diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA.srt
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index 0000000000000000000000000000000000000000..244467fc28a6b7fe9fc3ab8e13fea37743ba2098
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+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA.srt
@@ -0,0 +1,1619 @@
+1
+00:00:21,240 --> 00:00:27,440
+لازلنا في تشابتر ستة وهو الـ isomorphism المرة اللي 
+
+2
+00:00:27,440 --> 00:00:33,520
+فاتت عرفنا الـ automorphism وعرفنا أنه عبارة عن
+
+3
+00:00:33,520 --> 00:00:37,880
+isomorphism لكن من الـ group إلى نفس الـ group
+
+4
+00:00:37,880 --> 00:00:43,720
+وبالتالي سميناه automorphism عرفنا كمان الـ Inner
+
+5
+00:00:43,720 --> 00:00:48,560
+Automorphism induced by an element of a group G
+
+6
+00:00:48,560 --> 00:00:55,940
+وقلنا الـ Phi A of X يساوي A X A inverse وسمينا
+
+7
+00:00:55,940 --> 00:01:02,640
+هذا الـ Inner Automorphism من G الآن لو جمعنا كل
+
+8
+00:01:02,640 --> 00:01:08,570
+الـ Automorphism في G وسميناهم الـ Automorphism لـ G
+
+9
+00:01:08,570 --> 00:01:14,310
+جمعنا كل الـ inner automorphism وسميناهم الـ inner
+
+10
+00:01:14,310 --> 00:01:18,750
+automorphism of G يفجر الرمز اللي قدام الـ
+
+11
+00:01:18,750 --> 00:01:24,110
+automorphism لـ G كل الـ automorphism اللي موجودة في
+
+12
+00:01:24,110 --> 00:01:28,910
+الـ group G الـ inner automorphism لـ G كل الـ inner
+
+13
+00:01:28,910 --> 00:01:34,490
+automorphism of group G النظرية اللي عندنا بتقول لو
+
+14
+00:01:34,490 --> 00:01:38,210
+كانت جي جروب يبقى الـ automorphism والـ inner
+
+15
+00:01:38,210 --> 00:01:45,270
+automorphism لجروب جي كل واحد فيهم عبارة عن جروب
+
+16
+00:01:45,770 --> 00:01:49,370
+بدي أحاول أثبت النقطة الأولى ومن ثم أثبت النقطة
+
+17
+00:01:49,370 --> 00:01:53,170
+الثانية طبع الكتاب تركها .. تركه ملكه as an
+
+18
+00:01:53,170 --> 00:01:57,170
+exercise يعني حطه الـ .. الـ .. الـ .. في التمرين
+
+19
+00:01:57,170 --> 00:02:02,190
+تبعت ميم تبعت الكتاب على أساس أحله كـ exercise
+
+20
+00:02:02,190 --> 00:02:07,070
+احنا هنبره إنه برهان عادي يبقى الخطوة الأولى بدي
+
+21
+00:02:07,070 --> 00:02:11,590
+أثبت له إن الـ automorphism is a group يعني بدي أثبت
+
+22
+00:02:11,590 --> 00:02:16,150
+إن الـ binary operation اللي على الـ automorphism اللي
+
+23
+00:02:16,150 --> 00:02:20,150
+جيه is a binary operation associative الـ identity
+
+24
+00:02:20,150 --> 00:02:25,050
+element الـ inverse element وهكذا نجي للنقطة
+
+25
+00:02:25,050 --> 00:02:31,510
+الأولى لذلك بدي أقوله let فاي واحد وفاي اتنين
+
+26
+00:02:31,510 --> 00:02:39,110
+موجودات في الـ automorphism اللاجئ يبقى
+
+27
+00:02:39,110 --> 00:02:44,530
+بناء عليه مدام automorphism يبقى كل من فاي واحد وفاي
+
+28
+00:02:44,530 --> 00:02:53,530
+اتنين is one to one and onto يبقى then فاي واحد وفاي
+
+29
+00:02:53,530 --> 00:03:01,210
+اتنين is one to one and onto هذا بيعطينا من مبادئ
+
+30
+00:03:01,210 --> 00:03:06,910
+الرياضيات إن الـ composition فيما بينهما فاي واحد في
+
+31
+00:03:06,910 --> 00:03:14,510
+اتنين is one to one and onto كذلك من مبادئ
+
+32
+00:03:14,510 --> 00:03:18,330
+الرياضيات لو كان عندي two functions كل واحدة فيهم
+
+33
+00:03:18,330 --> 00:03:21,730
+one to one and onto يبقى الـ composition عليهم
+
+34
+00:03:21,730 --> 00:03:26,450
+بيعطينا one to one and onto function بدي أشوف
+
+35
+00:03:26,450 --> 00:03:31,110
+هالهدى بتخدم خاصية الـ isomorphism ولا لأ إن خدمت
+
+36
+00:03:31,110 --> 00:03:36,000
+يبقى بصير هدى هذه موجودة في الـ automorphism
+
+37
+00:03:44,810 --> 00:03:53,910
+يبقى بناء عليه هذي بتعطينا فاي وان لـ فاي تو of XY ليش
+
+38
+00:03:53,910 --> 00:03:57,970
+هذا تعريف الـ composition of functions اللي أخدناه
+
+39
+00:03:57,970 --> 00:04:05,810
+في calculus A هذا الكلام يساوي فاي واحد of  فاي
+
+40
+00:04:05,810 --> 00:04:11,070
+اتنين أنا فرضه Automorphism لـ جي يعني Isomorphism إذا
+
+41
+00:04:11,070 --> 00:04:15,110
+بناء عليه لما يأثر على الـ X و Y يبدو يساوي فاي في
+
+42
+00:04:15,110 --> 00:04:23,790
+تو of X فاي في تو of Y يبقى فاي تو of X فاي في تو of
+
+43
+00:04:23,790 --> 00:04:33,230
+Y ليش؟ since لإن الـ فاي تو is isomorphism طيب هذا
+
+44
+00:04:33,230 --> 00:04:42,890
+الكلام يساوي يساوي فاي وان لـ فاي two of x وكمان فاي
+
+45
+00:04:42,890 --> 00:04:51,370
+وان لـ فاي two of y لنفس السبب نظرا لإن فاي وان is
+
+46
+00:04:51,370 --> 00:04:57,510
+an isomorphism يبقى هذا الكلام since فاي وان is an
+
+47
+00:04:57,510 --> 00:05:01,930
+isomorphism طيب بدا الشغلانة الـ composition of
+
+48
+00:05:01,930 --> 00:05:06,930
+functions بده رجعهم إلى أصلهم يبقى هذا معناه فاي
+
+49
+00:05:06,930 --> 00:05:12,890
+واحد في اتنين كله as a function of x و فاي واحد في
+
+50
+00:05:12,890 --> 00:05:19,290
+اتنين as a function of y يبقى بناء عليه أصبح فاي
+
+51
+00:05:19,290 --> 00:05:23,950
+واحد في اتنين في اتنين is an isomorphism وبالتالي
+
+52
+00:05:23,950 --> 00:05:30,380
+Automorphism يبقى الـ automorphism لـ G is closed under
+
+53
+00:05:30,380 --> 00:05:34,500
+the composition of functions أو الـ composition of
+
+54
+00:05:34,500 --> 00:05:38,940
+functions is a binary operation على مين؟ على G
+
+55
+00:05:38,940 --> 00:05:45,220
+يبقى يا بتروح تقولي هنا الـ automorphism
+
+56
+00:05:45,220 --> 00:05:54,740
+automorphism لـ G is closed under the
+
+57
+00:05:59,540 --> 00:06:06,340
+composition of functions يعني إذا كان بدل العبارة
+
+58
+00:06:06,340 --> 00:06:09,300
+هذه بتقدر تقولي so the composition of a function
+
+59
+00:06:09,300 --> 00:06:14,700
+is a binary operation على مين على الـ automorphism لمين
+
+60
+00:06:14,700 --> 00:06:20,300
+إلى دي يعني إحنا حتى الآن أثبتنا مين الخاصية
+
+61
+00:06:20,300 --> 00:06:25,210
+الأولى إن الـ operation is a binary operation بتقدر
+
+62
+00:06:25,210 --> 00:06:30,030
+تقولها بينجو سين حطها binary operation عندك مشان
+
+63
+00:06:30,030 --> 00:06:34,390
+تتأكد إن هذه الخطوة هي الخطوة الأولى في إثبات الـ
+
+64
+00:06:34,390 --> 00:06:40,690
+group الخطوة الثانية خاصية associativity we know
+
+65
+00:06:40,690 --> 00:06:50,950
+that احنا بنعرف إن that the composition of
+
+66
+00:06:50,950 --> 00:06:52,870
+functions 
+
+67
+00:06:54,160 --> 00:06:59,880
+is associative يبقى فيش داعي أروح نعملها لإننا
+
+68
+00:06:59,880 --> 00:07:05,000
+عارفين إنها هذه يبقى اتحققت من الخاصية الثانية
+
+69
+00:07:05,000 --> 00:07:10,660
+بدنا نروح نجيب خاصية الـ identity element الآن الـ I
+
+70
+00:07:10,660 --> 00:07:20,440
+من G إلى G هذه is the identity function
+
+71
+00:07:21,740 --> 00:07:24,580
+خليني أسألكم السؤال اللي طالع لما أخدتم مبادئ
+
+72
+00:07:24,580 --> 00:07:27,460
+الرياضية الـ identity function one to one and onto
+
+73
+00:07:27,460 --> 00:07:34,460
+ولا لأ؟ مظبوط؟ يبقى هذه الـ identity function which
+
+74
+00:07:34,460 --> 00:07:44,920
+is one to one and onto مش عجبا هكذا and الـ I لو
+
+75
+00:07:44,920 --> 00:07:50,000
+أثرت على الـ X في Y، أيش بتعطيه لك؟ الـ X في Y لأن
+
+76
+00:07:50,000 --> 00:07:56,920
+الـ Identity function الـ X هذه ليست I of X وهذه I
+
+77
+00:07:56,920 --> 00:08:02,520
+of Y إذا حققت الخاصية تبع الـ isomorphism صار one
+
+78
+00:08:02,520 --> 00:08:08,260
+to one and onto و حقق الخاصية و من الـ group لنفسها
+
+79
+00:08:08,260 --> 00:08:15,880
+يبقى هنا الـ I موجود في الـ automorphism الجيب يبقى
+
+80
+00:08:15,880 --> 00:08:21,440
+أصبحت الـ I عبارة عن automorphism هذا هو الـ identity
+
+81
+00:08:21,440 --> 00:08:26,600
+element يبقى is the identity
+
+82
+00:08:35,120 --> 00:08:42,320
+Element of الـ automorphism
+
+83
+00:08:42,320 --> 00:08:49,620
+اللي جيه بدك تعمل تشك تاخد الـ identity مع automorphism
+
+84
+00:08:49,620 --> 00:08:52,740
+تاني و تعمل بينهم composites بينهم مالوش تأثير
+
+85
+00:08:52,740 --> 00:08:58,900
+مافيش مشكلة طب الآن بدنا نيجي لمين؟ للمعكوس، الآن
+
+86
+00:08:58,900 --> 00:09:09,160
+اف فاي موجود في الـ automorphism لجيب أحاول أن أثبت إن
+
+87
+00:09:09,160 --> 00:09:13,300
+الـ Phi Inverse عبارة عن Automorphism إذا أثبتت إن
+
+88
+00:09:13,300 --> 00:09:16,780
+الـ Phi Inverse عبارة عن Automorphism يبقى أثارة
+
+89
+00:09:16,780 --> 00:09:21,860
+الـ Automorphism is a group وانتهينا من المثلة يعني
+
+90
+00:09:21,860 --> 00:09:27,060
+كأننا نشتغل الآن ما أشتغلناه في الشابتر الثاني بعد
+
+91
+00:09:27,060 --> 00:09:34,080
+تشابتر المقدمة وهو تشابتر الـ group يبقى then Phi is
+
+92
+00:09:34,080 --> 00:09:40,910
+one to one and onto مش على جد هيك مادام فاي one to
+
+93
+00:09:40,910 --> 00:09:47,350
+one and one to one يبقى معاكسه as one to one and
+
+94
+00:09:47,350 --> 00:09:53,650
+one to كذلك function يبقى one to one and onto
+
+95
+00:09:53,650 --> 00:09:58,590
+function هذا معناه إنه فاي انفرس عبارة عن one to
+
+96
+00:09:58,590 --> 00:10:03,510
+one and onto function ضايل علينا مين؟ ضايل علينا
+
+97
+00:10:03,510 --> 00:10:07,670
+نثبت إن فاي انفرس is an isomorphism يعني فاي انفرس
+
+98
+00:10:07,670 --> 00:10:11,250
+of x y هو فاي انفرس of x وفاي انفرس of y أظن
+
+99
+00:10:11,250 --> 00:10:16,590
+أثبتناها في النظرية قبل الماضية أو السبع نقاط
+
+100
+00:10:16,590 --> 00:10:20,810
+أثبتناها فيهم طيب و
+
+101
+00:10:23,400 --> 00:10:31,860
+Prove that احنا برهننا كذلك إن فاي انفرس of x y
+
+102
+00:10:31,860 --> 00:10:40,780
+يساوي فاي انفرس of x فاي في انفرس of y برهنها سابقا
+
+103
+00:10:40,780 --> 00:10:47,440
+يبقى صارت فاي انفرس exist وفي نفس الوقت حققت خاصية
+
+104
+00:10:47,440 --> 00:10:52,570
+الـ isomorphism يبقى ه أو الـ automorphism هذا معناه
+
+105
+00:10:52,570 --> 00:10:59,690
+إن فاي انفرس موجود في الـ automorphism لمام الاجيه صار
+
+106
+00:10:59,690 --> 00:11:03,510
+الـ automorphism الاجيه closed under the operation
+
+107
+00:11:03,510 --> 00:11:08,850
+العملية associative الـ identity element موجود
+
+108
+00:11:08,850 --> 00:11:15,170
+المعكوس لأي element موجود في الـ automorphism موجود يبقى
+
+109
+00:11:15,170 --> 00:11:23,170
+الـ automorphism مالها is a group يبقى الـ automorphism لدي
+
+110
+00:11:23,170 --> 00:11:34,990
+is a group under the composition of
+
+111
+00:11:34,990 --> 00:11:36,790
+functions
+
+112
+00:11:38,510 --> 00:11:44,830
+طيب كويس انتهينا من الأولى نيجي لنقطة ثانية الـ inner
+
+113
+00:11:44,830 --> 00:11:50,910
+automorphism لـ G the set of all elements Phi A
+
+114
+00:11:50,910 --> 00:11:58,610
+such that الـ Phi A of X بده يساوي الـ A X A inverse
+
+115
+00:11:58,610 --> 00:12:05,960
+وهذا الكلام لكل الـ X اللي موجودة في G هذه عرفناها
+
+116
+00:12:05,960 --> 00:12:09,380
+المرة اللي فاتت بالشكل اللي عنها ده، بدي أحاول
+
+117
+00:12:09,380 --> 00:12:14,840
+أثبت إنه هذه is a group طب خليني أسألكوا السؤال
+
+118
+00:12:14,840 --> 00:12:19,960
+التالي، لو قدرت أثبت إن الـ inner automorphism اللي
+
+119
+00:12:19,960 --> 00:12:25,000
+جي subgroup من الـ automorphism اللي جي مش الـ inner
+
+120
+00:12:25,000 --> 00:12:32,000
+بصير group لأن الـ subgroup هي مجموعة جزئية من
+
+121
+00:12:32,000 --> 00:12:36,560
+المجموعة الأصلية بس تحت نفس العملية إذا لو قدرت
+
+122
+00:12:36,560 --> 00:12:41,540
+أثبت إن الـ inner automorphisms اللي جيه هي عبارة عن
+
+123
+00:12:41,540 --> 00:12:45,580
+subgroup من الـ automorphism اللي جيه بصير هذه group
+
+124
+00:12:45,580 --> 00:12:52,360
+ونكون انتهينا من المسألة هذه يبقى بدنا نروح نثبتها
+
+125
+00:12:52,760 --> 00:13:00,500
+بدنا نثبت إن الـ inner هذه is a group مشان أثبتها 
+
+126
+00:13:00,500 --> 00:13:04,440
+group بدأ أثبتها sub group من ال-atom morphism لـ G
+
+127
+00:13:04,440 --> 00:13:14,920
+الـ inner atom morphism لـ G is non-empty 
+
+128
+00:13:14,920 --> 00:13:16,280
+ليش؟ because
+
+129
+00:13:19,280 --> 00:13:27,680
+الـ Phi E موجودة في الـ Inner Atomorphism لـ جي يعني
+
+130
+00:13:27,680 --> 00:13:36,440
+هذا هو الـ identity element because and الـ Phi E is
+
+131
+00:13:36,440 --> 00:13:47,260
+the identity element and الـ Inner
+
+132
+00:13:47,260 --> 00:13:49,740
+Atomorphism لـ G
+
+133
+00:14:01,130 --> 00:14:05,330
+أنا بدعي أنه الـ identity element الآن بدي بين أن
+
+134
+00:14:05,330 --> 00:14:10,470
+هذا هو الـ identity element تبع الـ atomorphism يبقى
+
+135
+00:14:10,470 --> 00:14:17,110
+هذا بدي يعطيني أن الـ phi E of X يساوي الـ X يساوي
+
+136
+00:14:17,110 --> 00:14:22,410
+شريك الـ X هذه لو ضربت في الـ identity element تتغير
+
+137
+00:14:22,410 --> 00:14:30,360
+يعني لو قلت لك هذه E X صح ولا غلط؟ مية المية طب لو
+
+138
+00:14:30,360 --> 00:14:34,440
+قلت لك كمان ضربت في معكوس الـ identity element مين
+
+139
+00:14:34,440 --> 00:14:39,600
+معكوس الـ identity element الـ identity element نفسه
+
+140
+00:14:39,600 --> 00:14:47,140
+يبقى سعر الـ Phi E ده موجود في الـ inner atom
+
+141
+00:14:47,140 --> 00:14:51,880
+morphism لـ G ومن هنا الـ inner atom morphism لـ G is
+
+142
+00:14:51,880 --> 00:14:59,450
+non-empty طب كويس الآن بدأ أخد two elements موجودات
+
+143
+00:14:59,450 --> 00:15:05,190
+في الـ inner و أثبت أن الأول في معكوس الثاني موجود
+
+144
+00:15:05,190 --> 00:15:13,910
+يبقى بداجي أقوله let code لفاي a وفاي b موجودات
+
+145
+00:15:13,910 --> 00:15:18,750
+في الـ inner atomorphism لـ جي then
+
+146
+00:15:20,330 --> 00:15:28,470
+بدي أخد فاي a فاي b inverse كله as a function of x
+
+147
+00:15:28,470 --> 00:15:34,330
+وشوف هل هذا موجود في الـ inner ولا لأ بمعنى آخر هل
+
+148
+00:15:34,330 --> 00:15:40,430
+بقدر أكتب حصل الضرب هذا على شكل inner atomorphism
+
+149
+00:15:40,430 --> 00:15:47,060
+والله ما أقدرش هذا ما سنجيب عليه طيب هذا الكلام يساوي
+
+150
+00:15:47,060 --> 00:15:52,820
+as a
+
+151
+00:15:52,820 --> 00:15:58,700
+function of x طبعًا برهنا هذا الكلام سابقًا في
+
+152
+00:15:58,700 --> 00:16:03,440
+نظريات السابقة بينا أن فاي a inverse الانفرس
+
+153
+00:16:03,440 --> 00:16:08,720
+بنزله على من؟ على الـ element يبقى هاي نزلنا الـ
+
+154
+00:16:08,720 --> 00:16:12,470
+inverse على من؟ على الـ element اللي جواهذا
+
+155
+00:16:12,470 --> 00:16:20,610
+composition of functions يبقى فاي a لمين لفاي b
+
+156
+00:16:20,610 --> 00:16:27,150
+inverse as a function of x يبقى هذه الـ فاي اللي برا
+
+157
+00:16:27,150 --> 00:16:32,810
+هذه الـ فاي اللي برا a واللي جوا هذي بده أطبق عليها
+
+158
+00:16:32,810 --> 00:16:38,560
+التعريف اللي احنا جايلينه هنا يبقى هذه عبارة عن B
+
+159
+00:16:38,560 --> 00:16:46,220
+inverse X B inverse Inverse طبق لهذا التعريف Phi A
+
+160
+00:16:46,220 --> 00:16:51,800
+الـ element A X A inverse يبقى هذا الـ element X الـ
+
+161
+00:16:51,800 --> 00:16:57,850
+element inverse بالشكل اللي عندنا هذا الآن بدي أطبق
+
+162
+00:16:57,850 --> 00:17:04,110
+التعريف كمان مرة يبقى هذا بدي يعطيني الـ a b
+
+163
+00:17:04,110 --> 00:17:13,250
+inverse x b inverse x b inverse inverse كل هذا
+
+164
+00:17:13,250 --> 00:17:20,410
+الكلام في من؟ في الـ a inverse يبقى اعتبرت هذا كله
+
+165
+00:17:20,410 --> 00:17:24,790
+element في domain الـ phi of A طبقت عليه التعريف
+
+166
+00:17:24,790 --> 00:17:30,030
+اللي هناك A نفس الـ element الـ A inverse الآن
+
+167
+00:17:30,030 --> 00:17:35,170
+بالدالي لخاصية الـ associativity يبقى بناء عليه هذا
+
+168
+00:17:35,170 --> 00:17:42,120
+بقدر أقول A B inverse في الـ X فيه أطلع لي هذا الـ
+
+169
+00:17:42,120 --> 00:17:45,660
+element inverse و هذا الـ element inverse بقدر
+
+170
+00:17:45,660 --> 00:17:51,360
+أجمعهم بـ inverse واحد بعد ما أغير أو أبدل مواقعهم
+
+171
+00:17:51,360 --> 00:17:57,740
+يبقى هذا الكلام اللي هو الـ a b inverse الكل
+
+172
+00:17:57,740 --> 00:18:02,480
+inverse بالشكل اللي عندنا هذا يبقى هذا inverse و
+
+173
+00:18:02,480 --> 00:18:07,160
+هذا inverse جلبت وضعهم و خلت inverse للكل أطلع لي
+
+174
+00:18:07,160 --> 00:18:12,120
+للمقدار بين القوسين هو هذا ولا لا يبقى صار الـ
+
+175
+00:18:12,120 --> 00:18:18,180
+element هذا هو الـ element هذا بس inverse أليس هو
+
+176
+00:18:18,180 --> 00:18:25,760
+تعريف inner atomorphism يعني هذا كأنه مين كأنه في
+
+177
+00:18:25,760 --> 00:18:32,300
+a b inverse of x تمام
+
+178
+00:18:32,970 --> 00:18:40,210
+يبقى ابتدأت بـ element في معكوسه الثاني طلع عندي Phi
+
+179
+00:18:40,210 --> 00:18:45,910
+of AB inverse يعني إيش؟ يعني اللي هو inner
+
+180
+00:18:45,910 --> 00:18:53,370
+atomorphism إذا هذا موجود في inner atomorphism لـ G
+
+181
+00:18:55,870 --> 00:19:00,910
+ثبت هنا أنه non-empty أخدت الـ elements موجودات في
+
+182
+00:19:00,910 --> 00:19:06,350
+الـ inner فردت الأول في معكوس الثاني طلع موجود وين
+
+183
+00:19:06,350 --> 00:19:12,810
+في الـ inner atomorphism يبقى بناء عليه الـ inner
+
+184
+00:19:12,810 --> 00:19:20,150
+atomorphism لـ جي is a subgroup من الـ atomorphism
+
+185
+00:19:20,150 --> 00:19:22,970
+لـ جي هذا بيعطينا
+
+186
+00:19:48,290 --> 00:19:52,050
+حد لو يتسائل بالنسبة للنظرية
+
+187
+00:19:55,710 --> 00:20:02,030
+علي صوتك شوية عشان
+
+188
+00:20:02,030 --> 00:20:13,110
+نثبت أنها non-empty ممتاز تعال
+
+189
+00:20:13,110 --> 00:20:17,810
+هنا تعال تعال الحق الحق قول
+
+190
+00:20:26,310 --> 00:20:31,150
+أنا ادعيت أن هذا هو الـ identity element هايو جايلك
+
+191
+00:20:31,150 --> 00:20:34,990
+هذا is identity element أن جي جيت قلت لك مدام
+
+192
+00:20:34,990 --> 00:20:39,410
+identity يبقى بده يساوي هيك مظبوط تأثيره على الـ
+
+193
+00:20:39,410 --> 00:20:43,350
+element بيساوي الـ element هذه النتيجة بدي أحاول أحط
+
+194
+00:20:43,350 --> 00:20:49,510
+على شكل inner atomorphism فروحت قلت الـ Phi يساوي X
+
+195
+00:20:49,510 --> 00:20:54,670
+يساوي E X E inverse هذا شكل inner atomorphism
+
+196
+00:20:54,670 --> 00:21:02,070
+وبالتالي هذا موجود هنا قسمة عالمية أربعة بيصير
+
+197
+00:21:02,070 --> 00:21:09,380
+في A X بيساوي E X E inverse فاي E هي الـ identity هي
+
+198
+00:21:09,380 --> 00:21:14,840
+جايلك من الأول في E موجودة وهي الـ identity مش الـ
+
+199
+00:21:14,840 --> 00:21:19,620
+E الـ E هو الـ identity تبع الـ group لكن في E هو
+
+200
+00:21:19,620 --> 00:21:23,020
+الـ identity element تبع الـ atom morphism وتبع الـ
+
+201
+00:21:23,020 --> 00:21:26,800
+inner atom morphism در بالك يعني هدول functions
+
+202
+00:21:26,800 --> 00:21:32,580
+وليست elements عادية تمام لكن صورها هي الـ elements
+
+203
+00:21:32,580 --> 00:21:36,400
+اللي موجودة وين في نفس الـ group اللي عندنا جي حد
+
+204
+00:21:36,400 --> 00:21:41,380
+يلاقي تساوي الآخر؟ طيب بدنا نروح و نوضع هذا الكلام
+
+205
+00:21:41,380 --> 00:21:49,800
+بمثال example
+
+206
+00:22:12,580 --> 00:22:22,400
+بقول الـ D4 بده يساوي الـ R0 R90 R180 و
+
+207
+00:22:22,400 --> 00:22:35,360
+R270 H V D D prime find find أو
+
+208
+00:22:35,360 --> 00:22:38,340
+جد ليه الـ inner
+
+209
+00:22:41,510 --> 00:22:47,710
+لـ D4 بدنا الـ inner atomorphism لـ D4
+
+210
+00:22:47,710 --> 00:22:53,550
+solution
+
+211
+00:23:03,160 --> 00:23:08,840
+تعال نشوف اللي هو الـ elements المختلفة اللي بدنا
+
+212
+00:23:08,840 --> 00:23:13,480
+نجيبها من خلال الـ elements اللي عندنا نتكلم احنا
+
+213
+00:23:13,480 --> 00:23:17,620
+على الـ inner مدام على الـ inner يبقى نتكلم على
+
+214
+00:23:17,620 --> 00:23:23,560
+functions كلها بهذا الشكل تمام؟ بدي أروح أجيب هنا
+
+215
+00:23:23,560 --> 00:23:34,730
+فاي R0 as a function of x طبعًا الـ X مين يا
+
+216
+00:23:34,730 --> 00:23:41,130
+شباب الـ X أي عنصر من هدول مين ما كان يكون يبقى هذا
+
+217
+00:23:41,130 --> 00:23:45,870
+لكل الـ X اللي موجودة في G يبقى هذا حسب الـ
+
+218
+00:23:45,870 --> 00:23:52,890
+definition بده يساوي R0 X R0 inverse حد
+
+219
+00:23:52,890 --> 00:23:59,030
+فيكم يقدر يقول لي قداش الناتج؟ قداش؟ X لأن هذا هو الـ
+
+220
+00:23:59,030 --> 00:24:02,450
+identity element ومعكوس الـ identity element الـ
+
+221
+00:24:02,450 --> 00:24:06,210
+identity element نفسه ويضربه في أي element بيعطينا
+
+222
+00:24:06,210 --> 00:24:12,790
+نفس الـ element طيب كويس إذا تأثير في R0 على
+
+223
+00:24:12,790 --> 00:24:17,350
+جميع عناصر جي بيعطيني جميع عناصر دي حط على شجرة
+
+224
+00:24:17,350 --> 00:24:24,350
+الآن بداجة أخد في R180 as a function of
+
+225
+00:24:24,350 --> 00:24:33,860
+X يبقى هذا الكلام يبدو يساوي R180 X R180 Inverse
+
+226
+00:24:33,860 --> 00:24:41,360
+السؤال هو قبل ما أسافر أعطيتكم الـ center تبع الـ D4
+
+227
+00:24:41,360 --> 00:24:46,860
+أو الـ Dn قلنا لكم إذا الـ N فردي يبقى الـ center
+
+228
+00:24:46,860 --> 00:24:53,340
+ما فيه إلا الـ identity element وإذا الـ Dn الـ N
+
+229
+00:24:53,340 --> 00:24:58,140
+زوجي يبقى فيها الـ Identity Element والـ R180 صحيح
+
+230
+00:24:58,140 --> 00:25:02,860
+ولا لأ؟ إذا الـ R180 هذه موجودة في الـ Center يعني
+
+231
+00:25:02,860 --> 00:25:10,100
+كوميوتس مع جميع عناصر D4 إذا هذه لو بدلتها هنا بيصير
+
+232
+00:25:10,100 --> 00:25:14,400
+X R180 R180 Inverse اللي هي بالـ Identity يبقى ناتج
+
+233
+00:25:14,400 --> 00:25:15,660
+كده بده يعطينا
+
+234
+00:25:19,650 --> 00:25:27,540
+لأن الـ R 180 موجودة في الـ Center تبع الـ D4 طب من
+
+235
+00:25:27,540 --> 00:25:33,520
+الاثنين هدول إذا الناتج هو نفسه معناته في R0
+
+236
+00:25:33,520 --> 00:25:37,200
+تأثيرها على الـ elements بتساوي في R0 تأثيرها
+
+237
+00:25:37,200 --> 00:25:40,920
+على الـ R180 تأثيرها على الـ elements يبقى
+
+238
+00:25:40,920 --> 00:25:49,640
+أصبح في R0 بتساوي في R180 تمام يبقى
+
+239
+00:25:49,640 --> 00:25:53,600
+هدول في الـ atom morphism عنصرين ولا عنصر واحد
+
+240
+00:25:54,780 --> 00:26:01,440
+عنصرين ولا واحد واحد ممتاز جدًا طيب تعال نشوف فاي
+
+241
+00:26:01,440 --> 00:26:10,120
+R270 تأثيرها على X يبقى هذه
+
+242
+00:26:10,120 --> 00:26:19,700
+R270 X R270 inverse وتساوي إيش
+
+243
+00:26:19,700 --> 00:26:28,240
+رأيك الـ R270 بقدر أكتبها R180 مضروبة في R90 صحيح
+
+244
+00:26:28,240 --> 00:26:33,500
+ولا لا؟ لأن هذه نفسها الـ rotation هو نفسه ما عناه مش
+
+245
+00:26:33,500 --> 00:26:39,960
+مشكلة طيب هنا الـ X الـ R270 .. اه هذه R270 و
+
+246
+00:26:39,960 --> 00:26:45,220
+سبعين inverse حسب التعريف طبعًا يبقى R270 و
+
+247
+00:26:45,220 --> 00:26:49,120
+سبعين inverse في الـ H مش خليني أسألكم السؤال
+
+248
+00:26:49,120 --> 00:26:56,640
+التالي R270 كده إيش تساوي يا شباب R0
+
+249
+00:26:56,640 --> 00:27:06,420
+طبعًا طيب R0 لو ضربتها في R90 inverse بيصير الـ
+
+250
+00:27:06,420 --> 00:27:17,440
+R270 تساوي الـ R90 inverse يعني ضربت 
+
+251
+00:27:17,440 --> 00:27:24,200
+الطرفين في مين؟ R تسعين انفرس يبقى بناء عليه الـ R
+
+252
+00:27:24,200 --> 00:27:30,500
+ميتين وسبعين انفرس، الـ R ميتين وسبعين انفرس لو بدأ
+
+253
+00:27:30,500 --> 00:27:35,660
+أخد الانفرس هنا، يقول هيعطيني من الانفرس هنا يبقى
+
+254
+00:27:35,660 --> 00:27:43,180
+الـ R ميتين وسبعين انفرس بده يساوي الـ R تسعين طيب
+
+255
+00:27:45,430 --> 00:27:54,010
+هذا الكلام بده يساوي هذه الـ R التي هي
+
+256
+00:27:54,010 --> 00:28:02,850
+R تسعين inverse في R مية وتمانين inverseالـ 
+
+257
+00:28:02,850 --> 00:28:07,570
+موجودة مع الـ Center يبقى لو جيب تهادي معهدش بصير
+
+258
+00:28:07,570 --> 00:28:15,670
+الـ Identity Element يبقى بصير الناتج R 90 X R 90
+
+259
+00:28:15,670 --> 00:28:21,410
+Inverse أليس تهادي على الصيغة اللي موجودة عندنا
+
+260
+00:28:21,410 --> 00:28:31,640
+هذه؟ يبقى هذه Φ R تسعين يبقى هذه Φ R تسعين as a
+
+261
+00:28:31,640 --> 00:28:39,440
+function of X يبقى بناء عليه أصبح عند هنا مين Φ
+
+262
+00:28:39,440 --> 00:28:48,640
+R ميتين وسبعين بده يساوي Φ R تسعين هذه بروزناها
+
+263
+00:28:48,640 --> 00:28:54,030
+وهذه بروزناها النتيجة اللي حصلنا عليها يبقى خلصنا
+
+264
+00:28:54,030 --> 00:28:59,650
+من R نود ومن R تسعين ومن R مية وتمانين ومن R
+
+265
+00:28:59,650 --> 00:29:07,710
+ميتين وسبعين بدنا نجي لامام لـ Φ H as a function
+
+266
+00:29:07,710 --> 00:29:19,670
+of X يبقى H X H inverse هذا الكلام يساوي بالدجل الـ
+
+267
+00:29:19,670 --> 00:29:26,360
+H عندنا ورحت فتحت على الجدول صفحة واحد وثلاثين
+
+268
+00:29:26,360 --> 00:29:33,100
+تابع الكتاب اللامان لـ دي فور صفحة واحد وثلاثين
+
+269
+00:29:33,100 --> 00:29:40,460
+وروح تدور على H ممكن تساوي هلاجيها R مية وتمانين
+
+270
+00:29:40,460 --> 00:29:47,490
+في V يبقى R مية وتمانين في V هي الـ H إذا ممكن
+
+271
+00:29:47,490 --> 00:29:56,890
+أشيلها وأكتب R مية وتمانين V في الـ X في الـ R مية
+
+272
+00:29:56,890 --> 00:30:05,800
+وتمانين V inverse  كلها طب ليش كتبتها هيك؟ عشان أسهل
+
+273
+00:30:05,800 --> 00:30:10,180
+عملية الاختصارات يعني بدي أحاول أكتبها بدلالة من؟
+
+274
+00:30:10,180 --> 00:30:14,560
+بدلالة الـ R180 كون الـ R180 في الـ center إذا
+
+275
+00:30:14,560 --> 00:30:20,780
+بتختصرني نص الشيء اللي موجود طيب هذا الكلام يساوي
+
+276
+00:30:20,780 --> 00:30:23,060
+R180
+
+277
+00:30:25,010 --> 00:30:33,570
+في V في الـ X هذه الـ inverse الـ V inverse R مية و
+
+278
+00:30:33,570 --> 00:30:40,030
+تمانين inverse طب هذه لو جبت عندها دي بقى كم بصير
+
+279
+00:30:40,030 --> 00:30:48,770
+بالـ identity ايش بصير عندنا هنا VX V inverse يبقى
+
+280
+00:30:48,770 --> 00:30:57,900
+هذه مين هذه Φ V of X يبقى بناء عليه أصبح عندي Φ
+
+281
+00:30:57,900 --> 00:31:06,700
+H هي عبارة عن Φ V بقى اللي عندي أخر حاجة Φ D
+
+282
+00:31:06,700 --> 00:31:14,780
+Prime as a function of X يبقى هي D Prime X D Prime
+
+283
+00:31:14,780 --> 00:31:21,100
+Inverse بنفس الطريقة اللي جبت فيها H بدي أروح أجيب
+
+284
+00:31:21,100 --> 00:31:28,460
+D' بروح بفتح الجدول صفحة واحد وثلاثين على الـ D'
+
+285
+00:31:29,220 --> 00:31:35,820
+على من؟ على الـ D' بدي R مية وتمانين عشان يجيب لي
+
+286
+00:31:35,820 --> 00:31:42,530
+D' بصير R مية وتمانين في D يبقى بشيلها وبكتب
+
+287
+00:31:42,530 --> 00:31:51,250
+بدالها R مية وتمانين في D في X في الـ R مية و
+
+288
+00:31:51,250 --> 00:31:58,270
+تمانين في D كل هذا الكلام inverse يبقى هذا الكلام
+
+289
+00:31:58,270 --> 00:32:02,370
+بيصير R مية وتمانين في D
+
+290
+00:32:12,070 --> 00:32:18,930
+يبقى هذه مع هذه بمين؟ بالـ identity element تمام
+
+291
+00:32:18,930 --> 00:32:26,920
+يبقى النتيجة هتعطيك DX D inverse هذه هي عبارة عن
+
+292
+00:32:26,920 --> 00:32:35,380
+Φ D of x يبقى بناء عليه أصبح Φ D prime
+
+293
+00:32:35,380 --> 00:32:38,300
+بده يساوي Φ D
+
+294
+00:32:40,110 --> 00:32:45,830
+يبقى الثمانية inner automorphism
+
+295
+00:32:45,830 --> 00:32:54,030
+صاروا كده؟ أربعة وليست ثمانية، الأربع صاروا على
+
+296
+00:32:54,030 --> 00:32:55,850
+الشكل التالي
+
+297
+00:33:11,130 --> 00:33:19,170
+يبقى هنا صار الـ inner automorphism لـ D4 هو عبارة
+
+298
+00:33:19,170 --> 00:33:26,130
+عن الـ Φ R نوت طبعًا يساوي Φ R مية وتمانين والثاني
+
+299
+00:33:26,130 --> 00:33:33,850
+Φ R تسعين اللي يساوي Φ R ميتين وسبعين والثالث
+
+300
+00:33:33,850 --> 00:33:39,690
+اللي هو Φ H والرابع اللي هو Φ D بهذا الشكل
+
+301
+00:33:40,480 --> 00:33:46,740
+يبقى هدول الـ inner automorphism لمن؟ لـ G السؤال هو
+
+302
+00:33:46,740 --> 00:33:53,380
+هل الـ inner automorphism لـ G أقل من ذلك واللهيهم
+
+303
+00:33:53,380 --> 00:33:58,720
+الأربعة فيش غيرهم بمعنى آخر هل الأربعة هدول بقدر
+
+304
+00:33:58,720 --> 00:34:04,040
+أخسرهم لثلاثة ولا لاثنين تعالوا نشوفوا نتأكد من
+
+305
+00:34:04,040 --> 00:34:09,640
+هذا الكلام أنا أدعي أن هذه الأربعة are distinct
+
+306
+00:34:10,700 --> 00:34:21,380
+يبقى هنا this أو the elements له five R node وfive
+
+307
+00:34:21,380 --> 00:34:29,580
+R تسعين وfive H and five
+
+308
+00:34:29,580 --> 00:34:31,260
+D are distinct
+
+309
+00:34:34,120 --> 00:34:38,580
+إذا Distinct معناته ايه؟ معناته إنه فعلا الـ
+
+310
+00:34:38,580 --> 00:34:43,080
+Inner Automorphism فيه الـ D والـ G ما فيش فيه إلا
+
+311
+00:34:43,080 --> 00:34:49,600
+الأربع عناصر هدول أو الأربع Inner Automorphism مشان
+
+312
+00:34:49,600 --> 00:34:54,540
+أثبتهم Distinct يكفيني counter example واحد لكل
+
+313
+00:34:54,540 --> 00:34:59,670
+واحدة فيهم تعالوا نشوفوا الآن أنا أدعي إنهم هذول
+
+314
+00:34:59,670 --> 00:35:06,830
+distinct إذا لو جيت قلت Φ R نود وبده أخليه
+
+315
+00:35:06,830 --> 00:35:15,910
+يأثر مثلًا على H أخد H عشوائيًا من الـ D4 يبقى هذا
+
+316
+00:35:15,910 --> 00:35:23,290
+بده يساوي R نود H R نود اللي هو Φ H الآن
+
+317
+00:35:23,290 --> 00:35:31,170
+بدأ أخد Φ R تسعين as a function of H يبقى هذا
+
+318
+00:35:31,170 --> 00:35:39,850
+الكلام بده يساوي R تسعين H R تسعين inverse ويساوي
+
+319
+00:35:39,850 --> 00:35:46,370
+برضه بده أرجع للجدول R تسعين H اللي في صفحة واحدة
+
+320
+00:35:46,370 --> 00:35:55,890
+وثلاثين R تسعين HR تسعين تضربها في H بيطلع D
+
+321
+00:35:55,890 --> 00:36:02,590
+Prime يبقى هذه D Prime R تسعين inverse اللي هي
+
+322
+00:36:02,590 --> 00:36:09,250
+بمين؟ بـ R ميتين والسبعين يبقى R ميتين والسبعين الـ D
+
+323
+00:36:09,250 --> 00:36:13,950
+Prime في الـ R ميتين والسبعين عندك D Prime في الـ R
+
+324
+00:36:13,950 --> 00:36:20,340
+ميتين والسبعين اللي هو بيعطيلك V بيعطيلك V هذه
+
+325
+00:36:20,340 --> 00:36:29,460
+أعطتني H وهذه أعطتني V إذا لا يمكن للـ R لـ Φ R
+
+326
+00:36:29,460 --> 00:36:37,460
+تسعين إنه يساوي مين؟ إنه يساوي الـ Φ R نود الآن
+
+327
+00:36:37,460 --> 00:36:45,240
+بالمثل لو جيت قلت Φ R تسعين بدي أبحثها مع مين؟ مع
+
+328
+00:36:45,240 --> 00:36:50,710
+Φ H بدي أثبت إنه ما فيش تساوي فيما بينهما يبقى Φ R
+
+329
+00:36:50,710 --> 00:36:57,030
+تسعين مثلًا لو خلتها تأثر على R تسعين يبقى ما بيصيرش
+
+330
+00:36:57,030 --> 00:37:05,510
+R تسعين R تسعين R تسعين inverse اللي هو بقد ايش؟ R
+
+331
+00:37:05,510 --> 00:37:14,770
+تسعين الآن بدي أنا أخد Φ H R تسعين يبقى هذا
+
+332
+00:37:14,770 --> 00:37:24,750
+الكلام يساوي H R تسعين H inverse يبقى
+
+333
+00:37:24,750 --> 00:37:30,090
+H inverse Y يساوي بالدجل الـ H R تسعين برضه من
+
+334
+00:37:30,090 --> 00:37:37,710
+صفحة واحدة وثلاثين بدي من؟ بدي الـ H R تسعين عندك الـ
+
+335
+00:37:37,710 --> 00:37:46,570
+H R تسعين اللي هي بـ D' طب والـ H inverse مش هي
+
+336
+00:37:46,570 --> 00:37:54,720
+H يا شباب ولا لا؟ سكت الشعب العناصر اللي عندنا هذه
+
+337
+00:37:54,720 --> 00:37:59,260
+هو الـ H تربيعها تساوي V تربيعها تساوي D تربيعها 
+
+338
+00:37:59,260 --> 00:38:03,460
+تساوي D' تربيعها تساوي الـ identity قلنا يبقى الـ H
+
+339
+00:38:03,460 --> 00:38:06,900
+والـ H inverse D' D inverse V' V inverse D prime يا D
+
+340
+00:38:06,900 --> 00:38:10,480
+prime inverse، مظبوط؟ إذا أشيلتها وحطيت قيمتها،
+
+341
+00:38:10,480 --> 00:38:16,680
+الآن بدي أشوف الـ DH مين هي، يبقى لو جيت لـ D في H،
+
+342
+00:38:16,680 --> 00:38:25,460
+D في H باللي بقى 270 يبقى هذه بدها تساوي الـ R 270
+
+343
+00:38:25,460 --> 00:38:30,980
+وسبعين يبقى من الاثنين هدول معناه هذا الكلام اللي
+
+344
+00:38:30,980 --> 00:38:37,780
+هو Φ R تسعين لا يمكن أن تساوي الـ Φ H اللي
+
+345
+00:38:37,780 --> 00:38:43,590
+عندنا بقى اللي عندنا مين بقى الـ Φ D الآن احنا
+
+346
+00:38:43,590 --> 00:38:47,850
+بياننا هي الثانية الأولى نياتي وهي الثانية
+
+347
+00:38:47,850 --> 00:38:53,850
+الثانية وهي الثانية اللي بعضهم Φ R تسعين برضه
+
+348
+00:38:53,850 --> 00:38:59,770
+بده يخلي يأثر على R تسعين أعطاني R تسعين itself
+
+349
+00:38:59,770 --> 00:39:08,140
+بده أخد آخر واحدة Φ D لما تأثر على R تسعين يبقى
+
+350
+00:39:08,140 --> 00:39:16,660
+هذا الكلام يساوي DR تسعين D inverse هو يساوي بدي
+
+351
+00:39:16,660 --> 00:39:22,760
+أجيب له الـ D R تسعين من الجدول الـ D R تسعين عبارة
+
+352
+00:39:22,760 --> 00:39:30,140
+عن V يبقى هذه V والـ D inverse هي عبارة عن D بدي
+
+353
+00:39:30,140 --> 00:39:38,300
+أجيب له الـ V في D يبقى الـ V في D اللي يبقى R ميتين
+
+354
+00:39:38,300 --> 00:39:46,120
+وسبعين يبقى هذه تساوي R ميتين وسبعين ملي الاثنين هدول
+
+355
+00:39:46,120 --> 00:39:54,260
+بس تنتج إن الـ Φ R تسعين لا يمكن أن تساوي الـ Φ D
+
+356
+00:39:55,610 --> 00:40:00,970
+اللي عملته أنا لسه شغلة أثبت إن الـ Φ R تسعين لا
+
+357
+00:40:00,970 --> 00:40:05,030
+بتساوي هذه ولا بتساوي هذه ولا بتساوي هذه الآن أنت
+
+358
+00:40:05,030 --> 00:40:09,710
+بتكتب إن الـ Φ H ما تساويش هذه Φ H ما تساويش هذه وΦ
+
+359
+00:40:09,710 --> 00:40:14,590
+H ما تساويش هذه وبعدين Φ D يبقى بروح بقوله
+
+360
+00:40:14,590 --> 00:40:15,910
+similarly
+
+361
+00:40:18,410 --> 00:40:28,530
+similarly for اللي هو Φ H and Φ D thus وهكذا
+
+362
+00:40:28,530 --> 00:40:35,850
+هكذا الـ inner automorphism اللي D4 هو عبارة
+
+363
+00:40:35,850 --> 00:40:46,050
+عن الـ Φ R نود والـ Φ R تسعين والـ Φ H و
+
+364
+00:40:46,050 --> 00:40:55,540
+الـ Φ D فقط لا غير طيب بدي أسأل السؤال التالي أنا
+
+365
+00:40:55,540 --> 00:41:01,360
+أخد تأثير الـ R node على H والـ R node على H طب لو
+
+366
+00:41:01,360 --> 00:41:08,060
+غيرت الـ H هذه يمكن يطلع اثنين زي بعض اه دير بالك
+
+367
+00:41:08,060 --> 00:41:13,370
+اصبر شوية اصبر عليّ شوية أنا هنا أثبت له إن الـ R
+
+368
+00:41:13,370 --> 00:41:18,690
+نود الـ R نود هي الـ R مية وتمانين على مين؟ على
+
+369
+00:41:18,690 --> 00:41:25,270
+X هل الـ X اخترت رمز معين ولا جيت على ثمانية رموز
+
+370
+00:41:25,270 --> 00:41:30,770
+على ثمانية ممتاز إذا إذا أنا لما أقول هذه لا تساوي
+
+371
+00:41:30,770 --> 00:41:36,190
+قد تساوي على بعض الرموز ولا تساوي على البعض الآخر
+
+372
+00:41:36,190 --> 00:41:41,050
+يبقى أنا بس جبت counter example أنها لا تساوي in
+
+373
+00:41:41,050 --> 00:41:46,430
+general لكن قد يحدث تساوي آخر لا مشكلة في ذلك لأن
+
+374
+00:41:46,430 --> 00:41:52,620
+أنا بدي عدم التساوي يكون على الكل بلا استثناء إذا
+
+375
+00:41:52,620 --> 00:41:58,260
+لو لجيت رمز واحد من الثمانية التساوي غير حاصل زي 
+
+376
+00:41:58,260 --> 00:42:04,160
+ما شوفت هنا يبقى هدول يمكن أن يتساوى رغم أن هم
+
+377
+00:42:04,160 --> 00:42:08,680
+ممكن يتساوى على بعض العناصر لكن in general على D4
+
+378
+00:42:08,680 --> 00:42:15,720
+كلها بحصلش تساوي واضح كلامي؟ أيوة مش سامع إيش 
+
+379
+00:42:15,720 --> 00:42:18,220
+بتقول هل صوتك
+
+380
+00:42:23,350 --> 00:42:24,650
+مين المتساوين؟
+
+381
+00:42:33,630 --> 00:42:38,550
+ماعنديش مشكلة أنا بقول لك أنه ممكن يحصل تساوي لكن
+
+382
+00:42:38,550 --> 00:42:42,710
+إذا بدك التساوي على جميع العناصر وليس على بعضها
+
+383
+00:42:42,710 --> 00:42:47,130
+عشان يحصل التساوي طبعا إذا أنا من الثمان عناصر
+
+384
+00:42:47,130 --> 00:42:52,650
+فبعد if لو جيت عنصر واحد التساوي غير حاصل إذا in
+
+385
+00:42:52,650 --> 00:42:56,670
+general التساوي غير حاصل عشان يكون تساوي بدي يكون
+
+386
+00:42:56,670 --> 00:43:02,510
+لجميع العناصر X يعني جميع عناصر D4 الثمانية بلا
+
+387
+00:43:02,510 --> 00:43:06,710
+استثناء يبقى بناء عليه هدول عناصر ال inner
+
+388
+00:43:06,710 --> 00:43:11,790
+automorphism تبعت منهم تبعات ال D4 اللي هو طلبهم
+
+389
+00:43:11,790 --> 00:43:18,570
+وبالتالي انتهى هذا السؤال ننتقل الآن إلى سؤال
+
+390
+00:43:20,250 --> 00:43:24,970
+السؤال الآخر وهو very important ولو أنه لم يبقى
+
+391
+00:43:24,970 --> 00:43:45,030
+له وقت السؤال الآخر بيقول ما يأتي خليه
+
+392
+00:43:45,030 --> 00:43:47,330
+بلكن كمان example
+
+393
+00:43:51,320 --> 00:44:02,000
+example بقول الكمبيوتر احسب لي ال automorphism لـ Z
+
+394
+00:44:02,000 --> 00:44:04,080
+منين لـ Z عشرة
+
+395
+00:44:12,500 --> 00:44:17,500
+أنا بدي احسب له كل الـ automorphism لـ Z10 يعني أنا بدي
+
+396
+00:44:17,500 --> 00:44:24,460
+function من Z10 إلى Z10 تبقى وأنت وأنت وأنت و تخدم
+
+397
+00:44:24,460 --> 00:44:29,800
+خاصية من الـ isomorphism كل function بهذه الطريقة
+
+398
+00:44:29,800 --> 00:44:35,480
+بتبقى موجود وين؟ في الـ automorphism لمين؟ لـ Z10 طبعا
+
+399
+00:44:35,480 --> 00:44:41,590
+هنثبت أن هدول أربعة فقط لغيروهذا ما سيكون في
+
+400
+00:44:41,590 --> 00:44:45,690
+المحاضرة بعض الظهر لإنه ما ضلش معانا واجد إلا تمام؟
+
+401
+00:44:45,690 --> 00:44:49,230
+هذا أنا بغششك من الحين إذا معاك الكتاب موجودة في
+
+402
+00:44:49,230 --> 00:44:53,890
+الكتاب تمر عليها ولن تفهم منها إلا القليل أنا
+
+403
+00:44:53,890 --> 00:44:58,290
+متأكد مش هتفهم إن هو كتاب إلا القليل لكن إن شاء
+
+404
+00:44:58,290 --> 00:45:02,510
+الله بنوضحها لك وبنفهمها لك في المحاضرة القادمة
+
+405
+00:45:02,510 --> 00:45:04,170
+إن شاء الله يعطيكم العفو 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb8b7560dc99eae89925cd2595a93c7ddf35d0c9
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_postprocess.srt
@@ -0,0 +1,1508 @@
+1
+00:00:21,290 --> 00:00:25,850
+بسم الله الرحمن الرحيم نستكمل الموضوع اللى بدأناه
+
+2
+00:00:25,850 --> 00:00:31,590
+الصبح وهو موضوع ال external direct product بعد ما
+
+3
+00:00:31,590 --> 00:00:35,770
+أخدنا أمثلة من خلالها بنعين ال order لل element
+
+4
+00:00:35,770 --> 00:00:42,070
+وكذلك عدد اللى هو ال elements ب order معين وعدد ال
+
+5
+00:00:42,070 --> 00:00:46,830
+cyclic groups ب order معين ننتقل الآن الى هذه
+
+6
+00:00:46,830 --> 00:00:51,500
+النظريةالنظرية بتقول يفترض ان جي و اتش بيه finite
+
+7
+00:00:51,500 --> 00:00:55,140
+cyclic groups يبقى كل واحدة فيها عدد محدود من
+
+8
+00:00:55,140 --> 00:01:00,060
+العناصر والتنتين are cyclic groups بيقول في هذه
+
+9
+00:01:00,060 --> 00:01:05,080
+الحلقين ال جي eccentric product مع اتش is cyclic
+
+10
+00:01:05,080 --> 00:01:08,760
+in fact تقول يف ال order جي و ال order اتش are
+
+11
+00:01:08,760 --> 00:01:13,240
+relatively prime يبقى من الآن فصاعدا لو ال two
+
+12
+00:01:13,240 --> 00:01:17,080
+groups جي و اتشتنين ال order اللي هم are
+
+13
+00:01:17,080 --> 00:01:19,840
+relatively prime اللي يبقى ال external product
+
+14
+00:01:19,840 --> 00:01:25,960
+معناه is a cyclic group مباشرة و العكس لو كانت
+
+15
+00:01:25,960 --> 00:01:28,860
+cyclic groups يبقى ال two orders are relatively
+
+16
+00:01:28,860 --> 00:01:35,620
+prime هذا اللي عايزين نثبته الآن يبقى لذلك نثبته
+
+17
+00:01:35,620 --> 00:01:41,040
+افترض ان ال H لها order معين و ال G كذلك لها order
+
+18
+00:01:41,040 --> 00:01:47,800
+معين و نشوف كيف بدنا نعمليبقى let ال order لل G
+
+19
+00:01:47,800 --> 00:01:55,680
+بده يساوي ال M and ال order لل H بده يساوي ال N
+
+20
+00:01:55,680 --> 00:02:00,200
+then
+
+21
+00:02:00,200 --> 00:02:11,180
+لو بده اجيب ال order لل G with H يبقى thenالأردر
+
+22
+00:02:11,180 --> 00:02:16,380
+للـ G External Hierarchical Product مع H كده يسوى
+
+23
+00:02:16,380 --> 00:02:20,040
+هذا يا شباب مكتوب معاكم من المرة اللي فاتت الأردر
+
+24
+00:02:20,040 --> 00:02:26,400
+للأولى في الأردر لثانية يبقى هذا الكلام يسوى ال M
+
+25
+00:02:26,400 --> 00:02:33,020
+في Nهذه المعلومة حطيتها قبل المبدأ و الأن بدي أبدأ
+
+26
+00:02:33,020 --> 00:02:38,360
+لإيش حطيتها؟ لأن كل شغل بالحب هو لازمانه الأن بدنا
+
+27
+00:02:38,360 --> 00:02:48,400
+نقول Assume that الـG external product مع الـH is
+
+28
+00:02:48,400 --> 00:02:54,540
+cyclicماذا أريد أن أثبت؟ أن الـ order اللي جي و ال
+
+29
+00:02:54,540 --> 00:02:58,560
+order اللي اتش اتنين are relatively prime يعني
+
+30
+00:02:58,560 --> 00:03:01,520
+أريد أن أثبت أن ال Euclides common divisor ما بين
+
+31
+00:03:01,520 --> 00:03:05,920
+الاتنين سيكون كم؟ سيكون واحد، صحيح طب افترضنا هذه
+
+32
+00:03:05,920 --> 00:03:10,040
+Cyclic مدام الـ Cyclic يبقى لها generator صح ولا
+
+33
+00:03:10,040 --> 00:03:14,600
+لا؟ يبقى Cyclic assume
+
+34
+00:03:15,770 --> 00:03:25,370
+أفترض كذلك إن الـ G والـ H is a generator is a
+
+35
+00:03:25,370 --> 00:03:33,870
+generator for اللي هو external product للـ H مع G
+
+36
+00:03:34,700 --> 00:03:38,460
+ما دام هذا generator يبقى ال order اللي بده يساوي
+
+37
+00:03:38,460 --> 00:03:43,860
+منين ال order لل G موديل لل G external direct
+
+38
+00:03:43,860 --> 00:03:50,920
+product مع H هذا معناه ان ال order لل G والH بده
+
+39
+00:03:50,920 --> 00:03:56,600
+يساوي ال order لل G external direct product مع من؟
+
+40
+00:03:56,600 --> 00:04:05,990
+مع ال H هذا بده يعطيني طيب ال order لل Gوالـ H بدي
+
+41
+00:04:05,990 --> 00:04:11,410
+يساوي ال least common multiple لل order تبع ال G
+
+42
+00:04:11,410 --> 00:04:18,870
+وال order تبع ال H يبقى
+
+43
+00:04:18,870 --> 00:04:23,050
+ال order لل G وال order تبع ال H بالشكل اللي عندنا
+
+44
+00:04:23,050 --> 00:04:28,730
+هذا اللي هو بدي يساوي ال order لهذه قداش اللي م في
+
+45
+00:04:28,730 --> 00:04:34,700
+نيبقى أنا بقول ال order لل element هذا بيساوي ال
+
+46
+00:04:34,700 --> 00:04:38,300
+order لل element هذه بيبقى بناء عليه ال order لل
+
+47
+00:04:38,300 --> 00:04:42,520
+element g و h بيساوي ال least common multiple ما
+
+48
+00:04:42,520 --> 00:04:46,360
+بين ال two orders طبقا للنظرية السابقة اللي
+
+49
+00:04:46,360 --> 00:04:51,340
+برهنناها طيب هذا ال order هو عبارة عن مين؟ عن m في
+
+50
+00:04:51,340 --> 00:04:57,020
+n خلي هذه المعلومة في دماغك و هنرجعلها بعد قليل
+
+51
+00:04:57,020 --> 00:05:05,640
+طيب الآنالـ order للـ G ال order للـ G يقسم ال
+
+52
+00:05:05,640 --> 00:05:11,840
+order للـ G كبتار صح ولا لا يبقى divide ال order
+
+53
+00:05:11,840 --> 00:05:19,250
+للـ G اللي هو بدي ساوي قداشM يعني ال order اللي
+
+54
+00:05:19,250 --> 00:05:25,670
+جيه بده يقسم من ال M وفي نفس الوقت ال order ل ال H
+
+55
+00:05:25,670 --> 00:05:33,390
+بده يقسم من بده يقسم ال order ل من ل ال H اللي هو
+
+56
+00:05:33,390 --> 00:05:38,870
+بده يساوي ال N إذا
+
+57
+00:05:38,870 --> 00:05:44,710
+ما هو علاقة least common multiple لل two orders مع
+
+58
+00:05:44,710 --> 00:05:45,970
+M و N
+
+59
+00:05:48,440 --> 00:05:52,340
+الليز كومل ملتبل لل اوضة مع الليز كومل ملتبل لل M
+
+60
+00:05:52,340 --> 00:05:55,360
+و N مين اللي اصغر و مين اللي اكبر؟ لليز كومل ملتبل
+
+61
+00:05:55,360 --> 00:06:01,800
+لمن؟ لل H و G مية لمية اصغر من من؟من ال least
+
+62
+00:06:01,800 --> 00:06:06,840
+common multiple لل M و N تمام؟ يبقى هذا يطيء
+
+63
+00:06:06,840 --> 00:06:12,840
+لكمين؟ ان ال least common multiple لل order تبع ال
+
+64
+00:06:12,840 --> 00:06:24,040
+G وال order تبع ال H هذا كله ماله أقل من أو يساوي
+
+65
+00:06:24,040 --> 00:06:32,930
+ال least common multiple لل M و Nتمام طيب ال least
+
+66
+00:06:32,930 --> 00:06:40,450
+common multiple لهذا اللي هو قداش M في N يبقى بناء
+
+67
+00:06:40,450 --> 00:06:47,950
+عليه So ال M في N أقل من أو يسوى ال least common
+
+68
+00:06:47,950 --> 00:06:56,450
+multiple لمن؟ لل M و N اعتبر هذه المعادلة رقم Star
+
+69
+00:06:58,800 --> 00:07:06,940
+السؤال هو احنا لان جيبنا ال M و ال N اقل من ال
+
+70
+00:07:06,940 --> 00:07:12,720
+least common multiple لمن؟ لل M و N طب in general
+
+71
+00:07:12,720 --> 00:07:24,720
+but و لكن we know that ان ال least common multiple
+
+72
+00:07:24,720 --> 00:07:26,840
+لل M و N
+
+73
+00:07:30,950 --> 00:07:35,450
+100% صحيح ولا لأ؟ دائما و أبدا ال least common ..
+
+74
+00:07:35,450 --> 00:07:39,430
+أقصى حاجة حصل ضربهم و دائما و أبدا بيكون أقل من
+
+75
+00:07:39,430 --> 00:07:44,870
+هيك يعني المضاعف المشترك أحيان بيكون كبيره في أقل
+
+76
+00:07:44,870 --> 00:07:51,630
+ما يمكن يبقى هذا أقل من مين؟ من M في N و هذه
+
+77
+00:07:51,630 --> 00:07:56,550
+العلاقة التانية هي رقم Star إذا من الإتنين مع بعض
+
+78
+00:07:56,550 --> 00:08:02,130
+بقول إن إتنين هدول ما لهماريكم يبقى هنا سوا ال
+
+79
+00:08:02,130 --> 00:08:09,150
+least common multiple لل M و N بده يساوي ال M في N
+
+80
+00:08:11,690 --> 00:08:17,290
+طيب نرجع بالذاكرة اصبر علينا شوية نرجع بالذاكرة
+
+81
+00:08:17,290 --> 00:08:22,650
+للوراء خلف الاول chapter اذا بتذكروا هنا قلنا ل
+
+82
+00:08:22,650 --> 00:08:26,290
+grace is common divided between عددين في least
+
+83
+00:08:26,290 --> 00:08:29,990
+common multiple العدين بيعطينا مين؟ نفس العددين
+
+84
+00:08:29,990 --> 00:08:40,950
+يبقى هنا باجي بقوله بط ولكن و لاthat لابنعرف ان
+
+85
+00:08:40,950 --> 00:08:47,530
+الـ greatest common divisor لل M والN مضروب في
+
+86
+00:08:47,530 --> 00:08:55,510
+least common multiple لل M وN بده يساوي M في N هذا
+
+87
+00:08:55,510 --> 00:09:01,790
+بده يعطيناالان ال least common multiple هو M في N
+
+88
+00:09:01,790 --> 00:09:07,570
+يبقى هذا بدي اعطيك انه ال greatest common divisor
+
+89
+00:09:07,570 --> 00:09:13,070
+لل M و N في ال least common multiple اللي هو M في
+
+90
+00:09:13,070 --> 00:09:20,040
+N بده يسوى ال M في Nيبقى هذا يعطينا common divisor
+
+91
+00:09:20,040 --> 00:09:25,980
+لل M و N يبقى كمية طب ال M مش ال order تبع ال G و
+
+92
+00:09:25,980 --> 00:09:32,260
+ال N هو ال order تبع ال H يبقى هذا معناه ان ال M
+
+93
+00:09:32,260 --> 00:09:44,640
+and ال N are relatively prime هذا يعطيناهذا بدي
+
+94
+00:09:44,640 --> 00:09:51,120
+يعطينا ان ال order ل capital G لل group كلها and
+
+95
+00:09:51,120 --> 00:09:57,700
+ال order ل ال H are relatively right
+
+96
+00:10:03,000 --> 00:10:07,320
+أحنا خلصنا الاتجاه الأول في النظرية، وهو أنه لو
+
+97
+00:10:07,320 --> 00:10:14,100
+كان الـ G إكسيندرايكالبرودك مع H is cyclic يبقى
+
+98
+00:10:14,100 --> 00:10:17,080
+الأوردر لـ G و الأوردر لـ H are relatively
+
+99
+00:10:17,080 --> 00:10:22,010
+primary، لأننا بدأ نمشي العملية العكسيةأثبت و افرض
+
+100
+00:10:22,010 --> 00:10:27,250
+ان اتنين هدول are relatively prime ذاتس يعني ايش
+
+101
+00:10:27,250 --> 00:10:32,030
+ذاتس؟ لجريس ال common divisor لل M و N بده يساوي
+
+102
+00:10:32,030 --> 00:10:37,350
+كده ايش؟ بده يساوي واحد صحيح طيب في حاجة موجودة في
+
+103
+00:10:37,350 --> 00:10:42,690
+النصر وحتى الآن لم نستخدمها اشيو .. اللي كل واحدة
+
+104
+00:10:42,690 --> 00:10:47,350
+من ال two groups اتنين هدول cycling مدام كل واحدة
+
+105
+00:10:47,350 --> 00:10:56,270
+cycling اذا كل واحدة فيهاgenerator يبقى since ال g
+
+106
+00:10:56,270 --> 00:10:59,350
+since
+
+107
+00:10:59,350 --> 00:11:07,070
+ال g is cyclic we have since ال .. خلي ال g باتنين
+
+108
+00:11:07,070 --> 00:11:15,950
+مرة واحدة since ال g and ال h and ال h are cyclic
+
+109
+00:11:15,950 --> 00:11:24,510
+we haveإن الـ G هذه في الها generator وليكن small
+
+110
+00:11:24,510 --> 00:11:33,050
+g and ال H الهاهاها اللي هو generator وليكن main
+
+111
+00:11:33,050 --> 00:11:38,110
+وليكن H طيب
+
+112
+00:11:38,110 --> 00:11:46,110
+إذا قداش ال order ل G small M و ال order ل H M
+
+113
+00:11:46,110 --> 00:11:52,630
+يكويس يبقى هذا بده يعطيناإن ال order للـ G بده
+
+114
+00:11:52,630 --> 00:11:58,430
+يساوي ال M and ال order ل H بده يساوي ال main بده
+
+115
+00:11:58,430 --> 00:12:05,390
+يساوي ال N طيب كويس يبقى أنا بده أجي لل order تبع
+
+116
+00:12:05,390 --> 00:12:11,630
+ال G و ال H مرة واحدة يبقى هذا الكلام بده يساوي
+
+117
+00:12:11,630 --> 00:12:16,950
+least common multiple لل order بتبع ال G و ال
+
+118
+00:12:16,950 --> 00:12:23,120
+order بتبع ال Hيبقى هذا الكلام بدي يسوى ال least
+
+119
+00:12:23,120 --> 00:12:30,180
+common multiple ال least common multiple لمين؟ لل
+
+120
+00:12:30,180 --> 00:12:39,940
+M و لل N أنا أدعي ان M في N طيب ليش؟ لأن ال common
+
+121
+00:12:39,940 --> 00:12:47,400
+divisor يسوى 1 يبقى هذا ليش؟ لأنإن الـ common
+
+122
+00:12:47,400 --> 00:12:54,480
+divisor لـ M و لـ N يبدو يساوي واحد صحيح طب هذا
+
+123
+00:12:54,480 --> 00:13:00,120
+الـ M في الـ N هو عبارة عن ال order لمن؟ ال order
+
+124
+00:13:00,120 --> 00:13:03,970
+لل group اللي هو نسميه هايوهو عبارة عن الـ order
+
+125
+00:13:03,970 --> 00:13:09,850
+للجروب يبقى هذا الكلام يساوي ال order للـ G
+
+126
+00:13:09,850 --> 00:13:15,530
+external direct product لمن؟ لل H يبقى ال gate
+
+127
+00:13:15,530 --> 00:13:20,630
+element موجود في ال external direct product ال
+
+128
+00:13:20,630 --> 00:13:26,150
+order له يساوي ال order لمن؟ لل group يبقى ال
+
+129
+00:13:26,150 --> 00:13:31,250
+group هذا ما يصير؟ Cyclic وهذا generator يبقى هنا
+
+130
+00:13:31,250 --> 00:13:43,780
+ساالـ G والـ H is a generator for اللي هو الـ G
+
+131
+00:13:43,780 --> 00:13:50,320
+external direct product مع مين مع H هذا بده يعطيلك
+
+132
+00:13:50,320 --> 00:13:57,620
+انه G external direct product مع H is cyclic وهو
+
+133
+00:13:57,620 --> 00:14:05,720
+المطلوبإذا قلت لك إثبت
+
+134
+00:14:05,720 --> 00:14:11,100
+الـexternal هذا direct product is cyclic تمام؟
+
+135
+00:14:11,100 --> 00:14:15,520
+بعدين بقوله إذا والله التنتين كل واحدة فيهم cyclic
+
+136
+00:14:15,520 --> 00:14:18,940
+وال order تبع كل واحدة فيهم مع التاني اتنين
+
+137
+00:14:18,940 --> 00:14:22,570
+relatively primeor than automatic على طول الخطب
+
+138
+00:14:22,570 --> 00:14:27,210
+هذه النظرية ال external direct product is cyclic
+
+139
+00:14:27,210 --> 00:14:31,670
+group يبقى الشرط ال external direct product أن
+
+140
+00:14:31,670 --> 00:14:36,270
+يكون cyclic group أمرين الأمر الأول كل واحدة فيهم
+
+141
+00:14:36,270 --> 00:14:41,190
+تبقى cyclic الأمر الثاني ال order لل group الأولى
+
+142
+00:14:41,190 --> 00:14:43,850
+و ال order لل group التاني يكونوا اتنين معاهم
+
+143
+00:15:00,200 --> 00:15:05,820
+النظرية هذه أثبتناها لمين لتو group طب لو صاروا
+
+144
+00:15:05,820 --> 00:15:11,810
+تلاتةتلاتة groups والله أربعة والله خمسة والله in
+
+145
+00:15:11,810 --> 00:15:16,550
+من ال groups فالنظرية صحيحة وهذا الموضوع ل
+
+146
+00:15:16,550 --> 00:15:27,390
+crawlery رقم واحد يبقى crawlery رقم واحد بتقول ان
+
+147
+00:15:27,390 --> 00:15:34,230
+external direct product ان external direct
+
+148
+00:15:35,820 --> 00:15:44,680
+a product external direct product g one external
+
+149
+00:15:44,680 --> 00:15:50,520
+direct product مع g two external direct product مع
+
+150
+00:15:50,520 --> 00:16:03,000
+مين مع g n of a finite of a finite number
+
+151
+00:16:04,660 --> 00:16:20,060
+finite number of finite cyclic groups is
+
+152
+00:16:20,060 --> 00:16:33,660
+cyclic if and only ifالـ order للـ G I and ال
+
+153
+00:16:33,660 --> 00:16:46,100
+order للـ G J are relatively a prime are
+
+154
+00:16:46,100 --> 00:16:54,380
+relatively a prime when ال I لا تساوي مين؟ لا
+
+155
+00:16:54,380 --> 00:17:02,540
+تساوي ال Gكمان كرولري تانية بتقول
+
+156
+00:17:02,540 --> 00:17:10,240
+let اللي هو ال M عملناها تحليل صارت N واحد في N
+
+157
+00:17:10,240 --> 00:17:18,760
+اتنين في N K then ال
+
+158
+00:17:18,760 --> 00:17:31,150
+ZM ال ZM isomorphicلمن؟ ل z n one external product
+
+159
+00:17:31,150 --> 00:17:43,350
+مع z n two external product مع من؟ مع z n k if and
+
+160
+00:17:43,350 --> 00:17:53,930
+only if if and only if ال n i and ال n j are
+
+161
+00:17:53,930 --> 00:18:06,240
+relatively primeare relatively prime when
+
+162
+00:18:06,240 --> 00:18:11,100
+I لا تساوي الجهة
+
+163
+00:18:38,860 --> 00:18:44,120
+الكرولري الأولى هي تعميم للنظرية الكرولري الثانية
+
+164
+00:18:44,120 --> 00:18:48,760
+كأنه تطبيق مباشر عالمين على النظرية تعالى نشوف
+
+165
+00:18:48,760 --> 00:18:53,640
+التعميم في الأول ومن ثم بنروح للكرولري التانية
+
+166
+00:18:53,640 --> 00:18:59,380
+اللى هي رقم اتنين يبقى هذه الكرولري الرقم اتنين
+
+167
+00:19:00,650 --> 00:19:03,590
+تعالى اكررلى رقم واحد بيقول ان external direct
+
+168
+00:19:03,590 --> 00:19:08,770
+product لمجموعة من ال group of a finite number
+
+169
+00:19:08,770 --> 00:19:13,330
+يبقى عدد محدود من ال groups وكل group has finite
+
+170
+00:19:13,330 --> 00:19:18,490
+order كل واحدة اللى عدد تبعها محدود يبقى هذا ال
+
+171
+00:19:18,490 --> 00:19:21,710
+external direct product بيكون cyclic if and only
+
+172
+00:19:21,710 --> 00:19:26,230
+if ال order لجي اي and ال order لجي جي are
+
+173
+00:19:26,230 --> 00:19:31,510
+relatively primeوان ال I لا تساوي ال جيه يعني بديش
+
+174
+00:19:31,510 --> 00:19:36,650
+اقول لجروبه نفسه هى المقصود I لا تساوي الجيه يعني
+
+175
+00:19:36,650 --> 00:19:40,570
+هاد الجروب تختلف تماما مع من مع هاد الجروب طب احنا
+
+176
+00:19:40,570 --> 00:19:47,290
+عندنا كام جروبأي واحدة مع التانية بيكون relatively
+
+177
+00:19:47,290 --> 00:19:50,270
+prime يعني الأولى مع التانية الأولى مع التالتة
+
+178
+00:19:50,270 --> 00:19:54,350
+الأولى مع العاشرة التانية مع التالتة التانية مع ..
+
+179
+00:19:54,350 --> 00:19:58,950
+كله are relatively prime تمام ال order تبع كل
+
+180
+00:19:58,950 --> 00:20:01,550
+واحدة منهم مع ال order مع التانية بيكون are
+
+181
+00:20:01,550 --> 00:20:05,420
+relatively primeوهو تعميم للنظرية النظرية كانت
+
+182
+00:20:05,420 --> 00:20:08,620
+عالميا على two groups اللي هي GUH عمّمناها
+
+183
+00:20:08,620 --> 00:20:11,800
+خلّيناهم تلاتة خلّيناهم أربعة خلّيناهم خمسة مش
+
+184
+00:20:11,800 --> 00:20:16,900
+مشكلة قد ما يكون العدد يبقى هذه النظرية صحيح عليهم
+
+185
+00:20:16,900 --> 00:20:21,700
+وهي هذه النتيجة رقم واحد الا للنتيجة رقم اتنين
+
+186
+00:20:21,700 --> 00:20:27,780
+بيقول لو عندك رقم M حللته إلى حاصل ضرب أعداد زي
+
+187
+00:20:27,780 --> 00:20:33,700
+ايش مثلا زي تلاتينتلاتين بقدر اقول اتنين في تلاتة
+
+188
+00:20:33,700 --> 00:20:38,780
+في خمسة يبقى هاي حلته لحاصل ضرب ثلاثة اعداد
+
+189
+00:20:38,780 --> 00:20:43,480
+والثلاثة اعداد ما لهم؟ Primes اتنين والتلاتة
+
+190
+00:20:43,480 --> 00:20:48,500
+والخمسة are primes ايش بقول هنا؟لو حللت ال M لحاصل
+
+191
+00:20:48,500 --> 00:20:58,140
+ضرب أعداد يبقى ZM isomorphic ل ZN1, ZN2, ZN3, ZNK,
+
+192
+00:20:58,400 --> 00:21:04,080
+F and only F كل عدد من هذه الأعداد are relatively
+
+193
+00:21:04,080 --> 00:21:10,580
+prime مع بعضهم البعض يعني ليس بالضرورة أن يكونوا
+
+194
+00:21:10,580 --> 00:21:15,240
+primes وإنما يكونوا relatively primesيعني ممكن اخد
+
+195
+00:21:15,240 --> 00:21:21,360
+اللي هو العدد اتنين مع العدد سبعة ممكن اخد ستة و
+
+196
+00:21:21,360 --> 00:21:24,800
+خمسة ستة و خمسة اتنين relatively primes رغم انه
+
+197
+00:21:24,800 --> 00:21:29,980
+خمسة primes ستة لأ تمام يبقى ليس بالضرورة ان تكون
+
+198
+00:21:29,980 --> 00:21:35,420
+هذه الاعداد primes مثل ما حللنا اش التلاتين يبقى
+
+199
+00:21:35,420 --> 00:21:40,310
+ممكن يكون اربعة و عشرينأربعة و عشرين هو تلاتة في
+
+200
+00:21:40,310 --> 00:21:45,110
+تمان يعني اتنين في تلاتة في اربع مظبوط يبقى الاربع
+
+201
+00:21:45,110 --> 00:21:47,730
+و عشرين اتنين في تلاتة في ستة في اربع و اربع و
+
+202
+00:21:47,730 --> 00:21:53,010
+عشرين الان يبقى هذول اتنين في تلاتة في ستة اتنين و
+
+203
+00:21:53,010 --> 00:21:57,810
+تلاتة هذول الـprimes بس إيش بيصير اتنين مع الأربع
+
+204
+00:21:57,810 --> 00:22:01,880
+are not relatively primeيبقى بصير كل ابن هذا صحيح
+
+205
+00:22:01,880 --> 00:22:06,600
+ولا مش صحيح؟ مش صحيح لازم تاخد أي رقمين منهم
+
+206
+00:22:06,600 --> 00:22:10,640
+ودمكونوا مع بعض اتنين معاهم relatively a primes
+
+207
+00:22:10,640 --> 00:22:16,220
+وليس بالضرورة ان يكونوا a primes يبقى مرة تانية
+
+208
+00:22:16,220 --> 00:22:22,740
+بقول حللت ال M الى حاصل ضرب اعدادمدام حللت يجزد ام
+
+209
+00:22:22,740 --> 00:22:30,040
+الأصلية isomorphic لمام لل external direct product
+
+210
+00:22:30,040 --> 00:22:35,340
+اللي هم كلهم هدول if and only if أي اتنين منهم
+
+211
+00:22:35,340 --> 00:22:39,640
+بدهم يكونوا relatively prime مع بعضهم البعض الان
+
+212
+00:22:39,640 --> 00:22:46,020
+نعطيك تمثيل عددي شغل عددي كيف هذا الكلام example
+
+213
+00:22:53,570 --> 00:22:58,310
+هذا هو التوضيح اللي قال لو جيت ل z دي اتنين
+
+214
+00:22:58,310 --> 00:23:04,670
+external like product مع z دي اتنين external like
+
+215
+00:23:04,670 --> 00:23:11,390
+product مع z تلاتة external like product مع مين؟
+
+216
+00:23:11,390 --> 00:23:14,590
+مع z خمسة بالشكل اللي عندنا
+
+217
+00:23:17,820 --> 00:23:21,800
+بدي أكوّن من هذه مجموعة milligroups بيكونوا
+
+218
+00:23:21,800 --> 00:23:27,260
+isomorphic لها باجي بقول والله كويس شرايك التنتين
+
+219
+00:23:27,260 --> 00:23:31,200
+هذول are relatively prime اتنين والتلاتة ولا لأ
+
+220
+00:23:31,200 --> 00:23:38,460
+اذا هذه isomorphic لمين زد ستة زد ستة لأن انا قولك
+
+221
+00:23:38,460 --> 00:23:44,580
+M و هذا M فين بس أصغر شوية واحدة واحدةيبقى هذه
+
+222
+00:23:44,580 --> 00:23:53,600
+isomorphic لمين؟ لزد اتنين كما هي لزد اتنين
+
+223
+00:23:53,600 --> 00:24:00,340
+اكستيرنا ال product لزد ستة اكستيرنا ال product
+
+224
+00:24:00,340 --> 00:24:11,060
+لمن؟ لزد خمسة ليش؟ since اتنين and التلاتة are
+
+225
+00:24:11,430 --> 00:24:21,670
+relatively prime طيب ..الان هذى بدي اجيب كمان
+
+226
+00:24:21,670 --> 00:24:28,630
+group اخرى isomorphic لهاوهذه كمان isomorphic لزد
+
+227
+00:24:28,630 --> 00:24:32,750
+اتنين external by product هدول اتنين are
+
+228
+00:24:32,750 --> 00:24:39,110
+relatively prime يبقى زد مين؟ زد تلاتين حاصلة ضرب
+
+229
+00:24:39,110 --> 00:24:49,230
+يبقى هذه لزد تلاتين يبقى ليش؟ since الستة and
+
+230
+00:24:49,230 --> 00:24:53,650
+الخمسة are relatively
+
+231
+00:24:57,660 --> 00:25:04,940
+السؤال هو هل هذا ايزو مورفك لزد ستين لأ ليش لأن
+
+232
+00:25:04,940 --> 00:25:12,080
+هذا ليس عشان ايزو مورفك لزد ستين وستين وهي هذا ليس
+
+233
+00:25:12,080 --> 00:25:24,880
+عشان ايزو مورفك لزد ستين لأن السبب ان الاتنين and
+
+234
+00:25:25,300 --> 00:25:30,240
+الثلاثين ليسوا
+
+235
+00:25:30,240 --> 00:25:41,180
+مرتفعين بشكل عام طيب
+
+236
+00:25:41,180 --> 00:25:47,640
+ايش رايك؟ بدي اخلق كمان groups اخرى ايزو مورفة
+
+237
+00:25:47,640 --> 00:25:57,570
+لهذه ال group also لو جيت اخدتاللي هو Z اتنين
+
+238
+00:25:57,570 --> 00:26:03,490
+external by-product لزد اتنين external by-product
+
+239
+00:26:03,490 --> 00:26:10,010
+لزد تلاتة external by-product لزد خمسة is
+
+240
+00:26:10,010 --> 00:26:15,910
+isomorphic قلنا قبل قليل زد اتنين external by
+
+241
+00:26:15,910 --> 00:26:21,850
+-product is ستة external by-product لمن لزد خمسة
+
+242
+00:26:23,460 --> 00:26:27,620
+هذا اللي قلناها قبل قليل من هذه بدي أخلق groups
+
+243
+00:26:27,620 --> 00:26:32,320
+أخرى تبقى isomorphic لنفس ال group كيف كانت تالية
+
+244
+00:26:32,320 --> 00:26:39,840
+أطلع لي هنا بقدر أكتب هذه Z2 زي ما هي هذه Z6 انقول
+
+245
+00:26:39,840 --> 00:26:45,980
+Z2 external dichromate مع Z3 ولا Z3 external مع Z2
+
+246
+00:26:45,980 --> 00:26:50,160
+نفس الشيء لأنه حصل ضربهم يسوء 6 و 2 are relatively
+
+247
+00:26:50,160 --> 00:26:54,690
+prime بنفس النظرية اللي هي قبل قليليبقى بناءً عليه
+
+248
+00:26:54,690 --> 00:27:00,210
+هذه بقدر أقول بدل ما هي z6 بدي أقول عليها z3
+
+249
+00:27:00,210 --> 00:27:05,690
+external by-product مع z2 external by-product مع
+
+250
+00:27:05,690 --> 00:27:16,790
+z5 طيب هذه isomorphic لمن؟ طلعلي لهذه relatively
+
+251
+00:27:16,790 --> 00:27:24,330
+primeيبقى هذول الـ Z6 External Direct Product مع
+
+252
+00:27:24,330 --> 00:27:30,610
+Z2 External Direct Product مع Z5 يبقى هذه جروب
+
+253
+00:27:30,610 --> 00:27:37,130
+جديدة بدي أطلع كمان جروب تاني يبقى هذه isomorphic
+
+254
+00:27:37,130 --> 00:27:45,770
+كمان لمين؟ لـ Z6 External Direct Product 2 5 يبقى
+
+255
+00:27:45,770 --> 00:27:54,900
+مع Z10ليش؟ لأنه الستة والخمسة are .. لأنه الاتنين
+
+256
+00:27:54,900 --> 00:28:00,140
+والخمسة are relatively prime يبقى هذا sense اتنين
+
+257
+00:28:00,140 --> 00:28:10,160
+and خمسة are relatively primeوالخطوة الأولى اللى
+
+258
+00:28:10,160 --> 00:28:13,380
+عندنا زد ستة لإنه اتنين و تلاتة relatively prime
+
+259
+00:28:13,380 --> 00:28:20,600
+هذا كتبناه قبل قليل طب السؤال هو هل هذه isomorphic
+
+260
+00:28:20,600 --> 00:28:28,340
+لزد ستين ما يفيها ستين عنصر طبعا لأ السبب because
+
+261
+00:28:29,790 --> 00:28:40,350
+إن الستة و العشرة ليسوا مرتبطين بشكل
+
+262
+00:28:40,350 --> 00:28:40,370
+عام
+
+263
+00:28:47,410 --> 00:28:53,090
+بقول isomorphic وين هي؟ لأ لأ كله isomorphic يا
+
+264
+00:28:53,090 --> 00:28:57,310
+شباب ماعنديش ماقلتش يساوي يبقى لو قلت يساوي معناته
+
+265
+00:28:57,310 --> 00:29:03,170
+كل عنصر يساوي نظيره لكن هذه group تختلف عن هذه
+
+266
+00:29:03,170 --> 00:29:08,050
+يعني مثلا عنصر اللي هنا لو بده أخد الواحد و من هنا
+
+267
+00:29:08,050 --> 00:29:12,010
+بده أخد اتنين و من هنا بده أخد ال zero و من هنا
+
+268
+00:29:12,010 --> 00:29:16,350
+بده أخد الأربعة مثلابيختلف عن هذا اللي هنا وهكذا
+
+269
+00:29:16,350 --> 00:29:20,810
+إذا أي زمار فيك يعني لجروب الأولى و لجروب التانية
+
+270
+00:29:20,810 --> 00:29:27,730
+لها نفس الخواص الرياضية يبقى هاي كل اللي بنقوله
+
+271
+00:29:27,730 --> 00:29:33,530
+بناسمة يعني هذا مثال عملي على الشغلانة طيب ننتقل
+
+272
+00:29:33,530 --> 00:29:39,110
+الآن لنقطة برضه لها علاقة بهذا الموضوع
+
+273
+00:29:58,550 --> 00:30:02,970
+في هنا تعريف أخدناه سابقا في chapter of subgroup
+
+274
+00:30:02,970 --> 00:30:11,090
+نذكره لأنه بدنا نبني الشغل عليه definition تعريف
+
+275
+00:30:11,090 --> 00:30:17,810
+يقول if ال K is a divisor of N if ال K is a
+
+276
+00:30:17,810 --> 00:30:30,020
+divisor of N لو كان ال K قاسم لل N وdefine بدنا
+
+277
+00:30:30,020 --> 00:30:40,800
+نروح انعرف ال U K of N هو كل العناصر X اللي موجودة
+
+278
+00:30:40,800 --> 00:30:48,740
+في U M X اللي موجودة في U N such that X modulo K
+
+279
+00:30:48,740 --> 00:30:57,410
+بده ساوي مين بده ساوي الواحدوهذا شباب sub group من
+
+280
+00:30:57,410 --> 00:30:58,850
+ال UN
+
+281
+00:31:20,410 --> 00:31:23,750
+طلعلي في الكلام اللى احنا كتبينه من أول و جديد
+
+282
+00:31:23,750 --> 00:31:29,610
+بدنا نعطي تعريف و هذا التعريف مر علينا قبل هيك
+
+283
+00:31:29,610 --> 00:31:35,150
+يبقى احنا بس بنذكر بالذكر بقول لو كان عندي K هو
+
+284
+00:31:35,150 --> 00:31:40,010
+divisor لل N يبقى الشرط أساسي ان ال K لازم يقسمين
+
+285
+00:31:42,860 --> 00:31:49,420
+بنعرف ستة جديدة سميتها U K of N U N نعرفينها كل
+
+286
+00:31:49,420 --> 00:31:53,220
+الإعداد اللي هي relatively prime مع M بس U K دخلت
+
+287
+00:31:53,220 --> 00:31:59,960
+على خط بيقول لمينكل ال X's اللي موجودة في UN يبقى
+
+288
+00:31:59,960 --> 00:32:04,720
+عناصر من UN بحيث ال X modulo K بيسوي جداش واحد
+
+289
+00:32:04,720 --> 00:32:09,800
+يعني كل الأعداد اللي الفرق بينها وبين الواحد يسوي
+
+290
+00:32:09,800 --> 00:32:15,880
+مضاعفات ال K كل الأعداد اللي موجودة في UN اللي
+
+291
+00:32:15,880 --> 00:32:19,740
+الفرق بينها وبين الواحد هي مضاعفات ال K يعني Zero
+
+292
+00:32:20,270 --> 00:32:26,410
+طبعا يعني لو طرحت هذا العدد من الواحد بدي يطلعلي
+
+293
+00:32:26,410 --> 00:32:32,030
+مضاعفات ال K يطلعلي K يطلعلي 2K مضاعفات يعني كأنه
+
+294
+00:32:32,030 --> 00:32:35,130
+المضاعفات ال K زائد واحد صحيح يبقى الفرق بينهم
+
+295
+00:32:35,130 --> 00:32:43,210
+بيساوي Zero نعطي مثال let ال
+
+296
+00:32:43,210 --> 00:32:50,020
+G بدها تساوي U أربعينU اربعين مين عناصرها شباب طيب
+
+297
+00:32:50,020 --> 00:32:57,220
+find بدنا تمانية بدنا عدد يقسم الاربعين وليكن
+
+298
+00:32:57,220 --> 00:33:05,100
+تمانية مثلا find U تمانية of اربعين هي اللي بدنا
+
+299
+00:33:05,100 --> 00:33:06,440
+solution
+
+300
+00:33:12,160 --> 00:33:16,040
+الأول اللي بدنا نعرفه هو عناصر الـU40 ومنهم بدنا
+
+301
+00:33:16,040 --> 00:33:22,480
+نبدأ نجّه يبقى بداجة أقول له الـU40 عناصرها اللي
+
+302
+00:33:22,480 --> 00:33:31,680
+هي واحد اتنين تلاتة أربع خمسة ستة انسة سبعة تمانية
+
+303
+00:33:31,680 --> 00:33:44,690
+تسعة11 .. 13 .. 14 .. 15 .. 16 .. 17 .. 19 .. 21
+
+304
+00:33:44,690 --> 00:33:47,710
+..
+
+305
+00:33:47,710 --> 00:33:59,490
+23 .. 24 .. 25 .. 26 .. 27 ..وكمان تسعة و عشرين
+
+306
+00:33:59,490 --> 00:34:07,490
+تلاتين انسى واحد و تلاتين اتنين و تلاتين تلاتة و
+
+307
+00:34:07,490 --> 00:34:12,670
+تلاتين اربعة و تلاتين خمسة و تلاتين ستة و تلاتين
+
+308
+00:34:12,670 --> 00:34:18,910
+سبعة و تلاتين تسعة و تلاتين يبقى هذه عناصر من
+
+309
+00:34:18,910 --> 00:34:21,050
+عناصر ال U اربعين
+
+310
+00:34:27,390 --> 00:34:33,650
+أحنا بنشرح للكل مش لوحد، كنا بنشرح للكل، الضعيف
+
+311
+00:34:33,650 --> 00:34:37,190
+والوسط والقوي كله موجود، بدك تحكي كلام يتناسب مع
+
+312
+00:34:37,190 --> 00:34:41,010
+الجميعماشي يعني انا كان بيبقى مكان يقولك ده هي
+
+313
+00:34:41,010 --> 00:34:44,270
+دغري خد اللي هي الرقمين تلاتة و اقولك ده هم لكنها
+
+314
+00:34:44,270 --> 00:34:49,790
+بناشك بننفم كل خطوة بنعملها كيف جت هالي طيب قاللي
+
+315
+00:34:49,790 --> 00:34:54,410
+احسبلي قداش ال U تمانية و أربعين فباجي بقوله U
+
+316
+00:34:54,410 --> 00:35:05,110
+تمانية و أربعين بده تساوي U ساوي هل الواحد منهملو
+
+317
+00:35:05,110 --> 00:35:11,130
+قلت لي لأ هقولها غلط لأن قبل قليل جالك هذه ال
+
+318
+00:35:11,130 --> 00:35:16,510
+group تحتوي على ال identity اتنين واحد ناقص واحد
+
+319
+00:35:16,510 --> 00:35:22,090
+يسوى جداش ال zero له مضاعفات الأربعين أو مضاعفات
+
+320
+00:35:22,090 --> 00:35:26,310
+ال K مضاعفات التمانية اللي عندنا يبقى الواحد منهم
+
+321
+00:35:27,330 --> 00:35:33,470
+يالا تسعة لو شيلت من أواها بصير تمانية تمام يبقى
+
+322
+00:35:33,470 --> 00:35:39,190
+هذه التسعة أحداشر تلتاشر سبعتاشر شيلت من أواها بضل
+
+323
+00:35:39,190 --> 00:35:44,600
+كده ستاشر هي مضاعفات التمانيةيبقى ايه سبعتاشر
+
+324
+00:35:44,600 --> 00:35:52,080
+تسعتاشر لأ واحد و عشرين تلاتة و عشرين سبعة و عشرين
+
+325
+00:35:52,080 --> 00:36:00,260
+تسعة و عشرين واحد و تلاتين تلاتة و تلاتين اه تلاتة
+
+326
+00:36:00,260 --> 00:36:06,160
+و تلاتين منهمتلاتة و تلاتين لإن لو أقل منها واحد
+
+327
+00:36:06,160 --> 00:36:10,780
+فتبقى اتنين و تلاتين تسمع تمانية ستة و تلاتين لأ
+
+328
+00:36:10,780 --> 00:36:16,160
+تمانية و تلاتين لأ يبقى ماعنديش إلا الأربعة عناصر
+
+329
+00:36:16,160 --> 00:36:19,820
+اللي قدامي يعني يبقى إذن ال U تمانية و أربعين هي
+
+330
+00:36:19,820 --> 00:36:23,860
+واحد و تسعة و سبتاشر و تلاتة و تلاتين و كل منها
+
+331
+00:36:23,860 --> 00:36:29,490
+يحقق منالمعادلة او حسبناهم بناء على التعريف اللى
+
+332
+00:36:29,490 --> 00:36:37,550
+اعطناه ل UKM هذا كلام مهم لان بدنا نبني عليه شغل
+
+333
+00:36:37,550 --> 00:36:42,230
+تاني بعد قليل الان بدنا نيجي لنظرية اخرى في هذا
+
+334
+00:36:42,230 --> 00:36:47,350
+الشبتر النظرية بتقول ما يأتي IRM
+
+335
+00:36:52,330 --> 00:37:06,230
+theorem suppose that suppose that ان ال S and T ال
+
+336
+00:37:06,230 --> 00:37:18,490
+S and T are relatively prime are relatively prime
+
+337
+00:37:20,290 --> 00:37:31,510
+are relatively prime then then
+
+338
+00:37:31,510 --> 00:37:40,830
+ال U S T ال U S T isomorphic
+
+339
+00:37:40,830 --> 00:37:50,770
+لل U S external product مع مين مع U Tmoreover
+
+340
+00:37:50,770 --> 00:37:54,230
+وأكثر
+
+341
+00:37:54,230 --> 00:37:59,050
+من ذلك ال
+
+342
+00:37:59,050 --> 00:38:12,930
+subgroup U S of ST isomorphic ل U T and ال U Tلمن
+
+343
+00:38:12,930 --> 00:38:22,170
+لل ST isomorphic لمن ل US الشكل اللي عندنا انا
+
+344
+00:38:22,170 --> 00:38:32,050
+isomorphic ل US وفي نتيجة عليها ك رولري بتقول
+
+345
+00:38:32,050 --> 00:38:44,170
+ما يأتي let ال M بدأ تساوي N واحد N اتنينولغاية NK
+
+346
+00:38:44,170 --> 00:38:55,190
+ان واحد ان اتنين لغاية NK where حيث لجلس ال common
+
+347
+00:38:55,190 --> 00:39:08,010
+divisor لل N I و N J بدها تساوي واحد for I لاتساوي
+
+348
+00:39:08,010 --> 00:39:09,810
+جي then
+
+349
+00:39:11,580 --> 00:39:19,920
+الـ UM ايزو مورفك لمن؟ لل U N 1 اكستاناضايك برودك
+
+350
+00:39:19,920 --> 00:39:28,200
+مع U N 2 اكستاناضايك برودك مع مين؟ مع U N K بالشكل
+
+351
+00:39:28,200 --> 00:39:28,860
+اللي عندنا هنا
+
+352
+00:39:42,060 --> 00:39:48,760
+مرة تانية بقول بقول لو عندك رقمين S وT are
+
+353
+00:39:48,760 --> 00:39:57,880
+relatively prime then ال U S T يبقى ال group اللي
+
+354
+00:39:57,880 --> 00:40:03,080
+عندنا ال U S T isomorphic لل externa تاكرودك تبقى
+
+355
+00:40:03,080 --> 00:40:09,120
+حاصل الضرب زي ايش مثلا لو قلتلك U خمستاشربقدر
+
+356
+00:40:09,120 --> 00:40:15,260
+اكتبها U تلاتة في خمسة مظبوط اذا هذه ال U خمساش
+
+357
+00:40:15,260 --> 00:40:19,820
+ايزو مورفك ل U تلاته اكسترنه ضايقة ضعفك مع مين مع
+
+358
+00:40:19,820 --> 00:40:24,740
+U خمسه هتقولي تلاته و خمسه relatively prime بقولك
+
+359
+00:40:24,740 --> 00:40:33,900
+ماشي اش رايك U تلاتين تساوي U خمسه في ستة صح خمسه
+
+360
+00:40:33,900 --> 00:40:39,070
+في ستة او عشرة في تلاتههذه وهذه او اتنين في
+
+361
+00:40:39,070 --> 00:40:43,410
+خمستاشر كلها أرقام are relatively prime اذا ال U
+
+362
+00:40:43,410 --> 00:40:47,930
+تلاتين isomorphic الى U عشرة في تلاتة او
+
+363
+00:40:47,930 --> 00:40:53,830
+isomorphic ل U خمسة في ستة او isomorphic للاتنين
+
+364
+00:40:53,830 --> 00:40:58,390
+في U اتنين external like product مع U خمستاشر و
+
+365
+00:40:58,390 --> 00:41:03,670
+هكذامدام الرقامين او التلاتة اللى عندك تلاتة من
+
+366
+00:41:03,670 --> 00:41:08,790
+اين جبتها دى؟ جبتها من الكرولري الكرولري بتقول اذا
+
+367
+00:41:08,790 --> 00:41:11,490
+ما عندك ليس بضرر رقامين ممكن الرقام اللى عندك
+
+368
+00:41:11,490 --> 00:41:16,090
+تحلله الى حصل ضرب ثلاثة رقام او اربعة ارقام او
+
+369
+00:41:16,090 --> 00:41:21,690
+خمسة او عشرة او كم من الأرقام حلل قد ما بدكيبقى لو
+
+370
+00:41:21,690 --> 00:41:27,990
+عندي الـ M هذا حللناه إلى حاصل ضرب N من الأرقام N1
+
+371
+00:41:27,990 --> 00:41:32,450
+N2 لغاية NK بحيث الـ greatest common divisor بين
+
+372
+00:41:32,450 --> 00:41:37,250
+أي اتنين بدي يكون relatively prime بدي يكون واحد
+
+373
+00:41:37,250 --> 00:41:41,690
+صحيح يعني الاتنين هذول are relatively prime يبقى
+
+374
+00:41:41,690 --> 00:41:46,830
+ال U M isomorphic ل U of الرقم الأول كستانادايكو
+
+375
+00:41:46,830 --> 00:41:51,030
+برودك U مع الرقم التاني كستانادايكو برودكمع الرقم
+
+376
+00:41:51,030 --> 00:41:55,250
+كي و هكذا المرة الجاية ان شاء الله بناخد أمثلة
+
+377
+00:41:55,250 --> 00:41:59,890
+توضحية على كيفية استخدام الكلام اللي عندنا هذا
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/AWHAVt1fZHw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/AWHAVt1fZHw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a995b828869b702f2c2199918b41bd976e808439
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/AWHAVt1fZHw.srt
@@ -0,0 +1,1747 @@
+1
+00:00:21,110 --> 00:00:24,390
+السلام عليكم ورحمة الله وبركاته محاضرتنا اليوم
+
+2
+00:00:24,390 --> 00:00:27,610
+إن شاء الله هتكون استكمالًا للشِعبة خمسة آخر حاجة 
+
+3
+00:00:27,610 --> 00:00:30,630
+اتكلمنا عنها المرة الماضية أخذنا مثال اللي هو ال
+
+4
+00:00:30,630 --> 00:00:36,010
+S3 وآخر كلمة كتبناها قلنا إن الـ S3 هي نفسها من
+
+5
+00:00:36,010 --> 00:00:42,190
+الـ D3 طبعًا قلنا ليه طبعًا هنثبت هذا الكلام الفكرة
+
+6
+00:00:42,190 --> 00:00:50,330
+في الإثبات أن الـ S3 هي نفسها الـ D3 احنا كتبنا ال
+
+7
+00:00:50,330 --> 00:00:56,150
+multiplication table للـ S3 write the
+
+8
+00:00:56,150 --> 00:01:00,610
+multiplication table 
+
+9
+00:01:00,610 --> 00:01:11,110
+of d3 then حاول تعمل يعني مقارنات بين الـ two
+
+10
+00:01:11,110 --> 00:01:16,650
+multiplication table then we can show that
+
+11
+00:01:18,600 --> 00:01:25,280
+أنّ الـ identity كانت بتقابل مين هاي الـ S3 وهي الـ D3
+
+12
+00:01:25,280 --> 00:01:30,860
+الـ S3 في الـ identity بتقابل الـ R نوت في الـ Alpha
+
+13
+00:01:30,860 --> 00:01:39,120
+بتقابل مين الـ R مي عشيد وفي الـ Alpha تغبيع بتقابل
+
+14
+00:01:39,120 --> 00:01:45,130
+مين الـ R240 في كان عند الـ Beta وفي الـ Alpha Beta
+
+15
+00:01:45,130 --> 00:01:51,310
+وفي الـ Alpha Beta أو الـ Alpha تغبيق Beta لو
+
+16
+00:01:51,310 --> 00:01:54,230
+اتكلمنا احنا عن الـ DC اللي عبارة عن دوران المثلث
+
+17
+00:01:54,230 --> 00:02:00,710
+ذكرنا المثلث اللي أخذناه كيف كان؟ كان 1 2 3 من أين
+
+18
+00:02:00,710 --> 00:02:06,250
+بيبدأ الـ 1؟ 1 2 3 لو جينا نقول F1
+
+19
+00:02:10,260 --> 00:02:14,640
+ماذا يعني اف واحد؟ انعكاس حول النقطة واحد هتصير
+
+20
+00:02:14,640 --> 00:02:20,620
+عبارة عن مين؟ واحد، تلاتة، اتنين، شوف لمين بتقابل
+
+21
+00:02:20,620 --> 00:02:26,080
+حسب الجدول واحد، اتنين، تلاتة، وندي باف في اتنين،
+
+22
+00:02:26,080 --> 00:02:30,340
+انعكاس حولين اتنين، ماذا يحصل معايا؟ هاي اتنين
+
+23
+00:02:30,340 --> 00:02:38,530
+وهاي تلاتة وهاي واحد، وانعكاس اللي هو واحد اتنين
+
+24
+00:02:38,530 --> 00:02:45,330
+تلاتة و الـ F تلاتة هاسي معايا بهذا الشكل اللي هو
+
+25
+00:02:45,330 --> 00:02:52,050
+تلاتة اتنين واحد ذكرني ايش كانت الـ beta الـ beta
+
+26
+00:02:52,050 --> 00:02:56,190
+ايش أخذناها كانت
+
+27
+00:02:56,190 --> 00:03:03,550
+تابعة عن ايش كانت أعتقد واحد تلاتة ال
+
+28
+00:03:03,550 --> 00:03:12,100
+beta كانت اللي هو أو جينا هنا الـ beta كانت واحد
+
+29
+00:03:12,100 --> 00:03:20,160
+اتنين تلاتة ثبتنا مين فيها ثبتنا الواحد يعني
+
+30
+00:03:20,160 --> 00:03:25,460
+عبارة عن مين الواحد ثابت فغيرنا التاني و التلاتة
+
+31
+00:03:25,460 --> 00:03:33,600
+هي F1 فهذه عبارة عن F1 طب والـ alpha beta ايش كانت
+
+32
+00:03:33,600 --> 00:03:42,630
+كانت عبارة عن 1,2,3 بعد ما ضربنا كان الناتج 2,1,3
+
+33
+00:03:42,630 --> 00:03:48,950
+مين اللي اتثبت هان التلاتة يعني هذا عبارة عن أف
+
+34
+00:03:48,950 --> 00:03:53,910
+تلاتة و الـ alpha تربيع beta هيكون عبارة عن ايش
+
+35
+00:03:53,910 --> 00:04:03,370
+هنثبت التنين هذه بس مش 1,2,3 1,3,2 و
+
+36
+00:04:03,370 --> 00:04:06,890
+الـ alpha تربيع beta هنثبت الواحد هيروح
+
+37
+00:04:20,220 --> 00:04:24,100
+بنفس الطريقة لو بنشتغل على D4
+
+38
+00:04:32,950 --> 00:04:38,090
+عدد عناصر الـ D4 بدي يساوي تمانية لكن عدد عناصر ال
+
+39
+00:04:38,090 --> 00:04:48,270
+S4 24 فمش تساوي طب مش لا علاقة لأ عناصر اللي هنا
+
+40
+00:04:48,270 --> 00:04:53,070
+هدول R0 R90 R270 إلى آخرها وهدول عبارة عن
+
+41
+00:04:53,070 --> 00:04:56,750
+permutationان أنا بدي اتكلم عن إن كله علاقة جزئية و
+
+42
+00:04:56,750 --> 00:05:01,630
+لأ مش صحيح لكن في نوع من ايش من التشابه إن عناصر
+
+43
+00:05:01,630 --> 00:05:06,530
+الـ D4 بيقابلوا عناصر وين في الـ S4 الـ D4 عبارة عن
+
+44
+00:05:06,530 --> 00:05:16,630
+ايش الـ R0 الـ R90 الـ R80 180 الـ R270 ومين عندي
+
+45
+00:05:16,630 --> 00:05:23,590
+كمان H وD وD'
+
+46
+00:05:23,590 --> 00:05:35,330
+وD وD' طيب لو اتكلمنا عن الـ R تسعين تساشر
+
+47
+00:05:35,330 --> 00:05:39,970
+إن الـ D فور مبارح عن ايش دورانات وعكسات وين في
+
+48
+00:05:39,970 --> 00:05:44,170
+المربع لو أنا بدأت المربع بهذا الشكل واحد اتنين
+
+49
+00:05:44,170 --> 00:05:51,270
+تلاتة أربعة وR90 يعني دوران بزاوية 90 درجة عكس
+
+50
+00:05:51,270 --> 00:05:56,970
+عقارب الساعة السماعية 1 2 3 4 يعني أنا اتكلمت أنا
+
+51
+00:05:56,970 --> 00:06:05,230
+ك permutation 1 2 3 4 الواحد ايش صار مكانه الواحد
+
+52
+00:06:05,230 --> 00:06:09,850
+لمين راح؟ للاربع الاتنين
+
+53
+00:06:11,790 --> 00:06:16,370
+هذه اتنين ايه صار مكان اتنين صار مكان واحد التلاتة
+
+54
+00:06:16,370 --> 00:06:28,350
+صار اتنين والاربع للتلاتة خدلي هذه Alpha هو
+
+55
+00:06:28,350 --> 00:06:33,810
+شوية بس لأ احنا أخطأنا في الـ .. في الـ .. في الـ ..
+
+56
+00:06:34,060 --> 00:06:38,500
+في الدورانات هو الواحد هي مكانه وصار مدال مين
+
+57
+00:06:38,500 --> 00:06:43,200
+الواحد انتقل وين مكانه كان مكانه هنا لما انتقل صار
+
+58
+00:06:43,200 --> 00:06:47,520
+مكان مين الاتنين فالواحد انتقل للاتنين الاتنين
+
+59
+00:06:47,520 --> 00:06:52,260
+انتقل لمين للتلاتة التلاتة انتقل للاربع والاربع
+
+60
+00:06:52,260 --> 00:06:56,200
+انتقل لمين لل
+
+61
+00:06:56,200 --> 00:07:07,800
+لا باتكلم على هنا بس طيب الـ alpha تربيع R180
+
+62
+00:07:07,800 --> 00:07:20,280
+الـ alpha تكعيب R90 الـ alpha تكعيب R270 الـ alpha أربعة ال
+
+63
+00:07:20,280 --> 00:07:22,400
+identity
+
+64
+00:07:23,340 --> 00:07:28,080
+البصارة عندك أول أربع عناصر في الـ D4 مثلتهم أنا
+
+65
+00:07:28,080 --> 00:07:33,140
+بمين؟ بالـ alpha والـ alpha تربيع والـ alpha تكعيب ومين؟ وال
+
+66
+00:07:33,140 --> 00:07:39,840
+identity ناخذ مثلًا الـ beta بهذا الشكل ونشوف ايش
+
+67
+00:07:39,840 --> 00:07:45,420
+بتمثلها في المربع واحد اتنين تلاتة أربعة اتنين واحد
+
+68
+00:07:45,420 --> 00:07:49,000
+أربعة تلاتة يعني
+
+69
+00:07:52,190 --> 00:07:57,990
+هي واحد هي اتنين هي تلاتة هي أربعة اصبر
+
+70
+00:07:57,990 --> 00:08:04,710
+شوية بس ايش صارت الواحد انتقل لمين الواحد انتقل
+
+71
+00:08:04,710 --> 00:08:09,270
+للتنين والتنين انتقل للواحد التلاتة والاربعة
+
+72
+00:08:09,270 --> 00:08:17,530
+اتبدلوا يعني هذا لانعكاس انعكاس horizontal ليه مين
+
+73
+00:08:17,530 --> 00:08:25,920
+H يعني هذه بتمثل مين الـ H طبعًا الـ beta تربيع
+
+74
+00:08:25,920 --> 00:08:31,000
+هيعطينا الـ identity بنفس الطريقة في عندي Alpha
+
+75
+00:08:31,000 --> 00:08:38,900
+Beta و Alpha تربيع Beta و Alpha تكعيب Beta كل
+
+76
+00:08:38,900 --> 00:08:45,600
+واحدة هتمثل لي حاجة من هدول طبعًا
+
+77
+00:08:45,600 --> 00:08:49,060
+بإمكانك تحسبهم Calculate
+
+78
+00:08:52,900 --> 00:09:03,620
+المحصلة إن الـ D4 بتشابه الـ identity Alpha Alpha
+
+79
+00:09:03,620 --> 00:09:09,180
+تربيع Alpha تكعيب Alpha Beta Alpha تربيع Beta
+
+80
+00:09:09,180 --> 00:09:13,080
+Alpha تكعيب Beta طبعًا الـ Alpha Beta والـ Alpha تربيع
+
+81
+00:09:13,080 --> 00:09:17,820
+Beta والـ Alpha تكعيب Beta هيمثلوا أحد اللي هو الـ V
+
+82
+00:09:17,820 --> 00:09:20,780
+والـ D والـ D'
+
+83
+00:09:24,720 --> 00:09:37,920
+8 أنا ناسي أحط الـ beta هدول
+
+84
+00:09:37,920 --> 00:09:44,320
+جزء من الـ S4 مش الـ S4 يعني هدا قدامي لما ناخدوا
+
+85
+00:09:44,320 --> 00:09:49,940
+isomorphism هسينا نتعامل مع الـ DN as a copy of
+
+86
+00:09:49,940 --> 00:09:57,290
+subgroup of SN الـ DN هتصير copy لـ sub group الـ SN
+
+87
+00:09:57,290 --> 00:10:05,730
+طبعًا سؤال الـ DN أشمالها not abelian وهي بتشابه جزء
+
+88
+00:10:05,730 --> 00:10:09,770
+من الـ SN من هذا المنطلق بتقدر تقول إن الـ SN
+
+89
+00:10:09,770 --> 00:10:15,250
+أشمالها not abelian تكون الـ SN not abelian
+
+90
+00:10:27,870 --> 00:10:37,850
+cycle notation موضوع
+
+91
+00:10:37,850 --> 00:10:41,110
+الـ cycle notation شباب له يعني بعض الأهميات
+
+92
+00:10:41,110 --> 00:10:47,230
+الأهمية الأولى إنه أنا بإمكاني أسهل طريقة الكتابة
+
+93
+00:10:47,230 --> 00:10:51,790
+بدل ما أكتب سطرين و واحد اتنين تلاتة أربعة لأنه
+
+94
+00:10:51,790 --> 00:10:54,290
+وبعدين أشوف الواحد لمين بيروح والتاني لمين بيروح
+
+95
+00:10:54,290 --> 00:11:01,530
+بإمكاني أكتبها بطريقة مختصرة الأهمية الثانية من
+
+96
+00:11:01,530 --> 00:11:05,510
+خلال الكتابة هذه بقدر أحدد الـ order بشكل سهل من
+
+97
+00:11:05,510 --> 00:11:10,360
+دون ما أروح أنا أقول إنه أداروا في نفس مرة ومرتين أو
+
+98
+00:11:10,360 --> 00:11:15,240
+تلاتة عشان أصل الـ order شغل تالتة بتفيدني في عملية
+
+99
+00:11:15,240 --> 00:11:21,860
+إيجاد الـ cyclic subgroup من الـ SN طبعًا الـ SN مش
+
+100
+00:11:21,860 --> 00:11:27,240
+abelian زي ما قلنا وبالتالي لما أبدأ أتعامل مع
+
+101
+00:11:27,240 --> 00:11:33,070
+subgroup منها وأشوف الـ cyclic subgroup لأ مش قصة
+
+102
+00:11:33,070 --> 00:11:36,070
+أصعب المعنى الـ الـ لما تكون الـ group مش
+
+103
+00:11:36,070 --> 00:11:40,150
+abelian وبدي أتعامل معاها داخليًا فالأفضل أتعامل
+
+104
+00:11:40,150 --> 00:11:44,910
+مع مين؟ مع الحاجات اللي التعامل معاها أسهل الأسهل
+
+105
+00:11:44,910 --> 00:11:50,210
+في التعامل هو الـ abelian ثم أكثر سهولة ليه ومين؟
+
+106
+00:11:50,210 --> 00:11:57,240
+الـ cycle شغل يعني ثاني احنا قلنا عن الـ order بصي
+
+107
+00:11:57,240 --> 00:12:04,860
+عندي سهولة في حسابه في عملية الضرب عشان أعرف إنه
+
+108
+00:12:04,860 --> 00:12:07,980
+هل alpha في beta بتساوي beta في alpha والله
+
+109
+00:12:07,980 --> 00:12:11,640
+مابتساويش الـ cyclic notation أو الـ cycle notation
+
+110
+00:12:11,640 --> 00:12:17,880
+بريّحني الفكرة هان كانت التالي لو أنا خدت alpha بهذا
+
+111
+00:12:17,880 --> 00:12:24,180
+الشكل واحد اتنين تلاتة أربعة خمسة ستة سبعة نكبّرها
+
+112
+00:12:24,180 --> 00:12:25,140
+مثلًا لتمانية
+
+113
+00:12:30,110 --> 00:12:34,090
+خلّي الواحد يروح للتنين التنين للسبعة والتلاتة
+
+114
+00:12:34,090 --> 00:12:40,630
+للخمسة والاربعة للواحد والخمسة للستة والستة
+
+115
+00:12:40,630 --> 00:12:45,050
+للتمانية وخلّي السبعة يروح للتلاتة والتمانية يروح
+
+116
+00:12:45,050 --> 00:12:51,950
+للاربعة لو أنا هادي permutation لو أنا بدي أروح
+
+117
+00:12:51,950 --> 00:12:56,190
+أسهلها في الـ cycle notation بمكاني أقول التالي
+
+118
+00:12:56,190 --> 00:13:04,290
+أفتح قوس وأبدأ بالواحد الواحد لمن بيروح؟ للتانين
+
+119
+00:13:04,290 --> 00:13:10,150
+باجع التانين لمن بيروح؟ للسبعة باجع السبعة لمن
+
+120
+00:13:10,150 --> 00:13:17,530
+بتروح؟ للتلاتة طب التلاتة لمن؟ للخمسة باجع الخمسة
+
+121
+00:13:17,530 --> 00:13:23,530
+لمن؟ للستة الستة لمن؟ للتمانية والتمانية لمن؟
+
+122
+00:13:23,530 --> 00:13:29,930
+للاربعة طبعًا أنا بقدر أفهم مباشرة إن الواحد بيروح
+
+123
+00:13:29,930 --> 00:13:35,650
+للتنين التنين للسبعة التلاتة للخمسة الأربعة للواحد
+
+124
+00:13:35,650 --> 00:13:40,790
+الخمسة للستة الستة للتمانية والسبعة للتلاتة
+
+125
+00:13:40,790 --> 00:13:45,030
+والتمانية لمين للاربع يعني بدل ما أنا أكتب في هذا 
+
+126
+00:13:45,030 --> 00:13:51,070
+الشكل ممكن أن يسهل عملية الكتابة طيب لو كانت زي
+
+127
+00:13:51,070 --> 00:13:51,450
+هيك
+
+128
+00:13:57,220 --> 00:14:01,860
+الواحد لنفسه، الاثنين للثلاثة، الثلاثة للخمسة
+
+129
+00:14:01,860 --> 00:14:10,620
+والأربعة للـ .. والأربعة للثلاثة، الخمسة مثلا للثنين
+
+130
+00:14:10,620 --> 00:14:17,400
+الستة للسبعة، السبعة للستة، والثمانية لنفسه، كيف بدي 
+
+131
+00:14:17,400 --> 00:14:26,800
+أكتبها؟ ببدأ بالشكل هذا، الواحد لمن لنفسه، بسكرلأ
+
+132
+00:14:26,800 --> 00:14:31,760
+ماجولش واحد واحد كيف؟
+
+133
+00:14:31,760 --> 00:14:38,400
+مين اللي ناجى صين دي هان؟ الأربعة خلي الاثنين
+
+134
+00:14:38,400 --> 00:14:45,400
+للأربعة، والأربعة للثلاثة، نبدأ بالاثنين، الاثنين
+
+135
+00:14:45,400 --> 00:14:52,040
+هتروح لمين؟ للأربعة، والأربعة والثلاثة للخمسة، الخمسة
+
+136
+00:14:52,040 --> 00:14:58,100
+لمين؟ انصر موجود معايا، بسكرطيب، بعد كده، واحد،
+
+137
+00:14:58,100 --> 00:15:02,020
+اثنين، ثلاثة، أربعة، خمسة، خلصتهم، مين بعده؟
+
+138
+00:15:02,020 --> 00:15:07,140
+الستة، لمين؟ السبعة لمين بترجع؟ للستة، والثمانية
+
+139
+00:15:07,140 --> 00:15:16,980
+لمين؟ للزوج اللي فيه عنصر واحد، بلزمنيش،
+
+140
+00:15:16,980 --> 00:15:20,930
+الواحد والثمانية بإمكاني أشيلهم، أو بتقلي
+
+141
+00:15:20,930 --> 00:15:24,610
+بفهم أنا إنه أنا عشان الواحد مش موجود، والتمانية
+
+142
+00:15:24,610 --> 00:15:40,190
+مش موجودة إنه يشملهم، يروحوا لنفسهم، طب تعالي نضغط لو 
+
+143
+00:15:40,190 --> 00:15:45,090
+قلت Alpha في Beta عبارة عن إيش؟ واحد اثنين ثلاثة
+
+144
+00:15:45,090 --> 00:15:51,570
+أربعة خمسة ستة سبعة ثمانية، واحد اثنين ثلاثة أربعة
+
+145
+00:15:51,570 --> 00:15:59,390
+خمسة ستة سبعة ثمانية، وهنا نجّلني اثنين سبعة خمسة 
+
+146
+00:15:59,390 --> 00:16:08,870
+واحد ستة ثمانية ثلاثة أربعة، واللي بعدها واحد 
+
+147
+00:16:08,870 --> 00:16:16,930
+أربعة خمسة ثلاثة اثنين سبعة ستة ثمانية، زي ما تعلمت
+
+148
+00:16:16,930 --> 00:16:24,590
+أنا واحد، اثنين، ثلاثة، أربعة، خمسة، ستة، سبعة،
+
+149
+00:16:24,590 --> 00:16:31,750
+ثمانية، ببدأ من هنا، الواحد لمين؟ للواحد، باجي هنا
+
+150
+00:16:31,750 --> 00:16:38,010
+الواحد لمين؟ يجب الواحد للثنين، الاثنين لمين؟
+
+151
+00:16:38,010 --> 00:16:43,330
+للأربعة، والأربعة يجب الاثنين للواحد، الثلاثة لمين؟
+
+152
+00:16:44,030 --> 00:16:48,650
+للخمسة، والخمسة لمن؟ يكبر الثلاثة للستة، الأربعة
+
+153
+00:16:48,650 --> 00:16:53,650
+للثلاثة، والثلاثة للخمسة، يكبر الأربعة لمن؟ للخمسة
+
+154
+00:16:53,650 --> 00:16:58,710
+الخمسة للثنين، والثنين للسبعة، يكبر الخمسة للسبعة
+
+155
+00:16:58,710 --> 00:17:02,950
+الستة للسبعة، والسبعة للثلاثة، يكبر الستة هتروح
+
+156
+00:17:02,950 --> 00:17:08,690
+لمين؟ للثلاثة، السبعة للستة، والستة للثمانية، يكبر
+
+157
+00:17:08,690 --> 00:17:13,830
+السبعة لمن؟ للثمانية، والثمانية للثمانية، والثمانية للأربعة
+
+158
+00:17:13,830 --> 00:17:18,370
+يكبر الثمانية لمن؟ للأربعة، أما الacyclic أو cycle
+
+159
+00:17:18,370 --> 00:17:23,130
+notation، الواحد للثنين، والثنين بيرجع للواحد
+
+160
+00:17:23,130 --> 00:17:31,870
+الثلاثة للستة، والستة لمن؟ للثلاثة، الأربعة للخمسة 
+
+161
+00:17:31,870 --> 00:17:39,090
+والخمسة لمن؟ للسبعة، والسبعة لمن؟ للثمانية، طب لاحظ
+
+162
+00:17:39,090 --> 00:17:43,610
+إن أنا هنا بدرب مين في الوضع الجديد، تبقى السطرين
+
+163
+00:17:43,610 --> 00:17:52,990
+هل بقدر أضرب في الوضع الجديد using cycle notation
+
+164
+00:17:52,990 --> 00:17:59,370
+الـ alpha في الـ beta عبارة عن إيش؟ خط الـ alpha واحد
+
+165
+00:17:59,370 --> 00:18:10,320
+اثنين سبعة ثلاثة خمسة ستة ثمانية أربعة، الـفيتا اثنين
+
+166
+00:18:10,320 --> 00:18:21,820
+أربعة ثلاثة خمسة ستة سبعة، كيف بده يضغط، مادام
+
+167
+00:18:21,820 --> 00:18:26,700
+نقدر كيف نضغط؟ ببدأ
+
+168
+00:18:26,700 --> 00:18:33,400
+بنفس الأسلوب، الواحد، الواحد هلا مين بيروح؟ مش موجود
+
+169
+00:18:33,400 --> 00:18:39,040
+ولا نفسه، بكمل طبعا، ببدأ من وين دايمًا؟ من البعيد
+
+170
+00:18:39,040 --> 00:18:46,500
+الواحد بيروح هنا لمين؟ لنفسه، طيب هنا لنفسه وهنا
+
+171
+00:18:46,500 --> 00:18:53,660
+للثنين، طيب هنا الاثنين لمن بيروح؟ لهنا، هنا هنا
+
+172
+00:18:53,660 --> 00:18:59,660
+هنا، باجي هنا؟ باجي الأربعة لمن بيرجع؟ للواحد
+
+173
+00:18:59,660 --> 00:19:08,040
+بسّكّف، ثلاثة، ثلاثة لمن بيروح؟ ماشي يكبر ثلاثة لثلاثة
+
+174
+00:19:08,040 --> 00:19:15,100
+هنا للخمسة، يكبر ثلاثة لثلاثة للخمسة، خمسة لستة
+
+175
+00:19:15,100 --> 00:19:23,220
+بسّكن الأربعة لمين؟ لنفسه، يكبر أربعة لأربعة، يكبر أربعة
+
+176
+00:19:23,220 --> 00:19:29,840
+لأربعة لثلاثة، ثلاثة لخمسة، يكبر أربعة لأربعة لثلاثة
+
+177
+00:19:29,840 --> 00:19:38,820
+لخمسة، طيب الخمسة، خمسة لخمسة، خمسة لخمسة للاثنين، خمسة
+
+178
+00:19:38,820 --> 00:19:47,420
+لخمسة للاثنين للسبعة، طيب السبعة لستة، ستة لستة، و
+
+179
+00:19:47,420 --> 00:19:54,320
+الستة لمين؟ للثمانية، خلصوا، خلصوا، طلع النتيجة اللي
+
+180
+00:19:54,320 --> 00:19:58,860
+هنا، والنتيجة اللي هنا، مين أسهل أتعامل مع الشكل
+
+181
+00:19:58,860 --> 00:20:03,370
+هذا ولا الشكل هذا؟ طيب تعالي نضرب الـ beta alpha
+
+182
+00:20:03,370 --> 00:20:08,190
+بالسماء لل cycle عبارة
+
+183
+00:20:08,190 --> 00:20:19,250
+عن 2 4 3 5 في 6 7 في 1 2 7 3 5 6 8 4، نبدأ الواحد
+
+184
+00:20:19,250 --> 00:20:25,070
+لمين بيروح؟ هذا مش السؤال، هذا أنا بشرح كيف نضرب
+
+185
+00:20:25,070 --> 00:20:29,070
+بال cycle notation، يعني هذا بس شرح الطريقة ضمن مثال
+
+186
+00:20:30,370 --> 00:20:34,390
+الواحد لمين بيروح؟ للاثنين، للاثنين يكبر واحد للاثنين
+
+187
+00:20:34,390 --> 00:20:41,250
+اثنين للاثنين، اثنين لمين؟ يكبر واحد لأربعة، طيب غلط
+
+188
+00:20:41,250 --> 00:20:49,230
+إني أسكت، همسك الأربعة، أربعة لمين؟ للواحد، واحد لمين؟
+
+189
+00:20:49,230 --> 00:20:53,430
+لنفسه، واحد لمين؟ يكبر دي من الأربعة ورجعت لمين؟
+
+190
+00:20:53,430 --> 00:20:58,010
+للواحد، طيب
+
+191
+00:20:58,010 --> 00:21:06,060
+اثنين، اثنين لمين؟ لا سبعة، سبعة لمين؟ ستة لمين؟ لنفسه
+
+192
+00:21:06,060 --> 00:21:11,180
+يكبر اثنين لمين؟ لا ستة، ستة للثمانية، ثمانية لنفسه
+
+193
+00:21:11,180 --> 00:21:15,880
+ثمانية لنفسه، يكبر ستة للثمانية، ثمانية للأربعة، أربعة
+
+194
+00:21:15,880 --> 00:21:20,640
+لنفسها، أربعة لثلاثة، يكبر ثمانية لمين؟ لثلاثة، ثلاثة
+
+195
+00:21:20,640 --> 00:21:25,940
+لخمسة، خمسة لخمسة، خمسة للاثنين، وبسكر أنا حاسيب
+
+196
+00:21:25,940 --> 00:21:30,030
+الثلاثة لمين؟ تروح للثانية، واحد اثنين ثلاثة أربعة
+
+197
+00:21:30,030 --> 00:21:35,310
+نبدأ بالخمسة، خمسة لستة، ستة لسبعة، سبعة لنفسها، يبقى
+
+198
+00:21:35,310 --> 00:21:42,230
+خمسة لسبعة، سبعة خلصه، لأن سبعة هتروح للثلاثة، ثلاثة
+
+199
+00:21:42,230 --> 00:21:46,690
+لنفسها، ثلاثة ترجع لمين؟ ده الخمسة، طبعا هذه ممكن
+
+200
+00:21:46,690 --> 00:21:47,670
+أكتبها زي هيك
+
+201
+00:21:55,620 --> 00:22:01,340
+يجب الواحد هتروح لمين؟ للأربعة، الثانية للستة
+
+202
+00:22:01,340 --> 00:22:08,540
+الثلاثة للثانية، الأربعة للواحد، الخمسة للسبعة، الستة
+
+203
+00:22:08,540 --> 00:22:14,200
+للثمانية، والسبعة للخمسة، والثمانية لمين؟ للثلاثة
+
+204
+00:22:14,200 --> 00:22:20,020
+جرب اعكس واضغط وشوف هل هيطلع معاك هذا الكلام ولا
+
+205
+00:22:20,020 --> 00:22:26,430
+لأ، كيف طلعت من هالهال، الواحد لمين بيروح؟ ده الأربعة
+
+206
+00:22:26,430 --> 00:22:31,190
+إيه واحد؟ ده الأربعة، طيب الاثنين كيف ضربت من هالـ ..
+
+207
+00:22:31,190 --> 00:22:36,990
+من هال لهال؟ بدنا بالواحد، واحد لمين؟ للاثنين، واحد
+
+208
+00:22:36,990 --> 00:22:40,150
+للاثنين، اثنين للاثنين، يكبر واحد للاثنين، اثنين اثنين
+
+209
+00:22:40,150 --> 00:22:43,710
+لأربعة، يكبر واحد للاثنين، اثنين لأربعة، يكبر واحد
+
+210
+00:22:43,710 --> 00:22:47,050
+لأربعة، نبدأ بالثنين، اثنين لسبعة
+
+211
+00:22:50,640 --> 00:22:54,820
+عشان يفهم إن واحد للاثنين، والاثنين راحت للثنين، و
+
+212
+00:22:54,820 --> 00:22:58,580
+بعدين الاثنين في الأخيرة راحت للأربعة، هي خطوة واحدة
+
+213
+00:22:58,580 --> 00:23:05,020
+بس هو عشان يستوعبها مثلا هنا لو جيت هنا هقول واحد
+
+214
+00:23:05,020 --> 00:23:08,560
+لواحد، وبعدين واحد لواحد، هيفكرني إن أنا كل مرة
+
+215
+00:23:08,560 --> 00:23:12,880
+ببدأ بالواحد، إن أنا مثلا هنا واحد لواحد، وبعدين
+
+216
+00:23:12,880 --> 00:23:16,780
+واحد لواحد، وبعدين واحد للاثنين، يكبر واحد للاثنين لأ
+
+217
+00:23:16,780 --> 00:23:22,510
+مش شكال، الفكرة إنه علشان الاثنين مثلا مش موجودة أو
+
+218
+00:23:22,510 --> 00:23:26,030
+الواحد مش موجودة هنا، فبتروح لنفسها، فلما أقول واحد
+
+219
+00:23:26,030 --> 00:23:29,290
+لواحد، واحد لواحد، واحد للاثنين، هيفكرني دايمًا ببدأ
+
+220
+00:23:29,290 --> 00:23:37,170
+بمين؟ بالواحد، أكمل، خلصت من الواحد راحت للأربعة
+
+221
+00:23:37,170 --> 00:23:42,860
+هل جيت للأربعة؟ الأربعة راحت لـ .. للواحد، والواحد
+
+222
+00:23:42,860 --> 00:23:45,780
+رجعت للواحد، والواحد رجعت للواحد، يقبل محصلة إنها
+
+223
+00:23:45,780 --> 00:23:50,860
+هي الأربعة بترجع لمن؟ للواحد، كمل، اثنين لسبعة، سبعة
+
+224
+00:23:50,860 --> 00:23:55,880
+لستة، وستة لنفسها، يقبل، اثنين لستة، ستة للثمانية
+
+225
+00:23:55,880 --> 00:23:59,340
+ثمانية لنفسها، وثمانية لنفسها، يقبل ستة، وهكذا
+
+226
+00:23:59,340 --> 00:24:04,040
+واضح؟ فضل، أنا الأربعة راحت للواحد، الواحد راحت
+
+227
+00:24:04,040 --> 00:24:08,600
+للواحد، وأنا في الأخير الأربعة راحت للإنزال، وين؟
+
+228
+00:24:08,600 --> 00:24:15,670
+بسلوة شوية، بس الواحد راح للأربعة، الواحد راح للثنين
+
+229
+00:24:15,670 --> 00:24:20,370
+والثنين راحت للثنين، إيش بقى؟ انتقلت واحد للاثنين
+
+230
+00:24:20,370 --> 00:24:24,250
+والثنين راح للثنين، والثنين لمين راح؟ إيش بقاش
+
+231
+00:24:24,250 --> 00:24:29,670
+المحصلة؟ واحد للأربعة، اللي بعدها الأربعة لمين
+
+232
+00:24:29,670 --> 00:24:39,590
+راحت؟ الأربعة للواحد، والواحد لمين؟ والواحد لمين؟
+
+233
+00:24:39,590 --> 00:24:40,870
+إيش؟ بالـ أربعة لمين راحت؟
+
+234
+00:24:44,260 --> 00:24:50,980
+مضحك؟ عشان مش موجوده بقى هو محايد،
+
+235
+00:24:50,980 --> 00:24:55,220
+هو مش موجود هنفل لنفسه، مش موجود هنبقى لنفسه
+
+236
+00:25:17,120 --> 00:25:23,740
+ملاحظة، الـ identity إيش بيساوي؟ الـ identity عبارة عن
+
+237
+00:25:23,740 --> 00:25:28,280
+مثلا واحد اثنين ثلاثة لعند إن الواحد لواحد، اثنين
+
+238
+00:25:28,280 --> 00:25:33,300
+للاثنين، ثلاثة لثلاثة، لأن لأن يعني واحد اثنين ثلاثة
+
+239
+00:25:33,300 --> 00:25:39,640
+بعدين في الآخر لأن، هذه طريقة كتابة الـ identity على
+
+240
+00:25:39,640 --> 00:25:41,720
+شكل cycle
+
+241
+00:25:45,440 --> 00:25:53,380
+theorem خمسة واحد من
+
+242
+00:25:53,380 --> 00:25:59,020
+الـ أنفا ساعدا، غالبية شغل هيكون فيهاش في الـ cycle
+
+243
+00:25:59,020 --> 00:26:03,220
+notation إنه أسهل في الكتابة وأسرع في الحسابات
+
+244
+00:26:03,220 --> 00:26:07,760
+theorem خمسة واحد بتقول التالي، خلينا نكتبها وبعدين
+
+245
+00:26:07,760 --> 00:26:11,360
+نفهم عن إيش بتكلم، every permutation
+
+246
+00:26:16,440 --> 00:26:23,200
+of a finite set، طبعا وإحنا حصرنا شغلنا من أول ال
+
+247
+00:26:23,200 --> 00:26:35,300
+section في ال finite set a can be written as a
+
+248
+00:26:35,300 --> 00:26:43,920
+cycle or a product of
+
+249
+00:26:43,920 --> 00:26:45,860
+disjoint
+
+250
+00:27:05,390 --> 00:27:12,250
+cycles، شباب إحنا أثناء الشرح قدرنا نعمل كلام هذا 
+
+251
+00:27:12,250 --> 00:27:17,330
+إن أي permutation اشتغلنا عليها في المثال الأمثلة
+
+252
+00:27:17,330 --> 00:27:24,910
+السابقة كنا قادرين نحطها في شكل cycles طبعا ممكن
+
+253
+00:27:24,910 --> 00:27:29,750
+cycle واحدة زي الـ alpha أو
+
+254
+00:27:29,750 --> 00:27:32,090
+disjoint cycles زي ما أقول disjoint cycles يعني
+
+255
+00:27:32,090 --> 00:27:38,610
+ما فيش عناصر مشتركة زي الـ beta بنحط التشريع اللي
+
+256
+00:27:38,610 --> 00:27:43,170
+بيقول إنه هذا الكلام دائما بقدر أعمله يعني إنه
+
+257
+00:27:43,170 --> 00:27:45,930
+عملية إن أنا أقدر أكتب cycle notation الـ
+
+258
+00:27:45,930 --> 00:27:49,970
+permutation مش فقط خاص في الـ alpha و الـ beta تبعتي
+
+259
+00:27:49,970 --> 00:27:55,110
+المثال هذا لأي permutation على finite set بقدر
+
+260
+00:27:55,110 --> 00:28:01,230
+أعمل هذا الكلام عليه نيجي للإثبات أنا عشان أثبت أن
+
+261
+00:28:01,230 --> 00:28:05,450
+every permutation of a finite set A هاخد واحدة let
+
+262
+00:28:05,450 --> 00:28:14,650
+alpha be a permutation on
+
+263
+00:28:14,650 --> 00:28:23,730
+the set A بيساوي واحد اثنين ثلاثة ده عندي أنا هي أنا
+
+264
+00:28:23,730 --> 00:28:31,590
+أخذت permutation على finite set طيب
+
+265
+00:28:31,590 --> 00:28:34,730
+حاجات
+
+266
+00:28:34,730 --> 00:28:40,570
+الـ permutation عبارة عن ايش؟ نرجع للسجن المحاضر
+
+267
+00:28:40,570 --> 00:28:48,610
+الماضي عبارة عن اقتران اقتران ايش بيعمله؟ بينقل
+
+268
+00:28:48,610 --> 00:28:56,330
+الواحد لقيمة ثانية لقيمة ثانية ثلاثة لقيمة ثالثة
+
+269
+00:28:56,330 --> 00:28:56,470
+لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة
+
+270
+00:28:56,470 --> 00:29:00,550
+لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة
+
+271
+00:29:00,550 --> 00:29:00,890
+ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة
+
+272
+00:29:00,890 --> 00:29:03,550
+ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة
+
+273
+00:29:03,550 --> 00:29:05,590
+ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة
+
+274
+00:29:05,590 --> 00:29:10,150
+ثالثة لقيمة ثالثة لقيمة ثالثة لقيمة
+
+275
+00:29:10,150 --> 00:29:12,910
+ثالثة لقيمة ت
+
+276
+00:29:17,240 --> 00:29:22,600
+الـ alpha هينقل الـ 1 لـ a1 و ينقل الـ a1 alpha a1
+
+277
+00:29:22,600 --> 00:29:28,660
+هيروح لـ a2 هينقل الـ a2 طبعا لما أقول مثلا الـ 1 لـ
+
+278
+00:29:28,660 --> 00:29:33,760
+a1 بـ alpha يعني لو كنت بقول alpha الـ 1 يساوي a1 بدي
+
+279
+00:29:33,760 --> 00:29:37,640
+أكمل الـ alpha على a1 و أوصل لـ a2 يعني أنا بدي أقول
+
+280
+00:29:37,640 --> 00:29:43,380
+الـ alpha a1 دي ساوي a2 يعني الـ alpha الواحد و دي
+
+281
+00:29:43,380 --> 00:29:48,180
+ساوي a2 يعني الـ alpha تربيع الواحد و دي ساوي a2
+
+282
+00:29:48,180 --> 00:29:54,800
+طيب كمل الـ a2 بالـ alpha هيروح لـ a3 بالـ alpha لـ a4
+
+283
+00:29:54,800 --> 00:30:00,820
+بالـ alpha لـ a5 بس أنساش إنك تشوف وين يعني في لحظة
+
+284
+00:30:00,820 --> 00:30:07,620
+معينة هترجع لمن؟ للواحد يعني هتبقى لك شغال alpha
+
+285
+00:30:07,620 --> 00:30:13,720
+مثلا أس N للواحد، ايش هيساوي؟ ايش يعني؟ يعني مثلا
+
+286
+00:30:13,720 --> 00:30:22,720
+الواحد بيروح لمن؟ لـ A واحد الـ A واحد لـ A اثنين الـ
+
+287
+00:30:22,720 --> 00:30:28,480
+A اثنين لـ A ثلاثة لعند من؟ A N اللي هو مين هيكون؟
+
+288
+00:30:29,110 --> 00:30:32,150
+أنا بإمكان أروح ألفها و أقول إن هاد a واحد و هاد
+
+289
+00:30:32,150 --> 00:30:39,610
+مين a and بس في غلط الـ and أنا مستعمله غلط
+
+290
+00:30:39,610 --> 00:30:44,770
+الـ and مستعمله فبدل ما أقول and هقول مثلا m a and
+
+291
+00:30:44,770 --> 00:30:52,910
+طيب شوية بس دائما
+
+292
+00:30:52,910 --> 00:30:53,890
+بنبدأ بالواحد
+
+293
+00:30:57,290 --> 00:31:04,890
+خلصت عناصر الـ A نضمنش فجأة عناصر الـ A قد تكون
+
+294
+00:31:04,890 --> 00:31:10,930
+خلصت من الـ AM ويمكن ما تخلصش ناخد مثلا B واحد لا
+
+295
+00:31:10,930 --> 00:31:15,550
+ينتمي لهذول الالفش
+
+296
+00:31:15,550 --> 00:31:20,010
+هتعمل في الـ B واحد هتنجلها لـ B اثنين بعدين
+
+297
+00:31:20,010 --> 00:31:24,920
+هتنجلها لـ B ثلاثة بعدين هترجع في النهاية ل مين؟ لـ
+
+298
+00:31:24,920 --> 00:31:30,540
+B1 يعني ممكن في الآخر يقول B1 تروح لـ B2 لـ B3 لـ
+
+299
+00:31:30,540 --> 00:31:34,600
+B1000 و تجف خلصنا
+
+300
+00:31:35,630 --> 00:31:41,190
+هي نخلصنا خلصوا عناصر الـ a فبنجف و بنقول إن الـ
+
+301
+00:31:41,190 --> 00:31:47,510
+alpha تبعتنا عبارة عن هدول هدفي هدف مخلصش باخد C1
+
+302
+00:31:47,510 --> 00:31:52,050
+لا ينتمي لا لها دول ولا لها دول بكمل يطلع C1 ع C2
+
+303
+00:31:52,050 --> 00:31:59,960
+لأن CT مثلا خلصت هي خلصت مخلصتش بتاخد D1 في النهاية
+
+304
+00:31:59,960 --> 00:32:05,060
+لازم تخلص، ليش؟ لأنك بتشغل أنت فين؟ finite set ففي
+
+305
+00:32:05,060 --> 00:32:09,340
+الآخر، قول مثلا نخلصنا عند الـ C، هتكون الـ A1 لعن
+
+306
+00:32:09,340 --> 00:32:16,360
+الـ A M، B1 لعن الـ B L، C1 لعن الـ C T، و تنساش إنه
+
+307
+00:32:16,360 --> 00:32:22,750
+ولا واحد من هدول هان، ليش؟ بتتكلم عن لما أخذت الـ P
+
+308
+00:32:22,750 --> 00:32:28,630
+واحد ما أخدتهاش من هنا فجد ما تلف الـ P واحد مستحيل
+
+309
+00:32:28,630 --> 00:32:33,950
+تجي لقيمة هنا أيضا الـ C واحد أنت لا أخدت لا من هنا
+
+310
+00:32:33,950 --> 00:32:37,870
+ولا هنا فجد ما تلف الـ C واحد مستحيل تساوي أي A
+
+311
+00:32:37,870 --> 00:32:43,210
+مستحيل تساوي أي P وبالتالي هدولة disjoint مش
+
+312
+00:32:43,210 --> 00:32:48,220
+هتلاقي ولا عنصر هنا موجود هنا أو موجود هنا و بتعني
+
+313
+00:32:48,220 --> 00:32:52,520
+الكلام اللي أنا قلته إنه أي permutation بقدر
+
+314
+00:32:52,520 --> 00:32:55,640
+أكتبها disjoint cycle بقدر أعملها لأي
+
+315
+00:32:55,640 --> 00:33:02,280
+permutation أنا باخدها نلخص الكلام هذا بشكل مختصر
+
+316
+00:33:02,280 --> 00:33:06,960
+لقيت؟
+
+317
+00:33:08,530 --> 00:33:13,030
+A1 ينتمي الـ A احنا طبعا عشان نشرح و نبدأ صائم
+
+318
+00:33:13,030 --> 00:33:16,470
+نبدأ بشكل سهل أنت ممكن تتصرفي و بدأنا بواحد و
+
+319
+00:33:16,470 --> 00:33:21,130
+روحنا لـ A1 و بعدين قلنا AN-1 لو أخدت أي عدد بدل
+
+320
+00:33:21,130 --> 00:33:25,590
+الواحد مقدر أعمل كلام هد عليه let A1 ينتمي الـ A
+
+321
+00:33:25,590 --> 00:33:30,090
+then let
+
+322
+00:33:30,090 --> 00:33:37,410
+A2 عبارة عن Alpha A1 A3 عبارة عن Alpha A2 يعني
+
+323
+00:33:37,410 --> 00:33:45,530
+Alpha Alpha A1 اللي هو عبارة عن Alpha تربيع A1 A4
+
+324
+00:33:45,530 --> 00:33:58,190
+هيصير Alpha A3 يعني Alpha تكعيب A1 Continue
+
+325
+00:33:58,190 --> 00:34:01,850
+until
+
+326
+00:34:01,850 --> 00:34:04,130
+we get that
+
+327
+00:34:07,710 --> 00:34:19,610
+A1 بيساوي Alpha أس M لـ A1 This must be happened
+
+328
+00:34:19,610 --> 00:34:32,940
+since A1 Alpha أس M since the set A is finite أنا
+
+329
+00:34:32,940 --> 00:34:37,120
+بضلني شغال جوا الـ a ألف جواها واحد لا اثنين لا
+
+330
+00:34:37,120 --> 00:34:42,360
+ثلاثة لا أربعة لا عند مثلا A M بضلني جواها
+
+331
+00:34:42,360 --> 00:34:55,940
+النتيجة since
+
+332
+00:34:55,940 --> 00:35:01,280
+we must get for some
+
+333
+00:35:04,170 --> 00:35:09,690
+I and J ذات مدام أنا بشرب finite فلازم في لحظة
+
+334
+00:35:09,690 --> 00:35:15,270
+معينة أحصل على تكرار إنه بيصير معايا Alpha I لـ A1
+
+335
+00:35:15,270 --> 00:35:22,510
+بيساوي Alpha J لـ A1 طبعا تنساش إن الـ Alpha one to
+
+336
+00:35:22,510 --> 00:35:29,070
+one على finite set فهي bijection معناته إلها inverse
+
+337
+00:35:29,070 --> 00:35:32,490
+فأنا بقدر أتعامل مع الـ inverse بشكل سهل ايك فانا
+
+338
+00:35:32,490 --> 00:35:39,730
+بصير عندي مثلا الـ alpha J ناقص الـ I عند الـ A أو الـ
+
+339
+00:35:39,730 --> 00:35:44,770
+I ناقص الـ J عند الـ A واحد بيساوي Alpha صفر عند
+
+340
+00:35:44,770 --> 00:35:51,310
+الـ A واحد وبالتالي هذا بيعطيني مين A واحد take M
+
+341
+00:35:51,310 --> 00:35:57,060
+بيساوي I ناقص J و حطها نجوس وحطها نجوس عشان يكون
+
+342
+00:35:57,060 --> 00:36:05,300
+ما بين الجثين جملة اعتراضية بتفسر الكلام هنا we
+
+343
+00:36:05,300 --> 00:36:20,260
+get the cycle A واحد اثنين لعند مين A M طيب
+
+344
+00:36:20,260 --> 00:36:21,200
+choose
+
+345
+00:36:23,540 --> 00:36:34,620
+B1 لا ينتمي لـ A1 A2 لا ينتمي لـ AM B اثنين
+
+346
+00:36:34,620 --> 00:36:41,340
+عبارة عن الف B واحد B
+
+347
+00:36:41,340 --> 00:36:46,900
+ثلاثة عبارة عن الف تربيع B واحد until we stop لأن
+
+348
+00:36:46,900 --> 00:36:53,120
+ما فيش manager to get another
+
+349
+00:36:55,780 --> 00:37:05,140
+cycle B واحد B اثنين لعند B K
+
+350
+00:37:05,140 --> 00:37:16,500
+B اثنين لعند B K B اثنين لعند B K B اثنين لعند
+
+351
+00:37:16,500 --> 00:37:26,420
+B K B اثنين لعند B K B اثنين لعند B K وهو
+
+352
+00:37:26,420 --> 00:37:31,560
+المطلب بنضلنا
+
+353
+00:37:31,560 --> 00:37:37,880
+شغالين لما يخلصوا كل عناصر الـ A و بحصل على مين؟
+
+354
+00:37:37,880 --> 00:37:43,180
+disjoint cycles ليش disjoint يا شباب؟ ليش
+
+355
+00:37:43,180 --> 00:37:49,180
+disjoint؟ لأن ما فيش عناصر مشتركة بين الـ A ولا الـ B
+
+356
+00:37:49,180 --> 00:37:50,580
+ولا الـ C
+
+357
+00:38:36,020 --> 00:38:40,820
+شباب أنا لما بأجي بأخد في permutation ما و بكتب
+
+358
+00:38:40,820 --> 00:38:45,980
+على شكل cycle عادة
+
+359
+00:38:45,980 --> 00:38:51,480
+ببدأ بواحد و بخلص لفة الواحد و بعدين ببدأ باللي
+
+360
+00:38:51,480 --> 00:38:55,460
+بيظل مثلا خلصتين أو ثلاثة مثلا الأربعة ما كانش موجود
+
+361
+00:38:55,460 --> 00:39:00,460
+ببدأ بالأربعة و بخلص لفة الأربعة و هكذا طب واحد
+
+362
+00:39:00,460 --> 00:39:06,350
+ما يبدأش بالواحد بدأ بالسبعة هيحصل على لفة السبعة و
+
+363
+00:39:06,350 --> 00:39:10,610
+بعدين هيجي الواحد في لفته الجديدة بصار مثلا عندي
+
+364
+00:39:10,610 --> 00:39:16,910
+بدأ لفة الواحد و بعدين لفة السابعة بهذا الشكل واحد
+
+365
+00:39:16,910 --> 00:39:23,150
+بدأ بالسبعة فأجت معا لفة السابعة و لفة الواحد فهي
+
+366
+00:39:23,150 --> 00:39:27,730
+نفس الـ permutation بس
+
+367
+00:39:27,730 --> 00:39:34,000
+إن كانت مكان ضيقة طب ايش الـ .. يعني معناته بدي أقول
+
+368
+00:39:34,000 --> 00:39:37,020
+إن واحد اثنين ثلاثة في سبعة ستة خمسة بدي ساوي سبعة
+
+369
+00:39:37,020 --> 00:39:40,800
+ستة خمسة في واحد اثنين ثلاثة يعني هو كأنه لو أخدت
+
+370
+00:39:40,800 --> 00:39:45,940
+هذه الف واحد و هذه الف اثنين ايش بقى الف واحد الف
+
+371
+00:39:45,940 --> 00:39:49,320
+اثنين بدي ساوي الف اثنين الف واحد ايش بقى ايش صار
+
+372
+00:39:49,320 --> 00:39:56,040
+صار عملية تبديل بين الف واحد و الف اثنين طيب السبب
+
+373
+00:39:56,040 --> 00:40:03,340
+طلع لـ الف واحد و الف اثنين في عناصر مشتركة اللي
+
+374
+00:40:03,340 --> 00:40:07,440
+خلاني أقدر أعمل عملية التبديل إن هم disjoint و هذه
+
+375
+00:40:07,440 --> 00:40:12,560
+نظرية 5-2 إن أنا لو بدرب disjoint cycles فانا بقدر
+
+376
+00:40:12,560 --> 00:40:25,720
+أجري العملية بالإبدال if alpha بساوي a1 a2 لـ n a
+
+377
+00:40:25,720 --> 00:40:35,730
+and and هو حتى ما أخدها أنا أم بيتاعبارة عن P1 P2
+
+378
+00:40:35,730 --> 00:40:48,990
+لأن P and R are disjoint cycles then Alpha Beta
+
+379
+00:40:48,990 --> 00:40:51,250
+يتساوى Beta Alpha
+
+380
+00:41:11,730 --> 00:41:19,350
+طيب ده نظرية سهلة تلات أربع دقائق مخلص طيب let
+
+381
+00:41:19,350 --> 00:41:33,210
+alpha and beta be two disjoint cycles on the set a
+
+382
+00:41:33,210 --> 00:41:37,130
+بده تساوي ال a هي واحد اثنين ثلاث أربع لـ n
+
+383
+00:41:37,130 --> 00:41:45,130
+هرتبه بالشكل التالي a واحد a اثنين b واحد b اثنين
+
+384
+00:41:45,130 --> 00:41:52,630
+b n والباقي ما
+
+385
+00:41:52,630 --> 00:41:56,290
+هو أحيانا مثلا أنت واخدنا ال cycles ما يأخذ كل
+
+386
+00:41:56,290 --> 00:42:02,530
+العناصر يعني هدول مثلا الالفة بتأخذ لفة من ال A1
+
+387
+00:42:02,530 --> 00:42:06,110
+لعندي ال AM والباقي بالنسبة لل alpha بيروحوا
+
+388
+00:42:06,110 --> 00:42:11,350
+لنفسهم ال beta بتأخذ لفة ال B والباقي بالنسبة ل
+
+389
+00:42:11,350 --> 00:42:16,070
+beta يشملهم لنفسهم طبعا هدول العناصر اللي هم
+
+390
+00:42:16,070 --> 00:42:23,410
+بالنسبة لل alpha و بالنسبة لل beta ثابتين we will
+
+391
+00:42:23,410 --> 00:42:30,940
+show that alpha beta بتساوي beta alpha شباب أنا
+
+392
+00:42:30,940 --> 00:42:35,900
+بتعامل مع مين؟ مع functions إيش يعني؟ يعني Alpha
+
+393
+00:42:35,900 --> 00:42:42,240
+Beta لل X بدي أساوي Beta Alpha لل X لكل X في A بس
+
+394
+00:42:42,240 --> 00:42:46,140
+هذه عملية .. عملية composition يعني Alpha Beta لل
+
+395
+00:42:46,140 --> 00:42:53,540
+X بدي أساوي Beta ل Alpha X ال
+
+396
+00:42:53,540 --> 00:42:55,480
+X في A كم حالة قدامها
+
+397
+00:42:58,010 --> 00:43:10,350
+ثلاث حالات يا من ال A يا من ال B يا من ال C Case 1
+
+398
+00:43:10,350 --> 00:43:13,830
+ال
+
+399
+00:43:13,830 --> 00:43:22,750
+X بتنتمي ل A1 A2 لـ A M معناته Alpha Beta لل X اللي
+
+400
+00:43:22,750 --> 00:43:29,830
+Alpha ما هي كده هتصير ال X مثلا بتساوي AI يعني ال
+
+401
+00:43:29,830 --> 00:43:38,310
+Alpha Beta لل X عبارة عن Alpha Beta ال AI شباب ال
+
+402
+00:43:38,310 --> 00:43:43,290
+AI بالنسبة لل Beta إيش مالها؟ ال Beta بتأخذ ال AI
+
+403
+00:43:43,290 --> 00:43:48,670
+لمين؟ لنفسها لأن ال AI مش من ضمن ال Beta يعني بقى
+
+404
+00:43:48,670 --> 00:43:54,130
+هتعرف عبارة عن Alpha AI طيب ال Alpha بتأخذ ال AI
+
+405
+00:43:54,130 --> 00:44:00,780
+لمين؟ للي بعدها ماشي احنا بناخد A1 A2 يكبر AI
+
+406
+00:44:00,780 --> 00:44:08,620
+لمين ل AI زاد الواحد طيب ال Beta Alpha لل X يعني
+
+407
+00:44:08,620 --> 00:44:16,380
+Beta Alpha لل AI ال Alpha هتاخد ال AI لمين ل AI
+
+408
+00:44:16,380 --> 00:44:22,640
+زاد الواحد يعني Beta AI زاد الواحد و ال Beta
+
+409
+00:44:22,640 --> 00:44:27,550
+بتأخذ ال AI زاد الواحد لمين؟ تساوي والله ما تساويش
+
+410
+00:44:27,550 --> 00:44:33,990
+تساوي كيس اثنين ال
+
+411
+00:44:33,990 --> 00:44:41,910
+X بتنتمي لمين B واحد B اثنين وصولا لـ B n طيب
+
+412
+00:44:41,910 --> 00:44:50,230
+يعني ال X بتساوي مثلا بي جيه مثلا طيب Alpha Beta لل
+
+413
+00:44:50,230 --> 00:44:55,780
+X يعني Alpha Beta لل بي جيه الـ beta هتاخد ال بي جيه
+
+414
+00:44:55,780 --> 00:45:01,600
+لمين؟ لـ بي جيه زائد الواحد يعني هذه alpha بي جيه
+
+415
+00:45:01,600 --> 00:45:05,740
+زائد الواحد طيب ال بي جيه زائد الواحد ال alpha
+
+416
+00:45:05,740 --> 00:45:11,590
+هتاخدها لمين؟ لنفسها واحد هيسألني طب و لو كانت ال
+
+417
+00:45:11,590 --> 00:45:16,170
+J بتساوي N فال B J زائد الواحد يا B N زائد ال
+
+418
+00:45:16,170 --> 00:45:21,670
+واحد مش موجودة إيش هتعمل؟ هترجع لمين؟ لـ B واحد طيب
+
+419
+00:45:21,670 --> 00:45:28,610
+Beta Alpha ل X يعني Beta ل Alpha B J ال Alpha
+
+420
+00:45:28,610 --> 00:45:34,830
+هتاخد ال B J لمين؟ لنفسها إذن بقى Beta ل B J و ال
+
+421
+00:45:34,830 --> 00:45:38,690
+B J هتاخد لمين؟ لـ B J زائد الواحد و إشملهم
+
+422
+00:45:40,130 --> 00:45:49,690
+متساويين آخر حالة كالـثلاثة
+
+423
+00:45:49,690 --> 00:46:00,390
+ال X تنتمي لـ C1 C2 لعند C احنا قلنا K طيب يعني ال
+
+424
+00:46:00,390 --> 00:46:08,710
+X مدى تساوي CT فوق صمتي Alpha Beta لل X يعني Alpha
+
+425
+00:46:09,520 --> 00:46:14,840
+لـ Beta الـ CT شباب ال Beta بتأخذ ال CT لمين؟
+
+426
+00:46:14,840 --> 00:46:19,560
+لنفسها لنفسها يعني بقى Alpha CT وال Alpha بتأخذها
+
+427
+00:46:19,560 --> 00:46:25,520
+لـ CT ال Beta Alpha لل X يعني Beta ل Alpha ال CT
+
+428
+00:46:25,520 --> 00:46:34,840
+يعني عبارة عن عبارة
+
+429
+00:46:34,840 --> 00:46:43,180
+عن Beta لل CT و ال beta هتاخد ال ct لمين؟ ومافيه
+
+430
+00:46:43,180 --> 00:46:50,120
+بينهم إيه بقى في كل الحالات عندي مساواة و بالتالي
+
+431
+00:46:50,120 --> 00:46:55,120
+alpha beta لـ ال x بدأت ساوي beta alpha لـ ال x لكل x
+
+432
+00:46:55,120 --> 00:47:00,800
+في a و بالتالي alpha beta بدأت ساوي beta alpha و هو
+
+433
+00:47:00,800 --> 00:47:05,260
+المطلوب و هذه نهاية النظرية خمسة اثنين إن شاء الله
+
+434
+00:47:05,260 --> 00:47:07,580
+في المحاضرة الثانية اللي هناخدها اليوم من اثنا عشر
+
+435
+00:47:07,580 --> 00:47:11,040
+الواحدة إن شاء الله هناخدها في المحاضرة الثانية من
+
+436
+00:47:11,040 --> 00:47:15,020
+اثنا عشر الواحدة تكملة ال chapter هنحاول ننهيه إن
+
+437
+00:47:15,020 --> 00:47:16,020
+شاء الله يعطيكم الأفراح 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc54dc7714996ff9de24e88b7a15fa146ff6dd67
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.json
@@ -0,0 +1 @@
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تقسم الـ N والـ N لا تساوي 7 الـ N مثلا تساوي 7K الـ N ماذا تساوي؟ 7K حيث ك أكبر من 1", "tokens": [10721, 15730, 5551, 16572, 3215, 2423, 39184, 426, 2423, 39184, 1614, 6055, 4587, 38251, 2423, 39184, 426, 16070, 39184, 426, 20193, 6055, 3794, 995, 45865, 1614, 2423, 39184, 426, 50113, 15040, 6055, 3794, 995, 45865, 1614, 42, 2423, 39184, 426, 3714, 45636, 995, 6055, 3794, 995, 45865, 22807, 1614, 42, 11331, 1829, 12984, 9122, 5551, 4117, 26890, 9154, 502], "avg_logprob": -0.38151042759418485, "compression_ratio": 1.6699029126213591, "no_speech_prob": 0.0, "words": [{"start": 344.67, "end": 344.93, "word": "أذا", "probability": 0.155303955078125}, {"start": 344.93, "end": 345.35, "word": " أريد", "probability": 0.6869303385416666}, {"start": 345.35, "end": 346.01, "word": " الـ", "probability": 0.39007568359375}, {"start": 346.01, "end": 346.93, "word": " N", "probability": 0.54638671875}, {"start": 346.93, "end": 347.29, "word": " الـ", "probability": 0.4505615234375}, {"start": 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"start": 584.88, "end": 599.64, "text": "حسب النظريات اللي عندي لكل قاسم فيه subgroup الارض لهذه ال subgroup بيساوي القاسم ال K رقم طب و السبعة؟ ال K قاسم تان غير السبعة", "tokens": [5016, 35457, 28239, 19913, 16572, 9307, 13672, 1829, 18871, 16254, 5296, 28820, 12174, 32277, 2304, 8978, 3224, 1422, 17377, 2423, 9640, 11242, 46740, 24192, 2423, 1422, 17377, 4724, 1829, 3794, 995, 45865, 25062, 32277, 2304, 2423, 591, 12602, 4587, 2304, 23032, 3555, 4032, 21136, 3555, 27884, 22807, 2423, 591, 12174, 32277, 2304, 6055, 7649, 32771, 13546, 21136, 3555, 27884], "avg_logprob": -0.4028645808498065, "compression_ratio": 1.5323741007194245, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 584.88, "end": 585.58, "word": "حسب", "probability": 0.56182861328125}, {"start": 585.58, "end": 586.08, "word": " النظريات", "probability": 0.9141845703125}, {"start": 586.08, "end": 586.2, "word": " اللي", "probability": 0.74560546875}, {"start": 586.2, "end": 586.46, "word": " عندي", 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سبعة is replaced by بيه ال order ل j هي سوى بيه تربيه لو بنستبدل السبعة بيه هيكون ال order عبارة عن بيه تربيه سؤال خمس عشر", "tokens": [9566, 1829, 3555, 16490, 2304, 3794, 6225, 46309, 718, 361, 312, 364, 23842, 1594, 412, 1472, 437, 393, 291, 584, 498, 8608, 3555, 27884, 307, 10772, 538, 4724, 1829, 3224, 2423, 1668, 5296, 361, 39896, 8608, 2407, 7578, 4724, 1829, 3224, 6055, 2288, 21292, 3224, 45164, 44945, 14851, 44510, 1211, 21136, 3555, 27884, 4724, 1829, 3224, 39896, 30544, 2423, 1668, 6225, 3555, 9640, 3660, 18871, 4724, 1829, 3224, 6055, 2288, 21292, 3224, 8608, 33604, 6027, 16490, 2304, 3794, 6225, 46309], "avg_logprob": -0.2849151175699116, "compression_ratio": 1.5542857142857143, "no_speech_prob": 0.0, "words": [{"start": 603.16, "end": 603.5, "word": "طيب", "probability": 0.7455240885416666}, {"start": 603.5, "end": 603.8, "word": " خمس", "probability": 0.8377278645833334}, {"start": 603.8, "end": 604.2, "word": " عشر", "probability": 0.453369140625}, {"start": 604.2, "end": 605.04, "word": " let", "probability": 0.2191162109375}, {"start": 605.04, "end": 605.34, "word": " j", "probability": 0.66259765625}, {"start": 605.34, "end": 605.54, "word": " be", "probability": 0.671875}, {"start": 605.54, "end": 605.84, "word": " an", "probability": 0.1632080078125}, {"start": 605.84, "end": 606.2, "word": " appealing", "probability": 0.48388671875}, {"start": 606.2, "end": 606.74, "word": " group", "probability": 0.9814453125}, {"start": 606.74, "end": 607.0, "word": " at", "probability": 0.411865234375}, {"start": 607.0, "end": 607.26, "word": " rest", "probability": 0.66943359375}, {"start": 607.26, "end": 608.32, "word": " what", "probability": 0.35595703125}, {"start": 608.32, "end": 609.96, "word": " can", "probability": 0.95947265625}, {"start": 609.96, "end": 610.3, "word": " you", "probability": 0.94580078125}, {"start": 610.3, "end": 610.82, "word": " say", "probability": 0.966796875}, {"start": 610.82, "end": 611.08, "word": " if", "probability": 0.958984375}, {"start": 611.08, "end": 611.42, "word": " سبعة", "probability": 0.7029622395833334}, {"start": 611.42, "end": 611.6, "word": " is", "probability": 0.82958984375}, {"start": 611.6, "end": 611.92, "word": " replaced", "probability": 0.927734375}, {"start": 611.92, "end": 612.38, "word": " by", "probability": 0.9814453125}, {"start": 612.38, "end": 612.76, "word": " بيه", "probability": 0.5811360677083334}, {"start": 612.76, "end": 613.28, "word": " ال", "probability": 0.6337890625}, {"start": 613.28, "end": 613.66, "word": " order", "probability": 0.943359375}, {"start": 613.66, "end": 613.86, "word": " ل", "probability": 0.88671875}, {"start": 613.86, "end": 614.24, "word": " j", "probability": 0.53759765625}, {"start": 614.24, "end": 614.86, "word": " هي", "probability": 0.8056640625}, {"start": 614.86, "end": 615.16, "word": " سوى", "probability": 0.72705078125}, {"start": 615.16, "end": 615.44, "word": " بيه", "probability": 0.8251953125}, {"start": 615.44, "end": 615.9, "word": " تربيه", "probability": 0.829345703125}, {"start": 615.9, "end": 617.92, "word": " لو", "probability": 0.568359375}, {"start": 617.92, "end": 619.04, "word": " بنستبدل", "probability": 0.822021484375}, {"start": 619.04, "end": 619.38, "word": " السبعة", "probability": 0.8924153645833334}, {"start": 619.38, "end": 620.12, "word": " بيه", "probability": 0.7650553385416666}, {"start": 620.12, "end": 620.8, "word": " هيكون", "probability": 0.84423828125}, {"start": 620.8, "end": 620.92, "word": " ال", "probability": 0.96630859375}, {"start": 620.92, "end": 621.28, "word": " order", "probability": 0.97607421875}, {"start": 621.28, "end": 621.8, "word": " عبارة", "probability": 0.9473876953125}, {"start": 621.8, "end": 622.14, "word": " عن", "probability": 0.98095703125}, {"start": 622.14, "end": 622.7, "word": " بيه", "probability": 0.9285481770833334}, {"start": 622.7, "end": 623.84, "word": " تربيه", "probability": 0.977783203125}, {"start": 623.84, "end": 624.54, "word": " سؤال", "probability": 0.8033854166666666}, {"start": 624.54, "end": 624.82, "word": " خمس", "probability": 0.9601236979166666}, {"start": 624.82, "end": 625.22, "word": " عشر", "probability": 0.953369140625}], "temperature": 1.0}, {"id": 23, "seek": 65743, "start": 630.23, "end": 657.43, "text": "suppose that a cyclic group J أو JAB يعني group و ال H عبارة عن كل ال J في ال J حيث ال order ل J يقسم 12 prove that H is a subgroup of J", "tokens": [36622, 541, 300, 257, 38154, 1050, 1594, 508, 34051, 508, 13868, 37495, 22653, 1594, 4032, 2423, 389, 6225, 3555, 9640, 3660, 18871, 28242, 2423, 508, 8978, 2423, 508, 11331, 1829, 12984, 2423, 1668, 5296, 508, 7251, 4587, 38251, 2272, 7081, 300, 389, 307, 257, 1422, 17377, 295, 508], "avg_logprob": -0.2672193974864726, "compression_ratio": 1.223021582733813, "no_speech_prob": 0.0, "words": [{"start": 630.23, "end": 630.91, "word": "suppose", "probability": 0.85595703125}, {"start": 630.91, "end": 631.21, "word": " that", "probability": 0.8203125}, {"start": 631.21, "end": 631.37, "word": " a", "probability": 0.8212890625}, {"start": 631.37, "end": 631.87, "word": " cyclic", "probability": 0.6795654296875}, {"start": 631.87, "end": 632.39, "word": " group", "probability": 0.974609375}, {"start": 632.39, "end": 632.73, "word": " J", "probability": 0.253662109375}, {"start": 632.73, "end": 633.07, "word": " أو", "probability": 0.4140625}, {"start": 633.07, "end": 634.09, "word": " JAB", "probability": 0.509521484375}, {"start": 634.09, "end": 634.33, "word": " يعني", "probability": 0.7705078125}, {"start": 634.33, "end": 634.77, "word": " group", "probability": 0.90087890625}, {"start": 634.77, "end": 641.97, "word": " و", "probability": 0.66162109375}, {"start": 641.97, "end": 642.29, "word": " ال", "probability": 0.693359375}, {"start": 642.29, "end": 642.73, "word": " H", "probability": 0.73876953125}, {"start": 642.73, "end": 644.11, "word": " عبارة", "probability": 0.9212646484375}, {"start": 644.11, "end": 644.33, "word": " عن", "probability": 0.99853515625}, {"start": 644.33, "end": 644.61, "word": " كل", "probability": 0.966796875}, {"start": 644.61, "end": 644.83, "word": " ال", "probability": 0.5}, {"start": 644.83, "end": 645.15, "word": " J", "probability": 0.853515625}, {"start": 645.15, "end": 646.27, "word": " في", "probability": 0.9365234375}, {"start": 646.27, "end": 646.39, "word": " ال", "probability": 0.71875}, {"start": 646.39, "end": 646.61, "word": " J", "probability": 0.6650390625}, {"start": 646.61, "end": 647.29, "word": " حيث", "probability": 0.95947265625}, {"start": 647.29, "end": 649.25, "word": " ال", "probability": 0.33056640625}, {"start": 649.25, "end": 650.05, "word": " order", "probability": 0.94970703125}, {"start": 650.05, "end": 650.25, "word": " ل", "probability": 0.81103515625}, {"start": 650.25, "end": 650.57, "word": " J", "probability": 0.66064453125}, {"start": 650.57, "end": 651.99, "word": " يقسم", "probability": 0.9723307291666666}, {"start": 651.99, "end": 652.65, "word": " 12", "probability": 0.59033203125}, {"start": 652.65, "end": 654.73, "word": " prove", "probability": 0.5625}, {"start": 654.73, "end": 655.01, "word": " that", "probability": 0.955078125}, {"start": 655.01, "end": 655.37, "word": " H", "probability": 0.91259765625}, {"start": 655.37, "end": 655.59, "word": " is", "probability": 0.94091796875}, {"start": 655.59, "end": 655.79, "word": " a", "probability": 0.951171875}, {"start": 655.79, "end": 656.27, "word": " subgroup", "probability": 0.77392578125}, {"start": 656.27, "end": 656.63, "word": " of", "probability": 0.97412109375}, {"start": 656.63, "end": 657.43, "word": " J", "probability": 0.9033203125}], "temperature": 1.0}, {"id": 24, "seek": 68759, "start": 658.29, "end": 687.59, "text": "مطلوب ان اثبت هل ممكن نغير 12 بأي رقم هل ممكن نغير 12 بأي رقم هل ممكن نغير 12 بأي رقم", "tokens": [2304, 9566, 1211, 37746, 16472, 1975, 12984, 3555, 2655, 8032, 1211, 3714, 43020, 8717, 17082, 13546, 2272, 4724, 10721, 1829, 12602, 4587, 2304, 8032, 1211, 3714, 43020, 8717, 17082, 13546, 2272, 4724, 10721, 1829, 12602, 4587, 2304, 8032, 1211, 3714, 43020, 8717, 17082, 13546, 2272, 4724, 10721, 1829, 12602, 4587, 2304], "avg_logprob": -0.3118990436196327, "compression_ratio": 2.028169014084507, "no_speech_prob": 0.0, "words": [{"start": 658.29, "end": 658.73, "word": "مطلوب", "probability": 0.74517822265625}, {"start": 658.73, "end": 658.85, "word": " ان", "probability": 0.572265625}, {"start": 658.85, "end": 659.77, "word": " اثبت", "probability": 0.931396484375}, {"start": 659.77, "end": 662.45, "word": " هل", "probability": 0.32672119140625}, {"start": 662.45, "end": 668.77, "word": " ممكن", "probability": 0.759521484375}, {"start": 668.77, "end": 669.09, "word": " نغير", "probability": 0.8338216145833334}, {"start": 669.09, "end": 669.43, "word": " 12", "probability": 0.50341796875}, {"start": 669.43, "end": 669.65, "word": " بأي", "probability": 0.7008463541666666}, {"start": 669.65, "end": 670.21, "word": " رقم", "probability": 0.99072265625}, {"start": 670.21, "end": 671.61, "word": " هل", "probability": 0.3736572265625}, {"start": 671.61, "end": 671.67, "word": " ممكن", "probability": 0.977294921875}, {"start": 671.67, "end": 672.89, "word": " نغير", "probability": 0.96875}, {"start": 672.89, "end": 672.93, "word": " 12", "probability": 0.947265625}, {"start": 672.93, "end": 673.07, "word": " بأي", "probability": 0.9658203125}, {"start": 673.07, "end": 673.07, "word": " رقم", "probability": 0.9964192708333334}, {"start": 673.07, "end": 674.81, "word": " هل", "probability": 0.407867431640625}, {"start": 674.81, "end": 687.59, "word": " ممكن", "probability": 0.991943359375}, {"start": 687.59, "end": 687.59, "word": " نغير", "probability": 0.9912109375}, {"start": 687.59, "end": 687.59, "word": " 12", "probability": 0.9892578125}, {"start": 687.59, "end": 687.59, "word": " بأي", "probability": 0.9879557291666666}, {"start": 687.59, "end": 687.59, "word": " رقم", "probability": 0.99755859375}], "temperature": 1.0}, {"id": 25, "seek": 71731, "start": 688.31, "end": 717.31, "text": "المجموعة بتمثل subgroup كل العناصر اللي في j اللي ال order اللي هي بيقسم 12 طيب تبدأ تبتنوعش subgroup موضوع تقليدي first H لا يسوى 5 since ال identity في ال H since ال order لل identity بيسوى 1 يقسم 12", "tokens": [45340, 7435, 2304, 2407, 27884, 39894, 2304, 12984, 1211, 1422, 17377, 28242, 18863, 1863, 33546, 2288, 13672, 1829, 8978, 361, 13672, 1829, 2423, 1668, 13672, 1829, 39896, 4724, 1829, 4587, 38251, 2272, 23032, 1829, 3555, 6055, 44510, 10721, 6055, 3555, 2655, 1863, 2407, 3615, 8592, 1422, 17377, 3714, 2407, 11242, 45367, 6055, 4587, 20292, 16254, 700, 389, 20193, 7251, 3794, 2407, 7578, 1025, 1670, 2423, 6575, 8978, 2423, 389, 1670, 2423, 1668, 24976, 6575, 4724, 1829, 3794, 2407, 7578, 502, 7251, 4587, 38251, 2272], "avg_logprob": -0.30790440054500806, "compression_ratio": 1.5913978494623655, "no_speech_prob": 0.0, "words": [{"start": 688.31, "end": 689.13, "word": "المجموعة", "probability": 0.81357421875}, {"start": 689.13, "end": 690.47, "word": " بتمثل", "probability": 0.8101806640625}, {"start": 690.47, "end": 691.33, "word": " subgroup", "probability": 0.736572265625}, {"start": 691.33, "end": 692.11, "word": " كل", "probability": 0.767578125}, {"start": 692.11, "end": 693.09, "word": " العناصر", "probability": 0.8392333984375}, {"start": 693.09, "end": 693.83, "word": " اللي", "probability": 0.832763671875}, {"start": 693.83, "end": 693.95, "word": " في", "probability": 0.9609375}, {"start": 693.95, "end": 694.27, "word": " j", "probability": 0.401123046875}, {"start": 694.27, "end": 694.89, "word": " اللي", "probability": 0.792236328125}, {"start": 694.89, "end": 695.01, "word": " ال", "probability": 0.75732421875}, {"start": 695.01, "end": 695.31, "word": " order", "probability": 0.916015625}, {"start": 695.31, "end": 695.55, "word": " اللي", "probability": 0.740478515625}, {"start": 695.55, "end": 695.63, "word": " هي", "probability": 0.56689453125}, {"start": 695.63, "end": 696.29, "word": " بيقسم", "probability": 0.9173583984375}, {"start": 696.29, "end": 697.53, "word": " 12", "probability": 0.29638671875}, {"start": 697.53, "end": 699.81, "word": " طيب", "probability": 0.6962483723958334}, {"start": 699.81, "end": 700.65, "word": " تبدأ", "probability": 0.7976888020833334}, {"start": 700.65, "end": 701.13, "word": " تبتنوعش", "probability": 0.6880580357142857}, {"start": 701.13, "end": 701.67, "word": " subgroup", "probability": 0.88037109375}, {"start": 701.67, "end": 703.27, "word": " موضوع", "probability": 0.5374755859375}, {"start": 703.27, "end": 703.87, "word": " تقليدي", "probability": 0.9302978515625}, {"start": 703.87, "end": 705.13, "word": " first", "probability": 0.37890625}, {"start": 705.13, "end": 707.97, "word": " H", "probability": 0.52734375}, {"start": 707.97, "end": 708.15, "word": " لا", "probability": 0.83154296875}, {"start": 708.15, "end": 708.55, "word": " يسوى", "probability": 0.68145751953125}, {"start": 708.55, "end": 708.91, "word": " 5", "probability": 0.7470703125}, {"start": 708.91, "end": 710.39, "word": " since", "probability": 0.6767578125}, {"start": 710.39, "end": 711.63, "word": " ال", "probability": 0.97412109375}, {"start": 711.63, "end": 712.09, "word": " identity", "probability": 0.94775390625}, {"start": 712.09, "end": 712.31, "word": " في", "probability": 0.84619140625}, {"start": 712.31, "end": 712.45, "word": " ال", "probability": 0.904296875}, {"start": 712.45, "end": 712.71, "word": " H", "probability": 0.86279296875}, {"start": 712.71, "end": 713.33, "word": " since", "probability": 0.7587890625}, {"start": 713.33, "end": 714.95, "word": " ال", "probability": 0.98046875}, {"start": 714.95, "end": 715.27, "word": " order", "probability": 0.95849609375}, {"start": 715.27, "end": 715.43, "word": " لل", "probability": 0.642578125}, {"start": 715.43, "end": 715.83, "word": " identity", "probability": 0.9248046875}, {"start": 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0.9625244140625}, {"start": 825.33, "end": 825.79, "word": " مضعفة", "probability": 0.80625}, {"start": 825.79, "end": 826.09, "word": " لو", "probability": 0.51171875}, {"start": 826.09, "end": 826.59, "word": " حطيت", "probability": 0.9671223958333334}, {"start": 826.59, "end": 826.87, "word": " 7", "probability": 0.7265625}, {"start": 826.87, "end": 827.15, "word": " بدل", "probability": 0.908203125}, {"start": 827.15, "end": 827.51, "word": " 12،", "probability": 0.730224609375}, {"start": 827.51, "end": 827.65, "word": " في", "probability": 0.411865234375}, {"start": 827.65, "end": 829.55, "word": " مشكلة؟", "probability": 0.984619140625}, {"start": 829.55, "end": 830.13, "word": " لو", "probability": 0.53076171875}, {"start": 830.13, "end": 830.63, "word": " حطيت", "probability": 0.9889322916666666}, {"start": 830.63, "end": 831.87, "word": " 1000؟", "probability": 0.50830078125}, {"start": 831.87, "end": 832.11, "word": " مافيش", "probability": 0.8662109375}, {"start": 832.11, "end": 832.69, "word": " مشكلة،", "probability": 0.870361328125}, {"start": 832.69, "end": 833.13, "word": " 12", "probability": 0.619140625}], "temperature": 1.0}, {"id": 30, "seek": 85918, "start": 834.86, "end": 859.18, "text": "is not special يعني ممكن تبدل ال 12 بأي رقم مين الحاجة الضرورية هنا ال abelian مش ال 12 لو مش abelian ماقدرتش انا اعمل الفكرة هذه طيب", "tokens": [271, 406, 2121, 37495, 22653, 3714, 43020, 6055, 44510, 1211, 2423, 2272, 4724, 10721, 1829, 12602, 4587, 2304, 3714, 9957, 21542, 26108, 3660, 6024, 114, 2288, 13063, 10632, 34105, 2423, 410, 338, 952, 37893, 2423, 2272, 45164, 37893, 410, 338, 952, 19446, 28543, 43500, 8592, 1975, 8315, 1975, 25957, 1211, 27188, 4117, 25720, 29538, 23032, 1829, 3555], "avg_logprob": -0.26872306034482757, "compression_ratio": 1.412162162162162, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 834.86, "end": 835.14, "word": "is", "probability": 0.453125}, {"start": 835.14, "end": 835.48, "word": " not", "probability": 0.7353515625}, {"start": 835.48, "end": 836.68, "word": " special", "probability": 0.88720703125}, {"start": 836.68, "end": 838.96, "word": " يعني", "probability": 0.8583984375}, {"start": 838.96, "end": 839.26, "word": " ممكن", "probability": 0.901123046875}, {"start": 839.26, "end": 839.68, "word": " تبدل", "probability": 0.859375}, {"start": 839.68, "end": 839.76, "word": " ال", "probability": 0.63330078125}, {"start": 839.76, "end": 839.96, "word": " 12", "probability": 0.454833984375}, {"start": 839.96, "end": 840.24, "word": " بأي", "probability": 0.8513997395833334}, {"start": 840.24, "end": 840.6, "word": " رقم", "probability": 0.9869791666666666}, {"start": 840.6, "end": 841.48, "word": " مين", "probability": 0.779296875}, {"start": 841.48, "end": 842.1, "word": " الحاجة", "probability": 0.978515625}, {"start": 842.1, "end": 842.8, "word": " الضرورية", "probability": 0.86171875}, {"start": 842.8, "end": 843.14, "word": " هنا", "probability": 0.2073974609375}, {"start": 843.14, 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868.48, "word": " 12", "probability": 0.270751953125}, {"start": 868.48, "end": 868.64, "word": " مش", "probability": 0.9912109375}, {"start": 868.64, "end": 868.96, "word": " special", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 32, "seek": 91628, "start": 890.82, "end": 916.28, "text": "أه اللى خلانى أقدر أشتغل هنا بالأسلوب أو و أطلع النتيجة اللى موجودة قدامك هو أنه لجروب قابيل يعنى 17 complete the statement order ال A بتيسار order ال A ترمي if and only if order ال A is is ايش", "tokens": [10721, 3224, 13672, 7578, 16490, 1211, 7649, 7578, 5551, 28543, 2288, 5551, 8592, 2655, 17082, 1211, 34105, 20666, 10721, 3794, 1211, 37746, 34051, 4032, 5551, 9566, 1211, 3615, 28239, 31371, 7435, 3660, 13672, 7578, 3714, 29245, 23328, 3660, 12174, 3215, 10943, 4117, 31439, 14739, 3224, 5296, 7435, 32887, 3555, 12174, 16758, 26895, 37495, 1863, 7578, 3282, 3566, 264, 5629, 1668, 2423, 316, 39894, 1829, 3794, 9640, 1668, 2423, 316, 6055, 2288, 2304, 1829, 498, 293, 787, 498, 1668, 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"probability": 0.595947265625}, {"start": 1322.96, "end": 1323.2, "word": " N", "probability": 0.66455078125}, {"start": 1323.2, "end": 1323.86, "word": " بيساوي", "probability": 0.89814453125}, {"start": 1323.86, "end": 1324.12, "word": " N", "probability": 0.884765625}, {"start": 1324.12, "end": 1324.28, "word": " على", "probability": 0.6337890625}, {"start": 1324.28, "end": 1324.4, "word": " ال", "probability": 0.716796875}, {"start": 1324.4, "end": 1325.32, "word": " divisor", "probability": 0.55047607421875}, {"start": 1325.32, "end": 1325.42, "word": " ل", "probability": 0.367919921875}, {"start": 1325.42, "end": 1325.62, "word": " K", "probability": 0.79638671875}, {"start": 1325.62, "end": 1325.74, "word": " و", "probability": 0.9228515625}, {"start": 1325.74, "end": 1325.98, "word": " N", "probability": 0.7958984375}, {"start": 1325.98, "end": 1326.6, "word": " يعني", "probability": 0.6033935546875}, {"start": 1326.6, "end": 1326.68, "word": " ال", "probability": 0.1666259765625}, {"start": 1326.68, "end": 1326.9, "word": " order", "probability": 0.58447265625}, {"start": 1326.9, "end": 1327.06, "word": " ل", "probability": 0.66357421875}, {"start": 1327.06, "end": 1327.6, "word": " A", "probability": 0.83154296875}, {"start": 1327.6, "end": 1327.6, "word": " أُس", "probability": 0.93310546875}, {"start": 1327.6, "end": 1327.6, "word": " K", "probability": 0.9453125}, {"start": 1327.6, "end": 1328.46, "word": " بيساوي", "probability": 0.92880859375}, {"start": 1328.46, "end": 1328.68, "word": " order", "probability": 0.8525390625}, {"start": 1328.68, "end": 1328.68, "word": " ل", "probability": 0.93701171875}, {"start": 1328.68, "end": 1328.68, "word": " A", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 48, "seek": 137146, "start": 1342.78, "end": 1371.46, "text": "سؤال تسعة عشر سهل بتشوف ال generators للعناصر في U تلاتين او بتمسك العناصر بتشوف ايش بولته سؤال عشرين suppose that J is a pelian group of order خمسة و تلاتين and every element of J satisfies the equation X وخمسة و تلاتين دي ساوي identity proof that J is cyclic order لل J دي ساوي خمسة و تلاتين", "tokens": [3794, 33604, 6027, 6055, 3794, 27884, 6225, 46309, 8608, 3224, 1211, 39894, 8592, 38688, 2423, 38662, 24976, 3615, 1863, 33546, 2288, 8978, 624, 6055, 1211, 9307, 9957, 1975, 2407, 39894, 2304, 3794, 4117, 18863, 1863, 33546, 2288, 39894, 8592, 38688, 1975, 1829, 8592, 4724, 12610, 47395, 8608, 33604, 6027, 6225, 46309, 9957, 7297, 300, 508, 307, 257, 6178, 952, 1594, 295, 1668, 16490, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 293, 633, 4478, 295, 508, 44271, 264, 5367, 1783, 4032, 9778, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 11778, 1829, 8608, 995, 45865, 6575, 8177, 300, 508, 307, 38154, 1050, 1668, 24976, 508, 11778, 1829, 8608, 995, 45865, 16490, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957], "avg_logprob": -0.26015623634060225, "compression_ratio": 1.7280334728033473, "no_speech_prob": 0.0, "words": [{"start": 1342.78, "end": 1343.2, "word": "سؤال", "probability": 0.9002278645833334}, {"start": 1343.2, "end": 1343.46, "word": " تسعة", "probability": 0.6328938802083334}, {"start": 1343.46, "end": 1343.72, "word": " عشر", "probability": 0.81103515625}, {"start": 1343.72, "end": 1344.1, "word": " سهل", "probability": 0.9744466145833334}, {"start": 1344.1, "end": 1345.44, "word": " بتشوف", "probability": 0.8228352864583334}, {"start": 1345.44, "end": 1345.56, "word": " ال", "probability": 0.91552734375}, {"start": 1345.56, "end": 1346.18, "word": " generators", "probability": 0.69189453125}, {"start": 1346.18, "end": 1347.68, "word": " للعناصر", "probability": 0.695458984375}, {"start": 1347.68, "end": 1347.84, "word": " في", "probability": 0.953125}, {"start": 1347.84, "end": 1347.96, "word": " U", "probability": 0.64697265625}, {"start": 1347.96, "end": 1348.42, "word": " تلاتين", "probability": 0.90576171875}, {"start": 1348.42, "end": 1349.74, "word": " او", "probability": 0.734375}, {"start": 1349.74, "end": 1350.28, "word": " بتمسك", "probability": 0.902587890625}, {"start": 1350.28, "end": 1350.72, "word": " العناصر", "probability": 0.9718017578125}, {"start": 1350.72, "end": 1351.5, "word": " بتشوف", "probability": 0.721435546875}, {"start": 1351.5, "end": 1352.06, "word": " ايش", "probability": 0.7256673177083334}, {"start": 1352.06, "end": 1352.56, "word": " بولته", "probability": 0.9103190104166666}, {"start": 1352.56, "end": 1353.64, "word": " سؤال", "probability": 0.9415690104166666}, {"start": 1353.64, "end": 1354.24, "word": " عشرين", "probability": 0.9352213541666666}, {"start": 1354.24, "end": 1354.94, "word": " suppose", "probability": 0.2047119140625}, {"start": 1354.94, "end": 1355.52, "word": " that", "probability": 0.89208984375}, {"start": 1355.52, "end": 1355.72, "word": " J", "probability": 0.71484375}, {"start": 1355.72, "end": 1355.86, "word": " is", "probability": 0.8798828125}, {"start": 1355.86, "end": 1356.0, "word": " a", "probability": 0.83251953125}, 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1359.12, "end": 1359.62, "word": " satisfies", "probability": 0.498779296875}, {"start": 1359.62, "end": 1359.84, "word": " the", "probability": 0.8779296875}, {"start": 1359.84, "end": 1360.32, "word": " equation", "probability": 0.9736328125}, {"start": 1360.32, "end": 1361.04, "word": " X", "probability": 0.83642578125}, {"start": 1361.04, "end": 1361.48, "word": " وخمسة", "probability": 0.73695068359375}, {"start": 1361.48, "end": 1361.52, "word": " و", "probability": 0.96630859375}, {"start": 1361.52, "end": 1361.82, "word": " تلاتين", "probability": 0.9884033203125}, {"start": 1361.82, "end": 1362.0, "word": " دي", "probability": 0.5845947265625}, {"start": 1362.0, "end": 1362.26, "word": " ساوي", "probability": 0.8001302083333334}, {"start": 1362.26, "end": 1363.12, "word": " identity", "probability": 0.76953125}, {"start": 1363.12, "end": 1363.5, "word": " proof", "probability": 0.215576171875}, {"start": 1363.5, "end": 1363.76, "word": " that", "probability": 0.9130859375}, 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X في J X و 35 يساوي ال identity يثبت ان J صحيح هل 35 special تعالى نشوف", "tokens": [41, 307, 2847, 338, 952, 5296, 28820, 1783, 8978, 508, 1783, 4032, 6976, 7251, 3794, 995, 45865, 2423, 6575, 7251, 12984, 3555, 2655, 16472, 508, 20328, 5016, 1829, 5016, 8032, 1211, 6976, 2121, 37279, 6027, 7578, 8717, 8592, 38688], "avg_logprob": -0.49570309817790986, "compression_ratio": 1.0427350427350428, "no_speech_prob": 0.0, "words": [{"start": 1372.1, "end": 1372.44, "word": "J", "probability": 0.0838623046875}, {"start": 1372.44, "end": 1372.72, "word": " is", "probability": 0.6259765625}, {"start": 1372.72, "end": 1373.34, "word": " Abelian", "probability": 0.7491048177083334}, {"start": 1373.34, "end": 1379.54, "word": " لكل", "probability": 0.85205078125}, {"start": 1379.54, "end": 1381.1, "word": " X", "probability": 0.677734375}, {"start": 1381.1, "end": 1381.36, "word": " في", "probability": 0.935546875}, {"start": 1381.36, "end": 1381.68, "word": " J", "probability": 0.8974609375}, {"start": 1381.68, "end": 1383.14, "word": " X", "probability": 0.7822265625}, {"start": 1383.14, "end": 1383.3, "word": " و", "probability": 0.13037109375}, {"start": 1383.3, "end": 1384.24, "word": " 35", "probability": 0.8076171875}, {"start": 1384.24, "end": 1386.34, "word": " يساوي", "probability": 0.618408203125}, {"start": 1386.34, "end": 1386.42, "word": " ال", "probability": 0.88427734375}, {"start": 1386.42, "end": 1386.96, "word": " identity", "probability": 0.59814453125}, {"start": 1386.96, "end": 1388.98, "word": " يثبت", "probability": 0.7684326171875}, {"start": 1388.98, "end": 1390.14, "word": " ان", "probability": 0.42578125}, {"start": 1390.14, "end": 1390.4, "word": " J", "probability": 0.49072265625}, {"start": 1390.4, "end": 1391.02, "word": " صحيح", "probability": 0.66693115234375}, {"start": 1391.02, "end": 1395.8, "word": " هل", "probability": 0.706298828125}, {"start": 1395.8, "end": 1396.18, "word": " 35", "probability": 0.7890625}, {"start": 1396.18, "end": 1396.88, "word": " special", "probability": 0.33642578125}, {"start": 1396.88, "end": 1398.18, "word": " تعالى", "probability": 0.6119791666666666}, {"start": 1398.18, "end": 1398.5, "word": " نشوف", "probability": 0.9752604166666666}], "temperature": 1.0}, {"id": 50, "seek": 143155, "start": 1404.15, "end": 1431.55, "text": "جي أبيليان وكل عنصر فيها بيحقق العلاقة ان اكسوس خمسة و تلاتين بيساوي ال identity هل ال جي Cyclic عشان اثبت ان الجي Cyclic لازم يلاقي عنصر يعني المطلوب prove that يوجد جي في الجي او ا في الجي", "tokens": [7435, 1829, 5551, 21292, 20292, 7649, 4032, 28820, 18871, 9381, 2288, 8978, 11296, 4724, 1829, 5016, 4587, 4587, 18863, 15040, 28671, 16472, 1975, 4117, 3794, 41779, 16490, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 4724, 1829, 3794, 995, 45865, 2423, 6575, 8032, 1211, 2423, 10874, 1829, 10295, 66, 1050, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 16472, 25724, 1829, 10295, 66, 1050, 5296, 31377, 2304, 7251, 15040, 38436, 18871, 9381, 2288, 37495, 22653, 9673, 9566, 1211, 37746, 7081, 300, 7251, 29245, 3215, 10874, 1829, 8978, 25724, 1829, 1975, 2407, 1975, 8978, 25724, 1829], "avg_logprob": -0.23930921240856773, "compression_ratio": 1.6473684210526316, "no_speech_prob": 0.0, "words": [{"start": 1404.15, "end": 1404.43, "word": "جي", "probability": 0.400543212890625}, {"start": 1404.43, "end": 1405.03, "word": " أبيليان", "probability": 0.82421875}, {"start": 1405.03, "end": 1405.51, "word": " وكل", "probability": 0.591552734375}, {"start": 1405.51, "end": 1405.87, "word": " عنصر", "probability": 0.9669596354166666}, {"start": 1405.87, "end": 1406.11, "word": " فيها", "probability": 0.864990234375}, {"start": 1406.11, "end": 1406.55, "word": " بيحقق", "probability": 0.8994140625}, {"start": 1406.55, "end": 1406.99, "word": " العلاقة", "probability": 0.7479654947916666}, {"start": 1406.99, "end": 1407.13, "word": " ان", "probability": 0.3984375}, {"start": 1407.13, "end": 1407.67, "word": " اكسوس", "probability": 0.8118896484375}, {"start": 1407.67, "end": 1408.15, "word": " خمسة", "probability": 0.8917236328125}, {"start": 1408.15, "end": 1408.25, "word": " و", "probability": 0.51025390625}, {"start": 1408.25, "end": 1408.89, "word": " تلاتين", "probability": 0.902587890625}, {"start": 1408.89, "end": 1410.63, "word": " بيساوي", "probability": 0.8134765625}, {"start": 1410.63, "end": 1410.85, "word": " ال", "probability": 0.94482421875}, {"start": 1410.85, "end": 1411.47, "word": " identity", "probability": 0.8408203125}, {"start": 1411.47, "end": 1414.17, "word": " هل", "probability": 0.90478515625}, {"start": 1414.17, "end": 1416.19, "word": " ال", "probability": 0.465576171875}, {"start": 1416.19, "end": 1416.63, "word": " جي", "probability": 0.7236328125}, {"start": 1416.63, "end": 1418.01, "word": " Cyclic", "probability": 0.6590983072916666}, {"start": 1418.01, "end": 1419.71, "word": " عشان", "probability": 0.8986002604166666}, {"start": 1419.71, "end": 1420.47, "word": " اثبت", "probability": 0.876953125}, {"start": 1420.47, "end": 1420.57, "word": " ان", "probability": 0.86865234375}, {"start": 1420.57, "end": 1420.81, "word": " الجي", "probability": 0.6695556640625}, {"start": 1420.81, "end": 1421.23, "word": " Cyclic", "probability": 0.9222005208333334}, {"start": 1421.23, "end": 1421.53, "word": " لازم", "probability": 0.9874674479166666}, {"start": 1421.53, "end": 1421.79, "word": " يلاقي", "probability": 0.5833333333333334}, {"start": 1421.79, "end": 1422.43, "word": " عنصر", "probability": 0.9938151041666666}, {"start": 1422.43, "end": 1423.55, "word": " يعني", "probability": 0.927490234375}, {"start": 1423.55, "end": 1424.97, "word": " المطلوب", "probability": 0.983154296875}, {"start": 1424.97, "end": 1425.89, "word": " prove", "probability": 0.720703125}, {"start": 1425.89, "end": 1427.53, "word": " that", "probability": 0.93017578125}, {"start": 1427.53, "end": 1429.21, "word": " يوجد", "probability": 0.978515625}, {"start": 1429.21, "end": 1429.63, "word": " جي", 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"probability": 0.683349609375}, {"start": 1475.45, "end": 1476.39, "word": " زائد", "probability": 0.8732096354166666}, {"start": 1476.39, "end": 1478.29, "word": " الأخضر", "probability": 0.64996337890625}, {"start": 1478.29, "end": 1478.55, "word": " خمس", "probability": 0.8087565104166666}, {"start": 1478.55, "end": 1478.63, "word": " و", "probability": 0.5029296875}, {"start": 1478.63, "end": 1479.01, "word": " تلاتين", "probability": 0.95458984375}, {"start": 1479.01, "end": 1479.39, "word": " طيب", "probability": 0.9251302083333334}, {"start": 1479.39, "end": 1479.89, "word": " زائد", "probability": 0.9619140625}, {"start": 1479.89, "end": 1482.09, "word": " ان", "probability": 0.63916015625}, {"start": 1482.09, "end": 1486.49, "word": " كل", "probability": 0.48486328125}, {"start": 1486.49, "end": 1487.35, "word": " العناصر", "probability": 0.8541259765625}], "temperature": 1.0}, {"id": 53, "seek": 151257, "start": 1488.53, "end": 1512.57, "text": "بحقق ان اكسوس خمسة و تلاتين بدي ساوي ال identity انا بدي اثبت انه يوجد عنصر ال order له خمسة و تلاتين كيف؟ فكروا", "tokens": [49628, 4587, 4587, 16472, 1975, 4117, 3794, 41779, 16490, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 4724, 16254, 8608, 995, 45865, 2423, 6575, 1975, 8315, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 7251, 29245, 3215, 18871, 9381, 2288, 2423, 1668, 46740, 16490, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 9122, 33911, 22807, 6156, 37983, 14407], "avg_logprob": -0.22590042726468232, "compression_ratio": 1.4242424242424243, "no_speech_prob": 0.0, "words": [{"start": 1488.53, "end": 1489.11, "word": "بحقق", "probability": 0.85400390625}, {"start": 1489.11, "end": 1489.27, "word": " ان", "probability": 0.76611328125}, {"start": 1489.27, "end": 1489.67, "word": " اكسوس", "probability": 0.84674072265625}, {"start": 1489.67, "end": 1489.97, "word": " خمسة", "probability": 0.8258056640625}, {"start": 1489.97, "end": 1490.05, "word": " و", "probability": 0.5966796875}, {"start": 1490.05, "end": 1490.37, "word": " تلاتين", "probability": 0.953125}, {"start": 1490.37, "end": 1490.63, "word": " بدي", "probability": 0.5810546875}, {"start": 1490.63, "end": 1491.13, "word": " ساوي", "probability": 0.91162109375}, {"start": 1491.13, "end": 1492.25, "word": " ال", "probability": 0.91943359375}, {"start": 1492.25, "end": 1492.79, "word": " identity", "probability": 0.84228515625}, {"start": 1492.79, "end": 1494.17, "word": " انا", "probability": 0.760498046875}, {"start": 1494.17, "end": 1494.33, "word": " بدي", "probability": 0.95263671875}, {"start": 1494.33, "end": 1494.65, "word": " اثبت", "probability": 0.927978515625}, {"start": 1494.65, "end": 1495.03, "word": " انه", "probability": 0.788818359375}, {"start": 1495.03, "end": 1495.47, "word": " يوجد", "probability": 0.9899088541666666}, {"start": 1495.47, "end": 1496.15, "word": " عنصر", "probability": 0.78076171875}, {"start": 1496.15, "end": 1496.43, "word": " ال", "probability": 0.94970703125}, {"start": 1496.43, "end": 1496.81, "word": " order", "probability": 0.955078125}, {"start": 1496.81, "end": 1497.21, "word": " له", "probability": 0.13037109375}, {"start": 1497.21, "end": 1498.47, "word": " خمسة", "probability": 0.9605712890625}, {"start": 1498.47, "end": 1498.57, "word": " و", "probability": 0.91015625}, {"start": 1498.57, "end": 1499.19, "word": " تلاتين", "probability": 0.981201171875}, {"start": 1499.19, "end": 1508.07, "word": " كيف؟", "probability": 0.6612141927083334}, {"start": 1508.07, "end": 1512.57, "word": " فكروا", "probability": 0.6968587239583334}], "temperature": 1.0}, {"id": 54, "seek": 153823, "start": 1515.71, "end": 1538.23, "text": "أسس الطريقة لإثبات جمل بهذا الشكل هي تنقض هفترض ان لا يوجد عنصر ال order الو 35 تنساش انه ال .. لو بدي اخد اي عنصر هنا و يكون عندك x و 35 يساوي ال identity", "tokens": [10721, 3794, 3794, 41950, 16572, 28671, 5296, 28814, 12984, 3555, 9307, 10874, 42213, 39627, 15730, 25124, 28820, 39896, 6055, 1863, 4587, 11242, 8032, 5172, 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{"start": 1528.87, "end": 1530.93, "word": " ال", "probability": 0.37939453125}, {"start": 1530.93, "end": 1531.59, "word": " ..", "probability": 0.439208984375}, {"start": 1531.59, "end": 1532.73, "word": " لو", "probability": 0.92431640625}, {"start": 1532.73, "end": 1532.91, "word": " بدي", "probability": 0.7322998046875}, {"start": 1532.91, "end": 1533.23, "word": " اخد", "probability": 0.8684895833333334}, {"start": 1533.23, "end": 1533.47, "word": " اي", "probability": 0.8515625}, {"start": 1533.47, "end": 1533.89, "word": " عنصر", "probability": 0.9920247395833334}, {"start": 1533.89, "end": 1534.21, "word": " هنا", "probability": 0.966796875}, {"start": 1534.21, "end": 1535.49, "word": " و", "probability": 0.9541015625}, {"start": 1535.49, "end": 1535.77, "word": " يكون", "probability": 0.92431640625}, {"start": 1535.77, "end": 1536.11, "word": " عندك", "probability": 0.86669921875}, {"start": 1536.11, "end": 1536.43, "word": " x", "probability": 0.77880859375}, {"start": 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"end": 1652.68, "word": " اللي", "probability": 0.8330078125}, {"start": 1652.68, "end": 1652.72, "word": " له", "probability": 0.59814453125}, {"start": 1652.72, "end": 1653.28, "word": " خمسة", "probability": 0.9888916015625}, {"start": 1653.28, "end": 1653.84, "word": " و", "probability": 0.94775390625}, {"start": 1653.84, "end": 1653.96, "word": " في", "probability": 0.6337890625}, {"start": 1653.96, "end": 1654.3, "word": " عنصر", "probability": 0.9798177083333334}, {"start": 1654.3, "end": 1654.4, "word": " ال", "probability": 0.982421875}, {"start": 1654.4, "end": 1654.62, "word": " order", "probability": 0.96533203125}, {"start": 1654.62, "end": 1654.86, "word": " اللي", "probability": 0.958984375}, {"start": 1654.86, "end": 1654.98, "word": " له", "probability": 0.95458984375}, {"start": 1654.98, "end": 1656.8, "word": " سبعة", "probability": 0.9757486979166666}, {"start": 1656.8, "end": 1657.52, "word": " خدها", "probability": 0.7864583333333334}, {"start": 1657.52, "end": 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{"id": 61, "seek": 172250, "start": 1696.7, "end": 1722.5, "text": "X و 35 يساوي ال identity لكل X في J معناته order X هيقسم 35 لكل X في J order X يساوي 35 لكل X في J if X لا يساوي ال identity", "tokens": [55, 4032, 6976, 7251, 3794, 995, 45865, 2423, 6575, 5296, 28820, 1783, 8978, 508, 20449, 8315, 47395, 1668, 1783, 39896, 4587, 38251, 6976, 5296, 28820, 1783, 8978, 508, 1668, 1783, 7251, 3794, 995, 45865, 6976, 5296, 28820, 1783, 8978, 508, 498, 1783, 20193, 7251, 3794, 995, 45865, 2423, 6575], "avg_logprob": -0.31937500834465027, "compression_ratio": 1.638095238095238, "no_speech_prob": 0.0, "words": [{"start": 1696.7, "end": 1697.16, "word": "X", "probability": 0.39990234375}, {"start": 1697.16, "end": 1697.36, "word": " و", "probability": 0.0618896484375}, {"start": 1697.36, "end": 1698.22, "word": " 35", "probability": 0.69970703125}, {"start": 1698.22, "end": 1698.96, "word": " يساوي", "probability": 0.547149658203125}, {"start": 1698.96, "end": 1699.08, "word": " ال", "probability": 0.75244140625}, {"start": 1699.08, "end": 1699.54, "word": " identity", "probability": 0.5322265625}, {"start": 1699.54, "end": 1700.8, "word": " لكل", "probability": 0.852783203125}, {"start": 1700.8, "end": 1701.2, "word": " X", "probability": 0.83154296875}, {"start": 1701.2, "end": 1701.48, "word": " في", "probability": 0.90087890625}, {"start": 1701.48, "end": 1701.76, "word": " J", "probability": 0.4833984375}, {"start": 1701.76, "end": 1703.12, "word": " معناته", "probability": 0.6476236979166666}, {"start": 1703.12, "end": 1703.62, "word": " order", "probability": 0.5556640625}, {"start": 1703.62, "end": 1704.26, "word": " X", "probability": 0.62841796875}, {"start": 1704.26, "end": 1704.94, "word": " هيقسم", "probability": 0.7572428385416666}, {"start": 1704.94, "end": 1705.84, "word": " 35", "probability": 0.6943359375}, {"start": 1705.84, "end": 1707.3, "word": " لكل", "probability": 0.888916015625}, {"start": 1707.3, "end": 1707.6, "word": " X", 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"probability": 0.925537109375}, {"start": 1738.01, "end": 1739.13, "word": " خمسة", "probability": 0.9642333984375}, {"start": 1739.13, "end": 1739.39, "word": " و", "probability": 0.5703125}, {"start": 1739.39, "end": 1739.91, "word": " تلاتين", "probability": 0.8814697265625}, {"start": 1739.91, "end": 1740.79, "word": " يكبر", "probability": 0.50921630859375}, {"start": 1740.79, "end": 1741.23, "word": " جميع", "probability": 0.9837239583333334}, {"start": 1741.23, "end": 1742.49, "word": " العناصر", "probability": 0.9093017578125}, {"start": 1742.49, "end": 1742.89, "word": " مع", "probability": 0.947265625}, {"start": 1742.89, "end": 1743.21, "word": " عدل", "probability": 0.84912109375}, {"start": 1743.21, "end": 1743.83, "word": " identity", "probability": 0.5263671875}, {"start": 1743.83, "end": 1744.23, "word": " يعني", "probability": 0.53436279296875}, {"start": 1744.23, "end": 1744.37, "word": " ال", "probability": 0.70849609375}, {"start": 1744.37, "end": 1744.69, "word": " order", "probability": 0.8994140625}, {"start": 1744.69, "end": 1744.95, "word": " له", "probability": 0.6240234375}, {"start": 1744.95, "end": 1745.59, "word": " خمسة", "probability": 0.9739990234375}, {"start": 1745.59, "end": 1746.29, "word": " او", "probability": 0.834716796875}, {"start": 1746.29, "end": 1746.71, "word": " سبعة", "probability": 0.9658203125}, {"start": 1746.71, "end": 1747.71, "word": " اجازة", "probability": 0.5994873046875}, {"start": 1747.71, "end": 1747.79, "word": " اللي", "probability": 0.87939453125}, {"start": 1747.79, "end": 1748.41, "word": " هنعمله", "probability": 0.8994140625}, {"start": 1748.41, "end": 1749.09, "word": " كانت", "probability": 0.91015625}, {"start": 1749.09, "end": 1749.47, "word": " تالي", "probability": 0.8126627604166666}, {"start": 1749.47, "end": 1750.73, "word": " We", "probability": 0.463623046875}, {"start": 1750.73, "end": 1752.11, "word": " will", "probability": 0.7958984375}, {"start": 1752.11, "end": 1753.23, "word": " show", "probability": 0.9345703125}, {"start": 1753.23, "end": 1753.65, "word": " that", "probability": 0.91015625}], "temperature": 1.0}, {"id": 63, "seek": 178631, "start": 1759.91, "end": 1786.31, "text": "أحنا هننفيها عشان نشرع الخمسة و السابعة لحالنا و نصلّى تناقض لهذه الجملة اللي نفنها We will show that there is elements in D with order", "tokens": [10721, 5016, 8315, 8032, 1863, 1863, 5172, 1829, 11296, 6225, 8592, 7649, 8717, 46309, 3615, 33962, 2304, 3794, 3660, 4032, 21136, 16758, 27884, 5296, 5016, 6027, 8315, 4032, 8717, 36520, 11703, 7578, 6055, 8315, 4587, 11242, 46740, 24192, 25724, 2304, 37977, 13672, 1829, 8717, 5172, 1863, 11296, 492, 486, 855, 300, 456, 307, 4959, 294, 413, 365, 1668], "avg_logprob": -0.3029661067461563, "compression_ratio": 1.2993630573248407, "no_speech_prob": 0.0, "words": [{"start": 1759.91, "end": 1760.61, "word": "أحنا", "probability": 0.6168009440104166}, {"start": 1760.61, "end": 1761.23, "word": " هننفيها", "probability": 0.6761474609375}, {"start": 1761.23, "end": 1761.45, "word": " عشان", "probability": 0.8987630208333334}, {"start": 1761.45, "end": 1761.79, "word": " نشرع", "probability": 0.7168782552083334}, {"start": 1761.79, "end": 1762.15, "word": " الخمسة", "probability": 0.9041748046875}, {"start": 1762.15, "end": 1762.21, "word": " و", "probability": 0.63623046875}, {"start": 1762.21, "end": 1762.47, "word": " السابعة", "probability": 0.72900390625}, {"start": 1762.47, "end": 1763.19, "word": " لحالنا", "probability": 0.61480712890625}, {"start": 1763.19, "end": 1763.49, "word": " و", "probability": 0.845703125}, {"start": 1763.49, "end": 1763.93, "word": " نصلّى", "probability": 0.7515869140625}, {"start": 1763.93, "end": 1764.67, "word": " تناقض", "probability": 0.9656982421875}, {"start": 1764.67, "end": 1766.59, "word": " لهذه", "probability": 0.834716796875}, {"start": 1766.59, "end": 1766.85, "word": " الجملة", "probability": 0.9514973958333334}, {"start": 1766.85, "end": 1766.97, "word": " اللي", "probability": 0.92431640625}, {"start": 1766.97, "end": 1767.47, "word": " نفنها", "probability": 0.701416015625}, {"start": 1767.47, "end": 1768.41, "word": " We", "probability": 0.346435546875}, {"start": 1768.41, "end": 1768.65, "word": " will", "probability": 0.8876953125}, {"start": 1768.65, "end": 1768.93, "word": " show", "probability": 0.96484375}, {"start": 1768.93, "end": 1769.61, "word": " that", "probability": 0.94970703125}, {"start": 1769.61, "end": 1775.69, "word": " there", "probability": 0.6298828125}, {"start": 1775.69, "end": 1777.49, "word": " is", "probability": 0.9287109375}, {"start": 1777.49, "end": 1779.97, "word": " elements", "probability": 0.8701171875}, {"start": 1779.97, "end": 1782.33, "word": " in", "probability": 0.90625}, {"start": 1782.33, "end": 1782.61, "word": " D", "probability": 0.77880859375}, {"start": 1782.61, "end": 1784.31, "word": " with", "probability": 0.9072265625}, {"start": 1784.31, "end": 1786.31, "word": " order", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 64, "seek": 181461, "start": 1787.65, "end": 1814.61, "text": "خمسة and elements with order سبعة هاتبت انه يوجد عناصر ال order له خمسة و يوجد عناصر ال order له ايش سبعة برضه هشغل هالجتنا في داخلي هانفي انه .. يعني هقول انه مافيش order سبعة يعني كل ال order خمسة to show that", "tokens": [9778, 2304, 3794, 3660, 293, 4959, 365, 1668, 8608, 3555, 27884, 8032, 9307, 3555, 2655, 16472, 3224, 7251, 29245, 3215, 18871, 33546, 2288, 2423, 1668, 46740, 16490, 2304, 3794, 3660, 4032, 7251, 29245, 3215, 18871, 33546, 2288, 2423, 1668, 46740, 1975, 1829, 8592, 8608, 3555, 27884, 4724, 43042, 3224, 8032, 8592, 17082, 1211, 8032, 6027, 7435, 2655, 8315, 8978, 11778, 47283, 20292, 8032, 7649, 41185, 16472, 3224, 4386, 37495, 22653, 8032, 39648, 16472, 3224, 19446, 41185, 8592, 1668, 8608, 3555, 27884, 37495, 22653, 28242, 2423, 1668, 16490, 2304, 3794, 3660, 281, 855, 300], "avg_logprob": -0.24069149570262177, "compression_ratio": 1.7868852459016393, "no_speech_prob": 0.0, "words": [{"start": 1787.65, "end": 1788.41, "word": "خمسة", "probability": 0.789794921875}, {"start": 1788.41, "end": 1789.31, "word": " and", "probability": 0.1895751953125}, {"start": 1789.31, "end": 1790.15, "word": " elements", "probability": 0.8076171875}, {"start": 1790.15, "end": 1793.09, "word": " with", "probability": 0.86669921875}, {"start": 1793.09, "end": 1793.73, "word": " order", "probability": 0.9287109375}, {"start": 1793.73, "end": 1796.05, "word": " سبعة", "probability": 0.8562825520833334}, {"start": 1796.05, "end": 1797.83, "word": " هاتبت", "probability": 0.50970458984375}, {"start": 1797.83, "end": 1798.05, "word": " انه", "probability": 0.573974609375}, {"start": 1798.05, "end": 1798.35, "word": " يوجد", "probability": 0.9820963541666666}, {"start": 1798.35, "end": 1798.79, "word": " عناصر", "probability": 0.9794921875}, {"start": 1798.79, "end": 1798.89, "word": " ال", "probability": 0.7490234375}, {"start": 1798.89, "end": 1799.11, "word": " order", "probability": 0.8388671875}, {"start": 1799.11, "end": 1799.33, "word": " له", "probability": 0.529296875}, {"start": 1799.33, "end": 1799.89, "word": " خمسة", "probability": 0.974853515625}, {"start": 1799.89, "end": 1800.97, "word": " و", "probability": 0.92626953125}, {"start": 1800.97, "end": 1801.33, "word": " يوجد", "probability": 0.792724609375}, {"start": 1801.33, "end": 1801.85, "word": " عناصر", "probability": 0.9925130208333334}, {"start": 1801.85, "end": 1801.97, "word": " ال", "probability": 0.9765625}, {"start": 1801.97, "end": 1802.27, "word": " order", "probability": 0.9521484375}, {"start": 1802.27, "end": 1802.55, "word": " له", "probability": 0.81494140625}, {"start": 1802.55, "end": 1802.93, "word": " ايش", "probability": 0.6714680989583334}, {"start": 1802.93, "end": 1803.91, "word": " سبعة", "probability": 0.8416341145833334}, {"start": 1803.91, "end": 1804.67, "word": " برضه", "probability": 0.9342447916666666}, {"start": 1804.67, "end": 1805.13, "word": " هشغل", "probability": 0.96044921875}, {"start": 1805.13, "end": 1805.63, "word": " هالجتنا", "probability": 0.710791015625}, {"start": 1805.63, "end": 1805.77, "word": " في", "probability": 0.63037109375}, {"start": 1805.77, "end": 1806.29, "word": " داخلي", "probability": 0.9383138020833334}, {"start": 1806.29, "end": 1807.49, "word": " هانفي", "probability": 0.3623860677083333}, {"start": 1807.49, "end": 1807.79, "word": " انه", "probability": 0.81005859375}, {"start": 1807.79, "end": 1807.93, "word": " ..", "probability": 0.40771484375}, {"start": 1807.93, "end": 1808.19, "word": " يعني", "probability": 0.933349609375}, {"start": 1808.19, "end": 1808.57, "word": " هقول", "probability": 0.8779296875}, {"start": 1808.57, "end": 1808.79, "word": " انه", "probability": 0.88623046875}, {"start": 1808.79, "end": 1808.99, "word": " مافيش", "probability": 0.768798828125}, {"start": 1808.99, "end": 1809.37, "word": " order", "probability": 0.81640625}, {"start": 1809.37, "end": 1809.81, "word": " سبعة", "probability": 0.9744466145833334}, {"start": 1809.81, "end": 1810.63, "word": " يعني", "probability": 0.962158203125}, {"start": 1810.63, "end": 1810.97, "word": " كل", "probability": 0.9609375}, {"start": 1810.97, "end": 1811.11, "word": " ال", "probability": 0.91845703125}, {"start": 1811.11, "end": 1811.61, "word": " order", "probability": 0.97265625}, {"start": 1811.61, "end": 1812.89, "word": " خمسة", "probability": 0.9644775390625}, {"start": 1812.89, "end": 1813.91, "word": " to", "probability": 0.8779296875}, {"start": 1813.91, "end": 1814.19, "word": " show", "probability": 0.96826171875}, {"start": 1814.19, "end": 1814.61, "word": " that", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 65, "seek": 184605, "start": 1817.33, "end": 1846.05, "text": "we will first assume that there is no elements in J with order 7 assume that all", "tokens": [826, 486, 700, 6552, 300, 456, 307, 572, 4959, 294, 508, 365, 1668, 1614, 6552, 300, 439], "avg_logprob": -0.238498255610466, "compression_ratio": 1.1594202898550725, "no_speech_prob": 0.0, "words": [{"start": 1817.33, "end": 1817.75, "word": "we", "probability": 0.174072265625}, {"start": 1817.75, "end": 1818.89, "word": " will", "probability": 0.9169921875}, {"start": 1818.89, "end": 1820.37, "word": " first", "probability": 0.919921875}, {"start": 1820.37, "end": 1822.51, "word": " assume", "probability": 0.92626953125}, {"start": 1822.51, "end": 1825.89, "word": " that", "probability": 0.9248046875}, {"start": 1825.89, "end": 1827.67, "word": " there", "probability": 0.9189453125}, {"start": 1827.67, "end": 1829.45, "word": " is", "probability": 0.9501953125}, {"start": 1829.45, "end": 1830.85, "word": " no", "probability": 0.9482421875}, {"start": 1830.85, "end": 1831.85, "word": " elements", "probability": 0.89404296875}, {"start": 1831.85, "end": 1834.63, "word": " in", "probability": 0.9580078125}, {"start": 1834.63, "end": 1834.99, "word": " J", "probability": 0.494384765625}, {"start": 1834.99, "end": 1836.49, "word": " with", "probability": 0.90771484375}, {"start": 1836.49, "end": 1838.57, "word": " order", "probability": 0.65234375}, {"start": 1838.57, "end": 1839.01, "word": " 7", "probability": 0.75830078125}, {"start": 1839.01, "end": 1840.01, "word": " assume", "probability": 0.7939453125}, {"start": 1840.01, "end": 1843.83, "word": " that", "probability": 0.9443359375}, {"start": 1843.83, "end": 1846.05, "word": " all", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 66, "seek": 187568, "start": 1848.4, "end": 1875.68, "text": "x لا يساوي ال identity in j has order خمسة Note that if order ال x بدى يساوي خمسة then order ال x تربع بدى يساوي order ال x تكعي بدى يساوي order ال x أربعة بدى يساوي خمسة", "tokens": [87, 20193, 7251, 3794, 995, 45865, 2423, 6575, 294, 361, 575, 1668, 16490, 2304, 3794, 3660, 11633, 300, 498, 1668, 2423, 2031, 47525, 7578, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 550, 1668, 2423, 2031, 6055, 25513, 3615, 47525, 7578, 7251, 3794, 995, 45865, 1668, 2423, 2031, 6055, 4117, 3615, 1829, 47525, 7578, 7251, 3794, 995, 45865, 1668, 2423, 2031, 5551, 25513, 27884, 47525, 7578, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660], "avg_logprob": -0.3060416579246521, "compression_ratio": 1.952, "no_speech_prob": 0.0, "words": [{"start": 1848.4, "end": 1848.88, "word": "x", "probability": 0.10528564453125}, {"start": 1848.88, "end": 1849.3, "word": " لا", "probability": 0.79736328125}, {"start": 1849.3, "end": 1849.82, "word": " يساوي", "probability": 0.71051025390625}, {"start": 1849.82, "end": 1849.9, "word": " ال", "probability": 0.91845703125}, {"start": 1849.9, "end": 1850.48, "word": " identity", "probability": 0.67529296875}, {"start": 1850.48, "end": 1851.18, "word": " in", "probability": 0.1851806640625}, {"start": 1851.18, "end": 1851.58, "word": " j", "probability": 0.576171875}, {"start": 1851.58, "end": 1853.16, "word": " has", "probability": 0.1512451171875}, {"start": 1853.16, "end": 1854.74, "word": " order", "probability": 0.83544921875}, {"start": 1854.74, "end": 1856.48, "word": " خمسة", "probability": 0.9190673828125}, {"start": 1856.48, "end": 1860.78, "word": " Note", "probability": 0.375732421875}, {"start": 1860.78, "end": 1861.5, "word": " that", "probability": 0.9130859375}, {"start": 1861.5, "end": 1865.08, "word": " if", "probability": 0.73974609375}, {"start": 1865.08, "end": 1865.7, "word": " order", "probability": 0.96044921875}, {"start": 1865.7, "end": 1865.96, "word": " ال", "probability": 0.4189453125}, {"start": 1865.96, "end": 1866.22, "word": " x", "probability": 0.63525390625}, {"start": 1866.22, "end": 1866.5, "word": " بدى", "probability": 0.3155517578125}, {"start": 1866.5, "end": 1866.86, "word": " يساوي", "probability": 0.956787109375}, {"start": 1866.86, "end": 1867.3, "word": " خمسة", "probability": 0.9637451171875}, {"start": 1867.3, "end": 1867.62, "word": " then", "probability": 0.56103515625}, {"start": 1867.62, "end": 1869.2, "word": " order", "probability": 0.94189453125}, {"start": 1869.2, "end": 1869.44, "word": " ال", "probability": 0.88330078125}, {"start": 1869.44, "end": 1869.64, "word": " x", "probability": 0.9619140625}, {"start": 1869.64, "end": 1870.22, "word": " تربع", "probability": 0.625732421875}, {"start": 1870.22, "end": 1870.5, "word": " بدى", "probability": 0.803955078125}, {"start": 1870.5, "end": 1870.72, "word": " يساوي", "probability": 0.960693359375}, {"start": 1870.72, "end": 1871.02, "word": " order", "probability": 0.8642578125}, {"start": 1871.02, "end": 1871.24, "word": " ال", "probability": 0.83056640625}, {"start": 1871.24, "end": 1871.46, "word": " x", "probability": 0.9853515625}, {"start": 1871.46, "end": 1871.78, "word": " تكعي", "probability": 0.50830078125}, {"start": 1871.78, "end": 1872.02, "word": " بدى", "probability": 0.745361328125}, {"start": 1872.02, "end": 1872.26, "word": " يساوي", "probability": 0.987060546875}, {"start": 1872.26, "end": 1872.58, "word": " order", "probability": 0.9462890625}, {"start": 1872.58, "end": 1872.86, "word": " ال", "probability": 0.9189453125}, {"start": 1872.86, "end": 1873.06, "word": " x", "probability": 0.98486328125}, {"start": 1873.06, "end": 1873.8, "word": " أربعة", "probability": 0.8037923177083334}, {"start": 1873.8, "end": 1874.92, "word": " بدى", "probability": 0.873291015625}, {"start": 1874.92, "end": 1875.18, "word": " يساوي", "probability": 0.9852294921875}, {"start": 1875.18, "end": 1875.68, "word": " خمسة", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 67, "seek": 190635, "start": 1877.07, "end": 1906.35, "text": "طبعا هذه بدأ اثبات prove it اثباتها سهل ال order لexos k بدي ساوي ال o اللي هو n اللي هي خمسة على order لجيسكم و ال divisor ل الخمسة و الكيه في نهاية تصل لكلام هذا هذا معناته the order خمسة is found in", "tokens": [9566, 3555, 3615, 995, 29538, 47525, 10721, 1975, 12984, 3555, 9307, 7081, 309, 1975, 12984, 3555, 9307, 11296, 8608, 3224, 1211, 2423, 1668, 5296, 3121, 329, 350, 4724, 16254, 8608, 995, 45865, 2423, 277, 13672, 1829, 31439, 297, 13672, 1829, 39896, 16490, 2304, 3794, 3660, 15844, 1668, 5296, 7435, 1829, 3794, 24793, 4032, 2423, 25974, 284, 5296, 33962, 2304, 3794, 3660, 4032, 33251, 1829, 3224, 8978, 8717, 11296, 10632, 6055, 36520, 5296, 28820, 10943, 23758, 23758, 20449, 8315, 47395, 264, 1668, 16490, 2304, 3794, 3660, 307, 1352, 294], "avg_logprob": -0.30389746387353106, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1877.07, "end": 1877.41, "word": "طبعا", "probability": 0.83837890625}, {"start": 1877.41, "end": 1877.75, "word": " هذه", "probability": 0.62646484375}, {"start": 1877.75, "end": 1878.39, "word": " بدأ", "probability": 0.7080078125}, {"start": 1878.39, "end": 1878.91, "word": " اثبات", "probability": 0.7998046875}, {"start": 1878.91, "end": 1879.45, "word": " prove", "probability": 0.453369140625}, {"start": 1879.45, "end": 1880.49, "word": " it", "probability": 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{"start": 2056.63, "end": 2057.31, "word": " واحد", "probability": 0.58551025390625}, {"start": 2057.31, "end": 2057.51, "word": " أو", "probability": 0.453125}, {"start": 2057.51, "end": 2058.61, "word": " خمسة", "probability": 0.9578857421875}, {"start": 2058.61, "end": 2059.11, "word": " ايش", "probability": 0.59423828125}, {"start": 2059.11, "end": 2059.91, "word": " يعني؟", "probability": 0.84423828125}, {"start": 2059.91, "end": 2060.85, "word": " مش", "probability": 0.8154296875}, {"start": 2060.85, "end": 2061.27, "word": " الكل", "probability": 0.733154296875}, {"start": 2061.27, "end": 2061.75, "word": " واحد", "probability": 0.98583984375}, {"start": 2061.75, "end": 2061.91, "word": " مش", "probability": 0.59228515625}, {"start": 2061.91, "end": 2062.21, "word": " الكل", "probability": 0.908935546875}, {"start": 2062.21, "end": 2062.91, "word": " خمسة،", "probability": 0.83984375}, {"start": 2062.91, "end": 2063.29, "word": " مافيش", "probability": 0.7858072916666666}, {"start": 2063.29, "end": 2063.61, "word": " خمسة", "probability": 0.871337890625}, {"start": 2063.61, "end": 2063.67, "word": " و", "probability": 0.82373046875}, {"start": 2063.67, "end": 2064.13, "word": " تلاتين،", "probability": 0.86435546875}, {"start": 2064.13, "end": 2064.19, "word": " إيش", "probability": 0.7661946614583334}, {"start": 2064.19, "end": 2065.85, "word": " هيضل؟", "probability": 0.765380859375}, {"start": 2065.85, "end": 2066.01, "word": " إيش", "probability": 0.6199544270833334}, {"start": 2066.01, "end": 2066.43, "word": " بقى؟", "probability": 0.939208984375}, {"start": 2066.43, "end": 2066.63, "word": " at", "probability": 0.89208984375}, {"start": 2066.63, "end": 2067.29, "word": " least", "probability": 0.9697265625}, {"start": 2067.29, "end": 2069.39, "word": " there", "probability": 0.8759765625}, {"start": 2069.39, "end": 2070.07, "word": " is", "probability": 0.95458984375}, {"start": 2070.07, "end": 2071.81, "word": " a", "probability": 0.6416015625}, {"start": 2071.81, "end": 2073.19, "word": " ينتمي", "probability": 0.981201171875}, {"start": 2073.19, "end": 2073.37, "word": " لل", "probability": 0.8427734375}, {"start": 2073.37, "end": 2073.71, "word": " j", "probability": 0.55712890625}, {"start": 2073.71, "end": 2074.59, "word": " and", "probability": 0.87646484375}, {"start": 2074.59, "end": 2075.89, "word": " order", "probability": 0.94970703125}, {"start": 2075.89, "end": 2076.17, "word": " ال", "probability": 0.9052734375}, {"start": 2076.17, "end": 2076.35, "word": " a", "probability": 0.71435546875}, {"start": 2076.35, "end": 2076.51, "word": " بدي", "probability": 0.5528564453125}, {"start": 2076.51, "end": 2076.77, "word": " يساوي", "probability": 0.60247802734375}, {"start": 2076.77, "end": 2077.17, "word": " سبعة", "probability": 0.9549153645833334}], "temperature": 1.0}, {"id": 74, "seek": 210712, "start": 2078.32, "end": 2107.12, "text": "أعطيها نجمة Similarly بنفس الطريقة there is P إذا فيها نكسة لا اطلع فيها اجيت على الواجب فادي there is P أنتمي نرجع with order ال P بدي ساوي خمسة", "tokens": [10721, 3615, 9566, 1829, 11296, 8717, 7435, 46007, 13157, 44945, 36178, 41950, 16572, 28671, 456, 307, 430, 11933, 15730, 8978, 11296, 8717, 4117, 3794, 3660, 20193, 1975, 9566, 1211, 3615, 8978, 11296, 1975, 7435, 36081, 15844, 2423, 2407, 26108, 3555, 6156, 995, 16254, 456, 307, 430, 14739, 39237, 1829, 8717, 47341, 3615, 365, 1668, 2423, 430, 4724, 16254, 8608, 995, 45865, 16490, 2304, 3794, 3660], "avg_logprob": -0.3499053170283635, "compression_ratio": 1.3865030674846626, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2078.32, "end": 2078.72, "word": "أعطيها", "probability": 0.8003662109375}, {"start": 2078.72, "end": 2079.1, "word": " نجمة", "probability": 0.9195963541666666}, {"start": 2079.1, "end": 2082.62, "word": " Similarly", "probability": 0.357666015625}, {"start": 2082.62, "end": 2083.6, "word": " بنفس", "probability": 0.883056640625}, {"start": 2083.6, "end": 2084.4, "word": " 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"end": 2232.42, "text": "أشماله يقسم الخمسة و تلاتين خلصناش case واحد order ال AB بدي ساوي واحد", "tokens": [10721, 8592, 2304, 6027, 3224, 7251, 4587, 38251, 33962, 2304, 3794, 3660, 4032, 6055, 1211, 9307, 9957, 16490, 1211, 9381, 1863, 33599, 1389, 36764, 24401, 1668, 2423, 13838, 4724, 16254, 8608, 995, 45865, 36764, 24401], "avg_logprob": -0.4296875124176343, "compression_ratio": 1.1717171717171717, "no_speech_prob": 0.0, "words": [{"start": 2221.46, "end": 2222.54, "word": "أشماله", "probability": 0.580804443359375}, {"start": 2222.54, "end": 2223.62, "word": " يقسم", "probability": 0.8546549479166666}, {"start": 2223.62, "end": 2224.2, "word": " الخمسة", "probability": 0.8570556640625}, {"start": 2224.2, "end": 2224.26, "word": " و", "probability": 0.38818359375}, {"start": 2224.26, "end": 2225.68, "word": " تلاتين", "probability": 0.7901611328125}, {"start": 2225.68, "end": 2226.84, "word": " خلصناش", "probability": 0.65263671875}, {"start": 2226.84, "end": 2227.74, "word": " 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0.69873046875}, {"start": 2685.01, "end": 2685.35, "word": " X1", "probability": 0.31396484375}, {"start": 2685.35, "end": 2686.11, "word": " مش", "probability": 0.21484375}, {"start": 2686.11, "end": 2686.49, "word": " الأقدر", "probability": 0.716796875}, {"start": 2686.49, "end": 2686.57, "word": " ال", "probability": 0.765625}, {"start": 2686.57, "end": 2686.71, "word": " X", "probability": 0.986328125}, {"start": 2686.71, "end": 2687.41, "word": " كمسة", "probability": 0.78558349609375}, {"start": 2687.41, "end": 2687.63, "word": " ف", "probability": 0.492431640625}, {"start": 2687.63, "end": 2688.07, "word": " X5", "probability": 0.6650390625}, {"start": 2688.07, "end": 2688.23, "word": " يبقوا", "probability": 0.77099609375}, {"start": 2688.23, "end": 2688.47, "word": " عليا", "probability": 0.591552734375}, {"start": 2688.47, "end": 2690.03, "word": " أي", "probability": 0.75146484375}, {"start": 2690.03, "end": 2692.65, "word": " سؤال", "probability": 0.9306640625}, {"start": 2692.65, "end": 2692.73, "word": " يا", "probability": 0.96826171875}, {"start": 2692.73, "end": 2693.21, "word": " شباب؟", "probability": 0.8775634765625}, {"start": 2693.21, "end": 2694.61, "word": " أي", "probability": 0.826171875}, {"start": 2694.61, "end": 2695.99, "word": " سؤال؟", "probability": 0.8724365234375}, {"start": 2695.99, "end": 2697.29, "word": " واضح؟", "probability": 0.945068359375}, {"start": 2697.29, "end": 2697.49, "word": " يا", "probability": 0.6748046875}, {"start": 2697.49, "end": 2697.65, "word": " عزيزي", "probability": 0.8287109375}, {"start": 2697.65, "end": 2697.77, "word": " يا", "probability": 0.1124267578125}, {"start": 2697.77, "end": 2697.93, "word": " عزيزي", "probability": 0.85625}, {"start": 2697.93, "end": 2698.05, "word": " يا", "probability": 0.41650390625}, {"start": 2698.05, "end": 2698.21, "word": " شباب", "probability": 0.86669921875}, {"start": 2698.21, "end": 2698.33, "word": " من", "probability": 0.162841796875}, {"start": 2698.33, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..86253b0662203cd0ddef09ea5d5c183ab5bed962
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_raw.srt
@@ -0,0 +1,1680 @@
+1
+00:00:21,350 --> 00:00:24,670
+السلام عليكم بسم الله الرحمن الرحيم طبعا هنكمل ان
+
+2
+00:00:24,670 --> 00:00:28,250
+شاء الله زي ما اتفقنا في المحاضرة تبعت الصبح هنكمل
+
+3
+00:00:28,250 --> 00:00:33,030
+مناقشة الوحدة الرابعة اعتقد وصلنا لسؤال تلتاش سؤال
+
+4
+00:00:33,030 --> 00:00:38,610
+اتناش خلصناه سؤال تلتاش اربعتاش خمستاش خليني بس
+
+5
+00:00:38,610 --> 00:00:40,750
+اشوف المورجة تبعت الاسئلة اللي حطناها
+
+6
+00:00:45,690 --> 00:00:51,590
+سؤال 12 او 13 انزد 24 find a generator of
+
+7
+00:00:51,590 --> 00:00:58,070
+generated by 21 and generated by 10 خلينا نجيب
+
+8
+00:00:58,070 --> 00:01:02,770
+generated by 21 generated by 21 يا شباب هي عبارة
+
+9
+00:01:02,770 --> 00:01:08,650
+عن generated by مين ال
+
+10
+00:01:08,650 --> 00:01:14,790
+21والاربع و عشرين ايش الجريس ال common divisor لهم
+
+11
+00:01:14,790 --> 00:01:20,690
+تلاتة هذا عبارة عن generated by واحد اص واحد و
+
+12
+00:01:20,690 --> 00:01:23,890
+عشرين اللي يجب ان يساوي generated by واحد اص جريس
+
+13
+00:01:23,890 --> 00:01:28,910
+ال common divisor لواحد و عشرين واربع و عشرين اللي
+
+14
+00:01:28,910 --> 00:01:33,030
+generated by واحد اص تلاتة كان generated by تلاتة
+
+15
+00:01:33,030 --> 00:01:42,440
+مين يا generated by تلاتةidentity 3 6 9 12 15 18
+
+16
+00:01:42,440 --> 00:01:48,800
+21 و بس نفس القصة generated by 10 هنكتشف انها
+
+17
+00:01:48,800 --> 00:01:57,560
+generated by 2 اللي هي عبارة عن identity 2 4 6 8 و
+
+18
+00:01:57,560 --> 00:02:03,860
+22 لو بتجيب التقاطع generated by 21 تقاطع
+
+19
+00:02:03,860 --> 00:02:11,420
+generated by 10هنصف ال identity ستة و اتناش و
+
+20
+00:02:11,420 --> 00:02:17,180
+تمانتاش هذا generated by مين يا شباب؟
+
+21
+00:02:17,180 --> 00:02:26,240
+ستة بتقدر تعمم تكمل
+
+22
+00:02:26,240 --> 00:02:31,220
+السؤال بتقدر تعمم generated by a to m تقاضع
+
+23
+00:02:31,220 --> 00:02:34,580
+generated by a to n عبارة عن ايش؟
+
+24
+00:02:42,150 --> 00:02:47,150
+generated by a to m and generated by a to nتقاطع
+
+25
+00:02:47,150 --> 00:02:51,650
+generated by مين لاحظ ان احنا هنا وصلنا لgenerated
+
+26
+00:02:51,650 --> 00:02:56,990
+by تلاتة وgenerated by تنين يعني واحد وثلاثة وواحد
+
+27
+00:02:56,990 --> 00:03:01,210
+واثنين لو قولنا a والثلاثة و a والثانين يعني a
+
+28
+00:03:01,210 --> 00:03:04,810
+والستة اللي هو least common multiple يعني هذا
+
+29
+00:03:04,810 --> 00:03:08,890
+عبارة عن generated by a ال least common multiple
+
+30
+00:03:08,890 --> 00:03:15,980
+لأ مهموهذا حصير fact generated by a to m تقعده
+
+31
+00:03:15,980 --> 00:03:20,680
+generated by a to n هي generated by a قص ال least
+
+32
+00:03:20,680 --> 00:03:25,540
+common multiple ل m قص ال least common multiple ل
+
+33
+00:03:25,540 --> 00:03:26,080
+m قص ال least common multiple ل M قص ال least
+
+34
+00:03:26,080 --> 00:03:28,680
+common multiple ل M قص ال least common multiple ل
+
+35
+00:03:28,680 --> 00:03:32,620
+M قص ال least common multiple ل M قص ال least
+
+36
+00:03:32,620 --> 00:03:32,720
+common multiple ل M قص ال least common multiple ل
+
+37
+00:03:32,720 --> 00:03:32,720
+M قص ال least common multiple ل M قص ال least
+
+38
+00:03:32,720 --> 00:03:32,720
+common multiple ل M قص ال least common multiple ل
+
+39
+00:03:32,720 --> 00:03:32,720
+M قص ال least common multiple ل M قص ال least
+
+40
+00:03:32,720 --> 00:03:32,720
+common multiple ل M قص ال least common multiple ل
+
+41
+00:03:32,720 --> 00:03:32,720
+M قص ال least common multiple ل M قص ال least
+
+42
+00:03:32,720 --> 00:03:33,380
+common multiple ل M قص ال least common multiple ل
+
+43
+00:03:33,380 --> 00:03:33,380
+M قص ال least common multiple ل M قص ال least
+
+44
+00:03:33,380 --> 00:03:33,380
+common multiple ل M قص ال least common multiple ل
+
+45
+00:03:33,380 --> 00:03:33,380
+M قص ال least common multiple ل M قص ال least
+
+46
+00:03:33,380 --> 00:03:33,520
+common multiple ل M قص ال least common multiple ل
+
+47
+00:03:33,520 --> 00:03:36,860
+M قص ال least common multiple ل M قص ال least
+
+48
+00:03:36,860 --> 00:03:37,280
+common multiple
+
+49
+00:03:40,270 --> 00:03:47,850
+الـ 0 تنتشر في Z أربعة و عشرين نفس
+
+50
+00:03:47,850 --> 00:03:52,870
+الشيء بعده أربعة عاشر suppose that a cyclic group
+
+51
+00:03:52,870 --> 00:03:56,990
+J has exactly three subgroups J identity and a
+
+52
+00:03:56,990 --> 00:04:03,810
+subgroup of order سبعة what is order J J cyclic
+
+53
+00:04:03,810 --> 00:04:08,690
+generated by ال A اللي هو only
+
+54
+00:04:11,530 --> 00:04:25,630
+subgroups of j are ال identity و ال h حيث order ال
+
+55
+00:04:25,630 --> 00:04:33,250
+h بيساوي سبعة and j itself المطلوب
+
+56
+00:04:33,250 --> 00:04:33,990
+order ال j
+
+57
+00:04:47,620 --> 00:04:53,640
+فكروا انلخص معلوماتنا قولنا لو انا بشتغل في cyclic
+
+58
+00:04:53,640 --> 00:04:59,760
+group ال subgroups كلهم cyclic ال subgroups ال
+
+59
+00:04:59,760 --> 00:05:04,160
+order اللي يقسم ال order لل group وكل قاسم ل order
+
+60
+00:05:04,160 --> 00:05:10,280
+ال group اللي قاسم ال order له هذا القاسم let
+
+61
+00:05:10,280 --> 00:05:17,430
+order الجي بده يساوي nتجمع المعلومات السبعة تقسم
+
+62
+00:05:17,430 --> 00:05:22,730
+الان ليش H subgroup من الجيه و order ال H ودي
+
+63
+00:05:22,730 --> 00:05:34,610
+ساوية سبعة تانية الان لا يساوي سبعة ليش لإن H
+
+64
+00:05:34,610 --> 00:05:40,050
+proper subgroup من الجيه ليش proper لإن جالي فيه
+
+65
+00:05:40,050 --> 00:05:46,930
+ال H و فيه ال جيه و التنتين مختلفةأذا أريد الـ N
+
+66
+00:05:46,930 --> 00:05:56,430
+الـ 7 تقسم الـ N والـ N لا تساوي 7 الـ
+
+67
+00:05:56,430 --> 00:06:03,930
+N مثلا تساوي 7K الـ
+
+68
+00:06:03,930 --> 00:06:14,630
+N ماذا تساوي؟ 7K حيث ك أكبر من 1ليش K أكبر من
+
+69
+00:06:14,630 --> 00:06:23,150
+الواحد؟ لأن الان لا يساوي سبعة But J is cyclic إيش
+
+70
+00:06:23,150 --> 00:06:33,130
+يعني؟ يعني يوجد subgroup T من ال J and other T
+
+71
+00:06:38,280 --> 00:06:42,520
+قدامي تلات خيارات يا إما T بده تساوي ال identity
+
+72
+00:06:42,520 --> 00:06:50,980
+وبالتالي K بده يساوي واحد وهذا تناقض أو
+
+73
+00:06:50,980 --> 00:06:57,580
+T بده تساوي H وبالتالي
+
+74
+00:06:57,580 --> 00:07:03,120
+K بده يساوي سبعة وانا الآن بده يساوي تسعة واربعين
+
+75
+00:07:03,120 --> 00:07:07,080
+وهذا مافيش فيه مشكلة أو
+
+76
+00:07:08,540 --> 00:07:19,940
+كيس واحد هذا كيس اتنين وهذا كيس ثلاثة ال T بتتساوي
+
+77
+00:07:19,940 --> 00:07:25,600
+ال G نفسها هذا
+
+78
+00:07:25,600 --> 00:07:37,640
+ماعنته ان ال K بتتساوي N ايش يعني؟ يعني سبعة Kمش
+
+79
+00:07:37,640 --> 00:07:42,220
+الان بده تساوي 7k وبالتالي واحد بده يساوي سبعة وده
+
+80
+00:07:42,220 --> 00:07:45,520
+عبارة عن ايش؟ من الحالة الوحيدة اللي مافيش فيها
+
+81
+00:07:45,520 --> 00:07:49,240
+تناقض الان
+
+82
+00:07:49,240 --> 00:07:57,580
+بده تساوي تسعة او اربعين وهذا هو الحل السليماني
+
+83
+00:07:57,580 --> 00:08:03,820
+طيب نايد المعطيات تبعت السؤال بيقول لي يوجد ال
+
+84
+00:08:03,820 --> 00:08:10,400
+cyclic groupالها فقط تلاتة subgroup ال identity و
+
+85
+00:08:10,400 --> 00:08:13,700
+subgroup H ال order اللي لها سبعة و ال J نفسها
+
+86
+00:08:13,700 --> 00:08:17,860
+بهيك بيقول لإنه ال J ال order اللي لها أكبر من
+
+87
+00:08:17,860 --> 00:08:23,560
+السبعة و السبعة بتقسم ال order لل J لإن هو J
+
+88
+00:08:23,560 --> 00:08:28,120
+Cyclic بس الآن بدأت تساوي سبعة K و ال K أكبر من
+
+89
+00:08:28,120 --> 00:08:33,800
+الواحد حاجة ال J Cyclic فأكيد لازم تلاقي subgroup
+
+90
+00:08:33,800 --> 00:08:39,250
+ال order اللي لهاK طيب هذه ال sub group يا بده
+
+91
+00:08:39,250 --> 00:08:44,050
+تساوي ال identity انه مافيش غير تلاتها دول وهذا
+
+92
+00:08:44,050 --> 00:08:50,690
+تناقض هيخللي ال K بساوي واحد او ال H بده تساوي او
+
+93
+00:08:50,690 --> 00:08:54,850
+ال T بده تساوي ال H وانا مافيش مشاكل بيعطيني ال
+
+94
+00:08:54,850 --> 00:08:58,950
+Ant سواء باين او ال H هي نفس ال J وانا بيعطيني
+
+95
+00:08:58,950 --> 00:09:03,170
+تناقض يعني بالحالة الوحيدة اللي زبطت معايا هي مين
+
+96
+00:09:03,170 --> 00:09:08,990
+الحالة التانيةوالان بتطلع جديش؟ تسعة واربعين واضحة
+
+97
+00:09:08,990 --> 00:09:19,870
+هذى؟ واضحة يا شباب؟ طيب ايش
+
+98
+00:09:19,870 --> 00:09:26,930
+يا شمش ده؟ ايش .. وان بتكتب؟ هنا؟ احنا بنشد ..
+
+99
+00:09:44,880 --> 00:09:48,500
+حسب النظريات اللي عندي لكل قاسم فيه subgroup الارض
+
+100
+00:09:48,500 --> 00:09:53,820
+لهذه ال subgroup بيساوي القاسم ال
+
+101
+00:09:53,820 --> 00:09:59,640
+K رقم طب و السبعة؟ ال K قاسم تان غير السبعة
+
+102
+00:10:03,160 --> 00:10:07,260
+طيب خمس عشر let j be an appealing group at rest
+
+103
+00:10:07,260 --> 00:10:13,280
+what can you say if سبعة is replaced by بيه ال
+
+104
+00:10:13,280 --> 00:10:20,120
+order ل j هي سوى بيه تربيه لو بنستبدل السبعة بيه
+
+105
+00:10:20,120 --> 00:10:25,220
+هيكون ال order عبارة عن بيه تربيه سؤال خمس عشر
+
+106
+00:10:30,230 --> 00:10:41,970
+suppose that a cyclic group J أو JAB يعني group و
+
+107
+00:10:41,970 --> 00:10:50,570
+ال H عبارة عن كل ال J في ال J حيث ال order ل J
+
+108
+00:10:50,570 --> 00:10:58,850
+يقسم 12 prove that H is a subgroup of Jمطلوب ان
+
+109
+00:10:58,850 --> 00:11:08,770
+اثبت هل ممكن
+
+110
+00:11:08,770 --> 00:11:27,590
+نغير 12 بأي رقم هل ممكن نغير 12 بأي رقم هل ممكن
+
+111
+00:11:27,590 --> 00:11:33,090
+نغير 12 بأي رقمالمجموعة بتمثل subgroup كل العناصر
+
+112
+00:11:33,090 --> 00:11:40,650
+اللي في j اللي ال order اللي هي بيقسم 12 طيب تبدأ
+
+113
+00:11:40,650 --> 00:11:48,910
+تبتنوعش subgroup موضوع تقليدي first H لا يسوى 5
+
+114
+00:11:48,910 --> 00:11:55,430
+since ال identity في ال H since ال order لل
+
+115
+00:11:55,430 --> 00:11:57,310
+identity بيسوى 1 يقسم 12
+
+116
+00:12:00,090 --> 00:12:10,230
+طيب ف a و b ينتمي لل H يعني ال order ل a و ال
+
+117
+00:12:10,230 --> 00:12:16,870
+order ل b كلاهما بيقسم مين ال 12 ايش بدي اشوف انا
+
+118
+00:12:16,870 --> 00:12:23,770
+هذا معناته ان a و 12 بيساوي ال identity بيساوي b و
+
+119
+00:12:23,770 --> 00:12:29,810
+12بغض النظر لو اقدر اتنين، تلاتة، ستة، اربعة،
+
+120
+00:12:29,810 --> 00:12:33,650
+اتناش، لأ بهمني ان ال a أُس اتناش و ال b أُس اتناش
+
+121
+00:12:33,650 --> 00:12:41,070
+بيعطيني مين؟ ال identity for a P inverse اللي هي
+
+122
+00:12:41,070 --> 00:12:49,990
+one step ال a P inverse أُس اتناش عبارة عن a أُس
+
+123
+00:12:49,990 --> 00:12:59,640
+اتناش P inverse أُس اتناش هذا السببعلى سبب ايش؟
+
+124
+00:12:59,640 --> 00:13:06,020
+ليش اقدرت اعمل هذه الحركة؟ عشان ال B يعني طيب ال A
+
+125
+00:13:06,020 --> 00:13:13,180
+وصلة و اتناش identity ال B وصلة و اتناش هذا
+
+126
+00:13:13,180 --> 00:13:17,440
+هيساوة ال identity في B وصلة و اتناش inverse يعني
+
+127
+00:13:17,440 --> 00:13:24,830
+identity inverse هيساوة identity ال A P inverseالـ
+
+128
+00:13:24,830 --> 00:13:31,150
+order اللي بيقسم الـ 12 a,b,in,out ينتمي لمين؟ للـ
+
+129
+00:13:31,150 --> 00:13:38,490
+H فبالتالي الـ H sub group من مين؟ من الـ G هل
+
+130
+00:13:38,490 --> 00:13:45,070
+الرقم 12 special؟ لو بدلت 12 بأي رقم تاني؟ مش
+
+131
+00:13:45,070 --> 00:13:50,630
+ضروري مضعفة لو حطيت 7 بدل 12، في مشكلة؟ لو حطيت
+
+132
+00:13:50,630 --> 00:13:59,680
+1000؟ مافيش مشكلة، 12is not special يعني ممكن تبدل
+
+133
+00:13:59,680 --> 00:14:05,000
+ال 12 بأي رقم مين الحاجة الضرورية هنا ال abelian
+
+134
+00:14:05,000 --> 00:14:13,000
+مش ال 12 لو مش abelian ماقدرتش انا اعمل الفكرة هذه
+
+135
+00:14:13,000 --> 00:14:19,180
+طيب
+
+136
+00:14:20,740 --> 00:14:25,380
+ليش 12 مش special؟ شيل 12 وحط أي رقم بدك إياها،
+
+137
+00:14:25,380 --> 00:14:28,960
+بيفرق معاك؟ طيب، هيك ب 12 مش special
+
+138
+00:14:50,820 --> 00:14:56,200
+أه اللى خلانى أقدر أشتغل هنا بالأسلوب أو و أطلع
+
+139
+00:14:56,200 --> 00:15:05,020
+النتيجة اللى موجودة قدامك هو أنه لجروب قابيل يعنى
+
+140
+00:15:05,020 --> 00:15:10,720
+17 complete the statement order ال A بتيسار order
+
+141
+00:15:10,720 --> 00:15:16,280
+ال A ترمي if and only if order ال A is is ايش
+
+142
+00:15:20,770 --> 00:15:24,890
+17 complete the following statement order A بيسوي
+
+143
+00:15:24,890 --> 00:15:38,950
+order A تربيع if and only if order A is يبسط
+
+144
+00:15:38,950 --> 00:15:47,750
+ال order لإيه؟ طلع معايا نشوف بعض الحلات و نجمعهم
+
+145
+00:15:47,750 --> 00:15:51,940
+عشان نحط كيس واحدةأردر الـ A بيسوي أردر ال A تربيه
+
+146
+00:15:51,940 --> 00:15:58,780
+مين ممكن تلاقي تحت هذا الإطار ممكن نضمه أولا
+
+147
+00:15:58,780 --> 00:16:04,260
+الـidentity أردر ال E بيسوي أردر ال E تربيه بيسوي
+
+148
+00:16:04,260 --> 00:16:09,620
+واحدة اتنين لو
+
+149
+00:16:09,620 --> 00:16:16,460
+أردر ال A infinite برضه
+
+150
+00:16:16,460 --> 00:16:17,580
+أردر ال E تربيه infinite
+
+151
+00:16:22,670 --> 00:16:28,250
+بس ايش بيظل عندي حالة؟ حالة ال finite في ال finite
+
+152
+00:16:28,250 --> 00:16:34,930
+كام كيس عندي؟ فردي و زوجي لو كان أرضر ال a زوجي هل
+
+153
+00:16:34,930 --> 00:16:41,270
+هذا كلام يكون صحيح؟ لو أرضر ال a بدت سوى 2q فأرضر
+
+154
+00:16:41,270 --> 00:16:48,190
+ال a تقريبا بدت سوى q إيه كده؟ بدي أنفذ زوجيطب
+
+155
+00:16:48,190 --> 00:16:53,670
+نشوف الفردي لو order ال A تسوى 2Q زي 1 برضه order
+
+156
+00:16:53,670 --> 00:17:01,370
+ال A تربية 2Q زي 1 ايك بقى ال identity زبطت طب
+
+157
+00:17:01,370 --> 00:17:06,550
+هتنساش ان ال identity ممكن تدخل وين في حالة ال
+
+158
+00:17:06,550 --> 00:17:12,930
+order الفردي ال identity ال order الهيش واحد و ال
+
+159
+00:17:12,930 --> 00:17:17,160
+infiniteيجب الفردي بظبط و ال infinite بظبط مين
+
+160
+00:17:17,160 --> 00:17:23,760
+اللي بظبط ايش يجب ايش نقول if order a is not even
+
+161
+00:17:23,760 --> 00:17:30,840
+if and سبعة عاشر بدك تكملها if and only if order a
+
+162
+00:17:30,840 --> 00:17:34,700
+is not even
+
+163
+00:17:34,700 --> 00:17:39,780
+ركز معايا مافيش infinite even مافيش infinite even
+
+164
+00:17:39,780 --> 00:17:44,910
+و oddالـ Infinite مش فيه even أو odd الـ Infinite
+
+165
+00:17:44,910 --> 00:17:49,570
+Infinite واضح؟
+
+166
+00:17:49,570 --> 00:17:52,850
+يعني هي لو حالة واحدة كانت قولت if and only if
+
+167
+00:17:52,850 --> 00:17:56,890
+order الـ A infinite مثلا لو نفيت هذه وهذه بس أنا
+
+168
+00:17:56,890 --> 00:18:01,230
+نفيت واحدة و أثبتت تنتين فبدل ما أقول if and only
+
+169
+00:18:01,230 --> 00:18:05,150
+if order ال A is infinite أو order ال A is odd
+
+170
+00:18:05,150 --> 00:18:09,190
+بقول لأ not even بغيّر حالي طب كيف الوضع اللي قلت
+
+171
+00:18:09,190 --> 00:18:15,350
+من ال Q يعني؟order a بيبقى اثنين اثنين اثنين اثنين
+
+172
+00:18:15,350 --> 00:18:18,650
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+173
+00:18:18,650 --> 00:18:20,710
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+174
+00:18:20,710 --> 00:18:20,750
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+175
+00:18:20,750 --> 00:18:22,010
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+176
+00:18:22,010 --> 00:18:22,010
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+177
+00:18:22,010 --> 00:18:24,130
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+178
+00:18:24,130 --> 00:18:30,430
+اثنين اثنين ا
+
+179
+00:18:39,470 --> 00:18:45,210
+بتساوي order of a تربيع هجيت قدامي order of a تلت
+
+180
+00:18:45,210 --> 00:18:53,290
+حالات even, odd, infinite هجيت هذه بتظبط وهذه
+
+181
+00:18:53,290 --> 00:19:00,950
+بتظبط وهذه لأ فأوحان في هذه if and only if order
+
+182
+00:19:00,950 --> 00:19:08,530
+of a is not even طيب
+
+183
+00:19:11,590 --> 00:19:17,390
+مش فاهم مش فاهم ال even و ال odd ده مش يعني even
+
+184
+00:19:17,390 --> 00:19:24,990
+طيب فلو كان order ال A بده سوى اتنين Q يعني A أُس
+
+185
+00:19:24,990 --> 00:19:28,610
+اتنين Q بده سوى ال identity يعني A تربيه أُس Q بده
+
+186
+00:19:28,610 --> 00:19:34,250
+سوى ال identity فorder ال A تربيه على الأكثر Q أقل
+
+187
+00:19:34,250 --> 00:19:38,450
+من order ال A إيه؟ فلو كان order ال A even هذه
+
+188
+00:19:38,450 --> 00:19:47,360
+مابتنفعشهذه غير مفيدة، واضحة؟ حجزت، لو كان order
+
+189
+00:19:47,360 --> 00:19:51,120
+الـA بيتساوي ماله نهاية فأكيد order الـA تربيه
+
+190
+00:19:51,120 --> 00:19:58,680
+ماله نهاية يقبل even، مابتنفعش ال infinite بتنفع،
+
+191
+00:19:58,680 --> 00:20:04,160
+بيضال مين؟ ال odd حجزت order الـA بيتساوي un وun
+
+192
+00:20:04,160 --> 00:20:10,990
+odd ف order الـA بيتساوي order الـAقص K حيث ان
+
+193
+00:20:10,990 --> 00:20:16,770
+اجيز common divisor ل K و M يساوي 1 صح ولا لأ؟ طب
+
+194
+00:20:16,770 --> 00:20:24,070
+حط بدل K 2 هل هذا كلام صحيح؟ خلط يجب ان اقضر ل A
+
+195
+00:20:24,070 --> 00:20:30,890
+تربيع لكي اجيز common divisor ل 2 و 1 يساوي 2 و M
+
+196
+00:20:30,890 --> 00:20:34,590
+يساوي 1 بس بسرعة
+
+197
+00:20:38,830 --> 00:20:44,910
+لو في عندك J Cyclic يوجد
+
+198
+00:20:44,910 --> 00:20:51,370
+A في الـ J ال order لـ A يساوي مانا نهاية اكم عنصر
+
+199
+00:20:51,370 --> 00:20:56,630
+ال order له finite في ال J طالع معايا ال A ال
+
+200
+00:20:56,630 --> 00:21:00,570
+order له infinite ف A و A تربية و A تكيب و A أس
+
+201
+00:21:00,570 --> 00:21:05,250
+خمسة و A أس أي حاجة هيكون ال order له infinite بعد
+
+202
+00:21:05,250 --> 00:21:19,540
+مين ال identitythe only element of finite order is
+
+203
+00:21:19,540 --> 00:21:26,120
+E هذا فقط في الـ cyclic لو انت بتشتغل في group مش
+
+204
+00:21:26,120 --> 00:21:30,700
+cyclic ممكن تلاقي عناصر ال order اللي هم finite
+
+205
+00:21:30,700 --> 00:21:36,580
+حتى لو كانت ال group infinite حتى لو كانت ال group
+
+206
+00:21:36,580 --> 00:21:41,020
+infiniteإذا أسمي كل جريس كمان بقايا سلطانة، فالأمر
+
+207
+00:21:41,020 --> 00:21:44,440
+مافيه سواء حد؟
+
+208
+00:21:57,580 --> 00:22:01,480
+عشان يكون ال order ل A أُس K بيساوي order ل A يعني
+
+209
+00:22:01,480 --> 00:22:05,980
+بيساوي N فال N بيساوي N على ال divisor ل K و N
+
+210
+00:22:05,980 --> 00:22:08,680
+يعني ال order ل A أُس K بيساوي order ل A
+
+211
+00:22:22,780 --> 00:22:27,960
+سؤال تسعة عشر سهل بتشوف ال generators للعناصر في U
+
+212
+00:22:27,960 --> 00:22:34,240
+تلاتين او بتمسك العناصر بتشوف ايش بولته سؤال عشرين
+
+213
+00:22:34,240 --> 00:22:37,500
+suppose that J is a pelian group of order خمسة و
+
+214
+00:22:37,500 --> 00:22:39,840
+تلاتين and every element of J satisfies the
+
+215
+00:22:39,840 --> 00:22:43,500
+equation X وخمسة و تلاتين دي ساوي identity proof
+
+216
+00:22:43,500 --> 00:22:49,340
+that J is cyclic order
+
+217
+00:22:49,340 --> 00:22:59,540
+لل J دي ساوي خمسة و تلاتينJ is Abelian لكل
+
+218
+00:22:59,540 --> 00:23:15,800
+X في J X و 35 يساوي ال identity يثبت ان J صحيح هل
+
+219
+00:23:15,800 --> 00:23:18,500
+35 special تعالى نشوف
+
+220
+00:23:24,150 --> 00:23:27,670
+جي أبيليان وكل عنصر فيها بيحقق العلاقة ان اكسوس
+
+221
+00:23:27,670 --> 00:23:38,010
+خمسة و تلاتين بيساوي ال identity هل ال جي Cyclic
+
+222
+00:23:38,010 --> 00:23:43,550
+عشان اثبت ان الجي Cyclic لازم يلاقي عنصر يعني
+
+223
+00:23:43,550 --> 00:23:52,770
+المطلوب prove that يوجد جي في الجي او ا في الجيو
+
+224
+00:23:52,770 --> 00:24:07,990
+اخضر انتي ابني سنة و خمسة و تلاتين هاطوني
+
+225
+00:24:07,990 --> 00:24:15,910
+حلولكم لم احضر السؤال او اعتبوني ماشوفتش السؤال
+
+226
+00:24:15,910 --> 00:24:18,890
+قبل هيك فكوا معايا
+
+227
+00:24:21,730 --> 00:24:29,470
+I'm here و لا انا ايش
+
+228
+00:24:29,470 --> 00:24:36,390
+نعمل ايش الموضوع اللي عندك يا شباب جيابيليان زائد
+
+229
+00:24:36,390 --> 00:24:46,490
+الأخضر خمس و تلاتين طيب زائد ان كل
+
+230
+00:24:46,490 --> 00:24:52,250
+العناصربحقق ان اكسوس خمسة و تلاتين بدي ساوي ال
+
+231
+00:24:52,250 --> 00:24:57,210
+identity انا بدي اثبت انه يوجد عنصر ال order له
+
+232
+00:24:57,210 --> 00:25:08,070
+خمسة و تلاتين كيف؟
+
+233
+00:25:08,070 --> 00:25:12,570
+فكروا
+
+234
+00:25:15,710 --> 00:25:22,530
+أسس الطريقة لإثبات جمل بهذا الشكل هي تنقض هفترض ان
+
+235
+00:25:22,530 --> 00:25:32,730
+لا يوجد عنصر ال order الو 35 تنساش انه ال .. لو
+
+236
+00:25:32,730 --> 00:25:37,730
+بدي اخد اي عنصر هنا و يكون عندك x و 35 يساوي ال
+
+237
+00:25:37,730 --> 00:25:43,490
+identityو X في الـ J معناته order كل العناصر
+
+238
+00:25:43,490 --> 00:25:48,270
+الموجودين في الـ J قواسم للخمس و تلاتين قلنا مافيش
+
+239
+00:25:48,270 --> 00:25:52,070
+عنصر ال order له خمس و تلاتين فكل عنصر انا باخد
+
+240
+00:25:52,070 --> 00:25:58,810
+غير ال identity ال order له اما خمسة
+
+241
+00:25:58,810 --> 00:26:07,610
+او سبعة هجي التواجد العناصر حسب ال order خمسة بيجي
+
+242
+00:26:07,610 --> 00:26:08,890
+في أي شكل
+
+243
+00:26:11,690 --> 00:26:15,170
+عناصر ال order يلهم خمسة، لو كان عند ال X ال order
+
+244
+00:26:15,170 --> 00:26:22,430
+يلهم خمسة أكمل عنصر زي بلاج ال order يلهم خمسة X X
+
+245
+00:26:22,430 --> 00:26:29,570
+تربية X تكييب X أربعةهدولة كلهم ال order اللي هم
+
+246
+00:26:29,570 --> 00:26:33,850
+خمسة لو انا لو أخدت X في هذه لجوب ال order اللي هو
+
+247
+00:26:33,850 --> 00:26:37,770
+خمسة و أخدت ال generated by X اللي هو ال identity
+
+248
+00:26:37,770 --> 00:26:41,550
+هو X و X تربيه و X تكيبه و X أربعة مع هذا ال
+
+249
+00:26:41,550 --> 00:26:45,270
+identity الأربع عناصر هدولة اللي هم فيها الخمسة ال
+
+250
+00:26:45,270 --> 00:26:49,150
+order اللي هم خمسة يجب تواجد ال order الخمسة هيكون
+
+251
+00:26:49,150 --> 00:26:53,810
+في إيش؟ في أربعات شيل ال identity من الخمسة
+
+252
+00:26:53,810 --> 00:27:04,360
+وتلاتين كده هيظلأربعة وتلاتين، شيل كل الأربعات،
+
+253
+00:27:04,360 --> 00:27:11,660
+يجب مش كل العناصر ال order لهم خمسة، بنفس الطريقة
+
+254
+00:27:11,660 --> 00:27:18,020
+ال order سبعة بيجي في ستاتX تربيه لإن X هو الستة
+
+255
+00:27:18,020 --> 00:27:22,940
+شيل الستات من الاربعة وتلاتين بيضال أربعة يكبر مش
+
+256
+00:27:22,940 --> 00:27:26,620
+كل العناصر ال order اللي لهم سبعة مش كل العناصر ال
+
+257
+00:27:26,620 --> 00:27:31,680
+order اللي لهم خمسة فش ال order خمسة و تلاتين يكبر
+
+258
+00:27:31,680 --> 00:27:34,620
+في عنصر ال order اللي له خمسة و في عنصر ال order
+
+259
+00:27:34,620 --> 00:27:40,920
+اللي له سبعة خدها ده A اخدها ده B ال order ل A و B
+
+260
+00:27:40,920 --> 00:27:45,260
+هيكون كده؟ خمسة و تلاتين و هو هيكون ال generator
+
+261
+00:27:46,570 --> 00:27:52,910
+فجهز حالك السؤال ده في شغل Assume
+
+262
+00:27:52,910 --> 00:28:06,930
+that there is no element in J with order خمسة و
+
+263
+00:28:06,930 --> 00:28:13,430
+تلاتين فش أنصر في الـ J ال order الو خمسة و تلاتين
+
+264
+00:28:13,430 --> 00:28:15,110
+since
+
+265
+00:28:16,700 --> 00:28:24,260
+X و 35 يساوي ال identity لكل X في J معناته order X
+
+266
+00:28:24,260 --> 00:28:32,920
+هيقسم 35 لكل X في J order
+
+267
+00:28:32,920 --> 00:28:42,500
+X يساوي 35 لكل X في J if X لا يساوي ال identity
+
+268
+00:28:45,790 --> 00:28:52,070
+Order of X بدي يساوي خمسة Or order of X بدي يساوي
+
+269
+00:28:52,070 --> 00:28:59,910
+سبعة طبعا اكيد order of X لا يساوي خمسة و تلاتين
+
+270
+00:28:59,910 --> 00:29:04,950
+يكبر جميع العناصر مع عدل identity يعني ال order له
+
+271
+00:29:04,950 --> 00:29:12,110
+خمسة او سبعة اجازة اللي هنعمله كانت تالي We will
+
+272
+00:29:12,110 --> 00:29:13,650
+show that
+
+273
+00:29:19,910 --> 00:29:23,490
+أحنا هننفيها عشان نشرع الخمسة و السابعة لحالنا و
+
+274
+00:29:23,490 --> 00:29:28,930
+نصلّى تناقض لهذه الجملة اللي نفنها We will show
+
+275
+00:29:28,930 --> 00:29:35,690
+that there
+
+276
+00:29:35,690 --> 00:29:46,310
+is elements in D with order
+
+277
+00:29:47,650 --> 00:29:58,350
+خمسة and elements with order سبعة هاتبت انه يوجد
+
+278
+00:29:58,350 --> 00:30:02,550
+عناصر ال order له خمسة و يوجد عناصر ال order له
+
+279
+00:30:02,550 --> 00:30:07,930
+ايش سبعة برضه هشغل هالجتنا في داخلي هانفي انه ..
+
+280
+00:30:07,930 --> 00:30:11,610
+يعني هقول انه مافيش order سبعة يعني كل ال order
+
+281
+00:30:11,610 --> 00:30:14,610
+خمسة to show that
+
+282
+00:30:17,330 --> 00:30:25,890
+we will first assume that
+
+283
+00:30:25,890 --> 00:30:43,830
+there is no elements in J with order 7 assume that
+
+284
+00:30:43,830 --> 00:30:46,050
+all
+
+285
+00:30:48,400 --> 00:31:00,780
+x لا يساوي ال identity in j has order خمسة Note
+
+286
+00:31:00,780 --> 00:31:05,080
+that if
+
+287
+00:31:05,080 --> 00:31:10,500
+order ال x بدى يساوي خمسة then order ال x تربع بدى
+
+288
+00:31:10,500 --> 00:31:13,800
+يساوي order ال x تكعي بدى يساوي order ال x أربعة
+
+289
+00:31:13,800 --> 00:31:22,530
+بدى يساوي خمسةطبعا هذه بدأ اثبات prove it اثباتها
+
+290
+00:31:22,530 --> 00:31:30,370
+سهل ال order لexos k بدي ساوي ال o اللي هو n اللي
+
+291
+00:31:30,370 --> 00:31:34,430
+هي خمسة على order لجيسكم و ال divisor ل الخمسة و
+
+292
+00:31:34,430 --> 00:31:41,170
+الكيه في نهاية تصل لكلام هذا هذا معناته the order
+
+293
+00:31:41,170 --> 00:31:46,350
+خمسة is found in
+
+294
+00:31:47,360 --> 00:32:02,040
+J in six contains four elements هذا
+
+295
+00:32:02,040 --> 00:32:10,580
+معناته J هتساوي ال identity اتحاد X1 X1 تربية X2
+
+296
+00:32:10,580 --> 00:32:29,670
+X1 تكييبX1 اقص 4 اتحاد X2 X2 تربيع X2 تكييب لان X2
+
+297
+00:32:29,670 --> 00:32:43,030
+اقص 4 اتحاد وصولا ل XI او XT XT تربيع XT تكييب
+
+298
+00:32:59,740 --> 00:33:04,000
+X لا يساوي X تربيه X لا يساوي X تكيب
+
+299
+00:33:06,760 --> 00:33:12,100
+X تربيه لا يساوي X تكريب X تربيه لا يساوي X أربعة
+
+300
+00:33:12,100 --> 00:33:17,800
+X تكريب لا يساوي X أربعة عشان ماحدش يقولي هدول
+
+301
+00:33:17,800 --> 00:33:22,000
+ممكن يكونوا مكررين ولا واحد من ربعي هذا بيساوي
+
+302
+00:33:22,000 --> 00:33:26,880
+التاني لا هذا بيساوي هدول ولا هذا بيساوي هدول ولا
+
+303
+00:33:26,880 --> 00:33:33,940
+هذا بيساوي هذا هذا معناته order ال J بيساوي أربعة
+
+304
+00:33:33,940 --> 00:33:44,120
+T زاد واحدواحد زياد اربعة زياد اربعة بعد الواحد
+
+305
+00:33:44,120 --> 00:33:48,860
+بصيح تجمع اربعات يعني الخمسة و تلاتين بديوا يساوي
+
+306
+00:33:48,860 --> 00:33:56,360
+ايش اربعة T زياد الواحد تنين T بدي يساوي سبعتعش
+
+307
+00:33:56,360 --> 00:34:02,580
+وهذا تناقض هذا
+
+308
+00:34:02,580 --> 00:34:07,620
+تناقض so not
+
+309
+00:34:08,250 --> 00:34:19,910
+all elements in j has order واحد أو خمسة ايش يعني؟
+
+310
+00:34:19,910 --> 00:34:24,130
+مش الكل واحد مش الكل خمسة، مافيش خمسة و تلاتين،
+
+311
+00:34:24,130 --> 00:34:33,710
+إيش هيضل؟ إيش بقى؟ at least there is a ينتمي لل j
+
+312
+00:34:33,710 --> 00:34:42,620
+and order ال a بدي يساوي سبعةأعطيها نجمة Similarly
+
+313
+00:34:42,620 --> 00:34:49,820
+بنفس الطريقة there
+
+314
+00:34:49,820 --> 00:34:58,440
+is P إذا فيها نكسة لا اطلع فيها اجيت على الواجب
+
+315
+00:34:58,440 --> 00:35:06,300
+فادي there is P أنتمي نرجع with order ال P بدي
+
+316
+00:35:06,300 --> 00:35:11,830
+ساوي خمسةطبعا نفس الطريقة بفترض انه فيش order خمسة
+
+317
+00:35:11,830 --> 00:35:16,310
+فكله يا سبعات يا واحد ال order تبع السبعات بيجي
+
+318
+00:35:16,310 --> 00:35:22,050
+فياش؟ هشيل ال واحد ال order تبع السبعات بيجي فياش؟
+
+319
+00:35:22,050 --> 00:35:26,190
+في شكل مجموعات كل مجموعة فيها ست عناصر بيكون عندك
+
+320
+00:35:26,190 --> 00:35:29,750
+خمسة و تلاتين بيكون ستة T زاد الواحد ستة T بيكون
+
+321
+00:35:29,750 --> 00:35:36,190
+اربعة و تلاتين انا هى السبعة و ايه الخمسة؟ستة T
+
+322
+00:35:36,190 --> 00:35:38,310
+بدت ساوي اربع تلات تلات تلات تلات تلات تلات تلات
+
+323
+00:35:38,310 --> 00:35:38,770
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+324
+00:35:38,770 --> 00:35:39,390
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+325
+00:35:39,390 --> 00:35:47,630
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+326
+00:35:47,630 --> 00:35:53,070
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+327
+00:35:53,070 --> 00:35:53,070
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+328
+00:35:53,070 --> 00:35:53,070
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+329
+00:35:53,070 --> 00:35:54,910
+تلات تلات تلات تلات
+
+330
+00:36:05,570 --> 00:36:10,470
+لأ واحدة تتلاتة اربعة التيش ده تكون، عداد، العداد
+
+331
+00:36:10,470 --> 00:36:18,750
+ينتمي لان مش لل Z كمان طيب claim order
+
+332
+00:36:18,750 --> 00:36:22,990
+ال A B بدي ساوي خمسة و تلاتين طبعا اتباع ال claim
+
+333
+00:36:22,990 --> 00:36:25,710
+بصير تناقض مع مين؟ مع الاسيوم
+
+334
+00:36:31,200 --> 00:36:35,160
+Since ال order ل ال A بدي تسوى خمسة أو ال A بدي
+
+335
+00:36:35,160 --> 00:36:41,620
+تسوى سبعة ال order ل ال B بدي تسوى خمسة لو قلنا ال
+
+336
+00:36:41,620 --> 00:36:46,160
+A بيقص خمسة و تلاتين عبارة عن A أقص خمسة و تلاتين
+
+337
+00:36:46,160 --> 00:36:52,000
+في B أقص خمسة و تلاتين identity في identity ايش
+
+338
+00:36:52,000 --> 00:36:57,640
+بدي تسوى identity هذا معناته order ل ال A بي
+
+339
+00:37:01,460 --> 00:37:10,920
+أشماله يقسم الخمسة و تلاتين خلصناش case واحد order
+
+340
+00:37:10,920 --> 00:37:17,190
+ال AB بدي ساوي واحديكبى a,b بدي يسوى ال identity a
+
+341
+00:37:17,190 --> 00:37:23,290
+بدي يسوى b inverse يكبى o الخمسة بدي تسوى او
+
+342
+00:37:23,290 --> 00:37:27,450
+السبعة بدي تسوى order ال a اللي هو order ال b
+
+343
+00:37:27,450 --> 00:37:30,430
+inverse اللي هو order ال b بدي يسوى خمسة وهذا
+
+344
+00:37:30,430 --> 00:37:39,330
+تناقض case اتنين ال
+
+345
+00:37:39,330 --> 00:37:47,120
+order لل a,bبدي ساوي خمسة ال
+
+346
+00:37:47,120 --> 00:37:51,200
+order لل a,b بدي ساوي خمسة ده اش معناته هذا معناته
+
+347
+00:37:51,200 --> 00:37:59,180
+a,b أس خمسة بدي ساوي ال identity a,b أس خمسة بدي
+
+348
+00:37:59,180 --> 00:38:06,560
+ساوي ال identity اش يعني يعني a أس خمسة,b أس خمسة
+
+349
+00:38:06,560 --> 00:38:10,640
+بدي ساوي ال identity يعني a أس خمسة بدي ساوي ال
+
+350
+00:38:10,640 --> 00:38:17,320
+identityهذا معناته السبعة بديساوي order ال a أقل
+
+351
+00:38:17,320 --> 00:38:26,680
+أو يساوي الخمسة و هذا تناقض case ثلاثة order ال a
+
+352
+00:38:26,680 --> 00:38:31,780
+,b بديساوي سبعة order
+
+353
+00:38:31,780 --> 00:38:36,300
+ال a,b بديساوي سبعة يعني a,b والسبعة بديساوي ال
+
+354
+00:38:36,300 --> 00:38:36,720
+identity
+
+355
+00:38:42,000 --> 00:38:46,340
+ماذا يعني؟ يعني a والسبعة بيه السبعة بدي يسووا ال
+
+356
+00:38:46,340 --> 00:38:50,980
+identity يعني ال identity في بيه الخمسة في بيه
+
+357
+00:38:50,980 --> 00:38:55,020
+تربيه بدي يسووا ال identity بيه تربيه بدي يسووا ال
+
+358
+00:38:55,020 --> 00:39:00,980
+identity هذا معناته خمسة تسوي order ال بيه فقال لو
+
+359
+00:39:00,980 --> 00:39:08,240
+يسووا اتنين تنقض مين ضال؟ الواحد لأ الخمسة لأ
+
+360
+00:39:08,240 --> 00:39:17,150
+السبعة لأهذا معناته order ال a,b يسوى 35 هدف نقض
+
+361
+00:39:17,150 --> 00:39:23,810
+مين contradiction contradiction
+
+362
+00:39:23,810 --> 00:39:29,850
+مع مين مع الفرض اللي انا فرضه ان ال a,b او فيش
+
+363
+00:39:29,850 --> 00:39:38,230
+عنصر اللي orderedه 35 with the assumption that
+
+364
+00:39:38,230 --> 00:39:44,700
+there is noX ينتمي من ال J و أغضر ال X بالساعة 35
+
+365
+00:39:44,700 --> 00:39:48,040
+الفرض
+
+366
+00:39:48,040 --> 00:39:56,220
+اللي أنا فرضه خاطئ، إيش الصواب؟ عكسه طب إيش عكسه؟
+
+367
+00:39:56,220 --> 00:40:02,860
+أنا قولت فش الأغضر 35؟يوجد X ينتمي للـ J Order X
+
+368
+00:40:02,860 --> 00:40:08,540
+يتساوي خمسة وتلاتين Order X يتساوي order جي جي
+
+369
+00:40:08,540 --> 00:40:20,060
+جنيريتد by الـ X جي الصارت
+
+370
+00:40:20,060 --> 00:40:24,340
+طبعا
+
+371
+00:40:24,340 --> 00:40:27,540
+هل الخمسة وتلاتين special
+
+372
+00:40:32,600 --> 00:40:38,240
+لو جربت التلاتة و تلاتين مش هينفع لأ، من التلاتة و
+
+373
+00:40:38,240 --> 00:40:41,700
+تلاتين عندك التلاتة و ال 11 التلاتة بتكون موجودة
+
+374
+00:40:41,700 --> 00:40:49,460
+في إيش؟ في أزواج طيب،
+
+375
+00:40:49,460 --> 00:40:54,320
+معناته ممكن يكون عندك حالة يكون الأرض إلها تلاتة؟
+
+376
+00:40:54,320 --> 00:41:06,180
+إيه الشعير؟هل 35 special ولا لا؟
+
+377
+00:41:06,180 --> 00:41:09,980
+تلاتة
+
+378
+00:41:09,980 --> 00:41:14,660
+وتلاتين هل
+
+379
+00:41:14,660 --> 00:41:23,300
+ايه special؟
+
+380
+00:41:23,300 --> 00:41:29,040
+اه
+
+381
+00:41:29,040 --> 00:41:41,320
+شبابو نعمل تلاتة آلاف تسيتيش حاجة طيب و
+
+382
+00:41:41,320 --> 00:41:47,520
+دم هناخد نظرية تجاوب على السؤال هدا هنشتغل على ال
+
+383
+00:41:47,520 --> 00:41:51,760
+ground theorem هنشتغل على ال factor جوهر بالنسبالي
+
+384
+00:41:51,760 --> 00:41:56,100
+التلاتة و تلاتين انا
+
+385
+00:41:56,100 --> 00:42:01,560
+بقدر اجزم دائماإنه يوجد عنصر الأرض غيله تلاتة إن
+
+386
+00:42:01,560 --> 00:42:04,920
+اشتغلت على إحدى عشات، الإحدى عشات بتتواجد فيها في
+
+387
+00:42:04,920 --> 00:42:09,020
+شكل عشرات فدائما بيظل عنصر الأرض غيله تلاتة طب هل
+
+388
+00:42:09,020 --> 00:42:12,200
+كل العناصر لو اشتغلت على التلاتات، التلاتات
+
+389
+00:42:12,200 --> 00:42:19,800
+يتواجدوا في أزواج فبيظل ال identity لكن هل ده يعني
+
+390
+00:42:19,800 --> 00:42:25,100
+ممكن انا لاي .. بالطريقة اللي اشتغلت فيهاأصل لقنع
+
+391
+00:42:25,100 --> 00:42:31,980
+أنه بقدر يكون كل group الأردن والعصر فيه تلتات هل
+
+392
+00:42:31,980 --> 00:42:35,280
+ممكن أن احصل على group فيها تلت و تلتين عنصر و
+
+393
+00:42:35,280 --> 00:42:38,920
+الأردن غيره تلتات؟
+
+394
+00:42:38,920 --> 00:42:43,960
+ايش رايكو؟ انا
+
+395
+00:42:43,960 --> 00:42:47,260
+مش حاجة تجربك على السؤال هذا لما اتأكد منه بس انا
+
+396
+00:42:47,260 --> 00:42:54,310
+على اعتقادي ان الخمسة و تلتين قد تكون specialيعني
+
+397
+00:42:54,310 --> 00:43:02,050
+ممكن يكون عند جروب ال order إلها P في Q ومش Cyclic
+
+398
+00:43:02,050 --> 00:43:14,890
+تلاتة
+
+399
+00:43:14,890 --> 00:43:20,980
+تلاتين عند تلاتة بيزيدشطب انا يا جد هبطمن ان ال 4
+
+400
+00:43:20,980 --> 00:43:23,720
+جديد و 3 جديد معايا يردوا يطلحوا مش 7 انا انا
+
+401
+00:43:23,720 --> 00:43:29,000
+معايا بحنا يا جد قولنا لو كل 1 و 5 ال 1 و 5
+
+402
+00:43:29,000 --> 00:43:33,460
+هيكونوا على الاكتر جداش تنين و تلاتين زي 1 تلات و
+
+403
+00:43:33,460 --> 00:43:40,260
+تلاتين هيضال عنصرين هدول العنصرين يا 7 يا 35 انا
+
+404
+00:43:40,260 --> 00:43:45,520
+نافل 35 فإيش بيضال عندي سبعة فهي كده انا اجزمت انه
+
+405
+00:43:45,520 --> 00:43:48,950
+في عنصر قدرله سبعةعشان ايه كده ان انا فيت ال 35 في
+
+406
+00:43:48,950 --> 00:43:53,570
+الأول عشان نشر على السبعة لحالي عشان ماقلتش كل
+
+407
+00:43:53,570 --> 00:43:58,030
+شوية جولة أبقى لو ال 35 خلصت لو مش 35 ف7 لأ لما
+
+408
+00:43:58,030 --> 00:44:03,910
+فيت ال 35 ضايحت حالي لما جيت جولة لكل سبعة واحد ال
+
+409
+00:44:03,910 --> 00:44:07,890
+maximum تبقى مجدهاش 31 بيبقى الأربعة أكيد منهم
+
+410
+00:44:07,890 --> 00:44:12,570
+الخمسة فدائما في سبعة دائما في خمسة هات واحد سبعة
+
+411
+00:44:12,570 --> 00:44:16,650
+و واحد خمسة بيطلع ال .. طبعا فادات نهانة كتير مين
+
+412
+00:44:17,540 --> 00:44:21,340
+موضوع ال abelian لو مش abelian بقدرش أشغل الشغل
+
+413
+00:44:21,340 --> 00:44:25,200
+اللي موجود هنا في ال cases اللي موجودين في الحالة
+
+414
+00:44:25,200 --> 00:44:30,160
+اللي موجودة ضمن الكلام واضح؟
+
+415
+00:44:30,160 --> 00:44:36,080
+أي سؤال؟ صحيح
+
+416
+00:44:36,080 --> 00:44:41,580
+قفتلك إياها؟ طب عشان حكينا دلوقتي لأن وكسوس خمسة
+
+417
+00:44:41,580 --> 00:44:46,710
+موجهة identityو X6 برجع ال X و X1 مش الأقدر ال X
+
+418
+00:44:46,710 --> 00:44:55,990
+كمسة ف X5 يبقوا عليا أي سؤال يا شباب؟ أي سؤال؟
+
+419
+00:44:55,990 --> 00:44:58,750
+واضح؟ يا عزيزي يا عزيزي يا شباب من كام اليوم
+
+420
+00:44:58,750 --> 00:44:59,990
+اتنين؟
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8fe68afd3ce0fb124a1d45838d28849db409521a
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_raw.srt
@@ -0,0 +1,1980 @@
+1
+00:00:21,400 --> 00:00:25,980
+الان بنرجع لشبتر ال permutation groups اللى خدتهم
+
+2
+00:00:25,980 --> 00:00:31,800
+مع الأستاذ محمود السرساوي ونقش لكوا أول عشرة مسائل
+
+3
+00:00:31,800 --> 00:00:37,780
+بنحاول نناقش بقية المسائل ان شاء الله وتبرك وتعالى
+
+4
+00:00:38,220 --> 00:00:42,540
+اللي انا بنيجي لسؤال 11، السؤال 11 بيقولي خدلي a
+
+5
+00:00:42,540 --> 00:00:47,060
+positive integer و
+
+6
+00:00:47,060 --> 00:00:53,580
+if ال a is odd و في عندى cycle طولها n طبعا
+
+7
+00:00:56,780 --> 00:01:01,840
+السؤال بيقول مرة تانية السؤال 11 بيقول ال n
+
+8
+00:01:01,840 --> 00:01:09,380
+positive integer و ال a is odd والا ال alpha is
+
+9
+00:01:09,380 --> 00:01:17,260
+odd و طولها n cycle ف ال n cycle هد بتبقى odd والا
+
+10
+00:01:17,260 --> 00:01:21,820
+even قالي بالك معاك الآن
+
+11
+00:01:22,280 --> 00:01:30,160
+أنا عندي ال n مااخد ليه اللي هو positive integer
+
+12
+00:01:30,160 --> 00:01:40,410
+لو كان ال n is oddو أنا عندي ال cycle ال cycle هذه
+
+13
+00:01:40,410 --> 00:01:49,190
+طولها n يعني بمعنى a1 a2 و لغاية an بهذا الشكل هل
+
+14
+00:01:49,190 --> 00:01:55,070
+ال permutation هذه بتبقى even والله قد علما ان ان
+
+15
+00:01:55,070 --> 00:02:01,620
+هذه عبارة عن aعن odd هذا هو السؤال طب لو كانت in
+
+16
+00:02:01,620 --> 00:02:06,580
+even برضه إيش اللي بد يكون يبقى ال on سواء كانت
+
+17
+00:02:06,580 --> 00:02:12,580
+odd و الله even بدنا نعرف هذه إيش بدتكون إذا بدي
+
+18
+00:02:12,580 --> 00:02:18,380
+أخد الحالة الأولى لو كانت ال on ال in is is odd
+
+19
+00:02:18,380 --> 00:02:24,200
+يبقى هدول عددهم odd أكم Transposition بقدر أسوي
+
+20
+00:02:24,200 --> 00:02:30,460
+منهملما يكون عددهم in a chemical composition او
+
+21
+00:02:30,460 --> 00:02:36,900
+two cycles بقدر اعمل منهم قداش عددهم يعني
+
+22
+00:02:36,900 --> 00:02:41,540
+اكتر من عددهم مقدار واحد والله اقل من عددهم مقدار
+
+23
+00:02:41,540 --> 00:02:46,120
+واحد اقل من عددهم مقدار واحد طب لو كان in فردي
+
+24
+00:02:46,120 --> 00:02:52,720
+يبقى الاقل منه بواحد ايش بيكون زوجي يبقى هنا if ال
+
+25
+00:02:52,720 --> 00:03:01,250
+in is odd او evenيبقى هذه بتبقى is even أو odd
+
+26
+00:03:01,250 --> 00:03:02,870
+permutation
+
+27
+00:03:05,030 --> 00:03:10,890
+يعني يعني عكس العدد اللي عندنا هذا لو كان العدد زي
+
+28
+00:03:10,890 --> 00:03:14,310
+مثال و ذلك لو قلت انا اشير انزل سايكل فيها واحد
+
+29
+00:03:14,310 --> 00:03:19,390
+اتنين تلاتة هيبقى هذه الطول فردي مظبوط اكمل
+
+30
+00:03:19,390 --> 00:03:23,170
+ترانسبوزش ان بقدر اعمل واحد تلاتة واحد اتنين يبقى
+
+31
+00:03:23,170 --> 00:03:28,620
+اتنين فقط يبقى هذه بيصير even permutationيبقى إذا
+
+32
+00:03:28,620 --> 00:03:33,520
+ال cycle عدد العناصر فيها odd أو الطول تبعها عبارة
+
+33
+00:03:33,520 --> 00:03:37,520
+عن odd يبقى عدد ال transposition is even أو ال
+
+34
+00:03:37,520 --> 00:03:42,160
+permutation هذه بقول عنها even وإن كان العدد هذا
+
+35
+00:03:42,160 --> 00:03:45,840
+even يبقى ال permutation بقول عنهاأو odd و هكذا
+
+36
+00:03:45,840 --> 00:03:51,100
+يبقى هذا المقصود بسؤال 11 اذا كان السؤال 12 يقول
+
+37
+00:03:51,100 --> 00:03:56,040
+لو كان ال alpha even شوف لل alpha inverse او اثبت
+
+38
+00:03:56,040 --> 00:03:59,820
+ان ال alpha inverse even و لو كانت ال alpha odd
+
+39
+00:03:59,820 --> 00:04:07,260
+اثبت ان ال alpha inverse is even يبقى هنا سؤال 12
+
+40
+00:04:07,260 --> 00:04:15,830
+يقول if ال alpha is even او oddthen ال alpha
+
+41
+00:04:15,830 --> 00:04:22,930
+inverse is even او اقل هذا اللي عايزين ان تبدأ
+
+42
+00:04:22,930 --> 00:04:29,450
+يبقى هنا solution حليت
+
+43
+00:04:29,450 --> 00:04:32,690
+السؤال هذا انت يا أبو الأعداد هذي طب هذي أعداد
+
+44
+00:04:32,690 --> 00:04:38,190
+even و odd يعني حليت السؤال هذا مش مستاهل كلام
+
+45
+00:04:38,190 --> 00:04:43,660
+ذاري يعنيانت عندك الان لو افترضت انه alpha even
+
+46
+00:04:43,660 --> 00:04:51,600
+يبقى if ال alpha is even معناته ان ال alpha هذه
+
+47
+00:04:51,600 --> 00:04:56,980
+بقدر اكتبها alpha one alpha اتنين لغاية alpha
+
+48
+00:04:56,980 --> 00:05:04,180
+اتنين and هدول مالهم two cycles او transpositions
+
+49
+00:05:04,180 --> 00:05:08,720
+مظبوطيبقى هذه ال alpha واحد وال alpha اتنين و
+
+50
+00:05:08,720 --> 00:05:12,240
+لغاية ال alpha اتنين ان كل واحدة فيهم الطول تبقى
+
+51
+00:05:12,240 --> 00:05:17,620
+اتنينيبقى كتبت على شكل في ال cycles أوى
+
+52
+00:05:17,620 --> 00:05:22,240
+transpositions طب ليش كتبت اتنين in لأنه قال لي
+
+53
+00:05:22,240 --> 00:05:28,080
+alpha is even يعني عدد هدول كلهم اتنين in اللي انا
+
+54
+00:05:28,080 --> 00:05:32,480
+بده اجيب المعكوس تبعها يبقى باجي بقوله ال alpha
+
+55
+00:05:32,480 --> 00:05:37,780
+inverse بدها تساوي alpha واحد alpha اتنين alpha
+
+56
+00:05:37,780 --> 00:05:40,640
+اتنين in و كله inverse
+
+57
+00:05:45,080 --> 00:05:50,420
+الأن ال inverse لهذه بعيد كتابتهم من الخلف إلى
+
+58
+00:05:50,420 --> 00:05:56,580
+الأمام على الشكل التالي Alpha 2 N inverse اللي
+
+59
+00:05:56,580 --> 00:06:01,400
+جابله Alpha 2 N ناقص واحد inverse بضل ماشي لغاية
+
+60
+00:06:01,400 --> 00:06:07,770
+Alpha 2 inverse Alpha 1 inverseالسؤال هو اخدته في
+
+61
+00:06:07,770 --> 00:06:12,850
+الجزء النظري انه ال transposition المعكوس تبع هو
+
+62
+00:06:12,850 --> 00:06:18,250
+نفسه ولا بيختلف نفسه اذا بقدر اشيل كل واحد و احط
+
+63
+00:06:18,250 --> 00:06:23,670
+main و احط اللي هو نفسه اذا هذا الكلام بده يساوي
+
+64
+00:06:23,670 --> 00:06:30,550
+Alpha 2N Alpha 2N minus ال one لغاية Alpha 2 Alpha
+
+65
+00:06:30,550 --> 00:06:38,790
+واحد قداش عددهم هدول؟عددهم اتنين ان يعني even يبقى
+
+66
+00:06:38,790 --> 00:06:45,310
+هذا even تمام اذا لو كانت ال alpha even ال alpha
+
+67
+00:06:45,310 --> 00:06:50,510
+inverse even لو كانت ال alpha odd يبقى ال alpha
+
+68
+00:06:50,510 --> 00:06:57,190
+inverse كذلك odd similarly بنفس الطريقة similarly
+
+69
+00:06:57,190 --> 00:07:07,710
+if ال alpha is oddthen alpha inverse is odd
+
+70
+00:07:07,710 --> 00:07:14,490
+وانتهينا من هذه الشغلة هذه صعبة يعني برضه صعبة
+
+71
+00:07:14,490 --> 00:07:19,670
+تجيب ال inverse تبعها وترده لأصله طيب هذا سؤال
+
+72
+00:07:19,670 --> 00:07:26,310
+اتناش نيجي لسؤال سبعتاش ماتيني alpha و beta سؤال
+
+73
+00:07:26,310 --> 00:07:33,600
+سبعتاشمعطيلي Alpha و Beta Alpha تساوي اللي هي ال
+
+74
+00:07:33,600 --> 00:07:38,660
+permutation من واحد لغاية ستة اتنين تلاتة اربعة
+
+75
+00:07:38,660 --> 00:07:43,720
+خمسة ستة والصفر تانية اتنين واحد تلاتة خمسة اتنين
+
+76
+00:07:43,720 --> 00:07:53,110
+واحد تلاتة خمسة اربعة و هنا ستة و Beta تساويبارضه
+
+77
+00:07:53,110 --> 00:07:58,670
+من واحد لستة اتنين تلاتة اربعة خمسة ستة والصفر
+
+78
+00:07:58,670 --> 00:08:03,210
+التاني ستة واحد اتنين اربعة ستة واحد اتنين اربعة
+
+79
+00:08:03,210 --> 00:08:08,670
+تلاتة خمسة بالشكل اللي عندنا هنا طلب مني تلات
+
+80
+00:08:08,670 --> 00:08:13,170
+شغلات alpha inverse و beta alpha و alpha beta طلب
+
+81
+00:08:13,170 --> 00:08:21,510
+find alpha inverse و alpha beta و beta alpha
+
+82
+00:08:30,000 --> 00:08:34,020
+الخيار يا بنجيب ال alpha مباشرة من هذا الوضع يا
+
+83
+00:08:34,020 --> 00:08:38,400
+بنحولها لل cycles و بعدين بنجيب ال inverse على زي
+
+84
+00:08:38,400 --> 00:08:42,000
+ما بدك ع الشكتين ماشي طيب احنا الان لو بدنا نجيب
+
+85
+00:08:42,000 --> 00:08:48,400
+معكوس هذين مباشرة كيف بنجيب معكوس هذين؟ حد بيعرف؟
+
+86
+00:08:48,400 --> 00:08:50,320
+نفس نفسه
+
+87
+00:08:54,870 --> 00:08:59,970
+كيف بنجيب معكس الفيريماتيش اللى بتبقى مكتوبة صفين؟
+
+88
+00:08:59,970 --> 00:09:03,190
+يعني
+
+89
+00:09:03,190 --> 00:09:06,870
+إيش قالكوا لأستاذ محمود إيش بنعمل مشان يجيب المعكس
+
+90
+00:09:06,870 --> 00:09:13,650
+تبعها؟ إيش بنعمل؟ cycle كيش يا راجل؟ أنا ماعطيك
+
+91
+00:09:13,650 --> 00:09:16,750
+فيريماتيش اللي لأ .. ماحولتهاش لcycles، بدأتش
+
+92
+00:09:16,750 --> 00:09:21,290
+يبهيكد مباشرة بدون cycles كل واحد لواحد يعني واحد
+
+93
+00:09:21,290 --> 00:09:28,900
+لواحديعني ايش نسوي بالظبط فاهمني على اي حال كلمتين
+
+94
+00:09:28,900 --> 00:09:33,020
+اصغار مفيش غيرهم ببدل الصف الأول مكان التاني
+
+95
+00:09:33,020 --> 00:09:36,900
+والتاني مكان الأول وبعيد ترتيب ال permutation بس
+
+96
+00:09:36,900 --> 00:09:43,140
+جلها الكوالا ماجلهاش الكهاجر ماحسبش الكوالا معكوس
+
+97
+00:09:43,140 --> 00:09:48,340
+ل permutation كيف؟ بتاعة ال cycles
+
+98
+00:09:52,010 --> 00:09:55,090
+استفيد كمان هذه المعلومة مدى ما قالكوا الطريقة هذه
+
+99
+00:09:55,090 --> 00:09:59,730
+خدها الطريقة هذه يبقى بدى اخد ال alpha inverse
+
+100
+00:09:59,730 --> 00:10:04,810
+يبقى يساوي الصفر تاني اثنين واحد تلاتة خمسة اربعة
+
+101
+00:10:04,810 --> 00:10:09,550
+ستة واحد اتنين تلاتة اربعة خمسة ستة يبقى هذا
+
+102
+00:10:09,550 --> 00:10:15,490
+المعكوس بس بدى اعيد الترتيب بحيث فعلا الصف الأول
+
+103
+00:10:15,490 --> 00:10:22,550
+يكون هو الأرقام اللي اهالمرتبة ترتيب حسب وضعها
+
+104
+00:10:22,550 --> 00:10:27,690
+يفجأي واحد اتنين تلاتة اربعة خمسة ستة وهيجفلنا
+
+105
+00:10:27,690 --> 00:10:32,510
+الواحد ايش صورته؟ اتنين يفجأي اتنين اتنين ايش
+
+106
+00:10:32,510 --> 00:10:39,050
+صورتها؟ واحد الان التلاتة صورتها تلاتةالخمسة
+
+107
+00:10:39,050 --> 00:10:44,050
+صورتها اش لأ قبلها الأربعة صورتها اش صورتها خمسة
+
+108
+00:10:44,050 --> 00:10:49,530
+والخمسة صورتها اربعة والستة صورتها ستة اذا هذا
+
+109
+00:10:49,530 --> 00:10:54,150
+المعكوس تبع ال ال permutation طب ده تاكد حل الصح و
+
+110
+00:10:54,150 --> 00:10:58,150
+الله غلط ما عليك اللي تمسك هذه و تضربها في هذه
+
+111
+00:10:58,150 --> 00:11:05,620
+لازم يطلع مينidentity permutation 123456 123456
+
+112
+00:11:05,620 --> 00:11:11,820
+تمام؟ يبقى ده تشكلك اعمليه وشوف هذه صح ولا غلط بدك
+
+113
+00:11:11,820 --> 00:11:15,220
+عن طريق ال cycles ماعناش مشكلة زي ما علمك عن طريق
+
+114
+00:11:15,220 --> 00:11:23,300
+ال cycles اللي علموهلك كلام صحيح مئة بالمئة على
+
+115
+00:11:23,300 --> 00:11:28,420
+أي حال هذا المطلوب اللي مطلوب التاني قاللي بده
+
+116
+00:11:28,420 --> 00:11:34,050
+الفا بيتاالان بدنا نجيبله alpha beta ماعليك إلا
+
+117
+00:11:34,050 --> 00:11:39,350
+تعمل ال permutations مباشرة أوي تحولهم إلى ال
+
+118
+00:11:39,350 --> 00:11:43,650
+cycle و تجيب إيه عشان ال composition تبعهم حسبلكوا
+
+119
+00:11:43,650 --> 00:11:47,250
+ال composition مباشرة زي هيك و لا زي .. يعني
+
+120
+00:11:47,250 --> 00:11:52,950
+حسبلكوا هذه طيب ماشي يا سيديهي هذه الأولى هي ال
+
+121
+00:11:52,950 --> 00:11:58,350
+alpha واحد اتنين تلاتة اربعة خمسة ستة اتنين واحد
+
+122
+00:11:58,350 --> 00:12:05,290
+تلاتة خمسة اربعة ستة والتاني واحد اتنين تلاتة
+
+123
+00:12:05,290 --> 00:12:12,630
+اربعة خمسة ستة الصف التاني ستة واحد اتنين اربعة
+
+124
+00:12:12,630 --> 00:12:20,820
+تلاتة خمسة ويساوي بذكر تذكير يبقىبعدين ابدأ هاي
+
+125
+00:12:20,820 --> 00:12:26,840
+واحد اتنين تلاتة اربعة خمسة ستة وهيجفلنا الان ببدأ
+
+126
+00:12:26,840 --> 00:12:32,580
+بالواحد ببدأ من اليمين للشمال الواحد صورته اه ستة
+
+127
+00:12:32,580 --> 00:12:37,740
+باجي طالع هنا على الستة صورتها صورتها اه يبقى
+
+128
+00:12:37,740 --> 00:12:42,740
+الواحد صورته ستة بعدين بدي اجي للاتنين اتنين
+
+129
+00:12:42,740 --> 00:12:47,860
+صورتها واحد والواحد صورتها اهأتنين يبقى اتنين ده
+
+130
+00:12:47,860 --> 00:12:52,220
+يجي اللي بعده التلاتة صورته اتنين و اتنين صورته
+
+131
+00:12:52,220 --> 00:12:56,560
+واحد بالشكل اللي عندنا اللي بعده وصلنا للاربعة
+
+132
+00:12:56,560 --> 00:13:01,580
+الاربعة صورتها اربعة و الاربعة صورتها خمسة الخمسة
+
+133
+00:13:01,580 --> 00:13:06,460
+صورتها تلاتة و التلاتة صورتها تلاتة الستة صورتها
+
+134
+00:13:06,460 --> 00:13:11,910
+خمسة و الخمسة صورتها اربعة زي ما انت شايفيبقى هذا
+
+135
+00:13:11,910 --> 00:13:14,230
+ال composition انت تلاحظ انه لما تجيب ال
+
+136
+00:13:14,230 --> 00:13:19,770
+composition ولا رقم يتكرر مرتين الرقم لا يظهر الا
+
+137
+00:13:19,770 --> 00:13:22,530
+المرة الواحدة لأن ال permutation هي عبارة عن
+
+138
+00:13:22,530 --> 00:13:26,670
+function وهذه ال function one to one and unto
+
+139
+00:13:26,670 --> 00:13:31,350
+بتغطي لجميع العناصر ومافيش عنصر يشتركوا في نفس
+
+140
+00:13:31,350 --> 00:13:36,330
+الصورة على الإطلاقيبقى هذا بالنسبة لل alpha beta
+
+141
+00:13:36,330 --> 00:13:40,530
+من ال beta alpha زيها ماعنديش مشكلة فيها طيب هذا
+
+142
+00:13:40,530 --> 00:13:46,530
+كان سؤال سبعتاش بدنا نروح لتسعتاش قل اتش subgroup
+
+143
+00:13:46,530 --> 00:13:57,390
+من ال sn سؤال تسعتاش قل اتش subgroup من ال sn هذا
+
+144
+00:13:57,390 --> 00:14:11,740
+بده يعطيلك اللي هو anyElement of H is even or half
+
+145
+00:14:11,740 --> 00:14:16,920
+elements of
+
+146
+00:14:16,920 --> 00:14:21,740
+S and R are even
+
+147
+00:14:31,780 --> 00:14:39,360
+قبل ما نبدأ الشغل الـ Sn فيها permutations إيش
+
+148
+00:14:39,360 --> 00:14:45,360
+even وإيش odd؟ روحنا أثبتنا له من خلال جزء النظري
+
+149
+00:14:45,360 --> 00:14:49,600
+أن الـ set of all even permutations ودّيناها الرمز
+
+150
+00:14:49,600 --> 00:14:55,940
+An is a subgroup من مين؟ من ال Snوفي المقابل قلنا
+
+151
+00:14:55,940 --> 00:14:59,080
+له the set of all odd permutation is not a
+
+152
+00:14:59,080 --> 00:15:03,560
+subgroup ليش؟ مافيش فيها ال identity ال identity
+
+153
+00:15:03,560 --> 00:15:08,780
+even permutation تمام اتنين لو ضربتوا odd
+
+154
+00:15:08,780 --> 00:15:12,740
+permutation يعطيني even يعني ال operation عليها is
+
+155
+00:15:12,740 --> 00:15:18,260
+not a binary operation او is not closed under the
+
+156
+00:15:18,260 --> 00:15:21,580
+composition of functions او of permutations
+
+157
+00:15:21,930 --> 00:15:25,570
+وبالتالي مجموعة الـ odd permutation لا يمكن تكون
+
+158
+00:15:25,570 --> 00:15:28,030
+في يوم من الأيام اللي هي ال subgroup هذا السؤال
+
+159
+00:15:28,030 --> 00:15:34,710
+الموجود عندك في التمرينالان بيقولش انها خدنا h
+
+160
+00:15:34,710 --> 00:15:40,310
+subgroup من sn يبدأك تروح تثبتلي انه كل element من
+
+161
+00:15:40,310 --> 00:15:44,190
+h بيكون even permutation وهو واضح على الطبيعي لإن
+
+162
+00:15:44,190 --> 00:15:47,330
+ال odd permutations عمرهم مش بيعملولي ال subgroup
+
+163
+00:15:47,330 --> 00:15:57,330
+بدكش بلاش اثبتلي ان ال elements of h نص عناصر sn
+
+164
+00:15:57,330 --> 00:16:03,740
+بدهم يكونوا evenيعني لو كانت ال sn فيها عشرين عنصر
+
+165
+00:16:03,740 --> 00:16:08,680
+فعشرة even وعشرة odd هاي اللي بقوله يثبته بقوله
+
+166
+00:16:08,680 --> 00:16:13,140
+بسيطة جدا يبقى بقوليش اثبت لإثنين بقولي بكفيني منك
+
+167
+00:16:13,140 --> 00:16:17,960
+واحد اللي تقدر تثبته فيهم لإنه or or تعني هذا او
+
+168
+00:16:17,960 --> 00:16:22,470
+هذاطيب ماشي تمام انا بدي احاول اتنطلع ان نص
+
+169
+00:16:22,470 --> 00:16:28,210
+العناصر تبع ال SN بيكونوا even وبالتالي عدد ال odd
+
+170
+00:16:28,210 --> 00:16:32,250
+permutation جد عدد ال even permutation واعتقد ان
+
+171
+00:16:32,250 --> 00:16:35,490
+الأستاذ محمود جالكوا في الجزء النظري ان ال order
+
+172
+00:16:35,490 --> 00:16:40,870
+لل alternating group AN هو عبارة عن N factorial
+
+173
+00:16:40,870 --> 00:16:45,890
+على اتنين مظبوط طيب مدام جالكوا احنا بدأنا بتهدى
+
+174
+00:16:45,890 --> 00:16:52,720
+عمليا ال Aمش هنتبت عمليا بضروح افترض اني عندي odd
+
+175
+00:16:52,720 --> 00:17:03,260
+permutation beta يبقى assume that ان ال beta is an
+
+176
+00:17:03,260 --> 00:17:10,040
+odd permutation كويس
+
+177
+00:17:12,170 --> 00:17:18,110
+طيب انا عندي odd وعندي even بدي اعرف function من
+
+178
+00:17:18,110 --> 00:17:23,090
+ال even permutations لل odd permutations واذا طلعت
+
+179
+00:17:23,090 --> 00:17:26,870
+هذه ال function one to one and unto يبقى عدد ال
+
+180
+00:17:26,870 --> 00:17:32,270
+odd بصير جد عدد من ال even يبقى عدد ال even بيكون
+
+181
+00:17:32,270 --> 00:17:37,770
+نص عدد اللي هو ال S انه بيكون خلصنا مظبوط يبقى
+
+182
+00:17:37,770 --> 00:17:39,630
+بداجي اقوله define
+
+183
+00:17:44,730 --> 00:17:50,370
+من الـ Alternating group of degree n إلى الـ set
+
+184
+00:17:50,370 --> 00:17:58,970
+of all odd permutations للـ S ناقص الـ An هذه ال
+
+185
+00:17:58,970 --> 00:18:03,730
+group هذه ال set كلها
+
+186
+00:18:03,730 --> 00:18:11,520
+طيب مين هي هذا يا شباب؟الـ Sn لما شيل منها الـ
+
+187
+00:18:11,520 --> 00:18:16,320
+even مين بيظل الـ odd يبقى هدول الـ set of all odd
+
+188
+00:18:16,320 --> 00:18:21,260
+permutations و هدى ال set of all even permutations
+
+189
+00:18:21,260 --> 00:18:33,920
+باي فاي of alpha بده يسوى alpha beta مثلا بتتأكد
+
+190
+00:18:33,920 --> 00:18:38,450
+تعريفي صح ولا غلطأنا معرف Function Phi من ال set
+
+191
+00:18:38,450 --> 00:18:41,490
+of all even permutation لل set of all odd
+
+192
+00:18:41,490 --> 00:18:46,090
+permutation باي Phi of Alpha يبقى Alpha ياش even
+
+193
+00:18:46,090 --> 00:18:52,390
+موجودة في ال a in بدت روح لمين لل odd الآن هذه
+
+194
+00:18:52,390 --> 00:18:57,850
+even وهذه ايش فرضها انا odd طب odd في even ايش
+
+195
+00:18:57,850 --> 00:19:05,090
+بيعطيني odd في evenأد يبقى اد يبقى مية المية هذه
+
+196
+00:19:05,090 --> 00:19:09,170
+موجودة هنا يبقى تعريف يسليم مائة بالمائة هذه ال
+
+197
+00:19:09,170 --> 00:19:11,790
+function لو جلسنا نثبت انها one to one and انتوا
+
+198
+00:19:11,790 --> 00:19:16,030
+بيقول خلصنا بصير عدد ال odd permutation جد عدد ال
+
+199
+00:19:16,030 --> 00:19:21,110
+even permutation يبقى مص عناصر s ان بصيروا even
+
+200
+00:19:21,110 --> 00:19:24,210
+permutation بصيروا even permutation او odd
+
+201
+00:19:24,210 --> 00:19:29,520
+permutationزي ما بدك وهذا يتفق مع عدد ال a n يسوى
+
+202
+00:19:29,520 --> 00:19:33,440
+n factorial على اتنين اللي اقالكمين الأستاذ محمود
+
+203
+00:19:33,440 --> 00:19:39,480
+يبقى الآن انا بتدعي ان فاي is one to one مشان هيك
+
+204
+00:19:39,480 --> 00:19:47,180
+بدأت أخد صورتين متساويتين assume that ان في of
+
+205
+00:19:47,180 --> 00:19:53,130
+alpha one يسوى في of alpha twoإذا قلت أثبت أن ألف
+
+206
+00:19:53,130 --> 00:19:58,430
+وان يتساوي ألف اتو بتم المطلوب يبقى بناء عليه هذا
+
+207
+00:19:58,430 --> 00:20:05,910
+معناته أن ألف وان بيتا يساوي ألف اتو بيتا بال
+
+208
+00:20:05,910 --> 00:20:10,170
+right cancellation law يبقى هذا ما يريد أن يعطيك
+
+209
+00:20:10,170 --> 00:20:17,270
+أن ألف وان يتساوي ألف اتو لذلك فاي هو واحد اتو
+
+210
+00:20:17,270 --> 00:20:26,390
+واحدبدى اثبت الان الـ fi is unto يفجر بروح اخد let
+
+211
+00:20:26,390 --> 00:20:33,030
+هه بديش اقول بي تبدى سميها مثلا جامع موجودة في
+
+212
+00:20:33,030 --> 00:20:39,330
+الاس ان نقص الام يعني اخدت element موجود في ال
+
+213
+00:20:39,330 --> 00:20:44,110
+code domain تبع ال function و بدي اثبت انه له أصل
+
+214
+00:20:44,110 --> 00:20:46,890
+في ال domain اللى عندنا then
+
+215
+00:20:50,300 --> 00:20:56,780
+الـ gamma is odd مظبوط ولا لأ؟ ليش؟ لإنها موجودة
+
+216
+00:20:56,780 --> 00:21:02,120
+في ال set of all odd permutation implies that ممكن
+
+217
+00:21:02,120 --> 00:21:10,190
+أكتب الجامعة هذه على الشكل alpha betaيعني حاصل ضرب
+
+218
+00:21:10,190 --> 00:21:15,470
+even في قد اللي هو مين قد صح ولا لأ يبقى هالكلام
+
+219
+00:21:15,470 --> 00:21:20,310
+هذا ممكن ولا غير ممكن الإجابة ممكن لإن هذه قد وهذه
+
+220
+00:21:20,310 --> 00:21:26,830
+قد فعلا طب حسب ال definition هذه بتعطينا مينفاي of
+
+221
+00:21:26,830 --> 00:21:31,610
+alpha يبقى جامل حتى في ال code main لقيت اللي أصل
+
+222
+00:21:31,610 --> 00:21:35,990
+في ال domain اللي هو alpha يبقى بناء عليه فاي is
+
+223
+00:21:35,990 --> 00:21:44,150
+unto يبقى بناء عليه اللي هو الفاي is one to one
+
+224
+00:21:44,150 --> 00:21:50,430
+and untoمدام one to one and one to hada بده يعطينا
+
+225
+00:21:50,430 --> 00:21:57,530
+ان ال order لل AN بده ساوي ال order لل SN ناقص ال
+
+226
+00:21:57,530 --> 00:22:09,610
+AM هذا بده يعطينا اللي هو half of the elements of
+
+227
+00:22:09,610 --> 00:22:18,670
+SN is evenيبقى نصهم بيكون even مثل ما طلب في
+
+228
+00:22:18,670 --> 00:22:31,410
+السؤال وهو المطلوب طيب
+
+229
+00:22:31,410 --> 00:22:39,930
+هذا كان سؤال تسعتاشالان بعد تسعة اتاش انا سؤال
+
+230
+00:22:39,930 --> 00:22:45,530
+اتنين وعشرين مائتين alpha و beta موجودة في sn و
+
+231
+00:22:45,530 --> 00:22:49,490
+اثبت ان ال alpha inverse beta inverse alpha beta
+
+232
+00:22:49,490 --> 00:22:55,890
+even permutation على طول الخط الان سؤال اتنين
+
+233
+00:22:55,890 --> 00:23:03,130
+وعشرين بقولي alpha و beta موجودة في ال sn اثبت انه
+
+234
+00:23:03,830 --> 00:23:11,190
+Alpha inverse Beta inverse Alpha Beta is even
+
+235
+00:23:11,190 --> 00:23:12,350
+دائما وأبدا
+
+236
+00:23:26,840 --> 00:23:29,940
+محطليش ميودة على alpha و beta اللهم إلا
+
+237
+00:23:29,940 --> 00:23:34,240
+permutation موجودة في ال sn هل even و odd خد زي ما
+
+238
+00:23:34,240 --> 00:23:39,820
+بدك اذا انا عندي ثلاث احتمالات العربي عليها
+
+239
+00:23:39,820 --> 00:23:44,060
+الاحتمال الأول ان alpha و beta التنتين even
+
+240
+00:23:44,060 --> 00:23:48,800
+الاحتمال الثاني ان alpha و beta التنتين odd
+
+241
+00:23:48,800 --> 00:23:54,450
+الاحتمال الثالث واحدة odd واحدة even مش هيكعلى كده
+
+242
+00:23:54,450 --> 00:23:58,290
+الاحتمالات الثلاثة بدي اثبت له انه حصل ضربة ده او
+
+243
+00:23:58,290 --> 00:24:02,810
+حصل composition ما بين الأربع permutation even
+
+244
+00:24:02,810 --> 00:24:09,990
+تمام يبقى الآن بداية اخدله المقطة الأولى if alpha
+
+245
+00:24:09,990 --> 00:24:19,150
+and beta are even then ال alpha inverse beta
+
+246
+00:24:19,150 --> 00:24:26,090
+inverse alpha betaتوا قبل قليل أثبتنا أنه لو كانت
+
+247
+00:24:26,090 --> 00:24:29,990
+ال alpha even يبقى معكوسة even لو كانت ال alpha
+
+248
+00:24:29,990 --> 00:24:36,030
+odd يبقى معكوسة odd كذلك إذا هذه الأولى even
+
+249
+00:24:36,030 --> 00:24:43,350
+والتانية even والتالتة even والرابعة even يبقى
+
+250
+00:24:43,350 --> 00:24:50,310
+ناتج جداش يبقى إن كانوا التنتين even في المجموع او
+
+251
+00:24:50,310 --> 00:24:55,900
+ال composition ما بينهم evenالحالة الثانية لو كانت
+
+252
+00:24:55,900 --> 00:25:05,880
+ال alpha and ال beta are both odd تمام then ايش
+
+253
+00:25:05,880 --> 00:25:11,000
+اللي بدي يحصل ال alpha inverse beta inverse alpha
+
+254
+00:25:11,000 --> 00:25:16,640
+beta بتبقى على الشكل التالي الحين التنتين odd يبقى
+
+255
+00:25:16,640 --> 00:25:24,380
+المعكوس تبعهم odd تمام يبقى oddوالتانية odd
+
+256
+00:25:24,380 --> 00:25:32,200
+والتالتة odd والرابعة odd لكن odd زائد odd إيش
+
+257
+00:25:32,200 --> 00:25:38,500
+بتعطينا؟ even و odd زائد odd التانية بتعطينا؟ و
+
+258
+00:25:38,500 --> 00:25:42,440
+even زائد even إيش بتعطينا؟ even يبقى على كل
+
+259
+00:25:42,440 --> 00:25:46,360
+الأمرين سواء التنتين odd أو التنتين even الناتج
+
+260
+00:25:46,360 --> 00:25:54,050
+even وصلنا للحالة الثالثة والأخيرةلو كانت ال alpha
+
+261
+00:25:54,050 --> 00:26:03,330
+is odd and beta is even then بدنا ناخد alpha
+
+262
+00:26:03,330 --> 00:26:09,370
+inverse beta inverse alpha beta الان alpha odd
+
+263
+00:26:09,370 --> 00:26:18,080
+يبقى معكوسة كذلك oddالان beta even يبقى مع كوسة
+
+264
+00:26:18,080 --> 00:26:25,140
+even alpha قلنا عليها odd و beta even هذا الكلام
+
+265
+00:26:25,140 --> 00:26:31,420
+بده يساوي اطلعلي لهذه اض زائد اد شو بتعطينا even
+
+266
+00:26:31,420 --> 00:26:40,520
+يبقى evenهو عندك زائد even زائد even يبقى كل وش
+
+267
+00:26:40,520 --> 00:26:45,880
+بيعطيلك even على كل الاحتمالات الممكنة فإن ال
+
+268
+00:26:45,880 --> 00:26:50,260
+composition بين الأربعة permutations دائما و أبدا
+
+269
+00:26:50,260 --> 00:26:57,680
+even هي permutationيبقى هنا س ال alpha inverse
+
+270
+00:26:57,680 --> 00:27:04,400
+beta inverse alpha beta is even لكل ال alpha و
+
+271
+00:27:04,400 --> 00:27:10,300
+beta اللي موجودة في مين موجودة في sn بلا استثناء
+
+272
+00:27:34,070 --> 00:27:39,810
+طيب هذا كان سؤال اتنين وعشرين الان بدنا نروح لسؤال
+
+273
+00:27:39,810 --> 00:27:44,810
+ستة وعشرين بيقول لي اثبت ان ال cycle واحد اتنين
+
+274
+00:27:44,810 --> 00:27:51,290
+تلاتة اربعة is not the product of three cycle يبقى
+
+275
+00:27:51,290 --> 00:28:00,270
+هنا ستة وعشرين show that ان واحد اتنين تلاتة اربعة
+
+276
+00:28:00,270 --> 00:28:10,170
+is notis a product of three cycles هذا الكلام مش
+
+277
+00:28:10,170 --> 00:28:17,990
+ممكن يحصل أبدا طيب تعالى نشوف صحة هذا الكلام الان
+
+278
+00:28:17,990 --> 00:28:24,030
+ال permutation هادي even والله odd يا شباب odd
+
+279
+00:28:24,030 --> 00:28:30,530
+اتكلمتش عن ال order لها ال order لها يسبب أربعة
+
+280
+00:28:30,530 --> 00:28:36,710
+صحيحوهو طول ال cycle مظبوط انا اتكلمت اكمتوا cycle
+
+281
+00:28:36,710 --> 00:28:43,310
+بتقدر تكون منها تلاتة اذا هذه odd فباجي بقوله هنا
+
+282
+00:28:43,310 --> 00:28:50,950
+solution يبقى the cycle او the permutation
+
+283
+00:28:50,950 --> 00:28:54,470
+permutation
+
+284
+00:28:54,470 --> 00:29:02,430
+اللي هو واحد اتنين تلاتة او اربعة is oddأد ليش؟
+
+285
+00:29:02,430 --> 00:29:10,470
+لأنه تلاتة transpositions هي تلاتة اللي هو واحد
+
+286
+00:29:10,470 --> 00:29:15,570
+اربعة واحد تلاتة واحد اتنين تمام يبقى هذه اد بدي
+
+287
+00:29:15,570 --> 00:29:23,310
+افترض جدلا ان جدرت اكتب هذه على شكل cycle واحدة
+
+288
+00:29:23,310 --> 00:29:27,730
+طولها يساوي تلاتة يبقى لما اكتب ال cycle طولها
+
+289
+00:29:27,730 --> 00:29:32,150
+تلاتة even والله اديعني بنفعل permutation تكون
+
+290
+00:29:32,150 --> 00:29:37,530
+even و odd معناته فيه شغل غلط يبقى اللي فرضته أنا
+
+291
+00:29:37,530 --> 00:29:42,110
+هذا غلط و عكسه هو الصح إذا لا يمكن كتابة ال
+
+292
+00:29:42,110 --> 00:29:46,630
+permutation اللي عندي على شكل three cycle وماقلش
+
+293
+00:29:46,630 --> 00:29:51,030
+three cycle قال لي product وين قال لي product of
+
+294
+00:29:51,030 --> 00:29:57,000
+three cycle بدي أفترضي الآنان بقدر اكتبها على شكل
+
+295
+00:29:57,000 --> 00:30:02,160
+product of three cycles وشوف هذا فرضي بوصلني الى
+
+296
+00:30:02,160 --> 00:30:06,980
+نتيجة صحيحة ولا الى نتيجة خاطئة اذا وصلني الى
+
+297
+00:30:06,980 --> 00:30:12,260
+نتيجة صحيحة معناته شغل صح وصلني الى نتيجة خاطئة
+
+298
+00:30:12,260 --> 00:30:17,060
+معناته فرض اللي انا فرضته خطأ وعكسه ايه هو الصح
+
+299
+00:30:17,060 --> 00:30:19,920
+اذا هروح اقول assume
+
+300
+00:30:22,800 --> 00:30:32,800
+إن الواحد اتنين تلاتة أربعة is a product of three
+
+301
+00:30:32,800 --> 00:30:41,400
+cycles that is I N الواحد اتنين تلاتة أربعة بدي
+
+302
+00:30:41,400 --> 00:30:51,420
+أكتب على شكل ABC في DEF بالشكل اللي عندناهي
+
+303
+00:30:51,420 --> 00:30:59,900
+product of three cycles then الان
+
+304
+00:30:59,900 --> 00:31:09,060
+ال a,b,c في d,e,f يساوي بدي اكتبها على شكل
+
+305
+00:31:09,060 --> 00:31:17,800
+transposition يبقى هذا بدي يعطينا a,c و هنا a,b و
+
+306
+00:31:17,800 --> 00:31:26,210
+التانية d,fوالتالتة دي ايه؟ كده عددهم؟ اربعة يعني
+
+307
+00:31:26,210 --> 00:31:32,930
+even صح ولا لا؟ يعني معناته هذه even permutation
+
+308
+00:31:32,930 --> 00:31:41,070
+ايش
+
+309
+00:31:41,070 --> 00:31:45,090
+رأيك؟ وصلنا للتناقض ولا لا؟ مش واحد اتنين تلاتة
+
+310
+00:31:45,090 --> 00:31:51,130
+اربعة قدلما كتبت على شكل three ال cycle صارت ايش؟
+
+311
+00:31:51,130 --> 00:31:56,810
+صارت even يبقى هذه even تسمح له أنه وصلنا إلى
+
+312
+00:31:56,810 --> 00:32:02,510
+contradiction يبقى هذا تناقض معناته فرض اللي انا
+
+313
+00:32:02,510 --> 00:32:10,250
+فرضته هذا صح ولا غلط؟ غلط يبقى هنا so الواحد اتنين
+
+314
+00:32:10,250 --> 00:32:24,680
+تلاتة اربع كانت ب writtenas a product of three
+
+315
+00:32:24,680 --> 00:32:31,250
+cyclesطيب يجي واحد تاني يقولي انت خدتين تانى طب
+
+316
+00:32:31,250 --> 00:32:34,690
+انا ممكن احط كمان واحدة تالتة اقوله حط مش تالتة حط
+
+317
+00:32:34,690 --> 00:32:37,990
+رابعة او خمسة او سادة او زى ما بدك الحين اللى ما
+
+318
+00:32:37,990 --> 00:32:41,230
+تحطلي كمان واحدة three cycle هدول عددهم اربعة
+
+319
+00:32:41,230 --> 00:32:46,530
+الواحدة بتجيبلي قداش two transposition بتصير قداش؟
+
+320
+00:32:46,530 --> 00:32:50,910
+ستة يعني even لو اخدتين تانى مش واحدة بتجيبلك
+
+321
+00:32:50,910 --> 00:32:55,650
+اربعة او اربعة تمانية evenوهكذا يعني أيش ما تحط في
+
+322
+00:32:55,650 --> 00:33:00,070
+three cycles بتطلع even يبقى هذا الكلام غير ممكن
+
+323
+00:33:00,070 --> 00:33:05,570
+على الإطلاق وبالتالي هذه مالها دائما و أبدا لا
+
+324
+00:33:05,570 --> 00:33:13,670
+يمكن كتابت على شكل product of three cycles طيب هذا
+
+325
+00:33:13,670 --> 00:33:19,870
+كان سؤال ستة و عشرين سبعة و عشرين جالي beta موجودة
+
+326
+00:33:19,870 --> 00:33:28,970
+في S7جالي سبعة و عشرين Beta موجودة في أس سبعة
+
+327
+00:33:28,970 --> 00:33:37,730
+وزيادة على ذلك جالي ال Beta أس أربعة ال Beta أس
+
+328
+00:33:37,730 --> 00:33:41,990
+أربعة ليه اتنين واحد اربعة تلاتة اتنين واحد اربعة
+
+329
+00:33:41,990 --> 00:33:50,630
+تلاتة خمسة ستة سبعة خمسة ستة سبعة جالي find Beta
+
+330
+00:33:53,520 --> 00:33:58,940
+بيتا بده اعرف البيتا هذه ايه شكلها يعني ما هي شكل
+
+331
+00:33:58,940 --> 00:34:06,020
+العناصر او قداش ما هي العناصر الموجودة في اللي هو
+
+332
+00:34:06,020 --> 00:34:09,720
+بيتا علم ان بيتا أقصى أربعة بالشكل اللي عندنا هذا
+
+333
+00:34:09,720 --> 00:34:16,480
+حد فيك وحل السؤال هذا احليت يعني ايوة احكي الفكرة
+
+334
+00:34:16,480 --> 00:34:20,940
+شوف مربع البيت أربعة وربيحها ال CBS تانية وعند ال
+
+335
+00:34:20,940 --> 00:34:28,640
+order البيت سبعةأشعرفك أن ال order لل بيسم يعني كل
+
+336
+00:34:28,640 --> 00:34:36,700
+element موجود في ال سبعة ال order له سبعة هي
+
+337
+00:34:36,700 --> 00:34:42,300
+موجودة في السبعة أنا موافق أنها موجودة في السبعة
+
+338
+00:34:42,300 --> 00:34:45,020
+لكن هل ال order له يسوى سبعة
+
+339
+00:34:50,030 --> 00:34:53,610
+أنا منافق إنها سبعة بس كيف جيبتها بك تثبتها مش
+
+340
+00:34:53,610 --> 00:34:58,210
+عشوائية و اخ بتطلع غير انه طلعت سبعة ها هي سبعة صح
+
+341
+00:34:58,210 --> 00:35:03,410
+بس كيف نثبتها بتثبت ان ال order ل beta يساوي سبعة
+
+342
+00:35:03,410 --> 00:35:09,470
+حتى يطلع كلامك صحيح الحين هذي beta أُس أربعة ال
+
+343
+00:35:09,470 --> 00:35:13,730
+order لها كمان يساوي سبعة ليش ان هاي هال cycle
+
+344
+00:35:13,730 --> 00:35:19,260
+كلها سبعة و كلهم are disjoint elements مظبوطيعني
+
+345
+00:35:19,260 --> 00:35:23,860
+هذه permutation او cycle موجودة في السبعة صحيح وال
+
+346
+00:35:23,860 --> 00:35:27,960
+order الها يساوي طولها يساوي السبعة صحيح هذا ال
+
+347
+00:35:27,960 --> 00:35:32,520
+order ل beta اربعة يساوي سبعة انا بد ال order ل
+
+348
+00:35:32,520 --> 00:35:37,340
+beta وبالتالي اذا جبت ال order ل beta صارت قصتنا
+
+349
+00:35:37,340 --> 00:35:44,670
+بسيطة تمام طيب نرجع هنانرجع هنا مرة تانية من خلال
+
+350
+00:35:44,670 --> 00:35:49,370
+الكلام اللي احنا كتبينه خليني اسألكوا سؤال لستاذ
+
+351
+00:35:49,370 --> 00:35:55,050
+محمود حسبلكوا جداش ال order .. اي جداش ال order لل
+
+352
+00:35:55,050 --> 00:36:01,110
+elements لل S7 جداش
+
+353
+00:36:01,110 --> 00:36:05,170
+ال orders الممكنة لعناصر S7
+
+354
+00:36:07,770 --> 00:36:11,930
+جديش؟ مش عدد العناصر بتكلمش عن عدد العناصر،
+
+355
+00:36:11,930 --> 00:36:14,530
+العناصر كله عارف أنه السبعة فقه سبعة factorial
+
+356
+00:36:14,530 --> 00:36:22,130
+بقول ال order لعناصر ل group السبعة، جيش ال orders
+
+357
+00:36:22,130 --> 00:36:30,150
+الممكنة؟ من واحد لسبعة بس، مزيدش أكتر من هيك؟ طب
+
+358
+00:36:30,150 --> 00:36:34,750
+احنا مشان نجيب ال order ل cycles كيف بجيب ال order
+
+359
+00:36:34,750 --> 00:36:40,290
+لcycles مضربات في بعض؟two cycles مثلا هذه طولها
+
+360
+00:36:40,290 --> 00:36:44,610
+تلاتة وهذه طولها خمسة وموافق التنتين دوس جوينت
+
+361
+00:36:44,610 --> 00:36:48,150
+تلاتة وخمسة يعني التنتين دوس جوينت ال least common
+
+362
+00:36:48,150 --> 00:36:53,810
+multiple ممتاز جدا يبقى لو عندي cycle واحدة فال
+
+363
+00:36:53,810 --> 00:36:58,770
+order لها يساوي طولها إذا عندي تنتين والتنتين are
+
+364
+00:36:58,770 --> 00:37:02,630
+disjoint بجيب ال least common multiple للإتنين
+
+365
+00:37:02,630 --> 00:37:06,590
+بيكون هو ال order لل permutationلو كانوا التلاتة
+
+366
+00:37:06,590 --> 00:37:10,410
+والتلاتة are disjoint بجيب ال is common multiple
+
+367
+00:37:10,410 --> 00:37:15,290
+للتلاتة وبالتالي هذا هو ال order لهم تمام يبقى
+
+368
+00:37:15,290 --> 00:37:20,630
+الآن ما هي ال orders الممكنة لعناصر السبعة هذا
+
+369
+00:37:20,630 --> 00:37:25,030
+ضروري لازم لفي العلم لازم اعرفهم وهو مثال محلول
+
+370
+00:37:25,030 --> 00:37:29,770
+عندك في الكتاب يعني الأستاذ محمود لازم يكون شرحه
+
+371
+00:37:29,770 --> 00:37:37,080
+مائة بالمائةأه مين مذكر ال orders يعني مغششك في
+
+372
+00:37:37,080 --> 00:37:42,160
+صفحة قداش كمان يا سيدي هذا في الكتاب موجود عندك
+
+373
+00:37:42,160 --> 00:37:49,080
+تفصيليا المثال يا سيدي المثال في الكتاب اللي هو
+
+374
+00:37:49,080 --> 00:37:58,080
+صفحة 102 و 103 example 4 صفحة 102 و 103 أكيد
+
+375
+00:37:58,080 --> 00:38:00,500
+شرحلكوا تفصيليا
+
+376
+00:38:02,040 --> 00:38:07,740
+أي نعم اتنين ناقش لكل مسائل من واحد الى عشر اطلعلي
+
+377
+00:38:07,740 --> 00:38:12,180
+في سؤال سبعة في الأسئلة بتلاقي نفس السؤال السؤال
+
+378
+00:38:12,180 --> 00:38:15,520
+السابعة بيقولي what are the possible orders of the
+
+379
+00:38:15,520 --> 00:38:22,420
+elements of A6 وA6 و what about A7 يعني معناته إذا
+
+380
+00:38:22,420 --> 00:38:26,340
+ما انشرحش في النظري انحل في المحاضرة بس انت مش
+
+381
+00:38:26,340 --> 00:38:29,850
+قاري هذه القصة تانية بتقول اعداد ما هذه اعدادطب
+
+382
+00:38:29,850 --> 00:38:34,810
+تروح تراجع في الكتاب و ال orders واحد اتنين تلتة
+
+383
+00:38:34,810 --> 00:38:42,250
+اربعة خمسة ستة سبعة عشر اتناش هدول بس يبقى الان
+
+384
+00:38:42,250 --> 00:38:47,390
+solution the
+
+385
+00:38:47,390 --> 00:38:52,650
+possible orders
+
+386
+00:38:52,650 --> 00:39:04,140
+the possible orders ofthe elements of
+
+387
+00:39:04,140 --> 00:39:11,540
+السبعة are الواحد والاتنين والتلاتة والاربعة
+
+388
+00:39:11,540 --> 00:39:18,460
+والخمسة والستة والسبعة والعشرة والاثمان عشر خلّي
+
+389
+00:39:18,460 --> 00:39:24,000
+هؤلاء العشقاء نعود لهم بعد قليل الان نعود لمين؟
+
+390
+00:39:24,000 --> 00:39:30,080
+لصاحبتنا هذا البيت أربعةالان ال order ل beta 4
+
+391
+00:39:30,080 --> 00:39:38,020
+يساوي طولها كم طولها سبعة يبقى سبعة هذا معناته ان
+
+392
+00:39:38,020 --> 00:39:43,140
+beta أس أربعة أس سبعة ستعطي ال identity
+
+393
+00:39:43,140 --> 00:39:51,110
+permutationهذا معناته ان بيتا اص تمانية وعشرين بده
+
+394
+00:39:51,110 --> 00:39:57,590
+يساوي ال identity السؤال هو ما علاقة ال order تبع
+
+395
+00:39:57,590 --> 00:40:04,790
+بيتا بالتمانية وعشرين يجي اسمه ممتاز جدا الان هذا
+
+396
+00:40:04,790 --> 00:40:11,450
+بده يعطينا ان ال order لبيتا divide التمانية
+
+397
+00:40:11,450 --> 00:40:19,360
+وعشرينطيب كل ال possible orders هاي هم قدامي يبقى
+
+398
+00:40:19,360 --> 00:40:25,720
+بده أروح أدور مين منهم بيقسم ال 28 يبقى باجي بقول
+
+399
+00:40:25,720 --> 00:40:31,540
+saw the possible orders
+
+400
+00:40:31,540 --> 00:40:42,300
+of beta R الواحد بيقسم ال 28والاتنين يقسم الـ 28
+
+401
+00:40:42,300 --> 00:40:50,880
+والاربعة يقسم الـ 28 والسبعة يقسم الـ 28 في غيرهم
+
+402
+00:40:50,880 --> 00:40:56,240
+تقول الـ 14 بقولك الـ 14 مش منهم مافيش عندي
+
+403
+00:40:56,240 --> 00:41:01,140
+permutation في السبعة ال order الى يسوى 14يبقى انا
+
+404
+00:41:01,140 --> 00:41:06,780
+بدي اخد من هدول الارقام اللي بتقسم للتمانية وعشرين
+
+405
+00:41:06,780 --> 00:41:12,040
+طلعت هذه الان اذا استبعدت الواحد واتنين والاربعة
+
+406
+00:41:12,040 --> 00:41:17,120
+بيصير ال order ل beta هو سبعة مظبوط هيك دي اخ
+
+407
+00:41:17,120 --> 00:41:23,780
+العران شو اسمك انت؟ على ايش؟ على ابعودة على ابعودة
+
+408
+00:41:23,780 --> 00:41:29,380
+خلانا نعود الى السؤال من جديديعني احنا بدنا نوصل
+
+409
+00:41:29,380 --> 00:41:32,840
+لكلام اللى قاله ان ال order يساوي سبعة واني بصمته
+
+410
+00:41:32,840 --> 00:41:36,580
+بس سألنا كيف قال خبطها من عندى مافيش حاجة يسمع
+
+411
+00:41:36,580 --> 00:41:41,880
+خبطها ماتش تشتغل رياضى سليم تمام الان بداجي اقوله
+
+412
+00:41:41,880 --> 00:41:48,780
+if ال order ل beta كان يساوي واحد هل هذا ممكن ولا
+
+413
+00:41:48,780 --> 00:41:54,700
+غير ممكنغير ممكن ان بيتا لا يمكن يسوى ال identity
+
+414
+00:41:54,700 --> 00:42:00,980
+بدليل ان بيتا أص أربعة تسوى هذه لو كانت بيتا تسوى
+
+415
+00:42:00,980 --> 00:42:04,280
+ال identity ليه كان بيتا أص أربعة يسوى ال identity
+
+416
+00:42:04,280 --> 00:42:11,480
+يبقى ال order لبيتا يسوى واحد impossible غير ممكن
+
+417
+00:42:11,480 --> 00:42:19,500
+السبب becauseان بيتا لا يساوي ال identity
+
+418
+00:42:19,500 --> 00:42:24,460
+permutation لأن لو كانت ال beta بال identity يبقى
+
+419
+00:42:24,460 --> 00:42:28,640
+beta و أربعة بال identity يبقى هذا مستبعد تماما
+
+420
+00:42:28,640 --> 00:42:41,880
+طيب نيجي ناخد الاحتمال الثاني بعدك
+
+421
+00:42:41,880 --> 00:42:48,750
+باجي بقوله لو كانال order ل beta بده يساوي أربعة
+
+422
+00:42:48,750 --> 00:42:57,190
+اسمع يا راجل then تمام ال beta أُص أربعة بده يساوي
+
+423
+00:42:57,190 --> 00:43:01,870
+ال identity هذا كلام حقيقي لأ لأن beta أُص أربعة
+
+424
+00:43:01,870 --> 00:43:14,310
+هيها يبقى هنا this is impossible ليش becauseإن الـ
+
+425
+00:43:14,310 --> 00:43:20,890
+beta أُس أربعة ليست ال identity وإنما تساوي وراحت
+
+426
+00:43:20,890 --> 00:43:26,790
+اتنين واحد اربعة تلاتة اتنين واحد اربعة تلاتة خمسة
+
+427
+00:43:26,790 --> 00:43:32,550
+ستة سبعة هذا اللي مستعجل عليه الاحتمال الثالث اللي
+
+428
+00:43:32,550 --> 00:43:40,430
+هو Fبتا تربيع بده يساوي اتنين ثم بتا تربيع بده
+
+429
+00:43:40,430 --> 00:43:43,690
+يساوي اتنين ثم بتا تربيع بده يساوي اتنين ثم بتا
+
+430
+00:43:43,690 --> 00:43:51,930
+تربيع بده يساوي اتنين ثم بتا تربيع بده يساوي اتنين
+
+431
+00:43:52,550 --> 00:43:58,650
+يبقى سؤال order ل beta كده؟ سبعة يبقى سؤال order ل
+
+432
+00:43:58,650 --> 00:44:03,850
+beta بده يسوى السبعة يعني معناته beta و السبعة بده
+
+433
+00:44:03,850 --> 00:44:10,310
+يسوى من ال identity element طب انا بدي beta بقدر
+
+434
+00:44:10,310 --> 00:44:17,790
+اجيب او اخلك من هنا beta؟ كيف؟واضرب في Beta يبقى
+
+435
+00:44:17,790 --> 00:44:24,470
+لو ضربت في Beta بصير Beta أس تمانية بده يساوي Beta
+
+436
+00:44:24,470 --> 00:44:32,150
+يبقى صارت Beta بدها تساوي Beta أس أربعة في Beta أس
+
+437
+00:44:32,150 --> 00:44:38,160
+أربعة ليه Beta أس تمانية؟مظبوط هذا معناه ان بيتا
+
+438
+00:44:38,160 --> 00:44:43,000
+تساوي بيتا وصة أربعة هي جاهزة عندنا اتنين واحد
+
+439
+00:44:43,000 --> 00:44:49,940
+اربعة تلاتة خمسة ستة سبعة خمسة ستة سبعة اتنين واحد
+
+440
+00:44:49,940 --> 00:44:59,690
+اربعة تلاتة خمسة ستة سبعةيبقى صورة beta تساوي يبقى
+
+441
+00:44:59,690 --> 00:45:03,890
+صورة
+
+442
+00:45:03,890 --> 00:45:14,650
+تساوي
+
+443
+00:45:14,650 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+444
+00:45:15,290 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+445
+00:45:15,290 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+446
+00:45:15,290 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+447
+00:45:15,290 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+448
+00:45:15,290 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+449
+00:45:15,290 --> 00:45:20,350
+يبقتمام الان وصلتي التلاتة التلاتة موجودة هنا
+
+450
+00:45:20,350 --> 00:45:26,070
+موجودة صورتها مين؟ و الخمسة مين صورتها؟ هاي الستة
+
+451
+00:45:26,070 --> 00:45:31,130
+الستة صورتها سبعة و السبعة صورتها اتنين صورته واحد
+
+452
+00:45:31,130 --> 00:45:36,270
+و الواحد صورته الأربع صورته تلاتة و التلاتة صورته
+
+453
+00:45:36,270 --> 00:45:41,830
+الخمسة صورته ستة و الستة صورتها سبعة السبعة صورتها
+
+454
+00:45:41,830 --> 00:45:46,770
+اتنين و اتنين صورتها واحد جفلتطب السؤال هو خلصنا و
+
+455
+00:45:46,770 --> 00:45:51,070
+لا ضايق الأرقام واحد اتنين تلتة اربعة خمسة ستة
+
+456
+00:45:51,070 --> 00:45:55,390
+سبعة تمام خلصنا يبقى ايه ال cycle يبقى هذه ال beta
+
+457
+00:45:55,390 --> 00:46:01,110
+اللي عندنا تمام يبقى هذا الشغل الرياضي بيخرج شمال
+
+458
+00:46:01,110 --> 00:46:06,950
+ولا واحد بيقدر يقولكإنه في شغلة ضعيفة أو شغلة غلطة
+
+459
+00:46:06,950 --> 00:46:11,670
+بس تقولي إنها سبعة مباشرة هحطلك علامة تفهم لو كان
+
+460
+00:46:11,670 --> 00:46:16,210
+السؤال يجيلك ويقولك why يعني كيف نزلت من السماء ال
+
+461
+00:46:16,210 --> 00:46:20,550
+order يساوي سبعة لأ هو لو قلتلي ال order ل beta
+
+462
+00:46:20,550 --> 00:46:23,470
+أقصى أربعة يساوي سبعة ده ال order ل beta يساوي
+
+463
+00:46:23,470 --> 00:46:24,670
+سبعة هو كلام غلط
+
+464
+00:46:28,000 --> 00:46:34,400
+طيب، هذا كان سؤال سبعة وعشرين، الآن وصلنا لسؤال
+
+465
+00:46:34,400 --> 00:46:39,100
+تسعة وعشرين وما أدرك ما تسعة وعشرين، ها يا أخويا
+
+466
+00:46:39,100 --> 00:46:44,480
+عدوا، وشوفوا كيف حلتوا هذا، هاي السؤال تسعة وعشرين
+
+467
+00:46:46,720 --> 00:46:51,700
+تسعة و عشرين بيقول اجالي find the element sigma
+
+468
+00:46:51,700 --> 00:46:58,660
+اللي موجودة في S تسعة بدنا sigma اللي موجودة في S
+
+469
+00:46:58,660 --> 00:47:09,260
+تسعة such that اللي هو sigma تقريب بده يساوي واحد
+
+470
+00:47:09,260 --> 00:47:16,230
+خمسة سبعة واحد خمسة سبعةاتنين تمانية تلاتة اتنين
+
+471
+00:47:16,230 --> 00:47:23,770
+تمانية تلاتة و هنا اربعة ستة تسعة اربعة ستة تسعة
+
+472
+00:47:27,170 --> 00:47:32,670
+أه في عندنا sigma موجودة في اس تسعة بحيث sigma
+
+473
+00:47:32,670 --> 00:47:39,390
+تقريب يسوى هذا الرقم قلي هاتلي تلت سيجمات بحيث
+
+474
+00:47:39,390 --> 00:47:45,890
+يعطونا الرقم هذا والسيجمات هدول موجودة وانفي S9
+
+475
+00:47:45,890 --> 00:47:55,210
+يعني بدي تلاتة permutations من S9 لو لو كعبت
+
+476
+00:47:55,210 --> 00:48:00,250
+الواحدة فيهم تعطيني حاصل ضرب ل three cycles اللي
+
+477
+00:48:00,250 --> 00:48:05,910
+عندنا هذون خلص
+
+478
+00:48:05,910 --> 00:48:12,410
+الوقت طيب بدي أعطيك واحدة لبعد الظهر تجيبلي كمان
+
+479
+00:48:12,410 --> 00:48:16,980
+غيرها تمامو الواحدة بدي أخذها من الأرقام اللي
+
+480
+00:48:16,980 --> 00:48:24,180
+قدامك يبقى اخذ هي sigma one sigma one شوف كيف بدي
+
+481
+00:48:24,180 --> 00:48:29,400
+أخذها طلع معايا هي جوس بدي أبدأ بالواحد هنا
+
+482
+00:48:29,400 --> 00:48:36,680
+والواحد هنا يعني أول رقم يبقى هي واحد اتنين اربع
+
+483
+00:48:36,680 --> 00:48:45,290
+بدي أبدأ بالتانيخمسة تمانية ستة التالت سبعة تلاتة
+
+484
+00:48:45,290 --> 00:48:54,490
+تسعة تمام تقولك كمان واحدة طيب سيجما اتنين من هذه
+
+485
+00:48:54,490 --> 00:48:59,830
+بدي اجيبهابدي أخلي الواحد ثابت زي ما هو بدي أقول
+
+486
+00:48:59,830 --> 00:49:05,090
+اربعة اتنين بدلت اتنين مع بعض الخمسة ثابت زي ما هو
+
+487
+00:49:05,090 --> 00:49:10,810
+ستة تمانية بدل الستة تمانية السابعة ثابت تسعة
+
+488
+00:49:10,810 --> 00:49:18,410
+تلاتة تاخد لك كمان واحدة سجمة تلاتة بجيبلك ستة مش
+
+489
+00:49:18,410 --> 00:49:23,830
+تلاتة بجيبلك جد ببدأك مرتينتمام يبقى sigma تلاتة
+
+490
+00:49:23,830 --> 00:49:28,710
+انا بدأت هنا بالواحد بدأ ابدأ بالاتنين يبقى لو قلت
+
+491
+00:49:28,710 --> 00:49:35,530
+اتنين اه اه واحد اربع بدأ ابدأ باللي في المص يبقى
+
+492
+00:49:35,530 --> 00:49:41,110
+تمانية خمسة ستة يبقى بدأ اخد اللي في المص يبقى
+
+493
+00:49:41,110 --> 00:49:47,050
+تلاتة سبعة تسعةالحين انت من هنا لبعد الظهر مسكلي
+
+494
+00:49:47,050 --> 00:49:52,450
+أي واحدة فيهم وضربها في نفسها تلت مرات إذا ما
+
+495
+00:49:52,450 --> 00:49:55,330
+طالعشي الجواب هذا بتيجي قرجعني
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6c224458254a9edbb556b2d57a4fdff5511e4f2d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48.srt
@@ -0,0 +1,2075 @@
+1
+00:00:22,310 --> 00:00:28,070
+في محاضرة الصبح قبل ساعتين بدأنا في موضوع ال
+
+2
+00:00:28,070 --> 00:00:31,530
+groups اللي هو أول موضوع في ال alphabet algebra
+
+3
+00:00:31,530 --> 00:00:37,070
+المقرر علينا،  مشان نعرف ال group لازم نعرف حاجة
+
+4
+00:00:37,070 --> 00:00:41,750
+اسمها binary operation وبعد ذلك بندخل إلى موضوع
+
+5
+00:00:41,750 --> 00:00:47,070
+ال group عرفنا ال binary operation على set هي عبارة
+
+6
+00:00:47,070 --> 00:00:52,710
+عن function من ال S cross ال S إلى set أخرى بحيث
+
+7
+00:00:52,710 --> 00:00:55,990
+ال order paired اللي في ال S cross ال S بيكون 
+
+8
+00:00:55,990 --> 00:01:01,450
+موجود وين؟ في ال set itself وعطينا على ذلك مثالين
+
+9
+00:01:01,450 --> 00:01:07,000
+وهذا هو المثال رقم 3، يبقى أنا عرفت ال function star
+
+10
+00:01:07,000 --> 00:01:12,480
+من Z cross Z إلى Z by a star b يساوي a b ناقص واحد
+
+11
+00:01:12,480 --> 00:01:16,880
+يعني ال star صارت عبارة عن عمليتين في أنا واحد،
+
+12
+00:01:16,880 --> 00:01:20,160
+عملية الضرب ما بين ال a و ال b وعملية الطرح من
+
+13
+00:01:20,160 --> 00:01:26,640
+واحد، لكن على set of integers السؤال هو: لما اضرب ال
+
+14
+00:01:26,640 --> 00:01:31,100
+a في b حصل ضرب two integers بيعطيني integer ولا
+
+15
+00:01:31,100 --> 00:01:35,970
+بيعطيني شغل تانية، اطرح منه واحد بيظل integer ولا بيبقى
+
+16
+00:01:35,970 --> 00:01:40,730
+يصير integer؟ معناته هذه binary operation، يبقى هذه
+
+17
+00:01:40,730 --> 00:01:50,350
+الـ ... then ... then star is a binary operation
+
+18
+00:01:50,350 --> 00:01:59,030
+السبب because إن العدد اللي عندنا a b ناقص ال one
+
+19
+00:01:59,030 --> 00:02:03,140
+موجود في Z، ما دام موجود في Z يبقى هذه ال operation
+
+20
+00:02:03,140 --> 00:02:09,440
+is a binary operation، طيب نتطلع الأمثلة شوية، مثال
+
+21
+00:02:09,440 --> 00:02:25,060
+رقم أربعة بيقول: let ال X ب any non-empty set، any
+
+22
+00:02:25,060 --> 00:02:28,240
+non-empty set، define
+
+23
+00:02:31,160 --> 00:02:36,600
+capital P of X to
+
+24
+00:02:36,600 --> 00:02:43,020
+be the
+
+25
+00:02:43,020 --> 00:02:56,140
+power set، فئة القوة، of set X اللي عندنا، يعني اللي 
+
+26
+00:02:56,140 --> 00:03:07,960
+هي the set of all the set of all subsets of X
+
+27
+00:03:07,960 --> 00:03:11,260
+define
+
+28
+00:03:11,260 --> 00:03:14,820
+star
+
+29
+00:03:14,820 --> 00:03:19,120
+by
+
+30
+00:03:19,120 --> 00:03:22,900
+a
+
+31
+00:03:22,900 --> 00:03:33,460
+star b بده يساوي a union b لكل ال a و ال b اللي
+
+32
+00:03:33,460 --> 00:03:44,040
+موجودة في ال power set of X، ال power set of X، then
+
+33
+00:03:44,040 --> 00:03:47,220
+star
+
+34
+00:03:47,220 --> 00:03:57,140
+then star هذه is a binary operation
+
+35
+00:03:58,950 --> 00:04:07,810
+binary operation on the power set لل X because
+
+36
+00:04:41,540 --> 00:04:46,380
+طبعًا ال power set اللي هي فئة القوة أو فئة القوى
+
+37
+00:04:46,380 --> 00:04:51,520
+درسناها في مبدأ الرياضيات والآن بنعيد دراستها مرة
+
+38
+00:04:51,520 --> 00:04:57,380
+ثانية، فلو أخدت ال X أي non-empty set، ركز على non
+
+39
+00:04:57,380 --> 00:05:03,260
+-empty يعني ليست فيها عناصر، بدي أعرف ال power
+
+40
+00:05:03,260 --> 00:05:07,940
+set of X هي ال power set of X أو the set of all
+
+41
+00:05:07,940 --> 00:05:12,520
+subset of X، يبقى بداجي على ال set X أشوف عناصرها
+
+42
+00:05:12,520 --> 00:05:18,540
+أجيب كل ال subsets الممكنة بما فيهم phi و ال X
+
+43
+00:05:18,540 --> 00:05:23,000
+itself، هذه بسميها ال trivial subset وهذه أكبر
+
+44
+00:05:23,000 --> 00:05:26,840
+subset من ال X because أخدنا في مادة الرياضيات أن 
+
+45
+00:05:26,840 --> 00:05:32,180
+ال X is a subset of itself، يبقى كل ال subsets اللي
+
+46
+00:05:32,180 --> 00:05:37,240
+عنده بيكونوله ميهم، بيكونوله ال power set لل X، بدا
+
+47
+00:05:37,240 --> 00:05:41,480
+أعرف اللي هو ال relation اللي ... ال operation اللي
+
+48
+00:05:41,480 --> 00:05:47,450
+عندنا a star b بده يساوي a union b لكل ال a و ال b
+
+49
+00:05:47,450 --> 00:05:51,570
+اللي موجودة في ال power set، السؤال هو: هل star هذه
+
+50
+00:05:51,570 --> 00:05:56,980
+binary operation ولا لا؟ بقول والله إذا نتيجة a star
+
+51
+00:05:56,980 --> 00:06:01,640
+b جبت لي عنصر دائمًا وأبدًا وهذا العنصر موجود في ال
+
+52
+00:06:01,640 --> 00:06:06,280
+power set، إذا هذه binary operation، يعني نتيجة
+
+53
+00:06:06,280 --> 00:06:12,220
+للعملية ما بين الاتنين لعملية ال union ههه بدها
+
+54
+00:06:12,220 --> 00:06:15,900
+تجيب لي عنصر موجود في ال power set، إذا هذه binary
+
+55
+00:06:15,900 --> 00:06:20,580
+operation، لو جبت عنصر طالع برا يبقى ليست binary
+
+56
+00:06:20,580 --> 00:06:25,300
+operation، يبقى ال operation a star b a union b لكل
+
+57
+00:06:25,300 --> 00:06:29,280
+ال a و ال b اللي موجودة في ال P of x، then star is
+
+58
+00:06:29,280 --> 00:06:32,900
+a binary operation على power set because نجي نشوف
+
+59
+00:06:32,900 --> 00:06:39,120
+ما هو السبب الآن، ال operation a star b بدي يساوي a
+
+60
+00:06:39,120 --> 00:06:44,800
+union b، السؤال هو: a union b هل هذه ال subset من X
+
+61
+00:06:44,800 --> 00:06:52,390
+يا شباب؟ لو أخدت any two subsets من ال X وجبت لهم
+
+62
+00:06:52,390 --> 00:06:56,870
+ال union يكون موجود في ال X itself ولا بتطلع برا؟
+
+63
+00:06:56,870 --> 00:07:00,710
+لا تطلعش برا، يبقى هذا موجود دائمًا وأبدًا في X، طب
+
+64
+00:07:00,710 --> 00:07:07,700
+و ال X هذه أليس subset من ال power set of X؟ يبقى
+
+65
+00:07:07,700 --> 00:07:15,340
+star، ال element هذا موجود في ال power set، ال X هذه
+
+66
+00:07:15,340 --> 00:07:21,700
+as a أعلى، مش subset، ال X هذه belongs موجودة في ال
+
+67
+00:07:21,700 --> 00:07:25,700
+power set، لكن ال a union b ال subset من ال X وال X
+
+68
+00:07:25,700 --> 00:07:31,500
+belong في ال power set of X، معناه هذا كلام، ال star
+
+69
+00:07:31,500 --> 00:07:35,320
+is a binary operation، طب السؤال هو: هل ال
+
+70
+00:07:35,320 --> 00:07:41,520
+intersection ما بين ال two sets a و b is a subset؟
+
+71
+00:07:41,520 --> 00:07:48,080
+يعني هل هو موجود في ال power set؟ ليش؟ على أسوأ
+
+72
+00:07:48,080 --> 00:07:53,100
+الاحتمالات، بدي يطلع في phi ولا لأ، في subset من ال
+
+73
+00:07:53,100 --> 00:07:58,760
+X ولا لأ، يبقى في موجودة في ال power set، وبناء عليه
+
+74
+00:07:58,760 --> 00:08:02,620
+سعر ال intersection كمان also is a binary
+
+75
+00:08:02,620 --> 00:08:07,320
+operation، يبقى باجي بقول إن similarly كمان شغلة
+
+76
+00:08:07,320 --> 00:08:13,550
+تانية، similarly، ال
+
+77
+00:08:13,550 --> 00:08:21,930
+... ال ... ال star أو a star b، ال a star b بدي يساوي
+
+78
+00:08:21,930 --> 00:08:32,130
+a intersection b، ها دي is a binary is a binary
+
+79
+00:08:32,130 --> 00:08:33,930
+operation
+
+80
+00:08:40,500 --> 00:08:44,000
+بارضه بنفس الطريقة، ليش؟ إن ال intersection ما بين
+
+81
+00:08:44,000 --> 00:08:48,520
+ال A وال B موجود في ال set X
+
+82
+00:08:54,460 --> 00:09:01,960
+بسبب أن a intersection b هو subset من set X وهذا
+
+83
+00:09:01,960 --> 00:09:14,020
+سيعطينا أن a intersection b هو subset من set X، طيب
+
+84
+00:09:14,020 --> 00:09:21,390
+ناخد كمان مثال بيختلف عن شكل هذه الأمثلة كليًا، let
+
+85
+00:09:21,390 --> 00:09:29,970
+خمسة، let الجي capital G بدي يساوي كل ال real
+
+86
+00:09:29,970 --> 00:09:34,010
+numbers X اللي موجودة في ال set of real numbers
+
+87
+00:09:34,010 --> 00:09:42,690
+بحيث إن ال X أكبر من أو تساوي واحد، define عرف لي a
+
+88
+00:09:42,690 --> 00:09:45,750
+star by
+
+89
+00:09:48,020 --> 00:10:01,220
+X star Y يساوي X Y ناقص X ناقص Y زائد 2، then
+
+90
+00:10:01,220 --> 00:10:13,680
+star اللي عندنا هذا is a binary operation is
+
+91
+00:10:13,680 --> 00:10:16,880
+a binary operation because
+
+92
+00:10:26,450 --> 00:10:34,230
+السبب؟ خلي بالك هنا، الآن أنا اخد ست جديدة على غير
+
+93
+00:10:34,230 --> 00:10:40,710
+الأمثلة السابقة، سميتها G، مين هي G؟ أخدت عناصر من
+
+94
+00:10:40,710 --> 00:10:44,830
+set of real numbers، اللي مين هم العناصر؟ كلهم اللي
+
+95
+00:10:44,830 --> 00:10:50,470
+بيكونوا دائمًا وأبدًا أكبر من الواحد الصحيح، كسور، مش
+
+96
+00:10:50,470 --> 00:10:54,870
+كسور، اللي وهم أعداد موجبة دائمًا وأبدًا وكلها أكبر
+
+97
+00:10:54,870 --> 00:11:00,950
+من الواحد الصحيح، عرفنا star على ال G cross ال G إلى
+
+98
+00:11:00,950 --> 00:11:06,630
+G على الشكل التالي: X star Y بده يساوي XY ناقص X
+
+99
+00:11:06,630 --> 00:11:12,830
+ناقص Y زائد 2، يبقى عملية ضرب وطرح وجمع في آن
+
+100
+00:11:12,830 --> 00:11:18,270
+واحد، من هذه ال star عرفتها بهذه الطريقة، أنا أدعي
+
+101
+00:11:28,250 --> 00:11:35,690
+السبب: إذا طلع هذا ال element موجود في G بقى كلامي
+
+102
+00:11:35,690 --> 00:11:41,310
+صح، ما طلع موجود في G بقى كلامي ماله؟ مش صحيح، بمعنى
+
+103
+00:11:41,310 --> 00:11:46,750
+آخر، لو طلع هذا المقدار كله أكبر من الواحد الصحيح
+
+104
+00:11:46,750 --> 00:11:51,610
+معناته موجود في G، ما طلع يبقى كلامي ماله؟ ليس صحيحًا
+
+105
+00:11:51,610 --> 00:11:56,370
+ممتاز جدًا، يبقى باجي بقوله: بدي أبيله ليش هذه binary
+
+106
+00:11:56,370 --> 00:12:06,430
+operation because if X و Y موجودة في G then ال X
+
+107
+00:12:06,430 --> 00:12:11,650
+هذا تبقى أكبر من الواحد وفي نفس الوقت ال Y أكبر
+
+108
+00:12:11,650 --> 00:12:17,890
+من الواحد، بسبب ال definition تبع ال G، ماخد two
+
+109
+00:12:17,890 --> 00:12:22,290
+elements موجودات في G، يبقى ال two elements كل
+
+110
+00:12:22,290 --> 00:12:27,970
+واحد يوم أكبر من مين؟ من الواحد، طيب هذا معناته إن
+
+111
+00:12:27,970 --> 00:12:33,330
+ال X greater than one and ال Y ناقص واحد أكبر من
+
+112
+00:12:33,330 --> 00:12:38,430
+مين؟ من ال zero، إذا هذا ال term موجب والله سالم
+
+113
+00:12:40,620 --> 00:12:45,140
+أكبر من Zero، موجب ولا عمره حتى بيصير Zero، يعني لا
+
+114
+00:12:45,140 --> 00:12:50,420
+Zero ولا سالب، هذا موجب، طب لو مسكت هذا الرقم الموجب
+
+115
+00:12:50,420 --> 00:12:54,360
+وضربته في ال inequality هذه بتتغير ولا بيظلها زي
+
+116
+00:12:54,360 --> 00:13:00,060
+ما هي؟ يعني الأكبر من هذه بتتغير ولا بتغير إلى أقل
+
+117
+00:13:00,060 --> 00:13:04,340
+منه ولا بتظل أكبر منه؟ يبقى بدي أمسك ال term هذا وأ
+
+118
+00:13:04,340 --> 00:13:09,020
+ضربه في ال inequality هذه، يبقى بدي أشوف هذا ايش
+
+119
+00:13:09,020 --> 00:13:14,000
+بيعطينا، يبقى مشان أوضح لك الصورة بدي أقول لك multiply
+
+120
+00:13:14,000 --> 00:13:23,560
+apply the inequality المتباينة
+
+121
+00:13:23,560 --> 00:13:31,690
+X greater than one by Y minus one we get بنحصل على
+
+122
+00:13:31,690 --> 00:13:39,390
+يبقى هذا ال X في Y ناقص ال one أكبر من ال Y ناقص
+
+123
+00:13:39,390 --> 00:13:44,310
+ال one، مظبوط؟
+
+124
+00:13:44,310 --> 00:13:51,010
+طيب، ايش رأيك؟ بدي أفك الطرف الشمال، يبقى XY ناقص X
+
+125
+00:13:51,010 --> 00:13:57,410
+ايش رأيك؟ هجيب ال Y على الشجة التانية، ناقص Y أكبر
+
+126
+00:13:57,410 --> 00:13:59,870
+من اللي هو سالب واحد
+
+127
+00:14:03,300 --> 00:14:11,750
+طيب ايش رأيك لو أضفت للطرفين اثنين؟ مرة واحدة بضيف
+
+128
+00:14:11,750 --> 00:14:15,310
+رقم هنا زي ما أضيف رقم هنا عادي جدا واثنين 
+
+129
+00:14:15,310 --> 00:14:17,590
+positive positive ولا negative في حالة الجمع
+
+130
+00:14:17,590 --> 00:14:22,010
+ما تفرقش عندي المشكلة في حالة الضرب أو القسمة يبقى
+
+131
+00:14:22,010 --> 00:14:29,670
+هنا لو أضفت اثنين بيصير x في y ناقص x ناقص y زائد 
+
+132
+00:14:29,670 --> 00:14:36,330
+اثنين أكبر من قداش أضفت اثنين للطرفين طب الطرف هذا
+
+133
+00:14:36,330 --> 00:14:42,130
+مش هو هذا يبقى star العدد اللي عندي هذا أكبر من
+
+134
+00:14:42,130 --> 00:14:49,670
+واحد يبقى موجود في G يبقى هذا بده يعطيك أن الـ X 
+
+135
+00:14:49,670 --> 00:14:57,330
+Y ناقص X ناقص Y زائد اثنين belongs to G لذلك star
+
+136
+00:14:57,330 --> 00:15:02,190
+is a binary operation لأنها تحت العملية اللي عندنا
+
+137
+00:15:02,190 --> 00:15:06,210
+هذه الـ star طلع الناتج موجود في G إذا هذه مالها
+
+138
+00:15:06,210 --> 00:15:12,400
+binary operation طيب احنا مهدينا للـ group بموضوع الـ
+
+139
+00:15:12,400 --> 00:15:17,380
+binary operation الآن بدنا ندخل في صميم الموضوع و
+
+140
+00:15:17,380 --> 00:15:23,580
+هو تعريف الـ group الجروب يا شباب هي الـ set بدي أضع
+
+141
+00:15:23,580 --> 00:15:30,580
+عليها binary operation بحيث تحقق لي ثلاثة شروط أن 
+
+142
+00:15:30,580 --> 00:15:35,400
+تحققت ثلاثة شروط بسمي الـ set مع الـ binary
+
+143
+00:15:35,400 --> 00:15:41,540
+operation is a group ايش الشروط الثلاثة؟ أول شيء 
+
+144
+00:15:41,540 --> 00:15:47,270
+الـ binary operation هذه بتبقى associative إدمجية
+
+145
+00:15:47,270 --> 00:15:54,150
+تمام أو تجميعية زي ما بتسموها أنتم اثنين في عنصر
+
+146
+00:15:54,150 --> 00:15:59,270
+بده اسميه عنصر الوحدة الـ identity element أنتم
+
+147
+00:15:59,270 --> 00:16:04,260
+بالعربي بجهة السماوية الثانوية العنصر المحايد يبقى
+
+148
+00:16:04,260 --> 00:16:08,720
+المحايد أو الوحدة هو الـ identity element الشرط
+
+149
+00:16:08,720 --> 00:16:14,260
+الثالث كل عنصر في الـ group تحت هذه العملية بدي
+
+150
+00:16:14,260 --> 00:16:20,400
+يكون له معكوس بحيث لو ضربت عنصر في معكوسه بدي يطلع لي
+
+151
+00:16:20,400 --> 00:16:25,080
+من عنصر المحايد الـ identity element لو تحققت
+
+152
+00:16:25,080 --> 00:16:30,020
+الشروط هذه الثلاثة بقول يبقى الجروب اللي عندي is a
+
+153
+00:16:30,020 --> 00:16:34,390
+group الكلام اللي سمعته بنروح نكتبه لإنه كل الـ
+
+154
+00:16:34,390 --> 00:16:39,490
+section مبني على مين؟ على الكلمتين اللي سمعتهم يبقى
+
+155
+00:16:39,490 --> 00:16:50,510
+بدنا نجي للـ definition يبقى definition let the G be a
+
+156
+00:16:50,510 --> 00:16:56,830
+non empty non empty set
+
+157
+00:16:58,880 --> 00:17:09,840
+and let the star be a
+
+158
+00:17:09,840 --> 00:17:17,640
+binary operation
+
+159
+00:17:17,640 --> 00:17:24,840
+on اللي هو G على set G then
+
+160
+00:17:27,230 --> 00:17:33,170
+الـ G والـ star مع بعض هدول يعني الـ set G والـ star
+
+161
+00:17:33,170 --> 00:17:43,230
+عملية عليها هدول is called a group بنسميها مجموعة
+
+162
+00:17:43,230 --> 00:17:50,750
+if the following properties
+
+163
+00:17:55,710 --> 00:18:00,170
+if the following properties are satisfied are
+
+164
+00:18:00,170 --> 00:18:08,230
+satisfied ايش
+
+165
+00:18:08,230 --> 00:18:18,110
+الخواص هذه اللي هو الخاصية الأولى the star is
+
+166
+00:18:18,110 --> 00:18:24,030
+associative associative
+
+167
+00:18:24,800 --> 00:18:29,100
+that is
+
+168
+00:18:29,100 --> 00:18:42,300
+a star b star c بدو يساوي a star b star c لكل
+
+169
+00:18:42,300 --> 00:18:49,140
+الـ a و الـ b و الـ c اللي موجودة في الـ group G الـ
+
+170
+00:18:49,140 --> 00:18:50,760
+condition الثاني
+
+171
+00:18:52,870 --> 00:19:09,190
+condition الثاني there is an element such
+
+172
+00:19:09,190 --> 00:19:12,550
+that
+
+173
+00:19:12,550 --> 00:19:23,830
+بحيث أن a star e يساوي e star a يساوي الـ a نفسها
+
+174
+00:19:23,830 --> 00:19:33,730
+لكل الـ a الموجودة في G بلا استثناء يبقى الـ E is
+
+175
+00:19:33,730 --> 00:19:42,330
+called the identity element
+
+176
+00:19:42,330 --> 00:19:45,530
+of
+
+177
+00:19:46,970 --> 00:20:11,510
+G condition
+
+178
+00:20:11,510 --> 00:20:13,330
+الثالث والأخير
+
+179
+00:20:20,360 --> 00:20:34,280
+for each a الموجود في G there exists b in G such
+
+180
+00:20:34,280 --> 00:20:45,800
+that بحيث أن such that a star b بده يساوي b star
+
+181
+00:20:45,800 --> 00:20:53,500
+a بده يساوي الـ identity e بيه
+
+182
+00:20:53,500 --> 00:20:58,880
+is called يبقى
+
+183
+00:20:58,880 --> 00:21:09,490
+بيه في هذه الحالة بنسميه is the inverse element of
+
+184
+00:21:09,490 --> 00:21:21,950
+a معكوس العنصر a and denoted by الـ b بده يساوي الـ
+
+185
+00:21:21,950 --> 00:21:26,870
+a inverse command
+
+186
+00:21:26,870 --> 00:21:30,970
+definition the group
+
+187
+00:21:33,590 --> 00:21:39,610
+الـ G is called abelian
+
+188
+00:21:39,610 --> 00:21:45,090
+if
+
+189
+00:21:45,090 --> 00:21:54,250
+x star y متساوي y star x لكل الـ x و الـ y الموجودة في الـ
+
+190
+00:21:54,250 --> 00:21:55,450
+group G
+
+191
+00:22:25,540 --> 00:22:31,040
+يبقى احنا ابتداء من هذا التعريف بكون بدأنا ندخل في
+
+192
+00:22:31,040 --> 00:22:35,680
+علم الـ groups أو علم المجموعات اللي هو موضوع
+
+193
+00:22:35,680 --> 00:22:40,220
+دراستنا لهذا الفصل اللي هو الـ abstract algebra
+
+194
+00:22:40,220 --> 00:22:44,460
+يبقى أول موضوع في موضوع الجبر اللي هو الموضوع
+
+195
+00:22:44,460 --> 00:22:50,330
+المجموعات الآن نعرف المجموعة وبعدين ناخذ أمثلة
+
+196
+00:22:50,330 --> 00:22:54,310
+متعددة على المجموعة بدل المثال عشر أو أحد الأمثلة
+
+197
+00:22:54,310 --> 00:23:00,010
+وبعد ذلك ناخذ بعض خواص المجموعات البسيطة يبقى
+
+198
+00:23:00,010 --> 00:23:04,470
+التعريف بيقول ما يتفترض أن G هو عبارة عن non-empty
+
+199
+00:23:04,470 --> 00:23:10,230
+set يبقى ليست الفئة الخاوية وإنما على الأقل فيها
+
+200
+00:23:10,230 --> 00:23:15,000
+ولو عنصر واحد and let the star be a binary
+
+201
+00:23:15,000 --> 00:23:20,760
+operation على الـ G الـ set
+
+202
+00:23:20,760 --> 00:23:26,400
+G مع الـ star مع بعض هدول بيكونوا لي a group إذا
+
+203
+00:23:26,400 --> 00:23:32,990
+تحققت عندي ثلاثة خواص أو ثلاثة شروط الشروط أو 
+
+204
+00:23:32,990 --> 00:23:37,790
+الخواص دي لـ star اللي عندي is associative يبقى
+
+205
+00:23:37,790 --> 00:23:43,430
+هي عملية إدماجية بمعنى أن a star b star c يساوي
+
+206
+00:23:43,430 --> 00:23:48,250
+يعني بتخلي a تأثر على b في الأول حسب تعريف الـ star
+
+207
+00:23:48,360 --> 00:23:52,300
+والعنصر اللي ينتج تخليه يأثر على مين؟ على c
+
+208
+00:23:52,300 --> 00:23:57,580
+النتيجة تماما كما لو b أثرت على c طالع عنصر جديد
+
+209
+00:23:57,580 --> 00:24:01,820
+هذا العنصر بدأ يأثر عليه بإيه لازم يكون اثنين are
+
+210
+00:24:01,820 --> 00:24:06,140
+equal إن حدث ذلك يبقى بقوله خاصية الـ associativity
+
+211
+00:24:06,140 --> 00:24:11,160
+الصحيحة لجميع العناصر يعني لما بدأ أخذ a و b و c مش
+
+212
+00:24:11,160 --> 00:24:15,060
+بدأ اختارهم عناصر محددة فلان وفلان بدأ أخذ أي
+
+213
+00:24:15,060 --> 00:24:20,770
+عناصر بغض النظر شو شكلها النقطة الثانية بيقول لي
+
+214
+00:24:20,770 --> 00:24:26,570
+there is an element E بحيث إذا لجيت عنصر أعطيته
+
+215
+00:24:26,570 --> 00:24:32,090
+الرمز E بس هذا إله خواص طبعا العنصر هذا موجود في
+
+216
+00:24:32,090 --> 00:24:38,570
+G itself بحيث أن لو أثرت بالـ a على الـ E بالـ star
+
+217
+00:24:38,570 --> 00:24:44,330
+هذه تماما كما لو أثرت بالـ E على a والنتج طالع الـ a
+
+218
+00:24:44,330 --> 00:24:49,240
+itself يبقى هذا اللي كنا بنسميه عنصر المحايد لا
+
+219
+00:24:49,240 --> 00:24:54,200
+يتأثر أي element في المجموعة بهذا الـ element تحت
+
+220
+00:24:54,200 --> 00:24:58,300
+العملية star أثر عليه star بهذا العنصر ويبقى الـ
+
+221
+00:24:58,300 --> 00:25:02,780
+element كما هو يبقى إن حدث ذلك هذا بسميه عنصر
+
+222
+00:25:02,780 --> 00:25:07,040
+المحايد أو في لغة الـ groups احنا هنسميه identity
+
+223
+00:25:07,040 --> 00:25:12,390
+element اللي هو عنصر الوحدة لهذه المجموعة بنضل عند
+
+224
+00:25:12,390 --> 00:25:18,210
+الـ condition الثالث والأخير قال لي 4 each اللي موجود
+
+225
+00:25:18,210 --> 00:25:24,290
+في G لأي عنصر a موجود في G هلاقي عنصر ثاني اسمه b
+
+226
+00:25:24,290 --> 00:25:29,830
+موجود في G بحيث لو ضربته من اليمين أو من الشمال a
+
+227
+00:25:29,830 --> 00:25:34,590
+star b بلاقي النتيجة هو b star a يساوي الـ identity
+
+228
+00:25:34,590 --> 00:25:39,450
+element itself يبقى هذا بده يعطيني عنصر الوحدة
+
+229
+00:25:39,450 --> 00:25:47,580
+نفسه إن حدث ذلك يبقى هذا العنصر معكوس العنصر a يبقى
+
+230
+00:25:47,580 --> 00:25:51,980
+في هذه الحالة الـ b is called the inverse element
+
+231
+00:25:51,980 --> 00:25:52,520
+of a
+
+232
+00:25:58,500 --> 00:26:01,920
+هذا الـ a كلها اللي فوق واسه اللي بسميه the
+
+233
+00:26:01,920 --> 00:26:07,460
+inverse element of a معكوس العنصر a يبقى b اللي
+
+234
+00:26:07,460 --> 00:26:12,460
+لجيته هذا بدي أسميه معكوس العنصر اللي هو a طب
+
+235
+00:26:12,460 --> 00:26:19,980
+السؤال هو هل كل عنصر في G لازم يجيه معكوس يعني مش
+
+236
+00:26:19,980 --> 00:26:26,940
+بالضرورة بعضهم ما و بعضهم لأ طب ايش جاي الـ a لأ for
+
+237
+00:26:26,940 --> 00:26:32,260
+each لكل عنصر يبقى كل عنصر في G بدأت تجيله معكوس
+
+238
+00:26:32,260 --> 00:26:38,020
+مش بعضهم له و بعضهم ما له كل عنصر في G له معكوس
+
+239
+00:26:38,020 --> 00:26:45,080
+يعني لو تصورت أن G هذه خمس عناصر يبقى فيهم اللي
+
+240
+00:26:45,080 --> 00:26:49,020
+هو أربعة واحد معكوس للتاني والـ identity element
+
+241
+00:26:49,020 --> 00:26:55,290
+معكوس لنفسه لو كانوا ستة يبقى ثلاثة معكوسات الثلاثة
+
+242
+00:26:55,290 --> 00:27:01,430
+الثانية وهكذا يبقى كل عنصر في الـ group G حلقيله
+
+243
+00:27:01,430 --> 00:27:05,990
+معكوس موجود في G بعد لو ضربت العنصر في معكوسه من
+
+244
+00:27:05,990 --> 00:27:10,290
+الشمال والله لمين بدي يطلع عنصر الوحدة طب عنصر
+
+245
+00:27:10,290 --> 00:27:15,960
+الوحدة هذا هو الصفر ولا واحد صح؟ بيقول حسب الـ
+
+246
+00:27:15,960 --> 00:27:20,600
+operation المعرفة على الـ group يبقى حسب الـ group
+
+247
+00:27:20,600 --> 00:27:23,820
+وحسب الـ operation اللي عليها ملاقي الـ identity
+
+248
+00:27:23,820 --> 00:27:27,570
+اللي يمكن الـ identity is zero يمكن الـ identity يطلع
+
+249
+00:27:27,570 --> 00:27:33,750
+واحد يمكن الـ identity يطلع عشرة مثلا هادئ جدا يبقى
+
+250
+00:27:33,750 --> 00:27:37,930
+حسب الـ operation اللي موجودة عندك وقد نستغرب هذا
+
+251
+00:27:37,930 --> 00:27:41,950
+لأن نستغرب ولا حاجة وحنُوريك بعض الأمثلة نحسب فيها
+
+252
+00:27:41,950 --> 00:27:47,550
+الـ identity element وما يطلعش لا zero ولا واحد يبقى
+
+253
+00:27:47,550 --> 00:27:52,430
+هذا يعني أن الشخص ما يكون شكله يكون بهمنيّش يبقى الـ
+
+254
+00:27:52,430 --> 00:27:55,570
+identity يعتمد على الـ group ويعتمد على الـ
+
+255
+00:27:55,570 --> 00:28:00,790
+operation على الـ group اتفضل معناته
+
+256
+00:28:00,790 --> 00:28:07,410
+مش معكوس يبقى ليست group يبقى إذا اختل أي شرط من
+
+257
+00:28:07,410 --> 00:28:11,550
+الشروط الثلاثة بالضبط ستصبح group يبقى مشان تكون
+
+258
+00:28:11,550 --> 00:28:16,810
+الـ group بدي any non zero set والثلاثة شروط يتحققوا
+
+259
+00:28:16,810 --> 00:28:21,190
+هدول بدي الـ operation هذه تبقى binary operation
+
+260
+00:28:21,190 --> 00:28:25,830
+نمرا واحد لو ما كانتش binary operation الصبح أخذنا
+
+261
+00:28:25,830 --> 00:28:29,030
+مثل ماهيّاش binary operation يبقى ده مينفعش يتكون
+
+262
+00:28:29,030 --> 00:28:35,060
+الـ group لازم نبقى binary operation أولا ثم تتحقق
+
+263
+00:28:35,060 --> 00:28:40,240
+الشروط الثلاثة تطلع الشجرة التعريف جينامتستاتار بي
+
+264
+00:28:40,240 --> 00:28:44,880
+binary operation يبقى هذه بسميها group لو تحققت
+
+265
+00:28:44,880 --> 00:28:48,340
+الشروط الثلاثة يبقى أنا في الحقيقة عندي ثلاثة شروط
+
+266
+00:28:48,340 --> 00:28:54,260
+ولا أربعة أربعة بدك هدى binary operation لستار
+
+267
+00:28:54,260 --> 00:28:59,780
+بتبقى associative أو اختصارا بروح بقول هم الثلاثة
+
+268
+00:28:59,780 --> 00:29:04,000
+لستار هدى بدي associative binary operation يبقى
+
+269
+00:29:04,000 --> 00:29:08,020
+جمعت الشرطين مين بشرط واحد اثنين وجود الـ identity
+
+270
+00:29:08,020 --> 00:29:13,200
+element ثلاثة وجود معكوس العنصر لأي عنصر موجود وين
+
+271
+00:29:13,200 --> 00:29:18,130
+موجود في الـ group G إن حدث ذلك بقول يبقى الـ 6G
+
+272
+00:29:18,130 --> 00:29:22,350
+اللي عندنا هذه مالها is A group وحتى أرسخ هذا
+
+273
+00:29:22,350 --> 00:29:27,330
+المفهوم من دماغك وأسحب المفهوم اللي في دماغك أن
+
+274
+00:29:27,330 --> 00:29:31,690
+الـ operation هذه هي عملية ضرب لحالها أو عملية قسمة
+
+275
+00:29:31,690 --> 00:29:36,290
+لحالها أو عملية طرح لحالها هتشوف أمثلة مختلفة و
+
+276
+00:29:36,290 --> 00:29:42,070
+عديدة حتى مصبح احنا مقيدين بشكل الـ six اللي عندنا
+
+277
+00:29:42,070 --> 00:29:46,650
+وماناش دعوة في الـ six الأخرى اثنين مقيدين بالـ
+
+278
+00:29:46,650 --> 00:29:49,070
+binary operation اللي عندنا وغيرها من الـ
+
+279
+00:29:49,070 --> 00:29:53,550
+operations ماليش علاقة فيهم تمام؟ وهذا يختلف من
+
+280
+00:29:53,550 --> 00:29:58,890
+group إلى الأخرى نعطي أول مثال على ذلك قبله نعطي
+
+281
+00:29:58,890 --> 00:30:04,910
+أول مثال كلمة Abelian Abelian بالعربي يعني ابدالي
+
+282
+00:30:04,910 --> 00:30:10,190
+ابدالي زي ما يقول commutative ابدالي فبجي بقول
+
+283
+00:30:10,190 --> 00:30:15,430
+group G is called abelian إذا كان الـ X في Y بده
+
+284
+00:30:15,430 --> 00:30:19,730
+يساوي Y في X لكل الـ X و Y اللي موجودة بلا استثناء
+
+285
+00:30:19,730 --> 00:30:25,210
+يعني لو جيت شباب اللي في القاعة خمسين طالب تمام لو
+
+286
+00:30:25,210 --> 00:30:29,150
+بدل كل واحد مقعد ومكان الثاني ما صار تغيير عندي
+
+287
+00:30:29,150 --> 00:30:34,520
+ولا حاجة كويس يبقى ما عدش فيه طول ولا قصر مع تبديل
+
+288
+00:30:34,520 --> 00:30:38,920
+مقعده ولا نقص من مقامه لا يبقى طالب زي ما هو مسجل
+
+289
+00:30:38,920 --> 00:30:43,480
+المادة وقاعد عندنا إذا لما بدل واحد مكان الثاني
+
+290
+00:30:43,480 --> 00:30:49,480
+لجيته يساوي نفس التبديل الأصلي إن حدث ذلك يبقى هذا
+
+291
+00:30:49,480 --> 00:30:53,960
+بقول عنك commutative group أو abelian group لكن
+
+292
+00:30:53,960 --> 00:30:59,810
+بقولش commutative commutative بقول عن درجات التسمية
+
+293
+00:30:59,810 --> 00:31:04,550
+أو التعريف في حالة الـ rings اللي هو تبعت الفصل
+
+294
+00:31:04,550 --> 00:31:08,450
+الثاني إن شاء الله إن شاء الله اللي باخد جبر حديثة
+
+295
+00:31:08,450 --> 00:31:12,790
+نمسكو الـ commutative ring لكن في الـ group هسميها
+
+296
+00:31:12,790 --> 00:31:17,640
+abelian group نسبة للعالم هي ابيل اللي اكتشف هالشغل
+
+297
+00:31:17,640 --> 00:31:23,340
+هذه وسميت باسمه ابيليان جروب إذا من حد ما تسمع
+
+298
+00:31:23,340 --> 00:31:28,120
+كلمة ابيليان جروب بدك تفهم أن العناصر بقدر أبدلهم
+
+299
+00:31:28,120 --> 00:31:33,000
+مكان بعض بدون أي مشاكل تمام؟ فهذا معنى ابيليان
+
+300
+00:31:33,000 --> 00:31:40,150
+جروبنأخد أبسط الأمثلة ونتدرج إلى الأثقال فالأثقال
+
+301
+00:31:40,150 --> 00:31:45,310
+فالأثقال حتى نصل إلى أمثلة مختلفة يبقى examples
+
+302
+00:31:45,310 --> 00:31:48,990
+أمثلة
+
+303
+00:31:48,990 --> 00:31:58,170
+أول مثال على ذلك الآن الـ Z والـ Q and set of real
+
+304
+00:31:58,170 --> 00:32:09,760
+numbers هذول under usual addition تحت عملية الجمع
+
+305
+00:32:09,760 --> 00:32:17,740
+العادي under usual addition اللي هو الـ plus are
+
+306
+00:32:17,740 --> 00:32:26,160
+abelian groups are
+
+307
+00:32:26,160 --> 00:32:28,580
+abelian groups because
+
+308
+00:32:36,540 --> 00:32:42,300
+السبب يبقى أنا أدعي أن زد تحت عملية الجامعة
+
+309
+00:32:42,300 --> 00:32:46,020
+العادي أقول لك usual addition الجامعة العادي تبع
+
+310
+00:32:46,020 --> 00:32:51,060
+الـ real number الـ Q تحت الجامعة العادي الـ R تحت
+
+311
+00:32:51,060 --> 00:32:54,020
+الجامعة العادي يعني عملش معرف على الـ set of
+
+312
+00:32:54,020 --> 00:32:56,680
+integers ومعرف على الـ set of rational numbers
+
+313
+00:32:56,680 --> 00:32:59,440
+ومعرف على الـ set of .. يعني هدول يعتبروا إيه؟
+
+314
+00:32:59,440 --> 00:33:05,620
+ثلاثة أمثلة يعني هدول three groups تحت العملية الـ
+
+315
+00:33:05,620 --> 00:33:09,780
+plus هذا والـ groups هدول are abelian احنا بنعرف
+
+316
+00:33:09,780 --> 00:33:14,270
+لما أقول A زائد B يعني اثنين زائد ثلاثة يساوي ثلاثة
+
+317
+00:33:14,270 --> 00:33:18,890
+زي اثنين جامعة عادي صح ولا لا هذا على زد لو جيت
+
+318
+00:33:18,890 --> 00:33:24,610
+على الـ IQ اثنين عدديا نسبيا مجموعهم عدد نسبي كذلك
+
+319
+00:33:24,610 --> 00:33:29,610
+لو جيت مجموع عددين حقيقيا بيعطينا إيه؟ عدد حقيقي
+
+320
+00:33:29,610 --> 00:33:35,860
+بجهة دي binary operation يبقى هنا بقوله because a
+
+321
+00:33:35,860 --> 00:33:43,060
+plus is a by أو associative بالمرة كمان is
+
+322
+00:33:43,060 --> 00:33:46,080
+associative
+
+323
+00:33:46,080 --> 00:33:53,300
+binary operation
+
+324
+00:33:53,300 --> 00:33:56,320
+on
+
+325
+00:33:56,320 --> 00:34:07,850
+z والـ q وكذلك من الـ set of real numbers طب كويس
+
+326
+00:34:07,850 --> 00:34:11,170
+أظن
+
+327
+00:34:11,170 --> 00:34:14,730
+أخذنا هذه الكثير حكاية الـ associativity للأعداد
+
+328
+00:34:14,730 --> 00:34:18,730
+الحقيقية ما هي النسبية والصحيحة جزء من الأعداد
+
+329
+00:34:18,730 --> 00:34:22,510
+الحقيقية يبقى الأعداد الحقيقية لما أقول اثنين زي
+
+330
+00:34:22,510 --> 00:34:26,650
+الثلاثة زي الخمسة هو ثلاثة زي الخمسة والإنتاج يضيف
+
+331
+00:34:26,650 --> 00:34:30,410
+له اثنين عادي جدا ما فيش فيها مشكلة يبقى هذه بالنسبة
+
+332
+00:34:30,410 --> 00:34:35,590
+للـ associative طب مين الـ identity element في حالة
+
+333
+00:34:35,590 --> 00:34:43,310
+الجامعة الـ zero يبقى هنا is هذه النقطة الأولى
+
+334
+00:34:43,310 --> 00:34:49,810
+النقطة الثانية النقطة الثانية الـ zero is the
+
+335
+00:34:49,810 --> 00:34:56,310
+identity element because
+
+336
+00:35:00,180 --> 00:35:07,120
+الـ zero زائد الـ بي مثلا يساوي بي زائد الـ zero بده
+
+337
+00:35:07,120 --> 00:35:15,720
+يساوي الـ بي itself الكلام هذا for all بي اللي
+
+338
+00:35:15,720 --> 00:35:24,240
+موجودة في z أوي q and الـ a طيب النقطة الثالثة
+
+339
+00:35:27,080 --> 00:35:33,000
+لو أخدت element a موجود في أي منهما من المعكوس
+
+340
+00:35:33,000 --> 00:35:38,940
+تبعه يعني مين العدد اللي بدي أضيفه إليه يطلع من؟
+
+341
+00:35:38,940 --> 00:35:50,730
+يطلع zero سالم العدد يبقى هنا the inverse of أي
+
+342
+00:35:50,730 --> 00:36:00,010
+اللي موجود في الـ Z أو الـ Q and ال R is سالب A
+
+343
+00:36:00,010 --> 00:36:10,770
+since لأن الـ A زائد ناقص A يساوي ناقص A زائد A يساوي
+
+344
+00:36:10,770 --> 00:36:17,490
+Zero لهمين الـ identity element طيب
+
+345
+00:36:17,490 --> 00:36:26,910
+نمر اثنين نروح ناخد مثال آخر لو أخدت الآن z وتحت
+
+346
+00:36:26,910 --> 00:36:35,250
+عملية الضرب العادي z is
+
+347
+00:36:35,250 --> 00:36:46,010
+not a group يبقى هذه ماهيّاش group under usual
+
+348
+00:36:46,010 --> 00:36:47,810
+multiplication
+
+349
+00:36:50,890 --> 00:37:00,830
+تحت عملية الضرب العادية ليش؟ because because
+
+350
+00:37:00,830 --> 00:37:14,270
+if الـ a موجود في z and الـ a لا يساوي واحد وبحيث الـ
+
+351
+00:37:14,270 --> 00:37:20,450
+a لا يساوي واحد الآن تحت عملية الضرب من الـ identity
+
+352
+00:37:20,450 --> 00:37:25,650
+element الواحد ممتاز جدا يبقى هذا واحد لأن أي عدد
+
+353
+00:37:25,650 --> 00:37:29,910
+اضربه في واحد بيطلع نفسي لوحده السؤال هو هل بقدر
+
+354
+00:37:29,910 --> 00:37:34,370
+ألاقي element اضربه في أي عدد يطلع واحد
+
+355
+00:37:37,270 --> 00:37:43,510
+أنا بدي في Z أنا بحكي على Z فقط أنا مقيد بالـ 6
+
+356
+00:37:43,510 --> 00:37:47,590
+بتبعتي الـ 6 الأخرى ماليش علاقة فيها ومقيد بالـ
+
+357
+00:37:47,590 --> 00:37:52,950
+operation اللي عندي بقدر ألاقي في الشمكانية يبقى F
+
+358
+00:37:52,950 --> 00:37:59,150
+الـ A موجودة under الـ A لا تساوي واحد then there is
+
+359
+00:37:59,150 --> 00:38:12,610
+أو there exists no element B اللي هو z such that
+
+360
+00:38:12,610 --> 00:38:21,170
+بحيث أن الـ a في b بده يساوي الواحد الصحيح يعني for
+
+361
+00:38:21,170 --> 00:38:25,830
+example if
+
+362
+00:38:25,830 --> 00:38:33,190
+الـ a تساوي ثلاثة بقدر ألاقي عدد بي اضروف ثلاثة يطلع
+
+363
+00:38:33,190 --> 00:38:39,390
+واحد بس بحيث العدد فيه z فالـ a تساوي ثلاثة then
+
+364
+00:38:39,390 --> 00:38:45,910
+there is no integer
+
+365
+00:38:45,910 --> 00:38:55,950
+بي such that بحيث أن ثلاثة بي بده يساوي واحد
+
+366
+00:38:55,950 --> 00:39:03,250
+مالاجيش هذا العدد بتاتا يبقى هذه زد تحت عملية ضرب
+
+367
+00:39:03,250 --> 00:39:11,270
+مالها طيب خليني أسأل كمان سؤال لو قلت لك الـ set of
+
+368
+00:39:11,270 --> 00:39:16,770
+real numbers كويس؟ بس أصبر شوية الـ set of real
+
+369
+00:39:16,770 --> 00:39:26,430
+numbers تحت عملية الضرب هل هي group؟ ليش؟ بالنسبة
+
+370
+00:39:26,430 --> 00:39:29,750
+للصفر بلا جيش ولا inverse ليش أن الـ identity قلت
+
+371
+00:39:29,750 --> 00:39:34,890
+هو مين بلا جيش ولا عدد اضربه في الصفر يطلع واحد
+
+372
+00:39:34,890 --> 00:39:40,730
+صحيح يدي ليست جروب وهكذا إذا احنا الـ set مقيدين
+
+373
+00:39:40,730 --> 00:39:45,410
+بالـ set بشكل الأعداد اللي موجودة فيها مقيد بالـ
+
+374
+00:39:45,410 --> 00:39:48,750
+identity اللي عندي فيها مقيد بالـ binary
+
+375
+00:39:48,750 --> 00:39:52,150
+operational اللي موجودة عندي حققت الشروط بقول جروب
+
+376
+00:39:52,150 --> 00:39:58,830
+ما حققت بقوله ماهيّاش جروب طب لو جيت قولت لك تلاتة
+
+377
+00:39:58,830 --> 00:40:06,490
+let i تساوي الجذر التربيعي للسالب واحد define
+
+378
+00:40:06,490 --> 00:40:10,090
+define
+
+379
+00:40:10,090 --> 00:40:17,610
+usual multiplication multiplication
+
+380
+00:40:17,610 --> 00:40:19,550
+on
+
+381
+00:40:38,180 --> 00:40:46,550
+عرفت حصل الضرب على set of complex numbers واحد ناقص
+
+382
+00:40:46,550 --> 00:40:51,330
+واحد i ناقص i ناقص i حيث i هو الجذر التربيعي
+
+383
+00:40:51,330 --> 00:40:56,550
+للسالب واحد يبقى دول complex ولا لا وعليهم عملية
+
+384
+00:40:56,550 --> 00:41:01,430
+ضرب العادية تبع ال complex number السؤال هو هل هذه
+
+385
+00:41:01,430 --> 00:41:05,470
+group ولا لا في الأول بدي أشوف هل ال
+
+386
+00:41:05,470 --> 00:41:12,990
+multiplication هذه لو ضربت أي عددين في بعض من دول
+
+387
+00:41:12,990 --> 00:41:18,430
+بيبقى complex ولا بيبطل يصير complex any real
+
+388
+00:41:18,430 --> 00:41:22,270
+number is complex هذا complex وهذا complex وهذا
+
+389
+00:41:22,270 --> 00:41:25,670
+complex وهذا complex وهذا complex يبقى العملية هذه
+
+390
+00:41:25,670 --> 00:41:30,790
+طيب لو ضربت ال i في ناقص i أليست مثل ناقص i في i
+
+391
+00:41:30,790 --> 00:41:34,950
+لأن العملية إبدالية هذا ناقص واحد في i زي i في
+
+392
+00:41:34,950 --> 00:41:40,230
+ناقص واحد سياد يبقى هذه اللي هي عبارة عن
+
+393
+00:41:40,230 --> 00:41:45,610
+associative binary operation يبقى let then
+
+394
+00:41:52,020 --> 00:41:58,380
+النقطة الآن هي نقطة
+
+395
+00:41:58,380 --> 00:42:03,500
+عملية عملية عملية عملية عملية عملية
+
+396
+00:42:03,500 --> 00:42:06,700
+عملية عملية
+
+397
+00:42:10,880 --> 00:42:17,480
+طب كويس، مين ال identity element؟ واحد، يبقى واحد
+
+398
+00:42:17,480 --> 00:42:22,740
+is the identity element
+
+399
+00:42:24,480 --> 00:42:28,440
+يبقى الواحد هو عنصر الواحد اللي دي لو ضربته في أي
+
+400
+00:42:28,440 --> 00:42:32,580
+واحد من هدول بيطلع نفس الواحد هدول طيب السؤال مين
+
+401
+00:42:32,580 --> 00:42:38,060
+معكوس السالب واحد؟ السالب واحد itself يبقى السالب واحد
+
+402
+00:42:38,060 --> 00:42:44,740
+is the inverse of itself يبقى هو معكوس لنفسي هنا
+
+403
+00:42:44,740 --> 00:42:55,030
+سالب واحد is the inverse of itself طيب مين معكوس
+
+404
+00:42:55,030 --> 00:42:58,590
+الواحد؟ الواحد نفسه، ضربه نفسه بيطلع واحد، ما عنديش
+
+405
+00:42:58,590 --> 00:43:01,650
+أمر يبقى هذا ال identity دائما و أبدا شباب ال
+
+406
+00:43:01,650 --> 00:43:06,150
+identity هو معكوسه لنفسه، يتدورش عليه أي group
+
+407
+00:43:06,150 --> 00:43:08,810
+تطلع في الدنيا عندك ال identity إن هو معكوسه
+
+408
+00:43:08,810 --> 00:43:13,490
+لنفسها طيب الآن مين معكوس ال i؟ ال سالب i طب و
+
+409
+00:43:13,490 --> 00:43:20,880
+السالب i؟ لو ضربت i في i ب i تربيع اللي بسالب واحد و
+
+410
+00:43:20,880 --> 00:43:27,520
+عندك سالب بصير موجبة بواحد يبقى هنا باجي بقول له ال
+
+411
+00:43:27,520 --> 00:43:34,580
+i is the inverse of سالب i
+
+412
+00:43:39,980 --> 00:43:46,020
+من هذول التلاتة مع اللي فوق يبقى صلة هذه ال group
+
+413
+00:43:46,020 --> 00:43:52,260
+تحت عملية ضرب is a group يبقى هذا بدي يعطيلك إن g
+
+414
+00:43:52,260 --> 00:43:59,920
+تحت عملية الضرب اللي عندنا هذه is a group يبقى هذه
+
+415
+00:43:59,920 --> 00:44:02,160
+عبارة عن مجموعة
+
+416
+00:44:17,760 --> 00:44:23,720
+مثال رقم أربعة مثال
+
+417
+00:44:23,720 --> 00:44:31,880
+رقم أربعة هذا سؤال تلاتة من الكتاب بيقول لي show
+
+418
+00:44:31,880 --> 00:44:41,860
+that the set اللي هي مين؟ واحد واثنين وتلاتة
+
+419
+00:44:41,860 --> 00:44:45,680
+وأربعة under
+
+420
+00:44:50,830 --> 00:45:01,410
+multiplication modulo خمسة modulo خمسة is an
+
+421
+00:45:01,410 --> 00:45:14,950
+abelian group is an abelian group but ولكن اللي هو
+
+422
+00:45:14,950 --> 00:45:26,710
+واحد واثنين و تلاتة under multiplication
+
+423
+00:45:26,710 --> 00:45:30,410
+modulo
+
+424
+00:45:30,410 --> 00:45:34,850
+أربعة
+
+425
+00:45:34,850 --> 00:45:39,970
+is not a group
+
+426
+00:46:15,380 --> 00:46:20,710
+سؤال مرة ثانية السؤال يعتبر سؤالين عندما أعطيني
+
+427
+00:46:20,710 --> 00:46:25,010
+أربعة أعداد واحد اثنين تلاتة عرفنا عليهم عملية ضرب
+
+428
+00:46:25,010 --> 00:46:30,430
+modulo خمسة عملية ضرب بالمقياس خمسة قال لي أثبت إن
+
+429
+00:46:30,430 --> 00:46:34,050
+هذه عبارة عن abelian group abelian سهلة تلاتة في
+
+430
+00:46:34,050 --> 00:46:36,550
+اثنين هي اثنين في تلاتة تلاتة في أربع هي أربع في
+
+431
+00:46:36,550 --> 00:46:40,050
+تلاتة اثنين في أربع هي أربع في اثنين والباقي في
+
+432
+00:46:40,050 --> 00:46:43,070
+واحد ما هي بطلع نفسها تمام؟ إذا أنا حكيت ال
+
+433
+00:46:43,070 --> 00:46:46,630
+abelian هذه تحصيل حاصل يبقى أنا بالزمن ال
+
+434
+00:46:46,630 --> 00:46:51,690
+associative و بالزمن من؟ ال binary operation في
+
+435
+00:46:51,690 --> 00:46:55,830
+الأول و لزمنا ال identity و المعكوس بقوله بسيطة
+
+436
+00:46:55,830 --> 00:47:00,370
+جدا الآن بدي أشوف هل هي associ .. هي قبل ال
+
+437
+00:47:00,370 --> 00:47:04,190
+associative هل هي binary operation ولا لا بقوله
+
+438
+00:47:04,190 --> 00:47:10,110
+الله كويس يعني لو تعرفت أي عنصرين في بعضهم بدي
+
+439
+00:47:10,110 --> 00:47:14,170
+يكون ناتج داخل الستة دي إن حدث ذلك بقوله هذه
+
+440
+00:47:14,170 --> 00:47:18,880
+binary operation الآن تعال خدلي اثنين في واحد اثنين
+
+441
+00:47:18,880 --> 00:47:21,840
+موجودة تلاتة في واحد تلاتة موجودة أربعة في واحد
+
+442
+00:47:21,840 --> 00:47:26,960
+بأربعة موجودة نمسك اثنين اثنين في تلاتة ستة modulo
+
+443
+00:47:26,960 --> 00:47:31,740
+خمسة بيظل قداش؟ واحد موجود اثنين في أربعة تمانية
+
+444
+00:47:31,740 --> 00:47:36,080
+modulo خمسة تلاتة موجود خلصنا اثنين ضربنا في تلاتة
+
+445
+00:47:36,080 --> 00:47:39,940
+و أربعة لأن تلاتة في أربعة باطمعشر modulo خمسة
+
+446
+00:47:39,940 --> 00:47:45,980
+بأثنين موجود يبقى داشت صارت binary operation يبقى
+
+447
+00:47:45,980 --> 00:47:55,650
+باجي بقوله أول شيء ال multiplication modulo
+
+448
+00:47:55,650 --> 00:48:12,890
+خمسة is a binary operation on the set اللي واحد
+
+449
+00:48:12,890 --> 00:48:17,950
+واثنين وتلاتة وأربعة because السبب
+
+450
+00:48:20,570 --> 00:48:29,870
+ال a, b modulo خمسة موجود في الست واحد واثنين
+
+451
+00:48:29,870 --> 00:48:35,430
+وتلاتة وأربعة لكل ال a و ال b شو رأيك أسميها
+
+452
+00:48:35,430 --> 00:48:41,430
+للسهولة أسميها s و هذا يبدأ أسميها s يبغى لكل ال a
+
+453
+00:48:41,430 --> 00:48:47,850
+و ال b اللي موجودة وين في s يبقى حاصل ضرب أي اثنين
+
+454
+00:48:47,850 --> 00:48:52,430
+كله موجود وين؟ موجود لذلك بايناري وبرجانت اثنين هذا
+
+455
+00:48:52,430 --> 00:48:55,870
+ضرب عادي بس باخد الموديولو في الآخر يبقى
+
+456
+00:48:55,870 --> 00:49:03,570
+associative ولا لا يبقى هنا كمان لاحظ إن note إن
+
+457
+00:49:03,570 --> 00:49:09,510
+multiplication modulo
+
+458
+00:49:09,510 --> 00:49:12,310
+خمسة
+
+459
+00:49:15,220 --> 00:49:21,640
+is associative بدك
+
+460
+00:49:21,640 --> 00:49:25,640
+تشكل بساطرة هذا ما في مشكلة احنا ال i هو ال
+
+461
+00:49:25,640 --> 00:49:29,040
+identity الواحد يبقى هذا سهل لكن ضالي عند مين
+
+462
+00:49:29,040 --> 00:49:31,700
+الاثنين والتلاتة والاربعة يبقى بقدر أخدهم مع بعض
+
+463
+00:49:31,700 --> 00:49:37,040
+أو يبقى خلصت ال group كله مظبوط يعني for example
+
+464
+00:49:40,060 --> 00:49:49,900
+لو أخدت اثنين أستار تلاتة أستار أربعة طيب، هذا
+
+465
+00:49:49,900 --> 00:49:56,040
+اثنين في تلاتة بستة موديولو خمسة صح ولا لأ؟ يبقى
+
+466
+00:49:56,040 --> 00:50:02,220
+ستة موديولو خمسة فيها قداش؟ واحد يبقى بظل واحد
+
+467
+00:50:02,220 --> 00:50:11,280
+أستار أربعة أربعة مد يولو خمسة يبقى هذا بده يساوي
+
+468
+00:50:11,280 --> 00:50:18,860
+أربعة and لو أخدت اثنين star تلاتة star أربعة
+
+469
+00:50:18,860 --> 00:50:27,510
+ويساوي تلاتة في أربعة ب 12 modulo 5 ب 2 يبقى يساوي 2
+
+470
+00:50:27,510 --> 00:50:35,110
+star 2 يعني 2 في 2 ب 4 modulo 5 اللي هي ب 4 يبقى هذا
+
+471
+00:50:35,110 --> 00:50:41,450
+بده يعطينا 4 يبقى star هذه هي نفس هذه بالظبط يبقى
+
+472
+00:50:41,450 --> 00:50:44,750
+العملية أساسية وضل بس دور مين الواحد واحد اللي
+
+473
+00:50:44,750 --> 00:50:47,490
+هيقدمه لأخر بالنسبة لعملية الدور لأن هو ال
+
+474
+00:50:47,490 --> 00:50:53,510
+identity element يبقى على طول الخطبة نقول واحد is
+
+475
+00:50:53,510 --> 00:51:01,430
+the identity element لأن
+
+476
+00:51:01,430 --> 00:51:05,250
+الواحد في أي رقم من الباقي modulo وخمسة هيعطيني
+
+477
+00:51:05,250 --> 00:51:12,230
+نفس الرقم مش هيغير حاجة طيب مين معكوس أي واحد فيهم
+
+478
+00:51:12,230 --> 00:51:14,270
+يلا شوف
+
+479
+00:51:17,900 --> 00:51:24,760
+من معكوس أي رقم من هذه الأرقام اثنين
+
+480
+00:51:24,760 --> 00:51:30,440
+والتلاتة معكوسات لبعض لأن اثنين في تلاتة modulo
+
+481
+00:51:30,440 --> 00:51:34,040
+وخمسة بطلع قداش؟ واحد اللي هو ال identity element
+
+482
+00:51:34,040 --> 00:51:42,230
+طب والأربعة في أربعة يبقى أربعة معكوس لنفسه و اثنين
+
+483
+00:51:42,230 --> 00:51:46,430
+معكوس للتلاتة و ال identity هو معكوس لنفسه إذا صار
+
+484
+00:51:46,430 --> 00:51:56,550
+كل عنصر له معكوس يبقى هنا باجي بقول every element
+
+485
+00:51:56,550 --> 00:52:05,310
+in s has an inverse
+
+486
+00:52:07,290 --> 00:52:22,690
+since الواحد is the inverse of واحد بعدها
+
+487
+00:52:22,690 --> 00:52:35,280
+اثنين is the inverse of تلاتة since لأن اثنين في
+
+488
+00:52:35,280 --> 00:52:43,720
+تلاتة modulo خمسة بده يساوي واحد and الأربعة is
+
+489
+00:52:43,720 --> 00:52:58,530
+the inverse of itself since اللي هما مين؟ أربعة مضروبة
+
+490
+00:52:58,530 --> 00:53:06,150
+في أربعة modulo خمسة يساوي واحد يبقى كل عنصر له
+
+491
+00:53:06,150 --> 00:53:14,310
+معكوس يبقى بناء عليه أصبحت هذه group يبقى هنا ال s
+
+492
+00:53:14,310 --> 00:53:23,330
+تساوي واحد واثنين وتلاتة وأربعة is a group under
+
+493
+00:53:29,300 --> 00:53:33,920
+multiplication multiplication modulo
+
+494
+00:53:35,390 --> 00:53:41,550
+خمسة طب أنا لسه خلصت الشطر الأول من السؤال جالي
+
+495
+00:53:41,550 --> 00:53:47,530
+لكن المجموعة هذه modulo أربعة is not a group بقوله
+
+496
+00:53:47,530 --> 00:53:52,670
+كويس إيش عرفك؟ بدي ولو شرط واحد يختل من الشروط
+
+497
+00:53:52,670 --> 00:53:59,510
+اللي عندي بتبطل تصير a group صح ولا لا؟ طيب حد
+
+498
+00:53:59,510 --> 00:54:01,530
+بقدر يجيب لي هذا الشرط
+
+499
+00:54:06,800 --> 00:54:11,660
+ممتاز جدا تعال نشوف تلاتة هذه بيقول ما لهاش معكوس
+
+500
+00:54:11,660 --> 00:54:17,320
+ليش؟ لأني قلت تلاتة في تلاتة تسعة تسعة شيل منهم
+
+501
+00:54:17,320 --> 00:54:24,200
+أربعتين بيظل واحد إذا التلاتة معكوس لنفسي صح يبقى
+
+502
+00:54:24,200 --> 00:54:31,020
+معكوسها اتنين في تلاتة ايه بستة شيل منهم أربعة
+
+503
+00:54:31,020 --> 00:54:35,500
+بيطلع اتنين يبقى ده مش اتنين معكسه مش التلاتة لكن
+
+504
+00:54:35,500 --> 00:54:41,720
+اتنين في اتنين أربعة تعني زيرو يبقى اتنين أو هذه
+
+505
+00:54:41,720 --> 00:54:45,680
+ماهيّاش closed under يعني هذه ال operation ماهيّاش
+
+506
+00:54:45,680 --> 00:54:50,780
+binary operation لأن ال element موجود في نفس ال set
+
+507
+00:54:50,780 --> 00:54:57,180
+يبقى هذه بقول له that set اللي هو واحد و اتنين و
+
+508
+00:54:57,180 --> 00:55:11,200
+تلاتة under multiplication modulo أربعة is not
+
+509
+00:55:11,200 --> 00:55:15,920
+a group since
+
+510
+00:55:18,430 --> 00:55:25,610
+الاتنين مستار اتنين يساوي أربعة modulo أربعة ليه
+
+511
+00:55:25,610 --> 00:55:30,730
+تساوي زيرو وهذا does not belong للست واحد واتنين 
+
+512
+00:55:30,730 --> 00:55:34,930
+وتلاتة يبقى الشرط الأول تبقى binary operation لأنه
+
+513
+00:55:34,930 --> 00:55:38,110
+تحت عملية ضرب modulo أربعة التي بيكون موجود في
+
+514
+00:55:38,110 --> 00:55:43,260
+الست هذه هذا مش موجود يبقى يبعتلك الله لازلنا في
+
+515
+00:55:43,260 --> 00:55:48,000
+الأمثلة السهلة حتى هذه اللحظة لسه عندنا أمثلة
+
+516
+00:55:48,000 --> 00:55:53,000
+كثيرة بدنا على قلبي كمان محاضرتين مشان نخلص
+
+517
+00:55:53,000 --> 00:55:57,500
+الأمثلة على موضوع ال group لأن هذا الأساس اللي
+
+518
+00:55:57,500 --> 00:56:02,420
+بدنا نبني عليه كل دراستنا في موضوع ال groups بعد
+
+519
+00:56:02,420 --> 00:56:04,080
+ذلك يعطيكم العجب 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..164b23432c32dd3524b0cc727f91d5bd40780c86
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_postprocess.srt
@@ -0,0 +1,1472 @@
+1
+00:00:22,730 --> 00:00:27,590
+المرة الماضية أخدنا نظرية على ال subgroups
+
+2
+00:00:27,590 --> 00:00:33,590
+ومختصرها إن ال H لو كانت non-empty هال condition
+
+3
+00:00:33,590 --> 00:00:37,470
+الأول و ال condition التانيلو أخدت two elements في
+
+4
+00:00:37,470 --> 00:00:42,090
+ال group أو في ال subgroup و أثبت انه حصل ضرب
+
+5
+00:00:42,090 --> 00:00:45,770
+الأول في معكس الثاني موجود في هذه ال subset اللي
+
+6
+00:00:45,770 --> 00:00:50,010
+هي ال H يبقى ال H بتكون is a subgroup و أخدنا على
+
+7
+00:00:50,010 --> 00:00:55,500
+ذلك أربعة أمثلة وهذا هو المثال رقم خمسةالمثال رقم
+
+8
+00:00:55,500 --> 00:00:59,800
+خمسة جيئ به في إحدى الامتحانات في إحدى السنوات
+
+9
+00:00:59,800 --> 00:01:04,180
+السابقة اللي هو في الجامعة الإسلامية عندنا هنا
+
+10
+00:01:04,180 --> 00:01:10,580
+ولذلك أحببت أن أحل هذا السؤال كمثال على موضوع هذه
+
+11
+00:01:10,580 --> 00:01:15,050
+النظريةالسؤال بيقول little h بيبقى subset of a
+
+12
+00:01:15,050 --> 00:01:19,610
+group g بيبقى احنا اخدنا h subset من ال group g
+
+13
+00:01:19,610 --> 00:01:25,310
+اخدنا ال element او ال set a هي كل العناصر a اللي
+
+14
+00:01:25,310 --> 00:01:31,630
+موجودة في g بحيث ان ال a h تساوي h a يعني كل
+
+15
+00:01:31,630 --> 00:01:37,190
+العناصر اللي بتبقى commutative مع عناصر h فقط
+
+16
+00:01:52,630 --> 00:01:56,840
+الخطوة الأولى بدي أثبت ان الـ H is non-emptyبعدين
+
+17
+00:01:56,840 --> 00:02:04,440
+باخد اشياء موجودة في a و اثبت ان الاول في معكس
+
+18
+00:02:04,440 --> 00:02:09,280
+الثاني موجود في a يفجر بعدين بقول له solution
+
+19
+00:02:09,280 --> 00:02:19,400
+الخطوة الأولى ان ال a is non empty السبب because
+
+20
+00:02:22,540 --> 00:02:28,180
+طبعا ال identity elements مع ناسر g كلها وبالتالي
+
+21
+00:02:28,180 --> 00:02:37,440
+مع ناسر h because ال E موجود في ال A since السبب
+
+22
+00:02:37,440 --> 00:02:43,740
+في ذلك ان ال E في ال H هو ال H في ال E طب ال H في
+
+23
+00:02:43,740 --> 00:02:44,940
+E ايش بيعطينا
+
+24
+00:02:53,110 --> 00:02:58,350
+هذه النقطة الأولى هي a non empty النقطة الثانية
+
+25
+00:02:58,350 --> 00:03:05,530
+بدي اخد عنصرين موجودين في ال set a يبقى بداجي اقول
+
+26
+00:03:05,530 --> 00:03:12,070
+افترض ان ال a و ال b موجودات في ال aطيب هذا معناه
+
+27
+00:03:12,070 --> 00:03:21,110
+then ال a h بده يساوي ال h a and ال b h بده يساوي
+
+28
+00:03:21,110 --> 00:03:27,530
+ال h b هذا معناه بدالي امسك هذا ال element اللي
+
+29
+00:03:27,530 --> 00:03:32,410
+عندنا هذالو ذهبت و ضربت من جهة الشمال في ال B
+
+30
+00:03:32,410 --> 00:03:37,670
+inverse و ضربت من جهة اليمين في ال B inverse بدي
+
+31
+00:03:37,670 --> 00:03:42,010
+أشوف الدوصل ليه طب انت بكتره في ال B inverse ليش؟
+
+32
+00:03:42,010 --> 00:03:46,930
+بقوله اه انا فرض ان A و B موجودة في A إذا هي
+
+33
+00:03:46,930 --> 00:03:52,220
+موجودة وين؟فتش موجودة في a يعني موجودة في g
+
+34
+00:03:52,220 --> 00:03:58,080
+الأصلية لأن كل عناصر a موجودة في g اذا هذه موجودة
+
+35
+00:03:58,080 --> 00:04:04,960
+في g يبقى ال b inverse موجود في g لكن انا بدي اثبت
+
+36
+00:04:04,960 --> 00:04:10,680
+ان ال a b inverse موجود في a بمعنى اخر ان ال a b
+
+37
+00:04:10,680 --> 00:04:15,240
+inverse في ال set a بدي ساوي ال a في ال a b
+
+38
+00:04:15,240 --> 00:04:20,810
+inverseإن أثبت هذا الكلام بيتم المطلوب يبقى بده
+
+39
+00:04:20,810 --> 00:04:25,050
+أجعل هذه و أضرب من جهة اليمين في ال B inverse و من
+
+40
+00:04:25,050 --> 00:04:29,510
+جهة الشمال كمان وين في ال B inverse يبقى هذا معناه
+
+41
+00:04:29,510 --> 00:04:36,350
+انه B inverse في BH بده يساوي هاي ضربنا من جهة
+
+42
+00:04:36,350 --> 00:04:43,730
+الشمال يبقى بنتجينا B inverse H BH يبقى ضربنا خليا
+
+43
+00:04:43,730 --> 00:04:47,830
+من جهة الشمالمرة جيب نضرب من جهة اليمين ولا يمك
+
+44
+00:04:47,830 --> 00:04:53,530
+ولا نضربهم مرة واحدة رياحة انها اضرب من جهة الشمال
+
+45
+00:04:53,530 --> 00:04:58,990
+ومن جهة اليمين في ال B inverse يبقى بدي جينا كمان
+
+46
+00:04:58,990 --> 00:05:05,290
+هنا B inverse بدي ساوي ال B inverse في ال BH بدي
+
+47
+00:05:05,290 --> 00:05:12,010
+ساوي ال B inverse H في ال BB inverse بالشكل اللي
+
+48
+00:05:12,010 --> 00:05:18,260
+عندنابالدراجة هذا ال element فيه معكوس ويش بيعطينا
+
+49
+00:05:18,260 --> 00:05:24,500
+ال identity يبقى هذا بدري يعطينا ان ال E H B
+
+50
+00:05:24,500 --> 00:05:26,640
+inverse بدري ساوي
+
+51
+00:05:38,550 --> 00:05:44,150
+بإنفرس هذي مباشرة هذه ضربت من جهة الشمال و من جهة
+
+52
+00:05:44,150 --> 00:05:48,790
+اليمين هنا ضربت من جهة الشمال و من جهة اليمين طيب
+
+53
+00:05:48,790 --> 00:05:53,050
+هذه الان ال بي بي انفرس بتعطينا ال identity يبقى
+
+54
+00:05:53,050 --> 00:05:59,630
+هدف السوى بي انفرس heبناءً عليه الـ identity في أي
+
+55
+00:05:59,630 --> 00:06:03,250
+element و الله في أي set بيعطينا نفس ال element أو
+
+56
+00:06:03,250 --> 00:06:09,750
+نفس ال set يبقى هذا معناه ان ال H P inverse بده
+
+57
+00:06:09,750 --> 00:06:12,250
+يساوي P inverse H
+
+58
+00:06:21,020 --> 00:06:26,020
+أنا بدي أثبت أن الـ A B inverse موجود في الـ A
+
+59
+00:06:26,020 --> 00:06:30,560
+بمعنى أن الـ A B inverse مضروب في الـ H بيساوي الـ
+
+60
+00:06:30,560 --> 00:06:35,440
+H في الـ A B inverse المعادلة هذه مافيش فيها Aلكن
+
+61
+00:06:35,440 --> 00:06:40,420
+لو ضربت الطرفين في A بوصل لمن؟ للمطلوب اذا حاجة
+
+62
+00:06:40,420 --> 00:06:45,980
+لهذه و اروح اضرب الطرفين من جهة الشمال في من؟ في
+
+63
+00:06:45,980 --> 00:06:52,900
+ال A يبقى هذا بدي اعطيك انه A H B inverse بدي ساوي
+
+64
+00:06:52,900 --> 00:07:00,430
+A B inverse H بالشكل اللي عندناطب احنا فيها معلومة
+
+65
+00:07:00,430 --> 00:07:08,070
+حتى الآن لم نستخدمها ليمين ال a h بده يسوي h a إذا
+
+66
+00:07:08,070 --> 00:07:15,460
+بقدر أشيل هذه ال a h و أكتب بدالها ال h aيبقى هذا
+
+67
+00:07:15,460 --> 00:07:23,360
+معناه ان ال a h بده اكتبها h a في ال b inverse بده
+
+68
+00:07:23,360 --> 00:07:28,840
+يساوي من خاصية ال associativity بقدر اقول هذه a b
+
+69
+00:07:28,840 --> 00:07:33,420
+inverse مضروب في ال h يبقى هذه بده يساوي a b
+
+70
+00:07:33,420 --> 00:07:39,140
+inverse مضروبة في مين في ال hيبقى بناء عليه كمان
+
+71
+00:07:39,140 --> 00:07:44,300
+مرة من خاصية ال associativity بصير عندنا ال H في
+
+72
+00:07:44,300 --> 00:07:51,140
+ال A B inverse بده يساوي ال A B inverse في ال H
+
+73
+00:07:51,140 --> 00:07:55,720
+ايش تفسير كل ذلك؟ معناه ان ال A B inverse موجود
+
+74
+00:07:55,720 --> 00:08:04,310
+وين؟في a يبقى سا ال a بي انفرس موجود في ال a هذا
+
+75
+00:08:04,310 --> 00:08:10,710
+بدي يعطينا ان ال a is a sub group من g أثبتنا في
+
+76
+00:08:10,710 --> 00:08:14,450
+الأول ان ال a is non empty وجدنا فيها ال identity
+
+77
+00:08:14,450 --> 00:08:18,970
+element أخدنا two elements موجودة في a أثبتنا ان
+
+78
+00:08:18,970 --> 00:08:23,390
+الأول في معكوس الثاني موجود في اللي هو ال a
+
+79
+00:08:23,630 --> 00:08:28,690
+وبالتالي ال ASA subgroup من مين؟ من G و مرة تانية
+
+80
+00:08:28,690 --> 00:08:34,570
+بقول هذا السؤال جئنا به في إحدى الامتحانات السابقة
+
+81
+00:08:34,570 --> 00:08:40,470
+على أي حال احنا حتى الآن أثبتنا نظرية واحدةبواسطة
+
+82
+00:08:40,470 --> 00:08:45,030
+تحالية بدل المثال خمسة على إثبات إن الـ subset
+
+83
+00:08:45,030 --> 00:08:47,850
+اللي باخدها كيف هي ال subgroup من ال group
+
+84
+00:08:47,850 --> 00:08:52,290
+الأساسية عن طريق إثبات نقطتين النقطة الأولى إن ال
+
+85
+00:08:52,290 --> 00:08:55,930
+subset اللي باخدها non empty والنقطة الثانية لو
+
+86
+00:08:55,930 --> 00:08:59,430
+أخدت elements في هذه ال set بدي أثبت إن الأول في
+
+87
+00:08:59,430 --> 00:09:05,750
+معكوس الثاني موجود في هذه ال set طيب نجي الآن
+
+88
+00:09:05,750 --> 00:09:12,590
+لنظرية ثانيةيبقى ال theorem النظرية
+
+89
+00:09:12,590 --> 00:09:25,190
+التانية بتقول مات let ال H be a non empty subset
+
+90
+00:09:25,190 --> 00:09:28,630
+of
+
+91
+00:09:28,630 --> 00:09:31,990
+a group G
+
+92
+00:09:38,050 --> 00:09:47,510
+الـ H is a subgroup من G if and only if ال A و ال
+
+93
+00:09:47,510 --> 00:09:54,450
+B موجودة في H whenever عندما
+
+94
+00:09:54,450 --> 00:10:04,690
+ال A و ال B موجود في H and ال A inverse belongs to
+
+95
+00:10:04,690 --> 00:10:07,230
+H whenever
+
+96
+00:10:10,270 --> 00:10:16,730
+الـ A موجودة
+
+97
+00:10:16,730 --> 00:10:17,450
+في إتش
+
+98
+00:10:32,050 --> 00:10:34,830
+النظرية الثانية اللي عندنا بالنسبة للـ subgroups
+
+99
+00:10:34,830 --> 00:10:40,430
+بتقول ما يأتي H non-empty subset of A group G يبقى
+
+100
+00:10:40,430 --> 00:10:44,690
+نفس ال condition الأول تبع من؟ تبع النظرية السابقة
+
+101
+00:10:44,690 --> 00:10:48,670
+الآن كان عندي condition واحد في النظرية السابقة
+
+102
+00:10:48,670 --> 00:10:52,790
+حاصل ضرب الأول في معكوس الثاني موجود في H إذا two
+
+103
+00:10:52,790 --> 00:10:56,870
+elements موجودات في H هنا هذا ال condition فصل على
+
+104
+00:10:56,870 --> 00:11:03,060
+شكل two conditionsH Subgroup من G F and only F
+
+105
+00:11:03,060 --> 00:11:09,660
+حاصل ضرب A في B في H لأي عنصرين A وB موجودة في H
+
+106
+00:11:09,660 --> 00:11:14,280
+والمعكوس لأي element موجود في H إذا كان هذا ال
+
+107
+00:11:14,280 --> 00:11:19,560
+element موجود في H بتطلع للنظرية بتقول F and only
+
+108
+00:11:19,560 --> 00:11:24,840
+F يبقى البرهان بيصير في اتجاهينيبقى بدي أخد
+
+109
+00:11:24,840 --> 00:11:31,100
+الاتجاه الأول بدي أقول له assume افترض ان ال H is
+
+110
+00:11:31,100 --> 00:11:38,380
+a subgroup من G مدام subgroup من G لو أخدت أي two
+
+111
+00:11:38,380 --> 00:11:42,820
+elements موجودة في H حصل ضربه في H ولا لا لأن
+
+112
+00:11:42,820 --> 00:11:50,550
+عليها binary operation بدي يطلع في H يبقى thenالـ
+
+113
+00:11:50,550 --> 00:11:58,570
+A B موجود في H الـ for all A و B اللي موجودة في H
+
+114
+00:11:58,570 --> 00:12:06,230
+and الـ B inverse موجود في H لكل الـ B اللي موجودة
+
+115
+00:12:06,230 --> 00:12:12,310
+في H يبقى الاتجاه الأول مافيش فيه مشكلةإذا هذه الـ
+
+116
+00:12:12,310 --> 00:12:16,010
+subgroup يبقى لو أخدت any two elements موجودات في
+
+117
+00:12:16,010 --> 00:12:21,070
+H بدي يكون A star B موجود في H والأمر الثاني مادام
+
+118
+00:12:21,070 --> 00:12:25,950
+subgroup يعني هي group تحت نفس ال operation يبقى
+
+119
+00:12:25,950 --> 00:12:30,330
+أي عنصر فيها له معكوس إذا ال B inverse موجود فيهش
+
+120
+00:12:30,330 --> 00:12:35,690
+لان بدنا نمشي لعملية العكسية يبقى conversely
+
+121
+00:12:35,690 --> 00:12:38,870
+assume
+
+122
+00:12:38,870 --> 00:12:47,710
+أفترضإن ال A B موجود في H لكل ال A و ال B اللي
+
+123
+00:12:47,710 --> 00:12:55,230
+belong to H and ال B inverse موجود في H لكل ال B
+
+124
+00:12:55,230 --> 00:12:56,730
+اللي موجودة في H
+
+125
+00:13:01,210 --> 00:13:07,290
+ماذا بدنا نثبت؟ الـ H Subgroup ممتاز جدا طيب بدأجي
+
+126
+00:13:07,290 --> 00:13:12,090
+أقوله الأولاني بدي أحاول أستفيد من كل معطية معطية
+
+127
+00:13:12,090 --> 00:13:16,390
+عندنا هنا أنا عندي أخدت elements ضربتهم وجدتهم في
+
+128
+00:13:16,390 --> 00:13:20,910
+H أخدت element في الـ H وجدته بعكوس في H بقولي تحت
+
+129
+00:13:20,910 --> 00:13:25,150
+ال two conditions الاتنين هذول بدي أثبت ان الـ H
+
+130
+00:13:25,150 --> 00:13:32,730
+is a subgroup من من جي الأصليةبقوله كويس الان
+
+131
+00:13:32,730 --> 00:13:41,810
+since ال B موجود في H بما ان B موجود في H we have
+
+132
+00:13:41,810 --> 00:13:49,810
+ال B انفرس موجود في H طب من وين جبت الكلام هذا من
+
+133
+00:13:49,810 --> 00:13:53,530
+ال second condition من ال condition الثاني يبقى
+
+134
+00:13:53,530 --> 00:13:59,510
+هذا from the second condition
+
+135
+00:14:02,590 --> 00:14:08,590
+طيب احنا ماخدين هنا ال a و ال b موجودة في h الآن
+
+136
+00:14:08,590 --> 00:14:20,190
+ال a موجودة في h كويس؟ and ال a في b belongs to h
+
+137
+00:14:20,190 --> 00:14:25,850
+لكل اللي هو ال a و ال b اللي موجودة في h implies
+
+138
+00:14:25,850 --> 00:14:33,430
+هذا الآن موجود في h صح؟و هذا موجود في H و ال
+
+139
+00:14:33,430 --> 00:14:38,030
+condition هذا حاصل ضرب اي عنصر من H موجود في H إذا
+
+140
+00:14:38,030 --> 00:14:43,930
+بدي أضرب الاتنين هدول في بعض ي بجا بدي أصير A B
+
+141
+00:14:43,930 --> 00:14:51,740
+inverse موجود في Hالان الـ H non-empty مُعطَى أخدت
+
+142
+00:14:51,740 --> 00:14:56,400
+الـ two elements موجودات في H وجدت حصل ضرب الأول
+
+143
+00:14:56,400 --> 00:14:59,480
+في التاني موجودة في H يبقى الـ H is a subgroup
+
+144
+00:14:59,480 --> 00:15:05,680
+بالنظرية السابقة يبقى هذا بدّي يعطينا أن الـ H is
+
+145
+00:15:05,680 --> 00:15:11,660
+a subgroup من G from the previous
+
+146
+00:15:13,190 --> 00:15:17,590
+الثيوريم يبقى بالنظرية السابقة هذه سارة subgroup
+
+147
+00:15:17,590 --> 00:15:28,470
+وهو المطلوب نعطي مثال توضيحي example let
+
+148
+00:15:28,470 --> 00:15:39,110
+ال g بدها تساوي r star اللي بدها تساوي ال r ناقص
+
+149
+00:15:39,110 --> 00:15:41,370
+ال zero under
+
+150
+00:15:46,570 --> 00:15:56,170
+multiplication تحت عملية الضرب little h بدها تساوي
+
+151
+00:15:56,170 --> 00:16:03,510
+كل العناصر x اللي موجودة في g بحيث ان ال x بدها
+
+152
+00:16:03,510 --> 00:16:08,070
+تساوي واحد or ال x is irrational
+
+153
+00:16:11,120 --> 00:16:21,100
+عدد غير نسبي and ال k بدأت ساوي كل ال x اللي
+
+154
+00:16:21,100 --> 00:16:26,280
+موجودة فيه بحيث ان ال x greater than or equal to
+
+155
+00:16:26,280 --> 00:16:34,160
+oneالسؤال هل هدول subgroups ام لا R
+
+156
+00:16:34,160 --> 00:16:44,840
+H N K subgroups of
+
+157
+00:16:44,840 --> 00:16:50,240
+G هل هدول subgroups من G ولا لأ solution
+
+158
+00:17:10,540 --> 00:17:14,980
+خلّيني أقول لكم هنا الست اللي انا للا أسطار اللي
+
+159
+00:17:14,980 --> 00:17:19,540
+مجموعة الأعداد الحقيقية بدي أشيل منها من ال zero و
+
+160
+00:17:19,540 --> 00:17:22,940
+ال binary operation اللي هي عملية الضرب العادية
+
+161
+00:17:22,940 --> 00:17:26,500
+بدي أعملية الضرب على مجموعة الأعداد الحقيقية بعد
+
+162
+00:17:26,500 --> 00:17:31,280
+ما أشيل منها ال zero أخدت منها subset مجموعة جزية
+
+163
+00:17:31,280 --> 00:17:35,750
+submitted مين هي هذه؟هي كل العناصر اللي موجودة في
+
+164
+00:17:35,750 --> 00:17:39,650
+هذه ال element يوعبه إيه؟ ال X بده يساوي واحد اللي
+
+165
+00:17:39,650 --> 00:17:43,870
+هو ال identity element تبع عملية الضرب أو ال X
+
+166
+00:17:43,870 --> 00:17:50,470
+يكون irrational طيب التانية ال K كل ال X اللي
+
+167
+00:17:50,470 --> 00:17:55,390
+موجودة في G بحيث ال X greater than or equal to 1
+
+168
+00:17:55,390 --> 00:18:01,390
+بيسأل هل هدول subgroups أم لا؟ بنقوله كويس المثال
+
+169
+00:18:01,390 --> 00:18:05,790
+هذا جاي بعد مين؟بعد النظرية اذا انا بدي احاول اطبق
+
+170
+00:18:05,790 --> 00:18:09,730
+النظرية هذه واشوف شو اللي بيصير اذا تطبقت النظرية
+
+171
+00:18:09,730 --> 00:18:13,270
+بيبقى هم ال seven groups اختل اي شرط من الشروط
+
+172
+00:18:13,270 --> 00:18:17,590
+اللي موجودة فيها يبقى ماهياش seven groups طيب لأ
+
+173
+00:18:17,590 --> 00:18:21,310
+لو جيت هنا على ال H بيقول لي اما ال X بدي اسيه
+
+174
+00:18:21,310 --> 00:18:25,830
+واحد وهو ال identity elementهذا هو وضع الطبيعي or
+
+175
+00:18:25,830 --> 00:18:29,290
+الـ x يجب أن يكون irrational يعني هذا عندما نحب
+
+176
+00:18:29,290 --> 00:18:34,410
+الـ or تعني ال union يبقى العناصر هم الواحد الصحيح
+
+177
+00:18:34,410 --> 00:18:39,570
+وال irrational number تمام؟ أريد أن أشوف هل هذه
+
+178
+00:18:39,570 --> 00:18:44,570
+closed under multiplication بمعنى أنه لو أخذت two
+
+179
+00:18:44,570 --> 00:18:50,730
+elements موجودات في ال group هل حاصل ضربه ما يكون
+
+180
+00:18:50,730 --> 00:18:54,500
+في ال group ولا لأ؟السؤال هو، ضروري الـ two
+
+181
+00:18:54,500 --> 00:18:58,560
+elements اللي أخدهم يكونوا مختلفات عن بعض؟ ليس
+
+182
+00:18:58,560 --> 00:19:03,600
+بالضرورة، ممكن ال element و نفسه، تمام؟ ممكن مشان
+
+183
+00:19:03,600 --> 00:19:06,320
+تبقى close، سواء ضربته في نفسه إن شاء الله تضربه
+
+184
+00:19:06,320 --> 00:19:09,860
+في نفسه عشرين مرة ولا تضربه في أي element آخر، بدي
+
+185
+00:19:09,860 --> 00:19:15,160
+يكون موجود في H إن كانت subgroup طيب، الآن أنا
+
+186
+00:19:15,160 --> 00:19:22,590
+أدعي إن الـH هذه is not a subgroup من هناانا ادعى
+
+187
+00:19:22,590 --> 00:19:29,570
+طيب شو السبب because جذر
+
+188
+00:19:29,570 --> 00:19:34,390
+تلاتة موجود في itch ولا لا يا شباب مش جذر تلاتة
+
+189
+00:19:34,390 --> 00:19:42,930
+irrational number and جذر تلاتة مضروب في جذر تلاتة
+
+190
+00:19:42,930 --> 00:19:49,110
+بده يساوي قدر هل التلاتة irrational number لأ مش
+
+191
+00:19:49,110 --> 00:19:57,470
+موجود في itchيبقى أنا أخدت عنصرين من H لجأت حاصل
+
+192
+00:19:57,470 --> 00:20:03,030
+ضربهما مش موجود في H معناته الـ H هذه ما هياش
+
+193
+00:20:03,030 --> 00:20:06,750
+subgroup يختل ال condition الأول في النظرية اللي
+
+194
+00:20:06,750 --> 00:20:13,070
+ذكرناها قبل قليل الأن أنا ده أدعي كذلك أن الـ H is
+
+195
+00:20:13,070 --> 00:20:15,410
+not a subgroup من G
+
+196
+00:20:19,030 --> 00:20:27,950
+السؤال لماذا؟ لأن اي
+
+197
+00:20:27,950 --> 00:20:37,690
+element يأتي في بالي موجود في كيه لأن الست هذه
+
+198
+00:20:37,690 --> 00:20:43,930
+موجودة في كيه لأن عناصر كيه من واحد واطلع
+
+199
+00:20:46,730 --> 00:20:53,790
+أنا روحت أخدت الستة موجودة هادئة في كتر شو معكوس
+
+200
+00:20:53,790 --> 00:21:00,660
+الستة؟ سُدسانه ضرب عملية الضرب العادية يبقى هذا
+
+201
+00:21:00,660 --> 00:21:06,680
+بده يعطينا انه معكوس الستة ليه ستة inverse يساوي
+
+202
+00:21:06,680 --> 00:21:10,320
+واحد على ستة لإنه ستة في سُدس هو اللي بالساوية
+
+203
+00:21:10,320 --> 00:21:16,680
+واحدة صحيح السؤال هو هل السُدس هذا موجود في ك؟ لأ
+
+204
+00:21:16,680 --> 00:21:22,540
+لإنه واحد واطلعهذا أقل من الواحد يبقى هذا does not
+
+205
+00:21:22,540 --> 00:21:27,540
+belong to K معناته اختلت الشرط الثاني اذا اخدت
+
+206
+00:21:27,540 --> 00:21:32,540
+element ال H لقيته معكوسه ما هوش في H اذا لا يمكن
+
+207
+00:21:32,540 --> 00:21:38,220
+لهذه الست او هذه ان تكون subgroup ملي جروب اللي
+
+208
+00:21:38,220 --> 00:21:42,940
+موجودة نيجي ناخد النظرية رقم تلاتة على ال
+
+209
+00:21:42,940 --> 00:21:53,460
+subgroups بيقول ال Hبا non-empty نفس ال condition
+
+210
+00:21:53,460 --> 00:22:00,900
+هو هو في النظريات الثلاث non-empty بس أضافنا عليها
+
+211
+00:22:00,900 --> 00:22:06,180
+finite subset
+
+212
+00:22:06,180 --> 00:22:09,320
+of
+
+213
+00:22:09,320 --> 00:22:11,480
+a group G
+
+214
+00:22:18,370 --> 00:22:32,950
+ثم الـ H هو مجلد من G إذا كان الـ H مقفل
+
+215
+00:22:32,950 --> 00:22:40,370
+تحت عمل
+
+216
+00:22:40,370 --> 00:22:43,650
+G
+
+217
+00:23:02,130 --> 00:23:09,910
+مرة تانية بقول جالي H non-empty زاد على نظريتين
+
+218
+00:23:09,910 --> 00:23:16,190
+الجالي finite subset يبقى عدد المحدود في هذه الست
+
+219
+00:23:16,190 --> 00:23:21,470
+عدد ال subset اللي أخدته محدود تمام بيقول لذن ال H
+
+220
+00:23:21,470 --> 00:23:26,010
+is a subgroup إذا كانت ال H closed under the
+
+221
+00:23:26,010 --> 00:23:29,510
+operation شو يعني closed under the operation يعني
+
+222
+00:23:29,510 --> 00:23:35,110
+ال condition هذاهذا يعني أن الـ H مقفل تحت الـ
+
+223
+00:23:35,110 --> 00:23:40,570
+operation يعني A*)B يكون موجود في H لكل الـ A والـ
+
+224
+00:23:40,570 --> 00:23:45,630
+B الموجودة في H يبقى في المقابل شال ال condition
+
+225
+00:23:45,630 --> 00:23:51,130
+التاني هذا واستعاد عنه بمين بأن الـ H is finite
+
+226
+00:23:51,130 --> 00:23:56,290
+إذن لو كانت ال group finite يا شباب و ال subsidy
+
+227
+00:23:56,290 --> 00:24:00,530
+اللي أخدته من ال group كان إجباري هيصير finite
+
+228
+00:24:01,220 --> 00:24:06,040
+مظبوط يبقى كان ال subgroup non-empty وفي نفس الوقت
+
+229
+00:24:06,040 --> 00:24:12,060
+هيكون finite يعني عدد العناصر فيه عددا محدودا بدي
+
+230
+00:24:12,060 --> 00:24:16,580
+اثبت ان هذا ال subgroup يكفي انه تاخد two elements
+
+231
+00:24:16,580 --> 00:24:22,920
+موجودات في H و تثبت ان حاصل ضربهما موجود في H طبقا
+
+232
+00:24:22,920 --> 00:24:28,800
+لهذه النظرية ان تم ذلك يبقى ال H is a subgroupيبقى
+
+233
+00:24:28,800 --> 00:24:34,380
+الآن احنا بداية اقوله افترض ان ال a و ال b موجود
+
+234
+00:24:34,380 --> 00:24:45,220
+في h and ال a و ال b موجود في h تمام يبقى انا اخد
+
+235
+00:24:45,220 --> 00:24:53,580
+اي عنصرين في جي و افرض انه حاصل ضاربهميعني هذا
+
+236
+00:24:53,580 --> 00:24:58,840
+اللي معناه ان ال H is closed under the operation
+
+237
+00:24:58,840 --> 00:25:05,320
+تمام؟ يبقى هي المعنى تبعها طيب بيقوللي اثبت ان هذه
+
+238
+00:25:05,320 --> 00:25:10,780
+عبارة عن ايه؟ عن ال subgroup بقوله كويس يبقى الآن
+
+239
+00:25:10,780 --> 00:25:17,340
+انا بدي احاول اطبق النظرية الأولى مثلا كيف النظرية
+
+240
+00:25:17,340 --> 00:25:17,880
+الأولى؟
+
+241
+00:25:22,290 --> 00:25:28,350
+أو حاصل ضرب الأول في الثاني موجود في H أو حاصل
+
+242
+00:25:28,350 --> 00:25:35,170
+الضرب موجود في H يكفيني أن أثبت أن معكوس أي عنصر
+
+243
+00:25:35,170 --> 00:25:39,030
+موجود في H إذا طبقًا لهذه النظرية تصبح هذه
+
+244
+00:25:39,030 --> 00:25:41,390
+subgroup موجودة
+
+245
+00:25:44,750 --> 00:25:49,710
+يبقى الـ condition الأول متحقق ضايل عليه أثبت مين
+
+246
+00:25:49,710 --> 00:25:54,690
+ال condition التاني بنكون خلصه يعني لو أخد أي عنصر
+
+247
+00:25:54,690 --> 00:25:59,350
+موجود في itch أثبت أنه معكوس موجود في itch بقدر
+
+248
+00:25:59,350 --> 00:26:05,430
+أطبق النظرية هذه مباشرة لذلك هروحض أي عنصر موجود
+
+249
+00:26:05,430 --> 00:26:10,630
+وين في itch وشوف وين بتوجه الدنيايبقى باجي بقوله
+
+250
+00:26:10,630 --> 00:26:17,070
+little a موجود في itch من ال a أنا مش عارف يبقى
+
+251
+00:26:17,070 --> 00:26:23,590
+باجي بقوله if ال a بدرساه ال identity لو طلع
+
+252
+00:26:23,590 --> 00:26:34,150
+لأخدته عشوائيا هذا هو ال identity then أخدته
+
+253
+00:26:34,150 --> 00:26:41,590
+في itch طلع من ال identity يبقى thenالـ A Inverse
+
+254
+00:26:41,590 --> 00:26:46,570
+موجود
+
+255
+00:26:46,570 --> 00:26:51,450
+في H يعني انه اتطبق من ال condition التاني
+
+256
+00:26:51,450 --> 00:26:58,680
+وبالتالي صارت الـ H is Aيبقى هذا بده يعطينا ان ال
+
+257
+00:26:58,680 --> 00:27:03,600
+h sub group من جيه هذا لو طلع ال element اللي هو
+
+258
+00:27:03,600 --> 00:27:11,280
+ال identity طيب لو ما طلعش يبقى f ال a لا تساوي ال
+
+259
+00:27:11,280 --> 00:27:18,120
+a بمعنى اخر لا يمكن يكون ال order لل a واحد صحيح
+
+260
+00:27:18,120 --> 00:27:22,330
+لان لو كان واحد صحيح بطلع فعلاطيب احنا في عندنا
+
+261
+00:27:22,330 --> 00:27:28,470
+معلومة حتى الآن لم نستخدمها اللي هو مين؟ finite
+
+262
+00:27:28,470 --> 00:27:34,170
+يعني عدد العناصر في H محدود طب استنى شوية ايش
+
+263
+00:27:34,170 --> 00:27:39,610
+بيقول هنا انه حاصل ضرب اي عددين من H موجود في H
+
+264
+00:27:39,610 --> 00:27:46,870
+السؤال هو هل A تربيع موجود في H؟ لأنه ايه فيه؟ طب
+
+265
+00:27:46,870 --> 00:27:52,680
+هل A تكييب موجود في H؟لأن a تربية في h و a في h
+
+266
+00:27:52,680 --> 00:27:57,940
+يبقى a تربية هل a أس أربعة موجود في a كل a أربعة
+
+267
+00:27:57,940 --> 00:28:04,500
+أو أي أس يطلع موجود في h يبقى f في a لا تساوي ال a
+
+268
+00:28:04,500 --> 00:28:16,000
+then according طبقا to the condition
+
+269
+00:28:17,640 --> 00:28:24,480
+طبقا للشرط ان ال a بي موجود في h لكل ال a و ال b
+
+270
+00:28:24,480 --> 00:28:32,040
+اللي موجودة في h بقول we have ان ال a و ال a تربيع
+
+271
+00:28:32,040 --> 00:28:40,960
+و ال a تكيب ومشي لجد ما بدك are all in h كلهم هذول
+
+272
+00:28:40,960 --> 00:28:48,250
+موجودات في ايه؟ موجودات في h ممتاز جداطيب الان ال
+
+273
+00:28:48,250 --> 00:28:53,990
+H finite افترض فيها خمسين عنصر وانا حاطيت ا
+
+274
+00:28:53,990 --> 00:29:02,030
+والسبعين بدي يكون موجود فيها ولا لا؟ ليش؟ مش ال H
+
+275
+00:29:02,030 --> 00:29:07,870
+عدد العناصر خمسين يبقى عنصر حاطيت فلوس عشرة و الله
+
+276
+00:29:07,870 --> 00:29:12,130
+عشرين و الله خمسمية بدي يكون فيهامظبوط ولا لأ بس
+
+277
+00:29:12,130 --> 00:29:17,170
+ماهي اللي بدى يحصل ان ال a سبعين هذه متساوي اعشرين
+
+278
+00:29:17,170 --> 00:29:22,090
+مظبوط ولا لأ زى ايه زى عملية المقياس a modulo n
+
+279
+00:29:22,090 --> 00:29:26,210
+بعد ما زيت ال n كله برجع بصير فيها مظبوط ولا لأ
+
+280
+00:29:26,210 --> 00:29:31,240
+طيب ايه اللي حكمنا يا عزيزي لأن هذه finiteفاينيت
+
+281
+00:29:31,240 --> 00:29:36,980
+يبقى a مرفوعة لأي أس عندك بدي يكون من ضمن هدول بدي
+
+282
+00:29:36,980 --> 00:29:42,520
+يكون موجود وين؟ موجود في إتش شئنا أم أبينا تمام
+
+283
+00:29:42,520 --> 00:29:50,640
+يبقى هنا هذا معناته these elements
+
+284
+00:29:50,640 --> 00:29:54,020
+are
+
+285
+00:29:54,020 --> 00:29:59,420
+not all disjoint
+
+286
+00:30:00,850 --> 00:30:04,530
+مش كل هدول بدهم يكونوا كل واحد مختلف عن التاني
+
+287
+00:30:04,530 --> 00:30:10,110
+لازم ألاجي بعضهم الأس تبعه مختلف عن التاني لكن
+
+288
+00:30:10,110 --> 00:30:14,710
+موجود في H مش
+
+289
+00:30:14,710 --> 00:30:23,630
+كلهم يبقى let ال A I بده يساوي A J مثلا افترض ان
+
+290
+00:30:23,630 --> 00:30:30,540
+ال I بيساوي ال J و ال I هذي أكبر من Jهي الكبيرة
+
+291
+00:30:30,540 --> 00:30:39,920
+فيهم طيب هذا يعني لو ضربت الطرفين من جهة اليمين في
+
+292
+00:30:39,920 --> 00:30:50,320
+معكوس هذه يبقاش بدرسي يعني AI AJ inverse بدرساوي
+
+293
+00:30:50,320 --> 00:30:54,380
+AJ AJ inverse
+
+294
+00:30:56,640 --> 00:31:03,440
+هذا معناه a i في a سالب j يساوي ال element في
+
+295
+00:31:03,440 --> 00:31:10,980
+معكوسه كم يعطينا ال identity يبقى هذا يعطينا a i
+
+296
+00:31:10,980 --> 00:31:18,760
+minus j يساوي ال identity element طب السؤال هو لما
+
+297
+00:31:18,760 --> 00:31:24,880
+أقول i ناقص j معقول يكون الفرق بينهم واحد يا شباب
+
+298
+00:31:28,780 --> 00:31:36,160
+لو كان الفرق بينهم واحد لأصبح
+
+299
+00:31:36,160 --> 00:31:42,500
+A أس واحد يسوى ال identity بيطلع من أن ال A هو بال
+
+300
+00:31:42,500 --> 00:31:48,130
+E لكن أنا شرقإن الـ A لا يمكن أن يكون الـ E إذا لا
+
+301
+00:31:48,130 --> 00:31:53,270
+يمكن أن يكون الفرق فيما بينهما واحد صحيح يبقى
+
+302
+00:31:53,270 --> 00:31:59,330
+الفرق فيما بينهم ماله أكبر من واحد يبقى ال I نقص
+
+303
+00:31:59,330 --> 00:32:04,830
+ال J أكبر من واحد على الأقل بيكون اتنين تلاتة
+
+304
+00:32:04,830 --> 00:32:12,660
+أربعة الاخرينبما أن الـ I ناقص D أكبر من 1 يبقى
+
+305
+00:32:12,660 --> 00:32:19,580
+هذا بطل يصير الـ identity بطل بلاش هذا معناه ان
+
+306
+00:32:19,580 --> 00:32:28,240
+الـ A I minus G يساوي الـ A في الـ A I minus G
+
+307
+00:32:28,240 --> 00:32:35,100
+minus الـ 1 خلته A أس واحد في الـ A أس I ناقص D
+
+308
+00:32:35,100 --> 00:32:41,980
+ناقص واحدتمام؟ مظبوط هيك؟ طلعت منهم ايه فقط و لا
+
+309
+00:32:41,980 --> 00:32:48,860
+غير هذا الكلام كله بسوى جداش ال identity element،
+
+310
+00:32:48,860 --> 00:32:55,050
+مظبوط؟طيب لو روحت ضربت في ال A inverse ضربت
+
+311
+00:32:55,050 --> 00:33:01,330
+المعادلة هذه في ال A inverse من جهة الشمال يبقى
+
+312
+00:33:01,330 --> 00:33:08,450
+ايش بيصير عندنا A I ناقص D ناقص 1 يسوى ال A
+
+313
+00:33:08,450 --> 00:33:17,530
+inverse السؤال هو هذا ههه هو عنصر من هذول ولا لا
+
+314
+00:33:20,970 --> 00:33:26,050
+هو واحد منهم صحيح ولا لأ؟ لأن الـH finite يبقى هذا
+
+315
+00:33:26,050 --> 00:33:33,150
+العنصر لازم يكون واحد من هذول هذا معناه ان الـA I
+
+316
+00:33:33,150 --> 00:33:40,130
+minus D minus 1 belongs to H مدان belongs to H
+
+317
+00:33:40,130 --> 00:33:47,170
+يبقى الـA inverse موجود في H يبقى تحقق ال
+
+318
+00:33:47,170 --> 00:33:51,130
+condition الثاني ولا لأ؟يبقى باجي بقوله by the
+
+319
+00:33:51,130 --> 00:33:55,850
+above theorem هذي صارت ال sub group يبقى هنا باجي
+
+320
+00:33:55,850 --> 00:34:04,250
+بقوله by the above theorem ال
+
+321
+00:34:04,250 --> 00:34:07,670
+H is a sub group من جي
+
+322
+00:34:14,000 --> 00:34:18,700
+عشان اللي كان سارح ياخد باله كويس اللي فاتته حاجة
+
+323
+00:34:18,700 --> 00:34:25,150
+يفهمها خلي بالك كدهأنا لم أجد non-empty مثل
+
+324
+00:34:25,150 --> 00:34:29,530
+النظريتين اللي فاتوا زيادة على ذلك ال subset اللي
+
+325
+00:34:29,530 --> 00:34:35,410
+أخدت عدد عناصرها finite عددا محدودا لو أخدت two
+
+326
+00:34:35,410 --> 00:34:39,550
+elements موجودة في اتش ولا جيت حاصل ضربهما موجودة
+
+327
+00:34:39,550 --> 00:34:42,510
+في اتش تحت هذا ال condition أو تحت ال condition
+
+328
+00:34:42,510 --> 00:34:46,290
+finite اللي اتش بتبقى ال subgroup من G هذا اللي
+
+329
+00:34:46,290 --> 00:34:51,850
+عايزين نثبتهيبقى انا عندي معطيات اتنين H non-empty
+
+330
+00:34:51,850 --> 00:34:55,950
+زي اللي جاب الهدا لكن ال non-empty هذا finite
+
+331
+00:34:55,950 --> 00:35:00,910
+وحاصل ضرب اي عنصر من H بلا G في H هذا ال condition
+
+332
+00:35:00,910 --> 00:35:05,250
+الثاني تحت ال two condition بثبت ان هذه السابع
+
+333
+00:35:05,250 --> 00:35:08,930
+جروس قلت له ماشي افترض ان ال A و ال B موجودة في ال
+
+334
+00:35:08,930 --> 00:35:11,750
+H و ال A و ال B موجودة في ال H هذه هي المعطيات
+
+335
+00:35:16,010 --> 00:35:20,050
+خُد element موجود في H
+
+336
+00:35:23,260 --> 00:35:27,300
+يبقى إذا كان بال identity يبقى ال identity هو
+
+337
+00:35:27,300 --> 00:35:34,400
+معكوس لنفسه إذا ال A inverse هو ال A وبالتالي ال A
+
+338
+00:35:34,400 --> 00:35:38,820
+inverse هي ال A inverse موجودة في H يبقى طبق ال
+
+339
+00:35:38,820 --> 00:35:43,260
+condition التاني التابع لنظرية H الصحيحةهذا لو كان
+
+340
+00:35:43,260 --> 00:35:48,880
+بكل بساطة أن A تساوية طب لو كانت ال A لا تساوي ال
+
+341
+00:35:48,880 --> 00:35:53,640
+E، إيش بدك تعمل؟ بقول أه طبقا لمن ال condition
+
+342
+00:35:53,640 --> 00:35:59,260
+لأنه حاصل ضرب لأي two elements في H هو موجود في H،
+
+343
+00:35:59,260 --> 00:36:02,720
+بدي أجي لل A و أضربه في نفسه يعني بدي أضربه في
+
+344
+00:36:02,720 --> 00:36:06,260
+نفسه، بيطلع A تربيع موجود في H أضربه كمان في A،
+
+345
+00:36:06,260 --> 00:36:10,070
+بيطلع A تكعيب موجود في H أضرب و أضرب و هكذاهذا
+
+346
+00:36:10,070 --> 00:36:15,310
+يعني أن الـA و الـA³ و الـA³ كلهم هدول جد ما تحط
+
+347
+00:36:15,310 --> 00:36:20,070
+أسس لكن أنا مادام الـH finite افترض فيها خمسين
+
+348
+00:36:20,070 --> 00:36:24,350
+عنصر مثل ما قلت لكن أنا بضلماجي خمسين و واحد و
+
+349
+00:36:24,350 --> 00:36:29,570
+خمسين و سبعين و تمانين إلى آخرين إذاً هيطلع كله
+
+350
+00:36:29,570 --> 00:36:35,530
+موجود في H وبالتالي بعض العناصر لازم تتساوىعنصر من
+
+351
+00:36:35,530 --> 00:36:41,470
+بعد الخمسين يساوي عنصر من قبل الخمسين
+
+352
+00:36:50,940 --> 00:36:55,240
+بيكونوا مش كلهم disjoint are not all of them مش
+
+353
+00:36:55,240 --> 00:37:01,340
+كلهم disjoint لذلك هيطلع عندي كتير فيهم اتنين بسوا
+
+354
+00:37:01,340 --> 00:37:06,400
+بعض اختي اتنين عشوائيا اختي ال ai بده يساوي ال aj
+
+355
+00:37:06,400 --> 00:37:11,380
+واختي ال i اكبر من مين اكبر من جي اكبر واحد باتنين
+
+356
+00:37:11,380 --> 00:37:15,900
+وبتلات الله أعلم اللي هم انه اكبر منه دائما وابدا
+
+357
+00:37:16,340 --> 00:37:24,420
+الان اذا جيت للمعادلة دربتها في معكوس الـaj الولى
+
+358
+00:37:24,420 --> 00:37:28,900
+صغير يبقى دربتها في معكوس الaj وهنا دربتها هذا
+
+359
+00:37:28,900 --> 00:37:34,220
+بيعطينا ال identity element هذا بيعطينا اللى هو ai
+
+360
+00:37:34,220 --> 00:37:39,880
+في a ناقص g اللى هو ai ناقص g بده يسوى من ال
+
+361
+00:37:39,880 --> 00:37:44,800
+identity element والi ناقص g اكبر من الواحد اكبر
+
+362
+00:37:44,800 --> 00:37:49,680
+من الواحد ليش؟لأنه لو طلع هذا بواحد معناته ايه؟
+
+363
+00:37:49,680 --> 00:37:52,680
+اذا واحد يساوي ال identity يبقى ايه هو ال
+
+364
+00:37:52,680 --> 00:37:58,140
+identity؟ لكن احنا شرطنا انه ايه؟ مش ممكن، اذا هذا
+
+365
+00:37:58,140 --> 00:38:02,530
+الكلام دائما وأبداأكبر من واحد ممكن يكون اتنين
+
+366
+00:38:02,530 --> 00:38:08,230
+تلاتة اربعة الاخري ما علينا اكبر من الواحد اذا ال
+
+367
+00:38:08,230 --> 00:38:14,430
+a ij طبعا هتقدر تقولي هذا اكبر من واحد مشان ماتوش
+
+368
+00:38:14,430 --> 00:38:21,450
+تقولي because السبب ان ال a بسويش ال a
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/KpzIv297Rbw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/KpzIv297Rbw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..62123a3db94af27e98b77c9b3c90b3ac4f64bf09
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/KpzIv297Rbw.srt
@@ -0,0 +1,1663 @@
+1
+00:00:21,400 --> 00:00:24,020
+بسم الله الرحمن الرحيم إن شاء الله شباب اليوم
+
+2
+00:00:24,020 --> 00:00:28,240
+هنفوت في الوحدة الرابعة اللي عنوانها cyclic groups
+
+3
+00:00:28,240 --> 00:00:31,580
+خلينا بس نراجع شوية معروفاتنا في اللي درسناها 
+
+4
+00:00:31,580 --> 00:00:35,300
+سابقا في الوحدة الثالثة و الوحدة الثانية و وحدة
+
+5
+00:00:35,300 --> 00:00:42,900
+المقدمة يمكن لو طلعت على ال..النص التاريخي هنا أو
+
+6
+00:00:42,900 --> 00:00:45,760
+المقولة اللي موجودة لواحد اسمه Alex مش عارف أشهرها
+
+7
+00:00:45,760 --> 00:00:50,540
+في العام 1991 بتكلم عن لفظة الـ group نفسها اللي
+
+8
+00:00:50,540 --> 00:00:54,080
+صارت أهم من لفظة physics وchemistry وحتى
+
+9
+00:00:54,080 --> 00:00:57,900
+mathematics itself الفكرة هنا يا شباب بالنسبة لل
+
+10
+00:00:57,900 --> 00:01:02,820
+chapter الرابع or the cyclic groups هي كالتالي في
+
+11
+00:01:02,820 --> 00:01:06,680
+..عند أهل الرياضيات في عندهم هوث بحاجة اسمها
+
+12
+00:01:06,680 --> 00:01:08,540
+classification أو التصنيف
+
+13
+00:01:11,260 --> 00:01:15,680
+يعني لما بنيجي بنعرف هيكل جبري أو هيكل تحليلي
+
+14
+00:01:15,680 --> 00:01:20,040
+مجموعة عليها بعض الخصائص والشروط بنحاول نصنف
+
+15
+00:01:20,040 --> 00:01:25,960
+الأنواع هذه المجموعات يعني مثلا في شغلنا مفهوم
+
+16
+00:01:25,960 --> 00:01:35,620
+للـ group هي مجموعة زائد عملية زائد
+
+17
+00:01:35,620 --> 00:01:37,860
+أربع شروط
+
+18
+00:01:40,810 --> 00:01:47,590
+هنلاحظ فيه عدد كبير من الحاجات اللي زي هيك أو
+
+19
+00:01:47,590 --> 00:01:51,310
+المجموعات اللي معرفة عليها عملية وبتحقق الأربع
+
+20
+00:01:51,310 --> 00:01:55,910
+شروط واللي بنسميها group لكن هل هذه كلها زي بعض؟
+
+21
+00:01:55,910 --> 00:02:04,430
+هل هي نفس الشيء؟ هل هي صور مختلفة لنفس المفهوم؟
+
+22
+00:02:04,430 --> 00:02:09,040
+بيجي هنا السؤال لما بدأت أتعامل مع الـ groups لجأت
+
+23
+00:02:09,040 --> 00:02:14,740
+أنه عندي فرصة أني أصنع groups بأي order بدي إياها ممكن
+
+24
+00:02:14,740 --> 00:02:21,120
+أبدأ بـ order 1,2,3,4,N أو بنتكلم عن ZN ممكن أتكلم
+
+25
+00:02:21,120 --> 00:02:27,160
+عن الـ groups الـ order إلى infinity طيب هي نوع من
+
+26
+00:02:27,160 --> 00:02:32,370
+أنواع التصنيف أني أصنف الـ group حسب عدد عناصرها في
+
+27
+00:02:32,370 --> 00:02:38,010
+نوع ثاني أني هصنف الـ group حسب العملية نفسها بتحقق
+
+28
+00:02:38,010 --> 00:02:44,430
+شرط إضافي ولا لأ زي مين الـ abelian والـ non
+
+29
+00:02:44,430 --> 00:02:52,430
+abelian وكان عندي قسم لـ groups لصنفين صنف abelian
+
+30
+00:02:52,430 --> 00:02:58,030
+وصنف non abelian الـ abelian نفسه بدنا نصنف فيه
+
+31
+00:02:58,030 --> 00:03:05,360
+أيضا يعني في الـ abelian أنا بإمكاني ألاقي نوعين نوع
+
+32
+00:03:05,360 --> 00:03:14,640
+زي الـ R مع الجمع ونوع زي الـ Z برضه مع الجمع
+
+33
+00:03:14,640 --> 00:03:20,860
+لاحظوا نفس العملية وهذه أصلا جزء من ..يعني الـ Z
+
+34
+00:03:20,860 --> 00:03:27,790
+جزء من مين؟ من الـ R لكن الـ Z مع الجمع بتحقق
+
+35
+00:03:27,790 --> 00:03:35,050
+خاصية أنه جميع العناصر بقدر أكتبهم تركيبة معينة من
+
+36
+00:03:35,050 --> 00:03:40,330
+عنصر ما يعني كل العناصر في الـ Z عبارة عن power
+
+37
+00:03:40,330 --> 00:03:45,550
+لمين؟ للواحد طبعا الـ N عبارة عن واحد plus N ليه؟ N
+
+38
+00:03:45,550 --> 00:03:51,670
+في واحد لأن عملية الضرب هنا تتحول ليش؟ لجمع في
+
+39
+00:03:51,670 --> 00:03:56,050
+القارة ده كلام مش ممكن أعملهما عنده تنتين abelian
+
+40
+00:03:56,050 --> 00:04:02,450
+فأنا لازم أصنف الـ groups اللي بتحقق هذا الكلام تحت
+
+41
+00:04:02,450 --> 00:04:06,830
+إطار معين والـ groups اللي بتحققش هذا الكلام تحت
+
+42
+00:04:06,830 --> 00:04:12,630
+إطار آخر الإطار تبع الـ group Z ومثيلاتها هنسميه الـ
+
+43
+00:04:12,630 --> 00:04:20,330
+cyclic groups وهذا هيكون abelian لكن إيش ماله؟ مش
+
+44
+00:04:20,330 --> 00:04:26,350
+cyclic  ناخد من الـ Z الخاصية الأهم اللي خلتها
+
+45
+00:04:26,350 --> 00:04:31,550
+مختلفة عن الـ R وهي أن كل العناصر تركيبة خطية من
+
+46
+00:04:31,550 --> 00:04:36,230
+الواحد ونقول أن الـ group علشان تكون cyclic لازم
+
+47
+00:04:36,230 --> 00:04:40,990
+تكون كل العناصر تركيبة خطية من عنصر معاه يعني
+
+48
+00:04:40,990 --> 00:04:44,270
+بنسمي هذا العنصر اللي العناصر تركيبة ..أو مش
+
+49
+00:04:44,270 --> 00:04:48,490
+تركيبة خطية منه power لهذا العنصر هذا العنصر هسميه
+
+50
+00:04:48,490 --> 00:04:55,820
+مولد أو generator للـ group نجي للأهمية، ليش احنا
+
+51
+00:04:55,820 --> 00:05:04,560
+بَندرس التصنيف؟ سببين، السبب الأول، هذا بهمني لما
+
+52
+00:05:04,560 --> 00:05:08,740
+أدرس لاحقا عملية الـ isomorphism والـ homomorphism،
+
+53
+00:05:08,740 --> 00:05:14,260
+وبهمني لمعرفة أنه هدول الـ groups زي بعض فبحطهم مع
+
+54
+00:05:14,260 --> 00:05:19,080
+بعض وبصير أتعامل مع رأس لهم وما ينطبق عليه ينطبق
+
+55
+00:05:19,080 --> 00:05:23,960
+على الباقي الشغلة الثانية بسهل علي التعامل مع
+
+56
+00:05:23,960 --> 00:05:28,310
+التركيبة الداخلية للـ groups كيف يعني؟ يعني أنا لو
+
+57
+00:05:28,310 --> 00:05:32,890
+بشرط على group Cyclic الجروب الـ Cyclic بتحقق خصائص
+
+58
+00:05:32,890 --> 00:05:37,290
+بتخليني هذه الخصائص بسهولة أقدر أتعامل مع الـ
+
+59
+00:05:37,290 --> 00:05:43,430
+orders تبعت العناصر أتعامل مع خصائص العنصر نفسه
+
+60
+00:05:43,430 --> 00:05:48,070
+لحل المعادلات المتعلقة بالعناصر الموجودة ضمن هذه
+
+61
+00:05:48,070 --> 00:05:49,550
+الـ groups
+
+62
+00:05:52,750 --> 00:05:58,030
+في حين مثلا اللي أبيه لأنه مش cyclic مقدرش أنفذ
+
+63
+00:05:58,030 --> 00:06:04,370
+هذا الكلام إلا لما بدي أخد نظريات أكثر تقدما في الـ
+
+64
+00:06:04,370 --> 00:06:10,130
+chapter الرابع اليوم ابنهي كل ما يتعلق بالـ cyclic
+
+65
+00:06:10,130 --> 00:06:15,410
+groups من ناحية التركيب الداخلي في chapter عشرة أو
+
+66
+00:06:15,410 --> 00:06:20,530
+chapter 11 تحديدًا بنتناول ما يتعلق بالـ Ability
+
+67
+00:06:20,530 --> 00:06:26,250
+Group الـ finite من ناحية التركيب الداخلي بظل
+
+68
+00:06:26,250 --> 00:06:32,150
+الصعوبة في التعامل مع مين؟ مع شغلتين الـ Ability
+
+69
+00:06:32,150 --> 00:06:36,960
+Infinite والـ non-abelian طبعا الناس اللي بيشتغلوا
+
+70
+00:06:36,960 --> 00:06:39,680
+في الجبر الحديث اللي هم نظرياتهم واللي هم شغلهم
+
+71
+00:06:39,680 --> 00:06:42,980
+في هذا الموضوع اللي احنا مش هنتطرق له في هذا
+
+72
+00:06:42,980 --> 00:06:47,180
+المساق إذا ضال وجد احنا هناخد شبطة راح دعش ما
+
+73
+00:06:47,180 --> 00:06:49,480
+يتعلق بالـ finite abelian group لكن على الأقل
+
+74
+00:06:49,480 --> 00:06:54,700
+هننهي من الـ cyclic groups بالنسبة للتعريف التعريف
+
+75
+00:06:54,700 --> 00:06:59,560
+مر علينا سابقا خلال الوحدة السابقة اتكلمنا عن إيش
+
+76
+00:06:59,560 --> 00:07:10,510
+بتعني كلمة cyclic Ego أي سؤال يا شباب؟ في أي سؤال؟
+
+77
+00:07:10,510 --> 00:07:20,830
+طيب نلخص بعض الأمور كمثال
+
+78
+00:07:20,830 --> 00:07:31,830
+واحد لو أخذنا Z with addition
+
+79
+00:07:34,660 --> 00:07:47,520
+أخذنا Z مع عملية الجمع we can show that for any x
+
+80
+00:07:47,520 --> 00:07:57,220
+أو N ينتمي لـ Z that الـ N بتتساوي واحد أس N أو
+
+81
+00:07:57,220 --> 00:08:04,250
+عبارة عن الـ N في واحد أيضا الـ N بتتساوي سالب واحد
+
+82
+00:08:04,250 --> 00:08:10,570
+أو سالب N اللي عبارة عن سالب N بسالب واحد يعني
+
+83
+00:08:10,570 --> 00:08:22,610
+each element in Z is a power of
+
+84
+00:08:22,610 --> 00:08:33,480
+واحد and a power of سالب واحد هذا بيخلينا نقول أن
+
+85
+00:08:33,480 --> 00:08:43,260
+واحد و سالب واحد are generators of
+
+86
+00:08:43,260 --> 00:08:48,120
+the group Z
+
+87
+00:08:48,120 --> 00:08:58,580
+عبارة عن مولدات لعناصر الـ group Z and Z is a
+
+88
+00:08:58,580 --> 00:08:59,200
+cyclic
+
+89
+00:09:06,930 --> 00:09:13,870
+الجروب مثال آخر برضه على Z لكن على مين؟ على ZN لو
+
+90
+00:09:13,870 --> 00:09:19,770
+جيت أنا قلت ZN اللي عبارة عن zero واحد اثنين
+
+91
+00:09:19,770 --> 00:09:27,070
+ثلاثة land in minus one we
+
+92
+00:09:27,070 --> 00:09:30,750
+can show also
+
+93
+00:09:32,960 --> 00:09:48,720
+that any element in ZN is a power of واحد هل
+
+94
+00:09:48,720 --> 00:09:54,200
+الواحد وبس لأ بقدر ألاقي عناصر أخرى هنطلق لها
+
+95
+00:09:54,200 --> 00:09:57,780
+لاحقا هكون الواحد is a generator
+
+96
+00:10:00,210 --> 00:10:10,030
+of Zn and Zn is cyclic طبعا ZN لما بتناولها من دون
+
+97
+00:10:10,030 --> 00:10:14,190
+ما أحط عليها شروط إضافية فأنا بتكلم عن ZN مع عملية
+
+98
+00:10:14,190 --> 00:10:25,850
+عملية الجمع modulo N طيب لو أخذنا مثلا
+
+99
+00:10:31,850 --> 00:10:43,490
+U عشرة الـ U عشرة مين فيها؟ واحد، ثلاثة، سبعة،
+
+100
+00:10:43,490 --> 00:10:49,370
+تسعة طبعا أنا مقدرش أقول generated by واحد، لأن
+
+101
+00:10:49,370 --> 00:10:54,040
+الواحد عبارة عن إيش؟ على الـ identity لكن أنا مقدر
+
+102
+00:10:54,040 --> 00:10:58,880
+أقول أن ثلاثة أس واحد بتساوي ثلاثة ثلاثة أس اثنين
+
+103
+00:10:58,880 --> 00:11:05,600
+ثلاثة فثلاثة جدّيش تسعة ثلاثة أس ثلاثة عبارة عن
+
+104
+00:11:05,600 --> 00:11:10,940
+سبعة وعشرين بضار جدّيش سبعة ثلاثة أس أربعة واحد
+
+105
+00:11:10,940 --> 00:11:19,120
+معناته U عشرة بتساوي generated by ثلاثة أيضا هي
+
+106
+00:11:19,120 --> 00:11:28,660
+generated by مين؟ U10 Generated by 7 وبالتالي U10 is
+
+107
+00:11:28,660 --> 00:11:31,780
+Cyclic
+
+108
+00:11:31,780 --> 00:11:40,220
+U10
+
+109
+00:11:40,220 --> 00:11:43,260
+Cyclic لكن هل كل الـ UN Cyclic
+
+110
+00:11:48,530 --> 00:11:56,790
+U10 Cyclic هل كل الـ U N Cyclic؟ أعطيني مثال
+
+111
+00:11:56,790 --> 00:12:05,390
+على U U8 N مش Cyclic نجرب الـ U8 مين فيها الـ U8؟
+
+112
+00:12:05,390 --> 00:12:09,590
+طيب
+
+113
+00:12:09,590 --> 00:12:15,550
+هلاحظ أنه ثلاثة أس واحد ثلاثة ثلاثة تربيع عبارة عن
+
+114
+00:12:15,550 --> 00:12:20,510
+واحد خمسة أس واحد خمسة لكن خمسة تربيع عبارة عن
+
+115
+00:12:20,510 --> 00:12:27,450
+واحد سبعة أس واحد سبعة لكن سبعة تربيع برضه واحد
+
+116
+00:12:27,450 --> 00:12:33,550
+وبالتالي U ثمانية ليست generated by ثلاثة وليست
+
+117
+00:12:33,550 --> 00:12:40,410
+generated by خمسة وليست generated by سبعة هذا
+
+118
+00:12:40,410 --> 00:12:43,830
+معناته U ثمانية is not
+
+119
+00:12:46,600 --> 00:12:55,140
+Cyclic ليست جروب ولجروب هذه Cyclic الأربع أمثلة
+
+120
+00:12:55,140 --> 00:13:02,940
+اللي كتبناها بتوضح ليه أن زد Cyclic زد N دائما
+
+121
+00:13:02,940 --> 00:13:07,620
+Cyclic لأي N المثال الثالث والرابع بيقول الـ UN قد
+
+122
+00:13:07,620 --> 00:13:14,140
+تكون Cyclic وقد لا تكون Cyclic واضح
+
+123
+00:13:17,290 --> 00:13:24,110
+واضح شباب؟ طبعا
+
+124
+00:13:24,110 --> 00:13:39,630
+هي الأمثلة الموجودة قدامك هنبدأ
+
+125
+00:13:39,630 --> 00:13:45,050
+بعد هذا المثال في أولى نظريات الوحدة الرابعة 
+
+126
+00:13:45,050 --> 00:13:45,910
+theorem
+
+127
+00:13:49,560 --> 00:13:50,400
+أربعة واحدة
+
+128
+00:14:08,250 --> 00:14:12,370
+عشان أنا أقدر أتناول في نظرية لاحقة بعد نظرية 4-1
+
+129
+00:14:12,370 --> 00:14:16,850
+اسمها الـ fundamental theorem of cyclic groups
+
+130
+00:14:16,850 --> 00:14:22,870
+النظرية الأساسية للزمر الدورية لازم أنا أتناول
+
+131
+00:14:22,870 --> 00:14:31,180
+مسألة وقتاش two powers لعنصر ما بيتساوى وقتاش بقول 
+
+132
+00:14:31,180 --> 00:14:37,660
+إن الـ A<sup>i</sup> بتساوي الـ A<sup>j</sup> في أي group لو أخدت أي عنصر هذا
+
+133
+00:14:37,660 --> 00:14:44,860
+قدامه خيارين يا إما infinite order يا إما finite 
+
+134
+00:14:44,860 --> 00:14:50,720
+order بدنا نتناول في حالة الـ infinite order وقتاش
+
+135
+00:14:52,330 --> 00:14:56,690
+الـ A<sup>i</sup> بيتساوى الـ A<sup>j</sup> مين هو الـ i والـ j اللي بيخلي
+
+136
+00:14:56,690 --> 00:15:01,050
+هذا الكلام صحيح وفي حالة الـ finite الـ A<sup>i</sup> والـ A<sup>j</sup>
+
+137
+00:15:01,050 --> 00:15:06,670
+وإمتى بيتساوى وإيش علاقة الـ i والـ j في هذه
+
+138
+00:15:06,670 --> 00:15:15,550
+الحالة كنص النظرية خلينا نكتبه let G be
+
+139
+00:15:15,550 --> 00:15:18,730
+a group
+
+140
+00:15:22,250 --> 00:15:32,050
+A ينتمي للـ G الحالة الأولى if order الـ A بيساوي
+
+141
+00:15:32,050 --> 00:15:40,370
+infinite يعني الـ A has infinite order then A<sup>i</sup>
+
+142
+00:15:40,370 --> 00:15:50,930
+بتساوي A<sup>j</sup> if and only if الـ i بيساوي الـ j and
+
+143
+00:15:55,120 --> 00:16:02,260
+generated by a بتبدأ بالـ identity a هي تربية هي
+
+144
+00:16:02,260 --> 00:16:09,300
+تكيب ولا تنتهي أما
+
+145
+00:16:09,300 --> 00:16:15,080
+في حالة ما يكون الـ order finite الوضع شوية بيتغير
+
+146
+00:16:15,080 --> 00:16:21,480
+تنين
+
+147
+00:16:21,480 --> 00:16:32,290
+if order الـ a بيساوي n then A<sup>i</sup>
+
+148
+00:16:32,290 --> 00:16:41,850
+بتساوي A<sup>j</sup> if and only if الـ n تقسم الـ i - j مش
+
+149
+00:16:41,850 --> 00:16:49,910
+بس هيك and generated by a ده تساوي الـ identity a
+
+150
+00:16:49,910 --> 00:17:00,830
+a<sup>2</sup> and a and a<sup>-1</sup> في كل
+
+151
+00:17:00,830 --> 00:17:08,370
+حالة بالنسبة لـ a<sup>i</sup> بيساوي a<sup>j</sup> في نتائج
+
+152
+00:17:08,370 --> 00:17:19,970
+وإمتى بيتساوى الجزء الأول assume that أن order الـ a
+
+153
+00:17:19,970 --> 00:17:28,160
+بدأ تساوي infinite هذا معناه إن a<sup>n</sup> لا يساوي الـ 
+
+154
+00:17:28,160 --> 00:17:38,480
+identity for any n في الـ Z في
+
+155
+00:17:38,480 --> 00:17:46,250
+اتجاه سهل if i بيساوي j to i بيبقى تساوي a<sup>j</sup> 
+
+156
+00:17:46,250 --> 00:17:50,090
+العكسي إنه i بيساوي j بيقودني إنه a<sup>i</sup> بيساوي
+
+157
+00:17:50,090 --> 00:17:54,910
+a<sup>j</sup> وهذا أمر منطقي نجي لاتجاه الثاني Assume
+
+158
+00:17:54,910 --> 00:18:06,190
+that a<sup>i</sup> بيبقى تساوي  لا يساوي بلاش في z بيحطها
+
+159
+00:18:06,190 --> 00:18:09,190
+في الـ natural number اتكلم عن الـ order يكون
+
+160
+00:18:09,190 --> 00:18:17,180
+positive assume that a<sup>i</sup> بدأت تساوي a<sup>j</sup> هذا
+
+161
+00:18:17,180 --> 00:18:30,360
+معناه let أو assume that إن j أو i لا يساوي j
+
+162
+00:18:30,360 --> 00:18:34,300
+أنا
+
+163
+00:18:34,300 --> 00:18:38,480
+بدي أثبت إن i بيساوي j هفتخد إن i لا يساوي j
+
+164
+00:18:42,320 --> 00:18:51,960
+without loss of generality بدون فقدان التعميم ذات
+
+165
+00:18:51,960 --> 00:18:59,660
+i أكبر من j ما هو الـ i لا يساوي الـ j يا الـ i أكبر
+
+166
+00:18:59,660 --> 00:19:06,840
+يا الـ j أكبر فحنفترض أنه الـ i أكبر حاجة الـ A<sup>i</sup> بدأت
+
+167
+00:19:06,840 --> 00:19:16,070
+تساوي A<sup>j</sup> يعني A<sup>i-j</sup> بدأت تساوي الـ identity هداش
+
+168
+00:19:16,070 --> 00:19:22,170
+حيخليني أقول but
+
+169
+00:19:22,170 --> 00:19:32,190
+a<sup>n</sup> لا يساوي الـ identity لكل n في الـ N هداش
+
+170
+00:19:32,190 --> 00:19:37,190
+معناه معناه لازم الـ i - الـ j تساوي zero
+
+171
+00:19:37,190 --> 00:19:39,390
+وبالتالي
+
+172
+00:19:42,900 --> 00:19:49,260
+إذا حسيني أندي تناقض هان كيف بقول كيف
+
+173
+00:19:49,260 --> 00:19:53,700
+بقول إن الـ i - الـ j بتساوي الـ identity والـ i
+
+174
+00:19:53,700 --> 00:20:00,460
+- j ينتمي للـ N والـ A<sup>n</sup> لا يساوي الـ identity
+
+175
+00:20:00,460 --> 00:20:08,140
+لأي n في N هذا contradiction فاني أعملها هان
+
+176
+00:20:08,140 --> 00:20:12,440
+وبالتالي i بدأت تساوي
+
+177
+00:20:17,690 --> 00:20:24,410
+طيب هذا معناه إن generated by a بتتساوي الـ
+
+178
+00:20:24,410 --> 00:20:33,450
+identity ايه تربية ايه تكييب and a<sup>i</sup> and a<sup>j</sup>
+
+179
+00:20:33,450 --> 00:20:38,610
+are distinct خلي
+
+180
+00:20:38,610 --> 00:20:44,810
+اعمله since a<sup>i</sup> and a<sup>j</sup> are distinct from
+
+181
+00:20:44,810 --> 00:20:45,290
+any
+
+182
+00:20:50,630 --> 00:21:00,130
+i يساوي j هجات الـ powers للـ A A<sup>i</sup> و A<sup>j</sup>
+
+183
+00:21:00,130 --> 00:21:04,730
+لا يتساوى إلا لو تساوى الـ i و الـ j لما الـ i و
+
+184
+00:21:04,730 --> 00:21:08,170
+الـ j ما يتساووش هذه القيم اللي بتطلع معاش بتكون
+
+185
+00:21:08,850 --> 00:21:15,310
+مختلفة ما بوصلش في لحظة معينة لعنصر موجود قبل هيك كل
+
+186
+00:21:15,310 --> 00:21:19,550
+مرة باعطي power جديد بيعطي ناشر عنصر جديد وبالتالي
+
+187
+00:21:19,550 --> 00:21:25,650
+هذه المجموعة مش هتنتهي وبهيك تكون خلص إثبات الجزء
+
+188
+00:21:25,650 --> 00:21:35,250
+الأول أي
+
+189
+00:21:35,250 --> 00:21:35,950
+سؤال؟
+
+190
+00:21:46,140 --> 00:21:50,120
+عشان الـ order بيساوي infinity مدام الـ order بيساوي
+
+191
+00:21:50,120 --> 00:21:53,220
+infinity مش هيساوي عدد محدود يعني ما فيش power للـ a
+
+192
+00:21:53,220 --> 00:21:59,980
+بيعطيك الـ identity غير الـ zero عشان إنالو أنا
+
+193
+00:21:59,980 --> 00:22:03,020
+خلّيتها N ينتمي لـ Z طب ما هو أصلاً A و zero
+
+194
+00:22:03,020 --> 00:22:06,620
+بيعطيني الـ identity فاخدتها في الـ N حد هيقول لي
+
+195
+00:22:06,620 --> 00:22:09,920
+طيب والأعداد السالبة ما هو أصلاً لو الـ A<sup>-</sup>
+
+196
+00:22:09,920 --> 00:22:13,360
+n بيساوي الـ identity فالـ A<sup>n</sup> هيساوي الـ identity
+
+197
+00:22:13,360 --> 00:22:18,320
+وبالتالي لما أنا أقول n في الـ N ف أنا بلغ الموجب و
+
+198
+00:22:18,320 --> 00:22:28,500
+بلغ السالب وبكتفي بمين بالصفر جزء الثاني assume
+
+199
+00:22:30,900 --> 00:22:40,420
+that هو أخضر الـ A بدأت تساوي الـ n يعني A<sup>n</sup>
+
+200
+00:22:40,420 --> 00:22:46,840
+بدأت تساوي الـ Identity إيش المطلوب يثبته نرجع للنص
+
+201
+00:22:46,840 --> 00:22:49,880
+أنه
+
+202
+00:22:49,880 --> 00:22:55,540
+A<sup>i</sup> بتساوي A<sup>j</sup> if and only if الـ n بتقسم الـ
+
+203
+00:22:55,540 --> 00:23:05,690
+i - j في اتجاه سهل إذا i بيساوي الـ j ثم A<sup>i</sup>
+
+204
+00:23:05,690 --> 00:23:10,770
+بيبقى بيساوي A<sup>j</sup> لحظة، أنا هبدأ بنفس البداية،
+
+205
+00:23:10,770 --> 00:23:19,130
+بنفس الطريقة اللي بدأتها جهة ثانية Assume that A
+
+206
+00:23:19,130 --> 00:23:21,930
+<sup>i</sup> بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى
+
+207
+00:23:21,930 --> 00:23:23,430
+بيبقى بيبقى بيبقى بيبقى بيبقى بيبقى A<sup>j</sup>
+
+208
+00:23:27,170 --> 00:23:33,150
+هنثبت إن الـ i - الـ j من مضاعفات الـ n أو الـ n
+
+209
+00:23:33,150 --> 00:23:43,730
+بتقسم الـ i - j هذا معناه الـ A<sup>i-j</sup>
+
+210
+00:23:43,730 --> 00:23:46,090
+إيش ده تساوي الـ identity
+
+211
+00:23:49,390 --> 00:23:55,070
+طيب حاجة الجيت أشغل على الأن هنمسح الجملة هذه
+
+212
+00:23:55,070 --> 00:24:00,190
+كتبناها ونرجع نكتب جملة بعدها نكتبها الـ i - j
+
+213
+00:24:00,190 --> 00:24:04,070
+مدام
+
+214
+00:24:04,070 --> 00:24:08,730
+أنا ما حطيت الشروط على i و j فهذا قد يكون سالب وقد
+
+215
+00:24:08,730 --> 00:24:14,850
+يكون موجب قد يكون zero أنا علشان أبعد عن حالتين
+
+216
+00:24:14,850 --> 00:24:19,110
+حالة الـ zero وحالة السالب هفترض زي ما فرضت هنا أن
+
+217
+00:24:19,110 --> 00:24:22,470
+الـ i أكبر من الـ j إفتراض إن الـ i أكبر من الـ j يعني
+
+218
+00:24:22,470 --> 00:24:28,270
+إن أنا دخلت على أسلوب الإثبات الغير مباشر يعني بال
+
+219
+00:24:28,270 --> 00:24:31,790
+contradiction وبالتالي لازم أفترض إن الـ i لا يساوي
+
+220
+00:24:31,790 --> 00:24:38,630
+الـ j assume in contrary that
+
+221
+00:24:40,640 --> 00:24:56,260
+إن الـ i لا يساوي j c الـ i أكبر من الـ j Now A
+
+222
+00:24:56,260 --> 00:25:02,080
+<sup>i</sup> بيبقى تساوي A<sup>j</sup> يعني A<sup>i-j</sup>
+
+223
+00:25:02,080 --> 00:25:07,660
+إيش بديه يساوي الـ identity طبعاً تنساش إن الـ i
+
+224
+00:25:07,660 --> 00:25:21,810
+- j أكبر من الصفر يعني بينتمي لمين ينتمي طيب
+
+225
+00:25:21,810 --> 00:25:26,910
+using اللي
+
+226
+00:25:26,910 --> 00:25:36,090
+هو الـ division algorithm سمعني
+
+227
+00:25:36,090 --> 00:25:41,770
+الـ division algorithm أنا بقدر أقول إن الـ i -
+
+228
+00:25:41,770 --> 00:25:45,570
+j بدأت
+
+229
+00:25:45,570 --> 00:25:52,150
+تساوي الـ qn + r والـ r أقل من الـ n وأكبر
+
+230
+00:25:52,150 --> 00:26:00,690
+من الصفر صح؟ في غلط إن
+
+231
+00:26:00,690 --> 00:26:03,970
+أنا شيلت اليسار لما أنا بدي أقول إن اليسار مش
+
+232
+00:26:03,970 --> 00:26:05,910
+موجود بدي مبرر
+
+233
+00:26:08,360 --> 00:26:15,240
+بدي وبقى طب و ليش أنا بدي أثبتها هنا هل أنا محتاج
+
+234
+00:26:15,240 --> 00:26:28,960
+أنفيها طيب
+
+235
+00:26:28,960 --> 00:26:34,500
+يبدو إني بدأت خطأ ممكن أنا أجاوب لعدل بعد هيك طيب
+
+236
+00:26:34,500 --> 00:26:46,500
+now A<sup>r</sup> عبارة عن A<sup>i-j</sup> - qn بدأت
+
+237
+00:26:46,500 --> 00:26:53,580
+تساوي A<sup>i-j</sup> × A<sup>-qn</sup> اللي عبارة
+
+238
+00:26:53,580 --> 00:26:58,920
+عن الـ identity × A<sup>n</sup><sup>-q</sup> identity ×
+
+239
+00:26:58,920 --> 00:27:07,270
+identity بدأت تساوي إيش identity يعني A<sup>r</sup> ده يساوي
+
+240
+00:27:07,270 --> 00:27:12,330
+الـ identity طيب
+
+241
+00:27:12,330 --> 00:27:17,350
+تعالوا نشوف وين الأخطاء اللي وجعنا فيها أول حاجة
+
+242
+00:27:17,350 --> 00:27:22,130
+شباب أناش المطلوب يثبته مش
+
+243
+00:27:22,130 --> 00:27:27,270
+المطلوب يثبته أول حاجة المطلوب أثبت إن الـ n تقسم
+
+244
+00:27:27,270 --> 00:27:32,470
+الـ i - الـ j أناش
+
+245
+00:27:32,470 --> 00:27:32,970
+فرضت
+
+246
+00:27:39,300 --> 00:27:43,240
+ما شيله علاقة؟ إيش اللي علاقة؟ يعني بقى هذا أول خطأ
+
+247
+00:27:43,240 --> 00:27:47,580
+شوية
+
+248
+00:27:47,580 --> 00:27:52,440
+بس وهذا الخطأ جاب وراه أخطاء ثانية فرض إن الـ i لا
+
+249
+00:27:52,440 --> 00:27:59,880
+يساوي j وقولت إن الـ i أكبر من الـ j طبعاً
+
+250
+00:27:59,880 --> 00:28:05,860
+وهذا مبني على هذا أنا مطلوب إني أثبت إن الـ n تقسم 
+
+251
+00:28:05,860 --> 00:28:11,460
+هل لو الـ I أكبر من الـ J، الـ N قد لا 
+
+252
+00:28:11,460 --> 00:28:16,280
+تقسم الـ I minus J، ما لهوش
+
+253
+00:28:16,280 --> 00:28:22,740
+علاقة. إذاً، فبنرجع نعدل فرضياتنا ونعدل الدزق هذا
+
+254
+00:28:22,740 --> 00:28:25,920
+بناء على الفرض اللي احنا فرضناه، إذاً فأنا بدي أفترض
+
+255
+00:28:25,920 --> 00:28:34,650
+هنا إيش؟ أن الـ N لا تقسم الـ I minus J، تقسم أو لا
+
+256
+00:28:34,650 --> 00:28:41,970
+تقسم؟ لا تقسم. هل هذي هي الازمة هالجيت؟ لأ لأ
+
+257
+00:28:41,970 --> 00:28:48,110
+هجيت الـ A أُس I minus الـ J، بدي أساوي الـ E. أنا لما
+
+258
+00:28:48,110 --> 00:28:52,550
+قلت إنه I minus الـ J في الـ .. بناء على إيش؟ على
+
+259
+00:28:52,550 --> 00:28:58,130
+إنه الـ I أكبر من الـ J. طيب بصراحة، الـ I أكبر من
+
+260
+00:28:58,130 --> 00:29:00,210
+الـ J، يبقى دي ونحن سيه؟ في الـ Z
+
+261
+00:29:04,420 --> 00:29:08,320
+Using Division Algorithm معرفة على مين؟ عزد في هذه
+
+262
+00:29:08,320 --> 00:29:14,580
+الخطوة. سليمة. هرجت. هنرجع هان لما أنا قلت لك إنه
+
+263
+00:29:14,580 --> 00:29:18,860
+ممنوع نشيل المساواة إلا بمبرر. صار المبرر موجود ولا
+
+264
+00:29:18,860 --> 00:29:24,480
+لأ. الشغلة إنه الآن لو تقسم الـ I minus J، فأنا بروحش
+
+265
+00:29:24,480 --> 00:29:31,810
+بعمل هان، بشيل المساواة، بكمل: a-r بيساوي a-i-j-q-n
+
+266
+00:29:31,810 --> 00:29:40,350
+بصل إن a-r بيساوي الـ identity، since r أكبر أو 
+
+267
+00:29:40,350 --> 00:29:46,950
+يساوي الـ zero. a-r بيساوي الـ identity. طبعاً، الـ r ما
+
+268
+00:29:46,950 --> 00:29:51,150
+بين الـ n وأكبر من الـ zero. الـ a-r بيساوي الـ
+
+269
+00:29:51,150 --> 00:29:53,990
+identity order للـ a بيساوي n
+
+270
+00:29:57,830 --> 00:30:01,950
+A contradiction. مين
+
+271
+00:30:01,950 --> 00:30:07,110
+هو الـ contradiction؟ هذا الـ order هو n، وصار عندي
+
+272
+00:30:07,110 --> 00:30:13,990
+عدد مش صفري أقل من الـ n بيعطينا الـ identity. so وين
+
+273
+00:30:13,990 --> 00:30:23,600
+الخلل؟ إنه لازم الـ R يساوي zero، والـ N تقسم الـ I
+
+274
+00:30:23,600 --> 00:30:27,340
+minus J، وبالتالي الجزئية الأولى من المرحلة
+
+275
+00:30:27,340 --> 00:30:33,000
+الثانية تم إثباتها. أعيد بسرعة عشان .. أعيد بسرعة
+
+276
+00:30:33,000 --> 00:30:39,040
+لأنه طريقة الإثبات صار فيها تعديل. أنا فرضت ..
+
+277
+00:30:39,040 --> 00:30:43,380
+بالعمد. يعني أنت عمد فيك ولا عشان تتعلم ولا .. مش
+
+278
+00:30:43,380 --> 00:30:45,880
+دائماً بكون عاملة بالعمد. أحياناً أنا بخ .. ب .. يعني
+
+279
+00:30:45,880 --> 00:30:52,700
+أنا أخلطت في شغلة وبرجع أعدلها. طيب، فعرضت هنا إن الـ
+
+280
+00:30:52,700 --> 00:30:58,460
+A Os I بدأ تساوي A Os J، فأنا بشتغل على عكس المطلوب
+
+281
+00:30:58,460 --> 00:31:03,360
+فرضت إن الـ N لا تقسم الـ I minus J، وصلت إن I minus
+
+282
+00:31:03,360 --> 00:31:07,620
+J بده يساوي الـ identity، والـ I minus J في الـ Z، والـ N
+
+283
+00:31:07,620 --> 00:31:11,560
+عدد طبيعي، فأنا بقدر أشتغل بالـ division algorithm، و
+
+284
+00:31:11,560 --> 00:31:15,540
+أكتب هذا الكلام. وعلشان الـ N لا تقسم I minus J
+
+285
+00:31:15,540 --> 00:31:19,760
+الـ r لازم تساوي Zero. وصلت بعد الحسابات إن I minus
+
+286
+00:31:19,760 --> 00:31:23,560
+R بده يساوي الـ identity. طيب، I minus R بده يساوي الـ
+
+287
+00:31:23,560 --> 00:31:31,230
+identity، والـ R عدد طبيعي، يعني يكون أكبر من الـ
+
+288
+00:31:31,230 --> 00:31:36,210
+order. لكن هو أصغر من الـ order، فصار تناقض. يعني لازم
+
+289
+00:31:36,210 --> 00:31:43,870
+الـ R يساوي 0، والـ N تقسم الـ I minus G. الجهة
+
+290
+00:31:43,870 --> 00:31:48,630
+الثانية بسطر واحد. لو الـ I بيساوي الـ G، فالـ A و I
+
+291
+00:31:48,630 --> 00:31:49,990
+بيساوي A و G
+
+292
+00:31:57,620 --> 00:32:05,680
+خلّيني أكتب الجهة الثانية مرة أخرى. Assume أن
+
+293
+00:32:05,680 --> 00:32:15,420
+N تقسم I minus J، معناته إن I minus J تتساوي Q
+
+294
+00:32:15,420 --> 00:32:26,520
+ضربناها في N، والـ T من أين؟ من Z. الجهة A أُس I minus
+
+295
+00:32:26,520 --> 00:32:31,240
+الـ J عبارة عن A أُس T N، يعني عبارة عن A أُس N أُس
+
+296
+00:32:31,240 --> 00:32:36,020
+T، بدت تساوي الـ Identity. A أُس I minus الـ J بدت تساوي
+
+297
+00:32:36,020 --> 00:32:44,700
+الـ Identity. A أُس I بدت تساوي A أُس G. طيب، 
+
+298
+00:32:44,700 --> 00:32:49,260
+فضل هذه؟
+
+299
+00:32:49,260 --> 00:32:55,310
+ركز معايا. فرضت إن الـ A أُس I بيبقى تساوي A أُس J
+
+300
+00:32:55,310 --> 00:33:02,950
+فرضت
+
+301
+00:33:02,950 --> 00:33:09,290
+الـ B. فرضت إن الـ A أُس I بيبقى تساوي A أُس J. فرضت
+
+302
+00:33:09,290 --> 00:33:09,690
+أن الـ B. فرضت إن الـ A أُس I بيبقى تساوي A أُس J
+
+303
+00:33:09,690 --> 00:33:12,050
+فرضت إن الـ N تقسم الـ I minus J. فرضت إن الـ N لا
+
+304
+00:33:12,050 --> 00:33:19,000
+تقسم الـ I minus J. يبقى a-i يبقى a-j يبقى a-j يبقى
+
+305
+00:33:19,000 --> 00:33:20,000
+a-j يبقى a-j يبقى a-j يبقى
+
+306
+00:33:20,000 --> 00:33:20,200
+يبقى a-j يبقى a-j يبقى a-j يبقى a-j يبقى a-j يبقى
+
+307
+00:33:20,200 --> 00:33:21,480
+a-j يبقى a-j يبقى a-j يبقى a-j يبقى a-j يبقى a-j
+
+308
+00:33:21,480 --> 00:33:22,100
+يبقى a-j يبقى a-j يبقى a-j يبقى a-j يبقى a-j يبقى
+
+309
+00:33:22,100 --> 00:33:30,580
+a-j يبقى a-j يبقى a-j يبقى a-j يبقى
+
+310
+00:33:30,580 --> 00:33:38,510
+a-j يبقى a-j يبقى a-j. الـ A أُس I minus الـ G
+
+311
+00:33:38,510 --> 00:33:42,570
+Identity. A أُس سالب Q N عبارة عن A أُس N أُس سالب
+
+312
+00:33:42,570 --> 00:33:46,630
+Q، برضه Identity. Identity في Identity بيعطيك الـ
+
+313
+00:33:46,630 --> 00:33:50,610
+Identity. يكبر A أُس R بيبقى يساوي الـ Identity. هجيت
+
+314
+00:33:50,610 --> 00:33:54,850
+أي عدد طبيعي برفع الـ A له وبيعطيني الـ Identity
+
+315
+00:33:54,850 --> 00:33:59,470
+لازم يكون أكبر من مين؟ من الـ order، لأن الـ order هو
+
+316
+00:33:59,470 --> 00:34:03,230
+أصغر عدد طبيعي بيخلي الـ A يروح لمين؟
+
+317
+00:34:05,600 --> 00:34:08,900
+هو المفروض يكون أكبر، لكن حسب الـ Divisional Root
+
+318
+00:34:08,900 --> 00:34:14,080
+ما هو أصغر، فصار عندي تناقض، وبالتالي لازم الـ R
+
+319
+00:34:14,080 --> 00:34:19,860
+تساوي صفر، والـ order أو الـ A، الـ N تقسم الـ I minus
+
+320
+00:34:19,860 --> 00:34:30,620
+J. تجاه العكس سهل، يعني ما فيش فيه تأخير. كيف؟ ما
+
+321
+00:34:30,620 --> 00:34:34,600
+هو حسب الـ Divisional Root، مستحيل يساوي الـ N، طالما
+
+322
+00:34:34,600 --> 00:34:38,820
+بتجسم الباقي دائماً أقل من اللي بتجسم عليه، وإلا لو
+
+323
+00:34:38,820 --> 00:34:44,820
+بيساوي اللي بتجسم عليه، هيظل باقي بتضالي
+
+324
+00:34:44,820 --> 00:34:53,820
+الجزئية الأخيرة يا شباب
+
+325
+00:34:53,820 --> 00:34:59,060
+أنا بدي أثبت إنه generated by A بس هدول هذه
+
+326
+00:34:59,060 --> 00:35:04,390
+خطوتين. الخطوة الأولى إنه كل واحد من هدول مختلف عن
+
+327
+00:35:04,390 --> 00:35:13,210
+الثاني. الخطوة الثانية إنه أي واحد من برا، يعني أي 
+
+328
+00:35:13,210 --> 00:35:19,970
+power أقل من الصفر أو أكبر من الـ N-1، لازم يكون
+
+329
+00:35:19,970 --> 00:35:25,510
+موجود هنا. طيب now four
+
+330
+00:35:26,720 --> 00:35:35,540
+أني I أقل من الـ N، أكبر أو يساوي الصفر. J أقل من الـ
+
+331
+00:35:35,540 --> 00:35:51,020
+N، أكبر أو يساوي الصفر. if I لا يساوي J، then I minus
+
+332
+00:35:51,020 --> 00:35:59,650
+J من الـ N وبين السالب N، والـ I minus J لا يساوي Zero
+
+333
+00:35:59,650 --> 00:36:02,810
+وبالتالي
+
+334
+00:36:02,810 --> 00:36:08,230
+A أس I minus J مش هيساوي الـ identity
+
+335
+00:36:11,870 --> 00:36:15,810
+العدد الوحيد اللي ما ترفع الـ a له يعطيك الـ
+
+336
+00:36:15,810 --> 00:36:20,350
+identity من هو؟ الصفر بس. الصفر الـ i minus الـ j لا
+
+337
+00:36:20,350 --> 00:36:24,330
+تساوي إيه، بمعناته الـ a أُس i minus الـ j ما بيسويش
+
+338
+00:36:24,330 --> 00:36:31,630
+الـ identity، و بالتالي a أُس i لا يساوي a أُس j، يعني
+
+339
+00:36:31,630 --> 00:36:41,760
+if i لا يساوي j، والـ I بين الـ N والـ 0، والـ J بين
+
+340
+00:36:41,760 --> 00:36:48,320
+الـ N والـ 0. المحصلة A أُس I and A أُس J are
+
+341
+00:36:48,320 --> 00:36:57,300
+distinct، يعني هدولة كلهم مختلفين ولا واحد فيهم
+
+342
+00:36:57,300 --> 00:37:00,180
+بيساوي الثاني. now
+
+343
+00:37:02,790 --> 00:37:12,250
+إذا M أكبر أو يساوي الـ N أو M أصغر من الـ Zero، ثم
+
+344
+00:37:12,250 --> 00:37:16,430
+بمعالجة
+
+345
+00:37:16,430 --> 00:37:21,590
+الـ Division الـ
+
+346
+00:37:21,590 --> 00:37:32,410
+M بدأ تساوي مثلاً الـ Q شرطة N زاد R شرطة، والـ R شرطة
+
+347
+00:37:32,410 --> 00:37:41,550
+بين الـ N والـ 0. أي عدد غير هدول الـ 0,1,2,N,N-1
+
+348
+00:37:41,550 --> 00:37:48,250
+لما بدي أجسمه على الـ N، هيدلر المين ضار بين مين؟
+
+349
+00:37:48,250 --> 00:37:55,810
+طيب الـ A أُس M بدت تساوي A أُس Q شرطة N زاد R شرطة
+
+350
+00:37:55,810 --> 00:38:01,930
+A أُس N أُس Q شرطة في A أُس R شرطة، هذا بيساوي الـ
+
+351
+00:38:01,930 --> 00:38:14,790
+identity في A أُس R شرطة. A أُس R شرطة، وهذا ينتمي، يعني
+
+352
+00:38:14,790 --> 00:38:20,630
+بأي M أكبر من الـ N، أصغر من الصفر، موجود هنا ولا مش
+
+353
+00:38:20,630 --> 00:38:26,070
+موجود هنا؟ يجب كل الـ powers للـ A اللي محصورين بين
+
+354
+00:38:26,070 --> 00:38:31,010
+الصفر والـ N-1 مختلفين وموجودين، لكن الـ powers
+
+355
+00:38:31,010 --> 00:38:37,090
+اللي جابوا للصفر وبعد الـ N برضه مكررين بالسماء
+
+356
+00:38:37,090 --> 00:38:43,810
+الواحد من هدول. النتيجة إنه generated by A موجود
+
+357
+00:38:43,810 --> 00:38:44,630
+فيه بس هدول
+
+358
+00:38:49,050 --> 00:38:53,310
+طبعاً، لأن أنا عملت خطوتين: أثبتت إن هدول موجودين، و
+
+359
+00:38:53,310 --> 00:38:56,990
+أثبتت إنه مش موجود غيرهم. كيف أثبتت إنهم موجودين؟
+
+360
+00:38:56,990 --> 00:39:02,450
+أثبتتهم distinct، مختلفين. مدام مختلفين، مش مكررين، و
+
+361
+00:39:02,450 --> 00:39:08,770
+بالتالي كل واحد موجود بشخصه. طبعاً، اللي غيرهم، كل واحد
+
+362
+00:39:08,770 --> 00:39:15,210
+من الـ powers اللي جاب لي الصفر بعد الـ N، موجود له
+
+363
+00:39:17,180 --> 00:39:23,000
+power مساوي في هذه المجموعة أو في السرد اللي موجود
+
+364
+00:39:23,000 --> 00:39:29,700
+قدامك، وبالتالي بهذه الخطوة أنا بكون أنهيت النظرية
+
+365
+00:39:29,700 --> 00:39:36,700
+الأولى أو نظرية 4-1، أي
+
+366
+00:39:36,700 --> 00:39:41,200
+سؤال أي
+
+367
+00:39:41,200 --> 00:39:41,980
+سؤال يا شباب
+
+368
+00:39:57,040 --> 00:40:06,240
+هنا؟ طيب، اللي هي الجزء الأخير هذا. هذا جزئين، الجزء
+
+369
+00:40:06,240 --> 00:40:12,960
+الأول اللي هو المربع هذا، الموجودين
+
+370
+00:40:12,960 --> 00:40:16,880
+مختلفين
+
+371
+00:40:16,880 --> 00:40:23,840
+يعني العناصر هذه، أشملها مختلفة. ما عادش بعدك تقول يا
+
+372
+00:40:23,840 --> 00:40:28,440
+عم إيه أو السبعة أو إيه أو الستمانتاش زي بعض، فأنت
+
+373
+00:40:28,440 --> 00:40:33,440
+ليش حاططهم؟ الخطوة الثانية اللي المربع الأزرق
+
+374
+00:40:33,440 --> 00:40:41,400
+الوا .. والباقي
+
+375
+00:40:41,400 --> 00:40:51,200
+القوة مكررة. ماذا يعني؟ أي أُس آخر غير هدول موجود
+
+376
+00:40:51,200 --> 00:40:58,600
+لكناش بشكل تاني في two corollaries على هذه النظرية
+
+377
+00:40:58,600 --> 00:41:05,260
+corollary
+
+378
+00:41:05,260 --> 00:41:05,800
+واحد
+
+379
+00:41:15,560 --> 00:41:30,080
+إن order of a بيسوي order generated by a if
+
+380
+00:41:30,080 --> 00:41:33,120
+order
+
+381
+00:41:33,120 --> 00:41:37,720
+of a بيسوي infinity then order generated by a
+
+382
+00:41:37,720 --> 00:41:43,780
+عبارة عن order المجموعة هذه كده
+
+383
+00:41:43,780 --> 00:41:45,220
+عدد العناصر هنا يا شباب
+
+384
+00:41:48,100 --> 00:41:54,200
+final طيب لو كان order ال a بدي يساوي n then
+
+385
+00:41:54,200 --> 00:42:01,240
+order generated by a اللي هو ال order لل e a a
+
+386
+00:42:01,240 --> 00:42:05,320
+تربية ل عند a and n minus one كده عدد العناصر هنا
+
+387
+00:42:05,320 --> 00:42:13,280
+برضه and المحصرة ان order ال a بيساوي order
+
+388
+00:42:13,280 --> 00:42:15,720
+generated by a
+
+389
+00:42:30,400 --> 00:42:36,480
+corollary 2 زمان
+
+390
+00:42:36,480 --> 00:42:44,920
+يا شباب لما كنا نشتغل على order
+
+391
+00:42:44,920 --> 00:42:50,480
+العنصر و نقول انه بيساوي n فأي power بيعطيك ان
+
+392
+00:42:50,480 --> 00:42:54,740
+العنصر بيساوي identity كنا نقول ان هذا ال power
+
+393
+00:42:54,740 --> 00:42:59,760
+أكبر من ال n هل جيت مش هنقول اكبر من الان هنقول ان
+
+394
+00:42:59,760 --> 00:43:04,760
+الان يقسمه هذا بذكرني في نظرية الاعداد لما شغلت
+
+395
+00:43:04,760 --> 00:43:07,940
+على الجريس greatest common divisor في التعريف تبع الجريس
+
+396
+00:43:07,940 --> 00:43:13,760
+greatest common divisor كان اي greatest common divisor اخر للجريس
+
+397
+00:43:13,760 --> 00:43:18,280
+greatest common divisor اكبر منه بعدين اصبح الجريس greatest
+
+398
+00:43:18,280 --> 00:43:25,720
+common divisor مضاعف لهذا ال greatest common divisor الاخر هنا نفس
+
+399
+00:43:25,720 --> 00:43:33,910
+الفكرةفإذا أردر الـ A هو N و A أُس K هو الـ
+
+400
+00:43:33,910 --> 00:43:43,770
+Identity فإن N يقسم الـ K إثبات سهل إذا
+
+401
+00:43:43,770 --> 00:43:50,250
+أردر ال A هو N و A أُس K هو الـ Identity فإن N
+
+402
+00:43:50,250 --> 00:43:51,510
+تقسم الـ K
+
+403
+00:43:57,750 --> 00:44:06,590
+كيف؟ النظرية مباشرة كمثال
+
+404
+00:44:06,590 --> 00:44:12,590
+سريع جامع من المحاضرة لو كان ال order لل A بدي
+
+405
+00:44:12,590 --> 00:44:18,390
+ساوي ستة ف generated by ال A عبارة عن ال identity
+
+406
+00:44:18,390 --> 00:44:25,930
+A A تربيع A تكعيب A أس أربعة A أس خمسة طبعا ليش
+
+407
+00:44:25,930 --> 00:44:31,810
+سموها Cyclic او زمر دوارة؟ هاي ال identity يا شباب
+
+408
+00:44:31,810 --> 00:44:41,800
+هان ال a هان ال a تربيع هان ال a تكعيب ال a أس 4 الـ
+
+409
+00:44:41,800 --> 00:44:47,240
+A أس 5 الـ Identity اللي هو A أس 6 بلف مرتين على A أس
+
+410
+00:44:47,240 --> 00:44:52,320
+7 الـ A أس 2 هو نفسه A أس 8 الـ A أس 3 عبارة عن الـ
+
+411
+00:44:52,320 --> 00:44:57,820
+A أس 9 الـ A أس 4 عبارة عن الـ A أس 10 و هكذا بتصير
+
+412
+00:44:57,820 --> 00:45:05,850
+القوة اشمالها بتلف في دائرةيعطيكوا العافية طبعا هي
+
+413
+00:45:05,850 --> 00:45:10,070
+كده احنا انهينا الجزء الاول في الوحدة الرابعة
+
+414
+00:45:10,070 --> 00:45:13,810
+وحاضرة جهة ان شاء الله هناخد الجزء التاني هناخد ال
+
+415
+00:45:13,810 --> 00:45:18,850
+fundamental theorem of cyclic groups يعطيكوا
+
+416
+00:45:18,850 --> 00:45:19,170
+العافية 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eb17cd298178d470db928b0139b6da4bc9ea3de7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk.srt
@@ -0,0 +1,1619 @@
+1
+00:00:21,500 --> 00:00:25,180
+الرحيم استكملنا محاضرة الصبح، تكلمنا في البداية عن
+
+2
+00:00:25,180 --> 00:00:32,480
+بعض الأسئلة ودخلنا في شكل قصير وسريع عن الواحدة
+
+3
+00:00:32,480 --> 00:00:35,240
+الخامسة، الـ permutation الـ group  عن جديد اللي ما كانش 
+
+4
+00:00:35,240 --> 00:00:39,820
+موجود، الفكرة أن أنا بدي أروح أصنع group فيه
+
+5
+00:00:39,820 --> 00:00:44,440
+functions مع عملية الـ composition فعلشان أنا أقدر
+
+6
+00:00:44,440 --> 00:00:49,540
+أتعامل مع الكلام هذا، لازم أتعامل كـ function بهذا
+
+7
+00:00:49,540 --> 00:00:55,310
+الشكل، من مجموعة لنفسها، وعشان عملية الـ composition
+
+8
+00:00:55,310 --> 00:00:59,410
+بعد كده لو بدأ آخد J تانية مثلا، لو بدأ أقول F من X
+
+9
+00:00:59,410 --> 00:01:03,670
+لـ Y، لازم J تكون من Y لحاجة تانية، وعلشان أنا بدأ
+
+10
+00:01:03,670 --> 00:01:07,830
+أشغل بحيث أن أحقق عملية الـ .. الـ .. اللي هو الـ
+
+11
+00:01:07,830 --> 00:01:10,230
+pile  تكون موجودة، وتكون العملية مغلقة على
+
+12
+00:01:10,230 --> 00:01:15,120
+المجموعة، لازم أثبت شغلي على مجموعة واحدة اللي بتكون 
+
+13
+00:01:15,120 --> 00:01:21,160
+من المجموعة لمين؟ لنفسها طبعا، الـ identity موجود، الـ
+
+14
+00:01:21,160 --> 00:01:24,680
+associative موجود، الـ closed موجود، بيبقى شغلة الـ
+
+15
+00:01:24,680 --> 00:01:29,020
+inverse، عشان أقدر أعرف F inverse لازم F يكون إيش؟
+
+16
+00:01:29,020 --> 00:01:32,720
+one to one، وعشان يكون الـ inverse معرف كـ function
+
+17
+00:01:32,720 --> 00:01:35,920
+من الـ X نفسه، لازم يكون الـ onto موجود، فأنا بدي
+
+18
+00:01:35,920 --> 00:01:44,480
+أتكلم عن J بتحتوي من كل الـ projections، F من X لـ X، و
+
+19
+00:01:44,480 --> 00:01:50,720
+f is bijection، و
+
+20
+00:01:50,720 --> 00:01:57,780
+أقول أن الـ J مع الـ composition تمثل الـ group، هجيت
+
+21
+00:01:57,780 --> 00:02:03,220
+في هذا الـ chapter، هروح أقول أن الـ x finite فقط
+
+22
+00:02:03,220 --> 00:02:07,420
+عشان
+
+23
+00:02:07,420 --> 00:02:12,670
+احنا نتعامل مع مساقلة undergraduates، فاحنا نتعامل
+
+24
+00:02:12,670 --> 00:02:16,070
+مع الـ finite set، والـ functions عليها تكون
+
+25
+00:02:16,070 --> 00:02:24,830
+بيجيكشن، الـ function اللي بتكون بهذا الشكل بنسميها
+
+26
+00:02:24,830 --> 00:02:29,770
+permutation، يعني لما تكون الـ function one to one
+
+27
+00:02:29,770 --> 00:02:34,570
+على مجموعة، بنقول طبعا لو بيشتغل من مجموعة لنفسها
+
+28
+00:02:34,570 --> 00:02:39,450
+أو لجزء أكبر منها، بنسميها permutation، فحروح أقول
+
+29
+00:02:39,450 --> 00:02:47,760
+أن أي function من X لـ X، في مساقنا الـ X finite، و
+
+30
+00:02:47,760 --> 00:02:51,740
+تكون one to one، هذه هنسميها إيش؟ permutation، طبعا
+
+31
+00:02:51,740 --> 00:02:55,100
+في ميزة أن لو كانت الـ function one to one على
+
+32
+00:02:55,100 --> 00:02:59,260
+finite set، فالـ on two موجود، الـ one to one على
+
+33
+00:02:59,260 --> 00:03:04,060
+finite set يؤدي إلى الـ on two، فتخيل مجموعة محدودة
+
+34
+00:03:04,060 --> 00:03:10,240
+زي هيك مثلا A B C D، أنا بدي أصنع function من الـ X
+
+35
+00:03:10,240 --> 00:03:17,760
+لنفسها، الـ A هتروح لمين؟ لـ F الـ A، الـ B لـ F الـ
+
+36
+00:03:17,760 --> 00:03:25,860
+B، الـ C لـ F الـ D، ايه الـ C؟ الـ D لـ F الـ D، هجيت
+
+37
+00:03:25,860 --> 00:03:29,700
+F الـ A، وF الـ B، وF الـ C، وF الـ D هم نفسهم الـ
+
+38
+00:03:29,700 --> 00:03:32,960
+A، والـ B، والـ C، والـ D، فالـ F الـ A كم احتمال
+
+39
+00:03:32,960 --> 00:03:43,470
+له؟ لأ، أربعة يا A يا B يا C يا D، طيب لو ايه؟ اخد F في
+
+40
+00:03:43,470 --> 00:03:47,530
+ايه؟ اخد واحد من هدول، يكبر هذا أربعة احتمالات، F في
+
+41
+00:03:47,530 --> 00:03:51,770
+الـ B كم احتمال هيكون له؟ تلاتة، لإن واحد واحد فضله
+
+42
+00:03:51,770 --> 00:03:57,590
+تلاتة، F في الـ C اتنين، وF في الـ D يكبر، كم function
+
+43
+00:03:57,590 --> 00:04:02,370
+بقدر أصنع هنا؟ أربعة في تلاتة في اتنين في واحد، أربعة
+
+44
+00:04:02,370 --> 00:04:07,150
+factorial، أنا بقدر أصنع أربعة factorial من
+
+45
+00:04:07,150 --> 00:04:10,970
+الاقترانات على مجموعة فيها أربعة عناصر، وتكون هذه
+
+46
+00:04:10,970 --> 00:04:13,330
+الاقترانات one to one، أو one to one، أو one to one
+
+47
+00:04:13,330 --> 00:04:14,290
+أو one to one، أو one to one، أو one to one، أو one
+
+48
+00:04:14,290 --> 00:04:15,250
+to one، أو one to one، أو one to one، أو one to one
+
+49
+00:04:15,250 --> 00:04:15,270
+to one، أو one to one، أو one to one، أو one to one
+
+50
+00:04:15,270 --> 00:04:15,670
+أو one to one، أو one to one، أو one to one، أو one
+
+51
+00:04:15,670 --> 00:04:15,890
+أو one to one، أو one to one، أو one to one، أو one
+
+52
+00:04:15,890 --> 00:04:29,730
+to one، أو one to one، أو one
+
+53
+00:04:29,730 --> 00:04:35,250
+to one، ما هي مش هتفرق معايا كتير، هذا ايه؟ أو أي واحد
+
+54
+00:04:35,250 --> 00:04:38,690
+أو أي اتنين، أو أي إن كانت قيمته هتظل نفس النتاج
+
+55
+00:04:38,690 --> 00:04:44,990
+متحققة، نخلي العناصر هذه بهذا الشكل، واحد و اتنين و
+
+56
+00:04:44,990 --> 00:04:51,030
+تلاتة، يعني أنا باشتغل المجموعة اللي فيها الأرقام
+
+57
+00:04:51,030 --> 00:04:55,850
+واحد، لأنه واخدت جميع الاقترانات اللي بتكون one to
+
+58
+00:04:55,850 --> 00:05:02,600
+one، نقنتوا على هذه المجموعة، هحطها في مجموعة اسمها
+
+59
+00:05:02,600 --> 00:05:12,840
+Sn اللي هي the set of all one to one functions on
+
+60
+00:05:12,840 --> 00:05:19,480
+واحد اتنين لعند n، هذه الـ Sn هنسميها symmetry
+
+61
+00:05:19,480 --> 00:05:25,340
+group، أو
+
+62
+00:05:25,340 --> 00:05:31,500
+symmetry n group، هنظبط تسميها كما شوية، هذه هي مجلة
+
+63
+00:05:31,500 --> 00:05:37,220
+شغلنا اليوم، سواء كانت على مجموع 1,2,3 لـ N، أو كانت
+
+64
+00:05:37,220 --> 00:05:41,340
+الـ A1,A2 and An، مش عارف مين بالظبط، هذه اللي أنا
+
+65
+00:05:41,340 --> 00:05:45,860
+هسميهم permutation، طبعا احنا درسنا شغلة زيها قبل
+
+66
+00:05:45,860 --> 00:05:55,200
+هيك، درسنا لـ group D3، إيش كان فيها؟ R0
+
+67
+00:05:58,110 --> 00:06:03,930
+R120، R240، F1
+
+68
+00:06:03,930 --> 00:06:12,370
+F2، F3، D3 عبارة عن إيش؟ تعامل مع المثلث، إذا قلنا 1
+
+69
+00:06:12,370 --> 00:06:24,160
+2 3، إيش الـ R0؟ بتظل مكاني، طيب تعالي أفهمش يعني اظل
+
+70
+00:06:24,160 --> 00:06:28,660
+مكاني، الواحد ظل مكانه في الواحد، يعني أف الواحد
+
+71
+00:06:28,660 --> 00:06:34,860
+ممكن اعتبره واحد، اتنين ظل وين؟ يعني أف التنين، و
+
+72
+00:06:34,860 --> 00:06:40,140
+التلاتة ظل وين؟ مكانه، يعني أف التلاتة بيساو تلاتة
+
+73
+00:06:40,140 --> 00:06:45,320
+يعني أنا بتكلم عن مين؟ يعني أنا بتكلم عن لو خدت
+
+74
+00:06:45,320 --> 00:06:50,030
+مثلا المجموعة J، واتكلمت عن الـ identity function، و
+
+75
+00:06:50,030 --> 00:06:59,210
+أخطّلها رمز إبسلون زي هيك، طيب لو قلنا الـ R Zero
+
+76
+00:06:59,210 --> 00:07:06,170
+هذا هي الـ R مية وعشرين، أبدا يش دوران بمقدار مية و
+
+77
+00:07:06,170 --> 00:07:11,890
+عشرين درجة، في أي اتجاه؟ عكس عقارب الساعة، يعني هيك
+
+78
+00:07:11,890 --> 00:07:18,990
+يعني حاسيب معايا واحد اتنين تلاتة، وكأنه F الواحد
+
+79
+00:07:18,990 --> 00:07:26,010
+صار تلاتة، وF التنين صار واحد، وF التلاتة صار
+
+80
+00:07:26,010 --> 00:07:30,010
+اتنين، طبعا أنا هذا الاقتران واحد اتنين تلاتة
+
+81
+00:07:30,010 --> 00:07:34,730
+الواحد إيش صار؟ تلاتة، التلاتة إيش صار؟ 
+
+82
+00:07:37,450 --> 00:07:40,430
+ممكن اكتبه بدل من أقول F الواحد يساوي، F التانين، F
+
+83
+00:07:40,430 --> 00:07:45,210
+التلاتة، أكتب الواحد والتانين والتلاتة، غيّر ترتيبهم
+
+84
+00:07:45,210 --> 00:07:51,630
+لتلاتة واحد اتنين، فهذا الـ identity عبارة عن إيش؟
+
+85
+00:07:51,630 --> 00:07:56,370
+الواحد مكانه، التانين مكانه، التلاتة مكانه، يعني هذا
+
+86
+00:07:56,370 --> 00:08:02,970
+هو واحد اتنين تلاتة، واحد اتنين تلاتة، لكن الـ R
+
+87
+00:08:02,970 --> 00:08:08,830
+ميعني عشرين، صارت الواحد اتنين تلاتة صارت إيش؟ تلاتة
+
+88
+00:08:08,830 --> 00:08:16,310
+واحد اتنين، مش صارت ترتيبه زي هيك؟ طيب هذه بالنسبالي
+
+89
+00:08:16,310 --> 00:08:24,590
+الـ R0، الـ R 240 كمان لفة، واحد اتنين تلاتة يعني F
+
+90
+00:08:24,590 --> 00:08:29,150
+الواحد صارت اتنين، F التنين صارت تلاتة، F التلاتة
+
+91
+00:08:29,150 --> 00:08:36,050
+صارت إيش؟ واحد، يعني واحد اتنين تلاتة صارت اتنين
+
+92
+00:08:36,050 --> 00:08:42,610
+تلاتة واحد، طيب
+
+93
+00:08:42,610 --> 00:08:47,930
+شوية بس، مين رجع مكانه؟ محدش، هدول رجع مكانه يعني
+
+94
+00:08:47,930 --> 00:08:53,590
+اللي لف التالتة، ماهترج على identity، اه بس أنا خلصت
+
+95
+00:08:53,590 --> 00:08:59,040
+دورانات، هفوت على مين؟ هالجير؟ ع reflections، هي أنا
+
+96
+00:08:59,040 --> 00:09:02,900
+لما بدي آجي أعمل هي واحد اتنين تلاتة، بدي أعمل
+
+97
+00:09:02,900 --> 00:09:07,560
+reflection بالنسبة للواحد، وأجلب، هتصير واحد تلاتة
+
+98
+00:09:07,560 --> 00:09:12,880
+اتنين، يعني أف الواحد زي ما هي، أف التانين تلاتة، أف
+
+99
+00:09:12,880 --> 00:09:17,660
+التلاتة اتنين، يعني واحد اتنين تلاتة، واحد تلاتة
+
+100
+00:09:17,660 --> 00:09:24,150
+اتنين، حاجة أقول واحد تلاتة اتنين، وهذه بالنسبة لي
+
+101
+00:09:24,150 --> 00:09:27,270
+محايدة، ضالت مكانها، الواحد ضال مكانه، مايكبهاش
+
+102
+00:09:27,270 --> 00:09:32,350
+التبديلة صارت تلاتة واتنين، تلاتة واتنين، يعني
+
+103
+00:09:32,350 --> 00:09:36,850
+وكانها تلاتة واتنين، طبعا اللي بعدها هتكون واحد و
+
+104
+00:09:36,850 --> 00:09:42,070
+تلاتة وواحد واتنين فعليا،
+
+105
+00:09:42,070 --> 00:09:47,190
+طبعا هذه تنساش عبارة عن مين؟ S3، إن صارت مجموعة
+
+106
+00:09:47,190 --> 00:09:52,890
+التباديل للمجموعة اللي فيها مين؟ 1 2 3، الـ D3 والـ
+
+107
+00:09:52,890 --> 00:10:00,390
+S3 هما واحد، هما نفس الـ group، لكن هذا منطلع إلها من
+
+108
+00:10:00,390 --> 00:10:07,970
+الزاوية، وهذا منطلع من زاوية، طيب هل ممكن أنعمم؟ هل
+
+109
+00:10:07,970 --> 00:10:18,030
+الـ D4 هتصير S4؟ تعال نشوف الـ D4 كم هنصه فيها الـ S4
+
+110
+00:10:18,030 --> 00:10:21,210
+الـ
+
+111
+00:10:21,210 --> 00:10:26,710
+D4 مش هي الـ S4، لأ، هتكون جزء من الـ S4، هناخد في مثال
+
+112
+00:10:26,710 --> 00:10:31,110
+كمان شوية، كيف هذا الكلام يكون واقعي، هنكتب التعريف
+
+113
+00:10:31,110 --> 00:10:37,350
+ناخد إنثلاف بعدك، إذا ضال وقت هنصل لمثال الـ D4 إن
+
+114
+00:10:37,350 --> 00:10:43,630
+شاء الله، كيف؟
+
+115
+00:10:52,890 --> 00:10:59,990
+definition، C4، مش الأسفار دي، واحد
+
+116
+00:10:59,990 --> 00:11:06,490
+a permutation of
+
+117
+00:11:06,490 --> 00:11:12,730
+a set A، زي ما قلنا، is a function
+
+118
+00:11:16,040 --> 00:11:33,840
+from A to A that is both one to one and unto، كلمة
+
+119
+00:11:33,840 --> 00:11:41,760
+واحدة، يعني إيش؟ projection، تانين، الـ Permutation group
+
+120
+00:11:44,770 --> 00:11:48,590
+هنا تكلمنا عن الـ permutation نفسها، الـ permutation الـ
+
+121
+00:11:48,590 --> 00:11:53,810
+group عبارة عن مجموعة بتحتوي permutation مع عملية مين؟
+
+122
+00:11:53,810 --> 00:11:59,030
+الـ composition، لأن أنا بتكلم عن functions، وأنا
+
+123
+00:11:59,030 --> 00:12:02,370
+أصلًا صنعت الموضوع هذا عشان أتناول عملية الـ
+
+124
+00:12:02,370 --> 00:12:06,250
+composition، وأخليها ضمن الـ group، الـ permutation
+
+125
+00:12:06,250 --> 00:12:13,880
+group عبارة عن جروب طبعا تحت عملية الـ composition
+
+126
+00:12:13,880 --> 00:12:17,700
+العناصر اللي فيها عبارة عن permutation على مجموعة
+
+127
+00:12:17,700 --> 00:12:27,320
+ما permutation group of a set
+
+128
+00:12:27,320 --> 00:12:33,740
+permutation group of a set a is
+
+129
+00:12:40,670 --> 00:12:49,470
+a set of permutations on
+
+130
+00:12:49,470 --> 00:13:02,790
+a that form a group under
+
+131
+00:13:02,790 --> 00:13:06,510
+function
+
+132
+00:13:06,510 --> 00:13:09,010
+composition
+
+133
+00:13:17,160 --> 00:13:22,380
+عبارة عن مجموعة
+
+134
+00:13:22,380 --> 00:13:29,020
+بتعمل جروب مع عملية تركيب الدوال في هذا ال chapter
+
+135
+00:13:29,020 --> 00:13:43,560
+we study here the case where a is finite يعني في
+
+136
+00:13:43,560 --> 00:13:48,660
+مصرّحنا شباب هندرس الحالة اللي بيكون فيها المجموعة
+
+137
+00:13:48,660 --> 00:13:53,200
+مثال ناخد
+
+138
+00:13:53,200 --> 00:13:58,160
+مثال على permutation وبعد هيك ناخد مثال على
+
+139
+00:13:58,160 --> 00:14:03,880
+permutation group كيف؟
+
+140
+00:14:05,440 --> 00:14:10,260
+لأ في هذا المثال تحديدًا هنشتغل يعني ال A عبارة عن
+
+141
+00:14:10,260 --> 00:14:14,680
+واحد اثنين ثلاثة لعند N طبعًا أنا شرحت في البداية
+
+142
+00:14:14,680 --> 00:14:17,860
+ليش اخترت واحد اثنين ثلاثة لعند N لو كان بدل واحد
+
+143
+00:14:17,860 --> 00:14:21,580
+اثنين ثلاثة A واحد اثنين لعند AN نفس الخصائص
+
+144
+00:14:21,580 --> 00:14:25,990
+الموجودة ممكن تكون موجودة على المجموعة من واحد
+
+145
+00:14:25,990 --> 00:14:31,790
+لا ثنين لثلاثة لعند N هي هي أنا مش هاهتم كثير عنصر
+
+146
+00:14:31,790 --> 00:14:36,570
+ايش قيمته بدي أنا هان خصائص اللي هي التبديل على
+
+147
+00:14:36,570 --> 00:14:41,710
+هذه العناصر فبختار مجموعة سهلة عشان أقدر أتعامل
+
+148
+00:14:41,710 --> 00:14:49,930
+و تكون الكتابة أسهل طيب ناخد ال A اولدت ال A
+
+149
+00:14:49,930 --> 00:14:57,160
+عبارة عن الواحد واثنين وثلاثة وأربعة let alpha from a
+
+150
+00:14:57,160 --> 00:15:05,800
+to a be given as alpha الواحد بدي أساوي ثلاثة alpha
+
+151
+00:15:05,800 --> 00:15:09,600
+اثنين بدي أساوي واحد alpha التلاتة بدي أساوي أربعة
+
+152
+00:15:09,600 --> 00:15:12,640
+و alpha
+
+153
+00:15:12,640 --> 00:15:17,140
+الأربعة بدي أساوي اثنين
+
+154
+00:15:21,680 --> 00:15:31,740
+بيتا from a to a be given as بيتا الاثنين أو بيتا
+
+155
+00:15:31,740 --> 00:15:38,260
+الواحد بدت أساوي واحد بيتا الاثنين بدت أساوي ثلاثة
+
+156
+00:15:38,260 --> 00:15:44,060
+بيتا التلاتة بدت أساوي أربعة وبيتا الأربعة بدت
+
+157
+00:15:44,060 --> 00:15:48,100
+أساوي اثنين these functions clearly
+
+158
+00:15:52,440 --> 00:16:05,880
+alpha and beta are permutations on a ليش ال one to
+
+159
+00:16:05,880 --> 00:16:09,700
+one و ال onto واضح من التعريف التعريف موجود عندك
+
+160
+00:16:09,700 --> 00:16:13,760
+بطريقة السرد ولا عنصر بيروح ل .. ولا .. مافيش
+
+161
+00:16:13,760 --> 00:16:18,660
+عنصرين بيروحوا لنفس القيمة طبعا و لعملية onto
+
+162
+00:16:24,210 --> 00:16:30,290
+طيب ال alpha و ال beta ممكن أكتبهم كتابة we can
+
+163
+00:16:30,290 --> 00:16:40,430
+write ال alpha عبارة عن واحد اثنين ثلاثة أربعة ال
+
+164
+00:16:40,430 --> 00:16:46,250
+الواحد لمين بيروح لمين بيروح الواحد الثانية لمين
+
+165
+00:16:46,250 --> 00:17:01,430
+بيروح التلاتة والاربعة طيب ال beta 1,2,3,4 ال 1,2,3
+
+166
+00:17:01,430 --> 00:17:12,710
+,4,2 هذا هي ال alpha وهذا هي ال beta طيب for
+
+167
+00:17:12,710 --> 00:17:18,390
+alpha beta طبعا أنا هجيت هتعامل alpha permutation
+
+168
+00:17:18,390 --> 00:17:22,460
+و beta permutation العملية اللي بينهم عملية ايش
+
+169
+00:17:22,460 --> 00:17:27,900
+composition المفروض أن يكون Alpha Beta عبارة عن
+
+170
+00:17:27,900 --> 00:17:37,640
+اقتران من A ل A with Alpha Beta ل X عبارة عن Alpha
+
+171
+00:17:37,640 --> 00:17:41,060
+Beta
+
+172
+00:17:41,060 --> 00:17:50,960
+ل X لأن العملية Alpha Beta فعليا هو Alpha Composite
+
+173
+00:17:50,960 --> 00:17:55,980
+Beta طب ليش؟ هذا كانت الزمرة الدليل قال لأ يا عمي
+
+174
+00:17:55,980 --> 00:18:00,380
+هو تعريف العملية أنا ما نتّش أحط هنا نقطة ال Alpha
+
+175
+00:18:00,380 --> 00:18:03,740
+في Beta عبارة عن أنصف ال group و أنصف ال group
+
+176
+00:18:03,740 --> 00:18:06,540
+العملية اللي بينهم عملية composition بين function
+
+177
+00:18:06,540 --> 00:18:12,880
+و function طيب طب تعال نشوف Alpha Beta للواحد
+
+178
+00:18:12,880 --> 00:18:19,140
+عبارة عن Alpha Beta الواحد Beta الواحد يا ديش يا
+
+179
+00:18:19,140 --> 00:18:25,470
+شباب Beta الواحد واحد طب Alpha الواحد قد ايش ثلاثة طب
+
+180
+00:18:25,470 --> 00:18:32,610
+Alpha Beta and الاثنين عبارة عن Alpha Beta الاثنين Beta
+
+181
+00:18:32,610 --> 00:18:39,210
+الاثنين قد ايش ثلاثة طب و Alpha الأربع التلاتة أربعة طب
+
+182
+00:18:39,210 --> 00:18:45,850
+Alpha Beta and التلاتة عبارة عن Alpha Beta التلاتة
+
+183
+00:18:45,850 --> 00:18:52,280
+Beta التلاتة قد ايش Beta التلاتة كده؟ أربعة Alpha
+
+184
+00:18:52,280 --> 00:18:56,160
+الأربعة Alpha
+
+185
+00:18:56,160 --> 00:19:02,640
+Beta للأربعة عبارة عن Alpha Beta يعني Alpha الاثنين
+
+186
+00:19:02,640 --> 00:19:12,060
+Alpha الاثنين كده؟ واحد طيب هذا معناته أن Alpha Beta
+
+187
+00:19:12,060 --> 00:19:17,620
+بقدر أكتب زي كده واحد اثنين ثلاثة أربعة الواحد لمين
+
+188
+00:19:17,620 --> 00:19:26,830
+راح؟ الواحد لمين للتلاتة والاثنين والتلاتة والاربعة
+
+189
+00:19:26,830 --> 00:19:41,870
+للواحد طيب تعال نشوف Beta Alpha for Beta Alpha هو
+
+190
+00:19:41,870 --> 00:19:47,930
+مش قاعدة إنهم يتساوي هي مش قاعدة إنهم يتساوي تعال
+
+191
+00:19:47,930 --> 00:19:56,830
+نشوف Beta Alpha للواحد عبارة
+
+192
+00:19:56,830 --> 00:20:02,330
+عن Beta Alpha الواحد Alpha الواحد كده؟ Alpha الواحد
+
+193
+00:20:02,330 --> 00:20:09,710
+ثلاثة Beta التلاتة أربعة طيب Beta Alpha للتانين يعني
+
+194
+00:20:09,710 --> 00:20:17,250
+Beta Alpha التانين Alpha التانين كده؟ واحد Beta للواحد
+
+195
+00:20:21,150 --> 00:20:28,410
+Beta Alpha للتلاتة Beta Alpha التلاتة Beta Alpha
+
+196
+00:20:28,410 --> 00:20:35,770
+التلاتة قد ايش؟ طيب Beta Alpha للأربعة Beta Alpha
+
+197
+00:20:35,770 --> 00:20:42,550
+للأربعة Alpha للأربعة قد ايش؟ اثنين و Beta التالين
+
+198
+00:20:42,550 --> 00:20:50,610
+Beta Alpha عبارة عن واحد اثنين ثلاثة أربعة الواحد
+
+199
+00:20:50,610 --> 00:20:58,350
+للاربعة اثنين الواحد واثنين وثلاثة ايش بتلاحظ؟ in
+
+200
+00:20:58,350 --> 00:21:05,290
+general Alpha
+
+201
+00:21:05,290 --> 00:21:11,810
+Beta ليسوا Beta Alpha ليش قلت in general؟ قد يكون
+
+202
+00:21:11,810 --> 00:21:12,710
+هناك حالات
+
+203
+00:21:16,150 --> 00:21:20,970
+أو هناك حالات لـ .. لـ .. لت .. أن كل عملية تبديلية
+
+204
+00:21:20,970 --> 00:21:24,650
+هذا
+
+205
+00:21:24,650 --> 00:21:29,690
+مش صورة، هذا مثال مثال لنفهم العملية كده بالتمثيل، بس
+
+206
+00:21:39,190 --> 00:21:43,670
+هل كل مرة يا شباب بدي أقدر أعرف لك Alpha Beta and
+
+207
+00:21:43,670 --> 00:21:46,570
+الواحد يعني Alpha Beta الواحد يعني Alpha مثلا
+
+208
+00:21:46,570 --> 00:21:53,870
+الواحد يعني مستوى تلاتة لأ how to
+
+209
+00:21:53,870 --> 00:22:00,950
+do this using
+
+210
+00:22:00,950 --> 00:22:11,090
+the notation واحد اثنين تلاتة Alpha الواحد Alpha التاني
+
+211
+00:22:11,090 --> 00:22:18,170
+الاند Alpha أنا كيف نستعمل ال notation هذا في الحساب
+
+212
+00:22:18,170 --> 00:22:27,490
+نحسب Alpha Beta Alpha Beta عبارة عن مين هاي ال Alpha كده
+
+213
+00:22:27,490 --> 00:22:34,530
+ال Alpha هنا ثلاثة واحد أربعة اثنين و Beta واحد اثنين
+
+214
+00:22:34,530 --> 00:22:39,310
+ثلاثة أربعة كده ايش؟ واحد .. ثلاثة .. أربعة .. اثنين
+
+215
+00:22:39,310 --> 00:22:42,990
+كيف بدي أتم الأمر هذا؟ هي واحد .. هي اثنين .. هي
+
+216
+00:22:42,990 --> 00:22:48,470
+ثلاثة .. هي أربعة؟ بنبدأ من وين؟ الواحد مين أقرب
+
+217
+00:22:48,470 --> 00:22:51,990
+للواحد
+
+218
+00:22:51,990 --> 00:22:57,990
+هنا؟ ال Alpha ولا ال Beta؟ ال Beta بنبدأ ال Beta وان
+
+219
+00:22:57,990 --> 00:23:02,670
+بتاخد الواحد؟ للواحد بنجي هنا ال Alpha وان بتاخد
+
+220
+00:23:02,670 --> 00:23:04,850
+الواحد؟ يجب الواحد يروح للتلاتة
+
+221
+00:23:07,750 --> 00:23:11,730
+الواحد باجي من هنا بروح للواحد باجي هنا الواحد لمن
+
+222
+00:23:11,730 --> 00:23:18,510
+بيروح؟ للتلاتة طيب التنين التلاتة لمن؟ اثنين
+
+223
+00:23:18,510 --> 00:23:23,270
+تلاتة تلاتة أربعة يكبر اثنين للاربعة تلاتة للاربعة
+
+224
+00:23:23,270 --> 00:23:27,490
+اربعة للتنين يكبر تلاتة للتنين أربعة للتنين واثنين
+
+225
+00:23:27,490 --> 00:23:33,190
+للواحد يكبر أربعة لمن؟ للواحد ماشي بس بدون الكتابة
+
+226
+00:23:33,190 --> 00:23:35,930
+هذه كلها بدون الكتابة هذه كلها
+
+227
+00:23:40,500 --> 00:23:45,000
+نبدأ بالواحد الواحد لمين بيروح أنا؟ بمسك الواحد أنا
+
+228
+00:23:45,000 --> 00:23:49,400
+و بطلع فيه فوق لمين هيروح؟ يجب أحد لمين؟ أنا بتبدأ
+
+229
+00:23:49,400 --> 00:23:54,880
+من ال Beta اه من ال Beta التاني لمين؟ للتلاتة
+
+230
+00:23:54,880 --> 00:23:59,980
+لمين؟ يجب اثنين للاربعة تلاتة أربعة أربعة اثنين
+
+231
+00:23:59,980 --> 00:24:04,300
+يجب تلاتة للتانين أربعة اثنين اثنين واحد يجب أربعة
+
+232
+00:24:04,300 --> 00:24:12,180
+للواحد طيب نفس الطريقة Beta Alpha واحد اثنين تلاتة
+
+233
+00:24:12,180 --> 00:24:19,240
+اربعة واحد تلاتة أربعة اثنين فيه
+
+234
+00:24:19,240 --> 00:24:26,980
+واحد اثنين تلاتة أربعة تلاتة واحد أربعة اثنين طيب
+
+235
+00:24:26,980 --> 00:24:30,680
+واحد
+
+236
+00:24:30,680 --> 00:24:36,740
+اثنين تلاتة أربعة الواحد لمن بيروح تلاتة لمن هيروح
+
+237
+00:24:36,740 --> 00:24:41,630
+يقبل واحد تلاتة تلاتة أربعة يقبل واحد للاربعة طيب
+
+238
+00:24:41,630 --> 00:24:46,250
+اثنين واحد واحد واحد يكبر اثنين للواحد تلاتة
+
+239
+00:24:46,250 --> 00:24:50,690
+للأربعة واربعة للتانين يكبر تلاتة لمن للتانين
+
+240
+00:24:50,690 --> 00:24:56,490
+اربعة للتانين واثنين للتلاتة يكبر أربعة لمن بيروح
+
+241
+00:24:56,490 --> 00:25:08,910
+بيروح للتلاتة واضح
+
+242
+00:25:18,740 --> 00:25:25,980
+symmetric group etc طبعا المثال هذا شباب تعاملنا
+
+243
+00:25:25,980 --> 00:25:30,460
+معاه مع ال permutation على شكل عناصر permutation و
+
+244
+00:25:30,460 --> 00:25:32,340
+permutation ثانية كيف بنضرب كيف
+
+245
+00:25:32,340 --> 00:25:43,100
+ببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببب
+
+246
+00:25:43,500 --> 00:25:47,360
+يعني ناخد مجموعة تكون جروب و فيها permutation
+
+247
+00:25:47,360 --> 00:25:57,040
+الثلاثة is the set of all طب أنا ما قلت all يعني كل
+
+248
+00:25:57,040 --> 00:26:00,160
+ال permutation الممكنة لكن أنا ما قلت a set of
+
+249
+00:26:00,160 --> 00:26:03,400
+permutations on يعني مجموعة permutation على
+
+250
+00:26:03,400 --> 00:26:08,840
+المجموعة قد يكونوا كلهم وقد يكون جزء الثلاثة is
+
+251
+00:26:08,840 --> 00:26:11,440
+the set of all permutations
+
+252
+00:26:16,490 --> 00:26:29,850
+on the set واحد اثنين ثلاثة which
+
+253
+00:26:29,850 --> 00:26:34,010
+called هذه 
+
+254
+00:26:34,010 --> 00:26:44,110
+الاستثنائية بسميها the symmetric group
+
+255
+00:26:45,820 --> 00:26:52,420
+of order ثلاثة طب أنا بقول هنا of order ثلاثة مش 
+
+256
+00:26:52,420 --> 00:26:56,280
+القصد إنه عدد العناصر ثلاثة لأ ال order ثلاثة يعني
+
+257
+00:26:56,280 --> 00:27:01,780
+order المجموعة اللي أنا اشتغلت عليها مش order ال
+
+258
+00:27:01,780 --> 00:27:08,700
+permutation اللي بيطلع معايا هبدأ بالـ E عبارة عن
+
+259
+00:27:08,700 --> 00:27:12,600
+واحد اثنين ثلاثة واحد اثنين ثلاثة اللي هو
+
+260
+00:27:16,300 --> 00:27:19,800
+الـ E نفسه الواحد بيروح للواحد الثاني بيروح للثاني
+
+261
+00:27:19,800 --> 00:27:26,400
+الثلاثة بتروح لمين؟ و آخد الـ alpha واحد اثنين ثلاثة 
+
+262
+00:27:26,400 --> 00:27:32,360
+و الواحد هيروح للثاني و الثاني هيروح للثلاثة
+
+263
+00:27:32,360 --> 00:27:39,620
+و الثلاثة هيروح للواحد هذا عبارة عن ايش؟ عن دوران R
+
+264
+00:27:39,620 --> 00:27:46,410
+ميّاشي و آخد الـ beta  إبعاداً 1 2 3 أدخل الواحد يذهب
+
+265
+00:27:46,410 --> 00:27:52,070
+لنفسة و الثاني يذهب للثالث و الثالث للثاني يعني هذه 
+
+266
+00:27:52,070 --> 00:27:56,610
+عبارة عن الـ identity و دوران و reflection و أنتم
+
+267
+00:27:56,610 --> 00:28:01,990
+عارفين أن الـ D<sub>n</sub> بتكونه بدوران و reflection و بيصير
+
+268
+00:28:01,990 --> 00:28:06,630
+تعمل دوران تتكرر مع بعضها و كل تكرار متكررات الدوران
+
+269
+00:28:06,630 --> 00:28:11,450
+مع reflection الأولاني يعطيك reflection جديد تعال
+
+270
+00:28:11,450 --> 00:28:12,450
+نشوف Alpha تربيع
+
+271
+00:28:18,920 --> 00:28:26,320
+Alpha تربيع عبارة عن الـ Alpha في Alpha عشان
+
+272
+00:28:26,320 --> 00:28:29,020
+شرحنا الكلام في الأول فاحنا فاهمين إنه هذا
+
+273
+00:28:29,020 --> 00:28:32,760
+reflection لكن مفترض إنه أنا أشر عليه و أتفاجأ إنه 
+
+274
+00:28:32,760 --> 00:28:38,880
+هذا reflection بس احنا ضيعنا المفاجأة يعني واحد
+
+275
+00:28:38,880 --> 00:28:45,540
+اثنين ثلاثة واحد اثنين ثلاثة هذا اثنين ثلاثة واحد
+
+276
+00:28:45,540 --> 00:28:52,360
+اثنين ثلاثة واحد هذا عبارة عن ايش؟ واحد اثنين ثلاثة
+
+277
+00:28:52,360 --> 00:28:56,880
+الواحد للثاني و الثاني للثلاثة الثاني للثلاثة 
+
+278
+00:28:56,880 --> 00:29:01,700
+و الثلاثة للواحد الثلاثة للواحد و الواحد للثاني
+
+279
+00:29:01,700 --> 00:29:08,700
+هيبقى بنكتبه بهذا الشكل طيب الـ alpha تكعيب عبارة
+
+280
+00:29:08,700 --> 00:29:16,400
+عن alpha تربيع في alpha يعني واحد اثنين ثلاثة 
+
+281
+00:29:16,400 --> 00:29:25,510
+ثلاثة واحد اثنين 1 2 3 2 3 1 1 للثاني و اثنين 
+
+282
+00:29:25,510 --> 00:29:29,050
+للواحد يعني واحد للواحد اثنين للثلاثة و ثلاثة للثاني
+
+283
+00:29:29,050 --> 00:29:33,570
+يجب اثنين للثاني ثلاثة للثلاثة اللي هو مين؟ الـ identity
+
+284
+00:29:33,570 --> 00:29:41,350
+الـ identity طيب Beta تربيع يعني 
+
+285
+00:29:41,350 --> 00:29:53,170
+1 2 3 و 1 3 2 1 2 3 1 3 2 هيعطيك 1 2 3 1 2 3 اللي هو ال
+
+286
+00:29:53,170 --> 00:30:02,170
+identity سهل هذه لو جينا حسبنا alpha beta يعني 1 2 3
+
+287
+00:30:02,170 --> 00:30:06,790
+1 3 2
+
+288
+00:30:06,790 --> 00:30:15,430
+أو احنا كنا الـ alpha في الأول 2 3 1 و الـ beta 1 2 3
+
+289
+00:30:15,430 --> 00:30:22,230
+1 3 2 يعمل العملية هذه ايش
+
+290
+00:30:22,230 --> 00:30:29,950
+هيعطيك؟ المطلوب يعطينا مركز صحيح واحد لواحد واحد
+
+291
+00:30:29,950 --> 00:30:33,930
+لاثنين يكبر واحد للاثنين اثنين للثلاثة و ثلاثة للاثنين
+
+292
+00:30:33,930 --> 00:30:37,730
+لواحد يكبر اثنين لمين؟ لواحد ثلاثة للاثنين و ثلاثة 
+
+293
+00:30:37,730 --> 00:30:41,250
+للثلاثة يكبر ثلاثة لمين؟ للثلاثة
+
+294
+00:30:50,810 --> 00:30:55,490
+طب على المفروض يا شباب S<sub>3</sub> هيكون كام عنصر؟ ستة تعال
+
+295
+00:30:55,490 --> 00:31:00,870
+نشوف كام عنصر و حصلنا عليه ستة هي الأول هي الثاني
+
+296
+00:31:00,870 --> 00:31:08,650
+هي الثالث هي الرابع هي الخامس لإن هي خمس عناصر
+
+297
+00:31:08,650 --> 00:31:12,810
+مختلفة ايه يا ابو عزوز بيتا ألفا كيف تجدها ألفا بيتا
+
+298
+00:31:12,810 --> 00:31:18,130
+ألفا زي ما عملت عمال يضغبها نفس الفكرة تعالوا ببيتا
+
+299
+00:31:18,130 --> 00:31:18,550
+ألفا
+
+300
+00:31:24,260 --> 00:31:30,780
+واحد اثنين ثلاثة واحد اثنين ثلاثة الـ alpha عبارة
+
+301
+00:31:30,780 --> 00:31:36,260
+عن ثلاثة أو اثنين ثلاثة واحد و أنا واحد ثلاثة اثنين
+
+302
+00:31:36,260 --> 00:31:44,500
+أعمل عملية واحد اثنين ثلاثة واحد للثاني ثاني
+
+303
+00:31:44,500 --> 00:31:48,380
+للثلاثة واحد للثلاثة ثاني للثلاثة و ثلاثة للثاني
+
+304
+00:31:48,380 --> 00:31:52,400
+نجمة ثاني للثاني ثلاثة للواحد هذا أنصار جديد ولا 
+
+305
+00:31:52,400 --> 00:31:59,390
+لأ؟ بدا نضمن إنه مافيش تكرار يعني المفروض احنا
+
+306
+00:31:59,390 --> 00:32:02,870
+هالجيت Alpha Beta المفروض أنا احسب Alpha تربيع
+
+307
+00:32:02,870 --> 00:32:06,350
+Beta Alpha
+
+308
+00:32:06,350 --> 00:32:12,250
+تربيع Beta عبارة عن ايش الـ Alpha تربيع؟ واحد اثنين
+
+309
+00:32:12,250 --> 00:32:19,630
+ثلاثة ايه؟ ثلاثة واحد اثنين واحد اثنين ثلاثة و ال
+
+310
+00:32:19,630 --> 00:32:22,310
+Beta عبارة عن واحد ثلاثة اثنين تحسب
+
+311
+00:32:25,380 --> 00:32:30,200
+واحد لواحد و واحد لثلاثة اثنين لثلاثة اثنين و
+
+312
+00:32:30,200 --> 00:32:34,700
+ثلاثة للاثنين اللي هو الـ Beta Alpha ايش يعني
+
+313
+00:32:34,700 --> 00:32:43,080
+يعني Alpha تربيع Beta يساوي Beta Alpha يعني إنص و واحد
+
+314
+00:32:43,080 --> 00:32:54,200
+يعني كم إنص عندي هنا أنا
+
+315
+00:32:54,200 --> 00:32:54,280
+أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا أنا
+
+316
+00:32:54,280 --> 00:32:55,370
+أنا أنا أنا أنا أنا أنا أنا أنا افيه ال
+
+317
+00:32:55,370 --> 00:33:00,890
+identity وفيه الـ alpha وفيه الـ alpha تربيع وفيه ال
+
+318
+00:33:00,890 --> 00:33:07,190
+beta وفيه الـ alpha beta وفيه الـ alpha تربيع beta
+
+319
+00:33:07,190 --> 00:33:21,150
+الـ S<sub>3</sub> فيها كم عنصر؟ ست عناصر زي ما أنت شايف طيب
+
+320
+00:33:24,580 --> 00:33:27,820
+ايش أهمية القاعدة اللي أنا حطيتها غير دي إنه Alpha
+
+321
+00:33:27,820 --> 00:33:33,420
+تربيع Beta يساوي Beta Alpha؟
+
+322
+00:33:33,420 --> 00:33:38,260
+ايش أهميتها؟
+
+323
+00:33:38,260 --> 00:33:41,440
+هي
+
+324
+00:33:41,440 --> 00:33:46,400
+الأهمية أنا ما كتبتها عبثاً يعني أهميتها إنه أنا لما
+
+325
+00:33:46,400 --> 00:33:51,600
+بدي أجي أضغط Powers ثانيها يجيب كل الـ powers ال
+
+326
+00:33:51,600 --> 00:33:55,780
+alpha كبير و اثنين و الـ beta كبير و واحد يعني
+
+327
+00:33:55,780 --> 00:34:00,760
+alpha تكعيب يعني على الـ identity و beta تكعيب على
+
+328
+00:34:00,760 --> 00:34:07,280
+الـ identity تخيل مثلاً أنا بدي أضرب alpha beta مثلاً
+
+329
+00:34:07,280 --> 00:34:13,220
+alpha beta بدي أضربه في alpha تكعيب من beta هذا
+
+330
+00:34:13,220 --> 00:34:19,180
+ايش بدي أساوي؟ هذا عبارة عن في Beta في Beta Alpha يعني
+
+331
+00:34:19,180 --> 00:34:24,480
+Alpha Beta تربيع طبعاً هذه عملية composition و هي
+
+332
+00:34:24,480 --> 00:34:28,720
+associative Beta تربيع يبقى بعناش يعني Alpha
+
+333
+00:34:28,720 --> 00:34:34,480
+Identity Alpha Alpha تربيع يعني أنا لو بدي أعمل
+
+334
+00:34:34,480 --> 00:34:39,100
+هنا multiplication table بقدر من خلال العلاقة هذه
+
+335
+00:34:39,100 --> 00:34:47,320
+أنا أحصل بهذا الشكل هي الـ identity هي الـ Alpha هي
+
+336
+00:34:47,320 --> 00:34:52,960
+الـ alpha تربيع هي الـ beta هي الـ beta تربيع أو ال
+
+337
+00:34:52,960 --> 00:34:57,280
+alpha beta تربيع أو الـ alpha beta قصدي و alpha
+
+338
+00:34:57,280 --> 00:35:03,620
+تربيع beta و هنا الـ identity و هنا الـ alpha و هنا ال
+
+339
+00:35:03,620 --> 00:35:08,580
+alpha تربيع و حط هنا الـ alpha beta أو الـ beta في
+
+340
+00:35:08,580 --> 00:35:15,180
+الأول و الـ alpha beta و الـ alpha تربيع beta و كمل
+
+341
+00:35:15,180 --> 00:35:15,620
+الجدول
+
+342
+00:35:18,300 --> 00:35:23,640
+تعال نشوف مش هيطلع معايا طب الـ identity نفس
+
+343
+00:35:23,640 --> 00:35:35,560
+العناصر عملت
+
+344
+00:35:35,560 --> 00:35:41,960
+ضغم اللي هو صف بعدين عمود هجت ألفا في ألفا ألفا في
+
+345
+00:35:41,960 --> 00:35:49,810
+ألفا ألفا تربيع ألفا في ألفا تربيع identity Alpha في
+
+346
+00:35:49,810 --> 00:35:56,410
+Beta Alpha Beta Alpha في Alpha Beta Alpha تربيع
+
+347
+00:35:56,410 --> 00:36:02,450
+Beta Alpha في Alpha تربيع Beta Alpha تكعيب Beta
+
+348
+00:36:02,450 --> 00:36:09,300
+Identity في Beta Beta Alpha تربيع في Alpha Identity
+
+349
+00:36:09,300 --> 00:36:13,180
+ألفا تربيع في ألفا تربيع ألفا تكعيب أربعة أربعة
+
+350
+00:36:13,180 --> 00:36:14,180
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+351
+00:36:14,180 --> 00:36:14,440
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+352
+00:36:14,440 --> 00:36:16,300
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+353
+00:36:16,300 --> 00:36:20,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+354
+00:36:20,360 --> 00:36:22,680
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+355
+00:36:22,680 --> 00:36:24,120
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+356
+00:36:24,120 --> 00:36:28,080
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+357
+00:36:28,080 --> 00:36:37,820
+أرب
+
+358
+00:36:38,830 --> 00:36:51,650
+بيتا ألفا بقالها معايا حاجة بيتا عبارة
+
+359
+00:36:51,650 --> 00:36:56,530
+عن بيتا ألفا ألفا عبارة عن بيتا ألفا عبارة عن ايش
+
+360
+00:36:56,530 --> 00:37:04,050
+ألفا تربيع بيتا عبارة عن ألفا تربيع في ألفا تربيع
+
+361
+00:37:04,050 --> 00:37:06,950
+بيتا يعني ألفا بيتا
+
+362
+00:37:10,200 --> 00:37:14,920
+Beta في Beta Identity
+
+363
+00:37:14,920 --> 00:37:22,000
+Beta في Alpha Beta عبارة عن ايش؟ عبارة عن Alpha
+
+364
+00:37:22,000 --> 00:37:25,460
+تربيع Beta في Beta يعني Alpha تربيع في الـ identity
+
+365
+00:37:25,460 --> 00:37:33,360
+يعني Alpha تربيع مين ضال هان؟ ضال الـ Alpha طيب
+
+366
+00:37:33,360 --> 00:37:38,880
+Alpha Beta في Alpha وين؟
+
+367
+00:37:48,030 --> 00:37:54,210
+مش فاهمش .. اه .. صحيح
+
+368
+00:37:54,210 --> 00:38:01,690
+.. صحيح .. صحيح .. احنا .. لأ أنت خربطني يا شيخ ..
+
+369
+00:38:01,690 --> 00:38:04,250
+صحيح .. بيتا ألفا تربيع .. يعني بيتا ألفا في ألفا
+
+370
+00:38:04,250 --> 00:38:08,250
+.. هذه ألفا .. ألفا تربيع بيتا .. لأ بيصيح ألف
+
+371
+00:38:08,250 --> 00:38:12,560
+تكعيب في بيتا .. كل المسلمينهجت الـ Alpha Beta
+
+372
+00:38:12,560 --> 00:38:17,160
+هادي عبارة عن Alpha تربيع في Beta يعني Alpha أُص
+
+373
+00:38:17,160 --> 00:38:21,680
+أربع في Beta يعني Alpha Beta مين؟
+
+374
+00:38:21,680 --> 00:38:27,440
+في واحدة عملناها اللي بيتا Alpha Beta عبارة عن
+
+375
+00:38:27,440 --> 00:38:34,380
+Alpha تربيع Beta في Beta بتساوي Alpha تربيع مين
+
+376
+00:38:34,380 --> 00:38:39,920
+جاي يعني أنها هجيت Alpha Beta في Alpha عبارة عن
+
+377
+00:38:39,920 --> 00:38:47,660
+بدّل هادي Beta Alpha Alpha في Alpha تربيع Beta اللي 
+
+378
+00:38:47,660 --> 00:38:58,560
+هي Beta طبعا Alpha Beta في Alpha تربيع عبارة 
+
+379
+00:38:58,560 --> 00:39:05,000
+عن أيش Alpha Beta Alpha في Alpha اللي عبارة عن
+
+380
+00:39:05,000 --> 00:39:09,180
+Alpha Alpha تربيع Beta في Alpha عبارة عن Beta
+
+381
+00:39:09,180 --> 00:39:14,170
+Alpha Beta Alpha عبارة عن أيش Alpha تربيع Beta
+
+382
+00:39:14,170 --> 00:39:18,550
+Alpha
+
+383
+00:39:18,550 --> 00:39:23,250
+في Beta في Beta Alpha Alpha Beta في Alpha Beta
+
+384
+00:39:23,250 --> 00:39:26,630
+Alpha
+
+385
+00:39:26,630 --> 00:39:34,170
+Beta Alpha تربيع Alpha Beta Alpha Alpha
+
+386
+00:39:34,170 --> 00:39:36,730
+Beta Alpha Alpha Beta Alpha Alpha Alpha Alpha
+
+387
+00:39:36,730 --> 00:39:38,250
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+388
+00:39:38,250 --> 00:39:40,910
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+389
+00:39:40,910 --> 00:39:41,130
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+390
+00:39:41,130 --> 00:39:41,410
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+391
+00:39:41,410 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+392
+00:39:41,430 --> 00:39:46,460
+Alpha Alpha Alpha  تين هدول بيتا
+
+393
+00:39:46,460 --> 00:39:51,880
+ألف عبارة عن ألف تربيع بيتا بيتا
+
+394
+00:39:51,880 --> 00:39:56,040
+ألف عبارة عن ألف تربيع بيتا ألف ألف مع ألف تربيع
+
+395
+00:39:56,040 --> 00:40:00,380
+identity و بيتا ألف بيظل طبعا الجواب أنها ألف
+
+396
+00:40:00,380 --> 00:40:07,940
+تربيع بيتا ألف بيتا في ألف بيتا عبارة عن ألف ألف
+
+397
+00:40:07,940 --> 00:40:10,100
+تربيع بيتا بيتا بي سوى ال identity
+
+398
+00:40:12,800 --> 00:40:16,640
+و أنا هيظل alpha تربيع طبعا تقدر تكمل الجدول هجت
+
+399
+00:40:16,640 --> 00:40:22,300
+لحالك أنا هيكون identity و أنا alpha أنا alpha 
+
+400
+00:40:22,300 --> 00:40:32,160
+تربيع و أنا beta و أنا alpha beta طبعا
+
+401
+00:40:32,160 --> 00:40:35,300
+we
+
+402
+00:40:35,300 --> 00:40:41,020
+will show later that
+
+403
+00:40:43,140 --> 00:40:56,800
+S3 and D3 is the same thing
+
+404
+00:40:56,800 --> 00:41:00,200
+ماشي
+
+405
+00:41:00,200 --> 00:41:05,960
+نفس الحاجة يعطيكوا العفو يا شباب 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e749a61c5e9ec72646b12f19e3a13be4ae55a864
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.srt
@@ -0,0 +1,1848 @@
+1
+00:00:21,090 --> 00:00:25,950
+أحنا واصل ما بدأنا فيه المرة الماضية و هو حل اللي
+
+2
+00:00:25,950 --> 00:00:30,570
+هو المسائل على شبتر تمانية الاكستاناداركت برودرك
+
+3
+00:00:30,570 --> 00:00:35,110
+وصلنا لسؤال واحد واربعين بقول express automorphism
+
+4
+00:00:35,110 --> 00:00:40,070
+ل U خمسة وعشرين in the form ZM اكستاناداركت برودرك
+
+5
+00:00:40,070 --> 00:00:41,390
+مع ZN
+
+6
+00:00:43,960 --> 00:00:48,680
+بمعنى اخر بدي اجيب جروب لجروب هذه تبقى isomorphic
+
+7
+00:00:48,680 --> 00:00:54,060
+لمام لل U خمسة وعشرين طب احنا عندنا ال U خمسة
+
+8
+00:00:54,060 --> 00:00:59,680
+وعشرين solution عندنا
+
+9
+00:00:59,680 --> 00:01:07,500
+ال U خمسة وعشرين اللي هو U خمسة لكل تربيع الشكل
+
+10
+00:01:07,500 --> 00:01:16,670
+اللي عندنا هذه isomorphicأو ال atomorphism ل U
+
+11
+00:01:16,670 --> 00:01:23,730
+خمسة وعشرين هذه تساوي U خمسة تربيع مباشرة طبعا
+
+12
+00:01:23,730 --> 00:01:32,770
+اخدت عندك ان ال U مرفوعة ل prime P ومرفوعة ل أس N
+
+13
+00:01:32,770 --> 00:01:39,550
+U P أس N ناقص P أس N minus ال one كتبناها معاكم
+
+14
+00:01:39,550 --> 00:01:45,390
+المرة الماضيةفي آخر محاضرة تجدها موجودة معاك نحاول
+
+15
+00:01:45,390 --> 00:01:50,950
+نطبق هذا الكلام عالميا على أرض الواقع يبقى بناء
+
+16
+00:01:50,950 --> 00:01:55,330
+عليه يو خمسة وعشرين كتبناها بالشكل هذه بقدر اقول
+
+17
+00:01:55,330 --> 00:01:58,070
+هذه isomorphic لمين
+
+18
+00:02:02,510 --> 00:02:09,870
+Isomorphic لزد P اللي هي خمسة تربيع ناقص خمسة أس
+
+19
+00:02:09,870 --> 00:02:14,390
+اتنين ناقص واحد بالشكل اللي عندنا هنايبقى هذا
+
+20
+00:02:14,390 --> 00:02:19,790
+الكلام هذه تساوي من خمسة ترابيع ليه خمسة وعشرين
+
+21
+00:02:19,790 --> 00:02:27,090
+وهذه خمسة وسواحد يبقى زد عشرين شكل اللي عندنا هنا
+
+22
+00:02:27,090 --> 00:02:31,710
+هذا U خمسة وعشرين انا مابدي U خمسة وعشرين بدي
+
+23
+00:02:31,710 --> 00:02:38,540
+اتومورفزم ل U خمسة وعشرينإذا بناء عليه atomorphism
+
+24
+00:02:38,540 --> 00:02:47,580
+ل U خمسة وعشرين اللي هي isomorphic لمهم اللي هو
+
+25
+00:02:47,580 --> 00:02:54,750
+atomorphism ل Z عشرين الشكل اللي عندنا هناأخذنا
+
+26
+00:02:54,750 --> 00:03:03,470
+كمان نظرية سابقة اتومورفزم ل ZN ايزو مورفك ل UN
+
+27
+00:03:03,470 --> 00:03:10,830
+شبطر اللي قبله اخر نظرية يبقى هذا ايزو مورفك ل U20
+
+28
+00:03:11,920 --> 00:03:19,120
+U20 هذه اللي بقدر اكتبها اللي هي تساوي U أربعة في
+
+29
+00:03:19,120 --> 00:03:25,440
+خمسة والاربعة خمسة are relatively prime يبقى هذه
+
+30
+00:03:25,440 --> 00:03:34,070
+isomorphic لمينلأ اللي هو isomorphic او هدى تساوي
+
+31
+00:03:34,070 --> 00:03:39,990
+او isomorphic دُغري لمهم ل U أربعة external
+
+32
+00:03:39,990 --> 00:03:49,530
+product مع U خمسة مرة تانية ل U أربعة هدى U تنين
+
+33
+00:03:49,530 --> 00:03:58,130
+تربيعهذه اخدناها ايزو مورفك لمين لزد دي اتنين وهذه
+
+34
+00:03:58,130 --> 00:04:03,170
+بتطبق عليها القاعدة اللي طبقناها فوق تماما يبقى
+
+35
+00:04:03,170 --> 00:04:10,730
+بالداجي اقول هذا زد خمسة أس واحد ناقص خمسة أس واحد
+
+36
+00:04:10,730 --> 00:04:17,180
+ناقص واحدهذا الكلام يساوي زد اتنين external by
+
+37
+00:04:17,180 --> 00:04:22,880
+product هذه خمسة وهذه خمسة وزيرو خمسة وزيرو أبواحد
+
+38
+00:04:22,880 --> 00:04:29,420
+خمسة ناقص واحد اللي هي أربعة زد اربعة زد اربعة اه
+
+39
+00:04:29,420 --> 00:04:35,300
+زد اربعة يبقى هذه زد اربعة معناه هذا الكلام ان ال
+
+40
+00:04:35,300 --> 00:04:41,050
+atomorphism ليه خمسة وعشرين isomorphic لمهملزد
+
+41
+00:04:41,050 --> 00:04:45,490
+اتنين external product زد اربعة وبالتالي عندي
+
+42
+00:04:45,490 --> 00:04:50,030
+تمانية atomorphism من ال U خمسة وعشرين الى ال U
+
+43
+00:04:50,030 --> 00:04:54,910
+خمسة وعشرين اتسل بغض النظر عن شكلهم قال لي اكتبلي
+
+44
+00:04:54,910 --> 00:05:01,170
+ال atomorphism ل U خمسة وعشرين على شكل ZM في ZN
+
+45
+00:05:01,170 --> 00:05:05,310
+يبقى هي كتبتله بالشكل هذا باستخدام القواعد اللي
+
+46
+00:05:05,310 --> 00:05:08,130
+أخدناها المرة الماضية
+
+47
+00:05:10,010 --> 00:05:20,890
+بعدها بيقول ليه في 46 يبقى 46 بيقول ما يأتي بيقول
+
+48
+00:05:20,890 --> 00:05:28,510
+هاتلي isomorphism بدنا isomorphism من وين لوين في
+
+49
+00:05:28,510 --> 00:05:34,770
+من اللي هو ال group Z12 إلى مين
+
+50
+00:05:37,910 --> 00:05:46,330
+السؤال ستة اربع يقول ز أربع في ز تلاتة يبقى ز أربع
+
+51
+00:05:46,330 --> 00:05:52,270
+كستينو دايكا product مع ز تلاتة مع ز تلاتة بقول
+
+52
+00:05:52,270 --> 00:05:56,740
+عرف ليه اللي هو isomorphismمن ال group هذه لل
+
+53
+00:05:56,740 --> 00:06:01,240
+group هذه انا بعطيك ال function وانت عليك تثبت
+
+54
+00:06:01,240 --> 00:06:05,620
+انها one to one and انت وتخدم خاصيات ال
+
+55
+00:06:05,620 --> 00:06:08,680
+isomorphism ال function اللي بتقول عليها شبه
+
+56
+00:06:08,680 --> 00:06:14,630
+بالشكل التالي phi of x يبقى x وين موجودة هذه؟في
+
+57
+00:06:14,630 --> 00:06:19,810
+Z12 بدي أجسمها إلى مركبتين واحدة موجودة في Z4
+
+58
+00:06:19,810 --> 00:06:25,390
+واحدة موجودة في Z3 يبقى بقدر أقول له هذه على الشكل
+
+59
+00:06:25,390 --> 00:06:33,210
+التالي طبعا العدد اللي هنا في Z12 اللي هو مين اللي
+
+60
+00:06:33,210 --> 00:06:38,470
+هو العدد قد يكون من عند ال zero لغاية من ال 11
+
+61
+00:06:38,470 --> 00:06:44,350
+وهكذاإذا بدى أخلي مركبة موجودة في Z4 و مركبة
+
+62
+00:06:44,350 --> 00:06:51,030
+موجودة في Z3 إذا بقدر أقول هذا X modulo 4 و
+
+63
+00:06:51,030 --> 00:06:57,070
+المركبة التانية X modulo 3 يعني العدد اللى باخده
+
+64
+00:06:57,070 --> 00:07:04,230
+من Z12 أكبر من 4 ولا أكبر من 3 افترض كان 2يبقى
+
+65
+00:07:04,230 --> 00:07:07,830
+باجي بقول فاي اف اتنين يسوى اتنين موديوله أربعة
+
+66
+00:07:07,830 --> 00:07:11,130
+اللي هو باتنين و اتنين موديوله تلاتة اللي هو
+
+67
+00:07:11,130 --> 00:07:16,510
+باتنين لكن لو قلتله خمسة فاي خمسة بدي يكون هنا
+
+68
+00:07:16,510 --> 00:07:20,370
+واحد و هنا كداش و هنا اتنين و هكذا يبقى هاي
+
+69
+00:07:20,370 --> 00:07:23,490
+المقصودة هاي ال function قدامك بس تبتليها one to
+
+70
+00:07:23,490 --> 00:07:30,670
+one and on to وتخدم خاصية ال isomorphismهذا قال له
+
+71
+00:07:30,670 --> 00:07:35,210
+ستة واربعين تمانية واربعين بيقولوا show that five
+
+72
+00:07:35,210 --> 00:07:42,310
+is an isomorphism
+
+73
+00:07:42,310 --> 00:07:48,650
+من زد تلاتة cross زد خمسة لزد خمستاشر يبقى تمانية
+
+74
+00:07:48,650 --> 00:07:59,630
+واربعين ان في من من زد تلاتة external productمع
+
+75
+00:07:59,630 --> 00:08:07,090
+مين؟ مع z خمسة لمن؟ ل z خمستاشر بالشكل اللي عندنا
+
+76
+00:08:07,090 --> 00:08:14,410
+هذا z خمستاشر و بحيث انه ال five of اتنين و تلاتة
+
+77
+00:08:14,410 --> 00:08:20,370
+بده يسوى اتنين بقول find an element a و b في هذا
+
+78
+00:08:20,370 --> 00:08:26,050
+بحيث ال maps to one يبقى انا بدي اوجداللي هو
+
+79
+00:08:26,050 --> 00:08:31,950
+element a و b صورته main صورته الواحد او five of a
+
+80
+00:08:31,950 --> 00:08:36,570
+و b اللي بتعطينا main بتعطينا الواحد
+
+81
+00:08:41,470 --> 00:08:46,970
+سؤال مرة تانية في انا isomorphism ال isomorphism
+
+82
+00:08:46,970 --> 00:08:55,090
+من ال group z3 external to z5 إلى z15 وفي انا معطع
+
+83
+00:08:55,090 --> 00:08:58,810
+ان فيلم اتأثر على الاتنين والتلاتة النتيجة تساوي
+
+84
+00:08:58,810 --> 00:09:05,390
+اتنين جليهات للعنصر a وb لصورته من؟ لصورته الواحد
+
+85
+00:09:05,390 --> 00:09:09,190
+الصحيح حد فيكو حل هذا السؤال
+
+86
+00:09:12,670 --> 00:09:19,130
+أه يعني مدن امتحانات مش داعي للحل كويس طيب على أي
+
+87
+00:09:19,130 --> 00:09:24,310
+حال أنا مرة حلتلكوا سؤال شبيه بهذا في اللي قبل لما
+
+88
+00:09:24,310 --> 00:09:28,110
+أخدنا ال isomorphism حلتكوا سؤال شبيه به بس هذا
+
+89
+00:09:28,110 --> 00:09:33,060
+الفرق بينه وبين هذا هذا مكون من مين منorder pair
+
+90
+00:09:33,060 --> 00:09:36,880
+order pair والله مش order pair بتفرجش عنها شوف يا
+
+91
+00:09:36,880 --> 00:09:41,180
+سيدي انا بدي العنصر a و b اللي صورته تحت أثير الفا
+
+92
+00:09:41,180 --> 00:09:47,540
+يساوي واحد هناك كان بدي شكل ال isomorphism عبارة
+
+93
+00:09:47,540 --> 00:09:51,440
+عن إيش كان في السؤال اللي جابله لكن هذا لأ بدي ال
+
+94
+00:09:51,440 --> 00:09:57,040
+order a و b اللي صورته تساوي مين تساوي واحد صحيح
+
+95
+00:09:57,460 --> 00:10:02,300
+بقول كويس بحاول استخدام المعلومة هذه بقدر الإمكان
+
+96
+00:10:02,300 --> 00:10:08,820
+ولذلك بحاول أجيب المعطى هذا اللي هو واحد في الصورة
+
+97
+00:10:08,820 --> 00:10:12,920
+اللي قدامي هنا يعني بدي أجيب علقة تربط بين الواحد
+
+98
+00:10:12,920 --> 00:10:18,140
+واتنين اللي عندنا حتى نقدر نحسب كم هذا ال element
+
+99
+00:10:18,140 --> 00:10:24,930
+الان لو جيت واحد الواحد هذا موجود في أي groupفنيات
+
+100
+00:10:24,930 --> 00:10:31,430
+زد خمستاشر هل هذا الواحد يكافئ رقم تاني اللي هو
+
+101
+00:10:31,430 --> 00:10:37,490
+مين ستاشر ممتاز يعني الواحد هذا بالضبط هو عبارة عن
+
+102
+00:10:37,490 --> 00:10:45,610
+ستاشر modulo خمستاشر تمام الستاشر مش هي عبارة عن
+
+103
+00:10:45,610 --> 00:10:53,640
+تمانية في اتنين modulo خمستاشرتمام طب اتنين مديله
+
+104
+00:10:53,640 --> 00:10:58,380
+خمستاشر ما هو اتنين صح ولا لأ يبقى اتنين اللي عندي
+
+105
+00:10:58,380 --> 00:11:02,580
+هذه بقدر اشيلها و اكتر بدلها في او في اتنين و
+
+106
+00:11:02,580 --> 00:11:08,740
+تلاتة يبقى هذا الكلام بدي يساوي تمانية في في او في
+
+107
+00:11:08,740 --> 00:11:16,810
+اتنين و تلاتة كأن المثل ايشكأنه تمانية انا هدم
+
+108
+00:11:16,810 --> 00:11:21,250
+طلعها من جوا الجوس وطلعها مين؟ برا وزي ما كنا نقول
+
+109
+00:11:21,250 --> 00:11:27,190
+Alpha of خمسة يسوى خمسة في Alpha of واحد تمام هنا
+
+110
+00:11:27,190 --> 00:11:31,850
+نفس الفكرة بالضبط تماما كأنه تمانية كانت جوا وانا
+
+111
+00:11:31,850 --> 00:11:36,310
+طلعتها برا اذا بدأ دخلها جوا يبقى لو دخلتها جوا
+
+112
+00:11:36,310 --> 00:11:41,710
+هضربها وين في كل عنصر من هذه العناصر بس اتنين هذه
+
+113
+00:11:41,710 --> 00:11:47,790
+موجودة وينفي زد تلاتة والتلاتة هذه موجودة في زد
+
+114
+00:11:47,790 --> 00:11:51,730
+خمسة إذا عند الضرب بدك اتراعي من؟ بدك اتراعي
+
+115
+00:11:51,730 --> 00:11:57,430
+النتيجة إذا هذا الكلام بده يساوي بيده يساوي five
+
+116
+00:11:57,430 --> 00:12:04,190
+تمانية في اتنين modulo الأولى اللي هي تلاتة
+
+117
+00:12:04,190 --> 00:12:11,000
+والمركبة التانية تمانية في تلاتة modulo خمسةهذا
+
+118
+00:12:11,000 --> 00:12:16,680
+الكلام بده يسوى five تمانية في اتنين بستعش مضيله
+
+119
+00:12:16,680 --> 00:12:22,800
+تلاتة بيبقى واحد يبقى واحد و تلاتة في تمانية اربعة
+
+120
+00:12:22,800 --> 00:12:28,320
+وعشرين مضيله خمسة اللي هو اربع يبقى الواحد اللي
+
+121
+00:12:28,320 --> 00:12:33,520
+عندي هو صورة ال order per man واحد واربعة هذا
+
+122
+00:12:33,520 --> 00:12:40,200
+معناه ان ال a و ال b بده يسوى جداش واحد واربع
+
+123
+00:12:45,820 --> 00:12:52,020
+طيب هذا كان سؤال اللي هو تمانية واربعين بدنا نروح
+
+124
+00:12:52,020 --> 00:12:57,840
+لسؤال تمانية وخمسينتمانية و خمسين بيقول لي without
+
+125
+00:12:57,840 --> 00:13:02,100
+doing any calculations in atomorphism Z عشرين
+
+126
+00:13:02,100 --> 00:13:07,940
+determine how many elements of atomorphism Z عشرين
+
+127
+00:13:07,940 --> 00:13:16,560
+ال order لهم يساوي أربعة بدي سؤال تمانية و خمسين
+
+128
+00:13:16,560 --> 00:13:31,780
+the number of elements ofOrder four in atomorphism
+
+129
+00:13:31,780 --> 00:13:33,640
+لزاد عشرين
+
+130
+00:13:40,950 --> 00:13:46,130
+بقول اجيبلي اكام انصر في الاتومورفزم لزد عشرين ال
+
+131
+00:13:46,130 --> 00:13:51,070
+order اللي لهم يساوي اربعة بدونها بدون ما اروح
+
+132
+00:13:51,070 --> 00:13:56,330
+تبحث في شكل الاتومورفزم هدول بدك تعرفلي كده بدون
+
+133
+00:13:56,330 --> 00:14:01,850
+ما تعرفلي شكل ولا function بقوله كويسيبقى solution
+
+134
+00:14:01,850 --> 00:14:07,150
+يبقى معنى هذا الكلام انا بدي استخدم اي شغلة لها
+
+135
+00:14:07,150 --> 00:14:11,470
+علاقة بال atomorphism ل Z عشرين احنا عندنا ال
+
+136
+00:14:11,470 --> 00:14:16,790
+atomorphism ل Z عشرين ايزو مورفك لمين يا شباب ل ال
+
+137
+00:14:16,790 --> 00:14:23,750
+U عشرين ممتاز و ال U عشرين هذه اللي هي U اللي هي
+
+138
+00:14:23,750 --> 00:14:31,010
+عبارة عن U اربعة في خمسةوالاربعة في الخمسة are
+
+139
+00:14:31,010 --> 00:14:35,870
+relatively primeمدام relatively prime يبقى هذه
+
+140
+00:14:35,870 --> 00:14:47,070
+isomorphic لمام ل U4 external product مع U5 ال U4
+
+141
+00:14:47,070 --> 00:14:54,570
+هذه اللي هي isomorphic لمام ل Z2 external product
+
+142
+00:14:54,570 --> 00:14:56,230
+مع U5
+
+143
+00:15:00,200 --> 00:15:05,120
+عشان أضيع وقت فيها يبقى isomorphic لزد اربعة اذا
+
+144
+00:15:05,120 --> 00:15:11,720
+عندي تمانية اتومورفزم لمان لزد عشرين بدى ادور من
+
+145
+00:15:11,720 --> 00:15:17,440
+التمانية هدول يبقى ما ينطبق على الاتومورفزم لزد
+
+146
+00:15:17,440 --> 00:15:23,540
+عشرين ينطبق على الاتومورفزم لمانلزد اتنين اكس تانو
+
+147
+00:15:23,540 --> 00:15:28,120
+ضايق product مع مين مع زد اربعة معناه هذا الكلام
+
+148
+00:15:28,120 --> 00:15:34,060
+مادام هذه ايزو مورفك لهذه اذا لو لجيت جديش عدد
+
+149
+00:15:34,060 --> 00:15:38,300
+العناصر في ال group هذه لل order إلهم يساوي أربعة
+
+150
+00:15:38,300 --> 00:15:42,340
+بكون جبت عدد ال atom morphisms اللي ال order إلهم
+
+151
+00:15:42,340 --> 00:15:48,060
+يساوي مين أربعة يعني هذه صعب العمل فيها لكن هذه
+
+152
+00:15:48,060 --> 00:15:54,020
+سهل العمل فيهاومن هنا التحويلات هذه بتنقلنا من
+
+153
+00:15:54,020 --> 00:15:59,480
+جروب صعب التعامل معاها إلى جروب سهل التعامل معاها
+
+154
+00:16:01,670 --> 00:16:05,970
+أنا بدي أبحث من العناصر اللي في Z2 Extended
+
+155
+00:16:05,970 --> 00:16:11,390
+Product كده عددهم ال order لهم بده يساوي من؟ بده
+
+156
+00:16:11,390 --> 00:16:16,970
+يساوي الأربعة يبقى بداتي أقول له assume افترض انه
+
+157
+00:16:16,970 --> 00:16:23,250
+عندي element a و b موجود في Z2 Extended Product مع
+
+158
+00:16:23,250 --> 00:16:31,480
+Z4 such that بحيث انالأردر لـ A و لـ B اللي هو
+
+159
+00:16:31,480 --> 00:16:36,660
+لساوي ال least common multiple للأردر بتابع ال A
+
+160
+00:16:36,660 --> 00:16:41,340
+والأردر بتابع ال B هذا الكلام دي ساوي كده؟ دي ساوي
+
+161
+00:16:41,340 --> 00:16:45,220
+أربعة الأردر
+
+162
+00:16:45,220 --> 00:16:56,900
+المحتملة ال orders of A are مين يا شباب؟ كده؟ واحد
+
+163
+00:16:56,900 --> 00:17:02,030
+و كده؟واحد واثنين هذه الـ elements بتاع الـ z
+
+164
+00:17:02,030 --> 00:17:05,630
+اتنين Zero و واحد Zero هو ال identity ال order له
+
+165
+00:17:05,630 --> 00:17:09,230
+بواحد و الواحد له ال order اتنين اللي لو جمعت واحد
+
+166
+00:17:09,230 --> 00:17:11,830
+زي واحد يسوى اتنين فزي اتنين ب Zero اللي هو ال
+
+167
+00:17:11,830 --> 00:17:16,090
+identity يبقى ال orders المحتملة اللي هي واحد و
+
+168
+00:17:16,090 --> 00:17:28,660
+اتنين and ال orders of B areممكن واحد واتنين واربع
+
+169
+00:17:28,660 --> 00:17:32,760
+تمام تلاتة مافيش حاجة لإن التلاتة لا تقسم الأربع
+
+170
+00:17:32,760 --> 00:17:36,740
+يبقى اما ال order اي واحد او اتنين او اربع طيب
+
+171
+00:17:36,740 --> 00:17:40,140
+هدول الرقامين لو بدى اجيب ال least common multiple
+
+172
+00:17:40,140 --> 00:17:45,620
+مع هدول بشكلولي مشكلة؟لأ واحد اتنين هي واحد و
+
+173
+00:17:45,620 --> 00:17:49,900
+اتنين اذا هدال بدون تفكير بدي اخد الانصارين زي ما
+
+174
+00:17:49,900 --> 00:17:55,280
+هم لكن بدي ادور هنا الارقام اللي بتعملي ال least
+
+175
+00:17:55,280 --> 00:17:58,920
+common multiple مع مين مع هدول بيعطيني اربعة
+
+176
+00:17:58,920 --> 00:18:03,180
+السؤال هو لو كان خدت العناصر ال order اللي لهم
+
+177
+00:18:03,180 --> 00:18:08,020
+واحد و اتنين بيجيبولي عناصر يبقى مفيش insert يبقى
+
+178
+00:18:08,020 --> 00:18:12,980
+مفيش اخد الا اللي ال order له يسوى manأربعة فقط و
+
+179
+00:18:12,980 --> 00:18:16,760
+هدول بدي أخدهم هم اتنين زي ما هم كويس هدول شوف
+
+180
+00:18:16,760 --> 00:18:20,860
+هدول بيعطوني تبدل تان او بيعطوني اتنين على طول
+
+181
+00:18:20,860 --> 00:18:27,940
+الخط و هدول تعالى نشوف ايش بدي نعمل فيهم الآن z
+
+182
+00:18:27,940 --> 00:18:34,100
+four هذا كم أنصر ال order اللي بيساوي أربعة في z
+
+183
+00:18:34,100 --> 00:18:43,270
+four و مين كمانوالتلاتة فيش غيرهم فيش غيرهم يبقى
+
+184
+00:18:43,270 --> 00:18:51,870
+ال Z for has واحد and تلاتة of order أربع يعني كام
+
+185
+00:18:51,870 --> 00:18:58,170
+خيار عندى؟ اتنين يبقى ال A لها خيارات two choices
+
+186
+00:18:58,170 --> 00:19:06,930
+for A for B هذا بدي يعطينا two choices for Bطيب كم
+
+187
+00:19:06,930 --> 00:19:10,530
+بقى كم خيار لإيه؟ خد زي ما بدك لإن order واحد
+
+188
+00:19:10,530 --> 00:19:14,990
+واتنين بيفرجوش معايا مع الأربع يبقى هنا كمان two
+
+189
+00:19:14,990 --> 00:19:24,550
+choices for b إذن عدد العدد تبعهم يساوي يبقى هنا
+
+190
+00:19:24,550 --> 00:19:35,450
+the number of elements of order for
+
+191
+00:19:37,350 --> 00:19:44,950
+is اتنين في اتنين ويساوي اربعة elements يبقى
+
+192
+00:19:44,950 --> 00:19:49,650
+ماعنديش الا اربعة عناصر ال order لهم يساوي four
+
+193
+00:19:49,650 --> 00:19:54,110
+وبالتالي ال atom morphism لزد عشرين يوجد فيه جداش
+
+194
+00:19:54,110 --> 00:19:59,690
+يبقى اربعة عناصر ال order لها بده يساوي مان بده
+
+195
+00:19:59,690 --> 00:20:05,310
+يساوي عشرين تمام يبقى هذا اللي عندنا
+
+196
+00:20:12,060 --> 00:20:17,500
+لاحظ ان هذه الأسئلة كلها تطبيق مباشر على ما درسناه
+
+197
+00:20:17,500 --> 00:20:23,240
+في الجزء النظري في آخر محاضرة في هذا section الآن
+
+198
+00:20:23,240 --> 00:20:30,840
+ننتقل إلى الشبتر اللذي يليه وهو شبتر تسعة تسعة
+
+199
+00:20:30,840 --> 00:20:37,300
+normal subgroups
+
+200
+00:20:37,300 --> 00:20:40,680
+and factor
+
+201
+00:20:44,630 --> 00:20:49,990
+and factor groups
+
+202
+00:20:49,990 --> 00:20:56,610
+definition
+
+203
+00:20:56,610 --> 00:21:01,010
+a
+
+204
+00:21:01,010 --> 00:21:05,670
+subgroup H
+
+205
+00:21:05,670 --> 00:21:13,250
+of a group G is called
+
+206
+00:21:16,320 --> 00:21:29,000
+is called a normal is called a normal subgroup of
+
+207
+00:21:29,000 --> 00:21:40,680
+g subgroup of g f ال a h بده يساوي ال h a لكل
+
+208
+00:21:40,680 --> 00:21:50,920
+ال a اللي موجودة في g b لا استخدامwe denote this
+
+209
+00:21:50,920 --> 00:22:02,720
+by ال H is a normal subgroup of G note
+
+210
+00:22:02,720 --> 00:22:05,880
+ال
+
+211
+00:22:05,880 --> 00:22:11,680
+A H دي ساوي ال H A does not
+
+212
+00:22:15,740 --> 00:22:21,240
+imply that ان
+
+213
+00:22:21,240 --> 00:22:36,120
+ال a h بدر يساوي ال h a but means that ان ال a h
+
+214
+00:22:36,120 --> 00:22:41,700
+one بدر يساوي ال h two a
+
+215
+00:22:44,410 --> 00:22:50,070
+أول نظرية theorem a
+
+216
+00:22:50,070 --> 00:22:54,430
+subgroup a
+
+217
+00:22:54,430 --> 00:23:07,070
+subgroup H a subgroup H of G is normal is normal
+
+218
+00:23:07,070 --> 00:23:18,730
+in G if and only ifالـ X H X inverse subset من H
+
+219
+00:23:18,730 --> 00:23:24,870
+لكل ال X اللي موجودة في ال group G
+
+220
+00:24:16,580 --> 00:24:22,060
+نرجع مرة تانيةيبقى انا عندى جروب جديدة هسميها
+
+221
+00:24:22,060 --> 00:24:27,040
+normal subgroup اللى بتحققلى الشرط معين ال factor
+
+222
+00:24:27,040 --> 00:24:32,640
+group بدى انشئ جروب جديدة بواسطة ال subgroup اللى
+
+223
+00:24:32,640 --> 00:24:36,340
+عرفته دى فخلينا في الأول مع ال normal subgroup
+
+224
+00:24:36,340 --> 00:24:41,720
+وهتلعب دور كبير في علم الجبر وخاصة في موضوع الجروب
+
+225
+00:24:41,720 --> 00:24:46,880
+ال subgroup H من الجروب G بسميها normal subgroup
+
+226
+00:24:46,880 --> 00:24:53,390
+من Gإذا كان الـ A H هو الـ H A for all A belongs
+
+227
+00:24:53,390 --> 00:24:57,970
+to G يعني إذا كان ال right coset هي ال left coset
+
+228
+00:24:57,970 --> 00:25:04,280
+لجميع عناصر G يبقى بقول هذابقول عليها ال normal
+
+229
+00:25:04,280 --> 00:25:10,660
+subgroup من G طبعا احنا سابقا بقين اقول ال A H ليس
+
+230
+00:25:10,660 --> 00:25:15,300
+بالضرورة ان تكون subgroup لكن ان كانت normal يبقى
+
+231
+00:25:15,300 --> 00:25:21,240
+automatic هذا subgroup انت معمل يبقى ال H اللي هي
+
+232
+00:25:21,240 --> 00:25:26,010
+subgroup من G بقول عليها normal subgroupإذا كان
+
+233
+00:25:26,010 --> 00:25:30,510
+الـ left coset يساوي الـ right coset واختصارا بدل
+
+234
+00:25:30,510 --> 00:25:34,910
+ما أقول الـ H is a normal subgroup من G بدي أعبر
+
+235
+00:25:34,910 --> 00:25:41,230
+بالرمز المثلث قاعدته جهة G والرأس تبعه جهة من؟ جهة
+
+236
+00:25:41,230 --> 00:25:44,950
+H قعدي لبالك مش حيال الله تخلي القاعدة تحت و الرأس
+
+237
+00:25:44,950 --> 00:25:50,570
+فوقالرأس دائما جهة ال subgroup والقاعدة جهة من جهة
+
+238
+00:25:50,570 --> 00:25:54,950
+ال group طب في شغل ممكن يفهمها الواحد غلط من خلال
+
+239
+00:25:54,950 --> 00:25:58,610
+ال condition اللي حاطه هذا ايش الحاجة الغلط لو جيت
+
+240
+00:25:58,610 --> 00:26:04,790
+قولتك a h يساوي h a هذا كلام خطأ انا لما اقول a h
+
+241
+00:26:04,790 --> 00:26:08,370
+بيساوي شي يعني ال left coset بيساوي ال right coset
+
+242
+00:26:08,370 --> 00:26:14,570
+اذا بدى اتكلم بلغة ال elements بيقول a h one يساوي
+
+243
+00:26:16,110 --> 00:26:20,010
+هو الـ H2 رقم تاني و element تاني ليس نفس ال
+
+244
+00:26:20,010 --> 00:26:24,930
+element قد يكون نفس ال element لكن in general لأ
+
+245
+00:26:24,930 --> 00:26:31,370
+مش صحيح يبقى لما أقول هذه H بيسوي HA يعني AH1
+
+246
+00:26:31,370 --> 00:26:37,290
+بيسوي H2A رقم تاني أو element تاني غير ال element
+
+247
+00:26:37,290 --> 00:26:42,350
+اللي عندنا يبقى بقولش AH بيسوي HA و لما بقول AH1
+
+248
+00:26:42,350 --> 00:26:45,090
+يسوى 100 H2A
+
+249
+00:26:46,550 --> 00:26:51,370
+التعريف هذا اللي عندنا بدي أحاول أصيغه صياغة أخرى،
+
+250
+00:26:51,370 --> 00:26:55,910
+تمام؟ ليهاشي الصياغة الأخرى؟ بل بدل الصياغة تلاتة
+
+251
+00:26:56,420 --> 00:27:01,320
+أيش الصيغة الأخرى؟ أنا بإمكاني هنا لو ضربت في ال A
+
+252
+00:27:01,320 --> 00:27:05,300
+inverse من جهة اليمين أو A inverse من جهة الشمال
+
+253
+00:27:05,300 --> 00:27:10,540
+فبصير عندي A H A inverse يساوي من؟ يساوي ال H شرط
+
+254
+00:27:10,540 --> 00:27:15,920
+ال normality أو لو ضربت من جهة الشمال بصير ال H
+
+255
+00:27:15,920 --> 00:27:23,260
+يساوي A inverse H A شرطاني لل normality ممكن أقول
+
+256
+00:27:23,260 --> 00:27:31,150
+AH small A inverse موجودة في H كابتل لأن هذا
+
+257
+00:27:31,150 --> 00:27:36,170
+بيستوى H يبقى ال A H small A inverse ك element
+
+258
+00:27:36,170 --> 00:27:42,450
+موجود في H برضه شرط اللي اللي هو صيغة أخرى
+
+259
+00:27:42,450 --> 00:27:46,550
+للnormalty نظريها ده إيش بتقولي بقول افترض ال H
+
+260
+00:27:46,550 --> 00:27:50,070
+normal subgroup أو ال H هي normal subgroup من G if
+
+261
+00:27:50,070 --> 00:27:55,300
+and only ifالـ X H X inverse subset من مين؟ من H
+
+262
+00:27:55,300 --> 00:28:00,140
+ما هو إن كان التساوي حاصل إذن automatic هدي مين؟
+
+263
+00:28:00,140 --> 00:28:04,420
+هذه subset من هذه طبعا التساوي حصل من هنا قلتلك لو
+
+264
+00:28:04,420 --> 00:28:08,480
+ضربت في ال A inverse من اليمين أو لشمال بيطلع
+
+265
+00:28:08,480 --> 00:28:12,800
+التساوي أنا بدأ أختصر و لا أقول التساوي بدأ أقول
+
+266
+00:28:12,800 --> 00:28:17,220
+ال subset رغم أن التساوي كمان صحيح طيب مشان هيك
+
+267
+00:28:17,220 --> 00:28:23,480
+بنروح نثبت صحة هذا الكلاميبقى بداجي أقوله أسيوم
+
+268
+00:28:23,480 --> 00:28:30,780
+اللي هو ال H is a normal subgroup من G then
+
+269
+00:28:34,230 --> 00:28:39,130
+يبقى انا فرضت ان الـ H هذه normal subgroup من G
+
+270
+00:28:39,130 --> 00:28:45,790
+يبقى بناء عليه بدي أصير عندي A H يساوي H A حسب مام
+
+271
+00:28:45,790 --> 00:28:52,070
+حسب ال definition او مشان خلي نفس الرموز يبقى بده
+
+272
+00:28:52,070 --> 00:28:58,950
+اقول X H بدي يساوي الـ H X لكل ال X اللي موجودة في
+
+273
+00:28:58,950 --> 00:29:01,090
+G بلا استثناء
+
+274
+00:29:03,680 --> 00:29:10,640
+طيب تمام انا بدي اخلق في المثلة X H X inverse يبقى
+
+275
+00:29:10,640 --> 00:29:15,440
+بناء عليه لو ضربت الطرفين من جهتي اليمين في X
+
+276
+00:29:15,440 --> 00:29:21,840
+inverse ايش اللي بدي يصير؟ بدي يصير عندي ال X H X
+
+277
+00:29:21,840 --> 00:29:26,950
+inverse بدي ساوي ماين؟بدى يساوي ال H هذا معناه
+
+278
+00:29:26,950 --> 00:29:34,030
+مدام تساوي يبقى ال X H X inverse subset من مين من
+
+279
+00:29:34,030 --> 00:29:39,110
+ال H و ال H subset من ال X H X inverse ما علينا
+
+280
+00:29:39,110 --> 00:29:43,770
+يبقى هاي جيبتله مين الشرط الأول بدي أجيبله الشرط
+
+281
+00:29:43,770 --> 00:29:45,630
+الثاني conversely
+
+282
+00:29:49,190 --> 00:29:57,170
+assume افترض ان الـ X H X inverse subset من مين؟
+
+283
+00:29:57,170 --> 00:30:03,330
+subset من H بدي احاول اثبت ان الـ H هذه معلها is a
+
+284
+00:30:03,330 --> 00:30:09,690
+normal subgroup من جي طيب بجي بقوله then
+
+285
+00:30:12,460 --> 00:30:19,120
+أو قبل then هذه الصحيحة احنا فرضينها لكل ال X اللي
+
+286
+00:30:19,120 --> 00:30:24,920
+موجود أويا في ال group G بدي أسأل السؤال التالي ال
+
+287
+00:30:24,920 --> 00:30:28,680
+X inverse موجودة في G ولا لا؟ لإن ال G جروبه
+
+288
+00:30:28,680 --> 00:30:35,210
+المعكس موجود يبقى بجي بقوله thenالـ X inverse
+
+289
+00:30:35,210 --> 00:30:41,390
+موجودة في G implies بدي اطبق عليها الشرط هذا يبقى
+
+290
+00:30:41,390 --> 00:30:47,370
+لو جيت طبقت عليها الشرط هذا بصير X inverse H X
+
+291
+00:30:47,370 --> 00:30:52,850
+inverse inverse اللي هو subset من من؟ subset من H
+
+292
+00:30:55,030 --> 00:31:02,150
+او بمعنى اخر بقدر اقول هنا main ان ال X inverse H
+
+293
+00:31:02,150 --> 00:31:11,830
+X subset من main subset من main من H طيب
+
+294
+00:31:11,830 --> 00:31:19,130
+كويسيبقى هذه الخطوة الأولى لو جبت او قدرت اثبت ان
+
+295
+00:31:19,130 --> 00:31:26,430
+ال H هي ال subset من من ال X inverse HX بتم
+
+296
+00:31:26,430 --> 00:31:31,550
+المطلوب يبقى بدي اعتبر هذه الخطوة رقم واحد بدي اجي
+
+297
+00:31:31,550 --> 00:31:38,030
+للخطوة رقم اتنين الخطوة رقم واحدلو ضربتها في X من
+
+298
+00:31:38,030 --> 00:31:45,830
+جهة الشمال يبقى ايش بيصير ال X X inverse في من؟ في
+
+299
+00:31:45,830 --> 00:31:54,050
+ال H وهنا X بدي تبقى subset من ال X H ضربت من جهة
+
+300
+00:31:54,050 --> 00:31:58,610
+الشمال في X يبقى هذا ايش بدي يعطيلك؟ هذا بدي
+
+301
+00:31:58,610 --> 00:32:06,330
+يعطيلك ان ال H X subset من ال X Hبنفس الطريقة اضرب
+
+302
+00:32:06,330 --> 00:32:12,090
+من جهة اليمين في الـ X inverse يبقى لو ضربنا في ال
+
+303
+00:32:12,090 --> 00:32:19,250
+X inverse بصير ال H هي subset من X H X inverse و
+
+304
+00:32:19,250 --> 00:32:22,550
+هذه العلاقة رقم اتنين اتطلع ليه في الواحد و اتنين
+
+305
+00:32:22,550 --> 00:32:33,120
+يبقى باجي بقوله هنا from واحد and اتنين we haveإن
+
+306
+00:32:33,120 --> 00:32:40,620
+ال X H X inverse بده يساوي مين؟ بده يساوي ال H طب
+
+307
+00:32:40,620 --> 00:32:47,100
+أضرب للطرفين في X من جهتي اليامين يبقى X H بده
+
+308
+00:32:47,100 --> 00:32:52,780
+يساوي H X هالتعريف مين؟ ال normal هذا بده يعطيلك
+
+309
+00:32:52,780 --> 00:32:57,660
+إن ال H is a normal subgroup من مين؟ من G و أنت
+
+310
+00:32:57,660 --> 00:33:00,120
+هنا من المسألة
+
+311
+00:33:04,330 --> 00:33:12,130
+الان خدلي هالملاحظة اللي قلتلك قبل قليل وهي صورة
+
+312
+00:33:12,130 --> 00:33:17,030
+من صورة ال normality بيقولي the above theorem the
+
+313
+00:33:17,030 --> 00:33:26,450
+above theorem the above theorem can be written as
+
+314
+00:33:26,450 --> 00:33:36,160
+can bewritten as ممكن نكتبها على الشكل ا التالي ان
+
+315
+00:33:36,160 --> 00:33:46,820
+ال a او ال h is a normal subgroup من g if and only
+
+316
+00:33:46,820 --> 00:33:56,180
+if ال x h x inversebelongs لمن؟ belongs ل ال H لكل
+
+317
+00:33:56,180 --> 00:34:01,340
+ال X اللي موجود وين في جيب لا استثناء
+
+318
+00:34:18,040 --> 00:34:25,960
+مرة تانية الملاحظة هذه بتقول ان التعريف ال
+
+319
+00:34:25,960 --> 00:34:32,640
+normality استنتج من النظريةالنظرية الآن أنا بدي
+
+320
+00:34:32,640 --> 00:34:37,240
+أصيغها هذه مرة تانية فبجي بقول ال H normal
+
+321
+00:34:37,240 --> 00:34:42,220
+subgroup من G إذا كان X H يا small يعني element من
+
+322
+00:34:42,220 --> 00:34:47,460
+H في X inverse بقول belong to H لأنه صار عنصر
+
+323
+00:34:47,460 --> 00:34:51,640
+العنصر بقولش substitute انما بقول main belong to H
+
+324
+00:34:51,640 --> 00:34:55,760
+يعني حصل ضرب ال X اللي هو من G في ال element اللي
+
+325
+00:34:55,760 --> 00:34:58,580
+هو من H في معكوس ال element تبع ال G التلاتة
+
+326
+00:34:58,580 --> 00:35:02,970
+بديكون oneموجود في H وهي الموضوع تبعها هذي normal
+
+327
+00:35:02,970 --> 00:35:07,290
+إذا كان ال X H X inverse belongs to the main للـH
+
+328
+00:35:07,290 --> 00:35:12,130
+يبقى لو قلي من الآن فصادم اثبت ان ال H is a normal
+
+329
+00:35:12,130 --> 00:35:18,130
+subgroup من G يكفيني main هذا الشرطأو هذا الشرط أو
+
+330
+00:35:18,130 --> 00:35:22,190
+هذا الشرط يبقى اللي تقدر عليه من التلت اشتغله
+
+331
+00:35:22,190 --> 00:35:26,970
+وتوكل على الله طيب بدنا نبدأ ناخد بعض الأمثلة
+
+332
+00:35:26,970 --> 00:35:32,330
+ونبدأ بأبسط أنواع الأمثلة السؤال هو لو عندي group
+
+333
+00:35:32,330 --> 00:35:37,470
+abelian والجروب هذه أخدت منها ال subgroup السؤال
+
+334
+00:35:37,470 --> 00:35:45,270
+هو هل ال subgroup هذه بتبقى normalيعني هل يتحقق ال
+
+335
+00:35:45,270 --> 00:35:50,160
+condition اللي عندي هذاليش؟ لأن أبيليان انا بقول
+
+336
+00:35:50,160 --> 00:35:55,420
+بقدر ابدل هدول ايه مكان بعض لو بدلتهم بصير H XX
+
+337
+00:35:55,420 --> 00:36:00,320
+inverse لو H في E لهو بـH يبقى H موجودة وان موجودة
+
+338
+00:36:00,320 --> 00:36:03,720
+في H وبالتالي الشرط متحقق إذا ال group هذي ايه؟
+
+339
+00:36:03,720 --> 00:36:08,580
+normal group يبقى أول قاعدة باخدها انه لو كانت ال
+
+340
+00:36:08,580 --> 00:36:13,940
+group أبيليان يبقى any sub group is normal يبقى
+
+341
+00:36:13,940 --> 00:36:29,400
+أول مثال بيقول anysubgroup of an abelian group is
+
+342
+00:36:29,400 --> 00:36:36,380
+normal مثال
+
+343
+00:36:36,380 --> 00:36:42,000
+اتنين طبعا
+
+344
+00:36:42,000 --> 00:36:47,080
+ال condition هيه عندك اقولك هذهلو تحقق ال
+
+345
+00:36:47,080 --> 00:36:51,820
+condition هنا موجود الان ابيليان بقدر ابدله
+
+346
+00:36:51,820 --> 00:36:58,420
+وبالتالي بيبقى عندى H موجود فيه H طيب النقطة
+
+347
+00:36:58,420 --> 00:37:02,600
+الثانية ال center تبع ال group هل هو ال sub group
+
+348
+00:37:02,600 --> 00:37:03,460
+من ال group G
+
+349
+00:37:06,550 --> 00:37:14,770
+الـ Center تبع بجروب الـ Z of G أنا أدعي أن الـ A
+
+350
+00:37:14,770 --> 00:37:18,510
+normal sub group منين؟ من G
+
+351
+00:37:21,130 --> 00:37:24,530
+ماجي بقوله كويس اذا اتحقق اي condition من ال
+
+352
+00:37:24,530 --> 00:37:28,850
+conditions اللي عندي هدول بكون خلصنا امن الموضوع
+
+353
+00:37:28,850 --> 00:37:34,670
+تمام كيف الان خلاني نحقق اي condition هادي هادي
+
+354
+00:37:34,670 --> 00:37:40,550
+هادي السيانة بتفرجش عننا الان لو روحت اخد اي عنصر
+
+355
+00:37:40,550 --> 00:37:44,550
+عندي في ال group G و بدي اضربه في ال center طبع ال
+
+356
+00:37:44,550 --> 00:37:47,350
+H هنا solution
+
+357
+00:37:50,630 --> 00:38:00,150
+الان Z of G هو مجلد من G بدي اعمل left coset عندى
+
+358
+00:38:00,150 --> 00:38:08,330
+يبقى بادي بقوله لات ال X موجود في G then ال X في
+
+359
+00:38:08,330 --> 00:38:16,500
+ال center بتابع ال G بده يساويأظن الـ X هذي تتعامل
+
+360
+00:38:16,500 --> 00:38:23,060
+مع جميع عناصر Z أو عناصر Z of G تتعامل مع جميع
+
+361
+00:38:23,060 --> 00:38:28,820
+عناصر G إذا هذي تتعامل مع الـ Z كلها اللي عندنا
+
+362
+00:38:28,820 --> 00:38:37,780
+يبقى هذا بده يعطيني Z of G Z of G في X الشكل اللي
+
+363
+00:38:37,780 --> 00:38:42,440
+عندنا هنا كان بإمكاني أبدأ غير هيكأروح أقول له
+
+364
+00:38:42,440 --> 00:38:49,540
+تعالى نشوف X Z of G X inverse شو بده تعطيني و أجيب
+
+365
+00:38:49,540 --> 00:38:54,260
+من و أجيب ال X أبدلها بالشكل هذا بتيجي ال X يعني
+
+366
+00:38:54,260 --> 00:38:59,060
+كان بإمكاني بدل ما أقول هيك أقول تعالى نشوف ال
+
+367
+00:38:59,060 --> 00:39:04,100
+group يعني و أروح أحط هنا من X inverse أشوف وين
+
+368
+00:39:04,100 --> 00:39:09,030
+بده توصلني يعنيبقول لك كويس هذا الكلام ال X كميوت
+
+369
+00:39:09,030 --> 00:39:14,850
+مع جميع العناصر اللي موجودة في Z إذا هذه بقدر أقول
+
+370
+00:39:14,850 --> 00:39:21,320
+Z of G وهنا X وهذه ال X انفرس اللي عندناهذه
+
+371
+00:39:21,320 --> 00:39:26,380
+بتعطينا مين ال identity element ال identity
+
+372
+00:39:26,380 --> 00:39:31,580
+element في أي subgroup والله بتعطيني نفس ال
+
+373
+00:39:31,580 --> 00:39:38,320
+subgroup تمام يبقى أسار X Z of G X inverse بدي
+
+374
+00:39:38,320 --> 00:39:44,480
+أسوأ من Z of G أضرب من جهة اليمين في X هذا بدي
+
+375
+00:39:44,480 --> 00:39:52,350
+يعطيكإن ال X في Z of G في ال X inverse بده تجيلك
+
+376
+00:39:52,350 --> 00:39:59,750
+كمان X بده يساوي Z of G في من في ال X هذا بده
+
+377
+00:39:59,750 --> 00:40:06,210
+يعطيلك إن ال X في Z of Gطلعلي هذا الشي بيعطينا ال
+
+378
+00:40:06,210 --> 00:40:10,250
+identity في أي element من نفس ال element و الطرف
+
+379
+00:40:10,250 --> 00:40:17,650
+اليمين Z of G أو ال X في .. هذا بيعطيك Z of G في
+
+380
+00:40:17,650 --> 00:40:23,550
+من؟ في ال X هذا بدي أعطيلك ان Z of G is a normal
+
+381
+00:40:23,550 --> 00:40:27,590
+subgroup من G يعني .. يعني قلت الفكرة البسيطة
+
+382
+00:40:27,590 --> 00:40:31,710
+الأولى اللي قلناها أوي الثانية كله بيأدي إلى نفس
+
+383
+00:40:31,710 --> 00:40:37,100
+الموضوعوالله بيكفل اللي قلناها بس احنا مسحناها
+
+384
+00:40:37,100 --> 00:40:43,080
+القطب اللي كنا .. هذه الان X Z X inverse بده سوى
+
+385
+00:40:43,080 --> 00:40:47,080
+مين؟ بده سوى ..
+
+386
+00:40:47,080 --> 00:40:51,160
+خليكم معايا احنا هذي ال sub group أخدنا X في G
+
+387
+00:40:51,160 --> 00:40:55,440
+وقلنا تعالي شوف المقدر هذا إيش بيعطينا يعني أنا
+
+388
+00:40:55,440 --> 00:41:00,220
+جيت اشوف هذا شو بدي يعطينا امشي طلع مين طلع هو Z
+
+389
+00:41:00,220 --> 00:41:06,350
+of G اللي هي النظرية subsetالنظرية صبست وماقلناش
+
+390
+00:41:06,350 --> 00:41:12,730
+تساوي لإن احنا الصبس جيبنا من اليساوي لو قدرت تثبت
+
+391
+00:41:12,730 --> 00:41:17,230
+هذا الكلام إن هذا بيساوي هذا بيكون قد الواجب بس
+
+392
+00:41:17,230 --> 00:41:21,710
+أنا بدي أحاول أحطلك التعريف كلام صح مظبوط ماحدش
+
+393
+00:41:21,710 --> 00:41:24,790
+بيقدر يقول غلط فيه هذا بس أنا حبيت أجيب التعريف
+
+394
+00:41:24,790 --> 00:41:28,910
+الأساسي لكن لو قلت لحد هنا يبقى normal خلاصنا ولا
+
+395
+00:41:28,910 --> 00:41:34,440
+واحد اللي اعترض عليكيبقى هذا بالنسبة للمثال رقم
+
+396
+00:41:34,440 --> 00:41:40,000
+اتنين طب نجيب لك مثال رقم تلاتة انا بدي اجيبلك من
+
+397
+00:41:40,000 --> 00:41:44,800
+الشغلات اللي مرت عليك بدنا مش نبعد لسه سمعت بال
+
+398
+00:41:44,800 --> 00:41:49,000
+special linear group of two by two matrices over R
+
+399
+00:41:49,000 --> 00:41:56,770
+انا ادعي ان هذه كمان normalالان ال special linear
+
+400
+00:41:56,770 --> 00:42:02,150
+group of two by two matrices over R هذي normal من
+
+401
+00:42:02,150 --> 00:42:06,070
+ال general linear group of two by two matrices
+
+402
+00:42:06,070 --> 00:42:11,990
+over R ليش هذي؟ بدي اثبت شرطين الشرط الأول انها
+
+403
+00:42:11,990 --> 00:42:17,230
+subgroup اتنين بدي اثبت خاصية ال normality يبقى
+
+404
+00:42:17,230 --> 00:42:19,450
+الان solution
+
+405
+00:42:22,250 --> 00:42:26,870
+بتروح تقول ايه ال special linear group of two by
+
+406
+00:42:26,870 --> 00:42:31,330
+two matrices over R sub group من ال general linear
+
+407
+00:42:31,330 --> 00:42:38,350
+group of two by two matrices over R وهذه مثال
+
+408
+00:42:38,350 --> 00:42:47,010
+سابق هذه أثبتناها قبل ذلكطب كويس الان بروح اخد
+
+409
+00:42:47,010 --> 00:42:51,990
+element من G و بدي اخد element من ال special و
+
+410
+00:42:51,990 --> 00:42:55,690
+اشوف حصل ضرب ال element من G في ال element من ال
+
+411
+00:42:55,690 --> 00:43:00,390
+special في معكوس ال element تبعي انطلع والله ال
+
+412
+00:43:00,390 --> 00:43:03,330
+determinant ايه اللي بدي يساوي واحد بيكون حصل
+
+413
+00:43:03,330 --> 00:43:06,260
+الضرب هذا موجود وانفي ال special وبالتالي ال
+
+414
+00:43:06,260 --> 00:43:11,840
+special هه normal subgroup من main من G يبقى
+
+415
+00:43:11,840 --> 00:43:14,480
+بالداخل اكتب لك الحل على الشجرة التانية
+
+416
+00:43:28,720 --> 00:43:34,740
+أفترض أن ال A موجودة في ال general linear group of
+
+417
+00:43:34,740 --> 00:43:41,000
+2 by 2 matrices over R ويكون موجودة في ال special
+
+418
+00:43:41,000 --> 00:43:48,000
+linear group of 2 by 2 matrices over Rأريد أن أخذ
+
+419
+00:43:48,000 --> 00:43:54,640
+الـ A بـ A إنفرس إذا كنت أثبت إن هذه موجودة في الـ
+
+420
+00:43:54,640 --> 00:43:58,860
+Special يبقى هو الشرط اللي قلنا عليه الشرط التالت
+
+421
+00:43:58,860 --> 00:44:03,200
+هو المساحنة أه هذه موجودة تمام يبقى بدي أحاول
+
+422
+00:44:03,200 --> 00:44:09,300
+أثبتها فبدي أخدي determinant لمين لهذه المصوفة
+
+423
+00:44:09,300 --> 00:44:15,530
+يبقى حسب الجبرة الخاطية هذه determinant للـ Aفى
+
+424
+00:44:15,530 --> 00:44:19,970
+الـ determinant للـ B فى الـ determinant للـ A
+
+425
+00:44:19,970 --> 00:44:23,650
+inverse صاروا هدور الـ real numbers الـ real
+
+426
+00:44:23,650 --> 00:44:28,350
+numbers are commutes يبقى هذا الـ determinant للـ
+
+427
+00:44:28,350 --> 00:44:33,070
+A فى الـ determinant للـ A inverse فى الـ
+
+428
+00:44:33,070 --> 00:44:37,870
+determinant للـ B يبقى .. بدى أرجعه إلى أصله يبقى
+
+429
+00:44:37,870 --> 00:44:42,170
+الـ determinant للـ A فى الـ A inverse فى الـ
+
+430
+00:44:42,170 --> 00:44:47,280
+determinant للـ Bالمصوفة فيما عكوزها بالـ
+
+431
+00:44:47,280 --> 00:44:52,240
+determinant لمصوفة الوحدة في الـ determinant للـ P
+
+432
+00:44:52,240 --> 00:44:58,920
+محدد مصوفة الوحدة جداش؟ واحد صحيح محدد المصوفة بـ
+
+433
+00:44:58,920 --> 00:45:03,320
+B برضه بواحد لأنها موجودة وين؟بالـ Special يبقى
+
+434
+00:45:03,320 --> 00:45:09,800
+الـ
+
+435
+00:45:09,800 --> 00:45:14,980
+ABA inverse موجودة في الـ Special Linear Group of
+
+436
+00:45:14,980 --> 00:45:20,280
+2x2 matrices over R بناء عليه الـ Special Linear
+
+437
+00:45:20,280 --> 00:45:25,400
+Group of 2x2 matrices over R is a normal subgroup
+
+438
+00:45:25,400 --> 00:45:30,620
+من الـ General Linear Group of 2x2 matrices over R
+
+439
+00:45:31,450 --> 00:45:38,970
+يبقى هذا مثال آخر على ال .. على اللي عندنا خد مثال
+
+440
+00:45:38,970 --> 00:45:43,390
+أربعة مثال
+
+441
+00:45:43,390 --> 00:45:49,030
+أربعة the alternating
+
+442
+00:45:49,030 --> 00:45:53,490
+group
+
+443
+00:45:53,490 --> 00:45:59,850
+the alternating group اربعة
+
+444
+00:46:04,190 --> 00:46:10,170
+التاني جروب AN is
+
+445
+00:46:10,170 --> 00:46:19,130
+a normal subgroup من من ال SN ليش
+
+446
+00:46:19,130 --> 00:46:22,450
+هذي normal باجي بقوله because
+
+447
+00:46:26,200 --> 00:46:31,900
+بدي اخد element في sn و element في an طبعا انا
+
+448
+00:46:31,900 --> 00:46:36,460
+اخدناها سابقا انها ال subgroup مظبوط ال a for
+
+449
+00:46:36,460 --> 00:46:42,680
+because ال an هدى ال subgroup من ال sn and
+
+450
+00:46:45,520 --> 00:46:55,140
+Alpha موجودة في الـS in and Beta موجودة في الـA in
+
+451
+00:46:55,140 --> 00:47:05,920
+thenأخذ العنصر SN والعنصر AN ومعكس العنصر SM لو
+
+452
+00:47:05,920 --> 00:47:11,420
+طلع هذا الكلام even يبقى هذا حصلت ضربوين في SN
+
+453
+00:47:11,420 --> 00:47:19,110
+يكون خلصنا يبقى هذا الكلام هادئةقد تكون even وقد
+
+454
+00:47:19,110 --> 00:47:24,150
+تكون odd لنا في ال sense إن كان even يبقى معكوسة
+
+455
+00:47:24,150 --> 00:47:28,370
+even هذه even ماعنديش مشكلة إن كان هذه odd هذه
+
+456
+00:47:28,370 --> 00:47:32,370
+even هذه odd يبقى المجموع اللي هو even وبالتالي
+
+457
+00:47:32,370 --> 00:47:36,770
+هذه موجودة على طول الخططبعا أثبتناها قبل إيه
+
+458
+00:47:36,770 --> 00:47:44,930
+أخدناها سؤال وحلناه يبقى then هذه موجودة في الان
+
+459
+00:47:44,930 --> 00:47:54,870
+because السبب أن even زائد even زائد even بده
+
+460
+00:47:54,870 --> 00:48:05,410
+يساوي even and odd زائد evenزائد اد بده يعطينا
+
+461
+00:48:05,410 --> 00:48:10,870
+even مشان هيك هذه normal طبعا بنكمل في المحاضرة
+
+462
+00:48:10,870 --> 00:48:12,950
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d3c8766e6763d36a78d2158bef028baa66809313
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3706, "start": 21.58, "end": 37.06, "text": "بسم الله الرحمن الرحيم في نهاية المحاضرة الماضية أخدنا نظرية النظرية بتقول لو عندي رقمين S و T are relatively prime يبقى ال U S T isomorphic", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 8717, 11296, 10632, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 5551, 9778, 3215, 8315, 8717, 19913, 2288, 10632, 28239, 19913, 2288, 10632, 39894, 39648, 45164, 18871, 16254, 12602, 4587, 2304, 9957, 318, 4032, 314, 366, 7226, 5835, 7251, 3555, 4587, 7578, 2423, 624, 318, 314, 307, 32702, 299], "avg_logprob": -0.1745233076103663, "compression_ratio": 1.4350649350649352, "no_speech_prob": 0.0, "words": [{"start": 21.58, "end": 21.9, "word": "بسم", "probability": 0.691650390625}, {"start": 21.9, "end": 22.12, "word": " الله", "probability": 0.95556640625}, {"start": 22.12, "end": 22.52, "word": " الرحمن", "probability": 0.9275716145833334}, {"start": 22.52, "end": 23.34, "word": " الرحيم", "probability": 0.9921875}, {"start": 23.34, "end": 24.34, "word": " في", "probability": 0.66650390625}, {"start": 24.34, "end": 24.78, "word": " نهاية", "probability": 0.9612630208333334}, {"start": 24.78, "end": 25.6, "word": " المحاضرة", "probability": 0.9884033203125}, {"start": 25.6, "end": 26.4, "word": " الماضية", "probability": 0.95849609375}, {"start": 26.4, "end": 26.94, "word": " أخدنا", "probability": 0.8621826171875}, {"start": 26.94, "end": 27.6, "word": " نظرية", "probability": 0.98486328125}, {"start": 27.6, "end": 28.72, "word": " النظرية", "probability": 0.8388671875}, {"start": 28.72, "end": 29.16, "word": " بتقول", "probability": 0.935791015625}, {"start": 29.16, "end": 29.54, "word": " لو", "probability": 0.8115234375}, {"start": 29.54, "end": 30.1, "word": " عندي", "probability": 0.6405029296875}, {"start": 30.1, "end": 30.84, "word": " رقمين", "probability": 0.952392578125}, {"start": 30.84, "end": 31.2, "word": " S", "probability": 0.4248046875}, {"start": 31.2, 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Product لمن؟ لـ two groups لـ three groups لـ four groups وما إلى ذلك بشرط يكون ال S و ال T are relatively a prime", "tokens": [1211, 1211, 39184, 2546, 48277, 22005, 20449, 9154, 20449, 2423, 39184, 35514, 37495, 22653, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 2423, 39184, 8229, 15844, 20328, 1829, 17082, 3660, 48277, 22005, 5296, 27842, 22807, 5296, 39184, 732, 3935, 5296, 39184, 1045, 3935, 5296, 39184, 1451, 3935, 4032, 15042, 30731, 29910, 23275, 4724, 46309, 9566, 7251, 30544, 2423, 318, 4032, 2423, 314, 366, 7226, 257, 5835], "avg_logprob": -0.3991477236603246, "compression_ratio": 1.4285714285714286, "no_speech_prob": 0.0, "words": [{"start": 37.27, "end": 37.69, "word": "للـ", "probability": 0.3546549479166667}, {"start": 37.69, "end": 37.97, "word": " US", "probability": 0.71484375}, {"start": 37.97, "end": 38.77, "word": " External", "probability": 0.246826171875}, {"start": 38.77, "end": 39.29, "word": " Product", "probability": 0.1529541015625}, {"start": 39.29, "end": 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"seek": 8310, "start": 57.24, "end": 83.1, "text": "واخدنا كمان نقطة ان U S T على S isomorphic ل U T وكذلك U T ل U S T isomorphic ل U S وزيادة على ذلك رولر عليها بنقول لو عندنا الرقم M واستطعنا ال M نكتبه على الشكل التالي يبقى M بده يسوى N واحد", "tokens": [2407, 47283, 3215, 8315, 9122, 2304, 7649, 8717, 47432, 3660, 16472, 624, 318, 314, 15844, 318, 307, 32702, 299, 5296, 624, 314, 4032, 4117, 8848, 23275, 624, 314, 5296, 624, 318, 314, 307, 32702, 299, 5296, 624, 318, 4032, 11622, 1829, 18513, 3660, 15844, 29910, 23275, 12602, 12610, 2288, 25894, 11296, 44945, 39648, 45164, 43242, 8315, 34892, 4587, 2304, 376, 4032, 995, 14851, 9566, 3615, 8315, 2423, 376, 8717, 4117, 2655, 3555, 3224, 15844, 25124, 28820, 16712, 6027, 1829, 7251, 3555, 4587, 7578, 376, 47525, 3224, 7251, 3794, 2407, 7578, 426, 36764, 24401], "avg_logprob": -0.24551196982885928, "compression_ratio": 1.644808743169399, "no_speech_prob": 0.0, "words": [{"start": 57.24, "end": 57.84, "word": "واخدنا", "probability": 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0.90185546875}, {"start": 395.05, "end": 395.59, "word": " وعشرين", "probability": 0.9580078125}, {"start": 395.59, "end": 396.01, "word": " اتنين", "probability": 0.895751953125}, {"start": 396.01, "end": 396.37, "word": " relative", "probability": 0.95947265625}, {"start": 396.37, "end": 396.61, "word": " to", "probability": 0.955078125}, {"start": 396.61, "end": 396.65, "word": " the", "probability": 0.8271484375}, {"start": 396.65, "end": 396.85, "word": " prime", "probability": 0.9228515625}, {"start": 396.85, "end": 397.39, "word": " والتلاتة", "probability": 0.857763671875}, {"start": 397.39, "end": 397.95, "word": " وعشرين", "probability": 0.97265625}, {"start": 397.95, "end": 398.59, "word": " يبقى", "probability": 0.8707275390625}, {"start": 398.59, "end": 398.93, "word": " فعلا", "probability": 0.92333984375}, {"start": 398.93, "end": 399.57, "word": " الستة", "probability": 0.7464192708333334}, {"start": 399.57, "end": 400.21, "word": " واربعين", "probability": 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following facts دي عندي حقائق مهمة جدا", "tokens": [41185, 43242, 8315, 4386, 13672, 1829, 31439, 4386, 13672, 1829, 31439, 12174, 995, 22488, 3660, 25062, 995, 22488, 3660, 29538, 23032, 3555, 3615, 995, 4724, 2288, 3224, 29399, 8978, 11933, 24401, 7578, 9673, 2288, 26108, 3615, 38392, 1975, 34268, 2304, 3215, 25894, 11296, 23758, 33251, 2655, 16758, 35525, 8848, 23275, 47525, 8315, 8717, 47283, 3215, 11296, 9122, 5016, 4587, 16373, 4587, 321, 362, 264, 3480, 5570, 34051, 264, 3480, 9130, 11778, 1829, 18871, 16254, 11331, 4587, 16373, 4587, 3714, 16095, 3660, 10874, 28259], "avg_logprob": -0.15299478936053457, "compression_ratio": 1.6428571428571428, "no_speech_prob": 0.0, "words": [{"start": 790.27, "end": 790.61, "word": "في", "probability": 0.217041015625}, {"start": 790.61, "end": 791.39, "word": " عندنا", "probability": 0.91845703125}, {"start": 791.39, "end": 791.53, "word": " ..", "probability": 0.14404296875}, {"start": 791.53, "end": 791.75, "word": " اللي", "probability": 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external", "probability": 0.377685546875}, {"start": 1420.88, "end": 1421.22, "word": " product", "probability": 0.66650390625}, {"start": 1421.22, "end": 1422.04, "word": " لزد", "probability": 0.8338216145833334}, {"start": 1422.04, "end": 1422.42, "word": " أربع", "probability": 0.80419921875}, {"start": 1422.42, "end": 1422.84, "word": " external", "probability": 0.213623046875}, {"start": 1422.84, "end": 1423.38, "word": " product", "probability": 0.9580078125}, {"start": 1423.38, "end": 1423.88, "word": " لزد", "probability": 0.9698893229166666}, {"start": 1423.88, "end": 1424.48, "word": " ستة", "probability": 0.9615885416666666}, {"start": 1424.48, "end": 1425.2, "word": " external", "probability": 0.67236328125}, {"start": 1425.2, "end": 1425.6, "word": " product", "probability": 0.96142578125}, {"start": 1425.6, "end": 1426.54, "word": " لزد", "probability": 0.9762369791666666}, {"start": 1426.54, "end": 1427.08, "word": " أربع", "probability": 0.876953125}, {"start": 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element", "probability": 0.9287109375}, {"start": 1446.62, "end": 1446.94, "word": " ال", "probability": 0.8046875}, {"start": 1446.94, "end": 1447.38, "word": " order", "probability": 0.95703125}, {"start": 1447.38, "end": 1447.8, "word": " الو", "probability": 0.5411376953125}, {"start": 1447.8, "end": 1448.14, "word": " كذا", "probability": 0.93603515625}, {"start": 1448.14, "end": 1448.3, "word": " في", "probability": 0.853515625}, {"start": 1448.3, "end": 1448.84, "word": " سبعمية", "probability": 0.9559326171875}, {"start": 1448.84, "end": 1449.48, "word": " وعشرين", "probability": 0.9722900390625}], "temperature": 1.0}, {"id": 61, "seek": 146896, "start": 1450.0, "end": 1468.96, "text": "بروح على هذه هذه سهل التعامل معاها بس ليه 720 صعب التعامل معاها إذا بجيب هذه المكافئة لها ومن خلالها بقدر أجيب من اللي هو ال element اللي ال order عنده يعطيني إياه في السؤال", "tokens": [26890, 2407, 5016, 15844, 29538, 29538, 8608, 3224, 1211, 16712, 3615, 10943, 1211, 20449, 995, 11296, 4724, 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نعطيك", "probability": 0.90419921875}, {"start": 1489.73, "end": 1490.27, "word": " مثال", "probability": 0.962158203125}, {"start": 1490.27, "end": 1490.51, "word": " على", "probability": 0.880859375}, {"start": 1490.51, "end": 1490.87, "word": " هذا", "probability": 0.9658203125}, {"start": 1490.87, "end": 1491.53, "word": " الكلام", "probability": 0.9337565104166666}], "temperature": 1.0}, {"id": 63, "seek": 152193, "start": 1492.17, "end": 1521.93, "text": "وبالتالي المثال انت تعودت على external product مكوّن من رقمين احنا هنعطيك سنة من تلاتة من اربعة اكثر من ذلك يبقى باجي بقول example how many elements of order", "tokens": [37746, 6027, 2655, 6027, 1829, 9673, 12984, 6027, 16472, 2655, 37279, 23328, 2655, 15844, 8320, 1674, 3714, 4117, 2407, 11703, 1863, 9154, 12602, 4587, 2304, 9957, 1975, 5016, 8315, 8032, 1863, 3615, 9566, 1829, 4117, 8608, 1863, 3660, 9154, 6055, 1211, 9307, 3660, 9154, 1975, 25513, 27884, 1975, 4117, 49115, 9154, 29910, 23275, 7251, 3555, 4587, 7578, 4724, 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"probability": 0.84637451171875}, {"start": 1498.79, "end": 1499.49, "word": " احنا", "probability": 0.88818359375}, {"start": 1499.49, "end": 1500.11, "word": " هنعطيك", "probability": 0.9551595052083334}, {"start": 1500.11, "end": 1500.51, "word": " سنة", "probability": 0.568115234375}, {"start": 1500.51, "end": 1500.75, "word": " من", "probability": 0.9921875}, {"start": 1500.75, "end": 1501.51, "word": " تلاتة", "probability": 0.948974609375}, {"start": 1501.51, "end": 1501.81, "word": " من", "probability": 0.89306640625}, {"start": 1501.81, "end": 1502.45, "word": " اربعة", "probability": 0.85302734375}, {"start": 1502.45, "end": 1503.45, "word": " اكثر", "probability": 0.92529296875}, {"start": 1503.45, "end": 1503.75, "word": " من", "probability": 0.994140625}, {"start": 1503.75, "end": 1504.31, "word": " ذلك", "probability": 0.9931640625}, {"start": 1504.31, "end": 1505.33, "word": " يبقى", "probability": 0.881591796875}, {"start": 1505.33, "end": 1505.73, "word": " باجي", 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"probability": 0.937744140625}, {"start": 1606.62, "end": 1606.76, "word": " هو", "probability": 0.98828125}, {"start": 1606.76, "end": 1607.22, "word": " السؤال", "probability": 0.99267578125}, {"start": 1607.22, "end": 1607.48, "word": " هذا", "probability": 0.85791015625}], "temperature": 1.0}, {"id": 67, "seek": 161717, "start": 1608.03, "end": 1617.17, "text": "الان solution from the above example", "tokens": [6027, 7649, 3827, 490, 264, 3673, 1365], "avg_logprob": -0.5566406399011612, "compression_ratio": 0.8333333333333334, "no_speech_prob": 0.0, "words": [{"start": 1608.03, "end": 1608.55, "word": "الان", "probability": 0.75048828125}, {"start": 1608.55, "end": 1609.05, "word": " solution", "probability": 0.154052734375}, {"start": 1609.05, "end": 1611.93, "word": " from", "probability": 0.46484375}, {"start": 1611.93, "end": 1613.93, "word": " the", "probability": 0.3662109375}, {"start": 1613.93, "end": 1615.49, "word": " above", "probability": 0.9560546875}, {"start": 1615.49, "end": 1617.17, "word": " example", "probability": 0.96142578125}], "temperature": 1.0}, {"id": 68, "seek": 163947, "start": 1618.67, "end": 1639.47, "text": "من المثال اللي فوق الـ U720 أيزو مورفك ل Z2 Extended like product مع Z4 Extended like product مع Z6 Extended like product مع Z4", "tokens": [27842, 9673, 12984, 6027, 13672, 1829, 6156, 30543, 2423, 39184, 624, 22, 2009, 5551, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 1176, 17, 9881, 3502, 411, 1674, 20449, 1176, 19, 9881, 3502, 411, 1674, 20449, 1176, 21, 9881, 3502, 411, 1674, 20449, 1176, 19], "avg_logprob": -0.3371263554562693, "compression_ratio": 1.5631067961165048, "no_speech_prob": 0.0, "words": [{"start": 1618.67, "end": 1618.99, "word": "من", "probability": 0.350830078125}, {"start": 1618.99, "end": 1619.61, "word": " المثال", "probability": 0.9568684895833334}, {"start": 1619.61, "end": 1619.81, "word": " اللي", "probability": 0.66357421875}, {"start": 1619.81, "end": 1620.35, "word": " فوق", "probability": 0.723388671875}, {"start": 1620.35, "end": 1621.31, "word": " الـ", "probability": 0.4908447265625}, {"start": 1621.31, "end": 1623.57, "word": " U720", "probability": 0.64697265625}, {"start": 1623.57, "end": 1624.65, "word": " أيزو", "probability": 0.678466796875}, {"start": 1624.65, "end": 1625.41, "word": " مورفك", "probability": 0.7877197265625}, {"start": 1625.41, "end": 1625.99, "word": " ل", "probability": 0.87841796875}, {"start": 1625.99, "end": 1627.09, "word": " Z2", "probability": 0.6512451171875}, {"start": 1627.09, "end": 1628.03, "word": " Extended", "probability": 0.550048828125}, {"start": 1628.03, "end": 1628.35, "word": " like", "probability": 0.2469482421875}, {"start": 1628.35, "end": 1629.11, "word": " product", "probability": 0.76611328125}, {"start": 1629.11, "end": 1629.81, "word": " مع", "probability": 0.84765625}, {"start": 1629.81, "end": 1631.23, "word": " Z4", "probability": 0.964599609375}, {"start": 1631.23, "end": 1632.51, "word": " Extended", "probability": 0.93701171875}, {"start": 1632.51, "end": 1632.89, "word": " like", "probability": 0.92529296875}, {"start": 1632.89, "end": 1633.59, "word": " product", "probability": 0.95654296875}, {"start": 1633.59, "end": 1634.23, "word": " مع", "probability": 0.9736328125}, {"start": 1634.23, "end": 1635.21, "word": " Z6", "probability": 0.98876953125}, {"start": 1635.21, "end": 1636.11, "word": " Extended", "probability": 0.95751953125}, {"start": 1636.11, "end": 1636.47, "word": " like", "probability": 0.9462890625}, {"start": 1636.47, "end": 1637.09, "word": " product", "probability": 0.9580078125}, {"start": 1637.09, "end": 1637.35, "word": " مع", "probability": 0.98779296875}, {"start": 1637.35, "end": 1639.47, "word": " Z4", "probability": 0.909423828125}], "temperature": 1.0}, {"id": 69, "seek": 167266, "start": 1642.86, "end": 1672.66, "text": "أى element هنا ال order إليه يساوي اتناش يبقى بناء عليه يبدو لو حسب فيه التانية يبقى so the number of elements of order اتناش in u سبعمية او عشرين", "tokens": [10721, 7578, 4478, 34105, 2423, 1668, 11933, 20292, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 33599, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 7251, 44510, 2407, 45164, 11331, 35457, 8978, 3224, 16712, 7649, 10632, 7251, 3555, 4587, 7578, 370, 264, 1230, 295, 4959, 295, 1668, 1975, 2655, 1863, 33599, 294, 344, 8608, 3555, 25957, 10632, 1975, 2407, 6225, 46309, 9957], "avg_logprob": -0.4029738047430592, "compression_ratio": 1.4473684210526316, "no_speech_prob": 0.0, "words": [{"start": 1642.86, "end": 1643.38, "word": "أى", "probability": 0.4554443359375}, {"start": 1643.38, "end": 1644.06, "word": " element", "probability": 0.69140625}, {"start": 1644.06, "end": 1644.48, "word": " هنا", "probability": 0.61767578125}, {"start": 1644.48, "end": 1644.7, "word": " ال", "probability": 0.69482421875}, {"start": 1644.7, "end": 1645.04, "word": " order", "probability": 0.8408203125}, {"start": 1645.04, "end": 1645.48, "word": " إليه", "probability": 0.4498087565104167}, {"start": 1645.48, "end": 1645.78, "word": " يساوي", "probability": 0.8304443359375}, {"start": 1645.78, "end": 1646.3, "word": " اتناش", "probability": 0.684722900390625}, {"start": 1646.3, "end": 1647.52, "word": " يبقى", "probability": 0.7093505859375}, {"start": 1647.52, "end": 1651.92, "word": " بناء", "probability": 0.5141448974609375}, {"start": 1651.92, "end": 1652.52, "word": " عليه", "probability": 0.8466796875}, {"start": 1652.52, "end": 1653.06, "word": " يبدو", "probability": 0.4399820963541667}, {"start": 1653.06, "end": 1653.2, "word": " لو", "probability": 0.57470703125}, {"start": 1653.2, "end": 1653.58, "word": " حسب", "probability": 0.908935546875}, {"start": 1653.58, "end": 1653.86, "word": " فيه", "probability": 0.861572265625}, {"start": 1653.86, "end": 1654.26, "word": " التانية", "probability": 0.712890625}, {"start": 1654.26, "end": 1656.24, "word": " يبقى", "probability": 0.92138671875}, {"start": 1656.24, "end": 1656.78, "word": " so", "probability": 0.1943359375}, {"start": 1656.78, "end": 1658.18, "word": " the", "probability": 0.77587890625}, {"start": 1658.18, "end": 1659.52, "word": " number", "probability": 0.9775390625}, {"start": 1659.52, "end": 1661.38, "word": " of", "probability": 0.9609375}, {"start": 1661.38, "end": 1663.1, "word": " elements", "probability": 0.8486328125}, {"start": 1663.1, "end": 1664.8, "word": " of", "probability": 0.95166015625}, {"start": 1664.8, "end": 1666.34, "word": " order", "probability": 0.94580078125}, {"start": 1666.34, "end": 1668.48, "word": " اتناش", "probability": 0.857666015625}, {"start": 1668.48, "end": 1669.04, "word": " in", "probability": 0.896484375}, {"start": 1669.04, "end": 1670.1, "word": " u", "probability": 0.5107421875}, {"start": 1670.1, "end": 1671.18, "word": " سبعمية", "probability": 0.9031982421875}, {"start": 1671.18, "end": 1671.62, "word": " او", "probability": 0.7132568359375}, {"start": 1671.62, "end": 1672.66, "word": " عشرين", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 70, "seek": 168928, "start": 1674.98, "end": 1689.28, "text": "equal of the number of elements of order", "tokens": [12816, 304, 295, 264, 1230, 295, 4959, 295, 1668], "avg_logprob": -0.5316406488418579, "compression_ratio": 0.9302325581395349, "no_speech_prob": 0.0, "words": [{"start": 1674.98, "end": 1676.38, "word": "equal", "probability": 0.59161376953125}, {"start": 1676.38, "end": 1676.76, "word": " of", "probability": 0.2298583984375}, {"start": 1676.76, "end": 1678.36, "word": " the", "probability": 0.1580810546875}, {"start": 1678.36, "end": 1680.06, "word": " number", "probability": 0.9365234375}, {"start": 1680.06, "end": 1682.56, "word": " of", "probability": 0.9638671875}, {"start": 1682.56, "end": 1684.66, "word": " elements", "probability": 0.8603515625}, {"start": 1684.66, "end": 1687.68, "word": " of", "probability": 0.90966796875}, {"start": 1687.68, "end": 1689.28, "word": " order", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 71, "seek": 171526, "start": 1706.26, "end": 1715.26, "text": "طب احنا اخدنا اول نظرية في هذا section وكان مشان اجيب ال order لل element", "tokens": [9566, 3555, 1975, 5016, 8315, 1975, 9778, 3215, 8315, 1975, 12610, 8717, 19913, 2288, 10632, 8978, 23758, 3541, 4032, 41361, 37893, 7649, 1975, 7435, 1829, 3555, 2423, 1668, 24976, 4478], "avg_logprob": -0.2266885099872466, "compression_ratio": 1.153061224489796, "no_speech_prob": 0.0, "words": [{"start": 1706.26, "end": 1707.3, "word": "طب", "probability": 0.5054931640625}, {"start": 1707.3, "end": 1707.7, "word": " احنا", "probability": 0.9029947916666666}, {"start": 1707.7, "end": 1708.66, "word": " اخدنا", "probability": 0.8717041015625}, {"start": 1708.66, "end": 1708.96, "word": " اول", "probability": 0.8662109375}, {"start": 1708.96, "end": 1709.44, "word": " نظرية", "probability": 0.9779052734375}, {"start": 1709.44, "end": 1709.64, "word": " في", "probability": 0.73876953125}, {"start": 1709.64, "end": 1709.96, "word": " هذا", "probability": 0.79296875}, {"start": 1709.96, "end": 1710.48, "word": " section", "probability": 0.31640625}, {"start": 1710.48, "end": 1711.62, "word": " وكان", "probability": 0.89794921875}, {"start": 1711.62, "end": 1712.14, "word": " مشان", "probability": 0.88232421875}, {"start": 1712.14, "end": 1712.88, "word": " اجيب", "probability": 0.9412841796875}, {"start": 1712.88, "end": 1713.74, "word": " ال", "probability": 0.6767578125}, {"start": 1713.74, "end": 1714.32, "word": " order", "probability": 0.9443359375}, {"start": 1714.32, "end": 1714.7, "word": " لل", "probability": 0.5703125}, {"start": 1714.7, "end": 1715.26, "word": " element", "probability": 0.8935546875}], "temperature": 1.0}, {"id": 72, "seek": 173393, "start": 1716.63, "end": 1733.93, "text": "المُركّب مثلا من مُركّبة هنا بجيب ال list common multiple لمن ل ال two orders اللي عنده وبالتالي بكون جابت ال order لل element اللي موجود في ال external direct product لذلك بروح أخد element هنا", "tokens": [45340, 10859, 31747, 11703, 3555, 50113, 15040, 9154, 3714, 10859, 31747, 11703, 49401, 34105, 4724, 7435, 1829, 3555, 2423, 1329, 2689, 3866, 5296, 27842, 5296, 2423, 732, 9470, 13672, 1829, 43242, 3224, 46599, 6027, 2655, 6027, 1829, 4724, 30544, 10874, 16758, 2655, 2423, 1668, 24976, 4478, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 8320, 2047, 1674, 5296, 8848, 23275, 4724, 32887, 5016, 5551, 9778, 3215, 4478, 34105], "avg_logprob": -0.3235294060672031, "compression_ratio": 1.486910994764398, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1716.6299999999999, "end": 1717.53, "word": "المُركّب", "probability": 0.56717529296875}, {"start": 1717.53, "end": 1718.03, "word": " مثلا", "probability": 0.55780029296875}, {"start": 1718.03, "end": 1718.19, "word": " من", "probability": 0.45263671875}, {"start": 1718.19, "end": 1718.95, "word": " مُركّبة", "probability": 0.91953125}, {"start": 1718.95, "end": 1719.17, "word": " هنا", "probability": 0.587890625}, {"start": 1719.17, "end": 1719.99, "word": " بجيب", "probability": 0.66021728515625}, {"start": 1719.99, "end": 1720.09, "word": " ال", "probability": 0.5283203125}, {"start": 1720.09, "end": 1720.33, "word": " list", "probability": 0.81787109375}, {"start": 1720.33, "end": 1720.73, "word": " common", "probability": 0.2008056640625}, {"start": 1720.73, "end": 1721.45, "word": " multiple", "probability": 0.771484375}, {"start": 1721.45, "end": 1722.51, "word": " لمن", "probability": 0.4744873046875}, {"start": 1722.51, "end": 1722.97, "word": " ل", "probability": 0.443359375}, {"start": 1722.97, "end": 1723.11, "word": " ال", "probability": 0.336181640625}, {"start": 1723.11, "end": 1723.37, "word": " two", "probability": 0.7744140625}, {"start": 1723.37, "end": 1723.97, "word": " orders", "probability": 0.8564453125}, {"start": 1723.97, "end": 1724.25, "word": " اللي", "probability": 0.844970703125}, {"start": 1724.25, "end": 1724.59, "word": " عنده", "probability": 0.908447265625}, {"start": 1724.59, "end": 1725.05, "word": " وبالتالي", "probability": 0.9330078125}, {"start": 1725.05, "end": 1725.49, "word": " بكون", "probability": 0.951904296875}, {"start": 1725.49, "end": 1726.03, "word": " جابت", "probability": 0.9554036458333334}, {"start": 1726.03, "end": 1726.53, "word": " ال", "probability": 0.8876953125}, {"start": 1726.53, "end": 1726.97, "word": " order", "probability": 0.96337890625}, {"start": 1726.97, "end": 1727.33, "word": " لل", "probability": 0.62255859375}, {"start": 1727.33, "end": 1727.87, "word": " element", "probability": 0.95361328125}, {"start": 1727.87, "end": 1728.19, "word": " اللي", "probability": 0.9306640625}, {"start": 1728.19, "end": 1728.59, "word": " موجود", "probability": 0.98486328125}, {"start": 1728.59, "end": 1728.71, "word": " في", "probability": 0.80419921875}, {"start": 1728.71, "end": 1728.85, "word": " ال", "probability": 0.419921875}, {"start": 1728.85, "end": 1729.39, "word": " external", "probability": 0.9560546875}, {"start": 1729.39, "end": 1730.03, "word": " direct", "probability": 0.61962890625}, {"start": 1730.03, "end": 1730.69, "word": " product", "probability": 0.96923828125}, {"start": 1730.69, "end": 1731.85, "word": " لذلك", "probability": 0.9539388020833334}, {"start": 1731.85, "end": 1732.29, "word": " بروح", "probability": 0.8400065104166666}, {"start": 1732.29, "end": 1732.73, "word": " أخد", "probability": 0.8277994791666666}, {"start": 1732.73, "end": 1733.33, "word": " element", "probability": 0.974609375}, {"start": 1733.33, "end": 1733.93, "word": " هنا", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 73, "seek": 175003, "start": 1734.43, "end": 1750.03, "text": "و افترض ان هذا ال element ال order له يساوي 12 و ابحث عن ال orders المختلفة في هذه الحالة يبقى بداجي اقول له let ال a و ال b و ال c", "tokens": [2407, 1975, 5172, 2655, 43042, 16472, 23758, 2423, 4478, 2423, 1668, 46740, 7251, 3794, 995, 45865, 2272, 4032, 48127, 5016, 12984, 18871, 2423, 9470, 9673, 46456, 46538, 3660, 8978, 29538, 21542, 6027, 3660, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 46740, 718, 2423, 257, 4032, 2423, 272, 4032, 2423, 269], "avg_logprob": -0.31279482031768224, "compression_ratio": 1.4265734265734267, "no_speech_prob": 0.0, "words": [{"start": 1734.43, "end": 1735.43, "word": "و", "probability": 0.1802978515625}, {"start": 1735.43, "end": 1736.07, "word": " افترض", "probability": 0.78607177734375}, {"start": 1736.07, "end": 1736.35, "word": " ان", "probability": 0.876953125}, {"start": 1736.35, "end": 1736.69, "word": " هذا", "probability": 0.68017578125}, {"start": 1736.69, "end": 1736.83, "word": " ال", "probability": 0.78857421875}, {"start": 1736.83, "end": 1737.21, "word": " element", "probability": 0.3759765625}, {"start": 1737.21, "end": 1737.49, "word": " ال", "probability": 0.529296875}, {"start": 1737.49, "end": 1737.93, "word": " order", "probability": 0.9501953125}, {"start": 1737.93, "end": 1738.29, "word": " له", "probability": 0.1356201171875}, {"start": 1738.29, "end": 1738.81, "word": " يساوي", "probability": 0.8978271484375}, {"start": 1738.81, "end": 1739.29, "word": " 12", "probability": 0.62451171875}, {"start": 1739.29, "end": 1739.85, "word": " و", "probability": 0.465576171875}, {"start": 1739.85, "end": 1740.43, "word": " ابحث", "probability": 0.8665364583333334}, {"start": 1740.43, "end": 1740.73, "word": " عن", "probability": 0.99560546875}, {"start": 1740.73, "end": 1740.93, "word": " ال", "probability": 0.927734375}, {"start": 1740.93, "end": 1741.71, "word": " orders", "probability": 0.80859375}, {"start": 1741.71, "end": 1743.01, "word": " المختلفة", "probability": 0.9862060546875}, {"start": 1743.01, "end": 1743.23, "word": " في", "probability": 0.93359375}, {"start": 1743.23, "end": 1743.71, "word": " هذه", "probability": 0.90087890625}, {"start": 1743.71, "end": 1744.63, "word": " الحالة", "probability": 0.9381510416666666}, {"start": 1744.63, "end": 1745.49, "word": " يبقى", "probability": 0.912109375}, {"start": 1745.49, "end": 1745.91, "word": " بداجي", "probability": 0.4921061197916667}, {"start": 1745.91, "end": 1746.17, "word": " اقول", "probability": 0.91796875}, {"start": 1746.17, "end": 1746.37, "word": " له", "probability": 0.52685546875}, {"start": 1746.37, "end": 1746.83, "word": " let", "probability": 0.412109375}, {"start": 1746.83, "end": 1748.03, "word": " ال", "probability": 0.82275390625}, {"start": 1748.03, "end": 1748.41, "word": " a", "probability": 0.63818359375}, {"start": 1748.41, "end": 1748.71, "word": " و", "probability": 0.50830078125}, {"start": 1748.71, "end": 1748.91, "word": " ال", "probability": 0.841796875}, {"start": 1748.91, "end": 1749.21, "word": " b", "probability": 0.9853515625}, {"start": 1749.21, "end": 1749.53, "word": " و", "probability": 0.982421875}, {"start": 1749.53, "end": 1749.73, "word": " ال", "probability": 0.94921875}, {"start": 1749.73, "end": 1750.03, "word": " c", "probability": 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"word": " order", "probability": 0.97216796875}, {"start": 2022.44, "end": 2022.74, "word": " ال", "probability": 0.619140625}, {"start": 2022.74, "end": 2022.96, "word": " list", "probability": 0.6083984375}, {"start": 2022.96, "end": 2023.24, "word": " common", "probability": 0.94873046875}, {"start": 2023.24, "end": 2023.68, "word": " multiple", "probability": 0.97412109375}, {"start": 2023.68, "end": 2023.82, "word": " اللى", "probability": 0.756591796875}, {"start": 2023.82, "end": 2024.04, "word": " بده", "probability": 0.587158203125}, {"start": 2024.04, "end": 2024.3, "word": " يطلع", "probability": 0.9920654296875}, {"start": 2024.3, "end": 2024.78, "word": " اتناش", "probability": 0.798095703125}, {"start": 2024.78, "end": 2025.52, "word": " خد", "probability": 0.6162109375}, {"start": 2025.52, "end": 2026.06, "word": " الحالة", "probability": 0.9903971354166666}, {"start": 2026.06, "end": 2026.48, "word": " التانية", "probability": 0.9754231770833334}], "temperature": 1.0}, {"id": 87, "seek": 204320, "start": 2026.82, "end": 2043.2, "text": "ممكن يكون ال order اللي دي هو أربعة و ال C له تلاتة و ستة مش هيك وارد تمام و الباقي اللي هو اللي بيتحصيل حاصل بسيط تمام يبقى بدنا نيجي نشتغل الشغل اللي عندنا هادي", "tokens": [2304, 43020, 7251, 30544, 2423, 1668, 13672, 1829, 11778, 1829, 31439, 5551, 25513, 27884, 4032, 2423, 383, 46740, 6055, 1211, 9307, 3660, 4032, 8608, 2655, 3660, 37893, 39896, 4117, 4032, 9640, 3215, 46811, 10943, 4032, 29739, 995, 38436, 13672, 1829, 31439, 13672, 1829, 4724, 36081, 5016, 9381, 26895, 11331, 33546, 1211, 4724, 3794, 1829, 9566, 46811, 10943, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 1829, 7435, 1829, 8717, 8592, 2655, 17082, 1211, 25124, 17082, 1211, 13672, 1829, 43242, 8315, 8032, 995, 16254], "avg_logprob": -0.26750751791230165, "compression_ratio": 1.6946107784431137, "no_speech_prob": 0.0, "words": [{"start": 2026.82, "end": 2027.34, "word": "ممكن", "probability": 0.746826171875}, {"start": 2027.34, "end": 2027.76, "word": " يكون", "probability": 0.846435546875}, {"start": 2027.76, "end": 2027.94, "word": " ال", "probability": 0.45263671875}, {"start": 2027.94, "end": 2028.46, "word": " order", "probability": 0.76416015625}, {"start": 2028.46, "end": 2028.84, "word": " اللي", "probability": 0.484375}, {"start": 2028.84, "end": 2029.46, "word": " دي", "probability": 0.81884765625}, {"start": 2029.46, "end": 2029.76, "word": " هو", "probability": 0.9462890625}, {"start": 2029.76, "end": 2030.52, "word": " أربعة", "probability": 0.7587890625}, {"start": 2030.52, "end": 2031.02, "word": " و", "probability": 0.716796875}, {"start": 2031.02, "end": 2031.24, "word": " ال", "probability": 0.6357421875}, {"start": 2031.24, "end": 2031.52, "word": " C", "probability": 0.47900390625}, {"start": 2031.52, "end": 2031.94, "word": " له", "probability": 0.2149658203125}, {"start": 2031.94, "end": 2032.56, "word": " تلاتة", "probability": 0.9097900390625}, {"start": 2032.56, "end": 2032.7, "word": " و", "probability": 0.94091796875}, {"start": 2032.7, "end": 2033.22, "word": " ستة", "probability": 0.91162109375}, {"start": 2033.22, "end": 2033.48, "word": " مش", "probability": 0.658203125}, {"start": 2033.48, "end": 2033.76, "word": " هيك", "probability": 0.55615234375}, {"start": 2033.76, "end": 2034.18, "word": " وارد", "probability": 0.8489583333333334}, {"start": 2034.18, "end": 2035.2, "word": " تمام", "probability": 0.66455078125}, {"start": 2035.2, "end": 2035.6, "word": " و", "probability": 0.402587890625}, {"start": 2035.6, "end": 2036.14, "word": " الباقي", "probability": 0.80029296875}, {"start": 2036.14, "end": 2036.38, "word": " اللي", "probability": 0.9765625}, {"start": 2036.38, "end": 2036.56, "word": " هو", "probability": 0.6064453125}, {"start": 2036.56, "end": 2036.72, "word": " اللي", "probability": 0.978271484375}, {"start": 2036.72, "end": 2037.36, "word": " بيتحصيل", "probability": 0.73955078125}, {"start": 2037.36, "end": 2037.9, "word": " حاصل", "probability": 0.8924153645833334}, {"start": 2037.9, "end": 2038.4, "word": " بسيط", "probability": 0.908447265625}, {"start": 2038.4, "end": 2039.18, "word": " تمام", "probability": 0.8681640625}, {"start": 2039.18, "end": 2039.88, "word": " يبقى", "probability": 0.8646240234375}, {"start": 2039.88, "end": 2040.2, "word": " بدنا", "probability": 0.8564453125}, {"start": 2040.2, "end": 2040.52, "word": " نيجي", "probability": 0.896484375}, {"start": 2040.52, "end": 2041.44, "word": " نشتغل", "probability": 0.8875}, {"start": 2041.44, "end": 2042.06, "word": " الشغل", "probability": 0.8562825520833334}, {"start": 2042.06, "end": 2042.24, "word": " اللي", "probability": 0.978515625}, {"start": 2042.24, "end": 2042.74, "word": " عندنا", "probability": 0.919677734375}, {"start": 2042.74, "end": 2043.2, "word": " هادي", "probability": 0.5537109375}], "temperature": 1.0}, {"id": 88, "seek": 208179, "start": 2053.77, "end": 2081.79, "text": "الان قلنا بالنسبة للأولى اللي اسمها multiple تحصيل حصل يبقى دي مش هتدخل في الحساب عندنا يبقى we have two cases هي عندي حالتين الحالة الأولى ان ال order لل B بده يسوى الأربعة و ال order ل C يا إما تلاتة يا إما ستة", "tokens": [6027, 7649, 12174, 1211, 8315, 20666, 1863, 35457, 3660, 24976, 10721, 12610, 7578, 2423, 20292, 24525, 2304, 11296, 3866, 6055, 5016, 9381, 26895, 11331, 36520, 7251, 3555, 4587, 7578, 11778, 1829, 37893, 8032, 2655, 3215, 9778, 1211, 8978, 21542, 3794, 16758, 43242, 8315, 7251, 3555, 4587, 7578, 321, 362, 732, 3331, 39896, 18871, 16254, 11331, 6027, 2655, 9957, 21542, 6027, 3660, 16247, 12610, 7578, 16472, 2423, 1668, 24976, 363, 47525, 3224, 7251, 3794, 2407, 7578, 16247, 25513, 27884, 4032, 2423, 1668, 5296, 383, 35186, 11933, 15042, 6055, 1211, 9307, 3660, 35186, 11933, 15042, 8608, 2655, 3660], "avg_logprob": -0.23518040745528704, "compression_ratio": 1.6634615384615385, "no_speech_prob": 0.0, "words": [{"start": 2053.77, "end": 2054.43, "word": "الان", "probability": 0.72705078125}, {"start": 2054.43, "end": 2055.03, "word": " قلنا", "probability": 0.6650390625}, {"start": 2055.03, "end": 2055.63, "word": " بالنسبة", "probability": 0.96826171875}, {"start": 2055.63, "end": 2056.35, "word": " للأولى", "probability": 0.896728515625}, {"start": 2056.35, "end": 2056.79, "word": " اللي", "probability": 0.4769287109375}, {"start": 2056.79, "end": 2057.15, "word": " اسمها", "probability": 0.5608723958333334}, {"start": 2057.15, "end": 2057.43, "word": " multiple", "probability": 0.4072265625}, {"start": 2057.43, "end": 2058.01, "word": " تحصيل", "probability": 0.9447021484375}, {"start": 2058.01, "end": 2058.29, "word": " حصل", "probability": 0.631591796875}, {"start": 2058.29, "end": 2058.47, "word": " يبقى", "probability": 0.903564453125}, {"start": 2058.47, "end": 2058.65, "word": " دي", "probability": 0.6048583984375}, {"start": 2058.65, "end": 2058.85, "word": " مش", "probability": 0.97314453125}, {"start": 2058.85, "end": 2059.57, "word": " هتدخل", "probability": 0.9873046875}, {"start": 2059.57, "end": 2059.73, "word": " في", "probability": 0.8916015625}, {"start": 2059.73, "end": 2060.29, "word": " الحساب", "probability": 0.8430989583333334}, {"start": 2060.29, "end": 2060.87, "word": " عندنا", "probability": 0.933349609375}, {"start": 2060.87, "end": 2061.89, "word": " يبقى", "probability": 0.9705810546875}, {"start": 2061.89, "end": 2062.19, "word": " we", "probability": 0.451171875}, {"start": 2062.19, "end": 2064.21, "word": " have", "probability": 0.93896484375}, {"start": 2064.21, "end": 2065.71, "word": " two", "probability": 0.900390625}, {"start": 2065.71, "end": 2070.05, "word": " cases", "probability": 0.80712890625}, {"start": 2070.05, "end": 2070.63, "word": " هي", "probability": 0.25634765625}, {"start": 2070.63, "end": 2071.09, "word": " عندي", "probability": 0.8828125}, {"start": 2071.09, "end": 2071.89, "word": " حالتين", "probability": 0.9818115234375}, {"start": 2071.89, "end": 2073.07, "word": " الحالة", "probability": 0.95361328125}, {"start": 2073.07, "end": 2073.59, "word": " الأولى", "probability": 0.9814453125}, {"start": 2073.59, "end": 2073.91, "word": " ان", "probability": 0.509765625}, {"start": 2073.91, "end": 2074.13, "word": " ال", "probability": 0.87353515625}, {"start": 2074.13, "end": 2074.55, "word": " order", "probability": 0.96484375}, {"start": 2074.55, "end": 2074.97, "word": " لل", "probability": 0.72509765625}, {"start": 2074.97, "end": 2075.31, "word": " B", "probability": 0.281982421875}, {"start": 2075.31, "end": 2075.91, "word": " بده", "probability": 0.50048828125}, {"start": 2075.91, "end": 2076.25, "word": " يسوى", "probability": 0.7923583984375}, {"start": 2076.25, "end": 2076.89, "word": " الأربعة", "probability": 0.8929036458333334}, {"start": 2076.89, "end": 2077.43, "word": " و", "probability": 0.50146484375}, {"start": 2077.43, "end": 2077.59, "word": " ال", "probability": 0.82421875}, {"start": 2077.59, "end": 2078.03, "word": " order", "probability": 0.97216796875}, {"start": 2078.03, "end": 2078.49, "word": " ل", "probability": 0.630859375}, {"start": 2078.49, "end": 2078.71, "word": " C", "probability": 0.66064453125}, {"start": 2078.71, "end": 2079.07, "word": " يا", "probability": 0.513671875}, {"start": 2079.07, "end": 2079.35, "word": " إما", "probability": 0.73486328125}, {"start": 2079.35, "end": 2080.21, "word": " تلاتة", "probability": 0.9476318359375}, {"start": 2080.21, "end": 2080.69, "word": " يا", "probability": 0.859375}, {"start": 2080.69, "end": 2081.15, "word": " إما", "probability": 0.9658203125}, {"start": 2081.15, "end": 2081.79, "word": " ستة", "probability": 0.9886067708333334}], "temperature": 1.0}, {"id": 89, "seek": 210405, "start": 2082.31, "end": 2104.05, "text": "يبقى تلاتة واربعة الـ least common multiple يبقى 12 الستة والاربعة ال least common multiple يبقى 12 يبقى هدول يجيبولي ال element ال order يسوى كم؟ ال 12 طب أكم انصر في زيد أربعة ال order يسوى أربعة؟ بس", "tokens": [1829, 3555, 4587, 7578, 6055, 1211, 9307, 3660, 4032, 9640, 3555, 27884, 2423, 39184, 1935, 2689, 3866, 7251, 3555, 4587, 7578, 2272, 2423, 14851, 3660, 16070, 9640, 3555, 27884, 2423, 1935, 2689, 3866, 7251, 3555, 4587, 7578, 2272, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 7251, 7435, 1829, 3555, 12610, 1829, 2423, 4478, 2423, 1668, 7251, 3794, 2407, 7578, 9122, 2304, 22807, 2423, 2272, 23032, 3555, 5551, 24793, 16472, 9381, 2288, 8978, 30767, 25708, 5551, 25513, 27884, 2423, 1668, 7251, 3794, 2407, 7578, 5551, 25513, 27884, 22807, 4724, 3794], "avg_logprob": -0.4500000105963813, "compression_ratio": 1.81437125748503, "no_speech_prob": 0.0, "words": [{"start": 2082.31, "end": 2082.89, "word": "يبقى", "probability": 0.77093505859375}, {"start": 2082.89, "end": 2083.57, "word": " تلاتة", "probability": 0.8045654296875}, {"start": 2083.57, "end": 2084.23, "word": " واربعة", "probability": 0.7137451171875}, {"start": 2084.23, "end": 2084.41, "word": " الـ", "probability": 0.217437744140625}, {"start": 2084.41, "end": 2084.59, "word": " least", "probability": 0.180908203125}, {"start": 2084.59, "end": 2084.87, "word": " common", "probability": 0.947265625}, {"start": 2084.87, "end": 2085.35, "word": " multiple", "probability": 0.95654296875}, {"start": 2085.35, "end": 2085.59, "word": " يبقى", "probability": 0.68634033203125}, {"start": 2085.59, "end": 2085.97, "word": " 12", "probability": 0.202392578125}, {"start": 2085.97, "end": 2087.23, "word": " الستة", "probability": 0.4868977864583333}, {"start": 2087.23, "end": 2087.73, "word": " والاربعة", "probability": 0.84136962890625}, {"start": 2087.73, "end": 2087.87, "word": " ال", "probability": 0.9248046875}, {"start": 2087.87, "end": 2088.07, "word": " least", "probability": 0.548828125}, {"start": 2088.07, "end": 2088.33, "word": " common", "probability": 0.93359375}, {"start": 2088.33, "end": 2088.73, "word": " multiple", "probability": 0.87890625}, {"start": 2088.73, "end": 2089.03, "word": " يبقى", "probability": 0.900634765625}, {"start": 2089.03, "end": 2089.51, "word": " 12", "probability": 0.791015625}, {"start": 2089.51, "end": 2089.87, "word": " يبقى", "probability": 0.81134033203125}, {"start": 2089.87, "end": 2090.35, "word": " هدول", "probability": 0.6090494791666666}, {"start": 2090.35, "end": 2090.99, "word": " يجيبولي", "probability": 0.7001953125}, {"start": 2090.99, "end": 2091.07, "word": " ال", "probability": 0.927734375}, {"start": 2091.07, "end": 2091.49, "word": " element", "probability": 0.69970703125}, {"start": 2091.49, "end": 2092.05, "word": " ال", "probability": 0.54443359375}, {"start": 2092.05, "end": 2092.55, "word": " order", "probability": 0.8037109375}, {"start": 2092.55, "end": 2093.29, "word": " يسوى", "probability": 0.629638671875}, {"start": 2093.29, "end": 2093.99, "word": " كم؟", "probability": 0.42919921875}, {"start": 2093.99, "end": 2094.19, "word": " ال", "probability": 0.37158203125}, {"start": 2094.19, "end": 2094.57, "word": " 12", "probability": 0.7529296875}, {"start": 2094.57, "end": 2095.55, "word": " طب", "probability": 0.530029296875}, {"start": 2095.55, "end": 2096.17, "word": " أكم", "probability": 0.755859375}, {"start": 2096.17, "end": 2097.17, "word": " انصر", "probability": 0.7589518229166666}, {"start": 2097.17, "end": 2097.65, "word": " في", "probability": 0.92236328125}, {"start": 2097.65, "end": 2098.15, "word": " زيد", "probability": 0.640869140625}, {"start": 2098.15, "end": 2098.75, "word": " أربعة", "probability": 0.7537434895833334}, {"start": 2098.75, "end": 2098.93, "word": " ال", "probability": 0.8544921875}, {"start": 2098.93, "end": 2099.37, "word": " order", "probability": 0.955078125}, {"start": 2099.37, "end": 2100.19, "word": " يسوى", "probability": 0.883544921875}, {"start": 2100.19, "end": 2102.87, "word": " أربعة؟", "probability": 0.6549072265625}, {"start": 2102.87, "end": 2104.05, "word": " بس", "probability": 0.600830078125}], "temperature": 1.0}, {"id": 90, "seek": 213485, "start": 2105.61, "end": 2134.85, "text": "أتنين هو الواحد والتلاتة 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0.84375}, {"start": 2356.45, "end": 2357.17, "word": " تلاتة", "probability": 0.89599609375}, {"start": 2357.17, "end": 2357.41, "word": " يا", "probability": 0.82421875}, {"start": 2357.41, "end": 2357.73, "word": " اما", "probability": 0.938232421875}, {"start": 2357.73, "end": 2359.71, "word": " ستة", "probability": 0.9835611979166666}, {"start": 2359.71, "end": 2366.91, "word": " يبقى", "probability": 0.85491943359375}, {"start": 2366.91, "end": 2367.17, "word": " في", "probability": 0.8974609375}, {"start": 2367.17, "end": 2367.53, "word": " هذه", "probability": 0.94384765625}, {"start": 2367.53, "end": 2368.13, "word": " الحالة", "probability": 0.9728190104166666}, {"start": 2368.13, "end": 2368.69, "word": " لما", "probability": 0.875732421875}, {"start": 2368.69, "end": 2368.85, "word": " ال", "probability": 0.9814453125}, {"start": 2368.85, "end": 2369.23, "word": " order", "probability": 0.98095703125}, {"start": 2369.23, "end": 2369.59, "word": " اللى", "probability": 0.98095703125}, {"start": 2369.59, "end": 2369.99, "word": " دى", "probability": 0.90869140625}, {"start": 2369.99, "end": 2370.47, "word": " بدى", "probability": 0.5521240234375}, {"start": 2370.47, "end": 2370.93, "word": " يساوي", "probability": 0.73016357421875}, {"start": 2370.93, "end": 2371.65, "word": " اربعة", "probability": 0.8839518229166666}, {"start": 2371.65, "end": 2372.09, "word": " اكم", "probability": 0.5706787109375}, {"start": 2372.09, "end": 2372.55, "word": " element", "probability": 0.83544921875}, {"start": 2372.55, "end": 2373.25, "word": " بيعطينا", "probability": 0.8412109375}, {"start": 2373.25, "end": 2375.65, "word": " اتنين", "probability": 0.85205078125}, {"start": 2375.65, "end": 2376.73, "word": " مظبوط", "probability": 0.83759765625}], "temperature": 1.0}, {"id": 101, "seek": 240323, "start": 2376.98, "end": 2403.24, "text": "يبقى هنا في عندي اتنين elements طيب لما يكون هنا في عندي جداش؟ جداش؟ اربع elements طيب نيجي لل a جداش؟ اربع elements اتنين elements نيجي لل b جداش عندي؟ اتنين elements", "tokens": [1829, 3555, 4587, 7578, 34105, 8978, 18871, 16254, 1975, 2655, 1863, 9957, 4959, 23032, 1829, 3555, 5296, 15042, 7251, 30544, 34105, 8978, 18871, 16254, 10874, 3215, 33599, 22807, 10874, 3215, 33599, 22807, 1975, 25513, 3615, 4959, 23032, 1829, 3555, 8717, 1829, 7435, 1829, 24976, 257, 10874, 3215, 33599, 22807, 1975, 25513, 3615, 4959, 1975, 2655, 1863, 9957, 4959, 8717, 1829, 7435, 1829, 24976, 272, 10874, 3215, 33599, 18871, 16254, 22807, 1975, 2655, 1863, 9957, 4959], "avg_logprob": -0.15995065240483536, "compression_ratio": 2.139344262295082, "no_speech_prob": 0.0, "words": [{"start": 2376.98, "end": 2377.56, "word": "يبقى", "probability": 0.8616943359375}, {"start": 2377.56, "end": 2377.9, "word": " هنا", "probability": 0.908203125}, {"start": 2377.9, "end": 2378.14, "word": " في", "probability": 0.2373046875}, {"start": 2378.14, "end": 2378.6, "word": " عندي", "probability": 0.785888671875}, {"start": 2378.6, "end": 2379.5, "word": " اتنين", "probability": 0.9288330078125}, {"start": 2379.5, "end": 2380.12, "word": " elements", "probability": 0.83740234375}, {"start": 2380.12, "end": 2382.38, "word": " طيب", "probability": 0.9280598958333334}, {"start": 2382.38, "end": 2382.96, "word": " لما", "probability": 0.87255859375}, {"start": 2382.96, "end": 2383.32, "word": " يكون", "probability": 0.98681640625}, {"start": 2383.32, "end": 2383.62, "word": " هنا", "probability": 0.9736328125}, {"start": 2383.62, "end": 2383.78, "word": " في", "probability": 0.818359375}, {"start": 2383.78, "end": 2384.0, "word": " عندي", "probability": 0.9658203125}, {"start": 2384.0, "end": 2386.08, "word": " جداش؟", "probability": 0.626708984375}, {"start": 2386.08, "end": 2387.36, "word": " جداش؟", "probability": 0.8846435546875}, {"start": 2387.36, "end": 2388.1, "word": " اربع", "probability": 0.6691080729166666}, {"start": 2388.1, "end": 2388.74, "word": " elements", "probability": 0.9248046875}, {"start": 2388.74, "end": 2392.44, "word": " طيب", "probability": 0.9749348958333334}, {"start": 2392.44, "end": 2392.78, "word": " نيجي", "probability": 0.904541015625}, {"start": 2392.78, "end": 2393.02, "word": " لل", "probability": 0.8447265625}, {"start": 2393.02, "end": 2393.38, "word": " a", "probability": 0.57666015625}, {"start": 2393.38, "end": 2395.16, "word": " جداش؟", "probability": 0.92919921875}, {"start": 2395.16, "end": 2395.6, "word": " اربع", "probability": 0.8704427083333334}, {"start": 2395.6, "end": 2395.96, "word": " elements", "probability": 0.5693359375}, {"start": 2395.96, "end": 2396.84, "word": " اتنين", "probability": 0.9188232421875}, {"start": 2396.84, "end": 2397.6, "word": " elements", "probability": 0.92822265625}, {"start": 2397.6, "end": 2399.2, "word": " نيجي", "probability": 0.9852294921875}, {"start": 2399.2, "end": 2399.42, "word": " لل", "probability": 0.916015625}, {"start": 2399.42, "end": 2399.82, "word": " b", "probability": 0.8623046875}, {"start": 2399.82, "end": 2400.58, "word": " جداش", "probability": 0.9480794270833334}, {"start": 2400.58, "end": 2401.28, "word": " عندي؟", "probability": 0.931640625}, {"start": 2401.28, "end": 2402.58, "word": " اتنين", "probability": 0.989990234375}, {"start": 2402.58, "end": 2403.24, "word": " elements", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 102, "seek": 242980, "start": 2405.8, "end": 2429.8, "text": "يبقى صغر الآن اتنين اخدناها اربعة مع الخطوة اللي قبلها اه اخدناها اربعة مع الخطوة اللي قبلها لاش نكررها لان التكرار هذا بجيب شغلات اكتر من اللازم يبقى so we have العنصر الأولاني اتنين والتاني اربعة واللي بعده اتنين واللي بعده اتنين", "tokens": [1829, 3555, 4587, 7578, 20328, 17082, 2288, 6024, 48506, 1975, 2655, 1863, 9957, 1975, 9778, 3215, 8315, 11296, 1975, 25513, 27884, 20449, 33962, 9566, 2407, 3660, 13672, 1829, 12174, 36150, 11296, 1975, 3224, 1975, 9778, 3215, 8315, 11296, 1975, 25513, 27884, 20449, 33962, 9566, 2407, 3660, 13672, 1829, 12174, 36150, 11296, 5296, 33599, 8717, 37983, 2288, 11296, 5296, 7649, 16712, 37983, 9640, 23758, 4724, 7435, 1829, 3555, 13412, 17082, 1211, 9307, 1975, 4117, 2655, 2288, 9154, 13672, 31377, 2304, 7251, 3555, 4587, 7578, 370, 321, 362, 18863, 1863, 9381, 2288, 16247, 12610, 7649, 1829, 1975, 2655, 1863, 9957, 16070, 2655, 7649, 1829, 1975, 25513, 27884, 16070, 20292, 39182, 3224, 1975, 2655, 1863, 9957, 16070, 20292, 39182, 3224, 1975, 2655, 1863, 9957], "avg_logprob": -0.18685962491836705, "compression_ratio": 2.2085561497326203, "no_speech_prob": 0.0, "words": [{"start": 2405.8, "end": 2406.4, "word": "يبقى", "probability": 0.8660888671875}, {"start": 2406.4, "end": 2406.82, "word": " صغر", "probability": 0.5589599609375}, {"start": 2406.82, "end": 2407.42, "word": " الآن", "probability": 0.6217041015625}, {"start": 2407.42, "end": 2408.68, "word": " اتنين", "probability": 0.883056640625}, {"start": 2408.68, "end": 2412.76, "word": " اخدناها", "probability": 0.711767578125}, {"start": 2412.76, "end": 2413.12, "word": " اربعة", "probability": 0.7057291666666666}, {"start": 2413.12, "end": 2413.26, "word": " مع", "probability": 0.59521484375}, {"start": 2413.26, "end": 2413.62, "word": " الخطوة", "probability": 0.95166015625}, {"start": 2413.62, "end": 2413.76, "word": " اللي", "probability": 0.828369140625}, {"start": 2413.76, "end": 2414.86, "word": " قبلها", "probability": 0.9000651041666666}, {"start": 2414.86, "end": 2415.46, "word": " اه", "probability": 0.3890380859375}, {"start": 2415.46, "end": 2415.88, "word": " اخدناها", "probability": 0.94013671875}, {"start": 2415.88, "end": 2416.08, "word": " اربعة", "probability": 0.9108072916666666}, {"start": 2416.08, "end": 2416.24, "word": " مع", "probability": 0.89990234375}, {"start": 2416.24, "end": 2416.46, "word": " الخطوة", "probability": 0.9774169921875}, {"start": 2416.46, "end": 2416.56, "word": " اللي", "probability": 0.9755859375}, {"start": 2416.56, "end": 2416.68, "word": " قبلها", "probability": 0.9803059895833334}, {"start": 2416.68, "end": 2416.88, "word": " لاش", "probability": 0.26348876953125}, {"start": 2416.88, "end": 2417.46, "word": " نكررها", "probability": 0.8739013671875}, {"start": 2417.46, "end": 2417.72, "word": " لان", "probability": 0.6602783203125}, {"start": 2417.72, "end": 2418.46, "word": " التكرار", "probability": 0.8587239583333334}, {"start": 2418.46, "end": 2418.9, "word": " هذا", "probability": 0.93212890625}, {"start": 2418.9, "end": 2419.58, "word": " بجيب", "probability": 0.9505615234375}, {"start": 2419.58, "end": 2420.02, "word": " شغلات", "probability": 0.880615234375}, {"start": 2420.02, "end": 2420.38, "word": " اكتر", "probability": 0.9630126953125}, {"start": 2420.38, "end": 2420.54, "word": " من", "probability": 0.97119140625}, {"start": 2420.54, "end": 2420.94, "word": " اللازم", "probability": 0.96435546875}, {"start": 2420.94, "end": 2422.2, "word": " يبقى", "probability": 0.9788818359375}, {"start": 2422.2, "end": 2422.44, "word": " so", "probability": 0.255615234375}, {"start": 2422.44, "end": 2422.78, "word": " we", "probability": 0.95849609375}, {"start": 2422.78, "end": 2423.46, "word": " have", "probability": 0.96728515625}, {"start": 2423.46, "end": 2424.3, "word": " العنصر", "probability": 0.966552734375}, {"start": 2424.3, "end": 2425.02, "word": " الأولاني", "probability": 0.8746337890625}, {"start": 2425.02, "end": 2425.48, "word": " اتنين", "probability": 0.9783935546875}, {"start": 2425.48, "end": 2426.52, "word": " والتاني", "probability": 0.900634765625}, {"start": 2426.52, "end": 2427.1, "word": " اربعة", "probability": 0.8819986979166666}, {"start": 2427.1, "end": 2427.52, "word": " واللي", "probability": 0.71875}, {"start": 2427.52, "end": 2427.88, "word": " بعده", "probability": 0.94677734375}, {"start": 2427.88, "end": 2428.4, "word": " اتنين", "probability": 0.99169921875}, {"start": 2428.4, "end": 2428.94, "word": " واللي", "probability": 0.893310546875}, {"start": 2428.94, "end": 2429.34, "word": " بعده", "probability": 0.961181640625}, {"start": 2429.34, "end": 2429.8, "word": " اتنين", "probability": 0.991943359375}], "temperature": 1.0}, {"id": 103, "seek": 244321, "start": 2430.27, "end": 2443.21, "text": "يبقى تمانية في أربعة بجداش بتنين و تلاتين element of order اللي هو أتناشر طب إذا على بعضهم جداش", "tokens": [1829, 3555, 4587, 7578, 46811, 7649, 10632, 8978, 5551, 25513, 27884, 4724, 7435, 3215, 33599, 39894, 1863, 9957, 4032, 6055, 1211, 9307, 9957, 4478, 295, 1668, 13672, 1829, 31439, 5551, 2655, 1863, 33599, 2288, 23032, 3555, 11933, 15730, 15844, 45030, 11242, 16095, 10874, 3215, 33599], "avg_logprob": -0.27055028340090875, "compression_ratio": 1.264, "no_speech_prob": 0.0, "words": [{"start": 2430.27, "end": 2430.89, "word": "يبقى", "probability": 0.8447265625}, {"start": 2430.89, "end": 2431.41, "word": " تمانية", "probability": 0.8600260416666666}, {"start": 2431.41, "end": 2431.57, "word": " في", "probability": 0.64013671875}, {"start": 2431.57, "end": 2431.97, "word": " أربعة", "probability": 0.78515625}, {"start": 2431.97, "end": 2432.61, "word": " بجداش", "probability": 0.720703125}, {"start": 2432.61, "end": 2433.21, "word": " بتنين", "probability": 0.7950032552083334}, {"start": 2433.21, "end": 2433.37, "word": " و", "probability": 0.472900390625}, {"start": 2433.37, "end": 2434.51, "word": " تلاتين", "probability": 0.95458984375}, {"start": 2434.51, "end": 2435.35, "word": " element", "probability": 0.7080078125}, {"start": 2435.35, "end": 2436.43, "word": " of", "probability": 0.9736328125}, {"start": 2436.43, "end": 2437.77, "word": " order", "probability": 0.95703125}, {"start": 2437.77, "end": 2438.95, "word": " اللي", "probability": 0.77734375}, {"start": 2438.95, "end": 2439.27, "word": " هو", "probability": 0.96728515625}, {"start": 2439.27, "end": 2440.61, "word": " أتناشر", "probability": 0.68720703125}, {"start": 2440.61, "end": 2441.17, "word": " طب", "probability": 0.76025390625}, {"start": 2441.17, "end": 2441.41, "word": " إذا", "probability": 0.83447265625}, {"start": 2441.41, "end": 2441.65, "word": " على", "probability": 0.385498046875}, {"start": 2441.65, "end": 2442.23, "word": " بعضهم", "probability": 0.8670247395833334}, {"start": 2442.23, "end": 2443.21, "word": " جداش", "probability": 0.9806315104166666}], "temperature": 1.0}, {"id": 104, "seek": 246801, "start": 2445.41, "end": 2468.01, "text": "يو سبعمية وعشرين has اللي هو قداش في الأول اربعة وستين زائد اتنين وتلاتين ويساوي ستة وتسعين element of order اللي هو اتناشر", "tokens": [1829, 2407, 8608, 3555, 25957, 10632, 4032, 3615, 46309, 9957, 575, 13672, 1829, 31439, 12174, 3215, 33599, 8978, 16247, 12610, 1975, 25513, 27884, 4032, 14851, 9957, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 4032, 2655, 1211, 9307, 9957, 4032, 1829, 3794, 995, 45865, 8608, 2655, 3660, 34683, 3794, 3615, 9957, 4478, 295, 1668, 13672, 1829, 31439, 1975, 2655, 1863, 33599, 2288], "avg_logprob": -0.17578125120170654, "compression_ratio": 1.4475524475524475, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2445.41, "end": 2446.07, "word": "يو", "probability": 0.32940673828125}, {"start": 2446.07, "end": 2446.95, "word": " سبعمية", "probability": 0.893310546875}, {"start": 2446.95, "end": 2447.95, "word": " وعشرين", "probability": 0.88623046875}, {"start": 2447.95, "end": 2449.41, "word": " has", "probability": 0.3212890625}, {"start": 2449.41, "end": 2450.37, "word": " اللي", "probability": 0.80908203125}, {"start": 2450.37, "end": 2450.53, "word": " هو", "probability": 0.97314453125}, {"start": 2450.53, "end": 2450.93, "word": " قداش", "probability": 0.6315104166666666}, {"start": 2450.93, "end": 2451.05, "word": " في", "probability": 0.85986328125}, {"start": 2451.05, "end": 2451.53, "word": " الأول", "probability": 0.94921875}, {"start": 2451.53, "end": 2452.27, "word": " اربعة", "probability": 0.7310384114583334}, {"start": 2452.27, "end": 2453.33, "word": " وستين", "probability": 0.953125}, {"start": 2453.33, "end": 2454.47, "word": " 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249787, "start": 2477.69, "end": 2497.87, "text": "يبقى بناء عليها من الآن فصاعدا لو قاللي شوف لقداش عدد العناصر اللي ال order لهم يساوية رقم معين في UN ال UN ال N مينما كانت تكون بدي احولها الى مين؟ بدي احولها الى ال cyclic groups", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 25894, 11296, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995, 45164, 50239, 20292, 13412, 38688, 5296, 28543, 33599, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 13672, 1829, 2423, 1668, 5296, 16095, 7251, 3794, 995, 2407, 10632, 12602, 4587, 2304, 20449, 9957, 8978, 8229, 2423, 8229, 2423, 426, 3714, 9957, 15042, 25961, 2655, 6055, 30544, 4724, 16254, 1975, 5016, 12610, 11296, 2423, 7578, 3714, 9957, 22807, 4724, 16254, 1975, 5016, 12610, 11296, 2423, 7578, 2423, 38154, 1050, 3935], "avg_logprob": -0.2764136840899785, "compression_ratio": 1.6358695652173914, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2477.69, "end": 2478.11, "word": "يبقى", "probability": 0.79541015625}, {"start": 2478.11, 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of H بده يساوي ال external direct product لل E تبع ال G", "tokens": [1211, 2407, 10874, 36081, 5551, 9778, 3215, 2655, 47525, 1211, 8978, 5551, 9778, 3215, 2655, 50113, 15040, 13672, 1829, 31439, 2423, 479, 9154, 2423, 389, 30731, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 460, 2108, 2423, 389, 538, 2423, 479, 295, 389, 47525, 3224, 7251, 3794, 995, 45865, 2423, 8320, 2047, 1674, 24976, 462, 6055, 3555, 3615, 2423, 460], "avg_logprob": -0.2311197889347871, "compression_ratio": 1.4203821656050954, "no_speech_prob": 0.0, "words": [{"start": 2624.53, "end": 2624.97, "word": "لو", "probability": 0.83935546875}, {"start": 2624.97, "end": 2625.31, "word": " جيت", "probability": 0.911376953125}, {"start": 2625.31, "end": 2625.89, "word": " أخدت", "probability": 0.82275390625}, {"start": 2625.89, "end": 2626.35, "word": " بدل", "probability": 0.952880859375}, {"start": 2626.35, "end": 2626.89, "word": " في", "probability": 0.212890625}, {"start": 2626.89, "end": 2627.79, "word": " أخدت", 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إذا أثبتنا الأول بصير التاني حرفيا زيه", "tokens": [1211, 1211, 39184, 316, 6055, 16758, 3615, 2423, 39184, 460, 4032, 389, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 1975, 2407, 4724, 1211, 33599, 8032, 11536, 23758, 1975, 1829, 3224, 10874, 2407, 11622, 37037, 15730, 1975, 1829, 3224, 10874, 1829, 4032, 389, 10874, 2407, 11622, 3714, 3555, 33599, 25720, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 12984, 3555, 2655, 9154, 23758, 23032, 3555, 3615, 995, 11933, 15730, 5551, 12984, 3555, 2655, 8315, 16247, 12610, 4724, 9381, 13546, 16712, 7649, 1829, 11331, 28480, 25528, 30767, 1829, 3224], "avg_logprob": -0.34037642350251024, "compression_ratio": 1.748427672955975, "no_speech_prob": 0.0, "words": [{"start": 2652.02, "end": 2652.54, "word": "للـ", "probability": 0.3560384114583333}, {"start": 2652.54, "end": 2652.72, "word": " A", "probability": 0.296875}, {"start": 2652.72, "end": 2653.32, "word": " تابع", "probability": 0.78076171875}, {"start": 2653.32, "end": 2653.7, "word": 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diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..98be588c7d84edf7db119a5358c4ab16eb8c2171
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.json
@@ -0,0 +1 @@
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51.66, "word": " subgroup", "probability": 0.69482421875}, {"start": 51.66, "end": 52.46, "word": " من", "probability": 0.90966796875}, {"start": 52.46, "end": 53.0, "word": " cyclic", "probability": 0.6856689453125}, {"start": 53.0, "end": 53.4, "word": " group", "probability": 0.9599609375}, {"start": 53.4, "end": 53.94, "word": " بتكون", "probability": 0.831298828125}, {"start": 53.94, "end": 54.62, "word": " cyclic", "probability": 0.841552734375}, {"start": 54.62, "end": 56.26, "word": " اي", "probability": 0.71142578125}, {"start": 56.26, "end": 56.94, "word": " subgroup", "probability": 0.95068359375}, {"start": 56.94, "end": 57.12, "word": " من", "probability": 0.990234375}, {"start": 57.12, "end": 57.74, "word": " cyclic", "probability": 0.90625}, {"start": 57.74, "end": 58.08, "word": " group", "probability": 0.9814453125}, {"start": 58.08, "end": 58.48, "word": " بتكون", "probability": 0.966064453125}, {"start": 58.48, "end": 59.06, "word": " cyclic", "probability": 0.89794921875}, {"start": 59.06, "end": 59.86, "word": " الجزء", "probability": 0.9630533854166666}, {"start": 59.86, "end": 60.44, "word": " التانى", "probability": 0.9108072916666666}, {"start": 60.44, "end": 61.62, "word": " اي", "probability": 0.854736328125}, {"start": 61.62, "end": 62.74, "word": " subgroup", "probability": 0.96630859375}, {"start": 62.74, "end": 63.92, "word": " هيكون", "probability": 0.91357421875}, {"start": 63.92, "end": 64.06, "word": " ال", "probability": 0.93798828125}, {"start": 64.06, "end": 64.44, "word": " order", "probability": 0.96630859375}, {"start": 64.44, "end": 65.48, "word": " لها", "probability": 0.6346435546875}, {"start": 65.48, "end": 66.44, "word": " بيقسم", "probability": 0.9449462890625}, {"start": 66.44, "end": 66.9, "word": " ال", "probability": 0.97216796875}, {"start": 66.9, "end": 67.34, "word": " order", "probability": 0.9775390625}, {"start": 67.34, "end": 67.76, "word": " لل", "probability": 0.80615234375}, {"start": 67.76, "end": 68.02, "word": " group", "probability": 0.9580078125}, {"start": 68.02, "end": 68.2, "word": " في", "probability": 0.78564453125}, {"start": 68.2, "end": 68.52, "word": " حالة", "probability": 0.9514973958333334}, {"start": 68.52, "end": 68.8, "word": " طبعا", "probability": 0.8804931640625}, {"start": 68.8, "end": 68.92, "word": " ال", "probability": 0.76416015625}, {"start": 68.92, "end": 69.38, "word": " cyclic", "probability": 0.8603515625}, {"start": 69.38, "end": 69.88, "word": " group", "probability": 0.98876953125}, {"start": 69.88, "end": 70.6, "word": " الشغل", "probability": 0.6803385416666666}, {"start": 70.6, "end": 71.22, "word": " التالتة", "probability": 0.8897705078125}, {"start": 71.22, "end": 71.6, "word": " لو", "probability": 0.86767578125}, {"start": 71.6, "end": 71.84, "word": " كان", "probability": 0.9775390625}, {"start": 71.84, "end": 72.12, "word": " عندي", "probability": 0.913818359375}, {"start": 72.12, "end": 72.86, "word": " قاسم", "probability": 0.8756510416666666}, {"start": 72.86, "end": 73.18, "word": " لل", "probability": 0.9306640625}, {"start": 73.18, "end": 73.68, "word": " order", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 3, "seek": 10241, "start": 74.33, "end": 102.41, "text": "لأ الجروب او الـ cyclic group انا بقدر عليها جيونيكسة بالجروب داخل الـ cyclic group و بيكون لها نفس ال order هناخد مثال سريع في هذه الجزئية هنقول التالي example let j generated by a with order ال a", "tokens": [1211, 10721, 25724, 32887, 3555, 1975, 2407, 2423, 39184, 38154, 1050, 1594, 1975, 8315, 4724, 28543, 2288, 25894, 11296, 10874, 1829, 11536, 1829, 4117, 3794, 3660, 20666, 7435, 32887, 3555, 11778, 47283, 1211, 2423, 39184, 38154, 1050, 1594, 4032, 4724, 1829, 30544, 5296, 11296, 8717, 36178, 2423, 1668, 8032, 1863, 47283, 3215, 50113, 6027, 8608, 16572, 3615, 8978, 29538, 25724, 11622, 19986, 10632, 8032, 1863, 39648, 16712, 6027, 1829, 1365, 718, 361, 10833, 538, 257, 365, 1668, 2423, 257], "avg_logprob": -0.2904296815395355, "compression_ratio": 1.5336787564766838, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 74.33, "end": 74.79, "word": "لأ", "probability": 0.72119140625}, {"start": 74.79, "end": 75.49, "word": " الجروب", "probability": 0.5600789388020834}, {"start": 75.49, "end": 75.77, "word": " او", "probability": 0.80224609375}, {"start": 75.77, "end": 75.91, "word": " الـ", "probability": 0.60302734375}, {"start": 75.91, "end": 76.23, "word": " cyclic", "probability": 0.6651611328125}, {"start": 76.23, "end": 76.67, "word": " group", "probability": 0.9560546875}, {"start": 76.67, "end": 77.19, "word": " انا", "probability": 0.879150390625}, {"start": 77.19, "end": 77.51, "word": " بقدر", "probability": 0.9700520833333334}, {"start": 77.51, "end": 77.75, "word": " عليها", "probability": 0.6463623046875}, {"start": 77.75, "end": 78.49, "word": " جيونيكسة", "probability": 0.6400844029017857}, {"start": 78.49, "end": 79.03, "word": " بالجروب", "probability": 0.8079833984375}, {"start": 79.03, "end": 80.25, "word": " داخل", "probability": 0.95263671875}, {"start": 80.25, "end": 80.59, "word": " الـ", "probability": 0.801025390625}, {"start": 80.59, "end": 80.97, "word": " cyclic", "probability": 0.8681640625}, {"start": 80.97, "end": 81.45, "word": " group", "probability": 0.98974609375}, {"start": 81.45, "end": 81.91, "word": " و", "probability": 0.62548828125}, {"start": 81.91, "end": 82.19, "word": " بيكون", "probability": 0.6639811197916666}, {"start": 82.19, "end": 82.63, "word": " لها", "probability": 0.773193359375}, {"start": 82.63, "end": 83.11, "word": " نفس", "probability": 0.997314453125}, {"start": 83.11, "end": 83.35, "word": " ال", "probability": 0.919921875}, {"start": 83.35, "end": 83.59, "word": " order", "probability": 0.88623046875}, {"start": 83.59, "end": 84.47, "word": " هناخد", "probability": 0.8359375}, {"start": 84.47, "end": 84.85, "word": " مثال", "probability": 0.987060546875}, {"start": 84.85, "end": 85.57, "word": " سريع", "probability": 0.8935546875}, {"start": 85.57, "end": 86.31, "word": " في", "probability": 0.876953125}, {"start": 86.31, "end": 86.77, "word": " هذه", "probability": 0.95166015625}, {"start": 86.77, "end": 88.79, "word": " الجزئية", "probability": 0.9447021484375}, {"start": 88.79, "end": 89.57, "word": " هنقول", "probability": 0.7058919270833334}, {"start": 89.57, "end": 90.27, "word": " التالي", "probability": 0.9202473958333334}, {"start": 90.27, "end": 92.01, "word": " example", "probability": 0.70556640625}, {"start": 92.01, "end": 94.63, "word": " let", "probability": 0.783203125}, {"start": 94.63, "end": 95.43, "word": " j", "probability": 0.53173828125}, {"start": 95.43, "end": 96.65, "word": " generated", "probability": 0.77880859375}, {"start": 96.65, "end": 97.03, "word": " by", "probability": 0.908203125}, {"start": 97.03, "end": 97.43, "word": " a", "probability": 0.8583984375}, {"start": 97.43, "end": 99.15, "word": " with", "probability": 0.90234375}, {"start": 99.15, "end": 101.83, "word": " order", "probability": 0.92919921875}, {"start": 101.83, "end": 102.11, "word": " ال", "probability": 0.39111328125}, {"start": 102.11, "end": 102.41, "word": " a", "probability": 0.6396484375}], "temperature": 1.0}, {"id": 4, "seek": 13307, "start": 104.51, "end": 133.07, "text": "بساوة تلاتين المطلوب list all subgroups of G عندي group Cyclic الـ all ضاقينها تلاتين المطلوب مني أجيب كل group Cyclic من الـ G تعالوا نشوف قليل الحل قبل أن نبدأ الحل", "tokens": [3555, 3794, 995, 2407, 3660, 6055, 1211, 9307, 9957, 9673, 9566, 1211, 37746, 1329, 439, 1422, 17377, 82, 295, 460, 18871, 16254, 1594, 10295, 66, 1050, 2423, 39184, 439, 48812, 995, 4587, 9957, 11296, 6055, 1211, 9307, 9957, 9673, 9566, 1211, 37746, 9154, 1829, 5551, 7435, 1829, 3555, 28242, 1594, 10295, 66, 1050, 9154, 2423, 39184, 460, 37279, 6027, 14407, 8717, 8592, 38688, 12174, 20292, 1211, 21542, 1211, 12174, 36150, 14739, 8717, 44510, 10721, 21542, 1211], "avg_logprob": -0.38534901204047267, "compression_ratio": 1.5421686746987953, "no_speech_prob": 0.0, "words": [{"start": 104.51, "end": 105.09, "word": "بساوة", "probability": 0.722802734375}, {"start": 105.09, "end": 105.61, "word": " تلاتين", "probability": 0.8404541015625}, {"start": 105.61, "end": 106.99, "word": " المطلوب", "probability": 0.8641357421875}, {"start": 106.99, "end": 108.07, "word": " list", "probability": 0.35986328125}, {"start": 108.07, "end": 110.79, "word": " all", "probability": 0.76025390625}, {"start": 110.79, "end": 115.77, "word": " subgroups", "probability": 0.8479817708333334}, {"start": 115.77, "end": 116.11, "word": " of", "probability": 0.88818359375}, {"start": 116.11, "end": 117.27, "word": " G", "probability": 0.36767578125}, {"start": 117.27, "end": 120.75, "word": " عندي", "probability": 0.803466796875}, {"start": 120.75, "end": 120.99, "word": " group", "probability": 0.763671875}, {"start": 120.99, "end": 121.25, "word": " Cyclic", "probability": 0.5761006673177084}, {"start": 121.25, "end": 122.07, "word": " الـ", "probability": 0.2886962890625}, {"start": 122.07, "end": 122.19, "word": " all", "probability": 0.309814453125}, {"start": 122.19, "end": 122.61, "word": " ضاقينها", "probability": 0.5388671875}, {"start": 122.61, "end": 123.19, "word": " تلاتين", "probability": 0.95263671875}, {"start": 123.19, "end": 124.21, "word": " المطلوب", "probability": 0.9249267578125}, {"start": 124.21, "end": 124.63, "word": " مني", "probability": 0.725830078125}, {"start": 124.63, "end": 125.31, "word": " أجيب", "probability": 0.879150390625}, {"start": 125.31, "end": 126.15, "word": " كل", "probability": 0.8349609375}, {"start": 126.15, "end": 126.59, "word": " group", "probability": 0.17724609375}, {"start": 126.59, "end": 127.17, "word": " Cyclic", "probability": 0.8702799479166666}, {"start": 127.17, "end": 128.65, "word": " من", "probability": 0.89111328125}, {"start": 128.65, "end": 129.27, "word": " الـ", "probability": 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subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups subgroups", "tokens": [1344, 66, 1050, 1594, 4032, 4724, 3215, 2407, 11703, 3615, 15844, 2423, 1422, 17377, 82, 13672, 1829, 3714, 29245, 23328, 9957, 48812, 27842, 2423, 1594, 11933, 1829, 8592, 39896, 30544, 14407, 2423, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 82, 1422, 17377, 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0.860107421875}, {"start": 457.32, "end": 457.62, "word": " G", "probability": 0.78466796875}, {"start": 457.62, "end": 459.7, "word": " نفسها", "probability": 0.7180989583333334}, {"start": 459.7, "end": 461.28, "word": " طبعا", "probability": 0.77069091796875}, {"start": 461.28, "end": 461.58, "word": " يكسر", "probability": 0.4564666748046875}, {"start": 461.58, "end": 461.84, "word": " عندي", "probability": 0.8798828125}, {"start": 461.84, "end": 462.4, "word": " listing", "probability": 0.85888671875}, {"start": 462.4, "end": 463.34, "word": " لكل", "probability": 0.92919921875}, {"start": 463.34, "end": 463.62, "word": " ال", "probability": 0.689453125}, {"start": 463.62, "end": 464.18, "word": " cyclic", "probability": 0.6220703125}, {"start": 464.18, "end": 464.9, "word": " subgroup", "probability": 0.7490234375}, {"start": 464.9, "end": 465.24, "word": " او", "probability": 0.7291259765625}, {"start": 465.24, "end": 465.52, "word": " لكل", "probability": 0.9052734375}, {"start": 465.52, "end": 465.66, "word": " ال", "probability": 0.865234375}, {"start": 465.66, "end": 466.28, "word": " subgroup", "probability": 0.90771484375}, {"start": 466.28, "end": 467.2, "word": " من", "probability": 0.9375}, {"start": 467.2, "end": 468.02, "word": " ال", "probability": 0.44970703125}, {"start": 468.02, "end": 468.36, "word": " group", "probability": 0.95263671875}, {"start": 468.36, "end": 468.68, "word": " J", "probability": 0.6396484375}, {"start": 468.68, "end": 468.94, "word": " اللي", "probability": 0.679931640625}, {"start": 468.94, "end": 469.04, "word": " ال", "probability": 0.748046875}, {"start": 469.04, "end": 469.32, "word": " order", "probability": 0.9541015625}, {"start": 469.32, "end": 470.16, "word": " لها", "probability": 0.7000732421875}, {"start": 470.16, "end": 471.04, "word": " بساوي", "probability": 0.83056640625}, {"start": 471.04, "end": 471.9, "word": " 30", "probability": 0.69677734375}, {"start": 471.9, "end": 472.6, "word": " اي", "probability": 0.6632080078125}, {"start": 472.6, "end": 472.86, "word": " سؤال", "probability": 0.9830729166666666}, {"start": 472.86, "end": 472.96, "word": " يا", "probability": 0.85693359375}, {"start": 472.96, "end": 475.16, "word": " شباب؟", "probability": 0.8358154296875}, {"start": 475.16, "end": 479.62, "word": " اي", "probability": 0.887451171875}, {"start": 479.62, "end": 480.24, "word": " سؤال؟", "probability": 0.972900390625}], "temperature": 1.0}, {"id": 18, "seek": 51313, "start": 483.65, "end": 513.13, "text": "طيب لو خلنا هذا نفس المثال لكن على group معروف ال generator إلها بشكل واضح يعني مش a كرقم لو قولنا مثلا find all subgroups of Z 13 إيش هنعمل؟", "tokens": [9566, 1829, 3555, 45164, 16490, 1211, 8315, 23758, 8717, 36178, 9673, 12984, 6027, 44381, 15844, 1594, 20449, 32887, 5172, 2423, 19265, 11933, 1211, 11296, 4724, 8592, 28820, 4032, 46958, 5016, 37495, 22653, 37893, 257, 9122, 2288, 4587, 2304, 45164, 12174, 12610, 8315, 50113, 15040, 915, 439, 1422, 17377, 82, 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{"start": 492.35, "end": 492.61, "word": " ال", "probability": 0.78125}, {"start": 492.61, "end": 493.03, "word": " generator", "probability": 0.966796875}, {"start": 493.03, "end": 493.57, "word": " إلها", "probability": 0.710693359375}, {"start": 493.57, "end": 495.23, "word": " بشكل", "probability": 0.97998046875}, {"start": 495.23, "end": 495.77, "word": " واضح", "probability": 0.9441731770833334}, {"start": 495.77, "end": 495.97, "word": " يعني", "probability": 0.839599609375}, {"start": 495.97, "end": 496.23, "word": " مش", "probability": 0.9443359375}, {"start": 496.23, "end": 496.53, "word": " a", "probability": 0.345703125}, {"start": 496.53, "end": 497.45, "word": " كرقم", "probability": 0.9727783203125}, {"start": 497.45, "end": 498.71, "word": " لو", "probability": 0.88623046875}, {"start": 498.71, "end": 499.01, "word": " قولنا", "probability": 0.7483723958333334}, {"start": 499.01, "end": 499.51, "word": " مثلا", "probability": 0.976806640625}, {"start": 499.51, "end": 502.31, "word": " find", "probability": 0.763671875}, {"start": 502.31, "end": 504.17, "word": " all", "probability": 0.93994140625}, {"start": 504.17, "end": 507.51, "word": " subgroups", "probability": 0.8888346354166666}, {"start": 507.51, "end": 508.39, "word": " of", "probability": 0.97265625}, {"start": 508.39, "end": 509.37, "word": " Z", "probability": 0.399658203125}, {"start": 509.37, "end": 510.07, "word": " 13", "probability": 0.269775390625}, {"start": 510.07, "end": 512.47, "word": " إيش", "probability": 0.7467447916666666}, {"start": 512.47, "end": 513.13, "word": " هنعمل؟", "probability": 0.964453125}], "temperature": 1.0}, {"id": 19, "seek": 54326, "start": 514.62, "end": 543.26, "text": "هنعمل نفس الفكرة اللي اشتغلناها مع فرق واحد ان الـ A أشماله الـ A معروف هو الواحد solution الـ Z 30 عبارة عن generated Pi الواحد و ال order للواحد 100", "tokens": [3224, 1863, 25957, 1211, 8717, 36178, 27188, 4117, 25720, 13672, 1829, 1975, 8592, 2655, 17082, 1211, 8315, 11296, 20449, 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"probability": 0.67431640625}, {"start": 537.56, "end": 538.26, "word": " 30", "probability": 0.1495361328125}, {"start": 538.26, "end": 539.36, "word": " عبارة", "probability": 0.804840087890625}, {"start": 539.36, "end": 539.56, "word": " عن", "probability": 0.9921875}, {"start": 539.56, "end": 540.02, "word": " generated", "probability": 0.412841796875}, {"start": 540.02, "end": 540.36, "word": " Pi", "probability": 0.3076171875}, {"start": 540.36, "end": 540.92, "word": " الواحد", "probability": 0.8732096354166666}, {"start": 540.92, "end": 541.88, "word": " و", "probability": 0.2479248046875}, {"start": 541.88, "end": 542.0, "word": " ال", "probability": 0.56201171875}, {"start": 542.0, "end": 542.4, "word": " order", "probability": 0.869140625}, {"start": 542.4, "end": 542.94, "word": " للواحد", "probability": 0.93798828125}, {"start": 542.94, "end": 543.26, "word": " 100", "probability": 0.26416015625}], "temperature": 1.0}, {"id": 20, "seek": 56898, "start": 544.64, "end": 568.98, "text": "تلاتين using the same method in the last example we get the following cyclic subgroups", "tokens": [2655, 1211, 9307, 9957, 1228, 264, 912, 3170, 294, 264, 1036, 1365, 321, 483, 264, 3480, 38154, 1050, 1422, 17377, 82], "avg_logprob": -0.14319957521828738, "compression_ratio": 1.0454545454545454, "no_speech_prob": 0.0, "words": [{"start": 544.64, "end": 545.2, "word": "تلاتين", "probability": 0.8218994140625}, {"start": 545.2, "end": 546.12, "word": " using", "probability": 0.487548828125}, {"start": 546.12, "end": 549.68, "word": " the", "probability": 0.90234375}, {"start": 549.68, "end": 550.24, "word": " same", "probability": 0.9296875}, {"start": 550.24, "end": 552.46, "word": " method", "probability": 0.9716796875}, {"start": 552.46, "end": 554.86, "word": " in", "probability": 0.9375}, {"start": 554.86, "end": 555.0, "word": " the", "probability": 0.94384765625}, {"start": 555.0, "end": 555.62, "word": " last", "probability": 0.892578125}, {"start": 555.62, "end": 558.72, "word": " example", "probability": 0.97607421875}, {"start": 558.72, "end": 561.0, "word": " we", "probability": 0.74658203125}, {"start": 561.0, "end": 561.52, "word": " get", "probability": 0.9423828125}, {"start": 561.52, "end": 562.16, "word": " the", "probability": 0.923828125}, {"start": 562.16, "end": 562.9, "word": " following", "probability": 0.86328125}, {"start": 562.9, "end": 566.52, "word": " cyclic", "probability": 0.90673828125}, {"start": 566.52, "end": 568.98, "word": " subgroups", "probability": 0.9051106770833334}], "temperature": 1.0}, {"id": 21, "seek": 59875, "start": 572.67, "end": 598.75, "text": "generated by الواحد الـ H1 الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا مين 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{"start": 741.81, "end": 742.43, "word": " الواحد", "probability": 0.9612630208333334}], "temperature": 1.0}, {"id": 27, "seek": 77165, "start": 743.07, "end": 771.65, "text": "generated by التنين generated by الأربعة generated by الخمسة and generated by العشرة and generated by الأشعين دول هم ال only cyclic subgroups ل ال z أشعين أيه السؤال يا شباب", "tokens": [21848, 770, 538, 16712, 1863, 9957, 10833, 538, 16247, 25513, 27884, 10833, 538, 33962, 2304, 3794, 3660, 293, 10833, 538, 18863, 8592, 25720, 293, 10833, 538, 16247, 8592, 3615, 9957, 11778, 12610, 8032, 2304, 2423, 787, 38154, 1050, 1422, 17377, 82, 5296, 2423, 710, 5551, 8592, 3615, 9957, 36632, 3224, 21136, 33604, 6027, 35186, 13412, 3555, 16758], "avg_logprob": -0.36503234094586867, "compression_ratio": 1.7153284671532847, "no_speech_prob": 0.0, "words": [{"start": 743.07, "end": 743.69, "word": "generated", "probability": 0.73828125}, {"start": 743.69, "end": 743.91, "word": " by", "probability": 0.9814453125}, {"start": 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753.29, "end": 753.73, "word": " generated", "probability": 0.8681640625}, {"start": 753.73, "end": 754.77, "word": " by", "probability": 0.98583984375}, {"start": 754.77, "end": 756.49, "word": " الأشعين", "probability": 0.54638671875}, {"start": 756.49, "end": 758.27, "word": " دول", "probability": 0.60076904296875}, {"start": 758.27, "end": 759.37, "word": " هم", "probability": 0.70263671875}, {"start": 759.37, "end": 760.09, "word": " ال", "probability": 0.751953125}, {"start": 760.09, "end": 761.83, "word": " only", "probability": 0.76171875}, {"start": 761.83, "end": 762.83, "word": " cyclic", "probability": 0.770263671875}, {"start": 762.83, "end": 764.27, "word": " subgroups", "probability": 0.8068033854166666}, {"start": 764.27, "end": 764.53, "word": " ل", "probability": 0.7705078125}, {"start": 764.53, "end": 765.67, "word": " ال", "probability": 0.1748046875}, {"start": 765.67, "end": 765.85, "word": " z", "probability": 0.34765625}, {"start": 765.85, "end": 766.75, "word": " أشعين", "probability": 0.773681640625}, {"start": 766.75, "end": 770.99, "word": " أيه", "probability": 0.5966796875}, {"start": 770.99, "end": 771.23, "word": " السؤال", "probability": 0.9031575520833334}, {"start": 771.23, "end": 771.35, "word": " يا", "probability": 0.9521484375}, {"start": 771.35, "end": 771.65, "word": " شباب", "probability": 0.9928385416666666}], "temperature": 1.0}, {"id": 28, "seek": 79681, "start": 773.65, "end": 796.81, "text": "أي سؤال سؤال عالسريع find the number of subgroups of j generated by a if order a بسوى خمسة وعشرين", "tokens": [10721, 1829, 8608, 33604, 6027, 8608, 33604, 6027, 6225, 6027, 3794, 16572, 3615, 915, 264, 1230, 295, 1422, 17377, 82, 295, 361, 10833, 538, 257, 498, 1668, 257, 4724, 3794, 2407, 7578, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957], "avg_logprob": -0.2578125058150873, "compression_ratio": 1.1130434782608696, "no_speech_prob": 0.0, "words": [{"start": 773.65, "end": 773.97, "word": "أي", "probability": 0.638427734375}, {"start": 773.97, "end": 774.51, "word": " سؤال", "probability": 0.9933268229166666}, {"start": 774.51, "end": 776.11, "word": " سؤال", "probability": 0.811279296875}, {"start": 776.11, "end": 776.93, "word": " عالسريع", "probability": 0.710205078125}, {"start": 776.93, "end": 779.91, "word": " find", "probability": 0.46435546875}, {"start": 779.91, "end": 781.83, "word": " the", "probability": 0.82568359375}, {"start": 781.83, "end": 782.43, "word": " number", "probability": 0.9619140625}, {"start": 782.43, "end": 784.75, "word": " of", "probability": 0.97216796875}, {"start": 784.75, "end": 787.43, "word": " subgroups", "probability": 0.86767578125}, {"start": 787.43, "end": 789.21, "word": " of", "probability": 0.9609375}, {"start": 789.21, "end": 789.69, "word": " j", "probability": 0.513671875}, {"start": 789.69, "end": 790.79, "word": " generated", "probability": 0.83203125}, {"start": 790.79, "end": 791.19, "word": " by", "probability": 0.98583984375}, {"start": 791.19, "end": 791.75, "word": " a", "probability": 0.5791015625}, {"start": 791.75, "end": 793.33, "word": " if", "probability": 0.89892578125}, {"start": 793.33, "end": 793.97, "word": " order", "probability": 0.95751953125}, {"start": 793.97, "end": 794.65, "word": " a", "probability": 0.81005859375}, {"start": 794.65, "end": 795.75, "word": " بسوى", "probability": 0.53204345703125}, {"start": 795.75, "end": 796.29, "word": " خمسة", "probability": 0.83941650390625}, {"start": 796.29, "end": 796.81, "word": " وعشرين", "probability": 0.85400390625}], "temperature": 1.0}, {"id": 29, "seek": 83156, "start": 802.1, "end": 831.56, "text": "أوجد عدد الـ subgroups اللي موجودين في الجروب جيه اللي ال order لل generator إلها عبارة عن 25 نجيب عدد قواسم الخمسة وعشرين ويكون هو عدد ال subgroups the divisors of خمسة وعشرين are واحد خمسة وخمسة وعشرين يجب كموحدة", "tokens": [10721, 29245, 3215, 6225, 3215, 3215, 2423, 39184, 1422, 17377, 82, 13672, 1829, 3714, 29245, 23328, 9957, 8978, 25724, 32887, 3555, 10874, 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" اللي", "probability": 0.862060546875}, {"start": 806.46, "end": 807.02, "word": " موجودين", "probability": 0.983642578125}, {"start": 807.02, "end": 807.14, "word": " في", "probability": 0.83203125}, {"start": 807.14, "end": 807.52, "word": " الجروب", "probability": 0.6748860677083334}, {"start": 807.52, "end": 808.38, "word": " جيه", "probability": 0.677734375}, {"start": 808.38, "end": 808.68, "word": " اللي", "probability": 0.860595703125}, {"start": 808.68, "end": 808.78, "word": " ال", "probability": 0.72119140625}, {"start": 808.78, "end": 809.14, "word": " order", "probability": 0.6884765625}, {"start": 809.14, "end": 809.38, "word": " لل", "probability": 0.7021484375}, {"start": 809.38, "end": 809.84, "word": " generator", "probability": 0.91845703125}, {"start": 809.84, "end": 810.48, "word": " إلها", "probability": 0.6964518229166666}, {"start": 810.48, "end": 811.6, "word": " عبارة", "probability": 0.9288330078125}, {"start": 811.6, "end": 811.8, "word": " عن", "probability": 0.9580078125}, {"start": 811.8, "end": 812.36, "word": " 25", "probability": 0.6318359375}, {"start": 812.36, "end": 813.62, "word": " نجيب", "probability": 0.783355712890625}, {"start": 813.62, "end": 813.86, "word": " عدد", "probability": 0.9894205729166666}, {"start": 813.86, "end": 816.66, "word": " قواسم", "probability": 0.6725260416666666}, {"start": 816.66, "end": 817.14, "word": " الخمسة", "probability": 0.725341796875}, {"start": 817.14, "end": 817.52, "word": " وعشرين", "probability": 0.77294921875}, {"start": 817.52, "end": 817.86, "word": " ويكون", "probability": 0.47021484375}, {"start": 817.86, "end": 818.04, "word": " هو", "probability": 0.2288818359375}, {"start": 818.04, "end": 818.4, "word": " عدد", "probability": 0.9933268229166666}, {"start": 818.4, "end": 818.52, "word": " ال", "probability": 0.69580078125}, {"start": 818.52, "end": 819.4, "word": " subgroups", "probability": 0.6298828125}, {"start": 819.4, "end": 819.5, "word": " the", "probability": 0.2359619140625}, {"start": 819.5, "end": 820.96, "word": " divisors", "probability": 0.78271484375}, {"start": 820.96, "end": 824.04, "word": " of", "probability": 0.74267578125}, {"start": 824.04, "end": 824.48, "word": " خمسة", "probability": 0.9058837890625}, {"start": 824.48, "end": 825.12, "word": " وعشرين", "probability": 0.889892578125}, {"start": 825.12, "end": 826.1, "word": " are", "probability": 0.281982421875}, {"start": 826.1, "end": 827.12, "word": " واحد", "probability": 0.781005859375}, {"start": 827.12, "end": 828.7, "word": " خمسة", "probability": 0.9056396484375}, {"start": 828.7, "end": 829.44, "word": " وخمسة", "probability": 0.91015625}, {"start": 829.44, "end": 829.96, "word": " وعشرين", "probability": 0.9398193359375}, {"start": 829.96, "end": 830.9, "word": " يجب", "probability": 0.8317057291666666}, {"start": 830.9, "end": 831.56, "word": " كموحدة", "probability": 0.82734375}], "temperature": 1.0}, {"id": 30, "seek": 85905, "start": 832.41, "end": 859.05, "text": "there are only three subgroups of G فقط تلاتة cyclic subgroups أو subgroups موجودين هنا أنهينا السؤال المتعلق بعدد ال cyclic subgroup بيجي سؤال تاني", "tokens": [15456, 366, 787, 1045, 1422, 17377, 82, 295, 460, 6156, 47432, 6055, 1211, 9307, 3660, 38154, 1050, 1422, 17377, 82, 34051, 1422, 17377, 82, 3714, 29245, 23328, 9957, 34105, 14739, 3224, 1829, 8315, 21136, 33604, 6027, 9673, 2655, 30241, 4587, 4724, 22488, 3215, 2423, 38154, 1050, 1422, 17377, 4724, 1829, 7435, 1829, 8608, 33604, 6027, 6055, 7649, 1829], "avg_logprob": -0.19849046660681902, "compression_ratio": 1.4137931034482758, "no_speech_prob": 0.0, "words": [{"start": 832.41, "end": 832.87, "word": "there", "probability": 0.396240234375}, {"start": 832.87, "end": 835.01, "word": " are", "probability": 0.9462890625}, {"start": 835.01, "end": 835.65, "word": " only", "probability": 0.91064453125}, {"start": 835.65, "end": 836.79, "word": " three", "probability": 0.783203125}, {"start": 836.79, "end": 842.19, "word": " subgroups", "probability": 0.7947591145833334}, {"start": 842.19, "end": 842.41, "word": " of", "probability": 0.80322265625}, {"start": 842.41, "end": 842.71, "word": " G", "probability": 0.677734375}, {"start": 842.71, "end": 845.17, "word": " فقط", "probability": 0.76171875}, {"start": 845.17, "end": 846.77, "word": " تلاتة", "probability": 0.9365234375}, {"start": 846.77, "end": 847.47, "word": " cyclic", "probability": 0.616455078125}, {"start": 847.47, "end": 848.39, "word": " subgroups", "probability": 0.8518880208333334}, {"start": 848.39, "end": 848.53, "word": " أو", "probability": 0.4267578125}, {"start": 848.53, "end": 849.91, "word": " subgroups", "probability": 0.8665364583333334}, {"start": 849.91, "end": 851.29, "word": " موجودين", "probability": 0.962646484375}, {"start": 851.29, "end": 852.43, "word": " هنا", "probability": 0.26708984375}, {"start": 852.43, "end": 853.65, "word": " أنهينا", "probability": 0.83856201171875}, {"start": 853.65, "end": 854.33, "word": " السؤال", "probability": 0.9915364583333334}, {"start": 854.33, "end": 855.07, "word": " المتعلق", "probability": 0.9808349609375}, {"start": 855.07, "end": 855.73, "word": " بعدد", "probability": 0.88671875}, {"start": 855.73, "end": 856.13, "word": " ال", "probability": 0.802734375}, {"start": 856.13, "end": 856.63, "word": " cyclic", "probability": 0.6495361328125}, {"start": 856.63, "end": 857.13, "word": " subgroup", "probability": 0.964599609375}, {"start": 857.13, "end": 858.29, "word": " بيجي", "probability": 0.8897705078125}, {"start": 858.29, "end": 858.59, "word": " سؤال", "probability": 0.98681640625}, {"start": 858.59, "end": 859.05, "word": " تاني", "probability": 0.9108072916666666}], "temperature": 1.0}, {"id": 31, "seek": 86419, "start": 860.27, "end": 864.19, "text": "سؤال الأول هو قداش عدد ال generator في ال cyclic group؟", "tokens": [3794, 33604, 6027, 16247, 12610, 31439, 12174, 3215, 33599, 6225, 3215, 3215, 2423, 19265, 8978, 2423, 38154, 1050, 1594, 22807], "avg_logprob": -0.3234746910276867, "compression_ratio": 1.0126582278481013, "no_speech_prob": 0.0, "words": [{"start": 860.27, "end": 860.71, "word": "سؤال", "probability": 0.9152018229166666}, {"start": 860.71, "end": 861.17, "word": " الأول", "probability": 0.913818359375}, {"start": 861.17, "end": 861.53, "word": " هو", "probability": 0.7509765625}, {"start": 861.53, "end": 861.93, "word": " قداش", "probability": 0.604736328125}, {"start": 861.93, "end": 862.25, "word": " عدد", "probability": 0.9698893229166666}, {"start": 862.25, "end": 862.35, "word": " ال", "probability": 0.5400390625}, {"start": 862.35, "end": 862.85, "word": " generator", "probability": 0.95703125}, {"start": 862.85, "end": 863.09, "word": " في", "probability": 0.904296875}, {"start": 863.09, "end": 863.21, "word": " ال", "probability": 0.814453125}, {"start": 863.21, "end": 863.67, "word": " cyclic", "probability": 0.509490966796875}, {"start": 863.67, "end": 864.19, "word": " group؟", "probability": 0.881103515625}], "temperature": 1.0}, {"id": 32, "seek": 89451, "start": 865.69, "end": 894.51, "text": "سؤال التاني لو كان عندي قاسم لل order لل group cyclic نقول لو كان عندي قاسم فانا بلاقي sub group ال order لهذا القاسم لما اقول sub group من cyclic و ال order لهذا القاسم معناته انها generator وهذا ال generator ال order له بيساوي القاسم يعني لكل قاسم ل order ال finite group cyclic بلاقي عنصر جوا", "tokens": [3794, 33604, 6027, 16712, 7649, 1829, 45164, 25961, 18871, 16254, 12174, 32277, 2304, 24976, 1668, 24976, 1594, 38154, 1050, 8717, 39648, 45164, 25961, 18871, 16254, 12174, 32277, 2304, 6156, 7649, 995, 4724, 15040, 38436, 1422, 1594, 2423, 1668, 46740, 15730, 25062, 32277, 2304, 5296, 15042, 1975, 39648, 1422, 1594, 9154, 38154, 1050, 4032, 2423, 1668, 46740, 15730, 25062, 32277, 2304, 20449, 8315, 47395, 16472, 11296, 19265, 37037, 15730, 2423, 19265, 2423, 1668, 46740, 4724, 1829, 3794, 995, 45865, 25062, 32277, 2304, 37495, 22653, 5296, 28820, 12174, 32277, 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multiplicative", "probability": 0.91357421875}, {"start": 1184.63, "end": 1185.33, "word": " functions", "probability": 0.8486328125}, {"start": 1185.33, "end": 1185.83, "word": " و", "probability": 0.6298828125}, {"start": 1185.83, "end": 1186.47, "word": " بعض", "probability": 0.949951171875}, {"start": 1186.47, "end": 1186.97, "word": " الأمور", "probability": 0.9501953125}, {"start": 1186.97, "end": 1187.15, "word": " من", "probability": 0.96826171875}, {"start": 1187.15, "end": 1187.41, "word": " هذا", "probability": 0.88525390625}, {"start": 1187.41, "end": 1187.71, "word": " النوع", "probability": 0.833984375}, {"start": 1187.71, "end": 1194.37, "word": " طيب", "probability": 0.7110595703125}, {"start": 1194.37, "end": 1194.69, "word": " ايش", "probability": 0.7330729166666666}, {"start": 1194.69, "end": 1195.03, "word": " دخل", "probability": 0.9874674479166666}, {"start": 1195.03, "end": 1195.25, "word": " ال", "probability": 0.9833984375}, {"start": 1195.25, "end": 1195.85, "word": " function", "probability": 0.947265625}, {"start": 1195.85, "end": 1196.19, "word": " هذه", "probability": 0.2861328125}, {"start": 1196.19, "end": 1196.37, "word": " في", "probability": 0.7509765625}, {"start": 1196.37, "end": 1196.95, "word": " موضوعنا", "probability": 0.94462890625}, {"start": 1196.95, "end": 1197.55, "word": " هتيجي", "probability": 0.918212890625}, {"start": 1197.55, "end": 1198.01, "word": " النظرية", "probability": 0.931640625}, {"start": 1198.01, "end": 1198.33, "word": " اربع", "probability": 0.6185709635416666}, {"start": 1198.33, "end": 1198.91, "word": " اربع", "probability": 0.9384765625}, {"start": 1198.91, "end": 1200.67, "word": " و", "probability": 0.5283203125}, {"start": 1200.67, "end": 1201.23, "word": " توضح", "probability": 0.8411458333333334}], "temperature": 1.0}, {"id": 44, "seek": 121809, "start": 1205.04, "end": 1218.1, "text": "بنخلصه ان شاء الله بضايق نظرية واحدة بيساوي رقم معين let J بيساوي generated by ال A و أخضر ال A بيساوي N", "tokens": [3555, 1863, 9778, 1211, 9381, 3224, 16472, 13412, 16606, 21984, 4724, 11242, 47302, 4587, 8717, 19913, 2288, 10632, 36764, 24401, 3660, 4724, 1829, 3794, 995, 45865, 12602, 4587, 2304, 20449, 9957, 718, 508, 4724, 1829, 3794, 995, 45865, 10833, 538, 2423, 316, 4032, 5551, 9778, 11242, 2288, 2423, 316, 4724, 1829, 3794, 995, 45865, 426], "avg_logprob": -0.2811104937323502, "compression_ratio": 1.2923076923076924, "no_speech_prob": 1.3113021850585938e-06, "words": [{"start": 1205.04, "end": 1205.68, "word": "بنخلصه", "probability": 0.7716878255208334}, {"start": 1205.68, "end": 1205.74, "word": " ان", "probability": 0.7216796875}, {"start": 1205.74, "end": 1205.94, "word": " شاء", "probability": 0.916748046875}, {"start": 1205.94, "end": 1206.06, "word": " الله", "probability": 0.95654296875}, {"start": 1206.06, "end": 1206.76, "word": " بضايق", "probability": 0.49041748046875}, {"start": 1206.76, "end": 1207.12, "word": " نظرية", "probability": 0.9713134765625}, {"start": 1207.12, "end": 1207.6, "word": " واحدة", "probability": 0.95947265625}, {"start": 1207.6, "end": 1209.04, "word": " بيساوي", "probability": 0.834765625}, {"start": 1209.04, "end": 1209.44, "word": " رقم", "probability": 0.9736328125}, {"start": 1209.44, "end": 1209.94, "word": " معين", "probability": 0.958251953125}, {"start": 1209.94, "end": 1210.84, "word": " let", "probability": 0.466552734375}, {"start": 1210.84, "end": 1212.38, "word": " J", "probability": 0.217041015625}, {"start": 1212.38, "end": 1213.28, "word": " بيساوي", "probability": 0.884765625}, {"start": 1213.28, "end": 1213.78, "word": " generated", "probability": 0.689453125}, {"start": 1213.78, "end": 1214.2, "word": " by", "probability": 0.9169921875}, {"start": 1214.2, "end": 1214.38, "word": " ال", "probability": 0.80810546875}, {"start": 1214.38, "end": 1214.62, "word": " A", "probability": 0.7197265625}, {"start": 1214.62, "end": 1216.08, "word": " و", "probability": 0.609375}, {"start": 1216.08, "end": 1216.64, "word": " أخضر", "probability": 0.67974853515625}, {"start": 1216.64, "end": 1216.86, "word": " ال", "probability": 0.90576171875}, {"start": 1216.86, "end": 1217.12, "word": " A", "probability": 0.93994140625}, {"start": 1217.12, "end": 1217.82, "word": " بيساوي", "probability": 0.789697265625}, {"start": 1217.82, "end": 1218.1, "word": " N", "probability": 0.625}], "temperature": 1.0}, {"id": 45, "seek": 124908, "start": 1221.78, "end": 1249.08, "text": "دى يقسم الان طبعا دى يقسم الان احنا هيك بنقول ان يوجد only one sub group of order دى namely generated by a to n على d هيت السؤال جداش عدد ال generator then the elements او the number of elements", "tokens": [3215, 7578, 7251, 4587, 38251, 2423, 7649, 23032, 3555, 3615, 995, 11778, 7578, 7251, 4587, 38251, 2423, 7649, 1975, 5016, 8315, 39896, 4117, 44945, 39648, 16472, 7251, 29245, 3215, 787, 472, 1422, 1594, 295, 1668, 11778, 7578, 20926, 10833, 538, 257, 281, 297, 15844, 274, 39896, 2655, 21136, 33604, 6027, 10874, 3215, 33599, 6225, 3215, 3215, 2423, 19265, 550, 264, 4959, 1975, 2407, 264, 1230, 295, 4959], "avg_logprob": -0.26976103554753694, "compression_ratio": 1.5086705202312138, "no_speech_prob": 0.0, "words": [{"start": 1221.78, "end": 1222.14, "word": "دى", "probability": 0.33245849609375}, {"start": 1222.14, "end": 1222.5, "word": " يقسم", "probability": 0.8458658854166666}, {"start": 1222.5, "end": 1222.88, "word": " الان", "probability": 0.905517578125}, {"start": 1222.88, "end": 1223.72, "word": " طبعا", "probability": 0.89306640625}, {"start": 1223.72, "end": 1223.9, "word": " دى", "probability": 0.859619140625}, {"start": 1223.9, "end": 1224.18, "word": " يقسم", "probability": 0.98828125}, {"start": 1224.18, "end": 1224.46, "word": " الان", "probability": 0.93115234375}, {"start": 1224.46, "end": 1224.68, "word": " احنا", "probability": 0.8349609375}, {"start": 1224.68, "end": 1224.92, "word": " هيك", "probability": 0.80517578125}, {"start": 1224.92, "end": 1225.24, "word": " بنقول", "probability": 0.5872802734375}, {"start": 1225.24, "end": 1225.38, "word": " ان", "probability": 0.7802734375}, {"start": 1225.38, "end": 1225.74, "word": " يوجد", "probability": 0.8888346354166666}, {"start": 1225.74, "end": 1226.14, "word": " only", "probability": 0.68798828125}, {"start": 1226.14, "end": 1227.06, "word": " one", "probability": 0.93115234375}, {"start": 1227.06, "end": 1227.38, "word": " sub", "probability": 0.8896484375}, {"start": 1227.38, "end": 1227.76, "word": " group", "probability": 0.54638671875}, {"start": 1227.76, "end": 1227.94, "word": " of", "probability": 0.9580078125}, {"start": 1227.94, "end": 1228.4, "word": " order", "probability": 0.95068359375}, {"start": 1228.4, "end": 1228.86, "word": " دى", "probability": 0.771728515625}, {"start": 1228.86, "end": 1229.6, "word": " namely", "probability": 0.66943359375}, {"start": 1229.6, "end": 1230.72, "word": " generated", "probability": 0.76708984375}, {"start": 1230.72, "end": 1230.96, "word": " by", "probability": 0.98583984375}, {"start": 1230.96, "end": 1231.34, "word": " a", "probability": 0.64599609375}, {"start": 1231.34, "end": 1231.5, "word": " to", "probability": 0.501953125}, {"start": 1231.5, "end": 1231.68, "word": " n", "probability": 0.73583984375}, {"start": 1231.68, "end": 1231.84, "word": " على", "probability": 0.77197265625}, {"start": 1231.84, "end": 1232.08, "word": " d", "probability": 0.6611328125}, {"start": 1232.08, "end": 1233.06, "word": " هيت", "probability": 0.551513671875}, {"start": 1233.06, "end": 1233.62, "word": " السؤال", "probability": 0.9884440104166666}, {"start": 1233.62, "end": 1234.12, "word": " جداش", "probability": 0.6920572916666666}, {"start": 1234.12, "end": 1234.38, "word": " عدد", "probability": 0.9812825520833334}, {"start": 1234.38, "end": 1234.5, "word": " ال", "probability": 0.67822265625}, {"start": 1234.5, "end": 1234.96, "word": " generator", "probability": 0.98681640625}, {"start": 1234.96, "end": 1236.84, "word": " then", "probability": 0.76220703125}, {"start": 1236.84, "end": 1240.6, "word": " the", "probability": 0.8076171875}, {"start": 1240.6, "end": 1241.44, "word": " elements", "probability": 0.85400390625}, {"start": 1241.44, "end": 1244.08, "word": " او", "probability": 0.6669921875}, {"start": 1244.08, "end": 1244.22, "word": " the", "probability": 0.66845703125}, {"start": 1244.22, "end": 1244.64, "word": " number", "probability": 0.966796875}, {"start": 1244.64, "end": 1248.32, "word": " of", "probability": 0.97802734375}, {"start": 1248.32, "end": 1249.08, "word": " elements", "probability": 0.89404296875}], "temperature": 1.0}, {"id": 46, "seek": 127769, "start": 1251.85, "end": 1277.69, "text": "in J with order D is فاية D عدد العناصر في J اللي ال order لهم بيساوي D بيساوياش فاية D نيجي نتبت نيجي نتبت العلاقة", "tokens": [259, 508, 365, 1668, 413, 307, 6156, 995, 10632, 413, 6225, 3215, 3215, 18863, 8315, 9381, 2288, 8978, 508, 13672, 1829, 2423, 1668, 5296, 16095, 4724, 1829, 3794, 995, 45865, 413, 4724, 1829, 3794, 995, 45865, 33599, 6156, 995, 10632, 413, 8717, 1829, 7435, 1829, 8717, 2655, 3555, 2655, 8717, 1829, 7435, 1829, 8717, 2655, 3555, 2655, 18863, 15040, 28671], "avg_logprob": -0.33043032786885246, "compression_ratio": 1.5083333333333333, "no_speech_prob": 0.0, "words": [{"start": 1251.85, "end": 1252.13, "word": "in", "probability": 0.1162109375}, {"start": 1252.13, "end": 1252.45, "word": " J", "probability": 0.3232421875}, {"start": 1252.45, "end": 1254.13, "word": " with", "probability": 0.853515625}, {"start": 1254.13, "end": 1254.83, "word": " order", "probability": 0.9306640625}, {"start": 1254.83, "end": 1256.55, "word": " D", "probability": 0.5791015625}, {"start": 1256.55, "end": 1257.57, "word": " is", "probability": 0.68505859375}, {"start": 1257.57, "end": 1259.63, "word": " فاية", "probability": 0.3465983072916667}, {"start": 1259.63, "end": 1259.83, "word": " D", "probability": 0.8583984375}, {"start": 1259.83, "end": 1262.21, "word": " عدد", "probability": 0.9443359375}, {"start": 1262.21, "end": 1263.15, "word": " العناصر", "probability": 0.8302001953125}, {"start": 1263.15, "end": 1263.83, "word": " في", "probability": 0.8291015625}, {"start": 1263.83, "end": 1264.19, "word": " J", "probability": 0.89404296875}, {"start": 1264.19, "end": 1265.15, "word": " اللي", "probability": 0.945068359375}, {"start": 1265.15, "end": 1265.31, "word": " ال", "probability": 0.578125}, {"start": 1265.31, "end": 1265.73, "word": " order", "probability": 0.94873046875}, {"start": 1265.73, "end": 1266.43, "word": " لهم", "probability": 0.700439453125}, {"start": 1266.43, "end": 1267.49, "word": " بيساوي", "probability": 0.89404296875}, {"start": 1267.49, "end": 1267.77, "word": " D", "probability": 0.8017578125}, {"start": 1267.77, "end": 1269.21, "word": " بيساوياش", "probability": 0.8541259765625}, {"start": 1269.21, "end": 1270.83, "word": " فاية", "probability": 0.8458658854166666}, {"start": 1270.83, "end": 1271.35, "word": " D", "probability": 0.984375}, {"start": 1271.35, "end": 1272.11, "word": " نيجي", "probability": 0.6709136962890625}, {"start": 1272.11, "end": 1272.61, "word": " نتبت", "probability": 0.8291015625}, {"start": 1272.61, "end": 1276.27, "word": " نيجي", "probability": 0.73333740234375}, {"start": 1276.27, "end": 1277.29, "word": " نتبت", "probability": 0.994140625}, {"start": 1277.29, "end": 1277.69, "word": " العلاقة", "probability": 0.8767903645833334}], "temperature": 1.0}, {"id": 47, "seek": 131009, "start": 1280.74, "end": 1310.1, "text": "اربع تلاتة part c ايش ال part c في النظرية هذه بيقول؟ there exist a unique .. طبعا there exist unique subgroup of j with order d namely", "tokens": [9640, 3555, 3615, 6055, 1211, 9307, 3660, 644, 269, 1975, 1829, 8592, 2423, 644, 269, 8978, 28239, 19913, 2288, 10632, 29538, 4724, 1829, 39648, 22807, 456, 2514, 257, 3845, 4386, 23032, 3555, 3615, 995, 456, 2514, 3845, 1422, 17377, 295, 361, 365, 1668, 274, 20926], "avg_logprob": -0.32727582623129303, "compression_ratio": 1.2214285714285715, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1280.74, "end": 1281.2, "word": "اربع", "probability": 0.6944986979166666}, {"start": 1281.2, "end": 1281.86, "word": " تلاتة", "probability": 0.9375}, {"start": 1281.86, "end": 1282.66, "word": " part", "probability": 0.7509765625}, {"start": 1282.66, "end": 1284.26, "word": " c", "probability": 0.41357421875}, {"start": 1284.26, "end": 1286.78, "word": " ايش", "probability": 0.699462890625}, {"start": 1286.78, "end": 1286.9, "word": " ال", "probability": 0.62109375}, {"start": 1286.9, "end": 1287.08, "word": " part", "probability": 0.9580078125}, {"start": 1287.08, "end": 1287.28, "word": " c", "probability": 0.8896484375}, {"start": 1287.28, "end": 1287.42, "word": " في", "probability": 0.85888671875}, {"start": 1287.42, "end": 1287.84, "word": " النظرية", "probability": 0.932373046875}, {"start": 1287.84, "end": 1288.02, "word": " هذه", "probability": 0.28125}, {"start": 1288.02, "end": 1288.98, "word": " بيقول؟", "probability": 0.728271484375}, {"start": 1288.98, "end": 1290.26, "word": " there", "probability": 0.59326171875}, {"start": 1290.26, "end": 1290.9, "word": " exist", "probability": 0.505859375}, {"start": 1290.9, "end": 1293.82, "word": " a", "probability": 0.890625}, {"start": 1293.82, "end": 1294.48, "word": " unique", "probability": 0.8662109375}, {"start": 1294.48, "end": 1294.56, "word": " ..", "probability": 0.2110595703125}, {"start": 1294.56, "end": 1295.28, "word": " طبعا", "probability": 0.842041015625}, {"start": 1295.28, "end": 1295.46, "word": " there", "probability": 0.66357421875}, {"start": 1295.46, "end": 1295.76, "word": " exist", "probability": 0.87646484375}, {"start": 1295.76, "end": 1296.26, "word": " unique", "probability": 0.59716796875}, {"start": 1296.26, "end": 1297.46, "word": " subgroup", "probability": 0.77734375}, {"start": 1297.46, "end": 1302.04, "word": " of", "probability": 0.94482421875}, {"start": 1302.04, "end": 1302.64, "word": " j", "probability": 0.71728515625}, {"start": 1302.64, "end": 1304.5, "word": " with", "probability": 0.91357421875}, {"start": 1304.5, "end": 1305.24, "word": " order", "probability": 0.97021484375}, {"start": 1305.24, "end": 1308.44, "word": " d", "probability": 0.482666015625}, {"start": 1308.44, "end": 1310.1, "word": " namely", "probability": 0.80712890625}], "temperature": 1.0}, {"id": 48, "seek": 133135, "start": 1313.03, "end": 1331.35, "text": "generated by a to n على d طيب هل جيت؟ مده مافيش غير هذه ال subgroup ال order اللي هي دي فالعناصر لل order اللي هي دي ممكن تكون موجودة برا", "tokens": [21848, 770, 538, 257, 281, 297, 15844, 274, 23032, 1829, 3555, 8032, 1211, 10874, 36081, 22807, 3714, 3215, 3224, 19446, 41185, 8592, 32771, 13546, 29538, 2423, 1422, 17377, 2423, 1668, 13672, 1829, 39896, 11778, 1829, 6156, 6027, 3615, 8315, 9381, 2288, 24976, 1668, 13672, 1829, 39896, 11778, 1829, 3714, 43020, 6055, 30544, 3714, 29245, 23328, 3660, 4724, 23557], "avg_logprob": -0.25820974374221545, "compression_ratio": 1.4482758620689655, "no_speech_prob": 0.0, "words": [{"start": 1313.03, "end": 1313.67, "word": "generated", "probability": 0.681640625}, {"start": 1313.67, "end": 1314.27, "word": " by", "probability": 0.9716796875}, {"start": 1314.27, "end": 1315.71, "word": " a", "probability": 0.62890625}, {"start": 1315.71, "end": 1317.25, "word": " to", "probability": 0.437255859375}, {"start": 1317.25, "end": 1317.51, "word": " n", "probability": 0.73388671875}, {"start": 1317.51, "end": 1317.73, "word": " على", "probability": 0.7197265625}, {"start": 1317.73, "end": 1317.95, "word": " d", "probability": 0.6689453125}, {"start": 1317.95, "end": 1321.27, "word": " طيب", "probability": 0.76611328125}, {"start": 1321.27, "end": 1323.29, "word": " هل", "probability": 0.83544921875}, {"start": 1323.29, "end": 1324.17, "word": " جيت؟", "probability": 0.71484375}, {"start": 1324.17, "end": 1324.43, "word": " مده", "probability": 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generators are of the form", "tokens": [13267, 498, 10833, 538, 316, 281, 426, 15844, 413, 3714, 43020, 1975, 4117, 2655, 3555, 11296, 10833, 538, 430, 365, 1668, 2423, 430, 4724, 16254, 8608, 2407, 413, 550, 264, 661, 38662, 366, 295, 264, 1254], "avg_logprob": -0.2749155502061586, "compression_ratio": 1.1774193548387097, "no_speech_prob": 0.0, "words": [{"start": 1425.29, "end": 1425.83, "word": "Now", "probability": 0.1783447265625}, {"start": 1425.83, "end": 1429.09, "word": " if", "probability": 0.50634765625}, {"start": 1429.09, "end": 1430.53, "word": " generated", "probability": 0.73388671875}, {"start": 1430.53, "end": 1431.55, "word": " by", "probability": 0.97265625}, {"start": 1431.55, "end": 1431.97, "word": " A", "probability": 0.421142578125}, {"start": 1431.97, "end": 1432.41, "word": " to", "probability": 0.90869140625}, {"start": 1432.41, "end": 1432.63, "word": " N", "probability": 0.85546875}, {"start": 1432.63, "end": 1432.85, "word": " على", "probability": 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order", "probability": 0.95654296875}, {"start": 1529.59, "end": 1530.51, "word": " D", "probability": 0.94189453125}, {"start": 1530.51, "end": 1531.55, "word": " is", "probability": 0.93603515625}, {"start": 1531.55, "end": 1532.63, "word": " فاية", "probability": 0.8894856770833334}, {"start": 1532.63, "end": 1533.03, "word": " D", "probability": 0.96044921875}, {"start": 1533.03, "end": 1535.11, "word": " وهو", "probability": 0.690673828125}, {"start": 1535.11, "end": 1535.51, "word": " المطلوب", "probability": 0.9898681640625}], "temperature": 1.0}, {"id": 56, "seek": 156843, "start": 1542.17, "end": 1568.43, "text": "اللي صار كانت تانية يا شباب انا بدور على عناصر لل order الهدى نقلت المسألة من اني ابحث في ال ج كلها لاني ابحث وين في ال sub group لل order الهدى ميزة العناصر هنا لل order الهدى انها generator انا عشان اعدى كام generator باخد واحد من هذه ال generators فليكن بيه و باقى ال generators عبارة عن P to K و ال K relative لبرايم مع مين", "tokens": [6027, 20292, 20328, 9640, 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1939.23, "word": " إن", "probability": 0.4501953125}, {"start": 1939.23, "end": 1939.67, "word": " الطالب", "probability": 0.99365234375}, {"start": 1939.67, "end": 1940.73, "word": " يقدر", "probability": 0.9957682291666666}, {"start": 1940.73, "end": 1942.69, "word": " يعرفها", "probability": 0.88525390625}, {"start": 1942.69, "end": 1943.73, "word": " لوحده", "probability": 0.8362630208333334}], "temperature": 1.0}, {"id": 70, "seek": 199104, "start": 1963.42, "end": 1991.04, "text": "السؤال الأول find all generator of z6, z8, z20 طبعا ال generator غيرنا عبارة عن مين؟ لو طلعنا على نظرية أو corollary لنظرية الأولى كان بيقولك ال generator ل zn هي عبارة عن مين؟ عن الأرقام اللي relative ل برايم مع ال n اللي هي فعليا عبارة عناش؟ عناصر ال UN", "tokens": [6027, 3794, 33604, 6027, 16247, 12610, 915, 439, 19265, 295, 710, 21, 11, 710, 23, 11, 710, 2009, 23032, 3555, 3615, 995, 2423, 19265, 32771, 13546, 8315, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 45164, 23032, 1211, 3615, 8315, 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واربعين مدة عشرين جديش؟ تسعة", "tokens": [1829, 2407, 6225, 46309, 9957, 10874, 16254, 8592, 35186, 13412, 3555, 16758, 22807, 36764, 24401, 12399, 6055, 1211, 9307, 3660, 12399, 8608, 3555, 27884, 12399, 6055, 3794, 27884, 12399, 11778, 33599, 2288, 12399, 6055, 1211, 2655, 33599, 2288, 12399, 8608, 3555, 34268, 33599, 2288, 12399, 6055, 3794, 27884, 12399, 1975, 2655, 33599, 2288, 17668, 264, 4959, 295, 10833, 538, 6055, 1211, 9307, 3660, 4032, 35457, 27884, 8717, 47283, 3215, 10833, 538, 8608, 3555, 27884, 50113, 15040, 13672, 1829, 6225, 3555, 9640, 3660, 18871, 2423, 14407, 24401, 21136, 3555, 27884, 8608, 3555, 27884, 6055, 17082, 21292, 3615, 10874, 16254, 8592, 22807, 6055, 3794, 27884, 4032, 9640, 3555, 3615, 9957, 3714, 41891, 6225, 46309, 9957, 10874, 16254, 8592, 22807, 6055, 3794, 27884], "avg_logprob": -0.2125516459961568, "compression_ratio": 1.964824120603015, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2119.21, "end": 2119.49, "word": "يو", "probability": 0.509521484375}, {"start": 2119.49, "end": 2119.73, "word": " عشرين", "probability": 0.7166341145833334}, {"start": 2119.73, "end": 2120.05, "word": " جديش", "probability": 0.5483805338541666}, {"start": 2120.05, "end": 2120.15, "word": " يا", "probability": 0.9306640625}, {"start": 2120.15, "end": 2121.23, "word": " شباب؟", "probability": 0.91552734375}, {"start": 2121.23, "end": 2121.87, "word": " واحد،", "probability": 0.7345377604166666}, {"start": 2121.87, "end": 2122.45, "word": " تلاتة،", "probability": 0.95546875}, {"start": 2122.45, "end": 2123.35, "word": " سبعة،", "probability": 0.9273681640625}, {"start": 2123.35, "end": 2124.25, "word": " تسعة،", "probability": 0.9678955078125}, {"start": 2124.25, "end": 2124.79, "word": " داشر،", "probability": 0.826416015625}, {"start": 2124.79, "end": 2125.41, "word": " تلتاشر،", "probability": 0.863037109375}, {"start": 2125.41, "end": 2126.37, "word": " سبعتاشر،", "probability": 0.927978515625}, {"start": 2126.37, "end": 2127.63, "word": " تسعة،", "probability": 0.81475830078125}, {"start": 2127.63, "end": 2128.13, "word": " اتاشر", "probability": 0.7889404296875}, {"start": 2128.13, "end": 2129.33, "word": " List", "probability": 0.226806640625}, {"start": 2129.33, "end": 2130.01, "word": " the", "probability": 0.8701171875}, {"start": 2130.01, "end": 2130.43, "word": " elements", "probability": 0.8837890625}, {"start": 2130.43, "end": 2130.65, "word": " of", "probability": 0.8193359375}, {"start": 2130.65, "end": 2131.11, "word": " generated", "probability": 0.8056640625}, {"start": 2131.11, "end": 2131.61, "word": " by", "probability": 0.9765625}, {"start": 2131.61, "end": 2132.17, "word": " تلاتة", "probability": 0.8997802734375}, {"start": 2132.17, "end": 2132.77, "word": " وسبعة", "probability": 0.7275390625}, {"start": 2132.77, "end": 2133.47, "word": " ناخد", "probability": 0.9156901041666666}, {"start": 2133.47, "end": 2133.87, "word": " generated", "probability": 0.78125}, {"start": 2133.87, "end": 2134.13, "word": " by", "probability": 0.98388671875}, {"start": 2134.13, "end": 2134.43, "word": " سبعة", "probability": 0.9381510416666666}, {"start": 2134.43, "end": 2135.41, "word": " مثلا", "probability": 0.93896484375}, {"start": 2135.41, "end": 2136.73, "word": " اللي", "probability": 0.702880859375}, {"start": 2136.73, "end": 2137.19, "word": " عبارة", "probability": 0.9886474609375}, {"start": 2137.19, "end": 2137.97, "word": " عن", "probability": 0.9970703125}, {"start": 2137.97, "end": 2138.65, "word": " الواحد", "probability": 0.984375}, {"start": 2138.65, "end": 2139.47, "word": " السبعة", "probability": 0.7750651041666666}, {"start": 2139.47, "end": 2140.67, "word": " سبعة", "probability": 0.8758138020833334}, {"start": 2140.67, "end": 2141.89, "word": " تغبيع", "probability": 0.77093505859375}, {"start": 2141.89, "end": 2143.25, "word": " جديش؟", "probability": 0.72259521484375}, {"start": 2143.25, "end": 2144.61, "word": " تسعة", "probability": 0.95458984375}, {"start": 2144.61, "end": 2145.15, "word": " واربعين", "probability": 0.8580078125}, {"start": 2145.15, "end": 2145.67, "word": " مدة", "probability": 0.51708984375}, {"start": 2145.67, "end": 2146.05, "word": " عشرين", "probability": 0.70751953125}, {"start": 2146.05, "end": 2146.67, "word": " جديش؟", "probability": 0.9346923828125}, {"start": 2146.67, "end": 2147.63, "word": " تسعة", "probability": 0.9837239583333334}], "temperature": 1.0}, {"id": 77, "seek": 217798, "start": 2148.44, "end": 2177.98, "text": "سبعة تكيب يعني سبعة في تسعة تلاتة قصتين تلاتة سبعة أربعة يعني سبعة في تلاتة يعني واحد و عشرين و واحد طبعا generated by تلاتة عبارة عن من؟ واحد تلاتة تلاتة تربية تسعة بعدين سبعة و عشرين سبعة بعدين حتيجة", "tokens": [35457, 27884, 6055, 4117, 1829, 3555, 37495, 22653, 8608, 3555, 27884, 8978, 6055, 3794, 27884, 6055, 1211, 9307, 3660, 12174, 9381, 2655, 9957, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 5551, 25513, 27884, 37495, 22653, 8608, 3555, 27884, 8978, 6055, 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"probability": 0.9845377604166666}, {"start": 2151.7, "end": 2153.74, "word": " تلاتة", "probability": 0.861572265625}, {"start": 2153.74, "end": 2155.02, "word": " قصتين", "probability": 0.56610107421875}, {"start": 2155.02, "end": 2157.72, "word": " تلاتة", "probability": 0.77587890625}, {"start": 2157.72, "end": 2159.54, "word": " سبعة", "probability": 0.8424479166666666}, {"start": 2159.54, "end": 2161.54, "word": " أربعة", "probability": 0.6748860677083334}, {"start": 2161.54, "end": 2162.32, "word": " يعني", "probability": 0.82275390625}, {"start": 2162.32, "end": 2162.62, "word": " سبعة", "probability": 0.94970703125}, {"start": 2162.62, "end": 2162.74, "word": " في", "probability": 0.966796875}, {"start": 2162.74, "end": 2163.1, "word": " تلاتة", "probability": 0.9730224609375}, {"start": 2163.1, "end": 2163.24, "word": " يعني", "probability": 0.8916015625}, {"start": 2163.24, "end": 2163.48, "word": " واحد", "probability": 0.96337890625}, {"start": 2163.48, "end": 2163.58, 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" تلاتة", "probability": 0.9056396484375}, {"start": 2173.34, "end": 2174.02, "word": " تلاتة", "probability": 0.9111328125}, {"start": 2174.02, "end": 2174.36, "word": " تربية", "probability": 0.8956705729166666}, {"start": 2174.36, "end": 2174.8, "word": " تسعة", "probability": 0.97705078125}, {"start": 2174.8, "end": 2175.58, "word": " بعدين", "probability": 0.6116943359375}, {"start": 2175.58, "end": 2175.82, "word": " سبعة", "probability": 0.9557291666666666}, {"start": 2175.82, "end": 2175.94, "word": " و", "probability": 0.93017578125}, {"start": 2175.94, "end": 2176.2, "word": " عشرين", "probability": 0.93212890625}, {"start": 2176.2, "end": 2176.64, "word": " سبعة", "probability": 0.9129231770833334}, {"start": 2176.64, "end": 2177.6, "word": " بعدين", "probability": 0.919921875}, {"start": 2177.6, "end": 2177.98, "word": " حتيجة", "probability": 0.67816162109375}], "temperature": 1.0}, {"id": 78, "seek": 220942, "start": 2181.63, "end": 2209.43, "text": "طيب سؤال السادس what do exercises تلاتة و أربعة و خمسة have in common try to make a generalization that includes these three cases انت لما تحل سؤال تلاتة و أربعة و خمسة ايش بتستنتجه؟ ايش السنتجات اللي ممكن تستنتجها؟ لو طلعنا على خمسة", "tokens": [9566, 1829, 3555, 8608, 33604, 6027, 21136, 18513, 3794, 437, 360, 11900, 6055, 1211, 9307, 3660, 4032, 5551, 25513, 27884, 4032, 16490, 2304, 3794, 3660, 362, 294, 2689, 853, 281, 652, 257, 2674, 2144, 300, 5974, 613, 1045, 3331, 16472, 2655, 5296, 15042, 6055, 5016, 1211, 8608, 33604, 6027, 6055, 1211, 9307, 3660, 4032, 5551, 25513, 27884, 4032, 16490, 2304, 3794, 3660, 1975, 1829, 8592, 39894, 14851, 29399, 7435, 3224, 22807, 1975, 1829, 8592, 21136, 29399, 7435, 9307, 13672, 1829, 3714, 43020, 6055, 14851, 29399, 7435, 11296, 22807, 45164, 23032, 1211, 3615, 8315, 15844, 16490, 2304, 3794, 3660], "avg_logprob": -0.13920454545454544, "compression_ratio": 1.6428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2181.6299999999997, "end": 2182.49, "word": 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{"id": 83, "seek": 234709, "start": 2321.15, "end": 2347.09, "text": "let a be an element of a group and let order a بسوا 15 compute the orders of the following طبعا هذا سهل مثلا ال order ل a أس 9 عبارة عن عبارة عن إيش ال order ل a أس k عبارة عن إيش في نظرية في أول واحدة خدناها and على", "tokens": [2631, 257, 312, 364, 4478, 295, 257, 1594, 293, 718, 1668, 257, 4724, 3794, 14407, 2119, 14722, 264, 9470, 295, 264, 3480, 23032, 3555, 3615, 995, 23758, 8608, 3224, 1211, 50113, 15040, 2423, 1668, 5296, 257, 5551, 3794, 1722, 6225, 3555, 9640, 3660, 18871, 6225, 3555, 9640, 3660, 18871, 11933, 1829, 8592, 2423, 1668, 5296, 257, 5551, 3794, 350, 6225, 3555, 9640, 3660, 18871, 11933, 1829, 8592, 8978, 8717, 19913, 2288, 10632, 8978, 5551, 12610, 36764, 24401, 3660, 16490, 3215, 8315, 11296, 293, 15844], "avg_logprob": -0.26158087113324335, "compression_ratio": 1.588235294117647, "no_speech_prob": 0.0, "words": [{"start": 2321.15, "end": 2321.45, "word": "let", "probability": 0.43603515625}, 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"end": 2365.05, "word": " نفس", "probability": 0.80126953125}, {"start": 2365.05, "end": 2365.83, "word": " القصة", "probability": 0.9873046875}, {"start": 2365.83, "end": 2367.21, "word": " في", "probability": 0.94873046875}, {"start": 2367.21, "end": 2367.45, "word": " c", "probability": 0.939453125}], "temperature": 1.0}, {"id": 85, "seek": 239889, "start": 2373.53, "end": 2398.89, "text": "سؤال تسعة how many subgroups of Z20 توحى لنا توحى لنا شباب في Z20 كام subgroup اللي أجى؟ عوام ال 20 عوام ال 20 و لا عوام ال 20؟ لأ عوام ال 20 generator لكن subgroup احنا قلنا فيه عددين عدد ال subgroups اللي هو عدد القواسم", "tokens": [3794, 33604, 6027, 6055, 3794, 27884, 577, 867, 1422, 17377, 82, 295, 1176, 2009, 6055, 2407, 5016, 7578, 5296, 8315, 6055, 2407, 5016, 7578, 5296, 8315, 13412, 3555, 16758, 8978, 1176, 2009, 9122, 10943, 1422, 17377, 13672, 1829, 5551, 7435, 7578, 22807, 6225, 2407, 10943, 2423, 945, 6225, 2407, 10943, 2423, 945, 4032, 20193, 6225, 2407, 10943, 2423, 945, 22807, 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"probability": 0.4996337890625}, {"start": 2378.95, "end": 2379.21, "word": " لنا", "probability": 0.7286376953125}, {"start": 2379.21, "end": 2381.33, "word": " توحى", "probability": 0.80133056640625}, {"start": 2381.33, "end": 2381.65, "word": " لنا", "probability": 0.9873046875}, {"start": 2381.65, "end": 2381.99, "word": " شباب", "probability": 0.8321940104166666}, {"start": 2381.99, "end": 2383.07, "word": " في", "probability": 0.65673828125}, {"start": 2383.07, "end": 2383.51, "word": " Z20", "probability": 0.936767578125}, {"start": 2383.51, "end": 2383.75, "word": " كام", "probability": 0.5169677734375}, {"start": 2383.75, "end": 2384.17, "word": " subgroup", "probability": 0.938720703125}, {"start": 2384.17, "end": 2384.33, "word": " اللي", "probability": 0.5865478515625}, {"start": 2384.33, "end": 2386.07, "word": " أجى؟", "probability": 0.54302978515625}, {"start": 2386.07, "end": 2386.63, "word": " عوام", "probability": 0.761962890625}, {"start": 2386.63, "end": 2386.71, 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ال", "probability": 0.9091796875}, {"start": 2391.67, "end": 2391.85, "word": " 20", "probability": 0.92333984375}, {"start": 2391.85, "end": 2392.31, "word": " generator", "probability": 0.64453125}, {"start": 2392.31, "end": 2393.31, "word": " لكن", "probability": 0.329345703125}, {"start": 2393.31, "end": 2394.01, "word": " subgroup", "probability": 0.781494140625}, {"start": 2394.01, "end": 2394.23, "word": " احنا", "probability": 0.85888671875}, {"start": 2394.23, "end": 2394.41, "word": " قلنا", "probability": 0.700927734375}, {"start": 2394.41, "end": 2394.83, "word": " فيه", "probability": 0.8330078125}, {"start": 2394.83, "end": 2395.65, "word": " عددين", "probability": 0.9014892578125}, {"start": 2395.65, "end": 2396.41, "word": " عدد", "probability": 0.9469401041666666}, {"start": 2396.41, "end": 2396.53, "word": " ال", "probability": 0.83349609375}, {"start": 2396.53, "end": 2397.49, "word": " subgroups", "probability": 0.84521484375}, {"start": 2397.49, "end": 2397.89, "word": " اللي", "probability": 0.95751953125}, {"start": 2397.89, "end": 2397.99, "word": " هو", "probability": 0.8828125}, {"start": 2397.99, "end": 2398.23, "word": " عدد", "probability": 0.9890950520833334}, {"start": 2398.23, "end": 2398.89, "word": " القواسم", "probability": 0.9148763020833334}], "temperature": 1.0}, {"id": 86, "seek": 242841, "start": 2400.01, "end": 2428.41, "text": "لكن عدد ال generator اللي هو ال file عدد القواسم من ال 20 جديش 6 1 2 4 5 10 و 20 طبعا سهل انك تتعامل مع هذا السؤال سؤال 10 انزد 24 list all generator سؤال 10 زي سؤال 9 سؤال 11 generated by ال A inverse ممكن تساوي generated by D", "tokens": [1211, 19452, 6225, 3215, 3215, 2423, 19265, 13672, 1829, 31439, 2423, 3991, 6225, 3215, 3215, 25062, 14407, 38251, 9154, 2423, 945, 10874, 16254, 8592, 1386, 502, 568, 1017, 1025, 1266, 4032, 945, 23032, 3555, 3615, 995, 8608, 3224, 1211, 16472, 4117, 6055, 2655, 3615, 10943, 1211, 20449, 23758, 21136, 33604, 6027, 8608, 33604, 6027, 1266, 16472, 11622, 3215, 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diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8d357fcbd38a0214a8e1da63133d734c60213d9e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.json
@@ -0,0 +1 @@
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"temperature": 1.0}, {"id": 5, "seek": 12239, "start": 103.47, "end": 122.39, "text": "النقطة الثانية لو كان الـG abelian فإن الـG bar abelian والعكس صحيح لو كان الـG bar abelian يبقى الـG abelian يبقى الـG is abelian if and only if الـG bar is abelian بالمثل الـG is cyclic if and only if الـG bar is cyclic", "tokens": [6027, 1863, 47432, 3660, 6024, 104, 7649, 10632, 45164, 25961, 2423, 39184, 38, 410, 338, 952, 6156, 28814, 1863, 2423, 39184, 38, 2159, 410, 338, 952, 16070, 3615, 4117, 3794, 20328, 5016, 1829, 5016, 45164, 25961, 2423, 39184, 38, 2159, 410, 338, 952, 7251, 3555, 4587, 7578, 2423, 39184, 38, 410, 338, 952, 7251, 3555, 4587, 7578, 2423, 39184, 38, 307, 410, 338, 952, 498, 293, 787, 498, 2423, 39184, 38, 2159, 307, 410, 338, 952, 20666, 2304, 12984, 1211, 2423, 39184, 38, 307, 38154, 1050, 498, 293, 787, 498, 2423, 39184, 38, 2159, 307, 38154, 1050], "avg_logprob": -0.1563297245575457, "compression_ratio": 2.0774647887323945, "no_speech_prob": 0.0, "words": [{"start": 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نحاول نبرهن النقاط الأربع اللي عندنا و بدنا نأتي إلى النقطة الأولى النقطة الأولى بدنا نعتمد في برهانها على ما نعرف من مبادئ الرياضية", "tokens": [6027, 7649, 47525, 8315, 8717, 5016, 995, 12610, 8717, 26890, 3224, 1863, 28239, 4587, 41193, 16247, 25513, 3615, 13672, 1829, 43242, 8315, 4032, 47525, 8315, 8717, 10721, 31371, 30731, 28239, 47432, 3660, 16247, 12610, 7578, 28239, 47432, 3660, 16247, 12610, 7578, 47525, 8315, 8717, 34268, 2304, 3215, 8978, 4724, 2288, 3224, 7649, 11296, 15844, 19446, 8717, 3615, 28480, 9154, 3714, 3555, 18513, 19986, 2423, 16572, 46958, 10632], "avg_logprob": -0.14200367910020492, "compression_ratio": 1.9044117647058822, "no_speech_prob": 0.0, "words": [{"start": 149.31, "end": 149.77, "word": "الان", "probability": 0.8876953125}, {"start": 149.77, "end": 150.07, "word": " بدنا", "probability": 0.6484375}, {"start": 150.07, "end": 150.47, "word": " نحاول", "probability": 0.83551025390625}, {"start": 150.47, "end": 151.03, "word": " نبرهن", "probability": 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الأولين", "probability": 0.8782552083333334}, {"start": 357.42, "end": 357.54, "word": " يا", "probability": 0.86865234375}, {"start": 357.54, "end": 357.94, "word": " شباب", "probability": 0.9921875}, {"start": 357.94, "end": 359.12, "word": " تأثير", "probability": 0.7222900390625}, {"start": 359.12, "end": 360.32, "word": " الفاي", "probability": 0.914306640625}], "temperature": 1.0}, {"id": 17, "seek": 38143, "start": 360.51, "end": 381.43, "text": "على الفاي انفرس عشان اه فايفاي انفرس عشان اه فايفاي انفرس عشان اه فايفاي انفرس عشان اه فايفاي انفرس عشان اه فايفاي انفرس عشان اه فايفاي انفرس عشان اه", "tokens": [3615, 23942, 27188, 47302, 16472, 5172, 2288, 3794, 6225, 8592, 7649, 1975, 3224, 6156, 995, 33911, 47302, 16472, 5172, 2288, 3794, 6225, 8592, 7649, 1975, 3224, 6156, 995, 33911, 47302, 16472, 5172, 2288, 3794, 6225, 8592, 7649, 1975, 3224, 6156, 995, 33911, 47302, 16472, 5172, 2288, 3794, 6225, 8592, 7649, 1975, 3224, 6156, 995, 33911, 47302, 16472, 5172, 2288, 3794, 6225, 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374.59, "word": " اه", "probability": 0.947265625}, {"start": 374.59, "end": 377.99, "word": " فايفاي", "probability": 0.8316650390625}, {"start": 377.99, "end": 378.67, "word": " انفرس", "probability": 0.993408203125}, {"start": 378.67, "end": 379.53, "word": " عشان", "probability": 0.9754231770833334}, {"start": 379.53, "end": 379.53, "word": " اه", "probability": 0.955078125}, {"start": 379.53, "end": 380.07, "word": " فايفاي", "probability": 0.857421875}, {"start": 380.07, "end": 380.71, "word": " انفرس", "probability": 0.9935302734375}, {"start": 380.71, "end": 381.05, "word": " عشان", "probability": 0.9757486979166666}, {"start": 381.05, "end": 381.43, "word": " اه", "probability": 0.960693359375}], "temperature": 1.0}, {"id": 18, "seek": 41156, "start": 383.42, "end": 411.56, "text": "يبقى بناء عليه هذا الكلام يساوي انا عندي في is an isomorphism معناته في لما تأثر على حصر ضرب two elements يساوي تأثير الفي على الأولى مضروب في تأثير الفي على الثانية يبقى هذا بده يعطينا في لفي inverse of a في في لمين لفي inverse of b", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 47356, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 1975, 8315, 18871, 16254, 8978, 307, 364, 307, 32702, 1434, 20449, 8315, 47395, 8978, 5296, 15042, 6055, 10721, 49115, 15844, 11331, 9381, 2288, 48812, 25513, 732, 4959, 7251, 3794, 995, 45865, 6055, 10721, 12984, 13546, 27188, 1829, 15844, 16247, 12610, 7578, 3714, 11242, 32887, 3555, 8978, 6055, 10721, 12984, 13546, 27188, 1829, 15844, 6024, 104, 7649, 10632, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 8978, 5296, 41185, 17340, 295, 257, 8978, 8978, 32767, 9957, 5296, 41185, 17340, 295, 272], "avg_logprob": -0.17140151454944802, "compression_ratio": 1.8106796116504855, "no_speech_prob": 0.0, "words": [{"start": 383.42, "end": 383.96, "word": "يبقى", "probability": 0.8111572265625}, {"start": 383.96, "end": 384.4, "word": " بناء", "probability": 0.8828125}, {"start": 384.4, "end": 385.02, "word": " عليه", "probability": 0.77490234375}, {"start": 385.02, "end": 385.42, "word": " هذا", "probability": 0.86962890625}, {"start": 385.42, "end": 386.02, "word": " الكلام", "probability": 0.8680013020833334}, {"start": 386.02, "end": 386.64, "word": " يساوي", "probability": 0.9359130859375}, {"start": 386.64, "end": 387.06, "word": " انا", "probability": 0.6895751953125}, {"start": 387.06, "end": 387.58, "word": " عندي", "probability": 0.83544921875}, {"start": 387.58, "end": 388.1, "word": " في", "probability": 0.325927734375}, {"start": 388.1, "end": 389.06, "word": " is", "probability": 0.312255859375}, {"start": 389.06, "end": 389.46, "word": " an", "probability": 0.7685546875}, {"start": 389.46, "end": 390.52, "word": " isomorphism", "probability": 0.9674479166666666}, {"start": 390.52, "end": 391.58, "word": " معناته", "probability": 0.8098958333333334}, {"start": 391.58, "end": 391.9, "word": " في", "probability": 0.927734375}, {"start": 391.9, "end": 392.14, "word": " لما", "probability": 0.763671875}, {"start": 392.14, "end": 392.54, "word": " تأثر", "probability": 0.7335611979166666}, {"start": 392.54, "end": 392.74, "word": " على", "probability": 0.92333984375}, {"start": 392.74, "end": 393.3, "word": " حصر", "probability": 0.8235677083333334}, {"start": 393.3, "end": 393.6, "word": " ضرب", "probability": 0.88525390625}, {"start": 393.6, "end": 393.82, "word": " two", "probability": 0.689453125}, {"start": 393.82, "end": 394.2, "word": " elements", "probability": 0.95654296875}, {"start": 394.2, "end": 394.66, "word": " يساوي", "probability": 0.924560546875}, {"start": 394.66, "end": 395.22, "word": " تأثير", "probability": 0.915283203125}, {"start": 395.22, "end": 395.64, "word": " الفي", "probability": 0.6937255859375}, {"start": 395.64, "end": 395.84, "word": " على", "probability": 0.92333984375}, {"start": 395.84, "end": 396.34, "word": " الأولى", "probability": 0.9376627604166666}, {"start": 396.34, "end": 396.74, "word": " مضروب", "probability": 0.862060546875}, {"start": 396.74, "end": 396.86, "word": " في", "probability": 0.88134765625}, {"start": 396.86, "end": 397.32, "word": " تأثير", "probability": 0.981201171875}, {"start": 397.32, "end": 397.9, "word": " الفي", "probability": 0.939208984375}, {"start": 397.9, "end": 398.7, "word": " على", "probability": 0.91748046875}, {"start": 398.7, "end": 399.48, "word": " الثانية", "probability": 0.968994140625}, {"start": 399.48, "end": 400.38, "word": " يبقى", "probability": 0.9796142578125}, {"start": 400.38, "end": 400.7, "word": " هذا", "probability": 0.94091796875}, {"start": 400.7, "end": 401.12, "word": " بده", "probability": 0.5467529296875}, {"start": 401.12, "end": 401.88, "word": " يعطينا", "probability": 0.932861328125}, {"start": 401.88, "end": 402.72, "word": " في", "probability": 0.8974609375}, {"start": 402.72, "end": 403.64, "word": " لفي", "probability": 0.890625}, {"start": 403.64, "end": 404.54, "word": " inverse", "probability": 0.916015625}, {"start": 404.54, "end": 405.12, "word": " of", "probability": 0.96435546875}, {"start": 405.12, "end": 405.56, "word": " a", "probability": 0.75146484375}, {"start": 405.56, "end": 406.56, "word": " في", "probability": 0.81689453125}, {"start": 406.56, "end": 407.26, "word": " في", "probability": 0.90087890625}, {"start": 407.26, "end": 408.44, "word": " لمين", "probability": 0.82568359375}, {"start": 408.44, "end": 409.24, "word": " لفي", "probability": 0.94091796875}, {"start": 409.24, "end": 410.26, "word": " inverse", "probability": 0.90771484375}, {"start": 410.26, "end": 411.22, "word": " of", "probability": 0.98291015625}, {"start": 411.22, "end": 411.56, "word": " b", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 19, "seek": 43494, "start": 412.24, "end": 434.94, "text": "الكلام هذا ليش؟ نظرا لإن الـ Phi is an isomorphism نظرا لإن Phi is isomorphism قدرت أكتبها بالشكل اللي عندنا هذا فبهذا التعريف ال composition of function يبقى بيظل Phi Phi inverse of A وهنا من", "tokens": [6027, 28820, 10943, 23758, 32239, 8592, 22807, 8717, 19913, 23557, 5296, 28814, 1863, 2423, 39184, 41435, 307, 364, 307, 32702, 1434, 8717, 19913, 23557, 5296, 28814, 1863, 41435, 307, 307, 32702, 1434, 12174, 3215, 43500, 5551, 4117, 2655, 3555, 11296, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 6156, 3555, 3224, 15730, 16712, 3615, 16572, 5172, 2423, 12686, 295, 2445, 7251, 3555, 4587, 7578, 4724, 1829, 19913, 1211, 41435, 41435, 17340, 295, 316, 37037, 8315, 9154], "avg_logprob": -0.2568993413603151, "compression_ratio": 1.5027027027027027, "no_speech_prob": 0.0, "words": [{"start": 412.24, "end": 412.92, "word": "الكلام", "probability": 0.8650716145833334}, {"start": 412.92, "end": 413.28, "word": " هذا", "probability": 0.748046875}, {"start": 413.28, "end": 413.9, "word": " ليش؟", "probability": 0.74267578125}, {"start": 413.9, "end": 414.74, "word": " نظرا", "probability": 0.890625}, {"start": 414.74, "end": 415.56, "word": " لإن", "probability": 0.7100423177083334}, {"start": 415.56, "end": 416.38, "word": " الـ", "probability": 0.5352783203125}, {"start": 416.38, "end": 416.42, "word": " Phi", "probability": 0.203125}, {"start": 416.42, "end": 417.38, "word": " is", "probability": 0.7001953125}, {"start": 417.38, "end": 418.28, "word": " an", "probability": 0.79736328125}, {"start": 418.28, "end": 420.02, "word": " isomorphism", "probability": 0.9326171875}, {"start": 420.02, "end": 421.22, "word": " نظرا", "probability": 0.9322916666666666}, {"start": 421.22, "end": 421.58, "word": " لإن", "probability": 0.9425455729166666}, {"start": 421.58, "end": 421.92, "word": " Phi", "probability": 0.80712890625}, {"start": 421.92, "end": 422.16, "word": " is", "probability": 0.52197265625}, {"start": 422.16, "end": 422.86, "word": " isomorphism", "probability": 0.8225911458333334}, {"start": 422.86, "end": 423.3, "word": " قدرت", "probability": 0.8203125}, {"start": 423.3, "end": 423.86, "word": " أكتبها", "probability": 0.92109375}, {"start": 423.86, "end": 424.42, "word": " بالشكل", "probability": 0.9484049479166666}, {"start": 424.42, "end": 424.6, "word": " اللي", "probability": 0.93701171875}, {"start": 424.6, "end": 425.18, "word": " عندنا", "probability": 0.9345703125}, {"start": 425.18, "end": 425.64, "word": " هذا", "probability": 0.92822265625}, {"start": 425.64, "end": 426.96, "word": " فبهذا", "probability": 0.6060791015625}, {"start": 426.96, "end": 427.44, "word": " التعريف", "probability": 0.9354248046875}, {"start": 427.44, "end": 427.6, "word": " ال", "probability": 0.4755859375}, {"start": 427.6, "end": 428.22, "word": " composition", "probability": 0.84033203125}, {"start": 428.22, "end": 428.76, "word": " of", "probability": 0.97998046875}, {"start": 428.76, "end": 429.4, "word": " function", "probability": 0.87109375}, {"start": 429.4, "end": 429.8, "word": " يبقى", "probability": 0.969482421875}, {"start": 429.8, "end": 430.42, "word": " بيظل", "probability": 0.658935546875}, {"start": 430.42, "end": 431.1, "word": " Phi", "probability": 0.87939453125}, {"start": 431.1, "end": 431.82, "word": " Phi", "probability": 0.60302734375}, {"start": 431.82, "end": 432.62, "word": " inverse", "probability": 0.87060546875}, {"start": 432.62, "end": 433.14, "word": " of", "probability": 0.97119140625}, {"start": 433.14, "end": 433.7, "word": " A", "probability": 0.609375}, {"start": 433.7, "end": 434.74, "word": " وهنا", "probability": 0.7010498046875}, {"start": 434.74, "end": 434.94, "word": " من", "probability": 0.6240234375}], "temperature": 1.0}, {"id": 20, "seek": 46048, "start": 435.42, "end": 460.48, "text": "وهنا كذلك في لفي انفرس of بي بالشكل اللي عندنا هذا الكلام يساوي طبعا في في انفرس هتطلع ال identity function يبقى هنا مش هيضل عندي إلا ال element a و هنا في في انفرس هيعطينا ال identity function تأثيره على بي مش هيعطينا إلا من إلا بي", "tokens": [2407, 3224, 8315, 9122, 8848, 23275, 8978, 5296, 41185, 16472, 5172, 2288, 3794, 295, 4724, 1829, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 23032, 3555, 3615, 995, 8978, 8978, 16472, 5172, 2288, 3794, 8032, 2655, 9566, 1211, 3615, 2423, 6575, 2445, 7251, 3555, 4587, 7578, 34105, 37893, 39896, 11242, 1211, 18871, 16254, 11933, 15040, 2423, 4478, 257, 4032, 34105, 8978, 8978, 16472, 5172, 2288, 3794, 39896, 3615, 9566, 1829, 8315, 2423, 6575, 2445, 6055, 10721, 12984, 13546, 3224, 15844, 4724, 1829, 37893, 39896, 3615, 9566, 1829, 8315, 11933, 15040, 9154, 11933, 15040, 4724, 1829], "avg_logprob": -0.20995145486396494, "compression_ratio": 1.8656716417910448, "no_speech_prob": 0.0, "words": [{"start": 435.42, "end": 436.06, "word": "وهنا", "probability": 0.6144205729166666}, {"start": 436.06, "end": 436.84, "word": " كذلك", "probability": 0.9015299479166666}, {"start": 436.84, "end": 437.4, "word": " في", "probability": 0.223876953125}, {"start": 437.4, "end": 438.62, "word": " لفي", "probability": 0.55224609375}, {"start": 438.62, "end": 439.74, "word": " انفرس", "probability": 0.7103271484375}, {"start": 439.74, "end": 440.38, "word": " of", "probability": 0.693359375}, {"start": 440.38, "end": 441.28, "word": " بي", "probability": 0.662841796875}, {"start": 441.28, "end": 442.1, "word": " بالشكل", "probability": 0.7664388020833334}, {"start": 442.1, "end": 442.24, "word": " اللي", "probability": 0.929931640625}, {"start": 442.24, "end": 442.58, "word": " عندنا", "probability": 0.737060546875}, {"start": 442.58, "end": 443.56, "word": " هذا", "probability": 0.6064453125}, {"start": 443.56, "end": 444.22, "word": " الكلام", "probability": 0.9461263020833334}, {"start": 444.22, "end": 444.76, "word": " يساوي", "probability": 0.77392578125}, {"start": 444.76, "end": 445.82, "word": " طبعا", "probability": 0.9549560546875}, {"start": 445.82, "end": 446.1, "word": " في", "probability": 0.489501953125}, {"start": 446.1, "end": 446.38, "word": " في", "probability": 0.96142578125}, {"start": 446.38, "end": 446.86, "word": " انفرس", "probability": 0.976806640625}, {"start": 446.86, "end": 447.42, "word": " هتطلع", "probability": 0.936328125}, {"start": 447.42, "end": 447.56, "word": " ال", "probability": 0.95654296875}, {"start": 447.56, "end": 448.1, "word": " identity", "probability": 0.78369140625}, {"start": 448.1, "end": 448.96, "word": " function", "probability": 0.95703125}, {"start": 448.96, "end": 449.8, "word": " يبقى", "probability": 0.9512939453125}, {"start": 449.8, "end": 450.06, "word": " هنا", "probability": 0.9306640625}, {"start": 450.06, "end": 450.26, "word": " مش", "probability": 0.9248046875}, {"start": 450.26, "end": 450.68, "word": " هيضل", "probability": 0.7194010416666666}, {"start": 450.68, "end": 451.0, "word": " عندي", "probability": 0.852783203125}, {"start": 451.0, "end": 451.24, "word": " إلا", "probability": 0.68408203125}, {"start": 451.24, "end": 451.44, "word": " ال", "probability": 0.96826171875}, {"start": 451.44, "end": 451.96, "word": " element", "probability": 0.9443359375}, {"start": 451.96, "end": 452.4, "word": " a", "probability": 0.7236328125}, {"start": 452.4, "end": 452.96, "word": " و", "probability": 0.58349609375}, {"start": 452.96, "end": 453.18, "word": " هنا", "probability": 0.521484375}, {"start": 453.18, "end": 453.48, "word": " في", "probability": 0.90771484375}, {"start": 453.48, "end": 453.76, "word": " في", "probability": 0.984375}, {"start": 453.76, "end": 454.2, "word": " انفرس", "probability": 0.989013671875}, {"start": 454.2, "end": 454.72, "word": " هيعطينا", "probability": 0.87294921875}, {"start": 454.72, "end": 454.86, "word": " ال", "probability": 0.97705078125}, {"start": 454.86, "end": 455.34, "word": " identity", "probability": 0.91796875}, {"start": 455.34, "end": 456.14, "word": " function", "probability": 0.96240234375}, {"start": 456.14, "end": 457.12, "word": " تأثيره", "probability": 0.9537109375}, {"start": 457.12, "end": 457.42, "word": " على", "probability": 0.890625}, {"start": 457.42, "end": 457.7, "word": " بي", "probability": 0.8828125}, {"start": 457.7, "end": 457.9, "word": " مش", "probability": 0.93603515625}, {"start": 457.9, "end": 458.48, "word": " هيعطينا", "probability": 0.8974609375}, {"start": 458.48, "end": 458.76, "word": " إلا", "probability": 0.970947265625}, {"start": 458.76, "end": 459.16, "word": " من", "probability": 0.34375}, {"start": 459.16, "end": 460.12, "word": " إلا", "probability": 0.820556640625}, {"start": 460.12, "end": 460.48, "word": " بي", "probability": 0.982421875}], "temperature": 1.0}, {"id": 21, "seek": 48627, "start": 460.99, "end": 486.27, "text": "أطلع للنقطة الأولى هذه star والنقطة هذه اللي بدي أسميها double star هذه بتساوي AB وهذه بتساوي AB يبقى الطرف الشمال بتساوي من؟ الطرف الشمال اللي عندنا هذا يبقى باجي بقوله هنا from star and double star we have", "tokens": [10721, 9566, 1211, 3615, 24976, 1863, 47432, 3660, 16247, 12610, 7578, 29538, 3543, 16070, 1863, 47432, 3660, 29538, 13672, 1829, 4724, 16254, 5551, 38251, 1829, 11296, 3834, 3543, 29538, 39894, 3794, 995, 45865, 13838, 37037, 24192, 39894, 3794, 995, 45865, 13838, 7251, 3555, 4587, 7578, 41950, 28480, 25124, 2304, 6027, 39894, 3794, 995, 45865, 9154, 22807, 41950, 28480, 25124, 2304, 6027, 13672, 1829, 43242, 8315, 23758, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 490, 3543, 293, 3834, 3543, 321, 362], "avg_logprob": -0.2974264846128576, "compression_ratio": 1.8186813186813187, "no_speech_prob": 0.0, "words": [{"start": 460.99, "end": 461.77, "word": "أطلع", "probability": 0.5858154296875}, {"start": 461.77, "end": 462.67, "word": " للنقطة", "probability": 0.79193115234375}, {"start": 462.67, "end": 463.25, "word": " الأولى", "probability": 0.9840494791666666}, {"start": 463.25, "end": 463.61, "word": " هذه", "probability": 0.3896484375}, {"start": 463.61, "end": 464.29, "word": " star", "probability": 0.2462158203125}, {"start": 464.29, "end": 465.47, "word": " والنقطة", "probability": 0.833251953125}, {"start": 465.47, "end": 465.75, "word": " هذه", "probability": 0.66845703125}, {"start": 465.75, "end": 465.89, "word": " اللي", "probability": 0.704345703125}, {"start": 465.89, "end": 466.05, "word": " بدي", "probability": 0.572998046875}, {"start": 466.05, "end": 466.89, "word": " أسميها", "probability": 0.8690185546875}, {"start": 466.89, "end": 467.43, "word": " double", "probability": 0.56689453125}, {"start": 467.43, "end": 468.27, "word": " star", "probability": 0.935546875}, {"start": 468.27, "end": 470.23, "word": " هذه", "probability": 0.80517578125}, {"start": 470.23, "end": 470.87, "word": " بتساوي", "probability": 0.7667236328125}, {"start": 470.87, "end": 471.31, "word": " AB", "probability": 0.1988525390625}, {"start": 471.31, "end": 471.75, "word": " وهذه", "probability": 0.74560546875}, {"start": 471.75, "end": 472.31, "word": " بتساوي", "probability": 0.923828125}, {"start": 472.31, "end": 472.75, "word": " AB", "probability": 0.83740234375}, {"start": 472.75, "end": 473.21, "word": " يبقى", "probability": 0.69683837890625}, {"start": 473.21, "end": 473.65, "word": " الطرف", "probability": 0.89990234375}, {"start": 473.65, "end": 474.25, "word": " الشمال", "probability": 0.978515625}, {"start": 474.25, "end": 474.87, "word": " بتساوي", "probability": 0.748809814453125}, {"start": 474.87, "end": 475.49, "word": " من؟", "probability": 0.4107666015625}, {"start": 475.49, "end": 476.03, "word": " الطرف", "probability": 0.9619140625}, {"start": 476.03, "end": 476.61, "word": " الشمال", "probability": 0.98876953125}, {"start": 476.61, "end": 476.79, "word": " اللي", "probability": 0.944580078125}, {"start": 476.79, "end": 477.23, "word": " عندنا", "probability": 0.984375}, {"start": 477.23, "end": 477.55, "word": " هذا", "probability": 0.95361328125}, {"start": 477.55, "end": 478.31, "word": " يبقى", "probability": 0.945068359375}, {"start": 478.31, "end": 478.71, "word": " باجي", "probability": 0.8427734375}, {"start": 478.71, "end": 479.25, "word": " بقوله", "probability": 0.82373046875}, {"start": 479.25, "end": 479.57, "word": " هنا", "probability": 0.9794921875}, {"start": 479.57, "end": 480.13, "word": " from", "probability": 0.87158203125}, {"start": 480.13, "end": 482.47, "word": " star", "probability": 0.430908203125}, {"start": 482.47, "end": 483.41, "word": " and", "probability": 0.9501953125}, {"start": 483.41, "end": 484.61, "word": " double", "probability": 0.919921875}, {"start": 484.61, "end": 485.63, "word": " star", "probability": 0.9677734375}, {"start": 485.63, "end": 485.87, "word": " we", "probability": 0.70263671875}, {"start": 485.87, "end": 486.27, "word": " have", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 22, "seek": 51014, "start": 487.48, "end": 510.14, "text": "هنحصل على ما يأتي انه فاي لفاي inverse of a b بدر ساوي فا بدر ساوي مين بدر ساوي فاي لفاي inverse of a في فاي inverse of b بالشكل اللي عندها", "tokens": [3224, 1863, 5016, 36520, 15844, 19446, 7251, 10721, 31371, 16472, 3224, 6156, 47302, 5296, 5172, 47302, 17340, 295, 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"seek": 53365, "start": 512.17, "end": 533.65, "text": "طب الآن أنا طلعت قيمتين متساويتين السؤال هو فاي هدي one to one ولا لأ؟ مظبوط لأنها isomorphism يبقى فاي one to one وعندي صورتين متساويتين يبقى الأصل ماله متساوي يبقى هذا بده يعطيني مين؟", "tokens": [9566, 3555, 6024, 48506, 41850, 23032, 1211, 34268, 12174, 32640, 2655, 9957, 44650, 3794, 995, 2407, 36081, 9957, 21136, 33604, 6027, 31439, 6156, 47302, 8032, 16254, 472, 281, 472, 49429, 5296, 10721, 22807, 3714, 19913, 3555, 2407, 9566, 5296, 33456, 11296, 307, 32702, 1434, 7251, 3555, 4587, 7578, 6156, 47302, 472, 281, 472, 4032, 3615, 1863, 16254, 20328, 13063, 2655, 9957, 44650, 3794, 995, 2407, 36081, 9957, 7251, 3555, 4587, 7578, 16247, 36520, 3714, 6027, 3224, 44650, 3794, 995, 45865, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 7251, 3615, 9566, 1829, 22653, 3714, 9957, 22807], "avg_logprob": -0.2236328087747097, "compression_ratio": 1.7657142857142858, "no_speech_prob": 0.0, "words": [{"start": 512.17, "end": 512.49, "word": 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الشمال بدي اسوي أصل الطرف اليمين اللي هو في انفرس of a في في انفرس ماله of b هذا الكلام ليش؟ because في is one to one", "tokens": [3555, 16254, 37495, 9566, 1829, 22653, 16472, 3224, 8978, 16472, 5172, 2288, 3794, 295, 257, 11, 65, 13672, 1829, 31439, 5551, 36520, 41950, 28480, 25124, 2304, 6027, 4724, 16254, 24525, 45865, 5551, 36520, 41950, 28480, 2423, 32640, 9957, 13672, 1829, 31439, 8978, 16472, 5172, 2288, 3794, 295, 257, 8978, 8978, 16472, 5172, 2288, 3794, 3714, 6027, 3224, 295, 272, 23758, 2423, 28820, 10943, 32239, 8592, 22807, 570, 8978, 307, 472, 281, 472], "avg_logprob": -0.2870291095890411, "compression_ratio": 1.78, "no_speech_prob": 0.0, "words": [{"start": 533.86, "end": 534.32, "word": "بدي", "probability": 0.231719970703125}, {"start": 534.32, "end": 535.02, "word": " يعطيني", "probability": 0.7200927734375}, {"start": 535.02, "end": 535.48, "word": " انه", "probability": 0.430419921875}, {"start": 535.48, "end": 535.82, "word": " في", "probability": 0.21630859375}, 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" الطرف", "probability": 0.974365234375}, {"start": 542.32, "end": 543.08, "word": " اليمين", "probability": 0.8274739583333334}, {"start": 543.08, "end": 543.56, "word": " اللي", "probability": 0.929931640625}, {"start": 543.56, "end": 543.72, "word": " هو", "probability": 0.986328125}, {"start": 543.72, "end": 544.12, "word": " في", "probability": 0.904296875}, {"start": 544.12, "end": 544.82, "word": " انفرس", "probability": 0.9827880859375}, {"start": 544.82, "end": 545.1, "word": " of", "probability": 0.9443359375}, {"start": 545.1, "end": 545.58, "word": " a", "probability": 0.98291015625}, {"start": 545.58, "end": 546.08, "word": " في", "probability": 0.85888671875}, {"start": 546.08, "end": 546.6, "word": " في", "probability": 0.943359375}, {"start": 546.6, "end": 547.48, "word": " انفرس", "probability": 0.9884033203125}, {"start": 547.48, "end": 547.98, "word": " ماله", "probability": 0.8714192708333334}, {"start": 547.98, "end": 548.66, "word": " of", "probability": 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وهكذا في inverse is an isomorphism وبالتالي أثبتنا النقطة الأولى", "tokens": [4587, 11242, 1829, 8315, 5551, 12984, 3555, 2655, 8315, 34105, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 17340, 23758, 5551, 9381, 49628, 6225, 3555, 9640, 3660, 18871, 307, 32702, 1434, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 4724, 39648, 3224, 8807, 37037, 4117, 15730, 8978, 17340, 307, 364, 307, 32702, 1434, 46599, 6027, 2655, 6027, 1829, 5551, 12984, 3555, 2655, 8315, 28239, 47432, 3660, 16247, 12610, 7578], "avg_logprob": -0.17267923341954455, "compression_ratio": 1.5592105263157894, "no_speech_prob": 0.0, "words": [{"start": 556.3, "end": 556.72, "word": "قضينا", "probability": 0.62017822265625}, {"start": 556.72, "end": 557.26, "word": " أثبتنا", "probability": 0.871630859375}, {"start": 557.26, "end": 557.58, "word": " هنا", "probability": 0.80126953125}, {"start": 557.58, "end": 559.0, "word": " أثبتنا", "probability": 0.92822265625}, {"start": 559.0, "end": 559.3, "word": " أن", "probability": 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"word": " generated", "probability": 0.85986328125}, {"start": 952.04, "end": 952.78, "word": " by", "probability": 0.96044921875}, {"start": 952.78, "end": 953.34, "word": " Phi", "probability": 0.224365234375}, {"start": 953.34, "end": 953.74, "word": " of", "probability": 0.92041015625}, {"start": 953.74, "end": 954.22, "word": " A", "probability": 0.9013671875}, {"start": 954.22, "end": 955.34, "word": " طب", "probability": 0.6624755859375}, {"start": 955.34, "end": 955.56, "word": " إن", "probability": 0.64501953125}, {"start": 955.56, "end": 956.04, "word": " حدث", "probability": 0.9930013020833334}, {"start": 956.04, "end": 956.58, "word": " ذلك", "probability": 0.9833984375}, {"start": 956.58, "end": 956.94, "word": " يبقى", "probability": 0.9361572265625}, {"start": 956.94, "end": 957.14, "word": " G", "probability": 0.66943359375}, {"start": 957.14, "end": 957.44, "word": " bar", "probability": 0.9228515625}, {"start": 957.44, "end": 958.12, "word": " مالها", "probability": 0.8400065104166666}, {"start": 958.12, "end": 959.64, "word": " مال", "probability": 0.75537109375}, {"start": 959.64, "end": 959.84, "word": " G", "probability": 0.414306640625}, {"start": 959.84, "end": 960.12, "word": " bar", "probability": 0.94140625}, {"start": 960.12, "end": 960.3, "word": " في", "probability": 0.93896484375}, {"start": 960.3, "end": 960.62, "word": " هذه", "probability": 0.9697265625}, {"start": 960.62, "end": 961.46, "word": " الحالة", "probability": 0.99365234375}, {"start": 961.46, "end": 962.04, "word": " if", "probability": 0.75048828125}, {"start": 962.04, "end": 962.42, "word": " and", "probability": 0.892578125}, {"start": 962.42, "end": 962.84, "word": " only", "probability": 0.90869140625}, {"start": 962.84, "end": 963.34, "word": " if", "probability": 0.96923828125}, {"start": 963.34, "end": 963.74, "word": " الـ", "probability": 0.867431640625}, {"start": 963.74, "end": 964.16, "word": " G", "probability": 0.87548828125}, {"start": 964.16, "end": 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{"start": 986.19, "end": 986.53, "word": " order", "probability": 0.97216796875}, {"start": 986.53, "end": 986.97, "word": " لـG", "probability": 0.9246419270833334}, {"start": 986.97, "end": 987.27, "word": " bar", "probability": 0.71923828125}, {"start": 987.27, "end": 988.09, "word": " كل", "probability": 0.89990234375}, {"start": 988.09, "end": 988.51, "word": " هذا", "probability": 0.9423828125}, {"start": 988.51, "end": 988.97, "word": " تحت", "probability": 0.994384765625}, {"start": 988.97, "end": 989.73, "word": " تأثير", "probability": 0.9810791015625}, {"start": 989.73, "end": 990.35, "word": " أن", "probability": 0.492919921875}, {"start": 990.35, "end": 990.57, "word": " ال", "probability": 0.69140625}, {"start": 990.57, "end": 990.85, "word": " Phi", "probability": 0.671875}, {"start": 990.85, "end": 991.05, "word": " اللي", "probability": 0.897216796875}, {"start": 991.05, "end": 991.51, "word": " عندها", "probability": 0.78662109375}, {"start": 991.51, "end": 992.15, "word": " عبارة", "probability": 0.85003662109375}, {"start": 992.15, "end": 992.75, "word": " عن", "probability": 0.9892578125}, {"start": 992.75, "end": 994.63, "word": " isomorphism", "probability": 0.8385416666666666}], "temperature": 1.0}, {"id": 43, "seek": 100751, "start": 995.37, "end": 1007.51, "text": "بذلك نصل الى النقطة الرابعة حد يلو سؤال هنا قبل ان ننتقل الى النقطة الرابعة اللى بحب يسألى سؤال هنا فيش بلاش", "tokens": [3555, 8848, 23275, 8717, 36520, 2423, 7578, 28239, 47432, 3660, 34892, 16758, 27884, 11331, 3215, 7251, 1211, 2407, 8608, 33604, 6027, 34105, 12174, 36150, 16472, 8717, 29399, 4587, 1211, 2423, 7578, 28239, 47432, 3660, 34892, 16758, 27884, 13672, 7578, 4724, 5016, 3555, 7251, 3794, 10721, 23942, 8608, 33604, 6027, 34105, 6156, 1829, 8592, 4724, 1211, 33599], "avg_logprob": -0.24205044487066435, "compression_ratio": 1.8055555555555556, "no_speech_prob": 0.0, "words": [{"start": 995.37, "end": 996.05, "word": "بذلك", "probability": 0.8082682291666666}, {"start": 996.05, "end": 996.59, "word": " نصل", "probability": 0.960205078125}, {"start": 996.59, "end": 996.93, "word": " الى", "probability": 0.6676025390625}, {"start": 996.93, "end": 997.49, "word": " النقطة", "probability": 0.90380859375}, {"start": 997.49, "end": 997.91, "word": " الرابعة", "probability": 0.9718424479166666}, {"start": 997.91, "end": 998.49, "word": " حد", "probability": 0.684814453125}, {"start": 998.49, "end": 998.77, "word": " يلو", "probability": 0.548583984375}, {"start": 998.77, "end": 999.13, "word": " سؤال", "probability": 0.93798828125}, {"start": 999.13, "end": 999.41, "word": " هنا", "probability": 0.7529296875}, {"start": 999.41, "end": 999.79, "word": " قبل", "probability": 0.98779296875}, {"start": 999.79, "end": 999.99, "word": " ان", "probability": 0.5}, {"start": 999.99, "end": 1000.47, "word": " ننتقل", "probability": 0.8529052734375}, {"start": 1000.47, "end": 1000.63, "word": " الى", "probability": 0.9140625}, {"start": 1000.63, "end": 1001.09, "word": " النقطة", "probability": 0.96826171875}, {"start": 1001.09, "end": 1001.69, "word": " الرابعة", "probability": 0.9853515625}, {"start": 1001.69, "end": 1002.71, "word": " اللى", "probability": 0.791748046875}, {"start": 1002.71, "end": 1003.03, "word": " بحب", "probability": 0.92578125}, {"start": 1003.03, "end": 1003.49, "word": " يسألى", "probability": 0.753173828125}, {"start": 1003.49, "end": 1003.95, "word": " سؤال", "probability": 0.9895833333333334}, {"start": 1003.95, "end": 1004.43, "word": " هنا", "probability": 0.98828125}, {"start": 1004.43, "end": 1006.01, "word": " فيش", "probability": 0.4503987630208333}, {"start": 1006.01, "end": 1007.51, "word": " بلاش", "probability": 0.80615234375}], "temperature": 1.0}, {"id": 44, "seek": 103285, "start": 1008.18, "end": 1032.86, "text": "نجي للنقطة الرابعة بيقول لو كان capital K هو subgroup من J فإن في of capital K كل العناصر في of small k بحيث ك موجود في ك كابتل عبارة عن subgroup من جي بار إذا بنحاول نثبت إن الست اللي عندنا هذه ال subgroup من جي بار", "tokens": [1863, 7435, 1829, 24976, 1863, 47432, 3660, 34892, 16758, 27884, 4724, 1829, 39648, 45164, 25961, 4238, 591, 31439, 1422, 17377, 9154, 508, 6156, 28814, 1863, 8978, 295, 4238, 591, 28242, 18863, 1863, 33546, 2288, 8978, 295, 1359, 350, 4724, 5016, 1829, 12984, 9122, 3714, 29245, 23328, 8978, 9122, 9122, 16758, 2655, 1211, 6225, 3555, 9640, 3660, 18871, 1422, 17377, 9154, 10874, 1829, 4724, 9640, 11933, 15730, 44945, 5016, 995, 12610, 8717, 12984, 3555, 2655, 36145, 2423, 14851, 13672, 1829, 43242, 8315, 29538, 2423, 1422, 17377, 9154, 10874, 1829, 4724, 9640], "avg_logprob": -0.3061469832619468, "compression_ratio": 1.67, "no_speech_prob": 0.0, "words": [{"start": 1008.18, "end": 1008.66, "word": "نجي", "probability": 0.4264322916666667}, {"start": 1008.66, "end": 1009.24, "word": " للنقطة", "probability": 0.83404541015625}, {"start": 1009.24, "end": 1009.54, "word": " الرابعة", "probability": 0.9383138020833334}, {"start": 1009.54, 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1016.54, "word": " capital", "probability": 0.468994140625}, {"start": 1016.54, "end": 1017.16, "word": " K", "probability": 0.90185546875}, {"start": 1017.16, "end": 1017.64, "word": " كل", "probability": 0.8984375}, {"start": 1017.64, "end": 1018.46, "word": " العناصر", "probability": 0.8824462890625}, {"start": 1018.46, "end": 1018.72, "word": " في", "probability": 0.93359375}, {"start": 1018.72, "end": 1019.02, "word": " of", "probability": 0.9541015625}, {"start": 1019.02, "end": 1019.46, "word": " small", "probability": 0.765625}, {"start": 1019.46, "end": 1019.76, "word": " k", "probability": 0.7685546875}, {"start": 1019.76, "end": 1020.22, "word": " بحيث", "probability": 0.884521484375}, {"start": 1020.22, "end": 1020.46, "word": " ك", "probability": 0.441650390625}, {"start": 1020.46, "end": 1020.94, "word": " موجود", "probability": 0.9254557291666666}, {"start": 1020.94, "end": 1021.1, "word": " في", "probability": 0.9130859375}, {"start": 1021.1, "end": 1021.34, "word": " 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"probability": 0.574951171875}, {"start": 1028.18, "end": 1028.5, "word": " اللي", "probability": 0.9072265625}, {"start": 1028.5, "end": 1028.94, "word": " عندنا", "probability": 0.935546875}, {"start": 1028.94, "end": 1029.22, "word": " هذه", "probability": 0.419189453125}, {"start": 1029.22, "end": 1029.4, "word": " ال", "probability": 0.6328125}, {"start": 1029.4, "end": 1029.98, "word": " subgroup", "probability": 0.900634765625}, {"start": 1029.98, "end": 1030.22, "word": " من", "probability": 0.9833984375}, {"start": 1030.22, "end": 1032.52, "word": " جي", "probability": 0.74853515625}, {"start": 1032.52, "end": 1032.86, "word": " بار", "probability": 0.98828125}], "temperature": 1.0}, {"id": 45, "seek": 104827, "start": 1033.71, "end": 1048.27, "text": "لما كنا بنثبت ال subgroup كان عندي اكثر من طريقة لإثبات ال subgroup أبسطهم و أسرعهم اني أثبت نقطتين ان ال 6 اللي عندها دي is none امتى الخطوة الأولى", "tokens": [1211, 15042, 9122, 8315, 44945, 12984, 3555, 2655, 2423, 1422, 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identity element تبع ال K هو ال identity element تبع من؟", "tokens": [6027, 7649, 21136, 33604, 6027, 31439, 591, 29538, 2423, 1422, 1594, 9154, 460, 44945, 5172, 3615, 7251, 30544, 1422, 1594, 4032, 15042, 8978, 11296, 6575, 4478, 22807, 44945, 5172, 3615, 22807, 5296, 10721, 7251, 3555, 4587, 7578, 1422, 1594, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 591, 31439, 2423, 6575, 4478, 6055, 3555, 3615, 9154, 22807], "avg_logprob": -0.23396381997225577, "compression_ratio": 1.6338028169014085, "no_speech_prob": 0.0, "words": [{"start": 1076.83, "end": 1077.37, "word": "الان", "probability": 0.6771240234375}, {"start": 1077.37, "end": 1077.87, "word": " السؤال", "probability": 0.9547526041666666}, {"start": 1077.87, "end": 1078.29, "word": " هو", "probability": 0.9326171875}, {"start": 1078.29, "end": 1079.15, "word": " K", "probability": 0.2080078125}, {"start": 1079.15, "end": 1079.59, "word": " هذه", "probability": 0.62109375}, {"start": 1079.59, "end": 1079.83, "word": " ال", 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is", "probability": 0.67626953125}, {"start": 1597.75, "end": 1598.23, "word": " called", "probability": 0.91259765625}, {"start": 1598.23, "end": 1598.73, "word": " an", "probability": 0.86865234375}, {"start": 1598.73, "end": 1600.05, "word": " atomorphism", "probability": 0.6806640625}, {"start": 1600.05, "end": 1600.35, "word": " ايش", "probability": 0.6955159505208334}, {"start": 1600.35, "end": 1601.25, "word": " رأيك؟", "probability": 0.797802734375}, {"start": 1601.25, "end": 1601.53, "word": " احنا", "probability": 0.9851888020833334}, {"start": 1601.53, "end": 1601.91, "word": " خدنا", "probability": 0.8301595052083334}, {"start": 1601.91, "end": 1602.41, "word": " مثال", "probability": 0.974365234375}, {"start": 1602.41, "end": 1602.59, "word": " على", "probability": 0.7626953125}, {"start": 1602.59, "end": 1602.77, "word": " ال", "probability": 0.9677734375}, {"start": 1602.77, "end": 1603.77, "word": " atomorphism", "probability": 0.9280598958333334}, {"start": 1603.77, "end": 1603.91, "word": " و", "probability": 0.677734375}, {"start": 1603.91, "end": 1604.05, "word": " احنا", "probability": 0.8875325520833334}, {"start": 1604.05, "end": 1604.25, "word": " مش", "probability": 0.9892578125}, {"start": 1604.25, "end": 1604.77, "word": " دارين", "probability": 0.9685872395833334}], "temperature": 1.0}, {"id": 69, "seek": 163194, "start": 1605.5, "end": 1631.94, "text": "أخدنا المثال أعتقد رقم خمسة أو رقم أربع معاك في الأمثلة تبع الـ isomorphism يبقى أول example الخدنا define اللي هو five من ال special linear group of two by two matrices over R لل special linear group of two by two matrices over R", "tokens": [10721, 9778, 3215, 8315, 9673, 12984, 6027, 5551, 34268, 28543, 12602, 4587, 2304, 16490, 2304, 3794, 3660, 34051, 12602, 4587, 2304, 5551, 25513, 3615, 20449, 995, 4117, 8978, 16247, 2304, 12984, 37977, 6055, 3555, 3615, 2423, 39184, 307, 32702, 1434, 7251, 3555, 4587, 7578, 5551, 12610, 1365, 33962, 3215, 8315, 6964, 13672, 1829, 31439, 1732, 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"temperature": 1.0}, {"id": 70, "seek": 165796, "start": 1633.92, "end": 1657.96, "text": "Define Phi by عرفنا اللي هو Phi M of A بدي ساوي الـ M A M inverse والـ M هذه مصفوفة نظامها 2 في 2 قد تكون في ال special و قد لا تكون لكن نظامها 2 في 2", "tokens": [35, 5666, 533, 41435, 538, 6225, 28480, 8315, 13672, 1829, 31439, 41435, 376, 295, 316, 4724, 16254, 8608, 995, 45865, 2423, 39184, 376, 316, 376, 17340, 16070, 39184, 376, 29538, 3714, 9381, 5172, 38688, 3660, 8717, 19913, 10943, 11296, 568, 8978, 568, 12174, 3215, 6055, 30544, 8978, 2423, 2121, 4032, 12174, 3215, 20193, 6055, 30544, 44381, 8717, 19913, 10943, 11296, 568, 8978, 568], "avg_logprob": -0.3010253864340484, "compression_ratio": 1.414012738853503, "no_speech_prob": 0.0, "words": [{"start": 1633.92, "end": 1634.76, "word": "Define", "probability": 0.6730143229166666}, {"start": 1634.76, "end": 1635.24, "word": " Phi", "probability": 0.65673828125}, {"start": 1635.24, "end": 1635.84, "word": " by", "probability": 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{"start": 1646.2, "end": 1647.0, "word": " M", "probability": 0.96533203125}, {"start": 1647.0, "end": 1647.82, "word": " inverse", "probability": 0.64892578125}, {"start": 1647.82, "end": 1649.82, "word": " والـ", "probability": 0.587646484375}, {"start": 1649.82, "end": 1650.02, "word": " M", "probability": 0.94921875}, {"start": 1650.02, "end": 1650.34, "word": " هذه", "probability": 0.84375}, {"start": 1650.34, "end": 1650.9, "word": " مصفوفة", "probability": 0.8345703125}, {"start": 1650.9, "end": 1651.54, "word": " نظامها", "probability": 0.98828125}, {"start": 1651.54, "end": 1652.0, "word": " 2", "probability": 0.77978515625}, {"start": 1652.0, "end": 1652.38, "word": " في", "probability": 0.439453125}, {"start": 1652.38, "end": 1652.76, "word": " 2", "probability": 0.9921875}, {"start": 1652.76, "end": 1653.26, "word": " قد", "probability": 0.957763671875}, {"start": 1653.26, "end": 1653.58, "word": " تكون", "probability": 0.971923828125}, {"start": 1653.58, "end": 1653.72, "word": " في", "probability": 0.95068359375}, {"start": 1653.72, "end": 1653.82, "word": " ال", "probability": 0.98193359375}, {"start": 1653.82, "end": 1654.2, "word": " special", "probability": 0.7705078125}, {"start": 1654.2, "end": 1654.44, "word": " و", "probability": 0.9736328125}, {"start": 1654.44, "end": 1654.66, "word": " قد", "probability": 0.78271484375}, {"start": 1654.66, "end": 1654.82, "word": " لا", "probability": 0.7841796875}, {"start": 1654.82, "end": 1655.36, "word": " تكون", "probability": 0.968017578125}, {"start": 1655.36, "end": 1656.1, "word": " لكن", "probability": 0.75830078125}, {"start": 1656.1, "end": 1656.74, "word": " نظامها", "probability": 0.8817138671875}, {"start": 1656.74, "end": 1657.4, "word": " 2", "probability": 0.293701171875}, {"start": 1657.4, "end": 1657.66, "word": " في", "probability": 0.95947265625}, {"start": 1657.66, "end": 1657.96, "word": " 2", "probability": 0.986328125}], "temperature": 1.0}, {"id": 71, "seek": 168456, "start": 1658.66, "end": 1684.56, "text": "يبقى هاي ال function اللي عندنا نظرا اثبتناها احنا isomorphism وهيها من ال group الى نفس ال group يبقى في is an atomorphism يبقى هنا بدي بقوله since في م is an isomorphism وهذا previous", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 2423, 2445, 13672, 1829, 43242, 8315, 8717, 19913, 23557, 1975, 12984, 3555, 2655, 8315, 11296, 1975, 5016, 8315, 307, 32702, 1434, 37037, 1829, 11296, 9154, 2423, 1594, 2423, 7578, 8717, 36178, 2423, 1594, 7251, 3555, 4587, 7578, 8978, 307, 364, 12018, 18191, 1434, 7251, 3555, 4587, 7578, 34105, 4724, 16254, 4724, 39648, 3224, 1670, 8978, 3714, 307, 364, 307, 32702, 1434, 37037, 15730, 3894], "avg_logprob": -0.24801937207369737, "compression_ratio": 1.6196319018404908, "no_speech_prob": 0.0, "words": [{"start": 1658.66, "end": 1659.26, "word": "يبقى", "probability": 0.8448486328125}, {"start": 1659.26, "end": 1659.5, "word": " هاي", "probability": 0.5252685546875}, {"start": 1659.5, "end": 1659.66, "word": " ال", "probability": 0.95849609375}, {"start": 1659.66, "end": 1660.04, "word": " function", "probability": 0.55126953125}, {"start": 1660.04, "end": 1660.36, "word": " اللي", "probability": 0.828369140625}, {"start": 1660.36, "end": 1660.68, "word": " عندنا", "probability": 0.864013671875}, {"start": 1660.68, "end": 1661.44, "word": " نظرا", "probability": 0.9532877604166666}, {"start": 1661.44, "end": 1662.74, "word": " اثبتناها", "probability": 0.9165852864583334}, {"start": 1662.74, "end": 1663.22, "word": " احنا", "probability": 0.9773763020833334}, {"start": 1663.22, "end": 1664.56, "word": " isomorphism", "probability": 0.8028971354166666}, {"start": 1664.56, "end": 1665.8, "word": " وهيها", "probability": 0.85205078125}, {"start": 1665.8, "end": 1666.08, "word": " من", "probability": 0.86181640625}, {"start": 1666.08, "end": 1666.24, "word": " ال", "probability": 0.66650390625}, {"start": 1666.24, "end": 1666.74, "word": " group", "probability": 0.966796875}, {"start": 1666.74, "end": 1667.18, "word": " الى", "probability": 0.7021484375}, {"start": 1667.18, "end": 1667.5, "word": " نفس", "probability": 0.95068359375}, {"start": 1667.5, "end": 1667.7, "word": " ال", "probability": 0.84423828125}, {"start": 1667.7, "end": 1668.06, "word": " group", "probability": 0.986328125}, {"start": 1668.06, "end": 1668.7, "word": " يبقى", "probability": 0.952392578125}, {"start": 1668.7, "end": 1669.12, "word": " في", "probability": 0.335205078125}, {"start": 1669.12, "end": 1669.64, "word": " is", "probability": 0.49609375}, {"start": 1669.64, "end": 1670.16, "word": " an", "probability": 0.61572265625}, {"start": 1670.16, "end": 1671.46, "word": " atomorphism", "probability": 0.66259765625}, {"start": 1671.46, "end": 1672.7, "word": " يبقى", "probability": 0.977783203125}, {"start": 1672.7, "end": 1673.06, "word": " هنا", "probability": 0.94970703125}, {"start": 1673.06, "end": 1673.42, "word": " بدي", "probability": 0.61376953125}, {"start": 1673.42, "end": 1674.24, "word": " بقوله", "probability": 0.83984375}, {"start": 1674.24, "end": 1674.96, "word": " since", "probability": 0.76904296875}, {"start": 1674.96, "end": 1676.66, "word": " في", "probability": 0.466064453125}, {"start": 1676.66, "end": 1677.46, "word": " م", "probability": 0.2734375}, {"start": 1677.46, "end": 1679.18, "word": " is", "probability": 0.92333984375}, {"start": 1679.18, "end": 1680.24, "word": " an", "probability": 0.8330078125}, {"start": 1680.24, "end": 1682.68, "word": " isomorphism", "probability": 0.9680989583333334}, {"start": 1682.68, "end": 1683.76, "word": " وهذا", "probability": 0.671875}, {"start": 1683.76, "end": 1684.56, "word": " previous", "probability": 0.62646484375}], "temperature": 1.0}, {"id": 72, "seek": 171307, "start": 1686.03, "end": 1713.07, "text": "example مش هنقعد هنا أعيد فيه تاني and الـ phi m من ال special linear group لل special linear group هيها نفسها يبقى we have أنه phi is an atomorphism", "tokens": [3121, 335, 781, 37893, 8032, 1863, 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1767.01, "end": 1767.65, "word": " group", "probability": 0.9638671875}, {"start": 1767.65, "end": 1769.43, "word": " هذا", "probability": 0.384033203125}, {"start": 1769.43, "end": 1769.71, "word": " لما", "probability": 0.9306640625}, {"start": 1769.71, "end": 1770.21, "word": " اتروح", "probability": 0.916748046875}, {"start": 1770.21, "end": 1770.37, "word": " في", "probability": 0.953125}, {"start": 1770.37, "end": 1770.95, "word": " الدار", "probability": 0.864990234375}, {"start": 1770.95, "end": 1772.25, "word": " شيكلي", "probability": 0.7095947265625}, {"start": 1772.25, "end": 1772.69, "word": " عليها", "probability": 0.9912109375}, {"start": 1772.69, "end": 1772.87, "word": " و", "probability": 0.7978515625}, {"start": 1772.87, "end": 1773.59, "word": " اتأكد", "probability": 0.87412109375}], "temperature": 1.0}, {"id": 75, "seek": 179881, "start": 1773.97, "end": 1798.81, "text": "انه هذه عبارة عن group define a function phi من ال R square لل R square by phi of A و B بده يساوي ال B و ال A", "tokens": [7649, 3224, 29538, 6225, 3555, 9640, 3660, 18871, 1594, 6964, 257, 2445, 13107, 9154, 2423, 497, 3732, 24976, 497, 3732, 538, 13107, 295, 316, 4032, 363, 47525, 3224, 7251, 3794, 995, 45865, 2423, 363, 4032, 2423, 316], "avg_logprob": -0.3830181023007945, "compression_ratio": 1.1932773109243697, "no_speech_prob": 0.0, "words": [{"start": 1773.97, "end": 1774.43, "word": "انه", "probability": 0.426513671875}, {"start": 1774.43, "end": 1774.73, "word": " هذه", "probability": 0.326171875}, {"start": 1774.73, "end": 1775.21, "word": " عبارة", "probability": 0.986572265625}, {"start": 1775.21, "end": 1775.45, "word": " عن", "probability": 0.99658203125}, {"start": 1775.45, "end": 1775.97, "word": " group", "probability": 0.5068359375}, {"start": 1775.97, "end": 1777.93, "word": " define", "probability": 0.71044921875}, {"start": 1777.93, "end": 1781.79, "word": " a", "probability": 0.318359375}, {"start": 1781.79, "end": 1782.99, "word": " function", 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one and one to one تخدم خاصية ال isomorphism إذا بدي أبدأ أول شغلة بفي is one to one", "tokens": [1829, 3555, 4587, 7578, 37893, 48812, 47302, 4587, 5296, 3615, 9957, 8315, 8717, 12984, 3555, 2655, 11933, 15040, 8978, 6225, 3555, 9640, 3660, 18871, 307, 32702, 1434, 36145, 5551, 12984, 3555, 2655, 8315, 11296, 307, 32702, 1434, 39894, 9381, 13546, 12018, 18191, 1434, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 8978, 472, 281, 472, 293, 472, 281, 472, 6055, 9778, 40448, 16490, 33546, 10632, 2423, 307, 32702, 1434, 11933, 15730, 4724, 16254, 5551, 44510, 10721, 5551, 12610, 13412, 17082, 37977, 4724, 41185, 307, 472, 281, 472], "avg_logprob": -0.2185837745349458, "compression_ratio": 1.7206703910614525, "no_speech_prob": 0.0, "words": [{"start": 1867.62, "end": 1867.96, "word": "يبقى", "probability": 0.76324462890625}, {"start": 1867.96, "end": 1868.22, "word": " مش", "probability": 0.974609375}, {"start": 1868.22, "end": 1868.5, "word": " 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0.52685546875}, {"start": 2197.24, "end": 2197.9, "word": " التانية", "probability": 0.8123372395833334}, {"start": 2197.9, "end": 2198.22, "word": " d", "probability": 0.89794921875}, {"start": 2198.22, "end": 2198.54, "word": " و", "probability": 0.9931640625}, {"start": 2198.54, "end": 2199.14, "word": " c", "probability": 0.919921875}, {"start": 2199.14, "end": 2199.68, "word": " هي", "probability": 0.9169921875}, {"start": 2199.68, "end": 2200.36, "word": " عبارة", "probability": 0.9962158203125}, {"start": 2200.36, "end": 2200.62, "word": " عن", "probability": 0.9951171875}, {"start": 2200.62, "end": 2201.14, "word": " five", "probability": 0.93798828125}, {"start": 2201.14, "end": 2201.58, "word": " of", "probability": 0.984375}, {"start": 2201.58, "end": 2201.98, "word": " c", "probability": 0.97607421875}, {"start": 2201.98, "end": 2202.34, "word": " و", "probability": 0.98779296875}, {"start": 2202.34, "end": 2202.66, "word": " d", "probability": 0.849609375}], "temperature": 1.0}, {"id": 92, "seek": 222687, "start": 2203.59, "end": 2226.87, "text": "طب ايش اللي عملنا؟ طلع هنا أخدت مجموع اللي هو two ordered pair لجيت تأثير الفي عليهم يسوى تأثير الفي على ال element الأول زي تأثير الفي على ال element الثاني هنا ظلت النقطة الأخيرة يبقى since", "tokens": [9566, 3555, 1975, 1829, 8592, 13672, 1829, 6225, 42213, 8315, 22807, 23032, 1211, 3615, 34105, 5551, 9778, 3215, 2655, 3714, 7435, 2304, 45367, 13672, 1829, 31439, 732, 8866, 6119, 5296, 7435, 36081, 6055, 10721, 12984, 13546, 27188, 1829, 25894, 16095, 7251, 3794, 2407, 7578, 6055, 10721, 12984, 13546, 27188, 1829, 15844, 2423, 4478, 16247, 12610, 30767, 1829, 6055, 10721, 12984, 13546, 27188, 1829, 15844, 2423, 4478, 6024, 104, 7649, 1829, 34105, 1357, 116, 1211, 2655, 28239, 47432, 3660, 16247, 9778, 48923, 7251, 3555, 4587, 7578, 1670], "avg_logprob": -0.18750000102766629, "compression_ratio": 1.768361581920904, "no_speech_prob": 0.0, "words": [{"start": 2203.59, "end": 2203.89, "word": "طب", "probability": 0.5460205078125}, {"start": 2203.89, "end": 2204.09, "word": " ايش", "probability": 0.7528483072916666}, {"start": 2204.09, "end": 2204.27, "word": " اللي", "probability": 0.896728515625}, {"start": 2204.27, "end": 2205.13, "word": " عملنا؟", "probability": 0.73583984375}, {"start": 2205.13, "end": 2205.65, "word": " طلع", "probability": 0.8430989583333334}, {"start": 2205.65, "end": 2206.03, "word": " هنا", "probability": 0.96728515625}, {"start": 2206.03, "end": 2207.41, "word": " أخدت", "probability": 0.79449462890625}, {"start": 2207.41, "end": 2208.51, "word": " مجموع", "probability": 0.94189453125}, {"start": 2208.51, "end": 2209.23, "word": " اللي", "probability": 0.91015625}, {"start": 2209.23, "end": 2209.47, "word": " هو", "probability": 0.98486328125}, {"start": 2209.47, "end": 2209.79, "word": " two", "probability": 0.79248046875}, {"start": 2209.79, "end": 2210.39, "word": " ordered", "probability": 0.45556640625}, {"start": 2210.39, "end": 2210.93, "word": " pair", "probability": 0.6005859375}, {"start": 2210.93, "end": 2211.71, "word": " لجيت", "probability": 0.5941569010416666}, {"start": 2211.71, "end": 2212.23, "word": " تأثير", "probability": 0.9818115234375}, {"start": 2212.23, "end": 2212.63, "word": " الفي", "probability": 0.362060546875}, {"start": 2212.63, "end": 2213.25, "word": " عليهم", "probability": 0.97265625}, {"start": 2213.25, "end": 2214.15, "word": " يسوى", "probability": 0.8690185546875}, {"start": 2214.15, "end": 2214.91, "word": " تأثير", "probability": 0.9896240234375}, {"start": 2214.91, "end": 2216.03, "word": " الفي", "probability": 0.88671875}, {"start": 2216.03, "end": 2216.57, "word": " على", "probability": 0.71484375}, {"start": 2216.57, "end": 2216.81, "word": " ال", "probability": 0.96923828125}, {"start": 2216.81, "end": 2217.25, "word": " element", "probability": 0.9169921875}, {"start": 2217.25, "end": 2218.01, "word": " الأول", "probability": 0.975341796875}, {"start": 2218.01, "end": 2218.73, "word": " زي", "probability": 0.95166015625}, {"start": 2218.73, "end": 2219.39, "word": " تأثير", "probability": 0.9801025390625}, {"start": 2219.39, "end": 2219.87, "word": " الفي", "probability": 0.959228515625}, {"start": 2219.87, "end": 2220.13, "word": " على", "probability": 0.88720703125}, {"start": 2220.13, "end": 2220.37, "word": " ال", "probability": 0.97265625}, {"start": 2220.37, "end": 2221.01, "word": " element", "probability": 0.97216796875}, {"start": 2221.01, "end": 2222.51, "word": " الثاني", "probability": 0.9488525390625}, {"start": 2222.51, "end": 2223.39, "word": " هنا", "probability": 0.94091796875}, {"start": 2223.39, "end": 2223.93, "word": " ظلت", "probability": 0.7808837890625}, {"start": 2223.93, "end": 2224.53, "word": " النقطة", "probability": 0.9869791666666666}, {"start": 2224.53, "end": 2225.31, "word": " الأخيرة", "probability": 0.9547526041666666}, {"start": 2225.31, "end": 2226.19, "word": " يبقى", "probability": 0.98583984375}, {"start": 2226.19, "end": 2226.87, "word": " since", "probability": 0.56640625}], "temperature": 1.0}, {"id": 93, "seek": 224496, "start": 2227.36, "end": 2244.96, "text": "فاي من R تربية الى R تربية is an isomorphism يبقى الفاي is an atomorphism وهو المطلوب", "tokens": [5172, 47302, 9154, 497, 6055, 25513, 10632, 2423, 7578, 497, 6055, 25513, 10632, 307, 364, 307, 32702, 1434, 7251, 3555, 4587, 7578, 27188, 47302, 307, 364, 12018, 18191, 1434, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.2224392423199283, "compression_ratio": 1.3406593406593406, "no_speech_prob": 0.0, "words": [{"start": 2227.36, "end": 2228.1, "word": "فاي", "probability": 0.3055419921875}, {"start": 2228.1, "end": 2228.78, "word": " من", "probability": 0.9384765625}, {"start": 2228.78, "end": 2229.32, "word": " R", "probability": 0.46923828125}, {"start": 2229.32, "end": 2230.1, "word": " تربية", "probability": 0.8289388020833334}, {"start": 2230.1, "end": 2230.74, "word": " الى", "probability": 0.74853515625}, {"start": 2230.74, "end": 2231.26, "word": " R", "probability": 0.88037109375}, {"start": 2231.26, "end": 2232.04, "word": " تربية", "probability": 0.97119140625}, {"start": 2232.04, "end": 2232.94, "word": " is", "probability": 0.865234375}, {"start": 2232.94, "end": 2233.72, "word": " an", "probability": 0.783203125}, {"start": 2233.72, "end": 2235.36, "word": " isomorphism", "probability": 0.9588216145833334}, {"start": 2235.36, "end": 2236.48, "word": " يبقى", "probability": 0.961181640625}, {"start": 2236.48, "end": 2237.26, "word": " الفاي", "probability": 0.74462890625}, {"start": 2237.26, "end": 2238.02, "word": " is", "probability": 0.9423828125}, {"start": 2238.02, "end": 2239.4, "word": " an", "probability": 0.837890625}, {"start": 2239.4, "end": 2241.98, "word": " atomorphism", "probability": 0.7566731770833334}, {"start": 2241.98, "end": 2244.4, "word": " وهو", "probability": 0.8076171875}, {"start": 2244.4, "end": 2244.96, "word": " المطلوب", "probability": 0.981689453125}], "temperature": 1.0}, {"id": 94, "seek": 227460, "start": 2246.92, "end": 2274.6, "text": "يبقى من الأنفا صاعدا مشان أثبت أنه في اتو مورفزم بدي أتأكد أنه لازم تبقى من ال group لنفس ال group و بعد هيك ايزو مورفزم فباقى عندنا في هذه المحاضرة تعريف له علاقة بهذه النقطة تعريف بقول ما يأتي definition little gb group", "tokens": [1829, 3555, 4587, 7578, 9154, 16247, 1863, 5172, 995, 20328, 995, 22488, 995, 37893, 7649, 5551, 12984, 3555, 2655, 14739, 3224, 8978, 1975, 2655, 2407, 3714, 13063, 5172, 11622, 2304, 4724, 16254, 5551, 2655, 10721, 4117, 3215, 14739, 3224, 5296, 31377, 2304, 6055, 3555, 4587, 7578, 9154, 2423, 1594, 5296, 1863, 36178, 2423, 1594, 4032, 39182, 39896, 4117, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 11622, 2304, 6156, 3555, 995, 4587, 7578, 43242, 8315, 8978, 29538, 9673, 5016, 46958, 25720, 37279, 16572, 5172, 46740, 11203, 995, 28671, 39627, 24192, 28239, 47432, 3660, 37279, 16572, 5172, 4724, 39648, 19446, 7251, 10721, 31371, 7123, 707, 290, 65, 1594], "avg_logprob": -0.15683410964279532, "compression_ratio": 1.7428571428571429, "no_speech_prob": 0.0, "words": [{"start": 2246.92, "end": 2247.32, "word": "يبقى", "probability": 0.8638916015625}, {"start": 2247.32, "end": 2247.48, "word": " من", "probability": 0.95263671875}, {"start": 2247.48, "end": 2248.04, "word": " الأنفا", "probability": 0.775390625}, {"start": 2248.04, "end": 2248.7, "word": " صاعدا", "probability": 0.8121337890625}, {"start": 2248.7, "end": 2249.58, "word": " مشان", "probability": 0.586669921875}, {"start": 2249.58, "end": 2250.12, "word": " أثبت", "probability": 0.9644775390625}, {"start": 2250.12, "end": 2250.46, "word": " أنه", "probability": 0.697509765625}, {"start": 2250.46, "end": 2250.74, "word": " في", "probability": 0.84423828125}, {"start": 2250.74, "end": 2251.64, "word": " اتو", "probability": 0.4186197916666667}, {"start": 2251.64, "end": 2252.52, "word": " مورفزم", "probability": 0.85732421875}, {"start": 2252.52, "end": 2253.38, "word": " بدي", "probability": 0.722412109375}, {"start": 2253.38, "end": 2254.2, "word": " أتأكد", "probability": 0.91572265625}, {"start": 2254.2, "end": 2254.66, "word": " أنه", "probability": 0.713134765625}, {"start": 2254.66, "end": 2254.98, "word": " لازم", "probability": 0.98095703125}, {"start": 2254.98, "end": 2255.38, "word": " تبقى", "probability": 0.9713134765625}, {"start": 2255.38, "end": 2255.62, "word": " من", "probability": 0.88623046875}, {"start": 2255.62, "end": 2255.78, "word": " ال", "probability": 0.5673828125}, {"start": 2255.78, "end": 2256.08, "word": " group", "probability": 0.8759765625}, {"start": 2256.08, "end": 2256.62, "word": " لنفس", "probability": 0.9661458333333334}, {"start": 2256.62, "end": 2256.8, "word": " ال", "probability": 0.9306640625}, {"start": 2256.8, "end": 2257.24, "word": " group", "probability": 0.97412109375}, {"start": 2257.24, "end": 2257.64, "word": " و", "probability": 0.59814453125}, {"start": 2257.64, "end": 2258.0, "word": " بعد", "probability": 0.82080078125}, {"start": 2258.0, "end": 2258.52, "word": " هيك", "probability": 0.878662109375}, {"start": 2258.52, "end": 2259.12, "word": " ايزو", "probability": 0.88916015625}, {"start": 2259.12, "end": 2259.98, "word": " مورفزم", "probability": 0.9810546875}, {"start": 2259.98, "end": 2261.62, "word": " فباقى", "probability": 0.8689453125}, {"start": 2261.62, "end": 2261.96, "word": " عندنا", "probability": 0.93896484375}, {"start": 2261.96, "end": 2262.08, "word": " في", "probability": 0.98046875}, {"start": 2262.08, "end": 2262.34, "word": " هذه", "probability": 0.92041015625}, {"start": 2262.34, "end": 2263.04, "word": " المحاضرة", "probability": 0.9906005859375}, {"start": 2263.04, "end": 2263.7, "word": " تعريف", "probability": 0.9889322916666666}, {"start": 2263.7, "end": 2264.02, "word": " له", "probability": 0.98583984375}, {"start": 2264.02, "end": 2264.78, "word": " علاقة", "probability": 0.9822591145833334}, {"start": 2264.78, "end": 2265.52, "word": " بهذه", "probability": 0.9609375}, {"start": 2265.52, "end": 2266.88, "word": " النقطة", "probability": 0.9850260416666666}, {"start": 2266.88, "end": 2267.52, "word": " تعريف", "probability": 0.9832356770833334}, {"start": 2267.52, "end": 2268.3, "word": " بقول", "probability": 0.93408203125}, {"start": 2268.3, "end": 2268.72, "word": " ما", "probability": 0.96923828125}, {"start": 2268.72, "end": 2269.36, "word": " يأتي", "probability": 0.8976236979166666}, {"start": 2269.36, "end": 2270.68, "word": " definition", "probability": 0.75439453125}, {"start": 2270.68, "end": 2273.36, "word": " little", "probability": 0.583984375}, {"start": 2273.36, "end": 2273.96, "word": " gb", "probability": 0.76953125}, {"start": 2273.96, "end": 2274.6, "word": " group", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 95, "seek": 230282, "start": 2274.9, "end": 2302.82, "text": "let الـ G بي A group and let ال A موجود في هذه ال group define a function فاي A من ال group G إلى ال group G by", "tokens": [2631, 2423, 39184, 460, 4724, 1829, 316, 1594, 293, 718, 2423, 316, 3714, 29245, 23328, 8978, 29538, 2423, 1594, 6964, 257, 2445, 6156, 47302, 316, 9154, 2423, 1594, 460, 30731, 2423, 1594, 460, 538], "avg_logprob": -0.3111607142857143, "compression_ratio": 1.3523809523809525, "no_speech_prob": 0.0, "words": [{"start": 2274.9, "end": 2275.58, "word": "let", "probability": 0.3330078125}, {"start": 2275.58, "end": 2276.06, "word": " الـ", "probability": 0.5782470703125}, {"start": 2276.06, "end": 2276.42, "word": " G", "probability": 0.472900390625}, {"start": 2276.42, "end": 2277.46, "word": " بي", "probability": 0.625}, {"start": 2277.46, "end": 2278.4, "word": " A", "probability": 0.23681640625}, {"start": 2278.4, "end": 2279.04, "word": " group", "probability": 0.794921875}, {"start": 2279.04, "end": 2282.42, "word": " and", "probability": 0.72705078125}, {"start": 2282.42, "end": 2284.22, "word": " let", "probability": 0.8935546875}, {"start": 2284.22, "end": 2284.82, "word": " ال", "probability": 0.8896484375}, {"start": 2284.82, "end": 2285.2, "word": " A", "probability": 0.85302734375}, {"start": 2285.2, "end": 2285.96, "word": " موجود", "probability": 0.9895833333333334}, {"start": 2285.96, "end": 2286.22, "word": " في", "probability": 0.8544921875}, {"start": 2286.22, "end": 2286.7, "word": " هذه", "probability": 0.8154296875}, {"start": 2286.7, "end": 2286.94, "word": " ال", "probability": 0.87646484375}, {"start": 2286.94, "end": 2287.36, "word": " group", "probability": 0.9716796875}, {"start": 2287.36, "end": 2290.04, "word": " define", "probability": 0.95263671875}, {"start": 2290.04, "end": 2292.3, "word": " a", "probability": 0.9423828125}, {"start": 2292.3, "end": 2293.38, "word": " function", "probability": 0.97705078125}, {"start": 2293.38, "end": 2295.14, "word": " فاي", "probability": 0.4041748046875}, {"start": 2295.14, "end": 2295.88, "word": " A", "probability": 0.77294921875}, {"start": 2295.88, "end": 2298.1, "word": " من", 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29245, 23328, 8978, 290, 20666, 995, 14851, 12984, 1863, 16606, 7251, 3555, 4587, 7578, 550, 6156, 47302, 257, 307, 1219, 307, 1219, 364], "avg_logprob": -0.28817471861839294, "compression_ratio": 1.2372881355932204, "no_speech_prob": 0.0, "words": [{"start": 2305.0, "end": 2306.4, "word": "فاي", "probability": 0.4580078125}, {"start": 2306.4, "end": 2307.8, "word": " a", "probability": 0.244140625}, {"start": 2307.8, "end": 2308.52, "word": " of", "probability": 0.8193359375}, {"start": 2308.52, "end": 2309.12, "word": " x", "probability": 0.90185546875}, {"start": 2309.12, "end": 2310.22, "word": " يساوي", "probability": 0.69158935546875}, {"start": 2310.22, "end": 2310.86, "word": " a", "probability": 0.42919921875}, {"start": 2310.86, "end": 2311.7, "word": " x", "probability": 0.7734375}, {"start": 2311.7, "end": 2312.32, "word": " a", "probability": 0.8818359375}, {"start": 2312.32, "end": 2313.12, "word": " inverse", "probability": 0.71728515625}, {"start": 2313.12, "end": 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is", "probability": 0.91357421875}, {"start": 2326.74, "end": 2327.56, "word": " called", "probability": 0.93212890625}, {"start": 2327.56, "end": 2329.32, "word": " is", "probability": 0.7890625}, {"start": 2329.32, "end": 2330.42, "word": " called", "probability": 0.91064453125}, {"start": 2330.42, "end": 2332.12, "word": " an", "probability": 0.60888671875}], "temperature": 1.0}, {"id": 97, "seek": 236167, "start": 2334.79, "end": 2361.67, "text": "و الله is called the inner the inner atomorphism atomorphism of g induced by a ناخد مثال", "tokens": [2407, 21984, 307, 1219, 264, 7284, 264, 7284, 12018, 18191, 1434, 12018, 18191, 1434, 295, 290, 33991, 538, 257, 8717, 47283, 3215, 50113, 6027], "avg_logprob": -0.1900000047683716, "compression_ratio": 1.188235294117647, "no_speech_prob": 0.0, "words": [{"start": 2334.79, "end": 2335.03, "word": "و", "probability": 0.67578125}, {"start": 2335.03, "end": 2335.19, "word": " الله", "probability": 0.81005859375}, {"start": 2335.19, "end": 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في تسعين من D4 إلى D4 by في تسعين of X ساوي", "tokens": [20595, 533, 257, 2445, 8978, 6055, 3794, 3615, 9957, 9154, 413, 19, 30731, 413, 19, 538, 8978, 6055, 3794, 3615, 9957, 295, 1783, 8608, 995, 45865], "avg_logprob": -0.21961806107450416, "compression_ratio": 1.135135135135135, "no_speech_prob": 0.0, "words": [{"start": 2426.7, "end": 2428.1, "word": "define", "probability": 0.7171630859375}, {"start": 2428.1, "end": 2429.5, "word": " a", "probability": 0.297119140625}, {"start": 2429.5, "end": 2430.84, "word": " function", "probability": 0.974609375}, {"start": 2430.84, "end": 2432.86, "word": " في", "probability": 0.328857421875}, {"start": 2432.86, "end": 2434.1, "word": " تسعين", "probability": 0.977783203125}, {"start": 2434.1, "end": 2436.56, "word": " من", "probability": 0.9541015625}, {"start": 2436.56, "end": 2437.98, "word": " D4", "probability": 0.752685546875}, {"start": 2437.98, "end": 2438.64, "word": " إلى", "probability": 0.8271484375}, {"start": 2438.64, "end": 2440.24, "word": " D4", "probability": 0.978759765625}, {"start": 2440.24, "end": 2442.64, "word": " by", "probability": 0.7646484375}, {"start": 2442.64, "end": 2444.82, "word": " في", "probability": 0.51513671875}, {"start": 2444.82, "end": 2446.12, "word": " تسعين", "probability": 0.9952392578125}, {"start": 2446.12, "end": 2446.74, "word": " of", "probability": 0.85693359375}, {"start": 2446.74, "end": 2447.32, "word": " X", "probability": 0.82568359375}, {"start": 2447.32, "end": 2448.8, "word": " ساوي", "probability": 0.8976236979166666}], "temperature": 1.0}, {"id": 101, "seek": 247233, "start": 2450.75, "end": 2472.33, "text": "ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين", "tokens": [2288, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957, 12602, 6055, 3794, 3615, 9957], "avg_logprob": -0.3988715302613046, "compression_ratio": 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1.0}, {"id": 109, "seek": 266219, "start": 2639.21, "end": 2662.19, "text": "إذا ميدالي ل R تسعين R نود هي عبارة عن R تسعين R نود R تسعين inverse ال R نود مش هدا ال identity طب وال R تسعين فيه R تسعين inverse يبقى ده هيطلع ال R نود itself", "tokens": [28814, 15730, 3714, 25708, 6027, 1829, 5296, 497, 6055, 3794, 3615, 9957, 497, 8717, 23328, 39896, 6225, 3555, 9640, 3660, 18871, 497, 6055, 3794, 3615, 9957, 497, 8717, 23328, 497, 6055, 3794, 3615, 9957, 17340, 2423, 497, 8717, 23328, 37893, 8032, 28259, 2423, 6575, 23032, 3555, 16070, 497, 6055, 3794, 3615, 9957, 8978, 3224, 497, 6055, 3794, 3615, 9957, 17340, 7251, 3555, 4587, 7578, 11778, 3224, 39896, 9566, 1211, 3615, 2423, 497, 8717, 23328, 2564], "avg_logprob": -0.15902549616600337, "compression_ratio": 1.7272727272727273, "no_speech_prob": 0.0, "words": [{"start": 2639.21, "end": 2639.53, "word": "إذا", "probability": 0.64501953125}, {"start": 2639.53, "end": 2640.11, "word": " ميدالي", "probability": 0.70208740234375}, {"start": 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\ No newline at end of file
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@@ -0,0 +1,1843 @@
+1
+00:00:20,650 --> 00:00:24,730
+الله رحمة ورحمة أنهينا في المحاضرة الماضية chapter
+
+2
+00:00:24,730 --> 00:00:28,550
+ثمانية كجزء نظري والآن هذه المحاضرة إن شاء الله 
+
+3
+00:00:28,550 --> 00:00:35,150
+سنناقش بعض الأسئلة بقدر ما نستطيع خلال هذه الساعة
+
+4
+00:00:35,150 --> 00:00:43,140
+إن شاء الله تعالى نبدأ بالأسئلة على Chapter 8 والتي
+
+5
+00:00:43,140 --> 00:00:47,920
+تتعلق بالـ product external direct هو نبدأ بالسؤال
+
+6
+00:00:47,920 --> 00:00:52,620
+السادس مثلًا بيقول prove by comparing orders of the
+
+7
+00:00:52,620 --> 00:00:57,200
+element يبقى اللي بدك تستخدم طريقة المقارنة بين
+
+8
+00:00:57,200 --> 00:01:08,610
+العناصر لإثبات أنه لإثبات أن Z8 external direct
+
+9
+00:01:08,610 --> 00:01:17,670
+product مع Z2 is not isomorphic
+
+10
+00:01:17,670 --> 00:01:18,970
+إلى Z4
+
+11
+00:01:23,930 --> 00:01:28,970
+يبقى دلني على طريقة يقول لي استخدم لي الـ orders لل
+
+12
+00:01:28,970 --> 00:01:33,270
+element في كلا الـ two groups للحكم على أن الـ group
+
+13
+00:01:33,270 --> 00:01:37,930
+الأولى ليست isomorphic للـ group الثانية فمثلًا لو
+
+14
+00:01:37,930 --> 00:01:41,810
+جيت للـ group الأولى هل فيها element of order
+
+15
+00:01:41,810 --> 00:01:49,270
+ثمانية بالمرة Z ثمانية × ثانية direct product مع Z
+
+16
+00:01:49,270 --> 00:01:49,730
+اثنين
+
+17
+00:01:53,360 --> 00:01:59,800
+بس فيها .. فيها اثنين والثمانية ولا جزاك؟ ثمانية
+
+18
+00:01:59,800 --> 00:02:05,740
+واتنين الواحد
+
+19
+00:02:05,740 --> 00:02:09,080
+والواحد
+
+20
+00:02:09,080 --> 00:02:14,500
+كويس، في غيره؟ الواحد والصفر يبقى عندي بدل الـ
+
+21
+00:02:14,500 --> 00:02:18,020
+element اثنين الـ orders اللي هم يساووا ثمانية
+
+22
+00:02:18,020 --> 00:02:22,560
+الواحد في الـ Z ثمانية الـ order اللي هو ثمانية الـ
+
+23
+00:02:22,560 --> 00:02:25,280
+zero الـ order اللي هو واحد الـ least common
+
+24
+00:02:25,280 --> 00:02:28,660
+multiple بين الثمانية والواحد اللي هو ثمانية مظبوط
+
+25
+00:02:28,660 --> 00:02:35,800
+يبقى هنا عندي الـ element واحد و zero موجود في Z
+
+26
+00:02:35,800 --> 00:02:42,970
+ثمانية external direct product with order اللي هو
+
+27
+00:02:42,970 --> 00:02:48,030
+ثمانية الـ order لهذا الـ element ثمانية الآن بنجي لـ
+
+28
+00:02:48,030 --> 00:02:52,590
+Z أربعة direct product مع Z أربعة هل بتلاقي في
+
+29
+00:02:52,590 --> 00:02:56,430
+element الـ order اللي بيساوي ثمانية رغم أنه ستة
+
+30
+00:02:56,430 --> 00:03:02,410
+عشر عنصر ها في element Z أربعة الـ order لهم يا إما
+
+31
+00:03:02,410 --> 00:03:06,790
+واحد يا إما اثنين يا أربعة والتاني واحد واثنين
+
+32
+00:03:06,790 --> 00:03:10,410
+وأربعة هل في least common multiple فيهم أكثر من
+
+33
+00:03:10,410 --> 00:03:15,710
+أربعة الذي يسكب الملتقب لهذه الـ order فيه أكثر من
+
+34
+00:03:15,710 --> 00:03:24,090
+أربعة ما عندهوش يبقى باجي بقول له بطولكن الـ Z أربعة
+
+35
+00:03:24,090 --> 00:03:34,830
+external product مع Z أربعة has no element of
+
+36
+00:03:34,830 --> 00:03:38,990
+order ثمانية because
+
+37
+00:03:41,450 --> 00:03:54,550
+The maximum order in Z4 is 4
+
+38
+00:03:57,180 --> 00:04:00,700
+لأن الـ order للـ element بيقسم الـ order للـ group
+
+39
+00:04:00,700 --> 00:04:04,580
+إذا Z أربعة لا يوجد فيها إلا الـ elements الـ order
+
+40
+00:04:04,580 --> 00:04:09,580
+الواحد اللي هو الـ identity والاثنين اللي هو العدد
+
+41
+00:04:09,580 --> 00:04:13,740
+اثنين وكذلك الأربعة اللي هو العدد واحد وثلاثة
+
+42
+00:04:13,740 --> 00:04:19,380
+تمام؟ يبقى من هنا أقصى order عندي في Z أربعة direct
+
+43
+00:04:19,380 --> 00:04:23,760
+product كبيرة زي Z أربعة هو أربعة وهذه ثمانية يبقى
+
+44
+00:04:23,760 --> 00:04:29,010
+اثنين هذول ما لهم isomorphic يبقى التزام في
+
+45
+00:04:29,010 --> 00:04:33,810
+الكلام اللي قالي وصلت للنتيجة بدنا نروح لسؤال
+
+46
+00:04:33,810 --> 00:04:42,490
+أربعة عشر سؤال أربعة عشر بيقول ما يأتي suppose الـ G1
+
+47
+00:04:42,490 --> 00:04:53,490
+isomorphic إلى G2 و group ثانية H1 isomorphic لمن؟
+
+48
+00:04:53,490 --> 00:05:03,330
+لـ H2 هو H1 isomorphic لـ H2 prove that اثبت أنه الـ
+
+49
+00:05:03,330 --> 00:05:10,530
+G1 external direct product مع H1 isomorphic لـ G2
+
+50
+00:05:10,530 --> 00:05:19,550
+external direct product مع H2 هذا اللي احنا بدنا نروح
+
+51
+00:05:19,550 --> 00:05:26,330
+نثبته إذا دائمًا وأبدًا بنحاول نستفيد من المعطيات
+
+52
+00:05:26,330 --> 00:05:31,190
+اللي عندنا في إثبات المطلوب هذول two groups are
+
+53
+00:05:31,190 --> 00:05:35,790
+isomorphic هذول two groups are isomorphic أخذت الـ
+
+54
+00:05:35,790 --> 00:05:38,830
+external product ما بين الـ group الأولى و الـ group
+
+55
+00:05:38,830 --> 00:05:42,280
+الأولى من المجموعة الثانية والجروب الثانية مع
+
+56
+00:05:42,280 --> 00:05:46,480
+الجروب الثانية بدي أثبت أنه اللي هو الـ external
+
+57
+00:05:46,480 --> 00:05:50,460
+product هذا ما له isomorphic للـ external product
+
+58
+00:05:50,460 --> 00:05:55,480
+اللي عندنا هذا يبقى الحلقة التالية solution
+
+59
+00:06:00,220 --> 00:06:09,660
+أفترض أن الـ Alpha من الـ G1 إلى الـ G2 و الـ Beta
+
+60
+00:06:09,660 --> 00:06:18,860
+من الـ H1 إلى الـ H2 هم isomorphism
+
+61
+00:06:20,010 --> 00:06:24,330
+يبقى بدي أفترض إن هذول الاثنين isomorphism الآن
+
+62
+00:06:24,330 --> 00:06:29,750
+هذا مشان أثبت إن اثنين isomorphism بدي أعرف
+
+63
+00:06:29,750 --> 00:06:33,530
+function من الجروب الأولى إلى الجروب الثانية وأثبت
+
+64
+00:06:33,530 --> 00:06:37,390
+أنها one to one and one to one وتخدم خاصية الـ isomorphism
+
+65
+00:06:37,390 --> 00:06:40,710
+إذا بدي أقول له define
+
+66
+00:06:43,180 --> 00:06:52,220
+A function في من الـ G1 و H1 كـ external direct product
+
+67
+00:06:52,220 --> 00:06:55,760
+من
+
+68
+00:06:55,760 --> 00:07:05,860
+الـ G1 و H1 لمين؟ لـ G2 كـ external direct product مع H2
+
+69
+00:07:05,860 --> 00:07:16,200
+بـ في of بدي آخذ element من G1 وليكن G و H فعلي ما
+
+70
+00:07:16,200 --> 00:07:24,520
+تأثر على G و H بدي أوديها وين؟ في الـ group G2 و H2
+
+71
+00:07:24,520 --> 00:07:31,280
+طيب G2 هذه مش هي G2 هذه صح؟ إذا الـ element اللي
+
+72
+00:07:31,280 --> 00:07:37,350
+هنا هو صورة لـ element من هنا الفانكشن من هنا لهنا
+
+73
+00:07:37,350 --> 00:07:44,510
+شو سميتها Alpha يبقى هذه بقدر آخذها Alpha of G
+
+74
+00:07:44,510 --> 00:07:52,690
+يبقى هذه بقدر أقول Alpha of G ليش؟ لأن Alpha of G G
+
+75
+00:07:52,690 --> 00:07:59,210
+موجودة في G1 واحنا عندنا هنا G موجودة في G1 يبقى
+
+76
+00:07:59,210 --> 00:08:04,350
+هنا صورتها في G2 صورتها في G2 اللي Alpha of G
+
+77
+00:08:05,900 --> 00:08:12,960
+بتداجر للـ H الـ H موجودة في الـ H1 تمام أنا عندي
+
+78
+00:08:12,960 --> 00:08:18,140
+Beta من H1 إلى H2 يبقى H اللي موجودة في H1 صورتها
+
+79
+00:08:18,140 --> 00:08:25,520
+تبقى Beta of H يبقى هذا Beta of H بالشكل اللي
+
+80
+00:08:25,520 --> 00:08:32,520
+عندنا يبقى هكذا عرفت الدالة تعريفًا سليمًا الآن هذه
+
+81
+00:08:32,520 --> 00:08:37,400
+الدالة بدي أحاول أثبت أنها one to one and onto
+
+82
+00:08:37,400 --> 00:08:42,120
+وتخدم خاصية الـ isomorphism إن تم لذلك يبقى بيكونوا
+
+83
+00:08:42,120 --> 00:08:45,660
+اثنين هذول are isomorphic وبكون أنت هنا من هالشغل
+
+84
+00:08:45,660 --> 00:08:51,020
+هادى يبقى بدي آجي للخطوة الأولى بدي أثبت له إن فاي
+
+85
+00:08:51,020 --> 00:08:58,240
+is one to one مشان هيك بدي آخذ صورتين متساويتين
+
+86
+00:08:58,240 --> 00:09:08,360
+Assume Phi of G و H بدي أساوي Phi of X و Y مثلًا إذا
+
+87
+00:09:08,360 --> 00:09:14,420
+قدرت أثبت إن الـ ordered pair G و H هو الـ ordered pair X
+
+88
+00:09:14,420 --> 00:09:16,540
+و Y بكون انتهينا من الشغل يعني
+
+89
+00:09:19,880 --> 00:09:25,740
+بتداجي لصورة الـ element الأول حسب التعريف يبقى
+
+90
+00:09:25,740 --> 00:09:35,420
+Alpha of G و Beta of H يبقى هذه تبقى Alpha of G و
+
+91
+00:09:35,420 --> 00:09:41,760
+Beta of H بالشكل اللي عندنا هنا الـ Phi of X بنفس
+
+92
+00:09:41,760 --> 00:09:51,500
+الطريقة يبقى هادي Alpha of X الصورة والثانية Beta
+
+93
+00:09:51,500 --> 00:09:53,920
+of Y الشكل اللي عندها
+
+94
+00:09:57,060 --> 00:10:01,740
+بناء على هذا الكلام صار عندي two ordered pair are
+
+95
+00:10:01,740 --> 00:10:05,240
+equal يبقى المركبة الأولى هتساوي المركبة الأولى
+
+96
+00:10:05,240 --> 00:10:10,020
+والمركبة الثانية هتساوي المركبة الثانية يبقى بناء
+
+97
+00:10:10,020 --> 00:10:17,900
+عليه Alpha of G بديه يساوي Alpha of X and Beta of
+
+98
+00:10:17,900 --> 00:10:24,180
+H بديه يساوي Beta of Y شوف هذا شو بديه يعطينا الآن
+
+99
+00:10:24,180 --> 00:10:29,940
+الـ Alpha هذي isomorphism يبقى one to one and onto
+
+100
+00:10:29,940 --> 00:10:34,960
+إذا مدام one to one يبقى الـ G بده يساوي اللي هو
+
+101
+00:10:34,960 --> 00:10:42,960
+الـ X يبقى هنا الـ G بده يساوي الـ X and الـ H
+
+102
+00:10:42,960 --> 00:10:51,920
+بده يساوي الـ Y السبب بسبب أن Alpha و Beta هم one
+
+103
+00:10:51,920 --> 00:10:57,500
+to one ما دام صورتين متساويتين إذا الأصل متساوي لأن
+
+104
+00:10:57,500 --> 00:11:02,000
+الـ Alpha one to one و كذلك الـ Beta is one to one
+
+105
+00:11:02,000 --> 00:11:08,360
+يبقى بناء عليه هذا بديه يعطينا لو أخذت الـ G و الـ H
+
+106
+00:11:08,360 --> 00:11:15,900
+as an ordered الـ G عبارة عن مين؟ X و الـ H عبارة عن
+
+107
+00:11:15,900 --> 00:11:20,420
+مين؟ Y عبارة عن Y بالشكل اللي عندنا هذا يبقى أخذ
+
+108
+00:11:20,420 --> 00:11:26,890
+صورتين متساويتين واثبت إن أصل هماله متساوي لذلك
+
+109
+00:11:26,890 --> 00:11:28,630
+فاي is one to one
+
+110
+00:11:34,980 --> 00:11:43,220
+يبقى أنا بأخذ element في الـ G2 و X2 و H2 يبقى
+
+111
+00:11:43,220 --> 00:11:50,340
+بالدرجة يقول لو أخذت الـ X موجود مثلًا في الـ G2
+
+112
+00:11:50,340 --> 00:12:00,280
+external product مع H2 بشكل لعين هذا يبقى then بدي
+
+113
+00:12:00,280 --> 00:12:06,570
+أدور على شكل هذا الـ element يبقى شكل الـ element X
+
+114
+00:12:06,570 --> 00:12:12,370
+هذا بده يساوي element من G2 و element من H2
+
+115
+00:12:12,370 --> 00:12:20,370
+يبقى هذا الكلام بده يساوي element وليكن G2 و H2 من
+
+116
+00:12:20,370 --> 00:12:30,200
+H2 طيب هذا الكلام يساوي الـ G2 موجودة في G2 تمام و
+
+117
+00:12:30,200 --> 00:12:38,180
+Alpha is onto يبقى هذا الـ element له أصل في G1
+
+118
+00:12:38,180 --> 00:12:43,260
+صحيح ولا لأ يبقى هذا الكلام بقدر أشيل الـ G2 و
+
+119
+00:12:43,260 --> 00:12:51,940
+أكتبها Alpha of G1 مثلًا و بقدر أكتب هذا Beta of
+
+120
+00:12:51,940 --> 00:12:57,180
+each one شو السبب في ذلك لأن Alpha and Beta are
+
+121
+00:12:57,180 --> 00:13:10,440
+onto يبقى هنا since الـ Alpha and Beta are onto هذا
+
+122
+00:13:10,440 --> 00:13:15,400
+الكلام لو رجعته إلى أصله بلاقي هو التعريف اللي أنا
+
+123
+00:13:15,400 --> 00:13:21,100
+قايله هنا يبقى الأصل اللي بتابعه هو عبارة عن Phi
+
+124
+00:13:21,100 --> 00:13:28,960
+of G1 و H1 يبقى الـ element اللي أخدته في G2 و H2 اللي
+
+125
+00:13:28,960 --> 00:13:36,600
+جات له أصل في G1 و H1 اللي هو G1 و H1 صغير يبقى Phi
+
+126
+00:13:36,600 --> 00:13:41,600
+is in two ضايل عليه نثبت أن Phi is an isomorphism
+
+127
+00:13:41,600 --> 00:13:50,020
+يبقى باقي بقول Phi is an isomorphism يبقى بدي أنا 
+
+128
+00:13:50,020 --> 00:13:55,920
+آخذ اللي هو الـPhi of حاصل ضرب two elements ال
+
+129
+00:13:55,920 --> 00:14:01,100
+element الأول اللي هو بدك تأخذه من هنا من مكان
+
+130
+00:14:01,100 --> 00:14:08,120
+يكون يبقى لو جئت قلت G وH مضروب في element ثاني
+
+131
+00:14:08,120 --> 00:14:14,720
+وليكن مثلا G prime وH prime بالشكل اللي عندنا هذا
+
+132
+00:14:15,810 --> 00:14:21,390
+يبقى هذا الكلام بده يساوي Phi of هذا الضرب عليه
+
+133
+00:14:21,390 --> 00:14:25,770
+بنضرب component wise حسب ما عرفنا عملية الضرب على
+
+134
+00:14:25,770 --> 00:14:32,350
+ال external product يبقى G G prime و H H prime
+
+135
+00:14:32,350 --> 00:14:39,440
+بالشكل اللي عندنا هذا هذا الكلام بده يساوي Phi لما
+
+136
+00:14:39,440 --> 00:14:43,900
+تأثر على هذا ال element يبقى Alpha للأول و Beta 
+
+137
+00:14:43,900 --> 00:14:52,700
+للثاني يبقى هذا Alpha of G G prime و Beta of H H
+
+138
+00:14:52,700 --> 00:14:58,950
+prime  الألف والبيتا كل واحدة فيهم isomorphism مدام
+
+139
+00:14:58,950 --> 00:15:04,790
+كل واحدة فيهم isomorphism إذا هذه Alpha of G وهذه
+
+140
+00:15:04,790 --> 00:15:14,430
+Alpha of G' وهذه Beta of H وهذه Beta of H' بالشكل
+
+141
+00:15:14,430 --> 00:15:19,000
+اللي عندنا هنا يبقى أثر على شكل order pair السؤال
+
+142
+00:15:19,000 --> 00:15:25,600
+هو هل ال order pair هذا بقدر أكتبه على شكل حاصل
+
+143
+00:15:25,600 --> 00:15:31,240
+ضرب two ordered pairs؟ الإجابة نعم، كيف؟ كالتالي،
+
+144
+00:15:31,240 --> 00:15:36,140
+شوفوا يا سيدتي، هاي باجي بقوله هنا Alpha of G بدي
+
+145
+00:15:36,140 --> 00:15:43,870
+آخذها مع Beta of H عشان الترتيب وهنا Alpha of G
+
+146
+00:15:43,870 --> 00:15:50,450
+prime بدي آخذها مع Beta of H prime يبقى هاي كتبتهم
+
+147
+00:15:50,450 --> 00:15:55,830
+على شكل حاصل ضرب قوسية يبقى هذا الكلام بده يساوي
+
+148
+00:15:55,830 --> 00:16:04,650
+الآن لو جئت للقوس الأول يبقى هذا Phi of GH يبقى هذا
+
+149
+00:16:04,650 --> 00:16:16,880
+Phi of GH الثاني عبارة عن Phi of G' وH'  أطلع بدأت
+
+150
+00:16:16,880 --> 00:16:22,020
+بحاصل ضرب القوسين وصلت لـPhi الأول مضروبة في مين
+
+151
+00:16:22,020 --> 00:16:26,700
+في Phi التانية يبقى بناء عليه Phi is an
+
+152
+00:16:26,700 --> 00:16:29,640
+isomorphism يبقى
+
+153
+00:16:34,510 --> 00:16:42,450
+Isomorphism that is أي أن الـ G1 external product
+
+154
+00:16:42,450 --> 00:16:51,850
+مع H1 isomorphic ل G2 external product مع G2 وهو
+
+155
+00:16:51,850 --> 00:16:57,590
+المطلوب الشغل مش صعب سهل بس طويل شوية يعني بده
+
+156
+00:16:57,590 --> 00:17:07,460
+تمشي بدقة كبيرة طيب كان هذا هو السؤال رقم 14 خذ لي
+
+157
+00:17:07,460 --> 00:17:15,260
+16 بيقول في ال group Z 40 Z 30 هات لي two subgroups
+
+158
+00:17:15,260 --> 00:17:20,980
+of order 12 and
+
+159
+00:17:20,980 --> 00:17:24,360
+هذا
+
+160
+00:17:24,360 --> 00:17:33,400
+سؤال كده ايش قلنا؟ 16 16 يبقى in z 40 external
+
+161
+00:17:33,400 --> 00:17:42,880
+product مع z 30 find two subgroups
+
+162
+00:17:42,880 --> 00:17:47,780
+of order 12
+
+163
+00:17:57,100 --> 00:18:02,960
+طيب جالي في ال group هذي Z 30 Z 40 Extended like a
+
+164
+00:18:02,960 --> 00:18:07,480
+project مع Z 30 هات لي two sub groups of order 12
+
+165
+00:18:07,480 --> 00:18:11,720
+لا جالي Cyclic ولا غير Cyclic لكن اللي أسهل ليه أن
+
+166
+00:18:11,720 --> 00:18:17,660
+أجيب Cyclic إن جدرتها طيب بقوله كويسة طب كيف بدي
+
+167
+00:18:17,660 --> 00:18:21,440
+أجيب Cyclic ال order اللي هي سوية 12 بقوله كويسة
+
+168
+00:18:21,440 --> 00:18:27,530
+إذا بتقدريجب أن أجرب الـ order لـ element فيها
+
+169
+00:18:27,530 --> 00:18:30,910
+أربعة والتاني تلاتة يبقى الـ least common
+
+170
+00:18:30,910 --> 00:18:35,270
+multiple المجداش اتناش وكفى الله المنقتل هذا ال
+
+171
+00:18:35,270 --> 00:18:40,390
+element وولد ال subgroup من المطلوب إذا أنا بدي
+
+172
+00:18:40,390 --> 00:18:46,710
+أدور على عناصر من زد أربعين ال order اللي يكون
+
+173
+00:18:46,710 --> 00:18:53,750
+جداش أربعة صح؟ طيب مين العناصر اللي في Z أربعين
+
+174
+00:18:53,750 --> 00:18:59,530
+اللي ال order لهم يساوي أربعة حد بيقدر يجيب لي ولو
+
+175
+00:18:59,530 --> 00:19:07,200
+عنصر واحد عشرة ممتاز جدا يبقى عشرة موجودة في Z
+
+176
+00:19:07,200 --> 00:19:14,560
+أربعين وال order للعشرة بده يساوي أربعة ممتاز جدا
+
+177
+00:19:14,560 --> 00:19:21,220
+إذا أنا بده أروح على Z ثلاثين كمان برضه عشرة طيب
+
+178
+00:19:21,220 --> 00:19:27,980
+العشرة موجودة في Z ثلاثين and ال order للعشرة بده
+
+179
+00:19:27,980 --> 00:19:34,370
+يساوي كدهش بده يساوي ثلاثة إذا ال element اللي هو
+
+180
+00:19:34,370 --> 00:19:40,370
+عشرة وعشرة موجود في Z أربعين External Direct
+
+181
+00:19:40,370 --> 00:19:50,070
+Product مع Z ثلاثين ال order للعشرة وعشرة هو عبارة
+
+182
+00:19:50,070 --> 00:19:55,130
+عن ال least common multiple للأربعة والثلاثة اللي
+
+183
+00:19:55,130 --> 00:20:00,470
+هو يساوي قداش اتناش إذا هذا ال element بيعطيني ال
+
+184
+00:20:00,470 --> 00:20:02,910
+cyclic subgroup of order اتناش
+
+185
+00:20:05,800 --> 00:20:14,800
+يبقى (عشرة،عشرة) (عشرة،عشرة) هو عبارة عن
+
+186
+00:20:14,800 --> 00:20:26,480
+Cyclic Subgroup Cyclic Subgroup of order اثنا عشر
+
+187
+00:20:26,480 --> 00:20:34,000
+بدي أدور على غيره بدي أدور كمان على عنصر ثاني
+
+188
+00:20:38,630 --> 00:20:47,730
+كيف؟ اثنين وستة .. لا بدك .. ستة وأربعة ماشي ..
+
+189
+00:20:47,730 --> 00:20:51,470
+ستة وأربعة ماشي .. واحد واثنا عشر ماشي .. بس يلا
+
+190
+00:20:51,470 --> 00:20:55,250
+نلاقي .. يبقى الآن بدي أروح أدور على مين على
+
+191
+00:20:55,250 --> 00:21:04,750
+orders أخرى طيب ال order تبع العشرة هو أربعة نقدر
+
+192
+00:21:04,750 --> 00:21:10,550
+نجيب من z ثلاثين واحد ال order إله ستة أربعة وستة
+
+193
+00:21:10,550 --> 00:21:13,250
+ال order اللي مصير اثنا عشر least common multiple
+
+194
+00:21:13,250 --> 00:21:21,010
+مظبوط يبقى هنا مرة ثانية also أيضا العشرة أو ال
+
+195
+00:21:21,010 --> 00:21:28,440
+order للعشرة بده يساوي أربعة في z أربعين الآن
+
+196
+00:21:28,440 --> 00:21:37,500
+الخمسة الخامسة ال order إيه يساوي قداش؟ ستة مظبوط
+
+197
+00:21:37,670 --> 00:21:45,150
+ال order له يساوي ستة في Z ثلاثين يبقى إذا ال
+
+198
+00:21:45,150 --> 00:21:51,910
+order للعشرة وخمسة بده يساوي ال least common
+
+199
+00:21:51,910 --> 00:21:58,630
+multiple اللي هو من الأربعة والستة اللي هو كده
+
+200
+00:21:58,630 --> 00:22:04,970
+اثنا عشر يبقى إذا ال sub group generated by عشرة
+
+201
+00:22:04,970 --> 00:22:19,620
+وخمسة is a cyclic group of order اثنا عشر يبقى بناء
+
+202
+00:22:19,620 --> 00:22:24,000
+عليه هاي طلعنا له اثنتين subgroups ورغم أنه
+
+203
+00:22:24,000 --> 00:22:28,120
+ما اشترطش وقال هات لي subgroups وخلصنا يبقى أنا
+
+204
+00:22:28,120 --> 00:22:33,620
+جبت له subgroups وجبتهم له اثنتين زيادة على مقال أنه
+
+205
+00:22:33,620 --> 00:22:39,160
+اثنتين cyclic subgroups ال order لهم يساوي 12
+
+206
+00:22:39,160 --> 00:22:45,120
+اعتمدت في ذلك على من على ال order لل elements وهم
+
+207
+00:22:45,120 --> 00:22:48,540
+اللي رايحين في من في الحل
+
+208
+00:22:51,060 --> 00:23:04,520
+طيب كان هذا سؤال ستة عشر خذ لي سؤال ستة وعشرين سؤال
+
+209
+00:23:04,520 --> 00:23:12,180
+ستة وعشرين ستة وعشرين بيقول لي هات لي ال subgroup من z
+
+210
+00:23:12,180 --> 00:23:16,400
+أربعة بدي مثلا subgroup
+
+211
+00:23:18,720 --> 00:23:28,460
+of subgroup من مين من z4 external direct product
+
+212
+00:23:28,460 --> 00:23:35,640
+z4 external direct product مع z دي اثنين that is
+
+213
+00:23:35,640 --> 00:23:46,880
+not of the form not in the form اللي هو H external
+
+214
+00:23:46,880 --> 00:23:59,480
+product ل K حيث حياته where ال H subgroup من
+
+215
+00:23:59,480 --> 00:24:10,530
+Z4 and ال K subgroup من main subgroup من z2 و ال k
+
+216
+00:24:10,530 --> 00:24:17,230
+sub group من من z2
+
+217
+00:24:17,230 --> 00:24:27,190
+شوفوا يا سيدي نرجع مرة ثانية أنا عندي الآن ال z4
+
+218
+00:24:27,190 --> 00:24:33,250
+external direct product مع z2 هذه group الآن بدي
+
+219
+00:24:33,250 --> 00:24:39,410
+subgroup من هذه ال group بحيث ما تكونش على الشكل H
+
+220
+00:24:39,410 --> 00:24:45,890
+اللي هو external product مع K حيث H subgroup من Z
+
+221
+00:24:45,890 --> 00:24:51,590
+أربعة وال K subgroup من من من Z يعني بدي جيب لي ال
+
+222
+00:24:51,590 --> 00:24:56,910
+subgroup ثانية غير ال external product تبع هدول
+
+223
+00:24:58,090 --> 00:25:03,850
+تعال نشوف كيف بدنا نحل السؤال السؤال يحتاج إلى
+
+224
+00:25:03,850 --> 00:25:09,720
+تفكير ومن التفكير بنقدر نوصل للمطلب Z أربعة
+
+225
+00:25:09,720 --> 00:25:14,100
+external product ل Z اثنين not in the form ليست في
+
+226
+00:25:14,100 --> 00:25:17,840
+هذا الشكل احنا ده جبنا ال subgroup وجبنا ال
+
+227
+00:25:17,840 --> 00:25:20,820
+subgroup بنجيب لهم ال external product بنطلع
+
+228
+00:25:20,820 --> 00:25:25,200
+subgroup جديدة بقول ال subgroup الجديدة بديش إياها
+
+229
+00:25:25,200 --> 00:25:28,830
+ولا واحدة منها دول اللي أنت بتقول عليهم قلت له
+
+230
+00:25:28,830 --> 00:25:32,410
+تعال نشوف مين هم ال subgroups وبعدين بصير خير
+
+231
+00:25:32,410 --> 00:25:38,710
+تمام الآن لو جئت على z4 بدي أدور مين هم ال
+
+232
+00:25:38,710 --> 00:25:44,990
+subgroups تبعات z4 فبقى اجيب يقوله the only
+
+233
+00:25:44,990 --> 00:25:56,370
+subgroups of z4 are اللي ال order إلها واحد واللي
+
+234
+00:25:56,370 --> 00:25:59,590
+ال order إلها اثنين واللي ال order إلها أربعة
+
+235
+00:25:59,590 --> 00:26:06,190
+مظبوط يبقى اللي ال order إلها واحد هي ال identity
+
+236
+00:26:06,190 --> 00:26:12,170
+واللي ال order إلها اثنين هي ال sub group
+
+237
+00:26:12,170 --> 00:26:18,630
+generated by اثنين ايش ضال عندي؟ واحد وثلاثة واحد
+
+238
+00:26:18,630 --> 00:26:23,230
+وثلاثة بوالدولي نفس ال subgroup z أربعة يبقى هدول
+
+239
+00:26:23,230 --> 00:26:28,650
+ثلاثة لكن في الحقيقة هي واحدة بس يبقى الثالثة اللي
+
+240
+00:26:28,650 --> 00:26:37,930
+هي main z أربعة itself تمام؟ طيب الآن also the
+
+241
+00:26:37,930 --> 00:26:51,930
+only subgroups only subgroups of z2 are طبعا ال
+
+242
+00:26:51,930 --> 00:26:56,950
+identity ومين كمان والاثنين اللي هي ال subgroup
+
+243
+00:26:56,950 --> 00:27:04,350
+generated by one اللي هي z2 itself z2 itself طيب
+
+244
+00:27:04,350 --> 00:27:09,850
+لو بدي أكونه ال external product هذا يبقى بدي
+
+245
+00:27:09,850 --> 00:27:18,330
+أقوله الأولى مع الأولى اللي هي zero طبعا هذه فيش
+
+246
+00:27:18,330 --> 00:27:23,570
+فيها إلا مين عنصر واحد صحيح ال cyclic وفيش فيها
+
+247
+00:27:23,570 --> 00:27:28,730
+أقل عنصر واحد بدي أمسك الثانية الثانية اللي هي ال
+
+248
+00:27:28,730 --> 00:27:35,230
+zero نفسها مع ال subject ال zero نفسها مع z2
+
+249
+00:27:35,230 --> 00:27:41,450
+standard product مع z2 الثالثة خلصنا منها اللي
+
+250
+00:27:41,450 --> 00:27:46,710
+هي ال subgroup generated by اثنين external like 
+
+251
+00:27:46,710 --> 00:27:55,350
+product مع من؟ مع الـ zero الـ subgroup generated by
+
+252
+00:27:55,350 --> 00:28:01,390
+اتنين external like product مع من؟ مع زد اتنين الآن
+
+253
+00:28:01,390 --> 00:28:07,950
+الـ z4 external product مع الـ zero آخر حاجة الـ
+
+254
+00:28:07,950 --> 00:28:16,830
+z4 external product مع الـ z2 هؤلاء كل الـ
+
+255
+00:28:16,830 --> 00:28:20,990
+subgroups اللي على الشكل اللي قدامي هذا جالي هذا
+
+256
+00:28:20,990 --> 00:28:25,480
+اللي بديش منهم ولا واحدة ولا واحدة من هدول قال لي
+
+257
+00:28:25,480 --> 00:28:29,080
+بيدي الـ subgroup من هذا ماهياش على الشكل اللي
+
+258
+00:28:29,080 --> 00:28:34,180
+عندنا هنا بقوله تعالي ندور الآن لو جالس له قوله
+
+259
+00:28:34,180 --> 00:28:39,780
+consider خد لي أول شيء الـ subgroup لازم يكون فيها
+
+260
+00:28:39,780 --> 00:28:46,750
+الـ identity element identity element تمام طيب لو
+
+261
+00:28:46,750 --> 00:28:58,130
+جيت أخد عندي هنا مثلا الـ zero و الـ one الـ zero
+
+262
+00:28:58,130 --> 00:29:04,650
+أخدته من z ولا أخدت خليك معايا بدي أخدي اتنين و
+
+263
+00:29:04,650 --> 00:29:11,500
+الـ zero اتنين وزيرو موجود في زد أربعة external
+
+264
+00:29:11,500 --> 00:29:16,300
+product لزيد دي اتنين وزيد أربعة لزيد تلاتة
+
+265
+00:29:16,300 --> 00:29:25,590
+اتاكد لي بالله سؤال جديد شو قلنا ستة وعشرين.. ستة
+
+266
+00:29:25,590 --> 00:29:32,910
+وعشرين.. ستة وعشرين.. ستة وعشرين.. ستة وعشرين
+
+267
+00:29:32,910 --> 00:29:40,130
+..ستة وعشرين.. ستة وعشرين.. ستة وعشرين.. ستة
+
+268
+00:29:40,130 --> 00:29:40,870
+وعشرين.. ستة وعشرين.. ستة وعشرين.. ستة وعشرين
+
+269
+00:29:40,870 --> 00:29:41,150
+وعشرين.. ستة وعشرين.. ستة وعشرين.. ستة وعشرين
+
+270
+00:29:41,150 --> 00:29:42,010
+..ستة وعشرين.. ستة وعشرين.. ستة وعشرين.. ستة
+
+271
+00:29:42,010 --> 00:29:47,740
+وعشرين.. ستة وعشرين.. ستة وعشرين.. طيب يبقى الآن
+
+272
+00:29:47,740 --> 00:29:54,880
+بدي أخد الـ element zero و zero بدي أخد element
+
+273
+00:29:54,880 --> 00:30:01,140
+ثاني اتنين و zero موجود في واحدة من هدول اتنين
+
+274
+00:30:01,140 --> 00:30:05,380
+موجود فيها ده استنى شوية لأ لأ بدي أجيب هو قال لي
+
+275
+00:30:05,380 --> 00:30:08,840
+النقط ماهياش في الشكل اللي عندنا هل هادي الـ
+
+276
+00:30:08,840 --> 00:30:13,480
+subgroup هادي الـ subgroup صحيح بس استنى نشوفها هي
+
+277
+00:30:13,480 --> 00:30:14,440
+هادي ولا لأ
+
+278
+00:30:17,170 --> 00:30:23,010
+لأ لأ لأ استنى شوف بدنا نغيرها لو جيت قول واحد
+
+279
+00:30:23,010 --> 00:30:30,790
+وزيرو وزيرو وواحد وواحد وواحد الشكل اللي عندنا
+
+280
+00:30:30,790 --> 00:30:38,370
+نيجي نشوف هل هذه تساوي أي واحدة من هدول ولا لأ لأ
+
+281
+00:30:38,370 --> 00:30:42,970
+لو جيت لهذه خلصنا منها Zero واتنين يعني Zero Zero
+
+282
+00:30:42,970 --> 00:30:49,360
+Zero واحدة هذه ما فيش إلا عنصرين فيها طيب هذه برضه
+
+283
+00:30:49,360 --> 00:30:57,140
+كذلك ما فيش فيها إلا زت اتنين برضه عنصرين طيب هذه
+
+284
+00:30:57,140 --> 00:31:02,130
+اللي هي زت اتنين مع زت اتنين الكثير اللي بيكبره في
+
+285
+00:31:02,130 --> 00:31:07,050
+الـ Z أربعة اللي هو بالـ identity Zero وبعدين اتنين
+
+286
+00:31:07,050 --> 00:31:12,130
+بس عنصرين مع عنصرين أربعة عناصر اللي هم مين اللي هم
+
+287
+00:31:12,130 --> 00:31:21,090
+Zero و Zero Zero و واحد وبعدها بيجيني اتنين اتنين
+
+288
+00:31:21,090 --> 00:31:27,180
+مش من هدول يبقى ليست هذه والـ Z أربعة فيها أربعة
+
+289
+00:31:27,180 --> 00:31:31,720
+عناصر طبعا مش هادي والـ Z أربعة مع Z two طبعا
+
+290
+00:31:31,720 --> 00:31:36,140
+ماهياش هادي يبقى هذه ليست ولا واحدة من هدول اللي
+
+291
+00:31:36,140 --> 00:31:41,120
+عندنا يبقى هذه هي الـ sub group المطلوبة وهي ليست
+
+292
+00:31:41,120 --> 00:31:43,660
+أي واحدة من الست الأولين أيوة
+
+293
+00:31:49,130 --> 00:31:54,590
+لو بدك subgroup من هدفك بنفس الطريقة هذه بقصة
+
+294
+00:31:54,590 --> 00:31:59,850
+بتطول، ليش؟ إنه عندك عناصر كثير، أربعين في تلاتين،
+
+295
+00:31:59,850 --> 00:32:04,850
+ألف وميتين عنصر، مش سهلة، بس دول تمان عناصر مش
+
+296
+00:32:04,850 --> 00:32:08,890
+كثير، تمانية زي ألف وميتين، في السوق اللي هو محل
+
+297
+00:32:08,890 --> 00:32:12,690
+لهم من الإعراب، ايه نعم، هذا بزهج، بصدق
+
+298
+00:32:17,470 --> 00:32:27,870
+أنا ممتاز طب شوف الهدف
+
+299
+00:32:27,870 --> 00:32:32,630
+من ذلك الهدف من ذلك أن أنت ما تكونش عليه الشكل هذا
+
+300
+00:32:32,630 --> 00:32:37,490
+هي الأشكال كلها كتبناها بدك تجيب أي subgroup تكون
+
+301
+00:32:37,490 --> 00:32:42,490
+تستبعد منها هذه الأشكال طبعا الـ subgroup يال order
+
+302
+00:32:42,490 --> 00:32:47,530
+إلا واحد يا اتنين، يا أربعة، يا تمانية، لأنه زد
+
+303
+00:32:47,530 --> 00:32:51,950
+أربعة كسنوات بتمان عناصر، مظبوط؟ يبقى بدك تجيب لك
+
+304
+00:32:51,950 --> 00:32:57,210
+واحدة من هدول، أي نعم، لو بدك تسامد الآن اللي هو
+
+305
+00:32:57,210 --> 00:33:02,370
+الـ order اللي هو سوى تمانية، ليش؟ لأن هي هيه،
+
+306
+00:33:02,370 --> 00:33:06,630
+يبقى صف على شجرة، بدك تجي واحد أو اتنين أو أربع،
+
+307
+00:33:06,630 --> 00:33:11,430
+الـ order اللي هي واحد هيها يبقى صف على شجرة يبقى بضل
+
+308
+00:33:11,430 --> 00:33:14,710
+اتنين والاربعة اتنين هاي هاي بضلش إلا الاربعة
+
+309
+00:33:14,710 --> 00:33:20,150
+عناصر يبقى إجباري إينا أيوة هذه مش مغنقة
+
+310
+00:33:23,720 --> 00:33:27,000
+لو عملت العنصر الثاني مع العنصر الأخير فتبقى لك
+
+311
+00:33:27,000 --> 00:33:34,560
+اتنين واحد العنصر الثاني مع الأخير يبقى هذا طبعا
+
+312
+00:33:34,560 --> 00:33:39,960
+الأملاني اللي اتجمع يبقى بصير اتنين واحد استنى
+
+313
+00:33:39,960 --> 00:33:45,400
+شوية هذا طب لو قلت هذه اتنين.. لأ لو قلت هذه
+
+314
+00:33:45,400 --> 00:33:51,400
+اتنين واحد التانية طب
+
+315
+00:33:51,400 --> 00:33:58,760
+استنى نشوف هذه الآن واحد و اتنين بيصير تلاتة موجودة
+
+316
+00:33:58,760 --> 00:34:04,200
+تلاتة و واحد مش مشكلة كمان مرة اه هذه بيصير انيا
+
+317
+00:34:04,200 --> 00:34:13,600
+اتنين و قلت هذه اه ايش هذه؟ اتنين و صفر فعلا شوف طب
+
+318
+00:34:13,600 --> 00:34:19,180
+اتنين تربيع بصير أربعة و زيرو موجودة اتنين و اتنين
+
+319
+00:34:19,180 --> 00:34:25,340
+اللي هو بصير زيرو واحد زيرو واحد موجود صحيح وهذا
+
+320
+00:34:25,340 --> 00:34:29,260
+لو بدنا نربعها بصير أربعة و اتنين زيرو زيرو مظبوط
+
+321
+00:34:29,260 --> 00:34:36,500
+صحيح ايش تلاتة و واحد لأ لأ ماشي هيك ماشي مقبول
+
+322
+00:34:36,500 --> 00:34:41,880
+فصحيح وين
+
+323
+00:34:41,880 --> 00:34:47,260
+صفر و واحد؟ ضرب اتنين و واحد هنا جامعة جامعة مش
+
+324
+00:34:47,260 --> 00:34:51,380
+ضاربة اه اه الصفر هي موجود اه الـ operation عليها
+
+325
+00:34:51,380 --> 00:34:59,970
+عملية جامعة وهي كده طيب هذا سؤال ستة و عشرين خدي
+
+326
+00:34:59,970 --> 00:35:05,470
+سؤال 28 بيقول لي هات لي كل الـ subgroups اللي الـ order
+
+327
+00:35:05,470 --> 00:35:12,450
+إلها 4 في z 4 external direct product مع z 4 يبقى
+
+328
+00:35:12,450 --> 00:35:23,690
+سؤال 28 28 بيقول لي find all subgroups بدنا الـ all
+
+329
+00:35:23,690 --> 00:35:25,970
+subgroups
+
+330
+00:35:28,190 --> 00:35:38,450
+of order أربعة in z أربعة external product مع z
+
+331
+00:35:38,450 --> 00:35:39,030
+أربعة
+
+332
+00:35:41,620 --> 00:35:45,240
+سؤال مرة ثانية زد أربعة كتير نضالك الـ product مع
+
+333
+00:35:45,240 --> 00:35:50,940
+زد أربعة فيها ستة عشر عنصر، مظبوط؟ الآن بدي كل الـ
+
+334
+00:35:50,940 --> 00:35:54,520
+sub groups اللي الـ order اللي لهم يساوي أربعة
+
+335
+00:35:54,520 --> 00:36:01,040
+تعالى نفكر احنا وإياكم تفكير بهذا الشكل الآن لو
+
+336
+00:36:01,040 --> 00:36:08,500
+جيت للعنصر اللي هو واحد و zero كداش الـ order له؟
+
+337
+00:36:12,150 --> 00:36:17,190
+أربعة يبقى هذا بيولد لي الـ sub group الـ order إلها
+
+338
+00:36:17,190 --> 00:36:24,710
+يساوي أربعة طيب لو جيت لـ zero و واحد أربعة يبقى
+
+339
+00:36:24,710 --> 00:36:32,030
+بالشكل اللي عندنا هنا طيب لو جيت لمين لـ الـ واحد و
+
+340
+00:36:32,030 --> 00:36:39,710
+واحد أربعة subgroup generated by واحد وواحد أربعة
+
+341
+00:36:39,710 --> 00:36:44,290
+طب لو قلت لك subgroup generated by واحد واتنين
+
+342
+00:36:44,290 --> 00:36:47,950
+أربعة
+
+343
+00:36:47,950 --> 00:36:54,390
+طب لو قلت لك subgroup generated by اتنين وواحد
+
+344
+00:36:54,390 --> 00:36:55,370
+أربعة
+
+345
+00:36:58,860 --> 00:37:06,840
+طب لو قلت لك subgroup generated by واحد و تلاتة
+
+346
+00:37:06,840 --> 00:37:15,150
+طيب لو قلت لك subgroup generated by تلاتة و واحد و
+
+347
+00:37:15,150 --> 00:37:18,010
+نفس الـ group زد أربع زد أربع هي نفسها اللي بسهل
+
+348
+00:37:18,010 --> 00:37:23,530
+العملية أي نعم جداش صاروا هدول اتنين أربع خمسة و
+
+349
+00:37:23,530 --> 00:37:28,910
+اتنين سبعة طيب خد لك هال group هذه مش زيهم cyclic
+
+350
+00:37:28,910 --> 00:37:35,170
+عادي زي ما جيبنا هذه لو جيت قلت لك zero و zero و
+
+351
+00:37:35,170 --> 00:37:41,510
+zero و اتنين و اتنين و zero و اتنين و اتنين تعال
+
+352
+00:37:41,510 --> 00:37:45,370
+في الأول نشوفها subgroup ولا لأ طبع الـ order اللي
+
+353
+00:37:45,370 --> 00:37:51,150
+هيها يساوي أربعة تمام لو جاتي لهذه اتنين و اتنين
+
+354
+00:37:51,150 --> 00:37:58,190
+جمعنا بصير كده اتنين و اتنين نربعها يعني لو بتضرب
+
+355
+00:37:58,190 --> 00:38:04,450
+العنصر في نفسه يبقى بيطلع 00 هي موجود طبعا طب لو
+
+356
+00:38:04,450 --> 00:38:10,590
+هذا مع هذا بصير الـ zero و أربعة يعني اتنين و zero
+
+357
+00:38:10,590 --> 00:38:17,320
+اتنين و zero هي موجود تمام؟ لو جيت قلت لي zero و
+
+358
+00:38:17,320 --> 00:38:21,400
+اتنين أو اتنين أو زيرو في هذا هتلاقي موجود تمام؟
+
+359
+00:38:21,400 --> 00:38:24,640
+طب لو هده ضربت بنفسه أربعة و أربعة هي zero و zero
+
+360
+00:38:24,640 --> 00:38:29,360
+يبقى هو الـ sub group على طول الخط لكن هدى مش زيهم
+
+361
+00:38:29,360 --> 00:38:34,860
+ماهياش cyclic تعال امسك أي element آخر اللي يمكن
+
+362
+00:38:34,860 --> 00:38:39,370
+تلاقي يجيبك ايه اش أربع عناظر فمثلا هات لي أي
+
+363
+00:38:39,370 --> 00:38:43,330
+element غير اللي قدامك في الـ group هذه نشوف وكم
+
+364
+00:38:43,330 --> 00:38:50,030
+عنصر بده يجيب يلا اختاروا أي رقم غير الارقام أي
+
+365
+00:38:50,030 --> 00:38:56,070
+عنصر غير العناصر هذه تلاتة و تلاتة موجودة تلاتة و
+
+366
+00:38:56,070 --> 00:39:03,230
+تلاتة تربيع يعني ستة و ستة جامعة يعني ستة و ستة
+
+367
+00:39:03,230 --> 00:39:09,010
+يعني اتنين و اتنين تلاتة و تلاتة كعيب يعني تسعة
+
+368
+00:39:10,910 --> 00:39:17,470
+تسعة و تسعة اللي هي واحد و واحد و واحد و واحد طيب
+
+369
+00:39:17,470 --> 00:39:25,890
+لو جيت قول تلاتة و تلاتة يبقى اللي هي تلاتة
+
+370
+00:39:25,890 --> 00:39:28,310
+و أربعة اللي هي الصفر و الصفر مظبوط اللي هو الـ
+
+371
+00:39:28,310 --> 00:39:33,010
+identity كمان هذه منهم ولا لا اه هذه طلعت كمان
+
+372
+00:39:33,010 --> 00:39:39,700
+منهم و قال لي كل الـ sub group اللي الـ order إلها طب
+
+373
+00:39:39,700 --> 00:39:46,380
+اتنين و اتنين ما هو
+
+374
+00:39:46,380 --> 00:39:49,860
+السهل إنك تحط العناصر قدامك و تبدأ تدور فيهم فيش
+
+375
+00:39:49,860 --> 00:39:51,200
+شغلة محددة
+
+376
+00:40:00,460 --> 00:40:03,360
+هذه الخطوة مختلفة عن هذه الخطوة وهي سهلة للغاية
+
+377
+00:40:03,360 --> 00:40:07,620
+لكن هذه الخطوة بتجيبها من أين؟ أنا بحط قدامي عناصر
+
+378
+00:40:07,620 --> 00:40:09,980
+الـ group اللي كلها زي أربعة كسنوات أو أربعة كسنوات
+
+379
+00:40:09,980 --> 00:40:10,200
+أو أربعة كسنوات أو أربعة كسنوات أو أربعة كسنوات أو
+
+380
+00:40:10,200 --> 00:40:12,500
+أربعة كسنوات أو أربعة كسنوات أو أربعة كسنوات أو
+
+381
+00:40:12,500 --> 00:40:12,720
+أربعة كسنوات أو أربعة كسنوات أو أربعة كسنوات أو
+
+382
+00:40:12,720 --> 00:40:13,140
+أربعة كسنوات أو أربعة كسنوات أو أربعة كسنوات أو
+
+383
+00:40:13,140 --> 00:40:17,680
+أربعة كسنوات أو أربعة
+
+384
+00:40:17,680 --> 00:40:23,570
+كسنوات أو أربعة كالحين دلت مننا ناله ثلاثة وثلاثة
+
+385
+00:40:23,570 --> 00:40:29,030
+الآن كمان هذه ثلاثة وثلاثة نسيناها يبقى الـ sub
+
+386
+00:40:29,030 --> 00:40:33,650
+group generated by ثلاثة وثلاثة طيب لأنه فيه
+
+387
+00:40:33,650 --> 00:40:37,850
+قبلها واحد وواحد لكن اثنين واثنين لا اثنين الـ
+
+388
+00:40:37,850 --> 00:40:40,770
+order إليها يساوي اثنين يبقى كل الـ sub groups
+
+389
+00:40:40,770 --> 00:40:47,050
+الممكنة اللي عندنا طيب لو جاء صفر وثلاثة
+
+390
+00:40:54,230 --> 00:40:59,930
+أه أربعة أربعة ليش ما تكونش منهم الـ صفر والثلاثة
+
+391
+00:40:59,930 --> 00:41:05,650
+والثلاثة وصفر كمان أه حط عليهم الـ صفر و
+
+392
+00:41:05,650 --> 00:41:13,310
+الثلاثة and ثلاثة وصفر طب ليش اختارت ثلاثة
+
+393
+00:41:13,310 --> 00:41:17,310
+ليش ما اختارت اثنين لأن ثلاثة والواحد هدول
+
+394
+00:41:17,310 --> 00:41:24,600
+relatively prime مع الـ main مع اللي هو أربعة يبقى هدول
+
+395
+00:41:24,600 --> 00:41:29,020
+كلهم اش ما تاخد صفر واحد وواحد وصفر أخدناه مش 
+
+396
+00:41:29,020 --> 00:41:32,440
+هيك هاي أول مبادئنا فيهم يبقى ما فيش مشكلة هيك
+
+397
+00:41:32,440 --> 00:41:36,700
+بيكون خلصنا كل اللي هو الـ subgroups اللي الـ order
+
+398
+00:41:36,700 --> 00:41:40,480
+اللي يساوي أربعة في الـ group اللي عندنا
+
+399
+00:41:51,560 --> 00:41:57,420
+طيب هذا سؤال ثمانية وعشرين سؤال اثنين وثلاثين
+
+400
+00:41:57,420 --> 00:42:04,380
+find a subgroup من z12, z4, z15 الـ order لها يساوي
+
+401
+00:42:04,380 --> 00:42:17,760
+تسعة يبقى سؤال اثنين وثلاثين بدنا subgroup of z12
+
+402
+00:42:19,790 --> 00:42:25,210
+External Direct Product مع زد أربعة External
+
+403
+00:42:25,210 --> 00:42:31,710
+Direct Product مع زد خمسة عشر
+
+404
+00:42:31,710 --> 00:42:38,590
+that has order
+
+405
+00:42:38,590 --> 00:42:48,190
+تسعة خلي
+
+406
+00:42:48,190 --> 00:42:52,930
+بالك هنا كويس خليني أسألكم سؤال ثاني، هل في
+
+407
+00:42:52,930 --> 00:42:58,470
+element هنا الـ order إيه اللي بيساوي تسعة؟ ولا بدي
+
+408
+00:42:58,470 --> 00:43:02,850
+أشوف، أنا بحكي عليه هادي بس، لأن تسعة دقيقة مش
+
+409
+00:43:02,850 --> 00:43:07,200
+اثناش ولا element هنا الـ order يساوي تسعة ولا
+
+410
+00:43:07,200 --> 00:43:11,520
+element هنا الـ order يساوي تسعة يبقى ما عنديش ولا
+
+411
+00:43:11,520 --> 00:43:15,920
+element الـ order يساوي تسعة في أي من الـ group
+
+412
+00:43:15,920 --> 00:43:20,920
+المنفردات الثلاثة اللي عندنا هذه طيب أنا مش هنجيب
+
+413
+00:43:20,920 --> 00:43:25,300
+الـ order تسعة مش هنجيب الـ order تسعة تبع هذه الـ
+
+414
+00:43:25,300 --> 00:43:33,410
+sub group بدي يكون عندي هدول ثلاثة ثلاثة أو ثلاثة
+
+415
+00:43:33,410 --> 00:43:35,850
+أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو
+
+416
+00:43:35,850 --> 00:43:39,370
+ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة
+
+417
+00:43:39,370 --> 00:43:42,410
+أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو
+
+418
+00:43:42,410 --> 00:43:43,570
+ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة
+
+419
+00:43:43,570 --> 00:43:44,930
+أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو ثلاثة أو
+
+420
+00:43:44,930 --> 00:43:53,390
+ثلاثة أو ثلاثة أو ثلاثة أو
+
+421
+00:43:53,390 --> 00:43:56,850
+ثلاثة
+
+422
+00:43:57,140 --> 00:44:01,440
+لو أخدت group الـ order إلها ثلاثة وواحدة الـ order
+
+423
+00:44:01,440 --> 00:44:05,140
+إلها واحد وواحدة الـ order إلها ثلاثة بيصير عندي
+
+424
+00:44:05,140 --> 00:44:12,590
+قد ايش الـ order للـ external product تسعة الـ order
+
+425
+00:44:12,590 --> 00:44:17,110
+للـ group كلها بصير تسعة مش باخدش elements باخد
+
+426
+00:44:17,110 --> 00:44:21,150
+group كاملة الـ order لها ثلاثة أو sub group تمام
+
+427
+00:44:21,150 --> 00:44:27,370
+يعني بناء عليه لا يمكن ألاقي sub group من الـ
+
+428
+00:44:27,370 --> 00:44:32,150
+groups هدول الـ order لها يساوي تسعة مش إمكانية لكن
+
+429
+00:44:32,150 --> 00:44:36,750
+بنعمل عملية تحايل بالداجة الأولى بدي أخد منها الـ
+
+430
+00:44:36,750 --> 00:44:41,020
+sub group الـ order لها يساوي ثلاثة ومن الثانية الـ
+
+431
+00:44:41,020 --> 00:44:45,020
+subgroup الـ order إلها يساوي ثلاثة أو ثلاثة في شيء
+
+432
+00:44:45,020 --> 00:44:48,760
+ممكن نقول واحد مثلا والثالثة بتاخد subgroup الـ
+
+433
+00:44:48,760 --> 00:44:51,760
+order إلها يساوي ثلاثة يبقى دول لو ضربتها مكون
+
+434
+00:44:51,760 --> 00:44:57,300
+جديش تسعة تقدر تجيب أه بقدر ليش لأن زد اثناش وزد
+
+435
+00:44:57,300 --> 00:45:01,820
+أربعة وزد خمسة عشر كلهم cyclic group وفي نظرية كانت في
+
+436
+00:45:01,820 --> 00:45:06,840
+chapter أربعة بتقولي أي subgroup من cyclic group
+
+437
+00:45:06,840 --> 00:45:11,380
+بتكون cyclic تمام باجي بقوله كويسة الآن لو جيت
+
+438
+00:45:11,380 --> 00:45:26,980
+أخطط الـ HBA subgroup of Z12 with order مثلا with
+
+439
+00:45:26,980 --> 00:45:39,970
+order ثلاثة and k is a subgroup من z4 with order
+
+440
+00:45:39,970 --> 00:45:49,510
+واحد والـ
+
+441
+00:45:49,510 --> 00:45:59,370
+subgroup من z15 with order واحد ثلاثة طبعا كله ممكن
+
+442
+00:45:59,370 --> 00:46:04,030
+لأن ثلاثة بتجسم الخمسة عشر والواحد بيجسم الأربعة
+
+443
+00:46:04,030 --> 00:46:11,990
+وثلاثة بتجسم الاثناش يعني for example for
+
+444
+00:46:11,990 --> 00:46:17,190
+example الـ
+
+445
+00:46:17,190 --> 00:46:21,450
+group generated by أربعة الـ order اللي قد ايش يساوي
+
+446
+00:46:21,450 --> 00:46:21,810
+هنا
+
+447
+00:46:24,580 --> 00:46:30,860
+ثلاثة تمام هاي ليش أربعة الـ صفر أربعة ثمانية يبقى
+
+448
+00:46:30,860 --> 00:46:37,000
+الـ order لها تساوي ثلاثة والـ صفر الـ order له
+
+449
+00:46:37,000 --> 00:46:43,230
+يساوي كده ايش واحد من الثانية هذه والثالثة بداخل من
+
+450
+00:46:43,230 --> 00:46:48,510
+خمسة عشر بداخل الـ group generated by خمسة الـ order
+
+451
+00:46:48,510 --> 00:46:54,250
+كمان يساوي كم؟ يساوي ثلاثة يبقى الـ order يساوي
+
+452
+00:46:54,250 --> 00:46:58,670
+ثلاثة بالشكل اللي عندنا هنا يبقى الـ least يبقى الـ
+
+453
+00:46:58,670 --> 00:47:04,610
+order للـ external direct product الـ order للـ
+
+454
+00:47:04,610 --> 00:47:13,540
+external direct product مع من؟ مع الـ صفر مع من؟
+
+455
+00:47:13,540 --> 00:47:18,280
+مع الـ subgroup generated by خمسة الـ order لها
+
+456
+00:47:18,280 --> 00:47:23,140
+يساوي الـ order للـ subgroup generated by أربعة لمن
+
+457
+00:47:23,140 --> 00:47:28,100
+الـ order لـ الـ صفر في الـ order للـ subgroup
+
+458
+00:47:28,100 --> 00:47:34,100
+generated by خمسة ويساوي ثلاثة في واحد في ثلاثة و
+
+459
+00:47:34,100 --> 00:47:38,660
+يساوي تسعة يبقى هي جبتله subgroup من الـ group
+
+460
+00:47:38,660 --> 00:47:44,260
+الأصلية الـ order إلها يساوي تسعة كان هذا سؤال
+
+461
+00:47:44,260 --> 00:47:46,360
+اثنين وثلاثين 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..44acf2dad16cfafa698a02de2262adee7e628cfd
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.json
@@ -0,0 +1 @@
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236.21, "end": 258.11, "text": "و كذلك ال a b بده يسوي a c implies ان ال a prime في ال a b بده يسوي ال a prime في ال a c من خاصية ال associativity هذا يعني ان ال a prime a", "tokens": [2407, 9122, 8848, 23275, 2423, 257, 272, 47525, 3224, 7251, 3794, 45865, 257, 269, 18779, 16472, 2423, 257, 5835, 8978, 2423, 257, 272, 47525, 3224, 7251, 3794, 45865, 2423, 257, 5835, 8978, 2423, 257, 269, 9154, 16490, 33546, 10632, 2423, 4180, 30142, 23758, 37495, 22653, 16472, 2423, 257, 5835, 257], "avg_logprob": -0.23590685690150542, "compression_ratio": 1.603305785123967, "no_speech_prob": 0.0, "words": [{"start": 236.21, "end": 236.59, "word": "و", "probability": 0.595703125}, {"start": 236.59, "end": 237.51, "word": " كذلك", "probability": 0.8116861979166666}, {"start": 237.51, "end": 238.31, "word": " ال", "probability": 0.8134765625}, {"start": 238.31, "end": 239.37, "word": " a", "probability": 0.38916015625}, {"start": 239.37, "end": 240.03, "word": " b", "probability": 0.40234375}, {"start": 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ضربت واحدة من اليمين و واحدة من الشمال، انت فريقش عننا بس إن كان الضرب من اليمين، الثاني من اليمين، الضرب من الشمال، الطرف التاني من الشمال زي ما أنت شايف", "tokens": [1211, 2407, 50239, 1829, 5296, 7435, 32887, 3555, 5551, 21292, 20292, 16472, 48812, 25513, 2655, 36764, 24401, 3660, 9154, 45595, 2304, 9957, 4032, 36764, 24401, 3660, 9154, 25124, 2304, 6027, 12399, 16472, 2655, 6156, 16572, 4587, 8592, 18871, 8315, 4724, 3794, 36145, 25961, 6024, 114, 25513, 9154, 45595, 2304, 9957, 12399, 6024, 104, 7649, 1829, 9154, 45595, 2304, 9957, 12399, 6024, 114, 25513, 9154, 25124, 2304, 6027, 12399, 41950, 28480, 16712, 7649, 1829, 9154, 25124, 2304, 6027, 30767, 1829, 19446, 14739, 2655, 13412, 995, 33911], "avg_logprob": -0.27416424349296925, "compression_ratio": 2.1266666666666665, "no_speech_prob": 0.0, "words": [{"start": 282.32, "end": 282.76, "word": "لو", "probability": 0.8193359375}, {"start": 282.76, "end": 283.06, "word": " قالي", "probability": 0.423248291015625}, {"start": 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بيساوي ال identity E هذا حسب تعريف من؟ حسب تعريف المعكوس الآن هذا ال element", "tokens": [6027, 39184, 316, 363, 4724, 1829, 3794, 995, 45865, 363, 316, 2423, 39184, 316, 363, 4724, 1829, 3794, 995, 45865, 363, 316, 4724, 1829, 3794, 995, 45865, 2423, 6575, 462, 293, 2423, 39184, 316, 383, 4724, 1829, 3794, 995, 45865, 383, 8978, 316, 4724, 1829, 3794, 995, 45865, 2423, 6575, 462, 23758, 11331, 35457, 37279, 16572, 5172, 9154, 22807, 11331, 35457, 37279, 16572, 5172, 9673, 3615, 4117, 41779, 6024, 48506, 23758, 2423, 4478], "avg_logprob": -0.26668075492253174, "compression_ratio": 1.8625954198473282, "no_speech_prob": 0.0, "words": [{"start": 506.86, "end": 507.36, "word": "الـ", "probability": 0.800048828125}, {"start": 507.36, "end": 507.74, "word": " A", "probability": 0.42578125}, {"start": 507.74, "end": 508.16, "word": " B", "probability": 0.5048828125}, {"start": 508.16, "end": 510.06, "word": " بيساوي", "probability": 0.38292236328125}, {"start": 510.06, "end": 510.58, "word": 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"start": 988.42, "end": 1017.28, "text": "بترجع مرة تانية لهذه النقاط الأساسية الثمانية لأن هذه الأساسية عندنا بتظل معانا طيلة شغلنا في علم الجبار من الآن فسعدم أن نتفق على هذه النقاط مرة أخرى يبقى النقطة الأخرى احنا بنشغل داخل ال group وليس داخل ال set of real number احنا بنشغل داخل ال group من ما كانت ال group تكون هذه", "tokens": [3555, 2655, 47341, 3615, 3714, 25720, 6055, 7649, 10632, 46740, 24192, 28239, 4587, 41193, 16247, 3794, 32277, 10632, 6024, 104, 2304, 7649, 10632, 5296, 33456, 29538, 16247, 3794, 32277, 10632, 43242, 8315, 39894, 19913, 1211, 20449, 7649, 995, 23032, 26895, 3660, 13412, 17082, 1211, 8315, 8978, 11203, 2304, 25724, 3555, 9640, 9154, 6024, 48506, 6156, 3794, 22488, 2304, 14739, 8717, 2655, 5172, 4587, 15844, 29538, 28239, 4587, 41193, 3714, 25720, 5551, 34740, 7578, 7251, 3555, 4587, 7578, 28239, 47432, 3660, 16247, 34740, 7578, 1975, 5016, 8315, 44945, 8592, 17082, 1211, 11778, 47283, 1211, 2423, 1594, 4032, 20292, 3794, 11778, 47283, 1211, 2423, 992, 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من الأن فساعدا هنرمزله بالرمز G inverse وليس G أسالب واحد يعني هذه ليست واحد على جي تمام ايوة مشان متوهش بين غسيل اكتب ل G inverse لا تساوي واحد على جي", "tokens": [3555, 39648, 45164, 25961, 2655, 10874, 1829, 10874, 32887, 3555, 4032, 47283, 3215, 2655, 18871, 9381, 2288, 10874, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 7251, 3555, 4587, 7578, 20449, 4117, 41779, 25724, 1829, 9154, 16247, 1863, 6156, 3794, 995, 22488, 995, 8032, 1863, 2288, 2304, 11622, 43761, 20666, 2288, 2304, 11622, 460, 17340, 4032, 20292, 3794, 460, 5551, 3794, 6027, 3555, 36764, 24401, 37495, 22653, 29538, 32239, 14851, 36764, 24401, 15844, 10874, 1829, 46811, 10943, 1975, 1829, 2407, 3660, 37893, 7649, 44650, 2407, 3224, 8592, 49374, 32771, 3794, 26895, 1975, 4117, 2655, 3555, 5296, 460, 17340, 20193, 6055, 3794, 995, 45865, 36764, 24401, 15844, 10874, 1829], "avg_logprob": -0.2586805414822366, "compression_ratio": 1.7345971563981042, "no_speech_prob": 0.0, "words": [{"start": 1018.1, "end": 1018.52, 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N positive integer عدد صحيح موجب يبقى المقصود ب G N هي G star G star G star G N من المرات يعني بدي أطبق ال binary operation على ال element هذا N من المرات", "tokens": [32640, 19452, 8978, 45030, 11242, 16712, 3615, 16572, 5172, 9307, 39896, 11296, 20328, 5016, 1829, 5016, 2423, 39184, 460, 17340, 36764, 24401, 15844, 460, 4724, 3794, 294, 2674, 2423, 28820, 10943, 23758, 32239, 3794, 20328, 5016, 1829, 5016, 995, 14111, 23032, 1829, 3555, 28239, 47432, 3660, 16712, 7649, 10632, 45164, 25961, 2655, 2423, 426, 3353, 24922, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 7251, 3555, 4587, 7578, 9673, 4587, 9381, 23328, 4724, 460, 426, 39896, 460, 3543, 460, 3543, 460, 3543, 460, 426, 9154, 9673, 2288, 9307, 37495, 22653, 4724, 16254, 5551, 9566, 3555, 4587, 2423, 17434, 6916, 15844, 2423, 4478, 23758, 426, 9154, 9673, 2288, 9307], "avg_logprob": -0.18046171681301013, "compression_ratio": 1.6561264822134387, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 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التالتة الـ A element في ال group G لو حطيت له الأس Zero بدي يعطيني دائما و أبدا ال identity element", "tokens": [6027, 1863, 47432, 3660, 16712, 6027, 2655, 3660, 2423, 39184, 316, 4478, 8978, 2423, 1594, 460, 45164, 11331, 9566, 36081, 46740, 16247, 3794, 17182, 4724, 16254, 7251, 3615, 9566, 1829, 22653, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 2423, 6575, 4478], "avg_logprob": -0.4274553713344392, "compression_ratio": 1.2213740458015268, "no_speech_prob": 0.0, "words": [{"start": 1070.75, "end": 1071.51, "word": "النقطة", "probability": 0.8935546875}, {"start": 1071.51, "end": 1072.51, "word": " التالتة", "probability": 0.93701171875}, {"start": 1072.51, "end": 1073.07, "word": " الـ", "probability": 0.4010009765625}, {"start": 1073.07, "end": 1073.29, "word": " A", "probability": 0.204833984375}, {"start": 1073.29, "end": 1073.89, "word": " element", "probability": 0.54833984375}, {"start": 1073.89, "end": 1074.15, "word": " في", "probability": 0.90087890625}, {"start": 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هذه ليست ضربة وإنما ما المقصود بيها Star GM Star GN يبقى GM زائد M", "tokens": [6027, 1863, 47432, 3660, 33962, 10943, 3794, 3660, 16609, 3714, 11242, 32887, 49401, 8978, 46411, 7251, 3555, 4587, 7578, 44945, 7435, 2304, 3615, 16247, 3794, 3794, 10874, 10943, 27884, 29538, 32239, 14851, 48812, 25513, 3660, 4032, 28814, 1863, 15042, 19446, 9673, 4587, 9381, 23328, 4724, 1829, 11296, 5705, 16609, 5705, 46411, 7251, 3555, 4587, 7578, 16609, 30767, 16373, 3215, 376], "avg_logprob": -0.2565317759748365, "compression_ratio": 1.3873239436619718, "no_speech_prob": 0.0, "words": [{"start": 1102.34, "end": 1103.58, "word": "النقطة", "probability": 0.836181640625}, {"start": 1103.58, "end": 1104.52, "word": " الخامسة", "probability": 0.940673828125}, {"start": 1104.52, "end": 1105.0, "word": " GM", "probability": 0.472412109375}, {"start": 1105.0, "end": 1105.76, "word": " مضروبة", "probability": 0.8914794921875}, {"start": 1105.76, "end": 1106.0, "word": " في", "probability": 0.869140625}, 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نروح نثبت صحة هذا الكلام يبقى باجي بقوله ل ال professor", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 39648, 46740, 8978, 2423, 1594, 460, 20449, 4117, 41779, 9673, 3615, 4117, 41779, 4724, 40228, 9566, 1829, 8315, 16247, 36520, 316, 17340, 16472, 5172, 2288, 3794, 4724, 40228, 9566, 1829, 8315, 316, 12174, 36150, 19446, 6055, 29245, 3215, 316, 9673, 3615, 4117, 41779, 6055, 3555, 3615, 3224, 7251, 3555, 4587, 7578, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995, 20449, 4117, 41779, 20449, 4117, 41779, 2423, 4478, 4724, 13546, 7435, 3615, 22653, 24976, 4478, 2564, 47525, 8315, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 2423, 28820, 10943, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 5296, 2423, 8304], "avg_logprob": -0.2660472946124034, "compression_ratio": 1.7321428571428572, "no_speech_prob": 0.0, "words": [{"start": 1745.53, "end": 1745.89, "word": "خلّيني", "probability": 0.6263671875}, {"start": 1745.89, "end": 1746.11, "word": " 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لل element اللي موجود في ال group أول شي بالبلد هيك قبل ما نكتب", "tokens": [7435, 16254, 41891, 12174, 36150, 14739, 8717, 44510, 10721, 8978, 2423, 39184, 1422, 17377, 82, 11331, 26108, 3660, 24525, 46007, 2423, 1668, 24976, 1594, 16070, 1668, 24976, 4478, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 1594, 5551, 12610, 44049, 20666, 36150, 3215, 39896, 4117, 12174, 36150, 19446, 8717, 4117, 2655, 3555], "avg_logprob": -0.28109976706596523, "compression_ratio": 1.4444444444444444, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 2131.09, "end": 2131.99, "word": "جديدة", "probability": 0.5848388671875}, {"start": 2131.99, "end": 2132.51, "word": " قبل", "probability": 0.99072265625}, {"start": 2132.51, "end": 2132.77, "word": " أن", "probability": 0.40869140625}, {"start": 2132.77, "end": 2133.29, "word": " نبدأ", "probability": 0.9464518229166666}, {"start": 2133.29, "end": 2133.55, "word": " في", "probability": 0.81640625}, {"start": 2133.55, "end": 2134.79, "word": " 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216630, "start": 2147.9, "end": 2166.3, "text": "لو أردت ال order لجروب فأذهب بعد عناصرها جداش ال order لجروب هو عدد العناصر في الجروب جروب فيها أربع عناصر يبقى ال order لها يساوي أربعة جروب فيها عشر عناصر يبقى ال order لها يساوي عشرة و هكذا", "tokens": [1211, 2407, 5551, 2288, 3215, 2655, 2423, 1668, 5296, 7435, 32887, 3555, 6156, 10721, 24192, 3555, 45030, 3215, 18871, 33546, 2288, 11296, 10874, 3215, 33599, 2423, 1668, 5296, 7435, 32887, 3555, 31439, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 8978, 25724, 32887, 3555, 10874, 32887, 3555, 8978, 11296, 5551, 25513, 3615, 18871, 33546, 2288, 7251, 3555, 4587, 7578, 2423, 1668, 5296, 11296, 7251, 3794, 995, 45865, 5551, 25513, 27884, 10874, 32887, 3555, 8978, 11296, 6225, 46309, 18871, 33546, 2288, 7251, 3555, 4587, 7578, 2423, 1668, 5296, 11296, 7251, 3794, 995, 45865, 6225, 8592, 25720, 4032, 8032, 4117, 15730], "avg_logprob": -0.2840909211322515, "compression_ratio": 2.2027027027027026, "no_speech_prob": 1.1920928955078125e-07, 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"أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب", "tokens": [10721, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 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{"start": 2203.42, "end": 2203.42, "word": " عدد", "probability": 0.9944661458333334}, {"start": 2203.42, "end": 2203.42, "word": " صحيح", "probability": 0.9892578125}, {"start": 2203.42, "end": 2203.42, "word": " موجب", "probability": 0.9944661458333334}, {"start": 2203.42, "end": 2203.42, "word": " أصغر", "probability": 0.9892578125}, {"start": 2203.42, "end": 2203.42, "word": " عدد", "probability": 0.994140625}, {"start": 2203.42, "end": 2203.6, "word": " صحيح", "probability": 0.98779296875}, {"start": 2203.6, "end": 2203.6, "word": " موجب", "probability": 0.9944661458333334}, {"start": 2203.6, "end": 2203.6, "word": " أصغر", "probability": 0.9896240234375}, {"start": 2203.6, "end": 2203.6, "word": " عدد", "probability": 0.9934895833333334}, {"start": 2203.6, "end": 2203.98, "word": " صحيح", "probability": 0.9857177734375}, {"start": 2203.98, "end": 2205.12, "word": " موجب", "probability": 0.99462890625}, {"start": 2205.12, "end": 2206.02, "word": " أصغر", "probability": 0.9892578125}, {"start": 2206.02, "end": 2209.64, "word": " عدد", "probability": 0.99267578125}, {"start": 2209.64, "end": 2210.58, "word": " صحيح", "probability": 0.984130859375}, {"start": 2210.58, "end": 2211.7, "word": " موجب", "probability": 0.9943033854166666}], "temperature": 1.0}, {"id": 90, "seek": 223805, "start": 2212.87, "end": 2238.05, "text": "G as the number of elements in G which is denoted by", "tokens": [38, 382, 264, 1230, 295, 4959, 294, 460, 597, 307, 1441, 23325, 538], "avg_logprob": -0.4118303507566452, "compression_ratio": 0.9122807017543859, "no_speech_prob": 0.0, "words": [{"start": 2212.87, "end": 2213.41, "word": "G", "probability": 0.225830078125}, {"start": 2213.41, "end": 2216.27, "word": " as", "probability": 0.10394287109375}, {"start": 2216.27, "end": 2216.47, "word": " the", "probability": 0.7470703125}, {"start": 2216.47, "end": 2221.29, "word": " number", "probability": 0.97119140625}, {"start": 2221.29, "end": 2222.95, "word": " of", "probability": 0.96923828125}, {"start": 2222.95, "end": 2228.95, "word": " elements", "probability": 0.89013671875}, {"start": 2228.95, "end": 2230.07, "word": " in", "probability": 0.4580078125}, {"start": 2230.07, "end": 2231.83, "word": " G", "probability": 0.83544921875}, {"start": 2231.83, "end": 2233.25, "word": " which", "probability": 0.8955078125}, {"start": 2233.25, "end": 2235.21, "word": " is", "probability": 0.96044921875}, {"start": 2235.21, "end": 2237.33, "word": " denoted", "probability": 0.952392578125}, {"start": 2237.33, "end": 2238.05, "word": " by", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 91, "seek": 226919, "start": 2242.8, "end": 2269.2, "text": "by جيه ما بين خطين و تقرأ ال order لجيه مش absolute value لجيه يبقى هذا هو ال order لجيه command definition تاني ال order لل element the order of an element of an element", "tokens": [2322, 10874, 1829, 3224, 19446, 49374, 16490, 9566, 9957, 4032, 6055, 4587, 2288, 10721, 2423, 1668, 5296, 7435, 1829, 3224, 37893, 8236, 2158, 5296, 7435, 1829, 3224, 7251, 3555, 4587, 7578, 23758, 31439, 2423, 1668, 5296, 7435, 1829, 3224, 5622, 7123, 6055, 7649, 1829, 2423, 1668, 24976, 4478, 264, 1668, 295, 364, 4478, 295, 364, 4478], "avg_logprob": -0.3437499916344358, "compression_ratio": 1.5416666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2242.8, "end": 2243.96, "word": "by", "probability": 0.2308349609375}, {"start": 2243.96, "end": 2245.12, "word": " جيه", "probability": 0.3988037109375}, {"start": 2245.12, "end": 2245.38, "word": " ما", "probability": 0.0966796875}, {"start": 2245.38, "end": 2245.74, "word": " بين", "probability": 0.97705078125}, {"start": 2245.74, "end": 2246.48, "word": " خطين", "probability": 0.8728841145833334}, {"start": 2246.48, "end": 2247.1, "word": " و", "probability": 0.23828125}, {"start": 2247.1, "end": 2247.7, "word": " تقرأ", "probability": 0.75628662109375}, {"start": 2247.7, "end": 2247.86, "word": " ال", "probability": 0.458740234375}, {"start": 2247.86, "end": 2248.36, "word": " order", "probability": 0.833984375}, {"start": 2248.36, "end": 2248.92, "word": " لجيه", "probability": 0.64739990234375}, {"start": 2248.92, "end": 2249.12, "word": " مش", "probability": 0.7890625}, {"start": 2249.12, "end": 2249.6, "word": " absolute", "probability": 0.86279296875}, {"start": 2249.6, "end": 2250.06, "word": " value", "probability": 0.984375}, {"start": 2250.06, "end": 2250.8, "word": " لجيه", "probability": 0.9031982421875}, {"start": 2250.8, "end": 2251.48, "word": " يبقى", "probability": 0.9417724609375}, {"start": 2251.48, "end": 2251.8, "word": " هذا", "probability": 0.89208984375}, {"start": 2251.8, "end": 2252.12, "word": " هو", "probability": 0.982421875}, {"start": 2252.12, "end": 2252.38, "word": " ال", "probability": 0.79443359375}, {"start": 2252.38, "end": 2252.96, "word": " order", "probability": 0.97265625}, {"start": 2252.96, "end": 2254.4, "word": " لجيه", "probability": 0.874755859375}, {"start": 2254.4, "end": 2255.14, "word": " command", "probability": 0.40673828125}, {"start": 2255.14, "end": 2255.86, "word": " definition", "probability": 0.94921875}, {"start": 2255.86, "end": 2256.58, "word": " تاني", "probability": 0.9309895833333334}, {"start": 2256.58, "end": 2256.98, "word": " ال", "probability": 0.3642578125}, {"start": 2256.98, "end": 2257.38, "word": " order", "probability": 0.96728515625}, {"start": 2257.38, "end": 2257.66, "word": " لل", "probability": 0.61181640625}, {"start": 2257.66, "end": 2258.18, "word": " element", "probability": 0.94921875}, {"start": 2258.18, "end": 2259.44, "word": " the", "probability": 0.68359375}, {"start": 2259.44, "end": 2261.08, "word": " order", "probability": 0.9619140625}, {"start": 2261.08, "end": 2262.98, "word": " of", "probability": 0.97900390625}, {"start": 2262.98, "end": 2264.6, "word": " an", "probability": 0.89990234375}, {"start": 2264.6, "end": 2266.86, "word": " element", "probability": 0.96533203125}, {"start": 2266.86, "end": 2268.22, "word": " of", "probability": 0.9384765625}, {"start": 2268.22, "end": 2268.64, "word": " an", "probability": 0.953125}, {"start": 2268.64, "end": 2269.2, "word": " element", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 92, "seek": 228758, "start": 2270.92, "end": 2287.58, "text": "اللي موجود في G is the smallest positive integer", "tokens": [6027, 20292, 3714, 29245, 23328, 8978, 460, 307, 264, 16998, 3353, 24922], "avg_logprob": -0.5366586355062631, "compression_ratio": 0.921875, "no_speech_prob": 0.0, "words": [{"start": 2270.92, "end": 2272.32, "word": "اللي", "probability": 0.247314453125}, {"start": 2272.32, "end": 2273.16, "word": " موجود", "probability": 0.96533203125}, {"start": 2273.16, "end": 2273.38, "word": " في", "probability": 0.93115234375}, {"start": 2273.38, "end": 2273.72, "word": " G", "probability": 0.28271484375}, {"start": 2273.72, "end": 2275.1, "word": " is", "probability": 0.284912109375}, {"start": 2275.1, "end": 2276.46, "word": " the", "probability": 0.72705078125}, {"start": 2276.46, "end": 2278.32, "word": " smallest", "probability": 0.9462890625}, {"start": 2278.32, "end": 2284.04, "word": " positive", "probability": 0.77783203125}, {"start": 2284.04, "end": 2287.58, "word": " integer", "probability": 0.935546875}], "temperature": 1.0}, {"id": 93, "seek": 232489, "start": 2317.95, "end": 2324.89, "text": "بنروح نكتب ال order لا جي بده يساوي ال in", "tokens": [3555, 1863, 32887, 5016, 8717, 4117, 2655, 3555, 2423, 1668, 20193, 10874, 1829, 47525, 3224, 7251, 3794, 995, 45865, 2423, 294], "avg_logprob": -0.5820312770930204, "compression_ratio": 0.9428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2317.9500000000003, "end": 2319.15, "word": "بنروح", "probability": 0.4825439453125}, {"start": 2319.15, "end": 2319.77, "word": " نكتب", "probability": 0.9810791015625}, {"start": 2319.77, "end": 2320.13, "word": " ال", "probability": 0.4912109375}, {"start": 2320.13, "end": 2320.71, "word": " order", "probability": 0.83740234375}, {"start": 2320.71, "end": 2321.35, "word": " لا", "probability": 0.31298828125}, {"start": 2321.35, "end": 2321.77, "word": " جي", "probability": 0.5982666015625}, {"start": 2321.77, "end": 2322.65, "word": " بده", "probability": 0.6953125}, {"start": 2322.65, "end": 2323.05, "word": " يساوي", "probability": 0.8831787109375}, {"start": 2323.05, "end": 2324.47, "word": " ال", "probability": 0.73779296875}, {"start": 2324.47, "end": 2324.89, "word": " in", "probability": 0.1239013671875}], "temperature": 1.0}, {"id": 94, "seek": 235110, "start": 2326.2, "end": 2351.1, "text": "في عندنا بعض ال notes البسيطة أول واحدة if the operation on g is addition is addition عملية الجامعة then", "tokens": [41185, 43242, 8315, 45030, 11242, 2423, 5570, 29739, 3794, 1829, 9566, 3660, 5551, 12610, 36764, 24401, 3660, 498, 264, 6916, 322, 290, 307, 4500, 307, 4500, 6225, 42213, 10632, 25724, 10943, 27884, 550], "avg_logprob": -0.1652113913613207, "compression_ratio": 1.2016806722689075, "no_speech_prob": 0.0, "words": [{"start": 2326.2, "end": 2326.44, "word": "في", "probability": 0.5087890625}, {"start": 2326.44, "end": 2326.78, "word": " عندنا", "probability": 0.6519775390625}, {"start": 2326.78, "end": 2327.16, "word": " بعض", "probability": 0.98876953125}, {"start": 2327.16, "end": 2327.34, "word": " ال", "probability": 0.9521484375}, {"start": 2327.34, "end": 2327.76, "word": " notes", "probability": 0.8291015625}, {"start": 2327.76, "end": 2329.44, "word": " البسيطة", "probability": 0.9869140625}, {"start": 2329.44, "end": 2330.36, "word": " أول", "probability": 0.769287109375}, {"start": 2330.36, "end": 2332.48, "word": " واحدة", "probability": 0.9716796875}, {"start": 2332.48, "end": 2333.48, "word": " if", "probability": 0.7744140625}, {"start": 2333.48, "end": 2335.5, "word": " the", "probability": 0.85546875}, {"start": 2335.5, "end": 2337.66, "word": " operation", "probability": 0.9697265625}, {"start": 2337.66, "end": 2339.96, "word": " on", "probability": 0.88037109375}, {"start": 2339.96, "end": 2341.3, "word": " g", "probability": 0.55029296875}, {"start": 2341.3, "end": 2342.92, "word": " is", "probability": 0.93994140625}, {"start": 2342.92, "end": 2343.74, "word": " addition", "probability": 0.951171875}, {"start": 2343.74, "end": 2345.56, "word": " is", "probability": 0.6845703125}, {"start": 2345.56, "end": 2348.02, "word": " addition", "probability": 0.86279296875}, {"start": 2348.02, "end": 2348.98, "word": " عملية", "probability": 0.9733072916666666}, {"start": 2348.98, "end": 2349.72, "word": " الجامعة", "probability": 0.8693033854166666}, {"start": 2349.72, "end": 2351.1, "word": " then", "probability": 0.806640625}], "temperature": 1.0}, {"id": 95, "seek": 238125, "start": 2370.23, "end": 2381.25, "text": "النقطة الثانية is the order of identity", "tokens": [6027, 1863, 47432, 3660, 6024, 104, 7649, 10632, 307, 264, 1668, 295, 6575], "avg_logprob": -0.305524542927742, "compression_ratio": 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-0.26548549852200914, "compression_ratio": 1.1, "no_speech_prob": 0.0, "words": [{"start": 2382.6, "end": 2383.26, "word": "Element", "probability": 0.5}, {"start": 2383.26, "end": 2385.72, "word": " E", "probability": 0.482177734375}, {"start": 2385.72, "end": 2387.56, "word": " is", "probability": 0.60302734375}, {"start": 2387.56, "end": 2388.6, "word": " واحدة", "probability": 0.7217610677083334}, {"start": 2388.6, "end": 2389.1, "word": " صحية", "probability": 0.9078776041666666}, {"start": 2389.1, "end": 2390.66, "word": " مقطة", "probability": 0.7918294270833334}, {"start": 2390.66, "end": 2391.86, "word": " تالتة", "probability": 0.905029296875}, {"start": 2391.86, "end": 2393.54, "word": " if", "probability": 0.658203125}, {"start": 2393.54, "end": 2396.22, "word": " there", "probability": 0.88525390625}, {"start": 2396.22, "end": 2396.7, "word": " is", "probability": 0.94970703125}, {"start": 2396.7, "end": 2400.5, "word": " if", "probability": 0.8544921875}, {"start": 2400.5, "end": 2400.92, "word": " there", "probability": 0.93115234375}, {"start": 2400.92, "end": 2401.48, "word": " is", "probability": 0.9638671875}, {"start": 2401.48, "end": 2402.44, "word": " no", "probability": 0.904296875}, {"start": 2402.44, "end": 2404.66, "word": " positive", "probability": 0.93798828125}, {"start": 2404.66, "end": 2407.48, "word": " integer", "probability": 0.94091796875}, {"start": 2407.48, "end": 2410.38, "word": " in", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 97, "seek": 242927, "start": 2411.81, "end": 2429.27, "text": "such that الـ G to the power N بده سوى ال identity then ال order لجي is infinite", "tokens": [39974, 300, 2423, 39184, 460, 281, 264, 1347, 426, 47525, 3224, 8608, 2407, 7578, 2423, 6575, 550, 2423, 1668, 5296, 7435, 1829, 307, 13785], "avg_logprob": -0.538125, "compression_ratio": 1.0105263157894737, "no_speech_prob": 0.0, "words": [{"start": 2411.81, "end": 2412.27, "word": "such", "probability": 0.047271728515625}, {"start": 2412.27, "end": 2413.79, "word": " that", "probability": 0.9560546875}, {"start": 2413.79, "end": 2417.31, "word": " الـ", "probability": 0.5362548828125}, {"start": 2417.31, "end": 2417.49, "word": " G", "probability": 0.373779296875}, {"start": 2417.49, "end": 2417.67, "word": " to", "probability": 0.2247314453125}, {"start": 2417.67, "end": 2417.91, "word": " the", "probability": 0.9228515625}, {"start": 2417.91, "end": 2418.29, "word": " power", "probability": 0.90185546875}, {"start": 2418.29, "end": 2418.57, "word": " N", "probability": 0.288330078125}, {"start": 2418.57, "end": 2418.99, "word": " بده", "probability": 0.5115966796875}, {"start": 2418.99, "end": 2419.31, "word": " سوى", "probability": 0.8828125}, {"start": 2419.31, "end": 2419.43, "word": " ال", "probability": 0.953125}, {"start": 2419.43, "end": 2420.33, "word": " identity", "probability": 0.56103515625}, {"start": 2420.33, "end": 2421.89, "word": " then", "probability": 0.47705078125}, {"start": 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ما علينا لسه بعيد عننا شوية يبقى باجي بقول ال order لل element U هو اصغر smallest و positive integer in such that g to the power n بده يساوي ال ايه و حدله الرمز", "tokens": [6027, 39184, 25905, 507, 13672, 7578, 10874, 36081, 32771, 13546, 3224, 3714, 6027, 1829, 8592, 11203, 995, 28671, 8978, 16095, 4032, 12174, 3215, 10943, 13412, 2407, 10632, 8032, 1863, 39648, 5296, 4117, 16472, 2423, 1668, 23758, 4724, 1829, 4587, 38251, 1975, 1829, 12602, 4587, 2304, 6055, 7649, 1829, 7251, 5016, 9566, 3224, 9122, 32277, 19986, 12610, 3224, 4032, 7251, 3615, 9566, 1829, 8315, 2423, 6575, 19446, 25894, 8315, 5296, 3794, 3224, 45030, 25708, 18871, 8315, 13412, 2407, 10632, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 2423, 1668, 24976, 4478, 624, 31439, 1975, 9381, 17082, 2288, 16998, 4032, 3353, 24922, 294, 1270, 300, 290, 281, 264, 1347, 297, 47525, 3224, 7251, 3794, 995, 45865, 2423, 1975, 1829, 3224, 4032, 11331, 3215, 43761, 34892, 2304, 11622], "avg_logprob": -0.30536416149514867, 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{"start": 2657.65, "end": 2658.07, "word": " هنقول", "probability": 0.8663736979166666}, {"start": 2658.07, "end": 2658.27, "word": " لك", "probability": 0.667236328125}, {"start": 2658.27, "end": 2658.45, "word": " ان", "probability": 0.5517578125}, {"start": 2658.45, "end": 2658.65, "word": " ال", "probability": 0.93408203125}, {"start": 2658.65, "end": 2659.09, "word": " order", "probability": 0.8662109375}, {"start": 2659.09, "end": 2659.61, "word": " هذا", "probability": 0.78955078125}, {"start": 2659.61, "end": 2660.57, "word": " بيقسم", "probability": 0.88916015625}, {"start": 2660.57, "end": 2661.05, "word": " اي", "probability": 0.642822265625}, {"start": 2661.05, "end": 2661.63, "word": " رقم", "probability": 0.99560546875}, {"start": 2661.63, "end": 2662.03, "word": " تاني", "probability": 0.8818359375}, {"start": 2662.03, "end": 2662.55, "word": " يحطه", "probability": 0.746337890625}, {"start": 2662.55, "end": 2663.09, "word": " كاسئوله", "probability": 0.70283203125}, 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{"start": 2668.73, "end": 2669.09, "word": " بقول", "probability": 0.893310546875}, {"start": 2669.09, "end": 2669.25, "word": " ال", "probability": 0.96875}, {"start": 2669.25, "end": 2669.59, "word": " order", "probability": 0.95849609375}, {"start": 2669.59, "end": 2669.87, "word": " لل", "probability": 0.4892578125}, {"start": 2669.87, "end": 2670.29, "word": " element", "probability": 0.9208984375}, {"start": 2670.29, "end": 2670.71, "word": " U", "probability": 0.5234375}, {"start": 2670.71, "end": 2671.07, "word": " هو", "probability": 0.9326171875}, {"start": 2671.07, "end": 2672.19, "word": " اصغر", "probability": 0.864990234375}, {"start": 2672.19, "end": 2673.47, "word": " smallest", "probability": 0.55224609375}, {"start": 2673.47, "end": 2673.91, "word": " و", "probability": 0.295654296875}, {"start": 2673.91, "end": 2674.51, "word": " positive", "probability": 0.54345703125}, {"start": 2674.51, "end": 2675.61, "word": " integer", "probability": 0.89990234375}, {"start": 2675.61, "end": 2676.29, "word": " in", "probability": 0.6982421875}, {"start": 2676.29, "end": 2676.69, "word": " such", "probability": 0.88134765625}, {"start": 2676.69, "end": 2677.01, "word": " that", "probability": 0.75390625}, {"start": 2677.01, "end": 2677.31, "word": " g", "probability": 0.08514404296875}, {"start": 2677.31, "end": 2677.51, "word": " to", "probability": 0.339599609375}, {"start": 2677.51, "end": 2677.69, "word": " the", "probability": 0.90869140625}, {"start": 2677.69, "end": 2677.95, "word": " power", "probability": 0.89892578125}, {"start": 2677.95, "end": 2678.21, "word": " n", "probability": 0.7119140625}, {"start": 2678.21, "end": 2678.49, "word": " بده", "probability": 0.5074462890625}, {"start": 2678.49, "end": 2678.87, "word": " يساوي", "probability": 0.80401611328125}, {"start": 2678.87, "end": 2679.03, "word": " ال", "probability": 0.489501953125}, {"start": 2679.03, "end": 2679.55, "word": " ايه", "probability": 0.7123616536458334}, {"start": 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خمستاش في تلاتة وخمسة واربعين يطلع أربعة", "tokens": [1829, 3555, 4587, 7578, 20666, 11242, 3555, 9566, 8608, 3555, 27884, 1975, 41779, 36764, 24401, 7251, 3794, 995, 45865, 8608, 3555, 27884, 31439, 8608, 3555, 27884, 6055, 2288, 21292, 3615, 7251, 3794, 995, 45865, 6055, 3794, 27884, 4032, 9640, 3555, 3615, 9957, 3714, 2407, 16254, 12610, 2407, 16490, 2304, 14851, 33599, 16490, 2304, 14851, 33599, 8978, 6055, 1211, 9307, 3660, 4032, 9778, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 7251, 9566, 1211, 3615, 5551, 25513, 27884], "avg_logprob": -0.2998798138056046, "compression_ratio": 1.8031496062992125, "no_speech_prob": 0.0, "words": [{"start": 3023.69, "end": 3025.03, "word": "يبقى", "probability": 0.62689208984375}, {"start": 3025.03, "end": 3025.39, "word": " بالضبط", "probability": 0.712158203125}, {"start": 3025.39, "end": 3026.01, "word": " سبعة", "probability": 0.7224934895833334}, {"start": 3026.01, "end": 3026.35, "word": " اوس", "probability": 0.3302001953125}, {"start": 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3117.28, "word": " كذلك", "probability": 0.9412434895833334}, {"start": 3117.28, "end": 3117.68, "word": " 4", "probability": 0.849609375}, {"start": 3117.68, "end": 3117.92, "word": " و", "probability": 0.7373046875}, {"start": 3117.92, "end": 3118.6, "word": " هكذا", "probability": 0.86083984375}, {"start": 3118.6, "end": 3119.32, "word": " طب", "probability": 0.869384765625}, {"start": 3119.32, "end": 3119.76, "word": " خلينا", "probability": 0.764892578125}, {"start": 3119.76, "end": 3120.14, "word": " نسأل", "probability": 0.9583740234375}, {"start": 3120.14, "end": 3120.3, "word": " ال", "probability": 0.90087890625}, {"start": 3120.3, "end": 3120.62, "word": " order", "probability": 0.9736328125}, {"start": 3120.62, "end": 3120.84, "word": " ل", "probability": 0.7109375}, {"start": 3120.84, "end": 3121.54, "word": " 11", "probability": 0.58349609375}, {"start": 3121.54, "end": 3126.74, "word": " 11", "probability": 0.6796875}, {"start": 3126.74, "end": 3126.9, "word": " و", "probability": 0.73388671875}, {"start": 3126.9, "end": 3127.34, "word": " 11", "probability": 0.87109375}, {"start": 3127.34, "end": 3129.74, "word": " 121", "probability": 0.841552734375}, {"start": 3129.74, "end": 3130.26, "word": " 121", "probability": 0.713623046875}, {"start": 3130.26, "end": 3130.42, "word": " مش", "probability": 0.7490234375}, {"start": 3130.42, "end": 3130.84, "word": " بتكسبها", "probability": 0.703857421875}, {"start": 3130.84, "end": 3131.24, "word": " 15", "probability": 0.8876953125}, {"start": 3131.24, "end": 3132.36, "word": " لأنها", "probability": 0.4623209635416667}, {"start": 3132.36, "end": 3132.8, "word": " بتكسبها", "probability": 0.9447021484375}, {"start": 3132.8, "end": 3133.42, "word": " 30", "probability": 0.96435546875}, {"start": 3133.42, "end": 3133.66, "word": " و", "probability": 0.7470703125}, {"start": 3133.66, "end": 3134.04, "word": " 30", "probability": 0.55419921875}, {"start": 3134.04, "end": 3134.78, "word": " يبقى", "probability": 0.943359375}], "temperature": 1.0}, {"id": 126, "seek": 314907, "start": 3135.31, "end": 3149.07, "text": "يبقى واحد يبقى ال order للإحداش هو اتنين و ال order للإحداش بده يساوي اتنين فقط و هكذا يلا بنكمل ان شاء الله بعد الظهر", "tokens": [1829, 3555, 4587, 7578, 36764, 24401, 7251, 3555, 4587, 7578, 2423, 1668, 24976, 28814, 24401, 33599, 31439, 1975, 2655, 1863, 9957, 4032, 2423, 1668, 24976, 28814, 24401, 33599, 47525, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 6156, 47432, 4032, 8032, 4117, 15730, 7251, 15040, 44945, 24793, 1211, 16472, 13412, 16606, 21984, 39182, 6024, 116, 3224, 2288], "avg_logprob": -0.1930614467394554, "compression_ratio": 1.5419847328244274, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3135.31, "end": 3135.87, "word": "يبقى", "probability": 0.84991455078125}, {"start": 3135.87, "end": 3136.15, "word": " واحد", "probability": 0.777587890625}, {"start": 3136.15, "end": 3136.35, "word": " يبقى", "probability": 0.82696533203125}, {"start": 3136.35, "end": 3136.45, "word": " ال", "probability": 0.802734375}, {"start": 3136.45, "end": 3136.71, "word": " order", "probability": 0.96728515625}, {"start": 3136.71, "end": 3137.29, "word": " للإحداش", "probability": 0.679107666015625}, {"start": 3137.29, "end": 3137.59, "word": " هو", "probability": 0.9345703125}, {"start": 3137.59, "end": 3138.49, "word": " اتنين", "probability": 0.9541015625}, {"start": 3138.49, "end": 3139.51, "word": " و", "probability": 0.416259765625}, {"start": 3139.51, "end": 3140.25, "word": " ال", "probability": 0.80078125}, {"start": 3140.25, "end": 3140.81, "word": " order", "probability": 0.97900390625}, {"start": 3140.81, "end": 3141.89, "word": " للإحداش", "probability": 0.9521484375}, {"start": 3141.89, "end": 3142.63, "word": " بده", "probability": 0.5670166015625}, {"start": 3142.63, "end": 3143.03, "word": " يساوي", "probability": 0.8204345703125}, {"start": 3143.03, "end": 3143.55, "word": " اتنين", "probability": 0.97998046875}, {"start": 3143.55, "end": 3144.03, "word": " فقط", "probability": 0.99267578125}, {"start": 3144.03, "end": 3144.29, "word": " و", "probability": 0.69482421875}, {"start": 3144.29, "end": 3145.25, "word": " هكذا", "probability": 0.95166015625}, {"start": 3145.25, "end": 3147.09, "word": " يلا", "probability": 0.641357421875}, {"start": 3147.09, "end": 3147.71, "word": " بنكمل", "probability": 0.9427083333333334}, {"start": 3147.71, "end": 3147.87, "word": " ان", "probability": 0.8603515625}, {"start": 3147.87, "end": 3148.19, "word": " شاء", "probability": 0.9873046875}, {"start": 3148.19, "end": 3148.31, "word": " الله", "probability": 0.96533203125}, {"start": 3148.31, "end": 3148.63, "word": " بعد", "probability": 0.916015625}, {"start": 3148.63, "end": 3149.07, "word": " الظهر", "probability": 0.9403076171875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3151.45875, "duration_after_vad": 2971.4431249999893}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aa0f572e72021946c040afd5be843668bba4085e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.srt
@@ -0,0 +1,1708 @@
+1
+00:00:21,290 --> 00:00:25,550
+بسم الله الرحمن الرحيم نكمل chapter عشرة اللي كنا
+
+2
+00:00:25,550 --> 00:00:30,790
+بنتحدث فيه المرة اللي فاتت و آخر مرة أعطينا نظرية
+
+3
+00:00:30,790 --> 00:00:34,710
+أو أول نظرية في ال isomorphism vs isomorphism
+
+4
+00:00:34,710 --> 00:00:38,270
+theorem ثم أخدنا بعد ذلك كرولري عليها و الآن
+
+5
+00:00:38,270 --> 00:00:42,690
+بنواصل في نفس ال chapter في هنا مثال بيقول هاتلي
+
+6
+00:00:42,690 --> 00:00:49,520
+كل ال homomorphism من z12 إلى z13يبقى بدي اقول
+
+7
+00:00:49,520 --> 00:00:59,220
+الحلقة التالية solution assume افترض ان الـ Phi من
+
+8
+00:00:59,220 --> 00:01:09,720
+Z12 الى Z13 هو homomorphism افترض ان هذا هو
+
+9
+00:01:09,720 --> 00:01:15,260
+homomorphism و بدي اعرف ما هو شكل هذه ال
+
+10
+00:01:15,260 --> 00:01:20,620
+homomorphismالان شكل الـ homomorphism هو الـ 5
+
+11
+00:01:20,620 --> 00:01:26,820
+يؤثر على element من مين؟ من Z12 ال element هذا قد
+
+12
+00:01:26,820 --> 00:01:32,060
+يكون 0، قد يكون 1، 2، 3، لغاية كدهش، لغاية كدهش،
+
+13
+00:01:32,060 --> 00:01:37,160
+لو افترضنا خمسة ده اقول five of خمسة الخمسة بقدر
+
+14
+00:01:37,160 --> 00:01:40,280
+اكتبها واحد زائد واحد زائد واحد زائد واحد زائد
+
+15
+00:01:40,280 --> 00:01:42,800
+واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد
+
+16
+00:01:42,800 --> 00:01:43,280
+واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد
+
+17
+00:01:43,280 --> 00:01:43,400
+واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد
+
+18
+00:01:43,400 --> 00:01:47,960
+واحدهي عملية الجمع اذا بقدر اقول مدام homomorphism
+
+19
+00:01:47,960 --> 00:01:50,960
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+20
+00:01:50,960 --> 00:01:55,880
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+21
+00:01:55,880 --> 00:01:57,780
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+22
+00:01:57,780 --> 00:02:01,180
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+23
+00:02:01,180 --> 00:02:02,820
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+24
+00:02:02,820 --> 00:02:03,020
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+25
+00:02:03,020 --> 00:02:03,760
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+26
+00:02:03,760 --> 00:02:05,080
+فاي اف واحد زاد فاي اف واحد زاد فاي اف واحد زاد
+
+27
+00:02:05,080 --> 00:02:10,530
+فاي اف واحد زاد فاي اإذا شكل ال homomorphism اللي
+
+28
+00:02:10,530 --> 00:02:14,930
+عندنا لو عرفت ما هو شكل ال five of one بكون عرفت
+
+29
+00:02:14,930 --> 00:02:23,210
+شكل مين اللي هو شكل ال homomorphism طيب we shall
+
+30
+00:02:24,890 --> 00:02:33,810
+Find نحاول ان نجد Form of Phi of 1 بدي اعرف ايه
+
+31
+00:02:33,810 --> 00:02:40,390
+شكل Phi of 1 اللي عندنا هنا طيب كويس الآن Phi of 1
+
+32
+00:02:40,390 --> 00:02:46,730
+موجودة في Z12 ولا في Z30؟زي التلاتين ممتاز جدا
+
+33
+00:02:46,730 --> 00:02:52,230
+يبقى ال order ل five of واحد بده يقسم ال order
+
+34
+00:02:52,230 --> 00:02:56,650
+للواحد مش هيك اخدنا ال order لل five of جي بيقسم
+
+35
+00:02:56,650 --> 00:03:03,370
+ال order لل جي لذلك بروح بقوله ال order لل five of
+
+36
+00:03:03,370 --> 00:03:10,990
+one divides ال order لل one ال order لل one قداش
+
+37
+00:03:15,020 --> 00:03:21,100
+معنى هذا الكلام ان ال order ل five of one بده
+
+38
+00:03:21,100 --> 00:03:26,880
+يساوي مادام يقسم اتناش يبغى قد يكون واحد وقد يكون
+
+39
+00:03:26,880 --> 00:03:33,880
+اتنينوقد يكون تلاتة اربعة طبعا واربعة كذلك فتقسم
+
+40
+00:03:33,880 --> 00:03:41,060
+اتناش خمسة ستة اتناش يبقى كل هدول قواسمين الاتناش
+
+41
+00:03:41,060 --> 00:03:45,100
+جبتها من العلاقة ال order لل five of one divides
+
+42
+00:03:45,100 --> 00:03:53,660
+ال order لل one but ولكن ال five of one هذا موجود
+
+43
+00:03:53,660 --> 00:04:00,840
+اين؟فزي التلاتين معناه هذا الكلام ان ال order لفاي
+
+44
+00:04:00,840 --> 00:04:04,260
+of one divide زي التلاتين
+
+45
+00:04:06,850 --> 00:04:11,550
+يبقى معنى هذا الكلام ان ال order للـfive of one
+
+46
+00:04:11,550 --> 00:04:16,830
+كذلك بدنا نشوف قواصم التلاتين اللي هي واحد واتنين
+
+47
+00:04:16,830 --> 00:04:23,790
+وتلاتة طبعا أربعة لأ ولكن تجينا خمسة وستة وعشرة
+
+48
+00:04:23,790 --> 00:04:31,370
+وخمستاشر وتلاتينكل هدول قواسمين قواسم اللي هو
+
+49
+00:04:31,370 --> 00:04:37,930
+التلاتين من الاتنين هدول مع بعض بقدر استنتج ان ال
+
+50
+00:04:37,930 --> 00:04:46,260
+orderللـ 5 of 1 اللي هو بده يساوي واحد واتنين
+
+51
+00:04:46,260 --> 00:04:53,600
+وتلاتة طبعا أربعة وخمسة لأو ستة بهذا الشكل في غير
+
+52
+00:04:53,600 --> 00:04:59,720
+هيك؟ مافيش يبقى هذه القواسم المشتركة ما بين ال two
+
+53
+00:04:59,720 --> 00:05:05,160
+orders يبقى كل احتمالات الممكنة لل order لل 5 of 1
+
+54
+00:05:05,160 --> 00:05:12,390
+ان يكون واحد واتنينو تلاتة و كذلك مين و كذلك ستة
+
+55
+00:05:12,390 --> 00:05:18,010
+هى العناصر او هى الأعداد او الأرقام المشتركة ما
+
+56
+00:05:18,010 --> 00:05:22,450
+بين النقطة الأولى و النقطة الثانية طيب في of one
+
+57
+00:05:22,450 --> 00:05:27,210
+احنا بنقول هذه قبل قليل موجودة وين في زي التلاتين
+
+58
+00:05:27,210 --> 00:05:32,150
+اذا بروح في زي التلاتين سهل جدا ادور على العناصر
+
+59
+00:05:32,150 --> 00:05:34,570
+اللى ال order إلها بدى يسوى مين
+
+60
+00:05:39,930 --> 00:05:45,210
+معنى هذا الكلام ان ال five of one قد يكون ال one
+
+61
+00:05:45,210 --> 00:05:51,810
+مظبوط لأن ال one ال order عليه عفوًا ستكون ال zero
+
+62
+00:05:51,810 --> 00:05:57,600
+وليس ال one قد يكون ال zeroتمام يبقى five of one
+
+63
+00:05:57,600 --> 00:06:02,280
+قد يكون zero ليش؟ لأن ال order لل zero سيكون كم؟
+
+64
+00:06:02,280 --> 00:06:07,000
+واحد طب مين ال element اللي ال order له يسوى
+
+65
+00:06:07,000 --> 00:06:13,020
+اتنين؟ هل يوجد غير الخمستاشة هذا؟ لأ يبقى zero أو
+
+66
+00:06:13,020 --> 00:06:18,900
+خمستاشة نجي للتلاتة مين العناصر اللي ال order لها
+
+67
+00:06:18,900 --> 00:06:24,460
+يسوى تلاتة في زي التلاتين؟ مين؟ عشرين طب و عشرة؟
+
+68
+00:06:25,460 --> 00:06:31,520
+وكمان عشرين لأن ال order للعشرة هو تلاتة وال order
+
+69
+00:06:31,520 --> 00:06:36,040
+للعشرين كذلك هو تلاتة ضايل عليه باسمين ال order
+
+70
+00:06:36,040 --> 00:06:43,180
+اللي هو ستة مين العنصر ال order يسوى ستة خمسة ماشي
+
+71
+00:06:43,180 --> 00:06:50,340
+موافقين طيب في غيره هذا بالمرة طيب ستة في خمسة
+
+72
+00:06:50,340 --> 00:06:51,440
+وعشرين بقداش
+
+73
+00:06:54,600 --> 00:06:58,200
+ما هي او خمسة مضعفات التلاتين ولا لا يبقى الخمسة
+
+74
+00:06:58,200 --> 00:07:05,280
+وعشرين منهم يبقى الخمسة وعشرين في غيرهم امسك كل
+
+75
+00:07:05,280 --> 00:07:09,940
+عناصر الـ Z تلاتين ما تجد الا عناصر هذه ال order
+
+76
+00:07:09,940 --> 00:07:14,940
+الوساء واحد ال order اتنين هذول اتنين تلاتة هذا
+
+77
+00:07:14,940 --> 00:07:20,350
+اللي هو الستة يبقى هي العناصركم واحدة دول؟ اربعة
+
+78
+00:07:20,350 --> 00:07:26,370
+وستة يعني معناته كم همومورفزم يكون عندنا؟ ستة
+
+79
+00:07:26,370 --> 00:07:38,710
+همومورفزم يبقى هنا اذا نحن لدينا ستة همومورفزم من
+
+80
+00:07:38,710 --> 00:07:45,850
+هم يبقى بدي اسميه فاي وان اف اكس بدي اساوي قداش
+
+81
+00:07:45,850 --> 00:07:53,930
+زيروالتانى بده يسمى فاي تو اف اكس يساوي الخمستاشر
+
+82
+00:07:53,930 --> 00:08:01,970
+اكس التالت اللى هو فاي ثري اف اكس بده يساوي عشرة
+
+83
+00:08:01,970 --> 00:08:09,740
+اكسعشر اكس وده خمساشر اكس الان الفاي أربعة of X
+
+84
+00:08:09,740 --> 00:08:17,560
+بده يسوى كده؟ بده يسوى عشرين اكس فاي خمسة of X بده
+
+85
+00:08:17,560 --> 00:08:25,640
+يسوى خمسة اكس والان في of .. والله في ستة of X بده
+
+86
+00:08:25,640 --> 00:08:30,660
+يسوى خمسة وعشرين اكس يبقى هذه الستة homomorphisms
+
+87
+00:08:31,360 --> 00:08:36,440
+اللي عندنا اللي استطعنا نستنتجهم من خلال معرفتنا
+
+88
+00:08:36,440 --> 00:08:41,200
+لشكل الـPhi 1 يبقى هدول جيبناهم من وين جيبناهم
+
+89
+00:08:41,200 --> 00:08:45,240
+الكلام اللي جالينه احنا انه Phi of X تساوي ال X في
+
+90
+00:08:45,240 --> 00:08:51,080
+Phi of 1 يبقى شيلت قيمة كل Phi of 1 وحطيت قيمتها
+
+91
+00:08:51,080 --> 00:08:56,380
+هنا وبالتالي حصلت على مين؟ على الستة homomorphisms
+
+92
+00:08:56,380 --> 00:09:04,110
+اللي عندنا تبعات هذه ال groupبدأ نيجي لآخر نظرية
+
+93
+00:09:04,110 --> 00:09:12,410
+في هذا ال section بتقول ما يأتي theorem every
+
+94
+00:09:12,410 --> 00:09:22,810
+normal subgroup of
+
+95
+00:09:22,810 --> 00:09:23,570
+A group
+
+96
+00:09:30,050 --> 00:09:41,470
+جي ملي جروب جي is the kernel is the kernel of a
+
+97
+00:09:41,470 --> 00:09:50,650
+homomorphism of a homomorphism of g in particular
+
+98
+00:09:50,650 --> 00:09:58,110
+in
+
+99
+00:09:58,110 --> 00:10:06,000
+particulara normal subgroup بقى a normal subgroup
+
+100
+00:10:06,000 --> 00:10:09,020
+بدي
+
+101
+00:10:09,020 --> 00:10:14,580
+أعطيها الرمز n a normal subgroup is the kernel is
+
+102
+00:10:14,580 --> 00:10:25,520
+the kernel of the mapping kernel of the mapping
+
+103
+00:10:26,970 --> 00:10:36,010
+اللي هو فاي من جي إلى جي موديولر N given by ..
+
+104
+00:10:36,010 --> 00:10:46,010
+given by فاي of جي بدي ساوي جي في ال N
+
+105
+00:10:59,320 --> 00:11:04,200
+نجي لنفس النظرية مرة تانية يبقى النظرية مرة تانية
+
+106
+00:11:04,200 --> 00:11:10,080
+بتقول every normal subgroup of a group G is the
+
+107
+00:11:10,080 --> 00:11:15,260
+kernel of a homomorphism of G يعني لو عندي normal
+
+108
+00:11:15,260 --> 00:11:19,940
+subgroup من a group G و ال G عليها homomorphism
+
+109
+00:11:19,940 --> 00:11:24,400
+لازم يكون ال normal subgroup اللي عندنا هي kernel
+
+110
+00:11:24,400 --> 00:11:30,150
+لواحد من mainمن الـ Homomorphism قلنا نعطيك توضيح
+
+111
+00:11:30,150 --> 00:11:35,050
+in particular كمثال على ذلك لو كانت ال N هي normal
+
+112
+00:11:35,050 --> 00:11:40,670
+subgroup يبقى ال N هي ال kernel لل function Phi من
+
+113
+00:11:40,670 --> 00:11:45,830
+G إلى G modulo N والتي تُعطى بالشكل التالي Phi of
+
+114
+00:11:45,830 --> 00:11:50,270
+G يسوى lift cost من ال factor group اللي عندنا
+
+115
+00:11:50,270 --> 00:12:00,200
+اللي هو من GNبدنا نحاول نثبت بعد ما نفرض ان ال N
+
+116
+00:12:00,200 --> 00:12:05,220
+is a normal subgroup من G بدنا نحاول نحسب ال
+
+117
+00:12:05,220 --> 00:12:11,660
+kernel لهذه ال Phi و نثبت انه ميناللي هو ال
+
+118
+00:12:11,660 --> 00:12:16,400
+subgroup اللي عندنا بالضبط تماما هذه يبقى باجي
+
+119
+00:12:16,400 --> 00:12:21,320
+بقوله أول شيء بدي أبيله أن هذا homomorphism و بعد
+
+120
+00:12:21,320 --> 00:12:25,640
+هيك بدي أروح أجيب main ال kernel له يبقى باجي
+
+121
+00:12:25,640 --> 00:12:30,240
+بقوله Phi is homomorphism هذا اللي بدي أروح إيه
+
+122
+00:12:30,240 --> 00:12:37,840
+أثبته لذلك لو روحت أخد Phi of G1 G2يبقى حسب
+
+123
+00:12:37,840 --> 00:12:48,240
+التعريف اللي عندنا بيصير G1 G2 في N طيب ليش؟ لأنها
+
+124
+00:12:48,240 --> 00:12:51,180
+normal لو ماكنتش normal اللي بصي كلامك مش صحيح
+
+125
+00:12:51,180 --> 00:13:00,160
+يبقى هذا الكلام بده يساوي G1 N في G2 N السبب في
+
+126
+00:13:00,160 --> 00:13:07,880
+ذلك since ال N is a normal subgroup من Gهذه هي الـ
+
+127
+00:13:07,880 --> 00:13:14,860
+Main لـ Phi of G1 وهذه Phi of G2 لذلك Phi
+
+128
+00:13:14,860 --> 00:13:22,340
+Homomorphism نحسب الـ Kernel لهذا الـ Phi يبقى هو
+
+129
+00:13:22,340 --> 00:13:30,090
+كل الـ X الموجودة في الـ Group G بحيث أناللي هو
+
+130
+00:13:30,090 --> 00:13:36,390
+Phi of X بده يساوي ال identity element تبع ال G
+
+131
+00:13:36,390 --> 00:13:43,090
+modulo N يبقى هذا الكلام كل ال X اللي موجودة في ال
+
+132
+00:13:43,090 --> 00:13:48,170
+group G such that ال Phi of X اللي هي مين عندنا ال
+
+133
+00:13:48,170 --> 00:13:54,090
+X N بده يساوي ال identity element تبع ال factor
+
+134
+00:13:54,090 --> 00:14:00,910
+group هذي اللي هو مينمن الـ identity هنا؟ N كويس
+
+135
+00:14:00,910 --> 00:14:06,230
+يبقى مادام N هذا شو معناه اللي بقول X N يساوي ال N
+
+136
+00:14:06,230 --> 00:14:11,550
+هذا الكلام صحيح إذا ال X موجودة في ال N يبقى هذا
+
+137
+00:14:11,550 --> 00:14:19,210
+اللي هو كل ال X اللي موجودة في G such ذات ال X
+
+138
+00:14:19,210 --> 00:14:25,430
+موجودة في ال Nيبقى هذا بدي يسوي ال in itself يبقى
+
+139
+00:14:25,430 --> 00:14:28,750
+معنى هذا الكلام الكيرني لهذا ال function هو عبارة
+
+140
+00:14:28,750 --> 00:14:33,530
+عن مين؟ عن ال normal subgroup اللي عمناه الآن في
+
+141
+00:14:33,530 --> 00:14:39,650
+two definitions آخر two definitions بيقول الأول ما
+
+142
+00:14:39,650 --> 00:14:47,530
+يأتي definition let ال h be a subgroup من ال group
+
+143
+00:14:47,530 --> 00:14:53,860
+Gيبقى هذا الـ sub-group من مين؟ من جيه الـ
+
+144
+00:14:53,860 --> 00:14:55,940
+Normalizer of
+
+145
+00:15:13,820 --> 00:15:17,340
+الشكل التالي هو
+
+146
+00:15:34,250 --> 00:15:44,750
+وبدنا نعرف التعريف الثاني and the centralizer يا
+
+147
+00:15:44,750 --> 00:15:55,570
+رحمكم الله and the centralizer of HNG is defined
+
+148
+00:15:55,570 --> 00:16:03,940
+byبنروح نعرفه على الشكل التالي الـ Centralizer للـ
+
+149
+00:16:03,940 --> 00:16:11,700
+H وكل الـ X اللي موجودة في G such that بحيث أن الـ
+
+150
+00:16:11,700 --> 00:16:19,560
+X H X inverse بده يساوي H itself لكل الـ H اللي
+
+151
+00:16:19,560 --> 00:16:26,680
+موجودة في ال subgroup H example
+
+152
+00:16:34,430 --> 00:16:42,450
+لت الـ H بي ايه ال sub group من G define a mapping
+
+153
+00:16:42,450 --> 00:16:50,810
+define a mapping define
+
+154
+00:16:50,810 --> 00:16:58,490
+a mapping ابسعي من ال normalizer بتبع ال H الى ال
+
+155
+00:16:58,490 --> 00:17:06,790
+inner atom morphismالـ Inner Atomorphism لمن؟ للـ
+
+156
+00:17:06,790 --> 00:17:20,490
+H باي إبساي of X بده يساوي فاي X where حيث الفاي X
+
+157
+00:17:20,490 --> 00:17:33,600
+من الـ H إلى His defined by as defined by five X
+
+158
+00:17:33,600 --> 00:17:45,700
+of H بده يساوي ال X H X H X inverse لكل ال H اللي
+
+159
+00:17:45,700 --> 00:17:53,880
+موجودة في capital H السؤال هو show that بيلي انه
+
+160
+00:17:54,950 --> 00:18:03,050
+النقطة الأولى إبساي is a homomorphism النقطة
+
+161
+00:18:03,050 --> 00:18:07,190
+الثانية بدنا
+
+162
+00:18:07,190 --> 00:18:17,090
+نثبت إن كيرنل للإبساي بد سواء ال centralizer of
+
+163
+00:18:17,090 --> 00:18:18,850
+main of it
+
+164
+00:19:09,240 --> 00:19:13,520
+نعود للتعريف اللى بين أيدنا هذا مرة تانية احنا
+
+165
+00:19:13,520 --> 00:19:18,240
+خدنا الـcentralizer لل element لكن ما خدناهوش لل
+
+166
+00:19:18,240 --> 00:19:22,220
+subgroup خدنا ال normalizer لل element لكن لل
+
+167
+00:19:22,220 --> 00:19:29,640
+subgroupومن هنا بدنا نجي نعطي تعريف لل centralizer
+
+168
+00:19:29,640 --> 00:19:34,680
+لل subgroup H وال normalizer كذلك لل subgroup H
+
+169
+00:19:34,680 --> 00:19:39,680
+التعريف بقول ما ياتي the normalizer of subgroup H
+
+170
+00:19:39,680 --> 00:19:45,220
+اللي أخدناها منجي هو عبارة عنthe set of all
+
+171
+00:19:45,220 --> 00:19:49,940
+elements x اللي belongs to G such that ال X H X
+
+172
+00:19:49,940 --> 00:19:55,460
+inverse بده يسوى من ال H يعني كل العناصر اللي
+
+173
+00:19:55,460 --> 00:20:01,460
+موجودة في G والتي تحقق هذه المعادلة بتكون هي عناصر
+
+174
+00:20:01,460 --> 00:20:06,820
+ال normalizer شو هذه العناصر هذه لو ضربتها في H من
+
+175
+00:20:06,820 --> 00:20:11,040
+جهة الشمال لو ضربت معكوسها في H من جهة الجميل تبقى
+
+176
+00:20:11,040 --> 00:20:17,940
+ال H كما هيإن حدث ذلك يبقى كل هذه العناصر بتعطين
+
+177
+00:20:17,940 --> 00:20:24,040
+إيمان الـ Normalizer طب السؤال هو هل ال identity
+
+178
+00:20:24,040 --> 00:20:28,180
+element موجود في ال normalizer؟ نعم ليش؟ ال
+
+179
+00:20:28,180 --> 00:20:32,980
+identity المعكوس تبع هو نفسه اضربه في ال subgroup
+
+180
+00:20:32,980 --> 00:20:36,840
+يمين و الله شمال تبقى ال subgroup كما هي لإن ال
+
+181
+00:20:36,840 --> 00:20:41,850
+identity موجود وراموجود في الـ H itself وبالتالي
+
+182
+00:20:41,850 --> 00:20:46,330
+أبسط حاجة عند ال identity element موجود في ال
+
+183
+00:20:46,330 --> 00:20:51,330
+normalizer أو أحد عناصر منه ال normalizer تعني دي
+
+184
+00:20:51,330 --> 00:20:55,330
+لل centralizer تبع ال subgroup H في G بنعرفه
+
+185
+00:20:55,330 --> 00:21:01,660
+كالتاليبارضه كل العناصر اللي موجودة في X بس عنا X
+
+186
+00:21:01,660 --> 00:21:07,960
+H X inverse بدي سوى mean H لكل ال H اللي موجودة في
+
+187
+00:21:07,960 --> 00:21:14,340
+H او ممكن اصيغ هذا مرة تانية و اقول لو ضربت في X
+
+188
+00:21:14,340 --> 00:21:21,600
+من جهة اليمين H بصيرال XH بدى يسوى مين؟ HX يعني كل
+
+189
+00:21:21,600 --> 00:21:29,300
+العناصر اللى موجودة في في G و اللى بتبقى commutes
+
+190
+00:21:29,300 --> 00:21:35,040
+مع جميع عناصر H بلا استثناء فلما أقول XH بقدر أقول
+
+191
+00:21:35,040 --> 00:21:42,500
+يسوى HX يبقى كل ال X's اللى موجودة في Gولكميوتس مع
+
+192
+00:21:42,500 --> 00:21:47,720
+جميع عناصر H بلا استثناء اذا هذا يختلف عن هذا ولو
+
+193
+00:21:47,720 --> 00:21:53,840
+انه في ظاهره كأنه هو لكن لو بدأجي اطبق هذا عمليا
+
+194
+00:21:53,840 --> 00:22:01,540
+بقول X H X inverse بقولش H بقول H one يعني element
+
+195
+00:22:01,540 --> 00:22:06,360
+تاني ليس بالضرورة يكون نفس ال element بس هنا نفس
+
+196
+00:22:06,360 --> 00:22:10,470
+ال element بالضبط تمامالأن الـ Centralizer جاء من
+
+197
+00:22:10,470 --> 00:22:14,850
+كلمة Center المركز و احنا عرفنا الـ Center كل
+
+198
+00:22:14,850 --> 00:22:18,910
+العناصر الـ commutes مع مين مع جميع العناصر إذا
+
+199
+00:22:18,910 --> 00:22:23,410
+هنا جبنا الـ Center لمن؟ للجروب و جبنا الـ
+
+200
+00:22:23,410 --> 00:22:26,850
+Centralizer ل element في الجروب بس هنا الـ
+
+201
+00:22:26,850 --> 00:22:31,250
+Centralizer لل subgroup كله يبقى كل ال X اللي
+
+202
+00:22:31,250 --> 00:22:36,070
+موجود في G و الذي يحقق المعادل X H X inverse بدي
+
+203
+00:22:36,070 --> 00:22:41,700
+سوى من؟ بدي سوى Hمثال يرتبط بالاتنين هذول بيقول خد
+
+204
+00:22:41,700 --> 00:22:47,100
+الاتش subgroup وعرفلي ده لإبساى من ال normalizer
+
+205
+00:22:47,100 --> 00:22:52,980
+لل inner atomorphism لجي باي إبساى of X يبقى هذا
+
+206
+00:22:52,980 --> 00:22:57,420
+normalizer عناصر اللي فيه يقول بدي أقول إبساى of X
+
+207
+00:22:57,420 --> 00:23:02,520
+بدي اوديها وين؟على ال inner ال inner هذا كل
+
+208
+00:23:02,520 --> 00:23:06,240
+العناصر اللي فيها عبارة عن functions و ال
+
+209
+00:23:06,240 --> 00:23:11,400
+functions هذه بتحقق العلاقة اللي عندنا هذه يبقى ال
+
+210
+00:23:11,400 --> 00:23:14,780
+inner عبارة عن في اكس من ال group او من ال sub
+
+211
+00:23:14,780 --> 00:23:19,540
+group الى نفسها بحيث ان ال a في اكس of h بده سوى
+
+212
+00:23:19,540 --> 00:23:22,960
+ال x اتش انفرطة خدناها قبل هيك يعني مش جديدة علينا
+
+213
+00:23:22,960 --> 00:23:29,710
+لكل ال h اللي موجود في gإذا إبساى of X بدي ساوي في
+
+214
+00:23:29,710 --> 00:23:35,770
+X قال يبينلي إن إبساى is a homomorphism يبقى بدروح
+
+215
+00:23:35,770 --> 00:23:43,560
+أثبتله من الخطوة الأولى يبقى ل proofوبدي اخد
+
+216
+00:23:43,560 --> 00:23:50,740
+النقطة الأولى بدي اخد a psi of حصل ضرب to elements
+
+217
+00:23:50,740 --> 00:23:56,400
+حسب ال operation اللي موجود عالميا على g يبقى هذا
+
+218
+00:23:56,400 --> 00:24:04,020
+الكلام بده يساوي phi x y حسب التعريفتمام؟ طيب
+
+219
+00:24:04,020 --> 00:24:08,860
+سيبلي هذه على الشكة و بدنا نرجع لها بعد قليل لو
+
+220
+00:24:08,860 --> 00:24:16,860
+جيت قولتلك في x y as a function of h ايش بدي
+
+221
+00:24:16,860 --> 00:24:24,020
+اعطيني؟ حسب التاريف x y h x y inverse يعني هذا
+
+222
+00:24:24,020 --> 00:24:31,360
+الكلام يعني x y h y inverse x inverse بالشكل اللي
+
+223
+00:24:31,360 --> 00:24:37,530
+عندنا هذاالان هذا بده اعتبره كله element واحد يبقى
+
+224
+00:24:37,530 --> 00:24:41,130
+لو اعتبرته كله element واحد بيصير هذا
+
+225
+00:24:48,320 --> 00:24:56,820
+اللي هو H Y inverse هذا الكلام بدي يساوي في X of
+
+226
+00:24:56,820 --> 00:25:03,280
+هذا كله اللي هو عبارة عن اين في Y as a function of
+
+227
+00:25:03,280 --> 00:25:10,910
+X يعني هذا بالضبط هو في X composition في Yكله as a
+
+228
+00:25:10,910 --> 00:25:16,810
+function of x لذلك كان عندنا مين؟ كان عندنا f psi
+
+229
+00:25:16,810 --> 00:25:26,610
+of x y بيسوي في x y يسوي يبقى في x y هو في x في
+
+230
+00:25:26,610 --> 00:25:33,470
+مين؟ في في yطب فاي إكس حسب ال definition لإب ساي
+
+231
+00:25:33,470 --> 00:25:38,930
+of إكس و الفاي of واي يبقى هي إب ساي of واي لذلك
+
+232
+00:25:38,930 --> 00:25:46,230
+الإب ساي is a homomorphism يبقى سائل إب ساي is a
+
+233
+00:25:46,230 --> 00:25:51,330
+homomorphismأنت هنا من النقطة الأولى النقطة
+
+234
+00:25:51,330 --> 00:25:56,050
+الثانية قال يحسب لل kernel تبع هذا الإبصاى يبقى
+
+235
+00:25:56,050 --> 00:26:01,070
+باجي بقوله ال kernel بتبع الإبصاى هو
+
+236
+00:26:06,680 --> 00:26:14,900
+يبقى كل الـ X الموجودة في Normalizer للـ H بحيث أن
+
+237
+00:26:14,900 --> 00:26:21,540
+صورتها Epsi of X بده يساوي الـ Identity Element
+
+238
+00:26:21,540 --> 00:26:27,200
+تبع الـ Innerطب شكل ال function في ال inner هيك أو
+
+239
+00:26:27,200 --> 00:26:32,220
+بمعنى أخر هيك يبقى ياش بد يكون ال identity تبع ال
+
+240
+00:26:32,220 --> 00:26:38,080
+inner هو مين ال inner نفسه مين ال inner نفسه هذا؟
+
+241
+00:26:38,990 --> 00:26:47,930
+هه ليس هو فاي اي ليش انه فاي اي of X فاي اي of X
+
+242
+00:26:47,930 --> 00:26:54,590
+بديساوي E H X inverse اللي هيعطيك ال H itself يبقى
+
+243
+00:26:54,590 --> 00:26:59,550
+هذا وعملتها لكوا قبل هيك أكتر من مرة عدة مرات يبقى
+
+244
+00:26:59,550 --> 00:27:05,190
+Psi of X بديساوي مين؟ فاي اي طب هذا الكلام بديساوي
+
+245
+00:27:05,190 --> 00:27:10,580
+مين؟بتساوي كل العناصر اللي موجودة في الـ
+
+246
+00:27:10,580 --> 00:27:16,960
+Normalizer للـ H بحيث ان ال Epsilon of X هي مين
+
+247
+00:27:16,960 --> 00:27:26,630
+فاي X بتساوي فاي Eأو بمعنى آخر هذه كل العناصر X
+
+248
+00:27:26,630 --> 00:27:33,910
+اللي موجودة في ال Normalizer للـH بحيث أن فاي X of
+
+249
+00:27:33,910 --> 00:27:40,830
+H بدها تساوي فاي E of H لكل الـH اللي موجود في
+
+250
+00:27:40,830 --> 00:27:46,670
+الـH بلا استثناء ليش عملت هك؟ لأن فاي X أصلا من
+
+251
+00:27:46,670 --> 00:27:52,320
+من؟ من الـH إلى الـH أو من الـH إلى الـH itselfهذا
+
+252
+00:27:52,320 --> 00:27:56,940
+الكلام بده يساوي كل العناصر اللي موجودة في الـ
+
+253
+00:27:56,940 --> 00:28:04,160
+Normalizer للـ H بحيث أن الـ X H X Inverse بده
+
+254
+00:28:04,160 --> 00:28:10,160
+يساوي الـ E H E Inverse لكل الـ H اللي Belongs to
+
+255
+00:28:10,160 --> 00:28:16,260
+من The H أو بمعنى آخر كل الـ X اللي موجودة في الـ
+
+256
+00:28:16,260 --> 00:28:22,480
+Normalizerاللي موجودة في الـ Normalizer للـ H بحيث
+
+257
+00:28:22,480 --> 00:28:29,360
+ان الـ X H X inverse يساوي هذي كلها بقداش؟ بـ H
+
+258
+00:28:29,360 --> 00:28:35,330
+لكل الـ H اللي موجود وان في H، السؤال هوطلّعلي في
+
+259
+00:28:35,330 --> 00:28:40,450
+تعريف الـcentralizer كل العناصر اللي موجودة في جيب
+
+260
+00:28:40,450 --> 00:28:46,890
+بحيث تحقق هذه العلاقة إذا هذا يعتبر الـmain يعتبر
+
+261
+00:28:46,890 --> 00:28:51,830
+الـcentralizer لمن؟ لـH يبقى هذا يعتبر
+
+262
+00:28:51,830 --> 00:28:59,930
+الـcentralizer لمن؟ لـH وهو المقلوب طبعا بالنخاطر
+
+263
+00:28:59,930 --> 00:29:05,520
+نحلنا احنا هيك انتهينا بنحلنا كمانأكمل سؤال من
+
+264
+00:29:05,520 --> 00:29:08,260
+مسائل التمرين
+
+265
+00:29:52,800 --> 00:30:00,460
+خد يا للسؤال التالي اللي هو السؤال أربعة عشر من
+
+266
+00:30:00,460 --> 00:30:12,960
+التمرين بقول X plane X plane Y اللي هو في من زد
+
+267
+00:30:12,960 --> 00:30:26,550
+اتناش إلى زد عشرة defined bydefined by phi of x
+
+268
+00:30:26,550 --> 00:30:36,310
+يساوي تلاتة x phi of x يساوي تلاتة x is not a
+
+269
+00:30:36,310 --> 00:30:42,610
+homomorphism اثبتلي ليش هذه ماهياش homomorphism
+
+270
+00:30:44,250 --> 00:30:48,310
+أحنا أخدنا نظريات الهمومورفزم الأساسيات اللي هما
+
+271
+00:30:48,310 --> 00:30:52,670
+تنتين واحدة فيها ست نقاط وواحدة فيها تسعة نقاط
+
+272
+00:30:52,670 --> 00:30:59,090
+يعني خمس عشر نقطة و أثبتناهم عمليا لو لجينا تناقض
+
+273
+00:30:59,090 --> 00:31:04,510
+بين هذا التعريف و أي نقطة من هذه التناقض بيبطل
+
+274
+00:31:04,510 --> 00:31:10,100
+يصير homomorphism، مظبوط؟هو يدعى لماذا هذا اللي
+
+275
+00:31:10,100 --> 00:31:14,560
+عرفناه بشكل انه هو homomorphism نقوله بسيطة تعالى
+
+276
+00:31:14,560 --> 00:31:21,680
+نشوف إيش ممكن يتناقض معنا طبعا احنا أخدنا اللي هو
+
+277
+00:31:21,680 --> 00:31:22,600
+solution
+
+278
+00:31:24,720 --> 00:31:31,180
+أخدنا اللي هو main sentence فى of الـG to the
+
+279
+00:31:31,180 --> 00:31:39,320
+power N بده يساوي فى of G كله to the power N هذا
+
+280
+00:31:39,320 --> 00:31:49,580
+الكلام لكل الـN اللى موجودة في Zمش هذه الخاصية رقم
+
+281
+00:31:49,580 --> 00:31:56,220
+اتنين في أول نظرية تمام يبقى هذه الخاصية نشوف هل
+
+282
+00:31:56,220 --> 00:32:01,440
+هذه الخاصية تنطبق على الدعاء انه homomorphism ولا
+
+283
+00:32:01,440 --> 00:32:09,180
+لا ماشي نقوله ماشي خدلي مثلا five of أربعة تكعيب
+
+284
+00:32:09,180 --> 00:32:16,000
+الأربعة موجودة في Z12وحطتلها أس in طبعا ال
+
+285
+00:32:16,000 --> 00:32:20,560
+operation اللي عزد 12 هي عملية من جامعة يبقى الأس
+
+286
+00:32:20,560 --> 00:32:27,880
+هذا بتحول الي يمين five of تلاتة في أربعة مش أربعة
+
+287
+00:32:27,880 --> 00:32:31,400
+أس تلاتة وإنما تلاتة ضرب أربعة تلاتة في أربعة
+
+288
+00:32:31,400 --> 00:32:39,200
+بقداش اتناش تاني قداشzero طب أول خاصية من خواص ال
+
+289
+00:32:39,200 --> 00:32:44,300
+homomorphism أن ال identity هو صوت ال identity صح
+
+290
+00:32:44,300 --> 00:32:47,820
+ولا لأ يبقى ال five of zero يساوي قداش هدى مباشرة
+
+291
+00:32:47,820 --> 00:32:54,440
+قداش zero ال zero تبع مين زد عشرة و هذا هو ال zero
+
+292
+00:32:54,440 --> 00:33:00,320
+تبع مين تبع زد اتناشر هذا الفرق بينهم طيب تعالى
+
+293
+00:33:00,320 --> 00:33:12,860
+خدلي five of أربعةالكل تكعيب يساوي تلاتة في فاي of
+
+294
+00:33:12,860 --> 00:33:21,680
+أربعة هذا الكلام يساوي تلاتة فيه نجي لفاي of أربعة
+
+295
+00:33:21,680 --> 00:33:29,660
+اللي تلاتة في أربعة يبقى هذا تلاتة في أربعةاللي هو
+
+296
+00:33:29,660 --> 00:33:34,960
+بده يساوي تلاتة في تلاتة في أربعة في قداش اتناش
+
+297
+00:33:34,960 --> 00:33:38,720
+هذي في الأول ولا في التانية في التانية مادام في
+
+298
+00:33:38,720 --> 00:33:43,580
+التانية يبقى هذا باتنين يعني هذا اتناشر موديله
+
+299
+00:33:43,580 --> 00:33:49,440
+عشرة يبقى هذا اتنين تلاتة في اتنين في قداش بستة
+
+300
+00:33:49,440 --> 00:33:54,080
+الستة موجودة في زد عشرة ميلي اتنين هدول ايش بقدر
+
+301
+00:33:54,080 --> 00:34:01,190
+استنتجإن الـ Phi of أربعة تكييب لا تسوى Phi of
+
+302
+00:34:01,190 --> 00:34:08,390
+أربعة لكل تكييب هذا يعني إن Phi of X بدى يسوى
+
+303
+00:34:08,390 --> 00:34:17,630
+تلاتة X is not a homomorphismطبعا يبقى هذا كان
+
+304
+00:34:17,630 --> 00:34:27,570
+سؤال اربعتاشر من الكتاب خدلي سؤال تاني سؤال خمسة
+
+305
+00:34:27,570 --> 00:34:34,950
+وتلاتين سؤال خمسة وتلاتين بيقول prove that the
+
+306
+00:34:34,950 --> 00:34:39,690
+mapping النقطة الأولى prove that
+
+307
+00:34:55,650 --> 00:35:04,990
+Proof Proof that the mapping Phi من Z external
+
+308
+00:35:04,990 --> 00:35:16,770
+product لZ إلى Z given byوالمعطاه بالتعريف التالي
+
+309
+00:35:16,770 --> 00:35:25,330
+Phi of A وB بديساوي الـ A ناقص الـ B as a
+
+310
+00:35:25,330 --> 00:35:32,810
+homomorphism النقطة الثانية النقطة
+
+311
+00:35:32,810 --> 00:35:40,970
+الثانية Find ال kernel لـ Phi النقطة التالتة
+
+312
+00:35:40,970 --> 00:35:42,770
+Describe
+
+313
+00:35:45,300 --> 00:35:53,960
+describe the set اللي هو في
+
+314
+00:35:53,960 --> 00:35:56,820
+انفرس من تلاتة
+
+315
+00:36:38,410 --> 00:36:43,810
+السؤال مرة تانية في عندنا function من z اكترين او
+
+316
+00:36:43,810 --> 00:36:48,150
+like product مع z الى z موطع بالشكل التاليفي of a
+
+317
+00:36:48,150 --> 00:36:53,730
+و b بده يسوى ال a ناقص ال b وهدي homomorphism بدنا
+
+318
+00:36:53,730 --> 00:36:57,550
+نثبتهابعد أن نثبت تهمورفازيا بنا نجيب لها ال
+
+319
+00:36:57,550 --> 00:37:02,370
+kernel بعد ال kernel بنا نوصف مين هي ال 6 اللي
+
+320
+00:37:02,370 --> 00:37:07,330
+عندنا هذه خلينا مع النقطة الأولى بجباجي للنقطة
+
+321
+00:37:07,330 --> 00:37:13,150
+الأولىمشان اثبتها انها homomorphism بدروح اخد fi
+
+322
+00:37:13,150 --> 00:37:19,290
+of بداخل عنصر اول يبقى بقوله ال a و ال b ال
+
+323
+00:37:19,290 --> 00:37:24,310
+operation اللي عزدها دي كلها هي عملية من الجامع
+
+324
+00:37:24,310 --> 00:37:31,170
+ولا الضرب الجامع يبقى بدروح اقوله زائد c و d
+
+325
+00:37:31,170 --> 00:37:36,880
+بالشكل اللي عندنايبقى هي أخد تأثير الفاي على two
+
+326
+00:37:36,880 --> 00:37:42,980
+elements هذا الكلام بده يساوي في of هذا بده يجمع
+
+327
+00:37:42,980 --> 00:37:53,700
+component wise يبقى a زائد c و b زائد d حسب تعريف
+
+328
+00:37:53,700 --> 00:38:01,650
+الفاي اللي عندنا هذا يبقى الأول ناقص الثانييعني
+
+329
+00:38:01,650 --> 00:38:09,750
+مين؟ يعني ال A زائد ال C نقص ال B نقص ال D اللي
+
+330
+00:38:09,750 --> 00:38:15,910
+بقدر أكتبها على الشكل التالي ال A نقص ال B في قوس
+
+331
+00:38:15,910 --> 00:38:23,130
+وال C نقص ال D في قوس أخر السؤال هو هذا هو التعريف
+
+332
+00:38:23,130 --> 00:38:31,810
+اللي فوقيبقى هذا الكلام Phi of A وB زائد التاني
+
+333
+00:38:31,810 --> 00:38:38,930
+Phi of C وD لذلك Phi is A homomorphism بدنا نروح
+
+334
+00:38:38,930 --> 00:38:45,430
+نجيب له mainالكيرنل للفاي يبقى الكيرنل للفاي كل
+
+335
+00:38:45,430 --> 00:38:52,910
+العناصر a و b اللي موجودة في z external by product
+
+336
+00:38:52,910 --> 00:39:01,890
+مع z such that الفاي of a و b بده يسوى ال identity
+
+337
+00:39:01,890 --> 00:39:06,950
+element تبع man تبع ال z من ال identity element
+
+338
+00:39:06,950 --> 00:39:14,180
+تبع ال z اللي هو ال zeroطيب هذا الكلام كل العناصر
+
+339
+00:39:14,180 --> 00:39:21,380
+a و b اللي موجودة في z external like product مع z
+
+340
+00:39:21,380 --> 00:39:28,600
+such that ال a ناقص ال b بده يساوي ال zeroيبقى كل
+
+341
+00:39:28,600 --> 00:39:34,560
+العناصر a وb اللي موجودة في z external like
+
+342
+00:39:34,560 --> 00:39:41,870
+product مع z such that ال a تساوي ال bيعني
+
+343
+00:39:41,870 --> 00:39:46,250
+المُركّبة الأولى تسوى مين؟ المُركّبة الثانية يبقى
+
+344
+00:39:46,250 --> 00:39:52,950
+هذا الكلام يبقى the set of all a و a such ذات ال a
+
+345
+00:39:52,950 --> 00:39:59,710
+عنصر من مين؟ من ال z المُركّبتين زي بعض يبقى the
+
+346
+00:39:59,710 --> 00:40:04,510
+set of all are pair a و a b و b c و c زي ما بدك
+
+347
+00:40:04,510 --> 00:40:07,410
+يعني بيطلعوا هدول عناصر منهم
+
+348
+00:40:11,840 --> 00:40:19,580
+ونقص اتنين ونقص واحد ونقص واحد وزيرو وزيرو وكذلك
+
+349
+00:40:19,580 --> 00:40:25,640
+واحد وواحد اتنين واتنين وهكذا الى ما شاء الله نعم
+
+350
+00:40:25,640 --> 00:40:30,640
+هذه كلها عناصر من عناصر الكيرن يعني كم عنصر فيه
+
+351
+00:40:31,430 --> 00:40:35,790
+مالة نهاية من ال elements يبقى ال order لل kernel
+
+352
+00:40:35,790 --> 00:40:41,730
+في هذه الحالة infinite وليس finite حسب ناله ال
+
+353
+00:40:41,730 --> 00:40:48,490
+kernel مطلوب التاني بدنا نروح للمطلوب التالت ايش
+
+354
+00:40:48,490 --> 00:40:54,910
+بقول هنا هاتل الست اللي عندنا هذه باجي بيقوله ال
+
+355
+00:40:54,910 --> 00:41:01,420
+phi inverse of تلاتةال fire inverse of ثلاثة
+
+356
+00:41:01,420 --> 00:41:05,900
+موجودة و هنا يا شبابفي زد والله في زد external
+
+357
+00:41:05,900 --> 00:41:09,400
+like a product مع زد في ال external لأن هذا
+
+358
+00:41:09,400 --> 00:41:16,380
+بترجعها من زد إلى يبجي كل العناصر the set of all
+
+359
+00:41:16,380 --> 00:41:21,960
+elements a و b اللي موجودة في زد external like a
+
+360
+00:41:21,960 --> 00:41:30,840
+product مع زد such that بحيث ان ال fi of a و b
+
+361
+00:41:30,840 --> 00:41:40,480
+بدها تسوي تلاتةمظبوط يبقى كل العناصر اللي صورتها
+
+362
+00:41:40,480 --> 00:41:46,980
+بدها تساوي تلاتة يعني مين يعني كل العناصر a و b
+
+363
+00:41:46,980 --> 00:41:53,920
+اللي موجودة في z external like product إلى z such
+
+364
+00:41:53,920 --> 00:41:59,520
+that fi of a و b اللي هو مين ال a ناقص ال b بده
+
+365
+00:41:59,520 --> 00:42:08,660
+يساوي مينيبقى هذا الكلام كل العناصر a وb اللي
+
+366
+00:42:08,660 --> 00:42:15,580
+موجودة في z external by product مع z such ذات ال a
+
+367
+00:42:15,580 --> 00:42:22,760
+بدها تساوي ال b زائد التلاتةيعني بالبلد يطلع من
+
+368
+00:42:22,760 --> 00:42:29,360
+هدول يبقى هدول the set of all المُركّبة الأولى بدا
+
+369
+00:42:29,360 --> 00:42:35,160
+تبقى بي زائد تلاتة والمُركّبة التانية اللي هي مين
+
+370
+00:42:35,160 --> 00:42:42,400
+اللي هي بي itself و ال بي هذه موجودة وان موجود في
+
+371
+00:42:42,400 --> 00:42:49,430
+زد يعني خدلي أي رقم موجود في زدوحط هو المركبة
+
+372
+00:42:49,430 --> 00:42:54,330
+التانية وحط للمركبة الأولى نفس هذه المركبة واضيف
+
+373
+00:42:54,330 --> 00:42:58,650
+عليها ماذا؟ اضيف عليها .. كم عنصر هدول بيطلعون؟
+
+374
+00:42:58,650 --> 00:43:03,490
+برضه مالة نهاية يبني مالة نهاية من العناصر كلهم
+
+375
+00:43:03,490 --> 00:43:08,810
+يروح لماذا؟ للعنصر التلاتة أو لصورتهم بتكون تلاتة
+
+376
+00:43:09,160 --> 00:43:14,200
+خدلي سؤال قريب يعني أو حوالين هذا السؤال كمان
+
+377
+00:43:14,200 --> 00:43:20,620
+السؤال اللى بعضه على طوله سؤال 36 بيقولي suppose
+
+378
+00:43:20,620 --> 00:43:31,010
+that suppose that افترض انه ال five منZ external
+
+379
+00:43:31,010 --> 00:43:38,050
+by-product إلى Z لمين لا group G وعليها عملية
+
+380
+00:43:38,050 --> 00:43:53,290
+الجامعة is a homomorphism such that بحيث أن الـ
+
+381
+00:43:53,290 --> 00:43:56,230
+Phi of تلاتة واثنين
+
+382
+00:44:17,490 --> 00:44:25,890
+سؤال مرة تانيةجال افترض في عنا function في من زد
+
+383
+00:44:25,890 --> 00:44:30,970
+external like product مع زد إلى group مين ماكانت
+
+384
+00:44:30,970 --> 00:44:35,090
+ال group ماحددش شكلها لكن ال operation اللي عليها
+
+385
+00:44:35,090 --> 00:44:41,070
+اللي هي عملية منعملية الجمع تمام افترض ان هذا هو
+
+386
+00:44:41,070 --> 00:44:46,650
+homomorphism وعندي ان في of تلاتة واثنين بده يساوي
+
+387
+00:44:46,650 --> 00:44:52,430
+ال a طبعا ال a وين موجودة لان في g وعندي في of
+
+388
+00:44:52,430 --> 00:44:56,330
+اتنين واحد اللي موجودة اللي بده تساوي بيه موجودة
+
+389
+00:44:56,330 --> 00:45:01,330
+في g كذلك قالي هت لل في of اربعة واربعةطبعا
+
+390
+00:45:01,330 --> 00:45:05,290
+الفيديو في اربع واربع حاجيهم دلالة مين؟ A و B لإن
+
+391
+00:45:05,290 --> 00:45:10,390
+A و B أنا مش عارفهم يعني عناصر، مين هم؟ الله أعلم
+
+392
+00:45:10,390 --> 00:45:13,930
+بحالهما، يبقى باجي بقول solution
+
+393
+00:45:19,590 --> 00:45:24,750
+بدي أحاول أستفيد من المعطيات اللي عندنا five of
+
+394
+00:45:24,750 --> 00:45:29,590
+تلاتة و اتنين و five of اتنين و واحد و أربطهم بمين
+
+395
+00:45:29,590 --> 00:45:37,770
+بfive of أربعة و أربعة الأن لو جيت ليه ال five of
+
+396
+00:45:37,770 --> 00:45:46,570
+تلاتة و اتنين ناقص five of اتنين و واحد أشوف قداش
+
+397
+00:45:46,570 --> 00:45:48,390
+هذا الكلام بده يساوي
+
+398
+00:45:52,580 --> 00:45:57,700
+هذا ال element موجود في جي و هذا ال element موجود
+
+399
+00:45:57,700 --> 00:46:02,720
+في جي اذا المجموع تبعهم او الفرق بينهم هذا معكوس
+
+400
+00:46:02,720 --> 00:46:06,980
+سالب ال phi of اتنين و احد هو معكوس ال phi of
+
+401
+00:46:06,980 --> 00:46:10,140
+اتنين و احد لان ال operation اللي عليها عملية جي
+
+402
+00:46:10,140 --> 00:46:14,820
+وبالتالي ماحدش الا اعتراض عنها السؤال هو مش phi
+
+403
+00:46:14,820 --> 00:46:22,510
+homomorphism يبقى هذا معناه phi ofالتلاتة و اتنين
+
+404
+00:46:22,510 --> 00:46:29,070
+بدي اطرح منها اتنين و واحد يسوى five of اللي هو
+
+405
+00:46:29,070 --> 00:46:36,210
+مين تلاتة ناقص اتنين و اتنين ناقص واحد يبقى هذا
+
+406
+00:46:36,210 --> 00:46:45,190
+الكلام بدي يسوى five of واحد واحدإذا الفرق ما بين
+
+407
+00:46:45,190 --> 00:46:50,570
+الصورتين هدول تلاتية صورة العنصر واحد وواحد الان
+
+408
+00:46:50,570 --> 00:46:56,470
+الواحد وواحد له علاقة بالفاي اربعة واربعة بقدر
+
+409
+00:46:56,470 --> 00:46:59,690
+أجيب العلاقة اللي بتربط منهم توقبل يا قليل إذا
+
+410
+00:46:59,690 --> 00:47:04,750
+كنتم ذاكرين قولنا في of x يسوى ال x في في of one
+
+411
+00:47:04,960 --> 00:47:10,380
+يبقى نفس المفهوم اللي عندنا، الأن بروح أخدله five
+
+412
+00:47:10,380 --> 00:47:16,620
+of أربعة وأربعة، أليست أربعة في ال five of one
+
+413
+00:47:16,620 --> 00:47:24,470
+one؟طيب احنا طلعنا هنا الـ five of one و one اللي
+
+414
+00:47:24,470 --> 00:47:32,050
+هو الفرق ما بين الاتنين هدول يبقى هذه العلاقة رقم
+
+415
+00:47:32,050 --> 00:47:37,170
+واحد بدي اجيب العلاقة اللي فوق لما اقول five of
+
+416
+00:47:37,170 --> 00:47:43,230
+تلاتة و اتنين ناقص five of اتنين و واحد أليس ال A
+
+417
+00:47:43,230 --> 00:47:49,350
+ناقص ال B؟ مش الاولة A والتانية Bيبقى هذه العلاقة
+
+418
+00:47:49,350 --> 00:47:54,410
+اللى عندنا اللى هي الرقم اتنين طب الفرق ما بين
+
+419
+00:47:54,410 --> 00:48:01,110
+هدول طالع مين يبقى من الاتنين هدول مع بعض بس تنتج
+
+420
+00:48:01,110 --> 00:48:08,450
+ما يأتي هذه عبارة عن ال five of أربعة وأربعة بدها
+
+421
+00:48:08,450 --> 00:48:15,550
+تساوي أربعة في five of one one وتساوي أربعة فيه
+
+422
+00:48:16,570 --> 00:48:22,830
+فاية أربعة واحد واحد الفرق فيه ما بينهم لهمين a
+
+423
+00:48:22,830 --> 00:48:31,030
+ناقص ال b يبقى النتيجة تساوي أربعة a ناقص أربعة b
+
+424
+00:48:31,030 --> 00:48:37,730
+إذا بنانا عليه صورة الفاية أربعة وأربعة هي أربعة
+
+425
+00:48:37,730 --> 00:48:44,630
+مضروبة في ال a ناقص ال b لحد هنا انتهى ال section
+
+426
+00:48:45,380 --> 00:48:50,120
+والله يعطيكوا العافية ونسامحوا أو يسامحوا بعضنا
+
+427
+00:48:50,120 --> 00:48:54,920
+بعضا إن كان صار فيه خطأ أو تقسير أو ما إلى ذلك
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aaf3eaaafa4dca00108a6cfa5e4b84dc89b8fbaf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc.srt
@@ -0,0 +1,1543 @@
+1
+00:00:22,140 --> 00:00:26,780
+بسم الله الرحمن الرحيم المرة اللي فاتت أعطينا
+
+2
+00:00:26,780 --> 00:00:31,760
+ساعتين فيه اللي هو الـ chapter 7 اللي بتحدث عن
+
+3
+00:00:31,760 --> 00:00:38,300
+Cosets and Lagrange theorem، و عرفنا الـ coset و
+
+4
+00:00:38,300 --> 00:00:42,520
+حسبنا الـ cosets لمجموعة من الـ subgroups يعني
+
+5
+00:00:42,520 --> 00:00:47,080
+أعطينا بدل المثال ثلاثة ثم انتقلنا بعد ذلك إلى
+
+6
+00:00:47,080 --> 00:00:51,500
+Lagrange theorem وهذه النظرية في الجبر مشهورة في
+
+7
+00:00:51,500 --> 00:00:56,980
+كل كتب الجبر نظرية
+
+8
+00:00:56,980 --> 00:01:00,320
+Lagrange ما بعرف إيش كان نص اللي قاعد بيقرا هذا
+
+9
+00:01:00,320 --> 00:01:04,450
+إيش كان نص Lagrange theorem يعني؟ طبعا جى finite
+
+10
+00:01:04,450 --> 00:01:10,310
+group هذه البداية وبعدها بصرشو اه
+
+11
+00:01:10,310 --> 00:01:13,570
+اشتر
+
+12
+00:01:13,570 --> 00:01:23,130
+نظرية لاجرانج إيش كان نصنا طريقة Lagrange؟ هاي
+
+13
+00:01:23,130 --> 00:01:27,570
+بدر أضائلكوا يعني الطريقة Lagrange theorem بيقول
+
+14
+00:01:27,570 --> 00:01:31,870
+لو أخدت أي subgroup من الـ group اللي عندك فإن الـ
+
+15
+00:01:31,870 --> 00:01:36,170
+order للـ subgroup يقسم الـ order للـ group وهذا ما
+
+16
+00:01:36,170 --> 00:01:40,560
+برهنّاه في المرة الماضية يعني لو أنا عندي group G
+
+17
+00:01:40,560 --> 00:01:45,360
+و أخدت any subgroup إن شاء الله لـ trivial subgroup
+
+18
+00:01:45,360 --> 00:01:50,060
+كويس؟ يبقى الـ order لهذه الـ subgroup بيقسم الـ
+
+19
+00:01:50,060 --> 00:01:54,760
+order للي group تمام؟ هذا كان نص نظرية Lagrange
+
+20
+00:01:54,760 --> 00:02:00,360
+أعطينا عليها بدل المثال اثنين الآن بدنا نيجي لأول
+
+21
+00:02:00,360 --> 00:02:04,380
+Corollary عندنا مجموعة من الـ corollaries على نظرية
+
+22
+00:02:04,380 --> 00:02:08,890
+Lagrange يعني مجموعة من النتائج النتيجة الأولى بيقول
+
+23
+00:02:08,890 --> 00:02:12,950
+في الـ finite group the order of each element of
+
+24
+00:02:12,950 --> 00:02:16,170
+the group divides the order of the group that is
+
+25
+00:02:16,170 --> 00:02:21,030
+لو كان عندي element x موجود في الـ group g يبقى الـ
+
+26
+00:02:21,030 --> 00:02:26,050
+order لـ x بدّه يقسمين بدّه يقسم الـ order لـ g يعني
+
+27
+00:02:26,050 --> 00:02:30,270
+لاجرانج قال لي الـ order تبع الـ sub group بيقسمين
+
+28
+00:02:30,270 --> 00:02:34,370
+الـ order للـ group النتيجة هذه تقول لي لأ الـ order
+
+29
+00:02:34,370 --> 00:02:37,790
+للـ element كذلك لأي element في الـ group بدّه يقسم
+
+30
+00:02:37,790 --> 00:02:43,070
+إياه بدّه يقسم الـ order للـ group بدنا نبرهن صحة هذا
+
+31
+00:02:43,070 --> 00:02:48,130
+الكلام مشان نبرهن صحة هذا الكلام بدي أقول له افترض
+
+32
+00:02:48,130 --> 00:02:54,530
+أن X هذا موجود في الـ group بدي أثبت أن الـ order
+
+33
+00:02:54,530 --> 00:02:58,710
+لهذا الـ element بدّه يقسم إياه الـ order للـ group
+
+34
+00:02:58,710 --> 00:03:06,550
+بقول له ماشي then الـ H هذه اللي بدي أخدها subgroup
+
+35
+00:03:06,550 --> 00:03:14,810
+اللي عبارة عن الـ subgroup generated by X تمام هذه
+
+36
+00:03:14,810 --> 00:03:24,610
+الآن subgroup الـ H هذه is a subgroup of G طيب
+
+37
+00:03:24,610 --> 00:03:29,290
+تمام بالـ Lagrange theorem الـ order لـ H بدّه يقسم
+
+38
+00:03:29,290 --> 00:03:36,020
+من الـ order لـ G يبقى بروح بقوله هنا by Lagrange
+
+39
+00:03:36,020 --> 00:03:39,400
+theorem
+
+40
+00:03:39,400 --> 00:03:51,300
+الـ order للـ H divides الـ order لـ G طيب لما تبقى
+
+41
+00:03:51,300 --> 00:03:55,160
+هذه الـ cyclic شو علاقة ما بين الـ order لـ H و الـ
+
+42
+00:03:55,160 --> 00:04:03,270
+order لـ X متساوية بقوله هنا بطء ولكن الـ order لـ H
+
+43
+00:04:03,270 --> 00:04:10,070
+بدّه يساوي الـ order لـ X يبقى هذا بدّه يعطيني بدل ما
+
+44
+00:04:10,070 --> 00:04:13,810
+يقول الـ order تبع الـ H بدّه يقسم الـ G بدّه يشيل الـ
+
+45
+00:04:13,810 --> 00:04:17,970
+order تبع الـ H و يكتب بداله الـ order لـ X
+
+46
+00:04:17,970 --> 00:04:24,500
+divides الـ order لـ G وكان الله بالسر علينا إذا من
+
+47
+00:04:24,500 --> 00:04:28,980
+الآن أساعد إن بديك تعرف إن لو عندي group خدت منها
+
+48
+00:04:28,980 --> 00:04:32,540
+subgroup يبقى الـ order لهذا الـ subgroup يقسم لـ
+
+49
+00:04:32,540 --> 00:04:37,180
+group وفي المقابل لو كان عندي أي element x موجود
+
+50
+00:04:37,180 --> 00:04:41,920
+في الـ group g يبقى الـ order لـ x كمان يقسم الـ
+
+51
+00:04:41,920 --> 00:04:46,200
+order لـ g نيجي لـ الـ corollary الثانية
+
+52
+00:04:50,810 --> 00:04:57,570
+Corollary اثنين بتقول a group of a prime order a
+
+53
+00:04:57,570 --> 00:05:08,570
+group of a prime order is
+
+54
+00:05:08,570 --> 00:05:10,230
+cyclic
+
+55
+00:05:13,050 --> 00:05:19,910
+يعني أي group الـ order لها بتكون الـ prime اثنين،
+
+56
+00:05:19,910 --> 00:05:24,450
+ثلاثة، خمسة، سبعة، أحد عشر، ثلاثة عشر دائما تبقى
+
+57
+00:05:24,450 --> 00:05:29,710
+Cyclic وإذا Cyclic يبقى abelian لأنه أخدناه قبل ذلك
+
+58
+00:05:29,710 --> 00:05:35,950
+في chapter 4 أن any cyclic group is abelian لكن العكس
+
+59
+00:05:35,950 --> 00:05:40,310
+ما هوّاش صحيح طيب a group of a prime order is
+
+60
+00:05:40,310 --> 00:05:44,850
+cyclic بدنا نروح نثبت هذا الكلام بدي أجي أقوله
+
+61
+00:05:44,850 --> 00:06:02,150
+assume that افترض أن الـ g is a group with order P
+
+62
+00:06:02,150 --> 00:06:10,640
+that is that is الـ
+
+63
+00:06:10,640 --> 00:06:19,540
+order لـ g بدّه يساوي الـ P and الـ P is prime
+
+64
+00:06:19,540 --> 00:06:25,600
+يبقى الـ order لـ g هو عبارة عن عدد أول اثنين
+
+65
+00:06:25,600 --> 00:06:30,520
+ثلاثة خمسة سبعة أحد عشر ثلاثة عشر سبعة عشر تسعة عشر زي
+
+66
+00:06:30,520 --> 00:06:37,650
+ما بدّك يبقى g group with order P و الـ P هذا عبارة
+
+67
+00:06:37,650 --> 00:06:42,990
+عن a prime number كويس؟ بدي أثبت أن هذا الـ group
+
+68
+00:06:42,990 --> 00:06:48,470
+دائما و أبدا تبقى Cyclic، كويس؟ يبقى بدي أجي أقوله
+
+69
+00:06:48,470 --> 00:06:56,210
+خذ لي عنصر a موجود في G طب العنصر a هذا بيولد لي الـ
+
+70
+00:06:56,210 --> 00:06:57,650
+subgroup ولا لأ؟
+
+71
+00:07:00,140 --> 00:07:03,500
+أي element في الجروب بيولد ليه subgroup صحيح ولا
+
+72
+00:07:03,500 --> 00:07:07,240
+لأ؟ يمكن يكون فيش فيها إلا الـ identity يمكن عنصرين
+
+73
+00:07:07,240 --> 00:07:12,260
+يمكن ثلاثة يمكن أربعة إلى آخره تمام يبقى little a
+
+74
+00:07:12,260 --> 00:07:23,880
+belongs to g then هذه هي is a is a cyclic subgroup
+
+75
+00:07:26,920 --> 00:07:35,500
+cyclic subgroup of G يبقى
+
+76
+00:07:35,500 --> 00:07:43,660
+الـ order لها يقسم من الـ order لـ G يبقى then الـ
+
+77
+00:07:43,660 --> 00:07:48,520
+order للـ subgroup generated by A divides
+
+78
+00:07:51,870 --> 00:07:59,770
+divide الـ order لـ g اللي بدّه يساوي الـ P إيش قواسم
+
+79
+00:07:59,770 --> 00:08:08,310
+الـ P واحد و الـ P itself يبقى هنّا لو قلنا little a
+
+80
+00:08:08,310 --> 00:08:14,750
+belongs to g و قلنا الـ a لا يساوي الـ identity كمان
+
+81
+00:08:14,750 --> 00:08:20,410
+أضيف عليها أن الـ a لا يساوي الـ identity حتى لا نقع
+
+82
+00:08:20,410 --> 00:08:26,920
+في أي مشكلة بعد ذلك تمام طيب يبقى الـ order لـ g
+
+83
+00:08:26,920 --> 00:08:33,460
+بدّه يساوي الـ P معناه هذا الكلام أن الـ order لـ الـ
+
+84
+00:08:33,460 --> 00:08:39,920
+subgroup generated by A بدّه يساوي واحد or P يبقى
+
+85
+00:08:39,920 --> 00:08:46,060
+هاي القواسم اللي بتقسم الـ P الآن هل يمكن لهذا الـ
+
+86
+00:08:46,060 --> 00:08:51,020
+order أنّه يساوي واحد لأ لأنه اشتراط مع أن الـ e لا
+
+87
+00:08:51,020 --> 00:08:58,970
+يساوي الـ identity بقول له ولكن الـ order للـ subgroup
+
+88
+00:08:58,970 --> 00:09:05,210
+generated by a لا يمكن أن يساوي الواحد السبب لأنّ
+
+89
+00:09:05,210 --> 00:09:11,470
+الـ a does not equal to e يبقى هذا شو بدّه يعطينا
+
+90
+00:09:11,470 --> 00:09:15,530
+هذا بدّه يعطينا أن الـ order للـ subgroup generated
+
+91
+00:09:15,530 --> 00:09:21,050
+by a بدّه يساوي 100 بدّه يساوي الـ P طب هذا إيش بدّه
+
+92
+00:09:21,050 --> 00:09:25,750
+يعطينا صار الـ order لهذه الـ sub group بدّه يساوي الـ
+
+93
+00:09:25,750 --> 00:09:29,850
+P يبقى الـ sub group هذه عبارة عن مين عبارة عن G
+
+94
+00:09:29,850 --> 00:09:36,510
+itself تمام يبقى هذا بدّه يعطينا أن الـ sub group
+
+95
+00:09:36,510 --> 00:09:41,610
+generated by A هي عبارة عن مين الـ G itself لأنّ الـ
+
+96
+00:09:41,610 --> 00:09:45,550
+order لـ G بدّه يساوي الـ P و الـ order للـ sub group
+
+97
+00:09:45,550 --> 00:09:50,080
+هذا بدّه يساوي الـ P يبقى الاثنين are equal يبقى هذا
+
+98
+00:09:50,080 --> 00:09:59,080
+معناه إيش؟ معناه إنّ الـ g لـ group الـ G is cyclic لو
+
+99
+00:09:59,080 --> 00:10:02,780
+كان السؤال أثبتها إنها abelian، بدي أثبتها إنها
+
+100
+00:10:02,780 --> 00:10:08,180
+الـ cyclic ومن ثم بقول لما دام cyclic، يبقى abelian
+
+101
+00:10:08,180 --> 00:10:12,780
+هذه الـ corollary رقم اثنين، بدنا نروح للـ corollary رقم
+
+102
+00:10:12,780 --> 00:10:16,420
+ثلاثة يبقى الـ corollary
+
+103
+00:10:18,200 --> 00:10:24,040
+رقم ثلاثة أو النتيجة رقم ثلاثة بتقول little g be a
+
+104
+00:10:24,040 --> 00:10:34,440
+finite group little g be a finite group يبقى
+
+105
+00:10:34,440 --> 00:10:42,020
+group محدودة العدد من العناصر little g be a finite
+
+106
+00:10:42,020 --> 00:10:45,220
+group and let and
+
+107
+00:10:51,350 --> 00:10:57,830
+يبقى الـ a أصل order لـ g يبقى الـ a أصل order
+
+108
+00:10:57,830 --> 00:11:01,430
+لـ g يبقى الـ a أصل order لـ g
+
+109
+00:11:09,240 --> 00:11:13,740
+يعني لو أخدت أي element من الـ group و حطيت له أس
+
+110
+00:11:13,740 --> 00:11:18,920
+الـ order تبع الـ group دائما و أبدا بدّه يساوي الـ
+
+111
+00:11:18,920 --> 00:11:28,960
+identity طيب
+
+112
+00:11:28,960 --> 00:11:34,990
+كويس نشوف نؤكد على صحة ما تكلّمنا نقول إيش احنا عندنا
+
+113
+00:11:34,990 --> 00:11:39,410
+g finite group و الـ a belongs to g قال لي أثبت أن
+
+114
+00:11:39,410 --> 00:11:43,890
+الـ a مرفوعة للأردر السابع الـ g بتساوي مين الـ
+
+115
+00:11:43,890 --> 00:11:47,430
+identity element الـ a لو جيت على الـ a corollary
+
+116
+00:11:47,430 --> 00:11:53,770
+one يبقى الـ order للـ a بتقسمين الـ order لـ g يبقى
+
+117
+00:11:53,770 --> 00:11:59,970
+by a corollary one
+
+118
+00:12:01,250 --> 00:12:10,590
+الـ order للـ a divides الـ order للـ g هذا معناته
+
+119
+00:12:10,590 --> 00:12:16,390
+أن الـ order للـ g بدّه يساوي الـ order للـ a في رقم و
+
+120
+00:12:16,390 --> 00:12:25,970
+ليكن k for some positive integer
+
+121
+00:12:25,970 --> 00:12:27,990
+k
+
+122
+00:12:29,620 --> 00:12:35,640
+for some positive integer k الآن أنا بدي أثبت
+
+123
+00:12:35,640 --> 00:12:43,060
+أن الـ a مرفوعة للأس اللي هو الـ order للـ g بدّه 
+
+124
+00:12:43,060 --> 00:12:48,220
+يساوي الـ identity بناء عليها بقدر أقول هذا ايه الـ
+
+125
+00:12:48,220 --> 00:12:54,260
+order للـ g اللي هو عبارة عن الـ order للـ a مضروب في
+
+126
+00:12:54,260 --> 00:13:01,570
+مين مضروب في K هذا معناه أن ال A مرفوعة لل order
+
+127
+00:13:01,570 --> 00:13:08,350
+تبع ال A كل هذا أس K طب ال A لما يكون مرفوع لل
+
+128
+00:13:08,350 --> 00:13:13,070
+order تبعه كده بيعطينا ال identity يبقى هذا
+
+129
+00:13:13,070 --> 00:13:17,310
+بيعطينا ال identity أس K ال identity أس K بيعطينا
+
+130
+00:13:17,310 --> 00:13:23,230
+من ال identity يبقى بناء علي أسار ال A أس ال order
+
+131
+00:13:23,230 --> 00:13:27,970
+لل G دائما و أبدا بدي يعطينا ماذا؟ بدي يعطينا ال
+
+132
+00:13:27,970 --> 00:13:33,850
+identity element تمام بدي أخاطر قبل مفروض نعطي بعض
+
+133
+00:13:33,850 --> 00:13:39,310
+الأمثلة على هذه ال crawlers بدنا نيجي لأول مثال
+
+134
+00:13:39,310 --> 00:13:42,090
+examples او example one
+
+135
+00:13:45,840 --> 00:13:52,120
+example one بيقول show that
+
+136
+00:13:52,120 --> 00:14:00,260
+بيّن لي أن every group
+
+137
+00:14:00,260 --> 00:14:09,300
+of order less than or equal to 5
+
+138
+00:14:16,890 --> 00:14:32,590
+less than or equal to five is abelian يعني
+
+139
+00:14:32,590 --> 00:14:35,550
+بنثبت أن أي group
+
+140
+00:14:38,460 --> 00:14:43,920
+الـ order تبعها بده يساوي خمسة دائما و أبدا أو أقل
+
+141
+00:14:43,920 --> 00:14:47,440
+من خمسة is abelian يعني لو عندي group فيها عنصر
+
+142
+00:14:47,440 --> 00:14:51,540
+واحد أو group فيها عنصرين أو group فيها ثلاثة عناصر
+
+143
+00:14:51,540 --> 00:14:55,880
+أو أربعة عناصر أو خمسة عناصر كل هذه الأنموعة من ال
+
+144
+00:14:55,880 --> 00:15:01,600
+group تبقى دائما و أبدا abelian طيب الآن solution
+
+145
+00:15:06,050 --> 00:15:11,890
+أخذ الآن لو ال order اللي جى هو عبارة عن واحد يعني
+
+146
+00:15:11,890 --> 00:15:15,930
+ايش فيها فقط ال identity element و ال identity
+
+147
+00:15:15,930 --> 00:15:21,310
+الموجودة مع نفسه صحيح ولا لأ يبقى أبيل يعني يبقى
+
+148
+00:15:21,310 --> 00:15:27,180
+هنا بدأ أخد النقطة الأولى لو كان ال order لل G
+
+149
+00:15:27,180 --> 00:15:33,360
+بده يساوي واحد صحيح then ال G بده يساوي ال identity
+
+150
+00:15:33,360 --> 00:15:42,340
+فقط لا غير و هذا بده يعطينا أن ال G is abelian طيب
+
+151
+00:15:42,340 --> 00:15:51,100
+لو كان ال order لل G بده يساوي اثنين و ثلاثة or
+
+152
+00:15:51,100 --> 00:15:59,130
+خمسة يبقى كل هما دول مالهم primes then ال order لل
+
+153
+00:15:59,130 --> 00:16:05,970
+G is prime في الحالات الثلاثة ايش بيقول ال crawler
+
+154
+00:16:05,970 --> 00:16:10,790
+اثنين ال group of prime order is cyclic يبقى هذا
+
+155
+00:16:10,790 --> 00:16:17,250
+بده يعطينا أن ال G is cyclic طب و إذا ال G is
+
+156
+00:16:17,250 --> 00:16:18,910
+cyclic أبيليان يعني
+
+157
+00:16:23,770 --> 00:16:29,690
+يبقى الآن اثبتنا أن في حالة الواحد و الاثنين و الثلاثة
+
+158
+00:16:29,690 --> 00:16:34,710
+والخمسة أبيليان ضلت ايه؟ ضلت الأربعة يبقى بداجي
+
+159
+00:16:34,710 --> 00:16:41,010
+أقول له هنا لو كان ال order لل G بده يساوي أربعة
+
+160
+00:16:44,930 --> 00:16:51,590
+لو افترضت أن ال order للجي يكون 4 لو أخذت أي non
+
+161
+00:16:51,590 --> 00:16:56,470
+identity element في ال group جي كده احتمال ال
+
+162
+00:16:56,470 --> 00:17:02,890
+order يكون له واحد استبعدناه أنا قلت non identity
+
+163
+00:17:02,890 --> 00:17:07,750
+ليه بيبقى فيش إلا اثنين أو أربعة طب لو كان ال
+
+164
+00:17:07,750 --> 00:17:14,810
+order لل element يساوي 4 بيكون generator لـ G لأن ال
+
+165
+00:17:14,810 --> 00:17:17,990
+order يبقى الـ G الـ cyclic وبالتالي أبدا طلت
+
+166
+00:17:17,990 --> 00:17:24,390
+المشكلة وين عند اثنين فبداش أقول له هنا if يبقى if
+
+167
+00:17:24,390 --> 00:17:33,590
+ال order لـ G بده يساوي أربعة then any non identity
+
+168
+00:17:33,590 --> 00:17:39,490
+element has
+
+169
+00:17:40,760 --> 00:17:44,540
+order اثنين
+
+170
+00:17:44,540 --> 00:17:50,560
+أو أربعة if
+
+171
+00:17:50,560 --> 00:18:01,960
+order لأ بدو يساوي أربعة then order لأ بدو يساوي 
+
+172
+00:18:01,960 --> 00:18:09,370
+order لـ G معنى هذا الكلام أن الـ G هذه بدها تساوي ل
+
+173
+00:18:09,370 --> 00:18:16,010
+group generated by A هذا يعني أن الـ G هو Cyclic
+
+174
+00:18:16,010 --> 00:18:25,910
+و هذا يعني أن الـ G هو Abelian بلت مشكلتنا وين؟
+
+175
+00:18:25,910 --> 00:18:40,540
+أيوة يبقى لو كان الـ A موجود في G with ال order للـ A
+
+176
+00:18:40,540 --> 00:18:48,760
+بده يساوي اثنين then ال A تربيع بده يساوي ال
+
+177
+00:18:48,760 --> 00:18:55,660
+identity مظبوط يعني ال A صار بده يساوي ال A
+
+178
+00:18:55,660 --> 00:18:56,060
+inverse
+
+179
+00:19:01,020 --> 00:19:07,280
+يبقى أنا باخد two elements من G و أثبت أن ال X في
+
+180
+00:19:07,280 --> 00:19:12,460
+Y بيساوي ال Y X باستخدام المعلومة اللي عندنا هذا
+
+181
+00:19:12,460 --> 00:19:19,100
+يبقى بروح اقول له افترض أن ال X و ال Y عناصر موجودة
+
+182
+00:19:19,100 --> 00:19:19,580
+عندنا
+
+183
+00:19:37,640 --> 00:19:47,160
+بدايه اقول له let ال X و ال Y موجودة في G then ال X
+
+184
+00:19:47,160 --> 00:19:56,920
+Y موجودة في G if ال order لل X Y يساوي اثنين then
+
+185
+00:19:56,920 --> 00:20:05,460
+ال X Y لكل تربيع يساوي من؟ يساوي ال identity طب ال
+
+186
+00:20:05,460 --> 00:20:11,760
+X Y تربيع هذا بقدر أقول X تربيع Y تربيع لا تبقى
+
+187
+00:20:11,760 --> 00:20:16,980
+بيلا ما هي أشباه لاني بقدرش مظبوط لكن كل اللي بقدر
+
+188
+00:20:16,980 --> 00:20:23,960
+أقول له then اللي هو من ال X Y في ال X Y يساوي ال
+
+189
+00:20:23,960 --> 00:20:31,570
+identity تمام طب لو ضربت الطرفين في y inverse من
+
+190
+00:20:31,570 --> 00:20:39,630
+جهة اليمين يبقى بيصير عندي x y x بده يساوي e في y
+
+191
+00:20:39,630 --> 00:20:45,010
+inverse اللي هو بمين؟ ب y inverse طب اضرب كمان في
+
+192
+00:20:45,010 --> 00:20:51,350
+x inverse من جهة اليمين هذا يعني أن ال x في y بده
+
+193
+00:20:51,350 --> 00:20:57,090
+يساوي ال y inverse في ال x inverse الآن احنا قلنا
+
+194
+00:20:57,090 --> 00:21:02,790
+هنا ايش أن ال element اللي ال order له يساوي اثنين
+
+195
+00:21:02,790 --> 00:21:09,650
+ال element يساوي معكوسه تمام طيب بناء عليه هذا بده
+
+196
+00:21:09,650 --> 00:21:16,030
+يعطينا أن ال x في ال y بده يساوي من ال y في ال x
+
+197
+00:21:17,170 --> 00:21:23,450
+يعني شيلت كل X وحطيت بدلها X وشيلت كل Y وحطيت
+
+198
+00:21:23,450 --> 00:21:31,830
+بدلها Y هذا يعني أن ال G is abelian يبقى معنى هذا
+
+199
+00:21:31,830 --> 00:21:35,950
+الكلام أن الـ G abelian سواء كان ال order لها
+
+200
+00:21:35,950 --> 00:21:39,470
+واحد ولا اثنين ولا ثلاثة ولا أربعة ولا خمسة من
+
+201
+00:21:39,470 --> 00:21:44,470
+الآن فصاعدا بدك تاخدها قاعدة أي group ال order
+
+202
+00:21:44,470 --> 00:21:48,750
+اللي هيساوي خمسة أو أقل من خمسة يبقى هذه ال group
+
+203
+00:21:48,750 --> 00:21:54,330
+عبارة عن abelian group خد كمان مثال، المثال هذا هو
+
+204
+00:21:54,330 --> 00:22:02,450
+أحد أسئلة الكتاب يبقى example two example 2 هو
+
+205
+00:22:02,450 --> 00:22:10,690
+عبارة عن سؤال 26 من الكتاب بيقول let g
+
+206
+00:22:10,690 --> 00:22:25,890
+be a group of order 25 prove that
+
+207
+00:22:25,890 --> 00:22:34,580
+أثبت أن الـ G is cyclic
+
+208
+00:22:34,580 --> 00:22:40,580
+or الـ
+
+209
+00:22:40,580 --> 00:22:48,600
+G أس خمسة بده يساوي ال identity for all G اللي
+
+210
+00:22:48,600 --> 00:22:49,720
+belongs to G
+
+211
+00:23:04,000 --> 00:23:09,320
+خلّيني أبقى معناه هنا السؤال مرة ثانية أنا عندي
+
+212
+00:23:09,320 --> 00:23:14,300
+group فيها خمسة وعشرين عنصر ال order لها يساوي خمسة
+
+213
+00:23:14,300 --> 00:23:20,800
+وعشرين قال لي بتثبت أن جي هذه Cyclic يا إما الجي
+
+214
+00:23:20,800 --> 00:23:24,940
+أس خمسة بده يساوي ال identity لكل الجي اللي belongs
+
+215
+00:23:24,940 --> 00:23:30,640
+to جي إذا أنا بدي استبعد واحد وأثبت مين لأنه قال
+
+216
+00:23:30,640 --> 00:23:35,230
+لي or هذا أو هذا يبقى أنا لو روحته قلت له هنا
+
+217
+00:23:35,230 --> 00:23:46,330
+assume افترض أن ال G is non-cyclic ماهي 
+
+218
+00:23:46,330 --> 00:23:54,310
+cyclic and ال order لل G بده يساوي خمسة وعشرين
+
+219
+00:23:54,310 --> 00:24:01,760
+يبقاش بتثبت يا شباب ال جي أس خمسة يساوي من ال identity
+
+220
+00:24:01,760 --> 00:24:06,500
+element الآن ال G موجود في G يبقى ال order له
+
+221
+00:24:06,500 --> 00:24:14,680
+يقسم من الخمسة و العشرين يبقى هنا since لما أن ال G
+
+222
+00:24:14,680 --> 00:24:19,660
+belongs to G ال order لل G divide
+
+223
+00:24:21,710 --> 00:24:26,870
+اللي هو الخمسة و العشرين معنى هذا الكلام أن ال order
+
+224
+00:24:26,870 --> 00:24:35,230
+لل G يا إما واحد يا إما خمسة or خمسة و عشرين بنستبعد
+
+225
+00:24:35,230 --> 00:24:40,550
+لخمسة و عشرين لأن لو كان ال order خمسة و عشرين لصار ال
+
+226
+00:24:40,550 --> 00:24:45,630
+G Cyclic قال لا هي ما هي ال Cyclic إذا لا يمكن
+
+227
+00:24:45,630 --> 00:24:52,330
+لل order تبع ال element هذا أنه يساوي من ال order ل
+
+228
+00:24:52,330 --> 00:24:56,110
+G small هذا يا شباب مش جي كتر ال جي كتر هي خمسة و عشرين
+
+229
+00:24:56,110 --> 00:25:00,050
+ال order لل element يا بده يساوي واحد يا إما خمسة
+
+230
+00:25:00,050 --> 00:25:06,310
+يا إما خمسة و عشرين الآن أنا باجي بقول له ال order لل
+
+231
+00:25:06,310 --> 00:25:13,770
+G بده يساوي خمسة و عشرين impossible هذا الكلام غير
+
+232
+00:25:13,770 --> 00:25:26,190
+ممكن because السبب أن ال G is not cyclic يبقى الـ G
+
+233
+00:25:26,190 --> 00:25:30,690
+ما هيش Cycle طيب استبعدنا منين؟ الخمسة و العشرين
+
+234
+00:25:30,690 --> 00:25:36,250
+ضلت عندنا الـ G ال order له بده يساوي واحد بده
+
+235
+00:25:36,250 --> 00:25:45,550
+يساوي خمسة الآن لو كان ال order لو كان ال order لل G
+
+236
+00:25:45,550 --> 00:25:51,260
+بده يساوي واحد then لما يكون ال order اللي جي بده
+
+237
+00:25:51,260 --> 00:25:54,680
+يساوي واحد يبقى مين هي جي هذه ال identity element
+
+238
+00:25:54,680 --> 00:26:01,260
+يبقى then الجي بدها تساوي ال identity element يبقى
+
+239
+00:26:01,260 --> 00:26:07,660
+الجي أس خمسة بده يساوي ال identity element أس خمسة
+
+240
+00:26:07,660 --> 00:26:12,600
+يبقى جي أس خمسة ال identity أس خمسة من بال
+
+241
+00:26:12,600 --> 00:26:19,940
+identity وهو المطلوب الحالة الثانية لو كان ال
+
+242
+00:26:19,940 --> 00:26:26,180
+order للـ G بده يساوي خمسة then الـ G أس خمسة بده
+
+243
+00:26:26,180 --> 00:26:32,180
+يساوي ال identity و هو المطلوب يبقى بناء عليه مدام
+
+244
+00:26:32,180 --> 00:26:37,200
+الـ G non-cyclic الـ G أس خمسة بده يساوي ال
+
+245
+00:26:37,200 --> 00:26:41,140
+identity element دائما و أبدا
+
+246
+00:27:02,160 --> 00:27:09,020
+طب ننتقل إلى تعريف جديد أو لكرولري رقم أربعة كرولري
+
+247
+00:27:09,020 --> 00:27:18,180
+رقم أربعة بسموها
+
+248
+00:27:18,180 --> 00:27:23,420
+Fermat Fermat's
+
+249
+00:27:23,420 --> 00:27:26,260
+little theorem
+
+250
+00:27:31,620 --> 00:27:39,240
+نصها كالتالي بيقول for every integer a for every
+
+251
+00:27:39,240 --> 00:27:56,220
+integer a and every prime p and every prime p الـ a
+
+252
+00:27:56,220 --> 00:28:05,260
+to the power p modulo p بدو يساوي الـ a modulo p
+
+253
+00:28:05,260 --> 00:28:08,480
+بدنا
+
+254
+00:28:08,480 --> 00:28:11,720
+نبرهن صحّيتها ل proof
+
+255
+00:28:16,540 --> 00:28:21,300
+هذه سمّيت باسم Fermat's Little Theorem لأنّ الاكتشاف هذه الشغلة
+
+256
+00:28:21,300 --> 00:28:26,420
+وسمّيت Little لأنّي بُصغّر الرقم الكبير أنا عندي رقم
+
+257
+00:28:26,420 --> 00:28:32,620
+كبير ضخم بُصغّره على طول الخط يعني بجيب رقم مكافئ له
+
+258
+00:28:32,620 --> 00:28:38,980
+في حالة إذا كان المقياس هو P فبقول أي integer A و
+
+259
+00:28:38,980 --> 00:28:43,630
+every prime P الـ A to the power of P modulo P
+
+260
+00:28:43,630 --> 00:28:49,090
+اللاّحظ الـ modulo P هو الأس اللي عندي هذا و هذا
+
+261
+00:28:49,090 --> 00:28:54,040
+لازم يكون الـ prime number شرط أساسي مش أي رقم إن
+
+262
+00:28:54,040 --> 00:28:59,300
+حدث ذلك يبقى بقوله هذا a modulo p يعني هذا الـ p
+
+263
+00:28:59,300 --> 00:29:03,800
+بكون اتخلّصت منها وبالتالي الرقم الضخم هذا صغّرته
+
+264
+00:29:03,800 --> 00:29:08,260
+إلى رقم a modulo p الـ a هذه يمكن تكون أكبر من الـ p
+
+265
+00:29:08,260 --> 00:29:12,980
+ويمكن تكون أصغر من الـ p محطّ الشرط عندي كل اللي 
+
+266
+00:29:12,980 --> 00:29:17,480
+حطّوا أنّ integer و الـ p is a prime نروح نسبة صحة
+
+267
+00:29:17,480 --> 00:29:22,090
+هذا الكلام بأني بدي أخد حالتين الحالة الأولى لو كان
+
+268
+00:29:22,090 --> 00:29:27,790
+الـ A أقل من P و الحالة الثانية لو كان الـ A أكبر من
+
+269
+00:29:27,790 --> 00:29:34,610
+P بدي أدرس إيه الحالة الثانية طب لو يساوي لو الـ A يساوي
+
+270
+00:29:34,610 --> 00:29:38,790
+الـ P يبقى من 100 لما يبقى Zero بدي أساوي Zero على
+
+271
+00:29:38,790 --> 00:29:43,710
+طول الخطّ طيب يبقى بدي أجي يبقى ما عنديش مشكلة في
+
+272
+00:29:43,710 --> 00:29:47,930
+حالة الـ Zero ليش بصراحة خلاص Zero بساوي Zero طيب
+
+273
+00:29:47,930 --> 00:29:59,460
+بدي أخد F الـ P less than 0 لأ
+
+274
+00:29:59,460 --> 00:30:08,740
+لو كان less than A لو كان F الـ A less than P لو
+
+275
+00:30:08,740 --> 00:30:19,080
+كان الـ A أقل من P then الـ P الـ .. الـ A هذه بتكون
+
+276
+00:30:19,080 --> 00:30:25,500
+موجودة في مجموعة الأعداد 1 و 2 و 3 و
+
+277
+00:30:25,500 --> 00:30:33,740
+لغاية P minus الـ 1 أكيد مية المية مدام A integer
+
+278
+00:30:33,740 --> 00:30:38,820
+أصغر من P يبقى A موجود في المجموعة هذه طب مين هي
+
+279
+00:30:38,820 --> 00:30:46,580
+المجموعة هذه مش UP يبقى هذه اللي هي تساوي UP
+
+280
+00:30:49,020 --> 00:30:59,020
+يبقى معنى هذا الكلام أنّ الـ a موجود في الـ U P طيب
+
+281
+00:30:59,020 --> 00:31:08,500
+يبقى قداش الـ order لـ U P نقص واحد، كويس هذا بيقين
+
+282
+00:31:08,500 --> 00:31:20,930
+اللي عندي الـ order لـ U P بيساوي P ناقص واحد طبعًا طيب
+
+283
+00:31:20,930 --> 00:31:26,950
+الآن أنّ يأتي crawler فيهم هذه اللي قالت لي اه
+
+284
+00:31:26,950 --> 00:31:31,070
+مشحناها اللي هو a أو زي ما أظنّ الـ crawler رقم 3
+
+285
+00:31:31,070 --> 00:31:36,270
+الـ a أو الـ order للـ a بدو يساوي الـ ID 3 طيب
+
+286
+00:31:36,270 --> 00:31:43,790
+هنا from crawler ثلاثة
+
+287
+00:31:43,790 --> 00:31:52,450
+أي element بدي أخد مرفوع للـ order تبع الـ U P بدي
+
+288
+00:31:52,450 --> 00:32:00,810
+يساوي الـ identity اللي هو 1 هذا الكلام
+
+289
+00:32:00,810 --> 00:32:06,510
+إيش معناه؟ معناه الـ A أس الـ P ناقص 1 بدو يساوي
+
+290
+00:32:06,510 --> 00:32:15,030
+1 طيب لو ضربت الطرفين في A إيش بيصير عندي؟ A أس
+
+291
+00:32:15,030 --> 00:32:21,900
+P بدو يساوي الـ A يبقى معناه هذا الكلام أنّ a is p
+
+292
+00:32:21,900 --> 00:32:28,960
+modulo p بدو يساوي a modulo p مادة ما الرقمين هذا
+
+293
+00:32:28,960 --> 00:32:33,320
+اللي بيساووا بعض إذا بدي يكون هذا modulo p بدو يساوي
+
+294
+00:32:33,320 --> 00:32:38,060
+هذا modulo p تمامًا وهو المطلوب هذا لو كانت إيش الـ
+
+295
+00:32:38,060 --> 00:32:44,840
+a أقل من p طب لو كانت الـ a أكبر من p يبقى f الـ a
+
+296
+00:32:44,840 --> 00:32:46,940
+greater than p
+
+297
+00:32:51,570 --> 00:32:57,570
+يعني الـ A هذه P زائد شوية 2 P زائد شوية 3 P
+
+298
+00:32:57,570 --> 00:33:01,970
+20 P زائد زائد شوية تمام يبقى بالـ division
+
+299
+00:33:01,970 --> 00:33:09,730
+algorithm بقول له then الـ A هذا بدو يساوي الـ M P
+
+300
+00:33:09,730 --> 00:33:15,870
+زائد الـ R يعني مضاعفة الـ P زائد الـ R و الـ R هذه
+
+301
+00:33:15,870 --> 00:33:25,010
+أكبر من أو تساوي Zero أقل من مين؟ أقل من P طيب لو
+
+302
+00:33:25,010 --> 00:33:31,190
+جيت مدام عرفت زيك اللي هو أخدت الآن الـ A modulo P
+
+303
+00:33:31,190 --> 00:33:39,730
+كده إيش بدو يساوي؟ R أنا عندي الـ A بدو يساوي MP زي
+
+304
+00:33:39,730 --> 00:33:43,630
+ده أنا أخدت الـ A modulo P بقى مضاعفات الـ P بطيّرها
+
+305
+00:33:43,630 --> 00:33:49,810
+إيش بيظهر عندي؟ بيظهر عندي R يبقى هذا بيبقى عندي مين؟
+
+306
+00:33:49,810 --> 00:33:56,570
+بيبقى عندي R فقط لا غير طيب الآن الـ R محصورة من
+
+307
+00:33:56,570 --> 00:34:01,590
+أين إلى أين؟ من Zero إلى P وأنا جايل أنّ الـ A
+
+308
+00:34:01,590 --> 00:34:08,210
+modulo P بدو يساوي الـ R الـ R يعني موجودة وين؟ في الـ
+
+309
+00:34:08,210 --> 00:34:17,490
+U P صح ولا لا؟ موجودة في الـ U P ليش؟ لأنّها محصورة
+
+310
+00:34:17,490 --> 00:34:25,050
+من صفر إلى P طبعًا طيب مدام محصورة هذه تساوي هذه
+
+311
+00:34:25,050 --> 00:34:31,030
+وهذه موجودة هنا إذا automatic على طول الخط إيش قلنا
+
+312
+00:34:31,030 --> 00:34:35,970
+هنا لو كان في البرهان الأول بقول لما تبقى الـ a
+
+313
+00:34:35,970 --> 00:34:41,750
+موجودة في الـ U P استنتجنا أنّ هذا الكلام ما له صحيح
+
+314
+00:34:41,750 --> 00:34:52,610
+تمام يبقى باجي بقول from the above from من البرهان
+
+315
+00:34:52,610 --> 00:35:00,500
+أعلاه يبقى الـ a modulo p modulo p بدو يساوي a أس p
+
+316
+00:35:00,500 --> 00:35:07,300
+modulo p وانتهينا منها يبقى على كلّ الأمر يعني سواء
+
+317
+00:35:07,300 --> 00:35:12,360
+كان الـ a أكبر من p ولا أصغر من p فإنّ الـ a to the
+
+318
+00:35:12,360 --> 00:35:18,220
+power p modulo p بدو يساوي منها الـ a modulo p حد
+
+319
+00:35:18,220 --> 00:35:24,110
+يلاقي أيّ استفسار هنا طب نحاول نعطي أكثر من مثال على
+
+320
+00:35:24,110 --> 00:35:30,770
+هذه النقطة المثال الأول يبقى
+
+321
+00:35:30,770 --> 00:35:41,150
+examples find
+
+322
+00:35:41,150 --> 00:35:54,640
+the exact value متجدّدش القيمة الحقيقية of 15
+
+323
+00:35:54,640 --> 00:36:04,480
+أس 11 modulo 11 of وهذا يجب أن أعتبرها إيه
+
+324
+00:36:04,480 --> 00:36:11,760
+ويجب أن نأتي إلى الـ B يجب أن يكون 7 أس 13
+
+325
+00:36:11,760 --> 00:36:15,880
+modulo 11
+
+326
+00:36:29,550 --> 00:36:35,690
+خلّي أبقى لك هنا بقول هات للقيمة الحقيقية للـ 15
+
+327
+00:36:35,690 --> 00:36:41,550
+أس 11 modulo 11 وكذلك 7 أس 13 modulo
+
+328
+00:36:41,550 --> 00:36:47,610
+11 الحل كالتالي بيروح أخد إيه؟ نمر إيه؟ نمر
+
+329
+00:36:47,610 --> 00:36:54,530
+إيه؟ بدي أخد له الـ 15 أس 11 modulo 11
+
+330
+00:36:54,530 --> 00:37:01,420
+النتج 15 modulo 11 صحّيك يا شباب
+
+331
+00:37:05,780 --> 00:37:11,120
+لو كان هذا P و هذا P يتماثل نفس بعض يبقى هذا يقول
+
+332
+00:37:11,120 --> 00:37:17,060
+إلى E modulo P يبقى أنا عندي 15 و 11 modulo
+
+333
+00:37:17,060 --> 00:37:20,380
+11 يبقى أنا عندي 15 modulo 11 يبقى أنا
+
+334
+00:37:20,380 --> 00:37:20,420
+عندي 15 modulo 11 يبقى أنا عندي 15
+
+335
+00:37:20,420 --> 00:37:23,320
+modulo 11 هي 15 modulo 11 15 modulo
+
+336
+00:37:23,320 --> 00:37:28,240
+11 أكبر من الـ 11 إذا بدي أشيل منها الـ 11 أو
+
+337
+00:37:28,240 --> 00:37:32,840
+مضاعفات الـ 11 كدهش بطلع يبقى النتيجة تساوي 4
+
+338
+00:37:33,130 --> 00:37:39,010
+يبقى هذا سؤال direct مباشر لكن قد يكون السؤال غير
+
+339
+00:37:39,010 --> 00:37:46,030
+مباشر غير مباشر كيف؟ زي ما قال لي 7 أس 13
+
+340
+00:37:46,030 --> 00:37:56,510
+modulo 11 بدو يساوي يعني
+
+341
+00:37:56,510 --> 00:37:59,850
+ما نفعش أقول الجواب اللي هو 7 modulo 11؟
+
+342
+00:37:59,850 --> 00:38:02,290
+خلط؟
+
+343
+00:38:03,320 --> 00:38:09,060
+غلط ونصف بدو يكون الرقم هذا الأس هو المقياس اللي
+
+344
+00:38:09,060 --> 00:38:15,220
+عندي طيب يعني إيش؟ يعني 7 أس 13 بدي أكتبها
+
+345
+00:38:15,220 --> 00:38:21,920
+بدلالة 7 أس 11 يبقى هذه بدها تساوي 7 أس
+
+346
+00:38:21,920 --> 00:38:30,490
+11 كدهش بيظلّ 7 تربيع كلّ modulo 11 هذه هي
+
+347
+00:38:30,490 --> 00:38:37,810
+عبارة عن 7 أس 11 modulo 11 مضروبة في
+
+348
+00:38:37,810 --> 00:38:46,530
+من في 7 تربيع modulo 11 يبقى حولتها إلى حصل
+
+349
+00:38:46,530 --> 00:38:50,850
+ضرب الرقمين اللي عندنا الآن من Fermat's Little Theorem هذه
+
+350
+00:38:50,850 --> 00:38:55,210
+شكلها شكل Fermat's Little Theorem يبقى هذا 7 modulo
+
+351
+00:38:55,210 --> 00:39:01,570
+11 يبقى هنا 7 modulo 11 من Fermat's
+
+352
+00:39:01,570 --> 00:39:07,610
+Little Theorem وهذه 7 تربيع يعني 49 modulo
+
+353
+00:39:07,610 --> 00:39:14,600
+من 11 يبقى هذا الكلام يساوي الآن هذه الـ 7
+
+354
+00:39:14,600 --> 00:39:20,400
+modulo 11 لأنّ 49 modulo 11 فيها
+
+355
+00:39:20,400 --> 00:39:27,020
+قداش؟ لأنّ 11 في 4 من 49 بيظلّ 5
+
+356
+00:39:27,020 --> 00:39:34,180
+يبقى مضروبة في من؟ مضروبة في 5 modulo 11
+
+357
+00:39:37,280 --> 00:39:44,860
+35 عبارة
+
+358
+00:39:44,860 --> 00:39:51,290
+عن 11 في 3 33 زائد 2 يبقى
+
+359
+00:39:51,290 --> 00:39:56,130
+النتج كله يساوي 2 يبقى هالرقم الضخم اللي
+
+360
+00:39:56,130 --> 00:40:00,650
+عندنا هذا اللي هو 7 أس 13 يعني بدي أضرب
+
+361
+00:40:00,650 --> 00:40:04,990
+7 في نفسها 13 مرة وأجيبلها الموديل
+
+362
+00:40:04,990 --> 00:40:09,150
+11 اختصرناها وقلنا ناتج يساوي قداش؟ يساوي
+
+363
+00:40:09,150 --> 00:40:11,490
+2 على طول الخطّ
+
+364
+00:40:16,940 --> 00:40:24,100
+تحسب شو ما عليكش قيود مدام أنت ماشي سليم يبقى احسب
+
+365
+00:40:24,100 --> 00:40:29,680
+اللي بدك ياه متى لازم القمع عارف قصده لو حطينا
+
+366
+00:40:29,680 --> 00:40:35,960
+element وحطينا له قوّة كبير وبتصغّر هذا القوّة قصده اه
+
+367
+00:40:35,960 --> 00:40:43,830
+طيب في عندنا خد بالك شغلة بدي أشير إليها نظرية
+
+368
+00:40:43,830 --> 00:40:50,950
+Lagrange بتقول الـ order للـ subgroup بيقسم من؟
+
+369
+00:40:50,950 --> 00:40:57,230
+بيقسم لـ group السؤال هو هل في هذه الحلقة كلّ قاسم
+
+370
+00:40:57,230 --> 00:41:03,490
+لـ group بديّه جاب له subgroup؟ بالتأكيد؟ يعني عكس
+
+371
+00:41:03,490 --> 00:41:08,550
+النظرية صحية؟ في شفتر 4 هيك؟ طيب
+
+372
+00:41:13,820 --> 00:41:20,700
+هذا كلامك مش صحيح بدليل مثال 5 على الـ section
+
+373
+00:41:20,700 --> 00:41:25,480
+الآن وصلنا له لأنّ عكس نظرية Lagrange غير صحيح
+
+374
+00:41:25,480 --> 00:41:30,100
+وعندك مثال تطلع عليه في الكتاب اللي هو مثال 5
+
+375
+00:41:30,100 --> 00:41:37,280
+بالكتاب يعني .. يعني .. يعني لو عندي قواسم للـ order 
+
+376
+00:41:37,280 --> 00:41:41,780
+تبع الـ .. تبع الـ group ليس بالضرورة أنه الذي يأتي الـ
+
+377
+00:41:41,780 --> 00:41:47,220
+sub group الـ order الذي  هيسوي هذا القواسم قد .. يا
+
+378
+00:41:47,220 --> 00:41:53,010
+شيخ أنت اسمعني شوية بقى ..أحنا بيقول ما يأتي أنا
+
+379
+00:41:53,010 --> 00:41:56,750
+وك تفهم أن عكس نظرية لاجرانج ليس صحيح في حالة ما هو
+
+380
+00:41:56,750 --> 00:42:01,310
+عكس نظرية لاجرانج لو جبت قواسم الـ order ليلي جروب
+
+381
+00:42:01,310 --> 00:42:07,090
+ليس بالضرورة كل قاسم يجيب له sub group قد يكون و قد
+
+382
+00:42:07,090 --> 00:42:11,110
+لا يكون ممكن بعض القواسم يجيلهم sub group يحمل نفس
+
+383
+00:42:11,110 --> 00:42:15,200
+الـ order لكن بعض الآخر ممكن ما يجي له أعطى مثال
+
+384
+00:42:15,200 --> 00:42:20,940
+عندك الـ اللي هو على الـ A4 تمام؟ يبقى ما عليك إلا أن
+
+385
+00:42:20,940 --> 00:42:26,320
+تطلع على هذا المثال و لنا إلى ذلك عودة إن شاء الله
+
+386
+00:42:26,320 --> 00:42:28,500
+على نفس الموضوع في المحاضرة القادمة 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f79016766d7eb115f92f454f79b777e930aa61f7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.srt
@@ -0,0 +1,1544 @@
+1
+00:00:22,140 --> 00:00:26,780
+بسم الله الرحمن الرحيم المرة اللي فاتت أعطينا
+
+2
+00:00:26,780 --> 00:00:31,760
+ساعتين فيه اللي هو ال chapter 7 اللي بتحدث عن
+
+3
+00:00:31,760 --> 00:00:38,300
+Cossets and Lagrange theoremو أعرفنا ال coset و
+
+4
+00:00:38,300 --> 00:00:42,520
+حسبنا ال cosets لمجموعة من ال subgroups يعني
+
+5
+00:00:42,520 --> 00:00:47,080
+أعطينا بدل المثال ثلاثة ثم انتقلنا بعد ذلك إلى
+
+6
+00:00:47,080 --> 00:00:51,500
+Lagrange theorem وهذه النظرية في الجبر مشهورة في
+
+7
+00:00:51,500 --> 00:00:56,980
+كل كتب الجبر نظرية
+
+8
+00:00:56,980 --> 00:01:00,320
+Lagrange ما بعرف إيش كان نص اللي قاعد بيقرا هذا
+
+9
+00:01:00,320 --> 00:01:04,450
+إيش كان نص Lagrange theorem يعنيطبعا جى finite
+
+10
+00:01:04,450 --> 00:01:10,310
+group هذه البداية وبعدها بصرشو اه
+
+11
+00:01:10,310 --> 00:01:13,570
+اشتر
+
+12
+00:01:13,570 --> 00:01:23,130
+نصرية لجراجأيش كان نصنا طريقة Lagrange؟ هاي
+
+13
+00:01:23,130 --> 00:01:27,570
+بدر أضائلكوا يعني الطريقة Lagrange theorem بيقول
+
+14
+00:01:27,570 --> 00:01:31,870
+لو أخدت أي subgroup من ال group اللي عندك فإن ال
+
+15
+00:01:31,870 --> 00:01:36,170
+order لل subgroup يقسم ال order لل group وهذا ما
+
+16
+00:01:36,170 --> 00:01:40,560
+برناه في المرة الماضيةيعني لو أنا عندي group G
+
+17
+00:01:40,560 --> 00:01:45,360
+واخدت any subgroup ان شاء الله ل trivial subgroup
+
+18
+00:01:45,360 --> 00:01:50,060
+كويس؟ يبقى ال order لهذه ال subgroup بيقسم ال
+
+19
+00:01:50,060 --> 00:01:54,760
+order للي group تمام؟ هذا كان نص نظرية Lagrange
+
+20
+00:01:54,760 --> 00:02:00,360
+أعطينا عليها بدل المثال اتنين الآن بدنا نيجي لأول
+
+21
+00:02:00,360 --> 00:02:04,380
+crawlerي عندنا مجموعة من ال crawlers على نظرية
+
+22
+00:02:04,380 --> 00:02:08,890
+Lagrange يعني مجموعة من النتائج النتيجة الأولىبقول
+
+23
+00:02:08,890 --> 00:02:12,950
+في الـ finite group the order of each element of
+
+24
+00:02:12,950 --> 00:02:16,170
+the group divides the order of the group that is
+
+25
+00:02:16,170 --> 00:02:21,030
+لو كان عندي element x موجود في ال group g يبقى ال
+
+26
+00:02:21,030 --> 00:02:26,050
+order ل x بدي يقسمين بدي يقسم ال order ل g يعني
+
+27
+00:02:26,050 --> 00:02:30,270
+الأجران قال لي ال order تبع ال sub group بيقسمين
+
+28
+00:02:30,270 --> 00:02:34,370
+ال order لل group النتيجة هذه تقول لي لأالـ order
+
+29
+00:02:34,370 --> 00:02:37,790
+للـ element كذلك لأي element في ال group بدي أقسم
+
+30
+00:02:37,790 --> 00:02:43,070
+إياه بدي أقسم ال order لل group بدنا نبره صحة هذا
+
+31
+00:02:43,070 --> 00:02:48,130
+الكلام مشان نبره صحة هذا الكلام بدي أقول له افترض
+
+32
+00:02:48,130 --> 00:02:54,530
+ان X هذا موجود في ال group بدي أثبت أن ال order
+
+33
+00:02:54,530 --> 00:02:58,710
+لهذا ال element بدي أقسم إياه ال order لل group
+
+34
+00:02:58,710 --> 00:03:06,550
+بقول له ماشي thenالـ H هذه اللي بدي أخدها subgroup
+
+35
+00:03:06,550 --> 00:03:14,810
+اللي عبارة عن ال subgroup generated by X تمام هذه
+
+36
+00:03:14,810 --> 00:03:24,610
+الآن subgroup الـ H هذه is a subgroup of G طيب
+
+37
+00:03:24,610 --> 00:03:29,290
+تمام بال Lagrange theorem ال order لـ H بدي يقسم
+
+38
+00:03:29,290 --> 00:03:36,020
+من ال order ل Gيبقى بروح بقوله هنا by Lagrange
+
+39
+00:03:36,020 --> 00:03:39,400
+theorem
+
+40
+00:03:39,400 --> 00:03:51,300
+ال order لل H divides ال order ل G طيب لما تبقى
+
+41
+00:03:51,300 --> 00:03:55,160
+هذه ال cyclic شو علاقة ما بين ال order ل H و ال
+
+42
+00:03:55,160 --> 00:04:03,270
+order ل X متساوية بقوله هنا بطء ولكنالأردر لل H
+
+43
+00:04:03,270 --> 00:04:10,070
+بده يساوي الأردر لل X يبقى هذا بده يعطيني بدل ما
+
+44
+00:04:10,070 --> 00:04:13,810
+يقول ال order تبع ال H بده يقسم ال G بده يشيل ال
+
+45
+00:04:13,810 --> 00:04:17,970
+order تبع ال H و يكتب بداله man ال order ل X
+
+46
+00:04:17,970 --> 00:04:24,500
+dividesالأردر لجي وكان الله بالسر علينا إذا من
+
+47
+00:04:24,500 --> 00:04:28,980
+الآن أساعد ان بديك تعرف ان لو عندي group خدت منها
+
+48
+00:04:28,980 --> 00:04:32,540
+subgroup يبقى ال order لهذا ال subgroup يقسم ل
+
+49
+00:04:32,540 --> 00:04:37,180
+group وفي المقابل لو كان عندي أي element x موجود
+
+50
+00:04:37,180 --> 00:04:41,920
+في ال group جي يبقى ال order ل x كمان يقسم ال
+
+51
+00:04:41,920 --> 00:04:46,200
+order ل جي نجي ل ال crawler التانية
+
+52
+00:04:50,810 --> 00:04:57,570
+corollar اتنين بتقول a group of a prime order a
+
+53
+00:04:57,570 --> 00:05:08,570
+group of a prime order is
+
+54
+00:05:08,570 --> 00:05:10,230
+cyclic
+
+55
+00:05:13,050 --> 00:05:19,910
+يعني اي group ال order لها بتكون ال prime اتنين،
+
+56
+00:05:19,910 --> 00:05:24,450
+تلاتة، خمسة، سبعة، احداشر، تلتاشر دائما تبقى
+
+57
+00:05:24,450 --> 00:05:29,710
+Cyclic وإذا Cyclic يبقى abelian لأنه أخدته قبل ذلك
+
+58
+00:05:29,710 --> 00:05:35,950
+في chapter 4 ان any cyclic group isأبيلن لكن العكس
+
+59
+00:05:35,950 --> 00:05:40,310
+ما هواش صحيح طيب a group of a prime order is
+
+60
+00:05:40,310 --> 00:05:44,850
+cyclic بدنا نروح نثبت هذا الكلام بدي أجي أقوله
+
+61
+00:05:44,850 --> 00:06:02,150
+assume that افترض ان ال g is a group with order P
+
+62
+00:06:02,150 --> 00:06:10,640
+that isthat is ال
+
+63
+00:06:10,640 --> 00:06:19,540
+order اللى جى بدى يساوي ال P and ال P is prime
+
+64
+00:06:19,540 --> 00:06:25,600
+يبقى ال order اللى جى هو عبارة عن عدد اول اتنين
+
+65
+00:06:25,600 --> 00:06:30,520
+تلاتة خمسة سبعة احداشر تلاتاشر سبعتاشر تسعتاشر زى
+
+66
+00:06:30,520 --> 00:06:37,650
+ما بدكيبقى جي جروب with order P و ال P هذا عبارة
+
+67
+00:06:37,650 --> 00:06:42,990
+عن a prime number كويس؟ بدي أثبت أن هذا ال group
+
+68
+00:06:42,990 --> 00:06:48,470
+دائما و أبدا تبقى Cycling، كويس؟ يبقى بدأجي أقوله
+
+69
+00:06:48,470 --> 00:06:56,210
+خدلي عنصر A موجود في G طب العنصر A هذا بولدلي ال
+
+70
+00:06:56,210 --> 00:06:57,650
+sub group ولا لأ؟
+
+71
+00:07:00,140 --> 00:07:03,500
+أى element في الجروب بيولد ليه subgroup صحيح ولا
+
+72
+00:07:03,500 --> 00:07:07,240
+لأ يمكن يكون فيش فيها إلا ال identity يمكن عنصرين
+
+73
+00:07:07,240 --> 00:07:12,260
+يمكن تلاتة يمكن أربعة إلى آخرين تمام يبقى little a
+
+74
+00:07:12,260 --> 00:07:23,880
+belongs to g then هذه هي is a is a cyclic subgroup
+
+75
+00:07:26,920 --> 00:07:35,500
+cyclic subgroup of G يبقى
+
+76
+00:07:35,500 --> 00:07:43,660
+ال order لها يقسم من ال order ل G يبقى then ال
+
+77
+00:07:43,660 --> 00:07:48,520
+order لل subgroup generated by A divides
+
+78
+00:07:51,870 --> 00:07:59,770
+divide ال order لجى اللى بده يساوي ال P إيش قواسم
+
+79
+00:07:59,770 --> 00:08:08,310
+ال P واحد و ال P itself يبقى هنالو قلنا little a
+
+80
+00:08:08,310 --> 00:08:14,750
+belongs to g و قللي ال a لا يسوى ال identity كمان
+
+81
+00:08:14,750 --> 00:08:20,410
+اضيف عليها ان ال a لا يسوى ال identity حتى لا نقع
+
+82
+00:08:20,410 --> 00:08:26,920
+في اي مشكلة بعد ذلك تمامطيب يبقى ال order اللى جيه
+
+83
+00:08:26,920 --> 00:08:33,460
+بده يساوي ال P معناه هذا الكلام ان ال order ل ال
+
+84
+00:08:33,460 --> 00:08:39,920
+sub group generated by A بده يساوي واحد or P يبقى
+
+85
+00:08:39,920 --> 00:08:46,060
+هاي القواسم اللى بتقسم ال P الآن هل يمكن لهذا ال
+
+86
+00:08:46,060 --> 00:08:51,020
+order انه يساوي واحد لأ لأنه اشتراط مع ان ال E لا
+
+87
+00:08:51,020 --> 00:08:58,970
+يساوي ال identityبقول له ولكن ال order لل subgroup
+
+88
+00:08:58,970 --> 00:09:05,210
+generated by a لا يمكن أن يساوي الواحد السبب لإن
+
+89
+00:09:05,210 --> 00:09:11,470
+ال a does not equal to a يبقى هذا شو بدي يعطينا
+
+90
+00:09:11,470 --> 00:09:15,530
+هذا بدي يعطينا ان ال order لل subgroup generated
+
+91
+00:09:15,530 --> 00:09:21,050
+by a بدي ساوي 100بدي يساوي ال P طب هذا ايش بدي
+
+92
+00:09:21,050 --> 00:09:25,750
+يعطينا صار ال order لهذه ال sub group بدي يساوي ال
+
+93
+00:09:25,750 --> 00:09:29,850
+P يبقى ال sub group هذه عبارة عن مين عبارة عن G
+
+94
+00:09:29,850 --> 00:09:36,510
+itself تمام يبقى هذا بدي يعطينا ان ال sub group
+
+95
+00:09:36,510 --> 00:09:41,610
+generated by A هي عبارة عن مين ال G itself لإن ال
+
+96
+00:09:41,610 --> 00:09:45,550
+order ل G بدي يساوي ال P و ال order لل sub group
+
+97
+00:09:45,550 --> 00:09:50,080
+هذا بدي يساوي ال Pيبقى الاتنين are equal يبقى هذا
+
+98
+00:09:50,080 --> 00:09:59,080
+معناه إيش؟ معناه إن الـG لجروب الـG is cyclic لو
+
+99
+00:09:59,080 --> 00:10:02,780
+كان السؤال اثبتها إنها abelian، بدي أثبتها إنها
+
+100
+00:10:02,780 --> 00:10:08,180
+الـcyclic ومن ثم بقول لما دام cyclic، يبقى abelian
+
+101
+00:10:08,180 --> 00:10:12,780
+هذه الكرولري رقم اتنين، بدنا نروح للكرولري رقم
+
+102
+00:10:12,780 --> 00:10:16,420
+تلاتة يبقى الكرولري
+
+103
+00:10:18,200 --> 00:10:24,040
+رقم تلاتة او النتيجة رقم تلاتة بتقول little g be a
+
+104
+00:10:24,040 --> 00:10:34,440
+finite group little g be a finite group يبقى
+
+105
+00:10:34,440 --> 00:10:42,020
+group محدودة العدد من العناصر little g be a finite
+
+106
+00:10:42,020 --> 00:10:45,220
+group and let and
+
+107
+00:10:51,350 --> 00:10:57,830
+يبقى الـ A أُصل order للـ G يبقى الـ A أُصل order
+
+108
+00:10:57,830 --> 00:11:01,430
+للـ G يبقى الـ A أُصل order للـ G
+
+109
+00:11:09,240 --> 00:11:13,740
+يعني لو أخدت أي element من ال group و حطيت له أس
+
+110
+00:11:13,740 --> 00:11:18,920
+ال order تبع ال group دائما و أبدا بده يسوى ال
+
+111
+00:11:18,920 --> 00:11:28,960
+identity طيب
+
+112
+00:11:28,960 --> 00:11:34,990
+كويس نشوف نؤكد على صحة ما تكونبنقول ايش احنا عندنا
+
+113
+00:11:34,990 --> 00:11:39,410
+g finite group و ال a belongs to g قال لي اثبت ان
+
+114
+00:11:39,410 --> 00:11:43,890
+ال a مرفوعة للأردر السابع ال g بتساومين ال
+
+115
+00:11:43,890 --> 00:11:47,430
+identity element ال ا لو جيت على ال a corollary
+
+116
+00:11:47,430 --> 00:11:53,770
+one يبقى ال order لل a بتقسمين ال order ل g يبقى
+
+117
+00:11:53,770 --> 00:11:59,970
+by a corollary one
+
+118
+00:12:01,250 --> 00:12:10,590
+الـ order للـ A divides ال order لل G هذا معناته
+
+119
+00:12:10,590 --> 00:12:16,390
+ان ال order لل G بده ساوي ال order لل A في رقم و
+
+120
+00:12:16,390 --> 00:12:25,970
+ليكن K for some positive integer
+
+121
+00:12:25,970 --> 00:12:27,990
+K
+
+122
+00:12:29,620 --> 00:12:35,640
+for some positive integer لكيه الان انا بدى اثبت
+
+123
+00:12:35,640 --> 00:12:43,060
+ان ال a مرفوعة لل أس اللى هو ال order لل g بدى
+
+124
+00:12:43,060 --> 00:12:48,220
+يساوي ال identity بناء عليها بقدر اقول هذا ايه ال
+
+125
+00:12:48,220 --> 00:12:54,260
+order لل g اللى هو عبارة عن ال order لل a مضروب في
+
+126
+00:12:54,260 --> 00:13:01,570
+مينمضروب في K هذا معناه ان ال A مرفوعة لل order
+
+127
+00:13:01,570 --> 00:13:08,350
+تبع ال A كل هذا أس K طب ال A لما يكون مرفوع لل
+
+128
+00:13:08,350 --> 00:13:13,070
+order تبعه كده بيعطينا ال identity يبقى هذا
+
+129
+00:13:13,070 --> 00:13:17,310
+بيعطينا ال identity أس K ال identity أس K بيعطينا
+
+130
+00:13:17,310 --> 00:13:23,230
+من ال identity يبقى بناء علي أسار ال A أس ال order
+
+131
+00:13:23,230 --> 00:13:27,970
+لل Gدائما و أبدا بدي أعطينا ماذا؟ بدي أعطينا ال
+
+132
+00:13:27,970 --> 00:13:33,850
+identity element تمام بدي أخاطر قبل مفروض نعطي بعض
+
+133
+00:13:33,850 --> 00:13:39,310
+الأمثلة على هذه ال crawlers بدنا نيجي لأول مثال
+
+134
+00:13:39,310 --> 00:13:42,090
+examples او example one
+
+135
+00:13:45,840 --> 00:13:52,120
+example one بيقول show that
+
+136
+00:13:52,120 --> 00:14:00,260
+بيّلي ان every group
+
+137
+00:14:00,260 --> 00:14:09,300
+of order less than or equal to 5
+
+138
+00:14:16,890 --> 00:14:32,590
+less than or equal to five is abelian يعني
+
+139
+00:14:32,590 --> 00:14:35,550
+بنثبت أن أي group
+
+140
+00:14:38,460 --> 00:14:43,920
+الـ order تبعها بده يساوي خمسة دائما و أبدا أو أقل
+
+141
+00:14:43,920 --> 00:14:47,440
+من خمسة is abelian يعني لو عندي group فيها عنصر
+
+142
+00:14:47,440 --> 00:14:51,540
+واحد أو group فيها عنصرين أو group فيها تلتة عناصر
+
+143
+00:14:51,540 --> 00:14:55,880
+أو أربعة عناصر أو خمسة عناصر كل هذه الأنموعة من ال
+
+144
+00:14:55,880 --> 00:15:01,600
+group تبقى دائما و أبدا abelian طيب الآن solution
+
+145
+00:15:06,050 --> 00:15:11,890
+أخذ الان لو ال order اللى جى هو عبارة عن واحد يعني
+
+146
+00:15:11,890 --> 00:15:15,930
+ايش فيها فقط ال identity element و ال identity
+
+147
+00:15:15,930 --> 00:15:21,310
+الموجودة مع نفسه صحيح ولا لأ يبقى أبيل يعني يبقى
+
+148
+00:15:21,310 --> 00:15:27,180
+هنا بدأ أخد النقطة الأولى Fلو كان ال order لل G
+
+149
+00:15:27,180 --> 00:15:33,360
+بده يسوي واحد صحيح then ال G بده يسوي ال identity
+
+150
+00:15:33,360 --> 00:15:42,340
+فقط لا غير و هذا بده يعطينا ان ال G is abelian طيب
+
+151
+00:15:42,340 --> 00:15:51,100
+لو كان ال order لل G بده يسوي اتنين و تلاتة or
+
+152
+00:15:51,100 --> 00:15:59,130
+خمسةيبقى كل هما دول مالهم primes then ال order لل
+
+153
+00:15:59,130 --> 00:16:05,970
+G is prime في الحالات التلاتة ايش بيقول ال crawler
+
+154
+00:16:05,970 --> 00:16:10,790
+اتنين ال group of prime order is cyclic يبقى هذا
+
+155
+00:16:10,790 --> 00:16:17,250
+بده يعطينا ان ال G is cyclic طب و اذا ال G is
+
+156
+00:16:17,250 --> 00:16:18,910
+cyclic ابيه يعني
+
+157
+00:16:23,770 --> 00:16:29,690
+يبقى الان اثبتنا ان في حالة الواحد واتنين والتلاتة
+
+158
+00:16:29,690 --> 00:16:34,710
+والخمسة ابيليان ضالت ايه؟ ضالت الأربعة يبقى بداجي
+
+159
+00:16:34,710 --> 00:16:41,010
+اقوله هنا F ال order لل G بده يساوي أربعة
+
+160
+00:16:44,930 --> 00:16:51,590
+لو افترضت ان ال order للجي يكون 4 لو اخذت اي non
+
+161
+00:16:51,590 --> 00:16:56,470
+identity element في ال group جي كده احتمال ال
+
+162
+00:16:56,470 --> 00:17:02,890
+order يكون له واحد استبعدناه انا قلت non identity
+
+163
+00:17:02,890 --> 00:17:07,750
+ليه بيبقى فيش الا اتنين او اربعة طب لو كان ال
+
+164
+00:17:07,750 --> 00:17:14,810
+order لل element يسوى 4بكون generator لـ G لأن ال
+
+165
+00:17:14,810 --> 00:17:17,990
+order يبقى الـ G الـ cyclic وبالتالي أبدا طلت
+
+166
+00:17:17,990 --> 00:17:24,390
+المشكلة وين عند اتنين فبداش أقوله هنا if يبقى if
+
+167
+00:17:24,390 --> 00:17:33,590
+ال order لـ G بده يسوى أربعة then any non identity
+
+168
+00:17:33,590 --> 00:17:39,490
+element has
+
+169
+00:17:40,760 --> 00:17:44,540
+order اتنين
+
+170
+00:17:44,540 --> 00:17:50,560
+واربع if
+
+171
+00:17:50,560 --> 00:18:01,960
+order لأ بدوا يساوي اربع then order لأ بدوا يساوي
+
+172
+00:18:01,960 --> 00:18:09,370
+order لجيمعنى هذا الكلام ان الـ G هذه بدها تساوي ل
+
+173
+00:18:09,370 --> 00:18:16,010
+group generated by A هذا يعني ان الـ G هو Cyclic
+
+174
+00:18:16,010 --> 00:18:25,910
+وهذا يعني ان الـ G هو Abelian بلت مشكلتنا وين؟
+
+175
+00:18:25,910 --> 00:18:40,540
+ايوة يبقى Fالـ A موجود في G with ال order للـ A
+
+176
+00:18:40,540 --> 00:18:48,760
+بده يساوي اتنين then ال A تربيه بده يساوي ال
+
+177
+00:18:48,760 --> 00:18:55,660
+identity مظبوط يعني ال A صار بده يساوي ال A
+
+178
+00:18:55,660 --> 00:18:56,060
+inverse
+
+179
+00:19:01,020 --> 00:19:07,280
+يبقى انا باخد two elements من G و اثبت ان ال X في
+
+180
+00:19:07,280 --> 00:19:12,460
+Y بيساوي ال Y X باستخدام المعلومة اللي عندنا هذا
+
+181
+00:19:12,460 --> 00:19:19,100
+يبقى بروح اقوله افترض ان ال X و ال Y عناصر موجودة
+
+182
+00:19:19,100 --> 00:19:19,580
+عندنا
+
+183
+00:19:37,640 --> 00:19:47,160
+داجة اقول له let ال X و ال Y موجودة في G then ال X
+
+184
+00:19:47,160 --> 00:19:56,920
+Y موجودة في G if ال order لل X Y يساوي اتنين then
+
+185
+00:19:56,920 --> 00:20:05,460
+ال X Y لكل تربيع يساوي من؟ يساوي ال identityطب ال
+
+186
+00:20:05,460 --> 00:20:11,760
+X Y تربيع هذا بقدر اقول X تربيع Y تربيع لا تبقى
+
+187
+00:20:11,760 --> 00:20:16,980
+بيلا ما هي اشابه لاني بقدرش مظبوط لكن كل اللي بقدر
+
+188
+00:20:16,980 --> 00:20:23,960
+اقوله then اللي هو من ال X Y في ال X Y يسوى ال
+
+189
+00:20:23,960 --> 00:20:31,570
+identity تمامطب لو ضربت الطرفين في y inverse من
+
+190
+00:20:31,570 --> 00:20:39,630
+جهة اليمين يبقى بيصير عندي x y x بده يساوي e في y
+
+191
+00:20:39,630 --> 00:20:45,010
+inverse اللي هو بمين؟ ب y inverse طب اضرب كمان في
+
+192
+00:20:45,010 --> 00:20:51,350
+x inverse من جهة اليمين هذا يعني ان ال x في y بده
+
+193
+00:20:51,350 --> 00:20:57,090
+يساوي ال y inverse في ال x inverseالان احنا قلنا
+
+194
+00:20:57,090 --> 00:21:02,790
+هنا ايش ان ال element اللي ال order له يساوي اتنين
+
+195
+00:21:02,790 --> 00:21:09,650
+ال element يساوي معكوسه تمام طيب بناء عليه هذا بده
+
+196
+00:21:09,650 --> 00:21:16,030
+يعطينا ان ال x في ال y بده يساوي من ال y في ال x
+
+197
+00:21:17,170 --> 00:21:23,450
+يعني شيلت كل X وحطيت بدلها X وشيلت كل Y وحطيت
+
+198
+00:21:23,450 --> 00:21:31,830
+بدلها Y هذا يعني ان ال G is abelianيبقى معنى هذا
+
+199
+00:21:31,830 --> 00:21:35,950
+الكلام أن الـ G abelian سواء كان ال order إلها
+
+200
+00:21:35,950 --> 00:21:39,470
+واحد و لا اتنين و لا تلاتة و لا أربع و لا خمسة من
+
+201
+00:21:39,470 --> 00:21:44,470
+الآن فصاعدا بدك تاخدها قاعدة أي group ال order
+
+202
+00:21:44,470 --> 00:21:48,750
+اللي هيسوي خمسة أو أقل من خمسة يبقى هذه ال group
+
+203
+00:21:48,750 --> 00:21:54,330
+عبارة عن abelian group خد كمان مثال، المثال هذا هو
+
+204
+00:21:54,330 --> 00:22:02,450
+أحد أسئلة الكتاب يبقى example twoexample 2 هو
+
+205
+00:22:02,450 --> 00:22:10,690
+عبارة عن سؤال 26 من الكتاب بيقول let g
+
+206
+00:22:10,690 --> 00:22:25,890
+be a group of order 25 prove that
+
+207
+00:22:25,890 --> 00:22:34,580
+اثبت انهالـ G is cyclic
+
+208
+00:22:34,580 --> 00:22:40,580
+or الـ
+
+209
+00:22:40,580 --> 00:22:48,600
+G فُس خمسة بده يساوي ال identity for all G اللي
+
+210
+00:22:48,600 --> 00:22:49,720
+belongs to G
+
+211
+00:23:04,000 --> 00:23:09,320
+خلّيني أبقى معناه هنا السؤال مرة تانية انا عندي
+
+212
+00:23:09,320 --> 00:23:14,300
+group فيها خمسة وعشرين عنصر ال order لها يسوى خمسة
+
+213
+00:23:14,300 --> 00:23:20,800
+وعشرين قال لي بتثبت ان جي هذي Cyclic يا اما الجي
+
+214
+00:23:20,800 --> 00:23:24,940
+أسخمسة بده يسوى ال identity لكل الجي اللي belongs
+
+215
+00:23:24,940 --> 00:23:30,640
+to جي اذا انا بدي استبعد واحد و اثبت مين لانه قال
+
+216
+00:23:30,640 --> 00:23:35,230
+لي or هذا او هذايبقى انا لو روحته قولتله هنا
+
+217
+00:23:35,230 --> 00:23:46,330
+assume افترض ان ال G is non-cyclic ماهياش
+
+218
+00:23:46,330 --> 00:23:54,310
+cyclic and ال order لل G بده يساوي خمسة وعشرين
+
+219
+00:23:54,310 --> 00:24:01,760
+يبقاش بتثبت يا شبابالجيوس خمسة يسوى من ال identity
+
+220
+00:24:01,760 --> 00:24:06,500
+element الان ال جي موجود في جي يبقى ال order له
+
+221
+00:24:06,500 --> 00:24:14,680
+يقسم من الخمسة وعشرين يبقى هنا since لما ان ال جي
+
+222
+00:24:14,680 --> 00:24:19,660
+belongs to جي ال order لل جي divide
+
+223
+00:24:21,710 --> 00:24:26,870
+اللي هو الخمسة وعشرين معنى هذا الكلام ان ال order
+
+224
+00:24:26,870 --> 00:24:35,230
+للجي يا اما واحد يا اما خمسة or خمسة وعشرينبنستبعد
+
+225
+00:24:35,230 --> 00:24:40,550
+لخمسة وعشرين لأن لو كان ال order خمسة وعشرين لصارة
+
+226
+00:24:40,550 --> 00:24:45,630
+ال G Cyclic قال لا هي ما هي ال Cyclic إذا لا يمكن
+
+227
+00:24:45,630 --> 00:24:52,330
+لل order تبع ال element هذا أنه يسوى من ال order ل
+
+228
+00:24:52,330 --> 00:24:56,110
+G small هذا شباب مش جي كتر الجي كتر هي خمسة وعشرين
+
+229
+00:24:56,110 --> 00:25:00,050
+ال order لل element يا بده يسوى واحد يا إما خمسة
+
+230
+00:25:00,050 --> 00:25:06,310
+يا إما خمسة وعشرينالان انا باجي بقوله ال order لل
+
+231
+00:25:06,310 --> 00:25:13,770
+G بدي سوى خمسة و عشرين impossible هذا الكلام غير
+
+232
+00:25:13,770 --> 00:25:26,190
+ممكن because السبب ان ال G is not cyclicيبقى الـ G
+
+233
+00:25:26,190 --> 00:25:30,690
+ما هياش Cycle طيب استبعدنا منين؟ الخمسة و عشرين
+
+234
+00:25:30,690 --> 00:25:36,250
+ضايلة عندنا الـ G ال order له يبدو يساوي واحد يبدو
+
+235
+00:25:36,250 --> 00:25:45,550
+يساوي خمسة الان لو كان ال order F ال order ل ال G
+
+236
+00:25:45,550 --> 00:25:51,260
+يبدو يساوي واحد thenلما يكون الارض اللي جي بده
+
+237
+00:25:51,260 --> 00:25:54,680
+يساوي واحد يبقى مين هي جي هذه ال identity element
+
+238
+00:25:54,680 --> 00:26:01,260
+يبقى then الجي بدها تساوي ال identity element يبقى
+
+239
+00:26:01,260 --> 00:26:07,660
+الجي أس خمسة بده يساوي ال identity element أس خمسة
+
+240
+00:26:07,660 --> 00:26:12,600
+يبقى جي أس خمسة ال identity أس خمسة من بال
+
+241
+00:26:12,600 --> 00:26:19,940
+identity وهو المطلوب الحالة التانية لو كانالـ
+
+242
+00:26:19,940 --> 00:26:26,180
+order للـ G بده يساوي خمسة then الـ G أُس خمسة بده
+
+243
+00:26:26,180 --> 00:26:32,180
+يساوي ال identity و هو المفتوح يبقى بناء عليه مدام
+
+244
+00:26:32,180 --> 00:26:37,200
+الـ G non-cyclic الـ G أُس خمسة بده يساوي ال
+
+245
+00:26:37,200 --> 00:26:41,140
+identity element دائما و أبدا
+
+246
+00:27:02,160 --> 00:27:09,020
+طب ننتقل الى تعريف جئى او لكرولري رقم اربعة كرولري
+
+247
+00:27:09,020 --> 00:27:18,180
+رقم اربعة بسموها
+
+248
+00:27:18,180 --> 00:27:23,420
+Fermat Fermat's
+
+249
+00:27:23,420 --> 00:27:26,260
+little theorem
+
+250
+00:27:31,620 --> 00:27:39,240
+نصها كتالة بيقول for every integer a for every
+
+251
+00:27:39,240 --> 00:27:56,220
+integer a and every prime p and every prime p ال a
+
+252
+00:27:56,220 --> 00:28:05,260
+to the power p modulo pبدو يساوي ال a modulo p
+
+253
+00:28:05,260 --> 00:28:08,480
+بدنا
+
+254
+00:28:08,480 --> 00:28:11,720
+نبرهم صحيتها ل proof
+
+255
+00:28:16,540 --> 00:28:21,300
+هذه سميت باسم FairMaths لانه الاكتشاف هذه الشغلة
+
+256
+00:28:21,300 --> 00:28:26,420
+وسميت little لان انا بظغر الرقم الكبير انا عند رقم
+
+257
+00:28:26,420 --> 00:28:32,620
+كبير ضخم بظغره على طول الخط يعني بجيب رقم مكافئ له
+
+258
+00:28:32,620 --> 00:28:38,980
+في حالة اذا كان المقياس هو P فبقول أي integer A و
+
+259
+00:28:38,980 --> 00:28:43,630
+every prime Pالـ A to the power of P موديولو P
+
+260
+00:28:43,630 --> 00:28:49,090
+اللاحظ ال موديولو P هو الأس اللي عندى هذا و هذا
+
+261
+00:28:49,090 --> 00:28:54,040
+لازم يكون ال prime number شرط أساسي مش أي رقمإن
+
+262
+00:28:54,040 --> 00:28:59,300
+حدث ذلك يبقى بقوله هذا a modulo p يعني هذا ال p
+
+263
+00:28:59,300 --> 00:29:03,800
+بكون اتخلصت منها وبالتالي الرقم الضخم هذا صغرته
+
+264
+00:29:03,800 --> 00:29:08,260
+إلى رقم a modulo p ال a هذه يمكن تكون أكبر من ال p
+
+265
+00:29:08,260 --> 00:29:12,980
+ويمكن تكون أصغر من ال p محط الشرط عندى كل اللي
+
+266
+00:29:12,980 --> 00:29:17,480
+حطوا انه انتجار و ال p is a prime نروح نسبة صحة
+
+267
+00:29:17,480 --> 00:29:22,090
+هذا الكلام بأنا بدي أخد حالتينالحالة الأولى لو كان
+
+268
+00:29:22,090 --> 00:29:27,790
+ال A أقل من P و الحالة الثانية لو كان ال A أكبر من
+
+269
+00:29:27,790 --> 00:29:34,610
+P بدي أدرس ايه الحالة تانية طب لو يساو لو ال A ساو
+
+270
+00:29:34,610 --> 00:29:38,790
+ال P يبقى من 100 لما يبقى Zero بدي أساوي Zero على
+
+271
+00:29:38,790 --> 00:29:43,710
+طول الخطط طيب يبقى بدي أجي يبقى ماعنديش مشكلة في
+
+272
+00:29:43,710 --> 00:29:47,930
+حالة ال Zero ليش بصيحة خلاص Zero بساوي Zero طيب
+
+273
+00:29:47,930 --> 00:29:59,460
+بدي أخد Fالـ P less than 0 لأ
+
+274
+00:29:59,460 --> 00:30:08,740
+لو كان less than A لو كان F ال A less than P لو
+
+275
+00:30:08,740 --> 00:30:19,080
+كان ال A أقل من P then ال P ال .. ال A هذابتكون
+
+276
+00:30:19,080 --> 00:30:25,500
+موجود في مجموعته الأعداد واحد و اتنين و تلاتة و
+
+277
+00:30:25,500 --> 00:30:33,740
+لغاية P minus ال one أكيد مية المية مدام A integer
+
+278
+00:30:33,740 --> 00:30:38,820
+أصغر من P يبقى A موجود في المجموعة هذه طب مين هي
+
+279
+00:30:38,820 --> 00:30:46,580
+المجموعة هذه مش UP يبقى هذه اللي هي تساوي UP
+
+280
+00:30:49,020 --> 00:30:59,020
+يبقى معنى هذا الكلام ان ال a موجود في ال U P طيب
+
+281
+00:30:59,020 --> 00:31:08,500
+يبقى قداش ال order ل U P نقص واحد، كويس هذا بيقين
+
+282
+00:31:08,500 --> 00:31:20,930
+اللي عند ال order ل U P بيسوي P ناقص واحدطبعا طيب
+
+283
+00:31:20,930 --> 00:31:26,950
+الآن ان يأتي crawler فيهم هذه اللي قالتلي اه
+
+284
+00:31:26,950 --> 00:31:31,070
+مشحناها اللي هو a او زي اظن ال crawler رقم تلاتة
+
+285
+00:31:31,070 --> 00:31:36,270
+ال a او ال order لل a بدو يشتوي ال ID تلاتة طيب
+
+286
+00:31:36,270 --> 00:31:43,790
+هنا from crawler ثلاثة
+
+287
+00:31:43,790 --> 00:31:52,450
+اي element بد أخد امرفوع لل order تبع ال U P بدي
+
+288
+00:31:52,450 --> 00:32:00,810
+يسوى ال identity اللي هو واحد هذا الكلام
+
+289
+00:32:00,810 --> 00:32:06,510
+ايش معناه؟ معناه ال A أس ال P ناقص واحد بدي يسوى
+
+290
+00:32:06,510 --> 00:32:15,030
+واحد طيب لو ضربت الطرفين في A ايش بيصير عندي؟ A أس
+
+291
+00:32:15,030 --> 00:32:21,900
+P بدي يسوى ال Aيبقى معناه هذا كلمة ان a is p
+
+292
+00:32:21,900 --> 00:32:28,960
+modulo p بدي سوى a modulo p مادة ما الرقمين هذا
+
+293
+00:32:28,960 --> 00:32:33,320
+اللي بيسووا بعض اذا بدي يكون هذا modulo p بدي سوى
+
+294
+00:32:33,320 --> 00:32:38,060
+هذا modulo p تماما وهو المطلوب هذا لو كانت ايش ال
+
+295
+00:32:38,060 --> 00:32:44,840
+a اقل من p طب لو كانت ال a اكبر من p يبقى f ال a
+
+296
+00:32:44,840 --> 00:32:46,940
+greater than p
+
+297
+00:32:51,570 --> 00:32:57,570
+يعني ال A هذي P زائد شوية اتنين P زائد شوية تلتة P
+
+298
+00:32:57,570 --> 00:33:01,970
+عشرين P زائد زائد شوية تمام يبقى بال division
+
+299
+00:33:01,970 --> 00:33:09,730
+algorithm بقول له then ال A هذا بده يساوي ال M P
+
+300
+00:33:09,730 --> 00:33:15,870
+زائد ال R يعني مضاعفة ال P زائد ال R و ال R هذي
+
+301
+00:33:15,870 --> 00:33:25,010
+اكبر من أو تساوي Zero اقل من مينأقل من P طيب لو
+
+302
+00:33:25,010 --> 00:33:31,190
+جيت مدام عرفت زيك اللي هو خدت الآن ال A modulo P
+
+303
+00:33:31,190 --> 00:33:39,730
+كده ايش بده تساوي؟ R انا عند ال A بده تساوي MP زي
+
+304
+00:33:39,730 --> 00:33:43,630
+ده انا خدت ال A modulo P بقى مضاعفات ال P بطيروا
+
+305
+00:33:43,630 --> 00:33:49,810
+ايش بظهر عندي؟ بظهر عندي Rيبقى هذا بيبقى عندى مين؟
+
+306
+00:33:49,810 --> 00:33:56,570
+بيبقى عندى R فقط لا غير طيب الان ال R محصورة من
+
+307
+00:33:56,570 --> 00:34:01,590
+اين الى اين؟ من Zero الى P وانا جايل ان ال A
+
+308
+00:34:01,590 --> 00:34:08,210
+modulo P بده ساوى ال R ال R يعني موجودة وين؟ في ال
+
+309
+00:34:08,210 --> 00:34:17,490
+U P صح ولا لا؟موجودة في ال U P ليش؟ لأنها محصورة
+
+310
+00:34:17,490 --> 00:34:25,050
+من صفر إلى P طبعا طيب مدام محصورة هذه تساوي هذه
+
+311
+00:34:25,050 --> 00:34:31,030
+وهذه موجودة هنا اذا automatic على طول الخطأيش قلنا
+
+312
+00:34:31,030 --> 00:34:35,970
+هنا لو كان في البرهان الأول بقول لما تبقى ال a
+
+313
+00:34:35,970 --> 00:34:41,750
+موجودة في ال U P استنتجنا ان هذا الكلام ماله صحيح
+
+314
+00:34:41,750 --> 00:34:52,610
+تمام يبقى باجي بقول from the above from من البرهان
+
+315
+00:34:52,610 --> 00:35:00,500
+أعلاهيبقى ال a modulo p modulo p بدى يسوى a أس p
+
+316
+00:35:00,500 --> 00:35:07,300
+modulo p وانتهينا منها يبقى على كل الأمر يعنى سواء
+
+317
+00:35:07,300 --> 00:35:12,360
+كان ال a أكبر من p ولا أصغر من p فإن ال a to the
+
+318
+00:35:12,360 --> 00:35:18,220
+power p modulo p بدى يسوى منها ال a modulo p حد
+
+319
+00:35:18,220 --> 00:35:24,110
+يلقى أي استفسار هناطب نحاول نعطي اكثر من مثال على
+
+320
+00:35:24,110 --> 00:35:30,770
+هذه النقطة المثال الأول يبقى
+
+321
+00:35:30,770 --> 00:35:41,150
+examples find
+
+322
+00:35:41,150 --> 00:35:54,640
+the exact value متجددش القيمة الحقيقيةof خمستاشر
+
+323
+00:35:54,640 --> 00:36:04,480
+أس احداش موديولو أحداش of وهذا يجب أن أعتبرها ايه
+
+324
+00:36:04,480 --> 00:36:11,760
+ويجب أن نأتي إلى الـ B يجب أن يكون سبعة أس تلتاش
+
+325
+00:36:11,760 --> 00:36:15,880
+موديولو أحداش
+
+326
+00:36:29,550 --> 00:36:35,690
+خلّي أبقى لك هنا بقول هات للقيمة الحقيقية للخمستاش
+
+327
+00:36:35,690 --> 00:36:41,550
+أس احداش موديولو أحداش وكذلك سبعة أس تلتاش موديولو
+
+328
+00:36:41,550 --> 00:36:47,610
+أحداش الحل كالتالي بيروح أخد إيه؟ نمر إيه؟ نمر
+
+329
+00:36:47,610 --> 00:36:54,530
+إيه؟ بدي أخدله الخمستاشر أس إحداش موديولو أحداش
+
+330
+00:36:54,530 --> 00:37:01,420
+النتج خمستاشروديولو أحداشر صحيك يا شباب
+
+331
+00:37:05,780 --> 00:37:11,120
+لو كان هذا P و هذا P يتماين نفس بعض يبقى هذا يقول
+
+332
+00:37:11,120 --> 00:37:17,060
+الى E modulo P يبقى انا عندي خمستاش و احداش modulo
+
+333
+00:37:17,060 --> 00:37:20,380
+احداش يبقى انا عندي خمستاش modulo احداش يبقى انا
+
+334
+00:37:20,380 --> 00:37:20,420
+عندي خمستاش modulo احداش يبقى انا عندي خمستاش
+
+335
+00:37:20,420 --> 00:37:23,320
+modulo احداش هي خمستاش modulo احداش خمستاش modulo
+
+336
+00:37:23,320 --> 00:37:28,240
+احداش اكبر من الاحداش اذا بدى اشيل منها الاحداش او
+
+337
+00:37:28,240 --> 00:37:32,840
+مضاعفات الاحداش كدهش بطلع يبقى النتيجة تساوي اربع
+
+338
+00:37:33,130 --> 00:37:39,010
+يبقى هذا سؤال direct مباشر لكن قد يكون السؤال غير
+
+339
+00:37:39,010 --> 00:37:46,030
+مباشر غير مباشر كيف؟ زي ما قال لي سبعة أس تلتاشر
+
+340
+00:37:46,030 --> 00:37:56,510
+موديولو أحداش بده يساوي يعني
+
+341
+00:37:56,510 --> 00:37:59,850
+مانفعش أقول الجواب اللي هو سبعة موديولو أحداش؟
+
+342
+00:37:59,850 --> 00:38:02,290
+خلط؟
+
+343
+00:38:03,320 --> 00:38:09,060
+غلطة و نصف بدي يكون الرقم هذا الأس هو المقياس اللي
+
+344
+00:38:09,060 --> 00:38:15,220
+عندي طيب يعني ايش؟ يعني سبعة أس تلتاش بدي اكتبها
+
+345
+00:38:15,220 --> 00:38:21,920
+بدلالة سبعة أس أحداش يبقى هذه بدها تساوي سبعة أسي
+
+346
+00:38:21,920 --> 00:38:30,490
+أحداش كدهش بيظل سبعة ترابيع كل موديولو أحداشهذه هي
+
+347
+00:38:30,490 --> 00:38:37,810
+عبارة عن سبعة أوسى احداش موديولو احداش مضروبة في
+
+348
+00:38:37,810 --> 00:38:46,530
+من في سبعة ترابية موديولو احداشيبقى حولتها إلى حصل
+
+349
+00:38:46,530 --> 00:38:50,850
+ضرب الرقمين اللي عندنا الان من firmat theorem هذه
+
+350
+00:38:50,850 --> 00:38:55,210
+شكلة شكل firmat theorem يبقى هذا سبعة موديولو
+
+351
+00:38:55,210 --> 00:39:01,570
+احداش يبقى هنا سبعة موديولو احداش من firmat
+
+352
+00:39:01,570 --> 00:39:07,610
+theorem وهذه سبعة تربية يعني تسعة واربعين موديولو
+
+353
+00:39:07,610 --> 00:39:14,600
+من احداش يبقى هذا الكلام يسامالان هذه السابعة
+
+354
+00:39:14,600 --> 00:39:20,400
+موديولو احداش لان تسعة واربعين موديولو احداش فيها
+
+355
+00:39:20,400 --> 00:39:27,020
+قداش لان احداش في اربعة من تسعة واربعين بظال خمسة
+
+356
+00:39:27,020 --> 00:39:34,180
+يبقى مضروبة في من مضروبة في خمسة موديولو احداش
+
+357
+00:39:37,280 --> 00:39:44,860
+خمسة و تلاتين عبارة
+
+358
+00:39:44,860 --> 00:39:51,290
+عن أحد عشر في تلاتة تلاتة و تلاتين زائدأتنين يبقى
+
+359
+00:39:51,290 --> 00:39:56,130
+الناتج كله يساوي اتنين يبقى هالرقم الضخم اللى
+
+360
+00:39:56,130 --> 00:40:00,650
+عندنا هذا اللى هو سبعة أس طلع تاشر يعني بدي أضرب
+
+361
+00:40:00,650 --> 00:40:04,990
+سبعة في نفسها طلع تاشر مرة و أجيبلها الموديل
+
+362
+00:40:04,990 --> 00:40:09,150
+أحداشر اختصرناها و قولنا ناتج يساوي قداشر يساوي
+
+363
+00:40:09,150 --> 00:40:11,490
+اتنين على طول الخط
+
+364
+00:40:16,940 --> 00:40:24,100
+تحسب شو ماعليكش قيود مدام انت ماشي سليم يبقى احسب
+
+365
+00:40:24,100 --> 00:40:29,680
+اللي بدك يام متى لازم القمع عارف قصده لو حطينا
+
+366
+00:40:29,680 --> 00:40:35,960
+element وحطينا له قص كبير وبتصغر هذا القص قصده اه
+
+367
+00:40:35,960 --> 00:40:43,830
+طيب في عندنا خد بالك شغلة بدي اشير اليهانظرية
+
+368
+00:40:43,830 --> 00:40:50,950
+Lagrange بتقول ال order لل subgroup بيقسم من؟
+
+369
+00:40:50,950 --> 00:40:57,230
+بيقسم ل group السؤال هو هل في هذه الحلقة كل خاسم
+
+370
+00:40:57,230 --> 00:41:03,490
+لل group بديه جابله subgroup؟ بالتأكيد؟ يعني عكس
+
+371
+00:41:03,490 --> 00:41:08,550
+النظرية الصحية؟ في شفتر أربعة هيك؟ طيب
+
+372
+00:41:13,820 --> 00:41:20,700
+هذا كلامك مش صحيح بدليل مثال خمسة على ال section
+
+373
+00:41:20,700 --> 00:41:25,480
+الان وصلنا له لأن عكس نظرية Lagrange غير صحيح
+
+374
+00:41:25,480 --> 00:41:30,100
+وعندك مثال اتطلع عليه في الكتاب اللي هو مثال خمسة
+
+375
+00:41:30,100 --> 00:41:37,280
+بالكتابيعني .. يعني .. يعني لو عندي قواسم لل order
+
+376
+00:41:37,280 --> 00:41:41,780
+تبع ال .. تبع ال group ليس بالضرورة انه الاجي ال
+
+377
+00:41:41,780 --> 00:41:47,220
+sub group ال order اللي هيسوي هذا القواسم قد .. يا
+
+378
+00:41:47,220 --> 00:41:53,010
+شيخ انت اسمعلي شوية بقى ..أحنا بيقول ما ياتي انا
+
+379
+00:41:53,010 --> 00:41:56,750
+وك تفهم ان عكس نظرية لاجراني ليس صحيح حالة ما هو
+
+380
+00:41:56,750 --> 00:42:01,310
+عكس نظرية لاجراني لو جيبت قواسم ال order ليلي جروب
+
+381
+00:42:01,310 --> 00:42:07,090
+ليس بالضرورة كل قاسم يجيبله sub group قد يكون و قد
+
+382
+00:42:07,090 --> 00:42:11,110
+لا يكون ممكن بعض القواسم يجيلهم sub group يحمل نفس
+
+383
+00:42:11,110 --> 00:42:15,200
+ال orderلكن بعض الأخر ممكن مالاجيش له أعطى مثال
+
+384
+00:42:15,200 --> 00:42:20,940
+عندك اللى هو على ال A4 تمام؟ يبقى ماعلك إلا أن
+
+385
+00:42:20,940 --> 00:42:26,320
+تطلع على هذا المثال و لنا إلى ذلك عودة ان شاء الله
+
+386
+00:42:26,320 --> 00:42:28,500
+على نفس الموضوع في المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f1b90dc798900cf8111cd8134acf3609b254055b
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM.srt
@@ -0,0 +1,1807 @@
+1
+00:00:21,330 --> 00:00:26,210
+بسم الله الرحمن الرحيم المرة الماضية آخر حاجة 
+
+2
+00:00:26,210 --> 00:00:29,750
+تكلمنا فيها أعطينا definition للـ center للـ group
+
+3
+00:00:30,390 --> 00:00:36,030
+نعيد هذا الـ definition ومن ثم نأخذ نظرية عليه
+
+4
+00:00:36,030 --> 00:00:41,050
+فقلنا المرة اللي فاتت أن الـ center تبع الـ group G
+
+5
+00:00:41,050 --> 00:00:47,610
+نديله رمز Z of G وقلنا هو كل العناصر الـ A اللي
+
+6
+00:00:47,610 --> 00:00:55,510
+موجودة في G بحيث أن الـ AX بيساوي الـ XA لكل الـ X
+
+7
+00:00:55,510 --> 00:01:02,150
+اللي belongs to the group G إذا ما معنى الـ
+
+8
+00:01:02,150 --> 00:01:05,510
+Center تبع الـ Group؟ معنى الـ Center تبع الـ 
+
+9
+00:01:05,510 --> 00:01:11,070
+Group هو كل الـ elements اللي كميوتس مع بقية
+
+10
+00:01:11,070 --> 00:01:15,090
+عناصر الـ Group يعني لو أخذت element وجيته كميوتس
+
+11
+00:01:15,090 --> 00:01:18,030
+مع جميع عناصر الـ Group بقول هذا من الـ Center
+
+12
+00:01:18,030 --> 00:01:22,970
+اللي بعده اللي بعده لغاية ما يطلع كل العناصر اللي
+
+13
+00:01:22,970 --> 00:01:28,500
+بتكون كميوتس مع جميع عناصر الـ Group يبقى هذول
+
+14
+00:01:28,500 --> 00:01:32,560
+بيكونوا مين؟ بيكونوا الـ center تبع الـ group أبسط
+
+15
+00:01:32,560 --> 00:01:37,380
+الأشياء الـ identity element موجود في مين؟ في الـ
+
+16
+00:01:37,380 --> 00:01:40,260
+center تبع الـ group لأن الـ identity elements
+
+17
+00:01:40,260 --> 00:01:45,740
+commutes with all elements of G يبقى كل العناصر
+
+18
+00:01:45,740 --> 00:01:51,520
+اللي موجودة في G واللي بتبقى commutes مع أي عنصر
+
+19
+00:01:51,520 --> 00:01:56,490
+موجود في G يبقى هذا بسميه الـ center of G الآن في
+
+20
+00:01:56,490 --> 00:02:01,530
+نظرية بتقول الـ center هذا هو الـ subgroup فبدنا
+
+21
+00:02:01,530 --> 00:02:06,670
+نروح نبرهن صحة هذا الكلام يبقى النظرية بتقول ما
+
+22
+00:02:06,670 --> 00:02:13,070
+يأتي theorem Z
+
+23
+00:02:13,070 --> 00:02:18,430
+of G the
+
+24
+00:02:18,430 --> 00:02:23,570
+center of 
+
+25
+00:02:23,570 --> 00:02:33,340
+a group G is a
+
+26
+00:02:33,340 --> 00:02:39,720
+subgroup of
+
+27
+00:02:39,720 --> 00:02:41,020
+G
+
+28
+00:02:51,670 --> 00:02:56,290
+يبقى أنا مشان أثبت أن الـ Z المعرفة بالشكل هنا
+
+29
+00:02:56,290 --> 00:03:02,490
+subgroup من الـ group الأساسية دي بدي أثبت النقطتين
+
+30
+00:03:02,490 --> 00:03:08,810
+أول شيء أن Z of G non-empty الأمر الثاني بدي أثبت
+
+31
+00:03:08,810 --> 00:03:15,350
+أن أي عنصر لو أخذته أو أي عنصرين لو أخذته من
+
+32
+00:03:15,350 --> 00:03:18,750
+الـ center بدي يكون الأول في معكوس الثاني موجود
+
+33
+00:03:18,750 --> 00:03:25,220
+وين؟ موجود في الـ center يبقى أول شيء أنا أدعي أن الـ
+
+34
+00:03:25,220 --> 00:03:32,400
+Z of G is non-empty وهذه هي النقطة الأولى في
+
+35
+00:03:32,400 --> 00:03:40,150
+البرهان non-empty ليش؟ because الـ E موجود في الـ Z
+
+36
+00:03:40,150 --> 00:03:47,610
+of G لإيش؟ لأن الـ EX بيساوي X E لكل الـ X
+
+37
+00:03:47,610 --> 00:03:56,650
+اللي موجود لأن الـ EX بيساوي الـ X في الـ E
+
+38
+00:03:56,650 --> 00:04:04,040
+لكل الـ X اللي موجودة في G بلا استثناء يبقى نظرا
+
+39
+00:04:04,040 --> 00:04:07,780
+لأنه يحقق الخاصية تبع الـ center تبع الـ group إذا
+
+40
+00:04:07,780 --> 00:04:13,680
+على الأقل فيها element واحد اللي هو الـ E الآن 
+
+41
+00:04:13,680 --> 00:04:20,700
+بتروح تأخذ two elements النقطة الثانية let a و b
+
+42
+00:04:20,700 --> 00:04:27,960
+belongs to Z of G لما أقول two elements هذول
+
+43
+00:04:27,960 --> 00:04:34,760
+موجودات في Z of G يبقى بد يكون عندنا الـ AX بد
+
+44
+00:04:34,760 --> 00:04:44,800
+يساوي الـ XA and الـ BX بيساوي X B لكل الـ X اللي
+
+45
+00:04:44,800 --> 00:04:47,400
+موجود في G بي less تتنعى
+
+46
+00:04:50,150 --> 00:04:54,250
+يبقى هذا الـ element موجود في الـ center إذا بدي
+
+47
+00:04:54,250 --> 00:04:58,790
+أحقق للخاصية اللي فوق تبعت الـ center بي موجود في
+
+48
+00:04:58,790 --> 00:05:03,590
+الـ center إذا بدي أحقق لنفس الخاصية يبقى أنا أخذت
+
+49
+00:05:03,590 --> 00:05:08,050
+عنصرين موجودات في الـ center تبع الـ group بدي أثبت
+
+50
+00:05:08,050 --> 00:05:13,350
+إن الأول في معكوسه الثاني موجود في مين؟ في الـ center
+
+51
+00:05:13,350 --> 00:05:21,040
+بمعنى آخر أريد أن أثبت أن a b inverse x هو x a b
+
+52
+00:05:21,040 --> 00:05:27,360
+inverse لكل x موجودة في g بلا استثناء يبقى بدي أجي
+
+53
+00:05:27,360 --> 00:05:34,740
+أقول له consider خد أن a b inverse x
+
+54
+00:05:38,410 --> 00:05:46,950
+بتشوف هذا بدي أثبت و بدي أثبت و بدي أثبت
+
+55
+00:05:46,950 --> 00:05:48,290
+و بدي أثبت و بدي أثبت و بدي أثبت و بدي أثبت و بدي
+
+56
+00:05:48,290 --> 00:05:57,150
+أثبت و بدي أثبت و بدي أثبت
+
+57
+00:05:57,980 --> 00:06:03,900
+يبقى هذا الكلام بيساوي بدي أحاول أربط ما بين الـ
+
+58
+00:06:03,900 --> 00:06:08,780
+X والـ B اللي عندنا يبقى لو جيت قلت هذا A B
+
+59
+00:06:08,780 --> 00:06:16,420
+inverse الـ X أخدتها X inverse inverse طبعا برهناها
+
+60
+00:06:16,420 --> 00:06:23,600
+سابقا يبقى هذا الكلام بيساوي A فاهمين؟ فبيصير X 
+
+61
+00:06:23,600 --> 00:06:30,770
+inverse B inverse هذه إنفرس وهذه إنفرس يبقى
+
+62
+00:06:30,770 --> 00:06:35,330
+رجعتهم للأصل اللي بتبعهم بالشكل اللي عندنا هذا طيب
+
+63
+00:06:35,330 --> 00:06:40,170
+الآن B موجودة في الـ center ولا لأ؟ يبقى commutes مع
+
+64
+00:06:40,170 --> 00:06:43,270
+الـ X والـ X inverse لأنها موجودة في الـ center يعني
+
+65
+00:06:43,270 --> 00:06:47,910
+commutes مع any element موجود في الـ group G يبقى
+
+66
+00:06:47,910 --> 00:06:56,670
+هذا الكلام بيساوي A وهنا B X inverse الكل inverse
+
+67
+00:07:00,860 --> 00:07:05,520
+ليش هذه الخطوة عملتها؟ لأن B موجودة في الـ Center
+
+68
+00:07:05,520 --> 00:07:11,600
+يبقى هذه الـ sense B موجودة في الـ Center تبع الـ
+
+69
+00:07:11,600 --> 00:07:17,580
+G هذا الكلام بيساوي لو جيت لي هذا الآن بيساوي بدي أطبق
+
+70
+00:07:17,580 --> 00:07:22,940
+عليه تعريف المعكوس لحظة حصل ضرب two elements يبقى
+
+71
+00:07:22,940 --> 00:07:26,020
+هذا بيصير A في X
+
+72
+00:07:28,710 --> 00:07:37,090
+inverse inverse وهنا اللي هو B inverse يبقى وزعت الـ
+
+73
+00:07:37,090 --> 00:07:42,210
+inverse لكل واحدة من هذول يبقى هذه انتقلت يبقى
+
+74
+00:07:42,210 --> 00:07:49,770
+هذه إيش بيصير AX في الـ B inverse الآن أنا عندي من
+
+75
+00:07:49,770 --> 00:07:57,330
+المعطيات أن AX يساوي X A يبقى هذا الكلام بدي
+
+76
+00:07:57,330 --> 00:08:06,810
+يعطينا X A في الـ B inverse ليش هذا الـ sense الـ A
+
+77
+00:08:06,810 --> 00:08:13,150
+موجودة في الـ center تبع الـ G طيب هذا الكلام بدي
+
+78
+00:08:13,150 --> 00:08:19,770
+يساوي من خاصية الـ associativity XAB inverse بالشكل
+
+79
+00:08:19,770 --> 00:08:25,090
+اللي عندنا طب إيش اللي عملته أنا حتى اللحظة أخذت A
+
+80
+00:08:25,090 --> 00:08:31,250
+B inverse X وجيته يساوي X A B inverse هذا الكلام
+
+81
+00:08:31,250 --> 00:08:37,590
+صحيح لكل الـ X اللي موجودة في G plus تتنى إيش
+
+82
+00:08:37,590 --> 00:08:42,370
+تفسيرك لهذا الكلام يبقى الـ A B inverse موجود وين
+
+83
+00:08:42,370 --> 00:08:45,990
+في الـ center تبع الـ group وبالتالي الـ center عبارة
+
+84
+00:08:45,990 --> 00:08:53,880
+عن subgroup يبقى هنا سويا الـ A B inverse belongs للـ
+
+85
+00:08:53,880 --> 00:09:03,920
+Z of G and hence ومن ثم الـ Z of G is a subgroup من
+
+86
+00:09:03,920 --> 00:09:05,060
+G وهو المطلوب
+
+87
+00:09:08,760 --> 00:09:14,200
+يبقى من الآن فصاعدا الـ center تبع الـ group هو sub
+
+88
+00:09:14,200 --> 00:09:20,440
+group من الـ group الأساسية طيب يا شباب في عندنا
+
+89
+00:09:20,440 --> 00:09:28,000
+سؤال السؤال لو كانت G أبيليان G أبيليان يبقى الـ
+
+90
+00:09:28,000 --> 00:09:34,040
+center تبع الـ group بيكون كل الـ group يبقى هذه اكتبها
+
+91
+00:09:34,040 --> 00:09:46,500
+ملاحظة Note If الـ G is abelian then الـ center تبع
+
+92
+00:09:46,500 --> 00:09:53,280
+الـ G بيساوي الـ G itself كلها بلا استثناء نبدأ
+
+93
+00:09:53,280 --> 00:10:04,080
+نأخذ أمثلة examples أول مثال بيقول let الـ G هي الـ
+
+94
+00:10:04,080 --> 00:10:09,550
+general linear group of two by two matrices over R
+
+95
+00:10:09,550 --> 00:10:21,390
+Then بدنا Z of G بدي Z of G هو عبارة عن مين؟ أنا
+
+96
+00:10:21,390 --> 00:10:31,090
+أدعي أن Z of G كل المصفوفة على صيغة A 0 0 A وبحيث الـ
+
+97
+00:10:31,090 --> 00:10:41,300
+A موجود في R والـ A هذا لا يساوي Zero الكلام
+
+98
+00:10:41,300 --> 00:10:44,760
+هذا صحيح ولا ما هو؟ مش صحيح والله أنا أدعي
+
+99
+00:10:44,760 --> 00:10:51,040
+ادعاء باجي بقول والله إذا لقيت هذه المصفوفات كلهم
+
+100
+00:10:51,040 --> 00:10:56,540
+اللي موجودة في Z of G commutes with any element في
+
+101
+00:10:56,540 --> 00:11:00,180
+الـ general linear group يصيب كلامنا صحيح من اليمين
+
+102
+00:11:00,180 --> 00:11:05,450
+ومن الشمال ما طلع يبقى كلامنا معله غير صحيح لذلك
+
+103
+00:11:05,450 --> 00:11:11,310
+بأجي بقول لك هذا الكلام because بدي أجي الـ element
+
+104
+00:11:11,310 --> 00:11:17,230
+اللي موجود في الـ center A 0 0 A بدي أضربه في
+
+105
+00:11:17,230 --> 00:11:21,230
+أي element موجود في الـ general linear group بدي
+
+106
+00:11:21,230 --> 00:11:28,810
+آخذ B, C, D, F مثلا بديش أكتب الـ A بلاش تقول لي إيه
+
+107
+00:11:28,810 --> 00:11:34,160
+هذا هو الـ identity element إذا هذه لو جيت ضربتها
+
+108
+00:11:34,160 --> 00:11:40,400
+بدها تساوي الصف الأول في العمود الأول اللي هو AB
+
+109
+00:11:40,400 --> 00:11:47,560
+الصف الأول في العمود الثاني يبقى BC الصف الثاني
+
+110
+00:11:47,560 --> 00:11:53,260
+في العمود الأول يبقى AD الصف الثاني في العمود
+
+111
+00:11:53,260 --> 00:12:06,450
+الثاني AF اللي بقدر أكتبها A في B, C, D, F الآن بدأت
+
+112
+00:12:06,450 --> 00:12:16,420
+آخذ له اللي هو B, C, D, F في الـ A, 0, 0, A يبقى هذا معناه
+
+113
+00:12:16,420 --> 00:12:23,180
+صف الأول في العمود الأول BA الصف الأول في العمود
+
+114
+00:12:23,180 --> 00:12:29,960
+الثاني CA الصف الثاني في العمود الأول DA الصف
+
+115
+00:12:29,960 --> 00:12:37,240
+الثاني في العمود الثاني يبقى FA لو أخذت الـ A من كل
+
+116
+00:12:37,240 --> 00:12:42,340
+element موجود داخل المصفوفة بيظهر لنا مين؟ بي بي بي
+
+117
+00:12:42,340 --> 00:12:43,680
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+118
+00:12:43,680 --> 00:12:50,000
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+119
+00:12:50,780 --> 00:12:56,080
+ما دام أريكوا المعناته فعلا هذا يمثل main الـ 
+
+120
+00:12:56,080 --> 00:13:01,480
+center أو المصفوفة اللي عندنا هذه هي element موجود
+
+121
+00:13:01,480 --> 00:13:07,380
+وإن موجود في الـ center هذا بدي أعطيك أن any
+
+122
+00:13:07,380 --> 00:13:09,140
+element
+
+123
+00:13:11,320 --> 00:13:22,860
+in Z of G is in the form على الشكل اللي هو A 0
+
+124
+00:13:22,860 --> 00:13:30,410
+0 A والـ A does not equal to zero يبقى من الآن
+
+125
+00:13:30,410 --> 00:13:34,110
+فصاعدا لما بدي الـ center للـ general linear group of 
+
+126
+00:13:34,110 --> 00:13:38,670
+two by two matrices over R بيكون عندي واحد زيرو
+
+127
+00:13:38,670 --> 00:13:43,030
+زيرو واحد اتنين زيرو زيرو واحد  مص زيرو زيرو واحد
+
+128
+00:13:43,030 --> 00:13:48,310
+واحد على مية زيرو زيرو واحد على مية وهكذا يبقى كل
+
+129
+00:13:48,310 --> 00:13:53,590
+العناصر القطر الرئيسي بيكون عناصرهم متساوية وهذه
+
+130
+00:13:53,590 --> 00:13:59,170
+بقينا نسميها في ال linear algebra بقينا نسميها 
+
+131
+00:13:59,170 --> 00:14:05,830
+المصفوفة شو اسمها؟ مصفوفة الواحد القطرية
+
+132
+00:14:05,830 --> 00:14:12,150
+لما العناصر القطر الرئيسي يكونوا متساوية بقينا 
+
+133
+00:14:12,150 --> 00:14:14,330
+نسميها مثلثية
+
+134
+00:14:17,700 --> 00:14:24,520
+بنسميها scalar matrix أو مقياسية
+
+135
+00:14:24,520 --> 00:14:28,940
+لو كان القطرين غير متساويين بيقول diagonal matrix
+
+136
+00:14:28,940 --> 00:14:31,240
+diagonal matrix هي فعلا diagonal matrix في المصفوف
+
+137
+00:14:31,240 --> 00:14:36,060
+القطرية بس إذا تساوت عناصر القطر الرئيسي بنسميها
+
+138
+00:14:36,060 --> 00:14:41,070
+scalar matrix يبقى كل scalar matrix في ال general
+
+139
+00:14:41,070 --> 00:14:44,790
+linear group of two by two matrices بيكونولي main
+
+140
+00:14:44,790 --> 00:14:50,790
+بيكونولي ال center لل group اللي عندنا طيب نمرتنا
+
+141
+00:14:50,790 --> 00:15:01,990
+example two بدنا z of D4 يساوي أكيد ال R node منهم
+
+142
+00:15:01,990 --> 00:15:07,240
+هذا كل مجمع ليه لأنه ال identity حد بيقدر يجيبلي
+
+143
+00:15:07,240 --> 00:15:16,240
+كمان element آخر تسعين commutes مع الكل تسعين
+
+144
+00:15:16,240 --> 00:15:19,860
+commutes مع المية وتمانين ومع الميتين وسبعين مع ال
+
+145
+00:15:19,860 --> 00:15:25,580
+rotations نعم لكن مع ال reflections ليس صحيحا
+
+146
+00:15:25,580 --> 00:15:31,960
+وأثبت لك أن R تسعين في H ليسوا ال H في R تسعين
+
+147
+00:15:31,960 --> 00:15:39,720
+وحسبتهم لك أنت الـ R180 فقط لا غير يبقى هذه والـ
+
+148
+00:15:39,720 --> 00:15:48,060
+R180 فقط لا غير يبقى هدول بس عناصر الـ Center تبعي
+
+149
+00:15:48,060 --> 00:15:52,600
+الـ D4 غير هيك ما فيش ولا elements طبعا لو رجعت
+
+150
+00:15:52,600 --> 00:15:58,720
+للجدول اللي في الصفحة واحدة و تلاتين الكليتابل للـ
+
+151
+00:15:58,720 --> 00:16:05,880
+D4 بتلاقي أن ال R180 هي ال commutes مع جميع عناصر
+
+152
+00:16:05,880 --> 00:16:10,280
+D4 بالإضافة إلى ال identity element اللي هو main
+
+153
+00:16:10,670 --> 00:16:16,350
+اللي هو Arnold يبقى هذول ال two elements هم اللي
+
+154
+00:16:16,350 --> 00:16:21,890
+commutes مع جميع عناصر D4 فقط لا غير طيب إيش رأيك
+
+155
+00:16:21,890 --> 00:16:27,650
+بدي أعملك هالشغل هذه بدل ما آخذ D4 بدي آخذ DN
+
+156
+00:16:27,650 --> 00:16:35,950
+يبقى الآن in general لو 
+
+157
+00:16:35,950 --> 00:16:46,670
+أخذت ال Z of DM هذه أحد أمرين يا إما الـ Arnold والـ 
+
+158
+00:16:46,670 --> 00:16:55,750
+مية و تمانين فقط يا إما الـ Arnold السؤال هو متى يحدث
+
+159
+00:16:55,750 --> 00:17:01,950
+هذا ومتى يحدث هذا الآن في D4 الرقم هذا زوجي والله
+
+160
+00:17:01,950 --> 00:17:09,870
+فردي زوجي يبقى هذا يحدث لو كان ال n فرديا يبقى هنا
+
+161
+00:17:09,870 --> 00:17:21,630
+هذا الكلام if n is even أو هذا if ال n is odd
+
+162
+00:17:21,630 --> 00:17:29,050
+فقط لا غير طبعا يمكن يسأل واحد بعض منكم لماذا هذا
+
+163
+00:17:29,050 --> 00:17:29,750
+الكلام
+
+164
+00:17:40,760 --> 00:17:46,140
+الإجابة بدنا نعطي تفسير ليش هذا الكلام ما فيش غرض
+
+165
+00:17:46,140 --> 00:17:54,220
+يبقى اكتب لي this is because يبقى this is because
+
+166
+00:17:54,220 --> 00:18:05,940
+هذا الكلام لأنه this is because every rotation in
+
+167
+00:18:05,940 --> 00:18:07,680
+DN
+
+168
+00:18:09,750 --> 00:18:19,790
+is a power is a power of
+
+169
+00:18:19,790 --> 00:18:28,450
+R تلت مية و ستين على N and
+
+170
+00:18:28,450 --> 00:18:37,790
+rotations and rotations commute
+
+171
+00:18:42,200 --> 00:18:49,400
+and the rotations commute with each other with
+
+172
+00:18:49,400 --> 00:18:59,060
+each other نجي
+
+173
+00:18:59,060 --> 00:19:03,760
+الآن لو كان حاصل ضرب rotation في reflection بدا
+
+174
+00:19:03,760 --> 00:19:10,280
+أقول لك بدا أعطي تسمية التالية little r b any
+
+175
+00:19:12,530 --> 00:19:31,450
+rotation in DN and let ال F be any reflection برضه
+
+176
+00:19:31,450 --> 00:19:36,290
+in DN in DN
+
+177
+00:19:49,990 --> 00:19:57,070
+مرة أخرى ندعي أن الـ Center تبع ال group D ان سواء
+
+178
+00:19:57,070 --> 00:20:04,330
+كانت D3، D4، D5، D6، جد ما يكون يكون طبعا ال N هذه
+
+179
+00:20:04,330 --> 00:20:10,410
+أكبر من أو تساوي تلاتة ال N اللي عندنا أكبر من أو
+
+180
+00:20:10,410 --> 00:20:15,330
+تساوي تلاتة يعني ممكن يكون مثلث منتظم مربع منتظم
+
+181
+00:20:15,330 --> 00:20:20,390
+مخلص منتظم مسدس منتظم إلى آخرهم إذا والله ال N
+
+182
+00:20:20,390 --> 00:20:28,030
+موجبة زي D4, D6, D8, D10 إلى آخره يبقى العناصر
+
+183
+00:20:28,030 --> 00:20:33,070
+اللي في ال center بس Arnold و R180 الأقل لو كانت
+
+184
+00:20:33,070 --> 00:20:36,670
+ال N فردي تلاتة خمسة سبعة تسعة إلى آخره يبقى لا
+
+185
+00:20:36,670 --> 00:20:40,990
+يوجد في ال center إلا عنصر الوحدة اللي همين Arnold
+
+186
+00:20:40,990 --> 00:20:46,720
+ليش هذا؟ لأن أي روتاشن يتعامل مع أي روتاشن آخر مثلا
+
+187
+00:20:46,720 --> 00:20:52,220
+في D4 إذا قلت لك R90 يتعامل مع R180 ويتعامل مع
+
+188
+00:20:52,220 --> 00:20:57,520
+R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+189
+00:20:57,520 --> 00:21:01,300
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+190
+00:21:01,300 --> 00:21:02,380
+يتعامل مع R270 وR270 يتعامل مع R270 وR270 يتعامل
+
+191
+00:21:02,380 --> 00:21:03,200
+مع R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+192
+00:21:03,200 --> 00:21:07,000
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+193
+00:21:07,000 --> 00:21:12,500
+يتعامل مع R270 وR270 يتعامل مع R270
+
+194
+00:21:12,500 --> 00:21:17,410
+وR2 يبقى ده commutes باجي بقوله بدي آجي آخذ R هي any
+
+195
+00:21:17,410 --> 00:21:23,670
+rotation يعني جرب لك الفكرة لو كان ال D4 عندنا يبقى
+
+196
+00:21:23,670 --> 00:21:27,610
+ال R هادي أما R تسعين أو مية و تمانين أو ميتين و
+
+197
+00:21:27,610 --> 00:21:34,730
+سبعين أي واحدة منهم تمام؟ يبقى ال F في كذلك any
+
+198
+00:21:34,730 --> 00:21:39,670
+reflection أي انقلاب سواء كان H أو لا V أو لا D أو لا
+
+199
+00:21:39,670 --> 00:21:45,430
+D' أي واحدة منهم مكتوب معك أن reflection ضرب
+
+200
+00:21:45,430 --> 00:21:51,530
+rotation يساوي rotation ضرب reflection كله بيعطيني
+
+201
+00:21:51,530 --> 00:21:55,850
+reflection ما أقولش يساوي يعني على كل الأمرين بيطلع لي
+
+202
+00:21:55,850 --> 00:21:59,090
+reflection لو ضربت rotation في reflection بده
+
+203
+00:21:59,090 --> 00:22:01,570
+يطلع لي reflection، لو ضربت reflection في rotation
+
+204
+00:22:01,570 --> 00:22:05,170
+بده يطلع لي reflection على كلا الأمرين ومكتوبة
+
+205
+00:22:05,170 --> 00:22:08,130
+معاك هذه كتبناها قبل ذلك
+
+206
+00:22:10,970 --> 00:22:16,690
+أي rotation في D4 هو power of r 360 على n إيش
+
+207
+00:22:16,690 --> 00:22:24,630
+360 على n باجي بقول اه لو كانت n تساوي 4 مثلا يبقى
+
+208
+00:22:24,630 --> 00:22:29,230
+360 على 4 فيها قداش 90 إذا ال rotation الواحدة
+
+209
+00:22:29,230 --> 00:22:35,080
+بتسعين درجة هذا لما يكون مربع طب لو كان مثلث بدي
+
+210
+00:22:35,080 --> 00:22:39,660
+أقسم على تلاتة يبقى ال rotation مقداش مية وعشرين
+
+211
+00:22:39,660 --> 00:22:45,740
+درجة لو كان مخمس لو كان مسدس منتظم يبقى تلاتمية و
+
+212
+00:22:45,740 --> 00:22:49,460
+ستين على ست اللي فيه مقداش ستين يبقى بيصير عندي R
+
+213
+00:22:49,460 --> 00:22:55,740
+node R ستين R مية وعشرين R مية وتمانين R ميتين و أربعين
+
+214
+00:22:55,740 --> 00:23:02,820
+R300 R node وهكذا يبقى هكذا تكتب من العناصر وبعدين
+
+215
+00:23:02,820 --> 00:23:06,800
+بروح بدور من ال reflections إلى آخرين ما علينا
+
+216
+00:23:06,800 --> 00:23:13,880
+يبقى المقصود من R360 على N أطلع قداش مقدار الزاوية
+
+217
+00:23:13,880 --> 00:23:18,250
+اللي بأعمل بها الدورالة المضلع المنتظم اللي عندي
+
+218
+00:23:18,250 --> 00:23:23,830
+مين مكان إيه يكون تمام أي rotation هديها الرمز R
+
+219
+00:23:23,830 --> 00:23:30,150
+أي reflection هديها إيه هديها الرمز F تمام طيب
+
+220
+00:23:30,150 --> 00:23:36,890
+الآن rotation بدي أقول any rotation في reflection
+
+221
+00:23:36,890 --> 00:23:41,930
+بيعطينا reflection أو أي reflection في rotation
+
+222
+00:23:41,930 --> 00:23:44,250
+بيعطينا reflection
+
+223
+00:23:58,780 --> 00:24:03,600
+Arnold ال identity element اتحرك مع أي element آخر
+
+224
+00:24:03,600 --> 00:24:10,860
+في ال group Arnold هو دوران بصفر درجة يبقى هذا هو ال
+
+225
+00:24:10,860 --> 00:24:15,860
+identity element كنت حاضر يوم شرحنا ال D4 هذه؟
+
+226
+00:24:15,860 --> 00:24:24,180
+بعون الله طيب ولا قريتها كمان؟ ماشي طيب هذه دلوقتي
+
+227
+00:24:24,180 --> 00:24:28,440
+عمود فقري روح اقرأها ثاني غلبتك حاجة حتى وتعالي
+
+228
+00:24:28,440 --> 00:24:32,980
+نشرح لك ما عندناش مشكلة المهم لأن هذه عمود فقري كل
+
+229
+00:24:32,980 --> 00:24:37,860
+شوية لجروب وهي طالعة بدنا نشتغل عليها تمام؟ طيب
+
+230
+00:24:38,150 --> 00:24:43,490
+نرجع لموضوعنا احنا بندعي الآن أن ال center لدى N
+
+231
+00:24:43,490 --> 00:24:47,690
+إذا كانت N عددا زوجيا ما عنديش إلا Arnold وR180
+
+232
+00:24:47,690 --> 00:24:53,970
+وإذا كان فرديا ما عنديش إلا من Arnold الآن بنقول ال
+
+233
+00:24:53,970 --> 00:24:58,950
+rotation ب commutes مع أي rotation أخرى وضربت لك من
+
+234
+00:24:58,950 --> 00:25:04,490
+93 مع 180 مع 270 كلهم commutes هدول مع بعض مع ال
+
+235
+00:25:04,490 --> 00:25:09,480
+Arnold كمان اللي هو ال identity الآن أي rotation
+
+236
+00:25:09,480 --> 00:25:15,000
+حديها الرمز R أي reflection حديها الرمز F الآن
+
+237
+00:25:15,000 --> 00:25:22,600
+احنا سابقا برضه باجي بقول since اللي هو ال R في F
+
+238
+00:25:22,600 --> 00:25:25,800
+is a reflection
+
+239
+00:25:28,280 --> 00:25:32,260
+هذه reflection يعني حاصل ضرب ال rotation في ال
+
+240
+00:25:32,260 --> 00:25:36,860
+reflection بيعطيني reflection أو العكس لو كان F في
+
+241
+00:25:36,860 --> 00:25:41,700
+R كمان بيعطينا مين reflection وما إلى ذلك يبقى
+
+242
+00:25:41,700 --> 00:25:46,300
+نظرا لإن ال R في F is a reflection معناته هذا
+
+243
+00:25:46,300 --> 00:25:55,630
+العنصر معكسه قداشي بيعطينا معكس العنصر هذا ارجع ال
+
+244
+00:25:55,630 --> 00:26:00,450
+D4 مش ال D4 قولنا H تربيعه يساوي ال identity يبقى
+
+245
+00:26:00,450 --> 00:26:05,530
+ال H inverse يبقى كده بال H itself يبقى هو معكوس
+
+246
+00:26:05,530 --> 00:26:12,210
+لنفس يبقى في هذه لأ it's a reflection we have
+
+247
+00:26:12,210 --> 00:26:22,430
+يبقى بده يصير ال RF بده يساوي ال RF لكل inverse يبقى
+
+248
+00:26:22,430 --> 00:26:29,210
+باجي بقول يبقى صار ال RF بده يساوي ال RF في
+
+249
+00:26:29,210 --> 00:26:35,290
+الكل inverse وبلغة ال F inverse هذا هو ال F inverse
+
+250
+00:26:35,290 --> 00:26:40,190
+في ال R inverse بلغة المعكوس بتنقل بيقول معكوس 
+
+251
+00:26:40,190 --> 00:26:45,290
+الأول للآخر طب الـ F reflection لما تبقى الـ F
+
+252
+00:26:45,290 --> 00:26:51,340
+reflection يبقى F square قداش مديوطن يا شباب اللي
+
+253
+00:26:51,340 --> 00:26:55,420
+هنضل هو الـ identity يعني لو جيت قلت الـ identity
+
+254
+00:26:55,420 --> 00:27:00,880
+يبقى الـ F بالصير هي الـ F inverse ولا لا يعني لو
+
+255
+00:27:00,880 --> 00:27:04,480
+ضربت الطرفين في الـ F inverse من جهة اليمين أو من
+
+256
+00:27:04,480 --> 00:27:09,220
+جهة الشمال يبقى هنا بظل قداش بظل F والطرف اليامين
+
+257
+00:27:09,220 --> 00:27:13,620
+هي G F inverse مكتوب معاك هذا V تربية تسوى الـ
+
+258
+00:27:13,620 --> 00:27:17,420
+identity في D4 يبقى V بتسوى V inverse H تربية تسوى 
+
+259
+00:27:17,420 --> 00:27:20,200
+الـ identity يبقى H تسوى H inverse D تربية تسوى الـ
+
+260
+00:27:20,200 --> 00:27:23,340
+identity يبقى D بتسوى D الـ inverse وD prime زيهم
+
+261
+00:27:23,340 --> 00:27:29,300
+يبقى كل هذا مكتوب معاك يوم أخدنا D4 يبقى بناء عليه
+
+262
+00:27:29,300 --> 00:27:34,320
+لما كانت الـ F هي reflection يبقى الـ F و الـ F
+
+263
+00:27:34,320 --> 00:27:41,300
+inverse الشي العلاقة بينهما اتنين are الـ F و الـ F 
+
+264
+00:27:41,300 --> 00:27:42,540
+inverse الـ reflection
+
+265
+00:27:47,690 --> 00:27:52,230
+ماذا يحصل علاقة بينهم؟ علاقة تساوي يعني بقدر أشيل
+
+266
+00:27:52,230 --> 00:27:55,590
+الـ F و أحط مكانها F inverse و بقدر أشيل F inverse
+
+267
+00:27:55,590 --> 00:27:59,730
+و أحط مكانها الـ F هيها قدامك هي على اللوح مكتوبة
+
+268
+00:27:59,730 --> 00:28:09,470
+يبقى بقدر بناء عليه أقول هذه هي الـ F R inverse طيب
+
+269
+00:28:09,470 --> 00:28:10,510
+استنى شوية
+
+270
+00:28:27,180 --> 00:28:29,980
+مصبوط هكذا؟
+
+271
+00:28:38,160 --> 00:28:46,100
+طيب هذا كلام صحيح if and only if الـ R F بدها تساوي
+
+272
+00:28:47,590 --> 00:28:53,690
+وين الـ ار اف هيها؟ كده اش طالع بيساوي؟ اف ار انفرس،
+
+273
+00:28:53,690 --> 00:29:03,130
+مظبوط؟ يبقى هذه اف ار اف بدي ساوي ال .. إذا كانت
+
+274
+00:29:03,130 --> 00:29:09,630
+الـ ار اف بدي ساوي الاف ار طيب وين الاف ار؟ طيب
+
+275
+00:29:09,630 --> 00:29:16,200
+خليها ماشية بنجب نقول هذا الكلام الـ RF بدي ساوي
+
+276
+00:29:16,200 --> 00:29:20,220
+الـ
+
+277
+00:29:20,220 --> 00:29:27,760
+FR inverse بالشكل اللي عندنا هنا يبقى هذا الكلام
+
+278
+00:29:27,760 --> 00:29:33,570
+صحيء إذا كان الـ RF بدي ساومين الـ FR inverse طيب
+
+279
+00:29:33,570 --> 00:29:40,070
+الآن أنا بقدر أشيل الـ F و احط مكانها من الـ F
+
+280
+00:29:40,070 --> 00:29:46,290
+inverse و ارجعها كيف ده سيه لحظة شوية طيب عندك الـ
+
+281
+00:29:46,290 --> 00:29:51,230
+RF يسوى الـ FR inverse مظبوط الـ R كما نسميه إذا كان
+
+282
+00:29:51,230 --> 00:29:58,350
+الـ FR بديه يسوى إذا كان الـ FR بديه يسوى RF استنى
+
+283
+00:29:58,350 --> 00:30:01,130
+شوية إذا كان الـ F
+
+284
+00:30:04,870 --> 00:30:19,850
+فار فار فار فار فار فار فار فار فار فار فار
+
+285
+00:30:28,490 --> 00:30:34,610
+الـ R F Inverse لأيش؟ لأن الـ F هي تساوي مين؟
+
+286
+00:30:34,610 --> 00:30:40,450
+تساوي الـ F Inverse itself تمام؟ يبقى هذا بيساوي
+
+287
+00:30:40,450 --> 00:30:47,150
+الـ R Inverse F itself يبقى أصار F R Inverse
+
+288
+00:30:50,680 --> 00:30:57,700
+يبقى فان الـ F R بدينا فيها بدي يساوي R F وهذا R F
+
+289
+00:30:57,700 --> 00:31:07,380
+اللي عندنا يساوي F R Inverse هذي بدي يساوي F R
+
+290
+00:31:07,380 --> 00:31:12,680
+Inverse هي الكلام صحيح يبقى أنا بديت هدول التنين
+
+291
+00:31:12,680 --> 00:31:18,160
+كموسي ده كان الـ F R بدي يساوي من R F هذا الكلام
+
+292
+00:31:18,160 --> 00:31:24,080
+يساوي هاي RF من فوق شيلتها و جيبت بدالها مين؟ F R
+
+293
+00:31:24,080 --> 00:31:30,340
+inverse يبقى اطلعلي لهذه و اطلعلي لهذه تمام؟ بال
+
+294
+00:31:30,340 --> 00:31:35,360
+lift cancellation law يبقى هذه الـ F بتروح مع هذه
+
+295
+00:31:35,360 --> 00:31:43,480
+بظل F and only F الـ R بدها تساوي R inverse إذا كان
+
+296
+00:31:43,480 --> 00:31:49,820
+الـ R يسوى الـ R inverse الـ R يسوى
+
+297
+00:31:49,820 --> 00:31:57,820
+الـ R inverse بس في حالة الـ 180 يبقى هذا معناه أن R
+
+298
+00:31:57,820 --> 00:32:06,440
+تسوى R 180 درجة وهذا الكلام صحيح لو كانت الـ N is
+
+299
+00:32:06,440 --> 00:32:19,190
+even فقط this is a true فالن is even يبقى بناء عليه
+
+300
+00:32:19,190 --> 00:32:27,310
+z of d فالـ z of dn بدي يسوى رن ورمية و تمانين في
+
+301
+00:32:27,310 --> 00:32:34,730
+حالة الزوجي والارنود في حالة من في حالة الفردي طيب
+
+302
+00:32:34,730 --> 00:32:39,990
+فينا تعريف جديد برضه جريب من الـ center بس بيسميه
+
+303
+00:32:39,990 --> 00:32:46,610
+centralizer يبقى definition let
+
+304
+00:32:46,610 --> 00:32:55,270
+الـ a be a fixed element
+
+305
+00:32:55,270 --> 00:32:58,350
+of
+
+306
+00:32:58,350 --> 00:33:01,330
+a group G
+
+307
+00:33:04,040 --> 00:33:18,140
+the centralizer of
+
+308
+00:33:18,140 --> 00:33:28,120
+الـ element a اللي موجود في g هديله الرمز center of
+
+309
+00:33:28,120 --> 00:33:28,600
+a
+
+310
+00:33:31,400 --> 00:33:42,920
+is the set of all elements the set of all elements
+
+311
+00:33:42,920 --> 00:33:53,620
+in G that commute with
+
+312
+00:33:53,620 --> 00:33:57,700
+A with
+
+313
+00:33:57,700 --> 00:34:01,020
+A that is
+
+314
+00:34:03,590 --> 00:34:12,050
+Centralizer لإيه كل العناصر جي اللي موجودة في جي
+
+315
+00:34:12,050 --> 00:34:18,790
+بحيث أن جي في ايه ساوي ايه في جي
+
+316
+00:34:48,240 --> 00:34:52,400
+نعود للتعريف اللي قلناه و نعود له ثاني و نشوف شو
+
+317
+00:34:52,400 --> 00:34:58,360
+بيقول التعريف بيقول خدلي a fixed element من الـ
+
+318
+00:34:58,360 --> 00:35:02,660
+group g بيبقى أخدت عنصر من g سميته a the
+
+319
+00:35:02,660 --> 00:35:08,840
+centralizer of a اللي موجود فيه g يبقى أنا بدي
+
+320
+00:35:08,840 --> 00:35:15,540
+أدور على العناصر اللي بتبقى commutes مع a فقط وبدي
+
+321
+00:35:15,540 --> 00:35:20,900
+أسميهم الـ centralizer بهذا الـ element a بتعطيه C of
+
+322
+00:35:20,900 --> 00:35:25,400
+A يبقى C of A the centralizer of the element A مين
+
+323
+00:35:25,400 --> 00:35:30,900
+هي؟ هي كل العناصر اللي موجودة في G that commutes
+
+324
+00:35:30,900 --> 00:35:37,060
+with A اللي بتعمل عملية تبديل فقط مع العنصر A مش
+
+325
+00:35:37,060 --> 00:35:40,700
+مع باقي عناصر يبقى فيه فرق ما بين الـ center
+
+326
+00:35:40,700 --> 00:35:44,940
+والـ centralizer الـ element اللي موجود في الـ center
+
+327
+00:35:44,940 --> 00:35:50,460
+commutes مع جميع عناصر A مع جميع عناصر الجروب G
+
+328
+00:35:50,460 --> 00:35:54,960
+لكن الـ centralizer ليه؟ بس العناصر ي commutes مع
+
+329
+00:35:54,960 --> 00:36:01,260
+مين؟ مع A فقط لغير ذلك قلنا الـ Centralizer لكل
+
+330
+00:36:01,260 --> 00:36:05,180
+العناصر اللي موجودة في جيه اللي بتبقى commutes مع
+
+331
+00:36:05,180 --> 00:36:11,260
+مين مع ايه فقط بناء على ذلك سنطرح بعض الأسئلة
+
+332
+00:36:11,260 --> 00:36:16,120
+السؤال الأول مين
+
+333
+00:36:16,120 --> 00:36:19,840
+اللي أكبر الـ center ولا الـ centralizer في الـ group
+
+334
+00:36:19,840 --> 00:36:28,240
+العادي الـ Center أكبر يعني بلاقي في عناصر أكثر من
+
+335
+00:36:28,240 --> 00:36:31,020
+عناصر الـ Centralizer لإيه؟
+
+336
+00:36:34,970 --> 00:36:40,990
+طيب سؤال سؤال بدي أجيب نفس السؤال بصيغة أخرى لو
+
+337
+00:36:40,990 --> 00:36:46,550
+أخد element في الـ center تبع الـ group بلاجيه في الـ
+
+338
+00:36:46,550 --> 00:36:50,410
+centralizer تبع الـ ايه؟ بلاجيه طب نعمل العملية
+
+339
+00:36:50,410 --> 00:36:54,430
+العكسية بدي أخد element في الـ centralizer هل
+
+340
+00:36:54,430 --> 00:36:57,170
+بلاجيه موجود في الـ center؟
+
+341
+00:37:00,330 --> 00:37:05,270
+يعني قد يكون و قد لا يكون موجود، مظبوط؟ إذا صار الـ
+
+342
+00:37:05,270 --> 00:37:10,630
+center صغير لأنه بدكم يسمع جميع عناصر جهة بس هدا
+
+343
+00:37:10,630 --> 00:37:14,650
+كم يسمع عنصر واحد فقط يبقى الـ center هيكون في
+
+344
+00:37:14,650 --> 00:37:18,710
+عناصر كثيرة بدليل أخدت أوسع عنصر من الـ center
+
+345
+00:37:18,710 --> 00:37:21,970
+وجدته موجود في الـ centralizer لكن إذا ذهبت لختم
+
+346
+00:37:21,970 --> 00:37:25,210
+الـ centralizer ليس بالضرورة أن يكون وين في
+
+347
+00:37:25,210 --> 00:37:29,850
+الـ center يبقى أول ملاحظة أن الـ center تبع لجروب
+
+348
+00:37:29,850 --> 00:37:36,030
+هو الـ subset من الـ centralizer تمام؟ يبقى باجي
+
+349
+00:37:36,030 --> 00:37:37,750
+بقوله هنا note
+
+350
+00:37:40,820 --> 00:37:48,020
+النقطة الأولى الـ center تبع الـ group G subset من
+
+351
+00:37:48,020 --> 00:37:51,200
+الـ
+
+352
+00:37:51,200 --> 00:37:59,660
+centralizer لـ A و الـ A عنصر موجود في جي مش الـ A و
+
+353
+00:37:59,660 --> 00:38:03,300
+لا الـ B و الـ C يعني هذا كلام صحيح لكل الـ A اللي
+
+354
+00:38:03,300 --> 00:38:08,940
+موجود في جي بدل هيك بقول لكل الـ A اللي موجودة في
+
+355
+00:38:08,940 --> 00:38:15,310
+جي يعني لو روحت لأي عنصر غيرت لإيه بعنصر ثاني و
+
+356
+00:38:15,310 --> 00:38:18,830
+جبتله الـ centralizer بلاج الـ center subset منه و
+
+357
+00:38:18,830 --> 00:38:22,210
+روحت جبت الـ centralizer لعنصر ثالث و جبت الـ
+
+358
+00:38:22,210 --> 00:38:24,770
+central group بلاج الـ central subset من الـ
+
+359
+00:38:24,770 --> 00:38:29,070
+centralizer للعنصر الثالث و هكذا هي اللي قصدناه من
+
+360
+00:38:29,070 --> 00:38:36,050
+هنا طيب كمان سؤال لو كانت الـ جي أبيليان قداش الـ
+
+361
+00:38:36,050 --> 00:38:42,450
+centralizer للـ إيه؟ جي جي كلها طب و الـ center؟ جي
+
+362
+00:38:42,450 --> 00:38:46,080
+كلها يبقى صرت سما بين الـ Central و الـ Centralizer
+
+363
+00:38:46,080 --> 00:38:50,740
+يبقى إذا كانت الـ G Abelian فإن الـ Center يسوى
+
+364
+00:38:50,740 --> 00:38:55,540
+الـ Centralizer و يساوى الجروب G كله لكن لو ماكنتش
+
+365
+00:38:55,540 --> 00:38:59,840
+Abelian بيظل الـ Center تبع الجروب هو الـ Subset
+
+366
+00:38:59,840 --> 00:39:06,220
+قد يسوى و قد لا يسوى تمام؟ يبقى بناء عليه بقول هذه
+
+367
+00:39:06,220 --> 00:39:14,040
+النقطة الأولى النقطة الثانية If G is Abelian Then
+
+368
+00:39:14,040 --> 00:39:20,220
+الـ Center تبع لـ Group G هو بالضبط الـ
+
+369
+00:39:20,220 --> 00:39:26,060
+Centralizer لـ A لكل الـ A اللي موجودة في G وهذا
+
+370
+00:39:26,060 --> 00:39:31,500
+بده يساوي G itself هذا في حالة ما تكون A ما تكون
+
+371
+00:39:31,500 --> 00:39:39,200
+Abelian Group طيب ناخد مثال بسيط example let
+
+372
+00:39:44,050 --> 00:39:52,830
+الـ G تسوي الـ D4 الـ D4 ثم بدي
+
+373
+00:39:52,830 --> 00:40:02,670
+الـ Centralizer للـ R نوت مين بيطلع دي كلها طيب هل
+
+374
+00:40:02,670 --> 00:40:10,150
+هو الـ Centralizer للـ R 180 صحيح لغرمية ابنكم يسمع
+
+375
+00:40:10,150 --> 00:40:16,270
+الكل يريد عن جديكوا بس و هذا بدي يسوي D4 كله يبقى 
+
+376
+00:40:16,270 --> 00:40:22,070
+هذا بدي يعطينا D4 كله طب لو بدي الـ centralizer للـ
+
+377
+00:40:22,070 --> 00:40:28,270
+R90 هل 
+
+378
+00:40:28,270 --> 00:40:34,710
+هذا هو الـ centralizer للـ R270؟
+
+379
+00:40:38,690 --> 00:40:46,030
+انظروا معاكوسه طب بدّ العناصر تبعتهم مين هم؟ ارونود و
+
+380
+00:40:46,030 --> 00:40:54,230
+R180 والـ R90 كمان لأن الـ R90 يسمع نفسه صحيح ولا 
+
+381
+00:40:54,230 --> 00:41:00,540
+لا؟ ضل عليك كمان واحد بسحد معاه الجدول يطلع لبسه 
+
+382
+00:41:00,540 --> 00:41:04,000
+فتش الجدول وبتعرف الإجابة منه في صفحة واحد و
+
+383
+00:41:04,000 --> 00:41:09,500
+ثلاثين يبقى لو رجعنا بنلاقي بس اللي هي الـ R ميتين
+
+384
+00:41:09,500 --> 00:41:16,710
+وسبعين يبقى هذه الـ R ميتين وسبعين هذا الكلام يعني
+
+385
+00:41:16,710 --> 00:41:20,230
+ايش مين بدي أعطيه لك؟ بدي أعطيه لك الـ subgroup
+
+386
+00:41:20,230 --> 00:41:26,470
+generated by R 90 وفي نفس الوقت هي الـ subgroup
+
+387
+00:41:26,470 --> 00:41:36,590
+generated by R 270 مظبوط؟ R 90 تربيع 180 R 90 
+
+388
+00:41:36,590 --> 00:41:42,400
+تكعيب 270 R أس 4 بالـ identity يبقى لو بدي
+
+389
+00:41:42,400 --> 00:41:46,780
+أجيب كمان الـ centralizer لمين؟ للـ H يبقى
+
+390
+00:41:46,780 --> 00:41:55,200
+الـ centralizer للـ H اللي عندنا هذه يبقى هذا بده
+
+391
+00:41:55,200 --> 00:42:00,140
+يعطيك الـ R nought والـ R100U80 
+
+392
+00:42:00,140 --> 00:42:03,700
+والـ H وحط عليها الـ V كمان
+
+393
+00:42:06,390 --> 00:42:13,330
+أليس هذا هو الـ centralizer للـ V كذلك؟ لو الجدول
+
+394
+00:42:13,330 --> 00:42:17,970
+معك كان عرفت لحالك جدول في صفحة واحد وثلاثين
+
+395
+00:42:17,970 --> 00:42:22,390
+بالمثل لو روحنا جبنا الـ centralizer لـ D
+
+396
+00:42:22,390 --> 00:42:30,450
+الـ centralizer لـ D هو عبارة عن الـ R nought والـ R مية
+
+397
+00:42:30,450 --> 00:42:38,000
+وثمانين والـ D itself والـ D prime هذا سيكون الـ
+
+398
+00:42:38,000 --> 00:42:46,540
+Centralizer لـ D' من هذا الكلام بقدر استنتج أن H
+
+399
+00:42:46,540 --> 00:42:54,040
+في V سيكون V في H وبقدر استنتج من هذا اللي تحت أن
+
+400
+00:42:54,040 --> 00:43:02,460
+D D' سيكون D' D يبقى هذا استنتاج من خلال الكلام
+
+401
+00:43:02,460 --> 00:43:03,760
+اللي عندنا هنا
+
+402
+00:43:23,420 --> 00:43:30,680
+الآن آخر نظرية موجودة في هذا الـ chapter وهي أن الـ 
+
+403
+00:43:30,680 --> 00:43:39,220
+centralizer عبارة عن subgroup يبقى theorem for
+
+404
+00:43:39,220 --> 00:43:51,840
+any element a اللي موجود في جيب الـ centralizer لـ a 
+
+405
+00:43:53,260 --> 00:44:02,720
+is a subgroup من G من من من من من 
+
+406
+00:44:02,720 --> 00:44:03,440
+من من من من من من من من من من من من من من من من 
+
+407
+00:44:03,440 --> 00:44:03,500
+من من من من من من من من من من من من من من من من
+
+408
+00:44:03,500 --> 00:44:08,840
+من من من من من من من من من من من
+
+409
+00:44:08,840 --> 00:44:08,920
+من من من من من من من من من من من من من من من من
+
+410
+00:44:08,920 --> 00:44:10,740
+من من من من من من من من من من من من من من من من
+
+411
+00:44:10,740 --> 00:44:14,560
+من من من من من من من من من من
+
+412
+00:44:14,560 --> 00:44:15,840
+من من من
+
+413
+00:44:36,070 --> 00:44:43,020
+النقطة الثانية بداية ياخد let عشان ناخد الـ a ونقول
+
+414
+00:44:43,020 --> 00:44:51,400
+x y لت الـ x y موجود في الـ centralizer لـ a then الـ
+
+415
+00:44:51,400 --> 00:45:02,980
+x a بده يساوي الـ a x and الـ y a بده يساوي الـ a y ايش
+
+416
+00:45:02,980 --> 00:45:09,100
+بدنا نثبت؟ بنثبت أن الـ xy inverse موجود في
+
+417
+00:45:09,100 --> 00:45:14,360
+الـ centralizer لإيه؟ يعني بنثبت أن الـ xy inverse a
+
+418
+00:45:14,360 --> 00:45:20,360
+بدو يساوي الـ axy inverse يبقى فرضنا هدول الاثنين 
+
+419
+00:45:20,360 --> 00:45:30,020
+بيساووا بعض يبقى now لو أجى أخدت الـ ya بدو يساوي
+
+420
+00:45:30,020 --> 00:45:37,890
+الـ ay هذا بدي يعطينا شرايك بدي أضرب في الـ y inverse
+
+421
+00:45:37,890 --> 00:45:44,690
+من جهة اليمين يبقى بيصير y a y inverse يساوي قداش
+
+422
+00:45:44,690 --> 00:45:50,210
+يساوي الـ a بدي أضرب في y inverse من جهة اليسار
+
+423
+00:45:50,210 --> 00:45:56,310
+يبقى لو ضربت من جهة اليسار بيظل a y inverse تساوي
+
+424
+00:45:56,310 --> 00:46:03,130
+y inverse في a يبقى ايش معنى هذا الكلام أن الـ y 
+
+425
+00:46:03,130 --> 00:46:09,370
+inverse موجود في الـ centralizer لإيه هذا معناه أن
+
+426
+00:46:09,370 --> 00:46:14,450
+الـ y inverse موجود في الـ centralizer لإيه يبقى
+
+427
+00:46:14,450 --> 00:46:20,870
+بناء عليه الـ element y موجود في الـ centralizer
+
+428
+00:46:20,870 --> 00:46:27,030
+لإيه إذا معكوسه يكون كذلك موجود في الـ centralizer
+
+429
+00:46:27,030 --> 00:46:31,110
+لإيه هذا معناته أن y inverse موجود في الـ
+
+430
+00:46:31,110 --> 00:46:37,710
+centralizer لإيه واعتبر لهذه الهيمينة النقطة الأولى
+
+431
+00:46:37,710 --> 00:46:45,670
+يبقى نكتب الكلمة اللي قولناها يبقى this means that
+
+432
+00:46:45,670 --> 00:46:52,710
+هذا يعني أن if الـ y موجود في الـ centralizer لـ a
+
+433
+00:46:52,710 --> 00:47:03,380
+then الـ Y موجود في الـ Centralizer لـ
+
+434
+00:47:03,380 --> 00:47:10,880
+A ثم الـ Y Inverse ثم أو الـ Y موجودة في الـ
+
+435
+00:47:10,880 --> 00:47:17,780
+Centralizer لـ A Inverse لا لا الـ Y Inverse
+
+436
+00:47:17,780 --> 00:47:24,550
+موجودة في الـ Centralizer لـ A تمام الآن لو جيت
+
+437
+00:47:24,550 --> 00:47:39,110
+قلت لك consider خد لي اللي هو الـ X Y inverse A هذا
+
+438
+00:47:39,110 --> 00:47:45,310
+الكلام بدو يساوي إذا قدرت أثبت أن الـ x y inverse a
+
+439
+00:47:45,310 --> 00:47:52,290
+بيكون a x y inverse بيتم المطلوب يبقى هذا x y
+
+440
+00:47:52,290 --> 00:47:58,010
+inverse الـ a بقدر أكتبها a inverse inverse يبقى
+
+441
+00:47:58,010 --> 00:48:07,470
+هذا الكلام بيكون x وهنا a inverse y الكل inverse
+
+442
+00:48:07,470 --> 00:48:09,510
+مظبوط
+
+443
+00:48:10,530 --> 00:48:16,310
+يعني جمعت هنا الـ inverse inverse رجعتهم لأصلهم
+
+444
+00:48:16,310 --> 00:48:24,110
+واحدة بالشكل هنا الآن أنا عندي هنا a inverse
+
+445
+00:48:24,110 --> 00:48:30,990
+مكتوبة اه سنة سنة شوية ايش اللي سويتها؟ a inverse y
+
+446
+00:48:30,990 --> 00:48:34,990
+طيب هنا قلت دي اسم الالكترون موجود في الـ
+
+447
+00:48:34,990 --> 00:48:38,910
+centralizer then y inverse موجود
+
+448
+00:48:45,110 --> 00:48:56,690
+كيف؟ بدي واحد بس يحكي، واحد يحكي بقى، ايه؟ اه،
+
+449
+00:48:56,690 --> 00:49:00,850
+يعني هيك، برضه مظبوط، ممكن ناخد x,y وممكن ناخد x,y
+
+450
+00:49:00,850 --> 00:49:04,090
+inverse مرة واحد، عشقتين، يا ناس ضرورة، ممكن
+
+451
+00:49:04,090 --> 00:49:06,770
+استفيد من هذه، أن الـ A 
+
+452
+00:49:17,330 --> 00:49:22,150
+على أي حال بنكمل المرة القادمة إن شاء الله
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..26bb8de9fbfc1ebc9b092069fbc45f53e3ebec1b
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_postprocess.srt
@@ -0,0 +1,1808 @@
+1
+00:00:21,330 --> 00:00:26,210
+بسم الله الرحمن الرحيم المرة الماضية اخر حاجة
+
+2
+00:00:26,210 --> 00:00:29,750
+اتكلمنا فيها اعطينا definition لل center لل group
+
+3
+00:00:30,390 --> 00:00:36,030
+بنعيد هذا ال definition ومن ثم ناخد نظرية عليه
+
+4
+00:00:36,030 --> 00:00:41,050
+فقلنا المرة اللي فاتت ان ال center تبع ال group G
+
+5
+00:00:41,050 --> 00:00:47,610
+هديله رمز Z of G وقلنا هو كل العلاصر ال A اللي
+
+6
+00:00:47,610 --> 00:00:55,510
+موجودة في G بحيث ان ال AX بده يساوي ال XA لكل ال X
+
+7
+00:00:55,510 --> 00:01:02,150
+اللي belongs to main to group Gإذا ما معنى الـ
+
+8
+00:01:02,150 --> 00:01:05,510
+Center تبع الـ Group؟ معنى الـ Center تبع الـ
+
+9
+00:01:05,510 --> 00:01:11,070
+Group هو كل ال elements اللي كميوتس عمّا بقية
+
+10
+00:01:11,070 --> 00:01:15,090
+عناصر الـ Group يعني لو أخدت element لجيته كميوتس
+
+11
+00:01:15,090 --> 00:01:18,030
+مع جميع عناصر الـ Group بقول هذا من الـ Center
+
+12
+00:01:18,030 --> 00:01:22,970
+اللي بعد اللي بعد لغاية ما طلع كل العناصر اللي
+
+13
+00:01:22,970 --> 00:01:28,500
+بتكون كميوتس مع جميع عناصر الـ Groupيبقى هذول
+
+14
+00:01:28,500 --> 00:01:32,560
+بيكونول مين؟ بيكونول ال center تبع ال group أبسط
+
+15
+00:01:32,560 --> 00:01:37,380
+الأشياء ال identity element موجود في مين؟ في ال
+
+16
+00:01:37,380 --> 00:01:40,260
+center تبع ال group لأن ال identity elements
+
+17
+00:01:40,260 --> 00:01:45,740
+commutes with all elements of G يبقى كل العناصر
+
+18
+00:01:45,740 --> 00:01:51,520
+اللي موجودة في G و اللي بتبقى commutes مع أي عنصر
+
+19
+00:01:51,520 --> 00:01:56,490
+موجود في G يبقى هذا بسميه ال center of Gالان في
+
+20
+00:01:56,490 --> 00:02:01,530
+نظرية بتقول الـ center هذا هو الـ subgroup فبدنا
+
+21
+00:02:01,530 --> 00:02:06,670
+نروح نبره انصحة هذا الكلام يبقى النظرية بتقول ما
+
+22
+00:02:06,670 --> 00:02:13,070
+يأتي theorem z
+
+23
+00:02:13,070 --> 00:02:18,430
+of g the
+
+24
+00:02:18,430 --> 00:02:23,570
+center of
+
+25
+00:02:23,570 --> 00:02:33,340
+a groupG is a
+
+26
+00:02:33,340 --> 00:02:39,720
+subgroup of
+
+27
+00:02:39,720 --> 00:02:41,020
+G
+
+28
+00:02:51,670 --> 00:02:56,290
+يبقى انا مشان اثبت انه ال 6 المعرفة بالشكل هنا
+
+29
+00:02:56,290 --> 00:03:02,490
+subgroup من لجروب الأساسية دي بدي اثبت النقطتين
+
+30
+00:03:02,490 --> 00:03:08,810
+اول شئ انه Z of G none empty الأمر الثاني بدي اثبت
+
+31
+00:03:08,810 --> 00:03:15,350
+انه انه اي عنصر لو أخدته او اي عنصرين لو أخدته من
+
+32
+00:03:15,350 --> 00:03:18,750
+ال center بدي يكون الأول في معكوس الثاني موجود
+
+33
+00:03:18,750 --> 00:03:25,220
+وين؟ موجود في ال centerيبقى أول شي أنا أدعي ان ال
+
+34
+00:03:25,220 --> 00:03:32,400
+z of g is non-empty وهذه هي النقطة الأولى في
+
+35
+00:03:32,400 --> 00:03:40,150
+البرهان non-empty ليش؟ becauseالـ E موجود في الـ Z
+
+36
+00:03:40,150 --> 00:03:47,610
+of G لأيش؟ لأن الـ E X بده يساوي X E لكل الـ X
+
+37
+00:03:47,610 --> 00:03:56,650
+اللي موجود لأن الـ E X بده يساوي الـ X في الـ E
+
+38
+00:03:56,650 --> 00:04:04,040
+لكل الـ X اللي موجودة في G بلا استثناءيبقى نظرا
+
+39
+00:04:04,040 --> 00:04:07,780
+لإنه يحقق الخاصية تبع الـ center تبع ال group إذا
+
+40
+00:04:07,780 --> 00:04:13,680
+على الأقل فيها element واحد اللي هو ال E الآن
+
+41
+00:04:13,680 --> 00:04:20,700
+بتروح اخد two elements النقطة الثانية let a و b
+
+42
+00:04:20,700 --> 00:04:27,960
+belongs to z of gلما أقول two elements هدول
+
+43
+00:04:27,960 --> 00:04:34,760
+موجودات في Z of G يبقى بد يكون عندنا ال A X بد
+
+44
+00:04:34,760 --> 00:04:44,800
+يساوي ال X A and ال B X بد يساوي X B لكل ال X اللي
+
+45
+00:04:44,800 --> 00:04:47,400
+موجود في G بي less تتنعى
+
+46
+00:04:50,150 --> 00:04:54,250
+يبقى هذا ال element موجود في ال center إذا بدي
+
+47
+00:04:54,250 --> 00:04:58,790
+أحقق للخاصية اللي فوق تبعت ال center بي موجود في
+
+48
+00:04:58,790 --> 00:05:03,590
+ال center إذا بدي أحقق لنفس الخاصية يبقى أنا أخدت
+
+49
+00:05:03,590 --> 00:05:08,050
+عنصرين موجودات في ال center تبع ال group بدي أثبت
+
+50
+00:05:08,050 --> 00:05:13,350
+إن الأول في معكوسي ثاني موجود في مين في ال center
+
+51
+00:05:13,350 --> 00:05:21,040
+بمعنى آخرأريد أن أثبت أن a b inverse x هو x a b
+
+52
+00:05:21,040 --> 00:05:27,360
+inverse لكل x موجودة في g بلا استثناء يبقى بداجي
+
+53
+00:05:27,360 --> 00:05:34,740
+أقول له consider خد أن a b inverse x
+
+54
+00:05:38,410 --> 00:05:46,950
+بتشوف هذا بدي أثبت و بدي أثبت و بدي أثبت
+
+55
+00:05:46,950 --> 00:05:48,290
+و بدي أثبت و بدي أثبت و بدي أثبت و بدي أثبت و بدي
+
+56
+00:05:48,290 --> 00:05:57,150
+أثبت و بدي أثبت و بدي أثبت
+
+57
+00:05:57,980 --> 00:06:03,900
+يبقى هذا الكلام بده يساوي بدي أحاول أربط ما بين ال
+
+58
+00:06:03,900 --> 00:06:08,780
+X و ال B اللي عندنا يبقى لو جيت قولت هذا A B
+
+59
+00:06:08,780 --> 00:06:16,420
+inverse ال X أخدتها X inverse inverse طبعا برهنها
+
+60
+00:06:16,420 --> 00:06:23,600
+سابقا يبقى هذا الكلام بده يساوي A فاهمين؟ فبصير X
+
+61
+00:06:23,600 --> 00:06:30,770
+inverse B لكل inverseهذه انفرس وهذه انفرس يبقى
+
+62
+00:06:30,770 --> 00:06:35,330
+رجعتهم للأصل اللي بتبعهم بالشكل اللي عندنا هذا طيب
+
+63
+00:06:35,330 --> 00:06:40,170
+الآن P موجودة في ال center ولا لأ يبقى commutes مع
+
+64
+00:06:40,170 --> 00:06:43,270
+ال X وال X انفرس لأنها موجودة في ال center يعني
+
+65
+00:06:43,270 --> 00:06:47,910
+commutes مع any element موجود في ال group G يبقى
+
+66
+00:06:47,910 --> 00:06:56,670
+هذا الكلام بده يساوي A و هنا B X انفرس الكل انفرس
+
+67
+00:07:00,860 --> 00:07:05,520
+ليش هذا الخطوة عملتها؟ لأن بي موجودة في الـ Center
+
+68
+00:07:05,520 --> 00:07:11,600
+يبقى هذه الـ Sense بي موجودة في الـ Center تبع الـ
+
+69
+00:07:11,600 --> 00:07:17,580
+G هذا الكلام بده يساوي لو جيتلي هذا الآن بده أطبق
+
+70
+00:07:17,580 --> 00:07:22,940
+عليها تعريف المعكوس لحظة حصل ضرب two elements يبقى
+
+71
+00:07:22,940 --> 00:07:26,020
+هذا بيصير A في X
+
+72
+00:07:28,710 --> 00:07:37,090
+إنفرس إنفرس وهنا اللي هو بي انفرس يبقى وزعة ال
+
+73
+00:07:37,090 --> 00:07:42,210
+inverse لكل واحدة من هدول يبقى هذه ابتنقلة يبقى
+
+74
+00:07:42,210 --> 00:07:49,770
+هذه إيش بصير ax في ال b inverseالان انا عندى من
+
+75
+00:07:49,770 --> 00:07:57,330
+المعطيات ان a x يساوي main x a يبقى هذا الكلام بدي
+
+76
+00:07:57,330 --> 00:08:06,810
+يعطينا x a في ال b inverse ليش هذا ال sense ال a
+
+77
+00:08:06,810 --> 00:08:13,150
+موجودة في ال center تبع ال gطيب هذا الكلام بده
+
+78
+00:08:13,150 --> 00:08:19,770
+يساوي من خاصية ال associativity XAB inverse بالشكل
+
+79
+00:08:19,770 --> 00:08:25,090
+اللي عندناطب ايش اللي عملته انا حتى اللحظة اخدت a
+
+80
+00:08:25,090 --> 00:08:31,250
+b inverse x لجيته يساوي x a b inverse هذا الكلام
+
+81
+00:08:31,250 --> 00:08:37,590
+صحيح لكل ال x اللي موجودة في g plus تتنى ايش
+
+82
+00:08:37,590 --> 00:08:42,370
+تفسيرك لهذا الكلام يبقى ال a b inverse موجود وين
+
+83
+00:08:42,370 --> 00:08:45,990
+في ال center تبع ال group وبالتالي ال center عبارة
+
+84
+00:08:45,990 --> 00:08:53,880
+عن sub groupيبقى هنا سوا ال a b inverse belongs لل
+
+85
+00:08:53,880 --> 00:09:03,920
+z of g and hence ومن ثم ال z of g is a subgroup من
+
+86
+00:09:03,920 --> 00:09:05,060
+g وهو المطلوب
+
+87
+00:09:08,760 --> 00:09:14,200
+يبقى من الآن فصاعدا ال center تبع ال group هو sub
+
+88
+00:09:14,200 --> 00:09:20,440
+group من من ال group الأساسية طيب يا شباب في عندنا
+
+89
+00:09:20,440 --> 00:09:28,000
+سؤال السؤال لو كانت جي أبيليان جي أبيليان يبقى ال
+
+90
+00:09:28,000 --> 00:09:34,040
+center تبع ال group بيكون كل group يبقى هذه اكتبها
+
+91
+00:09:34,040 --> 00:09:46,500
+ملاحظة not fالـ G is abelian then ال center تبع
+
+92
+00:09:46,500 --> 00:09:53,280
+الـ G بده يسوي الـ G itself كلها بلا استثناء نبدأ
+
+93
+00:09:53,280 --> 00:10:04,080
+ناخد أمثلة examples أول مثال بيقول let ال G هي ال
+
+94
+00:10:04,080 --> 00:10:09,550
+generalLinear group of two by two matrices over R
+
+95
+00:10:09,550 --> 00:10:21,390
+Then بدنا Z of G بد Z of G هو عبارة عن مين أنا
+
+96
+00:10:21,390 --> 00:10:31,090
+أدعي أن Z of G كل المصوفة على صيغة A 00A و بحيث ال
+
+97
+00:10:31,090 --> 00:10:41,300
+A موجود في Rوالـ A هذا لا يساوي Zero الكلام
+
+98
+00:10:41,300 --> 00:10:44,760
+هذا صحيح ولا ما هو مش صحيح الله وعلا أنا أدعي
+
+99
+00:10:44,760 --> 00:10:51,040
+ادعاء باجي بقول والله إذا لقيت هذا المصوفات كلهم
+
+100
+00:10:51,040 --> 00:10:56,540
+اللي موجودة في Z of G commutes with any element في
+
+101
+00:10:56,540 --> 00:11:00,180
+ال general linear غروب يصيب كلامنا صحيح من اليمين
+
+102
+00:11:00,180 --> 00:11:05,450
+ومن الشمال ماطلة يبقى كلامنا معله غير صحيحلذلك
+
+103
+00:11:05,450 --> 00:11:11,310
+بأجي بقولك هذا الكلام because بدي أجي ال element
+
+104
+00:11:11,310 --> 00:11:17,230
+اللي موجود في ال center a zero zero a بدي أضربه في
+
+105
+00:11:17,230 --> 00:11:21,230
+أي element موجود في ال general linear group بدي
+
+106
+00:11:21,230 --> 00:11:28,810
+أخد b, c, d, f مثلا بديش اكتب ال a بلاش تقولي ايه
+
+107
+00:11:28,810 --> 00:11:34,160
+هذا هو ال identity elementإذا هذه لو جيت ضربتها
+
+108
+00:11:34,160 --> 00:11:40,400
+بدها تساوي الصف الأول في العمود الأول اللي هو AB
+
+109
+00:11:40,400 --> 00:11:47,560
+الصف الأول في العمود الثاني يبقى بAC الصف الثاني
+
+110
+00:11:47,560 --> 00:11:53,260
+في العمود الأول يبقى بAD الصف الثاني في العمود
+
+111
+00:11:53,260 --> 00:12:06,450
+الثاني بAFاللي بقدر اكتبها a في b,c,d,f الان بداتي
+
+112
+00:12:06,450 --> 00:12:16,420
+اخدله اللي هو b,c,d,f في ال a,0,0,aيبقى هذا معناه
+
+113
+00:12:16,420 --> 00:12:23,180
+صف الأول في العمود الأول BA الصف الأول في العمود
+
+114
+00:12:23,180 --> 00:12:29,960
+الثاني CA الصف الثاني في العمود الأول DA الصف
+
+115
+00:12:29,960 --> 00:12:37,240
+الثاني في العمود الثاني يبقى FAلو أخدت ال a من كل
+
+116
+00:12:37,240 --> 00:12:42,340
+element موجود داخل المصوفة بيظهر لنا مين بي بي بي
+
+117
+00:12:42,340 --> 00:12:43,680
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+118
+00:12:43,680 --> 00:12:50,000
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+119
+00:12:50,780 --> 00:12:56,080
+ما دام اريكوا المعناته فعلا هذا يمثل main ال
+
+120
+00:12:56,080 --> 00:13:01,480
+center او المصفوفة اللي عندنا هذه هي element موجود
+
+121
+00:13:01,480 --> 00:13:07,380
+وان موجود في ال center هذا بدي اعطيلك ان any
+
+122
+00:13:07,380 --> 00:13:09,140
+element
+
+123
+00:13:11,320 --> 00:13:22,860
+in z of g is in the form على الشكل اللي هو a zero
+
+124
+00:13:22,860 --> 00:13:30,410
+zero aوالـ A does not equal to zero يبقى من الأن
+
+125
+00:13:30,410 --> 00:13:34,110
+فصاعدا لما بد ال center لل general linear group of
+
+126
+00:13:34,110 --> 00:13:38,670
+two by two matrices over R بيكون عندي واحد زيرو
+
+127
+00:13:38,670 --> 00:13:43,030
+زيرو واحد اتنين زيرو زيرو واحد مص زيرو زيرو واحد
+
+128
+00:13:43,030 --> 00:13:48,310
+واحد على مية زيرو زيرو واحد على مية و هكذايبقى كل
+
+129
+00:13:48,310 --> 00:13:53,590
+العناصر القطرة الرئيسى بيكون عناصرهم متساوية وهذه
+
+130
+00:13:53,590 --> 00:13:59,170
+بقينا نسميها في ال linear algebra بقيناها نسميها
+
+131
+00:13:59,170 --> 00:14:05,830
+المصوفة شو اسمها؟ مصوفة الواحدة قطرية
+
+132
+00:14:05,830 --> 00:14:12,150
+لما العناصر القطرة الرئيسى يكونوا متساوية بقيناش
+
+133
+00:14:12,150 --> 00:14:14,330
+نسميها مثلثية
+
+134
+00:14:17,700 --> 00:14:24,520
+بنسميها scalar matrix او مقياسية
+
+135
+00:14:24,520 --> 00:14:28,940
+لو كان القطرين غير متسوين بيقول دياجون الماتريك
+
+136
+00:14:28,940 --> 00:14:31,240
+دياجون الماتريك هي فعلا دياجون الماتريك في المصحوف
+
+137
+00:14:31,240 --> 00:14:36,060
+القطرية بس إذا تسابق عناصر القطر الرئيسي بنسميها
+
+138
+00:14:36,060 --> 00:14:41,070
+scalar matrixيبقى كل scalar matrix في ال general
+
+139
+00:14:41,070 --> 00:14:44,790
+linear group of two by two matrices بيكونولي main
+
+140
+00:14:44,790 --> 00:14:50,790
+بيكونولي ال center لل group اللي عندنا طيب نمرتنا
+
+141
+00:14:50,790 --> 00:15:01,990
+example two بدنا z of D4 يساوي أكيد ال R node منهم
+
+142
+00:15:01,990 --> 00:15:07,240
+هذا كل مجمع ليه لأنه ال identityحد بيقدر يجيبلي
+
+143
+00:15:07,240 --> 00:15:16,240
+كمان element اخر تسعين commutes مع الكل تسعين
+
+144
+00:15:16,240 --> 00:15:19,860
+commutes مع المية وتمانين ومع الميتين وسبعين مع ال
+
+145
+00:15:19,860 --> 00:15:25,580
+rotations نعم لكن مع ال reflections ليس صحيحا
+
+146
+00:15:25,580 --> 00:15:31,960
+واثبتلك ان ر تسعين في H ليسوا ال H في R تسعين
+
+147
+00:15:31,960 --> 00:15:39,720
+وحسبتهم لك انتالـ R180 فقط لا غير يبقى هذه والـ
+
+148
+00:15:39,720 --> 00:15:48,060
+R180 فقط لا غير يبقى هدول بس عناصر الـ Center تبعي
+
+149
+00:15:48,060 --> 00:15:52,600
+الـ D4 غير هيك مافيش ولا elements طبعا لو رجعت
+
+150
+00:15:52,600 --> 00:15:58,720
+للجدول اللي في الصفحة واحدة و تلاتين الكليتابل للـ
+
+151
+00:15:58,720 --> 00:16:05,880
+D4بتلاقي ان ال R180 هي ال commutes مع جميع عناصر
+
+152
+00:16:05,880 --> 00:16:10,280
+D4 بالاضافة الى ال identity element اللي هو main
+
+153
+00:16:10,670 --> 00:16:16,350
+اللي هو Arnold يبقى هذول ال two elements هم اللي
+
+154
+00:16:16,350 --> 00:16:21,890
+commutes مع جميع عناصر D4 فقط لا غير طيب إيش رأيك
+
+155
+00:16:21,890 --> 00:16:27,650
+بدي أعمملك هالشغل هذه بدل ما أاخد D4 بدي أاخد DN
+
+156
+00:16:27,650 --> 00:16:35,950
+يبقى الآن in general لو
+
+157
+00:16:35,950 --> 00:16:46,670
+أخدت ال Z of DMهذه أحد أمرين يا إما الارنود والار
+
+158
+00:16:46,670 --> 00:16:55,750
+مية و تمانين فقط يا إما الارنود السؤال هو متى يحدث
+
+159
+00:16:55,750 --> 00:17:01,950
+هذا و متى يحدث هذا الان في D4 الرقم هذا زوجي والله
+
+160
+00:17:01,950 --> 00:17:09,870
+فردي زوجييبقى هذا يحدث لو كان ال in فرديا يبقى هنا
+
+161
+00:17:09,870 --> 00:17:21,630
+هذا الكلام if in is even او هذا if ال in is odd
+
+162
+00:17:21,630 --> 00:17:29,050
+فقط لا غير طبعا يمكن يسأل واحد بعض منكم لماذا هذا
+
+163
+00:17:29,050 --> 00:17:29,750
+الكلام
+
+164
+00:17:40,760 --> 00:17:46,140
+الإجابة بدنا نعطي تفسير ليش هذا الكلام مافيش غرض
+
+165
+00:17:46,140 --> 00:17:54,220
+يبقى اكتب لي this is because يبقى this is because
+
+166
+00:17:54,220 --> 00:18:05,940
+هذا الكلام لإنه this is because every rotation in
+
+167
+00:18:05,940 --> 00:18:07,680
+DN
+
+168
+00:18:09,750 --> 00:18:19,790
+is a power is a power of
+
+169
+00:18:19,790 --> 00:18:28,450
+R تلت مية و ستين على N and
+
+170
+00:18:28,450 --> 00:18:37,790
+rotations and rotations commute
+
+171
+00:18:42,200 --> 00:18:49,400
+and the rotations commute with each other with
+
+172
+00:18:49,400 --> 00:18:59,060
+each other نجي
+
+173
+00:18:59,060 --> 00:19:03,760
+الان لو كان حاصل ضبر rotation في reflection بدا
+
+174
+00:19:03,760 --> 00:19:10,280
+اقولك بدا اعطي تسمية التالية little r b any
+
+175
+00:19:12,530 --> 00:19:31,450
+rotation in DN and let ال F be any reflection برضه
+
+176
+00:19:31,450 --> 00:19:36,290
+in DN in DN
+
+177
+00:19:49,990 --> 00:19:57,070
+مرة أخرى ندعي أن الـ Center تبع ال group D ان سواء
+
+178
+00:19:57,070 --> 00:20:04,330
+كانت D3، D4، D5، D6، جد ما يكون يكون طبعا ال N هذه
+
+179
+00:20:04,330 --> 00:20:10,410
+أكبر من أو تساوي تلاتة ال N اللي عندنا أكبر من أو
+
+180
+00:20:10,410 --> 00:20:15,330
+تساوي تلاتة يعني ممكن يكون مثلث منتظم مربع منتظم
+
+181
+00:20:15,330 --> 00:20:20,390
+مخلص منتظم مسدس منتظم إلى آخرهمإذا والله ال N
+
+182
+00:20:20,390 --> 00:20:28,030
+موجبة زي D4, D6, D8, D10 إلى آخره يبقى العناصر
+
+183
+00:20:28,030 --> 00:20:33,070
+اللي في ال center بس Arnold و R180 الأقل لو كانت
+
+184
+00:20:33,070 --> 00:20:36,670
+ال N فردي تلاتة خمسة سبعة تسعة إلى آخره يبقى لا
+
+185
+00:20:36,670 --> 00:20:40,990
+يوجد في ال center إلا عنصر الوحدة اللي همين Arnold
+
+186
+00:20:40,990 --> 00:20:46,720
+ليش هذا؟لأن أي روتاشن يتعامل مع أي روتاشن أخر مثلا
+
+187
+00:20:46,720 --> 00:20:52,220
+في D4 اذا قلت لك R90 يتعامل مع R180 ويتعامل مع
+
+188
+00:20:52,220 --> 00:20:57,520
+R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+189
+00:20:57,520 --> 00:21:01,300
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+190
+00:21:01,300 --> 00:21:02,380
+يتعامل مع R270 وR270 يتعامل مع R270 وR270 يتعامل
+
+191
+00:21:02,380 --> 00:21:03,200
+مع R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+192
+00:21:03,200 --> 00:21:07,000
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+193
+00:21:07,000 --> 00:21:12,500
+يتعامل مع R270 وR270 يتعامل مع R270
+
+194
+00:21:12,500 --> 00:21:17,410
+وR2يبقى ده كميوس باجي بقوله بدي اجي اخد R هي any
+
+195
+00:21:17,410 --> 00:21:23,670
+rotation يعني جربلك الفكرة لو كان ال D4 عندنا يبقى
+
+196
+00:21:23,670 --> 00:21:27,610
+ال R هادي اما R تسعين او مية و تمانين او ميتين و
+
+197
+00:21:27,610 --> 00:21:34,730
+سبعين اي واحدة منهم تمام؟يبقى ال F في كذلك any
+
+198
+00:21:34,730 --> 00:21:39,670
+reflection أي انقلاب سواء كان H و لا V و لا D و لا
+
+199
+00:21:39,670 --> 00:21:45,430
+D' أي واحدة منهم مكتوب معاك ان reflection ضرب
+
+200
+00:21:45,430 --> 00:21:51,530
+rotation يساوي rotation ضرب reflection كله بيعطيني
+
+201
+00:21:51,530 --> 00:21:55,850
+reflection ماقولش يساوي يعني على كل الأمرين بطلعلي
+
+202
+00:21:55,850 --> 00:21:59,090
+reflectionلو ضربت rotation في reflection بده
+
+203
+00:21:59,090 --> 00:22:01,570
+يطلعلي reflection، لو ضربت reflection في rotation
+
+204
+00:22:01,570 --> 00:22:05,170
+بده يطلعلي reflection على كلا الأمرين و مكتوبة
+
+205
+00:22:05,170 --> 00:22:08,130
+معاك هذه كتبناها قبل ذلك
+
+206
+00:22:10,970 --> 00:22:16,690
+أي rotation في ديو 4 هو power of r 360 على n ايش
+
+207
+00:22:16,690 --> 00:22:24,630
+360 على n باجي بقول اه لو كانت n تساوي 4 مثلا يبقى
+
+208
+00:22:24,630 --> 00:22:29,230
+360 على 4 فيها جداش 90 اذا ال rotation الواحدة
+
+209
+00:22:29,230 --> 00:22:35,080
+بتسعين درجةهذا لما يكون مربع طب لو كان مثلث بدي
+
+210
+00:22:35,080 --> 00:22:39,660
+اقسم على تلاتة يبقى ال rotation مقداش مية و عشرين
+
+211
+00:22:39,660 --> 00:22:45,740
+درجة لو كان مخمس لو كان مسدس منتظر يبقى تلاتمية و
+
+212
+00:22:45,740 --> 00:22:49,460
+ستين على ست اللي فيه مقداش ستين يبقى بصير عندي R
+
+213
+00:22:49,460 --> 00:22:55,740
+نوت R ستين R مية و عشرين R مية و تمانين R متينو40
+
+214
+00:22:55,740 --> 00:23:02,820
+R300 R node وهكذا يبقى هكذا تكتب من العناصر وبعدين
+
+215
+00:23:02,820 --> 00:23:06,800
+بروح بدور من ال reflections إلى آخرين ما علينا
+
+216
+00:23:06,800 --> 00:23:13,880
+يبقى المقصود من R360 على N أطلع جداش مقدار الزاوية
+
+217
+00:23:13,880 --> 00:23:18,250
+اللي بأعملبها الدورالة المضلع المنتظم اللي عندي
+
+218
+00:23:18,250 --> 00:23:23,830
+مين مكان ايه يكون تمام اي rotation هديها الرمز R
+
+219
+00:23:23,830 --> 00:23:30,150
+اي reflection هديها ايه هديها الرمز R تمام طيب
+
+220
+00:23:30,150 --> 00:23:36,890
+الان rotation بدي اقول any rotation في reflection
+
+221
+00:23:36,890 --> 00:23:41,930
+بيعطينا reflection او اي reflection في rotation
+
+222
+00:23:41,930 --> 00:23:44,250
+بيعطينا reflection
+
+223
+00:23:58,780 --> 00:24:03,600
+ارنود ال identity element اتحرك مع اي element اخر
+
+224
+00:24:03,600 --> 00:24:10,860
+في ال group ارنود هو دوران بصفر درجةيبقى هذا هو ال
+
+225
+00:24:10,860 --> 00:24:15,860
+identity element كنت حاضر يوم شرحنا ال D4 هذه؟
+
+226
+00:24:15,860 --> 00:24:24,180
+بعوض الله طيب ولا قريتها كمان؟ ماشي طيب هذه دلوقتي
+
+227
+00:24:24,180 --> 00:24:28,440
+عمود فقري روح اقراها تاني غلبتك حاجة حتى و تعالي
+
+228
+00:24:28,440 --> 00:24:32,980
+نشرحلك ماعناش مشكلة المهم لأن هذه عمود فقري كل
+
+229
+00:24:32,980 --> 00:24:37,860
+شوية لجروب و هيطلعانة بدنا نشتغل عليها تمام؟ طيب
+
+230
+00:24:38,150 --> 00:24:43,490
+نرجع لموضوعنا احنا بندعي الان ان ال center لدى N
+
+231
+00:24:43,490 --> 00:24:47,690
+اذا كانت N عددا زوجين ماعنديش الا Arnold وR180
+
+232
+00:24:47,690 --> 00:24:53,970
+واذا كان فاردي ماعنديش الا من Arnold الان بنقول ال
+
+233
+00:24:53,970 --> 00:24:58,950
+rotation ب commutes مع اي rotation اخرى وضربتلك من
+
+234
+00:24:58,950 --> 00:25:04,490
+93 مع 180 مع 270 كلهم commutes هدول مع بعض مع ال
+
+235
+00:25:04,490 --> 00:25:09,480
+Arnold كمان اللي هو ال identityالان اي rotation
+
+236
+00:25:09,480 --> 00:25:15,000
+حديها الرمز R اي reflection حديها الرمز F الان
+
+237
+00:25:15,000 --> 00:25:22,600
+احنا سابقا برضه باجي بقول since اللي هو ال R في F
+
+238
+00:25:22,600 --> 00:25:25,800
+is a reflection
+
+239
+00:25:28,280 --> 00:25:32,260
+هذه reflection يعني حاصر ضرب ال rotation في ال
+
+240
+00:25:32,260 --> 00:25:36,860
+reflection بيعطيني reflection أو العكس لو كان F في
+
+241
+00:25:36,860 --> 00:25:41,700
+R كمان بيعطينا مين reflection و ما إلى ذلك يبقى
+
+242
+00:25:41,700 --> 00:25:46,300
+نظرا لإن ال R في F is a reflection معناته هذا
+
+243
+00:25:46,300 --> 00:25:55,630
+العنصر معكسه قداشي بيعطينا معكس العنصر هذاأرجع ال
+
+244
+00:25:55,630 --> 00:26:00,450
+D4 مش ال D4 قولنا H تربيعه يسوى ال identity يبقى
+
+245
+00:26:00,450 --> 00:26:05,530
+ال H inverse يبقى كده بال H itself يبقى هو معكوس
+
+246
+00:26:05,530 --> 00:26:12,210
+لنفسه يبقى في هذه لأ it's a reflection we have
+
+247
+00:26:12,210 --> 00:26:22,430
+يبقى بده يصير ال RF بده يسوى ال RF لكل inverseيبقى
+
+248
+00:26:22,430 --> 00:26:29,210
+باجي بقول يبقى صار الار اف بده يساوي الار اف في
+
+249
+00:26:29,210 --> 00:26:35,290
+الكل انفرست وبلغة ال F inverse هذا هو ال F inverse
+
+250
+00:26:35,290 --> 00:26:40,190
+في الار انفرست بلغة المعكوس بتنقل بيقول معكوس
+
+251
+00:26:40,190 --> 00:26:45,290
+الأول للآخر طب ال F reflection لما تبقى ال F
+
+252
+00:26:45,290 --> 00:26:51,340
+reflection يبقى F square قداش مديوطن يا شباباللي
+
+253
+00:26:51,340 --> 00:26:55,420
+هنضل هو ال identity يعني لو جيت قلت ال identity
+
+254
+00:26:55,420 --> 00:27:00,880
+يبقى ال F بالصير هي ال F inverse ولا لا يعني لو
+
+255
+00:27:00,880 --> 00:27:04,480
+ضربت الطرفين في ال F inverse من جهة اليمين او من
+
+256
+00:27:04,480 --> 00:27:09,220
+جهة الشماليبقى هنا بظل قداش بظل F والطرف اليامين
+
+257
+00:27:09,220 --> 00:27:13,620
+هي G F inverse مكتوب معاك هذا V تربية تسوى ال
+
+258
+00:27:13,620 --> 00:27:17,420
+identity في D4 يبقى V بتسوى V inverse H تربية تسوى
+
+259
+00:27:17,420 --> 00:27:20,200
+ال identity يبقى H تسوى H inverse D تربية تسوى ال
+
+260
+00:27:20,200 --> 00:27:23,340
+identity يبقى D بتسوى D ال inverse وD prime زيهم
+
+261
+00:27:23,340 --> 00:27:29,300
+يبقى كل هذا مكتوب معاك يوم أخدنا D4يبقى بناء عليه
+
+262
+00:27:29,300 --> 00:27:34,320
+لما كانت ال F هي reflection يبقى ال F و ال F
+
+263
+00:27:34,320 --> 00:27:41,300
+inverse الشي العلاقة بينهما اتنين are ال F و ال F
+
+264
+00:27:41,300 --> 00:27:42,540
+inverse ال reflection
+
+265
+00:27:47,690 --> 00:27:52,230
+ماذا يحصل علاقة بينهم؟ علاقة تساوي يعني بقدر أشيل
+
+266
+00:27:52,230 --> 00:27:55,590
+ال F و أحط مكانها F inverse و بقدر أشيل F inverse
+
+267
+00:27:55,590 --> 00:27:59,730
+و أحط مكانها ال F هيها قدامك هي على اللوح مكتوبة
+
+268
+00:27:59,730 --> 00:28:09,470
+يبقى بقدر بناء عليه أقول هذه هي ال F R inverse طيب
+
+269
+00:28:09,470 --> 00:28:10,510
+استنى شوية
+
+270
+00:28:27,180 --> 00:28:29,980
+مصبوط هكذا؟
+
+271
+00:28:38,160 --> 00:28:46,100
+طيب هذا كلام صحيح if and only if ال R F بدها تساوي
+
+272
+00:28:47,590 --> 00:28:53,690
+وين الار اف هيها؟ كده اش طالع بيساوي؟ اف ار انفرس،
+
+273
+00:28:53,690 --> 00:29:03,130
+مظبوط؟ يبقى هذه اف ار اف بدي ساوي ال .. اذا كانت
+
+274
+00:29:03,130 --> 00:29:09,630
+الار اف بدي ساوي الاف ار طيب وين الاف ار؟ طيب
+
+275
+00:29:09,630 --> 00:29:16,200
+خليها ماشيةبنجب نقول هذا الكلام الـ RF بدي ساوي
+
+276
+00:29:16,200 --> 00:29:20,220
+الـ
+
+277
+00:29:20,220 --> 00:29:27,760
+FR inverse بالشكل اللي عندنا هنا يبقى هذا الكلام
+
+278
+00:29:27,760 --> 00:29:33,570
+صحيء إذا كان الـ RF بدي ساومين الـ FR inverseطيب
+
+279
+00:29:33,570 --> 00:29:40,070
+الان انا بقدر اشيل ال F و احط مكانها من ال F
+
+280
+00:29:40,070 --> 00:29:46,290
+inverse و ارجعها كيف ده سيه لحظة شوية طيب عندك ال
+
+281
+00:29:46,290 --> 00:29:51,230
+RF يسوى ال FR inverse مظبوط ال R كما نسميه اذا كان
+
+282
+00:29:51,230 --> 00:29:58,350
+ال FR بديه يسوى اذا كان ال FR بديه يسوى RF استنى
+
+283
+00:29:58,350 --> 00:30:01,130
+شوية اذا كان ال F
+
+284
+00:30:04,870 --> 00:30:19,850
+فار فار فار فار فار فار فار فار فار فار فار
+
+285
+00:30:28,490 --> 00:30:34,610
+الـ R F Inverse لأيش؟ لأن الـ F هي تساوي مين؟
+
+286
+00:30:34,610 --> 00:30:40,450
+تساوي الـ F Inverse itself تمام؟ يبقى هذا بيساوي
+
+287
+00:30:40,450 --> 00:30:47,150
+الـ R Inverse F itself يبقى أصار F R Inverse
+
+288
+00:30:50,680 --> 00:30:57,700
+يبقى فان ال F R بدينا فيها بدي يساوي R F وهذا R F
+
+289
+00:30:57,700 --> 00:31:07,380
+اللي عندنا يساوي F R Inverse هذي بدي يساوي F R
+
+290
+00:31:07,380 --> 00:31:12,680
+Inverse هي الكلام صحيح يبقى أنا بديت هدول التنين
+
+291
+00:31:12,680 --> 00:31:18,160
+كموسي ده كان ال F R بدي يساوي من R Fهذا الكلام
+
+292
+00:31:18,160 --> 00:31:24,080
+يساوي هاي RF من فوق شيلتها و جيبت بدالها مين؟ F R
+
+293
+00:31:24,080 --> 00:31:30,340
+inverse يبقى اطلعلي لهذه و اطلعلي لهذه تمام؟ بال
+
+294
+00:31:30,340 --> 00:31:35,360
+lift cancellation law يبقى هذه ال F بتروح مع هذه
+
+295
+00:31:35,360 --> 00:31:43,480
+بظل F and only F ال R بدها تساوي R inverseإذا كان
+
+296
+00:31:43,480 --> 00:31:49,820
+الـR يسوى الـR inverse الـR يسوى
+
+297
+00:31:49,820 --> 00:31:57,820
+الـR inverse بس في حالة الـ180 يبقى هذا معناه أن R
+
+298
+00:31:57,820 --> 00:32:06,440
+تسوى R 180 درجة وهذا الكلام صحيح لو كانت الـN is
+
+299
+00:32:06,440 --> 00:32:19,190
+even فقط this is a trueفالن is even يبقى بناء عليه
+
+300
+00:32:19,190 --> 00:32:27,310
+z of d فالz of dn بدي يسوى رن ورمية و تمانين في
+
+301
+00:32:27,310 --> 00:32:34,730
+حالة الزوجي والارنود في حالة من في حالة الفرديطب
+
+302
+00:32:34,730 --> 00:32:39,990
+فينا تعريف جديد برضه جريب من ال center بس بيسميه
+
+303
+00:32:39,990 --> 00:32:46,610
+centralizer يبقى definition let
+
+304
+00:32:46,610 --> 00:32:55,270
+ال a be a fixed element
+
+305
+00:32:55,270 --> 00:32:58,350
+of
+
+306
+00:32:58,350 --> 00:33:01,330
+a group G
+
+307
+00:33:04,040 --> 00:33:18,140
+the centralizer of
+
+308
+00:33:18,140 --> 00:33:28,120
+ال element a اللي موجود في g هديله الرمز center of
+
+309
+00:33:28,120 --> 00:33:28,600
+a
+
+310
+00:33:31,400 --> 00:33:42,920
+is the set of all elements the set of all elements
+
+311
+00:33:42,920 --> 00:33:53,620
+in G that commute with
+
+312
+00:33:53,620 --> 00:33:57,700
+A with
+
+313
+00:33:57,700 --> 00:34:01,020
+A that is
+
+314
+00:34:03,590 --> 00:34:12,050
+Centralizer لإيه كل العناصر جي اللي موجودة في جي
+
+315
+00:34:12,050 --> 00:34:18,790
+بحيث ان جي في ايه ساوي ايه في جي
+
+316
+00:34:48,240 --> 00:34:52,400
+نعود للتعريف اللي قلناه و نعود له تاني و نشوف شو
+
+317
+00:34:52,400 --> 00:34:58,360
+بيقولالتعريف بيقول خدلي a fixed element من ال
+
+318
+00:34:58,360 --> 00:35:02,660
+group g بيبقى أخدت عنصر من g سميته a the
+
+319
+00:35:02,660 --> 00:35:08,840
+centralizer of a اللي موجود فيه g يبقى أنا بدى
+
+320
+00:35:08,840 --> 00:35:15,540
+أدور على العناصر اللي بتبقى commutes مع a فقط وبدى
+
+321
+00:35:15,540 --> 00:35:20,900
+أسميهم ال centralizer بهذا ال element aبتعطيه C of
+
+322
+00:35:20,900 --> 00:35:25,400
+A يبقى C of A the centralizer of the element A مين
+
+323
+00:35:25,400 --> 00:35:30,900
+هي؟ هي كل العناصر اللي موجودة في G that commutes
+
+324
+00:35:30,900 --> 00:35:37,060
+with A اللي بتعمل عملية تبديل فقط مع العنصر A مش
+
+325
+00:35:37,060 --> 00:35:40,700
+مع باقي عناصريبقى فيه فرق ما بين الـcenter
+
+326
+00:35:40,700 --> 00:35:44,940
+والـcentralizer الـelement اللي موجود في الـcenter
+
+327
+00:35:44,940 --> 00:35:50,460
+commutes مع جميع عناصر A مع جميع عناصر الجروب G
+
+328
+00:35:50,460 --> 00:35:54,960
+لكن الـcentralizer ليه؟ بس العناصر ي commutes مع
+
+329
+00:35:54,960 --> 00:36:01,260
+مين؟ مع A فقط لغيروالذالك قلنا الـ Centralizer لكل
+
+330
+00:36:01,260 --> 00:36:05,180
+العناصر اللي موجودة في جيه اللي بتبقى commutes مع
+
+331
+00:36:05,180 --> 00:36:11,260
+مين مع ايه فقط بناء على ذلك سنطرح بعض الأسئلة
+
+332
+00:36:11,260 --> 00:36:16,120
+السؤال الأول مين
+
+333
+00:36:16,120 --> 00:36:19,840
+اللي أكبر ال center ولا ال centralizer في ال group
+
+334
+00:36:19,840 --> 00:36:28,240
+العادىالـ Center أكبر يعني بلاقي في عناصر أكتر من
+
+335
+00:36:28,240 --> 00:36:31,020
+عناصر الـ Centralizer لإيه؟
+
+336
+00:36:34,970 --> 00:36:40,990
+طيب سؤال سؤال بدي أجيب نفس السؤال بصيغة أخرى لو
+
+337
+00:36:40,990 --> 00:36:46,550
+أخد element في ال center تبع ال group بلاجيه في ال
+
+338
+00:36:46,550 --> 00:36:50,410
+centralizer تبع ال ايه؟ بلاجية طب نعمل العملية
+
+339
+00:36:50,410 --> 00:36:54,430
+العكسية بدي أخد element في ال centralizer هل
+
+340
+00:36:54,430 --> 00:36:57,170
+بلاجيه موجود في ال center؟
+
+341
+00:37:00,330 --> 00:37:05,270
+يعني قد يكون و قد لا يكون موجود، مظبوط؟ إذا صار ال
+
+342
+00:37:05,270 --> 00:37:10,630
+center صغير لأنه بدكم يسمع جميع عناصر جهة بس هدا
+
+343
+00:37:10,630 --> 00:37:14,650
+كم يسمع عنصر واحد فقط يبقى ال center هيكون في
+
+344
+00:37:14,650 --> 00:37:18,710
+عناصر كتيرة بدليل أخدت أوسع عنصر من ال center
+
+345
+00:37:18,710 --> 00:37:21,970
+وجدته موجود في ال centralizerلكن اذا ذهبت لختم
+
+346
+00:37:21,970 --> 00:37:25,210
+الـcentralizer ليس بالضرورة ان يكون وين في
+
+347
+00:37:25,210 --> 00:37:29,850
+الـcenter يبقى اول ملاحظة ان الـcenter تبع لجروب
+
+348
+00:37:29,850 --> 00:37:36,030
+هو الـsubset من الـcentralizer تمام؟ يبقى باجي
+
+349
+00:37:36,030 --> 00:37:37,750
+بقوله هنا note
+
+350
+00:37:40,820 --> 00:37:48,020
+النقطة الأولى ال center تبع ال group G subset من
+
+351
+00:37:48,020 --> 00:37:51,200
+ال
+
+352
+00:37:51,200 --> 00:37:59,660
+centralizer ل A و ال A عنصر موجود في جي مش ال A و
+
+353
+00:37:59,660 --> 00:38:03,300
+لا ال B و ال C يعني هذا كلام صحيح لكل ال A اللي
+
+354
+00:38:03,300 --> 00:38:08,940
+موجود في جي بدل هيك بقول لكل ال A اللي موجودة في
+
+355
+00:38:08,940 --> 00:38:15,310
+جييعني لو روحت لأى عنصر غيرت لإيه بعنصر تانى و
+
+356
+00:38:15,310 --> 00:38:18,830
+جبتله ال centralizer بلاج ال center subset منه و
+
+357
+00:38:18,830 --> 00:38:22,210
+روحت جبت ال centralizer لعنصر تالت و جبت ال
+
+358
+00:38:22,210 --> 00:38:24,770
+central group بلاج ال central subset من ال
+
+359
+00:38:24,770 --> 00:38:29,070
+centralizer للعنصر التالت و هكذاهى اللى قصدناه من
+
+360
+00:38:29,070 --> 00:38:36,050
+هنا طيب كمان سؤال لو كانت ال جي أبيليان قداش ال
+
+361
+00:38:36,050 --> 00:38:42,450
+centralizer لل إيه؟ جي جي كلها طب و ال center؟ جي
+
+362
+00:38:42,450 --> 00:38:46,080
+كلهايبقى صرت سما بين الـ Central و الـ Centralizer
+
+363
+00:38:46,080 --> 00:38:50,740
+يبقى إذا كانت الـ G Abelian فإن الـ Center يسوى
+
+364
+00:38:50,740 --> 00:38:55,540
+الـ Centralizer و يسوى الجروب G كله لكن لو ماكنتش
+
+365
+00:38:55,540 --> 00:38:59,840
+Abelian بيظل الـ Center تبع الجروب هو الـ Subset
+
+366
+00:38:59,840 --> 00:39:06,220
+قد يسوى و قد لا يسوى تمام؟ يبقى بناء عليه بقول هذه
+
+367
+00:39:06,220 --> 00:39:14,040
+النقطة الأولى النقطة التانية F G is AbelianThen
+
+368
+00:39:14,040 --> 00:39:20,220
+الـ Center تبع لـ Group G هو بالضبط الـ
+
+369
+00:39:20,220 --> 00:39:26,060
+Centralizer لـ A لكل الـ A اللي موجودة في G وهذا
+
+370
+00:39:26,060 --> 00:39:31,500
+بده يساوي G itself هذا في حالة ما تكون A ما تكون
+
+371
+00:39:31,500 --> 00:39:39,200
+Abelian Group طيب ناخد مثال بسيط example let
+
+372
+00:39:44,050 --> 00:39:52,830
+الـ G تسوي الـ D4 الـ D4 ثم بدّي
+
+373
+00:39:52,830 --> 00:40:02,670
+الـ Centralizer للـ R نوت مين بيطلع دي كلها طيب هل
+
+374
+00:40:02,670 --> 00:40:10,150
+هو الـ Centralizer للـ R 180صحيح لغرمية ابنكم يسمع
+
+375
+00:40:10,150 --> 00:40:16,270
+الكل يريد عن جديكوا بس و هذا بدي يسوي D4 كله يبقى
+
+376
+00:40:16,270 --> 00:40:22,070
+هذا بدي يعطينا D4 كله طب لو بدي ال centralizer لل
+
+377
+00:40:22,070 --> 00:40:28,270
+R90 هل
+
+378
+00:40:28,270 --> 00:40:34,710
+هذا هو ال centralizer لل R270؟
+
+379
+00:40:38,690 --> 00:40:46,030
+انظروا معاكوسه طب بد العناصر تبعتهم مين هم ارنود و
+
+380
+00:40:46,030 --> 00:40:54,230
+R180 و ال R90 كمان لأن ال R90 يسمع نفسه صحيح ولا
+
+381
+00:40:54,230 --> 00:41:00,540
+لا؟ ضل عليك كمان واحد بسحد معاه الجدول يطلع لبسه
+
+382
+00:41:00,540 --> 00:41:04,000
+فتش الجدول و بتعرف الإجابة منه في صفحة واحد و
+
+383
+00:41:04,000 --> 00:41:09,500
+تلاتين يبقى لو رجعنا بنلاقي بس اللي هي ال R ميتين
+
+384
+00:41:09,500 --> 00:41:16,710
+و سبعين يبقى هذه ال R ميتين و سبعينهذا الكلام يعني
+
+385
+00:41:16,710 --> 00:41:20,230
+ايش مين بدي اعطيه لك؟ بدي اعطيه لك ال subgroup
+
+386
+00:41:20,230 --> 00:41:26,470
+generated by R 90 وفي نفس الوقت هي ال subgroup
+
+387
+00:41:26,470 --> 00:41:36,590
+generated by R 270 مظبوط؟ R 90 R 90 تربية 180 R 90
+
+388
+00:41:36,590 --> 00:41:42,400
+تكيب 270 R أسبوع أربعة بال identityيبقى لو بدى
+
+389
+00:41:42,400 --> 00:41:46,780
+اجيب كمان الـcentralizer لمين للـH يبقى
+
+390
+00:41:46,780 --> 00:41:55,200
+الـcentralizer للـH اللى عندنا هذه يبقى هذا بده
+
+391
+00:41:55,200 --> 00:42:00,140
+يعطيلك الـR non والـR100U80
+
+392
+00:42:00,140 --> 00:42:03,700
+والـH وحط عليها الـV كمان
+
+393
+00:42:06,390 --> 00:42:13,330
+أليس هذا هو الـcentralizer للـ V كذلك؟ لو الجدول
+
+394
+00:42:13,330 --> 00:42:17,970
+معاك كان عرفت لحالك جدول في صفحة واحد و تلاتيه
+
+395
+00:42:17,970 --> 00:42:22,390
+بالمثل لو روحنا جيبنا الـcentralizer ل D
+
+396
+00:42:22,390 --> 00:42:30,450
+الـcentralizer ل D هو عبارة عن الـR node والـR مية
+
+397
+00:42:30,450 --> 00:42:38,000
+و تمانين والـD itself والـD primeهذا سيكون الـ
+
+398
+00:42:38,000 --> 00:42:46,540
+Centralizer لـ D' من هذا الكلام بقدر استنتج ان H
+
+399
+00:42:46,540 --> 00:42:54,040
+في V سيكون V في H و بقدر استنتج من هذا اللي تحت ان
+
+400
+00:42:54,040 --> 00:43:02,460
+D D' سيكون D' D يبقى هذا استنتاج من خلال الكلام
+
+401
+00:43:02,460 --> 00:43:03,760
+اللي عندنا هنا
+
+402
+00:43:23,420 --> 00:43:30,680
+الآن اخر نظرية موجودة في هذا ال chapter وهي ان ال
+
+403
+00:43:30,680 --> 00:43:39,220
+centralizer عبارة عن subgroup يبقى theorem for
+
+404
+00:43:39,220 --> 00:43:51,840
+any element a اللي موجود في جيب ال centralizer ل a
+
+405
+00:43:53,260 --> 00:44:02,720
+is a subgroup من G من من من من من
+
+406
+00:44:02,720 --> 00:44:03,440
+من من من من من من من من من من من من من من من من من
+
+407
+00:44:03,440 --> 00:44:03,500
+من من من من من من من من من من من من من من من من من
+
+408
+00:44:03,500 --> 00:44:08,840
+من من من من من من من من من من من من
+
+409
+00:44:08,840 --> 00:44:08,920
+من من من من من من من من من من من من من من من من من
+
+410
+00:44:08,920 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+411
+00:44:10,740 --> 00:44:14,560
+من من من من من من من من من من من
+
+412
+00:44:14,560 --> 00:44:15,840
+من من من
+
+413
+00:44:36,070 --> 00:44:43,020
+النقطة الثانية بداية ياخد letعشان ناخد ال a و نقول
+
+414
+00:44:43,020 --> 00:44:51,400
+x y لت ال x y موجود في ال centralizer ل a then ال
+
+415
+00:44:51,400 --> 00:45:02,980
+x a بده ساوي ال a x and ال y a بده ساوي ال a y ايش
+
+416
+00:45:02,980 --> 00:45:09,100
+بدنا نثبت؟بنثبت ان الـxy inverse موجود في
+
+417
+00:45:09,100 --> 00:45:14,360
+الـcentralizer لإيه يعني بنثبت ان الـxy inverse a
+
+418
+00:45:14,360 --> 00:45:20,360
+بدو يساوي الaxy inverse يبقى فرضنا هدول الاتنين
+
+419
+00:45:20,360 --> 00:45:30,020
+بيساووا بعض يبقى now لو أجى أخدت الـya بدو يساوي
+
+420
+00:45:30,020 --> 00:45:37,890
+الayهذا بدى يعطينا شرايك بدى اضرب في ال y inverse
+
+421
+00:45:37,890 --> 00:45:44,690
+من جهة اليمين يبقى بيصير y a y inverse يساوي قداش
+
+422
+00:45:44,690 --> 00:45:50,210
+يساوي ال a بدى اضرب في y inverse من جهة الشمال
+
+423
+00:45:50,210 --> 00:45:56,310
+يبقى لو ضربت من جهة الشمال بيظل a y inverse تساوي
+
+424
+00:45:56,310 --> 00:46:03,130
+y inverse في aيبقى ايش معنى هذا الكلام ان ال y
+
+425
+00:46:03,130 --> 00:46:09,370
+inverse موجود في ال centralizer لإيه هذا معناه ان
+
+426
+00:46:09,370 --> 00:46:14,450
+ال y inverse موجود في ال centralizer لإيه يبقى
+
+427
+00:46:14,450 --> 00:46:20,870
+بناء عليهالـ element y موجود في الـ centralizer
+
+428
+00:46:20,870 --> 00:46:27,030
+لإيه إذا معكسه يكون كذلك موجود في الـ centralizer
+
+429
+00:46:27,030 --> 00:46:31,110
+لإيه هذا معناته أن y inverse موجود في الـ
+
+430
+00:46:31,110 --> 00:46:37,710
+centralizer لإيه واعتبر لهذه الهيمينةالنقطة الأولى
+
+431
+00:46:37,710 --> 00:46:45,670
+يبقى نكتب الكلمة اللى قولناها يبقى this means that
+
+432
+00:46:45,670 --> 00:46:52,710
+هذا يعني ان if ال y موجود في ال centralizer ل a
+
+433
+00:46:52,710 --> 00:47:03,380
+thenالـ Y موجود في الـ Centralizer لـ
+
+434
+00:47:03,380 --> 00:47:10,880
+A ثم الـ Y Inverse ثم أو الـ Y موجودة في الـ
+
+435
+00:47:10,880 --> 00:47:17,780
+Centralizer لـ A Inverse لا لا الـ Y Inverse
+
+436
+00:47:17,780 --> 00:47:24,550
+موجودة في الـ Centralizer لـ Aتمام الان لو جيت
+
+437
+00:47:24,550 --> 00:47:39,110
+قولتلك consider خدلي اللي هو ال X Y inverse A هذا
+
+438
+00:47:39,110 --> 00:47:45,310
+الكلام بده يساويإذا قدرت أثبت ان الـ x y inverse a
+
+439
+00:47:45,310 --> 00:47:52,290
+بيكون a x y inverse بيتم المطلوب يبقى هذا x y
+
+440
+00:47:52,290 --> 00:47:58,010
+inverse ال a بقدر أكتبها a inverse inverse يبقى
+
+441
+00:47:58,010 --> 00:48:07,470
+هذا الكلام بيكون x و هنا a inverse y الكل inverse
+
+442
+00:48:07,470 --> 00:48:09,510
+مظبوط
+
+443
+00:48:10,530 --> 00:48:16,310
+يعني جمعت هنا ال inverse inverse رجعتهم لأصلهم
+
+444
+00:48:16,310 --> 00:48:24,110
+واحدة بالشكل هنا الان انا عندي هنا a inverse
+
+445
+00:48:24,110 --> 00:48:30,990
+مكتوبا اه سنة سنة شوية ايش اللي سويتها a inverse y
+
+446
+00:48:30,990 --> 00:48:34,990
+طيب هنا قلت دي اسم الالكترون موجود في ال
+
+447
+00:48:34,990 --> 00:48:38,910
+centralizer then y inverse موجود
+
+448
+00:48:45,110 --> 00:48:56,690
+كيف؟ بدي واحد بس يحكي، واحد يحكي بقى، ايه؟ اه،
+
+449
+00:48:56,690 --> 00:49:00,850
+يعني هيك، برضه مظبوط، ممكن ناخد x,y وممكن ناخد x,y
+
+450
+00:49:00,850 --> 00:49:04,090
+inverse مرة واحد، عشقتين، يا ناس بضرورة، ممكن
+
+451
+00:49:04,090 --> 00:49:06,770
+استفيد من هذه، ان الـA
+
+452
+00:49:17,330 --> 00:49:22,150
+على أي حال بنكمل المرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aca2fe6445fb8001de82a7d9d3ea2ff48f26e60c
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_postprocess.srt
@@ -0,0 +1,1576 @@
+1
+00:00:21,210 --> 00:00:26,110
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في
+
+2
+00:00:26,110 --> 00:00:30,870
+المحاضرة السابقة عرفنا ال isomorphism أخدنا عليه
+
+3
+00:00:30,870 --> 00:00:36,030
+خمسة أمثلة في الفترة الصبحية الآن بدنا نيجي لأول
+
+4
+00:00:36,030 --> 00:00:42,150
+نظرية هذه النظرية نظرية كيلي تنص على ما يتيح أن أي
+
+5
+00:00:42,150 --> 00:00:47,310
+group تبقى isomorphic to a group of permutations
+
+6
+00:00:48,010 --> 00:00:53,130
+الجروب of permutations بدي أنشئها من خلال الجروب
+
+7
+00:00:53,130 --> 00:00:58,570
+اللي عندي طبعا هذا بيختلف عن كل ما سبق انه لم يبين
+
+8
+00:00:58,570 --> 00:01:03,210
+ايش شكل الجروب ولا مبين شكل الجروب of permutation
+
+9
+00:01:03,210 --> 00:01:07,890
+مش مبين عندي ولا عاجز لذلك بدنا نبدأ البرهان
+
+10
+00:01:07,890 --> 00:01:14,430
+كالتالي فبجي بقول let G بي أ grow
+
+11
+00:01:17,890 --> 00:01:32,690
+for any g اللي موجودة فيه g define a function TG
+
+12
+00:01:32,690 --> 00:01:46,470
+من G إلى G by TG of X بده ساوي GXلكل الـ X اللي
+
+13
+00:01:46,470 --> 00:01:55,050
+موجود في جي يبقى
+
+14
+00:01:55,050 --> 00:02:01,030
+أنا الأن بدي أسعى إلى أكون من ال group of
+
+15
+00:02:01,030 --> 00:02:06,390
+permutation من ال group اللي موجودة لذلك فرط ال
+
+16
+00:02:06,390 --> 00:02:13,420
+group اللي موجودة عند جي بدي أكونبالتالي يجب أن
+
+17
+00:02:13,420 --> 00:02:18,020
+يكون الجروب of all permutations التي تعتمد على
+
+18
+00:02:18,020 --> 00:02:22,660
+الجروب اللي عندنا لذلك لو أخدت أي جي موجود في جي
+
+19
+00:02:22,660 --> 00:02:28,960
+يجب أن أعرف الدالة كالتالي تجي من جي إلى جي باي
+
+20
+00:02:28,960 --> 00:02:34,140
+يجب أن أعرفها كالتالي تجي of x يساوي جي of x لكل
+
+21
+00:02:34,140 --> 00:02:38,650
+ال x الموجود في جيالسؤال هو هل هذا التعريف صحيح
+
+22
+00:02:38,650 --> 00:02:44,910
+ولا غير صحيح الإجابة التعريف صحيح لأن الـTG من G
+
+23
+00:02:44,910 --> 00:02:50,710
+إلى G الـG و الـX موجودات في G إذا حصل ضربهما
+
+24
+00:02:50,710 --> 00:02:55,550
+موجود في G لأنه G closed under multiplication أو
+
+25
+00:02:55,550 --> 00:02:58,550
+ال operation اللي على G هي عبارة عن binary
+
+26
+00:02:58,550 --> 00:03:03,500
+operation يبقى الـG في X موجودة في ال groupاللي
+
+27
+00:03:03,500 --> 00:03:09,380
+عندنا يبقى تعريفي هذا صحيح الان انا ادعي ان هذه ال
+
+28
+00:03:09,380 --> 00:03:15,900
+function is a permutation انا ادعي ان تيجي هذه
+
+29
+00:03:15,900 --> 00:03:19,980
+عبارة عن permutation طيب هي ال permutation عبارة
+
+30
+00:03:19,980 --> 00:03:23,780
+عن ايش؟ function و ال function بتكبر one to one
+
+31
+00:03:23,780 --> 00:03:27,620
+and on two اذا طلعت هذه ال function one to one and
+
+32
+00:03:27,620 --> 00:03:32,500
+on two يبقى بال فهي تكون permutation مظبوط؟يبقى
+
+33
+00:03:32,500 --> 00:03:45,080
+هنا باجي بقول now ال TG is a permutation طبعا؟
+
+34
+00:03:45,080 --> 00:03:55,740
+طيب ليش؟ because السبب النقطة الأولىالـ TG هادي is
+
+35
+00:03:55,740 --> 00:04:02,960
+one to one الـ TG is one to one بدنا نثبت صحة هذا
+
+36
+00:04:02,960 --> 00:04:11,500
+الكلام يبقى باجي بقوله let الـ TG of X يساوي TG of
+
+37
+00:04:11,500 --> 00:04:20,520
+Y then حسب التعريف الـ TG of X بده يساوي الـ G في
+
+38
+00:04:20,520 --> 00:04:29,350
+Xالـ TG of Y بده ساوي GYبالـ left cancellation law
+
+39
+00:04:29,350 --> 00:04:35,470
+بنقدر نشطب الجي والجي يطلع لنا قداش ان ال X بده
+
+40
+00:04:35,470 --> 00:04:40,130
+يساوي ال Y او كون الجي في الجي والجي اجروا بيبقى
+
+41
+00:04:40,130 --> 00:04:44,110
+جي انفرست موجود يبقى لو ضربت الطرفين في جي انفرست
+
+42
+00:04:44,110 --> 00:04:48,830
+هيعطينا ان X يساوي Y معناه هذا الكلام ان TG is one
+
+43
+00:04:48,830 --> 00:04:53,230
+to one لانه خدت صورتين متساويتين اثبتت ان اصلهم
+
+44
+00:04:53,570 --> 00:05:01,690
+متساوين الان بدنا نثبت النقطة الثانية انه تي جي is
+
+45
+00:05:01,690 --> 00:05:11,290
+onto لذلك بدروح اخد element في جي و اثبت انه اصل
+
+46
+00:05:11,290 --> 00:05:19,440
+في جي يبقى باجي بقوله let y موجودة في جيفي جيله من
+
+47
+00:05:19,440 --> 00:05:24,360
+الـcodomain تبع الـTG يعني في الـG التانية هذه
+
+48
+00:05:24,360 --> 00:05:32,380
+ماهي هذه هي هذه كويس موجود في الـTG then الـY
+
+49
+00:05:32,380 --> 00:05:40,650
+تساوي بدي أحاولأكتب الـ Y هذه كصورة لعنصر من G
+
+50
+00:05:40,650 --> 00:05:48,590
+الأولى إذا لو جيت قلت لك ال Y هذه قلت لك هي G G
+
+51
+00:05:48,590 --> 00:05:56,910
+inverse Y بنفع؟ بنفع؟ لإيش؟ لأن الـ G G inverse هو
+
+52
+00:05:56,910 --> 00:06:01,350
+ال identity element و ال identity element تضربه في
+
+53
+00:06:01,350 --> 00:06:06,210
+أي element بيعطيك نفس ال elementإذا بقدر أقول هذه
+
+54
+00:06:06,210 --> 00:06:10,490
+G في G inverse Y
+
+55
+00:06:13,170 --> 00:06:17,550
+فباش رأيك هذا اللي بين قصيره؟ بدي أسميه أي عنصر
+
+56
+00:06:17,550 --> 00:06:24,990
+آخر للسهولة إذا بقدر أقول هذه جي إكس مثلا إذا
+
+57
+00:06:24,990 --> 00:06:31,030
+العنصر هذا شيلته و حاطه بدله مين؟ إكس طيب جي إكس
+
+58
+00:06:31,030 --> 00:06:39,080
+هذه عبارة عن مين؟ عبارة عن تجي of إكسيبقى ال
+
+59
+00:06:39,080 --> 00:06:44,740
+element y اللي موجود في ال group g لجت له أصل x
+
+60
+00:06:44,740 --> 00:06:51,000
+موجود في g التانية يبقى بناء عليه في is onto يبقى
+
+61
+00:06:51,000 --> 00:06:56,340
+صار في عندي function من g إلى g هذه one to one and
+
+62
+00:06:56,340 --> 00:07:00,060
+onto واحنا لما عرفنا ال permutation قلنا هي
+
+63
+00:07:00,060 --> 00:07:05,630
+functionعبارة عن one to one and on to يبقى بناء
+
+64
+00:07:05,630 --> 00:07:12,050
+عليه ال TG هذي عبارة عن ايش permutation يبقى ال
+
+65
+00:07:12,050 --> 00:07:18,090
+element G من الجروب جاب لي permutation اسمها مين
+
+66
+00:07:18,090 --> 00:07:25,870
+اسمها TG الآن بده لم هدول كل ال permutation و بده
+
+67
+00:07:25,870 --> 00:07:34,750
+حطهم في set يبقى الآنconsider جي
+
+68
+00:07:34,750 --> 00:07:44,650
+بار جي بار هذي بتعطيها الرمز SG مين ال SG هذي كل ت
+
+69
+00:07:44,650 --> 00:07:52,550
+جي بحيث الجي موجودة في جي يعني
+
+70
+00:07:53,310 --> 00:07:58,270
+لو جينا قولنا الـ G هذه فيها خمسين elements مثلا
+
+71
+00:07:58,270 --> 00:08:02,910
+يبقى ابو دي اطلع هنا كم element عندى؟ خمسين
+
+72
+00:08:02,910 --> 00:08:08,570
+elements لإنه TG1, TG2, TG3, TG4 لغاية مكمله
+
+73
+00:08:08,570 --> 00:08:14,390
+الخمسين يبقى ال SG هذي mean the set of all
+
+74
+00:08:14,390 --> 00:08:20,210
+permutations اللي محطوطة على ال group G هذه the
+
+75
+00:08:20,210 --> 00:08:28,300
+setof all permutations
+
+76
+00:08:28,300 --> 00:08:32,060
+of
+
+77
+00:08:32,060 --> 00:08:40,640
+G كل ال permutations اللي على G الان انا هتدعي ان
+
+78
+00:08:40,640 --> 00:08:47,450
+SG هدى is a groupوبنفعش تدعى يا صاحبي بدك تبين انه
+
+79
+00:08:47,450 --> 00:08:52,810
+فعلا انه SG هذه ايه هي group لانه اذا اثبتت انها
+
+80
+00:08:52,810 --> 00:08:58,150
+group وصلت للنص اللى انا بقول عنه كل group
+
+81
+00:08:58,150 --> 00:09:02,210
+isomorphic الى permutation group او ال group of
+
+82
+00:09:02,210 --> 00:09:08,190
+permutation تمام يبقى الخطوة التالية بعد ما خلقت
+
+83
+00:09:08,590 --> 00:09:13,950
+permutations لكل عنصر موجود في دي خلقتله
+
+84
+00:09:13,950 --> 00:09:18,230
+permutation اقبلهالـ Perimotations حطيتهم في ست
+
+85
+00:09:18,230 --> 00:09:24,930
+واحدة سميتها G bar أو سميتها SG من العناصر تبعتها
+
+86
+00:09:24,930 --> 00:09:30,190
+كل الـ Perimotations اللي خلقتهم على ال group G
+
+87
+00:09:30,190 --> 00:09:37,510
+الآن أنا بتدعي ان SG هذه is a group يبقى بدى أشوف
+
+88
+00:09:37,510 --> 00:09:44,450
+هل ال SG بتحقق شروط ال group ولا لايبقى أول شيء ال
+
+89
+00:09:44,450 --> 00:09:47,370
+operation اللي عليها madam permutation هو ال
+
+90
+00:09:47,370 --> 00:09:52,690
+composition of functions الآن ال composition of
+
+91
+00:09:52,690 --> 00:09:57,430
+functions بدي أثبت إنها binary operation إيش يعني
+
+92
+00:09:57,430 --> 00:10:01,430
+binary operation؟ يعني لو جبت composition بين two
+
+93
+00:10:01,430 --> 00:10:06,190
+permutations بدي أعطيني مين؟ permutation واحدة إن
+
+94
+00:10:06,190 --> 00:10:10,590
+حدث ذلك يبقى فعلا تبقى ال operation اللي عليها هي
+
+95
+00:10:10,590 --> 00:10:22,300
+binaryoperation يبقى we a claim that اكليم يدعي ان
+
+96
+00:10:22,300 --> 00:10:32,520
+ال SG is a group under the
+
+97
+00:10:32,520 --> 00:10:38,240
+composition of
+
+98
+00:10:38,240 --> 00:10:39,100
+functions
+
+99
+00:10:41,910 --> 00:10:47,890
+انا هتدعي ان اس جي هدى is a group تحت عملية تحصيل
+
+100
+00:10:47,890 --> 00:10:53,770
+او تركيب من ال function بيدروح اثبت هذا الكلام
+
+101
+00:10:53,770 --> 00:11:02,990
+يبقى باجي بقوله for all جي و H اللى موجودة في جي
+
+102
+00:11:02,990 --> 00:11:04,190
+we have
+
+103
+00:11:20,200 --> 00:11:24,840
+البيانات مضربات ضرب لكن في الحقيقة هي عبارة عن
+
+104
+00:11:26,540 --> 00:11:34,960
+composition تحصيل يبقى بناء عليه هذا بيصير تجي of
+
+105
+00:11:34,960 --> 00:11:45,440
+th of x composition يبقى بناء عليه هذا بيعطيني تجي
+
+106
+00:11:45,440 --> 00:11:55,980
+of th of x حسب التعريف بيعطيني ال h of xتمام حسب
+
+107
+00:11:55,980 --> 00:12:04,760
+التعريف كمان بده يعطيني g of h of x ال g و ال h و
+
+108
+00:12:04,760 --> 00:12:09,420
+ال x موجودات في g ولا لأ و ال g associative ال
+
+109
+00:12:09,420 --> 00:12:15,920
+operation اللي عليها يبقى هذا بده يعطيني gh في x
+
+110
+00:12:15,920 --> 00:12:26,650
+يبقى هذا بده يعطيني th of xهذه موجودة في SD ولا لأ
+
+111
+00:12:26,650 --> 00:12:34,570
+يبقى هذه موجودة في SD يبقى بناء عليه ال
+
+112
+00:12:34,570 --> 00:12:38,250
+composition of function is a binary operation على
+
+113
+00:12:38,250 --> 00:12:48,750
+main على SD يبقى ال composition of
+
+114
+00:12:48,750 --> 00:12:57,500
+functions isa binary operation
+
+115
+00:12:57,500 --> 00:13:00,540
+on
+
+116
+00:13:00,540 --> 00:13:08,540
+SG طب إيش رأيك؟ ال composition of function قبلك
+
+117
+00:13:08,540 --> 00:13:12,300
+أخدناها كثير associative ولا لأ؟ associative
+
+118
+00:13:12,300 --> 00:13:20,460
+associative also وكذلك we know that
+
+119
+00:13:22,880 --> 00:13:29,140
+the composition of
+
+120
+00:13:29,140 --> 00:13:38,660
+functions is associative يبقى
+
+121
+00:13:38,660 --> 00:13:46,260
+مش ضايق اللي عندى ال identity element يبقى TE is
+
+122
+00:13:46,260 --> 00:13:52,380
+the identity element
+
+123
+00:13:54,350 --> 00:14:03,070
+ن اس جي ليش because بتاخد
+
+124
+00:14:03,070 --> 00:14:11,050
+تي في تي اتش as a function of x هشوف كده الشي
+
+125
+00:14:11,050 --> 00:14:19,050
+يعطيني يبقى هذا بده يعطيني تي في تي اتش of x يبقى
+
+126
+00:14:19,050 --> 00:14:26,320
+تي في ال اتش اكس هذه حسب التعريفوحسب التعريف كذلك
+
+127
+00:14:26,320 --> 00:14:36,620
+E في HX اللي هو بده يساوي HX يبقى TH of X يبقى
+
+128
+00:14:36,620 --> 00:14:43,220
+بناء عليه TE في TH of X هتانمين TH of X هذا لو كان
+
+129
+00:14:43,220 --> 00:14:49,880
+الضرب من جهة الشمال لو كان من جهة اليامين and TH
+
+130
+00:14:59,520 --> 00:15:16,000
+يبقى هذا الكلام يبقى تي اتش تي
+
+131
+00:15:16,000 --> 00:15:20,190
+اتش تي اتش تي اتش تي اتش تي اتش تي اتشإذا لو ضربت
+
+132
+00:15:20,190 --> 00:15:26,970
+من اليمين وضربت من الشمال بيعطيني ته of x يبقى ته
+
+133
+00:15:26,970 --> 00:15:35,230
+هو الوضع الوحدة الوحدة الوحدة الوحدة
+
+134
+00:15:35,230 --> 00:15:41,630
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+135
+00:15:41,630 --> 00:15:46,210
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+136
+00:15:46,210 --> 00:15:46,570
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+137
+00:15:46,570 --> 00:15:46,590
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+138
+00:15:46,590 --> 00:15:47,270
+الو
+
+139
+00:15:52,000 --> 00:16:02,180
+تعالى نشوف الان ال TG انفرس TG as a function of X
+
+140
+00:16:02,180 --> 00:16:13,040
+يبقى هذا بدى يعطينا TG انفرس ل TG of Xهذا الكلام
+
+141
+00:16:13,040 --> 00:16:21,780
+بدي اعطينا تجي انفرست تجي of x هيها بمين بجي اكس
+
+142
+00:16:21,780 --> 00:16:25,160
+يبقى
+
+143
+00:16:25,160 --> 00:16:31,420
+صار الجي اكس كله element في domain تجي انفرست يبقى
+
+144
+00:16:31,420 --> 00:16:39,230
+هذا الكلام بدي اساوي جي انفرست لجي اكسهدول الـ
+
+145
+00:16:39,230 --> 00:16:44,010
+three elements كلهم موجودات في ال group G خاصية ال
+
+146
+00:16:44,010 --> 00:16:48,730
+associativity عليها الصحيحة يبقى هذا الكلام بده
+
+147
+00:16:48,730 --> 00:16:56,610
+يعطينا G inverse G في ال X يبقى هذا بده يعطينا E X
+
+148
+00:16:56,610 --> 00:17:06,160
+ال E X هي عبارة عن T E of Xإذا حصل ضرب الـElement
+
+149
+00:17:06,160 --> 00:17:13,200
+في معكوسه إعطاني الـIdentity Element بالمثل يبقى
+
+150
+00:17:13,200 --> 00:17:26,900
+and الـTG of X في الـTG and الـTG في الـTG inverse
+
+151
+00:17:26,900 --> 00:17:36,560
+as a function of Xهذا الكلام بدي يعطيني TG في TG
+
+152
+00:17:36,560 --> 00:17:46,020
+inverse of X هذا الكلام بيساوي اي TG اللي برا و
+
+153
+00:17:46,020 --> 00:17:51,580
+اللي جوا هادي اللي هي في G inverse X طبقا لل
+
+154
+00:17:51,580 --> 00:17:58,980
+definition اللي عنديهذا الكلام بده يساوي جي للجي
+
+155
+00:17:58,980 --> 00:18:05,560
+انفرست اكس هذا نظرة لخاصية ال associativity بده
+
+156
+00:18:05,560 --> 00:18:12,140
+يساوي جي جي انفرست اكس الجي جي انفرست بتعطيني ال
+
+157
+00:18:12,140 --> 00:18:20,930
+identity element يبقى هذه بتعطيني ax لte of xإذا
+
+158
+00:18:20,930 --> 00:18:29,000
+أصبح تجي انفرس هو هو بالضبط تجي لكل انفرسليش ان
+
+159
+00:18:29,000 --> 00:18:33,000
+ضربته من اليمين و الشمال اعطاني نفس ال identity
+
+160
+00:18:33,000 --> 00:18:38,020
+element اذا binary operation associative ال
+
+161
+00:18:38,020 --> 00:18:41,600
+identity element ال inverse element لكل element
+
+162
+00:18:41,600 --> 00:18:46,360
+يبقى ال SG صارت مالها a group under the
+
+163
+00:18:46,360 --> 00:18:54,540
+composition of functions يبقى هنا so ال SG is a
+
+164
+00:18:54,540 --> 00:19:05,910
+groupunder the composition of
+
+165
+00:19:05,910 --> 00:19:16,570
+functions خلصنا يا شباب؟ لسه مخلصناش احنا جبنا
+
+166
+00:19:16,570 --> 00:19:21,430
+جروب جي وجبنا جروب تاني اللي هو the set of all
+
+167
+00:19:21,430 --> 00:19:25,960
+permutationsلجروبة المكوّنة من permutation الأن
+
+168
+00:19:25,960 --> 00:19:31,940
+بدي أثبت أنه اتنين هذول are isomorphic أي اللي
+
+169
+00:19:31,940 --> 00:19:42,600
+بديها يبقى الأن بقوله define a function Phi من G
+
+170
+00:19:42,600 --> 00:19:45,520
+إلى SG by
+
+171
+00:19:51,950 --> 00:20:01,320
+5 of G بدر ساوي TG ال elementاللي في ال group
+
+172
+00:20:01,320 --> 00:20:07,680
+capital يبدأ يسميه G ال element اللي في S G ال S G
+
+173
+00:20:07,680 --> 00:20:15,820
+قلنا وين حطنا لها تعرف قلنا ال S G where are the
+
+174
+00:20:15,820 --> 00:20:19,940
+composition binary operations اه ال S G وين
+
+175
+00:20:19,940 --> 00:20:25,780
+كتبناها this is a group اه هي ال S G يبقى ال
+
+176
+00:20:25,780 --> 00:20:30,900
+element اللي في S G على شكلاللي هو الـ permutation
+
+177
+00:20:30,900 --> 00:20:37,820
+TG يبقى لكل element جي موجود في G عرفنا منهم اللي
+
+178
+00:20:37,820 --> 00:20:43,540
+هو الـ TG اللي موجودة في SG الان انا بدى ابين ان
+
+179
+00:20:43,540 --> 00:20:50,080
+هذه ال function is well defined يبقى الخطوة الأولى
+
+180
+00:20:50,080 --> 00:20:58,740
+Phi is well definedWell-defined يعني معرفة تعريفا
+
+181
+00:20:58,740 --> 00:21:05,960
+صحيحاكيف تعريفا صحيحا كالتالي بدأ أخد عنصرين
+
+182
+00:21:05,960 --> 00:21:12,860
+متساوين و أثبت أنه إلهم نفس الصورة على عكس مين ال
+
+183
+00:21:12,860 --> 00:21:17,000
+one to one ال one to one بتاخد صورتين و بتثبت أن
+
+184
+00:21:17,000 --> 00:21:26,920
+أصلهم متساوي يبقى هنا F ال G و H موجودات في ال G
+
+185
+00:21:29,890 --> 00:21:36,850
+إن الـ G بده يساوي الـ H then بده يتأثر الـ Phi
+
+186
+00:21:36,850 --> 00:21:45,730
+على الطرفين يبقى Phi of G بده يساوي Phi of H حسب
+
+187
+00:21:45,730 --> 00:21:51,590
+ال definition Phi of G بده يساوي TG
+
+188
+00:21:53,140 --> 00:22:00,700
+فاي اف اتش تساوي ت اتش اذا العنصرين المتساويين في
+
+189
+00:22:00,700 --> 00:22:06,140
+جيوز صورتهم متساوي تبقى ال function معرفة تعريفا
+
+190
+00:22:06,140 --> 00:22:12,540
+صحيا بعد ذلك اثبت ان هذا isomorphism يعني ال
+
+191
+00:22:12,540 --> 00:22:17,620
+function f صارت موجودة شو ضايل عندى one to one
+
+192
+00:22:18,000 --> 00:22:22,720
+وانتوا وتخدم خاصية الهيزمورفزيوم لإيه فاي of a بي
+
+193
+00:22:22,720 --> 00:22:27,940
+بده يساوي فاي of a في فاي of b يبقى بالدرجة يقوله
+
+194
+00:22:27,940 --> 00:22:35,980
+فاي النقطة الثانية is one to one يبقى بالدرجة
+
+195
+00:22:35,980 --> 00:22:45,700
+يقوله assume افترض ان فاي of g بده يساوي فاي of h
+
+196
+00:22:46,380 --> 00:22:55,240
+بدي احاول اثبتله ان الـ G تساوي مين تساوي ال H ثم
+
+197
+00:22:55,240 --> 00:23:06,800
+الـ Phi of G اللي هي TG بيديها تساوي THتمام إذا تي
+
+198
+00:23:06,800 --> 00:23:11,700
+جي لما تأثر على أي element بده يسوى تأثير تي إتش
+
+199
+00:23:11,700 --> 00:23:15,680
+على أي element سواء كان ال element هذا ال identity
+
+200
+00:23:15,680 --> 00:23:19,980
+element أو أي element موجود في ال group يعني لو
+
+201
+00:23:19,980 --> 00:23:26,200
+قلت لك تي جي of اي أو قلت لك تي جي of اكسيان هذه
+
+202
+00:23:26,200 --> 00:23:31,190
+والله هذه الاتنين هيأديني إلى نفس النتيجةهذا بده
+
+203
+00:23:31,190 --> 00:23:45,350
+يعطينا ان TG of X بده يساوي TH of X هذا
+
+204
+00:23:45,350 --> 00:23:51,770
+بده يعطينا ان G of X بده تساوي H
+
+205
+00:23:58,390 --> 00:24:04,470
+بال right cancellation law يبقى هذا معناه ان ال G
+
+206
+00:24:04,470 --> 00:24:12,850
+بده يساوي ال H إذا أخدنا صورتين متساويتين أثبتنا
+
+207
+00:24:12,850 --> 00:24:19,070
+أن الأصل متساوي يبقى Phi is one to one النقطة
+
+208
+00:24:19,070 --> 00:24:22,510
+الثالثة Phi is onto
+
+209
+00:24:28,880 --> 00:24:37,080
+أظن هذه لا تحتاج برهان لماذا؟ لأن كل element في S
+
+210
+00:24:37,080 --> 00:24:48,460
+G يعتمد على element من جي؟ من جي يبقى because any
+
+211
+00:24:48,460 --> 00:24:50,600
+element
+
+212
+00:24:53,320 --> 00:24:59,140
+any element تي جي اللي موجود في اس جي
+
+213
+00:24:59,140 --> 00:25:05,660
+corresponding to
+
+214
+00:25:05,660 --> 00:25:19,520
+جي اللي موجودة في جي يعني بمعنى أخر اللي هو ال ال
+
+215
+00:25:19,520 --> 00:25:28,860
+five is onليش؟ لأن كل element من SG له أصل في جي
+
+216
+00:25:28,860 --> 00:25:34,720
+اللي هو جي يبقى إيش ضايل علينا؟ الخاصية الأخيرة
+
+217
+00:25:34,720 --> 00:25:41,600
+الخاصية الأخيرة كانت تالية يبقى بدي أجي أخد Phi
+
+218
+00:25:41,600 --> 00:25:53,740
+الخاصية الرابعة بدي أخد Phi of HG أو GH سيانيبقى
+
+219
+00:25:53,740 --> 00:26:02,520
+هذه حسب ال definition بدأت تساوي تي اتش جي تمام تي
+
+220
+00:26:02,520 --> 00:26:09,580
+اتش جي لو رجعتها الاصلة بصير تي اتش composition تي
+
+221
+00:26:09,580 --> 00:26:16,980
+جي تي اتش حسب التعريف اللي عرفناه هنا اللي هو تي
+
+222
+00:26:16,980 --> 00:26:18,480
+جي هي في
+
+223
+00:26:21,140 --> 00:26:30,370
+of H في التانية Phi of Gهذا الكلام صحيح لكل الـ H
+
+224
+00:26:30,370 --> 00:26:37,930
+والـ G اللي موجودة في G يبقى بناء عليه أثبتنا الآن
+
+225
+00:26:37,930 --> 00:26:44,230
+إن Phi of HG بدأ يساوي Phi of H في Phi of G يبقى
+
+226
+00:26:44,230 --> 00:26:51,210
+بناء عليه هذا يعني إن خواص الأيزومورفزم تحصلت يبقى
+
+227
+00:26:51,210 --> 00:27:00,060
+باني بقوله غاصوهكذا اللي هو من الـG isomorphic
+
+228
+00:27:00,060 --> 00:27:08,840
+لمن؟ للـSG اللي هي the set of all permutations أظن
+
+229
+00:27:08,840 --> 00:27:14,500
+دوّقتكوا شوية النظرية هيك لذلك بنروح أعيدها لكم
+
+230
+00:27:14,500 --> 00:27:21,160
+مرة تانية حتى نثبت هذه المعلومات عندكمطبعا هي من
+
+231
+00:27:21,160 --> 00:27:27,120
+أطول النظريات برهانة اللى موجودة فى الكتاب ليش
+
+232
+00:27:27,120 --> 00:27:31,960
+لأنها تحدث عن نقطة واحدة وليس عن مجموعة من النقاط
+
+233
+00:27:31,960 --> 00:27:38,700
+النظرية بتقول ما يأتي every group is isomorphic to
+
+234
+00:27:38,700 --> 00:27:42,480
+group if permutation هو هذا اللى ما قلناه فى الآخر
+
+235
+00:27:42,910 --> 00:27:46,810
+إنه ال group G isomorphic لل set of all
+
+236
+00:27:46,810 --> 00:27:52,590
+permutations اللي كوّنها على G اللي وعطناها الرمز
+
+237
+00:27:52,590 --> 00:28:00,370
+من SD لما أنا قاعد أقرا النص هذا بقول group G ماشي
+
+238
+00:28:00,370 --> 00:28:04,690
+لكن ال group permutation مش عارف الشكلها يبقى أنا
+
+239
+00:28:04,690 --> 00:28:08,890
+بدأ أخلق ال group هذي وبعد هيك نبدأ نتفاهم على
+
+240
+00:28:08,890 --> 00:28:11,410
+حكاية من ال isomorphism
+
+241
+00:28:14,910 --> 00:28:21,690
+أخذ أي عنصر جي موجود في جي من مكان يكون عرفت عليه
+
+242
+00:28:21,690 --> 00:28:26,830
+function TG من جي إلى جي by TG of X ساوية G of X
+
+243
+00:28:26,830 --> 00:28:31,470
+التعريف هذا صحيح لأن X و G موجودات في الجي والجي
+
+244
+00:28:31,470 --> 00:28:35,070
+group closed under multiplication يبقى فعلا ال
+
+245
+00:28:35,070 --> 00:28:41,300
+element هذا موجود في جيبعدين بقول و الله لو كانت
+
+246
+00:28:41,300 --> 00:28:46,740
+ال function هذه one to one and unto يبقى بيصير
+
+247
+00:28:46,740 --> 00:28:51,260
+permutation لأن لما نعرفنا ال permutation على set
+
+248
+00:28:51,260 --> 00:28:55,340
+قلنا هي function من ال set إلى نفسها بعدين تبقى
+
+249
+00:28:55,340 --> 00:28:59,900
+one to one and unto هي function من ال set إلى
+
+250
+00:28:59,900 --> 00:29:03,740
+نفسها يبقى ضال علي بس أثبت إنها one to one هذه ال
+
+251
+00:29:03,740 --> 00:29:09,070
+functionوكذلك on to يبقى روحت لل one to one قولت
+
+252
+00:29:09,070 --> 00:29:15,330
+افترض صوتين متساويتين بدي اثبت ان ال X يساوي Y حسب
+
+253
+00:29:15,330 --> 00:29:18,830
+التعريف اللي احنا جايليه يبقى هذا G X بدي اساوي
+
+254
+00:29:18,830 --> 00:29:22,450
+main G Y بال left cancellation اللي هو يبقى ال X
+
+255
+00:29:22,450 --> 00:29:28,090
+يساوي Y يبقى ال T G one to one بدي اثبتها انها on
+
+256
+00:29:28,090 --> 00:29:34,450
+to فاخدت Y موجود في Gالـ Y بدي أحاول أصيغه بصيغة
+
+257
+00:29:34,450 --> 00:29:41,650
+تعطيني TG of X كيف؟ قلت الـ Y يسوى ال identity في
+
+258
+00:29:41,650 --> 00:29:48,760
+Y ال identity بقدر أقول عليها GG inverseبعد ذلك
+
+259
+00:29:48,760 --> 00:29:56,460
+باخد اتنين هذول مع بعض جي انفرس واي وجي لحاله باجي
+
+260
+00:29:56,460 --> 00:30:02,930
+بقول هذول لو سميتم تاسم جديدة XZW اللي بدكيايبقى
+
+261
+00:30:02,930 --> 00:30:09,050
+اقولنا X مثلا يبقى جي X باجي لجي X من التعريف
+
+262
+00:30:09,050 --> 00:30:15,930
+عبارة عن TG of X يبقى سارة TG of X يبقى ال element
+
+263
+00:30:15,930 --> 00:30:21,850
+Y اللي موجود في جي اللي عندنا هذه اللي جاتله أصل X
+
+264
+00:30:21,850 --> 00:30:27,070
+موجود في جي الأولى يبقى بناء عليه الدالة هذه is
+
+265
+00:30:27,070 --> 00:30:33,500
+ontoبناء عليه هذه الـ function أصبحت تشكل ليه
+
+266
+00:30:33,500 --> 00:30:38,480
+permutationتمام؟ جيت على ال permutations هدول و
+
+267
+00:30:38,480 --> 00:30:43,900
+حطيتهم كلهم في مين؟ في ستة جديدة روحت سميتها SG
+
+268
+00:30:43,900 --> 00:30:50,400
+سميتها SG مشان العناصر تبعات G يكونوا من مين
+
+269
+00:30:50,400 --> 00:30:56,540
+ناخدهم من G itself من عناصرها كل ال permutations
+
+270
+00:30:56,540 --> 00:31:01,530
+اللي حصلنا عليها في القطغة الأولىيبقى لما يقولي
+
+271
+00:31:01,530 --> 00:31:05,130
+isomorphic to group of perimutations يبقى الجروب
+
+272
+00:31:05,130 --> 00:31:10,990
+هذه خلقتها جديد وسميتها SG بس أنا مش عارفة اللي هي
+
+273
+00:31:10,990 --> 00:31:15,390
+group ولا .. هي صارت عندي set و ال set فيها مجموعة
+
+274
+00:31:15,390 --> 00:31:20,130
+من العناظة بدي أثبتله إنها group إذا أثبتله إنها
+
+275
+00:31:20,130 --> 00:31:24,570
+group بصير هي عندي groupوجروب تانية بقدر اعمل ال
+
+276
+00:31:24,570 --> 00:31:29,630
+isomorphism ما بين الاتنين طب سؤال هامشي هيه جاب
+
+277
+00:31:29,630 --> 00:31:34,930
+المكمل بنفع اعمل isomorphism ما بين جروب و ما بين
+
+278
+00:31:34,930 --> 00:31:38,150
+set؟
+
+279
+00:31:38,150 --> 00:31:43,700
+بنفعلا يمكن ينفع لأن هذه عليها binary operation
+
+280
+00:31:43,700 --> 00:31:47,820
+وهذه ما عليها اش احنا بيقول isomorphism الأولى
+
+281
+00:31:47,820 --> 00:31:52,100
+والتانية كله لهم نفس القواصة الرياضية فكيف علي هذه
+
+282
+00:31:52,100 --> 00:31:56,380
+binary operation وهذه لأ إذا لا يمكن أن يكون هناك
+
+283
+00:31:56,380 --> 00:31:59,720
+isomorphism ما بين group ما بين set لازم يكون
+
+284
+00:31:59,720 --> 00:32:06,800
+التنتين are groups طيب نرجع الأن لل SG أنا أدعىإن
+
+285
+00:32:06,800 --> 00:32:11,400
+الـ Sجي هذي اللي كونها مالها is a group تحت ال
+
+286
+00:32:11,400 --> 00:32:18,020
+composition of function لذلك أخد GH بدي أثبت إنها
+
+287
+00:32:18,020 --> 00:32:25,820
+closed under multiplication أو closed underأخد تي
+
+288
+00:32:25,820 --> 00:32:36,360
+جي composition th of x يساوي تي جي في th of x
+
+289
+00:32:36,360 --> 00:32:42,540
+استخدم تعريف th of x اللي هو hx وبعدين استخدم
+
+290
+00:32:42,540 --> 00:32:48,850
+تعريفأو تي جي فسرة جي اتش اكس او جي اتش كله في اكس
+
+291
+00:32:48,850 --> 00:32:53,030
+او تي جي اتش كله في اكس لان جي في اتش يعطينا
+
+292
+00:32:53,030 --> 00:32:57,830
+element من جي يبقى بناء عليه هذا موجود في S يبقى
+
+293
+00:32:57,830 --> 00:33:02,030
+ال S جي is a closed under multiplication أو ال
+
+294
+00:33:02,030 --> 00:33:05,770
+operation اللي عليها ال composition of function is
+
+295
+00:33:05,770 --> 00:33:13,220
+a binary operationالان صار عندنا binary operation
+
+296
+00:33:13,220 --> 00:33:15,800
+كمان ال composition of a function ثم نعرف انها
+
+297
+00:33:15,800 --> 00:33:19,440
+associative يبقى ماضلش عندي الا main two
+
+298
+00:33:19,440 --> 00:33:26,480
+conditions ال identity elementانا ادعي ان TA هو ال
+
+299
+00:33:26,480 --> 00:33:31,400
+identity element وروح نثبتنا ان هو ال identity
+
+300
+00:33:31,400 --> 00:33:37,420
+element اتدعيت ان تجي انفرس بالضبط هو ت وال انفرس
+
+301
+00:33:37,420 --> 00:33:42,860
+بحطه على ال elementمن اين لك هذا روحت اثبتته وهيه
+
+302
+00:33:42,860 --> 00:33:48,620
+وهيه كله طلع ليه ال identity element يبقى فعلا كل
+
+303
+00:33:48,620 --> 00:33:54,460
+element في SG له معكوس يبقى بناء عليه ال SG the
+
+304
+00:33:54,460 --> 00:33:59,540
+group of permutation صارت group إذا مدام صارت
+
+305
+00:33:59,540 --> 00:34:05,980
+group وعند group بقدر اكون ايش isomorphismتعرف الـ
+
+306
+00:34:05,980 --> 00:34:11,860
+Function Phi من G إلى SG بـPhi of G بيسوء من T of
+
+307
+00:34:11,860 --> 00:34:18,780
+G جي هذه موجودة في جي الـTG موجودة في SG بدي أروح
+
+308
+00:34:18,780 --> 00:34:23,300
+أبين إنه فعلا هذه الـ Function معرفة من هنا إلى
+
+309
+00:34:23,300 --> 00:34:28,950
+هناباخد عنصرين متساوين و بثبت ان عنصرته متساوية ان
+
+310
+00:34:28,950 --> 00:34:34,210
+حدث ذلك بقول هذه well-defined function يعني ال
+
+311
+00:34:34,210 --> 00:34:39,990
+function معرفة تعريفا صحيحا فجيه تقول خد لي G و H
+
+312
+00:34:39,990 --> 00:34:44,470
+موجودات بحيث الـ G يستوى الـ H أثر على الطرفين بـ
+
+313
+00:34:44,470 --> 00:34:49,800
+Phi Phi of G بده سوى TGوهذه تساوي الـTH يبقى صورة
+
+314
+00:34:49,800 --> 00:34:53,580
+الأنصار الأول تساوي صورة الأنصار التانية يبقى Phi
+
+315
+00:34:53,580 --> 00:34:58,160
+is well defined ال one to one خد لي صورتين
+
+316
+00:34:58,160 --> 00:35:03,240
+متساويتين وبدأ أثبت أن أصلهم متساوي يبقى TG بدأ
+
+317
+00:35:03,240 --> 00:35:07,260
+يساوي TH بدأ أخلي كل واحد أتأثر على X عشان أقدر
+
+318
+00:35:07,260 --> 00:35:13,100
+أطبق التعريف اللي عندنا هذا فصار عندنا TG of X بده
+
+319
+00:35:13,100 --> 00:35:21,120
+يساوياللي هو TH of X تمام
+
+320
+00:35:21,120 --> 00:35:26,800
+يبقى GX يساوي HX بدنا ن cancel ال X من الطرفين
+
+321
+00:35:26,800 --> 00:35:30,660
+يبقى ال G يساوي ال H وبالتالي Phi is one to one
+
+322
+00:35:30,660 --> 00:35:36,120
+الانتوا صحيحة لإن كل TG في SG بده يقابله main
+
+323
+00:35:36,470 --> 00:35:40,050
+الخطوة الأخيرة موجودة في جيو مين و جيونتو موجودة
+
+324
+00:35:40,050 --> 00:35:46,310
+في جيو
+
+325
+00:35:46,310 --> 00:35:56,560
+مين و جيونتو موجودة في جيونتوأي كتاب جبر تلاقيه في
+
+326
+00:35:56,560 --> 00:36:00,620
+المكتب على النت بس اكتب Kiley theorem بفتح لك
+
+327
+00:36:00,620 --> 00:36:05,740
+علامين على Kiley theorem نظرية اللي هو العالم كيلي
+
+328
+00:36:05,740 --> 00:36:11,260
+اللي اكتشفها اللي انا انا بدي اعطيك مثال تطبيقي
+
+329
+00:36:11,260 --> 00:36:15,680
+على الشغل هذي تمام؟ ايوة تعال هنا اللي هو تعال
+
+330
+00:36:20,700 --> 00:36:24,500
+أيوة جيد كويس
+
+331
+00:36:24,500 --> 00:36:30,230
+أثبتنا ان فاي is onto تبع التعريف هذاهي التعريف
+
+332
+00:36:30,230 --> 00:36:36,270
+هذه file is under كيف أثبتنا هذا؟ لأن أي element
+
+333
+00:36:36,270 --> 00:36:41,950
+في Sجي هيه هذا بيعتمد على مين؟ على G جي من وين جي
+
+334
+00:36:41,950 --> 00:36:48,790
+بناها؟ من G كبتر يبقى كل permutation هنا تعتمد على
+
+335
+00:36:48,790 --> 00:36:53,070
+element من اللي هناك يعني لا يمكن أن يكون هنا
+
+336
+00:36:53,070 --> 00:36:57,610
+permutation ما لم يكن مناظر إلها element من G
+
+337
+00:36:57,610 --> 00:37:04,720
+فضعت؟أه حد بدى يسأل تانى طب نعطى مثال عددي توضيحى
+
+338
+00:37:04,720 --> 00:37:13,680
+كيف نحسب هالشغل هذه example
+
+339
+00:37:48,300 --> 00:37:59,760
+find الاجرب SG where ال
+
+340
+00:37:59,760 --> 00:38:04,540
+G بدأت ساوي ال U عشرة
+
+341
+00:38:17,140 --> 00:38:23,660
+أظهر لو وجدنا عناصر SG بيصير الجيل الأصلي اللي هي
+
+342
+00:38:23,660 --> 00:38:30,600
+U10 isomorphic لمين؟ للـ SG حسب نظرية كلب الأن لو
+
+343
+00:38:30,600 --> 00:38:40,340
+جيت للـU10 مين عناصرها؟ الواحد، اتنين، تلاتة،
+
+344
+00:38:40,340 --> 00:38:49,730
+أربعة، خمسة، ستة، سبعة، تسعة، في غيرهم؟طيب يبقى
+
+345
+00:38:49,730 --> 00:38:59,910
+بناء عليه ال S G ال S G أو ال S U عشرة بدها تساوي
+
+346
+00:38:59,910 --> 00:39:09,110
+T واحد و T تلاتة و T سبعة و T تسعة بس مين T واحد و
+
+347
+00:39:09,110 --> 00:39:14,530
+T تلاتة و T سبعة مش عارفين بدنا نعرف تمام باجي
+
+348
+00:39:14,530 --> 00:39:15,950
+بقولهم where
+
+349
+00:39:18,450 --> 00:39:26,230
+حيث الـ T1 هذه هي ال identity permutation الصف
+
+350
+00:39:26,230 --> 00:39:31,070
+الأول بقولش واحد اتنين تلاتة اربعة العناصر هذه
+
+351
+00:39:31,070 --> 00:39:38,110
+تبعات الـ G لإن هذه ال permutation على ال group مش
+
+352
+00:39:38,110 --> 00:39:43,990
+على أعداد عادية يبقى الصف الأول واحد تلاتة سبعة
+
+353
+00:39:43,990 --> 00:39:52,810
+تسعة انتهينابدي اجيب صورهم تمام؟ قبل شوية عرفنا ان
+
+354
+00:39:52,810 --> 00:40:00,870
+TG of X بده يساوي حصل ضرب G في X مظبوط؟ يبقى انا
+
+355
+00:40:00,870 --> 00:40:08,730
+ايش؟ بدي T واحد of واحد بدي اعطيك الواحدT1 of
+
+356
+00:40:08,730 --> 00:40:15,130
+تلاتة سبعة تسعة كما هي ال identity كل شي بده ينزل
+
+357
+00:40:15,130 --> 00:40:21,010
+زي ما هو كيف؟
+
+358
+00:40:21,010 --> 00:40:29,650
+واحد في تلاتة واحد في سبعة واحد في تسعة بين إيش؟
+
+359
+00:40:29,650 --> 00:40:38,000
+طيب يبقى هذه ال identity هذه ال T1بدي هنا T ثلاثة
+
+360
+00:40:38,000 --> 00:40:47,340
+بده يساوي الصف الأول واحد تلاتة سبعة تسعة طيب
+
+361
+00:40:47,340 --> 00:40:53,480
+بدي أجيب الصف الثاني بقول لي T G of X بده يساوي GX
+
+362
+00:40:53,480 --> 00:41:00,160
+يعني أنا بدي أحسبله T تلاتة of واحد يبقى تلاتة في
+
+363
+00:41:00,160 --> 00:41:07,720
+واحد يبقى تلاتة يبقى العنصر هنا تلاتةبدي T ثلاثة و
+
+364
+00:41:07,720 --> 00:41:12,740
+ثلاثة يبقى ثلاثة في ثلاثة اللي هو تسعة يبقى هنا
+
+365
+00:41:12,740 --> 00:41:19,640
+تسعة بدي T ثلاثة و سبعة اللي هو تلاتة في سبعة
+
+366
+00:41:19,640 --> 00:41:27,060
+بقدرش؟ واحد و عشري مضيله عشرة بواحد يبقى هذه تساوي
+
+367
+00:41:27,060 --> 00:41:33,500
+واحد إذا هنا واحدبجيلك هنا T ثلاثة و تسعة يبقى
+
+368
+00:41:33,500 --> 00:41:38,020
+ثلاثة في تسعة في قدر؟ سبعة و عشرين موديه العاشرة
+
+369
+00:41:38,020 --> 00:41:44,900
+بسبعة يبقى هنا السبعة لاحظ مجانيش ولا رقم الا اللي
+
+370
+00:41:44,900 --> 00:41:50,340
+موجودة في الصف الأول اتنين لم يتكرر اي رقم مرتين
+
+371
+00:41:50,340 --> 00:41:56,120
+على الإطلاق ليش انها one to one and unto طيب لو
+
+372
+00:41:56,120 --> 00:42:04,270
+بدنا الآن T سبعةيبقى واحد ثلاثة سبعة تسعة نحسبهم
+
+373
+00:42:04,270 --> 00:42:08,910
+بنفس الطريقة اللي هناك ت سبعة وواحد يبقى سبعة في
+
+374
+00:42:08,910 --> 00:42:15,170
+واحد بسبعة الان ت سبعة تلاتة يعني سبعة في تلاتة
+
+375
+00:42:15,170 --> 00:42:21,500
+بواحد وعشرين مضيوله عشرةأب واحد سبعة في سبعة بتسعة
+
+376
+00:42:21,500 --> 00:42:27,340
+واربعين موديولو سبعة ابتسعة سبعة في تسعة بتلاتة
+
+377
+00:42:27,340 --> 00:42:32,760
+وستين موديولو عشرة بتلاتة اللي هي بجداش بتلاتة
+
+378
+00:42:32,760 --> 00:42:40,940
+ضالت عندنا مين تتسعة واحد تلاتة سبعة تسعةتسعة في
+
+379
+00:42:40,940 --> 00:42:46,580
+واحد بتسعة، تسعة في تلاتة بسبعة وعشرين، سبعة في
+
+380
+00:42:46,580 --> 00:42:51,260
+تسعة على تسعة في سبعة بتلاتة وستين، تسعة في تسعة
+
+381
+00:42:51,260 --> 00:43:00,650
+بواحد وتمانينيبقى الأن عرفنا كيف بنكوّم الـT1 وT3
+
+382
+00:43:00,650 --> 00:43:08,110
+وT7 يبقى الـSG بكتب كل عنصر فيهم بدلالة عناصر G
+
+383
+00:43:08,110 --> 00:43:12,980
+مين ما تكون جيهش ما يكون شكل هيكونيبقى بقول TG1
+
+384
+00:43:12,980 --> 00:43:18,740
+TG2 TG3 TG4 لغاية ما أخلصهم كلهم كيف بحسب كل واحد
+
+385
+00:43:18,740 --> 00:43:23,520
+منهم؟ بالطريقة اللي عندنا هنا بحط الصف الأول عناصر
+
+386
+00:43:23,520 --> 00:43:28,280
+G و بعدين بخلي ال T تأثر على العنصر الأول التاني
+
+387
+00:43:28,280 --> 00:43:33,660
+التالت الرابع و بكتب الصفوف يبقى هذه العناصر يبقى
+
+388
+00:43:33,660 --> 00:43:38,020
+في هذه الحالة باي كلي
+
+389
+00:43:39,710 --> 00:43:46,930
+أو Keyless theorem الـ U عشرة الـ U عشرة
+
+390
+00:43:46,930 --> 00:43:57,550
+isomorphic للـ S U عشرة هاي المقصود يعني يبقى G
+
+391
+00:43:57,550 --> 00:44:03,330
+isomorphic للست of all permutations اللي كوّنها
+
+392
+00:44:03,330 --> 00:44:08,780
+على ال group عشرة و كذايبقى فهمنا كيف تطبيق
+
+393
+00:44:08,780 --> 00:44:15,540
+النظرية، الآن بدنا نخش لنظرية مكونة من سبعة نقاط
+
+394
+00:44:15,540 --> 00:44:19,560
+للمرة القادمة، ان شاء الله مافيش إمكانية اليوم
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..16d118339c772600b0e3d0ed9ee73a9b51c21d53
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8.srt
@@ -0,0 +1,1955 @@
+1
+00:00:20,690 --> 00:00:24,770
+بسم الله الرحمن الرحيم عودنا على البدء في المحاضرات في
+
+2
+00:00:24,770 --> 00:00:29,010
+الفترة الصباحية كتبنا نظرية عبارة عن ست نقاط
+
+3
+00:00:29,010 --> 00:00:33,450
+نقطتين كانتا مبرهناتين سابقا في موضوع ال isomorphism
+
+4
+00:00:33,450 --> 00:00:38,870
+مبرهننا نقطتين وهذه هي النقطة الخامسة يبقى النقطة
+
+5
+00:00:38,870 --> 00:00:42,430
+الخامسة بتقول إنه phi of a بدو يساوي phi of b if
+
+6
+00:00:42,430 --> 00:00:46,990
+and only if ال a في ال kernel بدو يساوي ال b في ال
+
+7
+00:00:46,990 --> 00:00:52,660
+kernel يبقى بدنا نبرهن صحة هذه النقطة فباجي بقول له
+
+8
+00:00:52,660 --> 00:00:59,340
+ال proof لو كان ال phi of a بده يساوي ال phi of b
+
+9
+00:00:59,340 --> 00:01:06,210
+هذا الكلام صحيح if and only if لو ضربنا في المعكوس
+
+10
+00:01:06,210 --> 00:01:11,990
+تبعها من جهة الشمال بيكون مين؟ بيكون phi of b
+
+11
+00:01:11,990 --> 00:01:18,190
+لكل inverse في phi of a بدو يساوي ال identity
+
+12
+00:01:18,190 --> 00:01:25,690
+element تبع من؟ تبع الـG bar لأن phi of a وفي phi of b
+
+13
+00:01:25,690 --> 00:01:32,440
+موجودة تاتوين في الـG bar الكلام هذا صحيح if and
+
+14
+00:01:32,440 --> 00:01:48,720
+only if الكلام
+
+15
+00:01:48,720 --> 00:01:53,570
+هذا صحيح if and only if الـ Phi أول ما أخذناها هو
+
+16
+00:01:53,570 --> 00:02:03,110
+Homomorphism، إذا phi of b inverse a بدل
+
+17
+00:02:03,110 --> 00:02:08,650
+سبب من الـ Identity Element تبع الـ G¯  إيش تفسيرك
+
+18
+00:02:08,650 --> 00:02:13,810
+لهذه العبارة phi لما أثرت على element أعطتني ال
+
+19
+00:02:13,810 --> 00:02:17,510
+identity element يبقى هذا ال element وين موجود؟ ال
+
+20
+00:02:17,510 --> 00:02:22,950
+kernel يبقى هذا .. والله هذا معناته if and only if
+
+21
+00:02:22,950 --> 00:02:28,770
+كله ماشيين ب if and only if ال b inverse a موجود
+
+22
+00:02:28,770 --> 00:02:35,190
+في ال kernel للـphi معنـى هذا الكلام أن الـb inverse
+
+23
+00:02:35,190 --> 00:02:41,030
+a في الـkernel للـphi بده يساوي الـkernel للـphi
+
+24
+00:02:41,030 --> 00:02:46,350
+itself لو ضربنا الطرفين في الـb من جهتي الشمال
+
+25
+00:02:46,350 --> 00:02:50,650
+يبقى بصير if and only if الـa في الkernel للـphi
+
+26
+00:02:50,650 --> 00:02:56,130
+بده يساوي b في الkernel للـphi أظن وهو المطلوب
+
+27
+00:02:56,130 --> 00:03:05,820
+النقطة السادسة النقطة السادسة بتقول ما يأتي لو كان
+
+28
+00:03:05,820 --> 00:03:12,220
+الـ phi of g بده يساوي الـ g prime ال phi of g بده
+
+29
+00:03:12,220 --> 00:03:20,470
+يساوي ال g prime الـphi inverse of g' بدو يساوي الـg
+
+30
+00:03:20,470 --> 00:03:24,430
+في الـKernel للـphi وراح المعرفة هذه كل الـx اللي
+
+31
+00:03:24,430 --> 00:03:27,750
+موجودة في g بيحيط الـphi of x بدو يساوي مين؟ بدو
+
+32
+00:03:27,750 --> 00:03:33,490
+يساوي g' بدنا نروح نثبت صحة هذا الكلام النقطة هذه
+
+33
+00:03:33,490 --> 00:03:38,030
+تعال نشوف إيش مفهومها قبل ما نبرهن بدنا نفهم ما
+
+34
+00:03:38,030 --> 00:03:42,770
+هو موضوع هذه النقطة شوف يا سيدي إحنا عندنا phi من
+
+35
+00:03:42,770 --> 00:03:48,150
+ال group g إلى ال group g bar تمام قال لي phi of g
+
+36
+00:03:48,150 --> 00:03:52,200
+بده يساوي g prime يقول لي g prime وين موجودة؟ في الـg
+
+37
+00:03:52,200 --> 00:03:56,840
+bar والـg هذه موجودة في الـg طيب كويس إذا هذه
+
+38
+00:03:56,840 --> 00:04:02,140
+معلومة الآن إيش بقول لي بقى؟ بدي يكون الـphi inverse
+
+39
+00:04:02,140 --> 00:04:07,960
+للـg prime تساوي g مضروبة في ال kernel يعني لما نأخذ phi
+
+40
+00:04:07,960 --> 00:04:11,260
+inverse للطرفين مش هروح أقول phi inverse of g
+
+41
+00:04:11,260 --> 00:04:16,930
+prime تساوي g ليش؟ ليش؟ لأنها كانت one to one صحيح هذا
+
+42
+00:04:16,930 --> 00:04:20,250
+ليس isomorphism، إن هؤلاء عبارة عن مجموعة من
+
+43
+00:04:20,250 --> 00:04:24,690
+النقاط صورتهم الـIdentity. إذن عندما أدخل للعكس،
+
+44
+00:04:24,690 --> 00:04:28,170
+فإن الـphi inverse لهذا العلم سيكون مجموعة من
+
+45
+00:04:28,170 --> 00:04:33,490
+النقاط وليس نقطة واحدة. وهذا ما سنثبته بعد قليل في
+
+46
+00:04:33,490 --> 00:04:38,420
+النظرية القادمة. يبقى phi inverse g prime يبقى مين
+
+47
+00:04:38,420 --> 00:04:41,680
+يساوي g في ال kernel اللي في هذا اللي عايزين إن تبدو
+
+48
+00:04:41,680 --> 00:04:45,340
+هدول two sets are equal يبقى بدي اروح أأخذ element
+
+49
+00:04:45,340 --> 00:04:48,800
+هنا أثبت إنه موجود هنا وأعمل الأعمال العكسية آخذ
+
+50
+00:04:48,800 --> 00:04:52,840
+element هنا وأثبت إنه موجود هنا يبقى مشان هيك
+
+51
+00:04:52,840 --> 00:04:59,900
+باجي أقول له let ال x موجودة في phi inverse g prime
+
+52
+00:05:01,340 --> 00:05:09,260
+طبعا يبقى لو أثرت بمين؟ ب phi على الطرفين بصير phi
+
+53
+00:05:09,260 --> 00:05:17,880
+of x بدها تساوي g prime طيب هذا معناه إنه phi of x
+
+54
+00:05:17,880 --> 00:05:24,500
+يساوي أظن g prime مواطعه ما أقدرش ب phi of g يبقى هذا
+
+55
+00:05:24,500 --> 00:05:31,090
+phi of g بالشكل اللي عندنا هنا طيب لو رحت من هذا
+
+56
+00:05:31,090 --> 00:05:37,250
+الكلام ضربت الطرفين في معكوس هذا ال element يبقى
+
+57
+00:05:37,250 --> 00:05:45,810
+بده يصير phi of g الكل inverse في ال
+
+58
+00:05:45,810 --> 00:05:50,290
+phi of x بده يساوي الطرف اليمين اللي هو ال
+
+59
+00:05:50,290 --> 00:05:56,610
+identity element تبع g bar تبع ال g بعضه بنفس المفهوم
+
+60
+00:05:56,610 --> 00:06:02,810
+هذا إيش معناه؟ معناه إنه phi of g inverse في phi
+
+61
+00:06:02,810 --> 00:06:08,310
+of x بده يساوي ال identity element تبع ال g bar أو
+
+62
+00:06:08,310 --> 00:06:15,250
+إن شئتم فقولوا phi of g inverse x بده يساوي ال
+
+63
+00:06:15,250 --> 00:06:20,470
+identity element تبع ال g bar معنى هذا الكلام أن
+
+64
+00:06:20,470 --> 00:06:24,690
+هذا ال element بين القوسين وين موجود؟ في ال kernel
+
+65
+00:06:24,690 --> 00:06:29,690
+لأنه صورته ال identity يبقى بده يصير g inverse x
+
+66
+00:06:29,690 --> 00:06:36,490
+موجود في ال kernel للـphi طب لو ضربت الطرفين في g
+
+67
+00:06:36,490 --> 00:06:42,130
+من جهة الشمال يبقى بظل x موجود في ال g في
+
+68
+00:06:42,130 --> 00:06:48,480
+ال kernel للـphi يبقى أنا أخذت x موجود في ال phi
+
+69
+00:06:48,480 --> 00:06:53,940
+inverse للـg' لقيته موجود وين؟ في g في ال kernel
+
+70
+00:06:53,940 --> 00:07:00,020
+معناته الست الأولانية subset من الست الثانية يبقى
+
+71
+00:07:00,020 --> 00:07:08,060
+هنا phi inverse of g' subset من مين؟ من ال g في
+
+72
+00:07:08,060 --> 00:07:13,580
+ال kernel للـphi اعتبر هذه هي النقطة الأولى بالدرجة
+
+73
+00:07:13,580 --> 00:07:21,300
+للنقطة الثانية on the other hand بالدرجة
+
+74
+00:07:21,300 --> 00:07:28,940
+يأخذ x موجودة في ال g في ال kernel للـphi خذ لل x
+
+75
+00:07:28,940 --> 00:07:35,380
+موجودة في ال g في ال kernel للـphi إذا كنت أثبت إن
+
+76
+00:07:35,380 --> 00:07:39,700
+ال x هذه موجودة هنا بيكون تم المطلوب يكون انتهينا
+
+77
+00:07:39,700 --> 00:07:45,600
+من المسألة اللي عندنا يبقى then ال x هذه يا شباب
+
+78
+00:07:45,600 --> 00:07:51,200
+بقدر أقول هي ال g مضروبة في element من مين؟ من
+
+79
+00:07:51,200 --> 00:07:59,080
+ال kernel تبع الـphi وليكن اللي هو k يبقى x بدأت
+
+80
+00:07:59,080 --> 00:08:09,660
+تساوي gk for some for some k اللي موجودة في ال kernel
+
+81
+00:08:09,660 --> 00:08:17,100
+ل phi طيب شو رأيك أثر على التنتين ب phi يبقى إيش بده
+
+82
+00:08:17,100 --> 00:08:25,960
+يصير؟ بده يصير phi of x بده يساوي phi of g في phi of k يعني
+
+83
+00:08:25,960 --> 00:08:32,540
+معنى هذا الكلام إنه phi of x بده يساوي phi of g في
+
+84
+00:08:32,540 --> 00:08:42,240
+phi of .. اللي هو small k هذا الكلام يساوي أو هذا
+
+85
+00:08:42,240 --> 00:08:49,680
+بده يعطينا الطرف الشمال phi of x الطرف اليمين phi
+
+86
+00:08:49,680 --> 00:08:55,860
+of g كده معطى من رأس المسألة؟ g prime يبقى
+
+87
+00:08:55,860 --> 00:09:04,900
+هذا phi of g بده يساوي g prime طيب phi of k كده إيش؟
+
+88
+00:09:04,900 --> 00:09:10,080
+طلع ليه هنا؟ إحنا جبناها من وين ال k هذا؟ موجودة
+
+89
+00:09:10,080 --> 00:09:13,200
+في ال kernel for some k الموجودة في ال kernel
+
+90
+00:09:13,200 --> 00:09:18,880
+يبقى phi of k بقد إيش؟ بال identity يبقى هذا بال
+
+91
+00:09:18,880 --> 00:09:27,880
+identity تبع ال g bar ليش؟ since اللي هو ال k هذه
+
+92
+00:09:27,880 --> 00:09:33,300
+موجودة في ال kernel للـphi النظر اللي موجودة هنا
+
+93
+00:09:33,300 --> 00:09:39,400
+بتعطينا ال identity element يبقى هنا الساعة ال
+
+94
+00:09:39,400 --> 00:09:45,860
+phi of x بده يساوي من ال g' ليش؟ إن ال g' موجودة
+
+95
+00:09:45,860 --> 00:09:50,380
+في g' وال identity هي تبع ال g' يبقى حاصل الضرب
+
+96
+00:09:50,380 --> 00:09:58,050
+بيعطينا من g' يبقى معنى هذا الكلام إن ال x بتكون
+
+97
+00:09:58,050 --> 00:10:06,270
+موجودة في ال phi inverse of g' لاحظ ما يأتي إيش
+
+98
+00:10:06,270 --> 00:10:11,070
+كتبت أنا السطر الأخير أنا وصلت لغاية هنا phi of x
+
+99
+00:10:11,070 --> 00:10:15,470
+بده يساوي g' في ال identity يبقى phi of x بده
+
+100
+00:10:15,470 --> 00:10:22,230
+يساوي g' إيش رحت كتبتي؟ يبقى ال x ما كتبتش تساوي في
+
+101
+00:10:22,230 --> 00:10:27,490
+inverse of g' كتبت ال x موجودة في ال phi inverse of g'
+
+102
+00:10:27,890 --> 00:10:33,270
+ليش؟ إن ال phi inverse of g' عدة نقاط مش نقطة واحدة لو
+
+103
+00:10:33,270 --> 00:10:39,650
+كانت نقطة واحدة لكتبت إيش؟ لكتبت اليساوي تمام إذا x
+
+104
+00:10:41,450 --> 00:10:43,270
+ماشي ولو وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+105
+00:10:43,270 --> 00:10:44,270
+وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+106
+00:10:44,270 --> 00:10:44,630
+وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+107
+00:10:44,630 --> 00:10:45,630
+وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+108
+00:10:45,630 --> 00:10:47,230
+وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+109
+00:10:47,230 --> 00:10:50,470
+وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+110
+00:10:50,470 --> 00:10:54,770
+وانت وانت وانت وانت 
+
+111
+00:11:02,630 --> 00:11:07,710
+اللي هو subset من مين؟ من ال phi inverse of g
+
+112
+00:11:07,710 --> 00:11:12,990
+prime وهذه العلاقة رقم اتنين يبقى باجي بقول from
+
+113
+00:11:12,990 --> 00:11:23,810
+واحد and اتنين we have إن ال phi inverse of g
+
+114
+00:11:23,810 --> 00:11:28,510
+prime بده يساوي g في ال kernel للـphi
+
+115
+00:11:34,710 --> 00:11:38,890
+نعطيك مثال توضيح على ذلك لأن هي خلصت النظرية
+
+116
+00:11:38,890 --> 00:11:44,870
+example بقول
+
+117
+00:11:44,870 --> 00:11:49,610
+suppose that
+
+118
+00:11:49,610 --> 00:12:01,130
+افترض أن phi من z ثلاثين إلى z ثلاثين A
+
+119
+00:12:01,130 --> 00:12:07,730
+homomorphism suppose that phi is a homomorphism
+
+120
+00:12:07,730 --> 00:12:12,510
+and ال kernel
+
+121
+00:12:12,510 --> 00:12:22,390
+للفاي هي العناصر zero و عشرة و عشرين بيقول ل f إذا
+
+122
+00:12:22,390 --> 00:12:30,290
+كان ال phi ل 23 هي عبارة عن 9 السؤال هو
+
+123
+00:12:30,290 --> 00:12:33,990
+determine
+
+124
+00:12:33,990 --> 00:12:38,510
+all
+
+125
+00:12:41,760 --> 00:12:51,300
+elements that map maps to تسعة كل ال elements اللي 
+
+126
+00:12:51,300 --> 00:13:02,040
+هم maps to تسعة السؤال
+
+127
+00:13:02,040 --> 00:13:06,480
+مرة تانية فيها النفاي من Z 30 ل Z 30
+
+128
+00:13:06,480 --> 00:13:10,870
+homomorphism وهذا حسبنا له كيرن اللي جينا كيرنه
+
+129
+00:13:10,870 --> 00:13:16,190
+zero وعشرة وعشرين هذه معلومة وزيادة على ذلك five
+
+130
+00:13:16,190 --> 00:13:20,590
+of تلاتة وعشرين يساوي تسعة قال لي هاتلي كل ال
+
+131
+00:13:20,590 --> 00:13:25,250
+elements اللي maps to تسعة يعني بدي كل العناصر
+
+132
+00:13:25,250 --> 00:13:29,810
+اللي في زد تلاتين واللي صارتهم بتكون مان تسعة يعني
+
+133
+00:13:29,810 --> 00:13:33,750
+مش ع جد تلاتة وعشرين يبقى باقي ال elements اللي
+
+134
+00:13:33,750 --> 00:13:39,990
+وصرتهم بتكون تسعة تطلعلي في النقطة الأخيرة رقم ستة
+
+135
+00:13:39,990 --> 00:13:45,270
+وخليها في دماغك أنا عندي في of G يساوي G prime كأنه
+
+136
+00:13:45,270 --> 00:13:50,030
+G هذه main تلاتة وعشرين وال G prime هي main التسعة
+
+137
+00:13:50,030 --> 00:13:55,510
+يبقى ال في inverse of G prime بده يساوي ال G في ال
+
+138
+00:13:55,510 --> 00:14:00,750
+kernel للفي يبقى بناء عليه أنا عندي فاي of تلاتة
+
+139
+00:14:00,750 --> 00:14:07,250
+وعشرين يساوي تسعة شو رايك آخذ معكوس الفاي للطرفين
+
+140
+00:14:07,250 --> 00:14:14,370
+يبقى ايش بصير عندي بصير الفاي inverse of تسعة بده
+
+141
+00:14:14,370 --> 00:14:18,930
+يساوي ال element اللي عندنا اللي هو تلاتة وعشرين
+
+142
+00:14:18,930 --> 00:14:27,530
+في ال kernel للفايتمام؟ لكن لما كانت العملية عملية
+
+143
+00:14:27,530 --> 00:14:31,890
+جامعة إذا ما بكتبش تلاتة وعشرين مضروبة في ال
+
+144
+00:14:31,890 --> 00:14:37,990
+kernel وإنما بكتب تلاتة وعشرين زائد ال kernel لمن؟
+
+145
+00:14:37,990 --> 00:14:44,890
+لل في يبقى هذا الكلام بدرساوي تلاتة وعشرين زائد ال
+
+146
+00:14:44,890 --> 00:14:53,110
+kernel لل في هي موجود فوق يبقى zero وعشرة وعشرين مش
+
+147
+00:14:53,110 --> 00:14:57,070
+تروح تقول هنا فاينفرس وتسعة الفاينفرس وتضرع
+
+148
+00:14:57,070 --> 00:14:57,650
+الفاينفرس وتضرع الفاينفرس تضرع الفاينفرس تضرع
+
+149
+00:14:57,650 --> 00:14:57,950
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+150
+00:14:57,950 --> 00:14:58,630
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+151
+00:14:58,630 --> 00:14:59,010
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+152
+00:14:59,010 --> 00:15:01,730
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+153
+00:15:01,730 --> 00:15:07,210
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+154
+00:15:07,210 --> 00:15:14,830
+الفاينفرس تضرع الفاينفرس
+
+155
+00:15:14,830 --> 00:15:18,880
+تفي المثل لأن ال operation عملية جمع هذا الكلام
+
+156
+00:15:18,880 --> 00:15:22,460
+بده يساوي بده يجمع كل عنصر مع نظيره يبقى هذا
+
+157
+00:15:22,460 --> 00:15:27,460
+تلاتة وعشرين تلاتة وعشرين وعشرة تلاتة وتلاتين في
+
+158
+00:15:27,460 --> 00:15:32,980
+زد تلاتين بيطلع تلاتة وتلاتين واربعين في زي التلاتين
+
+159
+00:15:32,980 --> 00:15:37,340
+بيطلع تلاتاش بيطلع تلاتاش إذا العناصر لو صرتهم
+
+160
+00:15:37,340 --> 00:15:42,140
+تسعة هي تلاتة وعشرين وهي معطاة وكذلك في of تلاتة
+
+161
+00:15:42,140 --> 00:15:46,160
+وفي of تلاتاش هي اللي بتساويهم هي اللي بتساوي تسعة
+
+162
+00:15:46,160 --> 00:15:52,240
+يبقى دير بالك من هذه النقطة ننتقل الآن إلى النظرية
+
+163
+00:15:52,240 --> 00:15:56,480
+التالية يبقى بالداجي ل theorem
+
+164
+00:15:59,090 --> 00:16:07,770
+هذه نظرية بتتحدث عن properties of
+
+165
+00:16:07,770 --> 00:16:15,270
+subgroups under
+
+166
+00:16:15,270 --> 00:16:18,470
+homomorphism
+
+167
+00:16:27,200 --> 00:16:36,600
+تنص على مياتي لت الفاي ب homomorphism
+
+168
+00:16:36,600 --> 00:16:47,240
+from a group g to a group g bar
+
+169
+00:17:02,150 --> 00:17:10,650
+النقطة الأولى فاي اف اتش كابتل اتش اللي هي كل
+
+170
+00:17:10,650 --> 00:17:19,080
+العناصر في اف اتش بحيث الاتش موجودة في الاتش is a
+
+171
+00:17:19,080 --> 00:17:24,240
+subgroup من الـ G bar يبقى هذه ال subgroup من ال G
+
+172
+00:17:24,240 --> 00:17:34,120
+bar النقطة الثانية لو كانت ال H Cyclic F ال H is
+
+173
+00:17:34,120 --> 00:17:43,340
+Cyclic لو كانت ال H Cyclic then Phi of H صورتها is
+
+174
+00:17:43,340 --> 00:17:56,420
+Cyclic النقطة التالتة لو كانت ال h is abelian then
+
+175
+00:17:56,420 --> 00:18:04,740
+لو five of h is abelian five of h is abelian
+
+176
+00:18:04,740 --> 00:18:14,120
+النقطة الرابعة لو كانت الـ H is a normal subgroup
+
+177
+00:18:14,120 --> 00:18:25,200
+من G then Phi of H is a normal subgroup من Phi of
+
+178
+00:18:25,200 --> 00:18:28,620
+G النقطة
+
+179
+00:18:28,620 --> 00:18:42,540
+الخامسة إذا كانت أعضاء كيرنال فيا هي نة ثم فيا ثم
+
+180
+00:18:42,540 --> 00:18:56,080
+فيا هي نة إلى واحدة نة إلى واحدة مابينج من
+
+181
+00:18:58,300 --> 00:19:10,500
+from g to phi of g النقطة
+
+182
+00:19:10,500 --> 00:19:22,480
+السادسة بيقول if ال order لل H كان يساوي N then ال
+
+183
+00:19:22,480 --> 00:19:27,420
+order لل phi of H بده يقسم
+
+184
+00:19:29,960 --> 00:19:33,980
+الـ N النقطة
+
+185
+00:19:33,980 --> 00:19:46,000
+السابعة بيقول لي if ال K bar if ال K bar is a
+
+186
+00:19:46,000 --> 00:19:55,620
+subgroup من ال G bar then الـ Phi inverse of الـ K
+
+187
+00:19:55,620 --> 00:20:05,940
+bar اللي هو كل ال K اللي موجودة في G such that Phi
+
+188
+00:20:05,940 --> 00:20:16,410
+of K Phi of K موجودة في ال K bar ما لها هذه is a
+
+189
+00:20:16,410 --> 00:20:28,390
+subgroup of G يبقى هذه is a subgroup of G النقطة
+
+190
+00:20:28,390 --> 00:20:35,370
+الثامنة بقول لو كان ال K bar is a normal subgroup
+
+191
+00:20:35,370 --> 00:20:43,010
+if ال K bar is a normal subgroup من ال G bar then
+
+192
+00:20:45,860 --> 00:20:54,920
+then الـ Phi inverse of K bar هذه
+
+193
+00:20:54,920 --> 00:21:04,360
+كل العناصر K اللي موجودة في G بحيث ان Phi of K
+
+194
+00:21:04,360 --> 00:21:07,620
+موجود في K bar
+
+195
+00:21:24,440 --> 00:21:31,720
+النقطة التاسعة والأخيرة بقول لو كانت الفاي is onto
+
+196
+00:21:31,720 --> 00:21:39,240
+f الفاي is onto لو كانت الـphi صندوق الـ and
+
+197
+00:21:39,240 --> 00:21:42,260
+الكيرنل
+
+198
+00:21:42,260 --> 00:21:49,120
+للـphi بده يساوي الـ identity element تبع الـG
+
+199
+00:22:03,460 --> 00:22:14,140
+من اين الى اين من جيه لجيه بار من جيه
+
+200
+00:22:14,140 --> 00:22:16,980
+لجيه بار
+
+201
+00:22:41,150 --> 00:22:48,850
+Nigel will prove the
+
+202
+00:22:48,850 --> 00:23:02,990
+parts الواحد واتنين and تلاتة are identical
+
+203
+00:23:02,990 --> 00:23:05,510
+to
+
+204
+00:23:07,260 --> 00:23:17,740
+are identical to the probes of أربعة
+
+205
+00:23:17,740 --> 00:23:27,640
+واتنين and واحد of
+
+206
+00:23:27,640 --> 00:23:40,060
+theorem of theorem ستة تلاتة بصفحات
+
+207
+00:23:40,060 --> 00:23:44,540
+مية وسبعة وعشرين respectively
+
+208
+00:24:12,850 --> 00:24:16,630
+نرجع ثاني للنظرية اللي احنا كاتبينها نحاول نقرأها
+
+209
+00:24:16,630 --> 00:24:21,250
+كمان مرة نتفهم كل ما فيها بعد هيك بنروح إلى
+
+210
+00:24:21,250 --> 00:24:26,610
+البرهان المرة اللي فاتت النظرية اللي فاتت كانت
+
+211
+00:24:26,610 --> 00:24:29,610
+بيشتغل على ال elements homomorphism على ال
+
+212
+00:24:29,610 --> 00:24:34,010
+elements هنا ال subgroups under ال homomorphism
+
+213
+00:24:34,010 --> 00:24:36,970
+يجيب جال ال homomorphism يشتغل عالميا على ال
+
+214
+00:24:36,970 --> 00:24:41,500
+subgroups وليس على ال elements مقول لو كانت فاي من
+
+215
+00:24:41,500 --> 00:24:46,180
+جي إلى جي بار هي hemomorphism وكانت ال H subgroup
+
+216
+00:24:46,180 --> 00:24:52,620
+من جي then فاي of H، H هذه sub set من مين أو
+
+217
+00:24:52,620 --> 00:24:56,260
+subgroup من جي إذا صورتها إذا كنت أريد أن تكون
+
+218
+00:24:56,260 --> 00:25:02,380
+موجودة في جي بار في جي بار في جي بار في جي بار في
+
+219
+00:25:02,380 --> 00:25:06,980
+جي بار في جي بار في جي بار في جي بار في جي بار في
+
+220
+00:25:06,980 --> 00:25:13,870
+جي بار من الجيل المقابل يبقى ال subgroup صورتها
+
+221
+00:25:13,870 --> 00:25:18,130
+subgroup أخرى تحت تأثير ال homomorphism الناحية
+
+222
+00:25:18,130 --> 00:25:22,650
+الثانية لو كانت هذه ال subgroup cyclic يبقى صورتها
+
+223
+00:25:22,650 --> 00:25:27,570
+كمان cyclic يعني ليست فقط subgroup و كذلك cycle
+
+224
+00:25:27,570 --> 00:25:32,530
+group طب لو كانت ال H abelian يبقى صورتها كذلك ما
+
+225
+00:25:32,530 --> 00:25:37,520
+لها abelian group هذول واحد واتنين وتلاتة برهنهم
+
+226
+00:25:37,520 --> 00:25:43,680
+قبل هيك في النظرية اللي في صفحة 127 نظرية 6 3 لذلك
+
+227
+00:25:43,680 --> 00:25:48,000
+النقطة الأولى مكافئة هي نفس النقطة 4 في النظرية
+
+228
+00:25:48,000 --> 00:25:53,670
+النقطة 2 هي 2 النقطة 3 هي نقطة 1 لو رجعنا لهذه
+
+229
+00:25:53,670 --> 00:25:57,530
+النظرية في صحفة 127 من الكتاب نجد التلاتة اللي
+
+230
+00:25:57,530 --> 00:26:01,410
+عندنا هذا نجي للربع الرابع بيقول لو كانت ال H
+
+231
+00:26:01,410 --> 00:26:06,990
+normal subgroup يجي صورتها normal في صورة ال G
+
+232
+00:26:06,990 --> 00:26:12,810
+كلها لأن ال Phi of G ليس بالضرورة أن تغطي كل
+
+233
+00:26:12,810 --> 00:26:17,730
+عناصر G برشوية منهم وممكن تغطيهم كلهم سيان سواء
+
+234
+00:26:17,730 --> 00:26:21,840
+كان لكن احنا in general بيقول لأ طيب يبقى لو كانت
+
+235
+00:26:21,840 --> 00:26:27,620
+هذه normal صورتها normal في صورة G طب لو كان ال
+
+236
+00:26:27,620 --> 00:26:33,200
+kernel في N من العناصر ال order له يساوي N يبقى ال
+
+237
+00:26:33,200 --> 00:26:35,300
+N هدول بدهم يروحوا لوين؟
+
+238
+00:26:37,710 --> 00:26:42,050
+لوين؟ للـ identity ممتاز جدا يبقى آثار ال
+
+239
+00:26:42,050 --> 00:26:47,010
+homomorphism N to 1 التلاتة أو الأربعة أو العشرة
+
+240
+00:26:47,010 --> 00:26:50,490
+راحوا العنصر واحد يبقى بقول عشرة to one مش one to
+
+241
+00:26:50,490 --> 00:26:54,950
+one بقول الأربعة to one أو الخمسة to one أو الستة
+
+242
+00:26:54,950 --> 00:26:59,950
+جدما يكون ال order one to one mapping من ال G on
+
+243
+00:26:59,950 --> 00:27:04,840
+two انتوا هادي دي بالك مش هنقول انتوا انه وخلاص
+
+244
+00:27:04,840 --> 00:27:09,280
+وننسى لابد تغطي جميع عناصر five of G وهذا اللي
+
+245
+00:27:09,280 --> 00:27:12,540
+مطلوب مش روح نبره ان هدى وننسى هدى لأ لأ لأ هدول
+
+246
+00:27:12,540 --> 00:27:18,020
+نقطتين وليست نقطة واحدة السادسة لو كان ال order ل
+
+247
+00:27:18,020 --> 00:27:23,620
+in بده يساوي ال H يبقى ال order للصورة بده يقسم ال
+
+248
+00:27:23,620 --> 00:27:28,640
+order تبع من؟ تبع ال H أظن حلينا مثال شبيه بوا قبل
+
+249
+00:27:28,640 --> 00:27:36,540
+شوية الآن لو كانت كيابار subgroup من جيبار يبقى
+
+250
+00:27:36,540 --> 00:27:40,780
+صورتها subgroup ولو كانت هذه ال subgroup normal 
+
+251
+00:27:40,780 --> 00:27:46,400
+يبقى صورتها normal اتنين هذول بنقدر ندمجهم بـ band
+
+252
+00:27:46,400 --> 00:27:47,060
+واحد
+
+253
+00:28:06,500 --> 00:28:12,150
+النقطة الأخيرة لو كانت Phi is onto والـ Kernel
+
+254
+00:28:12,150 --> 00:28:15,930
+مافيش فيه إلا الـ Identity Element يبقى الـ Phi
+
+255
+00:28:15,930 --> 00:28:20,970
+عبارة عن إيش؟ Isomorphism طب هي أعطاني Phi أنتم
+
+256
+00:28:20,970 --> 00:28:25,710
+و أعطاني هنا Phi همومورفزم بقى عليه باسمين يعني لو
+
+257
+00:28:25,710 --> 00:28:29,470
+أثبتت أن Phi one to one بيكون خلصنا من الموضوع
+
+258
+00:28:29,470 --> 00:28:33,910
+بيكون خلاص انتهينا منه يبقى بس مطلوب أثبت أن Phi
+
+259
+00:28:33,910 --> 00:28:38,240
+one to one طيب نيجي للبرهان يبقى أول ثلاث نقاط
+
+260
+00:28:38,240 --> 00:28:42,260
+تفاجئنا عليهم نيجي للرابعة الرابعة H Normal بدي أثبت
+
+261
+00:28:42,260 --> 00:28:46,760
+أن الـ Phi of H هذي إيه اللي همالها normal
+
+262
+00:28:46,760 --> 00:28:51,700
+subgroup من main من الـ Phi of G لذلك بدي أروح
+
+263
+00:28:51,700 --> 00:28:57,080
+أخدلي element في H و أخد element من G و أشوف لوين
+
+264
+00:28:57,080 --> 00:29:03,160
+بده يوصل هالدنيا هذه يبقى باجي بقوله هنا لو أخدنا
+
+265
+00:29:03,160 --> 00:29:15,050
+الـ G موجود في G و أخدنا الـ H موجود في H then إيش
+
+266
+00:29:15,050 --> 00:29:18,710
+شرايك في الـ GHG inverse؟
+
+267
+00:29:22,660 --> 00:29:29,260
+بينتمي لمين؟ أيوة يبقى هذا belongs to H السبب
+
+268
+00:29:29,260 --> 00:29:35,860
+because أن الـ H is a normal subgroup من G طب احنا
+
+269
+00:29:35,860 --> 00:29:40,260
+لما نتكلم على Phiات يبقى نبدأ ناخد الـ Phiات هنا يبقى
+
+270
+00:29:40,260 --> 00:29:47,560
+لو روحت أخدت الـ phi of GHG inverse هيكون موجود في
+
+271
+00:29:47,560 --> 00:29:55,310
+الـ phi of H طب الـ Phi homomorphism يبقى بدي أفك
+
+272
+00:29:55,310 --> 00:30:04,710
+هدول يبقاش بصير أن ها Phi of G Phi of H Phi of G
+
+273
+00:30:04,710 --> 00:30:14,450
+inverse هذا موجود في مين؟ في الـ Phi of H طيب، ألسا
+
+274
+00:30:14,450 --> 00:30:23,910
+هذا Phi of G Phi of H Phi of G لكل Inverse موجود
+
+275
+00:30:23,910 --> 00:30:30,950
+في Phi of H تعالوا نشوف تعالوا نشوف هذا وين موجود يا
+
+276
+00:30:30,950 --> 00:30:37,790
+شباب؟ في الـ Phi of G يبقى هذا belongs to Phi of G
+
+277
+00:30:37,790 --> 00:30:46,670
+طيب هذا Phi of H belongs to Phi of H هذا بـ belongs
+
+278
+00:30:46,670 --> 00:30:54,540
+to Phi of G صح؟ طيب ممتاز جدا يبقى الآن أنا هاي
+
+279
+00:30:54,540 --> 00:30:59,000
+اللي بدفتها الـ normality يبقى أخدت element من هنا
+
+280
+00:30:59,000 --> 00:31:03,220
+و element من هنا ضربت الـ element من هنا في الـ
+
+281
+00:31:03,220 --> 00:31:07,180
+element من هنا في معكوس هذا الـ element لجته موجود
+
+282
+00:31:07,180 --> 00:31:12,760
+في Phi H يبقى إيش تفتيرك لهذا الكلام أن Phi H is
+
+283
+00:31:12,760 --> 00:31:18,830
+normal يبقى هذا بده يعطينا الـ Phi of H is a normal
+
+284
+00:31:18,830 --> 00:31:24,670
+subgroup من من الـ Phi of G طبعا رب واحد فيكم قاعد
+
+285
+00:31:24,670 --> 00:31:28,910
+بيفكر هيك و قال لي طب استنى شوية أنت جبت نص البرهان
+
+286
+00:31:28,910 --> 00:31:32,890
+و أين النص الثاني بقوله إيش النص الثاني قال لي الـ
+
+287
+00:31:32,890 --> 00:31:36,070
+Phi of H is a subgroup بقوله اه ما هي هو عندك رقم
+
+288
+00:31:36,070 --> 00:31:40,110
+واحد هذا مطلوب، هيبقى باعتباره مثبت، هيبقى مثبت
+
+289
+00:31:40,110 --> 00:31:45,790
+معاك وإن لم يكن مثبتًا، لأثبتناه أولًا، ثم أثبتنا
+
+290
+00:31:45,790 --> 00:31:50,430
+مين؟ الـ Normality يبقى هي الكلام صحيح، هذا النقطة
+
+291
+00:31:50,430 --> 00:31:55,370
+أربعة بدنا نروح للنقطة رقم خمسة النقطة رقم خمسة
+
+292
+00:31:55,370 --> 00:31:58,770
+بتقول لي لو كان assume
+
+293
+00:32:23,000 --> 00:32:24,960
+إذا أردت أن أردت أن أردت أن أردت أن أردت أن أردت
+
+294
+00:32:24,960 --> 00:32:25,500
+أن أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+295
+00:32:25,500 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+296
+00:32:25,840 --> 00:32:30,720
+أردت أن أردت أن الـ Kernel لـ Phi يجب أن يساوي،
+
+297
+00:32:30,720 --> 00:32:34,320
+يجب أن أضع فيه N من العناصر، أظن أن الـ Identity
+
+298
+00:32:34,320 --> 00:32:41,520
+تبع الـ G منهم يبقى G منهم، ويجب أن أقول G1 و G2
+
+299
+00:32:41,520 --> 00:32:43,280
+ويبقى مازالة مازالة مازالة مازالة مازالة مازالة
+
+300
+00:32:43,280 --> 00:32:43,920
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+301
+00:32:43,920 --> 00:32:48,960
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+302
+00:32:48,960 --> 00:32:49,280
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+303
+00:32:49,280 --> 00:32:49,320
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+304
+00:32:49,320 --> 00:32:53,270
+مازالة مازالة مازالة مازاليبقى let الكلام then هذا
+
+305
+00:32:53,270 --> 00:32:59,450
+إيش معناه؟ معناه أن الـ Phi of الـ identity element
+
+306
+00:32:59,450 --> 00:33:03,510
+تبع الـ G بده يساوي الـ identity element تبع الـ G
+
+307
+00:33:03,510 --> 00:33:09,430
+bar والـ Phi of G1 بده يساوي الـ identity element
+
+308
+00:33:09,430 --> 00:33:15,110
+تبع الـ G bar والـ Phi of G2 بده يساوي الـ identity
+
+309
+00:33:15,110 --> 00:33:20,820
+element تبع الـ G bar والـ Phi of G N minus الـ one
+
+310
+00:33:20,820 --> 00:33:26,600
+بده يساوي الـ identity تبع الـ G bar يبقى أنا صار
+
+311
+00:33:26,600 --> 00:33:30,980
+عندي N من العناصر لهم صورة واحدة يبقى الـ Phi is
+
+312
+00:33:30,980 --> 00:33:41,960
+into one يبقى هذا this means that أن الـ Phi is
+
+313
+00:33:41,960 --> 00:33:45,440
+into one
+
+314
+00:33:52,040 --> 00:34:02,440
+يبقى هايات مثلا من G لـ G من from G to G bar ولم
+
+315
+00:34:02,440 --> 00:34:09,970
+أقول unto G bar يبقى دي قصة الـ onto هذه بدها
+
+316
+00:34:09,970 --> 00:34:15,270
+إثبات يبقى بدأ أروح أخد element في Phi of G و
+
+317
+00:34:15,270 --> 00:34:24,870
+أثبت أنه له أصل وين في G طيب كويس اه مش بدنا نثبت
+
+318
+00:34:24,870 --> 00:34:30,760
+أنها onto لـ G bar لأ في of G هي من عناصر G bar
+
+319
+00:34:30,760 --> 00:34:35,380
+جزء منها لكن هل تسويها أو لا تسويها قد يكون و قد
+
+320
+00:34:35,380 --> 00:34:41,120
+لا يكون يعني يا شباب لو اتخيلنا أن هذه كلها هي G
+
+321
+00:34:41,120 --> 00:34:49,500
+bar و أنا عندي Phi من الـ G من الـ G إلى الـ G bar يمكن
+
+322
+00:34:49,500 --> 00:34:57,460
+هدول هذا كله يطلع هو Phi of G لكن هذا هنا مافيش ولا
+
+323
+00:34:57,460 --> 00:35:04,100
+عنصر تمام يبقى جزء بقول لذلك أنا مركز على Phi of G
+
+324
+00:35:04,100 --> 00:35:10,160
+on to Phi of G يعني كل element في هذه الـ set بدي
+
+325
+00:35:10,160 --> 00:35:15,580
+أثبت أنه له أصل وين في G كويس لذلك مضاجي أقوله
+
+326
+00:35:15,580 --> 00:35:25,360
+خدلي y الآن بدي أثبت له أن فاي is onto يبقى بداجة
+
+327
+00:35:25,360 --> 00:35:34,880
+أقوله let مثلا y belongs to فاي of g فاي of كابتل
+
+328
+00:35:34,880 --> 00:35:44,120
+G تمام؟ then الـ y هذه بدها تساوي فاي of g for some
+
+329
+00:35:44,120 --> 00:35:52,310
+g اللي موجودة في G مصبوط هيك يبقى أنا أخدت element
+
+330
+00:35:52,310 --> 00:35:56,610
+في الصورة و روحت أخدت element من هنا يبقى الـ five
+
+331
+00:35:56,610 --> 00:36:02,890
+ده سواء five of g for some أيوة طيب أنا بدي إيش الـ
+
+332
+00:36:02,890 --> 00:36:07,490
+element اللي أخدته في الـ five of g بدي أثبت أنه له
+
+333
+00:36:07,490 --> 00:36:13,810
+أصل في g أو له أصول ممكن يكون أصول مش أصل ممكن يكون
+
+334
+00:36:13,810 --> 00:36:20,230
+كتار أنتم أثبتنا أن أنتم يبقى أصول وليس أصل تمام
+
+335
+00:36:20,230 --> 00:36:29,110
+يبقى الـ Phi inverse يبقى بناء على لو أخدت الـ Phi inverse
+
+336
+00:36:29,110 --> 00:36:35,230
+of Y يبقى الـ Phi inverse of Y عشان بده يساوي G في الـ
+
+337
+00:36:35,230 --> 00:36:40,450
+Kernel ها دي ربالك يبقى هذا بده يساوي الـ Phi
+
+338
+00:36:40,450 --> 00:36:46,970
+inverse of Y بده يساوي الـ G في الـ Kernel لمين؟ في
+
+339
+00:36:46,970 --> 00:36:52,490
+الـ Kernel للـ Phi معناه هذا الكلام أنه طبعا Phi
+
+340
+00:36:52,490 --> 00:36:57,850
+inverse of Y مش عنصر واحد لو بدي أشتغل حرفي لو
+
+341
+00:36:57,850 --> 00:37:02,830
+بقول عنصر واحد لكن هذه عناصر وبالتالي كثير من
+
+342
+00:37:02,830 --> 00:37:08,390
+العناصر اللي هو الـ Y هذه قد يكون هو صورتها فبجي
+
+343
+00:37:08,390 --> 00:37:15,650
+بقوله يبقى الـ order للـ Phi inverse of Y بده يساوي
+
+344
+00:37:15,650 --> 00:37:22,990
+الـ order للـ G في الـ kernel للـ Phi. مظبوط ولا لا؟
+
+345
+00:37:22,990 --> 00:37:29,150
+طب إيش العلاقة؟ الآن هذا ليس left coset G في
+
+346
+00:37:29,150 --> 00:37:33,350
+الـ Kernel الـ Phi مش left coset صح ولا لا؟ طب إذا الـ
+
+347
+00:37:33,350 --> 00:37:37,990
+order إيه اللي هيساوي الـ order لـ الـ subgroup نفسه
+
+348
+00:37:37,990 --> 00:37:43,090
+يبقى هذا الكلام بدي يساوي الـ order للـ Kernel الـ Phi
+
+349
+00:37:43,090 --> 00:37:49,190
+اللي هو جداش الـ N يعني معنى هذا الكلام إن الـ Y
+
+350
+00:37:49,190 --> 00:37:55,770
+اللي عندي أخدت هذه لجتلها أصول عددهم N تمام يبقى
+
+351
+00:37:55,770 --> 00:38:04,900
+on to يبقى this means that .. يبقى this means that
+
+352
+00:38:04,900 --> 00:38:08,240
+أن
+
+353
+00:38:08,240 --> 00:38:16,600
+الـ Phi maps in elements from
+
+354
+00:38:18,360 --> 00:38:26,080
+G to Y اللي موجود وين في G bar أو موجود في Phi
+
+355
+00:38:26,080 --> 00:38:37,560
+of G بالتحديد موجود في Phi of G so Phi is onto طيب،
+
+356
+00:38:37,560 --> 00:38:43,320
+هذه النقطة إيه؟ النقطة الخامسة اللي خاطر مدام حلنا
+
+357
+00:38:43,320 --> 00:38:48,680
+زيها يبقى النقطة السادسة هذه أقول لكم exercise طبعا
+
+358
+00:38:48,680 --> 00:38:52,780
+مبرهنة في الكتاب، بس بعمل restriction على الـ Phi
+
+359
+00:38:52,780 --> 00:38:56,700
+يعني بيخليهاش على إطلاقها، بس على عناصر إيش، يبقى
+
+360
+00:38:56,700 --> 00:39:02,300
+يا ريت من الكتاب تروح تجرها وترتب أمورها الآن كي
+
+361
+00:39:02,300 --> 00:39:07,660
+بار سابق روب من G bar يبقى Phi inverse of K بده
+
+362
+00:39:07,660 --> 00:39:12,780
+أثبتها سابق روب من مين؟ من الـ G طيب مشان أثبتها
+
+363
+00:39:12,780 --> 00:39:18,600
+السابق روب بده أثبته conditions يبقى بدي أروح لمين؟
+
+364
+00:39:18,600 --> 00:39:24,620
+للنقطة السابعة مشان أروح للنقطة السابعة بدي أثبت
+
+365
+00:39:24,620 --> 00:39:31,160
+هذه Phi inverse subgroup من مين؟ من الـ G هذا اللي
+
+366
+00:39:31,160 --> 00:39:35,460
+عايزيني أثبته مشان هيك بدي أثبت له أن هذه non-empty
+
+367
+00:39:35,460 --> 00:39:39,000
+و لو أخدت عنصرين منها بدي أثبت أن الأول في معكوس الثاني موجود فيها وبالتالي بيصير a subgroup
+
+368
+00:39:39,000 --> 00:39:43,020
+وبالتالي بيصير a subgroup
+
+369
+00:39:45,060 --> 00:39:52,840
+يبقى بضاجي أقول له assume أفترض أن الـ K bar هي
+
+370
+00:39:52,840 --> 00:40:01,600
+عبارة عن subgroup من الـ G bar يبقى
+
+371
+00:40:01,600 --> 00:40:10,020
+هذه subgroup من الـ G bar then الـ Phi inverse of K
+
+372
+00:40:10,020 --> 00:40:14,180
+bar is non-empty
+
+373
+00:40:20,320 --> 00:40:25,200
+الـ Phi of الـ Identity تبع الـ G بده يعطيني مين
+
+374
+00:40:25,200 --> 00:40:33,300
+الـ Identity تبع من؟ تبع الـ G bar يعني إيش؟ هذا
+
+375
+00:40:33,300 --> 00:40:43,430
+بده يعطيك أن الـ Phi Inverse of الـ Identity تبع 
+
+376
+00:40:43,430 --> 00:40:48,190
+الـ G Bar بدي أسوي الـ Identity Element تبع الـ G
+
+377
+00:40:48,190 --> 00:40:55,030
+مظبوط؟ يبقى معنا هذا الكلام إن الـ Identity تبع
+
+378
+00:40:55,030 --> 00:41:02,830
+الـ G موجود في الـ Phi Inverse of الـ K Bar بعد
+
+379
+00:41:02,830 --> 00:41:10,120
+هيك بتروح أخد two elements الـ X و الـ Y موجودة في
+
+380
+00:41:10,120 --> 00:41:18,780
+الـ Phi inverse of الـ K bar معنى هذا الكلام أن
+
+381
+00:41:18,780 --> 00:41:28,520
+الـ X بده يساوي Phi inverse of K1 مثلا و الـ Y بده 
+
+382
+00:41:28,520 --> 00:41:32,800
+يساوي Phi inverse of K2
+
+383
+00:41:36,280 --> 00:41:42,310
+كويس يبقى بدي أروح أخد الـ X Y inverse أشوف هل
+
+384
+00:41:42,310 --> 00:41:45,930
+موجودة هنا ولا لأ إذا طلعت موجودة بيكون كفى الله
+
+385
+00:41:45,930 --> 00:41:53,370
+المؤمنين يبقى بدي أروح أخد له الـ X Y inverse يبقى
+
+386
+00:41:53,370 --> 00:41:59,190
+أو الـ Phi خلّي 
+
+387
+00:41:59,190 --> 00:42:03,610
+أشوف الـ X Y inverse يبقى الـ X اللي عبارة عن Phi
+
+388
+00:42:03,610 --> 00:42:12,100
+inverse of الكوانفي الـ Phi inverse of K2 لكل
+
+389
+00:42:12,100 --> 00:42:25,400
+inverse يبقى هذا الكلام بده يساوي هذا
+
+390
+00:42:25,400 --> 00:42:31,900
+الكلام بده يساوي Phi inverse of K1 في Phi inverse
+
+391
+00:42:31,900 --> 00:42:40,870
+of K2 inverse هذا الكلام بده يساوي في انفرس of K1
+
+392
+00:42:40,870 --> 00:42:49,640
+K2 انفرس هذا كله مين؟ اللي هو الـ X Y inverse هل
+
+393
+00:42:49,640 --> 00:43:00,080
+هذا الآن موجود في الـ Phi inverse of K bar؟ ليش؟
+
+394
+00:43:00,080 --> 00:43:04,740
+لأن هدول حاصل ضربهم موجود في K bar لأن أول ما جينا
+
+395
+00:43:04,740 --> 00:43:09,220
+كنا K bar ما لها subgroup من G بقى closed under
+
+396
+00:43:09,220 --> 00:43:13,480
+multiplication يبقى هذا موجود في الـPhi inverse of
+
+397
+00:43:13,480 --> 00:43:22,060
+K bar يبقى بناء عليه الـPhi inverse of K bar is a 
+
+398
+00:43:22,060 --> 00:43:27,160
+subgroup من جيه؟ من G وانتهينا منها بدنا نروح
+
+399
+00:43:27,160 --> 00:43:36,840
+للنقطة اللي بعدها وهي خاصية ال normality أيوة عرف
+
+400
+00:43:36,840 --> 00:43:42,730
+لو ماكنتش homomorphism أمرها ما بيصير كلامها ده
+
+401
+00:43:42,730 --> 00:43:51,470
+صحيح وحسب
+
+402
+00:43:51,470 --> 00:43:55,670
+التعريف اللي عندك حسب التعريف يعني عرفنا الـPhi
+
+403
+00:43:55,670 --> 00:44:00,210
+Inverse وين عرفناه والله مسحنا.. مسحنا.. لا
+
+404
+00:44:00,210 --> 00:44:04,230
+أيوة أيوة كل الـK اللي موجودة في جبهات الـPhi of K
+
+405
+00:44:04,230 --> 00:44:07,670
+موجودة وين؟ في الـK bar أيوة
+
+406
+00:44:14,620 --> 00:44:30,300
+تاني تاني سؤالك سطر التاني هنا لفوق اه اه
+
+407
+00:44:30,300 --> 00:44:37,200
+هذا يا ابني أنا بقول يساوي ال identity تبع ال جي
+
+408
+00:44:37,200 --> 00:44:42,220
+بار اثر على الطرفين بالفاي انفرس لا مانعثرنا بفعل
+
+409
+00:44:42,220 --> 00:44:46,900
+مش هتاطنين ال identity يعني اللي هو .. هذا لو كنت
+
+410
+00:44:46,900 --> 00:44:51,000
+أريد مورفزم، عنصر واحد. أنا بهمني العنصر، بدي أجيب
+
+411
+00:44:51,000 --> 00:44:55,000
+عنصر، بديش أجيب كثير، بكفيني منك عنصر، هذا همشي أن
+
+412
+00:44:55,000 --> 00:45:02,260
+أثبت أنها non-empty، تمام؟ طيب، أنا إلي وجهة نظر
+
+413
+00:45:02,260 --> 00:45:07,980
+أخرى، إلي وجهة نظر أخرى في هذا الكلام، يعني لو
+
+414
+00:45:07,980 --> 00:45:12,820
+بدنا نشك في هذا هل هو homomorphism ولا لا، بنقدر
+
+415
+00:45:12,820 --> 00:45:18,450
+نقول الخطوة هذه استني شوية، الحين لو جيت هنا فاي of
+
+416
+00:45:18,450 --> 00:45:26,950
+ال X Y inverse أليست هي فاي لفاي inverse of K1 K2
+
+417
+00:45:26,950 --> 00:45:35,530
+inverse صح ولا لا أثر هنا بفاي و أثر هنا بفاي يبقى
+
+418
+00:45:35,530 --> 00:45:40,250
+النتيجة
+
+419
+00:45:40,250 --> 00:45:47,640
+K1 K2 Inverse اللي موجودة في الـK bar صح ولا لا
+
+420
+00:45:47,640 --> 00:45:55,440
+يبقى صار عندك اللي هو ال X Y inverse موجودة ال X Y
+
+421
+00:45:55,440 --> 00:46:05,560
+inverse بدها تساوي اللي بدها تساوي أو هذه مو ..
+
+422
+00:46:05,560 --> 00:46:11,190
+استني شوية بدي ألغي هذه ألغيتها بمين أثرت عليها فهي
+
+423
+00:46:11,190 --> 00:46:16,070
+أصبحت X Y inverse بدي أجيبها هنا يبقى بدها تساوي
+
+424
+00:46:16,070 --> 00:46:24,030
+الـ Phi of الـ K واحد K اتنين inverse اللي هي هذه
+
+425
+00:46:24,030 --> 00:46:32,490
+موجودة في المين في ال Phi of Phi of K وPhi of K
+
+426
+00:46:32,490 --> 00:46:43,590
+Phi of K لأ احنا احنا خليك معايا احنا خليك .. هاي
+
+427
+00:46:43,590 --> 00:46:49,270
+اللي وصلنا X Y inverse بده يساوي في انفرست ل K1 K2
+
+428
+00:46:49,270 --> 00:46:53,830
+بده اثر هنا بفي و اثر هنا بفي هاي اثرنا بفي و
+
+429
+00:46:53,830 --> 00:46:59,390
+اثرنا هنا بفي هذه هتلغي التانية بصير اللي هو X Y
+
+430
+00:46:59,390 --> 00:47:06,100
+inverse بده يساوي في of K1 K2 inverse تمام؟ يبقى
+
+431
+00:47:06,100 --> 00:47:20,100
+هذه موجودة في Phi of K و Phi of K لحظة
+
+432
+00:47:20,100 --> 00:47:25,880
+شوية عندك اعتراض على هذه العبارة؟ الخطوة اللي بعدها
+
+433
+00:47:25,880 --> 00:47:31,680
+تمام أنا جيت اثره بفاي على XY inverse طب هدى تساوي
+
+434
+00:47:31,680 --> 00:47:35,460
+هدى مشينا لغاية هنا لو قلنا مش عارفين هي
+
+435
+00:47:35,460 --> 00:47:40,240
+homomorphism ولا لأ يبقى كان صار كل الشغل هدى مش
+
+436
+00:47:40,240 --> 00:47:45,350
+صحيح إذا هي homomorphism غصب على ما يرضى وإلا كان
+
+437
+00:47:45,350 --> 00:47:48,530
+هذا الكلام .. لقد قلت ال inverse صح لكن مصير هذا
+
+438
+00:47:48,530 --> 00:47:52,910
+الكلام صحيح ليس صحيحا إلا إذا كانت homomorphism
+
+439
+00:47:52,910 --> 00:48:00,130
+تمام؟ على .. أيوة ال homomorphism مش ضروري يكون
+
+440
+00:48:00,130 --> 00:48:04,010
+مدبن صحيح لما تجيب في انفص بطل افتران أصلا مصير
+
+441
+00:48:04,010 --> 00:48:08,490
+الواحد اللي عند الصور مظبوط مش متبطل اختراع أصلا مش
+
+442
+00:48:08,490 --> 00:48:12,350
+متبطل homomorphism متبطل اختراع معرف أصلا تصير
+
+443
+00:48:12,350 --> 00:48:15,470
+الصورة العنصر اللي هو أكثر من الصورة فكيف أنت
+
+444
+00:48:15,470 --> 00:48:18,130
+بتاخد اللي هو أكثر من الصورة العنصر اللي هو أكثر
+
+445
+00:48:18,130 --> 00:48:21,210
+من الصورة احنا بنحكي homomorphism وليس function
+
+446
+00:48:21,210 --> 00:48:27,050
+إذا قلنا function ماهو isomorphism function يعني
+
+447
+00:48:27,050 --> 00:48:30,230
+مية المية بس ال homomorphism قد يكون و قد لا يكون
+
+448
+00:48:31,440 --> 00:48:36,400
+أه قد يكون و قد لا يكون تمام طيب احنا هذه النقطة
+
+449
+00:48:36,400 --> 00:48:42,740
+رقم قداش هي سبعة النقطة هذه رقم سبعة رقم سبعة
+
+450
+00:48:42,740 --> 00:48:50,600
+ماشيين كله صح وهذه تمام واخدنا x y inverse و أثرنا
+
+451
+00:48:50,600 --> 00:48:55,180
+عليها بفاية و طلع ك واحد كتنين اللي موجودة في ك
+
+452
+00:48:55,180 --> 00:49:01,270
+مظبوط يبقى من هذا الكلام بنقدر نقول X Y inverse
+
+453
+00:49:01,270 --> 00:49:08,490
+موجودة في الـ Phi في ال Phi of K صحيح يبقى بنقول
+
+454
+00:49:08,490 --> 00:49:16,550
+هنا النقطة الأخيرة أن ال X Y inverse هذه موجودة في
+
+455
+00:49:16,550 --> 00:49:25,650
+ال Phi inverse في ال Phi inverse في ال Phi inverse
+
+456
+00:49:25,650 --> 00:49:31,360
+of K بار اللي فوق بالظبط تماما خلاص يبقى ليش يعيدها
+
+457
+00:49:31,360 --> 00:49:36,220
+هذي كلها مالاش نزول هي ال X Y انفرست موجودة في
+
+458
+00:49:36,220 --> 00:49:40,840
+الفاي انفرست هذا كله زيادة صوتنا هذه الخطوة زيادة
+
+459
+00:49:40,840 --> 00:49:45,660
+تمام يبقى موجودة في الـ Phi inverse of K bar يبقى
+
+460
+00:49:45,660 --> 00:49:50,920
+بناء اللي عليه Phi inverse of K bar is a subgroup
+
+461
+00:49:50,920 --> 00:49:59,100
+يبقى هنا Phi inverse of K bar is a subgroup من
+
+462
+00:49:59,100 --> 00:50:05,840
+مين؟ من ال G بدنا نيجي للنقطة الثامنة خلي بالك
+
+463
+00:50:05,840 --> 00:50:10,900
+معايا النقطة الثامنة اللي جبناها هذه الـ subgroup
+
+464
+00:50:10,900 --> 00:50:16,160
+من G بنا نثبت أنها normal بس بشرط أن ال K bar
+
+465
+00:50:16,160 --> 00:50:23,320
+normal من G يبقى باجي بقوله assume افترض أن ال K
+
+466
+00:50:23,320 --> 00:50:30,840
+bar is a normal subgroup من G bar بالدالي اثبت أن
+
+467
+00:50:30,840 --> 00:50:38,520
+الفاي
+
+468
+00:50:38,520 --> 00:50:49,580
+انفرس of K bar is a normal subgroup من من من ال G
+
+469
+00:50:50,950 --> 00:51:00,270
+كويس لذلك بدروع أخد let الجي موجودة في جي and ال X
+
+470
+00:51:00,270 --> 00:51:11,210
+موجود في الفاي انفرس of الكبار then الجي موجودة في
+
+471
+00:51:11,210 --> 00:51:20,950
+الجي و الـ X هذه بدها تساوي في انفرس في انفرس of K
+
+472
+00:51:20,950 --> 00:51:29,760
+على سبيل المثال يبقى هذا معناه أن جي موجود في جي
+
+473
+00:51:29,760 --> 00:51:37,360
+and فاي of اكس فاي of اكس بده يساوي كم؟ بده يساوي
+
+474
+00:51:37,360 --> 00:51:44,700
+كم طب لو أخدت الجي اكس جي انفرس مشان اثبات ال
+
+475
+00:51:44,700 --> 00:51:51,000
+normality واخد تأثير الـ Phi عليها يبقى هذا الكلام
+
+476
+00:51:51,000 --> 00:51:59,700
+بدل يساوي Phi of G Phi of X Phi of G inverse يبقى
+
+477
+00:51:59,700 --> 00:52:06,420
+هذا الكلام بدل يساوي Phi of G Phi of X اللي هي
+
+478
+00:52:06,420 --> 00:52:12,400
+main اللي هي اب K Phi of X اللي هي و ال K normal
+
+479
+00:52:12,400 --> 00:52:21,200
+اللي هو K و الـ Phi هذه of G لكل inverse بالشكل اللي
+
+480
+00:52:21,200 --> 00:52:28,620
+عندنا هنا تمام؟ الحين هذه موجودة في G وهذه موجودة
+
+481
+00:52:28,620 --> 00:52:36,240
+في الـPhi inverse of K وهذه موجودة في G أخدنا
+
+482
+00:52:36,240 --> 00:52:41,720
+تأثير الـPhi عليهم وطلع عندنا هذا الـElement وهذا
+
+483
+00:52:41,720 --> 00:52:49,100
+وهذا الـK bar أنا جال عليها normal يبقى لو أخدت
+
+484
+00:52:49,100 --> 00:52:56,580
+element من G bar هذا موجود في G bar وهذا موجود في
+
+485
+00:52:56,580 --> 00:53:04,000
+جي بار وهذا موجود في الفاي انفرس هذا موجود في
+
+486
+00:53:04,000 --> 00:53:10,460
+الفاي انفرس of K إذا هذا كله موجود في الفاي انفرس
+
+487
+00:53:10,460 --> 00:53:17,680
+of K بار بالشكل اللي عندنا K بار يبقى بناء عليه
+
+488
+00:53:17,680 --> 00:53:21,500
+الفاي
+
+489
+00:53:21,890 --> 00:53:30,270
+إنفرست من K بار هو عضو عام من جيه
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c.srt
new file mode 100644
index 0000000000000000000000000000000000000000..44797273c7e3d96c84f2cbcee597e557ac462576
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c.srt
@@ -0,0 +1,2127 @@
+1
+00:00:21,600 --> 00:00:25,960
+بسم الله الرحمن الرحيم عودة على بدء في الفترة
+
+2
+00:00:25,960 --> 00:00:31,280
+الصباحية أخذنا ثلاث نظريات اللي هو على ال
+
+3
+00:00:31,280 --> 00:00:35,260
+subgroups لأن الدرس الحديث على نفس الموضوع
+
+4
+00:00:35,910 --> 00:00:39,090
+النظرية اللي عندنا بتقول لي  g  مجموعة  وخد 
+
+5
+00:00:39,090 --> 00:00:44,710
+ل a أي عنصر موجود في g then the set  ال set
+
+6
+00:00:44,710 --> 00:00:49,350
+اللي هي مولدة ب a يبقى هذه بنسميها ال cycle
+
+7
+00:00:49,350 --> 00:00:54,620
+ك group مولدة ب a مين هي؟ بروح نعرفها لأن
+
+8
+00:00:54,620 --> 00:01:01,140
+العنصر a اللي موجود في g بس بدي أرفعه للأس n  و ال n
+
+9
+00:01:01,140 --> 00:01:09,220
+موجود في z  ال a هو عنصر ثابت لكن ال n عدد متغير أي
+
+10
+00:01:09,220 --> 00:01:13,940
+عدد من ذات سواء كان صفر أو موجب أو سالب يبقى الست
+
+11
+00:01:13,940 --> 00:01:18,020
+اللي عندنا بهذا الشكل بتبقى subgroup من g بدنا
+
+12
+00:01:18,020 --> 00:01:22,140
+نثبتها هذه ال subgroup بنسميه ال cyclic subgroup
+
+13
+00:01:22,140 --> 00:01:27,620
+مولدة ب a  يبقى هي مجموعة جزئية دورية مولدة
+
+14
+00:01:27,620 --> 00:01:31,480
+بالعنصر a  طبعا ال cyclic groups
+
+15
+00:01:31,480 --> 00:01:36,360
+الشطر الجاي كله ال cyclic groups من أوله إلى آخره
+
+16
+00:01:36,360 --> 00:01:41,220
+و النظريات و أمثلة وما إلى ذلك لكن إذا روح نثبت هذه
+
+17
+00:01:41,220 --> 00:01:45,720
+بقى أنا بدي أثبت نقطتين النقطة الأولى بدي أثبت إن
+
+18
+00:01:45,720 --> 00:01:52,360
+ال set هذه ليست خالية non-empty اثنين بدي أخد منها
+
+19
+00:01:52,360 --> 00:01:56,120
+two elements و أثبت إن الأول في معكوس الثاني موجود
+
+20
+00:01:56,120 --> 00:02:02,680
+فيها لذلك بجي بقول هنا ال subgroup generated by a is
+
+21
+00:02:02,680 --> 00:02:14,040
+non-empty بما أن الـ a to the power of 0 هي
+
+22
+00:02:14,040 --> 00:02:17,140
+على
+
+23
+00:02:17,140 --> 00:02:26,000
+الشكل a<sup>0</sup> و 0 موجود في z يبقى هذا موجود في a لذلك ال
+
+24
+00:02:26,000 --> 00:02:30,520
+subgroup generated by a is non empty النقطة
+
+25
+00:02:30,520 --> 00:02:37,020
+الثانية بدي أخد two elements يبقى let ال X و Y
+
+26
+00:02:37,020 --> 00:02:42,180
+موجودة في ال subgroup generated by A أو موجودة في
+
+27
+00:02:42,180 --> 00:02:48,620
+الست اللي هي مولدة ب A يبقى then ال X هذه
+
+28
+00:02:48,620 --> 00:02:54,740
+بدها تساوي A to the power N and ال Y تساوي A to
+
+29
+00:02:54,740 --> 00:03:01,740
+the power M الآن بدي أثبت إن الأول في معكوس الثاني
+
+30
+00:03:01,740 --> 00:03:08,500
+موجود في هذه الست مشان هيك بدي آخذ له consider
+
+31
+00:03:08,500 --> 00:03:16,460
+آخذ لي XY inverse يبقى بناء عليه هذا بدي يساوي ال A<sup>N</sup>
+
+32
+00:03:16,460 --> 00:03:23,110
+فال A<sup>M</sup> inverse من معلوماتنا السابقة في ال chapter
+
+33
+00:03:23,110 --> 00:03:29,810
+الأول في ال groups هذا بدي يعطينا a<sup>m</sup> a<sup>-m</sup>
+
+34
+00:03:29,810 --> 00:03:40,130
+أو إنشاءتهم فقولوا a<sup>n-m</sup> الآن هذا موجود
+
+35
+00:03:40,130 --> 00:03:49,510
+في ال group generated by a بسبب إن ال M أو ال N
+
+36
+00:03:49,510 --> 00:03:55,710
+ناقص ال M هو integer موجود في ال Z إذا صار ال
+
+37
+00:03:55,710 --> 00:04:00,530
+identity element موجود هنا أخذت عنصرين موجودات في
+
+38
+00:04:00,530 --> 00:04:03,370
+ال group generated by A اللي جت الأول في معكوس
+
+39
+00:04:03,370 --> 00:04:09,350
+الثاني موجود فيها يبقى by a previous
+
+40
+00:04:12,500 --> 00:04:19,180
+theorem بنظرية سابقة اللي هو ال group generated by
+
+41
+00:04:19,180 --> 00:04:27,020
+a is a subgroup يبقى هذه ال subgroup و بقول هذه
+
+42
+00:04:27,020 --> 00:04:33,160
+مولدة بالعنصر a يعني ال a بيجيب كل العناصر بتبعته
+
+43
+00:04:33,160 --> 00:04:35,800
+remarks
+
+44
+00:04:41,190 --> 00:04:49,050
+النقطة الأولى لو كانت ال G كلها بدأ تساوي ال
+
+45
+00:04:49,050 --> 00:04:59,630
+subgroup generated by A نقول إن ال
+
+46
+00:04:59,630 --> 00:05:10,490
+G is cyclic ال G is cyclic and the element
+
+47
+00:05:15,070 --> 00:05:26,150
+and the element a is a generator for اللي هو ال
+
+48
+00:05:26,150 --> 00:05:32,330
+group g النقطة
+
+49
+00:05:32,330 --> 00:05:40,130
+الثانية النقطة
+
+50
+00:05:40,130 --> 00:05:42,250
+الثانية every
+
+51
+00:05:45,790 --> 00:05:53,190
+cyclic group is
+
+52
+00:05:53,190 --> 00:06:00,070
+abelian روح
+
+53
+00:06:00,070 --> 00:06:10,110
+ندب صحة هذا الكلام ال
+
+54
+00:06:10,110 --> 00:06:15,780
+remark اللي عنها عبارة عن نقطتين النقطة الأولى بقول
+
+55
+00:06:15,780 --> 00:06:22,180
+لو كانت ال G هي ال subgroup generated by A يعني
+
+56
+00:06:22,180 --> 00:06:26,300
+عناصر هنا لو جيت دورت عليهم فكتهم بدهم يطلعوا
+
+57
+00:06:26,300 --> 00:06:32,720
+عناصر G الأصلية بروح نقول ال G is cyclic يبقى ال
+
+58
+00:06:32,720 --> 00:06:38,040
+group G بقول عليها مجموعة دورية and element A وال A
+
+59
+00:06:38,040 --> 00:06:44,080
+بقول generator ل G يعني ال A مولد لمين ل G لما نقول
+
+60
+00:06:44,080 --> 00:06:49,280
+a مولد لجيه يعني هذا ال element a بيخلق لي جميع
+
+61
+00:06:49,280 --> 00:06:54,800
+عناصر ال group جيه كيف لو قلت a أس صفر a أس 
+
+62
+00:06:54,800 --> 00:07:00,000
+واحد a تربيع a تكعيب بده يجيب لي كل العناصر نتيجة
+
+63
+00:07:00,000 --> 00:07:04,680
+لهذه الأساس بدهم يجيب لي عناصر جيه كلها إن حدث ذلك
+
+64
+00:07:04,680 --> 00:07:09,660
+يبقى بقول ال G هذه Cyclic group يبقى هذا بناء
+
+65
+00:07:09,660 --> 00:07:16,040
+عليه هو تعريف ال Cyclic group generated by A يعني
+
+66
+00:07:16,040 --> 00:07:21,500
+المجموعة الدورية المولدة بالعنصر a؟ نقطة ثانية
+
+67
+00:07:21,500 --> 00:07:26,500
+بيقول أي cycling group أو every cycling group is
+
+68
+00:07:26,500 --> 00:07:31,460
+abelian طيب أنا الآن بدي أثبت صحة هذا الكلام عشان
+
+69
+00:07:31,460 --> 00:07:35,500
+أعتمد عليه بعد ذلك من حد ما يقول ال cycling group
+
+70
+00:07:35,500 --> 00:07:40,660
+بدي أفهم إنها abelian طيب هل العكس صحيح؟ العكس ليه
+
+71
+00:07:40,660 --> 00:07:46,010
+صحيح؟ قد تكون abelian وليست cycling وهكذا طيب لو
+
+72
+00:07:46,010 --> 00:07:55,250
+جيت الآن بدأت أقول له let ال g be a cyclic group
+
+73
+00:07:55,250 --> 00:08:08,630
+then ال g بدها تساوي ال subgroup generated by a for some a اللي موجود في g
+
+74
+00:08:11,870 --> 00:08:17,310
+مرة ثانية أنا مفترض إن جيه ال cyclic group يبقى
+
+75
+00:08:17,310 --> 00:08:21,430
+جيه اللي هي شكل معين ما هو هذا الشكل جيه اللي هي
+
+76
+00:08:21,430 --> 00:08:27,240
+ال subgroup generated by A طيب، إيش يعني؟ يعني
+
+77
+00:08:27,240 --> 00:08:33,900
+معناته إنه هلاقي عنصر على الأقل في G أو أكثر لكن
+
+78
+00:08:33,900 --> 00:08:39,960
+ما قلتش جميع العناصر فروحت قلت for some لبعض عناصر
+
+79
+00:08:39,960 --> 00:08:46,500
+G على أي حال بعد شوية هنثبت إنه على الأقل كل group
+
+80
+00:08:46,500 --> 00:08:52,080
+فيها two generators يعني مش كل عناصر لجروب بنفع
+
+81
+00:08:52,080 --> 00:08:56,620
+يكونوا generators البعض نعم والبعض لا تمام فإيش
+
+82
+00:08:56,620 --> 00:09:00,240
+بقى يجب أقول مدام فرضتها ال cyclic يبقى لازم ألاقي
+
+83
+00:09:00,240 --> 00:09:05,060
+element A موجود في G بحيث هذا ال element يجيب لمين
+
+84
+00:09:05,060 --> 00:09:11,770
+جميع عناصر G أنا الآن بدي أثبت إن هذي ال G is
+
+85
+00:09:11,770 --> 00:09:16,750
+abelian بمعنى لو أخذت عنصرين فيها بدي أثبت إن ال X
+
+86
+00:09:16,750 --> 00:09:23,630
+في Y يساوي ال Y في X يبقى باجي بقول له ال X و Y
+
+87
+00:09:23,630 --> 00:09:28,910
+موجودات في ال group generated by A طيب ال group
+
+88
+00:09:28,910 --> 00:09:35,690
+generated by a لها تعريف في التعريف إذا كل x هذا
+
+89
+00:09:35,690 --> 00:09:45,010
+then ال x يساوي معناته a مرفوعة ل integer يبقى هذا
+
+90
+00:09:45,010 --> 00:09:53,090
+بده يساوي a<sup>i</sup> مثلا and ال y بدها تساوي a<sup>j</sup>
+
+91
+00:09:55,520 --> 00:10:00,040
+لإيش؟ لأن ال subgroup هذا a مرفوع ل أس ال أس هذا
+
+92
+00:10:00,040 --> 00:10:05,520
+بدي يجينا مين؟ من z يعني integer كويس أنا شو بدي
+
+93
+00:10:05,520 --> 00:10:14,960
+أثبت؟ بدي أثبت إن ال x y inverse موجودة ال x y بدي
+
+94
+00:10:14,960 --> 00:10:23,390
+أساوي y x كويس then الآن بدي أقول لك خذ لي consider
+
+95
+00:10:23,390 --> 00:10:32,030
+ال X Y هشوف شو بده يساوي ال X هو a<sup>i</sup> تمام؟ طيب هو
+
+96
+00:10:32,030 --> 00:10:40,070
+هذا الكلام ال Y اللي هي a<sup>j</sup> هذا
+
+97
+00:10:40,070 --> 00:10:48,270
+الكلام يساوي a<sup>i+j</sup> هذا الكلام يساوي a أس
+
+98
+00:10:48,270 --> 00:10:53,870
+الله أعلم الآن ال I و ال J integers ولا لا؟ و J
+
+99
+00:10:53,870 --> 00:10:58,790
+مجموعة two integers ب Integer اثنين لما أقول I
+
+100
+00:10:58,790 --> 00:11:04,170
+زائد J و لا J زائد I في Integers بختلف الوضع؟ لأ
+
+101
+00:11:04,170 --> 00:11:11,640
+يبقى هذا الكلام بقدر أقول a<sup>j+i</sup> تمام؟ هذا
+
+102
+00:11:11,640 --> 00:11:21,840
+الكلام بقدر أقول a<sup>j</sup> a<sup>i</sup> برجع a<sup>j</sup> هو Y و a<sup>i</sup>
+
+103
+00:11:21,840 --> 00:11:30,360
+هو X يبقى صار ال X في Y يساوي Y في X لكل ال X و Y
+
+104
+00:11:30,360 --> 00:11:35,660
+اللي موجودة في ال group generated by A معناة ال
+
+105
+00:11:35,660 --> 00:11:41,630
+group هذه مالها؟ أبليان يبقى هنا sir ال group
+
+106
+00:11:41,630 --> 00:11:51,190
+generated by a is an abelian group يبقى من الآن
+
+107
+00:11:51,190 --> 00:11:54,830
+فصاعدا نستفيد من المعلومة لو كانت ال group cyclic
+
+108
+00:11:54,830 --> 00:12:01,410
+فهي abelian ناخذ الآن مجموعة من الأمثلة examples
+
+109
+00:12:01,410 --> 00:12:05,090
+أول
+
+110
+00:12:05,090 --> 00:12:15,140
+مثال بقول let ال G بده يساوي U<sub>10</sub> U<sub>10</sub>
+
+111
+00:12:15,140 --> 00:12:27,280
+عناصرها عارفينها اللي هي 1 و 3 و 7 و 9 خلي
+
+112
+00:12:27,280 --> 00:12:35,310
+بالكم عليها أحاول أن أجلب ال subgroup مختلفة لهذه
+
+113
+00:12:35,310 --> 00:12:41,670
+ال group الآن لو جبت ال subgroup generated by 1
+
+114
+00:12:41,670 --> 00:12:46,690
+من هو ال  ⟨1⟩ بالنسبة لل group هذا؟ ماهو بيطلع هذا؟
+
+115
+00:12:46,690 --> 00:12:51,850
+ال identity element ممتاز جدا يبقى لما أريد أن أضع
+
+116
+00:12:51,850 --> 00:12:55,470
+1 أس 1، 1 أس 2، 1 أس 0، 1 أس 
+
+117
+00:12:55,470 --> 00:12:59,520
+10، 1 أس 2، يبقى ال order اللي هو 1
+
+118
+00:12:59,520 --> 00:13:05,060
+يبقى هذه ال set لا يوجد فيها إلا عنصر وحيد اللي هو
+
+119
+00:13:05,060 --> 00:13:10,960
+ال 1 itself ال group أو ال subgroup اللي
+
+120
+00:13:10,960 --> 00:13:14,860
+فيهاش إلا ال identity element بنسميها ال trivial
+
+121
+00:13:14,860 --> 00:13:23,820
+subgroup تمام؟ يبقى هذه اسمها is a trivial
+
+122
+00:13:23,820 --> 00:13:25,940
+subgroup
+
+123
+00:13:27,300 --> 00:13:32,260
+يبقى هذه ال group ال بدية هي أو التارية 2 مين
+
+124
+00:13:32,260 --> 00:13:36,520
+بيجيني بعد ال 1 بيجيني 3 بدي subgroup
+
+125
+00:13:36,520 --> 00:13:42,440
+generated by 3 أنا 
+
+126
+00:13:42,440 --> 00:13:51,200
+أَدَّعِي أنّها the subgroup generated by سبعة وأَدَّعِي كذلك
+
+127
+00:13:51,200 --> 00:14:00,030
+أنّها هي واحد وثلاثة وسبعة وتسعة كما هيطيب استنى
+
+128
+00:14:00,030 --> 00:14:05,650
+نشوف كلامنا صح ولا غلط لأ لو جئت ثلاثة أس زيرو
+
+129
+00:14:05,650 --> 00:14:14,130
+ثلاثة أس واحد ثلاثة ثلاثة تربيع برجع ال operation
+
+130
+00:14:14,130 --> 00:14:19,330
+اللي هنا عملية من الضرب module عشرة يبقى ثلاثة
+
+131
+00:14:19,330 --> 00:14:25,610
+تربيع بتسعة هي تمام يبقى سبعة لسه مظاهرات ثلاثة أس
+
+132
+00:14:25,610 --> 00:14:26,430
+أربعة
+
+133
+00:14:29,150 --> 00:14:34,710
+احنا قلنا ثلاثة تربيع بتسعة ثلاثة تكعيب بسبعة
+
+134
+00:14:34,710 --> 00:14:39,910
+و20 شيل 20 بيطلع سبعة اللي هو ال element
+
+135
+00:14:39,910 --> 00:14:47,330
+هذا يبقى كل العناصر ظاهروا طيب ثلاثة أس أربعة اللي
+
+136
+00:14:47,330 --> 00:14:54,200
+هو واحد مظبوط يبقى حط أسس زي ما بدك دايما لما بطلعه
+
+137
+00:14:54,200 --> 00:14:58,040
+هدول يبقى السار ال subgroup جينا تبقى ثلاثة هي
+
+138
+00:14:58,040 --> 00:15:03,080
+واحد وثلاثة وسبعة وتسعة في شغيرهم طب لو جيت
+
+139
+00:15:03,080 --> 00:15:10,090
+للسبعة بنفس الطريقة سبعة أس Zero بواحد سبعة أس واحد بسبعة سبعة تربيع بتسعة وأربعين شيل أربع عشرات
+
+140
+00:15:10,090 --> 00:15:16,430
+بيظل تسعة هايا يظل عندنا تسعة سبعة تكعيب اللي هو
+
+141
+00:15:16,430 --> 00:15:23,250
+تسعة وأربعين في سبعة أو تسعة في سبعة اللي ظل عندنا
+
+142
+00:15:23,250 --> 00:15:29,350
+في سبعة ثلاثة وستين شيل ست عشرات بيظل 3 هايا
+
+143
+00:15:29,350 --> 00:15:34,890
+تعالى لتسعة أس أربعة بتلاقي طالع يبقى كده؟ واحد
+
+144
+00:15:36,770 --> 00:15:41,970
+صحيح يبقى ال subgroup generated by ثلاثة ال
+
+145
+00:15:41,970 --> 00:15:45,510
+subgroup generated by سبعة وتعتبر subgroup واحدة
+
+146
+00:15:45,510 --> 00:15:49,090
+مش اثنتين الاثنتين بس are equivalent طيب إيش
+
+147
+00:15:49,090 --> 00:15:52,510
+رأيك؟ ما علاقة الاثنين هدول بال group الأصلي؟ إذا
+
+148
+00:15:52,510 --> 00:15:58,830
+ال subgroup ثوت لجروب الأصلية بنسميها improper
+
+149
+00:15:58,830 --> 00:16:03,290
+subgroup يبقى هذي هذي is called improper subgroup
+
+150
+00:16:03,290 --> 00:16:15,570
+أو subgroup يبقى ال subgroup generated by ثلاثة أو
+
+151
+00:16:15,570 --> 00:16:21,290
+ال subgroup generated by سبعة بنسميها improper
+
+152
+00:16:21,290 --> 00:16:24,190
+subgroup أي cyclic group تحسبها وتجدها تساوي لجروب
+
+153
+00:16:24,190 --> 00:16:30,010
+الأصلية بسميها improper subgroup يعني كان ال
+
+154
+00:16:30,010 --> 00:16:33,950
+subgroup غير فعلية يعني أنت ما جبتش جديد ليش؟ لأن
+
+155
+00:16:33,950 --> 00:16:38,850
+any set is a subset of itself improper يعني غير
+
+156
+00:16:38,850 --> 00:16:44,210
+فعلي طيب إيش ضايل عندنا؟ ما ظلش إلا التسعة يبقى
+
+157
+00:16:44,210 --> 00:16:50,390
+الآن لو جئت لل subgroup generated by تسعة بدي يكون
+
+158
+00:16:50,390 --> 00:16:55,810
+تسعة أس صفر بواحد وتسعة أس واحد بتسعة تربيع
+
+159
+00:16:55,810 --> 00:17:02,490
+يعني واحد وهي وها كده حط التسعة الأس اللي عجبك ودي
+
+160
+00:17:03,110 --> 00:17:09,470
+يطلع يا واحد يا تسعة طب هدول شو اسمها اللي طلعت أقل
+
+161
+00:17:09,470 --> 00:17:14,890
+من ال group الأصلية يبقى هي ال proper subgroup
+
+162
+00:17:14,890 --> 00:17:18,310
+يبقى subgroup فعليا يبقى هدول trivial هدول improper هدول
+
+163
+00:17:18,310 --> 00:17:24,050
+proper يبقى واحد وتسعة is a proper subgroup
+
+164
+00:17:24,050 --> 00:17:32,630
+طيب خلينا نبدأ الملاحظات التالية على هذه النتيجة
+
+165
+00:17:35,700 --> 00:17:40,160
+التي توصلنا إليها هنجاوب على سؤالك واحنا بنحكي إن
+
+166
+00:17:40,160 --> 00:17:44,160
+شاء الله تمام؟ من دون ما أعرف شو السؤال تمام؟ يبقى
+
+167
+00:17:44,160 --> 00:17:49,220
+أنا باجي بتطلع اللي عندنا اللي لقيت ال subgroup
+
+168
+00:17:49,220 --> 00:17:52,140
+generated by ثلاثة هي ال subgroup generated by
+
+169
+00:17:52,140 --> 00:17:55,220
+السبعة طيب فيه عشرة شو العلاقة بين الثلاثة
+
+170
+00:17:55,220 --> 00:17:59,140
+والسبعة؟ بيقربوا لبعض؟ أه واحد فيهم معكوس الثاني
+
+171
+00:17:59,140 --> 00:18:05,220
+معناته ال subgroup generated بال element هي ال
+
+172
+00:18:05,220 --> 00:18:09,180
+subgroup generated بال inverse لهذا ال element يبقى
+
+173
+00:18:09,180 --> 00:18:15,790
+هنا هي الثلاثة والسبعة بواحدة وعشرين شيل عشرتين
+
+174
+00:18:15,790 --> 00:18:20,170
+بيطلع ال identity element إذا الثلاثة is the
+
+175
+00:18:20,170 --> 00:18:23,910
+inverse of سبعة وبالتالي ال subgroup generated by
+
+176
+00:18:23,910 --> 00:18:28,030
+ثلاثة هي ال subgroup generated by سبعة يبقى هنا
+
+177
+00:18:28,030 --> 00:18:32,730
+بقول not that لاحظ أنّ الثلاثة is the inverse of
+
+178
+00:18:32,730 --> 00:18:44,440
+سبعة modulo عشرة هذا هو معكوسه ده ومن هنا كان ال
+
+179
+00:18:44,440 --> 00:18:51,800
+subgroup هادي مين هي ال subgroup اللي عندنا هادي
+
+180
+00:18:51,800 --> 00:18:56,060
+بالضبط هذه الملاحظة هادي يبقى هادي هي هادي بالضبط
+
+181
+00:18:56,060 --> 00:19:01,860
+تماما كأنه هذا كنت باكتساله هات السؤال ممتاز
+
+182
+00:19:01,860 --> 00:19:09,240
+جدا السؤال إليك السؤال إليك استنى شوية بس هل group
+
+183
+00:19:09,240 --> 00:19:15,740
+هذه التي كشبابفهو بقى is on cyclic ليش؟ بس يصبر
+
+184
+00:19:15,740 --> 00:19:20,440
+شوية ليش؟ لأن لقيت فيها بدل ال generator اثنين
+
+185
+00:19:20,440 --> 00:19:26,560
+اللي هم مين؟ ثلاثة وسبعة يبقى باجي بقوله هنا
+
+186
+00:19:26,560 --> 00:19:31,720
+النقطة الثانية note that هذه اعتبرها رقم واحد رقم
+
+187
+00:19:31,720 --> 00:19:38,380
+اثنين ال U عشرة is cyclic and
+
+188
+00:19:38,380 --> 00:19:44,620
+ثلاثة and سبعة are generators يبقى
+
+189
+00:19:46,290 --> 00:19:56,610
+دول بيجيبولي كل group تمام يبقى ملاحظة صار أنّ
+
+190
+00:19:56,610 --> 00:20:02,360
+الثلاثة هو المعكوس تبع السبعة ولذلك ال subgroup
+
+191
+00:20:02,360 --> 00:20:06,800
+generated by ثلاثة هي ال subgroup generated by
+
+192
+00:20:06,800 --> 00:20:10,240
+سبعة وفي هذه الحالة بقول لجروب الأصلية تبقى
+
+193
+00:20:10,240 --> 00:20:15,720
+عندنا ال cyclic لأن اللي جيت فيها two generators
+
+194
+00:20:15,720 --> 00:20:19,480
+طب السؤال هو تسعة generators لأ يعني معنى هذا
+
+195
+00:20:19,480 --> 00:20:24,730
+الكلام لما تبقى ال group cyclic مش كل element
+
+196
+00:20:24,730 --> 00:20:28,970
+بيكون generator بعضهم بيكون generator ولبعضهم
+
+197
+00:20:28,970 --> 00:20:33,030
+بيكونش generator إذا على الأقل ال group فيها two
+
+198
+00:20:33,030 --> 00:20:38,010
+generators ال element والمعكوس واضح؟ الآن نعطي
+
+199
+00:20:38,010 --> 00:20:43,770
+مزيدا من الأمثلة على ال subgroup generated by any
+
+200
+00:20:43,770 --> 00:20:51,160
+element in the group مثال
+
+201
+00:20:51,160 --> 00:21:04,300
+اثنين let
+
+202
+00:21:04,300 --> 00:21:10,000
+g بدها تساوي Z 12 شباب اللي هي ال
+
+203
+00:21:10,000 --> 00:21:18,240
+0 1 2 3 4 5 6 7 8
+
+204
+00:21:18,240 --> 00:21:25,580
+9 10 11 كويس
+
+205
+00:21:25,580 --> 00:21:32,860
+الآن لو جئت سألتك بالله قداش ال subgroup generated
+
+206
+00:21:32,860 --> 00:21:39,160
+by zero كم عنصر فيها؟ عنصر واحد فقط، ما فيش غيره يبقى
+
+207
+00:21:39,160 --> 00:21:47,980
+هذا ال trivial subgroup
+
+208
+00:21:47,980 --> 00:21:54,440
+يبقى هذا ال subgroup البديهي طب لو بدأنا ال subgroup
+
+209
+00:21:54,440 --> 00:22:00,260
+generated by one العملية
+
+210
+00:22:00,260 --> 00:22:05,860
+عليها عملية جمع Z 12 عشان تكون الجروب عليها
+
+211
+00:22:05,860 --> 00:22:10,560
+عملية جمع لكن ضرب يبعت الله
+
+212
+00:22:10,560 --> 00:22:12,760
+كلها من أولها إلى آخرها Z 12 كلها
+
+213
+00:22:15,630 --> 00:22:24,530
+من أولها إلى آخرها Z 12 كلها
+
+214
+00:22:24,530 --> 00:22:26,250
+من أولها إلى آخرها Z 12 كلها
+
+215
+00:22:26,250 --> 00:22:26,370
+من أولها إلى آخرها Z 12 كلها
+
+216
+00:22:26,370 --> 00:22:27,010
+من أولها إلى آخرها Z 12 كلها
+
+217
+00:22:27,010 --> 00:22:28,770
+من أولها إلى آخرها Z 12 كلها
+
+218
+00:22:28,770 --> 00:22:29,290
+من أولها إلى آخرها Z 12 كلها
+
+219
+00:22:29,290 --> 00:22:29,570
+من أولها إلى آخرها Z 12 كلها
+
+220
+00:22:29,570 --> 00:22:32,450
+من أولها إلى آخرها Z 12 كلها
+
+221
+00:22:32,450 --> 00:22:40,710
+من أولها إلى آخرها Z 12 كلها
+
+222
+00:22:40,710 --> 00:22:47,800
+منتحت عملية الجمع 11 يبقى 11 بده يجيب كمان
+
+223
+00:22:47,800 --> 00:22:52,960
+مين لجروب كله يبقى هذا بده يساوي ال subgroup
+
+224
+00:22:52,960 --> 00:23:04,140
+generated by 11 طيب احنا الآن بده يجي 1 2 3 4 بده
+
+225
+00:23:04,140 --> 00:23:06,580
+ال subgroup generated by 5
+
+226
+00:23:13,980 --> 00:23:20,000
+خمسة و Zero تعني Zero في خمسة بقداش؟ ب Zero يبقى هذا
+
+227
+00:23:20,000 --> 00:23:24,780
+ال element موجود فيها خمسة أس واحد يعني واحد في
+
+228
+00:23:24,780 --> 00:23:29,960
+خمسة خمسة تربيع راح ال element خمسة تربيع تعني خمسة
+
+229
+00:23:29,960 --> 00:23:35,130
+زائد خمسة هي ال element اللي عندنا هنا تمام
+
+230
+00:23:35,130 --> 00:23:40,270
+الآن هذا خمسة تكعيب خمسة تكعيب تكعيب تكعيب تكعيب
+
+231
+00:23:40,270 --> 00:23:41,330
+تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب
+
+232
+00:23:41,330 --> 00:23:42,130
+تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب
+
+233
+00:23:42,130 --> 00:23:43,830
+تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب
+
+234
+00:23:43,830 --> 00:23:44,370
+تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب
+
+235
+00:23:44,370 --> 00:23:45,350
+تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب تكعيب
+
+236
+00:23:45,350 --> 00:23:49,990
+تكعيب تكعيب تكعيب تكعيب تكعيب الآن خمسة أس أربعة
+
+237
+00:23:49,990 --> 00:23:54,270
+يعني أربعة في خمسة اللي هو ب 20 بنشيل 12 بيطلع
+
+238
+00:23:54,270 --> 00:23:59,470
+قداش؟ 8 خمسة أس خمسة يعني خمسة في خمسة ب 25
+
+239
+00:23:59,470 --> 00:24:05,630
+بدي أشيل من 24 بيطلع قداش؟ 5
+
+240
+00:24:05,630 --> 00:24:10,750
+و 30
+
+241
+00:24:10,750 --> 00:24:17,170
+و 5
+
+242
+00:24:17,170 --> 00:24:22,270
+و 30 و 5 و 30
+
+243
+00:24:26,960 --> 00:24:32,440
+خمسة أس 8 اللي 8 في 5 ب 40 بدّه
+
+244
+00:24:32,440 --> 00:24:37,860
+أشيل 36 بتطلع من 4 خمسة أس 9 اللي
+
+245
+00:24:37,860 --> 00:24:42,750
+خمسة في 40 ببدأ يزيل منهم 36 ويبقى
+
+246
+00:24:42,750 --> 00:24:49,270
+الجديد 9 الآن خمسة أس 9 هنا خمسة أس 10 اللي
+
+247
+00:24:49,270 --> 00:24:52,390
+ب 50 أربعة في 12 ب 48 ويبقى له
+
+248
+00:24:52,390 --> 00:24:58,810
+2 يبقى له 2 هيا الآن خمسة أس 11 ب 55
+
+249
+00:24:58,810 --> 00:25:02,250
+من 48 ويبقى له 7 يبقى هذه
+
+250
+00:25:02,250 --> 00:25:06,310
+السبعة خمسة 12 ب 60 تعني Zero يبقى بدأنا من 
+
+251
+00:25:06,310 --> 00:25:12,690
+أول وجديد في عنصر مظاهره، لو روحت حسبت مين المعكوس
+
+252
+00:25:12,690 --> 00:25:18,650
+تبع الخمسة يبقى بده يطلع كمان هذا سبعة subgroup
+
+253
+00:25:18,650 --> 00:25:25,190
+generated by سبعة طيب by اللي عندي فيه relatively
+
+254
+00:25:25,190 --> 00:25:29,870
+prime للأتناشر غير هدول الخمسة والسبعة والأحداش
+
+255
+00:25:29,870 --> 00:25:34,170
+ماشي، هالفاش غيرهم تمام، يبقى هذا الكلام بده
+
+256
+00:25:34,170 --> 00:25:43,110
+يساوي Z اتناشر بالضبط تماما، يبقى هذول عبارة عن ايش؟
+
+257
+00:25:43,110 --> 00:25:52,050
+improper subgroups، يبقى بعدي بقوله these subgroups
+
+258
+00:25:52,050 --> 00:25:54,710
+are improper
+
+259
+00:25:57,830 --> 00:26:02,830
+يبقى يا شباب هدول الأربعة، لكن في الحقيقة واحد، يبقى
+
+260
+00:26:02,830 --> 00:26:07,350
+subgroup واحدة، و ال zero هي تنتين، تنتين subgroup
+
+261
+00:26:07,350 --> 00:26:11,890
+فقط من ال group هذه، تعالى نشوف الباقية بعد الواحد
+
+262
+00:26:11,890 --> 00:26:16,450
+بيجيني اتنين subgroup generated by اتنين اللي هو
+
+263
+00:26:16,450 --> 00:26:23,010
+zero، اتنين، اربعة، ستة، تمانية، عاشرة، متأكد، متأكد ونص
+
+264
+00:26:24,160 --> 00:26:28,660
+2×0 بزير و 2×1 باتنين و 2 تربية و 2×2 باربعة و 2
+
+265
+00:26:28,660 --> 00:26:31,860
+تكيبة و 2×3 بستة و 2 اتنين و 4 اربعة و 2 تمانية
+
+266
+00:26:31,860 --> 00:26:38,200
+لغاية العشرة تمام؟ بدي اجي اشوف مين هم، هل في غيرها
+
+267
+00:26:38,200 --> 00:26:42,780
+هدى و الله فيش غيرها، باجي بسأل نفسي هو مين معكس 2
+
+268
+00:26:42,780 --> 00:26:48,440
+في 8عشرة، يبقى لو روحت حسبت العشرة بدهم يطلعوا
+
+269
+00:26:48,440 --> 00:26:51,860
+العناصر اللي عندك كانت، يعني لو روحت حسبت ال
+
+270
+00:26:51,860 --> 00:26:57,280
+subgroup generated by عشرة بدها تطلع هذه بالضبط
+
+271
+00:26:57,280 --> 00:27:02,840
+جرب عشرة و Zero و واحد عشرة و اس واحد بعشرة هذا
+
+272
+00:27:02,840 --> 00:27:10,080
+راح ال zero و راح العشرة، عشرة تربيع بعشرة زائد
+
+273
+00:27:10,080 --> 00:27:15,900
+عشرة تانية عشرين، فزد اتناشر بكمانية هذه الثمانية
+
+274
+00:27:15,900 --> 00:27:18,940
+والعشرة تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+275
+00:27:18,940 --> 00:27:22,680
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+276
+00:27:22,680 --> 00:27:27,140
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+277
+00:27:27,140 --> 00:27:27,200
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+278
+00:27:27,200 --> 00:27:27,220
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+279
+00:27:27,220 --> 00:27:28,360
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+280
+00:27:28,360 --> 00:27:37,360
+تقريبا تقريبا، الأن اقصد خمسة يعني خمسين، اربع في
+
+281
+00:27:37,360 --> 00:27:41,180
+اتناشر تمانية واربعين، بيظل اتنين اللي بعدها ستين
+
+282
+00:27:41,180 --> 00:27:45,700
+بيزيروا، يبقى فعلا هذه ال sub group generated by
+
+283
+00:27:45,700 --> 00:27:52,410
+عشرة هي ال sub group generated by اتنين تمام؟ طيب،
+
+284
+00:27:52,410 --> 00:27:56,850
+الآن، يبقى صاروا كام subgroup عندي؟ تلاتة بس مافيش
+
+285
+00:27:56,850 --> 00:28:00,910
+غيرهم، دير بالك أنا بمهد لل chapter اللي بعده ال
+
+286
+00:28:00,910 --> 00:28:05,550
+chapter هتبع ربوحيه تجيك أسئلة يقول لك list all
+
+287
+00:28:05,550 --> 00:28:09,470
+the subgroups of ال group الفلانية، مش هتروح تحطهم
+
+288
+00:28:09,470 --> 00:28:12,390
+اتناشر واحدة، يمكن بيطلعوش غير اربعة، يمكن بيطلعوش
+
+289
+00:28:12,390 --> 00:28:16,130
+غير خمسة، يمكن غير ستة، يبقى أنت تتقيد بالموجودة،
+
+290
+00:28:16,130 --> 00:28:21,180
+هدول كلهم، الاربع يعتبر واحدة وليس اربع، يبقى واحدة
+
+291
+00:28:21,180 --> 00:28:26,220
+فقط، ده يعني طيب، الان لو جيت قلت لك بدي ال subgroup
+
+292
+00:28:26,220 --> 00:28:34,080
+generated by خلصنا واحد واثنين، بدنا تلاتة، يبقى هي
+
+293
+00:28:34,080 --> 00:28:41,380
+Zero و تلاتة و ستة و تسعة، في غيرهم؟ لأ، طيب هذه
+
+294
+00:28:41,380 --> 00:28:45,900
+تعتبر ال subgroup generated by معكوس التلاتة من
+
+295
+00:28:45,900 --> 00:28:49,780
+تسعة، يبقى ال subgroup generated by .. يبقى هدول
+
+296
+00:28:49,780 --> 00:28:55,840
+تين تين، لكن يعتبروا ايش؟ واحدة فقط لا غير، طب لو
+
+297
+00:28:55,840 --> 00:29:01,300
+بدي أديب ال subgroup generated by أربعة، زيرو، أربعة
+
+298
+00:29:01,300 --> 00:29:06,860
+تمانية، في غيرهم، أربعة في زيرو بزيرو، أربعة في أحد
+
+299
+00:29:06,860 --> 00:29:10,480
+بأربعة، أربعة في اتنين تمانية، أربعة في تلاتة بزيرو
+
+300
+00:29:10,480 --> 00:29:16,340
+يبقى ما عنديش إلا التلت عناصر هدول بالضبط تماما، طيب
+
+301
+00:29:16,340 --> 00:29:21,340
+بعد الأربعة، الخمسة خلصنا منها، بدي ال sub group
+
+302
+00:29:21,340 --> 00:29:28,180
+generated by ستة اللي همين زيرو وستة، في غيرهم، مش
+
+303
+00:29:28,180 --> 00:29:34,460
+غيرهم، في كمان subgroup غير هدول ولا واحدة تمام
+
+304
+00:29:34,460 --> 00:29:41,740
+يبقى هي واحدة، هي تنتين، هي تلاتة، هذا أربعة، هذا خمسة
+
+305
+00:29:41,740 --> 00:29:48,660
+هذا ستة، بس ستة subgroup، تمانية ما حسبناهاش، طيب هذه
+
+306
+00:29:48,660 --> 00:29:53,580
+تساوي subgroup generated by تمانية، فعلا في ضايق
+
+307
+00:29:53,580 --> 00:29:59,950
+الحاجة ما حسبناهاش، شكله إن حسب، تمام، طيب هذا كل ال
+
+308
+00:29:59,950 --> 00:30:03,370
+subgroups، الان لو جيت أنت هدول هدول قلنا عليهم
+
+309
+00:30:03,370 --> 00:30:10,470
+improper، هدى و هدى و هدى و هدى و هدى، كلهم proper
+
+310
+00:30:10,470 --> 00:30:20,530
+subgroups، يبقى هنا ال subgroups اللي هم ال zero
+
+311
+00:30:20,530 --> 00:30:23,290
+وال اتنين
+
+312
+00:30:25,560 --> 00:30:32,760
+والتلاتة و ال group generated by أربعة وال group
+
+313
+00:30:32,760 --> 00:30:40,500
+generated by and ال group generated by ستة are
+
+314
+00:30:40,500 --> 00:30:49,650
+proper، كلهم دول proper sub groups، يبقى برضه لاحظنا
+
+315
+00:30:49,650 --> 00:30:55,930
+ان اي subgroup تولد بعنصر كذلك تولد بمعكوس هذا
+
+316
+00:30:55,930 --> 00:31:01,290
+العنصر، هذا الشيء اللي هو موجود عندنا وشيء أساسي
+
+317
+00:31:01,290 --> 00:31:06,550
+لازم نعرفه، يبقى عرفنا ال trivial subgroup وعرفنا
+
+318
+00:31:06,550 --> 00:31:11,450
+ال proper subgroup وعرفنا ال improper subgroup
+
+319
+00:31:11,450 --> 00:31:22,710
+كذلك نجي ل group تانية كمان، مجددش نمرة تلاتة Z
+
+320
+00:31:22,710 --> 00:31:29,110
+وعليها
+
+321
+00:31:29,110 --> 00:31:38,730
+عملية الجمع، Z وعليها عملية الجمع، فاكرولي؟ هل هذه
+
+322
+00:31:38,730 --> 00:31:44,470
+Cyclic ولا لأ؟ وإذا كانت Cyclic من هم ال generator
+
+323
+00:32:02,420 --> 00:32:07,100
+cyclic مش هاتولى generator واحد بس تحت عملية
+
+324
+00:32:07,100 --> 00:32:14,320
+الجامعة، مش الدرب، not cyclic، not cyclic، طيب اذا
+
+325
+00:32:14,320 --> 00:32:18,820
+احنا عاملنا contradiction للكلام اللي بتقوله، بتصير
+
+326
+00:32:18,820 --> 00:32:25,100
+ايش؟ بتصير cyclic ونافع انها cyclic، انا هادعى انها
+
+327
+00:32:25,100 --> 00:32:30,420
+cyclic، انا ادعى ان السيكلف كاكن، بدنا نثبت صحة تلك
+
+328
+00:32:30,420 --> 00:32:36,780
+هم، و بدي اجيبلك بدل ال generator اتنين، و هم ال
+
+329
+00:32:36,780 --> 00:32:44,800
+generators فقط لا، لا يوجد غيرهما، واحد و سلب واحد
+
+330
+00:32:44,800 --> 00:32:50,560
+على طول الخط، يبقى هذه in the group، هذه the
+
+331
+00:32:50,560 --> 00:32:52,240
+generators
+
+332
+00:32:56,770 --> 00:33:04,450
+are one and سالب one، طيب ليش one و سالب one كل
+
+333
+00:33:04,450 --> 00:33:07,630
+واحد فيهم معكوسة لآخر، أنت قلت الساعة في السنة اللي
+
+334
+00:33:07,630 --> 00:33:10,990
+قبله أي element مالاجيه generator مالاجيه معكوسة و
+
+335
+00:33:10,990 --> 00:33:14,250
+generator، يبقى هنا الواحد و السالب واحد هيقول
+
+336
+00:33:14,250 --> 00:33:18,690
+الواحد كيف سالب واحد generator لل group كله، بنقوله
+
+337
+00:33:18,690 --> 00:33:25,610
+كالتالي، أنا الآن بدي ال sub group generated by سالب
+
+338
+00:33:25,610 --> 00:33:31,400
+one، بدي أسولك السلب one، وانت تبقى at one one مع ال
+
+339
+00:33:31,400 --> 00:33:38,180
+one اللي ضايلة، يبقى هذه عناصرها كتالة، بدي أبدأ بـ-1
+
+340
+00:33:38,180 --> 00:33:47,620
+أس 0، و-1 أس 1، و-1 أس 2، و-1 أس 3، وضلك ماشي إلى
+
+341
+00:33:47,620 --> 00:33:55,440
+ما شاء الله، وأرجع على الشمال، يبقى -1 أس 1، و-1
+
+342
+00:33:55,440 --> 00:34:04,830
+أس 2، و-1 أس 3، وضلك ماشي إلى ما شاء الله، الان
+
+343
+00:34:04,830 --> 00:34:09,670
+العملية عملية جمع، قولنا لكم في عملية الجمع كتبنا
+
+344
+00:34:09,670 --> 00:34:14,030
+في نهاية آخر حاجة في الخاصية رقم أربعة في نهاية
+
+345
+00:34:14,030 --> 00:34:19,110
+الشابتر الماضي، قولنا الأس اللي فوق تضرب، وتضرب لل
+
+346
+00:34:19,110 --> 00:34:25,060
+element لأن هذا تعني انك بتجمع هذا مرتين، وما إلى
+
+347
+00:34:25,060 --> 00:34:30,000
+ذاك تلاتة إلى آخرية، يبقى هذه لو بدها اعيد صياغتها
+
+348
+00:34:30,000 --> 00:34:36,540
+بتكون هي ال elements سالب تلاتة في سالب واحد، اللي
+
+349
+00:34:36,540 --> 00:34:42,980
+بعده سالب اتنين في سالب واحد، اللي بعده بيكون سالب
+
+350
+00:34:42,980 --> 00:34:48,920
+واحد في سالب واحد، اللي بعده Zero في سالب واحد، واحد
+
+351
+00:34:48,920 --> 00:34:57,340
+في سالب واحد، اتنين في سالب واحد، تلاتة في سالب واحد
+
+352
+00:34:57,340 --> 00:35:02,540
+و هكذا، يبقى أصبحت ال group generated أو ال sub
+
+353
+00:35:02,540 --> 00:35:09,470
+group generated by سالب واحد هي هنا سالب تلاتة في
+
+354
+00:35:09,470 --> 00:35:16,230
+سالب واحد اللي هي قداش؟ تلاتة، اتنين، واحد، زيرو، سالب
+
+355
+00:35:16,230 --> 00:35:22,050
+واحد، سالب اتنين، سالب تلاتة، واضدلك ماشي الى ما شاء
+
+356
+00:35:22,050 --> 00:35:26,570
+الله، بس مش مرتبة يعني خلى الموجة في الأول والسلم
+
+357
+00:35:26,570 --> 00:35:33,370
+في الآخر، لكن كل العناصر موجودة، هدف تعطيك Z itself
+
+358
+00:35:33,370 --> 00:35:41,990
+يبقى هدول improper ولا proper subgroup، يبقى
+
+359
+00:35:41,990 --> 00:35:48,970
+هنا سالـ group generated by one بدها تساوي ال
+
+360
+00:35:48,970 --> 00:35:55,710
+subgroup generated by سالب one، هدول are improper
+
+361
+00:35:55,710 --> 00:35:59,090
+subgroups
+
+362
+00:35:59,090 --> 00:36:08,350
+طب هل هذه تحتوي على proper subgroup، proper
+
+363
+00:36:10,920 --> 00:36:15,540
+ممتاز جدا، اتنين بيجيبليش الا الزوجيات، اتنين، اربعة
+
+364
+00:36:15,540 --> 00:36:19,640
+ستة، تمانية، Zero، سالب اتنين، سالب اربعة، سالب ستة
+
+365
+00:36:19,640 --> 00:36:22,860
+سالب تمانية، Improper، والتلاتة والاربعة والخاطر
+
+366
+00:36:22,860 --> 00:36:27,280
+كلهم improper subgroup، يبقى هدول the only
+
+367
+00:36:27,280 --> 00:36:32,850
+generators، و هدول الـ improper subgroups، و هدول
+
+368
+00:36:32,850 --> 00:36:37,350
+اللي بيجيبولي عناصر ال group كل، ما خل ذلك بيجيبولي
+
+369
+00:36:37,350 --> 00:36:44,610
+جزء من ال groups تمام؟ يبقى هذا z لا يوجد فيها
+
+370
+00:36:44,610 --> 00:36:48,490
+generators إلا اتنين، واحد و سالب واحد، غير هيك
+
+371
+00:36:48,490 --> 00:36:52,350
+يبعتلك الله، تلاتة بيصير زيرو تلاتة ستة تسعة، نقص
+
+372
+00:36:52,350 --> 00:36:56,190
+تلاتة، نقص ستة، نقص تسعة، subgroup generated by اربعة
+
+373
+00:36:56,190 --> 00:36:59,450
+زيرو اربعة تمانية اتنانية، زيرو سالب اربعة سالب
+
+374
+00:36:59,450 --> 00:37:03,930
+تمانية سالب اتنانية، ونضلك مالي وهكذا، تمام، يبقى لا
+
+375
+00:37:03,930 --> 00:37:09,250
+يوجد generators لا زد تحت عمل الجامعة الا two
+
+376
+00:37:09,250 --> 00:37:14,380
+generators و البيت كلهم ما فيش يمكن لجنوب حاجة
+
+377
+00:37:14,380 --> 00:37:19,340
+ما تطلعش Cyclic هه أعطيك لجنوب ما تطلعش Cyclic خد لي
+
+378
+00:37:19,340 --> 00:37:25,810
+هنا مثلًا اعتبر هذا كمان مثال الـ U أربعة تمانية
+
+379
+00:37:25,810 --> 00:37:33,270
+عناصرها واحد و ثلاثة و خمسة و سبعة شوف هذه Cyclic
+
+380
+00:37:33,270 --> 00:37:42,170
+ولا لا الآن ثلاثة تربيع يعني واحد طيب خمسة تربيع
+
+381
+00:37:42,170 --> 00:37:48,970
+يعني واحد ثلاثة ثمانية سبعة تربيع تسعة وعشرين يعني
+
+382
+00:37:48,970 --> 00:37:54,110
+واحد يبقى ولا واحد فيهم generator يبقى معناه دي
+
+383
+00:37:54,110 --> 00:38:06,070
+مهنياش Cyclic يبقى هذه as not cyclic because أن ال
+
+384
+00:38:06,070 --> 00:38:11,870
+X تربيع تساوي واحد for all X اللي موجودة في U
+
+385
+00:38:11,870 --> 00:38:18,200
+تمامًا مين ما تكون تكون ربع بيطلع ال identity تمام؟
+
+386
+00:38:18,200 --> 00:38:22,500
+يعني سبعة تربيع تساوي ثلاثة تربيع تساوي خمسة تربيع
+
+387
+00:38:22,500 --> 00:38:26,840
+تساوي واحد تربيع كله بال identity إذا ولا واحد فيهم
+
+388
+00:38:26,840 --> 00:38:36,380
+generator كويس نواصل الحكي في هذا الموضوع نمرة
+
+389
+00:38:36,380 --> 00:38:45,020
+هذه اعتبرتها أربعة يبقى نمرة خمسة نمرة خمسة in دي
+
+390
+00:38:45,020 --> 00:38:55,090
+أن في دي أن اللي هي دي دايهدرال دايهدرال
+
+391
+00:38:55,090 --> 00:39:05,550
+جروب of order اثنين أن جداش الآن بتضرب في اثنين
+
+392
+00:39:05,550 --> 00:39:14,790
+let الـ R بيه rotation بيه rotation
+
+393
+00:39:17,820 --> 00:39:26,140
+أعظه ثلاثمئة و ستين على in degree ثلاثمئة و ستين
+
+394
+00:39:26,140 --> 00:39:38,640
+على in degree then جاب
+
+395
+00:39:38,640 --> 00:39:45,200
+المبدأ اللي أنا بديه الآن أنا جاي الـ DN هي dihydral
+
+396
+00:39:45,200 --> 00:39:50,180
+group اللي هو المجموعة ثنائية السطوح من ال order 2
+
+397
+00:39:50,180 --> 00:40:02,650
+احنا خدنا مثال عليها قبل ذلك اللي هو مين؟ D4 D4 D4
+
+398
+00:40:02,650 --> 00:40:13,490
+D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 D4 أربعة
+
+399
+00:40:13,490 --> 00:40:18,670
+أضلاع هو مضلع منتظم مقسم من أربعة أضلاع إذا بقسم
+
+400
+00:40:18,670 --> 00:40:23,830
+الـ 360 على أربعة بيصير قداش يبقى ال element of
+
+401
+00:40:23,830 --> 00:40:30,630
+rotation بيكون R تسعين طيب لو قلت مخمس منتظم بدي
+
+402
+00:40:30,630 --> 00:40:35,590
+أقسم على خمسة يبقى بدي أقسم ثلاثمئة و ستين على
+
+403
+00:40:35,590 --> 00:40:41,330
+خمسة فيها الست في خمسة بتلاتين فيها فيها الست فيها
+
+404
+00:40:41,330 --> 00:40:48,270
+الست على خمسة على خمسة فيها السبعة يبقى فيها
+
+405
+00:40:48,270 --> 00:40:53,250
+السبعة في خمسة بتلاتي يبقى اثنين و سبعين درجة أنا
+
+406
+00:40:53,250 --> 00:40:58,270
+بدي أعمل دوران في المخمس بزاوية 72 درجة و بصير
+
+407
+00:40:58,270 --> 00:41:09,350
+عندي R0 R72 R144 و هكذا لغاية ما أوصل إلى R4 R5
+
+408
+00:41:09,350 --> 00:41:14,730
+بتعود من جديد اللي هي R0 طب لو قلت مثلث متساوي
+
+409
+00:41:14,730 --> 00:41:22,910
+الأضلاع يبقى بصير هذه DN يعني فيها اثنين في ثلاثة
+
+410
+00:41:22,910 --> 00:41:29,370
+ستة عناصر فقط لا غير ليش بقسم ثلاثمئة و ستين على
+
+411
+00:41:29,370 --> 00:41:34,010
+ثلاثة بصير مئة و عشرين يبقى دوران بيكون مئة و عشرين
+
+412
+00:41:34,010 --> 00:41:39,270
+درجة و ليس تسعين و هكذا و كله counter clockwise
+
+413
+00:41:39,270 --> 00:41:46,780
+تمام يبقى بصير عندي R نود و R مئة و عشرين و R مئتين
+
+414
+00:41:46,780 --> 00:41:51,800
+و أربعين و بعدين بروح ايش لل reflections و هكذا
+
+415
+00:41:51,800 --> 00:41:55,800
+بيضلوا ثلاثة reflections ماشي الحالة يبقى هذا
+
+416
+00:41:55,800 --> 00:42:04,390
+المقصود بالـ DN الآن أنا لو جيت قلت لك الـ RN يعني
+
+417
+00:42:04,390 --> 00:42:11,950
+أنا اللي أيضًا مثلث مربع مخمس منتظم مسدس منتظم لو
+
+418
+00:42:11,950 --> 00:42:18,580
+عملت ايه من المرات دوران؟ مين بيعطيني هنا؟ يعني زي
+
+419
+00:42:18,580 --> 00:42:24,520
+R تسعين R تسعين أس أربعة بقداش ال identity له الـ R
+
+420
+00:42:24,520 --> 00:42:30,720
+نود يبقى هذا الـ R تسعين الـ R N يساوي ال identity
+
+421
+00:42:30,720 --> 00:42:37,080
+element اللي رمزنا له بالرمز R نود طب لو ضربت
+
+422
+00:42:37,080 --> 00:42:45,980
+الطرفين في R يبقى هذا معناه أن R N زائد واحد يساوي
+
+423
+00:42:45,980 --> 00:42:58,100
+R رن زائد اثنين ر تربيع رن زائد ثلاثة رن زائد أربعة
+
+424
+00:42:58,100 --> 00:43:02,580
+رتبة رتبة
+
+425
+00:43:02,580 --> 00:43:07,760
+رتبة
+
+426
+00:43:07,760 --> 00:43:16,220
+رتبة رتبة رتبة رتبة رتبة رتبة
+
+427
+00:43:20,650 --> 00:43:28,910
+رن ناقص واحد يساوي الـ R inverse رن
+
+428
+00:43:28,910 --> 00:43:32,490
+ناقص
+
+429
+00:43:32,490 --> 00:43:38,580
+واحد يساوي الـ R inverse إذا بناء عليه الدوران لغاية أن
+
+430
+00:43:38,580 --> 00:43:43,720
+ما زاد على ذلك يعتبر عنصر من مين من العنصر اللي قبل
+
+431
+00:43:43,720 --> 00:43:48,060
+يبقى بناء عليه اللي لو جيت قلت لك الـ subgroup
+
+432
+00:43:48,060 --> 00:43:53,900
+generated by R R هذه any rotation ها يا شباب يعني
+
+433
+00:43:53,900 --> 00:44:00,700
+قد تكون R 120 وقد تكون R 90 وقد تكون R 72 وقد تكون
+
+434
+00:44:00,700 --> 00:44:05,440
+R 60 وقد وقد إلى آخرين يبقى مين مكان ال rotations
+
+435
+00:44:05,440 --> 00:44:09,480
+ليش؟ لأن احنا لما أخذنا دي for goal فيه أربع
+
+436
+00:44:09,480 --> 00:44:14,380
+rotations و أربع reflections، من ذاكرين؟ سكات
+
+437
+00:44:14,380 --> 00:44:23,290
+الشعباربع rotation واربع reflection يبقى
+
+438
+00:44:23,290 --> 00:44:33,630
+أربع rotation يبقى أربع rotation واربع reflection يبقى
+
+439
+00:44:33,630 --> 00:44:38,870
+أربع rotation وكتبت معكم في الدفتر أن لو ضربت ال
+
+440
+00:44:38,870 --> 00:44:43,290
+reflection في ال rotation أو ال rotation في ال
+
+441
+00:44:43,290 --> 00:44:47,970
+reflection على كل الأمرين بده يطلع مين reflection
+
+442
+00:44:47,970 --> 00:44:54,290
+تمام يبقى ارى اللي عندها دي rotation بتسعين بتنين
+
+443
+00:44:54,290 --> 00:44:58,210
+وسبعين بمئة وعشرين أنت حر مين ما تكون ال rotation
+
+444
+00:44:58,210 --> 00:45:03,090
+داك معنى هذا الكلام أن ال rotation commutes مع
+
+445
+00:45:03,090 --> 00:45:09,130
+نفسها مع أي rotation أخرى لكن مع ال reflection مش
+
+446
+00:45:09,130 --> 00:45:15,750
+صحيح يعني لما كنا نقول مثلًا R تسعين في H هل هي H
+
+447
+00:45:15,750 --> 00:45:16,750
+في R تسعين؟
+
+448
+00:45:21,120 --> 00:45:28,800
+العملية ليست إبدالية لما نقل rotation مع نفسه إذا
+
+449
+00:45:28,800 --> 00:45:33,940
+قلت ر تسعين في ر مئة و ثمانين أليست ر مئة و ثمانين
+
+450
+00:45:33,940 --> 00:45:35,160
+في ر تسعين؟
+
+451
+00:45:42,590 --> 00:45:47,930
+يعني يعني الإبدال مع ال rotation مئة بالمئة ما عناه
+
+452
+00:45:47,930 --> 00:45:53,210
+مشكلة إذا لما أقول الـ subgroup generated by R هذه
+
+453
+00:45:53,210 --> 00:45:59,010
+هتعطيني مين؟ هتعطيني ال identity element اللي
+
+454
+00:45:59,010 --> 00:46:05,240
+هسميه مين؟ اللي هسميه Arnold وبعدين هتعطيني ر اتسل
+
+455
+00:46:05,240 --> 00:46:10,900
+وبعدين هتعطيني ر تربيع وهتعطيني ر تكعيب وهضل
+
+456
+00:46:10,900 --> 00:46:19,120
+ماشي لغاية ر N minus الـ one لأن ر N بتعطيني مين الـ
+
+457
+00:46:19,120 --> 00:46:24,200
+identity اللي هو Arnold بنرجع لهذا يبقى مهما كانت
+
+458
+00:46:24,200 --> 00:46:29,400
+القيمة N ال integer اللي عندك تبدأ تبدأ تدور ايه؟ من
+
+459
+00:46:29,400 --> 00:46:34,600
+جديد يبقى ال rotation is a cyclic subgroup أي
+
+460
+00:46:34,600 --> 00:46:39,660
+rotation و خلينا معاه R أربعة اللي أخذناها مع D
+
+461
+00:46:39,660 --> 00:46:44,860
+أربعة غزنة يبقى الـ R node cyclic group generated
+
+462
+00:46:44,860 --> 00:46:49,780
+by R node ما فيش فيها إلا element واحد الـ R تسعين
+
+463
+00:46:49,780 --> 00:46:56,350
+cyclic subgroup فيها كام عنصر R تسعين R تسعين تبع
+
+464
+00:46:56,350 --> 00:47:01,170
+الـ D4 نتكلم عن الـ D4 يبقى فيه الـ R تسعين Cyclic
+
+465
+00:47:01,170 --> 00:47:06,210
+subgroup generated by تسعين فيها كام element؟ R
+
+466
+00:47:06,210 --> 00:47:11,590
+تسعين أربعة عناصر أربعة عناصر لأن ال order لـ R
+
+467
+00:47:11,590 --> 00:47:17,490
+تسعين هو أربعة يعني R أس R تسعين أس أربعة هو بال
+
+468
+00:47:17,490 --> 00:47:21,090
+identity element يقول ما عنديش إلا مين؟ أربعة طب R
+
+469
+00:47:21,090 --> 00:47:22,190
+مين و ثمانين؟
+
+470
+00:47:24,690 --> 00:47:29,670
+ما فيش إلا ال identity و الـ R 180 itself طب الـ R
+
+471
+00:47:29,670 --> 00:47:35,010
+272 الـ cyclic هذي أكثر .. اللي هي مين؟ ارتسايل
+
+472
+00:47:35,010 --> 00:47:40,110
+لأنه التنتين معكوسات لبعض و هكذا و نقيس على ذلك دي
+
+473
+00:47:40,110 --> 00:47:44,010
+أن مهما كانت دي ثلاثة، دي خمسة، دي ستة، دي سبعة،
+
+474
+00:47:44,010 --> 00:47:48,120
+جد ما يكون كله بنفس الفكرة اللي عندنا يبقى هذه
+
+475
+00:47:48,120 --> 00:47:54,120
+Cyclic group generated by قصدته من ذلك أنه are any
+
+476
+00:47:54,120 --> 00:48:00,860
+rotation سواء كانت R90 ولا R72 ولا R120 ولا R60
+
+477
+00:48:00,860 --> 00:48:06,380
+يبقى هذه مين ما يكون المثل عندك DN خلاصنا؟ يبقى
+
+478
+00:48:06,380 --> 00:48:10,220
+هذا ال elements اللي عندنا طيب بدنا نيجي الآن
+
+479
+00:48:10,220 --> 00:48:16,520
+لتعريف جديد يا شباب بدنا ندور على مركز لجروب ال
+
+480
+00:48:16,520 --> 00:48:23,020
+center احنا
+
+481
+00:48:23,020 --> 00:48:28,900
+ما قلناش أنه دي in cyclic قلنا بعض ال subgroups
+
+482
+00:48:28,900 --> 00:48:34,700
+cyclic و البعض الآخر ماهيّاش cyclic يعني مثلًا
+
+483
+00:48:34,700 --> 00:48:40,930
+ارتسين cyclic group طب هل الـ R 180 .. الـ cyclic
+
+484
+00:48:40,930 --> 00:48:43,630
+group صحيح و ما فيش فيها إلا أربعة أن الـ cyclic sub
+
+485
+00:48:43,630 --> 00:48:47,290
+group طب و الـ R 180؟ الـ cyclic sub group و ما فيش
+
+486
+00:48:47,290 --> 00:48:52,490
+فيها إلا عنصرين لكن هل فيهم أي واحد بدي أجيب لل
+
+487
+00:48:52,490 --> 00:48:57,710
+group الأصلية اللي هي دي ولا واحد يعني دي ان ليست
+
+488
+00:48:57,710 --> 00:49:02,930
+cyclic group و لو كان الـ cyclic لصارت قابل يعني
+
+489
+00:49:02,930 --> 00:49:08,010
+لأن الصبح أثبتنا أن أنا الـ cyclic group is أبيليان و
+
+490
+00:49:08,010 --> 00:49:11,270
+احنا كل حياتنا من يوم أخذنا D4 بنقول ماهيّاش
+
+491
+00:49:11,270 --> 00:49:19,250
+أبيليان، تمام؟ يعني الـ D4 أو الـ D in .. in has no
+
+492
+00:49:19,250 --> 00:49:23,790
+generator، ليش؟ لأنه ماهيّاش Cyclic ولا إلا لو كان
+
+493
+00:49:23,790 --> 00:49:28,860
+فيها generator واحد كان جاب لي لجروبنا لكن ممكن يكون
+
+494
+00:49:28,860 --> 00:49:33,560
+ال subgroups بعضهم cyclic اه صحيح بصير بعضهم
+
+495
+00:49:33,560 --> 00:49:39,120
+cyclic رغم أن الأصلية ماهيّاش cyclic تمام لكن أن
+
+496
+00:49:39,120 --> 00:49:43,440
+شاء الله جاي آكو نظرية الشبطريت جاي لو كانت
+
+497
+00:49:43,440 --> 00:49:48,800
+الأصلية cyclic يبقى أي subgroup منها بتبقى cyclic
+
+498
+00:49:50,860 --> 00:49:54,380
+الشبتر الجامعي مش الشبتر هذا يعني احنا هذا مجرد بس
+
+499
+00:49:54,380 --> 00:49:59,180
+معلومة بسيطة نخليك تفكر على أي حال بدنا عشان أبعد
+
+500
+00:49:59,180 --> 00:50:03,780
+كتير definition definition 
+
+501
+00:50:03,780 --> 00:50:08,740
+the center
+
+502
+00:50:08,740 --> 00:50:20,420
+the center اللي هو حديد Z of G أدي الرمز هذا of A
+
+503
+00:50:20,420 --> 00:50:37,780
+center of G is the subset of G consisting
+
+504
+00:50:37,780 --> 00:50:42,260
+of
+
+505
+00:50:42,260 --> 00:50:46,040
+those elements
+
+506
+00:50:47,470 --> 00:50:59,630
+يتكون من العناصر of g of g that that
+
+507
+00:50:59,630 --> 00:51:05,770
+commutes with
+
+508
+00:51:05,770 --> 00:51:11,310
+commutes with every
+
+509
+00:51:11,310 --> 00:51:23,690
+element of G with every element of
+
+510
+00:51:23,690 --> 00:51:35,040
+G that is بتصير هذا الكلام رياضيا فباجي بقول Z of G
+
+511
+00:51:35,040 --> 00:51:41,280
+أو الـ Center تبع لجروب G كل العناصر A اللي موجودة
+
+512
+00:51:41,280 --> 00:51:50,900
+في G بحيث أن ال A X بده يساوي ال X A لكل ال X اللي
+
+513
+00:51:50,900 --> 00:51:53,500
+موجود في G
+
+514
+00:52:01,760 --> 00:52:06,940
+مرة تانية نجي لحاجة اسمها ال center تبع ال group
+
+515
+00:52:06,940 --> 00:52:13,380
+مركز ال group مركز ال group هو كل العناصر اللي
+
+516
+00:52:13,380 --> 00:52:19,460
+بتبقى commutes مع جميع عناصر ال group حد فيكم بقدر
+
+517
+00:52:19,460 --> 00:52:24,990
+يجيب ليه element commute مع جميع عناصر ال group الـ
+
+518
+00:52:24,990 --> 00:52:28,490
+identity element ممتاز يبقى ال identity element
+
+519
+00:52:28,490 --> 00:52:33,870
+دائما و أبدا موجود في ال center تبع ال group تمام
+
+520
+00:52:33,870 --> 00:52:39,270
+يبقى هناك عناصر أخرى بس احنا بنضرب مثال بعضهم مش
+
+521
+00:52:39,270 --> 00:52:43,510
+هتلاقي غير ال identity element البعض الآخر هتلاقي
+
+522
+00:52:43,510 --> 00:52:49,710
+عناصر أخرى طيب سؤال لو كانت ال group abelian
+
+523
+00:52:52,230 --> 00:52:55,270
+يبقى الـ center تبع ال group بيساوي ال group كلها
+
+524
+00:52:55,270 --> 00:52:59,970
+كل عناصر ال group ليش؟ لأنه بيقولك كل العناصر اللي
+
+525
+00:52:59,970 --> 00:53:05,870
+موجود في ال group بحيث ax بيساوي xa لكل ال x اللي
+
+526
+00:53:05,870 --> 00:53:10,490
+موجود يعني ال element مشان يكون في ال center بديكم
+
+527
+00:53:10,490 --> 00:53:15,750
+يسمع جميع عناصر دي بلا استثناء مش واحد أو واحد لأ
+
+528
+00:53:16,790 --> 00:53:20,850
+هذا كده واحد أو واحد لأ في تسمية جديدة بدنا نسميها
+
+529
+00:53:20,850 --> 00:53:25,650
+إن شاء الله كويس للمرة القادمة عليها المرة القادمة
+
+530
+00:53:25,650 --> 00:53:31,030
+سنثبت أن ال center هذا هو ال sub group من ال group
+
+531
+00:53:31,030 --> 00:53:36,530
+الأساسية إن شاء الله تعالى ماشي يبقى stop المرة
+
+532
+00:53:36,530 --> 00:53:38,670
+القادمة بنكمل إن شاء الله
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..a5fe16cb5cb017c699c44af87b71c6102a2bdbab
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/_TZ6gd4sw_c_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3526, "start": 21.6, "end": 35.26, "text": "بسم الله الرحمن الرحيم عود على بدء في الفترة الصباحية أخدنا ثلاث نظريات اللي هو على ال subgroups لأن المواصل الحديث على نفس الموضوع", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6225, 23328, 15844, 47525, 38207, 8978, 27188, 2655, 25720, 31767, 3555, 39319, 10632, 5551, 9778, 3215, 8315, 38637, 1211, 5718, 104, 8717, 19913, 16572, 9307, 13672, 1829, 31439, 15844, 2423, 1422, 17377, 82, 5296, 33456, 9673, 2407, 33546, 1211, 21542, 16254, 12984, 15844, 8717, 36178, 9673, 2407, 11242, 45367], "avg_logprob": -0.17333157082735481, "compression_ratio": 1.5333333333333334, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 21.6, "end": 21.92, "word": "بسم", "probability": 0.621826171875}, {"start": 21.92, "end": 22.14, "word": " الله", "probability": 0.9658203125}, {"start": 22.14, "end": 22.54, "word": " الرحمن", "probability": 0.9498697916666666}, {"start": 22.54, "end": 23.1, 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"end": 222.13, "word": " generated", "probability": 0.86669921875}, {"start": 222.13, "end": 222.81, "word": " by", "probability": 0.9873046875}, {"start": 222.81, "end": 223.33, "word": " a", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 10, "seek": 24935, "start": 223.69, "end": 249.35, "text": "بسبب ان الـ M أو الـ N ناقص الـ M هو انتجر موجود في الـ Z إذا صار الـ identity element موجود هنا خدت عنصرين موجودات في ال group generated by A اللي جت الأول في معكس التاني موجود فيها يبقى by a previous", "tokens": [3555, 35457, 3555, 16472, 2423, 39184, 376, 34051, 2423, 39184, 426, 8717, 995, 4587, 9381, 2423, 39184, 376, 31439, 16472, 2655, 7435, 2288, 3714, 29245, 23328, 8978, 2423, 39184, 1176, 11933, 15730, 20328, 9640, 2423, 39184, 6575, 4478, 3714, 29245, 23328, 34105, 16490, 3215, 2655, 18871, 9381, 2288, 9957, 3714, 29245, 23328, 9307, 8978, 2423, 1594, 10833, 538, 316, 13672, 1829, 10874, 2655, 16247, 12610, 8978, 20449, 4117, 3794, 16712, 7649, 1829, 3714, 29245, 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بتبعتها remarks", "tokens": [3322, 37956, 44945, 19913, 2288, 10632, 8608, 16758, 28671, 13672, 1829, 31439, 2423, 1594, 10833, 538, 257, 307, 257, 1422, 17377, 7251, 3555, 4587, 7578, 29538, 2423, 1422, 17377, 4032, 4724, 39648, 29538, 33427, 1211, 2655, 20666, 3615, 1863, 9381, 2288, 257, 37495, 22653, 2423, 257, 4724, 1829, 7435, 1829, 3555, 28242, 18863, 1863, 33546, 2288, 39894, 3555, 34268, 11296, 19151], "avg_logprob": -0.18724797690106976, "compression_ratio": 1.4838709677419355, "no_speech_prob": 0.0, "words": [{"start": 252.49999999999997, "end": 253.73999999999998, "word": "theorem", "probability": 0.62548828125}, {"start": 253.73999999999998, "end": 254.98, "word": " بنظرية", "probability": 0.8695068359375}, {"start": 254.98, "end": 256.08, "word": " سابقة", "probability": 0.9778645833333334}, {"start": 256.08, "end": 257.04, "word": " اللي", "probability": 0.6474609375}, {"start": 257.04, "end": 257.32, "word": " هو", "probability": 0.93310546875}, {"start": 257.32, "end": 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273.16, "end": 275.8, "word": " remarks", "probability": 0.654296875}], "temperature": 1.0}, {"id": 12, "seek": 31049, "start": 281.19, "end": 310.49, "text": "النقطة الأولى لو كانت الـ G كلها بدأ تساوي ال subgroup generated by A نقول ان الـ G is cyclic الـ G is cyclic and the element", "tokens": [6027, 1863, 47432, 3660, 16247, 12610, 7578, 45164, 25961, 2655, 2423, 39184, 460, 28242, 11296, 47525, 10721, 6055, 3794, 995, 45865, 2423, 1422, 17377, 10833, 538, 316, 8717, 39648, 16472, 2423, 39184, 460, 307, 38154, 1050, 2423, 39184, 460, 307, 38154, 1050, 293, 264, 4478], "avg_logprob": -0.3603940230348836, "compression_ratio": 1.2835820895522387, "no_speech_prob": 0.0, "words": [{"start": 281.19, "end": 281.91, "word": "النقطة", "probability": 0.8262939453125}, {"start": 281.91, "end": 282.91, "word": " الأولى", "probability": 0.9534505208333334}, {"start": 282.91, "end": 285.09, "word": " لو", "probability": 0.62548828125}, {"start": 285.09, "end": 286.19, "word": " كانت", 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{"start": 293.19, "end": 299.63, "word": " الـ", "probability": 0.58984375}, {"start": 299.63, "end": 300.41, "word": " G", "probability": 0.94287109375}, {"start": 300.41, "end": 301.79, "word": " is", "probability": 0.149169921875}, {"start": 301.79, "end": 303.31, "word": " cyclic", "probability": 0.811767578125}, {"start": 303.31, "end": 304.61, "word": " الـ", "probability": 0.6785888671875}, {"start": 304.61, "end": 304.75, "word": " G", "probability": 0.943359375}, {"start": 304.75, "end": 305.07, "word": " is", "probability": 0.609375}, {"start": 305.07, "end": 305.85, "word": " cyclic", "probability": 0.8974609375}, {"start": 305.85, "end": 307.17, "word": " and", "probability": 0.78125}, {"start": 307.17, "end": 308.87, "word": " the", "probability": 0.4462890625}, {"start": 308.87, "end": 310.49, "word": " element", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 13, "seek": 34225, "start": 315.07, "end": 342.25, "text": "and the element a is a generator for اللي هو ال group g النقطة الثانية النقطة الثانية every", "tokens": [474, 264, 4478, 257, 307, 257, 19265, 337, 13672, 1829, 31439, 2423, 1594, 290, 28239, 47432, 3660, 6024, 104, 7649, 10632, 28239, 47432, 3660, 6024, 104, 7649, 10632, 633], "avg_logprob": -0.26770833830038704, "compression_ratio": 1.3736263736263736, "no_speech_prob": 0.0, "words": [{"start": 315.07, "end": 315.41, "word": "and", "probability": 0.157470703125}, {"start": 315.41, "end": 315.67, "word": " the", "probability": 0.58203125}, {"start": 315.67, "end": 316.25, "word": " element", "probability": 0.9091796875}, {"start": 316.25, "end": 317.27, "word": " a", "probability": 0.55419921875}, {"start": 317.27, "end": 318.47, "word": " is", "probability": 0.884765625}, {"start": 318.47, "end": 319.69, "word": " a", "probability": 0.927734375}, {"start": 319.69, "end": 322.09, "word": " generator", "probability": 0.97509765625}, {"start": 322.09, "end": 324.19, "word": " for", "probability": 0.95166015625}, {"start": 324.19, "end": 325.73, "word": " اللي", "probability": 0.56134033203125}, {"start": 325.73, "end": 325.97, "word": " هو", "probability": 0.94287109375}, {"start": 325.97, "end": 326.15, "word": " ال", "probability": 0.58203125}, {"start": 326.15, "end": 326.53, "word": " group", "probability": 0.8544921875}, {"start": 326.53, "end": 327.39, "word": " g", "probability": 0.415771484375}, {"start": 327.39, "end": 332.33, "word": " النقطة", "probability": 0.95556640625}, {"start": 332.33, "end": 333.81, "word": " الثانية", "probability": 0.9681396484375}, {"start": 333.81, "end": 340.13, "word": " النقطة", "probability": 0.94140625}, {"start": 340.13, "end": 340.83, "word": " الثانية", "probability": 0.980224609375}, {"start": 340.83, "end": 342.25, "word": " every", "probability": 0.640625}], "temperature": 1.0}, {"id": 14, "seek": 37265, "start": 345.79, "end": 372.65, "text": "cyclic group is abelian روح ندب صحة هذا الكلام ال remark اللي عنها عبارة عن نقطتين", "tokens": [1344, 66, 1050, 1594, 307, 410, 338, 952, 12602, 2407, 5016, 8717, 3215, 3555, 20328, 5016, 3660, 23758, 2423, 28820, 10943, 2423, 7942, 13672, 1829, 18871, 11296, 6225, 3555, 9640, 3660, 18871, 8717, 47432, 2655, 9957], "avg_logprob": -0.29138512546951706, "compression_ratio": 1.0884955752212389, "no_speech_prob": 0.0, "words": [{"start": 345.79, "end": 347.19, "word": "cyclic", "probability": 0.78466796875}, {"start": 347.19, "end": 348.59, "word": " group", "probability": 0.53857421875}, {"start": 348.59, "end": 353.19, "word": " is", "probability": 0.78564453125}, {"start": 353.19, "end": 355.85, "word": " abelian", "probability": 0.7423502604166666}, {"start": 355.85, "end": 360.07, "word": " روح", "probability": 0.6358642578125}, {"start": 360.07, "end": 360.37, "word": " ندب", "probability": 0.76025390625}, {"start": 360.37, "end": 360.93, "word": " صحة", "probability": 0.623779296875}, {"start": 360.93, "end": 361.21, "word": " هذا", "probability": 0.62158203125}, {"start": 361.21, "end": 363.43, "word": " الكلام", "probability": 0.9075520833333334}, {"start": 363.43, "end": 370.11, "word": " ال", "probability": 0.83642578125}, {"start": 370.11, "end": 370.45, "word": " remark", "probability": 0.70556640625}, {"start": 370.45, "end": 370.71, "word": " اللي", "probability": 0.883544921875}, {"start": 370.71, "end": 371.05, "word": " عنها", "probability": 0.59613037109375}, {"start": 371.05, "end": 371.55, "word": " عبارة", "probability": 0.8883056640625}, {"start": 371.55, "end": 371.77, "word": " عن", "probability": 0.9931640625}, {"start": 371.77, "end": 372.65, "word": " نقطتين", "probability": 0.963134765625}], "temperature": 1.0}, {"id": 15, "seek": 40312, "start": 373.56, "end": 403.12, "text": "النقطة الأولى بقول لو كانت ال G هي ال sub group generated by A يعني عناصر هنا لو جيت دورت عليهم فكتهم بدهم يطلعوا عناصر G الأصلية بروح نقول ال G is cyclic يبقى ال group G بقول عليها دالة دورية and element A وال A بقول generator ل G يعني ال A مولد لمين ل G", "tokens": [6027, 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"probability": 0.794921875}, {"start": 884.75, "end": 885.61, "word": " أربعة", "probability": 0.8572591145833334}, {"start": 885.61, "end": 887.33, "word": " اللي", "probability": 0.823974609375}, {"start": 887.33, "end": 887.47, "word": " هو", "probability": 0.8955078125}, {"start": 887.47, "end": 887.97, "word": " واحد", "probability": 0.962646484375}], "temperature": 1.0}, {"id": 36, "seek": 90858, "start": 889.82, "end": 908.58, "text": "مظبوط يبقى حط أسس زي ما بدك دايما لما بطلعه هدول يبقى السار ال sub group جينا تبقى تلتة هي واحد و تلتة و سبعة و تسعة في شغيرهم طب لو جيت للسبعة بنفس الطريقة سبعة أس Zero بواحد", "tokens": [2304, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 11331, 9566, 5551, 3794, 3794, 30767, 1829, 19446, 47525, 4117, 11778, 47302, 15042, 5296, 15042, 4724, 9566, 1211, 3615, 3224, 8032, 3215, 12610, 7251, 3555, 4587, 7578, 21136, 9640, 2423, 1422, 1594, 10874, 1829, 8315, 6055, 3555, 4587, 7578, 6055, 1211, 2655, 3660, 39896, 36764, 24401, 4032, 6055, 1211, 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بيظل", "probability": 0.949951171875}, {"start": 933.27, "end": 933.89, "word": " جداش", "probability": 0.6663411458333334}, {"start": 933.89, "end": 934.89, "word": " هايا", "probability": 0.712890625}], "temperature": 1.0}, {"id": 38, "seek": 95641, "start": 936.77, "end": 956.41, "text": "تعالى لتسعة أقص أربعة بتلاقي طالع يبقى كده؟ واحد صحيح يبقى ال subgroup generated by تلاتية ال subgroup generated by سبعة وتعتبر subgroup واحدة مش تنتين التنتين بس are equivalent طيب إيه إيش رأيك؟ ما علاقة الإتنين هدول بال group الأصلي؟", "tokens": [2655, 3615, 6027, 7578, 5296, 2655, 3794, 27884, 5551, 4587, 9381, 5551, 25513, 27884, 39894, 15040, 38436, 23032, 6027, 3615, 7251, 3555, 4587, 7578, 9122, 3215, 3224, 22807, 36764, 24401, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 2423, 1422, 17377, 10833, 538, 6055, 1211, 9307, 10632, 2423, 1422, 17377, 10833, 538, 8608, 3555, 27884, 34683, 34268, 26890, 1422, 17377, 36764, 24401, 3660, 37893, 6055, 29399, 9957, 16712, 29399, 9957, 4724, 3794, 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إيه", "probability": 0.7706705729166666}, {"start": 952.39, "end": 952.51, "word": " إيش", "probability": 0.6039225260416666}, {"start": 952.51, "end": 953.09, "word": " رأيك؟", "probability": 0.911328125}, {"start": 953.09, "end": 953.27, "word": " ما", "probability": 0.7197265625}, {"start": 953.27, "end": 953.83, "word": " علاقة", "probability": 0.9630533854166666}, {"start": 953.83, "end": 954.59, "word": " الإتنين", "probability": 0.758056640625}, {"start": 954.59, "end": 954.89, "word": " هدول", "probability": 0.90771484375}, {"start": 954.89, "end": 955.05, "word": " بال", "probability": 0.97705078125}, {"start": 955.05, "end": 955.29, "word": " group", "probability": 0.83251953125}, {"start": 955.29, "end": 956.41, "word": " الأصلي؟", "probability": 0.833984375}], "temperature": 1.0}, {"id": 39, "seek": 97747, "start": 956.91, "end": 977.47, "text": "إذا الـ subgroup ثوت لجروب الأصلية بنسميها improper subgroup يبقى هذي هذي is called improper subgroup او subgroup", "tokens": 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ال subgroup generated by سبعة بنسميها improper subgroup أي cyclic group تحسبها وتجدها تساوي لجروب الأصلية بسميها improper subgroup يعني كان ال subgroup غير فعلية يعني انت ماجيبتش جديد ليش؟ لأن any set is a subset of itself improper يعني غير فعلي", "tokens": [1829, 3555, 4587, 7578, 2423, 1422, 17377, 10833, 538, 6055, 1211, 9307, 3660, 34051, 2423, 1422, 17377, 10833, 538, 8608, 3555, 27884, 44945, 38251, 1829, 11296, 40651, 1422, 17377, 36632, 38154, 1050, 1594, 6055, 5016, 35457, 11296, 34683, 7435, 3215, 11296, 6055, 3794, 995, 45865, 5296, 7435, 32887, 3555, 16247, 36520, 10632, 4724, 38251, 1829, 11296, 40651, 1422, 17377, 37495, 22653, 25961, 2423, 1422, 17377, 32771, 13546, 6156, 30241, 10632, 37495, 22653, 16472, 2655, 3714, 26108, 1829, 3555, 2655, 8592, 10874, 16254, 3215, 32239, 8592, 22807, 5296, 33456, 604, 992, 307, 257, 25993, 295, 2564, 40651, 37495, 22653, 32771, 13546, 6156, 3615, 20292], "avg_logprob": -0.21003606328024313, "compression_ratio": 1.7937219730941705, 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{"start": 998.05, "end": 998.59, "word": " ليش؟", "probability": 0.7742513020833334}, {"start": 998.59, "end": 998.85, "word": " لأن", "probability": 0.825439453125}, {"start": 998.85, "end": 999.49, "word": " any", "probability": 0.63525390625}, {"start": 999.49, "end": 999.91, "word": " set", "probability": 0.95947265625}, {"start": 999.91, "end": 1000.21, "word": " is", "probability": 0.94970703125}, {"start": 1000.21, "end": 1000.53, "word": " a", "probability": 0.96240234375}, {"start": 1000.53, "end": 1000.99, "word": " subset", "probability": 0.93701171875}, {"start": 1000.99, "end": 1001.41, "word": " of", "probability": 0.9794921875}, {"start": 1001.41, "end": 1002.13, "word": " itself", "probability": 0.865234375}, {"start": 1002.13, "end": 1003.25, "word": " improper", "probability": 0.61572265625}, {"start": 1003.25, "end": 1003.71, "word": " يعني", "probability": 0.980712890625}, {"start": 1003.71, "end": 1004.21, "word": " غير", "probability": 0.996826171875}, {"start": 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subgroup", "probability": 0.635986328125}, {"start": 1072.14, "end": 1072.76, "word": " generated", "probability": 0.8125}, {"start": 1072.76, "end": 1073.08, "word": " by", "probability": 0.97509765625}, {"start": 1073.08, "end": 1073.56, "word": " تلاتة", "probability": 0.76531982421875}, {"start": 1073.56, "end": 1073.72, "word": " هي", "probability": 0.7568359375}, {"start": 1073.72, "end": 1073.9, "word": " ال", "probability": 0.86767578125}, {"start": 1073.9, "end": 1074.36, "word": " subgroup", "probability": 0.939453125}, {"start": 1074.36, "end": 1074.86, "word": " generated", "probability": 0.87841796875}, {"start": 1074.86, "end": 1075.22, "word": " by", "probability": 0.98681640625}, {"start": 1075.22, "end": 1075.78, "word": " السبعة", "probability": 0.8894856770833334}, {"start": 1075.78, "end": 1076.56, "word": " طيب", "probability": 0.9620768229166666}, {"start": 1076.56, "end": 1076.88, "word": " فيه", "probability": 0.87939453125}, {"start": 1076.88, "end": 1077.32, 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التلاتة والسبعة بواحدة وعشرين شيل عشرتين بيطلع ال identity element إذا التلاتة is the inverse of سبعة وبالتالي ال subgroup generated by تلاتة هي ال subgroup generated by سبعة يبقى هنا بقول not that", "tokens": [1829, 3555, 4587, 7578, 34105, 39896, 16712, 1211, 9307, 3660, 16070, 35457, 27884, 4724, 14407, 24401, 3660, 4032, 3615, 46309, 9957, 13412, 26895, 6225, 8592, 43500, 9957, 4724, 1829, 9566, 1211, 3615, 2423, 6575, 4478, 11933, 15730, 16712, 1211, 9307, 3660, 307, 264, 17340, 295, 8608, 3555, 27884, 46599, 6027, 2655, 6027, 1829, 2423, 1422, 17377, 10833, 538, 6055, 1211, 9307, 3660, 39896, 2423, 1422, 17377, 10833, 538, 8608, 3555, 27884, 7251, 3555, 4587, 7578, 34105, 4724, 39648, 406, 300], "avg_logprob": -0.21334876248865953, "compression_ratio": 1.7303370786516854, "no_speech_prob": 0.0, "words": [{"start": 1094.95, "end": 1095.79, "word": "يبقى", "probability": 0.7816162109375}, {"start": 1095.79, "end": 1096.13, "word": " هنا", "probability": 0.8427734375}, {"start": 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"word": " cyclic", "probability": 0.863525390625}, {"start": 1183.26, "end": 1184.62, "word": " and", "probability": 0.96484375}], "temperature": 1.0}, {"id": 49, "seek": 119839, "start": 1186.29, "end": 1198.39, "text": "تلاتة and سبعة are generators يبقى دول بيجيبولي كل group", "tokens": [2655, 1211, 9307, 3660, 293, 8608, 3555, 27884, 366, 38662, 7251, 3555, 4587, 7578, 11778, 12610, 4724, 1829, 7435, 1829, 3555, 12610, 1829, 28242, 1594], "avg_logprob": -0.15640023809212905, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 1186.29, "end": 1187.45, "word": "تلاتة", "probability": 0.769744873046875}, {"start": 1187.45, "end": 1188.09, "word": " and", "probability": 0.76171875}, {"start": 1188.09, "end": 1189.53, "word": " سبعة", "probability": 0.9674479166666666}, {"start": 1189.53, "end": 1190.51, "word": " are", "probability": 0.90283203125}, {"start": 1190.51, "end": 1192.25, "word": " generators", "probability": 0.98388671875}, {"start": 1192.25, "end": 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1648.36, "end": 1650.88, "word": " تقريبا", "probability": 0.98671875}, {"start": 1650.88, "end": 1651.94, "word": " تقري", "probability": 0.9762369791666666}], "temperature": 1.0}, {"id": 69, "seek": 167094, "start": 1652.04, "end": 1670.94, "text": "الان اقصد خمسة يعني خمسين اربع في اتناشر تمانية واربعين بيظل اتنين اللي بعدها ستين بيزيروا يبقى فعلا هذه ال sub group generated by عشرة هي ال sub group generated by اتنين تمام؟", "tokens": [6027, 7649, 1975, 4587, 9381, 3215, 16490, 2304, 3794, 3660, 37495, 22653, 16490, 2304, 3794, 9957, 1975, 25513, 3615, 8978, 1975, 2655, 1863, 33599, 2288, 46811, 7649, 10632, 4032, 9640, 3555, 3615, 9957, 4724, 1829, 19913, 1211, 1975, 2655, 1863, 9957, 13672, 1829, 39182, 11296, 8608, 2655, 9957, 4724, 1829, 11622, 13546, 14407, 7251, 3555, 4587, 7578, 6156, 3615, 15040, 29538, 2423, 1422, 1594, 10833, 538, 6225, 8592, 25720, 39896, 2423, 1422, 1594, 10833, 538, 1975, 2655, 1863, 9957, 46811, 10943, 22807], "avg_logprob": -0.2724021062793502, "compression_ratio": 1.6588235294117648, "no_speech_prob": 0.0, "words": [{"start": 1652.04, "end": 1652.96, "word": "الان", "probability": 0.7197265625}, {"start": 1652.96, "end": 1655.24, "word": " اقصد", "probability": 0.41943359375}, {"start": 1655.24, "end": 1655.88, "word": " خمسة", "probability": 0.83978271484375}, {"start": 1655.88, "end": 1656.28, "word": " يعني", "probability": 0.6553955078125}, {"start": 1656.28, "end": 1656.86, "word": " خمسين", "probability": 0.94921875}, {"start": 1656.86, "end": 1657.22, "word": " اربع", "probability": 0.7240397135416666}, {"start": 1657.22, "end": 1657.36, "word": " في", "probability": 0.40380859375}, {"start": 1657.36, "end": 1657.76, "word": " اتناشر", "probability": 0.91572265625}, {"start": 1657.76, "end": 1658.2, "word": " تمانية", "probability": 0.54302978515625}, {"start": 1658.2, "end": 1658.66, "word": " واربعين", "probability": 0.91796875}, {"start": 1658.66, "end": 1659.56, "word": " بيظل", "probability": 0.6953125}, {"start": 1659.56, "end": 1659.88, "word": " اتنين", "probability": 0.9476318359375}, {"start": 1659.88, "end": 1660.04, "word": " اللي", "probability": 0.583251953125}, {"start": 1660.04, "end": 1660.48, "word": " بعدها", "probability": 0.891845703125}, {"start": 1660.48, "end": 1661.18, "word": " ستين", "probability": 0.96435546875}, {"start": 1661.18, "end": 1661.88, "word": " بيزيروا", "probability": 0.82529296875}, {"start": 1661.88, "end": 1662.72, "word": " يبقى", "probability": 0.8944091796875}, {"start": 1662.72, "end": 1663.12, "word": " فعلا", "probability": 0.9571940104166666}, {"start": 1663.12, "end": 1663.64, "word": " هذه", "probability": 0.5478515625}, {"start": 1663.64, "end": 1664.18, "word": " ال", "probability": 0.75146484375}, {"start": 1664.18, "end": 1664.48, "word": " sub", "probability": 0.70703125}, {"start": 1664.48, "end": 1664.84, "word": " group", "probability": 0.470947265625}, {"start": 1664.84, "end": 1665.42, "word": " generated", "probability": 0.84619140625}, {"start": 1665.42, "end": 1665.7, "word": " by", "probability": 0.947265625}, {"start": 1665.7, "end": 1666.1, "word": " عشرة", "probability": 0.8797200520833334}, {"start": 1666.1, "end": 1666.3, "word": " هي", "probability": 0.8447265625}, {"start": 1666.3, "end": 1666.46, "word": " ال", "probability": 0.72021484375}, {"start": 1666.46, "end": 1666.66, "word": " sub", "probability": 0.87109375}, {"start": 1666.66, "end": 1667.06, "word": " group", "probability": 0.97265625}, {"start": 1667.06, "end": 1667.94, "word": " generated", "probability": 0.85693359375}, {"start": 1667.94, "end": 1668.82, "word": " by", "probability": 0.9736328125}, {"start": 1668.82, "end": 1670.16, "word": " اتنين", "probability": 0.967529296875}, {"start": 1670.16, "end": 1670.94, "word": " تمام؟", "probability": 0.8536783854166666}], "temperature": 1.0}, {"id": 70, "seek": 169721, "start": 1671.21, "end": 1697.21, "text": "طيب، الان يبقى صاروا كام subgroup عندى؟ تلاتة بس مافيش غيرهم، دير بالك انا بمهد لل chapter اللى بعده ال chapter هتبع ربوحيه تجيك أسئلة يقول لك list all the subgroups of ال group الفلانية مش هتروح تحطهم اتناشر واحدة يمكن بيطلعوش غير اربعة يمكن بيطلعوش غير خمسة يمكن غير ستة يبقى أنت تتقيد بالموجودة، هدول كلهم", "tokens": [9566, 1829, 3555, 12399, 2423, 7649, 7251, 3555, 4587, 7578, 20328, 9640, 14407, 9122, 10943, 1422, 17377, 43242, 7578, 22807, 6055, 1211, 9307, 3660, 4724, 3794, 19446, 41185, 8592, 32771, 13546, 16095, 12399, 11778, 13546, 20666, 4117, 1975, 8315, 4724, 2304, 3224, 3215, 24976, 7187, 13672, 7578, 39182, 3224, 2423, 7187, 8032, 2655, 3555, 3615, 12602, 3555, 2407, 5016, 1829, 3224, 6055, 7435, 1829, 4117, 5551, 3794, 19986, 37977, 7251, 39648, 5296, 4117, 1329, 439, 264, 1422, 17377, 82, 295, 2423, 1594, 27188, 1211, 7649, 10632, 37893, 8032, 2655, 32887, 5016, 6055, 5016, 9566, 16095, 1975, 2655, 1863, 33599, 2288, 36764, 24401, 3660, 7251, 43020, 4724, 1829, 9566, 1211, 3615, 2407, 8592, 32771, 13546, 1975, 25513, 27884, 7251, 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1675.03, "end": 1675.97, "word": " تلاتة", "probability": 0.905029296875}, {"start": 1675.97, "end": 1676.35, "word": " بس", "probability": 0.95361328125}, {"start": 1676.35, "end": 1676.85, "word": " مافيش", "probability": 0.732666015625}, {"start": 1676.85, "end": 1677.77, "word": " غيرهم،", "probability": 0.84759521484375}, {"start": 1677.77, "end": 1677.97, "word": " دير", "probability": 0.604736328125}, {"start": 1677.97, "end": 1678.35, "word": " بالك", "probability": 0.87353515625}, {"start": 1678.35, "end": 1678.71, "word": " انا", "probability": 0.703125}, {"start": 1678.71, "end": 1679.21, "word": " بمهد", "probability": 0.75787353515625}, {"start": 1679.21, "end": 1679.41, "word": " لل", "probability": 0.81005859375}, {"start": 1679.41, "end": 1679.75, "word": " chapter", "probability": 0.9658203125}, {"start": 1679.75, "end": 1680.05, "word": " اللى", "probability": 0.88623046875}, {"start": 1680.05, "end": 1680.49, "word": " بعده", "probability": 0.89990234375}, {"start": 1680.49, "end": 1680.91, "word": " ال", "probability": 0.4912109375}, {"start": 1680.91, "end": 1681.21, "word": " chapter", "probability": 0.87646484375}, {"start": 1681.21, "end": 1681.85, "word": " هتبع", "probability": 0.66790771484375}, {"start": 1681.85, "end": 1682.59, "word": " ربوحيه", "probability": 0.7354329427083334}, {"start": 1682.59, "end": 1682.97, "word": " تجيك", "probability": 0.849853515625}, {"start": 1682.97, "end": 1683.37, "word": " أسئلة", "probability": 0.870849609375}, {"start": 1683.37, "end": 1683.71, "word": " يقول", "probability": 0.833740234375}, {"start": 1683.71, "end": 1684.23, "word": " لك", "probability": 0.7451171875}, {"start": 1684.23, "end": 1684.89, "word": " list", "probability": 0.892578125}, {"start": 1684.89, "end": 1685.55, "word": " all", "probability": 0.89794921875}, {"start": 1685.55, "end": 1685.77, "word": " the", "probability": 0.84130859375}, {"start": 1685.77, "end": 1686.75, "word": " subgroups", "probability": 0.8932291666666666}, {"start": 1686.75, "end": 1686.89, "word": " of", "probability": 0.97802734375}, {"start": 1686.89, "end": 1687.03, "word": " ال", "probability": 0.6787109375}, {"start": 1687.03, "end": 1687.25, "word": " group", "probability": 0.93115234375}, {"start": 1687.25, "end": 1688.09, "word": " الفلانية", "probability": 0.89208984375}, {"start": 1688.09, "end": 1688.73, "word": " مش", "probability": 0.73486328125}, {"start": 1688.73, "end": 1689.05, "word": " هتروح", "probability": 0.9493408203125}, {"start": 1689.05, "end": 1689.47, "word": " تحطهم", "probability": 0.756072998046875}, {"start": 1689.47, "end": 1690.01, "word": " اتناشر", "probability": 0.81875}, {"start": 1690.01, "end": 1690.31, "word": " واحدة", "probability": 0.8953450520833334}, {"start": 1690.31, "end": 1690.45, "word": " يمكن", "probability": 0.7218017578125}, {"start": 1690.45, "end": 1690.87, "word": " بيطلعوش", "probability": 0.8291364397321429}, {"start": 1690.87, "end": 1691.05, "word": " غير", "probability": 0.89208984375}, {"start": 1691.05, "end": 1691.47, "word": " اربعة", "probability": 0.6988932291666666}, {"start": 1691.47, "end": 1692.01, "word": " يمكن", "probability": 0.76025390625}, {"start": 1692.01, "end": 1692.39, "word": " بيطلعوش", "probability": 0.9752371651785714}, {"start": 1692.39, "end": 1692.57, "word": " غير", "probability": 0.9560546875}, {"start": 1692.57, "end": 1693.09, "word": " خمسة", "probability": 0.92822265625}, {"start": 1693.09, "end": 1693.23, "word": " يمكن", "probability": 0.84716796875}, {"start": 1693.23, "end": 1693.41, "word": " غير", "probability": 0.9248046875}, {"start": 1693.41, "end": 1693.95, "word": " ستة", "probability": 0.9920247395833334}, {"start": 1693.95, "end": 1694.61, "word": " يبقى", "probability": 0.9560546875}, {"start": 1694.61, "end": 1694.93, "word": " أنت", "probability": 0.704833984375}, {"start": 1694.93, "end": 1695.55, "word": " تتقيد", "probability": 0.9151611328125}, {"start": 1695.55, "end": 1696.13, "word": " بالموجودة،", "probability": 0.8241780598958334}, {"start": 1696.13, "end": 1696.63, "word": " هدول", "probability": 0.9772135416666666}, {"start": 1696.63, "end": 1697.21, "word": " كلهم", "probability": 0.98779296875}], "temperature": 1.0}, {"id": 71, "seek": 171124, "start": 1697.42, "end": 1711.24, "text": "الاربع يعتبر واحدة وليس اربع يبقى واحدة فقط ده يعني طيب الان لو جيت قولتلك بد ال subgroup generated by خلصنا واحد واثنين بدنا تلاتة", "tokens": [6027, 9640, 3555, 3615, 7251, 34268, 26890, 36764, 24401, 3660, 4032, 20292, 3794, 1975, 25513, 3615, 7251, 3555, 4587, 7578, 36764, 24401, 3660, 6156, 47432, 11778, 3224, 37495, 22653, 23032, 1829, 3555, 2423, 7649, 45164, 10874, 36081, 12174, 12610, 2655, 23275, 47525, 2423, 1422, 17377, 10833, 538, 16490, 1211, 9381, 8315, 36764, 24401, 4032, 5718, 104, 1863, 9957, 47525, 8315, 6055, 1211, 9307, 3660], "avg_logprob": -0.23064903846153847, "compression_ratio": 1.489795918367347, "no_speech_prob": 0.0, "words": [{"start": 1697.42, "end": 1698.02, "word": "الاربع", "probability": 0.7525634765625}, {"start": 1698.02, "end": 1698.5, "word": " يعتبر", "probability": 0.7201334635416666}, {"start": 1698.5, "end": 1699.24, "word": " واحدة", "probability": 0.884765625}, {"start": 1699.24, "end": 1699.96, "word": " وليس", "probability": 0.8797200520833334}, {"start": 1699.96, "end": 1700.4, "word": " اربع", "probability": 0.81298828125}, {"start": 1700.4, "end": 1700.68, "word": " يبقى", "probability": 0.8167724609375}, {"start": 1700.68, "end": 1701.18, "word": " واحدة", "probability": 0.92822265625}, {"start": 1701.18, "end": 1701.64, "word": " فقط", "probability": 0.9384765625}, {"start": 1701.64, "end": 1701.9, "word": " ده", "probability": 0.599365234375}, {"start": 1701.9, "end": 1702.18, "word": " يعني", "probability": 0.7138671875}, {"start": 1702.18, "end": 1703.5, "word": " طيب", "probability": 0.8933919270833334}, {"start": 1703.5, "end": 1703.98, "word": " الان", "probability": 0.6978759765625}, {"start": 1703.98, "end": 1704.16, "word": " لو", "probability": 0.97412109375}, {"start": 1704.16, "end": 1704.44, "word": " جيت", "probability": 0.96337890625}, {"start": 1704.44, "end": 1704.96, "word": " قولتلك", "probability": 0.68560791015625}, {"start": 1704.96, "end": 1705.22, "word": " بد", "probability": 0.64013671875}, {"start": 1705.22, "end": 1705.44, "word": " ال", "probability": 0.69189453125}, {"start": 1705.44, "end": 1706.22, "word": " subgroup", "probability": 0.549072265625}, {"start": 1706.22, "end": 1707.38, "word": " generated", "probability": 0.82080078125}, {"start": 1707.38, "end": 1708.04, "word": " by", "probability": 0.98779296875}, {"start": 1708.04, "end": 1708.66, "word": " خلصنا", "probability": 0.968994140625}, {"start": 1708.66, "end": 1709.0, "word": " واحد", "probability": 0.948486328125}, {"start": 1709.0, "end": 1709.56, "word": " واثنين", "probability": 0.8326171875}, {"start": 1709.56, "end": 1710.46, "word": " بدنا", "probability": 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ولا لأ وإذا كانت Cyclic من هم ال generator", "tokens": [2304, 7435, 3215, 3215, 8592, 8717, 2304, 25720, 6055, 1211, 9307, 3660, 1176, 4032, 3615, 20292, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 1176, 4032, 3615, 20292, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 6156, 995, 37983, 12610, 1829, 8032, 1211, 29538, 10295, 66, 1050, 49429, 5296, 10721, 4032, 28814, 15730, 25961, 2655, 10295, 66, 1050, 9154, 8032, 2304, 2423, 19265], "avg_logprob": -0.3162802424161665, "compression_ratio": 1.5037593984962405, "no_speech_prob": 0.0, "words": [{"start": 1876.57, "end": 1877.15, "word": "مجددش", "probability": 0.54892578125}, {"start": 1877.15, "end": 1877.53, "word": " نمرة", "probability": 0.80908203125}, {"start": 1877.53, "end": 1879.87, "word": " تلاتة", "probability": 0.9254150390625}, {"start": 1879.87, "end": 1882.71, "word": " Z", "probability": 0.058502197265625}, {"start": 1882.71, "end": 1889.11, "word": " وعليها", "probability": 0.6749267578125}, {"start": 1889.11, "end": 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"end": 1934.56, "word": " احنا", "probability": 0.9495442708333334}, {"start": 1934.56, "end": 1934.94, "word": " عاملنا", "probability": 0.76416015625}, {"start": 1934.94, "end": 1935.78, "word": " contradiction", "probability": 0.9091796875}, {"start": 1935.78, "end": 1936.64, "word": " للكلام", "probability": 0.8753255208333334}, {"start": 1936.64, "end": 1936.82, "word": " اللى", "probability": 0.984375}, {"start": 1936.82, "end": 1938.14, "word": " بتقوله", "probability": 0.9876302083333334}, {"start": 1938.14, "end": 1938.82, "word": " بتصير", "probability": 0.9012044270833334}, {"start": 1938.82, "end": 1939.36, "word": " ايش؟", "probability": 0.76416015625}, {"start": 1939.36, "end": 1940.24, "word": " بتصير", "probability": 0.8621419270833334}, {"start": 1940.24, "end": 1940.94, "word": " cyclic", "probability": 0.81201171875}, {"start": 1940.94, "end": 1942.32, "word": " ونافع", "probability": 0.71783447265625}, {"start": 1942.32, "end": 1942.64, "word": " انها", 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فيها فيها الست فيها الست على خمسة على خمسة فيها السبعة يبقى فيها السبعة في خمسة بتلاتي يبقى تنين و سبعين درجة", "tokens": [3555, 16254, 1975, 4587, 38251, 15844, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 4587, 38251, 6055, 1211, 9307, 2304, 10632, 4032, 8608, 2655, 9957, 15844, 16490, 2304, 3794, 3660, 8978, 11296, 21136, 2655, 8978, 16490, 2304, 3794, 3660, 39894, 1211, 9307, 1829, 8978, 11296, 8978, 11296, 21136, 2655, 8978, 11296, 21136, 2655, 15844, 16490, 2304, 3794, 3660, 15844, 16490, 2304, 3794, 3660, 8978, 11296, 21136, 3555, 27884, 7251, 3555, 4587, 7578, 8978, 11296, 21136, 3555, 27884, 8978, 16490, 2304, 3794, 3660, 39894, 1211, 9307, 1829, 7251, 3555, 4587, 7578, 6055, 1863, 9957, 4032, 8608, 3555, 3615, 9957, 11778, 47341, 3660], "avg_logprob": -0.13549106802259173, "compression_ratio": 2.6929133858267718, "no_speech_prob": 0.0, "words": [{"start": 2430.15, "end": 2430.63, "word": "بدي", "probability": 0.542236328125}, {"start": 2430.63, "end": 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" rotations", "probability": 0.98486328125}, {"start": 2650.26, "end": 2650.46, "word": " و", "probability": 0.86767578125}, {"start": 2650.46, "end": 2650.86, "word": " أربع", "probability": 0.9015299479166666}, {"start": 2650.86, "end": 2651.96, "word": " reflections،", "probability": 0.796142578125}, {"start": 2651.96, "end": 2652.04, "word": " من", "probability": 0.63330078125}, {"start": 2652.04, "end": 2653.92, "word": " ذاكرين؟", "probability": 0.89697265625}, {"start": 2653.92, "end": 2654.38, "word": " سكات", "probability": 0.6156412760416666}, {"start": 2654.38, "end": 2654.86, "word": " الشعب", "probability": 0.9879557291666666}], "temperature": 1.0}, {"id": 112, "seek": 267585, "start": 2655.79, "end": 2675.85, "text": "اربع روتيشن واربع رفليكشن يبقى اربع روتيشن يبقى اربع روتيشن واربع رفليكشن يبقى اربع روتيشن", "tokens": [9640, 3555, 3615, 12602, 35473, 1829, 8592, 1863, 4032, 9640, 3555, 3615, 12602, 5172, 20292, 4117, 8592, 1863, 7251, 3555, 4587, 7578, 1975, 25513, 3615, 12602, 35473, 1829, 8592, 1863, 7251, 3555, 4587, 7578, 1975, 25513, 3615, 12602, 35473, 1829, 8592, 1863, 4032, 9640, 3555, 3615, 12602, 5172, 20292, 4117, 8592, 1863, 7251, 3555, 4587, 7578, 1975, 25513, 3615, 12602, 35473, 1829, 8592, 1863], "avg_logprob": -0.2899038461538462, "compression_ratio": 2.721311475409836, "no_speech_prob": 0.0, "words": [{"start": 2655.79, "end": 2656.41, "word": "اربع", "probability": 0.6514892578125}, {"start": 2656.41, "end": 2657.07, "word": " روتيشن", "probability": 0.695849609375}, {"start": 2657.07, "end": 2657.67, "word": " واربع", "probability": 0.9017333984375}, {"start": 2657.67, "end": 2658.45, "word": " رفليكشن", "probability": 0.8636881510416666}, {"start": 2658.45, "end": 2663.29, "word": " يبقى", "probability": 0.6915435791015625}, {"start": 2663.29, "end": 2663.67, "word": " اربع", "probability": 0.6648356119791666}, {"start": 2663.67, "end": 2664.51, "word": " روتيشن", "probability": 0.897265625}, {"start": 2664.51, "end": 2665.27, "word": " يبقى", "probability": 0.73779296875}, {"start": 2665.27, "end": 2665.69, "word": " اربع", "probability": 0.9436848958333334}, {"start": 2665.69, "end": 2666.25, "word": " روتيشن", "probability": 0.978515625}, {"start": 2666.25, "end": 2668.01, "word": " واربع", "probability": 0.7418441772460938}, {"start": 2668.01, "end": 2669.03, "word": " رفليكشن", "probability": 0.9853515625}, {"start": 2669.03, "end": 2673.63, "word": " يبقى", "probability": 0.8936767578125}, {"start": 2673.63, "end": 2673.99, "word": " اربع", "probability": 0.9768880208333334}, {"start": 2673.99, "end": 2675.85, "word": " روتيشن", "probability": 0.983984375}], "temperature": 1.0}, {"id": 113, "seek": 269865, "start": 2675.97, "end": 2698.65, "text": "و كتبت معاكم في الدفتر ان لو ضربت ال reflection فى ال rotation او ال rotation فى ال reflection على كل الأمرين بده يطلع مين reflection تمام يبقى ارى اللى عندها دى rotation بتسعين بتنين وسبعين بمية وعشرين انت حر مين ما تكون ال rotation داك", "tokens": [2407, 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{"start": 2696.85, "end": 2697.09, "word": " حر", "probability": 0.9833984375}, {"start": 2697.09, "end": 2697.31, "word": " مين", "probability": 0.768310546875}, {"start": 2697.31, "end": 2697.43, "word": " ما", "probability": 0.80322265625}, {"start": 2697.43, "end": 2697.67, "word": " تكون", "probability": 0.976318359375}, {"start": 2697.67, "end": 2697.79, "word": " ال", "probability": 0.97705078125}, {"start": 2697.79, "end": 2698.21, "word": " rotation", "probability": 0.99267578125}, {"start": 2698.21, "end": 2698.65, "word": " داك", "probability": 0.76025390625}], "temperature": 1.0}, {"id": 114, "seek": 271675, "start": 2698.95, "end": 2716.75, "text": "معنى هذا الكلام ان ال rotation commutes مع نفسها مع أي rotation أخرى لكن مع ال reflection مش صحيح يعني لما كنا نقول مثلا R تسعين في H هل هي H في R تسعين؟", "tokens": [2304, 3615, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 2423, 12447, 800, 1819, 20449, 8717, 36178, 11296, 20449, 36632, 12447, 5551, 34740, 7578, 44381, 20449, 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0.9638671875}, {"start": 2703.09, "end": 2703.99, "word": " نفسها", "probability": 0.9724934895833334}, {"start": 2703.99, "end": 2704.51, "word": " مع", "probability": 0.66015625}, {"start": 2704.51, "end": 2704.95, "word": " أي", "probability": 0.4931640625}, {"start": 2704.95, "end": 2706.05, "word": " rotation", "probability": 0.90234375}, {"start": 2706.05, "end": 2706.83, "word": " أخرى", "probability": 0.9285481770833334}, {"start": 2706.83, "end": 2707.21, "word": " لكن", "probability": 0.76953125}, {"start": 2707.21, "end": 2707.43, "word": " مع", "probability": 0.974609375}, {"start": 2707.43, "end": 2707.57, "word": " ال", "probability": 0.73291015625}, {"start": 2707.57, "end": 2708.09, "word": " reflection", "probability": 0.89599609375}, {"start": 2708.09, "end": 2709.13, "word": " مش", "probability": 0.54296875}, {"start": 2709.13, "end": 2709.75, "word": " صحيح", "probability": 0.994873046875}, {"start": 2709.75, "end": 2710.45, "word": " يعني", "probability": 0.88720703125}, {"start": 2710.45, "end": 2710.65, "word": " لما", "probability": 0.890869140625}, {"start": 2710.65, "end": 2710.97, "word": " كنا", "probability": 0.902099609375}, {"start": 2710.97, "end": 2711.31, "word": " نقول", "probability": 0.95068359375}, {"start": 2711.31, "end": 2711.69, "word": " مثلا", "probability": 0.903564453125}, {"start": 2711.69, "end": 2712.17, "word": " R", "probability": 0.48681640625}, {"start": 2712.17, "end": 2713.41, "word": " تسعين", "probability": 0.8961181640625}, {"start": 2713.41, "end": 2714.01, "word": " في", "probability": 0.96142578125}, {"start": 2714.01, "end": 2714.63, "word": " H", "probability": 0.91259765625}, {"start": 2714.63, "end": 2715.23, "word": " هل", "probability": 0.8447265625}, {"start": 2715.23, "end": 2715.43, "word": " هي", "probability": 0.77783203125}, {"start": 2715.43, "end": 2715.75, "word": " H", "probability": 0.759765625}, {"start": 2715.75, "end": 2715.95, "word": " في", "probability": 0.435791015625}, {"start": 2715.95, "end": 2716.07, "word": " R", "probability": 0.96923828125}, {"start": 2716.07, "end": 2716.75, "word": " تسعين؟", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 115, "seek": 273516, "start": 2721.12, "end": 2735.16, "text": "العملية ليست إبدالية لما نقل روتيشن مع نفسه اذا قلت ر تسعين في ر مية و تمانين أليست ر مية و تمانين في ر تسعين؟", "tokens": [6027, 3615, 42213, 10632, 32239, 14851, 11933, 44510, 6027, 10632, 5296, 15042, 8717, 4587, 1211, 12602, 35473, 1829, 8592, 1863, 20449, 8717, 36178, 3224, 1975, 15730, 12174, 1211, 2655, 12602, 6055, 3794, 3615, 9957, 8978, 12602, 3714, 10632, 4032, 46811, 7649, 9957, 5551, 20292, 14851, 12602, 3714, 10632, 4032, 46811, 7649, 9957, 8978, 12602, 6055, 3794, 3615, 9957, 22807], "avg_logprob": -0.47864582935969036, "compression_ratio": 1.7345132743362832, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2721.12, "end": 2722.0, "word": "العملية", "probability": 0.570587158203125}, {"start": 2722.0, "end": 2722.84, "word": " ليست", "probability": 0.7421875}, {"start": 2722.84, "end": 2724.02, "word": " إبدالية", "probability": 0.7841796875}, {"start": 2724.02, "end": 2726.74, "word": " لما", "probability": 0.32611083984375}, {"start": 2726.74, "end": 2727.2, "word": " نقل", "probability": 0.5763346354166666}, {"start": 2727.2, "end": 2728.02, "word": " روتيشن", "probability": 0.64832763671875}, {"start": 2728.02, "end": 2728.18, "word": " مع", "probability": 0.603515625}, {"start": 2728.18, "end": 2728.62, "word": " نفسه", "probability": 0.7647298177083334}, {"start": 2728.62, "end": 2728.8, "word": " اذا", "probability": 0.53936767578125}, {"start": 2728.8, "end": 2729.2, "word": " قلت", "probability": 0.92236328125}, {"start": 2729.2, "end": 2729.42, "word": " ر", "probability": 0.1553955078125}, {"start": 2729.42, "end": 2730.14, "word": " تسعين", "probability": 0.9385986328125}, {"start": 2730.14, "end": 2730.74, "word": " في", "probability": 0.80419921875}, {"start": 2730.74, "end": 2731.22, "word": " ر", "probability": 0.37744140625}, {"start": 2731.22, "end": 2731.82, "word": " مية", "probability": 0.891845703125}, {"start": 2731.82, "end": 2731.96, "word": " و", "probability": 0.64990234375}, {"start": 2731.96, "end": 2732.38, "word": " تمانين", "probability": 0.9435221354166666}, {"start": 2732.38, "end": 2732.94, "word": " أليست", "probability": 0.4269612630208333}, {"start": 2732.94, "end": 2733.18, "word": " ر", "probability": 0.74560546875}, {"start": 2733.18, "end": 2733.42, "word": " مية", "probability": 0.880126953125}, {"start": 2733.42, "end": 2733.52, "word": " و", "probability": 0.9765625}, {"start": 2733.52, "end": 2733.94, "word": " تمانين", "probability": 0.982421875}, {"start": 2733.94, "end": 2734.1, "word": " في", "probability": 0.93408203125}, {"start": 2734.1, "end": 2734.26, "word": " ر", "probability": 0.76025390625}, {"start": 2734.26, "end": 2735.16, "word": " تسعين؟", "probability": 0.88505859375}], "temperature": 1.0}, {"id": 116, "seek": 276185, "start": 2742.59, "end": 2761.85, "text": "يعني يعني الإبدال مع ال rotation مية المية ماعناه مشكلة إذا لما أقول ال subgroup generated by R هذه هتعطيني مين؟ هتعطيني ال identity element اللي هسميه مين؟ اللي هسميه Arnold", "tokens": [40228, 22653, 37495, 22653, 33688, 44510, 6027, 20449, 2423, 12447, 3714, 10632, 9673, 10632, 19446, 3615, 8315, 3224, 37893, 28820, 3660, 11933, 15730, 5296, 15042, 5551, 39648, 2423, 1422, 17377, 10833, 538, 497, 29538, 8032, 2655, 3615, 9566, 9957, 1829, 3714, 9957, 22807, 8032, 2655, 3615, 9566, 9957, 1829, 2423, 6575, 4478, 13672, 1829, 8032, 38251, 1829, 3224, 3714, 9957, 22807, 13672, 1829, 8032, 38251, 1829, 3224, 30406], "avg_logprob": -0.2506793409154035, "compression_ratio": 1.5549132947976878, "no_speech_prob": 0.0, "words": [{"start": 2742.59, "end": 2743.13, "word": "يعني", "probability": 0.5692138671875}, {"start": 2743.13, "end": 2744.11, "word": " يعني", "probability": 0.537353515625}, {"start": 2744.11, "end": 2745.47, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck.srt
new file mode 100644
index 0000000000000000000000000000000000000000..89bc7c438a5b02dce01e56b3732f8e0951bbbdfe
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck.srt
@@ -0,0 +1,1491 @@
+1
+00:00:20,970 --> 00:00:25,690
+بسم الله الرحمن الرحيم مواصلة ما ابتدأنا به في ال
+
+2
+00:00:25,690 --> 00:00:29,650
+chapter الأول وهو الـ chapter المقدمة التأسيسية
+
+3
+00:00:29,650 --> 00:00:35,190
+لموضوع الـ groups وصلنا إلى النقطة الأخيرة من هذا
+
+4
+00:00:35,190 --> 00:00:39,170
+الـ chapter وهي موضوع الـ functions أو الـ mapping
+
+5
+00:00:39,170 --> 00:00:45,310
+يعني الدوال أو الاقترانات، طبعًا الدالة أخذنا تعريف
+
+6
+00:00:45,310 --> 00:00:50,230
+في Calculus A وأخذنا إيش معنى one to one function
+
+7
+00:00:50,230 --> 00:00:54,970
+وبعد ذلك على مبادئ الرياضيات رجعنا أخذنا تعريف الـ
+
+8
+00:00:54,970 --> 00:00:58,330
+function كمان مرة وعرفنا ما هي الـ one to one
+
+9
+00:00:58,330 --> 00:01:02,890
+function وما هي الـ one to function والـ composition
+
+10
+00:01:02,890 --> 00:01:07,590
+ما بين two functions، اليوم نظرة لأهمية الموضوع
+
+11
+00:01:07,590 --> 00:01:14,270
+للموضوع الذي سيساعدنا الموضوعين سيأتيانِ فيما بعد، و
+
+12
+00:01:14,270 --> 00:01:19,030
+خاصة موضوع الـ isomorphism والـ homomorphism، بدنا
+
+13
+00:01:19,030 --> 00:01:24,350
+نرجع نؤسس مرة ثانية أو نذكر إيه اللي ناسي بما سبق
+
+14
+00:01:24,350 --> 00:01:29,050
+دراسته، فبأجي أول شيء لتعريف الـ function، فبأجي بقول
+
+15
+00:01:29,050 --> 00:01:34,490
+في من الـ set A إلى الـ set B is a rule that assigns
+
+16
+00:01:34,490 --> 00:01:40,290
+تعين أو تخصص لكل عنصر موجود في الـ set A بالضبط
+
+17
+00:01:40,290 --> 00:01:45,650
+عنصر واحد فقط لا غير، بي موجود في الـ set B، وبروح
+
+18
+00:01:45,650 --> 00:01:49,910
+نكتب أنه في of a بدها تساوي مين؟ بدها تساوي بي
+
+19
+00:01:49,910 --> 00:01:55,380
+خليني أتوقف عشان نقف
+
+20
+00:01:55,380 --> 00:02:00,640
+على كل نقطة في هذا التعريف، بيقول لي هادي في من الـ
+
+21
+00:02:00,640 --> 00:02:07,280
+6a إلى الـ 6b، بقول عليها function لو هدي خصصة لكل
+
+22
+00:02:07,280 --> 00:02:13,860
+عنصر من الـ 6a، يبقى في هتأثر على جميع عناصر الـ 6a
+
+23
+00:02:13,860 --> 00:02:20,700
+ولا على بعضها دون البعض الآخر؟ على من؟ على الكل؟ والله
+
+24
+00:02:20,700 --> 00:02:26,560
+على بعضهم، على الكل، نجي to each element لكل عنصر
+
+25
+00:02:26,560 --> 00:02:31,460
+في الـ set A، إذا الـ fi ستؤثر على جميع عناصر الـ set
+
+26
+00:02:31,460 --> 00:02:36,940
+A، الـ set A، هدي هسميها domain الـ function، المجال
+
+27
+00:02:36,940 --> 00:02:41,100
+تبع الـ function، طيب لما تأثر على هذا العنصر بدي
+
+28
+00:02:41,100 --> 00:02:47,670
+يطلع لمين؟ exactly one element B موجود في B، يبقى
+
+29
+00:02:47,670 --> 00:02:53,650
+عنصرًا واحدًا بالضبط في الـ set B، تمام؟ هذا بدي أطرح
+
+30
+00:02:53,650 --> 00:02:59,130
+لنا مجموعة من المسائل، السؤال الأول: هل يمكن لعنصر
+
+31
+00:02:59,130 --> 00:03:05,590
+من الـ set A أن تكون له صورتان في الـ set B؟ لا، لأنه
+
+32
+00:03:05,590 --> 00:03:10,550
+قال exactly بالضبط one element، يبقى العنصر الواحد
+
+33
+00:03:10,550 --> 00:03:16,590
+في الـ set B سنجد له صورة واحدة فقط في الـ set B، لو
+
+34
+00:03:16,590 --> 00:03:21,610
+حصل أن العنصر لاجي ناله صورتين، يبقى هذه ليست
+
+35
+00:03:21,610 --> 00:03:26,790
+function، طب السؤال الثاني: هل يمكن لعنصرين من الـ
+
+36
+00:03:26,790 --> 00:03:34,260
+set A أن يشتركا في صورة واحدة من الـ set B؟ صحيح، لأنه
+
+37
+00:03:34,260 --> 00:03:39,420
+لم يشترط ذلك، إذا يمكن لعنصرين وممكن ثلاثة وممكن
+
+38
+00:03:39,420 --> 00:03:43,440
+أربعة وممكن كل عناصر A تطلع لهم نفس الصورة عادي
+
+39
+00:03:43,440 --> 00:03:47,780
+جدا، زي إيش مثلا؟ لو جينا نقول لك أنا عندي function
+
+40
+00:03:47,780 --> 00:03:52,200
+من الـ set of real numbers للـ set of real numbers معرفة
+
+41
+00:03:52,200 --> 00:03:56,060
+كتلة f of x يساوي خمسة، اللي هي الـ constant function
+
+42
+00:03:56,060 --> 00:03:59,600
+يبقى جميع عناصر الـ set of real numbers بدها تروح
+
+43
+00:03:59,600 --> 00:04:06,260
+لمين؟ إذا عنصر واحد ظهر كصورة لجميع عناصر الـ set
+
+44
+00:04:06,260 --> 00:04:09,620
+الأولى اللي هو الـ domain تبعها، يبقى معناها مشكلة
+
+45
+00:04:09,620 --> 00:04:16,020
+إذا يمكن لعنصر أو أكثر أو كل العناصر يشتركوا في
+
+46
+00:04:16,020 --> 00:04:21,420
+نفس الصورة، لكن لا يمكن لعنصر واحد أن تظهر له صورتان
+
+47
+00:04:21,420 --> 00:04:27,060
+ممتاز جدا، طيب هل اشترط في هذا التعريف أن جميع
+
+48
+00:04:27,060 --> 00:04:33,340
+عناصر بي تظهروا كصور لعناصر A؟ لا، لم يقل ذلك، مجالش
+
+49
+00:04:33,340 --> 00:04:39,800
+ذلك، ولذلك لما أقول أنا عندي في من الـ set A للـ set
+
+50
+00:04:39,800 --> 00:04:45,400
+B، يعني لو جيت قلت هذه الـ set A وهذه مثلا الـ set
+
+51
+00:04:45,400 --> 00:04:50,340
+B على سبيل المثال، إذا لو افترضت أنه ما عنديش إلا
+
+52
+00:04:50,340 --> 00:04:56,960
+ثلاثة عناصر هنا وهنا عندي مجموعة من العناصر، وليكن
+
+53
+00:04:56,960 --> 00:05:01,900
+خمسة، إذا الثلاثة هدول ممكن تطلع لهم صورة واحدة، و
+
+54
+00:05:01,900 --> 00:05:06,760
+ممكن صورتين، وممكن ثلاث صور، أكثر من هيك ممكن، ما فيش
+
+55
+00:05:06,760 --> 00:05:12,000
+إمكانية، إذا ممكن هذا العنصر تطلع صورته هذه، وهذا
+
+56
+00:05:12,000 --> 00:05:16,320
+العنصر تطلع صورته هذه، وهذا العنصر تطلع صورته هذه
+
+57
+00:05:16,320 --> 00:05:21,980
+إذا الاثنين اللي في النص دول ما لهم، لم يظهر كصور
+
+58
+00:05:21,980 --> 00:05:29,160
+لعناصر من الـ set A، إذا هذه الـ set B بسميها الـ co-
+
+59
+00:05:29,160 --> 00:05:33,820
+domain، المجال المصاحب أو المجال المناظر، لمين؟
+
+60
+00:05:35,850 --> 00:05:42,590
+العناصر التي ظهرت كصور بسميها الـ range، المدى، تبع
+
+61
+00:05:42,590 --> 00:05:47,610
+من؟ تبع الـ function Φ، يبقى هذه كل الأسئلة التي مرت علينا
+
+62
+00:05:47,610 --> 00:05:52,450
+قبل ذلك، حبيت أذكرها هنا، في بعض الملاحظات على هذا
+
+63
+00:05:52,740 --> 00:05:57,140
+التعريف، الملاحظة الأولى أن الـ A بسمي الـ domain
+
+64
+00:05:57,140 --> 00:06:02,020
+والـ B بسميه co-domain للـ function Φ
+
+65
+00:06:02,020 --> 00:06:06,720
+المجال والمجال المناظر، المجال والمجال المصاحب
+
+66
+00:06:06,720 --> 00:06:13,800
+النقطة الثانية: العنصر B هذا، يعني لو جيت قلت هذه
+
+67
+00:06:13,800 --> 00:06:20,620
+النقطة A، هذه اللي ظهرت عندنا اللي هي B تساوي الـ F
+
+68
+00:06:20,620 --> 00:06:26,960
+of A، يبقى الـ element بي اللي موجود في بي بسميه
+
+69
+00:06:26,960 --> 00:06:33,980
+image of a under Φ، يعني صورة العنصر a تحت تأثير
+
+70
+00:06:33,980 --> 00:06:39,220
+الـ function Φ، في لما أثرت على العنصر a اللي عندنا
+
+71
+00:06:39,220 --> 00:06:46,640
+هذا خلت صورته منب مين؟ هي بي، هي f of a، يبقى هي
+
+72
+00:06:46,640 --> 00:06:52,640
+العنصر اللي نتج نتيجة لتأثير الـ Φ على العنصر a
+
+73
+00:06:52,640 --> 00:06:58,320
+اللي موجود وين؟ في domain، إذا بي هي الـ image تبعت
+
+74
+00:06:58,320 --> 00:07:01,380
+لمين؟ يعني هي صورة العنصر a
+
+75
+00:07:05,090 --> 00:07:11,830
+الآن لو جيت أخذت كل الصور تبعت عناصر A، بطلع عند
+
+76
+00:07:11,830 --> 00:07:16,770
+من؟ بطلع عند الـ range تبع الـ Φ، يبقى أنا عند
+
+77
+00:07:16,770 --> 00:07:20,110
+العناصر الثلاثة، الـ range عندهم الثلاث عناصر هدول
+
+78
+00:07:20,110 --> 00:07:23,770
+يبقى الثلاث عناصر اللي من بي هدول بسميهم إيه؟
+
+79
+00:07:23,770 --> 00:07:29,470
+بسميهم الـ range تبع من؟ تبع الـ function Φ، إذا
+
+80
+00:07:29,470 --> 00:07:32,750
+بالنسبة للتعريف الأول، بدنا نجي للتعريف الثاني
+
+81
+00:07:32,750 --> 00:07:38,030
+Gallify من الـ set A إلى الـ set B و Epsilon من B إلى C
+
+82
+00:07:38,030 --> 00:07:42,910
+عبارة عن functions، بدي أكون من الـ two functions
+
+83
+00:07:42,910 --> 00:07:47,950
+function جديدة بسميها الدالة المحصلة أو الدالة
+
+84
+00:07:47,950 --> 00:07:53,160
+التركيبية، الـ composite function، يبقى هدول بدي أكون
+
+85
+00:07:53,160 --> 00:07:56,460
+منهم دالة اسمها الـ Composite Function اللي هي
+
+86
+00:07:56,460 --> 00:08:01,180
+الدالة المحصلة أو الدالة التركيبية، وبديها الرمز
+
+87
+00:08:01,180 --> 00:08:07,820
+Epsilon Composition Phi، واختصارًا هقول Epsilon Phi بدون
+
+88
+00:08:07,820 --> 00:08:11,710
+لفظ كلمة الـ composition، لكن بديك تفهم إن هذه
+
+89
+00:08:11,710 --> 00:08:16,610
+محصلة الـ two functions، مش حاصل ضربهما، حاصل ضرب
+
+90
+00:08:16,610 --> 00:08:19,530
+two functions غير الـ composition of two functions
+
+91
+00:08:19,530 --> 00:08:22,770
+أنا مش هتكلم اللي هو حاصل ضرب functions، كلام عتيق، هذا
+
+92
+00:08:22,770 --> 00:08:26,590
+هذا في Calculus A، أنا بهمّني الـ composition of two
+
+93
+00:08:26,590 --> 00:08:31,650
+functions، يبقى في من a إلى b، إبصي من b إلى c، بدي
+
+94
+00:08:31,650 --> 00:08:36,790
+أجيب المحصلة تبعتهم، اللي هي إبصي، هتكون من الـ set a
+
+95
+00:08:36,790 --> 00:08:41,810
+إلى الـ set c، يبقى في من الـ set a إلى الـ set c is defined
+
+96
+00:08:41,810 --> 00:08:47,470
+by Φ، إبصي Φ of a يساوي، اللي في domain مين؟ 
+
+97
+00:08:49,760 --> 00:08:55,760
+في domain الـ Φ، لأن هاي Φ هنا من a إلى b، يبقى الـ a
+
+98
+00:08:55,760 --> 00:09:01,540
+small موجود وين؟ في الـ a كفترة، إذا العنصر a موجود
+
+99
+00:09:01,540 --> 00:09:07,200
+في domain الـ Φ وبالتالي الـ Φ هتقدر تأثر عليه، بيبقى
+
+100
+00:09:07,200 --> 00:09:13,480
+هذا بيبقى يساوي Epsilon لـ Φ of a، Φ of A كلها بيصير
+
+101
+00:09:13,480 --> 00:09:17,560
+عنصر في domain Epsilon، بس Epsilon، يبقى الـ Epsilon بس، Epsilon بتقدر تأثر
+
+102
+00:09:17,560 --> 00:09:20,700
+عليه كيف؟ عنصر في domain اللي هو الـ Epsilon بس، Epsilon
+
+103
+00:09:26,170 --> 00:09:32,150
+العنصر اللي موجود في a صار صورته في b، تمام؟ بي هي الـ
+
+104
+00:09:32,150 --> 00:09:36,610
+domain تبع مين؟ تبع ليه؟ إبصي، إذا إبصي تقدر تأثر على
+
+105
+00:09:36,610 --> 00:09:41,690
+هذا العنصر، يبقى إبصي لـ Φ of a لكل الـ a اللي موجود
+
+106
+00:09:41,690 --> 00:09:47,990
+في الـ set A، تعريف آخر بنعرف حاجة اسمها الـ one to one
+
+107
+00:09:47,990 --> 00:09:53,300
+function، يبقى الـ Φ من الـ set A إلى الـ set B is called
+
+108
+00:09:53,300 --> 00:09:57,540
+one to one، بعض الناس بيختصروها في الكتابة، و
+
+109
+00:09:57,540 --> 00:10:01,260
+بيقولوا واحد لواحد، واحد لواحد، والله one to one
+
+110
+00:10:01,260 --> 00:10:06,340
+ممكن تفهم نفس المعنى، بعض الكتب بتكتبها بشكل آخر
+
+111
+00:10:06,340 --> 00:10:10,300
+بتكتب هذه injective
+
+112
+00:10:11,240 --> 00:10:15,460
+يبقى لو وجدت في أحد كتب مبادئ الرياضة ولا أي كتاب
+
+113
+00:10:15,460 --> 00:10:20,140
+جبر الكلمة injective function، تفهم منها إيش؟ هذه
+
+114
+00:10:20,140 --> 00:10:25,760
+one to one function، if for every a1 و a2 اللي
+
+115
+00:10:25,760 --> 00:10:31,710
+موجودة في a، هذه فاصلة طبعًا، إذا كان الـ a واحد لا
+
+116
+00:10:31,710 --> 00:10:35,810
+يساوي الـ a 2، يبقى then الـ f of 1 لا يساوي
+
+117
+00:10:35,810 --> 00:10:41,970
+الـ f of 2، بالبلدي هيك، بنجي نقول في كل كلّاسيك
+
+118
+00:10:41,970 --> 00:10:44,470
+أول ما جيتوا على الجامعة، بنجي نقول العناصر
+
+119
+00:10:44,470 --> 00:10:51,290
+المختلفة لها صور مختلفة، يبقى الـ a1 لا يساوي a2
+
+120
+00:10:51,290 --> 00:10:57,210
+imply الصورة الـ a1 هي f of a1 لا يساوي f of a2
+
+121
+00:10:57,210 --> 00:11:02,850
+وهذا معنى العناصر المختلفة لها صور مختلفة، or
+
+122
+00:11:02,850 --> 00:11:10,940
+equivalently، يعني في تعريف آخر مكافئ لهذا التعريف
+
+123
+00:11:10,940 --> 00:11:19,300
+وهو لو كانت صورتان متساويتان فإن أصلهما متساويان
+
+124
+00:11:19,620 --> 00:11:25,380
+يعني F of F of F 1 of A 1 بده يساوي F of A
+
+125
+00:11:25,380 --> 00:11:29,640
+2، يبقى إذا أن الـ A 1 بده يساوي مين؟ يعني 
+
+126
+00:11:29,640 --> 00:11:33,460
+بالبلد هيك زي ما أخذت في مبادئ الرياضيات ال
+
+127
+00:11:33,460 --> 00:11:37,300
+counter positive يعني أنا بدي أمشي في الاتجاه من
+
+128
+00:11:37,300 --> 00:11:43,080
+العكس اطلع a واحد لا يساوي f في اتنين هذا بيطلب f في
+
+129
+00:11:43,080 --> 00:11:47,220
+a واحد لا يساوي f في اتنين يبقى لو نفيت هذه بدها
+
+130
+00:11:47,220 --> 00:11:52,260
+تعطيني مين؟ نفي هذه، هذه المكافئة، نفي لهذه اللي هو
+
+131
+00:11:52,260 --> 00:11:57,760
+التساوي، يبقى هاهم بيساوي بعض بدها تعطيني التساوي
+
+132
+00:11:57,760 --> 00:12:02,600
+هذه تماما، يعني عكس هذه بدها يعطيك عكس هذه، هذا اللي
+
+133
+00:12:02,600 --> 00:12:06,770
+كنا في مادة الرياضة بنسميه ال contrapositive طيب
+
+134
+00:12:06,770 --> 00:12:14,350
+تعرف اللي هو الأخير بيقول ال function Φ من A إلى
+
+135
+00:12:14,350 --> 00:12:19,190
+B is said to be onto أنتم بالعربي يعني ده الفوقية
+
+136
+00:12:19,190 --> 00:12:24,230
+فوقية يعني بمعنى آخر بتغطي جميع عناصر ال co-domain
+
+137
+00:12:24,230 --> 00:12:28,870
+هنا في الرسم هذه ما غطّت جميع عناصر، غطّت بعضهم
+
+138
+00:12:28,870 --> 00:12:34,750
+إذا مشان تبقى onto لازم تمر على جميع عناصر ال B بلا
+
+139
+00:12:34,750 --> 00:12:41,640
+استثناء، هذه ال onto بعض الكتب بتكتبها surjective
+
+140
+00:12:41,640 --> 00:12:45,360
+يبقى
+
+141
+00:12:45,360 --> 00:12:50,640
+أنتو أو onto كما هي، يبقى ده شو تعريفه؟ يبقى ده Φ
+
+142
+00:12:50,640 --> 00:12:57,500
+من a إلى b بنسميها onto إذا كان كل عنصر في b بدي
+
+143
+00:12:57,500 --> 00:13:03,060
+يظهر كصورة لمين؟ للعنصر من A، في كل element في B is
+
+144
+00:13:03,060 --> 00:13:07,720
+the image of at least one element of A. لماذا قلت
+
+145
+00:13:07,720 --> 00:13:10,900
+at least one element؟ لأن الـ Φ هذه ممكن ما
+
+146
+00:13:10,900 --> 00:13:15,500
+تكونش one to one، صح ولا لأ؟ يعني ممكن لعنصرين أن
+
+147
+00:13:15,500 --> 00:13:19,640
+يشتركا في نفس الصورة، إذا العنصر اللي بتاخده
+
+148
+00:13:19,640 --> 00:13:24,100
+مابيه، بدي كله على الأقل أصل واحد اللي لم يكن
+
+149
+00:13:24,100 --> 00:13:28,360
+اثنين، ثلاثة، أربعة موجودات وين؟ موجودات في الـ set
+
+150
+00:13:28,360 --> 00:13:32,800
+A يبقى لو قال لي اثبت أن هذه ال function اللي عندي
+
+151
+00:13:32,800 --> 00:13:37,960
+هي onto function بروح بجيب له element عشوائي أي
+
+152
+00:13:37,960 --> 00:13:42,360
+element من ال co-domain وبحاول أثبت أنه له أصل
+
+153
+00:13:42,360 --> 00:13:46,480
+في ال domain، إن حدث ذلك يبقى هذه الـ function بصير
+
+154
+00:13:46,480 --> 00:13:52,100
+مالها onto function، that is أي أنه بدي أعيد صياغة
+
+155
+00:13:52,100 --> 00:13:56,100
+التعريف، بقول الـΦ من A إلى B بقول عليها onto
+
+156
+00:13:56,100 --> 00:14:03,240
+function إذا كان لكل B موجود في B there exist يوجد
+
+157
+00:14:03,240 --> 00:14:07,560
+at least A موجود في A بحيث الـB بدها تساوي من إيه؟
+
+158
+00:14:07,560 --> 00:14:12,050
+الـΦ of A، يبقى ال element هذا اللي أخذته من b
+
+159
+00:14:12,050 --> 00:14:17,430
+اللي جاته أصل فيه a capital اللي هو a small بحيث
+
+160
+00:14:17,430 --> 00:14:22,630
+أن Φ of a بدها تساوي بدها تساوي ال b خليك
+
+161
+00:14:22,630 --> 00:14:27,450
+على الملاحظة دي الآن، لو ال function من a ل b كانت one
+
+162
+00:14:27,450 --> 00:14:31,570
+to one and onto يبقى حققت التعريف اللي عندها و
+
+163
+00:14:31,570 --> 00:14:35,770
+التعريف اللي فوق اتنين في آن واحد، يبقى بنسميها ال
+
+164
+00:14:35,770 --> 00:14:41,890
+function one to one correspondence طب السؤال هو ال
+
+165
+00:14:41,890 --> 00:14:47,970
+one to one بنسميها injective وال onto surjective ال
+
+166
+00:14:47,970 --> 00:14:53,570
+one to one correspondence bijective يبقى هادي هاي
+
+167
+00:14:53,570 --> 00:14:57,950
+ال one to one correspondence هادي بنسميها
+
+168
+00:14:57,950 --> 00:15:00,090
+bijective
+
+169
+00:15:01,970 --> 00:15:06,050
+يبقى لو لقيت في الكتاب عند أي لحظة تمام by
+
+170
+00:15:06,050 --> 00:15:10,510
+adjective بدك تفهم أنها one to one and onto في نفس
+
+171
+00:15:10,510 --> 00:15:15,850
+الوقت، نعطي بعض الأمثلة البسيطة لل one to one و ال
+
+172
+00:15:15,850 --> 00:15:19,730
+onto و ال one to one correspondence الدالة يا شباب
+
+173
+00:15:19,730 --> 00:15:24,060
+يمكن تبقى one to one لكن ما تكونش onto وممكن تكون
+
+174
+00:15:24,060 --> 00:15:30,760
+onto وممكن تكون one to one and onto في نفس
+
+175
+00:15:30,760 --> 00:15:35,800
+الوقت، كل الاحتمالات واردة عنها، نعطي المثال الأول
+
+176
+00:15:35,800 --> 00:15:46,540
+define عرف لي ال function، define ال f من ال set of
+
+177
+00:15:46,540 --> 00:15:52,180
+integers Z ل set of integers Z by
+
+178
+00:15:54,160 --> 00:16:06,120
+ف by f of x، f of x يساوي 2x السؤال هو هل هذه
+
+179
+00:16:06,120 --> 00:16:10,560
+one to one يعني
+
+180
+00:16:10,560 --> 00:16:15,600
+هل يمكن لعنصرين يشتركا في نفس الصورة؟ مش ممكنية على
+
+181
+00:16:15,600 --> 00:16:20,620
+الإطلاق، هذه one to one السؤال هو هل هي onto؟ لأ
+
+182
+00:16:20,620 --> 00:16:25,220
+لأن كل الأعداد الفردية ما بتظهرش، ليه؟ ال X لو كان فردي
+
+183
+00:16:25,220 --> 00:16:28,200
+أو زوجي تضربه في 2 بتصير زوجي، يبقى كل
+
+184
+00:16:28,200 --> 00:16:34,060
+الأعداد الفردية مش حتظهر كصور لعناصر من اللي هو Z
+
+185
+00:16:34,060 --> 00:16:44,640
+يبقى هذه is one to one but not onto because
+
+186
+00:16:44,640 --> 00:16:57,280
+مثلا for example كمثال بسيط أن التلاتة does not
+
+187
+00:16:57,280 --> 00:17:05,980
+image ماهو صورة for any .. والله is not image
+
+188
+00:17:05,980 --> 00:17:15,340
+يبقى هذه is not image for any element
+
+189
+00:17:20,140 --> 00:17:25,100
+انتهينا مشان ننفي هذا الكلام يا شباب يا بنجيب counter
+
+190
+00:17:25,100 --> 00:17:29,060
+example يا بنبرهن، احنا جبنا counter example بسيط
+
+191
+00:17:29,060 --> 00:17:35,620
+بيؤكد الكلام اللي احنا بنقوله، نواصل برضه الأمثلة
+
+192
+00:17:49,540 --> 00:17:54,000
+المثال الثاني برضه
+
+193
+00:17:54,000 --> 00:17:58,540
+define الـ
+
+194
+00:17:58,540 --> 00:18:05,240
+function g من set of integer Z إلى set of integer
+
+195
+00:18:05,240 --> 00:18:18,640
+Z by G of X بدها تساوي أحد أمرين يا إما ال X if ال X
+
+196
+00:18:18,640 --> 00:18:33,040
+is odd يا إما ال X على 2 if ال X is even then
+
+197
+00:18:37,650 --> 00:18:47,630
+الـ G هو هل الـ G هذه one to one؟ طيب، تقدر الـ G
+
+198
+00:18:47,630 --> 00:18:53,970
+of counter example؟ 3 و 6، 3 فردة، G of
+
+199
+00:18:53,970 --> 00:18:58,710
+3 بدها تساوي 3، G of 6 زوجي، 6 على 2
+
+200
+00:18:58,710 --> 00:19:03,150
+بطلع 3، إذا وصلت ل 3 وصلت ل 6 نفس الشيء،
+
+201
+00:19:03,150 --> 00:19:06,410
+يبقى الـ G not one to one طب، Z on to؟
+
+202
+00:19:11,290 --> 00:19:17,070
+معقول؟ طيب 8 على 2 ما بتطلع؟ 4 على 2
+
+203
+00:19:17,070 --> 00:19:22,130
+يبقى ظهروا even ولا لأ؟ يبقى هذي onto but not one
+
+204
+00:19:22,130 --> 00:19:32,050
+to one يبقى هذي G is onto but not one to one
+
+205
+00:19:32,050 --> 00:19:32,490
+because
+
+206
+00:19:35,340 --> 00:19:42,280
+نظراً لأن الـG of 3 بدها تساوي الـG of 6
+
+207
+00:19:42,280 --> 00:19:50,500
+والتي بدها تساوي كم؟ بدها تساوي 3 and ال 3
+
+208
+00:19:50,500 --> 00:19:56,080
+لا تساوي 6، هاي جبنا صورتين متساويتين لكن أصلهم
+
+209
+00:19:56,080 --> 00:20:01,140
+غير متساوي، يبقى هذا يتناقض مع مين؟ مع التعريف اللي
+
+210
+00:20:01,140 --> 00:20:09,880
+قلنا احنا، طيب خد لي مثال 3 لو أخذت Φ من ال
+
+211
+00:20:09,880 --> 00:20:17,980
+set of real numbers define اللي هو Φ من ال set
+
+212
+00:20:17,980 --> 00:20:25,240
+of real number ل set of real number مثلا by Φ
+
+213
+00:20:25,240 --> 00:20:32,940
+of x يساوي حط أي دالة خطية بدك إياها، أي دالة خطية تجي
+
+214
+00:20:32,940 --> 00:20:40,180
+في بالك، مثلا 2x زائد 3، السؤال هو هذه one
+
+215
+00:20:40,180 --> 00:20:45,740
+to one ولا لأ، onto ولا لأ؟ يبقى onto كمان لأن
+
+216
+00:20:45,740 --> 00:20:49,260
+ما في عندي ولا element إيش ما تكون ال X تكون
+
+217
+00:20:49,260 --> 00:21:01,580
+يبقى هذه then ال Φ is one to one and onto طيب خد
+
+218
+00:21:01,580 --> 00:21:11,070
+مثال 4 لو قلت لك دي Φ من الـ set of real
+
+219
+00:21:11,070 --> 00:21:16,430
+numbers إلى ال set of positive real numbers يعني
+
+220
+00:21:16,430 --> 00:21:21,610
+ليس بالضرورة تبقى نفس اللي هو ال set، بدخل ال set
+
+221
+00:21:21,610 --> 00:21:30,190
+تانية by Φ of X دي تساوي e of X ال exponential
+
+222
+00:21:30,190 --> 00:21:32,390
+function تبع ال calculus بنسميه
+
+223
+00:21:36,170 --> 00:21:42,470
+هل هذه عمرها بتاخد قيم سالبة؟ مش إمكانية طبعا لو
+
+224
+00:21:42,470 --> 00:21:48,630
+ذكرتك برسمتها هيك، هذا محور X هذا محور Y هذه نقطة
+
+225
+00:21:48,630 --> 00:21:54,520
+الأصل، الدالة بتيجي ماشية هيك، عند الـ zero بتبقى هذه
+
+226
+00:21:54,520 --> 00:21:59,580
+النقطة اللي هي zero أو 1، إحداثية النقطة هذه
+
+227
+00:21:59,580 --> 00:22:05,940
+وهذه الدالة اللي هي e of x ال domain تبعها بياخد كل
+
+228
+00:22:05,940 --> 00:22:09,840
+ال real line والـ Range تبعها بياخد من وين؟ من وين؟
+
+229
+00:22:09,840 --> 00:22:14,680
+من zero ل Infinity يبقى one to one and onto ولا لأ؟
+
+230
+00:22:14,680 --> 00:22:20,180
+لا طيب نذكر بال one to one بيجي نقول هندسيا لو
+
+231
+00:22:20,180 --> 00:22:25,840
+رسمت أي horizontal line ممنوع يقطع المنحنى إلا في
+
+232
+00:22:25,840 --> 00:22:30,460
+نقطة واحدة، فلو قطع في نقطتين أو أكثر بالطبع ليست
+
+233
+00:22:30,460 --> 00:22:37,580
+one to one، إذا هذه ال function كذلك one to one يبقى
+
+234
+00:22:37,580 --> 00:22:45,440
+then اللي هو ال Φ is one to one and onto كذلك
+
+235
+00:22:46,030 --> 00:22:50,730
+يبقى يعطيك العديد من الأمثلة ممكن تبقى one to
+
+236
+00:22:50,730 --> 00:22:56,710
+one وما تبقاش onto وممكن تكون onto وما تكونش
+
+237
+00:22:56,710 --> 00:23:02,290
+one to one وممكن تكون one to one and onto وهكذا
+
+238
+00:23:02,290 --> 00:23:07,410
+وأنا جبت لك دوال بسيطة ماهي دوال معقدة لأن أنا
+
+239
+00:23:07,410 --> 00:23:15,980
+بدي المفهوم يثبت عندك، طيب ننتقل الآن إلى نظرية
+
+240
+00:23:15,980 --> 00:23:23,940
+بتقول ما يأتي، theorem هذه النظرية بتتكلم عن خواص
+
+241
+00:23:23,940 --> 00:23:32,260
+ال functions اللي هي ال properties of
+
+242
+00:23:32,260 --> 00:23:36,480
+functions خواص الدوال
+
+243
+00:23:41,350 --> 00:23:58,170
+بقول ال α من a إلى b and β من b إلى c و
+
+244
+00:23:58,170 --> 00:24:11,110
+γ من c إلى d and γ من c إلى d من c إلى d are
+
+245
+00:24:11,110 --> 00:24:20,610
+functions كلهم كانوا دوال then النقطة
+
+246
+00:24:20,610 --> 00:24:34,270
+الأولى α β عفوا γ γ β α
+
+247
+00:24:41,110 --> 00:24:55,730
+النقطة الثانية if α and β are one to one
+
+248
+00:24:55,730 --> 00:25:06,830
+are one to one then β α is one to one نمرة
+
+249
+00:25:06,830 --> 00:25:20,830
+3 if α and β are onto are
+
+250
+00:25:20,830 --> 00:25:36,900
+onto then β α is onto النقطة الرابعة إذا كانت
+
+251
+00:25:36,900 --> 00:25:45,580
+ألفة واحدة واحدة وانتم ثم
+
+252
+00:25:45,580 --> 00:25:50,000
+يوجد
+
+253
+00:25:50,000 --> 00:26:00,920
+مفعول Alpha inverse من Beta إلى A بحيث
+
+254
+00:26:03,330 --> 00:26:15,570
+بحيث أن ال alpha inverse of a بده يساوي a لكل
+
+255
+00:26:15,570 --> 00:26:20,090
+الـ a الموجودة في الـ A and
+
+256
+00:26:44,670 --> 00:26:47,410
+الفا الفا الفا الفا الفا الفا الفا الفا الفا الفا
+
+257
+00:26:47,410 --> 00:26:47,970
+الفا الفا الفا الفا الفا الفا الفا الفا الفا الفا
+
+258
+00:26:47,970 --> 00:26:48,030
+الفا الفا الفا الفا الفا الفا الفا الفا الفا الفا
+
+259
+00:26:48,030 --> 00:26:48,050
+الفا الفا الفا الفا الفا الفا الفا الفا الفا الفا
+
+260
+00:26:48,050 --> 00:26:48,070
+الفا الفا الفا الفا الفا الفا الفا الفا الفا الفا
+
+261
+00:26:48,070 --> 00:26:58,680
+الفا الفا and one to one and on to and alpha
+
+262
+00:26:58,680 --> 00:27:05,960
+of a بده يساوي الـ b then الـ
+
+263
+00:27:05,960 --> 00:27:09,720
+a يساوي alpha inverse of b
+
+264
+00:27:46,960 --> 00:27:50,800
+الآن بدنا نجي لبعض الخواص الخاصة بالـ functions و
+
+265
+00:27:50,800 --> 00:27:57,320
+التي درست في مبادئ الرياضيات بيقول لو كان في عندي
+
+266
+00:27:57,320 --> 00:28:01,800
+three functions Alpha و Beta و Gamma Alpha من A
+
+267
+00:28:01,800 --> 00:28:07,560
+إلى B Beta من B إلى C Gamma من C إلى D كلهم كانوا
+
+268
+00:28:07,560 --> 00:28:12,800
+functions then Gamma Beta Alpha بيساوي Gamma Beta
+
+269
+00:28:12,800 --> 00:28:18,130
+Alpha شو اسم الخاصية هذه؟ في علم الرياضيات جابر
+
+270
+00:28:18,130 --> 00:28:25,550
+الخاطي إيش اسمها؟ خاصية إيش؟ واحد بدي يحكي يرفع يده،
+
+271
+00:28:25,550 --> 00:28:28,710
+بدي واحد يرى يرفع يده باسم ويحكي يقول لي، حتى نقول
+
+272
+00:28:28,710 --> 00:28:34,550
+إن التناقش هنيوة صح ولا غلطأيوة تفضل، خاصية تجميع،
+
+273
+00:28:34,550 --> 00:28:39,330
+لكن القزيشو معناها؟ associative، وهذه خاصية الـ
+
+274
+00:28:39,330 --> 00:28:45,030
+associativity، خاصية الدمج أو التجميع، يبقى هذه
+
+275
+00:28:45,030 --> 00:28:49,870
+اسمها الـ associative property
+
+276
+00:28:52,440 --> 00:28:57,780
+يبقى هذه اسمها خاصية التجميع تمام يبقى خاصية
+
+277
+00:28:57,780 --> 00:29:02,900
+التجميع تنطبق على الـ functions كما تنطبق على ضرب
+
+278
+00:29:02,900 --> 00:29:07,960
+المصفوفات كما تنطبق على جمع المصفوفات إلى آخره طيب
+
+279
+00:29:07,960 --> 00:29:11,520
+النقطة الثانية لو كان alpha و beta are one and one
+
+280
+00:29:11,520 --> 00:29:15,220
+is two وجبنا الـ composition ما بين beta و alpha
+
+281
+00:29:15,220 --> 00:29:21,020
+هذا هيعطينا مين هيعطيني one to one يمكن واحد يسألني
+
+282
+00:29:21,020 --> 00:29:25,240
+طب يقول لي beta alpha one to one ولا لأ باجي بسألك
+
+283
+00:29:25,240 --> 00:29:30,010
+يا beta alpha exist ولا does not exist على طول الخط
+
+284
+00:29:30,010 --> 00:29:34,470
+يبقى في الشمكانية يبقى هنا بيتا لو كانت تنتين one
+
+285
+00:29:34,470 --> 00:29:38,290
+to one يبقى الـ composition تبعهم one to one بالمثل
+
+286
+00:29:38,290 --> 00:29:42,070
+لو كانوا on two يبقى الـ composition تبعهم on two
+
+287
+00:29:42,070 --> 00:29:47,090
+الان النقطة الرابعة لو كانت alpha one to one
+
+288
+00:29:47,090 --> 00:29:52,990
+and on to نرجع لـ calculus إيه الشرط الـ existence
+
+289
+00:29:52,990 --> 00:29:59,740
+لمعكوس الدالة تبقى دالة one to one مظبوط يبقى one
+
+290
+00:29:59,740 --> 00:30:05,580
+to one وعناصرها كلهم يظهروا كصور لعناصرها لو
+
+291
+00:30:05,580 --> 00:30:11,140
+اتحقق الشرطين هدول بقول يبقى المعكوس موجود يبقى لو
+
+292
+00:30:11,140 --> 00:30:15,120
+كانت alpha one to one and on to يبقى مضمون
+
+293
+00:30:15,120 --> 00:30:19,180
+المعكوس موجودة على طول القط يبقى there exist a
+
+294
+00:30:19,180 --> 00:30:24,320
+function بسميها مش ال alpha والسلب واحد ألفا انفرس
+
+295
+00:30:24,320 --> 00:30:29,200
+معكوسة ده لألفا من beta إلى a بحيث تأثير ال alpha
+
+296
+00:30:29,200 --> 00:30:32,660
+inverse alpha على a بده يساوي الـ a يعني الـ
+
+297
+00:30:32,660 --> 00:30:36,540
+composition ما بين ال alpha inverse وال alpha بده
+
+298
+00:30:36,540 --> 00:30:40,840
+يساوي الـ a بده يساوي الـ a لكل الـ a اللي موجودة في a
+
+299
+00:30:40,840 --> 00:30:45,860
+طبعا الـ a في domain مين يا شباب هنا إيه؟ في الـ
+
+300
+00:30:45,860 --> 00:30:49,980
+domain الـ Alpha لأنه Alpha فوق اللي من A إلى B
+
+301
+00:30:49,980 --> 00:30:54,220
+وفي نفس الوقت Alpha Alpha inverse of B بده يساوي B
+
+302
+00:30:54,220 --> 00:30:58,820
+لكل الـ B اللي موجودة في الـ domain الـ Alpha
+
+303
+00:30:58,820 --> 00:31:03,210
+Inverse الآن الملاحظة دي لو كانت ال alpha is one to
+
+304
+00:31:03,210 --> 00:31:07,230
+one and one to one كان عندي alpha of a بده يساوي
+
+305
+00:31:07,230 --> 00:31:13,010
+الـ b لو بده اجيب العنصر a بأثر على الطرفين بمين بـ
+
+306
+00:31:13,010 --> 00:31:18,620
+alpha inverse بصير alpha inverse ألفا انفرس أو ألفا
+
+307
+00:31:18,620 --> 00:31:22,820
+انفرس أو ألفا انفرس أو ألفا انفرس أو ألفا انفرس أو
+
+308
+00:31:22,820 --> 00:31:35,180
+ألفا انفرس أو ألفا انفرس
+
+309
+00:31:35,380 --> 00:31:39,780
+كل اللي سمعتوه هذا في الغالب ضروري جدا لدراستنا
+
+310
+00:31:39,780 --> 00:31:44,020
+خلال الجبر كما سترونه خلال دراستنا الآن بدنا نروح
+
+311
+00:31:44,020 --> 00:31:48,480
+إلى الـ chapter 2 اللي هو الجديد chapter لـ groups
+
+312
+00:31:48,480 --> 00:31:56,700
+يبقى chapter 2 اللي هو لـ groups المجموعات
+
+313
+00:31:56,700 --> 00:32:00,400
+definition
+
+314
+00:32:00,400 --> 00:32:00,620
+let
+
+315
+00:32:05,230 --> 00:32:12,410
+جي بي اي ست جي
+
+316
+00:32:12,410 --> 00:32:18,310
+بي
+
+317
+00:32:18,310 --> 00:32:22,770
+اي ست جي بي اي ست جي
+
+318
+00:32:22,770 --> 00:32:28,610
+بي
+
+319
+00:32:28,610 --> 00:32:39,170
+اي ست is a function a star من g cross الـ g إلى g
+
+320
+00:32:39,170 --> 00:32:48,190
+that is أن it
+
+321
+00:32:48,190 --> 00:32:58,750
+is a rule it is a rule that assigns that
+
+322
+00:33:03,660 --> 00:33:14,900
+to each ordered pair to each ordered pair
+
+323
+00:33:14,900 --> 00:33:26,500
+لأي زوج مرتب a و b اللي موجود في g cross الـ g an
+
+324
+00:33:26,500 --> 00:33:27,340
+element
+
+325
+00:33:31,010 --> 00:33:35,910
+A Star B in G
+
+326
+00:34:19,780 --> 00:34:23,960
+نعود مرة أخرى لموضوعنا، موضوع الـ groups الـ group
+
+327
+00:34:23,960 --> 00:34:28,780
+الشباب هي عبارة عن ست عادية والست هذه بنحط عليها
+
+328
+00:34:28,780 --> 00:34:33,760
+عملية رياضية العملية قد تكون جمع، طرح، ضرب، قسمة،
+
+329
+00:34:33,760 --> 00:34:39,420
+جمع وطرح، جمع وطرح وضرب وقسمة مع بعض، رفع أسس، أخذ
+
+330
+00:34:39,420 --> 00:34:44,300
+جذور، أخذ جذور، أي عملية رياضية العملية الرياضية
+
+331
+00:34:44,300 --> 00:34:49,080
+هذه بدي أعطيها الرمز اللي هو star binary operation
+
+332
+00:34:49,080 --> 00:34:56,380
+عملية ثنائية عملية ثنائية رياضية يبقى g ست عادية a
+
+333
+00:34:56,380 --> 00:35:01,720
+binary operation هأعطيها الرمز star على g is a
+
+334
+00:35:01,720 --> 00:35:07,180
+function star من الـ 6 g cross الـ g إلى g يبقى
+
+335
+00:35:07,180 --> 00:35:12,020
+العملية الثنائية على ست جيهة عبارة عن function من
+
+336
+00:35:12,020 --> 00:35:17,120
+الـ cross product G cross الـ G إلى G شو شكلها إيش
+
+337
+00:35:17,120 --> 00:35:22,640
+ما يكون شكلها يكون أي شغلة رياضية that is it is a
+
+338
+00:35:22,640 --> 00:35:29,040
+rule هي صيغة تعين أو تحدد أو تخصص لكل زوج A وB
+
+339
+00:35:29,040 --> 00:35:34,300
+موجود في G cross الـ G عنصر واحد A star B وهذا
+
+340
+00:35:34,300 --> 00:35:38,470
+العنصر لازم يكون مالهم موجود في جيبجا مشان تكون
+
+341
+00:35:38,470 --> 00:35:44,890
+binary operation تحت هذه العملية نتيجة لجمع عنصرين
+
+342
+00:35:44,890 --> 00:35:49,990
+لطرح عنصرين لضربهم أو ضربهم مع طرحهم كده بدي يكون
+
+343
+00:35:49,990 --> 00:35:54,850
+موجود داخل مين يعني جيبجا closed under this
+
+344
+00:35:54,850 --> 00:35:58,950
+operation إن حدث ذلك بقول يبقى هذه ال operation ما
+
+345
+00:35:58,950 --> 00:36:03,420
+لها binary operation هيعطيك طبعا عدة binary
+
+346
+00:36:03,420 --> 00:36:06,740
+operations ونشوف أحيان تنفع تكون binary operations
+
+347
+00:36:06,740 --> 00:36:11,700
+وأحيان بتكونش binary operations أول مثال لو جيت
+
+348
+00:36:11,700 --> 00:36:20,040
+قلت خدلي set g هي set of integer z define عرف لي
+
+349
+00:36:20,040 --> 00:36:29,100
+اللي هو ال star من set z cross z إلى z itself by
+
+350
+00:36:41,990 --> 00:36:50,040
+لو جمعت العنصرين هدول يعني مجموع two integers بيظل
+
+351
+00:36:50,040 --> 00:36:55,980
+integer ولا بيصير complex مجموع two integers إيش
+
+352
+00:36:55,980 --> 00:37:00,340
+بيظل integer يبقى هذه ال operation binary operation
+
+353
+00:37:00,340 --> 00:37:08,020
+يبقى هنا then the operation
+
+354
+00:37:14,080 --> 00:37:27,740
+star is a binary operation السبب because
+
+355
+00:37:27,740 --> 00:37:38,220
+the sum of two integers
+
+356
+00:37:40,560 --> 00:37:51,520
+is an integer طب السؤال نفس العملية على set of
+
+357
+00:37:51,520 --> 00:37:56,160
+natural number و set of real number و set of
+
+358
+00:37:56,160 --> 00:38:03,080
+rational number هل هذه كمان binary operation؟ يبقى
+
+359
+00:38:03,080 --> 00:38:15,740
+باجي بقوله also star is a binary operation is a
+
+360
+00:38:15,740 --> 00:38:27,770
+binary operation on the sets اللي هو الـ Q and الـ
+
+361
+00:38:27,770 --> 00:38:31,910
+R يعني على مجموعة الأعداد النسبية وكذلك مجموعة
+
+362
+00:38:31,910 --> 00:38:37,370
+الأعداد الحقيقية طب مثال اثنين إيه إيش رأيك؟
+
+363
+00:38:37,370 --> 00:38:43,850
+Subtraction Subtraction
+
+364
+00:38:43,850 --> 00:38:49,490
+هل هو binary operation على set of natural numbers؟
+
+365
+00:38:49,490 --> 00:38:56,690
+لا يبقى Subtraction is not a binary
+
+366
+00:39:01,000 --> 00:39:07,700
+operation on set of natural number اللي هو N
+
+367
+00:39:07,700 --> 00:39:12,580
+because if
+
+368
+00:39:12,580 --> 00:39:21,660
+star معرفة من N cross الـ N إلى N by
+
+369
+00:39:33,680 --> 00:39:37,440
+أربعة وسبعة موجودة في N
+
+370
+00:39:41,310 --> 00:39:48,690
+أنا جالس بتركشن طرح أربعة ناقص سبعة يساوي قداش ناقص
+
+371
+00:39:48,690 --> 00:39:53,210
+ثلاثة هل هذه موجودة في الـ N مش موجودة في الـ N إذا
+
+372
+00:39:53,210 --> 00:39:57,290
+عملية طرح على set of natural numbers is not a
+
+373
+00:39:57,290 --> 00:40:02,450
+binary operation المرة الجاية نعطي مزيد من الأمثلة 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..b20d627c66b100ea1ee556e2bbb0392c31c376c8
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_raw.json
@@ -0,0 +1 @@
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600.44, "word": " لواحد", "probability": 0.955078125}, {"start": 600.44, "end": 600.78, "word": " والله", "probability": 0.73876953125}, {"start": 600.78, "end": 600.98, "word": " one", "probability": 0.90625}, {"start": 600.98, "end": 601.12, "word": " to", "probability": 0.96484375}, {"start": 601.12, "end": 601.26, "word": " one", "probability": 0.9521484375}, {"start": 601.26, "end": 601.48, "word": " ممكن", "probability": 0.439453125}, {"start": 601.48, "end": 601.82, "word": " تفهم", "probability": 0.9835611979166666}, {"start": 601.82, "end": 602.16, "word": " نفس", "probability": 0.990478515625}, {"start": 602.16, "end": 602.68, "word": " المعنى", "probability": 0.95654296875}, {"start": 602.68, "end": 603.44, "word": " بعض", "probability": 0.915771484375}, {"start": 603.44, "end": 603.86, "word": " الكتب", "probability": 0.9913736979166666}, {"start": 603.86, "end": 604.88, "word": " بتكتبها", "probability": 0.9751953125}, {"start": 604.88, "end": 605.84, "word": " بشكل", 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3714, 29245, 23328, 3660, 8978, 257, 29538, 6156, 33546, 37977, 23032, 3555, 3615, 995], "avg_logprob": -0.2816723105875221, "compression_ratio": 1.3891891891891892, "no_speech_prob": 0.0, "words": [{"start": 611.24, "end": 611.82, "word": "يبقى", "probability": 0.74945068359375}, {"start": 611.82, "end": 612.0, "word": " لو", "probability": 0.8134765625}, {"start": 612.0, "end": 612.58, "word": " وجدت", "probability": 0.7093098958333334}, {"start": 612.58, "end": 612.68, "word": " في", "probability": 0.93310546875}, {"start": 612.68, "end": 612.98, "word": " أحد", "probability": 0.804931640625}, {"start": 612.98, "end": 613.32, "word": " كتب", "probability": 0.9794921875}, {"start": 613.32, "end": 613.84, "word": " مبادئ", "probability": 0.969970703125}, {"start": 613.84, "end": 614.48, "word": " الرياضة", "probability": 0.73370361328125}, {"start": 614.48, "end": 614.68, "word": " ولا", "probability": 0.2181396484375}, {"start": 614.68, "end": 615.06, "word": " اي", "probability": 0.679443359375}, {"start": 615.06, "end": 615.46, "word": " كتاب", "probability": 0.98583984375}, {"start": 615.46, "end": 615.7, "word": " جبر", "probability": 0.570068359375}, {"start": 615.7, "end": 616.34, "word": " الكلمة", "probability": 0.8544921875}, {"start": 616.34, "end": 617.54, "word": " injective", "probability": 0.757568359375}, {"start": 617.54, "end": 618.28, "word": " function", "probability": 0.78515625}, {"start": 618.28, "end": 619.26, "word": " تفهم", "probability": 0.5546875}, {"start": 619.26, "end": 619.52, "word": " منها", "probability": 0.829833984375}, {"start": 619.52, "end": 619.8, "word": " ايش", "probability": 0.7552083333333334}, {"start": 619.8, "end": 620.14, "word": " هذه", "probability": 0.42236328125}, {"start": 620.14, "end": 621.0, "word": " one", "probability": 0.67919921875}, {"start": 621.0, "end": 621.38, "word": " to", "probability": 0.87109375}, {"start": 621.38, "end": 621.78, "word": " one", "probability": 0.95458984375}, {"start": 621.78, "end": 622.62, "word": " function", "probability": 0.93603515625}, {"start": 622.62, "end": 623.46, "word": " if", "probability": 0.457763671875}, {"start": 623.46, "end": 623.76, "word": " for", "probability": 0.87060546875}, {"start": 623.76, "end": 624.06, "word": " every", "probability": 0.83056640625}, {"start": 624.06, "end": 624.82, "word": " a1", "probability": 0.53436279296875}, {"start": 624.82, "end": 625.04, "word": " و", "probability": 0.8212890625}, {"start": 625.04, "end": 625.42, "word": " a2", "probability": 0.931884765625}, {"start": 625.42, "end": 625.76, "word": " اللي", "probability": 0.760986328125}, {"start": 625.76, "end": 626.64, "word": " موجودة", "probability": 0.978515625}, {"start": 626.64, "end": 627.0, "word": " في", "probability": 0.9619140625}, {"start": 627.0, "end": 627.52, "word": " a", "probability": 0.802734375}, {"start": 627.52, "end": 628.06, "word": " هذه", "probability": 0.65283203125}, {"start": 628.06, "end": 628.64, "word": " فاصلة", "probability": 0.9744466145833334}, {"start": 628.64, "end": 629.06, "word": " طبعا", "probability": 0.9901123046875}], "temperature": 1.0}, {"id": 28, "seek": 64547, "start": 629.81, "end": 645.47, "text": "إذا كان ال a واحد لا يساوي ال a اتنين يبقى then ال f of واحد لا يساوي ال f of اتنين بالبلد هيك بجينا نقول في كل كلاصية أول ما جيتوا على الجامعة بجينا نقول العناصر المختلفة", "tokens": [28814, 15730, 25961, 2423, 257, 36764, 24401, 20193, 7251, 3794, 995, 45865, 2423, 257, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 550, 2423, 283, 295, 36764, 24401, 20193, 7251, 3794, 995, 45865, 2423, 283, 295, 1975, 2655, 1863, 9957, 20666, 36150, 3215, 39896, 4117, 4724, 7435, 1829, 8315, 8717, 39648, 8978, 28242, 28242, 33546, 10632, 5551, 12610, 19446, 10874, 36081, 14407, 15844, 25724, 10943, 27884, 4724, 7435, 1829, 8315, 8717, 39648, 18863, 1863, 33546, 2288, 9673, 46456, 46538, 3660], "avg_logprob": -0.2264660523261553, "compression_ratio": 1.808641975308642, "no_speech_prob": 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"word": " ال", "probability": 0.783203125}, {"start": 633.95, "end": 634.21, "word": " f", "probability": 0.58544921875}, {"start": 634.21, "end": 634.41, "word": " of", "probability": 0.66162109375}, {"start": 634.41, "end": 634.85, "word": " واحد", "probability": 0.976318359375}, {"start": 634.85, "end": 635.15, "word": " لا", "probability": 0.81689453125}, {"start": 635.15, "end": 635.81, "word": " يساوي", "probability": 0.9539794921875}, {"start": 635.81, "end": 635.95, "word": " ال", "probability": 0.86474609375}, {"start": 635.95, "end": 636.31, "word": " f", "probability": 0.88525390625}, {"start": 636.31, "end": 638.19, "word": " of", "probability": 0.75927734375}, {"start": 638.19, "end": 638.93, "word": " اتنين", "probability": 0.864990234375}, {"start": 638.93, "end": 639.97, "word": " بالبلد", "probability": 0.8356119791666666}, {"start": 639.97, "end": 640.27, "word": " هيك", "probability": 0.859130859375}, {"start": 640.27, "end": 640.65, "word": " بجينا", "probability": 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{"start": 1033.38, "end": 1035.34, "word": " element", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 45, "seek": 105561, "start": 1040.14, "end": 1055.62, "text": "انزد مشان تنفي هذا كلام الشباب يا بنجيب counter example يا بنبرهن احنا جيبنا counter example بسيط يؤكد الكلام اللي احنا بنقوله نواصل برضه الأمثلة", "tokens": [7649, 11622, 3215, 37893, 7649, 6055, 1863, 41185, 23758, 28242, 10943, 25124, 3555, 16758, 35186, 44945, 7435, 1829, 3555, 5682, 1365, 35186, 44945, 26890, 3224, 1863, 1975, 5016, 8315, 10874, 1829, 3555, 8315, 5682, 1365, 4724, 3794, 1829, 9566, 7251, 33604, 4117, 3215, 2423, 28820, 10943, 13672, 1829, 1975, 5016, 8315, 44945, 39648, 3224, 8717, 2407, 33546, 1211, 4724, 43042, 3224, 16247, 2304, 12984, 37977], "avg_logprob": -0.15506629239429126, "compression_ratio": 1.576158940397351, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1040.1400000000003, "end": 1041.2600000000002, "word": "انزد", "probability": 0.5883382161458334}, {"start": 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"word": " الأمثلة", "probability": 0.9410400390625}], "temperature": 1.0}, {"id": 46, "seek": 108776, "start": 1069.54, "end": 1087.76, "text": "المثال الثاني برضه define الـ function g من set of integer z إلى set of integer z by", "tokens": [45340, 12984, 6027, 6024, 104, 7649, 1829, 4724, 43042, 3224, 6964, 2423, 39184, 2445, 290, 9154, 992, 295, 24922, 710, 30731, 992, 295, 24922, 710, 538], "avg_logprob": -0.2792245259991399, "compression_ratio": 1.1868131868131868, "no_speech_prob": 0.0, "words": [{"start": 1069.54, "end": 1070.2, "word": "المثال", "probability": 0.9148763020833334}, {"start": 1070.2, "end": 1070.98, "word": " الثاني", "probability": 0.9493408203125}, {"start": 1070.98, "end": 1074.0, "word": " برضه", "probability": 0.6286214192708334}, {"start": 1074.0, "end": 1074.9, "word": " define", "probability": 0.46484375}, {"start": 1074.9, "end": 1078.54, "word": " الـ", "probability": 0.665283203125}, {"start": 1078.54, "end": 1078.98, "word": " function", 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سالبة؟ مش إمكانية طبعا لو ذكرتك برسمتها هك هذا محور X هذا محور Y هذا نقطة الأصل الدالة بتيجي ماشية هك", "tokens": [3224, 1211, 29538, 6225, 29973, 11296, 39894, 47283, 3215, 12174, 32640, 8608, 6027, 49401, 22807, 37893, 11933, 2304, 41361, 10632, 23032, 3555, 3615, 995, 45164, 29910, 37983, 2655, 4117, 4724, 2288, 38251, 2655, 11296, 8032, 4117, 23758, 3714, 5016, 13063, 1783, 23758, 3714, 5016, 13063, 398, 23758, 8717, 47432, 3660, 16247, 36520, 32748, 6027, 3660, 4724, 31371, 7435, 1829, 3714, 33599, 10632, 8032, 4117], "avg_logprob": -0.24350961538461538, "compression_ratio": 1.5347222222222223, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1296.17, "end": 1297.25, "word": "هل", "probability": 0.35546875}, {"start": 1297.25, "end": 1297.63, "word": " هذه", "probability": 0.66552734375}, {"start": 1297.63, "end": 1298.05, "word": " عمرها", "probability": 0.8787434895833334}, {"start": 1298.05, "end": 1298.57, "word": " بتاخد", "probability": 0.861328125}, {"start": 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اللي هي EOSX ال domain تبعها بياخد كل ال real line", "tokens": [2407, 3615, 41260, 2423, 39184, 4018, 39894, 3555, 4587, 7578, 29538, 28239, 47432, 3660, 13672, 1829, 39896, 4018, 34051, 36764, 24401, 1975, 24401, 5718, 104, 10632, 28239, 47432, 3660, 29538, 37037, 24192, 32748, 6027, 3660, 13672, 1829, 39896, 462, 4367, 55, 2423, 9274, 6055, 3555, 3615, 11296, 4724, 1829, 47283, 3215, 28242, 2423, 957, 1622], "avg_logprob": -0.3175223113170692, "compression_ratio": 1.4657534246575343, "no_speech_prob": 0.0, "words": [{"start": 1312.38, "end": 1313.02, "word": "وعند", "probability": 0.4378255208333333}, {"start": 1313.02, "end": 1313.3, "word": " الـ", "probability": 0.65087890625}, {"start": 1313.3, "end": 1313.54, "word": " zero", "probability": 0.391357421875}, {"start": 1313.54, "end": 1314.14, "word": " بتبقى", "probability": 0.758270263671875}, {"start": 1314.14, "end": 1314.52, "word": " هذه", "probability": 0.76904296875}, {"start": 1314.52, "end": 1315.8, "word": " النقطة", 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associative، و هذه خاصية ال associativity، خاصية الدمج أو التجميع، يبقى هذه اسمها ال associative property", "tokens": [10721, 1829, 2407, 3660, 6055, 5172, 11242, 1211, 12399, 16490, 33546, 10632, 6055, 7435, 2304, 40228, 12399, 44381, 25062, 11622, 1829, 8592, 2407, 20449, 8315, 11296, 22807, 4180, 1166, 12399, 4032, 29538, 16490, 33546, 10632, 2423, 4180, 30142, 12399, 16490, 33546, 10632, 32748, 2304, 7435, 34051, 16712, 7435, 2304, 40228, 12399, 7251, 3555, 4587, 7578, 29538, 24525, 2304, 11296, 2423, 4180, 1166, 4707], "avg_logprob": -0.23486328008584678, "compression_ratio": 1.5743243243243243, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1710.95, "end": 1712.55, "word": "أيوة", "probability": 0.6800994873046875}, {"start": 1712.55, "end": 1713.29, "word": " تفضل،", "probability": 0.78603515625}, {"start": 1713.29, "end": 1714.11, "word": " خاصية", "probability": 0.9446614583333334}, {"start": 1714.11, "end": 1714.55, "word": " تجميع،", "probability": 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2203.39, "word": "لو", "probability": 0.431884765625}, {"start": 2203.39, "end": 2204.03, "word": " جمعت", "probability": 0.97412109375}, {"start": 2204.03, "end": 2205.03, "word": " العنصرين", "probability": 0.98095703125}, {"start": 2205.03, "end": 2205.75, "word": " هدول", "probability": 0.7080078125}], "temperature": 1.0}, {"id": 90, "seek": 222802, "start": 2206.46, "end": 2228.02, "text": "يعني مجموع two integers بيظل انتجر ولا بيصير complex مجموع two integers ايش بيظل انتجر يبقى هذه ال operation binary operation يبقى هنا then the operation", "tokens": [40228, 22653, 3714, 7435, 2304, 45367, 732, 41674, 4724, 1829, 19913, 1211, 16472, 2655, 7435, 2288, 49429, 4724, 1829, 9381, 13546, 3997, 3714, 7435, 2304, 45367, 732, 41674, 1975, 1829, 8592, 4724, 1829, 19913, 1211, 16472, 2655, 7435, 2288, 7251, 3555, 4587, 7578, 29538, 2423, 6916, 17434, 6916, 7251, 3555, 4587, 7578, 34105, 550, 264, 6916], "avg_logprob": -0.26562500418278207, "compression_ratio": 1.5820895522388059, 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"word": " integers", "probability": 0.947265625}, {"start": 2215.62, "end": 2215.98, "word": " ايش", "probability": 0.7599283854166666}, {"start": 2215.98, "end": 2216.34, "word": " بيظل", "probability": 0.77197265625}, {"start": 2216.34, "end": 2217.64, "word": " انتجر", "probability": 0.9771728515625}, {"start": 2217.64, "end": 2218.04, "word": " يبقى", "probability": 0.912841796875}, {"start": 2218.04, "end": 2218.36, "word": " هذه", "probability": 0.60498046875}, {"start": 2218.36, "end": 2218.52, "word": " ال", "probability": 0.91357421875}, {"start": 2218.52, "end": 2219.0, "word": " operation", "probability": 0.66357421875}, {"start": 2219.0, "end": 2219.5, "word": " binary", "probability": 0.6298828125}, {"start": 2219.5, "end": 2220.34, "word": " operation", "probability": 0.625}, {"start": 2220.34, "end": 2221.48, "word": " يبقى", "probability": 0.98388671875}, {"start": 2221.48, "end": 2222.0, "word": " هنا", "probability": 0.9853515625}, {"start": 2222.0, "end": 2223.22, "word": " then", "probability": 0.7890625}, {"start": 2223.22, "end": 2225.1, "word": " the", "probability": 0.72705078125}, {"start": 2225.1, "end": 2228.02, "word": " operation", "probability": 0.25634765625}], "temperature": 1.0}, {"id": 91, "seek": 225821, "start": 2234.08, "end": 2258.22, "text": "أسطار is a binary operation السبب because the sum of two integers", "tokens": [10721, 3794, 9566, 9640, 307, 257, 17434, 6916, 21136, 3555, 3555, 570, 264, 2408, 295, 732, 41674], "avg_logprob": -0.4427083333333333, "compression_ratio": 0.9375, "no_speech_prob": 0.0, "words": [{"start": 2234.08, "end": 2235.16, "word": "أسطار", "probability": 0.355438232421875}, {"start": 2235.16, "end": 2236.66, "word": " is", "probability": 0.1947021484375}, {"start": 2236.66, "end": 2237.7, "word": " a", "probability": 0.90966796875}, {"start": 2237.7, "end": 2238.68, "word": " binary", "probability": 0.89892578125}, {"start": 2238.68, "end": 2240.92, "word": " operation", "probability": 0.904296875}, {"start": 2240.92, "end": 2242.94, "word": " السبب", "probability": 0.9890950520833334}, {"start": 2242.94, "end": 2247.74, "word": " because", "probability": 0.7568359375}, {"start": 2247.74, "end": 2250.12, "word": " the", "probability": 0.787109375}, {"start": 2250.12, "end": 2252.12, "word": " sum", "probability": 0.95703125}, {"start": 2252.12, "end": 2254.68, "word": " of", "probability": 0.9794921875}, {"start": 2254.68, "end": 2256.28, "word": " two", "probability": 0.9306640625}, {"start": 2256.28, "end": 2258.22, "word": " integers", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 92, "seek": 228167, "start": 2260.56, "end": 2281.68, "text": "is an integer طب السؤال نفس العملية على set of natural number و set of real number و set of rational number هل هذه كمان binary operation؟", "tokens": [271, 364, 24922, 23032, 3555, 21136, 33604, 6027, 8717, 36178, 18863, 42213, 10632, 15844, 992, 295, 3303, 1230, 4032, 992, 295, 957, 1230, 4032, 992, 295, 15090, 1230, 8032, 1211, 29538, 9122, 2304, 7649, 17434, 6916, 22807], "avg_logprob": -0.25760690397337865, "compression_ratio": 1.328125, "no_speech_prob": 0.0, "words": [{"start": 2260.56, "end": 2261.26, "word": "is", "probability": 0.09722900390625}, {"start": 2261.26, "end": 2262.76, "word": " an", "probability": 0.69580078125}, {"start": 2262.76, "end": 2264.18, "word": " integer", "probability": 0.8916015625}, {"start": 2264.18, "end": 2267.0, "word": " طب", "probability": 0.5020751953125}, {"start": 2267.0, "end": 2267.5, "word": " السؤال", "probability": 0.9905598958333334}, {"start": 2267.5, "end": 2268.98, "word": " نفس", "probability": 0.96875}, {"start": 2268.98, "end": 2269.96, "word": " العملية", "probability": 0.9658203125}, {"start": 2269.96, "end": 2270.76, "word": " على", "probability": 0.61181640625}, {"start": 2270.76, "end": 2271.26, "word": " set", "probability": 0.5947265625}, {"start": 2271.26, "end": 2271.52, "word": " of", "probability": 0.9609375}, {"start": 2271.52, "end": 2272.14, "word": " natural", "probability": 0.8671875}, {"start": 2272.14, "end": 2272.82, "word": " number", "probability": 0.5}, {"start": 2272.82, "end": 2273.3, "word": " و", "probability": 0.86083984375}, {"start": 2273.3, "end": 2273.74, "word": " set", "probability": 0.71826171875}, {"start": 2273.74, "end": 2274.04, "word": " of", "probability": 0.978515625}, {"start": 2274.04, "end": 2274.32, "word": " real", "probability": 0.9462890625}, {"start": 2274.32, "end": 2275.08, "word": " number", "probability": 0.90966796875}, {"start": 2275.08, "end": 2275.44, "word": " و", "probability": 0.962890625}, {"start": 2275.44, "end": 2275.84, "word": " set", "probability": 0.93896484375}, {"start": 2275.84, "end": 2276.16, "word": " of", "probability": 0.97900390625}, {"start": 2276.16, "end": 2278.08, "word": " rational", "probability": 0.85888671875}, {"start": 2278.08, "end": 2278.94, "word": " number", "probability": 0.9208984375}, {"start": 2278.94, "end": 2279.62, "word": " هل", "probability": 0.94189453125}, {"start": 2279.62, "end": 2279.96, "word": " هذه", "probability": 0.71484375}, {"start": 2279.96, "end": 2280.38, "word": " كمان", "probability": 0.9357096354166666}, {"start": 2280.38, "end": 2280.72, "word": " binary", "probability": 0.787109375}, {"start": 2280.72, "end": 2281.68, "word": " operation؟", "probability": 0.634033203125}], "temperature": 1.0}, {"id": 93, "seek": 230634, "start": 2282.54, "end": 2306.34, "text": "يبقى باجي بقوله also listar is a binary operation is a binary operation on the sets اللي هو الكيو and", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 611, 1329, 289, 307, 257, 17434, 6916, 307, 257, 17434, 6916, 322, 264, 6352, 13672, 1829, 31439, 33251, 1829, 2407, 293], "avg_logprob": -0.26635743491351604, "compression_ratio": 1.288659793814433, "no_speech_prob": 0.0, "words": [{"start": 2282.54, "end": 2283.08, "word": "يبقى", "probability": 0.89794921875}, {"start": 2283.08, "end": 2283.46, "word": " باجي", "probability": 0.7569986979166666}, {"start": 2283.46, "end": 2284.18, "word": " بقوله", "probability": 0.9148763020833334}, {"start": 2284.18, "end": 2285.08, "word": " also", "probability": 0.7265625}, {"start": 2285.08, "end": 2287.78, "word": " listar", "probability": 0.48760986328125}, {"start": 2287.78, "end": 2288.76, "word": " is", "probability": 0.93310546875}, {"start": 2288.76, "end": 2289.52, "word": " a", "probability": 0.97998046875}, {"start": 2289.52, "end": 2290.4, "word": " binary", "probability": 0.8828125}, {"start": 2290.4, "end": 2292.84, "word": " operation", "probability": 0.9619140625}, {"start": 2292.84, "end": 2295.2, "word": " is", "probability": 0.517578125}, {"start": 2295.2, "end": 2295.74, "word": " a", "probability": 0.9921875}, {"start": 2295.74, "end": 2296.28, "word": " binary", "probability": 0.8583984375}, {"start": 2296.28, "end": 2297.52, "word": " operation", "probability": 0.94482421875}, {"start": 2297.52, "end": 2298.72, "word": " on", "probability": 0.9287109375}, {"start": 2298.72, "end": 2300.8, "word": " the", "probability": 0.74853515625}, {"start": 2300.8, "end": 2302.34, "word": " sets", "probability": 0.85302734375}, {"start": 2302.34, "end": 2303.54, "word": " اللي", "probability": 0.962890625}, {"start": 2303.54, "end": 2303.82, "word": " هو", "probability": 0.95654296875}, {"start": 2303.82, "end": 2304.7, "word": " الكيو", "probability": 0.6477864583333334}, {"start": 2304.7, "end": 2306.34, "word": " and", "probability": 0.92822265625}], "temperature": 1.0}, {"id": 94, "seek": 233669, "start": 2307.33, "end": 2336.69, "text": "الـ R يعني على مجموعة الاعداد النسبية و كذلك مجموعة الاعداد الحقيقية طب مثال اتنين ايه اش رايك؟ Subtraction Subtraction هل هو binary operation على set of natural numbers؟ لأ يبقى Subtraction is not a binary", "tokens": [6027, 39184, 497, 37495, 22653, 15844, 3714, 7435, 2304, 2407, 27884, 42963, 22488, 18513, 28239, 35457, 10632, 4032, 9122, 8848, 23275, 3714, 7435, 2304, 2407, 27884, 42963, 22488, 18513, 21542, 38436, 4587, 10632, 23032, 3555, 50113, 6027, 1975, 2655, 1863, 9957, 1975, 1829, 3224, 1975, 8592, 12602, 47302, 4117, 22807, 8511, 83, 26766, 8511, 83, 26766, 8032, 1211, 31439, 17434, 6916, 15844, 992, 295, 3303, 3547, 22807, 5296, 10721, 7251, 3555, 4587, 7578, 8511, 83, 26766, 307, 406, 257, 17434], "avg_logprob": -0.22067901528911826, "compression_ratio": 1.5797872340425532, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2307.33, "end": 2307.77, "word": "الـ", "probability": 0.4241943359375}, {"start": 2307.77, "end": 2308.11, "word": " R", "probability": 0.293212890625}, {"start": 2308.11, "end": 2308.83, "word": " يعني", "probability": 0.8955078125}, {"start": 2308.83, "end": 2309.05, "word": " على", "probability": 0.8837890625}, {"start": 2309.05, "end": 2309.69, "word": " مجموعة", "probability": 0.9490234375}, {"start": 2309.69, "end": 2310.25, "word": " الاعداد", "probability": 0.7522786458333334}, {"start": 2310.25, "end": 2310.77, "word": " النسبية", "probability": 0.94384765625}, {"start": 2310.77, "end": 2310.91, "word": " و", "probability": 0.95947265625}, {"start": 2310.91, "end": 2311.37, "word": " كذلك", "probability": 0.791015625}, {"start": 2311.37, "end": 2311.91, "word": " مجموعة", "probability": 0.93583984375}, {"start": 2311.91, "end": 2312.69, "word": " الاعداد", "probability": 0.9695638020833334}, {"start": 2312.69, "end": 2313.73, "word": " الحقيقية", "probability": 0.9854736328125}, {"start": 2313.73, "end": 2314.51, "word": " طب", "probability": 0.8046875}, {"start": 2314.51, "end": 2314.93, "word": " مثال", "probability": 0.966064453125}, {"start": 2314.93, "end": 2315.59, "word": " اتنين", "probability": 0.960205078125}, {"start": 2315.59, "end": 2316.45, "word": " ايه", "probability": 0.7434895833333334}, {"start": 2316.45, "end": 2316.61, "word": " اش", "probability": 0.53759765625}, {"start": 2316.61, "end": 2317.37, "word": " رايك؟", "probability": 0.69873046875}, {"start": 2317.37, "end": 2318.71, "word": " Subtraction", "probability": 0.7335611979166666}, {"start": 2318.71, "end": 2323.85, "word": " Subtraction", "probability": 0.8004557291666666}, {"start": 2323.85, "end": 2325.35, "word": " هل", "probability": 0.97265625}, {"start": 2325.35, "end": 2325.61, "word": " هو", "probability": 0.98779296875}, {"start": 2325.61, "end": 2326.25, "word": " binary", "probability": 0.78076171875}, {"start": 2326.25, "end": 2326.89, "word": " operation", "probability": 0.96728515625}, {"start": 2326.89, "end": 2327.17, "word": " على", "probability": 0.85546875}, {"start": 2327.17, "end": 2327.71, "word": " set", "probability": 0.53271484375}, {"start": 2327.71, "end": 2327.97, "word": " of", "probability": 0.97265625}, {"start": 2327.97, "end": 2328.51, "word": " natural", "probability": 0.90478515625}, {"start": 2328.51, "end": 2329.49, "word": " numbers؟", "probability": 0.619384765625}, {"start": 2329.49, "end": 2330.51, "word": " لأ", "probability": 0.6611328125}, {"start": 2330.51, "end": 2331.35, "word": " يبقى", "probability": 0.965087890625}, {"start": 2331.35, "end": 2332.09, "word": " Subtraction", "probability": 0.796630859375}, {"start": 2332.09, "end": 2332.93, "word": " is", "probability": 0.9208984375}, {"start": 2332.93, "end": 2334.83, "word": " not", "probability": 0.94580078125}, {"start": 2334.83, "end": 2335.87, "word": " a", "probability": 0.97412109375}, {"start": 2335.87, "end": 2336.69, "word": " binary", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 95, "seek": 236166, "start": 2341.0, "end": 2361.66, "text": "operation on set of natural number اللي هو N because if star معرفة من N نقرص ال N إلى N by", "tokens": [7192, 399, 322, 992, 295, 3303, 1230, 13672, 1829, 31439, 426, 570, 498, 3543, 20449, 28480, 3660, 9154, 426, 8717, 4587, 2288, 9381, 2423, 426, 30731, 426, 538], "avg_logprob": -0.4657866379310345, "compression_ratio": 1.018181818181818, "no_speech_prob": 0.0, "words": [{"start": 2341.0000000000005, "end": 2342.2000000000003, "word": "operation", "probability": 0.4745025634765625}, {"start": 2342.2000000000003, "end": 2343.4, "word": " on", "probability": 0.796875}, {"start": 2343.4, "end": 2345.54, "word": " set", "probability": 0.58203125}, {"start": 2345.54, "end": 2345.84, "word": " of", "probability": 0.9443359375}, {"start": 2345.84, "end": 2346.36, "word": " natural", "probability": 0.89599609375}, {"start": 2346.36, "end": 2346.98, "word": " number", "probability": 0.496337890625}, {"start": 2346.98, "end": 2347.18, "word": " اللي", "probability": 0.5625}, {"start": 2347.18, "end": 2347.38, "word": " هو", "probability": 0.9404296875}, {"start": 2347.38, "end": 2347.7, "word": " N", "probability": 0.36181640625}, {"start": 2347.7, "end": 2349.36, "word": " because", "probability": 0.6298828125}, {"start": 2349.36, "end": 2352.58, "word": " if", "probability": 0.8818359375}, {"start": 2352.58, "end": 2354.96, "word": " star", "probability": 0.50439453125}, {"start": 2354.96, "end": 2356.92, "word": " معرفة", "probability": 0.9471028645833334}, {"start": 2356.92, "end": 2357.36, "word": " من", "probability": 0.97314453125}, {"start": 2357.36, "end": 2357.86, "word": " N", "probability": 0.7275390625}, {"start": 2357.86, "end": 2358.58, "word": " نقرص", "probability": 0.529510498046875}, {"start": 2358.58, "end": 2358.96, "word": " ال", "probability": 0.8232421875}, {"start": 2358.96, "end": 2359.46, "word": " N", "probability": 0.8505859375}, {"start": 2359.46, "end": 2360.06, "word": " إلى", "probability": 0.85693359375}, {"start": 2360.06, "end": 2360.66, "word": " N", "probability": 0.95703125}, {"start": 2360.66, "end": 2361.66, "word": " by", "probability": 0.86181640625}], "temperature": 1.0}, {"id": 96, "seek": 237744, "start": 2373.68, "end": 2377.44, "text": "أربعة و سبعة موجودة في N", "tokens": [10721, 25513, 27884, 4032, 8608, 3555, 27884, 3714, 29245, 23328, 3660, 8978, 426], "avg_logprob": -0.41545758289950235, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2373.6800000000003, "end": 2374.78, "word": "أربعة", "probability": 0.4742431640625}, {"start": 2374.78, "end": 2375.34, "word": " و", "probability": 0.59326171875}, {"start": 2375.34, "end": 2375.88, "word": " سبعة", "probability": 0.810546875}, {"start": 2375.88, "end": 2376.62, "word": " موجودة", "probability": 0.9437255859375}, {"start": 2376.62, "end": 2376.92, "word": " في", "probability": 0.93310546875}, {"start": 2376.92, "end": 2377.44, "word": " N", "probability": 0.301025390625}], "temperature": 1.0}, {"id": 97, "seek": 240244, "start": 2381.31, "end": 2402.45, "text": "أنا جالس بتركشن طرح أربعة ناقص سبعة يسوي قداش ناقص ثلاثة هل هذه موجودة في ال N مش موجودة في ال N إذا عملية طرح على set of natural numbers is not a binary operation المرة الجاية نعطي مزيد من الأمثلة", "tokens": [10721, 8315, 10874, 6027, 3794, 39894, 2288, 4117, 8592, 1863, 23032, 2288, 5016, 5551, 25513, 27884, 8717, 995, 4587, 9381, 8608, 3555, 27884, 7251, 3794, 45865, 12174, 3215, 33599, 8717, 995, 4587, 9381, 38637, 1211, 5718, 104, 3660, 8032, 1211, 29538, 3714, 29245, 23328, 3660, 8978, 2423, 426, 37893, 3714, 29245, 23328, 3660, 8978, 2423, 426, 11933, 15730, 6225, 42213, 10632, 23032, 2288, 5016, 15844, 992, 295, 3303, 3547, 307, 406, 257, 17434, 6916, 9673, 25720, 25724, 995, 10632, 8717, 3615, 9566, 1829, 3714, 11622, 25708, 9154, 16247, 2304, 12984, 37977], "avg_logprob": -0.18427309329095093, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2381.31, "end": 2381.63, "word": "أنا", "probability": 0.6175537109375}, {"start": 2381.63, "end": 2382.05, "word": " جالس", "probability": 0.8898111979166666}, {"start": 2382.05, "end": 2382.79, "word": " بتركشن", "probability": 0.594580078125}, {"start": 2382.79, "end": 2383.29, "word": " طرح", "probability": 0.783203125}, {"start": 2383.29, "end": 2384.67, "word": " أربعة", "probability": 0.8167317708333334}, {"start": 2384.67, "end": 2385.77, "word": " ناقص", "probability": 0.9383544921875}, {"start": 2385.77, "end": 2386.17, "word": " سبعة", "probability": 0.9558919270833334}, {"start": 2386.17, "end": 2386.57, "word": " يسوي", "probability": 0.77294921875}, {"start": 2386.57, "end": 2387.19, "word": " قداش", "probability": 0.6787109375}, {"start": 2387.19, "end": 2388.69, "word": " ناقص", "probability": 0.932861328125}, {"start": 2388.69, "end": 2389.27, "word": " ثلاثة", "probability": 0.9513671875}, {"start": 2389.27, "end": 2389.65, "word": " هل", "probability": 0.867431640625}, {"start": 2389.65, "end": 2390.01, "word": " هذه", "probability": 0.724609375}, {"start": 2390.01, "end": 2390.65, "word": " موجودة", "probability": 0.9818115234375}, {"start": 2390.65, "end": 2390.79, "word": " في", "probability": 0.8974609375}, {"start": 2390.79, "end": 2390.91, "word": " ال", "probability": 0.92626953125}, {"start": 2390.91, "end": 2391.17, "word": " N", "probability": 0.331298828125}, {"start": 2391.17, "end": 2392.11, "word": " مش", "probability": 0.50537109375}, {"start": 2392.11, "end": 2392.61, "word": " موجودة", "probability": 0.9852294921875}, {"start": 2392.61, "end": 2392.73, "word": " في", "probability": 0.78369140625}, {"start": 2392.73, "end": 2392.81, "word": " ال", "probability": 0.92041015625}, {"start": 2392.81, "end": 2392.93, "word": " N", "probability": 0.8720703125}, {"start": 2392.93, "end": 2393.21, "word": " إذا", "probability": 0.7646484375}, {"start": 2393.21, "end": 2393.69, "word": " عملية", "probability": 0.9615885416666666}, {"start": 2393.69, "end": 2394.05, "word": " طرح", "probability": 0.9443359375}, {"start": 2394.05, "end": 2394.21, "word": " على", "probability": 0.7939453125}, {"start": 2394.21, "end": 2394.55, "word": " set", "probability": 0.4462890625}, {"start": 2394.55, "end": 2394.79, "word": " of", "probability": 0.96923828125}, {"start": 2394.79, "end": 2395.17, "word": " natural", "probability": 0.8447265625}, {"start": 2395.17, "end": 2395.91, "word": " numbers", "probability": 0.54345703125}, {"start": 2395.91, "end": 2396.51, "word": " is", "probability": 0.896484375}, {"start": 2396.51, "end": 2396.93, "word": " not", "probability": 0.96630859375}, {"start": 2396.93, "end": 2397.29, "word": " a", "probability": 0.97021484375}, {"start": 2397.29, "end": 2397.89, "word": " binary", "probability": 0.853515625}, {"start": 2397.89, "end": 2399.01, "word": " operation", "probability": 0.951171875}, {"start": 2399.01, "end": 2399.97, "word": " المرة", "probability": 0.970458984375}, {"start": 2399.97, "end": 2400.53, "word": " الجاية", "probability": 0.873046875}, {"start": 2400.53, "end": 2401.15, "word": " نعطي", "probability": 0.95361328125}, {"start": 2401.15, "end": 2401.61, "word": " مزيد", "probability": 0.9334309895833334}, {"start": 2401.61, "end": 2401.79, "word": " من", "probability": 0.97802734375}, {"start": 2401.79, "end": 2402.45, "word": " الأمثلة", "probability": 0.9681396484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2403.35825, "duration_after_vad": 2225.5131249999913}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c73a3003bda2e8d5b8f39d6b1580a8a18eee6454
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_postprocess.srt
@@ -0,0 +1,1796 @@
+1
+00:00:21,180 --> 00:00:26,920
+بسم الله الرحمن الرحيم انتهينا من شبتر ستة اللي هو
+
+2
+00:00:26,920 --> 00:00:32,320
+ال isomorphism والآن بندخل لشبتر سبعة شبتر سبعة
+
+3
+00:00:32,320 --> 00:00:36,640
+اللي هو Cossets and Lagrange theorem بتكلم عن
+
+4
+00:00:36,640 --> 00:00:41,980
+نقطتين والنقطتين مرتبطتين مع بعض ارتباطا وثيقا كما
+
+5
+00:00:41,980 --> 00:00:49,330
+سنرى Cosset بالعربي يعني الفئة المرافقةلقرنج
+
+6
+00:00:49,330 --> 00:00:53,410
+theorem نظرية لقرنج بالنسبة للعالم الرياضي لقرنج
+
+7
+00:00:53,410 --> 00:00:59,970
+الذي اكتشف هذه النظرية اليوم خلينا مع ال quesets و
+
+8
+00:00:59,970 --> 00:01:04,030
+المرة القادمة ان شاء الله تتكلم عن لقرنج theorem
+
+9
+00:01:04,650 --> 00:01:11,170
+بنقدر نعطي تعريف للـ Cosets ثم نبدأ بملاحظاتنا على
+
+10
+00:01:11,170 --> 00:01:15,750
+الـ Cosets in general يبقى التعريف يقول ياخد الـ H
+
+11
+00:01:15,750 --> 00:01:22,330
+subgroup من G وروحت أخد أي element A في G بضروح
+
+12
+00:01:22,330 --> 00:01:27,950
+أعرف ال Coset اللي هي AHيعني الـ subgroup بدأ
+
+13
+00:01:27,950 --> 00:01:33,670
+ضربها من جهة الشمال في أي element من G وليكن A من
+
+14
+00:01:33,670 --> 00:01:38,530
+ال set هذه A H يبقى the set of all elements A H
+
+15
+00:01:38,530 --> 00:01:43,570
+such that ال H small موجودة في H capital يعني
+
+16
+00:01:43,570 --> 00:01:51,350
+عناصر ال A H هوالـ Element A مضروب في من في عنصر
+
+17
+00:01:51,350 --> 00:01:55,890
+من عناصر H من ما يكون شكله A يكون بالشكل اللي
+
+18
+00:01:55,890 --> 00:02:00,330
+عندنا هذا الدرب من جهة الشمال لذلك هذه بسميها left
+
+19
+00:02:00,330 --> 00:02:06,370
+coset of H in G وهذه left coset تحتوي دائما و أبدا
+
+20
+00:02:06,370 --> 00:02:11,810
+عالميا على العنصر A حد بيقدر يقول لي ليش هذه
+
+21
+00:02:11,810 --> 00:02:17,210
+بتحتوي على العنصر Aلأن فيها الـ Identity الـ A في
+
+22
+00:02:17,210 --> 00:02:20,710
+الـ Identity بيعطينا الـ A itself يبقى الـ left
+
+23
+00:02:20,710 --> 00:02:26,310
+coset دائما و أبدا ال element A موجود فيها بالمثل
+
+24
+00:02:26,310 --> 00:02:29,770
+مثل ما عرفنا الـ left coset بتروح أعرفها الـ right
+
+25
+00:02:29,770 --> 00:02:34,690
+coset فبقول الـ H capital A هي عبارة عن H A such
+
+26
+00:02:34,690 --> 00:02:38,410
+that الـ H belonged to H وهذه بسميها الـ right
+
+27
+00:02:38,410 --> 00:02:44,460
+coset of H in G وفي نفس الوقت containing Aلاحظ لما
+
+28
+00:02:44,460 --> 00:02:50,800
+اقول a h او h a ال operation اللي بين ال a و ال h
+
+29
+00:02:50,800 --> 00:02:54,500
+هي نفس ال operation اللي موجودة على g و اللي
+
+30
+00:02:54,500 --> 00:03:02,390
+موجودة على h يعني اذا كان ضرب بدأ اقول ضربإذا جامع
+
+31
+00:03:02,390 --> 00:03:07,490
+يبقى الـ binary operation ما بين ال element a و ال
+
+32
+00:03:07,490 --> 00:03:12,310
+element h حسب ال operation اللي موجودة في g أو ال
+
+33
+00:03:12,310 --> 00:03:16,610
+operation اللي موجودة في hطيب الـ a اللي خلّج ال
+
+34
+00:03:16,610 --> 00:03:20,510
+left coset سواء كان ال right و الله left بسمي ايه
+
+35
+00:03:20,510 --> 00:03:25,670
+ال element ايه بسميه the coset representative of a
+
+36
+00:03:25,670 --> 00:03:30,350
+H أو ال H إيه سواء كان ال left أو ال right بتفرجش
+
+37
+00:03:30,350 --> 00:03:37,330
+أمنا طب نروح نبدي ذلك عمليا بمثال و نتوقف مع هذا
+
+38
+00:03:37,330 --> 00:03:44,080
+المثالنوعا ما و ناقش بعض الشغلات ماعطيني G هي S3
+
+39
+00:03:44,080 --> 00:03:50,180
+وهي كتبناها بالكامل ليها ستة عناصر واخد ال H هي ال
+
+40
+00:03:50,180 --> 00:03:55,700
+sub group ال E والواحد و تلاتةقال هاتلي كل ال left
+
+41
+00:03:55,700 --> 00:04:01,300
+cosets of H in S3 بقوله كويس اذا بدى ابدا مدام
+
+42
+00:04:01,300 --> 00:04:05,620
+قاله هاتلي كل ال left cosets اذا بدى ابدا بمعنى
+
+43
+00:04:05,620 --> 00:04:10,320
+بالعنصر الاول بدى اضربه في H واشوف شو بيعطيني يبقى
+
+44
+00:04:10,320 --> 00:04:18,570
+بداتي اخدله E H يبقى هذا E في E واحد و تلاتةطبعا
+
+45
+00:04:18,570 --> 00:04:22,910
+ال identity element لما اضربه فيه ال element بطلع
+
+46
+00:04:22,910 --> 00:04:27,530
+نفس ال element اضربه في التاني بدي يطلع نفس التاني
+
+47
+00:04:27,530 --> 00:04:33,730
+ال هد مين هي يا شباباللي هي H itself طيب اضرب الان
+
+48
+00:04:33,730 --> 00:04:39,430
+واحد و تلاتة ال permutation في ال H يبقى هذا
+
+49
+00:04:39,430 --> 00:04:44,970
+الكلام بده يساوي لما اضربها بده يطلع واحد و تلاتة
+
+50
+00:04:44,970 --> 00:04:50,750
+و هنا من واحد و تلاتة في واحد و تلاتة بالشكل اللي
+
+51
+00:04:50,750 --> 00:04:56,580
+عندناهذه هتعطينا مين؟ هتعطينا الو ال permutation
+
+52
+00:04:56,580 --> 00:05:01,700
+واحد، تلاتة، طب هذه نفسها إيش بتعطينا؟ ال
+
+53
+00:05:01,700 --> 00:05:06,560
+identity، تمام يبقى هذه عطتنا ال identity، طلعت
+
+54
+00:05:06,560 --> 00:05:14,480
+مين؟نفس الـ H يبقى هذه طلعت نفس الـ H itself يبقى
+
+55
+00:05:14,480 --> 00:05:20,680
+بناء عليه بقدر استنتج من هذا الكلام ان ال E في H
+
+56
+00:05:20,680 --> 00:05:27,920
+ساوة واحد تلاتة في H ساوة الـ H itself وهذا بدي
+
+57
+00:05:27,920 --> 00:05:34,740
+أحط علامة استفهام سارجع لها بعد قليلطيب الان بده
+
+58
+00:05:34,740 --> 00:05:39,240
+اخد ال elements الأخرى بدل ما اخدنا واحد و تلاتة
+
+59
+00:05:39,240 --> 00:05:45,320
+بده اخد واحد و اتنين في h اشوف ايش بده يعطينا يبقى
+
+60
+00:05:45,320 --> 00:05:51,420
+هذا بده يعطينا واحد و اتنين واحد و اتنين مضروبة في
+
+61
+00:05:51,420 --> 00:05:56,000
+من؟ في واحد و تلاتة يبقى واحد و اتنين في ال
+
+62
+00:05:56,000 --> 00:05:59,340
+identity بواحد و اتنين واحد اتنين في واحد تلاتة
+
+63
+00:05:59,340 --> 00:06:03,840
+بواحد اتنين واحد تلاتةهذا الكلام بدي يعطينا الواحد
+
+64
+00:06:03,840 --> 00:06:09,200
+اتنين كما هي وهذه بدي اجيب ال composition ما بين
+
+65
+00:06:09,200 --> 00:06:14,180
+ال two transpositions الاتنين هدول يبقى باجي بقول
+
+66
+00:06:14,180 --> 00:06:20,170
+هاي الواحد الواحد صورتهوالتلاتة صورتها تلاتة يبقى
+
+67
+00:06:20,170 --> 00:06:26,050
+هي التلاتة التلاتة صورتها واحد والواحد صورته اتنين
+
+68
+00:06:26,050 --> 00:06:30,630
+يبقى هي الاتنين الان اتنين صورته اتنين واتنين
+
+69
+00:06:30,630 --> 00:06:35,890
+صورته هي موجود يبقى جفلة بالشكل اللي عندنا هنا
+
+70
+00:06:35,890 --> 00:06:43,940
+تمام؟لاحظ ان هذا بالضبط تماما هو واحد تلات اثنين
+
+71
+00:06:43,940 --> 00:06:52,540
+كما لو ضربت في main ضربت في Hبناء على يسار واحد
+
+72
+00:06:52,540 --> 00:06:58,240
+اتنين اتش هو واحد تلات اتنين اتش يبقى هذا بدي
+
+73
+00:06:58,240 --> 00:07:03,780
+يعطيك ان واحد اتنين ال permutation لما تضربها في
+
+74
+00:07:03,780 --> 00:07:09,800
+اتش كليا بدي يساوي واحد تلات اتنين كما لو ضربتها
+
+75
+00:07:09,800 --> 00:07:17,240
+في اتش وهذا كمان بدي يولد علامة استفهام اخرى نكمل
+
+76
+00:07:18,800 --> 00:07:24,440
+بدي اجي لليه اتنين و تلاتة بدي اضربها في مين فاتش
+
+77
+00:07:24,440 --> 00:07:32,100
+يبقى الناتج اتنين تلاتة و اتنين تلاتة واحد تلاتة و
+
+78
+00:07:32,100 --> 00:07:37,750
+يساوي اتنين تلاتة واحديبقى اتنين تلاتة في اتش
+
+79
+00:07:37,750 --> 00:07:42,050
+باتنين تلاتة لان ال identity بعدها اتنين تلاتة في
+
+80
+00:07:42,050 --> 00:07:47,030
+واحد تلاتة هي اذا ان النتج يساوي هي اتنين تلاتة
+
+81
+00:07:47,030 --> 00:07:51,130
+الأولانية ال permutation الأولى وهذه بضروح اجيب ال
+
+82
+00:07:51,130 --> 00:07:55,830
+composition في ما بينهما اذا ببدأ بالواحد الواحد
+
+83
+00:07:55,830 --> 00:08:02,130
+صورته والتلاتة صورتها اتنين يبقى هي واحد اتنين
+
+84
+00:08:02,640 --> 00:08:08,840
+تلاتة صورته اتنين و اتنين صورته تلاتة الان بالداجي
+
+85
+00:08:08,840 --> 00:08:14,400
+التلاتة صورتها واحد و الواحد صورته هي موجود اذا
+
+86
+00:08:14,400 --> 00:08:20,370
+انقفلت بالشكل اللي عندنا هذاهذا بالضبط تماماً بده
+
+87
+00:08:20,370 --> 00:08:26,010
+يساوي اللي هو واحد اتنين تلاتة كما لو ضربتها في H
+
+88
+00:08:26,010 --> 00:08:32,730
+اعمل ال H كانت كويس؟ يبقى هاي خلاصنا ضايل فيه شيء؟
+
+89
+00:08:33,500 --> 00:08:39,680
+كل element هيو مبروب عندى من جهة الشمال فيه H بناء
+
+90
+00:08:39,680 --> 00:08:53,770
+عليه صار the left cosets of H in S3R أول واحد Hهه
+
+91
+00:08:53,770 --> 00:08:59,450
+H او ال E في ال H او واحد تلاتة H ال element
+
+92
+00:08:59,450 --> 00:09:06,990
+الثاني اللي هو من واحد اتنين في من في H وال
+
+93
+00:09:06,990 --> 00:09:15,330
+element التالت اللي هو اتنين تلاتة كله في Hأحنا
+
+94
+00:09:15,330 --> 00:09:21,690
+هكذا خلصنا المتوقع كان من البداية أنه لما أضرب ال
+
+95
+00:09:21,690 --> 00:09:25,490
+elements الستة اللي عندنا تبعات ال agromfets يطلع
+
+96
+00:09:25,490 --> 00:09:30,150
+عندى الست elements مظبوط طلعوا الست elements بس ما
+
+97
+00:09:30,150 --> 00:09:34,570
+هماش disjoint هاي الملاحظة الأولى لأن هدول طلعوا
+
+98
+00:09:34,570 --> 00:09:39,600
+اشي بيساوي بعضه هاي طلعوا هاي تلاتة بيساوي بعضهذول
+
+99
+00:09:39,600 --> 00:09:43,700
+اتنين بيسووا بعض، هذول اتنين كمان بيسووا بعض،
+
+100
+00:09:43,700 --> 00:09:48,220
+تمام؟ إذا ليس بالضرورة لما أجيب ال left corset ال
+
+101
+00:09:48,220 --> 00:09:53,650
+elements يكونوا disjointهذه الملاحظة الأولى
+
+102
+00:09:53,650 --> 00:09:58,170
+الملاحظة التانية اتطلعلي في الحالتين الاتنين هدول
+
+103
+00:09:58,170 --> 00:10:03,430
+هنا ضربت في ايه و هنا ضربت في واحد تلاتة يعني ضربت
+
+104
+00:10:03,430 --> 00:10:10,330
+في عناصر H إذا لو أخدت element من H و ضربته في H
+
+105
+00:10:10,330 --> 00:10:16,680
+بدي أطلع منهمEach itself مش واحدة تانية اطلع عندي
+
+106
+00:10:16,680 --> 00:10:22,080
+ايه اتش ثوات لمين اتش itself الواحد تلاتة فيه اتش
+
+107
+00:10:22,080 --> 00:10:27,100
+ثوات لمين الواحد تلاتة يعني اتش itself يبقى ال
+
+108
+00:10:27,100 --> 00:10:31,880
+left coset لو ضربت اللي هو ال subgroup في element
+
+109
+00:10:31,880 --> 00:10:35,820
+من نفس ال subgroup دي يطلع مين ال subgroup هاي
+
+110
+00:10:35,820 --> 00:10:42,520
+الملاحظة التانية الملاحظة التالتةإن الليفت كو سيتس
+
+111
+00:10:42,520 --> 00:10:49,180
+ممكن يتساوى رغم أن العنصر اللي ضرب فيه مش نفسه طلع
+
+112
+00:10:49,180 --> 00:10:54,280
+لي هنا هي عندي واحد اتنين ضربتها في H سواتلي مام
+
+113
+00:10:54,280 --> 00:10:59,220
+واحد تلات اتنين في H هل الواحد اتنين هو الواحد
+
+114
+00:10:59,220 --> 00:11:05,600
+تلات اتنين؟ لأ مختلف إذا ليس بالضرورة لو قلتلك A H
+
+115
+00:11:05,600 --> 00:11:11,370
+يسوى BH إذا ال A يسوى ال B صح ولا غلط؟غلط قد يحدث
+
+116
+00:11:11,370 --> 00:11:16,450
+انه صح بس in general غلط يعني ممكن تحصل حالة علتين
+
+117
+00:11:16,450 --> 00:11:21,870
+تلاتة تبقى صح لكن in general ليس صحيحا يبقى هذه
+
+118
+00:11:21,870 --> 00:11:25,750
+الملاحظة هذه انه في حالة ال left cosets ممكن
+
+119
+00:11:25,750 --> 00:11:30,470
+يتساوي ال two left cosets لكن ال a ليساوي ال b وهي
+
+120
+00:11:30,470 --> 00:11:36,050
+الكلام واضح قدامنا وهكذايبقى هذه ملاحظات أساسية
+
+121
+00:11:36,050 --> 00:11:40,890
+موجودة من خلال هذا المثال و بنقدر نسحبها على
+
+122
+00:11:40,890 --> 00:11:49,210
+course sets أخرى نعطي مثال أخرى example
+
+123
+00:11:49,210 --> 00:11:59,280
+two example two بيقولالـ G تساوي D4 و D4 احنا
+
+124
+00:11:59,280 --> 00:12:05,540
+عارفين عناصرها اللي هي R نود و R تسعين و R مية و
+
+125
+00:12:05,540 --> 00:12:14,800
+تمانين و R متين و سبعين و H و V و D و D Primeو بدي
+
+126
+00:12:14,800 --> 00:12:21,740
+اخد اللي هو K subgroup اللي هي subgroup generated
+
+127
+00:12:21,740 --> 00:12:32,800
+by R180 اللي عناصرها Arnold وR180 فقط لا غير تمام؟
+
+128
+00:12:32,800 --> 00:12:41,600
+find the left cosets of
+
+129
+00:12:54,930 --> 00:12:59,790
+الان بدي ابدا بال elements كلهم قاللي هاتلي lift
+
+130
+00:12:59,790 --> 00:13:06,950
+cos 6 يبقى انا بدي اجيبله ارناد في كابتل كهي كابتة
+
+131
+00:13:06,950 --> 00:13:11,930
+ال K موجودة عندى ارنود في ارنود مين بتعطينا ارنود
+
+132
+00:13:11,930 --> 00:13:16,410
+في مية و تمانين بتعطينا مين R مية و تمانين اللى هى
+
+133
+00:13:16,410 --> 00:13:25,190
+ال K itself طيب خذى R مية و تمانين مية و تمانين في
+
+134
+00:13:25,190 --> 00:13:31,550
+اللى هو K يبقى هذا الكلام بده يساوي R مية و تمانين
+
+135
+00:13:31,550 --> 00:13:39,080
+والتانية بصير Arnoldلأن الـ R 180 هو R 180 و R 360
+
+136
+00:13:39,080 --> 00:13:46,720
+هو الـ R node طلعت من هذا الـ K نفسه من الاتنين
+
+137
+00:13:46,720 --> 00:13:55,510
+هذول نستنتج الـ R node Kبدي يساوي R180K بدي يساوي
+
+138
+00:13:55,510 --> 00:14:00,350
+K itself أظن هذا يتفق مع النتيجة اللي توصلنا لها
+
+139
+00:14:00,350 --> 00:14:04,890
+هنا أنه لو ضربت ال subgroup في أي element من ال
+
+140
+00:14:04,890 --> 00:14:09,310
+subgroup بتطلع نفس من نفس ال subgroup وهذا اللي
+
+141
+00:14:09,310 --> 00:14:13,330
+حصل في الحالتين الأثنين هذول زي المثال اللي هناك
+
+142
+00:14:13,330 --> 00:14:20,020
+بالضبط تماماطيب الان لو جيت اخدت ال R ميتين و
+
+143
+00:14:20,020 --> 00:14:25,940
+سبعين في K مثلا يبقى هذا الكلام بده يسوي بده اضربه
+
+144
+00:14:25,940 --> 00:14:31,840
+هنا يبقى بده يعطيني R ميتين و سبعين و عندك R مية و
+
+145
+00:14:31,840 --> 00:14:37,540
+تمانين في R ميتين و سبعين اللي هي من R تسعين
+
+146
+00:14:39,600 --> 00:14:45,860
+270×180 خُد منها R 90 بيصير هذه R 360 ال identity
+
+147
+00:14:45,860 --> 00:14:54,920
+بيظل 100 بيظل R 90 السؤال هو هل هذا الكلام هو R 90
+
+148
+00:14:54,920 --> 00:15:02,760
+في K ام لا اضرب هاي R 90 وR 90 في R 180 بR 270
+
+149
+00:15:04,630 --> 00:15:10,250
+مظبوط ولا لا؟ يبقى من هذا الكلام بس تنتج ان ال R
+
+150
+00:15:10,250 --> 00:15:19,810
+ميتين وسبعين K هي عبارة عن ال R تسعين K بالشكل
+
+151
+00:15:19,810 --> 00:15:25,070
+اللي عندناتمام يبقى هدول مش أربعة هدول بس تنتين
+
+152
+00:15:25,070 --> 00:15:29,950
+left cosets لإن واحدة بتساوي التانية طيب بدأت أخد
+
+153
+00:15:29,950 --> 00:15:36,450
+الآن اللي هو ال H في K أشوف إيش بدها تعطينا ال H
+
+154
+00:15:36,450 --> 00:15:44,630
+في R نوت بال H وهذه H في R مية و تمانين هذه بدها
+
+155
+00:15:44,630 --> 00:15:47,730
+تساوي H وهذه نجي نشوف
+
+156
+00:15:51,960 --> 00:15:58,420
+HVR180 تفتح الكتاب صفحة واحد و تلاتين واحد و
+
+157
+00:15:58,420 --> 00:16:03,500
+تلاتين على ال table ال table بتاعة ال product ما
+
+158
+00:16:03,500 --> 00:16:10,550
+بين اللي هو عناصر ال D4 مع بعضها البعضيبقى احنا
+
+159
+00:16:10,550 --> 00:16:15,850
+بدنا H في R مية و تمانين يبقى عندنا H في R مية و
+
+160
+00:16:15,850 --> 00:16:20,410
+تمانين وين راحت؟ H في R مية و تمانين اللي هي ب V
+
+161
+00:16:20,410 --> 00:16:28,650
+يبقى هذا الكلام بد يساوي H و Vطب خليني اخد VK
+
+162
+00:16:28,650 --> 00:16:33,910
+واشوف ايش بدها تساوي يبقى ال VK الشكل اللي عندنا
+
+163
+00:16:33,910 --> 00:16:40,670
+هذا بدها تساوي ال V و ال V في من في ال R مية و
+
+164
+00:16:40,670 --> 00:16:45,970
+تمانينهذا الكلام بده يعطينا V و نجي ال V في ال R
+
+165
+00:16:45,970 --> 00:16:55,370
+180 ال V في ال R 180 بتعطينا H يبقى ناتج هو H ايش
+
+166
+00:16:55,370 --> 00:17:01,130
+بتلاحظوا على الاتنين هذول اتنين متساويين يبقى هذا
+
+167
+00:17:01,130 --> 00:17:09,360
+بده يعطينا ان ال HK بده يساوي ال VKبنفس الطريقة
+
+168
+00:17:09,360 --> 00:17:19,080
+اعملها similarly بدي يكون ال D K هتلاقي هو ال D' K
+
+169
+00:17:19,080 --> 00:17:28,020
+كذلك تمام؟ بناء عليه بقدر اقوله the left corsets
+
+170
+00:17:28,020 --> 00:17:36,360
+of the left corsets of
+
+171
+00:17:38,820 --> 00:17:49,140
+the left cosets of اللي هو K and D for R الأولى
+
+172
+00:17:49,140 --> 00:17:56,760
+الـ K itself والتانية اللي هو ال R تسعين في K
+
+173
+00:17:56,760 --> 00:18:05,600
+والتالتة لHK والرابعة اللي هو DKيبقى هذا left
+
+174
+00:18:05,600 --> 00:18:10,680
+cursive فقط لا غير اطلع على الملاحظات اللي عندك
+
+175
+00:18:10,680 --> 00:18:17,920
+هنا تجدها منطبقة تماما هيتنتين متساويتين رغم ان ال
+
+176
+00:18:17,920 --> 00:18:22,510
+element هذا مش هو ال element ال H بيختلف عن Vهنا
+
+177
+00:18:22,510 --> 00:18:26,830
+برضه ال D كي بده يسوي D' رغم ان ال D تختلف عاميا
+
+178
+00:18:26,830 --> 00:18:33,030
+عن D' و هكذا يعني ال two left cosets are equal رغم
+
+179
+00:18:33,030 --> 00:18:35,670
+ان ال element اللي مضروب فيه اتش يختلف عن ال
+
+180
+00:18:35,670 --> 00:18:39,710
+element الثاني اللي مضروب فيه اتش الحالة الثانية
+
+181
+00:18:39,710 --> 00:18:44,550
+لو أخدنا ال K اللي عندنا و ضربناها في عنصر من
+
+182
+00:18:44,550 --> 00:18:50,790
+عناصر K تبقى K كما هي وهذه الملاحظة اللي عندناطيب
+
+183
+00:18:50,790 --> 00:18:55,470
+السؤال هو هل ال right corset ممكن تساوي ال left
+
+184
+00:18:55,470 --> 00:19:02,070
+corset؟ بتساوي يعني؟ تعالي نجرب قد يحدث بس in
+
+185
+00:19:02,070 --> 00:19:07,310
+general مش صحيح في هدول أول تنتين صحيح بمظبوط
+
+186
+00:19:07,310 --> 00:19:10,850
+الكلام ليش انه من نفس ال group أو من نفس ال
+
+187
+00:19:10,850 --> 00:19:14,450
+subgroup بس بدي أجيب element من برا وبين انه هذا
+
+188
+00:19:14,450 --> 00:19:20,190
+الكلام مش صحيح فمثلاأحنا أخدنا وين R تسعين في K
+
+189
+00:19:20,190 --> 00:19:27,630
+هذه R تسعين في K واخدنا H كيه وغيره إلى آخرين طب
+
+190
+00:19:27,630 --> 00:19:33,030
+بدى أجرب K في H أشوف إيش بتعطيني هنا now
+
+191
+00:19:34,850 --> 00:19:41,830
+بدأ أخد اللي هو K في H يبقى هذا الكلام بده يساوي
+
+192
+00:19:41,830 --> 00:19:54,310
+اللي هو ال K في H بده يساوي H و هنا R مية و تمانين
+
+193
+00:19:54,310 --> 00:20:00,800
+في من في Hنجي نشوف اش بده يساوي هذا الكلام بده
+
+194
+00:20:00,800 --> 00:20:07,520
+يساوي H وال R مية و تمانين في H ال R مية و تمانين
+
+195
+00:20:07,520 --> 00:20:16,840
+في H في H بطلع كده؟ بطلع V بطلع V طيب طلعت هذه هي
+
+196
+00:20:16,840 --> 00:20:24,540
+بالضبط هذه V و H حد بقدر يقول لي ليش؟ ايوةمية مية
+
+197
+00:20:24,540 --> 00:20:29,960
+المي أر مية و تمانين في ال center وبالتالي هذا طلع
+
+198
+00:20:29,960 --> 00:20:34,840
+متساوين لكن لو برا ال center بصير كلام هذا معلوم
+
+199
+00:20:34,840 --> 00:20:39,020
+ليس صحيحا يبقى in general هذا الكلام ليس صحيحا
+
+200
+00:20:39,020 --> 00:20:43,840
+الممكن أخد من هنا هذا مافيش فيها ال center هذه S3
+
+201
+00:20:43,840 --> 00:20:47,380
+مافيش فيها إلا ال identity element تعالي ناخد من
+
+202
+00:20:47,380 --> 00:20:54,770
+هنا هى الصارة عندك هذا يعنيإن ال K في H بده يساوي
+
+203
+00:20:54,770 --> 00:20:56,230
+ال H في K
+
+204
+00:20:59,010 --> 00:21:08,290
+ولكن لو جيت من المثال الأول أخدت واحد اتنين
+
+205
+00:21:08,290 --> 00:21:15,610
+هذا مضروب في اتش ان اتش قداش طلع واحد اتنين في اتش
+
+206
+00:21:15,610 --> 00:21:21,390
+طلع واحد تلاتة اتنين اتش طلع واحد تلاتة اتنين في
+
+207
+00:21:21,390 --> 00:21:28,700
+اتش andبدي اخد H في main في واحد اتنين يبقى H في
+
+208
+00:21:28,700 --> 00:21:34,440
+ال permutation واحد اتنين بدي يعطينا واحد اتنين
+
+209
+00:21:34,440 --> 00:21:40,760
+والان اللي هو ال H قولنا هناك بقداش بواحد تلاتة
+
+210
+00:21:40,760 --> 00:21:48,220
+يبقى واحد تلاتة في واحد اتنين لأن الضرب من وين؟ من
+
+211
+00:21:48,220 --> 00:21:54,510
+جهتي اليمينيبقى هذا الكلام بده يعطينا واحد اتنين و
+
+212
+00:21:54,510 --> 00:21:59,630
+هذا بده يعطينا الواحد صورته اتنين و اتنين صورته
+
+213
+00:21:59,630 --> 00:22:05,050
+اتنين الان اتنين صورته الواحد و الواحد صورته تلاتة
+
+214
+00:22:05,050 --> 00:22:11,680
+التلاتة صورتها تلاتة و التلاتة واحد قفلت هديهااللي
+
+215
+00:22:11,680 --> 00:22:18,860
+هو واحد اتنين تلاتة في H اطلع شوف لي واحد اتنين في
+
+216
+00:22:18,860 --> 00:22:25,200
+H هل هي H في واحد اتنين طب لا هذه واحد تلاتة اتنين
+
+217
+00:22:25,200 --> 00:22:30,000
+هذه واحد اتنين تلاتة يبقى بيسووش بعض يبقى باجي
+
+218
+00:22:30,000 --> 00:22:37,600
+بقوله هنا سا واحد اتنين في H does not equal لل H
+
+219
+00:22:37,600 --> 00:22:43,660
+في واحد اتنينيبقى in general الـ left cosets
+
+220
+00:22:43,660 --> 00:22:48,960
+والright cosets are not equal يعني قد يحدث تساوي
+
+221
+00:22:48,960 --> 00:22:54,540
+وقد لا يحدث سبب التساوي في النقطة الأولى اللي
+
+222
+00:22:54,540 --> 00:23:00,600
+أخدناها من D4 أن الـR180 كانت في ال center
+
+223
+00:23:00,600 --> 00:23:05,640
+وبالتالي حصل التساوي النقطة الثانية ليست في ال
+
+224
+00:23:05,640 --> 00:23:11,600
+center وبالتالي لم يحدث تساوينعطي كمان مثال تلاتة
+
+225
+00:23:11,600 --> 00:23:23,820
+example تلاتة بيقول خدلي G هو هي Z تسعة تمام and
+
+226
+00:23:23,820 --> 00:23:31,230
+ال H هي ال sub group generated by تلاتةهات لل left
+
+227
+00:23:31,230 --> 00:23:44,070
+cosets find the left cosets of H and the تسعة
+
+228
+00:23:47,960 --> 00:23:52,880
+خلّى بالا كدا بدنا نجيب اللفت كو ستس اللى عندنا
+
+229
+00:23:52,880 --> 00:24:00,180
+طبعا جي معروفة زد تسعة هي عبارة عن زير و واحد و
+
+230
+00:24:00,180 --> 00:24:05,900
+اتنين لغاية تمانينتمام الان ال H ال sub group
+
+231
+00:24:05,900 --> 00:24:11,560
+generated by تلاتة هي زيرو تلاتة و ستة و تسعة اللي
+
+232
+00:24:11,560 --> 00:24:16,480
+هي زيرو و هكذا بدنا نروح نجيب ال left cosets ال
+
+233
+00:24:16,480 --> 00:24:21,300
+operation على Z تسعة جامع ولا ضاربة جامع ممدر جدا
+
+234
+00:24:21,610 --> 00:24:29,110
+يبقى انا بدي ابدأ بالعنصر الأول Zero زائد H يعني
+
+235
+00:24:29,110 --> 00:24:35,050
+اللي هو Zero زائد ال sub group generated by تلاتة
+
+236
+00:24:35,050 --> 00:24:41,230
+من عناصرها هيهم بدي اضيف Zero لكل عنصر من هذه
+
+237
+00:24:41,230 --> 00:24:47,820
+العناصر بتغير اشييقول تطلع H itself يبقى هذا بده
+
+238
+00:24:47,820 --> 00:24:53,780
+يعطينا H itself ليش؟ لإن ال zero موجود في H طيب لو
+
+239
+00:24:53,780 --> 00:25:00,840
+روحت قولتلك أليس هذا هو تلاتة زائد H؟نفسه ولا لا؟
+
+240
+00:25:00,840 --> 00:25:05,460
+لأن تلاتة تضيف فلك كل عمصر تلاتة زائد زيرو بتلاتة
+
+241
+00:25:05,460 --> 00:25:09,700
+تلاتة زائد تلاتة بستة تلاتة زائد تسعة بزيرو يبقى
+
+242
+00:25:09,700 --> 00:25:16,200
+zero, six, تلاتة، تمام؟ طيب، أليست هذه هي ستة زائد
+
+243
+00:25:16,200 --> 00:25:23,570
+H كذلك؟ يبقى هاي تلاتة، هاي واحدةوهي تنتين وهي
+
+244
+00:25:23,570 --> 00:25:28,950
+تلاتة وهي الأصلية كلهم بيساوي بعض مرة واحدة طب لو
+
+245
+00:25:28,950 --> 00:25:36,000
+جيت واحد زائد Hيبقى هذا الكلام بده يساوي واحد زائد
+
+246
+00:25:36,000 --> 00:25:40,840
+zero بواحد، واحد زائد تلاتة باربعة، واحد زائد ستة
+
+247
+00:25:40,840 --> 00:25:47,960
+بسبعة السؤال هو شوف ليه، احنا أخدنا هنا، هل شوف
+
+248
+00:25:47,960 --> 00:25:53,910
+ليه هل هو اربعة زائد each ولا لأ، تعالى نشوفأربعة
+
+249
+00:25:53,910 --> 00:25:58,770
+زائد Zero باربعة هيها أربعة زائد تلاتة بسبعة هيها
+
+250
+00:25:58,770 --> 00:26:04,450
+أربعة زائد ستة بعاشرة في زي التسعة بواحد هيها تمام
+
+251
+00:26:04,450 --> 00:26:13,270
+طيب شوف ليه هل هذا بالضبط سبعة زائد Hنفس الفكرة طب
+
+252
+00:26:13,270 --> 00:26:19,510
+لو روحت لان للي اتنين زائد H يبقى هذا الكلام بده
+
+253
+00:26:19,510 --> 00:26:24,110
+يسويه بده اجي هنا و اضيف لكل واحد اتنين يبقى هذه
+
+254
+00:26:24,110 --> 00:26:32,190
+بصير اتنين و هنا خمسة و هنا تمانيةطب شوف لبالله
+
+255
+00:26:32,190 --> 00:26:40,250
+هذه هل هي خمسة زائد H أم لا وشوف هل هي تمانية زائد
+
+256
+00:26:40,250 --> 00:26:47,730
+H أم لا هي نفسها يبقى ماعنديش إلا رغم هذه تسع
+
+257
+00:26:47,730 --> 00:26:52,310
+عناصر لكن رغم ذلك ماعنديش إلا تلاتة left cosets
+
+258
+00:26:52,310 --> 00:27:02,300
+يبقى بجي بقوله so the left cosets areاللي هو مين
+
+259
+00:27:02,300 --> 00:27:08,760
+ال H نفسه Zero زاد H ال H نفسه و ال واحد زاد H و
+
+260
+00:27:08,760 --> 00:27:16,780
+اتنين زاد H فقط لا غير لا يوجد غيرها طيب
+
+261
+00:27:16,780 --> 00:27:23,540
+الان اللاحظ هدى و هدى و هدى و هدى كلهم دول are
+
+262
+00:27:23,540 --> 00:27:27,360
+equal ليش؟لأن الـ element اللي هنا ده أخدناه من
+
+263
+00:27:27,360 --> 00:27:32,440
+داخل الـ H لما انطلعنا برا الـ H لجيت واحد زادتش
+
+264
+00:27:32,440 --> 00:27:36,600
+يساوي أربعة زادتش رغم أن الواحد لاتساوي أربعة في
+
+265
+00:27:36,600 --> 00:27:41,640
+زي التسعة و لجينا هذا الكلام يساوي سبعة زادتش رغم
+
+266
+00:27:41,640 --> 00:27:46,480
+أن السبعة لاتساوي أربعة لاتساوي واحد وهكذا بالنسبة
+
+267
+00:27:46,480 --> 00:27:51,070
+للآخر هذا يتفق مع الكلام اللي قلناه قبل قليلان ال
+
+268
+00:27:51,070 --> 00:27:56,970
+A H لو كانت تساوي B H ليس بالضرورة ان A تساوي B
+
+269
+00:27:56,970 --> 00:28:02,430
+يعني قد يكون و قد لا يكون in general حد ايه له اي
+
+270
+00:28:02,430 --> 00:28:03,810
+سؤال هنا شباب؟
+
+271
+00:28:19,180 --> 00:28:23,240
+حاجة بقول بدي أحب أسالها سؤال؟ طيب احنا من حاب
+
+272
+00:28:23,240 --> 00:28:28,600
+نسألها الحينالسؤال اللى بدنا نعطيك لمّة ونروح
+
+273
+00:28:28,600 --> 00:28:35,240
+نبرهن عناصرها وحنسأل واحنا بنبرهن ان شاء الله يبقى
+
+274
+00:28:35,240 --> 00:28:40,860
+أول لمّة في هذا ال section بتتكلم عن ما يأتي عن
+
+275
+00:28:40,860 --> 00:28:47,520
+خواص ال cosets يبقى اللمّة اللي هي عبارة عن the
+
+276
+00:28:47,520 --> 00:28:52,940
+properties of cosets
+
+277
+00:28:54,980 --> 00:29:07,360
+أيش الخواص هذه بيقول let ال h be a subgroup of g
+
+278
+00:29:07,360 --> 00:29:10,700
+let
+
+279
+00:29:10,700 --> 00:29:19,240
+ال a will be موجودة في ال group g then النقطة
+
+280
+00:29:19,240 --> 00:29:29,050
+الأولىالـ A موجود في الـ H بنفس الطريقة بقدر أقوله
+
+281
+00:29:29,050 --> 00:29:34,170
+الـ A موجودة في الـ H سواء كان هذه و الله هذه
+
+282
+00:29:34,170 --> 00:29:42,050
+سيامة النقطة الثانية الـ A H بده يساوي الـ H if
+
+283
+00:29:42,050 --> 00:29:50,600
+and only if الـ A موجود في الـ Hالنقطة التالتة ال
+
+284
+00:29:50,600 --> 00:29:59,880
+A H بده يساوي B H if and only if ال A موجودة في ال
+
+285
+00:29:59,880 --> 00:30:10,300
+B H النقطة الرابعة ال A H بده يساوي ال B HO ال A H
+
+286
+00:30:10,300 --> 00:30:20,400
+intersection BH بده يساوي الفايالنقطة الخامسة
+
+287
+00:30:20,400 --> 00:30:30,000
+بتقول ال A H بده يساوي ال B H if and only if A
+
+288
+00:30:30,000 --> 00:30:38,380
+inverse B belongs to H النقطة السادسة بتقول ان ال
+
+289
+00:30:38,380 --> 00:30:45,740
+order لل A H بده يساوي ال order لل B H النقطة
+
+290
+00:30:45,740 --> 00:30:55,500
+السابعةبتقول ان الـ A H بده يساوي الـ H A if and
+
+291
+00:30:55,500 --> 00:31:02,360
+only if if and only if الـ H بده يساوي الـ A H A
+
+292
+00:31:02,360 --> 00:31:09,400
+inverse النقطة الثامنة والاخيرة بيقول الـ A H is a
+
+293
+00:31:09,400 --> 00:31:17,050
+subgroup main G if and only ifF and only F ال A
+
+294
+00:31:17,050 --> 00:31:22,350
+موجودة في H Approved
+
+295
+00:31:39,310 --> 00:31:43,790
+خلّي بالك معانا كويس هنا الان انا عندي H subgroup
+
+296
+00:31:43,790 --> 00:31:49,370
+من G أخدت عنصرين موجودات فيه G النقطة الأولى بتقول
+
+297
+00:31:49,370 --> 00:31:53,190
+ال A موجود في ال H طبعا احنا قرناها في التعريف لكم
+
+298
+00:31:53,190 --> 00:31:59,470
+النتبه رياضيا ال A H بده يساوي ال H إذا كان ال A
+
+299
+00:31:59,470 --> 00:32:03,530
+موجود في H يعني لو ضاربت ال subgroup في element
+
+300
+00:32:03,530 --> 00:32:07,550
+منها بيطلع نفس ال H وشوفنا تو في الثلاثة أمثلة نفس
+
+301
+00:32:07,550 --> 00:32:12,790
+الكلامبس احنا بنثبت نظرية للجميع النقطة التالتة A
+
+302
+00:32:12,790 --> 00:32:17,670
+H بدي تسوى BH إذا كان ال A موجود وان في ال BH
+
+303
+00:32:17,670 --> 00:32:23,430
+الرابعة any two left cosets يا إما اتنين بتسووا
+
+304
+00:32:23,430 --> 00:32:27,490
+بالكامل يا إما ال intersection تبعهم بدي تسوى فاي
+
+305
+00:32:27,490 --> 00:32:32,570
+طلع في نهاية كل مثال قولنا يبقى left cosets كذا
+
+306
+00:32:32,570 --> 00:32:37,710
+طلع فش ولا عنصر مشترك ما بين التلاتة فالمثال الأول
+
+307
+00:32:48,150 --> 00:32:54,550
+تساوى لو حدث يبقى a inverse b موجود في h عدد
+
+308
+00:32:54,550 --> 00:32:59,050
+العناصر في كل left coset يسوى عدد العناصر في left
+
+309
+00:32:59,050 --> 00:33:04,280
+coset a الثانية بالضبط تماماهذا الـ A H بده يساوي
+
+310
+00:33:04,280 --> 00:33:08,280
+H A إذا كان الـ H بده يساوي يعني ال right coset
+
+311
+00:33:08,280 --> 00:33:12,600
+تساوي ال left coset إذا كان ال H قدرت أكتبها على
+
+312
+00:33:12,600 --> 00:33:18,180
+صيغة A H A inverse الأمر الأخير أنه الـ A H
+
+313
+00:33:18,180 --> 00:33:23,180
+subgroup من G إذا كان ال A موجود في H يعني ال left
+
+314
+00:33:23,180 --> 00:33:28,040
+cosets اللي حسبناهم قبل قليل بعضهم subgroup وبعضهم
+
+315
+00:33:28,040 --> 00:33:32,550
+لأو subgroup وقتاش لما كان ال element اللى بنضرب
+
+316
+00:33:32,550 --> 00:33:35,970
+فيه جاي من نفس ال subgroup لإنه بطلع لنفس ال
+
+317
+00:33:35,970 --> 00:33:40,830
+subgroup لكن لما نيجي من برا ماهواش subgroup اطلع
+
+318
+00:33:40,830 --> 00:33:45,610
+مثلا للواحد اتنين في ال H في أول مثالإذا أعطاني
+
+319
+00:33:45,610 --> 00:33:49,930
+two elements فاش فيهم ال identity element إذا هذه
+
+320
+00:33:49,930 --> 00:33:55,370
+ليست subgroup يبقى أنا بقول coset وليست subgroup
+
+321
+00:33:55,370 --> 00:33:59,630
+إذا ال coset in general ليست بالضرورة تكون
+
+322
+00:33:59,630 --> 00:34:03,450
+subgroup تكون subgroup لو كان ال element من نفس ال
+
+323
+00:34:03,450 --> 00:34:08,900
+subgroup itselfنجي للنقطة الأولى بيقول يثبت أن ال
+
+324
+00:34:08,900 --> 00:34:13,780
+a موجودة في ال a h باجي بقوله ال a اللي عندنا هذه
+
+325
+00:34:13,780 --> 00:34:19,760
+مش بقدر اكتبها ال a في ال identity element صح ولا
+
+326
+00:34:19,760 --> 00:34:24,720
+لا طيب ال identity element هذا المنظر فيه أليس
+
+327
+00:34:24,720 --> 00:34:32,180
+موجود في ال a hلأن أي subgroup تحتوي على الـ
+
+328
+00:34:32,180 --> 00:34:36,640
+Identity Element. إذاً الـ E هدى موجود في H و A هي
+
+329
+00:34:36,640 --> 00:34:42,600
+A نفسها. بناءً عليه الـ A صارت موجودة في الـ H وهو
+
+330
+00:34:42,600 --> 00:34:48,700
+المطلوب يبقى الـ A belongs to H.وبالفعل احنا لما
+
+331
+00:34:48,700 --> 00:34:52,800
+اخدنا ال subgroup تاو قبل شوية وضربنا ال element
+
+332
+00:34:52,800 --> 00:34:57,960
+في ال identity طالع من نفس ال element موجود فيها
+
+333
+00:34:57,960 --> 00:35:02,680
+طيب هذا النقطة الأولى بسيطة نيجي للنقطة الثانية
+
+334
+00:35:03,090 --> 00:35:06,970
+النقطة الثانية بيقول ال A H بده يساوي ال H if and
+
+335
+00:35:06,970 --> 00:35:12,210
+only if ال A belongs to H بنقوله كويس يبقى البرهان
+
+336
+00:35:12,210 --> 00:35:16,890
+بده يصير في اتجاهين لإنه if and only if يبقى
+
+337
+00:35:16,890 --> 00:35:22,210
+الاتجاه الأول بداجي أقوله assume ال A H بده يساوي
+
+338
+00:35:22,210 --> 00:35:28,820
+ال H itself ايش بدي أثباته؟الـ A موجود في الـ H
+
+339
+00:35:28,820 --> 00:35:37,900
+الـ A لو جت من النقطة الأولى from oneالـ A موجود
+
+340
+00:35:37,900 --> 00:35:44,680
+في مين؟ في الـ H طيب و الـ H ايش تساوي؟ يبقى الـ A
+
+341
+00:35:44,680 --> 00:35:49,140
+موجودة في الـ H يبقى هذا بدي يعطيني ان الـ A
+
+342
+00:35:49,140 --> 00:35:59,040
+موجودة في الـ H ليش since H او الـ H بدها ساوي H
+
+343
+00:35:59,040 --> 00:36:03,540
+بدها موجود هنا اذا موجود هنا هذا الاتجاه الأولنجي
+
+344
+00:36:03,540 --> 00:36:11,560
+لاتجاه الثاني conversely assume
+
+345
+00:36:11,560 --> 00:36:21,640
+افترض ان ال a موجود في ال Hماذا نريد أن نثبت؟ نريد
+
+346
+00:36:21,640 --> 00:36:27,920
+أن نثبت أن الـ H هي subgroup من الـ H تساوي H
+
+347
+00:36:27,920 --> 00:36:31,780
+itself طبعا في المبادئ الرياضية دخلنا لما بدأ أثبت
+
+348
+00:36:31,780 --> 00:36:35,520
+أنه two sets are equal باخد element هنا بثبته في
+
+349
+00:36:35,520 --> 00:36:38,400
+التاني بيصير الأولى أعصاب ساتمة التانية هو العملية
+
+350
+00:36:38,400 --> 00:36:42,220
+العكسية بنفس الطريقة بدأ أثبت أنه التانية أعصاب
+
+351
+00:36:42,220 --> 00:36:47,660
+ساتمة الأولى بيحدث تساوي يبقى الخطوة الأولى بدأ
+
+352
+00:36:47,660 --> 00:36:54,300
+أحاول أثبت أنهالـ A H subset من من؟ subset من ال H
+
+353
+00:36:54,300 --> 00:37:05,710
+طيب ال N from one ال A موجودة في ال A Hمظبوط؟ وانا
+
+354
+00:37:05,710 --> 00:37:10,790
+عند ايش؟ وانا عند ال A H انا فرضها بتسوى 100 .. لا
+
+355
+00:37:10,790 --> 00:37:12,310
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+356
+00:37:12,310 --> 00:37:12,590
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+357
+00:37:12,590 --> 00:37:14,650
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+358
+00:37:14,650 --> 00:37:15,290
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+359
+00:37:15,290 --> 00:37:15,490
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+360
+00:37:15,490 --> 00:37:15,590
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+361
+00:37:15,590 --> 00:37:21,630
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+362
+00:37:21,630 --> 00:37:21,690
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+363
+00:37:21,690 --> 00:37:31,710
+لا .. لا ..الان ال a كذلك from واحد موجودة في مين؟
+
+364
+00:37:31,710 --> 00:37:37,730
+في ال a H و ال a موجودة في H يبقى معنا هذا الكلام
+
+365
+00:37:37,730 --> 00:37:46,670
+ان ال a H صبست من مين؟ صبست من ال Hيبقى أنا عندي A
+
+366
+00:37:46,670 --> 00:37:52,370
+موجودة في ال H من الواحد ومن الفرض تبعي A موجودة
+
+367
+00:37:52,370 --> 00:37:57,870
+في H إذا ال A H subset من من؟ subset من ال H هذا
+
+368
+00:37:57,870 --> 00:38:03,310
+الاتجاه السهل الاتجاه الصعب الثاني يبقى هنا on the
+
+369
+00:38:03,310 --> 00:38:08,830
+other hand on the other hand
+
+370
+00:38:13,180 --> 00:38:19,160
+الان لما اقول يا شباب ان ال a موجودة في H هذا معطى
+
+371
+00:38:19,160 --> 00:38:24,540
+طب H sub group ولا لا يبقى معكوس ال element هذا
+
+372
+00:38:24,540 --> 00:38:30,060
+موجود صح ولا لا يبقى then
+
+373
+00:38:31,810 --> 00:38:38,330
+اللي هو الـ A inverse موجود في H طيب بدا أجي أقوله
+
+374
+00:38:38,330 --> 00:38:44,710
+خدلي X موجود في H أنا بدي أثبت إن H subset من مين؟
+
+375
+00:38:44,710 --> 00:38:50,670
+من الـ H يبقى خت element موجود في وين؟ في الـ H
+
+376
+00:38:50,670 --> 00:38:51,650
+then
+
+377
+00:38:54,840 --> 00:39:00,800
+then هلحين هذا موجود في H و هذا موجود في H إذا حصل
+
+378
+00:39:00,800 --> 00:39:08,760
+ضربهم موجود في H يبقى then A inverse X موجود وين؟
+
+379
+00:39:08,760 --> 00:39:18,000
+موجود في H هذا معناه إن ال A inverse X بده يساوي H
+
+380
+00:39:18,000 --> 00:39:29,930
+for somefor some h اللي موجودة في h مادام هذا في h
+
+381
+00:39:29,930 --> 00:39:36,170
+اذا هيساوي ال h طيب هذا معناه انا بدي ال x يبقى
+
+382
+00:39:36,170 --> 00:39:42,190
+هذا معناه ان ال x تساوي لو ضربت الطرفين في العنصر
+
+383
+00:39:42,190 --> 00:39:48,630
+a يبقى بضل على شمال x وهنا بجينا mean a h هذه h
+
+384
+00:39:48,630 --> 00:39:55,960
+وين موجودة؟موجودة في اله يبقى انا فرض x في h لجيت
+
+385
+00:39:55,960 --> 00:40:02,600
+ال x موجود وان في اله يبقى هذا معناه ان اله هذه ال
+
+386
+00:40:02,600 --> 00:40:09,540
+subset من اله اطلع لي سميلي هذه star وسميلي هذه
+
+387
+00:40:09,540 --> 00:40:13,840
+double star من التنتين مع بعض from
+
+388
+00:40:28,680 --> 00:40:33,490
+الشكل اللي عندنا هناطيب هذه هي النقطة الثانية دير
+
+389
+00:40:33,490 --> 00:40:37,970
+بالك هتلزمنا كتير خلال البراهين بده اروح للنقطة
+
+390
+00:40:37,970 --> 00:40:44,570
+التالتة النقطة التالتة بيقول ال a h ال a ال a h
+
+391
+00:40:44,570 --> 00:40:50,510
+بده يساوي ال ال b h f عنده اللي f ال a موجودة في b
+
+392
+00:40:50,510 --> 00:40:57,670
+h يبقى بداجي اقوله assume افترض ان ال a h بده
+
+393
+00:40:57,670 --> 00:41:03,560
+يساوي b hبدي احاول اثبت ان ال a موجودة في ال بي
+
+394
+00:41:03,560 --> 00:41:10,520
+اتش الان يا شباب from واحد ال a موجودة في ال اتش
+
+395
+00:41:10,520 --> 00:41:17,260
+صح؟ و اللي عند ال a اتش بدي يسوي ال بي اتش يبقى
+
+396
+00:41:17,260 --> 00:41:22,040
+هذا معناه ان ال a موجودة في ال بي اتش و هو المطلوب
+
+397
+00:41:23,190 --> 00:41:29,710
+مظبوط؟ طيب الاتجاه الثاني يبقى هنا أخدنا الاتجابات
+
+398
+00:41:29,710 --> 00:41:36,130
+دي اجي اقوله هنا و الرقاهي رقم تلاتة conversely
+
+399
+00:41:39,490 --> 00:41:48,910
+conversely ا assume افترض ان ال a موجودة في ال bh
+
+400
+00:41:48,910 --> 00:41:55,430
+بده احاول اثبت ان ال aH بده سوى مين بيه ال aH
+
+401
+00:41:55,430 --> 00:42:05,210
+موجودة في بي كابتل H تمامطيب assume كذا then ال a
+
+402
+00:42:05,210 --> 00:42:13,490
+هذه بدها تساوي bh for some h اللي belongs to man
+
+403
+00:42:13,490 --> 00:42:21,250
+لل h طب لو ضربت الطرفين في hيبقى باجي بقوله هذا
+
+404
+00:42:21,250 --> 00:42:29,790
+معناه ان ال a capital H بده يساوي bh capital H هذا
+
+405
+00:42:29,790 --> 00:42:37,130
+معناه ان ال aH بده يساوي bh في H من خاصية ال
+
+406
+00:42:37,130 --> 00:42:44,700
+associativityهذا معناه ان الـ a h بده يساوي بي ال
+
+407
+00:42:44,700 --> 00:42:49,700
+element h لما يكون في h و تضربه في h بتظهر زي مهي
+
+408
+00:42:49,700 --> 00:42:55,300
+h كابتن يبقى هدف بيه اتش عزيزي و هو المطلوب خلصنا
+
+409
+00:42:55,300 --> 00:43:00,820
+الاتجاهين طيب الان بدنا نجي لنقطة رابعالنقطة
+
+410
+00:43:00,820 --> 00:43:05,540
+الرابعة بيقول يا إما ال two left cosets بدوا
+
+411
+00:43:05,540 --> 00:43:09,560
+يتساووا يا إما ال intersection تبعهم بدوا يساووا
+
+412
+00:43:09,560 --> 00:43:15,480
+ماين فاي إذا لو نفيت واحدة منهم بدي أثبت إيه تانية
+
+413
+00:43:15,480 --> 00:43:22,040
+يبقى بالداجة أقوله أسيوم افترض ان ال a h
+
+414
+00:43:22,040 --> 00:43:30,160
+intersection ب a h لا يساوي الفايلا يساو الفاى
+
+415
+00:43:30,160 --> 00:43:36,080
+معناته في عناصر مشتركة ما بين الاتنين يبقى هنا
+
+416
+00:43:36,080 --> 00:43:41,540
+بداية اقوله افترض ان ال X موجود في ال A H
+
+417
+00:43:41,540 --> 00:43:47,660
+intersection B H معناه هذا الكلام ان ال X موجود في
+
+418
+00:43:47,660 --> 00:43:55,840
+ال A H و ال X موجود في ال B Hمعنى هذا الكلام ان ال
+
+419
+00:43:55,840 --> 00:44:07,320
+X بده يساوي A H1 مثلا and ال X بده يساوي B H2 مش
+
+420
+00:44:07,320 --> 00:44:12,290
+هنا ميز فيه ما بينهم مش نفس ال elementطب كويس مدام
+
+421
+00:44:12,290 --> 00:44:17,710
+هذا بيساوي هذا إذا الاتنين are equal يبقى لإن
+
+422
+00:44:17,710 --> 00:44:26,170
+الطرف الشمال كله X يبقى A H1 بده يساوي ال B H2طيب
+
+423
+00:44:26,170 --> 00:44:33,570
+هذا لو جيت قولت A H 1 بضربته في H بديه ساوي ال B H
+
+424
+00:44:33,570 --> 00:44:40,190
+2 كله في H من خاصية ال associativity يبقى ال A في
+
+425
+00:44:40,190 --> 00:44:48,330
+ال H 1 H بديه ساوي B في ال H 2 H يبقى هذا الكلام
+
+426
+00:44:48,330 --> 00:44:54,770
+بديه يعطينا انه A H بديه ساوي من BH وهو المطلوب
+
+427
+00:44:55,410 --> 00:45:00,810
+يبقى هنا فيت واحدة و أثبت له main الثانية طيب بدنا
+
+428
+00:45:00,810 --> 00:45:06,610
+نيجي لرقم خمسة رقم خمسة بيقول ايه اتش بيبقى طيب
+
+429
+00:45:06,610 --> 00:45:13,630
+هنا ال a h بده يسوى b h f and only f
+
+430
+00:45:16,890 --> 00:45:23,450
+ما هو رأيك لو ضربت الطرفين في a inverse يبقى عندي
+
+431
+00:45:23,450 --> 00:45:31,270
+a inverse في الاح بده يساوي ال a inverse في ال bh
+
+432
+00:45:32,250 --> 00:45:37,870
+من خاصية ال associative طبعا هذا if and only if ال
+
+433
+00:45:37,870 --> 00:45:47,310
+a inverse a في ال h بده ساوي a inverse b في ال h
+
+434
+00:45:47,310 --> 00:45:51,970
+الشكل اللي عندنا هناطيب هذا بيعطينا مين؟ ال
+
+435
+00:45:51,970 --> 00:45:56,630
+identity لما اضربه في H بدي يطلع مين؟ بدي يطلع ال
+
+436
+00:45:56,630 --> 00:46:03,970
+H itself يبقى if and only if if and only if ال H
+
+437
+00:46:03,970 --> 00:46:13,300
+هذه بدها تساوي A inverse B في ال H فلسنايبقى هنا
+
+438
+00:46:13,300 --> 00:46:20,880
+إيش بيقولي هذا يتساوى إذا كان لجيت ال A inverse B
+
+439
+00:46:20,880 --> 00:46:27,240
+في H بده يساوي ال H لو رجعت للخاصية الرقم اتنين
+
+440
+00:46:27,240 --> 00:46:36,280
+يبقى F and قولي F ال A inverse B هذا موجود وين؟
+
+441
+00:46:36,300 --> 00:46:43,560
+موجود في الـ H وهذا من ال property اتنين بالشكل
+
+442
+00:46:43,560 --> 00:46:53,810
+اللي عندنا هذاطيب ستة هه ستة بدك اتعرف function ما
+
+443
+00:46:53,810 --> 00:46:58,910
+بين الاتنين و الناس بينها one to one and unto يبقى
+
+444
+00:46:58,910 --> 00:47:09,010
+بداجي اقوله define a function phi من ال a h الى ال
+
+445
+00:47:09,010 --> 00:47:19,260
+b h byfive of a h بده يساوي بي اتش واثبتلي انها
+
+446
+00:47:19,260 --> 00:47:23,560
+one to one and unto اذا اثبتناها one to one and
+
+447
+00:47:23,560 --> 00:47:29,640
+unto يحصلوا التساوي بصير ال order للأولى بده يساوي
+
+448
+00:47:29,640 --> 00:47:35,800
+من ال order للثانية بنكمل المرة الجاية ان شاء الله
+
+449
+00:47:35,800 --> 00:47:36,300
+و تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d98682abfffdab6a05fd5e39e8b65a33aa864355
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4716, "start": 21.18, "end": 47.16, "text": "بسم الله الرحمن الرحيم انتهينا من شبتر ستة اللي هو ال isomorphism والآن بندخل لشبتر سبعة شبتر سبعة اللي هو Cossets and Lagrange theorem بتكلم عن نقطتين والنقطتين مرتبطتين مع بعض ارتباطا وثيقا كما سنرى Cosset بالعربي يعني الفئة المرافقة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 47395, 1829, 8315, 9154, 13412, 3555, 2655, 2288, 8608, 2655, 3660, 13672, 1829, 31439, 2423, 307, 32702, 1434, 16070, 148, 48506, 44945, 3215, 9778, 1211, 5296, 8592, 3555, 2655, 2288, 8608, 3555, 27884, 13412, 3555, 2655, 2288, 8608, 3555, 27884, 13672, 1829, 31439, 383, 772, 1385, 293, 24886, 14521, 20904, 39894, 4117, 19528, 18871, 8717, 47432, 2655, 9957, 16070, 1863, 47432, 2655, 9957, 3714, 43500, 3555, 9566, 2655, 9957, 20449, 45030, 11242, 1975, 43500, 3555, 41193, 995, 4032, 12984, 1829, 4587, 995, 9122, 15042, 8608, 1863, 2288, 7578, 383, 772, 302, 20666, 3615, 2288, 21292, 37495, 22653, 27188, 19986, 3660, 9673, 23557, 5172, 28671], "avg_logprob": -0.20706521039423736, "compression_ratio": 1.7844036697247707, "no_speech_prob": 0.0, "words": [{"start": 21.18, "end": 21.5, "word": "بسم", "probability": 0.646728515625}, {"start": 21.5, "end": 21.74, "word": " الله", "probability": 0.9462890625}, {"start": 21.74, "end": 22.16, "word": " الرحمن", "probability": 0.94775390625}, {"start": 22.16, "end": 22.66, "word": " الرحيم", "probability": 0.9938151041666666}, {"start": 22.66, "end": 24.72, "word": " انتهينا", "probability": 0.78131103515625}, {"start": 24.72, "end": 25.06, "word": " من", "probability": 0.9677734375}, {"start": 25.06, "end": 25.78, "word": " شبتر", "probability": 0.606201171875}, {"start": 25.78, "end": 26.64, "word": " ستة", "probability": 0.87890625}, {"start": 26.64, "end": 26.8, "word": " اللي", "probability": 0.6002197265625}, {"start": 26.8, "end": 26.92, "word": " هو", "probability": 0.951171875}, {"start": 26.92, "end": 27.04, "word": " ال", "probability": 0.45263671875}, {"start": 27.04, "end": 27.88, "word": " isomorphism", "probability": 0.80908203125}, {"start": 27.88, "end": 28.78, "word": " والآن", "probability": 0.5293782552083334}, {"start": 28.78, "end": 29.34, "word": " بندخل", "probability": 0.932861328125}, {"start": 29.34, "end": 30.16, "word": " لشبتر", "probability": 0.97490234375}, {"start": 30.16, "end": 30.72, "word": " سبعة", "probability": 0.95703125}, {"start": 30.72, "end": 31.78, "word": " شبتر", "probability": 0.885986328125}, {"start": 31.78, "end": 32.32, "word": " سبعة", "probability": 0.9625651041666666}, {"start": 32.32, "end": 32.86, "word": " اللي", "probability": 0.84716796875}, {"start": 32.86, "end": 33.0, "word": " هو", "probability": 0.91943359375}, {"start": 33.0, "end": 33.62, "word": " Cossets", "probability": 0.6032918294270834}, {"start": 33.62, "end": 34.02, "word": " and", "probability": 0.9052734375}, {"start": 34.02, "end": 34.58, "word": " Lagrange", "probability": 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"end": 77.17, "word": " G", "probability": 0.435546875}, {"start": 77.17, "end": 78.21, "word": " وروحت", "probability": 0.6005045572916666}, {"start": 78.21, "end": 78.75, "word": " أخد", "probability": 0.8268229166666666}, {"start": 78.75, "end": 79.17, "word": " أي", "probability": 0.6474609375}, {"start": 79.17, "end": 79.93, "word": " element", "probability": 0.78369140625}, {"start": 79.93, "end": 80.43, "word": " A", "probability": 0.88330078125}, {"start": 80.43, "end": 80.73, "word": " في", "probability": 0.986328125}, {"start": 80.73, "end": 81.31, "word": " G", "probability": 0.685546875}, {"start": 81.31, "end": 82.33, "word": " بضروح", "probability": 0.7467041015625}, {"start": 82.33, "end": 82.97, "word": " أعرف", "probability": 0.7939453125}, {"start": 82.97, "end": 83.41, "word": " ال", "probability": 0.87744140625}, {"start": 83.41, "end": 84.21, "word": " Coset", "probability": 0.6968994140625}, {"start": 84.21, "end": 84.55, "word": " اللي", "probability": 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96.99, "end": 97.61, "word": " elements", "probability": 0.8701171875}, {"start": 97.61, "end": 98.11, "word": " A", "probability": 0.78271484375}, {"start": 98.11, "end": 98.53, "word": " H", "probability": 0.970703125}, {"start": 98.53, "end": 99.25, "word": " such", "probability": 0.51806640625}, {"start": 99.25, "end": 99.85, "word": " that", "probability": 0.923828125}, {"start": 99.85, "end": 100.03, "word": " ال", "probability": 0.818359375}, {"start": 100.03, "end": 100.31, "word": " H", "probability": 0.64111328125}, {"start": 100.31, "end": 100.81, "word": " small", "probability": 0.74609375}, {"start": 100.81, "end": 101.43, "word": " موجودة", "probability": 0.9822998046875}, {"start": 101.43, "end": 101.65, "word": " في", "probability": 0.92529296875}, {"start": 101.65, "end": 102.07, "word": " H", "probability": 0.8525390625}, {"start": 102.07, "end": 102.61, "word": " capital", "probability": 0.4697265625}, {"start": 102.61, "end": 103.57, "word": " يعني", "probability": 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نبدي", "probability": 0.8359375}, {"start": 213.07, "end": 213.57, "word": " ذلك", "probability": 0.996337890625}, {"start": 213.57, "end": 214.73, "word": " عمليا", "probability": 0.88330078125}, {"start": 214.73, "end": 215.55, "word": " بمثال", "probability": 0.9818115234375}, {"start": 215.55, "end": 215.83, "word": " و", "probability": 0.98095703125}, {"start": 215.83, "end": 216.75, "word": " نتوقف", "probability": 0.9490966796875}, {"start": 216.75, "end": 216.99, "word": " مع", "probability": 0.99169921875}, {"start": 216.99, "end": 217.33, "word": " هذا", "probability": 0.9638671875}, {"start": 217.33, "end": 218.01, "word": " المثال", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 10, "seek": 23368, "start": 218.16, "end": 233.68, "text": "نوعا ما و ناقش بعض الشغلات ماعطيني G هي S3 وهي كتبناها بالكامل ليها ستة عناصر واخد ال H هي ال sub group ال E والواحد و تلاتة", "tokens": [1863, 45367, 995, 19446, 4032, 8717, 995, 4587, 8592, 45030, 11242, 25124, 17082, 1211, 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951.96, "end": 969.04, "text": "HVR180 تفتح الكتاب صفحة واحد و تلاتين واحد و تلاتين على ال table ال table بتاعة ال product ما بين اللي هو عناصر ال D4 مع بعضها البعض", "tokens": [39, 44358, 37078, 6055, 5172, 2655, 5016, 33251, 2655, 16758, 20328, 5172, 5016, 3660, 36764, 24401, 4032, 6055, 1211, 9307, 9957, 36764, 24401, 4032, 6055, 1211, 9307, 9957, 15844, 2423, 3199, 2423, 3199, 39894, 995, 27884, 2423, 1674, 19446, 49374, 13672, 1829, 31439, 18871, 33546, 2288, 2423, 413, 19, 20449, 45030, 11242, 11296, 29739, 3615, 11242], "avg_logprob": -0.19983553258996262, "compression_ratio": 1.452054794520548, "no_speech_prob": 0.0, "words": [{"start": 951.9599999999999, "end": 953.06, "word": "HVR180", "probability": 0.5956217447916666}, {"start": 953.06, "end": 954.16, "word": " تفتح", "probability": 0.8919677734375}, {"start": 954.16, "end": 954.7, "word": " الكتاب", "probability": 0.8116861979166666}, {"start": 954.7, "end": 955.34, "word": " صفحة", "probability": 0.90185546875}, {"start": 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"يبقى احنا بدنا H في R مية و تمانين يبقى عندنا H في R مية و تمانين وين راحت؟ H في R مية و تمانين اللي هي ب V يبقى هذا الكلام بد يساوي H و V", "tokens": [1829, 3555, 4587, 7578, 1975, 5016, 8315, 47525, 8315, 389, 8978, 497, 3714, 10632, 4032, 46811, 7649, 9957, 7251, 3555, 4587, 7578, 43242, 8315, 389, 8978, 497, 3714, 10632, 4032, 46811, 7649, 9957, 4032, 9957, 12602, 995, 33753, 22807, 389, 8978, 497, 3714, 10632, 4032, 46811, 7649, 9957, 13672, 1829, 39896, 4724, 691, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 7251, 3794, 995, 45865, 389, 4032, 691], "avg_logprob": -0.16439732078995023, "compression_ratio": 1.925, "no_speech_prob": 0.0, "words": [{"start": 969.47, "end": 970.03, "word": "يبقى", "probability": 0.8916015625}, {"start": 970.03, "end": 970.55, "word": " احنا", "probability": 0.9205729166666666}, {"start": 970.55, "end": 971.13, "word": " بدنا", "probability": 0.9287109375}, {"start": 971.13, "end": 971.47, "word": " H", "probability": 0.60791015625}, 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تمانين", "probability": 0.9874674479166666}, {"start": 976.91, "end": 977.97, "word": " وين", "probability": 0.2767333984375}, {"start": 977.97, "end": 978.41, "word": " راحت؟", "probability": 0.6981201171875}, {"start": 978.41, "end": 978.61, "word": " H", "probability": 0.85791015625}, {"start": 978.61, "end": 978.73, "word": " في", "probability": 0.97021484375}, {"start": 978.73, "end": 978.85, "word": " R", "probability": 0.97900390625}, {"start": 978.85, "end": 979.05, "word": " مية", "probability": 0.96435546875}, {"start": 979.05, "end": 979.11, "word": " و", "probability": 0.98876953125}, {"start": 979.11, "end": 979.57, "word": " تمانين", "probability": 0.990234375}, {"start": 979.57, "end": 979.75, "word": " اللي", "probability": 0.88916015625}, {"start": 979.75, "end": 979.93, "word": " هي", "probability": 0.69482421875}, {"start": 979.93, "end": 980.09, "word": " ب", "probability": 0.75}, {"start": 980.09, "end": 980.41, "word": " V", "probability": 0.88818359375}, 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بده", "probability": 0.884033203125}, {"start": 1024.93, "end": 1025.61, "word": " يساوي", "probability": 0.9237060546875}, {"start": 1025.61, "end": 1025.91, "word": " ال", "probability": 0.876953125}, {"start": 1025.91, "end": 1027.01, "word": " VK", "probability": 0.931884765625}], "temperature": 1.0}, {"id": 48, "seek": 105635, "start": 1027.74, "end": 1056.36, "text": "بنفس الطريقة اعملها similarly بدي يكون ال D K هتلاقي هو ال D' K كذلك تمام؟ بناء عليه بقدر اقوله the left corsets of the left corsets of", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 1975, 25957, 1211, 11296, 14138, 4724, 16254, 7251, 30544, 2423, 413, 591, 8032, 2655, 15040, 38436, 31439, 2423, 413, 6, 591, 9122, 8848, 23275, 46811, 10943, 22807, 44945, 16606, 47356, 4724, 28543, 2288, 1975, 39648, 3224, 264, 1411, 46511, 1385, 295, 264, 1411, 46511, 1385, 295], "avg_logprob": -0.2697523494936385, "compression_ratio": 1.3221476510067114, "no_speech_prob": 0.0, "words": [{"start": 1027.74, "end": 1028.4, 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"word": " D'", "probability": 0.984375}, {"start": 1038.5, "end": 1039.08, "word": " K", "probability": 0.9091796875}, {"start": 1039.08, "end": 1040.08, "word": " كذلك", "probability": 0.9656575520833334}, {"start": 1040.08, "end": 1041.42, "word": " تمام؟", "probability": 0.7840169270833334}, {"start": 1041.42, "end": 1041.84, "word": " بناء", "probability": 0.9345703125}, {"start": 1041.84, "end": 1042.36, "word": " عليه", "probability": 0.8994140625}, {"start": 1042.36, "end": 1042.86, "word": " بقدر", "probability": 0.9845377604166666}, {"start": 1042.86, "end": 1043.9, "word": " اقوله", "probability": 0.7450358072916666}, {"start": 1043.9, "end": 1044.4, "word": " the", "probability": 0.583984375}, {"start": 1044.4, "end": 1046.32, "word": " left", "probability": 0.9111328125}, {"start": 1046.32, "end": 1048.02, "word": " corsets", "probability": 0.5384521484375}, {"start": 1048.02, "end": 1049.78, "word": " of", "probability": 0.9853515625}, {"start": 1049.78, "end": 1051.3, 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{"start": 1069.76, "end": 1070.04, "word": " K", "probability": 0.625}, {"start": 1070.04, "end": 1071.06, "word": " itself", "probability": 0.7265625}, {"start": 1071.06, "end": 1072.74, "word": " والتانية", "probability": 0.921630859375}, {"start": 1072.74, "end": 1073.4, "word": " اللي", "probability": 0.830322265625}, {"start": 1073.4, "end": 1073.6, "word": " هو", "probability": 0.97900390625}, {"start": 1073.6, "end": 1073.8, "word": " ال", "probability": 0.791015625}, {"start": 1073.8, "end": 1074.28, "word": " R", "probability": 0.66357421875}, {"start": 1074.28, "end": 1075.64, "word": " تسعين", "probability": 0.9771728515625}, {"start": 1075.64, "end": 1076.2, "word": " في", "probability": 0.96435546875}, {"start": 1076.2, "end": 1076.76, "word": " K", "probability": 0.939453125}, {"start": 1076.76, "end": 1078.46, "word": " والتالتة", "probability": 0.90361328125}, {"start": 1078.46, "end": 1080.1, "word": " لHK", "probability": 0.558349609375}, {"start": 1080.1, "end": 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"avg_logprob": -0.21750452898550723, "compression_ratio": 1.4742857142857142, "no_speech_prob": 0.0, "words": [{"start": 1084.4, "end": 1085.04, "word": "يبقى", "probability": 0.83282470703125}, {"start": 1085.04, "end": 1085.3, "word": " هذا", "probability": 0.81494140625}, {"start": 1085.3, "end": 1085.6, "word": " left", "probability": 0.52978515625}, {"start": 1085.6, "end": 1086.24, "word": " cursive", "probability": 0.41253662109375}, {"start": 1086.24, "end": 1086.98, "word": " فقط", "probability": 0.960205078125}, {"start": 1086.98, "end": 1087.48, "word": " لا", "probability": 0.57568359375}, {"start": 1087.48, "end": 1087.94, "word": " غير", "probability": 0.97265625}, {"start": 1087.94, "end": 1088.98, "word": " اطلع", "probability": 0.6654052734375}, {"start": 1088.98, "end": 1089.14, "word": " على", "probability": 0.88818359375}, {"start": 1089.14, "end": 1090.04, "word": " الملاحظات", "probability": 0.9814453125}, {"start": 1090.04, "end": 1090.24, "word": " اللي", 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"word": " هذا", "probability": 0.7841796875}, {"start": 1098.84, "end": 1099.08, "word": " مش", "probability": 0.8876953125}, {"start": 1099.08, "end": 1099.34, "word": " هو", "probability": 0.9443359375}, {"start": 1099.34, "end": 1099.46, "word": " ال", "probability": 0.8759765625}, {"start": 1099.46, "end": 1099.68, "word": " element", "probability": 0.95263671875}, {"start": 1099.68, "end": 1099.86, "word": " ال", "probability": 0.92138671875}, {"start": 1099.86, "end": 1100.1, "word": " H", "probability": 0.400390625}, {"start": 1100.1, "end": 1100.82, "word": " بيختلف", "probability": 0.9210205078125}, {"start": 1100.82, "end": 1101.1, "word": " عن", "probability": 0.9697265625}, {"start": 1101.1, "end": 1101.4, "word": " V", "probability": 0.8828125}], "temperature": 1.0}, {"id": 51, "seek": 113017, "start": 1101.77, "end": 1130.17, "text": "هنا برضه ال D كي بده يسوي D' رغم ان ال D تختلف عاميا عن D' و هكذا يعني ال two left cosets are equal رغم ان ال element اللي مضروب فيه اتش 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0.96923828125}, {"start": 1372.64, "end": 1373.26, "word": " النقطة", "probability": 0.9796549479166666}, {"start": 1373.26, "end": 1373.92, "word": " الأولى", "probability": 0.9866536458333334}, {"start": 1373.92, "end": 1374.54, "word": " اللي", "probability": 0.817138671875}, {"start": 1374.54, "end": 1375.44, "word": " أخدناها", "probability": 0.96171875}, {"start": 1375.44, "end": 1375.94, "word": " من", "probability": 0.96630859375}, {"start": 1375.94, "end": 1376.82, "word": " D4", "probability": 0.904541015625}, {"start": 1376.82, "end": 1377.42, "word": " أن", "probability": 0.43701171875}, {"start": 1377.42, "end": 1378.84, "word": " الـR180", "probability": 0.6102294921875}, {"start": 1378.84, "end": 1379.82, "word": " كانت", "probability": 0.97509765625}, {"start": 1379.82, "end": 1379.94, "word": " في", "probability": 0.9765625}, {"start": 1379.94, "end": 1380.16, "word": " ال", "probability": 0.95166015625}, {"start": 1380.16, "end": 1380.6, "word": " center", 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"end": 1391.6, "word": " تلاتة", "probability": 0.9298095703125}, {"start": 1391.6, "end": 1392.76, "word": " example", "probability": 0.61181640625}, {"start": 1392.76, "end": 1395.66, "word": " تلاتة", "probability": 0.923828125}, {"start": 1395.66, "end": 1397.12, "word": " بيقول", "probability": 0.9601236979166666}, {"start": 1397.12, "end": 1397.96, "word": " خدلي", "probability": 0.8914388020833334}, {"start": 1397.96, "end": 1398.9, "word": " G", "probability": 0.361572265625}, {"start": 1398.9, "end": 1399.7, "word": " هو", "probability": 0.46533203125}, {"start": 1399.7, "end": 1400.08, "word": " هي", "probability": 0.81494140625}, {"start": 1400.08, "end": 1400.7, "word": " Z", "probability": 0.37060546875}, {"start": 1400.7, "end": 1401.54, "word": " تسعة", "probability": 0.9599609375}, {"start": 1401.54, "end": 1402.86, "word": " تمام", "probability": 0.88818359375}, {"start": 1402.86, "end": 1403.82, "word": " and", "probability": 0.87060546875}, {"start": 1403.82, "end": 1405.06, "word": " ال", "probability": 0.92724609375}, {"start": 1405.06, "end": 1405.74, "word": " H", "probability": 0.94384765625}, {"start": 1405.74, "end": 1406.66, "word": " هي", "probability": 0.953125}, {"start": 1406.66, "end": 1406.92, "word": " ال", "probability": 0.7958984375}, {"start": 1406.92, "end": 1407.18, "word": " sub", "probability": 0.79296875}, {"start": 1407.18, "end": 1407.68, "word": " group", "probability": 0.62353515625}, {"start": 1407.68, "end": 1408.5, "word": " generated", "probability": 0.8349609375}, {"start": 1408.5, "end": 1408.96, "word": " by", "probability": 0.97998046875}, {"start": 1408.96, "end": 1409.82, "word": " تلاتة", "probability": 0.980712890625}], "temperature": 1.0}, {"id": 64, "seek": 142407, "start": 1410.33, "end": 1424.07, "text": "هات لل left cosets find the left cosets of H and the تسعة", "tokens": [3224, 9307, 24976, 1411, 3792, 1385, 915, 264, 1411, 3792, 1385, 295, 389, 293, 264, 6055, 3794, 27884], "avg_logprob": 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1428.62, "word": " بالا", "probability": 0.4840087890625}, {"start": 1428.62, "end": 1428.84, "word": " كدا", "probability": 0.5650634765625}, {"start": 1428.84, "end": 1430.42, "word": " بدنا", "probability": 0.5654296875}, {"start": 1430.42, "end": 1431.06, "word": " نجيب", "probability": 0.81268310546875}, {"start": 1431.06, "end": 1431.5, "word": " اللفت", "probability": 0.5125325520833334}, {"start": 1431.5, "end": 1431.8, "word": " كو", "probability": 0.7763671875}, {"start": 1431.8, "end": 1432.14, "word": " ستس", "probability": 0.7823893229166666}, {"start": 1432.14, "end": 1432.34, "word": " اللى", "probability": 0.83203125}, {"start": 1432.34, "end": 1432.88, "word": " عندنا", "probability": 0.934814453125}, {"start": 1432.88, "end": 1434.04, "word": " طبعا", "probability": 0.901611328125}, {"start": 1434.04, "end": 1435.04, "word": " جي", "probability": 0.678955078125}, {"start": 1435.04, "end": 1436.1, "word": " معروفة", "probability": 0.971435546875}, {"start": 1436.1, "end": 1436.92, "word": " زد", "probability": 0.530029296875}, {"start": 1436.92, "end": 1437.52, "word": " تسعة", "probability": 0.8580729166666666}, {"start": 1437.52, "end": 1438.22, "word": " هي", "probability": 0.78271484375}, {"start": 1438.22, "end": 1438.7, "word": " عبارة", "probability": 0.9898681640625}, {"start": 1438.7, "end": 1438.98, "word": " عن", "probability": 0.96875}, {"start": 1438.98, "end": 1439.3, "word": " زير", "probability": 0.584716796875}, {"start": 1439.3, "end": 1439.46, "word": " و", "probability": 0.658203125}, {"start": 1439.46, "end": 1439.94, "word": " واحد", "probability": 0.87548828125}, {"start": 1439.94, "end": 1440.18, "word": " و", "probability": 0.94873046875}, {"start": 1440.18, "end": 1440.56, "word": " اتنين", "probability": 0.882568359375}, {"start": 1440.56, "end": 1441.08, "word": " لغاية", "probability": 0.98046875}, {"start": 1441.08, "end": 1441.78, "word": " تمانين", "probability": 0.7652180989583334}], "temperature": 1.0}, {"id": 66, "seek": 146130, "start": 1442.3, "end": 1461.3, "text": "تمام الان ال H ال sub group generated by تلاتة هي زيرو تلاتة و ستة و تسعة اللي هي زيرو و هكذا بدنا نروح نجيب ال left cosets ال operation على Z تسعة جامع ولا ضاربة جامع ممدر جدا", "tokens": [2655, 15042, 2304, 2423, 7649, 2423, 389, 2423, 1422, 1594, 10833, 538, 6055, 1211, 9307, 3660, 39896, 30767, 13546, 2407, 6055, 1211, 9307, 3660, 4032, 8608, 2655, 3660, 4032, 6055, 3794, 27884, 13672, 1829, 39896, 30767, 13546, 2407, 4032, 8032, 4117, 15730, 47525, 8315, 8717, 32887, 5016, 8717, 7435, 1829, 3555, 2423, 1411, 3792, 1385, 2423, 6916, 15844, 1176, 6055, 3794, 27884, 10874, 10943, 3615, 49429, 48812, 9640, 49401, 10874, 10943, 3615, 3714, 2304, 3215, 2288, 10874, 28259], "avg_logprob": -0.33900317285634296, "compression_ratio": 1.583815028901734, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1442.3, "end": 1442.9, "word": "تمام", "probability": 0.441162109375}, {"start": 1442.9, "end": 1444.14, "word": " الان", "probability": 0.6092529296875}, {"start": 1444.14, "end": 1444.64, "word": " ال", "probability": 0.74658203125}, {"start": 1444.64, "end": 1445.0, "word": " H", "probability": 0.26171875}, {"start": 1445.0, "end": 1445.3, "word": " ال", "probability": 0.458984375}, {"start": 1445.3, "end": 1445.52, "word": " sub", "probability": 0.5712890625}, {"start": 1445.52, "end": 1445.9, "word": " group", "probability": 0.6328125}, {"start": 1445.9, "end": 1446.54, "word": " generated", "probability": 0.5830078125}, {"start": 1446.54, "end": 1447.0, "word": " by", "probability": 0.9033203125}, {"start": 1447.0, "end": 1447.72, "word": " تلاتة", "probability": 0.79534912109375}, {"start": 1447.72, "end": 1447.98, "word": " هي", "probability": 0.76318359375}, {"start": 1447.98, "end": 1448.7, "word": " زيرو", "probability": 0.5564778645833334}, {"start": 1448.7, "end": 1449.42, "word": " تلاتة", "probability": 0.94482421875}, {"start": 1449.42, "end": 1449.58, "word": " و", "probability": 0.9013671875}, {"start": 1449.58, "end": 1450.28, "word": " ستة", "probability": 0.8427734375}, {"start": 1450.28, "end": 1450.84, "word": " و", "probability": 0.256103515625}, {"start": 1450.84, "end": 1451.34, "word": " تسعة", "probability": 0.9759114583333334}, {"start": 1451.34, "end": 1451.56, "word": " اللي", "probability": 0.7034912109375}, {"start": 1451.56, "end": 1451.84, "word": " هي", "probability": 0.857421875}, {"start": 1451.84, "end": 1452.44, "word": " زيرو", "probability": 0.8522135416666666}, {"start": 1452.44, "end": 1452.62, "word": " و", "probability": 0.66748046875}, {"start": 1452.62, "end": 1453.4, "word": " هكذا", "probability": 0.9070638020833334}, {"start": 1453.4, "end": 1454.2, "word": " بدنا", "probability": 0.85546875}, {"start": 1454.2, "end": 1454.48, "word": " نروح", "probability": 0.9801432291666666}, {"start": 1454.48, "end": 1454.86, "word": " نجيب", "probability": 0.976318359375}, {"start": 1454.86, "end": 1455.02, "word": " ال", "probability": 0.78466796875}, {"start": 1455.02, "end": 1455.26, "word": " left", "probability": 0.449951171875}, {"start": 1455.26, "end": 1455.98, "word": " cosets", "probability": 0.537109375}, {"start": 1455.98, "end": 1456.48, "word": " ال", "probability": 0.91845703125}, {"start": 1456.48, "end": 1456.98, "word": " operation", "probability": 0.9365234375}, {"start": 1456.98, "end": 1457.36, "word": " على", "probability": 0.77685546875}, {"start": 1457.36, "end": 1457.68, "word": " Z", "probability": 0.52490234375}, {"start": 1457.68, "end": 1458.26, "word": " تسعة", "probability": 0.9552408854166666}, {"start": 1458.26, "end": 1458.64, "word": " جامع", "probability": 0.8839518229166666}, {"start": 1458.64, "end": 1458.86, "word": " ولا", "probability": 0.93212890625}, {"start": 1458.86, "end": 1459.42, "word": " ضاربة", "probability": 0.6692708333333334}, {"start": 1459.42, "end": 1460.32, "word": " جامع", "probability": 0.7245279947916666}, {"start": 1460.32, "end": 1460.92, "word": " ممدر", 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نفسه و ال واحد زاد H و اتنين زاد H فقط لا غير لا يوجد غيرها طيب الان اللاحظ هدى و هدى و هدى و هدى كلهم دول are equal ليش؟", "tokens": [6027, 20292, 31439, 3714, 9957, 2423, 389, 8717, 36178, 3224, 17182, 30767, 18513, 389, 2423, 389, 8717, 36178, 3224, 4032, 2423, 36764, 24401, 30767, 18513, 389, 4032, 1975, 2655, 1863, 9957, 30767, 18513, 389, 6156, 47432, 20193, 32771, 13546, 20193, 7251, 29245, 3215, 32771, 13546, 11296, 23032, 1829, 3555, 2423, 7649, 13672, 39319, 19913, 8032, 3215, 7578, 4032, 8032, 3215, 7578, 4032, 8032, 3215, 7578, 4032, 8032, 3215, 7578, 28242, 16095, 11778, 12610, 366, 2681, 32239, 8592, 22807], "avg_logprob": -0.29410600662231445, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1621.48, "end": 1621.86, "word": "اللي", "probability": 0.5452880859375}, {"start": 1621.86, "end": 1622.04, "word": " هو", "probability": 0.7265625}, {"start": 1622.04, "end": 1622.3, "word": " مين", "probability": 0.68701171875}, {"start": 1622.3, 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هو الـ A inverse موجود في H طيب بدا أجي أقوله خدلي X موجود في H أنا بدي أثبت إن H subset من مين؟ من الـ H يبقى خت element موجود في وين؟ في الـ H then", "tokens": [6027, 20292, 31439, 2423, 39184, 316, 17340, 3714, 29245, 23328, 8978, 389, 23032, 1829, 3555, 4724, 28259, 5551, 7435, 1829, 5551, 39648, 3224, 16490, 3215, 20292, 1783, 3714, 29245, 23328, 8978, 389, 41850, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 389, 25993, 9154, 3714, 9957, 22807, 9154, 2423, 39184, 389, 7251, 3555, 4587, 7578, 16490, 2655, 4478, 3714, 29245, 23328, 8978, 4032, 9957, 22807, 8978, 2423, 39184, 389, 550], "avg_logprob": -0.3473214192049844, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 2311.81, "end": 2312.23, "word": "اللي", "probability": 0.2396240234375}, {"start": 2312.23, "end": 2312.61, "word": " هو", "probability": 0.955078125}, {"start": 2312.61, "end": 2313.11, "word": " الـ", "probability": 0.6160888671875}, {"start": 2313.11, "end": 2313.39, "word": " 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"probability": 0.9920247395833334}, {"start": 2351.48, "end": 2352.34, "word": " إن", "probability": 0.4853515625}, {"start": 2352.34, "end": 2352.72, "word": " ال", "probability": 0.89404296875}, {"start": 2352.72, "end": 2353.3, "word": " A", "probability": 0.90478515625}, {"start": 2353.3, "end": 2354.86, "word": " inverse", "probability": 0.80712890625}, {"start": 2354.86, "end": 2355.7, "word": " X", "probability": 0.98193359375}, {"start": 2355.7, "end": 2356.62, "word": " بده", "probability": 0.7099609375}, {"start": 2356.62, "end": 2357.3, "word": " يساوي", "probability": 0.9434814453125}, {"start": 2357.3, "end": 2358.0, "word": " H", "probability": 0.97119140625}, {"start": 2358.0, "end": 2359.24, "word": " for", "probability": 0.9072265625}, {"start": 2359.24, "end": 2360.5, "word": " some", "probability": 0.87158203125}], "temperature": 1.0}, {"id": 107, "seek": 238996, "start": 2362.03, "end": 2389.97, "text": "for some h اللي موجودة في h مادام هذا في h اذا هيساوي ال h طيب هذا معناه انا بدي ال x يبقى هذا معناه ان ال x تساوي لو ضربت الطرفين في العنصر a يبقى بضل على شمال x وهنا بجينا mean a h هذه h وين موجودة؟", "tokens": [2994, 512, 276, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 276, 3714, 18513, 10943, 23758, 8978, 276, 1975, 15730, 39896, 3794, 995, 45865, 2423, 276, 23032, 1829, 3555, 23758, 20449, 8315, 3224, 1975, 8315, 4724, 16254, 2423, 2031, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 2423, 2031, 6055, 3794, 995, 45865, 45164, 48812, 25513, 2655, 41950, 28480, 9957, 8978, 18863, 1863, 9381, 2288, 257, 7251, 3555, 4587, 7578, 4724, 11242, 1211, 15844, 13412, 2304, 6027, 2031, 37037, 8315, 4724, 7435, 1829, 8315, 914, 257, 276, 29538, 276, 4032, 9957, 3714, 29245, 23328, 3660, 22807], "avg_logprob": -0.23453608739007378, "compression_ratio": 1.8032786885245902, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2362.03, "end": 2362.57, "word": "for", "probability": 0.42626953125}, {"start": 2362.57, "end": 2363.79, "word": 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2390.12, "end": 2413.84, "text": "موجودة في اله يبقى انا فرض x في h لجيت ال x موجود وان في اله يبقى هذا معناه ان اله هذه ال subset من اله اطلع لي سميلي هذه star وسميلي هذه double star من التنتين مع بعض from", "tokens": [2304, 29245, 23328, 3660, 8978, 2423, 3224, 7251, 3555, 4587, 7578, 1975, 8315, 6156, 43042, 2031, 8978, 276, 5296, 7435, 36081, 2423, 2031, 3714, 29245, 23328, 4032, 7649, 8978, 2423, 3224, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 2423, 3224, 29538, 2423, 25993, 9154, 2423, 3224, 1975, 9566, 1211, 3615, 32239, 8608, 2304, 1829, 20292, 29538, 3543, 4032, 38251, 1829, 20292, 29538, 3834, 3543, 9154, 16712, 29399, 9957, 20449, 45030, 11242, 490], "avg_logprob": -0.23666667262713115, "compression_ratio": 1.7267080745341614, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2390.12, "end": 2391.08, "word": "موجودة", "probability": 0.786224365234375}, {"start": 2391.08, "end": 2391.32, "word": " في", "probability": 0.92822265625}, {"start": 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اقوله", "probability": 0.77587890625}, {"start": 2490.73, "end": 2491.25, "word": " هنا", "probability": 0.9853515625}, {"start": 2491.25, "end": 2491.91, "word": " و", "probability": 0.67529296875}, {"start": 2491.91, "end": 2492.61, "word": " الرقاهي", "probability": 0.6419677734375}, {"start": 2492.61, "end": 2493.01, "word": " رقم", "probability": 0.9884440104166666}, {"start": 2493.01, "end": 2494.13, "word": " تلاتة", "probability": 0.9405517578125}, {"start": 2494.13, "end": 2496.13, "word": " conversely", "probability": 0.899658203125}], "temperature": 1.0}, {"id": 113, "seek": 251921, "start": 2499.49, "end": 2519.21, "text": "conversely ا assume افترض ان ال a موجودة في ال bh بده احاول اثبت ان ال aH بده سوى مين بيه ال aH موجودة في بي كابتل H تمام", "tokens": [1671, 840, 736, 1975, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 257, 3714, 29245, 23328, 3660, 8978, 2423, 41221, 47525, 3224, 1975, 5016, 995, 12610, 1975, 12984, 3555, 2655, 16472, 2423, 257, 39, 47525, 3224, 8608, 2407, 7578, 3714, 9957, 4724, 1829, 3224, 2423, 257, 39, 3714, 29245, 23328, 3660, 8978, 4724, 1829, 9122, 16758, 2655, 1211, 389, 46811, 10943], "avg_logprob": -0.28329916664811433, "compression_ratio": 1.450381679389313, "no_speech_prob": 0.0, "words": [{"start": 2499.49, "end": 2500.45, "word": "conversely", "probability": 0.6375325520833334}, {"start": 2500.45, "end": 2501.41, "word": " ا", "probability": 0.3642578125}, {"start": 2501.41, "end": 2502.23, "word": " assume", "probability": 0.6142578125}, {"start": 2502.23, "end": 2503.77, "word": " افترض", "probability": 0.9376220703125}, {"start": 2503.77, "end": 2504.75, "word": " ان", "probability": 0.9169921875}, {"start": 2504.75, "end": 2505.13, "word": " ال", "probability": 0.9228515625}, {"start": 2505.13, "end": 2505.53, "word": " a", "probability": 0.59375}, {"start": 2505.53, "end": 2507.29, "word": " موجودة", "probability": 0.9735107421875}, {"start": 2507.29, "end": 2507.77, "word": " في", "probability": 0.87255859375}, {"start": 2507.77, "end": 2508.11, "word": " ال", "probability": 0.92431640625}, {"start": 2508.11, "end": 2508.91, "word": " bh", "probability": 0.5849609375}, {"start": 2508.91, "end": 2509.81, "word": " بده", "probability": 0.4471435546875}, {"start": 2509.81, "end": 2510.13, "word": " احاول", "probability": 0.939208984375}, {"start": 2510.13, "end": 2510.57, "word": " اثبت", "probability": 0.9705810546875}, {"start": 2510.57, "end": 2510.73, "word": " ان", "probability": 0.93408203125}, {"start": 2510.73, "end": 2510.93, "word": " ال", "probability": 0.97900390625}, {"start": 2510.93, "end": 2511.41, "word": " aH", "probability": 0.5760498046875}, {"start": 2511.41, "end": 2511.73, "word": " بده", "probability": 0.75244140625}, {"start": 2511.73, "end": 2512.05, "word": " سوى", "probability": 0.7099609375}, {"start": 2512.05, "end": 2512.49, "word": " مين", "probability": 0.6695556640625}, {"start": 2512.49, "end": 2513.69, "word": " بيه", "probability": 0.54736328125}, {"start": 2513.69, "end": 2514.87, "word": " ال", "probability": 0.88720703125}, {"start": 2514.87, "end": 2515.43, "word": " aH", "probability": 0.824462890625}, {"start": 2515.43, "end": 2516.21, "word": " موجودة", "probability": 0.9833984375}, {"start": 2516.21, "end": 2516.51, "word": " في", "probability": 0.89208984375}, {"start": 2516.51, "end": 2516.93, "word": " بي", "probability": 0.652587890625}, {"start": 2516.93, "end": 2517.79, "word": " كابتل", "probability": 0.8819580078125}, {"start": 2517.79, "end": 2518.27, "word": " H", "probability": 0.72216796875}, {"start": 2518.27, "end": 2519.21, "word": " تمام", "probability": 0.93115234375}], "temperature": 1.0}, {"id": 114, "seek": 253785, "start": 2520.67, "end": 2537.85, "text": "طيب assume كذا then ال a هذه بدها تساوي bh for some h اللي belongs to man لل h طب لو ضربت الطرفين في h", "tokens": [9566, 1829, 3555, 6552, 9122, 15730, 550, 2423, 257, 29538, 47525, 11296, 6055, 3794, 995, 45865, 41221, 337, 512, 276, 13672, 1829, 12953, 281, 587, 24976, 276, 23032, 3555, 45164, 48812, 25513, 2655, 41950, 28480, 9957, 8978, 276], "avg_logprob": -0.2700320375271333, "compression_ratio": 1.1885245901639345, "no_speech_prob": 0.0, "words": [{"start": 2520.67, "end": 2521.23, "word": "طيب", "probability": 0.7372233072916666}, {"start": 2521.23, "end": 2522.49, "word": " assume", "probability": 0.228515625}, {"start": 2522.49, "end": 2522.91, "word": " كذا", "probability": 0.909423828125}, {"start": 2522.91, "end": 2523.55, "word": " then", "probability": 0.7568359375}, {"start": 2523.55, "end": 2524.79, "word": " ال", "probability": 0.921875}, {"start": 2524.79, "end": 2525.21, "word": " a", "probability": 0.63671875}, {"start": 2525.21, "end": 2525.83, "word": " هذه", "probability": 0.60693359375}, {"start": 2525.83, "end": 2526.69, "word": " بدها", "probability": 0.835693359375}, {"start": 2526.69, "end": 2527.29, "word": " تساوي", "probability": 0.813232421875}, {"start": 2527.29, "end": 2528.15, "word": " bh", "probability": 0.353515625}, {"start": 2528.15, "end": 2529.27, "word": " for", "probability": 0.9326171875}, {"start": 2529.27, "end": 2530.59, "word": " some", "probability": 0.880859375}, {"start": 2530.59, "end": 2531.71, "word": " h", "probability": 0.82470703125}, {"start": 2531.71, "end": 2532.15, "word": " اللي", "probability": 0.926513671875}, {"start": 2532.15, "end": 2532.71, "word": " belongs", "probability": 0.66162109375}, {"start": 2532.71, "end": 2533.07, "word": " to", "probability": 0.9658203125}, {"start": 2533.07, "end": 2533.49, "word": " man", "probability": 0.40185546875}, {"start": 2533.49, "end": 2534.23, "word": " لل", "probability": 0.8154296875}, {"start": 2534.23, "end": 2534.75, "word": " h", "probability": 0.346923828125}, {"start": 2534.75, "end": 2535.81, "word": " طب", "probability": 0.797607421875}, {"start": 2535.81, "end": 2535.99, "word": " لو", "probability": 0.99365234375}, {"start": 2535.99, "end": 2536.45, "word": " ضربت", "probability": 0.99365234375}, {"start": 2536.45, "end": 2537.07, "word": " الطرفين", "probability": 0.94921875}, {"start": 2537.07, "end": 2537.35, "word": " في", "probability": 0.95263671875}, {"start": 2537.35, "end": 2537.85, "word": " h", "probability": 0.830078125}], "temperature": 1.0}, {"id": 115, "seek": 255801, "start": 2538.91, "end": 2558.01, "text": "يبقى باجي بقوله هذا معناه ان ال a capital H بده يساوي bh capital H هذا معناه ان ال aH بده يساوي bh في H من خاصية ال associativity", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 23758, 20449, 8315, 3224, 16472, 2423, 257, 4238, 389, 47525, 3224, 7251, 3794, 995, 45865, 41221, 4238, 389, 23758, 20449, 8315, 3224, 16472, 2423, 257, 39, 47525, 3224, 7251, 3794, 995, 45865, 41221, 8978, 389, 9154, 16490, 33546, 10632, 2423, 4180, 30142], "avg_logprob": -0.21933962601535725, "compression_ratio": 1.5691056910569106, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2538.91, "end": 2539.45, "word": "يبقى", "probability": 0.8614501953125}, {"start": 2539.45, "end": 2539.87, "word": " باجي", "probability": 0.6648763020833334}, {"start": 2539.87, "end": 2540.63, "word": " بقوله", "probability": 0.8297526041666666}, {"start": 2540.63, "end": 2541.25, "word": " هذا", "probability": 0.88623046875}, {"start": 2541.25, "end": 2542.09, "word": " معناه", "probability": 0.98681640625}, {"start": 2542.09, "end": 2542.55, "word": " ان", "probability": 0.6708984375}, {"start": 2542.55, "end": 2542.89, "word": " ال", "probability": 0.91845703125}, {"start": 2542.89, "end": 2543.23, "word": " a", "probability": 0.396728515625}, {"start": 2543.23, "end": 2543.87, "word": " capital", "probability": 0.552734375}, {"start": 2543.87, "end": 2544.57, "word": " H", "probability": 0.64306640625}, {"start": 2544.57, "end": 2545.43, "word": " بده", "probability": 0.40618896484375}, {"start": 2545.43, "end": 2546.05, "word": " يساوي", "probability": 0.8321533203125}, {"start": 2546.05, "end": 2546.99, "word": " bh", "probability": 0.52099609375}, {"start": 2546.99, "end": 2548.09, "word": " capital", "probability": 0.830078125}, {"start": 2548.09, "end": 2548.67, "word": " H", "probability": 0.97021484375}, {"start": 2548.67, "end": 2549.79, "word": " هذا", "probability": 0.76611328125}, {"start": 2549.79, "end": 2550.67, "word": " معناه", "probability": 0.9563802083333334}, {"start": 2550.67, "end": 2551.13, "word": " ان", "probability": 0.84326171875}, {"start": 2551.13, "end": 2551.47, "word": " ال", "probability": 0.98095703125}, {"start": 2551.47, "end": 2552.35, "word": " aH", "probability": 0.6451416015625}, {"start": 2552.35, "end": 2552.89, "word": " بده", "probability": 0.92529296875}, {"start": 2552.89, "end": 2553.41, "word": " يساوي", "probability": 0.98681640625}, {"start": 2553.41, "end": 2554.33, "word": " bh", "probability": 0.9091796875}, {"start": 2554.33, "end": 2555.09, "word": " في", "probability": 0.857421875}, {"start": 2555.09, "end": 2555.61, "word": " H", "probability": 0.9013671875}, {"start": 2555.61, "end": 2556.33, "word": " من", "probability": 0.9453125}, {"start": 2556.33, "end": 2556.91, "word": " خاصية", "probability": 0.9930013020833334}, {"start": 2556.91, "end": 2557.13, "word": " ال", "probability": 0.95947265625}, {"start": 2557.13, "end": 2558.01, "word": " associativity", "probability": 0.832763671875}], "temperature": 1.0}, {"id": 116, "seek": 257969, "start": 2559.14, "end": 2579.7, "text": "هذا معناه ان الـ a h بده يساوي بي ال element h لما يكون في h و تضربه في h بتظهر زي مهي h كابتن يبقى هدف بيه اتش عزيزي و هو المطلوب خلصنا الاتجاهين طيب الان بدنا نجي لنقطة رابع", "tokens": [3224, 15730, 20449, 8315, 3224, 16472, 2423, 39184, 257, 276, 47525, 3224, 7251, 3794, 995, 45865, 4724, 1829, 2423, 4478, 276, 5296, 15042, 7251, 30544, 8978, 276, 4032, 6055, 11242, 25513, 3224, 8978, 276, 39894, 19913, 3224, 2288, 30767, 1829, 3714, 3224, 1829, 276, 9122, 16758, 2655, 1863, 7251, 3555, 4587, 7578, 8032, 3215, 5172, 4724, 1829, 3224, 1975, 2655, 8592, 6225, 11622, 1829, 11622, 1829, 4032, 31439, 9673, 9566, 1211, 37746, 16490, 1211, 9381, 8315, 2423, 9307, 7435, 40294, 9957, 23032, 1829, 3555, 2423, 7649, 47525, 8315, 8717, 7435, 1829, 5296, 1863, 47432, 3660, 12602, 16758, 3615], "avg_logprob": -0.3563762770758735, "compression_ratio": 1.6141304347826086, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2559.14, "end": 2560.06, "word": "هذا", "probability": 0.5638427734375}, {"start": 2560.06, "end": 2560.82, "word": " معناه", "probability": 0.8042805989583334}, {"start": 2560.82, "end": 2561.26, "word": " ان", "probability": 0.6845703125}, {"start": 2561.26, "end": 2561.64, "word": " الـ", "probability": 0.50885009765625}, {"start": 2561.64, "end": 2561.86, "word": " a", "probability": 0.284423828125}, {"start": 2561.86, "end": 2562.32, "word": " h", "probability": 0.30615234375}, {"start": 2562.32, "end": 2562.78, "word": " بده", "probability": 0.397430419921875}, {"start": 2562.78, "end": 2563.54, "word": " يساوي", "probability": 0.95751953125}, {"start": 2563.54, "end": 2564.04, "word": " بي", "probability": 0.74462890625}, {"start": 2564.04, "end": 2564.7, "word": " ال", "probability": 0.478759765625}, {"start": 2564.7, "end": 2565.18, "word": " element", "probability": 0.8232421875}, {"start": 2565.18, "end": 2565.56, "word": " h", "probability": 0.70703125}, {"start": 2565.56, "end": 2565.92, "word": " لما", "probability": 0.81494140625}, {"start": 2565.92, "end": 2566.34, "word": " يكون", "probability": 0.92919921875}, {"start": 2566.34, "end": 2566.56, "word": " في", "probability": 0.89306640625}, {"start": 2566.56, "end": 2566.82, "word": " h", "probability": 0.6591796875}, {"start": 2566.82, "end": 2566.98, "word": " و", "probability": 0.60888671875}, {"start": 2566.98, "end": 2567.52, "word": " تضربه", "probability": 0.9468994140625}, {"start": 2567.52, "end": 2567.68, "word": " في", "probability": 0.93310546875}, {"start": 2567.68, "end": 2568.12, "word": " h", "probability": 0.80908203125}, {"start": 2568.12, "end": 2569.04, "word": " بتظهر", "probability": 0.624481201171875}, {"start": 2569.04, "end": 2569.44, "word": " زي", "probability": 0.6314697265625}, {"start": 2569.44, "end": 2569.7, "word": " مهي", "probability": 0.5595703125}, {"start": 2569.7, "end": 2569.98, "word": " h", "probability": 0.39404296875}, {"start": 2569.98, "end": 2570.58, "word": " كابتن", "probability": 0.6603469848632812}, {"start": 2570.58, "end": 2571.52, "word": " يبقى", "probability": 0.9371337890625}, {"start": 2571.52, "end": 2572.02, "word": " هدف", "probability": 0.7565104166666666}, {"start": 2572.02, "end": 2572.48, "word": " بيه", "probability": 0.8953450520833334}, {"start": 2572.48, "end": 2572.7, "word": " اتش", "probability": 0.6576741536458334}, {"start": 2572.7, "end": 2573.0, "word": " عزيزي", "probability": 0.630322265625}, {"start": 2573.0, "end": 2573.08, "word": " و", "probability": 0.55078125}, {"start": 2573.08, "end": 2573.22, "word": " هو", "probability": 0.93017578125}, {"start": 2573.22, "end": 2574.28, "word": " المطلوب", "probability": 0.9798583984375}, {"start": 2574.28, "end": 2575.3, "word": " خلصنا", "probability": 0.9267578125}, {"start": 2575.3, "end": 2576.3, "word": " الاتجاهين", "probability": 0.9259765625}, {"start": 2576.3, "end": 2577.36, "word": " طيب", "probability": 0.8935546875}, {"start": 2577.36, "end": 2577.9, "word": " الان", "probability": 0.6805419921875}, {"start": 2577.9, "end": 2578.18, "word": " بدنا", "probability": 0.74462890625}, {"start": 2578.18, "end": 2578.5, "word": " نجي", "probability": 0.7724609375}, {"start": 2578.5, "end": 2579.22, "word": " لنقطة", "probability": 0.8797607421875}, {"start": 2579.22, "end": 2579.7, "word": " رابع", "probability": 0.7696940104166666}], "temperature": 1.0}, {"id": 117, "seek": 260628, "start": 2580.08, "end": 2606.28, "text": "النقطة الرابعة بيقول يا إما ال two left cosets بدوا يتساووا يا إما ال intersection تبعهم بدوا يساووا ماين فاي إذا لو نفيت واحدة منهم بدي أثبت إيه تانية يبقى بالداجة أقوله أسيوم افترض ان ال a h intersection ب a h لا يساوي الفاي", "tokens": [6027, 1863, 47432, 3660, 34892, 16758, 27884, 4724, 1829, 39648, 35186, 11933, 15042, 2423, 732, 1411, 3792, 1385, 47525, 14407, 7251, 2655, 3794, 995, 2407, 14407, 35186, 11933, 15042, 2423, 15236, 6055, 3555, 3615, 16095, 47525, 14407, 7251, 3794, 995, 2407, 14407, 19446, 9957, 6156, 47302, 11933, 15730, 45164, 8717, 5172, 36081, 36764, 24401, 3660, 9154, 16095, 4724, 16254, 5551, 12984, 3555, 2655, 11933, 1829, 3224, 6055, 7649, 10632, 7251, 3555, 4587, 7578, 20666, 3215, 26108, 3660, 5551, 39648, 3224, 5551, 3794, 1829, 20498, 1975, 5172, 2655, 43042, 16472, 2423, 257, 276, 15236, 4724, 257, 276, 20193, 7251, 3794, 995, 45865, 27188, 47302], "avg_logprob": -0.2976261961918611, "compression_ratio": 1.7311320754716981, "no_speech_prob": 0.0, "words": [{"start": 2580.08, "end": 2580.82, "word": "النقطة", "probability": 0.9033203125}, {"start": 2580.82, "end": 2581.3, "word": " الرابعة", "probability": 0.97509765625}, {"start": 2581.3, "end": 2581.82, "word": " بيقول", "probability": 0.7200520833333334}, {"start": 2581.82, "end": 2582.26, "word": " يا", "probability": 0.35302734375}, {"start": 2582.26, "end": 2582.98, "word": " إما", "probability": 0.69580078125}, {"start": 2582.98, "end": 2583.78, "word": " ال", "probability": 0.9287109375}, {"start": 2583.78, "end": 2584.02, "word": " two", "probability": 0.465576171875}, {"start": 2584.02, "end": 2584.38, "word": " left", "probability": 0.87841796875}, {"start": 2584.38, "end": 2584.98, "word": " cosets", "probability": 0.617919921875}, {"start": 2584.98, "end": 2585.54, "word": " بدوا", "probability": 0.5306396484375}, {"start": 2585.54, "end": 2586.66, "word": " يتساووا", "probability": 0.8807779947916666}, {"start": 2586.66, "end": 2587.12, "word": " يا", "probability": 0.61865234375}, {"start": 2587.12, "end": 2587.44, "word": " إما", "probability": 0.980712890625}, {"start": 2587.44, 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{"start": 2785.44, "end": 2786.24, "word": " الرقم", "probability": 0.9363606770833334}, {"start": 2786.24, "end": 2787.24, "word": " اتنين", "probability": 0.8936767578125}, {"start": 2787.24, "end": 2789.22, "word": " يبقى", "probability": 0.9559326171875}, {"start": 2789.22, "end": 2789.64, "word": " F", "probability": 0.7216796875}, {"start": 2789.64, "end": 2790.3, "word": " and", "probability": 0.9541015625}, {"start": 2790.3, "end": 2791.04, "word": " قولي", "probability": 0.6131998697916666}, {"start": 2791.04, "end": 2791.5, "word": " F", "probability": 0.87744140625}, {"start": 2791.5, "end": 2792.24, "word": " ال", "probability": 0.8642578125}, {"start": 2792.24, "end": 2792.76, "word": " A", "probability": 0.97607421875}, {"start": 2792.76, "end": 2793.6, "word": " inverse", "probability": 0.83349609375}, {"start": 2793.6, "end": 2794.26, "word": " B", "probability": 0.978515625}, {"start": 2794.26, "end": 2795.1, "word": " هذا", "probability": 0.82080078125}, {"start": 2795.1, "end": 2795.68, "word": " موجود", "probability": 0.98779296875}, {"start": 2795.68, "end": 2796.28, "word": " وين؟", "probability": 0.8743489583333334}], "temperature": 1.0}, {"id": 127, "seek": 280486, "start": 2796.3, "end": 2804.86, "text": "موجود في الـ H وهذا من ال property اتنين بالشكل اللي عندنا هذا", "tokens": [2304, 29245, 23328, 8978, 2423, 39184, 389, 37037, 15730, 9154, 2423, 4707, 1975, 2655, 1863, 9957, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.40531250953674314, "compression_ratio": 1.1195652173913044, "no_speech_prob": 0.0, "words": [{"start": 2796.3, "end": 2797.18, "word": "موجود", "probability": 0.7605794270833334}, {"start": 2797.18, "end": 2797.36, "word": " في", "probability": 0.80859375}, {"start": 2797.36, "end": 2797.58, "word": " الـ", "probability": 0.46429443359375}, {"start": 2797.58, "end": 2797.86, "word": " H", "probability": 0.55322265625}, {"start": 2797.86, "end": 2798.54, "word": " وهذا", "probability": 0.6636962890625}, {"start": 2798.54, "end": 2799.04, "word": " من", "probability": 0.23779296875}, {"start": 2799.04, "end": 2799.38, "word": " ال", "probability": 0.861328125}, {"start": 2799.38, "end": 2801.12, "word": " property", "probability": 0.798828125}, {"start": 2801.12, "end": 2802.62, "word": " اتنين", "probability": 0.7950439453125}, {"start": 2802.62, "end": 2803.56, "word": " بالشكل", "probability": 0.88818359375}, {"start": 2803.56, "end": 2803.74, "word": " اللي", "probability": 0.904296875}, {"start": 2803.74, "end": 2804.34, "word": " عندنا", "probability": 0.87646484375}, {"start": 2804.34, "end": 2804.86, "word": " هذا", "probability": 0.8994140625}], "temperature": 1.0}, {"id": 128, "seek": 283143, "start": 2806.75, "end": 2831.43, "text": "طيب ستة هه ستة بدك اتعرف function ما بين الاتنين و الناس بينها one to one and unto يبقى بداجي اقوله define a function phi من ال a h الى ال b h by", "tokens": [9566, 1829, 3555, 8608, 2655, 3660, 8032, 3224, 8608, 2655, 3660, 47525, 4117, 1975, 2655, 3615, 28480, 2445, 19446, 49374, 2423, 9307, 1863, 9957, 4032, 2423, 8315, 3794, 49374, 11296, 472, 281, 472, 293, 16521, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 3224, 6964, 257, 2445, 13107, 9154, 2423, 257, 276, 2423, 7578, 2423, 272, 276, 538], "avg_logprob": -0.31692708979050316, "compression_ratio": 1.4583333333333333, "no_speech_prob": 0.0, "words": [{"start": 2806.75, "end": 2807.35, "word": "طيب", "probability": 0.7049153645833334}, {"start": 2807.35, "end": 2808.53, "word": " ستة", "probability": 0.8907877604166666}, {"start": 2808.53, "end": 2809.69, "word": " هه", "probability": 0.399078369140625}, {"start": 2809.69, "end": 2811.55, "word": " ستة", "probability": 0.9039713541666666}, {"start": 2811.55, "end": 2812.45, "word": " بدك", "probability": 0.876708984375}, {"start": 2812.45, "end": 2812.97, "word": " اتعرف", "probability": 0.84576416015625}, {"start": 2812.97, "end": 2813.59, "word": " function", "probability": 0.47119140625}, {"start": 2813.59, "end": 2813.81, "word": " ما", "probability": 0.85205078125}, {"start": 2813.81, "end": 2814.01, "word": " بين", "probability": 0.96826171875}, {"start": 2814.01, "end": 2814.45, "word": " الاتنين", "probability": 0.82318115234375}, {"start": 2814.45, "end": 2814.57, "word": " و", "probability": 0.83642578125}, {"start": 2814.57, "end": 2814.75, "word": " الناس", "probability": 0.7383626302083334}, {"start": 2814.75, "end": 2815.29, "word": " بينها", "probability": 0.77001953125}, {"start": 2815.29, "end": 2815.67, "word": " one", "probability": 0.6923828125}, {"start": 2815.67, "end": 2816.05, "word": " to", "probability": 0.8935546875}, {"start": 2816.05, "end": 2816.47, "word": " one", "probability": 0.9541015625}, {"start": 2816.47, "end": 2817.17, "word": " and", "probability": 0.90380859375}, {"start": 2817.17, "end": 2817.95, "word": " unto", "probability": 0.41357421875}, {"start": 2817.95, "end": 2818.91, "word": " يبقى", "probability": 0.81854248046875}, {"start": 2818.91, "end": 2819.49, "word": " بداجي", "probability": 0.8045247395833334}, {"start": 2819.49, "end": 2820.19, "word": " اقوله", "probability": 0.900390625}, {"start": 2820.19, "end": 2821.05, "word": " define", "probability": 0.951171875}, {"start": 2821.05, "end": 2822.25, "word": " a", "probability": 0.95556640625}, {"start": 2822.25, "end": 2823.31, "word": " function", "probability": 0.98388671875}, {"start": 2823.31, "end": 2824.45, "word": " phi", "probability": 0.1572265625}, {"start": 2824.45, "end": 2825.49, "word": " من", "probability": 0.9892578125}, {"start": 2825.49, "end": 2826.41, "word": " ال", "probability": 0.96044921875}, {"start": 2826.41, "end": 2826.73, "word": " a", "probability": 0.40625}, {"start": 2826.73, "end": 2827.39, "word": " h", "probability": 0.64501953125}, {"start": 2827.39, "end": 2828.47, "word": " الى", "probability": 0.6376953125}, {"start": 2828.47, "end": 2829.01, "word": " ال", "probability": 0.9775390625}, {"start": 2829.01, "end": 2829.31, "word": " b", "probability": 0.90576171875}, {"start": 2829.31, "end": 2830.17, "word": " h", "probability": 0.9140625}, {"start": 2830.17, "end": 2831.43, "word": " by", "probability": 0.890625}], "temperature": 1.0}, {"id": 129, "seek": 285630, "start": 2832.4, "end": 2856.3, "text": "five of a h بده يساوي بي اتش واثبتلي انها one to one and unto اذا اثبتناها one to one and unto يحصلوا التساوي بصير ال order للأولى بده يساوي من ال order للثانية بنكمل المرة الجاية ان شاء الله و تعالى", "tokens": [18621, 295, 257, 276, 47525, 3224, 7251, 3794, 995, 45865, 4724, 1829, 1975, 2655, 8592, 4032, 5718, 104, 3555, 2655, 20292, 16472, 11296, 472, 281, 472, 293, 16521, 1975, 15730, 1975, 12984, 3555, 2655, 8315, 11296, 472, 281, 472, 293, 16521, 7251, 5016, 36520, 14407, 16712, 3794, 995, 45865, 4724, 9381, 13546, 2423, 1668, 24976, 10721, 12610, 7578, 47525, 3224, 7251, 3794, 995, 45865, 9154, 2423, 1668, 24976, 12984, 7649, 10632, 44945, 24793, 1211, 9673, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 4032, 37279, 6027, 7578], "avg_logprob": -0.26029829206791794, "compression_ratio": 1.7556818181818181, "no_speech_prob": 0.0, "words": [{"start": 2832.4, "end": 2833.2, "word": "five", "probability": 0.05670166015625}, {"start": 2833.2, "end": 2833.88, "word": " of", "probability": 0.81591796875}, {"start": 2833.88, "end": 2834.36, "word": " a", "probability": 0.261474609375}, {"start": 2834.36, "end": 2834.92, "word": " h", "probability": 0.5322265625}, {"start": 2834.92, "end": 2835.44, "word": " بده", "probability": 0.400787353515625}, {"start": 2835.44, "end": 2836.12, "word": " يساوي", "probability": 0.933837890625}, {"start": 2836.12, "end": 2836.58, "word": " بي", "probability": 0.582275390625}, {"start": 2836.58, "end": 2837.16, "word": " اتش", "probability": 0.8141276041666666}, {"start": 2837.16, "end": 2838.8, "word": " واثبتلي", "probability": 0.7358805338541666}, {"start": 2838.8, "end": 2839.26, "word": " انها", "probability": 0.45123291015625}, {"start": 2839.26, "end": 2839.78, "word": " one", "probability": 0.72607421875}, {"start": 2839.78, "end": 2840.12, "word": " to", "probability": 0.876953125}, {"start": 2840.12, "end": 2840.52, "word": " one", "probability": 0.95556640625}, {"start": 2840.52, "end": 2841.14, "word": " and", "probability": 0.88720703125}, {"start": 2841.14, "end": 2841.62, "word": " unto", "probability": 0.469970703125}, {"start": 2841.62, "end": 2841.88, "word": " اذا", "probability": 0.685302734375}, {"start": 2841.88, "end": 2842.56, "word": " اثبتناها", "probability": 0.932861328125}, {"start": 2842.56, "end": 2842.78, "word": " one", "probability": 0.6904296875}, {"start": 2842.78, "end": 2843.04, "word": " to", "probability": 0.9677734375}, {"start": 2843.04, "end": 2843.24, "word": " one", "probability": 0.95556640625}, {"start": 2843.24, "end": 2843.56, "word": " and", "probability": 0.93603515625}, {"start": 2843.56, "end": 2844.02, "word": " unto", "probability": 0.88623046875}, {"start": 2844.02, "end": 2845.26, "word": " يحصلوا", "probability": 0.870361328125}, {"start": 2845.26, "end": 2845.98, "word": " التساوي", "probability": 0.95166015625}, {"start": 2845.98, "end": 2847.24, "word": " بصير", "probability": 0.7190755208333334}, {"start": 2847.24, "end": 2847.38, "word": " ال", "probability": 0.89501953125}, {"start": 2847.38, "end": 2847.78, "word": " order", "probability": 0.96142578125}, {"start": 2847.78, "end": 2848.76, "word": " للأولى", "probability": 0.8603515625}, {"start": 2848.76, "end": 2849.3, "word": " بده", "probability": 0.916015625}, {"start": 2849.3, "end": 2849.64, "word": " يساوي", "probability": 0.966552734375}, {"start": 2849.64, "end": 2849.84, "word": " من", "probability": 0.9404296875}, {"start": 2849.84, "end": 2850.48, "word": " ال", "probability": 0.8232421875}, {"start": 2850.48, "end": 2851.4, "word": " order", "probability": 0.96923828125}, {"start": 2851.4, "end": 2852.86, "word": " للثانية", "probability": 0.949462890625}, {"start": 2852.86, "end": 2854.1, "word": " بنكمل", "probability": 0.8673502604166666}, {"start": 2854.1, "end": 2854.52, "word": " المرة", "probability": 0.9619140625}, {"start": 2854.52, "end": 2855.0, "word": " الجاية", "probability": 0.9111328125}, {"start": 2855.0, "end": 2855.32, "word": " ان", "probability": 0.7890625}, {"start": 2855.32, "end": 2855.64, "word": " شاء", "probability": 0.982177734375}, {"start": 2855.64, "end": 2855.8, "word": " الله", "probability": 0.92919921875}, {"start": 2855.8, "end": 2856.04, "word": " و", "probability": 0.35302734375}, {"start": 2856.04, "end": 2856.3, "word": " تعالى", "probability": 0.9318033854166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2856.89025, "duration_after_vad": 2738.4699999999925}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c36801918c55b958d04f571b1b262c63b85e1e6c
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4_raw.srt
@@ -0,0 +1,1808 @@
+1
+00:00:21,180 --> 00:00:26,920
+بسم الله الرحمن الرحيم انتهينا من شبتر ستة اللي هو
+
+2
+00:00:26,920 --> 00:00:32,320
+ال isomorphism والآن بندخل لشبتر سبعة شبتر سبعة
+
+3
+00:00:32,320 --> 00:00:36,640
+اللي هو Cossets and Lagrange theorem بتكلم عن
+
+4
+00:00:36,640 --> 00:00:41,980
+نقطتين والنقطتين مرتبطتين مع بعض ارتباطا وثيقا كما
+
+5
+00:00:41,980 --> 00:00:49,330
+سنرى Cosset بالعربي يعني الفئة المرافقةلقرنج
+
+6
+00:00:49,330 --> 00:00:53,410
+theorem نظرية لقرنج بالنسبة للعالم الرياضي لقرنج
+
+7
+00:00:53,410 --> 00:00:59,970
+الذي اكتشف هذه النظرية اليوم خلينا مع ال quesets و
+
+8
+00:00:59,970 --> 00:01:04,030
+المرة القادمة ان شاء الله تتكلم عن لقرنج theorem
+
+9
+00:01:04,650 --> 00:01:11,170
+بنقدر نعطي تعريف للـ Cosets ثم نبدأ بملاحظاتنا على
+
+10
+00:01:11,170 --> 00:01:15,750
+الـ Cosets in general يبقى التعريف يقول ياخد الـ H
+
+11
+00:01:15,750 --> 00:01:22,330
+subgroup من G وروحت أخد أي element A في G بضروح
+
+12
+00:01:22,330 --> 00:01:27,950
+أعرف ال Coset اللي هي AHيعني الـ subgroup بدأ
+
+13
+00:01:27,950 --> 00:01:33,670
+ضربها من جهة الشمال في أي element من G وليكن A من
+
+14
+00:01:33,670 --> 00:01:38,530
+ال set هذه A H يبقى the set of all elements A H
+
+15
+00:01:38,530 --> 00:01:43,570
+such that ال H small موجودة في H capital يعني
+
+16
+00:01:43,570 --> 00:01:51,350
+عناصر ال A H هوالـ Element A مضروب في من في عنصر
+
+17
+00:01:51,350 --> 00:01:55,890
+من عناصر H من ما يكون شكله A يكون بالشكل اللي
+
+18
+00:01:55,890 --> 00:02:00,330
+عندنا هذا الدرب من جهة الشمال لذلك هذه بسميها left
+
+19
+00:02:00,330 --> 00:02:06,370
+coset of H in G وهذه left coset تحتوي دائما و أبدا
+
+20
+00:02:06,370 --> 00:02:11,810
+عالميا على العنصر A حد بيقدر يقول لي ليش هذه
+
+21
+00:02:11,810 --> 00:02:17,210
+بتحتوي على العنصر Aلأن فيها الـ Identity الـ A في
+
+22
+00:02:17,210 --> 00:02:20,710
+الـ Identity بيعطينا الـ A itself يبقى الـ left
+
+23
+00:02:20,710 --> 00:02:26,310
+coset دائما و أبدا ال element A موجود فيها بالمثل
+
+24
+00:02:26,310 --> 00:02:29,770
+مثل ما عرفنا الـ left coset بتروح أعرفها الـ right
+
+25
+00:02:29,770 --> 00:02:34,690
+coset فبقول الـ H capital A هي عبارة عن H A such
+
+26
+00:02:34,690 --> 00:02:38,410
+that الـ H belonged to H وهذه بسميها الـ right
+
+27
+00:02:38,410 --> 00:02:44,460
+coset of H in G وفي نفس الوقت containing Aلاحظ لما
+
+28
+00:02:44,460 --> 00:02:50,800
+اقول a h او h a ال operation اللي بين ال a و ال h
+
+29
+00:02:50,800 --> 00:02:54,500
+هي نفس ال operation اللي موجودة على g و اللي
+
+30
+00:02:54,500 --> 00:03:02,390
+موجودة على h يعني اذا كان ضرب بدأ اقول ضربإذا جامع
+
+31
+00:03:02,390 --> 00:03:07,490
+يبقى الـ binary operation ما بين ال element a و ال
+
+32
+00:03:07,490 --> 00:03:12,310
+element h حسب ال operation اللي موجودة في g أو ال
+
+33
+00:03:12,310 --> 00:03:16,610
+operation اللي موجودة في hطيب الـ a اللي خلّج ال
+
+34
+00:03:16,610 --> 00:03:20,510
+left coset سواء كان ال right و الله left بسمي ايه
+
+35
+00:03:20,510 --> 00:03:25,670
+ال element ايه بسميه the coset representative of a
+
+36
+00:03:25,670 --> 00:03:30,350
+H أو ال H إيه سواء كان ال left أو ال right بتفرجش
+
+37
+00:03:30,350 --> 00:03:37,330
+أمنا طب نروح نبدي ذلك عمليا بمثال و نتوقف مع هذا
+
+38
+00:03:37,330 --> 00:03:44,080
+المثالنوعا ما و ناقش بعض الشغلات ماعطيني G هي S3
+
+39
+00:03:44,080 --> 00:03:50,180
+وهي كتبناها بالكامل ليها ستة عناصر واخد ال H هي ال
+
+40
+00:03:50,180 --> 00:03:55,700
+sub group ال E والواحد و تلاتةقال هاتلي كل ال left
+
+41
+00:03:55,700 --> 00:04:01,300
+cosets of H in S3 بقوله كويس اذا بدى ابدا مدام
+
+42
+00:04:01,300 --> 00:04:05,620
+قاله هاتلي كل ال left cosets اذا بدى ابدا بمعنى
+
+43
+00:04:05,620 --> 00:04:10,320
+بالعنصر الاول بدى اضربه في H واشوف شو بيعطيني يبقى
+
+44
+00:04:10,320 --> 00:04:18,570
+بداتي اخدله E H يبقى هذا E في E واحد و تلاتةطبعا
+
+45
+00:04:18,570 --> 00:04:22,910
+ال identity element لما اضربه فيه ال element بطلع
+
+46
+00:04:22,910 --> 00:04:27,530
+نفس ال element اضربه في التاني بدي يطلع نفس التاني
+
+47
+00:04:27,530 --> 00:04:33,730
+ال هد مين هي يا شباباللي هي H itself طيب اضرب الان
+
+48
+00:04:33,730 --> 00:04:39,430
+واحد و تلاتة ال permutation في ال H يبقى هذا
+
+49
+00:04:39,430 --> 00:04:44,970
+الكلام بده يساوي لما اضربها بده يطلع واحد و تلاتة
+
+50
+00:04:44,970 --> 00:04:50,750
+و هنا من واحد و تلاتة في واحد و تلاتة بالشكل اللي
+
+51
+00:04:50,750 --> 00:04:56,580
+عندناهذه هتعطينا مين؟ هتعطينا الو ال permutation
+
+52
+00:04:56,580 --> 00:05:01,700
+واحد، تلاتة، طب هذه نفسها إيش بتعطينا؟ ال
+
+53
+00:05:01,700 --> 00:05:06,560
+identity، تمام يبقى هذه عطتنا ال identity، طلعت
+
+54
+00:05:06,560 --> 00:05:14,480
+مين؟نفس الـ H يبقى هذه طلعت نفس الـ H itself يبقى
+
+55
+00:05:14,480 --> 00:05:20,680
+بناء عليه بقدر استنتج من هذا الكلام ان ال E في H
+
+56
+00:05:20,680 --> 00:05:27,920
+ساوة واحد تلاتة في H ساوة الـ H itself وهذا بدي
+
+57
+00:05:27,920 --> 00:05:34,740
+أحط علامة استفهام سارجع لها بعد قليلطيب الان بده
+
+58
+00:05:34,740 --> 00:05:39,240
+اخد ال elements الأخرى بدل ما اخدنا واحد و تلاتة
+
+59
+00:05:39,240 --> 00:05:45,320
+بده اخد واحد و اتنين في h اشوف ايش بده يعطينا يبقى
+
+60
+00:05:45,320 --> 00:05:51,420
+هذا بده يعطينا واحد و اتنين واحد و اتنين مضروبة في
+
+61
+00:05:51,420 --> 00:05:56,000
+من؟ في واحد و تلاتة يبقى واحد و اتنين في ال
+
+62
+00:05:56,000 --> 00:05:59,340
+identity بواحد و اتنين واحد اتنين في واحد تلاتة
+
+63
+00:05:59,340 --> 00:06:03,840
+بواحد اتنين واحد تلاتةهذا الكلام بدي يعطينا الواحد
+
+64
+00:06:03,840 --> 00:06:09,200
+اتنين كما هي وهذه بدي اجيب ال composition ما بين
+
+65
+00:06:09,200 --> 00:06:14,180
+ال two transpositions الاتنين هدول يبقى باجي بقول
+
+66
+00:06:14,180 --> 00:06:20,170
+هاي الواحد الواحد صورتهوالتلاتة صورتها تلاتة يبقى
+
+67
+00:06:20,170 --> 00:06:26,050
+هي التلاتة التلاتة صورتها واحد والواحد صورته اتنين
+
+68
+00:06:26,050 --> 00:06:30,630
+يبقى هي الاتنين الان اتنين صورته اتنين واتنين
+
+69
+00:06:30,630 --> 00:06:35,890
+صورته هي موجود يبقى جفلة بالشكل اللي عندنا هنا
+
+70
+00:06:35,890 --> 00:06:43,940
+تمام؟لاحظ ان هذا بالضبط تماما هو واحد تلات اثنين
+
+71
+00:06:43,940 --> 00:06:52,540
+كما لو ضربت في main ضربت في Hبناء على يسار واحد
+
+72
+00:06:52,540 --> 00:06:58,240
+اتنين اتش هو واحد تلات اتنين اتش يبقى هذا بدي
+
+73
+00:06:58,240 --> 00:07:03,780
+يعطيك ان واحد اتنين ال permutation لما تضربها في
+
+74
+00:07:03,780 --> 00:07:09,800
+اتش كليا بدي يساوي واحد تلات اتنين كما لو ضربتها
+
+75
+00:07:09,800 --> 00:07:17,240
+في اتش وهذا كمان بدي يولد علامة استفهام اخرى نكمل
+
+76
+00:07:18,800 --> 00:07:24,440
+بدي اجي لليه اتنين و تلاتة بدي اضربها في مين فاتش
+
+77
+00:07:24,440 --> 00:07:32,100
+يبقى الناتج اتنين تلاتة و اتنين تلاتة واحد تلاتة و
+
+78
+00:07:32,100 --> 00:07:37,750
+يساوي اتنين تلاتة واحديبقى اتنين تلاتة في اتش
+
+79
+00:07:37,750 --> 00:07:42,050
+باتنين تلاتة لان ال identity بعدها اتنين تلاتة في
+
+80
+00:07:42,050 --> 00:07:47,030
+واحد تلاتة هي اذا ان النتج يساوي هي اتنين تلاتة
+
+81
+00:07:47,030 --> 00:07:51,130
+الأولانية ال permutation الأولى وهذه بضروح اجيب ال
+
+82
+00:07:51,130 --> 00:07:55,830
+composition في ما بينهما اذا ببدأ بالواحد الواحد
+
+83
+00:07:55,830 --> 00:08:02,130
+صورته والتلاتة صورتها اتنين يبقى هي واحد اتنين
+
+84
+00:08:02,640 --> 00:08:08,840
+تلاتة صورته اتنين و اتنين صورته تلاتة الان بالداجي
+
+85
+00:08:08,840 --> 00:08:14,400
+التلاتة صورتها واحد و الواحد صورته هي موجود اذا
+
+86
+00:08:14,400 --> 00:08:20,370
+انقفلت بالشكل اللي عندنا هذاهذا بالضبط تماماً بده
+
+87
+00:08:20,370 --> 00:08:26,010
+يساوي اللي هو واحد اتنين تلاتة كما لو ضربتها في H
+
+88
+00:08:26,010 --> 00:08:32,730
+اعمل ال H كانت كويس؟ يبقى هاي خلاصنا ضايل فيه شيء؟
+
+89
+00:08:33,500 --> 00:08:39,680
+كل element هيو مبروب عندى من جهة الشمال فيه H بناء
+
+90
+00:08:39,680 --> 00:08:53,770
+عليه صار the left cosets of H in S3R أول واحد Hهه
+
+91
+00:08:53,770 --> 00:08:59,450
+H او ال E في ال H او واحد تلاتة H ال element
+
+92
+00:08:59,450 --> 00:09:06,990
+الثاني اللي هو من واحد اتنين في من في H وال
+
+93
+00:09:06,990 --> 00:09:15,330
+element التالت اللي هو اتنين تلاتة كله في Hأحنا
+
+94
+00:09:15,330 --> 00:09:21,690
+هكذا خلصنا المتوقع كان من البداية أنه لما أضرب ال
+
+95
+00:09:21,690 --> 00:09:25,490
+elements الستة اللي عندنا تبعات ال agromfets يطلع
+
+96
+00:09:25,490 --> 00:09:30,150
+عندى الست elements مظبوط طلعوا الست elements بس ما
+
+97
+00:09:30,150 --> 00:09:34,570
+هماش disjoint هاي الملاحظة الأولى لأن هدول طلعوا
+
+98
+00:09:34,570 --> 00:09:39,600
+اشي بيساوي بعضه هاي طلعوا هاي تلاتة بيساوي بعضهذول
+
+99
+00:09:39,600 --> 00:09:43,700
+اتنين بيسووا بعض، هذول اتنين كمان بيسووا بعض،
+
+100
+00:09:43,700 --> 00:09:48,220
+تمام؟ إذا ليس بالضرورة لما أجيب ال left corset ال
+
+101
+00:09:48,220 --> 00:09:53,650
+elements يكونوا disjointهذه الملاحظة الأولى
+
+102
+00:09:53,650 --> 00:09:58,170
+الملاحظة التانية اتطلعلي في الحالتين الاتنين هدول
+
+103
+00:09:58,170 --> 00:10:03,430
+هنا ضربت في ايه و هنا ضربت في واحد تلاتة يعني ضربت
+
+104
+00:10:03,430 --> 00:10:10,330
+في عناصر H إذا لو أخدت element من H و ضربته في H
+
+105
+00:10:10,330 --> 00:10:16,680
+بدي أطلع منهمEach itself مش واحدة تانية اطلع عندي
+
+106
+00:10:16,680 --> 00:10:22,080
+ايه اتش ثوات لمين اتش itself الواحد تلاتة فيه اتش
+
+107
+00:10:22,080 --> 00:10:27,100
+ثوات لمين الواحد تلاتة يعني اتش itself يبقى ال
+
+108
+00:10:27,100 --> 00:10:31,880
+left coset لو ضربت اللي هو ال subgroup في element
+
+109
+00:10:31,880 --> 00:10:35,820
+من نفس ال subgroup دي يطلع مين ال subgroup هاي
+
+110
+00:10:35,820 --> 00:10:42,520
+الملاحظة التانية الملاحظة التالتةإن الليفت كو سيتس
+
+111
+00:10:42,520 --> 00:10:49,180
+ممكن يتساوى رغم أن العنصر اللي ضرب فيه مش نفسه طلع
+
+112
+00:10:49,180 --> 00:10:54,280
+لي هنا هي عندي واحد اتنين ضربتها في H سواتلي مام
+
+113
+00:10:54,280 --> 00:10:59,220
+واحد تلات اتنين في H هل الواحد اتنين هو الواحد
+
+114
+00:10:59,220 --> 00:11:05,600
+تلات اتنين؟ لأ مختلف إذا ليس بالضرورة لو قلتلك A H
+
+115
+00:11:05,600 --> 00:11:11,370
+يسوى BH إذا ال A يسوى ال B صح ولا غلط؟غلط قد يحدث
+
+116
+00:11:11,370 --> 00:11:16,450
+انه صح بس in general غلط يعني ممكن تحصل حالة علتين
+
+117
+00:11:16,450 --> 00:11:21,870
+تلاتة تبقى صح لكن in general ليس صحيحا يبقى هذه
+
+118
+00:11:21,870 --> 00:11:25,750
+الملاحظة هذه انه في حالة ال left cosets ممكن
+
+119
+00:11:25,750 --> 00:11:30,470
+يتساوي ال two left cosets لكن ال a ليساوي ال b وهي
+
+120
+00:11:30,470 --> 00:11:36,050
+الكلام واضح قدامنا وهكذايبقى هذه ملاحظات أساسية
+
+121
+00:11:36,050 --> 00:11:40,890
+موجودة من خلال هذا المثال و بنقدر نسحبها على
+
+122
+00:11:40,890 --> 00:11:49,210
+course sets أخرى نعطي مثال أخرى example
+
+123
+00:11:49,210 --> 00:11:59,280
+two example two بيقولالـ G تساوي D4 و D4 احنا
+
+124
+00:11:59,280 --> 00:12:05,540
+عارفين عناصرها اللي هي R نود و R تسعين و R مية و
+
+125
+00:12:05,540 --> 00:12:14,800
+تمانين و R متين و سبعين و H و V و D و D Primeو بدي
+
+126
+00:12:14,800 --> 00:12:21,740
+اخد اللي هو K subgroup اللي هي subgroup generated
+
+127
+00:12:21,740 --> 00:12:32,800
+by R180 اللي عناصرها Arnold وR180 فقط لا غير تمام؟
+
+128
+00:12:32,800 --> 00:12:41,600
+find the left cosets of
+
+129
+00:12:54,930 --> 00:12:59,790
+الان بدي ابدا بال elements كلهم قاللي هاتلي lift
+
+130
+00:12:59,790 --> 00:13:06,950
+cos 6 يبقى انا بدي اجيبله ارناد في كابتل كهي كابتة
+
+131
+00:13:06,950 --> 00:13:11,930
+ال K موجودة عندى ارنود في ارنود مين بتعطينا ارنود
+
+132
+00:13:11,930 --> 00:13:16,410
+في مية و تمانين بتعطينا مين R مية و تمانين اللى هى
+
+133
+00:13:16,410 --> 00:13:25,190
+ال K itself طيب خذى R مية و تمانين مية و تمانين في
+
+134
+00:13:25,190 --> 00:13:31,550
+اللى هو K يبقى هذا الكلام بده يساوي R مية و تمانين
+
+135
+00:13:31,550 --> 00:13:39,080
+والتانية بصير Arnoldلأن الـ R 180 هو R 180 و R 360
+
+136
+00:13:39,080 --> 00:13:46,720
+هو الـ R node طلعت من هذا الـ K نفسه من الاتنين
+
+137
+00:13:46,720 --> 00:13:55,510
+هذول نستنتج الـ R node Kبدي يساوي R180K بدي يساوي
+
+138
+00:13:55,510 --> 00:14:00,350
+K itself أظن هذا يتفق مع النتيجة اللي توصلنا لها
+
+139
+00:14:00,350 --> 00:14:04,890
+هنا أنه لو ضربت ال subgroup في أي element من ال
+
+140
+00:14:04,890 --> 00:14:09,310
+subgroup بتطلع نفس من نفس ال subgroup وهذا اللي
+
+141
+00:14:09,310 --> 00:14:13,330
+حصل في الحالتين الأثنين هذول زي المثال اللي هناك
+
+142
+00:14:13,330 --> 00:14:20,020
+بالضبط تماماطيب الان لو جيت اخدت ال R ميتين و
+
+143
+00:14:20,020 --> 00:14:25,940
+سبعين في K مثلا يبقى هذا الكلام بده يسوي بده اضربه
+
+144
+00:14:25,940 --> 00:14:31,840
+هنا يبقى بده يعطيني R ميتين و سبعين و عندك R مية و
+
+145
+00:14:31,840 --> 00:14:37,540
+تمانين في R ميتين و سبعين اللي هي من R تسعين
+
+146
+00:14:39,600 --> 00:14:45,860
+270×180 خُد منها R 90 بيصير هذه R 360 ال identity
+
+147
+00:14:45,860 --> 00:14:54,920
+بيظل 100 بيظل R 90 السؤال هو هل هذا الكلام هو R 90
+
+148
+00:14:54,920 --> 00:15:02,760
+في K ام لا اضرب هاي R 90 وR 90 في R 180 بR 270
+
+149
+00:15:04,630 --> 00:15:10,250
+مظبوط ولا لا؟ يبقى من هذا الكلام بس تنتج ان ال R
+
+150
+00:15:10,250 --> 00:15:19,810
+ميتين وسبعين K هي عبارة عن ال R تسعين K بالشكل
+
+151
+00:15:19,810 --> 00:15:25,070
+اللي عندناتمام يبقى هدول مش أربعة هدول بس تنتين
+
+152
+00:15:25,070 --> 00:15:29,950
+left cosets لإن واحدة بتساوي التانية طيب بدأت أخد
+
+153
+00:15:29,950 --> 00:15:36,450
+الآن اللي هو ال H في K أشوف إيش بدها تعطينا ال H
+
+154
+00:15:36,450 --> 00:15:44,630
+في R نوت بال H وهذه H في R مية و تمانين هذه بدها
+
+155
+00:15:44,630 --> 00:15:47,730
+تساوي H وهذه نجي نشوف
+
+156
+00:15:51,960 --> 00:15:58,420
+HVR180 تفتح الكتاب صفحة واحد و تلاتين واحد و
+
+157
+00:15:58,420 --> 00:16:03,500
+تلاتين على ال table ال table بتاعة ال product ما
+
+158
+00:16:03,500 --> 00:16:10,550
+بين اللي هو عناصر ال D4 مع بعضها البعضيبقى احنا
+
+159
+00:16:10,550 --> 00:16:15,850
+بدنا H في R مية و تمانين يبقى عندنا H في R مية و
+
+160
+00:16:15,850 --> 00:16:20,410
+تمانين وين راحت؟ H في R مية و تمانين اللي هي ب V
+
+161
+00:16:20,410 --> 00:16:28,650
+يبقى هذا الكلام بد يساوي H و Vطب خليني اخد VK
+
+162
+00:16:28,650 --> 00:16:33,910
+واشوف ايش بدها تساوي يبقى ال VK الشكل اللي عندنا
+
+163
+00:16:33,910 --> 00:16:40,670
+هذا بدها تساوي ال V و ال V في من في ال R مية و
+
+164
+00:16:40,670 --> 00:16:45,970
+تمانينهذا الكلام بده يعطينا V و نجي ال V في ال R
+
+165
+00:16:45,970 --> 00:16:55,370
+180 ال V في ال R 180 بتعطينا H يبقى ناتج هو H ايش
+
+166
+00:16:55,370 --> 00:17:01,130
+بتلاحظوا على الاتنين هذول اتنين متساويين يبقى هذا
+
+167
+00:17:01,130 --> 00:17:09,360
+بده يعطينا ان ال HK بده يساوي ال VKبنفس الطريقة
+
+168
+00:17:09,360 --> 00:17:19,080
+اعملها similarly بدي يكون ال D K هتلاقي هو ال D' K
+
+169
+00:17:19,080 --> 00:17:28,020
+كذلك تمام؟ بناء عليه بقدر اقوله the left corsets
+
+170
+00:17:28,020 --> 00:17:36,360
+of the left corsets of
+
+171
+00:17:38,820 --> 00:17:49,140
+the left cosets of اللي هو K and D for R الأولى
+
+172
+00:17:49,140 --> 00:17:56,760
+الـ K itself والتانية اللي هو ال R تسعين في K
+
+173
+00:17:56,760 --> 00:18:05,600
+والتالتة لHK والرابعة اللي هو DKيبقى هذا left
+
+174
+00:18:05,600 --> 00:18:10,680
+cursive فقط لا غير اطلع على الملاحظات اللي عندك
+
+175
+00:18:10,680 --> 00:18:17,920
+هنا تجدها منطبقة تماما هيتنتين متساويتين رغم ان ال
+
+176
+00:18:17,920 --> 00:18:22,510
+element هذا مش هو ال element ال H بيختلف عن Vهنا
+
+177
+00:18:22,510 --> 00:18:26,830
+برضه ال D كي بده يسوي D' رغم ان ال D تختلف عاميا
+
+178
+00:18:26,830 --> 00:18:33,030
+عن D' و هكذا يعني ال two left cosets are equal رغم
+
+179
+00:18:33,030 --> 00:18:35,670
+ان ال element اللي مضروب فيه اتش يختلف عن ال
+
+180
+00:18:35,670 --> 00:18:39,710
+element الثاني اللي مضروب فيه اتش الحالة الثانية
+
+181
+00:18:39,710 --> 00:18:44,550
+لو أخدنا ال K اللي عندنا و ضربناها في عنصر من
+
+182
+00:18:44,550 --> 00:18:50,790
+عناصر K تبقى K كما هي وهذه الملاحظة اللي عندناطيب
+
+183
+00:18:50,790 --> 00:18:55,470
+السؤال هو هل ال right corset ممكن تساوي ال left
+
+184
+00:18:55,470 --> 00:19:02,070
+corset؟ بتساوي يعني؟ تعالي نجرب قد يحدث بس in
+
+185
+00:19:02,070 --> 00:19:07,310
+general مش صحيح في هدول أول تنتين صحيح بمظبوط
+
+186
+00:19:07,310 --> 00:19:10,850
+الكلام ليش انه من نفس ال group أو من نفس ال
+
+187
+00:19:10,850 --> 00:19:14,450
+subgroup بس بدي أجيب element من برا وبين انه هذا
+
+188
+00:19:14,450 --> 00:19:20,190
+الكلام مش صحيح فمثلاأحنا أخدنا وين R تسعين في K
+
+189
+00:19:20,190 --> 00:19:27,630
+هذه R تسعين في K واخدنا H كيه وغيره إلى آخرين طب
+
+190
+00:19:27,630 --> 00:19:33,030
+بدى أجرب K في H أشوف إيش بتعطيني هنا now
+
+191
+00:19:34,850 --> 00:19:41,830
+بدأ أخد اللي هو K في H يبقى هذا الكلام بده يساوي
+
+192
+00:19:41,830 --> 00:19:54,310
+اللي هو ال K في H بده يساوي H و هنا R مية و تمانين
+
+193
+00:19:54,310 --> 00:20:00,800
+في من في Hنجي نشوف اش بده يساوي هذا الكلام بده
+
+194
+00:20:00,800 --> 00:20:07,520
+يساوي H وال R مية و تمانين في H ال R مية و تمانين
+
+195
+00:20:07,520 --> 00:20:16,840
+في H في H بطلع كده؟ بطلع V بطلع V طيب طلعت هذه هي
+
+196
+00:20:16,840 --> 00:20:24,540
+بالضبط هذه V و H حد بقدر يقول لي ليش؟ ايوةمية مية
+
+197
+00:20:24,540 --> 00:20:29,960
+المي أر مية و تمانين في ال center وبالتالي هذا طلع
+
+198
+00:20:29,960 --> 00:20:34,840
+متساوين لكن لو برا ال center بصير كلام هذا معلوم
+
+199
+00:20:34,840 --> 00:20:39,020
+ليس صحيحا يبقى in general هذا الكلام ليس صحيحا
+
+200
+00:20:39,020 --> 00:20:43,840
+الممكن أخد من هنا هذا مافيش فيها ال center هذه S3
+
+201
+00:20:43,840 --> 00:20:47,380
+مافيش فيها إلا ال identity element تعالي ناخد من
+
+202
+00:20:47,380 --> 00:20:54,770
+هنا هى الصارة عندك هذا يعنيإن ال K في H بده يساوي
+
+203
+00:20:54,770 --> 00:20:56,230
+ال H في K
+
+204
+00:20:59,010 --> 00:21:08,290
+ولكن لو جيت من المثال الأول أخدت واحد اتنين
+
+205
+00:21:08,290 --> 00:21:15,610
+هذا مضروب في اتش ان اتش قداش طلع واحد اتنين في اتش
+
+206
+00:21:15,610 --> 00:21:21,390
+طلع واحد تلاتة اتنين اتش طلع واحد تلاتة اتنين في
+
+207
+00:21:21,390 --> 00:21:28,700
+اتش andبدي اخد H في main في واحد اتنين يبقى H في
+
+208
+00:21:28,700 --> 00:21:34,440
+ال permutation واحد اتنين بدي يعطينا واحد اتنين
+
+209
+00:21:34,440 --> 00:21:40,760
+والان اللي هو ال H قولنا هناك بقداش بواحد تلاتة
+
+210
+00:21:40,760 --> 00:21:48,220
+يبقى واحد تلاتة في واحد اتنين لأن الضرب من وين؟ من
+
+211
+00:21:48,220 --> 00:21:54,510
+جهتي اليمينيبقى هذا الكلام بده يعطينا واحد اتنين و
+
+212
+00:21:54,510 --> 00:21:59,630
+هذا بده يعطينا الواحد صورته اتنين و اتنين صورته
+
+213
+00:21:59,630 --> 00:22:05,050
+اتنين الان اتنين صورته الواحد و الواحد صورته تلاتة
+
+214
+00:22:05,050 --> 00:22:11,680
+التلاتة صورتها تلاتة و التلاتة واحد قفلت هديهااللي
+
+215
+00:22:11,680 --> 00:22:18,860
+هو واحد اتنين تلاتة في H اطلع شوف لي واحد اتنين في
+
+216
+00:22:18,860 --> 00:22:25,200
+H هل هي H في واحد اتنين طب لا هذه واحد تلاتة اتنين
+
+217
+00:22:25,200 --> 00:22:30,000
+هذه واحد اتنين تلاتة يبقى بيسووش بعض يبقى باجي
+
+218
+00:22:30,000 --> 00:22:37,600
+بقوله هنا سا واحد اتنين في H does not equal لل H
+
+219
+00:22:37,600 --> 00:22:43,660
+في واحد اتنينيبقى in general الـ left cosets
+
+220
+00:22:43,660 --> 00:22:48,960
+والright cosets are not equal يعني قد يحدث تساوي
+
+221
+00:22:48,960 --> 00:22:54,540
+وقد لا يحدث سبب التساوي في النقطة الأولى اللي
+
+222
+00:22:54,540 --> 00:23:00,600
+أخدناها من D4 أن الـR180 كانت في ال center
+
+223
+00:23:00,600 --> 00:23:05,640
+وبالتالي حصل التساوي النقطة الثانية ليست في ال
+
+224
+00:23:05,640 --> 00:23:11,600
+center وبالتالي لم يحدث تساوينعطي كمان مثال تلاتة
+
+225
+00:23:11,600 --> 00:23:23,820
+example تلاتة بيقول خدلي G هو هي Z تسعة تمام and
+
+226
+00:23:23,820 --> 00:23:31,230
+ال H هي ال sub group generated by تلاتةهات لل left
+
+227
+00:23:31,230 --> 00:23:44,070
+cosets find the left cosets of H and the تسعة
+
+228
+00:23:47,960 --> 00:23:52,880
+خلّى بالا كدا بدنا نجيب اللفت كو ستس اللى عندنا
+
+229
+00:23:52,880 --> 00:24:00,180
+طبعا جي معروفة زد تسعة هي عبارة عن زير و واحد و
+
+230
+00:24:00,180 --> 00:24:05,900
+اتنين لغاية تمانينتمام الان ال H ال sub group
+
+231
+00:24:05,900 --> 00:24:11,560
+generated by تلاتة هي زيرو تلاتة و ستة و تسعة اللي
+
+232
+00:24:11,560 --> 00:24:16,480
+هي زيرو و هكذا بدنا نروح نجيب ال left cosets ال
+
+233
+00:24:16,480 --> 00:24:21,300
+operation على Z تسعة جامع ولا ضاربة جامع ممدر جدا
+
+234
+00:24:21,610 --> 00:24:29,110
+يبقى انا بدي ابدأ بالعنصر الأول Zero زائد H يعني
+
+235
+00:24:29,110 --> 00:24:35,050
+اللي هو Zero زائد ال sub group generated by تلاتة
+
+236
+00:24:35,050 --> 00:24:41,230
+من عناصرها هيهم بدي اضيف Zero لكل عنصر من هذه
+
+237
+00:24:41,230 --> 00:24:47,820
+العناصر بتغير اشييقول تطلع H itself يبقى هذا بده
+
+238
+00:24:47,820 --> 00:24:53,780
+يعطينا H itself ليش؟ لإن ال zero موجود في H طيب لو
+
+239
+00:24:53,780 --> 00:25:00,840
+روحت قولتلك أليس هذا هو تلاتة زائد H؟نفسه ولا لا؟
+
+240
+00:25:00,840 --> 00:25:05,460
+لأن تلاتة تضيف فلك كل عمصر تلاتة زائد زيرو بتلاتة
+
+241
+00:25:05,460 --> 00:25:09,700
+تلاتة زائد تلاتة بستة تلاتة زائد تسعة بزيرو يبقى
+
+242
+00:25:09,700 --> 00:25:16,200
+zero, six, تلاتة، تمام؟ طيب، أليست هذه هي ستة زائد
+
+243
+00:25:16,200 --> 00:25:23,570
+H كذلك؟ يبقى هاي تلاتة، هاي واحدةوهي تنتين وهي
+
+244
+00:25:23,570 --> 00:25:28,950
+تلاتة وهي الأصلية كلهم بيساوي بعض مرة واحدة طب لو
+
+245
+00:25:28,950 --> 00:25:36,000
+جيت واحد زائد Hيبقى هذا الكلام بده يساوي واحد زائد
+
+246
+00:25:36,000 --> 00:25:40,840
+zero بواحد، واحد زائد تلاتة باربعة، واحد زائد ستة
+
+247
+00:25:40,840 --> 00:25:47,960
+بسبعة السؤال هو شوف ليه، احنا أخدنا هنا، هل شوف
+
+248
+00:25:47,960 --> 00:25:53,910
+ليه هل هو اربعة زائد each ولا لأ، تعالى نشوفأربعة
+
+249
+00:25:53,910 --> 00:25:58,770
+زائد Zero باربعة هيها أربعة زائد تلاتة بسبعة هيها
+
+250
+00:25:58,770 --> 00:26:04,450
+أربعة زائد ستة بعاشرة في زي التسعة بواحد هيها تمام
+
+251
+00:26:04,450 --> 00:26:13,270
+طيب شوف ليه هل هذا بالضبط سبعة زائد Hنفس الفكرة طب
+
+252
+00:26:13,270 --> 00:26:19,510
+لو روحت لان للي اتنين زائد H يبقى هذا الكلام بده
+
+253
+00:26:19,510 --> 00:26:24,110
+يسويه بده اجي هنا و اضيف لكل واحد اتنين يبقى هذه
+
+254
+00:26:24,110 --> 00:26:32,190
+بصير اتنين و هنا خمسة و هنا تمانيةطب شوف لبالله
+
+255
+00:26:32,190 --> 00:26:40,250
+هذه هل هي خمسة زائد H أم لا وشوف هل هي تمانية زائد
+
+256
+00:26:40,250 --> 00:26:47,730
+H أم لا هي نفسها يبقى ماعنديش إلا رغم هذه تسع
+
+257
+00:26:47,730 --> 00:26:52,310
+عناصر لكن رغم ذلك ماعنديش إلا تلاتة left cosets
+
+258
+00:26:52,310 --> 00:27:02,300
+يبقى بجي بقوله so the left cosets areاللي هو مين
+
+259
+00:27:02,300 --> 00:27:08,760
+ال H نفسه Zero زاد H ال H نفسه و ال واحد زاد H و
+
+260
+00:27:08,760 --> 00:27:16,780
+اتنين زاد H فقط لا غير لا يوجد غيرها طيب
+
+261
+00:27:16,780 --> 00:27:23,540
+الان اللاحظ هدى و هدى و هدى و هدى كلهم دول are
+
+262
+00:27:23,540 --> 00:27:27,360
+equal ليش؟لأن الـ element اللي هنا ده أخدناه من
+
+263
+00:27:27,360 --> 00:27:32,440
+داخل الـ H لما انطلعنا برا الـ H لجيت واحد زادتش
+
+264
+00:27:32,440 --> 00:27:36,600
+يساوي أربعة زادتش رغم أن الواحد لاتساوي أربعة في
+
+265
+00:27:36,600 --> 00:27:41,640
+زي التسعة و لجينا هذا الكلام يساوي سبعة زادتش رغم
+
+266
+00:27:41,640 --> 00:27:46,480
+أن السبعة لاتساوي أربعة لاتساوي واحد وهكذا بالنسبة
+
+267
+00:27:46,480 --> 00:27:51,070
+للآخر هذا يتفق مع الكلام اللي قلناه قبل قليلان ال
+
+268
+00:27:51,070 --> 00:27:56,970
+A H لو كانت تساوي B H ليس بالضرورة ان A تساوي B
+
+269
+00:27:56,970 --> 00:28:02,430
+يعني قد يكون و قد لا يكون in general حد ايه له اي
+
+270
+00:28:02,430 --> 00:28:03,810
+سؤال هنا شباب؟
+
+271
+00:28:19,180 --> 00:28:23,240
+حاجة بقول بدي أحب أسالها سؤال؟ طيب احنا من حاب
+
+272
+00:28:23,240 --> 00:28:28,600
+نسألها الحينالسؤال اللى بدنا نعطيك لمّة ونروح
+
+273
+00:28:28,600 --> 00:28:35,240
+نبرهن عناصرها وحنسأل واحنا بنبرهن ان شاء الله يبقى
+
+274
+00:28:35,240 --> 00:28:40,860
+أول لمّة في هذا ال section بتتكلم عن ما يأتي عن
+
+275
+00:28:40,860 --> 00:28:47,520
+خواص ال cosets يبقى اللمّة اللي هي عبارة عن the
+
+276
+00:28:47,520 --> 00:28:52,940
+properties of cosets
+
+277
+00:28:54,980 --> 00:29:07,360
+أيش الخواص هذه بيقول let ال h be a subgroup of g
+
+278
+00:29:07,360 --> 00:29:10,700
+let
+
+279
+00:29:10,700 --> 00:29:19,240
+ال a will be موجودة في ال group g then النقطة
+
+280
+00:29:19,240 --> 00:29:29,050
+الأولىالـ A موجود في الـ H بنفس الطريقة بقدر أقوله
+
+281
+00:29:29,050 --> 00:29:34,170
+الـ A موجودة في الـ H سواء كان هذه و الله هذه
+
+282
+00:29:34,170 --> 00:29:42,050
+سيامة النقطة الثانية الـ A H بده يساوي الـ H if
+
+283
+00:29:42,050 --> 00:29:50,600
+and only if الـ A موجود في الـ Hالنقطة التالتة ال
+
+284
+00:29:50,600 --> 00:29:59,880
+A H بده يساوي B H if and only if ال A موجودة في ال
+
+285
+00:29:59,880 --> 00:30:10,300
+B H النقطة الرابعة ال A H بده يساوي ال B HO ال A H
+
+286
+00:30:10,300 --> 00:30:20,400
+intersection BH بده يساوي الفايالنقطة الخامسة
+
+287
+00:30:20,400 --> 00:30:30,000
+بتقول ال A H بده يساوي ال B H if and only if A
+
+288
+00:30:30,000 --> 00:30:38,380
+inverse B belongs to H النقطة السادسة بتقول ان ال
+
+289
+00:30:38,380 --> 00:30:45,740
+order لل A H بده يساوي ال order لل B H النقطة
+
+290
+00:30:45,740 --> 00:30:55,500
+السابعةبتقول ان الـ A H بده يساوي الـ H A if and
+
+291
+00:30:55,500 --> 00:31:02,360
+only if if and only if الـ H بده يساوي الـ A H A
+
+292
+00:31:02,360 --> 00:31:09,400
+inverse النقطة الثامنة والاخيرة بيقول الـ A H is a
+
+293
+00:31:09,400 --> 00:31:17,050
+subgroup main G if and only ifF and only F ال A
+
+294
+00:31:17,050 --> 00:31:22,350
+موجودة في H Approved
+
+295
+00:31:39,310 --> 00:31:43,790
+خلّي بالك معانا كويس هنا الان انا عندي H subgroup
+
+296
+00:31:43,790 --> 00:31:49,370
+من G أخدت عنصرين موجودات فيه G النقطة الأولى بتقول
+
+297
+00:31:49,370 --> 00:31:53,190
+ال A موجود في ال H طبعا احنا قرناها في التعريف لكم
+
+298
+00:31:53,190 --> 00:31:59,470
+النتبه رياضيا ال A H بده يساوي ال H إذا كان ال A
+
+299
+00:31:59,470 --> 00:32:03,530
+موجود في H يعني لو ضاربت ال subgroup في element
+
+300
+00:32:03,530 --> 00:32:07,550
+منها بيطلع نفس ال H وشوفنا تو في الثلاثة أمثلة نفس
+
+301
+00:32:07,550 --> 00:32:12,790
+الكلامبس احنا بنثبت نظرية للجميع النقطة التالتة A
+
+302
+00:32:12,790 --> 00:32:17,670
+H بدي تسوى BH إذا كان ال A موجود وان في ال BH
+
+303
+00:32:17,670 --> 00:32:23,430
+الرابعة any two left cosets يا إما اتنين بتسووا
+
+304
+00:32:23,430 --> 00:32:27,490
+بالكامل يا إما ال intersection تبعهم بدي تسوى فاي
+
+305
+00:32:27,490 --> 00:32:32,570
+طلع في نهاية كل مثال قولنا يبقى left cosets كذا
+
+306
+00:32:32,570 --> 00:32:37,710
+طلع فش ولا عنصر مشترك ما بين التلاتة فالمثال الأول
+
+307
+00:32:48,150 --> 00:32:54,550
+تساوى لو حدث يبقى a inverse b موجود في h عدد
+
+308
+00:32:54,550 --> 00:32:59,050
+العناصر في كل left coset يسوى عدد العناصر في left
+
+309
+00:32:59,050 --> 00:33:04,280
+coset a الثانية بالضبط تماماهذا الـ A H بده يساوي
+
+310
+00:33:04,280 --> 00:33:08,280
+H A إذا كان الـ H بده يساوي يعني ال right coset
+
+311
+00:33:08,280 --> 00:33:12,600
+تساوي ال left coset إذا كان ال H قدرت أكتبها على
+
+312
+00:33:12,600 --> 00:33:18,180
+صيغة A H A inverse الأمر الأخير أنه الـ A H
+
+313
+00:33:18,180 --> 00:33:23,180
+subgroup من G إذا كان ال A موجود في H يعني ال left
+
+314
+00:33:23,180 --> 00:33:28,040
+cosets اللي حسبناهم قبل قليل بعضهم subgroup وبعضهم
+
+315
+00:33:28,040 --> 00:33:32,550
+لأو subgroup وقتاش لما كان ال element اللى بنضرب
+
+316
+00:33:32,550 --> 00:33:35,970
+فيه جاي من نفس ال subgroup لإنه بطلع لنفس ال
+
+317
+00:33:35,970 --> 00:33:40,830
+subgroup لكن لما نيجي من برا ماهواش subgroup اطلع
+
+318
+00:33:40,830 --> 00:33:45,610
+مثلا للواحد اتنين في ال H في أول مثالإذا أعطاني
+
+319
+00:33:45,610 --> 00:33:49,930
+two elements فاش فيهم ال identity element إذا هذه
+
+320
+00:33:49,930 --> 00:33:55,370
+ليست subgroup يبقى أنا بقول coset وليست subgroup
+
+321
+00:33:55,370 --> 00:33:59,630
+إذا ال coset in general ليست بالضرورة تكون
+
+322
+00:33:59,630 --> 00:34:03,450
+subgroup تكون subgroup لو كان ال element من نفس ال
+
+323
+00:34:03,450 --> 00:34:08,900
+subgroup itselfنجي للنقطة الأولى بيقول يثبت أن ال
+
+324
+00:34:08,900 --> 00:34:13,780
+a موجودة في ال a h باجي بقوله ال a اللي عندنا هذه
+
+325
+00:34:13,780 --> 00:34:19,760
+مش بقدر اكتبها ال a في ال identity element صح ولا
+
+326
+00:34:19,760 --> 00:34:24,720
+لا طيب ال identity element هذا المنظر فيه أليس
+
+327
+00:34:24,720 --> 00:34:32,180
+موجود في ال a hلأن أي subgroup تحتوي على الـ
+
+328
+00:34:32,180 --> 00:34:36,640
+Identity Element. إذاً الـ E هدى موجود في H و A هي
+
+329
+00:34:36,640 --> 00:34:42,600
+A نفسها. بناءً عليه الـ A صارت موجودة في الـ H وهو
+
+330
+00:34:42,600 --> 00:34:48,700
+المطلوب يبقى الـ A belongs to H.وبالفعل احنا لما
+
+331
+00:34:48,700 --> 00:34:52,800
+اخدنا ال subgroup تاو قبل شوية وضربنا ال element
+
+332
+00:34:52,800 --> 00:34:57,960
+في ال identity طالع من نفس ال element موجود فيها
+
+333
+00:34:57,960 --> 00:35:02,680
+طيب هذا النقطة الأولى بسيطة نيجي للنقطة الثانية
+
+334
+00:35:03,090 --> 00:35:06,970
+النقطة الثانية بيقول ال A H بده يساوي ال H if and
+
+335
+00:35:06,970 --> 00:35:12,210
+only if ال A belongs to H بنقوله كويس يبقى البرهان
+
+336
+00:35:12,210 --> 00:35:16,890
+بده يصير في اتجاهين لإنه if and only if يبقى
+
+337
+00:35:16,890 --> 00:35:22,210
+الاتجاه الأول بداجي أقوله assume ال A H بده يساوي
+
+338
+00:35:22,210 --> 00:35:28,820
+ال H itself ايش بدي أثباته؟الـ A موجود في الـ H
+
+339
+00:35:28,820 --> 00:35:37,900
+الـ A لو جت من النقطة الأولى from oneالـ A موجود
+
+340
+00:35:37,900 --> 00:35:44,680
+في مين؟ في الـ H طيب و الـ H ايش تساوي؟ يبقى الـ A
+
+341
+00:35:44,680 --> 00:35:49,140
+موجودة في الـ H يبقى هذا بدي يعطيني ان الـ A
+
+342
+00:35:49,140 --> 00:35:59,040
+موجودة في الـ H ليش since H او الـ H بدها ساوي H
+
+343
+00:35:59,040 --> 00:36:03,540
+بدها موجود هنا اذا موجود هنا هذا الاتجاه الأولنجي
+
+344
+00:36:03,540 --> 00:36:11,560
+لاتجاه الثاني conversely assume
+
+345
+00:36:11,560 --> 00:36:21,640
+افترض ان ال a موجود في ال Hماذا نريد أن نثبت؟ نريد
+
+346
+00:36:21,640 --> 00:36:27,920
+أن نثبت أن الـ H هي subgroup من الـ H تساوي H
+
+347
+00:36:27,920 --> 00:36:31,780
+itself طبعا في المبادئ الرياضية دخلنا لما بدأ أثبت
+
+348
+00:36:31,780 --> 00:36:35,520
+أنه two sets are equal باخد element هنا بثبته في
+
+349
+00:36:35,520 --> 00:36:38,400
+التاني بيصير الأولى أعصاب ساتمة التانية هو العملية
+
+350
+00:36:38,400 --> 00:36:42,220
+العكسية بنفس الطريقة بدأ أثبت أنه التانية أعصاب
+
+351
+00:36:42,220 --> 00:36:47,660
+ساتمة الأولى بيحدث تساوي يبقى الخطوة الأولى بدأ
+
+352
+00:36:47,660 --> 00:36:54,300
+أحاول أثبت أنهالـ A H subset من من؟ subset من ال H
+
+353
+00:36:54,300 --> 00:37:05,710
+طيب ال N from one ال A موجودة في ال A Hمظبوط؟ وانا
+
+354
+00:37:05,710 --> 00:37:10,790
+عند ايش؟ وانا عند ال A H انا فرضها بتسوى 100 .. لا
+
+355
+00:37:10,790 --> 00:37:12,310
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+356
+00:37:12,310 --> 00:37:12,590
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+357
+00:37:12,590 --> 00:37:14,650
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+358
+00:37:14,650 --> 00:37:15,290
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+359
+00:37:15,290 --> 00:37:15,490
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+360
+00:37:15,490 --> 00:37:15,490
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+361
+00:37:15,490 --> 00:37:15,590
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+362
+00:37:15,590 --> 00:37:21,630
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+363
+00:37:21,630 --> 00:37:21,630
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+364
+00:37:21,630 --> 00:37:21,630
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+365
+00:37:21,630 --> 00:37:21,690
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+366
+00:37:21,690 --> 00:37:31,710
+لا .. لا ..الان ال a كذلك from واحد موجودة في مين؟
+
+367
+00:37:31,710 --> 00:37:37,730
+في ال a H و ال a موجودة في H يبقى معنا هذا الكلام
+
+368
+00:37:37,730 --> 00:37:46,670
+ان ال a H صبست من مين؟ صبست من ال Hيبقى أنا عندي A
+
+369
+00:37:46,670 --> 00:37:52,370
+موجودة في ال H من الواحد ومن الفرض تبعي A موجودة
+
+370
+00:37:52,370 --> 00:37:57,870
+في H إذا ال A H subset من من؟ subset من ال H هذا
+
+371
+00:37:57,870 --> 00:38:03,310
+الاتجاه السهل الاتجاه الصعب الثاني يبقى هنا on the
+
+372
+00:38:03,310 --> 00:38:08,830
+other hand on the other hand
+
+373
+00:38:13,180 --> 00:38:19,160
+الان لما اقول يا شباب ان ال a موجودة في H هذا معطى
+
+374
+00:38:19,160 --> 00:38:24,540
+طب H sub group ولا لا يبقى معكوس ال element هذا
+
+375
+00:38:24,540 --> 00:38:30,060
+موجود صح ولا لا يبقى then
+
+376
+00:38:31,810 --> 00:38:38,330
+اللي هو الـ A inverse موجود في H طيب بدا أجي أقوله
+
+377
+00:38:38,330 --> 00:38:44,710
+خدلي X موجود في H أنا بدي أثبت إن H subset من مين؟
+
+378
+00:38:44,710 --> 00:38:50,670
+من الـ H يبقى خت element موجود في وين؟ في الـ H
+
+379
+00:38:50,670 --> 00:38:51,650
+then
+
+380
+00:38:54,840 --> 00:39:00,800
+then هلحين هذا موجود في H و هذا موجود في H إذا حصل
+
+381
+00:39:00,800 --> 00:39:08,760
+ضربهم موجود في H يبقى then A inverse X موجود وين؟
+
+382
+00:39:08,760 --> 00:39:18,000
+موجود في H هذا معناه إن ال A inverse X بده يساوي H
+
+383
+00:39:18,000 --> 00:39:29,930
+for somefor some h اللي موجودة في h مادام هذا في h
+
+384
+00:39:29,930 --> 00:39:36,170
+اذا هيساوي ال h طيب هذا معناه انا بدي ال x يبقى
+
+385
+00:39:36,170 --> 00:39:42,190
+هذا معناه ان ال x تساوي لو ضربت الطرفين في العنصر
+
+386
+00:39:42,190 --> 00:39:48,630
+a يبقى بضل على شمال x وهنا بجينا mean a h هذه h
+
+387
+00:39:48,630 --> 00:39:55,960
+وين موجودة؟موجودة في اله يبقى انا فرض x في h لجيت
+
+388
+00:39:55,960 --> 00:40:02,600
+ال x موجود وان في اله يبقى هذا معناه ان اله هذه ال
+
+389
+00:40:02,600 --> 00:40:09,540
+subset من اله اطلع لي سميلي هذه star وسميلي هذه
+
+390
+00:40:09,540 --> 00:40:13,840
+double star من التنتين مع بعض from
+
+391
+00:40:28,680 --> 00:40:33,490
+الشكل اللي عندنا هناطيب هذه هي النقطة الثانية دير
+
+392
+00:40:33,490 --> 00:40:37,970
+بالك هتلزمنا كتير خلال البراهين بده اروح للنقطة
+
+393
+00:40:37,970 --> 00:40:44,570
+التالتة النقطة التالتة بيقول ال a h ال a ال a h
+
+394
+00:40:44,570 --> 00:40:50,510
+بده يساوي ال ال b h f عنده اللي f ال a موجودة في b
+
+395
+00:40:50,510 --> 00:40:57,670
+h يبقى بداجي اقوله assume افترض ان ال a h بده
+
+396
+00:40:57,670 --> 00:41:03,560
+يساوي b hبدي احاول اثبت ان ال a موجودة في ال بي
+
+397
+00:41:03,560 --> 00:41:10,520
+اتش الان يا شباب from واحد ال a موجودة في ال اتش
+
+398
+00:41:10,520 --> 00:41:17,260
+صح؟ و اللي عند ال a اتش بدي يسوي ال بي اتش يبقى
+
+399
+00:41:17,260 --> 00:41:22,040
+هذا معناه ان ال a موجودة في ال بي اتش و هو المطلوب
+
+400
+00:41:23,190 --> 00:41:29,710
+مظبوط؟ طيب الاتجاه الثاني يبقى هنا أخدنا الاتجابات
+
+401
+00:41:29,710 --> 00:41:36,130
+دي اجي اقوله هنا و الرقاهي رقم تلاتة conversely
+
+402
+00:41:39,490 --> 00:41:48,910
+conversely ا assume افترض ان ال a موجودة في ال bh
+
+403
+00:41:48,910 --> 00:41:55,430
+بده احاول اثبت ان ال aH بده سوى مين بيه ال aH
+
+404
+00:41:55,430 --> 00:42:05,210
+موجودة في بي كابتل H تمامطيب assume كذا then ال a
+
+405
+00:42:05,210 --> 00:42:13,490
+هذه بدها تساوي bh for some h اللي belongs to man
+
+406
+00:42:13,490 --> 00:42:21,250
+لل h طب لو ضربت الطرفين في hيبقى باجي بقوله هذا
+
+407
+00:42:21,250 --> 00:42:29,790
+معناه ان ال a capital H بده يساوي bh capital H هذا
+
+408
+00:42:29,790 --> 00:42:37,130
+معناه ان ال aH بده يساوي bh في H من خاصية ال
+
+409
+00:42:37,130 --> 00:42:44,700
+associativityهذا معناه ان الـ a h بده يساوي بي ال
+
+410
+00:42:44,700 --> 00:42:49,700
+element h لما يكون في h و تضربه في h بتظهر زي مهي
+
+411
+00:42:49,700 --> 00:42:55,300
+h كابتن يبقى هدف بيه اتش عزيزي و هو المطلوب خلصنا
+
+412
+00:42:55,300 --> 00:43:00,820
+الاتجاهين طيب الان بدنا نجي لنقطة رابعالنقطة
+
+413
+00:43:00,820 --> 00:43:05,540
+الرابعة بيقول يا إما ال two left cosets بدوا
+
+414
+00:43:05,540 --> 00:43:09,560
+يتساووا يا إما ال intersection تبعهم بدوا يساووا
+
+415
+00:43:09,560 --> 00:43:15,480
+ماين فاي إذا لو نفيت واحدة منهم بدي أثبت إيه تانية
+
+416
+00:43:15,480 --> 00:43:22,040
+يبقى بالداجة أقوله أسيوم افترض ان ال a h
+
+417
+00:43:22,040 --> 00:43:30,160
+intersection ب a h لا يساوي الفايلا يساو الفاى
+
+418
+00:43:30,160 --> 00:43:36,080
+معناته في عناصر مشتركة ما بين الاتنين يبقى هنا
+
+419
+00:43:36,080 --> 00:43:41,540
+بداية اقوله افترض ان ال X موجود في ال A H
+
+420
+00:43:41,540 --> 00:43:47,660
+intersection B H معناه هذا الكلام ان ال X موجود في
+
+421
+00:43:47,660 --> 00:43:55,840
+ال A H و ال X موجود في ال B Hمعنى هذا الكلام ان ال
+
+422
+00:43:55,840 --> 00:44:07,320
+X بده يساوي A H1 مثلا and ال X بده يساوي B H2 مش
+
+423
+00:44:07,320 --> 00:44:12,290
+هنا ميز فيه ما بينهم مش نفس ال elementطب كويس مدام
+
+424
+00:44:12,290 --> 00:44:17,710
+هذا بيساوي هذا إذا الاتنين are equal يبقى لإن
+
+425
+00:44:17,710 --> 00:44:26,170
+الطرف الشمال كله X يبقى A H1 بده يساوي ال B H2طيب
+
+426
+00:44:26,170 --> 00:44:33,570
+هذا لو جيت قولت A H 1 بضربته في H بديه ساوي ال B H
+
+427
+00:44:33,570 --> 00:44:40,190
+2 كله في H من خاصية ال associativity يبقى ال A في
+
+428
+00:44:40,190 --> 00:44:48,330
+ال H 1 H بديه ساوي B في ال H 2 H يبقى هذا الكلام
+
+429
+00:44:48,330 --> 00:44:54,770
+بديه يعطينا انه A H بديه ساوي من BH وهو المطلوب
+
+430
+00:44:55,410 --> 00:45:00,810
+يبقى هنا فيت واحدة و أثبت له main الثانية طيب بدنا
+
+431
+00:45:00,810 --> 00:45:06,610
+نيجي لرقم خمسة رقم خمسة بيقول ايه اتش بيبقى طيب
+
+432
+00:45:06,610 --> 00:45:13,630
+هنا ال a h بده يسوى b h f and only f
+
+433
+00:45:16,890 --> 00:45:23,450
+ما هو رأيك لو ضربت الطرفين في a inverse يبقى عندي
+
+434
+00:45:23,450 --> 00:45:31,270
+a inverse في الاح بده يساوي ال a inverse في ال bh
+
+435
+00:45:32,250 --> 00:45:37,870
+من خاصية ال associative طبعا هذا if and only if ال
+
+436
+00:45:37,870 --> 00:45:47,310
+a inverse a في ال h بده ساوي a inverse b في ال h
+
+437
+00:45:47,310 --> 00:45:51,970
+الشكل اللي عندنا هناطيب هذا بيعطينا مين؟ ال
+
+438
+00:45:51,970 --> 00:45:56,630
+identity لما اضربه في H بدي يطلع مين؟ بدي يطلع ال
+
+439
+00:45:56,630 --> 00:46:03,970
+H itself يبقى if and only if if and only if ال H
+
+440
+00:46:03,970 --> 00:46:13,300
+هذه بدها تساوي A inverse B في ال H فلسنايبقى هنا
+
+441
+00:46:13,300 --> 00:46:20,880
+إيش بيقولي هذا يتساوى إذا كان لجيت ال A inverse B
+
+442
+00:46:20,880 --> 00:46:27,240
+في H بده يساوي ال H لو رجعت للخاصية الرقم اتنين
+
+443
+00:46:27,240 --> 00:46:36,280
+يبقى F and قولي F ال A inverse B هذا موجود وين؟
+
+444
+00:46:36,300 --> 00:46:43,560
+موجود في الـ H وهذا من ال property اتنين بالشكل
+
+445
+00:46:43,560 --> 00:46:53,810
+اللي عندنا هذاطيب ستة هه ستة بدك اتعرف function ما
+
+446
+00:46:53,810 --> 00:46:58,910
+بين الاتنين و الناس بينها one to one and unto يبقى
+
+447
+00:46:58,910 --> 00:47:09,010
+بداجي اقوله define a function phi من ال a h الى ال
+
+448
+00:47:09,010 --> 00:47:19,260
+b h byfive of a h بده يساوي بي اتش واثبتلي انها
+
+449
+00:47:19,260 --> 00:47:23,560
+one to one and unto اذا اثبتناها one to one and
+
+450
+00:47:23,560 --> 00:47:29,640
+unto يحصلوا التساوي بصير ال order للأولى بده يساوي
+
+451
+00:47:29,640 --> 00:47:35,800
+من ال order للثانية بنكمل المرة الجاية ان شاء الله
+
+452
+00:47:35,800 --> 00:47:36,300
+و تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..548fb0991b35217059cc643de7431b582cd4eba8
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.json
@@ -0,0 +1 @@
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"end": 267.37, "word": " المرة", "probability": 0.75439453125}, {"start": 267.37, "end": 267.51, "word": " اللي", "probability": 0.7294921875}, {"start": 267.51, "end": 267.69, "word": " فيها", "probability": 0.942626953125}, {"start": 267.69, "end": 268.41, "word": " تنظرية", "probability": 0.91650390625}, {"start": 268.41, "end": 269.31, "word": " أثبتنا", "probability": 0.96796875}, {"start": 269.31, "end": 269.51, "word": " إن", "probability": 0.47021484375}, {"start": 269.51, "end": 270.51, "word": " الـAutomorphism", "probability": 0.72119140625}, {"start": 270.51, "end": 272.23, "word": " لـZN", "probability": 0.61932373046875}, {"start": 272.23, "end": 273.43, "word": " isomorphic", "probability": 0.79541015625}, {"start": 273.43, "end": 274.21, "word": " لـUN،", "probability": 0.67083740234375}, {"start": 274.21, "end": 275.45, "word": " مظبوط؟", "probability": 0.8792317708333334}, {"start": 275.45, "end": 276.19, "word": " وبرأنها", "probability": 0.758984375}, {"start": 276.19, "end": 276.97, "word": " أنا", "probability": 0.6015625}, {"start": 276.97, "end": 277.29, "word": " بدي", "probability": 0.6553955078125}, {"start": 277.29, "end": 278.47, "word": " الـAutomorphism", "probability": 0.86494140625}, {"start": 278.47, "end": 279.05, "word": " لـZ", "probability": 0.955078125}, {"start": 279.05, "end": 280.07, "word": " isomorphic", "probability": 0.892578125}, {"start": 280.07, "end": 280.63, "word": " لمين؟", "probability": 0.77587890625}, {"start": 280.63, "end": 280.89, "word": " بدي", "probability": 0.940673828125}, {"start": 280.89, "end": 281.23, "word": " فيها", "probability": 0.990234375}, {"start": 281.23, "end": 282.15, "word": " عنصرين", "probability": 0.9775390625}, {"start": 282.15, "end": 284.11, "word": " وسمعت", "probability": 0.7994791666666666}, {"start": 284.11, "end": 284.53, "word": " أنت", "probability": 0.729248046875}, {"start": 284.53, "end": 284.97, "word": " قبل", "probability": 0.9814453125}, {"start": 284.97, "end": 285.49, "word": " قليل،", "probability": 0.79278564453125}, {"start": 285.49, "end": 286.53, "word": " مين؟", "probability": 0.8875325520833334}, {"start": 286.53, "end": 287.25, "word": " Z2", "probability": 0.7392578125}], "temperature": 1.0}, {"id": 12, "seek": 30205, "start": 287.75, "end": 302.05, "text": "يبقى هنا اتومورفزم هذه زيادة لزد ايزو مورفك فقط لزد تو فقط لغير طب هذا كان السؤال الثاني", "tokens": [1829, 3555, 4587, 7578, 34105, 1975, 2655, 20498, 13063, 5172, 11622, 2304, 29538, 30767, 1829, 18513, 3660, 5296, 11622, 3215, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 6156, 47432, 5296, 11622, 3215, 33427, 6156, 47432, 5296, 17082, 13546, 23032, 3555, 23758, 25961, 21136, 33604, 6027, 6024, 104, 7649, 1829], "avg_logprob": -0.21231617121135488, "compression_ratio": 1.485981308411215, "no_speech_prob": 0.0, "words": [{"start": 287.75, "end": 288.59, "word": "يبقى", "probability": 0.931640625}, {"start": 288.59, "end": 289.09, "word": " هنا", "probability": 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{"start": 300.09, "end": 300.33, "word": " هذا", "probability": 0.92578125}, {"start": 300.33, "end": 300.69, "word": " كان", "probability": 0.99169921875}, {"start": 300.69, "end": 301.31, "word": " السؤال", "probability": 0.9807942708333334}, {"start": 301.31, "end": 302.05, "word": " الثاني", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 13, "seek": 32335, "start": 304.27, "end": 323.35, "text": "السؤال اللى بعد السؤال الرابع بيقول لي ان U8 ليست isomorphic ل U10 يبقى السؤال الرابع U8 is not isomorphic ل U10 بدنا نثبت صحة هذا الكلام", "tokens": [6027, 3794, 33604, 6027, 13672, 7578, 39182, 21136, 33604, 6027, 34892, 16758, 3615, 4724, 1829, 39648, 32239, 16472, 624, 23, 32239, 14851, 307, 32702, 299, 5296, 624, 3279, 7251, 3555, 4587, 7578, 21136, 33604, 6027, 34892, 16758, 3615, 624, 23, 307, 406, 307, 32702, 299, 5296, 624, 3279, 47525, 8315, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 2423, 28820, 10943], "avg_logprob": -0.1246219830166909, "compression_ratio": 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"word": " ل", "probability": 0.884765625}, {"start": 311.29, "end": 312.21, "word": " U10", "probability": 0.85107421875}, {"start": 312.21, "end": 313.43, "word": " يبقى", "probability": 0.91943359375}, {"start": 313.43, "end": 314.01, "word": " السؤال", "probability": 0.99658203125}, {"start": 314.01, "end": 314.85, "word": " الرابع", "probability": 0.9890950520833334}, {"start": 314.85, "end": 316.11, "word": " U8", "probability": 0.94140625}, {"start": 316.11, "end": 317.15, "word": " is", "probability": 0.8916015625}, {"start": 317.15, "end": 317.77, "word": " not", "probability": 0.9697265625}, {"start": 317.77, "end": 319.69, "word": " isomorphic", "probability": 0.9485677083333334}, {"start": 319.69, "end": 319.95, "word": " ل", "probability": 0.97705078125}, {"start": 319.95, "end": 320.73, "word": " U10", "probability": 0.952392578125}, {"start": 320.73, "end": 321.25, "word": " بدنا", "probability": 0.779296875}, {"start": 321.25, "end": 321.73, "word": " نثبت", 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و", "probability": 0.94482421875}, {"start": 338.35, "end": 339.49, "word": " تلاتة", "probability": 0.9622802734375}, {"start": 339.49, "end": 339.87, "word": " و", "probability": 0.990234375}, {"start": 339.87, "end": 340.73, "word": " سبعة", "probability": 0.8722330729166666}, {"start": 340.73, "end": 341.11, "word": " و", "probability": 0.9384765625}, {"start": 341.11, "end": 341.59, "word": " تسعة", "probability": 0.9676106770833334}], "temperature": 1.0}, {"id": 15, "seek": 36136, "start": 343.84, "end": 361.36, "text": "مش هنثبت ان اتنين ليسوا ايزو مورفك بدي اجيب counter example يعني شغلة متحققة في احدى ال groups و غير متحققة في ال group التاني لو جيت ليه تمانية هل التلاتة هذا generator؟", "tokens": [2304, 8592, 8032, 1863, 12984, 3555, 2655, 16472, 1975, 2655, 1863, 9957, 32239, 3794, 14407, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 4724, 16254, 1975, 7435, 1829, 3555, 5682, 1365, 37495, 22653, 13412, 17082, 37977, 44650, 5016, 4587, 28671, 8978, 1975, 24401, 7578, 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{"start": 397.64, "end": 398.8, "word": " تلاتة", "probability": 0.972900390625}, {"start": 398.8, "end": 399.6, "word": " تكيب", "probability": 0.7939453125}, {"start": 399.6, "end": 401.0, "word": " بسبعة", "probability": 0.94970703125}, {"start": 401.0, "end": 401.94, "word": " يبقى", "probability": 0.93408203125}, {"start": 401.94, "end": 402.44, "word": " جابة", "probability": 0.8479817708333334}, {"start": 402.44, "end": 402.8, "word": " كل", "probability": 0.87060546875}, {"start": 402.8, "end": 403.42, "word": " العناصر", "probability": 0.80615234375}, {"start": 403.42, "end": 403.94, "word": " تلاتة", "probability": 0.96728515625}, {"start": 403.94, "end": 404.04, "word": " و", "probability": 0.9609375}, {"start": 404.04, "end": 404.16, "word": " اص", "probability": 0.856689453125}, {"start": 404.16, "end": 404.52, "word": " اربع", "probability": 0.7962239583333334}, {"start": 404.52, "end": 405.26, "word": " ليهمين", "probability": 0.7154947916666666}, {"start": 405.26, 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461.44, "end": 462.16, "word": " وبالتالي", "probability": 0.9236328125}], "temperature": 1.0}, {"id": 20, "seek": 47859, "start": 462.49, "end": 478.59, "text": "مافيش isomorphism ما بين الاتنين هذا كان السؤال الرابع و بعدين السؤال السادس G isomorphic ل H و H isomorphic ل K السؤال السادس", "tokens": [15042, 41185, 8592, 307, 32702, 1434, 19446, 49374, 2423, 9307, 1863, 9957, 23758, 25961, 21136, 33604, 6027, 34892, 16758, 3615, 4032, 39182, 9957, 21136, 33604, 6027, 21136, 18513, 3794, 460, 307, 32702, 299, 5296, 389, 4032, 389, 307, 32702, 299, 5296, 591, 21136, 33604, 6027, 21136, 18513, 3794], "avg_logprob": -0.13911033649833834, "compression_ratio": 1.7017543859649122, "no_speech_prob": 0.0, "words": [{"start": 462.49, "end": 463.15, "word": "مافيش", "probability": 0.95654296875}, {"start": 463.15, "end": 464.19, "word": " isomorphism", "probability": 0.91455078125}, {"start": 464.19, "end": 464.45, "word": " ما", "probability": 0.8046875}, {"start": 464.45, "end": 464.81, "word": " بين", "probability": 0.96142578125}, {"start": 464.81, "end": 465.59, "word": " الاتنين", "probability": 0.7640380859375}, {"start": 465.59, "end": 466.29, "word": " هذا", "probability": 0.5771484375}, {"start": 466.29, "end": 466.67, "word": " كان", "probability": 0.96826171875}, {"start": 466.67, "end": 467.23, "word": " السؤال", "probability": 0.9908854166666666}, {"start": 467.23, "end": 467.89, "word": " الرابع", "probability": 0.9933268229166666}, {"start": 467.89, "end": 468.01, "word": " و", "probability": 0.52978515625}, {"start": 468.01, "end": 468.35, "word": " بعدين", "probability": 0.785888671875}, {"start": 468.35, "end": 469.53, "word": " السؤال", "probability": 0.9886067708333334}, {"start": 469.53, "end": 470.41, "word": " السادس", "probability": 0.96923828125}, {"start": 470.41, "end": 472.21, "word": " G", "probability": 0.31201171875}, {"start": 472.21, "end": 473.33, "word": " isomorphic", "probability": 0.9226888020833334}, {"start": 473.33, "end": 473.47, "word": " ل", "probability": 0.87939453125}, {"start": 473.47, "end": 473.75, "word": " H", "probability": 0.54296875}, {"start": 473.75, "end": 473.97, "word": " و", "probability": 0.943359375}, {"start": 473.97, "end": 474.19, "word": " H", "probability": 0.85009765625}, {"start": 474.19, "end": 475.39, "word": " isomorphic", "probability": 0.9498697916666666}, {"start": 475.39, "end": 475.69, "word": " ل", "probability": 0.98193359375}, {"start": 475.69, "end": 476.21, "word": " K", "probability": 0.93017578125}, {"start": 476.21, "end": 477.71, "word": " السؤال", "probability": 0.9689127604166666}, {"start": 477.71, "end": 478.59, "word": " السادس", "probability": 0.9811197916666666}], "temperature": 1.0}, {"id": 21, "seek": 49339, "start": 479.75, "end": 493.39, "text": "عندك G isomorphic ل H و ال H isomorphic ل K بدنا نثبت ان ال G isomorphic لمن A ل K", "tokens": [3615, 41260, 4117, 460, 307, 32702, 299, 5296, 389, 4032, 2423, 389, 307, 32702, 299, 5296, 591, 47525, 8315, 8717, 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{"start": 486.21, "end": 486.71, "word": " K", "probability": 0.916015625}, {"start": 486.71, "end": 487.47, "word": " بدنا", "probability": 0.79296875}, {"start": 487.47, "end": 488.37, "word": " نثبت", "probability": 0.99462890625}, {"start": 488.37, "end": 488.79, "word": " ان", "probability": 0.6162109375}, {"start": 488.79, "end": 489.19, "word": " ال", "probability": 0.65283203125}, {"start": 489.19, "end": 489.63, "word": " G", "probability": 0.92333984375}, {"start": 489.63, "end": 491.23, "word": " isomorphic", "probability": 0.87841796875}, {"start": 491.23, "end": 492.31, "word": " لمن", "probability": 0.396484375}, {"start": 492.31, "end": 492.69, "word": " A", "probability": 0.80810546875}, {"start": 492.69, "end": 492.87, "word": " ل", "probability": 0.9501953125}, {"start": 492.87, "end": 493.39, "word": " K", "probability": 0.81201171875}], "temperature": 1.0}, {"id": 22, "seek": 51754, "start": 494.18, "end": 517.54, "text": "وهذه تسميناها الـtransitive property خاصية النقل أو بقنا نقول ال relation reflexive وtransitive and symmetric هذه هي حكاية لـtransitive لو كان الـG عيزومورفق لـH وH نفسها عيزومورفق لـK يبقى الـG عيزومورفق لمين؟ لـK", "tokens": [2407, 3224, 24192, 6055, 38251, 1829, 8315, 11296, 2423, 39184, 24999, 2187, 4707, 16490, 33546, 10632, 28239, 4587, 1211, 34051, 4724, 4587, 8315, 8717, 39648, 2423, 9721, 23802, 488, 4032, 24999, 2187, 293, 32330, 29538, 39896, 11331, 4117, 995, 10632, 5296, 39184, 24999, 2187, 45164, 25961, 2423, 39184, 38, 6225, 1829, 11622, 20498, 13063, 5172, 4587, 5296, 39184, 39, 4032, 39, 8717, 36178, 11296, 6225, 1829, 11622, 20498, 13063, 5172, 4587, 5296, 39184, 42, 7251, 3555, 4587, 7578, 2423, 39184, 38, 6225, 1829, 11622, 20498, 13063, 5172, 4587, 32767, 9957, 22807, 5296, 39184, 42], "avg_logprob": -0.28125001254834625, "compression_ratio": 1.6649484536082475, "no_speech_prob": 0.0, "words": [{"start": 494.18, "end": 494.8, "word": "وهذه", "probability": 0.5611165364583334}, {"start": 494.8, "end": 496.02, "word": " تسميناها", "probability": 0.6383544921875}, {"start": 496.02, "end": 497.18, "word": " الـtransitive", "probability": 0.486541748046875}, {"start": 497.18, "end": 497.92, "word": " property", "probability": 0.8671875}, {"start": 497.92, "end": 498.72, "word": " خاصية", "probability": 0.8850911458333334}, {"start": 498.72, "end": 499.34, "word": " النقل", "probability": 0.9607747395833334}, {"start": 499.34, "end": 500.18, "word": " أو", "probability": 0.68505859375}, {"start": 500.18, "end": 500.9, "word": " بقنا", "probability": 0.6195475260416666}, {"start": 500.9, "end": 501.32, "word": " نقول", "probability": 0.9462890625}, {"start": 501.32, "end": 501.56, "word": " ال", "probability": 0.70703125}, {"start": 501.56, "end": 502.04, "word": " relation", "probability": 0.796875}, {"start": 502.04, "end": 503.14, "word": " reflexive", "probability": 0.984375}, {"start": 503.14, "end": 504.1, "word": " وtransitive", "probability": 0.79541015625}, {"start": 504.1, "end": 504.5, "word": " and", "probability": 0.88525390625}, {"start": 504.5, "end": 505.1, "word": " symmetric", "probability": 0.75732421875}, {"start": 505.1, "end": 505.86, "word": " هذه", "probability": 0.419921875}, {"start": 505.86, "end": 505.98, "word": " هي", "probability": 0.4326171875}, {"start": 505.98, "end": 506.4, "word": " حكاية", "probability": 0.80963134765625}, {"start": 506.4, "end": 507.3, "word": " لـtransitive", "probability": 0.689697265625}, {"start": 507.3, "end": 507.98, "word": " لو", "probability": 0.693359375}, {"start": 507.98, "end": 508.32, "word": " كان", "probability": 0.95849609375}, {"start": 508.32, "end": 508.66, "word": " الـG", "probability": 0.7906901041666666}, {"start": 508.66, "end": 509.62, "word": " عيزومورفق", "probability": 0.6207449776785714}, {"start": 509.62, "end": 510.12, "word": " لـH", "probability": 0.8938802083333334}, {"start": 510.12, "end": 510.78, "word": " وH", "probability": 0.617431640625}, {"start": 510.78, "end": 511.28, "word": " نفسها", "probability": 0.7664388020833334}, {"start": 511.28, "end": 512.04, "word": " عيزومورفق", "probability": 0.9846540178571429}, {"start": 512.04, "end": 512.7, "word": " لـK", "probability": 0.8263346354166666}, {"start": 512.7, "end": 514.06, "word": " يبقى", "probability": 0.9635009765625}, {"start": 514.06, "end": 514.62, "word": " الـG", "probability": 0.9228515625}, {"start": 514.62, "end": 515.6, "word": " عيزومورفق", "probability": 0.9875139508928571}, {"start": 515.6, "end": 516.46, "word": " لمين؟", "probability": 0.6759440104166666}, {"start": 516.46, "end": 517.54, "word": " لـK", "probability": 0.9124348958333334}], "temperature": 1.0}, {"id": 23, "seek": 54754, "start": 518.16, "end": 547.54, "text": "يبقى بداجي اقول solution معناته بدنا نفترض assume ان في of واحد من g إلى h is an isomorphism and وفي نفس الوقت في اتنين من ال h إلى k is an isomorphism", "tokens": [1829, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 3827, 20449, 8315, 47395, 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547.54, "word": " isomorphism", "probability": 0.9656575520833334}], "temperature": 1.0}, {"id": 24, "seek": 57671, "start": 550.11, "end": 576.71, "text": "بدي أحاول أثبت أنه في عندي function من G إلى K تالي هذه ملاتبج isomorphism مدام هذا isomorphism و هذا isomorphism معناته أن الـPhi 1 و Phi 2 هم 1 to 1 and on 2 كويس", "tokens": [3555, 16254, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 14739, 3224, 8978, 18871, 16254, 2445, 9154, 460, 30731, 591, 6055, 6027, 1829, 29538, 3714, 1211, 9307, 3555, 7435, 307, 32702, 1434, 3714, 3215, 10943, 23758, 307, 32702, 1434, 4032, 23758, 307, 32702, 1434, 20449, 8315, 47395, 14739, 2423, 39184, 47, 4954, 502, 4032, 41435, 568, 8032, 2304, 502, 281, 502, 293, 322, 568, 9122, 45865, 3794], "avg_logprob": -0.4014246332294801, "compression_ratio": 1.4233128834355828, "no_speech_prob": 0.0, "words": [{"start": 550.11, "end": 550.47, "word": "بدي", "probability": 0.149383544921875}, {"start": 550.47, "end": 550.91, "word": " أحاول", "probability": 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"end": 558.69, "word": " isomorphism", "probability": 0.75341796875}, {"start": 558.69, "end": 559.75, "word": " مدام", "probability": 0.6953125}, {"start": 559.75, "end": 560.05, "word": " هذا", "probability": 0.6552734375}, {"start": 560.05, "end": 561.09, "word": " isomorphism", "probability": 0.9138997395833334}, {"start": 561.09, "end": 561.23, "word": " و", "probability": 0.5859375}, {"start": 561.23, "end": 561.57, "word": " هذا", "probability": 0.748046875}, {"start": 561.57, "end": 562.89, "word": " isomorphism", "probability": 0.9109700520833334}, {"start": 562.89, "end": 564.19, "word": " معناته", "probability": 0.9573567708333334}, {"start": 564.19, "end": 564.61, "word": " أن", "probability": 0.60302734375}, {"start": 564.61, "end": 565.35, "word": " الـPhi", "probability": 0.500946044921875}, {"start": 565.35, "end": 565.83, "word": " 1", "probability": 0.62744140625}, {"start": 565.83, "end": 566.51, "word": " و", "probability": 0.76708984375}, {"start": 566.51, "end": 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0.9017333984375}, {"start": 762.7, "end": 763.28, "word": " في", "probability": 0.91357421875}, {"start": 763.28, "end": 763.84, "word": " two", "probability": 0.95458984375}, {"start": 763.84, "end": 764.64, "word": " في", "probability": 0.9580078125}, {"start": 764.64, "end": 765.18, "word": " one", "probability": 0.9501953125}, {"start": 765.18, "end": 766.04, "word": " of", "probability": 0.9775390625}, {"start": 766.04, "end": 766.48, "word": " y", "probability": 0.939453125}, {"start": 766.48, "end": 767.26, "word": " يبقى", "probability": 0.986328125}, {"start": 767.26, "end": 767.76, "word": " صارت", "probability": 0.8094075520833334}, {"start": 767.76, "end": 769.16, "word": " isomorphism", "probability": 0.7416178385416666}, {"start": 769.16, "end": 769.98, "word": " يبقى", "probability": 0.9715576171875}, {"start": 769.98, "end": 770.38, "word": " هذا", "probability": 0.92578125}, {"start": 770.38, "end": 770.82, "word": " بده", "probability": 0.67529296875}, {"start": 770.82, "end": 771.6, "word": " يعطينا", "probability": 0.9583740234375}], "temperature": 1.0}, {"id": 33, "seek": 79988, "start": 771.84, "end": 799.88, "text": "إن الجي إيزو مورفك لكيه وهو المطلوب هو هذا اللي بيسميه في الرياضيات خاصية transit أنا عندي isomorphism من ال group الأولى إلى التانية وعندي isomorphism من التانية إلى التالتة إذا بصير عندي isomorphism من الأولى إلى الثالثة هذا كان سؤال ستة سؤال سبعة", "tokens": [28814, 1863, 25724, 1829, 11933, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 4117, 1829, 3224, 37037, 2407, 9673, 9566, 1211, 37746, 31439, 23758, 13672, 1829, 4724, 1829, 38251, 1829, 3224, 8978, 2423, 16572, 46958, 1829, 9307, 16490, 33546, 10632, 17976, 41850, 18871, 16254, 307, 32702, 1434, 9154, 2423, 1594, 16247, 12610, 7578, 30731, 16712, 7649, 10632, 4032, 3615, 1863, 16254, 307, 32702, 1434, 9154, 16712, 7649, 10632, 30731, 16712, 6027, 2655, 3660, 11933, 15730, 4724, 9381, 13546, 18871, 16254, 307, 32702, 1434, 9154, 16247, 12610, 7578, 30731, 2423, 12984, 6027, 12984, 3660, 23758, 25961, 8608, 33604, 6027, 8608, 2655, 3660, 8608, 33604, 6027, 8608, 3555, 27884], "avg_logprob": -0.21079282117662607, "compression_ratio": 2.019704433497537, "no_speech_prob": 0.0, "words": [{"start": 771.84, "end": 772.42, "word": "إن", "probability": 0.690673828125}, {"start": 772.42, "end": 773.24, "word": " الجي", "probability": 0.5538330078125}, {"start": 773.24, "end": 774.4, "word": " إيزو", "probability": 0.6728515625}, {"start": 774.4, "end": 775.18, "word": " مورفك", "probability": 0.8170166015625}, {"start": 775.18, "end": 776.46, "word": " لكيه", "probability": 0.6541748046875}, {"start": 776.46, "end": 777.02, "word": " وهو", "probability": 0.762939453125}, {"start": 777.02, "end": 777.82, "word": " المطلوب", "probability": 0.987060546875}, {"start": 777.82, "end": 778.48, "word": " هو", "probability": 0.397705078125}, {"start": 778.48, "end": 778.72, "word": " هذا", "probability": 0.6552734375}, {"start": 778.72, "end": 778.82, "word": " اللي", "probability": 0.7236328125}, {"start": 778.82, "end": 779.28, "word": " بيسميه", "probability": 0.84892578125}, {"start": 779.28, "end": 779.44, "word": " في", "probability": 0.9248046875}, {"start": 779.44, "end": 780.02, "word": " الرياضيات", "probability": 0.92841796875}, {"start": 780.02, "end": 781.0, "word": " خاصية", "probability": 0.94482421875}, {"start": 781.0, "end": 781.74, "word": " transit", "probability": 0.2421875}, {"start": 781.74, "end": 782.96, "word": " أنا", "probability": 0.60595703125}, {"start": 782.96, "end": 783.52, "word": " عندي", "probability": 0.858154296875}, {"start": 783.52, "end": 785.46, "word": " isomorphism", "probability": 0.8694661458333334}, {"start": 785.46, "end": 785.7, "word": " من", "probability": 0.97998046875}, {"start": 785.7, "end": 785.88, "word": " ال", "probability": 0.6767578125}, {"start": 785.88, "end": 786.12, "word": " group", "probability": 0.92529296875}, {"start": 786.12, "end": 786.6, "word": " الأولى", "probability": 0.966796875}, {"start": 786.6, "end": 786.76, "word": " إلى", "probability": 0.90234375}, {"start": 786.76, "end": 787.32, "word": " التانية", "probability": 0.9392903645833334}, {"start": 787.32, "end": 788.04, "word": " وعندي", "probability": 0.8995361328125}, {"start": 788.04, "end": 788.98, "word": " isomorphism", "probability": 0.9466145833333334}, {"start": 788.98, "end": 789.16, "word": " من", "probability": 0.99169921875}, {"start": 789.16, "end": 789.64, "word": " التانية", "probability": 0.9192708333333334}, {"start": 789.64, "end": 789.78, "word": " إلى", "probability": 0.85791015625}, {"start": 789.78, "end": 790.44, "word": " التالتة", "probability": 0.9573974609375}, {"start": 790.44, "end": 790.9, "word": " إذا", "probability": 0.697509765625}, {"start": 790.9, "end": 791.36, "word": " بصير", "probability": 0.645751953125}, {"start": 791.36, "end": 791.68, "word": " عندي", "probability": 0.888916015625}, {"start": 791.68, "end": 792.64, "word": " isomorphism", "probability": 0.9488932291666666}, {"start": 792.64, "end": 792.84, "word": " من", "probability": 0.98828125}, {"start": 792.84, "end": 793.72, "word": " الأولى", "probability": 0.9886067708333334}, {"start": 793.72, "end": 794.02, "word": " إلى", "probability": 0.96240234375}, {"start": 794.02, "end": 796.62, "word": " الثالثة", "probability": 0.778564453125}, {"start": 796.62, "end": 797.24, "word": " هذا", "probability": 0.869140625}, {"start": 797.24, "end": 797.8, "word": " كان", "probability": 0.97607421875}, {"start": 797.8, "end": 798.46, "word": " سؤال", "probability": 0.93212890625}, {"start": 798.46, "end": 798.9, "word": " ستة", "probability": 0.8673502604166666}, {"start": 798.9, "end": 799.34, "word": " سؤال", "probability": 0.9383138020833334}, {"start": 799.34, "end": 799.88, "word": " سبعة", "probability": 0.9578450520833334}], "temperature": 1.0}, {"id": 34, "seek": 81855, "start": 801.29, "end": 818.55, "text": "بيقول لي بييل لي ان ال S4 is not isomorphic ل D12 سؤال 7 S4 is not isomorphic ل D12", "tokens": [21292, 39648, 32239, 4724, 1829, 26895, 32239, 16472, 2423, 318, 19, 307, 406, 307, 32702, 299, 5296, 413, 4762, 8608, 33604, 6027, 1614, 318, 19, 307, 406, 307, 32702, 299, 5296, 413, 4762], "avg_logprob": -0.24770221552428076, "compression_ratio": 1.452054794520548, "no_speech_prob": 0.0, "words": [{"start": 801.29, "end": 801.79, "word": "بيقول", "probability": 0.5733642578125}, {"start": 801.79, "end": 801.93, "word": " لي", "probability": 0.302001953125}, {"start": 801.93, "end": 802.61, "word": " بييل", "probability": 0.6650390625}, {"start": 802.61, "end": 802.81, "word": " لي", "probability": 0.62060546875}, {"start": 802.81, "end": 803.05, "word": " ان", "probability": 0.55810546875}, {"start": 803.05, "end": 803.27, "word": " ال", "probability": 0.8828125}, {"start": 803.27, "end": 804.35, "word": " S4", "probability": 0.851318359375}, {"start": 804.35, "end": 805.11, "word": " is", "probability": 0.841796875}, {"start": 805.11, "end": 805.47, "word": " not", "probability": 0.958984375}, {"start": 805.47, "end": 806.79, "word": " isomorphic", "probability": 0.9254557291666666}, {"start": 806.79, "end": 807.01, "word": " ل", "probability": 0.92333984375}, {"start": 807.01, "end": 808.23, "word": " D12", "probability": 0.814208984375}, {"start": 808.23, "end": 809.35, "word": " سؤال", "probability": 0.9287109375}, {"start": 809.35, "end": 809.97, "word": " 7", "probability": 0.4609375}, {"start": 809.97, "end": 814.11, "word": " S4", "probability": 0.8759765625}, {"start": 814.11, "end": 814.65, "word": " is", "probability": 0.958984375}, {"start": 814.65, "end": 815.15, "word": " not", "probability": 0.96728515625}, {"start": 815.15, "end": 816.49, "word": " isomorphic", "probability": 0.9571940104166666}, {"start": 816.49, "end": 816.79, "word": " ل", "probability": 0.98046875}, {"start": 816.79, "end": 818.55, "word": " D12", "probability": 0.9404296875}], "temperature": 1.0}, {"id": 35, "seek": 84434, "start": 820.36, "end": 844.34, "text": "هذا يجعلني أسئل السؤال التالي ال S4 هذه ال S4 قداش أعلى order لأي element فيها S4 قداش أعلى order يلا يبدأ حل ال 4 3 1 2 2 2 1 1 قداش أعلى order لهم دول", "tokens": [3224, 15730, 7251, 7435, 30241, 22653, 5551, 3794, 19986, 1211, 21136, 33604, 6027, 16712, 6027, 1829, 2423, 318, 19, 29538, 2423, 318, 19, 12174, 3215, 33599, 5551, 3615, 23942, 1668, 5296, 10721, 1829, 4478, 8978, 11296, 318, 19, 12174, 3215, 33599, 5551, 3615, 23942, 1668, 7251, 15040, 7251, 44510, 10721, 11331, 1211, 2423, 1017, 805, 502, 568, 568, 568, 502, 502, 12174, 3215, 33599, 5551, 3615, 23942, 1668, 5296, 16095, 11778, 12610], "avg_logprob": -0.22431506522714276, "compression_ratio": 1.6571428571428573, "no_speech_prob": 0.0, "words": [{"start": 820.36, "end": 820.7, "word": "هذا", "probability": 0.76220703125}, {"start": 820.7, "end": 821.38, "word": " يجعلني", "probability": 0.70733642578125}, {"start": 821.38, "end": 821.74, "word": " أسئل", "probability": 0.8184814453125}, {"start": 821.74, "end": 822.28, "word": " السؤال", "probability": 0.9443359375}, {"start": 822.28, "end": 822.94, "word": " التالي", "probability": 0.9267578125}, {"start": 822.94, "end": 823.92, "word": " ال", "probability": 0.27490234375}, {"start": 823.92, "end": 824.96, "word": " S4", "probability": 0.6259765625}, {"start": 824.96, "end": 825.36, "word": " هذه", "probability": 0.287109375}, {"start": 825.36, "end": 825.98, "word": " ال", "probability": 0.61328125}, {"start": 825.98, "end": 827.02, "word": " S4", "probability": 0.923583984375}, {"start": 827.02, "end": 828.3, "word": " قداش", "probability": 0.6600748697916666}, {"start": 828.3, "end": 829.02, "word": " أعلى", "probability": 0.9514973958333334}, {"start": 829.02, "end": 829.96, "word": " order", "probability": 0.923828125}, {"start": 829.96, "end": 830.7, "word": " لأي", "probability": 0.93408203125}, {"start": 830.7, "end": 831.28, "word": " element", "probability": 0.9658203125}, {"start": 831.28, "end": 832.0, "word": " فيها", "probability": 0.975341796875}, {"start": 832.0, "end": 835.04, "word": " S4", "probability": 0.713134765625}, {"start": 835.04, "end": 836.18, "word": " قداش", "probability": 0.9503580729166666}, {"start": 836.18, "end": 836.42, "word": " أعلى", "probability": 0.9705403645833334}, {"start": 836.42, "end": 836.9, "word": " order", "probability": 0.974609375}, {"start": 836.9, "end": 838.0, "word": " يلا", "probability": 0.553955078125}, {"start": 838.0, "end": 838.38, "word": " يبدأ", "probability": 0.92333984375}, {"start": 838.38, "end": 838.72, "word": " حل", "probability": 0.8408203125}, {"start": 838.72, "end": 838.86, "word": " ال", "probability": 0.355224609375}, {"start": 838.86, "end": 839.3, "word": " 4", "probability": 0.654296875}, {"start": 839.3, "end": 839.86, "word": " 3", "probability": 0.611328125}, {"start": 839.86, "end": 840.4, "word": " 1", "probability": 0.95947265625}, {"start": 840.4, "end": 840.9, "word": " 2", "probability": 0.984375}, {"start": 840.9, "end": 841.48, "word": " 2", "probability": 0.974609375}, {"start": 841.48, "end": 841.9, "word": " 2", "probability": 0.60107421875}, {"start": 841.9, "end": 842.2, "word": " 1", "probability": 0.9462890625}, {"start": 842.2, "end": 842.54, "word": " 1", "probability": 0.9716796875}, {"start": 842.54, "end": 843.02, "word": " قداش", "probability": 0.9635416666666666}, {"start": 843.02, "end": 843.22, "word": " أعلى", "probability": 0.9791666666666666}, {"start": 843.22, "end": 843.64, "word": " order", "probability": 0.9755859375}, {"start": 843.64, "end": 843.96, "word": " لهم", "probability": 0.850830078125}, {"start": 843.96, "end": 844.34, "word": " دول", "probability": 0.8974609375}], "temperature": 1.0}, {"id": 36, "seek": 85767, "start": 846.39, "end": 857.67, "text": "الاربعة، تلاتة ولا واحد، اتنين واتنين، اتنين وواحد، كداش اعلى order؟ كداش؟ اعلى order لل S، اربعة", "tokens": [6027, 9640, 3555, 27884, 12399, 6055, 1211, 9307, 3660, 49429, 36764, 24401, 12399, 1975, 2655, 1863, 9957, 4032, 9307, 1863, 9957, 12399, 1975, 2655, 1863, 9957, 4032, 14407, 24401, 12399, 9122, 3215, 33599, 1975, 3615, 23942, 1668, 22807, 9122, 3215, 33599, 22807, 1975, 3615, 23942, 1668, 24976, 318, 12399, 1975, 25513, 27884], "avg_logprob": -0.27343749775076814, "compression_ratio": 1.6372549019607843, "no_speech_prob": 0.0, "words": [{"start": 846.39, "end": 847.31, "word": "الاربعة،", "probability": 0.617333984375}, {"start": 847.31, "end": 847.71, "word": " تلاتة", "probability": 0.83587646484375}, {"start": 847.71, "end": 847.89, "word": " ولا", "probability": 0.60009765625}, {"start": 847.89, "end": 848.43, "word": " واحد،", "probability": 0.7816569010416666}, {"start": 848.43, "end": 848.85, "word": " اتنين", "probability": 0.9537353515625}, {"start": 848.85, "end": 849.35, "word": " واتنين،", "probability": 0.80625}, {"start": 849.35, "end": 849.61, "word": " اتنين", "probability": 0.982177734375}, {"start": 849.61, "end": 850.01, "word": " وواحد،", "probability": 0.7310791015625}, {"start": 850.01, "end": 850.39, "word": " كداش", "probability": 0.457275390625}, {"start": 850.39, "end": 850.57, "word": " اعلى", "probability": 0.8553059895833334}, {"start": 850.57, "end": 852.13, "word": " order؟", "probability": 0.80810546875}, {"start": 852.13, "end": 855.31, "word": " كداش؟", "probability": 0.869140625}, {"start": 855.31, "end": 855.75, "word": " اعلى", "probability": 0.9541015625}, {"start": 855.75, "end": 856.25, "word": " order", "probability": 0.98193359375}, {"start": 856.25, "end": 856.73, "word": " لل", "probability": 0.87548828125}, {"start": 856.73, "end": 857.21, "word": " S،", "probability": 0.57763671875}, {"start": 857.21, "end": 857.67, "word": " اربعة", "probability": 0.85205078125}], "temperature": 1.0}, {"id": 37, "seek": 88161, "start": 858.35, "end": 881.61, "text": "مش جيبنا اعلى order لل S7 و S6 بالمثل بده يجيب اعلى order لل S4 يبقى بده يشوف قداش اكبر cycle في S4 اللي طولها أربع 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"probability": 0.84686279296875}, {"start": 1331.66, "end": 1332.16, "word": " هذه", "probability": 0.6796875}, {"start": 1332.16, "end": 1333.12, "word": " وهذه", "probability": 0.7353515625}, {"start": 1333.12, "end": 1333.28, "word": " اللي", "probability": 0.906494140625}, {"start": 1333.28, "end": 1333.58, "word": " هي", "probability": 0.826171875}, {"start": 1333.58, "end": 1334.06, "word": " من", "probability": 0.71435546875}, {"start": 1334.06, "end": 1335.06, "word": " I", "probability": 0.218505859375}, {"start": 1335.06, "end": 1335.54, "word": " of", "probability": 0.89892578125}, {"start": 1335.54, "end": 1335.88, "word": " A", "probability": 0.962890625}], "temperature": 1.0}, {"id": 58, "seek": 135958, "start": 1337.26, "end": 1359.58, "text": "طيب هذا لو كانت الـB موجبة كلامنا صح طب لو كانت الـB بـ0 يبقى باجي بقول له هذه الحالة الأولى الحالة الثانية لو كانت الـB تساوي 0 then بدي أخد الـA بواحد then", "tokens": [9566, 1829, 3555, 23758, 45164, 25961, 2655, 2423, 39184, 33, 3714, 29245, 49401, 28242, 10943, 8315, 20328, 5016, 23032, 3555, 45164, 25961, 2655, 2423, 39184, 33, 4724, 39184, 15, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 46740, 29538, 21542, 6027, 3660, 16247, 12610, 7578, 21542, 6027, 3660, 6024, 104, 7649, 10632, 45164, 25961, 2655, 2423, 39184, 33, 6055, 3794, 995, 45865, 1958, 550, 4724, 16254, 5551, 9778, 3215, 2423, 39184, 32, 4724, 14407, 24401, 550], "avg_logprob": -0.23457532165906367, "compression_ratio": 1.729032258064516, "no_speech_prob": 0.0, "words": [{"start": 1337.26, "end": 1337.66, "word": "طيب", "probability": 0.605224609375}, {"start": 1337.66, "end": 1338.02, "word": " هذا", "probability": 0.38525390625}, {"start": 1338.02, "end": 1338.22, "word": " لو", "probability": 0.92626953125}, {"start": 1338.22, "end": 1338.92, "word": " كانت", "probability": 0.91357421875}, {"start": 1338.92, "end": 1339.24, "word": " الـB", "probability": 0.4690755208333333}, {"start": 1339.24, "end": 1339.76, "word": " موجبة", "probability": 0.766357421875}, {"start": 1339.76, "end": 1340.5, "word": " كلامنا", "probability": 0.90478515625}, {"start": 1340.5, "end": 1340.96, "word": " صح", "probability": 0.937744140625}, {"start": 1340.96, "end": 1341.4, "word": " طب", "probability": 0.829345703125}, {"start": 1341.4, "end": 1341.66, "word": " لو", "probability": 0.986328125}, {"start": 1341.66, "end": 1342.18, "word": " كانت", "probability": 0.965087890625}, {"start": 1342.18, "end": 1342.54, "word": " الـB", "probability": 0.9547526041666666}, {"start": 1342.54, "end": 1343.4, "word": " بـ0", "probability": 0.6946614583333334}, {"start": 1343.4, "end": 1344.68, "word": " يبقى", "probability": 0.909912109375}, {"start": 1344.68, "end": 1345.14, "word": " باجي", "probability": 0.9088541666666666}, {"start": 1345.14, "end": 1345.6, "word": " بقول", "probability": 0.893310546875}, {"start": 1345.6, "end": 1345.74, "word": " له", "probability": 0.32080078125}, {"start": 1345.74, "end": 1345.96, "word": " هذه", "probability": 0.4228515625}, {"start": 1345.96, "end": 1346.48, "word": " الحالة", "probability": 0.9529622395833334}, {"start": 1346.48, "end": 1346.9, "word": " الأولى", "probability": 0.9794921875}, {"start": 1346.9, "end": 1347.62, "word": " الحالة", "probability": 0.90771484375}, {"start": 1347.62, "end": 1348.34, "word": " الثانية", "probability": 0.9720458984375}, {"start": 1348.34, "end": 1349.14, "word": " لو", "probability": 0.9091796875}, {"start": 1349.14, "end": 1349.76, "word": " كانت", "probability": 0.988037109375}, {"start": 1349.76, "end": 1350.32, "word": " الـB", "probability": 0.9690755208333334}, {"start": 1350.32, "end": 1351.48, "word": " تساوي", "probability": 0.9395751953125}, {"start": 1351.48, "end": 1352.22, "word": " 0", "probability": 0.406982421875}, {"start": 1352.22, "end": 1353.2, "word": " then", "probability": 0.5927734375}, {"start": 1353.2, "end": 1356.6, "word": " بدي", "probability": 0.4461669921875}, {"start": 1356.6, "end": 1357.0, "word": " أخد", "probability": 0.85205078125}, {"start": 1357.0, "end": 1357.48, "word": " الـA", "probability": 0.8732096354166666}, {"start": 1357.48, "end": 1358.32, "word": " بواحد", "probability": 0.9814453125}, {"start": 1358.32, "end": 1359.58, "word": " then", "probability": 0.80810546875}], "temperature": 1.0}, {"id": 59, "seek": 137300, "start": 1360.26, "end": 1373.0, "text": "اللي هو ال zero هذا بده يساوي لين أو بده يساوي لغا ريتم الواحد للأساس عشرة كيف؟", "tokens": [6027, 20292, 31439, 2423, 4018, 23758, 47525, 3224, 7251, 3794, 995, 45865, 5296, 9957, 34051, 47525, 3224, 7251, 3794, 995, 45865, 5296, 17082, 995, 12602, 36081, 2304, 2423, 14407, 24401, 24976, 10721, 3794, 32277, 6225, 8592, 25720, 9122, 33911, 22807], "avg_logprob": -0.23094511613613222, "compression_ratio": 1.3269230769230769, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1360.26, "end": 1360.78, "word": "اللي", "probability": 0.8720703125}, {"start": 1360.78, "end": 1361.06, "word": " هو", "probability": 0.97265625}, {"start": 1361.06, "end": 1361.3, "word": " ال", "probability": 0.9384765625}, {"start": 1361.3, "end": 1361.76, "word": " zero", "probability": 0.5693359375}, {"start": 1361.76, "end": 1362.48, "word": " هذا", "probability": 0.87060546875}, {"start": 1362.48, "end": 1363.46, "word": " بده", "probability": 0.48797607421875}, {"start": 1363.46, "end": 1363.92, "word": " يساوي", "probability": 0.929931640625}, {"start": 1363.92, "end": 1364.54, "word": " لين", "probability": 0.6002197265625}, {"start": 1364.54, "end": 1364.94, "word": " أو", "probability": 0.65478515625}, {"start": 1364.94, "end": 1365.44, "word": " بده", "probability": 0.899658203125}, {"start": 1365.44, "end": 1365.84, "word": " يساوي", "probability": 0.989013671875}, {"start": 1365.84, "end": 1366.58, "word": " لغا", "probability": 0.7542317708333334}, {"start": 1366.58, "end": 1367.18, "word": " ريتم", "probability": 0.7217610677083334}, {"start": 1367.18, "end": 1368.62, "word": " الواحد", "probability": 0.91552734375}, {"start": 1368.62, "end": 1369.78, "word": " للأساس", "probability": 0.8994140625}, {"start": 1369.78, "end": 1370.72, "word": " عشرة", "probability": 0.9111328125}, {"start": 1370.72, "end": 1373.0, "word": " كيف؟", "probability": 0.8683268229166666}], "temperature": 1.0}, {"id": 60, "seek": 139723, "start": 1375.21, "end": 1397.23, "text": "لغة راتب او لن اتنين نفس الرسمة كله يمر بهذه النقطة بس بيجرب على المحور او بيبعد عنها مديش غلبك هذا log X للاساس عشرة خليها هي ماشي ماهي ال log هي ال لن بس بتنضر في مقدار ثابت فقط لا غير", "tokens": [1211, 17082, 3660, 12602, 9307, 3555, 1975, 2407, 5296, 1863, 1975, 2655, 1863, 9957, 8717, 36178, 34892, 38251, 3660, 28242, 3224, 7251, 29973, 39627, 24192, 28239, 47432, 3660, 4724, 3794, 4724, 1829, 7435, 25513, 15844, 9673, 5016, 13063, 1975, 2407, 4724, 1829, 3555, 22488, 18871, 11296, 3714, 16254, 8592, 32771, 46152, 4117, 23758, 3565, 1783, 24976, 32277, 32277, 6225, 8592, 25720, 16490, 20292, 11296, 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{"start": 1385.59, "end": 1386.13, "word": " هذا", "probability": 0.65234375}, {"start": 1386.13, "end": 1386.97, "word": " log", "probability": 0.6748046875}, {"start": 1386.97, "end": 1388.13, "word": " X", "probability": 0.6259765625}, {"start": 1388.13, "end": 1389.15, "word": " للاساس", "probability": 0.8483072916666666}, {"start": 1389.15, "end": 1389.59, "word": " عشرة", "probability": 0.9264322916666666}, {"start": 1389.59, "end": 1390.15, "word": " خليها", "probability": 0.5967610677083334}, {"start": 1390.15, "end": 1390.45, "word": " هي", "probability": 0.82275390625}, {"start": 1390.45, "end": 1391.59, "word": " ماشي", "probability": 0.8211263020833334}, {"start": 1391.59, "end": 1392.25, "word": " ماهي", "probability": 0.7089029947916666}, {"start": 1392.25, "end": 1392.37, "word": " ال", "probability": 0.89453125}, {"start": 1392.37, "end": 1392.59, "word": " log", "probability": 0.921875}, {"start": 1392.59, "end": 1392.87, "word": " هي", "probability": 0.93896484375}, {"start": 1392.87, "end": 1393.11, "word": " ال", "probability": 0.787109375}, {"start": 1393.11, "end": 1393.35, "word": " لن", "probability": 0.61895751953125}, {"start": 1393.35, "end": 1393.63, "word": " بس", "probability": 0.98193359375}, {"start": 1393.63, "end": 1394.07, "word": " بتنضر", "probability": 0.7352294921875}, {"start": 1394.07, "end": 1394.27, "word": " في", "probability": 0.634765625}, {"start": 1394.27, "end": 1394.99, "word": " مقدار", "probability": 0.9716796875}, {"start": 1394.99, "end": 1395.83, "word": " ثابت", "probability": 0.9947916666666666}, {"start": 1395.83, "end": 1396.53, "word": " فقط", "probability": 0.986572265625}, {"start": 1396.53, "end": 1396.79, "word": " لا", "probability": 0.8662109375}, {"start": 1396.79, "end": 1397.23, "word": " غير", "probability": 0.974609375}], "temperature": 1.0}, {"id": 61, "seek": 142780, "start": 1398.26, "end": 1427.8, "text": "طيب يبقى صار ال zero بده يساوي log الواحد للأساس عشرة يعني هذا log ال a للأساس عشرة اللي هو بده يساوي في of a وال a تساوي واحد يبقى صارت في is onto طب لو كانت سالبة يبقى f ال b أقل من ال zero", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 20328, 9640, 2423, 4018, 47525, 3224, 7251, 3794, 995, 45865, 3565, 2423, 14407, 24401, 24976, 10721, 3794, 32277, 6225, 8592, 25720, 37495, 22653, 23758, 3565, 2423, 257, 24976, 10721, 3794, 32277, 6225, 8592, 25720, 13672, 1829, 31439, 47525, 3224, 7251, 3794, 995, 45865, 8978, 295, 257, 16070, 257, 6055, 3794, 995, 45865, 36764, 24401, 7251, 3555, 4587, 7578, 20328, 9640, 2655, 8978, 307, 3911, 23032, 3555, 45164, 25961, 2655, 8608, 6027, 49401, 7251, 3555, 4587, 7578, 283, 2423, 272, 5551, 4587, 1211, 9154, 2423, 4018], "avg_logprob": -0.2276545718152036, "compression_ratio": 1.802325581395349, "no_speech_prob": 0.0, "words": [{"start": 1398.26, "end": 1398.92, "word": "طيب", "probability": 0.6715291341145834}, {"start": 1398.92, "end": 1399.52, "word": " يبقى", "probability": 0.9093017578125}, {"start": 1399.52, "end": 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"word": " ألاقي", "probability": 0.8492838541666666}, {"start": 1457.94, "end": 1458.54, "word": " a", "probability": 0.6259765625}, {"start": 1458.54, "end": 1459.62, "word": " موجود", "probability": 0.9708658854166666}, {"start": 1459.62, "end": 1459.88, "word": " من", "probability": 0.9794921875}, {"start": 1459.88, "end": 1460.38, "word": " صفر", "probability": 0.9558919270833334}, {"start": 1460.38, "end": 1460.74, "word": " إلى", "probability": 0.90283203125}, {"start": 1460.74, "end": 1461.54, "word": " واحد", "probability": 0.9921875}, {"start": 1461.54, "end": 1462.32, "word": " such", "probability": 0.81103515625}, {"start": 1462.32, "end": 1463.08, "word": " that", "probability": 0.9384765625}, {"start": 1463.08, "end": 1464.28, "word": " بحيث", "probability": 0.9857177734375}, {"start": 1464.28, "end": 1464.72, "word": " أن", "probability": 0.556640625}, {"start": 1464.72, "end": 1465.76, "word": " ال", "probability": 0.9736328125}, {"start": 1465.76, "end": 1466.06, "word": " b", "probability": 0.421630859375}, {"start": 1466.06, "end": 1466.8, "word": " هذي", "probability": 0.6365559895833334}, {"start": 1466.8, "end": 1467.48, "word": " بده", "probability": 0.493896484375}, {"start": 1467.48, "end": 1468.0, "word": " يساوي", "probability": 0.7833251953125}, {"start": 1468.0, "end": 1468.4, "word": " log", "probability": 0.95556640625}, {"start": 1468.4, "end": 1468.78, "word": " a", "probability": 0.88134765625}, {"start": 1468.78, "end": 1469.68, "word": " للعساس", "probability": 0.9417724609375}, {"start": 1469.68, "end": 1470.34, "word": " عشرة", "probability": 0.935546875}, {"start": 1470.34, "end": 1470.96, "word": " اللي", "probability": 0.91552734375}, {"start": 1470.96, "end": 1471.3, "word": " هو", "probability": 0.9814453125}, {"start": 1471.3, "end": 1471.86, "word": " five", "probability": 0.25048828125}, {"start": 1471.86, "end": 1472.48, "word": " of", "probability": 0.95849609375}, {"start": 1472.48, "end": 1472.9, "word": " a", 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"end": 1880.19, "word": " جي", "probability": 0.913330078125}, {"start": 1880.19, "end": 1881.05, "word": " ايش", "probability": 0.7646484375}, {"start": 1881.05, "end": 1881.41, "word": " معنى", "probability": 0.9318033854166666}, {"start": 1881.41, "end": 1881.63, "word": " هذا", "probability": 0.96435546875}, {"start": 1881.63, "end": 1882.53, "word": " الكلام", "probability": 0.9524739583333334}, {"start": 1882.53, "end": 1883.71, "word": " انه", "probability": 0.6243896484375}, {"start": 1883.71, "end": 1884.05, "word": " جي", "probability": 0.848876953125}, {"start": 1884.05, "end": 1884.35, "word": " is", "probability": 0.84619140625}, {"start": 1884.35, "end": 1884.65, "word": " a", "probability": 0.841796875}, {"start": 1884.65, "end": 1884.99, "word": " billion", "probability": 0.8837890625}], "temperature": 1.0}, {"id": 80, "seek": 191288, "start": 1885.58, "end": 1912.88, "text": "يبقى هنا الـ g is abelian الان هذا الاتجاه الأول بروح نقوله conversely assume افترض that ان الـ g is abelian افترض ان الـ g is abelian ايش بده نثبت؟", "tokens": [1829, 3555, 4587, 7578, 34105, 2423, 39184, 290, 307, 410, 338, 952, 2423, 7649, 23758, 2423, 9307, 7435, 40294, 16247, 12610, 4724, 32887, 5016, 8717, 39648, 3224, 2615, 736, 6552, 1975, 5172, 2655, 43042, 300, 16472, 2423, 39184, 290, 307, 410, 338, 952, 1975, 5172, 2655, 43042, 16472, 2423, 39184, 290, 307, 410, 338, 952, 1975, 1829, 8592, 47525, 3224, 8717, 12984, 3555, 2655, 22807], "avg_logprob": -0.2443181745933764, "compression_ratio": 1.528169014084507, "no_speech_prob": 0.0, "words": [{"start": 1885.58, "end": 1886.34, "word": "يبقى", "probability": 0.928466796875}, {"start": 1886.34, "end": 1886.76, "word": " هنا", "probability": 0.9755859375}, {"start": 1886.76, "end": 1888.52, "word": " الـ", "probability": 0.5450439453125}, {"start": 1888.52, "end": 1888.7, "word": " g", "probability": 0.201904296875}, {"start": 1888.7, "end": 1890.22, "word": " is", "probability": 0.81103515625}, {"start": 1890.22, "end": 1891.48, "word": " abelian", "probability": 0.888671875}, {"start": 1891.48, "end": 1892.72, "word": " الان", "probability": 0.5743408203125}, {"start": 1892.72, "end": 1893.0, "word": " هذا", "probability": 0.6650390625}, {"start": 1893.0, "end": 1893.68, "word": " الاتجاه", "probability": 0.9083251953125}, {"start": 1893.68, "end": 1894.1, "word": " الأول", "probability": 0.831298828125}, {"start": 1894.1, "end": 1894.58, "word": " بروح", "probability": 0.8313802083333334}, {"start": 1894.58, "end": 1895.34, "word": " نقوله", "probability": 0.6092936197916666}, {"start": 1895.34, "end": 1897.6, "word": " conversely", "probability": 0.8671875}, {"start": 1897.6, "end": 1899.22, "word": " assume", "probability": 0.52978515625}, {"start": 1899.22, "end": 1900.88, "word": " افترض", "probability": 0.85552978515625}, {"start": 1900.88, "end": 1902.1, "word": " that", "probability": 0.50146484375}, {"start": 1902.1, "end": 1902.98, "word": " ان", "probability": 0.492919921875}, {"start": 1902.98, "end": 1903.42, "word": " الـ", "probability": 0.69482421875}, {"start": 1903.42, "end": 1903.92, "word": " g", "probability": 0.84765625}, {"start": 1903.92, "end": 1904.92, "word": " is", "probability": 0.93310546875}, {"start": 1904.92, "end": 1906.72, "word": " abelian", "probability": 0.970703125}, {"start": 1906.72, "end": 1910.02, "word": " افترض", "probability": 0.977294921875}, {"start": 1910.02, "end": 1910.24, "word": " ان", "probability": 0.93359375}, {"start": 1910.24, "end": 1910.5, "word": " الـ", "probability": 0.923828125}, {"start": 1910.5, "end": 1910.68, "word": " g", "probability": 0.9072265625}, {"start": 1910.68, "end": 1911.1, "word": " is", "probability": 0.880859375}, {"start": 1911.1, "end": 1911.54, "word": " abelian", "probability": 0.9689127604166666}, {"start": 1911.54, "end": 1911.88, "word": " ايش", "probability": 0.7431640625}, {"start": 1911.88, "end": 1912.14, "word": " بده", "probability": 0.7998046875}, {"start": 1912.14, "end": 1912.88, "word": " نثبت؟", "probability": 0.9337890625}], "temperature": 1.0}, {"id": 81, "seek": 193977, "start": 1915.09, "end": 1939.77, "text": "هذا isomorphism يعني بدي أثبت انه one to one وانتوا ويخدم خاصية مين ال isomorphism بعدين بقوله كويس يبقى بدي أروح أخدله اللي هو ال alpha is one to one بدي أحاول أثبتها لذلك بدي أقوله assume", "tokens": [3224, 15730, 307, 32702, 1434, 37495, 22653, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 3224, 472, 281, 472, 4032, 7649, 2655, 14407, 4032, 1829, 9778, 40448, 16490, 33546, 10632, 3714, 9957, 2423, 307, 32702, 1434, 39182, 9957, 4724, 39648, 3224, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 32887, 5016, 5551, 9778, 3215, 43761, 13672, 1829, 31439, 2423, 8961, 307, 472, 281, 472, 4724, 16254, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 11296, 5296, 8848, 23275, 4724, 16254, 5551, 39648, 3224, 6552], "avg_logprob": -0.20748546563608702, "compression_ratio": 1.6820809248554913, "no_speech_prob": 0.0, "words": [{"start": 1915.09, "end": 1915.57, "word": "هذا", "probability": 0.85400390625}, {"start": 1915.57, "end": 1916.67, "word": " isomorphism", "probability": 0.65423583984375}, {"start": 1916.67, "end": 1917.39, "word": " يعني", "probability": 0.864501953125}, {"start": 1917.39, "end": 1917.71, "word": " بدي", "probability": 0.53607177734375}, {"start": 1917.71, "end": 1918.19, "word": " أثبت", "probability": 0.92138671875}, {"start": 1918.19, "end": 1918.43, "word": " انه", "probability": 0.5928955078125}, {"start": 1918.43, "end": 1918.65, "word": " one", "probability": 0.75927734375}, {"start": 1918.65, "end": 1918.93, "word": " to", "probability": 0.85546875}, {"start": 1918.93, "end": 1919.31, "word": " one", "probability": 0.955078125}, {"start": 1919.31, "end": 1920.69, "word": " وانتوا", "probability": 0.70159912109375}, {"start": 1920.69, "end": 1921.31, "word": " ويخدم", "probability": 0.908935546875}, {"start": 1921.31, "end": 1922.01, "word": " خاصية", "probability": 0.9493815104166666}, {"start": 1922.01, "end": 1922.47, "word": " مين", "probability": 0.6551513671875}, {"start": 1922.47, "end": 1923.15, "word": " ال", "probability": 0.67431640625}, {"start": 1923.15, "end": 1924.37, "word": " isomorphism", "probability": 0.8857421875}, {"start": 1924.37, "end": 1925.39, "word": " بعدين", "probability": 0.603759765625}, {"start": 1925.39, "end": 1925.97, "word": " بقوله", "probability": 0.87744140625}, {"start": 1925.97, "end": 1926.69, "word": " كويس", "probability": 0.9431966145833334}, {"start": 1926.69, "end": 1927.85, "word": " يبقى", "probability": 0.876953125}, {"start": 1927.85, "end": 1928.19, "word": " بدي", "probability": 0.77783203125}, {"start": 1928.19, "end": 1928.65, "word": " أروح", "probability": 0.8497721354166666}, {"start": 1928.65, "end": 1929.67, "word": " أخدله", "probability": 0.856201171875}, {"start": 1929.67, "end": 1930.43, "word": " اللي", "probability": 0.917724609375}, {"start": 1930.43, "end": 1930.75, "word": " هو", "probability": 0.9833984375}, {"start": 1930.75, "end": 1930.99, "word": " ال", "probability": 0.8466796875}, {"start": 1930.99, "end": 1931.65, "word": " alpha", "probability": 0.8154296875}, {"start": 1931.65, "end": 1932.51, "word": " is", "probability": 0.90576171875}, {"start": 1932.51, "end": 1933.03, "word": " one", "probability": 0.95703125}, {"start": 1933.03, "end": 1933.45, "word": " to", "probability": 0.97314453125}, {"start": 1933.45, "end": 1934.25, "word": " one", "probability": 0.9560546875}, {"start": 1934.25, "end": 1935.75, "word": " بدي", "probability": 0.83740234375}, {"start": 1935.75, "end": 1936.15, "word": " أحاول", "probability": 0.962158203125}, {"start": 1936.15, "end": 1936.93, "word": " أثبتها", "probability": 0.972265625}, {"start": 1936.93, "end": 1938.05, "word": " لذلك", "probability": 0.9324544270833334}, {"start": 1938.05, "end": 1938.31, "word": " بدي", "probability": 0.9619140625}, {"start": 1938.31, "end": 1938.87, "word": " أقوله", "probability": 0.880859375}, {"start": 1938.87, "end": 1939.77, "word": " assume", "probability": 0.783203125}], "temperature": 1.0}, {"id": 82, "seek": 195928, "start": 1941.18, "end": 1959.28, "text": "افترض ان alpha of G1 يساوي alpha of G2 اذا قدرت اثبت له ان G1 يساوي G2 يكون اثبتنا انها alpha one to one", "tokens": [995, 5172, 2655, 43042, 16472, 8961, 295, 460, 16, 7251, 3794, 995, 45865, 8961, 295, 460, 17, 1975, 15730, 12174, 3215, 43500, 1975, 12984, 3555, 2655, 46740, 16472, 460, 16, 7251, 3794, 995, 45865, 460, 17, 7251, 30544, 1975, 12984, 3555, 2655, 8315, 16472, 11296, 8961, 472, 281, 472], "avg_logprob": -0.31124999761581423, "compression_ratio": 1.3761467889908257, "no_speech_prob": 0.0, "words": [{"start": 1941.18, "end": 1942.28, "word": "افترض", "probability": 0.747467041015625}, {"start": 1942.28, "end": 1943.12, "word": " ان", "probability": 0.86767578125}, {"start": 1943.12, "end": 1944.0, "word": " alpha", "probability": 0.196044921875}, {"start": 1944.0, "end": 1944.82, "word": " of", "probability": 0.88818359375}, {"start": 1944.82, "end": 1945.72, "word": " G1", "probability": 0.756103515625}, {"start": 1945.72, "end": 1947.02, "word": " يساوي", "probability": 0.548736572265625}, {"start": 1947.02, "end": 1947.68, "word": " alpha", "probability": 0.74951171875}, {"start": 1947.68, "end": 1948.4, "word": " of", "probability": 0.94873046875}, {"start": 1948.4, "end": 1949.26, "word": " G2", "probability": 0.9951171875}, {"start": 1949.26, "end": 1950.42, "word": " اذا", "probability": 0.852294921875}, {"start": 1950.42, "end": 1950.86, "word": " قدرت", "probability": 0.733154296875}, {"start": 1950.86, "end": 1951.42, "word": " اثبت", "probability": 0.923583984375}, {"start": 1951.42, "end": 1951.58, "word": " له", "probability": 0.2420654296875}, {"start": 1951.58, "end": 1951.78, "word": " ان", "probability": 0.88525390625}, {"start": 1951.78, "end": 1952.52, "word": " G1", "probability": 0.955810546875}, {"start": 1952.52, "end": 1953.66, "word": " يساوي", "probability": 0.948974609375}, {"start": 1953.66, "end": 1954.46, "word": " G2", "probability": 0.989013671875}, {"start": 1954.46, "end": 1954.92, "word": " يكون", "probability": 0.556640625}, {"start": 1954.92, "end": 1956.96, "word": " اثبتنا", "probability": 0.8861328125}, {"start": 1956.96, "end": 1957.32, "word": " انها", "probability": 0.77294921875}, {"start": 1957.32, "end": 1957.82, "word": " alpha", "probability": 0.66259765625}, {"start": 1957.82, "end": 1958.36, "word": " one", "probability": 0.615234375}, {"start": 1958.36, "end": 1958.74, "word": " to", "probability": 0.8642578125}, {"start": 1958.74, "end": 1959.28, "word": " one", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 83, "seek": 199013, "start": 1963.29, "end": 1990.13, "text": "حسب التعريف alpha of G1 إيش بتبقى G1 inverse و alpha of G2 بصير G2 inverse إيش رأيك بدي أضرب من جهة اليمين في G2 يبقى إيش بصير G1 inverse G2 بدي أسوأ ال identity صح؟", "tokens": [5016, 35457, 16712, 3615, 16572, 5172, 8961, 295, 460, 16, 11933, 1829, 8592, 39894, 3555, 4587, 7578, 460, 16, 17340, 4032, 8961, 295, 460, 17, 4724, 9381, 13546, 460, 17, 17340, 11933, 1829, 8592, 12602, 10721, 1829, 4117, 4724, 16254, 5551, 11242, 25513, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 8978, 460, 17, 7251, 3555, 4587, 7578, 11933, 1829, 8592, 4724, 9381, 13546, 460, 16, 17340, 460, 17, 4724, 16254, 5551, 3794, 2407, 10721, 2423, 6575, 20328, 5016, 22807], "avg_logprob": -0.17597656771540643, "compression_ratio": 1.460122699386503, "no_speech_prob": 0.0, "words": [{"start": 1963.29, "end": 1963.83, "word": "حسب", "probability": 0.878173828125}, {"start": 1963.83, "end": 1964.59, "word": " التعريف", "probability": 0.98681640625}, {"start": 1964.59, "end": 1964.99, "word": " alpha", "probability": 0.4501953125}, {"start": 1964.99, "end": 1965.43, "word": " of", "probability": 0.95751953125}, {"start": 1965.43, "end": 1965.93, "word": " G1", "probability": 0.742919921875}, {"start": 1965.93, "end": 1966.27, "word": " إيش", "probability": 0.695556640625}, {"start": 1966.27, "end": 1967.05, "word": " بتبقى", "probability": 0.9080810546875}, {"start": 1967.05, "end": 1968.23, "word": " G1", "probability": 0.768798828125}, {"start": 1968.23, "end": 1968.79, "word": " inverse", "probability": 0.7919921875}, {"start": 1968.79, "end": 1969.05, "word": " و", "probability": 0.646484375}, {"start": 1969.05, "end": 1969.43, "word": " alpha", "probability": 0.6708984375}, {"start": 1969.43, "end": 1969.91, "word": " of", "probability": 0.9814453125}, {"start": 1969.91, "end": 1970.69, "word": " G2", "probability": 0.98828125}, {"start": 1970.69, "end": 1971.73, "word": " بصير", "probability": 0.7406412760416666}, {"start": 1971.73, "end": 1973.15, "word": " G2", "probability": 0.9775390625}, {"start": 1973.15, "end": 1973.87, "word": " inverse", "probability": 0.8310546875}, {"start": 1973.87, "end": 1974.89, "word": " إيش", "probability": 0.8826497395833334}, {"start": 1974.89, "end": 1975.33, "word": " رأيك", "probability": 0.9659423828125}, {"start": 1975.33, "end": 1975.65, "word": " بدي", "probability": 0.687744140625}, {"start": 1975.65, "end": 1976.21, "word": " أضرب", "probability": 0.9620768229166666}, {"start": 1976.21, "end": 1976.47, "word": " من", "probability": 0.982421875}, {"start": 1976.47, "end": 1976.93, "word": " جهة", "probability": 0.98974609375}, {"start": 1976.93, "end": 1977.57, "word": " اليمين", "probability": 0.89111328125}, {"start": 1977.57, "end": 1977.85, "word": " في", "probability": 0.966796875}, {"start": 1977.85, "end": 1978.97, "word": " G2", "probability": 0.984130859375}, {"start": 1978.97, "end": 1980.49, "word": " يبقى", "probability": 0.9000244140625}, {"start": 1980.49, "end": 1980.55, "word": " إيش", "probability": 0.982421875}, {"start": 1980.55, "end": 1981.21, "word": " بصير", "probability": 0.9729817708333334}, {"start": 1981.21, "end": 1983.25, "word": " G1", "probability": 0.85009765625}, {"start": 1983.25, "end": 1984.41, "word": " inverse", "probability": 0.85791015625}, {"start": 1984.41, "end": 1986.11, "word": " G2", "probability": 0.90576171875}, {"start": 1986.11, "end": 1986.55, "word": " بدي", "probability": 0.6640625}, {"start": 1986.55, "end": 1986.89, "word": " أسوأ", "probability": 0.690673828125}, {"start": 1986.89, "end": 1987.03, "word": " ال", "probability": 0.943359375}, {"start": 1987.03, "end": 1987.79, "word": " identity", "probability": 0.8544921875}, {"start": 1987.79, "end": 1990.13, "word": " صح؟", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 84, "seek": 201323, "start": 1991.11, "end": 2013.23, "text": "طب بدى اضرب من جهة الشمال في G1 يبقى هذا معناته انه G2 بده يساوي ال G1 اظن و هو المطلوب طيب ضايق نثبت علينا الآن ان ال alpha هذه is on", "tokens": [9566, 3555, 47525, 7578, 1975, 11242, 25513, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 8978, 460, 16, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 47395, 16472, 3224, 460, 17, 47525, 3224, 7251, 3794, 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{"start": 2277.88, "end": 2278.4, "word": " اتش", "probability": 0.853515625}, {"start": 2278.4, "end": 2279.92, "word": " سؤال", "probability": 0.9475911458333334}, {"start": 2279.92, "end": 2281.12, "word": " اتناش", "probability": 0.8804931640625}, {"start": 2281.12, "end": 2282.64, "word": " بد", "probability": 0.66455078125}, {"start": 2282.64, "end": 2283.4, "word": " جي", "probability": 0.787841796875}, {"start": 2283.4, "end": 2284.36, "word": " ماهياش", "probability": 0.9752197265625}, {"start": 2284.36, "end": 2285.72, "word": " ايزومورفك", "probability": 0.98046875}, {"start": 2285.72, "end": 2286.02, "word": " لا", "probability": 0.9716796875}, {"start": 2286.02, "end": 2286.58, "word": " اتش", "probability": 0.9879557291666666}, {"start": 2286.58, "end": 2287.6, "word": " but", "probability": 0.78662109375}, {"start": 2287.6, "end": 2288.82, "word": " ولكن", "probability": 0.78466796875}], "temperature": 1.0}, {"id": 94, "seek": 231800, "start": 2289.56, "end": 2318.0, "text": "ولكن الـ Atomorphism لـ G isomorphic للـ Atomorphism بطل Atomorphism لل G isomorphic لل Atomorphism لل H لل Atomorphism لل H اللي عندنا هذا القصة بسيطة جدا", "tokens": [12610, 19452, 2423, 39184, 1711, 32702, 1434, 5296, 39184, 460, 307, 32702, 299, 24976, 39184, 1711, 32702, 1434, 4724, 9566, 1211, 1711, 32702, 1434, 24976, 460, 307, 32702, 299, 24976, 1711, 32702, 1434, 24976, 389, 24976, 1711, 32702, 1434, 24976, 389, 13672, 1829, 43242, 8315, 23758, 25062, 9381, 3660, 4724, 3794, 1829, 9566, 3660, 10874, 28259], "avg_logprob": -0.3034539390028569, "compression_ratio": 1.8636363636363635, "no_speech_prob": 0.0, "words": [{"start": 2289.56, "end": 2290.6, "word": "ولكن", "probability": 0.7330322265625}, {"start": 2290.6, "end": 2290.84, "word": " الـ", "probability": 0.572509765625}, {"start": 2290.84, "end": 2291.94, "word": " Atomorphism", "probability": 0.7320963541666666}, {"start": 2291.94, "end": 2292.26, "word": " لـ", "probability": 0.615478515625}, {"start": 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0.93212890625}, {"start": 2307.44, "end": 2308.06, "word": " H", "probability": 0.93896484375}, {"start": 2308.06, "end": 2309.06, "word": " لل", "probability": 0.8056640625}, {"start": 2309.06, "end": 2311.14, "word": " Atomorphism", "probability": 0.9010416666666666}, {"start": 2311.14, "end": 2311.7, "word": " لل", "probability": 0.93994140625}, {"start": 2311.7, "end": 2312.1, "word": " H", "probability": 0.94970703125}, {"start": 2312.1, "end": 2312.42, "word": " اللي", "probability": 0.73486328125}, {"start": 2312.42, "end": 2312.96, "word": " عندنا", "probability": 0.7139892578125}, {"start": 2312.96, "end": 2313.52, "word": " هذا", "probability": 0.374267578125}, {"start": 2313.52, "end": 2317.2, "word": " القصة", "probability": 0.8388671875}, {"start": 2317.2, "end": 2317.7, "word": " بسيطة", "probability": 0.9931640625}, {"start": 2317.7, "end": 2318.0, "word": " جدا", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 95, "seek": 234598, "start": 2318.72, "end": 2345.98, "text": "و لا نبعد كثير و نحاول نستخدم ما درسناه في آخر نظرية أخدناها في الشبتر آخر نظرية قلنا atomorphic ل ZN ايزو مورفك لمين لل UN الآن لو جيت قلت لك أخدت solution لو أخدت ال G تساوي ال Z6 and", "tokens": [2407, 20193, 8717, 3555, 22488, 9122, 12984, 13546, 4032, 8717, 5016, 995, 12610, 8717, 14851, 9778, 40448, 19446, 11778, 2288, 3794, 8315, 3224, 8978, 19753, 34740, 8717, 19913, 2288, 10632, 5551, 9778, 3215, 8315, 11296, 8978, 25124, 3555, 2655, 2288, 19753, 34740, 8717, 19913, 2288, 10632, 12174, 1211, 8315, 12018, 18191, 299, 5296, 1176, 45, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 32767, 9957, 24976, 8229, 6024, 48506, 45164, 10874, 36081, 12174, 1211, 2655, 5296, 4117, 5551, 9778, 3215, 2655, 3827, 45164, 5551, 9778, 3215, 2655, 2423, 460, 6055, 3794, 995, 45865, 2423, 1176, 21, 293], "avg_logprob": -0.3214285610889902, "compression_ratio": 1.532994923857868, "no_speech_prob": 0.0, "words": [{"start": 2318.72, "end": 2318.96, "word": "و", "probability": 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"end": 2352.21, "word": " ثلاثة", "probability": 0.75185546875}, {"start": 2352.21, "end": 2352.53, "word": " هل", "probability": 0.776123046875}, {"start": 2352.53, "end": 2352.99, "word": " الاتنين", "probability": 0.75103759765625}, {"start": 2352.99, "end": 2353.31, "word": " هذول", "probability": 0.7677408854166666}, {"start": 2353.31, "end": 2353.61, "word": " are", "probability": 0.479248046875}, {"start": 2353.61, "end": 2354.81, "word": " isomorphic؟", "probability": 0.81463623046875}, {"start": 2354.81, "end": 2355.81, "word": " لأن", "probability": 0.763671875}, {"start": 2355.81, "end": 2356.07, "word": " هذه", "probability": 0.380859375}, {"start": 2356.07, "end": 2356.41, "word": " فيها", "probability": 0.96533203125}, {"start": 2356.41, "end": 2356.81, "word": " ست", "probability": 0.94921875}, {"start": 2356.81, "end": 2357.35, "word": " عناصر", "probability": 0.9794921875}, {"start": 2357.35, "end": 2357.45, "word": " و", "probability": 0.47216796875}, {"start": 2357.45, "end": 2357.61, "word": " هذه", "probability": 0.7353515625}, {"start": 2357.61, "end": 2357.91, "word": " فيها", "probability": 0.974609375}, {"start": 2357.91, "end": 2358.71, "word": " كدهش؟", "probability": 0.67060546875}, {"start": 2358.71, "end": 2359.83, "word": " تلاتة", "probability": 0.9439697265625}, {"start": 2359.83, "end": 2361.41, "word": " يبقى", "probability": 0.929931640625}, {"start": 2361.41, "end": 2362.15, "word": " then", "probability": 0.60595703125}, {"start": 2362.15, "end": 2364.61, "word": " ال", "probability": 0.7060546875}, {"start": 2364.61, "end": 2366.27, "word": " then", "probability": 0.3056640625}, {"start": 2366.27, "end": 2366.55, "word": " ال", "probability": 0.798828125}, {"start": 2366.55, "end": 2367.15, "word": " order", "probability": 0.9501953125}, {"start": 2367.15, "end": 2367.49, "word": " اللي", "probability": 0.965087890625}, {"start": 2367.49, "end": 2368.21, "word": " هجيه", "probability": 0.63909912109375}, {"start": 2368.21, "end": 2368.65, "word": " بده", "probability": 0.840576171875}, {"start": 2368.65, "end": 2369.11, "word": " يساوي", "probability": 0.939208984375}, {"start": 2369.11, "end": 2369.79, "word": " ستة", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 97, "seek": 239784, "start": 2370.04, "end": 2397.84, "text": "وال order ل H بدي يسوى تلاتة هذا بدي يعطينا ان ال G is not isomorphic لمين لLH but ولكن ال atomorphism ل Z6 isomorphic لمين يا شباب ل U6 U6 من عناصر واحد", "tokens": [2407, 6027, 1668, 5296, 389, 4724, 16254, 7251, 3794, 2407, 7578, 6055, 1211, 9307, 3660, 23758, 4724, 16254, 37495, 9566, 1829, 8315, 16472, 2423, 460, 307, 406, 307, 32702, 299, 32767, 9957, 5296, 43, 39, 457, 35525, 19452, 2423, 12018, 18191, 1434, 5296, 1176, 21, 307, 32702, 299, 32767, 9957, 35186, 13412, 3555, 16758, 5296, 624, 21, 624, 21, 9154, 18871, 33546, 2288, 36764, 24401], "avg_logprob": -0.327651502959656, "compression_ratio": 1.3860759493670887, "no_speech_prob": 0.0, "words": 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2376.0, "end": 2376.38, "word": " G", "probability": 0.6611328125}, {"start": 2376.38, "end": 2377.2, "word": " is", "probability": 0.591796875}, {"start": 2377.2, "end": 2377.78, "word": " not", "probability": 0.9541015625}, {"start": 2377.78, "end": 2379.02, "word": " isomorphic", "probability": 0.9264322916666666}, {"start": 2379.02, "end": 2379.66, "word": " لمين", "probability": 0.6041259765625}, {"start": 2379.66, "end": 2381.64, "word": " لLH", "probability": 0.4846598307291667}, {"start": 2381.64, "end": 2383.0, "word": " but", "probability": 0.4453125}, {"start": 2383.0, "end": 2385.88, "word": " ولكن", "probability": 0.7587890625}, {"start": 2385.88, "end": 2387.12, "word": " ال", "probability": 0.9609375}, {"start": 2387.12, "end": 2389.06, "word": " atomorphism", "probability": 0.73583984375}, {"start": 2389.06, "end": 2389.5, "word": " ل", "probability": 0.95654296875}, {"start": 2389.5, "end": 2390.56, "word": " Z6", "probability": 0.756591796875}, {"start": 2390.56, "end": 2392.3, "word": " isomorphic", "probability": 0.8458658854166666}, {"start": 2392.3, "end": 2392.62, "word": " لمين", "probability": 0.883544921875}, {"start": 2392.62, "end": 2392.74, "word": " يا", "probability": 0.98779296875}, {"start": 2392.74, "end": 2393.34, "word": " شباب", "probability": 0.9886067708333334}, {"start": 2393.34, "end": 2394.76, "word": " ل", "probability": 0.58837890625}, {"start": 2394.76, "end": 2395.64, "word": " U6", "probability": 0.9365234375}, {"start": 2395.64, "end": 2396.28, "word": " U6", "probability": 0.889892578125}, {"start": 2396.28, "end": 2396.58, "word": " من", "probability": 0.59912109375}, {"start": 2396.58, "end": 2397.2, "word": " عناصر", "probability": 0.990234375}, {"start": 2397.2, "end": 2397.84, "word": " واحد", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 98, "seek": 242826, "start": 2399.48, "end": 2428.26, "text": "تلاتة، أربعة، خمسة، وايس الآن الـ Atomorphism لـ ZD3 Isomorphic لـ U3 U3 اللي هو واحد واتنين مافيش غيرهم طب اتطلعلي هذه هل هذا generator خمسة generator لـ U6", "tokens": [2655, 1211, 9307, 3660, 12399, 5551, 25513, 27884, 12399, 16490, 2304, 3794, 3660, 12399, 4032, 47302, 3794, 6024, 48506, 2423, 39184, 1711, 32702, 1434, 5296, 39184, 1176, 35, 18, 286, 539, 76, 18191, 299, 5296, 39184, 624, 18, 624, 18, 13672, 1829, 31439, 36764, 24401, 4032, 9307, 1863, 9957, 19446, 41185, 8592, 32771, 13546, 16095, 23032, 3555, 1975, 2655, 9566, 1211, 3615, 20292, 29538, 8032, 1211, 23758, 19265, 16490, 2304, 3794, 3660, 19265, 5296, 39184, 624, 21], "avg_logprob": -0.3567708230171448, "compression_ratio": 1.4082840236686391, "no_speech_prob": 0.0, "words": [{"start": 2399.48, "end": 2400.88, "word": "تلاتة،", "probability": 0.63310546875}, {"start": 2400.88, "end": 2401.94, "word": " أربعة،", "probability": 0.8294677734375}, {"start": 2401.94, "end": 2402.84, "word": " خمسة،", "probability": 0.853125}, {"start": 2402.84, "end": 2404.28, "word": " وايس", "probability": 0.3673502604166667}, {"start": 2404.28, "end": 2405.6, "word": " الآن", "probability": 0.5504150390625}, {"start": 2405.6, "end": 2406.4, "word": " الـ", "probability": 0.6064453125}, {"start": 2406.4, "end": 2408.56, "word": " Atomorphism", "probability": 0.6681315104166666}, {"start": 2408.56, "end": 2409.08, "word": " لـ", "probability": 0.773681640625}, {"start": 2409.08, "end": 2410.2, "word": " ZD3", "probability": 0.7527669270833334}, {"start": 2410.2, "end": 2412.42, "word": " Isomorphic", "probability": 0.7128662109375}, {"start": 2412.42, "end": 2412.96, "word": " لـ", "probability": 0.91796875}, {"start": 2412.96, "end": 2413.82, "word": " U3", "probability": 0.862548828125}, {"start": 2413.82, "end": 2414.94, "word": " U3", "probability": 0.927490234375}, {"start": 2414.94, "end": 2415.16, "word": " اللي", "probability": 0.5955810546875}, {"start": 2415.16, "end": 2415.36, "word": " هو", "probability": 0.97265625}, {"start": 2415.36, "end": 2415.74, "word": " واحد", "probability": 0.943359375}, {"start": 2415.74, "end": 2416.34, "word": " واتنين", "probability": 0.8499755859375}, {"start": 2416.34, "end": 2416.96, "word": " مافيش", "probability": 0.7577311197916666}, {"start": 2416.96, "end": 2417.88, "word": " غيرهم", "probability": 0.98583984375}, {"start": 2417.88, "end": 2419.28, "word": " طب", "probability": 0.8564453125}, {"start": 2419.28, "end": 2421.22, "word": " اتطلعلي", "probability": 0.68463134765625}, {"start": 2421.22, "end": 2421.62, "word": " هذه", "probability": 0.366943359375}, {"start": 2421.62, "end": 2422.96, "word": " هل", "probability": 0.928955078125}, {"start": 2422.96, "end": 2423.48, "word": " هذا", "probability": 0.58349609375}, {"start": 2423.48, "end": 2424.54, "word": " generator", "probability": 0.681640625}, {"start": 2424.54, "end": 2426.9, "word": " خمسة", "probability": 0.939453125}, {"start": 2426.9, "end": 2427.46, "word": " generator", "probability": 0.68994140625}, {"start": 2427.46, "end": 2427.8, "word": " لـ", "probability": 0.761474609375}, {"start": 2427.8, "end": 2428.26, "word": " U6", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 99, "seek": 243944, "start": 2431.26, "end": 2439.44, "text": "generator خمسة تربيع بتجيب لل identity الان هل اتنين generator ليه تلاتة؟", "tokens": [21848, 1639, 16490, 2304, 3794, 3660, 6055, 2288, 21292, 3615, 39894, 7435, 1829, 3555, 24976, 6575, 2423, 7649, 8032, 1211, 1975, 2655, 1863, 9957, 19265, 32239, 3224, 6055, 1211, 9307, 3660, 22807], "avg_logprob": -0.2765151515151515, "compression_ratio": 1.101010101010101, "no_speech_prob": 0.0, "words": [{"start": 2431.26, "end": 2432.14, "word": "generator", "probability": 0.5521240234375}, {"start": 2432.14, "end": 2433.32, "word": " خمسة", "probability": 0.8883056640625}, {"start": 2433.32, "end": 2433.66, "word": " تربيع", "probability": 0.7109375}, {"start": 2433.66, "end": 2433.98, "word": " بتجيب", "probability": 0.867431640625}, {"start": 2433.98, "end": 2434.14, "word": " لل", "probability": 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25513, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 4724, 9640, 3555, 27884, 4724, 1829, 9566, 1211, 3615, 36764, 24401, 2423, 6575, 4032, 8032, 4117, 15730, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 8032, 8848, 12610, 28242, 36764, 24401, 3660, 8978, 11296, 1975, 2655, 1863, 9957, 4032, 34105, 1975, 2655, 1863, 9957, 6575, 6575, 19265, 19265, 2423, 1668, 16247, 12610, 7251, 3794, 45865, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 8032, 8848, 12610, 366, 307, 32702, 299, 7251, 3555, 4587, 7578, 8032, 8848, 12610, 32239, 14851, 307, 32702, 299, 44381], "avg_logprob": -0.21344053832072657, "compression_ratio": 1.9, "no_speech_prob": 0.0, "words": [{"start": 2440.17, "end": 2440.77, "word": "هو", "probability": 0.4073486328125}, {"start": 2440.77, "end": 2441.05, "word": " برضه", "probability": 0.5671793619791666}, {"start": 2441.05, "end": 2441.43, "word": " عملية", "probability": 0.7333984375}, {"start": 2441.43, "end": 2441.69, "word": " ضرب", "probability": 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generator", "probability": 0.95849609375}, {"start": 2451.95, "end": 2452.51, "word": " ال", "probability": 0.9404296875}, {"start": 2452.51, "end": 2452.81, "word": " order", "probability": 0.947265625}, {"start": 2452.81, "end": 2453.21, "word": " الأول", "probability": 0.775634765625}, {"start": 2453.21, "end": 2453.47, "word": " يسوي", "probability": 0.5220540364583334}, {"start": 2453.47, "end": 2453.71, "word": " يبقى", "probability": 0.9830322265625}, {"start": 2453.71, "end": 2453.95, "word": " اتنين", "probability": 0.986572265625}, {"start": 2453.95, "end": 2454.25, "word": " هذول", "probability": 0.96337890625}, {"start": 2454.25, "end": 2454.83, "word": " are", "probability": 0.27490234375}, {"start": 2454.83, "end": 2457.13, "word": " isomorphic", "probability": 0.7833658854166666}, {"start": 2457.13, "end": 2457.91, "word": " يبقى", "probability": 0.9842529296875}, {"start": 2457.91, "end": 2458.37, "word": " هذول", "probability": 0.80126953125}, {"start": 2458.37, "end": 2459.03, "word": " ليست", "probability": 0.95361328125}, {"start": 2459.03, "end": 2460.35, "word": " isomorphic", "probability": 0.9402669270833334}, {"start": 2460.35, "end": 2460.93, "word": " لكن", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 101, "seek": 248210, "start": 2480.22, "end": 2482.1, "text": "وانتهينا الموضوع", "tokens": [2407, 7649, 47395, 1829, 8315, 9673, 2407, 11242, 45367], "avg_logprob": -0.2759765625, "compression_ratio": 0.8611111111111112, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2480.22, "end": 2481.62, "word": "وانتهينا", "probability": 0.7118896484375}, {"start": 2481.62, "end": 2482.1, "word": " الموضوع", "probability": 0.935791015625}], "temperature": 1.0}, {"id": 102, "seek": 250742, "start": 2482.45, "end": 2507.43, "text": "يعني ممكن هذا مثال هيعطينا ان two groups ليست isomorphic لكن ال atomorphism على ال group الأولى و ال atomorphism على ال group التانية اتنين are isomorphic هذا سؤال اتناشر السؤال الاربعتاش الشفوي قال لي هاتي ال atomorphism لمن ل Z6", "tokens": [40228, 22653, 3714, 43020, 23758, 50113, 6027, 39896, 3615, 9566, 1829, 8315, 16472, 732, 3935, 32239, 14851, 307, 32702, 299, 44381, 2423, 12018, 18191, 1434, 15844, 2423, 1594, 16247, 12610, 7578, 4032, 2423, 12018, 18191, 1434, 15844, 2423, 1594, 16712, 7649, 10632, 1975, 2655, 1863, 9957, 366, 307, 32702, 299, 23758, 8608, 33604, 6027, 1975, 2655, 1863, 33599, 2288, 21136, 33604, 6027, 2423, 9640, 3555, 34268, 33599, 25124, 5172, 45865, 50239, 32239, 8032, 9307, 1829, 2423, 12018, 18191, 1434, 5296, 27842, 5296, 1176, 21], "avg_logprob": -0.261213225476882, "compression_ratio": 1.824468085106383, "no_speech_prob": 0.0, "words": [{"start": 2482.45, "end": 2482.89, "word": "يعني", "probability": 0.6944580078125}, {"start": 2482.89, "end": 2483.43, "word": " ممكن", "probability": 0.91015625}, {"start": 2483.43, "end": 2483.79, "word": " هذا", "probability": 0.83203125}, {"start": 2483.79, "end": 2484.39, "word": " مثال", "probability": 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يبقى", "probability": 0.9735107421875}, {"start": 3015.01, "end": 3016.01, "word": " الـPhi", "probability": 0.5191650390625}, {"start": 3016.01, "end": 3016.51, "word": " of", "probability": 0.8525390625}, {"start": 3016.51, "end": 3017.03, "word": " X", "probability": 0.91455078125}, {"start": 3017.03, "end": 3018.33, "word": " يساوي", "probability": 0.827880859375}, {"start": 3018.33, "end": 3019.09, "word": " الـX", "probability": 0.66748046875}, {"start": 3019.09, "end": 3020.17, "word": " بدك", "probability": 0.785888671875}, {"start": 3020.17, "end": 3020.77, "word": " تخلي", "probability": 0.8603515625}, {"start": 3020.77, "end": 3021.29, "word": " الأس", "probability": 0.67138671875}, {"start": 3021.29, "end": 3021.87, "word": " فردي", "probability": 0.94873046875}, {"start": 3021.87, "end": 3022.75, "word": " تقدر", "probability": 0.8746744791666666}, {"start": 3022.75, "end": 3023.47, "word": " تقولي", "probability": 0.8160807291666666}, {"start": 3023.47, "end": 3024.07, "word": " اتنين", "probability": 0.80706787109375}, {"start": 3024.07, "end": 3024.51, "word": " N", "probability": 0.65869140625}, {"start": 3024.51, "end": 3025.29, "word": " زائد", "probability": 0.9138997395833334}, {"start": 3025.29, "end": 3025.99, "word": " واحد", "probability": 0.983642578125}, {"start": 3025.99, "end": 3026.91, "word": " is", "probability": 0.8603515625}, {"start": 3026.91, "end": 3027.91, "word": " an", "probability": 0.90478515625}, {"start": 3027.91, "end": 3030.27, "word": " Atomorphism", "probability": 0.6870930989583334}, {"start": 3030.27, "end": 3031.17, "word": " دير", "probability": 0.76220703125}, {"start": 3031.17, "end": 3031.55, "word": " بالك", "probability": 0.789306640625}, {"start": 3031.55, "end": 3031.71, "word": " في", "probability": 0.9638671875}, {"start": 3031.71, "end": 3031.99, "word": " حالة", "probability": 0.8855794270833334}, {"start": 3031.99, "end": 3032.43, "word": " الـX", "probability": 0.7291666666666666}, {"start": 3032.43, "end": 3033.23, "word": " السابعة", "probability": 0.715576171875}, {"start": 3033.23, "end": 3033.69, "word": " ها", "probability": 0.560546875}, {"start": 3033.69, "end": 3033.87, "word": " دي", "probability": 0.67333984375}], "temperature": 1.0}, {"id": 124, "seek": 306186, "start": 3034.58, "end": 3061.86, "text": "ها ها بدي أجيب identity فبصير لما أقولك x أُس أربعة بال identity بصير x أُس تمانية بجداش بال identity يبقى لما أجي أقوله ال x أُس تمانية اللي هي عبارة عن x في x أُس سبعة أو بدي x لحالها بضرب في x أس سالب سبعة بصير ال x هو x أس سالب سبعة و هكذا", "tokens": [3224, 995, 8032, 995, 4724, 16254, 5551, 7435, 1829, 3555, 6575, 6156, 3555, 9381, 13546, 5296, 15042, 5551, 39648, 4117, 2031, 5551, 10859, 3794, 5551, 25513, 27884, 20666, 6575, 4724, 9381, 13546, 2031, 5551, 10859, 3794, 46811, 7649, 10632, 4724, 7435, 3215, 33599, 20666, 6575, 7251, 3555, 4587, 7578, 5296, 15042, 5551, 7435, 1829, 5551, 39648, 3224, 2423, 2031, 5551, 10859, 3794, 46811, 7649, 10632, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 2031, 8978, 2031, 5551, 10859, 3794, 8608, 3555, 27884, 34051, 4724, 16254, 2031, 5296, 5016, 6027, 11296, 4724, 11242, 25513, 8978, 2031, 5551, 3794, 8608, 6027, 3555, 8608, 3555, 27884, 4724, 9381, 13546, 2423, 2031, 31439, 2031, 5551, 3794, 8608, 6027, 3555, 8608, 3555, 27884, 4032, 8032, 4117, 15730], "avg_logprob": -0.17581300546483294, "compression_ratio": 2.145945945945946, "no_speech_prob": 0.0, "words": [{"start": 3034.58, "end": 3035.08, "word": "ها", "probability": 0.29522705078125}, {"start": 3035.08, "end": 3035.9, "word": " ها", "probability": 0.6978759765625}, {"start": 3035.9, "end": 3036.32, "word": " بدي", "probability": 0.6239013671875}, {"start": 3036.32, "end": 3037.0, "word": " أجيب", "probability": 0.82806396484375}, {"start": 3037.0, "end": 3037.96, "word": " identity", "probability": 0.70556640625}, {"start": 3037.96, "end": 3038.82, "word": " فبصير", "probability": 0.8372802734375}, {"start": 3038.82, "end": 3039.06, "word": " لما", "probability": 0.794189453125}, {"start": 3039.06, "end": 3039.54, "word": " أقولك", "probability": 0.8009440104166666}, {"start": 3039.54, "end": 3039.86, "word": " x", "probability": 0.6142578125}, {"start": 3039.86, "end": 3040.22, "word": " أُس", "probability": 0.6025390625}, {"start": 3040.22, "end": 3040.7, "word": " أربعة", "probability": 0.7628580729166666}, {"start": 3040.7, "end": 3040.92, "word": " بال", "probability": 0.97021484375}, {"start": 3040.92, "end": 3041.4, "word": " identity", "probability": 0.91015625}, {"start": 3041.4, "end": 3041.88, "word": " بصير", "probability": 0.9348958333333334}, {"start": 3041.88, "end": 3042.32, "word": " x", "probability": 0.947265625}, {"start": 3042.32, "end": 3042.76, "word": " أُس", "probability": 0.8375651041666666}, {"start": 3042.76, "end": 3043.22, "word": " تمانية", "probability": 0.90234375}, {"start": 3043.22, "end": 3043.92, "word": " بجداش", "probability": 0.71435546875}, {"start": 3043.92, "end": 3044.98, "word": " بال", "probability": 0.92333984375}, {"start": 3044.98, "end": 3045.88, "word": " identity", "probability": 0.93896484375}, {"start": 3045.88, "end": 3046.82, "word": " يبقى", "probability": 0.78076171875}, {"start": 3046.82, "end": 3047.08, "word": " لما", "probability": 0.98681640625}, {"start": 3047.08, "end": 3047.58, "word": " أجي", "probability": 0.9093424479166666}, {"start": 3047.58, "end": 3048.2, "word": " أقوله", "probability": 0.8977864583333334}, {"start": 3048.2, "end": 3048.52, "word": " ال", "probability": 0.8994140625}, {"start": 3048.52, "end": 3048.84, "word": " x", "probability": 0.8115234375}, {"start": 3048.84, "end": 3049.2, "word": " أُس", "probability": 0.908203125}, {"start": 3049.2, "end": 3049.8, "word": " تمانية", "probability": 0.9690755208333334}, {"start": 3049.8, "end": 3049.98, "word": " اللي", "probability": 0.847900390625}, {"start": 3049.98, "end": 3050.12, "word": " هي", "probability": 0.498291015625}, {"start": 3050.12, "end": 3050.6, "word": " عبارة", "probability": 0.9959716796875}, {"start": 3050.6, "end": 3050.92, "word": " عن", "probability": 0.9951171875}, {"start": 3050.92, "end": 3051.48, "word": " x", "probability": 0.96044921875}, {"start": 3051.48, "end": 3051.74, "word": " في", "probability": 0.92138671875}, {"start": 3051.74, "end": 3052.16, "word": " x", "probability": 0.98974609375}, {"start": 3052.16, "end": 3052.68, "word": " أُس", "probability": 0.9459635416666666}, {"start": 3052.68, "end": 3053.18, "word": " سبعة", "probability": 0.8792317708333334}, {"start": 3053.18, "end": 3053.98, "word": " أو", "probability": 0.78271484375}, {"start": 3053.98, "end": 3054.38, "word": " بدي", "probability": 0.919189453125}, {"start": 3054.38, "end": 3054.82, "word": " x", "probability": 0.97900390625}, {"start": 3054.82, "end": 3055.8, "word": " لحالها", "probability": 0.9892578125}, {"start": 3055.8, "end": 3056.74, "word": " بضرب", "probability": 0.853515625}, {"start": 3056.74, "end": 3056.96, "word": " في", "probability": 0.9794921875}, {"start": 3056.96, "end": 3057.32, "word": " x", "probability": 0.98583984375}, {"start": 3057.32, "end": 3057.68, "word": " أس", "probability": 0.863037109375}, {"start": 3057.68, "end": 3058.02, "word": " سالب", "probability": 0.9108072916666666}, {"start": 3058.02, "end": 3058.4, "word": " سبعة", "probability": 0.97265625}, {"start": 3058.4, "end": 3058.92, "word": " بصير", "probability": 0.9641927083333334}, {"start": 3058.92, "end": 3059.1, "word": " ال", "probability": 0.94580078125}, {"start": 3059.1, "end": 3059.34, "word": " x", "probability": 0.88330078125}, {"start": 3059.34, "end": 3059.54, "word": " هو", "probability": 0.96044921875}, {"start": 3059.54, "end": 3059.88, "word": " x", "probability": 0.9931640625}, {"start": 3059.88, "end": 3060.2, "word": " أس", "probability": 0.974609375}, {"start": 3060.2, "end": 3060.58, "word": " سالب", "probability": 0.9654947916666666}, {"start": 3060.58, "end": 3061.0, "word": " سبعة", "probability": 0.9864908854166666}, {"start": 3061.0, "end": 3061.16, "word": " و", "probability": 0.68603515625}, {"start": 3061.16, "end": 3061.86, "word": " هكذا", "probability": 0.8323567708333334}], "temperature": 1.0}, {"id": 125, "seek": 307563, "start": 3062.29, "end": 3075.63, "text": "تمام؟ يعني نفس ال tactic اللي عملنا هنا للحالة الأولى بنروح نعمله لمين؟ للحالة التالتة والحالة التانية وبالتالي عبارة عن atomorphism", "tokens": [39237, 10943, 22807, 37495, 22653, 8717, 36178, 2423, 31012, 13672, 1829, 6225, 42213, 8315, 34105, 24976, 5016, 6027, 3660, 16247, 12610, 7578, 44945, 32887, 5016, 8717, 25957, 1211, 3224, 32767, 9957, 22807, 24976, 5016, 6027, 3660, 16712, 6027, 2655, 3660, 16070, 5016, 6027, 3660, 16712, 7649, 10632, 46599, 6027, 2655, 6027, 1829, 6225, 3555, 9640, 3660, 18871, 12018, 18191, 1434], "avg_logprob": -0.13383708527830782, "compression_ratio": 1.6214285714285714, "no_speech_prob": 0.0, "words": [{"start": 3062.29, "end": 3063.21, "word": "تمام؟", "probability": 0.6839192708333334}, {"start": 3063.21, "end": 3063.49, "word": " يعني", "probability": 0.960205078125}, {"start": 3063.49, "end": 3063.87, "word": " نفس", "probability": 0.998291015625}, {"start": 3063.87, "end": 3064.05, "word": " ال", "probability": 0.86376953125}, {"start": 3064.05, "end": 3064.43, "word": " tactic", "probability": 0.759765625}, {"start": 3064.43, "end": 3064.75, "word": " اللي", "probability": 0.791259765625}, {"start": 3064.75, "end": 3065.35, "word": " عملنا", "probability": 0.9949544270833334}, {"start": 3065.35, "end": 3065.85, "word": " هنا", "probability": 0.990234375}, {"start": 3065.85, "end": 3067.03, "word": " للحالة", "probability": 0.9495849609375}, {"start": 3067.03, "end": 3067.67, "word": " الأولى", "probability": 0.95166015625}, {"start": 3067.67, "end": 3068.35, "word": " بنروح", "probability": 0.84912109375}, {"start": 3068.35, "end": 3068.91, "word": " نعمله", "probability": 0.79437255859375}, {"start": 3068.91, "end": 3069.61, "word": " لمين؟", "probability": 0.82861328125}, {"start": 3069.61, "end": 3070.23, "word": " للحالة", "probability": 0.978759765625}, {"start": 3070.23, "end": 3070.69, "word": " التالتة", "probability": 0.970703125}, {"start": 3070.69, "end": 3071.51, "word": " والحالة", "probability": 0.86083984375}, {"start": 3071.51, "end": 3072.15, "word": " التانية", "probability": 0.9869791666666666}, {"start": 3072.15, "end": 3073.13, "word": " وبالتالي", "probability": 0.894873046875}, {"start": 3073.13, "end": 3073.75, "word": " عبارة", "probability": 0.997314453125}, {"start": 3073.75, "end": 3074.13, "word": " عن", "probability": 0.9912109375}, {"start": 3074.13, "end": 3075.63, "word": " atomorphism", "probability": 0.75390625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3076.87625, "duration_after_vad": 2904.884374999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1fe7affa6453c78fc7a509179f9a1f3da7efe3ad
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48_raw.srt
@@ -0,0 +1,1792 @@
+1
+00:00:21,800 --> 00:00:25,620
+بسم الله الرحمن الرحيم المرة اللى فاتت انتهينا من
+
+2
+00:00:25,620 --> 00:00:30,520
+chapter 6 كنظري والان فينا discussion لهذا ال
+
+3
+00:00:30,520 --> 00:00:35,280
+chapter وعطيناكم مجموعة من الأسئلة أول سؤال كان
+
+4
+00:00:35,280 --> 00:00:42,380
+سؤال اتنين قال لي هتل الautomorphism ل Z قال لي
+
+5
+00:00:42,380 --> 00:00:44,620
+exercises
+
+6
+00:00:45,860 --> 00:00:54,340
+اللي هو ستة سؤال التاني بدنا atomorphism ل z لو
+
+7
+00:00:54,340 --> 00:01:03,160
+جيت قولتك خدلي alpha من z إلى z بيان atomorphism
+
+8
+00:01:03,160 --> 00:01:06,620
+الان
+
+9
+00:01:06,620 --> 00:01:11,460
+بدي أعرف أيه الشكل ال atomorphism هدول السؤال هو
+
+10
+00:01:11,460 --> 00:01:14,560
+ال z هذا فيها كام generator
+
+11
+00:01:21,280 --> 00:01:30,020
+يبقى الان لو جيت ل alpha لما اتأثر على اي element
+
+12
+00:01:30,020 --> 00:01:37,700
+موجود في z وليكن alpha in يبقى بدها تجيب لي الصير
+
+13
+00:01:37,700 --> 00:01:45,710
+in في alpha of oneيبقى اي اتومورفزم بدى يعتمد على
+
+14
+00:01:45,710 --> 00:01:51,510
+شكل مين على شكل ال alpha of one اذا بدنا نعرف شكل
+
+15
+00:01:51,510 --> 00:02:00,830
+ال alpha of one الان الواحد generator for
+
+16
+00:02:00,830 --> 00:02:08,070
+z يبقى هذا معناته ان ال alpha of one is a
+
+17
+00:02:08,070 --> 00:02:14,280
+generatorمش غدناها نظرية لو كان عندك ال group
+
+18
+00:02:14,280 --> 00:02:18,580
+الأولى فيها generator يبقى الصورة وهو generator
+
+19
+00:02:18,580 --> 00:02:22,460
+لمن ال group التانية يبقى alpha of one is a
+
+20
+00:02:22,460 --> 00:02:31,320
+generator لمن لل atom morphism ل z طب
+
+21
+00:02:31,320 --> 00:02:38,260
+مدام هيك يبقى ال alpha of one أكم generator فيه في
+
+22
+00:02:38,260 --> 00:02:38,480
+z
+
+23
+00:02:42,310 --> 00:02:47,290
+يبقى ال alpha of one احتمال انها تكون واحد و
+
+24
+00:02:47,290 --> 00:02:54,610
+احتمال انها تكون جداش زائد واحد يبقى لو كان ال
+
+25
+00:02:54,610 --> 00:03:00,650
+alpha of one يساوي ال one يبقى معناته ان ال alpha
+
+26
+00:03:00,650 --> 00:03:07,080
+of n يساوي ال n يعني هذا ال identity functionلو
+
+27
+00:03:07,080 --> 00:03:13,220
+كان ال alpha of one يساوي ناقص one يبقى ال alpha
+
+28
+00:03:13,220 --> 00:03:19,400
+of n هيساوي كده؟ سالب n معناته هو كم automorphism
+
+29
+00:03:19,400 --> 00:03:25,240
+في عندى؟ اتنين فقط لا غير يبقى هنا
+
+30
+00:03:27,820 --> 00:03:36,600
+أتو مورفزمز لمين لازد هذي has two limits
+
+31
+00:03:42,590 --> 00:03:48,630
+بس عمصرين العمصر الأول هو alpha of n يساوي ال n
+
+32
+00:03:48,630 --> 00:03:54,150
+والتاني alpha of n يساوي ناقص n يعني two atom
+
+33
+00:03:54,150 --> 00:03:58,010
+morphisms فقط يعني two functions one to one and
+
+34
+00:03:58,010 --> 00:04:03,410
+unto وبتخدم خاصية ال isomorphismطب خليني أسأل كمان
+
+35
+00:04:03,410 --> 00:04:07,870
+سؤال مالهوش علاقة بسؤال الكتاب لكن يعتمد على اللي
+
+36
+00:04:07,870 --> 00:04:14,310
+قدامنا هذه حد فيكم بقدر يقولي atomorphism ل Z ايزو
+
+37
+00:04:14,310 --> 00:04:18,730
+مورفك ل مين؟
+
+38
+00:04:18,730 --> 00:04:25,710
+انصرين بس بد جروب فيها انصرين فقط لا غيروهي من
+
+39
+00:04:25,710 --> 00:04:29,510
+أبسط العناصر، المرة اللي فيها تنظرية أثبتنا إن
+
+40
+00:04:29,510 --> 00:04:35,450
+الـAutomorphism لـZN isomorphic لـUN، مظبوط؟
+
+41
+00:04:35,450 --> 00:04:40,070
+وبرأنها أنا بدي الـAutomorphism لـZ isomorphic
+
+42
+00:04:40,070 --> 00:04:47,250
+لمين؟ بدي فيها عنصرين وسمعت أنت قبل قليل، مين؟ Z2
+
+43
+00:04:47,750 --> 00:04:56,350
+يبقى هنا اتومورفزم هذه زيادة لزد ايزو مورفك فقط
+
+44
+00:04:56,350 --> 00:05:05,330
+لزد تو فقط لغير طب هذا كان السؤال الثانيالسؤال
+
+45
+00:05:05,330 --> 00:05:09,950
+اللى بعد السؤال الرابع بيقول لي ان U8 ليست
+
+46
+00:05:09,950 --> 00:05:17,770
+isomorphic ل U10 يبقى السؤال الرابع U8 is not
+
+47
+00:05:17,770 --> 00:05:24,770
+isomorphic ل U10 بدنا نثبت صحة هذا الكلامالان لو
+
+48
+00:05:24,770 --> 00:05:31,250
+جيت لعناصر ال U8 هو عبارة عن واحد و تلاتة و خمسة و
+
+49
+00:05:31,250 --> 00:05:39,490
+سبعة تمام؟ وعناصر ال U10 هو عبارة عن واحد و تلاتة
+
+50
+00:05:39,490 --> 00:05:48,280
+و سبعة و تسعةمش هنثبت ان اتنين ليسوا ايزو مورفك
+
+51
+00:05:48,280 --> 00:05:52,520
+بدي اجيب counter example يعني شغلة متحققة في احدى
+
+52
+00:05:52,520 --> 00:05:56,820
+ال groups و غير متحققة في ال group التاني لو جيت
+
+53
+00:05:56,820 --> 00:06:03,390
+ليه تمانية هل التلاتة هذا generator؟تلاتة وزيرة
+
+54
+00:06:03,390 --> 00:06:08,250
+بواحد، تلاتة وزيرة بواحد بتلاتة تلاتة تربيع اللي
+
+55
+00:06:08,250 --> 00:06:14,290
+هو بتسعة خمسة تربيع اللي هو بواحد، سبعة تربيع اللي
+
+56
+00:06:14,290 --> 00:06:24,070
+هو بواحد يبقى U تمانية Cyclic؟ لأ، U تمانية is not
+
+57
+00:06:24,070 --> 00:06:32,360
+cyclic يعني مافيهاش ولا generatorعشرة تلاتة وزيرة
+
+58
+00:06:32,360 --> 00:06:38,800
+بواحد تلاتة و اص واحد بواحد تلاتة ربيع بتسعة تلاتة
+
+59
+00:06:38,800 --> 00:06:44,520
+تكيب بسبعة يبقى جابة كل العناصر تلاتة و اص اربع
+
+60
+00:06:44,520 --> 00:06:49,190
+ليهمين بواحد تسعة فتسعة و احد تمانينيبقى هذه الـ
+
+61
+00:06:49,190 --> 00:06:55,110
+cyclic والتلاتة generator is not cyclic but اللي
+
+62
+00:06:55,110 --> 00:07:00,570
+هو U عشرة بدها تساوي ال group generated by تلاتة
+
+63
+00:07:00,570 --> 00:07:05,190
+اللي هي ال cyclic معناته هل ممكن اتنين يكونوا هدول
+
+64
+00:07:05,190 --> 00:07:10,990
+isomorphic طبعا لأ لإن واحدة cyclic والتانية لأ
+
+65
+00:07:10,990 --> 00:07:19,320
+يبقى هنا سواء ال U تمانيةالـ U8 is not isomorphic
+
+66
+00:07:19,320 --> 00:07:27,140
+لمن؟ لـ U10 ممكن مش بضرورة الـ cyclic ممكن تجيبلي
+
+67
+00:07:27,140 --> 00:07:31,140
+هنا مثلا two elements ال order اللي لهم يساوي
+
+68
+00:07:31,140 --> 00:07:34,600
+اتنين هنا تجيبلي two elements ولا اربعة elements
+
+69
+00:07:34,600 --> 00:07:37,940
+ال order اللي لهم يساوي اتنين يعني عدل عناصر اللي
+
+70
+00:07:37,940 --> 00:07:40,880
+لهم ال order هنا يختلف عن عدل عناصر اللي لهم ال
+
+71
+00:07:40,880 --> 00:07:45,590
+order هنا وبالتاليمافيش isomorphism ما بين الاتنين
+
+72
+00:07:45,590 --> 00:07:52,210
+هذا كان السؤال الرابع و بعدين السؤال السادس G
+
+73
+00:07:52,210 --> 00:07:58,590
+isomorphic ل H و H isomorphic ل K السؤال السادس
+
+74
+00:07:59,750 --> 00:08:07,470
+عندك G isomorphic ل H و ال H isomorphic ل K بدنا
+
+75
+00:08:07,470 --> 00:08:16,020
+نثبت ان ال G isomorphic لمن A ل Kوهذه تسميناها
+
+76
+00:08:16,020 --> 00:08:21,560
+الـtransitive property خاصية النقل أو بقنا نقول ال
+
+77
+00:08:21,560 --> 00:08:25,860
+relation reflexive وtransitive and symmetric هذه
+
+78
+00:08:25,860 --> 00:08:30,780
+هي حكاية لـtransitive لو كان الـG عيزومورفق لـH وH
+
+79
+00:08:30,780 --> 00:08:37,540
+نفسها عيزومورفق لـK يبقى الـG عيزومورفق لمين؟ لـK
+
+80
+00:08:38,160 --> 00:08:45,500
+يبقى بداجي اقول solution معناته بدنا نفترض assume
+
+81
+00:08:45,500 --> 00:08:56,940
+ان في of واحد من g إلى h is an isomorphism and وفي
+
+82
+00:08:56,940 --> 00:09:07,540
+نفس الوقت في اتنين من ال h إلى k is an isomorphism
+
+83
+00:09:10,110 --> 00:09:15,790
+بدي أحاول أثبت أنه في عندي function من G إلى K
+
+84
+00:09:15,790 --> 00:09:21,230
+تالي هذه ملاتبج isomorphism مدام هذا isomorphism و
+
+85
+00:09:21,230 --> 00:09:30,110
+هذا isomorphism معناته أن الـPhi 1 و Phi 2 هم 1 to
+
+86
+00:09:30,110 --> 00:09:36,710
+1 and on 2 كويس
+
+87
+00:09:37,460 --> 00:09:42,700
+يبقى في is one to one and unto معناه هذا الكلام ان
+
+88
+00:09:42,700 --> 00:09:49,060
+ال composition تبعهم في two في one is one to one
+
+89
+00:09:49,060 --> 00:09:56,800
+and unto في نفس الوقتطيب إذا طلع في 2 في 1 عبارة
+
+90
+00:09:56,800 --> 00:10:02,920
+عن isomorphism بتم المطلب طيب السؤال هو هل ال في 2
+
+91
+00:10:02,920 --> 00:10:09,540
+في 1 هي function من G إلى K؟ Calculus أيه هذا؟
+
+92
+00:10:09,540 --> 00:10:13,840
+مالوش دعوة بالجبه أنا عندي في function من هنا لهنا
+
+93
+00:10:13,840 --> 00:10:19,700
+يعني لو بجينا نقول لو أخدنا هذه ال Gو هذه ال H
+
+94
+00:10:19,700 --> 00:10:26,480
+وهذه ال K من هنا لهنا في function اسمها في one و
+
+95
+00:10:26,480 --> 00:10:31,820
+من هنا لهنا في function اسمها في two بدي function
+
+96
+00:10:31,820 --> 00:10:39,280
+من الأولى للثانية فباخد ما لا باخد في two ل في one
+
+97
+00:10:39,280 --> 00:10:45,840
+of xوالـ X موجودة في جروب G يبقى بدي يعطيني فاي
+
+98
+00:10:45,840 --> 00:10:50,700
+وان of X يبقى موجودة في H إذا هذه صارت domain
+
+99
+00:10:50,700 --> 00:10:55,140
+element في ضمن الـ FII يبقى FII بتقدر تأثر عليها
+
+100
+00:10:55,140 --> 00:11:00,700
+وبالتالي بصير FII و FII هي function من مين؟ من G
+
+101
+00:11:00,700 --> 00:11:08,440
+إلى K مباشرة يبقى أنا أثبتله أن FII و FII يبقى هنا
+
+102
+00:11:10,490 --> 00:11:18,070
+فاي تو في وان هي function من g إلى k إذا قلت أثبت
+
+103
+00:11:18,070 --> 00:11:21,410
+إنها بتخدم خاصية ال isomorphism بتتم المطموب أن
+
+104
+00:11:21,410 --> 00:11:28,790
+يثبت إنها y to one and on لذلك بتروح أخد فاي تو في
+
+105
+00:11:28,790 --> 00:11:38,370
+وان هذه كلها اللي عندنا as a function of x في yهل
+
+106
+00:11:38,370 --> 00:11:43,190
+هذه isomorphism ولا لا يبقى هذا الكلام بدل يساوي
+
+107
+00:11:43,190 --> 00:11:51,610
+في 2 لفي 1 of x في y هذا بدل يساوي في 2 والان في 1
+
+108
+00:11:51,610 --> 00:11:59,150
+عبارة عن isomorphism إذا تقدر تدخل على كل من ال x
+
+109
+00:11:59,150 --> 00:12:08,380
+وكذلك تدخل على ال yبالمثل في تو ايزو مورفزم و في
+
+110
+00:12:08,380 --> 00:12:14,020
+ون اكس و في ون اللي موجودة وين في H مدام ال H يبقى
+
+111
+00:12:14,020 --> 00:12:19,720
+في تو بتقدر تدخل عليهم يبقى هذا الكلام بده يساوي
+
+112
+00:12:19,720 --> 00:12:28,180
+في تو لفي ون of X وهنا في تو لفي ون of Y
+
+113
+00:12:30,800 --> 00:12:36,200
+طيب هذا الكلام لو جيت رجعتها الى أصلة هذا تعريف ال
+
+114
+00:12:36,200 --> 00:12:41,400
+composition of functions يبقى في two في one of x
+
+115
+00:12:41,400 --> 00:12:49,160
+والتانية في two في one of y يبقى صارت isomorphism
+
+116
+00:12:49,160 --> 00:12:57,020
+يبقى هذا بده يعطيناإن الجي إيزو مورفك لكيه وهو
+
+117
+00:12:57,020 --> 00:13:01,000
+المطلوب هو هذا اللي بيسميه في الرياضيات خاصية
+
+118
+00:13:01,000 --> 00:13:06,600
+transit أنا عندي isomorphism من ال group الأولى
+
+119
+00:13:06,600 --> 00:13:09,780
+إلى التانية وعندي isomorphism من التانية إلى
+
+120
+00:13:09,780 --> 00:13:14,020
+التالتة إذا بصير عندي isomorphism من الأولى إلى
+
+121
+00:13:14,020 --> 00:13:22,810
+الثالثة هذا كان سؤال ستة سؤال سبعةبيقول لي بييل لي
+
+122
+00:13:22,810 --> 00:13:34,110
+ان ال S4 is not isomorphic ل D12 سؤال 7 S4
+
+123
+00:13:34,110 --> 00:13:38,550
+is not isomorphic ل D12
+
+124
+00:13:40,360 --> 00:13:48,300
+هذا يجعلني أسئل السؤال التالي ال S4 هذه ال S4 قداش
+
+125
+00:13:48,300 --> 00:13:55,040
+أعلى order لأي element فيها S4
+
+126
+00:13:55,040 --> 00:14:02,540
+قداش أعلى order يلا يبدأ حل ال 4 3 1 2 2 2 1 1
+
+127
+00:14:02,540 --> 00:14:08,430
+قداش أعلى order لهم دولالاربعة، تلاتة ولا واحد،
+
+128
+00:14:08,430 --> 00:14:15,310
+اتنين واتنين، اتنين وواحد، كداش اعلى order؟ كداش؟
+
+129
+00:14:15,310 --> 00:14:20,710
+اعلى order لل S، اربعةمش جيبنا اعلى order لل S7 و
+
+130
+00:14:20,710 --> 00:14:26,470
+S6 بالمثل بده يجيب اعلى order لل S4 يبقى بده يشوف
+
+131
+00:14:26,470 --> 00:14:32,890
+قداش اكبر cycle في S4 اللي طولها أربع بعدها طولها
+
+132
+00:14:32,890 --> 00:14:36,170
+تلاتة في واحد بعدها طولها اتنين في اتنين بعدها
+
+133
+00:14:36,170 --> 00:14:39,450
+اتنين في واحد في واحد بعدها واحد واحد واحد قداش
+
+134
+00:14:39,450 --> 00:14:45,080
+اعلى order يعني في S4 الحين صاركداش؟ أربع، مافيش
+
+135
+00:14:45,080 --> 00:14:58,840
+غيره يبقى هنا ال maximum order of elements of S
+
+136
+00:14:58,840 --> 00:15:04,560
+أربع is أربع طيب، بالدجلة دي اتناشة كام element
+
+137
+00:15:04,560 --> 00:15:05,500
+فيها هذه؟
+
+138
+00:15:08,080 --> 00:15:13,420
+بلاش دي اتناش دي اربعة اكم element فيها تمانية
+
+139
+00:15:13,420 --> 00:15:17,560
+يعني قدها مرتين يبقى دي اتناش اكم element فيها
+
+140
+00:15:17,560 --> 00:15:23,240
+اربعة و عشرين element لما اقول دي اربعة هي E و R
+
+141
+00:15:23,240 --> 00:15:27,300
+تسعين و R مية و تمانين و R متين و سبعين و H و V و
+
+142
+00:15:27,300 --> 00:15:33,220
+D و D prime مظبوط يعني كأنه بدي اقول ان دي اربعة E
+
+143
+00:15:33,220 --> 00:15:38,410
+و رو و رو تربية و رو تكيب و فايوراه اتش وراه تربيه
+
+144
+00:15:38,410 --> 00:15:43,070
+اتش وراه تكيب اتش طب لو كان دي اتناش يبقى بده
+
+145
+00:15:43,070 --> 00:15:46,490
+اقوله ايه وراه وراه تربيه وراه تكيب لما اتموصل
+
+146
+00:15:46,490 --> 00:15:52,370
+لروح داش يبقى اعلى element في دي اتناش ال order
+
+147
+00:15:52,370 --> 00:16:05,570
+اللي قداش قداش اتناش هنا بقى the maximum order of
+
+148
+00:16:06,430 --> 00:16:15,170
+Elements of D12 is 12 يبقى هدول ممكن يكونوا are
+
+149
+00:16:15,170 --> 00:16:21,020
+isomorphicلا يمكن لأن أعلى order هنا بيجيب له أعلى
+
+150
+00:16:21,020 --> 00:16:26,100
+order هنا بالضبط تماما جده لو في isomorphism مافيش
+
+151
+00:16:26,100 --> 00:16:31,340
+يبقى لا يمكن يكون بينهم isomorphism يبقى هنا sole
+
+152
+00:16:31,340 --> 00:16:37,000
+S4 is not isomorphic الذي أطلعش هذا الكلام مامروش
+
+153
+00:16:37,000 --> 00:16:41,760
+هيحصل على الإطلاق رغم أنه عدد الأولى أربع وعشرين
+
+154
+00:16:41,760 --> 00:16:49,230
+element وعدد التانية أربع وعشرين elementكذلك طيب
+
+155
+00:16:49,230 --> 00:16:53,350
+هذا السؤال سبعة السؤال تمانية بييل لي اللي ال
+
+156
+00:16:53,350 --> 00:16:58,270
+group ال function a بالستوي الوريثمي is an
+
+157
+00:16:58,270 --> 00:17:05,590
+isomorphism ل R plus under multiplication to R
+
+158
+00:17:05,590 --> 00:17:12,700
+under addition هذه من ال R plus يبقى احناعن هذا
+
+159
+00:17:12,700 --> 00:17:22,530
+سؤال تمانية عن فايمانمن ال R plus اذا انا تموز
+
+160
+00:17:22,530 --> 00:17:31,010
+from R plus under multiplication تحت عملية الضرب
+
+161
+00:17:31,010 --> 00:17:39,230
+الى R تحت عملية من تحت عملية الجامعة معرفة بالتالي
+
+162
+00:17:39,230 --> 00:17:45,790
+Phi of A بده يساوي لغارتم الأيه للأساس عشرة؟ ساوي
+
+163
+00:17:45,790 --> 00:17:50,170
+اللغة ريتمال أيه للأساس عشرة؟ بدي أثبت إن هذا
+
+164
+00:17:50,170 --> 00:18:04,070
+عبارة عن isomorphism اه
+
+165
+00:18:04,070 --> 00:18:10,490
+ليه بدأت هنا؟الأن الـ operation هنا عملية ضرب على
+
+166
+00:18:10,490 --> 00:18:14,750
+مجموعة الأعداد الحقيقية الموجبة هنا ال operation
+
+167
+00:18:14,750 --> 00:18:17,510
+عملية تجمع على مجموعة الأعداد الحقيقية الموجبة
+
+168
+00:18:17,510 --> 00:18:22,090
+والسلبة والصفر كله الأعداد الحقيقية كلها عرفنا
+
+169
+00:18:22,090 --> 00:18:25,450
+function بالـPhi of a يساوي لغرتم الـa للأساس عشرة
+
+170
+00:18:25,450 --> 00:18:30,670
+بدي أثبت أن هذا عبارة عن isomorphism مشان أثبت أن
+
+171
+00:18:30,670 --> 00:18:36,560
+هو isomorphism بدي أثبت أن Phi is one to oneلذلك
+
+172
+00:18:36,560 --> 00:18:44,220
+بتروح اخد صورتين متساويتين assume ان فاي of a
+
+173
+00:18:44,220 --> 00:18:50,460
+بتساوي فاي of b thenطب لما أخدت صورتين متساوية
+
+174
+00:18:50,460 --> 00:18:55,880
+إمشانات بينها one to one إيش عايز أثبت؟ إن ال A
+
+175
+00:18:55,880 --> 00:19:02,740
+تساوي ال B يبقى بناء عليه Phi of A هي لغرتم ال A
+
+176
+00:19:02,740 --> 00:19:09,660
+للأساس عشرة وال Phi of B هو لغرتم ال B للأساس عشرة
+
+177
+00:19:10,420 --> 00:19:16,940
+معنى هذا الكلام هذي بقدر اكتبها بدلالة لن يبقى لن
+
+178
+00:19:16,940 --> 00:19:24,800
+ال a على لن على لن العشرة و هذي بدي يسوى لن ال b
+
+179
+00:19:24,800 --> 00:19:30,830
+على لن العشرةلو ضربت الطرفين في لن العشرة لأن لن
+
+180
+00:19:30,830 --> 00:19:37,070
+العشرة مقدارا ثابتا يبقى بده يصير لن ال A بده يسوى
+
+181
+00:19:37,070 --> 00:19:44,990
+لن ال B لو رفعت كل واحد فيهم كأس للعدد A يبقى هوصل
+
+182
+00:19:44,990 --> 00:19:51,740
+ان ال A بده يسوى 2بدو يساوي ال B وبناء عليه ال FI
+
+183
+00:19:51,740 --> 00:19:57,940
+is one to one بدي أحاول أثبتله الآن ان ال FI is
+
+184
+00:19:57,940 --> 00:20:05,080
+onto مشان هيك بدي أقعد أخد ال Y موجودة في من؟
+
+185
+00:20:05,080 --> 00:20:13,100
+موجودة في R او خليني أخد ال B خليني ال A و B خدلي
+
+186
+00:20:13,100 --> 00:20:19,350
+ال B موجودة في Rإذا بدأ أحاول أثبت إن الـ EPI اللي
+
+187
+00:20:19,350 --> 00:20:26,510
+أخدتها في R لها أصل في الـ R plus بقوله والله كويس
+
+188
+00:20:26,510 --> 00:20:30,530
+الـ P اللي موجودة في R احتمال تبقى positive
+
+189
+00:20:30,530 --> 00:20:36,090
+واحتمال تبقى negative واحتمال الـ zero مظبوط إذا
+
+190
+00:20:36,090 --> 00:20:39,770
+بدأ أحاول أدرس كل هذه الاحتمالات و أشوف هذه
+
+191
+00:20:39,770 --> 00:20:41,330
+بتوصلني إلى وين
+
+192
+00:20:44,240 --> 00:20:51,340
+يبقى بالضابط أقول له if الـB أكبر من الـZ يعني لو
+
+193
+00:20:51,340 --> 00:20:57,640
+كانت القيمة هذه قيمة موجبة اللي أخدتها يبقى then
+
+194
+00:20:57,640 --> 00:21:00,820
+الآن
+
+195
+00:21:00,820 --> 00:21:09,790
+هل الـB هذه تساوي أو then؟ there existاللي هو A
+
+196
+00:21:09,790 --> 00:21:17,150
+بحيث ال A يكون أكبر من ال واحد such that .. such
+
+197
+00:21:17,150 --> 00:21:25,330
+that ان ال B يسوى لغارتهم ال A للأساس عشرةهل هذا
+
+198
+00:21:25,330 --> 00:21:29,590
+الكلام ممكن و الله غير ممكن نشتغل Calculus احنا
+
+199
+00:21:29,590 --> 00:21:35,410
+الحين نشتغل Calculus بي لو رجعنا ل Calculus بي
+
+200
+00:21:35,410 --> 00:21:41,250
+منحنا الان كان بالشكل اللي عندك كده IY تسوى لن ال
+
+201
+00:21:41,250 --> 00:21:46,730
+X وهذا النقطة واحدة وهي Zero احنا بنقول لو كان ال
+
+202
+00:21:46,730 --> 00:21:54,280
+بي موجبة يبقى ال بي تسوى لغرتم عدد ده مظبوطوأجتاش
+
+203
+00:21:54,280 --> 00:21:59,820
+اللغة رتم هذا يكون موجبا إذا كان العدد اللي عندي
+
+204
+00:21:59,820 --> 00:22:05,300
+هذا معله أكبر من الواحد إذا لما أقول لو كانت ال B
+
+205
+00:22:05,300 --> 00:22:11,120
+موجبة يبقى هلاقي الرقم أكبر من الواحد بحيث B بده
+
+206
+00:22:11,120 --> 00:22:18,920
+يساوي هذه وهذه اللي هي من I of Aطيب هذا لو كانت
+
+207
+00:22:18,920 --> 00:22:25,140
+الـB موجبة كلامنا صح طب لو كانت الـB بـ0 يبقى باجي
+
+208
+00:22:25,140 --> 00:22:29,760
+بقول له هذه الحالة الأولى الحالة الثانية لو كانت
+
+209
+00:22:29,760 --> 00:22:36,600
+الـB تساوي 0 then بدي
+
+210
+00:22:36,600 --> 00:22:43,920
+أخد الـA بواحد thenاللي هو ال zero هذا بده يساوي
+
+211
+00:22:43,920 --> 00:22:53,000
+لين أو بده يساوي لغا ريتم الواحد للأساس عشرة كيف؟
+
+212
+00:22:55,210 --> 00:22:59,930
+لغة راتب او لن اتنين نفس الرسمة كله يمر بهذه
+
+213
+00:22:59,930 --> 00:23:05,590
+النقطة بس بيجرب على المحور او بيبعد عنها مديش غلبك
+
+214
+00:23:05,590 --> 00:23:12,870
+هذا log X للاساس عشرة خليها هي ماشي ماهي ال log هي
+
+215
+00:23:12,870 --> 00:23:19,520
+ال لن بس بتنضر في مقدار ثابت فقط لا غيرطيب يبقى
+
+216
+00:23:19,520 --> 00:23:25,520
+صار ال zero بده يساوي log الواحد للأساس عشرة يعني
+
+217
+00:23:25,520 --> 00:23:33,160
+هذا log ال a للأساس عشرة اللي هو بده يساوي في of a
+
+218
+00:23:33,160 --> 00:23:41,400
+وال a تساوي واحد يبقى صارت في is onto طب لو كانت
+
+219
+00:23:41,400 --> 00:23:53,810
+سالبة يبقى f ال b أقل من ال zerothen ال b تساوي أو
+
+220
+00:23:53,810 --> 00:24:02,370
+then there exist لازم ألاقي a أكبر من ال zero أقل
+
+221
+00:24:02,370 --> 00:24:07,620
+من ال واحد طلّالي على الفترة هذهالفترة هذه لما
+
+222
+00:24:07,620 --> 00:24:12,240
+تاخد ال log لأي رقم هنا إيش بيطلع قيمة موجبولة
+
+223
+00:24:12,240 --> 00:24:17,940
+سالبة يبقى قيمة سالبة معناه هذا الكلام لازم ألاقي
+
+224
+00:24:17,940 --> 00:24:26,800
+a موجود من صفر إلى واحد such that بحيث أن ال b هذي
+
+225
+00:24:26,800 --> 00:24:33,990
+بده يساوي log a للعساس عشرة اللي هو five of aيبقى
+
+226
+00:24:33,990 --> 00:24:39,250
+ليه جميع قيم بيه الموجبة والسلبة والصفر لقيت اللي
+
+227
+00:24:39,250 --> 00:24:44,650
+هي أصل اسمه Phi of A يبقى Phi of A او Phi is
+
+228
+00:24:44,650 --> 00:24:52,990
+hundred يبقى هنا ف Phi is hundredبقيت عند النقطة
+
+229
+00:24:52,990 --> 00:24:57,230
+الأخيرة لإنه اثبتله الآن انه في one two one
+
+230
+00:24:57,230 --> 00:25:02,210
+واثبتله انه في is on two مش ضايل عندنا إلا نثبت
+
+231
+00:25:02,210 --> 00:25:09,750
+خاصية من ال isomorphism الآن بدى أروح أاخدله ال في
+
+232
+00:25:09,750 --> 00:25:16,910
+of x في y طبعا كون ال في من الست اللي عليها الضرب
+
+233
+00:25:16,910 --> 00:25:22,510
+بدى أروح للست اللي عليها من الجامعةيبقى حسب ال
+
+234
+00:25:22,510 --> 00:25:30,550
+definition هذا الكلام بده يساوي log xy للأساس عشرة
+
+235
+00:25:32,030 --> 00:25:36,930
+نرجع لمعلوماتنا عن ال log ال log لحاصل الضرب يساوي
+
+236
+00:25:36,930 --> 00:25:43,310
+حاصل جمع ال two logs يبقى هذا الكلام يساوي log x
+
+237
+00:25:43,310 --> 00:25:49,950
+للأساس عشرة زائد log y للأساس عشرة هذه اللي هي
+
+238
+00:25:49,950 --> 00:25:57,560
+five of x وهذه اللي هي five of yيبقى بناء عليه
+
+239
+00:25:57,560 --> 00:26:08,060
+بقوله غص و هكذا ف I of A يسوى لج ال A للأساس عشرة
+
+240
+00:26:08,060 --> 00:26:18,200
+لج ال A للأساس عشرة is an isomorphism
+
+241
+00:26:45,420 --> 00:26:51,760
+هذا كان سؤال تمانية سؤال تسعة بثبتناه في المحاضرة
+
+242
+00:26:51,760 --> 00:26:59,600
+السؤال عاشرة بيقول لي ان جي جروب from the mapping
+
+243
+00:26:59,600 --> 00:27:09,200
+اللي هي the mapping Alpha G بتسوي G inverse for
+
+244
+00:27:09,200 --> 00:27:13,960
+all G is an atom morphism if and only if ال G is
+
+245
+00:27:13,960 --> 00:27:24,640
+abelianيبقى هذا سؤال عشرة سؤال عشرة Alpha of G بده
+
+246
+00:27:24,640 --> 00:27:32,820
+يساوي G inverse هذا معنى لكل الـG اللي معنى is
+
+247
+00:27:32,820 --> 00:27:41,540
+atomorphism is atomorphism if and only if الـG is
+
+248
+00:27:41,540 --> 00:27:52,100
+abelian الـGas abelian الـ G is abelian شوفوا يا
+
+249
+00:27:52,100 --> 00:27:55,380
+سيدي solution
+
+250
+00:27:55,380 --> 00:28:00,700
+بيقول
+
+251
+00:28:00,700 --> 00:28:05,940
+ال function اللي هي Alpha من G إلى G يعني Alpha
+
+252
+00:28:05,940 --> 00:28:12,120
+هذهمن جيه إلى جيه المعرفة alpha جيه ساوي جيه انفا
+
+253
+00:28:12,120 --> 00:28:17,800
+سابارع ان اتومورفزم اذا كانت الجيه is abelianكلمة
+
+254
+00:28:17,800 --> 00:28:22,240
+if and only if تعني ان البرهن سيصير في اتجاهين
+
+255
+00:28:22,240 --> 00:28:29,360
+تفكير بده اروح اخدني اتجاهي الاول assume that ان
+
+256
+00:28:29,360 --> 00:28:35,620
+ال alpha of g بده يساوي g inverse is an
+
+257
+00:28:35,620 --> 00:28:40,800
+atomorphism ايش بده نثبت؟
+
+258
+00:28:44,150 --> 00:28:48,310
+أنا بدي أثبت ان جي واحد جي اتنين يستوي جي اتنين جي
+
+259
+00:28:48,310 --> 00:28:54,890
+واحد for all جي واحد و جي اتنين اللي موجودة في جي
+
+260
+00:28:54,890 --> 00:29:00,950
+مادام alpha of g بيستوي g inverse لو جيت أخد alpha
+
+261
+00:29:00,950 --> 00:29:07,980
+of g واحد جي اتنينهذا الكلام بقدر اقول alpha of g
+
+262
+00:29:07,980 --> 00:29:13,880
+واحد في alpha of g اتنين صحيح هذا يا شباب صحيح لان
+
+263
+00:29:13,880 --> 00:29:19,160
+انا فرض ان alpha عبارة عن ايش atomorphism يعني
+
+264
+00:29:19,160 --> 00:29:25,660
+ايزو مورفيزم هذا الكلام صحيح since alpha is an
+
+265
+00:29:25,660 --> 00:29:33,400
+isomorphism طيب بطء ولكن ال alpha of g واحد g
+
+266
+00:29:33,400 --> 00:29:34,020
+اتنين
+
+267
+00:29:36,870 --> 00:29:46,150
+حسب التعريف بدها تساوي G1 G2 Inverse بلغة
+
+268
+00:29:46,150 --> 00:29:55,790
+المعكوسات يبقى هو G2 Inverse G1 Inverse يعني هذا
+
+269
+00:29:55,790 --> 00:30:05,520
+Alpha of G2 في Alpha of G1طب الطرف الشمال هذا هو
+
+270
+00:30:05,520 --> 00:30:10,920
+الطرف الشمال هنا إذا الطرف اليمين هو الطرف اليمين
+
+271
+00:30:10,920 --> 00:30:17,620
+يبقى هذا إيش بده يعطينا بده يعطينا Alpha of G1
+
+272
+00:30:17,620 --> 00:30:28,200
+Alpha of G2 بده يساوي Alpha of G2 Alpha of G1 طيب
+
+273
+00:30:28,200 --> 00:30:34,060
+ال Alpha هذا إيش فرضه أناAtomorphism يعني ايزو
+
+274
+00:30:34,060 --> 00:30:39,780
+مورفزم اذا بده ارجع كل واحد الى اصله يبقى هذا
+
+275
+00:30:39,780 --> 00:30:48,980
+معناته انه Alpha of G1 G2 بده يساوي Alpha of G2 G1
+
+276
+00:30:48,980 --> 00:30:55,120
+طب ال Alpha ايش جايل عليها انا Atomorphism يعني
+
+277
+00:30:55,120 --> 00:31:05,830
+one to one يبقى باطل ولكنالفا is one to one اذا
+
+278
+00:31:05,830 --> 00:31:12,570
+صورتين متساويتين يبقى جي واحد جي اتنين بتساوي جي
+
+279
+00:31:12,570 --> 00:31:19,490
+اتنين جي واحد لكل الجي واحد وجي اتنين اللي موجودات
+
+280
+00:31:19,490 --> 00:31:26,340
+فيه جي ايش معنى هذا الكلام انه جي is a billionيبقى
+
+281
+00:31:26,340 --> 00:31:34,580
+هنا الـ g is abelian الان هذا الاتجاه الأول بروح
+
+282
+00:31:34,580 --> 00:31:44,920
+نقوله conversely assume افترض that ان الـ g is
+
+283
+00:31:44,920 --> 00:31:50,020
+abelian افترض
+
+284
+00:31:50,020 --> 00:31:56,670
+ان الـ g is abelian ايش بده نثبت؟هذا isomorphism
+
+285
+00:31:56,670 --> 00:32:02,010
+يعني بدي أثبت انه one to one وانتوا ويخدم خاصية
+
+286
+00:32:02,010 --> 00:32:08,650
+مين ال isomorphism بعدين بقوله كويس يبقى بدي أروح
+
+287
+00:32:08,650 --> 00:32:16,150
+أخدله اللي هو ال alpha is one to one بدي أحاول
+
+288
+00:32:16,150 --> 00:32:25,720
+أثبتها لذلك بدي أقوله assumeافترض ان alpha of G1
+
+289
+00:32:25,720 --> 00:32:34,460
+يساوي alpha of G2 اذا قدرت اثبت له ان G1 يساوي G2
+
+290
+00:32:34,460 --> 00:32:39,280
+يكون اثبتنا انها alpha one to one
+
+291
+00:32:43,290 --> 00:32:49,050
+حسب التعريف alpha of G1 إيش بتبقى G1 inverse و
+
+292
+00:32:49,050 --> 00:32:56,470
+alpha of G2 بصير G2 inverse إيش رأيك بدي أضرب من
+
+293
+00:32:56,470 --> 00:33:06,550
+جهة اليمين في G2 يبقى إيش بصير G1 inverse G2 بدي
+
+294
+00:33:06,550 --> 00:33:10,130
+أسوأ ال identity صح؟
+
+295
+00:33:11,110 --> 00:33:17,670
+طب بدى اضرب من جهة الشمال في G1 يبقى هذا معناته
+
+296
+00:33:17,670 --> 00:33:27,630
+انه G2 بده يساوي ال G1 اظن و هو المطلوب طيب ضايق
+
+297
+00:33:27,630 --> 00:33:33,230
+نثبت علينا الآن ان ال alpha هذه is on
+
+298
+00:33:36,310 --> 00:33:43,410
+يبقى بدأ أخد element في g و أثبت أنه له أصل في g
+
+299
+00:33:43,410 --> 00:33:54,830
+يبقى لو جيت قلت لك little y belongs to g then بدأ
+
+300
+00:33:54,830 --> 00:34:01,110
+أحاول أثبت أن هذا ال element اللي أخدته هنا هنا له
+
+301
+00:34:01,110 --> 00:34:09,620
+أصل موجود هنايبقى روحت أخدت ال Y موجود في G then
+
+302
+00:34:09,620 --> 00:34:17,320
+ال Y بقدر أكتبها كيف؟
+
+303
+00:34:17,320 --> 00:34:21,440
+جي
+
+304
+00:34:21,440 --> 00:34:22,200
+جروب أيوة
+
+305
+00:34:25,220 --> 00:34:29,380
+هذا يعني جي اللي موجود في جي له معكوس لكن انا بدأ
+
+306
+00:34:29,380 --> 00:34:36,320
+اثبت ان هذا المعكوس هو يساوي فاي of شغله، مظبوط؟
+
+307
+00:34:36,320 --> 00:34:42,900
+هذا ليش اللي عايزين تفهمه؟ يبقى انا اخدت Y، then Y
+
+308
+00:34:42,900 --> 00:34:49,420
+inverse هذا بدي يكون موجود في جي، ليش؟ لأن الـG is
+
+309
+00:34:49,420 --> 00:34:50,340
+a group
+
+310
+00:34:56,530 --> 00:35:07,090
+طيب الان ال y هذه بقدر اكتبها y inverse inverse
+
+311
+00:35:07,090 --> 00:35:15,310
+بنفعله مانفعش 100% ايش رايك y inverse بدي اكتبها x
+
+312
+00:35:15,310 --> 00:35:20,570
+inverse يعني بدي اشيل اللي بين قسين و اكتب بدلها x
+
+313
+00:35:20,570 --> 00:35:29,800
+طب بين هي هذه مش هي alpha of xصح ولا لأ يبقى ال
+
+314
+00:35:29,800 --> 00:35:36,800
+element y اللي موجود في g لاجتله أصل x موجود في g
+
+315
+00:35:36,800 --> 00:35:43,100
+يبقى ال alpha is on it ضايل عليه فقط أن أثبت أن
+
+316
+00:35:43,100 --> 00:35:51,440
+alpha عبارة عن isomorphism finally أخيرا
+
+317
+00:35:51,440 --> 00:36:04,710
+بدي أخد alpha ofG1 G2 يساوي اللي هو ال G1 G2 كله
+
+318
+00:36:04,710 --> 00:36:13,030
+inverse تمام؟ يبقى هذا بده يعطيني G2 inverse G1
+
+319
+00:36:13,030 --> 00:36:20,690
+inverse السؤال هو هل هذا G1 inverse G2 inverse قلب
+
+320
+00:36:20,690 --> 00:36:27,580
+توضعها؟أه لماذا؟ لأنه فارض انا ان جي is abelian
+
+321
+00:36:27,580 --> 00:36:32,140
+وحتى هذه اللحظة اللي مستخدم قاضيها القاصية لماذا
+
+322
+00:36:32,140 --> 00:36:40,480
+هذا؟ since ال جي is abelian مدام
+
+323
+00:36:40,480 --> 00:36:51,040
+abelian يبقى الأول alpha of g1والتاني alpha of G2
+
+324
+00:36:51,040 --> 00:36:57,700
+يبقى sir alpha of G1 G2 هو alpha of G1 G2 بناء ان
+
+325
+00:36:57,700 --> 00:37:02,800
+علي ال alpha انا ماخدها من G الى G ان ال alpha
+
+326
+00:37:02,800 --> 00:37:09,860
+عبارة عن atomorphism thus ال alpha is an
+
+327
+00:37:09,860 --> 00:37:12,520
+atomorphism
+
+328
+00:37:41,820 --> 00:37:46,500
+طيب هذا كان سؤال عشرة من الكتاب السؤال اتناش for
+
+329
+00:37:46,500 --> 00:37:51,160
+two groups جي and ليش ساطجات الجي ليست اوم ايزوم
+
+330
+00:37:51,160 --> 00:37:57,880
+يعني بدنا two groups بحيث الجي ماهواش ايزومورفك لا
+
+331
+00:37:57,880 --> 00:38:07,600
+اتش سؤال اتناش بد جي ماهياش ايزومورفك لا اتش but
+
+332
+00:38:07,600 --> 00:38:15,480
+ولكنولكن الـ Atomorphism لـ G isomorphic للـ
+
+333
+00:38:15,480 --> 00:38:25,240
+Atomorphism بطل Atomorphism لل G isomorphic لل
+
+334
+00:38:25,240 --> 00:38:32,960
+Atomorphism لل H لل Atomorphism لل H اللي عندنا
+
+335
+00:38:32,960 --> 00:38:37,200
+هذا القصة
+
+336
+00:38:37,200 --> 00:38:44,420
+بسيطة جداو لا نبعد كثير و نحاول نستخدم ما درسناه
+
+337
+00:38:44,420 --> 00:38:49,280
+في آخر نظرية أخدناها في الشبتر آخر نظرية قلنا
+
+338
+00:38:49,280 --> 00:38:56,720
+atomorphic ل ZN ايزو مورفك لمين لل UN الآن لو جيت
+
+339
+00:38:56,720 --> 00:39:05,980
+قلت لك أخدت solution لو أخدت ال G تساوي ال Z6 and
+
+340
+00:39:06,790 --> 00:39:12,990
+الـ H اللي هي بدها تساوي الـ Z دي ثلاثة هل الاتنين
+
+341
+00:39:12,990 --> 00:39:17,610
+هذول are isomorphic؟ لأن هذه فيها ست عناصر و هذه
+
+342
+00:39:17,610 --> 00:39:27,490
+فيها كدهش؟ تلاتة يبقى then ال then ال order اللي
+
+343
+00:39:27,490 --> 00:39:34,420
+هجيه بده يساوي ستةوال order ل H بدي يسوى تلاتة هذا
+
+344
+00:39:34,420 --> 00:39:43,000
+بدي يعطينا ان ال G is not isomorphic لمين لLH but
+
+345
+00:39:43,000 --> 00:39:54,760
+ولكن ال atomorphism ل Z6 isomorphic لمين يا شباب ل
+
+346
+00:39:54,760 --> 00:40:05,600
+U6 U6 من عناصر واحدتلاتة، أربعة، خمسة، وايس الآن
+
+347
+00:40:05,600 --> 00:40:15,360
+الـ Atomorphism لـ ZD3 Isomorphic لـ U3 U3 اللي هو
+
+348
+00:40:15,360 --> 00:40:23,480
+واحد واتنين مافيش غيرهم طب اتطلعلي هذه هل هذا
+
+349
+00:40:23,480 --> 00:40:28,260
+generator خمسة generator لـ U6
+
+350
+00:40:31,260 --> 00:40:36,600
+generator خمسة تربيع بتجيب لل identity الان هل
+
+351
+00:40:36,600 --> 00:40:41,950
+اتنين generator ليه تلاتة؟هو برضه عملية ضرب اتنين
+
+352
+00:40:41,950 --> 00:40:46,010
+في اتنين باربعة بيطلع واحد ال identity و هكذا يبقى
+
+353
+00:40:46,010 --> 00:40:49,010
+اتنين هذول كل واحدة فيها اتنين و هنا اتنين
+
+354
+00:40:49,010 --> 00:40:52,810
+identity identity generator generator ال order
+
+355
+00:40:52,810 --> 00:40:57,910
+الأول يسوي يبقى اتنين هذول are isomorphic يبقى
+
+356
+00:40:57,910 --> 00:41:00,930
+هذول ليست isomorphic لكن
+
+357
+00:41:20,220 --> 00:41:26,250
+وانتهينا الموضوعيعني ممكن هذا مثال هيعطينا ان two
+
+358
+00:41:26,250 --> 00:41:31,830
+groups ليست isomorphic لكن ال atomorphism على ال
+
+359
+00:41:31,830 --> 00:41:35,050
+group الأولى و ال atomorphism على ال group التانية
+
+360
+00:41:35,050 --> 00:41:40,890
+اتنين are isomorphic هذا سؤال اتناشر السؤال
+
+361
+00:41:40,890 --> 00:41:46,430
+الاربعتاش الشفوي قال لي هاتي ال atomorphism لمن ل
+
+362
+00:41:46,430 --> 00:41:52,950
+Z6عظم زد ستة الاتمورفزم لزد ستة عرفنا ال
+
+363
+00:41:52,950 --> 00:41:56,010
+isomorphism اللي يعني مافيش فيها إلا إيه two
+
+364
+00:41:56,010 --> 00:42:02,110
+elements معناته أكم isomorphism في في اتمورفزم لزد
+
+365
+00:42:02,110 --> 00:42:07,310
+ستة كم واحد اتنين يبقى الأول يا إما ال alpha of
+
+366
+00:42:07,310 --> 00:42:11,770
+one بده يساوي ال one يا إما ال alpha one بده يساوي
+
+367
+00:42:11,770 --> 00:42:17,480
+الخمسة يبقى اتنين فقطيبقى السؤال الاربعتاش اللي هو
+
+368
+00:42:17,480 --> 00:42:25,140
+shuffle الآن السؤال ستاشه ال proof ان ال mapping
+
+369
+00:42:25,140 --> 00:42:30,540
+من U 16 الى ال self given by عبارة عن أتمورفزم
+
+370
+00:42:30,540 --> 00:42:39,300
+وماذا عن وماذا عن أعمم يبقى الآن بدنا نيجي للسؤال
+
+371
+00:42:39,300 --> 00:42:49,350
+تبع ستاشه16 بيقول ما يأتي ال mapping في من U 16
+
+372
+00:42:49,350 --> 00:42:58,390
+إلى U 16 من U 16 إلى U 16 is given by اللي هو
+
+373
+00:42:58,390 --> 00:43:08,360
+given byفاي او اكس يساوي الاكس تكعب و is an
+
+374
+00:43:08,360 --> 00:43:16,120
+atomorphism is atomorphism what about
+
+375
+00:43:17,650 --> 00:43:27,990
+five of x يساوي x أص خمسة and five of x يساوي x أص
+
+376
+00:43:27,990 --> 00:43:33,450
+سبعة مش بالك إيش رأيك في الاتنين هذول وبعد ذلك
+
+377
+00:43:33,450 --> 00:43:41,990
+بتقدر تعمم وبعد ذلك جينراليز عمم
+
+378
+00:43:41,990 --> 00:43:42,710
+هذا الكلام
+
+379
+00:43:47,860 --> 00:43:54,540
+خلّيني أقول لك هذا الان أنا عندي في من U16 إلى U16
+
+380
+00:43:54,540 --> 00:43:58,880
+مطابق فيوفيكسي يساوي XKM قال لي أثبت أن هذا
+
+381
+00:43:58,880 --> 00:44:03,940
+أتومورفزيوم وبعد ذلك شوفي إيش رأيك في هذه وإيش
+
+382
+00:44:03,940 --> 00:44:09,080
+رأيك في هذه وعامة من نتائجي التي توصلت إليها يبقى
+
+383
+00:44:09,080 --> 00:44:14,060
+خلّيني أثبت هذه في الأول وبعد ذلك بصير خير خلّيني
+
+384
+00:44:14,060 --> 00:44:17,000
+أقول لك U16 في الأول solution
+
+385
+00:44:19,900 --> 00:44:26,460
+الـ U 16 يا جماعة من عناصرها الواحد والتالتة
+
+386
+00:44:26,460 --> 00:44:36,920
+والخمسة، ستة، سبعة، تمانية، تسعة، عشرة، احداشر،
+
+387
+00:44:36,920 --> 00:44:48,540
+اتناشر، تلتاشر واربعتاشر وخمستاشر هذه
+
+388
+00:44:48,540 --> 00:44:55,600
+العناصرهي تمان عناصر الـ U 16 أنا عندي five من U
+
+389
+00:44:55,600 --> 00:45:02,220
+16 إلى U 16 مطابق X تكيب شوفوا لي بالله تلاتة أس
+
+390
+00:45:02,220 --> 00:45:09,080
+أربعة بقدرش بتطلع بال identity طيب شوفوا لي خمسة
+
+391
+00:45:09,080 --> 00:45:10,040
+أس أربعة
+
+392
+00:45:15,000 --> 00:45:17,360
+أربعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة
+
+393
+00:45:17,360 --> 00:45:18,520
+أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة
+
+394
+00:45:18,520 --> 00:45:19,680
+تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة
+
+395
+00:45:19,680 --> 00:45:28,680
+أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة
+
+396
+00:45:28,680 --> 00:45:29,400
+تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة
+
+397
+00:45:29,400 --> 00:45:29,400
+أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة
+
+398
+00:45:29,400 --> 00:45:29,460
+تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة
+
+399
+00:45:29,460 --> 00:45:40,120
+أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة
+
+400
+00:45:40,120 --> 00:45:48,850
+تسproperty الخاصية التالية ان الـ x أُص أربعة بده
+
+401
+00:45:48,850 --> 00:45:54,610
+يشوّن identity elementخلّي هذه المعلومة في دماغك و
+
+402
+00:45:54,610 --> 00:46:01,130
+بدنا نحاول نستفيد منها متى لازم الأمر و وقت أشي
+
+403
+00:46:01,130 --> 00:46:07,050
+بيلزم بدنا نحاول نستفيد منها طيب احنا بدنا نيجي
+
+404
+00:46:07,050 --> 00:46:16,190
+الـPhi of X يساوي X تكيب بدي أثبت ان الـPhi is one
+
+405
+00:46:16,190 --> 00:46:22,870
+to oneيبقى بالدرجة اقول له assume افترض انه five
+
+406
+00:46:22,870 --> 00:46:30,510
+of x يسوى five of y يعني معناته ان ال x تكييب بده
+
+407
+00:46:30,510 --> 00:46:36,530
+يسوى ال y تكييب معناته ال x بده يسوى main بده يسوى
+
+408
+00:46:36,530 --> 00:46:46,610
+ال y بعدين ال five is underأفترض أن ال Y موجودة في
+
+409
+00:46:46,610 --> 00:47:00,550
+U 16 يبقى ال Y أربعة تساوي كم؟ تساوي واحد بدي أثبت
+
+410
+00:47:00,550 --> 00:47:07,820
+أن ال Y هذه لها أصل في U 16بقول له كويس ايش رأيك
+
+411
+00:47:07,820 --> 00:47:13,540
+هذه بدل Y أُس أربعة بدي اخد Y واحدة يعني ايش اعمل
+
+412
+00:47:13,540 --> 00:47:21,640
+في المعادلة بدي اضرب في Y لسالب تلتة أو Y inverse
+
+413
+00:47:21,640 --> 00:47:28,660
+تكييب او Y تكييب inverseيبقى هذا بده يعطيك ان y
+
+414
+00:47:28,660 --> 00:47:35,480
+أربعة ل y سالب تلاتة بده يساوي ال y سالب تلاتة
+
+415
+00:47:35,480 --> 00:47:41,300
+يعني ضربنا الطرفين y سالب تلاتة هذا معناه ايش ان
+
+416
+00:47:41,300 --> 00:47:50,640
+ال y يساوي y inverse تكيبة ال y inverse بقدر اقول
+
+417
+00:47:50,640 --> 00:47:59,550
+عليها x تكيبةاللي بقدر أقول عليها في of X يبقى ال
+
+418
+00:47:59,550 --> 00:48:05,270
+element اللي أخدته Y اللي جيتله أصل هنا X يبقى في
+
+419
+00:48:05,270 --> 00:48:10,630
+is onto بالخاصية هذه أنا لما كتبتها ما كتبتاش بلاش
+
+420
+00:48:10,630 --> 00:48:17,230
+لزمتلي و لما لزمتلي روحت استخدمتها تمام يبقى في
+
+421
+00:48:17,230 --> 00:48:21,490
+one to one and onto مش ضايل إلا خاصية من ال
+
+422
+00:48:21,490 --> 00:48:30,430
+isomorphismيبقى بدي أخد finally أخيراً finally بدي
+
+423
+00:48:30,430 --> 00:48:38,090
+أخد ال five of XY يبقى هذا الكلام بدي يسوى XY لكل
+
+424
+00:48:38,090 --> 00:48:44,130
+تكييب السؤال هو هل بقدر اكتب X تكييب Y تكييب ولا
+
+425
+00:48:44,130 --> 00:48:56,080
+لا؟ بقدر اكتب هك؟ بقدر؟ طب ليش؟بقدر أكتب بالشكل
+
+426
+00:48:56,080 --> 00:49:01,520
+يعني هذا لإنه فاهم من وين لوين طب ال U 16 أبيلين
+
+427
+00:49:01,520 --> 00:49:08,140
+ولا non abelian ال UN in general أبيلين ولا non
+
+428
+00:49:08,140 --> 00:49:13,650
+abelianأبيليان ضرب أعداد عادي يبقى أبيليان يبقى
+
+429
+00:49:13,650 --> 00:49:20,470
+هذا الكلام صحيح since you 16 is a billion لو
+
+430
+00:49:20,470 --> 00:49:25,870
+ماكنتش أبيليان بصير هذا كلام ماله مش صحيح يبقى هذا
+
+431
+00:49:25,870 --> 00:49:33,410
+الكلام بدي أعطيك في of x في في of y يبقى دص وهكذا
+
+432
+00:49:33,410 --> 00:49:37,770
+الفي is an atomorphism
+
+433
+00:49:38,960 --> 00:49:43,920
+يقول لي ايش رأيك في هذا و ايش رأيك في هذا بنفس
+
+434
+00:49:43,920 --> 00:49:52,020
+الطريقة بنفس الطريقة يبقى similarly بنفس الطريقة
+
+435
+00:49:52,020 --> 00:50:00,400
+اللي هو five of x يساوي ال x أص خمسة and five of x
+
+436
+00:50:00,400 --> 00:50:06,720
+يساوي ال x أص سبعة are atomorphism
+
+437
+00:50:08,830 --> 00:50:16,510
+جالي عمّم مدام عمّم يبقى بده أقوله يبقى الـPhi of
+
+438
+00:50:16,510 --> 00:50:24,510
+X يساوي الـX بدك تخلي الأس فردي تقدر تقولي اتنين N
+
+439
+00:50:24,510 --> 00:50:32,430
+زائد واحد is an Atomorphism دير بالك في حالة الـX
+
+440
+00:50:32,430 --> 00:50:39,060
+السابعة ها ديها ها بدي أجيب identity فبصير لما
+
+441
+00:50:39,060 --> 00:50:43,220
+أقولك x أُس أربعة بال identity بصير x أُس تمانية
+
+442
+00:50:43,220 --> 00:50:49,200
+بجداش بال identity يبقى لما أجي أقوله ال x أُس
+
+443
+00:50:49,200 --> 00:50:54,820
+تمانية اللي هي عبارة عن x في x أُس سبعة أو بدي x
+
+444
+00:50:54,820 --> 00:51:00,200
+لحالها بضرب في x أس سالب سبعة بصير ال x هو x أس
+
+445
+00:51:00,200 --> 00:51:04,750
+سالب سبعة و هكذاتمام؟ يعني نفس ال tactic اللي
+
+446
+00:51:04,750 --> 00:51:10,230
+عملنا هنا للحالة الأولى بنروح نعمله لمين؟ للحالة
+
+447
+00:51:10,230 --> 00:51:14,130
+التالتة والحالة التانية وبالتالي عبارة عن
+
+448
+00:51:14,130 --> 00:51:15,630
+atomorphism
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7457537a253d61ae5b203ff199fc92774b0dc1ad
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.srt
@@ -0,0 +1,1856 @@
+1
+00:00:21,410 --> 00:00:27,670
+نكمل نبدأ في محاضرة الصباح وصلنا الى المثال
+
+2
+00:00:27,670 --> 00:00:33,930
+compute ال atomorphism لمن الى z عشرةمشان هيك روحت
+
+3
+00:00:33,930 --> 00:00:37,710
+افترض ان ال alpha من z عشرة الى z عشرة يبقى اعنى
+
+4
+00:00:37,710 --> 00:00:43,290
+atomorphism شو شكل ال alpha الله اعلم تمام يبقى
+
+5
+00:00:43,290 --> 00:00:48,010
+احنا بنبحث قداش ال alpha دي او ايش قيمتها شو تساوي
+
+6
+00:00:48,010 --> 00:00:54,990
+ماهو نوع هذه ال function فبجي بقول الان لو كان ال
+
+7
+00:00:54,990 --> 00:01:00,930
+k موجود في z عشرة thenيعني الـ K يبدو يساوي Zero
+
+8
+00:01:00,930 --> 00:01:05,830
+يا واحد اتنين تلاتة اربعة لغاية تسعة تمام؟ then لو
+
+9
+00:01:05,830 --> 00:01:13,010
+جيت أخدت Alpha of K لأن Alpha بدت أثر على K اللي
+
+10
+00:01:13,010 --> 00:01:18,810
+موجودة في Z عشرة يبقى هذا الكلام بده يساوي Alpha
+
+11
+00:01:18,810 --> 00:01:25,790
+of واحد زائد واحد زائد واحد كم مرة هدول؟ كم واحد
+
+12
+00:01:25,790 --> 00:01:35,250
+هدول؟ K من المراتيبقى هدول K times يبقى K من
+
+13
+00:01:35,250 --> 00:01:39,490
+المرات الان انا جاي ال alpha عبارة عن ايش
+
+14
+00:01:39,490 --> 00:01:45,210
+atomorphism atomorphism يعني isomorphism معناته
+
+15
+00:01:45,210 --> 00:01:51,910
+هذه هتساوي alpha of one زائد alpha of one زائد
+
+16
+00:01:51,910 --> 00:02:00,190
+زائد alpha of one كم مرة هدول كمان؟كتايمز يبقى هذا
+
+17
+00:02:00,190 --> 00:02:07,330
+الكلام بده يساوي ك في alpha of one ضالت مشكلتنا مع
+
+18
+00:02:07,330 --> 00:02:12,490
+alpha of one قائمة قداش alpha of one هذي بده تكون
+
+19
+00:02:12,490 --> 00:02:19,110
+الان alpha of one موجودة وين موجودة في z عشرة بده
+
+20
+00:02:19,110 --> 00:02:25,600
+اروح ادور على ال order تبعهايبقى باجي بقوله و ال
+
+21
+00:02:25,600 --> 00:02:34,680
+alpha of one موجودة في z عشرة طيب باجي بقول كمان
+
+22
+00:02:34,680 --> 00:02:42,820
+in z عشرة قداش ال order للواحد قداش ال order
+
+23
+00:02:42,820 --> 00:02:48,760
+للواحد في z عشرة مين ال operation اللي على z عشرة
+
+24
+00:02:49,640 --> 00:02:54,060
+أزايد الجامعة مظبوط الجامعة هي ال operation
+
+25
+00:02:54,060 --> 00:02:58,460
+الموجودة على ز عشرة إذا الواحد قداش ال order له
+
+26
+00:02:58,460 --> 00:03:05,440
+الواحد لو أشبهك كام مرة بيعطيني ال zero عشر مرات
+
+27
+00:03:05,440 --> 00:03:10,660
+يعني ال order للواحد يسوى قداش يسوى عشرة يبقى ال
+
+28
+00:03:10,660 --> 00:03:17,060
+order للواحد يسوى عشرة هذا بده يعطينا أن ال order
+
+29
+00:03:17,060 --> 00:03:24,120
+لل alpha of واحدخدنا في النظرية السابقة رقم خمسة
+
+30
+00:03:24,120 --> 00:03:28,900
+النظرية مش السابقة اللي قبلها اللي فيها السبع نقاط
+
+31
+00:03:28,900 --> 00:03:33,780
+النقطة رقم خمسة ال order اللي ايه بيساوي مين ال
+
+32
+00:03:33,780 --> 00:03:39,200
+order ل phi of اذا كان phi ايزو مورفزم انا افرض ان
+
+33
+00:03:39,200 --> 00:03:44,860
+اتومورفزم هو ايزو مورفزم من ال group الى نفسه هذا
+
+34
+00:03:44,860 --> 00:03:52,000
+بيعطينا ان هذا بيساوي عشرة becauseإن الـ order للـ
+
+35
+00:03:52,000 --> 00:03:57,940
+A بدي سوى ال order لـ Phi of A هذا previous
+
+36
+00:03:57,940 --> 00:03:58,780
+theorem
+
+37
+00:04:01,950 --> 00:04:07,450
+Theorem part 5 كان الجزء الخامس من النظرية اللي
+
+38
+00:04:07,450 --> 00:04:12,350
+فيها سبع نقاط يبقى ال order ل alpha of واحد بده
+
+39
+00:04:12,350 --> 00:04:17,410
+يساوي عشرة الان انا بقول ال alpha واحد وين موجود
+
+40
+00:04:17,410 --> 00:04:24,090
+في z عشرة مين العناصر اللي في z عشرة اللي ال order
+
+41
+00:04:24,090 --> 00:04:32,380
+اللي يساوي عشرة الواحد ومين كمانكل رقم relative
+
+42
+00:04:32,380 --> 00:04:36,740
+prime مع العشرة وانت بتجري مين كمان؟ relative
+
+43
+00:04:36,740 --> 00:04:44,040
+prime مع العشرة مين؟ مين؟ تلاتة والسبعة والتسعة
+
+44
+00:04:44,040 --> 00:04:48,220
+يبقى هدول بس يبقى alpha of one هتسوى واحد من
+
+45
+00:04:48,220 --> 00:04:55,320
+الأربع هدول فقط يبقى هذا بده يعطينا ان ال alpha of
+
+46
+00:04:55,320 --> 00:05:03,720
+one equalone او تلاتة او سبعة او تسعة because
+
+47
+00:05:03,720 --> 00:05:13,220
+السبب each of واحد و تلاتة و سبعة و تسعة is of
+
+48
+00:05:13,220 --> 00:05:21,920
+order عشر كويس مادام alpha of one ساوت يا واحد يا
+
+49
+00:05:21,920 --> 00:05:27,660
+تلاتة يا سبعة يا تسعة معناته اكم اوتومورفزم عندى
+
+50
+00:05:28,860 --> 00:05:36,460
+اربع فقط لا غير مافيش غيرهم يبقى بدي أروح أقول أن
+
+51
+00:05:36,460 --> 00:05:41,480
+ال alpha هذه لو أثرت على الواحد بدي أخلي صورتها
+
+52
+00:05:41,480 --> 00:05:45,720
+واحدلأن ال order اللي هذا بدي يسوى ال order اللي
+
+53
+00:05:45,720 --> 00:05:51,720
+هذا أو ال alpha لو أثرت على ال واحد بديت تبقى صورة
+
+54
+00:05:51,720 --> 00:05:58,040
+تلاتة هتكون ال order الاتنين كله كم؟ عشرة أو ال
+
+55
+00:05:58,040 --> 00:06:03,280
+alpha of واحد ممكن يتساوي السبعة أو ال alpha of
+
+56
+00:06:03,280 --> 00:06:09,340
+واحد ممكن الصورة كم؟ ممكن الصورة تسعة يبقى اكم
+
+57
+00:06:09,340 --> 00:06:15,670
+اتومورفزم الصار عندىأربعة ال alpha لو أثرت على ال
+
+58
+00:06:15,670 --> 00:06:18,770
+identity element تعطين ال identity element ال
+
+59
+00:06:18,770 --> 00:06:22,290
+alpha لو أثرت على ال identity element ممكن تكون
+
+60
+00:06:22,290 --> 00:06:25,950
+الصورة تلاتة عفوا مش ال identity لأن واحد مش ال
+
+61
+00:06:25,950 --> 00:06:29,970
+identity في زد عشر ال identity هو ال zero ال alpha
+
+62
+00:06:29,970 --> 00:06:33,750
+لما تأثر على واحد ممكن تكون الصورة واحد ال alpha
+
+63
+00:06:33,750 --> 00:06:36,350
+لما تأثر على واحد ممكن تكون الصورة تلاتة ال alpha
+
+64
+00:06:36,350 --> 00:06:39,670
+لو أثرت على واحد ممكن تكون الصورة سبعة ال alpha لو
+
+65
+00:06:39,670 --> 00:06:42,250
+أثرت على واحد ممكن تكون الصورة تسعة
+
+66
+00:06:59,950 --> 00:07:05,730
+مشان اميز في مابينهم ايش رايك هذا بده يسميه alpha
+
+67
+00:07:05,730 --> 00:07:12,530
+oneوهذا بدي أسميه Alpha 3 واللي بعده بدي أسميه
+
+68
+00:07:12,530 --> 00:07:19,270
+Alpha 7 واللي بعده بدي أسميه Alpha 9 عشان أميزهم
+
+69
+00:07:19,270 --> 00:07:28,250
+عن بعضهم هدول كلهم بدهم يشكلولي ال Atomorphism
+
+70
+00:07:28,250 --> 00:07:31,070
+لمن؟ لزد عشرة
+
+71
+00:07:35,390 --> 00:07:40,590
+يبقى هدول بدهم يشكلولي الـautomorphism لمن؟ لزد
+
+72
+00:07:40,590 --> 00:07:47,970
+عشرة الان انا بدي اتأكد ان كل واحد من هدول هو
+
+73
+00:07:47,970 --> 00:07:53,890
+عبارة عن automorphism تمام؟ مشان هيك بد ال alpha
+
+74
+00:07:53,890 --> 00:07:57,550
+كل واحدة فيهم الاولة او التانية او التالتة او
+
+75
+00:07:57,550 --> 00:08:03,120
+الرابعةبديها تبقى one to one و بديها انتوا و بديها
+
+76
+00:08:03,120 --> 00:08:09,400
+تخدم خاصية ال isomorphism تمام طيب انا بدى شيكلك
+
+77
+00:08:09,400 --> 00:08:13,560
+على واحدة اثبتها انها isomorphism و انت بتسوي
+
+78
+00:08:13,560 --> 00:08:18,370
+الباقي بنفس الطريقة اول شئهذه هو ال identity ليش؟
+
+79
+00:08:18,370 --> 00:08:21,530
+ان ال alpha of one بدي يساوي one هذه هي ال
+
+80
+00:08:21,530 --> 00:08:25,730
+identity function هذه دائما one to one and on two
+
+81
+00:08:25,730 --> 00:08:29,430
+و بتخدم خاصية ال isomorphism و قد رأينا ذلك في
+
+82
+00:08:29,430 --> 00:08:33,330
+النظرية تبعت الصبح يبقى أسيبني منها هذه شغلها سهل
+
+83
+00:08:33,330 --> 00:08:38,530
+بتروح أخد مين alpha 3 أو alpha 7 أو alpha 9 بعمل
+
+84
+00:08:38,530 --> 00:08:42,990
+واحدة منهم و التنتين التانيات بدي يكون بنفس
+
+85
+00:08:42,990 --> 00:08:55,210
+الطريقةيبقى باجي بقول هنا now we shall show that
+
+86
+00:08:55,210 --> 00:09:12,030
+each of the above four elements is an
+
+87
+00:09:17,630 --> 00:09:26,790
+Atomorphism يبقى بده اعمل check لمن لل alpha تلاتة
+
+88
+00:09:26,790 --> 00:09:34,470
+كويس طيب انا في الاول لما اخدت alpha من z الى عشرة
+
+89
+00:09:34,470 --> 00:09:41,440
+اعطيتها تعريفماتدهاش تعريف لكن بدي أروح أخذهلها ال
+
+90
+00:09:41,440 --> 00:09:51,980
+alpha تلاتة of of X بدي أسميها تلاتة X مثلا واحد
+
+91
+00:09:51,980 --> 00:09:56,340
+يقول استنى كله كيف استنى قال لي تعريفه غلط بقول
+
+92
+00:09:56,340 --> 00:10:02,620
+كيف تعريفه غلط بقول انت بتضرب ضربتلاتة في X بقوله
+
+93
+00:10:02,620 --> 00:10:07,480
+لأ مش صحيح انا قلت X زائد X زائد X لأن ال
+
+94
+00:10:07,480 --> 00:10:12,320
+operation على Z هي عملية الجامعة بس X زائد X زائد
+
+95
+00:10:12,320 --> 00:10:17,000
+X يعني قداش تلاتة X إذا تعريفه سليم مية المية ولا
+
+96
+00:10:17,000 --> 00:10:25,460
+يوجد فيه أي خطأ طيب الآن لما أقول Alpha تلاتة of
+
+97
+00:10:25,460 --> 00:10:30,580
+واحد بده يسوى قداش بده يسوى تلاتة يبقى هذا معناته
+
+98
+00:10:30,750 --> 00:10:39,710
+ألف تلاتة of واحد بده يساوي تلاتة سؤال التلاتة
+
+99
+00:10:39,710 --> 00:10:46,320
+generator لازد عشرة ولا لا؟يبقى ال alpha تلاتة one
+
+100
+00:10:46,320 --> 00:10:51,080
+to one and unto ليش انها generator اللي بتأثر
+
+101
+00:10:51,080 --> 00:10:54,040
+بتجيب element من z عشرة و التاني بتجيب element
+
+102
+00:10:54,040 --> 00:10:57,980
+تاني و التالت لما تجيبلي كل z عشرة صحيح ولا لا
+
+103
+00:10:57,980 --> 00:11:06,680
+يبقى هنا باجي بقوله since ال تلاتة is a generator
+
+104
+00:11:06,680 --> 00:11:11,760
+of z عشرة
+
+105
+00:11:16,370 --> 00:11:22,110
+الألف تلاتة على
+
+106
+00:11:22,110 --> 00:11:29,370
+طول الخط is one to one and one to function
+
+107
+00:11:39,060 --> 00:11:44,800
+one to one and unto كلمة function بدنا نثبتها انها
+
+108
+00:11:44,800 --> 00:11:50,060
+well defined يبقى اثبتها انها one to one and unto
+
+109
+00:11:50,060 --> 00:11:59,760
+and unto الان ال alpha تلاتة is well defined يبقى
+
+110
+00:11:59,760 --> 00:12:05,080
+بدنا نثبت انها معرفة الاصل اللي عملها قبل هذه
+
+111
+00:12:05,080 --> 00:12:10,010
+الخطوة لكن مافيش مشكلةطيب what do you find؟ بدأ
+
+112
+00:12:10,010 --> 00:12:16,090
+أخد عنصرين متساوين و أثبت أن صورتهم متساوية يبقى
+
+113
+00:12:16,090 --> 00:12:23,090
+باجب أقوله لو كان ال X مديله عشرة بده يساوي ال Y
+
+114
+00:12:23,090 --> 00:12:29,930
+مديله عشرة هذا إيش بيعطينا؟لو ضربت فيه تلاتة بيصير
+
+115
+00:12:29,930 --> 00:12:38,490
+تلاتة X modulo عشرة يسوى تلاتة Y modulo عشرة صحيح
+
+116
+00:12:38,490 --> 00:12:45,070
+ولا لا؟ طب انا معرفها هنا Alpha of X يسوى تلاتة X
+
+117
+00:12:45,070 --> 00:12:53,950
+معناته ان ال Alpha تلاتة of X بيسوى Alpha تلاتة of
+
+118
+00:12:53,950 --> 00:13:01,760
+Y تمام؟يبقى أخدت عنصرين متساويين اثبتت ان عنصرهم
+
+119
+00:13:01,760 --> 00:13:06,820
+متساويين يبقى في هذه الحالة في is well defined
+
+120
+00:13:06,820 --> 00:13:11,440
+يبقى well defined one to one and انتوا ايش ضايل
+
+121
+00:13:11,440 --> 00:13:14,860
+عليك بس الخاصية الأخيرة اللي هي خاصية ال
+
+122
+00:13:14,860 --> 00:13:21,680
+isomorphism لذلك بدأجي أقوله بدأ أخد finally بدأ
+
+123
+00:13:21,680 --> 00:13:30,800
+أخد alpha تلاتة ofA زائد B مثلا A زائد B نظرا لأن
+
+124
+00:13:30,800 --> 00:13:36,140
+العملية على زد N هي عملية الجامعة يبقى A زائد B
+
+125
+00:13:36,140 --> 00:13:41,600
+حسب ال definition تبعنا يبقى تلاتة في A زائد B
+
+126
+00:13:41,600 --> 00:13:49,020
+يبقى تلاتة A زائد تلاتة B هذه عبارة عن مين عبارة
+
+127
+00:13:49,020 --> 00:13:56,640
+عن Alpha تلاتة of Aوالتانية alpha 3 of b إذا ال
+
+128
+00:13:56,640 --> 00:14:02,320
+alpha 3 خدمت خاصية ال isomorphism بعد هيك ال alpha
+
+129
+00:14:02,320 --> 00:14:07,800
+احنا عرفناها من ال 6 إلى نفسها يبقى بناء عن عليه
+
+130
+00:14:07,800 --> 00:14:14,560
+alpha 3 is an atomorphism يبقى هذا بيعطينا أن
+
+131
+00:14:14,560 --> 00:14:20,940
+alpha 3 is an atomorphism
+
+132
+00:14:22,720 --> 00:14:31,600
+يبقى بنفس الطريقة similarly اللي هو من alpha 7 and
+
+133
+00:14:31,600 --> 00:14:37,900
+alpha 9 are automorphisms
+
+134
+00:14:37,900 --> 00:14:41,940
+where
+
+135
+00:14:41,940 --> 00:14:51,080
+كذلك حيثهم اللي هو ال alpha 1 is the identity
+
+136
+00:14:52,010 --> 00:14:52,570
+Animal
+
+137
+00:14:55,760 --> 00:15:03,020
+identity element يبقى الأن اثبتنا ان الاتومورفيزم
+
+138
+00:15:03,020 --> 00:15:06,020
+لزد عشرة بالضبط
+
+139
+00:15:25,840 --> 00:15:31,840
+يبقى هذه حسبتله مين الاتومورفزم لمين لزد عشرة
+
+140
+00:15:31,840 --> 00:15:36,680
+طلعته مافيش فيها الا اربعة عناصر وكل عنصر منها دول
+
+141
+00:15:36,680 --> 00:15:43,660
+عبارة عن اتومورفزم طيب خلينا نعطي بعض التوضيحات
+
+142
+00:15:43,660 --> 00:15:50,220
+اكتر اللي خاطر اشوف لحد هنا انتهى الشغللكن احنا
+
+143
+00:15:50,220 --> 00:15:54,180
+بدنا بعض التوضيحات، ايش بعض التوضيحات؟ هذه
+
+144
+00:15:54,180 --> 00:16:00,580
+isomorphic لمين؟ و لو ضربت ربعت هذه، ايش بدي يكون
+
+145
+00:16:00,580 --> 00:16:04,200
+الناتج؟ لو عملت composition ما بين الأولى
+
+146
+00:16:04,200 --> 00:16:07,140
+والتانية، شو بيكون الناتج؟ composition بين
+
+147
+00:16:07,140 --> 00:16:11,600
+التانية، هل بتبقى closed فعلا ولا لأ؟ بس مجرد
+
+148
+00:16:11,600 --> 00:16:17,110
+معلومات كيف بدنا نشتغل العناصر هدول مع بعضيبقى
+
+149
+00:16:17,110 --> 00:16:27,230
+ممكن اقوله زيادة على ذلك it should be noted that
+
+150
+00:16:27,230 --> 00:16:38,990
+من الملاحظة انه لو بدي alpha تلاتة تربيع of oneهذا
+
+151
+00:16:38,990 --> 00:16:42,450
+المقصود ليس تربية وضرب وفرقة المقصود هو
+
+152
+00:16:42,450 --> 00:16:48,310
+composition بين الاتنين يعني هذه معناها alpha تكيب
+
+153
+00:16:48,310 --> 00:16:55,610
+ل alpha تلاتة ل alpha تلاتة of one حسب تعريف ال
+
+154
+00:16:55,610 --> 00:17:00,730
+composition of function alpha تلاتة ل alpha تلاتة
+
+155
+00:17:00,730 --> 00:17:07,490
+of oneهذا الكلام بده يساوي Alpha تلاتة Alpha تلاتة
+
+156
+00:17:07,490 --> 00:17:13,450
+of one حسب التعريف Alpha تلاتة of X يساوي تلاتة في
+
+157
+00:17:13,450 --> 00:17:18,490
+X يبقى هذا ايش بده تكون تلاتة في واحد اللي هي
+
+158
+00:17:18,490 --> 00:17:23,590
+بتلاتة Alpha تلاتة of X بتصيب تلاتة في تلاتة اللي
+
+159
+00:17:23,590 --> 00:17:32,360
+هي بمين بتسعة هذه أليست Alpha تسعة of oneيبقى
+
+160
+00:17:32,360 --> 00:17:37,200
+الصار عندى alpha تلاتة تربيع of one هي alpha تسعة
+
+161
+00:17:37,200 --> 00:17:41,940
+of one يعني موجودة وين موجودة داخل الاتو مورفيزم
+
+162
+00:17:41,940 --> 00:17:47,080
+ال Z عشرة طب لو كعبدها تطلع واحدة من هدول والله
+
+163
+00:17:47,080 --> 00:17:53,320
+بتيجي برا تعالى نشوفلو جيت أخدتله alpha تكييب
+
+164
+00:17:53,320 --> 00:18:00,420
+تكييب of one يعني alpha تلاتة ل alpha تر تلاتة
+
+165
+00:18:00,420 --> 00:18:06,860
+تربيع of one ويساوي alpha تلاتة لبرا اللي جوا هيها
+
+166
+00:18:06,860 --> 00:18:09,940
+حسبناها قداشر طالت عنها تسعة
+
+167
+00:18:12,470 --> 00:18:17,970
+حسب التقريب في الجهد التالتة في التسعة سبعة وعشرين
+
+168
+00:18:17,970 --> 00:18:23,590
+سبعة وعشرين في الزد عشرة يعني بسبعة يعني بسبعة هذه
+
+169
+00:18:23,590 --> 00:18:29,770
+ال alpha سبعة of one إذا هذا ال element لما انكعت
+
+170
+00:18:30,250 --> 00:18:35,810
+جاب للعنصر هذه يعني لازالة closed و هكذا طب لو
+
+171
+00:18:35,810 --> 00:18:42,750
+جبتله هنا Alpha تكيب أس أربعة of one أليست Alpha
+
+172
+00:18:42,750 --> 00:18:51,070
+تلاتة في Alpha تلاتة تكيب of one تمام هذه تساوي
+
+173
+00:18:51,070 --> 00:18:58,230
+Alpha تلاتة ofالفا تلاتة كيب of one هاي امشي امشي
+
+174
+00:18:58,230 --> 00:19:04,550
+كده ايش كانت سبعة يبقى هذه السبعة حسب التعريف يبقى
+
+175
+00:19:04,550 --> 00:19:09,010
+تصير تلاتة في سبعة واحدة وعشرين شيل العشرين بتطلع
+
+176
+00:19:09,010 --> 00:19:15,830
+من اللي هو واحد اللي هو بدها تساوي alpha of one
+
+177
+00:19:20,890 --> 00:19:28,350
+أو Alpha one of one Alpha one of one يبقى بناء على
+
+178
+00:19:28,350 --> 00:19:34,670
+اليسار المقابل اتانمين ال identity element اذا صار
+
+179
+00:19:34,670 --> 00:19:42,010
+عندنا هذا سيعطيك ان Alpha تكيب ال order يساوي كم؟
+
+180
+00:19:42,010 --> 00:19:50,000
+يساوي أربعطيب ال order إلها يسوى أربعة يبقى هذه
+
+181
+00:19:50,000 --> 00:19:57,730
+إيش بتنفعGenerator لمن؟ لـAtomorphism لمن؟
+
+182
+00:19:57,730 --> 00:20:00,830
+لـAtomorphism
+
+183
+00:20:00,830 --> 00:20:05,890
+لـZ10 يبقى هذا .. ليش؟ لأنه مافيهاش الأربع عناصر
+
+184
+00:20:05,890 --> 00:20:11,450
+وكل مربع كعب بيطلع واحد من العنصر يبقى باستفيد من
+
+185
+00:20:11,450 --> 00:20:16,730
+هذا الكلام أن الـAtomorphism لـZ10 Cyclic ولا لأ؟
+
+186
+00:20:16,730 --> 00:20:24,610
+Cyclicيبقى هذا بده يعطيلك ان الاتمورفزم ل z عشرة
+
+187
+00:20:24,610 --> 00:20:33,450
+فيها generator اسمه alpha 3 يبقى هذا بده يعطيلك ان
+
+188
+00:20:33,450 --> 00:20:40,010
+الاتمورفزم ل z عشرة is cyclic
+
+189
+00:20:46,280 --> 00:20:53,240
+خلّيني أفكر قليلا، لدي أربعة عناصر، من من
+
+190
+00:20:53,240 --> 00:20:57,520
+الـgroups اللي مرت علينا و اللي ممكن يكون فيها صلة
+
+191
+00:20:57,520 --> 00:21:03,620
+قرابة بينها وبين الـgroup هذين، خلّيني أشوف U
+
+192
+00:21:03,620 --> 00:21:09,420
+عشرة، U عشرة من عناصرها؟ واحد و تلاتة وسبعة وتسعة،
+
+193
+00:21:09,420 --> 00:21:16,530
+تمام تمامإذا لو جيت لل group هذي و حسبت ال key ل
+
+194
+00:21:16,530 --> 00:21:33,490
+table لكل منها يبقى
+
+195
+00:21:33,490 --> 00:21:39,070
+ملاحظة هذي remark from
+
+196
+00:21:42,080 --> 00:21:53,900
+كالي تابل for U عشرة and اتومورفزم
+
+197
+00:21:53,900 --> 00:22:03,600
+لزد عشرة we have ان الاتومورفزم لزد عشرة
+
+198
+00:22:03,600 --> 00:22:11,710
+isomorphic ل U عشرةتعالى نعمل كيلة تابل طلعلي
+
+199
+00:22:11,710 --> 00:22:18,630
+الكيلة تابل هذا بدي اخد U عشرة عنصرها واحد و تلاتة
+
+200
+00:22:18,630 --> 00:22:24,730
+و سبعة و تسعة و هاي قفلنا و هنا واحد تلاتة سبعة
+
+201
+00:22:24,730 --> 00:22:29,550
+تسعة بالشكل اللي عندنا هنا وهذه التفصيل تبعها
+
+202
+00:22:29,550 --> 00:22:38,480
+كالتالي هذا الرأسهذا الشكل تعالى نحسبها واحد في
+
+203
+00:22:38,480 --> 00:22:44,620
+واحد بواحد تلاتة سابعة تسعة الان تلاتة في واحد
+
+204
+00:22:44,620 --> 00:22:48,600
+بتلاتة طبعا ال operation اللى علياه عشرة هي عملية
+
+205
+00:22:48,600 --> 00:22:53,660
+الضرب عارفينه مسبقا الان تلاتة في تلاتة بتسعة
+
+206
+00:22:53,660 --> 00:23:01,140
+تلاتة في سابعة كدهش؟يعني واحد تلاتة في تسعة سبعة
+
+207
+00:23:01,140 --> 00:23:06,180
+وعشرين شيل عشرتين بيظل سبعة الان سبعة في واحد
+
+208
+00:23:06,180 --> 00:23:10,840
+بسبعة سبعة في تلاتة بواحد وعشرين سبعة في سبعة
+
+209
+00:23:10,840 --> 00:23:17,320
+بتسعة واربعين سبعة في تسعة بتلاتة وستين الان تسعة
+
+210
+00:23:17,320 --> 00:23:22,640
+في واحد بتسعة تسعة في تلاتة بسبعة وعشرين تسعة في
+
+211
+00:23:22,640 --> 00:23:28,660
+سبعة بتلاتة وستين تسعة في تسعة بواحدو تمانين هذه
+
+212
+00:23:28,660 --> 00:23:35,560
+كيلي تابل لمين لـ U عشرة طب خدلي كيلي تابل لـ
+
+213
+00:23:35,560 --> 00:23:44,660
+Atomorphism لـ Z عشرة اللي هي Alpha واحد و Alpha
+
+214
+00:23:44,660 --> 00:23:53,440
+تلاتة و Alpha سبعة و Alpha تسعة تمام؟ و هنا هذه
+
+215
+00:23:53,440 --> 00:24:03,040
+Alpha واحدوهنا ألف تلاتة وهنا ألف سبعة وهنا ألف
+
+216
+00:24:03,040 --> 00:24:12,060
+تسعة شكل أنها طيب ألف واحد في ألف واحد بألف واحد
+
+217
+00:24:12,060 --> 00:24:18,320
+ألف واحد في ألف تلاتة بألف تلاتة ألف واحد في ألف
+
+218
+00:24:18,320 --> 00:24:25,150
+سبعة بألف سبعة ألف تسعةألف تلاتة في ألف واحد بألف
+
+219
+00:24:25,150 --> 00:24:31,890
+تلاتة ألف تلاتة في ألف تلاتة بألف تسعة ألف تلاتة
+
+220
+00:24:31,890 --> 00:24:38,710
+في ألف سبعة بألف واحد ألف تلاتة في ألف تسعة بألف
+
+221
+00:24:38,710 --> 00:24:47,020
+سبعة الآن ألف سبعة في ألف واحد بتديلك ألف سبعةو
+
+222
+00:24:47,020 --> 00:24:57,260
+هذه Alpha 1 وهذه Alpha 9 وهذه Alpha 3 وهذه Alpha 9
+
+223
+00:24:57,260 --> 00:25:09,540
+وهذه Alpha 7 وهذه Alpha 7 وهذه Alpha 3 وهذه Alpha
+
+224
+00:25:09,540 --> 00:25:13,440
+1 طيب
+
+225
+00:25:13,440 --> 00:25:19,930
+يعني احنالو عمليا اشتغلنا زى الشغل اللى عندنا هذا
+
+226
+00:25:19,930 --> 00:25:25,270
+وروحنا جيبنا alpha 3 في alpha 7 لازم يطلع عندك 100
+
+227
+00:25:25,270 --> 00:25:34,360
+alpha نعملها شفويألف تلاتة في ألف سبعة ألف سبعة من
+
+228
+00:25:34,360 --> 00:25:38,920
+واحد اللي هي بسبعة ألف تلاتة لا سبعة اللي هي بواحد
+
+229
+00:25:38,920 --> 00:25:43,120
+وعشرين بيبقى الواحد يبقى هي ألف واحد وهكذا بالنسبة
+
+230
+00:25:43,120 --> 00:25:47,340
+لمن؟ بالنسبة للباقي يعني لو بدي أضرب واحدة في
+
+231
+00:25:47,340 --> 00:25:51,740
+التانية هي نفسيطلع على هذا الجدول و هذا الجدول تجد
+
+232
+00:25:51,740 --> 00:25:56,320
+اتنين نفسي الخواص هذه فيها اربعة عناصر وهذه فيها
+
+233
+00:25:56,320 --> 00:26:00,720
+اربعة عناصر هذه Cyclic وهذه Cyclic مادام Cyclic
+
+234
+00:26:00,720 --> 00:26:03,940
+إذا أبيلن ال order of the element هنا هي ال order
+
+235
+00:26:03,940 --> 00:26:08,960
+of the element هنا يبقى اتنين هذول are isomorphic
+
+236
+00:26:08,960 --> 00:26:15,340
+مش عقدة اتنتين هذول حروحان عمّم هذا الكلام و بدل
+
+237
+00:26:15,340 --> 00:26:21,680
+ما هي Z عشرة هقول Z in و بدل ما هي و عشرة هقول U
+
+238
+00:26:21,680 --> 00:26:30,430
+in و نبرهن صحيتان الكلام as a theorem كنظريةأخر
+
+239
+00:26:30,430 --> 00:26:37,890
+نظرية في هذا الشبتر هي atomorphism ل ZN is
+
+240
+00:26:37,890 --> 00:26:52,150
+isomorphic للغروبيوين يا
+
+241
+00:26:52,150 --> 00:26:53,790
+أبقى بيدنا نيجي لtheorem
+
+242
+00:27:02,010 --> 00:27:09,650
+for every positive integer in for every positive
+
+243
+00:27:09,650 --> 00:27:14,970
+integer in
+
+244
+00:27:14,970 --> 00:27:26,890
+الـ Atomorphism لزد ان is isomorphic لمن لل UN
+
+245
+00:27:37,760 --> 00:27:48,780
+from the previous example من المثال السابق لاحظنا
+
+246
+00:27:48,780 --> 00:27:56,280
+ما يأتي any atomorphism
+
+247
+00:27:56,280 --> 00:27:58,620
+alpha
+
+248
+00:28:02,400 --> 00:28:10,380
+is determined determined
+
+249
+00:28:10,380 --> 00:28:24,760
+by the value of alpha of one اللي موجودة في ال UN
+
+250
+00:28:24,760 --> 00:28:28,220
+بدنا
+
+251
+00:28:28,220 --> 00:28:39,330
+نروح نقوله defineA mapping بنعرف function T من ال
+
+252
+00:28:39,330 --> 00:28:53,070
+atomorphism ل ZN إلى ال UN by كتالي T of alpha بده
+
+253
+00:28:53,070 --> 00:28:55,390
+يساوي alpha of one
+
+254
+00:28:59,500 --> 00:29:05,940
+بنثبت ان الـ T هادى is one to one and unto وكذلك
+
+255
+00:29:05,940 --> 00:29:11,640
+تخدم خاصية ال isomorphism لإن احنا مش هنثبت ال
+
+256
+00:29:11,640 --> 00:29:14,680
+isomorphism نثبت ان ال function لإنها one to one
+
+257
+00:29:14,680 --> 00:29:19,200
+and unto وتخدم الخاصية Phi of A بيبدى يساوي ال Phi
+
+258
+00:29:19,200 --> 00:29:26,020
+of A في ال Phi of B مرة تانيةمن خلال شغلنا في هذا
+
+259
+00:29:26,020 --> 00:29:32,600
+المثال لاحظنا ان قيمة Alpha تعتمد على قيمة Alpha
+
+260
+00:29:32,600 --> 00:29:39,580
+of 1 Alpha of 1 هي بتحدد شكل الـ Atomorphismفروح
+
+261
+00:29:39,580 --> 00:29:43,440
+نقول من المثال السابق any automorphism alpha is
+
+262
+00:29:43,440 --> 00:29:48,420
+determined by the value of alpha of one و alpha of
+
+263
+00:29:48,420 --> 00:29:54,960
+one لقناها موجودة في ال U N يعني alpha of z عاشرة
+
+264
+00:29:54,960 --> 00:30:00,390
+لقناها موجودة في ال U عاشرةيبقى Alpha of 1 موجودة
+
+265
+00:30:00,390 --> 00:30:04,230
+في الـ UN لذلك نروح نعرف Function من الـ
+
+266
+00:30:04,230 --> 00:30:09,170
+Atomorphism إلى ZN للـ UN بدي أخد ال element هنا
+
+267
+00:30:09,170 --> 00:30:12,730
+ال element هنا دي نالو الرمز اللي هو Alpha بدي
+
+268
+00:30:12,730 --> 00:30:17,670
+صورته في UN الصورة هي دائما و أبدا Alpha of 1 اللي
+
+269
+00:30:17,670 --> 00:30:24,030
+موجودة في TN الآن بدي أثبت ان T is one to one لكل
+
+270
+00:30:24,030 --> 00:30:28,370
+ال elements اللي موجودة في ال Atomorphism لمينالى
+
+271
+00:30:28,370 --> 00:30:37,350
+ZN يبقى بداجي اقوله ال N T is one to one مشان هيك
+
+272
+00:30:37,350 --> 00:30:45,630
+بداجي اقوله assume ان T of Alpha بده سوى T of Beta
+
+273
+00:30:45,630 --> 00:30:53,990
+بده احاول اثبت ان Alpha تسوى مين تسوى Betaهذا يعني
+
+274
+00:30:53,990 --> 00:31:04,070
+T of α لـ α of one هو beta of one هذا العلاقة رقم
+
+275
+00:31:04,070 --> 00:31:10,750
+واحد لكن لو رجعت ل ZN هي فيها بس ال one ولا فيها
+
+276
+00:31:10,750 --> 00:31:16,910
+اعداد كتيرةفيها اعداد كتيرة اذا انا بده اروح اثبت
+
+277
+00:31:16,910 --> 00:31:21,210
+ان ال alpha تساوي ال beta على كل الاعداد الكثيرة
+
+278
+00:31:21,210 --> 00:31:31,090
+وليست على ال one فقط فباجي بقوله لو كان ال K موجود
+
+279
+00:31:31,090 --> 00:31:41,220
+في Z then ال alpha of Kمش تساوي alpha ل واحد زائد
+
+280
+00:31:41,220 --> 00:31:46,900
+واحد زائد واحد يعني هذه بده تساوي k في alpha of
+
+281
+00:31:46,900 --> 00:31:57,180
+one مظبوط طيب بده اخد ال beta of k برضه تساوي ال k
+
+282
+00:31:57,180 --> 00:32:04,920
+في beta of one مظبوط طيب ايش رأيك من هذه beta of
+
+283
+00:32:04,920 --> 00:32:10,210
+one هي عبارة عن مين؟Alpha of one إذا بقدر أشيل هذه
+
+284
+00:32:10,210 --> 00:32:19,570
+و أكتب كيف Alpha of one هذه from one من ال one طب
+
+285
+00:32:19,570 --> 00:32:24,810
+اطلعلي في الطرف اليمين هذا و الطرف اليمين هذا إيش
+
+286
+00:32:24,810 --> 00:32:27,610
+بنستنتج ملي اتنين مع بعض
+
+287
+00:32:32,490 --> 00:32:39,490
+الشيء الوحيد اللي بدي اعطانيه هو alpha of K بيساوي
+
+288
+00:32:39,490 --> 00:32:46,070
+beta of KK هذا رقم عشوائي أخدته من كل زدن و أثبت
+
+289
+00:32:46,070 --> 00:32:52,010
+قبله أن Alpha of 1 يبقى أسوأ من Beta of 1 يبقى
+
+290
+00:32:52,010 --> 00:32:59,510
+أسوأ الـ Alpha تساوي Beta لكل الـ K الموجود في الـ
+
+291
+00:32:59,510 --> 00:33:03,630
+ZN طيب
+
+292
+00:33:03,630 --> 00:33:13,770
+بنا نيجي ناخد TS Onto مين اللي بيحكي و ايش بيقولمش
+
+293
+00:33:13,770 --> 00:33:19,910
+سامع لأ
+
+294
+00:33:19,910 --> 00:33:25,870
+كي رقم وليس اتومورفيزم ال alpha كي هو الاتومورفيزم
+
+295
+00:33:25,870 --> 00:33:26,930
+ال alpha كي هو الاتومورفيزم ال alpha كي هو
+
+296
+00:33:26,930 --> 00:33:29,910
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+297
+00:33:29,910 --> 00:33:30,990
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+298
+00:33:30,990 --> 00:33:30,990
+alpha كي هو الاتومورفيزم ال alpha كي هو
+
+299
+00:33:30,990 --> 00:33:32,070
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+300
+00:33:32,070 --> 00:33:32,090
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+301
+00:33:32,090 --> 00:33:32,090
+alpha كي هو الاتومورفيزم ال alpha كي هو
+
+302
+00:33:32,090 --> 00:33:34,630
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+303
+00:33:34,630 --> 00:33:40,990
+كي هو الاتومورفيزم ال alpha كي هو الفي ال code
+
+304
+00:33:40,990 --> 00:33:47,430
+domain و أثبت أنه له أصل في ال domain يبقى بالداجة
+
+305
+00:33:47,430 --> 00:33:58,190
+أقول له let ال R موجود في وين؟ في ال UN يبقى
+
+306
+00:33:58,190 --> 00:34:02,830
+أخدت ال R موجود في ال UN يبقى ال R هذا relatively
+
+307
+00:34:02,830 --> 00:34:10,380
+prime بالنسبة لمين؟ ل ال UN ل ال Nطيب، الآن بندروح
+
+308
+00:34:10,380 --> 00:34:15,160
+اعرف function من .. اه اه define
+
+309
+00:34:17,450 --> 00:34:26,530
+Alpha من ZN إلى ZN يعني بمعنى أخر بدي أخلق
+
+310
+00:34:26,530 --> 00:34:32,550
+Atomorphism علاقة بالأرض اللي عندنا هذه فقلت افترض
+
+311
+00:34:32,550 --> 00:34:42,970
+أن Alpha من ZN إلى ZM is a function defined by
+
+312
+00:34:47,820 --> 00:34:56,500
+Alpha of S مثلا ال S موجودة وين؟ هنا يبقى هذا
+
+313
+00:34:56,500 --> 00:35:08,500
+الكلام بده يساوي SR modulo N مرة
+
+314
+00:35:08,500 --> 00:35:13,820
+تانيةأنا خدت R موجودة في ال UN في ال code domain
+
+315
+00:35:13,820 --> 00:35:18,460
+هذا ال element بدي أثبت أنه له أصل هنا إيش يعني له
+
+316
+00:35:18,460 --> 00:35:23,600
+أصل هنا يعني لازم ألاقي atomorphism في ال
+
+317
+00:35:23,600 --> 00:35:29,100
+atomorphism لاجي بحيث ال R يكون صورة لمين صورة
+
+318
+00:35:29,100 --> 00:35:35,970
+لهذه ال function يبقى بتروح أخلقأتومورفزيوم هنا له
+
+319
+00:35:35,970 --> 00:35:41,550
+علاقة بالـ R هذه فاجينا نعرف فانكشن Alpha من Z إلى
+
+320
+00:35:41,550 --> 00:35:47,090
+N Z N نعرفها بالتالي Alpha لو أثرت على ال S بتساوي
+
+321
+00:35:47,090 --> 00:35:53,830
+ال SR modulo N تمام؟ بدنا نيجي نشوف هل هذه one to
+
+322
+00:35:53,830 --> 00:35:59,950
+one؟and unto وهل هي isomorphism ان تم ذلك يبقى هذه
+
+323
+00:35:59,950 --> 00:36:06,830
+صارت atomorphism الان بدنا نروح نثبت ان ال alpha
+
+324
+00:36:06,830 --> 00:36:13,810
+هذه is one to one كويس
+
+325
+00:36:14,530 --> 00:36:21,130
+الان مشان هيك بتروح اخد صورتين متساويتين يبقى
+
+326
+00:36:21,130 --> 00:36:28,890
+هقوله assume افترض انه alpha طبعا هذا يا شباب لكل
+
+327
+00:36:28,890 --> 00:36:35,230
+ال S اللي موجودة في ZN مشان نقولش ال S هذي من وين
+
+328
+00:36:35,230 --> 00:36:39,980
+جيبناهاهذه Alpha of S يساوي S R موضوعين لكل S
+
+329
+00:36:39,980 --> 00:36:45,440
+الموجودة في ZM الان انا ادعي ان Alpha is one to
+
+330
+00:36:45,440 --> 00:36:50,440
+one فبدي اثبت صحة هذا الكلام فقلنا افترض ان Alpha
+
+331
+00:36:50,440 --> 00:36:59,120
+of S1 يساوي Alpha of S2بدي احاول اثبت ان ال S1 بدى
+
+332
+00:36:59,120 --> 00:37:09,480
+يساوي S2 هذا معناه ايش alpha of S1 يعني S1R modulo
+
+333
+00:37:09,480 --> 00:37:18,040
+N بدى يساوي S2R modulo N ايش رأيك بدي اعملها
+
+334
+00:37:18,040 --> 00:37:24,150
+معادلة صفريةجابت داجي هذا ع الشجة التانية بإشارة
+
+335
+00:37:24,150 --> 00:37:32,990
+سالب يعني بقدر أقول S1 ناقص S2 أخدت R عامل مشترك
+
+336
+00:37:32,990 --> 00:37:38,930
+موديله N بده ساوي مين؟ بده ساوي Zero يعني كأني
+
+337
+00:37:38,930 --> 00:37:43,570
+نجلت هذه ع الشجة التانية و أخدت R من الطرفين عامل
+
+338
+00:37:43,570 --> 00:37:49,970
+مشترك الآن الـR أين موجود يا شباب؟ الها معكس ولا
+
+339
+00:37:49,970 --> 00:37:57,380
+لا؟ممتاز جدا يبقى هنا باجي بقوله since R موجودة في
+
+340
+00:37:57,380 --> 00:38:06,080
+ال UN we have ان ال R inverse موجودة في ال UN ايش
+
+341
+00:38:06,080 --> 00:38:11,200
+رايك المعادلة هذي بدي اضربها في R inverse هذي بدي
+
+342
+00:38:11,200 --> 00:38:19,900
+اسميها مثلا star يبقى بداجي اقوله multiply multi
+
+343
+00:38:22,080 --> 00:38:32,200
+ply star by R inverse we get لو ضربنا هنا في R
+
+344
+00:38:32,200 --> 00:38:40,920
+inverse بتروح معاها S واحد ناقص S اتنين موديولو N
+
+345
+00:38:40,920 --> 00:38:47,300
+بده يساوي Zero في R inverse اللي هو من من Zeroطيب
+
+346
+00:38:47,300 --> 00:38:54,780
+هذه بقدر افكها و احولها الى S1 modulo N بده يساوي
+
+347
+00:38:54,780 --> 00:39:04,720
+ال S2 modulo N يبقى هذا معناه ان ال S1 هي نفس ال
+
+348
+00:39:04,720 --> 00:39:13,440
+S2طبعا يبقى هك اثبت ان ال alpha is one to one بدنا
+
+349
+00:39:13,440 --> 00:39:25,640
+نثبت ان ال alpha is on الان
+
+350
+00:39:25,640 --> 00:39:33,480
+ال alpha is on هو ال
+
+351
+00:39:33,480 --> 00:39:41,790
+alpha من وين لوينمن ZN إلى Z وانا أخدت هنا S
+
+352
+00:39:41,790 --> 00:39:50,450
+موجودة في ZN يبقى باجي بقوله F ال S موجودة في ZN
+
+353
+00:39:50,450 --> 00:39:53,710
+then ال S تساوي
+
+354
+00:39:56,350 --> 00:40:08,010
+عشان رايك بقدر اكتبها هذه S مثلا في ال R inverse R
+
+355
+00:40:08,010 --> 00:40:18,410
+منفع الله مانفعش ايه انا السما عندي لسه بجمعش كويس
+
+356
+00:40:18,410 --> 00:40:22,370
+حتى اللحظة علي صوتك عشرين ايه
+
+357
+00:40:29,070 --> 00:40:36,890
+ممتاز لكن احنا بنشغل داخل مين هذا الكلام ورا in z
+
+358
+00:40:36,890 --> 00:40:42,210
+in بس يعني احنا بنشغل داخل دي اللي عناصر برا ماليش
+
+359
+00:40:42,210 --> 00:40:46,210
+علاقة فيها يعني علاقتي مع ال zero والواحد والاتنين
+
+360
+00:40:46,210 --> 00:40:57,910
+لغتي التسعةيبقى S1 تساوي S2 داخل Z10 يبقى
+
+361
+00:40:57,910 --> 00:41:08,730
+الـ S يساوي SR inverse Rطيب هذه ال S أنا ماخدها في
+
+362
+00:41:08,730 --> 00:41:17,130
+ZN يعني ال S modulo N تساوي ال S R inverse R كذلك
+
+363
+00:41:17,130 --> 00:41:24,930
+modulo N يعني هذه modulo N وهنا لو حطيت modulo N
+
+364
+00:41:24,930 --> 00:41:31,090
+مش مشكلةطيب إيش رأيك في SR inverse بدي أشيلها و
+
+365
+00:41:31,090 --> 00:41:38,350
+أكتب بدالها element 10 لو جيت كتبت بدالها S1R
+
+366
+00:41:38,350 --> 00:41:46,050
+modulo N ايوه
+
+367
+00:41:46,050 --> 00:41:51,510
+احنا بأي وسيلة رياضية بتحاول تثبت ان ال function
+
+368
+00:41:51,510 --> 00:41:57,070
+اللي عندك is on 2تمام؟ بدك تشتغل شغل صحيح ماحدش
+
+369
+00:41:57,070 --> 00:42:02,370
+يقدر يمسك عليك فيه غلطة ايوة اعلي
+
+370
+00:42:02,370 --> 00:42:09,490
+صوتك مش هنسمع تعالى شوف هنا شوف ايش بتقول بالظبط
+
+371
+00:42:09,490 --> 00:42:17,710
+اسمع يا شباب ايش بيقول اه احنا بدنا نوصل للرفض
+
+372
+00:42:17,710 --> 00:42:23,730
+الآن اقعد هتقولك ايش بيقولأنا قلت بس انت مااخدتش
+
+373
+00:42:23,730 --> 00:42:29,170
+بالك انا الأن ايش بدي أثبت بدي أثبت ان T is onto
+
+374
+00:42:30,060 --> 00:42:37,120
+قلت لك خد R موجود في UN بدي احاول اخلق atomorphism
+
+375
+00:42:37,120 --> 00:42:44,560
+في الـ set اللي عندنا هذه بحيث يكون صورة لل R اللي
+
+376
+00:42:44,560 --> 00:42:48,900
+انا اخدته هذا كل الفكرة في الموضوع تمام فروحت قلت
+
+377
+00:42:48,900 --> 00:42:53,420
+اعرف function بالشكل اللي عندنا هذا و بدور هل ال
+
+378
+00:42:53,420 --> 00:42:58,220
+function هذه atomorphism ولا لأ حتى هذه اللحظة لم
+
+379
+00:42:58,220 --> 00:43:03,660
+اثبت انها atomorphismمظبوط واذا طلعت atomorphism
+
+380
+00:43:03,660 --> 00:43:07,740
+بدي بيجيلك ان صورتها R اللى عندنا وبالتالي يكون
+
+381
+00:43:07,740 --> 00:43:13,280
+حلنا المشكلة واضحة تمام واضحة يا شباب هيك طيب يبقى
+
+382
+00:43:13,280 --> 00:43:17,680
+انا اخدت S موجودة في Z ان ال S بقدر اكتبها SR
+
+383
+00:43:17,680 --> 00:43:23,570
+inverse R modulo N عادي جداماعناش مشكلة طب ال S في
+
+384
+00:43:23,570 --> 00:43:31,130
+ال R inverse بدي أسميها S1R modulo N أليست هذه هي
+
+385
+00:43:31,130 --> 00:43:37,910
+Alpha of S1مش هي ال alpha of S يساوي SR modulo N
+
+386
+00:43:37,910 --> 00:43:47,130
+طلعناها S1R يبقى alpha of S1 يبقى صار ال element S
+
+387
+00:43:47,130 --> 00:43:55,250
+اللي أخدته في Z in لجتله أصل اسمه ايش اسمه S1 يبقى
+
+388
+00:43:55,250 --> 00:43:59,030
+ال alpha انتوا ولا لا يبقى ال alpha انتوا يبقى
+
+389
+00:43:59,030 --> 00:44:02,750
+أثبت الآن ان ال alpha اللي أخدتها دي one to one
+
+390
+00:44:02,750 --> 00:44:07,970
+and انتوا شو ضايل عندىأثبت أنه بتخدم خاصية ال
+
+391
+00:44:07,970 --> 00:44:14,790
+isomorphism لذلك بتروح أخد alpha of مثلا a زائد ال
+
+392
+00:44:14,790 --> 00:44:24,050
+.. او S1 زائد S2 خليها نفس الرمز خليها S1 و S2 S1
+
+393
+00:44:24,050 --> 00:44:31,430
+زائد S2 بده يساوي ال
+
+394
+00:44:31,430 --> 00:44:38,860
+S1 و ال S2 أرقام هذهمش هيك اه يعني بقدر اخدهم زي
+
+395
+00:44:38,860 --> 00:44:46,820
+ما بدي او خلينا بلاشي نغلط شوية هذه قولنا is on to
+
+396
+00:44:46,820 --> 00:44:53,940
+خلصنا منها S1 و S2 مظبوط حسب ال definition هذه
+
+397
+00:44:53,940 --> 00:45:05,740
+بدها تساوي S1 زي S2 في R modulo Nيعني هذه بقدر
+
+398
+00:45:05,740 --> 00:45:18,760
+اقول S1R زي S2R كله modulo N او ان شئتم فقولوا S1R
+
+399
+00:45:18,760 --> 00:45:30,060
+modulo N S2R modulo Nهلأيست هذه اللي هو Alpha of S
+
+400
+00:45:30,060 --> 00:45:36,160
+واحد وهذه Alpha of S اتنى؟ يبقى بناء عليها صارت
+
+401
+00:45:36,160 --> 00:45:42,600
+هذه ايش؟ صارت Atomorphism لأنها من ال group إلى
+
+402
+00:45:42,600 --> 00:45:51,860
+نفسها يبقى هنا Sir Alpha is an Atomorphism
+
+403
+00:45:57,050 --> 00:46:03,470
+يبقى حتى لأن خلقنا atomorphism موجود عندنا الان لو
+
+404
+00:46:03,470 --> 00:46:11,690
+جيت now لو أخدت alpha of S اللي هى مين قلنا عليها
+
+405
+00:46:11,690 --> 00:46:19,070
+اللي هى alpha of S اللي هى ال S R modulo N هذا بده
+
+406
+00:46:19,070 --> 00:46:26,340
+يعطيلكالـ alpha of S مش S موجود في ZN يعني هذا
+
+407
+00:46:26,340 --> 00:46:34,840
+الكلام بده يساوي S في alpha of one مظبوط؟
+
+408
+00:46:36,980 --> 00:46:42,940
+S α of خمسة يعني خمسة .. اي واحد واحد واحد أثر
+
+409
+00:46:42,940 --> 00:46:47,760
+alpha تأثر عليهم كلهم يبقى الرقم نفسه في alpha of
+
+410
+00:46:47,760 --> 00:46:55,140
+one بده يساوي مين؟ بده يساوي ال S R modulo M بال
+
+411
+00:46:55,140 --> 00:47:01,160
+left cancellation law شط بالأيسر يبقى alpha of one
+
+412
+00:47:01,160 --> 00:47:09,870
+بده يساوي ال R modulo Nهذه موجودة في UN ولا لا؟
+
+413
+00:47:09,870 --> 00:47:15,450
+موجودة في UN اللي احنا أخدناها من البداية وانراحت
+
+414
+00:47:15,450 --> 00:47:23,390
+تي وزنت أخدنا R موجودة في UN واحنا أخدنا T وانراحت
+
+415
+00:47:23,390 --> 00:47:30,070
+T of Alpha يسوى من؟ Alpha of one يبقى صار ال R
+
+416
+00:47:30,070 --> 00:47:37,870
+modulo N ال R modulo Nاللي هي تساوي Alpha of one
+
+417
+00:47:37,870 --> 00:47:44,230
+والـ Alpha of one هي T of Alpha هذا بده يعطيلك ان
+
+418
+00:47:44,230 --> 00:47:49,950
+T is onto يبقى
+
+419
+00:47:49,950 --> 00:47:55,950
+كلها اللف لفة مشان نوصل ان R هي عبارة عن T of
+
+420
+00:47:55,950 --> 00:48:02,030
+Alpha وبالتالي T of Alpha is onto خلصنا؟ما خلصناش،
+
+421
+00:48:02,030 --> 00:48:08,090
+ضالت خاصية الـ isomorphism إذا بدي أخد تأثير الـ T
+
+422
+00:48:08,090 --> 00:48:11,990
+على حاصل ضرب two permutations اللي هي او two
+
+423
+00:48:11,990 --> 00:48:17,730
+automorphisms Alpha و Beta يبقى بدي أخد finally
+
+424
+00:48:17,730 --> 00:48:21,010
+بدي
+
+425
+00:48:21,010 --> 00:48:27,610
+أخد T of Alpha Beta أو Beta Alpha سيئة Beta Alpha
+
+426
+00:48:28,150 --> 00:48:31,850
+اعتقد الكتاب ماخد alpha beta انا بدي اخد beta
+
+427
+00:48:31,850 --> 00:48:35,990
+alpha يعني على كل الأمرين الكلام صحيح لو اخدت
+
+428
+00:48:35,990 --> 00:48:40,470
+alpha beta ولا beta alpha بتفرقش عنها طيب هذا
+
+429
+00:48:40,470 --> 00:48:47,710
+الكلام بده يساويالان ايش بيقولي T لما تأثر على ال
+
+430
+00:48:47,710 --> 00:48:51,790
+.. وين راحت؟ T of Alpha بديه يساوي Alpha of one
+
+431
+00:48:51,790 --> 00:49:01,650
+يبقى هذا بديه يساوي Beta Alpha كله of one طيب
+
+432
+00:49:01,650 --> 00:49:08,990
+هذا الكلام بديه يساوي Beta في Alpha of one
+
+433
+00:49:12,500 --> 00:49:19,480
+طب alpha of one وين موجودة؟ وين موجودة؟ في UN
+
+434
+00:49:19,480 --> 00:49:26,020
+مظبوط ايه alpha of one حطناها موجودة وين؟ في UN
+
+435
+00:49:26,020 --> 00:49:34,280
+وين كتبناها؟ alpha وين راحت؟المهم كتبنا هاية Alpha
+
+436
+00:49:34,280 --> 00:49:38,540
+of one موجودة في UN يبقى Alpha of one لو قلنا مثلا
+
+437
+00:49:38,540 --> 00:49:44,140
+U عشرة يبقى يا واحد يا تلاتة يا سبعة يا تسعة وهكذا
+
+438
+00:49:44,140 --> 00:49:50,850
+قيص عليها الباقى إذا هذه هاهاهتساوي واحد زائد واحد
+
+439
+00:49:50,850 --> 00:49:58,390
+زائد واحد جديش Alpha of one times مظبوط يعني هذه
+
+440
+00:49:58,390 --> 00:50:05,550
+بدها تساوي Beta of واحد زائد واحد زائد واحد كام
+
+441
+00:50:05,550 --> 00:50:14,430
+مرة هذا كله Alpha of one times يعني لو كان Alpha
+
+442
+00:50:14,430 --> 00:50:21,550
+of one يساوي تلتةلو كانAlpha of one بده يسوى تلاتة
+
+443
+00:50:21,550 --> 00:50:27,450
+يبقى يصير واحد زي واحد زي واحد فقط لا غير طبعا طب
+
+444
+00:50:27,450 --> 00:50:33,510
+لو كان سبعة بدي اكتبها سبعة من المرات يعني قداش
+
+445
+00:50:33,510 --> 00:50:37,710
+بتكون النتيجة بدي اكرهها يعني Alpha of one times
+
+446
+00:50:37,710 --> 00:50:42,250
+ان كانت سبعة بدي اكررها سبعة مرات ان كانت تلاتة
+
+447
+00:50:42,250 --> 00:50:45,330
+تلات مرات ان كانت تسعة تسعة مرات ان كانت احداشر
+
+448
+00:50:45,330 --> 00:50:51,240
+احداشر مرة و هكذاطيب كويس هذا الكلام بده يشاوي
+
+449
+00:50:51,240 --> 00:51:00,460
+اللي هو beta of one زائد beta of one زائد زائد
+
+450
+00:51:00,460 --> 00:51:10,460
+beta of one هذا alpha of one كمان times اذا
+
+451
+00:51:10,460 --> 00:51:19,030
+هذا الكلام بده يشاوي اكمر هدولالفا of one و هدولة
+
+452
+00:51:19,030 --> 00:51:25,270
+كم واحدة في beta one يبقى هذا بده يساوي beta of
+
+453
+00:51:25,270 --> 00:51:33,230
+one في alpha of one beta of one امكررة alpha one
+
+454
+00:51:33,230 --> 00:51:42,170
+من المرات طيب ال beta of one ال beta of one أليس
+
+455
+00:51:42,170 --> 00:51:51,360
+تية T of betaيبقى هذه هي T of Beta والتانية هي T
+
+456
+00:51:51,360 --> 00:51:57,500
+of Alpha يبقى أثبتنا له أن T of Beta Alpha هي T
+
+457
+00:51:57,500 --> 00:52:02,860
+Beta Alpha لو روحت للكتاب هيكون جلب الوضع أخد لك T
+
+458
+00:52:02,860 --> 00:52:08,130
+Alpha Beta وهنا تقول لك T Alpha T فماعناش مشكلةبس
+
+459
+00:52:08,130 --> 00:52:10,830
+بدل ما اقول لك ان alpha of one times بقول لك beta
+
+460
+00:52:10,830 --> 00:52:15,870
+of one time اذا لا مشكلة انا اتعمد اجيبك بشكل هذا
+
+461
+00:52:15,870 --> 00:52:20,250
+حتى تتعرف انه ليس بالضرورة قرآن كريم لكن احنا
+
+462
+00:52:20,250 --> 00:52:30,070
+فهمنا هذا الكلام يبقى .. يبقى بناء عليه so T is an
+
+463
+00:52:30,070 --> 00:52:37,470
+isomorphism هذا بدي اعطيلك ان ال atomorphismلزد ان
+
+464
+00:52:37,470 --> 00:52:43,230
+ايزو مارفك ل يو ان من الآن فصاعدا
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a77a7919318f841e2012b9fba6720480c17a4f1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8.srt
@@ -0,0 +1,1791 @@
+1
+00:00:21,380 --> 00:00:26,260
+بسم الله الرحمن الرحيم المرة الماضية بدأنا نناقش
+
+2
+00:00:26,260 --> 00:00:30,500
+الأسئلة المتعلقة بشابتر ستة وهو الـ isomorphism
+
+3
+00:00:30,500 --> 00:00:36,220
+ووقفنا عند سؤال رقم تسعة عشر، سؤال تسعة عشر مختصر
+
+4
+00:00:36,220 --> 00:00:41,400
+بيقول في عندنا two isomorphism واحد اسمه Φ  والتاني 
+
+5
+00:00:41,400 --> 00:00:47,620
+اسمه  جامع من اللي هو الـ cycle group generated by a
+
+6
+00:00:47,620 --> 00:00:54,090
+إلى أي group أخرى، وعندي معلومة أن Φ(a) تساوي 
+
+7
+00:00:54,090 --> 00:00:59,750
+جامع(a)، قال لي اثبت أن Φ تساوي جامع.
+
+8
+00:01:00,460 --> 00:01:05,340
+بنقوله بسيطة، بنفكر في الموضوع الآن، فأيّ و جامع لما
+
+9
+00:01:05,340 --> 00:01:10,120
+يؤثروا على الـ subgroup generated by a معناته
+
+10
+00:01:10,120 --> 00:01:14,740
+a مرفوع لأس مظبوط، لإن ده الـ cycle group معناته الـ
+
+11
+00:01:14,740 --> 00:01:19,200
+a والـ a والـ a تربيع والـ a تكعيب وهكذا إلى آخره.
+
+12
+00:01:19,200 --> 00:01:29,180
+يبقى مناء عليه عندنا احنا هنا إيه اللي هو مثلا الـ a
+
+13
+00:01:29,180 --> 00:01:33,720
+to the power of k موجودة في الـ subgroup generated
+
+14
+00:01:33,720 --> 00:01:40,520
+by a معناته كل من Φ وجامع ستؤثر على من؟ على هذا
+
+15
+00:01:40,520 --> 00:01:50,160
+العنصر هذا، بده يعطينا إنه Φ(a<sup>k</sup>) أبصر قد إيش بده 
+
+16
+00:01:50,160 --> 00:01:56,390
+يساوي الله أعلم، تمام؟ طب بدي بقول هذا الكلام بده
+
+17
+00:01:56,390 --> 00:02:06,600
+يساوي اللي هو Φ(A) كله to the power of k  Φ(A) كله 
+
+18
+00:02:06,600 --> 00:02:11,000
+to the power of k وهذه نظرية سابقة أخذناها
+
+19
+00:02:11,000 --> 00:02:17,560
+وبرهناها، لكن في معطيات عندي بتقول لي Φ(a) تساوي
+
+20
+00:02:17,560 --> 00:02:23,080
+جامع(a)، إذا بقدر أشيل اللي هو Φ(a)  و أحط
+
+21
+00:02:23,080 --> 00:02:28,980
+بدلها جامع(a)، يبقى هذا الكلام بدي يعطيني جامع
+
+22
+00:02:28,980 --> 00:02:37,100
+(a) كله to the power of k يبقى أصبح عندي Φ(a) ك
+
+23
+00:02:37,100 --> 00:02:45,340
+بده يساوي جامع(a) كله to the power كل الـ k هذه
+
+24
+00:02:45,340 --> 00:02:54,910
+ممكن تنزل هنا، يبقى جامع كله لمن؟ للـ a<sup>k</sup> يبقى
+
+25
+00:02:54,910 --> 00:02:59,930
+معنى هذا الكلام إنه تأثير Φ على أي element في الـ
+
+26
+00:02:59,930 --> 00:03:06,050
+group هذي يساوي تأثير جامع على أي element موجود في
+
+27
+00:03:06,050 --> 00:03:11,810
+الـ subgroup generated by A، لكن بقدرش أقول التساو
+
+28
+00:03:11,810 --> 00:03:17,710
+ي حاصل نتيجة لهذا التساو لأن a عنصر محدد هو اللي ولد
+
+29
+00:03:17,710 --> 00:03:21,300
+الـ group لكن عندما أقول a to the power of k أي
+
+30
+00:03:21,300 --> 00:03:26,120
+element أخدت من الـ group عشوائيا من مكان يكون، إذا Φ
+
+31
+00:03:26,120 --> 00:03:30,440
+عند أي element موجود في الـ group ده تساوي جامع عند
+
+32
+00:03:30,440 --> 00:03:34,680
+نفس الـ element موجود في الـ group هذا، معناته أن Φ
+
+33
+00:03:34,680 --> 00:03:41,510
+تساوي جامع وهو المطلوب. يعني كل الفكرة كانت تبدل
+
+34
+00:03:41,510 --> 00:03:47,010
+تأثير بـ Φ على أي element من g بتأثير جامع على أي
+
+35
+00:03:47,010 --> 00:03:52,510
+element من g، هذا كان سؤال تسعة عشر، سؤال عشرين
+
+36
+00:03:52,510 --> 00:04:05,450
+بيقول لي سؤال عشرين بيقول لي Φ من Z<sub>50</sub> إلى Z<sub>50</sub>
+
+37
+00:04:05,450 --> 00:04:15,020
+خمسين عبارة عن Automorphism، هذا Automorphism وفي نفس
+
+38
+00:04:15,020 --> 00:04:23,620
+الوقت عندنا Φ(11) يساوي 13، وقال لي determine
+
+39
+00:04:23,620 --> 00:04:30,960
+the formula for Φ(x)، find Φ(x)، بدنا نعرف إيش
+
+40
+00:04:30,960 --> 00:04:33,740
+شكلها في هذه الحالة.
+
+41
+00:04:37,840 --> 00:04:44,420
+أنا عندي Φ من Z<sub>50</sub> إلى Z<sub>50</sub> عبارة عن Automorphism
+
+42
+00:04:44,420 --> 00:04:49,460
+عندي الـ Automorphism Φ تأثيره على الـ element 11
+
+43
+00:04:49,460 --> 00:04:55,260
+اللي موجود في Z<sub>50</sub> بده يساوي 13 اللي موجودة في Z<sub>50</sub>.
+
+44
+00:04:55,260 --> 00:05:00,690
+كذلك قال لي هات لي الصيغة لمين؟ للـ Automorphism Φ
+
+45
+00:05:00,690 --> 00:05:06,890
+(x)، بدي أعرف Φ(x) in general قد إيش بيساوي حتى
+
+46
+00:05:06,890 --> 00:05:13,350
+يكون Φ(11) بدي يساوي مين؟ بدي يساوي 13، طيب بدي 
+
+47
+00:05:13,350 --> 00:05:18,730
+أحاول أستفيد من المعطى هذا في حل المسألة حتى أعرف
+
+48
+00:05:18,730 --> 00:05:24,210
+أقدر أجيب من Φ(50) حد فكر في حل السؤال وجابه؟
+
+49
+00:05:24,210 --> 00:05:27,950
+يعني هيك؟ ولا واحد؟
+
+50
+00:05:31,180 --> 00:05:37,900
+كيف؟ ما وصلناش لنتيجة الساواة
+
+51
+00:05:37,900 --> 00:05:45,680
+قد إيش؟ ليش يعني x زي 2؟ لا، بدك تشغل رياضة صح أنت
+
+52
+00:05:45,680 --> 00:05:50,940
+بتشغل في Z<sub>50</sub> وZ<sub>50</sub> الـ operation عليها اللي هي
+
+53
+00:05:50,940 --> 00:05:56,100
+الجامعة طبعا، طيب خلي بالك هنا بنحاول نستفيد من
+
+54
+00:05:56,100 --> 00:05:59,300
+المعلومات اللي عندنا الحين يا جماعة، بقى أنا لما
+
+55
+00:05:59,300 --> 00:06:07,170
+أجي أقول ما يأتي إن Φ(11) بده يساوي 13
+
+56
+00:06:07,170 --> 00:06:12,050
+بقدر أكتب هذه المعادلة بالصيغة ثانية، هذه عبارة عن
+
+57
+00:06:12,050 --> 00:06:15,270
+إيش؟ Φ(1) زيادة 1 زيادة 1 زيادة 1 زيادة 1
+
+58
+00:06:15,270 --> 00:06:19,970
+أحد عشر مرة، Φ Automorphism حتى تدخل على كل واحد
+
+59
+00:06:19,970 --> 00:06:23,230
+فيهم، يبقى Φ(1) Φ(1) Φ(1)... كم مرة؟
+
+60
+00:06:23,230 --> 00:06:29,180
+يعني هذا كأن 11 مضروبة في Φ(1) يبقى هذا
+
+61
+00:06:29,180 --> 00:06:39,440
+معناته أن 11 × Φ(1) يساوي 13 تمام؟ إذا أنا هنا
+
+62
+00:06:39,440 --> 00:06:47,120
+Φ(11) يساوي 13 قدرت أكتبها بدلالة Φ(1)، لو
+
+63
+00:06:47,120 --> 00:06:53,120
+عرفت قد إيش Φ(1) بيتم المطلوب، لو عرفت قد إيش
+
+64
+00:06:53,120 --> 00:06:58,480
+القيمة العددية لـ Φ(1) بيتم المطلوب، بمعنى آخر لو
+
+65
+00:06:58,480 --> 00:07:03,760
+قدرت تخلص من الـ 11 هذه بيكون اه حصلنا على Φ(1)
+
+66
+00:07:03,760 --> 00:07:07,140
+هييجي واحد مثلا يقول أنت بتقسم على Φ(1)
+
+67
+00:07:07,760 --> 00:07:10,400
+وأقول لك شو هذه؟ 13 على 11، هذا Rational
+
+68
+00:07:10,400 --> 00:07:13,740
+Number احنا بنشتغل في Z<sub>50</sub> ماعناش Rational
+
+69
+00:07:13,740 --> 00:07:17,600
+مرة أنا ما عنديش إلا Z<sub>50</sub> يبقى هذا كلام فارغ
+
+70
+00:07:17,600 --> 00:07:24,140
+لكن بدي أخلق هنا رقم، الرقم يجزم على الـ 11
+
+71
+00:07:24,140 --> 00:07:28,100
+وعملت لكم مرة في الـ subgroups إذا كنتم بضروري، يبقى
+
+72
+00:07:28,100 --> 00:07:35,120
+بدي أفكر بنفس المفهوم، بمعنى آخر أنا بدي أدور على
+
+73
+00:07:35,120 --> 00:07:42,830
+رقم أضربه في 11 يطيني الـ 1 صحيح، يبقى هنا
+
+74
+00:07:42,830 --> 00:07:48,270
+أفترض أن
+
+75
+00:07:48,270 --> 00:07:58,630
+هناك n في حيث أن 11n  ≡ 1 (mod 50)
+
+76
+00:08:01,880 --> 00:08:05,720
+افترض أن عندي n بحيث 11n ≡ 1 (mod 50) افترض أن
+
+77
+00:08:05,720 --> 00:08:09,860
+عندي n بحيث 11n ≡ 1 (mod 
+
+78
+00:08:09,860 --> 00:08:15,900
+50) افترض أن عندي n بحيث 11n ≡ 1 (mod 50) افترض
+
+79
+00:08:15,900 --> 00:08:19,280
+أن عندي n بحيث 11n ≡ 1 (mod 50) افترض أن عندي n
+
+80
+00:08:19,280 --> 00:08:29,140
+بحيث 11n ≡ 1 (mod 50) افترض أن عندي n بحيث
+
+81
+00:08:29,790 --> 00:08:34,850
+إذا قدرت أتخلص من الـ 11 اللي عنها دي بكون حصلت على
+
+82
+00:08:34,850 --> 00:08:41,150
+n وبالتالي بكون جبت الرقم اللي لو ضربته في 11 بيطلع
+
+83
+00:08:41,150 --> 00:08:46,110
+1 صحيح، بضل عندي Φ(1) وبالتالي جبت
+
+84
+00:08:47,570 --> 00:08:54,090
+بالتالي سهل إيجاد Φ(x) لأن Φ(x) هي x × 
+
+85
+00:08:54,090 --> 00:08:59,710
+Φ(1) يعني كل مشكلة زي ما كان في الجزء النظري
+
+86
+00:08:59,710 --> 00:09:04,450
+بنا نروح نجيب α وندور عليها لف لف لما نطلع
+
+87
+00:09:04,450 --> 00:09:10,060
+نجيب قد إيش قيمتها وهذا المقصود عندنا هنا، طيب أنا
+
+88
+00:09:10,060 --> 00:09:15,480
+بدي أجيب رقم بدل هذا الرقم يكون يجزم على الـ 11
+
+89
+00:09:15,480 --> 00:09:23,220
+بحيث نجيب قيمة n، الآن أنا إيش عندي؟ عندي 11n
+
+90
+00:09:23,220 --> 00:09:31,640
+≡ 1 (mod 50) بده يساوي 1 ≡ 1 (mod 50)، هل بنقدر نجيب
+
+91
+00:09:31,640 --> 00:09:37,740
+رقم يكافئ الـ 1؟ اه بنقدر نحط خمسينات عليه زي ما بدك
+
+92
+00:09:38,090 --> 00:09:42,790
+زائد 50 زائد 100 زائد 150 زائد 200 صح؟
+
+93
+00:09:42,790 --> 00:09:46,310
+ولا لا؟ بس كله بيقسمش على الـ 11 اللي كان فيها
+
+94
+00:09:46,310 --> 00:09:51,890
+عندي رقم لو حطيته سهل جدا، بدل ما أضيف 50 بدي
+
+95
+00:09:51,890 --> 00:09:57,900
+أضيف سالب 50، بنفع ولا ما ينفعش؟ بنفع، يا بضيف
+
+96
+00:09:57,900 --> 00:10:02,180
+50 بالـ mod يا بضيف 50 بالسالب يبقى هذا لو ضفت
+
+97
+00:10:02,180 --> 00:10:08,080
+عليه 100 بيظل قد إيش؟ سالب 99، إذا سالب 99
+
+98
+00:10:08,080 --> 00:10:11,120
+بتكسب على 11 وبالتالي أتخلص من الـ 11
+
+99
+00:10:11,120 --> 00:10:17,560
+وحصلت على 100، حصلت على n يبقى الرقم المكافئ هذا
+
+100
+00:10:17,560 --> 00:10:22,140
+سالب 99 ≡ 1 (mod 50)
+
+101
+00:10:24,730 --> 00:10:31,310
+تمام، طيب الآن هذا بيقسم على الـ 11، لو قسمت كله على
+
+102
+00:10:31,310 --> 00:10:39,890
+الـ 11 بيصير n ≡ -9 (mod 50)
+
+103
+00:10:39,890 --> 00:10:46,530
+طب أنا ما عنديش سالب 9 ≡ 1 (mod 50)
+
+104
+00:10:46,530 --> 00:10:52,020
+أنا عندي أرقام موجبة، أضيف عليها 50 يبقى هذه العدد
+
+105
+00:10:52,020 --> 00:10:58,420
+المكافئ لها هو مين؟ هو 41 ≡ 1 (mod 50)
+
+106
+00:10:58,420 --> 00:11:04,500
+يبقى الآن هذا يا شباب لو كانت 41
+
+107
+00:11:04,500 --> 00:11:09,180
+وضربناها في الـ 11 اللي عندنا بضيع وبحصل على مين؟
+
+108
+00:11:09,180 --> 00:11:14,660
+على Φ(1) وبكون خلصنا القصة هذه تمام، يبقى
+
+109
+00:11:14,660 --> 00:11:22,090
+الآن بجي بقوله 11 × Φ(1) بده يساوي 13
+
+110
+00:11:22,090 --> 00:11:29,030
+implies إنه 41 × 11 × Φ(1)
+
+111
+00:11:29,030 --> 00:11:34,750
+طبعا كله ≡ 1 (mod 50) هذا بده يساوي اللي هو 41 × 13 ≡ 1 (mod 50) 
+
+112
+00:11:34,750 --> 00:11:41,850
+طب لو ضربت 41 × 11 إيش بتعطيك؟ هي 41 × 
+
+113
+00:11:41,850 --> 00:11:46,120
+11 بـ 451، 451 شيل منها خمسينات بضل قد إيش؟
+
+114
+00:11:46,120 --> 00:11:51,480
+في Φ(1)، يبقى Φ(1)، يبقى صار في
+
+115
+00:11:51,480 --> 00:11:56,120
+الطرف الشمال اللي عندنا Φ(1) اللي أنا بدور
+
+116
+00:11:56,120 --> 00:12:00,160
+عليه الآن، بنفس الطريقة بنضرب اللي هو الـ 1
+
+117
+00:12:00,160 --> 00:12:05,200
+و 41 × 13 وشوف إيش بتعطينا، يبقى لو جيت
+
+118
+00:12:05,200 --> 00:12:09,720
+1 × 41 × 13 3 × 4 بـ 12
+
+119
+00:12:09,720 --> 00:12:15,560
+وهنا 1 × 41 هنا 3، 3 × 4 بـ 12
+
+120
+00:12:15,560 --> 00:12:21,420
+وهنا 1 × 41 هنا 3، 3 × 4 بـ 12
+
+121
+00:12:21,420 --> 00:12:26,700
+وهنا 1، 41، هنا 3، 3 × 4 بـ 12
+
+122
+00:12:26,700 --> 00:12:31,940
+531 شيل منها عشر
+
+123
+00:12:31,940 --> 00:12:38,670
+خمسينات بضل قد إيش؟ بضل 31، Φ(1) اللي
+
+124
+00:12:38,670 --> 00:12:43,430
+أنا بدور عليه هو الرقم 31، طيب قال لي 
+
+125
+00:12:43,430 --> 00:12:49,930
+هات لي formula لـ Φ(x) بقوله هنا Φ(x) = x × 31
+
+126
+00:12:49,930 --> 00:12:56,130
+هذا موجود وإن في زد خمسين يعني رقم يبقى هذا الكلام
+
+127
+00:12:56,130 --> 00:13:03,900
+بده يساوي اكس في فاي اف وإن يبقى هذا الكلام يساوي X
+
+128
+00:13:03,900 --> 00:13:09,900
+في جداش في تلاتة و تلاتين يبقى أصبحت Phi of X
+
+129
+00:13:09,900 --> 00:13:15,900
+يساوي تلاتة و تلاتين X بالشكل اللي عندنا هذا يبقى
+
+130
+00:13:15,900 --> 00:13:21,400
+هذا صيغة تبعت من؟ تبعت Phi اللي عندنا وليست كما
+
+131
+00:13:21,400 --> 00:13:25,340
+زعمت X زائد تلاتة ولا X زائد اتنين عمرها ما
+
+132
+00:13:25,340 --> 00:13:31,140
+هتجيبها ولا هتجيبها يبقى هذا سؤال 19 فكرته كويسة
+
+133
+00:13:31,140 --> 00:13:36,880
+ومتعلقة بالجزء النظري اللي شرحناه  لكنّا نحسب في
+
+134
+00:13:36,880 --> 00:13:45,270
+alpha of one طيب هذا كان سؤال عشرين بعديها سؤال
+
+135
+00:13:45,270 --> 00:13:50,570
+أربع وعشرين approve or disapprove أن ال U عشرين
+
+136
+00:13:50,570 --> 00:13:56,990
+and ال U أربع وعشرين are isomorphic U عشرين و U
+
+137
+00:13:56,990 --> 00:14:04,850
+أربع وعشرين اه مش سامع تلاتة و تلاتين اكس اه مش
+
+138
+00:14:04,850 --> 00:14:11,490
+كاتب إن اكس اه تلاتة و تلاتين اكس كلام مظبوط يبقى هذا
+
+139
+00:14:11,490 --> 00:14:16,510
+الصيغة تبعت ثمين تبعت الدالة السؤال اللي بعده بيقول
+
+140
+00:14:16,510 --> 00:14:21,170
+لي اللي هو السؤال قداش ستة وعشرين ولا كان قلنا ليه
+
+141
+00:14:21,170 --> 00:14:26,410
+سؤال أربعة وعشرين سؤال أربعة وعشرين سؤال أربعة
+
+142
+00:14:26,410 --> 00:14:33,930
+وعشرين بيقول ليه عشرين وليه أربعة وعشرين شوف ليه
+
+143
+00:14:33,930 --> 00:14:39,750
+هدول isomorphic ولا not isomorphic السؤال هو الـ U
+
+144
+00:14:39,750 --> 00:14:44,430
+عشرين هذه عبارة عن مين؟ عبارة عن واحد، اتنين،
+
+145
+00:14:44,430 --> 00:14:51,830
+تلاتة، أربعة، خمسة، ستة، سبعة، تمانية، تسعة، عشرة،
+
+146
+00:14:51,830 --> 00:14:57,750
+أحداش، تلاتاش، أربعتاش، خمستاش، ستاش، سبعتاش،
+
+147
+00:14:57,750 --> 00:15:04,070
+تسعتاش، تمام؟ وهذه اللي هي عبارة عن مين؟ اللي هي
+
+148
+00:15:04,070 --> 00:15:11,640
+عبارة عن الواحد اتنين تلاتة أربعة خمسة ستة سبعة
+
+149
+00:15:11,640 --> 00:15:23,020
+تمانية تسعة عشرة أحداش تلاتاش أربعتاش خمستاش ستاش
+
+150
+00:15:23,020 --> 00:15:31,900
+سبعتاش وهنا تمانتاش تسعتاش عشرين واحد وعشرين اتنين
+
+151
+00:15:31,900 --> 00:15:38,370
+وعشرين تلاتة وعشرين تلاتة و تلاتة و اتنين تمانية
+
+152
+00:15:38,370 --> 00:15:44,210
+تلاتة و تلاتة و اتنين تمان عناصر و تمان عناصر هل
+
+153
+00:15:44,210 --> 00:15:49,190
+اتنين هدول are isomorphic ولا لأ تعالى نشوف الآن
+
+154
+00:15:49,190 --> 00:15:57,530
+لو جاتلي خمسة تربيع بواحد سبعة تربيع أحداش تربيع
+
+155
+00:15:57,530 --> 00:16:03,310
+تلتاش تربيع كل أي element من هدول تربيع بيعطينا
+
+156
+00:16:03,310 --> 00:16:09,090
+main ال identity element يبقى هذه cyclic لأ not
+
+157
+00:16:09,090 --> 00:16:17,950
+cyclic هذا not cyclic because any
+
+158
+00:16:17,950 --> 00:16:25,170
+non identity element
+
+159
+00:16:27,880 --> 00:16:35,360
+has order اتنين كله حطول الأس اتنين بصيلة ال
+
+160
+00:16:35,360 --> 00:16:41,120
+identity نجي لهذه تلاتة و زيره بواحد تلاتة و أس
+
+161
+00:16:41,120 --> 00:16:48,400
+واحد بتلاتة تلاتة ربيع بتسعة تلاتة كيب سبعة و
+
+162
+00:16:48,400 --> 00:16:55,320
+عشرين تمام؟ يعني السبعة تلاتة أس أربع بواحد و
+
+163
+00:16:55,320 --> 00:17:01,290
+تمانين واحد و تمانين الهمان الواحد و هكذا يبقى
+
+164
+00:17:01,290 --> 00:17:06,170
+التلاتة مرتين تلاتة و Zero بواحد تلاتة اص واحد
+
+165
+00:17:06,170 --> 00:17:11,190
+بواحد تلاتة تربيه بتسعة تلاتة تكيب بسبعة و عشرين
+
+166
+00:17:11,190 --> 00:17:15,530
+تلاتة اص اربع بواحد و تمانين يبقى ال order لتلاتة
+
+167
+00:17:15,530 --> 00:17:22,070
+كدهاش أربعة مظبوط لكن هنا ال order لأي element
+
+168
+00:17:22,070 --> 00:17:28,040
+كدهاش اتنين يبقى اتنين are isomorphic طبعاً لأ يبقى
+
+169
+00:17:28,040 --> 00:17:34,380
+هدول هذه التلاتة
+
+170
+00:17:34,380 --> 00:17:43,820
+is an element of order أربعة هذه أي element of
+
+171
+00:17:43,820 --> 00:17:47,680
+order له ساوى اتنين يبقى اتنين are isomorphic لأ
+
+172
+00:17:47,680 --> 00:17:52,700
+يبقى هذا بدى يعطينا إن ال U عشرين is not
+
+173
+00:17:52,700 --> 00:17:58,600
+isomorphic لـ U 24 يمكن نلاقيها الـ cyclic element
+
+174
+00:17:58,600 --> 00:18:04,380
+تانية الله أعلم أنا مش عارف قد يكون طيب هذا السؤال
+
+175
+00:18:04,380 --> 00:18:12,320
+اللي هو 24 بعد هيك عندنا سؤال 28 بيقول prove that
+
+176
+00:18:12,320 --> 00:18:21,700
+the group of equaterion سؤال 28 بيقول كيو اتثم
+
+177
+00:18:21,700 --> 00:18:29,680
+اثبت هذا الجروب أنه ليس ايزو مورفك ل D4 يبقى هذا
+
+178
+00:18:29,680 --> 00:18:37,400
+الجروب ليس ايزو مورفك .. ليس ايزو مورفك لمن؟ لدى
+
+179
+00:18:37,400 --> 00:18:43,640
+دا هدر الجروب اللي هو D4 لماذا؟ الأعلى جروب
+
+180
+00:18:43,640 --> 00:18:47,780
+افيكواتريون ما شفتهاش قبل هيك يبقى أول مرة
+
+181
+00:18:47,780 --> 00:18:55,540
+بينشوفها إذاً لـ Group هدهها لـ Q8 اللي هي عناصرها
+
+182
+00:18:55,540 --> 00:19:04,640
+زائد أو ناقص I زائد أو ناقص J زائد أو ناقص K زائد
+
+183
+00:19:04,640 --> 00:19:12,650
+أو ناقص L ايش ال I و ال J و ال K و ال L هذا سؤال و
+
+184
+00:19:12,650 --> 00:19:18,550
+إيش علاقتهم أبعاد أول شيء الآن ال I هذه هي مصفوفة
+
+185
+00:19:18,550 --> 00:19:23,810
+الوحدة من النظام اتنين في اتنين ناقص I هي مصفوفة
+
+186
+00:19:23,810 --> 00:19:27,650
+الوحدة نظامها اتنين في اتنين بس مضروبة في مين سالب
+
+187
+00:19:27,650 --> 00:19:34,540
+واحد الآن ال J من خلاصة إن ال j في ال k بده يعطينا
+
+188
+00:19:34,540 --> 00:19:44,200
+ال L و يساوي ناقص k في j يعني لو جلبتهم بيعطيني نفس
+
+189
+00:19:44,200 --> 00:19:50,380
+النتيجة بس ب ا ب سالب واحد بنفس الطريقة لو جت
+
+190
+00:19:50,380 --> 00:19:57,300
+قلت لك ال k في ال L بده يساوي j و اللي هو بده يساوي
+
+191
+00:19:57,300 --> 00:20:08,100
+ناقص L في k و كذلك لو جينا ل L في J يبقى L في J بده
+
+192
+00:20:08,100 --> 00:20:16,960
+يساوي K و يساوي ناقص J في L مش عاجزكوا بس و عندك J
+
+193
+00:20:16,960 --> 00:20:22,860
+تربيع بده يساوي K تربيع بده يساوي L تربيع بده
+
+194
+00:20:22,860 --> 00:20:24,520
+يساوي ناقص I
+
+195
+00:20:27,300 --> 00:20:31,120
+يبقى هذه الخواص الأساسية لهذه ال group اللي خاطر
+
+196
+00:20:31,120 --> 00:20:36,160
+اكتب لك مين ال I والJ والK كل واحدة مصفوفة نظامها
+
+197
+00:20:36,160 --> 00:20:47,400
+2 في 2 بحيث ال J هي المصفوفة اللي هي I 0 0 سالب I
+
+198
+00:20:48,010 --> 00:20:56,250
+الـ K هي المصفوفة اللي هي Zero واحد سالب واحد Zero
+
+199
+00:20:56,250 --> 00:21:03,470
+ال L هي المصفوفة Zero I I Zero بالشكل اللي عندي
+
+200
+00:21:04,720 --> 00:21:08,860
+الكتاب كتبها في عندك بالدلالة في الرموز A وB
+
+201
+00:21:08,860 --> 00:21:14,040
+ومخليها طلاس مش جايلك من ال A ومن ال B احنا
+
+202
+00:21:14,040 --> 00:21:19,300
+بنكتبها لك بصيغة أوضح هي ال Q وهي الخواص بتاعتها
+
+203
+00:21:19,300 --> 00:21:26,400
+الآن بيقول لي اثبت إن ال Q تمانية ل not isomorphic
+
+204
+00:21:26,400 --> 00:21:32,960
+لمين ل D4 ال Q تمانية كم element فيها هنا شباب كم
+
+205
+00:21:32,960 --> 00:21:38,240
+element تمانية زايد أو ناقص و D for فيها كمان قداش
+
+206
+00:21:38,240 --> 00:21:42,780
+تمانية ايه بقى دي هنا تمان عناصر و هنا تمان عناصر
+
+207
+00:21:42,780 --> 00:21:51,420
+امسكلي وين راحت ال J و ال K و ال L ال J هادي ال I
+
+208
+00:21:51,420 --> 00:21:54,760
+هادي يا شباب اللي هي الجدر التربيعي لسالب واحد ال
+
+209
+00:21:54,760 --> 00:22:00,780
+I يعني ال complex هي الجدر التربيعي لسالب واحد الآن
+
+210
+00:22:00,780 --> 00:22:05,500
+لو جيت هنا خاصية بيقول جيت تربيع يساوي كتربيع يساوي
+
+211
+00:22:05,500 --> 00:22:11,540
+ال تربيع يساوي قداش سالب I يبقى هذه ال order لها
+
+212
+00:22:11,540 --> 00:22:20,160
+قداش أربعة جيوس أربعة يعني سالب I في سالب I ب I
+
+213
+00:22:20,160 --> 00:22:23,820
+اللي هو ال identity يبقى هنا ال order لهذه أربعة
+
+214
+00:22:23,820 --> 00:22:27,300
+ال order لهذه أربعة ال order لهذه قداش أربعة
+
+215
+00:22:27,300 --> 00:22:32,650
+بالمثال ال order لسالب جي و ال order لسالب كي و ال order
+
+216
+00:22:32,650 --> 00:22:37,950
+لسالب ال كمان أربعة يبقى أنا عندي كم element ال
+
+217
+00:22:37,950 --> 00:22:44,010
+order اللي يساوي أربعة ستة elements ال order اللي
+
+218
+00:22:44,010 --> 00:22:50,110
+يساوي أربعة تعالوا نروح على D4 هل D4 فيها ستة
+
+219
+00:22:50,110 --> 00:22:55,850
+elements ال order اللي يساوي أربعة ال H وال V وال D
+
+220
+00:22:55,850 --> 00:22:59,660
+وال D prime ال order اللي يساوي اتنين و ال R مية و
+
+221
+00:22:59,660 --> 00:23:04,600
+تمانين ال order يسوي اتنين هاي سعر خمسة و ال
+
+222
+00:23:04,600 --> 00:23:08,020
+identity element ال order ايه لو واحد حطه على شجة
+
+223
+00:23:08,020 --> 00:23:12,980
+بيضلش عندي إلا مين إلا اتنين اللي هو ال R تسعين و
+
+224
+00:23:12,980 --> 00:23:15,560
+ال R متين و السبعين يبقى اتنين هل هو ال R
+
+225
+00:23:15,560 --> 00:23:23,850
+isomorphic لأ يبقى هنا الـ D أو الـ Q8 is not
+
+226
+00:23:23,850 --> 00:23:34,030
+isomorphic لـ D4 because اللي هو Q8 has six
+
+227
+00:23:34,030 --> 00:23:42,810
+elements أو ستة elements ستة elements اللي هم زد
+
+228
+00:23:42,810 --> 00:23:52,270
+أو نقص J وزادة أو ناقص k وزادة أو ناقص l of order
+
+229
+00:23:52,270 --> 00:24:09,050
+أربع but of order أربع but ال D4 has two elements
+
+230
+00:24:10,170 --> 00:24:21,750
+اللي هما main are 90 and are 270 of order 4 مدام
+
+231
+00:24:21,750 --> 00:24:26,510
+العدد هنا يختلف عن العدد هنا إذا الإثنين لا يمكن
+
+232
+00:24:26,510 --> 00:24:29,670
+يكونوا معاهم isomorphic
+
+233
+00:24:44,510 --> 00:24:51,370
+هذا كان سؤال سؤال تمانية وعشرين لأن عندنا سؤال
+
+234
+00:24:51,370 --> 00:24:56,510
+تلاتين سؤال تلاتين يعطينا ال R N هي ال components
+
+235
+00:24:56,510 --> 00:25:03,870
+من واحد لغاية M وقال لي بيان ال mapping Phi Phi
+
+236
+00:25:03,870 --> 00:25:12,690
+من من ال R N إلى ال R N عبارة عن اتومورفزمتحت
+
+237
+00:25:12,690 --> 00:25:18,050
+عملية الجامعة و هذا ال .. ال .. ال atomorphism
+
+238
+00:25:18,050 --> 00:25:25,610
+بنسميه ال inversion atomorphism يبقى سؤال تلاتين
+
+239
+00:25:25,610 --> 00:25:29,190
+سؤال
+
+240
+00:25:29,190 --> 00:25:43,320
+تلاتين بيقول ليش؟ بيقول لي في من ال rn لل rndefine
+
+241
+00:25:43,320 --> 00:25:53,920
+by فاي لما تأثر على ال element a1 و a2 و لغاية an
+
+242
+00:25:53,920 --> 00:26:02,960
+بيعطيني سالب a1 سالب a2 سالب an بالشكل اللي عندنا
+
+243
+00:26:02,960 --> 00:26:08,120
+هذا بيقول شو ذات ال mapping هذه عبارة عن
+
+244
+00:26:08,120 --> 00:26:13,350
+atomorphism على ال group under the component wise
+
+245
+00:26:13,350 --> 00:26:19,110
+addition تحت الجامعه العادى بالنسبه لمن؟ لل space
+
+246
+00:26:19,110 --> 00:26:23,130
+RN يبقى
+
+247
+00:26:23,130 --> 00:26:28,870
+أنا عندي function معرفه من RN الى RN بهذا الشكل
+
+248
+00:26:28,870 --> 00:26:33,470
+اللي بدي اطلب انه Phi one to one وانتوا وعباره عن
+
+249
+00:26:33,470 --> 00:26:38,680
+atomorphism يبقى الخطوة الأولى بدأت بيقوله أنه five
+
+250
+00:26:38,680 --> 00:26:46,160
+is one to one بدأ أروح آخذ assume اللي هو five of 
+
+251
+00:26:46,160 --> 00:26:52,960
+a واحد و a اتنين و لغاية a n بدر يساوي five of b
+
+252
+00:26:52,960 --> 00:27:03,930
+واحد و b اتنين و لغاية b n صورة الأول ناقص A1 ناقص
+
+253
+00:27:03,930 --> 00:27:15,610
+A2 ناقص AN ناقص B1 ناقص B2 ناقص BN ناقص من هذا
+
+254
+00:27:15,610 --> 00:27:21,130
+الكلام مش بستنتج، بستنتج أن ناقص A1 بدري يسوي ناقص
+
+255
+00:27:21,130 --> 00:27:28,650
+B1 يبقى ناقص A1 بدري يسوي ناقص B1 و ناقص A2 بدري
+
+256
+00:27:28,650 --> 00:27:35,250
+يسوي ناقص B2 و تظلك ماشي لغاية ناقص AN بدري يسوي
+
+257
+00:27:35,250 --> 00:27:43,040
+ناقص BN لو ضربنا هذا كله في إشارة ناقص بصير ال a1
+
+258
+00:27:43,040 --> 00:27:50,180
+بدر يساوي ال b1 وال a2 بدر يساوي ال b2 وال an بدر
+
+259
+00:27:50,180 --> 00:27:58,770
+يساوي ال bn بناء عليه لو أخدت ال order pair a1 و a2
+
+260
+00:27:58,770 --> 00:28:04,750
+و لغاية an هلاقيه يساويه هشيل ال a1 و أحط قيمتها
+
+261
+00:28:04,750 --> 00:28:11,330
+من ال b1 و أشيل ال a2 و أحط قيمتها اللي هي b2 و
+
+262
+00:28:11,330 --> 00:28:17,230
+أشيل ال an و أحط قيمتها bn إذا أخدت صورتين
+
+263
+00:28:17,230 --> 00:28:23,640
+متساويتين أثبت أن الاصل متساوي لذلك فاي is one to
+
+264
+00:28:23,640 --> 00:28:26,040
+one بدروح أخد element
+
+265
+00:28:34,730 --> 00:28:46,990
+let x1 و x2 و xn موجود في الارن بدي اثبت هذا أنه
+
+266
+00:28:46,990 --> 00:28:58,910
+ي لو اصل هذا الاصل موجود في ارن بقوله then ال
+
+267
+00:28:58,910 --> 00:29:09,270
+x1و X2 و XN بده يساوي شو رايك بنفع أقول هيك اللي
+
+268
+00:29:09,270 --> 00:29:18,570
+هو سالب X واحد و سالب X اتنين و لغاية سالب XN؟
+
+269
+00:29:18,570 --> 00:29:26,890
+بنفع؟ اه طيب مدام بنفع يبقى هيه كتبته بالشكل اللي
+
+270
+00:29:26,890 --> 00:29:33,860
+عندنا يبقى هذا الكلام بده يساوي اللي هو سالب برا
+
+271
+00:29:33,860 --> 00:29:39,860
+هذه سالب X واحد لو سميتها Y واحد والتانية Y اتنين
+
+272
+00:29:39,860 --> 00:29:47,020
+والاخيرة YN يعني هذه كتبت Y واحد وهذه Y اتنين وهذه
+
+273
+00:29:47,020 --> 00:29:53,040
+YN بالشكل اللي عندنا هنا يبقى هذا الكلام بده يساوي
+
+274
+00:29:53,040 --> 00:29:55,800
+اللي هو مين سالب Y واحد
+
+275
+00:30:01,060 --> 00:30:09,680
+أليس هذا هو صورة five of y واحد و y اتنين و لغاية
+
+276
+00:30:09,680 --> 00:30:17,660
+yn إذا ال element اللي أخدته في RN لجيت له أصل في
+
+277
+00:30:17,660 --> 00:30:24,660
+ال main في ال RN كذلك و هو Y1 و Y2 و هو ينحل من
+
+278
+00:30:24,660 --> 00:30:31,440
+بينهم Y1 هي سلب X1 و Y2 هي سلب X2 و YN هو سلب XN و
+
+279
+00:30:31,440 --> 00:30:37,300
+هكذا لذلك صارت أن ال main Phi is on it الآن بدي أجي
+
+280
+00:30:37,300 --> 00:30:44,940
+للنقطة الأخيرة five is an isomorphism بدي أروح أخد
+
+281
+00:30:44,940 --> 00:30:51,840
+five of مجموع two elements يبقى a واحد و a اتنين و
+
+282
+00:30:51,840 --> 00:31:02,600
+a n زائد b واحد و b اتنين و لغاية b n كتبتم ليه
+
+283
+00:31:02,600 --> 00:31:08,260
+شكل أن ال operation اللي على ال group هي عملية جمعة
+
+284
+00:31:08,260 --> 00:31:22,380
+طيب
+
+285
+00:31:22,380 --> 00:31:27,360
+الآن طب خل الجامعة اللي قال لي عليكم component wise
+
+286
+00:31:27,360 --> 00:31:36,430
+حاجة مع كل مركبة مع نظيرتها يبقى a1 زائد b1 a2 زائد
+
+287
+00:31:36,430 --> 00:31:45,910
+B2 وظل مستمر لغاية AN زائد BN بهذا الشكل الآن أصبح
+
+288
+00:31:45,910 --> 00:31:51,550
+هذا كله element واحد يبقى الصورة تبعته سالب هذا ال
+
+289
+00:31:51,550 --> 00:31:58,670
+element يبقى هذا الكلام بالدرس ساوي سالب A1 زائد
+
+290
+00:31:58,670 --> 00:32:02,850
+B1 سالب A2 زائد B2
+
+291
+00:32:11,310 --> 00:32:17,390
+بقدر أدخل السلب على كل term من هذه الترمات يبقى
+
+292
+00:32:17,390 --> 00:32:25,530
+هذا الكلام بده يساوي سالب a1 سالب b1 و سالب a2
+
+293
+00:32:38,400 --> 00:32:44,420
+هذا قوس واحد مكوّن من N من المُركّبات بدي أحاول
+
+294
+00:32:44,420 --> 00:32:50,040
+أحطه على صيغة مجموعة قوسين إذا لو روحت كتبته على
+
+295
+00:32:50,040 --> 00:32:57,700
+صيغة مجموعة قوسين بده يساوي a واحد أو سالب a واحد
+
+296
+00:32:58,410 --> 00:33:07,810
+سالب A1 سالب A2 ونظل ماشيين لغاية سالب AN كله زائد
+
+297
+00:33:07,810 --> 00:33:16,170
+اللي هو سالب B1 وسالب B2 ونظل ماشيين لغاية سالب BN
+
+298
+00:33:16,170 --> 00:33:24,390
+هذا الكلام يساوي الأول هذا هو عبارة عن Phi of A1
+
+299
+00:33:24,390 --> 00:33:36,900
+و A2 و لغاية AN زائد الثاني هو Phi of B1 و B2 و
+
+300
+00:33:36,900 --> 00:33:42,760
+لغاية BN بالشكل اللي عندنا يبقى بناءً أن عليه Phi
+
+301
+00:33:42,760 --> 00:33:49,660
+أصبح ماله Atomorphism لإن Phi من نفس ال group إلى
+
+302
+00:33:49,660 --> 00:33:56,890
+نفس ال group يبقى باجي بقوله هنا thus وهكذا فاي is
+
+303
+00:33:56,890 --> 00:34:03,310
+an atomorphism وانت هنا من مين؟ من المثلة بيسأل
+
+304
+00:34:03,310 --> 00:34:13,110
+بيقولي ما هو المعنى الهندسي لهذا ال atomorphism لو
+
+305
+00:34:13,110 --> 00:34:17,680
+اتخيلت أنا في ال space are in اللي جال عنه هنا وفي
+
+306
+00:34:17,680 --> 00:34:24,140
+عندي نقطة هنا إحداثيها أولاً إحداثيتها a1 و a2 و a3
+
+307
+00:34:24,140 --> 00:34:30,020
+و a4 و a5 لغاية an في المقابل صورتها نقطة ناقص a1
+
+308
+00:34:30,020 --> 00:34:33,260
+و ناقص a2 أو لا يعني إيش بيعمل ال homomorphism هذا
+
+309
+00:34:33,260 --> 00:34:40,740
+أو ليس homomorphism بيقلب النقطة عبر مين عبر نقطة
+
+310
+00:34:40,740 --> 00:34:52,360
+الاصل يبقى هنا هبروح بقوله لا meaning of this
+
+311
+00:34:52,360 --> 00:34:56,360
+atomorphism
+
+312
+00:34:56,360 --> 00:35:12,200
+reflect معنى هذا is the reflection of the points
+
+313
+00:35:12,200 --> 00:35:14,400
+أثرا
+
+314
+00:35:17,910 --> 00:35:26,350
+the origin يبقى كأننا نقلب النقاط عبر نقطة الأصل
+
+315
+00:35:26,350 --> 00:35:29,670
+اللي كانت على اليمين بنخليها على الشمال و اللي
+
+316
+00:35:29,670 --> 00:35:34,040
+كانت على الشمال بنوديها على اليمين وهكذا يعني
+
+317
+00:35:34,040 --> 00:35:40,780
+بنقلب وضع النقاط عبر نقطة الأصل، هذا كان هو سؤال
+
+318
+00:35:40,780 --> 00:35:47,000
+اللي هو تلاتين، عندك هنا سؤال خمسة و .. والله سؤال
+
+319
+00:35:47,000 --> 00:35:48,400
+تلاتة و تلاتين
+
+320
+00:36:05,810 --> 00:36:10,170
+يبقى السؤال تلاتة وتلاتين
+
+321
+00:36:25,230 --> 00:36:31,360
+سؤال مرة تانية بقول في عندي two inner atomorphism
+
+322
+00:36:31,360 --> 00:36:37,800
+الفاي جي والفاي زيد جي بقول اثبت أن الاتنين هدول
+
+323
+00:36:37,800 --> 00:36:42,880
+are equal علماً بأن الـ z هذه موجودة في ال center
+
+324
+00:36:42,880 --> 00:36:46,640
+تبع الجي الـ z موجودة في ال center تبع الجي يعني
+
+325
+00:36:46,640 --> 00:36:54,580
+commutes مع كل عناصر جي بلا استثناء الآن الـ Inner
+
+326
+00:36:54,580 --> 00:37:01,620
+Atomorphism Phi G of X بنذكر بتعريفه كان G X G
+
+327
+00:37:01,620 --> 00:37:06,140
+Inverse يبقى هذا ال Inner Atomorphism طيب تمام
+
+328
+00:37:06,140 --> 00:37:11,000
+الآن أنا بدي اثبت أن اتنين هذول are equal بمعنى
+
+329
+00:37:11,000 --> 00:37:16,620
+آخر تأثير لاتنين على أي element موجود في G بده
+
+330
+00:37:16,620 --> 00:37:21,430
+يتساوى مظبوط ولا لا يبقى المقصود فيهم يبقى باجي
+
+331
+00:37:21,430 --> 00:37:26,830
+بقوله هنا solution if
+
+332
+00:37:26,830 --> 00:37:33,490
+ال X موجود for all
+
+333
+00:37:33,490 --> 00:37:42,230
+لكل ال X اللي موجود في G لو جيت أخدت تأثير ال 5G
+
+334
+00:37:42,230 --> 00:37:48,250
+على X يبقى ال G X G inverse and
+
+335
+00:37:49,700 --> 00:38:00,500
+بتاخد تأثير الـ Phi ZG على X يبقى ZGX ZG inverse
+
+336
+00:38:00,500 --> 00:38:03,740
+تمام؟
+
+337
+00:38:03,740 --> 00:38:10,340
+يبقى هذا الكلام بده يساوي ZGX
+
+338
+00:38:10,340 --> 00:38:15,080
+G inverse Z inverse
+
+339
+00:38:17,430 --> 00:38:27,390
+هذا الكلام بده يساو G X G Inverse Z Inverse و هنا
+
+340
+00:38:27,390 --> 00:38:34,210
+Z ليش؟ لأن الـ Z موجودة في الـ Center يبقى هذا
+
+341
+00:38:34,210 --> 00:38:40,830
+الكلام صحيح لأن الـ Z موجودة في الـ Center تبع الـ
+
+342
+00:38:40,830 --> 00:38:45,290
+Group G يعني الـ Z مرتبط مع أي Element موجود في
+
+343
+00:38:45,290 --> 00:38:50,110
+الـ G وهذا كله Element موجود في الـ G يبقى خلينا
+
+344
+00:38:50,110 --> 00:38:54,110
+الـ Z تجوان على الناحية التانية الـ Element في
+
+345
+00:38:54,110 --> 00:39:01,940
+معكوسه من يعطينا؟ الـ Identity الـ GXG inverse في
+
+346
+00:39:01,940 --> 00:39:07,820
+الـ Identity Element اللي هو الـ GXG inverse الـ
+
+347
+00:39:07,820 --> 00:39:15,600
+GX inverse G مين هو عبارة عبارة عن Phi G of X يبقى
+
+348
+00:39:15,600 --> 00:39:21,260
+بناء عليه أصبح Phi ZG على جميع أناصر G يسوي تأثير
+
+349
+00:39:21,260 --> 00:39:27,160
+Phi G على جميع أناصر G يبقى معنا هذا الكلام إنه في
+
+350
+00:39:27,160 --> 00:39:33,280
+زد جي بده يساوي بين في جي وانت هنا من مين من
+
+351
+00:39:33,280 --> 00:39:40,940
+المسألة هذا كان سؤال تلاتة و تلاتين بعد سؤال خمسة و
+
+352
+00:39:40,940 --> 00:39:47,920
+تلاتين جي و اتش induce the same inner atomorphism
+
+353
+00:39:47,920 --> 00:39:57,280
+of جي يبقى الأسئلة
+
+354
+00:39:57,280 --> 00:40:04,180
+علاقة مباشرة بهذا السؤال خمسة و تلاتين خمسة و
+
+355
+00:40:04,180 --> 00:40:13,500
+تلاتين بيقول أن ال G and ال H اتنين هدول induce
+
+356
+00:40:13,500 --> 00:40:25,000
+the same inner atomorphism the same inner
+
+357
+00:40:25,000 --> 00:40:34,140
+atomorphism of G نقول prove هذا سيعطيك أن الـ H
+
+358
+00:40:34,140 --> 00:40:41,260
+inverse G موجود في الـ Center تبع الـ G بنا نثبت
+
+359
+00:40:41,260 --> 00:40:48,060
+أن هذا موجود في الـ Center تبع من؟ تبع الـ G طيب
+
+360
+00:40:48,060 --> 00:40:54,640
+اتنين هذول بيعملولي نفس ال Inner Atomorphism بمعنى
+
+361
+00:40:54,640 --> 00:40:57,820
+آخر أنه solution
+
+362
+00:41:00,540 --> 00:41:11,860
+إن الـ Phi G تأثيره على X بده يساوي Phi H تأثيره
+
+363
+00:41:11,860 --> 00:41:19,360
+على X هذا المقصود فيه لمن؟ هذا الكلام صحيح لكل X
+
+364
+00:41:19,360 --> 00:41:20,760
+الموجودة في G
+
+365
+00:41:24,660 --> 00:41:29,800
+تعريف ال inner atomorphism
+
+366
+00:41:29,800 --> 00:41:34,320
+بالشكل اللي عندنا يبقى اتنين هدول are equal مدام
+
+367
+00:41:34,320 --> 00:41:40,720
+are equal then الأولى اللي عبارة عن g x g inverse
+
+368
+00:41:40,720 --> 00:41:51,300
+والتاني عبارة عن مين عبارة عن h x h inverse قال لي
+
+369
+00:41:51,300 --> 00:41:56,940
+اثبت لي أن ال H inverse D موجودة في ال center يعني
+
+370
+00:41:56,940 --> 00:42:03,040
+ال H inverse G لما أثربها على أي انصار في G من
+
+371
+00:42:03,040 --> 00:42:07,950
+اليمين أو من الشمال يكونوا اتنين عريقين بنقوله بسيطة
+
+372
+00:42:07,950 --> 00:42:12,550
+جدا قال لي H inverse يبقى هذه ال H inverse مش هفرط
+
+373
+00:42:12,550 --> 00:42:17,170
+فيها لكن ال G inverse بده أفرط فيها مش أنا أفرط
+
+374
+00:42:17,170 --> 00:42:23,710
+فيها لو روحت ضربت اتنين من طرف اليمين في مام في ال
+
+375
+00:42:23,710 --> 00:42:33,530
+G يبقاش بيضل عند هنا G X وبده يساوي H X و هنا H 
+
+376
+00:42:33,530 --> 00:42:42,850
+inverse G يبقى ضرب من جهة اليمين الطرفين فقط في G
+
+377
+00:42:42,850 --> 00:42:47,790
+يبقى جي انفرس جي لو بال identity يبقى بظل عندي G X
+
+378
+00:42:47,790 --> 00:42:54,850
+بده يساوي ال H X H inverse بده أضربها في G يبقى
+
+379
+00:42:54,850 --> 00:43:00,190
+هيدربناها في G كمان ال H هذه مش لازمالي يبقى بيضروح
+
+380
+00:43:00,190 --> 00:43:06,210
+اضرب الطرفين في الـ H inverse إذا لو ضربت الطرفين
+
+381
+00:43:06,210 --> 00:43:13,630
+في الـ H inverse بيصير H inverse G X بده يساوي
+
+382
+00:43:13,630 --> 00:43:20,150
+ضربت الطرفين من جهتي الشمال يبقى بيصير H inverse
+
+383
+00:43:20,150 --> 00:43:27,810
+من جهتي الشمال بيصير هذه الـ X H inverse G يبقى
+
+384
+00:43:27,810 --> 00:43:32,170
+ضربت هنا H انفرس اتجيني H انفرس H اللي هي بال
+
+385
+00:43:32,170 --> 00:43:38,250
+identity بظهر X H انفرس G اطلعلي لهذا ال element
+
+386
+00:43:38,250 --> 00:43:44,190
+واطلعلي لهذا ال element هو نفسه و ال X هذه ايش
+
+387
+00:43:44,190 --> 00:43:51,120
+قلنا عليها أي x موجودة في جي يبقى هذا الكلام صحيح
+
+388
+00:43:51,120 --> 00:43:57,480
+لكل ال x اللي موجودة في جي ايش تفسيرك لهذا ان ال h
+
+389
+00:43:57,480 --> 00:44:02,660
+inverse g موجودة في ال center تبع الجي وهو المطلوب
+
+390
+00:44:02,660 --> 00:44:08,460
+هذا بده يعطيلك ان ال h inverse g موجودة في ال
+
+391
+00:44:08,460 --> 00:44:11,560
+center تبع الجي وهو المطلوب
+
+392
+00:44:36,580 --> 00:44:43,440
+هذا كان سؤال خمسة و ثلاثين الان عنا ثمانية و
+
+393
+00:44:43,440 --> 00:44:50,080
+ثلاثين أو عنا تسعة و ثلاثين بفضل نحل تسعة و ثلاثين
+
+394
+00:44:50,080 --> 00:44:54,440
+ونضل وقت نحل ثمانية و ثلاثين بس بعطيك ال function
+
+395
+00:44:54,440 --> 00:44:59,200
+تبع الثمانية و ثلاثين و انت بتكمل يبقى في ثمانية و
+
+396
+00:44:59,200 --> 00:45:06,270
+ثلاثين ال function عنا في من مين؟ من الست اللي
+
+397
+00:45:06,270 --> 00:45:13,630
+عناصرها اللي هو zero و زائد أو ناقص اثنين و زائد أو 
+
+398
+00:45:13,630 --> 00:45:20,610
+ناقص أربعة و زائد أو ناقص ستة إلى ما شاء الله هادي
+
+399
+00:45:20,610 --> 00:45:27,030
+بين هادي جي و هادي بدنا نسميها جي و الثانية H اللي
+
+400
+00:45:27,030 --> 00:45:33,770
+عناصرها زيرو زائد أو ناقص ثلاثة زائد أو ناقص ستة
+
+401
+00:45:33,770 --> 00:45:38,850
+زائد أو ناقص تسعة إلى ما شاء الله يبقى هذه الـ
+
+402
+00:45:38,850 --> 00:45:44,270
+five بده أعرفها كالتالي five of اثنين n يساوي
+
+403
+00:45:44,270 --> 00:45:50,710
+ثلاثة n يبقى هي ال element هنا موجود هنا حط n
+
+404
+00:45:50,710 --> 00:45:55,190
+بزيرو بيعطيك زيرو حط n بواحد بيعطيك اثنين حط n
+
+405
+00:45:55,190 --> 00:46:00,740
+باثنين بأربعة ثلاثة ستة تمام حط n بزيرو بصير ثلاثة
+
+406
+00:46:00,740 --> 00:46:05,780
+.. زيرو حط n بواحد بصير ثلاثة حط n باثنين بناقص
+
+407
+00:46:05,780 --> 00:46:09,320
+واحد بناقص كله تمام يبقى التعريف سليم مائة في
+
+408
+00:46:09,320 --> 00:46:16,620
+المائة باكتبت ان هذا عبارة عن ايزو مورفزم السؤال
+
+409
+00:46:16,620 --> 00:46:18,240
+تسعة و ثلاثين
+
+410
+00:46:20,220 --> 00:46:26,280
+سؤال تسعة و ثلاثين بيقول ليش بيقول ي support that
+
+411
+00:46:26,280 --> 00:46:35,100
+الفي is an atomorphism ل D4 يبقى في من D4 إلى D4
+
+412
+00:46:35,100 --> 00:46:43,500
+هذا atomorphism و such that الفي of R تسعين و الفي
+
+413
+00:46:43,500 --> 00:46:52,500
+of R تسعين بده يساوي R مئتين وسبعين مئتين وسبعين هو
+
+414
+00:46:52,500 --> 00:46:59,760
+عندك الفاي of V فاي of V بده يساوي ال V قال لي find
+
+415
+00:46:59,760 --> 00:47:08,520
+بدنا نوجد فاي of D و فاي of H فاي of D و فاي of H
+
+416
+00:47:08,520 --> 00:47:11,540
+هذا اللي عايزين نوجده
+
+417
+00:47:21,410 --> 00:47:25,930
+بلزمنا طبعا ال table في صفة واحد و ثلاثين تبع ال
+
+418
+00:47:25,930 --> 00:47:31,430
+day four الكل شوية ايه ابنه ارجعنا الان ميعطيني
+
+419
+00:47:31,430 --> 00:47:37,130
+هذا atomorphism وميعطيني قيمتين وطالب قيمتين
+
+420
+00:47:37,130 --> 00:47:42,390
+بنقوله بسيطة جدا يبقى هذا solution
+
+421
+00:47:49,780 --> 00:47:57,720
+السؤال هو هل بقدر اكتب D؟ بدلالة ال R تسعين و ال V
+
+422
+00:47:57,720 --> 00:47:58,560
+ولا لا
+
+423
+00:48:28,720 --> 00:48:35,000
+طب هو قال لي هذا في ايزو مورفزم يعني ايزو مورفزم
+
+424
+00:48:35,000 --> 00:48:42,680
+إذا هذا الكلام بدل يساوي في of R تسعين في في of V
+
+425
+00:48:43,580 --> 00:48:48,800
+الـ Phi of R90 هي R270
+
+426
+00:48:48,800 --> 00:48:54,920
+والـ Phi of V بدها تساوي الـ V itself برجع على
+
+427
+00:48:54,920 --> 00:49:00,720
+الجدول برضه بده أشوف R270 في V إيش بتعطينا يبقى
+
+428
+00:49:00,720 --> 00:49:10,250
+R270 في V بتعطينا D prime يبقى ناتج دي prime يبقى
+
+429
+00:49:10,250 --> 00:49:15,930
+هاي حسبت له فاي اف دي يساوي قداش دي prime الان قال
+
+430
+00:49:15,930 --> 00:49:22,710
+هات لي فاي اف اتش باجي بقول له فاي اف اتش يساوي فاي
+
+431
+00:49:22,710 --> 00:49:29,530
+اف هل بقدر اكتب ال H بدلالة ال R تسعين و ال V ولا
+
+432
+00:49:29,530 --> 00:49:37,650
+لأ تعالى نشوف R تسعين في إيش بتعطيني من ال H يبقى
+
+433
+00:49:37,650 --> 00:49:45,730
+هاي ال R تسعين ال H هي عبارة عن ال H هي عبارة عن R
+
+434
+00:49:45,730 --> 00:49:54,290
+تسعين في D يبقى R تسعين في D لأ احنا بدنا من؟ بدنا
+
+435
+00:49:54,290 --> 00:50:06,030
+R تسعين و V مظبوط؟ يعني بديها R تسعين في D كيف؟ مش
+
+436
+00:50:06,030 --> 00:50:12,310
+سامع احنا وجدناها بنفع برضه بنفع من فور كويس يبقى
+
+437
+00:50:12,310 --> 00:50:18,030
+أنا كل اللي عند ال H بقدر أشيله و اكتب له R تسعين
+
+438
+00:50:18,030 --> 00:50:26,910
+في D R تسعين في D يبقى هذه R تسعين في D يبقى هدف
+
+439
+00:50:26,910 --> 00:50:34,590
+تعطينا فاي of R تسعين في فاي of D و يساوي فاي of R
+
+440
+00:50:34,590 --> 00:50:40,090
+تسعين اللي هي R مئتين وسبعين و فاي of D حسبناها
+
+441
+00:50:40,090 --> 00:50:46,210
+اللي هي D prime يبقى بدي أشوف ر مئتين وسبعين في دي
+
+442
+00:50:46,210 --> 00:50:53,630
+prime قداش بتعطينا يبقى ر مئتين وسبعين في دي prime
+
+443
+00:50:53,630 --> 00:50:58,030
+اللي هي الأخيرة بتعطينا H
+
+444
+00:51:01,120 --> 00:51:08,160
+يبقى هذه بتعطينا H يبقى صار في of H يساوي من H
+
+445
+00:51:08,160 --> 00:51:15,940
+itself يبقى في of H يساوي من H itself هذه هنا في
+
+446
+00:51:15,940 --> 00:51:21,520
+of D يساوي من D prime
+
+447
+00:51:24,210 --> 00:51:29,170
+طيب المرة القادمة إن شاء الله بدنا نرجع لأسئلة ال
+
+448
+00:51:29,170 --> 00:51:30,930
+permutations
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..961c9bf40284b8a59cfbbd63b06cd1292d6324e1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_postprocess.srt
@@ -0,0 +1,1792 @@
+1
+00:00:21,380 --> 00:00:26,260
+بسم الله الرحمن الرحيم المرة الماضية بدأنا نناقش
+
+2
+00:00:26,260 --> 00:00:30,500
+الأسئلة المتعلقة بشبتر ستة وهو ال isomorphism
+
+3
+00:00:30,500 --> 00:00:36,220
+ووقفنا عند سؤال رقم تسعة عشر سؤال تسعة عشر مختصر
+
+4
+00:00:36,220 --> 00:00:41,400
+بيقول في عند two isomorphism واحد اسمه في والتاني
+
+5
+00:00:41,400 --> 00:00:47,620
+اسمه جامع من اللي هو ال cycle group generated by a
+
+6
+00:00:47,620 --> 00:00:54,090
+إلى أي group أخرىوعندى معلومة ان في او ا تساوي
+
+7
+00:00:54,090 --> 00:00:59,750
+جامعة او ا قاللي اثبت ان في تساوي ا تساوي جامعة
+
+8
+00:01:00,460 --> 00:01:05,340
+بنقوله بسيطة بنفكر فى الموضوع الآن فاى وجامع لما
+
+9
+00:01:05,340 --> 00:01:10,120
+يؤثروا على uniform subgroup generated by a معناته
+
+10
+00:01:10,120 --> 00:01:14,740
+a مرفوع لأس مظبوط لإن ده ال cycle group معناته ال
+
+11
+00:01:14,740 --> 00:01:19,200
+a و ال a و ال a تربيع و ال a تكعيب و هو إلى آخرى
+
+12
+00:01:19,200 --> 00:01:29,180
+يبقى مناء عليه عندنا احنا هنا ايه اللي هومثلا ال a
+
+13
+00:01:29,180 --> 00:01:33,720
+to the power of k موجودة في ال sub group generated
+
+14
+00:01:33,720 --> 00:01:40,520
+by a معناته كل من فاي وجامع ستؤثر على من؟ على هذا
+
+15
+00:01:40,520 --> 00:01:50,160
+العنصر هذا بده يعطينا انه فاي a of k أبصر قديش بده
+
+16
+00:01:50,160 --> 00:01:56,390
+يساوي الله أعلم تمامطب بدي بقول هذا الكلام بده
+
+17
+00:01:56,390 --> 00:02:06,600
+يساوي اللي هو Phi of A كله to the power Kof a كله
+
+18
+00:02:06,600 --> 00:02:11,000
+to the power of k وهذه نظرية السابقة أخدناها
+
+19
+00:02:11,000 --> 00:02:17,560
+وبرهناها لكن في معطيات عندى بتقولي في of a تسوى
+
+20
+00:02:17,560 --> 00:02:23,080
+جامعة of a إذا بقدر أشيل اللي هو في of a و أحط
+
+21
+00:02:23,080 --> 00:02:28,980
+بدلها جامعة of a يبقى هذا الكلام بدي يعطيني جامعة
+
+22
+00:02:28,980 --> 00:02:37,100
+of a كله to the power of kيبقى أصبح اندي في of ا ك
+
+23
+00:02:37,100 --> 00:02:45,340
+بده ساوي جامع of a كله to the power كل الكي هذه
+
+24
+00:02:45,340 --> 00:02:54,910
+ممكن تنزل هنا يبقى جامع كله لمن؟ لل a اص كييبقى
+
+25
+00:02:54,910 --> 00:02:59,930
+معنى هذا الكلام إنه تأثير في على أي element في ال
+
+26
+00:02:59,930 --> 00:03:06,050
+group هذي يسوى تأثير جامعة على أي element موجود في
+
+27
+00:03:06,050 --> 00:03:11,810
+ال subgroup generated by A لكن بقدرش أقول التسوي
+
+28
+00:03:11,810 --> 00:03:17,710
+حاصل نتيجة لهذا التسوي لأن A أنصر محدد هو اللي ولد
+
+29
+00:03:17,710 --> 00:03:21,300
+ال groupلكن عندما أقول a to the power of k أي
+
+30
+00:03:21,300 --> 00:03:26,120
+element أخدت من الجروب عشوائيا من مكان يكون إذا في
+
+31
+00:03:26,120 --> 00:03:30,440
+عند أي element موجود في الجروب ده تساوي جامع عند
+
+32
+00:03:30,440 --> 00:03:34,680
+نفس ال element موجود في الجروب هذا معناته أن في
+
+33
+00:03:34,680 --> 00:03:41,510
+تساوي جامع وهو المطلوبيعني كل الفكرة كانت تبدل
+
+34
+00:03:41,510 --> 00:03:47,010
+تأثير بفاي على أي element من g بتأثير جامعه على أي
+
+35
+00:03:47,010 --> 00:03:52,510
+element من g هذا كان سؤال تسعة عشر سؤال عشرين
+
+36
+00:03:52,510 --> 00:04:05,450
+بيقول لي سؤال عشرين بيقول لي فاي من z خمسين إلى z
+
+37
+00:04:05,450 --> 00:04:15,020
+خمسينعبارة عن اتومورفزم هذا اتومورفزم وفي نفس
+
+38
+00:04:15,020 --> 00:04:23,620
+الوقت عندنا في of 11 يسوى تلتاشر وقال لي determine
+
+39
+00:04:23,620 --> 00:04:30,960
+formula for في of x find في of x بدنا نعرف ايش
+
+40
+00:04:30,960 --> 00:04:33,740
+شكلها في هذه الحالة
+
+41
+00:04:37,840 --> 00:04:44,420
+أنا عندي في من z50 إلى z50 عبارة عن atomorphism
+
+42
+00:04:44,420 --> 00:04:49,460
+عندي ال atomorphism في تأثيره على ال element 11
+
+43
+00:04:49,460 --> 00:04:55,260
+اللي موجود في z50 بده يسوى 13 اللي موجودة في z50
+
+44
+00:04:55,260 --> 00:05:00,690
+كذلك قال لي هاتلي الصيغةلأ مين للـautomorphism في
+
+45
+00:05:00,690 --> 00:05:06,890
+of X بدي أعرف في of X in general قداش بيساوي حتى
+
+46
+00:05:06,890 --> 00:05:13,350
+يكون في of 11 بدي يساوي مين؟ بدي يساوي 13 طيب بدي
+
+47
+00:05:13,350 --> 00:05:18,730
+أحاول أستفيد من المعطى هذا في حل المسألة حتى أعرف
+
+48
+00:05:18,730 --> 00:05:24,210
+أقدر أجيب من في of 50 حد فكر في حل السؤال وجابه
+
+49
+00:05:24,210 --> 00:05:27,950
+يعني هك؟ ولا واحد؟
+
+50
+00:05:31,180 --> 00:05:37,900
+كيف؟ ماوصلناش لنا نتيجة الساوة
+
+51
+00:05:37,900 --> 00:05:45,680
+جداش؟ ليش يعني X زي 2؟لا بدك تشغل رياضة صح انت
+
+52
+00:05:45,680 --> 00:05:50,940
+بتشغل في Z50 و Z50 ال operation عليها اللي هي
+
+53
+00:05:50,940 --> 00:05:56,100
+الجامعة طبعا طيب خلي بالك هنا بنحاول نستفيد من
+
+54
+00:05:56,100 --> 00:05:59,300
+المعلومات اللي عندنا الحين يا جماعة بقى انا لما
+
+55
+00:05:59,300 --> 00:06:07,170
+اجي اقول ما يأتيإن الـ Phi of 11 بده يسوى تلتاشر
+
+56
+00:06:07,170 --> 00:06:12,050
+بقدر اكتب هذه المعادلة بالصيغة تانية هذه عبارة عن
+
+57
+00:06:12,050 --> 00:06:15,270
+ايش Phi of واحد زيادة واحد زيادة واحد زيادة واحد
+
+58
+00:06:15,270 --> 00:06:19,970
+احداشر مرة Phi atomorphism حتى تدخل على كل واحد
+
+59
+00:06:19,970 --> 00:06:23,230
+فيهم يبقى Phi of واحد Phi of واحد Phi .. كم مرة
+
+60
+00:06:23,230 --> 00:06:29,180
+يعني هذا كأن احداش مضروبة في Phi of واحديبقى هذا
+
+61
+00:06:29,180 --> 00:06:39,440
+معناته ان 11 في 5 of 1 يساوي 13 تمام؟ اذا انا هنا
+
+62
+00:06:39,440 --> 00:06:47,120
+5 of 11 يساوي 13 جدرت اكتبها بدلالة main 5 of 1 لو
+
+63
+00:06:47,120 --> 00:06:53,120
+عرفت قداش ال 5 of 1 بيتم المطلوب لو عرفت قداش
+
+64
+00:06:53,120 --> 00:06:58,480
+القيمة العددية ل 5 of 1 بتم المطلوب بمعنى اخرلو
+
+65
+00:06:58,480 --> 00:07:03,760
+قدرت تخلص من الاحداش هذي بيكون اه حصلنا على five
+
+66
+00:07:03,760 --> 00:07:07,140
+one هيجي واحد مثلا يقول انت بيكسب على five واحد
+
+67
+00:07:07,760 --> 00:07:10,400
+وأقول لك شو هذه تلتاشة على أحداشة هذا rational
+
+68
+00:07:10,400 --> 00:07:13,740
+number احنا بنشتغل في rational ماعناهش rational
+
+69
+00:07:13,740 --> 00:07:17,600
+مرة انا ماعنديش إلا زية خمسين يبقى هذا كلام فارغ
+
+70
+00:07:17,600 --> 00:07:24,140
+لكن بدي أخلق هنا رقم الرقم يجسم على الأحداشة
+
+71
+00:07:24,140 --> 00:07:28,100
+وعملتلكم مرة في ال subgroups إذا كنتم بضروري يبقى
+
+72
+00:07:28,100 --> 00:07:35,120
+بدي أفكر بنفس المفهوم بمعناه أخر أنا بدي أدور على
+
+73
+00:07:35,120 --> 00:07:42,830
+رقمأضربه في إحداش يطين الواحد الصحيح يبقى هنا
+
+74
+00:07:42,830 --> 00:07:48,270
+أفترض أن
+
+75
+00:07:48,270 --> 00:07:58,630
+هناك ن في حيث أن ال H في ال N يساوي الواحد الصحيح
+
+76
+00:08:01,880 --> 00:08:05,720
+افترض ان عندي N بحيث 11N موديولو خمسين افترض ان
+
+77
+00:08:05,720 --> 00:08:09,860
+عندي N بحيث 11N موديولو
+
+78
+00:08:09,860 --> 00:08:15,900
+خمسين افترض ان عندي N بحيث 11N موديولو خمسين افترض
+
+79
+00:08:15,900 --> 00:08:19,280
+ان عندي N بحيث 11N موديولو خمسين افترض ان عندي N
+
+80
+00:08:19,280 --> 00:08:29,140
+بحيث 11N موديولو خمسين افترض ان عندي N بحيث
+
+81
+00:08:29,790 --> 00:08:34,850
+إذا قدرت اتخلص من ال 11 اللي عنها دي بكون حصلت على
+
+82
+00:08:34,850 --> 00:08:41,150
+n وبالتالي بكون جبت الرقم اللي لو ضربته في 11 بطلع
+
+83
+00:08:41,150 --> 00:08:46,110
+واحد صحيح بضل عندي main phi of one وبالتالي جبت
+
+84
+00:08:47,570 --> 00:08:54,090
+بالتالي سهل إيجاد Phi of X لأن Phi of X هي X في
+
+85
+00:08:54,090 --> 00:08:59,710
+Phi of 1 يعني كل مشكلة زي ما كان في الجزء النظري
+
+86
+00:08:59,710 --> 00:09:04,450
+بكنا نروح نجيب Alpha و ندور عليها لف لف لما نطلع
+
+87
+00:09:04,450 --> 00:09:10,060
+نجيب قد إيش قيمتها وهذا المقصود عندنا هناطيب انا
+
+88
+00:09:10,060 --> 00:09:15,480
+بدى أجيب رقم بدل هذا الرقم يكون يجسم على ال 11
+
+89
+00:09:15,480 --> 00:09:23,220
+بحيث نجيب قيمة M الان انا ايش عندي عندي 11 N
+
+90
+00:09:23,220 --> 00:09:31,640
+modulo 50 بده يساوي ال 1 modulo 50 هل بنقدر نجيب
+
+91
+00:09:31,640 --> 00:09:37,740
+رقم يكافئ ال 1 اه بنقدر نحط خمسينات عليه زى ما بدك
+
+92
+00:09:38,090 --> 00:09:42,790
+زائد خمسين زائد مية زائد مية و خمسين زائد متين صح
+
+93
+00:09:42,790 --> 00:09:46,310
+ولا لا بس كله بيقسمش على الأحداث اللي كان فيها
+
+94
+00:09:46,310 --> 00:09:51,890
+عندي رقم لو حطيته سهل جدا بدل ما اضيف خمسين بدي
+
+95
+00:09:51,890 --> 00:09:57,900
+اضيف سالب خمسينتينبنفع ولا ماينفعش؟ بنفع يا بضيف
+
+96
+00:09:57,900 --> 00:10:02,180
+خمسين بالمود يا بضيف خمسين بالسالب يبقى هذا لو ضفت
+
+97
+00:10:02,180 --> 00:10:08,080
+عليه مية بيظل جداش سالب تسعة وتسعين إذا سالب تسعة
+
+98
+00:10:08,080 --> 00:10:11,120
+وتسعين بتكسب على أحداش وبالتالي اتخلص من الأحداش
+
+99
+00:10:11,120 --> 00:10:17,560
+وحصلت على مية حصلت على N يبقى الرقم المكافئ هذا
+
+100
+00:10:17,560 --> 00:10:22,140
+سالب تسعة وتسعين موديولو خمسين
+
+101
+00:10:24,730 --> 00:10:31,310
+تمام طيب الان هذا بيقسم على ال 11 لو قسمت كله على
+
+102
+00:10:31,310 --> 00:10:39,890
+ال 11 بيصير ال N modulo خمسين يساوي سالب تسعة
+
+103
+00:10:39,890 --> 00:10:46,530
+modulo خمسين طب انا ماعنديش سالب تسعة modulo خمسين
+
+104
+00:10:46,530 --> 00:10:52,020
+انا عندي ارقام مجمعةضيف عليها خمسين يبقى هذه العدد
+
+105
+00:10:52,020 --> 00:10:58,420
+المكافئ لها هو مين هو واحد واربعين موديولو خمسين
+
+106
+00:10:58,420 --> 00:11:04,500
+يبقى الآن هذا يا شباب لو كانت واحد واربعين
+
+107
+00:11:04,500 --> 00:11:09,180
+وضربناها في الاحداشر اللي عندنا بضيع وبحصل على مين
+
+108
+00:11:09,180 --> 00:11:14,660
+على five of واحد وبكون خلصنا القصة هذه تمام يبقى
+
+109
+00:11:14,660 --> 00:11:22,090
+الآنبجي بقوله احداشر five of one بده يساوي تلتاشر
+
+110
+00:11:22,090 --> 00:11:29,030
+implies انه واحد واربعين في احداشر في five of واحد
+
+111
+00:11:29,030 --> 00:11:34,750
+طبعا كله module وخمسين هذا بده يساوي اللي هو واحد
+
+112
+00:11:34,750 --> 00:11:41,850
+واربعين في تلتاشر module وخمسين طب لو ضربت واحد
+
+113
+00:11:41,850 --> 00:11:46,120
+واربعين في احداشر ايش بتعطيك هي واحد واربعينفي
+
+114
+00:11:46,120 --> 00:11:51,480
+احداشر بواحد واربعين وواحد واربعين اربعة خمسة وحدة
+
+115
+00:11:51,480 --> 00:11:56,120
+اربعمية وواحد وخمسين شيل من الخمسينات مضال قداشر
+
+116
+00:11:56,120 --> 00:12:00,160
+في five of واحد يبقى five of واحد يبقى صار في
+
+117
+00:12:00,160 --> 00:12:05,200
+الصرف الشمال اللي عندنا five of one اللي انا بدور
+
+118
+00:12:05,200 --> 00:12:09,720
+عليه الان بنفس الطريقة بنضرب اللي هو الواحد
+
+119
+00:12:09,720 --> 00:12:15,560
+واربعين في تلاتاشروشوف ايش بتعطينا يبقى لو جيت
+
+120
+00:12:15,560 --> 00:12:21,420
+واحد واربعين في تلتاش تلاتة و تلاتة في اربع باطناش
+
+121
+00:12:21,420 --> 00:12:26,700
+وهنا واحد واربعين هنا تلاتة تلاتة خمسمية و تلاتة و
+
+122
+00:12:26,700 --> 00:12:31,940
+تلاتين خمسمية و تلاتة و تلاتين شيل منها عشر
+
+123
+00:12:31,940 --> 00:12:38,670
+خمسينات بظل جدات بظل تلاتة و تلاتينفاي اف وان اللي
+
+124
+00:12:38,670 --> 00:12:43,430
+أنا بدور عليه هو الرقم تلاتة و تلاتين طيب قال لي
+
+125
+00:12:43,430 --> 00:12:49,930
+هاتلي formula لفاي اف اكس بقوله هنا فاي اف اكس اكس
+
+126
+00:12:49,930 --> 00:12:56,130
+هذا موجود وان في زد خمسين يعني رقم يبقى هذا الكلام
+
+127
+00:12:56,130 --> 00:13:03,900
+بده يساوي اكس في فاي اف وانيبقى هذا الكلام يساوي X
+
+128
+00:13:03,900 --> 00:13:09,900
+في جداش في تلاتة و تلاتين يبقى أصبحت Phi of X
+
+129
+00:13:09,900 --> 00:13:15,900
+يساوي تلاتة و تلاتين X بالشكل اللي عندنا هذا يبقى
+
+130
+00:13:15,900 --> 00:13:21,400
+هذا صيغة تبعت من؟ تبعت Phi اللي عندنا وليست كما
+
+131
+00:13:21,400 --> 00:13:25,340
+زعمت X زائد تلاتة و لا X زائد اتنين عمرها ما
+
+132
+00:13:25,340 --> 00:13:31,140
+هتجيبها ولا هتجيبهايبقى هذا سؤال 19 فكرته كويسة
+
+133
+00:13:31,140 --> 00:13:36,880
+ومتعلقة بالجزء النظري اللي شرحناه لكنا نحسب في
+
+134
+00:13:36,880 --> 00:13:45,270
+alpha of oneطيب هذا كان سؤال عشرين بعديها سؤال
+
+135
+00:13:45,270 --> 00:13:50,570
+اربع وعشرين approve or disapprove ان ال U عشرين
+
+136
+00:13:50,570 --> 00:13:56,990
+and ال U اربع وعشرين are isomorphic U عشرين و U
+
+137
+00:13:56,990 --> 00:14:04,850
+اربع وعشرين اه مش سامع تلاتة و تلاتين اكس اه مش
+
+138
+00:14:04,850 --> 00:14:11,490
+كتبين اكس اه تلاتة و تلاتين اكس كلام مظبوطيبقى هذا
+
+139
+00:14:11,490 --> 00:14:16,510
+الصيغة تبع ثمين تبعت الدالة السؤال اللي بعده بيقول
+
+140
+00:14:16,510 --> 00:14:21,170
+لي اللي هو السؤال قداش ستة وعشرين ولا كان قلنا ليه
+
+141
+00:14:21,170 --> 00:14:26,410
+سؤال اربعة وعشرين سؤال اربعة وعشرين سؤال اربعة
+
+142
+00:14:26,410 --> 00:14:33,930
+وعشرين بيقول ليه عشرين وليه اربعة وعشرين شوف ليه
+
+143
+00:14:33,930 --> 00:14:39,750
+هدول isomorphic ولا not isomorphic السؤال هوالـ U
+
+144
+00:14:39,750 --> 00:14:44,430
+عشرين هذه عبارة عن مين؟ عبارة عن واحد، اتنين،
+
+145
+00:14:44,430 --> 00:14:51,830
+تلاتة، اربع، خمسة، ستة، سبعة، تمانية، تسعة، عشرة،
+
+146
+00:14:51,830 --> 00:14:57,750
+احداش، تلاتاش، اربعتاش، خمستاش، ستاش، سبعتاش،
+
+147
+00:14:57,750 --> 00:15:04,070
+تسعتاش، تمام؟ وهذه اللي هي عبارة عن مين؟ اللي هي
+
+148
+00:15:04,070 --> 00:15:11,640
+عبارة عن الواحداتنين تلاتة اربعة خمسة ستة سابعة
+
+149
+00:15:11,640 --> 00:15:23,020
+تمانية تسعة عشرة احداش تلاتاش اربعتاش خمستاش ستاش
+
+150
+00:15:23,020 --> 00:15:31,900
+سبعتاش وهنا تمانتاش تسعتاش عشرين واحد وعشرين اتنين
+
+151
+00:15:31,900 --> 00:15:38,370
+وعشرين تلاتة وعشرينتلاتة و تلاتة و اتنين تمانية
+
+152
+00:15:38,370 --> 00:15:44,210
+تلاتة و تلاتة و اتنين تمان عناصر و تمان عناصر هل
+
+153
+00:15:44,210 --> 00:15:49,190
+اتنين هدول are isomorphic ولا لأ تعالى نشوف الان
+
+154
+00:15:49,190 --> 00:15:57,530
+لو جاتلي خمسة تربيع بواحد سبعة تربيعأحداش تربية
+
+155
+00:15:57,530 --> 00:16:03,310
+تلتاش تربية كل أي element من هدول تربية بيعطينا
+
+156
+00:16:03,310 --> 00:16:09,090
+main ال identity element يبقى هذه cyclic لأ not
+
+157
+00:16:09,090 --> 00:16:17,950
+cyclic هذا not cyclic because any
+
+158
+00:16:17,950 --> 00:16:25,170
+non identity element
+
+159
+00:16:27,880 --> 00:16:35,360
+has order اتنين كله حطول الأس اتنين بصيلة ال
+
+160
+00:16:35,360 --> 00:16:41,120
+identity نجي لهذه تلاتة و زيره بواحد تلاتة و أس
+
+161
+00:16:41,120 --> 00:16:48,400
+واحد بتلاتة تلاتة ربيع بتسعة تلاتة كيب سبعة و
+
+162
+00:16:48,400 --> 00:16:55,320
+عشرين تمام؟ يعني السبعة تلاتة أس أربع بواحد و
+
+163
+00:16:55,320 --> 00:17:01,290
+تمانينواحد و تمانين الهمان الواحد و هكذا يبقى
+
+164
+00:17:01,290 --> 00:17:06,170
+التلاتة مرتين تلاتة و Zero بواحد تلاتة اص واحد
+
+165
+00:17:06,170 --> 00:17:11,190
+بواحد تلاتة تربيه بتسعة تلاتة تكيب بسبعة و عشرين
+
+166
+00:17:11,190 --> 00:17:15,530
+تلاتة اص اربع بواحد و تمانين يبقى ال order لتلاتة
+
+167
+00:17:15,530 --> 00:17:22,070
+كدهاش اربعة مظبوط لكن هنا ال order لأي element
+
+168
+00:17:22,070 --> 00:17:28,040
+كدهاش اتنين يبقى اتنين are isomorphicطبعاً لأ يبقى
+
+169
+00:17:28,040 --> 00:17:34,380
+هدول هذه التلاتة
+
+170
+00:17:34,380 --> 00:17:43,820
+is an element of order أربعة هذه أي element of
+
+171
+00:17:43,820 --> 00:17:47,680
+order له ساوى اتنين يبقى اتنين are isomorphic لأ
+
+172
+00:17:47,680 --> 00:17:52,700
+يبقى هذا بدى يعطينا ان اليوم عشرينis not
+
+173
+00:17:52,700 --> 00:17:58,600
+isomorphic لـ U 24 يمكن نلاقيها الـ cyclic element
+
+174
+00:17:58,600 --> 00:18:04,380
+تانية الله أعلم أنا مش عارف قد يكون طيب هذا السؤال
+
+175
+00:18:04,380 --> 00:18:12,320
+اللي هو 24 بعد هيك عندنا سؤال 28 بيقول prove that
+
+176
+00:18:12,320 --> 00:18:21,700
+the group of equaterion سؤال 28 بيقول كيو اتثم
+
+177
+00:18:21,700 --> 00:18:29,680
+اثبت هذا الجروب انه ليس ايزو مورفك ل D4 يبقى هذا
+
+178
+00:18:29,680 --> 00:18:37,400
+الجروب ليس ايزو مورفك .. ليس ايزو مورفك لمن؟ لدى
+
+179
+00:18:37,400 --> 00:18:43,640
+دا هدر الجروب اللي هو D4 لماذا؟ الأعلى جروب
+
+180
+00:18:43,640 --> 00:18:47,780
+افيكواتريون ماشوفتهاش قبل هيك يبقى أول مرة
+
+181
+00:18:47,780 --> 00:18:55,540
+بينشوفهاإذاً لـ Group هدهها لـ Q8 اللي هي عناصرها
+
+182
+00:18:55,540 --> 00:19:04,640
+زائد أو ناقص I زائد أو ناقص J زائد أو ناقص K زائد
+
+183
+00:19:04,640 --> 00:19:12,650
+أو ناقص Lايش ال I و ال J و ال K و ال L هذا سؤال و
+
+184
+00:19:12,650 --> 00:19:18,550
+إيش علاقتهم أبعاد أول شيء الآن ال I هذه هي مصوفة
+
+185
+00:19:18,550 --> 00:19:23,810
+الوحدة من النظام هتنين في اتنين ناقص I هي مصوفة
+
+186
+00:19:23,810 --> 00:19:27,650
+الوحدة نظامها اتنين في اتنين بس مضروبة في مين سالب
+
+187
+00:19:27,650 --> 00:19:34,540
+واحد الآن ال Jمن خلاصة ان ال j في ال k بده يعطينا
+
+188
+00:19:34,540 --> 00:19:44,200
+ال L و يسوى ناقص k في j يعني لو جلبتهم بيعطيني نفس
+
+189
+00:19:44,200 --> 00:19:50,380
+النتيجة بس ب ا ب سالب واحد بنفس الطريقة لو جت
+
+190
+00:19:50,380 --> 00:19:57,300
+قلتلك ال k في ال L بده يسوى j و اللي هو بده يسوى
+
+191
+00:19:57,300 --> 00:20:08,100
+ناقص L في kو كذلك لو جينا ل L في J يبقى L في J بده
+
+192
+00:20:08,100 --> 00:20:16,960
+يساوي K و يساوي ناقص J في L مش عاجزكوا بس و عندك J
+
+193
+00:20:16,960 --> 00:20:22,860
+تربيع بده يساوي K تربيع بده يساوي L تربيع بده
+
+194
+00:20:22,860 --> 00:20:24,520
+يساوي ناقص I
+
+195
+00:20:27,300 --> 00:20:31,120
+يبقى هذه الخواصة الأساسية لهذه ال group اللي خاطر
+
+196
+00:20:31,120 --> 00:20:36,160
+اكتب لك مين ال I والJ والK كل واحدة مصفوفة نظامها
+
+197
+00:20:36,160 --> 00:20:47,400
+2 في 2 بحيث ال J هي المصفوفة اللي هي I 0 0 سالب I
+
+198
+00:20:48,010 --> 00:20:56,250
+الـ K هي المصفوفة اللي هي Zero واحد سلب واحد Zero
+
+199
+00:20:56,250 --> 00:21:03,470
+ال L هي المصفوفة Zero I I Zero بالشكل اللي عندي
+
+200
+00:21:04,720 --> 00:21:08,860
+الكتاب كتبها في عندك بالدلالة في الرموز A وB
+
+201
+00:21:08,860 --> 00:21:14,040
+ومخليها طلاس مش جايلك من ال A ومن ال B احنا
+
+202
+00:21:14,040 --> 00:21:19,300
+بنكتبها لك بصيغة اوضح هي ال Q وهي الخواص بتاعتها
+
+203
+00:21:19,300 --> 00:21:26,400
+الآن بيقوللي اثبت ان ال Q تمانية ل not isomorphic
+
+204
+00:21:26,400 --> 00:21:32,960
+لمين ل D4 ال Q تمانية كم element فيها هنا شباب كم
+
+205
+00:21:32,960 --> 00:21:38,240
+elementتمانية زايد او ناقص وD for فيها كمان قداش
+
+206
+00:21:38,240 --> 00:21:42,780
+تمانية ايه بقى دي هنا تمان عناصر و هنا تمان عناصر
+
+207
+00:21:42,780 --> 00:21:51,420
+امسكلي وين راحت ال J و ال K و ال L ال J هادي ال I
+
+208
+00:21:51,420 --> 00:21:54,760
+هادي يا شباب اللي هي الجدر التربيعي لسالب واحد ال
+
+209
+00:21:54,760 --> 00:22:00,780
+I يعني ال complex هي الجدر التربيعي لسالب واحدالان
+
+210
+00:22:00,780 --> 00:22:05,500
+لو جيت هنا خاصية بيقول جيت تربية يسوى كتربية يسوى
+
+211
+00:22:05,500 --> 00:22:11,540
+ال تربية يسوى قداش سالب I يبقى هذه ال order لها
+
+212
+00:22:11,540 --> 00:22:20,160
+قداش أربعة جيوس أربعة يعني سالب I في سالب I ب I
+
+213
+00:22:20,160 --> 00:22:23,820
+اللي هو ال identity يبقى هنا ال order لهذه أربعة
+
+214
+00:22:23,820 --> 00:22:27,300
+ال order لهذه أربعة ال order لهذه قداش أربعة
+
+215
+00:22:27,300 --> 00:22:32,650
+بالمثلالأردر لسالب جي والأردر لسالب كي والأردر
+
+216
+00:22:32,650 --> 00:22:37,950
+لسالب ال كمان أربعة يبقى أنا عندي كم element ال
+
+217
+00:22:37,950 --> 00:22:44,010
+order اللي يسوى أربعة ستة elements ال order اللي
+
+218
+00:22:44,010 --> 00:22:50,110
+يسوى أربعة تعالوا نروح على D4 هل D4 فيها ستة
+
+219
+00:22:50,110 --> 00:22:55,850
+elements ال order اللي يسوى أربعة ال H وال V وال D
+
+220
+00:22:55,850 --> 00:22:59,660
+وال D prime ال order اللي يسوى اتنينو ال R مية و
+
+221
+00:22:59,660 --> 00:23:04,600
+تمانين ال order يسوي اتنين هاي سعر خمسة و ال
+
+222
+00:23:04,600 --> 00:23:08,020
+identity element ال order ايه لو واحد حطه على شجة
+
+223
+00:23:08,020 --> 00:23:12,980
+بيضلش عندى الا مين الا اتنين اللي هو ال R تسعين و
+
+224
+00:23:12,980 --> 00:23:15,560
+ال R متين و السبعين يبقى اتنين هل هو ال R
+
+225
+00:23:15,560 --> 00:23:23,850
+isomorphic لأ يبقى هناالـ D أو الـ Q8 is not
+
+226
+00:23:23,850 --> 00:23:34,030
+isomorphic لـ D4 because اللي هو Q8 has six
+
+227
+00:23:34,030 --> 00:23:42,810
+elements أو ستة elements ستة elements اللي هم زد
+
+228
+00:23:42,810 --> 00:23:52,270
+أو نقص Jوزادة أو ناقص k وزادة أو ناقص l of order
+
+229
+00:23:52,270 --> 00:24:09,050
+أربع but of order أربع but ال D4 has two elements
+
+230
+00:24:10,170 --> 00:24:21,750
+اللي هما main are 90 and are 270 of order 4 مدام
+
+231
+00:24:21,750 --> 00:24:26,510
+العدد هنا يختلف عن العدد هنا إذا الإثنين لا يمكن
+
+232
+00:24:26,510 --> 00:24:29,670
+يكونوا معاهم isomorphic
+
+233
+00:24:44,510 --> 00:24:51,370
+هذا كان سؤال سؤال تمانية وعشرين لان عندنا سؤال
+
+234
+00:24:51,370 --> 00:24:56,510
+تلاتين سؤال تلاتين يعطينا ال R N هي ال components
+
+235
+00:24:56,510 --> 00:25:03,870
+من واحد لغاية M وقال لي بيانه ال mapping Phi Phi
+
+236
+00:25:03,870 --> 00:25:12,690
+من من ال R N إلى ال R N عبارة عن اتومورفزمتحت
+
+237
+00:25:12,690 --> 00:25:18,050
+عملية الجامعة و هذا ال .. ال .. ال atomorphism
+
+238
+00:25:18,050 --> 00:25:25,610
+بنسميه ال inversion atomorphism يبقى سؤال تلاتين
+
+239
+00:25:25,610 --> 00:25:29,190
+سؤال
+
+240
+00:25:29,190 --> 00:25:43,320
+تلاتين بيقول ليش؟ بيقوللي في من ال rn لل rndefine
+
+241
+00:25:43,320 --> 00:25:53,920
+by فاي لما تأثر على ال element a1 و a2 و لغاية an
+
+242
+00:25:53,920 --> 00:26:02,960
+بيعطيني سالب a1 سالب a2 سالب an بالشكل اللي عندنا
+
+243
+00:26:02,960 --> 00:26:08,120
+هذا بيقول شو ذات ال mapping هذه عبارة عن
+
+244
+00:26:08,120 --> 00:26:13,350
+atomorphismعلى ال group under the component wise
+
+245
+00:26:13,350 --> 00:26:19,110
+addition تحت الجامعه العادى بالنسبه لمن؟ لل space
+
+246
+00:26:19,110 --> 00:26:23,130
+RN يبقى
+
+247
+00:26:23,130 --> 00:26:28,870
+انا عندي function معرفه من RN الى RN بهذا الشكل
+
+248
+00:26:28,870 --> 00:26:33,470
+اللى بدى اطلب انه Phi one to one وانتوا وعباره عن
+
+249
+00:26:33,470 --> 00:26:38,680
+atomorphismيبقى الخطوة الأولى بدأت بيقوله أنه five
+
+250
+00:26:38,680 --> 00:26:46,160
+is one to one بدأ أروح أاخد assume اللي هو five of
+
+251
+00:26:46,160 --> 00:26:52,960
+a واحد و a اتنين و لغاية a n بدر يساوي five of b
+
+252
+00:26:52,960 --> 00:27:03,930
+واحد و b اتنين و لغاية b nصورة الأول ناقص A1 ناقص
+
+253
+00:27:03,930 --> 00:27:15,610
+A2 ناقص AN ناقص B1 ناقص B2 ناقص BN ناقصمن هذا
+
+254
+00:27:15,610 --> 00:27:21,130
+الكلام مش بستنتج، بستنتج ان ناقص A1 بدري يسوي ناقص
+
+255
+00:27:21,130 --> 00:27:28,650
+B1 يبقى ناقص A1 بدري يسوي ناقص B1 و ناقص A2 بدري
+
+256
+00:27:28,650 --> 00:27:35,250
+يسوي ناقص B2 و تظلك ماشي لغاية ناقص AN بدري يسوي
+
+257
+00:27:35,250 --> 00:27:43,040
+ناقص BMلو ضربنا هذا كله في إشارة ناقص بصير ال a1
+
+258
+00:27:43,040 --> 00:27:50,180
+بدر يساوي ال b1 وال a2 بدر يساوي ال b2 وال an بدر
+
+259
+00:27:50,180 --> 00:27:58,770
+يساوي ال bnبناء عليه لو أخدت ال order pair a1 و a2
+
+260
+00:27:58,770 --> 00:28:04,750
+و لغاية an هلاقيه يساويه هشيل ال a1 و أحط قيمتها
+
+261
+00:28:04,750 --> 00:28:11,330
+من ال b1 و أشيل ال a2 و أحط قيمتها اللي هي b2 و
+
+262
+00:28:11,330 --> 00:28:17,230
+أشيل ال an و أحط قيمتها bn إذا أخدت صورتين
+
+263
+00:28:17,230 --> 00:28:23,640
+متساويتينأثبت ان الاصل متساوي لذلك فاي is one to
+
+264
+00:28:23,640 --> 00:28:26,040
+one بدروح اخد element
+
+265
+00:28:34,730 --> 00:28:46,990
+let x1 و x2 و xn موجود في الارن بدي اثبت هذا انه
+
+266
+00:28:46,990 --> 00:28:58,910
+يلو اصل هذا الاصل موجود في ارن بقوله then ال
+
+267
+00:28:58,910 --> 00:29:09,270
+x1و X2 و XN بده يساوي شو رايك بنفع اقول هيك اللي
+
+268
+00:29:09,270 --> 00:29:18,570
+هو سالب X واحد و سالب X اتنين و لغاية سالب XN؟
+
+269
+00:29:18,570 --> 00:29:26,890
+بنفع؟ اه طيب مدام بنفع يبقى هيه كتبته بالشكل اللي
+
+270
+00:29:26,890 --> 00:29:33,860
+عندنايبقى هذا الكلام بده يساوي اللي هو سالب برا
+
+271
+00:29:33,860 --> 00:29:39,860
+هذه سالب X واحد لو سميتها Y واحد والتانية Y اتنين
+
+272
+00:29:39,860 --> 00:29:47,020
+والاخيرة YN يعني هذه كتبت Y واحد وهذه Y اتنين وهذه
+
+273
+00:29:47,020 --> 00:29:53,040
+YN بالشكل اللي عندنا هنا يبقى هذا الكلام بده يساوي
+
+274
+00:29:53,040 --> 00:29:55,800
+اللي هو مين سالب Y واحد
+
+275
+00:30:01,060 --> 00:30:09,680
+أليس هذا هو صورة five of y واحد و y اتنين و لغاية
+
+276
+00:30:09,680 --> 00:30:17,660
+ynإذا ال element اللي أخدته في RN لجيت له أصل في
+
+277
+00:30:17,660 --> 00:30:24,660
+ال main في ال RN كذلك و هو Y1 و Y2 و هو ينحل من
+
+278
+00:30:24,660 --> 00:30:31,440
+بينهم Y1 هي سلب X1 و Y2 هي سلب X2 و YN هو سلب XN و
+
+279
+00:30:31,440 --> 00:30:37,300
+هكذا لذلك صارت أن ال main Phi is on itالان بدي اجي
+
+280
+00:30:37,300 --> 00:30:44,940
+للنقطة الأخيرة five is an isomorphism بدي اروح اخد
+
+281
+00:30:44,940 --> 00:30:51,840
+five of مجموع two elements يبقى a واحد و a اتنين و
+
+282
+00:30:51,840 --> 00:31:02,600
+a n زائد b واحد و b اتنين و لغاية b n كتبتم ليه
+
+283
+00:31:02,600 --> 00:31:08,260
+شكل ان ال operation اللي على ال groupهي عملية جمعة
+
+284
+00:31:08,260 --> 00:31:22,380
+طيب
+
+285
+00:31:22,380 --> 00:31:27,360
+الان طب خل الجامعة اللي قاللي عليكم component wise
+
+286
+00:31:27,360 --> 00:31:36,430
+حاجة مع كل مركبة مع نظيرتها يبقى a1 زائد b1 a2زائد
+
+287
+00:31:36,430 --> 00:31:45,910
+B2 وظل مستمر لغاية AN زائد BN بهذا الشكل الآن أصبح
+
+288
+00:31:45,910 --> 00:31:51,550
+هذا كله element واحد يبقى الصورة تبعته سالب هذا ال
+
+289
+00:31:51,550 --> 00:31:58,670
+element يبقى هذا الكلام بالدرس ساوي سالب A1 زائد
+
+290
+00:31:58,670 --> 00:32:02,850
+B1 سالب A2 زائد B2
+
+291
+00:32:11,310 --> 00:32:17,390
+بقدر ادخل السلب على كل term من هذه الترمات يبقى
+
+292
+00:32:17,390 --> 00:32:25,530
+هذا الكلام بده يساوي سالب a1 سالب b1 و سالب a2
+
+293
+00:32:38,400 --> 00:32:44,420
+هذا قوس واحدمكوّن من N من المُركّبات بدي أحاول
+
+294
+00:32:44,420 --> 00:32:50,040
+أحطه على صيغة مجموعة قوسين إذا لو روحت كتبته على
+
+295
+00:32:50,040 --> 00:32:57,700
+صيغة مجموعة قوسين بده يساوي ا واحد أو سالب ا واحد
+
+296
+00:32:58,410 --> 00:33:07,810
+سالب A1 سالب A2 ونظل ماشيين لغاية سالب AN كله زائد
+
+297
+00:33:07,810 --> 00:33:16,170
+اللي هو سالب B1 وسالب B2 ونظل ماشيين لغاية سالب BM
+
+298
+00:33:16,170 --> 00:33:24,390
+هذا الكلام يساوي الأول هذا هو عبارة عن Phi of A1
+
+299
+00:33:24,390 --> 00:33:36,900
+وA2و لغاية AN زائد الاتاني هو Phi of B1 و B2 و
+
+300
+00:33:36,900 --> 00:33:42,760
+لغاية BN بالشكل اللي عندنا يبقى بناء ان عليه Phi
+
+301
+00:33:42,760 --> 00:33:49,660
+أصبح ماله Atomorphism لإن Phi من نفس ال group إلى
+
+302
+00:33:49,660 --> 00:33:56,890
+نفس ال groupيبقى باجي بقوله هنا thus وهكذا فاي is
+
+303
+00:33:56,890 --> 00:34:03,310
+an atomorphism وانت هنا من مين؟ من المثلة بيسأل
+
+304
+00:34:03,310 --> 00:34:13,110
+بيقولي ما هو المعنى الهندسي لهذا ال atomorphism لو
+
+305
+00:34:13,110 --> 00:34:17,680
+اتخيلت انا في ال space are in اللي جال عنه هناوفي
+
+306
+00:34:17,680 --> 00:34:24,140
+عندى نقطة هنا احداثيها اولا احداثيتها a1 و a2 و a3
+
+307
+00:34:24,140 --> 00:34:30,020
+و a4 و a5 لغاية an في المقابل صورتها نقطة ناقص a1
+
+308
+00:34:30,020 --> 00:34:33,260
+و ناقص a2 او لا يعني ايش بيعمل ال homomorphism هذا
+
+309
+00:34:33,260 --> 00:34:40,740
+او ليس homomorphism بيقلب النقطة عبر مين عبر نقطة
+
+310
+00:34:40,740 --> 00:34:52,360
+الاصل يبقى هنا هبروح بقوله لاmeaning of this
+
+311
+00:34:52,360 --> 00:34:56,360
+atomorphism
+
+312
+00:34:56,360 --> 00:35:12,200
+reflect معنى هذا is the reflection of the points
+
+313
+00:35:12,200 --> 00:35:14,400
+أثرا
+
+314
+00:35:17,910 --> 00:35:26,350
+the origin يبقى كأننا نقلب النقاط عبر نقطة الأصل
+
+315
+00:35:26,350 --> 00:35:29,670
+اللي كانت على اليمين بنخليها على الشمال و اللي
+
+316
+00:35:29,670 --> 00:35:34,040
+كانت على الشمال بنوديها على اليمين و هكذايعني
+
+317
+00:35:34,040 --> 00:35:40,780
+بنقلب وضع النقاط عبر نقطة الأصل، هذا كان هو سؤال
+
+318
+00:35:40,780 --> 00:35:47,000
+اللي هو تلاتين، عندك هنا سؤال خمسة و .. والله سؤال
+
+319
+00:35:47,000 --> 00:35:48,400
+تلاتة و تلاتين
+
+320
+00:36:05,810 --> 00:36:10,170
+يبقى السؤال تلاتة وتلاتين
+
+321
+00:36:25,230 --> 00:36:31,360
+سؤال مرة تانيةبقول في عندي two inner atomorphism
+
+322
+00:36:31,360 --> 00:36:37,800
+الفاي جي والفاي زيد جي بقول اثبت ان الاتنين هدول
+
+323
+00:36:37,800 --> 00:36:42,880
+are equal علما بان الـ z هذه موجودة في ال center
+
+324
+00:36:42,880 --> 00:36:46,640
+تبع الجي الـ z موجودة في ال center تبع الجي يعني
+
+325
+00:36:46,640 --> 00:36:54,580
+commutes مع كل عناصر جي بلا استثناءالأن الـ Inner
+
+326
+00:36:54,580 --> 00:37:01,620
+Atomorphism Phi G of X بنذكر بتعريفه كان G X G
+
+327
+00:37:01,620 --> 00:37:06,140
+Inverse يبقى هذا ال Inner Atomorphism طيب تمام
+
+328
+00:37:06,140 --> 00:37:11,000
+الان انا بدي اثبت ان اتنين هذول are equal بمعنى
+
+329
+00:37:11,000 --> 00:37:16,620
+اخر تأثير لاتنين على اي element موجود في G بده
+
+330
+00:37:16,620 --> 00:37:21,430
+يتساوى مظبوط ولا لا يبقى المقصود فيهميبقى باجي
+
+331
+00:37:21,430 --> 00:37:26,830
+بقوله هنا solution if
+
+332
+00:37:26,830 --> 00:37:33,490
+ال X موجود for all
+
+333
+00:37:33,490 --> 00:37:42,230
+لكل ال X اللي موجود في G لو جيت أخدت تأثير ال 5G
+
+334
+00:37:42,230 --> 00:37:48,250
+على X يبقى ال G X G inverse and
+
+335
+00:37:49,700 --> 00:38:00,500
+بتاخد تأثير الـ Phi ZG على X يبقى ZGX ZG inverse
+
+336
+00:38:00,500 --> 00:38:03,740
+تمام؟
+
+337
+00:38:03,740 --> 00:38:10,340
+يبقى هذا الكلام بده يساوي ZGX
+
+338
+00:38:10,340 --> 00:38:15,080
+G inverse Z inverse
+
+339
+00:38:17,430 --> 00:38:27,390
+هذا الكلام بده يساو G X G Inverse Z Inverse و هنا
+
+340
+00:38:27,390 --> 00:38:34,210
+Zليش؟ لأن الـ Z موجودة في الـ Center يبقى هذا
+
+341
+00:38:34,210 --> 00:38:40,830
+الكلام صحيح لأن الـ Z موجودة في الـ Center تبع الـ
+
+342
+00:38:40,830 --> 00:38:45,290
+Group G يعني الـ Z مرتبط مع أي Element موجود في
+
+343
+00:38:45,290 --> 00:38:50,110
+الـ G وهذا كله Element موجود في الـ G يبقى خلّينا
+
+344
+00:38:50,110 --> 00:38:54,110
+الـ Z تجوان على الناحية التانية الـ Element في
+
+345
+00:38:54,110 --> 00:39:01,940
+معكوسه من يعطينا؟الـ Identity الـ GXG inverse في
+
+346
+00:39:01,940 --> 00:39:07,820
+الـ Identity Element اللي هو الـ GXG inverse الـ
+
+347
+00:39:07,820 --> 00:39:15,600
+GX inverse G مين هو عبارة عبارة عن Phi G of X يبقى
+
+348
+00:39:15,600 --> 00:39:21,260
+بناء عليه أصبح Phi ZG على جميع أناصر G يسوي تأثير
+
+349
+00:39:21,260 --> 00:39:27,160
+Phi G على جميع أناصر G يبقى معنا هذا الكلامإنه في
+
+350
+00:39:27,160 --> 00:39:33,280
+زد جي بده يساوي بين في جي وانت هنا من مين من
+
+351
+00:39:33,280 --> 00:39:40,940
+المسألةهذا كان سؤال تلاتة و تلاتين بعد سؤال خمسة و
+
+352
+00:39:40,940 --> 00:39:47,920
+تلاتين جي و اتش induce the same inner atomorphism
+
+353
+00:39:47,920 --> 00:39:57,280
+of جي يبقى الاسئلة
+
+354
+00:39:57,280 --> 00:40:04,180
+علاقة مباشرة بهذا السؤالخمسة و تلاتين خمسة و
+
+355
+00:40:04,180 --> 00:40:13,500
+تلاتين بيقول ان ال G and ال H اتنين هدول induce
+
+356
+00:40:13,500 --> 00:40:25,000
+the same inner atomorphism the same inner
+
+357
+00:40:25,000 --> 00:40:34,140
+atomorphism of G نقول proveهذا سيعطيك ان الـ H
+
+358
+00:40:34,140 --> 00:40:41,260
+inverse G موجود في الـ Center تبع الـ G بنا نثبت
+
+359
+00:40:41,260 --> 00:40:48,060
+ان هذا موجود في الـ Center تبع من؟ تبع الـ G طيب
+
+360
+00:40:48,060 --> 00:40:54,640
+اتنين هذول بيعملولي نفس ال Inner Atomorphism بمعنى
+
+361
+00:40:54,640 --> 00:40:57,820
+اخر انه solution
+
+362
+00:41:00,540 --> 00:41:11,860
+إن الـ Phi G تأثيره على X بده يساوي Phi H تأثيره
+
+363
+00:41:11,860 --> 00:41:19,360
+على X هذا المقصود فيه لمن؟ هذا الكلام صحيح لكل X
+
+364
+00:41:19,360 --> 00:41:20,760
+الموجودة في G
+
+365
+00:41:24,660 --> 00:41:29,800
+تعريف ال inner atomorphism
+
+366
+00:41:29,800 --> 00:41:34,320
+بالشكل اللي عندنا يبقى اتنين هدول are equal مدام
+
+367
+00:41:34,320 --> 00:41:40,720
+are equal then الأولى اللي عبارة عن g x g inverse
+
+368
+00:41:40,720 --> 00:41:51,300
+والتانى عبارة عن مين عبارة عن h x h inverseقال لي
+
+369
+00:41:51,300 --> 00:41:56,940
+اثبتلي ان ال H inverse D موجودة في ال center يعني
+
+370
+00:41:56,940 --> 00:42:03,040
+ال H inverse G لما اثربها على اي انصار في G من
+
+371
+00:42:03,040 --> 00:42:07,950
+اليمين او من الشمال يكونوا اتنين عريقابنقوله بسيطة
+
+372
+00:42:07,950 --> 00:42:12,550
+جدا قال لي H inverse يبقى هذه ال H inverse مش هفرط
+
+373
+00:42:12,550 --> 00:42:17,170
+فيها لكن ال G inverse بده افرط فيها مش انا افرط
+
+374
+00:42:17,170 --> 00:42:23,710
+فيها لو روحت ضربت اتنين من طرف اليمين في مام في ال
+
+375
+00:42:23,710 --> 00:42:33,530
+G يبقاش بيضل عند هنا G X وبده يساوي H X و هنا H
+
+376
+00:42:33,530 --> 00:42:42,850
+inverse Gيبقى ضرب من جهة اليمين الطرفين فقط في G
+
+377
+00:42:42,850 --> 00:42:47,790
+يبقى جي انفرس جي لو بال identity يبقى بظل عندي G X
+
+378
+00:42:47,790 --> 00:42:54,850
+بده يساوي ال H X H inverse بده أضربها في G يبقى
+
+379
+00:42:54,850 --> 00:43:00,190
+هيدربناها في G كمان ال H هذه مش لازمالييبقى بيضروح
+
+380
+00:43:00,190 --> 00:43:06,210
+اضرب الطرفين في الـ H inverse إذا لو ضربت الطرفين
+
+381
+00:43:06,210 --> 00:43:13,630
+في الـ H inverse بيصير H inverse G X بده يساوي
+
+382
+00:43:13,630 --> 00:43:20,150
+ضربت الطرفين من جهتي الشمال يبقى بيصير H inverse
+
+383
+00:43:20,150 --> 00:43:27,810
+من جهتي الشمال بيصير هذه الـ X H inverse Gيبقى
+
+384
+00:43:27,810 --> 00:43:32,170
+ضربت هنا H انفرس اتجيني H انفرس H اللي هي بال
+
+385
+00:43:32,170 --> 00:43:38,250
+identity بظهر X H انفرس G اطلعلي لهذا ال element
+
+386
+00:43:38,250 --> 00:43:44,190
+واطلعلي لهذا ال element هو نفسه و ال X هذه ايش
+
+387
+00:43:44,190 --> 00:43:51,120
+قلنا عليهاأي x موجودة في جي يبقى هذا الكلام صحيح
+
+388
+00:43:51,120 --> 00:43:57,480
+لكل ال x اللي موجودة في جي ايش تفسيرك لهذا ان ال h
+
+389
+00:43:57,480 --> 00:44:02,660
+inverse g موجودة في ال center تبع الجي وهو المطلوب
+
+390
+00:44:02,660 --> 00:44:08,460
+هذا بده يعطيلك ان ال h inverse g موجودة في ال
+
+391
+00:44:08,460 --> 00:44:11,560
+center تبع الجي وهو المطلوب
+
+392
+00:44:36,580 --> 00:44:43,440
+هذا كان سؤال خمسة و تلاتين الان عنا تمانية و
+
+393
+00:44:43,440 --> 00:44:50,080
+تلاتين او عنا تسعة و تلاتين بفضل نحل تسعة و تلاتين
+
+394
+00:44:50,080 --> 00:44:54,440
+و نضل وقت نحل تمانية و تلاتين بس بعطيك ال function
+
+395
+00:44:54,440 --> 00:44:59,200
+تبع التمانية و تلاتين و انت بتكمل يبقى في تمانية و
+
+396
+00:44:59,200 --> 00:45:06,270
+تلاتين ال function عنا فيمن مين؟ من الست اللي
+
+397
+00:45:06,270 --> 00:45:13,630
+عناصرها اللي هو zero وزاد او ناقص اتنين وزاد او
+
+398
+00:45:13,630 --> 00:45:20,610
+ناقص اربع وزاد او ناقص ستة الى ما شاء الله هادي
+
+399
+00:45:20,610 --> 00:45:27,030
+بين هادي جي و هادي بدنا نسميها جي والتانية H اللي
+
+400
+00:45:27,030 --> 00:45:33,770
+عناصرهازيرو زائد او ناقص تلاتة زائد او ناقص ستة
+
+401
+00:45:33,770 --> 00:45:38,850
+زائد او ناقص تسعة إلى ما شاء الله يبقى هذه الـ
+
+402
+00:45:38,850 --> 00:45:44,270
+five بده اعرفها كالتالي five of اتنين ان يساوي
+
+403
+00:45:44,270 --> 00:45:50,710
+تلاتة ان يبقى هى ال element هنا موجود هنا حط ان
+
+404
+00:45:50,710 --> 00:45:55,190
+بزيرو بيعطيك زيرو حط ان بواحد بيعطيك اتنين حط ان
+
+405
+00:45:55,190 --> 00:46:00,740
+باثنين باربعة تلاتة ستة تمامحط ان بزيرو بصير تلات
+
+406
+00:46:00,740 --> 00:46:05,780
+.. زيرو حط ان بواحد بصير تلاتة حط ان باتنين بناقص
+
+407
+00:46:05,780 --> 00:46:09,320
+واحد بناقص كله تمام يبقى التعريف سليم مائة في
+
+408
+00:46:09,320 --> 00:46:16,620
+المائة باكتبت ان هذا عبارة عن ايزو مورفزم السؤال
+
+409
+00:46:16,620 --> 00:46:18,240
+تسعة وتلاتين
+
+410
+00:46:20,220 --> 00:46:26,280
+سؤال تسعة و تلاتين بيقول ليش بيقول ي support that
+
+411
+00:46:26,280 --> 00:46:35,100
+الفي is an atomorphism ل D4 يبقى في من D4 إلى D4
+
+412
+00:46:35,100 --> 00:46:43,500
+هذا atomorphism و such that الفي of R تسعين و الفي
+
+413
+00:46:43,500 --> 00:46:52,500
+of R تسعين بده يسوى R متين و سبعينمتين وسبعين هو
+
+414
+00:46:52,500 --> 00:46:59,760
+عندك الفاي of V فاي of V بده ساوي ال V قال لي find
+
+415
+00:46:59,760 --> 00:47:08,520
+بدنا نوجد فاي of D و فاي of H فاي of D و فاي of H
+
+416
+00:47:08,520 --> 00:47:11,540
+هذا اللي عايزين نوجده
+
+417
+00:47:21,410 --> 00:47:25,930
+بلزمنا طبعا ال table في صفة واحد و تلاتين تبع ال
+
+418
+00:47:25,930 --> 00:47:31,430
+day four الكل شوية ايه ابنه ارجعنا الان ميعطيني
+
+419
+00:47:31,430 --> 00:47:37,130
+هذا atomorphism وميعطيني قيمتين وطالب قيمتين
+
+420
+00:47:37,130 --> 00:47:42,390
+بنقوله بسيطة جدا يبقى هذا solution
+
+421
+00:47:49,780 --> 00:47:57,720
+السؤال هو هل بقدر اكتب D؟بدلالة ال R تسعين و ال V
+
+422
+00:47:57,720 --> 00:47:58,560
+ولا لا
+
+423
+00:48:28,720 --> 00:48:35,000
+طب هو قاللي هذا في ايزو مورفزم يعني ايزو مورفزم
+
+424
+00:48:35,000 --> 00:48:42,680
+اذا هذا الكلام بدل ساوي في of R تسعين في في of V
+
+425
+00:48:43,580 --> 00:48:48,800
+الـ Phi of R90 هي R270
+
+426
+00:48:48,800 --> 00:48:54,920
+والـ Phi of V بدها تساوي الـ V itself برجع على
+
+427
+00:48:54,920 --> 00:49:00,720
+الجدل برضه بده أشوف R270 في V إيش بتعطينا يبقى
+
+428
+00:49:00,720 --> 00:49:10,250
+R270 في V بتعطينا D primeيبقى ناتج دي prime يبقى
+
+429
+00:49:10,250 --> 00:49:15,930
+هاي حسبتله فاي اف دي يساوي قداش دي prime الان قال
+
+430
+00:49:15,930 --> 00:49:22,710
+هاتلي فاي اف اتش باجي بقوله فاي اف اتش يساوي فاي
+
+431
+00:49:22,710 --> 00:49:29,530
+اف هل بقدر اكتب ال H بدلالة ال R تسعين و ال V ولا
+
+432
+00:49:29,530 --> 00:49:37,650
+لأ تعالى نشوفR تسعين في إيش بتعطيني من ال H يبقى
+
+433
+00:49:37,650 --> 00:49:45,730
+هاي ال R تسعين ال H هي عبارة عن ال H هي عبارة عن R
+
+434
+00:49:45,730 --> 00:49:54,290
+تسعين في D يبقى R تسعين في D لأ احنا بدنا من؟ بدنا
+
+435
+00:49:54,290 --> 00:50:06,030
+R تسعين و V مظبوط؟يعني بديها R تسعين في D كيف؟ مش
+
+436
+00:50:06,030 --> 00:50:12,310
+سامع احنا وجدناها بنفع برضه بنفع من فور كويس يبقى
+
+437
+00:50:12,310 --> 00:50:18,030
+انا كل اللي عند ال H بقدر اشيله و اكتب له R تسعين
+
+438
+00:50:18,030 --> 00:50:26,910
+في D R تسعين في D يبقى هذه R تسعين في Dيبقى هدف
+
+439
+00:50:26,910 --> 00:50:34,590
+تعطينا فاي of R تسعين في فاي of D ويساوي فاي of R
+
+440
+00:50:34,590 --> 00:50:40,090
+تسعين اللي هي R ميتين وسبعين و فاي of D حسبناها
+
+441
+00:50:40,090 --> 00:50:46,210
+اللي هي D primeيبقى بدي اشوف ر متين و سبعين في دي
+
+442
+00:50:46,210 --> 00:50:53,630
+prime قدش بتعطينا يبقى ر متين و سبعين في دي prime
+
+443
+00:50:53,630 --> 00:50:58,030
+اللي هي الأخيرة بتعطينا H
+
+444
+00:51:01,120 --> 00:51:08,160
+يبقى هذي بتعطينا H يبقى صار في of H يساوي من H
+
+445
+00:51:08,160 --> 00:51:15,940
+itself يبقى في of H يساوي من H itself هذي هنا في
+
+446
+00:51:15,940 --> 00:51:21,520
+of D يساوي من D prime
+
+447
+00:51:24,210 --> 00:51:29,170
+طيب المرة القادمة ان شاء الله بدنا نرجع لأسئلة ال
+
+448
+00:51:29,170 --> 00:51:30,930
+permutations
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..486700ee3801e0e14d5e83e6618e6b8bc6e783ea
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5030, "start": 21.38, "end": 50.3, "text": "بسم الله الرحمن الرحيم المرة الماضية بدأنا نناقش الأسئلة المتعلقة بشبتر ستة وهو ال isomorphism ووقفنا عند سؤال رقم تسعة عشر سؤال تسعة عشر مختصر بيقول في عند two isomorphism واحد اسمه في والتاني اسمه جامع من اللي هو ال cycle group generated by a إلى أي group أخرى", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 9673, 46958, 10632, 47525, 10721, 8315, 8717, 8315, 4587, 8592, 16247, 3794, 19986, 37977, 9673, 2655, 30241, 28671, 4724, 8592, 3555, 2655, 2288, 8608, 2655, 3660, 37037, 2407, 2423, 307, 32702, 1434, 4032, 30543, 5172, 8315, 43242, 8608, 33604, 6027, 12602, 4587, 2304, 6055, 3794, 27884, 6225, 46309, 8608, 33604, 6027, 6055, 3794, 27884, 6225, 46309, 3714, 46456, 9381, 2288, 4724, 1829, 39648, 8978, 43242, 732, 307, 32702, 1434, 36764, 24401, 24525, 2304, 3224, 8978, 16070, 2655, 7649, 1829, 24525, 2304, 3224, 10874, 10943, 3615, 9154, 13672, 1829, 31439, 2423, 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" z50", "probability": 0.95703125}, {"start": 281.86, "end": 282.42, "word": " عبارة", "probability": 0.9879150390625}, {"start": 282.42, "end": 282.72, "word": " عن", "probability": 0.990234375}, {"start": 282.72, "end": 284.42, "word": " atomorphism", "probability": 0.70556640625}, {"start": 284.42, "end": 285.78, "word": " عندي", "probability": 0.805908203125}, {"start": 285.78, "end": 285.94, "word": " ال", "probability": 0.806640625}, {"start": 285.94, "end": 286.96, "word": " atomorphism", "probability": 0.8605143229166666}, {"start": 286.96, "end": 287.3, "word": " في", "probability": 0.8779296875}, {"start": 287.3, "end": 287.94, "word": " تأثيره", "probability": 0.9712890625}, {"start": 287.94, "end": 288.2, "word": " على", "probability": 0.83837890625}, {"start": 288.2, "end": 288.44, "word": " ال", "probability": 0.84228515625}, {"start": 288.44, "end": 288.82, "word": " element", "probability": 0.8623046875}, {"start": 288.82, "end": 289.46, "word": " 11", "probability": 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"اتنين تلاتة اربعة خمسة ستة سابعة تمانية تسعة عشرة احداش تلاتاش اربعتاش خمستاش ستاش سبعتاش وهنا تمانتاش تسعتاش عشرين واحد وعشرين اتنين وعشرين تلاتة وعشرين", "tokens": [995, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 8608, 16758, 27884, 46811, 7649, 10632, 6055, 3794, 27884, 6225, 8592, 25720, 1975, 24401, 33599, 6055, 1211, 9307, 33599, 1975, 25513, 34268, 33599, 16490, 2304, 14851, 33599, 8608, 2655, 33599, 8608, 3555, 34268, 33599, 37037, 8315, 46811, 7649, 2655, 33599, 6055, 3794, 34268, 33599, 6225, 46309, 9957, 36764, 24401, 4032, 3615, 46309, 9957, 1975, 2655, 1863, 9957, 4032, 3615, 46309, 9957, 6055, 1211, 9307, 3660, 4032, 3615, 46309, 9957], "avg_logprob": -0.11860795801674778, "compression_ratio": 2.41025641025641, "no_speech_prob": 0.0, "words": [{"start": 906.12, "end": 906.9, "word": "اتنين", "probability": 0.723419189453125}, {"start": 906.9, "end": 907.68, "word": " تلاتة", "probability": 0.911865234375}, 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999.34, "end": 999.88, "word": " بواحد", "probability": 0.9645182291666666}, {"start": 999.88, "end": 1000.9, "word": " تلاتة", "probability": 0.9532470703125}, {"start": 1000.9, "end": 1001.0, "word": " و", "probability": 0.49951171875}, {"start": 1001.0, "end": 1001.12, "word": " أس", "probability": 0.6517333984375}, {"start": 1001.12, "end": 1001.52, "word": " واحد", "probability": 0.961181640625}, {"start": 1001.52, "end": 1002.38, "word": " بتلاتة", "probability": 0.7453125}, {"start": 1002.38, "end": 1003.3, "word": " تلاتة", "probability": 0.9654541015625}, {"start": 1003.3, "end": 1004.34, "word": " ربيع", "probability": 0.9443359375}, {"start": 1004.34, "end": 1005.44, "word": " بتسعة", "probability": 0.9664713541666666}, {"start": 1005.44, "end": 1006.5, "word": " تلاتة", "probability": 0.98095703125}, {"start": 1006.5, "end": 1007.36, "word": " كيب", "probability": 0.9060872395833334}, {"start": 1007.36, "end": 1008.2, "word": " سبعة", "probability": 0.9637044270833334}, 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"probability": 0.70391845703125}, {"start": 1622.41, "end": 1623.09, "word": " A1", "probability": 0.5147705078125}, {"start": 1623.09, "end": 1623.93, "word": " ناقص", "probability": 0.91162109375}, {"start": 1623.93, "end": 1624.67, "word": " A2", "probability": 0.983642578125}, {"start": 1624.67, "end": 1625.49, "word": " ناقص", "probability": 0.98046875}, {"start": 1625.49, "end": 1626.19, "word": " AN", "probability": 0.42041015625}, {"start": 1626.19, "end": 1627.85, "word": " ناقص", "probability": 0.77264404296875}, {"start": 1627.85, "end": 1628.71, "word": " B1", "probability": 0.889892578125}, {"start": 1628.71, "end": 1629.89, "word": " ناقص", "probability": 0.9180908203125}, {"start": 1629.89, "end": 1630.77, "word": " B2", "probability": 0.99169921875}, {"start": 1630.77, "end": 1633.11, "word": " ناقص", "probability": 0.9232177734375}, {"start": 1633.11, "end": 1634.05, "word": " BN", "probability": 0.797119140625}, {"start": 1634.05, "end": 1634.61, "word": " ناقص", "probability": 0.9608154296875}], "temperature": 1.0}, {"id": 66, "seek": 165665, "start": 1634.63, "end": 1656.65, "text": "من هذا الكلام مش بستنتج، بستنتج ان ناقص A1 بدري يسوي ناقص B1 يبقى ناقص A1 بدري يسوي ناقص B1 و ناقص A2 بدري يسوي ناقص B2 و تظلك ماشي لغاية ناقص AN بدري يسوي ناقص BM", "tokens": [27842, 23758, 2423, 28820, 10943, 37893, 4724, 14851, 29399, 7435, 12399, 4724, 14851, 29399, 7435, 16472, 8717, 995, 4587, 9381, 316, 16, 47525, 16572, 7251, 3794, 45865, 8717, 995, 4587, 9381, 363, 16, 7251, 3555, 4587, 7578, 8717, 995, 4587, 9381, 316, 16, 47525, 16572, 7251, 3794, 45865, 8717, 995, 4587, 9381, 363, 16, 4032, 8717, 995, 4587, 9381, 316, 17, 47525, 16572, 7251, 3794, 45865, 8717, 995, 4587, 9381, 363, 17, 4032, 6055, 19913, 23275, 3714, 33599, 1829, 5296, 17082, 995, 10632, 8717, 995, 4587, 9381, 5252, 47525, 16572, 7251, 3794, 45865, 8717, 995, 4587, 9381, 15901], "avg_logprob": -0.16224747113507204, "compression_ratio": 2.140625, "no_speech_prob": 0.0, "words": 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"end": 1659.38, "word": " كله", "probability": 0.899658203125}, {"start": 1659.38, "end": 1659.6, "word": " في", "probability": 0.88427734375}, {"start": 1659.6, "end": 1660.38, "word": " إشارة", "probability": 0.9453125}, {"start": 1660.38, "end": 1661.1, "word": " ناقص", "probability": 0.9842529296875}, {"start": 1661.1, "end": 1662.24, "word": " بصير", "probability": 0.64990234375}, {"start": 1662.24, "end": 1662.46, "word": " ال", "probability": 0.9091796875}, {"start": 1662.46, "end": 1663.04, "word": " a1", "probability": 0.666748046875}, {"start": 1663.04, "end": 1663.52, "word": " بدر", "probability": 0.28125762939453125}, {"start": 1663.52, "end": 1663.92, "word": " يساوي", "probability": 0.74462890625}, {"start": 1663.92, "end": 1664.08, "word": " ال", "probability": 0.9306640625}, {"start": 1664.08, "end": 1664.74, "word": " b1", "probability": 0.966064453125}, {"start": 1664.74, "end": 1665.4, "word": " وال", "probability": 0.423583984375}, {"start": 1665.4, "end": 1666.24, "word": " a2", "probability": 0.871826171875}, {"start": 1666.24, "end": 1666.72, "word": " بدر", "probability": 0.93115234375}, {"start": 1666.72, "end": 1667.24, "word": " يساوي", "probability": 0.9881591796875}, {"start": 1667.24, "end": 1667.42, "word": " ال", "probability": 0.95947265625}, {"start": 1667.42, "end": 1668.1, "word": " b2", "probability": 0.99169921875}, {"start": 1668.1, "end": 1668.78, "word": " وال", "probability": 0.86083984375}, {"start": 1668.78, "end": 1669.66, "word": " an", "probability": 0.49462890625}, {"start": 1669.66, "end": 1670.18, "word": " بدر", "probability": 0.978271484375}, {"start": 1670.18, "end": 1670.86, "word": " يساوي", "probability": 0.9903564453125}, {"start": 1670.86, "end": 1671.14, "word": " ال", "probability": 0.94921875}, {"start": 1671.14, "end": 1672.08, "word": " bn", "probability": 0.919189453125}], "temperature": 1.0}, {"id": 68, "seek": 169847, "start": 1672.85, "end": 1698.47, "text": "بناء عليه لو أخدت ال order pair a1 و a2 و لغاية an هلاقيه يساويه هشيل ال a1 و أحط قيمتها من ال b1 و أشيل ال a2 و أحط قيمتها اللي هي b2 و أشيل ال an و أحط قيمتها bn إذا أخدت صورتين متساويتين", "tokens": [3555, 1863, 16606, 47356, 45164, 5551, 9778, 3215, 2655, 2423, 1668, 6119, 257, 16, 4032, 257, 17, 4032, 5296, 17082, 995, 10632, 364, 8032, 15040, 38436, 3224, 7251, 3794, 995, 45865, 3224, 8032, 8592, 26895, 2423, 257, 16, 4032, 5551, 5016, 9566, 12174, 32640, 2655, 11296, 9154, 2423, 272, 16, 4032, 5551, 8592, 26895, 2423, 257, 17, 4032, 5551, 5016, 9566, 12174, 32640, 2655, 11296, 13672, 1829, 39896, 272, 17, 4032, 5551, 8592, 26895, 2423, 364, 4032, 5551, 5016, 9566, 12174, 32640, 2655, 11296, 272, 77, 11933, 15730, 5551, 9778, 3215, 2655, 20328, 13063, 2655, 9957, 44650, 3794, 995, 45865, 2655, 9957], "avg_logprob": -0.19736043573583215, "compression_ratio": 1.8658536585365855, "no_speech_prob": 0.0, "words": [{"start": 1672.85, "end": 1673.43, "word": "بناء", "probability": 0.787109375}, {"start": 1673.43, "end": 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أشيل", "probability": 0.80224609375}, {"start": 1687.73, "end": 1687.97, "word": " ال", "probability": 0.8994140625}, {"start": 1687.97, "end": 1688.55, "word": " a2", "probability": 0.99560546875}, {"start": 1688.55, "end": 1688.81, "word": " و", "probability": 0.9501953125}, {"start": 1688.81, "end": 1689.13, "word": " أحط", "probability": 0.9786783854166666}, {"start": 1689.13, "end": 1689.77, "word": " قيمتها", "probability": 0.990966796875}, {"start": 1689.77, "end": 1689.97, "word": " اللي", "probability": 0.794189453125}, {"start": 1689.97, "end": 1690.19, "word": " هي", "probability": 0.693359375}, {"start": 1690.19, "end": 1690.77, "word": " b2", "probability": 0.896728515625}, {"start": 1690.77, "end": 1691.33, "word": " و", "probability": 0.94677734375}, {"start": 1691.33, "end": 1691.81, "word": " أشيل", "probability": 0.9485677083333334}, {"start": 1691.81, "end": 1692.13, "word": " ال", "probability": 0.986328125}, {"start": 1692.13, "end": 1692.73, "word": " an", "probability": 0.7294921875}, {"start": 1692.73, "end": 1693.01, "word": " و", "probability": 0.96337890625}, {"start": 1693.01, "end": 1693.41, "word": " أحط", "probability": 0.9825846354166666}, {"start": 1693.41, "end": 1694.11, "word": " قيمتها", "probability": 0.9947509765625}, {"start": 1694.11, "end": 1695.05, "word": " bn", "probability": 0.6689453125}, {"start": 1695.05, "end": 1695.87, "word": " إذا", "probability": 0.744384765625}, {"start": 1695.87, "end": 1696.63, "word": " أخدت", "probability": 0.84814453125}, {"start": 1696.63, "end": 1697.23, "word": " صورتين", "probability": 0.843017578125}, {"start": 1697.23, "end": 1698.47, "word": " متساويتين", "probability": 0.87890625}], "temperature": 1.0}, {"id": 69, "seek": 170604, "start": 1698.72, "end": 1706.04, "text": "أثبت ان الاصل متساوي لذلك فاي is one to one بدروح اخد element", "tokens": [10721, 12984, 3555, 2655, 16472, 2423, 33546, 1211, 44650, 3794, 995, 45865, 5296, 8848, 23275, 6156, 47302, 307, 472, 281, 472, 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"word": " A1", "probability": 0.589111328125}, {"start": 1980.53, "end": 1981.69, "word": " سالب", "probability": 0.896484375}, {"start": 1981.69, "end": 1982.59, "word": " A2", "probability": 0.98583984375}, {"start": 1982.59, "end": 1983.37, "word": " ونظل", "probability": 0.580322265625}, {"start": 1983.37, "end": 1983.77, "word": " ماشيين", "probability": 0.7557373046875}, {"start": 1983.77, "end": 1984.23, "word": " لغاية", "probability": 0.97900390625}, {"start": 1984.23, "end": 1984.89, "word": " سالب", "probability": 0.96337890625}, {"start": 1984.89, "end": 1985.73, "word": " AN", "probability": 0.53466796875}, {"start": 1985.73, "end": 1986.81, "word": " كله", "probability": 0.873291015625}, {"start": 1986.81, "end": 1987.81, "word": " زائد", "probability": 0.8753255208333334}, {"start": 1987.81, "end": 1988.53, "word": " اللي", "probability": 0.82958984375}, {"start": 1988.53, "end": 1988.75, "word": " هو", "probability": 0.9736328125}, {"start": 1988.75, "end": 1989.43, "word": " سالب", "probability": 0.92822265625}, {"start": 1989.43, "end": 1990.33, "word": " B1", "probability": 0.93603515625}, {"start": 1990.33, "end": 1991.55, "word": " وسالب", "probability": 0.8190104166666666}, {"start": 1991.55, "end": 1992.41, "word": " B2", "probability": 0.99462890625}, {"start": 1992.41, "end": 1993.21, "word": " ونظل", "probability": 0.94970703125}, {"start": 1993.21, "end": 1993.79, "word": " ماشيين", "probability": 0.947265625}, {"start": 1993.79, "end": 1994.41, "word": " لغاية", "probability": 0.99462890625}, {"start": 1994.41, "end": 1995.17, "word": " سالب", "probability": 0.9913736979166666}, {"start": 1995.17, "end": 1996.17, "word": " BM", "probability": 0.5673828125}, {"start": 1996.17, "end": 1997.17, "word": " هذا", "probability": 0.91552734375}, {"start": 1997.17, "end": 1997.87, "word": " الكلام", "probability": 0.9677734375}, {"start": 1997.87, "end": 1998.51, "word": " يساوي", "probability": 0.947998046875}, {"start": 1998.51, "end": 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0.908203125}, {"start": 2021.54, "end": 2021.82, "word": " بناء", "probability": 0.6400146484375}, {"start": 2021.82, "end": 2021.96, "word": " ان", "probability": 0.372314453125}, {"start": 2021.96, "end": 2022.22, "word": " عليه", "probability": 0.880859375}, {"start": 2022.22, "end": 2022.76, "word": " Phi", "probability": 0.84326171875}, {"start": 2022.76, "end": 2023.4, "word": " أصبح", "probability": 0.9632161458333334}, {"start": 2023.4, "end": 2023.94, "word": " ماله", "probability": 0.88232421875}, {"start": 2023.94, "end": 2026.02, "word": " Atomorphism", "probability": 0.68505859375}, {"start": 2026.02, "end": 2026.88, "word": " لإن", "probability": 0.8003743489583334}, {"start": 2026.88, "end": 2027.5, "word": " Phi", "probability": 0.625}, {"start": 2027.5, "end": 2027.88, "word": " من", "probability": 0.96240234375}, {"start": 2027.88, "end": 2028.3, "word": " نفس", "probability": 0.99560546875}, {"start": 2028.3, "end": 2028.56, "word": " ال", "probability": 0.8076171875}, {"start": 2028.56, "end": 2029.18, "word": " group", "probability": 0.84912109375}, {"start": 2029.18, "end": 2029.66, "word": " إلى", "probability": 0.84765625}, {"start": 2029.66, "end": 2030.16, "word": " نفس", "probability": 0.99658203125}, {"start": 2030.16, "end": 2030.42, "word": " ال", "probability": 0.87646484375}, {"start": 2030.42, "end": 2030.98, "word": " group", "probability": 0.986328125}], "temperature": 1.0}, {"id": 83, "seek": 205671, "start": 2031.31, "end": 2056.71, "text": "يبقى باجي بقوله هنا thus وهكذا فاي is an atomorphism وانت هنا من مين؟ من المثلة بيسأل بيقولي ما هو المعنى الهندسي لهذا ال atomorphism لو اتخيلت انا في ال space are in اللي جال عنه هنا", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 8807, 37037, 4117, 15730, 6156, 47302, 307, 364, 12018, 18191, 1434, 4032, 7649, 2655, 34105, 9154, 3714, 9957, 22807, 9154, 9673, 12984, 37977, 4724, 1829, 3794, 10721, 1211, 4724, 1829, 39648, 1829, 19446, 31439, 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"end": 2442.78, "word": " الـ", "probability": 0.87646484375}, {"start": 2442.78, "end": 2443.34, "word": " Center", "probability": 0.91357421875}, {"start": 2443.34, "end": 2443.86, "word": " تبع", "probability": 0.9671223958333334}, {"start": 2443.86, "end": 2444.6, "word": " من؟", "probability": 0.489013671875}, {"start": 2444.6, "end": 2445.2, "word": " تبع", "probability": 0.9754231770833334}, {"start": 2445.2, "end": 2445.66, "word": " الـ", "probability": 0.919921875}, {"start": 2445.66, "end": 2445.82, "word": " G", "probability": 0.88623046875}, {"start": 2445.82, "end": 2448.06, "word": " طيب", "probability": 0.8805338541666666}, {"start": 2448.06, "end": 2449.1, "word": " اتنين", "probability": 0.919677734375}, {"start": 2449.1, "end": 2449.76, "word": " هذول", "probability": 0.8282877604166666}, {"start": 2449.76, "end": 2451.54, "word": " بيعملولي", "probability": 0.89013671875}, {"start": 2451.54, "end": 2452.14, "word": " نفس", "probability": 0.996337890625}, {"start": 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0.98046875}, {"start": 3053.17, "end": 3053.63, "word": " prime", "probability": 0.80908203125}, {"start": 3053.63, "end": 3053.97, "word": " اللي", "probability": 0.932861328125}, {"start": 3053.97, "end": 3054.15, "word": " هي", "probability": 0.89501953125}, {"start": 3054.15, "end": 3054.81, "word": " الأخيرة", "probability": 0.9248046875}, {"start": 3054.81, "end": 3056.37, "word": " بتعطينا", "probability": 0.98525390625}, {"start": 3056.37, "end": 3058.03, "word": " H", "probability": 0.19580078125}], "temperature": 1.0}, {"id": 125, "seek": 308152, "start": 3061.12, "end": 3081.52, "text": "يبقى هذي بتعطينا H يبقى صار في of H يساوي من H itself يبقى في of H يساوي من H itself هذي هنا في of D يساوي من D prime", "tokens": [1829, 3555, 4587, 7578, 8032, 8848, 1829, 39894, 3615, 9566, 1829, 8315, 389, 7251, 3555, 4587, 7578, 20328, 9640, 8978, 295, 389, 7251, 3794, 995, 45865, 9154, 389, 2564, 7251, 3555, 4587, 7578, 8978, 295, 389, 7251, 3794, 995, 45865, 9154, 389, 2564, 8032, 8848, 1829, 34105, 8978, 295, 413, 7251, 3794, 995, 45865, 9154, 413, 5835], "avg_logprob": -0.2960668231906562, "compression_ratio": 1.6826923076923077, "no_speech_prob": 0.0, "words": [{"start": 3061.12, "end": 3061.8, "word": "يبقى", "probability": 0.874267578125}, {"start": 3061.8, "end": 3062.22, "word": " هذي", "probability": 0.339599609375}, {"start": 3062.22, "end": 3063.18, "word": " بتعطينا", "probability": 0.92392578125}, {"start": 3063.18, "end": 3063.84, "word": " H", "probability": 0.489990234375}, {"start": 3063.84, "end": 3064.8, "word": " يبقى", "probability": 0.9532470703125}, {"start": 3064.8, "end": 3065.22, "word": " صار", "probability": 0.68798828125}, {"start": 3065.22, "end": 3065.66, "word": " في", "probability": 0.1624755859375}, {"start": 3065.66, "end": 3066.04, "word": " of", "probability": 0.40087890625}, {"start": 3066.04, "end": 3066.36, "word": " H", "probability": 0.88037109375}, {"start": 3066.36, "end": 3066.9, "word": " يساوي", "probability": 0.7095947265625}, {"start": 3066.9, "end": 3067.28, "word": " من", "probability": 0.962890625}, {"start": 3067.28, "end": 3068.16, "word": " H", "probability": 0.86279296875}, {"start": 3068.16, "end": 3068.96, "word": " itself", "probability": 0.5537109375}, {"start": 3068.96, "end": 3070.0, "word": " يبقى", "probability": 0.96142578125}, {"start": 3070.0, "end": 3070.34, "word": " في", "probability": 0.794921875}, {"start": 3070.34, "end": 3070.76, "word": " of", "probability": 0.96484375}, {"start": 3070.76, "end": 3071.26, "word": " H", "probability": 0.97509765625}, {"start": 3071.26, "end": 3072.06, "word": " يساوي", "probability": 0.7928466796875}, {"start": 3072.06, "end": 3072.42, "word": " من", "probability": 0.994140625}, {"start": 3072.42, "end": 3073.36, "word": " H", "probability": 0.79541015625}, {"start": 3073.36, "end": 3074.08, "word": " itself", "probability": 0.5478515625}, {"start": 3074.08, "end": 3074.98, "word": " هذي", "probability": 0.7130533854166666}, {"start": 3074.98, "end": 3075.32, "word": " هنا", "probability": 0.8466796875}, {"start": 3075.32, "end": 3075.94, "word": " في", "probability": 0.87451171875}, {"start": 3075.94, "end": 3076.4, "word": " of", "probability": 0.951171875}, {"start": 3076.4, "end": 3076.72, "word": " D", "probability": 0.921875}, {"start": 3076.72, "end": 3078.02, "word": " يساوي", "probability": 0.912841796875}, {"start": 3078.02, "end": 3078.34, "word": " من", "probability": 0.9736328125}, {"start": 3078.34, "end": 3080.42, "word": " D", "probability": 0.64404296875}, {"start": 3080.42, "end": 3081.52, "word": " prime", "probability": 0.65380859375}], "temperature": 1.0}, {"id": 126, "seek": 309093, "start": 3084.21, "end": 3090.93, "text": "طيب المرة القادمة ان شاء الله بدنا نرجع لأسئلة ال permutations", "tokens": [9566, 1829, 3555, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 47525, 8315, 8717, 47341, 3615, 5296, 10721, 3794, 19986, 37977, 2423, 4784, 325, 763], "avg_logprob": -0.22468171627433212, "compression_ratio": 1.096774193548387, "no_speech_prob": 0.0, "words": [{"start": 3084.21, "end": 3084.69, "word": "طيب", "probability": 0.6895955403645834}, {"start": 3084.69, "end": 3085.25, "word": " المرة", "probability": 0.916748046875}, {"start": 3085.25, "end": 3085.87, "word": " القادمة", "probability": 0.98974609375}, {"start": 3085.87, "end": 3086.07, "word": " ان", "probability": 0.52001953125}, {"start": 3086.07, "end": 3086.37, "word": " شاء", "probability": 0.99169921875}, {"start": 3086.37, "end": 3086.81, "word": " الله", "probability": 0.95751953125}, {"start": 3086.81, "end": 3087.63, "word": " بدنا", "probability": 0.77685546875}, {"start": 3087.63, "end": 3088.03, "word": " نرجع", "probability": 0.984375}, {"start": 3088.03, "end": 3088.77, "word": " لأسئلة", "probability": 0.93623046875}, {"start": 3088.77, "end": 3089.17, "word": " ال", "probability": 0.982421875}, {"start": 3089.17, "end": 3090.93, "word": " permutations", "probability": 0.8128255208333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3092.20125, "duration_after_vad": 2959.943124999987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..14568af8e4489530c98d75df99cec53a860f2870
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_postprocess.srt
@@ -0,0 +1,1548 @@
+1
+00:00:21,500 --> 00:00:24,340
+السلام عليكم بسم الله الرحمن الرحيم اليوم ان شاء
+
+2
+00:00:24,340 --> 00:00:27,260
+الله هننهي المناقشة chapter رابع هنبدأ زي ما
+
+3
+00:00:27,260 --> 00:00:29,860
+اتوقفنا المرة الماضية السؤال سبعة و تلاتين حاليناه
+
+4
+00:00:29,860 --> 00:00:35,290
+هنبدأ من السؤال تمانية و تلاتينطبعا سؤال 38 ماعطيك
+
+5
+00:00:35,290 --> 00:00:40,210
+أربع عناصر في مجموعة بقولك أثبت إن هذي بتعمل group
+
+6
+00:00:40,210 --> 00:00:46,190
+مع عملية الضرب مد ال 20 عشان أنا أقدر أتعامل مع
+
+7
+00:00:46,190 --> 00:00:49,330
+هذا الأسئلة .. نوع من الأسئلة لما يعطيني group فيه
+
+8
+00:00:49,330 --> 00:00:53,090
+عدد محدود جدا من العناصر تلاتة أربعة خمسة ويثبت
+
+9
+00:00:53,090 --> 00:00:57,030
+إنها أو يطلب مني أن أثبت إنها group أسهل طريقة هي
+
+10
+00:00:57,030 --> 00:01:02,940
+multiplication table جدول الضربفبروح بحط التمانية
+
+11
+00:01:02,940 --> 00:01:09,060
+أو الأربعة في الأول التمانية والاتناش والستاش
+
+12
+00:01:09,060 --> 00:01:16,120
+واندي اربعة تمانية اتناش ستاش طبعا مدام الضرب
+
+13
+00:01:16,120 --> 00:01:21,920
+تقليدي يعني أنا بتعامل مع عملية ضرب صحيح مدة
+
+14
+00:01:21,920 --> 00:01:25,520
+العشرين لكن في نهاية أساسها عبارة عن إيش عن ضرب
+
+15
+00:01:25,520 --> 00:01:31,170
+أرقام فأكيد العملية هتكون إيشتبدلية اربع فى اربع
+
+16
+00:01:31,170 --> 00:01:34,730
+ستة عشر مدى العشرين ستة عشر اربع فى تمانية اتناش
+
+17
+00:01:34,730 --> 00:01:37,970
+اتنين و تلاتين مدى العشرين اتناش اربع فى اتناش
+
+18
+00:01:37,970 --> 00:01:42,810
+حياطين تمانية و اربع فى ستة عشر اربع تمانية فى
+
+19
+00:01:42,810 --> 00:01:45,850
+اربع اتنين و تلاتين باتناش تمانية فى تمانية اربع
+
+20
+00:01:45,850 --> 00:01:51,110
+وستين باربع تمانية فى اتناش بستة و تسعين يعني ستة
+
+21
+00:01:51,110 --> 00:01:57,240
+عشر و تمانية فى ستة عشر كدهشمية تمانية عشرين يعني
+
+22
+00:01:57,240 --> 00:02:01,500
+تمانية اتناش في اربعة تمانية واربعين يعني تمانية
+
+23
+00:02:01,500 --> 00:02:04,560
+اتناش في تمانية ستة وتسعين يعني ستة عشر اتناش
+
+24
+00:02:04,560 --> 00:02:08,600
+اتناش مية اربعة واربعين يعني اربعة اتناش في ستة
+
+25
+00:02:08,600 --> 00:02:13,420
+عشر هيظل اتناش طبعا ستة عشر في اربعة هيكون عبارة
+
+26
+00:02:13,420 --> 00:02:17,540
+عن اربعة وستين يظل اربعة ستة عشر في تمانية هيظل
+
+27
+00:02:17,540 --> 00:02:22,470
+تمانية واتناش وستة عشرمن الواضح انه اول حاجة
+
+28
+00:02:22,470 --> 00:02:27,070
+العملية عشانها اصلا ضرب عادي ف associative موجود
+
+29
+00:02:27,070 --> 00:02:31,050
+ال .. ال binary او ان العملية مغلقة على المجموعة
+
+30
+00:02:31,050 --> 00:02:34,390
+موجودة ماطلعش عناصر من برا المجموعة ال abelian
+
+31
+00:02:34,390 --> 00:02:43,330
+موجود في identity؟ في identity؟ في محايد؟ في ..
+
+32
+00:02:43,330 --> 00:02:49,390
+مين؟ ال 16 .. ليش؟ لأنه انا بضرب ال 16 في اي رقم
+
+33
+00:02:50,300 --> 00:02:55,120
+بيظل زي ما هو بيظل لدي ال inverse هل لكل رقم بلاجي
+
+34
+00:02:55,120 --> 00:02:59,260
+عنصر بضربه في نفسه بيعطيه ال identity بقدر أعرفه
+
+35
+00:02:59,260 --> 00:03:03,600
+لما أتأكد انه في كل سطر فيه ستة عشر وفي كل عمود
+
+36
+00:03:03,600 --> 00:03:10,400
+فيه ستة عشر وبالتالي هذا عبارة عن group ومش group
+
+37
+00:03:10,400 --> 00:03:16,840
+مش group بس لأ abelian abelian ال group what is
+
+38
+00:03:16,840 --> 00:03:19,560
+the identity هو الستة عشر هل هي ال cyclic
+
+39
+00:03:23,610 --> 00:03:28,370
+هل هي Cyclic؟ عشان تكون Cyclic شباب بديه أنصر
+
+40
+00:03:28,370 --> 00:03:33,370
+يولدها يعني بديه أنصر ال order ل 4 طبعا ال order ل
+
+41
+00:03:33,370 --> 00:03:42,090
+4 بنجيبه 4 في 4 16 بديه يساوي ال identity بقى ال
+
+42
+00:03:42,090 --> 00:03:48,270
+order ل 4 بديه يساوي 2 ال order ل 8 8 في 8 كدهش؟
+
+43
+00:03:48,990 --> 00:03:53,450
+أربعة ستين أربعة تمانية في تمانية في تمانية اتناش
+
+44
+00:03:53,450 --> 00:03:58,410
+تمانية في تمانية في تمانية في تمانية ستة عشريك
+
+45
+00:03:58,410 --> 00:04:03,630
+بأوردر التمانية بتساوي أربعة وبالتالي هذه الجروب
+
+46
+00:04:03,630 --> 00:04:10,310
+جيه generated by main من التمانية وبالتالي هي
+
+47
+00:04:10,310 --> 00:04:17,150
+Cyclic واضح السؤال ده واضح
+
+48
+00:04:17,150 --> 00:04:17,630
+السؤال
+
+49
+00:04:22,570 --> 00:04:26,490
+تسعة وتلاتين give an example of a group that has
+
+50
+00:04:26,490 --> 00:04:30,770
+that has exactly six subgroups including the
+
+51
+00:04:30,770 --> 00:04:34,210
+trivial subgroup and the group itself generalized
+
+52
+00:04:34,210 --> 00:04:38,050
+exactly any subgroup for any positive integer and
+
+53
+00:04:38,050 --> 00:04:48,690
+ايش رأيكم؟ بدك group J فيها only six subgroups
+
+54
+00:05:06,200 --> 00:05:11,860
+عشان اعطيك ال group انت تجيبها و تكون لها six
+
+55
+00:05:11,860 --> 00:05:17,100
+subgroup يعني القواسم عددهم ستة بالظبط ايش يعني
+
+56
+00:05:17,100 --> 00:05:22,260
+القواسم عددهم ستة صارت تمانية و تلاتين هذا صارت
+
+57
+00:05:22,260 --> 00:05:28,280
+تسعة و تلاتين يعني بدك ال group ال order الها n
+
+58
+00:05:29,840 --> 00:05:33,820
+وعدد قواسم الان بدي ساو ستة عشان تشتغل بناء على
+
+59
+00:05:33,820 --> 00:05:39,120
+انه تكون هادي الساكنك اعطيني جواب عدد القواسم تبع
+
+60
+00:05:39,120 --> 00:05:45,840
+ال order الها بساو ستة الاربع عشرين كام
+
+61
+00:05:45,840 --> 00:05:51,380
+قاسم؟ واحد، اتنين، تلاتة، اربع، ستة، تمانية،
+
+62
+00:05:51,380 --> 00:05:55,060
+اتناش، اربع عشرين، تمانية طيب عشان انا عارفش
+
+63
+00:05:55,060 --> 00:06:06,740
+البداية we needا group او a cyclic جيه
+
+64
+00:06:06,740 --> 00:06:17,280
+with order ال جيه بيساوي ان and الان has only six
+
+65
+00:06:17,280 --> 00:06:27,460
+divisors اعطيني group ال order لها ان والان له ستة
+
+66
+00:06:27,460 --> 00:06:28,180
+من القواسم
+
+67
+00:06:32,310 --> 00:06:38,210
+تعشى كام قاسم؟ واحد اتنين تلاتة اربع ستة اتناش
+
+68
+00:06:38,210 --> 00:06:47,010
+Take جبدة تساوياش؟ زد اتناش من ال six subgroup
+
+69
+00:06:47,010 --> 00:06:51,610
+هدول generated by واحد generated by تنين generated
+
+70
+00:06:51,610 --> 00:06:56,010
+by تلاتة generated by اربع generated by ستة
+
+71
+00:06:56,010 --> 00:07:00,410
+وgenerated by اتناش عمّمها لإيه ان؟
+
+72
+00:07:03,870 --> 00:07:13,010
+for n هنا في مشكلة شباب هنا
+
+73
+00:07:13,010 --> 00:07:17,990
+في مشكلة تبدأ
+
+74
+00:07:17,990 --> 00:07:28,730
+تشتغل على جروب عدد القواسم دي يكون إله n طيب كام
+
+75
+00:07:28,730 --> 00:07:29,450
+قاسم؟
+
+76
+00:07:32,370 --> 00:07:37,230
+خلصنا من الستة لنشغل على عدد القواسم يكونوا even
+
+77
+00:07:37,230 --> 00:07:42,270
+لو ال uneven فإيش
+
+78
+00:07:42,270 --> 00:07:49,110
+بيعمل تعالى نرجع شوية نظرية الأعداد إيش عدد
+
+79
+00:07:49,110 --> 00:07:56,750
+القواسم بيساوي؟ إيش رمز سبعة في الأول؟ تأولان؟طيب،
+
+80
+00:07:56,750 --> 00:08:04,050
+لو الان بدأ تساوي P1 P2 لعند PK K1 K2 لعند K إيش
+
+81
+00:08:04,050 --> 00:08:07,790
+تقوى الان بيساوي؟
+
+82
+00:08:07,790 --> 00:08:14,830
+إيش تقوى الان بيساوي؟ K1 زاد الواحد K2 زاد الواحد
+
+83
+00:08:14,830 --> 00:08:20,710
+لعند KR زاد الواحد عد
+
+84
+00:08:20,710 --> 00:08:30,810
+القواصم يا حبيبيعلى المهم هذا بدي ساوي N عدد
+
+85
+00:08:30,810 --> 00:08:41,830
+القواسم بدي ساوي الـ N المطلوبة اتبعوا فش غير واحد
+
+86
+00:08:41,830 --> 00:08:48,210
+زي هيك فانت بتشرح على مين N بدي تساوي K واحد زي
+
+87
+00:08:48,210 --> 00:08:52,110
+واحد خطة K زي واحديعني انت بدأت تشتغل على أن بدأت
+
+88
+00:08:52,110 --> 00:08:57,870
+تصير عندك P to K هتاخد الانبدو يساوي K زاد الواحد
+
+89
+00:08:57,870 --> 00:09:04,970
+اختار ال P بـPrime هتاخد مين أن بدأت تساوي تنين to
+
+90
+00:09:04,970 --> 00:09:08,530
+K جي
+
+91
+00:09:08,530 --> 00:09:11,910
+بدأت تساوي زد تنين to K
+
+92
+00:09:20,720 --> 00:09:26,220
+طبعا ال K بدأ تساوي N minus واحد تنين
+
+93
+00:09:26,220 --> 00:09:33,720
+to N minus واحد تنينوس N minus واحد has N divisors
+
+94
+00:09:33,720 --> 00:09:41,640
+من هما واحد، تنين، تنين تغبيع، تنين تكيب يعني تنين
+
+95
+00:09:41,640 --> 00:09:47,220
+N minus واحد هدول قواسم التنينوس N minus واحد
+
+96
+00:09:52,160 --> 00:09:59,300
+The n subgroups are generated by 1, generated by
+
+97
+00:09:59,300 --> 00:10:04,900
+2, generated by 4, generated by 8 لأن generated by
+
+98
+00:10:04,900 --> 00:10:11,320
+2 أُس n minus 1 وانت بتشغل في مين؟ في z 2 أُس n
+
+99
+00:10:11,320 --> 00:10:17,120
+minus كيف؟ اه وانا هي اللي حلته قدامك
+
+100
+00:10:22,180 --> 00:10:26,000
+أنا مش راحتش حاجة علاقة في نظرية الأعداد أنا مطلوب
+
+101
+00:10:26,000 --> 00:10:31,840
+مني أدور على رقم الو N من القواسم أي
+
+102
+00:10:31,840 --> 00:10:37,420
+P to N minus واحد الو N من القواسم احصل حالك في
+
+103
+00:10:37,420 --> 00:10:44,460
+prime واحد تمشي و بتجيب المطلوب واضح؟
+
+104
+00:10:44,460 --> 00:10:47,880
+مش
+
+105
+00:10:47,880 --> 00:10:48,500
+واضح؟
+
+106
+00:10:51,100 --> 00:10:58,260
+لأ هذا غير هذا مثال
+
+107
+00:10:58,260 --> 00:11:02,300
+بخص الستة لوحدها لو بدك تيجي على السبعة مش هتقدر
+
+108
+00:11:02,300 --> 00:11:06,460
+تيجي تاخد مثلا زد اربعة عاش لأ للستة هتقدر تاخد زد
+
+109
+00:11:06,460 --> 00:11:13,420
+تنين و نص خمس يعني زد اتنين و تلاتين اه جرب اتنين
+
+110
+00:11:13,420 --> 00:11:25,030
+اربعة اربعة اتنين اربعة تمانية16 و 32 هيهم 6 لكن
+
+111
+00:11:25,030 --> 00:11:28,990
+مش هي الوحيدة يعني مش هي الوحيدة معناه لو أخدت زد
+
+112
+00:11:28,990 --> 00:11:32,770
+تلاتة أثناء minus واحد بنفع زد سبعة أثناء minus
+
+113
+00:11:32,770 --> 00:11:40,070
+واحد بنفع في أكتر من واحدة طيب
+
+114
+00:11:40,070 --> 00:11:45,090
+سؤال 42 prove that an infinite group must have an
+
+115
+00:11:45,090 --> 00:11:51,210
+infinite number of subgroupsجي جنيريت باي الـ a و
+
+116
+00:11:51,210 --> 00:11:56,870
+order الـ a بدي يساوي مانا نهاية بدك infinite sub
+
+117
+00:11:56,870 --> 00:12:01,810
+group كيف؟
+
+118
+00:12:01,810 --> 00:12:09,030
+let a عبارة عن generated by a to i حيث اي is the
+
+119
+00:12:09,030 --> 00:12:13,770
+prime since
+
+120
+00:12:13,770 --> 00:12:27,110
+the numberof the primes is infinite عدد
+
+121
+00:12:27,110 --> 00:12:34,310
+لا نهائي فش في even أو odd and generated by a to i
+
+122
+00:12:34,310 --> 00:12:41,510
+لاتساوي generated by a to j forI لا يساوي J هل الـ
+
+123
+00:12:41,510 --> 00:12:45,130
+generated by A أو السبعة بيساوي generated by A أو
+
+124
+00:12:45,130 --> 00:12:50,090
+السحداش؟ صعب و مستحيل تقدرش تجيب ال A أو السبعة من
+
+125
+00:12:50,090 --> 00:12:52,830
+ال A أو السحداش ولا ال A أو السحداش من ال A أو
+
+126
+00:12:52,830 --> 00:12:59,990
+السبعة هدولة العداد تبعي لنهائي و أنا مافيش تكرار
+
+127
+00:12:59,990 --> 00:13:06,030
+النتيجة A has infinite number
+
+128
+00:13:08,470 --> 00:13:17,190
+of elements يوجد في ال a عدد لانهائي من العناصر كل
+
+129
+00:13:17,190 --> 00:13:22,390
+عنصر من هذه العناصر مش ممثلك where
+
+130
+00:13:22,390 --> 00:13:35,630
+each one is a cyclic subgroup of
+
+131
+00:13:35,630 --> 00:13:42,900
+Gالبعدد أنا طبعا بقدر ألاجي غيرهم بقدر لكن بشغل
+
+132
+00:13:42,900 --> 00:13:51,050
+أنا على هذا الشكل أو على هذا النمط أثر لييعني
+
+133
+00:13:51,050 --> 00:13:54,770
+اعطيك ايام مثال رقمى لو انت بتشغل في z في عندك
+
+134
+00:13:54,770 --> 00:13:58,390
+generated by تنين generated by تلاتة generated by
+
+135
+00:13:58,390 --> 00:14:03,910
+خمسة generated by سبعة generated by احداشر الى اخر
+
+136
+00:14:03,910 --> 00:14:07,690
+بتضلك الى ماله نهاية ولا واحد زى التانى هذا
+
+137
+00:14:07,690 --> 00:14:11,470
+مضاعفات الاتنين هذا مضاعفات التلاتة هذا مضاعفات
+
+138
+00:14:11,470 --> 00:14:19,480
+الخمسة هذا مضاعفات السبعةولا واحد زي فيه غيره بس
+
+139
+00:14:19,480 --> 00:14:37,400
+أنا اشتغلت عليه برايم علشان ما ..
+
+140
+00:14:37,400 --> 00:14:44,340
+سؤال خمسة واربعين بداك
+
+141
+00:14:44,340 --> 00:14:57,680
+العناصرفى z 40 اللى ال order بدى يساوي عشرة بنجيب
+
+142
+00:14:57,680 --> 00:15:04,440
+واحد اولش بنجيب عددهم و بنجيب واحد و بنرفع هذا
+
+143
+00:15:04,440 --> 00:15:10,440
+لمين ل relative prime مع العشرة the number of
+
+144
+00:15:10,440 --> 00:15:20,170
+elements in z 40with order عشرة is فايل عشرة
+
+145
+00:15:20,170 --> 00:15:25,770
+بديساوي أربع ليش
+
+146
+00:15:25,770 --> 00:15:36,630
+انت بتشغل في ZN و ZN شمالها Cyclic one of them is
+
+147
+00:15:36,630 --> 00:15:45,860
+مين A بديساوي أربعين على عشرة بديساوي الأربعالاربع
+
+148
+00:15:45,860 --> 00:15:53,580
+ال order إيه له عشرة باقي العناصر ال other
+
+149
+00:15:53,580 --> 00:15:58,780
+elements are
+
+150
+00:15:58,780 --> 00:16:03,980
+أربع أوس واحد أربع أوس ثلاثة أربع أوس سبعة أربع
+
+151
+00:16:03,980 --> 00:16:08,240
+أوس تسعة اللي هو ما عبارة عن الأربع والاتناشر
+
+152
+00:16:08,240 --> 00:16:13,940
+والتمانية وعشرين والستة وتلاتينهذا في سؤال في
+
+153
+00:16:13,940 --> 00:16:19,080
+التلخيص حلناه من هذا النمط لما تيجي تشتر على ال
+
+154
+00:16:19,080 --> 00:16:24,260
+order بيساوي أربعين list all the elements of that
+
+155
+00:16:24,260 --> 00:16:29,700
+have order عشرة هنا تعمين يعني في تكملة السؤال
+
+156
+00:16:29,700 --> 00:16:37,880
+هتاخد اللي هو اكسوس أربعةالـ X generated و X أُس
+
+157
+00:16:37,880 --> 00:16:47,000
+12 و X أُس 28 و X أُس 36 تكملة للسؤال
+
+158
+00:17:06,320 --> 00:17:11,680
+ماشي سؤال 47 بدنا نجيب عدد ال order للعناصر في D33
+
+159
+00:17:11,680 --> 00:17:19,800
+طبعا D33 عبارة عن 66 عنصر 33 منهم عبارة عن دورانات
+
+160
+00:17:19,800 --> 00:17:26,480
+و33 التانين عبارة عن reflection الدورانات بيبدو ب
+
+161
+00:17:26,480 --> 00:17:37,460
+R0 R 360 على 33 وصولنا ل R N-1يعني تنين و تلاتين
+
+162
+00:17:37,460 --> 00:17:43,240
+على تلاتة و تلاتين في تلات مية و ستين وبعدين بيبدو
+
+163
+00:17:43,240 --> 00:17:48,500
+ب F واحد F في اتنين لان F في تلاتة و تلاتين
+
+164
+00:17:48,500 --> 00:17:54,980
+الأولانية التواغنات والباجي عبارة عن reflections
+
+165
+00:17:54,980 --> 00:18:02,350
+ال order لأي F I بيساوي اتنينلأن انت لما تعمل
+
+166
+00:18:02,350 --> 00:18:09,130
+انعكاس وتعكس الانعكاس بيرجع مكانه ال order لري
+
+167
+00:18:09,130 --> 00:18:15,310
+ماشي بده يساوي طبعا
+
+168
+00:18:15,310 --> 00:18:22,130
+هدول عبارة عن ر اي في تلاتمية او تلاتمية وستين
+
+169
+00:18:22,130 --> 00:18:29,030
+مثلا ك على تلاتة و تلاتين والك
+
+170
+00:18:32,470 --> 00:18:40,730
+محصور بين الـ 32 والـ 0 بناجيب ال orders اللي باق
+
+171
+00:18:40,730 --> 00:18:45,250
+العناصر اللي هي عبارة عن الدورانات كل عنصر بهذا
+
+172
+00:18:45,250 --> 00:18:49,430
+الشكل ال order إلوش هيكون
+
+173
+00:18:55,620 --> 00:19:00,300
+انساش هدول شباب هذا أشبه بالـ Zero هذا بالواحد هذا
+
+174
+00:19:00,300 --> 00:19:05,380
+بالتنين هذا بالتنين و تلاتين يعني هم زي عناصر مين
+
+175
+00:19:05,380 --> 00:19:10,320
+ال Z تلاتة و تلاتين يعني هم كلهم أصلا هذا ال
+
+176
+00:19:10,320 --> 00:19:16,340
+answer ال R تلاتمية و ستين K ع تلاتة و تلاتين
+
+177
+00:19:16,340 --> 00:19:22,460
+عبارة عن ال R تلاتمية و ستين ع تلاتة و تلاتين أس K
+
+178
+00:19:25,710 --> 00:19:36,130
+طيب يعني لو أخدت انا لت مثلا A عبارة عن R 360 على
+
+179
+00:19:36,130 --> 00:19:43,110
+33 هيكون ال order لل A جديش اللي هو اللي بولد
+
+180
+00:19:43,110 --> 00:19:50,950
+الجزئية هذه من ال D 33 ال order له 33 فانت لما بدك
+
+181
+00:19:50,950 --> 00:19:52,570
+تيجي تتعامل مع ال order
+
+182
+00:19:57,580 --> 00:20:02,520
+لار تلاتمية و ستين كي على تلاتة و تلاتين اللي هو
+
+183
+00:20:02,520 --> 00:20:07,160
+عبارة عن ال order ل a to k ايش ال order ل a to k
+
+184
+00:20:07,160 --> 00:20:13,780
+عبارة عن تلاتة و تلاتين على الجريس common divisor
+
+185
+00:20:13,780 --> 00:20:19,940
+لكيه تلاتة و تلاتين و
+
+186
+00:20:19,940 --> 00:20:26,360
+حسب ايش في عندك عناصر هان بطلع ال order يلو بهذا
+
+187
+00:20:26,360 --> 00:20:32,610
+الشكلعيد بسرعة دي تلاتة و تلاتين جزئين جزء سهل
+
+188
+00:20:32,610 --> 00:20:36,150
+اللي هو reflections كل عنصر ال order له اتنين و
+
+189
+00:20:36,150 --> 00:20:43,990
+جزء بشابه مين ال zn فال order له لو انا اخدت اتبعت
+
+190
+00:20:43,990 --> 00:20:49,030
+ال a هو ال generator فكل عنصر مثلا عبارة عن ال a
+
+191
+00:20:49,030 --> 00:20:53,330
+تصم k و ال order ل a تكيه عبارة عن التلاتة و
+
+192
+00:20:53,330 --> 00:20:56,350
+تلاتين اللي هو order ال a على guess common divisor
+
+193
+00:20:56,350 --> 00:21:04,230
+لkو تلاتة و تلاتين طيب
+
+194
+00:21:04,230 --> 00:21:17,230
+تمانية
+
+195
+00:21:17,230 --> 00:21:21,170
+و أربعينif j is cyclic group and خمس طعش divide by
+
+196
+00:21:21,170 --> 00:21:24,950
+order of j then the number of solution of j of
+
+197
+00:21:24,950 --> 00:21:32,630
+equation x to خمس طعش سوى a j is cyclic خمس طعش
+
+198
+00:21:32,630 --> 00:21:41,530
+تقسم order of j وانا ب dash على x أُس خمس طعش بدي
+
+199
+00:21:41,530 --> 00:21:42,330
+سوى ال identity
+
+200
+00:21:54,710 --> 00:21:57,970
+أوجد عدد العناصر اللي بيحلوا المعادلة هذه في الـ j
+
+201
+00:21:57,970 --> 00:22:07,670
+طبعا since ال 15 تقسم ال order لل j و ال j is
+
+202
+00:22:07,670 --> 00:22:15,850
+cyclic هذا معناته يوجد a ينتمي لل j with a أُس 15
+
+203
+00:22:15,850 --> 00:22:21,750
+او with order ال a بدي يساوي 15 احنا قولنا نظريةأو
+
+204
+00:22:21,750 --> 00:22:25,990
+caller على نظرية لأي group لو في قاسم بيقسم ال
+
+205
+00:22:25,990 --> 00:22:30,370
+order إليها ففي عنصر في ال group هذه ال order اللي
+
+206
+00:22:30,370 --> 00:22:37,590
+بيسوي هذا القاسم هذا معناته the set H أو بلاش H
+
+207
+00:22:37,590 --> 00:22:41,830
+عشان ماتفكر أشهر بال group the set T عبارة عن كل X
+
+208
+00:22:41,830 --> 00:22:47,270
+في J X أُس 15 بدي يساوي ال identity is none أو is
+
+209
+00:22:47,270 --> 00:22:56,500
+not emptyهذه المجموعة غير خالية لماذا؟
+
+210
+00:22:56,500 --> 00:23:07,600
+لأن هناك أنصار موجودة فيها نستطيع أن نكتب T عبارة
+
+211
+00:23:07,600 --> 00:23:14,860
+عن ال identity اتحاد كل ال X في J أردر X يكون 3
+
+212
+00:23:16,060 --> 00:23:21,940
+اتحاد كل ال X في J order ال X بدي يساوي خمسة اتحاد
+
+213
+00:23:21,940 --> 00:23:28,120
+كل ال X في J order ال X بدي يساوي خمستاشر عشان
+
+214
+00:23:28,120 --> 00:23:31,600
+يكون ال X أس خمستاشر بدي يساوي ال identity ف order
+
+215
+00:23:31,600 --> 00:23:40,940
+ال X يا واحد يا تلاتة يا خمسة يا خمستاشر هذه
+
+216
+00:23:40,940 --> 00:23:47,950
+المجموعة كمانصور كمانصور هانأنصر واحد طب هذا كم
+
+217
+00:23:47,950 --> 00:23:58,690
+أنصر فايل تلاتة أكمن أنصر الأردر له خمسة فايل خمسة
+
+218
+00:23:58,690 --> 00:24:06,310
+أكمن أنصر الأردر له خمس عاش فايل خمس عاش إجبار عدد
+
+219
+00:24:06,310 --> 00:24:14,810
+عناصر ال T بيساوي واحد زاد فايل تلاتةفايل خمسة زاد
+
+220
+00:24:14,810 --> 00:24:19,910
+فايل خمستاش اللي هو واحد زاد اتنين زاد اربع فايل
+
+221
+00:24:19,910 --> 00:24:27,670
+خمستاش جديش برضه اربعة جديش المجموعة ده عشرة كم
+
+222
+00:24:27,670 --> 00:24:36,240
+انصر في ال J بحقق المعادلة ده عشرة انصرعيد بسرعة
+
+223
+00:24:36,240 --> 00:24:40,820
+علشان يكون عندى ال X أص خمس عشر بيساوي ال identity
+
+224
+00:24:40,820 --> 00:24:45,380
+أولا أنا متأكد أن في عندي عنصر ليش؟ لأن الخمس عشر
+
+225
+00:24:45,380 --> 00:24:49,360
+تقسم ال J وبالتالي في عنصر أردر الخمس عشر ممكن
+
+226
+00:24:49,360 --> 00:24:52,280
+أتأكد بطريقة تانية E أص خمس عشر بيساوي E
+
+227
+00:24:57,840 --> 00:25:01,320
+العناصر اللي بيحققوا ان X أص 15 يساوي ال identity
+
+228
+00:25:01,320 --> 00:25:05,380
+عشان انا بشتغل في ال group يا ال order واحد يا
+
+229
+00:25:05,380 --> 00:25:10,920
+تلاتة يا خمسة يا خمس عشر العناصر اللي ال order لهم
+
+230
+00:25:10,920 --> 00:25:14,440
+واحد عددهم واحد العناصر اللي ال order تلاتة فايل
+
+231
+00:25:14,440 --> 00:25:17,840
+تلاتة العناصر اللي ال order خمسة فايل خمسة
+
+232
+00:25:17,840 --> 00:25:22,020
+والعناصر اللي ال order خمس عشر فايل خمس عشر
+
+233
+00:25:22,020 --> 00:25:27,770
+المحصلةواحد زي اتنين زي اربعة زي اربعة ده عشر عنصر
+
+234
+00:25:27,770 --> 00:25:41,450
+عشان
+
+235
+00:25:41,450 --> 00:25:44,970
+تشتغل order بيسوي خمس عشر يعني اكسوس خمس عشر احنا
+
+236
+00:25:44,970 --> 00:25:47,910
+جولنا يبناها بطريقة ال order اكسوس خمس عشر سواء ال
+
+237
+00:25:47,910 --> 00:25:53,010
+identity بقى ال order يخسم الخمس عشر واحد و خمسين
+
+238
+00:25:54,660 --> 00:25:59,460
+عشان نرجع للسؤال رقم 51 no group can have exactly
+
+239
+00:25:59,460 --> 00:26:03,920
+two elements of order تنين يعني لو في عنصرين ال
+
+240
+00:26:03,920 --> 00:26:09,660
+order اللي لهم تنين ففي تالت لو في عنصرين ال order
+
+241
+00:26:09,660 --> 00:26:21,340
+اللي لهم اتنين ففي تالت let J be a group with
+
+242
+00:26:22,180 --> 00:26:27,120
+A وB ينتمي للـJ and order الـB بدي يساوي order
+
+243
+00:26:27,120 --> 00:26:33,500
+الـA بدي يساوي order الـB بدي يساوي ايش اتنين هذا
+
+244
+00:26:33,500 --> 00:26:43,860
+معناته انه A طبعا with عشان اتكلم عنهم A لا يساوي
+
+245
+00:26:43,860 --> 00:26:46,660
+بي note that
+
+246
+00:26:49,910 --> 00:26:54,430
+Order ال A بدي يسوى 2 يعني A inverse بدي يسوى A
+
+247
+00:26:54,430 --> 00:27:00,510
+Order ال B بدي يسوى 2 يعني B inverse بدي يسوى B
+
+248
+00:27:00,510 --> 00:27:03,790
+علشان ماحدش يقولي ماشي ال A لا يسوى B لأ ممكن يسوى
+
+249
+00:27:03,790 --> 00:27:12,010
+ال inverse مابيسويش ال inverse طيب
+
+250
+00:27:32,110 --> 00:27:39,730
+كيف نكمل ال A
+
+251
+00:27:39,730 --> 00:27:56,570
+و ال P بيسووا ال inverse تبعتهم مش
+
+252
+00:27:56,570 --> 00:27:56,890
+فاهم
+
+253
+00:28:03,880 --> 00:28:07,280
+طيب طب انا فرض انه فيه اثنين مدتبت انه فيه تالت لو
+
+254
+00:28:07,280 --> 00:28:12,860
+فرضت انه انه فش غير الاتنين هتروح جيب التالت و
+
+255
+00:28:12,860 --> 00:28:17,500
+تعمل تناقض يعني في نهاية نفس السياق فقط بتضيف جملة
+
+256
+00:28:17,500 --> 00:28:22,360
+و بتحط contradiction في الآخر فضل عاطف طب انا عارف
+
+257
+00:28:22,360 --> 00:28:26,820
+حال السؤال طيب
+
+258
+00:28:26,820 --> 00:28:28,140
+ايش حالك؟
+
+259
+00:28:31,380 --> 00:28:34,040
+تاخد عنصر تثبت ان ال order الأثنين غير ال a و ال b
+
+260
+00:28:34,040 --> 00:28:45,340
+زي مين a,b,a صحيح طيب now a
+
+261
+00:28:45,340 --> 00:28:51,920
+,b,a ينتمي لمين ده ال D تعالوا نشوف ال order ل a,b
+
+262
+00:28:51,920 --> 00:29:01,230
+,a a,b,a تربيع عبارة عن a,b,a,a,b,aالو عبارة عن a
+
+263
+00:29:01,230 --> 00:29:08,070
+b a تربيع بي a يعني a بي identity بي ايه a بي
+
+264
+00:29:08,070 --> 00:29:12,690
+تربيع ايه a identity ايه ايه تربيع بيسوي identity
+
+265
+00:29:12,690 --> 00:29:24,790
+معناته order ال a بي ايه مش بيسوي يا واحد يا اتنين
+
+266
+00:29:24,790 --> 00:29:33,280
+طبعا انا غلطت يعنيلأنه لو أنا بتعامل مع group
+
+267
+00:29:33,280 --> 00:29:38,860
+abelian فال a,b,a إيش هيساوي بيه أنا ماجيبتش إيش
+
+268
+00:29:38,860 --> 00:29:49,360
+جديد يقبل أنا بتضيف جملة if j is non abelian let و
+
+269
+00:29:49,360 --> 00:29:58,780
+then a,b,a في ال j طيب يقبل order ل a,b,a يا واحد
+
+270
+00:29:58,780 --> 00:29:59,260
+يا اتنين
+
+271
+00:30:02,100 --> 00:30:08,020
+ف order a,b,a بدي يسوى واحد a,b,a بدي يسوى ال
+
+272
+00:30:08,020 --> 00:30:13,200
+identity يعني a,b بدي تسوى a inverse بدي تسوى a
+
+273
+00:30:13,200 --> 00:30:17,640
+يعني a,b بدي تسوى a يعني b بدي يسوى ال identity
+
+274
+00:30:17,640 --> 00:30:28,960
+تناقض المحصلة ان order b,a بدي يسوى ايش اتنين
+
+275
+00:30:32,420 --> 00:30:36,760
+عشان اثبت ان هو انصر تالت ال order له اتنين لا بدي
+
+276
+00:30:36,760 --> 00:30:43,960
+يسوى ال a ولا بدي يسوى ال b if a,b,a بدي يسوى a,b
+
+277
+00:30:43,960 --> 00:30:47,460
+,a بدي يسوى ال identity,b بدي يسوى a inverse بدي
+
+278
+00:30:47,460 --> 00:30:56,360
+يسوى a,b بدي يسوى a تناقض if a,b,a بدي تسوى b
+
+279
+00:31:05,480 --> 00:31:10,640
+هذا معناته، مع أن النطق بيليان، مش ضروري أن ال A
+
+280
+00:31:10,640 --> 00:31:20,620
+بي تسوى بيه A، ليش بقاش راح لازم أعمل، أنا فرضت
+
+281
+00:31:20,620 --> 00:31:24,860
+أنه نمأ بيليان على مين؟ع الجيه كلها لما أنا بدي
+
+282
+00:31:24,860 --> 00:31:28,780
+أجي أقول لها انا a b بتسوى بي a inverse بتسوى بي
+
+283
+00:31:28,780 --> 00:31:34,440
+ايه يعني a b بتسوى بي ايه هذا لا يناقض انها non
+
+284
+00:31:34,440 --> 00:31:40,740
+abelian هذا لا يناقض انها non abelian طيب بدأ أروح
+
+285
+00:31:40,740 --> 00:31:44,900
+معناته أغير الفرض تبعي علشان يعطيني تناقض مع هذه
+
+286
+00:31:44,900 --> 00:31:55,060
+الجملة بدل ما أقول جيه non abelian اش عملAB لا
+
+287
+00:31:55,060 --> 00:32:01,320
+يساوي BA عشان هذه تصير تناقض مين؟ هذه وبالتالي
+
+288
+00:32:01,320 --> 00:32:13,040
+صارت تناقض so ABA is another element with
+
+289
+00:32:13,040 --> 00:32:26,570
+order 2 in J so we haveAt least كم واحد؟ الـ three
+
+290
+00:32:26,570 --> 00:32:35,850
+elements in J with order تنين
+
+291
+00:32:35,850 --> 00:32:42,530
+خلصنا؟ لأ أنا الحالة اللي ال A,B لا يساوي بيه A
+
+292
+00:32:42,530 --> 00:32:47,790
+أنهيتها طب الحالة التانية لما ال A,B يساوي بيه
+
+293
+00:32:47,790 --> 00:32:52,170
+اتفضلاللي بيساو بي إيه ليه التناقض دس فاطل التناقض
+
+294
+00:32:52,170 --> 00:33:01,090
+اللي بيساو بي إيه ليه التناقض دس فاطل
+
+295
+00:33:01,090 --> 00:33:04,270
+التناقض اللي بيساو بي إيه ليه التناقض اللي بيساو
+
+296
+00:33:04,270 --> 00:33:05,030
+بي إيه ليه التناقض اللي بيساو بي إيه ليه التناقض
+
+297
+00:33:05,030 --> 00:33:05,350
+اللي بيساو بي إيه ليه التناقض اللي بيساو بي إيه
+
+298
+00:33:05,350 --> 00:33:08,970
+ليه التناقض اللي بيساو بي إيه ليه التناقض اللي
+
+299
+00:33:08,970 --> 00:33:13,610
+بيساو بي إيه ليه التناقض اللي بيساو بي إيه ليه
+
+300
+00:33:13,610 --> 00:33:18,710
+التناقض اللي بيساو بي إيه ليه التناقض اللي بيساو ب
+
+301
+00:33:19,890 --> 00:33:25,590
+غير الـ a,b,a طيب
+
+302
+00:33:25,590 --> 00:33:36,950
+if a,b بدي سوا b,a then a,b ينتمي للـ j ال a,b
+
+303
+00:33:36,950 --> 00:33:43,670
+تربيع يعني a,b a,b يعني a تربيع b تربيع identity
+
+304
+00:33:43,670 --> 00:33:51,380
+في identity واحد عشان abelianطيب هذا معناته ان
+
+305
+00:33:51,380 --> 00:33:57,720
+order ال a,b بدت ساوي واحد او اتنين if order ال a
+
+306
+00:33:57,720 --> 00:33:59,620
+,b بدت ساوي واحد if order ال a,b بدت ساوي واحد if
+
+307
+00:33:59,620 --> 00:34:00,040
+order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+308
+00:34:00,040 --> 00:34:00,400
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+309
+00:34:00,400 --> 00:34:00,880
+ال a,b بدت ساوي واحد if order ال a,b بدت ساوي واحد
+
+310
+00:34:00,880 --> 00:34:01,900
+if order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+311
+00:34:01,900 --> 00:34:05,340
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+312
+00:34:05,340 --> 00:34:06,400
+ال a,b بدت ساوي واحد if order ال a,b بدت ساوي واحد
+
+313
+00:34:06,400 --> 00:34:09,800
+if order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+314
+00:34:09,800 --> 00:34:16,720
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+315
+00:34:16,720 --> 00:34:20,120
+الاب بدي يساوي ايه بدي بدي بدي بدي بدي بدي بدي بدي
+
+316
+00:34:20,120 --> 00:34:24,120
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+317
+00:34:24,120 --> 00:34:26,340
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+318
+00:34:26,340 --> 00:34:26,740
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+319
+00:34:26,740 --> 00:34:29,140
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+320
+00:34:29,140 --> 00:34:29,180
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+321
+00:34:29,180 --> 00:34:43,000
+بدي بدي
+
+322
+00:34:43,000 --> 00:34:50,630
+بدييجب في حالة ما يكونوا مش متبادلين بلاجي تلت
+
+323
+00:34:50,630 --> 00:34:55,310
+عناصر في حالة ما يكونوا متبادلين برضه بلاجي تلت
+
+324
+00:34:55,310 --> 00:35:00,550
+عناصر يجب مستحيل ألاجي عنصرينه بس دائما أي عنصرين
+
+325
+00:35:00,550 --> 00:35:06,490
+بيعطوني مين التالت هل في رابع خامس سادس مابخصنيش
+
+326
+00:35:06,490 --> 00:35:11,470
+بس أنا على الأقل عند مين تلتة هل ممكن ألاجي عنصر
+
+327
+00:35:11,470 --> 00:35:12,770
+واحد ال order الاتنين
+
+328
+00:35:15,280 --> 00:35:20,740
+بقدر؟ اه بقدر وين؟ مستقيل لإن معكوسه اتنين طبعا هو
+
+329
+00:35:20,740 --> 00:35:26,400
+بيساوي معكوسه في الزد اتنين في الزد اتنين اللي
+
+330
+00:35:26,400 --> 00:35:30,520
+فيها الصفر و الواحد يوجد عنصر واحد فقط ال order له
+
+331
+00:35:30,520 --> 00:35:36,060
+اتنين وهو الواحد
+
+332
+00:35:36,060 --> 00:35:41,840
+مستبدر
+
+333
+00:35:41,840 --> 00:35:44,700
+يا امان طيب
+
+334
+00:35:46,110 --> 00:35:51,350
+تنين و خمسين Given the fact that U تسعة و أربعين
+
+335
+00:35:51,350 --> 00:35:54,090
+is cyclic and has تنين و أربعين elements that use
+
+336
+00:35:54,090 --> 00:35:57,110
+the number of generator جديش عدد ال generator اللي
+
+337
+00:35:57,110 --> 00:36:03,250
+تبعون ال U تسعة و أربعين جديش ال U تسعة و أربعين
+
+338
+00:36:03,250 --> 00:36:05,770
+هي ال cyclic group و ال order لها تنين و أربعين
+
+339
+00:36:05,770 --> 00:36:13,140
+أكم generator لها فاية تنين و أربعينلما يكون عندك
+
+340
+00:36:13,140 --> 00:36:16,860
+Cyclic جروب ال order يلها N جديش عدد ال generator
+
+341
+00:36:16,860 --> 00:36:28,880
+فايل ان طبق مباشرة مانت
+
+342
+00:36:28,880 --> 00:36:37,190
+السؤال 52 الجواب تبع في 42سؤال 53 الـ A و ال B
+
+343
+00:36:37,190 --> 00:36:39,850
+elements in the group ال order ل A بدي سوى عشرة ال
+
+344
+00:36:39,850 --> 00:36:43,010
+order ل B بدي سوى واحد و عشرين show that انه
+
+345
+00:36:43,010 --> 00:36:45,590
+generated by ال A تقاطه generated by ال B بدي سوى
+
+346
+00:36:45,590 --> 00:36:52,290
+ال identity طيب يعني let X ينتمي لgenerated by ال
+
+347
+00:36:52,290 --> 00:36:57,770
+A تقاطه generated by ال B هذا
+
+348
+00:36:57,770 --> 00:37:03,380
+معناتهال X ينتمي ل generated by ال A يكبر order ال
+
+349
+00:37:03,380 --> 00:37:09,820
+X بيقسم order ال A بدي يسوي عداش عشرة ال X ينتمي ل
+
+350
+00:37:09,820 --> 00:37:14,540
+generated by ال B يكبر order ال X يقسم ال order ل
+
+351
+00:37:14,540 --> 00:37:19,220
+ال B بدي يسوي واحد و عشرين بنتو order ال X بدي
+
+352
+00:37:19,220 --> 00:37:22,320
+يقسم ل grease common divisor ل العشرة والواحد و
+
+353
+00:37:22,320 --> 00:37:27,060
+عشرين بدي يسوي واحد order ال X بدي يسوي واحد وال X
+
+354
+00:37:27,060 --> 00:37:30,770
+بدي يسوي ال identityاللي صار كالتالي انا بدي أثبت
+
+355
+00:37:30,770 --> 00:37:34,570
+ان التقاطع لا يوجد فيه غير المحايد أخدت عنصره ان
+
+356
+00:37:34,570 --> 00:37:38,930
+التقاطع ال order له بيقسم العشرة لإنه موجود في
+
+357
+00:37:38,930 --> 00:37:42,410
+group ال order له عشرة و ال order له بيقسم ال واحد
+
+358
+00:37:42,410 --> 00:37:45,690
+و عشرين لإنه موجود في group ال order له واحد و
+
+359
+00:37:45,690 --> 00:37:49,750
+عشرين بيقسم العشرة و ال واحد و عشرين هيقسم الجريس
+
+360
+00:37:49,750 --> 00:37:52,210
+common divisor لعشرة و ال واحد و عشرين و بيساوي
+
+361
+00:37:52,210 --> 00:37:58,500
+واحد مين عنصر ال order له واحد؟Generated by الـ A
+
+362
+00:37:58,500 --> 00:38:03,860
+تقاطع Generated by الـ B بيساوي ال Identity سؤال
+
+363
+00:38:03,860 --> 00:38:13,920
+54 تعميم ل 53 بس
+
+364
+00:38:13,920 --> 00:38:19,480
+بدل العشر والخمستعش M و N و ال M و N relative ال
+
+365
+00:38:19,480 --> 00:38:19,740
+prime
+
+366
+00:38:30,570 --> 00:38:39,010
+سؤال خمسة و خمسين what are possibilities of order
+
+367
+00:38:39,010 --> 00:38:44,030
+type؟
+
+368
+00:38:44,030 --> 00:38:49,510
+ال order لل a بيكون عشرة
+
+369
+00:38:49,860 --> 00:38:54,260
+فلو كان ال X ينتمي ل generated by ال A تقاطع
+
+370
+00:38:54,260 --> 00:38:58,000
+generated by ال B ف order ال X بيقسم ل grease
+
+371
+00:38:58,000 --> 00:39:03,980
+common divisor لل 24 و 10 جديش ف order ال X بيقسم
+
+372
+00:39:03,980 --> 00:39:09,060
+ل 2 يجب العلاصر اللي موجودة في التقاطع هذا ال
+
+373
+00:39:09,060 --> 00:39:18,530
+order إلا يا 1 يا 2 كم واحد؟طبعا انت بتتكلم عن
+
+374
+00:39:18,530 --> 00:39:22,130
+Cyclic group انت عندك Cyclic sub group ع Cyclic
+
+375
+00:39:22,130 --> 00:39:26,210
+sub group التقادر تبعهم Cyclic sub group هيكون ال
+
+376
+00:39:26,210 --> 00:39:31,970
+order له كم
+
+377
+00:39:31,970 --> 00:39:39,290
+أنصر ال identity هو أنصر ال order له جديش اتنين
+
+378
+00:39:39,290 --> 00:39:44,270
+يجب ال order له جديش اتنين انه هيساوي ال identity
+
+379
+00:39:47,930 --> 00:39:54,770
+و X و order X سيكون اتنين ايه بقى ال order ل هذا
+
+380
+00:39:54,770 --> 00:40:02,670
+ال generator سيكون اتنين ستة
+
+381
+00:40:02,670 --> 00:40:09,410
+و خمسين ال
+
+382
+00:40:09,410 --> 00:40:10,890
+E و تلانوس N is not
+
+383
+00:40:14,600 --> 00:40:18,520
+خلاص، ضال عندي أول سؤال ستة و خمسين، تمانية و
+
+384
+00:40:18,520 --> 00:40:20,900
+خمسين، تسعة و خمسين، أربعة، هذا سؤال مهم يا شباب
+
+385
+00:40:20,900 --> 00:40:24,820
+عشان الخامس أسئلة اللي ضايلة بنحلها في بداية
+
+386
+00:40:24,820 --> 00:40:28,900
+المحاضرة القادمة و بعد هيكت بنكمل أو بنفوض ان شاء
+
+387
+00:40:28,900 --> 00:40:30,520
+الله في الشبطة الخامس، أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..094732cb4b9dc269ff2e6b04475762cc72b9f502
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk_raw.srt
@@ -0,0 +1,1560 @@
+1
+00:00:21,500 --> 00:00:24,340
+السلام عليكم بسم الله الرحمن الرحيم اليوم ان شاء
+
+2
+00:00:24,340 --> 00:00:27,260
+الله هننهي المناقشة chapter رابع هنبدأ زي ما
+
+3
+00:00:27,260 --> 00:00:29,860
+اتوقفنا المرة الماضية السؤال سبعة و تلاتين حاليناه
+
+4
+00:00:29,860 --> 00:00:35,290
+هنبدأ من السؤال تمانية و تلاتينطبعا سؤال 38 ماعطيك
+
+5
+00:00:35,290 --> 00:00:40,210
+أربع عناصر في مجموعة بقولك أثبت إن هذي بتعمل group
+
+6
+00:00:40,210 --> 00:00:46,190
+مع عملية الضرب مد ال 20 عشان أنا أقدر أتعامل مع
+
+7
+00:00:46,190 --> 00:00:49,330
+هذا الأسئلة .. نوع من الأسئلة لما يعطيني group فيه
+
+8
+00:00:49,330 --> 00:00:53,090
+عدد محدود جدا من العناصر تلاتة أربعة خمسة ويثبت
+
+9
+00:00:53,090 --> 00:00:57,030
+إنها أو يطلب مني أن أثبت إنها group أسهل طريقة هي
+
+10
+00:00:57,030 --> 00:01:02,940
+multiplication table جدول الضربفبروح بحط التمانية
+
+11
+00:01:02,940 --> 00:01:09,060
+أو الأربعة في الأول التمانية والاتناش والستاش
+
+12
+00:01:09,060 --> 00:01:16,120
+واندي اربعة تمانية اتناش ستاش طبعا مدام الضرب
+
+13
+00:01:16,120 --> 00:01:21,920
+تقليدي يعني أنا بتعامل مع عملية ضرب صحيح مدة
+
+14
+00:01:21,920 --> 00:01:25,520
+العشرين لكن في نهاية أساسها عبارة عن إيش عن ضرب
+
+15
+00:01:25,520 --> 00:01:31,170
+أرقام فأكيد العملية هتكون إيشتبدلية اربع فى اربع
+
+16
+00:01:31,170 --> 00:01:34,730
+ستة عشر مدى العشرين ستة عشر اربع فى تمانية اتناش
+
+17
+00:01:34,730 --> 00:01:37,970
+اتنين و تلاتين مدى العشرين اتناش اربع فى اتناش
+
+18
+00:01:37,970 --> 00:01:42,810
+حياطين تمانية و اربع فى ستة عشر اربع تمانية فى
+
+19
+00:01:42,810 --> 00:01:45,850
+اربع اتنين و تلاتين باتناش تمانية فى تمانية اربع
+
+20
+00:01:45,850 --> 00:01:51,110
+وستين باربع تمانية فى اتناش بستة و تسعين يعني ستة
+
+21
+00:01:51,110 --> 00:01:57,240
+عشر و تمانية فى ستة عشر كدهشمية تمانية عشرين يعني
+
+22
+00:01:57,240 --> 00:02:01,500
+تمانية اتناش في اربعة تمانية واربعين يعني تمانية
+
+23
+00:02:01,500 --> 00:02:04,560
+اتناش في تمانية ستة وتسعين يعني ستة عشر اتناش
+
+24
+00:02:04,560 --> 00:02:08,600
+اتناش مية اربعة واربعين يعني اربعة اتناش في ستة
+
+25
+00:02:08,600 --> 00:02:13,420
+عشر هيظل اتناش طبعا ستة عشر في اربعة هيكون عبارة
+
+26
+00:02:13,420 --> 00:02:17,540
+عن اربعة وستين يظل اربعة ستة عشر في تمانية هيظل
+
+27
+00:02:17,540 --> 00:02:22,470
+تمانية واتناش وستة عشرمن الواضح انه اول حاجة
+
+28
+00:02:22,470 --> 00:02:27,070
+العملية عشانها اصلا ضرب عادي ف associative موجود
+
+29
+00:02:27,070 --> 00:02:31,050
+ال .. ال binary او ان العملية مغلقة على المجموعة
+
+30
+00:02:31,050 --> 00:02:34,390
+موجودة ماطلعش عناصر من برا المجموعة ال abelian
+
+31
+00:02:34,390 --> 00:02:43,330
+موجود في identity؟ في identity؟ في محايد؟ في ..
+
+32
+00:02:43,330 --> 00:02:49,390
+مين؟ ال 16 .. ليش؟ لأنه انا بضرب ال 16 في اي رقم
+
+33
+00:02:50,300 --> 00:02:55,120
+بيظل زي ما هو بيظل لدي ال inverse هل لكل رقم بلاجي
+
+34
+00:02:55,120 --> 00:02:59,260
+عنصر بضربه في نفسه بيعطيه ال identity بقدر أعرفه
+
+35
+00:02:59,260 --> 00:03:03,600
+لما أتأكد انه في كل سطر فيه ستة عشر وفي كل عمود
+
+36
+00:03:03,600 --> 00:03:10,400
+فيه ستة عشر وبالتالي هذا عبارة عن group ومش group
+
+37
+00:03:10,400 --> 00:03:16,840
+مش group بس لأ abelian abelian ال group what is
+
+38
+00:03:16,840 --> 00:03:19,560
+the identity هو الستة عشر هل هي ال cyclic
+
+39
+00:03:23,610 --> 00:03:28,370
+هل هي Cyclic؟ عشان تكون Cyclic شباب بديه أنصر
+
+40
+00:03:28,370 --> 00:03:33,370
+يولدها يعني بديه أنصر ال order ل 4 طبعا ال order ل
+
+41
+00:03:33,370 --> 00:03:42,090
+4 بنجيبه 4 في 4 16 بديه يساوي ال identity بقى ال
+
+42
+00:03:42,090 --> 00:03:48,270
+order ل 4 بديه يساوي 2 ال order ل 8 8 في 8 كدهش؟
+
+43
+00:03:48,990 --> 00:03:53,450
+أربعة ستين أربعة تمانية في تمانية في تمانية اتناش
+
+44
+00:03:53,450 --> 00:03:58,410
+تمانية في تمانية في تمانية في تمانية ستة عشريك
+
+45
+00:03:58,410 --> 00:04:03,630
+بأوردر التمانية بتساوي أربعة وبالتالي هذه الجروب
+
+46
+00:04:03,630 --> 00:04:10,310
+جيه generated by main من التمانية وبالتالي هي
+
+47
+00:04:10,310 --> 00:04:17,150
+Cyclic واضح السؤال ده واضح
+
+48
+00:04:17,150 --> 00:04:17,630
+السؤال
+
+49
+00:04:22,570 --> 00:04:26,490
+تسعة وتلاتين give an example of a group that has
+
+50
+00:04:26,490 --> 00:04:30,770
+that has exactly six subgroups including the
+
+51
+00:04:30,770 --> 00:04:34,210
+trivial subgroup and the group itself generalized
+
+52
+00:04:34,210 --> 00:04:38,050
+exactly any subgroup for any positive integer and
+
+53
+00:04:38,050 --> 00:04:48,690
+ايش رأيكم؟ بدك group J فيها only six subgroups
+
+54
+00:05:06,200 --> 00:05:11,860
+عشان اعطيك ال group انت تجيبها و تكون لها six
+
+55
+00:05:11,860 --> 00:05:17,100
+subgroup يعني القواسم عددهم ستة بالظبط ايش يعني
+
+56
+00:05:17,100 --> 00:05:22,260
+القواسم عددهم ستة صارت تمانية و تلاتين هذا صارت
+
+57
+00:05:22,260 --> 00:05:28,280
+تسعة و تلاتين يعني بدك ال group ال order الها n
+
+58
+00:05:29,840 --> 00:05:33,820
+وعدد قواسم الان بدي ساو ستة عشان تشتغل بناء على
+
+59
+00:05:33,820 --> 00:05:39,120
+انه تكون هادي الساكنك اعطيني جواب عدد القواسم تبع
+
+60
+00:05:39,120 --> 00:05:45,840
+ال order الها بساو ستة الاربع عشرين كام
+
+61
+00:05:45,840 --> 00:05:51,380
+قاسم؟ واحد، اتنين، تلاتة، اربع، ستة، تمانية،
+
+62
+00:05:51,380 --> 00:05:55,060
+اتناش، اربع عشرين، تمانية طيب عشان انا عارفش
+
+63
+00:05:55,060 --> 00:06:06,740
+البداية we needا group او a cyclic جيه
+
+64
+00:06:06,740 --> 00:06:17,280
+with order ال جيه بيساوي ان and الان has only six
+
+65
+00:06:17,280 --> 00:06:27,460
+divisors اعطيني group ال order لها ان والان له ستة
+
+66
+00:06:27,460 --> 00:06:28,180
+من القواسم
+
+67
+00:06:32,310 --> 00:06:38,210
+تعشى كام قاسم؟ واحد اتنين تلاتة اربع ستة اتناش
+
+68
+00:06:38,210 --> 00:06:47,010
+Take جبدة تساوياش؟ زد اتناش من ال six subgroup
+
+69
+00:06:47,010 --> 00:06:51,610
+هدول generated by واحد generated by تنين generated
+
+70
+00:06:51,610 --> 00:06:56,010
+by تلاتة generated by اربع generated by ستة
+
+71
+00:06:56,010 --> 00:07:00,410
+وgenerated by اتناش عمّمها لإيه ان؟
+
+72
+00:07:03,870 --> 00:07:13,010
+for n هنا في مشكلة شباب هنا
+
+73
+00:07:13,010 --> 00:07:17,990
+في مشكلة تبدأ
+
+74
+00:07:17,990 --> 00:07:28,730
+تشتغل على جروب عدد القواسم دي يكون إله n طيب كام
+
+75
+00:07:28,730 --> 00:07:29,450
+قاسم؟
+
+76
+00:07:32,370 --> 00:07:37,230
+خلصنا من الستة لنشغل على عدد القواسم يكونوا even
+
+77
+00:07:37,230 --> 00:07:42,270
+لو ال uneven فإيش
+
+78
+00:07:42,270 --> 00:07:49,110
+بيعمل تعالى نرجع شوية نظرية الأعداد إيش عدد
+
+79
+00:07:49,110 --> 00:07:56,750
+القواسم بيساوي؟ إيش رمز سبعة في الأول؟ تأولان؟طيب،
+
+80
+00:07:56,750 --> 00:08:04,050
+لو الان بدأ تساوي P1 P2 لعند PK K1 K2 لعند K إيش
+
+81
+00:08:04,050 --> 00:08:07,790
+تقوى الان بيساوي؟
+
+82
+00:08:07,790 --> 00:08:14,830
+إيش تقوى الان بيساوي؟ K1 زاد الواحد K2 زاد الواحد
+
+83
+00:08:14,830 --> 00:08:20,710
+لعند KR زاد الواحد عد
+
+84
+00:08:20,710 --> 00:08:30,810
+القواصم يا حبيبيعلى المهم هذا بدي ساوي N عدد
+
+85
+00:08:30,810 --> 00:08:41,830
+القواسم بدي ساوي الـ N المطلوبة اتبعوا فش غير واحد
+
+86
+00:08:41,830 --> 00:08:48,210
+زي هيك فانت بتشرح على مين N بدي تساوي K واحد زي
+
+87
+00:08:48,210 --> 00:08:52,110
+واحد خطة K زي واحديعني انت بدأت تشتغل على أن بدأت
+
+88
+00:08:52,110 --> 00:08:57,870
+تصير عندك P to K هتاخد الانبدو يساوي K زاد الواحد
+
+89
+00:08:57,870 --> 00:09:04,970
+اختار ال P بـPrime هتاخد مين أن بدأت تساوي تنين to
+
+90
+00:09:04,970 --> 00:09:08,530
+K جي
+
+91
+00:09:08,530 --> 00:09:11,910
+بدأت تساوي زد تنين to K
+
+92
+00:09:20,720 --> 00:09:26,220
+طبعا ال K بدأ تساوي N minus واحد تنين
+
+93
+00:09:26,220 --> 00:09:33,720
+to N minus واحد تنينوس N minus واحد has N divisors
+
+94
+00:09:33,720 --> 00:09:41,640
+من هما واحد، تنين، تنين تغبيع، تنين تكيب يعني تنين
+
+95
+00:09:41,640 --> 00:09:47,220
+N minus واحد هدول قواسم التنينوس N minus واحد
+
+96
+00:09:52,160 --> 00:09:59,300
+The n subgroups are generated by 1, generated by
+
+97
+00:09:59,300 --> 00:10:04,900
+2, generated by 4, generated by 8 لأن generated by
+
+98
+00:10:04,900 --> 00:10:11,320
+2 أُس n minus 1 وانت بتشغل في مين؟ في z 2 أُس n
+
+99
+00:10:11,320 --> 00:10:17,120
+minus كيف؟ اه وانا هي اللي حلته قدامك
+
+100
+00:10:22,180 --> 00:10:26,000
+أنا مش راحتش حاجة علاقة في نظرية الأعداد أنا مطلوب
+
+101
+00:10:26,000 --> 00:10:31,840
+مني أدور على رقم الو N من القواسم أي
+
+102
+00:10:31,840 --> 00:10:37,420
+P to N minus واحد الو N من القواسم احصل حالك في
+
+103
+00:10:37,420 --> 00:10:44,460
+prime واحد تمشي و بتجيب المطلوب واضح؟
+
+104
+00:10:44,460 --> 00:10:47,880
+مش
+
+105
+00:10:47,880 --> 00:10:48,500
+واضح؟
+
+106
+00:10:51,100 --> 00:10:58,260
+لأ هذا غير هذا مثال
+
+107
+00:10:58,260 --> 00:11:02,300
+بخص الستة لوحدها لو بدك تيجي على السبعة مش هتقدر
+
+108
+00:11:02,300 --> 00:11:06,460
+تيجي تاخد مثلا زد اربعة عاش لأ للستة هتقدر تاخد زد
+
+109
+00:11:06,460 --> 00:11:13,420
+تنين و نص خمس يعني زد اتنين و تلاتين اه جرب اتنين
+
+110
+00:11:13,420 --> 00:11:25,030
+اربعة اربعة اتنين اربعة تمانية16 و 32 هيهم 6 لكن
+
+111
+00:11:25,030 --> 00:11:28,990
+مش هي الوحيدة يعني مش هي الوحيدة معناه لو أخدت زد
+
+112
+00:11:28,990 --> 00:11:32,770
+تلاتة أثناء minus واحد بنفع زد سبعة أثناء minus
+
+113
+00:11:32,770 --> 00:11:40,070
+واحد بنفع في أكتر من واحدة طيب
+
+114
+00:11:40,070 --> 00:11:45,090
+سؤال 42 prove that an infinite group must have an
+
+115
+00:11:45,090 --> 00:11:51,210
+infinite number of subgroupsجي جنيريت باي الـ a و
+
+116
+00:11:51,210 --> 00:11:56,870
+order الـ a بدي يساوي مانا نهاية بدك infinite sub
+
+117
+00:11:56,870 --> 00:12:01,810
+group كيف؟
+
+118
+00:12:01,810 --> 00:12:09,030
+let a عبارة عن generated by a to i حيث اي is the
+
+119
+00:12:09,030 --> 00:12:13,770
+prime since
+
+120
+00:12:13,770 --> 00:12:27,110
+the numberof the primes is infinite عدد
+
+121
+00:12:27,110 --> 00:12:34,310
+لا نهائي فش في even أو odd and generated by a to i
+
+122
+00:12:34,310 --> 00:12:41,510
+لاتساوي generated by a to j forI لا يساوي J هل الـ
+
+123
+00:12:41,510 --> 00:12:45,130
+generated by A أو السبعة بيساوي generated by A أو
+
+124
+00:12:45,130 --> 00:12:50,090
+السحداش؟ صعب و مستحيل تقدرش تجيب ال A أو السبعة من
+
+125
+00:12:50,090 --> 00:12:52,830
+ال A أو السحداش ولا ال A أو السحداش من ال A أو
+
+126
+00:12:52,830 --> 00:12:59,990
+السبعة هدولة العداد تبعي لنهائي و أنا مافيش تكرار
+
+127
+00:12:59,990 --> 00:13:06,030
+النتيجة A has infinite number
+
+128
+00:13:08,470 --> 00:13:17,190
+of elements يوجد في ال a عدد لانهائي من العناصر كل
+
+129
+00:13:17,190 --> 00:13:22,390
+عنصر من هذه العناصر مش ممثلك where
+
+130
+00:13:22,390 --> 00:13:35,630
+each one is a cyclic subgroup of
+
+131
+00:13:35,630 --> 00:13:42,900
+Gالبعدد أنا طبعا بقدر ألاجي غيرهم بقدر لكن بشغل
+
+132
+00:13:42,900 --> 00:13:51,050
+أنا على هذا الشكل أو على هذا النمط أثر لييعني
+
+133
+00:13:51,050 --> 00:13:54,770
+اعطيك ايام مثال رقمى لو انت بتشغل في z في عندك
+
+134
+00:13:54,770 --> 00:13:58,390
+generated by تنين generated by تلاتة generated by
+
+135
+00:13:58,390 --> 00:14:03,910
+خمسة generated by سبعة generated by احداشر الى اخر
+
+136
+00:14:03,910 --> 00:14:07,690
+بتضلك الى ماله نهاية ولا واحد زى التانى هذا
+
+137
+00:14:07,690 --> 00:14:11,470
+مضاعفات الاتنين هذا مضاعفات التلاتة هذا مضاعفات
+
+138
+00:14:11,470 --> 00:14:19,480
+الخمسة هذا مضاعفات السبعةولا واحد زي فيه غيره بس
+
+139
+00:14:19,480 --> 00:14:37,400
+أنا اشتغلت عليه برايم علشان ما ..
+
+140
+00:14:37,400 --> 00:14:44,340
+سؤال خمسة واربعين بداك
+
+141
+00:14:44,340 --> 00:14:57,680
+العناصرفى z 40 اللى ال order بدى يساوي عشرة بنجيب
+
+142
+00:14:57,680 --> 00:15:04,440
+واحد اولش بنجيب عددهم و بنجيب واحد و بنرفع هذا
+
+143
+00:15:04,440 --> 00:15:10,440
+لمين ل relative prime مع العشرة the number of
+
+144
+00:15:10,440 --> 00:15:20,170
+elements in z 40with order عشرة is فايل عشرة
+
+145
+00:15:20,170 --> 00:15:25,770
+بديساوي أربع ليش
+
+146
+00:15:25,770 --> 00:15:36,630
+انت بتشغل في ZN و ZN شمالها Cyclic one of them is
+
+147
+00:15:36,630 --> 00:15:45,860
+مين A بديساوي أربعين على عشرة بديساوي الأربعالاربع
+
+148
+00:15:45,860 --> 00:15:53,580
+ال order إيه له عشرة باقي العناصر ال other
+
+149
+00:15:53,580 --> 00:15:58,780
+elements are
+
+150
+00:15:58,780 --> 00:16:03,980
+أربع أوس واحد أربع أوس ثلاثة أربع أوس سبعة أربع
+
+151
+00:16:03,980 --> 00:16:08,240
+أوس تسعة اللي هو ما عبارة عن الأربع والاتناشر
+
+152
+00:16:08,240 --> 00:16:13,940
+والتمانية وعشرين والستة وتلاتينهذا في سؤال في
+
+153
+00:16:13,940 --> 00:16:19,080
+التلخيص حلناه من هذا النمط لما تيجي تشتر على ال
+
+154
+00:16:19,080 --> 00:16:24,260
+order بيساوي أربعين list all the elements of that
+
+155
+00:16:24,260 --> 00:16:29,700
+have order عشرة هنا تعمين يعني في تكملة السؤال
+
+156
+00:16:29,700 --> 00:16:37,880
+هتاخد اللي هو اكسوس أربعةالـ X generated و X أُس
+
+157
+00:16:37,880 --> 00:16:47,000
+12 و X أُس 28 و X أُس 36 تكملة للسؤال
+
+158
+00:17:06,320 --> 00:17:11,680
+ماشي سؤال 47 بدنا نجيب عدد ال order للعناصر في D33
+
+159
+00:17:11,680 --> 00:17:19,800
+طبعا D33 عبارة عن 66 عنصر 33 منهم عبارة عن دورانات
+
+160
+00:17:19,800 --> 00:17:26,480
+و33 التانين عبارة عن reflection الدورانات بيبدو ب
+
+161
+00:17:26,480 --> 00:17:37,460
+R0 R 360 على 33 وصولنا ل R N-1يعني تنين و تلاتين
+
+162
+00:17:37,460 --> 00:17:43,240
+على تلاتة و تلاتين في تلات مية و ستين وبعدين بيبدو
+
+163
+00:17:43,240 --> 00:17:48,500
+ب F واحد F في اتنين لان F في تلاتة و تلاتين
+
+164
+00:17:48,500 --> 00:17:54,980
+الأولانية التواغنات والباجي عبارة عن reflections
+
+165
+00:17:54,980 --> 00:18:02,350
+ال order لأي F I بيساوي اتنينلأن انت لما تعمل
+
+166
+00:18:02,350 --> 00:18:09,130
+انعكاس وتعكس الانعكاس بيرجع مكانه ال order لري
+
+167
+00:18:09,130 --> 00:18:15,310
+ماشي بده يساوي طبعا
+
+168
+00:18:15,310 --> 00:18:22,130
+هدول عبارة عن ر اي في تلاتمية او تلاتمية وستين
+
+169
+00:18:22,130 --> 00:18:29,030
+مثلا ك على تلاتة و تلاتين والك
+
+170
+00:18:32,470 --> 00:18:40,730
+محصور بين الـ 32 والـ 0 بناجيب ال orders اللي باق
+
+171
+00:18:40,730 --> 00:18:45,250
+العناصر اللي هي عبارة عن الدورانات كل عنصر بهذا
+
+172
+00:18:45,250 --> 00:18:49,430
+الشكل ال order إلوش هيكون
+
+173
+00:18:55,620 --> 00:19:00,300
+انساش هدول شباب هذا أشبه بالـ Zero هذا بالواحد هذا
+
+174
+00:19:00,300 --> 00:19:05,380
+بالتنين هذا بالتنين و تلاتين يعني هم زي عناصر مين
+
+175
+00:19:05,380 --> 00:19:10,320
+ال Z تلاتة و تلاتين يعني هم كلهم أصلا هذا ال
+
+176
+00:19:10,320 --> 00:19:16,340
+answer ال R تلاتمية و ستين K ع تلاتة و تلاتين
+
+177
+00:19:16,340 --> 00:19:22,460
+عبارة عن ال R تلاتمية و ستين ع تلاتة و تلاتين أس K
+
+178
+00:19:25,710 --> 00:19:36,130
+طيب يعني لو أخدت انا لت مثلا A عبارة عن R 360 على
+
+179
+00:19:36,130 --> 00:19:43,110
+33 هيكون ال order لل A جديش اللي هو اللي بولد
+
+180
+00:19:43,110 --> 00:19:50,950
+الجزئية هذه من ال D 33 ال order له 33 فانت لما بدك
+
+181
+00:19:50,950 --> 00:19:52,570
+تيجي تتعامل مع ال order
+
+182
+00:19:57,580 --> 00:20:02,520
+لار تلاتمية و ستين كي على تلاتة و تلاتين اللي هو
+
+183
+00:20:02,520 --> 00:20:07,160
+عبارة عن ال order ل a to k ايش ال order ل a to k
+
+184
+00:20:07,160 --> 00:20:13,780
+عبارة عن تلاتة و تلاتين على الجريس common divisor
+
+185
+00:20:13,780 --> 00:20:19,940
+لكيه تلاتة و تلاتين و
+
+186
+00:20:19,940 --> 00:20:26,360
+حسب ايش في عندك عناصر هان بطلع ال order يلو بهذا
+
+187
+00:20:26,360 --> 00:20:32,610
+الشكلعيد بسرعة دي تلاتة و تلاتين جزئين جزء سهل
+
+188
+00:20:32,610 --> 00:20:36,150
+اللي هو reflections كل عنصر ال order له اتنين و
+
+189
+00:20:36,150 --> 00:20:43,990
+جزء بشابه مين ال zn فال order له لو انا اخدت اتبعت
+
+190
+00:20:43,990 --> 00:20:49,030
+ال a هو ال generator فكل عنصر مثلا عبارة عن ال a
+
+191
+00:20:49,030 --> 00:20:53,330
+تصم k و ال order ل a تكيه عبارة عن التلاتة و
+
+192
+00:20:53,330 --> 00:20:56,350
+تلاتين اللي هو order ال a على guess common divisor
+
+193
+00:20:56,350 --> 00:21:04,230
+لkو تلاتة و تلاتين طيب
+
+194
+00:21:04,230 --> 00:21:17,230
+تمانية
+
+195
+00:21:17,230 --> 00:21:21,170
+و أربعينif j is cyclic group and خمس طعش divide by
+
+196
+00:21:21,170 --> 00:21:24,950
+order of j then the number of solution of j of
+
+197
+00:21:24,950 --> 00:21:32,630
+equation x to خمس طعش سوى a j is cyclic خمس طعش
+
+198
+00:21:32,630 --> 00:21:41,530
+تقسم order of j وانا ب dash على x أُس خمس طعش بدي
+
+199
+00:21:41,530 --> 00:21:42,330
+سوى ال identity
+
+200
+00:21:54,710 --> 00:21:57,970
+أوجد عدد العناصر اللي بيحلوا المعادلة هذه في الـ j
+
+201
+00:21:57,970 --> 00:22:07,670
+طبعا since ال 15 تقسم ال order لل j و ال j is
+
+202
+00:22:07,670 --> 00:22:15,850
+cyclic هذا معناته يوجد a ينتمي لل j with a أُس 15
+
+203
+00:22:15,850 --> 00:22:21,750
+او with order ال a بدي يساوي 15 احنا قولنا نظريةأو
+
+204
+00:22:21,750 --> 00:22:25,990
+caller على نظرية لأي group لو في قاسم بيقسم ال
+
+205
+00:22:25,990 --> 00:22:30,370
+order إليها ففي عنصر في ال group هذه ال order اللي
+
+206
+00:22:30,370 --> 00:22:37,590
+بيسوي هذا القاسم هذا معناته the set H أو بلاش H
+
+207
+00:22:37,590 --> 00:22:41,830
+عشان ماتفكر أشهر بال group the set T عبارة عن كل X
+
+208
+00:22:41,830 --> 00:22:47,270
+في J X أُس 15 بدي يساوي ال identity is none أو is
+
+209
+00:22:47,270 --> 00:22:56,500
+not emptyهذه المجموعة غير خالية لماذا؟
+
+210
+00:22:56,500 --> 00:23:07,600
+لأن هناك أنصار موجودة فيها نستطيع أن نكتب T عبارة
+
+211
+00:23:07,600 --> 00:23:14,860
+عن ال identity اتحاد كل ال X في J أردر X يكون 3
+
+212
+00:23:16,060 --> 00:23:21,940
+اتحاد كل ال X في J order ال X بدي يساوي خمسة اتحاد
+
+213
+00:23:21,940 --> 00:23:28,120
+كل ال X في J order ال X بدي يساوي خمستاشر عشان
+
+214
+00:23:28,120 --> 00:23:31,600
+يكون ال X أس خمستاشر بدي يساوي ال identity ف order
+
+215
+00:23:31,600 --> 00:23:40,940
+ال X يا واحد يا تلاتة يا خمسة يا خمستاشر هذه
+
+216
+00:23:40,940 --> 00:23:47,950
+المجموعة كمانصور كمانصور هانأنصر واحد طب هذا كم
+
+217
+00:23:47,950 --> 00:23:58,690
+أنصر فايل تلاتة أكمن أنصر الأردر له خمسة فايل خمسة
+
+218
+00:23:58,690 --> 00:24:06,310
+أكمن أنصر الأردر له خمس عاش فايل خمس عاش إجبار عدد
+
+219
+00:24:06,310 --> 00:24:14,810
+عناصر ال T بيساوي واحد زاد فايل تلاتةفايل خمسة زاد
+
+220
+00:24:14,810 --> 00:24:19,910
+فايل خمستاش اللي هو واحد زاد اتنين زاد اربع فايل
+
+221
+00:24:19,910 --> 00:24:27,670
+خمستاش جديش برضه اربعة جديش المجموعة ده عشرة كم
+
+222
+00:24:27,670 --> 00:24:36,240
+انصر في ال J بحقق المعادلة ده عشرة انصرعيد بسرعة
+
+223
+00:24:36,240 --> 00:24:40,820
+علشان يكون عندى ال X أص خمس عشر بيساوي ال identity
+
+224
+00:24:40,820 --> 00:24:45,380
+أولا أنا متأكد أن في عندي عنصر ليش؟ لأن الخمس عشر
+
+225
+00:24:45,380 --> 00:24:49,360
+تقسم ال J وبالتالي في عنصر أردر الخمس عشر ممكن
+
+226
+00:24:49,360 --> 00:24:52,280
+أتأكد بطريقة تانية E أص خمس عشر بيساوي E
+
+227
+00:24:57,840 --> 00:25:01,320
+العناصر اللي بيحققوا ان X أص 15 يساوي ال identity
+
+228
+00:25:01,320 --> 00:25:05,380
+عشان انا بشتغل في ال group يا ال order واحد يا
+
+229
+00:25:05,380 --> 00:25:10,920
+تلاتة يا خمسة يا خمس عشر العناصر اللي ال order لهم
+
+230
+00:25:10,920 --> 00:25:14,440
+واحد عددهم واحد العناصر اللي ال order تلاتة فايل
+
+231
+00:25:14,440 --> 00:25:17,840
+تلاتة العناصر اللي ال order خمسة فايل خمسة
+
+232
+00:25:17,840 --> 00:25:22,020
+والعناصر اللي ال order خمس عشر فايل خمس عشر
+
+233
+00:25:22,020 --> 00:25:27,770
+المحصلةواحد زي اتنين زي اربعة زي اربعة ده عشر عنصر
+
+234
+00:25:27,770 --> 00:25:41,450
+عشان
+
+235
+00:25:41,450 --> 00:25:44,970
+تشتغل order بيسوي خمس عشر يعني اكسوس خمس عشر احنا
+
+236
+00:25:44,970 --> 00:25:47,910
+جولنا يبناها بطريقة ال order اكسوس خمس عشر سواء ال
+
+237
+00:25:47,910 --> 00:25:53,010
+identity بقى ال order يخسم الخمس عشر واحد و خمسين
+
+238
+00:25:54,660 --> 00:25:59,460
+عشان نرجع للسؤال رقم 51 no group can have exactly
+
+239
+00:25:59,460 --> 00:26:03,920
+two elements of order تنين يعني لو في عنصرين ال
+
+240
+00:26:03,920 --> 00:26:09,660
+order اللي لهم تنين ففي تالت لو في عنصرين ال order
+
+241
+00:26:09,660 --> 00:26:21,340
+اللي لهم اتنين ففي تالت let J be a group with
+
+242
+00:26:22,180 --> 00:26:27,120
+A وB ينتمي للـJ and order الـB بدي يساوي order
+
+243
+00:26:27,120 --> 00:26:33,500
+الـA بدي يساوي order الـB بدي يساوي ايش اتنين هذا
+
+244
+00:26:33,500 --> 00:26:43,860
+معناته انه A طبعا with عشان اتكلم عنهم A لا يساوي
+
+245
+00:26:43,860 --> 00:26:46,660
+بي note that
+
+246
+00:26:49,910 --> 00:26:54,430
+Order ال A بدي يسوى 2 يعني A inverse بدي يسوى A
+
+247
+00:26:54,430 --> 00:27:00,510
+Order ال B بدي يسوى 2 يعني B inverse بدي يسوى B
+
+248
+00:27:00,510 --> 00:27:03,790
+علشان ماحدش يقولي ماشي ال A لا يسوى B لأ ممكن يسوى
+
+249
+00:27:03,790 --> 00:27:12,010
+ال inverse مابيسويش ال inverse طيب
+
+250
+00:27:32,110 --> 00:27:39,730
+كيف نكمل ال A
+
+251
+00:27:39,730 --> 00:27:56,570
+و ال P بيسووا ال inverse تبعتهم مش
+
+252
+00:27:56,570 --> 00:27:56,890
+فاهم
+
+253
+00:28:03,880 --> 00:28:07,280
+طيب طب انا فرض انه فيه اثنين مدتبت انه فيه تالت لو
+
+254
+00:28:07,280 --> 00:28:12,860
+فرضت انه انه فش غير الاتنين هتروح جيب التالت و
+
+255
+00:28:12,860 --> 00:28:17,500
+تعمل تناقض يعني في نهاية نفس السياق فقط بتضيف جملة
+
+256
+00:28:17,500 --> 00:28:22,360
+و بتحط contradiction في الآخر فضل عاطف طب انا عارف
+
+257
+00:28:22,360 --> 00:28:26,820
+حال السؤال طيب
+
+258
+00:28:26,820 --> 00:28:28,140
+ايش حالك؟
+
+259
+00:28:31,380 --> 00:28:34,040
+تاخد عنصر تثبت ان ال order الأثنين غير ال a و ال b
+
+260
+00:28:34,040 --> 00:28:45,340
+زي مين a,b,a صحيح طيب now a
+
+261
+00:28:45,340 --> 00:28:51,920
+,b,a ينتمي لمين ده ال D تعالوا نشوف ال order ل a,b
+
+262
+00:28:51,920 --> 00:29:01,230
+,a a,b,a تربيع عبارة عن a,b,a,a,b,aالو عبارة عن a
+
+263
+00:29:01,230 --> 00:29:08,070
+b a تربيع بي a يعني a بي identity بي ايه a بي
+
+264
+00:29:08,070 --> 00:29:12,690
+تربيع ايه a identity ايه ايه تربيع بيسوي identity
+
+265
+00:29:12,690 --> 00:29:24,790
+معناته order ال a بي ايه مش بيسوي يا واحد يا اتنين
+
+266
+00:29:24,790 --> 00:29:33,280
+طبعا انا غلطت يعنيلأنه لو أنا بتعامل مع group
+
+267
+00:29:33,280 --> 00:29:38,860
+abelian فال a,b,a إيش هيساوي بيه أنا ماجيبتش إيش
+
+268
+00:29:38,860 --> 00:29:49,360
+جديد يقبل أنا بتضيف جملة if j is non abelian let و
+
+269
+00:29:49,360 --> 00:29:58,780
+then a,b,a في ال j طيب يقبل order ل a,b,a يا واحد
+
+270
+00:29:58,780 --> 00:29:59,260
+يا اتنين
+
+271
+00:30:02,100 --> 00:30:08,020
+ف order a,b,a بدي يسوى واحد a,b,a بدي يسوى ال
+
+272
+00:30:08,020 --> 00:30:13,200
+identity يعني a,b بدي تسوى a inverse بدي تسوى a
+
+273
+00:30:13,200 --> 00:30:17,640
+يعني a,b بدي تسوى a يعني b بدي يسوى ال identity
+
+274
+00:30:17,640 --> 00:30:28,960
+تناقض المحصلة ان order b,a بدي يسوى ايش اتنين
+
+275
+00:30:32,420 --> 00:30:36,760
+عشان اثبت ان هو انصر تالت ال order له اتنين لا بدي
+
+276
+00:30:36,760 --> 00:30:43,960
+يسوى ال a ولا بدي يسوى ال b if a,b,a بدي يسوى a,b
+
+277
+00:30:43,960 --> 00:30:47,460
+,a بدي يسوى ال identity,b بدي يسوى a inverse بدي
+
+278
+00:30:47,460 --> 00:30:56,360
+يسوى a,b بدي يسوى a تناقض if a,b,a بدي تسوى b
+
+279
+00:31:05,480 --> 00:31:10,640
+هذا معناته، مع أن النطق بيليان، مش ضروري أن ال A
+
+280
+00:31:10,640 --> 00:31:20,620
+بي تسوى بيه A، ليش بقاش راح لازم أعمل، أنا فرضت
+
+281
+00:31:20,620 --> 00:31:24,860
+أنه نمأ بيليان على مين؟ع الجيه كلها لما أنا بدي
+
+282
+00:31:24,860 --> 00:31:28,780
+أجي أقول لها انا a b بتسوى بي a inverse بتسوى بي
+
+283
+00:31:28,780 --> 00:31:34,440
+ايه يعني a b بتسوى بي ايه هذا لا يناقض انها non
+
+284
+00:31:34,440 --> 00:31:40,740
+abelian هذا لا يناقض انها non abelian طيب بدأ أروح
+
+285
+00:31:40,740 --> 00:31:44,900
+معناته أغير الفرض تبعي علشان يعطيني تناقض مع هذه
+
+286
+00:31:44,900 --> 00:31:55,060
+الجملة بدل ما أقول جيه non abelian اش عملAB لا
+
+287
+00:31:55,060 --> 00:32:01,320
+يساوي BA عشان هذه تصير تناقض مين؟ هذه وبالتالي
+
+288
+00:32:01,320 --> 00:32:13,040
+صارت تناقض so ABA is another element with
+
+289
+00:32:13,040 --> 00:32:26,570
+order 2 in J so we haveAt least كم واحد؟ الـ three
+
+290
+00:32:26,570 --> 00:32:35,850
+elements in J with order تنين
+
+291
+00:32:35,850 --> 00:32:42,530
+خلصنا؟ لأ أنا الحالة اللي ال A,B لا يساوي بيه A
+
+292
+00:32:42,530 --> 00:32:47,790
+أنهيتها طب الحالة التانية لما ال A,B يساوي بيه
+
+293
+00:32:47,790 --> 00:32:52,170
+اتفضلاللي بيساو بي إيه ليه التناقض دس فاطل التناقض
+
+294
+00:32:52,170 --> 00:33:01,090
+اللي بيساو بي إيه ليه التناقض دس فاطل
+
+295
+00:33:01,090 --> 00:33:04,270
+التناقض اللي بيساو بي إيه ليه التناقض اللي بيساو
+
+296
+00:33:04,270 --> 00:33:05,030
+بي إيه ليه التناقض اللي بيساو بي إيه ليه التناقض
+
+297
+00:33:05,030 --> 00:33:05,350
+اللي بيساو بي إيه ليه التناقض اللي بيساو بي إيه
+
+298
+00:33:05,350 --> 00:33:08,970
+ليه التناقض اللي بيساو بي إيه ليه التناقض اللي
+
+299
+00:33:08,970 --> 00:33:13,610
+بيساو بي إيه ليه التناقض اللي بيساو بي إيه ليه
+
+300
+00:33:13,610 --> 00:33:18,710
+التناقض اللي بيساو بي إيه ليه التناقض اللي بيساو ب
+
+301
+00:33:19,890 --> 00:33:25,590
+غير الـ a,b,a طيب
+
+302
+00:33:25,590 --> 00:33:36,950
+if a,b بدي سوا b,a then a,b ينتمي للـ j ال a,b
+
+303
+00:33:36,950 --> 00:33:43,670
+تربيع يعني a,b a,b يعني a تربيع b تربيع identity
+
+304
+00:33:43,670 --> 00:33:51,380
+في identity واحد عشان abelianطيب هذا معناته ان
+
+305
+00:33:51,380 --> 00:33:57,720
+order ال a,b بدت ساوي واحد او اتنين if order ال a
+
+306
+00:33:57,720 --> 00:33:59,620
+,b بدت ساوي واحد if order ال a,b بدت ساوي واحد if
+
+307
+00:33:59,620 --> 00:34:00,040
+order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+308
+00:34:00,040 --> 00:34:00,400
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+309
+00:34:00,400 --> 00:34:00,880
+ال a,b بدت ساوي واحد if order ال a,b بدت ساوي واحد
+
+310
+00:34:00,880 --> 00:34:01,900
+if order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+311
+00:34:01,900 --> 00:34:05,340
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+312
+00:34:05,340 --> 00:34:06,400
+ال a,b بدت ساوي واحد if order ال a,b بدت ساوي واحد
+
+313
+00:34:06,400 --> 00:34:09,800
+if order ال a,b بدت ساوي واحد if order ال a,b بدت
+
+314
+00:34:09,800 --> 00:34:16,720
+ساوي واحد if order ال a,b بدت ساوي واحد if order
+
+315
+00:34:16,720 --> 00:34:20,120
+الاب بدي يساوي ايه بدي بدي بدي بدي بدي بدي بدي بدي
+
+316
+00:34:20,120 --> 00:34:24,120
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+317
+00:34:24,120 --> 00:34:26,340
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+318
+00:34:26,340 --> 00:34:26,340
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+319
+00:34:26,340 --> 00:34:26,340
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+320
+00:34:26,340 --> 00:34:26,740
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+321
+00:34:26,740 --> 00:34:26,740
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+322
+00:34:26,740 --> 00:34:29,140
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+323
+00:34:29,140 --> 00:34:29,180
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+324
+00:34:29,180 --> 00:34:43,000
+بدي بدي
+
+325
+00:34:43,000 --> 00:34:50,630
+بدييجب في حالة ما يكونوا مش متبادلين بلاجي تلت
+
+326
+00:34:50,630 --> 00:34:55,310
+عناصر في حالة ما يكونوا متبادلين برضه بلاجي تلت
+
+327
+00:34:55,310 --> 00:35:00,550
+عناصر يجب مستحيل ألاجي عنصرينه بس دائما أي عنصرين
+
+328
+00:35:00,550 --> 00:35:06,490
+بيعطوني مين التالت هل في رابع خامس سادس مابخصنيش
+
+329
+00:35:06,490 --> 00:35:11,470
+بس أنا على الأقل عند مين تلتة هل ممكن ألاجي عنصر
+
+330
+00:35:11,470 --> 00:35:12,770
+واحد ال order الاتنين
+
+331
+00:35:15,280 --> 00:35:20,740
+بقدر؟ اه بقدر وين؟ مستقيل لإن معكوسه اتنين طبعا هو
+
+332
+00:35:20,740 --> 00:35:26,400
+بيساوي معكوسه في الزد اتنين في الزد اتنين اللي
+
+333
+00:35:26,400 --> 00:35:30,520
+فيها الصفر و الواحد يوجد عنصر واحد فقط ال order له
+
+334
+00:35:30,520 --> 00:35:36,060
+اتنين وهو الواحد
+
+335
+00:35:36,060 --> 00:35:41,840
+مستبدر
+
+336
+00:35:41,840 --> 00:35:44,700
+يا امان طيب
+
+337
+00:35:46,110 --> 00:35:51,350
+تنين و خمسين Given the fact that U تسعة و أربعين
+
+338
+00:35:51,350 --> 00:35:54,090
+is cyclic and has تنين و أربعين elements that use
+
+339
+00:35:54,090 --> 00:35:57,110
+the number of generator جديش عدد ال generator اللي
+
+340
+00:35:57,110 --> 00:36:03,250
+تبعون ال U تسعة و أربعين جديش ال U تسعة و أربعين
+
+341
+00:36:03,250 --> 00:36:05,770
+هي ال cyclic group و ال order لها تنين و أربعين
+
+342
+00:36:05,770 --> 00:36:13,140
+أكم generator لها فاية تنين و أربعينلما يكون عندك
+
+343
+00:36:13,140 --> 00:36:16,860
+Cyclic جروب ال order يلها N جديش عدد ال generator
+
+344
+00:36:16,860 --> 00:36:28,880
+فايل ان طبق مباشرة مانت
+
+345
+00:36:28,880 --> 00:36:37,190
+السؤال 52 الجواب تبع في 42سؤال 53 الـ A و ال B
+
+346
+00:36:37,190 --> 00:36:39,850
+elements in the group ال order ل A بدي سوى عشرة ال
+
+347
+00:36:39,850 --> 00:36:43,010
+order ل B بدي سوى واحد و عشرين show that انه
+
+348
+00:36:43,010 --> 00:36:45,590
+generated by ال A تقاطه generated by ال B بدي سوى
+
+349
+00:36:45,590 --> 00:36:52,290
+ال identity طيب يعني let X ينتمي لgenerated by ال
+
+350
+00:36:52,290 --> 00:36:57,770
+A تقاطه generated by ال B هذا
+
+351
+00:36:57,770 --> 00:37:03,380
+معناتهال X ينتمي ل generated by ال A يكبر order ال
+
+352
+00:37:03,380 --> 00:37:09,820
+X بيقسم order ال A بدي يسوي عداش عشرة ال X ينتمي ل
+
+353
+00:37:09,820 --> 00:37:14,540
+generated by ال B يكبر order ال X يقسم ال order ل
+
+354
+00:37:14,540 --> 00:37:19,220
+ال B بدي يسوي واحد و عشرين بنتو order ال X بدي
+
+355
+00:37:19,220 --> 00:37:22,320
+يقسم ل grease common divisor ل العشرة والواحد و
+
+356
+00:37:22,320 --> 00:37:27,060
+عشرين بدي يسوي واحد order ال X بدي يسوي واحد وال X
+
+357
+00:37:27,060 --> 00:37:30,770
+بدي يسوي ال identityاللي صار كالتالي انا بدي أثبت
+
+358
+00:37:30,770 --> 00:37:34,570
+ان التقاطع لا يوجد فيه غير المحايد أخدت عنصره ان
+
+359
+00:37:34,570 --> 00:37:38,930
+التقاطع ال order له بيقسم العشرة لإنه موجود في
+
+360
+00:37:38,930 --> 00:37:42,410
+group ال order له عشرة و ال order له بيقسم ال واحد
+
+361
+00:37:42,410 --> 00:37:45,690
+و عشرين لإنه موجود في group ال order له واحد و
+
+362
+00:37:45,690 --> 00:37:49,750
+عشرين بيقسم العشرة و ال واحد و عشرين هيقسم الجريس
+
+363
+00:37:49,750 --> 00:37:52,210
+common divisor لعشرة و ال واحد و عشرين و بيساوي
+
+364
+00:37:52,210 --> 00:37:58,500
+واحد مين عنصر ال order له واحد؟Generated by الـ A
+
+365
+00:37:58,500 --> 00:38:03,860
+تقاطع Generated by الـ B بيساوي ال Identity سؤال
+
+366
+00:38:03,860 --> 00:38:13,920
+54 تعميم ل 53 بس
+
+367
+00:38:13,920 --> 00:38:19,480
+بدل العشر والخمستعش M و N و ال M و N relative ال
+
+368
+00:38:19,480 --> 00:38:19,740
+prime
+
+369
+00:38:30,570 --> 00:38:39,010
+سؤال خمسة و خمسين what are possibilities of order
+
+370
+00:38:39,010 --> 00:38:44,030
+type؟
+
+371
+00:38:44,030 --> 00:38:49,510
+ال order لل a بيكون عشرة
+
+372
+00:38:49,860 --> 00:38:54,260
+فلو كان ال X ينتمي ل generated by ال A تقاطع
+
+373
+00:38:54,260 --> 00:38:58,000
+generated by ال B ف order ال X بيقسم ل grease
+
+374
+00:38:58,000 --> 00:39:03,980
+common divisor لل 24 و 10 جديش ف order ال X بيقسم
+
+375
+00:39:03,980 --> 00:39:09,060
+ل 2 يجب العلاصر اللي موجودة في التقاطع هذا ال
+
+376
+00:39:09,060 --> 00:39:18,530
+order إلا يا 1 يا 2 كم واحد؟طبعا انت بتتكلم عن
+
+377
+00:39:18,530 --> 00:39:22,130
+Cyclic group انت عندك Cyclic sub group ع Cyclic
+
+378
+00:39:22,130 --> 00:39:26,210
+sub group التقادر تبعهم Cyclic sub group هيكون ال
+
+379
+00:39:26,210 --> 00:39:31,970
+order له كم
+
+380
+00:39:31,970 --> 00:39:39,290
+أنصر ال identity هو أنصر ال order له جديش اتنين
+
+381
+00:39:39,290 --> 00:39:44,270
+يجب ال order له جديش اتنين انه هيساوي ال identity
+
+382
+00:39:47,930 --> 00:39:54,770
+و X و order X سيكون اتنين ايه بقى ال order ل هذا
+
+383
+00:39:54,770 --> 00:40:02,670
+ال generator سيكون اتنين ستة
+
+384
+00:40:02,670 --> 00:40:09,410
+و خمسين ال
+
+385
+00:40:09,410 --> 00:40:10,890
+E و تلانوس N is not
+
+386
+00:40:14,600 --> 00:40:18,520
+خلاص، ضال عندي أول سؤال ستة و خمسين، تمانية و
+
+387
+00:40:18,520 --> 00:40:20,900
+خمسين، تسعة و خمسين، أربعة، هذا سؤال مهم يا شباب
+
+388
+00:40:20,900 --> 00:40:24,820
+عشان الخامس أسئلة اللي ضايلة بنحلها في بداية
+
+389
+00:40:24,820 --> 00:40:28,900
+المحاضرة القادمة و بعد هيكت بنكمل أو بنفوض ان شاء
+
+390
+00:40:28,900 --> 00:40:30,520
+الله في الشبطة الخامس، أعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eNtIlTkhU3g_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eNtIlTkhU3g_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e1096da055f6a7354bf4915cda9df456588b4aaf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eNtIlTkhU3g_raw.json
@@ -0,0 +1 @@
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"text": "المعادلة هذه كلها بدى ضربها فى الرقم بى اللى انا بدى اثبت انه P بتقسمه يبقى لو ضربناه فى بيصير عندى A B S زايد B T B بدى يساوي من بى الان ال P بتقسم ال A فى B هذا معطى", "tokens": [45340, 3615, 18513, 37977, 29538, 28242, 11296, 47525, 7578, 48812, 25513, 11296, 6156, 7578, 34892, 4587, 2304, 4724, 7578, 13672, 7578, 1975, 8315, 47525, 7578, 1975, 12984, 3555, 2655, 16472, 3224, 430, 39894, 4587, 38251, 3224, 7251, 3555, 4587, 7578, 45164, 48812, 25513, 8315, 3224, 6156, 7578, 4724, 1829, 9381, 13546, 43242, 7578, 316, 363, 318, 30767, 995, 25708, 363, 314, 363, 47525, 7578, 7251, 3794, 995, 45865, 9154, 4724, 7578, 2423, 7649, 2423, 430, 39894, 4587, 38251, 2423, 316, 6156, 7578, 363, 23758, 20449, 9566, 7578], "avg_logprob": -0.3149857907132669, "compression_ratio": 1.7469135802469136, "no_speech_prob": 0.0, "words": [{"start": 625.28, "end": 625.94, "word": "المعادلة", "probability": 0.8773193359375}, {"start": 625.94, "end": 626.18, "word": " هذه", "probability": 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640.66, "word": " B", "probability": 0.83203125}, {"start": 640.66, "end": 641.08, "word": " هذا", "probability": 0.9345703125}, {"start": 641.08, "end": 642.06, "word": " معطى", "probability": 0.7989908854166666}], "temperature": 1.0}, {"id": 27, "seek": 66923, "start": 642.45, "end": 669.23, "text": "إذا ال P بتقسم الرقم هذا كله اتنين ال P بتقسم ال P تي بي معناته ال P بتقسم مجموعة الإتنين مدام تقسم مجموعة الإتنين إذا بتقسم بي وهو المطلوب طب السؤال هو لو P ماكنش prime هل اللمة هذه بتظل صحيحة أم لا هذا تساؤل", "tokens": [28814, 15730, 2423, 430, 39894, 4587, 38251, 34892, 4587, 2304, 23758, 28242, 3224, 1975, 2655, 1863, 9957, 2423, 430, 39894, 4587, 38251, 2423, 430, 6055, 1829, 4724, 1829, 20449, 8315, 47395, 2423, 430, 39894, 4587, 38251, 3714, 7435, 2304, 2407, 27884, 33688, 2655, 1863, 9957, 3714, 3215, 10943, 6055, 4587, 38251, 3714, 7435, 2304, 2407, 27884, 33688, 2655, 1863, 9957, 11933, 15730, 39894, 4587, 38251, 4724, 1829, 37037, 2407, 9673, 9566, 1211, 37746, 23032, 3555, 21136, 33604, 6027, 31439, 45164, 430, 19446, 19452, 8592, 5835, 8032, 1211, 13672, 2304, 3660, 29538, 39894, 19913, 1211, 20328, 5016, 1829, 5016, 3660, 5551, 2304, 20193, 23758, 6055, 3794, 5718, 97, 1211], "avg_logprob": -0.22290711610689076, "compression_ratio": 1.9836065573770492, "no_speech_prob": 0.0, "words": [{"start": 642.45, "end": 642.91, "word": "إذا", "probability": 0.55157470703125}, {"start": 642.91, "end": 643.15, "word": " ال", "probability": 0.521484375}, {"start": 643.15, "end": 643.33, "word": " P", "probability": 0.45263671875}, {"start": 643.33, "end": 643.95, "word": " بتقسم", "probability": 0.87353515625}, {"start": 643.95, "end": 644.53, "word": " الرقم", "probability": 0.9763997395833334}, {"start": 644.53, "end": 644.91, "word": " هذا", "probability": 0.79052734375}, {"start": 644.91, "end": 645.67, "word": " كله", "probability": 0.980224609375}, {"start": 645.67, "end": 646.45, "word": " اتنين", "probability": 0.7940673828125}, {"start": 646.45, "end": 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"probability": 0.82257080078125}, {"start": 653.67, "end": 654.33, "word": " مدام", "probability": 0.5935872395833334}, {"start": 654.33, "end": 654.79, "word": " تقسم", "probability": 0.96142578125}, {"start": 654.79, "end": 655.21, "word": " مجموعة", "probability": 0.93349609375}, {"start": 655.21, "end": 655.67, "word": " الإتنين", "probability": 0.9788818359375}, {"start": 655.67, "end": 655.91, "word": " إذا", "probability": 0.8193359375}, {"start": 655.91, "end": 656.51, "word": " بتقسم", "probability": 0.9197591145833334}, {"start": 656.51, "end": 657.91, "word": " بي", "probability": 0.6961669921875}, {"start": 657.91, "end": 658.71, "word": " وهو", "probability": 0.7822265625}, {"start": 658.71, "end": 659.61, "word": " المطلوب", "probability": 0.843994140625}, {"start": 659.61, "end": 659.85, "word": " طب", "probability": 0.580322265625}, {"start": 659.85, "end": 660.41, "word": " السؤال", "probability": 0.99658203125}, {"start": 660.41, "end": 660.73, "word": " هو", "probability": 0.97998046875}, {"start": 660.73, "end": 661.67, "word": " لو", "probability": 0.92236328125}, {"start": 661.67, "end": 662.01, "word": " P", "probability": 0.9736328125}, {"start": 662.01, "end": 662.81, "word": " ماكنش", "probability": 0.81103515625}, {"start": 662.81, "end": 663.53, "word": " prime", "probability": 0.5478515625}, {"start": 663.53, "end": 664.49, "word": " هل", "probability": 0.95166015625}, {"start": 664.49, "end": 665.05, "word": " اللمة", "probability": 0.636962890625}, {"start": 665.05, "end": 665.37, "word": " هذه", "probability": 0.7255859375}, {"start": 665.37, "end": 665.79, "word": " بتظل", "probability": 0.7234700520833334}, {"start": 665.79, "end": 666.63, "word": " صحيحة", "probability": 0.9806640625}, {"start": 666.63, "end": 666.97, "word": " أم", "probability": 0.78662109375}, {"start": 666.97, "end": 667.45, "word": " لا", "probability": 0.873046875}, {"start": 667.45, "end": 668.61, "word": " هذا", "probability": 0.347412109375}, {"start": 668.61, "end": 669.23, "word": " تساؤل", "probability": 0.88623046875}], "temperature": 1.0}, {"id": 28, "seek": 69720, "start": 670.26, "end": 697.2, "text": "في الشمكانية في الشمكانية يبقى ضروري لازم يكون P Prime طبعا هعطيك مثال على كل منها الان لو جينا قولنا خدلي الملاحظة هذه اللي احنا سألناكوا ياها فبعدين بقول note if ال P is not a prime", "tokens": [41185, 25124, 2304, 41361, 10632, 8978, 25124, 2304, 41361, 10632, 7251, 3555, 4587, 7578, 48812, 2288, 13063, 1829, 5296, 31377, 2304, 7251, 30544, 430, 9655, 23032, 3555, 3615, 995, 8032, 3615, 9566, 1829, 4117, 50113, 6027, 15844, 28242, 9154, 11296, 2423, 7649, 45164, 10874, 1829, 8315, 12174, 12610, 8315, 16490, 3215, 20292, 9673, 15040, 5016, 19913, 3660, 29538, 13672, 1829, 1975, 5016, 8315, 8608, 10721, 1211, 8315, 4117, 14407, 35186, 11296, 6156, 3555, 22488, 9957, 4724, 39648, 3637, 498, 2423, 430, 307, 406, 257, 5835], "avg_logprob": -0.22165698194226555, "compression_ratio": 1.6451612903225807, "no_speech_prob": 0.0, "words": [{"start": 670.26, "end": 670.48, "word": "في", "probability": 0.505859375}, {"start": 670.48, "end": 671.3, "word": " الشمكانية", "probability": 0.7196044921875}, {"start": 671.3, "end": 672.12, "word": " في", "probability": 0.45849609375}, {"start": 672.12, "end": 672.82, "word": " الشمكانية", "probability": 0.978759765625}, {"start": 672.82, "end": 673.3, "word": " يبقى", "probability": 0.9078369140625}, {"start": 673.3, "end": 673.92, "word": " ضروري", "probability": 0.959228515625}, {"start": 673.92, "end": 674.28, "word": " لازم", "probability": 0.83935546875}, {"start": 674.28, "end": 674.58, "word": " يكون", "probability": 0.982421875}, {"start": 674.58, "end": 674.76, "word": " P", "probability": 0.5576171875}, {"start": 674.76, "end": 675.12, "word": " Prime", "probability": 0.2333984375}, {"start": 675.12, "end": 675.72, "word": " طبعا", "probability": 0.9630126953125}, {"start": 675.72, "end": 676.18, "word": " هعطيك", "probability": 0.8179931640625}, {"start": 676.18, "end": 676.62, "word": " مثال", "probability": 0.982666015625}, {"start": 676.62, "end": 676.88, "word": " على", "probability": 0.86181640625}, {"start": 676.88, "end": 677.28, "word": " كل", "probability": 0.982421875}, {"start": 677.28, "end": 678.62, "word": " منها", "probability": 0.81201171875}, {"start": 678.62, "end": 679.82, "word": " الان", "probability": 0.6405029296875}, {"start": 679.82, "end": 680.58, "word": " لو", "probability": 0.9619140625}, {"start": 680.58, "end": 681.0, "word": " جينا", "probability": 0.9840494791666666}, {"start": 681.0, "end": 681.72, "word": " قولنا", "probability": 0.84521484375}, {"start": 681.72, "end": 682.38, "word": " خدلي", "probability": 0.7262369791666666}, {"start": 682.38, "end": 683.4, "word": " الملاحظة", "probability": 0.8966796875}, {"start": 683.4, "end": 683.84, "word": " هذه", "probability": 0.66015625}, {"start": 683.84, "end": 684.54, "word": " اللي", "probability": 0.923095703125}, {"start": 684.54, "end": 684.82, "word": " احنا", "probability": 0.8986002604166666}, {"start": 684.82, "end": 685.8, "word": " سألناكوا", "probability": 0.8229166666666666}, {"start": 685.8, "end": 686.42, "word": " ياها", "probability": 0.5960693359375}, {"start": 686.42, "end": 687.3, "word": " فبعدين", "probability": 0.8006591796875}, {"start": 687.3, "end": 687.78, "word": " بقول", "probability": 0.959228515625}, {"start": 687.78, "end": 688.46, "word": " note", "probability": 0.40673828125}, {"start": 688.46, "end": 691.62, "word": " if", "probability": 0.73583984375}, {"start": 691.62, "end": 693.12, "word": " ال", "probability": 0.73583984375}, {"start": 693.12, "end": 693.42, "word": " P", "probability": 0.966796875}, {"start": 693.42, "end": 694.64, "word": " is", "probability": 0.92724609375}, {"start": 694.64, "end": 695.98, "word": " not", "probability": 0.96337890625}, {"start": 695.98, "end": 696.68, "word": " a", "probability": 0.97021484375}, {"start": 696.68, "end": 697.2, "word": " prime", "probability": 0.76708984375}], "temperature": 1.0}, {"id": 29, "seek": 72183, "start": 698.39, "end": 721.83, "text": "لو ماكنش prime ليه above لما false يبقى هذه ماهياش صحيحة for example for example", "tokens": [1211, 2407, 19446, 19452, 8592, 5835, 32239, 3224, 3673, 5296, 15042, 7908, 7251, 3555, 4587, 7578, 29538, 19446, 3224, 1829, 33599, 20328, 5016, 1829, 5016, 3660, 337, 1365, 337, 1365], "avg_logprob": -0.2351310512711925, "compression_ratio": 1.1443298969072164, "no_speech_prob": 0.0, "words": [{"start": 698.39, "end": 698.81, "word": "لو", "probability": 0.937255859375}, {"start": 698.81, "end": 699.51, "word": " ماكنش", "probability": 0.77197265625}, {"start": 699.51, "end": 700.15, "word": " prime", "probability": 0.178466796875}, {"start": 700.15, "end": 701.91, "word": " ليه", "probability": 0.749267578125}, {"start": 701.91, "end": 704.21, "word": " above", "probability": 0.82568359375}, {"start": 704.21, "end": 707.01, "word": " لما", "probability": 0.7408447265625}, {"start": 707.01, "end": 709.79, "word": " false", "probability": 0.80517578125}, {"start": 709.79, "end": 711.71, "word": " يبقى", "probability": 0.8370361328125}, {"start": 711.71, "end": 712.01, "word": " هذه", "probability": 0.6416015625}, {"start": 712.01, "end": 712.69, "word": " ماهياش", "probability": 0.926513671875}, {"start": 712.69, "end": 713.65, "word": " صحيحة", "probability": 0.90087890625}, {"start": 713.65, "end": 714.59, "word": " for", "probability": 0.91259765625}, {"start": 714.59, "end": 715.31, "word": " example", "probability": 0.96826171875}, {"start": 715.31, "end": 720.03, "word": " for", "probability": 0.9287109375}, {"start": 720.03, "end": 721.83, "word": " example", "probability": 0.927734375}], "temperature": 1.0}, {"id": 30, "seek": 74017, "start": 724.51, "end": 740.17, "text": "الست بتقسم الأربعة ضرب تلاتة مظبوط أربعة في تلاتة باطماشي ستة بتقسم اتناشي but الست لا تقسم الأربعة", "tokens": [6027, 14851, 39894, 4587, 38251, 16247, 25513, 27884, 48812, 25513, 6055, 1211, 9307, 3660, 3714, 19913, 3555, 2407, 9566, 5551, 25513, 27884, 8978, 6055, 1211, 9307, 3660, 4724, 41193, 2304, 33599, 1829, 8608, 2655, 3660, 39894, 4587, 38251, 1975, 2655, 1863, 33599, 1829, 457, 2423, 14851, 20193, 6055, 4587, 38251, 16247, 25513, 27884], "avg_logprob": -0.22106481536670966, "compression_ratio": 1.7281553398058251, "no_speech_prob": 0.0, "words": [{"start": 724.51, "end": 725.33, "word": "الست", "probability": 0.80517578125}, {"start": 725.33, "end": 726.75, "word": " بتقسم", "probability": 0.888671875}, {"start": 726.75, "end": 727.55, "word": " الأربعة", "probability": 0.8746744791666666}, {"start": 727.55, "end": 728.01, "word": " ضرب", "probability": 0.9697265625}, {"start": 728.01, "end": 728.95, "word": " تلاتة", "probability": 0.9237060546875}, {"start": 728.95, "end": 730.49, "word": " مظبوط", "probability": 0.83251953125}, {"start": 730.49, "end": 731.57, "word": " أربعة", "probability": 0.76513671875}, {"start": 731.57, "end": 731.67, "word": " في", "probability": 0.7294921875}, {"start": 731.67, "end": 732.29, "word": " تلاتة", "probability": 0.985107421875}, {"start": 732.29, "end": 732.97, "word": " باطماشي", "probability": 0.503955078125}, {"start": 732.97, "end": 733.29, "word": " ستة", "probability": 0.7545572916666666}, {"start": 733.29, "end": 733.73, "word": " بتقسم", "probability": 0.9298502604166666}, {"start": 733.73, "end": 734.85, "word": " اتناشي", "probability": 0.8041015625}, {"start": 734.85, "end": 735.37, "word": " but", "probability": 0.406982421875}, {"start": 735.37, "end": 738.11, "word": " الست", "probability": 0.779052734375}, {"start": 738.11, "end": 738.61, "word": " لا", "probability": 0.89501953125}, {"start": 738.61, "end": 739.45, "word": " تقسم", "probability": 0.994140625}, {"start": 739.45, "end": 740.17, "word": " الأربعة", "probability": 0.9729817708333334}], "temperature": 1.0}, {"id": 31, "seek": 77089, "start": 741.25, "end": 770.89, "text": "و كذلك ال 6 لا تقسم ال 3 لماذا؟ لأن ال 6 ليس أمامي يبقى هنا لأن ال 6 ليس أمامي يبقى ضروري جدا لكي تقسم واحد منهم لازم تكون P عند أمامي", "tokens": [2407, 9122, 8848, 23275, 2423, 1386, 20193, 6055, 4587, 38251, 2423, 805, 32767, 45636, 995, 22807, 5296, 33456, 2423, 1386, 32239, 3794, 5551, 2304, 10943, 1829, 7251, 3555, 4587, 7578, 34105, 5296, 33456, 2423, 1386, 32239, 3794, 5551, 2304, 10943, 1829, 7251, 3555, 4587, 7578, 48812, 2288, 13063, 1829, 10874, 28259, 5296, 4117, 1829, 6055, 4587, 38251, 36764, 24401, 9154, 16095, 5296, 31377, 2304, 6055, 30544, 430, 43242, 5551, 2304, 10943, 1829], "avg_logprob": -0.2754708904109589, "compression_ratio": 1.7238805970149254, "no_speech_prob": 0.0, "words": [{"start": 741.25, "end": 741.65, "word": "و", "probability": 0.9091796875}, {"start": 741.65, "end": 742.91, "word": " كذلك", "probability": 0.7906087239583334}, {"start": 742.91, "end": 744.15, "word": " ال", "probability": 0.57861328125}, {"start": 744.15, "end": 744.61, "word": " 6", "probability": 0.321044921875}, {"start": 744.61, "end": 745.09, "word": " لا", "probability": 0.84716796875}, {"start": 745.09, "end": 746.03, "word": " تقسم", "probability": 0.97998046875}, {"start": 746.03, "end": 746.47, "word": " ال", "probability": 0.3701171875}, {"start": 746.47, "end": 748.05, "word": " 3", "probability": 0.662109375}, {"start": 748.05, "end": 749.25, "word": " لماذا؟", "probability": 0.74542236328125}, {"start": 749.25, "end": 749.59, "word": " لأن", "probability": 0.87939453125}, {"start": 749.59, "end": 749.73, "word": " ال", "probability": 0.243408203125}, {"start": 749.73, "end": 750.01, "word": " 6", "probability": 0.93115234375}, {"start": 750.01, "end": 750.65, "word": " ليس", "probability": 0.78125}, {"start": 750.65, "end": 751.47, "word": " أمامي", "probability": 0.3861083984375}, {"start": 751.47, "end": 752.63, "word": " يبقى", "probability": 0.8189697265625}, {"start": 752.63, "end": 753.07, "word": " هنا", "probability": 0.97412109375}, {"start": 753.07, "end": 754.49, "word": 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"probability": 0.88671875}, {"start": 1139.89, "end": 1140.29, "word": " form", "probability": 0.923828125}, {"start": 1140.29, "end": 1140.79, "word": " a", "probability": 0.80419921875}, {"start": 1140.79, "end": 1141.75, "word": " يسوى", "probability": 0.7823486328125}, {"start": 1141.75, "end": 1142.31, "word": " P1", "probability": 0.67724609375}, {"start": 1142.31, "end": 1142.99, "word": " α1", "probability": 0.5223388671875}, {"start": 1142.99, "end": 1143.61, "word": " P2", "probability": 0.906494140625}, {"start": 1143.61, "end": 1144.29, "word": " α2", "probability": 0.97998046875}, {"start": 1144.29, "end": 1144.83, "word": " مضرب", "probability": 0.7771809895833334}, {"start": 1144.83, "end": 1145.09, "word": " في", "probability": 0.90185546875}, {"start": 1145.09, "end": 1145.77, "word": " PN", "probability": 0.6715087890625}, {"start": 1145.77, "end": 1146.53, "word": " αN", "probability": 0.785888671875}], "temperature": 1.0}, {"id": 45, "seek": 115909, "start": 1146.82, "end": 1159.1, "text": "الـ P1 والـ P2 والـ PN كلهم الـ Primes وبدي أدرج من الأصغر للأكبر يعني مين أصغر الـ Prime عندى؟ اتنين اللي بعده .. اللي بعده", "tokens": [6027, 39184, 430, 16, 16070, 39184, 430, 17, 16070, 39184, 430, 45, 28242, 16095, 2423, 39184, 2114, 1532, 46599, 16254, 5551, 3215, 47341, 9154, 16247, 9381, 17082, 2288, 24976, 10721, 4117, 26890, 37495, 22653, 3714, 9957, 5551, 9381, 17082, 2288, 2423, 39184, 9655, 43242, 7578, 22807, 1975, 2655, 1863, 9957, 13672, 1829, 39182, 3224, 4386, 13672, 1829, 39182, 3224], "avg_logprob": -0.32447917660077413, "compression_ratio": 1.5338345864661653, "no_speech_prob": 0.0, "words": [{"start": 1146.82, "end": 1147.26, "word": "الـ", "probability": 0.5408935546875}, {"start": 1147.26, "end": 1147.68, "word": " P1", "probability": 0.8720703125}, {"start": 1147.68, "end": 1148.0, "word": " والـ", "probability": 0.53125}, {"start": 1148.0, "end": 1148.36, "word": " P2", "probability": 0.9775390625}, {"start": 1148.36, "end": 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موجود عندك بيقول حيث ال P1 أقل من P2 أقل من PN والأسس هذه ال exponents الأسس Alpha 1 و Alpha 2 كلهم بالموجة نبدأ ناخد مثلا أمثلة السابعة", "tokens": [6027, 20292, 39182, 3224, 37037, 4117, 15730, 47525, 3224, 7251, 19913, 1211, 3714, 33599, 1829, 23758, 2423, 5835, 11331, 10859, 9566, 11296, 24976, 10721, 3794, 3794, 13672, 1829, 47525, 4117, 1829, 11296, 11331, 35457, 23032, 21292, 27884, 34892, 4587, 2304, 13672, 1829, 3714, 29245, 23328, 43242, 4117, 4724, 1829, 39648, 11331, 1829, 12984, 2423, 430, 16, 5551, 4587, 1211, 9154, 430, 17, 5551, 4587, 1211, 9154, 430, 45, 16070, 10721, 3794, 3794, 29538, 2423, 12680, 791, 16247, 3794, 3794, 20588, 502, 4032, 20588, 568, 28242, 16095, 20666, 2304, 29245, 3660, 8717, 44510, 10721, 8717, 47283, 3215, 50113, 15040, 5551, 2304, 12984, 37977, 21136, 16758, 27884], "avg_logprob": -0.21786557334773946, "compression_ratio": 1.5974025974025974, "no_speech_prob": 0.0, "words": [{"start": 1159.51, "end": 1159.91, "word": "اللي", "probability": 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تمام أربعة اللي هي اتنين ترابيع في خمسة اللي هي اتنين prime والخمسة أس واحد واتنين أس اتنين يبقى Alpha واحد باتنين وAlpha اتنين بقداش بواحد يعني هنا لو جيت قولت for example", "tokens": [1829, 3555, 4587, 7578, 23758, 5835, 5296, 5016, 6027, 3224, 3714, 5016, 1211, 45164, 16490, 1211, 9381, 8978, 8592, 32771, 13546, 3224, 23032, 1829, 3555, 45164, 10874, 36081, 12174, 12610, 2655, 6225, 46309, 9957, 6225, 46309, 9957, 13672, 1829, 39896, 5551, 25513, 27884, 8978, 16490, 2304, 3794, 3660, 46811, 10943, 5551, 25513, 27884, 13672, 1829, 39896, 1975, 2655, 1863, 9957, 6055, 2288, 16758, 40228, 8978, 16490, 2304, 3794, 3660, 13672, 1829, 39896, 1975, 2655, 1863, 9957, 5835, 16070, 9778, 2304, 3794, 3660, 5551, 3794, 36764, 24401, 4032, 9307, 1863, 9957, 5551, 3794, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 20588, 36764, 24401, 4724, 9307, 1863, 9957, 4032, 9171, 7211, 1975, 2655, 1863, 9957, 4724, 28543, 33599, 4724, 14407, 24401, 37495, 22653, 34105, 45164, 10874, 36081, 12174, 12610, 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" واحد", "probability": 0.977783203125}, {"start": 1202.76, "end": 1203.4, "word": " واتنين", "probability": 0.89013671875}, {"start": 1203.4, "end": 1203.8, "word": " أس", "probability": 0.92822265625}, {"start": 1203.8, "end": 1204.4, "word": " اتنين", "probability": 0.96533203125}, {"start": 1204.4, "end": 1205.28, "word": " يبقى", "probability": 0.9871826171875}, {"start": 1205.28, "end": 1205.64, "word": " Alpha", "probability": 0.38330078125}, {"start": 1205.64, "end": 1206.36, "word": " واحد", "probability": 0.988037109375}, {"start": 1206.36, "end": 1207.14, "word": " باتنين", "probability": 0.8277587890625}, {"start": 1207.14, "end": 1207.68, "word": " وAlpha", "probability": 0.8108723958333334}, {"start": 1207.68, "end": 1208.12, "word": " اتنين", "probability": 0.949462890625}, {"start": 1208.12, "end": 1208.84, "word": " بقداش", "probability": 0.8429361979166666}, {"start": 1208.84, "end": 1209.96, "word": " بواحد", "probability": 0.9178059895833334}, {"start": 1209.96, "end": 1210.38, "word": " يعني", "probability": 0.947021484375}, {"start": 1210.38, "end": 1210.72, "word": " هنا", "probability": 0.697265625}, {"start": 1210.72, "end": 1210.98, "word": " لو", "probability": 0.958984375}, {"start": 1210.98, "end": 1211.3, "word": " جيت", "probability": 0.975830078125}, {"start": 1211.3, "end": 1211.74, "word": " قولت", "probability": 0.9464518229166666}, {"start": 1211.74, "end": 1212.0, "word": " for", "probability": 0.9248046875}, {"start": 1212.0, "end": 1212.64, "word": " example", "probability": 0.978515625}], "temperature": 1.0}, {"id": 48, "seek": 124355, "start": 1213.75, "end": 1243.55, "text": "for example لو جيت قلت عشرين عشرين تساوي أربعة في خمسة يساوي اتنين تربيع في خمسة اطلع الاتنين ال prime والخمسة ال prime الاتنين الأصغر والخمسة أكبر منه طبقا ل ال conditional والأسس اللي عندنا هذه موجبة طيب لو جيت قلت على سبيل المثال ستين", "tokens": [2994, 1365, 45164, 10874, 36081, 12174, 1211, 2655, 6225, 46309, 9957, 6225, 46309, 9957, 6055, 3794, 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"probability": 0.89453125}, {"start": 1233.67, "end": 1234.15, "word": " منه", "probability": 0.94775390625}, {"start": 1234.15, "end": 1235.11, "word": " طبقا", "probability": 0.8685302734375}, {"start": 1235.11, "end": 1235.15, "word": " ل", "probability": 0.260986328125}, {"start": 1235.15, "end": 1235.31, "word": " ال", "probability": 0.58837890625}, {"start": 1235.31, "end": 1235.75, "word": " conditional", "probability": 0.46484375}, {"start": 1235.75, "end": 1236.81, "word": " والأسس", "probability": 0.66510009765625}, {"start": 1236.81, "end": 1237.05, "word": " اللي", "probability": 0.85107421875}, {"start": 1237.05, "end": 1237.47, "word": " عندنا", "probability": 0.906494140625}, {"start": 1237.47, "end": 1237.77, "word": " هذه", "probability": 0.255615234375}, {"start": 1237.77, "end": 1239.03, "word": " موجبة", "probability": 0.8932291666666666}, {"start": 1239.03, "end": 1240.03, "word": " طيب", "probability": 0.95263671875}, {"start": 1240.03, "end": 1240.39, "word": " لو", "probability": 0.92431640625}, {"start": 1240.39, "end": 1240.73, "word": " جيت", "probability": 0.89306640625}, {"start": 1240.73, "end": 1241.09, "word": " قلت", "probability": 0.9855143229166666}, {"start": 1241.09, "end": 1241.31, "word": " على", "probability": 0.9306640625}, {"start": 1241.31, "end": 1241.67, "word": " سبيل", "probability": 0.9923502604166666}, {"start": 1241.67, "end": 1242.23, "word": " المثال", "probability": 0.94873046875}, {"start": 1242.23, "end": 1243.55, "word": " ستين", "probability": 0.9737955729166666}], "temperature": 1.0}, {"id": 49, "seek": 125814, "start": 1249.24, "end": 1258.14, "text": "أربعة في خمستاش بستين يعني أربعة في خمستاش", "tokens": [10721, 25513, 27884, 8978, 16490, 2304, 14851, 33599, 4724, 14851, 9957, 37495, 22653, 5551, 25513, 27884, 8978, 16490, 2304, 14851, 33599], "avg_logprob": -0.25408381901004096, "compression_ratio": 1.305084745762712, "no_speech_prob": 0.0, "words": [{"start": 1249.24, "end": 1250.64, "word": "أربعة", "probability": 0.63458251953125}, {"start": 1250.64, "end": 1250.74, "word": " في", "probability": 0.85693359375}, {"start": 1250.74, "end": 1251.58, "word": " خمستاش", "probability": 0.92919921875}, {"start": 1251.58, "end": 1253.72, "word": " بستين", "probability": 0.7683919270833334}, {"start": 1253.72, "end": 1254.82, "word": " يعني", "probability": 0.792724609375}, {"start": 1254.82, "end": 1256.1, "word": " أربعة", "probability": 0.8515625}, {"start": 1256.1, "end": 1256.72, "word": " في", "probability": 0.98486328125}, {"start": 1256.72, "end": 1258.14, "word": " خمستاش", "probability": 0.971923828125}], "temperature": 1.0}, {"id": 50, "seek": 128436, "start": 1258.79, "end": 1284.37, "text": "طب الأربعة هذه عبارة عن اتنين تربية و الخمستاشر تلاتة في خمسة يبقى تلاتة كذلك في خمسة يبقى اتنين تربية تلاتة في خمسة اتنين ا prime و التلاتة prime و الخمسة prime و الأسس اتنين واحد واحد عادي جدا لو جيتي قولتلك مش ستين كبرها كتير مثلا تلاتمية و ستين", "tokens": [9566, 3555, 16247, 25513, 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"probability": 0.939453125}, {"start": 1265.95, "end": 1266.85, "word": " تلاتة", "probability": 0.9791259765625}, {"start": 1266.85, "end": 1267.53, "word": " كذلك", "probability": 0.9401041666666666}, {"start": 1267.53, "end": 1267.75, "word": " في", "probability": 0.97607421875}, {"start": 1267.75, "end": 1268.39, "word": " خمسة", "probability": 0.9910888671875}, {"start": 1268.39, "end": 1269.11, "word": " يبقى", "probability": 0.9754638671875}, {"start": 1269.11, "end": 1269.73, "word": " اتنين", "probability": 0.963623046875}, {"start": 1269.73, "end": 1270.57, "word": " تربية", "probability": 0.90869140625}, {"start": 1270.57, "end": 1271.63, "word": " تلاتة", "probability": 0.9735107421875}, {"start": 1271.63, "end": 1271.83, "word": " في", "probability": 0.98681640625}, {"start": 1271.83, "end": 1272.47, "word": " خمسة", "probability": 0.996826171875}, {"start": 1272.47, "end": 1273.37, "word": " اتنين", "probability": 0.9588623046875}, {"start": 1273.37, "end": 1273.43, "word": " ا", "probability": 0.194580078125}, {"start": 1273.43, "end": 1273.75, "word": " prime", "probability": 0.347412109375}, {"start": 1273.75, "end": 1273.91, "word": " و", "probability": 0.53466796875}, {"start": 1273.91, "end": 1274.45, "word": " التلاتة", "probability": 0.9012451171875}, {"start": 1274.45, "end": 1274.85, "word": " prime", "probability": 0.6181640625}, {"start": 1274.85, "end": 1275.05, "word": " و", "probability": 0.9501953125}, {"start": 1275.05, "end": 1275.73, "word": " الخمسة", "probability": 0.980712890625}, {"start": 1275.73, "end": 1276.07, "word": " prime", "probability": 0.927734375}, {"start": 1276.07, "end": 1276.25, "word": " و", "probability": 0.92626953125}, {"start": 1276.25, "end": 1276.61, "word": " الأسس", "probability": 0.74462890625}, {"start": 1276.61, "end": 1277.01, "word": " اتنين", "probability": 0.9813232421875}, {"start": 1277.01, "end": 1277.37, "word": " واحد", "probability": 0.951904296875}, {"start": 1277.37, "end": 1277.81, 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0.9856770833333334}, {"start": 1367.73, "end": 1368.03, "word": " اسمه", "probability": 0.9228515625}, {"start": 1368.03, "end": 1368.77, "word": " المضاعف", "probability": 0.946044921875}, {"start": 1368.77, "end": 1369.73, "word": " المشترك", "probability": 0.984375}, {"start": 1369.73, "end": 1370.71, "word": " الأصغر", "probability": 0.9434814453125}], "temperature": 1.0}, {"id": 55, "seek": 139979, "start": 1371.01, "end": 1399.79, "text": "هذا اللي بيجي ناخده لما نوحد المقامات في المرحلة الابتدائية و الاعدادية مش خدناه هذا لما يكون عندك رقامين أو كاسرين بيبقى توحد المقامات و تشوف القاسرين قد إيش بتساوي يبقى هنعطي التعريف التالي اللي هو definition the least common multiple the least common multiple", "tokens": [3224, 15730, 13672, 1829, 4724, 1829, 7435, 1829, 8717, 47283, 3215, 3224, 5296, 15042, 8717, 2407, 24401, 9673, 4587, 10943, 9307, 8978, 9673, 2288, 5016, 37977, 42963, 3555, 2655, 3215, 16373, 10632, 4032, 42963, 22488, 18513, 10632, 37893, 16490, 3215, 8315, 3224, 23758, 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1372.51, "end": 1373.85, "word": " نوحد", "probability": 0.5227864583333334}, {"start": 1373.85, "end": 1375.07, "word": " المقامات", "probability": 0.9830322265625}, {"start": 1375.07, "end": 1375.53, "word": " في", "probability": 0.65966796875}, {"start": 1375.53, "end": 1376.07, "word": " المرحلة", "probability": 0.97998046875}, {"start": 1376.07, "end": 1376.89, "word": " الابتدائية", "probability": 0.8385009765625}, {"start": 1376.89, "end": 1377.11, "word": " و", "probability": 0.654296875}, {"start": 1377.11, "end": 1377.83, "word": " الاعدادية", "probability": 0.8740234375}, {"start": 1377.83, "end": 1378.03, "word": " مش", "probability": 0.57861328125}, {"start": 1378.03, "end": 1378.55, "word": " خدناه", "probability": 0.6978759765625}, {"start": 1378.55, "end": 1378.85, "word": " هذا", "probability": 0.68505859375}, {"start": 1378.85, "end": 1379.49, "word": " لما", "probability": 0.9375}, {"start": 1379.49, "end": 1379.77, "word": " يكون", "probability": 0.932861328125}, {"start": 1379.77, "end": 1380.27, "word": " عندك", "probability": 0.98486328125}, {"start": 1380.27, "end": 1381.07, "word": " رقامين", "probability": 0.8365478515625}, {"start": 1381.07, "end": 1381.27, "word": " أو", "probability": 0.54736328125}, {"start": 1381.27, "end": 1382.37, "word": " كاسرين", "probability": 0.8333740234375}, {"start": 1382.37, "end": 1382.57, "word": " بيبقى", "probability": 0.623486328125}, {"start": 1382.57, "end": 1383.09, "word": " توحد", "probability": 0.7102864583333334}, {"start": 1383.09, "end": 1383.79, "word": " المقامات", "probability": 0.968505859375}, {"start": 1383.79, "end": 1383.89, "word": " و", "probability": 0.404052734375}, {"start": 1383.89, "end": 1384.11, "word": " تشوف", "probability": 0.97265625}, {"start": 1384.11, "end": 1384.71, "word": " القاسرين", "probability": 0.78338623046875}, {"start": 1384.71, "end": 1384.93, "word": " قد", "probability": 0.6904296875}, {"start": 1384.93, "end": 1385.07, "word": " إيش", "probability": 0.7099202473958334}, {"start": 1385.07, "end": 1385.75, "word": " بتساوي", "probability": 0.6533203125}, {"start": 1385.75, "end": 1386.69, "word": " يبقى", "probability": 0.835205078125}, {"start": 1386.69, "end": 1387.19, "word": " هنعطي", "probability": 0.737109375}, {"start": 1387.19, "end": 1387.91, "word": " التعريف", "probability": 0.9715576171875}, {"start": 1387.91, "end": 1388.57, "word": " التالي", "probability": 0.98828125}, {"start": 1388.57, "end": 1388.77, "word": " اللي", "probability": 0.806640625}, {"start": 1388.77, "end": 1388.97, "word": " هو", "probability": 0.9853515625}, {"start": 1388.97, "end": 1389.69, "word": " definition", "probability": 0.71435546875}, {"start": 1389.69, "end": 1391.73, "word": " the", "probability": 0.6943359375}, {"start": 1391.73, "end": 1392.13, "word": " least", "probability": 0.9423828125}, {"start": 1392.13, "end": 1392.53, "word": " common", "probability": 0.916015625}, {"start": 1392.53, "end": 1393.39, "word": " multiple", "probability": 0.93115234375}, {"start": 1393.39, "end": 1394.23, "word": " the", "probability": 0.483154296875}, {"start": 1394.23, "end": 1395.95, "word": " least", "probability": 0.951171875}, {"start": 1395.95, "end": 1396.91, "word": " common", "probability": 0.923828125}, {"start": 1396.91, "end": 1399.79, "word": " multiple", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 56, "seek": 142472, "start": 1402.68, "end": 1424.72, "text": "least common multiple of two non-zero integers a and b is the smallest", "tokens": [306, 525, 2689, 3866, 295, 732, 2107, 12, 32226, 41674, 257, 293, 272, 307, 264, 16998], "avg_logprob": -0.3857996323529412, "compression_ratio": 1.0606060606060606, "no_speech_prob": 0.0, "words": [{"start": 1402.68, "end": 1403.22, "word": "least", "probability": 0.50634765625}, {"start": 1403.22, "end": 1403.56, "word": " common", "probability": 0.91259765625}, {"start": 1403.56, "end": 1404.22, "word": " multiple", "probability": 0.92578125}, {"start": 1404.22, "end": 1405.2, "word": " of", "probability": 0.908203125}, {"start": 1405.2, "end": 1409.42, "word": " two", "probability": 0.8408203125}, {"start": 1409.42, "end": 1410.86, "word": " non", "probability": 0.96337890625}, {"start": 1410.86, "end": 1412.52, "word": "-zero", "probability": 0.670654296875}, {"start": 1412.52, "end": 1414.72, "word": " integers", "probability": 0.9501953125}, {"start": 1414.72, "end": 1417.0, "word": " a", "probability": 0.373291015625}, {"start": 1417.0, "end": 1417.4, "word": " and", "probability": 0.87353515625}, {"start": 1417.4, "end": 1421.2, "word": " b", "probability": 0.994140625}, {"start": 1421.2, "end": 1422.56, "word": " is", "probability": 0.63623046875}, {"start": 1422.56, "end": 1423.78, "word": " the", "probability": 0.86767578125}, {"start": 1423.78, "end": 1424.72, "word": " smallest", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 57, "seek": 145927, "start": 1431.05, "end": 1459.27, "text": "positive integer positive integer that is multiple of both a and b", "tokens": [30010, 2187, 24922, 3353, 24922, 300, 307, 3866, 295, 1293, 257, 293, 272], "avg_logprob": -0.37081472149917055, "compression_ratio": 1.1578947368421053, "no_speech_prob": 0.0, "words": [{"start": 1431.05, "end": 1431.69, "word": "positive", "probability": 0.551605224609375}, {"start": 1431.69, "end": 1432.45, "word": " integer", "probability": 0.90087890625}, {"start": 1432.45, "end": 1438.93, "word": " positive", "probability": 0.48779296875}, {"start": 1438.93, "end": 1440.11, "word": " integer", "probability": 0.95458984375}, {"start": 1440.11, "end": 1442.31, "word": " that", "probability": 0.6513671875}, {"start": 1442.31, "end": 1444.99, "word": " is", "probability": 0.94775390625}, {"start": 1444.99, "end": 1447.89, "word": " multiple", "probability": 0.58642578125}, {"start": 1447.89, "end": 1452.09, "word": " of", "probability": 0.951171875}, {"start": 1452.09, "end": 1454.49, "word": " both", "probability": 0.86328125}, {"start": 1454.49, "end": 1457.35, "word": " a", "probability": 0.587890625}, {"start": 1457.35, "end": 1458.93, "word": " and", "probability": 0.8408203125}, {"start": 1458.93, "end": 1459.27, "word": " b", "probability": 0.84521484375}], "temperature": 1.0}, {"id": 58, "seek": 147531, "start": 1463.21, "end": 1475.31, "text": "we do not add by least common multiple لل a والb", "tokens": [826, 360, 406, 909, 538, 1935, 2689, 3866, 24976, 257, 16070, 65], "avg_logprob": -0.39212740384615385, "compression_ratio": 0.8688524590163934, "no_speech_prob": 0.0, "words": [{"start": 1463.21, "end": 1463.77, "word": "we", "probability": 0.4208984375}, {"start": 1463.77, "end": 1465.47, "word": " do", "probability": 0.5234375}, {"start": 1465.47, "end": 1466.17, "word": " not", "probability": 0.962890625}, {"start": 1466.17, "end": 1468.15, "word": " add", "probability": 0.52587890625}, {"start": 1468.15, "end": 1469.91, "word": " by", "probability": 0.9609375}, {"start": 1469.91, "end": 1471.33, "word": " least", "probability": 0.8583984375}, {"start": 1471.33, "end": 1471.91, "word": " common", "probability": 0.91259765625}, {"start": 1471.91, "end": 1472.81, "word": " multiple", "probability": 0.9375}, {"start": 1472.81, "end": 1473.95, "word": " لل", "probability": 0.4853515625}, {"start": 1473.95, "end": 1474.57, "word": " a", "probability": 0.253662109375}, {"start": 1474.57, "end": 1475.31, "word": " والb", "probability": 0.806884765625}], "temperature": 1.0}, {"id": 59, "seek": 151011, "start": 1494.47, "end": 1510.11, "text": "common مشترك least أقل multiple مضاعفة يبقى مسمى المضاعف المشترك الأصغر يعني بدي أشوف أصغر رقم بيقسم كل من الرقمين اللي عندنا", "tokens": [1112, 3317, 37893, 2655, 31747, 1935, 5551, 4587, 1211, 3866, 3714, 11242, 45761, 5172, 3660, 7251, 3555, 4587, 7578, 3714, 38251, 7578, 9673, 11242, 45761, 5172, 9673, 8592, 2655, 31747, 16247, 9381, 17082, 2288, 37495, 22653, 4724, 16254, 5551, 8592, 38688, 5551, 9381, 17082, 2288, 12602, 4587, 2304, 4724, 1829, 4587, 38251, 28242, 9154, 34892, 4587, 2304, 9957, 13672, 1829, 43242, 8315], "avg_logprob": -0.1853918679176815, "compression_ratio": 1.4383561643835616, "no_speech_prob": 0.0, "words": [{"start": 1494.47, "end": 1494.93, "word": "common", "probability": 0.675048828125}, {"start": 1494.93, "end": 1495.67, "word": " مشترك", "probability": 0.8603515625}, {"start": 1495.67, "end": 1496.83, "word": " least", "probability": 0.13720703125}, {"start": 1496.83, "end": 1497.65, "word": " أقل", "probability": 0.8956705729166666}, {"start": 1497.65, "end": 1498.35, "word": " multiple", "probability": 0.90185546875}, {"start": 1498.35, "end": 1499.35, "word": " مضاعفة", "probability": 0.95}, {"start": 1499.35, "end": 1499.97, "word": " يبقى", "probability": 0.69854736328125}, {"start": 1499.97, "end": 1500.41, "word": " مسمى", "probability": 0.6336263020833334}, {"start": 1500.41, "end": 1501.31, "word": " المضاعف", "probability": 0.9805908203125}, {"start": 1501.31, "end": 1502.15, "word": " المشترك", "probability": 0.98486328125}, {"start": 1502.15, "end": 1502.91, "word": " الأصغر", "probability": 0.975830078125}, {"start": 1502.91, "end": 1503.25, "word": " يعني", "probability": 0.864990234375}, {"start": 1503.25, "end": 1503.63, "word": " بدي", "probability": 0.6168212890625}, {"start": 1503.63, "end": 1504.31, "word": " أشوف", "probability": 0.9169921875}, {"start": 1504.31, "end": 1505.73, "word": " أصغر", "probability": 0.9666748046875}, {"start": 1505.73, "end": 1506.45, "word": " رقم", "probability": 0.9943033854166666}, {"start": 1506.45, "end": 1507.27, "word": " بيقسم", "probability": 0.92626953125}, {"start": 1507.27, "end": 1507.71, "word": " كل", "probability": 0.9287109375}, {"start": 1507.71, "end": 1508.19, "word": " من", "probability": 0.8427734375}, {"start": 1508.19, "end": 1509.31, "word": " الرقمين", "probability": 0.8529052734375}, {"start": 1509.31, "end": 1509.71, "word": " اللي", "probability": 0.9228515625}, {"start": 1509.71, "end": 1510.11, "word": " عندنا", "probability": 0.859130859375}], "temperature": 1.0}, {"id": 60, "seek": 152587, "start": 1510.61, "end": 1525.87, "text": "يبقى the least common multiple أصغر رقم يقسم non-zero integers a والb يبقى of two non-zero integers a and b", "tokens": [1829, 3555, 4587, 7578, 264, 1935, 2689, 3866, 5551, 9381, 17082, 2288, 12602, 4587, 2304, 7251, 4587, 38251, 2107, 12, 32226, 41674, 257, 16070, 65, 7251, 3555, 4587, 7578, 295, 732, 2107, 12, 32226, 41674, 257, 293, 272], "avg_logprob": -0.30108172924090654, "compression_ratio": 1.1415929203539823, "no_speech_prob": 0.0, "words": [{"start": 1510.61, "end": 1511.05, "word": "يبقى", "probability": 0.7938232421875}, {"start": 1511.05, "end": 1511.27, "word": " the", "probability": 0.2451171875}, {"start": 1511.27, "end": 1511.61, "word": " least", "probability": 0.7548828125}, {"start": 1511.61, "end": 1512.01, "word": " common", "probability": 0.85986328125}, {"start": 1512.01, 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1522.43, "end": 1522.73, "word": " non", "probability": 0.970703125}, {"start": 1522.73, "end": 1523.11, "word": "-zero", "probability": 0.83935546875}, {"start": 1523.11, "end": 1523.99, "word": " integers", "probability": 0.95751953125}, {"start": 1523.99, "end": 1524.71, "word": " a", "probability": 0.953125}, {"start": 1524.71, "end": 1525.53, "word": " and", "probability": 0.94140625}, {"start": 1525.53, "end": 1525.87, "word": " b", "probability": 0.330078125}], "temperature": 1.0}, {"id": 61, "seek": 154637, "start": 1530.19, "end": 1546.37, "text": "is the smallest positive integer أصغر عدد صحيح موجب that is a multiple of both a and b يبقى أصغر عدد يكون مضاعفات ال a والb في آن واحد", "tokens": [271, 264, 16998, 3353, 24922, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 300, 307, 257, 3866, 295, 1293, 257, 293, 272, 7251, 3555, 4587, 7578, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 7251, 30544, 3714, 11242, 45761, 5172, 9307, 2423, 257, 16070, 65, 8978, 19753, 1863, 36764, 24401], "avg_logprob": -0.1611328125, "compression_ratio": 1.251700680272109, "no_speech_prob": 0.0, "words": [{"start": 1530.19, "end": 1530.93, "word": "is", "probability": 0.0723876953125}, {"start": 1530.93, "end": 1531.49, "word": " the", "probability": 0.7724609375}, {"start": 1531.49, "end": 1531.99, "word": " smallest", "probability": 0.9501953125}, {"start": 1531.99, "end": 1532.55, "word": " positive", "probability": 0.92822265625}, {"start": 1532.55, "end": 1533.61, "word": " integer", "probability": 0.92041015625}, {"start": 1533.61, "end": 1534.91, "word": " أصغر", "probability": 0.843017578125}, {"start": 1534.91, "end": 1535.55, "word": " عدد", "probability": 0.9816080729166666}, {"start": 1535.55, "end": 1536.49, "word": " صحيح", "probability": 0.9820556640625}, {"start": 1536.49, "end": 1537.11, "word": " موجب", "probability": 0.9739583333333334}, {"start": 1537.11, "end": 1537.79, "word": " that", "probability": 0.50830078125}, {"start": 1537.79, "end": 1538.09, "word": " is", "probability": 0.95166015625}, {"start": 1538.09, "end": 1538.39, "word": " a", "probability": 0.6142578125}, {"start": 1538.39, "end": 1538.95, "word": " multiple", "probability": 0.90771484375}, {"start": 1538.95, "end": 1539.39, "word": " of", "probability": 0.97998046875}, {"start": 1539.39, "end": 1539.81, "word": " both", "probability": 0.90771484375}, {"start": 1539.81, "end": 1540.05, "word": " a", "probability": 0.8515625}, {"start": 1540.05, "end": 1540.31, "word": " and", "probability": 0.93701171875}, {"start": 1540.31, "end": 1540.59, "word": " b", "probability": 0.98974609375}, {"start": 1540.59, "end": 1541.29, "word": " يبقى", "probability": 0.963134765625}, {"start": 1541.29, "end": 1541.85, "word": " أصغر", "probability": 0.9849853515625}, {"start": 1541.85, "end": 1542.13, "word": " عدد", "probability": 0.9938151041666666}, {"start": 1542.13, "end": 1542.69, "word": " يكون", "probability": 0.975830078125}, {"start": 1542.69, "end": 1543.95, "word": " مضاعفات", "probability": 0.96953125}, {"start": 1543.95, "end": 1544.15, "word": " ال", "probability": 0.69677734375}, {"start": 1544.15, "end": 1544.43, "word": " a", "probability": 0.84228515625}, {"start": 1544.43, "end": 1544.91, "word": " والb", "probability": 0.573486328125}, {"start": 1544.91, "end": 1545.21, "word": " في", "probability": 0.90673828125}, {"start": 1545.21, "end": 1545.65, "word": " آن", "probability": 0.720947265625}, {"start": 1545.65, "end": 1546.37, "word": " واحد", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 62, "seek": 157002, "start": 1546.74, "end": 1570.02, "text": "we denote it by اللي هو main a و b يبقى هذا هندله الرمز least common multiple of a و b زي مجرسيس common divisor قدنا g,c,d هنا least common multiple يبقى l,c,m هو اختصار لل least common multiple نعطي مثال مثلا example", "tokens": [826, 45708, 309, 538, 13672, 1829, 31439, 2135, 257, 4032, 272, 7251, 3555, 4587, 7578, 23758, 8032, 41260, 43761, 34892, 2304, 11622, 1935, 2689, 3866, 295, 257, 4032, 272, 30767, 1829, 3714, 7435, 2288, 3794, 1829, 3794, 2689, 25974, 284, 12174, 3215, 8315, 290, 11, 66, 11, 67, 34105, 1935, 2689, 3866, 7251, 3555, 4587, 7578, 287, 11, 66, 11, 76, 31439, 1975, 46456, 9381, 9640, 24976, 1935, 2689, 3866, 8717, 3615, 9566, 1829, 50113, 6027, 50113, 15040, 1365], "avg_logprob": -0.3033203136175871, "compression_ratio": 1.5810055865921788, "no_speech_prob": 0.0, "words": [{"start": 1546.74, "end": 1547.04, "word": "we", "probability": 0.1282958984375}, {"start": 1547.04, "end": 1547.58, "word": " denote", "probability": 0.92431640625}, {"start": 1547.58, "end": 1547.94, "word": " it", "probability": 0.93701171875}, {"start": 1547.94, "end": 1548.5, "word": " by", "probability": 0.904296875}, {"start": 1548.5, "end": 1549.96, "word": " اللي", "probability": 0.473724365234375}, {"start": 1549.96, "end": 1550.18, "word": " هو", "probability": 0.921875}, {"start": 1550.18, "end": 1550.58, "word": " main", "probability": 0.51416015625}, {"start": 1550.58, "end": 1551.16, "word": " a", "probability": 0.671875}, {"start": 1551.16, "end": 1551.36, "word": " و", "probability": 0.765625}, {"start": 1551.36, "end": 1551.76, "word": " b", "probability": 0.59423828125}, {"start": 1551.76, "end": 1552.82, "word": " يبقى", "probability": 0.9227294921875}, {"start": 1552.82, "end": 1553.32, "word": " هذا", "probability": 0.86279296875}, {"start": 1553.32, "end": 1554.2, "word": " هندله", "probability": 0.4632975260416667}, {"start": 1554.2, "end": 1554.98, "word": " الرمز", "probability": 0.9246419270833334}, {"start": 1554.98, "end": 1555.44, "word": " least", "probability": 0.92626953125}, {"start": 1555.44, "end": 1555.88, "word": " common", "probability": 0.93359375}, {"start": 1555.88, "end": 1556.42, "word": " multiple", "probability": 0.9111328125}, {"start": 1556.42, "end": 1557.42, "word": " of", "probability": 0.93408203125}, {"start": 1557.42, "end": 1557.76, "word": " a", "probability": 0.90869140625}, {"start": 1557.76, "end": 1557.86, "word": " و", "probability": 0.8837890625}, {"start": 1557.86, "end": 1557.96, "word": " b", "probability": 0.8154296875}, {"start": 1557.96, "end": 1558.16, "word": " زي", "probability": 0.659912109375}, {"start": 1558.16, "end": 1558.86, "word": " مجرسيس", "probability": 0.6075846354166666}, {"start": 1558.86, "end": 1559.14, "word": " common", "probability": 0.8662109375}, {"start": 1559.14, "end": 1559.7, "word": " divisor", "probability": 0.802978515625}, {"start": 1559.7, "end": 1560.02, "word": " قدنا", "probability": 0.5210367838541666}, {"start": 1560.02, "end": 1560.22, "word": " g", "probability": 0.6787109375}, {"start": 1560.22, "end": 1560.62, "word": ",c", "probability": 0.443359375}, {"start": 1560.62, "end": 1560.98, "word": ",d", "probability": 0.984619140625}, {"start": 1560.98, "end": 1561.74, "word": " هنا", "probability": 0.833984375}, {"start": 1561.74, "end": 1562.48, "word": " least", "probability": 0.75341796875}, {"start": 1562.48, "end": 1563.12, "word": " common", "probability": 0.94482421875}, {"start": 1563.12, "end": 1563.74, "word": " multiple", "probability": 0.916015625}, {"start": 1563.74, "end": 1564.1, "word": " يبقى", "probability": 0.93798828125}, {"start": 1564.1, "end": 1564.4, "word": " l", "probability": 0.60498046875}, {"start": 1564.4, "end": 1564.66, "word": ",c", "probability": 0.830322265625}, {"start": 1564.66, "end": 1564.9, "word": ",m", "probability": 0.997802734375}, {"start": 1564.9, "end": 1565.08, "word": " هو", "probability": 0.8671875}, {"start": 1565.08, "end": 1565.68, "word": " اختصار", "probability": 0.9759521484375}, {"start": 1565.68, "end": 1565.86, "word": " لل", "probability": 0.487548828125}, {"start": 1565.86, "end": 1566.18, "word": " least", "probability": 0.7900390625}, {"start": 1566.18, "end": 1566.62, "word": " common", "probability": 0.9384765625}, {"start": 1566.62, "end": 1567.3, "word": " multiple", "probability": 0.943359375}, {"start": 1567.3, "end": 1568.26, "word": " نعطي", "probability": 0.951904296875}, {"start": 1568.26, "end": 1568.8, "word": " مثال", "probability": 0.955078125}, {"start": 1568.8, "end": 1569.3, "word": " مثلا", "probability": 0.962158203125}, {"start": 1569.3, "end": 1570.02, "word": " example", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 63, "seek": 160280, "start": 1574.42, "end": 1602.8, "text": "لو دي اتنين من واحد بدي ال least common multiple مثلا لست و اتناش ايش اول رقم بيقابلني بيقسم كله من الست و اتناش الواحد اتنين تلاتة بدي اول رقم اتنين هدول بيقسموه في انا واحد", "tokens": [1211, 2407, 11778, 1829, 1975, 2655, 1863, 9957, 9154, 36764, 24401, 4724, 16254, 2423, 1935, 2689, 3866, 50113, 15040, 5296, 14851, 4032, 1975, 2655, 1863, 33599, 1975, 1829, 8592, 1975, 12610, 12602, 4587, 2304, 4724, 1829, 4587, 16758, 1211, 22653, 4724, 1829, 4587, 38251, 28242, 3224, 9154, 2423, 14851, 4032, 1975, 2655, 1863, 33599, 2423, 14407, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 4724, 16254, 1975, 12610, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 8032, 3215, 12610, 4724, 1829, 4587, 38251, 2407, 3224, 8978, 1975, 8315, 36764, 24401], "avg_logprob": -0.2263049453824431, "compression_ratio": 1.8375, "no_speech_prob": 0.0, "words": [{"start": 1574.42, "end": 1574.82, "word": "لو", "probability": 0.658203125}, {"start": 1574.82, "end": 1575.0, "word": " دي", "probability": 0.6107177734375}, {"start": 1575.0, "end": 1575.34, "word": " اتنين", "probability": 0.65655517578125}, {"start": 1575.34, "end": 1575.44, "word": " من", "probability": 0.206787109375}, {"start": 1575.44, "end": 1575.8, "word": " واحد", "probability": 0.921875}, {"start": 1575.8, "end": 1576.84, "word": " بدي", "probability": 0.6793212890625}, {"start": 1576.84, "end": 1577.12, "word": " ال", "probability": 0.7841796875}, {"start": 1577.12, "end": 1577.58, "word": " least", "probability": 0.837890625}, {"start": 1577.58, "end": 1578.24, "word": " common", "probability": 0.96826171875}, {"start": 1578.24, "end": 1579.02, "word": " multiple", "probability": 0.89892578125}, {"start": 1579.02, "end": 1579.68, "word": " مثلا", "probability": 0.849853515625}, {"start": 1579.68, "end": 1580.26, "word": " لست", "probability": 0.777099609375}, {"start": 1580.26, "end": 1580.52, "word": " و", "probability": 0.35400390625}, {"start": 1580.52, "end": 1581.14, "word": " اتناش", "probability": 0.82440185546875}, {"start": 1581.14, "end": 1582.46, "word": " ايش", "probability": 0.8857421875}, {"start": 1582.46, "end": 1583.06, "word": " اول", "probability": 0.904541015625}, {"start": 1583.06, "end": 1583.68, "word": " رقم", "probability": 0.9962565104166666}, {"start": 1583.68, "end": 1584.88, "word": " بيقابلني", "probability": 0.9705403645833334}, {"start": 1584.88, "end": 1586.14, "word": " بيقسم", "probability": 0.9228515625}, {"start": 1586.14, "end": 1586.74, "word": " كله", "probability": 0.827392578125}, {"start": 1586.74, "end": 1586.92, "word": " من", "probability": 0.98974609375}, {"start": 1586.92, "end": 1587.4, "word": " الست", "probability": 0.789794921875}, {"start": 1587.4, "end": 1587.62, "word": " و", "probability": 0.80712890625}, {"start": 1587.62, "end": 1588.3, "word": " اتناش", "probability": 0.9334716796875}, {"start": 1588.3, "end": 1590.8, "word": " الواحد", "probability": 0.8629557291666666}, {"start": 1590.8, "end": 1592.42, "word": " اتنين", "probability": 0.81097412109375}, {"start": 1592.42, "end": 1595.06, "word": " تلاتة", "probability": 0.8582763671875}, {"start": 1595.06, "end": 1596.72, "word": " بدي", "probability": 0.60589599609375}, {"start": 1596.72, "end": 1597.48, "word": " اول", "probability": 0.929931640625}, {"start": 1597.48, "end": 1598.58, "word": " رقم", "probability": 0.9970703125}, {"start": 1598.58, "end": 1600.6, "word": " اتنين", "probability": 0.97265625}, {"start": 1600.6, "end": 1601.2, "word": " هدول", "probability": 0.9544270833333334}, {"start": 1601.2, "end": 1601.98, "word": " بيقسموه", "probability": 0.9256998697916666}, {"start": 1601.98, "end": 1602.12, "word": " في", "probability": 0.91259765625}, {"start": 1602.12, "end": 1602.38, "word": " انا", "probability": 0.35406494140625}, {"start": 1602.38, "end": 1602.8, "word": " واحد", "probability": 0.831298828125}], "temperature": 1.0}, {"id": 64, "seek": 162920, "start": 1603.14, "end": 1629.2, "text": "أيوة ممتاز جدا يبقى هنا هذا بدى يساوي كده اش او اتناش يبقى اتناش هو اول رقم بيقابلني الست بيقدر يقسمه و اتناش يعني هذا المضاعف المشترك الأصغر للاتنين طبعا طيب لو جيت قولتك بدي ال least common multiple للاربعة والست اتنين", "tokens": [10721, 1829, 2407, 3660, 3714, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 34105, 23758, 47525, 7578, 7251, 3794, 995, 45865, 9122, 3215, 3224, 1975, 8592, 1975, 2407, 1975, 2655, 1863, 33599, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 33599, 31439, 1975, 12610, 12602, 4587, 2304, 4724, 1829, 4587, 16758, 1211, 22653, 2423, 14851, 4724, 1829, 28543, 2288, 7251, 4587, 38251, 3224, 4032, 1975, 2655, 1863, 33599, 37495, 22653, 23758, 9673, 11242, 45761, 5172, 9673, 8592, 2655, 31747, 16247, 9381, 17082, 2288, 24976, 9307, 1863, 9957, 23032, 3555, 3615, 995, 23032, 1829, 3555, 45164, 10874, 36081, 12174, 12610, 2655, 4117, 4724, 16254, 2423, 1935, 2689, 3866, 24976, 9640, 3555, 27884, 16070, 14851, 1975, 2655, 1863, 9957], "avg_logprob": -0.17121292183459816, "compression_ratio": 1.7511520737327189, "no_speech_prob": 0.0, "words": [{"start": 1603.14, "end": 1603.76, "word": "أيوة", "probability": 0.75006103515625}, {"start": 1603.76, "end": 1604.36, "word": " ممتاز", "probability": 0.9459228515625}, {"start": 1604.36, "end": 1604.7, "word": " جدا", "probability": 0.988525390625}, {"start": 1604.7, "end": 1605.22, "word": " يبقى", "probability": 0.9139404296875}, {"start": 1605.22, "end": 1605.58, "word": " هنا", "probability": 0.9619140625}, {"start": 1605.58, "end": 1605.98, "word": " هذا", "probability": 0.84814453125}, {"start": 1605.98, "end": 1606.32, "word": " بدى", "probability": 0.44189453125}, {"start": 1606.32, "end": 1606.72, "word": " يساوي", "probability": 0.8681640625}, {"start": 1606.72, "end": 1607.24, "word": " كده", "probability": 0.6009928385416666}, {"start": 1607.24, "end": 1607.5, "word": " اش", "probability": 0.490966796875}, {"start": 1607.5, "end": 1607.8, "word": " او", "probability": 0.69189453125}, {"start": 1607.8, "end": 1608.3, "word": " اتناش", "probability": 0.8331298828125}, {"start": 1608.3, "end": 1609.36, "word": " يبقى", "probability": 0.9671630859375}, {"start": 1609.36, "end": 1609.82, "word": " اتناش", "probability": 0.947265625}, {"start": 1609.82, "end": 1610.06, "word": " هو", "probability": 0.97705078125}, {"start": 1610.06, "end": 1610.74, "word": " اول", "probability": 0.93310546875}, {"start": 1610.74, "end": 1611.2, "word": " رقم", "probability": 0.9949544270833334}, {"start": 1611.2, "end": 1611.98, "word": " بيقابلني", "probability": 0.8982747395833334}, {"start": 1611.98, "end": 1612.46, "word": " الست", "probability": 0.719970703125}, {"start": 1612.46, "end": 1613.02, "word": " بيقدر", "probability": 0.941162109375}, {"start": 1613.02, "end": 1613.82, "word": " يقسمه", "probability": 0.9591064453125}, {"start": 1613.82, "end": 1614.1, "word": " و", "probability": 0.489501953125}, {"start": 1614.1, "end": 1614.32, "word": " اتناش", "probability": 0.910888671875}, {"start": 1614.32, "end": 1614.58, "word": " يعني", "probability": 0.8408203125}, {"start": 1614.58, "end": 1614.86, "word": " هذا", "probability": 0.8408203125}, {"start": 1614.86, "end": 1615.5, "word": " المضاعف", "probability": 0.953857421875}, {"start": 1615.5, "end": 1616.14, "word": " المشترك", "probability": 0.985107421875}, {"start": 1616.14, "end": 1616.66, "word": " الأصغر", "probability": 0.8671875}, {"start": 1616.66, "end": 1617.46, "word": " للاتنين", "probability": 0.8125}, {"start": 1617.46, "end": 1618.34, "word": " طبعا", "probability": 0.7978515625}, {"start": 1618.34, "end": 1619.42, "word": " طيب", "probability": 0.90869140625}, {"start": 1619.42, "end": 1619.8, "word": " لو", "probability": 0.9765625}, {"start": 1619.8, "end": 1620.08, "word": " جيت", "probability": 0.93798828125}, {"start": 1620.08, "end": 1620.62, "word": " قولتك", "probability": 0.8323974609375}, {"start": 1620.62, "end": 1621.22, "word": " بدي", "probability": 0.78857421875}, {"start": 1621.22, "end": 1622.04, "word": " ال", "probability": 0.90478515625}, {"start": 1622.04, "end": 1622.52, "word": " least", "probability": 0.9853515625}, {"start": 1622.52, "end": 1623.38, "word": " common", "probability": 0.9619140625}, {"start": 1623.38, "end": 1624.64, "word": " multiple", "probability": 0.85888671875}, {"start": 1624.64, "end": 1626.48, "word": " للاربعة", "probability": 0.89404296875}, {"start": 1626.48, "end": 1627.3, "word": " والست", "probability": 0.818115234375}, {"start": 1627.3, "end": 1629.2, "word": " اتنين", "probability": 0.9498291015625}], "temperature": 1.0}, {"id": 65, "seek": 164051, "start": 1632.57, "end": 1640.51, "text": "الاربعة بتقسم اتنين بقولك اول رقم بيجابلك بحيث هالرقمين بدهم يقسموا هذا الرقم", "tokens": [6027, 9640, 3555, 27884, 39894, 4587, 38251, 1975, 2655, 1863, 9957, 4724, 39648, 4117, 1975, 12610, 12602, 4587, 2304, 4724, 1829, 7435, 16758, 23275, 4724, 5016, 1829, 12984, 8032, 6027, 2288, 4587, 2304, 9957, 47525, 16095, 7251, 4587, 38251, 14407, 23758, 34892, 4587, 2304], "avg_logprob": -0.21788194974263508, "compression_ratio": 1.4791666666666667, "no_speech_prob": 0.0, "words": [{"start": 1632.57, "end": 1633.15, "word": "الاربعة", "probability": 0.7967529296875}, {"start": 1633.15, "end": 1633.63, "word": " بتقسم", "probability": 0.9306640625}, {"start": 1633.63, "end": 1634.23, "word": " اتنين", "probability": 0.9000244140625}, {"start": 1634.23, "end": 1635.85, "word": " بقولك", "probability": 0.7605794270833334}, {"start": 1635.85, "end": 1636.33, "word": " اول", "probability": 0.861083984375}, {"start": 1636.33, "end": 1636.95, "word": " رقم", "probability": 0.9918619791666666}, {"start": 1636.95, "end": 1637.61, "word": " بيجابلك", "probability": 0.871875}, {"start": 1637.61, "end": 1637.97, "word": " بحيث", "probability": 0.8870849609375}, {"start": 1637.97, "end": 1638.71, "word": " هالرقمين", "probability": 0.7798665364583334}, {"start": 1638.71, "end": 1639.03, "word": " بدهم", "probability": 0.7467041015625}, {"start": 1639.03, "end": 1639.59, "word": " يقسموا", "probability": 0.9561767578125}, {"start": 1639.59, "end": 1639.81, "word": " هذا", "probability": 0.78515625}, {"start": 1639.81, "end": 1640.51, "word": " الرقم", "probability": 0.9796549479166666}], "temperature": 1.0}, {"id": 66, "seek": 166405, "start": 1646.37, "end": 1664.05, "text": "يبقى 12 هذا أول رقم بيقسم الأربعة والستة طبعا في أرقام بعده كتير في بعده لكن هذا هو أصغر رقم اللي .. اللي .. اللي اتنين هدول بيجسموه مثلا الأربعة والستة بتجسم الأربعة وعشرين", "tokens": 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الاثنين واحد فيهم مثل هيك لكن بعد هيك لازم يكون اكبر من الاثنين اكبر من الرقمين في انواع تطلع هنا اكبر من الأربعة و اكبر من الستة اكبر من التلاتة و اكبر من السبعة اكبر من الستة و اكبر من العشرة اكبر من العشرة و من الاطناش و هكذا", "tokens": [2407, 3224, 4117, 15730, 37495, 22653, 12174, 3215, 7251, 30544, 2423, 32277, 24793, 16070, 3866, 2423, 5718, 104, 1863, 9957, 36764, 24401, 8978, 16095, 50113, 1211, 39896, 4117, 44381, 39182, 39896, 4117, 5296, 31377, 2304, 7251, 30544, 1975, 4117, 26890, 9154, 2423, 5718, 104, 1863, 9957, 1975, 4117, 26890, 9154, 34892, 4587, 2304, 9957, 8978, 16472, 14407, 3615, 6055, 9566, 1211, 3615, 34105, 1975, 4117, 26890, 9154, 16247, 25513, 27884, 4032, 1975, 4117, 26890, 9154, 21136, 2655, 3660, 1975, 4117, 26890, 9154, 16712, 1211, 9307, 3660, 4032, 1975, 4117, 26890, 9154, 21136, 3555, 27884, 1975, 4117, 26890, 9154, 21136, 2655, 3660, 4032, 1975, 4117, 26890, 9154, 18863, 8592, 25720, 1975, 4117, 26890, 9154, 18863, 8592, 25720, 4032, 9154, 2423, 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0.9111328125}, {"start": 1757.94, "end": 1758.42, "word": " اكبر", "probability": 0.96728515625}, {"start": 1758.42, "end": 1758.58, "word": " من", "probability": 0.99658203125}, {"start": 1758.58, "end": 1759.06, "word": " التلاتة", "probability": 0.97119140625}, {"start": 1759.06, "end": 1759.18, "word": " و", "probability": 0.7724609375}, {"start": 1759.18, "end": 1759.46, "word": " اكبر", "probability": 0.9571940104166666}, {"start": 1759.46, "end": 1759.64, "word": " من", "probability": 0.99609375}, {"start": 1759.64, "end": 1760.14, "word": " السبعة", "probability": 0.9482421875}, {"start": 1760.14, "end": 1760.88, "word": " اكبر", "probability": 0.97216796875}, {"start": 1760.88, "end": 1761.06, "word": " من", "probability": 0.99755859375}, {"start": 1761.06, "end": 1761.48, "word": " الستة", "probability": 0.9318033854166666}, {"start": 1761.48, "end": 1761.58, "word": " و", "probability": 0.74951171875}, {"start": 1761.58, "end": 1761.86, "word": " اكبر", "probability": 0.9671223958333334}, {"start": 1761.86, "end": 1762.02, "word": " من", "probability": 0.9921875}, {"start": 1762.02, "end": 1762.4, "word": " العشرة", "probability": 0.748291015625}, {"start": 1762.4, "end": 1762.72, "word": " اكبر", "probability": 0.9326171875}, {"start": 1762.72, "end": 1762.84, "word": " من", "probability": 0.99462890625}, {"start": 1762.84, "end": 1763.26, "word": " العشرة", "probability": 0.9039713541666666}, {"start": 1763.26, "end": 1763.38, "word": " و", "probability": 0.9443359375}, {"start": 1763.38, "end": 1763.48, "word": " من", "probability": 0.8623046875}, {"start": 1763.48, "end": 1764.02, "word": " الاطناش", "probability": 0.6341552734375}, {"start": 1764.02, "end": 1764.24, "word": " و", "probability": 0.787109375}, {"start": 1764.24, "end": 1764.72, "word": " هكذا", "probability": 0.8658854166666666}], "temperature": 1.0}, {"id": 72, "seek": 179046, "start": 1765.04, "end": 1790.46, "text": "يعني أقل حاجة لازم يسوي واحد فيهم ولا يمكن ينزل عن أي واحد فيهم يعني مش ممكن يكون أقل من أي رقم راه وإنما أقل لما ننزل خلاص بدي يسوي مين بدي يسوي واحد فيهم يبقى هذا مين ال least common multiple في ملاحظة بدنا نقولها لك هنا ضرورة تكون ملمقة بها remark", "tokens": [40228, 22653, 5551, 4587, 1211, 11331, 26108, 3660, 5296, 31377, 2304, 7251, 3794, 45865, 36764, 24401, 8978, 16095, 49429, 7251, 43020, 7251, 1863, 11622, 1211, 18871, 36632, 36764, 24401, 8978, 16095, 37495, 22653, 37893, 3714, 43020, 7251, 30544, 5551, 4587, 1211, 9154, 36632, 12602, 4587, 2304, 12602, 40294, 4032, 28814, 1863, 15042, 5551, 4587, 1211, 5296, 15042, 8717, 1863, 11622, 1211, 16490, 1211, 33546, 4724, 16254, 7251, 3794, 45865, 3714, 9957, 4724, 16254, 7251, 3794, 45865, 36764, 24401, 8978, 16095, 7251, 3555, 4587, 7578, 23758, 3714, 9957, 2423, 1935, 2689, 3866, 8978, 3714, 15040, 5016, 19913, 3660, 47525, 8315, 8717, 39648, 11296, 5296, 4117, 34105, 48812, 2288, 13063, 3660, 6055, 30544, 3714, 19528, 28671, 4724, 11296, 7942], "avg_logprob": -0.18776483593855875, 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"word": " وإنما", "probability": 0.8056640625}, {"start": 1777.24, "end": 1778.04, "word": " أقل", "probability": 0.869140625}, {"start": 1778.04, "end": 1778.2, "word": " لما", "probability": 0.860107421875}, {"start": 1778.2, "end": 1778.56, "word": " ننزل", "probability": 0.820556640625}, {"start": 1778.56, "end": 1778.9, "word": " خلاص", "probability": 0.732421875}, {"start": 1778.9, "end": 1779.14, "word": " بدي", "probability": 0.613525390625}, {"start": 1779.14, "end": 1779.44, "word": " يسوي", "probability": 0.7367350260416666}, {"start": 1779.44, "end": 1779.76, "word": " مين", "probability": 0.6468505859375}, {"start": 1779.76, "end": 1780.42, "word": " بدي", "probability": 0.7890625}, {"start": 1780.42, "end": 1780.76, "word": " يسوي", "probability": 0.9342447916666666}, {"start": 1780.76, "end": 1781.06, "word": " واحد", "probability": 0.99462890625}, {"start": 1781.06, "end": 1781.36, "word": " فيهم", "probability": 0.983642578125}, {"start": 1781.36, "end": 1781.68, "word": " يبقى", "probability": 0.9547119140625}, {"start": 1781.68, "end": 1781.92, "word": " هذا", "probability": 0.8369140625}, {"start": 1781.92, "end": 1782.34, "word": " مين", "probability": 0.8359375}, {"start": 1782.34, "end": 1782.96, "word": " ال", "probability": 0.88916015625}, {"start": 1782.96, "end": 1783.32, "word": " least", "probability": 0.7041015625}, {"start": 1783.32, "end": 1783.86, "word": " common", "probability": 0.94482421875}, {"start": 1783.86, "end": 1784.7, "word": " multiple", "probability": 0.91357421875}, {"start": 1784.7, "end": 1785.3, "word": " في", "probability": 0.80078125}, {"start": 1785.3, "end": 1785.96, "word": " ملاحظة", "probability": 0.9828125}, {"start": 1785.96, "end": 1786.22, "word": " بدنا", "probability": 0.920654296875}, {"start": 1786.22, "end": 1786.74, "word": " نقولها", "probability": 0.761474609375}, {"start": 1786.74, "end": 1787.0, "word": " لك", "probability": 0.94580078125}, {"start": 1787.0, "end": 1787.34, "word": " هنا", "probability": 0.96826171875}, {"start": 1787.34, "end": 1787.92, "word": " ضرورة", "probability": 0.9490966796875}, {"start": 1787.92, "end": 1788.18, "word": " تكون", "probability": 0.721435546875}, {"start": 1788.18, "end": 1788.92, "word": " ملمقة", "probability": 0.67236328125}, {"start": 1788.92, "end": 1789.3, "word": " بها", "probability": 0.931640625}, {"start": 1789.3, "end": 1790.46, "word": " remark", "probability": 0.8505859375}], "temperature": 1.0}, {"id": 73, "seek": 181170, "start": 1792.92, "end": 1811.7, "text": "أنا عندي رقامين يا شباب ممكن أجيب ال list common multiple و ممكن أجيب ال grids common divisor لهم لو ضربت اتنين في بعض باطيني حصل ضربة الرقامين يبقى هنا باجي بقول الملاحظة ده بتقول", "tokens": [10721, 8315, 18871, 16254, 12602, 4587, 10943, 9957, 35186, 13412, 3555, 16758, 3714, 43020, 5551, 7435, 1829, 3555, 2423, 1329, 2689, 3866, 4032, 3714, 43020, 5551, 7435, 1829, 3555, 2423, 677, 3742, 2689, 25974, 284, 5296, 16095, 45164, 48812, 25513, 2655, 1975, 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"probability": 0.90234375}, {"start": 1803.26, "end": 1803.86, "word": " ضربت", "probability": 0.98974609375}, {"start": 1803.86, "end": 1804.42, "word": " اتنين", "probability": 0.8829345703125}, {"start": 1804.42, "end": 1804.64, "word": " في", "probability": 0.904296875}, {"start": 1804.64, "end": 1805.02, "word": " بعض", "probability": 0.98681640625}, {"start": 1805.02, "end": 1805.62, "word": " باطيني", "probability": 0.806396484375}, {"start": 1805.62, "end": 1806.22, "word": " حصل", "probability": 0.86865234375}, {"start": 1806.22, "end": 1806.8, "word": " ضربة", "probability": 0.93603515625}, {"start": 1806.8, "end": 1807.76, "word": " الرقامين", "probability": 0.9371337890625}, {"start": 1807.76, "end": 1809.02, "word": " يبقى", "probability": 0.9744873046875}, {"start": 1809.02, "end": 1809.44, "word": " هنا", "probability": 0.98974609375}, {"start": 1809.44, "end": 1810.14, "word": " باجي", "probability": 0.68115234375}, {"start": 1810.14, "end": 1810.46, "word": " بقول", "probability": 0.888671875}, {"start": 1810.46, "end": 1811.02, "word": " الملاحظة", "probability": 0.96494140625}, {"start": 1811.02, "end": 1811.14, "word": " ده", "probability": 0.6578369140625}, {"start": 1811.14, "end": 1811.7, "word": " بتقول", "probability": 0.926513671875}], "temperature": 1.0}, {"id": 74, "seek": 182683, "start": 1812.03, "end": 1826.83, "text": "Legacies common divisor للـA والـB مضروبة في ال list common multiple ل الأي والبي بدي سوى حصل ضرب الأي في البي for example", "tokens": [43, 1146, 20330, 2689, 25974, 284, 24976, 39184, 32, 16070, 39184, 33, 3714, 11242, 32887, 49401, 8978, 2423, 1329, 2689, 3866, 5296, 16247, 1829, 16070, 21292, 4724, 16254, 8608, 2407, 7578, 11331, 36520, 48812, 25513, 16247, 1829, 8978, 2423, 21292, 337, 1365], "avg_logprob": -0.37245640089345533, "compression_ratio": 1.2761194029850746, "no_speech_prob": 0.0, "words": [{"start": 1812.03, "end": 1813.07, "word": "Legacies", "probability": 0.53839111328125}, {"start": 1813.07, "end": 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"end": 2221.9, "word": " كداش؟", "probability": 0.8521728515625}, {"start": 2221.9, "end": 2222.86, "word": " Zero", "probability": 0.5849609375}, {"start": 2222.86, "end": 2223.7, "word": " تمام", "probability": 0.912841796875}, {"start": 2223.7, "end": 2224.56, "word": " يبقى", "probability": 0.938232421875}, {"start": 2224.56, "end": 2225.08, "word": " مثلا", "probability": 0.890380859375}, {"start": 2225.08, "end": 2225.78, "word": " لو", "probability": 0.9150390625}, {"start": 2225.78, "end": 2226.2, "word": " جيت", "probability": 0.9794921875}, {"start": 2226.2, "end": 2226.82, "word": " قلتلك", "probability": 0.767578125}, {"start": 2226.82, "end": 2227.24, "word": " هنا", "probability": 0.93212890625}, {"start": 2227.24, "end": 2228.22, "word": " 6", "probability": 0.54443359375}, {"start": 2228.22, "end": 2229.34, "word": " modulo", "probability": 0.763427734375}, {"start": 2229.34, "end": 2229.76, "word": " 2", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 91, 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" اتنين", "probability": 0.96630859375}, {"start": 2232.34, "end": 2232.68, "word": " يبقى", "probability": 0.710357666015625}, {"start": 2232.68, "end": 2232.96, "word": " انا", "probability": 0.812744140625}, {"start": 2232.96, "end": 2233.64, "word": " اخدت", "probability": 0.840576171875}, {"start": 2233.64, "end": 2234.26, "word": " المقياس", "probability": 0.8817138671875}, {"start": 2234.26, "end": 2234.9, "word": " قداش", "probability": 0.69677734375}, {"start": 2234.9, "end": 2236.2, "word": " اتنين", "probability": 0.89599609375}, {"start": 2236.2, "end": 2237.08, "word": " الستة", "probability": 0.73876953125}, {"start": 2237.08, "end": 2237.46, "word": " بتقسم", "probability": 0.97216796875}, {"start": 2237.46, "end": 2237.64, "word": " على", "probability": 0.7705078125}, {"start": 2237.64, "end": 2237.98, "word": " اتنين", "probability": 0.9852294921875}, {"start": 2237.98, "end": 2238.14, "word": " ولا", "probability": 0.9130859375}, {"start": 2238.14, "end": 2238.6, 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"end": 2254.08, "word": " الستة", "probability": 0.72412109375}, {"start": 2254.08, "end": 2254.36, "word": " هذه", "probability": 0.417236328125}, {"start": 2254.36, "end": 2255.02, "word": " يسوى", "probability": 0.81524658203125}, {"start": 2255.02, "end": 2255.6, "word": " اتنين", "probability": 0.95849609375}, {"start": 2255.6, "end": 2256.18, "word": " عندنا", "probability": 0.97119140625}, {"start": 2256.18, "end": 2256.8, "word": " مضروبة", "probability": 0.954833984375}, {"start": 2256.8, "end": 2257.02, "word": " في", "probability": 0.91796875}, {"start": 2257.02, "end": 2257.68, "word": " تلاتة", "probability": 0.9189453125}, {"start": 2257.68, "end": 2258.26, "word": " زائد", "probability": 0.8894856770833334}, {"start": 2258.26, "end": 2258.82, "word": " zero", "probability": 0.6025390625}, {"start": 2258.82, "end": 2260.06, "word": " ليش", "probability": 0.81103515625}, {"start": 2260.06, "end": 2260.36, "word": " هنا", "probability": 0.6025390625}, {"start": 2260.36, 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مثلا module تلاتة", "tokens": [10721, 7578, 12602, 4587, 2304, 34105, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 34892, 4587, 2304, 23758, 30767, 16373, 3215, 497, 2423, 39184, 497, 23758, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 2407, 7578, 17182, 36725, 4587, 1211, 9154, 34051, 7251, 3794, 2407, 7578, 9154, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 2423, 29837, 34105, 4724, 28543, 33599, 4724, 17182, 23032, 1829, 3555, 45164, 10874, 36081, 12174, 1211, 2655, 23275, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 34105, 6225, 33599, 25720, 50113, 15040, 10088, 6055, 1211, 9307, 3660], "avg_logprob": -0.17746710714540984, "compression_ratio": 1.6515151515151516, "no_speech_prob": 0.0, "words": [{"start": 2264.54, "end": 2265.0, "word": "أى", "probability": 0.4429931640625}, {"start": 2265.0, "end": 2265.52, "word": " رقم", "probability": 0.9912109375}, {"start": 2265.52, "end": 2265.82, "word": " هنا", "probability": 0.85205078125}, {"start": 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ضيف لل سالب تلاتة سبعة اللي هو مقدار المقياس سالب تلاتة سبعة بيضال قداش اربعة يبقى النتيجة تساوي اربعة بكوز سالب تلاتة يساوي سبعة في أبصر قداش زائد الأربعة اللي طلعت عندنا هذه", "tokens": [3555, 28820, 4724, 3794, 41193, 3660, 48812, 33911, 24976, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 13672, 1829, 31439, 3714, 28543, 9640, 9673, 4587, 25528, 3794, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 4724, 1829, 11242, 6027, 12174, 3215, 33599, 1975, 25513, 27884, 7251, 3555, 4587, 7578, 28239, 31371, 7435, 3660, 6055, 3794, 995, 45865, 1975, 25513, 27884, 4724, 4117, 2407, 11622, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 7251, 3794, 995, 45865, 8608, 3555, 27884, 8978, 5551, 3555, 9381, 2288, 12174, 3215, 33599, 30767, 16373, 3215, 16247, 25513, 27884, 13672, 1829, 23032, 1211, 34268, 43242, 8315, 29538], "avg_logprob": -0.15967261564163934, "compression_ratio": 2.036363636363636, "no_speech_prob": 0.0, "words": [{"start": 2327.7, "end": 2328.26, "word": 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{"start": 2466.96, "end": 2467.56, "word": " modulo", "probability": 0.947509765625}, {"start": 2467.56, "end": 2468.34, "word": " تمانية", "probability": 0.98779296875}, {"start": 2468.34, "end": 2469.46, "word": " واحد", "probability": 0.94189453125}, {"start": 2469.46, "end": 2469.86, "word": " وها", "probability": 0.4716796875}, {"start": 2469.86, "end": 2470.26, "word": " كده", "probability": 0.8818359375}, {"start": 2470.26, "end": 2470.86, "word": " يبقى", "probability": 0.9429931640625}, {"start": 2470.86, "end": 2471.28, "word": " فهمنا", "probability": 0.9337565104166666}, {"start": 2471.28, "end": 2471.62, "word": " عملية", "probability": 0.9895833333333334}, {"start": 2471.62, "end": 2472.4, "word": " الحسابات", "probability": 0.9857177734375}, {"start": 2472.4, "end": 2472.8, "word": " دي", "probability": 0.5001220703125}, {"start": 2472.8, "end": 2473.12, "word": " ربالة", "probability": 0.67559814453125}, {"start": 2473.12, "end": 2473.42, "word": " كده", "probability": 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integers with n greater than zero", "tokens": [2407, 16254, 16712, 3615, 16572, 5172, 7123, 718, 2423, 257, 16070, 65, 16070, 77, 312, 41674, 365, 297, 5044, 813, 4018], "avg_logprob": -0.4378551217642697, "compression_ratio": 1.0434782608695652, "no_speech_prob": 0.0, "words": [{"start": 2499.2, "end": 2499.74, "word": "ودي", "probability": 0.177734375}, {"start": 2499.74, "end": 2500.72, "word": " التعريف", "probability": 0.970703125}, {"start": 2500.72, "end": 2506.12, "word": " definition", "probability": 0.24951171875}, {"start": 2506.12, "end": 2511.4, "word": " let", "probability": 0.556640625}, {"start": 2511.4, "end": 2513.5, "word": " ال", "probability": 0.837890625}, {"start": 2513.5, "end": 2514.04, "word": " a", "probability": 0.560546875}, {"start": 2514.04, "end": 2516.0, "word": " والb", "probability": 0.571533203125}, {"start": 2516.0, "end": 2517.08, "word": " والn", "probability": 0.9443359375}, {"start": 2517.08, "end": 2518.74, "word": " be", "probability": 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"probability": 0.89208984375}, {"start": 2561.6, "end": 2562.02, "word": " same", "probability": 0.91552734375}, {"start": 2562.02, "end": 2562.84, "word": " remainder", "probability": 0.93017578125}, {"start": 2562.84, "end": 2564.3, "word": " upon", "probability": 0.90478515625}, {"start": 2564.3, "end": 2569.82, "word": " dividing", "probability": 0.92041015625}, {"start": 2569.82, "end": 2571.78, "word": " نتيجة", "probability": 0.8343505859375}, {"start": 2571.78, "end": 2572.78, "word": " لقسمة", "probability": 0.925048828125}, {"start": 2572.78, "end": 2574.64, "word": " each", "probability": 0.740234375}, {"start": 2574.64, "end": 2575.82, "word": " one", "probability": 0.90234375}, {"start": 2575.82, "end": 2578.72, "word": " of", "probability": 0.76904296875}, {"start": 2578.72, "end": 2580.58, "word": " a", "probability": 0.5869140625}, {"start": 2580.58, "end": 2582.3, "word": " and", "probability": 0.9072265625}, {"start": 2582.3, "end": 2583.34, "word": " b", 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الـ remainder هنا لازم يسوي main الـ remainder اللي هنا بيقول if they have the same remainder نفس الباقي نتيجة لقسمة كل واحد من A وB بيبقى على main على N مثال و ذلك", "tokens": [6027, 39184, 363, 15844, 426, 4724, 1829, 3555, 4587, 7578, 5296, 39184, 29837, 7251, 3555, 4587, 7578, 2423, 39184, 29837, 34105, 5296, 31377, 2304, 7251, 3794, 45865, 2135, 2423, 39184, 29837, 13672, 1829, 34105, 4724, 1829, 39648, 498, 436, 362, 264, 912, 29837, 8717, 36178, 29739, 995, 38436, 8717, 31371, 7435, 3660, 5296, 4587, 38251, 3660, 28242, 36764, 24401, 9154, 316, 4032, 33, 4724, 1829, 3555, 4587, 7578, 15844, 2135, 15844, 426, 50113, 6027, 4032, 29910, 23275], "avg_logprob": -0.32071313987939787, "compression_ratio": 1.655367231638418, "no_speech_prob": 0.0, "words": [{"start": 2627.27, "end": 2627.71, "word": "الـ", "probability": 0.4683837890625}, {"start": 2627.71, "end": 2627.87, "word": " B", "probability": 0.441650390625}, {"start": 2627.87, "end": 2628.15, "word": " على", "probability": 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"probability": 0.61962890625}, {"start": 2632.39, "end": 2632.71, "word": " remainder", "probability": 0.9208984375}, {"start": 2632.71, "end": 2633.01, "word": " اللي", "probability": 0.6982421875}, {"start": 2633.01, "end": 2633.29, "word": " هنا", "probability": 0.974609375}, {"start": 2633.29, "end": 2633.95, "word": " بيقول", "probability": 0.686767578125}, {"start": 2633.95, "end": 2634.27, "word": " if", "probability": 0.50439453125}, {"start": 2634.27, "end": 2634.53, "word": " they", "probability": 0.927734375}, {"start": 2634.53, "end": 2634.83, "word": " have", "probability": 0.96435546875}, {"start": 2634.83, "end": 2635.09, "word": " the", "probability": 0.919921875}, {"start": 2635.09, "end": 2635.57, "word": " same", "probability": 0.90966796875}, {"start": 2635.57, "end": 2636.31, "word": " remainder", "probability": 0.9482421875}, {"start": 2636.31, "end": 2636.99, "word": " نفس", "probability": 0.936279296875}, {"start": 2636.99, "end": 2638.29, "word": " الباقي", "probability": 0.9508463541666666}, {"start": 2638.29, "end": 2638.95, "word": " نتيجة", "probability": 0.9837646484375}, {"start": 2638.95, "end": 2639.79, "word": " لقسمة", "probability": 0.935791015625}, {"start": 2639.79, "end": 2640.27, "word": " كل", "probability": 0.916015625}, {"start": 2640.27, "end": 2640.71, "word": " واحد", "probability": 0.9970703125}, {"start": 2640.71, "end": 2640.93, "word": " من", "probability": 0.984375}, {"start": 2640.93, "end": 2641.15, "word": " A", "probability": 0.88525390625}, {"start": 2641.15, "end": 2641.57, "word": " وB", "probability": 0.812255859375}, {"start": 2641.57, "end": 2641.81, "word": " بيبقى", "probability": 0.7275390625}, {"start": 2641.81, "end": 2641.95, "word": " على", "probability": 0.82177734375}, {"start": 2641.95, "end": 2642.35, "word": " main", "probability": 0.62744140625}, {"start": 2642.35, "end": 2643.07, "word": " على", "probability": 0.86376953125}, {"start": 2643.07, "end": 2643.51, "word": " N", "probability": 0.87255859375}, {"start": 2643.51, "end": 2644.17, "word": " مثال", "probability": 0.950927734375}, {"start": 2644.17, "end": 2644.27, "word": " و", "probability": 0.67333984375}, {"start": 2644.27, "end": 2644.71, "word": " ذلك", "probability": 0.86181640625}], "temperature": 1.0}, {"id": 108, "seek": 265915, "start": 2645.41, "end": 2659.15, "text": "لو جاي تقولش لك مثلا سبعتاشر modulo ستة قداش بده يساوي هذا؟ خمسة، ستة و ستة و اتناش من سبعتاشر بيظل خمسة", "tokens": [1211, 2407, 10874, 47302, 6055, 39648, 8592, 5296, 4117, 50113, 15040, 8608, 3555, 34268, 33599, 2288, 1072, 13455, 8608, 2655, 3660, 12174, 3215, 33599, 47525, 3224, 7251, 3794, 995, 45865, 23758, 22807, 16490, 2304, 3794, 3660, 12399, 8608, 2655, 3660, 4032, 8608, 2655, 3660, 4032, 1975, 2655, 1863, 33599, 9154, 8608, 3555, 34268, 33599, 2288, 4724, 1829, 19913, 1211, 16490, 2304, 3794, 3660], "avg_logprob": -0.23181151924654841, "compression_ratio": 1.4596774193548387, "no_speech_prob": 0.0, "words": [{"start": 2645.41, "end": 2645.81, "word": "لو", "probability": 0.744140625}, {"start": 2645.81, "end": 2646.03, "word": " جاي", "probability": 0.5855712890625}, {"start": 2646.03, "end": 2646.49, "word": " تقولش", "probability": 0.83642578125}, {"start": 2646.49, "end": 2646.73, "word": " لك", "probability": 0.76171875}, {"start": 2646.73, "end": 2647.27, "word": " مثلا", "probability": 0.951171875}, {"start": 2647.27, "end": 2649.15, "word": " سبعتاشر", "probability": 0.9255859375}, {"start": 2649.15, "end": 2650.55, "word": " modulo", "probability": 0.649169921875}, {"start": 2650.55, "end": 2651.59, "word": " ستة", "probability": 0.86279296875}, {"start": 2651.59, "end": 2652.35, "word": " قداش", "probability": 0.7138671875}, {"start": 2652.35, "end": 2652.63, "word": " بده", "probability": 0.5704345703125}, {"start": 2652.63, "end": 2652.97, "word": " يساوي", "probability": 0.9031982421875}, {"start": 2652.97, "end": 2653.99, "word": " هذا؟", "probability": 0.7705078125}, {"start": 2653.99, "end": 2655.33, "word": " خمسة،", "probability": 0.836328125}, {"start": 2655.33, "end": 2655.85, "word": " ستة", "probability": 0.8790690104166666}, {"start": 2655.85, "end": 2655.93, "word": " و", "probability": 0.96826171875}, {"start": 2655.93, "end": 2656.25, "word": " ستة", "probability": 0.87890625}, {"start": 2656.25, "end": 2656.41, "word": " و", "probability": 0.5380859375}, {"start": 2656.41, "end": 2656.65, "word": " اتناش", "probability": 0.8599853515625}, {"start": 2656.65, "end": 2656.81, "word": " من", "probability": 0.71728515625}, {"start": 2656.81, "end": 2657.67, "word": " سبعتاشر", "probability": 0.961328125}, {"start": 2657.67, "end": 2658.21, "word": " بيظل", "probability": 0.8736572265625}, {"start": 2658.21, "end": 2659.15, "word": " خمسة", "probability": 0.971923828125}], "temperature": 1.0}, {"id": 109, "seek": 268046, "start": 2661.24, "end": 2680.46, "text": "لو جيت قولتلك مثلا تسعة وعشرين موديولو ستة برضه خمسة يبقى بناء عليه ايش بقدر استنتج انه السبعتاشر موديولو ستة بتساوي تسعة وعشرين موديولو ستة", "tokens": [1211, 2407, 10874, 36081, 12174, 12610, 2655, 23275, 50113, 15040, 6055, 3794, 27884, 4032, 3615, 46309, 9957, 3714, 2407, 16254, 12610, 2407, 8608, 2655, 3660, 4724, 43042, 3224, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 1975, 1829, 8592, 4724, 28543, 2288, 44713, 29399, 7435, 16472, 3224, 21136, 3555, 34268, 33599, 2288, 3714, 2407, 16254, 12610, 2407, 8608, 2655, 3660, 39894, 3794, 995, 45865, 6055, 3794, 27884, 4032, 3615, 46309, 9957, 3714, 2407, 16254, 12610, 2407, 8608, 2655, 3660], "avg_logprob": -0.2347515103328659, "compression_ratio": 1.8962962962962964, "no_speech_prob": 0.0, "words": [{"start": 2661.24, "end": 2661.64, "word": "لو", "probability": 0.60125732421875}, {"start": 2661.64, "end": 2661.94, "word": " جيت", "probability": 0.4200439453125}, {"start": 2661.94, "end": 2662.52, "word": " قولتلك", "probability": 0.557708740234375}, {"start": 2662.52, "end": 2663.0, "word": " مثلا", "probability": 0.6995849609375}, {"start": 2663.0, "end": 2663.7, "word": " تسعة", "probability": 0.9171549479166666}, {"start": 2663.7, "end": 2664.9, "word": " وعشرين", "probability": 0.8262939453125}, {"start": 2664.9, "end": 2666.16, "word": " موديولو", "probability": 0.8673828125}, {"start": 2666.16, "end": 2666.64, "word": " ستة", "probability": 0.94091796875}, {"start": 2666.64, "end": 2668.14, "word": " برضه", "probability": 0.80029296875}, {"start": 2668.14, "end": 2669.2, "word": " خمسة", "probability": 0.931884765625}, {"start": 2669.2, "end": 2669.76, "word": " يبقى", "probability": 0.9512939453125}, {"start": 2669.76, "end": 2670.2, "word": " بناء", "probability": 0.965576171875}, {"start": 2670.2, "end": 2670.7, "word": " عليه", "probability": 0.400634765625}, {"start": 2670.7, "end": 2670.96, "word": " ايش", "probability": 0.6584065755208334}, {"start": 2670.96, "end": 2671.38, "word": " بقدر", "probability": 0.7513834635416666}, {"start": 2671.38, "end": 2672.1, "word": " استنتج", "probability": 0.8759765625}, {"start": 2672.1, "end": 2673.08, "word": " انه", "probability": 0.747802734375}, {"start": 2673.08, "end": 2674.48, "word": " السبعتاشر", "probability": 0.74765625}, {"start": 2674.48, "end": 2675.62, "word": " موديولو", "probability": 0.987890625}, {"start": 2675.62, "end": 2676.48, "word": " ستة", "probability": 0.978515625}, {"start": 2676.48, "end": 2677.44, "word": " بتساوي", "probability": 0.6512451171875}, {"start": 2677.44, "end": 2678.06, "word": " تسعة", "probability": 0.98779296875}, {"start": 2678.06, "end": 2679.18, "word": " وعشرين", "probability": 0.9739990234375}, {"start": 2679.18, "end": 2680.0, "word": " موديولو", "probability": 0.99013671875}, {"start": 2680.0, "end": 2680.46, "word": " ستة", "probability": 0.9920247395833334}], "temperature": 1.0}, {"id": 110, "seek": 270949, "start": 2681.01, "end": 2709.49, "text": "يبقى هدول الرقمين بيسووا بقى يعني الرمين درهينة بدي يسوى مين بدي يسوى الرمين درهينة نفسه بدون تغيير طيب في عندنا سؤال في الكتاب السؤال بدي أعطيه لك كمثال سؤال رقم تسعة من الكتاب بدي أكتبه على شكل example مربوط مع الكلام اللي احنا بنقوله هذا السؤال تسعة من الكتاب بيقولي F ال A", "tokens": [1829, 3555, 4587, 7578, 8032, 3215, 12610, 34892, 4587, 2304, 9957, 4724, 1829, 3794, 2407, 14407, 4724, 4587, 7578, 37495, 22653, 34892, 2304, 9957, 11778, 2288, 3224, 9957, 3660, 4724, 16254, 7251, 3794, 2407, 7578, 3714, 9957, 4724, 16254, 7251, 3794, 2407, 7578, 34892, 2304, 9957, 11778, 2288, 3224, 9957, 3660, 8717, 36178, 3224, 47525, 11536, 6055, 17082, 1829, 13546, 23032, 1829, 3555, 8978, 43242, 8315, 8608, 33604, 6027, 8978, 33251, 2655, 16758, 21136, 33604, 6027, 4724, 16254, 5551, 3615, 9566, 1829, 3224, 5296, 4117, 9122, 2304, 12984, 6027, 8608, 33604, 6027, 12602, 4587, 2304, 6055, 3794, 27884, 9154, 33251, 2655, 16758, 4724, 16254, 5551, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 1365, 3714, 25513, 2407, 9566, 20449, 2423, 28820, 10943, 13672, 1829, 1975, 5016, 8315, 44945, 39648, 3224, 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0.54541015625}, {"start": 2685.57, "end": 2685.99, "word": " يسوى", "probability": 0.61370849609375}, {"start": 2685.99, "end": 2686.33, "word": " مين", "probability": 0.89111328125}, {"start": 2686.33, "end": 2686.61, "word": " بدي", "probability": 0.88916015625}, {"start": 2686.61, "end": 2687.07, "word": " يسوى", "probability": 0.9627685546875}, {"start": 2687.07, "end": 2687.53, "word": " الرمين", "probability": 0.9684244791666666}, {"start": 2687.53, "end": 2688.37, "word": " درهينة", "probability": 0.98564453125}, {"start": 2688.37, "end": 2689.29, "word": " نفسه", "probability": 0.96044921875}, {"start": 2689.29, "end": 2690.21, "word": " بدون", "probability": 0.9853515625}, {"start": 2690.21, "end": 2690.83, "word": " تغيير", "probability": 0.965576171875}, {"start": 2690.83, "end": 2691.85, "word": " طيب", "probability": 0.9552408854166666}, {"start": 2691.85, "end": 2692.11, "word": " في", "probability": 0.60546875}, {"start": 2692.11, "end": 2692.49, "word": " عندنا", "probability": 0.938720703125}, {"start": 2692.49, "end": 2692.87, "word": " سؤال", "probability": 0.9952799479166666}, {"start": 2692.87, "end": 2693.03, "word": " في", "probability": 0.79638671875}, {"start": 2693.03, "end": 2693.57, "word": " الكتاب", "probability": 0.9845377604166666}, {"start": 2693.57, "end": 2694.05, "word": " السؤال", "probability": 0.9246419270833334}, {"start": 2694.05, "end": 2694.39, "word": " بدي", "probability": 0.787353515625}, {"start": 2694.39, "end": 2694.79, "word": " أعطيه", "probability": 0.87939453125}, {"start": 2694.79, "end": 2695.09, "word": " لك", "probability": 0.875732421875}, {"start": 2695.09, "end": 2695.85, "word": " كمثال", "probability": 0.989501953125}, {"start": 2695.85, "end": 2696.83, "word": " سؤال", "probability": 0.9503580729166666}, {"start": 2696.83, "end": 2697.33, "word": " رقم", "probability": 0.9920247395833334}, {"start": 2697.33, "end": 2697.79, "word": " تسعة", "probability": 0.8898111979166666}, {"start": 2697.79, "end": 2698.09, "word": " من", "probability": 0.98876953125}, {"start": 2698.09, "end": 2698.65, "word": " الكتاب", "probability": 0.99267578125}, {"start": 2698.65, "end": 2698.97, "word": " بدي", "probability": 0.931640625}, {"start": 2698.97, "end": 2699.43, "word": " أكتبه", "probability": 0.84169921875}, {"start": 2699.43, "end": 2699.63, "word": " على", "probability": 0.9111328125}, {"start": 2699.63, "end": 2700.25, "word": " شكل", "probability": 0.979736328125}, {"start": 2700.25, "end": 2701.23, "word": " example", "probability": 0.9013671875}, {"start": 2701.23, "end": 2702.83, "word": " مربوط", "probability": 0.980224609375}, {"start": 2702.83, "end": 2703.15, "word": " مع", "probability": 0.9873046875}, {"start": 2703.15, "end": 2703.73, "word": " الكلام", "probability": 0.9326171875}, {"start": 2703.73, "end": 2703.93, "word": " اللي", "probability": 0.942626953125}, {"start": 2703.93, "end": 2704.19, "word": " احنا", "probability": 0.86474609375}, {"start": 2704.19, 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prove that اثبت انه", "tokens": [474, 2423, 363, 366, 41674, 1975, 22488, 18513, 20328, 5016, 1829, 5016, 3660, 293, 2423, 426, 307, 257, 3353, 24922, 3353, 24922, 7081, 300, 1975, 12984, 3555, 2655, 16472, 3224], "avg_logprob": -0.19707661963278247, "compression_ratio": 1.2842105263157895, "no_speech_prob": 0.0, "words": [{"start": 2710.26, "end": 2710.9, "word": "and", "probability": 0.69677734375}, {"start": 2710.9, "end": 2711.26, "word": " ال", "probability": 0.82958984375}, {"start": 2711.26, "end": 2711.62, "word": " B", "probability": 0.128662109375}, {"start": 2711.62, "end": 2713.46, "word": " are", "probability": 0.880859375}, {"start": 2713.46, "end": 2715.68, "word": " integers", "probability": 0.9697265625}, {"start": 2715.68, "end": 2717.48, "word": " اعداد", "probability": 0.7333170572916666}, {"start": 2717.48, "end": 2719.34, "word": " صحيحة", "probability": 0.987109375}, {"start": 2719.34, "end": 2720.22, "word": " and", "probability": 0.87939453125}, {"start": 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112, "seek": 276031, "start": 2737.43, "end": 2760.31, "text": "Proof that ال A modulo N بدو يساوي B modulo N if and only if ال N divides ال A minus ال B", "tokens": [12681, 2670, 300, 2423, 316, 1072, 13455, 426, 47525, 2407, 7251, 3794, 995, 45865, 363, 1072, 13455, 426, 498, 293, 787, 498, 2423, 426, 41347, 2423, 316, 3175, 2423, 363], "avg_logprob": -0.3528225902588137, "compression_ratio": 1.1931818181818181, "no_speech_prob": 0.0, "words": [{"start": 2737.43, "end": 2738.07, "word": "Proof", "probability": 0.36578369140625}, {"start": 2738.07, "end": 2738.59, "word": " that", "probability": 0.74755859375}, {"start": 2738.59, "end": 2739.41, "word": " ال", "probability": 0.61376953125}, {"start": 2739.41, "end": 2739.89, "word": " A", "probability": 0.361328125}, {"start": 2739.89, "end": 2741.53, "word": " modulo", "probability": 0.817138671875}, {"start": 2741.53, "end": 2741.99, "word": " N", "probability": 0.91943359375}, {"start": 2741.99, "end": 2748.13, "word": " بدو", 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a", "tokens": [6780, 1975, 5172, 2655, 43042, 16472, 2423, 257, 1072, 13455, 297, 47525, 3224, 7251, 3794, 995, 45865, 2423, 272, 1072, 13455, 297, 23032, 1829, 3555, 9122, 45865, 3794, 9154, 2423, 10044, 9284, 2423, 257, 8032, 995, 16254, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 19446, 7251, 10721, 31371, 16472, 2423, 257], "avg_logprob": -0.1912667416036129, "compression_ratio": 1.4191176470588236, "no_speech_prob": 0.0, "words": [{"start": 2847.06, "end": 2847.84, "word": "that", "probability": 0.30615234375}, {"start": 2847.84, "end": 2848.66, "word": " افترض", "probability": 0.9293212890625}, {"start": 2848.66, "end": 2849.14, "word": " ان", "probability": 0.89990234375}, {"start": 2849.14, "end": 2850.06, "word": " ال", "probability": 0.802734375}, {"start": 2850.06, "end": 2850.56, "word": " a", "probability": 0.47998046875}, {"start": 2850.56, "end": 2851.76, "word": " modulo", "probability": 0.864501953125}, {"start": 2851.76, "end": 2852.2, "word": " n", "probability": 0.90966796875}, {"start": 2852.2, "end": 2853.24, "word": " بده", "probability": 0.360107421875}, {"start": 2853.24, "end": 2853.9, "word": " يساوي", "probability": 0.822265625}, {"start": 2853.9, "end": 2854.12, "word": " ال", "probability": 0.78173828125}, {"start": 2854.12, "end": 2854.7, "word": " b", "probability": 0.9580078125}, {"start": 2854.7, "end": 2855.82, "word": " modulo", "probability": 0.912353515625}, {"start": 2855.82, "end": 2856.54, "word": " n", "probability": 0.9482421875}, {"start": 2856.54, "end": 2859.52, "word": " طيب", "probability": 0.9231770833333334}, {"start": 2859.52, "end": 2860.2, "word": " كويس", "probability": 0.9705403645833334}, {"start": 2860.2, "end": 2861.0, "word": " من", "probability": 0.96337890625}, {"start": 2861.0, "end": 2861.18, "word": " ال", "probability": 0.974609375}, {"start": 2861.18, "end": 2861.54, "word": " division", "probability": 0.87548828125}, {"start": 2861.54, "end": 2862.54, "word": " algorithm", "probability": 0.947265625}, {"start": 2862.54, "end": 2863.66, "word": " ال", "probability": 0.82275390625}, {"start": 2863.66, "end": 2864.14, "word": " a", "probability": 0.9580078125}, {"start": 2864.14, "end": 2864.88, "word": " هادي", "probability": 0.6546223958333334}, {"start": 2864.88, "end": 2865.98, "word": " يبقى", "probability": 0.97021484375}, {"start": 2865.98, "end": 2866.38, "word": " هذا", "probability": 0.80859375}, {"start": 2866.38, "end": 2866.86, "word": " بده", "probability": 0.8671875}, {"start": 2866.86, "end": 2867.56, "word": " يعطينا", "probability": 0.962890625}, {"start": 2867.56, "end": 2869.78, "word": " ما", "probability": 0.412841796875}, {"start": 2869.78, "end": 2870.66, "word": " يأتي", "probability": 0.86083984375}, {"start": 2870.66, "end": 2871.74, "word": " ان", "probability": 0.76806640625}, {"start": 2871.74, "end": 2872.14, "word": " ال", "probability": 0.94384765625}, {"start": 2872.14, "end": 2872.74, "word": " a", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 116, "seek": 288923, "start": 2873.37, "end": 2889.23, "text": "والله خلينا نقول there exist مثلا q1 و r1 في z such that بحيث أن", "tokens": [2407, 6027, 43761, 16490, 1211, 9957, 995, 8717, 39648, 456, 2514, 50113, 15040, 9505, 16, 4032, 367, 16, 8978, 710, 1270, 300, 4724, 5016, 1829, 12984, 14739], "avg_logprob": -0.37834820789950235, "compression_ratio": 1.011111111111111, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2873.37, "end": 2873.87, "word": "والله", "probability": 0.5659993489583334}, {"start": 2873.87, "end": 2874.29, "word": " خلينا", "probability": 0.677001953125}, {"start": 2874.29, "end": 2874.75, "word": " نقول", "probability": 0.99365234375}, {"start": 2874.75, "end": 2875.27, "word": " there", "probability": 0.708984375}, {"start": 2875.27, "end": 2876.17, "word": " exist", "probability": 0.84521484375}, {"start": 2876.17, "end": 2878.81, "word": " مثلا", "probability": 0.763916015625}, {"start": 2878.81, "end": 2880.25, "word": " q1", "probability": 0.21527099609375}, {"start": 2880.25, "end": 2881.05, "word": " و", "probability": 0.9560546875}, {"start": 2881.05, "end": 2882.37, "word": " r1", "probability": 0.754638671875}, {"start": 2882.37, "end": 2883.67, "word": " في", "probability": 0.96875}, {"start": 2883.67, "end": 2884.75, "word": " z", "probability": 0.87451171875}, {"start": 2884.75, "end": 2885.91, "word": " such", "probability": 0.9306640625}, {"start": 2885.91, "end": 2886.97, "word": " that", "probability": 0.958984375}, {"start": 2886.97, "end": 2888.73, "word": " بحيث", "probability": 0.989501953125}, {"start": 2888.73, "end": 2889.23, "word": " أن", "probability": 0.55517578125}], "temperature": 1.0}, {"id": 117, "seek": 291675, "start": 2890.85, "end": 2916.75, "text": "والله جيبها مرة واحدة كلها بلاش نقعد نفصل فيها اكتر يبقى there exist a q1 و q2 و r1 و r2 and z such that ال a بده يساوي q1n زائد r1 and", "tokens": [2407, 6027, 43761, 10874, 1829, 3555, 11296, 3714, 25720, 36764, 24401, 3660, 28242, 11296, 4724, 1211, 33599, 8717, 4587, 22488, 8717, 5172, 36520, 8978, 11296, 1975, 4117, 2655, 2288, 7251, 3555, 4587, 7578, 456, 2514, 257, 9505, 16, 4032, 9505, 17, 4032, 367, 16, 4032, 367, 17, 293, 710, 1270, 300, 2423, 257, 47525, 3224, 7251, 3794, 995, 45865, 9505, 16, 77, 30767, 16373, 3215, 367, 16, 293], "avg_logprob": -0.2127490933390631, "compression_ratio": 1.2774193548387096, "no_speech_prob": 0.0, "words": [{"start": 2890.85, "end": 2891.37, "word": "والله", "probability": 0.6765950520833334}, {"start": 2891.37, "end": 2891.71, "word": " جيبها", "probability": 0.853271484375}, {"start": 2891.71, "end": 2892.69, "word": " مرة", "probability": 0.8974609375}, {"start": 2892.69, "end": 2893.19, "word": " واحدة", "probability": 0.966796875}, {"start": 2893.19, "end": 2893.99, "word": " كلها", "probability": 0.75439453125}, {"start": 2893.99, "end": 2894.41, "word": " بلاش", "probability": 0.656494140625}, {"start": 2894.41, "end": 2894.75, "word": " نقعد", "probability": 0.8680013020833334}, {"start": 2894.75, "end": 2895.27, "word": " نفصل", "probability": 0.9488932291666666}, {"start": 2895.27, "end": 2895.57, "word": " فيها", "probability": 0.95458984375}, {"start": 2895.57, "end": 2895.99, "word": " اكتر", "probability": 0.8890380859375}, {"start": 2895.99, "end": 2897.11, "word": " يبقى", "probability": 0.968017578125}, {"start": 2897.11, "end": 2897.27, "word": " there", "probability": 0.6171875}, {"start": 2897.27, "end": 2897.93, "word": " exist", "probability": 0.78173828125}, {"start": 2897.93, "end": 2898.27, "word": " a", "probability": 0.85986328125}, {"start": 2898.27, "end": 2898.99, "word": " q1", "probability": 0.490478515625}, {"start": 2898.99, "end": 2899.67, "word": " و", "probability": 0.95458984375}, {"start": 2899.67, "end": 2900.59, "word": " q2", "probability": 0.88916015625}, {"start": 2900.59, "end": 2900.97, "word": " و", "probability": 0.9638671875}, {"start": 2900.97, "end": 2901.73, "word": " r1", "probability": 0.836669921875}, {"start": 2901.73, "end": 2902.29, "word": " و", "probability": 0.98828125}, {"start": 2902.29, "end": 2903.13, "word": " r2", "probability": 0.962646484375}, {"start": 2903.13, "end": 2903.67, "word": " and", "probability": 0.5458984375}, {"start": 2903.67, "end": 2904.33, "word": " z", "probability": 0.81884765625}, {"start": 2904.33, "end": 2905.35, "word": " such", "probability": 0.94677734375}, {"start": 2905.35, "end": 2905.95, "word": " that", "probability": 0.9521484375}, {"start": 2905.95, "end": 2909.21, "word": " ال", "probability": 0.7998046875}, {"start": 2909.21, "end": 2909.71, "word": " a", "probability": 0.69970703125}, {"start": 2909.71, "end": 2910.81, "word": " بده", "probability": 0.41064453125}, {"start": 2910.81, "end": 2911.23, "word": " يساوي", "probability": 0.85986328125}, {"start": 2911.23, "end": 2913.27, "word": " q1n", "probability": 0.7734375}, {"start": 2913.27, "end": 2914.49, "word": " زائد", "probability": 0.7890625}, {"start": 2914.49, "end": 2915.43, "word": " r1", "probability": 0.9833984375}, {"start": 2915.43, "end": 2916.75, "word": " and", "probability": 0.9521484375}], "temperature": 1.0}, {"id": 118, "seek": 292711, "start": 2917.53, "end": 2927.11, "text": "طبعا ال R1 هذه اكبر من أو تساوي ال zero و اقل من مين ان", "tokens": [9566, 3555, 3615, 995, 2423, 497, 16, 29538, 1975, 4117, 26890, 9154, 34051, 6055, 3794, 995, 45865, 2423, 4018, 4032, 1975, 4587, 1211, 9154, 3714, 9957, 16472], "avg_logprob": -0.2988281345793179, "compression_ratio": 1.0843373493975903, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2917.53, "end": 2918.31, "word": "طبعا", "probability": 0.86834716796875}, {"start": 2918.31, "end": 2918.95, "word": " ال", "probability": 0.90185546875}, {"start": 2918.95, "end": 2919.73, "word": " R1", "probability": 0.66064453125}, {"start": 2919.73, "end": 2920.25, "word": " هذه", "probability": 0.6171875}, {"start": 2920.25, "end": 2923.29, "word": " اكبر", "probability": 0.7213541666666666}, {"start": 2923.29, "end": 2923.57, "word": " من", "probability": 0.8818359375}, {"start": 2923.57, "end": 2923.89, "word": " أو", "probability": 0.5615234375}, {"start": 2923.89, "end": 2924.45, "word": " تساوي", "probability": 0.930908203125}, {"start": 2924.45, "end": 2924.59, "word": " ال", "probability": 0.84765625}, {"start": 2924.59, "end": 2924.95, "word": " zero", "probability": 0.61328125}, {"start": 2924.95, "end": 2925.57, "word": " و", "probability": 0.6953125}, {"start": 2925.57, "end": 2926.01, "word": " اقل", "probability": 0.9002278645833334}, {"start": 2926.01, "end": 2926.21, "word": " من", "probability": 0.99462890625}, {"start": 2926.21, "end": 2926.63, "word": " مين", "probability": 0.80712890625}, {"start": 2926.63, "end": 2927.11, "word": " ان", "probability": 0.287353515625}], "temperature": 1.0}, {"id": 119, "seek": 295807, "start": 2929.13, "end": 2958.07, "text": "وفي نفس الوقت ال B يبقى Q2N زائد R2 وR2 أكبر من أو تساوي 0 أقل من ال N يبقى هذول كخوارزمية القسمة إيش الفرض اللي عنده هنا بيقول افترض هذول بيسووا بعض يبقى معناته ال remainder هنا بيسووا ال remainder هنا يعني إيش؟", "tokens": [2407, 41185, 8717, 36178, 2423, 30543, 2655, 2423, 363, 7251, 3555, 4587, 7578, 1249, 17, 45, 30767, 16373, 3215, 497, 17, 4032, 49, 17, 5551, 4117, 26890, 9154, 34051, 6055, 3794, 995, 45865, 1958, 5551, 4587, 1211, 9154, 2423, 426, 7251, 3555, 4587, 7578, 8032, 8848, 12610, 9122, 9778, 2407, 9640, 11622, 2304, 10632, 25062, 38251, 3660, 11933, 1829, 8592, 27188, 43042, 13672, 1829, 43242, 3224, 34105, 4724, 1829, 39648, 1975, 5172, 2655, 43042, 8032, 8848, 12610, 4724, 1829, 3794, 2407, 14407, 45030, 11242, 7251, 3555, 4587, 7578, 20449, 8315, 47395, 2423, 29837, 34105, 4724, 1829, 3794, 2407, 14407, 2423, 29837, 34105, 37495, 22653, 11933, 1829, 8592, 22807], "avg_logprob": -0.27737957731299445, "compression_ratio": 1.7053140096618358, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2929.13, "end": 2929.55, "word": "وفي", "probability": 0.4852294921875}, {"start": 2929.55, "end": 2929.93, "word": " نفس", "probability": 0.99658203125}, {"start": 2929.93, "end": 2930.47, "word": " الوقت", "probability": 0.9778645833333334}, {"start": 2930.47, "end": 2930.75, "word": " ال", "probability": 0.8369140625}, {"start": 2930.75, "end": 2931.03, "word": " B", "probability": 0.2362060546875}, {"start": 2931.03, "end": 2931.95, "word": " يبقى", "probability": 0.59613037109375}, {"start": 2931.95, "end": 2933.87, "word": " Q2N", "probability": 0.5372721354166666}, {"start": 2933.87, "end": 2934.95, "word": " زائد", "probability": 0.5005238850911459}, {"start": 2934.95, "end": 2935.85, "word": " R2", "probability": 0.97021484375}, {"start": 2935.85, "end": 2938.17, "word": " وR2", "probability": 0.68310546875}, {"start": 2938.17, "end": 2938.89, "word": " أكبر", "probability": 0.89892578125}, {"start": 2938.89, "end": 2939.11, "word": " من", "probability": 0.8466796875}, {"start": 2939.11, "end": 2939.39, "word": " أو", "probability": 0.80517578125}, {"start": 2939.39, "end": 2939.97, "word": " تساوي", "probability": 0.7408447265625}, {"start": 2939.97, "end": 2940.41, "word": " 0", "probability": 0.219970703125}, {"start": 2940.41, "end": 2941.13, "word": " أقل", "probability": 0.9044596354166666}, {"start": 2941.13, "end": 2941.35, "word": " من", "probability": 0.9814453125}, {"start": 2941.35, "end": 2942.73, "word": " ال", "probability": 0.2276611328125}, {"start": 2942.73, "end": 2943.17, "word": " N", "probability": 0.54833984375}, {"start": 2943.17, "end": 2944.73, "word": " يبقى", "probability": 0.865966796875}, {"start": 2944.73, "end": 2945.33, "word": " هذول", "probability": 0.7967122395833334}, {"start": 2945.33, "end": 2946.63, "word": " كخوارزمية", "probability": 0.9501255580357143}, {"start": 2946.63, "end": 2947.75, "word": " القسمة", "probability": 0.9871419270833334}, {"start": 2947.75, "end": 2948.09, "word": " إيش", "probability": 0.723388671875}, {"start": 2948.09, "end": 2948.57, "word": " الفرض", "probability": 0.95751953125}, {"start": 2948.57, "end": 2948.81, "word": " اللي", "probability": 0.872802734375}, {"start": 2948.81, "end": 2949.27, "word": " عنده", "probability": 0.5037841796875}, {"start": 2949.27, "end": 2949.53, "word": " هنا", "probability": 0.7412109375}, {"start": 2949.53, "end": 2950.01, "word": " بيقول", "probability": 0.8645833333333334}, {"start": 2950.01, "end": 2951.09, "word": " افترض", "probability": 0.8895263671875}, {"start": 2951.09, "end": 2951.65, "word": " هذول", "probability": 0.978515625}, {"start": 2951.65, "end": 2952.29, "word": " بيسووا", "probability": 0.8240234375}, {"start": 2952.29, "end": 2952.77, "word": " بعض", "probability": 0.98974609375}, {"start": 2952.77, "end": 2953.55, "word": " يبقى", "probability": 0.9171142578125}, {"start": 2953.55, "end": 2954.07, "word": " معناته", "probability": 0.9013671875}, {"start": 2954.07, "end": 2954.23, "word": " ال", "probability": 0.75732421875}, {"start": 2954.23, "end": 2954.61, "word": " remainder", "probability": 0.8798828125}, {"start": 2954.61, "end": 2955.23, "word": " هنا", "probability": 0.8857421875}, {"start": 2955.23, "end": 2955.95, "word": " بيسووا", "probability": 0.680078125}, {"start": 2955.95, "end": 2956.07, "word": " ال", "probability": 0.366455078125}, {"start": 2956.07, "end": 2956.45, "word": " remainder", "probability": 0.95263671875}, {"start": 2956.45, "end": 2957.03, "word": " هنا", "probability": 0.98095703125}, {"start": 2957.03, "end": 2957.43, "word": " يعني", "probability": 0.948486328125}, {"start": 2957.43, "end": 2958.07, "word": " إيش؟", "probability": 0.8990478515625}], "temperature": 1.0}, {"id": 120, "seek": 297537, "start": 2958.39, "end": 2975.37, "text": "ار واحد تساوي ار اتنين يبقى باجي بقوله بما ان since ال a modulo n بده يساوي ال b modulo n we have", "tokens": [9640, 36764, 24401, 6055, 3794, 995, 45865, 1975, 2288, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 4724, 15042, 16472, 1670, 2423, 257, 1072, 13455, 297, 47525, 3224, 7251, 3794, 995, 45865, 2423, 272, 1072, 13455, 297, 321, 362], "avg_logprob": -0.2963654956092005, "compression_ratio": 1.2719298245614035, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2958.39, "end": 2958.51, "word": "ار", "probability": 0.10821533203125}, {"start": 2958.51, "end": 2959.75, "word": " واحد", "probability": 0.94970703125}, {"start": 2959.75, "end": 2960.27, "word": " تساوي", "probability": 0.763671875}, {"start": 2960.27, "end": 2960.75, "word": " ار", "probability": 0.61865234375}, {"start": 2960.75, "end": 2961.31, "word": " اتنين", "probability": 0.9747314453125}, {"start": 2961.31, "end": 2962.01, "word": " يبقى", "probability": 0.8013916015625}, {"start": 2962.01, "end": 2962.35, "word": " باجي", "probability": 0.87744140625}, {"start": 2962.35, "end": 2962.91, "word": " بقوله", "probability": 0.892578125}, {"start": 2962.91, 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{"start": 3079.62, "end": 3080.5, "word": " ان", "probability": 0.90576171875}, {"start": 3080.5, "end": 3080.9, "word": " ال", "probability": 0.95361328125}, {"start": 3080.9, "end": 3081.38, "word": " N", "probability": 0.884765625}, {"start": 3081.38, "end": 3082.14, "word": " divide", "probability": 0.91015625}, {"start": 3082.14, "end": 3082.58, "word": " ال", "probability": 0.9697265625}, {"start": 3082.58, "end": 3082.98, "word": " A", "probability": 0.96435546875}, {"start": 3082.98, "end": 3083.58, "word": " minus", "probability": 0.68701171875}, {"start": 3083.58, "end": 3083.9, "word": " ال", "probability": 0.91357421875}, {"start": 3083.9, "end": 3084.12, "word": " B", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 125, "seek": 310766, "start": 3085.66, "end": 3107.66, "text": "وبدى احاول اثبت ان ال a modulo n بدر سوى ال b modulo n يبجى هذا معناه ايه ان ال a نقص ال b بدر سوى ال aq في n وال aq موجودة وين في z في remainder", "tokens": [37746, 3215, 7578, 1975, 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"probability": 0.9869791666666666}], "temperature": 1.0}, {"id": 128, "seek": 317234, "start": 3154.1, "end": 3172.34, "text": "إن ال A modulo N بده ساوي ال B modulo N اللي هو ال remainder وهو المطلوب يبقى الاتجاه التاني أبسط من من الاتجاه الأول يعطيكوا العافية بنكمل ان شاء الله المرة القادمة", "tokens": [28814, 1863, 2423, 316, 1072, 13455, 426, 47525, 3224, 8608, 995, 45865, 2423, 363, 1072, 13455, 426, 13672, 1829, 31439, 2423, 29837, 37037, 2407, 9673, 9566, 1211, 37746, 7251, 3555, 4587, 7578, 2423, 9307, 7435, 40294, 16712, 7649, 1829, 5551, 3555, 3794, 9566, 9154, 9154, 2423, 9307, 7435, 40294, 16247, 12610, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 44945, 24793, 1211, 16472, 13412, 16606, 21984, 9673, 25720, 25062, 18513, 46007], "avg_logprob": -0.24913194278875986, "compression_ratio": 1.5689655172413792, "no_speech_prob": 3.49879264831543e-05, "words": [{"start": 3154.1, "end": 3154.68, "word": "إن", "probability": 0.53375244140625}, {"start": 3154.68, "end": 3155.0, "word": " ال", "probability": 0.68408203125}, {"start": 3155.0, "end": 3155.46, "word": " A", "probability": 0.209716796875}, {"start": 3155.46, "end": 3156.36, "word": " modulo", "probability": 0.808349609375}, {"start": 3156.36, "end": 3156.74, "word": " N", "probability": 0.8740234375}, {"start": 3156.74, "end": 3157.34, "word": " بده", "probability": 0.2418212890625}, {"start": 3157.34, "end": 3157.86, "word": " ساوي", "probability": 0.7763671875}, {"start": 3157.86, "end": 3158.06, "word": " ال", "probability": 0.6328125}, {"start": 3158.06, "end": 3158.44, "word": " B", "probability": 0.93798828125}, {"start": 3158.44, "end": 3159.32, "word": " modulo", "probability": 0.915283203125}, {"start": 3159.32, "end": 3159.62, "word": " N", "probability": 0.9853515625}, {"start": 3159.62, "end": 3159.78, "word": " اللي", "probability": 0.765625}, {"start": 3159.78, "end": 3159.94, "word": " هو", "probability": 0.98828125}, {"start": 3159.94, "end": 3160.08, "word": " ال", "probability": 0.56884765625}, {"start": 3160.08, "end": 3160.56, "word": " remainder", "probability": 0.89697265625}, {"start": 3160.56, "end": 3161.3, "word": " وهو", "probability": 0.75537109375}, {"start": 3161.3, "end": 3162.86, "word": " المطلوب", "probability": 0.9647216796875}, {"start": 3162.86, "end": 3163.96, "word": " يبقى", "probability": 0.9544677734375}, {"start": 3163.96, "end": 3164.48, "word": " الاتجاه", "probability": 0.82080078125}, {"start": 3164.48, "end": 3164.96, "word": " التاني", "probability": 0.9275716145833334}, {"start": 3164.96, "end": 3165.44, "word": " أبسط", "probability": 0.97705078125}, {"start": 3165.44, "end": 3165.64, "word": " من", "probability": 0.98046875}, {"start": 3165.64, "end": 3165.92, "word": " من", "probability": 0.332275390625}, {"start": 3165.92, "end": 3167.46, "word": " الاتجاه", "probability": 0.83544921875}, {"start": 3167.46, "end": 3167.82, "word": " الأول", "probability": 0.94384765625}, {"start": 3167.82, "end": 3168.32, "word": " يعطيكوا", "probability": 0.6990966796875}, {"start": 3168.32, "end": 3169.0, "word": " العافية", "probability": 0.9378255208333334}, {"start": 3169.0, "end": 3170.02, "word": " بنكمل", "probability": 0.88818359375}, {"start": 3170.02, "end": 3170.18, "word": " ان", "probability": 0.56494140625}, {"start": 3170.18, "end": 3170.5, "word": " شاء", "probability": 0.978515625}, {"start": 3170.5, "end": 3170.82, "word": " الله", "probability": 0.93603515625}, {"start": 3170.82, "end": 3171.66, "word": " المرة", "probability": 0.97607421875}, {"start": 3171.66, "end": 3172.34, "word": " القادمة", "probability": 0.9542643229166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3172.914, "duration_after_vad": 2902.6349999999907}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..002b7c191c184c1c6dba9f5e46f5776c464f6ec2
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM.srt
@@ -0,0 +1,2011 @@
+1
+00:00:20,790 --> 00:00:25,630
+بسم الله الرحمن الرحيم محاضرتنا اليوم إن شاء الله
+
+2
+00:00:25,630 --> 00:00:33,770
+تعالَ هي في جبر حديث واحد طبعًا إن بتعرفوا إن مادة
+
+3
+00:00:33,770 --> 00:00:38,930
+جبر الحديث الواحد وكذلك مادة تحليل حقيقي واحد
+
+4
+00:00:38,930 --> 00:00:43,010
+ومادة الـ topology هي أثقل ثلاث مواد بالنسبة
+
+5
+00:00:43,010 --> 00:00:47,990
+للرياضيات اللي أخذتوها كلصادة ما هو إلا بسكوتة
+
+6
+00:00:47,990 --> 00:00:53,040
+الرياضيات يعني بسيط جدًا إذا قيس بالجبر أو التحليل
+
+7
+00:00:53,040 --> 00:00:56,720
+أو الـ topology لكن إن شاء الله من خلال دراستنا
+
+8
+00:00:56,720 --> 00:01:01,520
+هلاقي المادة بسيطة لإنه سنحاول أن نبسطها إلى أبعد
+
+9
+00:01:01,520 --> 00:01:07,940
+الحدود بحيث تستوعبها وتفهمها تمامًا لكن قبل أن أبدأ
+
+10
+00:01:07,940 --> 00:01:13,340
+بدي كل واحد جوال يكون مغلق تحاول تلتزم بالحضور
+
+11
+00:01:13,340 --> 00:01:17,000
+الساعة تسعة يعني الساعة تسعة تمامًا طبعًا احنا
+
+12
+00:01:17,000 --> 00:01:20,840
+اتأخرنا خمس دقائق لأن ذهبت إلى المبنى الثاني و
+
+13
+00:01:20,840 --> 00:01:25,620
+كتبت إنتقال المحاضرة إلى قاعة التصوير فالأسبوع
+
+14
+00:01:25,620 --> 00:01:30,640
+الأربع ساعات بدنا ندومهم هنا المادة أربع ساعات وليس ثلاث
+
+15
+00:01:30,640 --> 00:01:34,960
+ساعات كما كانت من قبل قبل كانت ثلاث ساعات وساعات
+
+16
+00:01:34,960 --> 00:01:40,060
+مناقشة أربع ساعات اللي هي من ضمنهم المناقشة المدرس
+
+17
+00:01:40,060 --> 00:01:44,860
+هو الذي سيناقش معك المسائل مش المعيد كما كان في
+
+18
+00:01:44,860 --> 00:01:50,280
+الأعوام السابقة اليوم عندنا محاضرتين المحاضرة
+
+19
+00:01:50,280 --> 00:01:55,680
+الأولى هذه سنتكلم فيها الخطوط العريضة للمنهج
+
+20
+00:01:55,680 --> 00:01:58,920
+والمحاضرة الثانية اللي بتبدأ الساعة اثنا عشر إن شاء
+
+21
+00:01:58,920 --> 00:02:06,570
+الله سندخل في صميم المقرر طيب قبل أن نبدأ أحب أن
+
+22
+00:02:06,570 --> 00:02:12,830
+أركز على كيفية فهم المادة مشان تفهم المادة يجب أن
+
+23
+00:02:12,830 --> 00:02:17,910
+تحرص على الحضور مبكرًا الساعة تسعة يمكن تسعة و دقيقة
+
+24
+00:02:17,910 --> 00:02:21,650
+تلاقيني هنا إن تأخرت دقيقة بكون بس في الأسانسير
+
+25
+00:02:22,190 --> 00:02:26,230
+لكن الساعة تسعة بدي الكل .. ولو كنت تسعة و عشر
+
+26
+00:02:26,230 --> 00:02:30,210
+بكون أحسن أنا بعرف بدك تنتقل من مبنى إلى مبنى من
+
+27
+00:02:30,210 --> 00:02:34,450
+قاعة إلى قاعة ياخذ لك خمس دقائق المهم الساعة تسعة
+
+28
+00:02:34,450 --> 00:02:40,070
+بدك تجي قاعة أيه جاعد هنا في مقعدك تنتظر اللي هو
+
+29
+00:02:40,070 --> 00:02:46,530
+ما سيشرح أمامك حتى تستطيع أن تستوعب المادة مشان
+
+30
+00:02:46,530 --> 00:02:52,150
+تفهمها لازم تروح تجري المحاضرة بمجرد ما تاخدها
+
+31
+00:02:52,150 --> 00:02:57,190
+خلال المحاضرة بيطلع على ذهنك سؤال بتحب تناقشه بترفع
+
+32
+00:02:57,190 --> 00:03:02,370
+يدك بنقولك تفضل وما عنديش إجابة جماعية الإجابة
+
+33
+00:03:02,370 --> 00:03:05,470
+الفردية اللي هو السؤال فشان بترفع يدك بنقولك
+
+34
+00:03:05,470 --> 00:03:10,890
+تفضل حتى تكون الفائدة عامة للجميع بلا استثناء
+
+35
+00:03:11,240 --> 00:03:16,200
+واحنا كلامنا قصير ما نحبش إن يعني نجرّش الكلام
+
+36
+00:03:16,200 --> 00:03:23,500
+لكثير لأن أفضل الكلام يعني ما قلة عدده هو كثرة
+
+37
+00:03:23,500 --> 00:03:29,200
+معانيه ولذلك علمنا في معاني كثيرة إن شاء الله
+
+38
+00:03:29,200 --> 00:03:35,360
+سنتعرض لها من خلال دراستنا لمساق الجبر الحديث واحد
+
+39
+00:03:35,830 --> 00:03:40,250
+طيب روحنا على البيت الدراسة ليست أنك تقرأ المحاضرة
+
+40
+00:03:40,250 --> 00:03:45,070
+وتقرأ الأمثلة صحيح إن هذا ضروري جدًا لكن حل
+
+41
+00:03:45,070 --> 00:03:52,710
+الأسئلة له ضرورة كبيرة جدًا في فهم من الموضوع يعني
+
+42
+00:03:52,710 --> 00:03:57,310
+الـ definition النظرية اللي مليانة الفرضية المساعدة
+
+43
+00:03:57,310 --> 00:04:01,390
+النتيجة اللي موجودة على النظرية كلها قد تجد عليها
+
+44
+00:04:01,390 --> 00:04:05,270
+على كل واحدة فيها مجموعة من الأسئلة في التمرين
+
+45
+00:04:05,270 --> 00:04:11,000
+والحمد لله كتابنا مليان بالتمرين التطبيقي قد تكون
+
+46
+00:04:11,000 --> 00:04:17,600
+عددية وقد تكون نظرية طيب السؤال هو ما هو المساق
+
+47
+00:04:17,600 --> 00:04:23,140
+السابق الذي يعتمد عليه هذا المساق طبعًا سؤال وجيه
+
+48
+00:04:23,140 --> 00:04:27,780
+جدا وكتير منكم كان بإمكانه أو يدور في خلده أن يسأل
+
+49
+00:04:27,780 --> 00:04:33,190
+هذا السؤال المادة الأساسية اللي لازم لها لهذه المادة
+
+50
+00:04:33,190 --> 00:04:38,410
+هي مادة مبادئ الرياضيات Principle of mathematics
+
+51
+00:04:38,410 --> 00:04:42,910
+طبعًا ولذلك الـ chapter الأول عندنا في هذا الكتاب
+
+52
+00:04:42,910 --> 00:04:48,310
+يعتبر مراجعة لما سبقت دراسته في مبادئ الرياضيات
+
+53
+00:04:48,310 --> 00:04:54,610
+الأعداد الصحيحة الأعداد الطبيعية الأعداد الجذرية
+
+54
+00:04:54,610 --> 00:05:00,740
+مجموعة الأعداد الحقيقية مجموعة الأعداد التخيلية هذا
+
+55
+00:05:00,740 --> 00:05:06,520
+الأساس أو الخمس مجموعات هذه هو الذي أُسس عليها علم
+
+56
+00:05:06,520 --> 00:05:11,670
+الجبر اللي بين إيدينا هي لازم لنا بعض الشغلات البسيطة
+
+57
+00:05:11,670 --> 00:05:16,150
+مش كتير من مادة الـ Number theory نظرية الأعداد
+
+58
+00:05:16,150 --> 00:05:22,130
+ستكون في المقدمة ولذلك كل الأشياء الضرورية خلال
+
+59
+00:05:22,130 --> 00:05:26,150
+دراستنا في موضوع الجبر الحديث سنضعها لك في
+
+60
+00:05:26,150 --> 00:05:32,130
+chapter المقدمة وبعد هيك كل شوي بيطلعانة واحدة منهم
+
+61
+00:05:32,130 --> 00:05:37,380
+يكون إيه ملمين قبها أو ذكرنا بها في بداية دراستنا
+
+62
+00:05:37,380 --> 00:05:43,440
+هنا يبقى مبادئ الرياضيات أساسية جدا لفهم الجبر
+
+63
+00:05:43,440 --> 00:05:47,640
+والتحليل والـ topology كله بيعتمد على مادة مبادئ
+
+64
+00:05:47,640 --> 00:05:51,240
+الرياضيات وأنت في مبادئ الرياضيات في الشتر الأول
+
+65
+00:05:51,240 --> 00:05:56,780
+أخذت الطرق المختلفة للبراهين ولذلك الشغل هيكون
+
+66
+00:05:56,780 --> 00:06:01,480
+مليان براهين براهين كثيرة وكلها مطلوبة لإن أنت
+
+67
+00:06:01,480 --> 00:06:06,540
+إنسان متخصص وبعد سنة أو سنتين بدك تقف تشرح
+
+68
+00:06:06,540 --> 00:06:12,300
+للطلاب لذلك ضروري تكون تعرف تبرهن حتى تستطيع تبرهن
+
+69
+00:06:12,300 --> 00:06:15,900
+بعد سنة أو سنتين للطلاب سواء كان في المدارس
+
+70
+00:06:15,900 --> 00:06:21,580
+الإعدادية أو المدارس الثانوية أو ربما يكون بعضكم
+
+71
+00:06:21,580 --> 00:06:26,460
+معيدًا عندنا في الكلية ويطور نفسه وبعض ذلك يصبح
+
+72
+00:06:26,460 --> 00:06:32,160
+زميلًا لنا كما كثير منه الزملاء هم خريجي الجامعة
+
+73
+00:06:32,160 --> 00:06:37,100
+الإسلامية من عندنا واتدرسناهم والآن هاهم زملاء
+
+74
+00:06:37,100 --> 00:06:41,660
+لنا في القسم بل رئيس القسم الدكتور أحمد بابحوح هو
+
+75
+00:06:41,660 --> 00:06:46,400
+أحد خريجي الجامعة الإسلامية الدكتور الرائد قبله
+
+76
+00:06:46,400 --> 00:06:51,850
+برضه خريجي الجامعة الإسلامية وهكذا فيعني تستجلش
+
+77
+00:06:51,850 --> 00:06:55,670
+بنفسك لكن اللي بيشتغل هو اللي بيقدم اللي بيشتغلش
+
+78
+00:06:55,670 --> 00:06:59,030
+بيبقى قاعد وعمره ما بيقدم بيصير حاط على الكم زي
+
+79
+00:06:59,030 --> 00:07:03,470
+باقي الناس لكن اللي بيشغل مخ وبيشتغل هذا هو اللي
+
+80
+00:07:03,470 --> 00:07:07,870
+بيقدم أنت لأن في المستوى الثالث يبقى احرص على أن
+
+81
+00:07:07,870 --> 00:07:12,950
+المستوى الثالث والرابع ترفع معدلك حتى تتمكن من
+
+82
+00:07:12,950 --> 00:07:19,670
+العمل أو إكمال دراستك بعد ذلك يبقى هذه الأشياء
+
+83
+00:07:19,670 --> 00:07:23,770
+ضرورية نقرأ المحاضرة أن نفهم المحاضرة بقدر
+
+84
+00:07:23,770 --> 00:07:28,330
+الإمكان يصيب عليك شغل بتسألني بتروح على الدار بتقرأ
+
+85
+00:07:28,330 --> 00:07:32,130
+المحاضرة من جديد بتقرأ الأمثلة بتبدأ تحل
+
+86
+00:07:32,130 --> 00:07:36,570
+الأسئلة وفي نهاية كل Section بنخلي المحاضرة
+
+87
+00:07:36,570 --> 00:07:42,490
+للمناقشة خصوصًا الأصل اللي هنعطيك أرقامها بحيث تكون
+
+88
+00:07:42,490 --> 00:07:47,990
+مجهز حالك لحل هذه المسائل هذا بالنسبة للدراسة أما
+
+89
+00:07:47,990 --> 00:07:52,270
+بالنسبة للامتحانات فعندنا امتحانين أعمال فصل
+
+90
+00:07:52,270 --> 00:07:56,050
+الامتحان الأول بيكون حوالي أربعين يوم من بدء
+
+91
+00:07:56,050 --> 00:08:00,370
+الدراسة يعني اليوم السابعة تسعة أتوقع حوالي عشرين
+
+92
+00:08:00,370 --> 00:08:05,000
+عشرة قبله بيوم يومين أو بعده بيوم يومين ثلاثة هيكون
+
+93
+00:08:05,000 --> 00:08:08,860
+عندك الامتحان الأول كل امتحان عليه خمسة وعشرون
+
+94
+00:08:08,860 --> 00:08:14,660
+درجة يبقى امتحانين بخمسين درجة يبقى النهاية بقداش
+
+95
+00:08:14,660 --> 00:08:20,380
+بخمسين درجة طيب هذا بالنسبة لكيفية الدراسة و بنفسي
+
+96
+00:08:20,380 --> 00:08:26,070
+ولا الامتحان الحضور عندي أساسي وسأأخذ حضور وغياب
+
+97
+00:08:26,070 --> 00:08:30,030
+أول أسبوعين مشان السحب والإضافة بأخذ حضور وغياب
+
+98
+00:08:30,030 --> 00:08:34,810
+ابتداءً من اليوم الأول في الأسبوع الثالث بأخذ حضور و
+
+99
+00:08:34,810 --> 00:08:38,830
+غياب لو غيبت عندي خمسة وعشرون في المئة أعتبر حالك
+
+100
+00:08:38,830 --> 00:08:43,770
+مفصول على ذو الخط بنلغي تسجيلك لكن بنبلغك هذا أنا
+
+101
+00:08:43,770 --> 00:08:49,960
+ببلغ من اليوم الحضور عندي .. الحضور بد يكون لو غبت
+
+102
+00:08:49,960 --> 00:08:53,520
+خمسة وعشرون في المئة أعتبر حالك مفصول، مفصول من
+
+103
+00:08:53,520 --> 00:08:57,620
+المادة على طول القطب، منشطب تسجيلكم يقولك أنت مع
+
+104
+00:08:57,620 --> 00:09:02,540
+السلام بلزمكش تكون حاضر عن هنا، لأن الحضور أساسي،
+
+105
+00:09:02,540 --> 00:09:07,380
+طبعًا سيدعي بعض يكون أن أنا بأحضرها على التصوير ما هي
+
+106
+00:09:07,380 --> 00:09:11,820
+مصورة بالفيديو بتيجي بالصوت والصورة بقولك صحيح
+
+107
+00:09:11,820 --> 00:09:17,840
+الصورة ليست كالأصل يعني أنت حاضر هنا تطلع لنظرة
+
+108
+00:09:17,840 --> 00:09:23,220
+العين حركات اليدين المناقشة اللي بيصير بينه وبين
+
+109
+00:09:23,220 --> 00:09:27,420
+الغالب غالب كلها هذه بتفيدك لكن يمكن ما تسمعهاش
+
+110
+00:09:27,420 --> 00:09:31,640
+كويس في بيتكوا يمكن تقطيعات الوجه ما تظهرش تمامًا
+
+111
+00:09:31,640 --> 00:09:36,000
+أثناء السؤال والإجابة عليه فكل هذا له تأثير في
+
+112
+00:09:36,000 --> 00:09:42,410
+فهمك في فهم المساق يبقى الحضور عندي أساسي أول
+
+113
+00:09:42,410 --> 00:09:46,370
+أسبوعين أنا مسامحك لكن ابتداءً من الأسبوع الثالث حابد
+
+114
+00:09:46,370 --> 00:09:53,090
+آخذ الحضور والغياب إذا وصل غيابك لـ 25% بنبلغك أنك
+
+115
+00:09:53,090 --> 00:09:58,150
+مفصول حتى وإن كنت مقدم للامتحان النصفي تمام يبقى
+
+116
+00:09:58,150 --> 00:10:02,250
+الحضور أساسي هذا بالنسبة للحضور وبالنسبة لمن
+
+117
+00:10:02,250 --> 00:10:10,450
+وبالنسبة للدرجات وكذلك بالنسبة لطريقة الدراسة الآن
+
+118
+00:10:10,450 --> 00:10:15,580
+قبل أن أبدأ فيها إن حاجة اسمها ساعات مكتبية الساعات
+
+119
+00:10:15,580 --> 00:10:18,920
+المكتبية تجدني قاعد في المكتب بس تنسيتك تيجي
+
+120
+00:10:18,920 --> 00:10:24,640
+تسألني سؤال حلو حاجة ما أنت فاهمها نشرح لك أي
+
+121
+00:10:24,640 --> 00:10:30,040
+تساؤل حول المساق نحاول نفيدك فيه بقدر الإمكان أنا
+
+122
+00:10:30,040 --> 00:10:35,460
+متواجد في المكتب من الساعة الواحدة للساعتين سبت اثنين
+
+123
+00:10:35,460 --> 00:10:43,330
+أربع وكذلك متواجد في المكتب من الأحد عشر للاثنا عشر برضه
+
+124
+00:10:43,330 --> 00:10:49,030
+سبت اثنين أربع حسب جدول الطلاب والطالبات الوقت
+
+125
+00:10:49,030 --> 00:10:53,750
+المناسب بالنسبة لك تفضل احنا في انتظارك بس أعتقد 
+
+126
+00:10:53,750 --> 00:10:58,330
+المناسب اللي هو من الأحداش للاتناش مش هيك من
+
+127
+00:10:58,330 --> 00:11:05,330
+الأحداش للاتناش في المكتب تمام؟ يبقى هذا بالنسبة 
+
+128
+00:11:05,330 --> 00:11:09,850
+لمين؟ للساعات المكتبية، رقم المكتب تلاتمية و تلاتة
+
+129
+00:11:09,850 --> 00:11:16,370
+و عشرين اللي هي كلية العلوم الطابق الثالث الغرفة
+
+130
+00:11:16,370 --> 00:11:23,030
+رقمها 323 في الـ corridor التليفون الداخلي 2619
+
+131
+00:11:23,030 --> 00:11:28,930
+يعني بإمكانك من أي تليفون هنا تصل على 2619 تعرف
+
+132
+00:11:28,930 --> 00:11:32,770
+إنه متواجد في المكتب والله مش متواجد حتى لو كان
+
+133
+00:11:32,770 --> 00:11:39,210
+في غير الساعات المكتبية واضح كلامي؟ طيب نجي الآن
+
+134
+00:11:39,210 --> 00:11:45,590
+للموضوع موضوع الجبر الحديث الكتاب المقرر اسمه
+
+135
+00:11:45,590 --> 00:11:50,170
+Contemporary Abstract Algebra هكتب هلك الآن هذا
+
+136
+00:11:50,170 --> 00:11:55,570
+شكل الكتاب موجود الآن في مكتبة الطالب الجامعي
+
+137
+00:11:55,570 --> 00:12:00,660
+بتاعه ممكن تشتريه بعد نهاية المحاضرة تمام أو موجود
+
+138
+00:12:00,660 --> 00:12:05,340
+كمان في المكتبات اللي قدام الجامعة الإسلامية في
+
+139
+00:12:05,340 --> 00:12:09,560
+أحد المكتبات موجود فيها كمان نسخ اللي يريحك اشتريه
+
+140
+00:12:09,560 --> 00:12:14,760
+واللي تلاقيه أرخص اشتريه الكتاب هو Contemporary
+
+141
+00:12:14,760 --> 00:12:20,240
+Abstract Algebra المؤلف اسمه Joseph Gallian الطبعة
+
+142
+00:12:20,240 --> 00:12:27,770
+السابعة طبعا احنا دخلنا هذا الكتاب وقررنا منذ سنوات
+
+143
+00:12:27,770 --> 00:12:32,490
+منذ الطبعة الثانية لأن حسب ما شوفنا كتب جبر كثيرة
+
+144
+00:12:32,490 --> 00:12:38,590
+لجينا أن هذا أنسب كتاب بالنسبة للطالب وفيه عدد لا
+
+145
+00:12:38,590 --> 00:12:44,450
+بأس به من الأسئلة في التمرين الواحد ونصفها محلول
+
+146
+00:12:44,450 --> 00:12:49,530
+يعني حل بس حل مختصرا وأنواعيا في نهاية الكتاب
+
+147
+00:12:49,530 --> 00:12:55,020
+الأسئلة الفردية غالبها محلولة وبالتالي بيساعدك على
+
+148
+00:12:55,020 --> 00:13:00,720
+فهم المساق فهما صحيا يبقى اسم الكتاب Contemporary
+
+149
+00:13:00,720 --> 00:13:02,280
+Abstract Algebra
+
+150
+00:13:25,630 --> 00:13:39,950
+اسم المؤلف جوزيف جوزيف
+
+151
+00:13:39,950 --> 00:13:49,210
+جاليان الطبعة السابعة بجهة seven edition
+
+152
+00:13:57,810 --> 00:14:03,230
+again شوفتش شكل الكتاب وهذا الاسم المساكن
+
+153
+00:14:03,230 --> 00:14:06,230
+temporary abstract algebra الاسم اللي موجود على
+
+154
+00:14:06,230 --> 00:14:11,390
+الكتاب المؤلف اسمه Joseph Gallian الطبعة السابعة
+
+155
+00:14:11,390 --> 00:14:15,270
+احنا بنتعامل مع الكتاب منذ الطبعة الثانية والآن
+
+156
+00:14:15,270 --> 00:14:19,150
+وصلنا إلى الطبعة السابعة كل ما يصير تغيير بنتابع
+
+157
+00:14:19,150 --> 00:14:24,370
+هذا التغيير لأن العلم يتطور يوميا والعقل البشري كل
+
+158
+00:14:24,370 --> 00:14:29,110
+يوم يهتدي لشيء في الكون لم يكن قد اكتشفه من قبل
+
+159
+00:14:29,110 --> 00:14:35,210
+وهذه طبيعة البشر وطبيعة الكون الذي نحن فيه إلا
+
+160
+00:14:35,210 --> 00:14:38,850
+ابن نيجي ما هي الموضوعات التي سندرسها من هذا
+
+161
+00:14:38,850 --> 00:14:43,730
+الكتاب هذا الكتاب لجبر حديث واحد وجبر حديث اتنين
+
+162
+00:14:43,730 --> 00:14:49,950
+طبعا كلاب كلية العلوم مقرر عليهم المساقين طلاب كلية
+
+163
+00:14:49,950 --> 00:14:53,650
+التربية مقرر عليهم جبر حديث واحد جبر اتنين
+
+164
+00:14:53,650 --> 00:14:58,030
+optional اختياري تاخدها اهلا وسهلا بدكش بلاش لكن
+
+165
+00:14:58,030 --> 00:15:01,970
+العلوم إجباري عليهم جبر حديث اتنين
+
+166
+00:15:04,990 --> 00:15:11,750
+هذا الكتاب سندرس منه ten chapters يبقى عشر شباتر
+
+167
+00:15:11,750 --> 00:15:20,210
+سندرس من هذا الكتاب أول شبتر هو شبتر المقدمة
+
+168
+00:15:20,750 --> 00:15:27,010
+المقدمة اللي هنا هتلاقي مراجعة لما سبقت دراسته في
+
+169
+00:15:27,010 --> 00:15:33,630
+مبادئ الرياضيات زي ايش مثلا يبقى الشابتر الأول بيتكلم
+
+170
+00:15:33,630 --> 00:15:35,650
+عن الـ integers
+
+171
+00:15:37,860 --> 00:15:41,960
+اللي هو من مجموعة الأعداد الصحيحة طبعا احنا اول ما
+
+172
+00:15:41,960 --> 00:15:47,080
+نبدأ هنبدأ بنفسنا الـ number نعرفلك إياه المجموعة
+
+173
+00:15:47,080 --> 00:15:50,220
+الـ set of integers مجموعة الـ rational number الـ
+
+174
+00:15:50,220 --> 00:15:54,020
+real number الـ complex number الخمسة هدول اللي
+
+175
+00:15:54,020 --> 00:15:57,820
+علمنا في الجبر إن بنا عليهم اللي هي الأساسيات
+
+176
+00:15:57,820 --> 00:16:03,430
+الأساسية بعد ذلك نقوم بالإنتقال ناخد الـ prime
+
+177
+00:16:03,430 --> 00:16:07,730
+numbers الأعداد الأولية الـ division algorithm
+
+178
+00:16:07,730 --> 00:16:14,590
+خوارزمية القسمة modular arithmetic الحسابات بمقياس
+
+179
+00:16:14,590 --> 00:16:19,970
+معين الـ mathematical induction اللي هو الاستنتاج
+
+180
+00:16:19,970 --> 00:16:25,470
+الرياضي أو الاستقراء الرياضي الـ equivalence
+
+181
+00:16:25,470 --> 00:16:29,350
+relations اللي هي علاقات التكافؤ وبعدها الـ
+
+182
+00:16:29,350 --> 00:16:33,770
+functions يبقى هذه الملامح الأساسية لمين؟ للـ
+
+183
+00:16:33,770 --> 00:16:38,250
+chapter اللي عندنا يبقى في الـ integers بدنا ندرس لـ
+
+184
+00:16:38,250 --> 00:16:41,970
+prime الـ 
+
+185
+00:16:41,970 --> 00:16:50,070
+division اللي هو القسمة أو الـ division algorithm
+
+186
+00:16:50,070 --> 00:16:52,050
+خوارزمية القسمة
+
+187
+00:16:56,430 --> 00:17:00,430
+خوارزمية القسمة بناخد حاجة اسمها modular
+
+188
+00:17:00,430 --> 00:17:03,730
+arithmetic
+
+189
+00:17:03,730 --> 00:17:10,710
+اللي 
+
+190
+00:17:10,710 --> 00:17:18,130
+هو الحسابات الدورية بمقياس معين بعد الـ modular
+
+191
+00:17:18,130 --> 00:17:21,250
+بناخد حاجة اسمها mathematical induction
+
+192
+00:17:29,030 --> 00:17:34,570
+استنتاج أو الاستقراء الرياضي بعد الاستنتاج الرياضي
+
+193
+00:17:34,570 --> 00:17:44,610
+بنجي لحاجة اسمها الـ equivalence relations علاقات
+
+194
+00:17:44,610 --> 00:17:52,590
+التكافؤ آخر حاجة and functions اللي هم من الدولة
+
+195
+00:17:53,960 --> 00:17:59,360
+طبعا كل هذا مر عليك في مبادئ الرياضيات يعني هذا
+
+196
+00:17:59,360 --> 00:18:03,200
+الشابتر يعتبر مراجعة طبعا بتعرفوا مجموعة الأعداد
+
+197
+00:18:03,200 --> 00:18:08,360
+الصحيحة بتعرفوا الأعداد الأولية الـ prime numbers
+
+198
+00:18:08,360 --> 00:18:13,660
+بتعرفوا الخوارزمية القسمة كيف نكتب عددين بدلالة
+
+199
+00:18:13,660 --> 00:18:20,480
+بعض واحد بدلالة الثاني مضاعفات وزايد شيء معين علم
+
+200
+00:18:20,480 --> 00:18:26,110
+مقياس زي ايش مثلا زي العدد اتناش أظن كل اتناش ساعة
+
+201
+00:18:26,110 --> 00:18:29,650
+بتبدأ الساعة من جديد في الليل والنهار الساعة ..
+
+202
+00:18:29,650 --> 00:18:32,450
+بنبدأ من الساعة واحدة لغاية الساعة اتناش بعد
+
+203
+00:18:32,450 --> 00:18:34,610
+الساعة اتناش مايقولش الساعة تلاتاش مايقولش الساعة
+
+204
+00:18:34,610 --> 00:18:38,810
+واحدة وهكذا يبقى كل اتناش ساعة بتتدعت من هنا
+
+205
+00:18:38,810 --> 00:18:43,450
+الدورة من جديد طبعا المقياس هنا كان 12 ممكن تكون
+
+206
+00:18:43,450 --> 00:18:47,370
+المقياس تلاتة ممكن عشرة ممكن سبعة ممكن خمسة زي ما
+
+207
+00:18:47,370 --> 00:18:51,450
+بدك زي ما بدنا بناخد مقاسات وبناء عليه بنشغل
+
+208
+00:18:51,450 --> 00:18:56,110
+هالشغل هذه بعدين الاستنتاج الرياضي برضه هدرسنا في
+
+209
+00:18:56,110 --> 00:19:00,770
+مبادئ الرياضيات باختصار بنجي نقول نفرض انه أو
+
+210
+00:19:00,770 --> 00:19:05,370
+نحاول نثبت انه العدد صحيح عند الـ .. القاعدة
+
+211
+00:19:05,370 --> 00:19:09,270
+لمطلوبة صحية عند N تساوي واحد ثم نحاول .. نفرض
+
+212
+00:19:09,270 --> 00:19:14,770
+صحيتها عند N ونحاول اثبتها عند مين؟ عند N زائد واحد
+
+213
+00:19:14,770 --> 00:19:19,180
+وهاكذا يبقى هذا الـ mathematical induction الـ
+
+214
+00:19:19,180 --> 00:19:23,420
+equivalence relation بيقول إن الـ relation عدة أنواع
+
+215
+00:19:23,420 --> 00:19:27,000
+بيقول عن الـ relation إنّها equivalence relation إذا
+
+216
+00:19:27,000 --> 00:19:32,160
+حققت لي كام شرط؟ ثلاثة شرط الشرط الأول تبقى
+
+217
+00:19:32,160 --> 00:19:37,320
+الـ relation reflexive العنصر مرتبط مع نفسه تبقى
+
+218
+00:19:37,320 --> 00:19:41,360
+symmetric إذا الـ A مرتبطة مع الـ B يبقى الـ B
+
+219
+00:19:41,360 --> 00:19:45,120
+بتكون مرتبطة مع الـ A بالـ relation اللي عندنا
+
+220
+00:19:45,120 --> 00:19:49,640
+الأمر الثالث اللي هو الـ transitive لو الـ element A
+
+221
+00:19:49,640 --> 00:19:53,980
+مرتبط مع B و B مربوط مع C إذا الـ A مربوط مع C أو
+
+222
+00:19:53,980 --> 00:20:00,100
+في relation ما بينهم إذا تحققت الشروط التلاتة في
+
+223
+00:20:00,100 --> 00:20:02,700
+الـ relation بقول الـ relation اللي عندنا is an
+
+224
+00:20:02,700 --> 00:20:06,400
+equivalence relation بعد هيك بدنا نروح لمين؟ للـ
+
+225
+00:20:06,400 --> 00:20:09,980
+functions طبعا هنا في الـ calculus أخذنا الـ
+
+226
+00:20:09,980 --> 00:20:12,720
+functions وفي مبادئ الرياضيات أخذنا الـ functions
+
+227
+00:20:12,720 --> 00:20:17,200
+هنرجع نذكرك بتعريف الـ function الـ one to one function
+
+228
+00:20:17,200 --> 00:20:22,540
+الـ on to function هدول ضروريات جدا خلال دراستنا في
+
+229
+00:20:22,540 --> 00:20:26,420
+مساق الجبر يعني بدك تعرف شو الـ identity function
+
+230
+00:20:26,420 --> 00:20:29,300
+ايش الـ one to one function ايش الـ on to function
+
+231
+00:20:29,300 --> 00:20:32,780
+الـ composition ما بين الـ two functions لو كان one
+
+232
+00:20:32,780 --> 00:20:35,920
+to one هل الناتج one to one ولا لأ؟ لو كانوا
+
+233
+00:20:35,920 --> 00:20:39,120
+الاثنين onto هل الناتج onto ولا كل هذا الكلام
+
+234
+00:20:39,120 --> 00:20:44,440
+سنعرفه من خلال من؟ من خلال هذا الـ chapter ومن خلال
+
+235
+00:20:44,440 --> 00:20:48,360
+الجزء تبع من؟ تبع الـ functions يبقى هذه هي
+
+236
+00:20:48,360 --> 00:20:52,580
+المقدمات اللي عندنا بنجي للـ chapter الثاني الـ
+
+237
+00:20:52,580 --> 00:20:58,880
+chapter الثاني بناخد فيه الـ groups الـ groups اللي
+
+238
+00:20:58,880 --> 00:21:02,500
+هي المجموعات أو الترجمة الحقيقية حسب اللغة العربية
+
+239
+00:21:02,500 --> 00:21:09,470
+بنسميها الزمر الزمر اللي هي جمع .. جمع ايش؟ زمرة
+
+240
+00:21:09,470 --> 00:21:14,830
+الزمر هذه موجودة في القرآن الكريم؟ موجودة يعني في
+
+241
+00:21:14,830 --> 00:21:21,810
+صورة ايش؟ في صورة الزمر طيب ويعني قرآننا يشير إلى
+
+242
+00:21:21,810 --> 00:21:28,290
+هذا الموضوع ومش زمرتين في آخر ياتي صورة الزمر بيقول
+
+243
+00:21:28,290 --> 00:21:34,210
+ربنا سبحانه وتعالى وسيقى الذين كفروا إلى جهنم زمرة
+
+244
+00:21:34,210 --> 00:21:39,490
+يعني على شكل مجموعات وبعدها بيقول وسيقى الذين
+
+245
+00:21:39,490 --> 00:21:45,170
+اتقوا ربهم إلى الجنة زمرة كذلك على شكل مجموعات شكل
+
+246
+00:21:45,170 --> 00:21:51,490
+مجموعات ليه؟ لأنه جهنم دركات فالمجرمين اللي أكثر
+
+247
+00:21:51,490 --> 00:21:55,530
+جرمهم المنافقين بيكونوا في الدرك الأسفل من النار و
+
+248
+00:21:55,530 --> 00:22:00,950
+هدول عذابهم شديدة لفوق وخف لفوق وخف لفوق وخف لكن
+
+249
+00:22:00,950 --> 00:22:04,870
+الجنة بالعكس درجات الدرجة العليا هي اللي فوق
+
+250
+00:22:04,870 --> 00:22:09,990
+الفردوس الأعلى إذا سألتم الله سبحانه وتعالى فاسألوه 
+
+251
+00:22:09,990 --> 00:22:15,170
+الفردوس الأعلى يعني مثل ما أعمال الناس بتكون على
+
+252
+00:22:15,170 --> 00:22:19,810
+شكل اللي هو زمر أو مجموعات ويساقوا طبقا لهذه
+
+253
+00:22:19,810 --> 00:22:25,170
+الأعمال إلى الجنة أو إلى النار فكذلك الـ group إنها
+
+254
+00:22:25,170 --> 00:22:30,740
+عبارة عن مجموعة لها صفات معينة في أن ثلاثة شروط
+
+255
+00:22:30,740 --> 00:22:35,660
+بنحط على الـ set بالإضافة إلى العملية الثنائية على
+
+256
+00:22:35,660 --> 00:22:40,980
+الـ set بتصير عندنا group ويعني عندنا groups كثيرة كل
+
+257
+00:22:40,980 --> 00:22:45,420
+واحدة إلها صفات معينة لكن كلهم بدهم يشتركوا في
+
+258
+00:22:45,420 --> 00:22:49,720
+الشروط الثلاثة الأساسية اللي هنعرفها في حينها يبقى
+
+259
+00:22:49,720 --> 00:22:55,350
+في هذا الـ chapter هنعطي الـ groups و أمثلة عليها
+
+260
+00:22:55,350 --> 00:23:01,250
+على الـ groups و بعض الخواص عليها للـ groups زي إيش
+
+261
+00:23:01,250 --> 00:23:08,930
+مثلا كل group لدينا حاجة اسمها عنصر محايد identity
+
+262
+00:23:08,930 --> 00:23:15,450
+element وفي عندنا كل عنصر له معكوس inverse element
+
+263
+00:23:15,450 --> 00:23:19,730
+هل الـ inverse هذا وحيد ولا ممكن ألاقي العنصر له
+
+264
+00:23:19,730 --> 00:23:24,140
+أكثر من معكوس؟ طبعا ما فيش إلا واحد وهذا مثلا يعني هو
+
+265
+00:23:24,140 --> 00:23:27,760
+نثبته في حينه الـ identity element ما عنديش إلا 
+
+266
+00:23:27,760 --> 00:23:31,120
+identity واحد في الـ group لو وجود اثنين بدهم
+
+267
+00:23:31,120 --> 00:23:35,820
+يكونوا اثنين are equivalent اثنين نفس الشيء تمام
+
+268
+00:23:35,820 --> 00:23:39,260
+يبقى هذا بالنسبة للـ identity element وهكذا يعني
+
+269
+00:23:39,260 --> 00:23:45,820
+احنا هنعطي تعريف للـ group ثم نعطي بعض الأمثلة على
+
+270
+00:23:45,820 --> 00:23:51,040
+الـ group هذا وبعض الخصائص البسيطة لمن للـ group هذا
+
+271
+00:23:51,040 --> 00:23:57,240
+ما سيكون في هذا الـ chapter الـ chapter ثلاثة بدنا نيجي
+
+272
+00:23:57,240 --> 00:23:59,800
+لحاجة اسمها subgroups
+
+273
+00:24:03,000 --> 00:24:07,320
+subgroups يبقى أنا لجروب اللي عندي هذه يعني مثلا
+
+274
+00:24:07,320 --> 00:24:11,980
+كيف لو جيت قلت للطلاب اللي في القاعة هدول يمثلوا لي
+
+275
+00:24:11,980 --> 00:24:17,300
+لجروب طبعا خدت شوية منهم خدت الشجة هذه السبعة
+
+276
+00:24:17,300 --> 00:24:23,740
+هدول هل هدول بيصيروا إيه جروب تحت نفس العملية اللي
+
+277
+00:24:23,740 --> 00:24:28,130
+موجودة على الـ group الأصلية ولا لأ؟ بمعنى السبعة هذول
+
+278
+00:24:28,130 --> 00:24:33,750
+فيهم الـ identity element وفيهم كل عنصر له معكوس
+
+279
+00:24:33,750 --> 00:24:37,630
+ولا لأ؟ وعملية الـ associativity إن شاء الله هنشرحها
+
+280
+00:24:37,630 --> 00:24:41,550
+في هنا إذا انطبقت عليهم هذه اللي بقول هذول مثل الـ
+
+281
+00:24:41,550 --> 00:24:46,210
+subgroup لو اختل واحد من الشروط هذه بقول بطل يصير
+
+282
+00:24:46,210 --> 00:24:51,250
+subgroup هاي إيش بتصير؟ بتصير subset مجموعة جزئية
+
+283
+00:24:51,250 --> 00:24:56,680
+لكنها ليست subgroup إذا الـ subgroup هذه هي مجموعة
+
+284
+00:24:56,680 --> 00:25:01,920
+جزئية من الـ group اللي عندنا هذه وبدها ضالها group
+
+285
+00:25:01,920 --> 00:25:07,120
+تحت نفس العملية الرياضية المعرفة على الـ group
+
+286
+00:25:07,120 --> 00:25:12,380
+الأصلية إن حدث ذلك بقول هذه subgroup ما حدث يبقى
+
+287
+00:25:12,380 --> 00:25:17,200
+انسى الموضوع هذه الست عادية وخلاصنا وليست subgroup
+
+288
+00:25:17,200 --> 00:25:22,340
+بدنا نيجي لـ chapter أربعة حاجة اسمها الـ cyclic
+
+289
+00:25:22,340 --> 00:25:24,480
+groups
+
+290
+00:25:35,510 --> 00:25:42,650
+cyclic group يعني الزمرة الدائرية generator يعني
+
+291
+00:25:42,650 --> 00:25:49,010
+مولّد مولّد يعني بيولد لي جميع عناصرها main جميع عناصر
+
+292
+00:25:49,010 --> 00:25:52,810
+الـ group Cyclic group يعني إيش المقصود بالـ cyclic
+
+293
+00:25:52,810 --> 00:25:57,990
+group؟ group عادية هذه بس تحقق فيها شرط، إيش
+
+294
+00:25:57,990 --> 00:26:03,790
+الشرط؟ أخدت عنصر منها، العنصر هذا ربعته، قعدته، و
+
+295
+00:26:03,790 --> 00:26:07,230
+أس أربعة و أس خمسة و أس ستة و أس سبعة و أس عشرة و
+
+296
+00:26:07,230 --> 00:26:11,360
+إنّه جاب لي جميع العناصر اللي موجودة في الـ group إن
+
+297
+00:26:11,360 --> 00:26:16,920
+حدث ذلك بقول هذا العنصر هو generator للجروب يبقى
+
+298
+00:26:16,920 --> 00:26:21,140
+هذا العنصر هو اللي بيولد لي جميع عناصر الجروب بلا
+
+299
+00:26:21,140 --> 00:26:26,440
+استثناء يبقى إن حدث ذلك بقول هذا generator طب بدي
+
+300
+00:26:26,440 --> 00:26:31,220
+أسأل واحد يعني لو كانت الـ group cyclic كل عنصر بنفع
+
+301
+00:26:31,220 --> 00:26:38,350
+يكون generator الإجابة نعم ولا لا؟ لا يعني ممكن
+
+302
+00:26:38,350 --> 00:26:44,530
+تلاقي two generators فيها يعني أي group فيها أكثر
+
+303
+00:26:44,530 --> 00:26:49,910
+من عنصر على الأقل فيها two generators مين هم الـ
+
+304
+00:26:49,910 --> 00:26:54,790
+generators هدول؟ العنصر ومعكوسه يمكن الـ group الواحد
+
+305
+00:26:54,790 --> 00:26:59,190
+اللي أجي فيه إياه مولدين يمكن أربعة يمكن ستة
+
+306
+00:26:59,190 --> 00:27:03,930
+يبقى يمكن ثمانية بس ما تبقاش الـ trivial subgroup الـ
+
+307
+00:27:03,930 --> 00:27:07,630
+trivial subgroup اللي مش فيها إلا عنصر واحد اللي
+
+308
+00:27:07,630 --> 00:27:11,970
+هو main عنصر الواحدة تمام؟ يبقى هاي المقصود
+
+309
+00:27:11,970 --> 00:27:17,090
+بالـ cyclic group وكذلك الـ generators بعد الـ cyclic
+
+310
+00:27:17,090 --> 00:27:21,430
+group نيجي لحاجة اسمها الـ permutation group يبقى
+
+311
+00:27:21,430 --> 00:27:37,150
+chapter خمسة الحاجة اسمها الـ permutation group إيش
+
+312
+00:27:37,150 --> 00:27:43,070
+الـ permutation هذه؟ يبقى احنا بنيجي على set وفيها
+
+313
+00:27:43,070 --> 00:27:47,130
+مجموعة من العناصر افترض في عندي مثلا ثلاثة عناصر
+
+314
+00:27:47,790 --> 00:27:54,650
+الثلاثة عناصر كم تبديلة بقدر أسوي منهم بحيث ولا
+
+315
+00:27:54,650 --> 00:27:59,630
+واحد حتكون زي الثانية يعني مثلا لو جينا قلنا واحد
+
+316
+00:27:59,630 --> 00:28:04,630
+واثنين وثلاثة يبقى هذي بسميها تبديلة من التبديلة
+
+317
+00:28:04,630 --> 00:28:10,370
+هذي بقدر أخلّق مجموعة من التبديلات تعرف كم من
+
+318
+00:28:10,370 --> 00:28:14,750
+الثلاثة عناصر بتقدر تسوي تبديلات مرت عليكم بدأ
+
+319
+00:28:14,750 --> 00:28:20,930
+الرياضيات كم يعني؟ مضروب ثلاثة مضروب ثلاثة يبقى
+
+320
+00:28:20,930 --> 00:28:25,610
+ثلاثة في اثنين في واحد يبقى عندي ست تبديلات ممكن
+
+321
+00:28:25,610 --> 00:28:31,970
+أخلّق من هذه التبديلات احنا بدنا ننشي group على
+
+322
+00:28:31,970 --> 00:28:37,990
+التبديلات اللي عندنا هذه وندرس بعض المعلومات على
+
+323
+00:28:37,990 --> 00:28:42,450
+هذه التبديلات وهل التبديلات بتبقى even ولا odd
+
+324
+00:28:42,720 --> 00:28:48,500
+وقداش رتبت هذه التبديلة وقداش وقداش الأخرى يبقى
+
+325
+00:28:48,500 --> 00:28:52,180
+هذا شغلنا اللي يكون وين اللي هيكون في هذا الـ chapter
+
+326
+00:28:52,180 --> 00:28:56,900
+اللي هو الـ permutation group يبقى permutation
+
+327
+00:28:56,900 --> 00:29:02,540
+تبديلة permutation group اللي هي مجموعة التبديلات
+
+328
+00:29:02,540 --> 00:29:09,210
+أو زمرة التبديلات بنيجي لحاجة هنا اسمها isomorphisms
+
+329
+00:29:09,210 --> 00:29:14,570
+isomorphisms
+
+330
+00:29:14,570 --> 00:29:20,430
+وكذلك الـ atomorphisms
+
+331
+00:29:20,430 --> 00:29:26,470
+طيب
+
+332
+00:29:33,130 --> 00:29:38,230
+الترجمة العربية بتقول التشكل النمطي أو التشابه
+
+333
+00:29:38,230 --> 00:29:42,990
+النمطي ماذا يعني تشابه والنمط؟ يعني أنا عندي group
+
+334
+00:29:42,990 --> 00:29:48,270
+وعندي group ثانية اثنين فيهم تشابه مابينهما؟ إيش كيف
+
+335
+00:29:48,270 --> 00:29:52,790
+يعني تشابه؟ يعني هذا وهذا وهذا بنعم هذا؟ لأ مش
+
+336
+00:29:52,790 --> 00:29:57,590
+هيك في عندنا شروط الشروط لو تحققت على الـ two
+
+337
+00:29:57,590 --> 00:30:02,550
+groups بقول إن هم دول اثنين فيهم تشابه نمطين
+
+338
+00:30:02,550 --> 00:30:07,530
+تعرفوا زي إيش مثلا؟ يبقى لو جيت قلت هذه فيها سبعة
+
+339
+00:30:07,530 --> 00:30:13,710
+يبقى هذه فيها سبعة نفس العدد رتبة أي عنصر هنا زي
+
+340
+00:30:13,710 --> 00:30:19,390
+رتبة أي عنصر هنا عدد العناصر رتبتهم مثلا ستة جد
+
+341
+00:30:19,390 --> 00:30:23,250
+عدد العناصر اللي رتبتهم ستة عدد العناصر اللي
+
+342
+00:30:23,250 --> 00:30:27,830
+رتبتهم اثنين جد عدد العناصر اللي رتبتهم اثنين عدد
+
+343
+00:30:27,830 --> 00:30:31,450
+الـ subgroups هنا جد عدد الـ subgroups هنا ده اسمه
+
+344
+00:30:31,450 --> 00:30:37,230
+تشابه نمطي أو تشاكل نمطي طيب يبقى إيش يعني
+
+345
+00:30:37,230 --> 00:30:41,450
+isomorphism إن احنا شرحنا كلام بلدي لك رياضيا
+
+346
+00:30:41,450 --> 00:30:47,990
+بنقول الـ isomorphism هو function ما بين two groups
+
+347
+00:30:47,990 --> 00:30:55,300
+يبقى لو جيتي قلت لك افترض عندي function من الـ group
+
+348
+00:30:55,300 --> 00:31:02,280
+جي إلى الـ group جي بار مثلا كويس يبقى هذا عشان يكون
+
+349
+00:31:02,280 --> 00:31:07,000
+ايزو مورفزم تتحقق بعض الشروط أول شيء هي function
+
+350
+00:31:08,740 --> 00:31:15,860
+ثلاثة تبقى one to one ثلاثة تبقى onto إن حدث ذلك
+
+351
+00:31:15,860 --> 00:31:20,840
+بقول هذه الـ function one to one and onto كمان في
+
+352
+00:31:20,840 --> 00:31:27,860
+خاصية لازم أتحققها وهي في تأثيرها على الـ X Y في
+
+353
+00:31:27,860 --> 00:31:34,160
+تأثيرها على عنصر X في Y بتساوي في of X في of Y
+
+354
+00:31:35,360 --> 00:31:40,700
+تمام؟ هنا في عملية ما بين العنصرين ضرب جمع طرح
+
+355
+00:31:40,700 --> 00:31:45,920
+الجسم أخذها حسب ما هي معرفة على G هنا كمان في
+
+356
+00:31:45,920 --> 00:31:49,520
+عملية ما بين العنصر هذا والعنصر هذا هي العملية
+
+357
+00:31:49,520 --> 00:31:54,480
+المعرفة على G bar والتي قد تكون تاعة العملية G وقد
+
+358
+00:31:54,480 --> 00:32:00,470
+تكون غيرها وفي الغالب غيرها يبقى هذا الشرط مع الـ
+
+359
+00:32:00,470 --> 00:32:05,490
+one to one and one to two إن حدث ذلك تحققت الشروط
+
+360
+00:32:05,490 --> 00:32:11,370
+الثلاثة بقول الـ function عندي هذه isomorphism وبالتالي
+
+361
+00:32:11,370 --> 00:32:17,320
+بقول الـ جي والـ جي بار are isomorphic ايزو مورفك يعني
+
+362
+00:32:17,320 --> 00:32:22,280
+في ايزو مورفزم ما بين من؟ ما بين الـ two groups
+
+363
+00:32:22,280 --> 00:32:26,600
+يبقى معنا هذا الكلام لما جينا قلنا لكم هنا بدنا
+
+364
+00:32:26,600 --> 00:32:30,980
+نتكلم على الـ functions ونذكر بين one to one and
+
+365
+00:32:30,980 --> 00:32:35,310
+onto مش بلاش من ذاكرتنا يبقى هذه الأساسيات اللي
+
+366
+00:32:35,310 --> 00:32:38,770
+بتلزمنا للي قدام روح نعطيها لك في الـ chapter الأول
+
+367
+00:32:38,770 --> 00:32:43,350
+يبقى لما نجي أقول لك automatic phi is one to one
+
+368
+00:32:43,350 --> 00:32:46,450
+يبقى فيه one to one function يبقى كنت ماخذ الـ one
+
+369
+00:32:46,450 --> 00:32:50,410
+to one function في أول chapter في المقدمة إن قلت
+
+370
+00:32:50,410 --> 00:32:55,250
+لك phi is onto يبقى هنا فهمتك ما معنى onto
+
+371
+00:32:55,250 --> 00:32:58,590
+function لو جيت سؤال تعالى واحد يقولش يعني onto
+
+372
+00:32:58,590 --> 00:33:01,550
+function بيقول يعني ده الفوقية بيقول له ده ترجمة
+
+373
+00:33:01,550 --> 00:33:06,150
+عربية أنا ما أوديش ترجمة عربية أنا بدي ترجمة رياضية
+
+374
+00:33:06,150 --> 00:33:13,150
+حد فيكم يتذكر إيش يعني معنى onto function دي اللي
+
+375
+00:33:13,150 --> 00:33:18,310
+درسيه مبادئ onto function إيش معناها رياضيا؟ قولي
+
+376
+00:33:18,310 --> 00:33:21,350
+اللي أنت فاهم وموديش حافظ نص عن غيرك، بتفضل
+
+377
+00:33:28,820 --> 00:33:34,880
+أنا عندي ست a وست b في من a إلى b is a function
+
+378
+00:33:34,880 --> 00:33:37,200
+وقتش هدى بقول عليها أنتو
+
+379
+00:33:40,780 --> 00:33:46,420
+مية المية إذا جيت أخدت أي عنصر من الست بي لقيته
+
+380
+00:33:46,420 --> 00:33:50,620
+أصله وين في ايه يعني ما عندها كلام إن ال function دي
+
+381
+00:33:50,620 --> 00:33:56,500
+غطت جميع عناصر بي لستها لأن ال function يا شباب
+
+382
+00:33:56,500 --> 00:34:01,940
+من الست اي لست بي ليس بالضرورة تغطي لجميع عناصر بي
+
+383
+00:34:01,940 --> 00:34:05,840
+لكن بتغطي إجبار جميع عناصر اي لأن ال اي هو ال
+
+384
+00:34:05,840 --> 00:34:11,150
+domain تبعها تمام إذا مش هتكون onto يبقى يكون ال
+
+385
+00:34:11,150 --> 00:34:14,870
+range تبع هذه ال function هو نفس ال domain
+
+386
+00:34:14,870 --> 00:34:19,990
+بالضبط يعني جميع عناصر B كلهم بدهم يظهروا كصور
+
+387
+00:34:19,990 --> 00:34:25,130
+لعناصر A بالإضافة إلى هذا ال onto ال one to one
+
+388
+00:34:25,130 --> 00:34:29,690
+زواج كاثوليكي الواحد ما له إلا واحدة جوزة بس غير
+
+389
+00:34:29,690 --> 00:34:34,810
+هي كده ممنوع عندنا المسألة اه مش عندنا يبقى العنصر
+
+390
+00:34:34,810 --> 00:34:39,430
+الواحد له صورة واحدة ولا واحد بيشاركوا فيها مش
+
+391
+00:34:39,430 --> 00:34:43,010
+عنصرين بيشتركوا في نفس الصورة إذا اشترك عنصران في
+
+392
+00:34:43,010 --> 00:34:47,290
+نفس الصورة يبقى في هذه الحالة ال function ليست one
+
+393
+00:34:47,290 --> 00:34:51,310
+to one طب إذا العنصر طالع لصورتين يبقى ماهيّاش
+
+394
+00:34:51,310 --> 00:34:56,790
+function من الأساس يبقى ال five function بدأت تحقق
+
+395
+00:34:56,790 --> 00:35:01,760
+الخاصية هذه بتبقى one to one and onto وهذه من ال
+
+396
+00:35:01,760 --> 00:35:06,960
+group G إلى ال group G bar طبعًا وحنعطي أمثلة 
+
+397
+00:35:06,960 --> 00:35:11,950
+عديدة على ذلك وبعض النظريات المتعلقة بها بنجي لل
+
+398
+00:35:11,950 --> 00:35:18,470
+automorphism شو يعني automorphism هو function فاي بس
+
+399
+00:35:18,470 --> 00:35:24,230
+من جي إلى جي itself مش لوحدة تانية هنا جي و هنا جي
+
+400
+00:35:24,230 --> 00:35:28,550
+برضوا اختلفوا عن بعض تمامًا هاي شجة و هاي شجة تانية
+
+401
+00:35:28,550 --> 00:35:32,300
+وليهم مش علاقة ببعض ولا بقرب ولا بعض ولا غيره لكن
+
+402
+00:35:32,300 --> 00:35:36,920
+عندما أقول من ال group G إلى ال group G itself ال
+
+403
+00:35:36,920 --> 00:35:43,240
+isomorphism هذا بسميه ايه؟ بسميه automorphism يبقى
+
+404
+00:35:43,240 --> 00:35:48,500
+كأن ال automorphism هو حالة خاصة من isomorphism
+
+405
+00:35:48,500 --> 00:35:53,080
+ال isomorphism من group ل group تانية
+
+406
+00:35:53,080 --> 00:35:56,940
+لكن ال automorphism من ال group لنفس domain لنفس
+
+407
+00:35:56,940 --> 00:36:01,380
+group وهو isomorphism one to one و onto وبيحقق
+
+408
+00:36:01,380 --> 00:36:05,180
+لمين الخاصية اللي عندنا هذه إن حدث ذلك يبقى هذا
+
+409
+00:36:05,180 --> 00:36:11,140
+بسميه automorphism وسنحسب بعض ال automorphisms لمين
+
+410
+00:36:11,140 --> 00:36:19,550
+لبعض ال group بعد ذلك بنجي ل chapter 7 السابعة بنا
+
+411
+00:36:19,550 --> 00:36:26,210
+نيجي ناخد حاجة اسمها cosets and Lagrange theorem
+
+412
+00:36:26,210 --> 00:36:38,670
+coset
+
+413
+00:36:38,670 --> 00:36:44,690
+كلمة جديدة هنا set اللي فيها او مجموعة co مرافق
+
+414
+00:36:45,070 --> 00:36:51,750
+يبقى هي الست الجديدة وولدناها من شيء ما شو شيء ما؟
+
+415
+00:36:51,750 --> 00:36:57,710
+شايف عندي هذه ال subgroup أخدت عنصر من برا ال
+
+416
+00:36:57,710 --> 00:37:02,150
+subgroup لكن من نفس ال group ضربته في هذه ال
+
+417
+00:37:02,150 --> 00:37:06,590
+subgroup من جهة اليمين أو من جهة الشمال إن كان
+
+418
+00:37:06,590 --> 00:37:10,930
+الضرب من جهة الشمال بسميه left coset وإن كان
+
+419
+00:37:10,930 --> 00:37:16,690
+الضرب من جهة اليمين بسميها right coset الكوسيت هذي
+
+420
+00:37:16,690 --> 00:37:22,110
+يمكن تطلع subgroup ويمكن ما تطلعش subgroup يبقى in
+
+421
+00:37:22,110 --> 00:37:25,710
+general ال left coset أو ال right coset ليس
+
+422
+00:37:25,710 --> 00:37:31,430
+بالضرورة أن تكون subgroup من ال group الأصلية ما
+
+423
+00:37:31,430 --> 00:37:36,600
+علينا يبقى احنا جبنا حاجة جديدة اسمها coset ال
+
+424
+00:37:36,600 --> 00:37:40,620
+group الأصلية أخد جزء من أسره subgroup ال subgroup
+
+425
+00:37:40,620 --> 00:37:45,580
+جبت عنصر ضربته فيه عناصرها كلهم طلع عندي مين اللي
+
+426
+00:37:45,580 --> 00:37:52,280
+هو ال coset كويس يبقى ال coset هذي جبت عنصر تاني
+
+427
+00:37:52,280 --> 00:37:55,560
+طلعت coset تانية جبت عنصر تانية ضربته فيه طلع
+
+428
+00:37:55,560 --> 00:38:00,010
+coset تانية و هكذا طبعًا يبقى هذا مفهوم ال process
+
+429
+00:38:00,010 --> 00:38:04,190
+and Lagrange theory بنظرية Lagrange هذه بتلعب دور
+
+430
+00:38:04,190 --> 00:38:10,690
+كبير جديد في علم الجبر بالبلدي هيك باختصار بيقول ال
+
+431
+00:38:10,690 --> 00:38:13,370
+order ل sub group بيقسم
+
+432
+00:38:19,410 --> 00:38:25,290
+العدد العناصر في ال subgroup يقسم عدد العناصر في
+
+433
+00:38:25,290 --> 00:38:30,790
+ال group إذا كان العدد اللي هو finite عددا محدودا
+
+434
+00:38:30,790 --> 00:38:35,170
+يبقى هذه اللي بتقوله من؟ هذه اللي بتقوله نظرية
+
+435
+00:38:35,170 --> 00:38:40,180
+Lagrange هذه عمود فقري في علم الجبر وخاصة بالنسبة
+
+436
+00:38:40,180 --> 00:38:45,400
+لموضوع domain بالنسبة لموضوع group هذا بالنسبة ل
+
+437
+00:38:45,400 --> 00:38:49,420
+domain لنظرية Lagrange بنجي بعد ذلك حاجة اسم ال
+
+438
+00:38:49,420 --> 00:38:53,120
+external direct product يبقى ال chapter تمانية
+
+439
+00:38:53,120 --> 00:39:01,320
+حاجة اسمها ال external direct product
+
+440
+00:39:01,320 --> 00:39:08,310
+ايش ال external direct product يبقى أنا بدي أكون
+
+441
+00:39:08,310 --> 00:39:13,730
+group جديدة من two groups موجودة هذه group وهذه
+
+442
+00:39:13,730 --> 00:39:18,970
+group تانية ثانيًا منهم بدي أكون group جديدة عن
+
+443
+00:39:18,970 --> 00:39:24,210
+طريق حاجة اسمه حاصل الضرب الخارجي external خارجي
+
+444
+00:39:24,470 --> 00:39:29,750
+كيف يعني؟ بصير العنصر بدأ أقول هذه group G1 وهذه
+
+445
+00:39:29,750 --> 00:39:35,270
+group G2 يبقى G1 cross G2 هذا بدأ أرمز إلى مين؟
+
+446
+00:39:35,270 --> 00:39:40,810
+للضرب الخارج يمين عناصر وكل عنصر ordered pair زوج
+
+447
+00:39:40,810 --> 00:39:45,150
+مرتب عنصر هنا مع عنصر هنا اتنين تأور ضرب الكقص بقول
+
+448
+00:39:45,150 --> 00:39:49,070
+هذا عنصر واحد في مين؟ فال group الجديدة يعني
+
+449
+00:39:49,070 --> 00:39:55,690
+أنا بدي أنشئ group جديدة من two groups موجودة طيب
+
+450
+00:39:55,690 --> 00:40:00,570
+هذا هو حاصل الضرب الخارجي في حاصل ضرب داخلي اه في
+
+451
+00:40:00,570 --> 00:40:06,030
+حاصل ضرب داخلي وهذا مثلًا نشير إليه بعد قليل يبقى
+
+452
+00:40:06,030 --> 00:40:10,910
+هذا هو ال external direct product بدنا نيجي لتسعة
+
+453
+00:40:10,910 --> 00:40:15,730
+حاجة اسمها normal subgroups يبقى هنا normal
+
+454
+00:40:15,730 --> 00:40:19,350
+subgroups
+
+455
+00:40:21,580 --> 00:40:27,080
+هذه يا شباب أهم أنواع ال subgroups وبتلعب دور
+
+456
+00:40:27,080 --> 00:40:33,300
+كبير جدا في موضوع اللي هو ال groups إذا حصلت على
+
+457
+00:40:33,300 --> 00:40:38,880
+normal subgroup بقدر أنشئ group جديدة من المين
+
+458
+00:40:38,880 --> 00:40:42,820
+من كلمة اللي هو ال cosets اللي عندنا بقدر أعمل
+
+459
+00:40:42,820 --> 00:40:48,440
+cosets وال cosets يعملولي group جديدة بسميها ال
+
+460
+00:40:48,440 --> 00:40:56,210
+factor group factor group وزيادة
+
+461
+00:40:56,210 --> 00:41:00,670
+على ذلك باجي كمان نقطة أخرى internal direct
+
+462
+00:41:00,670 --> 00:41:08,530
+product وكذلك internal direct product
+
+463
+00:41:11,440 --> 00:41:15,580
+بس ال internal غير ال external external بجيب group
+
+464
+00:41:15,580 --> 00:41:19,100
+مع group تانية ال internal لأ داخل ال group
+
+465
+00:41:19,100 --> 00:41:23,640
+الواحدة بجيب subgroup وبجيب subgroup تانية طبعًا
+
+466
+00:41:23,640 --> 00:41:29,120
+ال two subgroups هذول بروح بدربهم في بعض لو كان
+
+467
+00:41:29,120 --> 00:41:33,480
+حاصل ضربهم يعطوني ال group الأساسية والتقاطهم
+
+468
+00:41:33,480 --> 00:41:37,910
+يعطوني بس عنصر واحدة بسمي هذا internal direct
+
+469
+00:41:37,910 --> 00:41:42,870
+product يعني احنا بنشتغل داخل ال group الواحدة
+
+470
+00:41:42,870 --> 00:41:48,250
+بطلع منها ال internal direct product تمام آخر
+
+471
+00:41:48,250 --> 00:41:56,550
+section عاشرة حاجة اسمها ال homomorphism
+
+472
+00:41:56,550 --> 00:42:04,200
+ايش ال homomorphism هو عبارة عن ال function هذه
+
+473
+00:42:04,200 --> 00:42:10,940
+Phi من G إلى G bar بس هذه مش لازم تكون one to one
+
+474
+00:42:10,940 --> 00:42:17,320
+ولو onto بس تحقق لي الشرط هنا اللهم إلا فقط لغاية
+
+475
+00:42:17,320 --> 00:42:25,950
+يبقى هنا Phi of XY بدل سوى Phi of X في Phi of Y إذا
+
+476
+00:42:25,950 --> 00:42:31,590
+تحقق هذا الشرط بقول هذا هو homomorphism وبرضه
+
+477
+00:42:31,590 --> 00:42:35,490
+عليه مجموعة من نظريات لباسية بها و section طويل
+
+478
+00:42:35,490 --> 00:42:39,670
+شوية يعني في مجموعة من البراهين ومجموعة من نظريات
+
+479
+00:42:39,670 --> 00:42:45,520
+ومجموعة من الشغلات يعني هذا اللي قدامك هو الإطار
+
+480
+00:42:45,520 --> 00:42:50,500
+العام لمين؟ لـ لمقرر في جبر حديث واحد كل الشغلات
+
+481
+00:42:50,500 --> 00:42:56,000
+اللتي سندرسها في اللي هو جبر حديث واحد بعد هيك
+
+482
+00:42:56,000 --> 00:43:00,940
+بيجينا جبر حديث اتنين للفصل الثاني وهذا مش الكل في
+
+483
+00:43:00,940 --> 00:43:06,280
+الكورس قبل آخر الان حد فيكم بيحب يسأل أي سؤال بالنسبة
+
+484
+00:43:06,280 --> 00:43:10,460
+للي سمعه اليوم في المحاضرة أو أي سؤال بيدور في
+
+485
+00:43:10,460 --> 00:43:11,180
+دماغك
+
+486
+00:43:19,140 --> 00:43:24,860
+والله عمود في قرية هذه كلها براهين وأنت أخذت في
+
+487
+00:43:24,860 --> 00:43:27,540
+المبادئ الرياضية اللي ما أخدش فيها حد يسمع ال
+
+488
+00:43:27,540 --> 00:43:32,040
+direct proof برهان مباشر في proof بال
+
+489
+00:43:32,040 --> 00:43:37,440
+contrapositive تمشي تمشي العكس في لا التناقض اسمه
+
+490
+00:43:37,440 --> 00:43:40,780
+ال contradiction طريقة تالتة اللي هي طريقة ال
+
+491
+00:43:40,780 --> 00:43:44,440
+contradiction إذا مش ماخد مبادئ رياضيات لا يمكن
+
+492
+00:43:44,440 --> 00:43:49,500
+أنك تفهم حاجة معانا هنا لأن شغلنا كله يعني قول
+
+493
+00:43:49,500 --> 00:43:55,780
+بنسبة 70% براهين كلها براهين مبادئ رياضية بتعلمك
+
+494
+00:43:55,780 --> 00:44:00,220
+كيف تبرهن بتعلمك هي ال logic المنطقة الرياضية
+
+495
+00:44:00,220 --> 00:44:03,920
+كيف يصير عندك منطقة رياضية تفهم وأنت ستطيع تبرهن
+
+496
+00:44:03,920 --> 00:44:07,640
+ما أنت مش ماخد مبادئ رياضيات يبقى أنت جاي على عمارة
+
+497
+00:44:07,640 --> 00:44:13,290
+بلا أساسات بس تطلع شوية بتيه تقدرش تتحمل ايه
+
+498
+00:44:13,290 --> 00:44:16,430
+الحمل يبقى احنا بيقولك إذا مش ماخد روح اسحب
+
+499
+00:44:16,430 --> 00:44:20,570
+المادة وروح سجل مبادئ رياضيات لأنها نازلة الحين
+
+500
+00:44:20,570 --> 00:44:26,110
+مع الدكتور أحمد المبحوح تمام؟ لكن إذا مسجل 
+
+501
+00:44:26,110 --> 00:44:29,790
+المادتين مع بعض ما فيش مشكلة لكن ما أنت مش مسجل
+
+502
+00:44:29,790 --> 00:44:34,130
+أديك، cancel الموضوع خلاص، حد عنده سؤال تاني؟
+
+503
+00:44:34,130 --> 00:44:38,230
+ننتظركم الساعة الثانية عشر إن شاء الله في هذا المكان
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d3ff79aec2705974cc0408f63c7d049b37b7b92
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8.srt
@@ -0,0 +1,1734 @@
+1
+00:00:21,280 --> 00:00:24,820
+بسم الله الرحمن الرحيم المرة التي فاتت واللي 
+
+2
+00:00:24,820 --> 00:00:29,380
+قبلها أخذنا تعريف لـ group وبدأنا نأخذ أمثلة على
+
+3
+00:00:29,380 --> 00:00:35,340
+ذلك، وأخذنا عشرة من الأمثلة، والآن بنكمل برضه بدل 
+
+4
+00:00:35,340 --> 00:00:39,360
+المثال اثنين على نفس الموضوع، المثال رقم أحد عشر
+
+5
+00:00:39,360 --> 00:00:47,210
+بيقول افترض جي كل الـ X اللي موجودة في الـ Q في الـ
+
+6
+00:00:47,210 --> 00:00:52,010
+set of rational numbers وليس فقط كل الـ X الموجودة
+
+7
+00:00:52,010 --> 00:00:57,390
+في الـ IQ بحيث الـ X لا تساوي واحد، يبقى احنا عندنا 
+
+8
+00:00:57,390 --> 00:01:04,070
+أعداد نسبية موجبة وسالبة وصفر ما عدا الواحد الصحيح
+
+9
+00:01:04,800 --> 00:01:08,880
+عرفنا binary operation star، يبقى أنا أعطيتك أنها
+
+10
+00:01:08,880 --> 00:01:13,540
+binary operation بالشكل أن a star b يساوي a زائد b
+
+11
+00:01:13,540 --> 00:01:19,500
+ناقص a b، يبقى مجموع العددين ناقص حاصل ضربهم
+
+12
+00:01:19,500 --> 00:01:23,500
+كلها على بعضها هذه بدي أسميها الـ operation star
+
+13
+00:01:23,500 --> 00:01:30,860
+لكل الـ a والـ b الموجودة في g، هل الـ G والـ Star هذه 
+
+14
+00:01:30,860 --> 00:01:36,260
+أي group ولا لأ، يبقى أنا بروح بسبحة الثلاثة شروط
+
+15
+00:01:36,260 --> 00:01:40,320
+لإعطانيها binary operation، بدي أشوف هل الـ
+
+16
+00:01:40,320 --> 00:01:44,380
+Star هذه associative، هل الـ identity element موجود
+
+17
+00:01:44,380 --> 00:01:50,320
+هل المعكوس لكل عنصر موجود أم لأ، يبقى solution
+
+18
+00:01:53,940 --> 00:01:58,880
+النقطة الأولى، هل العملية هذه associative ولا لأ
+
+19
+00:01:58,880 --> 00:02:04,740
+إذا بتروح تأخذ ثلاث عناصر موجودة في الـ group G، يبقى
+
+20
+00:02:04,740 --> 00:02:10,280
+بدنا نجي نقول له let الـ A والـ B والـ C موجودة في G، then
+
+21
+00:02:11,170 --> 00:02:18,770
+بتروح تأخذ a star b star c، أشوف كده شو ساوي، بدي أجي
+
+22
+00:02:18,770 --> 00:02:23,950
+الآن لـ a star b، a star b هي معرفة، يبقى بدي أشيلها 
+
+23
+00:02:23,950 --> 00:02:29,950
+وأحط اللي هي القيمة تبعها، يبقى a زائد الـ b ناقص
+
+24
+00:02:29,950 --> 00:02:38,060
+a b، هي الـ star، وهي c، الآن هذا كله صار عنصر جديد
+
+25
+00:02:38,060 --> 00:02:44,940
+في الـ group اللي عندنا جي أو في الـ set اللي عندنا جي
+
+26
+00:02:44,940 --> 00:02:50,280
+يبقى هذا العنصر بدي أعمله star مع c، الـ star بين 
+
+27
+00:02:50,280 --> 00:02:54,960
+two عنصر، يمكن أقول الأول زائد الثاني ناقص حاصل ضرب
+
+28
+00:02:54,960 --> 00:03:00,900
+الأول في الثاني، إذا هذا بدي يساوي الأول زائد b
+
+29
+00:03:00,900 --> 00:03:09,000
+ناقص a b زائد الثاني اللي هو C، تمام، ناقص حاصل
+
+30
+00:03:09,000 --> 00:03:15,900
+ضربهما، يبقى ناقص A زائد B ناقص a و b كله في 
+
+31
+00:03:15,900 --> 00:03:20,540
+مين؟ في c، يبقى هاي طبق للـ star طبق للـ
+
+32
+00:03:20,540 --> 00:03:25,370
+definition اللي فوق، بدي أشوف هذا شو بيساوي، يبقى هذا
+
+33
+00:03:25,370 --> 00:03:37,230
+بدي يساوي a زائد b زائد c ناقص ab ناقص ca عفواً
+
+34
+00:03:37,230 --> 00:03:49,420
+ناقص ac، ac بالترتيب ناقص bc زائد abc، هذا الـ term 
+
+35
+00:03:49,420 --> 00:03:55,520
+الأول، بدي أشوف الـ term الثاني، بدي أشوف الـ a star b
+
+36
+00:03:55,520 --> 00:04:01,670
+star c، شو بده يعطيني، يبقى بدي أروح أحسبه، بي ستار سي
+
+37
+00:04:01,670 --> 00:04:08,410
+يبقى هذا الـ a اللي برا وهذا الـ star وهيجي بي زائد
+
+38
+00:04:08,410 --> 00:04:15,690
+سي ناقص بي سي، طبق الـ definition اللي عرفناها الـ
+
+39
+00:04:15,690 --> 00:04:20,100
+operation أو الـ binary operation اللي عندنا، بتطبق
+
+40
+00:04:20,100 --> 00:04:24,680
+الـ binary operation كمان مرة، يبقى الأول زائد
+
+41
+00:04:24,680 --> 00:04:29,600
+الثاني ناقص حاصل ضرب الأول في الثاني، يبقى هذا
+
+42
+00:04:29,600 --> 00:04:38,720
+الأول زائد الثاني، ب زائد c، ناقص bc، ناقص حاصل ضرب
+
+43
+00:04:38,720 --> 00:04:48,280
+الأول في الثاني ب زائد c، ناقص bc، هذا الكلام يساوي a
+
+44
+00:04:49,470 --> 00:05:02,190
+زائد B زائد C ناقص BC ناقص AB ناقص AC زائد ABC
+
+45
+00:05:02,190 --> 00:05:10,430
+طلع لي هذه رقم واحد وهذه رقم اثنين، تعالوا نطلع على
+
+46
+00:05:10,430 --> 00:05:14,370
+رقم واحد ورقم اثنين، هل الاثنين نفس الشيء ولا
+
+47
+00:05:14,370 --> 00:05:20,530
+باختلفوا، a زائد b زائد c، a زائد b زائد c ناقص ab
+
+48
+00:05:20,530 --> 00:05:28,430
+ناقص ac ناقص bc، يبقى ناقص bc ناقص ab ناقص ac
+
+49
+00:05:28,430 --> 00:05:32,970
+الثلاثة دول هم هم، زائد حاصل ضرب الثلاثة، زائد حاصل
+
+50
+00:05:32,970 --> 00:05:38,950
+ضرب الثلاثة، يبقى بناء على الاثنين هذول مالهم؟ بيساووا 
+
+51
+00:05:38,950 --> 00:05:47,930
+بعض، يبقى بروح بقول له هنا from واحد and اثنين we
+
+52
+00:05:47,930 --> 00:06:00,720
+have أن a star b star c بده يساوي a star b star 
+
+53
+00:06:00,720 --> 00:06:06,600
+c، يبقى هذا معناه أن الـ star مالها؟ is associative
+
+54
+00:06:06,600 --> 00:06:18,360
+يبقى هنا so الـ star is an associative
+
+55
+00:06:18,360 --> 00:06:21,140
+binary operation
+
+56
+00:06:28,360 --> 00:06:32,280
+يبقى خلصنا النقطة الأولى، بدي أجل النقطة الثانية 
+
+57
+00:06:32,280 --> 00:06:40,240
+بدي أثبت أنه في عندي identity element، وطبقاً لهذه
+
+58
+00:06:40,240 --> 00:06:44,040
+العملية بدي أعرف إيه شكل هذا الـ identity element
+
+59
+00:06:44,040 --> 00:06:50,120
+إذا أنا هأفترض أن عندي identity element E، وأشوف الـ E
+
+60
+00:06:50,120 --> 00:06:54,450
+بقدر أجيب له قيمة ولا بقدرش، إذا قدرنا نجيب له قيمة 
+
+61
+00:06:54,450 --> 00:06:58,330
+معناه موجود، ما قدرنا معناه مش موجود، فرضي مش صحيح
+
+62
+00:06:58,330 --> 00:07:07,430
+يبقى بناء عليه بداية أقول له assume، أفترض that أن
+
+63
+00:07:07,430 --> 00:07:19,170
+الـ E is the identity element of
+
+64
+00:07:19,170 --> 00:07:26,450
+G، أفترض أن إيه الـ identity element في g، أفترض كمان
+
+65
+00:07:26,450 --> 00:07:42,690
+أن الـ a موجود في g، يبقى then الـ e star a بدي أعرف 
+
+66
+00:07:42,690 --> 00:07:50,190
+إيه شكل الـ e هذه، لذلك بروح آخذ أي واحدة من هذول، إذا 
+
+67
+00:07:50,190 --> 00:07:58,010
+لو أخذت الـ E star a يساوي a، implies إيه؟ بدي أطبق
+
+68
+00:07:58,010 --> 00:08:02,250
+تعريف الـ star اللي عندنا هذه على الجزء اللي عندنا
+
+69
+00:08:02,250 --> 00:08:10,290
+هذا، يبقى الأول زائد الثاني ناقص حاصل ضرب الأول في
+
+70
+00:08:10,290 --> 00:08:18,590
+الثاني، كل هذا بده يساوي مين؟ بده يساوي a itself، طيب
+
+71
+00:08:18,590 --> 00:08:24,110
+احنا بنشتغل في مين؟ في rational numbers، أعداد 
+
+72
+00:08:24,110 --> 00:08:30,770
+جذرية عادية، إذا هذا لو جبت عند هذا، بروح، إذا هذا
+
+73
+00:08:30,770 --> 00:08:37,490
+هيعطيني ما يأتي أن E ناقص E في a بيكون يساوي
+
+74
+00:08:37,490 --> 00:08:39,490
+كده؟ بيكون يساوي Zero
+
+75
+00:08:45,960 --> 00:08:52,440
+يبقى هذا معناه أن الـ E في 1 ناقص a يبقى يساوي
+
+76
+00:08:52,440 --> 00:08:57,320
+Zero، يبقى هذا معناه أن الـ E يساوي Zero على 1
+
+77
+00:08:57,320 --> 00:08:58,440
+ناقص a
+
+78
+00:09:02,280 --> 00:09:08,840
+لأن لو كان الواحد موجود لأصبح الـ E Undefined، يبقى
+
+79
+00:09:08,840 --> 00:09:17,900
+هذا معناه كم؟ Zero، يبقى هنا سواء الـ E Identity
+
+80
+00:09:17,900 --> 00:09:31,780
+Element of G، الـ E بده يساوي Zero، طيب، يبقى صار الـ
+
+81
+00:09:31,780 --> 00:09:36,700
+identity element exist، الآن بدنا نثبت أن الـ
+
+82
+00:09:36,700 --> 00:09:43,100
+inverse element كذلك ما له؟ exist، لذلك بدنا نجي نقول
+
+83
+00:09:43,100 --> 00:09:53,060
+هنا النقطة الثالثة والأخيرة، let B be the inverse
+
+84
+00:09:53,060 --> 00:09:57,780
+element of
+
+85
+00:09:58,350 --> 00:10:08,190
+أي اللي موجودة في g، then a star b يساوي b star a
+
+86
+00:10:08,190 --> 00:10:13,990
+يساوي الـ identity element اللي هو مين؟ الـ zero، هأخذ
+
+87
+00:10:13,990 --> 00:10:22,910
+أي واحدة فيهم، يبقى a star b بدي يساوي a زائد b
+
+88
+00:10:22,910 --> 00:10:29,430
+ناقص a b، بدي يساوي قداش؟ بدي يساوي zero، طلع لي
+
+89
+00:10:29,430 --> 00:10:35,510
+لهذه أنا ببحث عن مين؟ عن b، إذا بدي أخلي b في
+
+90
+00:10:35,510 --> 00:10:40,180
+ناحية والباقي كله في ناحية ثانية، يبقى هذه إيش
+
+91
+00:10:40,180 --> 00:10:48,890
+هتعطيني؟ هتعطيني أن a يساوي a في b ناقص b، أو الـ
+
+92
+00:10:48,890 --> 00:10:56,590
+a بدي يساوي اللي هو a ناقص 1 في b، أو الـ b بدي
+
+93
+00:10:56,590 --> 00:11:03,390
+يساوي a على a ناقص 1، يبقى هذا الشكل الـ inverse
+
+94
+00:11:03,390 --> 00:11:12,150
+element، يبقى b تساوي a على a ناقص 1 is the
+
+95
+00:11:12,150 --> 00:11:15,330
+inverse element
+
+96
+00:11:17,140 --> 00:11:26,860
+of a اللي موجود في main في g، طب إيش رأيك أنا جبت 
+
+97
+00:11:26,860 --> 00:11:31,160
+الـ zero element وجبت الـ inverse element، حابب
+
+98
+00:11:31,160 --> 00:11:37,220
+أتأكد شغلي هذا صح ولا لأ، أنا بدعي أنه صح 100% لكن 
+
+99
+00:11:37,220 --> 00:11:43,020
+حابب أتأكد، حابب أتأكد كيف؟ لو جبت a star zero لازم
+
+100
+00:11:43,020 --> 00:11:48,470
+يعطيني main الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+101
+00:11:48,470 --> 00:11:48,690
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+102
+00:11:48,690 --> 00:11:50,030
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+103
+00:11:50,030 --> 00:11:53,870
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+104
+00:11:53,870 --> 00:11:53,970
+أصح أو لا؟ الـ A
+
+105
+00:11:53,970 --> 00:11:57,170
+أصح أو لا؟ الـ A 
+
+106
+00:11:57,170 --> 00:12:01,620
+أصح أو لا؟ الـ A أصح أو لا، يبقى أنا بناء عليه بقدر
+
+107
+00:12:01,620 --> 00:12:11,480
+أقول رص وهكذا الـ g والـ star is a group، لكن لو 
+
+108
+00:12:11,480 --> 00:12:16,280
+جيت في الـ ه مش هيك، بدأت أتأكد من صحة كلامي، بدنا نجي
+
+109
+00:12:16,280 --> 00:12:23,600
+نأخذ a star is zero، هذا لازم يطلع قداش؟ a، مشان إيش؟
+
+110
+00:12:23,600 --> 00:12:29,500
+بالكلام الصحيح، يبقى هذا الكلام بده يساوي a زائد
+
+111
+00:12:29,500 --> 00:12:37,320
+zero ناقص a في zero، طبعاً هدف zero وهدف zero، يبقى
+
+112
+00:12:37,320 --> 00:12:42,660
+الجواب قداش؟ يبقى الجواب a وهو المطلوب، بالمثل 
+
+113
+00:12:42,660 --> 00:12:50,860
+similarly similarly الـ zero star a بده يساوي الـ a
+
+114
+00:12:50,860 --> 00:12:59,860
+and، بدي آخذ a star b، أنا ادعيت أن b هو معكوس الـ a
+
+115
+00:12:59,860 --> 00:13:03,740
+يبقى لما أنا أعمل star في مابينهما لازم يطلع الـ
+
+116
+00:13:03,740 --> 00:13:08,100
+identity element اللي هو mean الـ zero، يبقى هذا
+
+117
+00:13:08,100 --> 00:13:15,820
+الكلام بده يساوي a star b، هي موجودة عندي a على a
+
+118
+00:13:15,820 --> 00:13:21,800
+minus الـ one، يبقى حسب التعريف تبع الـ star هذا بده
+
+119
+00:13:21,800 --> 00:13:29,900
+يساوي العدد الأول زائد العدد الثاني ناقص حاصل
+
+120
+00:13:29,900 --> 00:13:39,370
+ضربهما، تمام؟ طيب هذا الكلام يساوي، لو وحدنا المقامات
+
+121
+00:13:39,370 --> 00:13:46,370
+للكل بصير a ناقص 1، بصير هنا a في a ناقص 1
+
+122
+00:13:46,370 --> 00:13:55,280
+زائد a ناقص a تربيع، هذه لو فكيتها بيصير a
+
+123
+00:13:55,280 --> 00:14:03,580
+تربيع ناقص a زائد a ناقص a تربيع كله على 
+
+124
+00:14:03,580 --> 00:14:12,340
+a ناقص 1، أظن كده البسط هذا بيطلع 0 على a-1، يبقى 
+
+125
+00:14:12,340 --> 00:14:17,560
+يساوي 0، يبقى فعلاً هذا هو معكوس الـ element اللي 
+
+126
+00:14:17,560 --> 00:14:21,800
+موجود هنا طبعا لم نأخذ في الأمثلة السابقة العشرة
+
+127
+00:14:21,800 --> 00:14:27,020
+أمثلة السابقة ولا مثال أخذنا بهذا الشكل لأن كان من
+
+128
+00:14:27,020 --> 00:14:30,720
+السهل أو بكل بساطة كان ممكن نجيب الـ identity
+
+129
+00:14:30,720 --> 00:14:34,700
+element والـ inverse element بس لما صارت الـ
+
+130
+00:14:34,700 --> 00:14:39,480
+operation هذا فيها نوع من التعقيد صارت عملية
+
+131
+00:14:39,480 --> 00:14:44,540
+الحسابات بهذا الشكل دقيقة يبقى بناء عليه لو أعطاك
+
+132
+00:14:44,540 --> 00:14:48,600
+أي binary operation بعد ذلك فيها تعقيد بدك تمشي
+
+133
+00:14:48,600 --> 00:14:51,680
+بنفس الـ tactic بعد ذلك تفترض أن عندك الـ identity
+
+134
+00:14:51,680 --> 00:14:56,400
+element تستنتج ما هو شكله بعد ذلك تفترض أن عندك
+
+135
+00:14:56,400 --> 00:15:01,760
+inverse element وتستنتج ما هو شكل هذا الـ inverse
+
+136
+00:15:01,760 --> 00:15:09,480
+element إذا هذا المثال هو نوع جديد من التفكير لكنه
+
+137
+00:15:09,480 --> 00:15:17,700
+تطبيق مباشر عالميا على هذه الخاصية الآن بنعطي مثال
+
+138
+00:15:17,700 --> 00:15:24,040
+آخر على الـ groups لكن هذا المثال very important كل
+
+139
+00:15:24,040 --> 00:15:28,500
+section هتلاقي طالع لك main سؤال على هذا المثال أو
+
+140
+00:15:28,500 --> 00:15:32,840
+معلومة على هذا المثال أو ما إلى ذلك المثال هذا
+
+141
+00:15:32,840 --> 00:15:40,320
+بنسميه symmetry of a square أو dihedral group يبقى
+
+142
+00:15:40,320 --> 00:15:41,920
+المثال الثاني عشر
+
+143
+00:16:07,260 --> 00:16:15,580
+الكتب بتسميها the dihedral 
+
+144
+00:16:18,660 --> 00:16:29,480
+the dihedral group of order اثنين في أربعة اللي هو
+
+145
+00:16:29,480 --> 00:16:30,800
+بده يساوي ثمانية
+
+146
+00:16:38,290 --> 00:16:42,490
+نجي للتسمية اللي احنا كاتبينها لـ group D4 لـ
+
+147
+00:16:42,490 --> 00:16:49,790
+symmetries of A² تماثل المربع تماثل المربع هذا خاص
+
+148
+00:16:49,790 --> 00:16:59,430
+بـ D4 لكن in general لو كان D2 D3 D4 D5 D6 DN
+
+149
+00:16:59,430 --> 00:17:06,420
+بسميها الـ dihydral group of order 2N يعني الرقم
+
+150
+00:17:06,420 --> 00:17:11,140
+اللي عندك هذا دائما وقبلها بتضربه في كده؟ في
+
+151
+00:17:11,140 --> 00:17:16,080
+اثنين اللي أنا بدنا نشوف ليش سميناها symmetries of
+
+152
+00:17:16,080 --> 00:17:22,380
+a² هذي الـ group أنت نشأ نتيجة لحركة مين؟ لحركة
+
+153
+00:17:22,380 --> 00:17:30,680
+مربع طب ايش معنى ايش معنى دايهدرال بالعربي؟
+
+154
+00:17:30,680 --> 00:17:37,480
+دايهدرال يعني ثنائي السطوح يعني إله وجهين أو إله
+
+155
+00:17:37,480 --> 00:17:43,340
+سطحين كما ستراونا بعد قليل من خلال الشغل شوف يا
+
+156
+00:17:43,340 --> 00:17:49,340
+سيدي أنا بدي آخذ مربع المربع هذا بالشكل اللي عندنا
+
+157
+00:17:49,340 --> 00:17:54,140
+هنا وبدي أعطيه تسميات مشان نتقيد بالتسمية اللي
+
+158
+00:17:54,140 --> 00:17:59,820
+بالكتاب مشان ما يصيرش مشاكل بيننا وبينه يبقى P وهنا
+
+159
+00:17:59,820 --> 00:18:03,300
+G وهنا B
+
+160
+00:18:09,690 --> 00:18:16,690
+هذا المربع بدي أعمل فيه دورانات يعني أنت قدامك وجه
+
+161
+00:18:16,690 --> 00:18:21,890
+مظبوط لكن الوجه في ناحية الثانية أحيانا بدي أخلي
+
+162
+00:18:21,890 --> 00:18:26,590
+هذا الوجه يبين وأحيانا بدي أخلي الوجه الثاني و
+
+163
+00:18:26,590 --> 00:18:34,100
+أحيانا بدي أخلي نفس الوجه بس بدي أغير مواقعه يبقى
+
+164
+00:18:34,100 --> 00:18:40,860
+هنا لو جيت قلت عملت rotation بزاوية مقدرها صفر
+
+165
+00:18:40,860 --> 00:18:48,720
+درجة هل سيتغير وضع هذا المربع؟ لا يبقى بدي أجي أسمي
+
+166
+00:18:48,720 --> 00:18:57,140
+حاجة عندي R node rotation
+
+167
+00:18:57,140 --> 00:19:05,570
+of صفر درجة rotation of صفر درجة يبقى دوران بصفر
+
+168
+00:19:05,570 --> 00:19:11,390
+درجة يبقى هنا بده أسميها no change in position
+
+169
+00:19:11,390 --> 00:19:19,630
+ما فيش تغيير في المكان no change in position ما فيش
+
+170
+00:19:19,630 --> 00:19:24,850
+تغيير في وضع المربع يبقى المربع هيصير عندنا بالشكل
+
+171
+00:19:24,850 --> 00:19:34,480
+اللي عندنا هذا هذا P هذا G هذا P وهذا W وهذا R نوت
+
+172
+00:19:34,480 --> 00:19:39,200
+يعني ما صارشي دوران يبقى بدي أسبب هذا الوضع الأساسي
+
+173
+00:19:39,200 --> 00:19:47,400
+طيب بدي أجي لـ R تسعين R تسعين درجة هو rotation of
+
+174
+00:19:47,400 --> 00:19:53,380
+تسعين درجة بس تسعين ممكن مع عقارب الساعة وممكن ضد
+
+175
+00:19:53,380 --> 00:19:58,980
+عقارب الساعة أنا بدي أمشي counter clockwise يبقى
+
+176
+00:19:58,980 --> 00:20:06,460
+هنا هذا counter clockwise
+
+177
+00:20:06,460 --> 00:20:15,340
+ضد عقارب الساعة يبقى هذا وضع المربع هذا P وهذا G
+
+178
+00:20:15,340 --> 00:20:23,920
+وهذا P وهذا W وهنا تحركت بزاوية تسعين درجة يبقى
+
+179
+00:20:23,920 --> 00:20:29,940
+الشكل المربع هيصير على الشكل اللي عندنا الـ P هتيجي
+
+180
+00:20:29,940 --> 00:20:36,780
+مكان G و G هتيجي مكان P و P مكان الـ W و الـ W مكان
+
+181
+00:20:36,780 --> 00:20:42,500
+مين مكان الـ P يبقى الـ P هتيجي هنا والـ G هتيجي هنا
+
+182
+00:20:42,500 --> 00:20:49,650
+والـ P هتيجي هنا والـ W هتيجي هنا يبقى هاي دوران
+
+183
+00:20:49,650 --> 00:20:57,070
+rotation بزاوية 90 درجة طب لو خلت الدوران R 180
+
+184
+00:20:57,070 --> 00:21:02,770
+درجة يبقى rotation of 180 درجة برضه counter
+
+185
+00:21:02,770 --> 00:21:08,690
+clockwise اللي هو ضد عقارب الساعة يبقى هذه حضريها
+
+186
+00:21:08,690 --> 00:21:13,690
+الرمزي التالي هذا المربع الأصلي اللي عندنا هذا P
+
+187
+00:21:13,690 --> 00:21:21,430
+وهذا G وهذا الـ B وهذه الـ W وهنا Rotation بزاوية
+
+188
+00:21:21,430 --> 00:21:29,090
+مقدرها 180 درجة بدي أجي عند المربع التالي من هنا
+
+189
+00:21:29,090 --> 00:21:33,170
+لهنا قولنا بقداش تسعين إذا بدي أمشي كمان من هنا
+
+190
+00:21:33,170 --> 00:21:39,370
+كمان تسعين إذا P بدي تيجي هنا تمام؟ الآن P بدي
+
+191
+00:21:39,370 --> 00:21:45,070
+تيجي هنا يبقى G بعد الـ P يبقى الـ G بدي تيجي هنا
+
+192
+00:21:45,520 --> 00:21:52,040
+الـ P بدها تيجي هنا الـ W بدها تيجي هنا تمام؟ يبقى
+
+193
+00:21:52,040 --> 00:21:59,700
+هذا دوران بزاوية مقدرها 180 درجة بدها GR 270 درجة
+
+194
+00:21:59,700 --> 00:22:05,680
+rotation بـ 270 counter clockwise يبقى هذا المربع
+
+195
+00:22:05,680 --> 00:22:14,850
+اللي عندنا الأصلي هذا P وهذا G وهذا P وهذا W يصير
+
+196
+00:22:14,850 --> 00:22:25,090
+بالشكل اللي عندنا هذا نتيجة للـ R 270 درجة P لما جت
+
+197
+00:22:25,090 --> 00:22:31,310
+هنا كان 180 270 بدنا ايه؟ كمان واحدة إذا الـ P بدها
+
+198
+00:22:31,310 --> 00:22:35,970
+تيجي هنا الـ G لما جت هنا كان مية و ثمانية يبقى
+
+199
+00:22:35,970 --> 00:22:41,450
+بتيجي مكان الـ P يبقى هنا بده يجينا الـ G وهنا بده
+
+200
+00:22:41,450 --> 00:22:48,470
+يجينا الـ P الـ P وهنا الـ W يبقى هاي الـ 270
+
+201
+00:22:48,470 --> 00:22:53,710
+والسبعين درجة طب لو 360 درجة برجع كما
+
+202
+00:22:53,710 --> 00:23:00,740
+كنت مظبوط يبقى بتطلع الـ R node اللي فوق طب أنا بدي
+
+203
+00:23:00,740 --> 00:23:08,160
+أعمل شغل ثاني بدي الآن آخذ دوران حول خط أفقي
+
+204
+00:23:08,160 --> 00:23:14,840
+ودوران حول خط رأسي ودوران حول من؟ حول الأقطار
+
+205
+00:23:32,710 --> 00:23:40,710
+واللي بقى لكن الآن بدي آخذ H اللي هو عبارة عن
+
+206
+00:23:40,710 --> 00:23:45,510
+rotation about
+
+207
+00:23:45,510 --> 00:23:49,770
+a
+
+208
+00:23:49,770 --> 00:24:00,270
+horizontal line about a horizontal line
+
+209
+00:24:01,580 --> 00:24:08,960
+حوالين خط مستقيم هذا المربع اللي عندك وهذه P وهذه
+
+210
+00:24:08,960 --> 00:24:20,260
+G وهذه P وهذه W هنا هذه الـ H بدي أجي كالمربع اللي عندك هنا خلي بالك هنا أنا بدي أدخلي
+
+211
+00:24:20,260 --> 00:24:26,490
+الدوران أهو الدوران horizontal حوالين الخط الأحمر
+
+212
+00:24:26,490 --> 00:24:32,050
+هذا بزاوية قداش rotation 180 درجة 180
+
+213
+00:24:32,050 --> 00:24:39,690
+درجة about a horizontal line يبقى أنا لما
+
+214
+00:24:39,690 --> 00:24:45,250
+أجي 180 درجة الـ G وين بتصير مكان الـ P والـ
+
+215
+00:24:45,250 --> 00:24:50,630
+B والـ W يعني بده يظهر الوجه الآخر للمربع السطح
+
+216
+00:24:58,330 --> 00:25:01,470
+اللي قبلنا هذا بده يصير هذا في الناحية الثانية والـ
+
+217
+00:25:01,470 --> 00:25:04,550
+لي كان الناحية الثانية بده يصير في وجهنا هو من
+
+218
+00:25:04,550 --> 00:25:10,210
+هنا سمينا dihydral ثنائي السطوح السطح اللي كان مش
+
+219
+00:25:10,210 --> 00:25:13,570
+ظاهر بده يصير هو الظاهر والسطح اللي كان ظاهر بده
+
+220
+00:25:13,570 --> 00:25:18,620
+يصير ما له مش ظاهر سمينا من هنا ثنائي السطوح يبقى
+
+221
+00:25:18,620 --> 00:25:23,780
+دوران حوال الخط بده يصير عندنا مين؟ بده يصير هذه G
+
+222
+00:25:23,780 --> 00:25:35,000
+وتحت هنا P وهنا B وهنا W طيب ما فيش أحسن حد من حد
+
+224
+00:25:35,000 --> 00:25:40,140
+مدام صورة دوران أفقي بده يخلي دوران حوال الخط
+
+225
+00:25:40,140 --> 00:25:45,880
+الرأسي يبقى لو جيت سميت الـ vertical اللي هو
+
+226
+00:25:45,880 --> 00:25:55,740
+rotation بـ 180 درجة about a vertical line
+
+227
+00:25:55,740 --> 00:26:01,980
+حوالين الخط الرأسي يبقى هذا المربع اللي عندنا هذا
+
+228
+00:26:01,980 --> 00:26:12,860
+P هذا G هذا W هذا P وهذا هو الخط الرأسي الـ
+
+229
+00:26:12,860 --> 00:26:19,200
+vertical يبقى بناء عليه بدي يصبح عندنا المربع على
+
+230
+00:26:19,200 --> 00:26:24,740
+الشكل التالي هذا V بدي يصير المربع بالشكل اللي
+
+231
+00:26:24,740 --> 00:26:30,120
+عندنا هنا الـ P بدي تيجي مكان الـ W والـ W مكان الـ P
+
+232
+00:26:30,120 --> 00:26:35,820
+يعني بدي نجليه رأسيًا تمام؟ يعني زي ما تقول هاي هذا
+
+233
+00:26:35,820 --> 00:26:40,860
+المربع لما نجليه رأسيًا حوالين النص بدي يصير دوران فوق
+
+234
+00:26:40,860 --> 00:26:44,670
+وتحت قبل كان دوران اللي قبل هي أمامي وأيسر لكن هي
+
+235
+00:26:44,670 --> 00:26:49,510
+منذ عامة الدوران فوق أو تحت معناته الـ P بده تيجي
+
+236
+00:26:49,510 --> 00:26:58,590
+مكان الـ W والـ W مكان الـ P تمام؟ والـ B بده تيجي
+
+237
+00:26:58,590 --> 00:27:04,930
+مكان الـ G والـ G مكان الـ B يبقى هذا اسمه vertical
+
+238
+00:27:04,930 --> 00:27:12,390
+rotation بـ 180 درجة طيب بدي أخلي دوران حوالين القطر
+
+239
+00:27:12,390 --> 00:27:19,210
+الرئيسي يبقى الحالة السابعة بدي أسميها اللي هي دي
+
+240
+00:27:19,210 --> 00:27:24,990
+يبقى هذه rotation 180
+
+241
+00:27:24,990 --> 00:27:33,910
+درجة about the main diagonal
+
+242
+00:27:36,260 --> 00:27:45,160
+حوالين القطر الرئيسي main main
+
+243
+00:27:45,160 --> 00:27:50,960
+diagonal حوالين القطر الرئيسي تمام يبقى المربع كان
+
+244
+00:27:50,960 --> 00:27:58,080
+بالشكل اللي عندنا هذا وهذه الرموز كما هي هنا P هنا
+
+245
+00:27:58,080 --> 00:28:08,270
+G هنا B هنا اللي هو W هذه بده يسميها اللي هو الرمز
+
+246
+00:28:08,270 --> 00:28:13,450
+D يبقى بده يصير المربع اللي عندنا على الشكل التالي
+
+247
+00:28:13,450 --> 00:28:20,610
+لما أقول يا شباب هذا هو القطر الرئيسي يبقى عندي
+
+248
+00:28:20,610 --> 00:28:26,110
+الدوران هل P و B بيحصل لهم حاجة يبقى هدول بيبقوا
+
+249
+00:28:26,110 --> 00:28:33,620
+ثوابت زي ما هم يبقى هذه بيبقى P وهذه B كما هي
+
+250
+00:28:33,620 --> 00:28:39,920
+ما فيش تغيير هذا التغيير بيصير بين مين ومين يبقى الـ W 
+
+251
+00:28:39,920 --> 00:28:45,300
+بتيجي هنا والـ G بتيجي هنا طيب بدنا نيجي أخر حاجة
+
+252
+00:28:45,300 --> 00:28:50,660
+اللي هي D prime اللي هو ال rotation about the
+
+253
+00:28:50,660 --> 00:28:59,000
+other diagonal على القطر الآخر يبقى باجي بقوله هذا
+
+254
+00:28:59,000 --> 00:29:09,540
+المربع وهذا الـ P G P G وهنا اللي هي الـ P وهنا
+
+255
+00:29:09,540 --> 00:29:16,440
+من الـ W يبقى هذه اللي هو D Prime المربع سيأخذ
+
+256
+00:29:16,440 --> 00:29:23,180
+الشكل التالي الدوران حوالين القطر الآخر اللي هو
+
+257
+00:29:23,180 --> 00:29:30,070
+القطر اللي عندنا هذا يبقى الـ G والـ P والـ W عند
+
+258
+00:29:30,070 --> 00:29:36,130
+الدوران تبقى كما هي اللي بده يتغير بس مين الـ P و
+
+259
+00:29:36,130 --> 00:29:42,750
+الـ B يبقى بده يصير الـ P وهنا مين وهنا الـ P
+
+260
+00:29:42,750 --> 00:29:49,410
+العناصر اللي شايفهم قدامك بيكونوا ال dihydral
+
+261
+00:29:49,410 --> 00:29:55,610
+group D4 وزي ما أنت شايف فيها ستة واتنين ثمانية
+
+262
+00:29:55,610 --> 00:30:03,440
+عناصر يبقى الآن الديهيدرالي جروب D4 عناصرها ال
+
+263
+00:30:03,440 --> 00:30:11,240
+identity element اللي حاط له الرمز R0 وبعدها R90 و
+
+264
+00:30:11,240 --> 00:30:12,560
+R180
+
+265
+00:30:16,180 --> 00:30:25,640
+وR270 وH وV وD وD prime هي ثمانية عناصر تبعات D4
+
+266
+00:30:25,640 --> 00:30:31,140
+طيب D3 يا شباب كام عنصر فيها؟ ستة كلّه ضرب في اثنين
+
+267
+00:30:31,140 --> 00:30:36,020
+دي عشرة فيها عشرين عنصر دي ثلاثين فيها ستين عنصر و
+
+268
+00:30:36,020 --> 00:30:42,040
+هكذا تمام يبقى هذه إيه؟ هذه الـ group اللي هي D4
+
+269
+00:30:42,530 --> 00:30:49,710
+تعالى نبدأ ببعض الملاحظات على هذه الـ group خلّينا
+
+270
+00:30:49,710 --> 00:30:55,470
+نبدأ بالاكتشاف هذا الـ identity element R تسعين هذي
+
+271
+00:30:55,470 --> 00:31:01,870
+بدي أعمل كم مرة بهذه الطريقة حتى أرجع للأصل؟ أربع
+
+272
+00:31:01,870 --> 00:31:07,050
+مرات يبقى هذه معناته R أس أربعة عارف تسعين أس أربعة
+
+273
+00:31:07,050 --> 00:31:14,610
+بدي أساويها من الـ identity طيب والـ 270 برضه كمان
+
+274
+00:31:14,610 --> 00:31:22,170
+أربع مرات يبقى هنا باجي بقوله some properties
+
+275
+00:31:22,170 --> 00:31:26,310
+of D4
+
+276
+00:31:28,510 --> 00:31:35,910
+الخاصية الأولى أن R تسعين أس أربعة هي R مئتين
+
+277
+00:31:35,910 --> 00:31:40,850
+وسبعين أس أربعة اللي تساوي الـ identity اللي هو
+
+278
+00:31:40,850 --> 00:31:49,790
+main R node الخاصية الثانية R مئة وثمانين تربيع
+
+279
+00:31:54,620 --> 00:31:59,400
+أرنود الأصلية H
+
+280
+00:31:59,400 --> 00:32:07,020
+تربيع أرنود الأصلية برضه الرد بتـرجع كما كانت مظبوط
+
+281
+00:32:07,020 --> 00:32:14,520
+طيب أدي تربيع الـ V تربيع نفسها
+
+282
+00:32:14,520 --> 00:32:22,480
+الـ identity طب أدي تربيع طيب أدي prime تربيع
+
+283
+00:32:25,950 --> 00:32:29,690
+يبقى الـ R مئة وثمانية تربيع هي الـ identity اللي
+
+284
+00:32:29,690 --> 00:32:35,790
+قلت بدي أعطيها إيه؟ بدي أسميها أرنود تمام؟ طيب والـ
+
+285
+00:32:35,790 --> 00:32:39,610
+H تربيع بتساوي أرنود والـ V تربيع ليش؟ أن لو لفيت
+
+286
+00:32:39,610 --> 00:32:44,390
+المربع كمان مرة برجع كمان كنت مظبوط يبقى من هنا
+
+287
+00:32:44,390 --> 00:32:51,510
+هذه كلها بالأرنود طيب إيش رأيك لو جيت قلت الـ R مئة
+
+288
+00:32:51,510 --> 00:32:57,190
+وثمانين تربيع بده يساوي الـ identity وضربت الطرفين
+
+289
+00:32:57,190 --> 00:33:03,190
+في R مئة وثمانين inverse قداش بيطلع؟ يعني لما أقول
+
+290
+00:33:03,190 --> 00:33:08,950
+G تربيع يساوي E يبقى لو ضربت inverse الطرفين بيصير
+
+291
+00:33:08,950 --> 00:33:14,780
+الطرف اليمين G inverse والطرف الشمالجي واحدة بس
+
+292
+00:33:14,780 --> 00:33:18,700
+يبقى بيصير G يساوي G inverse معناته الـ element
+
+293
+00:33:18,700 --> 00:33:24,540
+بيساوي مين؟ بيساوي معكوسه إذا للعناصر اللي عندك واحد
+
+294
+00:33:24,540 --> 00:33:29,780
+اثنين ثلاثة أربعة خمسة كل عنصر بيساوي إيه؟ بيساوي
+
+295
+00:33:29,780 --> 00:33:38,580
+معكوسه يبقى هذا معناه أن الـ R مئة وثمانين بيساوي
+
+296
+00:33:38,580 --> 00:33:44,700
+الـ R مئة وثمانين inverse واللي بعدها الـ H بده
+
+297
+00:33:44,700 --> 00:33:50,720
+يساوي الـ H inverse والـ V بده يساوي الـ V inverse و
+
+298
+00:33:50,720 --> 00:33:55,280
+الـ D بده يساوي الـ D inverse والـ D prime بده يساوي
+
+299
+00:33:55,280 --> 00:34:02,820
+D prime inverse هذا
+
+300
+00:34:02,820 --> 00:34:07,760
+كويس هذه المعلومات ديّ واخد بالك منها إن شاء الله الـ
+
+301
+00:34:07,760 --> 00:34:11,580
+section الجاي نبدأ الـ order لل element والـ order لل
+
+302
+00:34:11,580 --> 00:34:17,300
+group الـ order لل element أقل رقم بيرفعه عدد صحيح
+
+303
+00:34:17,300 --> 00:34:21,260
+موجب بيرفعه بيطلع بيعطيني الـ identity يعني معناته
+
+304
+00:34:21,260 --> 00:34:25,340
+بعد قليل المحاضرة القادمة يمكن ندخلها ويمكن لأ
+
+305
+00:34:39,090 --> 00:34:47,530
+طيب بدنا نروح لخاصية ثالثة غير هذه الخواص لو ضربت
+
+306
+00:34:47,530 --> 00:34:52,470
+أو قبل أن أضرب إيش رأيك هدول الأربعة واحد اثنين
+
+307
+00:34:52,470 --> 00:34:57,470
+ثلاثة أربعة أليست هذه حركة دورانية counter clockwise
+
+308
+00:34:57,470 --> 00:35:08,310
+يبقى هدول الأربع حالات كلهم بسميهم rotation دوران
+
+309
+00:35:09,580 --> 00:35:14,720
+وممكن اختصارًا أديهم الرمز R طب والأربع حالات اللي
+
+310
+00:35:14,720 --> 00:35:21,300
+بعدهم الاثنين هدول والاثنين هدول اسمهم من عاكس
+
+311
+00:35:21,300 --> 00:35:29,140
+reflection يبقى هدول بسميهم reflection وهدول
+
+312
+00:35:29,140 --> 00:35:36,760
+اثنين كمان reflection تمام
+
+313
+00:35:36,760 --> 00:35:45,190
+تمام طيب عشان نختار دوران مع reflection أشوف إيه
+
+314
+00:35:45,190 --> 00:35:49,750
+بيعطينا دوران يعني حاصل ضرب أي دوران من الدورانات
+
+315
+00:35:49,750 --> 00:35:53,790
+هدول في أي reflection من ال reflections الأربعة
+
+316
+00:35:53,790 --> 00:35:58,990
+أشوف إيه بيعطينا دوران؟ هل بيعطينا rotation دوران و
+
+317
+00:35:58,990 --> 00:36:04,730
+لّا بيعطينا reflection تعال نأخذ أختار لك أي رقم
+
+318
+00:36:04,730 --> 00:36:08,970
+من الدورانات اللي عندنا وبدي أختار أي reflection
+
+319
+00:36:08,970 --> 00:36:14,210
+منهم وأضرب اثنين في بعض أبسط الحالات لو أخد R
+
+320
+00:36:14,210 --> 00:36:19,230
+تسعين بدي
+
+321
+00:36:19,230 --> 00:36:25,480
+أضربها مثلًا في H في أول دوران أشوف إيش بيعطينا وين
+
+322
+00:36:25,480 --> 00:36:31,320
+الـ H اللي عندي طلع للـ H هي الـ H يبقى هذه الـ H اللي
+
+323
+00:36:31,320 --> 00:36:35,880
+عندنا هذه إيش بدي أعمل لها؟ بدي أعمل لها دوران
+
+324
+00:36:35,880 --> 00:36:41,760
+بتسعين درجة أشوف إيش هتعطينا هذه يبقى هذه الـ H هه
+
+325
+00:36:41,760 --> 00:36:48,780
+بدي أسوي لها دوران بتسعين درجة لما أسوي لها دوران
+
+326
+00:36:48,780 --> 00:36:53,790
+بتسعين درجة يبقى هنا بدها TGG وهنا بدها تجيني P
+
+327
+00:36:53,790 --> 00:36:59,930
+وهنا بدها تجي W وهنا بدها تجي تجيني B صحيح ولا لا؟
+
+328
+00:36:59,930 --> 00:37:06,410
+طيب بده أشوف هذه مين منهم تعال نطلع نشوف نشوف
+
+329
+00:37:06,410 --> 00:37:12,590
+تعال الـ D هذي هيها ولا لا هي؟ لأ هي هذي؟ اه هاي
+
+330
+00:37:12,590 --> 00:37:18,590
+GPW مية المية يبقى حاصل الضرب هذا بده يسوي قداش؟ D
+
+331
+00:37:18,590 --> 00:37:26,640
+Prime تمام؟ طيب واحد يقول ليه؟ طيب لو أخدت R تسعين
+
+332
+00:37:26,640 --> 00:37:32,100
+بدل ما أخدت الـ H خد لي الـ V أشوف إيش بده يعطيني هذا
+
+333
+00:37:32,100 --> 00:37:37,180
+حاصل الضرب بقوله اه وين الـ V؟ هاي الـ V اللي عندي
+
+334
+00:37:37,180 --> 00:37:45,610
+تمام؟ الـ V هذه بدي اهي الـ V بدي أعملها دوران بمقدار
+
+335
+00:37:45,610 --> 00:37:51,930
+الواحد فقط لا غير يعني دوران تسعين يبقى هذه هتاخد
+
+336
+00:37:51,930 --> 00:38:00,770
+الشكل التالي هذه الـ B وهذه الـ G وهذه الـ P أعلى فوق
+
+337
+00:38:00,770 --> 00:38:06,530
+استنى استنى استنى استنى يا شيخ استنى
+
+338
+00:38:09,060 --> 00:38:15,500
+احنا بدنا V وين الـ V؟ هاي الـ V تمام؟ يبقى هاد الـ V
+
+339
+00:38:15,500 --> 00:38:20,080
+بده أشوف إيش بده يصير لها يبقى هاد بده يصير بالشكل
+
+340
+00:38:20,080 --> 00:38:23,820
+اللي عندنا هنا بدي أعملها دوران تسعين يبقى الـ W
+
+341
+00:38:23,820 --> 00:38:30,020
+هتيجي هنا والـ P هتيجي هنا والـ G هتيجي هنا والـ P
+
+342
+00:38:30,020 --> 00:38:36,880
+هتيجي هنا بدي أشوف هاد مين منهم ديوارينا نشوف يبقى
+
+343
+00:38:36,880 --> 00:38:42,140
+وB هي تحت وP وG مظبوط يبقى هذا حصلت ضرب بده
+
+344
+00:38:42,140 --> 00:38:46,660
+يعطينا D يبقى هذا reflection وهذا كمان reflection
+
+345
+00:38:46,660 --> 00:38:55,740
+طيب لو جيت أخدت الـ R تسعين في من في الـ D هذه بده
+
+346
+00:38:55,740 --> 00:39:01,440
+يساوي يبقى وين الـ D؟ هيها كويس؟ بدي أعمل لها لفة
+
+347
+00:39:01,440 --> 00:39:08,600
+بمقدار تسعين يبقى هذه هتاخد الشكل التالي هنا P
+
+348
+00:39:08,600 --> 00:39:20,240
+وهنا W وهنا P وهنا G وين الـ P والـ W يبقى H ممتاز
+
+349
+00:39:20,240 --> 00:39:25,540
+يادن يبقى هذا الـ P W وG P مظبوط يبقى هذا الكلام
+
+350
+00:39:25,540 --> 00:39:32,420
+بده يساوي H بده يساوي H طيب لو جيت قلت لك N R
+
+351
+00:39:32,420 --> 00:39:39,160
+تسعين في D Prime راحة الـ H وراحة الـ D وهتظلش إلا
+
+352
+00:39:39,160 --> 00:39:44,300
+الـ V مظبوط يبقى ده هتلاقيه بده يساوي V يبقى الآن
+
+353
+00:39:44,300 --> 00:39:48,540
+حاصل ضرب rotation في reflection بيعطينا reflection
+
+354
+00:39:48,540 --> 00:39:53,740
+وأنت بتجري وهي كله دليل عدالة قدامك حتى لو أخدت
+
+355
+00:39:53,740 --> 00:39:59,640
+الـ R مئة وثمانين برضه بنفس الشيء يبقى هنا باجي
+
+356
+00:39:59,640 --> 00:40:03,840
+بقوله إيش؟ يبقى
+
+357
+00:40:03,840 --> 00:40:04,280
+remark
+
+358
+00:40:07,860 --> 00:40:15,900
+any rotation ضد
+
+359
+00:40:15,900 --> 00:40:26,180
+any reflection بده
+
+360
+00:40:26,180 --> 00:40:27,580
+يساوي reflection
+
+361
+00:40:32,020 --> 00:40:41,980
+طب مدام هيك شفوي شفوي هذا تربيع كده شو بيساوي؟
+
+362
+00:40:41,980 --> 00:40:47,260
+أيوه هذا تربيع كده إيش؟
+
+363
+00:40:47,260 --> 00:40:52,760
+أرنود مش هذا reflection صار reflection يعني قد إيه؟
+
+364
+00:40:52,760 --> 00:40:56,040
+D prime D prime تربيع بالـ identity على طول الخط
+
+365
+00:40:56,340 --> 00:40:59,960
+يبقى هذا تربيعه بالـ identity هذا تربيعه بالـ identity
+
+366
+00:40:59,960 --> 00:41:03,580
+هذا تربيعه بالـ identity هذا تربيعه بالـ identity على
+
+367
+00:41:03,580 --> 00:41:07,900
+طول الخط وأنت بتجيبها كده يعني هذه هنطلع منها شيء
+
+368
+00:41:07,900 --> 00:41:12,800
+كثير لسه احنا هذه بس نكشات بسيطة مشان تعرف يعني لو
+
+369
+00:41:12,800 --> 00:41:18,880
+قلت لك أي بدي أجي أضرب مثلًا R270 في D مثلًا كيف بدي
+
+370
+00:41:18,880 --> 00:41:22,950
+أضرب R270 في D؟ بنروح على الـ D وأنا دي هي دي
+
+371
+00:41:22,950 --> 00:41:26,910
+مئتين وسبعين بتخليها تلف اللي هو الثلاث أماكن و
+
+372
+00:41:26,910 --> 00:41:30,670
+أنا بتوصل بشوف مين من هدول بيكون جبت الجواب دوري
+
+373
+00:41:30,670 --> 00:41:35,870
+على أي حال هادي راح أعمل له فيها جدول في صفحة واحد
+
+374
+00:41:35,870 --> 00:41:39,600
+وثلاثين هذا فيكم معاه كتاب اللي معاه كتاب يفتح لي
+
+375
+00:41:39,600 --> 00:41:43,220
+على صفحة واحد وثلاثين اللي قبل ما ندخل في ال 
+
+376
+00:41:43,220 --> 00:41:46,120
+group الشابتر اللي ما رضيش هجيبلكم سيطة و أقولكم
+
+377
+00:41:46,120 --> 00:41:49,920
+هعطيكميها من خلال الشابتر القادر يعني مش هخليه
+
+378
+00:41:49,920 --> 00:41:54,700
+أفصله لحاله يبقى هذا هو إيه؟ هذا هو من الشابتر
+
+379
+00:41:54,700 --> 00:41:58,610
+السابق، إن ال chapter اللي قبله ما كناش واخدين حاجة
+
+380
+00:41:58,610 --> 00:42:03,390
+اسم مجرور لكن الآن أخدت هذه كحالة اللي من ال
+
+381
+00:42:03,390 --> 00:42:06,750
+holography جدول عندك في صفحة 23 حطيت
+
+382
+00:42:06,750 --> 00:42:12,110
+الـ 8 عناصر، والـ 8 عناصر، وحاصل ضربهم كله يبقى يا
+
+383
+00:42:12,110 --> 00:42:15,730
+ريت هذا تطلع لي على الجدول اللي بتعرف النتائج الـ 
+384
+00:42:15,730 --> 00:42:22,870
+كلها بلا استثناء يبقى بداجة أقول لك هنا lock the
+
+385
+00:42:22,870 --> 00:42:24,430
+table 
+
+386
+00:42:30,080 --> 00:42:36,940
+تعرف باقي الضربيات وكل الشغلات هذه حد
+
+387
+00:42:36,940 --> 00:42:40,800
+بيسال لي سؤال هنا يا شباب، لازلنا في نفس ال section
+
+388
+00:42:40,800 --> 00:42:44,920
+بس بدنا نخش على بعض الشغلات التي تهم خاص ال group
+
+389
+00:42:44,920 --> 00:42:48,980
+لحد هنا بدنا نوقف بالنسبة لمين؟ للأمثلة
+
+390
+00:43:27,730 --> 00:43:34,330
+بنجي لحاجة اسمها ال elementary properties
+
+391
+00:43:34,330 --> 00:43:39,490
+of 
+
+392
+00:43:39,490 --> 00:43:47,530
+groups هنعقد
+
+393
+00:43:47,530 --> 00:43:54,670
+أعطي نقاط فيها، النقطة الأولى: هي group g 
+
+394
+00:43:58,910 --> 00:44:21,370
+there is only one identity element احنا
+
+395
+00:44:21,370 --> 00:44:25,460
+المرة اللي فاتت لما عرفنا ال group قلنا لجروب فيها
+
+396
+00:44:25,460 --> 00:44:29,240
+identity element لكن ما قلناش هما اتنين، هو تلاتة، هو
+
+397
+00:44:29,240 --> 00:44:33,760
+واحد الآخر تمام، يبقى الخاصية الأولى من خاصة
+
+398
+00:44:33,760 --> 00:44:38,060
+الجروب بتقول لي ال identity element في الجروب يكون
+
+399
+00:44:38,060 --> 00:44:42,490
+وحيدا، يعني ال group الواحدة لا يوجد فيها إلا 
+
+400
+00:44:42,490 --> 00:44:47,350
+identity element واحد، in a group G there is only
+
+401
+00:44:47,350 --> 00:44:52,490
+one واحد فقط اللي هو identity element، طب بدنا نثبت
+
+402
+00:44:52,490 --> 00:44:56,850
+صحة هذا الكلام، مشان نثبت صحة هذا الكلام، مفروض إنه
+
+403
+00:44:56,850 --> 00:45:01,410
+عنده إيش؟ اتنين، وبثبت إن الاتنين هدول مالهم؟ are
+
+404
+00:45:01,410 --> 00:45:10,330
+equal، يبقى هنا بداجة أقول assume افترض that إن الـ
+
+405
+00:45:10,330 --> 00:45:25,050
+E والـ E prime are two identity elements of
+
+406
+00:45:25,050 --> 00:45:29,930
+the group G then
+
+407
+00:45:29,930 --> 00:45:33,830
+الـ
+
+408
+00:45:33,830 --> 00:45:42,880
+A star E بتساوي الـ A لكل الـ A الموجودة في G
+
+409
+00:45:42,880 --> 00:45:46,300
+مظبوط؟
+
+410
+00:45:46,300 --> 00:45:53,020
+طيب هذا الشيء بيعطيك الآن الـ A أسطري، أنا حتى الـ
+
+411
+00:45:53,020 --> 00:45:57,860
+E هو ال identity element هنا مظبوط؟ إذا الـ E
+
+412
+00:45:57,860 --> 00:46:02,740
+prime بيكون element عادي صح ولا لأ؟ بالنسبة لأني
+
+413
+00:46:02,740 --> 00:46:05,820
+إذا كان هذا هو ال identity element يبقى الـ E'
+
+414
+00:46:06,200 --> 00:46:10,620
+بيكون element عادي، يبقى بناء على اللي بدي يكون E'
+
+415
+00:46:11,440 --> 00:46:18,420
+أستار E بدي يساوي الـ E' يعني كأنه الـ E' حطيتها
+
+416
+00:46:18,420 --> 00:46:25,620
+مكان مين؟ مكان الـ E، الآن لو افترضت أن الـ E' هو
+
+417
+00:46:25,620 --> 00:46:36,400
+identity element يبقى and الـ E' أستار لأ لأ بدنا
+
+418
+00:46:36,400 --> 00:46:41,700
+نغيّر هذه يبقى
+
+419
+00:46:41,700 --> 00:46:48,420
+and ال and بدأ ياخد ال a star هو ال identity
+
+420
+00:46:48,420 --> 00:46:55,160
+element يبقى بدأ ياخد a star ال star a بده يسوي
+
+421
+00:46:55,160 --> 00:47:00,440
+من؟ بده يسوي ال a itself، يعني هنا أخدت ال a
+
+422
+00:47:00,440 --> 00:47:04,620
+identity element وهنا أخدت ال e prime identity
+
+423
+00:47:04,620 --> 00:47:11,850
+element يبقى هذا بده يعطينا إيه؟ لكل اللي موجودة في
+
+424
+00:47:11,850 --> 00:47:19,090
+فيجي الآن ال element E موجود في G إذا ينطبق عليه
+
+425
+00:47:19,090 --> 00:47:26,550
+هذه الخاصية يبقى معناته إن ال E prime star E بده
+
+426
+00:47:26,550 --> 00:47:32,530
+يساوي ال E itself، طب الاتنين هذول الطرف الشمال مش هو
+
+427
+00:47:32,530 --> 00:47:38,210
+نفسه، إذا الطرف اليمين هو نفسه، إذا هذا بده يعطيك
+
+428
+00:47:38,210 --> 00:47:45,400
+إن ال E تساوي مين؟ الـ E'، هو المطلوب، إذا من الآن
+
+429
+00:47:45,400 --> 00:47:49,960
+فصاعدا ال identity element في ال group G يكون
+
+430
+00:47:49,960 --> 00:47:54,680
+وحيدا ما فيش غيره، إن قلت هو ال zero هو ال identity
+
+431
+00:47:54,680 --> 00:47:58,590
+element إذا لا يوجد غير هذا الصفر، إن جدش ال group
+
+432
+00:47:58,590 --> 00:48:02,230
+فيها الواحد ال identity element يبقى الواحد ما فيش
+
+433
+00:48:02,230 --> 00:48:09,170
+غيره وهكذا تمام؟ في كمان نقطة ثانية ممكن نتعرض
+
+434
+00:48:09,170 --> 00:48:13,590
+إلى الآن بس بتاخد وقت شوية إذا نكتفي بهذا القدر
+
+435
+00:48:13,590 --> 00:48:19,070
+اليوم ونكمل المحاضرة القادمة إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..240486e75d7562808fcd8f57846aa529f031e292
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo_raw.srt
@@ -0,0 +1,1512 @@
+1
+00:00:21,720 --> 00:00:25,900
+السلام عليكم شباب ان شاء الله هنكمل ال .. بعد
+
+2
+00:00:25,900 --> 00:00:30,780
+أستاذ إسماعيل أصدر في مساقر جبر الحديث طبعا زي ما
+
+3
+00:00:30,780 --> 00:00:33,060
+أنا عارف و أنتوا عارفين أنه أستاذ إسماعيل وصل
+
+4
+00:00:33,060 --> 00:00:37,220
+لسؤال سبعتاشر مناقشة الوحدة التالتة اللي بتتكلم عن
+
+5
+00:00:37,220 --> 00:00:44,160
+finite group أو subgroups و ال finite groupسؤال 18
+
+6
+00:00:44,160 --> 00:00:48,020
+زي ما انت شايف قدامك if H and K are subgroups يعني
+
+7
+00:00:48,020 --> 00:00:52,860
+اندي two subgroups من الجيه H subgroup من الجيه ال
+
+8
+00:00:52,860 --> 00:00:56,640
+K subgroup من الجيه المطلوب في السؤال اثبت ان
+
+9
+00:00:56,640 --> 00:01:01,360
+اتقاطه عبارة عن subgroup معطياتي ان ال two
+
+10
+00:01:01,360 --> 00:01:04,900
+subgroups H وK مطلوب اثبت ان اتقاطه ولا ال two
+
+11
+00:01:04,900 --> 00:01:13,400
+subgroup بيعطيني ايضا subgroup لو بنرجع لالطرق
+
+12
+00:01:13,400 --> 00:01:16,160
+اللى من خلالها بثبت انه مجموعة ما عبارة عن
+
+13
+00:01:16,160 --> 00:01:19,940
+subgroup من group هبدأ بالوضع التقليدي ان اثبت
+
+14
+00:01:19,940 --> 00:01:24,440
+انها group تحت نفس العملية المعرفة على ال J اللى
+
+15
+00:01:24,440 --> 00:01:29,240
+هو التعريفبعد ذلك أخدنا تلت برق ال one step و ال
+
+16
+00:01:29,240 --> 00:01:33,120
+two step و ال finite subgroup test ال one step كان
+
+17
+00:01:33,120 --> 00:01:37,300
+بيعتمد على اثبات ان a-b في حالة الجامعة او a b
+
+18
+00:01:37,300 --> 00:01:41,160
+inverse في حالة ما تكون العملية عملية ضرب اثبت ان
+
+19
+00:01:41,160 --> 00:01:46,320
+لو ال a و ال b موجودين في المجموعة الجزئية ان a-b
+
+20
+00:01:46,320 --> 00:01:51,580
+او a b inverse موجودة فيها ال two step كان يعتمد
+
+21
+00:01:51,580 --> 00:01:57,300
+عليشعلى إثبات إن هذه المجموعة مغلطة على العملية
+
+22
+00:01:57,300 --> 00:02:05,200
+وعلى المعكوس طبعا في شغلة مهمة لازم يكون المجموعة
+
+23
+00:02:05,200 --> 00:02:09,600
+الجزئية اللي أنا بشرها هي مجموعة غير خالية لأنه
+
+24
+00:02:09,600 --> 00:02:12,420
+ماقدرش أثبت إن مجموعة خالية هي عبارة عن subgroup
+
+25
+00:02:12,420 --> 00:02:14,360
+بالنسبة لل finite
+
+26
+00:02:17,930 --> 00:02:22,550
+Test كنا نثبت فيه شرط واحد و هو ان المجموعة مغلقة
+
+27
+00:02:22,550 --> 00:02:28,970
+على العملية هل بإمكاني استعمل الطريقة الأولى و
+
+28
+00:02:28,970 --> 00:02:35,890
+الطريقة التانية First ال E ينتمي لل H ال E ينتمي
+
+29
+00:02:35,890 --> 00:02:39,990
+لل K صح ولا لأ المحايد موجود في ال H و المحايد
+
+30
+00:02:39,990 --> 00:02:44,670
+موجود في ال K النتيجة ان E موجود في التقاطع
+
+31
+00:02:44,670 --> 00:02:51,180
+وبالتالي التقاطعالـ two subgroups لا يساوي five
+
+32
+00:02:51,180 --> 00:03:02,500
+اختصارا للوقت هنستعمل الـ one step now let a و b
+
+33
+00:03:02,500 --> 00:03:08,660
+ينتمي للتقاطع هذا معناته حسب قوانين ال state
+
+34
+00:03:08,660 --> 00:03:14,800
+theory ان ال a و ال b ينتمي لل h and ال a و ال b
+
+35
+00:03:14,800 --> 00:03:19,820
+ينتمي لمين؟للكي تنساش ان ال H subgroup و ال K
+
+36
+00:03:19,820 --> 00:03:27,460
+subgroup معناته ال A B inverse موجودة وين في ال H
+
+37
+00:03:27,460 --> 00:03:33,200
+و موجودة وين في ال K ال A B inverse في ال H و ال A
+
+38
+00:03:33,200 --> 00:03:36,260
+B inverse في ال K ايه بال A B inverse وين موجود
+
+39
+00:03:36,260 --> 00:03:43,490
+موجود في التقاطعوبالتالي تقاطع مجموعة غير خالية
+
+40
+00:03:43,490 --> 00:03:50,170
+وفي نفس الوقت بتحقق شروط نظرية ال one step النتيجة
+
+41
+00:03:50,170 --> 00:04:01,590
+H تقاطع ال K sub group من ال G واضحة هذه؟ واضحة و
+
+42
+00:04:01,590 --> 00:04:02,470
+الله بدأت أوضيح؟
+
+43
+00:04:05,290 --> 00:04:09,770
+ما اثبتش ان ال B inverse ال H sub group و ال A و
+
+44
+00:04:09,770 --> 00:04:13,590
+ال B في ال H ف A B inverse في ال H بال one step
+
+45
+00:04:13,590 --> 00:04:21,970
+نتقل لسؤال 20 سؤال 20 يقول اثبت انه centralizer ال
+
+46
+00:04:21,970 --> 00:04:28,200
+A سو centralizer ال inverseهذا السؤال ممكنك تستعمل
+
+47
+00:04:28,200 --> 00:04:32,240
+أسلوبين للحلقة الأسلوب المباشر أن تكتب تعريف
+
+48
+00:04:32,240 --> 00:04:35,400
+المجموعة الأولى و تصل منها لتعريف المجموعة التانية
+
+49
+00:04:35,400 --> 00:04:39,880
+أو الأسلوب التاني الخاص بيثبت أنه الـcentralizer A
+
+50
+00:04:39,880 --> 00:04:42,640
+subset من الـcentralizer A inverse و
+
+51
+00:04:42,640 --> 00:04:45,500
+الـcentralizer A inverse subset من الـcentralizer
+
+52
+00:04:45,500 --> 00:04:51,500
+A أنا بفضل الأسلوب هذاCentralizer الـ A حسب
+
+53
+00:04:51,500 --> 00:04:56,200
+التعريف هذا عبارة عن كل ال X في J اللي بيكون
+
+54
+00:04:56,200 --> 00:05:04,460
+commute مع مين؟ مع ال A يعني AX بيساوي XA نشغل على
+
+55
+00:05:04,460 --> 00:05:09,940
+المجموعة نفسها هذا عبارة عن كل ال X في ال Jأضرب
+
+56
+00:05:09,940 --> 00:05:24,620
+ضغفين المساواة في a inverse اشتغلت
+
+57
+00:05:24,620 --> 00:05:29,200
+انا على المساواة اللى جوا ضربت في a inverse من
+
+58
+00:05:29,200 --> 00:05:35,950
+الجهتينهذا حاسيب معايا كل ال X في J حيث X A
+
+59
+00:05:35,950 --> 00:05:43,430
+Inverse بدي يساوي A Inverse X اجرأ تعريف المجموعة
+
+60
+00:05:43,430 --> 00:05:48,010
+هاد يشوف ايش بتاني لك هو كل ال X اللي في ال J اللي
+
+61
+00:05:48,010 --> 00:05:52,790
+بيكون commute مع مين؟ مع ال A Inverse وبالتالي هذا
+
+62
+00:05:52,790 --> 00:05:55,910
+عبارة عن Centralizer ال A Inverse
+
+63
+00:05:59,060 --> 00:06:04,400
+بإمكانك تفصل فيها و X في الأول ف X في التاني بعدين
+
+64
+00:06:04,400 --> 00:06:09,200
+X في التاني ثم X في الأول و تصل للمطلوب اثباته
+
+65
+00:06:09,200 --> 00:06:14,160
+واضح سؤال
+
+66
+00:06:14,160 --> 00:06:18,300
+23 سنحله
+
+67
+00:06:18,300 --> 00:06:26,030
+قدامك على الشاشة البيضة هذهعندي او هو زي ما انت
+
+68
+00:06:26,030 --> 00:06:30,730
+شايف معطيني جدول الضرب ل group j فيها العناصر من
+
+69
+00:06:30,730 --> 00:06:37,610
+واحد ل تمانية في عملية معرفة بغض النظر ايش التعريف
+
+70
+00:06:37,610 --> 00:06:42,790
+تبعها او القول تبعت العملية انا بهمني جدول الضرب
+
+71
+00:06:42,790 --> 00:06:46,750
+الموجود قدامي من خلال هذا الجدول بدي اجيب ال
+
+72
+00:06:46,750 --> 00:06:52,380
+centralizer لكل عنصر بدي اجيب ال centerتبع ال
+
+73
+00:06:52,380 --> 00:06:57,420
+group و بدى أجيب ال order لكل answer هذا السؤال
+
+74
+00:06:57,420 --> 00:07:02,340
+مهم جدا و كتير من الطلاب كانوا يغلطوا فيه نبدأ
+
+75
+00:07:02,340 --> 00:07:08,100
+بالفرع الأول find centralizer of each member of G
+
+76
+00:07:08,100 --> 00:07:12,660
+هنبدأ في البداية في ال identity من ال identity؟
+
+77
+00:07:13,910 --> 00:07:17,750
+واضح بالنسبة لي الواحد لإنه واحد مع أي عنصر
+
+78
+00:07:17,750 --> 00:07:25,510
+بيعطيني نفس العنصر طبعا centerizer الواحد عبارة عن
+
+79
+00:07:25,510 --> 00:07:34,910
+مين؟ ال group كله طبعا انا هستغل شغلة دراسة في سوء
+
+80
+00:07:34,910 --> 00:07:37,930
+ال 20 يعني انا لو جيب ال centralizer الاتنين
+
+81
+00:07:41,820 --> 00:07:46,700
+وعرفت ال inverse للتنين فبكون نفس ال centralizer
+
+82
+00:07:46,700 --> 00:07:55,740
+نبدأ بالتنين هاي التنين نبدأ
+
+83
+00:07:55,740 --> 00:08:02,060
+me commute مع التنين أكيد ال identity والتنين
+
+84
+00:08:02,060 --> 00:08:08,340
+نفسه لأن العنصر commute مع نفسه نبدأ التنين مع
+
+85
+00:08:08,340 --> 00:08:13,020
+التلاتة تنين مع التلاتة كده؟طيب تلاتة مع التنين
+
+86
+00:08:13,020 --> 00:08:19,280
+يكبر تلاتة برا مع الأربع تنين مع الأربع سبعة و
+
+87
+00:08:19,280 --> 00:08:25,920
+أربع مع التنين مش موجود مع الخمسة تنين مع الخمسة و
+
+88
+00:08:25,920 --> 00:08:32,200
+خمسة مع التنين ستة يكبر الستة موجود أو الخمسة طيب
+
+89
+00:08:33,200 --> 00:08:39,100
+التنين مع الستة .. التنين مع الستة كده؟ خمسة ..
+
+90
+00:08:39,100 --> 00:08:43,700
+التنين مع الستة خمسة .. طيب .. ستة مع التنين ..
+
+91
+00:08:43,700 --> 00:08:48,060
+إيه بقى برضه الستة موجود .. طيب .. تنين مع السبعة
+
+92
+00:08:48,060 --> 00:08:52,640
+.. السبعة مع الإتنين .. مانفعش .. تنين مع التمانية
+
+93
+00:08:52,640 --> 00:08:57,300
+.. تلاتة .. تنين أو تمانية مع التنين .. إيه بقى
+
+94
+00:08:57,300 --> 00:08:57,880
+بسكرها
+
+95
+00:09:01,430 --> 00:09:06,870
+تعالى نشوف مين العنصر اللى بدربه فى التنين بيعطينا
+
+96
+00:09:06,870 --> 00:09:11,310
+ال identity التنين يكبر ال centralizer التنين بدى
+
+97
+00:09:11,310 --> 00:09:14,170
+يساوي ال centralizer التنين inversely ليا تنين مش
+
+98
+00:09:14,170 --> 00:09:18,470
+هستفيد من الخاصية هذه ننتقل على التلاتة
+
+99
+00:09:23,130 --> 00:09:27,810
+أول حاجة الواحد موجود والتلاتة حد هيقول ليش
+
+100
+00:09:27,810 --> 00:09:32,450
+ماتعاملتش مع التنينالتلاتة مش موجودة في الـ
+
+101
+00:09:32,450 --> 00:09:37,090
+Centralizer التنين فأكيد التنين مش موجودة في الـ
+
+102
+00:09:37,090 --> 00:09:40,870
+Centralizer التلاتة طيب يجب الواحد والتانين
+
+103
+00:09:40,870 --> 00:09:45,430
+التلاتة خلصناهم التلاتة مع الأربعة ستة الأربعة مع
+
+104
+00:09:45,430 --> 00:09:49,130
+التلاتة تلاتة مانفعش أو الأربعة مع التلاتة اتنين
+
+105
+00:09:49,130 --> 00:09:56,240
+مانفعش التلاتة مع الخمسة سبعةالخمسة مع التلاتة ..
+
+106
+00:09:56,240 --> 00:10:01,860
+سبعة .. إيه بس؟ الخمسة موجود مع الستة .. تلاتة مع
+
+107
+00:10:01,860 --> 00:10:06,640
+الستة .. تمانية ستة مع التلاتة .. أربعة .. لأ
+
+108
+00:10:06,640 --> 00:10:11,580
+التلاتة مع السبعة .. واحد السبعة مع التلاتة .. إيه
+
+109
+00:10:11,580 --> 00:10:15,180
+بس؟ السبعة موجود طبعا والتمانية لأ بنفس الطريقة
+
+110
+00:10:15,180 --> 00:10:20,580
+هدف دي ساوي .. Centralize و التلاتة inverse مين
+
+111
+00:10:20,580 --> 00:10:26,710
+التلاتة inverse؟ السبعةليش؟ لأنه تلاتة في سبعة
+
+112
+00:10:26,710 --> 00:10:33,170
+واحد و سبعة في تلاتة واحد طيب خلصنا الواحد والتنين
+
+113
+00:10:33,170 --> 00:10:40,230
+والتلاتة والسبعة على الأربعة الاربعة
+
+114
+00:10:40,230 --> 00:10:47,490
+كميوت مع مين؟ نبدأ بالواحد والاربعة تنين والتلاتة
+
+115
+00:10:47,490 --> 00:10:52,840
+لألأن الأربعة لم توجد في الـ Centralizer 2 ولم
+
+116
+00:10:52,840 --> 00:10:57,720
+توجد في الـ Centralizer 3 نجرب مع الخمسة أربعة مع
+
+117
+00:10:57,720 --> 00:11:02,380
+الخمسة تمانية خمسة مع الأربعة تمانية اجبار الخمسة
+
+118
+00:11:02,380 --> 00:11:09,400
+موجود طيب الأربعة مع الستة سبعة و الستة مع الأربعة
+
+119
+00:11:09,400 --> 00:11:15,900
+تلاتة لأ الأربعة مع السبعة ستة و السبعة مع الأربعة
+
+120
+00:11:16,850 --> 00:11:21,530
+تنين لأ الاربع مع التمانية خمسة و التمانية مع
+
+121
+00:11:21,530 --> 00:11:26,130
+الأربعة يكبر تمانية هذا بني ساوز centralize و
+
+122
+00:11:26,130 --> 00:11:31,050
+الأربع inverse مين الأربع inverse الأربع مع نفسه
+
+123
+00:11:31,050 --> 00:11:37,050
+ماسفدناش اشيه centralize و الخمسة هلاحظ ان الواحد
+
+124
+00:11:37,050 --> 00:11:44,590
+و التنين الخمسة موجودة و التلاتة و الأربع و الخمسة
+
+125
+00:11:45,740 --> 00:11:50,580
+نجرب مع الستة خمسة مع الستة اتنين ستة مع الخمسة
+
+126
+00:11:50,580 --> 00:11:55,540
+اتنين طبعا الستة والسبعة والتمانية هدا بيساوي مين
+
+127
+00:11:55,540 --> 00:12:01,080
+الـ J بتظهر عندك الـ Centralizer الستة و
+
+128
+00:12:01,080 --> 00:12:05,640
+Centralizer التمانية هيتساوى بنفس الطريقة هيصيح
+
+129
+00:12:05,640 --> 00:12:15,160
+معاك واحد خمسة وستة وتمانية شوية بسهل التمانية
+
+130
+00:12:15,160 --> 00:12:19,800
+والستة ال inverse لهم زي بعض ستة في التمانية لأ لأ
+
+131
+00:12:19,800 --> 00:12:29,380
+لأ هانا حاسي معايا واحد خمسة و ستة و تمانية ان
+
+132
+00:12:29,380 --> 00:12:39,960
+الستة مع التمانية سبعة اتنين طيب
+
+133
+00:12:39,960 --> 00:12:47,630
+Centralizer بالتمانيةواحد وخمسة و تمانية واربع
+
+134
+00:12:47,630 --> 00:12:50,730
+واضح
+
+135
+00:12:50,730 --> 00:12:54,070
+كيف
+
+136
+00:12:54,070 --> 00:12:57,910
+الواحد
+
+137
+00:12:57,910 --> 00:13:02,400
+محايد بس الخمسةلأ من ال generator احنا اصلا
+
+138
+00:13:02,400 --> 00:13:06,760
+مابنتكلمش عن Cyclic group الخمسة commute مع الجميع
+
+139
+00:13:06,760 --> 00:13:11,780
+فلما نيجي نتكلم عن ثرع B زد الجيه مين العناصر
+
+140
+00:13:11,780 --> 00:13:18,140
+المشتركة في الكل واحد وخمسة الواحد و الخمسة هم
+
+141
+00:13:18,140 --> 00:13:27,280
+عناصر ال center يظل مين ال order ال order للواحد
+
+142
+00:13:27,280 --> 00:13:35,420
+كده؟ هذه سهلةطيب ال order للتنين هبدأ
+
+143
+00:13:35,420 --> 00:13:42,800
+بالتنين تنين مص تنين تنين في اتنين كده؟ لا يا عم
+
+144
+00:13:42,800 --> 00:13:50,320
+مش اربع تنين في اتنين واحد يكبر order التنين بدي
+
+145
+00:13:50,320 --> 00:13:51,140
+ساوى اتنين
+
+146
+00:13:56,000 --> 00:14:00,320
+شوف مدام انا مش عارف ايه العملية تحديدا من هي بشر
+
+147
+00:14:00,320 --> 00:14:06,640
+على ال general و هو ياش الضرب طيب ال order لتلاتة
+
+148
+00:14:06,640 --> 00:14:15,660
+تلاتة أست اتنين جديش تلاتة في تلاتة جديش خمسة طيب
+
+149
+00:14:15,660 --> 00:14:20,440
+تلاتة أست تلاتة عبارة عن تلاتة في تلاتة في تلاتة
+
+150
+00:14:20,440 --> 00:14:31,740
+خمسة في تلاتة جديشخمسة في تلاتة سبعة طيب نكمل يبقى
+
+151
+00:14:31,740 --> 00:14:39,660
+ال order مش اتنين و مش تلاتة نجرب اربعة تلاتة اص
+
+152
+00:14:39,660 --> 00:14:45,080
+اربعة تلاتة في تلاتة في تلاتة في تلاتة هنا خمسة و
+
+153
+00:14:45,080 --> 00:14:52,460
+هنا خمسة خمسة في خمسةOrder الاربعة هيساوي اربعة
+
+154
+00:14:52,460 --> 00:14:58,400
+Order الخامسة
+
+155
+00:14:58,400 --> 00:15:04,800
+هيساوي اتنين Order الستة هيساوي اتنين Order السبعة
+
+156
+00:15:04,800 --> 00:15:11,360
+هيساوي اربعة Order التمانية هيساوي اتنين بنفس
+
+157
+00:15:11,360 --> 00:15:16,980
+الطريقة تطلع ال orders زي ما انت شايف واضح؟
+
+158
+00:15:18,100 --> 00:15:22,760
+واضح ولا ما في حاجة محتاجة توضيح؟
+
+159
+00:15:22,760 --> 00:15:26,360
+مالو؟
+
+160
+00:15:26,360 --> 00:15:30,460
+how are these order are thematically related to
+
+161
+00:15:30,460 --> 00:15:32,880
+the order of the group؟ ايش ال orders اللي طلعت
+
+162
+00:15:32,880 --> 00:15:36,740
+معاك؟ واحد واتنين واربعة بيقسموا التمانية في
+
+163
+00:15:36,740 --> 00:15:40,740
+chapter سبعة هناخ نظرية بتقول ان order أي عنصر في
+
+164
+00:15:40,740 --> 00:15:45,000
+ال finite group بيقسم ال order تبع ال group نفسه
+
+165
+00:15:45,000 --> 00:15:47,000
+هذه نظرية اسمها نظرية Lagrang
+
+166
+00:15:50,850 --> 00:15:56,250
+طيب نيجي لسؤال 26 26
+
+167
+00:15:56,250 --> 00:16:01,990
+بيعمم
+
+168
+00:16:01,990 --> 00:16:07,970
+تعريف Centralizer العنصر و بينتقل منه ل
+
+169
+00:16:07,970 --> 00:16:13,430
+Centralizer المجموعة فلو كان عندي sub group من ال
+
+170
+00:16:13,430 --> 00:16:19,690
+Jف الـ centralizer الـ H عبارة عن الـ X في الـ J
+
+171
+00:16:19,690 --> 00:16:25,210
+اللي بيكون commute مع مين؟ مع كل عناصر الـ H يعني
+
+172
+00:16:25,210 --> 00:16:35,150
+XH بيساوي HX لكل H في H مطلوب من يثبت هنا أن الـ
+
+173
+00:16:35,150 --> 00:16:40,050
+centralizer للـ H عبارة عن subgroup
+
+174
+00:16:47,010 --> 00:16:52,610
+طيب في البداية لازم نثبت ان هذه المجموعة فيها
+
+175
+00:16:52,610 --> 00:17:03,250
+عناصر first ال E اكس او ال E ايه؟ ايه؟ ايه؟ ايه؟
+
+176
+00:17:03,250 --> 00:17:05,110
+ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟
+
+177
+00:17:05,110 --> 00:17:09,290
+ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟
+
+178
+00:17:09,290 --> 00:17:09,290
+ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟
+
+179
+00:17:09,290 --> 00:17:09,290
+ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟ ايه؟
+
+180
+00:17:09,290 --> 00:17:14,990
+ايه؟ ايه؟ ايه؟
+
+181
+00:17:15,820 --> 00:17:19,460
+يعني ينتمي لـ Centralizer الـ H وهذا يعني
+
+182
+00:17:19,460 --> 00:17:29,180
+Centralizer الـ H not empty كيف؟
+
+183
+00:17:29,180 --> 00:17:37,420
+H في H، A في J أنا فاهم، بس أنا بنتقل من إنه محايد
+
+184
+00:17:37,420 --> 00:17:39,560
+لكل الـ J فمحايد للجزء
+
+185
+00:17:46,120 --> 00:17:51,940
+طيب احنا بنشتغل ان ال X من ال H ولا من ال J طيب
+
+186
+00:17:51,940 --> 00:17:59,900
+انتقالي من هنا لهنا ان هو محيط للكل فمحيط للجزء
+
+187
+00:17:59,900 --> 00:18:03,660
+الجزئية
+
+188
+00:18:03,660 --> 00:18:12,280
+التانية ل A و B ينتمي ل Centralizer ال H هداش
+
+189
+00:18:12,280 --> 00:18:21,310
+معناتهمعناته ax بدي ساوي اك .. او h بدي ساوي ha ph
+
+190
+00:18:21,310 --> 00:18:30,250
+بدي ساوي hb لكل h small في h capital طيب .. هذا
+
+191
+00:18:30,250 --> 00:18:33,330
+هيخليني اقول ان aH
+
+192
+00:18:36,200 --> 00:18:41,760
+او هنا هنتقل منها بي انفرس بي اتش بي انفرس بدي
+
+193
+00:18:41,760 --> 00:18:51,180
+اساوي بي انفرس اتش بي بي انفرس حاسيب معايا بي
+
+194
+00:18:51,180 --> 00:18:58,420
+انفرس اتش بي انفرس بي انفرس اتش
+
+195
+00:19:00,880 --> 00:19:04,040
+علشان ال a b inverse يكون في ال centralizer و ال h
+
+196
+00:19:04,040 --> 00:19:11,140
+لازم ال a b inverse في h يساوي h a b inverse a b
+
+197
+00:19:11,140 --> 00:19:19,420
+inverse ال h عبارة عن a b inverse ال h اللي عبارة
+
+198
+00:19:19,420 --> 00:19:30,750
+عن a h b inverse يعني a h في b inverse يعني h aفي
+
+199
+00:19:30,750 --> 00:19:38,550
+B inverse او H AB inverse هذا معناته انه AB
+
+200
+00:19:38,550 --> 00:19:43,210
+inverse ينتمي لcentralizer الـH وبالتالي
+
+201
+00:19:43,210 --> 00:19:50,950
+centralizer الـH subgroup من الـG طبعا مش من
+
+202
+00:19:50,950 --> 00:19:55,690
+الضرورة ان عناصر centralizer الـH تكون في الـH
+
+203
+00:19:55,690 --> 00:20:02,430
+نفسهامش ضروري ان عناصر الـ centralizer الـ H تكون
+
+204
+00:20:02,430 --> 00:20:09,950
+في الـ H نفسها يعني
+
+205
+00:20:09,950 --> 00:20:13,910
+حتى ممكن يكون الـ centralizer عدد عناصره أكتر من
+
+206
+00:20:13,910 --> 00:20:19,630
+الـ H centralizer ال subgroup يكون فيه عناصر أكتر
+
+207
+00:20:19,630 --> 00:20:25,970
+من ال subgroup نفسها وين؟
+
+208
+00:20:28,090 --> 00:20:36,690
+رد يا مهر اقولك ايه انت ملاقيتش اتجاه
+
+209
+00:20:36,690 --> 00:20:42,230
+هذى عناصر الصندوق لازم من وين من جيه بس لازم تكون
+
+210
+00:20:42,230 --> 00:20:45,670
+تتبدل مع كل عناصر H طب هيا احنا انتقلنا من هتتبدل
+
+211
+00:20:45,670 --> 00:20:49,190
+مع كل عناصر جيه يعني مثلا العنصر بتتبدل مع كل
+
+212
+00:20:49,190 --> 00:20:52,590
+عناصر القاعة هيتبدل مع عناصر جيها ولا لأ
+
+213
+00:21:00,940 --> 00:21:06,040
+كيف ده اكتب هذه مش حاجة ده اكتب مباشرة لما انتقل
+
+214
+00:21:06,040 --> 00:21:14,040
+من معلومة انا متأكد منها 29 let J be an abelian
+
+215
+00:21:14,040 --> 00:21:17,000
+group with identity E and let N be some fixed
+
+216
+00:21:17,000 --> 00:21:19,800
+integer, both are the set of all elements of J
+
+217
+00:21:19,800 --> 00:21:26,040
+that satisfy the equation J
+
+218
+00:21:26,040 --> 00:21:26,740
+abelian
+
+219
+00:21:34,850 --> 00:21:42,210
+و الـ N ينتمي للـ national number أو حتى ينتمي للـ
+
+220
+00:21:42,210 --> 00:21:49,930
+Z بشكل عام The set of all elements in J يعني ال
+
+221
+00:21:49,930 --> 00:21:55,990
+set هذه خلّيني أعتبر عنها بغمز T هي كل ال X في J
+
+222
+00:21:55,990 --> 00:22:01,150
+اللي X أسن بدأ تساوي ال identity مطلوب أثبت أنه T
+
+223
+00:22:02,420 --> 00:22:08,400
+subgroup من الـ j مطلوب أثبت أن مجموعة حل معادلة
+
+224
+00:22:08,400 --> 00:22:13,400
+ما في group
+
+225
+00:22:13,400 --> 00:22:18,980
+بس بشغل أنها تكون abelian بيعطيني ال subgroup ماشي
+
+226
+00:22:18,980 --> 00:22:24,380
+proof طبعا السؤال اللي لتكمله أنه لو شيلنا كلمة
+
+227
+00:22:24,380 --> 00:22:31,760
+abelian ببطّر كلام هذا صحيح first ال team ده عنصر
+
+228
+00:22:33,560 --> 00:22:39,200
+الـ A أُس N بدي ساوي إيه؟ إجباليا تملة T وبالتالي
+
+229
+00:22:39,200 --> 00:22:48,520
+T ليست مجموعة خالية تقل الخطوة التانية لت A و B
+
+230
+00:22:48,520 --> 00:22:55,860
+تملة T إيش يعني؟ A أُس N بدي ساوي ال identity B
+
+231
+00:22:55,860 --> 00:23:02,260
+أُس N بدي ساوي ال identity طيبالـ A الـ B أُس أن
+
+232
+00:23:02,260 --> 00:23:06,860
+بدي يساوي ال identity بـ B أُس أن inverse بدي
+
+233
+00:23:06,860 --> 00:23:11,960
+يساوي ال identity inverse بدي يساوي ايش ال
+
+234
+00:23:11,960 --> 00:23:20,300
+identity بس هذه عبارة عن B inverse لكل أس أن ده
+
+235
+00:23:20,300 --> 00:23:27,540
+تساوي ال identity طيب احنا هنا بنجهزمعلومة معينة
+
+236
+00:23:27,540 --> 00:23:32,700
+نسميها الغرس علشان نستعملها في الإثبات التالي Now
+
+237
+00:23:32,700 --> 00:23:40,100
+A P inverse لكل أسن تنساش أن ال J is abelian هذا
+
+238
+00:23:40,100 --> 00:23:50,980
+عبارة عن A أسن P inverse أسن هذا ليش؟ J is abelian
+
+239
+00:23:50,980 --> 00:23:56,450
+طب ال A أسن إيش بتساوي؟الـ Identity والـ B inverse
+
+240
+00:23:56,450 --> 00:24:02,890
+أُس N برضه الـ Identity Identity في Identity سوى
+
+241
+00:24:02,890 --> 00:24:08,530
+الـ Identity وبالتالي A B inverse أُس N سوى الـ E
+
+242
+00:24:08,530 --> 00:24:17,970
+A B inverse يعني تامي للـ T تامي للـ T sub group
+
+243
+00:24:17,970 --> 00:24:24,380
+من الـ GT صارت subgroup لاحظ ان هذا الاسلوب
+
+244
+00:24:24,380 --> 00:24:29,620
+استعملته تلت مرات اليوم باستعمال ال first step
+
+245
+00:24:29,620 --> 00:24:35,600
+تكملت السؤال ايش بيقول ليه Give an example of a
+
+246
+00:24:35,600 --> 00:24:39,940
+group J in which the set of all elements of J that
+
+247
+00:24:39,940 --> 00:24:44,300
+satisfy the equation X تربيه بديه ساوي E doesn't
+
+248
+00:24:44,300 --> 00:24:49,220
+form a subgroup of J شوف
+
+249
+00:24:52,250 --> 00:24:56,550
+طلع المعطايا اللي أعطانيها المعطاء اللي بيخص ال
+
+250
+00:24:56,550 --> 00:25:00,830
+group نفسه انها إيش abelian فلو كانت ال group
+
+251
+00:25:00,830 --> 00:25:05,090
+abelian أكيد ال T sub group يعني بقى لما تديش تدور
+
+252
+00:25:05,090 --> 00:25:09,590
+على example تروحش تدور في ال abelian group هتدور
+
+253
+00:25:09,590 --> 00:25:13,730
+وين؟ في ال non abelian أكم non abelian sub group
+
+254
+00:25:13,730 --> 00:25:19,130
+أخدت حتى الآن واحدة واحدة بس طبعا هو في non
+
+255
+00:25:19,130 --> 00:25:25,250
+abelian sub group غيرهأخدت طبعا واحدة non-abelian
+
+256
+00:25:25,250 --> 00:25:31,630
+اللي هي JL2R أو SL2R لكن هنا حاجة صعوبة في حال
+
+257
+00:25:31,630 --> 00:25:37,330
+المعادلات في ال matrices عملية
+
+258
+00:25:37,330 --> 00:25:43,570
+الطرح بتعمليش جوب أصلا مع ال Z طيب
+
+259
+00:25:43,570 --> 00:25:52,170
+شوية بس الطرح لأ بتعملي جوب بتعملي جوب في الان لأ
+
+260
+00:25:53,410 --> 00:26:00,470
+هناخد الـ J عبارة عن الـ D4 لما يجي نشتغل T عبارة
+
+261
+00:26:00,470 --> 00:26:04,830
+عن كل ال X في الـ D4 اللي X تقريبا بيساوي ال
+
+262
+00:26:04,830 --> 00:26:09,170
+identity ارجع ال multiplication table للـ D4 هدي
+
+263
+00:26:09,170 --> 00:26:16,790
+هيعطيك ال R0 ال R رمية
+
+264
+00:26:16,790 --> 00:26:27,630
+و تمانينو ال H و ال V و ال D و ال D شغطة وهذه ليست
+
+265
+00:26:27,630 --> 00:26:32,610
+subgroup of
+
+266
+00:26:32,610 --> 00:26:38,070
+D4 هذه مستحيلة تكون subgroup لل D4 ليش؟ شوية بس
+
+267
+00:26:38,070 --> 00:26:44,570
+ليش مش هتكون subgroup من ال D4؟
+
+268
+00:26:44,570 --> 00:26:44,990
+اه
+
+269
+00:26:48,050 --> 00:26:52,430
+كل عنصر موجود هو معكوسه ال inverse exist لكن هل
+
+270
+00:26:52,430 --> 00:27:02,430
+المجموعة مغلقة فلو ضربت ال D في D شرطة شو هيعطيك D
+
+271
+00:27:02,430 --> 00:27:08,910
+في D شرطة هيعطيك يا R 90 يا R 270 حسب اتجاه الضرب
+
+272
+00:27:11,810 --> 00:27:14,330
+يعني في النهاية انت لو ضربت انتين من هدول في بعض
+
+273
+00:27:14,330 --> 00:27:18,870
+هعطيك ال R90 والـ R90 مش موجودة في ال T قبل T نطسة
+
+274
+00:27:18,870 --> 00:27:37,810
+بالجروب من ال D فافضل صحيح
+
+275
+00:27:37,810 --> 00:27:41,430
+طيب
+
+276
+00:27:43,770 --> 00:27:51,670
+مش في بعدها تلاتين طيب
+
+277
+00:27:51,670 --> 00:27:54,850
+سؤال تلاتين بيقول لصبوز a belong to the group ال
+
+278
+00:27:54,850 --> 00:28:01,130
+order ل ال a بيساوي خمسة ال
+
+279
+00:28:01,130 --> 00:28:07,350
+a في ال j و order ل ال a بيساوي خمسة center
+
+280
+00:28:07,350 --> 00:28:12,870
+centralizer ل a بيساوي centralizer
+
+281
+00:28:19,750 --> 00:28:25,490
+من عنده فكرة على السؤال هذا من عنده فكرة على
+
+282
+00:28:25,490 --> 00:28:27,930
+السؤال هذا من عنده فكرة على السؤال هذا من عنده
+
+283
+00:28:27,930 --> 00:28:28,630
+فكرة على السؤال هذا من عنده فكرة على السؤال هذا من
+
+284
+00:28:28,630 --> 00:28:28,790
+عنده فكرة على السؤال هذا من عنده فكرة على السؤال
+
+285
+00:28:28,790 --> 00:28:32,070
+هذا من عنده فكرة على السؤال هذا من عنده فكرة على
+
+286
+00:28:32,070 --> 00:28:39,090
+السؤال هذا من عنده فكرة على السؤال هذا من
+
+287
+00:28:39,090 --> 00:28:40,370
+عنده فكرة على السؤال هذا من عنده فكرة على السؤال
+
+288
+00:28:40,370 --> 00:28:40,970
+هذا من عنده فكرة على السؤال هذا من عنده فكرة على
+
+289
+00:28:40,970 --> 00:28:44,990
+السؤالorder لل inverse طيب بس ايش هتستفيد ان
+
+290
+00:28:44,990 --> 00:29:04,130
+هالكلام ايش هتستفيد تعالوا
+
+291
+00:29:04,130 --> 00:29:06,350
+نضبطها بالواضح لسلوب التقليدي انه
+
+292
+00:29:10,270 --> 00:29:15,410
+الأخضر ل ال A خمسة مش واحد ايش ده بتستفيد منها
+
+293
+00:29:15,410 --> 00:29:23,290
+تعلم ده بالاتجاه الأول او
+
+294
+00:29:23,290 --> 00:29:33,090
+خلينا اتجاه الأسل لين X ينتمي ل Centralizer A ده
+
+295
+00:29:33,090 --> 00:29:42,780
+اش معناته معناته AXبدي يساوي إيش؟ XA وبالتالي لما
+
+296
+00:29:42,780 --> 00:29:48,860
+نيجي نقول A تكييب X عبارة عن ال A في A في A في X A
+
+297
+00:29:48,860 --> 00:29:57,240
+في A في X في A A في X في A في A X في A في A في A X
+
+298
+00:29:57,240 --> 00:30:02,460
+A تكييب وين صارت ال X؟ في Centralizer ال A تكييب
+
+299
+00:30:03,400 --> 00:30:10,700
+وبتالي الـ Centralizer الـ A بيكون Subset من
+
+300
+00:30:10,700 --> 00:30:20,020
+Centralizer الـ A تكعيب وبتالي
+
+301
+00:30:20,020 --> 00:30:26,700
+خلصنا الاتجاه الأول انه Centralizer الـ A Subset
+
+302
+00:30:26,700 --> 00:30:35,290
+من Centralizer الـ A تكعيبمين عنده قدرة ان يثبت
+
+303
+00:30:35,290 --> 00:30:42,290
+للاتجاه التانى؟
+
+304
+00:30:42,290 --> 00:30:55,370
+اه
+
+305
+00:30:55,370 --> 00:30:59,850
+يا شباب فضل تطلعتوا كتاب؟
+
+306
+00:31:15,150 --> 00:31:17,630
+كبّي خطك و فمّا يجيب عليك
+
+307
+00:31:44,040 --> 00:31:49,720
+شوية بس .. شوية حاجات انت ضربت في الاتجاه اللي
+
+308
+00:31:49,720 --> 00:31:55,040
+نحيتي من اتجاه هذا لما ده تضرب هنا ده تضرب على نفس
+
+309
+00:31:55,040 --> 00:31:55,600
+الاتجاه
+
+310
+00:32:22,050 --> 00:32:30,630
+طيب، إيش سؤال؟ كان
+
+311
+00:32:30,630 --> 00:32:32,070
+سنجي اللي هو مش بروح لبنان
+
+312
+00:33:02,030 --> 00:33:05,650
+طب انت لما بدك تحطه ماناجك تستفيد انت بدك تنجل
+
+313
+00:33:05,650 --> 00:33:08,630
+تنتين ماتقدرش تنجل تنتين تنجل التلاتة لما تنجل
+
+314
+00:33:08,630 --> 00:33:14,450
+التلاتة هتصير X سواء X هتكمل
+
+315
+00:33:14,450 --> 00:33:21,950
+انا وانت بتحل وقعد في خطاين الخطأ الأول مابدتش صح
+
+316
+00:33:22,760 --> 00:33:25,200
+أنت لما بدك تيجي تبدأ وتثبت أن مجموعة بيساوي
+
+317
+00:33:25,200 --> 00:33:29,760
+مجموعة لازم تاخد عنصر من المجموعة هذه هتقول let X
+
+318
+00:33:29,760 --> 00:33:35,760
+ينتمي لـcentralizer الـ A تكعيب الخطأ التاني و أنت
+
+319
+00:33:35,760 --> 00:33:40,780
+بتشتغل مافكرتش تستعمل ال order أنت كتبت أن A X
+
+320
+00:33:40,780 --> 00:33:49,260
+تكعيب بيساوي A X A تكعيب بهذا
+
+321
+00:33:49,260 --> 00:33:49,620
+الشكل
+
+322
+00:33:53,180 --> 00:34:04,480
+طيب اضغط في X تكييب جهة في اي تكييب؟
+
+323
+00:34:04,480 --> 00:34:11,240
+هاي ال X ايش
+
+324
+00:34:11,240 --> 00:34:21,670
+حاسسي معاك هان؟ A6 X بدي ساوي A3 X A3الـ A أُس
+
+325
+00:34:21,670 --> 00:34:22,830
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+326
+00:34:22,830 --> 00:34:25,470
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+327
+00:34:25,470 --> 00:34:26,070
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+328
+00:34:26,070 --> 00:34:30,010
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+329
+00:34:30,010 --> 00:34:34,410
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+330
+00:34:34,410 --> 00:34:38,810
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+331
+00:34:38,810 --> 00:34:49,910
+ثلاثة الـ A أُس ثلاثة الـ
+
+332
+00:34:49,910 --> 00:34:56,040
+A أيجب اكس في Centralizer الـ A Centralizer الـ A
+
+333
+00:34:56,040 --> 00:35:03,020
+تكييب subset من Centralizer الـ A اعطيها 2 1 و 2
+
+334
+00:35:03,020 --> 00:35:08,680
+هيصير Centralizer الـ A بيساوي Centralizer الـ A
+
+335
+00:35:08,680 --> 00:35:17,240
+تكييب وهو المفروض واضح؟ واضح؟
+
+336
+00:35:17,240 --> 00:35:24,320
+واضح يا شباب؟لو كان ال order ل ال a سوى عشرة نفس
+
+337
+00:35:24,320 --> 00:35:28,080
+الكلمة كيف مش فاهم لو كان ال order ل ال a سوى عشرة
+
+338
+00:35:28,080 --> 00:35:32,600
+كيف ده توصلها يعني ال order ل ال a برضه متساوي
+
+339
+00:35:32,600 --> 00:35:36,680
+خمسة من جالك ال order ل ال a بيساوي عشرة بتستعمل
+
+340
+00:35:36,680 --> 00:35:41,920
+ان ال a plus خمسة بيساوي identity تقدرش كل اللي
+
+341
+00:35:41,920 --> 00:35:47,460
+بتقدر تثبته لو ال order ل ال a بيساوي عشرة انه ال
+
+342
+00:35:47,460 --> 00:35:50,380
+centralizer ل a تربيه او ال centralizer ل a تكعيب
+
+343
+00:35:50,380 --> 00:35:50,900
+متساوي
+
+344
+00:35:55,050 --> 00:36:00,210
+الـ A و الـ A تكيب جاجر طبعا ممكن منها توصل
+
+345
+00:36:00,210 --> 00:36:02,550
+الستغلال صغير ال A بساهم الستغلال صغير ال A تكيب
+
+346
+00:36:02,550 --> 00:36:06,130
+ممكن لكن ماقدرش انا اجزملك على هذا الكلام صحيح ولا
+
+347
+00:36:06,130 --> 00:36:12,890
+خطأ طيب
+
+348
+00:36:12,890 --> 00:36:22,860
+السؤال تلاتة و تلاتين اللي تكمل السؤال صحيحfind an
+
+349
+00:36:22,860 --> 00:36:26,180
+element a from subgroup such that in order الـ a
+
+350
+00:36:26,180 --> 00:36:29,900
+بيساوي 6 لكن الـ centralizer الـ a لا يساوي الـ
+
+351
+00:36:29,900 --> 00:36:37,960
+centralizer الـ a تكيب هات
+
+352
+00:36:37,960 --> 00:36:43,260
+مثال مدام
+
+353
+00:36:43,260 --> 00:36:46,820
+تشتغل على ال centralizer و بدكش مساواة اوعيك تجيب
+
+354
+00:36:46,820 --> 00:36:52,860
+مثال على abelian اوعيك تجيب مثالعلى abelian ايك
+
+355
+00:36:52,860 --> 00:36:57,240
+بدور على مين على مثال one abelian بعدين في الموضوع
+
+356
+00:36:57,240 --> 00:37:03,080
+الأردغ بدي يساوي 6 في
+
+357
+00:37:03,080 --> 00:37:09,920
+ال D3 في عنصر الأردغ له 6 لأ ايك بشر على D6 خد ال
+
+358
+00:37:09,920 --> 00:37:22,490
+J بدي يساوي D6 D6 عبارة عن R0 R 360 على 6 60120
+
+359
+00:37:22,490 --> 00:37:38,710
+180 240 و 6300 و عندك 6 دورانات و 6 انعكاسات كلها
+
+360
+00:37:38,710 --> 00:37:46,950
+R1 R2 R3 R4 R5 R6
+
+361
+00:37:50,560 --> 00:37:58,340
+عطينا عمصر ال order له 6 خد ال A بدي يساوي R120 ال
+
+362
+00:37:58,340 --> 00:38:04,740
+order لل A او R60 ال order لل A ايش بدي يساوي؟ 6
+
+363
+00:38:04,740 --> 00:38:19,620
+Centralizer ال A ايش بتساوي؟ R0 R60 R120 لعند R300
+
+364
+00:38:21,440 --> 00:38:25,180
+لكن الـ Centralizer الـ A تكعيب يعني الـ
+
+365
+00:38:25,180 --> 00:38:31,020
+Centralizer الـ R 180 عبارة عن الـ D6 كلها في
+
+366
+00:38:31,020 --> 00:38:35,100
+قاعدة أخدتها في قبل chapter أنه لو كانت الـ D N و
+
+367
+00:38:35,100 --> 00:38:39,760
+الـ N even فالـ Z تبع ال group أو الـ Center تبع
+
+368
+00:38:39,760 --> 00:38:47,300
+ال group عبارة عن R 0 و R 180 يعني بس Centralizer
+
+369
+00:38:47,300 --> 00:38:50,880
+الـ A لا يساوي الـ Centralizer الـ A تكعب
+
+370
+00:38:54,910 --> 00:39:03,250
+واضح؟ اه مهما فضل
+
+371
+00:39:03,250 --> 00:39:08,770
+الارض
+
+372
+00:39:08,770 --> 00:39:14,970
+لر ستين ر ستين مش ر ستة هذا حط ر ستين
+
+373
+00:39:21,640 --> 00:39:29,280
+مش كل المجموعة من R0
+
+374
+00:39:29,280 --> 00:39:34,820
+ل R300 R1
+
+375
+00:39:34,820 --> 00:39:45,040
+و R2 و R3 خليني اكتب بالسرد عشان اريحك بس
+
+376
+00:39:45,040 --> 00:39:50,520
+الدورانات مش الانعكاسات الدورانات ده فجأة واحدة
+
+377
+00:39:52,320 --> 00:39:55,000
+ماشي بقى بيعطيكوا العافية طبعا عشان الوقت انتهى
+
+378
+00:39:55,000 --> 00:39:57,380
+هنكمل السؤال و حضرة القادمة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7181e6096c7a0e7a4db824beb88de2957d9390c4
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4691, "start": 22.05, "end": 46.91, "text": "السلام عليكم اسمي الله الرحمن الرحيم طبعا اليوم هناخد ان شاء الله المحاضرة الأخيرة اللي هكون متواجد معاكم فيها المحاضرة القادمة هيكون أستاذ إسماعيل أصل هناخد بعض الأسئلة على الوحدة الخامسة permutation group بس قبل ما أفوض في الأسئلة بدأ أذكر للناس اللي ما كانوا موجودين المحاضرة الماضية بقواعد حساب ال orders في ال permutations", "tokens": [6027, 3794, 37440, 25894, 24793, 24525, 2304, 1829, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 23032, 3555, 3615, 995, 45595, 20498, 8032, 1863, 47283, 3215, 16472, 13412, 16606, 21984, 9673, 5016, 46958, 25720, 16247, 9778, 48923, 13672, 1829, 8032, 30544, 44650, 2407, 26108, 3215, 20449, 995, 24793, 8978, 11296, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 8032, 1829, 30544, 5551, 14851, 45636, 11933, 3794, 15042, 3615, 26895, 5551, 36520, 8032, 1863, 47283, 3215, 45030, 11242, 16247, 3794, 19986, 37977, 15844, 2423, 2407, 24401, 3660, 33962, 10943, 3794, 3660, 4784, 11380, 1594, 4724, 3794, 12174, 36150, 19446, 5551, 5172, 2407, 11242, 8978, 16247, 3794, 19986, 37977, 47525, 10721, 5551, 8848, 37983, 24976, 8315, 3794, 13672, 1829, 19446, 25961, 14407, 3714, 29245, 23328, 9957, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 4724, 4587, 14407, 22488, 11331, 3794, 16758, 2423, 9470, 8978, 2423, 4784, 325, 763], "avg_logprob": -0.15158420252717203, "compression_ratio": 1.9929577464788732, "no_speech_prob": 4.589557647705078e-06, "words": [{"start": 22.05, "end": 22.45, "word": "السلام", "probability": 0.80859375}, {"start": 22.45, "end": 22.99, "word": " عليكم", "probability": 0.95556640625}, {"start": 22.99, "end": 23.53, "word": " اسمي", "probability": 0.6397298177083334}, {"start": 23.53, "end": 23.61, "word": " الله", "probability": 0.736328125}, {"start": 23.61, "end": 23.91, "word": " الرحمن", "probability": 0.9064127604166666}, {"start": 23.91, "end": 24.31, "word": " الرحيم", "probability": 0.9913736979166666}, {"start": 24.31, "end": 25.47, "word": " طبعا", "probability": 0.965087890625}, {"start": 25.47, "end": 26.01, "word": " اليوم", "probability": 0.92919921875}, {"start": 26.01, "end": 26.51, "word": " هناخد", "probability": 0.885498046875}, {"start": 26.51, "end": 26.65, "word": " ان", "probability": 0.8193359375}, {"start": 26.65, "end": 26.85, "word": " شاء", "probability": 0.96533203125}, {"start": 26.85, "end": 26.97, "word": " الله", "probability": 0.95556640625}, {"start": 26.97, "end": 27.59, "word": " المحاضرة", "probability": 0.98388671875}, {"start": 27.59, "end": 27.91, "word": " الأخيرة", "probability": 0.9305013020833334}, {"start": 27.91, "end": 28.03, "word": " اللي", "probability": 0.853271484375}, {"start": 28.03, "end": 28.25, "word": " هكون", "probability": 0.794189453125}, {"start": 28.25, "end": 28.75, "word": " متواجد", "probability": 0.9591064453125}, {"start": 28.75, "end": 29.79, "word": " معاكم", "probability": 0.80712890625}, {"start": 29.79, "end": 30.19, "word": " فيها", "probability": 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36.09, "end": 36.61, "word": " permutation", "probability": 0.7890625}, {"start": 36.61, "end": 36.97, "word": " group", "probability": 0.83251953125}, {"start": 36.97, "end": 37.41, "word": " بس", "probability": 0.6944580078125}, {"start": 37.41, "end": 37.65, "word": " قبل", "probability": 0.6923828125}, {"start": 37.65, "end": 37.85, "word": " ما", "probability": 0.94970703125}, {"start": 37.85, "end": 38.35, "word": " أفوض", "probability": 0.71820068359375}, {"start": 38.35, "end": 38.47, "word": " في", "probability": 0.96923828125}, {"start": 38.47, "end": 38.81, "word": " الأسئلة", "probability": 0.99560546875}, {"start": 38.81, "end": 38.97, "word": " بدأ", "probability": 0.42431640625}, {"start": 38.97, "end": 39.43, "word": " أذكر", "probability": 0.8870442708333334}, {"start": 39.43, "end": 39.91, "word": " للناس", "probability": 0.9436848958333334}, {"start": 39.91, "end": 40.05, "word": " اللي", "probability": 0.970458984375}, {"start": 40.05, "end": 40.21, "word": " ما", 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"text": "أول شغلة لو كان عندي permutation بهذا الشكل a1, a2 اللي عند an فال order لل alpha بدي ساوي n الشغلة التانية", "tokens": [10721, 12610, 13412, 17082, 37977, 45164, 25961, 18871, 16254, 4784, 11380, 39627, 15730, 25124, 28820, 257, 16, 11, 257, 17, 13672, 1829, 43242, 364, 6156, 6027, 1668, 24976, 8961, 4724, 16254, 8608, 995, 45865, 297, 25124, 17082, 37977, 16712, 7649, 10632], "avg_logprob": -0.3115699269941875, "compression_ratio": 1.2330827067669172, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 47.65, "end": 47.97, "word": "أول", "probability": 0.81396484375}, {"start": 47.97, "end": 48.41, "word": " شغلة", "probability": 0.7459309895833334}, {"start": 48.41, "end": 49.07, "word": " لو", "probability": 0.59033203125}, {"start": 49.07, "end": 49.27, "word": " كان", "probability": 0.88330078125}, {"start": 49.27, "end": 49.49, "word": " عندي", "probability": 0.75390625}, {"start": 49.49, "end": 50.07, "word": " permutation", "probability": 0.966796875}, 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هي تلاتة و اربعة اتناش تلاتة و اتنين تلاتة و ستة ستة اربعة و خمسة بس هدولة بدهم يكونوا بدك تشتغلهم سرعة اللي انا همسح", "tokens": [2655, 1211, 9307, 3660, 1975, 4587, 36150, 1975, 2288, 3215, 2288, 6055, 1211, 9307, 3660, 2423, 1935, 2689, 3866, 39896, 6055, 1211, 9307, 3660, 4032, 1975, 25513, 27884, 1975, 2655, 1863, 33599, 6055, 1211, 9307, 3660, 4032, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 4032, 8608, 2655, 3660, 8608, 2655, 3660, 1975, 25513, 27884, 4032, 16490, 2304, 3794, 3660, 4724, 3794, 8032, 3215, 12610, 3660, 47525, 16095, 7251, 30544, 14407, 47525, 4117, 6055, 8592, 2655, 17082, 1211, 16095, 8608, 2288, 27884, 13672, 1829, 1975, 8315, 8032, 2304, 3794, 5016], "avg_logprob": -0.2886332489631988, "compression_ratio": 1.73125, "no_speech_prob": 0.0, "words": [{"start": 702.05, "end": 702.53, "word": "تلاتة", "probability": 0.739044189453125}, {"start": 702.53, "end": 702.85, "word": " اقبل", "probability": 0.468017578125}, {"start": 702.85, "end": 703.17, "word": " 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0.88134765625}, {"start": 794.29, "end": 794.89, "word": " لاربع", "probability": 0.9537353515625}, {"start": 794.89, "end": 795.31, "word": " وستة", "probability": 0.9207356770833334}, {"start": 795.31, "end": 795.87, "word": " جديش", "probability": 0.9694010416666666}], "temperature": 1.0}, {"id": 30, "seek": 80377, "start": 799.45, "end": 803.77, "text": "Show that A8 contains an element of order 15", "tokens": [27692, 300, 316, 23, 8306, 364, 4478, 295, 1668, 2119], "avg_logprob": -0.4474431818181818, "compression_ratio": 0.8461538461538461, "no_speech_prob": 0.0, "words": [{"start": 799.4499999999999, "end": 800.29, "word": "Show", "probability": 0.11260986328125}, {"start": 800.29, "end": 800.71, "word": " that", "probability": 0.90087890625}, {"start": 800.71, "end": 801.29, "word": " A8", "probability": 0.6197509765625}, {"start": 801.29, "end": 802.07, "word": " contains", "probability": 0.69140625}, {"start": 802.07, "end": 802.31, "word": " an", "probability": 0.9091796875}, 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{"start": 821.55, "end": 821.99, "word": " خمسة", "probability": 0.9798583984375}, {"start": 821.99, "end": 822.43, "word": " يجب", "probability": 0.8580729166666666}, {"start": 822.43, "end": 822.59, "word": " مين", "probability": 0.94580078125}, {"start": 822.59, "end": 823.19, "word": " هناخد", "probability": 0.862548828125}, {"start": 823.19, "end": 823.85, "word": " واحد", "probability": 0.75048828125}, {"start": 823.85, "end": 824.19, "word": " اتنين", "probability": 0.9681396484375}, {"start": 824.19, "end": 824.67, "word": " تلاتة", "probability": 0.92431640625}, {"start": 824.67, "end": 825.05, "word": " اربعة", "probability": 0.83349609375}, {"start": 825.05, "end": 825.89, "word": " خمسة", "probability": 0.9837646484375}, {"start": 825.89, "end": 826.59, "word": " ستة", "probability": 0.96337890625}, {"start": 826.59, "end": 826.83, "word": " سبعة", "probability": 0.8733723958333334}, {"start": 826.83, "end": 827.33, "word": " تمانية", "probability": 0.98876953125}, {"start": 827.33, "end": 828.23, "word": " و", "probability": 0.53466796875}, {"start": 828.23, "end": 828.41, "word": " هذه", "probability": 0.402587890625}, {"start": 828.41, "end": 828.53, "word": " ال", "probability": 0.94287109375}, {"start": 828.53, "end": 828.79, "word": " order", "probability": 0.95947265625}, {"start": 828.79, "end": 829.07, "word": " لها", "probability": 0.5784912109375}, {"start": 829.07, "end": 829.59, "word": " جديش", "probability": 0.6552734375}], "temperature": 1.0}, {"id": 32, "seek": 84681, "start": 831.79, "end": 846.81, "text": "What are the possible orders for the elements of S6 and A6؟", "tokens": [3748, 366, 264, 1944, 9470, 337, 264, 4959, 295, 318, 21, 293, 316, 21, 22807], "avg_logprob": -0.2927246131002903, "compression_ratio": 0.9230769230769231, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 831.79, "end": 832.65, "word": "What", "probability": 0.10943603515625}, {"start": 832.65, "end": 833.51, "word": " are", "probability": 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orders هدول موجودين permutation فيها عنصر واحد عنصرين تلاتة اربعة خمسة ستة هجيت نشوف التشكيلات", "tokens": [9566, 1829, 3555, 11331, 35457, 8717, 36178, 16247, 3794, 1211, 37746, 2423, 9470, 36764, 24401, 4032, 5718, 104, 1863, 9957, 4032, 2655, 1211, 9307, 3660, 4032, 9640, 3555, 27884, 4032, 9778, 2304, 3794, 3660, 4032, 14851, 3660, 7251, 2304, 6027, 16095, 2514, 2423, 9470, 8032, 3215, 12610, 3714, 29245, 23328, 9957, 4784, 11380, 8978, 11296, 18871, 9381, 2288, 36764, 24401, 18871, 9381, 2288, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 8032, 7435, 36081, 8717, 8592, 38688, 16712, 8592, 4117, 26895, 9307], "avg_logprob": -0.18593749619192548, "compression_ratio": 1.6685393258426966, "no_speech_prob": 0.0, "words": [{"start": 855.16, "end": 855.68, "word": "طيب", "probability": 0.7395833333333334}, {"start": 855.68, "end": 856.86, "word": " حسب", "probability": 0.890625}, {"start": 856.86, "end": 857.36, "word": " نفس", "probability": 0.9921875}, {"start": 857.36, "end": 858.18, "word": " الأسلوب", "probability": 0.9698486328125}, {"start": 858.18, "end": 858.74, "word": " ال", "probability": 0.79931640625}, {"start": 858.74, "end": 859.2, "word": " orders", "probability": 0.69140625}, {"start": 859.2, "end": 859.82, "word": " واحد", "probability": 0.724609375}, {"start": 859.82, "end": 860.22, "word": " واثنين", "probability": 0.8375}, {"start": 860.22, "end": 860.78, "word": " وتلاتة", "probability": 0.822265625}, {"start": 860.78, "end": 861.48, "word": " واربعة", "probability": 0.894287109375}, {"start": 861.48, "end": 862.88, "word": " وخمسة", "probability": 0.953515625}, {"start": 862.88, "end": 863.26, "word": " وستة", "probability": 0.9376627604166666}, {"start": 863.26, "end": 863.88, "word": " يمالهم", "probability": 0.668792724609375}, {"start": 863.88, "end": 865.54, "word": " exist", "probability": 0.59326171875}, {"start": 865.54, "end": 867.88, "word": " ال", "probability": 0.93505859375}, {"start": 867.88, "end": 868.36, "word": " orders", "probability": 0.85302734375}, {"start": 868.36, "end": 868.9, "word": " هدول", "probability": 0.9119466145833334}, {"start": 868.9, "end": 870.52, "word": " موجودين", "probability": 0.987548828125}, {"start": 870.52, "end": 871.38, "word": " permutation", "probability": 0.816650390625}, {"start": 871.38, "end": 871.9, "word": " فيها", "probability": 0.825927734375}, {"start": 871.9, "end": 872.2, "word": " عنصر", "probability": 0.8018391927083334}, {"start": 872.2, "end": 872.58, "word": " واحد", "probability": 0.984619140625}, {"start": 872.58, "end": 873.26, "word": " عنصرين", "probability": 0.74908447265625}, {"start": 873.26, "end": 873.78, "word": " تلاتة", "probability": 0.8984375}, {"start": 873.78, "end": 874.2, "word": " اربعة", "probability": 0.8826497395833334}, {"start": 874.2, "end": 875.04, "word": " خمسة", "probability": 0.9776611328125}, {"start": 875.04, "end": 876.4, "word": " ستة", "probability": 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"temperature": 1.0}, {"id": 38, "seek": 101789, "start": 995.15, "end": 1017.89, "text": "يعني ال .. ال permutation بروح بكتبه على شكل حاصل ضرب cycles كل واحدة منهم الطولة جدياش اتنين هانا مابفرجش معايا ال disjoint طبعا لو ال N even بقولي ال alpha even لو ال N odd بقولي ال alpha ash", "tokens": [40228, 22653, 2423, 4386, 2423, 4784, 11380, 4724, 32887, 5016, 4724, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 11331, 33546, 1211, 48812, 25513, 17796, 28242, 36764, 24401, 3660, 9154, 16095, 41950, 12610, 3660, 10874, 16254, 33599, 1975, 2655, 1863, 9957, 8032, 7649, 995, 3714, 16758, 5172, 47341, 8592, 20449, 995, 25528, 2423, 717, 48613, 23032, 3555, 3615, 995, 45164, 2423, 426, 754, 4724, 39648, 1829, 2423, 8961, 754, 45164, 2423, 426, 7401, 4724, 39648, 1829, 2423, 8961, 12588], "avg_logprob": -0.19363132722770113, "compression_ratio": 1.5076923076923077, "no_speech_prob": 0.0, "words": [{"start": 995.15, "end": 995.71, "word": "يعني", "probability": 0.8623046875}, {"start": 995.71, 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واحدة", "probability": 0.97998046875}, {"start": 1003.07, "end": 1003.37, "word": " منهم", "probability": 0.982666015625}, {"start": 1003.37, "end": 1004.01, "word": " الطولة", "probability": 0.8419596354166666}, {"start": 1004.01, "end": 1004.59, "word": " جدياش", "probability": 0.7107747395833334}, {"start": 1004.59, "end": 1005.51, "word": " اتنين", "probability": 0.9140625}, {"start": 1005.51, "end": 1006.07, "word": " هانا", "probability": 0.5751139322916666}, {"start": 1006.07, "end": 1006.67, "word": " مابفرجش", "probability": 0.835400390625}, {"start": 1006.67, "end": 1007.19, "word": " معايا", "probability": 0.9905598958333334}, {"start": 1007.19, "end": 1007.73, "word": " ال", "probability": 0.8623046875}, {"start": 1007.73, "end": 1008.33, "word": " disjoint", "probability": 0.792236328125}, {"start": 1008.33, "end": 1009.09, "word": " طبعا", "probability": 0.9853515625}, {"start": 1009.09, "end": 1009.23, "word": " لو", "probability": 0.93798828125}, {"start": 1009.23, 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"word": " ال", "probability": 0.9697265625}, {"start": 1017.15, "end": 1017.49, "word": " alpha", "probability": 0.49853515625}, {"start": 1017.49, "end": 1017.89, "word": " ash", "probability": 0.240478515625}], "temperature": 1.0}, {"id": 39, "seek": 104943, "start": 1021.29, "end": 1049.43, "text": "لو بدي اجي هان اول حاجة ال identity even يعني ال identity في اي ستة يجب ال order واحد موجود طيب ال order تنين هل بقدر الاقي عنصر ال order تنين في اي ستة بلاقي واحد اتنين تلاتة اربعة ينتمي لإي ستة", "tokens": [1211, 2407, 4724, 16254, 1975, 7435, 1829, 8032, 7649, 1975, 12610, 11331, 26108, 3660, 2423, 6575, 754, 37495, 22653, 2423, 6575, 8978, 1975, 1829, 8608, 2655, 3660, 7251, 7435, 3555, 2423, 1668, 36764, 24401, 3714, 29245, 23328, 23032, 1829, 3555, 2423, 1668, 6055, 1863, 9957, 8032, 1211, 4724, 28543, 2288, 1975, 15040, 38436, 18871, 9381, 2288, 2423, 1668, 6055, 1863, 9957, 8978, 1975, 1829, 8608, 2655, 3660, 4724, 15040, 38436, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 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في عندك تنتين من ال two cycle؟ ماحدش يجيجي يقولني ماهي ال order اتنين و قد لا انت من ايه ستة؟", "tokens": [1829, 7435, 3555, 2423, 1668, 1975, 2655, 1863, 9957, 1975, 1829, 8592, 3714, 6027, 3224, 22807, 4724, 43042, 3224, 3714, 29245, 23328, 32239, 8592, 23758, 18863, 1863, 9381, 2288, 30767, 29245, 1829, 35186, 13412, 3555, 16758, 22807, 32239, 8592, 23758, 30767, 29245, 1829, 22807, 5296, 33456, 3224, 6225, 3555, 9640, 3660, 18871, 6225, 3215, 3215, 30767, 29245, 1829, 9154, 2423, 732, 17796, 23758, 44945, 38251, 1829, 11296, 732, 6586, 4032, 23758, 44945, 38251, 1829, 11296, 732, 6586, 8978, 43242, 4117, 6055, 29399, 9957, 9154, 2423, 732, 6586, 22807, 19446, 24401, 8592, 7251, 7435, 1829, 7435, 1829, 7251, 39648, 22653, 19446, 3224, 1829, 2423, 1668, 1975, 2655, 1863, 9957, 4032, 12174, 3215, 20193, 16472, 2655, 9154, 1975, 1829, 3224, 8608, 2655, 3660, 22807], "avg_logprob": -0.21544714889875272, "compression_ratio": 1.9906542056074767, "no_speech_prob": 0.0, "words": [{"start": 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"probability": 0.97802734375}, {"start": 1075.21, "end": 1076.67, "word": " اتنين", "probability": 0.9730224609375}, {"start": 1076.67, "end": 1077.17, "word": " و", "probability": 0.50439453125}, {"start": 1077.17, "end": 1077.37, "word": " قد", "probability": 0.4468994140625}, {"start": 1077.37, "end": 1077.55, "word": " لا", "probability": 0.740234375}, {"start": 1077.55, "end": 1077.93, "word": " انت", "probability": 0.7152099609375}, {"start": 1077.93, "end": 1078.13, "word": " من", "probability": 0.74072265625}, {"start": 1078.13, "end": 1078.45, "word": " ايه", "probability": 0.7659505208333334}, {"start": 1078.45, "end": 1078.97, "word": " ستة؟", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 41, "seek": 110797, "start": 1079.93, "end": 1107.97, "text": "لأ يكفيني 1 عنصر 1 ال order اله 2 في ال a6 علشان اقول انه يوجد عنصر ال order اله 2 في ال a6 او ال order 2 موجود ضمن ال orders لعناصر ال a6 طيب ال order 3 123 هل هو في a6 لأ في a6 هذا عبارة عن 1312", "tokens": [1211, 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الأردر اتنين لكن انا الأردر تلاتة هذولا مش this joint يا شباب هذولا ال two permutation مش this joint", "tokens": [3224, 24192, 2423, 39184, 4784, 11380, 39894, 1863, 4117, 2655, 3555, 39627, 15730, 25124, 28820, 37037, 15730, 14739, 9381, 5172, 1975, 1829, 3224, 8608, 2655, 3660, 22807, 23758, 14739, 9381, 5172, 9122, 33911, 22807, 5296, 10721, 29538, 32771, 13546, 29538, 29538, 16247, 2288, 3215, 2288, 1975, 2655, 1863, 9957, 44381, 1975, 8315, 16247, 2288, 3215, 2288, 6055, 1211, 9307, 3660, 8032, 8848, 12610, 995, 37893, 341, 7225, 35186, 13412, 3555, 16758, 8032, 8848, 12610, 995, 2423, 732, 4784, 11380, 37893, 341, 7225], "avg_logprob": -0.2848268079470439, "compression_ratio": 1.739884393063584, "no_speech_prob": 0.0, "words": [{"start": 1110.9, "end": 1111.46, "word": "هذه", "probability": 0.767578125}, {"start": 1111.46, "end": 1111.82, "word": " الـ", "probability": 0.516845703125}, {"start": 1111.82, "end": 1112.46, "word": " permutation", "probability": 0.6964111328125}, 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طولها فردي بتكون permutation زوجية كل cycle طولها فردي اش يعني طولها طبعا بتكلم عن cycle واحدة مش حاصل ضرب cycles طولها فردي بتكون عنصر وين؟", "tokens": [6027, 3615, 1863, 9381, 2288, 23758, 13672, 1829, 2423, 1668, 11933, 43761, 16712, 1211, 9307, 3660, 3714, 29245, 23328, 8978, 318, 11778, 3224, 16490, 3215, 11296, 12174, 995, 22488, 3660, 28242, 6586, 23032, 12610, 11296, 6156, 2288, 16254, 39894, 30544, 4784, 11380, 30767, 29245, 10632, 28242, 6586, 23032, 12610, 11296, 6156, 2288, 16254, 1975, 8592, 37495, 22653, 23032, 12610, 11296, 23032, 3555, 3615, 995, 39894, 4117, 19528, 18871, 6586, 36764, 24401, 3660, 37893, 11331, 33546, 1211, 48812, 25513, 17796, 23032, 12610, 11296, 6156, 2288, 16254, 39894, 30544, 18871, 9381, 2288, 4032, 9957, 22807], "avg_logprob": -0.17237366799344409, "compression_ratio": 1.801047120418848, "no_speech_prob": 0.0, "words": [{"start": 1136.21, "end": 1137.25, "word": "العنصر", "probability": 0.851611328125}, {"start": 1137.25, "end": 1137.61, "word": 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" يعني", "probability": 0.8017578125}, {"start": 1152.21, "end": 1152.81, "word": " طولها", "probability": 0.9957682291666666}, {"start": 1152.81, "end": 1154.63, "word": " طبعا", "probability": 0.933837890625}, {"start": 1154.63, "end": 1155.37, "word": " بتكلم", "probability": 0.82275390625}, {"start": 1155.37, "end": 1155.53, "word": " عن", "probability": 0.9921875}, {"start": 1155.53, "end": 1155.87, "word": " cycle", "probability": 0.93408203125}, {"start": 1155.87, "end": 1156.33, "word": " واحدة", "probability": 0.9327799479166666}, {"start": 1156.33, "end": 1156.59, "word": " مش", "probability": 0.97802734375}, {"start": 1156.59, "end": 1157.09, "word": " حاصل", "probability": 0.736328125}, {"start": 1157.09, "end": 1157.33, "word": " ضرب", "probability": 0.896240234375}, {"start": 1157.33, "end": 1157.93, "word": " cycles", "probability": 0.62744140625}, {"start": 1157.93, "end": 1158.61, "word": " طولها", "probability": 0.9518229166666666}, {"start": 1158.61, "end": 1159.01, "word": " فردي", "probability": 0.94580078125}, {"start": 1159.01, "end": 1160.21, "word": " بتكون", "probability": 0.948486328125}, {"start": 1160.21, "end": 1160.57, "word": " عنصر", "probability": 0.9755859375}, {"start": 1160.57, "end": 1161.09, "word": " وين؟", "probability": 0.8575846354166666}], "temperature": 1.0}, {"id": 44, "seek": 118881, "start": 1162.03, "end": 1188.81, "text": "في A6 او في AN يعني طب ان ال order تلاتة exist طب ال order أربعة هذه لا ينتمي ل A6 هل هذا يعني ان مافيش order أربعة في عناصر ال A6 لأ هذا العنصر ينتمي ل A6", "tokens": [41185, 316, 21, 1975, 2407, 8978, 5252, 37495, 22653, 23032, 3555, 16472, 2423, 1668, 6055, 1211, 9307, 3660, 2514, 23032, 3555, 2423, 1668, 5551, 25513, 27884, 29538, 20193, 7251, 29399, 2304, 1829, 5296, 316, 21, 8032, 1211, 23758, 37495, 22653, 16472, 19446, 41185, 8592, 1668, 5551, 25513, 27884, 8978, 18871, 33546, 2288, 2423, 316, 21, 5296, 10721, 23758, 18863, 1863, 9381, 2288, 7251, 29399, 2304, 1829, 5296, 316, 21], 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اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد", "tokens": [14407, 24401, 5551, 25513, 27884, 4032, 14407, 24401, 6055, 1211, 9307, 3660, 4032, 14407, 24401, 1975, 2655, 1863, 9957, 4032, 14407, 24401, 16490, 2304, 3794, 3660, 9122, 2304, 33599, 6225, 3215, 3215, 16095, 8032, 3215, 12610, 16490, 2304, 3794, 3660, 9122, 33911, 6225, 42213, 39237, 15844, 23032, 12610, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 1975, 3215, 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1964.01, "word": " تلاتة", "probability": 0.9263916015625}, {"start": 1964.01, "end": 1965.05, "word": " وواحد", "probability": 0.7781575520833334}, {"start": 1965.05, "end": 1965.71, "word": " اتنين", "probability": 0.9456787109375}, {"start": 1965.71, "end": 1967.67, "word": " وواحد", "probability": 0.9119466145833334}, {"start": 1967.67, "end": 1968.29, "word": " خمسة", "probability": 0.958740234375}, {"start": 1968.29, "end": 1970.49, "word": " كماش", "probability": 0.4444986979166667}, {"start": 1970.49, "end": 1970.87, "word": " عددهم", "probability": 0.9405517578125}, {"start": 1970.87, "end": 1971.25, "word": " هدول", "probability": 0.8351236979166666}, {"start": 1971.25, "end": 1973.73, "word": " خمسة", "probability": 0.839111328125}, {"start": 1973.73, "end": 1974.55, "word": " كيف", "probability": 0.94287109375}, {"start": 1974.55, "end": 1974.87, "word": " عملتم", "probability": 0.8818359375}, {"start": 1974.87, "end": 1975.01, "word": " على", "probability": 0.90087890625}, {"start": 1975.01, "end": 1975.37, "word": " طول", "probability": 0.954345703125}, {"start": 1975.37, "end": 1975.91, "word": " اد", "probability": 0.2872314453125}, {"start": 1975.91, "end": 1976.19, "word": " اد", "probability": 0.837158203125}, {"start": 1976.19, "end": 1976.49, "word": " اد", "probability": 0.912841796875}, {"start": 1976.49, "end": 1976.91, "word": " اد", "probability": 0.889404296875}, {"start": 1976.91, "end": 1979.05, "word": " اد", "probability": 0.871826171875}, {"start": 1979.05, "end": 1979.15, "word": " اد", "probability": 0.896240234375}, {"start": 1979.15, "end": 1979.47, "word": " اد", "probability": 0.916748046875}, {"start": 1979.47, "end": 1979.53, "word": " اد", "probability": 0.934326171875}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.945068359375}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.9541015625}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.957275390625}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.958740234375}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.95947265625}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.960693359375}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.96240234375}, {"start": 1979.53, "end": 1979.53, "word": " اد", "probability": 0.96435546875}, {"start": 1979.53, "end": 1979.57, "word": " اد", "probability": 0.96630859375}, {"start": 1979.57, "end": 1979.57, "word": " اد", "probability": 0.968994140625}, {"start": 1979.57, "end": 1979.65, "word": " اد", "probability": 0.9716796875}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.9736328125}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.975830078125}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.9775390625}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.979248046875}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.98095703125}, {"start": 1979.65, "end": 1979.65, "word": " اد", "probability": 0.98193359375}, {"start": 1979.65, "end": 1979.67, "word": " اد", "probability": 0.982666015625}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.983642578125}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.984375}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.985107421875}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.985595703125}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.986083984375}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.986572265625}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.986572265625}, {"start": 1979.67, "end": 1979.67, "word": " اد", "probability": 0.9873046875}, {"start": 1979.67, "end": 1979.83, "word": " اد", "probability": 0.98779296875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.98828125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.98828125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.98876953125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.989013671875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9892578125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.989501953125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.98974609375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.989990234375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.989990234375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990234375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990478515625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990478515625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990478515625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.99072265625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.991455078125}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.9912109375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990966796875}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.99072265625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990478515625}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990234375}, {"start": 1979.83, "end": 1979.83, "word": " اد", "probability": 0.990234375}, {"start": 1979.83, "end": 1979.85, "word": " اد", "probability": 0.989990234375}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.98974609375}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.989501953125}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.989501953125}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.9892578125}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.9892578125}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.989013671875}, {"start": 1979.85, "end": 1979.85, "word": " اد", "probability": 0.98828125}, {"start": 1979.85, "end": 1979.95, "word": " اد", "probability": 0.9873046875}, {"start": 1979.95, "end": 1984.13, "word": " اد", "probability": 0.98681640625}, {"start": 1984.13, "end": 1984.13, "word": " اد", "probability": 0.983642578125}], "temperature": 1.0}, {"id": 74, "seek": 199559, "start": 1984.45, "end": 1995.59, "text": "طبعا في تكملة للسؤال هو ايه؟ المحاضرة القادمة ان شاء الله ساسمعيه بكملكوا بدءا السؤال عشرة يعطيكوا العافية", "tokens": [9566, 3555, 3615, 995, 8978, 6055, 24793, 37977, 24976, 3794, 33604, 6027, 31439, 1975, 1829, 3224, 22807, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 8608, 32277, 2304, 3615, 1829, 3224, 4724, 24793, 23275, 14407, 47525, 38207, 995, 21136, 33604, 6027, 6225, 8592, 25720, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.2795758896640369, "compression_ratio": 1.5234375, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1984.45, "end": 1985.37, "word": "طبعا", "probability": 0.8929443359375}, {"start": 1985.37, "end": 1985.49, "word": " في", "probability": 0.740234375}, {"start": 1985.49, "end": 1985.93, "word": " تكملة", "probability": 0.9235026041666666}, {"start": 1985.93, "end": 1986.51, "word": " للسؤال", "probability": 0.9503173828125}, {"start": 1986.51, "end": 1986.79, "word": " هو", "probability": 0.4609375}, {"start": 1986.79, "end": 1988.67, "word": " ايه؟", "probability": 0.694610595703125}, {"start": 1988.67, "end": 1989.19, "word": " المحاضرة", "probability": 0.9462890625}, {"start": 1989.19, "end": 1989.69, "word": " القادمة", "probability": 0.9892578125}, {"start": 1989.69, "end": 1989.83, "word": " ان", "probability": 0.767578125}, {"start": 1989.83, "end": 1989.99, "word": " شاء", "probability": 0.981201171875}, {"start": 1989.99, "end": 1990.09, "word": " الله", "probability": 0.9599609375}, {"start": 1990.09, "end": 1990.79, "word": " ساسمعيه", "probability": 0.4693705240885417}, {"start": 1990.79, "end": 1991.45, "word": " بكملكوا", "probability": 0.823974609375}, {"start": 1991.45, "end": 1992.03, "word": " بدءا", "probability": 0.8974609375}, {"start": 1992.03, "end": 1993.57, "word": " السؤال", "probability": 0.7722981770833334}, {"start": 1993.57, "end": 1994.39, "word": " عشرة", "probability": 0.8611653645833334}, {"start": 1994.39, "end": 1995.23, "word": " يعطيكوا", "probability": 0.795556640625}, {"start": 1995.23, "end": 1995.59, "word": " العافية", "probability": 0.75}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1997.101875, "duration_after_vad": 1850.2299999999955}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado.srt
new file mode 100644
index 0000000000000000000000000000000000000000..973b64c1c353279c2df78cfa4c896f1b2f9d0be2
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado.srt
@@ -0,0 +1,1627 @@
+1
+00:00:21,240 --> 00:00:24,600
+السلام عليكم ورحمة الله وبركاته هنكمل إن شاء 
+
+2
+00:00:24,600 --> 00:00:27,200
+الله في الجزء الثالث من ال chapter خمسة chapter
+
+3
+00:00:27,200 --> 00:00:30,980
+permutation groups آخر حاجة اتكلمنا عنها نظرية
+
+4
+00:00:30,980 --> 00:00:34,560
+خمسة اثنين اللي كانت بتتناول التالي أنه لو كان
+
+5
+00:00:34,560 --> 00:00:40,220
+عندي two permutations و هذول كانوا disjoint فهم
+
+6
+00:00:40,220 --> 00:00:44,620
+ايش مالهم؟ متبادلين، متبادلين يعني commuted العملية
+
+7
+00:00:44,620 --> 00:00:48,840
+بينهم تبادلية. نظرية خمسة ثلاثة بتتناول ال order
+
+8
+00:00:49,950 --> 00:00:56,750
+لحاصل ضرب two permutations the order طبعا ال session
+
+9
+00:00:56,750 --> 00:01:01,310
+أن أنا باشتغل وين؟ في finite groups، أن أنا باشتغل
+
+10
+00:01:01,310 --> 00:01:04,530
+على permutation على finite set فعددها على الأكثر
+
+11
+00:01:04,530 --> 00:01:11,630
+يعني 10 factorial فال order لأي عنصر finite the
+
+12
+00:01:11,630 --> 00:01:17,370
+order of a
+
+13
+00:01:17,370 --> 00:01:18,010
+permutation
+
+14
+00:01:24,100 --> 00:01:34,240
+of a finite set written as
+
+15
+00:01:34,240 --> 00:01:39,940
+a product of
+
+16
+00:01:39,940 --> 00:01:43,060
+disjoint
+
+17
+00:01:43,060 --> 00:01:51,480
+cycles is the least common
+
+18
+00:01:56,090 --> 00:02:08,350
+multiple of the length of
+
+19
+00:02:08,350 --> 00:02:13,870
+the
+
+20
+00:02:13,870 --> 00:02:14,370
+cycles
+
+21
+00:02:18,440 --> 00:02:22,600
+يعني لو كان عندي permutation و أنا كتبتها على شكل
+
+22
+00:02:22,600 --> 00:02:26,840
+disjoint cycles فال order اللي هيبقى عبارة عن ال
+
+23
+00:02:26,840 --> 00:02:30,120
+least common multiple لهذه الأطوال
+
+24
+00:02:34,080 --> 00:02:37,880
+طبعا أهمية النظرية هذه عشان أنا أقدر أعرف أوجد أي
+
+25
+00:02:37,880 --> 00:02:42,480
+permutation بأخليها عبارة عن disjoint cycles و
+
+26
+00:02:42,480 --> 00:02:44,580
+بأخذ ال least common multiple على طول من دون
+
+27
+00:02:44,580 --> 00:02:50,940
+مضطر أجرب ألف واحد، ألف أوس اثنين، ألف الآخر if ألف
+
+28
+00:02:50,940 --> 00:02:59,840
+عبارة عن ألف واحد اثنين and α is any cycle لما
+
+29
+00:02:59,840 --> 00:03:03,260
+أقول any cycle يعني عبارة عن permutation مكون من
+
+30
+00:03:03,260 --> 00:03:09,080
+cycle واحدة وعدد عناصرها n then order ال α
+
+31
+00:03:09,080 --> 00:03:15,880
+بيُصبح يساوي ايش؟ n طبعا ال α عشان أوصله
+
+32
+00:03:15,880 --> 00:03:18,780
+لل identity لازم أقوم بإجراءها من المرة n هو
+
+33
+00:03:18,780 --> 00:03:26,180
+عبارة عن ايش؟ دور ما عشان أرجع العنصر لمكانه بحتاج
+
+34
+00:03:26,180 --> 00:03:31,540
+n من الدورات لأن هنا a بيروح ل a1 ل a2 و a2
+
+35
+00:03:31,540 --> 00:03:35,800
+بيروح ل a3 لما أعمل α في α هيصير a1 يروح لمين؟
+
+36
+00:03:35,800 --> 00:03:42,120
+ل a3 كمان، ل a1 هيروح ل a4 بعد n من اللفات a1
+
+37
+00:03:42,120 --> 00:03:47,140
+هيصير يروح لمين؟ ل a1 و هيرجع لمكانه. طيب هذه أنا
+
+38
+00:03:47,140 --> 00:03:53,560
+هثبتها ل two cycles وبعد هيك التعميم تبعها بسيط
+
+39
+00:03:53,560 --> 00:04:02,200
+القادم we will proof this
+
+40
+00:04:02,200 --> 00:04:13,140
+result for a permutation consists
+
+41
+00:04:13,140 --> 00:04:19,940
+of two disjoint
+
+42
+00:04:19,940 --> 00:04:23,280
+cycles
+
+43
+00:04:23,280 --> 00:04:25,780
+يعني
+
+44
+00:04:30,100 --> 00:04:37,980
+we show that if order للألفا بيساوي m order
+
+45
+00:04:37,980 --> 00:04:44,320
+للبيتا بيساوي n then order للألفا في بيتا بـ
+
+46
+00:04:44,320 --> 00:04:50,740
+يساوي least common multiple ل m و n طبعا لو أنا أثبتت
+
+47
+00:04:50,740 --> 00:04:57,260
+اثنين لما ببدي أجيب واحدة ثالثة بأخذ ال least
+
+48
+00:04:57,260 --> 00:05:00,720
+common multiple الاثنين مع الثالثة لو بدنا نضيف
+
+49
+00:05:00,720 --> 00:05:07,760
+واحدة رابعة بيصير عملية عملية تكرارية assume that
+
+50
+00:05:07,760 --> 00:05:13,620
+أن order ال alpha beta بيساوي t وأن ال least
+
+51
+00:05:13,620 --> 00:05:19,440
+common multiple ل m و n بيساوي k
+
+52
+00:05:23,100 --> 00:05:28,120
+المطلوب أثبت أن أنا ايش؟ أن k بيساوي t شوف انتقل
+
+53
+00:05:28,120 --> 00:05:35,140
+الاثبات من جملة لفظية وقصة طويلة لايش لاثبات أنه
+
+54
+00:05:35,140 --> 00:05:40,100
+عقامين متساويين now since
+
+55
+00:05:40,100 --> 00:05:46,600
+Alpha و Beta are disjoint then
+
+56
+00:05:52,960 --> 00:06:02,840
+ألفا بيتا بتساوي ايش؟ بيتا ألفا so لو
+
+57
+00:06:02,840 --> 00:06:12,840
+أنا رفعت الالفا بيتا ل k هذا عبارة عن ألفا أس k في
+
+58
+00:06:12,840 --> 00:06:17,740
+بيتا أس k but
+
+59
+00:06:19,670 --> 00:06:25,710
+ال k عبارة عن ال least common multiple ل m و n يعني ال
+
+60
+00:06:25,710 --> 00:06:32,990
+k عبارة عن multiple ل m مثلا m في r وهي
+
+61
+00:06:32,990 --> 00:06:39,930
+نفسها ال n في s يكبر Alpha Beta أس k عبارة عن ايش؟
+
+62
+00:06:41,610 --> 00:06:47,750
+عن Alpha أس k Beta أس k يعني Alpha أس mr في
+
+63
+00:06:47,750 --> 00:06:54,390
+Beta أس ns يعني Alpha أس m أس r Beta أس n أس
+
+64
+00:06:54,390 --> 00:06:59,390
+s يعني Identity أس r في Identity أس s ايش
+
+65
+00:06:59,390 --> 00:07:04,290
+بيعطيني؟ معناته ال Alpha Beta أس k
+
+66
+00:07:07,390 --> 00:07:11,270
+بيساوي ال identity ايش ب order ال alpha beta
+
+67
+00:07:11,270 --> 00:07:23,330
+اللي هو عبارة عن ال t بيقسم ال k ال t بتقسم
+
+68
+00:07:23,330 --> 00:07:28,630
+ال k now order
+
+69
+00:07:28,630 --> 00:07:34,970
+ال alpha beta عبارة عن مين؟ عن ال t يعني ال alpha
+
+70
+00:07:34,970 --> 00:07:40,190
+Beta أس t بيساوي ال identity يعني Alpha أس t
+
+71
+00:07:40,190 --> 00:07:46,730
+لاحظ أنه أنهم disjoint هو اللي سهل عملية الرفع للأس
+
+72
+00:07:46,730 --> 00:07:53,490
+t و الرفع للأس k هذا بيساوي ايش؟ identity يعني ال
+
+73
+00:07:53,490 --> 00:08:01,190
+Alpha أس t بيساوي Beta أس t طيب
+
+74
+00:08:04,500 --> 00:08:14,720
+Alpha and beta are disjoint لما
+
+75
+00:08:14,720 --> 00:08:19,880
+يكون عندك two cycles و disjoint يعني عناصر ال
+
+76
+00:08:19,880 --> 00:08:25,980
+alpha غير عناصر ال beta فجد ما تلف ال alpha و تلف
+
+77
+00:08:25,980 --> 00:08:30,040
+ال beta مش هتلاقي عناصر مشتركة إلا في حالة واحدة
+
+78
+00:08:30,040 --> 00:08:34,260
+لما هاد تلف وتصل ال identity و هاد تلف وتصل ال
+
+79
+00:08:34,260 --> 00:08:45,850
+identity So we must have thatال α أس t بيبقى
+
+80
+00:08:45,850 --> 00:08:49,290
+تساوي ال Beta أس سالب t بيبقى تساوي ال Identity
+
+81
+00:08:49,290 --> 00:08:53,710
+Alpha أس t بيبقى تساوي ال Identity Beta أس t
+
+82
+00:08:53,710 --> 00:08:58,710
+أس سالب t بيبقى تساوي ال Identity Alpha أس t بـ
+
+83
+00:08:58,710 --> 00:09:06,190
+Identity Beta أس t بـ Identity يقبل m بيقسم ال t
+
+84
+00:09:06,190 --> 00:09:12,830
+Order ال Alpha بيبقى تساوي m بيقسم ال t Order ال
+
+85
+00:09:12,830 --> 00:09:20,870
+Beta بيساوي n بيقسم مين؟ ال t معناته ال t is a
+
+86
+00:09:20,870 --> 00:09:24,710
+common multiple
+
+87
+00:09:24,710 --> 00:09:33,830
+of m and n معناته ال least common multiple ل m و n
+
+88
+00:09:33,830 --> 00:09:39,610
+اللي هو عبارة عن k بيقسم ال t و أعطيها 2 هذه جهة
+
+89
+00:09:39,610 --> 00:09:43,050
+ال t بيقسم ال k ال k بيقسم ال t
+
+90
+00:10:01,620 --> 00:10:07,420
+وهو المطلوب إثباته وهو
+
+91
+00:10:07,420 --> 00:10:11,700
+المطلوب إثباته طبعا هنا لو كانوا اثنتين لو كانوا
+
+92
+00:10:11,700 --> 00:10:15,740
+ثلاثة لو كانوا أربعة لو كانوا أي عدد هيكون تعميم
+
+93
+00:10:15,740 --> 00:10:28,580
+لهذه النتيجة واضح مش 
+
+94
+00:10:28,580 --> 00:10:34,460
+ال identity function طيب
+
+95
+00:10:41,400 --> 00:10:45,300
+مش فاهم صحيح
+
+96
+00:10:45,300 --> 00:10:48,740
+power
+
+97
+00:10:48,740 --> 00:10:54,020
+من ال alpha هيجيب طالع معايا ال alpha الأخضر يله m
+
+98
+00:10:54,020 --> 00:10:57,920
+ف alpha أس m مش بيساوي طيب و ال beta الأخضر يله
+
+99
+00:10:57,920 --> 00:11:02,280
+n ف beta أس n مش بيساوي هاي power لل alpha و
+
+100
+00:11:02,280 --> 00:11:05,500
+power لل beta تساوي لكن ال alpha و ال beta و كل ال
+
+101
+00:11:05,500 --> 00:11:12,080
+powers مع ده الحالة الخاصة هذه إن المضاعفات ال m و
+
+102
+00:11:12,080 --> 00:11:15,880
+ال n مع بعض مش هيتساوى طيب احنا ال power أشمل أن
+
+103
+00:11:15,880 --> 00:11:17,840
+انتوا من أول مرة بتعطيني اللي بعد و ثاني بتعطيني
+
+104
+00:11:17,840 --> 00:11:18,120
+اللي بعد
+
+105
+00:11:22,370 --> 00:11:27,990
+هجيت Alpha بتاخد ال a1 ل a2 و ال a2 ل ال a3 لما
+
+106
+00:11:27,990 --> 00:11:32,530
+أحسب Alpha تربيع هتصير تاخد ال a1 ل a3 Alpha أس
+
+107
+00:11:32,530 --> 00:11:38,670
+أربعة ل a1 ل a4 هجيت Alpha أس n هتاخد ال a1 و تلف
+
+108
+00:11:38,670 --> 00:11:45,130
+ويرجع لمين؟ ل a1 وال a2 هتلف وترجع لمين؟ ل ال
+
+109
+00:11:45,130 --> 00:11:48,970
+a2 وال a3 ل ال a.. يعني انت حصلت على ال identity
+
+110
+00:11:48,970 --> 00:11:52,070
+عشان ال order لل alpha n مثلا أو حتى .. حتى أن ال
+
+111
+00:11:52,070 --> 00:11:57,690
+order m فانت بتتكلم عن مين؟ عن أس m واضح؟ القصد
+
+112
+00:11:57,690 --> 00:12:01,550
+هنا أن ال alpha و ال beta مش متساويين لكن في power
+
+113
+00:12:01,550 --> 00:12:05,050
+للألفا و power للبيتا بيعطيك ال identity يعني مثلا
+
+114
+00:12:05,050 --> 00:12:11,690
+في z7 أو بلاش z7 زد عشرين هل التلاتة و السبعة و ال
+
+115
+00:12:11,690 --> 00:12:16,950
+.. و ال .. و ال 11 متساوين لكن في power للتلاتة و
+
+116
+00:12:16,950 --> 00:12:19,830
+في power لل 11 طبعا أنا بتكلم عن power بتكلم عن
+
+117
+00:12:19,830 --> 00:12:24,510
+multiple هنا بتوديهم ل 100 للصفر أو بتوديهم ل .. ل
+
+118
+00:12:24,510 --> 00:12:27,250
+.. لقيم ما لكن هم نفسهم مش متساوين
+
+119
+00:12:45,760 --> 00:12:51,420
+كمثال لو أخذنا ال alpha تبعت الصبح اللي كانت عبارة
+
+120
+00:12:51,420 --> 00:12:57,600
+عن نجلونيها اللي كتبناها الصبح اللي كانت عبارة عن
+
+121
+00:12:57,600 --> 00:13:04,220
+ثمانية cycles كتبناها
+
+122
+00:13:04,220 --> 00:13:10,200
+الصبح في المثال المكان هذا 123
+
+123
+00:13:13,750 --> 00:13:17,930
+خمسة، ستة، ثمانية، أربعة ال O ضل الألف جديش يا 
+
+124
+00:13:17,930 --> 00:13:22,310
+شباب ثمانية، عدد عنصرها واحد، اثنين، ثلاثة،
+
+125
+00:13:22,310 --> 00:13:25,910
+أربعة، خمسة، ستة، سبعة، ثمانية طب ال beta إيش؟ 
+
+126
+00:13:25,910 --> 00:13:31,750
+كانت؟ نفس السؤال، نفس المثال، أظن واحد و اثنين
+
+127
+00:13:31,750 --> 00:13:41,470
+واحد لحالها هدول
+
+128
+00:13:41,470 --> 00:13:45,900
+مالهم مش لازمة طبعًا، فالـ order للـ beta عبارة عن ال
+
+129
+00:13:45,900 --> 00:13:51,640
+least common multiple لمن؟ لـ order هذه كم؟ أربع و
+
+130
+00:13:51,640 --> 00:13:56,160
+order هذه كم؟ الـ least common multiple كم؟ أربع
+
+131
+00:14:18,400 --> 00:14:24,420
+نظرية 5-4 يا جدعان، أي permutation بقدر أكتبها
+
+132
+00:14:24,420 --> 00:14:29,700
+على شكل حاصل ضرب disjoint cycles هل بقدر أتحكم في
+
+133
+00:14:29,700 --> 00:14:34,400
+طول الـ cycle لو شلت شرط الـ disjoint؟ يعني أنا بدي 
+
+134
+00:14:34,400 --> 00:14:37,840
+أسدّد وأقارب عشان أحصل على نتائج في كل حالة عشان
+
+135
+00:14:37,840 --> 00:14:41,040
+أكتبها على شكل disjoint بستفيد جثة التبديل وجثة
+
+136
+00:14:41,040 --> 00:14:44,670
+الـ order لكن أنا هجيت مش محتاج الـ order والتبديل
+
+137
+00:14:44,670 --> 00:14:51,030
+محتاج شغلات هنعرفها كمان شوية هل بقدر أتحكم في طول
+
+138
+00:14:51,030 --> 00:14:54,250
+الـ
+
+139
+00:14:54,250 --> 00:14:58,730
+permutation لو خدت permutation طولها اثنين بقدر
+
+140
+00:14:58,730 --> 00:15:04,950
+أخليه ثلاثة لأ واحد واثنين كيف بقدر أخليه ثلاثة
+
+141
+00:15:04,950 --> 00:15:09,980
+مش هتقدر تضيفي شيء يكبر له كان عندك permutation
+
+142
+00:15:09,980 --> 00:15:14,540
+ثلاثة تقدر تخليها permutation اثنين مثلًا واحد
+
+143
+00:15:14,540 --> 00:15:18,400
+اثنين ثلاثة الواحد اثنين ثلاثة أنا ممكن أخليها
+
+144
+00:15:18,400 --> 00:15:24,920
+واحد ثلاثة واحد اثنين وجرب واحد بيروح للاتنين و
+
+145
+00:15:24,920 --> 00:15:27,520
+اثنين بيروح لنفسه يجب واحد ده الاتنين اثنين بيروح
+
+146
+00:15:27,520 --> 00:15:29,820
+للواحد واحد بيروح للتلاتة واثنين بيروح للتلاتة
+
+147
+00:15:29,820 --> 00:15:33,780
+ثلاثة لنفسه وثلاثة للواحد يجب ثلاثة للواحد يكبر لو 
+
+148
+00:15:33,780 --> 00:15:38,220
+كانت الأرض يعني الطول أكثر من اثنين أنا ممكن أنزله
+
+149
+00:15:38,220 --> 00:15:42,360
+اثنين لكن صعب أني أرفع من صغير لكبير يكبر أنا
+
+150
+00:15:42,360 --> 00:15:46,560
+بإمكاني أتحكم وأخلي أي permutation لما أكتبها على
+
+151
+00:15:46,560 --> 00:15:50,160
+شكل disjoint cycles أروح الـ disjoint cycles هدول
+
+152
+00:15:50,160 --> 00:15:55,440
+أعملهم لحاجة إحنا بنسميها two cycles هذه نظرية خمسة
+
+153
+00:15:55,440 --> 00:15:57,740
+أربعة بتقول لك أي permutation
+
+154
+00:16:07,210 --> 00:16:16,990
+ن أسن حيث أن أكبر من الواحد can be written
+
+155
+00:16:16,990 --> 00:16:29,470
+as a product of two cycles two cycles يعني عبارة
+
+156
+00:16:29,470 --> 00:16:33,550
+عن إيش؟ عن cycle طولها كم؟ اثنين
+
+157
+00:16:38,270 --> 00:16:47,570
+إثبات سهل ومباشر proof أول شيء الـ identity الـ
+
+158
+00:16:47,570 --> 00:16:56,370
+identity ممكن أكتبها 1 2 2 1 طبعًا الأجهزة كله من
+
+159
+00:16:56,370 --> 00:17:00,610
+ثلاثة وأربعة بيروح لنفسه أنه مش مذكور هنا بيظل
+
+160
+00:17:00,610 --> 00:17:05,270
+الواحد والاتنين هذا بمكانك تعمله زي هيك واحد بيروح
+
+161
+00:17:05,270 --> 00:17:08,340
+للاتنين والاتنين بيروح للواحد يكبر واحد لواحدو
+
+162
+00:17:08,340 --> 00:17:16,240
+اثنين لـ اثنين وبالتالي صار الـ identity طيب now if
+
+163
+00:17:16,240 --> 00:17:23,380
+alpha عبارة عن a1 a2 اللي عند at أو ak في b1 b2
+
+164
+00:17:23,380 --> 00:17:31,240
+اللي عند pm في c1 c2 اللي عند cn كيبلك خلية two
+
+165
+00:17:31,240 --> 00:17:38,500
+cycles تعمل التالي بتبدأ أول عنصر تاخده مع الأخير
+
+166
+00:17:38,500 --> 00:17:41,740
+بعدين
+
+167
+00:17:41,740 --> 00:17:50,080
+أول عنصر مع قبل الأخير وبتضلك شغال لما تصل لمين لـ
+
+168
+00:17:50,080 --> 00:17:56,480
+واحد مع اثنين تجي على الـ B أول واحد مع الأخير أول
+
+169
+00:17:56,480 --> 00:18:03,510
+واحد مع قبل الأخير وبتضلك لما بتجيبه مع مين مع
+
+170
+00:18:03,510 --> 00:18:12,370
+التاني وبضلك نازل لما تصل لآخر cycle و
+
+171
+00:18:12,370 --> 00:18:16,090
+هدول
+
+172
+00:18:16,090 --> 00:18:24,090
+عبارة عن إيش كلهم cycles طولهم قد إيش؟ اثنين الـ
+
+173
+00:18:24,090 --> 00:18:28,190
+disjoint مش موجود هنا أنا هنا بيلزمنيش الـ disjoint
+
+174
+00:18:29,650 --> 00:18:34,210
+بيلزمن مين؟ فقط أني أكتب عليه شكل two cycles ليش؟
+
+175
+00:18:34,210 --> 00:18:39,730
+لأنه هعرف كمان شوية حاجة اسمها even permutation أو
+
+176
+00:18:39,730 --> 00:18:48,650
+odd permutation كمثال الـ alpha ها دي واحد اثنين سبعة
+
+177
+00:18:48,650 --> 00:18:55,310
+ثلاثة خمسة ستة ثمانية أربعة ممكن نكتبها واحد أربعة
+
+178
+00:18:55,310 --> 00:19:05,390
+واحد ثمانية واحد ستة واحد خمسة 1 3 1 7 1 2 طبعًا في
+
+179
+00:19:05,390 --> 00:19:08,430
+الدار جرب وحسبها هل هدول لما تضربهم بيعطوك هذي
+
+180
+00:19:08,430 --> 00:19:21,130
+ولا لأ أيضًا الـ beta اللي عبارة عن 2 4 3 5 6 7 2 5
+
+181
+00:19:21,130 --> 00:19:25,850
+2 3 2 4 وهذه جاهزة
+
+182
+00:19:28,510 --> 00:19:38,030
+أدوش محتاجة حسابات لما
+
+183
+00:19:56,270 --> 00:19:59,990
+هذه اللمة هناخدها بدون إثبات هنحتاجها في إثبات
+
+184
+00:19:59,990 --> 00:20:04,630
+شغلة قادمة أو نظرية لبعدها اللمة هذه بتقول الـ
+
+185
+00:20:04,630 --> 00:20:09,830
+identity لو قدرت تكتب على شكل two cycles فعدد الـ
+
+186
+00:20:09,830 --> 00:20:15,310
+two cycles هذا لازم يكون زوجي الـ identity لو قدرت
+
+187
+00:20:15,310 --> 00:20:19,430
+تكتب على شكل two cycles عدد الـ two cycles هدول
+
+188
+00:20:19,430 --> 00:20:26,110
+هيكون زوجي if الـ identity عبارة عن ألف واحد ألف
+
+189
+00:20:26,110 --> 00:20:38,490
+اثنين لعند ألف مثلًا R is a product of two cycles
+
+190
+00:20:38,490 --> 00:20:46,050
+then R is even لو
+
+191
+00:20:46,050 --> 00:20:50,590
+قدرت تكتب عيد الـ identity على شكل two cycles فعدد
+
+192
+00:20:50,590 --> 00:20:56,220
+الـ two cycles هدول لازم يكون زوجي أهميتها هي نظرية
+
+193
+00:20:56,220 --> 00:21:02,560
+5-5 theorem 5
+
+194
+00:21:02,560 --> 00:21:12,000
+-5 في نظرية 5-5 لو قدرت تكتب permutation بطريقتين
+
+195
+00:21:12,000 --> 00:21:18,380
+على شكل two cycles لو قدرت تكتب permutation على
+
+196
+00:21:18,380 --> 00:21:20,420
+شكل two cycles بطريقتين
+
+197
+00:21:23,020 --> 00:21:26,980
+ وعديت الـ two cycles في الطريقة الأولى وعديت الـ
+
+198
+00:21:26,980 --> 00:21:32,320
+two cycles في الطريقة الثانية يا اثنين
+
+199
+00:21:32,320 --> 00:21:42,040
+even يا اثنين odd if Alpha عبارة عن Alpha 1 Alpha 2
+
+200
+00:21:42,040 --> 00:21:49,780
+لعند Alpha R وهي نفسها Beta 1 Beta 2 لعند Beta S
+
+201
+00:21:49,780 --> 00:21:51,780
+where
+
+202
+00:21:53,300 --> 00:22:06,400
+أو is a product of two cycles in two ways then
+
+203
+00:22:06,400 --> 00:22:21,360
+both are and is even or both are
+
+204
+00:22:21,360 --> 00:22:28,740
+odd يعني لو كتبت الـ permutation على شكل two cycles
+
+205
+00:22:28,740 --> 00:22:35,260
+وضعتها زيكي لكي أميزها بطريقتين فعدد الـ two cycles
+
+206
+00:22:35,260 --> 00:22:38,340
+في الأولى وعدد الـ two cycles في الثانية يا اثنين
+
+207
+00:22:38,340 --> 00:22:46,980
+زوجي يا اثنين فردي ولا حاجة since Alpha بدي أساوي
+
+208
+00:22:46,980 --> 00:22:51,920
+Alpha واحد Alpha اثنين لعند Alpha R هو نفسه Beta
+
+209
+00:22:51,920 --> 00:23:01,010
+واحد Beta اثنين لأن BTS أجدع شباب الـ two cycle
+
+210
+00:23:01,010 --> 00:23:10,430
+الأخضر غير هجدع دي أش اثنين since
+
+211
+00:23:10,430 --> 00:23:24,540
+Alpha I عبارة عن a1i a2i وبيتا جي عبارة عن بي واحد
+
+212
+00:23:24,540 --> 00:23:31,200
+جي بيتنينين جي النتيجة order لـ ألف اي بيساوي order
+
+213
+00:23:31,200 --> 00:23:36,820
+لـ بيتا جي بيساوي اثنين لكل اي أقل أو يساوي ار جي أقل
+
+214
+00:23:36,820 --> 00:23:44,500
+أو يساوي اس هذا معناه إن ألف اي بيساوي ألف اي
+
+215
+00:23:44,500 --> 00:23:50,740
+inverse وبيتا جي بيساوي بيتا جي inverse يعني الـ
+
+216
+00:23:50,740 --> 00:23:53,820
+permutation اللي على شكل two cycles الميزة تبعتهم
+
+217
+00:23:53,820 --> 00:24:00,620
+إن الـ inverse تبعهم هو نفسهم هجيت نقول ألف واحد ألف
+
+218
+00:24:00,620 --> 00:24:07,200
+اثنين ألف ار بيتا واحد بيتا اثنين بيتاس اضرب في الـ
+
+219
+00:24:07,200 --> 00:24:10,120
+inverse تبعه دول حاسيب معايا ألف واحد ألف اثنين
+
+220
+00:24:10,120 --> 00:24:16,230
+ألف ار طبعًا إحنا بنضرب إيش؟ عكسي Beta S inverse
+
+221
+00:24:16,230 --> 00:24:20,670
+Beta S ناقص واحد inverse لعين Beta واحد inverse
+
+222
+00:24:20,670 --> 00:24:25,490
+هذا حساو مين اللي هو عبارة عن Alpha واحد Alpha
+
+223
+00:24:25,490 --> 00:24:31,470
+اثنين Alpha R Beta S Beta S ناقص واحد Beta واحد
+
+224
+00:24:31,470 --> 00:24:38,150
+إيش بتساوي الـ identity هذا معناه إن R زائد S is
+
+225
+00:24:38,150 --> 00:24:40,450
+even هذا by مين
+
+226
+00:24:43,820 --> 00:24:50,880
+طيب لما؟ لإنه صار الـ identity حاصل ضرب two cycles
+
+227
+00:24:50,880 --> 00:24:57,360
+عددهم قد إيش؟ R زيادة S حسب اللي لما لازم الـ R زيادة S
+
+228
+00:24:57,360 --> 00:25:03,500
+يكون even معناه both عشان يكون عندك عددين مجموعهم
+
+229
+00:25:03,500 --> 00:25:15,340
+زوجي يا اثنين even يا اثنين odd both R and S are even or
+
+230
+00:25:15,340 --> 00:25:25,040
+both are odd يا اثنين زوجي، يا اثنين فردي، فهمتوا فادي؟
+
+231
+00:25:25,040 --> 00:25:31,300
+طب
+
+232
+00:25:31,300 --> 00:25:35,160
+إيش الأهمية هنا؟
+
+233
+00:25:35,160 --> 00:25:40,820
+إن أي permutation لما أحطها كـ cycles two cycles
+
+234
+00:25:42,410 --> 00:25:46,530
+الحالة تبع الـ even والـ odd ثابتة دائمًا مدامها
+
+235
+00:25:46,530 --> 00:25:51,950
+ثابتة بإمكاني أنا أرفق الحالة بالعنصر يعني أقول
+
+236
+00:25:51,950 --> 00:25:56,790
+مدام حاصل ضرب even number of two cycles هقول عنه
+
+237
+00:25:56,790 --> 00:26:00,410
+even ومدام حاصل ضرب odd number of two cycles
+
+238
+00:26:00,410 --> 00:26:09,910
+هقول عنه إيش odd هيطلع معايا تعريف كالتالي الـ
+
+239
+00:26:09,910 --> 00:26:10,550
+permutation
+
+240
+00:26:15,680 --> 00:26:31,380
+الفا is called even بنفس النمط odd permutation if
+
+241
+00:26:31,380 --> 00:26:41,580
+الفا can be written as a product of
+
+242
+00:26:42,410 --> 00:26:50,110
+even في حالة الـ odd odd number of
+
+243
+00:26:50,110 --> 00:26:56,450
+two cycles يعني أنا لو قدرت أكتب الـ permutation
+
+244
+00:26:56,450 --> 00:27:02,910
+على شكل عدد معين من الـ two cycles هذا العدد لو كان
+
+245
+00:27:02,910 --> 00:27:07,090
+even بقول عن الـ permutation even لو كان هذا العدد
+
+246
+00:27:07,090 --> 00:27:14,350
+odd بقول عن الـ permutation لنرجع للمثال تبع توي الـ
+
+247
+00:27:14,350 --> 00:27:22,270
+alpha اللي كانت واحد اثنين سبعة ثلاثة و
+
+248
+00:27:22,270 --> 00:27:27,810
+الـ beta طبعًا هذه انكتبت خمسة ستة ثمانية أربعة
+
+249
+00:27:27,810 --> 00:27:33,790
+كتبناها واحد أربعة واحد ثمانية واحد ستة واحد خمسة
+
+250
+00:27:33,790 --> 00:27:38,930
+واحد ثلاثة واحد سبعة واحد اثنين كانت عددها هدول 
+
+251
+00:27:40,550 --> 00:27:49,350
+seven two cycles بألف شمالها odd لكن الـ beta 
+
+252
+00:27:49,350 --> 00:27:55,410
+اللي كانت عبارة عن اتنين اتنين
+
+253
+00:27:55,410 --> 00:28:00,690
+اربعة تلاتة خمسة يعني اتنين خمسة اتنين تلاتة اتنين
+
+254
+00:28:00,690 --> 00:28:04,090
+اربعة ستة سبعة beta شمالها
+
+255
+00:28:06,520 --> 00:28:15,720
+even هدول قداش for two cycles فكانت الـ beta ال
+
+256
+00:28:15,720 --> 00:28:27,040
+beta شمالها even طبعا
+
+257
+00:28:27,040 --> 00:28:35,860
+مثال تاني الـ identity is even allowed الـ identity
+
+258
+00:28:35,860 --> 00:28:42,180
+شوية بس الـ permutation بتكون even إذا كتبت على شكل
+
+259
+00:28:42,180 --> 00:28:47,060
+عدد زوجي من الـ two cycles طب الـ permutation اللي
+
+260
+00:28:47,060 --> 00:28:57,180
+هي الـ identity أكم two cycles كتبناها is even
+
+261
+00:28:57,180 --> 00:29:05,750
+by لما أصلا الـ identity ممكن تكتبها زي هيك هذا هو
+
+262
+00:29:05,750 --> 00:29:19,850
+even number of two cycles أصارت ايش even نرجع
+
+263
+00:29:19,850 --> 00:29:30,830
+للألف تبع التوي find
+
+264
+00:29:30,830 --> 00:29:34,070
+alpha inverse
+
+265
+00:29:48,860 --> 00:29:53,000
+دعونا ناخد هذه كمثال مشتق من القاعدة أصلا الـ
+
+266
+00:29:53,000 --> 00:30:07,440
+alpha عبارة عن 1 2 أو 1 4 1 8 1 6 1 5 1 3 1 7 1 2
+
+267
+00:30:07,440 --> 00:30:14,860
+الـ alpha inverse عبارة عن مين؟ عن واحد اربع واحد
+
+268
+00:30:14,860 --> 00:30:21,020
+ثمانية واحد ستة واحد خمسة واحد تلاتة واحد سبعة
+
+269
+00:30:21,020 --> 00:30:25,580
+واحد اتنين inverse شباب احنا عارفين ان الـ inverse
+
+270
+00:30:25,580 --> 00:30:31,720
+بتوزع الضرب لكن ما بتكون بالترتيب العكسي بيجيب هذه
+
+271
+00:30:31,720 --> 00:30:37,680
+عبارة عن واحد اتنين inverse واحد سبعة inverse واحد
+
+272
+00:30:37,680 --> 00:30:42,880
+تلاتة inverse واحد خمسة inverse واحد ستة inverse
+
+273
+00:30:42,880 --> 00:30:48,900
+واحد تمانية inverse واحد اربع inverse و هدول two
+
+274
+00:30:48,900 --> 00:30:53,780
+cycles الـ inverse ايه اللي هم شمالها الـ inverse لل
+
+275
+00:30:53,780 --> 00:30:56,620
+two cycles أي two cycle الـ inverse ايه اللي هاي
+
+276
+00:30:56,620 --> 00:31:02,500
+شمالهاها شباب الـ inverse لأي two cycles يساوي
+
+277
+00:31:02,500 --> 00:31:07,460
+نفسه يعني هذا عبارة عن واحد اتنين واحد ستة واحد
+
+278
+00:31:07,460 --> 00:31:14,220
+تلاتة واحد خمسة واحد ستة أو خدنا الـ واحد ستة احنا
+
+279
+00:31:14,220 --> 00:31:20,820
+اه هذه خربطت واحد اتنين واحد سبعة اه طيب واحد ستة
+
+280
+00:31:20,820 --> 00:31:25,720
+واحد تمانية واحد اربعة عارف هذه مين؟
+
+281
+00:31:32,810 --> 00:31:43,610
+طبها هذه واحد اتنين
+
+282
+00:31:43,610 --> 00:31:51,630
+سبعة تلاتة خمسة ستة تمانية اربعة
+
+283
+00:31:58,040 --> 00:32:00,900
+انت لو كتبت هادي على شكل two cycles مش هتاخد الأول
+
+284
+00:32:00,900 --> 00:32:06,400
+مع الآخر مع جبل الآخر اعملها بس بالعكس تنساش انه
+
+285
+00:32:06,400 --> 00:32:10,160
+الـ cycle انا ممكن اكتبها بطريقة هادي يعني انا ممكن
+
+286
+00:32:10,160 --> 00:32:13,140
+هادي اسير اربعة تمانية ستة خمسة تلاتة سبعة اتنين
+
+287
+00:32:13,140 --> 00:32:18,080
+واحد هي هي الاربعة بتروح للثمانية بتروح للثمانية
+
+288
+00:32:18,080 --> 00:32:22,100
+الـ ثمانية للستة للستة للخمسة الستة للخمسة ما فَرَجتش
+
+289
+00:32:22,100 --> 00:32:26,740
+كتير تطلع على هادي و تطلع على هادي تطلع ترتيب
+
+290
+00:32:26,740 --> 00:32:33,300
+العناصر بطلع على ترتيب العناصر بين هذه و هذه ايش
+
+291
+00:32:33,300 --> 00:32:37,920
+بتلاحظ؟ واحد اتنين سبعة تلاتة خمسة ستة تمانية
+
+292
+00:32:37,920 --> 00:32:42,000
+اربعة واحد اتنين سبعة تلاتة خمسة ستة تمانية اربعة
+
+293
+00:32:42,000 --> 00:32:46,720
+ايش بيصير؟ بنرتب العناصر لكن بالعكس وهذا ممكن نقول
+
+294
+00:32:46,720 --> 00:32:56,120
+fact if alpha بتساوي a1 a2 عند an then alpha
+
+295
+00:32:56,120 --> 00:33:06,230
+inverse عبارة عن anan-1 a2 a1 طيب
+
+296
+00:33:06,230 --> 00:33:12,390
+كمثال الـ beta تبع التوي اللي عبارة عن اتنين اربعة
+
+297
+00:33:12,390 --> 00:33:19,170
+تلاتة خمسة ستة سبعة الـ beta inverse عبارة عن اتنين
+
+298
+00:33:19,170 --> 00:33:25,700
+اربعة تلاتة خمسة في 6 7 inverse اللي عبارة عن 6 7
+
+299
+00:33:25,700 --> 00:33:37,880
+inverse 2 4 3 5 inverse 6 7 inverse مين هي نفسها و
+
+300
+00:33:37,880 --> 00:33:46,620
+2 4 3 5 inverse خمسة تلاتة اربعة اتنين خيال
+
+301
+00:33:48,310 --> 00:33:52,130
+و هدى صارت عندك أهمية تانية لكتابة الـ permutation
+
+302
+00:33:52,130 --> 00:34:03,470
+على شكل two cycles دي
+
+303
+00:34:03,470 --> 00:34:09,550
+theorem خمسة ستة بيجي
+
+304
+00:34:09,550 --> 00:34:14,650
+السؤال هل جيت الـ Sn فيها permutation even و فيها
+
+305
+00:34:14,650 --> 00:34:15,770
+permutation odd
+
+306
+00:34:19,310 --> 00:34:24,590
+هل الـ odd مع بعض بيعملولي subgroup؟ بيجي هنا
+
+307
+00:34:24,590 --> 00:34:30,470
+السؤال هل الـ even مع بعض بيعملولي subgroup؟ والله
+
+308
+00:34:30,470 --> 00:34:35,210
+لأ نظرية خمسة ستة بتقولك أنه لو أخدت الـ even مع
+
+309
+00:34:35,210 --> 00:34:39,780
+بعض هيعملوا subgroup إن الـ odd مع بعض ما بيعملش
+
+310
+00:34:39,780 --> 00:34:43,000
+subgroup هذا عبارة عن counter .. محتاج counter
+
+311
+00:34:43,000 --> 00:34:45,560
+example انه مش هيعمل subgroup موجود ضمن الأسئلة
+
+312
+00:34:45,560 --> 00:34:49,340
+هنثبت في نظرية ان الـ even بيعملوا subgroup و
+
+313
+00:34:49,340 --> 00:34:54,240
+بنستعطيها اسم اسم الـ alternating group of degree
+
+314
+00:34:54,240 --> 00:35:05,460
+theorem 5-6 that's it of all even permutations
+
+315
+00:35:11,480 --> 00:35:27,980
+ن أسن form a subgroup of أسن بتبقى سهلة let أن
+
+316
+00:35:27,980 --> 00:35:34,200
+عبارة عن كل الـ ألف حيث ألف ينتمي لأسن و ألف is even
+
+317
+00:35:39,340 --> 00:35:45,240
+الـ Identity ينتمي لان وبالتالي الان لا يسار فعلا
+
+318
+00:35:45,240 --> 00:35:50,700
+طبعا هنا for an أكبر من الواحد لأن لو an بيسار
+
+319
+00:35:50,700 --> 00:35:55,420
+واحد مافيش غير عنصر واحد هو الـ identity ايش بيظل
+
+320
+00:35:55,420 --> 00:36:04,440
+أثبت أنها جات؟ ان هيش هذي finite في الـ finite يكفي
+
+321
+00:36:04,440 --> 00:36:12,330
+نياش شرط واحد اللي هو الـ one step لأ انه closed انه
+
+322
+00:36:12,330 --> 00:36:18,290
+أي عنصرين بتاخدهم يكون حاصل ضربه معاها let alpha و
+
+323
+00:36:18,290 --> 00:36:28,230
+beta ينتمي ل a,n معناته alpha و beta is even يعني
+
+324
+00:36:28,230 --> 00:36:31,430
+alpha عبارة عن الـ alpha واحد الـ alpha اتنين اللي
+
+325
+00:36:31,430 --> 00:36:36,610
+عند الـ alpha اتنين ام beta بتساوي beta واحد beta
+
+326
+00:36:36,610 --> 00:36:39,270
+تنين اللي عند الـ beta تنين
+
+327
+00:36:41,610 --> 00:36:48,470
+مش هما even فعبارة عن where alpha
+
+328
+00:36:48,470 --> 00:36:58,870
+i and beta j شمالهم are two cycles
+
+329
+00:36:58,870 --> 00:37:05,550
+تعالوا
+
+330
+00:37:05,550 --> 00:37:06,450
+تقبل alpha في beta
+
+331
+00:37:10,320 --> 00:37:13,860
+الف في بيتا يبقى عن الف واحد الف اتنين لعند الف
+
+332
+00:37:13,860 --> 00:37:18,780
+اتنين ك بيتا واحد بيتا اتنين لعند بيتا اتنين ام في
+
+333
+00:37:18,780 --> 00:37:26,880
+الاول اتنين ام و اتنين ك كده اش عدد هدول اتنين ام
+
+334
+00:37:26,880 --> 00:37:35,800
+زائد ك من الـ two cycles اش يعني الف بيتا is even
+
+335
+00:37:35,800 --> 00:37:43,760
+يبقى الف بيتا وان موجود بسيط بسيط بسيط بسيط بسيط
+
+336
+00:37:43,760 --> 00:37:46,220
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+337
+00:37:46,220 --> 00:37:47,960
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+338
+00:37:47,960 --> 00:37:48,220
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+339
+00:37:48,220 --> 00:37:50,320
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+340
+00:37:50,320 --> 00:38:02,360
+بسيط
+
+341
+00:38:11,190 --> 00:38:22,930
+group of order نسميها الـ group المتذبذبة الـ order
+
+342
+00:38:22,930 --> 00:38:38,750
+تبعها بالساوي عشان
+
+343
+00:38:38,750 --> 00:38:39,210
+انهي
+
+344
+00:38:41,980 --> 00:38:53,240
+الشبتر تبقى نظرية واحدة هي نظرية خمسة سبعة theorem
+
+345
+00:38:53,240 --> 00:38:58,360
+خمسة
+
+346
+00:38:58,360 --> 00:39:03,720
+سبعة الشباب قال الـ a n sub group من الـ sn الـ sn
+
+347
+00:39:03,720 --> 00:39:10,540
+فيها n factorial من العناصر طب والـ a n كمنصر four
+
+348
+00:39:11,900 --> 00:39:20,880
+an أكبر من الواحد order الـ an بيساوي n! على 2 عدد
+
+349
+00:39:20,880 --> 00:39:35,600
+عناصر الـ an بيساوي نص عدد عناصر الـ sn let
+
+350
+00:39:35,600 --> 00:39:47,500
+طبعا clearly for n أكبر من الواحد ان الان sub group
+
+351
+00:39:47,500 --> 00:39:52,380
+من الاسن و proper ليش؟
+
+352
+00:39:52,380 --> 00:40:01,180
+لإن هذه ينتمي لاسن but لا ينتمي لان يعني هي proper
+
+353
+00:40:01,180 --> 00:40:05,900
+هي proper let
+
+354
+00:40:15,840 --> 00:40:21,600
+النتيجة Alpha is even يعني
+
+355
+00:40:21,600 --> 00:40:25,020
+Alpha عبارة عن Alpha واحد Alpha اتنين لعند Alpha
+
+356
+00:40:25,020 --> 00:40:31,080
+اتنين M هذا معناته if
+
+357
+00:40:31,080 --> 00:40:37,750
+Beta بدت ساوي واحد اتنين then Alpha في Beta يساوي
+
+358
+00:40:37,750 --> 00:40:41,290
+Alpha واحد Alpha اتنين لعند Alpha اتنين M طبعا
+
+359
+00:40:41,290 --> 00:40:47,950
+هدول عبارة عن إيش؟ Two cycles لإي Alpha I is two
+
+360
+00:40:47,950 --> 00:40:53,110
+cycle في
+
+361
+00:40:53,110 --> 00:41:00,490
+مين؟ في واحد و اتنين جداش عددهم هدول؟ تنين M زاد
+
+362
+00:41:00,490 --> 00:41:05,550
+الواحد of two cycles ايش يعني يا شباب؟
+
+363
+00:41:09,000 --> 00:41:16,580
+مش يعني؟ معناته Alpha Beta ايش مالها؟ is odd
+
+364
+00:41:16,580 --> 00:41:23,580
+permutation أخدت
+
+365
+00:41:23,580 --> 00:41:28,180
+انا even permutation وضربت في Beta طلعت Alpha في
+
+366
+00:41:28,180 --> 00:41:32,680
+Beta ايش؟ odd permutation يعني لكل permutation
+
+367
+00:41:32,680 --> 00:41:40,310
+even في جبالة واحدة odd طيب نعمل العكس if مثلا
+
+368
+00:41:40,310 --> 00:41:46,690
+gamma is odd permutation
+
+369
+00:41:46,690 --> 00:41:53,050
+ان أسأل يعني gamma مثلا عبارة عن gamma واحد gamma
+
+370
+00:41:53,050 --> 00:41:57,690
+اتنين لأن gamma اتنين k زاد الواحد النتيجة gamma
+
+371
+00:41:57,690 --> 00:42:01,970
+beta gamma واحد gamma اتنين لأن gamma اتنين k زاد
+
+372
+00:42:01,970 --> 00:42:08,250
+الواحد في واحد واتنين طبعا هدولة gamma jis two
+
+373
+00:42:08,250 --> 00:42:20,410
+cycle جداش عددهم هدول 2k زي 2 of two cycles يعني
+
+374
+00:42:20,410 --> 00:42:30,070
+gamma beta is even لكل واحدة even في واحدة odd لكل
+
+375
+00:42:30,070 --> 00:42:32,990
+واحدة odd في واحدة even ايش يعني
+
+376
+00:42:37,790 --> 00:42:42,150
+يعني عدد ال even بيساوي عدد ال odd تنساش أنه مافيش
+
+377
+00:42:42,150 --> 00:42:47,670
+واحدة even أو مافيش اثنتين even مختلفتين بيروحوا 
+
+378
+00:42:47,670 --> 00:42:51,330
+لاثنتين odd زي بعض يعني مافيش اثنتين even بيروحوا
+
+379
+00:42:51,330 --> 00:42:56,210
+لنفس ال odd لأنني أضاعف مين؟ في أنصر يعني لو كان
+
+380
+00:42:56,210 --> 00:43:01,930
+مثلا الف واحد beta بيساوي الف اثنين beta فالواحد
+
+381
+00:43:01,930 --> 00:43:06,830
+بيساوي الف اثنين فال even بيروح ل distinct even
+
+382
+00:43:06,830 --> 00:43:11,350
+بيروح ل distinct odd و distinct odd بيروح ليش ل
+
+383
+00:43:11,350 --> 00:43:18,430
+distinct even هذا معناه for any even permutation
+
+384
+00:43:18,430 --> 00:43:22,350
+there
+
+385
+00:43:22,350 --> 00:43:26,910
+is another
+
+386
+00:43:26,910 --> 00:43:45,740
+odd one and for any odd one we have another even 
+
+387
+00:43:45,740 --> 00:43:51,160
+one  ايش يعني؟ يعني عدد ال even بيساوي عدد ال odd
+
+388
+00:43:51,160 --> 00:43:54,820
+يعني
+
+389
+00:43:54,820 --> 00:44:01,700
+عدد ال even permutation بيساوي عدد ال odd 
+
+390
+00:44:02,670 --> 00:44:10,010
+permutation وبالتالي عدد ال even permutation مودي
+
+391
+00:44:10,010 --> 00:44:17,310
+يساوي نصف order ال sn يكفي order ال an مودي يساوي
+
+392
+00:44:17,310 --> 00:44:23,930
+order ال sn على اثنين يعني n! على اثنين وهو
+
+393
+00:44:23,930 --> 00:44:24,710
+المطلوب
+
+394
+00:44:35,020 --> 00:44:39,900
+طبعا عشان أنهي المحاضرة مثال لو قلنا ال S ثلاثة
+
+395
+00:44:39,900 --> 00:44:43,620
+مين
+
+396
+00:44:43,620 --> 00:44:52,100
+هي ال identity واحد و اثنين واحد و ثلاثة اثنين و
+
+397
+00:44:52,100 --> 00:44:58,780
+ثلاثة واحد و اثنين و ثلاثة واحد و ثلاثة اثنين من
+
+398
+00:44:58,780 --> 00:45:03,120
+ال AN مين
+
+399
+00:45:03,120 --> 00:45:09,750
+من هدول زوجيالـ Identity هذا فردي هذا فردي هذا
+
+400
+00:45:09,750 --> 00:45:16,750
+فردي بل واحد و اثنين و ثلاثة والواحد و ثلاثة و
+
+401
+00:45:16,750 --> 00:45:25,870
+اثنين بدي أسألك سؤال هل ال A ثلاثة ال A ثلاثة
+
+402
+00:45:25,870 --> 00:45:32,150
+Cyclic ولا مش Cyclic Cyclic
+
+403
+00:45:32,150 --> 00:45:37,910
+هذه Generated by واحد اثنين ثلاثة لحظة أن ال S
+
+404
+00:45:37,910 --> 00:45:45,410
+ثلاثة مش Abelian لكن ال A ثلاثة كانت ايش كانت
+
+405
+00:45:45,410 --> 00:45:50,070
+Cyclic هل هذا الكلام دائما صحيح لأ ال AN ما تكون
+
+406
+00:45:50,070 --> 00:45:57,470
+Abelian أصلا واضح؟ يا عظيم العافية هيك نهاية of
+
+407
+00:45:57,470 --> 00:45:58,910
+chapter خمسة
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6bc53ec3a607833cfaf72fab8268276fc278d852
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_postprocess.srt
@@ -0,0 +1,1628 @@
+1
+00:00:21,240 --> 00:00:24,600
+السلام عليكم باسم الله الرحمن الرحيم هنكمل ان شاء
+
+2
+00:00:24,600 --> 00:00:27,200
+الله في الجزء التالت من ال chapter خمسة chapter
+
+3
+00:00:27,200 --> 00:00:30,980
+permutation groups اخر حاجة اتكلمنا عنها نظرية
+
+4
+00:00:30,980 --> 00:00:34,560
+خمسة اتنين اللي كانت بتتناول التالي انه لو كان
+
+5
+00:00:34,560 --> 00:00:40,220
+عندي two permutations و هدولة كانوا disjoint فهم
+
+6
+00:00:40,220 --> 00:00:44,620
+ايش مالهم متبادلين متبادلين يعني commuted العملية
+
+7
+00:00:44,620 --> 00:00:48,840
+بينهم تبادلية نظرية خمسة تلاتة بتتناول ال order
+
+8
+00:00:49,950 --> 00:00:56,750
+لحاصل ضرب to permutation the order طبعا ال session
+
+9
+00:00:56,750 --> 00:01:01,310
+ان انا باشتغل وين في finite groups ان انا باشتغل
+
+10
+00:01:01,310 --> 00:01:04,530
+على permutation على finite set فعددها على ال أكتر
+
+11
+00:01:04,530 --> 00:01:11,630
+يعني 10 factorial فال order لأي عنصر finite the
+
+12
+00:01:11,630 --> 00:01:17,370
+order of a
+
+13
+00:01:17,370 --> 00:01:18,010
+permutation
+
+14
+00:01:24,100 --> 00:01:34,240
+of a finite set written as
+
+15
+00:01:34,240 --> 00:01:39,940
+a product of
+
+16
+00:01:39,940 --> 00:01:43,060
+disjoint
+
+17
+00:01:43,060 --> 00:01:51,480
+cycles is the least common
+
+18
+00:01:56,090 --> 00:02:08,350
+multiple of the length of
+
+19
+00:02:08,350 --> 00:02:13,870
+the
+
+20
+00:02:13,870 --> 00:02:14,370
+cycles
+
+21
+00:02:18,440 --> 00:02:22,600
+يعني لو كان عندي permutation و أنا كتبت على شكل
+
+22
+00:02:22,600 --> 00:02:26,840
+disjoint cycles فال order اللي هيبقى عبارة عن ال
+
+23
+00:02:26,840 --> 00:02:30,120
+least common multiple لهذه الأطوال
+
+24
+00:02:34,080 --> 00:02:37,880
+طبعا اهمية النظرية هذه عشان انا اقدر اعرف اغضر اي
+
+25
+00:02:37,880 --> 00:02:42,480
+permutation باخليها عبارة عن cycle destroyed و
+
+26
+00:02:42,480 --> 00:02:44,580
+باخد meaning least common multiple على طول من دون
+
+27
+00:02:44,580 --> 00:02:50,940
+مرض اجرب الف واحد الف اوس اتنين الف الاخر if الف
+
+28
+00:02:50,940 --> 00:02:59,840
+عبارة عن ا واحد اتنين and an is anyand cycle لما
+
+29
+00:02:59,840 --> 00:03:03,260
+اقول and cycle يعني عبارة عن permutation مكوّن من
+
+30
+00:03:03,260 --> 00:03:09,080
+cycle واحدة وعدد عناصرها and then order ال alpha
+
+31
+00:03:09,080 --> 00:03:15,880
+بدو يساوي ايش and طبعا ال ال ال alpha عشان اوصله
+
+32
+00:03:15,880 --> 00:03:18,780
+ال identity لازم اقوم باجراءها من المرة ان هو
+
+33
+00:03:18,780 --> 00:03:26,180
+عبارة عن ايش دور ما عشان ارجع العنصر لمكانه بحتاج
+
+34
+00:03:26,180 --> 00:03:31,540
+ايشان من الدورات لان هنا a بيروح ل a1 ل a2 و a2
+
+35
+00:03:31,540 --> 00:03:35,800
+بيروح ل a3 لما أعمل الف في الف فهيصير a1 يروح لمين
+
+36
+00:03:35,800 --> 00:03:42,120
+ل a3 كمان لف a1 هيروح ل a4 بعد ان من اللفات a1
+
+37
+00:03:42,120 --> 00:03:47,140
+هيصير يروح لمين ل a1 و هيرجع مكانه طيب هذه انا
+
+38
+00:03:47,140 --> 00:03:53,560
+هثبتها ل two cycles و بعد هيك التعميم تبعها بسيرة
+
+39
+00:03:53,560 --> 00:04:02,200
+القائمة we willproof this
+
+40
+00:04:02,200 --> 00:04:13,140
+result for a permutation consists
+
+41
+00:04:13,140 --> 00:04:19,940
+of two disjoint
+
+42
+00:04:19,940 --> 00:04:23,280
+cycles
+
+43
+00:04:23,280 --> 00:04:25,780
+يعني
+
+44
+00:04:30,100 --> 00:04:37,980
+we show that if order للألفة بدي ساوي M order
+
+45
+00:04:37,980 --> 00:04:44,320
+للبيتا بدي ساوي N then order للألفة في بيتا بدي
+
+46
+00:04:44,320 --> 00:04:50,740
+ساوي least common multiple ل M1 طبعا لو انا اثبتت
+
+47
+00:04:50,740 --> 00:04:57,260
+تلتين تين لما بدي اجيب واحدة تالتةبأخد ال least
+
+48
+00:04:57,260 --> 00:05:00,720
+common multiple التنتين مع التالتة لو بدنا نضيف
+
+49
+00:05:00,720 --> 00:05:07,760
+واحدة رابعة بيصير عملية عملية تكرارية assume that
+
+50
+00:05:07,760 --> 00:05:13,620
+ان order ال alpha بيتا بيدي ساوي T وان ال least
+
+51
+00:05:13,620 --> 00:05:19,440
+common multiple ل M و N بيساوي K
+
+52
+00:05:23,100 --> 00:05:28,120
+المطلوب اثبت ان انا اياش ان K بدي ساوي T شوف انتقل
+
+53
+00:05:28,120 --> 00:05:35,140
+الاثبات من جملة لفظية و قصة طويلة لاياش لاثبات انه
+
+54
+00:05:35,140 --> 00:05:40,100
+عقامين متساوين now since
+
+55
+00:05:40,100 --> 00:05:46,600
+Alpha و Beta are disjoint then
+
+56
+00:05:52,960 --> 00:06:02,840
+الفا بيتا بتسويش بيتا الفا so لو
+
+57
+00:06:02,840 --> 00:06:12,840
+انا رفعت الالفا بيتا ل k هذا عبارة عن الفا اص ك في
+
+58
+00:06:12,840 --> 00:06:17,740
+بيتا اص ك but
+
+59
+00:06:19,670 --> 00:06:25,710
+ال K عبارة عن ال least م multiple ل M و N يعني ال
+
+60
+00:06:25,710 --> 00:06:32,990
+K عبارة عن multiple ل M مثلا M في اختارة في R وهي
+
+61
+00:06:32,990 --> 00:06:39,930
+نفسها ال N في S يكبر Alpha Beta أس K عبارة عن إيش؟
+
+62
+00:06:41,610 --> 00:06:47,750
+عن Alpha أُس K Beta أُس K يعني Alpha أُس MR في
+
+63
+00:06:47,750 --> 00:06:54,390
+Beta أُس N S يعني Alpha أُس M أُس R Beta أُس N أُس
+
+64
+00:06:54,390 --> 00:06:59,390
+S يعني Identity أُس R في Identity أُس S إيش
+
+65
+00:06:59,390 --> 00:07:04,290
+بيعطيني؟ معناته ال Alpha Beta أُس K
+
+66
+00:07:07,390 --> 00:07:11,270
+بدي يساوي ال identity ايك ب order ال alpha beta
+
+67
+00:07:11,270 --> 00:07:23,330
+اللي هو عبارة عن ال T بيقسم ال K ال T بتقسم
+
+68
+00:07:23,330 --> 00:07:28,630
+ال K now order
+
+69
+00:07:28,630 --> 00:07:34,970
+ال alpha beta عبارة عن مين؟عن الـ T يعني الـ Alpha
+
+70
+00:07:34,970 --> 00:07:40,190
+Beta أس T بدي يساوي ال identity يعني Alpha أس T
+
+71
+00:07:40,190 --> 00:07:46,730
+لاحظ انه انهم disjoint هو اللي سهل عملية رفع للأس
+
+72
+00:07:46,730 --> 00:07:53,490
+T و رفع للأس K هذا بدي يساوي ايش identity يعني ال
+
+73
+00:07:53,490 --> 00:08:01,190
+Alpha أس T بدي يساوي Beta أس ثالث T طيب
+
+74
+00:08:04,500 --> 00:08:14,720
+Alpha and beta are disjoint لما
+
+75
+00:08:14,720 --> 00:08:19,880
+يكون عندك two cycles و disjoint يعني عناصر ال
+
+76
+00:08:19,880 --> 00:08:25,980
+alpha غير عناصر ال betaفجد ما تلف ال alpha و تلف
+
+77
+00:08:25,980 --> 00:08:30,040
+ال beta مش هتلاقي عناصر مشتركة إلا في حالة واحدة
+
+78
+00:08:30,040 --> 00:08:34,260
+لما هاد تلف و تصل ال identity و هاد تلف و تصل ال
+
+79
+00:08:34,260 --> 00:08:45,850
+identity So we must have thatالـ α أُس T بيبقى
+
+80
+00:08:45,850 --> 00:08:49,290
+تساوي الـ Beta أُس سالب T بيبقى تساوي الـ Identity
+
+81
+00:08:49,290 --> 00:08:53,710
+Alpha أُس T بيبقى تساوي الـ Identity Beta أُس T
+
+82
+00:08:53,710 --> 00:08:58,710
+أُس سالب T بيبقى تساوي الـ Identity Alpha أُس T بـ
+
+83
+00:08:58,710 --> 00:09:06,190
+Identity Beta أُس T بـ Identity يقبل M بيقسم الـ T
+
+84
+00:09:06,190 --> 00:09:12,830
+Order الـ Alpha بيبقى تساوي M بيقسم الـ T Order ال
+
+85
+00:09:12,830 --> 00:09:20,870
+Betaبدي ساوي N بيقسم مين ال T معناته ال T is a
+
+86
+00:09:20,870 --> 00:09:24,710
+common multiple
+
+87
+00:09:24,710 --> 00:09:33,830
+of M and N معناته ال least common multiple ل M و N
+
+88
+00:09:33,830 --> 00:09:39,610
+اللي هو عبارة عن K بيقسم ال T و أعطيها 2 هذه جهة
+
+89
+00:09:39,610 --> 00:09:43,050
+ال T بيقسم ال K ال K بيقسم ال T
+
+90
+00:10:01,620 --> 00:10:07,420
+وهو المطلوب اثبته وهو
+
+91
+00:10:07,420 --> 00:10:11,700
+المطلوب اثبتهطبعا هنا لو كانوا تنتين لو كانوا
+
+92
+00:10:11,700 --> 00:10:15,740
+تلاتة لو كانوا اربعة لو كانوا اي عدد هكون تعاميم
+
+93
+00:10:15,740 --> 00:10:28,580
+لهذه النتيجة واضح مش
+
+94
+00:10:28,580 --> 00:10:34,460
+ال identity function طيب
+
+95
+00:10:41,400 --> 00:10:45,300
+مش فاهم صحيح
+
+96
+00:10:45,300 --> 00:10:48,740
+power
+
+97
+00:10:48,740 --> 00:10:54,020
+من ال alphaهيجيب طالع معايا ال alpha الأخضر يلها M
+
+98
+00:10:54,020 --> 00:10:57,920
+ف alpha أُس M مش بيساوي طيب و ال beta الأخضر يلها
+
+99
+00:10:57,920 --> 00:11:02,280
+N ف beta أُس N مش بيساوي هاي power لل alpha و
+
+100
+00:11:02,280 --> 00:11:05,500
+power لل beta تساوى لكن ال alpha و ال beta و كل ال
+
+101
+00:11:05,500 --> 00:11:12,080
+powers مع ده الحالة الخاصة هذه إن المضاعفات ال M و
+
+102
+00:11:12,080 --> 00:11:15,880
+ال N مع بعض مش هيتساوى طيب أحنا ال power أشمل أن
+
+103
+00:11:15,880 --> 00:11:17,840
+أنتوا من أول مرة بتعطيني اللي بعد و أتاني بتعطيني
+
+104
+00:11:17,840 --> 00:11:18,120
+اللي بعد
+
+105
+00:11:22,370 --> 00:11:27,990
+هجيت Alpha بتاخد ال A1 ل A2 و ال A2 ل ال A3 لما
+
+106
+00:11:27,990 --> 00:11:32,530
+أحسب Alpha تربيه هتصير تاخد ال A1 ل A3 Alpha أُص
+
+107
+00:11:32,530 --> 00:11:38,670
+أربعة ل A1 ل A4 هجيت Alpha أُص N هتاخد ال A1 و تلف
+
+108
+00:11:38,670 --> 00:11:45,130
+و يترج و لمين ل A1و ال a2 هتلف و ترج ولا مين؟ ل ال
+
+109
+00:11:45,130 --> 00:11:48,970
+a2 و ال a3 ل ال a .. يعني انت حصلت على ال identity
+
+110
+00:11:48,970 --> 00:11:52,070
+عشان ال order لل alpha n مثلا او حتى .. حتى ان ال
+
+111
+00:11:52,070 --> 00:11:57,690
+order M فانت بتكلم عن مين؟ عن أُس M واضح؟ القصد
+
+112
+00:11:57,690 --> 00:12:01,550
+هنا أن ال alpha و ال beta مش متساويينلكن في power
+
+113
+00:12:01,550 --> 00:12:05,050
+للألفة و power للبيتا بيعطيك ال identity يعني مثلا
+
+114
+00:12:05,050 --> 00:12:11,690
+في z7 او بلاش z7 زد عشرين هل التلاتة و السبعة و ال
+
+115
+00:12:11,690 --> 00:12:16,950
+.. و ال .. و ال 11 متساوين لكن في power للتلاتة و
+
+116
+00:12:16,950 --> 00:12:19,830
+في power لل11 طبعا أنا بتكلم عن power بتكلم عن
+
+117
+00:12:19,830 --> 00:12:24,510
+multiple هنا بتوديهم ل 100 للصفر او بتوديهم ل .. ل
+
+118
+00:12:24,510 --> 00:12:27,250
+.. لقيم ما لكن هم نفسهم مش متساوين
+
+119
+00:12:45,760 --> 00:12:51,420
+كمثال لو أخدنا ال alpha تبعت الصبح اللي كانت عبارة
+
+120
+00:12:51,420 --> 00:12:57,600
+عن نجلونيها اللي كتبناها الصبح اللي كانت عبارة عن
+
+121
+00:12:57,600 --> 00:13:04,220
+تمانية cycles كتبناها
+
+122
+00:13:04,220 --> 00:13:10,200
+الصبح في المثال المكان هذا 123
+
+123
+00:13:13,750 --> 00:13:17,930
+خمسة، ستة، تمانية، أربعة الـ O ضل الألف جديش يا
+
+124
+00:13:17,930 --> 00:13:22,310
+شباب تمانية، عدد عنصرها، واحد، اتنين، تلاتة،
+
+125
+00:13:22,310 --> 00:13:25,910
+اربعة، خمسة، ستة، سبعة، تمانية طب ال beta إيش
+
+126
+00:13:25,910 --> 00:13:31,750
+كانت؟ نفس السؤال، نفس المثال، أظن واحد و اتنين
+
+127
+00:13:31,750 --> 00:13:41,470
+واحد لحالها هدول
+
+128
+00:13:41,470 --> 00:13:45,900
+مالهم مش لازمة طبعافال order لل beta عبارة عن ال
+
+129
+00:13:45,900 --> 00:13:51,640
+least common multiple لمن؟ ل order هذه كم؟ أربع و
+
+130
+00:13:51,640 --> 00:13:56,160
+order هذه كم؟ ال least common multiple كم؟ أربع
+
+131
+00:14:18,400 --> 00:14:24,420
+نظرية 5-4 يا جد شباب اي permutation بقدر اكتبها
+
+132
+00:14:24,420 --> 00:14:29,700
+على شكل حاصل ضرب disjoint cycles هل بقدر اتحكم في
+
+133
+00:14:29,700 --> 00:14:34,400
+طول ال cycle لو شلت شرط ال disjoint؟ يعني انا بدي
+
+134
+00:14:34,400 --> 00:14:37,840
+اسدد و اقارب عشان احصل على نتائج في كل حالة عشان
+
+135
+00:14:37,840 --> 00:14:41,040
+اكتبها على شكل disjoint بستفيد جثة التبديل و جثة
+
+136
+00:14:41,040 --> 00:14:44,670
+ال orderلكن انا هجيت مش محتاج ال order و التبديل
+
+137
+00:14:44,670 --> 00:14:51,030
+محتاج شغلات هنعرفها كمان شوية هل بقدر اتحكم في طول
+
+138
+00:14:51,030 --> 00:14:54,250
+ال
+
+139
+00:14:54,250 --> 00:14:58,730
+permutation لو خدت permutation طولها اتنين بقدر
+
+140
+00:14:58,730 --> 00:15:04,950
+اخليه تلاتة لأ واحد و اتنين كيف بقدر اخليه تلاتة
+
+141
+00:15:04,950 --> 00:15:09,980
+مش هتقدر تضيفي شيء يكبرلو كان عندك permutation
+
+142
+00:15:09,980 --> 00:15:14,540
+تلاتة تقدر تخليها permutation اتنين مثلا واحد
+
+143
+00:15:14,540 --> 00:15:18,400
+اتنين تلاتة الواحد اتنين تلاتة انا ممكن اخليها
+
+144
+00:15:18,400 --> 00:15:24,920
+واحد تلاتة واحد اتنين و جرب واحد بيروح للتنين و
+
+145
+00:15:24,920 --> 00:15:27,520
+اتنين بيروح للنفس يجب واحد ده التنين تنين بيروح
+
+146
+00:15:27,520 --> 00:15:29,820
+للواحد واحد بيروح للتلاتة و اتنين بيروح للتلاتة
+
+147
+00:15:29,820 --> 00:15:33,780
+تلاتة لنفسه و تلاتة للواحد يجب تلاتة للواحديكبر لو
+
+148
+00:15:33,780 --> 00:15:38,220
+كانت الأرض يعني الطول أكتر من اتنين أنا ممكن أنزله
+
+149
+00:15:38,220 --> 00:15:42,360
+اتنين لكن صعب أني أرفع من صغير لكبير يكبر أنا
+
+150
+00:15:42,360 --> 00:15:46,560
+بإمكاني أتحكم و أخلي أي permutation لما أكتبها على
+
+151
+00:15:46,560 --> 00:15:50,160
+شكل disjoint cycles أروح ال disjoint cycles هدول
+
+152
+00:15:50,160 --> 00:15:55,440
+عملهم لحاجة احنا بتسميها two cycles هذه نظرية خمسة
+
+153
+00:15:55,440 --> 00:15:57,740
+أربعة بتقولك اي permutation
+
+154
+00:16:07,210 --> 00:16:16,990
+ن أسن حيث أن أكبر من الواحد can be written
+
+155
+00:16:16,990 --> 00:16:29,470
+as a product of two cycles two cycles يعني عبارة
+
+156
+00:16:29,470 --> 00:16:33,550
+عن إيش؟ عن cycle طول طبعها كم؟ اتنين
+
+157
+00:16:38,270 --> 00:16:47,570
+اثبات سهل و مباشر proof اولش ال identity ال
+
+158
+00:16:47,570 --> 00:16:56,370
+identity ممكن اكتبها 1 2 2 1 طبعا اجهزة كله من
+
+159
+00:16:56,370 --> 00:17:00,610
+تلاتة و فور بيروح لنفسه انه مش مذكور هنا بيظل
+
+160
+00:17:00,610 --> 00:17:05,270
+الواحد والتانين هذا بمكانك تعمله زي هيك واحد بيروح
+
+161
+00:17:05,270 --> 00:17:08,340
+للتانين والتانين بيروح للواحد يكبر واحد لواحدو
+
+162
+00:17:08,340 --> 00:17:16,240
+اتنين ل اتنين وبالتالي صار ال identity طيب now if
+
+163
+00:17:16,240 --> 00:17:23,380
+alpha عبارة عن a1 a2 اللي عند at او ak في b1 b2
+
+164
+00:17:23,380 --> 00:17:31,240
+اللي عند pm في c1 c2 اللي عند cn كيبلك خلية two
+
+165
+00:17:31,240 --> 00:17:38,500
+cycles تعمل التاليبتبدأ أول عنصر تاخده مع الأخير
+
+166
+00:17:38,500 --> 00:17:41,740
+بعدين
+
+167
+00:17:41,740 --> 00:17:50,080
+أول عنصر مع قبل الأخير وبتضلك شغال لما تصل مين ا
+
+168
+00:17:50,080 --> 00:17:56,480
+واحد مع اتنين تجي على ال B أول واحد مع الأخير أول
+
+169
+00:17:56,480 --> 00:18:03,510
+واحد مع قبل الأخير وبتضلك لما بتجيبه مع مينمع
+
+170
+00:18:03,510 --> 00:18:12,370
+التاني و بضلك نازل لما تصل لآخر cycle و
+
+171
+00:18:12,370 --> 00:18:16,090
+هدول
+
+172
+00:18:16,090 --> 00:18:24,090
+عبارة عن ايش كلهم cycles طولهم جديش اتنين ال
+
+173
+00:18:24,090 --> 00:18:28,190
+disjoint مش موجود هان انا هان بلزمنيش ال disjoint
+
+174
+00:18:29,650 --> 00:18:34,210
+بالزمن مين؟ فقط أني أكتب عليه شكل two cycles ليش؟
+
+175
+00:18:34,210 --> 00:18:39,730
+لأنه هعرف كمان شوية حاجة اسمها even permutation أو
+
+176
+00:18:39,730 --> 00:18:48,650
+odd permutation كمثال الألف ها دي واحد اتنين سبعة
+
+177
+00:18:48,650 --> 00:18:55,310
+تلاتة خمسة ستة تمانية أربع ممكن نكتبها واحد أربع
+
+178
+00:18:55,310 --> 00:19:05,390
+واحد تمانية واحد ستة واحد خمسة1 3 1 7 1 2 طبعا في
+
+179
+00:19:05,390 --> 00:19:08,430
+الدار جرب و حسبها هل هدول لما تضربهم بيعطوك هذي
+
+180
+00:19:08,430 --> 00:19:21,130
+ولا لأ ايضا ال beta اللي عبارة عن 2 4 3 5 6 7 2 5
+
+181
+00:19:21,130 --> 00:19:25,850
+2 3 2 4 وهذه جاهزة
+
+182
+00:19:28,510 --> 00:19:38,030
+أدوش محتاجة حسابات لما
+
+183
+00:19:56,270 --> 00:19:59,990
+هذه اللمة هناخدها بدون اثبات هنحتاجها في اثبات
+
+184
+00:19:59,990 --> 00:20:04,630
+شغلة قادمة او نظرية لبعدها اللمة هذه بتقول ال
+
+185
+00:20:04,630 --> 00:20:09,830
+identity لو جدرت تكتب على شكل two cycles فعدد ال
+
+186
+00:20:09,830 --> 00:20:15,310
+two cycles هذا لازم يكون زوجي ال identity لو جدرت
+
+187
+00:20:15,310 --> 00:20:19,430
+تكتب على شكل two cycles عدد ال two cycles هدول
+
+188
+00:20:19,430 --> 00:20:26,110
+هيكون زوجي ifالـ identity عبارة عن ألف واحد ألف
+
+189
+00:20:26,110 --> 00:20:38,490
+اتنين لعند ألف مثلا R is a product of two cycles
+
+190
+00:20:38,490 --> 00:20:46,050
+then R is even لو
+
+191
+00:20:46,050 --> 00:20:50,590
+جدرت تكتب عيد ال identity على شكل two cycles فعدد
+
+192
+00:20:50,590 --> 00:20:56,220
+ال two cycles هدون لازم يكونزوجي أهميتها هي نظرية
+
+193
+00:20:56,220 --> 00:21:02,560
+5-5 theorem 5
+
+194
+00:21:02,560 --> 00:21:12,000
+-5 في نظرية 5-5 لو جدرت تكتب permutation بطريقتين
+
+195
+00:21:12,000 --> 00:21:18,380
+على شكل two cycles لو جدرت تكتب permutation على
+
+196
+00:21:18,380 --> 00:21:20,420
+شكل two cycles بطريقتين
+
+197
+00:21:23,020 --> 00:21:26,980
+و عديت ال two cycles في الطريقة الأولى و عديت ال
+
+198
+00:21:26,980 --> 00:21:32,320
+two cycles في الطريقة التانية ياتنين
+
+199
+00:21:32,320 --> 00:21:42,040
+even ياتنين odd if Alpha عبارة عن Alpha 1 Alpha 2
+
+200
+00:21:42,040 --> 00:21:49,780
+لعند Alpha R وهي نفسها Beta 1 Beta 2 لعند Beta S
+
+201
+00:21:49,780 --> 00:21:51,780
+where
+
+202
+00:21:53,300 --> 00:22:06,400
+أو is a product of two cycles in two ways then
+
+203
+00:22:06,400 --> 00:22:21,360
+both are and is even or both are
+
+204
+00:22:21,360 --> 00:22:28,740
+oddيعني لو كتبت ال permutation على شكل two cycles
+
+205
+00:22:28,740 --> 00:22:35,260
+وضعتها زيكي لكي أميزها بطريقتين فعدد ال two cycles
+
+206
+00:22:35,260 --> 00:22:38,340
+في الأولى وعدد ال two cycles في التانية يا اتنين
+
+207
+00:22:38,340 --> 00:22:46,980
+زوجي يا اتنين فردي ولا حاجة since Alpha بدي ساوي
+
+208
+00:22:46,980 --> 00:22:51,920
+Alpha واحد Alpha اتنين لعند Alpha R هو نفسه Beta
+
+209
+00:22:51,920 --> 00:23:01,010
+واحد Beta اتنينلأن BTS أجد شباب ال two cycle
+
+210
+00:23:01,010 --> 00:23:10,430
+الأخضر غير هجد دياش اتنين since
+
+211
+00:23:10,430 --> 00:23:24,540
+Alpha I عبارة عن a1i a2iوبيتا جي عبارة عن بي واحد
+
+212
+00:23:24,540 --> 00:23:31,200
+جي بيتينين جي النتيجة order لالف اي بيسوي order
+
+213
+00:23:31,200 --> 00:23:36,820
+لبيتا جي بيسوي اتنين لكل اي اقل او يسوي ار جي اقل
+
+214
+00:23:36,820 --> 00:23:44,500
+او يسوي اس هذا معناته ان الف اي بيسوي الف اي
+
+215
+00:23:44,500 --> 00:23:50,740
+inverse وبيتا جي بيسوي بيتا جي inverseيعني ال
+
+216
+00:23:50,740 --> 00:23:53,820
+permutation اللي على شكل two cycles الميزة تبعتهم
+
+217
+00:23:53,820 --> 00:24:00,620
+ان ال inverse تبعهم هو نفسهم هجت نقو الف واحد الف
+
+218
+00:24:00,620 --> 00:24:07,200
+اتنين الف ار بيتا واحد بيتا اتنين بيتاس اضرب في ال
+
+219
+00:24:07,200 --> 00:24:10,120
+inverse تبعه دول حاسيب معايا الف واحد الف اتنين
+
+220
+00:24:10,120 --> 00:24:16,230
+الف ار طبعا احنا بنضرب ايش؟عكسي Beta S inverse
+
+221
+00:24:16,230 --> 00:24:20,670
+Beta S minus واحد inverse لعين Beta واحد inverse
+
+222
+00:24:20,670 --> 00:24:25,490
+هذا حساو مين اللي هو عبارة عن Alpha واحد Alpha
+
+223
+00:24:25,490 --> 00:24:31,470
+اتنين Alpha R Beta S Beta S minus واحد Beta واحد
+
+224
+00:24:31,470 --> 00:24:38,150
+ايش بتساوي ال identity هذا معناته ان R زائد S is
+
+225
+00:24:38,150 --> 00:24:40,450
+even هذا by مين
+
+226
+00:24:43,820 --> 00:24:50,880
+طيب لما؟ لإنه صار ال identity حاصل ضرب two cycles
+
+227
+00:24:50,880 --> 00:24:57,360
+عددهم جديش؟ R زياد S حسب اللي لما لازم ال R زياد S
+
+228
+00:24:57,360 --> 00:25:03,500
+يكون even معناته both عشان يكون عندك عددين مجموعهم
+
+229
+00:25:03,500 --> 00:25:15,340
+زوجي يتنين even يتنين odd both R and Sare even or
+
+230
+00:25:15,340 --> 00:25:25,040
+both are good يا اتنين زوجي، يا اتنين اشمالهم فادي
+
+231
+00:25:25,040 --> 00:25:31,300
+طب
+
+232
+00:25:31,300 --> 00:25:35,160
+ايش الأهمية هنا؟
+
+233
+00:25:35,160 --> 00:25:40,820
+انه اي permutation لما حطها كcycles two cycles
+
+234
+00:25:42,410 --> 00:25:46,530
+الحالة تبع ال even و ال odd ثابتة دائما مدامها
+
+235
+00:25:46,530 --> 00:25:51,950
+ثابتة بإمكاني انا ارفق الحالة بالانصر يعني اقول
+
+236
+00:25:51,950 --> 00:25:56,790
+مدامه حاصل ضرب even number of two cycles هقول عنه
+
+237
+00:25:56,790 --> 00:26:00,410
+even و مدامه حاصل ضرب odd number of two cycles
+
+238
+00:26:00,410 --> 00:26:09,910
+هقول عنه ايش odd هيطلع معايا تعريف كالتالي ال
+
+239
+00:26:09,910 --> 00:26:10,550
+permutation
+
+240
+00:26:15,680 --> 00:26:31,380
+الفا is called even بنفس النمط odd permutation if
+
+241
+00:26:31,380 --> 00:26:41,580
+الفا can be written as a product of
+
+242
+00:26:42,410 --> 00:26:50,110
+even في حالة ال odd odd number of
+
+243
+00:26:50,110 --> 00:26:56,450
+two cycles يعني انا لو اقدرت اكتب ال permutation
+
+244
+00:26:56,450 --> 00:27:02,910
+على شكل عدد معين من ال two cycles هذا العدد لو كان
+
+245
+00:27:02,910 --> 00:27:07,090
+even بقول عن ال permutation even لو كان هذا العدد
+
+246
+00:27:07,090 --> 00:27:14,350
+odd بقول عن ال permutationلنرجع للمثال تبع توي ال
+
+247
+00:27:14,350 --> 00:27:22,270
+alpha اللي كانت واحد اتنين سبعة تلاتة و
+
+248
+00:27:22,270 --> 00:27:27,810
+ال beta طبعا هذه انكتبت خمسة ستة تمانية اربعة
+
+249
+00:27:27,810 --> 00:27:33,790
+كتبناها واحد اربعة واحد تمانية واحد ستة واحد خمسة
+
+250
+00:27:33,790 --> 00:27:38,930
+واحد تلاتة واحد سبعة واحد اتنين كانتش عددهم هدول
+
+251
+00:27:40,550 --> 00:27:49,350
+seven two cycles بألف a شمالها odd لكن ال beta
+
+252
+00:27:49,350 --> 00:27:55,410
+اللي كانت عبارة عن اتنين اتنين
+
+253
+00:27:55,410 --> 00:28:00,690
+اربعة تلاتة خمسة يعني اتنين خمسة اتنين تلاتة اتنين
+
+254
+00:28:00,690 --> 00:28:04,090
+اربعة ستة سبعة beta اشمالها
+
+255
+00:28:06,520 --> 00:28:15,720
+even هدول قداش for two cycles فكانت ال beta ال
+
+256
+00:28:15,720 --> 00:28:27,040
+beta شمالها even طبعا
+
+257
+00:28:27,040 --> 00:28:35,860
+مثال تاني ال identity is even allowedال identity
+
+258
+00:28:35,860 --> 00:28:42,180
+شوية بس ال permutation بتكون even إذا كتبت على شكل
+
+259
+00:28:42,180 --> 00:28:47,060
+عدد زوجي من ال two cycles طب ال permutation اللي
+
+260
+00:28:47,060 --> 00:28:57,180
+هي ال identity أكم two cycles كتبناها is even
+
+261
+00:28:57,180 --> 00:29:05,750
+by لما أصلا ال identity ممكن تكتبها زي هيكهذا هو
+
+262
+00:29:05,750 --> 00:29:19,850
+even number of two cycles أصارت ايش even نرجع
+
+263
+00:29:19,850 --> 00:29:30,830
+للألف تبع التوي find
+
+264
+00:29:30,830 --> 00:29:34,070
+alpha inverse
+
+265
+00:29:48,860 --> 00:29:53,000
+دعالوا ناخد هذه كمثال مشتق من القاعدة أصلا ال
+
+266
+00:29:53,000 --> 00:30:07,440
+alpha عبارة عن 1 2 او 1 4 1 8 1 6 1 5 1 3 1 7 1 2
+
+267
+00:30:07,440 --> 00:30:14,860
+ال alpha inverse عبارة عن مين؟عن واحد اربع واحد
+
+268
+00:30:14,860 --> 00:30:21,020
+تمانية واحد ستة واحد خمسة واحد تلاتة واحد سبعة
+
+269
+00:30:21,020 --> 00:30:25,580
+واحد اتنين inverse شباب احنا عارفين ان ال inverse
+
+270
+00:30:25,580 --> 00:30:31,720
+بتوزع الضغط لكن مبقاشبالترتيب العكسى بيجيب هذه
+
+271
+00:30:31,720 --> 00:30:37,680
+عبارة عن واحد اتنين inverse واحد سبعة inverse واحد
+
+272
+00:30:37,680 --> 00:30:42,880
+تلاتة inverse واحد خمسة inverse واحد ستة inverse
+
+273
+00:30:42,880 --> 00:30:48,900
+واحد تمانية inverse واحد اربع inverse و هدولة two
+
+274
+00:30:48,900 --> 00:30:53,780
+cycles ال inverse ايه اللي هم اشماله ال inverse لل
+
+275
+00:30:53,780 --> 00:30:56,620
+two cycles اي two cycle ال inverse ايه اللي هاي
+
+276
+00:30:56,620 --> 00:31:02,500
+اشمالهاها شباب ال inverse ل أي two cycles يساوي
+
+277
+00:31:02,500 --> 00:31:07,460
+نفسه يعني هذا عبارة عن واحد اتنين واحد ستة واحد
+
+278
+00:31:07,460 --> 00:31:14,220
+تلاتة واحد خمسة واحد ستة او خدنا ال واحد ستة احنا
+
+279
+00:31:14,220 --> 00:31:20,820
+اه هذه خربطت واحد اتنين واحد سبعة اه طيب واحد ستة
+
+280
+00:31:20,820 --> 00:31:25,720
+واحد تمانية واحد اربعة عارف هذه مين؟
+
+281
+00:31:32,810 --> 00:31:43,610
+طبها هذه واحد اتنين
+
+282
+00:31:43,610 --> 00:31:51,630
+سبعة تلاتة خمسة ستة تمانية اربعة
+
+283
+00:31:58,040 --> 00:32:00,900
+انت لو كتبت هادى على شكل two cycles مش هتاخد الأول
+
+284
+00:32:00,900 --> 00:32:06,400
+مع الأخر مع جبل الأخر اعملها بس بالعكس تنساش انه
+
+285
+00:32:06,400 --> 00:32:10,160
+ال cycle انا ممكن اكتبها بطريقة هادى يعني انا ممكن
+
+286
+00:32:10,160 --> 00:32:13,140
+هادى أسير اربعة تمانية ستة خمسة تلاتة سبعة اتنين
+
+287
+00:32:13,140 --> 00:32:18,080
+واحد هي هي الأربع بتروح لل تمانية بتروح لل تمانية
+
+288
+00:32:18,080 --> 00:32:22,100
+التمانية للستة للستة للخمسة الستة للخمسة مافرجتش
+
+289
+00:32:22,100 --> 00:32:26,740
+كتير تطلع على هادى و تطلع على هادى تطلع ترتيب
+
+290
+00:32:26,740 --> 00:32:33,300
+العناصربطلع على ترتيب العناصر بين هذه و هذه ايش
+
+291
+00:32:33,300 --> 00:32:37,920
+بتلاحظ؟ واحد اتنين سبعة تلاتة خمسة ستة تمانية
+
+292
+00:32:37,920 --> 00:32:42,000
+اربعة واحد اتنين سبعة تلاتة خمسة ستة تمانية اربعة
+
+293
+00:32:42,000 --> 00:32:46,720
+ايش بيصير؟ بنرتب العناصر لكن بالعكس وهذا ممكن نقول
+
+294
+00:32:46,720 --> 00:32:56,120
+fact if alpha بتساوي a1 a2 عند an then alpha
+
+295
+00:32:56,120 --> 00:33:06,230
+inverse عبارة عن anan-1 a2 a1 طيب
+
+296
+00:33:06,230 --> 00:33:12,390
+كمثال ال beta تبع التوي اللي عبارة عن اتنين اربعة
+
+297
+00:33:12,390 --> 00:33:19,170
+تلاتة خمسة ستة سبعة ال beta inverse عبارة عن اتنين
+
+298
+00:33:19,170 --> 00:33:25,700
+اربعة تلاتة خمسةفي 6 7 inverse اللي عبارة عن 6 7
+
+299
+00:33:25,700 --> 00:33:37,880
+inverse 2 4 3 5 inverse 6 7 inverse مين هي نفسها و
+
+300
+00:33:37,880 --> 00:33:46,620
+2 4 3 5 inverse خمسة تلاتة اربعة اتنين خيال
+
+301
+00:33:48,310 --> 00:33:52,130
+و هدى صارت عندك أهمية تانية لكتابة ال permutation
+
+302
+00:33:52,130 --> 00:34:03,470
+على شكل two cycles دى
+
+303
+00:34:03,470 --> 00:34:09,550
+theorem خمسة ستة بيجي
+
+304
+00:34:09,550 --> 00:34:14,650
+السؤال هل جيت ال Sn فيها permutation even و فيها
+
+305
+00:34:14,650 --> 00:34:15,770
+permutation odd
+
+306
+00:34:19,310 --> 00:34:24,590
+هل ال odd مع بعض بيعملولي subgroup؟ بيجي هانا
+
+307
+00:34:24,590 --> 00:34:30,470
+السؤال هل ال even مع بعض بيعملولي subgroup؟ والله
+
+308
+00:34:30,470 --> 00:34:35,210
+لأ نظرية خمسة ستة بتقولك أنه لو أخدت ال even مع
+
+309
+00:34:35,210 --> 00:34:39,780
+بعض هيعملوا subgroupإن الـ odd مع بعض ما بيعملش
+
+310
+00:34:39,780 --> 00:34:43,000
+subgroup هذا عبارة عن counter .. محتاج counter
+
+311
+00:34:43,000 --> 00:34:45,560
+example انه مش هيعمل subgroup موجود ضمن الأسئلة
+
+312
+00:34:45,560 --> 00:34:49,340
+هنثبت في نظرية ان ال even بيعملوا subgroup و
+
+313
+00:34:49,340 --> 00:34:54,240
+بنستعطيها اسم اسم ال alternating group of degree
+
+314
+00:34:54,240 --> 00:35:05,460
+theorem 5-6 that's it of all even permutations
+
+315
+00:35:11,480 --> 00:35:27,980
+ن أسن form a subgroup of أسن بتبقى سهل let أن
+
+316
+00:35:27,980 --> 00:35:34,200
+عبارة عن كل الألف حيث ألف ينتمي لأسن و ألف is even
+
+317
+00:35:39,340 --> 00:35:45,240
+الـ Identity ينتمي لان وبالتالي الان لا يسار فعلا
+
+318
+00:35:45,240 --> 00:35:50,700
+طبعا هنا for an أكبر من الواحد لأن لو an بيسار
+
+319
+00:35:50,700 --> 00:35:55,420
+واحد مافيش غير عنصر واحد هو ال identity أيش بيظل
+
+320
+00:35:55,420 --> 00:36:04,440
+أثبت أنها جات؟ ان هيش هذي finite في ال finite يكفي
+
+321
+00:36:04,440 --> 00:36:12,330
+نياش شرط واحد اللي هو ال one stepلأ انه closed انه
+
+322
+00:36:12,330 --> 00:36:18,290
+اي عنصرين بتاخدهم يكون حاصل ضربه معاها let alpha و
+
+323
+00:36:18,290 --> 00:36:28,230
+beta ينتمي ل a,n معناته alpha و beta is even يعني
+
+324
+00:36:28,230 --> 00:36:31,430
+alpha عبارة عن ال alpha واحد ال alpha اتنين اللي
+
+325
+00:36:31,430 --> 00:36:36,610
+عند ال alpha اتنين ام beta بتساوي beta واحد beta
+
+326
+00:36:36,610 --> 00:36:39,270
+تنين اللي عند ال beta تنين
+
+327
+00:36:41,610 --> 00:36:48,470
+مش هما even فعبارة عن where alpha
+
+328
+00:36:48,470 --> 00:36:58,870
+i and beta j اشملهم are two cycles
+
+329
+00:36:58,870 --> 00:37:05,550
+تعالوا
+
+330
+00:37:05,550 --> 00:37:06,450
+تقبلي alpha في beta
+
+331
+00:37:10,320 --> 00:37:13,860
+الف في بيتا يبقى عن الف واحد الف اتنين لعند الف
+
+332
+00:37:13,860 --> 00:37:18,780
+اتنين ك بيتا واحد بيتا اتنين لعند بيتا اتنين ام في
+
+333
+00:37:18,780 --> 00:37:26,880
+الاول اتنين ام و اتنين ك كده اش عدد هدول اتنين ام
+
+334
+00:37:26,880 --> 00:37:35,800
+زائد ك من ال two cycles اش يعني الف بيتا is even
+
+335
+00:37:35,800 --> 00:37:43,760
+يبقى الف بيتا وان موجودبسيط بسيط بسيط بسيط بسيط
+
+336
+00:37:43,760 --> 00:37:46,220
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+337
+00:37:46,220 --> 00:37:47,960
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+338
+00:37:47,960 --> 00:37:48,220
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+339
+00:37:48,220 --> 00:37:50,320
+بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط بسيط
+
+340
+00:37:50,320 --> 00:38:02,360
+بسيط
+
+341
+00:38:11,190 --> 00:38:22,930
+group of order نسميها الـ group المتذبذبة ال order
+
+342
+00:38:22,930 --> 00:38:38,750
+تبعها بالساوي عشان
+
+343
+00:38:38,750 --> 00:38:39,210
+أنهي
+
+344
+00:38:41,980 --> 00:38:53,240
+الشبتر تبقى نظرية واحدة هي نظرية خمسة سبعة theorem
+
+345
+00:38:53,240 --> 00:38:58,360
+خمسة
+
+346
+00:38:58,360 --> 00:39:03,720
+سبعة الشباب قال ال a n sub group من ال sn ال sn
+
+347
+00:39:03,720 --> 00:39:10,540
+فيها n factorial من العناصر طب وال a n كمنصر four
+
+348
+00:39:11,900 --> 00:39:20,880
+an أكبر من الواحد order ال an بيساوي n! على 2 عدد
+
+349
+00:39:20,880 --> 00:39:35,600
+عناصر ال an بيساوي نص عدد عناصر ال sn let
+
+350
+00:39:35,600 --> 00:39:47,500
+طبعا clearlyfor n أكبر من الواحد ان الان sub group
+
+351
+00:39:47,500 --> 00:39:52,380
+من الاسن و proper ليش؟
+
+352
+00:39:52,380 --> 00:40:01,180
+لإن هذه ينتمي لاسن but لا ينتمي لان يعني هي proper
+
+353
+00:40:01,180 --> 00:40:05,900
+هي proper let
+
+354
+00:40:15,840 --> 00:40:21,600
+النتيجة Alpha is even يعني
+
+355
+00:40:21,600 --> 00:40:25,020
+Alpha عبارة عن Alpha واحد Alpha اتنين لعند Alpha
+
+356
+00:40:25,020 --> 00:40:31,080
+اتنين M هذا معناته if
+
+357
+00:40:31,080 --> 00:40:37,750
+Beta بدت ساوي واحد اتنين thenAlpha في Beta يساوي
+
+358
+00:40:37,750 --> 00:40:41,290
+Alpha واحد Alpha اتنين لعند Alpha اتنين M طبعا
+
+359
+00:40:41,290 --> 00:40:47,950
+هدول عبارة عن إيش؟ Two cycles لإي Alpha I is two
+
+360
+00:40:47,950 --> 00:40:53,110
+cycle في
+
+361
+00:40:53,110 --> 00:41:00,490
+مين؟ في واحد و اتنين جداش عددهم هدول؟ تنين M زاد
+
+362
+00:41:00,490 --> 00:41:05,550
+الواحد of two cycles إيش يعني يا شباب؟
+
+363
+00:41:09,000 --> 00:41:16,580
+مش يعني؟ معناته Alpha Beta إيش مالها؟ is odd
+
+364
+00:41:16,580 --> 00:41:23,580
+permutation أخدت
+
+365
+00:41:23,580 --> 00:41:28,180
+أنا even permutation وضربت في Beta طلعت Alpha في
+
+366
+00:41:28,180 --> 00:41:32,680
+Beta إيش؟ odd permutation يعني لكل permutation
+
+367
+00:41:32,680 --> 00:41:40,310
+even في جبالة واحدة odd طيب نعمل العكسif مثلا
+
+368
+00:41:40,310 --> 00:41:46,690
+gamma is odd permutation
+
+369
+00:41:46,690 --> 00:41:53,050
+إن أسأل يعني gamma مثلا عبارة عن gamma واحد gamma
+
+370
+00:41:53,050 --> 00:41:57,690
+اتنين لأن gamma اتنين k زاد الواحد النتيجة gamma
+
+371
+00:41:57,690 --> 00:42:01,970
+beta gamma واحد gamma اتنين لأن gamma اتنين k زاد
+
+372
+00:42:01,970 --> 00:42:08,250
+الواحد في واحد واتنين طبعا هدولة gamma jis two
+
+373
+00:42:08,250 --> 00:42:20,410
+cycle جداش عددهم هدول 2k زي 2 of two cycles يعني
+
+374
+00:42:20,410 --> 00:42:30,070
+gamma beta is even لكل واحدة even في واحدة odd لكل
+
+375
+00:42:30,070 --> 00:42:32,990
+واحدة odd في واحدة even اش يعني
+
+376
+00:42:37,790 --> 00:42:42,150
+يعني عدد ال even بيساوي عدد ال odd تنساش انه مافيش
+
+377
+00:42:42,150 --> 00:42:47,670
+واحدة even او مافيش تنتين even مختلفات بيروحوا
+
+378
+00:42:47,670 --> 00:42:51,330
+لتنتين odd زي بعض يعني مافيش تنتين even بيروحوا
+
+379
+00:42:51,330 --> 00:42:56,210
+لنفس ال odd لأن انا بضغف مين؟ في أنصر يعني لو كان
+
+380
+00:42:56,210 --> 00:43:01,930
+مثلا الف واحد beta بيساوي الف اتنين beta فالواحد
+
+381
+00:43:01,930 --> 00:43:06,830
+بيساوي الف اتنينفال even بيروح ل destinect even
+
+382
+00:43:06,830 --> 00:43:11,350
+بيروح ل destinect odd و destinect odd بيروح ليش ل
+
+383
+00:43:11,350 --> 00:43:18,430
+destinect even هذا معناته for any even permutation
+
+384
+00:43:18,430 --> 00:43:22,350
+there
+
+385
+00:43:22,350 --> 00:43:26,910
+is another
+
+386
+00:43:26,910 --> 00:43:45,740
+odd one and for anyodd one we have another even
+
+387
+00:43:45,740 --> 00:43:51,160
+one اش يعني؟ يعني عدد ال even بساوي عدد ال odd
+
+388
+00:43:51,160 --> 00:43:54,820
+يعني
+
+389
+00:43:54,820 --> 00:44:01,700
+عدد ال even permutation بساوي عدد ال odd
+
+390
+00:44:02,670 --> 00:44:10,010
+Permutation وبالتالي عدد ال even permutation مودي
+
+391
+00:44:10,010 --> 00:44:17,310
+يساوي نص order ال sn يكفي order ال an مودي يساوي
+
+392
+00:44:17,310 --> 00:44:23,930
+order ال sn على اتنين يعني n! على اتنين وهو
+
+393
+00:44:23,930 --> 00:44:24,710
+المطلوب
+
+394
+00:44:35,020 --> 00:44:39,900
+طبعا عشان أنهي المحاضرة مثال لو قلنا ال S ثلاثة
+
+395
+00:44:39,900 --> 00:44:43,620
+مين
+
+396
+00:44:43,620 --> 00:44:52,100
+هي ال identity واحد و اتنين واحد و تلاتة اتنين و
+
+397
+00:44:52,100 --> 00:44:58,780
+تلاتة واحد و اتنين و تلاتة واحد و تلاتة اتنين من
+
+398
+00:44:58,780 --> 00:45:03,120
+ال AN مين
+
+399
+00:45:03,120 --> 00:45:09,750
+من هدولة زوجيالـ Identity هذا فردي هذا فردي هذا
+
+400
+00:45:09,750 --> 00:45:16,750
+فردي بل واحد و اتنين و تلاتة والواحد و تلاتة و
+
+401
+00:45:16,750 --> 00:45:25,870
+اتنين بدي اسألك سؤال هل ال A تلاتة ال A تلاتة
+
+402
+00:45:25,870 --> 00:45:32,150
+Cyclic ولا مش Cyclic Cyclic
+
+403
+00:45:32,150 --> 00:45:37,910
+هذي Generatedby واحد اتنين تلاتة لحظة ان ال S
+
+404
+00:45:37,910 --> 00:45:45,410
+تلاتة مش Abelian لكن ال A تلاتة كانت ايش كانت
+
+405
+00:45:45,410 --> 00:45:50,070
+Cyclic هل هذا كلام دائما صحيح لأ ال AN ماتكنش
+
+406
+00:45:50,070 --> 00:45:57,470
+Abelian أصلا واضح؟ يا عظيم العافية هيك نهاية of
+
+407
+00:45:57,470 --> 00:45:58,910
+chapter خمسة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ba27534e2c7edf275409c1c5dad2750642595d76
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_postprocess.srt
@@ -0,0 +1,1824 @@
+1
+00:00:21,510 --> 00:00:25,030
+بسم الله الرحمن الرحيم انتهينا في المرة الماضية من
+
+2
+00:00:25,030 --> 00:00:29,070
+شبتر تسعة والان بدنا نعمل discussion حول هذا
+
+3
+00:00:29,070 --> 00:00:35,390
+الشبتر بيقول ايش بيقول لو كان عندى ال cyclic group
+
+4
+00:00:35,390 --> 00:00:41,630
+G يبقى any factor group for this cyclic group is
+
+5
+00:00:41,630 --> 00:00:45,930
+cyclic يعني ايه؟ يعني لما نقول لو افترضنا G is a
+
+6
+00:00:45,930 --> 00:00:51,300
+cyclic group generated by Aوإفترضنا مشان يكون عندى
+
+7
+00:00:51,300 --> 00:00:55,020
+factor group لازم يكون عندى normal subgroup رغم
+
+8
+00:00:55,020 --> 00:00:59,320
+أنه ماقالش كل اللي قالوا show that any factor
+
+9
+00:00:59,320 --> 00:01:03,020
+group of a cyclic group is cyclic بس هاي كل الكلام
+
+10
+00:01:03,020 --> 00:01:07,120
+اللي قالوا يبقى معنى هذا الكلام أنه لو كانت جى ال
+
+11
+00:01:07,120 --> 00:01:11,340
+cyclic group وكانت each normal subgroup معناته
+
+12
+00:01:11,340 --> 00:01:15,480
+بقدر أكون اللي هو ال factor group أو ال quotient
+
+13
+00:01:15,480 --> 00:01:19,530
+group اللي قدامنا هذهيبقى لو كان الـ geocyclic بدي
+
+14
+00:01:19,530 --> 00:01:24,550
+أثبت إنه هذا إيه Cyclic بمعنى آخر بدي أحاول أثبت
+
+15
+00:01:24,550 --> 00:01:28,470
+إنه هذه إلها generator إذا قررنا نثبت إنها
+
+16
+00:01:28,470 --> 00:01:31,570
+generator يبقى بصير هذي الـcyclic وإذا كان يكون
+
+17
+00:01:31,570 --> 00:01:36,610
+وصلنا إيه للمطلوب اللي احنا بدنا يعني يبقى
+
+18
+00:01:36,610 --> 00:01:45,390
+solution بدي أقوله افترضان عندي element موجود
+
+19
+00:01:45,390 --> 00:01:52,010
+وليكن مثلا اللي هو H والله ساميه اللي بدك ايه
+
+20
+00:01:52,010 --> 00:01:58,450
+ساميه والله قبل ال BH بدي اقول ان اثبت ما ياتي
+
+21
+00:01:58,450 --> 00:02:08,300
+want to show thatto show that نحاول نبين ان الـ G
+
+22
+00:02:08,300 --> 00:02:14,400
+modulo H هي عبارة عن subgroup generated by any
+
+23
+00:02:14,400 --> 00:02:19,140
+element من مكان يكون الـ element هذا وليكن على
+
+24
+00:02:19,140 --> 00:02:26,900
+سبيل المثال H كويس
+
+25
+00:02:28,400 --> 00:02:33,480
+مشان هيك بدنا هذا تساوي لو قدت أثبت أن هذه subset
+
+26
+00:02:33,480 --> 00:02:38,700
+من هذه و هذه subset من هذه بيتم المطلوب تمام؟ الآن
+
+27
+00:02:38,700 --> 00:02:45,140
+السؤال هو هل الـAH هذه موجودة في الـG modulo H ولا
+
+28
+00:02:45,140 --> 00:02:51,860
+لأ؟ تمام يعني ال subgroup generated by AH بدها
+
+29
+00:02:51,860 --> 00:02:58,330
+تبقى subset من من subset من الـG modulo Hمظبوط
+
+30
+00:02:58,330 --> 00:03:02,110
+هكذا ال element موجود في ال group يبقى ال sub
+
+31
+00:03:02,110 --> 00:03:07,390
+group المتكونة بهذا ال element بتبقى ال subset من
+
+32
+00:03:07,390 --> 00:03:13,550
+من ال group الأساسية ويعتبر ان هذه رقم واحد بدنا
+
+33
+00:03:13,550 --> 00:03:18,050
+نعمل العملية العكسية بدنا ناخد element هنا ونحاول
+
+34
+00:03:18,050 --> 00:03:26,060
+نثبت انه موجود هنا اذا لو روحت quote letالـ B H
+
+35
+00:03:26,060 --> 00:03:33,220
+موجودة في الـ G modulo H إذا قدرت أثبت إن الـ B H
+
+36
+00:03:33,220 --> 00:03:39,800
+موجودة هنا بيتم المطلوب طيب كويس الآن احنا عندنا B
+
+37
+00:03:39,800 --> 00:03:48,870
+موجودة في الـ G مظبوط ولا لا؟ B موجودة في الـ Gأي
+
+38
+00:03:48,870 --> 00:03:54,510
+element أخدته من جهه يبقى شكل هذا ال element يعني
+
+39
+00:03:54,510 --> 00:04:04,580
+بيبدو يسوو ال a i for some i الموجودة في zليش؟
+
+40
+00:04:04,580 --> 00:04:09,080
+لأنه جيه الـCyclic يبقى أي element فيها بدي يكون
+
+41
+00:04:09,080 --> 00:04:17,760
+على شكل الـA ليش هذا الكلام؟ هذا الكلام لأن جيه
+
+42
+00:04:17,760 --> 00:04:22,500
+بدي تساوي ال subgroup generated by A مشان هيك
+
+43
+00:04:22,500 --> 00:04:26,760
+كتبناها على الشكل اللي عندنا هذا إذا بناء عليه
+
+44
+00:04:26,760 --> 00:04:36,410
+الـBH هذا بدي يساوي الـB عندى بقداش؟ بAIيبقى AI في
+
+45
+00:04:36,410 --> 00:04:45,990
+ال H AI في H عبارة عن A H A H A H I من المرات او
+
+46
+00:04:45,990 --> 00:04:55,940
+بمعنى اخر هذه بدها تساوي A H كله to the power Iإذا
+
+47
+00:04:55,940 --> 00:05:05,240
+هذه ال elements صار صورة من من ال a h بالشكل اللي
+
+48
+00:05:05,240 --> 00:05:05,920
+عندنا هنا
+
+49
+00:05:09,300 --> 00:05:14,740
+واضح يبقى الان اخدت element موجود في ال g h وجدته
+
+50
+00:05:14,740 --> 00:05:21,160
+في ال a h يبقى هذه النقطة رقم اتنين اذا من واحد
+
+51
+00:05:21,160 --> 00:05:25,880
+واتنين from واحد and اتنين
+
+52
+00:05:27,780 --> 00:05:33,580
+إن الـ G modulo H اللي بدها تساوي ال subgroup
+
+53
+00:05:33,580 --> 00:05:43,500
+generated by H يبقى هنا so ال G modulo H is cyclic
+
+54
+00:05:43,500 --> 00:05:51,820
+وانتهينا من السؤالإذا لو كانت G Cyclic وعملنا منها
+
+55
+00:05:51,820 --> 00:05:55,340
+أي quotient group فهذه ال quotient group كذلك
+
+56
+00:05:55,340 --> 00:05:59,220
+ستكون Cyclic group طبعا السؤال السابع اللي جابله
+
+57
+00:05:59,220 --> 00:06:06,760
+حلناه كمثال من خلال الأمثلة خد سؤال زي سؤال 14
+
+58
+00:06:06,760 --> 00:06:09,980
+سؤال
+
+59
+00:06:09,980 --> 00:06:16,910
+14بيقول what is the order of بدنا ال order تبع 14
+
+60
+00:06:16,910 --> 00:06:23,750
+زائد ال sub group generated by تمانية وهذا الكلام
+
+61
+00:06:23,750 --> 00:06:34,550
+في ال group اللي هو z 24 and z 24 module sub group
+
+62
+00:06:34,550 --> 00:06:36,290
+generated by تمانية
+
+63
+00:06:39,060 --> 00:06:44,380
+بنعرف قداش ال order لهذا ال element طبعا ليس
+
+64
+00:06:44,380 --> 00:06:48,180
+بالضرورة ان تبدأ انت تربع دغري و تكعب لغاية ما
+
+65
+00:06:48,180 --> 00:06:54,660
+توصل لل identity لكن بنظرة بسيطة ال 14 هذي بقدر
+
+66
+00:06:54,660 --> 00:07:01,520
+اكتبها بدلالة ال 8 يبقى باجي بقول الحل كتالي
+
+67
+00:07:01,520 --> 00:07:02,400
+solution
+
+68
+00:07:06,380 --> 00:07:10,620
+الاربعتاشر زي ال subgroup generated by تمانية
+
+69
+00:07:10,620 --> 00:07:17,020
+يساوي ستة زائد تمانية زي ال subgroup generated by
+
+70
+00:07:17,020 --> 00:07:25,100
+تمانية ال element هذا موجود هنا ولا لا يبقى هدول
+
+71
+00:07:25,100 --> 00:07:30,050
+إيش بدهم يعطوني؟Subgroup generated by تمانية
+
+72
+00:07:51,400 --> 00:07:57,160
+لو قلت الكلام هذا أستربية يعني معناته اتنين في ستة
+
+73
+00:07:57,160 --> 00:08:02,180
+اتنين في ستة لان اخدنا ال factor group ال A H في
+
+74
+00:08:02,180 --> 00:08:07,600
+BH بده يساوي A في BH يعني H بتظهر لثابتة و الدرب
+
+75
+00:08:07,600 --> 00:08:12,040
+يكون لمين للعنصر الان عندنا جمع يبقى لو جمعت ستة و
+
+76
+00:08:12,040 --> 00:08:18,170
+ستة اتناشتعطيني قداش تعطيني اربعة طب لو قلت تلاتة
+
+77
+00:08:18,170 --> 00:08:22,790
+في الستة بيبقى تمانتاش شيل منها ستاش بيبقى اتنين
+
+78
+00:08:22,790 --> 00:08:27,270
+لو قلت اربعة في الستة اربع عشرين اللي هي تلت
+
+79
+00:08:27,270 --> 00:08:30,470
+تمانية تبقى هذا بدي يعطيني التمانية إذا ال order
+
+80
+00:08:30,470 --> 00:08:36,330
+لهذا ال element يساوي قداش يساوي اربعةيبقى ال
+
+81
+00:08:36,330 --> 00:08:42,850
+order لل 14 زائد ال subgroup generated by 8 يبقى
+
+82
+00:08:42,850 --> 00:08:48,950
+ال order لل 6 زائد ال subgroup generated by 8 يبقى
+
+83
+00:08:48,950 --> 00:08:51,030
+ال order لل 6 زائد ال subgroup generated by 8 يبقى
+
+84
+00:08:51,030 --> 00:08:54,830
+ال order لل 6 زائد ال subgroup generated by 8
+
+85
+00:08:54,870 --> 00:09:00,830
+الأربعة في ستة زاد ال subgroup generated by تمانية
+
+86
+00:09:00,830 --> 00:09:05,530
+يساوي أربع وعشرين زاد ال subgroup generated by
+
+87
+00:09:05,530 --> 00:09:09,330
+تمانية يساوي ال subgroup generated by تمانية ال
+
+88
+00:09:09,330 --> 00:09:16,530
+identity element لذلك ال order يساوي أربعة
+
+89
+00:09:23,000 --> 00:09:29,120
+طب اروح لسؤال زي سؤال اربعة و عشرين هاي سؤال اربعة
+
+90
+00:09:29,120 --> 00:09:38,800
+و عشرين بيقول في ال group اللي هو Z اربعة external
+
+91
+00:09:38,800 --> 00:09:44,640
+product مع مين مع Z اتناشر module ال sub group
+
+92
+00:09:44,640 --> 00:09:49,740
+generated by اتنين و اتنين بالشكل اللي عندنا هذا
+
+93
+00:09:50,520 --> 00:09:57,540
+الجروب هذا ايزو مورفك لواحدة من ايزو مورفك لزد
+
+94
+00:09:57,540 --> 00:10:04,240
+تمانية والله زد اربعة external diet product مع زد
+
+95
+00:10:04,240 --> 00:10:10,260
+اتنين والله مع زد اتنين external diet product مع
+
+96
+00:10:10,260 --> 00:10:11,320
+زد اتنين
+
+97
+00:10:14,890 --> 00:10:19,630
+بسأل هل ال group هذي isomorphic ل واحدة من هذول ام
+
+98
+00:10:19,630 --> 00:10:24,910
+لا و determine which one by elimination يعني بدك
+
+99
+00:10:24,910 --> 00:10:29,270
+تحاول تحذف اللي هو تنتين وبالتالي تثبت عندك مين
+
+100
+00:10:29,270 --> 00:10:34,670
+تثبت عندك واحدة هي ال solution
+
+101
+00:10:40,640 --> 00:10:44,400
+الحين بدي اعرف هذه ال group فيها كام عنصر وبعد هيك
+
+102
+00:10:44,400 --> 00:10:49,940
+نتفهم على الباقي الان لو جيت سميت ال H هي ال
+
+103
+00:10:49,940 --> 00:10:56,400
+subgroup generated by 2 و 2 و بدي اشوف العناصر
+
+104
+00:10:56,400 --> 00:11:02,640
+تبعت هذه ال subgroup يبقى ال element الأول 00 ال
+
+105
+00:11:02,640 --> 00:11:08,620
+element التاني اللي هو 2 و 2الـ Element التالت
+
+106
+00:11:08,620 --> 00:11:19,580
+يبقى هذا التربيه يبقى 4 و 4 4 فى زد 4 تعني 0 فديك
+
+107
+00:11:19,580 --> 00:11:26,190
+فى زد 12 تعني 4 كما هيالان تكييب يعني اضرب في
+
+108
+00:11:26,190 --> 00:11:32,230
+تلاتة بيصير تلاتة في اتنين يبقى ستة و ستة الستة في
+
+109
+00:11:32,230 --> 00:11:38,770
+الزد اربعة باتنين وهديك ستة كما هي هذا تكييب لو
+
+110
+00:11:38,770 --> 00:11:45,600
+جيت أس اربعة بدي يعطيني هذا zero و هذا تمانيةالان
+
+111
+00:11:45,600 --> 00:11:51,180
+لو جيت أس خمسة بدي يعطيني عشرة و عشرة يبقى خمسة
+
+112
+00:11:51,180 --> 00:11:57,780
+هذه بيعطيني اتنين و عشرة يبقى أس ستة بيعطيني اتناش
+
+113
+00:11:57,780 --> 00:12:02,580
+و اتناش اللي هو ال identity و ال identity هيهيبقى
+
+114
+00:12:02,580 --> 00:12:07,920
+على هك انتهت من انتهت هذه ال subgroup يبقى زي ما
+
+115
+00:12:07,920 --> 00:12:12,380
+انت ملاحظ في عندي ال order اللي يساوي قداشر يساوي
+
+116
+00:12:12,380 --> 00:12:18,480
+ستة عناصر إذا لما بدي أجي لل factor group هذه ال
+
+117
+00:12:18,480 --> 00:12:24,760
+factor group external product لزد اتناش module ال
+
+118
+00:12:24,760 --> 00:12:30,050
+subgroup generated by اتنين و اتنينالـ Order لها
+
+119
+00:12:30,050 --> 00:12:35,990
+أربعة في اتناش بتمانية واربعين على ستة يبقى فيها
+
+120
+00:12:35,990 --> 00:12:41,450
+جداش فيها تمانية الان هذه ال group فيها ثمانية
+
+121
+00:12:41,450 --> 00:12:46,890
+عناصر بدنا نتعرف على هذه العناصر الثمانية اللي
+
+122
+00:12:46,890 --> 00:12:53,630
+عندنايبقى ال group اللي عندنا اللي هي z4 external
+
+123
+00:12:53,630 --> 00:13:00,990
+product مع z12 modulo h بدها تساوي مديش اكتبه
+
+124
+00:13:00,990 --> 00:13:08,380
+بالشكل هذا h اخف في الكتابة يبقى هذا hzero و واحد
+
+125
+00:13:08,380 --> 00:13:14,980
+اللي هو zero و واحد زائد ال H من operation عملية
+
+126
+00:13:14,980 --> 00:13:22,520
+جامعة واحد و زيرو زائد ال H واحد و واحد زائد ال H
+
+127
+00:13:23,920 --> 00:13:29,640
+واحد واتنين زائد
+
+128
+00:13:29,640 --> 00:13:39,280
+ال H اللي هو اتنين وواحد زائد ال H واحد وتلاتة
+
+129
+00:13:39,280 --> 00:13:49,160
+زائد ال H وكذلك اللي هو Zero واتنين زائد ال Hيبقى
+
+130
+00:13:49,160 --> 00:13:53,900
+هذه العناصر واحد اتنين تلاتة اربعة خمسة ستة سبعة
+
+131
+00:13:53,900 --> 00:13:59,300
+تمانية عناصر يبقى هذه تمانية عناصر عندنا تبعت ال
+
+132
+00:13:59,300 --> 00:14:04,860
+group هذه طبعا كيف عرفتها بدنا ناخد العناصر تبعات
+
+133
+00:14:04,860 --> 00:14:10,110
+ال group اللي عندنا ونبدأ نضربهم في مينفي ال H
+
+134
+00:14:10,110 --> 00:14:15,550
+طبعا هيطلعوا بعضهم يساوي بعض أو هيطلعوا الستة منهم
+
+135
+00:14:15,550 --> 00:14:20,750
+كل ستة بيساوي بعض فبيصف عنا مين؟ بيصف عنا التمانية
+
+136
+00:14:20,750 --> 00:14:25,310
+اللي قدامنا هدول يبقى هدول عناصر ال group اللي
+
+137
+00:14:25,310 --> 00:14:30,270
+عندك كان سؤال هو هذه isomorphic لمين؟ هل أزد
+
+138
+00:14:30,270 --> 00:14:35,880
+تمانية؟ والله لهذه والله لهذه تعالوا نشوفلو أخدت
+
+139
+00:14:35,880 --> 00:14:41,100
+عشوائيا أي element من هدول هتلاقي ال order له يا
+
+140
+00:14:41,100 --> 00:14:46,980
+واحد تلاتة انسى الموضوع تلاتة لأن هذه فيها تمانية
+
+141
+00:14:46,980 --> 00:14:50,300
+عناصر ال order لل element بدي اجسم ال order لل
+
+142
+00:14:50,300 --> 00:14:54,220
+group يا واحد يا اتنين يا اربعة يا تمانية مظبوط
+
+143
+00:14:54,220 --> 00:15:00,400
+السؤال هو هل هناك element ال order له يساوي تمانية
+
+144
+00:15:02,030 --> 00:15:10,770
+الله أعلم كل اللي بقوله انا each of these elements
+
+145
+00:15:15,310 --> 00:15:20,770
+this element has
+
+146
+00:15:20,770 --> 00:15:28,110
+orders ياما واحد، ياما اتنين، ياما اربعة فقط، لا
+
+147
+00:15:28,110 --> 00:15:32,550
+غير نجرب؟
+
+148
+00:15:32,550 --> 00:15:36,990
+حسب السؤال هذا كتير مش cycle انت مستخدم يكون
+
+149
+00:15:36,990 --> 00:15:43,280
+جناينك بتاعك cycle ما انت عشوائيابس في فن شوية هنا
+
+150
+00:15:43,280 --> 00:15:47,980
+عشوائيا خدلك اي element و تعالى نحسب ال order تبعه
+
+151
+00:15:47,980 --> 00:15:52,080
+تمام؟ و انت بعد هيك بدك تجرب ال order تبع الباقى
+
+152
+00:15:52,080 --> 00:15:55,700
+براحتك في البيت او احنا باقى المحاضرة نقعد نحسب ال
+
+153
+00:15:55,700 --> 00:16:01,240
+order كلهم لأ تعالى خد انتقلك اي واحد من هدول واحد
+
+154
+00:16:01,240 --> 00:16:05,440
+و تلاتة وين واحد و تلاتة هاي؟يبقى بيروح يدور على
+
+155
+00:16:05,440 --> 00:16:11,660
+ال order تبعه يبقى تاربيع جداش بيكون اتنين وستة
+
+156
+00:16:11,660 --> 00:16:16,920
+تمام اتنين وستة هل موجود هنا اتنين وستة اه ايه هنا
+
+157
+00:16:16,920 --> 00:16:21,830
+يبقى ال order له جداش باتنينطبعا هذا الواحد
+
+158
+00:16:21,830 --> 00:16:24,310
+والثالث والاثنين والستين هذين موجودين في الـH
+
+159
+00:16:24,310 --> 00:16:28,370
+موجود في الـH يبقى ال order له بس يساوي اتنين يعني
+
+160
+00:16:28,370 --> 00:16:32,970
+حصلت ضرب هذا التربيع بدي يعطيني الـH itself لأن
+
+161
+00:16:32,970 --> 00:16:36,350
+هذين أعطاني ال element اتنين والستين وغيره يبقى
+
+162
+00:16:36,350 --> 00:16:41,730
+هذا ال order له يساوي اتنين يلا طالك كمان عنصر
+
+163
+00:16:41,730 --> 00:16:46,730
+تاني اه ليه عجبك؟ أي واحد فيهم عشوائي اللي بدك
+
+164
+00:16:46,730 --> 00:16:53,480
+إياهقداش؟ اتنين و واحد طيب اتنين و واحديبقى بدي
+
+165
+00:16:53,480 --> 00:16:59,920
+أقوله تربيع بصير أربعة و إتنين، مظبوط؟ أربعة و
+
+166
+00:16:59,920 --> 00:17:05,360
+إتنين تعني زيرو و إتنين، زيرو و إتنين، وراح زيرو
+
+167
+00:17:05,360 --> 00:17:11,180
+أقل، مش موجود، يبقى تربيع بجيبليش زيرو و إتنين،
+
+168
+00:17:11,180 --> 00:17:16,020
+تمام؟ بجيبليش زيرو و إتنين، تمام، يبقى تكعيب، يبقى
+
+169
+00:17:16,020 --> 00:17:24,060
+بصير ستة و تلاتة، بس كيف؟ممتاز جدا يبقى الساعة
+
+170
+00:17:24,060 --> 00:17:27,880
+اتنين احطنا على الهشك يبقى وصلنا للاربعة يبقى هنا
+
+171
+00:17:27,880 --> 00:17:32,460
+اربعة في اتنين في تمانية و هنا اربعة يعني صفر
+
+172
+00:17:32,460 --> 00:17:36,760
+واربعة صفر واربعة هي موجودة يبقى ال order يساوي
+
+173
+00:17:36,760 --> 00:17:42,250
+كده؟ يساوي اربعة و هكذايبقى اي element من هدول ال
+
+174
+00:17:42,250 --> 00:17:46,730
+order يقولوا يا واحد يا اتنين يا اربع اذا هل ممكن
+
+175
+00:17:46,730 --> 00:17:50,950
+تبقى ال group هذه isomorphic ل Z تمانية؟ في
+
+176
+00:17:50,950 --> 00:17:54,430
+الشمكانية لأن Z تمانية فيها ال order تمانية هذه
+
+177
+00:17:54,430 --> 00:17:59,110
+فيهاش يبقى لا يمكن تبقى isomorphic لمين ل Z تمانية
+
+178
+00:17:59,110 --> 00:18:05,270
+طيب هذهأقصى order فيها جداش تنين يبقى هذه أربع
+
+179
+00:18:05,270 --> 00:18:09,510
+يبقى لا يمكن تكون isomorphic لهذه يبقى بضل إجباري
+
+180
+00:18:09,510 --> 00:18:14,530
+isomorphic لمين لزد أربع external product مع زد
+
+181
+00:18:14,530 --> 00:18:22,870
+اتنين يبقى هذا بده يعطينيالجروب اللي عندنا هو Z4
+
+182
+00:18:22,870 --> 00:18:31,510
+Xenodyic product لـ Z12 is not isomorphic لـ Z8
+
+183
+00:18:31,510 --> 00:18:36,590
+لأن Z8 فيها elements ال order لهم يسوى تمانية
+
+184
+00:18:39,300 --> 00:18:49,880
+الـ z4 external product مع z12 طبعا modulo h يا
+
+185
+00:18:49,880 --> 00:18:56,480
+شباب وهنا كمان modulo h لا يمكن تبقى isomorphic
+
+186
+00:18:56,480 --> 00:19:03,800
+إلى z2 external product مع z2 external product مع
+
+187
+00:19:03,800 --> 00:19:05,800
+z2 because
+
+188
+00:19:09,360 --> 00:19:24,180
+the last group has orders of .. والله has elements
+
+189
+00:19:24,180 --> 00:19:28,940
+of
+
+190
+00:19:28,940 --> 00:19:37,700
+orders واحد واتنين فقطيبقى بناء عليه بقول له thus
+
+191
+00:19:37,700 --> 00:19:46,180
+وهكذا z for external byproduct مع z12 modulo h is
+
+192
+00:19:46,180 --> 00:19:53,940
+isomorphic الى z4 external byproduct مع z2 يعني
+
+193
+00:19:53,940 --> 00:19:59,880
+حذفنا two groups ولاجناها isomorphic لواحدة من ال
+
+194
+00:19:59,880 --> 00:20:02,100
+groups الأخرى
+
+195
+00:20:16,060 --> 00:20:27,640
+هذا كان سؤال 24 خد لي سؤال 28 سؤال 28 حول نفس
+
+196
+00:20:27,640 --> 00:20:36,940
+الموضوع بيقول بيقول جي تساوي زد اربعة جي تساوي زد
+
+197
+00:20:36,940 --> 00:20:46,440
+اربعة external product مع زد اربعةو ال H ماعطينيها
+
+198
+00:20:46,440 --> 00:20:55,020
+هي Zero و Zero و Zero و اتنين و اتنين و Zero و
+
+199
+00:20:55,020 --> 00:21:01,360
+اتنين و Zero و كذلك اتنين و اتنين بالشكل اللي
+
+200
+00:21:01,360 --> 00:21:09,480
+عندنا هذا و ماعطيني K هي ال sub group generated by
+
+201
+00:21:09,480 --> 00:21:16,650
+واحدمين عناصرها مش مياطيني لكن انا بقدر اجيب عناصر
+
+202
+00:21:16,650 --> 00:21:23,210
+تبعتها يبقى اول شي هيكون Zero و Zero لإنها ال sub
+
+203
+00:21:23,210 --> 00:21:27,970
+group اللي بعده واحد و اتنين زي ما هو اللي بعده
+
+204
+00:21:27,970 --> 00:21:34,190
+تربيع بصير اتنين واربعة اتنين واربعة تعني ايه؟
+
+205
+00:21:34,190 --> 00:21:40,020
+تعني اتنين و Zeroيبقى تقريبا تقريبا تقريبا تقريبا
+
+206
+00:21:40,020 --> 00:21:48,580
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+207
+00:21:48,580 --> 00:21:54,040
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+208
+00:21:54,040 --> 00:21:54,840
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+209
+00:21:54,840 --> 00:21:58,320
+تقريبا تقريبا تقريبا تقريبا تقريبا
+
+210
+00:22:04,820 --> 00:22:12,480
+is g modulo
+
+211
+00:22:12,480 --> 00:22:22,080
+h isomorphic لمن لزد اربعة لزد اربعة و الله لزد
+
+212
+00:22:22,080 --> 00:22:31,370
+اتنين external product مع زد اتنين نمر باههل الجي
+
+213
+00:22:31,370 --> 00:22:40,230
+موديولوكا is الجي موديولوكا isomorphic لزد اربعة
+
+214
+00:22:40,230 --> 00:22:46,810
+والله لزد اتنين externa like product مع زد اتنين
+
+215
+00:22:46,810 --> 00:22:50,270
+كذلك يعني مع هذه بالضبط تماما
+
+216
+00:22:58,060 --> 00:23:04,680
+تعالى نشوف هذا الكلام solution يبقى
+
+217
+00:23:04,680 --> 00:23:09,720
+احنا عندنا group فيها 16 element وعندنا ال H فيها
+
+218
+00:23:09,720 --> 00:23:16,140
+اربعة element يبقى هذه فيها كام عنصر اربعة عناصر
+
+219
+00:23:16,140 --> 00:23:25,630
+يبقى بناء عليهبادى بقول هنا ال order لجى modulo H
+
+220
+00:23:25,630 --> 00:23:30,810
+بديه يسوى ال order لجى على ال order لل H و اللي هو
+
+221
+00:23:30,810 --> 00:23:36,510
+بديه يسوى 16 على 4 بديه يسوى كده؟ بديه يسوى 4
+
+222
+00:23:36,510 --> 00:23:44,330
+عناصر يبقى الجى modulo H عناصرها هي 00 اللي هو ال
+
+223
+00:23:44,330 --> 00:23:50,820
+identity elementفي عندك هنا zero واحد واحد و zero
+
+224
+00:23:50,820 --> 00:24:00,130
+و هنا واحد و واحدكله زائد H يبقى هذه الأولى اللى
+
+225
+00:24:00,130 --> 00:24:08,970
+هى H 00 اللى هى H itself و بعدها 01 زائد ال H
+
+226
+00:24:08,970 --> 00:24:18,070
+والتانية 100 زائد ال H والربع اللى هى 11 زائد ال H
+
+227
+00:24:18,070 --> 00:24:23,480
+بالشكل اللى عندنا هناهذه حداد العناصر الباقى
+
+228
+00:24:23,480 --> 00:24:27,760
+العناصر ايش ما تضرب هتطلع واحدة من الأربعة هدول
+
+229
+00:24:27,760 --> 00:24:33,500
+طيب يعني كل أربعة left cosets هيطلعوا are equal
+
+230
+00:24:33,500 --> 00:24:38,950
+بيسووا بعض ليش ان هذه العناصر عندى هنا أربعة؟طب
+
+231
+00:24:38,950 --> 00:24:43,910
+كويس الان لو جيت لهذه بدي اشوف ايزو مورفك لزد
+
+232
+00:24:43,910 --> 00:24:48,810
+اربعة ولا لزد اتنين اذا بدي اروح ادور عالمين لل
+
+233
+00:24:48,810 --> 00:24:54,750
+orders لهذه ال elements تعالى نشوف ال order لأي
+
+234
+00:24:54,750 --> 00:25:01,830
+element من هدول كده بيكوننقدر نشوفهم كلهم سيبك انه
+
+235
+00:25:01,830 --> 00:25:06,790
+ليه اتش هذه ال identity هذه ههه لو قلت تربيع بصير
+
+236
+00:25:06,790 --> 00:25:18,510
+ال 02 02 زائد ال H 02 02 موجودةهذه كل تربيع تعطي
+
+237
+00:25:18,510 --> 00:25:27,450
+الـ H نفسها هذي لما أربعها بصير Zero و اتنين زائد
+
+238
+00:25:27,450 --> 00:25:33,050
+الـ H Zero و اتنين موجودة في الـ H إذا بتعطيني H
+
+239
+00:25:33,050 --> 00:25:38,740
+يبقى ال order له بس قداشتيننمسك التاني، لو قلت
+
+240
+00:25:38,740 --> 00:25:46,540
+تربيع بيصير 2 و 0 زائد الـH 2 و 0 موجودة في الـH
+
+241
+00:25:46,540 --> 00:25:50,220
+يبقى هذا كمان هيعطيني من؟ هيعطيني الـH يبقى ال
+
+242
+00:25:50,220 --> 00:25:58,880
+order إله يساوي 2 لو جينا لهذه 2 و 2 يبقى كل non
+
+243
+00:25:58,880 --> 00:26:04,960
+identity element has order قداشت 2يبقى الـ orders
+
+244
+00:26:04,960 --> 00:26:08,880
+للـ element يا اما واحد يا اما اتنين يعني مايقول
+
+245
+00:26:08,880 --> 00:26:14,140
+تبقى isomorphic لزد اربعة؟ لأ مش ممكنية لزد اربعة
+
+246
+00:26:14,140 --> 00:26:21,160
+ال order واحد اتنين اربعة يبقى باجي بقول each of
+
+247
+00:26:21,160 --> 00:26:35,330
+this element has order اللي هو واحد orأتنين for
+
+248
+00:26:35,330 --> 00:26:40,950
+example كتوضيح for example لو بدنا نوضح الكلام
+
+249
+00:26:40,950 --> 00:26:49,330
+تبعنا خدلي أي واحد فيهم يبقى واحد وزيرو زائد H لكل
+
+250
+00:26:49,330 --> 00:26:58,310
+تربيع يبقى هذا بيصير اتنين في واحد وزيروزائد ال H
+
+251
+00:26:58,310 --> 00:27:06,370
+و يساوي اتنين و زيرو زائد ال H يبقى
+
+252
+00:27:06,370 --> 00:27:15,170
+ال order له يكون اتنين و زيرو زائد ال H يساوي
+
+253
+00:27:15,170 --> 00:27:23,890
+اتنينيبقى هنا الـ G modulo H isomorphic ل Z2
+
+254
+00:27:23,890 --> 00:27:30,610
+external product ل Z2 لأن أي element فيها is of
+
+255
+00:27:30,610 --> 00:27:37,670
+order 1 أو 2 طيب
+
+256
+00:27:37,670 --> 00:27:38,610
+نشوف التانية
+
+257
+00:27:47,280 --> 00:27:54,400
+بنشوف التانية اللي هي الـ G modulo K الأن برضه ال
+
+258
+00:27:54,400 --> 00:28:01,760
+order للـ G modulo K modulo K بده يساوي اللي هو
+
+259
+00:28:01,760 --> 00:28:07,320
+الست عشر على أربعة ويساوي كمان أربعة بدنا نشوف
+
+260
+00:28:07,320 --> 00:28:14,770
+عناصرها إذا الـ G modulo Kلو روحت دورت على عنصرها
+
+261
+00:28:14,770 --> 00:28:26,730
+هتلاقيها Zero و Zero و واحد و .. قصدي K يبقى
+
+262
+00:28:26,730 --> 00:28:35,910
+K و اللي هو واحد و واحد زائد K اتنين و اتنين زائد
+
+263
+00:28:35,910 --> 00:28:44,770
+K تلاتة و تلاتة زائد Kالان لو فكتهم و لا واحدة
+
+264
+00:28:44,770 --> 00:28:49,450
+عناصرها زي التانية يبقى كلهم الأربع هذول are
+
+265
+00:28:49,450 --> 00:28:54,810
+disjoint وبالتالي بقية 12 left cosets هيكون هنا
+
+266
+00:28:54,810 --> 00:28:59,470
+واحدة من الأربع اللي عندك كل واحدة هتساوي واحدة
+
+267
+00:28:59,470 --> 00:29:04,430
+طيب على اي حال الان بدى ادور على ال orders لبين
+
+268
+00:29:04,430 --> 00:29:10,470
+لأي element موجود هنا لو جيت لل element هذا كداشه
+
+269
+00:29:10,470 --> 00:29:11,350
+ال order له
+
+270
+00:29:14,660 --> 00:29:19,300
+الـ order ال order ال order له اتنين لانه يعطيني
+
+271
+00:29:19,300 --> 00:29:24,560
+اربعة و اربعة و احنا بنشتغل هنا و هنا على زد اربعة
+
+272
+00:29:24,560 --> 00:29:29,560
+يبقى هذا ال order له يساوي اتنين طيب ايش العلاقة
+
+273
+00:29:29,560 --> 00:29:34,690
+بين اتنين هدولواحد معكوس للتانى يبقى ال order
+
+274
+00:29:34,690 --> 00:29:38,910
+للأول بدو يساوي ال order للتانى قداش ال order لهذا
+
+275
+00:29:38,910 --> 00:29:43,530
+اربع يبقى لا يمكن يجب ايزو مورفك لزت اتنين اكسيران
+
+276
+00:29:43,530 --> 00:29:49,290
+زت اتنين وانما ايزو مورفك لمين لزت اربع يبقى هنا
+
+277
+00:29:49,290 --> 00:29:55,870
+ال order للواحد وواحد زائد كيه بدو يساوي ال order
+
+278
+00:29:56,320 --> 00:30:02,440
+لتلاتة و تلاتة زائد K وهذا الكلام كله بده يسوي
+
+279
+00:30:02,440 --> 00:30:08,720
+قداش؟ بده يسوي أربعة هذا automatic بده يعطينا ان
+
+280
+00:30:08,720 --> 00:30:15,600
+ال group اللي عندنا G modulo K is isomorphic إلى Z
+
+281
+00:30:15,600 --> 00:30:21,000
+أربعة وليس إلى Z اتنين external product مع Z اتنين
+
+282
+00:30:21,000 --> 00:30:21,860
+كيف؟
+
+283
+00:30:28,010 --> 00:30:35,010
+طيب هذا كان سؤال تمانية و عشرين شوفلي سؤال سبعة و
+
+284
+00:30:35,010 --> 00:30:43,910
+تلاتينسؤال سبعة و تلاتين بيقول ياخد ال G group و
+
+285
+00:30:43,910 --> 00:30:49,410
+ال H normal subgroup يبقى ال H normal subgroup من
+
+286
+00:30:49,410 --> 00:30:57,290
+G prove that ال order لل element GH prove ان ال
+
+287
+00:30:57,290 --> 00:31:04,850
+order لل element GH divides ال order لمين؟ ال
+
+288
+00:31:04,850 --> 00:31:05,850
+order ل G
+
+289
+00:31:09,110 --> 00:31:14,030
+عظمنا لما كنا نقول isomorphism بقينا نقول ال order
+
+290
+00:31:14,030 --> 00:31:18,550
+لل element يساوي ال order للصورة، مظبوط؟ يبقى هذا
+
+291
+00:31:18,550 --> 00:31:23,330
+في حالة مين؟ ال isomorphism هنا بختلف الكلام كليا
+
+292
+00:31:23,330 --> 00:31:28,510
+عندنا بيقول ال order لل left coset بده يقسم ال
+
+293
+00:31:28,510 --> 00:31:33,490
+order لمين؟ ال order لل element بدنا نروح نثبت صحة
+
+294
+00:31:33,490 --> 00:31:37,350
+هذا الكلام يبقى ال proof
+
+295
+00:31:43,840 --> 00:31:49,140
+لما قال الـ H normal subgroup من G يعني معناته
+
+296
+00:31:49,140 --> 00:31:54,840
+صارت الـ G modulo H اللي هذا أحد عناصرها exist
+
+297
+00:31:54,840 --> 00:31:57,920
+يعني ال factor group أو ال quotient group exist
+
+298
+00:31:57,920 --> 00:32:04,120
+وبالتالي هذا هو أحد العناصر اللي موجود فيهابنثبت
+
+299
+00:32:04,120 --> 00:32:10,220
+ان هذا ال element ال order اللي بده يقسم ال order
+
+300
+00:32:10,220 --> 00:32:15,960
+تبع ال element الثاني يعني ال order لل element في
+
+301
+00:32:15,960 --> 00:32:20,400
+ال quotient group بده يقسم ال order تبع ال element
+
+302
+00:32:20,400 --> 00:32:26,880
+اللي موجود في ال groupبنقوله كويس احنا لو روحنا
+
+303
+00:32:26,880 --> 00:32:33,720
+جينا وقلنا as you افترض ان ال order لل G بده يساوي
+
+304
+00:32:33,720 --> 00:32:40,780
+ال N that is اي ان ال G to the power N بده يساوي
+
+305
+00:32:40,780 --> 00:32:47,840
+مين؟ بده يساوي ال identity طيب لو روحنا وقلنا خدلي
+
+306
+00:32:47,840 --> 00:32:57,730
+GH كله to the power Nيبقى هذا الكلام بده يساوي GN
+
+307
+00:32:57,730 --> 00:33:05,610
+في ال Hالـ GN هي بالـ Identity Element في H بده
+
+308
+00:33:05,610 --> 00:33:11,610
+يسوى من؟ بده يسوى الـ H إذا الـ Order تبع الـ GH
+
+309
+00:33:11,610 --> 00:33:17,890
+شو علاقته بالـ N؟ يعني يقسم من؟ يقسم الـ N و قد
+
+310
+00:33:17,890 --> 00:33:22,950
+يسويها لو سواها كمان بيقسموا هذا معناته إن الـ
+
+311
+00:33:22,950 --> 00:33:31,990
+Order للـ GH Divides الـ Nهذا معناته ان ال order
+
+312
+00:33:31,990 --> 00:33:40,720
+لل GH divides من ال N هذهالـ order تبع الـ G يبقى
+
+313
+00:33:40,720 --> 00:33:45,820
+ال order تبع الـ G وهو المطلوب يبقى من الأن فصاعد
+
+314
+00:33:45,820 --> 00:33:50,180
+لما تحط في دماغك لما يكون عندك normal subgroup
+
+315
+00:33:50,180 --> 00:33:55,340
+وكوّننا ال factor group ال order لأي element في ال
+
+316
+00:33:55,340 --> 00:34:01,280
+factor group بيقسم نظيره من ال element اللي موجود
+
+317
+00:34:01,280 --> 00:34:04,740
+في ال group الأصلية
+
+318
+00:34:06,620 --> 00:34:13,180
+هذا كان سؤال سبعة و تلاتي بدنا نروح لسؤال أربعة و
+
+319
+00:34:13,180 --> 00:34:19,380
+أربعين بيقول يبيني ان دي تلتاش isomorphic لل inner
+
+320
+00:34:19,380 --> 00:34:24,340
+atomorphism اللي دي تلتاش يبقى السؤال أربعة و
+
+321
+00:34:24,340 --> 00:34:36,640
+أربعين show thatإن الـ D13 أيزو مورفك للـ Inner
+
+322
+00:34:36,640 --> 00:34:45,500
+Atomorphism لـ D13 أول
+
+323
+00:34:45,500 --> 00:34:50,220
+مرة نشوف سؤال زي هيك يعني ال Inner Atomorphism للي
+
+324
+00:34:50,220 --> 00:34:57,460
+جروب بدي يكون أيزو مورفك للي جروب itself طيب ممتاز
+
+325
+00:34:58,830 --> 00:35:03,650
+بنحاول انبرهن هذا الكلام من خلال الجزء النظري الذي
+
+326
+00:35:03,650 --> 00:35:11,190
+تعرضنا له في المحاضرات السابقة يبقى solution مرت
+
+327
+00:35:11,190 --> 00:35:16,050
+علينا نظرية فيها isomorphic لل inner atomorphism
+
+328
+00:35:16,050 --> 00:35:23,470
+لل G حد ماذا ذكرها يعني هك؟الـ G-modulus center
+
+329
+00:35:23,470 --> 00:35:30,110
+isomorphic للـ Inner Atomorphism للـ D4 صحيح يبقى
+
+330
+00:35:30,110 --> 00:35:37,590
+احنا أخدنا نظرية بتقول ايش؟ بتقول ان الـ G-modulus
+
+331
+00:35:37,590 --> 00:35:44,230
+center تبع الـ G isomorphic لل Inner Atomorphism
+
+332
+00:35:44,230 --> 00:35:53,800
+لمين؟ للـ Gهذا معناه ان دي تلتاش موديوله جداش ال
+
+333
+00:35:53,800 --> 00:36:02,140
+center تبع ال identity فقط مش السبب تلتاش odd لإن
+
+334
+00:36:02,140 --> 00:36:07,460
+ال center تبع ال D إن لا يوجد فيه إلا two elements
+
+335
+00:36:07,460 --> 00:36:12,220
+إن كان ال N even أو element واحد اللي هو ال
+
+336
+00:36:12,220 --> 00:36:20,750
+trivial إن كان ال N is oddيبقى هذا معناه ان ال D13
+
+337
+00:36:20,750 --> 00:36:29,650
+موديولو ارنود ايزو مورفك لان هذا ال center لمن لل
+
+338
+00:36:29,650 --> 00:36:38,720
+inner atom morphism ل D13 السبب becauseإن الـ
+
+339
+00:36:38,720 --> 00:36:45,920
+Center تبع الـ D13 لا يوجد فيه إلا الـ R node
+
+340
+00:36:45,920 --> 00:36:56,360
+since الـ D13 is odd ممتاز جدا يبقى صار D13 موديل
+
+341
+00:36:56,360 --> 00:37:02,260
+الـ R nodeما لها isomorphic للـ Inner Atomorphism
+
+342
+00:37:02,260 --> 00:37:09,180
+لمين لجى؟ طيب انا الآن لو قدرت اثبت ان جي
+
+343
+00:37:09,180 --> 00:37:14,880
+isomorphic لهذه ال group بصير جي الأصلية
+
+344
+00:37:14,880 --> 00:37:19,900
+isomorphic لمين؟للـ Inner Atomorphism لجيوب التالي
+
+345
+00:37:19,900 --> 00:37:25,360
+بيكون خلصنا يبقى if we show that انه D13
+
+346
+00:37:25,360 --> 00:37:31,920
+isomorphic ل D13 modulo R node then we have the
+
+347
+00:37:31,920 --> 00:37:36,330
+result بيكون حصلنا على من؟ على النتيجةطب كيف
+
+348
+00:37:36,330 --> 00:37:41,210
+بتسويها هذه؟ بسيط اعرف function و اثبت انها one to
+
+349
+00:37:41,210 --> 00:37:46,050
+one and on two و تخدم خاصية ال isomorphism و وصلنا
+
+350
+00:37:46,050 --> 00:37:55,190
+للمطلوب بسهولة كيف؟ ولا في أدفه منها هذا يعني
+
+351
+00:37:55,190 --> 00:37:56,590
+define
+
+352
+00:38:01,200 --> 00:38:11,960
+فاي من D13 الى D13 modulo R0
+
+353
+00:38:17,460 --> 00:38:23,080
+5 of X بدي اخد X موجود في D13 مين ما يكون شكله
+
+354
+00:38:23,080 --> 00:38:28,760
+يكون هذا بدي اودى وين في ال group هذى يبقى هذى
+
+355
+00:38:28,760 --> 00:38:34,020
+كعنصرها كلهم left cosets طبعا هذى مش subgroup
+
+356
+00:38:34,020 --> 00:38:39,040
+generated by Arnold قلتلها generated والله بس ال
+
+357
+00:38:39,040 --> 00:38:44,720
+Arnold ماهيها مافيش غيرهافيش غير هالأنصار هذا
+
+358
+00:38:44,720 --> 00:38:50,420
+تمام؟ بدي أعرفه يبقاش بدي أقوله left corsets يبقى
+
+359
+00:38:50,420 --> 00:38:57,440
+X في مين؟ في الارنر إيش رأيك في التعريف؟ صعب ولا
+
+360
+00:38:57,440 --> 00:39:04,990
+سهل؟ فيش هتفهم انه صحيح؟ليش؟ لأن الاردنود هذه
+
+361
+00:39:04,990 --> 00:39:09,450
+مافيش إلا عنصر واحد اللي هو ال identity element في
+
+362
+00:39:09,450 --> 00:39:15,350
+ال group لكن لو في عناصر تانية بصير هنا فيها كلام
+
+363
+00:39:17,300 --> 00:39:21,100
+طيب اعرفنا ال function هذه بدى اثبتله ان ال
+
+364
+00:39:21,100 --> 00:39:27,600
+function هذه فاي is one to one يبقى بدى اخد صورتين
+
+365
+00:39:27,600 --> 00:39:34,480
+متساويتين فاي اكس بده يساوي فاي واي و بده احاول
+
+366
+00:39:34,480 --> 00:39:40,680
+اثبتله ان ال X يساوي Y يبقى هذا معناه ان ال X في R
+
+367
+00:39:40,680 --> 00:39:47,970
+node بده يساوي ال Y في R nodeهذا الكلام يساوي لما
+
+368
+00:39:47,970 --> 00:39:54,170
+انت ضرب ال X في R node من بيعطيك X itself هذا بده
+
+369
+00:39:54,170 --> 00:39:59,830
+يعطينا هذه
+
+370
+00:39:59,830 --> 00:40:05,530
+تعطيك ال set اللي هي Y set فيش فيها غير عنصر و set
+
+371
+00:40:05,530 --> 00:40:10,610
+فيش فيها غير عنصر يبقوا اتنين متساويتين يبقى ال X
+
+372
+00:40:10,610 --> 00:40:15,580
+بالساوي Y وبالتالي ال Phi one to oneنجل فاي is
+
+373
+00:40:15,580 --> 00:40:20,900
+onto هذي well defined لو كان فيها عناصر لكن مافيش
+
+374
+00:40:20,900 --> 00:40:24,960
+غير ال identity كيف مظلوم فيش غير هو وبالتالي مش
+
+375
+00:40:24,960 --> 00:40:27,940
+محتاجة well defined اما لو كان فيها مجموعة عناصر
+
+376
+00:40:27,940 --> 00:40:37,920
+كلامك صحيح طيب الان فاي is ontoفايوز انتوا يبقى
+
+377
+00:40:37,920 --> 00:40:46,120
+بتروح اخد اللي هو element يبقى let ال element مثلا
+
+378
+00:40:46,120 --> 00:40:56,060
+X R node هذا هيك موجود في مين؟ موجود في ال D
+
+379
+00:40:56,060 --> 00:41:01,900
+تلتاشر modulo اللي هو ال R node
+
+380
+00:41:04,910 --> 00:41:09,010
+يبقى افترض ان هذا ال element موجود هنا
+
+381
+00:41:12,640 --> 00:41:19,120
+الـ X في الـ R نود حسب التعريف تبع الـ function هو
+
+382
+00:41:19,120 --> 00:41:25,220
+بيعطينا main فاي of X يبقى هذا بيعطينا الهو main
+
+383
+00:41:25,220 --> 00:41:31,540
+فاي of X يبقى بناء عليه فاي is onto ضالة النقطة
+
+384
+00:41:31,540 --> 00:41:39,320
+الأخيرة فاي is an isomorphism يبقى بده أروح أخد
+
+385
+00:41:39,320 --> 00:41:48,180
+فاي of XYيبقى هذا الكلام دي يساوي XY في ال R نوت R
+
+386
+00:41:48,180 --> 00:41:53,180
+نوت هو ال identity element يعني بقدر أقول ال X في
+
+387
+00:41:53,180 --> 00:41:58,500
+ال R نوت و في ال Y في ال R نوت بالشكل اللي عندنا
+
+388
+00:41:58,500 --> 00:42:03,280
+هنا و بقدر أشيل ال R نوت بالمرة كمان هذه لأن هو ال
+
+389
+00:42:03,280 --> 00:42:08,700
+identity element تبع ال D13طيب هذه بدها تعطينا
+
+390
+00:42:08,700 --> 00:42:14,440
+مين؟ في of X وهذه بدها تعطينا في of Y لذلك صورة
+
+391
+00:42:14,440 --> 00:42:23,810
+isomorphism يبقى صورة D13 ايزو مورفك ل D13موديولو
+
+392
+00:42:23,810 --> 00:42:33,290
+ارنود وهذه ايزو مورفك للانر اتو مورفزم لمن؟ لل D13
+
+393
+00:42:33,290 --> 00:42:41,370
+وهذا سيعطيك ان D13 ايزو مورفك للانر اتو مورفزم
+
+394
+00:42:41,370 --> 00:42:43,470
+لD13
+
+395
+00:42:46,940 --> 00:42:50,780
+طبعا لو جاءك هذا السؤال في الامتحان وانا جيتها مرة
+
+396
+00:42:50,780 --> 00:42:56,960
+بتسألني سؤالة لما؟ اقول لجروب تبقى isomorphism او
+
+397
+00:42:56,960 --> 00:43:02,140
+isomorphic لا ال inner-automorphism ما احنا بنقول
+
+398
+00:43:02,140 --> 00:43:06,360
+ها هتسألي السؤال انا بقولك اه ممكن هاي مثال يوضح
+
+399
+00:43:06,360 --> 00:43:12,460
+ان هذا الكلام ممكن يبقى هذا كان سؤال اللي هو اربعة
+
+400
+00:43:12,460 --> 00:43:13,840
+واربعين
+
+401
+00:43:16,470 --> 00:43:21,150
+سؤال 46 ستة
+
+402
+00:43:21,150 --> 00:43:29,050
+وأربعين بيقول لو كان جي a group و ال index بتابع
+
+403
+00:43:29,050 --> 00:43:36,070
+ال G ال index بتابع ال G في ال center بتابع ال G
+
+404
+00:43:36,070 --> 00:43:44,410
+بده يساوي قداش أربعة و كذلك كان prove that prove
+
+405
+00:43:44,410 --> 00:43:54,010
+thatبرهلي ان الـ G موديولوسينتر بتبع الـ G ايزو
+
+406
+00:43:54,010 --> 00:44:03,570
+مورفك لمن؟ ل Z2 external product مع من؟ مع Z2
+
+407
+00:44:36,980 --> 00:44:43,400
+خلّي بالقناة السؤال مرة تانية بيقول ال index تبع
+
+408
+00:44:43,400 --> 00:44:46,620
+ال center في ال group G هو أربعة يعني عندي كام
+
+409
+00:44:46,620 --> 00:44:51,200
+left coset؟ أربعة ا prove that ان ال G موديل ال
+
+410
+00:44:51,200 --> 00:44:56,380
+center isomorphic ل Z2 external product مع مين؟ مع
+
+411
+00:44:56,380 --> 00:45:03,420
+Z2 الآن لما أجي أقول ال order ل Z of G بده يساوي
+
+412
+00:45:03,420 --> 00:45:11,120
+أربعةهذا معناته ان ال order لجي موديولوس سنتر
+
+413
+00:45:11,120 --> 00:45:16,460
+بتابع الجي بده يساوي كدهاش؟ أربعة يبقى فيها أربعة
+
+414
+00:45:16,460 --> 00:45:24,300
+عناصر هذا معناه ان الجي موديولوس سنتر بتابع الجي
+
+415
+00:45:24,300 --> 00:45:31,800
+isomorphic يا إما لزد أربعة يا إما لزد اتنين
+
+416
+00:45:31,800 --> 00:45:37,610
+external product مع زد اتنينهذه فيها أربعة وهذه
+
+417
+00:45:37,610 --> 00:45:47,250
+فيها أربعة إذا هذه isomorphic لهذه أو لهذه كيف؟
+
+418
+00:45:47,250 --> 00:45:52,710
+يعني
+
+419
+00:45:52,710 --> 00:45:53,430
+زد أربعة
+
+420
+00:45:57,510 --> 00:46:01,710
+ماشي ماشي لكن انت لما تيجي تبقى ازواج مرتبة مظبوط
+
+421
+00:46:01,710 --> 00:46:07,110
+يعني ايه؟ ما ينطبق عليها ينطبق علي Z4 صح ولا لا
+
+422
+00:46:07,110 --> 00:46:11,710
+حرفيا حتى لو حطيت ال zero في الأول و ال Z في الآخر
+
+423
+00:46:11,710 --> 00:46:17,150
+اربعة نفسها يبقى هدول التنتين هادي و هادي فقط لغير
+
+424
+00:46:17,150 --> 00:46:22,110
+هادي isomorphic لل Z4 كسينوديكا product مع ال zero
+
+425
+00:46:22,110 --> 00:46:27,310
+و اثبتنا اصابق Robonormal قبل هيك كمانطيب يبقى يا
+
+426
+00:46:27,310 --> 00:46:31,750
+اما ايزومورفك لهذه ويا اما ايزومورفك لهذه لو
+
+427
+00:46:31,750 --> 00:46:38,010
+استبعدنا z4 بصير ايزومورفك لمين؟ ل z2 external
+
+428
+00:46:38,010 --> 00:46:45,140
+product مع z2تعالى نشوف هل ممكن نستبعد هذه والله
+
+429
+00:46:45,140 --> 00:46:51,080
+مش ممكن يعنى بدي استبعد انه ال G modula Z تبقى
+
+430
+00:46:51,080 --> 00:46:55,600
+isomorphic لمين ل Z أربعة والله ما احنا عارفين
+
+431
+00:46:55,600 --> 00:47:03,360
+نجرب يالا اقترح علينا نشوف ايش ممكن نسوي في هذه
+
+432
+00:47:05,650 --> 00:47:09,550
+يعني بدي افترض انها ماهياش isomorphic لزت اتنين
+
+433
+00:47:09,550 --> 00:47:12,410
+اكستران ضعية كبيرة لزت اتنين يبقى بيصير isomorphic
+
+434
+00:47:12,410 --> 00:47:19,150
+لمان لزت اربع صحيح ولا لأ طيب بدنا نجي نشوف قداش
+
+435
+00:47:19,150 --> 00:47:25,350
+او ايش ممكن نستنتج من هذا الكلامنشوف الكلام ان هذا
+
+436
+00:47:25,350 --> 00:47:34,590
+بيطلع صح ولا غلط طيب لو جيت قلت assume افترض ان
+
+437
+00:47:34,590 --> 00:47:40,930
+الـ G modulus center بتبع الـ G isomorphically زد
+
+438
+00:47:40,930 --> 00:47:45,750
+4 كويس؟
+
+439
+00:47:46,420 --> 00:47:52,160
+إذا عدد العناصر هنا بيساوي عدد العناصر هنا صحيح
+
+440
+00:47:52,160 --> 00:48:00,780
+ولا لا؟ طيب، الآن باجي بقوله إذا ال order لمن؟ لل
+
+441
+00:48:00,780 --> 00:48:08,060
+G modulo Z of G بيساوي ال order لل G على ال order
+
+442
+00:48:08,060 --> 00:48:14,100
+لل center بتابع ال G قداش ال order بتابع ال G؟
+
+443
+00:48:22,080 --> 00:48:27,860
+كل ال order لها يساوي أربعة هذا الكلام يعني كله
+
+444
+00:48:27,860 --> 00:48:31,460
+على بعض ال order لها يساوي أربعة
+
+445
+00:48:33,420 --> 00:48:37,680
+يبقى هذا كل القيمة بتساوي اربعة يعني معنى هذا
+
+446
+00:48:37,680 --> 00:48:43,680
+الكلام ان ال order ل G اللي انا مش عارفه على ال
+
+447
+00:48:43,680 --> 00:48:50,280
+center بتابع ال G ال G هذي قال ال order اه ماقلش
+
+448
+00:48:50,280 --> 00:48:56,160
+هذي G زد يعني كل اللي بدي اقوله ان ال order ل ال
+
+449
+00:48:56,160 --> 00:49:04,810
+center اه مش عارفينه قديش استنى شويةاستنى شوية طيب
+
+450
+00:49:04,810 --> 00:49:12,130
+احنا عندنا نظرية بتقول ما يأتي هذا الان الـG
+
+451
+00:49:12,130 --> 00:49:17,930
+modulus center يبقى isomorphic لل inner تبع من؟
+
+452
+00:49:17,930 --> 00:49:24,710
+تبع ال group G اللي عندنا صح؟خدنا نظرية اللى
+
+453
+00:49:24,710 --> 00:49:31,870
+توكننا من الحل عليها اللى هو الـ G-modulo الـ G
+
+454
+00:49:31,870 --> 00:49:35,690
+-modulo is center isomorphic للإنر أتو مورفزم
+
+455
+00:49:35,690 --> 00:49:41,150
+لمين؟ لـ G طيب على أي حال ايزال بدنا نحل هذا
+
+456
+00:49:41,150 --> 00:49:44,330
+السؤال وكمان سؤالين قادمات ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..58888a064502de1efeabf4511c3077bd4863fecc
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4863, "start": 21.51, "end": 48.63, "text": "بسم الله الرحمن الرحيم انتهينا في المرة الماضية من شبتر تسعة والان بدنا نعمل discussion حول هذا الشبتر بيقول ايش بيقول لو كان عندى ال cyclic group G يبقى any factor group for this cyclic group is cyclic يعني ايه؟ يعني لما نقول لو افترضنا G is a cyclic group generated by A", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 47395, 1829, 8315, 8978, 9673, 25720, 9673, 46958, 10632, 9154, 13412, 3555, 2655, 2288, 6055, 3794, 27884, 16070, 7649, 47525, 8315, 8717, 25957, 1211, 5017, 11331, 12610, 23758, 25124, 3555, 2655, 2288, 4724, 1829, 39648, 1975, 1829, 8592, 4724, 1829, 39648, 45164, 25961, 43242, 7578, 2423, 38154, 1050, 1594, 460, 7251, 3555, 4587, 7578, 604, 5952, 1594, 337, 341, 38154, 1050, 1594, 307, 38154, 1050, 37495, 22653, 1975, 1829, 3224, 22807, 37495, 22653, 5296, 15042, 8717, 39648, 45164, 1975, 5172, 2655, 43042, 8315, 460, 307, 257, 38154, 1050, 1594, 10833, 538, 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"probability": 0.6326904296875}, {"start": 110.91, "end": 111.37, "word": " ساميه", "probability": 0.697509765625}, {"start": 111.37, "end": 111.43, "word": " اللي", "probability": 0.97509765625}, {"start": 111.43, "end": 111.79, "word": " بدك", "probability": 0.94384765625}, {"start": 111.79, "end": 112.01, "word": " ايه", "probability": 0.6510416666666666}, {"start": 112.01, "end": 113.21, "word": " ساميه", "probability": 0.8128662109375}, {"start": 113.21, "end": 113.65, "word": " والله", "probability": 0.7763671875}, {"start": 113.65, "end": 113.97, "word": " قبل", "probability": 0.613525390625}, {"start": 113.97, "end": 114.15, "word": " ال", "probability": 0.9658203125}, {"start": 114.15, "end": 114.57, "word": " BH", "probability": 0.289794921875}, {"start": 114.57, "end": 116.27, "word": " بدي", "probability": 0.754638671875}, {"start": 116.27, "end": 116.81, "word": " اقول", "probability": 0.87841796875}, {"start": 116.81, "end": 117.03, "word": " ان", "probability": 0.36376953125}, {"start": 117.03, "end": 117.65, "word": " اثبت", "probability": 0.8355712890625}, {"start": 117.65, "end": 117.91, "word": " ما", "probability": 0.59765625}, {"start": 117.91, "end": 118.45, "word": " ياتي", "probability": 0.5723470052083334}, {"start": 118.45, "end": 118.81, "word": " want", "probability": 0.4755859375}, {"start": 118.81, "end": 119.05, "word": " to", "probability": 0.90771484375}, {"start": 119.05, "end": 119.33, "word": " show", "probability": 0.92724609375}, {"start": 119.33, "end": 119.85, "word": " that", "probability": 0.95068359375}], "temperature": 1.0}, {"id": 5, "seek": 14690, "start": 122.04, "end": 146.9, "text": "to show that نحاول نبين ان الـ G modulo H هي عبارة عن subgroup generated by any element من مكان يكون الـ element هذا وليكن على سبيل المثال H كويس", "tokens": [1353, 855, 300, 8717, 5016, 995, 12610, 8717, 3555, 9957, 16472, 2423, 39184, 460, 1072, 13455, 389, 39896, 6225, 3555, 9640, 3660, 18871, 1422, 17377, 10833, 538, 604, 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"end": 136.8, "word": " الـ", "probability": 0.704833984375}, {"start": 136.8, "end": 137.16, "word": " element", "probability": 0.88037109375}, {"start": 137.16, "end": 137.64, "word": " هذا", "probability": 0.9130859375}, {"start": 137.64, "end": 138.8, "word": " وليكن", "probability": 0.7584635416666666}, {"start": 138.8, "end": 139.14, "word": " على", "probability": 0.9580078125}, {"start": 139.14, "end": 139.78, "word": " سبيل", "probability": 0.98974609375}, {"start": 139.78, "end": 140.68, "word": " المثال", "probability": 0.9959309895833334}, {"start": 140.68, "end": 141.72, "word": " H", "probability": 0.70166015625}, {"start": 141.72, "end": 146.9, "word": " كويس", "probability": 0.90478515625}], "temperature": 1.0}, {"id": 6, "seek": 17694, "start": 148.4, "end": 176.94, "text": "مشان هيك بدنا هذا تساوي لو قدت أثبت أن هذه subset من هذه و هذه subset من هذه بيتم المطلوب تمام؟ الآن السؤال هو هل الـAH هذه موجودة في الـG modulo H ولا لأ؟ تمام يعني ال subgroup generated by AH بدها تبقى subset من من subset من الـG modulo H", "tokens": [2304, 8592, 7649, 39896, 4117, 47525, 8315, 23758, 6055, 3794, 995, 45865, 45164, 12174, 3215, 2655, 5551, 12984, 3555, 2655, 14739, 29538, 25993, 9154, 29538, 4032, 29538, 25993, 9154, 29538, 4724, 36081, 2304, 9673, 9566, 1211, 37746, 46811, 10943, 22807, 6024, 48506, 21136, 33604, 6027, 31439, 8032, 1211, 2423, 39184, 10566, 29538, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 38, 1072, 13455, 389, 49429, 5296, 10721, 22807, 46811, 10943, 37495, 22653, 2423, 1422, 17377, 10833, 538, 25888, 47525, 11296, 6055, 3555, 4587, 7578, 25993, 9154, 9154, 25993, 9154, 2423, 39184, 38, 1072, 13455, 389], "avg_logprob": -0.2745065858489589, "compression_ratio": 1.6990740740740742, "no_speech_prob": 0.0, "words": [{"start": 148.4, "end": 148.98, "word": "مشان", "probability": 0.6906331380208334}, {"start": 148.98, "end": 149.86, "word": " هيك", "probability": 0.86279296875}, {"start": 149.86, "end": 150.54, "word": " بدنا", "probability": 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element موجود في ال group يبقى ال sub group المتكونة بهذا ال element بتبقى ال subset من من ال group الأساسية ويعتبر ان هذه رقم واحد بدنا نعمل العملية العكسية بدنا ناخد element هنا ونحاول نثبت انه موجود هنا اذا لو روحت quote let", "tokens": [2304, 19913, 3555, 2407, 9566, 8032, 4117, 15730, 2423, 4478, 3714, 29245, 23328, 8978, 2423, 1594, 7251, 3555, 4587, 7578, 2423, 1422, 1594, 9673, 2655, 30544, 3660, 39627, 15730, 2423, 4478, 39894, 3555, 4587, 7578, 2423, 25993, 9154, 9154, 2423, 1594, 16247, 3794, 32277, 10632, 4032, 1829, 34268, 26890, 16472, 29538, 12602, 4587, 2304, 36764, 24401, 47525, 8315, 8717, 25957, 1211, 18863, 42213, 10632, 18863, 4117, 3794, 10632, 47525, 8315, 8717, 47283, 3215, 4478, 34105, 4032, 1863, 5016, 995, 12610, 8717, 12984, 3555, 2655, 16472, 3224, 3714, 29245, 23328, 34105, 1975, 15730, 45164, 12602, 2407, 33753, 6513, 718], "avg_logprob": -0.27588383958797263, "compression_ratio": 1.8238095238095238, "no_speech_prob": 0.0, "words": [{"start": 177.81, 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" المتكونة", "probability": 0.79156494140625}, {"start": 183.67, "end": 184.23, "word": " بهذا", "probability": 0.956298828125}, {"start": 184.23, "end": 184.51, "word": " ال", "probability": 0.90869140625}, {"start": 184.51, "end": 185.11, "word": " element", "probability": 0.96728515625}, {"start": 185.11, "end": 186.23, "word": " بتبقى", "probability": 0.814208984375}, {"start": 186.23, "end": 186.43, "word": " ال", "probability": 0.849609375}, {"start": 186.43, "end": 186.93, "word": " subset", "probability": 0.896484375}, {"start": 186.93, "end": 187.39, "word": " من", "probability": 0.97216796875}, {"start": 187.39, "end": 187.65, "word": " من", "probability": 0.4140625}, {"start": 187.65, "end": 188.39, "word": " ال", "probability": 0.654296875}, {"start": 188.39, "end": 188.67, "word": " group", "probability": 0.978515625}, {"start": 188.67, "end": 189.73, "word": " الأساسية", "probability": 0.944580078125}, {"start": 189.73, "end": 190.41, "word": " ويعتبر", "probability": 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كويس الآن احنا عندنا B موجودة في الـ G مظبوط ولا لا؟ B موجودة في الـ G", "tokens": [6027, 39184, 363, 389, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 460, 1072, 13455, 389, 11933, 15730, 12174, 3215, 43500, 5551, 12984, 3555, 2655, 36145, 2423, 39184, 363, 389, 3714, 29245, 23328, 3660, 34105, 4724, 36081, 2304, 9673, 9566, 1211, 37746, 23032, 1829, 3555, 9122, 45865, 3794, 6024, 48506, 1975, 5016, 8315, 43242, 8315, 363, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 460, 3714, 19913, 3555, 2407, 9566, 49429, 20193, 22807, 363, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 460], "avg_logprob": -0.21566358613379208, "compression_ratio": 1.773972602739726, "no_speech_prob": 0.0, "words": [{"start": 204.52, "end": 205.1, "word": "الـ", "probability": 0.751708984375}, {"start": 205.1, "end": 205.32, "word": " B", "probability": 0.2318115234375}, {"start": 205.32, "end": 206.06, "word": " H", "probability": 0.58447265625}, {"start": 206.06, "end": 207.12, "word": " موجودة", "probability": 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29313, "start": 273.79, "end": 293.13, "text": "يبقى AI في ال H AI في H عبارة عن A H A H A H I من المرات او بمعنى اخر هذه بدها تساوي A H كله to the power I", "tokens": [1829, 3555, 4587, 7578, 7318, 8978, 2423, 389, 7318, 8978, 389, 6225, 3555, 9640, 3660, 18871, 316, 389, 316, 389, 316, 389, 286, 9154, 9673, 2288, 9307, 1975, 2407, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 29538, 47525, 11296, 6055, 3794, 995, 45865, 316, 389, 28242, 3224, 281, 264, 1347, 286], "avg_logprob": -0.2223557669382829, "compression_ratio": 1.2764227642276422, "no_speech_prob": 0.0, "words": [{"start": 273.79, "end": 274.67, "word": "يبقى", "probability": 0.9556884765625}, {"start": 274.67, "end": 275.45, "word": " AI", "probability": 0.491943359375}, {"start": 275.45, "end": 276.41, "word": " في", "probability": 0.84619140625}, {"start": 276.41, "end": 276.87, "word": " ال", "probability": 0.462890625}, {"start": 276.87, "end": 277.71, "word": " H", "probability": 0.2169189453125}, {"start": 277.71, "end": 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11296, 6055, 3794, 995, 45865, 2423, 1422, 17377, 10833, 538, 389, 7251, 3555, 4587, 7578, 34105, 370, 2423, 460, 1072, 13455, 389, 307, 38154, 1050, 4032, 7649, 47395, 1829, 8315, 9154, 21136, 33604, 6027], "avg_logprob": -0.24490489583948385, "compression_ratio": 1.2213740458015268, "no_speech_prob": 0.0, "words": [{"start": 327.78, "end": 328.34, "word": "إن", "probability": 0.552032470703125}, {"start": 328.34, "end": 328.66, "word": " الـ", "probability": 0.624267578125}, {"start": 328.66, "end": 328.84, "word": " G", "probability": 0.73876953125}, {"start": 328.84, "end": 329.66, "word": " modulo", "probability": 0.839599609375}, {"start": 329.66, "end": 330.12, "word": " H", "probability": 0.93212890625}, {"start": 330.12, "end": 330.92, "word": " اللي", "probability": 0.680419921875}, {"start": 330.92, "end": 331.42, "word": " بدها", "probability": 0.830078125}, {"start": 331.42, "end": 332.22, "word": " تساوي", "probability": 0.970458984375}, {"start": 332.22, "end": 332.86, 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subgroup generated by تمانية يساوي ستة زائد تمانية زي ال subgroup generated by تمانية ال element هذا موجود هنا ولا لا يبقى هدول إيش بدهم يعطوني؟", "tokens": [6027, 9640, 3555, 34268, 33599, 2288, 30767, 1829, 2423, 1422, 17377, 10833, 538, 46811, 7649, 10632, 7251, 3794, 995, 45865, 8608, 2655, 3660, 30767, 16373, 3215, 46811, 7649, 10632, 30767, 1829, 2423, 1422, 17377, 10833, 538, 46811, 7649, 10632, 2423, 4478, 23758, 3714, 29245, 23328, 34105, 49429, 20193, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 11933, 1829, 8592, 47525, 16095, 37495, 9566, 11536, 1829, 22807], "avg_logprob": -0.23129735029104984, "compression_ratio": 1.585987261146497, "no_speech_prob": 0.0, "words": [{"start": 426.38, "end": 427.42, "word": "الاربعتاشر", "probability": 0.7037760416666666}, {"start": 427.42, "end": 427.7, "word": " زي", "probability": 0.804443359375}, {"start": 427.7, "end": 427.94, "word": " ال", "probability": 0.54541015625}, {"start": 427.94, "end": 428.66, "word": " subgroup", 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لهذه والله لهذه تعالوا نشوف", "tokens": [41185, 2423, 389, 23032, 3555, 3615, 995, 39896, 9566, 1211, 3615, 14407, 45030, 11242, 16095, 7251, 3794, 995, 45865, 45030, 11242, 34051, 39896, 9566, 1211, 3615, 14407, 21136, 2655, 3660, 9154, 16095, 28242, 8608, 2655, 3660, 4724, 1829, 3794, 995, 45865, 45030, 11242, 6156, 3555, 1829, 9381, 5172, 6225, 8315, 3714, 9957, 22807, 4724, 1829, 9381, 5172, 6225, 8315, 16712, 2304, 7649, 10632, 13672, 1829, 12174, 3215, 10943, 8315, 8032, 3215, 12610, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 18871, 33546, 2288, 2423, 1594, 13672, 1829, 43242, 4117, 25961, 8608, 33604, 6027, 31439, 29538, 307, 32702, 299, 32767, 9957, 22807, 8032, 1211, 5551, 11622, 3215, 46811, 7649, 10632, 22807, 16070, 43761, 46740, 24192, 16070, 43761, 46740, 24192, 37279, 6027, 14407, 8717, 8592, 38688], "avg_logprob": -0.22190019692624768, "compression_ratio": 1.918552036199095, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 848.83, "end": 849.13, "word": 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ل", "probability": 0.79638671875}, {"start": 1078.27, "end": 1078.57, "word": " Z", "probability": 0.72998046875}, {"start": 1078.57, "end": 1079.11, "word": " تمانية", "probability": 0.98974609375}, {"start": 1079.11, "end": 1079.79, "word": " طيب", "probability": 0.90625}, {"start": 1079.79, "end": 1080.21, "word": " هذه", "probability": 0.424560546875}], "temperature": 1.0}, {"id": 48, "seek": 109741, "start": 1080.93, "end": 1097.41, "text": "أقصى order فيها جداش تنين يبقى هذه أربع يبقى لا يمكن تكون isomorphic لهذه يبقى بضل إجباري isomorphic لمين لزد أربع external product مع زد اتنين يبقى هذا بده يعطيني", "tokens": [10721, 4587, 9381, 7578, 1668, 8978, 11296, 10874, 3215, 33599, 6055, 1863, 9957, 7251, 3555, 4587, 7578, 29538, 5551, 25513, 3615, 7251, 3555, 4587, 7578, 20193, 7251, 43020, 6055, 30544, 307, 32702, 299, 46740, 24192, 7251, 3555, 4587, 7578, 4724, 11242, 1211, 11933, 7435, 3555, 9640, 1829, 307, 32702, 299, 32767, 9957, 5296, 11622, 3215, 5551, 25513, 3615, 8320, 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0.8834228515625}, {"start": 1085.55, "end": 1085.69, "word": " لا", "probability": 0.440673828125}, {"start": 1085.69, "end": 1086.07, "word": " يمكن", "probability": 0.953369140625}, {"start": 1086.07, "end": 1086.53, "word": " تكون", "probability": 0.802490234375}, {"start": 1086.53, "end": 1087.57, "word": " isomorphic", "probability": 0.8055013020833334}, {"start": 1087.57, "end": 1088.03, "word": " لهذه", "probability": 0.853271484375}, {"start": 1088.03, "end": 1088.65, "word": " يبقى", "probability": 0.92529296875}, {"start": 1088.65, "end": 1088.99, "word": " بضل", "probability": 0.594970703125}, {"start": 1088.99, "end": 1089.51, "word": " إجباري", "probability": 0.93349609375}, {"start": 1089.51, "end": 1090.23, "word": " isomorphic", "probability": 0.8818359375}, {"start": 1090.23, "end": 1090.69, "word": " لمين", "probability": 0.7294921875}, {"start": 1090.69, "end": 1091.57, "word": " لزد", "probability": 0.3231608072916667}, {"start": 1091.57, "end": 1091.95, "word": " أربع", "probability": 0.7032877604166666}, {"start": 1091.95, "end": 1092.37, "word": " external", "probability": 0.66552734375}, {"start": 1092.37, "end": 1092.83, "word": " product", "probability": 0.763671875}, {"start": 1092.83, "end": 1093.65, "word": " مع", "probability": 0.66650390625}, {"start": 1093.65, "end": 1094.53, "word": " زد", "probability": 0.82666015625}, {"start": 1094.53, "end": 1095.03, "word": " اتنين", "probability": 0.9354248046875}, {"start": 1095.03, "end": 1095.83, "word": " يبقى", "probability": 0.9697265625}, {"start": 1095.83, "end": 1096.17, "word": " هذا", "probability": 0.86962890625}, {"start": 1096.17, "end": 1096.71, "word": " بده", "probability": 0.46600341796875}, {"start": 1096.71, "end": 1097.41, "word": " يعطيني", "probability": 0.7890625}], "temperature": 1.0}, {"id": 49, "seek": 111658, "start": 1097.75, "end": 1116.59, "text": "الجروب اللي عندنا هو Z4 Xenodyic product لـ Z12 is not isomorphic لـ Z8 لأن Z8 فيها elements ال order لهم يسوى تمانية", "tokens": [6027, 7435, 32887, 3555, 13672, 1829, 43242, 8315, 31439, 1176, 19, 1783, 268, 843, 299, 1674, 5296, 39184, 1176, 4762, 307, 406, 307, 32702, 299, 5296, 39184, 1176, 23, 5296, 33456, 1176, 23, 8978, 11296, 4959, 2423, 1668, 5296, 16095, 7251, 3794, 2407, 7578, 46811, 7649, 10632], "avg_logprob": -0.41080730470518273, "compression_ratio": 1.1267605633802817, "no_speech_prob": 0.0, "words": [{"start": 1097.75, "end": 1099.13, "word": "الجروب", "probability": 0.56939697265625}, {"start": 1099.13, "end": 1099.41, "word": " اللي", "probability": 0.635009765625}, {"start": 1099.41, "end": 1100.07, "word": " عندنا", "probability": 0.838623046875}, {"start": 1100.07, "end": 1101.27, "word": " هو", "probability": 0.369384765625}, {"start": 1101.27, "end": 1102.87, "word": " Z4", "probability": 0.4903564453125}, {"start": 1102.87, "end": 1104.01, "word": " Xenodyic", "probability": 0.465484619140625}, {"start": 1104.01, "end": 1104.65, "word": " product", "probability": 0.61572265625}, {"start": 1104.65, "end": 1105.49, "word": " لـ", "probability": 0.5186767578125}, {"start": 1105.49, "end": 1106.37, "word": " Z12", "probability": 0.804443359375}, {"start": 1106.37, "end": 1107.31, "word": " is", "probability": 0.55126953125}, {"start": 1107.31, "end": 1108.07, "word": " not", "probability": 0.9345703125}, {"start": 1108.07, "end": 1109.67, "word": " isomorphic", "probability": 0.8860677083333334}, {"start": 1109.67, "end": 1110.37, "word": " لـ", "probability": 0.80615234375}, {"start": 1110.37, "end": 1111.51, "word": " Z8", "probability": 0.900634765625}, {"start": 1111.51, "end": 1112.37, "word": " لأن", "probability": 0.803955078125}, {"start": 1112.37, "end": 1113.17, "word": " Z8", "probability": 0.9453125}, {"start": 1113.17, "end": 1113.69, "word": " فيها", "probability": 0.95361328125}, {"start": 1113.69, "end": 1114.17, "word": " elements", "probability": 0.79931640625}, {"start": 1114.17, "end": 1114.41, "word": " ال", "probability": 0.61669921875}, {"start": 1114.41, "end": 1114.81, "word": " order", "probability": 0.8232421875}, {"start": 1114.81, "end": 1115.31, "word": " لهم", "probability": 0.57354736328125}, {"start": 1115.31, "end": 1115.97, "word": " يسوى", "probability": 0.7845458984375}, {"start": 1115.97, "end": 1116.59, "word": " تمانية", "probability": 0.841796875}], "temperature": 1.0}, {"id": 50, "seek": 114580, "start": 1119.3, "end": 1145.8, "text": "الـ z4 external product مع z12 طبعا modulo h يا شباب وهنا كمان modulo h لا يمكن تبقى isomorphic إلى z2 external product مع z2 external product مع z2 because", "tokens": [6027, 39184, 710, 19, 8320, 1674, 20449, 710, 4762, 23032, 3555, 3615, 995, 1072, 13455, 276, 35186, 13412, 3555, 16758, 37037, 8315, 9122, 2304, 7649, 1072, 13455, 276, 20193, 7251, 43020, 6055, 3555, 4587, 7578, 307, 32702, 299, 30731, 710, 17, 8320, 1674, 20449, 710, 17, 8320, 1674, 20449, 710, 17, 570], "avg_logprob": -0.2762381940517785, "compression_ratio": 1.4411764705882353, "no_speech_prob": 0.0, "words": [{"start": 1119.3, "end": 1120.36, "word": "الـ", "probability": 0.4656982421875}, {"start": 1120.36, "end": 1121.84, "word": " z4", "probability": 0.3736572265625}, {"start": 1121.84, "end": 1123.34, "word": " external", "probability": 0.43017578125}, {"start": 1123.34, "end": 1123.94, "word": " product", "probability": 0.2254638671875}, {"start": 1123.94, "end": 1125.04, "word": " مع", "probability": 0.4609375}, {"start": 1125.04, "end": 1126.74, "word": " z12", "probability": 0.85400390625}, {"start": 1126.74, "end": 1127.36, "word": " طبعا", "probability": 0.8839111328125}, {"start": 1127.36, "end": 1127.7, "word": " modulo", "probability": 0.761962890625}, {"start": 1127.7, "end": 1129.58, "word": " h", "probability": 0.25390625}, {"start": 1129.58, "end": 1129.88, "word": " يا", "probability": 0.73046875}, {"start": 1129.88, "end": 1130.24, "word": " شباب", "probability": 0.9296875}, {"start": 1130.24, "end": 1131.16, "word": " وهنا", "probability": 0.790283203125}, {"start": 1131.16, "end": 1131.68, "word": " كمان", "probability": 0.9202473958333334}, {"start": 1131.68, "end": 1132.44, "word": " modulo", "probability": 0.927001953125}, {"start": 1132.44, "end": 1132.96, "word": " h", "probability": 0.90625}, {"start": 1132.96, "end": 1133.74, "word": " لا", "probability": 0.5791015625}, {"start": 1133.74, "end": 1134.38, "word": " يمكن", "probability": 0.814208984375}, {"start": 1134.38, "end": 1135.12, "word": " تبقى", "probability": 0.9464111328125}, {"start": 1135.12, "end": 1136.48, "word": " isomorphic", "probability": 0.8785807291666666}, {"start": 1136.48, "end": 1136.84, "word": " إلى", "probability": 0.59619140625}, {"start": 1136.84, "end": 1137.82, "word": " z2", "probability": 0.962646484375}, {"start": 1137.82, "end": 1138.52, "word": " external", "probability": 0.814453125}, {"start": 1138.52, "end": 1138.98, "word": " product", "probability": 0.908203125}, {"start": 1138.98, "end": 1140.24, "word": " مع", "probability": 0.8447265625}, {"start": 1140.24, "end": 1141.28, "word": " z2", "probability": 0.98486328125}, {"start": 1141.28, "end": 1141.98, "word": " external", "probability": 0.7109375}, {"start": 1141.98, "end": 1142.72, "word": " product", "probability": 0.96533203125}, {"start": 1142.72, "end": 1143.8, "word": " مع", "probability": 0.94873046875}, {"start": 1143.8, "end": 1144.76, "word": " z2", "probability": 0.988525390625}, {"start": 1144.76, "end": 1145.8, "word": " because", "probability": 0.81640625}], "temperature": 1.0}, {"id": 51, "seek": 117433, "start": 1149.36, "end": 1174.34, "text": "the last group has orders of .. والله has elements of orders واحد واتنين فقط", "tokens": [3322, 1036, 1594, 575, 9470, 295, 4386, 16070, 43761, 575, 4959, 295, 9470, 36764, 24401, 4032, 9307, 1863, 9957, 6156, 47432], "avg_logprob": -0.1928267086094076, "compression_ratio": 1.1325301204819278, "no_speech_prob": 0.0, "words": [{"start": 1149.36, "end": 1150.76, "word": "the", "probability": 0.34130859375}, {"start": 1150.76, "end": 1152.16, "word": " last", "probability": 0.884765625}, {"start": 1152.16, "end": 1153.98, "word": " group", "probability": 0.978515625}, {"start": 1153.98, "end": 1156.74, "word": " has", "probability": 0.86962890625}, {"start": 1156.74, "end": 1159.22, "word": " orders", "probability": 0.845703125}, {"start": 1159.22, "end": 1160.9, "word": " of", "probability": 0.85986328125}, {"start": 1160.9, "end": 1162.16, "word": " ..", "probability": 0.6953125}, {"start": 1162.16, "end": 1162.56, "word": " والله", "probability": 0.698974609375}, {"start": 1162.56, "end": 1162.98, "word": " has", "probability": 0.7548828125}, {"start": 1162.98, "end": 1164.18, "word": " elements", "probability": 0.92724609375}, {"start": 1164.18, "end": 1168.94, "word": " of", "probability": 0.97509765625}, {"start": 1168.94, "end": 1170.78, "word": " orders", "probability": 0.88818359375}, {"start": 1170.78, "end": 1172.86, "word": " واحد", "probability": 0.96728515625}, {"start": 1172.86, "end": 1173.82, "word": " واتنين", "probability": 0.8704833984375}, {"start": 1173.82, "end": 1174.34, "word": " فقط", "probability": 0.988037109375}], "temperature": 1.0}, {"id": 52, "seek": 120209, "start": 1175.22, "end": 1202.1, "text": "يبقى بناء عليه بقول له thus وهكذا z for external byproduct مع z12 modulo h is isomorphic الى z4 external byproduct مع z2 يعني حذفنا two groups ولاجناها isomorphic لواحدة من ال groups الأخرى", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 47356, 4724, 39648, 46740, 8807, 37037, 4117, 15730, 710, 337, 8320, 538, 33244, 20449, 710, 4762, 1072, 13455, 276, 307, 307, 32702, 299, 2423, 7578, 710, 19, 8320, 538, 33244, 20449, 710, 17, 37495, 22653, 11331, 8848, 5172, 8315, 732, 3935, 4032, 15040, 7435, 8315, 11296, 307, 32702, 299, 5296, 14407, 24401, 3660, 9154, 2423, 3935, 16247, 34740, 7578], "avg_logprob": -0.25970643216913397, "compression_ratio": 1.4078212290502794, "no_speech_prob": 0.0, "words": [{"start": 1175.22, "end": 1175.72, "word": "يبقى", "probability": 0.831298828125}, {"start": 1175.72, "end": 1176.2, "word": " بناء", "probability": 0.84228515625}, {"start": 1176.2, "end": 1176.6, "word": " عليه", "probability": 0.63525390625}, {"start": 1176.6, "end": 1177.04, "word": " بقول", "probability": 0.913330078125}, {"start": 1177.04, "end": 1177.24, "word": " له", "probability": 0.1956787109375}, {"start": 1177.24, "end": 1177.7, "word": " thus", "probability": 0.284912109375}, {"start": 1177.7, "end": 1178.84, "word": " وهكذا", "probability": 0.841796875}, {"start": 1178.84, "end": 1179.76, "word": " z", "probability": 0.515625}, {"start": 1179.76, "end": 1180.46, "word": " for", "probability": 0.64892578125}, {"start": 1180.46, "end": 1181.34, "word": " external", "probability": 0.6845703125}, {"start": 1181.34, "end": 1182.2, "word": " byproduct", "probability": 0.4140625}, {"start": 1182.2, "end": 1183.14, "word": " مع", "probability": 0.81396484375}, {"start": 1183.14, "end": 1184.02, "word": " z12", "probability": 0.667724609375}, {"start": 1184.02, "end": 1185.04, "word": " modulo", "probability": 0.73583984375}, {"start": 1185.04, "end": 1185.46, "word": " h", "probability": 0.79248046875}, {"start": 1185.46, "end": 1186.18, "word": " is", "probability": 0.9248046875}, {"start": 1186.18, "end": 1187.94, "word": " isomorphic", "probability": 0.9168294270833334}, {"start": 1187.94, "end": 1188.44, "word": " الى", "probability": 0.609619140625}, {"start": 1188.44, "end": 1189.58, "word": " z4", "probability": 0.96826171875}, {"start": 1189.58, "end": 1190.68, "word": " external", "probability": 0.880859375}, {"start": 1190.68, "end": 1191.78, "word": " byproduct", "probability": 0.84228515625}, {"start": 1191.78, "end": 1192.84, "word": " مع", "probability": 0.962890625}, {"start": 1192.84, "end": 1193.44, "word": " z2", "probability": 0.98193359375}, {"start": 1193.44, "end": 1193.94, "word": " يعني", "probability": 0.86181640625}, {"start": 1193.94, "end": 1194.66, "word": " حذفنا", "probability": 0.920654296875}, {"start": 1194.66, "end": 1195.04, "word": " two", "probability": 0.90625}, {"start": 1195.04, "end": 1195.72, "word": " groups", "probability": 0.94921875}, {"start": 1195.72, "end": 1196.96, "word": " ولاجناها", "probability": 0.720947265625}, {"start": 1196.96, "end": 1198.24, "word": " isomorphic", "probability": 0.9324544270833334}, {"start": 1198.24, "end": 1199.3, "word": " لواحدة", "probability": 0.8521728515625}, {"start": 1199.3, "end": 1199.64, "word": " من", "probability": 0.9951171875}, {"start": 1199.64, "end": 1199.88, "word": " ال", "probability": 0.85888671875}, {"start": 1199.88, "end": 1200.54, "word": " groups", "probability": 0.84716796875}, {"start": 1200.54, "end": 1202.1, "word": " الأخرى", "probability": 0.9366861979166666}], "temperature": 1.0}, {"id": 53, "seek": 124072, "start": 1216.06, "end": 1240.72, "text": "هذا كان سؤال 24 خد لي سؤال 28 سؤال 28 حول نفس الموضوع بيقول بيقول جي تساوي زد اربعة جي تساوي زد اربعة external product مع زد اربعة", "tokens": [3224, 15730, 25961, 8608, 33604, 6027, 4022, 16490, 3215, 32239, 8608, 33604, 6027, 7562, 8608, 33604, 6027, 7562, 11331, 12610, 8717, 36178, 9673, 2407, 11242, 45367, 4724, 1829, 39648, 4724, 1829, 39648, 10874, 1829, 6055, 3794, 995, 45865, 30767, 3215, 1975, 25513, 27884, 10874, 1829, 6055, 3794, 995, 45865, 30767, 3215, 1975, 25513, 27884, 8320, 1674, 20449, 30767, 3215, 1975, 25513, 27884], "avg_logprob": -0.26587302628017606, "compression_ratio": 1.618320610687023, "no_speech_prob": 0.0, "words": [{"start": 1216.06, "end": 1216.46, "word": "هذا", "probability": 0.716796875}, {"start": 1216.46, "end": 1216.9, "word": " كان", "probability": 0.86328125}, {"start": 1216.9, "end": 1217.86, "word": " سؤال", "probability": 0.9140625}, {"start": 1217.86, "end": 1218.76, "word": " 24", "probability": 0.308349609375}, {"start": 1218.76, "end": 1221.0, "word": " خد", "probability": 0.575927734375}, {"start": 1221.0, "end": 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"temperature": 1.0}, {"id": 85, "seek": 200919, "start": 1980.41, "end": 2009.19, "text": "الـ GN هي بالـ Identity Element في H بده يسوى من؟ بده يسوى الـ H إذا الـ Order تبع الـ GH شو علاقته بالـ N؟ يعني يقسم من؟ يقسم الـ N و قد يسويها لو سواها كمان بيقسموا هذا معناته إن الـ Order للـ GH Divides الـ N", "tokens": [6027, 39184, 46411, 39896, 20666, 39184, 25905, 507, 20900, 8978, 389, 47525, 3224, 7251, 3794, 2407, 7578, 9154, 22807, 47525, 3224, 7251, 3794, 2407, 7578, 2423, 39184, 389, 11933, 15730, 2423, 39184, 16321, 6055, 3555, 3615, 2423, 39184, 40690, 13412, 2407, 11203, 995, 38149, 3224, 20666, 39184, 426, 22807, 37495, 22653, 7251, 4587, 38251, 9154, 22807, 7251, 4587, 38251, 2423, 39184, 426, 4032, 12174, 3215, 7251, 3794, 45865, 11296, 45164, 8608, 14407, 11296, 9122, 2304, 7649, 4724, 1829, 4587, 38251, 14407, 23758, 20449, 8315, 47395, 36145, 2423, 39184, 16321, 24976, 39184, 40690, 9886, 1875, 2423, 39184, 426], "avg_logprob": -0.25781249969589465, "compression_ratio": 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"word": " N", "probability": 0.94921875}], "temperature": 1.0}, {"id": 86, "seek": 201753, "start": 2009.63, "end": 2017.53, "text": "هذا معناته ان ال order لل GH divides من ال N هذه", "tokens": [3224, 15730, 20449, 8315, 47395, 16472, 2423, 1668, 24976, 40690, 41347, 9154, 2423, 426, 29538], "avg_logprob": -0.46704101376235485, "compression_ratio": 1.0294117647058822, "no_speech_prob": 0.0, "words": [{"start": 2009.63, "end": 2010.19, "word": "هذا", "probability": 0.91064453125}, {"start": 2010.19, "end": 2010.93, "word": " معناته", "probability": 0.8582356770833334}, {"start": 2010.93, "end": 2011.25, "word": " ان", "probability": 0.58203125}, {"start": 2011.25, "end": 2011.47, "word": " ال", "probability": 0.62255859375}, {"start": 2011.47, "end": 2011.99, "word": " order", "probability": 0.763671875}, {"start": 2011.99, "end": 2012.45, "word": " لل", "probability": 0.6787109375}, {"start": 2012.45, "end": 2013.27, "word": " GH", "probability": 0.267333984375}, {"start": 2013.27, 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"word": " that", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 89, "seek": 209746, "start": 2070.14, "end": 2097.46, "text": "إن الـ D13 أيزو مورفك للـ Inner Atomorphism لـ D13 أول مرة نشوف سؤال زي هيك يعني ال Inner Atomorphism للي جروب بدي يكون أيزو مورفك للي جروب itself طيب ممتاز", "tokens": [28814, 1863, 2423, 39184, 413, 7668, 5551, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 24976, 39184, 36705, 1711, 32702, 1434, 5296, 39184, 413, 7668, 5551, 12610, 3714, 25720, 8717, 8592, 38688, 8608, 33604, 6027, 30767, 1829, 39896, 4117, 37495, 22653, 2423, 36705, 1711, 32702, 1434, 5296, 20292, 10874, 32887, 3555, 4724, 16254, 7251, 30544, 5551, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 20292, 10874, 32887, 3555, 2564, 23032, 1829, 3555, 3714, 2304, 2655, 31377], "avg_logprob": -0.25102797111398295, "compression_ratio": 1.5454545454545454, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2070.14, "end": 2070.6, "word": "إن", "probability": 0.61578369140625}, {"start": 2070.6, "end": 2070.9, "word": " الـ", "probability": 0.5662841796875}, {"start": 2070.9, "end": 2072.48, "word": " D13", "probability": 0.767822265625}, {"start": 2072.48, "end": 2074.42, "word": " أيزو", "probability": 0.6226043701171875}, {"start": 2074.42, "end": 2075.18, "word": " مورفك", "probability": 0.8447265625}, {"start": 2075.18, "end": 2076.24, "word": " للـ", "probability": 0.77587890625}, {"start": 2076.24, "end": 2076.64, "word": " Inner", "probability": 0.67138671875}, {"start": 2076.64, "end": 2078.36, "word": " Atomorphism", "probability": 0.8224283854166666}, {"start": 2078.36, "end": 2079.22, "word": " لـ", "probability": 0.801513671875}, {"start": 2079.22, "end": 2080.3, "word": " D13", "probability": 0.825927734375}, {"start": 2080.3, "end": 2085.5, "word": " أول", "probability": 0.91796875}, {"start": 2085.5, "end": 2085.76, "word": " مرة", "probability": 0.988037109375}, {"start": 2085.76, "end": 2086.04, "word": " نشوف", "probability": 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نظرية", "probability": 0.98681640625}, {"start": 2112.47, "end": 2113.05, "word": " فيها", "probability": 0.974609375}, {"start": 2113.05, "end": 2114.21, "word": " isomorphic", "probability": 0.8380533854166666}, {"start": 2114.21, "end": 2114.41, "word": " لل", "probability": 0.91064453125}, {"start": 2114.41, "end": 2114.81, "word": " inner", "probability": 0.7451171875}, {"start": 2114.81, "end": 2116.05, "word": " atomorphism", "probability": 0.5928548177083334}, {"start": 2116.05, "end": 2116.37, "word": " لل", "probability": 0.88427734375}, {"start": 2116.37, "end": 2116.69, "word": " G", "probability": 0.411865234375}, {"start": 2116.69, "end": 2117.75, "word": " حد", "probability": 0.748779296875}, {"start": 2117.75, "end": 2118.01, "word": " ماذا", "probability": 0.5638020833333334}, {"start": 2118.01, "end": 2118.55, "word": " ذكرها", "probability": 0.8590494791666666}, {"start": 2118.55, "end": 2118.89, "word": " يعني", "probability": 0.9140625}, {"start": 2118.89, "end": 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two", "probability": 0.69970703125}, {"start": 2166.78, "end": 2167.46, "word": " elements", "probability": 0.89501953125}, {"start": 2167.46, "end": 2168.06, "word": " إن", "probability": 0.57568359375}, {"start": 2168.06, "end": 2168.38, "word": " كان", "probability": 0.99072265625}, {"start": 2168.38, "end": 2168.68, "word": " ال", "probability": 0.9853515625}, {"start": 2168.68, "end": 2169.0, "word": " N", "probability": 0.379150390625}, {"start": 2169.0, "end": 2169.72, "word": " even", "probability": 0.83837890625}, {"start": 2169.72, "end": 2170.46, "word": " أو", "probability": 0.8095703125}, {"start": 2170.46, "end": 2171.18, "word": " element", "probability": 0.70703125}, {"start": 2171.18, "end": 2171.74, "word": " واحد", "probability": 0.98779296875}, {"start": 2171.74, "end": 2171.92, "word": " اللي", "probability": 0.9658203125}, {"start": 2171.92, "end": 2172.1, "word": " هو", "probability": 0.80908203125}, {"start": 2172.1, "end": 2172.22, "word": " ال", "probability": 0.1614990234375}, {"start": 2172.22, "end": 2172.9, "word": " trivial", "probability": 0.94482421875}, {"start": 2172.9, "end": 2173.58, "word": " إن", "probability": 0.8447265625}, {"start": 2173.58, "end": 2173.86, "word": " كان", "probability": 0.97021484375}, {"start": 2173.86, "end": 2174.2, "word": " ال", "probability": 0.56640625}, {"start": 2174.2, "end": 2174.62, "word": " N", "probability": 0.904296875}, {"start": 2174.62, "end": 2175.14, "word": " is", "probability": 0.69091796875}, {"start": 2175.14, "end": 2175.56, "word": " odd", "probability": 0.90478515625}], "temperature": 1.0}, {"id": 93, "seek": 219663, "start": 2176.03, "end": 2196.63, "text": "يبقى هذا معناه ان ال D13 موديولو ارنود ايزو مورفك لان هذا ال center لمن لل inner atom morphism ل D13 السبب because", "tokens": [1829, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 2423, 413, 7668, 3714, 2407, 16254, 12610, 2407, 1975, 2288, 1863, 23328, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 7649, 23758, 2423, 3056, 5296, 27842, 24976, 7284, 12018, 25778, 1434, 5296, 413, 7668, 21136, 3555, 3555, 570], "avg_logprob": -0.41390305149311923, "compression_ratio": 1.2686567164179106, "no_speech_prob": 0.0, "words": [{"start": 2176.03, "end": 2176.49, "word": "يبقى", "probability": 0.79107666015625}, {"start": 2176.49, "end": 2176.83, "word": " هذا", "probability": 0.91552734375}, {"start": 2176.83, "end": 2177.53, "word": " معناه", "probability": 0.95556640625}, {"start": 2177.53, "end": 2178.41, "word": " ان", "probability": 0.7353515625}, {"start": 2178.41, "end": 2179.49, "word": " ال", "probability": 0.75048828125}, {"start": 2179.49, "end": 2180.75, "word": " D13", "probability": 0.60888671875}, {"start": 2180.75, "end": 2182.35, "word": " موديولو", "probability": 0.619482421875}, {"start": 2182.35, "end": 2183.89, "word": " ارنود", "probability": 0.671142578125}, {"start": 2183.89, "end": 2185.91, "word": " ايزو", "probability": 0.72283935546875}, {"start": 2185.91, "end": 2186.61, "word": " مورفك", "probability": 0.877685546875}, {"start": 2186.61, "end": 2186.97, "word": " لان", "probability": 0.777099609375}, {"start": 2186.97, "end": 2187.37, "word": " هذا", "probability": 0.9072265625}, {"start": 2187.37, "end": 2187.59, "word": " ال", "probability": 0.8671875}, {"start": 2187.59, "end": 2188.07, "word": " center", "probability": 0.189208984375}, {"start": 2188.07, "end": 2188.99, "word": " لمن", "probability": 0.4959716796875}, {"start": 2188.99, "end": 2189.65, "word": " لل", "probability": 0.2171630859375}, {"start": 2189.65, "end": 2190.33, "word": " inner", "probability": 0.69921875}, {"start": 2190.33, "end": 2190.93, "word": " atom", "probability": 0.33203125}, {"start": 2190.93, "end": 2192.01, "word": " morphism", "probability": 0.60565185546875}, {"start": 2192.01, "end": 2192.73, "word": " ل", "probability": 0.828125}, {"start": 2192.73, "end": 2194.09, "word": " D13", "probability": 0.7042236328125}, {"start": 2194.09, "end": 2195.57, "word": " السبب", "probability": 0.9749348958333334}, {"start": 2195.57, "end": 2196.63, "word": " because", "probability": 0.35009765625}], "temperature": 1.0}, {"id": 94, "seek": 221780, "start": 2197.54, "end": 2217.8, "text": "إن الـ Center تبع الـ D13 لا يوجد فيه إلا الـ R node since الـ D13 is odd ممتاز جدا يبقى صار D13 موديل الـ R node", "tokens": [28814, 1863, 2423, 39184, 5169, 6055, 3555, 3615, 2423, 39184, 413, 7668, 20193, 7251, 29245, 3215, 8978, 3224, 11933, 15040, 2423, 39184, 497, 9984, 1670, 2423, 39184, 413, 7668, 307, 7401, 3714, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 20328, 9640, 413, 7668, 3714, 2407, 16254, 1211, 2423, 39184, 497, 9984], "avg_logprob": -0.30266204200409075, "compression_ratio": 1.3095238095238095, "no_speech_prob": 0.0, "words": [{"start": 2197.54, "end": 2198.1, "word": "إن", "probability": 0.502166748046875}, {"start": 2198.1, "end": 2198.72, "word": " الـ", "probability": 0.6104736328125}, {"start": 2198.72, "end": 2199.5, "word": " Center", "probability": 0.29443359375}, {"start": 2199.5, "end": 2200.62, "word": " تبع", "probability": 0.82568359375}, {"start": 2200.62, "end": 2200.9, "word": " الـ", "probability": 0.71630859375}, {"start": 2200.9, "end": 2202.16, "word": " D13", "probability": 0.879150390625}, {"start": 2202.16, "end": 2203.06, "word": " لا", "probability": 0.58984375}, {"start": 2203.06, "end": 2203.68, "word": " يوجد", "probability": 0.9365234375}, {"start": 2203.68, "end": 2204.1, "word": " فيه", "probability": 0.92724609375}, {"start": 2204.1, "end": 2204.66, "word": " إلا", "probability": 0.95703125}, {"start": 2204.66, "end": 2204.96, "word": " الـ", "probability": 0.825927734375}, {"start": 2204.96, "end": 2205.38, "word": " R", "probability": 0.5966796875}, {"start": 2205.38, "end": 2205.92, "word": " node", "probability": 0.37109375}, {"start": 2205.92, "end": 2207.2, "word": " since", "probability": 0.259521484375}, {"start": 2207.2, "end": 2208.74, "word": " الـ", "probability": 0.759765625}, {"start": 2208.74, "end": 2209.5, "word": " D13", "probability": 0.736572265625}, {"start": 2209.5, "end": 2210.16, "word": " is", "probability": 0.73974609375}, {"start": 2210.16, "end": 2210.76, "word": " odd", "probability": 0.80810546875}, {"start": 2210.76, "end": 2212.92, "word": " ممتاز", "probability": 0.8785400390625}, {"start": 2212.92, "end": 2213.26, "word": " جدا", "probability": 0.9697265625}, {"start": 2213.26, "end": 2214.18, "word": " يبقى", "probability": 0.9281005859375}, {"start": 2214.18, "end": 2214.62, "word": " صار", "probability": 0.6982421875}, {"start": 2214.62, "end": 2215.64, "word": " D13", "probability": 0.78369140625}, {"start": 2215.64, "end": 2216.36, "word": " موديل", "probability": 0.826904296875}, {"start": 2216.36, "end": 2216.76, "word": " الـ", "probability": 0.77099609375}, {"start": 2216.76, "end": 2217.22, "word": " R", "probability": 0.82666015625}, {"start": 2217.22, "end": 2217.8, "word": " node", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 95, "seek": 223650, "start": 2218.1, "end": 2236.5, "text": "ما لها isomorphic للـ Inner Atomorphism لمين لجى؟ طيب انا الآن لو قدرت اثبت ان جي isomorphic لهذه ال group بصير جي الأصلية isomorphic لمين؟", "tokens": [15042, 5296, 11296, 307, 32702, 299, 24976, 39184, 36705, 1711, 32702, 1434, 32767, 9957, 5296, 7435, 7578, 22807, 23032, 1829, 3555, 1975, 8315, 6024, 48506, 45164, 12174, 3215, 43500, 1975, 12984, 3555, 2655, 16472, 10874, 1829, 307, 32702, 299, 46740, 24192, 2423, 1594, 4724, 9381, 13546, 10874, 1829, 16247, 36520, 10632, 307, 32702, 299, 32767, 9957, 22807], "avg_logprob": -0.2815194063145539, "compression_ratio": 1.4195804195804196, "no_speech_prob": 0.0, "words": [{"start": 2218.1, "end": 2218.46, "word": "ما", "probability": 0.464599609375}, {"start": 2218.46, "end": 2218.86, "word": " لها", "probability": 0.822998046875}, {"start": 2218.86, "end": 2220.16, "word": " isomorphic", "probability": 0.74365234375}, {"start": 2220.16, "end": 2220.64, "word": " للـ", "probability": 0.637939453125}, {"start": 2220.64, "end": 2220.94, "word": " Inner", "probability": 0.251708984375}, {"start": 2220.94, "end": 2222.26, "word": " Atomorphism", "probability": 0.8312174479166666}, {"start": 2222.26, "end": 2223.36, "word": " لمين", "probability": 0.75732421875}, {"start": 2223.36, "end": 2224.32, "word": " لجى؟", "probability": 0.615966796875}, {"start": 2224.32, "end": 2224.78, "word": " طيب", "probability": 0.9186197916666666}, {"start": 2224.78, "end": 2225.18, "word": " انا", "probability": 0.6761474609375}, {"start": 2225.18, "end": 2225.7, "word": " الآن", "probability": 0.673828125}, {"start": 2225.7, "end": 2226.66, "word": " لو", "probability": 0.93017578125}, {"start": 2226.66, "end": 2227.3, "word": " قدرت", "probability": 0.8795572916666666}, {"start": 2227.3, "end": 2227.98, "word": " اثبت", "probability": 0.89892578125}, {"start": 2227.98, "end": 2228.66, "word": " ان", "probability": 0.8662109375}, {"start": 2228.66, "end": 2229.18, "word": " جي", "probability": 0.656982421875}, {"start": 2229.18, "end": 2230.8, "word": " isomorphic", "probability": 0.7552897135416666}, {"start": 2230.8, "end": 2231.58, "word": " لهذه", "probability": 0.952392578125}, {"start": 2231.58, "end": 2231.86, "word": " ال", "probability": 0.82958984375}, {"start": 2231.86, "end": 2232.6, "word": " group", "probability": 0.81640625}, {"start": 2232.6, "end": 2233.78, "word": " بصير", "probability": 0.83837890625}, {"start": 2233.78, "end": 2234.1, "word": " جي", "probability": 0.833740234375}, {"start": 2234.1, "end": 2234.88, "word": " الأصلية", "probability": 0.75537109375}, {"start": 2234.88, "end": 2235.62, "word": " isomorphic", "probability": 0.91357421875}, {"start": 2235.62, "end": 2236.5, "word": " لمين؟", "probability": 0.8938802083333334}], "temperature": 1.0}, {"id": 96, "seek": 225544, "start": 2236.64, "end": 2255.44, "text": "للـ Inner Atomorphism لجيوب التالي بيكون خلصنا يبقى if we show that انه D13 isomorphic ل D13 modulo R node then we have the result بيكون حصلنا على من؟ على النتيجة", "tokens": [1211, 1211, 39184, 36705, 1711, 32702, 1434, 5296, 7435, 1829, 37746, 16712, 6027, 1829, 4724, 1829, 30544, 16490, 1211, 9381, 8315, 7251, 3555, 4587, 7578, 498, 321, 855, 300, 16472, 3224, 413, 7668, 307, 32702, 299, 5296, 413, 7668, 1072, 13455, 497, 9984, 550, 321, 362, 264, 1874, 4724, 1829, 30544, 11331, 36520, 8315, 15844, 9154, 22807, 15844, 28239, 31371, 7435, 3660], "avg_logprob": -0.33159722127611674, "compression_ratio": 1.286549707602339, "no_speech_prob": 0.0, "words": [{"start": 2236.64, "end": 2237.08, "word": "للـ", "probability": 0.6021321614583334}, {"start": 2237.08, "end": 2237.34, "word": " Inner", "probability": 0.5419921875}, {"start": 2237.34, "end": 2238.84, "word": " Atomorphism", "probability": 0.8470052083333334}, {"start": 2238.84, "end": 2239.48, "word": " لجيوب", "probability": 0.66461181640625}, {"start": 2239.48, "end": 2239.9, "word": " التالي", "probability": 0.67919921875}, {"start": 2239.9, "end": 2240.28, "word": " بيكون", "probability": 0.6732584635416666}, {"start": 2240.28, "end": 2241.1, "word": " خلصنا", "probability": 0.8973388671875}, {"start": 2241.1, "end": 2242.14, "word": " يبقى", "probability": 0.80999755859375}, {"start": 2242.14, "end": 2242.4, "word": " if", "probability": 0.435546875}, {"start": 2242.4, "end": 2242.74, "word": " we", "probability": 0.7841796875}, {"start": 2242.74, "end": 2243.18, "word": " show", "probability": 0.96484375}, {"start": 2243.18, "end": 2243.62, "word": " that", "probability": 0.927734375}, {"start": 2243.62, "end": 2244.34, "word": " انه", "probability": 0.4752197265625}, {"start": 2244.34, "end": 2245.36, "word": " D13", "probability": 0.75}, {"start": 2245.36, "end": 2246.76, "word": " isomorphic", "probability": 0.8880208333333334}, {"start": 2246.76, "end": 2247.0, "word": " ل", "probability": 0.84716796875}, {"start": 2247.0, "end": 2248.38, "word": " D13", "probability": 0.607666015625}, {"start": 2248.38, "end": 2249.26, "word": " modulo", "probability": 0.6282958984375}, {"start": 2249.26, "end": 2250.04, "word": " R", "probability": 0.82958984375}, {"start": 2250.04, "end": 2250.64, "word": " node", "probability": 0.2030029296875}, {"start": 2250.64, "end": 2251.24, "word": " then", "probability": 0.65869140625}, {"start": 2251.24, "end": 2251.48, "word": " we", "probability": 0.916015625}, {"start": 2251.48, "end": 2251.72, "word": " have", "probability": 0.9443359375}, {"start": 2251.72, "end": 2251.92, "word": " the", "probability": 0.8896484375}, {"start": 2251.92, "end": 2252.4, "word": " result", "probability": 0.962890625}, {"start": 2252.4, "end": 2253.06, "word": " بيكون", "probability": 0.8681640625}, {"start": 2253.06, "end": 2253.54, "word": " حصلنا", "probability": 0.8898111979166666}, {"start": 2253.54, "end": 2253.72, "word": " على", "probability": 0.8310546875}, {"start": 2253.72, "end": 2254.22, "word": " من؟", "probability": 0.6353759765625}, {"start": 2254.22, "end": 2254.62, "word": " على", "probability": 0.8818359375}, {"start": 2254.62, "end": 2255.44, "word": " النتيجة", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 97, "seek": 227659, "start": 2255.81, "end": 2276.59, "text": "طب كيف بتسويها هذه؟ بسيط اعرف function و اثبت انها one to one and on two و تخدم خاصية ال isomorphism و وصلنا للمطلوب بسهولة كيف؟ ولا في أدفه منها هذا يعني define", "tokens": [9566, 3555, 9122, 33911, 39894, 3794, 45865, 11296, 29538, 22807, 4724, 3794, 1829, 9566, 1975, 3615, 28480, 2445, 4032, 1975, 12984, 3555, 2655, 16472, 11296, 472, 281, 472, 293, 322, 732, 4032, 6055, 9778, 40448, 16490, 33546, 10632, 2423, 307, 32702, 1434, 4032, 4032, 36520, 8315, 5296, 19528, 9566, 1211, 37746, 4724, 3794, 3224, 12610, 3660, 9122, 33911, 22807, 49429, 8978, 5551, 3215, 5172, 3224, 9154, 11296, 23758, 37495, 22653, 6964], "avg_logprob": -0.34440102842119, "compression_ratio": 1.3910614525139664, "no_speech_prob": 0.0, "words": [{"start": 2255.81, "end": 2256.07, "word": "طب", "probability": 0.54095458984375}, {"start": 2256.07, "end": 2256.33, "word": " كيف", "probability": 0.942138671875}, {"start": 2256.33, "end": 2257.13, "word": " بتسويها", "probability": 0.560821533203125}, {"start": 2257.13, "end": 2258.01, "word": " هذه؟", "probability": 0.5400390625}, {"start": 2258.01, "end": 2258.51, "word": " بسيط", "probability": 0.977783203125}, {"start": 2258.51, "end": 2259.23, "word": " اعرف", "probability": 0.6969807942708334}, {"start": 2259.23, "end": 2259.85, "word": " function", "probability": 0.131591796875}, {"start": 2259.85, "end": 2260.09, "word": " و", "probability": 0.7998046875}, {"start": 2260.09, "end": 2260.47, "word": " اثبت", "probability": 0.81640625}, {"start": 2260.47, "end": 2260.75, "word": " انها", "probability": 0.95166015625}, {"start": 2260.75, "end": 2260.95, "word": " one", "probability": 0.861328125}, {"start": 2260.95, "end": 2261.21, "word": " 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"probability": 0.819091796875}, {"start": 2538.72, "end": 2539.92, "word": " ايزو", "probability": 0.695281982421875}, {"start": 2539.92, "end": 2540.6, "word": " مورفك", "probability": 0.898193359375}, {"start": 2540.6, "end": 2540.86, "word": " ل", "probability": 0.5078125}, {"start": 2540.86, "end": 2542.3, "word": " D13", "probability": 0.6136474609375}], "temperature": 1.0}, {"id": 110, "seek": 256346, "start": 2542.79, "end": 2563.47, "text": "موديولو ارنود وهذه ايزو مورفك للانر اتو مورفزم لمن؟ لل D13 وهذا سيعطيك ان D13 ايزو مورفك للانر اتو مورفزم لD13", "tokens": [2304, 2407, 16254, 12610, 2407, 1975, 2288, 1863, 23328, 37037, 24192, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 24976, 7649, 2288, 1975, 2655, 2407, 3714, 13063, 5172, 11622, 2304, 5296, 27842, 22807, 24976, 413, 7668, 37037, 15730, 8608, 40228, 9566, 1829, 4117, 16472, 413, 7668, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 24976, 7649, 2288, 1975, 2655, 2407, 3714, 13063, 5172, 11622, 2304, 5296, 35, 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موديولوس سنتر بتابع الجي بده يساوي كدهاش؟ أربعة يبقى فيها أربعة عناصر هذا معناه ان الجي موديولوس سنتر بتابع الجي isomorphic يا إما لزد أربعة يا إما لزد اتنين external product مع زد اتنين", "tokens": [3224, 15730, 20449, 8315, 47395, 16472, 2423, 1668, 5296, 7435, 1829, 3714, 2407, 16254, 12610, 41779, 8608, 29399, 2288, 39894, 16758, 3615, 25724, 1829, 47525, 3224, 7251, 3794, 995, 45865, 9122, 3215, 3224, 33599, 22807, 5551, 25513, 27884, 7251, 3555, 4587, 7578, 8978, 11296, 5551, 25513, 27884, 18871, 33546, 2288, 23758, 20449, 8315, 3224, 16472, 25724, 1829, 3714, 2407, 16254, 12610, 41779, 8608, 29399, 2288, 39894, 16758, 3615, 25724, 1829, 307, 32702, 299, 35186, 11933, 15042, 5296, 11622, 3215, 5551, 25513, 27884, 35186, 11933, 15042, 5296, 11622, 3215, 1975, 2655, 1863, 9957, 8320, 1674, 20449, 30767, 3215, 1975, 2655, 1863, 9957], "avg_logprob": -0.25903799691620993, "compression_ratio": 1.898936170212766, "no_speech_prob": 0.0003523826599121094, "words": [{"start": 2704.6, 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28242, 3224, 15844, 45030, 11242, 2423, 1668, 5296, 11296, 7251, 3794, 995, 45865, 5551, 25513, 27884], "avg_logprob": -0.450223205770765, "compression_ratio": 1.5402298850574712, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2902.08, "end": 2903.16, "word": "كل", "probability": 0.38525390625}, {"start": 2903.16, "end": 2903.42, "word": " ال", "probability": 0.11236572265625}, {"start": 2903.42, "end": 2903.8, "word": " order", "probability": 0.34326171875}, {"start": 2903.8, "end": 2904.44, "word": " لها", "probability": 0.57843017578125}, {"start": 2904.44, "end": 2905.22, "word": " يساوي", "probability": 0.8153076171875}, {"start": 2905.22, "end": 2905.92, "word": " أربعة", "probability": 0.707275390625}, {"start": 2905.92, "end": 2906.52, "word": " هذا", "probability": 0.298095703125}, {"start": 2906.52, "end": 2907.0, "word": " الكلام", "probability": 0.8346354166666666}, {"start": 2907.0, "end": 2907.32, "word": " يعني", "probability": 0.8369140625}, {"start": 2907.32, "end": 2907.86, "word": " كله", "probability": 0.833251953125}, {"start": 2907.86, "end": 2908.14, "word": " على", "probability": 0.8984375}, {"start": 2908.14, "end": 2908.7, "word": " بعض", "probability": 0.993896484375}, {"start": 2908.7, "end": 2908.86, "word": " ال", "probability": 0.63330078125}, {"start": 2908.86, "end": 2909.24, "word": " order", "probability": 0.947265625}, {"start": 2909.24, "end": 2909.7, "word": " لها", "probability": 0.6009521484375}, {"start": 2909.7, "end": 2910.34, "word": " يساوي", "probability": 0.74237060546875}, {"start": 2910.34, "end": 2911.46, "word": " أربعة", "probability": 0.8753255208333334}], "temperature": 1.0}, {"id": 124, "seek": 293980, "start": 2913.42, "end": 2939.8, "text": "يبقى هذا كل القيمة بتساوي اربعة يعني معنى هذا الكلام ان ال order ل G اللي انا مش عارفه على ال center بتابع ال G ال G هذي قال ال order اه ماقلش هذي G زد يعني كل اللي بدي اقوله ان ال order ل ال center اه مش عارفينه قديش استنى شوية", "tokens": [1829, 3555, 4587, 7578, 23758, 28242, 25062, 32640, 3660, 39894, 3794, 995, 45865, 1975, 25513, 27884, 37495, 22653, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 2423, 1668, 5296, 460, 13672, 1829, 1975, 8315, 37893, 6225, 9640, 5172, 3224, 15844, 2423, 3056, 39894, 16758, 3615, 2423, 460, 2423, 460, 8032, 8848, 1829, 50239, 2423, 1668, 1975, 3224, 19446, 4587, 1211, 8592, 8032, 8848, 1829, 460, 30767, 3215, 37495, 22653, 28242, 13672, 1829, 4724, 16254, 1975, 39648, 3224, 16472, 2423, 1668, 5296, 2423, 3056, 1975, 3224, 37893, 6225, 9640, 5172, 9957, 3224, 12174, 16254, 8592, 44713, 1863, 7578, 13412, 2407, 10632], "avg_logprob": -0.2359220297029703, "compression_ratio": 1.9427083333333333, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2913.42, "end": 2913.92, "word": "يبقى", "probability": 0.783447265625}, {"start": 2913.92, "end": 2914.22, "word": " هذا", "probability": 0.6015625}, {"start": 2914.22, "end": 2914.54, "word": " كل", "probability": 0.744140625}, {"start": 2914.54, "end": 2915.06, "word": " القيمة", "probability": 0.9375}, {"start": 2915.06, "end": 2915.68, "word": " بتساوي", "probability": 0.59375}, {"start": 2915.68, "end": 2916.08, "word": " اربعة", "probability": 0.7047526041666666}, {"start": 2916.08, "end": 2916.74, "word": " يعني", "probability": 0.865966796875}, {"start": 2916.74, "end": 2917.3, "word": " معنى", "probability": 0.8929036458333334}, {"start": 2917.3, "end": 2917.68, "word": " هذا", "probability": 0.95947265625}, {"start": 2917.68, "end": 2918.5, "word": " الكلام", "probability": 0.9597981770833334}, {"start": 2918.5, "end": 2918.9, "word": " ان", "probability": 0.8232421875}, {"start": 2918.9, "end": 2919.2, "word": " ال", "probability": 0.83056640625}, {"start": 2919.2, "end": 2919.66, "word": " order", "probability": 0.86328125}, {"start": 2919.66, "end": 2920.0, "word": " ل", "probability": 0.73095703125}, {"start": 2920.0, "end": 2920.16, "word": " G", "probability": 0.399658203125}, {"start": 2920.16, "end": 2920.44, "word": " اللي", "probability": 0.891845703125}, {"start": 2920.44, "end": 2920.82, "word": " انا", "probability": 0.760986328125}, {"start": 2920.82, "end": 2921.16, "word": " مش", "probability": 0.99365234375}, {"start": 2921.16, "end": 2921.88, "word": " عارفه", "probability": 0.9940185546875}, {"start": 2921.88, "end": 2923.14, "word": " على", "probability": 0.78173828125}, {"start": 2923.14, "end": 2923.68, "word": " ال", "probability": 0.9560546875}, {"start": 2923.68, "end": 2924.12, "word": " center", "probability": 0.7587890625}, {"start": 2924.12, "end": 2924.96, "word": " بتابع", "probability": 0.8255208333333334}, {"start": 2924.96, "end": 2925.42, "word": " ال", "probability": 0.83203125}, {"start": 2925.42, "end": 2925.7, "word": " G", "probability": 0.93701171875}, {"start": 2925.7, "end": 2926.6, "word": " ال", "probability": 0.93017578125}, {"start": 2926.6, "end": 2926.88, "word": " G", "probability": 0.93994140625}, {"start": 2926.88, "end": 2927.42, "word": " هذي", "probability": 0.5699869791666666}, {"start": 2927.42, "end": 2927.62, "word": " قال", "probability": 0.90625}, {"start": 2927.62, "end": 2927.78, "word": " ال", "probability": 0.9462890625}, {"start": 2927.78, "end": 2928.42, "word": " order", "probability": 0.98193359375}, {"start": 2928.42, "end": 2929.48, "word": " اه", "probability": 0.767333984375}, {"start": 2929.48, "end": 2930.28, "word": " ماقلش", "probability": 0.62017822265625}, {"start": 2930.28, "end": 2930.72, "word": " هذي", "probability": 0.9169921875}, {"start": 2930.72, "end": 2931.06, "word": " G", "probability": 0.62744140625}, {"start": 2931.06, "end": 2931.98, "word": " زد", "probability": 0.69140625}, {"start": 2931.98, "end": 2933.28, "word": " يعني", "probability": 0.822998046875}, {"start": 2933.28, "end": 2933.66, "word": " كل", "probability": 0.94384765625}, {"start": 2933.66, "end": 2933.82, "word": " اللي", "probability": 0.98095703125}, {"start": 2933.82, "end": 2934.06, "word": " بدي", "probability": 0.6873779296875}, {"start": 2934.06, "end": 2934.52, "word": " اقوله", "probability": 0.8681640625}, {"start": 2934.52, "end": 2934.68, "word": " ان", "probability": 0.931640625}, {"start": 2934.68, "end": 2934.92, "word": " ال", "probability": 0.99072265625}, {"start": 2934.92, "end": 2935.46, "word": " order", "probability": 0.9794921875}, {"start": 2935.46, "end": 2935.84, "word": " ل", "probability": 0.56689453125}, {"start": 2935.84, "end": 2936.16, "word": " ال", "probability": 0.65087890625}, {"start": 2936.16, "end": 2937.08, "word": " center", "probability": 0.91015625}, {"start": 2937.08, "end": 2937.6, "word": " اه", "probability": 0.763427734375}, {"start": 2937.6, "end": 2937.78, "word": " مش", "probability": 0.9873046875}, {"start": 2937.78, "end": 2938.28, "word": " عارفينه", "probability": 0.9671875}, {"start": 2938.28, "end": 2938.82, "word": " قديش", "probability": 0.72216796875}, {"start": 2938.82, "end": 2939.4, "word": " استنى", "probability": 0.7936197916666666}, {"start": 2939.4, "end": 2939.8, "word": " شوية", "probability": 0.9127604166666666}], "temperature": 1.0}, {"id": 125, "seek": 296091, "start": 2942.27, "end": 2960.91, "text": "استنى شوية طيب احنا عندنا نظرية بتقول ما يأتي هذا الان الـG modulus center يبقى isomorphic لل inner تبع من؟ تبع ال group G اللي عندنا صح؟", "tokens": [995, 14851, 1863, 7578, 13412, 2407, 10632, 23032, 1829, 3555, 1975, 5016, 8315, 43242, 8315, 8717, 19913, 2288, 10632, 39894, 39648, 19446, 7251, 10721, 31371, 23758, 2423, 7649, 2423, 39184, 38, 42287, 3056, 7251, 3555, 4587, 7578, 307, 32702, 299, 24976, 7284, 6055, 3555, 3615, 9154, 22807, 6055, 3555, 3615, 2423, 1594, 460, 13672, 1829, 43242, 8315, 20328, 5016, 22807], "avg_logprob": -0.23078893051772822, "compression_ratio": 1.356687898089172, "no_speech_prob": 0.0, "words": [{"start": 2942.27, "end": 2943.13, "word": "استنى", "probability": 0.704132080078125}, {"start": 2943.13, "end": 2943.65, "word": " شوية", "probability": 0.93505859375}, {"start": 2943.65, "end": 2944.81, "word": " طيب", "probability": 0.766845703125}, {"start": 2944.81, "end": 2945.49, "word": " احنا", "probability": 0.9508463541666666}, {"start": 2945.49, "end": 2946.03, "word": " عندنا", "probability": 0.912841796875}, {"start": 2946.03, "end": 2946.89, "word": " نظرية", "probability": 0.986083984375}, {"start": 2946.89, "end": 2947.87, "word": " بتقول", "probability": 0.966064453125}, {"start": 2947.87, "end": 2948.13, "word": " ما", "probability": 0.9462890625}, {"start": 2948.13, "end": 2948.69, "word": " يأتي", "probability": 0.859375}, {"start": 2948.69, "end": 2950.63, "word": " هذا", "probability": 0.387451171875}, {"start": 2950.63, "end": 2951.23, "word": " الان", "probability": 0.58447265625}, {"start": 2951.23, "end": 2952.13, "word": " الـG", "probability": 0.526123046875}, {"start": 2952.13, "end": 2952.77, "word": " modulus", "probability": 0.383056640625}, {"start": 2952.77, "end": 2953.47, "word": " center", "probability": 0.5771484375}, {"start": 2953.47, "end": 2953.87, "word": " يبقى", "probability": 0.9520263671875}, {"start": 2953.87, "end": 2955.23, "word": " isomorphic", "probability": 0.8014322916666666}, {"start": 2955.23, "end": 2955.77, "word": " لل", "probability": 0.91650390625}, {"start": 2955.77, "end": 2956.45, "word": " inner", "probability": 0.70458984375}, {"start": 2956.45, "end": 2957.19, "word": " تبع", "probability": 0.90478515625}, {"start": 2957.19, "end": 2957.93, "word": " من؟", "probability": 0.83740234375}, {"start": 2957.93, "end": 2958.41, "word": " تبع", "probability": 0.98046875}, {"start": 2958.41, "end": 2958.57, "word": " ال", "probability": 0.406494140625}, {"start": 2958.57, "end": 2959.07, "word": " group", "probability": 0.92236328125}, {"start": 2959.07, "end": 2959.61, "word": " G", "probability": 0.81884765625}, {"start": 2959.61, "end": 2959.87, "word": " اللي", "probability": 0.777099609375}, {"start": 2959.87, "end": 2960.35, "word": " عندنا", "probability": 0.989990234375}, {"start": 2960.35, "end": 2960.91, "word": " صح؟", "probability": 0.8883463541666666}], "temperature": 1.0}, {"id": 126, "seek": 298433, "start": 2961.95, "end": 2984.33, "text": "خدنا نظرية اللى توكننا من الحل عليها اللى هو الـ G-modulo الـ G-modulo is center isomorphic للإنر أتو مورفزم لمين؟ لـ G طيب على أي حال ايزال بدنا نحل هذا السؤال وكمان سؤالين قادمات ان شاء الله", "tokens": [9778, 3215, 8315, 8717, 19913, 2288, 10632, 13672, 7578, 33427, 19452, 8315, 9154, 21542, 1211, 25894, 11296, 13672, 7578, 31439, 2423, 39184, 460, 12, 8014, 13455, 2423, 39184, 460, 12, 8014, 13455, 307, 3056, 307, 32702, 299, 24976, 28814, 1863, 2288, 5551, 2655, 2407, 3714, 13063, 5172, 11622, 2304, 32767, 9957, 22807, 5296, 39184, 460, 23032, 1829, 3555, 15844, 36632, 11331, 6027, 1975, 1829, 11622, 6027, 47525, 8315, 8717, 5016, 1211, 23758, 21136, 33604, 6027, 4032, 24793, 7649, 8608, 33604, 6027, 9957, 12174, 18513, 2304, 9307, 16472, 13412, 16606, 21984], "avg_logprob": -0.30339972330973697, "compression_ratio": 1.596938775510204, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2961.95, "end": 2962.43, "word": "خدنا", "probability": 0.69921875}, {"start": 2962.43, "end": 2963.25, "word": " نظرية", "probability": 0.973876953125}, {"start": 2963.25, "end": 2964.71, "word": " اللى", "probability": 0.4757080078125}, {"start": 2964.71, "end": 2965.27, "word": " توكننا", "probability": 0.62841796875}, {"start": 2965.27, "end": 2965.37, "word": " من", "probability": 0.63330078125}, {"start": 2965.37, "end": 2965.69, "word": " الحل", "probability": 0.72802734375}, {"start": 2965.69, "end": 2966.25, "word": " عليها", "probability": 0.979736328125}, {"start": 2966.25, "end": 2966.91, "word": " اللى", "probability": 0.908935546875}, {"start": 2966.91, "end": 2967.11, "word": " هو", "probability": 0.529296875}, {"start": 2967.11, "end": 2967.29, "word": " الـ", "probability": 0.718994140625}, {"start": 2967.29, "end": 2967.61, "word": " G", "probability": 0.76220703125}, {"start": 2967.61, "end": 2969.07, "word": "-modulo", "probability": 0.5777180989583334}, {"start": 2969.07, "end": 2971.01, "word": " الـ", "probability": 0.7099609375}, {"start": 2971.01, "end": 2971.87, "word": " G", "probability": 0.83056640625}, {"start": 2971.87, "end": 2972.47, "word": "-modulo", "probability": 0.9013671875}, {"start": 2972.47, "end": 2972.83, "word": " is", "probability": 0.5078125}, {"start": 2972.83, "end": 2973.31, "word": " center", "probability": 0.6748046875}, {"start": 2973.31, "end": 2974.35, "word": " isomorphic", "probability": 0.88330078125}, {"start": 2974.35, "end": 2974.87, "word": " للإنر", "probability": 0.6573486328125}, {"start": 2974.87, "end": 2975.23, "word": " أتو", "probability": 0.4777018229166667}, {"start": 2975.23, "end": 2975.69, "word": " مورفزم", "probability": 0.85556640625}, {"start": 2975.69, "end": 2976.55, "word": " لمين؟", "probability": 0.6819661458333334}, {"start": 2976.55, "end": 2976.79, "word": " لـ", "probability": 0.705322265625}, {"start": 2976.79, "end": 2977.03, "word": " G", "probability": 0.74365234375}, {"start": 2977.03, "end": 2978.49, "word": " طيب", "probability": 0.9163411458333334}, {"start": 2978.49, "end": 2978.69, "word": " على", "probability": 0.453857421875}, {"start": 2978.69, "end": 2978.85, "word": " أي", "probability": 0.8154296875}, {"start": 2978.85, "end": 2979.19, "word": " حال", "probability": 0.9384765625}, {"start": 2979.19, "end": 2979.67, "word": " ايزال", "probability": 0.5909423828125}, {"start": 2979.67, "end": 2980.03, "word": " بدنا", "probability": 0.9541015625}, {"start": 2980.03, "end": 2980.45, "word": " نحل", "probability": 0.98388671875}, {"start": 2980.45, "end": 2981.15, "word": " هذا", "probability": 0.556640625}, {"start": 2981.15, "end": 2981.61, "word": " السؤال", "probability": 0.9853515625}, {"start": 2981.61, "end": 2982.07, "word": " وكمان", "probability": 0.7425130208333334}, {"start": 2982.07, "end": 2982.67, "word": " سؤالين", "probability": 0.969970703125}, {"start": 2982.67, "end": 2983.67, "word": " قادمات", "probability": 0.9033203125}, {"start": 2983.67, "end": 2983.87, "word": " ان", "probability": 0.67578125}, {"start": 2983.87, "end": 2984.15, "word": " شاء", "probability": 0.98193359375}, {"start": 2984.15, "end": 2984.33, "word": " الله", "probability": 0.94921875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2984.9715, "duration_after_vad": 2798.6937499999913}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..beeb761f6aa048354b6ef7b3e28ce933ee2dccf5
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ.srt
@@ -0,0 +1,2118 @@
+1
+00:00:20,690 --> 00:00:26,090
+بسم الله الرحمن الرحيم نرجع ثانية إلى المحاضرة
+
+2
+00:00:26,090 --> 00:00:32,020
+الماضية و نكمل ما ابتدأنا به المرة الماضية، آخر حاجة 
+
+3
+00:00:32,020 --> 00:00:36,520
+أعطناها المرة الماضية كان تعريف الـcentralizer لـ
+
+4
+00:00:36,520 --> 00:00:40,900
+element موجود في الـ group وعرفنا الـ centralizer
+
+5
+00:00:40,900 --> 00:00:44,960
+لـ element A الموجود في الـ group على إن كل الـ G
+
+6
+00:00:44,960 --> 00:00:50,620
+اللي موجودة في G بحيث GA يساوي AG مكتوب معاكم 
+
+7
+00:00:50,620 --> 00:00:54,240
+المرة الماضية، مش الجديد وحتى نص النظرية مكتوب
+
+8
+00:00:54,240 --> 00:00:57,380
+معاكم المرة الماضية، يبقى حابيت أذكر لإنه بدنا نروح
+
+9
+00:00:57,380 --> 00:01:02,530
+نبرهن النظرية، النظرية بدنا نبرهن و نتابعها للمرة
+
+10
+00:01:02,530 --> 00:01:09,130
+القادمة، يبقى الـcentralizer لـA هو كل العناصر اللي
+
+11
+00:01:09,130 --> 00:01:14,670
+موجودة في G و اللي بتبقى commutes مع A، كل الـG
+
+12
+00:01:14,670 --> 00:01:20,320
+اللي موجودة في G بيعني الـG of A يساوي الـAG، الآن 
+
+13
+00:01:20,320 --> 00:01:24,780
+بنا نثبت تبقى لهذه النظرية، لو خت element A موجود
+
+14
+00:01:24,780 --> 00:01:29,300
+في ال group G، بدي ال centralizer ل A يبقى بدي أثبت 
+
+15
+00:01:29,300 --> 00:01:35,570
+ان ال centralizer ل A is a subgroup of G، يعني بدي
+
+16
+00:01:35,570 --> 00:01:39,430
+أحاول أثبت النقطتين تبعات الـ subgroup تبعات أول
+
+17
+00:01:39,430 --> 00:01:44,190
+نظرية وهو إن الـ centralizer ل A is non-empty،
+
+18
+00:01:44,190 --> 00:01:48,130
+اتنين، لو أخدت two elements في ال centralizer بدي
+
+19
+00:01:48,130 --> 00:01:51,970
+أحاول أثبت أن الأول في معكوس الثاني موجود في ال
+
+20
+00:01:51,970 --> 00:01:55,830
+centralizer ل A وبالتالي بيصبح ال centralizer ل
+
+21
+00:01:55,830 --> 00:02:02,500
+A is a subgroup of G، يبقى بيني ان انا اجي ال proof
+
+22
+00:02:02,500 --> 00:02:07,000
+اللي موجودة عندنا، يبقى النقطة الأولى بدي اقوله ال
+
+23
+00:02:07,000 --> 00:02:14,400
+centralizer لإيه is non-empty، non-empty ليش لإن
+
+24
+00:02:14,400 --> 00:02:19,940
+انا بدي احاول اجيبه ولو اللي هو element واحد موجود
+
+25
+00:02:19,940 --> 00:02:24,320
+في ال centralizer لإيه، مشان ادلل على هذا الكلام
+
+26
+00:02:24,320 --> 00:02:28,800
+اللي عندي، يبقى ال centralizer لإيه is non-empty،
+
+27
+00:02:28,800 --> 00:02:37,700
+sense الـ E موجود في الـ centralizer لـ A، شو السبب؟
+
+28
+00:02:37,700 --> 00:02:45,040
+because ان الـ E A بدر يساوي الـ A في الـ E، ال
+
+29
+00:02:45,040 --> 00:02:49,380
+identity element لو ضربناه في أي element يبقى من
+
+30
+00:02:49,380 --> 00:02:52,680
+اليمين او من الشمال بطلع نفس ال element اللي هو
+
+31
+00:02:52,680 --> 00:02:56,540
+الـ A، يبقى الـ E صارت موجودة في ال centralizer لـ
+
+32
+00:02:56,540 --> 00:03:00,120
+A، يبقى ال centralizer لـ A is non-empty،
+
+33
+00:03:04,840 --> 00:03:10,660
+عنصرين XY موجودة في الـ Centralizer لـ A،
+
+34
+00:03:29,260 --> 00:03:34,560
+إذا بدي أحاول أستخدم خاصية الـcentralizer اللي ايه
+
+35
+00:03:34,560 --> 00:03:39,980
+اللي فوق لمين الـtwo elements x و y، يبقى بناء عليه
+
+36
+00:03:39,980 --> 00:03:46,980
+بدي يصير x a بدي يساوي ax and اللي هو y a بدي
+
+37
+00:03:46,980 --> 00:03:52,800
+يساوي ay، طبق اللي تعرف من الـcentralizer لإن أخد
+
+38
+00:03:52,800 --> 00:03:57,350
+two elements موجودات في الـcentralizer، هذا هارجعله
+
+39
+00:03:57,350 --> 00:04:03,970
+بعد قليل، هذا هحاول أستفيد منه، مشان أستفيد منه بدي
+
+40
+00:04:03,970 --> 00:04:10,110
+أروح أضرب في A inverse من جهة الشمال و كذلك من جهة
+
+41
+00:04:10,110 --> 00:04:14,630
+اليمين، إذا لو ضربنا من جهة الشمال في A inverse
+
+42
+00:04:14,630 --> 00:04:23,570
+بيصير عند A inverse YA بده يساوي Y، ماذا فعلت؟ ضربت
+
+43
+00:04:23,570 --> 00:04:29,350
+من جهة الشمال في مين؟ في A inverse، الان بادرح اضرب
+
+44
+00:04:29,350 --> 00:04:33,950
+في جهة اليامين برضه في ال A inverse، مش الدرب
+
+45
+00:04:33,950 --> 00:04:36,950
+العادى اللى احنا عارفينه، لما اقول اضرب يعني بدي
+
+46
+00:04:36,950 --> 00:04:40,870
+اطبق ال binary operation اللى موجودة على جهة ضرب
+
+47
+00:04:40,870 --> 00:04:45,580
+جمع الجسم المهم ال operation اللى موجودة، يبقى هذا
+
+48
+00:04:45,580 --> 00:04:52,720
+بده يعطينا انه a inverse y يساوي y a inverse، ضربنا
+
+49
+00:04:52,720 --> 00:04:57,680
+من جهة اليمين في مين؟ في ال a inverse، بصير عندي a a
+
+50
+00:04:57,680 --> 00:05:01,520
+inverse اللي هو بال identity بضلش الا ال element
+
+51
+00:05:01,520 --> 00:05:06,800
+هذا، يبقى a inverse y بده يساوي y inverse، ايش
+
+52
+00:05:06,800 --> 00:05:12,940
+تفسيركوا للعبارة الأخيرة اللي وصلنا لها دي؟ لأ مش
+
+53
+00:05:12,940 --> 00:05:16,360
+هذا اللي بدنا نقوله، لأ احنا أخدنا y في ال
+
+54
+00:05:16,360 --> 00:05:23,760
+centralizer ل a، يعني طلع a y يسوى y a، وصلنا إلى a
+
+55
+00:05:23,760 --> 00:05:30,500
+inverse y يسوى y a inverse، يبقى ال y موجود في ال
+
+56
+00:05:30,500 --> 00:05:35,630
+centralizer ل a inverse، يبقى بناء عليه لو كان الـ
+
+57
+00:05:35,630 --> 00:05:39,750
+Element موجود في الـ Centralizer لـ A، هذا الـ
+
+58
+00:05:39,750 --> 00:05:44,470
+Element لازم يكون موجود في الـ Centralizer لمعكوس
+
+59
+00:05:44,470 --> 00:05:45,210
+الـ A
+
+60
+00:05:50,200 --> 00:05:54,980
+Y هذه I الموجودة في الـ Centralizer لـ A، هذا معناه
+
+61
+00:05:54,980 --> 00:06:01,420
+أن Y موجودة في الـ Centralizer لـ A وبالتالي يصبح
+
+62
+00:06:01,420 --> 00:06:05,160
+الـ Centralizer لـ A الـ subset من الـ Centralizer
+
+63
+00:06:05,160 --> 00:06:08,560
+لـ A inverse، دعوني أخبرك أن هناك سؤال في الكتاب
+
+64
+00:06:08,560 --> 00:06:11,580
+يقول أثبت أن الـ Centralizer لـ A
+
+65
+00:06:15,290 --> 00:06:20,370
+يبقى هذا نص البرهان، والاتجاه التاني هو النص الثاني
+
+66
+00:06:20,370 --> 00:06:25,370
+لما نيجي لسؤال رقم عشرين او ما بعرف جد ايش، المهم
+
+67
+00:06:26,570 --> 00:06:31,130
+يبقى تفسيرنا لهذه العبارة أنه إذا كان ال element
+
+68
+00:06:31,130 --> 00:06:36,890
+موجود في ال centralizer لإيه، فإن هذا ال element
+
+69
+00:06:36,890 --> 00:06:41,930
+يكون موجود في ال centralizer لإيه inverse، مجرد
+
+70
+00:06:41,930 --> 00:06:47,850
+استنتاج استنتجناه الآن، بس مجرد إشارة شرط له لكن
+
+71
+00:06:47,850 --> 00:06:52,270
+لازم هنا، مش لازم للكلام اللي أنا بقوله، طيب انا ليش
+
+72
+00:06:52,270 --> 00:06:58,490
+اللي بدياه بدي ادي اخد الآن، اللي هو مين بده ياخد
+
+73
+00:06:58,490 --> 00:07:09,150
+الـ X Y inverse في مين؟ في الـ A، إذا قدرت أثبت أن
+
+74
+00:07:09,150 --> 00:07:14,770
+هذا يسوي الـA في الـXY inverse، بتم المطلوب لأنه
+
+75
+00:07:14,770 --> 00:07:20,850
+بيصير الأول في معكوس الثاني، إذا قدرت أثبت أن الـXY
+
+76
+00:07:20,850 --> 00:07:25,290
+inverse A يسوي الـA XY inverse، بيصير ال element XY
+
+77
+00:07:25,290 --> 00:07:28,750
+inverse موجود في الـcentralizer لـA وبالتالي
+
+78
+00:07:28,750 --> 00:07:34,760
+الـcentralizer لـA بيصير subgroup، طيب ممتاز جدا، ايش
+
+79
+00:07:34,760 --> 00:07:42,160
+رايك هذي بقدر اكتبها x y inverse a inverse inverse
+
+80
+00:07:42,160 --> 00:07:48,680
+خدناها قبل ذلك وبرهناها، طب ايش رأيك في الـ two
+
+81
+00:07:48,680 --> 00:07:54,860
+elements دول بدي اجمعهم ب inverse واحد، بدي اخلّيهم
+
+82
+00:07:54,860 --> 00:07:58,460
+بدل ما في inverse و inverse بدي اخلّيهم inverse
+
+83
+00:07:58,460 --> 00:08:03,620
+واحد، يبقى حسب معلوماتنا في الشبتر الماضي هذا بدي
+
+84
+00:08:03,620 --> 00:08:10,040
+يصير مين؟ بدي يصير a inverse while كل inverse
+
+85
+00:08:10,040 --> 00:08:18,170
+مظبوط؟ طيب لكن ايش عندنا هنا احنا a inverse y هو
+
+86
+00:08:18,170 --> 00:08:22,750
+بواي a inverse، يبقى بقدر اشيل a inverse y و احط
+
+87
+00:08:22,750 --> 00:08:28,230
+بدالها مين؟ سميلي هذا على النقطة رقم واحد عشان
+
+88
+00:08:28,230 --> 00:08:34,870
+نستفيد منها، يبقى هذا الكلام بده يساوي x y a
+
+89
+00:08:34,870 --> 00:08:42,400
+inverse لكل inverse، هذا من وين؟ from one، من العلاقة
+
+90
+00:08:42,400 --> 00:08:48,670
+الأولى اللى عندنا، طيب ممتاز، بدى افك ال inverse هذا
+
+91
+00:08:48,670 --> 00:08:54,110
+مرة تانية، يبقى هذا ايش بيعطينا؟ هذا بيعطينا هاي ال
+
+92
+00:08:54,110 --> 00:08:59,670
+X اللي برا وهذا بيعطينا A inverse inverse Y
+
+93
+00:08:59,670 --> 00:09:06,110
+inverse، هذا بدي يعطينا X A Y inverse، الشكل اللي
+
+94
+00:09:06,110 --> 00:09:11,870
+عندنا هنا، لكن في معلومة حتى الآن لم نستفد منها شيء
+
+95
+00:09:11,870 --> 00:09:16,850
+المعلومة اللي هي المعلومة اللي عندنا هذه، إن الـ X
+
+96
+00:09:16,850 --> 00:09:21,190
+موجود في الـ Centralizer لـ A، مدام الـ X موجود
+
+97
+00:09:21,190 --> 00:09:26,310
+يبقى الـ X A بده يساوي A X، إذا بنقدر نبدل الأثنين
+
+98
+00:09:26,310 --> 00:09:33,150
+هذول مكان بعض، يبقى هذا الكلام بده يساوي A X Y
+
+99
+00:09:33,150 --> 00:09:38,670
+inverse، ليش هذا الكلام؟ since ال X موجود في ال
+
+100
+00:09:38,670 --> 00:09:50,240
+Centralizer ل A، هذا الكلام سيصبح A X Y Inverse، يبقى
+
+101
+00:09:50,240 --> 00:09:56,740
+انا بدأت هنا بال X Y inverse في A، لقيته يسوى ال A
+
+102
+00:09:56,740 --> 00:10:01,400
+في ال X Y inverse، ايش معنى هذا الكلام؟ ان ال X Y
+
+103
+00:10:01,400 --> 00:10:06,400
+inverse موجود في ال centralizer ل A، يبقى بدي بقوله
+
+104
+00:10:06,400 --> 00:10:13,440
+Sir ال X Y inverse belongs لل centralizer ل A، يبقى
+
+105
+00:10:13,440 --> 00:10:17,940
+تحقق ال condition الأول، تحقق ال condition التاني
+
+106
+00:10:17,940 --> 00:10:18,460
+by
+
+107
+00:10:25,940 --> 00:10:33,000
+بنظرية سابقة الـ Centralizer لـ A is a subgroup من
+
+108
+00:10:33,000 --> 00:10:40,310
+G وهو المطلوب، يبقى الآن اثبتنا ان الـcentre للجروب
+
+109
+00:10:40,310 --> 00:10:45,590
+هو الـsubgroup واثبتنا الـcentralizer لأي element
+
+110
+00:10:45,590 --> 00:10:50,930
+كذلك هو subgroup من مين؟ من الجروب الأساسية، لحد هنا
+
+111
+00:10:50,930 --> 00:10:55,910
+stop، انتهى الجزء النظري تبع ال section، ننتقل الآن
+
+112
+00:10:55,910 --> 00:11:00,210
+إلى الأسئلة، والمرة اللى فاتت اعطيتكوا أرقام
+
+113
+00:11:00,210 --> 00:11:01,330
+المسائل، مش هيك
+
+114
+00:11:09,830 --> 00:11:16,450
+طبعا كان مطلوب من ضمن الأسئلة، اول سؤال بيقول هاتلي
+
+115
+00:11:16,450 --> 00:11:21,330
+ال order لل group و ال order لكل element موجود في
+
+116
+00:11:21,330 --> 00:11:26,090
+ال group و ما شاء الله عليهم يعطينا خمس groups لكن
+
+117
+00:11:26,090 --> 00:11:29,930
+اول تنتهي انزلت اتناشوي و عشر هذه المحلولات معاك
+
+118
+00:11:29,930 --> 00:11:35,300
+كامثلة، يبقى احنا ممكن نتعرض واحدة من ال TNT اللي هي
+
+119
+00:11:35,300 --> 00:11:39,860
+واطماشي ويه عشرين واحدة منهم اللي بدك إياها و دي
+
+120
+00:11:39,860 --> 00:11:47,860
+فار معانا مشكلة فيها يه عشرين يه عشرين يا سيني
+
+121
+00:11:47,860 --> 00:11:51,440
+يبقى
+
+122
+00:11:51,440 --> 00:11:57,340
+السؤال الأول يه عشرين من اللي قال بديه عشرين فيكون
+
+123
+00:11:57,340 --> 00:12:07,730
+شوفأنت طب اعطيني العناصر تبعك واحد ثلاثة سبعة تسعة
+
+124
+00:12:07,730 --> 00:12:09,090
+اتناشر
+
+125
+00:12:11,330 --> 00:12:17,290
+أربعة عشر، خمسة عشر، ستة عشر، سبعة عشر، ثمانية عشر، 
+
+126
+00:12:17,290 --> 00:12:22,150
+تسعة عشر الآن واحد، اثنان، ثلاثة، أربعة، خمسة،
+
+127
+00:12:22,150 --> 00:12:27,450
+ستة، سبعة، ثمانية يبقى المطلوب الأول ال order ليه 
+
+128
+00:12:27,450 --> 00:12:34,030
+عشرين هو قداش ثمانية الآن بدك ال order لكل element
+
+129
+00:12:34,030 --> 00:12:38,960
+موجود في ال group عشان أقول ال order للواحد كده؟
+
+130
+00:12:38,960 --> 00:12:44,180
+واحد لإنه ال identity element بعدين أريد ال order
+
+131
+00:12:44,180 --> 00:12:48,440
+لثلاثة كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+132
+00:12:48,440 --> 00:12:48,680
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+133
+00:12:48,680 --> 00:12:53,360
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+134
+00:12:53,360 --> 00:12:56,830
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ ثلاثة
+
+135
+00:12:56,830 --> 00:13:04,010
+تربيع بتسعة موجود ثلاثة في سبعة ثلاثة أقصد ثلاثة
+
+136
+00:13:04,010 --> 00:13:09,530
+تربيع ثلاثة تكعيب سبعة وعشرين شيل منهم بيضل قداش
+
+137
+00:13:09,530 --> 00:13:16,250
+سبعة في ثلاثة بواحدة وعشرين اللي هو ال identity
+
+138
+00:13:16,250 --> 00:13:22,190
+يبقى قداش ال order لتلاتة أربعة يبقى هذا الكلام طب
+
+139
+00:13:22,190 --> 00:13:23,770
+مين معكوس الثلاثة؟
+
+140
+00:13:26,720 --> 00:13:31,080
+ثلاثة بيبقى معكوسه من اللي لو ضربت فيها بطلع ال
+
+141
+00:13:31,080 --> 00:13:37,260
+identity يبقى ال order لسبعة كمان أربعة يبقى يساوي
+
+142
+00:13:37,260 --> 00:13:42,380
+ال order لسبعة اللي هو مين اللي هو أربعة طيب تعال
+
+143
+00:13:42,380 --> 00:13:52,480
+تسعة قداش ال order إلها اثنان ثلاثة اختلف
+
+144
+00:13:52,480 --> 00:13:57,120
+الروايات هو تسعة في تسعة بقداش؟ واحد وثمانين شيل أربع
+
+145
+00:13:57,120 --> 00:14:03,180
+عشرينات بظل واحد يبقى ال order لستة اثنان يبقى ال
+
+146
+00:14:03,180 --> 00:14:08,680
+order لتسعة يساوي اثنان مين معكوس التسعة؟ تسعة
+
+147
+00:14:08,680 --> 00:14:14,000
+نفسها صحيح يبقى خلاصنا بدي بعد هيك ال order لليحدى عشر
+
+148
+00:14:14,000 --> 00:14:20,460
+هذا كمان يساوي ال order لليحدى عشر عشان موافقين هيك من
+
+149
+00:14:20,460 --> 00:14:25,480
+11 في 11 مئة وواحد وعشرين شيل ست عشرينات بظل واحد
+
+150
+00:14:25,480 --> 00:14:31,960
+ال identity يبقى ال order الى يساوي اثنان  الثلاثة عشر
+
+151
+00:14:31,960 --> 00:14:35,000
+أريحك 
+
+152
+00:14:35,000 --> 00:14:42,060
+شوية الثلاثة عشر modulo عشرين لو أضفتلها سالب عشرين
+
+153
+00:14:42,060 --> 00:14:47,360
+بطلع قداش؟ سالب سبعة يعني كانوا زي الشغل تبع سالب سبعة تمام
+
+154
+00:14:47,360 --> 00:14:53,870
+إذا لما أقوله ثلاثة عشر تربيع كأنه سالب سبعة تربيع
+
+155
+00:14:53,870 --> 00:15:00,330
+سالب سبعة تربيع بقداش؟ تسعة وأربعين يعني تسعة تسعة
+
+156
+00:15:00,330 --> 00:15:05,850
+فيه سالب سبعة اللي هو بسالب ثلاثة وستين بيظل سالب
+
+157
+00:15:05,850 --> 00:15:09,690
+ثلاثة تسعة سبعة بسالب واحد وعشرين يبقى ال order
+
+158
+00:15:09,690 --> 00:15:15,970
+أربعة تمام؟ يبقى كمان هذا بده يساوي ال order
+
+159
+00:15:15,970 --> 00:15:18,030
+لثلاثة عشر
+
+160
+00:15:20,900 --> 00:15:27,320
+وبالمثل ال order ل 17 و 19 بنفس الطريقة وأسهل 
+
+161
+00:15:27,320 --> 00:15:32,960
+بصير لأن ال 17 مرة عن سالب ثلاثة تمام؟ يبقى ال
+
+162
+00:15:32,960 --> 00:15:40,380
+order إحنا بقداش؟ بأربعة يبقى كمان هذا بده يساوي ال
+
+163
+00:15:40,380 --> 00:15:47,520
+order ل 17 ال 19 عبارة عن إيه؟ سالب واحد يبقى ال
+
+164
+00:15:47,520 --> 00:15:53,180
+order لها بس اثنان يبقى هذا بده يساوي ال order ل
+
+165
+00:15:53,180 --> 00:15:57,900
+19 خلصنا ماشي؟
+
+166
+00:15:57,900 --> 00:16:01,980
+طيب هاي خلصنا بالنسبة لل group الأولى نيجي لل
+
+167
+00:16:01,980 --> 00:16:04,860
+group الثانية اللي هو D4
+
+168
+00:16:07,490 --> 00:16:21,470
+D4 عناصرها اللي هي R0 وR90 وR180 وR270 وH وV وD
+
+169
+00:16:21,470 --> 00:16:30,730
+وD' طبعا كتبنالكوا قبل ذلك أن R أس 4 تساوي R270
+
+170
+00:16:30,730 --> 00:16:36,570
+تساوي ال identity يعني لو مسكنهم بالدور هذا بده
+
+171
+00:16:36,570 --> 00:16:43,850
+يعطيك إن ال order ل دي four بده يسوي ثمانية هنا ال
+
+172
+00:16:43,850 --> 00:16:49,670
+order لل R note بده يسوي واحد ال order لل R تسعين
+
+173
+00:16:49,670 --> 00:16:56,250
+هو ال order لمعكوسة R ميتين وسبعين هو أربعة الباقي
+
+174
+00:16:56,250 --> 00:17:02,310
+ال order ل R مية وتمانين هو ال order لل H هو ال
+
+175
+00:17:02,310 --> 00:17:07,980
+order لل V هو ال order ل D هو ال order ل D prime
+
+176
+00:17:07,980 --> 00:17:12,120
+هو اثنان مش هالول قولنا كل واحد تربيع بيعطينا ال
+
+177
+00:17:12,120 --> 00:17:17,440
+identity إذا ال order لهم يساوي اثنان يبقى كلام
+
+178
+00:17:17,440 --> 00:17:22,400
+كتبناه معك سابقا مجرد تحصيل حاصل هذا بالنسبة
+
+179
+00:17:22,400 --> 00:17:27,440
+للسؤال الأول بالنسبة للسؤال الرابع بقول prove that
+
+180
+00:17:27,440 --> 00:17:31,840
+in any group an element and its inverse have the
+
+181
+00:17:31,840 --> 00:17:33,260
+same order
+
+182
+00:17:36,320 --> 00:17:44,000
+يبقى السؤال الرابع بيقول لي show ان ال order لل A
+
+183
+00:17:44,000 --> 00:17:51,160
+هو ال order لل A inverse شايف السؤال هكذا؟ طيب،
+
+184
+00:17:51,160 --> 00:17:58,060
+الآن بدي أفترض أن هذا ال order له رقم وهذا رقم
+
+185
+00:17:58,060 --> 00:18:05,760
+ثاني وأحاول أثبت أن الرقمين متساويان، تمام؟ فمثلا
+
+186
+00:18:06,190 --> 00:18:13,150
+لو قلت let ال order لل A بده يسوي ال N and ال
+
+187
+00:18:13,150 --> 00:18:21,970
+order لل A inverse بده يسوي ال M شوف
+
+188
+00:18:21,970 --> 00:18:30,030
+يا سيد الآن بدي أضيف لـ A itself بدي أضيف كأس ل M
+
+189
+00:18:30,030 --> 00:18:35,230
+أو بدي أضيف M أس له وبدي أذهب لل A inverse و
+
+190
+00:18:35,230 --> 00:18:40,490
+أضيف هذا الأس N وأشوف أين تتوجه الدنيا إذا أنا
+
+191
+00:18:40,490 --> 00:18:50,060
+لو بدأت ب A inverse اللي هو أس N يبقى هذا إيش معناه
+
+192
+00:18:50,060 --> 00:18:59,080
+أن A أُس minus ال N مظبوط طيب هذا معناه A n
+
+193
+00:18:59,080 --> 00:19:07,710
+inverse طيب ال A n بجد إيش؟ ال Identity مش ال
+
+194
+00:19:07,710 --> 00:19:13,210
+Order ل A بده يسوي N يعني أقل عدد صحيح موجب بحط
+
+195
+00:19:13,210 --> 00:19:18,630
+أصل A بيعطيني ال Identity اللي هو مين؟ N يبقى هذا
+
+196
+00:19:18,630 --> 00:19:24,650
+الكلام بده يسوي E inverse اللي هو مين؟ ال E إيش
+
+197
+00:19:24,650 --> 00:19:30,470
+تفسيرك لهذا الكلام؟ إن ال Order لل A inverse يا
+
+198
+00:19:30,470 --> 00:19:37,150
+إما N يا إما أقل من ال N صحيح ولا لا؟ ليش؟ لأن أنا
+
+199
+00:19:37,150 --> 00:19:42,370
+بعرفش إن هذا هو أصغر رقم ولا فيه أصغر منه أنا
+
+200
+00:19:42,370 --> 00:19:47,550
+مفترض إن ال order لهذا main اللي هو M يبقى هذا
+
+201
+00:19:47,550 --> 00:19:53,670
+معناه إن ال order لل A inverse أقل من أو يساوي ال N
+
+202
+00:19:53,670 --> 00:20:01,760
+قد يكون ال N وقد يكون أقل منه طيب ال order ل A
+
+203
+00:20:01,760 --> 00:20:08,440
+inverse N عيش فرضه M يبقى صار ال M أقل من أو يساوي
+
+204
+00:20:08,440 --> 00:20:15,560
+ال N ودي المعادلة رقم واحد طيب تعال شوف للتجاه
+
+205
+00:20:15,560 --> 00:20:22,060
+الثاني يبقى لو جيت برضه أخد ال A أس M
+
+206
+00:20:25,070 --> 00:20:31,670
+يعني أنا حطيت الأس تبع ال A inverse لل A وحطيت ال
+
+207
+00:20:31,670 --> 00:20:37,230
+order تبع ال A لل A inverse وشوف وين بدنا نوصل
+
+208
+00:20:37,230 --> 00:20:44,590
+يبقى هذا الكلام بقدر أقول A inverse inverse كله أس
+
+209
+00:20:44,590 --> 00:20:48,270
+M أو
+
+210
+00:20:48,270 --> 00:21:03,060
+إن شئتم فقولوا A inverse لسالب M أو يساوي A-m لل A
+
+211
+00:21:03,060 --> 00:21:06,960
+inverse أو
+
+212
+00:21:06,960 --> 00:21:19,920
+بقدر أقول A m A m يبقى
+
+213
+00:21:19,920 --> 00:21:30,020
+هذه A-m inverse يبقى هذه A m وهنا inverse وهنا
+
+214
+00:21:30,020 --> 00:21:38,620
+inverse تمام ال A m ما بجدوش عند هنا ال A A لأ A
+
+215
+00:21:38,620 --> 00:21:44,940
+inverse m هذه استنى شوية استنى شوية هذه بدي أخليها
+
+216
+00:21:44,940 --> 00:21:51,160
+A inverse وهنا m تمام
+
+217
+00:21:51,760 --> 00:21:57,440
+يبقى هذا اللي بين جثيني بقداش؟ بال identity يبقى
+
+218
+00:21:57,440 --> 00:22:04,060
+هذا يعطيني E inverse اللي هو بال E يبقى A لما رفعت
+
+219
+00:22:04,060 --> 00:22:10,660
+للأس M اعطتني العدد E يبقى هذا معناته إيش؟ أن ال
+
+220
+00:22:10,660 --> 00:22:18,700
+order لل A أقل من أو يساوي ال M طيب ال order ل A
+
+221
+00:22:18,700 --> 00:22:25,970
+بقداش؟ N يبقى الآن أقل من أو يساوي M وهذه المعادلة
+
+222
+00:22:25,970 --> 00:22:32,050
+رقم اثنان نرجع لمبادئ الرياضيات لما أثبت أن هذا
+
+223
+00:22:32,050 --> 00:22:37,670
+أقل من هذا والمقلوب صحيح أن أقل من هذا يبقى
+
+224
+00:22:37,670 --> 00:22:43,090
+معاناة اثنين ما له equal يبقى هنا باجي بقوله from
+
+225
+00:22:43,090 --> 00:22:52,150
+واحد and اثنين يبقى ال N بده يساوي ال M هذا معناته
+
+226
+00:22:52,150 --> 00:22:57,350
+أن ال order ل A بده يساوي ال order ل A inverse وهو
+
+227
+00:22:57,350 --> 00:22:58,070
+المطلوب
+
+228
+00:23:04,320 --> 00:23:09,480
+يبقى شباب في الجبر هنا إحنا بنحاول نستخدم كل
+
+229
+00:23:09,480 --> 00:23:15,220
+المعلومات اللي درسناها في مبادئ الرياضيات متى لازم
+
+230
+00:23:15,220 --> 00:23:20,480
+الأمر وأين بنلزم بنروح نستخدمها يبقى هذا كان
+
+231
+00:23:20,480 --> 00:23:27,840
+السؤال رقم أربعة معانا الآن السؤال رقم ستة يبقى ستة
+
+232
+00:23:27,840 --> 00:23:36,100
+بيقول إيه؟ element موجود في ال group و A6 يساوي ال
+
+233
+00:23:36,100 --> 00:23:43,300
+identity element و what are the possible orders
+
+234
+00:23:43,300 --> 00:23:49,160
+for order A وقول لي ليش هذا بده يعطينا أن ال
+
+235
+00:23:49,160 --> 00:23:56,300
+order ل A الله أعلم بده
+
+236
+00:23:56,300 --> 00:24:04,160
+ال order ل A قد إيش ممكن يكون؟ الله أعلم طيب الحين
+
+237
+00:24:04,160 --> 00:24:10,020
+قد يكون ال A هذا هو ال identity element بقدر أقول
+
+238
+00:24:10,020 --> 00:24:15,900
+ال order يساوي ستة؟ قد يكون لكن ماقدرش أكد بقولي
+
+239
+00:24:15,900 --> 00:24:22,840
+ما هي الاحتمالات الممكنة لل order تبع ال A شو
+
+240
+00:24:22,840 --> 00:24:27,470
+الاحتمالات الممكنة لل order تبع ال A بقول له يمكن
+
+241
+00:24:27,470 --> 00:24:31,810
+يكون ال A هو ال identity إليه إذا ال order لا يبقى
+
+242
+00:24:31,810 --> 00:24:38,170
+بقداش؟ واحد اثنان قد يكون ال order ل A هو اثنان
+
+243
+00:24:38,170 --> 00:24:41,510
+معقول
+
+244
+00:24:41,510 --> 00:24:46,830
+ولا لا بصير اثنان تكعيب ال identity إذا الاحتمال
+
+245
+00:24:46,830 --> 00:24:53,810
+وارد قد يكون ال order ل A ثلاثة وارد
+
+246
+00:24:54,210 --> 00:25:01,310
+قد يكون ال order لإيه؟ أربعة خمسة ممكن؟ غير ممكن
+
+247
+00:25:01,310 --> 00:25:07,590
+على الإطلاق يبقى بيظل ستة أغششك شغلة سنثبتها كمان
+
+248
+00:25:07,590 --> 00:25:14,990
+قدام شوية دائما وأبدا لو كان عندك order ل element
+
+249
+00:25:14,990 --> 00:25:20,670
+واللي حطيت أس ثاني ل element هذا طلع ال
+
+250
+00:25:20,670 --> 00:25:25,630
+identity لازم ال order لل element يقسم هذا الرقم 
+
+251
+00:25:25,630 --> 00:25:32,750
+يعني كل الاحتمالات الممكنة هو the divisor الست يبقى
+
+252
+00:25:32,750 --> 00:25:38,240
+بصير ال identity هو واحد والـ A تربيع اللي هو اتنين
+
+253
+00:25:38,240 --> 00:25:41,940
+والـ A تكعيب اللي هو تلاتة والـ A والستة يبقى
+
+254
+00:25:41,940 --> 00:25:45,520
+الواحد والاتنين والتلاتة والستة هما ال possible
+
+255
+00:25:45,520 --> 00:25:52,900
+orders فقط لا غير يبقى باجي بقوله هنا the possible
+
+256
+00:25:52,900 --> 00:26:03,540
+orders are واحد و اتنين و تلاتة و ستة only فقط
+
+257
+00:26:03,540 --> 00:26:08,660
+مافيش غيرهم يعني لا بقدر أقول أربعة ولا بقدر أقول
+
+258
+00:26:08,660 --> 00:26:15,140
+خمسة ولا غيره كل هذه الأرقام بستطيعش أقولها أبدا
+
+259
+00:26:35,110 --> 00:26:41,430
+طيب ننتقل لسؤال ثمانية سؤال ثمانية بيقول ال X
+
+260
+00:26:41,430 --> 00:26:52,070
+موجود في group G و X تربيع لا 
+
+261
+00:26:52,070 --> 00:26:53,170
+يساوي
+
+262
+00:26:57,150 --> 00:27:01,590
+و X<sup>6</sup> يساوي E
+
+263
+00:27:10,650 --> 00:27:16,910
+هذا بده يعطينا ان ال X أس أربعة لا يمكن أن تساوي
+
+264
+00:27:16,910 --> 00:27:25,990
+الـ E and الـ X أس خمسة لا يمكن أن تساوي ال identity
+
+265
+00:27:25,990 --> 00:27:30,930
+element what can you say about the order of X بدي
+
+266
+00:27:30,930 --> 00:27:35,890
+كمان ال order ل X يساوي جداش عندنا
+
+267
+00:27:41,670 --> 00:27:48,450
+الآن المعطيات كالتالي هدول اتنين معطيات وهدول
+
+268
+00:27:48,450 --> 00:27:53,290
+التلاتة مطلوب يبقى أنا بدي احاول استخدام المعطيات
+
+269
+00:27:53,290 --> 00:27:58,870
+بقدر الامكان مشان أوصل للمطلوب يبقى ال X تربيع لا
+
+270
+00:27:58,870 --> 00:28:03,270
+يمكن أن يساوي ال identity element السؤال هو هل
+
+271
+00:28:03,270 --> 00:28:08,800
+يمكن لل X ان يكون ال identity؟ هو مستبعد تماما لأن
+
+272
+00:28:08,800 --> 00:28:12,560
+كل orders يبقى مربعه يعطينا ال identity وهذا مستبعد
+
+273
+00:28:12,560 --> 00:28:15,940
+يبقى استبعدنا ال identity element ان X يساوي ال
+
+274
+00:28:15,940 --> 00:28:20,100
+identity واستبعدنا كذلك ال X تربيع يساوي مايعنى ال
+
+275
+00:28:20,100 --> 00:28:24,480
+identity يعطينا بعد ذلك ان X<sup>6</sup> يساوي ال
+
+276
+00:28:24,480 --> 00:28:30,400
+identity هل بقدر أقول ان ال order لل X يساوي 6؟ لأ
+
+277
+00:28:30,400 --> 00:28:34,820
+طيب خلي ال order للاخر بس نثبت هدول قال لي اثبت لي
+
+278
+00:28:34,820 --> 00:28:39,820
+ان ال X أس 4 لا يمكن أن يساوي ال identity ولا حتى
+
+279
+00:28:39,820 --> 00:28:45,180
+ال X أس 6 ولا ال X أس 5 بدها تساوي ال identity
+
+280
+00:28:45,180 --> 00:28:50,320
+درجة لطرق ال proofs اللي تعلمناها في مبادئ الرياضيات
+
+281
+00:28:51,270 --> 00:28:54,930
+يا إما direct proof باخد المعطيات اللي عندي و امشي
+
+282
+00:28:54,930 --> 00:28:59,450
+بها مباشرة يا إما بمشي بال contradiction يا إما
+
+283
+00:28:59,450 --> 00:29:05,550
+بال contrapositive تمام الحين هو بيقول لي اثبت هذا طب
+
+284
+00:29:05,550 --> 00:29:11,070
+أنا بدي بدي أنفي هذا و لما أنفي هذا بدي أشوف
+
+285
+00:29:11,070 --> 00:29:16,030
+المسار هذا وين بدي يوصلني تمام يبقى بالطريقة دي أقول له
+
+286
+00:29:16,030 --> 00:29:16,570
+solution
+
+287
+00:29:21,500 --> 00:29:29,460
+assume أفترض أن X أس 4 يساوي ال identity إذا أدىني
+
+288
+00:29:29,460 --> 00:29:35,300
+هذا الكلام إلى تناقض معناته فرضي غلط وعكسه هو الصح
+
+289
+00:29:35,300 --> 00:29:44,160
+طيب then إيش رأيك لو قلت X أس 4 تربيع مش يساوي ال
+
+290
+00:29:44,160 --> 00:29:49,260
+identity تربيع اللي هو بال identity طيب هذا معناه
+
+291
+00:29:49,260 --> 00:29:56,240
+ايه؟ معناته ان X أس 8 يساوي ال identity طيب ال X
+
+292
+00:29:56,240 --> 00:30:01,820
+أس 8 مش هي عبارة عن X أس 6 في X تربيع يساوي ال
+
+293
+00:30:01,820 --> 00:30:09,030
+identity؟ الـ X أس 6 معطى بالـ Identity في الـ X
+
+294
+00:30:09,030 --> 00:30:13,370
+تربيع بدّه يساوي الـ Identity هذا بدّه يعطيك إن X
+
+295
+00:30:13,370 --> 00:30:19,370
+تربيع بدّه يساوي الـ Identity يبقى سارة ناقم يبقى
+
+296
+00:30:19,370 --> 00:30:26,490
+this is contradict أو contradiction
+
+297
+00:30:29,570 --> 00:30:36,910
+for ال X تربيع لا يساوي ال identity فرضي
+
+298
+00:30:36,910 --> 00:30:44,350
+غلط وعكسه هو الصح يبقى so ال X أس أربعة لا يمكن
+
+299
+00:30:44,350 --> 00:30:49,950
+أن تساوي ال identity على الاطلاق هذا نفس الطريقة
+
+300
+00:31:14,130 --> 00:31:18,230
+يبقى الهدف اللي اتعلمناه في ال exercise
+
+301
+00:31:20,500 --> 00:31:26,020
+بعدها جالي هتل ال order لل X بقول له والله كويس الآن
+
+302
+00:31:26,020 --> 00:31:31,600
+ال X تربيع لا يساوي ال identity وال X أس أربعة لا
+
+303
+00:31:31,600 --> 00:31:35,300
+يساوي ال identity وال X أس خمسة لا يساوي ال identity
+
+304
+00:31:35,300 --> 00:31:38,380
+وال X أس ستة لا يساوي ال identity إذا ما هي
+
+305
+00:31:38,380 --> 00:31:43,310
+الاحتمالات الممكنة لل order يا تلاتة يا ستة مفيش
+
+306
+00:31:43,310 --> 00:31:47,070
+غيرهم حتى لو كان تلاتة بصير X<sup>3</sup> كيف يساوي ال
+
+307
+00:31:47,070 --> 00:31:51,570
+identity وبالتالي مربعه يساوي X<sup>6</sup> اللي هو
+
+308
+00:31:51,570 --> 00:31:56,550
+بال identity وقلت لك قبل قليل ال order لل element
+
+309
+00:31:56,550 --> 00:32:02,010
+بجسم الرقم اللي بتحطه سبع مرات من ال identity إذا
+
+310
+00:32:02,010 --> 00:32:05,390
+بجي بقول له the possible
+
+311
+00:32:07,960 --> 00:32:19,260
+orders for x is تلاتة or ستة غير هيك يبعتلك الله
+
+312
+00:32:19,260 --> 00:32:26,560
+طيب هذا كان السؤال رقم ثمانية نروح للسؤال رقم أحد عشر
+
+313
+00:32:26,560 --> 00:32:36,040
+show that يبقى أحد عشر بيقول لي show that ان ال U كده
+
+314
+00:32:36,040 --> 00:32:40,340
+أش عشرين ولا عشرين وانسة ولا أحد عشر بيقول لي ان ال U
+
+315
+00:32:40,340 --> 00:32:52,080
+عشرين لا يمكن أن تجي تولد بعنصر واحد K و ال K 
+
+316
+00:32:52,080 --> 00:32:59,940
+هذا for any K موجود في ال U عشرين for any K اللي
+
+317
+00:32:59,940 --> 00:33:01,600
+موجود في ال U عشرين
+
+318
+00:33:06,720 --> 00:33:11,420
+طيب الآن بدي أعرف مين هي ال U عشرين بدي نقفها قبل
+
+319
+00:33:11,420 --> 00:33:16,960
+شوية و اماسحناها ال U عشرين قلنا هي واحد و تلاتة
+
+320
+00:33:16,960 --> 00:33:23,260
+و سبعة خمسة لا يا ابني أنا سبعة و تسعة و الاحد عشر
+
+321
+00:33:23,260 --> 00:33:29,780
+و تلتاشر و سبعة عشر و تسعة عشر او حسبنا لهم
+
+322
+00:33:29,780 --> 00:33:35,540
+ال orders قبل قليل مظبوط ال order كان يا إما واحد
+
+323
+00:33:35,540 --> 00:33:41,080
+يا إما اتنين يا إما أربعة مفيش غير هي كده إذا أي
+
+324
+00:33:41,080 --> 00:33:45,660
+واحد أعلى أس بتحطه له اللي هو أربعة بيعطينا ال
+
+325
+00:33:45,660 --> 00:33:50,800
+identity element بعد ذلك يبقى اللي هدول كام واحد
+
+326
+00:33:50,800 --> 00:33:56,940
+هدول تمانية يعني ماعنديش ولا element ال order اللي
+
+327
+00:33:56,940 --> 00:34:01,830
+يساوي ثمانية لو كان ال order له ثمانية فهو يجيب لي
+
+328
+00:34:01,830 --> 00:34:06,750
+كل عناصر ال group اللي عندنا هنا يبقى باجي بقول له
+
+329
+00:34:06,750 --> 00:34:14,150
+هذه ال U عشرين لا يمكن أن تساوي ال subgroup
+
+330
+00:34:14,150 --> 00:34:21,870
+generated by K و ال K موجود في U عشرين السبب because
+
+331
+00:34:21,870 --> 00:34:36,840
+any element in ال U عشرين has order هما طب
+
+332
+00:34:36,840 --> 00:34:47,060
+أنا بقول لك عمل هذا و هذا كيف ال U عشرين لا يساوي
+
+333
+00:34:47,060 --> 00:34:51,100
+صحيح يبقى ال U عشرين لا يساوي ال K و ال K because
+
+334
+00:34:51,100 --> 00:34:56,540
+any element من عند كلمة because هذا هو البرهان يبقى
+
+335
+00:34:56,540 --> 00:35:02,140
+because any element in U عشرين has order واحد أو
+
+336
+00:35:02,140 --> 00:35:09,340
+اتنين أو أربعة أو أربعة غير هيك ما عنديش مشان ال
+
+337
+00:35:09,340 --> 00:35:13,920
+element يجيب ل group كلها مشان يجيب الجروب كلها و
+
+338
+00:35:13,920 --> 00:35:19,500
+تبقى Cyclic ال orders اللي بدك ترفعه هنا بدي يكون
+
+339
+00:35:19,500 --> 00:35:23,880
+ثمانية بدي يساوي ال order لل group مشان يجيب كل
+
+340
+00:35:23,880 --> 00:35:27,760
+عناصر ال group غير هيك يبعتلك الله يعني زي ما شفنا
+
+341
+00:35:27,760 --> 00:35:30,720
+توسعة كل واحد بيجيب ليها عنصر يعنصرين يعني أربع
+
+342
+00:35:30,720 --> 00:35:35,280
+عناصر بس لا يوجد element من ال Z20 بيجيب ليه كل
+
+343
+00:35:35,280 --> 00:35:40,380
+عناصر ال Z20 وبالتالي هذه لا يمكن أن تكون Cyclic
+
+344
+00:35:41,300 --> 00:35:46,280
+طيب روحنا الآن لخمستاشر خمستاشر بيقول ال H proper
+
+345
+00:35:46,280 --> 00:35:52,260
+subgroup من Z under addition تحت عملية الجمع
+
+346
+00:35:52,260 --> 00:36:03,800
+يبقى سؤال خمستاشر ال H subgroup من Z تحت عملية
+
+347
+00:36:03,800 --> 00:36:10,660
+الجمع العادية under addition and ال H contains و
+
+348
+00:36:11,150 --> 00:36:20,170
+عندنا 12 و 30 و 40 و 50 كلهم موجودات
+
+349
+00:36:20,170 --> 00:36:26,070
+هدول وين في ال H بيقول لي what are the possibilities
+
+350
+00:36:26,070 --> 00:36:35,930
+for H ما هي إمكانيات أن ال H يكون شكلها ايه حد
+
+351
+00:36:35,930 --> 00:36:41,390
+فيكم بيقدر يجيب لي أي شكل من أشكال H طبعا عدة أشكال
+
+352
+00:36:41,390 --> 00:36:46,090
+دي واحد يجيب لي بس شكل واحد السؤال مرة تانية أنا
+
+353
+00:36:46,090 --> 00:36:51,650
+عند مجموعة اللي هي الأعداد الصحيحة ومعرف عليها الجمع أخدت
+
+354
+00:36:51,650 --> 00:36:57,390
+H هذه ال sub group منها ال H لجيت فيها العناصر 12
+
+355
+00:36:57,390 --> 00:37:03,350
+و 30 و 50 بيقول لي احتمال H تكون mean هذه
+
+356
+00:37:07,670 --> 00:37:13,390
+يجب أن يتجمع كل واحد صفر صفر ممكن ال H تبقى zero
+
+357
+00:37:13,390 --> 00:37:17,250
+يعني ليه trivial subgroup لا يعني صفر واحد ممكن
+
+358
+00:37:17,250 --> 00:37:21,550
+تبقى 0 0 0 0 0 0 0 0 0 0 0 0 
+
+359
+00:37:21,550 --> 00:37:24,970
+0 0 0 0 0 0 0 0 0 0 0 0
+
+360
+00:37:24,970 --> 00:37:30,050
+0 0 0 0 0 0 0 0 0 0 0 0
+
+361
+00:37:30,050 --> 00:37:32,150
+0 0 0 0 0 0 0 0 0 0 0 0
+
+362
+00:37:32,150 --> 00:37:37,360
+0 0 0 0 0 0 0 0 0 0 0 0 طبعا
+
+363
+00:37:37,360 --> 00:37:42,180
+كتير بلاجة مش واحد و واحد ايه
+
+364
+00:37:42,180 --> 00:37:45,220
+التاجمة
+
+365
+00:37:45,220 --> 00:37:48,580
+هتجيب له معكوس كلّه لازم تجيبه تقدر تجيب لي واحدة
+
+366
+00:37:48,580 --> 00:37:56,840
+ايوه 6 3 3 ماشي طب و 2 عملية جمع
+
+367
+00:37:56,840 --> 00:38:00,260
+2 4 6 8 بتجي على ال 30 و تجي على
+
+368
+00:38:00,260 --> 00:38:05,140
+40 و 50 ولا لأ طيب ممتاز طيب ال 3 3 6
+
+369
+00:38:05,140 --> 00:38:07,760
+9 تطلع تجي على ال 30 وال 40 و ال 50 ال 6
+
+370
+00:38:07,760 --> 00:38:13,460
+كمان يعني ايش يعني كأن أنا بجيب ل greatest common
+
+371
+00:38:13,460 --> 00:38:19,600
+divisors ما بين ال 30 و ال 40 و ال 50 جيب
+
+372
+00:38:19,600 --> 00:38:23,920
+ل greatest common مش ل greatest common divisor كل
+
+373
+00:38:23,920 --> 00:38:28,880
+ال common divisors المشتركان بتلاقيهم هم تبعت من؟
+
+374
+00:38:29,090 --> 00:38:35,590
+يبقى هنا بقول له يبقى ال H بدها تساوي subgroup
+
+375
+00:38:35,590 --> 00:38:42,050
+generated by 2 4 6 8 10 12 14 30 32 34 لغاية توصل
+
+376
+00:38:42,050 --> 00:38:48,170
+لـ 4 و 5 و تبقى ماشي، والاحتمال الآخر ممكن تكون الـ H 
+
+377
+00:38:48,170 --> 00:38:52,590
+في يمين الـ subgroup generated by 3، والاحتمال 
+
+378
+00:38:52,590 --> 00:38:56,810
+الثالث تبقى الـ subgroup generated by 6، كلها بتجيب 
+
+379
+00:38:56,810 --> 00:39:03,730
+لثلاثة أرقام، ما خلصت، ما تلاقيش تمام، فش .. إذا فضلت 
+
+380
+00:39:03,730 --> 00:39:07,710
+الستة، إذا فضلت ستة ما فيش إمكانية يصير أكثر من 
+
+381
+00:39:07,710 --> 00:39:12,650
+أطمعش مرتين أين؟ لذلك ما عنديش إلا التلاتة هذول كل 
+
+382
+00:39:12,650 --> 00:39:18,750
+الاحتمالات الممكنة للـ cyclic subgroups اللي بدي 
+
+383
+00:39:18,750 --> 00:39:22,630
+يكون العناصر التلاتة هذول موجودات فيها، كيف؟ الواحد 
+
+384
+00:39:22,630 --> 00:39:27,790
+الواحد بيجيبها يا راجل الجامعة، الواحد اه بيجيبها 
+
+385
+00:39:27,790 --> 00:39:34,950
+ليش ما ..بجيبها واحد، والواحد كمان زيادة على ذلك 
+
+386
+00:39:34,950 --> 00:39:40,010
+لإن الـ identity هنا هو الـ zero والواحد برضه، والـ H 
+
+387
+00:39:40,010 --> 00:39:45,810
+برضه احتمال يكون الواحد، كل اللي بتجيبها تمام؟ لكن 
+
+388
+00:39:45,810 --> 00:39:49,050
+أبسط حاجة 2، 3، 6، هذه لأول واحد الـ 
+
+389
+00:39:49,050 --> 00:39:53,710
+divisor بيجيبوا كل الباقي، لإن كل واحد من التلاتة 
+
+390
+00:39:53,710 --> 00:39:59,010
+عبارة عن الـ divisor مضروب في رقم، بيجيبوا دغري 
+
+391
+00:39:59,010 --> 00:40:04,890
+الواحد اللي هي بتجيب الكل، طيب الآن 
+
+392
+00:40:04,890 --> 00:40:11,070
+سؤال 17، سؤال 17، اه هذا very important لأن 
+
+393
+00:40:11,070 --> 00:40:25,830
+في معلومة جديدة، سؤال 
+
+394
+00:40:25,830 --> 00:40:26,610
+17
+
+395
+00:40:31,010 --> 00:40:37,430
+سؤال 17 يا شباب بيقول، لأنّ divisor K of N 
+
+396
+00:40:37,430 --> 00:40:49,630
+يبقى K بتقسم الـ N، ولات الـ UKN هي من؟ هي كل العناصر 
+
+397
+00:40:49,630 --> 00:40:57,920
+X اللي موجودة في الـ UN بحيث أن 
+
+398
+00:40:57,920 --> 00:41:06,320
+الـ x modulo k بده يساوي الواحدة الصحيحة، بقول for 
+
+399
+00:41:06,320 --> 00:41:10,480
+example بيعطيني u 3 تساوي كذا، و u 7 تساوي 
+
+400
+00:41:10,480 --> 00:41:18,900
+كذا، list the elements of 
+
+401
+00:41:18,900 --> 00:41:22,100
+u 
+
+402
+00:41:22,100 --> 00:41:31,630
+24، و يو 24، و يو 15، و يو 5 
+
+403
+00:41:31,630 --> 00:41:41,330
+20، و يو 5 30، و يو 5 30، و كذلك يو 
+
+404
+00:41:41,330 --> 00:41:49,750
+10 30، و يو 10 30، هذا المطلوب الأول، هذا 
+
+405
+00:41:49,750 --> 00:41:55,960
+نمرة ايه؟ بعدها نمرة B بيقول prove that هذي الـ sub 
+
+406
+00:41:55,960 --> 00:42:06,160
+group، نمرة B prove أن U KN sub group من الـ UN، وبعد 
+
+407
+00:42:06,160 --> 00:42:15,420
+ذلك خد الـ H نمرة C، الـ H تساوي كل العناصر X، كل 
+
+408
+00:42:15,420 --> 00:42:23,910
+العناصر X اللي موجودة في U 10 بحيث أن الـ X modulo 
+
+409
+00:42:23,910 --> 00:42:29,090
+3 تساوي 1، X modulo 3 تساوي 1، بيقول 
+
+410
+00:42:29,090 --> 00:42:38,050
+هل الـ H subgroup من 10 أم لا، is الـ H subgroup من 
+
+411
+00:42:38,050 --> 00:42:45,910
+U 10 أم لا، هي السؤال، يبقى في عندي ثلاث نقاط بدي 
+
+412
+00:42:45,910 --> 00:42:49,590
+أبدأ مع كل نقطة من النقاط الثلاثة
+
+413
+00:43:08,860 --> 00:43:16,400
+عندي K تقسم الـ N، وعندي الـ UKN كل العناصر اللي 
+
+414
+00:43:16,400 --> 00:43:22,700
+موجودة في U N اللي بتحقق X modulo K يساوي 1، يعني 
+
+415
+00:43:22,700 --> 00:43:30,800
+الفرق ما بين الـ X وما بين الـ 1 هو مضاعفات الـ K، بقول 
+
+416
+00:43:30,800 --> 00:43:33,420
+لي هات لي الـ elements طبعًا هو معطيني اثنتين، و 
+
+417
+00:43:33,420 --> 00:43:37,520
+حسبهم لي، وبعدين يقول لي يلا احسب الـ U 24، والـ 
+
+418
+00:43:37,520 --> 00:43:41,720
+U 15، والـ U 5 30، والـ U 10 
+
+419
+00:43:41,720 --> 00:43:46,180
+30، وما إلى ذلك، بقوله كويس، إذا بدي آجي للنقطة 
+
+420
+00:43:46,180 --> 00:43:50,520
+الأولى، مشان هيك بدي أجيب له U 20 في الأول، لإن 
+
+421
+00:43:50,520 --> 00:43:55,010
+الشغل بدي أكون عليها، يبقى بدي آجي إلى النقطة الأولى 
+
+422
+00:43:55,010 --> 00:44:00,470
+بدي أجيب له U 20، ودي حسبناها قبل قليل، 1 
+
+423
+00:44:00,470 --> 00:44:07,930
+3، 7، 9، 11، 13، 17، 19، 21، 23، 1، 2، 3، 4، وكمان 4، 8، مظبوط 
+
+424
+00:44:07,930 --> 00:44:12,190
+طيب الآن بدي آجي أجيب له U 24، يبقى U 
+
+425
+00:44:12,190 --> 00:44:18,610
+4
+426
+00:44:18,610 --> 00:44:20,090
+20 يساوي، تعالى التعريف بيقول U KN كل اللي 
+
+427
+00:44:24,580 --> 00:44:32,400
+موجودات في UN بحيث يكون الفرق بينها وبينها هو 
+
+428
+00:44:32,400 --> 00:44:37,580
+مضاعفات الـ K، يبقى بدي أشوف الأرقام اللي عندي من 
+
+429
+00:44:37,580 --> 00:44:42,220
+الفرق بينه وبين الواحد هو مضاعفات الأربعة طبعًا 
+
+430
+00:44:42,220 --> 00:44:47,340
+الواحد، لأن الفرق بينهم Zero، مضاعفات الأربعة، طيب 
+
+431
+00:44:47,340 --> 00:44:51,760
+هاي واحد، التلاتة اطرح من واحد يصير 2، هي مضاعفات 
+
+432
+00:44:51,760 --> 00:44:56,810
+الأربعة؟ لأ، السابعة اطرح من واحد 6، مضاعفات 
+
+433
+00:44:56,810 --> 00:45:00,330
+الأربعة؟ لأ، تسعة اطرح من واحد بضل قداش؟ 8 
+
+434
+00:45:00,330 --> 00:45:04,170
+مضاعفات الأربعة؟ لأ، تسعة اطرح من واحد بضل قداش؟ 8
+
+435
+00:45:04,170 --> 00:45:10,030
+مضاعفات الأربعة؟ لأ، التسعة، الآن 11، انسى
+
+436
+00:45:10,030 --> 00:45:15,900
+13، اه صحيح، يبقى 13 اطرح منها واحد 12، 
+
+437
+00:45:15,900 --> 00:45:22,420
+مضاعفات الأربعة، 17 نفس القصة، يبقى والـ 17، والـ 
+
+438
+00:45:22,420 --> 00:45:28,000
+19 بلاش منها تمام، يبقى هذه U 24، 
+
+439
+00:45:28,000 --> 00:45:32,980
+جيبناها، وبعدين قال لي هذه U 15، النقطة 
+
+440
+00:45:32,980 --> 00:45:41,100
+الثانية بدنا U 15، ويساوي الواحد، ونجي 
+
+441
+00:45:41,100 --> 00:45:45,810
+ندور للواحد، والـ 11، الواحد، والـ 11، الواحد 
+
+442
+00:45:45,810 --> 00:45:46,150
+الواحد، الواحد، الواحد، الواحد، الواحد، الواحد، الواحد
+
+443
+00:45:46,150 --> 00:45:47,430
+الواحد، الواحد، الواحد، الواحد، الواحد، الواحد، الواحد
+
+444
+00:45:47,430 --> 00:45:47,670
+الواحد، الواحد، الواحد، الواحد، الواحد، الواحد، الواحد
+
+445
+00:45:47,670 --> 00:45:51,070
+الواحد، الواحد، الواحد
+
+446
+00:45:51,070 --> 00:45:54,670
+الواحد
+
+447
+00:45:54,670 --> 00:45:55,190
+الواحد، الواحد، الواحد، الواحد، الواحد، الواحد، الواحد
+
+448
+00:45:55,190 --> 00:46:04,890
+الواحد، الواحد، الواحد، الواحد، الواحد، الواحد، الواحد
+
+449
+00:46:04,890 --> 00:46:08,450
+الواحد، الـ
+
+450
+00:46:09,610 --> 00:46:16,590
+وبعدين 8، 9، 19، 11، 13، 14، 
+
+451
+00:46:16,590 --> 00:46:25,150
+15، 16، 17، وحط 19، 20، 21، 
+
+452
+00:46:25,150 --> 00:46:30,530
+22، 23، 24، 25، 
+
+453
+00:46:30,530 --> 00:46:36,730
+26، 27، 28، 29، 
+
+454
+00:46:36,730 --> 00:46:41,210
+تبقى هذه، جبت له U 30، قال لي هات لي يو 5 
+
+455
+00:46:41,210 --> 00:46:48,510
+30، يو 5 30، يو يساوي الواحد منهم، وبدأ 
+
+456
+00:46:48,510 --> 00:46:57,270
+أروح أدور، يبقى قداش؟ 11، في غيرها؟ 12، 16، 
+
+457
+00:46:57,270 --> 00:47:01,370
+18، 22، 28، ولا واحدة 
+
+458
+00:47:01,370 --> 00:47:05,250
+بتكسب على 5 تمام؟ يبقى ما عنديش إلا الواحد 
+
+459
+00:47:05,250 --> 00:47:10,250
+والـ 11، بعدها تقول ياتي يو 10 30، يو 10 
+
+460
+00:47:10,250 --> 00:47:17,610
+30، موجودة يو 10 30 اللي هي برضه 1، و 
+
+461
+00:47:17,610 --> 00:47:19,070
+11، ما فيش غير 
+
+462
+00:47:22,780 --> 00:47:28,740
+هذه، وهذه كلها مختلفة، لكن النتيجة واحدة، لكن كل 
+
+463
+00:47:28,740 --> 00:47:35,380
+واحدة في موقع في set مختلفة عن الثانية، هذه يو 5 
+
+464
+00:47:35,380 --> 00:47:40,420
+20 جزء من الـ يو 20، هذه يو 5 30 جزء من 
+
+465
+00:47:40,420 --> 00:47:44,980
+الـ يو 30، يو 10 30 جزء من الـ يو 30، 
+
+466
+00:47:45,220 --> 00:47:49,940
+يبقى بقدرش أقول إنّ هذه، كل اللي بقدر أقوله إنّ هذه 
+
+467
+00:47:49,940 --> 00:47:53,380
+الـ subgroup هي الـ subgroup هذه، هذا بعد ما أثبتنا 
+
+468
+00:47:53,380 --> 00:47:57,340
+subgroup، لسه ما أثبتناش هذا، احنا جيبنا لسه المطلوب 
+
+469
+00:47:57,340 --> 00:48:01,180
+الأول، المطلوب التالي يقول أثبت لي إنّ هذه الـ 
+
+470
+00:48:01,180 --> 00:48:09,580
+subgroup، بقوله بصيغة باجلن أمره، أول شيء الـ UKN 
+
+471
+00:48:09,580 --> 00:48:15,900
+is non-empty فيها العنصر زي ما أنت شايف، واحنا بنحسب 
+
+472
+00:48:15,900 --> 00:48:20,160
+كل واحد واحد واحد، لإنه اطرح منه يصير مضاعفة الرقم 
+
+473
+00:48:20,160 --> 00:48:24,920
+اللي عندك، مين مكان يكون UK is non-empty since 
+
+474
+00:48:24,920 --> 00:48:28,940
+الواحد موجود في UKN
+
+475
+00:48:30,920 --> 00:48:38,460
+طيب الآن بدي أفترض هذه النقطة الأولى، بدي أخد list 
+
+476
+00:48:38,460 --> 00:48:46,280
+بدي أخد رقمين الـ a مثلاً أو الـ x والـ y موجودات في 
+
+477
+00:48:46,280 --> 00:48:50,800
+الـ UK then 
+
+478
+00:48:50,800 --> 00:48:53,920
+الـ
+
+479
+00:48:53,920 --> 00:49:02,990
+x modulo كيف بدي اسمه كده؟ والـ y modulo k يساوي كم؟ 
+
+480
+00:49:02,990 --> 00:49:11,630
+كمان واحد، طيب هذا معناه ايش؟ مش معناه أن الـ x يساوي 
+
+481
+00:49:11,630 --> 00:49:21,430
+q 1 K زائد 1؟ مظبوط، طيب والـ y أي q 2 K 
+
+482
+00:49:21,430 --> 00:49:29,030
+زائد 1؟ والـ Q1 موجودة في Z integer، والـ Q2 
+
+483
+00:49:29,030 --> 00:49:34,990
+موجودة في Z integer، طيب أنا بدي أشوف هل حاصل ضربهم 
+
+484
+00:49:34,990 --> 00:49:41,750
+موجود في الـ UK ولا لأ؟ بجي بقوله الآن بدي أخد الـ 
+
+485
+00:49:41,750 --> 00:49:51,450
+X في Y يساوي Q1 K زائد 1 في Q2 K زائد 1، هذا سوف 
+
+486
+00:49:51,450 --> 00:49:59,870
+يعطيك أن الـ XY يساوي نضرب يا شباب، يبقى Q1 Q2 K 
+
+487
+00:49:59,870 --> 00:50:11,990
+تربيع زائد Q1 K زائد Q2 K زائد 1، طيب هذا معناه 
+
+488
+00:50:11,990 --> 00:50:17,990
+أن الـ XY يساوي شرايك هذول التلاتة بدي أخد منهم K 
+
+489
+00:50:17,990 --> 00:50:24,380
+عامل مشترك، يبقى لو أخد كي عامل مشترك بيصير كي واحد 
+
+490
+00:50:24,380 --> 00:50:31,620
+كي و 2 كي زائد كي 1 زائد كي و 2 في كي 
+
+491
+00:50:31,620 --> 00:50:40,840
+زائد 1، ايش معنى هذا الكلام؟ أنّ x y موجودة أو الـ 
+
+492
+00:50:40,840 --> 00:50:49,360
+x y modulo k بدي يساوي قداش؟ إذا هذا معناه أن الـ XY 
+
+493
+00:50:49,360 --> 00:50:57,080
+موديولو K بدل يساوي الواحد، هذا معناه أن الـ XY موجود 
+
+494
+00:50:57,080 --> 00:50:59,120
+في الـ UKN
+
+495
+00:51:02,490 --> 00:51:07,690
+طب احنا الأصل نثبت الأول في معكوسه الثاني موجود 
+
+496
+00:51:07,690 --> 00:51:11,690
+لكن هذا إذا بدنا النظرية الأولى، لكن أخدنا نظرية 
+
+497
+00:51:11,690 --> 00:51:17,930
+ثانية، السؤال هو هل الـ UK infinite ولا ما هوش 
+
+498
+00:51:17,930 --> 00:51:23,150
+finite، finite لإن الـ UN أصلاً finite، أنت الحد الـ N 
+
+499
+00:51:23,150 --> 00:51:30,550
+ناقص 1 بتوقف، تبقى باجي بقوله الآن الـ UKN is 
+
+500
+00:51:30,550 --> 00:51:41,410
+finite، السبب finite because الـ UN is finite 
+
+501
+00:51:44,370 --> 00:51:50,490
+طيب هي الست اللي أخدناها non-empty واحد اثنين
+
+502
+00:51:50,490 --> 00:51:54,310
+أخذنا elements اللي جات حاصل ضرب الأول موجود فيها
+
+503
+00:51:54,310 --> 00:52:00,030
+ثلاثة الـ subset هذه مالها finite خلصنا مش في نظرية
+
+504
+00:52:00,030 --> 00:52:03,930
+بتقول هيك لأ non-empty finite subset وبكتابة
+
+505
+00:52:03,930 --> 00:52:06,430
+البيت لو أخدت عنصرين موجودات فيها أثبتنا يبقى
+
+506
+00:52:06,430 --> 00:52:12,030
+خلصنا يبقى بناء عليه الـ UK is a subgroup يبقى بروح
+
+507
+00:52:12,030 --> 00:52:13,310
+بقوله bye
+
+508
+00:52:24,590 --> 00:52:34,000
+الـ UKN is a subgroup من الـ UN خلاص المطلوب بيه
+
+509
+00:52:34,000 --> 00:52:38,760
+بدنا نروح للمطلوب C المطلوب C بيقول الـ X كل
+
+510
+00:52:38,760 --> 00:52:43,560
+العناصر اللي موجودة في عشرة في U عشرة إذا بدنا نروح
+
+511
+00:52:43,560 --> 00:52:50,860
+نحسب له من U عشرة عناصره ليه واحد وثلاثة وسبعة
+
+512
+00:52:50,860 --> 00:52:56,980
+وتسعة مظبوط هيك؟ يبقى بيقول الـ X اللي موجودة فيه
+
+513
+00:52:56,980 --> 00:53:03,340
+عشرة بحيث الـ X modulo ثلاثة بده يساوي مين؟ بده يساوي
+
+514
+00:53:03,340 --> 00:53:09,480
+واحد طيب هذا بده يعطينا أنه H تساوي الواحد منهم
+
+515
+00:53:10,050 --> 00:53:14,330
+وندور على الثاني ثلاثة لو شلنا واحد بيصير اثنين
+
+516
+00:53:14,330 --> 00:53:18,210
+ماهي مضاعفات الثلاث سبعة شلنا واحد بيصير ستة
+
+517
+00:53:18,210 --> 00:53:25,230
+آه سبعة منهم تسعة لأ هدأت الآن هل لئنها subgroup
+
+518
+00:53:25,230 --> 00:53:32,060
+أم لا؟ قولوا الله أعلم تعالوا نشوف الواحد فش مشكلة لو
+
+519
+00:53:32,060 --> 00:53:37,640
+ضربت السبعة في نفسه لو كانت الـ subgroup السبعة
+
+520
+00:53:37,640 --> 00:53:42,620
+هيكون هو المعكوس لنفسه يعني السبعة تربيعها بتعطيني
+
+521
+00:53:42,620 --> 00:53:48,120
+الـ identity element لكن سبعة في سبعة تسعة
+
+522
+00:53:48,120 --> 00:53:54,060
+و أربعين شيل أربع عشرات بيظل تسعة هل التسعة هذا
+
+523
+00:53:54,060 --> 00:54:00,280
+موجود في H؟ مش موجود في H يبقى أخدت element في H
+
+524
+00:54:00,280 --> 00:54:04,460
+ضربته بنفسه طلع يعني الـ H is not closed under the
+
+525
+00:54:04,460 --> 00:54:10,340
+operation يبقى هل هذه subgroup يبقى هذا بده يعطيلك
+
+526
+00:54:10,340 --> 00:54:18,000
+أن الـ H is not a subgroup من الـ U عشرة من الـ U
+
+527
+00:54:18,000 --> 00:54:19,060
+عشرة because
+
+528
+00:54:21,670 --> 00:54:33,690
+إن الـ H is not closed under the
+
+529
+00:54:33,690 --> 00:54:40,210
+operation on
+
+530
+00:54:40,210 --> 00:54:42,050
+الـ U عشرة 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f66d01d39adcd4aeb94ee1b03ec1906dd5b89ffc
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3071, "start": 20.69, "end": 30.71, "text": "بسم الله الرحمن الرحيم نرجع ثانية إلى المحاضرة الماضية و نكمل ما ابتدأنا به المرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 47341, 3615, 38637, 7649, 10632, 30731, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 4032, 8717, 24793, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.08471679557114839, "compression_ratio": 1.6464646464646464, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.69, "end": 21.03, "word": "بسم", "probability": 0.903076171875}, {"start": 21.03, "end": 21.25, "word": " الله", "probability": 0.9755859375}, {"start": 21.25, "end": 21.67, "word": " الرحمن", "probability": 0.921875}, {"start": 21.67, "end": 22.21, "word": " الرحيم", "probability": 0.9930013020833334}, {"start": 22.21, "end": 24.75, "word": " نرجع", "probability": 0.8699544270833334}, {"start": 24.75, "end": 25.15, "word": " ثانية", "probability": 0.8971354166666666}, {"start": 25.15, "end": 25.33, "word": " إلى", "probability": 0.5419921875}, {"start": 25.33, "end": 26.09, "word": " المحاضرة", "probability": 0.9915771484375}, {"start": 26.09, "end": 26.81, "word": " الماضية", "probability": 0.9944661458333334}, {"start": 26.81, "end": 27.61, "word": " و", "probability": 0.9482421875}, {"start": 27.61, "end": 28.29, "word": " نكمل", "probability": 0.9288736979166666}, {"start": 28.29, "end": 28.41, "word": " ما", "probability": 0.89990234375}, {"start": 28.41, "end": 28.99, "word": " ابتدأنا", "probability": 0.92490234375}, {"start": 28.99, "end": 29.27, "word": " به", "probability": 0.60400390625}, {"start": 29.27, "end": 29.99, "word": " المرة", "probability": 0.97705078125}, {"start": 29.99, "end": 30.71, "word": " الماضية", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 2, "seek": 5888, "start": 31.2, "end": 58.88, "text": "أخر حاجة أعطناها المرة الماضية كان تعريف الـcentralizer لـ element موجود في الـ group وعرفنا الـ centralizer لـ element A الموجود في الـ group على إن كل الـ G اللي موجودة في G بحيث GA يساوي AG مكتوب معاكم المرة الماضية مش الجديد وحتى نص النظرية مكتوب معاكم المرة الماضية يبقى حابيت أذكر لإنه بدنا نروح نبرهن النظرية", "tokens": [10721, 34740, 11331, 26108, 3660, 5551, 3615, 9566, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 25961, 37279, 16572, 5172, 2423, 39184, 2207, 2155, 6545, 5296, 39184, 4478, 3714, 29245, 23328, 8978, 2423, 39184, 1594, 4032, 3615, 28480, 8315, 2423, 39184, 5777, 6545, 5296, 39184, 4478, 316, 9673, 29245, 23328, 8978, 2423, 39184, 1594, 15844, 36145, 28242, 2423, 39184, 460, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 460, 4724, 5016, 1829, 12984, 22841, 7251, 3794, 995, 45865, 28406, 3714, 4117, 2655, 37746, 20449, 995, 24793, 9673, 25720, 9673, 46958, 10632, 37893, 25724, 16254, 3215, 4032, 33753, 7578, 8717, 9381, 28239, 19913, 2288, 10632, 3714, 4117, 2655, 37746, 20449, 995, 24793, 9673, 25720, 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36.52, "word": " لـ", "probability": 0.82470703125}, {"start": 36.52, "end": 36.86, "word": " element", "probability": 0.465576171875}, {"start": 36.86, "end": 37.54, "word": " موجود", "probability": 0.9716796875}, {"start": 37.54, "end": 38.06, "word": " في", "probability": 0.94384765625}, {"start": 38.06, "end": 38.52, "word": " الـ", "probability": 0.5838623046875}, {"start": 38.52, "end": 38.78, "word": " group", "probability": 0.7626953125}, {"start": 38.78, "end": 39.9, "word": " وعرفنا", "probability": 0.8145751953125}, {"start": 39.9, "end": 40.14, "word": " الـ", "probability": 0.891845703125}, {"start": 40.14, "end": 40.9, "word": " centralizer", "probability": 0.794189453125}, {"start": 40.9, "end": 41.26, "word": " لـ", "probability": 0.76220703125}, {"start": 41.26, "end": 41.74, "word": " element", "probability": 0.875}, {"start": 41.74, "end": 42.08, "word": " A", "probability": 0.53076171875}, {"start": 42.08, "end": 42.74, "word": " الموجود", "probability": 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لها", "probability": 0.7286376953125}, {"start": 310.0, "end": 310.24, "word": " دي", "probability": 0.693359375}], "temperature": 1.0}, {"id": 13, "seek": 33280, "start": 312.42, "end": 332.8, "text": "لأ مش هذا اللي بدنا نقوله لأ احنا أخدنا y في ال centralizer ل a يعني طلع a y يسوى y a وصلنا إلى a inverse y يسوى y a inverse يبقى ال y موجود في ال centralizer ل a inverse", "tokens": [1211, 10721, 37893, 23758, 13672, 1829, 47525, 8315, 8717, 39648, 3224, 5296, 10721, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 288, 8978, 2423, 5777, 6545, 5296, 257, 37495, 22653, 23032, 1211, 3615, 257, 288, 7251, 3794, 2407, 7578, 288, 257, 4032, 36520, 8315, 30731, 257, 17340, 288, 7251, 3794, 2407, 7578, 288, 257, 17340, 7251, 3555, 4587, 7578, 2423, 288, 3714, 29245, 23328, 8978, 2423, 5777, 6545, 5296, 257, 17340], "avg_logprob": -0.2643045741067806, "compression_ratio": 1.611842105263158, "no_speech_prob": 0.0, "words": [{"start": 312.42, "end": 312.78, "word": "لأ", "probability": 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"end": 317.48, "word": " ل", "probability": 0.93701171875}, {"start": 317.48, "end": 317.76, "word": " a", "probability": 0.603515625}, {"start": 317.76, "end": 318.88, "word": " يعني", "probability": 0.888671875}, {"start": 318.88, "end": 319.4, "word": " طلع", "probability": 0.7849934895833334}, {"start": 319.4, "end": 319.82, "word": " a", "probability": 0.283935546875}, {"start": 319.82, "end": 320.26, "word": " y", "probability": 0.52392578125}, {"start": 320.26, "end": 320.76, "word": " يسوى", "probability": 0.65960693359375}, {"start": 320.76, "end": 321.04, "word": " y", "probability": 0.89697265625}, {"start": 321.04, "end": 321.34, "word": " a", "probability": 0.880859375}, {"start": 321.34, "end": 322.96, "word": " وصلنا", "probability": 0.8515625}, {"start": 322.96, "end": 323.36, "word": " إلى", "probability": 0.52880859375}, {"start": 323.36, "end": 323.76, "word": " a", "probability": 0.92333984375}, {"start": 323.76, "end": 324.38, "word": " inverse", "probability": 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"word": " ل", "probability": 0.9560546875}, {"start": 332.04, "end": 332.3, "word": " a", "probability": 0.98046875}, {"start": 332.3, "end": 332.8, "word": " inverse", "probability": 0.84228515625}], "temperature": 1.0}, {"id": 14, "seek": 34521, "start": 333.35, "end": 345.21, "text": "يبقى بناء عليه لو كان الـ Element موجود في الـ Centralizer لـ A هذا الـ Element لازم يكون موجود في الـ Centralizer لمعكوس الـ A", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 47356, 45164, 25961, 2423, 39184, 20900, 3714, 29245, 23328, 8978, 2423, 39184, 9701, 6545, 5296, 39184, 316, 23758, 2423, 39184, 20900, 5296, 31377, 2304, 7251, 30544, 3714, 29245, 23328, 8978, 2423, 39184, 9701, 6545, 32767, 3615, 4117, 41779, 2423, 39184, 316], "avg_logprob": -0.26464844060440856, "compression_ratio": 1.5238095238095237, "no_speech_prob": 0.0, "words": [{"start": 333.35, "end": 333.89, "word": "يبقى", "probability": 0.65386962890625}, {"start": 333.89, "end": 334.23, "word": " بناء", "probability": 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دول بدي اجمعهم ب inverse واحد بدي اخلّيهم بدل ما في inverse و inverse بدي اخلّيهم inverse واحد يبقى حسب معلوماتنا في الشبتر الماضي هذا بدي يصير مين؟ بدي يصير a inverse while كل inverse مظبوط؟", "tokens": [9566, 3555, 1975, 1829, 8592, 12602, 10721, 1829, 4117, 8978, 2423, 39184, 732, 4959, 11778, 12610, 4724, 16254, 1975, 7435, 2304, 3615, 16095, 4724, 17340, 36764, 24401, 4724, 16254, 1975, 9778, 1211, 11703, 1829, 16095, 47525, 1211, 19446, 8978, 17340, 4032, 17340, 4724, 16254, 1975, 9778, 1211, 11703, 1829, 16095, 17340, 36764, 24401, 7251, 3555, 4587, 7578, 11331, 35457, 20449, 1211, 20498, 9307, 8315, 8978, 25124, 3555, 2655, 2288, 9673, 46958, 1829, 23758, 4724, 16254, 7251, 9381, 13546, 3714, 9957, 22807, 4724, 16254, 7251, 9381, 13546, 257, 17340, 1339, 28242, 17340, 3714, 19913, 3555, 2407, 9566, 22807], "avg_logprob": -0.24218750060821065, "compression_ratio": 1.7692307692307692, "no_speech_prob": 0.0, "words": [{"start": 467.1, "end": 467.44, "word": "طب", "probability": 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order ل R مية و تمانين هو ال order لل H هو ال order لل V", "tokens": [28814, 1863, 2423, 1668, 5296, 11778, 1829, 1451, 47525, 3224, 7251, 3794, 45865, 46811, 7649, 10632, 34105, 2423, 1668, 24976, 497, 3637, 47525, 3224, 7251, 3794, 45865, 36764, 24401, 2423, 1668, 24976, 497, 6055, 3794, 3615, 9957, 31439, 2423, 1668, 32767, 3615, 4117, 41779, 3660, 497, 3714, 36081, 9957, 4032, 35457, 3615, 9957, 31439, 5551, 25513, 27884, 29739, 995, 38436, 2423, 1668, 5296, 497, 3714, 10632, 4032, 46811, 7649, 9957, 31439, 2423, 1668, 24976, 389, 31439, 2423, 1668, 24976, 691], "avg_logprob": -0.206018524405397, "compression_ratio": 2.0526315789473686, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 997.53, "end": 998.05, "word": "إن", "probability": 0.5302734375}, {"start": 998.05, "end": 998.35, "word": " ال", "probability": 0.72998046875}, {"start": 998.35, "end": 999.07, "word": " order", "probability": 0.89794921875}, {"start": 999.07, "end": 999.53, "word": " ل", "probability": 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0.94482421875}, {"start": 1012.55, "end": 1013.01, "word": " ميتين", "probability": 0.8346354166666666}, {"start": 1013.01, "end": 1013.83, "word": " وسبعين", "probability": 0.9193115234375}, {"start": 1013.83, "end": 1014.47, "word": " هو", "probability": 0.90087890625}, {"start": 1014.47, "end": 1015.13, "word": " أربعة", "probability": 0.86865234375}, {"start": 1015.13, "end": 1016.25, "word": " الباقي", "probability": 0.8497721354166666}, {"start": 1016.25, "end": 1016.85, "word": " ال", "probability": 0.96923828125}, {"start": 1016.85, "end": 1017.37, "word": " order", "probability": 0.9814453125}, {"start": 1017.37, "end": 1017.63, "word": " ل", "probability": 0.8505859375}, {"start": 1017.63, "end": 1018.05, "word": " R", "probability": 0.8740234375}, {"start": 1018.05, "end": 1018.43, "word": " مية", "probability": 0.90283203125}, {"start": 1018.43, "end": 1018.63, "word": " و", "probability": 0.68359375}, {"start": 1018.63, "end": 1019.37, "word": " تمانين", "probability": 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بيعطينا ال identity إذا ال order لهم يساوي اتنين يبقى كلام كتبناه معاك سابقا مجرد تحصيل حاصل هذا بالنسبة للسؤال الأول بالنسبة للسؤال الرابع بقول prove that in any group an element and its inverse have the same order", "tokens": [3224, 2407, 2423, 1668, 5296, 16254, 3224, 31439, 2423, 1668, 5296, 16254, 3224, 5835, 31439, 1975, 2655, 1863, 9957, 37893, 8032, 6027, 12610, 12174, 12610, 8315, 28242, 36764, 24401, 6055, 25513, 10632, 4724, 40228, 9566, 1829, 8315, 2423, 6575, 11933, 15730, 2423, 1668, 5296, 16095, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 28242, 10943, 9122, 2655, 3555, 8315, 3224, 20449, 995, 4117, 8608, 16758, 4587, 995, 3714, 7435, 2288, 3215, 6055, 5016, 9381, 26895, 11331, 33546, 1211, 23758, 20666, 1863, 35457, 3660, 24976, 3794, 33604, 6027, 16247, 12610, 20666, 1863, 35457, 3660, 24976, 3794, 33604, 6027, 34892, 16758, 3615, 4724, 39648, 7081, 300, 294, 604, 1594, 364, 4478, 293, 1080, 17340, 362, 264, 912, 1668], "avg_logprob": 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"probability": 0.9287109375}, {"start": 1041.92, "end": 1042.4, "word": " بالنسبة", "probability": 0.8626708984375}, {"start": 1042.4, "end": 1043.34, "word": " للسؤال", "probability": 0.9261474609375}, {"start": 1043.34, "end": 1044.0, "word": " الأول", "probability": 0.9716796875}, {"start": 1044.0, "end": 1045.02, "word": " بالنسبة", "probability": 0.9871826171875}, {"start": 1045.02, "end": 1045.8, "word": " للسؤال", "probability": 0.9793701171875}, {"start": 1045.8, "end": 1046.3, "word": " الرابع", "probability": 0.9866536458333334}, {"start": 1046.3, "end": 1046.56, "word": " بقول", "probability": 0.5576171875}, {"start": 1046.56, "end": 1047.06, "word": " prove", "probability": 0.7841796875}, {"start": 1047.06, "end": 1047.44, "word": " that", "probability": 0.927734375}, {"start": 1047.44, "end": 1047.98, "word": " in", "probability": 0.875}, {"start": 1047.98, "end": 1048.26, "word": " any", "probability": 0.9296875}, {"start": 1048.26, "end": 1048.5, "word": " group", "probability": 0.96337890625}, {"start": 1048.5, "end": 1048.78, "word": " an", "probability": 0.83349609375}, {"start": 1048.78, "end": 1049.48, "word": " element", "probability": 0.96826171875}, {"start": 1049.48, "end": 1050.06, "word": " and", "probability": 0.9658203125}, {"start": 1050.06, "end": 1050.46, "word": " its", "probability": 0.9189453125}, {"start": 1050.46, "end": 1050.98, "word": " inverse", "probability": 0.88232421875}, {"start": 1050.98, "end": 1051.56, "word": " have", "probability": 0.939453125}, {"start": 1051.56, "end": 1051.84, "word": " the", "probability": 0.92822265625}, {"start": 1051.84, "end": 1052.7, "word": " same", "probability": 0.908203125}, {"start": 1052.7, "end": 1053.26, "word": " order", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 45, "seek": 108576, "start": 1056.32, "end": 1085.76, "text": "يبقى السؤال الرابع بيقول لي show ان ال order لل A هو ال order لل A inverse شايف السؤال هكذا؟ طيب، الان بدي افترض ان هذا ال order له رقم و هذا رقم تاني و احاول اثبت ان الرقمين متساويان، تمام؟ فمثلا", "tokens": [1829, 3555, 4587, 7578, 21136, 33604, 6027, 34892, 16758, 3615, 4724, 1829, 39648, 32239, 855, 16472, 2423, 1668, 24976, 316, 31439, 2423, 1668, 24976, 316, 17340, 13412, 995, 33911, 21136, 33604, 6027, 8032, 4117, 15730, 22807, 23032, 1829, 3555, 12399, 2423, 7649, 4724, 16254, 1975, 5172, 2655, 43042, 16472, 23758, 2423, 1668, 46740, 12602, 4587, 2304, 4032, 23758, 12602, 4587, 2304, 6055, 7649, 1829, 4032, 1975, 5016, 995, 12610, 1975, 12984, 3555, 2655, 16472, 34892, 4587, 2304, 9957, 44650, 3794, 995, 45865, 7649, 12399, 46811, 10943, 22807, 6156, 2304, 12984, 15040], "avg_logprob": -0.19802988871284152, "compression_ratio": 1.7180851063829787, "no_speech_prob": 0.0, "words": [{"start": 1056.32, "end": 1056.76, "word": "يبقى", "probability": 0.870361328125}, {"start": 1056.76, "end": 1057.26, "word": " السؤال", "probability": 0.9905598958333334}, {"start": 1057.26, "end": 1058.1, "word": " الرابع", "probability": 0.9913736979166666}, {"start": 1058.1, "end": 1059.58, "word": " بيقول", "probability": 0.7976888020833334}, {"start": 1059.58, "end": 1059.84, "word": " لي", "probability": 0.297119140625}, {"start": 1059.84, "end": 1060.44, "word": " show", "probability": 0.73486328125}, {"start": 1060.44, "end": 1061.6, "word": " ان", "probability": 0.54150390625}, {"start": 1061.6, "end": 1062.44, "word": " ال", "probability": 0.8798828125}, {"start": 1062.44, "end": 1063.12, "word": " order", "probability": 0.93994140625}, {"start": 1063.12, "end": 1063.58, "word": " لل", "probability": 0.6513671875}, {"start": 1063.58, "end": 1064.0, "word": " A", "probability": 0.296142578125}, {"start": 1064.0, "end": 1064.36, "word": " هو", "probability": 0.9765625}, {"start": 1064.36, "end": 1064.58, "word": " ال", "probability": 0.8076171875}, {"start": 1064.58, "end": 1065.06, "word": " order", "probability": 0.970703125}, {"start": 1065.06, "end": 1065.44, "word": " لل", "probability": 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0.9052734375}, {"start": 1074.96, "end": 1075.4, "word": " order", "probability": 0.97119140625}, {"start": 1075.4, "end": 1075.78, "word": " له", "probability": 0.77880859375}, {"start": 1075.78, "end": 1076.3, "word": " رقم", "probability": 0.9947916666666666}, {"start": 1076.3, "end": 1076.98, "word": " و", "probability": 0.442626953125}, {"start": 1076.98, "end": 1077.32, "word": " هذا", "probability": 0.86962890625}, {"start": 1077.32, "end": 1078.06, "word": " رقم", "probability": 0.984375}, {"start": 1078.06, "end": 1078.92, "word": " تاني", "probability": 0.8976236979166666}, {"start": 1078.92, "end": 1079.54, "word": " و", "probability": 0.94384765625}, {"start": 1079.54, "end": 1079.96, "word": " احاول", "probability": 0.85577392578125}, {"start": 1079.96, "end": 1080.56, "word": " اثبت", "probability": 0.9345703125}, {"start": 1080.56, "end": 1080.88, "word": " ان", "probability": 0.83056640625}, {"start": 1080.88, "end": 1081.88, "word": " الرقمين", "probability": 0.9337158203125}, {"start": 1081.88, "end": 1084.12, "word": " متساويان،", "probability": 0.8082682291666666}, {"start": 1084.12, "end": 1085.14, "word": " تمام؟", "probability": 0.8243815104166666}, {"start": 1085.14, "end": 1085.76, "word": " فمثلا", "probability": 0.9356689453125}], "temperature": 1.0}, {"id": 46, "seek": 110229, "start": 1086.19, "end": 1102.29, "text": "لو قلت let ال order لل A بده يسوي ال N and ال order لل A inverse بده يسوي ال M شوف يا سيد", "tokens": [1211, 2407, 12174, 1211, 2655, 718, 2423, 1668, 24976, 316, 47525, 3224, 7251, 3794, 45865, 2423, 426, 293, 2423, 1668, 24976, 316, 17340, 47525, 3224, 7251, 3794, 45865, 2423, 376, 13412, 38688, 35186, 8608, 25708], "avg_logprob": -0.258680565489663, "compression_ratio": 1.3763440860215055, "no_speech_prob": 0.0, "words": [{"start": 1086.19, "end": 1086.73, "word": "لو", "probability": 0.791259765625}, {"start": 1086.73, "end": 1087.21, "word": " قلت", "probability": 0.9404296875}, {"start": 1087.21, "end": 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"start": 1494.21, "end": 1509.33, "text": "قد يكون ال order لإيه؟ أربعة خمسة ممكن؟ غير ممكن على الإطلاق يبقى بيظل ستة أغششك شغلة سنثبتها كمان جدام شوية", "tokens": [28543, 7251, 30544, 2423, 1668, 5296, 28814, 1829, 3224, 22807, 5551, 25513, 27884, 16490, 2304, 3794, 3660, 3714, 43020, 22807, 32771, 13546, 3714, 43020, 15844, 33688, 9566, 15040, 4587, 7251, 3555, 4587, 7578, 4724, 1829, 19913, 1211, 8608, 2655, 3660, 5551, 17082, 8592, 8592, 4117, 13412, 17082, 37977, 8608, 1863, 12984, 3555, 2655, 11296, 9122, 2304, 7649, 10874, 3215, 10943, 13412, 2407, 10632], "avg_logprob": -0.16601562243886292, "compression_ratio": 1.3450704225352113, "no_speech_prob": 0.0, "words": [{"start": 1494.21, "end": 1494.57, "word": "قد", "probability": 0.71826171875}, {"start": 1494.57, "end": 1495.23, "word": " يكون", "probability": 0.987060546875}, {"start": 1495.23, "end": 1495.39, "word": " ال", "probability": 0.64404296875}, {"start": 1495.39, "end": 1495.93, "word": " order", "probability": 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أغششك", "probability": 0.9}, {"start": 1505.71, "end": 1506.13, "word": " شغلة", "probability": 0.93115234375}, {"start": 1506.13, "end": 1506.99, "word": " سنثبتها", "probability": 0.9642740885416666}, {"start": 1506.99, "end": 1507.59, "word": " كمان", "probability": 0.9803059895833334}, {"start": 1507.59, "end": 1508.77, "word": " جدام", "probability": 0.7906901041666666}, {"start": 1508.77, "end": 1509.33, "word": " شوية", "probability": 0.8274739583333334}], "temperature": 1.0}, {"id": 63, "seek": 153531, "start": 1509.91, "end": 1535.31, "text": "دائما و أبدا لو كان عندك order ل element و اللي حطيت أس تاني ل ال element هذا طلع ال identity لازم ال order ل ال element يقسم هذا الرقم يعني كل الاحتمالات الممكنة هو divisor الست يبقى بصير ال identity هو واحد", "tokens": [3215, 16373, 15042, 4032, 5551, 3555, 28259, 45164, 25961, 43242, 4117, 1668, 5296, 4478, 4032, 13672, 1829, 11331, 9566, 36081, 5551, 3794, 6055, 7649, 1829, 5296, 2423, 4478, 23758, 23032, 1211, 3615, 2423, 6575, 5296, 31377, 2304, 2423, 1668, 5296, 2423, 4478, 7251, 4587, 38251, 23758, 34892, 4587, 2304, 37495, 22653, 28242, 42963, 33753, 2304, 6027, 9307, 9673, 43020, 3660, 31439, 25974, 284, 2423, 14851, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 2423, 6575, 31439, 36764, 24401], "avg_logprob": -0.24759616148777497, "compression_ratio": 1.6842105263157894, "no_speech_prob": 0.0, "words": [{"start": 1509.91, "end": 1510.67, "word": "دائما", "probability": 0.7182210286458334}, {"start": 1510.67, "end": 1510.95, "word": " و", "probability": 0.6572265625}, {"start": 1510.95, "end": 1511.81, "word": " أبدا", "probability": 0.7858072916666666}, {"start": 1511.81, "end": 1512.67, "word": " لو", "probability": 0.62353515625}, {"start": 1512.67, "end": 1513.09, "word": " كان", "probability": 0.97509765625}, {"start": 1513.09, "end": 1513.59, "word": " عندك", "probability": 0.9765625}, {"start": 1513.59, "end": 1514.09, "word": " order", "probability": 0.9033203125}, {"start": 1514.09, "end": 1514.33, "word": " ل", "probability": 0.7060546875}, {"start": 1514.33, "end": 1514.99, "word": " element", "probability": 0.80859375}, {"start": 1514.99, "end": 1516.19, "word": " و", "probability": 0.6015625}, {"start": 1516.19, "end": 1516.43, "word": " اللي", "probability": 0.3753662109375}, {"start": 1516.43, "end": 1517.19, "word": " حطيت", "probability": 0.9127604166666666}, {"start": 1517.19, "end": 1517.75, "word": " أس", "probability": 0.341552734375}, {"start": 1517.75, "end": 1518.47, "word": " تاني", "probability": 0.86181640625}, {"start": 1518.47, "end": 1519.33, "word": " ل", "probability": 0.45458984375}, {"start": 1519.33, "end": 1519.53, "word": " ال", "probability": 0.78076171875}, {"start": 1519.53, "end": 1519.87, "word": " element", "probability": 0.9619140625}, {"start": 1519.87, "end": 1520.17, "word": " هذا", "probability": 0.78466796875}, {"start": 1520.17, "end": 1520.53, "word": " طلع", "probability": 0.87890625}, {"start": 1520.53, "end": 1520.67, "word": " ال", "probability": 0.978515625}, {"start": 1520.67, "end": 1521.31, "word": " identity", "probability": 0.83935546875}, {"start": 1521.31, "end": 1522.15, "word": " لازم", "probability": 0.8956705729166666}, {"start": 1522.15, "end": 1522.33, "word": " ال", "probability": 0.921875}, {"start": 1522.33, "end": 1522.69, "word": " order", "probability": 0.97900390625}, {"start": 1522.69, "end": 1522.87, "word": " ل", "probability": 0.68603515625}, {"start": 1522.87, "end": 1523.03, "word": " ال", "probability": 0.916015625}, {"start": 1523.03, "end": 1523.39, "word": " element", "probability": 0.98583984375}, {"start": 1523.39, "end": 1523.93, "word": " يقسم", "probability": 0.9881184895833334}, {"start": 1523.93, "end": 1524.27, "word": " هذا", "probability": 0.96728515625}, {"start": 1524.27, "end": 1525.63, "word": " الرقم", "probability": 0.9837239583333334}, {"start": 1525.63, "end": 1526.97, "word": " يعني", "probability": 0.57861328125}, {"start": 1526.97, "end": 1527.69, "word": " كل", "probability": 0.9765625}, {"start": 1527.69, "end": 1528.87, "word": " الاحتمالات", "probability": 0.94814453125}, {"start": 1528.87, "end": 1529.59, "word": " الممكنة", "probability": 0.9607747395833334}, {"start": 1529.59, "end": 1529.93, "word": " هو", "probability": 0.8203125}, {"start": 1529.93, "end": 1530.89, "word": " divisor", "probability": 0.82958984375}, {"start": 1530.89, "end": 1531.57, "word": " الست", "probability": 0.5546875}, {"start": 1531.57, "end": 1532.75, "word": " يبقى", "probability": 0.95556640625}, {"start": 1532.75, "end": 1533.39, "word": " بصير", "probability": 0.96044921875}, {"start": 1533.39, "end": 1534.01, "word": " ال", "probability": 0.79345703125}, {"start": 1534.01, "end": 1534.67, "word": " identity", "probability": 0.78857421875}, {"start": 1534.67, "end": 1534.93, "word": " هو", "probability": 0.36669921875}, {"start": 1534.93, "end": 1535.31, "word": " واحد", "probability": 0.953125}], "temperature": 1.0}, {"id": 64, "seek": 155746, "start": 1535.76, "end": 1557.46, "text": "والـ A تربيع اللي هو اتنين والـ A تكيب اللي هو تلاتة والـ A والستة يبقى الواحد والاتنين والتلاتة والستة هما ال possible orders فقط لا غير يبقى باجي بقوله هنا the possible orders are", "tokens": [2407, 6027, 39184, 316, 6055, 2288, 21292, 3615, 13672, 1829, 31439, 1975, 2655, 1863, 9957, 16070, 39184, 316, 6055, 4117, 1829, 3555, 13672, 1829, 31439, 6055, 1211, 9307, 3660, 16070, 39184, 316, 16070, 14851, 3660, 7251, 3555, 4587, 7578, 2423, 14407, 24401, 16070, 9307, 1863, 9957, 16070, 2655, 1211, 9307, 3660, 16070, 14851, 3660, 8032, 15042, 2423, 1944, 9470, 6156, 47432, 20193, 32771, 13546, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 264, 1944, 9470, 366], "avg_logprob": -0.21210937909781932, "compression_ratio": 1.8535031847133758, "no_speech_prob": 0.0, "words": [{"start": 1535.76, "end": 1536.22, "word": "والـ", "probability": 0.4182942708333333}, {"start": 1536.22, "end": 1536.42, "word": " A", "probability": 0.340087890625}, {"start": 1536.42, "end": 1537.12, "word": " تربيع", "probability": 0.850830078125}, {"start": 1537.12, "end": 1537.56, "word": " اللي", "probability": 0.839111328125}, {"start": 1537.56, "end": 1537.72, "word": " هو", "probability": 0.9638671875}, {"start": 1537.72, "end": 1538.24, "word": " اتنين", "probability": 0.8831787109375}, {"start": 1538.24, "end": 1538.68, "word": " والـ", "probability": 0.62353515625}, {"start": 1538.68, "end": 1538.9, "word": " A", "probability": 0.83984375}, {"start": 1538.9, "end": 1539.36, "word": " تكيب", "probability": 0.65869140625}, {"start": 1539.36, "end": 1539.48, "word": " اللي", "probability": 0.9599609375}, {"start": 1539.48, "end": 1539.58, "word": " هو", "probability": 0.97265625}, {"start": 1539.58, "end": 1540.08, "word": " تلاتة", "probability": 0.90966796875}, {"start": 1540.08, "end": 1540.3, "word": " والـ", "probability": 0.6632080078125}, {"start": 1540.3, "end": 1540.54, "word": " A", "probability": 0.888671875}, {"start": 1540.54, "end": 1541.46, "word": " والستة", "probability": 0.623291015625}, {"start": 1541.46, "end": 1541.94, "word": " يبقى", "probability": 0.9520263671875}, {"start": 1541.94, "end": 1542.44, "word": " الواحد", "probability": 0.9646809895833334}, {"start": 1542.44, "end": 1543.04, "word": " والاتنين", "probability": 0.8167724609375}, {"start": 1543.04, "end": 1543.72, "word": " والتلاتة", "probability": 0.95380859375}, {"start": 1543.72, "end": 1544.46, "word": " والستة", "probability": 0.9739583333333334}, {"start": 1544.46, "end": 1544.96, "word": " هما", "probability": 0.73193359375}, {"start": 1544.96, "end": 1545.16, "word": " ال", "probability": 0.87939453125}, {"start": 1545.16, "end": 1545.52, "word": " possible", "probability": 0.96142578125}, {"start": 1545.52, "end": 1546.3, "word": " orders", "probability": 0.79150390625}, {"start": 1546.3, "end": 1546.98, "word": " فقط", "probability": 0.98583984375}, {"start": 1546.98, "end": 1547.3, "word": " لا", "probability": 0.64111328125}, {"start": 1547.3, "end": 1547.68, "word": " غير", "probability": 0.9873046875}, {"start": 1547.68, "end": 1548.66, "word": " يبقى", "probability": 0.9366455078125}, {"start": 1548.66, "end": 1549.08, "word": " باجي", "probability": 0.86572265625}, {"start": 1549.08, "end": 1549.78, "word": " بقوله", "probability": 0.9384765625}, {"start": 1549.78, "end": 1550.38, "word": " هنا", "probability": 0.98388671875}, {"start": 1550.38, "end": 1551.24, "word": " the", "probability": 0.767578125}, {"start": 1551.24, "end": 1552.9, "word": " possible", "probability": 0.96923828125}, {"start": 1552.9, "end": 1555.62, "word": " orders", "probability": 0.8857421875}, {"start": 1555.62, "end": 1557.46, "word": " are", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 65, "seek": 157514, "start": 1558.02, "end": 1575.14, "text": "واحد و اتنين و تلاتة و ستة only فقط مافيش غيرهم يعني لا بقدر أقول أربعة ولا بقدر أقول خمسة ولا غيره كل هذه الأرقام بستطيعش أقولها أبدا", "tokens": [14407, 24401, 4032, 1975, 2655, 1863, 9957, 4032, 6055, 1211, 9307, 3660, 4032, 8608, 2655, 3660, 787, 6156, 47432, 19446, 41185, 8592, 32771, 13546, 16095, 37495, 22653, 20193, 4724, 28543, 2288, 5551, 39648, 5551, 25513, 27884, 49429, 4724, 28543, 2288, 5551, 39648, 16490, 2304, 3794, 3660, 49429, 32771, 13546, 3224, 28242, 29538, 16247, 2288, 4587, 10943, 4724, 14851, 9566, 40228, 8592, 5551, 39648, 11296, 5551, 3555, 28259], "avg_logprob": -0.15590532649965846, "compression_ratio": 1.6573426573426573, "no_speech_prob": 1.5676021575927734e-05, "words": [{"start": 1558.02, "end": 1558.7, "word": "واحد", "probability": 0.5709228515625}, {"start": 1558.7, "end": 1558.92, "word": " و", "probability": 0.8505859375}, {"start": 1558.92, "end": 1559.36, "word": " اتنين", "probability": 0.78704833984375}, {"start": 1559.36, "end": 1559.6, "word": " و", "probability": 0.763671875}, {"start": 1559.6, "end": 1560.3, "word": " تلاتة", "probability": 0.9320068359375}, {"start": 1560.3, "end": 1560.44, "word": " و", "probability": 0.95751953125}, {"start": 1560.44, "end": 1561.32, "word": " ستة", "probability": 0.8981119791666666}, {"start": 1561.32, "end": 1562.26, "word": " only", "probability": 0.3896484375}, {"start": 1562.26, "end": 1563.54, "word": " فقط", "probability": 0.927490234375}, {"start": 1563.54, "end": 1564.02, "word": " مافيش", "probability": 0.853515625}, {"start": 1564.02, "end": 1564.52, "word": " غيرهم", "probability": 0.947265625}, {"start": 1564.52, "end": 1565.34, "word": " يعني", "probability": 0.922119140625}, {"start": 1565.34, "end": 1565.5, "word": " لا", "probability": 0.62109375}, {"start": 1565.5, "end": 1565.88, "word": " بقدر", "probability": 0.9890950520833334}, {"start": 1565.88, "end": 1566.16, "word": " أقول", "probability": 0.7308349609375}, {"start": 1566.16, "end": 1566.82, "word": " أربعة", "probability": 0.8800455729166666}, {"start": 1566.82, "end": 1567.68, "word": " ولا", "probability": 0.89013671875}, {"start": 1567.68, "end": 1568.3, "word": " بقدر", "probability": 0.9861653645833334}, {"start": 1568.3, "end": 1568.66, "word": " أقول", "probability": 0.958740234375}, {"start": 1568.66, "end": 1569.54, "word": " خمسة", "probability": 0.9857177734375}, {"start": 1569.54, "end": 1570.18, "word": " ولا", "probability": 0.9365234375}, {"start": 1570.18, "end": 1570.7, "word": " غيره", "probability": 0.8837890625}, {"start": 1570.7, "end": 1570.98, "word": " كل", "probability": 0.85888671875}, {"start": 1570.98, "end": 1571.36, "word": " هذه", "probability": 0.93310546875}, {"start": 1571.36, "end": 1572.12, "word": " الأرقام", "probability": 0.9921875}, {"start": 1572.12, "end": 1573.76, "word": " بستطيعش", "probability": 0.91162109375}, {"start": 1573.76, "end": 1574.46, "word": " أقولها", "probability": 0.9775390625}, {"start": 1574.46, "end": 1575.14, "word": " أبدا", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 66, "seek": 161317, "start": 1595.11, "end": 1613.17, "text": "طيب ننتقل لسؤال تمانية سؤال تمانية بيقول ال X موجود في group G و X تربيع لا يساوي", "tokens": [9566, 1829, 3555, 8717, 29399, 4587, 1211, 5296, 3794, 33604, 6027, 46811, 7649, 10632, 8608, 33604, 6027, 46811, 7649, 10632, 4724, 1829, 39648, 2423, 1783, 3714, 29245, 23328, 8978, 1594, 460, 4032, 1783, 6055, 2288, 21292, 3615, 20193, 7251, 3794, 995, 45865], "avg_logprob": -0.2732558194981065, "compression_ratio": 1.3300970873786409, "no_speech_prob": 0.0, "words": [{"start": 1595.11, "end": 1595.47, "word": "طيب", "probability": 0.6549886067708334}, {"start": 1595.47, "end": 1596.13, "word": " ننتقل", "probability": 0.9283447265625}, {"start": 1596.13, "end": 1597.25, "word": " لسؤال", "probability": 0.80596923828125}, {"start": 1597.25, "end": 1598.03, "word": " تمانية", "probability": 0.78564453125}, {"start": 1598.03, "end": 1599.01, "word": " سؤال", "probability": 0.8318684895833334}, {"start": 1599.01, "end": 1599.59, "word": " تمانية", "probability": 0.97265625}, {"start": 1599.59, "end": 1600.17, "word": " بيقول", "probability": 0.9054361979166666}, {"start": 1600.17, "end": 1601.01, "word": " ال", "probability": 0.78271484375}, {"start": 1601.01, "end": 1601.43, "word": " X", "probability": 0.7109375}, {"start": 1601.43, "end": 1602.29, "word": " موجود", "probability": 0.9777018229166666}, {"start": 1602.29, "end": 1603.21, "word": " في", "probability": 0.86962890625}, {"start": 1603.21, "end": 1603.73, "word": " group", "probability": 0.8232421875}, {"start": 1603.73, "end": 1604.37, "word": " G", "probability": 0.9033203125}, {"start": 1604.37, "end": 1605.13, "word": " و", "probability": 0.446044921875}, {"start": 1605.13, "end": 1605.65, "word": " X", "probability": 0.64453125}, {"start": 1605.65, "end": 1606.59, "word": " تربيع", "probability": 0.84814453125}, {"start": 1606.59, "end": 1612.07, "word": " لا", "probability": 0.74462890625}, {"start": 1612.07, "end": 1613.17, "word": " يساوي", "probability": 0.8995361328125}], "temperature": 1.0}, {"id": 67, "seek": 162159, "start": 1617.15, "end": 1621.59, "text": "و X6 يساوي E", "tokens": [2407, 1783, 21, 7251, 3794, 995, 45865, 462], "avg_logprob": -0.6953125, "compression_ratio": 0.6666666666666666, "no_speech_prob": 0.0, "words": [{"start": 1617.15, "end": 1618.05, "word": "و", "probability": 0.65771484375}, {"start": 1618.05, "end": 1619.89, "word": " X6", "probability": 0.248931884765625}, {"start": 1619.89, "end": 1620.91, "word": " يساوي", "probability": 0.738433837890625}, {"start": 1620.91, "end": 1621.59, "word": " E", "probability": 0.50390625}], "temperature": 1.0}, {"id": 68, "seek": 165589, "start": 1630.65, "end": 1655.89, "text": "هذا بده يعطينا ان ال X أس أربعة لا يمكن أن تساوي ال E and ال X أس خمسة لا يمكن أن تساوي ال identity element what can you say about the order of X بدي كمان ال order ل X يساوي جداش عندنا", "tokens": [3224, 15730, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 1783, 5551, 3794, 5551, 25513, 27884, 20193, 7251, 43020, 14739, 6055, 3794, 995, 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[{"start": 1874.1299999999999, "end": 1875.53, "word": "يبقى", "probability": 0.635467529296875}, {"start": 1875.53, "end": 1875.95, "word": " الهدف", "probability": 0.7093048095703125}, {"start": 1875.95, "end": 1876.23, "word": " اللي", "probability": 0.603759765625}, {"start": 1876.23, "end": 1876.93, "word": " اتالج", "probability": 0.616546630859375}, {"start": 1876.93, "end": 1878.23, "word": " exercise", "probability": 0.1593017578125}], "temperature": 1.0}, {"id": 78, "seek": 190104, "start": 1880.5, "end": 1901.04, "text": "بعدها جالي هتل ال order لل X بقوله والله كويس الآن ال X تربيه لا يسوى ال identity وال X أص أربعة لا يسوى ال identity وال X أص خمسة لا يسوى ال identity وال X أص ستة لا يسوى ال identity إذا ما هي الاحتمالات الممكنة لل order", "tokens": [3555, 22488, 11296, 10874, 6027, 1829, 8032, 2655, 1211, 2423, 1668, 24976, 1783, 4724, 39648, 3224, 16070, 43761, 9122, 45865, 3794, 6024, 48506, 2423, 1783, 6055, 2288, 21292, 3224, 20193, 7251, 3794, 2407, 7578, 2423, 6575, 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subgroup generated by K والك موجود في U عشرين السبب because any element in", "tokens": [1211, 2407, 25961, 2423, 1668, 46740, 46811, 7649, 10632, 6156, 3224, 2407, 7251, 7435, 1829, 3555, 32239, 28242, 18871, 33546, 2288, 2423, 1594, 13672, 1829, 43242, 8315, 34105, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 46740, 29538, 2423, 624, 6225, 46309, 9957, 20193, 7251, 43020, 14739, 6055, 3794, 995, 45865, 2423, 1422, 17377, 10833, 538, 591, 16070, 4117, 3714, 29245, 23328, 8978, 624, 6225, 46309, 9957, 21136, 3555, 3555, 570, 604, 4478, 294], "avg_logprob": -0.30653781600688634, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2038.51, "end": 2039.03, "word": "لو", "probability": 0.3746337890625}, {"start": 2039.03, "end": 2039.43, "word": " كان", "probability": 0.96533203125}, {"start": 2039.43, "end": 2039.61, "word": " ال", "probability": 0.55224609375}, {"start": 2039.61, "end": 2039.93, "word": " order", "probability": 0.56787109375}, {"start": 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"temperature": 1.0}, {"id": 87, "seek": 214038, "start": 2112.14, "end": 2140.38, "text": "مشان يجيب الجروب كلها و تبقى Cyclic ال orders اللى بدك ترفع هنا بدي يكون تمانية بدي يساوي ال order لل group مشان يجيب كل عناصر ال group غير هيك بعتلك الله يعني زى ما شوفنا توسعة كل واحد بيجيب ليها عنصر يعنصرين يعني أربع عناصر بس لا يوجد element من ال Z20 بيجيب ليه كل عناصر ال Z20 وبالتالي هذه لا يمكن أن تكون Cyclic", "tokens": [2304, 8592, 7649, 7251, 7435, 1829, 3555, 25724, 32887, 3555, 28242, 11296, 4032, 6055, 3555, 4587, 7578, 10295, 66, 1050, 2423, 9470, 13672, 7578, 47525, 4117, 6055, 28480, 3615, 34105, 4724, 16254, 7251, 30544, 46811, 7649, 10632, 4724, 16254, 7251, 3794, 995, 45865, 2423, 1668, 24976, 1594, 37893, 7649, 7251, 7435, 1829, 3555, 28242, 18871, 33546, 2288, 2423, 1594, 32771, 13546, 39896, 4117, 4724, 34268, 23275, 21984, 37495, 22653, 30767, 7578, 19446, 13412, 38688, 8315, 33427, 3794, 27884, 28242, 36764, 24401, 4724, 1829, 7435, 1829, 3555, 32239, 11296, 18871, 9381, 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{"start": 2373.95, "end": 2374.37, "word": " زيادة", "probability": 0.9461669921875}, {"start": 2374.37, "end": 2374.53, "word": " على", "probability": 0.70751953125}, {"start": 2374.53, "end": 2374.95, "word": " ذلك", "probability": 0.973876953125}, {"start": 2374.95, "end": 2375.19, "word": " لإن", "probability": 0.724609375}, {"start": 2375.19, "end": 2375.31, "word": " ال", "probability": 0.95068359375}, {"start": 2375.31, "end": 2375.67, "word": " identity", "probability": 0.5595703125}, {"start": 2375.67, "end": 2376.07, "word": " هنا", "probability": 0.68359375}, {"start": 2376.07, "end": 2376.31, "word": " هو", "probability": 0.90380859375}, {"start": 2376.31, "end": 2376.43, "word": " ال", "probability": 0.71142578125}, {"start": 2376.43, "end": 2376.67, "word": " zero", "probability": 0.41455078125}, {"start": 2376.67, "end": 2378.11, "word": " والواحد", "probability": 0.80810546875}, {"start": 2378.11, "end": 2378.69, "word": " برضه", "probability": 0.95751953125}, {"start": 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{"start": 2446.55, "end": 2447.85, "word": " من؟", "probability": 0.70068359375}, {"start": 2447.85, "end": 2448.15, "word": " هي", "probability": 0.88037109375}, {"start": 2448.15, "end": 2448.59, "word": " كل", "probability": 0.98193359375}, {"start": 2448.59, "end": 2449.63, "word": " العناصر", "probability": 0.9495849609375}, {"start": 2449.63, "end": 2450.29, "word": " X", "probability": 0.97314453125}, {"start": 2450.29, "end": 2451.27, "word": " اللي", "probability": 0.8916015625}, {"start": 2451.27, "end": 2452.09, "word": " موجودة", "probability": 0.9893798828125}, {"start": 2452.09, "end": 2452.33, "word": " في", "probability": 0.96044921875}, {"start": 2452.33, "end": 2452.57, "word": " ال", "probability": 0.95751953125}, {"start": 2452.57, "end": 2453.27, "word": " UN", "probability": 0.69189453125}], "temperature": 1.0}, {"id": 100, "seek": 248336, "start": 2453.78, "end": 2483.36, "text": "بحيث ان الـ x modulo k بده يساوي الواحدة الصحية بقول for example بيعطيني u تلاتة تساوي كذا و u سبعة تساوي كذا list the elements of u أربعة عشرين", "tokens": [3555, 5016, 1829, 12984, 16472, 2423, 39184, 2031, 1072, 13455, 350, 47525, 3224, 7251, 3794, 995, 45865, 2423, 14407, 24401, 3660, 31767, 5016, 10632, 4724, 39648, 337, 1365, 4724, 1829, 3615, 9566, 9957, 1829, 344, 6055, 1211, 9307, 3660, 6055, 3794, 995, 45865, 9122, 15730, 4032, 344, 8608, 3555, 27884, 6055, 3794, 995, 45865, 9122, 15730, 1329, 264, 4959, 295, 344, 5551, 25513, 27884, 6225, 46309, 9957], "avg_logprob": -0.2656249912346111, "compression_ratio": 1.4166666666666667, "no_speech_prob": 0.0, "words": [{"start": 2453.78, "end": 2454.66, "word": "بحيث", "probability": 0.8404541015625}, {"start": 2454.66, "end": 2457.92, "word": " ان", "probability": 0.748046875}, {"start": 2457.92, "end": 2458.74, "word": " الـ", "probability": 0.344940185546875}, {"start": 2458.74, "end": 2459.12, "word": " x", "probability": 0.58251953125}, {"start": 2459.12, "end": 2460.44, "word": " modulo", "probability": 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0.709716796875}, {"start": 3042.44, "end": 3042.9, "word": " k", "probability": 0.75830078125}, {"start": 3042.9, "end": 3043.2, "word": " بدى", "probability": 0.3948974609375}, {"start": 3043.2, "end": 3043.42, "word": " يسوي", "probability": 0.8486328125}, {"start": 3043.42, "end": 3043.98, "word": " جداش", "probability": 0.5718587239583334}], "temperature": 1.0}, {"id": 122, "seek": 305912, "start": 3044.28, "end": 3059.12, "text": "إذا هذا معناه ان ال X Y موديولو K بدل سوى الواحد هذا معناه ان ال X Y موجود في ال U KN", "tokens": [28814, 15730, 23758, 20449, 8315, 3224, 16472, 2423, 1783, 398, 3714, 2407, 16254, 12610, 2407, 591, 47525, 1211, 8608, 2407, 7578, 2423, 14407, 24401, 23758, 20449, 8315, 3224, 16472, 2423, 1783, 398, 3714, 29245, 23328, 8978, 2423, 624, 26967], "avg_logprob": -0.40156250149011613, "compression_ratio": 1.5384615384615385, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3044.28, "end": 3045.56, "word": "إذا", "probability": 0.539794921875}, {"start": 3045.56, "end": 3046.1, "word": " هذا", "probability": 0.66162109375}, {"start": 3046.1, "end": 3047.02, "word": " معناه", "probability": 0.9267578125}, {"start": 3047.02, "end": 3047.86, "word": " ان", "probability": 0.499755859375}, {"start": 3047.86, "end": 3048.12, "word": " ال", "probability": 0.89892578125}, {"start": 3048.12, "end": 3048.58, "word": " X", "probability": 0.166015625}, {"start": 3048.58, "end": 3049.36, "word": " Y", "probability": 0.6396484375}, {"start": 3049.36, "end": 3050.86, "word": " موديولو", "probability": 0.73330078125}, {"start": 3050.86, "end": 3051.24, "word": " K", "probability": 0.365234375}, {"start": 3051.24, "end": 3051.94, "word": " بدل", "probability": 0.3582763671875}, {"start": 3051.94, "end": 3052.36, "word": " سوى", "probability": 0.7032877604166666}, {"start": 3052.36, "end": 3052.88, "word": " الواحد", "probability": 0.7101236979166666}, {"start": 3052.88, "end": 3053.6, "word": " هذا", "probability": 0.73388671875}, {"start": 3053.6, "end": 3054.38, "word": " معناه", "probability": 0.96923828125}, {"start": 3054.38, "end": 3055.02, "word": " ان", "probability": 0.69970703125}, {"start": 3055.02, "end": 3055.28, "word": " ال", "probability": 0.82470703125}, {"start": 3055.28, "end": 3055.72, "word": " X", "probability": 0.56884765625}, {"start": 3055.72, "end": 3056.28, "word": " Y", "probability": 0.91064453125}, {"start": 3056.28, "end": 3057.08, "word": " موجود", "probability": 0.9812825520833334}, {"start": 3057.08, "end": 3057.34, "word": " في", "probability": 0.951171875}, {"start": 3057.34, "end": 3057.58, "word": " ال", "probability": 0.96044921875}, {"start": 3057.58, "end": 3058.04, "word": " U", "probability": 0.58544921875}, {"start": 3058.04, "end": 3059.12, "word": " KN", "probability": 0.354736328125}], "temperature": 1.0}, {"id": 123, "seek": 308615, "start": 3062.49, "end": 3086.15, "text": "طب احنا الأصل نثبت الأول في معكوسي الثاني موجود لكن هذا إذا بدنا النظرية الأولى لكن أخدنا نظرية تانية السؤال هو هل ال UK infinite ولا ما هوش finite finite لإن ال UN أصلا finite انت الحد ال N ناقص واحد بتوقف تبقى باجي بقوله", "tokens": [9566, 3555, 1975, 5016, 8315, 16247, 36520, 8717, 12984, 3555, 2655, 16247, 12610, 8978, 20449, 4117, 41779, 1829, 6024, 104, 7649, 1829, 3714, 29245, 23328, 44381, 23758, 11933, 15730, 47525, 8315, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 44381, 5551, 9778, 3215, 8315, 8717, 19913, 2288, 10632, 6055, 7649, 10632, 21136, 33604, 6027, 31439, 8032, 1211, 2423, 7051, 13785, 49429, 19446, 31439, 8592, 19362, 19362, 5296, 28814, 1863, 2423, 8229, 5551, 9381, 15040, 19362, 16472, 2655, 21542, 3215, 2423, 426, 8717, 995, 4587, 9381, 36764, 24401, 39894, 30543, 5172, 6055, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224], "avg_logprob": -0.1715624986588955, "compression_ratio": 1.7912621359223302, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 3062.49, "end": 3062.81, "word": "طب", "probability": 0.62158203125}, {"start": 3062.81, 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{"start": 3069.33, "end": 3069.93, "word": " النظرية", "probability": 0.8812255859375}, {"start": 3069.93, "end": 3070.39, "word": " الأولى", "probability": 0.9778645833333334}, {"start": 3070.39, "end": 3070.57, "word": " لكن", "probability": 0.74365234375}, {"start": 3070.57, "end": 3071.03, "word": " أخدنا", "probability": 0.943359375}, {"start": 3071.03, "end": 3071.69, "word": " نظرية", "probability": 0.9898681640625}, {"start": 3071.69, "end": 3072.29, "word": " تانية", "probability": 0.9851888020833334}, {"start": 3072.29, "end": 3073.13, "word": " السؤال", "probability": 0.9793294270833334}, {"start": 3073.13, "end": 3073.45, "word": " هو", "probability": 0.97021484375}, {"start": 3073.45, "end": 3074.27, "word": " هل", "probability": 0.9541015625}, {"start": 3074.27, "end": 3074.47, "word": " ال", "probability": 0.9892578125}, {"start": 3074.47, "end": 3075.15, "word": " UK", "probability": 0.56640625}, {"start": 3075.15, "end": 3076.65, "word": " infinite", "probability": 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{"start": 3082.65, "end": 3082.87, "word": " ال", "probability": 0.93115234375}, {"start": 3082.87, "end": 3083.15, "word": " N", "probability": 0.6494140625}, {"start": 3083.15, "end": 3083.49, "word": " ناقص", "probability": 0.857177734375}, {"start": 3083.49, "end": 3083.75, "word": " واحد", "probability": 0.971923828125}, {"start": 3083.75, "end": 3084.33, "word": " بتوقف", "probability": 0.8048502604166666}, {"start": 3084.33, "end": 3085.01, "word": " تبقى", "probability": 0.77813720703125}, {"start": 3085.01, "end": 3085.43, "word": " باجي", "probability": 0.869140625}, {"start": 3085.43, "end": 3086.15, "word": " بقوله", "probability": 0.9534505208333334}], "temperature": 1.0}, {"id": 124, "seek": 310141, "start": 3086.55, "end": 3101.41, "text": "الان ال U K N is finite السبب finite because ال U N is finite", "tokens": [6027, 7649, 2423, 624, 591, 426, 307, 19362, 21136, 3555, 3555, 19362, 570, 2423, 624, 426, 307, 19362], "avg_logprob": -0.2724095520220305, "compression_ratio": 1.2758620689655173, "no_speech_prob": 0.0, "words": [{"start": 3086.55, "end": 3087.41, "word": "الان", "probability": 0.7025146484375}, {"start": 3087.41, "end": 3087.95, "word": " ال", "probability": 0.98828125}, {"start": 3087.95, "end": 3088.35, "word": " U", "probability": 0.285400390625}, {"start": 3088.35, "end": 3088.89, "word": " K", "probability": 0.1925048828125}, {"start": 3088.89, "end": 3089.79, "word": " N", "probability": 0.96142578125}, {"start": 3089.79, "end": 3090.55, "word": " is", "probability": 0.61962890625}, {"start": 3090.55, "end": 3092.17, "word": " finite", "probability": 0.98388671875}, {"start": 3092.17, "end": 3093.89, "word": " السبب", "probability": 0.9617513020833334}, {"start": 3093.89, "end": 3095.13, "word": " finite", "probability": 0.88623046875}, {"start": 3095.13, "end": 3096.79, "word": " because", "probability": 0.74365234375}, {"start": 3096.79, "end": 3099.41, "word": " ال", "probability": 0.98193359375}, {"start": 3099.41, "end": 3099.67, "word": " U", "probability": 0.84375}, {"start": 3099.67, "end": 3100.27, "word": " N", "probability": 0.98388671875}, {"start": 3100.27, "end": 3100.77, "word": " is", "probability": 0.94384765625}, {"start": 3100.77, "end": 3101.41, "word": " finite", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 125, "seek": 313331, "start": 3104.37, "end": 3133.31, "text": "طيب هى الست اللى أخدناها non-empty واحد اتنين أخدته elements اللى جت حاصل ضرب الأول موجود فيها تلاتة ال subset هذه مالها finite خلصنا مش في نظرية بتقول هيك لأ non-empty finite subset و بكتابت البيت لو أخدت عنصرين موجودات فيها أثبتنا يبقى خلصنا يبقى بناء عليه ال UK is a subgroup يبقى بروح بقوله bye", "tokens": [9566, 1829, 3555, 8032, 7578, 21136, 2655, 13672, 7578, 5551, 9778, 3215, 8315, 11296, 2107, 12, 4543, 88, 36764, 24401, 1975, 2655, 1863, 9957, 5551, 9778, 3215, 2655, 3224, 4959, 13672, 7578, 10874, 2655, 11331, 33546, 1211, 48812, 25513, 16247, 12610, 3714, 29245, 23328, 8978, 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هذا", "probability": 0.79248046875}, {"start": 3234.06, "end": 3234.7, "word": " موجود", "probability": 0.98828125}, {"start": 3234.7, "end": 3235.48, "word": " فيكش؟", "probability": 0.71990966796875}], "temperature": 1.0}, {"id": 131, "seek": 325906, "start": 3236.3, "end": 3259.06, "text": "مش موجود في هاتش يبقى أخدت element في h ضربته نفسي طوله يعني ال h is not closed under the operation يبقى هل هذه subgroup يبقى هذا بده يعطيلك ان ال h is not a subgroup من ال u عشرة من ال u عشرة because", "tokens": [2304, 8592, 3714, 29245, 23328, 8978, 8032, 9307, 8592, 7251, 3555, 4587, 7578, 5551, 9778, 3215, 2655, 4478, 8978, 276, 48812, 25513, 47395, 8717, 36178, 1829, 23032, 12610, 3224, 37495, 22653, 2423, 276, 307, 406, 5395, 833, 264, 6916, 7251, 3555, 4587, 7578, 8032, 1211, 29538, 1422, 17377, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 23275, 16472, 2423, 276, 307, 406, 257, 1422, 17377, 9154, 2423, 344, 6225, 8592, 25720, 9154, 2423, 344, 6225, 8592, 25720, 570], "avg_logprob": -0.24035493532816568, "compression_ratio": 1.5856353591160222, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3236.3, "end": 3236.66, "word": "مش", "probability": 0.53070068359375}, {"start": 3236.66, "end": 3237.22, "word": " موجود", "probability": 0.9874674479166666}, {"start": 3237.22, "end": 3237.4, "word": " في", "probability": 0.89404296875}, {"start": 3237.4, "end": 3237.66, "word": " هاتش", "probability": 0.558349609375}, {"start": 3237.66, "end": 3237.96, "word": " يبقى", "probability": 0.907958984375}, {"start": 3237.96, "end": 3238.68, "word": " أخدت", "probability": 0.54119873046875}, {"start": 3238.68, "end": 3239.34, "word": " element", "probability": 0.93212890625}, {"start": 3239.34, "end": 3240.02, "word": " في", "probability": 0.8603515625}, {"start": 3240.02, "end": 3240.28, "word": " h", "probability": 0.33984375}, {"start": 3240.28, "end": 3240.88, "word": " ضربته", "probability": 0.9563802083333334}, {"start": 3240.88, "end": 3241.3, "word": " نفسي", "probability": 0.9309895833333334}, {"start": 3241.3, "end": 3241.58, "word": " طوله", "probability": 0.6061197916666666}, {"start": 3241.58, "end": 3241.94, "word": " يعني", "probability": 0.873779296875}, {"start": 3241.94, "end": 3242.1, "word": " ال", "probability": 0.96826171875}, {"start": 3242.1, "end": 3242.32, "word": " h", "probability": 0.437255859375}, {"start": 3242.32, "end": 3242.66, "word": " is", "probability": 0.8828125}, {"start": 3242.66, "end": 3243.12, "word": " not", "probability": 0.96044921875}, {"start": 3243.12, "end": 3243.78, "word": " closed", "probability": 0.6044921875}, {"start": 3243.78, "end": 3244.22, "word": " under", "probability": 0.89453125}, {"start": 3244.22, "end": 3244.46, "word": " the", "probability": 0.89892578125}, {"start": 3244.46, "end": 3245.14, "word": " operation", "probability": 0.96630859375}, {"start": 3245.14, "end": 3245.78, "word": " يبقى", "probability": 0.974853515625}, {"start": 3245.78, "end": 3245.96, "word": " هل", "probability": 0.936279296875}, {"start": 3245.96, "end": 3246.2, "word": " هذه", "probability": 0.479248046875}, {"start": 3246.2, "end": 3246.94, "word": " subgroup", "probability": 0.7705078125}, {"start": 3246.94, "end": 3248.6, "word": " يبقى", "probability": 0.9222412109375}, {"start": 3248.6, "end": 3248.98, "word": " هذا", "probability": 0.6708984375}, {"start": 3248.98, "end": 3249.46, "word": " بده", "probability": 0.4659423828125}, {"start": 3249.46, "end": 3250.34, "word": " يعطيلك", "probability": 0.9144287109375}, {"start": 3250.34, "end": 3250.98, "word": " ان", "probability": 0.6953125}, {"start": 3250.98, "end": 3251.28, "word": " ال", "probability": 0.94140625}, {"start": 3251.28, "end": 3251.74, "word": " h", "probability": 0.67333984375}, {"start": 3251.74, "end": 3252.42, "word": " is", "probability": 0.9560546875}, {"start": 3252.42, "end": 3253.02, "word": " not", "probability": 0.96484375}, {"start": 3253.02, "end": 3253.48, "word": " a", "probability": 0.9365234375}, {"start": 3253.48, "end": 3254.62, "word": " subgroup", "probability": 0.96630859375}, {"start": 3254.62, "end": 3255.5, "word": " من", "probability": 0.99267578125}, {"start": 3255.5, "end": 3255.84, "word": " ال", "probability": 0.9208984375}, {"start": 3255.84, "end": 3256.1, "word": " u", "probability": 0.42529296875}, {"start": 3256.1, "end": 3257.04, "word": " عشرة", "probability": 0.9187825520833334}, {"start": 3257.04, "end": 3257.62, "word": " من", "probability": 0.85693359375}, {"start": 3257.62, "end": 3257.84, "word": " ال", "probability": 0.98876953125}, {"start": 3257.84, "end": 3258.0, "word": " u", "probability": 0.9375}, {"start": 3258.0, "end": 3258.56, "word": " عشرة", "probability": 0.9803059895833334}, {"start": 3258.56, "end": 3259.06, "word": " because", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 132, "seek": 328205, "start": 3261.67, "end": 3282.05, "text": "إن الـ H is not closed under the operation on ال U عشرة", "tokens": [28814, 1863, 2423, 39184, 389, 307, 406, 5395, 833, 264, 6916, 322, 2423, 624, 6225, 8592, 25720], "avg_logprob": -0.3611111177338494, "compression_ratio": 0.9166666666666666, "no_speech_prob": 0.0, "words": [{"start": 3261.67, "end": 3262.05, "word": "إن", "probability": 0.6016845703125}, {"start": 3262.05, "end": 3262.39, "word": " الـ", "probability": 0.6749267578125}, {"start": 3262.39, "end": 3262.79, "word": " H", "probability": 0.7705078125}, {"start": 3262.79, "end": 3263.73, "word": " is", "probability": 0.7509765625}, {"start": 3263.73, "end": 3265.21, "word": " not", "probability": 0.95068359375}, {"start": 3265.21, "end": 3267.49, "word": " closed", "probability": 0.5390625}, {"start": 3267.49, "end": 3269.59, "word": " under", "probability": 0.86376953125}, {"start": 3269.59, "end": 3273.69, "word": " the", "probability": 0.5908203125}, {"start": 3273.69, "end": 3275.99, "word": " operation", "probability": 0.9794921875}, {"start": 3275.99, "end": 3280.21, "word": " on", "probability": 0.78173828125}, {"start": 3280.21, "end": 3281.29, "word": " ال", "probability": 0.68115234375}, {"start": 3281.29, "end": 3281.49, "word": " U", "probability": 0.673828125}, {"start": 3281.49, "end": 3282.05, "word": " عشرة", "probability": 0.7483723958333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3286.0415, "duration_after_vad": 3129.0799999999876}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b34afff55a3205d77ceb9b92d904633115a99aa8
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos.srt
@@ -0,0 +1,2111 @@
+1
+00:00:20,990 --> 00:00:25,090
+بسم الله الرحمن الرحيم الآن نبدأ في الموضوع اللي 
+
+2
+00:00:25,090 --> 00:00:30,190
+أشرنا إليه الصبح وهو الـ chapter المقدمة اللي بتحدث عن
+
+3
+00:00:30,190 --> 00:00:35,210
+تذكير ببعض ما درس في مبادئ الرياضيات واللي هنأسس 
+
+4
+00:00:35,210 --> 00:00:40,850
+عليه دراستنا في علم algebra قبل أن نبدأ بأي نقطة
+
+5
+00:00:40,850 --> 00:00:45,230
+في هذا الـ chapter بحب نذكر بمجموعة الـ sets اللي
+
+6
+00:00:45,230 --> 00:00:49,350
+عليها بدنا نبني دراستنا إن شاء الله تبارك وتعالى
+
+7
+00:00:49,860 --> 00:00:55,140
+أول set من هذه الـ sets يبقى مضاجي أقول اللي هو الـ
+
+8
+00:00:55,140 --> 00:01:00,760
+sets المجموعات أول set من هذه الـ sets اللي هو the 
+
+9
+00:01:00,760 --> 00:01:04,560
+set of
+
+10
+00:01:04,560 --> 00:01:14,560
+natural numbers هذا هديها الرمز capital N
+
+11
+00:01:23,950 --> 00:01:33,190
+النقطة الثانية هي the set of integers مجموعة
+
+12
+00:01:33,190 --> 00:01:41,910
+الأعداد الصحيحة اللي هديها الرمز Z عناصرها هي: -3, -2, -1, 0, 1, 2,
+
+13
+00:01:41,910 --> 00:01:49,370
+3 إلى آخره يبقى مجموعة الأعداد الصحيحة الموجبة
+
+14
+00:01:49,370 --> 00:01:56,070
+والسالبة والصفر بنسميها the set of integers يبقى
+
+15
+00:01:56,070 --> 00:02:01,910
+اللي فوق أشهر بسميها شباب the set of positive
+
+16
+00:02:08,400 --> 00:02:16,200
+integers يعني ممكن أقول هذه هي Z+ Z plus يبقى
+
+17
+00:02:16,200 --> 00:02:20,720
+the set of positive integers يعني معناته مجموعة
+
+18
+00:02:20,720 --> 00:02:26,360
+الأعداد الصحيحة الموجبة اللي بتاخد الأعداد من هنا
+
+19
+00:02:26,360 --> 00:02:34,720
+و لغاية ما لا نهاية تمام المجموعة الثالثة the set of
+
+20
+00:02:34,720 --> 00:02:44,680
+rational numbers مجموعة الأعداد النسبية أو مجموعة
+
+21
+00:02:44,680 --> 00:02:49,620
+الأعداد الكسرية هنديلها رمز والرمز هذا هيظل معانا
+
+22
+00:02:49,620 --> 00:02:54,680
+موجود في الكتابة على طول الخط الرمز هذا capital Q
+
+23
+00:02:54,680 --> 00:03:00,910
+Equally the set of all elements A على B such
+
+24
+00:03:00,910 --> 00:03:07,570
+that الـ A والـ B belongs to Z and وفي نفس الوقت
+
+25
+00:03:07,570 --> 00:03:13,310
+الـ B ممنوع تساوي Zero على الإطلاق لأن لو الـ B 
+
+26
+00:03:13,310 --> 00:03:19,470
+ساوى Zero بصير إيه ماهياش معرفة يبقى كل الأعداد
+
+27
+00:03:19,470 --> 00:03:24,590
+اللي على الشكل A على B بحيث أهوا بأعداد صحيحة وفي
+
+28
+00:03:24,590 --> 00:03:30,910
+نفس الوقت B ممنوع يساوي Zero الـ set الرابع اللي هي
+
+29
+00:03:30,910 --> 00:03:36,150
+the set of real numbers
+
+30
+00:03:38,600 --> 00:03:44,020
+اللي هي مجموعة الأعداد الحقيقية يبقى لو جيت قلت
+
+31
+00:03:44,020 --> 00:03:50,220
+هذا الـ real life يبقى هنا Zero وهنا 1 وهنا
+
+32
+00:03:50,220 --> 00:03:55,240
+2 إلى آخره وسالب 1 سالب 2 والأعداد اللي
+
+33
+00:03:55,240 --> 00:04:01,010
+موجودة كذلك بينهما كل الـ rational و الـ irrational
+
+34
+00:04:01,010 --> 00:04:06,890
+numbers يعني الـ set of real numbers هذه هديها الرمز
+
+35
+00:04:06,890 --> 00:04:12,330
+capital R يبقى من حد ما نشوف capital R في الكتاب
+
+36
+00:04:12,330 --> 00:04:15,630
+اللي عندنا يبقى the set of real numbers مجموعة
+
+37
+00:04:15,630 --> 00:04:21,650
+الأعداد الحقيقية الصحيحة وغير الصحيحة نسبية وغير
+
+38
+00:04:21,650 --> 00:04:28,810
+النسبية بيجينا بعد هيك الأخيرة اللي هو the set of
+
+39
+00:04:28,810 --> 00:04:36,920
+complex numbers complex numbers مجموعة الأعداد
+
+40
+00:04:36,920 --> 00:04:43,240
+المركبة أو مجموعة الأعداد التخيلية يبقى هذه the
+
+41
+00:04:43,240 --> 00:04:51,500
+set of all elements a + bi بحيث أن الـ a والـ b
+
+42
+00:04:51,500 --> 00:04:58,660
+موجودة في R وفي نفس الوقت الـ I يساوي الجذر التربيعي
+
+43
+00:04:58,660 --> 00:05:05,360
+لمين؟ لسالب 1 يبقى بيان أقول زمان في الثانوية
+
+44
+00:05:05,360 --> 00:05:11,420
+العامة العدد المركب بالـ C + ص T حيث T اللي
+
+45
+00:05:11,420 --> 00:05:16,800
+هو الحرف الأول من كلمة تخيلي واحنا هنا A + Bi
+
+46
+00:05:16,800 --> 00:05:23,840
+حيث I العدد للحرف الأول من كلمة imaginary تخيلي
+
+47
+00:05:23,840 --> 00:05:30,490
+تمام يبقى الـ I هذا هو الـ square root لـ -1 يبقى 
+
+48
+00:05:30,490 --> 00:05:35,750
+هو الجذر التربيعي لـ -1 إيش بتلاحظوا على
+
+49
+00:05:35,750 --> 00:05:40,930
+الـ 6 الخمسة اللي عندنا هذه؟ شو العلاقة بين N و Z
+
+50
+00:05:40,930 --> 00:05:49,490
+ده؟ ممتاز يبقى N subset من Z طب Z ما عليك يوم subset
+
+51
+00:05:49,490 --> 00:05:56,330
+منها لإنه أي integer هو عبارة عن مين؟ عبارة عن اللي
+
+52
+00:05:56,330 --> 00:06:01,950
+هو rational number زي إيش مثلا؟ زي 5، الـ 5 بقدر
+
+53
+00:06:01,950 --> 00:06:06,530
+أكتب 5 على 1 يبقى صرت على الشكل A على B
+
+54
+00:06:06,530 --> 00:06:10,510
+الـ 5 والـ 1 موجودة في Z والمقام لا يساوي Zero
+
+55
+00:06:10,510 --> 00:06:15,200
+اللي هو 1 يبقى any integer is a rational number
+
+56
+00:06:15,200 --> 00:06:19,420
+but the converse is not necessarily true ليس
+
+57
+00:06:19,420 --> 00:06:26,160
+بالضرورة صحيحا بعد هيك الـ Q هذا subset من R ولا لا؟
+
+58
+00:06:26,160 --> 00:06:31,820
+أي عدد نسبي هو عبارة عن عدد حقيقي لكن العكس ليس
+
+59
+00:06:31,820 --> 00:06:37,310
+بالضرورة صحيحا يعني مثلا زي جذر 3 عدد غير نسبي
+
+60
+00:06:37,310 --> 00:06:42,330
+هذا زي باي عدد غير نسبي زي العدد إيه اللي هو 2
+
+61
+00:06:42,330 --> 00:06:47,010
+و 7 من عشرة وحط كسور إلى ما لا نهاية يبقى هذه كلها
+
+62
+00:06:47,010 --> 00:06:53,940
+أعداد irrational numbers أعداد غير نسبية طيب الآن الـ
+
+63
+00:06:53,940 --> 00:06:58,840
+R هي subset من مين؟ من الـ set of complex numbers
+
+64
+00:06:58,840 --> 00:07:04,360
+يعني any real number is a complex number بس الـ
+
+65
+00:07:04,360 --> 00:07:08,480
+converse is not necessarily true مثال وذلك لو جيت
+
+66
+00:07:08,480 --> 00:07:09,580
+قلت لك نصف
+
+67
+00:07:12,360 --> 00:07:18,960
+بقدر أكتب نصف + Zero في I يبقى النصف و Zero
+
+68
+00:07:18,960 --> 00:07:23,740
+موجودات في R والـ I يساوي الجذر التربيعي لـ سالب
+
+69
+00:07:23,740 --> 00:07:30,510
+1 يبقى أي عدد حقيقي هو عدد تخيلي أو هو عدد مركب
+
+70
+00:07:30,510 --> 00:07:36,010
+لكن العكس ليس بالضرورة صحيحا يبقى بناء عليه بروح
+
+71
+00:07:36,010 --> 00:07:44,050
+بقوله الـ N هذه هي subset من Z و Z هذه subset من الـ
+
+72
+00:07:44,050 --> 00:07:51,610
+Q و الـ Q subset من R و الـ R subset من set of complex
+
+73
+00:07:51,610 --> 00:07:56,050
+numbers يبقى هذه ما كتبناش رمزة بديها الرمز capital
+
+74
+00:07:56,050 --> 00:08:02,850
+من capital C يبقى N subset من Z, Z subset من الـ Q,
+
+75
+00:08:02,990 --> 00:08:06,730
+الـ Q subset من R, الـ R subset من C و complex
+
+76
+00:08:06,730 --> 00:08:12,680
+numbers capital C يبقى هذه الـ six الخمسة اللي وإن ما
+
+77
+00:08:12,680 --> 00:08:16,400
+نيجي واحنا خلال دراستنا في الجبر بيطلعولك الـ six
+
+78
+00:08:16,400 --> 00:08:21,060
+دول يطلع واحدة يطلع اثنتين يطلع تلاتة في كل مرة
+
+79
+00:08:21,060 --> 00:08:25,340
+بتطلع بعض الـ six اللي عندنا هذا بدنا نيجي لمين؟
+
+80
+00:08:25,340 --> 00:08:29,320
+للف properties of integers
+
+81
+00:08:30,870 --> 00:08:36,410
+يبقى بدنا نيجي لأول definition عندنا هنا بالنسبة
+
+82
+00:08:36,410 --> 00:08:44,610
+لل integers فبجي بقول a non-zero a non-zero
+
+83
+00:08:44,610 --> 00:08:52,190
+integer a
+
+84
+00:08:52,190 --> 00:09:03,460
+non-zero integer T is a divisor is a divisor of an
+
+85
+00:09:03,460 --> 00:09:23,060
+integer S if there is an integer U if there is an
+
+86
+00:09:23,060 --> 00:09:26,880
+integer U
+
+87
+00:09:29,260 --> 00:09:33,960
+such that
+
+88
+00:09:33,960 --> 00:09:47,580
+بحيث أن الـ S بده يساوي T في الـ U we
+
+89
+00:09:47,580 --> 00:09:56,680
+are right بروح نكتب أن T divides الـ S
+
+90
+00:10:00,660 --> 00:10:07,440
+if T does
+
+91
+00:10:07,440 --> 00:10:21,010
+not divide الـ S لو الـ T مقسمتش الـ S we write بنروح
+
+92
+00:10:21,010 --> 00:10:30,850
+نكتب أن الـ T does not divide الـ S definition ثاني
+
+93
+00:10:30,850 --> 00:10:34,050
+a
+
+94
+00:10:34,050 --> 00:10:41,290
+prime number P is
+
+95
+00:10:41,290 --> 00:10:44,970
+a positive integer
+
+96
+00:10:50,690 --> 00:10:58,950
+integer greater than
+
+97
+00:10:58,950 --> 00:11:07,830
+one أكبر من الواحد الصحيح who's only
+
+98
+00:11:07,830 --> 00:11:12,350
+positive divisors are
+
+99
+00:11:19,590 --> 00:11:30,810
+اللي هو main one and be itself be itself الـ
+
+100
+00:11:30,810 --> 00:11:37,670
+definition الثالث والأخير في هذه المجموعة an
+
+101
+00:11:37,670 --> 00:11:41,690
+integer S
+
+102
+00:11:41,690 --> 00:11:56,360
+is a multiple a multiple of is
+
+103
+00:11:56,360 --> 00:12:09,760
+a multiple of an integer T if there is if there is
+
+104
+00:12:09,760 --> 00:12:13,740
+if
+
+105
+00:12:13,740 --> 00:12:14,460
+there is
+
+106
+00:12:17,990 --> 00:12:32,950
+an integer U such that بحيث أن الـ S بدها تساوي T
+
+107
+00:12:32,950 --> 00:12:33,690
+في الـ U
+
+108
+00:12:55,300 --> 00:12:59,960
+هنا نجي لبعض الخواص على مين؟ على مجموعة الأعداد
+
+109
+00:12:59,960 --> 00:13:05,020
+الصحيحة الثانية اللي هي المجموعة Z في عندنا three
+
+110
+00:13:05,020 --> 00:13:10,120
+definitions هذه three definitions أساسية لها ما
+
+111
+00:13:10,120 --> 00:13:16,630
+بعدها أثناء دراستنا بنجي للتعريف الأول بدنا نعرف
+
+112
+00:13:16,630 --> 00:13:21,850
+العدد الذي يقسم عدد آخر شو معناه رياضيا التعريف
+
+113
+00:13:21,850 --> 00:13:25,890
+الثاني بيتكلم عن الأعداد الأولية التعريف الثالث
+
+114
+00:13:25,890 --> 00:13:31,350
+يتكلم عن مضاعفات الأعداد اللي هو في شبه بينه وبين
+
+115
+00:13:31,350 --> 00:13:36,680
+التعريف الأول إلى حد ما فبجي بقول a non-zero
+
+116
+00:13:36,680 --> 00:13:42,880
+integer T is a divisor of an integer S يبقى T و S
+
+117
+00:13:42,880 --> 00:13:50,760
+أعداد صحيحة يبقى كلهم موجودات في Z فبجي بقول T هو
+
+118
+00:13:50,760 --> 00:13:57,850
+قاسم للعدد S يعني بيقسم لعدد S إذا جدرت أنا لاجي
+
+119
+00:13:57,850 --> 00:14:01,870
+integer U
+
+120
+00:14:01,870 --> 00:14:10,030
+بحيث أن الـ S بده يساوي من T في U يعني الـ T بيقسم الـ
+
+121
+00:14:10,030 --> 00:14:15,500
+S إذا جدرت لاجي رقم ثاني اضربه في T يطلع من؟ يطلع
+
+122
+00:14:15,500 --> 00:14:21,440
+الـ S إن حدث ذلك بروح بكتب T تقسم الـ S يبقى هذه
+
+123
+00:14:21,440 --> 00:14:29,410
+الإشارة معناها Divide يقسم هذه معناها Divide يبقى
+
+124
+00:14:29,410 --> 00:14:36,590
+هنا T قاسم الـ S أو T بيقسم الـ S مثال وذلك لو جيت
+
+126
+00:14:36,590 --> 00:14:45,410
+تقول لك أربعة divide اللي هو من العشرين ليش؟ because
+
+127
+00:14:45,410 --> 00:14:49,390
+العشرين 
+
+128
+00:14:49,390 --> 00:14:55,130
+هذه بدها تساوي أربعة في عدد ثاني أبصر يطلع من؟
+
+129
+00:14:55,130 --> 00:14:57,350
+من يطلع؟ خمسة
+
+130
+00:15:00,230 --> 00:15:04,030
+يبقى أربعة في خمسة تساوي كده؟ تساوي عشرين أنا بدي 
+
+131
+00:15:04,030 --> 00:15:07,250
+أحط الخمسة بين قوسين حتى ما تقوليش هذه أربعة ونص
+
+132
+00:15:07,250 --> 00:15:15,730
+لأ المقصود هنا ضرب تمام زي مثلا لو جيت قلت لك مثلا
+
+133
+00:15:15,730 --> 00:15:22,490
+ناقص ثلاثين ناقص ثلاثين أو بديش أقول ناقص ثلاثين
+
+134
+00:15:22,490 --> 00:15:32,540
+بدي أقول الستة divides ناقص ثلاثين الستة تقسم ناقص
+
+135
+00:15:32,540 --> 00:15:41,700
+ثلاثين لماذا؟ لأن ناقص ثلاثين ساوي ستة أبصر في مين
+
+136
+00:15:41,700 --> 00:15:47,960
+ما هو الرقم اللي نرغب أن يكون في ستة سالب ثلاثين
+
+137
+00:15:47,960 --> 00:15:55,150
+واضح أنه سالب خمسة كذلك طيب يبقى في هذه الحالة بروح
+
+138
+00:15:55,150 --> 00:16:02,610
+نكتب أنه ستة بتقسم الثلاثين لكن هل الستة بتقسم
+
+139
+00:16:02,610 --> 00:16:06,950
+مثلا اللي هو ستة وعشرين مثلا؟
+
+140
+00:16:09,690 --> 00:16:15,650
+تقسمه؟ لأ يبقى برف أكتب الستة لا تقسم اللي هو من
+
+141
+00:16:15,650 --> 00:16:21,470
+الستة والعشرين لإنه لا يمكن ألاقي ناتج عدد صحيح
+
+142
+00:16:21,470 --> 00:16:26,430
+أضربه في الستة يطلع الجواب قد ستة وعشرين ما فيش
+
+143
+00:16:26,430 --> 00:16:29,310
+عندي بالمرة في هذه الحالة طيب
+
+144
+00:16:34,000 --> 00:16:38,960
+العدد الأول P هو عبارة عن positive integer greater
+
+145
+00:16:38,960 --> 00:16:43,780
+than one يبقى العدد الأول هو عدد الخصية الأولى
+
+146
+00:16:43,780 --> 00:16:48,900
+أكبر من الواحد الصحيح الخاصية الثانية بيقول who is
+
+147
+00:16:48,900 --> 00:16:54,820
+only positive divisors القواسم المشتركة لهذا العدد
+
+148
+00:16:54,820 --> 00:17:00,580
+الصحيح اثنين بس رقمين مين هما الواحد الصحيح هو
+
+149
+00:17:00,580 --> 00:17:06,660
+العدد في itself نفسه يبقى لا يوجد قواسم لهذا العدد
+
+150
+00:17:06,660 --> 00:17:12,000
+إلا العدد نفسه وكذلك مين الواحد الصحيح طيب ببناء
+
+151
+00:17:12,000 --> 00:17:17,880
+عليه هل اثنين يا شباب prime number اثنين عدد أولي؟
+
+152
+00:17:17,880 --> 00:17:23,060
+أه لأن هذا الصحيح أكبر من الواحد الصحيح و لا يقسم
+
+153
+00:17:23,060 --> 00:17:27,580
+إلا الواحد و الاثنين طب الثلاثه prime number؟ أه
+
+154
+00:17:27,580 --> 00:17:31,060
+طب الأربعة؟ لأ ماهو مش prime number لأن الأربعة
+
+155
+00:17:31,060 --> 00:17:35,300
+بتيجي اسمه اثنين غير حكاية الأربعة طب الخامسة؟
+
+156
+00:17:35,300 --> 00:17:42,790
+prime number؟ ستة؟ سبعة؟ صحيح ثمانية لأ تسعة لأ
+
+157
+00:17:42,790 --> 00:17:48,090
+برضه و لو أنه فردي تمام يبقى ال prime number هم
+
+158
+00:17:48,090 --> 00:17:53,570
+واحد اثنين صحيح غلط الواحد لا يستفيد واحد لازم يكون
+
+159
+00:17:53,570 --> 00:17:58,140
+أكبر من واحد يبقى ببدأ من ويمحط لي معلومتك أن اثنين
+
+160
+00:17:58,140 --> 00:18:03,860
+هو الرقم الزوجي الوحيد اللي هو prime number لو طلع
+
+161
+00:18:03,860 --> 00:18:08,040
+بعدك أربعة ستة ثمانية كلها بتقسم على اثنين تمام
+
+162
+00:18:08,040 --> 00:18:11,540
+يبقى العدد الزوجي الوحيد اللي هو prime number
+
+163
+00:18:11,540 --> 00:18:16,040
+ما فيش غير اثنين والباقي كلها أعداد فردية بس مش كل
+
+164
+00:18:16,040 --> 00:18:20,280
+الأعداد الفردية يبقى الأعداد ال prime number اثنين
+
+165
+00:18:20,280 --> 00:18:31,540
+ثلاثة خمسة سبعة أحد عشر ثلاثة عشر سبعة عشر تسعة عشر ثلاثة و
+
+166
+00:18:31,540 --> 00:18:39,040
+عشرين تسعة و عشرين واحد و ثلاثين و هكذا يبقى سبعة
+
+167
+00:18:39,040 --> 00:18:44,570
+و ثلاثين يبقى كلها هذه ال number يبقى العدد الأولي
+
+168
+00:18:44,570 --> 00:18:48,630
+هو العدد الذي لا يقسم إلا على نفسه وعلى الواحد
+
+169
+00:18:48,630 --> 00:18:54,210
+الصحيح تمام؟ يبقى هادمين دير بالك هيلعب دور كبير
+
+170
+00:18:54,210 --> 00:18:58,010
+عندنا لما نخش على الشطر الثاني وشطر ال groups
+
+171
+00:18:58,010 --> 00:19:03,570
+يبقى هنجيب groups الأعداد تبعها أعداد أولية دير
+
+172
+00:19:03,570 --> 00:19:08,250
+بالك يبقى صح صح من الآن هذه very important خلال
+
+173
+00:19:08,250 --> 00:19:14,960
+دراستنا طيب نجد ثانية أن integer S is a multiple of
+
+174
+00:19:14,960 --> 00:19:23,160
+an integer T يبقى ال S هو مضاعفات العدد T وقت إذا
+
+175
+00:19:23,160 --> 00:19:28,480
+جدرت لاجي عدد ثاني U بحيث ال S بدأ تساوي the T في U
+
+176
+00:19:28,480 --> 00:19:33,540
+أظن نفس الكلام اللي عندنا هنا صح ولا لا؟ يبقى
+
+177
+00:19:33,540 --> 00:19:39,320
+مضاعفات الأعداد الـ
+
+178
+00:19:39,320 --> 00:19:45,860
+S ومضاعفات العدد T إذا قدرت ألجن تجارب U بحيث الـ
+
+179
+00:19:45,860 --> 00:19:46,060
+S
+
+180
+00:19:49,810 --> 00:19:55,010
+العشرين هو مضاعفات الأربعة، لماذا؟ لأن العشرين
+
+181
+00:19:55,010 --> 00:20:00,730
+سيكونوا أربعة في رقم كان الخمسة، العدد ناقص ثلاثين
+
+182
+00:20:00,730 --> 00:20:05,810
+هو مضاعفات الستة، لماذا؟ لأن ناقص ثلاثين هو ستة في
+
+183
+00:20:05,810 --> 00:20:10,070
+من؟ في ناقص خمسة، يبقى العدد يطلع موجبة، والله سلم،
+
+184
+00:20:10,070 --> 00:20:14,770
+لا تفرج عندي، يبقى هذا معنى مضاعفات العدد يبقى
+
+185
+00:20:14,770 --> 00:20:18,630
+المعادلة تبعت مضاعفات العدد والمعادلة تبعت القسم
+
+186
+00:20:18,630 --> 00:20:24,110
+التنتين زي بعض بس كل واحدة إلها مفهوم هنا T بتقسم
+
+187
+00:20:24,110 --> 00:20:29,550
+العدد S يعني إيش؟ يعني لو قسمت S على T الناتج هو
+
+188
+00:20:29,550 --> 00:20:37,070
+عدد صحيح اسمه U هنا ال S هو مضاعفات ال T إذا جدرت
+
+189
+00:20:37,070 --> 00:20:41,630
+ألاقي رقم ثاني أضربه في T يطلع من عنده يطلع عند S
+
+190
+00:20:41,630 --> 00:20:50,200
+و هكذا يبقى هذا المثال اللي عندنا طيب إيش رأيك؟ أي
+
+191
+00:20:50,200 --> 00:20:52,640
+عدد عندي بيقسم ال zero ولا لأ؟
+
+192
+00:20:55,840 --> 00:21:00,340
+الخمسين بتقسم Zero ولا لا؟ Zero على خمسين بتساوى
+
+193
+00:21:00,340 --> 00:21:06,240
+Zero إذا أي رقم عندي صحيح بيقسم مين؟ بيقسم Zero
+
+194
+00:21:06,240 --> 00:21:10,240
+صحيح ولا غير صحيح حتى لو كان real number لكن ما دام
+
+195
+00:21:10,240 --> 00:21:15,300
+نتكلم في integers يبقى كلامنا على ال integers يبقى
+
+196
+00:21:15,300 --> 00:21:20,640
+اثنين هنا بقدر أقول every non zero integer every
+
+197
+00:21:20,640 --> 00:21:24,340
+non zero
+
+198
+00:21:26,530 --> 00:21:39,190
+integer وليكن n divides ال zero because السبب لأن
+
+199
+00:21:39,190 --> 00:21:48,010
+ال zero بده يساوي ال n في ال zero itself also
+
+200
+00:21:48,010 --> 00:22:01,540
+وكذلك الواحد بيقسم ال n ليش؟ because ال N تساوي
+
+201
+00:22:01,540 --> 00:22:16,020
+واحد ضرب ال N يعني
+
+202
+00:22:16,020 --> 00:22:19,500
+كل حاجة بنقدر نحطها على شكل المعادلة اللي عندنا
+
+203
+00:22:19,500 --> 00:22:23,360
+هذه و خلاص بيصير كلامنا صحيح
+
+204
+00:22:31,330 --> 00:22:35,710
+ننتقل إلى نقطة مهمة جدا وهي ال well ordering
+
+205
+00:22:35,710 --> 00:22:44,970
+principle حاجة اسمها ال well ordering principle
+
+206
+00:22:44,970 --> 00:22:50,670
+بتقول
+
+207
+00:22:50,670 --> 00:22:57,390
+ما ياتي every non zero every
+
+208
+00:22:57,390 --> 00:23:16,050
+non zero set of positive integers contains
+
+209
+00:23:16,050 --> 00:23:25,090
+a smallest member
+
+210
+00:23:39,830 --> 00:23:46,230
+قاعدة الترتيب الجيد لو
+
+211
+00:23:46,230 --> 00:23:52,250
+جينا قلنا بدنا ناخد set بس ال set هذي بيبقى non
+
+212
+00:23:52,250 --> 00:23:57,070
+-zero of positive integers يبقى أنا بدي أعداد
+
+213
+00:23:57,070 --> 00:24:02,520
+صحيحة كلها موجبة ولا يوجد فيها صفر لو أخدت هذه
+
+214
+00:24:02,520 --> 00:24:07,440
+المجموعة مثلا لو جيت مجموعة الشباب اللي هنا جيت
+
+215
+00:24:07,440 --> 00:24:12,720
+أخدت أعمارهم بقيت ولا واحد عمره زي الثاني وأخدتهم
+
+216
+00:24:12,720 --> 00:24:18,440
+مثلا بدي أخد شهور أو أيام أو سنين ليه السهولة بدي
+
+217
+00:24:18,440 --> 00:24:22,800
+أخد سنين طبعا كلهم نفس السنة تقريبا لكن أنا جدا
+
+218
+00:24:22,800 --> 00:24:26,840
+اللي بدي أسمي حالي لأ عمرهم مش زي بعض يبقى لو جيت
+
+219
+00:24:26,840 --> 00:24:31,470
+واحد عمره مثلا اللي هو سبعة عشر سنة واحد ثمانية عشر
+
+220
+00:24:31,470 --> 00:24:34,310
+سنة وواحد تسعة عشر سنة وواحد عشرين وواحد واثنين
+
+221
+00:24:34,310 --> 00:24:37,990
+وعشرين يبقى هذه المجموعة اللي خدتها لازم ألاقي
+
+222
+00:24:37,990 --> 00:24:44,310
+واحد فيهم عمره أقل ما يمكن بالنسبة لمين للآخرين
+
+223
+00:24:44,310 --> 00:24:47,470
+يبقى أي مجموعة من الأعداد تاخدها بالترتيب والله
+
+224
+00:24:47,470 --> 00:24:51,170
+عشوائي لو أخدت خمسين وثلاثة عشر وأربعة وعشرين واثنين
+
+225
+00:24:51,170 --> 00:24:55,440
+وثلاثين وواحد وستون ومئة وواحد وعشرين يبقى هذه
+
+226
+00:24:55,440 --> 00:24:59,000
+مجموعة الأرقام كلها non-zero انتجة لازم ألاقي واحد
+
+227
+00:24:59,000 --> 00:25:03,560
+فيهم بيكون أقل من باقي مين من باقي الأرقام هذه
+
+228
+00:25:03,560 --> 00:25:08,380
+الترتيب وبالتالي ممكن أرتبهم فعلا ترتيب جيد أو
+
+229
+00:25:08,380 --> 00:25:12,700
+ترتيب حسب واحد بعد الثاني حسب الأقل من اللي بعده
+
+230
+00:25:12,700 --> 00:25:16,200
+اللي بعده أقل من اللي بعده اللي بعده أقل من مين من
+
+231
+00:25:16,200 --> 00:25:20,760
+اللي بعده يبقى هذه المقصود فيها every non-zero set
+
+232
+00:25:20,760 --> 00:25:24,020
+of positive integers contains a smallest member
+
+233
+00:25:24,020 --> 00:25:28,300
+يبقى فيها عوضة أو فيها عنصر بيكون ماله أقل ما يمكن
+
+234
+00:25:28,300 --> 00:25:34,380
+من نفسه لمهم للعناصر الأخرى ننتقل الآن لنقطة مهمة
+
+235
+00:25:34,380 --> 00:25:38,400
+جدا خلال دراستنا في الجبر لزمان أكثر من اللي
+
+236
+00:25:38,400 --> 00:25:42,360
+قدامنا هذه كثيرة جدا اللي هي division algorithm
+
+237
+00:25:42,360 --> 00:25:48,740
+خوارزمية القسمة نشوف إيش بتقول و نعطي بعض التطبيقات
+
+238
+00:25:48,740 --> 00:25:56,320
+عليها يبقى بدنا نيجي لل division algorithm
+
+239
+00:25:56,320 --> 00:26:01,480
+خوارزمية
+
+240
+00:26:01,480 --> 00:26:10,660
+القسمة بتقول لمية الاتي ال a and ال b
+
+241
+00:26:34,100 --> 00:26:37,780
+يوجد unique integer
+
+242
+00:26:45,640 --> 00:26:58,240
+a unique integers اللي هو Q and ال R Q and ال R
+
+243
+00:26:58,240 --> 00:27:02,540
+with property
+
+244
+00:27:02,540 --> 00:27:15,170
+ذات with property ذات أن ال A بتساوي ال بي كيو زائد
+
+245
+00:27:15,170 --> 00:27:24,150
+ال R where حيث ال R أكبر من أو تساوي ال zero أقل
+
+246
+00:27:24,150 --> 00:27:34,870
+من مين و أقل من بي نقطة مهمة جدا هنا if ال بي
+
+247
+00:27:34,870 --> 00:27:47,720
+بتقسم ال a then الـ R بدها تساوي Zero That is I N ال
+
+248
+00:27:47,720 --> 00:27:52,240
+A بدها تساوي BQ في هذه الحالة
+
+249
+00:28:29,960 --> 00:28:37,500
+كلمة خوارزمية منسوبة إلى مؤسس علم الجبر اللي هو
+
+250
+00:28:37,500 --> 00:28:43,620
+مين؟ إيش اسمه؟ مين؟ اسمه محمد بن موسى الخوارزمي 
+
+251
+00:28:43,620 --> 00:28:49,080
+الذي عاش في العصر العباسي و الذي وضع كثيراً من قوانين
+
+252
+00:28:49,080 --> 00:28:55,200
+الرياضيات التي تدرس من ذلك الوقت وإلى يومنا هذا خاصة
+
+253
+00:28:55,200 --> 00:29:00,100
+في الـ calculus  وفي الجبر التابع للتنمية والإعدادية
+
+254
+00:29:00,100 --> 00:29:04,440
+وفي الهندسة يعني اللي هو خاصة حساب المثلثات هذه
+
+255
+00:29:04,440 --> 00:29:08,960
+الـ جيب الـ جتا هو أول من وضعها في التاريخ يبقى لما
+
+256
+00:29:08,960 --> 00:29:12,240
+أقول division algorithm خوارزمية القسمة أقول لو
+
+257
+00:29:12,240 --> 00:29:18,440
+أخذت أي عددين a و b بعد تبقى أعداد صحيحة و b دائماً
+
+258
+00:29:18,440 --> 00:29:24,450
+و أبداً ما له أكبر من الـ zero يبقى أخذت أعداد صحيحة ب
+
+259
+00:29:24,450 --> 00:29:29,250
+أكبر من الـ zero هل اشترطت a أكبر من الـ zero ليس 
+
+260
+00:29:29,250 --> 00:29:33,830
+بالضرورة ممكن يكون ال a بالسالب لكن بي بديها
+
+261
+00:29:33,830 --> 00:29:37,930
+بالموجب then there will exist a unique integers
+
+262
+00:29:37,930 --> 00:29:44,420
+هلاقي عددين وحيدين ما فيش غيرهم مرتبطين مع a و b كيف
+
+263
+00:29:44,420 --> 00:29:50,580
+اللي هم الخاصية التالية أن ال a تساوي b في ال q
+
+264
+00:29:50,580 --> 00:29:57,720
+يعني مضاعفات ال b زائد r حيث r هذه أكبر من أو 
+
+265
+00:29:57,720 --> 00:30:03,840
+تساوي zero  أقل من b لو ال r تساوي zero يبقى إيه
+
+266
+00:30:03,840 --> 00:30:10,350
+إيش بتساوي b في q صحيح ولا لأ ال r تساوي zero يبقى
+
+267
+00:30:10,350 --> 00:30:16,430
+ال a تساوي ال b في ال q معناه هذا الكلام أن ال a هي
+
+268
+00:30:16,430 --> 00:30:24,240
+مضاعفات من ال b أو ال b تقسم ال a أو تقسم ال a يبقى يا
+
+269
+00:30:24,240 --> 00:30:28,980
+شباب هذا ال condition ضروري جداً very important
+
+270
+00:30:28,980 --> 00:30:34,900
+دائماً يا بده يساوي zero يا أكبر من zero إذا ساوي
+
+271
+00:30:34,900 --> 00:30:40,380
+zero معناته ال b بتقسم ال a أو ال a هي مضاعفات ال
+
+272
+00:30:40,380 --> 00:30:47,060
+b إذا كان ال a ال b لا تقسم ال a يبقى ال r بدي
+
+273
+00:30:47,060 --> 00:30:52,260
+تأخذ قيمة أكبر من ال 0 لكن دائماً و أبداً ما لها أقل
+
+274
+00:30:52,260 --> 00:30:55,500
+من ال b لأن لو ساوي ال b بصير ال r ب 0 على طول
+
+275
+00:30:55,500 --> 00:30:59,940
+الخط يبقى ال r دائماً و أبداً محصورة ما بين ال 0 و
+
+276
+00:30:59,940 --> 00:31:05,280
+بين ال b اليومين العدد الثاني اللي عندنا تمام؟
+
+277
+00:31:05,280 --> 00:31:09,820
+يبقى هذه خوارزمية القسمة نعطي أمثلة examples
+
+278
+00:31:13,630 --> 00:31:18,670
+أول مثال بدي آخذ a برقم و آخذ b برقم و نشوف كيف
+
+279
+00:31:18,670 --> 00:31:24,430
+نسوي خوارزمية القسمة لو كان مثلاً ال a بده يساوي
+
+280
+00:31:24,430 --> 00:31:34,410
+تسعة عشر and ال b كان مثلاً بده يساوي خمسة يبقى
+
+281
+00:31:34,410 --> 00:31:39,750
+باجي بقوله the division algorithm
+
+282
+00:31:46,430 --> 00:31:53,370
+التسعة عشر هذه بدي أكتبها بدلالة مين؟ بدلالة الخمسة
+
+283
+00:31:53,370 --> 00:32:00,010
+يبقى هذه بدها تساوي الخمسة مضروبة أبصر في مين؟ زائد
+
+284
+00:32:00,010 --> 00:32:05,510
+رقم ثاني السؤال هو هل الخمسة بتقسم التسعة عشر؟ إذا
+
+285
+00:32:05,510 --> 00:32:09,470
+ال r اللي عندها لا يمكن أن تساوي 0 وإنما أكبر من
+
+286
+00:32:09,470 --> 00:32:17,270
+ال 0 أقل من ال b لخمسة ممتاز جداً يبقى خمسة في قداش
+
+287
+00:32:17,270 --> 00:32:22,850
+بدها تطلع أقل من تسعة عشر خمسة في ثلاثة يبقى خمسة في
+
+288
+00:32:22,850 --> 00:32:28,930
+ثلاثة بخمسة عشر يبقى أربعة يبقى بقوله زائد أربعة
+
+289
+00:32:28,930 --> 00:32:33,350
+و الأربعة زي ما أنتم شايفين أكبر من أو تساوي zero
+
+290
+00:32:33,350 --> 00:32:39,030
+أقل من المئة و أقل من الخمسة اللي عندنا يبقى ضروري
+
+291
+00:32:39,030 --> 00:32:45,010
+ينطبق الشرطان في قارنة واحدة مش ينطبق شرط التاني لأ
+
+292
+00:32:45,010 --> 00:32:53,530
+نعطيك مثال آخر مثال اثنين مثال اثنين لو أخذت ال a
+
+293
+00:32:53,530 --> 00:33:01,130
+تساوي ناقص تسعة عشر and ال b تساوي ثلاثة على سبيل
+
+294
+00:33:01,130 --> 00:33:12,870
+المثال يبقى the division algorithm is
+
+295
+00:33:12,870 --> 00:33:16,070
+ناقص
+
+296
+00:33:16,070 --> 00:33:23,340
+تسعة عشر بدها تساوي اللي هو ثلاثة أبصر في قداش زائد
+
+297
+00:33:23,340 --> 00:33:28,840
+أبصر قداش بدي
+
+298
+00:33:28,840 --> 00:33:35,510
+ناقص ستة عشر ثلاثة في قداش ممكن تعطيني سالب سبعة
+
+299
+00:33:35,510 --> 00:33:41,850
+سالب سبعة طيب لو قلت سالب سبعة يبقى بيصير قداش
+
+300
+00:33:41,850 --> 00:33:46,630
+سالب واحد و عشرين يبقى بدي أضيف لها قداش مشان يطلع
+
+301
+00:33:46,630 --> 00:33:53,670
+سالب تسعة عشر اثنين يبقى زائد اثنين و الاثنين هذه
+
+302
+00:33:53,670 --> 00:34:00,770
+أكبر من أو تساوي zero أقل من مين؟ أقل من ثلاثة طيب
+
+303
+00:34:01,270 --> 00:34:05,950
+هذا الكلام مئة بالمئة أنطبق الشرطان في آن واحد
+
+304
+00:34:05,950 --> 00:34:11,910
+يبقى بدي آجي أقوله إيش رأيك في ناقص تسعة و عشرين ها
+
+305
+00:34:11,910 --> 00:34:17,330
+ديها ناقص تسعة و عشرين بدي أكتبها بدل ما أقول ثلاثة
+
+306
+00:34:17,330 --> 00:34:24,470
+في ناقص سبعة بدي أقول ثلاثة في ناقص ستة ثلاثة في
+
+307
+00:34:24,470 --> 00:34:30,210
+ناقص ستة في قدر؟ الوصف عليه بتمانطعي زائد ناقص
+
+308
+00:34:30,210 --> 00:34:30,550
+واحد
+
+309
+00:34:33,520 --> 00:34:41,000
+مش هدول احنا بطلع سالب تسعة عشر بس يبقى هذه not
+
+310
+00:34:41,000 --> 00:34:46,760
+division يبقى
+
+311
+00:34:46,760 --> 00:34:51,360
+كتاب اللي هنا but ولكن ناقص تسعة و نصف division
+
+312
+00:34:51,360 --> 00:35:01,050
+algorithm السبب because أيوة شو اللي اختل عندي
+
+313
+00:35:01,050 --> 00:35:07,630
+السالب واحد السالب واحد هذا ما هو أكبر من أو
+
+314
+00:35:07,630 --> 00:35:15,300
+يساوي zero لكن فعلاً أقل من ثلاثة مظبوط أقل من ثلاثة
+
+315
+00:35:15,300 --> 00:35:20,780
+صحيح لكن سالب واحد ما هو أكبر من أو يساوي zero وإنما
+
+316
+00:35:20,780 --> 00:35:27,540
+أقل من zero إذا صارت تناقض لهذه الخاصية مع مين؟ مع
+
+317
+00:35:27,540 --> 00:35:32,300
+الخاصية اللي عندنا هذه تمام؟ يبقى هذه الأولى
+
+318
+00:35:32,300 --> 00:35:36,510
+الصحيحة و الثانية مالها؟ هذه خطأ ليست division
+
+319
+00:35:36,510 --> 00:35:41,610
+algorithm يعني يا شباب الزيادة لازم تكون بإشارة
+
+320
+00:35:41,610 --> 00:35:47,010
+موجبة وليست بإشارة سالبة دير بالك من النقطة هذه اللي
+
+321
+00:35:47,010 --> 00:35:50,770
+عندنا طيب بدنا نيجي لحاجة اسمها الـ greatest common
+
+322
+00:35:50,770 --> 00:35:57,690
+divisor definition the greatest common divisor the
+
+323
+00:35:57,690 --> 00:36:01,970
+greatest common
+
+324
+00:36:03,320 --> 00:36:16,100
+divisor القاسم المشترك الأعظم you
+
+325
+00:36:16,100 --> 00:36:24,840
+got the greatest common divisor of two non-zero
+
+326
+00:36:24,840 --> 00:36:26,560
+integers
+
+327
+00:36:38,640 --> 00:36:46,300
+is the largest
+
+328
+00:36:46,300 --> 00:37:00,580
+of all common divisors of all common divisors of
+
+329
+00:37:01,740 --> 00:37:13,560
+ال a و ال b and denoted by هنعطيهم
+
+330
+00:37:13,560 --> 00:37:24,800
+الرمز GCD لل a و ال b when
+
+331
+00:37:24,800 --> 00:37:27,840
+عندما
+
+332
+00:37:29,150 --> 00:37:34,250
+the greatest common divisor لل a و ال b يبدو يساوي
+
+333
+00:37:34,250 --> 00:37:45,370
+واحد we say that .. we say that بروح نقول أن ال a
+
+334
+00:37:45,370 --> 00:37:54,310
+and ال b are relatively prime
+
+335
+00:37:58,290 --> 00:38:03,070
+relatively prime examples
+
+336
+00:38:22,960 --> 00:38:27,360
+طبعاً هنا عندي شغلتين الشغلة الأولى ال greatest common
+
+337
+00:38:27,360 --> 00:38:30,900
+divisor الشغلة الثانية لو ال greatest common
+
+338
+00:38:30,900 --> 00:38:37,760
+divisor يساوي واحد شو تسمي هذه؟ تعريف الأول بقول
+
+339
+00:38:37,760 --> 00:38:42,360
+the greatest common divisors القاسم المشترك الأعظم
+
+340
+00:38:42,360 --> 00:38:47,460
+divisor قاسم common مشترك greatest اللي هو الأكبر
+
+341
+00:38:47,460 --> 00:38:51,520
+أو الأعظم يبقى القاسم المشترك الأعظم of two non
+
+342
+00:38:51,520 --> 00:38:57,440
+zero integers لعددين صحيحين غير صفريين a و b is
+
+343
+00:38:57,440 --> 00:39:03,500
+the largest أكبر واحد of all common divisors of a
+
+344
+00:39:03,500 --> 00:39:08,720
+and b يعني أنا عندي رقمين لقيت رقم بيقسم للاثنين
+
+345
+00:39:08,720 --> 00:39:12,260
+لقيت كمان رقم بيقسم للاثنين لقيت كمان رقم ... لقيت
+
+346
+00:39:12,260 --> 00:39:16,780
+كمان رقم بيقسم للاثنين أكبر واحد في هدول القواسم
+
+347
+00:39:16,780 --> 00:39:21,160
+بسميهم مين؟ ال greatest common divisor و هعطيله
+
+348
+00:39:21,160 --> 00:39:28,660
+الرمز GCD G greatest C جاء من common with B divisor
+
+349
+00:39:28,840 --> 00:39:31,860
+يبقى بدل ما أقول ال greatest common divisor
+
+350
+00:39:31,860 --> 00:39:37,820
+هأختصرهم إلى مين؟ الثلاثة أحرف و أحط العددين a و b
+
+351
+00:39:37,820 --> 00:39:43,060
+تمام تمام يبقى ال greatest common divisor هو أكبر
+
+352
+00:39:43,060 --> 00:39:48,540
+قاسم للعددين يعني عندي عدة قواسم للعددين أكبر واحد
+
+353
+00:39:48,540 --> 00:39:53,420
+فيهم بسميه ال greatest common divisor ممكن يحصل أن
+
+354
+00:39:53,420 --> 00:39:56,380
+ال greatest common divisor بين العددين يكون
+
+355
+00:39:56,380 --> 00:40:02,490
+ما عنديش إلا مين؟ إلا الواحد الصحيح إن حدث ذلك بقول
+
+356
+00:40:02,490 --> 00:40:09,750
+يبقى العددين a و b are relatively prime طيب كلمة
+
+357
+00:40:09,750 --> 00:40:14,510
+relatively prime يعني prime عدد أولي بس relatively
+
+358
+00:40:14,510 --> 00:40:19,960
+يعني نسبي يعني اثنين ال primes بالنسبة لبعض مش
+
+359
+00:40:19,960 --> 00:40:24,640
+اثنين ال primes أكيد العدد هذا و العدد هذا يعتبر
+
+360
+00:40:24,640 --> 00:40:29,840
+بالنسبة لبعض ال primes هي المقصود فيها مش كل واحد
+
+361
+00:40:29,840 --> 00:40:35,600
+فيهم لازم يكون ال prime لأ ليس بالضرورة تمام نعطي
+
+362
+00:40:35,600 --> 00:40:40,540
+توضيح لكل واحد من الكلام اللي عندنا هذا بأمثلة
+
+363
+00:40:40,540 --> 00:40:48,620
+عددية الآن لو جئت قلت لك خذ ال a تساوي مثلاً ستة عشر
+
+364
+00:40:48,620 --> 00:40:58,240
+and ال b تساوي الأربعة و عشرين then الواحد divide
+
+365
+00:40:58,240 --> 00:41:01,580
+الستة عشر
+
+366
+00:41:01,580 --> 00:41:07,380
+و الأربعة و عشرين صح ولا لأ؟ إيش بيجي بعد الواحد
+
+367
+00:41:07,380 --> 00:41:13,970
+بيقسم الاثنين؟ اثنين اثنين ال divisor الستة عشر و
+
+368
+00:41:13,970 --> 00:41:21,830
+الأربعة و عشرين بعد اثنين الثلاثة لأ الأربعة بتقسم
+
+369
+00:41:21,830 --> 00:41:29,790
+الستة عشر و الأربعة و عشرين الخمسة الستة السبعة
+
+370
+00:41:29,790 --> 00:41:40,650
+الثمانية آه ثمانية بتقسم ال 16 و كذلك ال 24 في أكثر
+
+371
+00:41:40,650 --> 00:41:45,650
+من هيك فشل لأنه ثمانية هو نصف العدد 16 من حد ما
+
+372
+00:41:45,650 --> 00:41:50,250
+تصل لنصف العدد stop بوجه تمشي ولا خطوة قدام لأنه
+
+373
+00:41:50,250 --> 00:41:54,050
+إذا زاد عن النصف لا يمكن أن يقسم العدد و يطلع عنده
+
+374
+00:41:54,050 --> 00:42:01,650
+عدد صحيح يبقى كم قاسم صار عنده هنا؟ أربعة أكبر واحد
+
+375
+00:42:01,650 --> 00:42:05,450
+فيهم بيقول هو ال greatest common divisor يبقى ال greatest
+
+376
+00:42:05,450 --> 00:42:08,390
+the common divisor للستة عشر والاربعين مين هو
+
+377
+00:42:08,390 --> 00:42:14,650
+ثمانية من هذا الكلام بقدر أقول يبقى ال greatest common divisor
+
+378
+00:42:14,650 --> 00:42:20,710
+ للستة عشر والاربعين هو العدد مين؟
+
+379
+00:42:20,710 --> 00:42:28,190
+العدد ثمانية طيب هذا المثال الأول بندخل لِمثال ثاني
+
+380
+00:42:29,950 --> 00:42:34,790
+بدي أجيبلك على حكاية إيه relatively prime لو جيت
+
+381
+00:42:34,790 --> 00:42:41,430
+قلت لك الآن the greatest common divisor للتلاتة والسبعة
+
+382
+00:42:41,430 --> 00:42:49,810
+قد إيش؟ في غيره؟ في غيره؟ لأ يبقى هذا يساوي الواحد
+
+383
+00:42:49,810 --> 00:42:58,910
+because التلاتة and السبعة are primes مش
+
+384
+00:42:58,910 --> 00:43:05,930
+relatively primes تمام؟ but ولكن the greatest common divisors
+
+385
+00:43:05,930 --> 00:43:12,650
+للأربعة والسبعة مثلا كده؟ في غيره؟
+
+386
+00:43:12,650 --> 00:43:17,410
+هو الواحد الوحيد اللي بيقسم العددين الاتنين هدول
+
+387
+00:43:17,410 --> 00:43:22,330
+يبقى يساوي واحد هل الأربعة prime number لكن
+
+388
+00:43:22,330 --> 00:43:26,010
+الأربعة والسبعة بالنسبة لبعض يعتبروا إيش prime
+
+389
+00:43:26,010 --> 00:43:33,960
+يبقى are relatively prime يبقى هنا because السبعة
+
+390
+00:43:33,960 --> 00:43:39,640
+and الأربعة are والله الأربعة and السبعة خلينا
+
+391
+00:43:39,640 --> 00:43:45,820
+بالترتيب ماشيين and السبعة are relatively
+
+392
+00:43:45,820 --> 00:43:49,240
+relatively
+
+393
+00:43:49,240 --> 00:43:53,960
+primes يبقى
+
+394
+00:43:53,960 --> 00:43:56,980
+شايف الفرق ما بين ال prime و relatively prime إيش
+
+395
+00:43:56,980 --> 00:43:57,520
+هتفضل
+
+396
+00:44:03,250 --> 00:44:08,970
+طب ما هي .. شوف في .. في غير الواحد؟
+
+397
+00:44:08,970 --> 00:44:15,580
+طب هو العوامل اللي هو .. هو السنة ممتاز جدا لك
+
+398
+00:44:15,580 --> 00:44:19,900
+الأربعة والسبعة في أكثر طيب ما فيش غيره يعني أنا 
+
+399
+00:44:19,900 --> 00:44:24,080
+بعطي مثال relatively prime لك المثال اللي جابله
+
+400
+00:44:24,080 --> 00:44:27,580
+جبت ال greatest common divisor لأي عددين بس ما طلعش
+
+401
+00:44:27,580 --> 00:44:31,540
+واحد طلع قد إيش؟ طلع ثمانية جبت الواحد والاتنين
+
+402
+00:44:31,540 --> 00:44:35,640
+والأربعة والثمانية أخدت الكبير فيهم طبقا للتعريف
+
+403
+00:44:35,640 --> 00:44:39,300
+تمام هنا ال greatest common divisor قد يكون واحد قد
+
+404
+00:44:39,300 --> 00:44:42,840
+يكون واحد في كام حالة؟ بدل الحالة حالتين الحالة
+
+405
+00:44:42,840 --> 00:44:46,700
+الأولى لو كانوا اتنين primes وفي هذه الحالة بقول
+
+406
+00:44:46,700 --> 00:44:50,520
+اتنين primes مثلا بقول relatively prime relatively
+
+407
+00:44:50,520 --> 00:44:55,120
+يعني في بنسبة واحد بالنسبة للتانية أخدت الأربعة
+
+408
+00:44:55,120 --> 00:45:01,460
+والسبعة أخدت الاحد عشر والخمسمية مثلا مثلا تسعة و
+
+409
+00:45:01,460 --> 00:45:05,520
+عشرة are relatively prime كلام صحيح يبقى أنا خدت
+
+410
+00:45:05,520 --> 00:45:08,420
+احد عشر و أخدت الخمسمية ما فيش قواسم بينهم إلا
+
+411
+00:45:08,420 --> 00:45:13,200
+الواحد الصحيح وهكذا تفضل كيف؟
+
+412
+00:45:14,710 --> 00:45:19,070
+automatically relatively prime لكن العكس ليس صحيحا
+
+413
+00:45:19,070 --> 00:45:25,190
+يبقى زميلكوف يقول هدول لما يكونوا are primes ما
+
+414
+00:45:25,190 --> 00:45:29,250
+بقدر أقول عليهم relatively primes لكن العكس ليس
+
+415
+00:45:29,250 --> 00:45:34,830
+صحيحا يبقى هذه الأمثلة على ال greatest common
+
+416
+00:45:34,830 --> 00:45:40,250
+divisors وعلى prime و relatively primes
+
+417
+00:46:07,100 --> 00:46:14,340
+طيب خد لها ملاحظة if
+
+418
+00:46:14,340 --> 00:46:23,880
+الـ N is an integer and
+
+419
+00:46:23,880 --> 00:46:34,570
+الـ N greater than zero ثم the greatest common divisor لل
+
+420
+00:46:34,570 --> 00:46:39,210
+N والـ 0 كده يا شباب؟
+
+421
+00:46:41,350 --> 00:46:49,330
+إن الواحد تقسم الـ N وتقسم الـ zero الـ N اتنين تقسم
+
+422
+00:46:49,330 --> 00:46:53,430
+الـ zero بس مضمون تقسم الـ N لا مش مضمون إيه
+
+423
+00:46:53,430 --> 00:46:59,010
+التلاتة الأربعة الـ N الـ N أكبر رقم بيقسم الـ N و
+
+424
+00:46:59,010 --> 00:47:04,550
+بيقسم الـ zero يبقى هنا هذا الكلام بدو يساوي الـ N
+
+425
+00:47:04,550 --> 00:47:10,250
+because الـ N is the
+
+426
+00:47:32,560 --> 00:47:45,550
+بقسم الاتنين في النظرية بتقول ما يأتي theorem for
+
+427
+00:47:45,550 --> 00:47:57,810
+any non zero integers a
+
+428
+00:47:57,810 --> 00:48:08,830
+and b there exist integers
+
+429
+00:48:11,450 --> 00:48:24,130
+بلاقي أعداد صحيحة S and T such that such that إن
+
+430
+00:48:24,130 --> 00:48:30,030
+ال greatest common divisor للـ A و الـ B بدو يساوي
+
+431
+00:48:30,030 --> 00:48:39,610
+الـ A في S زائد الـ B في T moreover
+
+432
+00:48:40,520 --> 00:48:48,920
+و أكثر من ذلك moreover the greatest common divisor
+
+433
+00:48:48,920 --> 00:48:55,080
+للـ a والـ b is the smallest positive integer is the
+
+434
+00:48:55,080 --> 00:49:02,900
+smallest positive integer
+
+435
+00:49:02,900 --> 00:49:06,040
+smallest
+
+436
+00:49:06,040 --> 00:49:17,910
+positive integer of form على الشكل aS زائد bT
+
+437
+00:49:17,910 --> 00:49:21,450
+quaternary
+
+438
+00:49:21,450 --> 00:49:24,950
+نتيجة
+
+439
+00:49:24,950 --> 00:49:38,030
+if الـ a and الـ b are relatively prime
+
+440
+00:49:39,750 --> 00:49:49,590
+relatively prime then there exist then there exist
+
+441
+00:49:49,590 --> 00:49:55,610
+integers s
+
+442
+00:49:55,610 --> 00:50:07,150
+and t s and t such that بحيث
+
+443
+00:50:07,150 --> 00:50:16,780
+إن الـ aS زائد الـ bT يساوي كده؟ يساوي واحد
+
+444
+00:51:06,130 --> 00:51:10,410
+طيب نرجع لنص النظرية بيقول for any non zero
+
+445
+00:51:10,410 --> 00:51:15,770
+integers a و b يبقى أنا عندي عددين صحيحين a و b
+
+446
+00:51:15,770 --> 00:51:21,250
+there exist integers لازم ألاقي عددين آخرين s and
+
+447
+00:51:21,250 --> 00:51:25,250
+t such that the greatest common divisor للـ a و الـ
+
+448
+00:51:25,250 --> 00:51:31,820
+b بدو يساوي a في الـ s زائد bT إيش يعني؟ بقول هنا
+
+449
+00:51:31,820 --> 00:51:36,440
+لل greatest common divisor بتقدر تكتبه على صيغة linear
+
+450
+00:51:36,440 --> 00:51:42,600
+combination من العددين A و B يعني بقدر ألاقي عدد
+
+451
+00:51:42,600 --> 00:51:47,120
+أضربه في A وعدد ثاني أضربه في B أجمع يطلع لي ال greatest common 
+
+452
+00:51:47,120 --> 00:51:52,460
+divisor هل حطيت قيود على الـ S و T؟
+
+453
+00:51:52,460 --> 00:51:56,160
+ما حطيتش، يعني يمكن يطلعوا اتنين سالب، يمكن واحد
+
+454
+00:51:56,160 --> 00:52:00,100
+موجب وواحد سالب المهم إن الهدف الصحيح بيهمنيش موجب
+
+455
+00:52:00,100 --> 00:52:05,320
+سالب غيره لكن بيهمنياش إنه فعلا يكون the greatest
+
+456
+00:52:05,320 --> 00:52:09,560
+common divisor هو linear combination من الرقمين
+
+457
+00:52:09,560 --> 00:52:15,350
+اللي عندي من A و B moreover greatest common divisor
+
+458
+00:52:15,350 --> 00:52:21,530
+هو أصغر رقم بقدر أكتبه على صيغة Linear Combination
+
+459
+00:52:21,530 --> 00:52:29,970
+aS زائد bT طيب النتيجة بتقول ليش؟ لو كان الـ a والـ b
+
+460
+00:52:29,970 --> 00:52:34,290
+relatively prime زي الأربعة والسبعة اللي قبل قليل
+
+461
+00:52:34,290 --> 00:52:38,750
+مثلا يبقى then there exists an integer S و T such
+
+462
+00:52:38,750 --> 00:52:43,450
+that يعني قصده يقول لك linear combination هذه الـ
+
+463
+00:52:43,450 --> 00:52:47,390
+greatest common divisor ده بيطلع بقد إيش؟ يبقى الواحد back
+
+464
+00:52:47,390 --> 00:52:53,730
+to record وعلى شكل aS زائد bT طبعا إنها تمثل لكل
+
+465
+00:52:53,730 --> 00:52:58,580
+من النظرية وكل من اللي هو .. وكذلك الـ corollary الـ
+
+466
+00:52:58,580 --> 00:53:02,480
+corollary يعني نتيجة يا شباب على نظرية يعني كانها حالة
+
+467
+00:53:02,480 --> 00:53:05,280
+خاصة الحالة الخاصة لو كان ال greatest common
+
+468
+00:53:05,280 --> 00:53:09,480
+divisor هدف واحد يبقى أقدر أكتب الواحد على صيغة
+
+469
+00:53:09,480 --> 00:53:13,680
+linear combination من مين؟ من الاتنين، هدول نعطي
+
+470
+00:53:13,680 --> 00:53:19,240
+أول مثال على ذلك يبقى example one لو كان الـ
+
+471
+00:53:19,240 --> 00:53:25,860
+greatest common divisor لمين؟ للاتناشر والثلاثين
+
+472
+00:53:26,910 --> 00:53:31,140
+قد إيش ال greatest common divisors كانوا بيلبسوا الـ 12 والـ 30 ستة
+
+473
+00:53:31,140 --> 00:53:38,200
+ممتازة يبقى الستة هذا أكبر رقم بيقسم كل من الاتنين
+
+474
+00:53:38,200 --> 00:53:43,740
+في آن واحد الستة هذا بدي أكتبه على صيغة linear
+
+475
+00:53:43,740 --> 00:53:49,120
+combination من مين؟ من الاتناشر والثلاثين بقوله آه
+
+476
+00:53:49,120 --> 00:53:55,880
+يبقى هذا بيساوي اتناشر في رقم زائد ثلاثين في رقم
+
+477
+00:53:55,880 --> 00:54:05,330
+آخر طيب اتناشر هذه لو ضربتها في سالب اتنين مثلا بصير
+
+478
+00:54:05,330 --> 00:54:11,240
+كده؟ سالب أربعة وعشرين يبقى الفرق بينهم بين
+
+479
+00:54:11,240 --> 00:54:15,960
+الثلاثين قد إيش؟ هو الستة تبعتنا يبقى بروح بضرب هنا
+
+480
+00:54:15,960 --> 00:54:22,380
+قد إيش؟ بواحد يبقى هذا الرقم هو عبارة عن S وهذا
+
+481
+00:54:22,380 --> 00:54:28,160
+الرقم هو عبارة عن مين؟ هو عبارة عن T يبقى للرقمين
+
+482
+00:54:28,160 --> 00:54:33,460
+اتناشر وثلاثين لجيت S بسالب اتنين و لجيت T تساوي
+
+483
+00:54:33,460 --> 00:54:37,090
+واحد بحيث اتناشر في السالب اتنين زائد الثلاثين في
+
+484
+00:54:37,090 --> 00:54:40,810
+واحد يعطينا ال greatest common divisor الرقم ستة الأولي greatest common
+
+485
+00:54:40,810 --> 00:54:46,590
+divisor للاتناشر وال greatest common divisor والثلاثين خد لي كمان مثال
+
+486
+00:54:46,590 --> 00:54:54,480
+آخر يبقى لو جيت قلت المثال رقم اتنين لو جيت الـ
+
+487
+00:54:54,480 --> 00:55:00,840
+greatest common divisor لمين؟ للأربعة والسبعتاشر
+
+488
+00:55:00,840 --> 00:55:06,880
+هدول ما لهم؟ relatively prime صحيح ولا لأ؟ يبقى دول
+
+489
+00:55:06,880 --> 00:55:13,110
+بدو يساوي واحدمش زي اللي هناك يساوي ستة يبقى هذا
+
+490
+00:55:13,110 --> 00:55:19,310
+بدو يساوي أربعة في أبصر قد إيش زائد سبعة عشر في أبصر
+
+491
+00:55:19,310 --> 00:55:28,070
+قد إيش وكذلك سالب أربعة في قد إيش سالب ستة وأنا عندي
+
+492
+00:55:28,070 --> 00:55:32,750
+هنا قد إيش يبقى السبعة عشر بدها قد إيش واحد ليس
+
+493
+00:55:32,750 --> 00:55:36,210
+بالضرورة دائما يطلع واحد ممكن يطلع أي رقم آخر يعني
+
+494
+00:55:36,210 --> 00:55:42,820
+بقدر الله المرة هذه طلع يبقى هذا يمثل الـ S وهذا
+
+495
+00:55:42,820 --> 00:55:48,760
+يمثل الـ T يبقى هاذول اتنين are relatively prime
+
+496
+00:55:48,760 --> 00:55:53,020
+قدرت أكتب الواحد على الشكل الأربعة مضروبة في
+
+497
+00:55:53,020 --> 00:55:57,040
+integer زائد سبعة عشر مضروبة في integer طبق اللي مين
+
+498
+00:55:57,040 --> 00:56:01,370
+لكورولري اللي عندي هذه وبالتالي ما عندي مشكلة في هذه
+
+499
+00:56:01,370 --> 00:56:07,790
+الحالة طيب يا شباب لو جيت قلت رقم تلاتة لو بدي الـ
+
+500
+00:56:07,790 --> 00:56:14,270
+greatest common divisor لمين؟ للاتنين تربيع في 
+
+501
+00:56:14,270 --> 00:56:22,450
+تلاتة تربيع في خمسة كل هذا ضرب والرقم الثاني اثنين
+
+502
+00:56:22,450 --> 00:56:27,150
+في تلاتة تربيع في سبعة تربيع
+
+503
+00:56:29,290 --> 00:56:34,450
+رقمين كبيرين يبقى لو كان عندي رقم كبير بحلله إلى
+
+504
+00:56:34,450 --> 00:56:38,010
+أبسط العوامل بشوف فيه كم اثنين وبعدين كم تلاتة
+
+505
+00:56:38,010 --> 00:56:44,390
+وكم خمسة وكم سبعة وهكذا طيب لو بدي أجيب الجنس
+
+506
+00:56:44,390 --> 00:56:49,510
+ال common divisor للاتنين هدول عشان أحسب هذا بجيب
+
+507
+00:56:49,510 --> 00:56:54,350
+قديش الجنس ال common divisor للاثنين تربيع واثنين
+
+508
+00:56:55,280 --> 00:57:03,200
+أكبر رقم بيقسم الاثنين هو الاثنين اثنين قديش لجريس 
+
+509
+00:57:03,200 --> 00:57:07,520
+ال common divisor للثلاثة تربيع والثلاثة تربيع
+
+510
+00:57:08,190 --> 00:57:14,710
+التسعة يعني ثلاثة تربيع يبقى هذا ثلاثة تربيع قديش
+
+511
+00:57:14,710 --> 00:57:18,870
+اللي جرس ال common divisor للخمسة والسبعة تربيع
+
+512
+00:57:18,870 --> 00:57:23,070
+سبعة يعني تسعة وأربعين مع خمسة  are
+
+513
+00:57:23,070 --> 00:57:27,810
+relatively primed قديش واحد يبقى الجرس ال common
+
+514
+00:57:27,810 --> 00:57:31,710
+divisor لهم اللي هو يساوي واحد تسعة في اثنين في
+
+515
+00:57:31,710 --> 00:57:36,570
+ثمانية عشر يبقى الجرس ال common divisor لهذين العددين
+
+516
+00:57:36,570 --> 00:57:41,630
+يساوي قديش ثمانية عشر وهكذا يبقى الجرس ال common
+
+517
+00:57:41,630 --> 00:57:44,670
+divisor لو كان مجموعة من الأعداد وعندي مجموعة من
+
+518
+00:57:44,670 --> 00:57:49,000
+الأعداد بقارن كل واحد بالجبل هو بطلع قديش لجريس
+
+519
+00:57:49,000 --> 00:57:52,420
+ال common divisor لكل اثنين متجاورين وبعدين بضربهم
+
+520
+00:57:52,420 --> 00:57:57,060
+في بعض بطلع قديش لجريس ال common divisor لمين؟ لكل
+
+521
+00:57:57,060 --> 00:58:01,420
+الأعداد يبقى لحد هنا أستوب المرة الجاية إن شاء
+
+522
+00:58:01,420 --> 00:58:06,120
+الله بنكمل يوم الاثنين وهجيك المرة الجاية هبدأ
+
+523
+00:58:06,410 --> 00:58:11,090
+بلمّة وبرهين نبدأ بنقول احنا حتى لا ما برهناش ولا
+
+524
+00:58:11,090 --> 00:58:14,730
+حاجة بنعطي بعض المعلومات الأساسية وبنحاول نثبت
+
+525
+00:58:14,730 --> 00:58:19,990
+هالمعلومة بواسطة من؟ بواسطة أمثلة مختلفة يمكن
+
+526
+00:58:19,990 --> 00:58:23,530
+الكلام اللي بقوله كثير منه تفتحه بتلاقيه أمثلة
+
+527
+00:58:23,530 --> 00:58:27,290
+لكن أنا بعطيك أمثلة مش هنثبت المعلومة عندك لأن
+
+528
+00:58:27,290 --> 00:58:31,010
+المعلومة القديمة عندك بس بنحاول نثبتها من خلال
+
+529
+00:58:31,010 --> 00:58:33,130
+الأمثلة يعطيكم العافية 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..609878a3c2f33441b1b144b42e9dabee5aeb4cf1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_postprocess.srt
@@ -0,0 +1,2116 @@
+1
+00:00:20,990 --> 00:00:25,090
+بسم الله الرحمن الرحيم الان نبدأ في الموضوع اللي
+
+2
+00:00:25,090 --> 00:00:30,190
+أشارناه الصبح وهو ال chapter المقدمة اللي بتحدث عن
+
+3
+00:00:30,190 --> 00:00:35,210
+تذكير ببعض ما درس في مبادئ الرياضيات و اللي هنأسس
+
+4
+00:00:35,210 --> 00:00:40,850
+عليه دراستنا في علم algebra قبل أن نبدأ بأي نقطة
+
+5
+00:00:40,850 --> 00:00:45,230
+في هذا ال chapter بحب نذكر بمجموعة ال sets اللي
+
+6
+00:00:45,230 --> 00:00:49,350
+عليها بدنا نبني دراستنا ان شاء الله تبارك وتعالى
+
+7
+00:00:49,860 --> 00:00:55,140
+أول set من هذه ال sets يبقى مضاجي أقول اللي هو ال
+
+8
+00:00:55,140 --> 00:01:00,760
+sets المجموعات أول set من هذه ال sets اللي هو the
+
+9
+00:01:00,760 --> 00:01:04,560
+set of
+
+10
+00:01:04,560 --> 00:01:14,560
+natural numbers هذا هديها الرمز capital N
+
+11
+00:01:23,950 --> 00:01:33,190
+النقطة التانية هي the set ofIntegers مجموعة
+
+12
+00:01:33,190 --> 00:01:41,910
+الاعداد الصحيحة اللي هديها الرمز Z عناصرها هي نقط
+
+13
+00:01:41,910 --> 00:01:49,370
+سالب تلاتة سالب اتنين سالب واحد زيرو واحد اتنين
+
+14
+00:01:49,370 --> 00:01:56,070
+تلاتة الى اخرىيبقى مجموعة الأعداد الصحيحة الموجبة
+
+15
+00:01:56,070 --> 00:02:01,910
+والسالبة والصفر بنسميها the set of integers يبقى
+
+16
+00:02:01,910 --> 00:02:08,400
+اللي فوق أشهر بسميها شبابthe set of positive
+
+17
+00:02:08,400 --> 00:02:16,200
+integers يعني ممكن اقول هذه هي z plus z plus يبقى
+
+18
+00:02:16,200 --> 00:02:20,720
+the set of positive integers يعني معناته مجموعة
+
+19
+00:02:20,720 --> 00:02:26,360
+الأعداد الصحيحة الموجبة اللي بتاخد الأعداد من هنا
+
+20
+00:02:26,360 --> 00:02:34,720
+و لغاية الخلف تمام المجموعة التالتة the setof
+
+21
+00:02:34,720 --> 00:02:44,680
+rational numbers مجموعة الأعداد النسبية او مجموعة
+
+22
+00:02:44,680 --> 00:02:49,620
+الأعداد الجذرية هنديلها رمز و الرمز هذا هيظل معانا
+
+23
+00:02:49,620 --> 00:02:54,680
+موجود في الكتابة على طول الخط الرمز هذا كاب تالي
+
+24
+00:02:54,680 --> 00:03:00,910
+كيوEqually the set of all elements A على B such
+
+25
+00:03:00,910 --> 00:03:07,570
+that الـ A والـ B belongs to Z and وفي نفس الوقت
+
+26
+00:03:07,570 --> 00:03:13,310
+الـ B ممنوع تساوي Zero على الإطلاقلأن لو ال بيه
+
+27
+00:03:13,310 --> 00:03:19,470
+سوى Zero بصير إيه ماهياش معرفة يبقى كل الأعداد
+
+28
+00:03:19,470 --> 00:03:24,590
+اللي على الشكل أعلى بيه بحيث أهوا بأعداد صحيحة وفي
+
+29
+00:03:24,590 --> 00:03:30,910
+نفس الوقت بيه ممنوع يساوي Zero الست الرابع اللي هي
+
+30
+00:03:30,910 --> 00:03:36,150
+the set of real numbers
+
+31
+00:03:38,600 --> 00:03:44,020
+اللي هي مجموعة الأعداد الحقيقية يبقى لو جيت قولت
+
+32
+00:03:44,020 --> 00:03:50,220
+هذا ال real life يبقى هنا zero و هنا واحد و هنا
+
+33
+00:03:50,220 --> 00:03:55,240
+اتنين الاخره و سالب واحد سالب اتنين و الأعداد اللي
+
+34
+00:03:55,240 --> 00:04:01,010
+موجودة كذلك بينهماكل ال rational و ال irrational
+
+35
+00:04:01,010 --> 00:04:06,890
+number يعني ال set of real numbers هذه حديها الرمز
+
+36
+00:04:06,890 --> 00:04:12,330
+capital Rيبقى من حد ما نشوف capital R في الكتاب
+
+37
+00:04:12,330 --> 00:04:15,630
+اللي عندنا يبقى the set of real numbers مجموعة
+
+38
+00:04:15,630 --> 00:04:21,650
+الأعداد الحقيقية الصحيحة و غير الصحيحة نسبية و غير
+
+39
+00:04:21,650 --> 00:04:28,810
+النسبية بيجينا بعد هيك الأخيرة اللي هو the set of
+
+40
+00:04:28,810 --> 00:04:36,920
+complex numbers complex numbersمجموعة الأعداد
+
+41
+00:04:36,920 --> 00:04:43,240
+المركبة أو مجموعة الأعداد التخيلية يبقى هذه the
+
+42
+00:04:43,240 --> 00:04:51,500
+set of all elements a زائد bi بحيث أن ال a وال b
+
+43
+00:04:51,500 --> 00:04:58,660
+موجودة في R وفي نفس الوقت ال I يسوى الجذر التربيع
+
+44
+00:04:58,660 --> 00:05:05,360
+لمين لسالب واحديبقى بيان اقول زمان في الثانوية
+
+45
+00:05:05,360 --> 00:05:11,420
+العامة العدو الموركة بالـC زائد صاد T حيث T اللي
+
+46
+00:05:11,420 --> 00:05:16,800
+هو الحرف الأول من كلمة تخيلي واحنا هنا A زائد Bi
+
+47
+00:05:16,800 --> 00:05:23,840
+حيث I العدد للحرف الأول من كلمة imaginary تخيلي
+
+48
+00:05:23,840 --> 00:05:30,490
+تمام يبقى ال I هذا هو ال square root زمان-1 يبقى
+
+49
+00:05:30,490 --> 00:05:35,750
+هو الجدرى التربية إلى أمام لـ-1 إيش بتلاحظوا على
+
+50
+00:05:35,750 --> 00:05:40,930
+ال 6 الخمسة اللي عندنا هذه شو العلاقة بين N و Z
+
+51
+00:05:40,930 --> 00:05:49,490
+ده؟ممتاز يبقى N subset من Z طب Z ماعليك يوم subset
+
+52
+00:05:49,490 --> 00:05:56,330
+منها لإنه أي integer هو عبارة عن مين عبارة عن اللي
+
+53
+00:05:56,330 --> 00:06:01,950
+هو rational number زي ايش مثلا زي خمسة الخمسة بقدر
+
+54
+00:06:01,950 --> 00:06:06,530
+كتب خمسة على واحد يبقى صرت على الشكل A على B
+
+55
+00:06:06,530 --> 00:06:10,510
+الخمسة والواحد موجودة في Z والمقام لا يساوي Zero
+
+56
+00:06:10,510 --> 00:06:15,200
+اللي هو واحديبقى any integer is a rational number
+
+57
+00:06:15,200 --> 00:06:19,420
+but the converse is not necessarily true ليس
+
+58
+00:06:19,420 --> 00:06:26,160
+بالضرورة صحيحا بعد هيك ال Q هذا subset من R ولا لا
+
+59
+00:06:26,160 --> 00:06:31,820
+اي عدد نسبي هو عبارة عن عدد حقيقي لكن العكس ليس
+
+60
+00:06:31,820 --> 00:06:37,310
+بالضرورة صحيحا يعني مثلا زي جدر تلاتةعدد غير نسبي
+
+61
+00:06:37,310 --> 00:06:42,330
+هذا زي باي عدد غير نسبي زي العدد ايه اللي هو اتنين
+
+62
+00:06:42,330 --> 00:06:47,010
+وسبعة من حشرة وحط كصور إلى مال نهاية يبجي هذه كلها
+
+63
+00:06:47,010 --> 00:06:53,940
+أعداد irrational number أعداد غير نسبيةطيب الآن ال
+
+64
+00:06:53,940 --> 00:06:58,840
+R هي subset من مين؟ من ال 6 of complex numbers
+
+65
+00:06:58,840 --> 00:07:04,360
+يعني any real number is a complex number بس ال
+
+66
+00:07:04,360 --> 00:07:08,480
+converse is not necessarily true مثال و ذلك لو جيت
+
+67
+00:07:08,480 --> 00:07:09,580
+قولتلك نص
+
+68
+00:07:12,360 --> 00:07:18,960
+بقدر اكتب نص زائد زيرو في I يبقى النص وزيرو
+
+69
+00:07:18,960 --> 00:07:23,740
+موجودات في R وال I يسوى الجدر التربية إلى سالب
+
+70
+00:07:23,740 --> 00:07:30,510
+واحديبقى أي عدد حقيقي هو عدد تخيلي أو هو عدد مركب
+
+71
+00:07:30,510 --> 00:07:36,010
+لكن العكس ليس بالضرورة صحيحا يبقى بناء عليه بروح
+
+72
+00:07:36,010 --> 00:07:44,050
+بقوله ال N هذه هي subset من Z و Z هذه subset من ال
+
+73
+00:07:44,050 --> 00:07:51,610
+Q و ال Q subset من R و ال R subset من 6 of complex
+
+74
+00:07:51,610 --> 00:07:56,050
+numberيبقى هذه ما كتبناش رمزة بديها الرمز capital
+
+75
+00:07:56,050 --> 00:08:02,850
+من capital C يبقى N subset من Z, Z subset من ال Q,
+
+76
+00:08:02,990 --> 00:08:06,730
+ال Q subset من R, ال R subset من Z و complex
+
+77
+00:08:06,730 --> 00:08:12,680
+number كابتل Cيبقى هذه ال six الخامسة اللي وان ما
+
+78
+00:08:12,680 --> 00:08:16,400
+نيجي و احنا خلال دراستنا في الجبر بيطلعولك ال six
+
+79
+00:08:16,400 --> 00:08:21,060
+دول يطلع واحدة يطلع سنتين يطلع تلاتة في كل مرة
+
+80
+00:08:21,060 --> 00:08:25,340
+بتطلع بعض ال six اللي عندنا هذا بدنا نيجي ل مين
+
+81
+00:08:25,340 --> 00:08:29,320
+للف reporties of انتجارز
+
+82
+00:08:30,870 --> 00:08:36,410
+يبقى بدنا نيجي لأول definition عندنا هنا بالنسبة
+
+83
+00:08:36,410 --> 00:08:44,610
+لل integers فبجي بقول a non zero a non zero
+
+84
+00:08:44,610 --> 00:08:52,190
+integer a
+
+85
+00:08:52,190 --> 00:09:03,460
+non zero integer T is a divisoris a divisor of an
+
+86
+00:09:03,460 --> 00:09:23,060
+integer s if there is an integer u if there is an
+
+87
+00:09:23,060 --> 00:09:26,880
+integer u
+
+88
+00:09:29,260 --> 00:09:33,960
+such that
+
+89
+00:09:33,960 --> 00:09:47,580
+بحيث ان ال S بده يساوي T في ال U we
+
+90
+00:09:47,580 --> 00:09:56,680
+are right بروح نكتب ان T divides ال S
+
+91
+00:10:00,660 --> 00:10:07,440
+if T does
+
+92
+00:10:07,440 --> 00:10:21,010
+not divide ال S لو ال T مقسمتش ال S we writeبنروح
+
+93
+00:10:21,010 --> 00:10:30,850
+نكتب ان الـ T does not divide ال S definition تاني
+
+94
+00:10:30,850 --> 00:10:34,050
+a
+
+95
+00:10:34,050 --> 00:10:41,290
+prime number P is
+
+96
+00:10:41,290 --> 00:10:44,970
+a positive integer
+
+97
+00:10:50,690 --> 00:10:58,950
+integer greater than
+
+98
+00:10:58,950 --> 00:11:07,830
+one أكبر من الواحد الصحيح who's only
+
+99
+00:11:07,830 --> 00:11:12,350
+positive divisors are
+
+100
+00:11:19,590 --> 00:11:30,810
+اللي هو main one and be itself be itself ال
+
+101
+00:11:30,810 --> 00:11:37,670
+definition الثالث والأخير في هذه المجموعة an
+
+102
+00:11:37,670 --> 00:11:41,690
+integer S
+
+103
+00:11:41,690 --> 00:11:56,360
+is a multiplea multiple of is
+
+104
+00:11:56,360 --> 00:12:09,760
+a multiple of an integer T if there is if there is
+
+105
+00:12:09,760 --> 00:12:13,740
+if
+
+106
+00:12:13,740 --> 00:12:14,460
+there is
+
+107
+00:12:17,990 --> 00:12:32,950
+and integer U such that بحيث ان ال S بدها تساوي T
+
+108
+00:12:32,950 --> 00:12:33,690
+في ال U
+
+109
+00:12:55,300 --> 00:12:59,960
+هنا نجي لبعض الخواص على مين على مجموعة الأعداد
+
+110
+00:12:59,960 --> 00:13:05,020
+الصحيحة الثانية اللي هي المجموعة Z في عندنا three
+
+111
+00:13:05,020 --> 00:13:10,120
+definitions هذه three definitions أساسية لها ما
+
+112
+00:13:10,120 --> 00:13:16,630
+بعدها أثناء دراستنابنجي للتعريف الأول بدنا نعرف
+
+113
+00:13:16,630 --> 00:13:21,850
+العدد الذي يقسم عدد أخر شو معناه رياضيا التعريف
+
+114
+00:13:21,850 --> 00:13:25,890
+التاني بتكلم عن الأعداد الأولية التعريف التالف
+
+115
+00:13:25,890 --> 00:13:31,350
+يتكلم عن مضاعفات الأعداد اللي هو في شبه بينه بين
+
+116
+00:13:31,350 --> 00:13:36,680
+التعريف الأول إلى حد مافبجي بقول a non zero
+
+117
+00:13:36,680 --> 00:13:42,880
+integer T is a divisor of an integer S يبقى T وS
+
+118
+00:13:42,880 --> 00:13:50,760
+أعداد صحيحة يبقى كلهم موجودات في Z فبجي بقول T هو
+
+119
+00:13:50,760 --> 00:13:57,850
+قاسم للعدد S يعني بيقسم لعدد Sإذا جدرت انا لاجي
+
+120
+00:13:57,850 --> 00:14:01,870
+integer U
+
+121
+00:14:01,870 --> 00:14:10,030
+بحيث ان ال S بده يسوى من T في U يعني ال T بيقسم ال
+
+122
+00:14:10,030 --> 00:14:15,500
+Sإذا جدرت لاجي رقم تاني اضربه في T يطلع من؟ يطلع
+
+123
+00:14:15,500 --> 00:14:21,440
+ال S إن حدث ذلك بروح بكتب T تقسم ال S يبقى هذه
+
+124
+00:14:21,440 --> 00:14:29,410
+الإشارة معناها Divide يقسم هذه معناها Divideيبقى
+
+125
+00:14:29,410 --> 00:14:36,590
+هنا T قاسم ال S او T بيقسم ال S مثال و ذلك لو جهت
+
+126
+00:14:36,590 --> 00:14:45,410
+تقولك اربعة divide اللي هو من العشرين ليش؟ because
+
+127
+00:14:45,410 --> 00:14:49,390
+العشرين
+
+128
+00:14:49,390 --> 00:14:55,130
+هذه بدها تساوي اربعة في عدد تاني ابصرية تطلع من؟
+
+129
+00:14:55,130 --> 00:14:57,350
+من يطلع؟ خمسة
+
+130
+00:15:00,230 --> 00:15:04,030
+يبقى اربعة في خمسة تساوي كده؟ تساوي عشرين انا بدي
+
+131
+00:15:04,030 --> 00:15:07,250
+احط الخمسة بين قصين حتى ما تقوليش هذه اربعة و نص
+
+132
+00:15:07,250 --> 00:15:15,730
+لأ المقصود هنا ضرب تمام زي مثلا لو جيت قولتلك مثلا
+
+133
+00:15:15,730 --> 00:15:22,490
+ناقص تلاتين ناقص تلاتين او بديش اقول ناقص تلاتين
+
+134
+00:15:22,490 --> 00:15:32,540
+بدي اقول الستة divides ناقص تلاتينالستة تقسم ناقص
+
+135
+00:15:32,540 --> 00:15:41,700
+تلاتين لماذا؟ لأن ناقص تلاتين ساوي ستة أبصر في مين
+
+136
+00:15:41,700 --> 00:15:47,960
+ما هو الرقم اللي نرغب أن يكون في ستة سالب تلاتين
+
+137
+00:15:47,960 --> 00:15:55,150
+واضح أنه سالب خمسة كذلكطيب يبقى في هذه الحالة بروح
+
+138
+00:15:55,150 --> 00:16:02,610
+نكتب انه ستة بتقسم التلاتين لكن هل الستة بتقسم
+
+139
+00:16:02,610 --> 00:16:06,950
+مثلا اللي هو ستة وعشرين مثلا؟
+
+140
+00:16:09,690 --> 00:16:15,650
+تقسمه؟ لأ يبقى برف أكتب الستة لا تقسم اللي هو من
+
+141
+00:16:15,650 --> 00:16:21,470
+الستة وعشرين لإنه لا يمكن ألاقي انتجار عدد صحيح
+
+142
+00:16:21,470 --> 00:16:26,430
+أضربه في الستة يطلع الجواب قد ستة وعشرين مافيش
+
+143
+00:16:26,430 --> 00:16:29,310
+عندى بالمرة في هذه الحالة طيب
+
+144
+00:16:34,000 --> 00:16:38,960
+العدد الأول P هو عبارة عن positive integer greater
+
+145
+00:16:38,960 --> 00:16:43,780
+than one يبقى العدد الأول هو عدد الخصية الأولى
+
+146
+00:16:43,780 --> 00:16:48,900
+أكبر من الواحد الصحيحالخاصية الثانية بيقول who is
+
+147
+00:16:48,900 --> 00:16:54,820
+only positive divisors القواسم المشتركة لهذا العدد
+
+148
+00:16:54,820 --> 00:17:00,580
+الصحيح اتنين بس رقمين مين هما الواحد الصحيح هو
+
+149
+00:17:00,580 --> 00:17:06,660
+العدد في itself نفسه يبقى لا يوجد قواسم لهذا العدد
+
+150
+00:17:06,660 --> 00:17:12,000
+إلا العدد نفسه وكذلك مين الواحد الصحيح طيب ببناء
+
+151
+00:17:12,000 --> 00:17:17,880
+عليه هل اتنين يا شباب prime numberتنين عدد أولى؟
+
+152
+00:17:17,880 --> 00:17:23,060
+أه لأن هذا الصحية أكبر من الواحد الصحية و لا يقسم
+
+153
+00:17:23,060 --> 00:17:27,580
+إلا الواحد و الاتنين طب التلاتة prime number؟ أه
+
+154
+00:17:27,580 --> 00:17:31,060
+طب الأربعة؟ لأ ماهواش prime number لأن الأربعة
+
+155
+00:17:31,060 --> 00:17:35,300
+بتيجي اسمه اتنين غير حكاية الأربعة طب الخامسة؟
+
+156
+00:17:35,300 --> 00:17:42,790
+prime number؟ ستة؟ سبعة؟صحيح تمانية لأ تسعة لأ
+
+157
+00:17:42,790 --> 00:17:48,090
+برضه و لو انه فردي تمام يبقى ال prime number هم
+
+158
+00:17:48,090 --> 00:17:53,570
+واحد اتنين صحيح غلط الواحد لا استفد واحد لازم يكون
+
+159
+00:17:53,570 --> 00:17:58,140
+اكبر واحد يبقى ببدأ من ويمحط لي معلومتك ان اتنين
+
+160
+00:17:58,140 --> 00:18:03,860
+هو الرقم الزوجي الوحيد اللي هو prime number لو طلع
+
+161
+00:18:03,860 --> 00:18:08,040
+بعدك اربعة ستة تمانية كلها بتقسم على اتنين تمام
+
+162
+00:18:08,040 --> 00:18:11,540
+يبقى العدد الزوجي الوحيد اللي هو prime number
+
+163
+00:18:11,540 --> 00:18:16,040
+مافيش غير اتنين والباجي كلها اعداد فردية بس مش كل
+
+164
+00:18:16,040 --> 00:18:20,280
+الاعداد الفردية يبقى الاعداد ال prime number اتنين
+
+165
+00:18:20,280 --> 00:18:31,540
+تلاتة خمسة سبعة احداشر تلتاشرسبعتاش تسعتاش تلاتة و
+
+166
+00:18:31,540 --> 00:18:39,040
+عشرين تسعة و عشرين واحد و تلاتين و هكذا يبقى سبعة
+
+167
+00:18:39,040 --> 00:18:44,570
+و تلاتين يبقى كلها هذه ال numberيبقى العدد الأولي
+
+168
+00:18:44,570 --> 00:18:48,630
+هو العدد اللذي لا يقسم إلا على نفسه وعلى الواحد
+
+169
+00:18:48,630 --> 00:18:54,210
+الصحيح تمام؟ يبقى هادمين دير بالك هتلعب دور كبير
+
+170
+00:18:54,210 --> 00:18:58,010
+عندنا لما نخش على الشبطر التاني وشبطر ال groups
+
+171
+00:18:58,010 --> 00:19:03,570
+يبقى هنجيب groups الأعداد تبعها أعداد أولية دير
+
+172
+00:19:03,570 --> 00:19:08,250
+بالك يبقى صح صح من الآن هذه very important خلال
+
+173
+00:19:08,250 --> 00:19:14,960
+دراستنا طيبنجد تانية أن integer S is a multiple of
+
+174
+00:19:14,960 --> 00:19:23,160
+an integer T يبقى ال S هو مضاعفات العدد T وقت إذا
+
+175
+00:19:23,160 --> 00:19:28,480
+جدرت لاجي عدد تاني U بحيث ال S بدأ تسوى 100 T في U
+
+176
+00:19:28,480 --> 00:19:33,540
+أظن نفس الكلام اللي عندنا هنا صح ولا لا؟يبقى
+
+177
+00:19:33,540 --> 00:19:39,320
+مضاعفات الأعداد الـ
+
+178
+00:19:39,320 --> 00:19:45,860
+S ومضاعفات العدد T إذا قدرت ألجن تجارب U بحيث الـ
+
+179
+00:19:45,860 --> 00:19:46,060
+S
+
+180
+00:19:49,810 --> 00:19:55,010
+العشرين هو مضاعفات الأربعة، لماذا؟ لأن العشرين
+
+181
+00:19:55,010 --> 00:20:00,730
+سيكونوا أربعة في رقم كان الخمسة، العدد ناقص تلاتين
+
+182
+00:20:00,730 --> 00:20:05,810
+هو مضاعفات الستة، لماذا؟ لأن ناقص تلاتين هو ستة في
+
+183
+00:20:05,810 --> 00:20:10,070
+من؟ في ناقص خمسة، يبقى العدد يطلع موجة، والله سلم،
+
+184
+00:20:10,070 --> 00:20:14,770
+لا تفرج عندي، يبقى هذا معنى مضاعفات العدديبقى
+
+185
+00:20:14,770 --> 00:20:18,630
+المعادلة تبعت مضاعفات العدد والمعادلة تبعت القسم
+
+186
+00:20:18,630 --> 00:20:24,110
+التنتين زي بعض بس كل واحدة إلها مفهوم هنا T بتقسم
+
+187
+00:20:24,110 --> 00:20:29,550
+العدد S يعني إيش؟ يعني لو قسمت S على T الناتج هو
+
+188
+00:20:29,550 --> 00:20:37,070
+عدد صحيح اسمه U هنا ال S هو مضاعفات ال T إذا جدرت
+
+189
+00:20:37,070 --> 00:20:41,630
+ألاقي رقم تاني أضربه في T يطلع من عنده يطلع عند S
+
+190
+00:20:41,630 --> 00:20:50,200
+و هكذايبقى هذا المثال اللي عندنا طيب إيش رأيك؟ أي
+
+191
+00:20:50,200 --> 00:20:52,640
+عدد عندى بيقسم ال zero ولا لأ؟
+
+192
+00:20:55,840 --> 00:21:00,340
+الخمسين بتقسم Zero ولا لا؟ Zero على خمسين بتسوى
+
+193
+00:21:00,340 --> 00:21:06,240
+Zero إذا أي رقم عندي صحيح بيقسم مين؟ بيقسم Zero
+
+194
+00:21:06,240 --> 00:21:10,240
+صحيح ولا غير صحيح حتى لو كان real number لكن مادام
+
+195
+00:21:10,240 --> 00:21:15,300
+نتكلم في integers يبقى كلامنا على ال integers يبقى
+
+196
+00:21:15,300 --> 00:21:20,640
+اتنين هنا بقدر اقول every non zero integer every
+
+197
+00:21:20,640 --> 00:21:24,340
+non zero
+
+198
+00:21:26,530 --> 00:21:39,190
+integer وليكن n divides ال zero because السبب لإن
+
+199
+00:21:39,190 --> 00:21:48,010
+ال zero بده يساوي ال n في ال zero itself also
+
+200
+00:21:48,010 --> 00:22:01,540
+وكذلك ال واحد بيقسم ال nلش؟ because ال N تساوي
+
+201
+00:22:01,540 --> 00:22:16,020
+واحد ضرب ال N يعني
+
+202
+00:22:16,020 --> 00:22:19,500
+كل حاجة بنقدر نحطها على شكل المعادلة اللي عندنا
+
+203
+00:22:19,500 --> 00:22:23,360
+هذه و خلاص بيصير كلامنا صحيح
+
+204
+00:22:31,330 --> 00:22:35,710
+ننتقل إلى نقطة مهمة جدا و هي ال will ordering
+
+205
+00:22:35,710 --> 00:22:44,970
+principle حاجة اسمها ال will ordering principle
+
+206
+00:22:44,970 --> 00:22:50,670
+بتقول
+
+207
+00:22:50,670 --> 00:22:57,390
+ما ياتي every non zero every
+
+208
+00:22:57,390 --> 00:23:16,050
+non zero setof positive integers contains
+
+209
+00:23:16,050 --> 00:23:25,090
+a smallest member
+
+210
+00:23:39,830 --> 00:23:46,230
+قاعدة الترتيب الجيد لو
+
+211
+00:23:46,230 --> 00:23:52,250
+جينا قولنا بدنا ناخد set بس ال set هذي بيبقى non
+
+212
+00:23:52,250 --> 00:23:57,070
+-zero of positive integers يبقى انا بدي اعداد
+
+213
+00:23:57,070 --> 00:24:02,520
+صحيحة كلها موجبة ولا يوجد فيها صفرلو أخدت هذه
+
+214
+00:24:02,520 --> 00:24:07,440
+المجموعة مثلا لو جيت مجموعة الشباب اللي هنا جيت
+
+215
+00:24:07,440 --> 00:24:12,720
+أخدت أعمارهم بقيت ولا واحد عمره زي التاني وأخدتهم
+
+216
+00:24:12,720 --> 00:24:18,440
+مثلا بدي أخد شهور أو أيام أو سنين ليه السهولة بدي
+
+217
+00:24:18,440 --> 00:24:22,800
+أخد سنين طبعا كلهم نفس السنة تقريبا لكن أنا جدا
+
+218
+00:24:22,800 --> 00:24:26,840
+اللي بدي أسمي حالي لأ عمرهم مش زي بعض يبقى لجيت
+
+219
+00:24:26,840 --> 00:24:31,470
+واحد عمره مثلا اللي هو سبعتاشر سنةواحد تمانتاشر
+
+220
+00:24:31,470 --> 00:24:34,310
+سنة وواحد تسعة عشر سنة وواحد عشرين وواحد واتنين
+
+221
+00:24:34,310 --> 00:24:37,990
+وعشرين يبقى هذه المجموعة اللى خدتها لازم ألاقي
+
+222
+00:24:37,990 --> 00:24:44,310
+واحد فيهم عمره أقل ما يمكن بالنسبة لمين للآخرين
+
+223
+00:24:44,310 --> 00:24:47,470
+يبقى أي مجموعة من الأعداد تاخدها بالترتيب والله
+
+224
+00:24:47,470 --> 00:24:51,170
+عشوائي لو أخدت خمسين وثلاثاشر واربع وعشرين واتنين
+
+225
+00:24:51,170 --> 00:24:55,440
+وتلاتين وواحد وستين ومية وواحد وعشرينيبقى هذه
+
+226
+00:24:55,440 --> 00:24:59,000
+مجموعة الأرقام كلها non-zero انتجة لازم ألاقي واحد
+
+227
+00:24:59,000 --> 00:25:03,560
+فيهم بيكون أقل من باقي مين من باقي الأرقام هذه
+
+228
+00:25:03,560 --> 00:25:08,380
+الترتيب وبالتالي ممكن أرتبهم فعلا ترتيب جيد أو
+
+229
+00:25:08,380 --> 00:25:12,700
+ترتيب حسب واحد بعد التاني حسب الأقل من اللي بعده
+
+230
+00:25:12,700 --> 00:25:16,200
+اللي بعده أقل من اللي بعده اللي بعده أقل من مين من
+
+231
+00:25:16,200 --> 00:25:20,760
+اللي بعده يبقى هذه المقصود فيهاevery non-zero set
+
+232
+00:25:20,760 --> 00:25:24,020
+of positive integers contains a smallest member
+
+233
+00:25:24,020 --> 00:25:28,300
+يبقى فيها عوضه أو فيها عنصر بيكون ماله أقل ما يمكن
+
+234
+00:25:28,300 --> 00:25:34,380
+من نفسه لمهم للعناصر الأخرى ننتقل الآن لنقطة مهمة
+
+235
+00:25:34,380 --> 00:25:38,400
+جدا خلال دراستنا في الجابرة لزمان أكتر من اللي
+
+236
+00:25:38,400 --> 00:25:42,360
+قدامنا هذه كثيرة جدا اللي هي division algorithm
+
+237
+00:25:42,360 --> 00:25:48,740
+خوارزمية القسمةنشوف ايش بتقول و نعطي بعض التطبيقات
+
+238
+00:25:48,740 --> 00:25:56,320
+عليها يبقى بدنا نيجي لل division algorithm
+
+239
+00:25:56,320 --> 00:26:01,480
+خوارزمية
+
+240
+00:26:01,480 --> 00:26:10,660
+القسمة بتقول لمية الات ال a and ال b
+
+241
+00:26:34,100 --> 00:26:37,780
+يوجد ايونيك انتجار
+
+242
+00:26:45,640 --> 00:26:58,240
+a unique integers اللي هو Q and ال R Q and ال R
+
+243
+00:26:58,240 --> 00:27:02,540
+with property
+
+244
+00:27:02,540 --> 00:27:15,170
+ذات with property ذات ان ال Aبتساوي ال بي كيو زائد
+
+245
+00:27:15,170 --> 00:27:24,150
+ال R where حيث ال R أكبر من أو تساوي ال zero أقل
+
+246
+00:27:24,150 --> 00:27:34,870
+من مين و أقل من بي نقطة مهمة جدا هنا if ال بي
+
+247
+00:27:34,870 --> 00:27:47,720
+بتقسم ال a thenالـ R بدا تساوي Zero That is I N ال
+
+248
+00:27:47,720 --> 00:27:52,240
+A بدا تساوي BQ في هذه الحالة
+
+249
+00:28:29,960 --> 00:28:37,500
+كلمة خوارزمية منسوبة إلى مؤسس علم الجبر اللى هو
+
+250
+00:28:37,500 --> 00:28:43,620
+مين؟ إيش اسمه؟ مين؟ اسمه محمد بن موسى الخوارزمى
+
+251
+00:28:43,620 --> 00:28:49,080
+اللى عاش في العصر العباسى واللى وضع كثير من قوانين
+
+252
+00:28:49,080 --> 00:28:55,200
+رياضيات اللى تدرس من ذلك الوقت وإلى يومنا هذاخاصة
+
+253
+00:28:55,200 --> 00:29:00,100
+في calculus ايه وفي الجبر تبع التنمية والاعدادية
+
+254
+00:29:00,100 --> 00:29:04,440
+وفي الهندسة يعني اللي هو خاصة حساب المثلثات هذه
+
+255
+00:29:04,440 --> 00:29:08,960
+الجوا الجتا هو اول من وضعها في التاريخ يبقى لما
+
+256
+00:29:08,960 --> 00:29:12,240
+اقول division algorithm خوارزمية القسم اقول لو
+
+257
+00:29:12,240 --> 00:29:18,440
+اخدت اي عددين a وb بعد تبقى اعداد صحيحة وb دائما
+
+258
+00:29:18,440 --> 00:29:24,450
+وابدا مالهأكبر من الـ zero يبقى أخدت أعداد صحية ب
+
+259
+00:29:24,450 --> 00:29:29,250
+أكبر من ال zero هل اشترت a أكبر من ال zero ليس
+
+260
+00:29:29,250 --> 00:29:33,830
+بالضرورة ممكن يكون ال a بالسالم لكن بي بديها
+
+261
+00:29:33,830 --> 00:29:37,930
+بالموجة then there will exist a unique integers
+
+262
+00:29:37,930 --> 00:29:44,420
+هلاجي عددين وحيدين مافيش غيرهممرتبطين مع a وb كيف
+
+263
+00:29:44,420 --> 00:29:50,580
+اللي هم الخاصية التالية ان ال a تساوي b في ال q
+
+264
+00:29:50,580 --> 00:29:57,720
+يعني مضاعفات ال b زائد r حيث ر هذي اكبر من او
+
+265
+00:29:57,720 --> 00:30:03,840
+تساوي zero اقل من b لو ال r تساوي zero يبقى ايه
+
+266
+00:30:03,840 --> 00:30:10,350
+ايش بتساويB في Q صحيح ولا لأ الار تسوى Zero يبقى
+
+267
+00:30:10,350 --> 00:30:16,430
+ال A يسوى ال B في ال Q معناه هذا الكلام ان ال A هي
+
+268
+00:30:16,430 --> 00:30:24,240
+مضعفات من ال B او ال B تقسم من تقسم ال Aيبقى يا
+
+269
+00:30:24,240 --> 00:30:28,980
+شباب هذا ال condition ضروري جدا very important
+
+270
+00:30:28,980 --> 00:30:34,900
+دايما يا بده يساوي zero يا أكبر من zero إذا سوى
+
+271
+00:30:34,900 --> 00:30:40,380
+zero معناته ال B بتقسم ال A أو ال A هي مضاعفات ال
+
+272
+00:30:40,380 --> 00:30:47,060
+Bإذا كان الـ A الـ B لا تقسيم الـ A يبقى الـ R بدي
+
+273
+00:30:47,060 --> 00:30:52,260
+أخذ قيمة أكبر من الـ 0 لكن دائما و أبدا مالها أقل
+
+274
+00:30:52,260 --> 00:30:55,500
+من الـ B لأن لو سوى الـ B بصير الـ R بـ 0 على طول
+
+275
+00:30:55,500 --> 00:30:59,940
+الخط يبقى الـ R دائما و أبدا محصورة ما بين الـ 0 و
+
+276
+00:30:59,940 --> 00:31:05,280
+بين الـ B اليومين العدد الثاني اللي عندنا تمام؟
+
+277
+00:31:05,280 --> 00:31:09,820
+يبقى هذه خوارزمية القسمة نعطي أمثلة examples
+
+278
+00:31:13,630 --> 00:31:18,670
+أول مثال بدي أخد a برقم و أخد b برقم و نشوف كيف
+
+279
+00:31:18,670 --> 00:31:24,430
+نسوي خوارزمية القسمة لو كان مثلا ال a بده يساوي
+
+280
+00:31:24,430 --> 00:31:34,410
+تسعة عشر and ال b كان مثلا بده يساوي خمسة يبقى
+
+281
+00:31:34,410 --> 00:31:39,750
+باجي بقوله the division algorithm
+
+282
+00:31:46,430 --> 00:31:53,370
+التسعة عشر هذه بدى اكتبها بدلالة مين بدلالة الخمسة
+
+283
+00:31:53,370 --> 00:32:00,010
+يبقى هذه بده تساوي الخمسة مضروبة أبصر في مين زائد
+
+284
+00:32:00,010 --> 00:32:05,510
+رقم تاني السؤال هو هل الخمسة بتقسم التسعة عشرإذا
+
+285
+00:32:05,510 --> 00:32:09,470
+الـR اللي عندها لا يمكن أن تساوي 0 وإنما أكبر من
+
+286
+00:32:09,470 --> 00:32:17,270
+الـ0 أقل من الـB لخمسة ممتاز جدا يبقى خمسة في قداش
+
+287
+00:32:17,270 --> 00:32:22,850
+بده يطلع أقل من تسعة عشر خمسة في تلاتةيبقى خمسة في
+
+288
+00:32:22,850 --> 00:32:28,930
+تلاتة بخمستاشر يبقى اربعة يبقى بقوله زائد اربعة
+
+289
+00:32:28,930 --> 00:32:33,350
+والاربعة زي ما انتوا شايفين اكبر من او تساوي zero
+
+290
+00:32:33,350 --> 00:32:39,030
+اقل من المئة و اقل من الخمسة اللي عندنا يبقى ضروري
+
+291
+00:32:39,030 --> 00:32:45,010
+ينطبق الشرطين في قارن واحد مش ينطبق شرطه التاني لأ
+
+292
+00:32:45,010 --> 00:32:53,530
+نعطيك مثال اخر مثال اتنينمثال اتنين لو أخدت ال a
+
+293
+00:32:53,530 --> 00:33:01,130
+تساوي ناقص تسعة عشر and ال b تساوي تلتة على سبيل
+
+294
+00:33:01,130 --> 00:33:12,870
+المثال يبقى the division algorithm is
+
+295
+00:33:12,870 --> 00:33:16,070
+ناقص
+
+296
+00:33:16,070 --> 00:33:23,340
+تسعة عشربدو يساوي اللي هو تلاتة أبصر في قداش زاد
+
+297
+00:33:23,340 --> 00:33:28,840
+أبصر قداش بدي
+
+298
+00:33:28,840 --> 00:33:35,510
+ناقص سنتاشر تلاتة في قداش ممكن تعطينيسالب سبعة
+
+299
+00:33:35,510 --> 00:33:41,850
+سالب سبعة طيب لو قلت سالب سبعة يبقى بيصير قداش
+
+300
+00:33:41,850 --> 00:33:46,630
+سالب واحد وعشرين يبقى بدي اضيفلها قداش مشان يطلع
+
+301
+00:33:46,630 --> 00:33:53,670
+سالب تسعة عشر اتنين يبقى زائد اتنين والاتنين هذه
+
+302
+00:33:53,670 --> 00:34:00,770
+اكبر من او تساوي zero اقل من مين اقل من تلاتة طيب
+
+303
+00:34:01,270 --> 00:34:05,950
+هذا الكلام مئة بالمئة انطبقه الشرطين في آن المؤهد
+
+304
+00:34:05,950 --> 00:34:11,910
+يبقى بداجي اقوله ايش رايك في ناقص تسعة واطعش ها
+
+305
+00:34:11,910 --> 00:34:17,330
+ديها ناقص تسعة واطعش بدي اكتبها بدل ما اقول تلاتة
+
+306
+00:34:17,330 --> 00:34:24,470
+في ناقص سبعة بدي اقول تلاتة في ناقص ستة تلاتة في
+
+307
+00:34:24,470 --> 00:34:30,210
+ناقص ستة في قدر؟ الوصف عليه بتمانطعي زائد ناقص
+
+308
+00:34:30,210 --> 00:34:30,550
+واحد
+
+309
+00:34:33,520 --> 00:34:41,000
+مش هدول احنا بطلع سلب تسعة عشر بس يبقى هذه not
+
+310
+00:34:41,000 --> 00:34:46,760
+division يبقى
+
+311
+00:34:46,760 --> 00:34:51,360
+كتاب اللي هنا but ولكن نقص تسعة ونصف division
+
+312
+00:34:51,360 --> 00:35:01,050
+algorithm السبب becauseايوة شو اللي اختل عندى
+
+313
+00:35:01,050 --> 00:35:07,630
+السالب واحد السالب واحد هذا ماهواش اكبر من او
+
+314
+00:35:07,630 --> 00:35:15,300
+يساوي zero لكن فعلا اقل من تلاتةمظبوط أقل من تلاتة
+
+315
+00:35:15,300 --> 00:35:20,780
+صحيح لكن سالب واحد ماهواش أكبر من سوى Zero وإنما
+
+316
+00:35:20,780 --> 00:35:27,540
+أقل من Zero إذا صارت تناقض لهذه الخاصية مع مين؟ مع
+
+317
+00:35:27,540 --> 00:35:32,300
+الخاصية اللي عندنا هذه تمام؟ يبقى هذه الأولى
+
+318
+00:35:32,300 --> 00:35:36,510
+الصحيحة والتانية مالها؟هذه خطأ ليست division
+
+319
+00:35:36,510 --> 00:35:41,610
+algorithm يعني يا شباب الزيادة لازم تكون بإشارة
+
+320
+00:35:41,610 --> 00:35:47,010
+موجبة وليست بإشارة سلبة ديربالك من النقطة هذه اللي
+
+321
+00:35:47,010 --> 00:35:50,770
+عندنا طيب بدنا نيجي لحاجة اسم ال greatest common
+
+322
+00:35:50,770 --> 00:35:57,690
+divisor definition the greatest common divisor the
+
+323
+00:35:57,690 --> 00:36:01,970
+greatest common
+
+324
+00:36:03,320 --> 00:36:16,100
+divisor القاسم المشترك الأعظم you
+
+325
+00:36:16,100 --> 00:36:24,840
+got the greatest common divisor of two non-zero
+
+326
+00:36:24,840 --> 00:36:26,560
+integers
+
+327
+00:36:38,640 --> 00:36:46,300
+is the largest
+
+328
+00:36:46,300 --> 00:37:00,580
+of all common divisors of all common divisors of
+
+329
+00:37:01,740 --> 00:37:13,560
+الـ A and ال B and denoted by هنعطيهم
+
+330
+00:37:13,560 --> 00:37:24,800
+الرمز GCD للـ A و ال B when
+
+331
+00:37:24,800 --> 00:37:27,840
+عندما
+
+332
+00:37:29,150 --> 00:37:34,250
+the greatest common divisor لل A والB يبدو يساوي
+
+333
+00:37:34,250 --> 00:37:45,370
+واحد we say that .. we say that بروح نقول ان ال A
+
+334
+00:37:45,370 --> 00:37:54,310
+and ال B are relatively prime
+
+335
+00:37:58,290 --> 00:38:03,070
+relatively prime examples
+
+336
+00:38:22,960 --> 00:38:27,360
+طبعا هنا عندي شغلتين الشغلة الأولى الجريس ال
+
+337
+00:38:27,360 --> 00:38:30,900
+common divisor الشغلة التانية لو كجريس ال common
+
+338
+00:38:30,900 --> 00:38:37,760
+divisor يساوي واحد شو تسمي هذه؟تعريف الأول بقول
+
+339
+00:38:37,760 --> 00:38:42,360
+the greatest common divisors القاسم المشترك الأعظم
+
+340
+00:38:42,360 --> 00:38:47,460
+divisor قاسم common مشترك greatest اللي هو الأكبر
+
+341
+00:38:47,460 --> 00:38:51,520
+أو الأعظم يبقى القاسم المشترك الأعظم of two non
+
+342
+00:38:51,520 --> 00:38:57,440
+zero integers لعددين صحيحين غير صفريين a و b is
+
+343
+00:38:57,440 --> 00:39:03,500
+the largest أكبر واحد of all common divisors of a
+
+344
+00:39:03,500 --> 00:39:08,720
+and bيعني انا عندي رقامين لقيت رقم بيقسم لإثنين
+
+345
+00:39:08,720 --> 00:39:12,260
+لقيت كمان رقم بيقسم لإثنين لقيت كمان رقم .. لقيت
+
+346
+00:39:12,260 --> 00:39:16,780
+كمان رقم بيقسم لإثنين أكبر واحد في هدول القواسم
+
+347
+00:39:16,780 --> 00:39:21,160
+بسميهمين الـ greatest common divisor و هعطيله
+
+348
+00:39:21,160 --> 00:39:28,660
+الرمز GCDG greatest C جاء من common with B divisor
+
+349
+00:39:28,840 --> 00:39:31,860
+يبقى بدل ما أقول الـ greatest common divisor
+
+350
+00:39:31,860 --> 00:39:37,820
+هأختصرهم إلى مين الثلاثة أحرف و أحط العددين A وB
+
+351
+00:39:37,820 --> 00:39:43,060
+تمام تمام يبقى ال greatest common divisor هو أكبر
+
+352
+00:39:43,060 --> 00:39:48,540
+قاسم للعددين يعني عندي عدة قواسم للعددين أكبر واحد
+
+353
+00:39:48,540 --> 00:39:53,420
+فيهم بسميه ال greatest common divisor ممكن يحصل أن
+
+354
+00:39:53,420 --> 00:39:56,380
+ال greatest common divisor بين العددين يكون
+
+355
+00:39:56,380 --> 00:40:02,490
+ماعنديش إلا مينإلا الواحد الصحيح إن حدث ذلك بقول
+
+356
+00:40:02,490 --> 00:40:09,750
+يبقى العددين a وb are relatively prime طيب كلمة
+
+357
+00:40:09,750 --> 00:40:14,510
+relatively prime يعني prime عدد أولي بس relatively
+
+358
+00:40:14,510 --> 00:40:19,960
+يعني نسبييعني اتنين الـprimes بالنسبة لبعض مش
+
+359
+00:40:19,960 --> 00:40:24,640
+اتنين الـprimes اكيد العدد هذا والعدد هذا يعتبر
+
+360
+00:40:24,640 --> 00:40:29,840
+بالنسبة لبعض الـprimes هي المقصود فيها مش كل واحد
+
+361
+00:40:29,840 --> 00:40:35,600
+فيهم لازم يكون الـprime لأ ليس بالضرورة تمام نعطي
+
+362
+00:40:35,600 --> 00:40:40,540
+توضيح لكل واحد من الكلام اللي عندنا هذا بأمثلة
+
+363
+00:40:40,540 --> 00:40:48,620
+عدديةالان لو جيت قولتلك خلط ال a تساوي مثلا ستاش
+
+364
+00:40:48,620 --> 00:40:58,240
+and ال b تساوي الأربعة و عشرين then الواحد divide
+
+365
+00:40:58,240 --> 00:41:01,580
+الستاش
+
+366
+00:41:01,580 --> 00:41:07,380
+and الأربعة و عشرين صح ولا لأ؟ ايش بيجي بعد الواحد
+
+367
+00:41:07,380 --> 00:41:13,970
+بيقسم اتنين؟ اتنينإتنين الـ device الستاش و
+
+368
+00:41:13,970 --> 00:41:21,830
+الأربعة و عشرين بعد إتنين التلاتة لأ الأربعة بتقسم
+
+369
+00:41:21,830 --> 00:41:29,790
+الستاش و الأربعة و عشرين الخامسة الستة السبعة
+
+370
+00:41:29,790 --> 00:41:40,650
+التمانية آه تمانيةبتقسم ال 16 و كذلك ال 24 في اكتر
+
+371
+00:41:40,650 --> 00:41:45,650
+من هيك فشل لإنه تمانية هو نص العدد 16 من حد ما
+
+372
+00:41:45,650 --> 00:41:50,250
+توصل لنص العدد stop بوجة تمشيش ولا خطوة قدام لإنه
+
+373
+00:41:50,250 --> 00:41:54,050
+إذا زاد عن نصف لا يمكن أن يقسم العدد و يطلع عنده
+
+374
+00:41:54,050 --> 00:42:01,650
+عدد صحيح يبجأ كم قاسم صار عنده هنااربع اكبر واحد
+
+375
+00:42:01,650 --> 00:42:05,450
+فيهم بيقول هو الجريس ال common divisor يبقى الجريس
+
+376
+00:42:05,450 --> 00:42:08,390
+ال common divisor للستاشر والاربع عشرين مين هو
+
+377
+00:42:08,390 --> 00:42:14,650
+تمانية من هذا الكلام بقدر اقول يبقى الجريس ال
+
+378
+00:42:14,650 --> 00:42:20,710
+common divisor للستاشر والاربع عشرين هو العدد مين؟
+
+379
+00:42:20,710 --> 00:42:28,190
+العدد تمانية طيب هذا المثال الأول بدأجي لمثال ثاني
+
+380
+00:42:29,950 --> 00:42:34,790
+بدي أجيبلك على حكاية إيه relatively prime لو جيت
+
+381
+00:42:34,790 --> 00:42:41,430
+قولتلك الآن ل greatest common divisor لتلاتة وسبعة
+
+382
+00:42:41,430 --> 00:42:49,810
+قد إيش؟في غيره؟ في غيره؟ لأ يبقى هذا يساوي الواحد
+
+383
+00:42:49,810 --> 00:42:58,910
+because التلاتة and السبعة are primes مش
+
+384
+00:42:58,910 --> 00:43:05,930
+relatively primes تمام؟ but ولكن ال aggressives
+
+385
+00:43:05,930 --> 00:43:12,650
+common divisors للأربعة والسبعة مثلا كدهش؟في شغيره
+
+386
+00:43:12,650 --> 00:43:17,410
+هو الواحد الوحيد اللي بيقسم العددين الاتنين هدول
+
+387
+00:43:17,410 --> 00:43:22,330
+يبقى يساوي واحد هل الأربعة prime number لكن
+
+388
+00:43:22,330 --> 00:43:26,010
+الأربعة والسبعة بالنسبة لبعض يعتبروا ايش prime
+
+389
+00:43:26,010 --> 00:43:33,960
+يبقى are relatively prime يبقى هنا becauseالسبعة
+
+390
+00:43:33,960 --> 00:43:39,640
+and الأربعة are والله الأربعة and السبعة خلينا
+
+391
+00:43:39,640 --> 00:43:45,820
+بالترتيب ماشيين and السبعة are relatively
+
+392
+00:43:45,820 --> 00:43:49,240
+relatively
+
+393
+00:43:49,240 --> 00:43:53,960
+primes يبقى
+
+394
+00:43:53,960 --> 00:43:56,980
+شايف الفرق ما بين ال prime و relatively prime ايش
+
+395
+00:43:56,980 --> 00:43:57,520
+هتفضل
+
+396
+00:44:03,250 --> 00:44:08,970
+طب ما هي .. شوف في .. في غير الواحد؟
+
+397
+00:44:08,970 --> 00:44:15,580
+طب هو العوامل اللي هو .. هو السنةممتاز جدا لك
+
+398
+00:44:15,580 --> 00:44:19,900
+الاربعة والسبعة في اكتر طيب مافيش غيره يعني انا
+
+399
+00:44:19,900 --> 00:44:24,080
+بعطي مثال relatively prime لك المثال اللي جابله
+
+400
+00:44:24,080 --> 00:44:27,580
+جبت ال grasses common divisor لأي عدنى بس ماطلعش
+
+401
+00:44:27,580 --> 00:44:31,540
+واحد طلع قداش طلع تمانية جبت الواحد والاتنين
+
+402
+00:44:31,540 --> 00:44:35,640
+والاربعة والتمانية أخدت الكبير فيهم طبقا للتعريف
+
+403
+00:44:35,640 --> 00:44:39,300
+تمام هنا ال grasses common divisor قد يكون واحد قد
+
+404
+00:44:39,300 --> 00:44:42,840
+يكون واحد في كام حالةبدل الحالة حالتين الحالة
+
+405
+00:44:42,840 --> 00:44:46,700
+الأولى لو كانوا اتنين primes وفي هذه الحالة بقول
+
+406
+00:44:46,700 --> 00:44:50,520
+اتنين primes مثلا بقول relatively prime relatively
+
+407
+00:44:50,520 --> 00:44:55,120
+يعني في بنسب واحد بالنسبة للتانية أخدت الأربعة
+
+408
+00:44:55,120 --> 00:45:01,460
+والسبعة أخدت الأحداشر والخمسمية مثلامثلا تسعة و
+
+409
+00:45:01,460 --> 00:45:05,520
+عشرة are relatively prime كلام صحيح يبقى انا خدت
+
+410
+00:45:05,520 --> 00:45:08,420
+احداشر و اخدت الخمسمية مافيش قواصم بينهم الا
+
+411
+00:45:08,420 --> 00:45:13,200
+الواحد الصحيح و هكذا تفضل كيف؟
+
+412
+00:45:14,710 --> 00:45:19,070
+automatic relatively prime لكن العكس ليس صحيحا
+
+413
+00:45:19,070 --> 00:45:25,190
+يبقى زميكوف يقول هدول لما يكونوا are primes ما
+
+414
+00:45:25,190 --> 00:45:29,250
+بقدر أقول عليهم relatively primes لكن العكس ليس
+
+415
+00:45:29,250 --> 00:45:34,830
+صحيحا يبقى هذه الأمثلة على ال grasses common
+
+416
+00:45:34,830 --> 00:45:40,250
+divisors وعلى main وrelatively primes
+
+417
+00:46:07,100 --> 00:46:14,340
+طيب خد لها الملاحظة if
+
+418
+00:46:14,340 --> 00:46:23,880
+ال N is an integer and
+
+419
+00:46:23,880 --> 00:46:34,570
+ال N greater than zeroثم لجرس ال common divisor لل
+
+420
+00:46:34,570 --> 00:46:39,210
+N وال0 كده يا شباب؟
+
+421
+00:46:41,350 --> 00:46:49,330
+ان الواحد تقسم الان و تقسم ال zero الان اتنين تقسم
+
+422
+00:46:49,330 --> 00:46:53,430
+ال zero بس مضمون تقسم ال ان لا مش مضمون ايه
+
+423
+00:46:53,430 --> 00:46:59,010
+التلاتة الأربعة ال ان ال ان اكبر رقم بيقسم ال ان و
+
+424
+00:46:59,010 --> 00:47:04,550
+بيقسم ال zero يبقى هنا هذا الكلام بدو يساوي ال in
+
+425
+00:47:04,550 --> 00:47:10,250
+because ال in is the
+
+426
+00:47:32,560 --> 00:47:45,550
+بقسم الاتنين في النظرية بتقول ما يأتيtheorem for
+
+427
+00:47:45,550 --> 00:47:57,810
+any none zero integers a
+
+428
+00:47:57,810 --> 00:48:08,830
+and b there exist integers
+
+429
+00:48:11,450 --> 00:48:24,130
+بلاقي أعداد صحيحة S and A T such that such that ان
+
+430
+00:48:24,130 --> 00:48:30,030
+ال aggressive common divisor لل A و ال B بدي ساوي
+
+431
+00:48:30,030 --> 00:48:39,610
+ال A في S زائد ال B في T moreover
+
+432
+00:48:40,520 --> 00:48:48,920
+و أكثر من ذلك moreover the greatest common divisor
+
+433
+00:48:48,920 --> 00:48:55,080
+لل a والb is the smallest positive integer is the
+
+434
+00:48:55,080 --> 00:49:02,900
+smallest positive integer
+
+435
+00:49:02,900 --> 00:49:06,040
+smallest
+
+436
+00:49:06,040 --> 00:49:17,910
+positive integer ofreform على الشكل as زائد bt
+
+437
+00:49:17,910 --> 00:49:21,450
+quaternary
+
+438
+00:49:21,450 --> 00:49:24,950
+نتيجة
+
+439
+00:49:24,950 --> 00:49:38,030
+if ال a and ال b are relatively prime
+
+440
+00:49:39,750 --> 00:49:49,590
+relatively prime then there exist then there exist
+
+441
+00:49:49,590 --> 00:49:55,610
+integers s
+
+442
+00:49:55,610 --> 00:50:07,150
+and t s and t such that بحيث
+
+443
+00:50:07,150 --> 00:50:16,780
+أنالـ AS زائد ال BT يساوي كده؟ يساوي واحد
+
+444
+00:51:06,130 --> 00:51:10,410
+طيب نرجع لنص النظرية بيقول for any non zero
+
+445
+00:51:10,410 --> 00:51:15,770
+integers a و b يبقى انا عندي عددين صحيحين a و b
+
+446
+00:51:15,770 --> 00:51:21,250
+there exist integers لازم الاقي عددين اخرين s and
+
+447
+00:51:21,250 --> 00:51:25,250
+t such that the greatest common divisor لل a و ال
+
+448
+00:51:25,250 --> 00:51:31,820
+b بدى يسوى a في ال s زائد bt ايش يعني؟بقول هنا
+
+449
+00:51:31,820 --> 00:51:36,440
+لجلس ال common divisor بتقدر تكتبه على صيغة linear
+
+450
+00:51:36,440 --> 00:51:42,600
+combination من العددين A وB يعني بقدر ألاقي عدد
+
+451
+00:51:42,600 --> 00:51:47,120
+أضربه في A وعدد تاني أضربه في B أجمع يطلع له لجلس
+
+452
+00:51:47,120 --> 00:51:52,460
+ال common divisorهل حطيت قيود على ال S و T؟
+
+453
+00:51:52,460 --> 00:51:56,160
+ماحطيتش، يعني يمكن يطلعوا اتنين سالب، يمكن واحد
+
+454
+00:51:56,160 --> 00:52:00,100
+موجب وواحد سالب المهم ان الهدف الصحيح بيهمنيش موجب
+
+455
+00:52:00,100 --> 00:52:05,320
+سالب غيره لكن بيهمنياش انه فعلا يكون the greatest
+
+456
+00:52:05,320 --> 00:52:09,560
+common divisor هو linear combination من الرقمين
+
+457
+00:52:09,560 --> 00:52:15,350
+اللي عندي من A وB moreoverGreece's Common Divisor
+
+458
+00:52:15,350 --> 00:52:21,530
+هو أصغر رقم بقدر أكتفه على صيغة Linear Combination
+
+459
+00:52:21,530 --> 00:52:29,970
+AS زائد BTطيب النتيجة بتقول ليش؟ لو كان ال a وال b
+
+460
+00:52:29,970 --> 00:52:34,290
+relatively prime زي الأربعة والسبعة اللي قبل قليل
+
+461
+00:52:34,290 --> 00:52:38,750
+مثلا يبقى then there exists an integer S و T such
+
+462
+00:52:38,750 --> 00:52:43,450
+that يعني قصده يقول لك linear combination هذي ال
+
+463
+00:52:43,450 --> 00:52:47,390
+aggressives common ده يغزلوا بقداشيبقى الواحد back
+
+464
+00:52:47,390 --> 00:52:53,730
+to record وعلى شكل AS بزاقة BT طبعا انها تامثل لكل
+
+465
+00:52:53,730 --> 00:52:58,580
+من النظرية وكل مناللي هو .. و كذلك الـ Crawler الـ
+
+466
+00:52:58,580 --> 00:53:02,480
+Crawler يعني نتيجة شباب على نظره يعني كانها حالة
+
+467
+00:53:02,480 --> 00:53:05,280
+خاصة الحالة الخاصة لو كان ال greatest common
+
+468
+00:53:05,280 --> 00:53:09,480
+divisor هدف واحد يبقى أقدر أكتب الواحد على صيغة
+
+469
+00:53:09,480 --> 00:53:13,680
+لينا ال combination من مين؟ من الاتنين، هدول نعطي
+
+470
+00:53:13,680 --> 00:53:19,240
+أول مثال على ذلك يبقى example one لو كان ال
+
+471
+00:53:19,240 --> 00:53:25,860
+greatest common divisor لمين؟ للأتناشر والتلاتين
+
+472
+00:53:26,910 --> 00:53:31,140
+قداش ال classes كانوا يلبسوا ال 12 وال 30ستة
+
+473
+00:53:31,140 --> 00:53:38,200
+ممتازة يبقى الستة هذا أكبر رقم بيقسم كل من الاتنين
+
+474
+00:53:38,200 --> 00:53:43,740
+في آن واحد الستة هذا بدأ كتبه على صيغة linear
+
+475
+00:53:43,740 --> 00:53:49,120
+combination من مين؟ من الاتناشر والتلاتين بقوله آه
+
+476
+00:53:49,120 --> 00:53:55,880
+يبقى هذا بيسوء اتناشر في رقم زائد تلاتين في رقم
+
+477
+00:53:55,880 --> 00:54:05,330
+آخرطيب اتناش هذه لو ضربتها في سالب اتنين مثلا بصير
+
+478
+00:54:05,330 --> 00:54:11,240
+كدهش؟سالب اربعة وعشرين يبقى الفرق بينهم بين
+
+479
+00:54:11,240 --> 00:54:15,960
+التلاتين جداش هو الستة تبعتنا يبقى بروح بضرب هنا
+
+480
+00:54:15,960 --> 00:54:22,380
+جداش يواحد يبقى هذا الرقم هو عبارة عن اس وهذا
+
+481
+00:54:22,380 --> 00:54:28,160
+الرقم هو عبارة عن مين هو عبارة عن تي يبقى للرقمين
+
+482
+00:54:28,160 --> 00:54:33,460
+اتناشر وتلاتين لجيت اس بسلب اتنين و لجيت تي تساوي
+
+483
+00:54:33,460 --> 00:54:37,090
+واحدبحيث اتناشر في السلبي اتنين زي التلاتين في
+
+484
+00:54:37,090 --> 00:54:40,810
+واحد يعطينا main الرقم ست الأولي greatest common
+
+485
+00:54:40,810 --> 00:54:46,590
+divisor لاتناشر وmain والتلاتين خد لي كمان مثال
+
+486
+00:54:46,590 --> 00:54:54,480
+آخريبقى لو جيت قلت المثال ارقم اتنين لو جيت ال
+
+487
+00:54:54,480 --> 00:55:00,840
+greatest common divisor لمن؟ للاربعة والسبعتاش
+
+488
+00:55:00,840 --> 00:55:06,880
+هدول ما لهم? rentable price صحيح ولا لأ؟ يبقى دول
+
+489
+00:55:06,880 --> 00:55:13,110
+بده يساوي واحدمش زي اللي هناك يساوي ستة يبقى هذا
+
+490
+00:55:13,110 --> 00:55:19,310
+بده يساوي أربعة في أبصر قداش زائد سبعتاشر في أبصر
+
+491
+00:55:19,310 --> 00:55:28,070
+قداش كذلك سالب أربعة قصير قداش سالب ستاش واني عندى
+
+492
+00:55:28,070 --> 00:55:32,750
+هنا قداش يبقى السبعتاشر بدها قداش واحد ليس
+
+493
+00:55:32,750 --> 00:55:36,210
+بالضرورة دايما يطلع واحد ممكن يطلع أي رقم آخر يعني
+
+494
+00:55:36,210 --> 00:55:42,820
+بقدر الله المرة هذه طلعيبقى هذا يمثل الـ S وهذا
+
+495
+00:55:42,820 --> 00:55:48,760
+يمثل الـ T يبقى هاي اتنين are relatively prime
+
+496
+00:55:48,760 --> 00:55:53,020
+قدرت اكتب الواحد على الشكل الأربعة مضروبة في
+
+497
+00:55:53,020 --> 00:55:57,040
+integer زاد سبعتاشر مضروبة في integer طبق اللي مين
+
+498
+00:55:57,040 --> 00:56:01,370
+لكرولري اللي عندى هذهوبالتالي ماعندي مشكلة في هذه
+
+499
+00:56:01,370 --> 00:56:07,790
+الحالة طيب يا شباب لو جيت قلت رقم تلاتة لو بد ال
+
+500
+00:56:07,790 --> 00:56:14,270
+degree is common divisor لمن؟ لليتنين تربيع في
+
+501
+00:56:14,270 --> 00:56:22,450
+تلاتة تربيع في خمسة كل هذا ضرب والرقم التاني اتنين
+
+502
+00:56:22,450 --> 00:56:27,150
+في تلاتة تربيع في سبعة تربيع
+
+503
+00:56:29,290 --> 00:56:34,450
+رقمين كبار يبقى لو كان عندى رقم كبير بحلله الى
+
+504
+00:56:34,450 --> 00:56:38,010
+أبسط العوامل بشوف فيه اكم اتنين و بعدين اكم تلاتة
+
+505
+00:56:38,010 --> 00:56:44,390
+و اكم خمسة و اكم سبعة و هكذا طيب لو بدى اجيب الجنس
+
+506
+00:56:44,390 --> 00:56:49,510
+ال common divisor للاتنين هدول عشان احسب هذا بجيب
+
+507
+00:56:49,510 --> 00:56:54,350
+قدش الجنس ال common divisor لتنين تربيع و اتنين
+
+508
+00:56:55,280 --> 00:57:03,200
+أكبر رقم بيقسم الاتنين هو الاتنين اتنين مقدش لجريس
+
+509
+00:57:03,200 --> 00:57:07,520
+ال common divisor للثلاثة تربيه والتلاتة تربيه
+
+510
+00:57:08,190 --> 00:57:14,710
+التسعة يعني تلاتة تربية يبقى هذا تلاتة تربية جداش
+
+511
+00:57:14,710 --> 00:57:18,870
+اللي جرس ال common divisor للخمسة والسبعة تربية
+
+512
+00:57:18,870 --> 00:57:23,070
+سبعة يعني تسعة واربعين مع خمسة اتنين are
+
+513
+00:57:23,070 --> 00:57:27,810
+relatively primed بجداشواحد يبقى الجرس ال common
+
+514
+00:57:27,810 --> 00:57:31,710
+divisor لهم اللي هو يساوي واحد تسعة في اتنين في
+
+515
+00:57:31,710 --> 00:57:36,570
+تمانتاش يبقى الجرس ال common divisor لهذين العددين
+
+516
+00:57:36,570 --> 00:57:41,630
+يساوي جداش تمانتاش و هكذا يبقى الجرس ال common
+
+517
+00:57:41,630 --> 00:57:44,670
+divisor لو كان مجموعة من الاعداد و عندي مجموعة من
+
+518
+00:57:44,670 --> 00:57:49,000
+الاعداد بقارن كل واحد بالاجبالهو بطلع جديش لجريس
+
+519
+00:57:49,000 --> 00:57:52,420
+ال common divisor لكل اتنين متنظرين وبعدين بضربهم
+
+520
+00:57:52,420 --> 00:57:57,060
+في بعض بطلع جديش لجريس ال common divisor لمين؟ لكل
+
+521
+00:57:57,060 --> 00:58:01,420
+الأعداد يبقى لحد هنا ا stop المرة الجاية ان شاء
+
+522
+00:58:01,420 --> 00:58:06,120
+الله بنكمل يوم الأتنين و هجيك المرة الجاية هبدأ
+
+523
+00:58:06,410 --> 00:58:11,090
+بلمة وبرهين نبدأ بنقول احنا حتى لا مابورهناش ولا
+
+524
+00:58:11,090 --> 00:58:14,730
+حاجة بنعطي بعض المعلومات الأساسية و بنحاول نثبت
+
+525
+00:58:14,730 --> 00:58:19,990
+هالمعلومة بواسطة من؟ بواسطة أمثلة مختلفة يمكن
+
+526
+00:58:19,990 --> 00:58:23,530
+الكلام اللي بقوله كثير منه تفتحت لك بتلاقيش أمثلة
+
+527
+00:58:23,530 --> 00:58:27,290
+لكن أنا بعطيك أمثلة مش هنثبت المعلومة عندك لإن
+
+528
+00:58:27,290 --> 00:58:31,010
+المعلومة القديمة عندك بس بنحاول نثبتها من خلال
+
+529
+00:58:31,010 --> 00:58:33,130
+الأمثلة يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f42e0aa7794724cdc8b509971f167478ad5818a6
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_raw.srt
@@ -0,0 +1,1872 @@
+1
+00:00:21,670 --> 00:00:27,730
+الان بنرجع مرة ثانية لما بدأنا بيه صباحا وهو اكمال
+
+2
+00:00:27,730 --> 00:00:31,950
+مناقشة مسائل ال permutations ان هنا سؤال تسعة و
+
+3
+00:00:31,950 --> 00:00:37,010
+عشرين في الفترة الصباحية وقلنالكوا احسبوا اضربوا
+
+4
+00:00:37,010 --> 00:00:40,850
+فينا ال sigma اللى طلعناها ضربة في نفسها تلت مرات
+
+5
+00:00:40,850 --> 00:00:44,690
+sigma تكيب تلاقيه على حاصل ضرب اللى هو ال three
+
+6
+00:00:44,690 --> 00:00:48,760
+cycles اللى موجودة عندكو بالفعل بعضكم قالوا
+
+7
+00:00:48,760 --> 00:00:52,620
+عملناها و طلعت زيه كما قلت تماما قلنا ماشي إذا
+
+8
+00:00:52,620 --> 00:00:57,500
+بننتقل الآن إلى السؤال واحد و تلاتين واحد و تلاتين
+
+9
+00:00:57,500 --> 00:01:02,980
+عرفلي ست جديدة سماها ال stabilizer لإيه و هي كل ال
+
+10
+00:01:02,980 --> 00:01:07,800
+alpha اللي موجودة فيه بحيث ان alpha of a بدي ساوي
+
+11
+00:01:07,800 --> 00:01:12,710
+ال aلما يقول الفا موجودة في جي الفا is a
+
+12
+00:01:12,710 --> 00:01:17,070
+permutation فلما يقول الفا of a بده يساوي ايه
+
+13
+00:01:17,070 --> 00:01:22,370
+معناته لسه بلازم تلاقي كل ال permutations اللي
+
+14
+00:01:22,370 --> 00:01:27,110
+بيكون فيهم ال a fixed ايش يعني fixed يعني ال
+
+15
+00:01:27,110 --> 00:01:32,940
+element هو صورة لنفسي الفا of a بده يساوي ايهأنا
+
+16
+00:01:32,940 --> 00:01:39,140
+بدي اذهب و ابحث في الـ SG على كل الـPermutations
+
+17
+00:01:39,140 --> 00:01:44,640
+التي تثبت منهم الانصار A بدي اذهب و اثبت ان هذا ال
+
+18
+00:01:44,640 --> 00:01:48,280
+list بلازر الـA هو عبارة عن subgroup من ال group
+
+19
+00:01:48,280 --> 00:01:53,760
+الأساسية اللي هي G بالرجوع إلى ذاكره إلى شبطر 3
+
+20
+00:01:53,760 --> 00:01:58,460
+بجينا ال subset من ال group نثبتها subgroup إذا
+
+21
+00:01:58,460 --> 00:02:02,660
+أثبتناتو conditions ال condition الأول أن ال
+
+22
+00:02:02,660 --> 00:02:06,500
+stabilizer لإيه is non-empty يعني على الأقل فيها و
+
+23
+00:02:06,500 --> 00:02:10,220
+لو عنصر واحد الأمر الثاني لو أخدت عنصرين في ال
+
+24
+00:02:10,220 --> 00:02:13,700
+stabilizer بدي أثبت أن الأول في معقولتي الثاني
+
+25
+00:02:13,700 --> 00:02:18,040
+موجود في ال stabilizer أن أثبتنا ذلك بيكون ال
+
+26
+00:02:18,040 --> 00:02:22,480
+stabilizer لإيه هي subgroup من من من ال group G
+
+27
+00:02:23,030 --> 00:02:27,910
+يبقى النقطة الأولى في الحل هو اثبات ان ال
+
+28
+00:02:27,910 --> 00:02:32,590
+stabilizer ل a is non-empty انا ادعي ان ال
+
+29
+00:02:32,590 --> 00:02:42,170
+stabilizer ل a is non-empty ليش؟ because ال
+
+30
+00:02:42,170 --> 00:02:48,810
+identity permutation موجودة في ال stabilizer ل ال
+
+31
+00:02:48,810 --> 00:02:55,070
+a senseالان ال identity permutation بيثبت اللي هو
+
+32
+00:02:55,070 --> 00:03:01,070
+بس هو اللي بيثبت كل العناصر كل العناصر بيثبت ..
+
+33
+00:03:01,070 --> 00:03:05,060
+اذا من بابا هو اللي بيثبت اللي هييبقى هنا non
+
+34
+00:03:05,060 --> 00:03:08,660
+-empty لأن الـ E موجودة في الاستبلايزر since ال
+
+35
+00:03:08,660 --> 00:03:12,760
+identity permutation لما اتأثر على ال element A
+
+36
+00:03:12,760 --> 00:03:19,060
+بتعطينا منه الـ A itself ومن ثم صار الاستبلايزر لـ
+
+37
+00:03:19,060 --> 00:03:25,760
+A فيها على الأقل ال identity permutation الان هذه
+
+38
+00:03:25,760 --> 00:03:31,490
+هي الخطوة الأولى الخطوة الثانيةبداية اقول ان ال
+
+39
+00:03:31,490 --> 00:03:36,350
+alpha و ال beta موجودة في ال stabilizer لل element
+
+40
+00:03:36,350 --> 00:03:44,110
+a تمام؟ اذا بناء عليه بقدر اقول له then ال alpha
+
+41
+00:03:44,110 --> 00:03:49,570
+لما تأثر على العنصر a بتعطينا العنصر a itself and
+
+42
+00:03:49,570 --> 00:03:54,550
+ال beta لما تأثر على العنصر a بتعطينا العنصر a
+
+43
+00:03:54,550 --> 00:04:01,640
+itselfأنا هاروح أخد المعلومة هذه واستنتج منها شغلة
+
+44
+00:04:01,640 --> 00:04:07,920
+تانية هذه ايش معناها لو جيت أثرت على الطرفين بال
+
+45
+00:04:07,920 --> 00:04:17,150
+beta inverse يبقى بيصيربيتا انفرس لبيتا of a يسوى
+
+46
+00:04:17,150 --> 00:04:26,150
+بيتا انفرس of a او بيتا انفرس لبيتا كلها لما اتأثر
+
+47
+00:04:26,150 --> 00:04:32,170
+على a بدها تسوى بيتا انفرس of a ال composition بين
+
+48
+00:04:32,170 --> 00:04:36,430
+ال permutation و معكوسة شو بعطينا ال identity
+
+49
+00:04:36,430 --> 00:04:40,650
+element لما اتأثر على ال element بعطيني نفس ال
+
+50
+00:04:40,650 --> 00:04:46,430
+elementيبقى هذا يطينا الـ beta inverse of a هذا
+
+51
+00:04:46,430 --> 00:04:53,070
+ايش معناه؟ ايش تفسيرك لهذه العبارة طبقا للتعريف
+
+52
+00:04:53,070 --> 00:04:57,710
+اللي احنا قيلينه؟ موجود كويس يبقى alpha inverse
+
+53
+00:04:57,710 --> 00:05:01,550
+موجودة في ال stabilizer لإيه؟ هاي معناها ليش انها
+
+54
+00:05:01,550 --> 00:05:08,560
+بتثبت العنصر a يبقى هذا معناهالـ beta inverse
+
+55
+00:05:08,560 --> 00:05:16,420
+موجودة في ال stabilizer لمن؟ لـ A الان consider خد
+
+56
+00:05:16,420 --> 00:05:22,060
+لمن؟ خد لل alpha beta inverse of A
+
+57
+00:05:25,670 --> 00:05:31,270
+يبقى انا اخدت العنصرين alpha و beta في موجودة في
+
+58
+00:05:31,270 --> 00:05:36,030
+ال stabilizer بدي اشوف هل ال alpha في beta inverse
+
+59
+00:05:36,030 --> 00:05:40,250
+بتثبت اللي ان ثبته خلاص موجودة في ال stabilizer و
+
+60
+00:05:40,250 --> 00:05:44,710
+التالي ال stabilizer عبارة عن subgroupيبقى هذا
+
+61
+00:05:44,710 --> 00:05:51,950
+الكلام بده يساوي alpha of beta inverse of a ويساوي
+
+62
+00:05:51,950 --> 00:05:57,830
+alpha of beta inverse of a عبارة عن ما؟ عبارة عن a
+
+63
+00:05:57,830 --> 00:06:04,530
+itself مدام عبارة عن a itself يبقى هذا a لكن أنا
+
+64
+00:06:04,530 --> 00:06:08,610
+عند هنا alpha موجودة في ال stabilizer يبقى alpha
+
+65
+00:06:08,610 --> 00:06:14,750
+of a بتعطيني ما؟ aإذا صار تأثير Alpha Beta Inverse
+
+66
+00:06:14,750 --> 00:06:18,230
+عليها سيكون الـ A itself، ما هو معناه هذا الكلام؟
+
+67
+00:06:18,230 --> 00:06:24,730
+أن Alpha Beta Inverse يبقى هذا معناه أن Alpha Beta
+
+68
+00:06:24,730 --> 00:06:30,430
+Inverse موجودة في ال stabilizer للـ Aمعنى هذا
+
+69
+00:06:30,430 --> 00:06:36,010
+الكلب ال stabilizer لإيه عبارة عن subgroup من G
+
+70
+00:06:36,010 --> 00:06:44,490
+يبقى ال stabilizer لمن؟ ال stabilizer لل a
+
+71
+00:06:44,490 --> 00:06:50,250
+subgroup من G و هو المطلوب إيه لخاطر أعطيك مثال
+
+72
+00:06:50,250 --> 00:06:54,910
+عملي و لو انه مش طالب و لا حاطب مثال عملي يوضح لك
+
+73
+00:06:54,910 --> 00:06:59,170
+إيش المقصود منه هذا فمثلا يعني for example
+
+74
+00:07:03,800 --> 00:07:11,560
+لو أخدت الـ G تساوي S3 S3 هي كم عنصر فيها يا شباب؟
+
+75
+00:07:11,560 --> 00:07:17,600
+ست عناصر اللي هو الأول اللي هو ال identity يبقى ال
+
+76
+00:07:17,600 --> 00:07:24,400
+identity والتاني اللي هو واحد اتنين تلاتة وبعد هيك
+
+77
+00:07:24,400 --> 00:07:31,000
+واحد اتنينوبعد هيك واحد تلاتة اتنين وبعد هيك واحد
+
+78
+00:07:31,000 --> 00:07:38,460
+تلاتة وبعد هيك اتنين تلاتة يبجي هي عناصر S3 كلهم
+
+79
+00:07:38,460 --> 00:07:45,010
+ستة عناصر S6 عناصريعني هاي الستة permutations اللي
+
+80
+00:07:45,010 --> 00:07:50,170
+موجودة وان في S3 الآن بدأ اجيب ال stabilizer
+
+81
+00:07:50,170 --> 00:07:55,970
+للواحد والستابليزر للاتنين والستابليزر للتلاتة هاي
+
+82
+00:07:55,970 --> 00:08:00,790
+العناصر اللي موجودة في اي permutation الان بدأ اجي
+
+83
+00:08:00,790 --> 00:08:08,120
+أخدله ال stabilizer لمن للواحد تساوي منالمقصود
+
+84
+00:08:08,120 --> 00:08:12,560
+بالـstabilizer للواحد يعني كل ال permutation اللي
+
+85
+00:08:12,560 --> 00:08:17,160
+فيهم الواحد fixed يعني صورة الواحد هي الواحد
+
+86
+00:08:17,160 --> 00:08:21,660
+itself ماشي
+
+87
+00:08:21,660 --> 00:08:25,600
+هو واحد اتنين تلاتة ال identity وال identity بتكون
+
+88
+00:08:25,600 --> 00:08:29,560
+واحد بين جثين او اتنين بين جثين او تلاتة بين جثين
+
+89
+00:08:29,560 --> 00:08:34,920
+هذه ال order اللي هيسوي تلاتة وبالتالي كيف خلتها
+
+90
+00:08:34,920 --> 00:08:39,820
+ال identity؟أما لو كنت واحد اتنين تلاتة واحد اتنين
+
+91
+00:08:39,820 --> 00:08:43,440
+تلاتة بيقولك هذا كلامك صح بس هذه معناته ان الواحد
+
+92
+00:08:43,440 --> 00:08:46,500
+صرت اتنين والاتنين صرت تلاتة والتلاتة صرت واحد
+
+93
+00:08:46,500 --> 00:08:50,000
+يبقى هذه ليست ال identity يبقى كتبناك ال identity
+
+94
+00:08:50,000 --> 00:08:56,110
+لحالك كان بإمكاني أقولك هذهو أسكت بدل ال E كان
+
+95
+00:08:56,110 --> 00:09:00,350
+ممكن أقولك اتنين و أسكت تلاتة و أسكت stop بقولش
+
+96
+00:09:00,350 --> 00:09:05,910
+أربعة و أسكت ليش؟ لأن ال S3 باس معمولة على ستم
+
+97
+00:09:05,910 --> 00:09:10,130
+تلاتة عناصر واحد اتنين تلاتة تمام؟ الان بدي أجيب
+
+98
+00:09:10,130 --> 00:09:13,950
+ال stabilizer اللي هو يعني مين هم ال permutation
+
+99
+00:09:13,950 --> 00:09:18,370
+اللي فيهم الواحد fixed يعني اللي الواحد صورته واحد
+
+100
+00:09:18,370 --> 00:09:23,400
+باجي ال identity هذهمنهم اه لان بيثبت الواحد
+
+101
+00:09:23,400 --> 00:09:27,100
+والاتنين والتلاتة مش ع جد الواحد يبقى باجي بقوله
+
+102
+00:09:27,100 --> 00:09:32,220
+ال identity pyramid اشتنام هذي بيثبت الواحد هذي
+
+103
+00:09:32,220 --> 00:09:38,100
+بيثبت الواحد هذي بيثبت الواحد هذي يبقى ايش اتنين
+
+104
+00:09:38,100 --> 00:09:42,820
+تلاتة هذي اللي فيها الواحد fixed مظهرليش يبقى هنا
+
+105
+00:09:42,820 --> 00:09:50,570
+اتنين وتلاتة تمامفي غيرهم؟ لأ طب لو بدي ال
+
+106
+00:09:50,570 --> 00:09:56,250
+stabilizer للي اتنين كل ال permitations المثبتة
+
+107
+00:09:56,250 --> 00:10:01,290
+للي اتنين ال identity واحدة و بداجة دولهذه اتنين
+
+108
+00:10:01,290 --> 00:10:05,590
+صورتة واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة
+
+109
+00:10:05,590 --> 00:10:06,290
+واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد
+
+110
+00:10:06,290 --> 00:10:07,010
+وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+111
+00:10:07,010 --> 00:10:07,010
+اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه اتنين
+
+112
+00:10:07,010 --> 00:10:07,010
+صورتة واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة
+
+113
+00:10:07,010 --> 00:10:07,070
+واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد
+
+114
+00:10:07,070 --> 00:10:07,610
+وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+115
+00:10:07,610 --> 00:10:12,070
+اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+116
+00:10:12,070 --> 00:10:20,610
+اتنين
+
+117
+00:10:20,610 --> 00:10:23,030
+صور
+
+118
+00:10:26,470 --> 00:10:31,930
+هذه لا تثبت هذه لا تثبت هذه لا تثبت التلاتة يبقى
+
+119
+00:10:31,930 --> 00:10:36,750
+مافيش غيرهم يبقى عرفنا أيش المقصود بال stabilizer
+
+120
+00:10:36,750 --> 00:10:42,170
+لل element يعني كل ال permutations اللي موجودة في
+
+121
+00:10:42,170 --> 00:10:46,210
+ال group اللي هنا بحيثهذه ال parameter يكون ال a
+
+122
+00:10:46,210 --> 00:10:51,470
+هذا رقم ثابت يعني fixed صورته هو نفسه فهمنا إيش
+
+123
+00:10:51,470 --> 00:10:56,590
+معنى stabilizer لإيه؟ طيب ننتقل الآن إلى السؤال
+
+124
+00:10:56,590 --> 00:11:05,610
+الذي يليه اللي هو 32 سؤال 32 بيقول ما يأتي أخدنا
+
+125
+00:11:05,610 --> 00:11:12,390
+beta تساوي واحد تلاتة خمسة سبعة تسعة تمانية ستة
+
+126
+00:11:24,410 --> 00:11:32,160
+مضروبة في اتنين اربع عاشرة2 4 10 بالشكل اللي عن
+
+127
+00:11:32,160 --> 00:11:36,560
+هنا بقول what is the smallest positive integer n
+
+128
+00:11:36,560 --> 00:11:47,440
+for which بحيث أن بيتا أس n يسوى بيتا أس ناقص خمسة
+
+129
+00:11:57,540 --> 00:12:02,820
+نرجع لسؤالنا مرة تانية ماتينا permutation beta
+
+130
+00:12:02,820 --> 00:12:09,680
+عبارة عن product of two disjoint cycles تمام و
+
+131
+00:12:09,680 --> 00:12:13,920
+واحد حطينا فواصل مرة هذه فواصل ليش مش هنا الرقم
+
+132
+00:12:13,920 --> 00:12:18,870
+عشرةرقمين بلاش تقول هذا اربع يعني طوله اربع وهذا
+
+133
+00:12:18,870 --> 00:12:22,790
+طوله جد ما يكون بقولها يبقى حاطين الفواصل مش
+
+134
+00:12:22,790 --> 00:12:27,570
+هنقولك ان العشرة عبارة عناش عنصر واحد ما علينا مش
+
+135
+00:12:27,570 --> 00:12:35,990
+مشكلةبقولي ما هو أصغر رقم N بحط اس ل Beta بده
+
+136
+00:12:35,990 --> 00:12:42,450
+يعطيني Beta أس سالب خمسة يعني حددتلك أصغر رقم ها
+
+137
+00:12:42,450 --> 00:12:47,970
+مش حيال لا رقام تمام بقولي بدي قديش قيمة N هذه
+
+138
+00:12:47,970 --> 00:12:53,190
+بقول و الله كويسة الآن احنا لو جينا لل order كبار
+
+139
+00:12:53,190 --> 00:12:53,570
+ال B
+
+140
+00:13:01,200 --> 00:13:07,960
+هل في بينهم عنصر مشتركيبقى ال order ل beta هو ال
+
+141
+00:13:07,960 --> 00:13:12,660
+least common multiple ما بين طول الأولى اتنين
+
+142
+00:13:12,660 --> 00:13:19,260
+اربعة ستة سبعة و طول التانية كده تلاتة يبقى ال
+
+143
+00:13:19,260 --> 00:13:24,540
+least common multiple لهم كده واحد وعشرين معناته
+
+144
+00:13:24,540 --> 00:13:29,700
+ال order ل beta بدي نسوي واحد وعشرين هذا معناه ان
+
+145
+00:13:29,700 --> 00:13:35,360
+beta أس واحد وعشرينيساوي ال identity والواحد
+
+146
+00:13:35,360 --> 00:13:41,200
+وعشرين هو أصغر الرقم حطيته لل أس بيتا اتانى مين
+
+147
+00:13:41,200 --> 00:13:46,160
+اتانى ال identity طيب ايش بيقولى فى السؤال ما هو
+
+148
+00:13:46,160 --> 00:13:52,880
+أصغر رقم ان بتحطه أس لبيتا بتطلع بيتا أس خمسة
+
+149
+00:13:52,880 --> 00:14:02,370
+بقوله آه الآنباجي بقوله ولكن ال beta أُس n بدها
+
+150
+00:14:02,370 --> 00:14:09,130
+تساوي beta أُس سالب خمسة implies شو رايك لو ضربت
+
+151
+00:14:09,130 --> 00:14:15,130
+الطرفين في beta أُس خمسة بس فيدي عندى هنا beta أُس
+
+152
+00:14:15,130 --> 00:14:21,990
+n زائد خمسة بده يساوي مين ال identity لما اطلع في
+
+153
+00:14:21,990 --> 00:14:27,840
+هذه هيك واطلع في هذه هيكو قال لي في السؤال بيتا
+
+154
+00:14:27,840 --> 00:14:34,660
+الان هذا أصغر رقم حاطيته كأس لبيتا طلع بيتا أس
+
+155
+00:14:34,660 --> 00:14:39,320
+سالب خمسة إذا ما هي العلاقة بين الرقمين الاتنين
+
+156
+00:14:39,320 --> 00:14:48,160
+هدول بيك اسمه والله بيسويه بيسويه لأنه أصغر رقم
+
+157
+00:14:48,160 --> 00:14:53,800
+لكن قال لي الان هذا رقم حيال اللهبقوله إذا ال 21
+
+158
+00:14:53,800 --> 00:14:58,580
+لازم تجسم من الرقم اللي عندنا هذا لكن كونه قاللي
+
+159
+00:14:58,580 --> 00:15:04,740
+إن أصغر الرقم و أني أثبت ان ال order ل beta هو 21
+
+160
+00:15:05,480 --> 00:15:11,400
+إذا هذا الرقم من الاتنين هدول مع بعض بستنتج ان ال
+
+161
+00:15:11,400 --> 00:15:17,360
+N زائد خمسة يساوي واحد وعشرين يبقى ال N تساوي كده؟
+
+162
+00:15:17,360 --> 00:15:26,840
+ستاشر إذا أصغر رقم بحط أس ل Beta بيطلع لي Beta أس
+
+163
+00:15:26,840 --> 00:15:33,880
+لخمسة هو الرقم اين؟ الرقماللي هو ستاشر طيب السؤال
+
+164
+00:15:33,880 --> 00:15:40,940
+اللي بعده نفس الفكرة بس ماقلش أصغر رقم هذا اتنين و
+
+165
+00:15:40,940 --> 00:15:47,250
+تلاتين تلاتة و تلاتين ماعطيني Alpha كتالةيبقى هذه
+
+166
+00:15:47,250 --> 00:15:52,250
+تلاتة و تلاتين ماتيني Alpha تساوي اللي هو واحد
+
+167
+00:15:52,250 --> 00:15:58,730
+تلاتة خمسة سبعة تسعة واحد تلاتة خمسة سبعة تسعة
+
+168
+00:15:58,730 --> 00:16:03,350
+بالشكل اللي عندنا هذا وهذه مضروبة في اتنين اربعة
+
+169
+00:16:03,350 --> 00:16:10,970
+ستة اتنين اربعة ستة وهذه مضروبة كمان في تمانية و
+
+170
+00:16:10,970 --> 00:16:16,870
+عشرة تمانية و عشرة بالشكل اللي عندنا هذاو بقول ليش
+
+171
+00:16:16,870 --> 00:16:27,330
+إذا كان ال A أُس M is a خمسة cycle is a خمسة cycle
+
+172
+00:16:27,330 --> 00:16:37,210
+يعني ال cycle طولها خمسة خمسة cycle what can you
+
+173
+00:16:37,210 --> 00:16:42,870
+say about M what
+
+174
+00:16:42,870 --> 00:16:53,220
+اللي هوwhat can you say
+
+175
+00:16:53,220 --> 00:17:00,840
+about M السؤال
+
+176
+00:17:00,840 --> 00:17:05,080
+هذا زي ما انت بلاحظ هو السؤال اللى جابله مع الفارق
+
+177
+00:17:05,080 --> 00:17:12,120
+شو الفارق هناك قالك ان أصغر رقم مظبوط هنا ماجليش M
+
+178
+00:17:12,120 --> 00:17:18,900
+كل اللى قالوه ليشجرح قال لي الام خمسة cycle يعني
+
+179
+00:17:18,900 --> 00:17:25,920
+ال order له يسوي كده؟ ال order لام خمسة تمام لإنه
+
+180
+00:17:25,920 --> 00:17:29,840
+قال له ال cycle طولة خمسة مدام طولة خمسة إذا ال
+
+181
+00:17:29,840 --> 00:17:35,180
+order لهذه ال cycle يسوي خمسة يعني a أس m أس خمسة
+
+182
+00:17:35,180 --> 00:17:40,590
+لازم يعطينا مين؟ ال islandالألفة بالشكل اللي عندها
+
+183
+00:17:40,590 --> 00:17:44,870
+ده باذي بتطلع في three cycles ولا element مشترك
+
+184
+00:17:44,870 --> 00:17:49,760
+فيه ما بينهماإذا على طول الخطب بروح بقوله ال order
+
+185
+00:17:49,760 --> 00:17:55,600
+لل alpha بده يساوي ال least common multiple لمن؟
+
+186
+00:17:55,600 --> 00:18:00,500
+لطول الأولى خمسة وطول الثانية تلاتة وطول الأخيرة
+
+187
+00:18:00,500 --> 00:18:05,460
+اتنين يبقى الرقم اللذي يقسم على او الرقم اللي
+
+188
+00:18:05,460 --> 00:18:10,560
+بيقسمه التلاتة في انا نواحد هو الرقم كم؟ تلاتين
+
+189
+00:18:10,560 --> 00:18:15,780
+ممتاز جدايبقى ال order ل alpha بده يسوى تلاتين
+
+190
+00:18:15,780 --> 00:18:20,800
+بيبقى ال alpha أس تلاتين بده يسوى من ال identity
+
+191
+00:18:20,800 --> 00:18:26,200
+هذا معناه ان ال alpha أس تلاتين بده يسوى ال
+
+192
+00:18:26,200 --> 00:18:32,240
+identity element والتلاتين أصغر رقم بحط أس ل alpha
+
+193
+00:18:32,240 --> 00:18:36,850
+بيطل من ال identity اللي أنا اشي قال ليهقال لي لو
+
+194
+00:18:36,850 --> 00:18:45,790
+كان ال AM is A خمسة cycle يعني ال AM لو جيت قلت له
+
+195
+00:18:45,790 --> 00:18:51,930
+مين هم الخمسة cycle قلت A B C D E هاي خمسة cycle
+
+196
+00:18:52,340 --> 00:18:59,020
+معناته ان ال order ل ال AM بده يسوي كده؟ بده يسوي
+
+197
+00:18:59,020 --> 00:19:06,880
+خمسة معناته ان ال AM أُس خمسة بده يعطي نمين ال
+
+198
+00:19:06,880 --> 00:19:13,280
+identity يعني معنى هذا الكلام أن A خمسة M بده يسوي
+
+199
+00:19:13,280 --> 00:19:19,740
+نمين ال identity elementهل حطينا قيود أو شروط على
+
+200
+00:19:19,740 --> 00:19:26,680
+M لا ماحطيناش على M ولا قيد ولا شرط اللهم إلا قلنا
+
+201
+00:19:26,680 --> 00:19:31,180
+Alpha أس M عبارة عن خمسة cycle يعني ال cycle طولها
+
+202
+00:19:31,180 --> 00:19:36,540
+يساوي خمسة طيب ماقلتش زي السؤال اللي جابله إن ال N
+
+203
+00:19:36,540 --> 00:19:41,910
+أصغر رقام لا ماحطيتش قيود على M بناء عليهلما يكون
+
+204
+00:19:41,910 --> 00:19:46,670
+عندى alpha أس تلاتين والتلاتين هو أصغر رقم بدي
+
+205
+00:19:46,670 --> 00:19:50,970
+يعطينا ال identity وال A أس خمسة M يساوي ال
+
+206
+00:19:50,970 --> 00:19:56,070
+identity إذا ما هي العلاقة ما بين التلاتين والخمسة
+
+207
+00:19:56,070 --> 00:20:05,910
+M تلاتين تقسم الخمسة M أو الخمسة M مضعفات التلاتين
+
+208
+00:20:05,910 --> 00:20:10,390
+هذه و هذه اتنين نفس الصورةاذا من الاتنين هدول بس
+
+209
+00:20:10,390 --> 00:20:18,990
+تنتج انه تلاتين تقسم خمسة M مين
+
+210
+00:20:18,990 --> 00:20:24,790
+اللي بيحكي؟ ايوة ايش بتقول؟ ال A بتسوي ال Alpha؟ و
+
+211
+00:20:24,790 --> 00:20:30,210
+مين ال A هذه؟ ال A أنا قلته سوي Alpha؟أنا ماقلتش
+
+212
+00:20:30,210 --> 00:20:35,490
+أنا الكلام هو قال لي a أُس m is a خمسة كلمة معناته
+
+213
+00:20:35,490 --> 00:20:40,610
+permutation والله alpha أُس m قال alpha أُس m هو
+
+214
+00:20:40,610 --> 00:20:46,720
+سؤال طب إذا alpha أُس m مظبوطالمقصود اللي قلتلك
+
+215
+00:20:46,720 --> 00:20:51,000
+ايه و الله اللي هيبقى هذا Alpha أس M خمسة cycle
+
+216
+00:20:51,000 --> 00:20:56,020
+على أي حال حتى لو قلنا A أس M يسوى خمسة cycle
+
+217
+00:20:56,020 --> 00:21:02,380
+معناته ال A permutation صح
+
+218
+00:21:02,380 --> 00:21:08,000
+هذه احنا عدلناها ألفة أس M is A خمسة cycle معناته
+
+219
+00:21:08,000 --> 00:21:16,440
+هذه Alpha أس M معناته هذه Alpha هذه Alphaيبقى هذه
+
+220
+00:21:16,440 --> 00:21:23,760
+alpha يبقى التلاتين التلاتين بتقسم الخمسة M لو
+
+221
+00:21:23,760 --> 00:21:31,540
+جسمنا كله على خمسة بيظل عناش ستة تقسم ال M إذا ال
+
+222
+00:21:31,540 --> 00:21:39,900
+M شو علاقتها بستة مضاعفاتها يبقى هنا ال M is a
+
+223
+00:21:39,900 --> 00:21:48,100
+multiple of 6يبقى الام اللي عندنا هذه هي مضاعفات
+
+224
+00:21:48,100 --> 00:21:53,260
+مين؟ مضاعفات العدد ستة شوف السؤال اللي جابله وقلنا
+
+225
+00:21:53,260 --> 00:21:59,920
+لأ تساوي مثلا ستة دوري بس هنا مضاعفاته ليش؟ لأنه
+
+226
+00:21:59,920 --> 00:22:05,440
+لهناك هو أصغر رقم يعني يدخل في ال order بس احنا
+
+227
+00:22:05,440 --> 00:22:10,160
+عندنا في هذا السؤال ال order تلاتين يبقى أي رقم
+
+228
+00:22:10,160 --> 00:22:16,570
+آخر التلاتين بتجسم مين؟تجسم هذا الرقم هذا كان سؤال
+
+229
+00:22:16,570 --> 00:22:22,610
+تلاتة وتلاتين سؤال ستة وتلاتين قال لي في S4 بدنا
+
+230
+00:22:22,610 --> 00:22:28,010
+Cyclic subgroup of order أربعة و non-cyclic of
+
+231
+00:22:28,010 --> 00:22:38,230
+order أربعة سؤال ستة وتلاتين سؤال ستة وتلاتين بدنا
+
+232
+00:22:38,230 --> 00:22:51,580
+Cyclic groupof order أربعة in S4 وبدنا non-cyclic
+
+233
+00:22:51,580 --> 00:23:02,660
+group of order أربعة برضه in S4 solution S4
+
+234
+00:23:02,660 --> 00:23:09,500
+أكام عنصر فيها شباببس تمانية اس اربعة وعشرين عنصر
+
+235
+00:23:09,500 --> 00:23:14,380
+اللي قال تمانية بتقدر تجيبلي ال sub group من ال S
+
+236
+00:23:14,380 --> 00:23:18,220
+أربعة ال order اللي هيساوي تمانية يعني مافيش فيها
+
+237
+00:23:18,220 --> 00:23:25,660
+إلا تمان عناصر وقد D4 صحيح الكلام صحيح يبقى D4 هي
+
+238
+00:23:25,660 --> 00:23:31,560
+ال sub group من ال S4 وال order اللي هيساوي تمانية
+
+239
+00:23:31,560 --> 00:23:38,610
+تمامأي subgroup من ال D4 هي subgroup من ال S4 يبقى
+
+240
+00:23:38,610 --> 00:23:43,570
+إذا بتجيبلي من ال D4 Cyclic group ال order اللي
+
+241
+00:23:43,570 --> 00:23:50,470
+هيساوي أربعة بكل قدّيت الواجب يلا هيغششناك من D4
+
+242
+00:23:50,470 --> 00:23:53,730
+بتقدر تجيبلي ال subgroup ال order اللي هيساوي
+
+243
+00:23:53,730 --> 00:23:54,350
+أربعة
+
+244
+00:24:07,840 --> 00:24:11,460
+D4D4R0R90R180R270HVDD' ممتاز جدا يبقى ال rotation
+
+245
+00:24:11,460 --> 00:24:18,080
+واحدة R290الأردر لها يساوي أربعة وتساوي ال
+
+246
+00:24:18,080 --> 00:24:22,100
+subgroup generated by R ميتين وسبعين لأن ال R
+
+247
+00:24:22,100 --> 00:24:26,080
+ميتين وسبعين هي ال inverse لمين يبقى احنا بدنا
+
+248
+00:24:26,080 --> 00:24:29,040
+واحدة بدناش تنتين بس تنتين واحدة والله يعطيك
+
+249
+00:24:29,040 --> 00:24:37,860
+العافية يبقى باجي بقوله الان the cyclic subgroup
+
+250
+00:24:37,860 --> 00:24:47,620
+اللي هي مينالـ R تسعين اللي عناصرها R نوت و R
+
+251
+00:24:47,620 --> 00:24:58,200
+تسعين و R مية و تمانين و R ميتين و سبعين هذه is of
+
+252
+00:24:58,200 --> 00:25:04,980
+order اللي هو أربعة إذا
+
+253
+00:25:04,980 --> 00:25:12,960
+بدك تكتبها على شكل cycle يبقى عندكالارت السعيد هي
+
+254
+00:25:12,960 --> 00:25:18,820
+عبارة عن واحد اتنين تلاتة اربع يبقى هي ال cycle
+
+255
+00:25:18,820 --> 00:25:24,140
+اللي عندنا هنا تمام يبقى هذه هي الارت السعيد هذا
+
+256
+00:25:24,140 --> 00:25:28,120
+لو حبيت تشتغل ال cycles حبيت مباشرة تشتغل مع الناس
+
+257
+00:25:28,120 --> 00:25:37,110
+مشكلة طيب بدنا non-cyclic يبقى دي non-cyclica
+
+258
+00:25:37,110 --> 00:25:45,170
+group of order أربعة أزم تقدر تجيب أكتر من واحدة
+
+259
+00:25:45,170 --> 00:25:50,970
+ال sub group تحتوي على ال identity الحين بقدر
+
+260
+00:25:50,970 --> 00:25:57,850
+أقولك ال identity are not وكمان are مية و تمانين
+
+261
+00:25:59,600 --> 00:26:08,640
+وحط عليهم H والر مية و تمانين فيه H الشكل اللي
+
+262
+00:26:08,640 --> 00:26:17,130
+عندنا هناهذه non-cyclic لأن الـR180S² بتعطيك ال
+
+263
+00:26:17,130 --> 00:26:21,470
+identity يبقى ماهياش generator هذه بتعطيك ال
+
+264
+00:26:21,470 --> 00:26:26,170
+identity التربية بتعطيك ال identity وهذه التربية
+
+265
+00:26:26,170 --> 00:26:30,730
+برضه بتعطيك ال identity طبعا هذه لو رجعت للجدول
+
+266
+00:26:30,730 --> 00:26:35,850
+صفة 31 يبقى R0 وR180
+
+267
+00:26:38,670 --> 00:26:42,510
+وهذه لو فتحنا الجدول في صفحة مية و واحد و تبقى في
+
+268
+00:26:42,510 --> 00:26:49,150
+صفحة واحد و تلاتين و طبعا حسبناها قبلك اللي هو ال
+
+269
+00:26:49,150 --> 00:26:55,250
+R مية و تمانين في H R مية و تمانين R مية و تمانين
+
+270
+00:26:55,250 --> 00:27:07,200
+في H بتعطيك V يبقى V طبعا لو حطيت ايشحط ما احنا
+
+271
+00:27:07,200 --> 00:27:11,260
+بقوله فيه كمان واحدة تانية يعني اول اتنين خليهم زي
+
+272
+00:27:11,260 --> 00:27:12,900
+ما هو ده اللي بتحطهم بنفع
+
+273
+00:27:16,940 --> 00:27:22,520
+أحنا أعطيتك كمثال بسيط يعني انت .. انت .. انت ..
+
+274
+00:27:22,520 --> 00:27:26,780
+بس لما تجيب عناصر بدك تتأكد انه لو وفعته لأي أس
+
+275
+00:27:26,780 --> 00:27:30,280
+بدي يكون موجود و لو ضربت اثنين في بعض بدي يكون
+
+276
+00:27:30,280 --> 00:27:34,100
+موجود فيها عشان تتأكد ان هذه فعلا subgroup ليها
+
+277
+00:27:34,100 --> 00:27:37,740
+closed under the operation أنا اختارت من D4 لإنه
+
+278
+00:27:37,740 --> 00:27:41,400
+أسهل ليه لإن D4 أنا ازهجت و أنا بشرح فيها و يمكن
+
+279
+00:27:41,400 --> 00:27:45,520
+يعطينا عليها مثال بدل مثال عشرة يبقى أصبحت محفوظة
+
+280
+00:27:45,520 --> 00:27:51,150
+بالنسبة لناومن هنا نجب لك هذا كمثال بسيط منها على
+
+281
+00:27:51,150 --> 00:27:57,310
+أي حال هذا كان سؤال اللي هو ستة و تلاتين بعده عندك
+
+282
+00:27:57,310 --> 00:28:04,430
+سبعة و أربعين وما أدراك سبعة و أربعين سؤال سبعة و
+
+283
+00:28:04,430 --> 00:28:11,010
+أربعين بيقول ما ياتي show that every elementالفة
+
+284
+00:28:11,010 --> 00:28:19,370
+الموجودة في الان أي element في الان can be
+
+285
+00:28:19,370 --> 00:28:23,930
+expressed as a three cycle or product of a three
+
+286
+00:28:23,930 --> 00:28:35,310
+cycle يبقى is written as a three cycle or product
+
+287
+00:28:35,310 --> 00:28:39,450
+of a three cycles
+
+288
+00:28:43,140 --> 00:28:48,560
+فكر معايا كويس السؤال ليس سهلا لكن بده تفكير
+
+289
+00:28:48,560 --> 00:28:56,400
+الحقيقة ومن خلال التفكير قد نصل الى النتيجة حد
+
+290
+00:28:56,400 --> 00:29:01,800
+فيكوا حلوا الدار هذا ايه او جاب فكرة يعنيطبعا
+
+291
+00:29:01,800 --> 00:29:06,160
+هيقول لي السؤال مش هذا دي؟ اه مش هذا دي صحيح رغم
+
+292
+00:29:06,160 --> 00:29:09,540
+انه فردي لكن مايعطيك hint في الكتاب لكن hint لن
+
+293
+00:29:09,540 --> 00:29:14,880
+تستفيد منها شيئا مش هتعرف تشغلها طيب على اي حال
+
+294
+00:29:14,880 --> 00:29:21,200
+السؤال مرة تانية بيقولي اي even permutation او اي
+
+295
+00:29:21,200 --> 00:29:25,580
+element موجود في a,nis written يابنك يمكن نكتبه
+
+296
+00:29:25,580 --> 00:29:29,800
+على شكل three cycle يعني ما product of three
+
+297
+00:29:29,800 --> 00:29:40,960
+cycles طيب يبقى الحل كتالي solution let
+
+298
+00:29:40,960 --> 00:29:52,510
+alpha موجودة في الثم الـ alpha is an even
+
+299
+00:29:52,510 --> 00:29:58,490
+permutation تمام؟
+
+300
+00:29:58,490 --> 00:30:03,530
+لما أقول لك even permutation يعني يمكن حصل ضرب two
+
+301
+00:30:03,530 --> 00:30:09,890
+transpositions صح؟ يمكن أربع transpositions مش
+
+302
+00:30:09,890 --> 00:30:15,210
+تلاتة انت لازم تصير goodيمكن ستة transpositions
+
+303
+00:30:15,210 --> 00:30:20,790
+يمكن تمانية قد ما يكون يكون أيوة يبقى هنا ال alpha
+
+304
+00:30:20,790 --> 00:30:26,750
+بكتبها على شكل أزواج من ايه من ال transpositions
+
+305
+00:30:26,750 --> 00:30:33,630
+يبقى باجي بقوله هذا بده يعطينا ان ال alpha is
+
+306
+00:30:33,630 --> 00:30:42,050
+written as a product of
+
+307
+00:30:43,150 --> 00:30:49,410
+pairs أزواج of two cycles أو transpositions
+
+308
+00:30:54,380 --> 00:31:00,520
+طيب بدي اخد زوج من هذه الأزواج يعني بدي اخد اتنين
+
+309
+00:31:00,520 --> 00:31:05,660
+transpositions واشوف هل بقدر اكتبهم على شكل three
+
+310
+00:31:05,660 --> 00:31:11,020
+cycles ولا لأ انه كان كل زوج بنقدر نكتبه على شكل
+
+311
+00:31:11,020 --> 00:31:15,480
+three cycles يبقى ال alpha فيها اتنين ولا اربع ولا
+
+312
+00:31:15,480 --> 00:31:22,220
+ستة ولا تمانية كلها بقدر اكتبها على شكلمشان هنا
+
+313
+00:31:22,220 --> 00:31:26,540
+قلت alpha بقدر اكتبها على شكل of pairs of two
+
+314
+00:31:26,540 --> 00:31:32,140
+cycle يعني الزوج يعني اتنين transpositions يبقى
+
+315
+00:31:32,140 --> 00:31:42,180
+هنا لو جيت قلت if ال a والb والc والd are distinct
+
+316
+00:31:42,180 --> 00:31:44,880
+then
+
+317
+00:31:46,690 --> 00:31:52,130
+this pair has
+
+318
+00:31:52,130 --> 00:32:02,670
+the following cases
+
+319
+00:32:02,670 --> 00:32:07,310
+أنا
+
+320
+00:32:07,310 --> 00:32:13,270
+عندي أربع عناصر مختلفة والزوج هذا يعني even
+
+321
+00:32:13,270 --> 00:32:21,520
+permutationإذا الاحتمال الأول انه يكون على شكل AB
+
+322
+00:32:21,520 --> 00:32:32,060
+في AB يعني أول عنصر مكررات AB زي CD CD CD CD زي A
+
+323
+00:32:32,060 --> 00:32:40,060
+B A B طب هدول حصل ضرب مش بيطينا مين ال
+
+324
+00:32:40,060 --> 00:32:43,320
+parameter one اتنين واحد اتنين لو ضربت في عضاش
+
+325
+00:32:43,320 --> 00:32:51,730
+بتعطيلهبتعطيك واحد اتنين؟ بتعطيلك مين؟identity
+
+326
+00:32:51,730 --> 00:32:55,510
+permutation مش قلنا ال identity permutation نستطيع
+
+327
+00:32:55,510 --> 00:32:59,450
+نسكبها على شكل زوجي ومكتوبة عندك في الكتاب واحد
+
+328
+00:32:59,450 --> 00:33:02,970
+اتنين واحد اتنين او واحد اتنين واحد اتنين تلاتة
+
+329
+00:33:02,970 --> 00:33:06,590
+اربعة تلاتة اربعة او خمسة ستة خمسة يعني بقدر
+
+330
+00:33:06,590 --> 00:33:11,350
+اكتبها على شكل زوج اذا هذه تعطينا اللي هو الاحتمال
+
+331
+00:33:11,350 --> 00:33:17,050
+الاول انه E لان ال E is an even permutation
+
+332
+00:33:17,050 --> 00:33:26,910
+الاحتمال الثانيإنه تبقى على الشكل ABC صح ولا لأ
+
+333
+00:33:26,910 --> 00:33:32,370
+لإحتمال التالت يكون فش عنصر فيما بينهما لإحتمال
+
+334
+00:33:32,370 --> 00:33:38,570
+الثالث والاخير ان يكون على الشكل ABCD
+
+335
+00:33:38,570 --> 00:33:45,750
+في غير هيك؟طيب في كل حالة من الحالات الثلاث انا
+
+336
+00:33:45,750 --> 00:33:50,070
+بدي أبيّلك انه بنكتبها على شكل product of three
+
+337
+00:33:50,070 --> 00:33:55,050
+cycles او three cycle واحدة تمام خلّينا نمسك
+
+338
+00:33:55,050 --> 00:34:01,710
+الحالة الأولى يبقى الحالة الأولى اللي هي a b a b
+
+339
+00:34:01,710 --> 00:34:08,930
+اللي هي ال identity permutation تمامأليست ال
+
+340
+00:34:08,930 --> 00:34:16,470
+identity permutation هي عبارة عن ال a,b,c الكل
+
+341
+00:34:16,470 --> 00:34:22,970
+تكييف؟مش هذه طولها تلاتة يبقى ال order اللي هي
+
+342
+00:34:22,970 --> 00:34:27,530
+تلاتة يبقى مكعبها بدي يعطينا ال identity يبقى كأنه
+
+343
+00:34:27,530 --> 00:34:32,230
+ضارب ال cycle ABC في ABC في ABC يبقى product of
+
+344
+00:34:32,230 --> 00:34:36,450
+three cycles مظبوط ولا لا؟ حد بيقدر يعترض على هذا
+
+345
+00:34:36,450 --> 00:34:41,330
+الكلام اللي عنده اعتراض يحكي حتى نفند هذا الاعتراض
+
+346
+00:34:41,330 --> 00:34:52,750
+يبقى هذا اسمه productof three cycles تمام؟ يبقى
+
+347
+00:34:52,750 --> 00:34:56,890
+خلاصه من النقطة الأولى شوف النقطة الأولى اعتمدت
+
+348
+00:34:56,890 --> 00:35:01,530
+على فهمك فلانت فاهم فعلا ان ال identity variation
+
+349
+00:35:01,530 --> 00:35:07,270
+is an even وكيف كتبناها لما صارت even طبعا مكتوب
+
+350
+00:35:07,270 --> 00:35:11,110
+عندك على التواب وشرحالكه لأستاذ محمود طيب نيجي
+
+351
+00:35:11,110 --> 00:35:17,040
+للنقطة الثانيةالنقطة الثانية اللى همين اللى هى ال
+
+352
+00:35:17,040 --> 00:35:24,140
+A B A C كويس بدي أجيب ال composition ما بين
+
+353
+00:35:24,140 --> 00:35:28,720
+الاتنين لإنه فى عنصر مشترك فى ما بينهما إذا هذول
+
+354
+00:35:28,720 --> 00:35:34,080
+are not disjoint بدي أخليهم disjoint يبقى لو جيت
+
+355
+00:35:34,080 --> 00:35:41,560
+قلتلك العنصر الأول هو AA ثورت مين؟ C الـC ثورتها
+
+356
+00:35:41,560 --> 00:35:49,720
+مين؟ C لأن الـC هنا مقفل، C بعد ذلك الـC ثورتها A
+
+357
+00:35:49,720 --> 00:35:57,120
+والـA ثورتها B بعد ذلك الـB مقفل ثورتها B والـB
+
+358
+00:35:57,120 --> 00:36:03,060
+ثورتها موجودة يبقى قفلة يبقى ال composition ما بين
+
+359
+00:36:03,060 --> 00:36:10,640
+اتنين هذول هي three cycleأولتين اتنين بساطة
+
+360
+00:36:10,640 --> 00:36:19,100
+المشكلة في التالتة يبقى التالتة هاية التالتة عنا A
+
+361
+00:36:19,100 --> 00:36:29,400
+B C D يوسام هذه الخبرة بتلعب دور كبير هل بقدر اكتب
+
+362
+00:36:29,400 --> 00:36:36,710
+هدولعلى شكل product of three cycles هذا السؤال حتى
+
+363
+00:36:36,710 --> 00:36:40,370
+و لو كان في بينهم عناصر مشتركة ماعنديش مشكلة المهم
+
+364
+00:36:40,370 --> 00:36:46,050
+ان اقدر اكتبها على شكل three cycles انا ازعم انه
+
+365
+00:36:46,050 --> 00:36:53,430
+بقدر بقدر اقوله a و هنا d و b و التاني بدي اخد a d
+
+366
+00:36:53,430 --> 00:36:59,890
+cطب زعمك هذا صحيح و الله ما يصحيح بقوله تعال خد ال
+
+367
+00:36:59,890 --> 00:37:03,270
+composition ما بين الأتنين M طلع الطرف هذا يبقى
+
+368
+00:37:03,270 --> 00:37:08,230
+كتابتي صح ماطلعش يبقى كتابتي غلط تمام؟ بقولك كويس
+
+369
+00:37:08,230 --> 00:37:14,070
+تعال ناخد ال M بدي أبدأ بالعنصر A ال A صورته و ال
+
+370
+00:37:14,070 --> 00:37:20,070
+D صورته هذا ال B ماجفلت شهر لسه بالداجة هنا ال B
+
+371
+00:37:20,070 --> 00:37:22,430
+صورتها B
+
+372
+00:37:24,280 --> 00:37:32,180
+الـ B صورتها B والـ B صورتها ايش؟ جفنة تمام خلصت
+
+373
+00:37:32,180 --> 00:37:36,970
+ال A و ال B بده روح لل Cالان هاي كتبت الـC الـC
+
+374
+00:37:36,970 --> 00:37:42,890
+صورتها A والـA صورتها D هذا الـD بدي أمسك الـD
+
+375
+00:37:42,890 --> 00:37:49,330
+الـD صورتها C والـC صورتها هاي يبقى قفلا يبقى
+
+376
+00:37:49,330 --> 00:37:54,750
+معناته فعلا هذول كتبتم على شكل product of three
+
+377
+00:37:54,750 --> 00:38:07,030
+cycles يبقى هذا productof three cycles إذا الزوج
+
+378
+00:38:07,030 --> 00:38:12,810
+تبع Transposition مهما كان شكله قدرت أكتبه يا إما
+
+379
+00:38:12,810 --> 00:38:17,630
+على شكل every cycle يا product of three cycles
+
+380
+00:38:17,630 --> 00:38:21,030
+السؤال سهل مع هذا النقطة الأخيرة النقطة الأخيرة
+
+381
+00:38:21,030 --> 00:38:24,950
+بيبقى تقعد تفكر كيف تكتب بحيث ال composition فيما
+
+382
+00:38:24,950 --> 00:38:30,660
+بينهمايعطيك مين؟ يعطيك الـ two transposition و هذه
+
+383
+00:38:30,660 --> 00:38:34,740
+عملية ليست سهلة أما الباقى مباشرة اتنين الأولانين
+
+384
+00:38:34,740 --> 00:38:42,320
+تمام؟ يبقى هنا لما ناخد كل اتنين كل زوج من ال two
+
+385
+00:38:42,320 --> 00:38:46,910
+transposition كل واحد بقدر اكتب على شكل مين؟3
+
+386
+00:38:46,910 --> 00:38:50,430
+cycle خد الزوج اللي بعده والزوج اللي بعده واللي
+
+387
+00:38:50,430 --> 00:38:54,910
+بعده قد ما بدك كله بتكتب ويش على شكل three cycles
+
+388
+00:38:54,910 --> 00:39:01,490
+لذلك أي element alpha موجود في الان is a three
+
+389
+00:39:01,490 --> 00:39:04,890
+cycle or a product of a three cycle أي التانية
+
+390
+00:39:04,890 --> 00:39:08,910
+كانت a three cycle الأولى والتالتة product of a
+
+391
+00:39:08,910 --> 00:39:11,770
+three cycle يبقى هنا
+
+392
+00:39:15,780 --> 00:39:24,260
+الخطوة الأولى اللى موجودة في a and is a three
+
+393
+00:39:24,260 --> 00:39:32,960
+cycle or product of a three cycles
+
+394
+00:39:36,830 --> 00:39:41,170
+السؤال على درجة من الأهمية لكن لو تركتك لحالك اللي
+
+395
+00:39:41,170 --> 00:39:44,130
+يوم تقدر تحلله يمكن تجيب الأولى والتانية بس
+
+396
+00:39:44,130 --> 00:39:48,930
+التالتة لا يمكن ان تأتي بيها يبقى هاي بساطنا حالك
+
+397
+00:39:48,930 --> 00:39:55,590
+الان نروح لسؤال ستة وخمسين سؤال ستة وخمسين
+
+398
+00:39:57,800 --> 00:40:02,060
+يقول ليش هذا عدد يا صاحب نشوف قال يقبل Alpha و
+
+399
+00:40:02,060 --> 00:40:07,580
+Beta موجودة في S4 Alpha و Beta ولا Jama و Beta
+
+400
+00:40:07,580 --> 00:40:14,940
+يبقى Beta و Jama Beta و Jama التنتين هذول ال
+
+401
+00:40:14,940 --> 00:40:21,940
+permutations موجودات في S4 وفي نفس الوقت Beta Jama
+
+402
+00:40:22,340 --> 00:40:29,000
+بيتا جاما بيتا تساوي واحد اربعة تلاتة اتنين واحد
+
+403
+00:40:29,000 --> 00:40:36,860
+اربعة تلاتة اتنين وجاما بيتا تساوي وجاما بيتا واحد
+
+404
+00:40:36,860 --> 00:40:43,600
+اتنين اربعة تلاتة واحد اتنينأربعة تلاتة وزيادة على
+
+405
+00:40:43,600 --> 00:40:48,540
+ذلك beta of واحد يساوي الأربعة و beta لما اتأثر
+
+406
+00:40:48,540 --> 00:40:54,600
+على الواحد بده يساوي الأربعة قال لي determine حدد
+
+407
+00:40:54,600 --> 00:41:01,440
+determine اللي هو beta and gamma بدي أعرف أيه شكل
+
+408
+00:41:01,440 --> 00:41:08,290
+ال beta و كذلك gammaبمعنى أخر أكتبها لي على شكل
+
+409
+00:41:08,290 --> 00:41:13,470
+الـcycle زي ما هؤلاء المكتوبات على شكل الـcycle حد
+
+410
+00:41:13,470 --> 00:41:20,010
+فيكوا حل السؤال هذا ؟ يالا يا أبو الأعدادات اللي
+
+411
+00:41:20,010 --> 00:41:21,670
+بتكلم بالأعداد
+
+412
+00:41:31,120 --> 00:41:37,720
+هو زوّق؟ طيب حد فيكوا حل السؤال هذا في البيت؟ none
+
+413
+00:41:37,720 --> 00:41:44,100
+علما انه very easy بس انت شغل مخك و الشيء هيو
+
+414
+00:41:44,100 --> 00:41:49,140
+قدامك الحل لا بد تفكير ولا هاجر بدنا نشتغل الشغل
+
+415
+00:41:49,140 --> 00:41:55,450
+روتينيانت عندك alpha و beta و جامعة في S4 و ال
+
+416
+00:41:55,450 --> 00:41:59,190
+composition ما بين اتنين من اليمين والشمال هيو على
+
+417
+00:41:59,190 --> 00:42:03,430
+شكل الcycle و ماطيك تأثير ال beta على الواحد يساوي
+
+418
+00:42:03,430 --> 00:42:08,190
+الأربعة قليهتلي شكل ال beta و شكل الجامعة يعني بدي
+
+419
+00:42:08,190 --> 00:42:10,790
+اشوف تأثير ال beta على واحد ايش بيعطينا و beta على
+
+420
+00:42:10,790 --> 00:42:13,170
+اتنين و beta على تلاتة و beta على اربعة وجامعة على
+
+421
+00:42:13,170 --> 00:42:15,050
+واحد وجامعة على اتنين وجامعة على تلاتة وجامعة على
+
+422
+00:42:15,050 --> 00:42:18,890
+اربعة القصة بسيطة جدا هاي solution
+
+423
+00:42:21,960 --> 00:42:27,100
+المعلومة اللى عندى ان ال beta of واحد بده ساوي
+
+424
+00:42:27,100 --> 00:42:34,780
+أربعة بنقدر نجيب gamma of أربعة جداش تساوي gamma
+
+425
+00:42:34,780 --> 00:42:43,020
+of أربعة نقدر يبقى أثر على الطرفين بجانب صح ولا لا
+
+426
+00:42:43,380 --> 00:42:48,700
+إذا لو أثرت على الطرفين بجامعة هذا بده يصبح على
+
+427
+00:42:48,700 --> 00:42:55,400
+الشكل ده جامعة beta of واحد يساوي جامعة of أربع
+
+428
+00:42:58,010 --> 00:43:02,930
+طيب جامة beta of واحد وين جامة beta هاي؟ جامة beta
+
+429
+00:43:02,930 --> 00:43:09,910
+of واحد صورتها ايش؟ اتنين يبقى هذا معناه انه اتنين
+
+430
+00:43:09,910 --> 00:43:17,550
+يساوي جامة of اربع هاي كان معلوم جديدة طيب سؤال
+
+431
+00:43:17,550 --> 00:43:23,760
+بنقدر نجيب beta of اتنينأثر على الطرفين بـ Beta
+
+432
+00:43:23,760 --> 00:43:30,400
+يبقى لو جينا يقولنا هنا Beta of اتنين يساوي Beta
+
+433
+00:43:30,400 --> 00:43:36,900
+Gamma of أربع يبقى معنى هذا الكلام أن ال Beta of
+
+434
+00:43:36,900 --> 00:43:43,380
+اتنين يساوي Beta Gamma of أربع بتعطينا مين؟ تلاتة
+
+435
+00:43:43,380 --> 00:43:56,220
+يبقى آي تلاتةالان بدنا جامع اوف تلاتة يبقى
+
+436
+00:43:56,220 --> 00:44:02,540
+هذه صارت جامع بيتا اوفي اتنين بده يسوي جامع اوف
+
+437
+00:44:02,540 --> 00:44:09,770
+تلاتة تمام هذا معناهان الجامعة beta of اتنين جامعة
+
+438
+00:44:09,770 --> 00:44:14,050
+beta of اتنين بيعطينا مين؟ بيعطينا أربعة يبقى
+
+439
+00:44:14,050 --> 00:44:21,210
+أربعة بده يساوي جامعة of تلاتة طيب ده أثر عليهم ب
+
+440
+00:44:21,210 --> 00:44:29,430
+beta يبقى بيصير beta of أربعة بده يساوي beta jama
+
+441
+00:44:29,430 --> 00:44:37,780
+of تلاتةهذا سيعطيك بيتا of أربعة يساوي بيتا جامعة
+
+442
+00:44:37,780 --> 00:44:47,420
+of ثلاثة بيعطيك اتنين طيب هذا سيعطيك بيتا جامعة of
+
+443
+00:44:47,420 --> 00:44:55,300
+أربعة يساوي جامعة of اتنين جامعة بيتا of أربعة
+
+444
+00:44:55,300 --> 00:45:08,290
+بيعطينايبقى تلاتة يبقى تلاتة يبقى يبقى يبقى يبقى
+
+445
+00:45:08,290 --> 00:45:21,590
+يبقى يبقى
+
+446
+00:45:21,590 --> 00:45:24,830
+يبقى
+
+447
+00:45:24,830 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+448
+00:45:26,130 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+449
+00:45:26,130 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+450
+00:45:26,130 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+451
+00:45:26,130 --> 00:45:30,390
+يبقى يبقى يبقى يبقى يبقىطيب هذا لو أثرت عليه ب
+
+452
+00:45:30,390 --> 00:45:38,010
+جامعة بيصير جامعة beta of تلاتة يساوي جامعة of
+
+453
+00:45:38,010 --> 00:45:44,830
+واحد هذا بده يعطيلك انه جامعة beta of تلاتة جامعة
+
+454
+00:45:44,830 --> 00:45:51,200
+beta of تلاتة بيعطيك واحديبقى الواحد يساوي جامعه
+
+455
+00:45:51,200 --> 00:45:55,300
+بواحد خلصنا هيك جامعه بواحد، جامعه باتنين، جامعه
+
+456
+00:45:55,300 --> 00:45:59,820
+بثلاثة، جامعه باربع، خلصنا البيتات هي هم كلهم يبقى
+
+457
+00:45:59,820 --> 00:46:05,240
+بناء العليا بقدر اكتب له بيته وجامعه يبقى بيته
+
+458
+00:46:05,240 --> 00:46:13,360
+بيدها تساوي بيته لو أثرت على الواحد ايش صورته؟
+
+459
+00:46:13,360 --> 00:46:21,150
+اربعطيب بيتا لو أثرت على الأربعاش تعطيك إتنين طيب
+
+460
+00:46:21,150 --> 00:46:26,570
+بيتا لو أثرت على الإتنين بتعطيك تلاتة طيب بيتا لو
+
+461
+00:46:26,570 --> 00:46:36,150
+أثرت على التلاتة بتعطيك قفلة تمام؟ يبقى أنداء ال
+
+462
+00:46:36,150 --> 00:46:43,520
+alpha تساوي بدي أخد الواحدالحين جامعة لو أثرت على
+
+463
+00:46:43,520 --> 00:46:51,660
+الواحد بتعطينا مين؟ يبقى قفلة، تمام؟ بعدها بتاخد
+
+464
+00:46:51,660 --> 00:46:58,360
+الاتنينجامع لو أثرت على الأتنين بتعطيني تلاتة جامع
+
+465
+00:46:58,360 --> 00:47:03,100
+لو أثرت على التلاتة بتعطيني أربعة جامع لو أثرت على
+
+466
+00:47:03,100 --> 00:47:07,340
+الأربعة بتعطيني اتنين، قفلة، يبقى هي ال cycle
+
+467
+00:47:07,340 --> 00:47:11,500
+اتنين، تلاتة، أربعة، واللي بيظهرش بيكون fixed
+
+468
+00:47:11,500 --> 00:47:19,100
+صعبها الشغل هذه؟ طيب، لحد هنا stop، انتهينا؟
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..93846c71468f003321a40dc25839ab8f039ff617
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_raw.srt
@@ -0,0 +1,1632 @@
+1
+00:00:21,750 --> 00:00:23,890
+بسم الله الرحمن الرحيم ان شاء الله يا شباب اليوم
+
+2
+00:00:23,890 --> 00:00:27,910
+هنكمل اللي بدناها في المحاضرة الماضية من مناقشة
+
+3
+00:00:27,910 --> 00:00:31,610
+اللي هو الوحدة التالتة المتعلقة بال subgroup طبعا
+
+4
+00:00:31,610 --> 00:00:35,230
+لذا وقفنا المرة الماضية عن سؤال تلاتة و تلاتين
+
+5
+00:00:35,230 --> 00:00:40,030
+كتبناه و ما حلناه نرجع نكتب السؤال السؤال بيقول
+
+6
+00:00:40,030 --> 00:00:46,710
+التاليإن لو كان عندي group وفيها two elements a وb
+
+7
+00:00:46,710 --> 00:00:51,170
+ال order ل ال a بدو يساوي اربع ال order ل ال b بدو
+
+8
+00:00:51,170 --> 00:00:55,490
+يساوي اتنين وعندي علاقة بتربط ال a و ال b بتقول ان
+
+9
+00:00:55,490 --> 00:01:02,450
+ال a تكايب بي بتساوي p في a المطلوب في السؤال find
+
+10
+00:01:02,450 --> 00:01:05,390
+order ال a,b
+
+11
+00:01:08,360 --> 00:01:11,440
+الطريقة اللى احنا بنتبعها لحساب ال order تبع أي
+
+12
+00:01:11,440 --> 00:01:16,500
+أنصر هو ان انا اشتغل على الانصر هذا و اعطيه powers
+
+13
+00:01:16,500 --> 00:01:21,480
+تنين تلاتة اربعة خمسة لما اصل لأقل او لأول عدد
+
+14
+00:01:21,480 --> 00:01:26,780
+صحيح موجب بيعطيني ال identity في البداية انا بدي
+
+15
+00:01:26,780 --> 00:01:32,420
+اثبت ان ال order لا يساوي واحد ا بي لا يساوي ال
+
+16
+00:01:32,420 --> 00:01:36,360
+identity claim هنحطها ك claim
+
+17
+00:01:41,470 --> 00:01:48,170
+تعالوا نثبتها Assume على النقيض that ان a,b بديوا
+
+18
+00:01:48,170 --> 00:01:54,850
+يساوي ال identity هذا معناته ان a بديت ساوي b
+
+19
+00:01:54,850 --> 00:02:00,110
+inverse وبالتالي order ال a بديه يساوي order ال b
+
+20
+00:02:00,110 --> 00:02:04,770
+inverse طبعا order ال b inverse هو ايش order ال b
+
+21
+00:02:04,770 --> 00:02:10,410
+وبالتالي الأربعة بديه يساوي اتنين وهذا ايش تنقدرة
+
+22
+00:02:11,450 --> 00:02:15,750
+صار عندى تناقض وبالتالي so ال a b لا يساوي ال
+
+23
+00:02:15,750 --> 00:02:21,550
+identity وبالتالي ال order لا يساوي واحد حد
+
+24
+00:02:21,550 --> 00:02:29,050
+هيسألني ليش انا كتبت هذا الشغل لان انا لما اكمل حل
+
+25
+00:02:29,050 --> 00:02:33,200
+الصورة اللى جيت هنكتشف ان ال order هيساوي اتنينلأن
+
+26
+00:02:33,200 --> 00:02:38,640
+AP تربية هيعطينا ال identity فالسؤال ان مادام ال
+
+27
+00:02:38,640 --> 00:02:42,440
+AP تربية هيعطينا ال identity فال order هيكون يا
+
+28
+00:02:42,440 --> 00:02:45,980
+اتنين يا واحد انا بأنفي هيكد ان يكون ال order
+
+29
+00:02:45,980 --> 00:02:54,820
+بيساوي واحد now لو قلنا AP الكل تربية عبارة عن ايش
+
+30
+00:02:54,820 --> 00:03:03,200
+عبارة عن AP AP زي ما احنا عارفين الدربأو العملية
+
+31
+00:03:03,200 --> 00:03:13,220
+بتحقيق خاصية التجميع هذا هي ساوي a في b a في b حسب
+
+32
+00:03:13,220 --> 00:03:19,080
+الخاصية لان بي اياش بتساويA في A تكيب في B في B
+
+33
+00:03:19,080 --> 00:03:24,700
+يعني A قص 4 في B تربيع ال identity في ال identity
+
+34
+00:03:24,700 --> 00:03:31,100
+بدي ساوي ال identity هذا معناته ان order ال AB أقل
+
+35
+00:03:31,100 --> 00:03:44,160
+او يساوي اتنين but order ال AB لا يساوي واحد واضح
+
+36
+00:03:44,160 --> 00:03:49,020
+هذا يا شبابأنا نفقت إن ال order يكون واحد و قلت إن
+
+37
+00:03:49,020 --> 00:03:52,360
+ال order هيبدأ من التنين و ينزل فيا التنين يا
+
+38
+00:03:52,360 --> 00:03:57,400
+الواحد و الواحد لأ هيظل عند مين؟ التنين لأ لأ مش
+
+39
+00:03:57,400 --> 00:04:02,900
+تجريب انت لما تيجي تتعامل مع ال order التعريف تبعه
+
+40
+00:04:02,900 --> 00:04:11,850
+أصغر عددطبيعي لما بترفع العنصر إله بيعطيك ال
+
+41
+00:04:11,850 --> 00:04:15,970
+identity انا بدأت بالواحد مانفعش الاتنين زبط
+
+42
+00:04:15,970 --> 00:04:20,210
+بالتجريب هو الأغلب بالتجريب إلا لو كان في عندك
+
+43
+00:04:20,210 --> 00:04:33,690
+شغلات مساعدة أخرى اشفهم
+
+44
+00:04:35,740 --> 00:04:40,000
+هي AB طيب
+
+45
+00:04:40,000 --> 00:04:52,180
+وحطه
+
+46
+00:04:52,180 --> 00:04:56,740
+بهذا الشكل وشوف عشان اللي انا عملتهلأ بدل التحذير
+
+47
+00:04:56,740 --> 00:04:59,340
+يعني انا مش .. انا ماعملتش .. ماعملتش تحذير انت
+
+48
+00:04:59,340 --> 00:05:03,240
+هتصل في النهاية ان ايه ال culture بيبقى بيساوي ال
+
+49
+00:05:03,240 --> 00:05:06,580
+identity تمام؟ يبقى ال order يا اتنين يا واحد
+
+50
+00:05:06,580 --> 00:05:09,500
+هتيجي تن في الواحد وبالتالي انت هو كأنك بدأت من
+
+51
+00:05:09,500 --> 00:05:13,800
+هان بعدين حلت هذا هي هي بدل التحذير اه في النهاية
+
+52
+00:05:13,800 --> 00:05:17,840
+ده برضه تحذير اش ضمنك انك هتصل لهذا نفس الضمان
+
+53
+00:05:17,840 --> 00:05:19,500
+اللي موجود هنا هو الضمان اللي موجود هنا
+
+54
+00:05:24,100 --> 00:05:29,300
+طيب ايش فيه سؤال بعده سؤال
+
+55
+00:05:29,300 --> 00:05:35,520
+اربعة و تلاتين suppose
+
+56
+00:05:35,520 --> 00:05:39,220
+a and p are group elements such that order a بدي
+
+57
+00:05:39,220 --> 00:05:42,240
+ساوي اتنين ال b لا يساوي ال identity هو a p a بدي
+
+58
+00:05:42,240 --> 00:05:48,200
+ساوي p تربيه find order ال b
+
+59
+00:05:52,030 --> 00:05:57,350
+ال order لل A بدي يساوي تنين ال B لا يساوي ال
+
+60
+00:05:57,350 --> 00:06:00,390
+identity طبعا هو رايحني من الجثة اللي انا عملتها
+
+61
+00:06:00,390 --> 00:06:05,910
+ال B لا يساوي ال identity يعني order ال B لا يساوي
+
+62
+00:06:05,910 --> 00:06:13,430
+ال واحد و عند ال علاقة التالية ان A PA بدي تساوي A
+
+63
+00:06:13,430 --> 00:06:18,430
+تربيع مين عنده أفكار لحل السؤال ده يا شباب مين
+
+64
+00:06:18,430 --> 00:06:19,110
+عنده أفكار
+
+65
+00:06:22,520 --> 00:06:28,460
+هنفكر طبعا بنفس الاسطوب اللي هان أفيدونا
+
+66
+00:06:28,460 --> 00:06:33,340
+أفادكم الله عشرة
+
+67
+00:06:33,340 --> 00:06:42,760
+أكتر طيب
+
+68
+00:06:42,760 --> 00:06:46,700
+A
+
+69
+00:06:46,700 --> 00:06:51,160
+تربية PA بيساوي طيب بعد ايه
+
+70
+00:06:54,360 --> 00:07:00,360
+تعالى نخربش تعمل ا بي ا بدي يساوي بي تربية هتضرب
+
+71
+00:07:00,360 --> 00:07:05,500
+الطرفين في a هصير a تربية بي ا بدي يساوي ا بي
+
+72
+00:07:05,500 --> 00:07:07,800
+تربية ال a تربية اللى على الناحية هذه بدها ايه
+
+73
+00:07:07,800 --> 00:07:19,680
+اتوح بدي صار عندى بي ا ا بي تربية طيب اش
+
+74
+00:07:19,680 --> 00:07:20,600
+ممكن يسي بعد هيك
+
+75
+00:07:24,000 --> 00:07:27,620
+تجرب تضغط على الشاشة التانية هصير بي ايه تربية
+
+76
+00:07:27,620 --> 00:07:33,780
+بتساوي ايه بي تربية ايه اللي هي بي بتساوي ايه بي
+
+77
+00:07:33,780 --> 00:07:45,740
+تربية ايه طيب اه كمان فكرة بس فكرة واحدة ضايلة وين
+
+78
+00:07:45,740 --> 00:07:54,770
+طب بدك تسفيد لأ هذه عبارة عن a b b a صح ولا لأاللي
+
+79
+00:07:54,770 --> 00:08:03,450
+عبارة عن a b identity b a اللي عبارة عن a b a
+
+80
+00:08:03,450 --> 00:08:09,350
+تربية بي
+
+81
+00:08:09,350 --> 00:08:15,830
+إيه هذي عبارة عن a b a a b a اللي a b a لكل تربية
+
+82
+00:08:15,830 --> 00:08:24,980
+اللي عبارة عن بي تربية تربية يعني بي قص أربعةيعني
+
+83
+00:08:24,980 --> 00:08:30,800
+انت وصلت ان P بيساو P وص 4 ال P لا يساو ال
+
+84
+00:08:30,800 --> 00:08:35,940
+identity بال cancellation law P تكئيب بيساو ال
+
+85
+00:08:35,940 --> 00:08:44,440
+identity وبالتالي هيصير ال order ل P يا
+
+86
+00:08:44,440 --> 00:08:52,790
+واحد يا اتنين يا تلاتة هذا مرفوض P مظلتانين في
+
+87
+00:08:52,790 --> 00:09:04,130
+التانين كنت هاي فكرة السؤال تعالى نغطبها ال
+
+88
+00:09:04,130 --> 00:09:14,050
+B تربية تربية انا هبدأ بالعكس عبارة عن A B A الكل
+
+89
+00:09:14,050 --> 00:09:29,640
+تربية عبارة عن ايش عن A B AA PA A PA الـ A إيش
+
+90
+00:09:29,640 --> 00:09:33,100
+بتساوي؟
+
+91
+00:09:33,100 --> 00:09:42,640
+إيش بتساوي؟ A P A تربيع PA يعني A P Identity PA
+
+92
+00:09:42,640 --> 00:09:51,500
+يعني A B تربيع A إيش ال B تربيع بتساوي؟هذا هتساوي
+
+93
+00:09:51,500 --> 00:09:58,180
+a في a p a a a تربية بي اي تربية بدي يساوي بي
+
+94
+00:09:58,180 --> 00:10:04,340
+المحصلة ان بي قص اربعة بدي تساوي بي وبالتالي بي تك
+
+95
+00:10:04,340 --> 00:10:10,520
+ايه بدي تساوي ال identity معناه to order ال بي يا
+
+96
+00:10:10,520 --> 00:10:19,100
+واحد يا اتنين يا تلاتة but order ال بي لا يساوي
+
+97
+00:10:19,100 --> 00:10:26,440
+واحدليش؟ لأن بي لا يساوي ال identity بيضايق قدامي
+
+98
+00:10:26,440 --> 00:10:35,040
+خيارين يا التنين يا التلاتة كيف ده ننفيه؟
+
+99
+00:10:35,040 --> 00:10:42,580
+if order ال بي بدت ساوي اتنين معناته بي تربيع ال
+
+100
+00:10:42,580 --> 00:10:47,960
+identity بيساوي بي تربيع اللي واش بيساوي بيساوي
+
+101
+00:10:47,960 --> 00:11:01,970
+ايه؟P A يعني E بدت ساوي A PA وبالتالي A تربيع
+
+102
+00:11:01,970 --> 00:11:07,270
+بدت ساوي A PA مش ال identity بيساوي A تربيع يعني A
+
+103
+00:11:07,270 --> 00:11:13,110
+في A بدت ساوي A PA المحصلة بعد ما تعمل
+
+104
+00:11:13,110 --> 00:11:19,410
+cancellation ال identity بدت ساوي P وهذا إيشتناقض
+
+105
+00:11:19,410 --> 00:11:24,490
+النتيجة order ال B لا يساوي اتنين المحصلة ان order
+
+106
+00:11:24,490 --> 00:11:36,010
+ال B ايش بتساوي تساوي تلاتة واضح؟ واضح؟
+
+107
+00:11:36,010 --> 00:11:39,110
+مين عنده اي شك او اي نقطة غير مفهومة؟
+
+108
+00:11:53,980 --> 00:11:59,260
+مش ال B تربيه بس هو APA شين ال B تربيه وحط ال APA
+
+109
+00:11:59,260 --> 00:12:06,980
+طيب
+
+110
+00:12:06,980 --> 00:12:10,460
+بالنسبة للسؤال تمانية و تلاتين انا هسيبه عليك يعني
+
+111
+00:12:10,460 --> 00:12:15,480
+هو هتحلوا بالسماء لل induction تمانية
+
+112
+00:12:15,480 --> 00:12:22,290
+و تلاتينمطلوب تثبت العلاقة هذه في SL2R ان cos θ
+
+113
+00:12:22,290 --> 00:12:28,850
+نقص sin θ sin θ cos θ أس N بيساوي cos Nθ سالب sin
+
+114
+00:12:28,850 --> 00:12:34,710
+Nθ sin Nθ cos Nθ بيستعمل ال induction بإمكانك
+
+115
+00:12:34,710 --> 00:12:39,290
+تثبته أثبت صحتها لما N بيساوي 2 بعدين افترض صحتها
+
+116
+00:12:39,290 --> 00:12:44,150
+لما N بيساوي K و أثبت صحتها بعدين لما N بيساوي K
+
+117
+00:12:44,150 --> 00:12:45,870
+زاد ال 1 using
+
+118
+00:12:47,910 --> 00:12:53,750
+mathematical induction فضل
+
+119
+00:12:53,750 --> 00:13:02,670
+الان على الطبيعي positive integer هو ايش جالك
+
+120
+00:13:02,670 --> 00:13:10,330
+positive integer طبعا هل هذه المصفوفة لها inverse
+
+121
+00:13:13,260 --> 00:13:18,780
+Cos θ سلب sin θ لها inverse لأن المحدد تبعها واحد
+
+122
+00:13:18,780 --> 00:13:22,000
+فانت ممكن ترفع لأس سالب بس لما ترفع لأس سالب
+
+123
+00:13:22,000 --> 00:13:29,240
+هتتعامل مع مين مع معكس المصفوفة واضح 41
+
+124
+00:13:29,240 --> 00:13:36,900
+D4
+
+125
+00:13:36,900 --> 00:13:42,140
+has seven cyclic subgroups list them هذا سؤال سهل
+
+126
+00:13:45,960 --> 00:13:52,180
+generated by R0 generated by R90 هو نفس ال
+
+127
+00:13:52,180 --> 00:13:57,440
+generated by R270 ال generated by R180 ال
+
+128
+00:13:57,440 --> 00:14:02,300
+generated by H ال generated by V ال generated by D
+
+129
+00:14:02,300 --> 00:14:07,820
+ال generated by D شرطة هم ال seven واحد اتنين
+
+130
+00:14:07,820 --> 00:14:12,640
+تلاتة اربعة خمسة ستة سبعة seven cyclic subgroup
+
+131
+00:14:26,150 --> 00:14:34,330
+طيب سؤال تنين و أربعين تنين و أربعين like سؤال
+
+132
+00:14:34,330 --> 00:14:42,450
+واحد و أربعين اللي هو خمسة عشر مين فيها عناصر واحد
+
+133
+00:14:42,450 --> 00:14:49,810
+اتنين اربع سبعة تمانية احداشر و تلتاشر و اربعة عشر
+
+134
+00:14:49,810 --> 00:14:58,260
+اتناشر لاطيب سؤال اربع و اربعين suppose j is a
+
+135
+00:14:58,260 --> 00:15:01,820
+group that has exactly eight elements of order
+
+136
+00:15:01,820 --> 00:15:05,720
+تلاتة how many subgroups of order تلاتة does j has
+
+137
+00:15:05,720 --> 00:15:14,940
+او have هذا السؤال حلو فيه أفكار عند group j have
+
+138
+00:15:14,940 --> 00:15:19,060
+او has عشان نكون ماشيين صح
+
+139
+00:15:22,470 --> 00:15:30,030
+exactly تمان element x with order x بدي تساوي
+
+140
+00:15:30,030 --> 00:15:39,690
+تلاتة say من هما x واحد x اتنين x تلاتة x اربع x
+
+141
+00:15:39,690 --> 00:15:44,990
+خمسة x ستة x سبعة و x تمانية
+
+142
+00:15:47,730 --> 00:15:53,230
+وال order ل X I يكون ثلاثة لكل I أقل أو يسوى
+
+143
+00:15:53,230 --> 00:16:01,330
+تمانية بقول ليه how many H
+
+144
+00:16:01,330 --> 00:16:12,070
+subgroup من ال J with H cyclic and ال order ل H
+
+145
+00:16:12,070 --> 00:16:15,070
+يكون ثلاثة
+
+146
+00:16:18,850 --> 00:16:25,870
+أكام جروب من هدولة أو subgroup من الـ Cyclic واللي
+
+147
+00:16:25,870 --> 00:16:31,190
+الأرضة غيرهم تلاتة موجودين في ERG قدام هناخد نظرية
+
+148
+00:16:31,190 --> 00:16:37,810
+تربط في chapter 4 أو chapter 7 بتحللك الأشكالية
+
+149
+00:16:37,810 --> 00:16:42,270
+هذه أنه بتقدر تحسبهم مباشرة بدون ما تقعد يتحذر زي
+
+150
+00:16:42,270 --> 00:16:48,400
+ما هنعمل هال game الحلقة التالية let Hsubgroup من
+
+151
+00:16:48,400 --> 00:16:54,020
+الجيه ال order لل H بدي يساوي تلاتة and H is
+
+152
+00:16:54,020 --> 00:17:00,660
+cyclic عشان اعرف كم واحدة من هدولة ال subgroup
+
+153
+00:17:00,660 --> 00:17:04,460
+المطلوبات هاخد واحدة منهم و اتكلم عن الهيكلية
+
+154
+00:17:04,460 --> 00:17:09,280
+الداخلية تبعتها هذا معناته ان ال H generated by
+
+155
+00:17:09,280 --> 00:17:14,470
+some Aو ال a ينتمي لل جيه و ال order لل a يبدو
+
+156
+00:17:14,470 --> 00:17:21,250
+يساوي تلاتة هذا معناته ان ال h أكم انصر فيها في
+
+157
+00:17:21,250 --> 00:17:27,570
+البداية ال identity و ال a تربيع اللي هو عبارة عن
+
+158
+00:17:27,570 --> 00:17:35,810
+ال a inverse مش
+
+159
+00:17:35,810 --> 00:17:41,240
+هذه sub group مغلقة على ال inverse ولا لأالـ A
+
+160
+00:17:41,240 --> 00:17:49,500
+موجودة والـ E موجودة و since طبعا هذه تفسيرها لإن
+
+161
+00:17:49,500 --> 00:17:54,380
+ال order ال A بدي ساوي تلاتة معناته A تكاري بدي
+
+162
+00:17:54,380 --> 00:17:57,660
+ساوي ال identity معناته A تغبيه بدي ساوي ال A
+
+163
+00:17:57,660 --> 00:18:06,830
+inverse تمام؟ alsoA لا يساوي الـ A inverse since
+
+164
+00:18:06,830 --> 00:18:15,630
+ال order لـ A يساوي ثلاثة مدام
+
+165
+00:18:15,630 --> 00:18:23,810
+ال A و ال A inverse موجودين هذا معناته ال order ل
+
+166
+00:18:23,810 --> 00:18:32,870
+A يساوي ثلاثة يقبل A يساوي some xi صح
+
+167
+00:18:32,870 --> 00:18:33,310
+ولا لأ؟
+
+168
+00:18:36,060 --> 00:18:40,360
+ال order لل a inverse بدي يساوي تلاتة و ال a لا
+
+169
+00:18:40,360 --> 00:18:45,920
+يساوي ال a inverse يكبر ال a inverse بدت ساوي xj و
+
+170
+00:18:45,920 --> 00:18:51,940
+ال j لا يساوي i هداش
+
+171
+00:18:51,940 --> 00:18:57,060
+معناته كل واحدة من اللي زي h أكمل أنصر ال order له
+
+172
+00:18:57,060 --> 00:19:03,680
+تلاتة موجود فيها يكبر every such
+
+173
+00:19:04,710 --> 00:19:11,370
+H contains two
+
+174
+00:19:11,370 --> 00:19:21,290
+elements of order تلاتة مش contain two ممكن اقول
+
+175
+00:19:21,290 --> 00:19:24,010
+احنا كمان contain exactly
+
+176
+00:19:30,600 --> 00:19:33,540
+كل واحدة من الـ H اللي أنا بدور عليهم فيها تنتين
+
+177
+00:19:33,540 --> 00:19:38,760
+طب هم مجددش كلهم هم
+
+178
+00:19:38,760 --> 00:19:44,240
+تمانية هذا
+
+179
+00:19:44,240 --> 00:19:52,040
+معناته يوجد تمانية على اتنين بيساوي اربعة such H
+
+180
+00:19:52,040 --> 00:19:58,960
+كم واحدة موجودة؟ اربعة
+
+181
+00:20:02,170 --> 00:20:08,790
+الـ Identity اللي هو ضغط له تلاتة ماشي
+
+182
+00:20:08,790 --> 00:20:15,130
+طالع معايا هم هيكون أربع group من ال H X واحد و X
+
+183
+00:20:15,130 --> 00:20:19,890
+واحد inverse مع ال identityX2 و X2 inverse مع ال
+
+184
+00:20:19,890 --> 00:20:25,810
+identity X3 و X3 inverse مع ال identity و X4 و X4
+
+185
+00:20:25,810 --> 00:20:29,190
+inverse مع ال identity هتقولي هدول تمانية مما هي
+
+186
+00:20:29,190 --> 00:20:34,650
+أول أربعة و الأربعة التانية مين ال inverse تبعهم
+
+187
+00:20:34,650 --> 00:20:38,290
+44 45
+
+188
+00:20:49,630 --> 00:20:55,850
+طيب خمسة و اربعين بسؤال
+
+189
+00:20:55,850 --> 00:21:01,190
+خمسة و اربعين H sub group من ال J و ال J finite
+
+190
+00:21:01,190 --> 00:21:04,310
+suppose
+
+191
+00:21:04,310 --> 00:21:14,930
+J تنتمي لل J و N is the smallest positive
+
+192
+00:21:25,380 --> 00:21:31,220
+مطلوب اثبت ان انت تقسم order ج
+
+193
+00:21:39,260 --> 00:21:43,940
+شباب أول ما نيجي نحل أسئلة من نوعية ال .. خصوصا في
+
+194
+00:21:43,940 --> 00:21:48,260
+الجبر الحديث أهم حاجة لازم أعرفها و أقدر أتعامل
+
+195
+00:21:48,260 --> 00:21:52,260
+معاها هو تفسيري للمواضيات اللي عندي إذا ما أقدرت
+
+196
+00:21:52,260 --> 00:21:56,460
+أفهم إيش المواضيات اللي في السؤال تتوقعش مني أعرف
+
+197
+00:21:56,460 --> 00:22:01,680
+أجيب المطلوب تتوقعش مني أعرف أجيب المطلوب
+
+198
+00:22:04,400 --> 00:22:08,180
+السؤال المعطلية اللوانية السهلات الـ H sub group
+
+199
+00:22:08,180 --> 00:22:11,560
+والـ J finite عشان أقدر أتعامل مع ال orders يوجد
+
+200
+00:22:11,560 --> 00:22:20,200
+عنصر في الـ J لكل عنصر من هذا النوع أصغر عدد طبيعي
+
+201
+00:22:20,200 --> 00:22:25,800
+بيخلي الـ J أُس N جوا الـ H هو N مطلوب أثبت أنه
+
+202
+00:22:25,800 --> 00:22:31,020
+الـ N تقسم ال order للـ J طيب تعالوا نشوف
+
+203
+00:22:35,740 --> 00:22:43,180
+let order j اختار له رقم خمسة
+
+204
+00:22:43,180 --> 00:22:53,000
+لأ اخي يعني اعطيه رمز خد دي دي و لا M المطلوب من
+
+205
+00:22:53,000 --> 00:23:02,060
+السؤال let n بدي يسوي ال smallest positive
+
+206
+00:23:03,860 --> 00:23:13,080
+Integral with J أس N ينتمي للـH المطلوب أن N تقسم
+
+207
+00:23:13,080 --> 00:23:17,660
+الـM ارجع
+
+208
+00:23:17,660 --> 00:23:21,700
+شوية بالذاكرة لنظرية الأعداد اللي أخدها كيف أثبت
+
+209
+00:23:21,700 --> 00:23:28,290
+أن N بيقسم الـMاسلوبين يا بلاجي عدد صحيح بضربه في
+
+210
+00:23:28,290 --> 00:23:32,550
+ال N بيعطيين ال M يا بثبت انه remainder عند عملية
+
+211
+00:23:32,550 --> 00:23:40,810
+القسمة يساوي صفر using division algorithm
+
+212
+00:23:40,810 --> 00:23:51,190
+let M بده تساوي QN زاد ال R ال R أقل من ال N وأصغر
+
+213
+00:23:51,190 --> 00:23:53,250
+من ال 0
+
+214
+00:23:57,090 --> 00:24:02,390
+الان الـ J to M بدي ساوي ال identity ينتمي لل H
+
+215
+00:24:02,390 --> 00:24:09,430
+الـ J to N ينتمي لل H هيخليني اقول ان الـ J to N
+
+216
+00:24:09,430 --> 00:24:16,530
+أس كيو ينتمي لل H عشان الـ H صب جوب فهي مغلقة على
+
+217
+00:24:16,530 --> 00:24:19,850
+العملية هذا معناته J
+
+218
+00:24:23,090 --> 00:24:35,110
+QN ينتمي للـH مش بس هيك يا شباب J قصة QN inverse
+
+219
+00:24:35,110 --> 00:24:44,750
+ينتمي للـH J قصة QN inverse عبارة عن أيش؟ J قصة
+
+220
+00:24:44,750 --> 00:24:50,710
+سالب QN ينتمي للـH أعطي هذا واحد و أعطي هذا اتنين
+
+221
+00:24:53,340 --> 00:24:59,920
+من واحد و اتنين عنصرين في ال H و ال H sub group
+
+222
+00:24:59,920 --> 00:25:06,600
+حصل ضرب و مون هيكون في ال H حاسيب معايا J أس M في
+
+223
+00:25:06,600 --> 00:25:15,920
+J سالب Q N هو عنصر من وين عنصر من ال H عند الضرب
+
+224
+00:25:15,920 --> 00:25:23,770
+ايش بيصير في الأسستجمع الأسس هاسي معايا J أُس M
+
+225
+00:25:23,770 --> 00:25:35,510
+minus Q N ينتمي لمن؟ للـH اطلح J أُس R ينتمي لمن؟
+
+226
+00:25:35,510 --> 00:25:43,270
+للـH هذا معناته N أقل أو يسوى R by the definition
+
+227
+00:25:43,270 --> 00:25:51,740
+of Nتعريف ال N بيقوللي أن ال N هو أصغر عدد طبيعي
+
+228
+00:25:51,740 --> 00:25:57,880
+أو positive integer بيخللي ال J أُس N جوه ال R فأي
+
+229
+00:25:57,880 --> 00:26:03,080
+أُس تاني لل J .. جوه ال H أي أُس تاني لل J بيكون
+
+230
+00:26:03,080 --> 00:26:07,620
+جوه ال H لازم هذا الأُس يكون أشماله أكبر من ال N
+
+231
+00:26:07,620 --> 00:26:16,020
+but R أقل من ال N قارن لأ
+
+232
+00:26:17,470 --> 00:26:25,070
+هنا أقل وهنا أقل أو يساوي كيف دي يكون الار أقل من
+
+233
+00:26:25,070 --> 00:26:29,650
+الان؟ هذه نقيض هذه يعني النفي تبقى هذا هيعطيني هذا
+
+234
+00:26:29,650 --> 00:26:41,210
+فصارت الجملة و نفيها contradiction so .. so إيش؟
+
+235
+00:26:41,210 --> 00:26:46,490
+الار يساوي
+
+236
+00:26:46,490 --> 00:26:56,610
+ستةوين الخلل في الإثبات؟ فيه سطر لازم نضيفه فيه
+
+237
+00:26:56,610 --> 00:27:04,750
+سطر في البداية بنضيفه بصير الحل سليم حاجة
+
+238
+00:27:04,750 --> 00:27:09,750
+هنا و اقول assume that
+
+239
+00:27:09,750 --> 00:27:17,750
+M أو N لا تقسم ال M هنا هنشيل هذه
+
+240
+00:27:23,100 --> 00:27:27,960
+لما نضيف أنا تقسم ال M معناته remainder مستحيل
+
+241
+00:27:27,960 --> 00:27:32,500
+يكون صفر واضح
+
+242
+00:27:32,500 --> 00:27:39,640
+يا عادي؟ واضح يا شباب؟ اللي ضفته؟
+
+243
+00:27:42,790 --> 00:27:48,270
+ليش فيه تناقض؟ طالع معايا ال N هو أصغر واحد بيحقق
+
+244
+00:27:48,270 --> 00:27:52,110
+العلاقة فأي واحد بيحقق العلاقة لازم يكون إشماله
+
+245
+00:27:52,110 --> 00:27:56,930
+أكبر منه ال R صار يحقق فصار ال R أكبر أو يساوي ال
+
+246
+00:27:56,930 --> 00:28:01,590
+N بس أنا أصلا بعرف أن ال R أصغر من ال N صار عندي
+
+247
+00:28:01,590 --> 00:28:02,090
+تناقض
+
+248
+00:28:14,570 --> 00:28:18,170
+كيف؟ و انا لما شيلت الشرق .. لما ضفت ان الان لا
+
+249
+00:28:18,170 --> 00:28:24,810
+يقسم الام صار remainder ليه ساوة صفر هلجيت؟ لما
+
+250
+00:28:24,810 --> 00:28:28,570
+انا اقول .. لما يصير تناقض يجب لازم يكون remainder
+
+251
+00:28:28,570 --> 00:28:31,430
+صفر و المحاصلة اللي احنا بدنا إياها مش انه قعد
+
+252
+00:28:31,430 --> 00:28:36,510
+بساوة صفر لأ ان الان تقسم الام هذا المطلوب مش انه
+
+253
+00:28:36,510 --> 00:28:37,730
+قعد بساوة صفر
+
+254
+00:28:42,020 --> 00:28:49,160
+طيب سؤال سبعة و أربعين خمسة و أربعين مطلوب مطلوب
+
+255
+00:28:49,160 --> 00:28:53,500
+خمسة و أربعين خمسة و أربعين حلناها سبعة و أربعين R
+
+256
+00:28:53,500 --> 00:28:59,320
+star be the group of non zero real number under
+
+257
+00:28:59,320 --> 00:29:07,500
+multiplication R star يا شباب عبارة عن Rمعدد Zero
+
+258
+00:29:07,500 --> 00:29:12,960
+والعملية عملية ضرب H عبارة عن كل X في R*) X تربيه
+
+259
+00:29:12,960 --> 00:29:20,020
+is rational يثبت أن H subgroup of R H عبارة عن كل
+
+260
+00:29:20,020 --> 00:29:27,520
+X في R*) X تربيه ينتمي ل Q المطلوب اثبات أن H
+
+261
+00:29:27,520 --> 00:29:36,050
+subgroup من R*)عارف ان السؤال هذا حلنا واحد زيه
+
+262
+00:29:36,050 --> 00:29:42,970
+مخضر الماضية لما قلنا عندي abelian group و هاد ال
+
+263
+00:29:42,970 --> 00:29:48,650
+R*) مع ضرب abelian فكل ال Xات اللي بيحققوله ان X
+
+264
+00:29:48,650 --> 00:29:54,630
+أس N بساوي ال identity بيعملوا له سبق ال group هذا
+
+265
+00:29:54,630 --> 00:29:59,750
+السؤال شبيه فيهبس ماجولش انه x تربيه بيسوي ال
+
+266
+00:29:59,750 --> 00:30:03,330
+identity لأ هان بقول انه x تربيه عبارة عن ايش
+
+267
+00:30:03,330 --> 00:30:09,550
+rational number اول شي ال
+
+268
+00:30:09,550 --> 00:30:18,170
+H لا يسوي فيه since واحد ينتمي لل H now if
+
+269
+00:30:22,520 --> 00:30:32,320
+A وB ينتمي للـH A تربيع ينتمي للـQ وB تربيع ينتمي
+
+270
+00:30:32,320 --> 00:30:44,440
+للـQ طيب ال AP inverse تربيع عبارة عن ايش عن A على
+
+271
+00:30:44,440 --> 00:30:48,740
+B لكل تربيع ليش انا عملت A على B
+
+272
+00:30:51,710 --> 00:30:55,510
+لان انا بشتغل مع العداد الحقيقية فال inverse لضرب
+
+273
+00:30:55,510 --> 00:31:04,470
+ماله تواحد على حسين على a تربيع على b تربيع وهذا
+
+274
+00:31:04,470 --> 00:31:10,050
+ينتمي ل ال Q ليش ينتمي ل ال Q عدد نسبي على عدد
+
+275
+00:31:10,050 --> 00:31:15,610
+نسبي عدد نسبي لانه اصلا عملية القسمة او عملية
+
+276
+00:31:15,610 --> 00:31:17,630
+الضرب مغلقة في ال Q
+
+277
+00:31:31,690 --> 00:31:37,870
+هل ممكن نبدل التنين بأي عدد صحيح
+
+278
+00:31:37,870 --> 00:31:38,590
+أخر؟
+
+279
+00:31:44,660 --> 00:31:49,620
+شيل اتنين و احط اي رقم او اي قيمة بالعداد الصحيح
+
+280
+00:31:49,620 --> 00:31:55,680
+الموجبه تكييب هتظل تكييب قص 17 هتظل قص 17 وهنا
+
+281
+00:31:55,680 --> 00:32:10,600
+مافيش مشكلة بقدر استبدل اتنين بعدد نسبي ليش بقدرش
+
+282
+00:32:10,600 --> 00:32:18,980
+اتعامل مع السوالبانا هنا بقدر yes we can replace
+
+283
+00:32:18,980 --> 00:32:29,540
+اتنين by any natural number بقدر ابدل اتنين بأي
+
+284
+00:32:29,540 --> 00:32:37,680
+عدد طبيعي سبعة
+
+285
+00:32:37,680 --> 00:32:39,020
+واربعين اتنين وخمسين
+
+286
+00:32:49,060 --> 00:32:58,000
+طب 52 ما أعتقد أنه فيه مشكلة يعني 52 و 53 سهلين سي
+
+287
+00:32:58,000 --> 00:33:05,840
+سؤال 47 حلين
+
+288
+00:33:05,840 --> 00:33:10,060
+أكتر من سؤال على حتى المحاضرة الماضية حلت تقريبا
+
+289
+00:33:10,060 --> 00:33:15,500
+تلت أسئلة على موضوع subgroup 56 و 57
+
+290
+00:33:18,570 --> 00:33:25,290
+تعالى نشوفهم 56 بيقول A زي P I حيث ال A P Positive
+
+291
+00:33:25,290 --> 00:33:35,270
+هل
+
+292
+00:33:35,270 --> 00:33:41,130
+هذا هل ال H سابقه مع ال C و الجامع
+
+293
+00:33:47,210 --> 00:33:52,410
+هل ال arch subgroup من ال C عشان اميزه احطله شرطا
+
+294
+00:33:52,410 --> 00:33:57,190
+مع الجامعة ايش رأيك؟
+
+295
+00:33:57,190 --> 00:34:06,250
+اه ايش رأيك؟
+
+296
+00:34:06,250 --> 00:34:16,540
+هل هذه subgroup من ال C مع الجامعة؟ اه فاكرهأول
+
+297
+00:34:16,540 --> 00:34:22,120
+حاجة ال identity موجود identity تبع الجامعة موجود
+
+298
+00:34:22,120 --> 00:34:27,740
+هيك
+
+299
+00:34:27,740 --> 00:34:33,740
+بقى مغلقة على وجود ال identity العملية associative
+
+300
+00:34:33,740 --> 00:34:41,840
+ولا لأ associative طب ال inverse موجود
+
+301
+00:34:42,610 --> 00:34:48,630
+لو ال A P موجب يعني A زاد P I في ال H سالب A سالب
+
+302
+00:34:48,630 --> 00:34:52,530
+P I برضه في ال H لإنه A P موجب فسالب A في سالب P
+
+303
+00:34:52,530 --> 00:34:57,910
+برضه موجب يجب أولي الخلل اللي ممكن يكون معانا في
+
+304
+00:34:57,910 --> 00:35:03,450
+إن العملية تكون مغلقة أصلا هلاحظ الشغل التالي سالب
+
+305
+00:35:03,450 --> 00:35:11,950
+واحد او واحد زاد اتنين I تامين ال H تمام؟
+
+306
+00:35:14,440 --> 00:35:24,880
+و سالب ثلاثة ناقص I برضه في الاتش خلي هذا A وهذا B
+
+307
+00:35:24,880 --> 00:35:31,840
+طيب A زاد ال B عبارة عن ايش سالب اتنين زاد ال I
+
+308
+00:35:31,840 --> 00:35:37,580
+هذا مش في الاتش وبالتالي
+
+309
+00:35:37,580 --> 00:35:42,860
+العملية مش مغلقة هنا مافيش اغلاق للعملية جوا الاتش
+
+310
+00:35:42,860 --> 00:35:49,630
+وبالتاليH not subgroup
+
+311
+00:35:49,630 --> 00:36:02,810
+of C و الجمهور مش subgroup لأنه
+
+312
+00:36:02,810 --> 00:36:06,850
+لو انت ضربت ال F انا هالخطأ ان اخدت A و B حطيليها
+
+313
+00:36:06,850 --> 00:36:13,010
+X و Y تعالوا
+
+314
+00:36:13,010 --> 00:36:18,400
+ضرب هدف يعني سلب 2 في 1سالف اتنين هل السالف اتنين
+
+315
+00:36:18,400 --> 00:36:24,380
+موجب او اكبر أو سوى الصفر سبعة و خمسين على نفس
+
+316
+00:36:24,380 --> 00:36:31,420
+المنطقة برضه بشتر على ال C مع ال multiplication
+
+317
+00:36:31,420 --> 00:36:39,720
+طبعا
+
+318
+00:36:39,720 --> 00:36:45,270
+هذه المجموعة شباب عبارة عن ايش؟A زي ات بي I حيث
+
+319
+00:36:45,270 --> 00:36:49,350
+ايه تر بي زي بي تر بي بيسوا واحد هذه بيسميها ال
+
+320
+00:36:49,350 --> 00:36:54,670
+unit circle دائرة الوحدة تم عظمها أخد complex هل
+
+321
+00:36:54,670 --> 00:36:59,930
+هذه sub group مع طبعا احنا هيك اتجاوبنا على الجزء
+
+322
+00:36:59,930 --> 00:37:02,410
+التاني من السؤال describe the element of H
+
+323
+00:37:02,410 --> 00:37:10,470
+geometrically دائرة الوحدة ال unit circle
+
+324
+00:37:10,470 --> 00:37:21,540
+هل هذه sub groupأنا بتعامل مع مين؟ مع الضنب أولش
+
+325
+00:37:21,540 --> 00:37:29,800
+المحايد هنا طبعا C Star عبارة عن C مع ده مين؟ الـ
+
+326
+00:37:29,800 --> 00:37:37,060
+Zero ال identity موجود مين ال identity هنا؟ ال A
+
+327
+00:37:37,060 --> 00:37:41,000
+بتتساوي واحد زي ال Zero I بتتساوي واحد هذا ينتمي
+
+328
+00:37:41,000 --> 00:37:47,220
+لل Hيقبل أش لا تساو فيه تنين ال identity موجود ولا
+
+329
+00:37:47,220 --> 00:37:55,340
+تساو فيه associative موجود طبعا لأنه جزء من الكبير
+
+330
+00:37:55,340 --> 00:38:07,420
+أش فيه ضالة شروط ال inverse ومي كمان ال inverse و
+
+331
+00:38:07,420 --> 00:38:12,970
+ال close ال inverse موجود يا شبابلو ال A زي ال P I
+
+332
+00:38:12,970 --> 00:38:17,950
+ينتمي لل H ف A تربيع زي ال P تربيع بسوء واحد طب ال
+
+333
+00:38:17,950 --> 00:38:22,610
+A زي ال P I inverse هذا عبارة عن A minus ال P I
+
+334
+00:38:22,610 --> 00:38:29,110
+على A تربيع زي ال P تربيع اللي هو عبارة عن A على A
+
+335
+00:38:29,110 --> 00:38:33,830
+تربيع زي ال P تربيع نقص ال P I على A تربيع زي ال P
+
+336
+00:38:33,830 --> 00:38:37,450
+تربيع بس هي أنا تحت الجزر
+
+337
+00:38:45,640 --> 00:38:54,960
+شوية بس مافيش جزايا طب
+
+338
+00:38:54,960 --> 00:38:59,480
+ماتنساش ان هذا ايش بيساوي واحد يكبر هذا عبارة عن
+
+339
+00:38:59,480 --> 00:39:04,300
+ال a minus bi و ال a تربيه زاد سالب ال b تربيه
+
+340
+00:39:04,300 --> 00:39:08,340
+بيساوي a تربيه زاد ال b تربيه بيساوي واحد يكبر a
+
+341
+00:39:08,340 --> 00:39:16,930
+زاد ال bi inverse ينتمي للhأول تلات شروط اتحققوا
+
+342
+00:39:16,930 --> 00:39:21,490
+طب أنا هنا مش راضي استعمل ليه ال notation تبعت ال
+
+343
+00:39:21,490 --> 00:39:25,290
+C أو تبعت ال complex analysis ان بعضهم هيقول انا
+
+344
+00:39:25,290 --> 00:39:31,610
+مااخدتش تحليل مُركّب اربعة لو أنا قولت ال X بيساوي
+
+345
+00:39:31,610 --> 00:39:36,450
+A زاد ال P I و ال Y بيساوي ال C زاد ال D I هدول
+
+346
+00:39:36,450 --> 00:39:43,020
+ينتموا لل H معناته A تربية زادالـ B تربيع بدي أسوأ
+
+347
+00:39:43,020 --> 00:39:49,360
+واحد بدي أسوأ C تربيع زاد ال D تربيع لو أنا جيت
+
+348
+00:39:49,360 --> 00:39:58,720
+أشتغل على XY XY عبارة عن إيش هذا
+
+349
+00:39:58,720 --> 00:40:10,380
+عبارة عن AC نقص BD زائد D في C زائد
+
+350
+00:40:11,860 --> 00:40:18,240
+تخربطوني هيك يا شباب A في D زائد
+
+351
+00:40:18,240 --> 00:40:23,440
+BC بي في CI تعالى نشوف هذا تربية زائد هذا تربية
+
+352
+00:40:23,440 --> 00:40:30,580
+ايش بيساوي AC نقص ال BD تربية زائد ال AD زائد ال
+
+353
+00:40:30,580 --> 00:40:36,000
+BC تربية ايش بيساوي A تربية C تربية نقص اتنين AC
+
+354
+00:40:36,000 --> 00:40:45,060
+BD زائد ال B تربية D تربية زائدA تربيع D تربيع زاد
+
+355
+00:40:45,060 --> 00:40:51,340
+اتنين ACPD زاد B تربيع C تربيع هذا مع هذا بيطير
+
+356
+00:40:51,340 --> 00:40:58,580
+بيظل عندي A تربيع في C تربيع زاد ال D تربيع زاد B
+
+357
+00:40:58,580 --> 00:41:04,520
+تربيع في C تربيع زاد ال D تربيع هذا واحد وهذا واحد
+
+358
+00:41:04,520 --> 00:41:10,020
+هيصيب معايا A تربيع زاد ال B تربيع مش بيساويهذا
+
+359
+00:41:10,020 --> 00:41:17,720
+معناته انه XY جوا ال H Identity موجود Associative
+
+360
+00:41:17,720 --> 00:41:25,480
+متحقق مغلقة على ال inverse مغلقة على العملية نفسها
+
+361
+00:41:25,480 --> 00:41:29,840
+يكبر H subgroup من C
+
+362
+00:41:35,920 --> 00:41:40,960
+أخدت complex analysis أخدت العدد المركب في
+
+363
+00:41:40,960 --> 00:41:45,280
+الثانوية ولا لأ كيف أجيب معكوس لعدد المركب بضغط في
+
+364
+00:41:45,280 --> 00:41:52,900
+المرافق فوق و تحت هو ال A زاد ال I B inverse هذا
+
+365
+00:41:52,900 --> 00:41:59,500
+عبارة عن واحد على A زاد ال I B واحد نقص ال .. و
+
+366
+00:41:59,500 --> 00:42:03,120
+بكمل قاضي
+
+367
+00:42:05,490 --> 00:42:15,010
+إيش بيظلاندي يا شباب؟ تسعة و خمسين جي
+
+368
+00:42:15,010 --> 00:42:19,910
+قلت
+
+369
+00:42:19,910 --> 00:42:33,990
+و اه؟ هذا سؤال فيه خربش كتير طيب
+
+370
+00:42:35,180 --> 00:42:42,220
+تسعة و خمسين اختار سؤال مثلا ايه بدك ال center او
+
+371
+00:42:42,220 --> 00:42:50,800
+ال centralizer ل 1110 حسب التعريف هذا عبارة عن كل
+
+372
+00:42:50,800 --> 00:43:03,430
+ال A في ال GL to R اللي A 1110 بيساوي 1110 في Aلو
+
+373
+00:43:03,430 --> 00:43:11,450
+انا خدت ال a عبارة عن a,b,c,d و جيت اشتغلت a,b,c,d
+
+374
+00:43:11,450 --> 00:43:25,150
+1110 هذا المفروض يساوي 1110 في a,b,c,d اضرب a زائد
+
+375
+00:43:25,150 --> 00:43:25,570
+ال b
+
+376
+00:43:29,260 --> 00:43:40,080
+C زائد D C هذا بـ D ساوي A زائد C واحد
+
+377
+00:43:40,080 --> 00:43:45,400
+واحد في B B زائد D A
+
+378
+00:43:45,400 --> 00:43:52,960
+B A
+
+379
+00:43:52,960 --> 00:43:57,580
+زائد C B زائد D A وB اعمل مساواة
+
+380
+00:44:24,230 --> 00:44:27,690
+هتستفيد من هذه و هذه شغلة واحدة ان ال B بيساوي ال
+
+381
+00:44:27,690 --> 00:44:27,830
+C
+
+382
+00:44:33,170 --> 00:44:38,950
+طب وهذه وهذه نفس
+
+383
+00:44:38,950 --> 00:44:44,230
+الفكرة لما تساوي a بساوي b زاد دي و a بساوي c زاد
+
+384
+00:44:44,230 --> 00:44:49,150
+دي طير دي من الطرفين مش هيظل عندك فقط المعلومة
+
+385
+00:44:49,150 --> 00:44:53,110
+الوحيدة اللي انت بتقدر تستفيدها نهيش ان ال b و ال
+
+386
+00:44:53,110 --> 00:45:03,870
+c متساوين وبالتالي ال centralizer لواحد واحدواحد
+
+387
+00:45:03,870 --> 00:45:16,710
+صفر عبارة عن كل ال a,b,b,d حيث a,b,d ينتموا لمين
+
+388
+00:45:16,710 --> 00:45:21,750
+هي كل
+
+389
+00:45:21,750 --> 00:45:29,290
+المصفوفات اللي ال b و ال c فيهم متساوية طبعا الفرع
+
+390
+00:45:29,290 --> 00:45:37,510
+b like الفرع aهيكون أسهل شوية طيب
+
+391
+00:45:37,510 --> 00:45:44,650
+الفرصية
+
+392
+00:45:44,650 --> 00:45:52,270
+ال center تبع JL2R
+
+393
+00:45:52,270 --> 00:45:59,230
+مين
+
+394
+00:45:59,230 --> 00:46:00,170
+بيقدر يعرفهم؟
+
+395
+00:46:03,410 --> 00:46:15,970
+من بيقدر يعرفه بس بس
+
+396
+00:46:15,970 --> 00:46:20,750
+بعد
+
+397
+00:46:20,750 --> 00:46:28,590
+شوية حسابات هنكتشف ان هذا عبارة عن كل a 00a حيث a
+
+398
+00:46:28,590 --> 00:46:29,030
+في r
+
+399
+00:46:32,520 --> 00:46:39,880
+هذا التوقعي بحاول المرة الجاية أكيدلك إياه أعتقد
+
+400
+00:46:39,880 --> 00:46:43,380
+أن هذا كلام صحي اللي لو كان في أمثلة أخرى خليني
+
+401
+00:46:43,380 --> 00:46:47,580
+أنا برضه أنه إيجي على بالي شغلة معينة ممكن تتحقق
+
+402
+00:46:47,580 --> 00:46:57,860
+كلام اللي بنحكي واضح؟ هذا اللي التأكد بأكيدها
+
+403
+00:46:57,860 --> 00:47:02,630
+المرة الجاية لأنه مايظلش وجهة عنديمناخش تفاصيلها
+
+404
+00:47:02,630 --> 00:47:07,590
+طب بنعطيكوا العافية محاضرة جاية ان شاء الله بنفوت
+
+405
+00:47:07,590 --> 00:47:12,890
+في الوحدة الرابعة بنتكلم فيها عن ال cyclic group و
+
+406
+00:47:12,890 --> 00:47:16,890
+بنتكلم فيها عن الهيكلية الداخلية لكل ال cyclic
+
+407
+00:47:16,890 --> 00:47:20,450
+group و التفاصيل الخاصة في هذا الموضوع بنعطيكوا
+
+408
+00:47:20,450 --> 00:47:21,850
+العافية السلام عليكم
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c6de8103a9474c222e8becb43d9d12df21a63860
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4261, "start": 20.99, "end": 42.61, "text": "بسم الله الرحمن الرحيم نرجع لمحاضرة ابتدناها في الفترة الصباحية و هو أنه بدأنا في chapter 3 اللي بتحدث عن ال subgroups طبعا أعطينا تعريف لل order لل group و order لل element اللي موجود داخل ال group", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 47341, 3615, 32767, 5016, 46958, 25720, 48127, 2655, 3215, 8315, 11296, 8978, 27188, 2655, 25720, 31767, 3555, 39319, 10632, 4032, 31439, 14739, 3224, 47525, 10721, 8315, 8978, 7187, 805, 13672, 1829, 39894, 24401, 12984, 18871, 2423, 1422, 17377, 82, 23032, 3555, 3615, 995, 5551, 3615, 9566, 1829, 8315, 37279, 16572, 5172, 24976, 1668, 24976, 1594, 4032, 1668, 24976, 4478, 13672, 1829, 3714, 29245, 23328, 11778, 47283, 1211, 2423, 1594], "avg_logprob": -0.16933594085276127, "compression_ratio": 1.6153846153846154, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 20.99, "end": 21.31, "word": "بسم", "probability": 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ايه له تلاتة سبعة ودي يطلع ال zero ها ال zero هو ال identity تمانية طيب يجي ال order للواحد بده يساوي تمانية طيب ال order ليه تلاتة", "tokens": [2655, 33753, 6225, 42213, 10632, 25724, 2304, 27884, 37495, 22653, 36764, 24401, 6055, 2288, 21292, 3615, 37495, 22653, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 3714, 2407, 16254, 43761, 46811, 7649, 7578, 46740, 10874, 3215, 33599, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 10874, 3215, 33599, 2423, 1668, 1975, 1829, 3224, 46740, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 4032, 16254, 7251, 9566, 1211, 3615, 2423, 4018, 8032, 995, 2423, 4018, 31439, 2423, 6575, 46811, 7649, 10632, 23032, 1829, 3555, 7251, 7435, 1829, 2423, 1668, 24976, 14407, 24401, 47525, 3224, 7251, 3794, 995, 45865, 46811, 7649, 10632, 23032, 1829, 3555, 2423, 1668, 32239, 3224, 6055, 1211, 9307, 3660], "avg_logprob": -0.21822034075098523, "compression_ratio": 2.1822916666666665, "no_speech_prob": 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"word": " ضربت", "probability": 0.89111328125}, {"start": 782.04, "end": 782.66, "word": " كمان", "probability": 0.970703125}, {"start": 782.66, "end": 782.88, "word": " في", "probability": 0.900390625}, {"start": 782.88, "end": 783.22, "word": " ايه", "probability": 0.766845703125}, {"start": 783.22, "end": 783.56, "word": " بصير", "probability": 0.7877604166666666}, {"start": 783.56, "end": 783.78, "word": " عندي", "probability": 0.679931640625}, {"start": 783.78, "end": 784.46, "word": " كم؟", "probability": 0.85107421875}, {"start": 784.46, "end": 785.32, "word": " اتكيب", "probability": 0.758203125}], "temperature": 1.0}, {"id": 32, "seek": 81325, "start": 785.83, "end": 813.25, "text": "طيب لو جيت قولت هذا بده يعطينا انه ايه تكييب بده يساوي اللي هو من Zero و واحد و سالب واحد و سالب واحد في سالب واحد سالب واحد واحد Zero و يساوي الصف الأول في العمود الأول يبقى Zero و هنا واحد هنا Zero و هنا Zero اللي هو ب Zero تمام", "tokens": [9566, 1829, 3555, 45164, 10874, 36081, 12174, 12610, 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"probability": 0.900390625}], "temperature": 1.0}, {"id": 33, "seek": 83188, "start": 813.74, "end": 831.88, "text": "هنا هي واحد وهنا سالب واحد يبقى zero الصف هذا في هذا بيطلع واحد وهنا واحد فقط لا غير يبقى ال order لإيه؟ تلاتة لإن هذه ال identity matrix يبقى similarly", "tokens": [3224, 8315, 39896, 36764, 24401, 37037, 8315, 8608, 6027, 3555, 36764, 24401, 7251, 3555, 4587, 7578, 4018, 31767, 5172, 23758, 8978, 23758, 4724, 1829, 9566, 1211, 3615, 36764, 24401, 37037, 8315, 36764, 24401, 6156, 47432, 20193, 32771, 13546, 7251, 3555, 4587, 7578, 2423, 1668, 5296, 28814, 1829, 3224, 22807, 6055, 1211, 9307, 3660, 5296, 28814, 1863, 29538, 2423, 6575, 8141, 7251, 3555, 4587, 7578, 14138], "avg_logprob": -0.2594696888417909, "compression_ratio": 1.5816993464052287, "no_speech_prob": 0.0, "words": [{"start": 813.74, "end": 814.46, "word": "هنا", "probability": 0.3629150390625}, {"start": 814.46, "end": 815.06, "word": " هي", "probability": 0.1663818359375}, {"start": 815.06, "end": 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"probability": 0.845458984375}, {"start": 822.48, "end": 823.22, "word": " واحد", "probability": 0.98193359375}, {"start": 823.22, "end": 823.9, "word": " فقط", "probability": 0.9912109375}, {"start": 823.9, "end": 824.2, "word": " لا", "probability": 0.65380859375}, {"start": 824.2, "end": 824.76, "word": " غير", "probability": 0.965576171875}, {"start": 824.76, "end": 825.38, "word": " يبقى", "probability": 0.9456787109375}, {"start": 825.38, "end": 825.46, "word": " ال", "probability": 0.765625}, {"start": 825.46, "end": 825.82, "word": " order", "probability": 0.96337890625}, {"start": 825.82, "end": 826.84, "word": " لإيه؟", "probability": 0.7146484375}, {"start": 826.84, "end": 827.84, "word": " تلاتة", "probability": 0.770172119140625}, {"start": 827.84, "end": 828.08, "word": " لإن", "probability": 0.814453125}, {"start": 828.08, "end": 828.38, "word": " هذه", "probability": 0.4443359375}, {"start": 828.38, "end": 828.54, "word": " ال", "probability": 0.6005859375}, {"start": 828.54, "end": 829.1, "word": " identity", "probability": 0.83642578125}, {"start": 829.1, "end": 829.8, "word": " matrix", "probability": 0.9482421875}, {"start": 829.8, "end": 830.98, "word": " يبقى", "probability": 0.9547119140625}, {"start": 830.98, "end": 831.88, "word": " similarly", "probability": 0.489501953125}], "temperature": 1.0}, {"id": 34, "seek": 85869, "start": 833.93, "end": 858.69, "text": "بنفس الطريقة similarly ال b square يساوي ال b square يبقى بدأ اضرب zero سالب واحد واحد zero في zero سالب واحد واحد zero ويساوي الصف الأول في العامل الأول zero سالب واحد بسالب واحد", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 14138, 2423, 272, 3732, 7251, 3794, 995, 45865, 2423, 272, 3732, 7251, 3555, 4587, 7578, 47525, 10721, 1975, 11242, 25513, 4018, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 4018, 8978, 4018, 8608, 6027, 3555, 36764, 24401, 36764, 24401, 4018, 4032, 1829, 3794, 995, 45865, 31767, 5172, 16247, 12610, 8978, 18863, 10943, 1211, 16247, 12610, 4018, 8608, 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"probability": 0.6728515625}, {"start": 844.73, "end": 845.07, "word": " يبقى", "probability": 0.8292236328125}, {"start": 845.07, "end": 845.39, "word": " بدأ", "probability": 0.4796142578125}, {"start": 845.39, "end": 845.81, "word": " اضرب", "probability": 0.8424479166666666}, {"start": 845.81, "end": 846.35, "word": " zero", "probability": 0.39892578125}, {"start": 846.35, "end": 847.07, "word": " سالب", "probability": 0.7820638020833334}, {"start": 847.07, "end": 847.59, "word": " واحد", "probability": 0.984375}, {"start": 847.59, "end": 848.57, "word": " واحد", "probability": 0.909423828125}, {"start": 848.57, "end": 849.17, "word": " zero", "probability": 0.478271484375}, {"start": 849.17, "end": 849.81, "word": " في", "probability": 0.84619140625}, {"start": 849.81, "end": 850.39, "word": " zero", "probability": 0.91064453125}, {"start": 850.39, "end": 851.09, "word": " سالب", "probability": 0.978515625}, {"start": 851.09, "end": 851.67, "word": " واحد", "probability": 0.993896484375}, {"start": 851.67, "end": 852.65, "word": " واحد", "probability": 0.94921875}, {"start": 852.65, "end": 853.41, "word": " zero", "probability": 0.7607421875}, {"start": 853.41, "end": 854.31, "word": " ويساوي", "probability": 0.9125}, {"start": 854.31, "end": 855.17, "word": " الصف", "probability": 0.95703125}, {"start": 855.17, "end": 855.57, "word": " الأول", "probability": 0.87841796875}, {"start": 855.57, "end": 855.71, "word": " في", "probability": 0.95458984375}, {"start": 855.71, "end": 856.11, "word": " العامل", "probability": 0.7981770833333334}, {"start": 856.11, "end": 856.41, "word": " الأول", "probability": 0.871337890625}, {"start": 856.41, "end": 856.89, "word": " zero", "probability": 0.49365234375}, {"start": 856.89, "end": 857.41, "word": " سالب", "probability": 0.96142578125}, {"start": 857.41, "end": 857.75, "word": " واحد", "probability": 0.9921875}, {"start": 857.75, "end": 858.33, "word": " بسالب", "probability": 0.81439208984375}, {"start": 858.33, "end": 858.69, "word": " واحد", "probability": 0.9921875}], "temperature": 1.0}, {"id": 35, "seek": 88239, "start": 859.17, "end": 882.39, "text": "زيرو وزيرو أب زيرو صف التاني زيرو وزيرو أب زيرو و هنا سالب واحد شكلنا ماطلعش ال identity element لكن الشافوي طلعلي هذه لو ضربت في نفسي مين بطلع مين تتوقع يطلع", "tokens": [11622, 13546, 2407, 4032, 11622, 13546, 2407, 5551, 3555, 30767, 13546, 2407, 20328, 5172, 16712, 7649, 1829, 30767, 13546, 2407, 4032, 11622, 13546, 2407, 5551, 3555, 30767, 13546, 2407, 4032, 34105, 8608, 6027, 3555, 36764, 24401, 13412, 28820, 8315, 3714, 41193, 1211, 3615, 8592, 2423, 6575, 4478, 44381, 25124, 31845, 45865, 23032, 1211, 3615, 20292, 29538, 45164, 48812, 25513, 2655, 8978, 8717, 36178, 1829, 3714, 9957, 4724, 9566, 1211, 3615, 3714, 9957, 6055, 2655, 30543, 3615, 7251, 9566, 1211, 3615], "avg_logprob": -0.2791280805328746, "compression_ratio": 1.7088607594936709, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 859.17, "end": 859.99, "word": "زيرو", "probability": 0.6024576822916666}, {"start": 859.99, "end": 861.07, "word": " وزيرو", "probability": 0.82421875}, {"start": 861.07, "end": 861.45, "word": " أب", "probability": 0.4822998046875}, {"start": 861.45, "end": 861.91, "word": " زيرو", "probability": 0.8876953125}, {"start": 861.91, "end": 862.67, "word": " صف", "probability": 0.74755859375}, {"start": 862.67, "end": 863.45, "word": " التاني", "probability": 0.6974283854166666}, {"start": 863.45, "end": 864.61, "word": " زيرو", "probability": 0.7576497395833334}, {"start": 864.61, "end": 865.61, "word": " وزيرو", "probability": 0.955810546875}, {"start": 865.61, "end": 865.95, "word": " أب", "probability": 0.938720703125}, {"start": 865.95, "end": 866.47, "word": " زيرو", "probability": 0.96826171875}, {"start": 866.47, "end": 866.97, "word": " و", "probability": 0.484375}, {"start": 866.97, "end": 867.33, "word": " هنا", "probability": 0.56103515625}, {"start": 867.33, "end": 868.21, "word": " سالب", "probability": 0.9228515625}, {"start": 868.21, "end": 868.91, "word": " واحد", "probability": 0.959228515625}, {"start": 868.91, "end": 870.11, "word": " شكلنا", "probability": 0.5546061197916666}, {"start": 870.11, "end": 871.11, "word": " ماطلعش", "probability": 0.774853515625}, {"start": 871.11, "end": 871.23, "word": " ال", "probability": 0.96142578125}, {"start": 871.23, "end": 871.75, "word": " identity", "probability": 0.7607421875}, {"start": 871.75, "end": 872.41, "word": " element", "probability": 0.9755859375}, {"start": 872.41, "end": 873.77, "word": " لكن", "probability": 0.7724609375}, {"start": 873.77, "end": 874.69, "word": " الشافوي", "probability": 0.7405598958333334}, {"start": 874.69, "end": 876.15, "word": " طلعلي", "probability": 0.8463134765625}, {"start": 876.15, "end": 876.55, "word": " هذه", "probability": 0.495849609375}, {"start": 876.55, "end": 877.13, "word": " لو", "probability": 0.8408203125}, {"start": 877.13, "end": 877.77, "word": " ضربت", "probability": 0.9485677083333334}, {"start": 877.77, "end": 877.95, "word": " في", "probability": 0.7607421875}, {"start": 877.95, "end": 878.49, "word": " نفسي", "probability": 0.8070475260416666}, {"start": 878.49, "end": 878.65, "word": " مين", "probability": 0.82470703125}, {"start": 878.65, "end": 879.33, "word": " بطلع", "probability": 0.7357177734375}, {"start": 879.33, "end": 881.35, "word": " مين", "probability": 0.7064208984375}, {"start": 881.35, "end": 881.85, "word": " تتوقع", "probability": 0.96923828125}, {"start": 881.85, "end": 882.39, "word": " يطلع", "probability": 0.9912109375}], "temperature": 1.0}, {"id": 36, "seek": 89519, "start": 883.03, "end": 895.19, "text": "الـ Identity Matrix على طول الخط يبقى لو روحت جبت ال بي أس أربع اوتوماتيك هيطلع واحد زيرو زيرو واحد", "tokens": [6027, 39184, 25905, 507, 36274, 15844, 23032, 12610, 33962, 9566, 7251, 3555, 4587, 7578, 45164, 12602, 2407, 33753, 10874, 3555, 2655, 2423, 4724, 1829, 5551, 3794, 5551, 25513, 3615, 1975, 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هذا بدي يقولك ان ال order ل a بدي ساوي تلاتة and ال order ل b بدي ساوي كده اربعة طيب ايش رايك لو ضربت التنتين في بعض و بدي اشوف ال order ايه الشطعة تبعه الا لو اخدت", "tokens": [3555, 1863, 16606, 16472, 47356, 23758, 4724, 16254, 7251, 39648, 4117, 16472, 2423, 1668, 5296, 257, 4724, 16254, 8608, 995, 45865, 6055, 1211, 9307, 3660, 293, 2423, 1668, 5296, 272, 4724, 16254, 8608, 995, 45865, 9122, 3215, 3224, 1975, 25513, 27884, 23032, 1829, 3555, 1975, 1829, 8592, 12602, 47302, 4117, 45164, 48812, 25513, 2655, 16712, 29399, 9957, 8978, 45030, 11242, 4032, 4724, 16254, 1975, 8592, 38688, 2423, 1668, 1975, 1829, 3224, 25124, 9566, 27884, 6055, 3555, 3615, 3224, 42963, 45164, 1975, 9778, 3215, 2655], "avg_logprob": -0.3733455924426808, "compression_ratio": 1.7337278106508875, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 895.76, "end": 896.64, "word": "بناء", "probability": 0.7115885416666666}, {"start": 896.64, "end": 896.82, "word": " ان", "probability": 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لو", "probability": 0.9765625}, {"start": 909.66, "end": 910.16, "word": " ضربت", "probability": 0.9814453125}, {"start": 910.16, "end": 910.8, "word": " التنتين", "probability": 0.8834635416666666}, {"start": 910.8, "end": 911.02, "word": " في", "probability": 0.87939453125}, {"start": 911.02, "end": 911.56, "word": " بعض", "probability": 0.996337890625}, {"start": 911.56, "end": 912.04, "word": " و", "probability": 0.7763671875}, {"start": 912.04, "end": 912.3, "word": " بدي", "probability": 0.775146484375}, {"start": 912.3, "end": 912.52, "word": " اشوف", "probability": 0.7449544270833334}, {"start": 912.52, "end": 912.64, "word": " ال", "probability": 0.90673828125}, {"start": 912.64, "end": 912.9, "word": " order", "probability": 0.96826171875}, {"start": 912.9, "end": 913.2, "word": " ايه", "probability": 0.7960611979166666}, {"start": 913.2, "end": 913.58, "word": " الشطعة", "probability": 0.7688802083333334}, {"start": 913.58, "end": 914.42, "word": " تبعه", "probability": 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"word": " subgroup", "probability": 0.95556640625}, {"start": 1417.92, "end": 1418.28, "word": " اتش", "probability": 0.5691731770833334}, {"start": 1418.28, "end": 1418.94, "word": " subgroup", "probability": 0.878662109375}, {"start": 1418.94, "end": 1419.74, "word": " من", "probability": 0.98779296875}, {"start": 1419.74, "end": 1420.02, "word": " G", "probability": 0.322509765625}], "temperature": 1.0}, {"id": 58, "seek": 143521, "start": 1421.19, "end": 1435.21, "text": "الـ H هذه يا شباب ممكن تساوي جي وممكن ما تساويش الجي إذا الـ H هذه ما سواتش الجي بنكتب H subgroup من جي وبنشيل اليساوي اللي عندنا", "tokens": [6027, 39184, 389, 29538, 35186, 13412, 3555, 16758, 3714, 43020, 6055, 3794, 995, 45865, 10874, 1829, 4032, 2304, 43020, 19446, 6055, 3794, 995, 45865, 8592, 25724, 1829, 11933, 15730, 2423, 39184, 389, 29538, 19446, 8608, 2407, 9307, 8592, 25724, 1829, 44945, 4117, 2655, 3555, 389, 1422, 17377, 9154, 10874, 1829, 4032, 3555, 1863, 8592, 26895, 45595, 3794, 995, 45865, 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1424.59, "end": 1425.29, "word": " تساويش", "probability": 0.789453125}, {"start": 1425.29, "end": 1425.95, "word": " الجي", "probability": 0.844482421875}, {"start": 1425.95, "end": 1427.61, "word": " إذا", "probability": 0.59259033203125}, {"start": 1427.61, "end": 1427.93, "word": " الـ", "probability": 0.766357421875}, {"start": 1427.93, "end": 1428.07, "word": " H", "probability": 0.74462890625}, {"start": 1428.07, "end": 1428.45, "word": " هذه", "probability": 0.90576171875}, {"start": 1428.45, "end": 1428.69, "word": " ما", "probability": 0.6494140625}, {"start": 1428.69, "end": 1429.23, "word": " سواتش", "probability": 0.7572021484375}, {"start": 1429.23, "end": 1429.99, "word": " الجي", "probability": 0.81884765625}, {"start": 1429.99, "end": 1430.91, "word": " بنكتب", "probability": 0.9051513671875}, {"start": 1430.91, "end": 1431.29, "word": " H", "probability": 0.73046875}, {"start": 1431.29, "end": 1432.09, "word": " subgroup", "probability": 0.66796875}, {"start": 1432.09, "end": 1432.29, "word": " من", "probability": 0.96875}, {"start": 1432.29, "end": 1432.53, "word": " جي", "probability": 0.921142578125}, {"start": 1432.53, "end": 1433.41, "word": " وبنشيل", "probability": 0.7705078125}, {"start": 1433.41, "end": 1434.25, "word": " اليساوي", "probability": 0.806396484375}, {"start": 1434.25, "end": 1434.51, "word": " اللي", "probability": 0.838623046875}, {"start": 1434.51, "end": 1435.21, "word": " عندنا", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 59, "seek": 145969, "start": 1437.73, "end": 1459.69, "text": "الـ HP في هذه الحالة بسميها proper subgroup يعني انا لو أخدت subgroup و لاقيتها لا تساوي لجروب الأصلية لأنه بناعرف احنا any set is a subset of itself صحيح ولا لأ؟ هي مجموعة جزئية من نفسها طلعت المجموعة هذه الجزئية أقل من نفسها", "tokens": [6027, 39184, 12557, 8978, 29538, 21542, 6027, 3660, 4724, 38251, 1829, 11296, 2296, 1422, 17377, 37495, 22653, 1975, 8315, 45164, 5551, 9778, 3215, 2655, 1422, 17377, 4032, 20193, 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{"start": 1439.05, "end": 1439.55, "word": " بسميها", "probability": 0.939208984375}, {"start": 1439.55, "end": 1440.09, "word": " proper", "probability": 0.6328125}, {"start": 1440.09, "end": 1441.05, "word": " subgroup", "probability": 0.839599609375}, {"start": 1441.05, "end": 1441.55, "word": " يعني", "probability": 0.890380859375}, {"start": 1441.55, "end": 1441.91, "word": " انا", "probability": 0.5394287109375}, {"start": 1441.91, "end": 1442.13, "word": " لو", "probability": 0.931640625}, {"start": 1442.13, "end": 1442.75, "word": " أخدت", "probability": 0.8756103515625}, {"start": 1442.75, "end": 1443.49, "word": " subgroup", "probability": 0.946533203125}, {"start": 1443.49, "end": 1444.23, "word": " و", "probability": 0.787109375}, {"start": 1444.23, "end": 1444.97, "word": " لاقيتها", "probability": 0.76470947265625}, {"start": 1444.97, "end": 1445.21, "word": " لا", "probability": 0.6328125}, {"start": 1445.21, "end": 1445.93, "word": " تساوي", "probability": 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"probability": 0.83447265625}, {"start": 1451.45, "end": 1452.09, "word": " صحيح", "probability": 0.984130859375}, {"start": 1452.09, "end": 1452.25, "word": " ولا", "probability": 0.9619140625}, {"start": 1452.25, "end": 1452.83, "word": " لأ؟", "probability": 0.5968424479166666}, {"start": 1452.83, "end": 1453.17, "word": " هي", "probability": 0.904296875}, {"start": 1453.17, "end": 1454.29, "word": " مجموعة", "probability": 0.95966796875}, {"start": 1454.29, "end": 1454.95, "word": " جزئية", "probability": 0.9715576171875}, {"start": 1454.95, "end": 1455.21, "word": " من", "probability": 0.99609375}, {"start": 1455.21, "end": 1455.87, "word": " نفسها", "probability": 0.99853515625}, {"start": 1455.87, "end": 1456.73, "word": " طلعت", "probability": 0.9544270833333334}, {"start": 1456.73, "end": 1457.43, "word": " المجموعة", "probability": 0.97841796875}, {"start": 1457.43, "end": 1457.67, "word": " هذه", "probability": 0.8896484375}, {"start": 1457.67, "end": 1458.13, "word": " الجزئية", "probability": 0.9744873046875}, {"start": 1458.13, "end": 1458.85, "word": " أقل", "probability": 0.9348958333333334}, {"start": 1458.85, "end": 1459.09, "word": " من", "probability": 0.99658203125}, {"start": 1459.09, "end": 1459.69, "word": " نفسها", "probability": 0.9977213541666666}], "temperature": 1.0}, {"id": 60, "seek": 148729, "start": 1459.85, "end": 1487.29, "text": "لاتساوي الأصلية يبقى في هذه الحالة بسميها proper subgroup طبعا طيب طب لو كده تلاقيتش تساوي جيه طبعا تلاقيتش جد الجيه بالضبط تماما يبقى بسميها بسميها improper subgroup هذه اسمها improper بقوم بلغيها زي ما نقول إن هذا possible ممكن ننفيها بنقول impossible غير ممكن", "tokens": [1211, 9307, 3794, 995, 45865, 16247, 9381, 1211, 10632, 7251, 3555, 4587, 7578, 8978, 29538, 21542, 6027, 3660, 4724, 38251, 1829, 11296, 2296, 1422, 17377, 23032, 3555, 3615, 995, 23032, 1829, 3555, 23032, 3555, 45164, 9122, 3215, 3224, 6055, 15040, 4587, 36081, 8592, 6055, 3794, 995, 45865, 10874, 1829, 3224, 23032, 3555, 3615, 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"end": 1463.23, "word": " الحالة", "probability": 0.9832356770833334}, {"start": 1463.23, "end": 1463.85, "word": " بسميها", "probability": 0.968505859375}, {"start": 1463.85, "end": 1464.95, "word": " proper", "probability": 0.45703125}, {"start": 1464.95, "end": 1466.39, "word": " subgroup", "probability": 0.85009765625}, {"start": 1466.39, "end": 1466.91, "word": " طبعا", "probability": 0.63922119140625}, {"start": 1466.91, "end": 1468.17, "word": " طيب", "probability": 0.88671875}, {"start": 1468.17, "end": 1468.73, "word": " طب", "probability": 0.8515625}, {"start": 1468.73, "end": 1468.89, "word": " لو", "probability": 0.9853515625}, {"start": 1468.89, "end": 1469.19, "word": " كده", "probability": 0.6742350260416666}, {"start": 1469.19, "end": 1469.63, "word": " تلاقيتش", "probability": 0.826318359375}, {"start": 1469.63, "end": 1470.19, "word": " تساوي", "probability": 0.9560546875}, {"start": 1470.19, "end": 1470.65, "word": " جيه", "probability": 0.6588541666666666}, {"start": 1470.65, "end": 1470.97, "word": " طبعا", "probability": 0.7744140625}, {"start": 1470.97, "end": 1471.41, "word": " تلاقيتش", "probability": 0.8662109375}, {"start": 1471.41, "end": 1471.71, "word": " جد", "probability": 0.920654296875}, {"start": 1471.71, "end": 1472.05, "word": " الجيه", "probability": 0.8761393229166666}, {"start": 1472.05, "end": 1472.49, "word": " بالضبط", "probability": 0.9473876953125}, {"start": 1472.49, "end": 1473.15, "word": " تماما", "probability": 0.9869791666666666}, {"start": 1473.15, "end": 1473.75, "word": " يبقى", "probability": 0.90087890625}, {"start": 1473.75, "end": 1474.75, "word": " بسميها", "probability": 0.978759765625}, {"start": 1474.75, "end": 1475.93, "word": " بسميها", "probability": 0.9007568359375}, {"start": 1475.93, "end": 1476.77, "word": " improper", "probability": 0.80419921875}, {"start": 1476.77, "end": 1477.63, "word": " subgroup", "probability": 0.961669921875}, {"start": 1477.63, "end": 1477.93, "word": " هذه", "probability": 0.4912109375}, {"start": 1477.93, "end": 1478.41, "word": " اسمها", "probability": 0.76708984375}, {"start": 1478.41, "end": 1479.25, "word": " improper", "probability": 0.64892578125}, {"start": 1479.25, "end": 1480.27, "word": " بقوم", "probability": 0.86083984375}, {"start": 1480.27, "end": 1480.99, "word": " بلغيها", "probability": 0.96923828125}, {"start": 1480.99, "end": 1481.57, "word": " زي", "probability": 0.962646484375}, {"start": 1481.57, "end": 1481.63, "word": " ما", "probability": 0.9716796875}, {"start": 1481.63, "end": 1481.99, "word": " نقول", "probability": 0.8798828125}, {"start": 1481.99, "end": 1482.33, "word": " إن", "probability": 0.406005859375}, {"start": 1482.33, "end": 1482.67, "word": " هذا", "probability": 0.5771484375}, {"start": 1482.67, "end": 1483.31, "word": " possible", "probability": 0.96533203125}, {"start": 1483.31, "end": 1483.99, "word": " ممكن", "probability": 0.9833984375}, {"start": 1483.99, "end": 1484.87, "word": " ننفيها", "probability": 0.8868408203125}, {"start": 1484.87, "end": 1485.25, "word": " بنقول", "probability": 0.904541015625}, {"start": 1485.25, "end": 1486.39, "word": " impossible", "probability": 0.90478515625}, {"start": 1486.39, "end": 1486.87, "word": " غير", "probability": 0.992431640625}, {"start": 1486.87, "end": 1487.29, "word": " ممكن", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 61, "seek": 151494, "start": 1487.7, "end": 1514.94, "text": "يبقى هذي ممكن احطها لك ملاحظة رقم تلاتة if ال H تساوي G then ال H is called improper subgroup يبقى هذي مسميها improper subgroup", "tokens": [1829, 3555, 4587, 7578, 8032, 8848, 1829, 3714, 43020, 1975, 5016, 9566, 11296, 5296, 4117, 3714, 15040, 5016, 19913, 3660, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 498, 2423, 389, 6055, 3794, 995, 45865, 460, 550, 2423, 389, 307, 1219, 40651, 1422, 17377, 7251, 3555, 4587, 7578, 8032, 8848, 1829, 3714, 38251, 1829, 11296, 40651, 1422, 17377], "avg_logprob": -0.23572197684953952, "compression_ratio": 1.3609022556390977, "no_speech_prob": 0.0, "words": [{"start": 1487.7, "end": 1488.24, "word": "يبقى", "probability": 0.77496337890625}, {"start": 1488.24, "end": 1488.46, "word": " هذي", "probability": 0.3536783854166667}, {"start": 1488.46, "end": 1488.8, "word": " ممكن", "probability": 0.927734375}, {"start": 1488.8, "end": 1489.26, "word": " احطها", "probability": 0.7552490234375}, {"start": 1489.26, "end": 1489.42, "word": " لك", "probability": 0.78271484375}, {"start": 1489.42, "end": 1489.98, "word": " ملاحظة", "probability": 0.96806640625}, {"start": 1489.98, "end": 1490.52, "word": " رقم", "probability": 0.947265625}, {"start": 1490.52, "end": 1491.52, "word": " تلاتة", "probability": 0.922119140625}, {"start": 1491.52, "end": 1492.38, "word": " if", "probability": 0.5732421875}, {"start": 1492.38, "end": 1493.6, "word": " ال", "probability": 0.84716796875}, {"start": 1493.6, "end": 1494.0, "word": " H", "probability": 0.353759765625}, {"start": 1494.0, "end": 1494.92, "word": " تساوي", "probability": 0.8389892578125}, {"start": 1494.92, "end": 1495.38, "word": " G", "probability": 0.8642578125}, {"start": 1495.38, "end": 1497.72, "word": " then", "probability": 0.6123046875}, {"start": 1497.72, "end": 1499.44, "word": " ال", "probability": 0.89013671875}, {"start": 1499.44, "end": 1499.92, "word": " H", "probability": 0.92919921875}, {"start": 1499.92, "end": 1500.68, "word": " is", "probability": 0.9326171875}, {"start": 1500.68, "end": 1501.96, "word": " called", "probability": 0.9033203125}, {"start": 1501.96, "end": 1504.18, "word": " improper", "probability": 0.7822265625}, {"start": 1504.18, "end": 1509.38, "word": " subgroup", "probability": 0.85693359375}, {"start": 1509.38, "end": 1513.02, "word": " يبقى", "probability": 0.943115234375}, {"start": 1513.02, "end": 1513.2, "word": " هذي", "probability": 0.725341796875}, {"start": 1513.2, "end": 1513.7, "word": " مسميها", "probability": 0.765380859375}, {"start": 1513.7, "end": 1514.18, "word": " improper", "probability": 0.845703125}, {"start": 1514.18, "end": 1514.94, "word": " subgroup", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 62, "seek": 153483, "start": 1516.35, "end": 1534.83, "text": "لو رحت أخدت ال identity وحدة لحاله و حطيته داخل set يبقى السعر عندي set لا يوجد فيها إلا ال identity element هل هذه ال subgroup في الأول؟ subgroup ليش؟ لأن ال identity موجود", "tokens": [1211, 2407, 12602, 33753, 5551, 9778, 3215, 2655, 2423, 6575, 4032, 24401, 3660, 5296, 5016, 6027, 3224, 4032, 11331, 9566, 36081, 3224, 11778, 47283, 1211, 992, 7251, 3555, 4587, 7578, 21136, 3615, 2288, 43242, 1829, 992, 20193, 7251, 29245, 3215, 8978, 11296, 11933, 15040, 2423, 6575, 4478, 8032, 1211, 29538, 2423, 1422, 17377, 8978, 16247, 12610, 22807, 1422, 17377, 32239, 8592, 22807, 5296, 33456, 2423, 6575, 3714, 29245, 23328], "avg_logprob": -0.22165178060531615, "compression_ratio": 1.5384615384615385, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 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0.76611328125}, {"start": 1604.4, "end": 1605.34, "word": " بنفع", "probability": 0.8219401041666666}, {"start": 1605.34, "end": 1605.56, "word": " أقول", "probability": 0.800048828125}, {"start": 1605.56, "end": 1605.88, "word": " عليها", "probability": 0.99072265625}, {"start": 1605.88, "end": 1606.32, "word": " proper", "probability": 0.955078125}], "temperature": 1.0}, {"id": 66, "seek": 163651, "start": 1607.39, "end": 1636.51, "text": "بنفع proper على كل خط بس لدرجة انها مسمية trivial subgroup وبالتالي مقولش عليها proper subgroup بدأ ناخد بعض الأمثلة التوضيحية على ذلك قبل أن ندخل إلى أول نظرية يبقى examples أول مثل بيقول z in under", "tokens": [3555, 1863, 5172, 3615, 2296, 15844, 28242, 16490, 9566, 4724, 3794, 5296, 3215, 47341, 3660, 16472, 11296, 3714, 38251, 10632, 26703, 1422, 17377, 46599, 6027, 2655, 6027, 1829, 3714, 39648, 8592, 25894, 11296, 2296, 1422, 17377, 47525, 10721, 8717, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 16712, 2407, 11242, 1829, 5016, 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"word": " الأمثلة", "probability": 0.97607421875}, {"start": 1617.37, "end": 1618.39, "word": " التوضيحية", "probability": 0.983154296875}, {"start": 1618.39, "end": 1619.07, "word": " على", "probability": 0.8544921875}, {"start": 1619.07, "end": 1619.71, "word": " ذلك", "probability": 0.992431640625}, {"start": 1619.71, "end": 1620.39, "word": " قبل", "probability": 0.9892578125}, {"start": 1620.39, "end": 1620.63, "word": " أن", "probability": 0.54150390625}, {"start": 1620.63, "end": 1621.35, "word": " ندخل", "probability": 0.9820556640625}, {"start": 1621.35, "end": 1622.05, "word": " إلى", "probability": 0.70166015625}, {"start": 1622.05, "end": 1624.07, "word": " أول", "probability": 0.7430419921875}, {"start": 1624.07, "end": 1624.73, "word": " نظرية", "probability": 0.984619140625}, {"start": 1624.73, "end": 1625.69, "word": " يبقى", "probability": 0.713409423828125}, {"start": 1625.69, "end": 1626.61, "word": " examples", "probability": 0.73681640625}, {"start": 1626.61, "end": 1629.73, "word": " أول", "probability": 0.835693359375}, {"start": 1629.73, "end": 1630.43, "word": " مثل", "probability": 0.958984375}, {"start": 1630.43, "end": 1632.83, "word": " بيقول", "probability": 0.8201497395833334}, {"start": 1632.83, "end": 1633.17, "word": " z", "probability": 0.5166015625}, {"start": 1633.17, "end": 1634.03, "word": " in", "probability": 0.52685546875}, {"start": 1634.03, "end": 1636.51, "word": " under", "probability": 0.783203125}], "temperature": 1.0}, {"id": 67, "seek": 166589, "start": 1639.25, "end": 1665.89, "text": "addition modulo n اللي هي توسعة رمز نالها بالرمز z in وعليها عملية الجمع modulo n هذه ماالها is not a subgroup of z", "tokens": [25224, 849, 1072, 13455, 297, 13672, 1829, 39896, 33427, 3794, 27884, 12602, 2304, 11622, 8717, 6027, 11296, 20666, 2288, 2304, 11622, 710, 294, 4032, 3615, 20292, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 1072, 13455, 297, 29538, 19446, 6027, 11296, 307, 406, 257, 1422, 17377, 295, 710], "avg_logprob": -0.2934570300082366, "compression_ratio": 1.32, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1639.2500000000002, "end": 1640.6100000000001, "word": "addition", "probability": 0.56201171875}, {"start": 1640.6100000000001, "end": 1641.97, "word": " modulo", "probability": 0.6492919921875}, {"start": 1641.97, "end": 1642.27, "word": " n", "probability": 0.6884765625}, {"start": 1642.27, "end": 1645.23, "word": " اللي", "probability": 0.427001953125}, {"start": 1645.23, "end": 1645.45, "word": " هي", "probability": 0.71435546875}, {"start": 1645.45, "end": 1646.23, "word": " توسعة", "probability": 0.8577473958333334}, {"start": 1646.23, "end": 1646.71, "word": " رمز", "probability": 0.8883463541666666}, {"start": 1646.71, "end": 1647.07, "word": " نالها", "probability": 0.9361979166666666}, {"start": 1647.07, "end": 1647.75, "word": " بالرمز", "probability": 0.976806640625}, {"start": 1647.75, "end": 1648.15, "word": " z", "probability": 0.615234375}, {"start": 1648.15, "end": 1648.83, "word": " in", "probability": 0.28759765625}, {"start": 1648.83, "end": 1650.13, "word": " وعليها", "probability": 0.84765625}, {"start": 1650.13, "end": 1650.93, "word": " عملية", "probability": 0.9832356770833334}, {"start": 1650.93, "end": 1651.61, "word": " الجمع", "probability": 0.87744140625}, {"start": 1651.61, "end": 1652.23, "word": " modulo", "probability": 0.86865234375}, {"start": 1652.23, "end": 1652.85, "word": " n", "probability": 0.8583984375}, {"start": 1652.85, "end": 1654.21, "word": " هذه", "probability": 0.63037109375}, {"start": 1654.21, "end": 1654.83, "word": " ماالها", "probability": 0.6283365885416666}, {"start": 1654.83, "end": 1655.51, "word": " is", "probability": 0.8623046875}, {"start": 1655.51, "end": 1655.91, "word": " not", "probability": 0.966796875}, {"start": 1655.91, "end": 1656.25, "word": " a", "probability": 0.94482421875}, {"start": 1656.25, "end": 1657.17, "word": " subgroup", "probability": 0.81494140625}, {"start": 1657.17, "end": 1664.09, "word": " of", "probability": 0.57177734375}, {"start": 1664.09, "end": 1665.89, "word": " z", "probability": 0.88134765625}], "temperature": 1.0}, {"id": 68, "seek": 169461, "start": 1667.15, "end": 1694.61, "text": "هو عليها عملية الجمع العادية هذه مش subgroup طب زد n عناصرها zero واحد واثنين وتلاتة لغاية n ناقص واحد زد هذه الموجب والسالب والصفر يبقى zn هي subset من من؟ subset من z بيتداعي هنا بيقول ماهياش subgroup حد بيقول لي ليش؟ ايوة", "tokens": [3224, 2407, 25894, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 18863, 18513, 10632, 29538, 37893, 1422, 17377, 23032, 3555, 30767, 3215, 297, 18871, 33546, 2288, 11296, 4018, 36764, 24401, 4032, 5718, 104, 1863, 9957, 4032, 2655, 1211, 9307, 3660, 5296, 17082, 995, 10632, 297, 8717, 995, 4587, 9381, 36764, 24401, 30767, 3215, 29538, 9673, 29245, 3555, 16070, 3794, 6027, 3555, 16070, 9381, 5172, 2288, 7251, 3555, 4587, 7578, 710, 77, 39896, 25993, 9154, 9154, 22807, 25993, 9154, 710, 4724, 36081, 28259, 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" زد", "probability": 0.6595458984375}, {"start": 1682.55, "end": 1682.77, "word": " هذه", "probability": 0.79296875}, {"start": 1682.77, "end": 1683.47, "word": " الموجب", "probability": 0.8629557291666666}, {"start": 1683.47, "end": 1684.21, "word": " والسالب", "probability": 0.90673828125}, {"start": 1684.21, "end": 1684.87, "word": " والصفر", "probability": 0.9683837890625}, {"start": 1684.87, "end": 1685.69, "word": " يبقى", "probability": 0.9560546875}, {"start": 1685.69, "end": 1686.41, "word": " zn", "probability": 0.4505615234375}, {"start": 1686.41, "end": 1686.77, "word": " هي", "probability": 0.91748046875}, {"start": 1686.77, "end": 1687.31, "word": " subset", "probability": 0.82763671875}, {"start": 1687.31, "end": 1687.71, "word": " من", "probability": 0.99365234375}, {"start": 1687.71, "end": 1688.49, "word": " من؟", "probability": 0.4892578125}, {"start": 1688.49, "end": 1688.95, "word": " subset", "probability": 0.89599609375}, {"start": 1688.95, "end": 1689.47, 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69, "seek": 171873, "start": 1695.73, "end": 1718.73, "text": "أيوة اختلفت العملية حسب التعريف اللي كتبناه لازم تبقى العملية على ال group الأصلية هي نفس العملية على من؟ على ال subset يبقى هنا Z under that is not a subgroup because the two operations", "tokens": [10721, 1829, 2407, 3660, 1975, 46456, 46538, 2655, 18863, 42213, 10632, 11331, 35457, 16712, 3615, 16572, 5172, 13672, 1829, 9122, 2655, 3555, 8315, 3224, 5296, 31377, 2304, 6055, 3555, 4587, 7578, 18863, 42213, 10632, 15844, 2423, 1594, 16247, 36520, 10632, 39896, 8717, 36178, 18863, 42213, 10632, 15844, 9154, 22807, 15844, 2423, 25993, 7251, 3555, 4587, 7578, 34105, 1176, 833, 300, 307, 406, 257, 1422, 17377, 570, 264, 732, 7705], "avg_logprob": -0.18928571322134563, "compression_ratio": 1.5909090909090908, "no_speech_prob": 0.0, "words": [{"start": 1695.73, "end": 1696.61, "word": "أيوة", "probability": 0.6676025390625}, {"start": 1696.61, "end": 1697.41, "word": " اختلفت", "probability": 0.913330078125}, {"start": 1697.41, 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و عليها عملية الجمع السؤال هو هل هذه صبست من هذه صحيح لأن any integer is a rational number ال operation نفسي ال operation ال identity هنا مين", "tokens": [474, 2423, 276, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 710, 4032, 25894, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 21136, 33604, 6027, 31439, 8032, 1211, 29538, 20328, 3555, 14851, 9154, 29538, 20328, 5016, 1829, 5016, 5296, 33456, 604, 24922, 307, 257, 15090, 1230, 2423, 6916, 8717, 36178, 1829, 2423, 6916, 2423, 6575, 34105, 3714, 9957], "avg_logprob": -0.2109375041827821, "compression_ratio": 1.4695121951219512, "no_speech_prob": 0.0, "words": [{"start": 1751.91, "end": 1752.73, "word": "and", "probability": 0.55224609375}, {"start": 1752.73, "end": 1754.29, "word": " ال", "probability": 0.50537109375}, {"start": 1754.29, "end": 1754.85, "word": " h", "probability": 0.1317138671875}, {"start": 1754.85, "end": 1755.51, "word": " هي", "probability": 0.83154296875}, {"start": 1755.51, "end": 1756.15, "word": " عبارة", 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let", "probability": 0.07843017578125}, {"start": 1793.13, "end": 1793.33, "word": " g", "probability": 0.60009765625}, {"start": 1793.33, "end": 1793.51, "word": " and", "probability": 0.2144775390625}, {"start": 1793.51, "end": 1794.15, "word": " then", "probability": 0.841796875}, {"start": 1794.15, "end": 1795.63, "word": " ال", "probability": 0.8525390625}, {"start": 1795.63, "end": 1796.11, "word": " H", "probability": 0.275390625}, {"start": 1796.11, "end": 1796.63, "word": " is", "probability": 0.8408203125}, {"start": 1796.63, "end": 1796.97, "word": " a", "probability": 0.974609375}, {"start": 1796.97, "end": 1797.87, "word": " subgroup", "probability": 0.957763671875}, {"start": 1797.87, "end": 1798.25, "word": " من", "probability": 0.98681640625}, {"start": 1798.25, "end": 1798.51, "word": " g", "probability": 0.5771484375}, {"start": 1798.51, "end": 1798.85, "word": " على", "probability": 0.95361328125}, {"start": 1798.85, "end": 1799.31, "word": " طول", "probability": 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Y inverse ب مين؟ ب B", "tokens": [3224, 15730, 2423, 28820, 10943, 7251, 14851, 45865, 2423, 1783, 1975, 8315, 1975, 5172, 43042, 11296, 4724, 28543, 33599, 22807, 4724, 316, 16070, 398, 17340, 4724, 3714, 9957, 22807, 4724, 363], "avg_logprob": -0.4514160109683871, "compression_ratio": 1.1354166666666667, "no_speech_prob": 0.0, "words": [{"start": 2571.36, "end": 2572.32, "word": "هذا", "probability": 0.67822265625}, {"start": 2572.32, "end": 2572.86, "word": " الكلام", "probability": 0.8603515625}, {"start": 2572.86, "end": 2573.32, "word": " يستوي", "probability": 0.7882486979166666}, {"start": 2573.32, "end": 2573.44, "word": " ال", "probability": 0.61669921875}, {"start": 2573.44, "end": 2573.7, "word": " X", "probability": 0.324951171875}, {"start": 2573.7, "end": 2573.94, "word": " انا", "probability": 0.4356689453125}, {"start": 2573.94, "end": 2574.34, "word": " افرضها", "probability": 0.85540771484375}, {"start": 2574.34, "end": 2575.4, "word": " بقداش؟", "probability": 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أثبتهم", "probability": 0.93046875}, {"start": 2698.51, "end": 2699.19, "word": " صحيح", "probability": 0.99462890625}, {"start": 2699.19, "end": 2699.93, "word": " بيصير", "probability": 0.71337890625}, {"start": 2699.93, "end": 2700.25, "word": " هذا", "probability": 0.69384765625}, {"start": 2700.25, "end": 2701.77, "word": " subgroup", "probability": 0.7200927734375}, {"start": 2701.77, "end": 2702.77, "word": " كيف؟", "probability": 0.7696940104166666}, {"start": 2702.77, "end": 2703.19, "word": " يعني", "probability": 0.90966796875}, {"start": 2703.19, "end": 2703.73, "word": " بيكتثبت", "probability": 0.6844656808035714}, {"start": 2703.73, "end": 2703.97, "word": " أولا", "probability": 0.8834635416666666}, {"start": 2703.97, "end": 2704.21, "word": " أن", "probability": 0.50244140625}, {"start": 2704.21, "end": 2704.41, "word": " ال", "probability": 0.76953125}, {"start": 2704.41, "end": 2704.73, "word": " subset", "probability": 0.93994140625}, {"start": 2704.73, "end": 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new file mode 100644
index 0000000000000000000000000000000000000000..50c99de5efb51f9d29203effc429bc9bbbca7ea1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_raw.json
@@ -0,0 +1 @@
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على", "probability": 0.67138671875}, {"start": 62.28, "end": 63.3, "word": " أولاقات", "probability": 0.9228515625}, {"start": 63.3, "end": 64.14, "word": " التكافؤ", "probability": 0.877197265625}, {"start": 64.14, "end": 65.04, "word": " بدنا", "probability": 0.792724609375}, {"start": 65.04, "end": 65.54, "word": " نعرف", "probability": 0.9645182291666666}, {"start": 65.54, "end": 66.0, "word": " أولاق", "probability": 0.95166015625}, {"start": 66.0, "end": 66.78, "word": " التكافؤ", "probability": 0.9263916015625}], "temperature": 1.0}, {"id": 3, "seek": 9337, "start": 66.97, "end": 93.37, "text": "و بعدين انا اخد مثال و اوضيها عليها بقول little s ب a6 يبقى اخدنا s كمجموعة جالي a subset R of s cross ال s يبقى انا على ال 6s بدي اعمل direct product ما بين ال s و ال s itself بصير كل element في ال s cross ال s عبارة عن order pair زوج مرتب", "tokens": [2407, 39182, 9957, 1975, 8315, 1975, 9778, 3215, 50113, 6027, 4032, 1975, 2407, 11242, 1829, 11296, 25894, 11296, 4724, 39648, 707, 262, 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"probability": 0.8404947916666666}, {"start": 86.61, "end": 87.05, "word": " كل", "probability": 0.97265625}, {"start": 87.05, "end": 87.77, "word": " element", "probability": 0.966796875}, {"start": 87.77, "end": 88.29, "word": " في", "probability": 0.8037109375}, {"start": 88.29, "end": 88.45, "word": " ال", "probability": 0.974609375}, {"start": 88.45, "end": 88.71, "word": " s", "probability": 0.81494140625}, {"start": 88.71, "end": 89.13, "word": " cross", "probability": 0.9365234375}, {"start": 89.13, "end": 89.31, "word": " ال", "probability": 0.98681640625}, {"start": 89.31, "end": 89.47, "word": " s", "probability": 0.890625}, {"start": 89.47, "end": 89.91, "word": " عبارة", "probability": 0.9884033203125}, {"start": 89.91, "end": 90.21, "word": " عن", "probability": 0.9833984375}, {"start": 90.21, "end": 90.91, "word": " order", "probability": 0.9521484375}, {"start": 90.91, "end": 91.61, "word": " pair", "probability": 0.841796875}, {"start": 91.61, "end": 92.61, "word": " زوج", "probability": 0.9287109375}, {"start": 92.61, "end": 93.37, "word": " مرتب", "probability": 0.9830729166666666}], "temperature": 1.0}, {"id": 4, "seek": 11234, "start": 93.6, "end": 112.34, "text": "يبقى ال R هي subset من ال S cross ال S وهذه بسميها equivalence relation on S إذا تحققت ثلاث خواص الخاصية الأولى هي خاصية reflexive التانية ال symmetric التالتة هي ال transitive", "tokens": [1829, 3555, 4587, 7578, 2423, 497, 39896, 25993, 9154, 2423, 318, 3278, 2423, 318, 37037, 24192, 4724, 38251, 1829, 11296, 9052, 655, 9721, 322, 318, 11933, 15730, 6055, 5016, 4587, 38149, 38637, 1211, 5718, 104, 16490, 2407, 33546, 33962, 33546, 10632, 16247, 12610, 7578, 39896, 16490, 33546, 10632, 23802, 488, 16712, 7649, 10632, 2423, 32330, 16712, 6027, 2655, 3660, 39896, 2423, 1145, 2187], "avg_logprob": -0.21142578148283064, "compression_ratio": 1.4545454545454546, "no_speech_prob": 0.0, "words": [{"start": 93.6, "end": 94.84, "word": "يبقى", "probability": 0.8621826171875}, {"start": 94.84, 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{"start": 99.76, "end": 100.56, "word": " relation", "probability": 0.9912109375}, {"start": 100.56, "end": 101.26, "word": " on", "probability": 0.9033203125}, {"start": 101.26, "end": 101.86, "word": " S", "probability": 0.958984375}, {"start": 101.86, "end": 102.24, "word": " إذا", "probability": 0.91845703125}, {"start": 102.24, "end": 103.22, "word": " تحققت", "probability": 0.9317626953125}, {"start": 103.22, "end": 104.52, "word": " ثلاث", "probability": 0.96630859375}, {"start": 104.52, "end": 105.2, "word": " خواص", "probability": 0.8048502604166666}, {"start": 105.2, "end": 106.5, "word": " الخاصية", "probability": 0.9728190104166666}, {"start": 106.5, "end": 106.96, "word": " الأولى", "probability": 0.9816080729166666}, {"start": 106.96, "end": 107.16, "word": " هي", "probability": 0.91162109375}, {"start": 107.16, "end": 107.74, "word": " خاصية", "probability": 0.87451171875}, {"start": 107.74, "end": 108.6, "word": " reflexive", "probability": 0.830810546875}, {"start": 108.6, "end": 109.52, "word": " التانية", "probability": 0.8367513020833334}, {"start": 109.52, "end": 109.66, "word": " ال", "probability": 0.433837890625}, {"start": 109.66, "end": 110.2, "word": " symmetric", "probability": 0.69775390625}, {"start": 110.2, "end": 111.12, "word": " التالتة", "probability": 0.9136962890625}, {"start": 111.12, "end": 111.38, "word": " هي", "probability": 0.81005859375}, {"start": 111.38, "end": 111.52, "word": " ال", "probability": 0.34716796875}, {"start": 111.52, "end": 112.34, "word": " transitive", "probability": 0.7364501953125}], "temperature": 1.0}, {"id": 5, "seek": 13478, "start": 112.72, "end": 134.78, "text": "تعالى نشوف شو يعني معنى reflexive property بيقول ال a و ال a موجودة في R يعني لو أخدت a موجود في S لازم يكون ال element a و a ك order pair موجود وام موجود في R يعني العنصر مرتبط مع مين؟ مع نفسه بهذه ال relation", "tokens": [2655, 3615, 6027, 7578, 8717, 8592, 38688, 13412, 2407, 37495, 22653, 20449, 1863, 7578, 23802, 488, 4707, 4724, 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"word": " ك", "probability": 0.7119140625}, {"start": 125.9, "end": 126.26, "word": " order", "probability": 0.87890625}, {"start": 126.26, "end": 126.68, "word": " pair", "probability": 0.8857421875}, {"start": 126.68, "end": 127.06, "word": " موجود", "probability": 0.9850260416666666}, {"start": 127.06, "end": 127.42, "word": " وام", "probability": 0.3843994140625}, {"start": 127.42, "end": 128.52, "word": " موجود", "probability": 0.9267578125}, {"start": 128.52, "end": 128.72, "word": " في", "probability": 0.9482421875}, {"start": 128.72, "end": 128.94, "word": " R", "probability": 0.966796875}, {"start": 128.94, "end": 129.42, "word": " يعني", "probability": 0.9697265625}, {"start": 129.42, "end": 130.4, "word": " العنصر", "probability": 0.9627685546875}, {"start": 130.4, "end": 131.34, "word": " مرتبط", "probability": 0.9888916015625}, {"start": 131.34, "end": 131.58, "word": " مع", "probability": 0.98291015625}, {"start": 131.58, "end": 132.42, "word": " مين؟", "probability": 0.771484375}, {"start": 132.42, "end": 132.9, "word": " مع", "probability": 0.9775390625}, {"start": 132.9, "end": 133.66, "word": " نفسه", "probability": 0.9249674479166666}, {"start": 133.66, "end": 134.2, "word": " بهذه", "probability": 0.796875}, {"start": 134.2, "end": 134.32, "word": " ال", "probability": 0.9599609375}, {"start": 134.32, "end": 134.78, "word": " relation", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 6, "seek": 16176, "start": 135.86, "end": 161.76, "text": "يقبل الـ A والـ A موجودة في الـ R لكل الـ A الموجودة في الـ Main في الـ S يعني لو أخدت أي element من الـ6S يكون هذا الـ element مربوط مع نفسه بالعلاقة من الـ R وهذا اللي نسميها العلاقة العاكسة reflexive property العلاقة العاكسة أو القصية العاكسة", "tokens": [1829, 4587, 36150, 2423, 39184, 316, 16070, 39184, 316, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 497, 5296, 28820, 2423, 39184, 316, 9673, 29245, 23328, 3660, 8978, 2423, 39184, 12383, 8978, 2423, 39184, 318, 37495, 22653, 45164, 5551, 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"word": " موجودة", "probability": 0.9124755859375}, {"start": 138.04, "end": 138.16, "word": " في", "probability": 0.89453125}, {"start": 138.16, "end": 138.34, "word": " الـ", "probability": 0.861083984375}, {"start": 138.34, "end": 138.52, "word": " R", "probability": 0.84423828125}, {"start": 138.52, "end": 139.4, "word": " لكل", "probability": 0.910888671875}, {"start": 139.4, "end": 139.84, "word": " الـ", "probability": 0.945068359375}, {"start": 139.84, "end": 140.14, "word": " A", "probability": 0.8193359375}, {"start": 140.14, "end": 141.08, "word": " الموجودة", "probability": 0.907470703125}, {"start": 141.08, "end": 141.24, "word": " في", "probability": 0.9326171875}, {"start": 141.24, "end": 141.44, "word": " الـ", "probability": 0.718017578125}, {"start": 141.44, "end": 141.56, "word": " Main", "probability": 0.35009765625}, {"start": 141.56, "end": 142.08, "word": " في", "probability": 0.146728515625}, {"start": 142.08, "end": 142.22, "word": " الـ", "probability": 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"end": 147.78, "word": " مربوط", "probability": 0.9739990234375}, {"start": 147.78, "end": 147.98, "word": " مع", "probability": 0.95751953125}, {"start": 147.98, "end": 148.5, "word": " نفسه", "probability": 0.9747721354166666}, {"start": 148.5, "end": 149.2, "word": " بالعلاقة", "probability": 0.908203125}, {"start": 149.2, "end": 149.64, "word": " من", "probability": 0.7958984375}, {"start": 149.64, "end": 150.28, "word": " الـ", "probability": 0.86865234375}, {"start": 150.28, "end": 150.68, "word": " R", "probability": 0.212158203125}, {"start": 150.68, "end": 151.46, "word": " وهذا", "probability": 0.4896240234375}, {"start": 151.46, "end": 151.56, "word": " اللي", "probability": 0.732666015625}, {"start": 151.56, "end": 152.34, "word": " نسميها", "probability": 0.7969970703125}, {"start": 152.34, "end": 153.48, "word": " العلاقة", "probability": 0.9676106770833334}, {"start": 153.48, "end": 154.78, "word": " العاكسة", "probability": 0.97548828125}, {"start": 154.78, "end": 157.24, "word": " reflexive", "probability": 0.6424560546875}, {"start": 157.24, "end": 157.86, "word": " property", "probability": 0.94921875}, {"start": 157.86, "end": 159.08, "word": " العلاقة", "probability": 0.89892578125}, {"start": 159.08, "end": 159.94, "word": " العاكسة", "probability": 0.99521484375}, {"start": 159.94, "end": 160.12, "word": " أو", "probability": 0.80810546875}, {"start": 160.12, "end": 160.82, "word": " القصية", "probability": 0.9269205729166666}, {"start": 160.82, "end": 161.76, "word": " العاكسة", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 7, "seek": 17550, "start": 163.08, "end": 175.5, "text": "الشرط التاني او الخاصية التانية لو كان عندي زوج مرتب a و b موجود في R لازم يكون المقلب اللي هو b و a موجودة في R", "tokens": [6027, 8592, 2288, 9566, 16712, 7649, 1829, 1975, 2407, 33962, 33546, 10632, 16712, 7649, 10632, 45164, 25961, 18871, 16254, 30767, 29245, 3714, 43500, 3555, 257, 4032, 272, 3714, 29245, 23328, 8978, 497, 5296, 31377, 2304, 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مرتب", "probability": 0.9620768229166666}, {"start": 168.56, "end": 168.82, "word": " a", "probability": 0.6533203125}, {"start": 168.82, "end": 168.98, "word": " و", "probability": 0.86328125}, {"start": 168.98, "end": 169.3, "word": " b", "probability": 0.5849609375}, {"start": 169.3, "end": 169.96, "word": " موجود", "probability": 0.984375}, {"start": 169.96, "end": 170.2, "word": " في", "probability": 0.9013671875}, {"start": 170.2, "end": 170.6, "word": " R", "probability": 0.52587890625}, {"start": 170.6, "end": 171.5, "word": " لازم", "probability": 0.92333984375}, {"start": 171.5, "end": 171.8, "word": " يكون", "probability": 0.99169921875}, {"start": 171.8, "end": 172.28, "word": " المقلب", "probability": 0.7827962239583334}, {"start": 172.28, "end": 172.48, "word": " اللي", "probability": 0.79150390625}, {"start": 172.48, "end": 172.6, "word": " هو", "probability": 0.955078125}, {"start": 172.6, "end": 172.96, "word": " b", "probability": 0.71044921875}, {"start": 172.96, "end": 173.26, "word": " و", "probability": 0.9638671875}, {"start": 173.26, "end": 173.7, "word": " a", "probability": 0.92626953125}, {"start": 173.7, "end": 174.88, "word": " موجودة", "probability": 0.9686279296875}, {"start": 174.88, "end": 175.2, "word": " في", "probability": 0.95068359375}, {"start": 175.2, "end": 175.5, "word": " R", "probability": 0.75927734375}], "temperature": 1.0}, {"id": 8, "seek": 20167, "start": 175.73, "end": 201.67, "text": "يبقى هذا يعطيك يعني المركبة التانية بيصير الأولى والأولى بيصير التانية وهذا ال element لازم يكون موجود في R يعني إن كان A وB موجود في R لازم يكون B وA كذلك موجود في R لكل ال A وB اللي موجودة في اسم وهذه بسميها علاقة التماثل symmetric property أو خاصية التماثل", "tokens": [1829, 3555, 4587, 7578, 23758, 7251, 3615, 9566, 1829, 4117, 37495, 22653, 9673, 31747, 49401, 16712, 7649, 10632, 4724, 1829, 9381, 13546, 16247, 12610, 7578, 16070, 10721, 12610, 7578, 4724, 1829, 9381, 13546, 16712, 7649, 10632, 37037, 15730, 2423, 4478, 5296, 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موجود", "probability": 0.97216796875}, {"start": 184.09, "end": 184.25, "word": " في", "probability": 0.94921875}, {"start": 184.25, "end": 184.37, "word": " R", "probability": 0.80126953125}, {"start": 184.37, "end": 184.67, "word": " يعني", "probability": 0.8779296875}, {"start": 184.67, "end": 184.87, "word": " إن", "probability": 0.434814453125}, {"start": 184.87, "end": 185.17, "word": " كان", "probability": 0.9765625}, {"start": 185.17, "end": 185.33, "word": " A", "probability": 0.58447265625}, {"start": 185.33, "end": 185.69, "word": " وB", "probability": 0.86767578125}, {"start": 185.69, "end": 186.13, "word": " موجود", "probability": 0.9886067708333334}, {"start": 186.13, "end": 186.29, "word": " في", "probability": 0.931640625}, {"start": 186.29, "end": 186.53, "word": " R", "probability": 0.97705078125}, {"start": 186.53, "end": 187.39, "word": " لازم", "probability": 0.96142578125}, {"start": 187.39, "end": 187.71, "word": " يكون", "probability": 0.978271484375}, {"start": 187.71, "end": 188.05, "word": " B", "probability": 0.8115234375}, {"start": 188.05, "end": 188.61, "word": " وA", "probability": 0.81787109375}, {"start": 188.61, "end": 189.29, "word": " كذلك", "probability": 0.9064127604166666}, {"start": 189.29, "end": 190.09, "word": " موجود", "probability": 0.9853515625}, {"start": 190.09, "end": 190.61, "word": " في", "probability": 0.9599609375}, {"start": 190.61, "end": 190.99, "word": " R", "probability": 0.98291015625}, {"start": 190.99, "end": 191.51, "word": " لكل", "probability": 0.95361328125}, {"start": 191.51, "end": 191.75, "word": " ال", "probability": 0.9208984375}, {"start": 191.75, "end": 191.87, "word": " A", "probability": 0.861328125}, {"start": 191.87, "end": 192.29, "word": " وB", "probability": 0.797119140625}, {"start": 192.29, "end": 192.43, "word": " اللي", "probability": 0.80908203125}, {"start": 192.43, "end": 193.03, "word": " موجودة", "probability": 0.9617919921875}, {"start": 193.03, "end": 193.33, "word": " في", "probability": 0.98193359375}, {"start": 193.33, "end": 193.87, "word": " اسم", "probability": 0.77001953125}, {"start": 193.87, "end": 194.53, "word": " وهذه", "probability": 0.591796875}, {"start": 194.53, "end": 195.09, "word": " بسميها", "probability": 0.9315185546875}, {"start": 195.09, "end": 195.87, "word": " علاقة", "probability": 0.8575846354166666}, {"start": 195.87, "end": 197.01, "word": " التماثل", "probability": 0.91533203125}, {"start": 197.01, "end": 197.79, "word": " symmetric", "probability": 0.37744140625}, {"start": 197.79, "end": 198.85, "word": " property", "probability": 0.84765625}, {"start": 198.85, "end": 199.61, "word": " أو", "probability": 0.69091796875}, {"start": 199.61, "end": 200.59, "word": " خاصية", "probability": 0.990234375}, {"start": 200.59, "end": 201.67, "word": " التماثل", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 9, "seek": 23083, "start": 202.31, "end": 230.83, "text": "الأمر الثالث والأخير لو كان ال order pair A وB موجود في R و ال B و C موجود في R لاحظ المركبة الثانية هنا هي المركبة الأولى هنا لو كانوا اتنين موجودات في R لازم يكون ال A و ال C موجود وان موجود في R وهذه بسميها Transitive Property خاصية النقل أو العلاقة التي حقق هذه الخاصية بسميها علاقة ناقلة", "tokens": [6027, 10721, 29973, 6024, 104, 6027, 12984, 16070, 10721, 9778, 13546, 45164, 25961, 2423, 1668, 6119, 316, 4032, 33, 3714, 29245, 23328, 8978, 497, 4032, 2423, 363, 4032, 383, 3714, 29245, 23328, 8978, 497, 20193, 5016, 19913, 9673, 31747, 49401, 6024, 104, 7649, 10632, 34105, 39896, 9673, 31747, 49401, 16247, 12610, 7578, 34105, 45164, 25961, 14407, 1975, 2655, 1863, 9957, 3714, 29245, 23328, 9307, 8978, 497, 5296, 31377, 2304, 7251, 30544, 2423, 316, 4032, 2423, 383, 3714, 29245, 23328, 4032, 7649, 3714, 29245, 23328, 8978, 497, 37037, 24192, 4724, 38251, 1829, 11296, 6531, 2187, 48966, 16490, 33546, 10632, 28239, 4587, 1211, 34051, 18863, 15040, 28671, 38392, 11331, 4587, 4587, 29538, 33962, 33546, 10632, 4724, 38251, 1829, 11296, 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"end": 229.29, "word": " بسميها", "probability": 0.9534912109375}, {"start": 229.29, "end": 230.09, "word": " علاقة", "probability": 0.9303385416666666}, {"start": 230.09, "end": 230.83, "word": " ناقلة", "probability": 0.9801025390625}], "temperature": 1.0}, {"id": 10, "seek": 24894, "start": 231.12, "end": 248.94, "text": "إذا الـ equivalence relation هي عبارة عن علاقة عاكسة وفي نفس الوقت علاقة متماثلة وفي نفس الوقت علاقة ناقلة إذا تحققت هذه الخواص الثلاثة بقول ال relation اللي عندنا is an equivalence relation", "tokens": [28814, 15730, 2423, 39184, 9052, 655, 9721, 39896, 6225, 3555, 9640, 3660, 18871, 11203, 995, 28671, 6225, 995, 4117, 3794, 3660, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 11203, 995, 28671, 44650, 2304, 5718, 104, 37977, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 11203, 995, 28671, 8717, 995, 4587, 37977, 11933, 15730, 6055, 5016, 4587, 38149, 29538, 33962, 2407, 33546, 6024, 104, 1211, 5718, 104, 3660, 4724, 39648, 2423, 9721, 13672, 1829, 43242, 8315, 307, 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كنا بنقول عليها جملة أدبية يعني equivalence relation بدنا نعطيها رمز وهذا الرمز بدي يصير متعرف عليها طبعا أن أكثر من رمز يمكن أن نرمز بهي ال equivalence relation لكن الدرجة الغالب هو رمز واحد", "tokens": [3224, 15730, 9052, 655, 9721, 44945, 3615, 26890, 18871, 11296, 4724, 9381, 1829, 17082, 3660, 12602, 1829, 46958, 10632, 39182, 19446, 9122, 8315, 44945, 39648, 25894, 11296, 10874, 2304, 37977, 5551, 3215, 3555, 10632, 37495, 22653, 9052, 655, 9721, 47525, 8315, 8717, 3615, 9566, 1829, 11296, 12602, 2304, 11622, 37037, 15730, 34892, 2304, 11622, 4724, 16254, 7251, 9381, 13546, 44650, 3615, 28480, 25894, 11296, 23032, 3555, 3615, 995, 14739, 5551, 4117, 49115, 9154, 12602, 2304, 11622, 7251, 43020, 14739, 8717, 2288, 2304, 11622, 39627, 1829, 2423, 9052, 655, 9721, 44381, 32748, 47341, 3660, 6024, 118, 6027, 3555, 31439, 12602, 2304, 11622, 36764, 24401], "avg_logprob": -0.18960336409509182, "compression_ratio": 1.8584905660377358, "no_speech_prob": 0.0, "words": [{"start": 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263.61, "end": 264.33, "word": " متعرف", "probability": 0.9462890625}, {"start": 264.33, "end": 264.67, "word": " عليها", "probability": 0.69970703125}, {"start": 264.67, "end": 265.25, "word": " طبعا", "probability": 0.9600830078125}, {"start": 265.25, "end": 265.85, "word": " أن", "probability": 0.66162109375}, {"start": 265.85, "end": 266.51, "word": " أكثر", "probability": 0.81982421875}, {"start": 266.51, "end": 266.71, "word": " من", "probability": 0.96875}, {"start": 266.71, "end": 267.17, "word": " رمز", "probability": 0.90185546875}, {"start": 267.17, "end": 267.55, "word": " يمكن", "probability": 0.954345703125}, {"start": 267.55, "end": 267.75, "word": " أن", "probability": 0.6884765625}, {"start": 267.75, "end": 268.17, "word": " نرمز", "probability": 0.97412109375}, {"start": 268.17, "end": 268.47, "word": " بهي", "probability": 0.590576171875}, {"start": 268.47, "end": 268.59, "word": " ال", "probability": 0.640625}, {"start": 268.59, "end": 269.19, "word": " equivalence", "probability": 0.97802734375}, {"start": 269.19, "end": 269.77, "word": " relation", "probability": 0.99365234375}, {"start": 269.77, "end": 270.47, "word": " لكن", "probability": 0.896484375}, {"start": 270.47, "end": 271.15, "word": " الدرجة", "probability": 0.7854817708333334}, {"start": 271.15, "end": 271.61, "word": " الغالب", "probability": 0.891357421875}, {"start": 271.61, "end": 271.81, "word": " هو", "probability": 0.73046875}, {"start": 271.81, "end": 272.31, "word": " رمز", "probability": 0.99169921875}, {"start": 272.31, "end": 272.69, "word": " واحد", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 12, "seek": 29716, "start": 273.14, "end": 297.16, "text": "مثال و ذلك لو قلنا ال R هي equivalence relation على ال 6S بالروح نكتب ان ال A are related with B هذي مش ال set of real numbers هذي R اللي هي العلاقة اللي عندي يعني بقول ان ال A و ال B مرتبطات مع بعض بالعلاقة R instead of بدلا مقول", "tokens": [2304, 12984, 6027, 4032, 29910, 23275, 45164, 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282.28, "word": " A", "probability": 0.8857421875}, {"start": 282.28, "end": 282.74, "word": " are", "probability": 0.2052001953125}, {"start": 282.74, "end": 283.36, "word": " related", "probability": 0.98046875}, {"start": 283.36, "end": 283.72, "word": " with", "probability": 0.87841796875}, {"start": 283.72, "end": 283.98, "word": " B", "probability": 0.572265625}, {"start": 283.98, "end": 284.68, "word": " هذي", "probability": 0.5638427734375}, {"start": 284.68, "end": 284.84, "word": " مش", "probability": 0.92236328125}, {"start": 284.84, "end": 285.1, "word": " ال", "probability": 0.90283203125}, {"start": 285.1, "end": 285.34, "word": " set", "probability": 0.66650390625}, {"start": 285.34, "end": 285.54, "word": " of", "probability": 0.96484375}, {"start": 285.54, "end": 285.82, "word": " real", "probability": 0.97705078125}, {"start": 285.82, "end": 286.48, "word": " numbers", "probability": 0.76953125}, {"start": 286.48, "end": 287.34, "word": " هذي", "probability": 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لأ ال a مرتبط مع مين مع بي يعني a are b يبقى a are related with b مرتبط تماما مع مين مع بي أو ممكن نعبر عنها بالصيغة هذه a are related with b و أحيانا بيعبروا بحكاية اليساوي و أحيانا بثلاثة", "tokens": [28814, 1863, 34892, 26108, 1211, 3714, 43500, 3555, 257, 4032, 272, 3714, 29245, 23328, 8978, 2423, 9640, 11242, 4724, 39648, 5296, 10721, 2423, 257, 3714, 43500, 3555, 9566, 20449, 3714, 9957, 20449, 4724, 1829, 37495, 22653, 257, 366, 272, 7251, 3555, 4587, 7578, 257, 366, 4077, 365, 272, 3714, 43500, 3555, 9566, 46811, 10943, 995, 20449, 3714, 9957, 20449, 4724, 1829, 34051, 3714, 43020, 8717, 3615, 26890, 18871, 11296, 20666, 9381, 1829, 17082, 3660, 29538, 257, 366, 4077, 365, 272, 4032, 5551, 5016, 1829, 7649, 995, 4724, 1829, 3615, 26890, 14407, 4724, 5016, 4117, 995, 10632, 45595, 3794, 995, 45865, 4032, 5551, 5016, 1829, 7649, 995, 4724, 12984, 1211, 5718, 104, 3660], "avg_logprob": -0.20271017910104938, "compression_ratio": 1.84, "no_speech_prob": 0.0, "words": [{"start": 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{"start": 383.86, "end": 384.04, "word": " مع", "probability": 0.98779296875}, {"start": 384.04, "end": 384.34, "word": " هذا", "probability": 0.955078125}, {"start": 384.34, "end": 384.92, "word": " العنصر", "probability": 0.9107666015625}, {"start": 384.92, "end": 385.42, "word": " فقط", "probability": 0.9951171875}, {"start": 385.42, "end": 386.2, "word": " وماليش", "probability": 0.80096435546875}, {"start": 386.2, "end": 386.48, "word": " دعوة", "probability": 0.83380126953125}, {"start": 386.48, "end": 386.6, "word": " في", "probability": 0.93408203125}, {"start": 386.6, "end": 387.08, "word": " الباقي", "probability": 0.8484700520833334}], "temperature": 1.0}, {"id": 17, "seek": 40482, "start": 387.36, "end": 404.82, "text": "يعني أنا طبقا لتأثير ال relation أو تحت أثير ال relation هذه في عندي عناصر بتكون مرتبطة مع العناصر هدول بيكونولي مجموعة لمجموعة هذه اللي بيسميها equivalence class فصل التكافئ لهذا الألم", "tokens": [40228, 22653, 41850, 23032, 3555, 4587, 995, 5296, 2655, 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"word": " relation", "probability": 0.935546875}, {"start": 390.04, "end": 390.4, "word": " أو", "probability": 0.7490234375}, {"start": 390.4, "end": 390.8, "word": " تحت", "probability": 0.978271484375}, {"start": 390.8, "end": 391.34, "word": " أثير", "probability": 0.8653971354166666}, {"start": 391.34, "end": 391.48, "word": " ال", "probability": 0.9873046875}, {"start": 391.48, "end": 391.94, "word": " relation", "probability": 0.990234375}, {"start": 391.94, "end": 392.44, "word": " هذه", "probability": 0.77099609375}, {"start": 392.44, "end": 393.08, "word": " في", "probability": 0.55419921875}, {"start": 393.08, "end": 393.6, "word": " عندي", "probability": 0.823486328125}, {"start": 393.6, "end": 394.18, "word": " عناصر", "probability": 0.9928385416666666}, {"start": 394.18, "end": 394.62, "word": " بتكون", "probability": 0.8935546875}, {"start": 394.62, "end": 395.44, "word": " مرتبطة", "probability": 0.96875}, {"start": 395.44, "end": 395.76, "word": " مع", "probability": 0.994140625}, {"start": 395.76, "end": 396.82, "word": " العناصر", "probability": 0.94873046875}, {"start": 396.82, "end": 397.28, "word": " هدول", "probability": 0.873046875}, {"start": 397.28, "end": 398.44, "word": " بيكونولي", "probability": 0.8423828125}, {"start": 398.44, "end": 398.98, "word": " مجموعة", "probability": 0.89736328125}, {"start": 398.98, "end": 399.56, "word": " لمجموعة", "probability": 0.78984375}, {"start": 399.56, "end": 399.96, "word": " هذه", "probability": 0.51416015625}, {"start": 399.96, "end": 400.22, "word": " اللي", "probability": 0.823486328125}, {"start": 400.22, "end": 400.78, "word": " بيسميها", "probability": 0.85634765625}, {"start": 400.78, "end": 401.5, "word": " equivalence", "probability": 0.84716796875}, {"start": 401.5, "end": 402.04, "word": " class", "probability": 0.9765625}, {"start": 402.04, "end": 402.84, "word": " فصل", "probability": 0.85205078125}, {"start": 402.84, "end": 403.66, "word": " التكافئ", "probability": 0.82666015625}, 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0.95947265625}, {"start": 425.23, "end": 425.61, "word": " أخدته", "probability": 0.87646484375}, {"start": 425.61, "end": 425.93, "word": " طبعا", "probability": 0.9224853515625}, {"start": 425.93, "end": 426.15, "word": " بعد", "probability": 0.89013671875}, {"start": 426.15, "end": 426.47, "word": " قليل", "probability": 0.9698893229166666}, {"start": 426.47, "end": 426.81, "word": " هعطيك", "probability": 0.9}, {"start": 426.81, "end": 427.27, "word": " مثال", "probability": 0.951904296875}, {"start": 427.27, "end": 427.83, "word": " كيف", "probability": 0.962890625}, {"start": 427.83, "end": 428.29, "word": " بنجيب", "probability": 0.977294921875}, {"start": 428.29, "end": 428.69, "word": " هذه", "probability": 0.9794921875}, {"start": 428.69, "end": 429.81, "word": " العناصر؟", "probability": 0.97177734375}], "temperature": 1.0}, {"id": 19, "seek": 45071, "start": 430.29, "end": 450.71, "text": "يبقى هذا ال element بنسميه ال equivalence class تبع ال 6S that contains A يعني ال equivalence class لل element لازم يحتوي على مين؟ يحتوي على ال element itself بالاضافة إلى مجموعة من العناصر الأخرى", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 4478, 44945, 38251, 1829, 3224, 2423, 9052, 655, 1508, 6055, 3555, 3615, 2423, 1386, 50, 300, 8306, 316, 37495, 22653, 2423, 9052, 655, 1508, 24976, 4478, 5296, 31377, 2304, 7251, 33753, 45865, 15844, 3714, 9957, 22807, 7251, 33753, 45865, 15844, 2423, 4478, 2564, 20666, 46958, 31845, 3660, 30731, 3714, 7435, 2304, 2407, 27884, 9154, 18863, 1863, 33546, 2288, 16247, 34740, 7578], "avg_logprob": -0.1878446656114915, "compression_ratio": 1.569060773480663, "no_speech_prob": 0.0, "words": [{"start": 430.29, "end": 430.77, "word": "يبقى", "probability": 0.778076171875}, {"start": 430.77, "end": 430.99, "word": " هذا", "probability": 0.900390625}, {"start": 430.99, "end": 431.13, "word": " ال", "probability": 0.9267578125}, {"start": 431.13, "end": 431.51, "word": " element", "probability": 0.53759765625}, {"start": 431.51, 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"word": " equivalence", "probability": 0.976318359375}, {"start": 439.63, "end": 440.23, "word": " class", "probability": 0.98876953125}, {"start": 440.23, "end": 440.51, "word": " لل", "probability": 0.60791015625}, {"start": 440.51, "end": 441.01, "word": " element", "probability": 0.970703125}, {"start": 441.01, "end": 441.83, "word": " لازم", "probability": 0.97705078125}, {"start": 441.83, "end": 442.49, "word": " يحتوي", "probability": 0.9763997395833334}, {"start": 442.49, "end": 442.71, "word": " على", "probability": 0.88427734375}, {"start": 442.71, "end": 443.55, "word": " مين؟", "probability": 0.6258138020833334}, {"start": 443.55, "end": 444.13, "word": " يحتوي", "probability": 0.9423828125}, {"start": 444.13, "end": 444.39, "word": " على", "probability": 0.93017578125}, {"start": 444.39, "end": 444.57, "word": " ال", "probability": 0.990234375}, {"start": 444.57, "end": 444.97, "word": " element", "probability": 0.98095703125}, {"start": 444.97, "end": 445.75, "word": " 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1223.3, "word": " مش", "probability": 0.986328125}, {"start": 1223.3, "end": 1223.62, "word": " كل", "probability": 0.98583984375}, {"start": 1223.62, "end": 1224.34, "word": " عناصر", "probability": 0.97509765625}, {"start": 1224.34, "end": 1224.76, "word": " z", "probability": 0.43115234375}, {"start": 1224.76, "end": 1225.88, "word": " شوية", "probability": 0.931640625}, {"start": 1225.88, "end": 1226.28, "word": " منهم", "probability": 0.943359375}], "temperature": 1.0}, {"id": 53, "seek": 123815, "start": 1226.89, "end": 1238.15, "text": "طيب إيش رايك ال equivalence relation بتعملي partition للست اللي عندها أو للزد اللي عندنا، إيش يعني partition", "tokens": [9566, 1829, 3555, 11933, 1829, 8592, 12602, 47302, 4117, 2423, 9052, 655, 9721, 39894, 25957, 20292, 24808, 24976, 14851, 13672, 1829, 43242, 11296, 34051, 24976, 11622, 3215, 13672, 1829, 43242, 8315, 12399, 11933, 1829, 8592, 37495, 22653, 24808], "avg_logprob": -0.25841346306678575, "compression_ratio": 1.3278688524590163, 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1364.91, "text": "collection of non-empty disjoint subsets of S", "tokens": [33891, 10183, 295, 2107, 12, 4543, 88, 717, 48613, 2090, 1385, 295, 318], "avg_logprob": -0.36997767857142855, "compression_ratio": 0.8823529411764706, "no_speech_prob": 0.0, "words": [{"start": 1337.39, "end": 1338.29, "word": "collection", "probability": 0.57635498046875}, {"start": 1338.29, "end": 1339.75, "word": " of", "probability": 0.95068359375}, {"start": 1339.75, "end": 1342.03, "word": " non", "probability": 0.75439453125}, {"start": 1342.03, "end": 1345.97, "word": "-empty", "probability": 0.8541666666666666}, {"start": 1345.97, "end": 1349.05, "word": " disjoint", "probability": 0.916748046875}, {"start": 1349.05, "end": 1356.27, "word": " subsets", "probability": 0.5635986328125}, {"start": 1356.27, "end": 1363.99, "word": " of", "probability": 0.951171875}, {"start": 1363.99, "end": 1364.91, "word": " S", "probability": 0.71630859375}], "temperature": 1.0}, {"id": 58, "seek": 139460, "start": 1366.3, "end": 1394.6, "text": "whose union is S itself طب كويس تعالى نوضح هذا المفهوم افترض ان انا عندى ال 6 وال6 بالشكل هذا هذا ال 6S قسمتها الى مجموعة من ال subsets", "tokens": [1363, 541, 11671, 307, 318, 2564, 23032, 3555, 9122, 45865, 3794, 37279, 6027, 7578, 8717, 2407, 11242, 5016, 23758, 9673, 5172, 3224, 20498, 1975, 5172, 2655, 43042, 16472, 1975, 8315, 43242, 7578, 2423, 1386, 16070, 21, 20666, 8592, 28820, 23758, 23758, 2423, 1386, 50, 12174, 38251, 2655, 11296, 2423, 7578, 3714, 7435, 2304, 2407, 27884, 9154, 2423, 2090, 1385], "avg_logprob": -0.25598957588275273, "compression_ratio": 1.358974358974359, "no_speech_prob": 0.0, "words": [{"start": 1366.3, "end": 1366.82, "word": "whose", "probability": 0.58935546875}, {"start": 1366.82, "end": 1367.4, "word": " union", "probability": 0.94775390625}, {"start": 1367.4, "end": 1374.04, "word": " is", "probability": 0.89599609375}, {"start": 1374.04, "end": 1375.02, "word": " S", "probability": 0.388671875}, {"start": 1375.02, "end": 1375.96, "word": " itself", "probability": 0.6142578125}, {"start": 1375.96, "end": 1380.62, "word": " طب", "probability": 0.58642578125}, {"start": 1380.62, "end": 1381.18, "word": " كويس", "probability": 0.9607747395833334}, {"start": 1381.18, "end": 1381.7, "word": " تعالى", "probability": 0.7876790364583334}, {"start": 1381.7, "end": 1382.16, "word": " نوضح", "probability": 0.9697265625}, {"start": 1382.16, "end": 1382.56, "word": " هذا", "probability": 0.87841796875}, {"start": 1382.56, "end": 1383.62, "word": " المفهوم", "probability": 0.9915771484375}, {"start": 1383.62, "end": 1385.02, "word": " افترض", "probability": 0.978271484375}, {"start": 1385.02, "end": 1385.88, "word": " ان", "probability": 0.89306640625}, {"start": 1385.88, "end": 1386.28, "word": " انا", "probability": 0.82763671875}, {"start": 1386.28, "end": 1386.8, "word": " عندى", "probability": 0.758056640625}, {"start": 1386.8, "end": 1386.96, "word": " ال", "probability": 0.45703125}, {"start": 1386.96, "end": 1387.22, "word": " 6", "probability": 0.431396484375}, {"start": 1387.22, "end": 1387.76, "word": " وال6", "probability": 0.6171875}, {"start": 1387.76, "end": 1388.34, "word": " بالشكل", "probability": 0.9033203125}, {"start": 1388.34, "end": 1388.72, "word": " هذا", "probability": 0.78955078125}, {"start": 1388.72, "end": 1389.1, "word": " هذا", "probability": 0.2010498046875}, {"start": 1389.1, "end": 1389.36, "word": " ال", "probability": 0.859375}, {"start": 1389.36, "end": 1390.28, "word": " 6S", "probability": 0.555908203125}, {"start": 1390.28, "end": 1392.54, "word": " قسمتها", "probability": 0.94775390625}, {"start": 1392.54, "end": 1392.86, "word": " الى", "probability": 0.756103515625}, {"start": 1392.86, "end": 1393.46, "word": " مجموعة", "probability": 0.92373046875}, {"start": 1393.46, "end": 1393.72, "word": " من", "probability": 0.990234375}, {"start": 1393.72, "end": 1393.94, "word": " ال", "probability": 0.900390625}, {"start": 1393.94, "end": 1394.6, "word": " subsets", "probability": 0.6966552734375}], "temperature": 1.0}, {"id": 59, "seek": 140038, "start": 1395.9, "end": 1400.38, "text": " وهذه واحدة وهذه واحدة وهذه واحدة وهذه واحدة.", "tokens": [37037, 24192, 36764, 24401, 3660, 4032, 3224, 24192, 36764, 24401, 3660, 4032, 3224, 24192, 36764, 24401, 3660, 4032, 3224, 24192, 36764, 24401, 3660, 13], "avg_logprob": -0.1657812452316284, "compression_ratio": 2.3823529411764706, "no_speech_prob": 0.0, "words": [{"start": 1395.9, "end": 1396.3, "word": " وهذه", "probability": 0.66796875}, {"start": 1396.3, "end": 1396.8, "word": " واحدة", "probability": 0.9781901041666666}, {"start": 1396.8, "end": 1397.24, "word": " وهذه", "probability": 0.779296875}, {"start": 1397.24, "end": 1397.88, "word": " واحدة", "probability": 0.9861653645833334}, {"start": 1397.88, "end": 1398.8, "word": " وهذه", "probability": 0.841796875}, {"start": 1398.8, "end": 1399.34, "word": " واحدة", "probability": 0.9920247395833334}, {"start": 1399.34, "end": 1399.92, 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"start": 1430.19, "end": 1453.83, "text": "طالعش بيقول الـ Partition of non-empty disjoint subsets يبقى كل واحدة فيها مجموعة من العناصر يبقى هنا في عندي عناصر و هنا في عندي عناصر و هنا في عناصر و هنا في عناصر و هكذا يبقى كل مجموعة لازم يكون على الأقل فيها ولو", "tokens": [9566, 6027, 3615, 8592, 4724, 1829, 39648, 2423, 39184, 4100, 849, 295, 2107, 12, 4543, 88, 717, 48613, 2090, 1385, 7251, 3555, 4587, 7578, 28242, 36764, 24401, 3660, 8978, 11296, 3714, 7435, 2304, 2407, 27884, 9154, 18863, 1863, 33546, 2288, 7251, 3555, 4587, 7578, 34105, 8978, 18871, 16254, 18871, 33546, 2288, 4032, 34105, 8978, 18871, 16254, 18871, 33546, 2288, 4032, 34105, 8978, 18871, 33546, 2288, 4032, 34105, 8978, 18871, 33546, 2288, 4032, 8032, 4117, 15730, 7251, 3555, 4587, 7578, 28242, 3714, 7435, 2304, 2407, 27884, 5296, 31377, 2304, 7251, 30544, 15844, 16247, 4587, 1211, 8978, 11296, 35525, 2407], "avg_logprob": -0.23169191196711378, "compression_ratio": 1.9344262295081966, "no_speech_prob": 0.0, "words": 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" اي", "probability": 0.8935546875}, {"start": 1528.07, "end": 1528.57, "word": " subset", "probability": 0.9384765625}, {"start": 1528.57, "end": 1528.79, "word": " و", "probability": 0.90185546875}, {"start": 1528.79, "end": 1529.17, "word": " التانية", "probability": 0.9861653645833334}, {"start": 1529.17, "end": 1529.51, "word": " بده", "probability": 0.5064697265625}, {"start": 1529.51, "end": 1529.75, "word": " يسوى", "probability": 0.70550537109375}, {"start": 1529.75, "end": 1530.41, "word": " قداش", "probability": 0.63671875}, {"start": 1530.41, "end": 1531.17, "word": " five", "probability": 0.1865234375}], "temperature": 1.0}, {"id": 65, "seek": 156011, "start": 1532.53, "end": 1560.11, "text": "إذا خدت ال union عليهم كلهم بدي يعطينا نفس ال 6S لا بيزيد عليها ولا بينقص عنها مافي إمكانية إن حدث ذلك يبقى هذا بسمي partition لمين لل 6S اللي عندنا طيب خلينا .. خلينا نيجي الآن نعطي شغل عملية على حكاية ال partition بس قبل هيك", "tokens": [28814, 15730, 16490, 3215, 2655, 2423, 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"text": "لأي partition P على ست S هما عناصر الـ equivalence classes يبقى ال equivalence class بتعمل partition على ست وعكسه صحية", "tokens": [1211, 10721, 1829, 24808, 430, 15844, 8608, 2655, 318, 8032, 15042, 18871, 33546, 2288, 2423, 39184, 9052, 655, 5359, 7251, 3555, 4587, 7578, 2423, 9052, 655, 1508, 39894, 25957, 1211, 24808, 15844, 8608, 2655, 4032, 3615, 4117, 3794, 3224, 20328, 5016, 10632], "avg_logprob": -0.49527616556300674, "compression_ratio": 1.296, "no_speech_prob": 0.0, "words": [{"start": 1795.29, "end": 1796.07, "word": "لأي", "probability": 0.7110188802083334}, {"start": 1796.07, "end": 1796.71, "word": " partition", "probability": 0.91162109375}, {"start": 1796.71, "end": 1797.07, "word": " P", "probability": 0.625}, {"start": 1797.07, "end": 1797.29, "word": " على", "probability": 0.673828125}, {"start": 1797.29, "end": 1797.67, "word": " ست", "probability": 0.49365234375}, {"start": 1797.67, "end": 1797.95, "word": " S", "probability": 0.86767578125}, {"start": 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1824.27, "end": 1824.67, "word": " أو", "probability": 0.6943359375}, {"start": 1824.67, "end": 1824.93, "word": " هو", "probability": 0.64599609375}, {"start": 1824.93, "end": 1825.35, "word": " عنصر", "probability": 0.96826171875}, {"start": 1825.35, "end": 1825.51, "word": " من", "probability": 0.9912109375}, {"start": 1825.51, "end": 1826.15, "word": " عناصر", "probability": 0.9903971354166666}, {"start": 1826.15, "end": 1826.57, "word": " ال", "probability": 0.68505859375}, {"start": 1826.57, "end": 1827.05, "word": " partition", "probability": 0.97607421875}, {"start": 1827.05, "end": 1827.37, "word": " على", "probability": 0.92626953125}, {"start": 1827.37, "end": 1827.83, "word": " الست", "probability": 0.878662109375}, {"start": 1827.83, "end": 1828.19, "word": " اللى", "probability": 0.904541015625}, {"start": 1828.19, "end": 1828.55, "word": " عندنا", "probability": 0.92578125}], "temperature": 1.0}, {"id": 76, "seek": 184741, "start": 1829.23, "end": 1847.41, "text": "الان الي خاطر اوضح هذا الكلام عمليا عمليا من وين انا اخد ال relation اللى عندنا احنا اخدنا اللى هو قولنا العمصر تسعة واخدنا المقياس مين اللى هو خمسة طب انا لما اخد المقياس خمسة", "tokens": [6027, 7649, 45595, 16490, 41193, 2288, 1975, 2407, 11242, 5016, 23758, 2423, 28820, 10943, 6225, 2304, 20292, 995, 6225, 2304, 20292, 995, 9154, 4032, 9957, 1975, 8315, 1975, 9778, 3215, 2423, 9721, 13672, 7578, 43242, 8315, 1975, 5016, 8315, 1975, 9778, 3215, 8315, 13672, 7578, 31439, 12174, 12610, 8315, 18863, 2304, 9381, 2288, 6055, 3794, 27884, 4032, 47283, 3215, 8315, 9673, 4587, 25528, 3794, 3714, 9957, 13672, 7578, 31439, 16490, 2304, 3794, 3660, 23032, 3555, 1975, 8315, 5296, 15042, 1975, 9778, 3215, 9673, 4587, 25528, 3794, 16490, 2304, 3794, 3660], "avg_logprob": -0.22767857535854802, "compression_ratio": 1.9135802469135803, "no_speech_prob": 0.0, "words": [{"start": 1829.23, "end": 1829.77, "word": "الان", "probability": 0.812255859375}, {"start": 1829.77, "end": 1830.19, "word": " الي", "probability": 0.04766845703125}, {"start": 1830.19, "end": 1830.67, "word": " خاطر", "probability": 0.9654947916666666}, {"start": 1830.67, "end": 1831.11, "word": " اوضح", "probability": 0.93017578125}, {"start": 1831.11, "end": 1831.35, "word": " هذا", "probability": 0.90234375}, {"start": 1831.35, "end": 1831.95, "word": " الكلام", "probability": 0.9440104166666666}, {"start": 1831.95, "end": 1832.93, "word": " عمليا", "probability": 0.879638671875}, {"start": 1832.93, "end": 1833.63, "word": " عمليا", "probability": 0.8302001953125}, {"start": 1833.63, "end": 1833.77, "word": " من", "probability": 0.95361328125}, {"start": 1833.77, "end": 1834.19, "word": " وين", "probability": 0.87255859375}, {"start": 1834.19, "end": 1834.79, "word": " انا", "probability": 0.320648193359375}, {"start": 1834.79, "end": 1835.25, "word": " اخد", "probability": 0.611083984375}, {"start": 1835.25, "end": 1835.35, "word": " ال", "probability": 0.5048828125}, {"start": 1835.35, "end": 1835.77, "word": " relation", "probability": 0.880859375}, {"start": 1835.77, "end": 1836.09, "word": " اللى", "probability": 0.728515625}, {"start": 1836.09, "end": 1836.51, "word": " عندنا", "probability": 0.956298828125}, {"start": 1836.51, "end": 1837.55, "word": " احنا", "probability": 0.624267578125}, {"start": 1837.55, "end": 1838.19, "word": " اخدنا", "probability": 0.8641357421875}, {"start": 1838.19, "end": 1838.87, "word": " اللى", "probability": 0.84033203125}, {"start": 1838.87, "end": 1839.05, "word": " هو", "probability": 0.595703125}, {"start": 1839.05, "end": 1839.43, "word": " قولنا", "probability": 0.853515625}, {"start": 1839.43, "end": 1840.03, "word": " العمصر", "probability": 0.810302734375}, {"start": 1840.03, "end": 1840.41, "word": " تسعة", "probability": 0.8896484375}, {"start": 1840.41, "end": 1840.95, "word": " واخدنا", "probability": 0.94970703125}, {"start": 1840.95, "end": 1841.55, "word": " المقياس", "probability": 0.867919921875}, {"start": 1841.55, "end": 1842.05, "word": " مين", "probability": 0.80419921875}, {"start": 1842.05, "end": 1842.67, "word": " اللى", "probability": 0.898681640625}, {"start": 1842.67, "end": 1842.85, "word": " هو", "probability": 0.9345703125}, {"start": 1842.85, "end": 1843.53, "word": " خمسة", "probability": 0.9581298828125}, {"start": 1843.53, "end": 1844.25, "word": " طب", "probability": 0.91845703125}, {"start": 1844.25, "end": 1844.51, "word": " انا", "probability": 0.933837890625}, {"start": 1844.51, "end": 1844.77, "word": " لما", "probability": 0.9697265625}, {"start": 1844.77, "end": 1845.49, "word": " اخد", "probability": 0.8956705729166666}, {"start": 1845.49, "end": 1846.45, "word": " المقياس", "probability": 0.94482421875}, {"start": 1846.45, "end": 1847.41, "word": " خمسة", "probability": 0.9837646484375}], "temperature": 1.0}, {"id": 77, "seek": 187598, "start": 1848.2, "end": 1875.98, "text": "لما نأخد المقياس خمسة يبقى العناصر Zero واحد واتنين وتلاتة واربعة خمسة بترجع مين؟ Zero ستة بترجع واحد سبعة بترجع اتنين تمانية بترجع تلاتة تسعة بترجع اربعة وهكذا نوضح هذا الكلام يبقى for example كمثال على ذلك from the", "tokens": [1211, 15042, 8717, 10721, 9778, 3215, 9673, 4587, 25528, 3794, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 18863, 1863, 33546, 2288, 17182, 36764, 24401, 4032, 9307, 1863, 9957, 4032, 2655, 1211, 9307, 3660, 4032, 9640, 3555, 27884, 16490, 2304, 3794, 3660, 39894, 47341, 3615, 3714, 9957, 22807, 17182, 8608, 2655, 3660, 39894, 47341, 3615, 36764, 24401, 8608, 3555, 27884, 39894, 47341, 3615, 1975, 2655, 1863, 9957, 46811, 7649, 10632, 39894, 47341, 3615, 6055, 1211, 9307, 3660, 6055, 3794, 27884, 39894, 47341, 3615, 1975, 25513, 27884, 37037, 4117, 15730, 8717, 2407, 11242, 5016, 23758, 2423, 28820, 10943, 7251, 3555, 4587, 7578, 337, 1365, 9122, 2304, 12984, 6027, 15844, 29910, 23275, 490, 264], "avg_logprob": -0.17602323430829345, "compression_ratio": 1.8542713567839195, "no_speech_prob": 0.0, "words": [{"start": 1848.2, "end": 1848.58, "word": "لما", 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"word": " بترجع", "probability": 0.9303385416666666}, {"start": 1855.88, "end": 1856.82, "word": " مين؟", "probability": 0.77978515625}, {"start": 1856.82, "end": 1857.3, "word": " Zero", "probability": 0.88623046875}, {"start": 1857.3, "end": 1858.24, "word": " ستة", "probability": 0.9269205729166666}, {"start": 1858.24, "end": 1858.86, "word": " بترجع", "probability": 0.9630533854166666}, {"start": 1858.86, "end": 1859.32, "word": " واحد", "probability": 0.98779296875}, {"start": 1859.32, "end": 1859.82, "word": " سبعة", "probability": 0.8118489583333334}, {"start": 1859.82, "end": 1860.4, "word": " بترجع", "probability": 0.9521484375}, {"start": 1860.4, "end": 1860.92, "word": " اتنين", "probability": 0.9766845703125}, {"start": 1860.92, "end": 1861.56, "word": " تمانية", "probability": 0.8951822916666666}, {"start": 1861.56, "end": 1861.96, "word": " بترجع", "probability": 0.9376627604166666}, {"start": 1861.96, "end": 1862.42, "word": " تلاتة", "probability": 0.9827880859375}, {"start": 1862.42, "end": 1862.72, "word": " تسعة", "probability": 0.92529296875}, {"start": 1862.72, "end": 1863.26, "word": " بترجع", "probability": 0.9710286458333334}, {"start": 1863.26, "end": 1863.68, "word": " اربعة", "probability": 0.89453125}, {"start": 1863.68, "end": 1864.48, "word": " وهكذا", "probability": 0.7332356770833334}, {"start": 1864.48, "end": 1865.48, "word": " نوضح", "probability": 0.9022216796875}, {"start": 1865.48, "end": 1865.78, "word": " هذا", "probability": 0.96923828125}, {"start": 1865.78, "end": 1866.28, "word": " الكلام", "probability": 0.9327799479166666}, {"start": 1866.28, "end": 1867.52, "word": " يبقى", "probability": 0.9737548828125}, {"start": 1867.52, "end": 1868.04, "word": " for", "probability": 0.68115234375}, {"start": 1868.04, "end": 1868.72, "word": " example", "probability": 0.9697265625}, {"start": 1868.72, "end": 1870.56, "word": " كمثال", "probability": 0.9891357421875}, {"start": 1870.56, "end": 1870.84, "word": " على", "probability": 0.86376953125}, {"start": 1870.84, "end": 1871.44, "word": " ذلك", "probability": 0.992919921875}, {"start": 1871.44, "end": 1874.44, "word": " from", "probability": 0.83251953125}, {"start": 1874.44, "end": 1875.98, "word": " the", "probability": 0.46728515625}], "temperature": 1.0}, {"id": 78, "seek": 190393, "start": 1877.11, "end": 1903.93, "text": "above example where ال S بدها تساوي Z وال N او and ال N بدها تساوي خمسة يبقى بجي بقوله هنا the equivalence", "tokens": [455, 1682, 1365, 689, 2423, 318, 47525, 11296, 6055, 3794, 995, 45865, 1176, 16070, 426, 1975, 2407, 293, 2423, 426, 47525, 11296, 6055, 3794, 995, 45865, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 4724, 7435, 1829, 4724, 39648, 3224, 34105, 264, 9052, 655], "avg_logprob": -0.23090277247958713, "compression_ratio": 1.2459016393442623, "no_speech_prob": 0.0, "words": [{"start": 1877.11, "end": 1878.05, "word": "above", "probability": 0.6510009765625}, {"start": 1878.05, "end": 1880.45, "word": " example", "probability": 0.83740234375}, {"start": 1880.45, "end": 1882.97, "word": " where", "probability": 0.92041015625}, {"start": 1882.97, "end": 1886.13, "word": " ال", "probability": 0.84521484375}, {"start": 1886.13, "end": 1886.79, "word": " S", "probability": 0.56103515625}, {"start": 1886.79, "end": 1888.85, "word": " بدها", "probability": 0.744140625}, {"start": 1888.85, "end": 1889.47, "word": " تساوي", "probability": 0.9521484375}, {"start": 1889.47, "end": 1889.97, "word": " Z", "probability": 0.73974609375}, {"start": 1889.97, "end": 1891.01, "word": " وال", "probability": 0.5791015625}, {"start": 1891.01, "end": 1891.67, "word": " N", "probability": 0.908203125}, {"start": 1891.67, "end": 1892.45, "word": " او", "probability": 0.60723876953125}, {"start": 1892.45, "end": 1893.19, "word": " and", "probability": 0.9365234375}, {"start": 1893.19, "end": 1895.51, "word": " ال", "probability": 0.43994140625}, {"start": 1895.51, "end": 1896.01, "word": " N", "probability": 0.9541015625}, {"start": 1896.01, "end": 1896.59, "word": " بدها", "probability": 0.9775390625}, {"start": 1896.59, "end": 1897.17, "word": " تساوي", "probability": 0.985107421875}, {"start": 1897.17, "end": 1898.67, "word": " خمسة", "probability": 0.9310302734375}, {"start": 1898.67, "end": 1899.59, "word": " يبقى", "probability": 0.9454345703125}, {"start": 1899.59, "end": 1899.95, "word": " بجي", "probability": 0.6761067708333334}, {"start": 1899.95, "end": 1900.51, "word": " بقوله", "probability": 0.7345377604166666}, {"start": 1900.51, "end": 1900.91, "word": " هنا", "probability": 0.99169921875}, {"start": 1900.91, "end": 1901.65, "word": " the", "probability": 0.65087890625}, {"start": 1901.65, "end": 1903.93, "word": " equivalence", "probability": 0.776123046875}], "temperature": 1.0}, {"id": 79, "seek": 193472, "start": 1905.62, "end": 1934.72, "text": "A classes are اللي هو الـ Zero والواحد والاتنين والتلاتة والاربعة فقط لغيرهم where حيثهم بدنا نعرف مين هو الـ Zero ال equivalence class تبع الـ Zero", "tokens": [32, 5359, 366, 13672, 1829, 31439, 2423, 39184, 17182, 16070, 14407, 24401, 16070, 9307, 1863, 9957, 16070, 2655, 1211, 9307, 3660, 16070, 9640, 3555, 27884, 6156, 47432, 5296, 17082, 13546, 16095, 689, 11331, 1829, 12984, 16095, 47525, 8315, 8717, 3615, 28480, 3714, 9957, 31439, 2423, 39184, 17182, 2423, 9052, 655, 1508, 6055, 3555, 3615, 2423, 39184, 17182], "avg_logprob": -0.2409752188571568, "compression_ratio": 1.527027027027027, "no_speech_prob": 0.0, "words": [{"start": 1905.62, "end": 1905.98, "word": "A", "probability": 0.05267333984375}, {"start": 1905.98, "end": 1907.04, "word": " classes", "probability": 0.72412109375}, {"start": 1907.04, "end": 1909.54, "word": " are", "probability": 0.84228515625}, {"start": 1909.54, "end": 1911.34, "word": " اللي", "probability": 0.5689697265625}, {"start": 1911.34, "end": 1911.52, "word": " هو", "probability": 0.9736328125}, {"start": 1911.52, "end": 1911.86, "word": " الـ", "probability": 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"probability": 0.92578125}, {"start": 1930.28, "end": 1930.54, "word": " هو", "probability": 0.99169921875}, {"start": 1930.54, "end": 1930.86, "word": " الـ", "probability": 0.7113037109375}, {"start": 1930.86, "end": 1931.04, "word": " Zero", "probability": 0.82763671875}, {"start": 1931.04, "end": 1932.5, "word": " ال", "probability": 0.7880859375}, {"start": 1932.5, "end": 1933.26, "word": " equivalence", "probability": 0.785400390625}, {"start": 1933.26, "end": 1933.74, "word": " class", "probability": 0.98193359375}, {"start": 1933.74, "end": 1934.22, "word": " تبع", "probability": 0.9410807291666666}, {"start": 1934.22, "end": 1934.52, "word": " الـ", "probability": 0.862548828125}, {"start": 1934.52, "end": 1934.72, "word": " Zero", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 80, "seek": 195318, "start": 1935.78, "end": 1953.18, "text": "بجي بقول هي ال zero حط ال zero ضيفله خمسات يبقاش بصير خمسة عشرة خمستاش و تضلك ماشي سالب خمسة سالب عشرة سالب خمستاش و تضلك ماشي", "tokens": [3555, 7435, 1829, 4724, 39648, 39896, 2423, 4018, 11331, 9566, 2423, 4018, 48812, 33911, 43761, 16490, 2304, 3794, 9307, 7251, 3555, 4587, 33599, 4724, 9381, 13546, 16490, 2304, 3794, 3660, 6225, 8592, 25720, 16490, 2304, 14851, 33599, 4032, 6055, 11242, 23275, 3714, 33599, 1829, 8608, 6027, 3555, 16490, 2304, 3794, 3660, 8608, 6027, 3555, 6225, 8592, 25720, 8608, 6027, 3555, 16490, 2304, 14851, 33599, 4032, 6055, 11242, 23275, 3714, 33599, 1829], "avg_logprob": -0.2006293400708172, "compression_ratio": 1.8632478632478633, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1935.78, "end": 1936.4, "word": "بجي", "probability": 0.39385986328125}, {"start": 1936.4, "end": 1936.92, "word": " بقول", "probability": 0.9033203125}, {"start": 1936.92, "end": 1937.24, "word": " هي", "probability": 0.408935546875}, {"start": 1937.24, "end": 1937.5, "word": " ال", "probability": 0.8193359375}, {"start": 1937.5, "end": 1937.84, "word": " zero", "probability": 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"probability": 0.7692057291666666}, {"start": 1946.4, "end": 1946.88, "word": " ماشي", "probability": 0.9327799479166666}, {"start": 1946.88, "end": 1947.74, "word": " سالب", "probability": 0.9169921875}, {"start": 1947.74, "end": 1948.44, "word": " خمسة", "probability": 0.9876708984375}, {"start": 1948.44, "end": 1949.26, "word": " سالب", "probability": 0.9744466145833334}, {"start": 1949.26, "end": 1949.88, "word": " عشرة", "probability": 0.98046875}, {"start": 1949.88, "end": 1950.74, "word": " سالب", "probability": 0.9889322916666666}, {"start": 1950.74, "end": 1951.78, "word": " خمستاش", "probability": 0.9853515625}, {"start": 1951.78, "end": 1952.3, "word": " و", "probability": 0.96142578125}, {"start": 1952.3, "end": 1952.7, "word": " تضلك", "probability": 0.9850260416666666}, {"start": 1952.7, "end": 1953.18, "word": " ماشي", "probability": 0.9493815104166666}], "temperature": 1.0}, {"id": 81, "seek": 198031, "start": 1953.87, "end": 1980.31, "text": "بعد ذلك يبدأ ال equivalence class للواحد يبقى بالدرجة اقول له هذه واحد وخمسة ستة وخمسة احداشر وخمسة ستة عشر وتبقى مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال مازال ماز", "tokens": [3555, 22488, 29910, 23275, 7251, 44510, 10721, 2423, 9052, 655, 1508, 24976, 14407, 24401, 7251, 3555, 4587, 7578, 20666, 3215, 47341, 3660, 1975, 39648, 46740, 29538, 36764, 24401, 4032, 9778, 2304, 3794, 3660, 8608, 2655, 3660, 4032, 9778, 2304, 3794, 3660, 1975, 24401, 33599, 2288, 4032, 9778, 2304, 3794, 3660, 8608, 2655, 3660, 6225, 46309, 4032, 2655, 3555, 4587, 7578, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 6027, 3714, 31377, 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0.57666015625}, {"start": 2368.22, "end": 2368.6, "word": " تعالى", "probability": 0.9495442708333334}, {"start": 2368.6, "end": 2369.66, "word": " طبعا", "probability": 0.9720458984375}, {"start": 2369.66, "end": 2369.94, "word": " الان", "probability": 0.75927734375}, {"start": 2369.94, "end": 2370.48, "word": " وصلنا", "probability": 0.9908854166666666}, {"start": 2370.48, "end": 2370.94, "word": " لموضوع", "probability": 0.9600830078125}, {"start": 2370.94, "end": 2371.12, "word": " ال", "probability": 0.97900390625}, {"start": 2371.12, "end": 2371.64, "word": " functions", "probability": 0.84716796875}, {"start": 2371.64, "end": 2372.02, "word": " في", "probability": 0.84033203125}, {"start": 2372.02, "end": 2372.66, "word": " المحاضرة", "probability": 0.91943359375}, {"start": 2372.66, "end": 2373.16, "word": " القادمة", "probability": 0.9910481770833334}, {"start": 2373.16, "end": 2373.44, "word": " يوم", "probability": 0.9853515625}, {"start": 2373.44, "end": 2373.94, "word": " السبت", "probability": 0.9324544270833334}, {"start": 2373.94, "end": 2375.04, "word": " بناخد", "probability": 0.9368489583333334}, {"start": 2375.04, "end": 2376.12, "word": " الموضوع", "probability": 0.906005859375}, {"start": 2376.12, "end": 2376.54, "word": " ال", "probability": 0.91943359375}, {"start": 2376.54, "end": 2377.0, "word": " functions", "probability": 0.79541015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2378.14125, "duration_after_vad": 2243.8349999999928}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c016e011ab4591d1209b8c4cbda84c6918eeb49f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_raw.srt
@@ -0,0 +1,1604 @@
+1
+00:00:20,970 --> 00:00:26,550
+بسم الله الرحمن الرحيم لازلنا في نفس ال chapter
+
+2
+00:00:26,550 --> 00:00:31,750
+الأول اللي هو بتحدث عن أساسيات لمساق الجبرة اللي
+
+3
+00:00:31,750 --> 00:00:36,670
+سندرسه و اليوم ان شاء الله سنتعرض الى ال
+
+4
+00:00:36,670 --> 00:00:41,190
+equivalence relations والتي سبقت دراستها في مبادئ
+
+5
+00:00:41,190 --> 00:00:46,100
+الرياضيةهنعطي تعريف نعرف شو يعني معنى equivalence
+
+6
+00:00:46,100 --> 00:00:51,080
+relation نعطي مثال نعرف شو يعني equivalence class
+
+7
+00:00:51,080 --> 00:00:55,660
+نعرف ما هو ال partition على ال set يعني هذا جمال
+
+8
+00:00:55,660 --> 00:01:00,000
+ما سندرسه في هذه المحاضرة ان شاء الله بنبدأ بال
+
+9
+00:01:00,000 --> 00:01:04,140
+equivalence relations اللي على أولاقات التكافؤ
+
+10
+00:01:04,140 --> 00:01:08,630
+بدنا نعرف أولاق التكافؤو بعدين انا اخد مثال و
+
+11
+00:01:08,630 --> 00:01:13,310
+اوضيها عليها بقول little s ب a6 يبقى اخدنا s
+
+12
+00:01:13,310 --> 00:01:19,970
+كمجموعة جالي a subset R of s cross ال s يبقى انا
+
+13
+00:01:19,970 --> 00:01:25,150
+على ال 6s بدي اعمل direct product ما بين ال s و ال
+
+14
+00:01:25,150 --> 00:01:29,910
+s itself بصير كل element في ال s cross ال s عبارة
+
+15
+00:01:29,910 --> 00:01:36,620
+عن order pair زوج مرتبيبقى ال R هي subset من ال S
+
+16
+00:01:36,620 --> 00:01:41,860
+cross ال S وهذه بسميها equivalence relation on S
+
+17
+00:01:41,860 --> 00:01:47,740
+إذا تحققت ثلاث خواص الخاصية الأولى هي خاصية
+
+18
+00:01:47,740 --> 00:01:51,520
+reflexive التانية ال symmetric التالتة هي ال
+
+19
+00:01:51,520 --> 00:01:55,020
+transitiveتعالى نشوف شو يعني معنى reflexive
+
+20
+00:01:55,020 --> 00:02:00,400
+property بيقول ال a و ال a موجودة في R يعني لو
+
+21
+00:02:00,400 --> 00:02:05,900
+أخدت a موجود في S لازم يكون ال element a و a ك
+
+22
+00:02:05,900 --> 00:02:11,340
+order pair موجود وام موجود في R يعني العنصر مرتبط
+
+23
+00:02:11,340 --> 00:02:17,520
+مع مين؟ مع نفسه بهذه ال relationيقبل الـ A والـ A
+
+24
+00:02:17,520 --> 00:02:22,080
+موجودة في الـ R لكل الـ A الموجودة في الـ Main في
+
+25
+00:02:22,080 --> 00:02:26,640
+الـ S يعني لو أخدت أي element من الـ6S يكون هذا
+
+26
+00:02:26,640 --> 00:02:31,460
+الـ element مربوط مع نفسه بالعلاقة من الـ R وهذا
+
+27
+00:02:31,460 --> 00:02:37,860
+اللي نسميها العلاقة العاكسة reflexive property
+
+28
+00:02:37,860 --> 00:02:44,300
+العلاقة العاكسة أو القصية العاكسةالشرط التاني او
+
+29
+00:02:44,300 --> 00:02:49,960
+الخاصية التانية لو كان عندي زوج مرتب a و b موجود
+
+30
+00:02:49,960 --> 00:02:55,500
+في R لازم يكون المقلب اللي هو b و a موجودة في R
+
+31
+00:02:55,730 --> 00:02:59,790
+يبقى هذا يعطيك يعني المركبة التانية بيصير الأولى
+
+32
+00:02:59,790 --> 00:03:03,650
+والأولى بيصير التانية وهذا ال element لازم يكون
+
+33
+00:03:03,650 --> 00:03:08,050
+موجود في R يعني إن كان A وB موجود في R لازم يكون B
+
+34
+00:03:08,050 --> 00:03:13,870
+وA كذلك موجود في R لكل ال A وB اللي موجودة في اسم
+
+35
+00:03:13,870 --> 00:03:19,610
+وهذه بسميها علاقة التماثل symmetric property أو
+
+36
+00:03:19,610 --> 00:03:25,510
+خاصية التماثلالأمر الثالث والأخير لو كان ال order
+
+37
+00:03:25,510 --> 00:03:30,410
+pair A وB موجود في R و ال B و C موجود في R لاحظ
+
+38
+00:03:30,410 --> 00:03:34,910
+المركبة الثانية هنا هي المركبة الأولى هنا لو كانوا
+
+39
+00:03:34,910 --> 00:03:39,710
+اتنين موجودات في R لازم يكون ال A و ال C موجود وان
+
+40
+00:03:39,710 --> 00:03:45,350
+موجود في R وهذه بسميها Transitive Property خاصية
+
+41
+00:03:45,350 --> 00:03:50,090
+النقل أو العلاقة التي حقق هذه الخاصية بسميها علاقة
+
+42
+00:03:50,090 --> 00:03:54,240
+ناقلةإذا الـ equivalence relation هي عبارة عن
+
+43
+00:03:54,240 --> 00:03:59,180
+علاقة عاكسة وفي نفس الوقت علاقة متماثلة وفي نفس
+
+44
+00:03:59,180 --> 00:04:03,860
+الوقت علاقة ناقلة إذا تحققت هذه الخواص الثلاثة
+
+45
+00:04:03,860 --> 00:04:08,240
+بقول ال relation اللي عندنا is an equivalence
+
+46
+00:04:08,240 --> 00:04:14,570
+relationهذا equivalence relation بنعبر عنها بصيغة
+
+47
+00:04:14,570 --> 00:04:18,730
+رياضية بعد ما كنا بنقول عليها جملة أدبية يعني
+
+48
+00:04:18,730 --> 00:04:22,710
+equivalence relation بدنا نعطيها رمز وهذا الرمز
+
+49
+00:04:22,710 --> 00:04:27,750
+بدي يصير متعرف عليها طبعا أن أكثر من رمز يمكن أن
+
+50
+00:04:27,750 --> 00:04:31,610
+نرمز بهي ال equivalence relation لكن الدرجة الغالب
+
+51
+00:04:31,610 --> 00:04:37,240
+هو رمز واحدمثال و ذلك لو قلنا ال R هي equivalence
+
+52
+00:04:37,240 --> 00:04:43,360
+relation على ال 6S بالروح نكتب ان ال A are related
+
+53
+00:04:43,360 --> 00:04:47,980
+with B هذي مش ال set of real numbers هذي R اللي هي
+
+54
+00:04:47,980 --> 00:04:52,920
+العلاقة اللي عندي يعني بقول ان ال A و ال B مرتبطات
+
+55
+00:04:52,920 --> 00:04:58,430
+مع بعض بالعلاقة R instead of بدلا مقولإن الراجل
+
+56
+00:04:58,430 --> 00:05:02,810
+مرتب a و b موجود في الارض بقول لأ ال a مرتبط مع
+
+57
+00:05:02,810 --> 00:05:08,310
+مين مع بي يعني a are b يبقى a are related with b
+
+58
+00:05:08,310 --> 00:05:13,410
+مرتبط تماما مع مين مع بي أو ممكن نعبر عنها بالصيغة
+
+59
+00:05:13,410 --> 00:05:18,750
+هذه a are related with b و أحيانا بيعبروا بحكاية
+
+60
+00:05:18,750 --> 00:05:23,490
+اليساوي و أحيانا بثلاثةاللي هي زي التكافو أو ما
+
+61
+00:05:23,490 --> 00:05:27,050
+إلى ذلك على أي حال لكن الدرج عندنا في كتابنا
+
+62
+00:05:27,050 --> 00:05:31,970
+بيحاول يستخدم him اللي هو الرمز اللي عندنا يبقى
+
+63
+00:05:31,970 --> 00:05:37,730
+هذا الرمز هو عبارة عن رمز يرمز لعلاقة التكافو اللي
+
+64
+00:05:37,730 --> 00:05:43,680
+هي reflexive و symmetric and transitiveطيب العلاقة
+
+65
+00:05:43,680 --> 00:05:48,080
+اللى عندنا هذه لما نجى على الست اللى عندنا هذه
+
+66
+00:05:48,080 --> 00:05:52,640
+ونقول عندنا العلاقة هذه العلاقة هذه بتعملى مجموعة
+
+67
+00:05:52,640 --> 00:05:57,780
+من ال equivalence classes اللي همين فصولي التكافئة
+
+68
+00:05:57,780 --> 00:06:02,660
+ايه قصة فصولي التكافئة هذا تعالي تشوفي دىلو كان ان
+
+69
+00:06:02,660 --> 00:06:06,300
+ال relation هذه عبارة عن equivalent relation على
+
+70
+00:06:06,300 --> 00:06:13,480
+ال 6S وخت أي عنصر موجود في ال 6S وليكن عنصر A
+
+71
+00:06:13,480 --> 00:06:19,940
+فبروح بعرف ال equivalence class لل 6A وكل العناصر
+
+72
+00:06:19,940 --> 00:06:24,340
+اللي موجودة في ال 6S و اللي بتكون مربوطة مع هذا
+
+73
+00:06:24,340 --> 00:06:28,800
+العنصر فقط وماليش دعوة في الباقييعني أنا طبقا
+
+74
+00:06:28,800 --> 00:06:33,080
+لتأثير ال relation أو تحت أثير ال relation هذه في
+
+75
+00:06:33,080 --> 00:06:38,440
+عندي عناصر بتكون مرتبطة مع العناصر هدول بيكونولي
+
+76
+00:06:38,440 --> 00:06:42,040
+مجموعة لمجموعة هذه اللي بيسميها equivalence class
+
+77
+00:06:42,040 --> 00:06:47,970
+فصل التكافئ لهذا الألميبقى لما نشوف element a
+
+78
+00:06:47,970 --> 00:06:53,390
+ومحطوط بين قسينك باربك تفهم هذا معناه equivalency
+
+79
+00:06:53,390 --> 00:06:56,490
+class نتيجة ال equivalency relation اللي موجودة
+
+80
+00:06:56,490 --> 00:07:01,190
+على ال S شو تعريفه؟ كل العناصر اللي موجودة في S و
+
+81
+00:07:01,190 --> 00:07:05,230
+اللي بتكون مرتبطة مع نفس العنصر هذا اللي هو A اللي
+
+82
+00:07:05,230 --> 00:07:08,690
+أخدته طبعا بعد قليل هعطيك مثال كيف بنجيب هذه
+
+83
+00:07:08,690 --> 00:07:13,210
+العناصر؟يبقى هذا ال element بنسميه ال equivalence
+
+84
+00:07:13,210 --> 00:07:18,830
+class تبع ال 6S that contains A يعني ال
+
+85
+00:07:18,830 --> 00:07:23,550
+equivalence class لل element لازم يحتوي على مين؟
+
+86
+00:07:23,550 --> 00:07:28,510
+يحتوي على ال element itself بالاضافة إلى مجموعة من
+
+87
+00:07:28,510 --> 00:07:33,120
+العناصر الأخرىنعطي مثال على ال equivalence
+
+88
+00:07:33,120 --> 00:07:36,140
+relation
+
+89
+00:07:36,140 --> 00:07:40,520
+و بعد ذلك نذهب نجيب ال equivalence class لأي
+
+90
+00:07:40,520 --> 00:07:45,960
+element موجود داخل ال set اللى بدنا ناخدها بقول لو
+
+91
+00:07:45,960 --> 00:07:52,000
+أخدت ال set of integers يبقى ال S هدفين ليه ال Z
+
+92
+00:07:52,000 --> 00:07:56,740
+مجموعة الأعداد الصحية الموجبة والسالمة والصفريعني
+
+93
+00:07:56,740 --> 00:08:02,620
+هذه صارت يا مين هي ال 6z اللى عرفنالكوا في أول
+
+94
+00:08:02,620 --> 00:08:07,860
+محاضرة قولنالكوا ال 6 اللى 6 of integer لت ال n
+
+95
+00:08:07,860 --> 00:08:12,660
+بيه positive integer أخدت ال n أي عدد صحيح موجه ب2
+
+96
+00:08:12,660 --> 00:08:19,800
+3 10 20 قد ما يكون تمامبناخد عنصرين موجودة في الست
+
+97
+00:08:19,800 --> 00:08:23,840
+S يعني ال A و ال B انتجرز يمكن يكونوا اتنين
+
+98
+00:08:23,840 --> 00:08:26,020
+بالموجة يمكن يكونوا اتنين بالسالي يمكن يكونوا واحد
+
+99
+00:08:26,020 --> 00:08:30,220
+موجة و واحد سالي مهمنيش ماليهمش قيود بدنا نروح و
+
+100
+00:08:30,220 --> 00:08:35,970
+نعرف ان ال A مرتبط مع ال B إذا كانالـ A modulo N
+
+101
+00:08:35,970 --> 00:08:41,030
+بيساوي ال B modulo N توجه لك ال relation يابن
+
+102
+00:08:41,030 --> 00:08:45,870
+أعطيها الرمز هذا يابن أعطيها الرمز هذا يابن أعطيها
+
+103
+00:08:45,870 --> 00:08:49,130
+الرمز هذا يابن أعطيها الرمز هذا هو راح أعطاها
+
+104
+00:08:49,130 --> 00:08:53,710
+الرمز اللي عندنا اللي هو رمز اليساوييعني الـ
+
+105
+00:08:53,710 --> 00:08:57,110
+remainder تبع الـ A يبقى يساوي الـ remainder تبع
+
+106
+00:08:57,110 --> 00:09:02,670
+الباقي نتيجة لقسمة الـ A على M نفس الباقي لو قسمنا
+
+107
+00:09:02,670 --> 00:09:08,850
+الـ B على M that is بدي أترجم هذا الكلام بصياغة
+
+108
+00:09:08,850 --> 00:09:15,730
+أخرىبعدين بقول ال A مرتبطة مع بي اف هذا أخدنا صيغة
+
+109
+00:09:15,730 --> 00:09:20,410
+مكافئة إلو و هي N بدأ تقسم الفرق ما بين ال A و
+
+110
+00:09:20,410 --> 00:09:24,070
+اللي بياخدناه المرة الماضية مظبوط إذا الصيغة بدل
+
+111
+00:09:24,070 --> 00:09:27,430
+ما صرت X صارت الصيغة اللي عندنا يعني بقول this
+
+112
+00:09:27,430 --> 00:09:32,140
+relation is an equivalence relation ليش؟يبقى قال
+
+113
+00:09:32,140 --> 00:09:35,880
+لي هذه equivalence relation بدنا نقيم الدليل على
+
+114
+00:09:35,880 --> 00:09:39,060
+إن هذا ال relation اللي عرفناها بهذا الشكل هي
+
+115
+00:09:39,060 --> 00:09:43,440
+عبارة عن equivalence relation بمعنى آخر بدي أروح
+
+116
+00:09:43,440 --> 00:09:47,260
+أحقق الشروط التلاتة أو الخواص التلاتة اللي عندنا
+
+117
+00:09:47,260 --> 00:09:51,160
+إذا تحققت الخواص التلاتة على ال relation هذي بيصير
+
+118
+00:09:51,160 --> 00:09:56,120
+هذه equivalence relation تمام؟ بنقوله كويس بدنا
+
+119
+00:09:56,120 --> 00:10:02,080
+نيجي للخاصية الأولىأنا بدي العنصر يكون مرتبط مع
+
+120
+00:10:02,080 --> 00:10:07,180
+نفسه كيف يعني مرتبط مع نفسه يعني لو طرحتي اتنين من
+
+121
+00:10:07,180 --> 00:10:13,460
+بعض الان بده تقسمين الفرق في ما بينهما يبقى بدي
+
+122
+00:10:13,460 --> 00:10:20,300
+اخد اول حاجة خاصية ال reflex يبقى باجي بقوله بدي
+
+123
+00:10:20,300 --> 00:10:25,760
+اجي اقوله الآن ال ا are related مع ا مرتبط مع ا شو
+
+124
+00:10:25,760 --> 00:10:34,380
+السبب becauseان ال N بتقسم ال A ناقص ال A يعني
+
+125
+00:10:34,380 --> 00:10:40,800
+مكان ال B حطينا مين حطينا بيه يعني ايش sense لإن
+
+126
+00:10:40,800 --> 00:10:46,660
+ال N بتقسم ال zero صحيح ولا لأمش ال N بتقسم ال
+
+127
+00:10:46,660 --> 00:10:50,960
+Zero ال Zero على N جدش يساوي Zero او لأن Zero
+
+128
+00:10:50,960 --> 00:10:56,300
+يساوي N في Zero عملناها برضه المرة اللي فاتت يبقى
+
+129
+00:10:56,300 --> 00:11:00,400
+لأن ال N بتقسم ال Zero يبقى هذا العنصر مرتبط مع
+
+130
+00:11:00,400 --> 00:11:07,960
+نفسه وهذه اللي سمنها reflexive property طيب نيجي
+
+131
+00:11:07,960 --> 00:11:11,620
+للخاصية التانية F
+
+132
+00:11:21,910 --> 00:11:33,070
+لما نقول ان ال N بدأ تقسم ال A minus ال B هذا
+
+133
+00:11:33,070 --> 00:11:40,070
+معناه ان ال A ناقص ال B بده يساوي ال N في ال Q
+
+134
+00:11:44,970 --> 00:11:51,910
+طب ايش رايك لو ضربت الطرفين في اشارة سالب انفك و
+
+135
+00:11:51,910 --> 00:11:56,350
+لو ضربت اتنين في اشارة سالب ايش بديصير؟ بيصير ال B
+
+136
+00:11:56,350 --> 00:12:03,030
+بالموجب و ال A بالسالب يبقى هذا بيصير B سالب ال A
+
+137
+00:12:03,030 --> 00:12:10,640
+هنا بقدر اقول انف ناقص Qماذا يعني هذا الكلام؟
+
+138
+00:12:10,640 --> 00:12:17,940
+معناته ان بتقسم من؟ ال b ناقص ال a هذا معناه ان ال
+
+139
+00:12:17,940 --> 00:12:24,000
+n بتقسم ال b ناقص ال a مدام هيك يبقى هذا معناه ان
+
+140
+00:12:24,000 --> 00:12:30,340
+ال b are related with a وهذا اللي بسميها symmetric
+
+141
+00:12:30,340 --> 00:12:32,880
+property
+
+142
+00:12:35,780 --> 00:12:40,340
+طيب كويس يبقى الأن تحققت الخاصية الثانية بتروح
+
+143
+00:12:40,340 --> 00:12:46,760
+لمين للخاصية التالتة يبقى بالداجة للخاصية التالتة
+
+144
+00:12:46,760 --> 00:12:55,280
+assume أفترض أن ال a are related with b and ال b
+
+145
+00:12:55,280 --> 00:13:02,940
+are related with c و ال a و ال b و ال c موجودات في
+
+146
+00:13:02,940 --> 00:13:12,090
+ال z اللي هو integersthen بقدر اقول ان ال N
+
+147
+00:13:12,090 --> 00:13:22,110
+divides ال A ناقص ال B and ال N divides ال B ناقص
+
+148
+00:13:22,110 --> 00:13:22,650
+ال C
+
+149
+00:13:25,490 --> 00:13:28,110
+مش هيك تعريف ال equivalence relation أو ال
+
+150
+00:13:28,110 --> 00:13:32,310
+relation اللي عندنا يبقى ال N بتقسم ال A ناقص ال B
+
+151
+00:13:32,310 --> 00:13:38,270
+وفي نفس الوقت ال N بتقسم ال B ناقص ال C هذا معناه
+
+152
+00:13:38,270 --> 00:13:53,680
+ان هناك Q1 و Q2 موجودة في Z such that بحيث انالـ A
+
+153
+00:13:53,680 --> 00:14:03,600
+minus ال B يساوي Q واحد في N and ال B ناقص ال C
+
+154
+00:14:03,600 --> 00:14:07,720
+بدر ساوي AQ اتنين في N
+
+155
+00:14:11,650 --> 00:14:18,370
+طيب انا ايش بدي؟ بدي الخاصية التالتة بدي A مرتبطة
+
+156
+00:14:18,370 --> 00:14:23,310
+مع مين؟ مع ال C يبقى بدي ال A تكون مرتبطة مع ال C
+
+157
+00:14:23,310 --> 00:14:28,220
+باجي بقول كويسة بدي اتطلع في هذه و هذهأظن لو جمعنا
+
+158
+00:14:28,220 --> 00:14:34,060
+الاتنين بيبقى من عنده ال A و ال C يبقى هذا يعطيك
+
+159
+00:14:34,060 --> 00:14:41,700
+لو جنا جمعنا هدول بيصير عند ال A ناقص ال C يساوي Q
+
+160
+00:14:41,700 --> 00:14:47,880
+واحد زائد Q اتنين كله مضروم في مين؟ مضروم في اين؟
+
+161
+00:14:48,090 --> 00:14:55,310
+معنى هذا الكلام ان ال N بتقسم ال A نقص ال C هذا
+
+162
+00:14:55,310 --> 00:15:04,300
+معناه ان ال N تقسم ال A نقص ال Cمدام الـ N مقاومة
+
+163
+00:15:04,300 --> 00:15:06,720
+الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ C
+
+164
+00:15:06,720 --> 00:15:08,960
+مقاومة الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ
+
+165
+00:15:08,960 --> 00:15:10,680
+C مقاومة الـ A مقاومة الـ C مقاومة الـ C مقاومة
+
+166
+00:15:10,680 --> 00:15:16,940
+الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ C
+
+167
+00:15:16,940 --> 00:15:20,500
+مقاومة الـ C مقاومة الـ C مقاومة الـ C مقاومة الـ
+
+168
+00:15:20,500 --> 00:15:23,220
+C مقاومة الـ C مقاومة الـ C مقاومة الـ C مقاومة
+
+169
+00:15:23,220 --> 00:15:24,400
+الـ C مقاومة الـ C مقاومة الـ C مقاومة الـ C
+
+170
+00:15:24,400 --> 00:15:29,300
+مقاومة الـ C مقإذا تحققت الشروط التلاتة اللي عندنا
+
+171
+00:15:29,300 --> 00:15:33,400
+يبقى ال relation هذي مالها is an equivalence
+
+172
+00:15:33,400 --> 00:15:39,280
+relation يبقى بقى دي بقوله ده و هكذا ان ال
+
+173
+00:15:39,280 --> 00:15:46,960
+relation اللي عندنا هذي is an equivalence relation
+
+174
+00:15:53,890 --> 00:15:58,170
+طب كويس يبقى يعطينا مثال على ال equivalence
+
+175
+00:15:58,170 --> 00:16:03,390
+relation بدنا نيجي نحسب ال equivalence class لأي
+
+176
+00:16:03,390 --> 00:16:09,610
+element موجود عندنا يعني بدي أروح أخد عنصر من Z و
+
+177
+00:16:09,610 --> 00:16:14,770
+أجيب كل العناصر اللي مرتبطة مع هذا العنصر طبق ال
+
+178
+00:16:14,770 --> 00:16:19,930
+main طبق ال definition اللي احنا معطينه طيب الآن
+
+179
+00:16:19,930 --> 00:16:22,750
+بدي أجي أطبق هذا التعريف
+
+180
+00:16:37,630 --> 00:16:41,530
+خلّيني أقول لكم هنا إحنا عندنا ال equivalence
+
+181
+00:16:41,530 --> 00:16:46,490
+class A كل العناصر X اللي موجودة في S يعني موجودة
+
+182
+00:16:46,490 --> 00:16:55,310
+في Z بحيث أن ال X are related with A طيب
+
+183
+00:16:55,310 --> 00:17:00,140
+احنا أخدنا هنا لما جينا أعرفنا ديقلنا إن الـ A
+
+184
+00:17:00,140 --> 00:17:06,840
+مرتبطة مع B إذا كانت الـ N تقسم الـ A نقص الـ B
+
+185
+00:17:06,840 --> 00:17:13,140
+يبقى الـ N بدي أخده كم قياس Modulo N بدي أخد
+
+186
+00:17:13,140 --> 00:17:18,740
+الأرقام هذه كلها Modulo M بس إن هذا رقم شايع بياخد
+
+187
+00:17:18,740 --> 00:17:23,880
+مالة نهاية من القيام أنا بقدر أحسب لرقم محدد اختار
+
+188
+00:17:23,880 --> 00:17:30,430
+لك رقم يجي في بالكقداش؟ خمسة ممتاز جدا يبقى صاحبنا
+
+189
+00:17:30,430 --> 00:17:38,570
+أخد الرقم خمسة بقوله آه يبقى الخمسة هذا طبقا لهذا
+
+190
+00:17:38,570 --> 00:17:43,950
+التعريف هو كل العناصر X اللي موجودة في S such ذات
+
+191
+00:17:43,950 --> 00:17:50,830
+ال X مرتبط مع مين؟ مع الخمسةطب كويس يعني هذا كل
+
+192
+00:17:50,830 --> 00:17:57,370
+العناصر X اللي موجودة في Z such that ال X بده
+
+193
+00:17:57,370 --> 00:18:02,930
+يساوي انت حتى المقياس خمسة والله المقياس كدهش؟
+
+194
+00:18:02,930 --> 00:18:06,690
+خمسة برضه؟ لأ إذا بناخد المقياس خمسة بده ناخد رقم
+
+195
+00:18:06,690 --> 00:18:10,690
+تاني مثلا بدي أخد تسعة
+
+196
+00:18:19,870 --> 00:18:31,330
+يبقى تسعة كل العناصر X بحيث X مرتبطة مع 9 يبقى كل
+
+197
+00:18:31,330 --> 00:18:41,550
+ال X الموجودة في Z بحيث X ساوي 9 زائدالرقم مضروب
+
+198
+00:18:41,550 --> 00:18:47,270
+في خمسة قد ما يكون يكون تمام يبقى بالداجي اقول Q
+
+199
+00:18:47,270 --> 00:18:55,080
+مضروب في خمسةيبقى هذا بجيبلي كل العناصر من أول ال
+
+200
+00:18:55,080 --> 00:18:59,660
+Z إلى آخرها اللي مرتبطة مع مين؟ مع التسعة طب انا
+
+201
+00:18:59,660 --> 00:19:05,120
+بدي شغل عملي الشغل العملي كالتالي باجي بقول هي
+
+202
+00:19:05,120 --> 00:19:09,060
+الست اللي عندنا و باجي بحط الرقم اللي عندنا اللي
+
+203
+00:19:09,060 --> 00:19:14,060
+هو تسعة في المصر و بصير اضيفله خمسات و اطرح منه
+
+204
+00:19:14,060 --> 00:19:22,370
+خمسات لإنه قلت تسعة زي ما هي زائد ل Q في خمسةليه Q
+
+205
+00:19:22,370 --> 00:19:29,130
+موجودة في Z يعني Q انتجر باجي بقوله لو التسعة
+
+206
+00:19:29,130 --> 00:19:37,420
+حاطتله خمسة قداش بصير اربعتاش وكمان خمسةوكمان خمسة
+
+207
+00:19:37,420 --> 00:19:42,600
+بيصير تسعة عشر وكمان خمسة بيصير أربعة وعشرين وكمان
+
+208
+00:19:42,600 --> 00:19:47,140
+خمسة بيصير تسعة وعشرين إلى ما شاء الله زي ما ضفت
+
+209
+00:19:47,140 --> 00:19:52,300
+خمسات بتطرح خمسات لو طرحت خمسة بيظل هنا جداش أربعة
+
+210
+00:19:52,300 --> 00:19:58,220
+بيظل سالب واحد بيظل سالب ستة بيظل سالب يحداش وهكذا
+
+211
+00:19:58,780 --> 00:20:04,160
+يبقى هي عناصر ال equivalency class كل العناصر هذول
+
+212
+00:20:04,160 --> 00:20:09,740
+أخدوا جزء من الست و الونتجر بس مش كلها أخدوا جزء
+
+213
+00:20:09,740 --> 00:20:13,880
+منها هذا الجزء أو هذه المجموعة هي اللي بنسميها ال
+
+214
+00:20:13,880 --> 00:20:18,540
+equivalency class يبقى ال equivalency class تبع
+
+215
+00:20:18,540 --> 00:20:24,340
+التسعة يحتوي على مجموعة من العناصر بس مش كل عناصر
+
+216
+00:20:24,340 --> 00:20:30,690
+z شوية منهمطيب إيش رايك ال equivalence relation
+
+217
+00:20:30,690 --> 00:20:36,730
+بتعملي partition للست اللي عندها أو للزد اللي
+
+218
+00:20:36,730 --> 00:20:41,310
+عندنا، إيش يعني partitionلو رجعنا لمبادئ رياضات
+
+219
+00:20:41,310 --> 00:20:46,390
+بقول لو عندي set و عليها partition partition يعني
+
+220
+00:20:46,390 --> 00:20:53,390
+مجموعة من ال subset اللي بتحقق شرطين الشرط الأول
+
+221
+00:20:53,390 --> 00:20:58,810
+لو أخدت ال union على كل ال subsets هذي بيطلع main
+
+222
+00:20:58,810 --> 00:21:04,510
+set الأصل يتنام لو عملت intersection على كل ال
+
+223
+00:21:04,510 --> 00:21:10,590
+subsets هذي بيطلع mainخلّيني اذكر بتعريف ال
+
+224
+00:21:10,590 --> 00:21:16,370
+partition و بعد هيك نحسبه للبعض يبقى بدنا نيجي
+
+225
+00:21:16,370 --> 00:21:21,450
+لحاجة اسمها اللي هو ال partition
+
+226
+00:21:46,380 --> 00:21:57,340
+هيبقى definition a
+
+227
+00:21:57,340 --> 00:22:05,040
+partition of
+
+228
+00:22:05,040 --> 00:22:11,500
+a set S is a collection
+
+229
+00:22:17,390 --> 00:22:25,970
+collection of non-empty
+
+230
+00:22:25,970 --> 00:22:29,050
+disjoint
+
+231
+00:22:29,050 --> 00:22:36,270
+subsets
+
+232
+00:22:36,270 --> 00:22:43,990
+of
+
+233
+00:22:43,990 --> 00:22:54,040
+Swhose union is
+
+234
+00:22:54,040 --> 00:23:00,620
+S itself طب
+
+235
+00:23:00,620 --> 00:23:07,220
+كويس تعالى نوضح هذا المفهوم افترض ان انا عندى ال 6
+
+236
+00:23:07,220 --> 00:23:13,940
+وال6 بالشكل هذا هذا ال 6S قسمتها الى مجموعة من ال
+
+237
+00:23:13,940 --> 00:23:19,920
+subsets وهذه واحدة وهذه واحدة وهذه واحدة وهذه
+
+238
+00:23:19,920 --> 00:23:30,220
+واحدة.و هكذا تمام سميتها S1 S2 S3 وظلت ماشي
+
+239
+00:23:30,220 --> 00:23:38,100
+للاخيرة اللي هي ال S N تمام يبقى ال partition
+
+240
+00:23:38,100 --> 00:23:45,660
+هديله الرمز بيه هو عبارة عن مجموعة S S1 و S2 و
+
+241
+00:23:45,660 --> 00:23:55,070
+لغاية S N بس بشرططالعش بيقول الـ Partition of non
+
+242
+00:23:55,070 --> 00:24:02,710
+-empty disjoint subsets يبقى كل واحدة فيها مجموعة
+
+243
+00:24:02,710 --> 00:24:06,910
+من العناصر يبقى هنا في عندي عناصر و هنا في عندي
+
+244
+00:24:06,910 --> 00:24:11,470
+عناصر و هنا في عناصر و هنا في عناصر و هكذا يبقى كل
+
+245
+00:24:11,470 --> 00:24:15,970
+مجموعة لازم يكون على الأقل فيها ولوعنصر واحد تمام
+
+246
+00:24:15,970 --> 00:24:21,350
+هذا المقصود non-empty this joint مافيش تقاطع فيما
+
+247
+00:24:21,350 --> 00:24:26,470
+بينهما تمام يبقى الشرط الأول مشان يكون هذا
+
+248
+00:24:26,470 --> 00:24:32,150
+partition الشرط الأولاني بدي يكون ال intersection
+
+249
+00:24:32,150 --> 00:24:39,650
+على ال S I و I تساوي واحد لغاية ال N بدي يساوي
+
+250
+00:24:39,650 --> 00:24:44,920
+قداشفاي ولا two subsets بتقاطعوا مع بعض مافيش
+
+251
+00:24:44,920 --> 00:24:51,720
+تنتين بتقاطعوا مع بعض على الإطلاق الشرط الثاني بدي
+
+252
+00:24:51,720 --> 00:24:57,860
+يكون ال union من I تساوي واحد لغاية ال N لل S I
+
+253
+00:24:57,860 --> 00:25:03,320
+بدي يساوي ال S itself ان حدث ذلك يبقى بقول هذا
+
+254
+00:25:03,320 --> 00:25:11,890
+بسمي partition على مين على Sيبقى ال partition على
+
+255
+00:25:11,890 --> 00:25:16,810
+set معينة هو تجزيه ال set هذه إلى مجموعة من ال
+
+256
+00:25:16,810 --> 00:25:21,210
+subsets بحيث ال subsets هدول بدوني محقولي شرطين
+
+257
+00:25:21,210 --> 00:25:25,670
+مافيش تداخل بين اي subset و التانية يعني ال
+
+258
+00:25:25,670 --> 00:25:30,410
+intersection بين اي subset و التانية بده يسوى قداش
+
+259
+00:25:30,410 --> 00:25:36,310
+fiveإذا خدت ال union عليهم كلهم بدي يعطينا نفس ال
+
+260
+00:25:36,310 --> 00:25:41,590
+6S لا بيزيد عليها ولا بينقص عنها مافي إمكانية إن
+
+261
+00:25:41,590 --> 00:25:47,790
+حدث ذلك يبقى هذا بسمي partition لمين لل 6S اللي
+
+262
+00:25:47,790 --> 00:25:57,230
+عندنا طيب خلينا .. خلينا نيجي الآن نعطي شغل عملية
+
+263
+00:25:57,230 --> 00:26:02,400
+على حكاية ال partition بس قبل هيكبدنا نعطي النقطة
+
+264
+00:26:02,400 --> 00:26:07,820
+الأخيرة قبل ما ناخد المثال العملي على ذلك في نظرية
+
+265
+00:26:07,820 --> 00:26:15,740
+بتقول لما يأتي theorem the
+
+266
+00:26:15,740 --> 00:26:18,700
+equivalence classes of an equivalence relation
+
+267
+00:26:18,700 --> 00:26:22,420
+equivalence
+
+268
+00:26:22,420 --> 00:26:30,000
+classes of an
+
+269
+00:26:37,750 --> 00:26:44,250
+equivalence classes of an equivalence relation on
+
+270
+00:26:44,250 --> 00:26:48,010
+a
+
+271
+00:26:48,010 --> 00:26:54,850
+set S على المجموعة S constitute a partition
+
+272
+00:27:21,730 --> 00:27:24,690
+العملية العكسية conversely
+
+273
+00:27:29,740 --> 00:27:39,920
+conversely for any partition
+
+274
+00:27:39,920 --> 00:27:46,160
+P
+
+275
+00:27:46,160 --> 00:27:49,880
+of
+
+276
+00:27:49,880 --> 00:27:54,460
+S there is
+
+277
+00:28:00,280 --> 00:28:15,400
+an equivalence relation there is
+
+278
+00:28:15,400 --> 00:28:24,760
+an equivalence relation on S على S whose
+
+279
+00:28:24,760 --> 00:28:26,300
+equivalence classes
+
+280
+00:28:32,590 --> 00:28:43,150
+equivalent classes فصول التكافئة تبعتها are the
+
+281
+00:28:43,150 --> 00:28:49,050
+elements of P
+
+282
+00:29:05,430 --> 00:29:10,810
+يبقى مرة تانية بنرجع الكلام اللى قلناه بنقول ال
+
+283
+00:29:10,810 --> 00:29:16,170
+partition على الست S هو collection of non-empty
+
+284
+00:29:16,170 --> 00:29:20,570
+disjoint subset لمين لل S اللي ال union تبعهم بدي
+
+285
+00:29:20,570 --> 00:29:25,030
+سوى مين S بالبلد هيك ال intersection على كل ال
+
+286
+00:29:25,030 --> 00:29:28,750
+subsets بدي سوى Phi و ال union بدي سوى ال S itself
+
+287
+00:29:29,700 --> 00:29:33,940
+النظرية بتقول لو كان ال equivalence classes اللي
+
+288
+00:29:33,940 --> 00:29:38,700
+نشأوا عن equivalence relation على ال 6S هدول
+
+289
+00:29:38,700 --> 00:29:44,420
+بيكونولي partition لمن؟ لل S يبقى مجموعة ال
+
+290
+00:29:44,420 --> 00:29:48,360
+equivalence classes اللي نتجوا عن ال equivalence
+
+291
+00:29:48,360 --> 00:29:52,540
+relation بيكونولي partition على ال 6S العملية
+
+292
+00:29:52,540 --> 00:29:57,950
+العكسية قال لي converselyلأي partition P على ست S
+
+293
+00:29:57,950 --> 00:30:03,210
+هما
+
+294
+00:30:03,210 --> 00:30:07,230
+عناصر الـ equivalence classes يبقى ال equivalence
+
+295
+00:30:07,230 --> 00:30:12,830
+class بتعمل partition على ست وعكسه صحيةلو كان عندى
+
+296
+00:30:12,830 --> 00:30:16,730
+partition على الست يبقى هذا ال partition بينشئ
+
+297
+00:30:16,730 --> 00:30:22,390
+equivalence classes كل equivalence class هو عضو من
+
+298
+00:30:22,390 --> 00:30:26,570
+أعضاء من ال partition أو هو عنصر من عناصر ال
+
+299
+00:30:26,570 --> 00:30:31,110
+partition على الست اللى عندناالان الي خاطر اوضح
+
+300
+00:30:31,110 --> 00:30:35,770
+هذا الكلام عمليا عمليا من وين انا اخد ال relation
+
+301
+00:30:35,770 --> 00:30:40,410
+اللى عندنا احنا اخدنا اللى هو قولنا العمصر تسعة
+
+302
+00:30:40,410 --> 00:30:45,490
+واخدنا المقياس مين اللى هو خمسة طب انا لما اخد
+
+303
+00:30:45,490 --> 00:30:50,800
+المقياس خمسةلما نأخد المقياس خمسة يبقى العناصر
+
+304
+00:30:50,800 --> 00:30:56,820
+Zero واحد واتنين وتلاتة واربعة خمسة بترجع مين؟
+
+305
+00:30:56,820 --> 00:31:01,960
+Zero ستة بترجع واحد سبعة بترجع اتنين تمانية بترجع
+
+306
+00:31:01,960 --> 00:31:07,520
+تلاتة تسعة بترجع اربعة وهكذا نوضح هذا الكلام يبقى
+
+307
+00:31:07,520 --> 00:31:20,450
+for example كمثال على ذلك from theabove example
+
+308
+00:31:20,450 --> 00:31:26,130
+where ال
+
+309
+00:31:26,130 --> 00:31:38,670
+S بدها تساوي Z وال N او and ال N بدها تساوي خمسة
+
+310
+00:31:38,670 --> 00:31:43,930
+يبقى بجي بقوله هنا the equivalence
+
+311
+00:31:45,620 --> 00:31:55,780
+A classes are اللي هو الـ Zero والواحد والاتنين
+
+312
+00:31:55,780 --> 00:32:05,240
+والتلاتة والاربعة فقط لغيرهم
+
+313
+00:32:05,240 --> 00:32:12,500
+where حيثهم بدنا نعرف مين هو الـ Zero ال
+
+314
+00:32:12,500 --> 00:32:17,840
+equivalence class تبع الـ Zeroبجي بقول هي ال zero
+
+315
+00:32:17,840 --> 00:32:25,460
+حط ال zero ضيفله خمسات يبقاش بصير خمسة عشرة خمستاش
+
+316
+00:32:25,460 --> 00:32:32,700
+و تضلك ماشي سالب خمسة سالب عشرة سالب خمستاش و تضلك
+
+317
+00:32:32,700 --> 00:32:37,910
+ماشيبعد ذلك يبدأ ال equivalence class للواحد يبقى
+
+318
+00:32:37,910 --> 00:32:43,290
+بالدرجة اقول له هذه واحد وخمسة ستة وخمسة احداشر
+
+319
+00:32:43,290 --> 00:32:46,670
+وخمسة ستة عشر وتبقى مازال مازال مازال مازال مازال
+
+320
+00:32:46,670 --> 00:32:47,490
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+321
+00:32:47,490 --> 00:32:48,110
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+322
+00:32:48,110 --> 00:32:48,970
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+323
+00:32:48,970 --> 00:32:50,350
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+324
+00:32:50,350 --> 00:32:50,970
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+325
+00:32:50,970 --> 00:32:55,850
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+326
+00:32:55,850 --> 00:33:04,460
+مازال مازتمام؟ طيب لو بد ال equivalence class للي
+
+327
+00:33:04,460 --> 00:33:12,000
+اتنين هو عبارة عن اتنين و خمسة سبعة اتناش سبعتاش
+
+328
+00:33:12,000 --> 00:33:17,700
+إلى ما شاء الله اضيف سالب خمسة بصير سالب تلاتة
+
+329
+00:33:17,700 --> 00:33:23,880
+سالب تمانية سالب تلتاش إلى ما شاء الله بد ال
+
+330
+00:33:23,880 --> 00:33:29,260
+equivalence class لمن؟ لتلاتةيبقى باجي بقول له هذه
+
+331
+00:33:29,260 --> 00:33:36,380
+التلاتة وخمسة تمانية تلتاش تمانتاش إلى ما شاء الله
+
+332
+00:33:36,380 --> 00:33:42,020
+و هنا نضيف سالب خمسة بصير السالب اتنين و هنا سالب
+
+333
+00:33:42,020 --> 00:33:47,700
+سبعة و هنا سالب اتناش إلى ما شاء الله بنوصل للعنصر
+
+334
+00:33:47,700 --> 00:33:52,510
+اللي هو مين؟ أربعيبقى العمصر أربعة، يبقى هذه
+
+335
+00:33:52,510 --> 00:33:59,150
+الأربعة وخمسة، تسعة، أربعتاشر، تسعتاشر إلى ما شاء
+
+336
+00:33:59,150 --> 00:34:06,210
+الله نرجع نضيف سالب خمسة وكمان سالب خمسة وكمان
+
+337
+00:34:06,210 --> 00:34:12,860
+سالب خمسة وهكذاطيب هذه العناصر اللي حطيتها من قبل
+
+338
+00:34:12,860 --> 00:34:17,680
+طيب بده اجي لخمسة يبقى بده احط خمسة يبقى بده احط
+
+339
+00:34:17,680 --> 00:34:26,380
+خمسة وخمسة وخمسة هي هذهو سالب خمسة زيرو و سالب
+
+340
+00:34:26,380 --> 00:34:30,260
+خمسة و سالب عشرة هى هذى ولا لا طيب لو جيت بعد
+
+341
+00:34:30,260 --> 00:34:36,260
+الخمسة بتاخدى الستة يبقى بتبدأ بستة و خمسة احداشر
+
+342
+00:34:36,260 --> 00:34:41,260
+هى ستة و خمسة احداشر وكمان خمسة بيطلع هذى يبقى
+
+343
+00:34:41,260 --> 00:34:46,000
+الستة هتطلع الواحد و السبعة هتطلع اتنين و التمانية
+
+344
+00:34:46,000 --> 00:34:50,660
+هتطلع التلاتة و التسعة تطلع الأربعة و العشرة ترجع
+
+345
+00:34:50,660 --> 00:34:57,410
+لزيرو و هكذاطيب يبقى هدول equivalency classes يبقى
+
+346
+00:34:57,410 --> 00:35:03,650
+هدول all equivalency
+
+347
+00:35:03,650 --> 00:35:09,270
+classes لو
+
+348
+00:35:09,270 --> 00:35:13,810
+جبتلي أي equivalency class أخر لأن الـ z فيها
+
+349
+00:35:13,810 --> 00:35:18,570
+ملنية من العناصر أي واحد فيهم هيطلع واحد من هدول
+
+350
+00:35:19,130 --> 00:35:24,790
+يبقى ماعنديش إلا مين إلا الخمسة هدول فقط لغية في
+
+351
+00:35:24,790 --> 00:35:31,190
+علم الجبره خلّي بالك في علم الجبره هذه الست مجموعة
+
+352
+00:35:31,190 --> 00:35:40,050
+العناصر هنقول عليها Z خمسة Z خمسة اللي هي عناصرها
+
+353
+00:35:40,050 --> 00:35:48,440
+Zero وواحد واتنين وتلاتة واربعة دائما وابنانطيب زد
+
+354
+00:35:48,440 --> 00:35:57,740
+خمسة ايش تمثلي بالنسبة لزد الأصلية ال partition
+
+355
+00:35:57,740 --> 00:36:05,220
+ممتاز جدا هلحين اي رقم يجي في بالك من الزد هتلاقيه
+
+356
+00:36:05,220 --> 00:36:08,880
+موجود في واحد من الخمسة هدول اي رقم يطلع على بالك
+
+357
+00:36:09,110 --> 00:36:14,950
+لازم تجد موجود في واحد من هدول هذه واحدة اثنين لن
+
+358
+00:36:14,950 --> 00:36:19,230
+تجد اي عنصر في اي equivalency class موجود في
+
+359
+00:36:19,230 --> 00:36:24,910
+التاني مافيش بالمرة طب لو عملت union عليهم كلهم
+
+360
+00:36:24,910 --> 00:36:30,400
+بيعطيني الذد الأصلي طلعهي عندك هنا كده ال zero هي
+
+361
+00:36:30,400 --> 00:36:35,080
+واحد اتنين تلاتة اربعة و هيجي خمسة ستة سبعة تمانية
+
+362
+00:36:35,080 --> 00:36:40,000
+بعدين بترجع مين وين التسعة في عنها هي التسعة و
+
+363
+00:36:40,000 --> 00:36:42,440
+عندك هنا هي العشرة و هي الاحداشر و هي اتناشر
+
+364
+00:36:42,440 --> 00:36:46,860
+تلاتاشر اربعتاشر خمساشر و السالب زيه يبقى هتلاقي
+
+365
+00:36:46,860 --> 00:36:52,720
+كل الأرقام هده لو أخدتلهم ال union بيعطيني مينالزد
+
+366
+00:36:52,720 --> 00:36:58,700
+الأصلي يتنين لا يوجد أي عنصر مشترك بين أي set و
+
+367
+00:36:58,700 --> 00:37:04,440
+أخرى من هذه ال sets يعني لا يوجد أي عنصر مشترك ما
+
+368
+00:37:04,440 --> 00:37:07,760
+بين ال equivalence classes طلع لما روحنا عرفنا ال
+
+369
+00:37:07,760 --> 00:37:12,320
+equivalence class هناهو ال equivalence class يقول
+
+370
+00:37:12,320 --> 00:37:17,200
+كل العناصر اللي بتبقى بس مرتبطة مع ايه تحت ال
+
+371
+00:37:17,200 --> 00:37:21,080
+relation اللي هي modulo خمسة يبقى انا جيبت بس
+
+372
+00:37:21,080 --> 00:37:24,100
+العنصر مرتبطة مع مين مع العنصر اللي بقى يعني انا
+
+373
+00:37:24,100 --> 00:37:29,570
+لما اقول zeroبدّى العناصر المرتبطة مع الـ zero تحت
+
+374
+00:37:29,570 --> 00:37:33,130
+أثير ال relation الهيموديولو خمسة غير هيك ماليش
+
+375
+00:37:33,130 --> 00:37:37,270
+علاقة فيه الواحد بدي أجيب كل العناصر المرتبطة مع
+
+376
+00:37:37,270 --> 00:37:41,610
+الواحد تحت أثير ال relation الهيموديولو خمسة وهكذا
+
+377
+00:37:41,610 --> 00:37:46,230
+بالنسبة للباقية إذا ال union عليهم كلهم بدي يعطيني
+
+378
+00:37:46,230 --> 00:37:52,570
+ال z بالكامل اتنينلا يوجد أي عنصر مشترك بين أي
+
+379
+00:37:52,570 --> 00:37:56,790
+equivalency class والثاني على الإطلاق مافيش بالمرة
+
+380
+00:37:56,790 --> 00:38:01,770
+يبقى فاهمني أيش معنى ال partition يبقى بناء عليه
+
+381
+00:38:01,770 --> 00:38:07,330
+هدول بيكونولي partition على من؟ على ال z يبقى باجي
+
+382
+00:38:07,330 --> 00:38:11,290
+بقول so the partition
+
+383
+00:38:13,850 --> 00:38:22,750
+of z is the six هي الست اللي حديلها الرمز capital
+
+384
+00:38:22,750 --> 00:38:28,890
+P و اللي هما ال class بتبع ال zero و ال class بتبع
+
+385
+00:38:28,890 --> 00:38:33,310
+ال واحد و ال class بتبع ال اتنين و ال class بتبع
+
+386
+00:38:33,310 --> 00:38:38,590
+التلاتة و ال class بتبع الاربعة غير هيك ماعنديش
+
+387
+00:38:38,590 --> 00:38:41,150
+طيب
+
+388
+00:38:41,900 --> 00:38:46,620
+لو روحت غيرت الموديولو الخامسة خليتها الموديولو
+
+389
+00:38:46,620 --> 00:38:53,260
+سبعة مثلا أكم عنصر هيطلع عندى؟ سبع عناصر أولى واحد
+
+390
+00:38:53,260 --> 00:38:56,990
+في اشتراك بينه وبين التانى واليولن انتبعهمالـ
+
+391
+00:38:56,990 --> 00:39:02,930
+union تبعهم بيساوي z itself و هكذا وهذا هيعطينا
+
+392
+00:39:02,930 --> 00:39:06,850
+group هسميها مستقبل ان شاء الله في الشبتر الجاي
+
+393
+00:39:06,850 --> 00:39:12,730
+هسميها z سبعة زي ما روحت سميتها لك هنا z خمسة يبقى
+
+394
+00:39:12,730 --> 00:39:15,530
+z خمسة على أسرها ال zero والواحد انا اختصارا
+
+395
+00:39:15,530 --> 00:39:18,630
+مكتوبهم زي هيك اما هي الاصل ال equivalence class
+
+396
+00:39:18,630 --> 00:39:20,850
+تبع ال zero ال equivalence class تبع ال واحد
+
+397
+00:39:20,850 --> 00:39:23,820
+والاثنين والتلاتة و هكذاهذه الجروب ان شاء الله
+
+398
+00:39:23,820 --> 00:39:27,820
+هتلعب دور كبير عندنا في ال chapter القادم ان شاء
+
+399
+00:39:27,820 --> 00:39:31,640
+الله و تعالى طبعا الان وصلنا لموضوع ال functions
+
+400
+00:39:31,640 --> 00:39:36,540
+في المحاضرة القادمة يوم السبت بناخد الموضوع ال
+
+401
+00:39:36,540 --> 00:39:37,000
+functions
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..3ca156639afceafebcb605f33ce5bdd3fbf01b59
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4743, "start": 21.55, "end": 47.43, "text": "بسم الله الرحمن الرحيم ننتقل الآن إلى ال chapter الثامن ال chapter الثامن بتحدث عن ال external direct products external طبعا خارجي direct product ضرب product ضرب direct مباشر يبقى الضرب المباشر الخارجي لمجموعة من ال groups سواء كانوا تين تين تلاتة أربعة جد ما يكونوا", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 29399, 4587, 1211, 6024, 48506, 30731, 2423, 7187, 6024, 104, 10943, 1863, 2423, 7187, 6024, 104, 10943, 1863, 39894, 24401, 12984, 18871, 2423, 8320, 2047, 3383, 8320, 23032, 3555, 3615, 995, 16490, 9640, 7435, 1829, 2047, 1674, 48812, 25513, 1674, 48812, 25513, 2047, 3714, 3555, 33599, 2288, 7251, 3555, 4587, 7578, 6024, 114, 25513, 9673, 3555, 33599, 2288, 33962, 9640, 7435, 1829, 32767, 7435, 2304, 2407, 27884, 9154, 2423, 3935, 8608, 2407, 16606, 25961, 14407, 6055, 9957, 6055, 9957, 6055, 1211, 9307, 3660, 5551, 25513, 27884, 10874, 3215, 19446, 7251, 30544, 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0.9231770833333334}, {"start": 119.9, "end": 120.28, "word": " M", "probability": 0.89892578125}], "temperature": 1.0}, {"id": 5, "seek": 14990, "start": 120.82, "end": 149.9, "text": "Where جي موجودة في جي اي يعني جي واحد موجودة في جي واحد جي اتنين موجودة في جي اتنين لغاية جي ان موجودة وين في جي ام إذا من الآن فصاعدا ال external product لمجموعة من ال groups هي عبارة عن ست جديدة هذه الست بعد قليل سنة شهيرة انها group كل عنصر من عناصر هذه ال group يتكون من inner tuple من ال elements", "tokens": [14436, 10874, 1829, 3714, 29245, 23328, 3660, 8978, 10874, 1829, 1975, 1829, 37495, 22653, 10874, 1829, 36764, 24401, 3714, 29245, 23328, 3660, 8978, 10874, 1829, 36764, 24401, 10874, 1829, 1975, 2655, 1863, 9957, 3714, 29245, 23328, 3660, 8978, 10874, 1829, 1975, 2655, 1863, 9957, 5296, 17082, 995, 10632, 10874, 1829, 16472, 3714, 29245, 23328, 3660, 4032, 9957, 8978, 10874, 1829, 1975, 2304, 11933, 15730, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995, 2423, 8320, 1674, 32767, 7435, 2304, 2407, 27884, 9154, 2423, 3935, 39896, 6225, 3555, 9640, 3660, 18871, 8608, 2655, 10874, 16254, 41891, 29538, 21136, 2655, 39182, 12174, 20292, 1211, 8608, 1863, 3660, 13412, 3224, 48923, 16472, 11296, 1594, 28242, 18871, 9381, 2288, 9154, 18871, 33546, 2288, 29538, 2423, 1594, 7251, 2655, 30544, 9154, 7714, 260, 2604, 781, 9154, 2423, 4959], "avg_logprob": -0.2112312012148979, "compression_ratio": 1.967479674796748, "no_speech_prob": 0.0, "words": [{"start": 120.82, "end": 121.4, "word": "Where", "probability": 0.108642578125}, {"start": 121.4, "end": 121.92, "word": " جي", "probability": 0.54229736328125}, {"start": 121.92, "end": 122.78, "word": " موجودة", "probability": 0.81707763671875}, {"start": 122.78, "end": 122.88, "word": " في", "probability": 0.9501953125}, {"start": 122.88, "end": 123.2, "word": " جي", "probability": 0.94921875}, {"start": 123.2, "end": 123.46, "word": " اي", "probability": 0.611083984375}, {"start": 123.46, "end": 123.78, "word": " يعني", "probability": 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"probability": 0.8232421875}, {"start": 132.88, "end": 133.5, "word": " external", "probability": 0.2239990234375}, {"start": 133.5, "end": 134.44, "word": " product", "probability": 0.93408203125}, {"start": 134.44, "end": 135.56, "word": " لمجموعة", "probability": 0.898046875}, {"start": 135.56, "end": 135.84, "word": " من", "probability": 0.91064453125}, {"start": 135.84, "end": 136.0, "word": " ال", "probability": 0.87890625}, {"start": 136.0, "end": 136.4, "word": " groups", "probability": 0.70458984375}, {"start": 136.4, "end": 136.72, "word": " هي", "probability": 0.71142578125}, {"start": 136.72, "end": 137.1, "word": " عبارة", "probability": 0.99365234375}, {"start": 137.1, "end": 137.42, "word": " عن", "probability": 0.99365234375}, {"start": 137.42, "end": 137.94, "word": " ست", "probability": 0.90478515625}, {"start": 137.94, "end": 138.76, "word": " جديدة", "probability": 0.85400390625}, {"start": 138.76, "end": 139.4, "word": " هذه", "probability": 0.60595703125}, {"start": 139.4, "end": 139.76, "word": " الست", "probability": 0.831787109375}, {"start": 139.76, "end": 140.04, "word": " بعد", "probability": 0.82275390625}, {"start": 140.04, "end": 140.42, "word": " قليل", "probability": 0.9881184895833334}, {"start": 140.42, "end": 140.7, "word": " سنة", "probability": 0.84814453125}, {"start": 140.7, "end": 140.94, "word": " شهيرة", "probability": 0.5924479166666666}, {"start": 140.94, "end": 141.4, "word": " انها", "probability": 0.68408203125}, {"start": 141.4, "end": 141.82, "word": " group", "probability": 0.89892578125}, {"start": 141.82, "end": 142.8, "word": " كل", "probability": 0.95849609375}, {"start": 142.8, "end": 143.4, "word": " عنصر", "probability": 0.99072265625}, {"start": 143.4, "end": 143.6, "word": " من", "probability": 0.994140625}, {"start": 143.6, "end": 144.26, "word": " عناصر", "probability": 0.9934895833333334}, {"start": 144.26, "end": 144.58, "word": " هذه", "probability": 0.98046875}, {"start": 144.58, "end": 144.78, "word": " ال", "probability": 0.87646484375}, {"start": 144.78, "end": 145.08, "word": " group", "probability": 0.783203125}, {"start": 145.08, "end": 146.02, "word": " يتكون", "probability": 0.8518880208333334}, {"start": 146.02, "end": 146.5, "word": " من", "probability": 0.990234375}, {"start": 146.5, "end": 147.14, "word": " inner", "probability": 0.29736328125}, {"start": 147.14, "end": 147.66, "word": " tuple", "probability": 0.883056640625}, {"start": 147.66, "end": 148.56, "word": " من", "probability": 0.9912109375}, {"start": 148.56, "end": 149.3, "word": " ال", "probability": 0.966796875}, {"start": 149.3, "end": 149.9, "word": " elements", "probability": 0.900390625}], "temperature": 1.0}, {"id": 6, "seek": 17179, "start": 150.39, "end": 171.79, "text": "يبقى كل element في ال group على شكل N-tuple يعني جوز مكوّن من مجموعة من المراكبات ال remark بتقول ال external product كله ان هذا is a group under the following operation يبقى بدنا نعرف binary operation على هذه ال set", "tokens": [1829, 3555, 4587, 7578, 28242, 4478, 8978, 2423, 1594, 15844, 13412, 28820, 426, 12, 9179, 781, 37495, 22653, 10874, 2407, 11622, 3714, 4117, 2407, 11703, 1863, 9154, 3714, 7435, 2304, 2407, 27884, 9154, 9673, 23557, 4117, 3555, 9307, 2423, 7942, 39894, 39648, 2423, 8320, 1674, 28242, 3224, 16472, 23758, 307, 257, 1594, 833, 264, 3480, 6916, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 3615, 28480, 17434, 6916, 15844, 29538, 2423, 992], "avg_logprob": -0.3548177178535197, "compression_ratio": 1.4285714285714286, "no_speech_prob": 0.0, "words": [{"start": 150.39, "end": 151.05, "word": "يبقى", "probability": 0.759429931640625}, {"start": 151.05, "end": 151.45, "word": " كل", "probability": 0.88671875}, {"start": 151.45, "end": 151.95, "word": " element", "probability": 0.5302734375}, {"start": 151.95, "end": 152.31, "word": " في", "probability": 0.8974609375}, {"start": 152.31, "end": 152.41, "word": " ال", "probability": 0.6259765625}, {"start": 152.41, "end": 152.69, "word": " group", "probability": 0.7041015625}, {"start": 152.69, "end": 153.03, "word": " على", "probability": 0.85400390625}, {"start": 153.03, "end": 153.67, "word": " شكل", "probability": 0.970947265625}, {"start": 153.67, "end": 154.21, "word": " N", "probability": 0.340087890625}, {"start": 154.21, "end": 155.15, "word": "-tuple", "probability": 0.5277913411458334}, {"start": 155.15, "end": 155.97, "word": " يعني", "probability": 0.814697265625}, {"start": 155.97, "end": 156.45, "word": " جوز", "probability": 0.636474609375}, {"start": 156.45, "end": 157.01, "word": " مكوّن", "probability": 0.75556640625}, {"start": 157.01, "end": 157.19, "word": " من", "probability": 0.98876953125}, {"start": 157.19, "end": 157.81, "word": " مجموعة", "probability": 0.91328125}, {"start": 157.81, "end": 158.17, "word": " من", "probability": 0.75927734375}, {"start": 158.17, "end": 159.25, "word": " المراكبات", "probability": 0.822314453125}, {"start": 159.25, "end": 159.95, "word": " ال", "probability": 0.599609375}, {"start": 159.95, "end": 160.33, "word": " remark", "probability": 0.669921875}, {"start": 160.33, "end": 160.85, "word": " بتقول", "probability": 0.957763671875}, {"start": 160.85, "end": 161.13, "word": " ال", "probability": 0.269775390625}, {"start": 161.13, "end": 161.63, "word": " external", "probability": 0.193359375}, {"start": 161.63, "end": 162.11, "word": " product", "probability": 0.301513671875}, {"start": 162.11, "end": 162.67, "word": " كله", "probability": 0.44140625}, {"start": 162.67, "end": 162.83, "word": " ان", "probability": 0.266845703125}, {"start": 162.83, "end": 163.15, "word": " هذا", "probability": 0.77197265625}, {"start": 163.15, "end": 163.65, "word": " is", "probability": 0.64990234375}, {"start": 163.65, "end": 164.01, "word": " a", "probability": 0.94384765625}, {"start": 164.01, "end": 164.49, "word": " group", "probability": 0.98046875}, {"start": 164.49, "end": 165.25, "word": " under", "probability": 0.87353515625}, {"start": 165.25, "end": 165.65, "word": " the", "probability": 0.91259765625}, {"start": 165.65, "end": 166.21, "word": " following", "probability": 0.91064453125}, {"start": 166.21, "end": 167.11, "word": " operation", "probability": 0.912109375}, {"start": 167.11, "end": 167.79, "word": " يبقى", "probability": 0.963134765625}, {"start": 167.79, "end": 168.03, "word": " بدنا", "probability": 0.6485595703125}, {"start": 168.03, "end": 168.45, "word": " نعرف", "probability": 0.9368489583333334}, {"start": 168.45, "end": 169.13, "word": " binary", "probability": 0.84912109375}, {"start": 169.13, "end": 169.93, "word": " operation", "probability": 0.951171875}, {"start": 169.93, "end": 170.43, "word": " على", "probability": 0.88330078125}, {"start": 170.43, "end": 170.93, "word": " هذه", "probability": 0.98291015625}, {"start": 170.93, "end": 171.43, "word": " ال", "probability": 0.38232421875}, {"start": 171.43, "end": 171.79, "word": " set", "probability": 0.6640625}], "temperature": 1.0}, {"id": 7, "seek": 19102, "start": 172.02, "end": 191.02, "text": "بحيث فعلًا يصبح هذه اللي عندنا اجروب كيف ال binary operation بدي اخد حاصل ضرب قوسين بالشكل اللي عندنا حاصل ضرب قوسين اللي عندنا بدي اضرب component wise كل مركبة في main في نظيرتها", "tokens": [3555, 5016, 1829, 12984, 6156, 30241, 14111, 995, 7251, 9381, 49628, 29538, 13672, 1829, 43242, 8315, 1975, 7435, 2288, 37746, 9122, 33911, 2423, 17434, 6916, 4724, 16254, 1975, 9778, 3215, 11331, 33546, 1211, 48812, 25513, 12174, 41779, 9957, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 11331, 33546, 1211, 48812, 25513, 12174, 41779, 9957, 13672, 1829, 43242, 8315, 4724, 16254, 1975, 11242, 25513, 6542, 10829, 28242, 3714, 31747, 49401, 8978, 2135, 8978, 8717, 19913, 13546, 2655, 11296], "avg_logprob": -0.34841721708124335, "compression_ratio": 1.6647727272727273, "no_speech_prob": 0.0, "words": [{"start": 172.02, "end": 172.56, "word": "بحيث", "probability": 0.592315673828125}, {"start": 172.56, "end": 173.18, "word": " فعلًا", "probability": 0.68133544921875}, {"start": 173.18, "end": 173.78, "word": " يصبح", "probability": 0.5619303385416666}, {"start": 173.78, "end": 174.08, "word": " هذه", "probability": 0.451416015625}, {"start": 174.08, "end": 174.18, "word": " اللي", "probability": 0.462493896484375}, {"start": 174.18, "end": 174.7, "word": " عندنا", "probability": 0.909912109375}, {"start": 174.7, "end": 176.04, "word": " اجروب", "probability": 0.5205078125}, {"start": 176.04, "end": 176.68, "word": " كيف", "probability": 0.8779296875}, {"start": 176.68, "end": 176.82, "word": " ال", "probability": 0.8037109375}, {"start": 176.82, "end": 177.2, "word": " binary", "probability": 0.489501953125}, {"start": 177.2, "end": 177.82, "word": " operation", "probability": 0.560546875}, {"start": 177.82, "end": 178.64, "word": " بدي", "probability": 0.3431396484375}, {"start": 178.64, "end": 178.96, "word": " اخد", "probability": 0.6798502604166666}, {"start": 178.96, "end": 179.76, "word": " حاصل", "probability": 0.7960611979166666}, {"start": 179.76, "end": 180.14, "word": " ضرب", "probability": 0.9755859375}, {"start": 180.14, "end": 180.88, "word": " قوسين", "probability": 0.98046875}, {"start": 180.88, "end": 181.42, "word": " بالشكل", "probability": 0.9427083333333334}, {"start": 181.42, "end": 181.58, "word": " اللي", "probability": 0.953857421875}, {"start": 181.58, "end": 181.9, "word": " عندنا", "probability": 0.862060546875}, {"start": 181.9, "end": 182.82, "word": " حاصل", "probability": 0.7803548177083334}, {"start": 182.82, "end": 183.08, "word": " ضرب", "probability": 0.994873046875}, {"start": 183.08, "end": 183.54, "word": " قوسين", "probability": 0.98583984375}, {"start": 183.54, "end": 183.66, "word": " اللي", "probability": 0.57391357421875}, {"start": 183.66, "end": 183.88, "word": " عندنا", "probability": 0.951171875}, {"start": 183.88, "end": 184.2, "word": " بدي", "probability": 0.80810546875}, {"start": 184.2, "end": 184.94, "word": " اضرب", "probability": 0.91650390625}, {"start": 184.94, "end": 186.26, "word": " component", "probability": 0.9228515625}, {"start": 186.26, "end": 187.04, "word": " wise", "probability": 0.451171875}, {"start": 187.04, "end": 187.86, "word": " كل", "probability": 0.86181640625}, {"start": 187.86, "end": 188.84, "word": " مركبة", "probability": 0.90673828125}, {"start": 188.84, "end": 189.12, "word": " في", "probability": 0.9716796875}, {"start": 189.12, "end": 189.46, "word": " main", "probability": 0.378173828125}, {"start": 189.46, "end": 189.8, "word": " في", "probability": 0.89306640625}, {"start": 189.8, "end": 191.02, "word": " نظيرتها", "probability": 0.95029296875}], "temperature": 1.0}, {"id": 8, "seek": 21942, "start": 191.38, "end": 219.42, "text": "يبقى بدى يصير حصر ضرب الشكل اللى عنها بدى اضرب جي واحد في جي واحد ال prime فاصلة جي اتنين في جي اتنين ال prime و هكذا لغاية ما نوصل الى جي ان بجي ان prime زى ما انت شايف طلع element موجود وان في ال external direct product يبقى هذه binary operation ضل عليك تعمل تشك هل هي associative ولا لأ وال identity element تبعها", "tokens": [1829, 3555, 4587, 7578, 47525, 7578, 7251, 9381, 13546, 11331, 9381, 2288, 48812, 25513, 25124, 28820, 13672, 7578, 18871, 11296, 47525, 7578, 1975, 11242, 25513, 10874, 1829, 36764, 24401, 8978, 10874, 1829, 36764, 24401, 2423, 5835, 6156, 33546, 37977, 10874, 1829, 1975, 2655, 1863, 9957, 8978, 10874, 1829, 1975, 2655, 1863, 9957, 2423, 5835, 4032, 8032, 4117, 15730, 5296, 17082, 995, 10632, 19446, 8717, 2407, 36520, 2423, 7578, 10874, 1829, 16472, 4724, 7435, 1829, 16472, 5835, 30767, 7578, 19446, 16472, 2655, 13412, 995, 33911, 23032, 1211, 3615, 4478, 3714, 29245, 23328, 4032, 7649, 8978, 2423, 8320, 2047, 1674, 7251, 3555, 4587, 7578, 29538, 17434, 6916, 48812, 1211, 25894, 4117, 6055, 25957, 1211, 6055, 8592, 4117, 8032, 1211, 39896, 4180, 1166, 49429, 5296, 10721, 16070, 6575, 4478, 6055, 3555, 3615, 11296], "avg_logprob": -0.2461831988269136, "compression_ratio": 1.7563636363636363, 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0.91259765625}, {"start": 530.83, "end": 531.15, "word": " بيكون", "probability": 0.8779296875}, {"start": 531.15, "end": 531.57, "word": " module", "probability": 0.80078125}, {"start": 531.57, "end": 532.05, "word": " main", "probability": 0.7021484375}, {"start": 532.05, "end": 532.63, "word": " ل", "probability": 0.90087890625}, {"start": 532.63, "end": 533.05, "word": " group", "probability": 0.85205078125}, {"start": 533.05, "end": 533.75, "word": " التانية", "probability": 0.9249674479166666}], "temperature": 1.0}, {"id": 23, "seek": 55457, "start": 534.01, "end": 554.57, "text": "يبقى هذا الكلام عبارة عن خمسة في سبعة في جداش بخمسة و تلاتين موديولو تمانية لأن الدرب هذا في الجروب الأولى و الدرب التاني في الجروب التانية سبعة في تسعة في جداش بتلاتة و ستين موديولو عشرة بالشكل اللي عندنا", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 6225, 3555, 9640, 3660, 18871, 16490, 2304, 3794, 3660, 8978, 8608, 3555, 27884, 8978, 10874, 3215, 33599, 4724, 9778, 2304, 3794, 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"text": "يبقى example two find خلّي المعلومة اللي سألتك عنها كم عنصر هذا كنت ل 16 خلّيها عندك لزمالي بعد قليل", "tokens": [1829, 3555, 4587, 7578, 1365, 732, 915, 16490, 1211, 11703, 1829, 9673, 30241, 20498, 3660, 13672, 1829, 8608, 10721, 1211, 2655, 4117, 18871, 11296, 9122, 2304, 18871, 9381, 2288, 23758, 9122, 29399, 5296, 3165, 16490, 1211, 11703, 1829, 11296, 43242, 4117, 5296, 11622, 2304, 6027, 1829, 39182, 12174, 20292, 1211], "avg_logprob": -0.20955882820428587, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 592.55, "end": 593.09, "word": "يبقى", "probability": 0.8609619140625}, {"start": 593.09, "end": 593.69, "word": " example", "probability": 0.7890625}, {"start": 593.69, "end": 594.33, "word": " two", "probability": 0.517578125}, {"start": 594.33, "end": 601.27, "word": " find", "probability": 0.6904296875}, {"start": 601.27, "end": 603.61, "word": " خلّي", "probability": 0.647216796875}, {"start": 603.61, "end": 604.33, "word": " المعلومة", "probability": 0.9434814453125}, {"start": 604.33, "end": 604.49, "word": " اللي", "probability": 0.893798828125}, {"start": 604.49, "end": 604.93, "word": " سألتك", "probability": 0.9392578125}, {"start": 604.93, "end": 605.27, "word": " عنها", "probability": 0.984375}, {"start": 605.27, "end": 605.51, "word": " كم", "probability": 0.683349609375}, {"start": 605.51, "end": 605.87, "word": " عنصر", "probability": 0.951171875}, {"start": 605.87, "end": 606.05, "word": " هذا", "probability": 0.2073974609375}, {"start": 606.05, "end": 606.27, "word": " كنت", "probability": 0.83984375}, {"start": 606.27, "end": 606.41, "word": " ل", "probability": 0.7060546875}, {"start": 606.41, "end": 606.99, "word": " 16", "probability": 0.310546875}, {"start": 606.99, "end": 607.91, "word": " خلّيها", "probability": 0.88134765625}, {"start": 607.91, "end": 608.27, "word": " عندك", "probability": 0.989013671875}, {"start": 608.27, "end": 609.07, "word": " لزمالي", "probability": 0.9138671875}, {"start": 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"end": 912.89, "word": " زد", "probability": 0.9775390625}, {"start": 912.89, "end": 913.65, "word": " تلاتة", "probability": 0.9857177734375}, {"start": 913.65, "end": 914.55, "word": " is", "probability": 0.67529296875}, {"start": 914.55, "end": 916.05, "word": " cyclic", "probability": 0.890869140625}], "temperature": 1.0}, {"id": 39, "seek": 93344, "start": 918.2, "end": 933.44, "text": "يبقى طلعت ال group اللي عندها هذه مالها اللي هو الـ cyclic group وبالتالي مدام ال cyclic وعدد العناصر إلها ستة بنقدر نقول إن هذه isomorphic لزد ستة", "tokens": [1829, 3555, 4587, 7578, 23032, 1211, 34268, 2423, 1594, 13672, 1829, 43242, 11296, 29538, 3714, 6027, 11296, 13672, 1829, 31439, 2423, 39184, 38154, 1050, 1594, 46599, 6027, 2655, 6027, 1829, 3714, 3215, 10943, 2423, 38154, 1050, 4032, 22488, 3215, 18863, 1863, 33546, 2288, 11933, 1211, 11296, 8608, 2655, 3660, 44945, 28543, 2288, 8717, 39648, 36145, 29538, 307, 32702, 299, 5296, 11622, 3215, 8608, 2655, 3660], "avg_logprob": 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"وبالتالي هذي الجروب صارت Cycle كمودام Cycle كمان قبيلية تمام السؤال هو هل فيها generator أخر ولا خلصنا .. أكيد؟ اللي هو مين؟ طيب احنا أخدنا واحد وواحد generator يبقى فيش غيره بيقول أبو غدر؟", "tokens": [37746, 6027, 2655, 6027, 1829, 8032, 8848, 1829, 2423, 7435, 32887, 3555, 20328, 9640, 2655, 10295, 2160, 9122, 2304, 23328, 10943, 10295, 2160, 9122, 2304, 7649, 12174, 21292, 1211, 10632, 46811, 10943, 21136, 33604, 6027, 31439, 8032, 1211, 8978, 11296, 19265, 5551, 34740, 49429, 16490, 1211, 9381, 8315, 4386, 5551, 4117, 25708, 22807, 13672, 1829, 31439, 3714, 9957, 22807, 23032, 1829, 3555, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 36764, 24401, 4032, 14407, 24401, 19265, 7251, 3555, 4587, 7578, 8978, 8592, 32771, 13546, 3224, 4724, 1829, 39648, 5551, 3555, 2407, 32771, 3215, 2288, 22807], "avg_logprob": -0.36513158333928963, "compression_ratio": 1.5858585858585859, "no_speech_prob": 0.0, "words": [{"start": 985.85, "end": 986.93, "word": "وبالتالي", "probability": 0.82783203125}, 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بمجرد النظر أكتر مرة سمعت منه لو عندك element و بيكون generator فمعكسه هو generator وقلنا أي group إذا فيها generator واحد معناته فيه كمان واحد يعني ال generator يظهر على شكل الأزواج إلا إذا كانت ل three sub group", "tokens": [45340, 34268, 43042, 9957, 7251, 39648, 11536, 8978, 3224, 3714, 16758, 1863, 3615, 8592, 8717, 7435, 25513, 4724, 2304, 7435, 2288, 3215, 28239, 19913, 2288, 5551, 4117, 2655, 2288, 3714, 25720, 8608, 2304, 34268, 9154, 3224, 45164, 43242, 4117, 4478, 4032, 4724, 1829, 30544, 19265, 6156, 2304, 3615, 4117, 3794, 3224, 31439, 19265, 4032, 4587, 1211, 8315, 36632, 1594, 11933, 15730, 8978, 11296, 19265, 36764, 24401, 20449, 8315, 47395, 8978, 3224, 9122, 2304, 7649, 36764, 24401, 37495, 22653, 2423, 19265, 7251, 19913, 3224, 2288, 15844, 13412, 28820, 16247, 11622, 2407, 26108, 11933, 15040, 11933, 15730, 25961, 2655, 5296, 1045, 1422, 1594], "avg_logprob": -0.2420343116802328, "compression_ratio": 1.7123893805309736, "no_speech_prob": 0.0, "words": [{"start": 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"word": " عليه", "probability": 0.9306640625}, {"start": 1111.05, "end": 1111.27, "word": " اي", "probability": 0.8623046875}, {"start": 1111.27, "end": 1111.47, "word": " واحد", "probability": 0.992431640625}, {"start": 1111.47, "end": 1111.85, "word": " تاني", "probability": 0.9368489583333334}, {"start": 1111.85, "end": 1112.27, "word": " بتروح", "probability": 0.8619791666666666}, {"start": 1112.27, "end": 1112.51, "word": " على", "probability": 0.564453125}, {"start": 1112.51, "end": 1113.35, "word": " معكوسه", "probability": 0.8614501953125}, {"start": 1113.35, "end": 1114.41, "word": " automatic", "probability": 0.79638671875}, {"start": 1114.41, "end": 1115.43, "word": " لقيت", "probability": 0.8777669270833334}, {"start": 1115.43, "end": 1116.07, "word": " معكوسه", "probability": 0.784423828125}, {"start": 1116.07, "end": 1116.37, "word": " بيكون", "probability": 0.8202311197916666}, {"start": 1116.37, "end": 1116.61, "word": " هو", "probability": 0.97509765625}, {"start": 1116.61, "end": 1116.83, "word": " ال", "probability": 0.93212890625}, {"start": 1116.83, "end": 1117.43, "word": " generator", "probability": 0.9951171875}, {"start": 1117.43, "end": 1118.95, "word": " الاخر", "probability": 0.792236328125}, {"start": 1118.95, "end": 1119.17, "word": " و", "probability": 0.703125}, {"start": 1119.17, "end": 1119.75, "word": " هكذا", "probability": 0.9034830729166666}, {"start": 1119.75, "end": 1121.15, "word": " تمام؟", "probability": 0.69775390625}, {"start": 1121.15, "end": 1121.45, "word": " طيب", "probability": 0.9412434895833334}, {"start": 1121.45, "end": 1121.73, "word": " هذا", "probability": 0.87841796875}, {"start": 1121.73, "end": 1122.03, "word": " كان", "probability": 0.98876953125}, {"start": 1122.03, "end": 1122.57, "word": " المثال", "probability": 0.96630859375}, {"start": 1122.57, "end": 1123.37, "word": " رقم", "probability": 0.9840494791666666}, {"start": 1123.37, "end": 1124.33, "word": " اتنين", "probability": 0.9609375}, {"start": 1124.33, "end": 1125.07, "word": " بدنا", "probability": 0.7607421875}, {"start": 1125.07, "end": 1125.35, "word": " نروح", "probability": 0.9931640625}, {"start": 1125.35, "end": 1126.01, "word": " لمثال", "probability": 0.8850911458333334}, {"start": 1126.01, "end": 1126.71, "word": " رقم", "probability": 0.9925130208333334}, {"start": 1126.71, "end": 1127.49, "word": " تلاتة", "probability": 0.8482666015625}], "temperature": 1.0}, {"id": 48, "seek": 115444, "start": 1128.04, "end": 1154.44, "text": "يبقى example three example three بيقول a group of order أربعة a group of order أربعة is isomorphic", "tokens": [1829, 3555, 4587, 7578, 1365, 1045, 1365, 1045, 4724, 1829, 39648, 257, 1594, 295, 1668, 5551, 25513, 27884, 257, 1594, 295, 1668, 5551, 25513, 27884, 307, 307, 32702, 299], "avg_logprob": -0.16145833532015483, "compression_ratio": 1.4096385542168675, "no_speech_prob": 0.0, "words": [{"start": 1128.04, "end": 1128.68, "word": "يبقى", "probability": 0.829345703125}, {"start": 1128.68, "end": 1129.26, "word": " example", "probability": 0.88720703125}, {"start": 1129.26, "end": 1130.16, "word": " three", "probability": 0.67724609375}, {"start": 1130.16, "end": 1139.1, "word": " example", "probability": 0.84326171875}, {"start": 1139.1, "end": 1139.82, "word": " three", "probability": 0.93798828125}, {"start": 1139.82, "end": 1141.04, "word": " بيقول", "probability": 0.9646809895833334}, {"start": 1141.04, "end": 1141.42, "word": " a", "probability": 0.44677734375}, {"start": 1141.42, "end": 1142.26, "word": " group", "probability": 0.982421875}, {"start": 1142.26, "end": 1145.24, "word": " of", "probability": 0.96044921875}, {"start": 1145.24, "end": 1146.86, "word": " order", "probability": 0.96142578125}, {"start": 1146.86, "end": 1148.62, "word": " أربعة", "probability": 0.73193359375}, {"start": 1148.62, "end": 1149.86, "word": " a", "probability": 0.578125}, {"start": 1149.86, "end": 1150.0, "word": " group", "probability": 0.98095703125}, {"start": 1150.0, "end": 1150.18, "word": " of", "probability": 0.91796875}, {"start": 1150.18, "end": 1150.34, "word": " order", "probability": 0.9462890625}, {"start": 1150.34, "end": 1150.62, "word": " أربعة", "probability": 0.9251302083333334}, {"start": 1150.62, "end": 1151.28, "word": " is", "probability": 0.95703125}, {"start": 1151.28, "end": 1154.44, "word": " isomorphic", "probability": 0.9412434895833334}], "temperature": 1.0}, {"id": 49, "seek": 116788, "start": 1158.44, "end": 1167.88, "text": "زد اربعة او زد اتنين اكستير نضعه ك product مع زد اتنين", "tokens": [11622, 3215, 1975, 25513, 27884, 1975, 2407, 30767, 3215, 1975, 2655, 1863, 9957, 1975, 4117, 14851, 13546, 8717, 11242, 3615, 3224, 9122, 1674, 20449, 30767, 3215, 1975, 2655, 1863, 9957], "avg_logprob": -0.333669368297823, "compression_ratio": 1.1538461538461537, "no_speech_prob": 0.0, "words": [{"start": 1158.4399999999998, "end": 1159.84, "word": "زد", "probability": 0.2967529296875}, {"start": 1159.84, "end": 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أسأل السؤال التالي بقول أي group من ما كانت تكون مدام ال order إلها أربعة يبقى يا enzomorphic إلى z أربعة يا isomorphic إلى z اتنين external like product مع z اتنين السؤال ليش خيرني بين هذه و هذه؟", "tokens": [7435, 16758, 9673, 44510, 10721, 25124, 17082, 1211, 8978, 29538, 25124, 17082, 37977, 47525, 10721, 5551, 3794, 10721, 1211, 21136, 33604, 6027, 16712, 6027, 1829, 4724, 39648, 36632, 1594, 9154, 19446, 25961, 2655, 6055, 30544, 3714, 3215, 10943, 2423, 1668, 11933, 1211, 11296, 5551, 25513, 27884, 7251, 3555, 4587, 7578, 35186, 465, 89, 32702, 299, 30731, 710, 5551, 25513, 27884, 35186, 307, 32702, 299, 30731, 710, 1975, 2655, 1863, 9957, 8320, 411, 1674, 20449, 710, 1975, 2655, 1863, 9957, 21136, 33604, 6027, 32239, 8592, 16490, 13546, 22653, 49374, 29538, 4032, 29538, 22807], "avg_logprob": -0.290826621875968, "compression_ratio": 1.6930232558139535, "no_speech_prob": 0.0, "words": [{"start": 1172.54, "end": 1172.94, "word": "جاب", "probability": 0.425201416015625}, {"start": 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{"start": 1184.04, "end": 1184.28, "word": " إلى", "probability": 0.66455078125}, {"start": 1184.28, "end": 1184.58, "word": " z", "probability": 0.2012939453125}, {"start": 1184.58, "end": 1185.3, "word": " أربعة", "probability": 0.9132486979166666}, {"start": 1185.3, "end": 1185.98, "word": " يا", "probability": 0.740234375}, {"start": 1185.98, "end": 1186.92, "word": " isomorphic", "probability": 0.8712565104166666}, {"start": 1186.92, "end": 1187.18, "word": " إلى", "probability": 0.9443359375}, {"start": 1187.18, "end": 1187.56, "word": " z", "probability": 0.96484375}, {"start": 1187.56, "end": 1188.02, "word": " اتنين", "probability": 0.8564453125}, {"start": 1188.02, "end": 1188.56, "word": " external", "probability": 0.75}, {"start": 1188.56, "end": 1189.0, "word": " like", "probability": 0.453857421875}, {"start": 1189.0, "end": 1189.6, "word": " product", "probability": 0.904296875}, {"start": 1189.6, "end": 1190.02, "word": " مع", "probability": 0.9736328125}, {"start": 1190.02, "end": 1190.56, "word": " z", "probability": 0.96044921875}, {"start": 1190.56, "end": 1191.4, "word": " اتنين", "probability": 0.9434814453125}, {"start": 1191.4, "end": 1192.16, "word": " السؤال", "probability": 0.9915364583333334}, {"start": 1192.16, "end": 1192.92, "word": " ليش", "probability": 0.872314453125}, {"start": 1192.92, "end": 1193.48, "word": " خيرني", "probability": 0.71630859375}, {"start": 1193.48, "end": 1193.74, "word": " بين", "probability": 0.97802734375}, {"start": 1193.74, "end": 1194.02, "word": " هذه", "probability": 0.80322265625}, {"start": 1194.02, "end": 1194.16, "word": " و", "probability": 0.6708984375}, {"start": 1194.16, "end": 1194.7, "word": " هذه؟", "probability": 0.854736328125}], "temperature": 1.0}, {"id": 51, "seek": 121683, "start": 1196.17, "end": 1216.83, "text": "أيوة Z4 هدى Cyclic تمام Z2 external dielectric product مع Z2 هدى is not cyclic بقدرش ألاقي فيها ولا generator إذا لو كانت ال group اللى ال order إلها يسوى 4 cyclic يبقى isomorphic لمين ل Z4", "tokens": [10721, 1829, 2407, 3660, 1176, 19, 8032, 3215, 7578, 10295, 66, 1050, 46811, 10943, 1176, 17, 8320, 978, 38421, 1674, 20449, 1176, 17, 8032, 3215, 7578, 307, 406, 38154, 1050, 4724, 28543, 2288, 8592, 5551, 15040, 38436, 8978, 11296, 49429, 19265, 11933, 15730, 45164, 25961, 2655, 2423, 1594, 13672, 7578, 2423, 1668, 11933, 1211, 11296, 7251, 3794, 2407, 7578, 1017, 38154, 1050, 7251, 3555, 4587, 7578, 307, 32702, 299, 32767, 9957, 5296, 1176, 19], "avg_logprob": -0.33041666269302367, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1196.1699999999998, "end": 1197.1299999999999, "word": "أيوة", "probability": 0.54046630859375}, {"start": 1197.1299999999999, "end": 1198.09, "word": " Z4", "probability": 0.48974609375}, {"start": 1198.09, "end": 1198.55, "word": " هدى", "probability": 0.5120442708333334}, {"start": 1198.55, "end": 1199.25, "word": " Cyclic", "probability": 0.7561848958333334}, {"start": 1199.25, "end": 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"end": 1255.87, "text": "دليل على ذلك لت الجي عناصر E وA وB وAV", "tokens": [3215, 20292, 1211, 15844, 29910, 23275, 5296, 2655, 25724, 1829, 18871, 33546, 2288, 462, 4032, 32, 4032, 33, 4032, 32, 53], "avg_logprob": -0.4410511322996833, "compression_ratio": 0.9841269841269841, "no_speech_prob": 0.0, "words": [{"start": 1247.35, "end": 1247.93, "word": "دليل", "probability": 0.7403157552083334}, {"start": 1247.93, "end": 1248.17, "word": " على", "probability": 0.88916015625}, {"start": 1248.17, "end": 1248.69, "word": " ذلك", "probability": 0.982421875}, {"start": 1248.69, "end": 1249.37, "word": " لت", "probability": 0.4825439453125}, {"start": 1249.37, "end": 1251.15, "word": " الجي", "probability": 0.59423828125}, {"start": 1251.15, "end": 1252.45, "word": " عناصر", "probability": 0.9601236979166666}, {"start": 1252.45, "end": 1252.79, "word": " E", "probability": 0.62109375}, {"start": 1252.79, "end": 1253.81, "word": " وA", "probability": 0.767333984375}, {"start": 1253.81, "end": 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و واحد طيب هل هذه Cyclic ولا لا انا مش عارف تعال تقدر تلاقي فيها generator طيب انا ادعي ان every non identity element has order to صح؟", "tokens": [2407, 39182, 39896, 4117, 17182, 4032, 36764, 24401, 4032, 39182, 39896, 4117, 2423, 14407, 24401, 4032, 17182, 4032, 36764, 24401, 4032, 36764, 24401, 23032, 1829, 3555, 8032, 1211, 29538, 10295, 66, 1050, 49429, 20193, 1975, 8315, 37893, 6225, 9640, 5172, 37279, 6027, 6055, 28543, 2288, 6055, 15040, 38436, 8978, 11296, 19265, 23032, 1829, 3555, 1975, 8315, 1975, 3215, 3615, 1829, 16472, 633, 2107, 6575, 4478, 575, 1668, 281, 20328, 5016, 22807], "avg_logprob": -0.23697916294137636, "compression_ratio": 1.547486033519553, "no_speech_prob": 0.0, "words": [{"start": 1459.94, "end": 1460.2, "word": "و", "probability": 0.471923828125}, {"start": 1460.2, "end": 1460.58, "word": " بعد", "probability": 0.90576171875}, {"start": 1460.58, "end": 1461.14, "word": " هيك", "probability": 0.587158203125}, {"start": 1461.14, "end": 1461.66, "word": " 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"probability": 0.94384765625}, {"start": 1487.6, "end": 1487.94, "word": " to", "probability": 0.322265625}, {"start": 1487.94, "end": 1489.7, "word": " صح؟", "probability": 0.8668619791666666}], "temperature": 1.0}, {"id": 63, "seek": 150759, "start": 1490.21, "end": 1507.59, "text": "لأن هنا جمع هذه تربية بتضرب في اتنين بيصير Zero وهنا اتنين Zero Zero هذه تربية برضه اتنين و Zero بيصير Zero Zero هذه اتنين بيصير اتنين و اتنين Zero Zero يبقى اي element من هناها", "tokens": [1211, 33456, 34105, 10874, 2304, 3615, 29538, 6055, 2288, 21292, 3660, 39894, 11242, 25513, 8978, 1975, 2655, 1863, 9957, 4724, 1829, 9381, 13546, 17182, 37037, 8315, 1975, 2655, 1863, 9957, 17182, 17182, 29538, 6055, 2288, 21292, 3660, 4724, 43042, 3224, 1975, 2655, 1863, 9957, 4032, 17182, 4724, 1829, 9381, 13546, 17182, 17182, 29538, 1975, 2655, 1863, 9957, 4724, 1829, 9381, 13546, 1975, 2655, 1863, 9957, 4032, 1975, 2655, 1863, 9957, 17182, 17182, 7251, 3555, 4587, 7578, 1975, 1829, 4478, 9154, 34105, 11296], 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وهنا", "probability": 0.784423828125}, {"start": 1496.13, "end": 1496.59, "word": " اتنين", "probability": 0.9622802734375}, {"start": 1496.59, "end": 1496.97, "word": " Zero", "probability": 0.83056640625}, {"start": 1496.97, "end": 1497.45, "word": " Zero", "probability": 0.86279296875}, {"start": 1497.45, "end": 1498.19, "word": " هذه", "probability": 0.484619140625}, {"start": 1498.19, "end": 1499.01, "word": " تربية", "probability": 0.9404296875}, {"start": 1499.01, "end": 1499.33, "word": " برضه", "probability": 0.8902994791666666}, {"start": 1499.33, "end": 1499.77, "word": " اتنين", "probability": 0.9918212890625}, {"start": 1499.77, "end": 1499.91, "word": " و", "probability": 0.978515625}, {"start": 1499.91, "end": 1500.15, "word": " Zero", "probability": 0.75830078125}, {"start": 1500.15, "end": 1500.61, "word": " بيصير", "probability": 0.93017578125}, {"start": 1500.61, "end": 1500.91, "word": " Zero", "probability": 0.9794921875}, {"start": 1500.91, "end": 1501.37, "word": " Zero", "probability": 0.97021484375}, {"start": 1501.37, "end": 1502.01, "word": " هذه", "probability": 0.646484375}, {"start": 1502.01, "end": 1502.33, "word": " اتنين", "probability": 0.98876953125}, {"start": 1502.33, "end": 1502.69, "word": " بيصير", "probability": 0.985595703125}, {"start": 1502.69, "end": 1503.05, "word": " اتنين", "probability": 0.991455078125}, {"start": 1503.05, "end": 1503.17, "word": " و", "probability": 0.9697265625}, {"start": 1503.17, "end": 1503.49, "word": " اتنين", "probability": 0.83251953125}, {"start": 1503.49, "end": 1503.79, "word": " Zero", "probability": 0.97265625}, {"start": 1503.79, "end": 1504.23, "word": " Zero", "probability": 0.978515625}, {"start": 1504.23, "end": 1505.03, "word": " يبقى", "probability": 0.963134765625}, {"start": 1505.03, "end": 1505.47, "word": " اي", "probability": 0.8642578125}, {"start": 1505.47, "end": 1506.27, "word": " element", "probability": 0.87841796875}, {"start": 1506.27, "end": 1506.67, "word": " من", "probability": 0.984375}, {"start": 1506.67, "end": 1507.59, "word": " هناها", "probability": 0.82275390625}], "temperature": 1.0}, {"id": 64, "seek": 153323, "start": 1508.03, "end": 1533.23, "text": "الـ order له يساوي اتنين يعني زي مين زي الكلام اللي قلناه هذا بالضبط تماما و هدول اربع عناصر و هدول اربع عناصر طب ايش رأيك؟ بدي اعرف function ما بين الاتنين و اثبت انها one to one ان انتوا وبالتالي بصير الجروب اللي عندها ده isomorphic لمين؟ لزد اتنين external direct product لزد", "tokens": [6027, 39184, 1668, 46740, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 37495, 22653, 30767, 1829, 3714, 9957, 30767, 1829, 2423, 28820, 10943, 13672, 1829, 12174, 1211, 8315, 3224, 23758, 20666, 11242, 3555, 9566, 46811, 10943, 995, 4032, 8032, 3215, 12610, 1975, 25513, 3615, 18871, 33546, 2288, 4032, 8032, 3215, 12610, 1975, 25513, 3615, 18871, 33546, 2288, 23032, 3555, 1975, 1829, 8592, 12602, 10721, 1829, 4117, 22807, 4724, 16254, 1975, 3615, 28480, 2445, 19446, 49374, 2423, 9307, 1863, 9957, 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" بين", "probability": 0.96484375}, {"start": 1522.11, "end": 1522.57, "word": " الاتنين", "probability": 0.86474609375}, {"start": 1522.57, "end": 1522.77, "word": " و", "probability": 0.94873046875}, {"start": 1522.77, "end": 1523.05, "word": " اثبت", "probability": 0.9053955078125}, {"start": 1523.05, "end": 1523.37, "word": " انها", "probability": 0.90869140625}, {"start": 1523.37, "end": 1523.65, "word": " one", "probability": 0.94091796875}, {"start": 1523.65, "end": 1523.85, "word": " to", "probability": 0.84423828125}, {"start": 1523.85, "end": 1524.01, "word": " one", "probability": 0.95361328125}, {"start": 1524.01, "end": 1524.23, "word": " ان", "probability": 0.41259765625}, {"start": 1524.23, "end": 1524.63, "word": " انتوا", "probability": 0.9025065104166666}, {"start": 1524.63, "end": 1525.47, "word": " وبالتالي", "probability": 0.944140625}, {"start": 1525.47, "end": 1526.33, "word": " بصير", "probability": 0.9440104166666666}, {"start": 1526.33, "end": 1526.77, "word": " الجروب", "probability": 0.82080078125}, {"start": 1526.77, "end": 1526.95, "word": " اللي", "probability": 0.9130859375}, {"start": 1526.95, "end": 1527.29, "word": " عندها", "probability": 0.779296875}, {"start": 1527.29, "end": 1527.53, "word": " ده", "probability": 0.780029296875}, {"start": 1527.53, "end": 1528.57, "word": " isomorphic", "probability": 0.7610677083333334}, {"start": 1528.57, "end": 1529.53, "word": " لمين؟", "probability": 0.6526692708333334}, {"start": 1529.53, "end": 1530.19, "word": " لزد", "probability": 0.673095703125}, {"start": 1530.19, "end": 1531.07, "word": " اتنين", "probability": 0.884765625}, {"start": 1531.07, "end": 1531.65, "word": " external", "probability": 0.71337890625}, {"start": 1531.65, "end": 1532.03, "word": " direct", "probability": 0.15087890625}, {"start": 1532.03, "end": 1532.59, "word": " product", "probability": 0.96826171875}, {"start": 1532.59, "end": 1533.23, "word": " لزد", "probability": 0.9392903645833334}], "temperature": 1.0}, {"id": 65, "seek": 155640, "start": 1533.68, "end": 1556.4, "text": "يبقى باجي بقوله ملاحظة بسيطة جدا ان زد اتنين external لزد اتنين is not cyclic because any element والله any non identity element", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 3714, 15040, 5016, 19913, 3660, 4724, 3794, 1829, 9566, 3660, 10874, 28259, 16472, 30767, 3215, 1975, 2655, 1863, 9957, 8320, 5296, 11622, 3215, 1975, 2655, 1863, 9957, 307, 406, 38154, 1050, 570, 604, 4478, 16070, 43761, 604, 2107, 6575, 4478], "avg_logprob": -0.22227328781988107, "compression_ratio": 1.330827067669173, "no_speech_prob": 0.0, "words": [{"start": 1533.68, "end": 1535.06, "word": "يبقى", "probability": 0.76129150390625}, {"start": 1535.06, "end": 1535.44, "word": " باجي", "probability": 0.78759765625}, {"start": 1535.44, "end": 1535.92, "word": " بقوله", "probability": 0.84912109375}, {"start": 1535.92, "end": 1536.64, "word": " ملاحظة", "probability": 0.9658203125}, {"start": 1536.64, "end": 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"end": 1612.05, "text": "أيه الـ function؟ فاي من الجي إلى زي ده to stay in a like product لزي ده to buy بدي أخلي الفاي تأثر على ال identity element بشكل فاي و بال identity كده اتوقع صورتها ده؟", "tokens": [10721, 1829, 3224, 2423, 39184, 2445, 22807, 6156, 47302, 9154, 25724, 1829, 30731, 30767, 1829, 11778, 3224, 281, 1754, 294, 257, 411, 1674, 5296, 11622, 1829, 11778, 3224, 281, 2256, 4724, 16254, 5551, 9778, 20292, 27188, 47302, 6055, 10721, 49115, 15844, 2423, 6575, 4478, 4724, 8592, 28820, 6156, 47302, 4032, 20666, 6575, 9122, 3215, 3224, 1975, 2655, 30543, 3615, 20328, 13063, 2655, 11296, 11778, 3224, 22807], "avg_logprob": -0.5046641968969089, "compression_ratio": 1.4497041420118344, "no_speech_prob": 0.0, "words": [{"start": 1588.43, "end": 1588.95, "word": "أيه", "probability": 0.519256591796875}, {"start": 1588.95, "end": 1588.95, "word": " الـ", "probability": 0.3966064453125}, {"start": 1588.95, "end": 1590.41, "word": " function؟", "probability": 0.6708984375}, {"start": 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"word": " zero", "probability": 0.56640625}, {"start": 1627.45, "end": 1627.83, "word": " و", "probability": 0.95166015625}, {"start": 1627.83, "end": 1628.25, "word": " zero", "probability": 0.73291015625}, {"start": 1628.25, "end": 1629.27, "word": " الان", "probability": 0.63916015625}, {"start": 1629.27, "end": 1629.95, "word": " Phi", "probability": 0.181884765625}, {"start": 1629.95, "end": 1630.61, "word": " of", "probability": 0.92236328125}, {"start": 1630.61, "end": 1631.19, "word": " A", "probability": 0.69580078125}], "temperature": 1.0}, {"id": 69, "seek": 165550, "start": 1649.72, "end": 1655.5, "text": "السؤال هو هل هذه one to one", "tokens": [6027, 3794, 33604, 6027, 31439, 8032, 1211, 29538, 472, 281, 472], "avg_logprob": -0.5533854216337204, "compression_ratio": 0.975609756097561, "no_speech_prob": 0.0, "words": [{"start": 1649.7199999999998, "end": 1651.12, "word": "السؤال", "probability": 0.6048431396484375}, {"start": 1651.12, "end": 1652.52, "word": " هو", 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"end": 1723.82, "text": "cyclic تمام طب قداش عدد العناصر هنا اربعة زد اتنين في زد تلاتة طلع ستة اللي قبلها اربعة واربعة طلع ستاشر اذا بقدر اجيب قداش ال order ل الاكسينو دايك افرضك ل two groups من خلال ال order لمين ل ال groups لذا بروح بقوله هذه ملاحظة بسيطة اللي هي remark", "tokens": [1344, 66, 1050, 46811, 10943, 23032, 3555, 12174, 3215, 33599, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 34105, 1975, 25513, 27884, 30767, 3215, 1975, 2655, 1863, 9957, 8978, 30767, 3215, 6055, 1211, 9307, 3660, 23032, 1211, 3615, 8608, 2655, 3660, 13672, 1829, 12174, 36150, 11296, 1975, 25513, 27884, 4032, 9640, 3555, 27884, 23032, 1211, 3615, 8608, 2655, 33599, 2288, 1975, 15730, 4724, 28543, 2288, 1975, 7435, 1829, 3555, 12174, 3215, 33599, 2423, 1668, 5296, 42963, 4117, 3794, 9957, 2407, 11778, 47302, 4117, 1975, 5172, 43042, 4117, 5296, 732, 3935, 9154, 16490, 1211, 6027, 2423, 1668, 32767, 9957, 5296, 2423, 3935, 5296, 15730, 4724, 32887, 5016, 4724, 39648, 3224, 29538, 3714, 15040, 5016, 19913, 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with", "probability": 0.40283203125}, {"start": 1868.41, "end": 1871.39, "word": " U6", "probability": 0.82275390625}, {"start": 1871.39, "end": 1874.07, "word": " with", "probability": 0.310302734375}, {"start": 1874.07, "end": 1876.03, "word": " Z3", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 79, "seek": 190803, "start": 1878.15, "end": 1908.03, "text": "يعني في حالة ال external ليس بالضرورة تبقى ال operation اللي على الأولى هي ال operation اللي على التانية هي اللي على التالتة لأ كل group قائمة بال operation الخاصة بيه اطلع هنا ال operation عملية ضرب هنا عملية ضرب هنا عملية اياش هنا عملية جمع بقولي اكم رقم بيكون او وجديش عدد العناصر في ال group اللي عندنا هذه اللي هو ال order", "tokens": [40228, 22653, 8978, 11331, 6027, 3660, 2423, 8320, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 6055, 3555, 4587, 7578, 2423, 6916, 13672, 1829, 15844, 16247, 12610, 7578, 39896, 2423, 6916, 13672, 1829, 15844, 16712, 7649, 10632, 39896, 13672, 1829, 15844, 16712, 6027, 2655, 3660, 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هذا", "probability": 0.69677734375}], "temperature": 1.0}, {"id": 96, "seek": 231879, "start": 2290.85, "end": 2318.79, "text": "نرجع للنص مرة تانية انا عندك product بدي ال order ل أي element ال order ل ال element يسوى least common multiple لل order لكل مركبة على حده يعني بدي أجيب ال order للعنصر الأول في ال N tuple ال order للعنصر الثاني في ال N tuple ال order في التالت ال order للرابع صار عندي مجموعة من ال order بتجيب ال least common multiple لهم كلهم بيكون هو", "tokens": [1863, 47341, 3615, 24976, 1863, 9381, 3714, 25720, 6055, 7649, 10632, 1975, 8315, 43242, 4117, 1674, 4724, 16254, 2423, 1668, 5296, 36632, 4478, 2423, 1668, 5296, 2423, 4478, 7251, 3794, 2407, 7578, 1935, 2689, 3866, 24976, 1668, 5296, 28820, 3714, 31747, 49401, 15844, 11331, 3215, 3224, 37495, 22653, 4724, 16254, 5551, 7435, 1829, 3555, 2423, 1668, 24976, 3615, 1863, 9381, 2288, 16247, 12610, 8978, 2423, 426, 2604, 781, 2423, 1668, 24976, 3615, 1863, 9381, 2288, 6024, 104, 7649, 1829, 8978, 2423, 426, 2604, 781, 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من ال groups هذه finite يعني فيها عدد محدود من العناصر كويس اتنين اخدت عدد محدود من ال groups هي المقصود فيها عدد محدود من ال groups", "tokens": [259, 257, 2047, 1674, 295, 257, 19362, 1230, 295, 19362, 3935, 7251, 3555, 7435, 1829, 1975, 8315, 18871, 16254, 28242, 1594, 9154, 2423, 3935, 29538, 19362, 37495, 22653, 8978, 11296, 6225, 3215, 3215, 3714, 24401, 23328, 9154, 18863, 1863, 33546, 2288, 9122, 45865, 3794, 1975, 2655, 1863, 9957, 1975, 9778, 3215, 2655, 6225, 3215, 3215, 3714, 24401, 23328, 9154, 2423, 3935, 39896, 9673, 4587, 9381, 23328, 8978, 11296, 6225, 3215, 3215, 3714, 24401, 23328, 9154, 2423, 3935], "avg_logprob": -0.16406250534913477, "compression_ratio": 1.8658536585365855, "no_speech_prob": 0.0, "words": [{"start": 2328.01, "end": 2328.53, "word": "in", "probability": 0.396728515625}, {"start": 2328.53, "end": 2329.03, "word": " a", "probability": 0.935546875}, {"start": 2329.03, "end": 2329.43, "word": " direct", "probability": 0.489501953125}, {"start": 2329.43, 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260546, "start": 2581.64, "end": 2605.46, "text": "يبقى صار عندك جي واحد أس تي بدأ تاني مين ال identity يبقى ال order لهذا ال element بدأ يقسم مين؟ بدأ يقسم ال T يبقى صار ال order لجي واحد divide ال T و ال order لجي اتنين divides", "tokens": [1829, 3555, 4587, 7578, 20328, 9640, 43242, 4117, 10874, 1829, 36764, 24401, 5551, 3794, 6055, 1829, 47525, 10721, 6055, 7649, 1829, 3714, 9957, 2423, 6575, 7251, 3555, 4587, 7578, 2423, 1668, 46740, 15730, 2423, 4478, 47525, 10721, 7251, 4587, 38251, 3714, 9957, 22807, 47525, 10721, 7251, 4587, 38251, 2423, 314, 7251, 3555, 4587, 7578, 20328, 9640, 2423, 1668, 5296, 7435, 1829, 36764, 24401, 9845, 2423, 314, 4032, 2423, 1668, 5296, 7435, 1829, 1975, 2655, 1863, 9957, 41347], "avg_logprob": -0.3345352694010123, "compression_ratio": 1.732484076433121, "no_speech_prob": 0.0, "words": [{"start": 2581.64, "end": 2582.32, "word": "يبقى", "probability": 0.881103515625}, {"start": 2582.32, "end": 2582.76, "word": " صار", "probability": 0.5484619140625}, 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"word": " means", "probability": 0.9169921875}, {"start": 2630.13, "end": 2631.93, "word": " that", "probability": 0.94921875}], "temperature": 1.0}, {"id": 111, "seek": 265539, "start": 2632.95, "end": 2655.39, "text": "إن الـ T is a common multiple of ال order لل G1 وال order لل G2 و ال order لل GM", "tokens": [28814, 1863, 2423, 39184, 314, 307, 257, 2689, 3866, 295, 2423, 1668, 24976, 460, 16, 16070, 1668, 24976, 460, 17, 4032, 2423, 1668, 24976, 16609], "avg_logprob": -0.3554687477075137, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 2632.95, "end": 2633.43, "word": "إن", "probability": 0.5828857421875}, {"start": 2633.43, "end": 2633.75, "word": " الـ", "probability": 0.4705810546875}, {"start": 2633.75, "end": 2634.15, "word": " T", "probability": 0.744140625}, {"start": 2634.15, "end": 2635.25, "word": " is", "probability": 0.67724609375}, {"start": 2635.25, "end": 2639.79, "word": " a", "probability": 0.92919921875}, {"start": 2639.79, "end": 2640.99, "word": " common", "probability": 0.93212890625}, {"start": 2640.99, "end": 2643.53, "word": " multiple", "probability": 0.93408203125}, {"start": 2643.53, "end": 2646.27, "word": " of", "probability": 0.888671875}, {"start": 2646.27, "end": 2647.27, "word": " ال", "probability": 0.720703125}, {"start": 2647.27, "end": 2647.79, "word": " order", "probability": 0.76708984375}, {"start": 2647.79, "end": 2648.05, "word": " لل", "probability": 0.6416015625}, {"start": 2648.05, "end": 2648.95, "word": " G1", "probability": 0.5665283203125}, {"start": 2648.95, "end": 2650.49, "word": " وال", "probability": 0.54443359375}, {"start": 2650.49, "end": 2651.13, "word": " order", "probability": 0.456298828125}, {"start": 2651.13, "end": 2651.51, "word": " لل", "probability": 0.92822265625}, {"start": 2651.51, "end": 2652.49, "word": " G2", "probability": 0.98291015625}, {"start": 2652.49, "end": 2653.29, "word": " و", "probability": 0.70556640625}, {"start": 2653.29, "end": 2653.77, "word": " ال", "probability": 0.48291015625}, {"start": 2653.77, "end": 2654.43, "word": " order", "probability": 0.962890625}, {"start": 2654.43, "end": 2654.83, "word": " لل", "probability": 0.9326171875}, {"start": 2654.83, "end": 2655.39, "word": " GM", "probability": 0.857421875}], "temperature": 1.0}, {"id": 112, "seek": 267809, "start": 2656.87, "end": 2678.09, "text": "طب أنا عندي least common multiple كدهش يبقى T مالها أكبر من S أو S أقل من أو يساوي T but ولكن S is the least common multiple", "tokens": [9566, 3555, 41850, 18871, 16254, 1935, 2689, 3866, 9122, 3215, 3224, 8592, 7251, 3555, 4587, 7578, 314, 19446, 1211, 11296, 5551, 4117, 26890, 9154, 318, 34051, 318, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 995, 45865, 314, 457, 35525, 19452, 318, 307, 264, 1935, 2689, 3866], "avg_logprob": -0.2365358998166754, "compression_ratio": 1.317829457364341, "no_speech_prob": 0.0, "words": [{"start": 2656.87, "end": 2657.17, "word": "طب", "probability": 0.6768798828125}, {"start": 2657.17, "end": 2657.33, "word": " أنا", "probability": 0.603515625}, {"start": 2657.33, "end": 2657.63, "word": " عندي", "probability": 0.7410888671875}, {"start": 2657.63, "end": 2658.13, "word": " least", "probability": 0.8583984375}, {"start": 2658.13, "end": 2658.51, "word": " common", "probability": 0.93359375}, {"start": 2658.51, "end": 2658.89, "word": " multiple", "probability": 0.93359375}, {"start": 2658.89, "end": 2659.51, "word": " كدهش", "probability": 0.73260498046875}, {"start": 2659.51, "end": 2661.03, "word": " يبقى", "probability": 0.8212890625}, {"start": 2661.03, "end": 2661.39, "word": " T", "probability": 0.72412109375}, {"start": 2661.39, "end": 2662.43, "word": " مالها", "probability": 0.614013671875}, {"start": 2662.43, "end": 2663.55, "word": " أكبر", "probability": 0.8211263020833334}, {"start": 2663.55, "end": 2663.79, "word": " من", "probability": 0.962890625}, {"start": 2663.79, "end": 2664.09, "word": " S", "probability": 0.92236328125}, {"start": 2664.09, "end": 2664.45, "word": " أو", "probability": 0.72998046875}, {"start": 2664.45, "end": 2664.95, "word": " S", "probability": 0.92138671875}, {"start": 2664.95, "end": 2665.67, "word": " أقل", "probability": 0.9537760416666666}, {"start": 2665.67, "end": 2665.93, "word": " من", "probability": 0.99169921875}, {"start": 2665.93, "end": 2666.23, "word": " أو", "probability": 0.81005859375}, {"start": 2666.23, "end": 2666.97, "word": " يساوي", "probability": 0.9228515625}, {"start": 2666.97, "end": 2667.37, "word": " T", "probability": 0.9619140625}, {"start": 2667.37, "end": 2668.45, "word": " but", "probability": 0.49169921875}, {"start": 2668.45, "end": 2669.57, "word": " ولكن", "probability": 0.776611328125}, {"start": 2669.57, "end": 2671.15, "word": " S", "probability": 0.87548828125}, {"start": 2671.15, "end": 2671.99, "word": " is", "probability": 0.9482421875}, {"start": 2671.99, "end": 2673.05, "word": " the", "probability": 0.892578125}, {"start": 2673.05, "end": 2674.51, "word": " least", "probability": 0.95751953125}, {"start": 2674.51, "end": 2675.79, "word": " common", "probability": 0.93115234375}, {"start": 2675.79, "end": 2678.09, "word": " multiple", "probability": 0.90869140625}], "temperature": 1.0}, {"id": 113, "seek": 269519, "start": 2681.33, "end": 2695.19, "text": "هذا سيعطيك ان ال S أقل من او يساوي ال T ومعدل رقم 2 يبقى باشر بقول from واحد", "tokens": [3224, 15730, 8608, 40228, 9566, 1829, 4117, 16472, 2423, 318, 5551, 4587, 1211, 9154, 1975, 2407, 7251, 3794, 995, 45865, 2423, 314, 4032, 2304, 22488, 1211, 12602, 4587, 2304, 568, 7251, 3555, 4587, 7578, 4724, 33599, 2288, 4724, 39648, 490, 36764, 24401], "avg_logprob": -0.46620639257652813, "compression_ratio": 1.2450980392156863, "no_speech_prob": 0.0, "words": [{"start": 2681.33, "end": 2681.77, "word": "هذا", "probability": 0.797119140625}, {"start": 2681.77, "end": 2682.77, "word": " سيعطيك", "probability": 0.7451171875}, {"start": 2682.77, "end": 2683.53, "word": " ان", "probability": 0.40283203125}, {"start": 2683.53, "end": 2684.41, "word": " ال", "probability": 0.6279296875}, {"start": 2684.41, "end": 2684.99, "word": " S", "probability": 0.10931396484375}, {"start": 2684.99, "end": 2685.97, "word": " أقل", "probability": 0.7688802083333334}, {"start": 2685.97, "end": 2686.21, "word": " من", "probability": 0.93896484375}, {"start": 2686.21, "end": 2686.55, "word": " او", "probability": 0.7271728515625}, {"start": 2686.55, "end": 2687.13, "word": " يساوي", "probability": 0.8553466796875}, {"start": 2687.13, "end": 2687.29, "word": " ال", "probability": 0.48291015625}, {"start": 2687.29, "end": 2687.53, "word": " T", "probability": 0.953125}, {"start": 2687.53, "end": 2688.53, "word": " ومعدل", "probability": 0.625244140625}, {"start": 2688.53, "end": 2689.05, "word": " رقم", "probability": 0.7920735677083334}, {"start": 2689.05, "end": 2689.31, "word": " 2", "probability": 0.78076171875}, {"start": 2689.31, "end": 2692.29, "word": " يبقى", "probability": 0.691162109375}, {"start": 2692.29, "end": 2692.59, "word": " باشر", "probability": 0.4463704427083333}, {"start": 2692.59, "end": 2692.95, "word": " بقول", "probability": 0.54595947265625}, {"start": 2692.95, "end": 2693.61, "word": " from", "probability": 0.75634765625}, {"start": 2693.61, "end": 2695.19, "word": " واحد", "probability": 0.88671875}], "temperature": 1.0}, {"id": 114, "seek": 271794, "start": 2697.12, "end": 2717.94, "text": "والاتنين يبقى T تساوي كده؟ ال S طب ال S هنا فرضه هو least common multiple و T هي الأقل يبقى اتنين ماله are equal و هو المفتوح يبقى بناء عليك بنكون برهنة النظرية و المرة جاها ان شاء الله بنكمل", "tokens": [2407, 6027, 9307, 1863, 9957, 7251, 3555, 4587, 7578, 314, 6055, 3794, 995, 45865, 9122, 3215, 3224, 22807, 2423, 318, 23032, 3555, 2423, 318, 34105, 6156, 43042, 3224, 31439, 1935, 2689, 3866, 4032, 314, 39896, 16247, 4587, 1211, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 3714, 6027, 3224, 366, 2681, 4032, 31439, 9673, 5172, 2655, 2407, 5016, 7251, 3555, 4587, 7578, 44945, 16606, 25894, 4117, 44945, 30544, 4724, 2288, 3224, 1863, 3660, 28239, 19913, 2288, 10632, 4032, 9673, 25720, 10874, 995, 11296, 16472, 13412, 16606, 21984, 44945, 24793, 1211], "avg_logprob": -0.34684066261563984, "compression_ratio": 1.6030927835051547, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2697.12, "end": 2698.0, "word": "والاتنين", "probability": 0.60302734375}, {"start": 2698.0, "end": 2698.88, "word": " يبقى", "probability": 0.900634765625}, {"start": 2698.88, "end": 2699.12, "word": " T", "probability": 0.459228515625}, {"start": 2699.12, "end": 2699.68, "word": " تساوي", "probability": 0.661376953125}, {"start": 2699.68, "end": 2700.5, "word": " كده؟", "probability": 0.5753173828125}, {"start": 2700.5, "end": 2701.38, "word": " ال", "probability": 0.319580078125}, {"start": 2701.38, "end": 2701.72, "word": " S", "probability": 0.80712890625}, {"start": 2701.72, "end": 2702.28, "word": " طب", "probability": 0.49462890625}, {"start": 2702.28, "end": 2702.42, "word": " ال", "probability": 0.94677734375}, {"start": 2702.42, "end": 2702.62, "word": " S", "probability": 0.9755859375}, {"start": 2702.62, "end": 2702.86, "word": " هنا", "probability": 0.88427734375}, {"start": 2702.86, "end": 2703.28, "word": " فرضه", "probability": 0.8824869791666666}, {"start": 2703.28, "end": 2703.46, "word": " هو", "probability": 0.87353515625}, {"start": 2703.46, "end": 2703.72, "word": " least", "probability": 0.466796875}, {"start": 2703.72, "end": 2704.06, "word": " common", "probability": 0.9599609375}, {"start": 2704.06, "end": 2704.66, "word": " multiple", "probability": 0.91162109375}, {"start": 2704.66, "end": 2705.2, "word": " و", "probability": 0.701171875}, {"start": 2705.2, "end": 2705.48, "word": " T", "probability": 0.5234375}, {"start": 2705.48, "end": 2705.68, "word": " هي", "probability": 0.88916015625}, {"start": 2705.68, "end": 2706.04, "word": " الأقل", "probability": 0.3683675130208333}, {"start": 2706.04, "end": 2706.4, "word": " يبقى", "probability": 0.878662109375}, {"start": 2706.4, "end": 2706.84, "word": " اتنين", "probability": 0.85577392578125}, {"start": 2706.84, "end": 2707.34, "word": " ماله", "probability": 0.5889485677083334}, {"start": 2707.34, "end": 2707.94, "word": " are", "probability": 0.71875}, {"start": 2707.94, "end": 2708.54, "word": " equal", "probability": 0.91796875}, {"start": 2708.54, "end": 2708.88, "word": " و", "probability": 0.469482421875}, {"start": 2708.88, "end": 2709.34, "word": " هو", "probability": 0.7470703125}, {"start": 2709.34, "end": 2710.26, "word": " المفتوح", "probability": 0.73134765625}, {"start": 2710.26, "end": 2711.02, "word": " يبقى", "probability": 0.9512939453125}, {"start": 2711.02, "end": 2711.32, "word": " بناء", "probability": 0.90087890625}, {"start": 2711.32, "end": 2712.04, "word": " عليك", "probability": 0.710205078125}, {"start": 2712.04, "end": 2712.56, "word": " بنكون", "probability": 0.796875}, {"start": 2712.56, "end": 2713.82, "word": " برهنة", "probability": 0.7544921875}, {"start": 2713.82, "end": 2715.28, "word": " النظرية", "probability": 0.82940673828125}, {"start": 2715.28, "end": 2715.9, "word": " و", "probability": 0.845703125}, {"start": 2715.9, "end": 2716.28, "word": " المرة", "probability": 0.78955078125}, {"start": 2716.28, "end": 2716.64, "word": " جاها", "probability": 0.5526529947916666}, {"start": 2716.64, "end": 2716.72, "word": " ان", "probability": 0.77734375}, {"start": 2716.72, "end": 2717.04, "word": " شاء", "probability": 0.907470703125}, {"start": 2717.04, "end": 2717.1, "word": " الله", "probability": 0.955078125}, {"start": 2717.1, "end": 2717.94, "word": " بنكمل", "probability": 0.9742838541666666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2719.33525, "duration_after_vad": 2585.4756249999873}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3cb4746b3f169251c45fd9b2a0b7f1380914232d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_postprocess.srt
@@ -0,0 +1,1640 @@
+1
+00:00:21,080 --> 00:00:24,480
+بسم الله الرحمن الرحيم سأكمل ما ابتدأنا به المرة
+
+2
+00:00:24,480 --> 00:00:31,120
+الماضية وهي النظرية المكونة من تسع نقاط أو من تسع
+
+3
+00:00:31,120 --> 00:00:35,140
+نقاط وصلنا إلى السابع والثامنة، بدي أحاول أدمج
+
+4
+00:00:35,140 --> 00:00:41,260
+التنتين بنقطة واحدة، النقطة الواحدة تتلخظ في أني
+
+5
+00:00:41,260 --> 00:00:45,160
+بدي أثبت أن Phi inverse of K bar عبارة عن normal
+
+6
+00:00:45,160 --> 00:00:49,810
+subgroup من ال group G، إذا أثبت نقطتينالنقطة
+
+7
+00:00:49,810 --> 00:00:56,090
+الأولى بدى أحاول أثبت أول شيء أنه الـ Phi inverse
+
+8
+00:00:56,090 --> 00:01:04,810
+of K bar هذي is a subgroup من G لذلك بدنا نروح
+
+9
+00:01:04,810 --> 00:01:10,270
+نثبت هذي أنها subgroup من G كالتالي النقطة الأولى
+
+10
+00:01:10,270 --> 00:01:17,290
+بروح بقوله Phi inverse of K bar is non-empty
+
+11
+00:01:18,030 --> 00:01:27,430
+مانأمتى ليش since او بدل since نقول because ..
+
+12
+00:01:27,430 --> 00:01:27,970
+because
+
+13
+00:01:31,280 --> 00:01:36,060
+الـ Phi of الـ Identity G بدل ساوي الـ Identity
+
+14
+00:01:36,060 --> 00:01:42,240
+تبع الـ G bar معناه هذا الكلام أن الـ Identity تبع
+
+15
+00:01:42,240 --> 00:01:48,880
+الـ G بدل ساوي Phi Inverse of الـ Identity Element
+
+16
+00:01:48,880 --> 00:01:55,580
+تبع الـ G bar وهذا الـ Element موجود في الجروب
+
+17
+00:01:55,580 --> 00:02:01,820
+اللي عندنا هذاوهذا موجود في الـ Phi inverse of K
+
+18
+00:02:01,820 --> 00:02:08,540
+bar بالشكل اللي عندنا بعدين افترض
+
+19
+00:02:08,540 --> 00:02:16,740
+ان ال X و ال Y موجودة في Phi inverse of K bar يبقى
+
+20
+00:02:16,740 --> 00:02:25,720
+thenالـ X هذي بيبقى تسوى في في انفرس of K1 for
+
+21
+00:02:25,720 --> 00:02:34,630
+some K1 اللي موجودة في K barوالـ y بدأت ساوي في
+
+22
+00:02:34,630 --> 00:02:45,030
+انفرس of k2 for some k2 اللي موجودة وين في k bar
+
+23
+00:02:45,030 --> 00:02:52,530
+كذلك من النقطتين هدول مع بعض بقدر اقول إذا في of x
+
+24
+00:02:52,530 --> 00:03:02,090
+بدأت ساوي k1 اللي موجودة في k bar andفاي واي بدها
+
+25
+00:03:02,090 --> 00:03:12,190
+تساوي كتو اللي موجودة في ك بارطيب هذه موجودة في كي
+
+26
+00:03:12,190 --> 00:03:18,450
+بار وكي بار هذه عبارة عن normal subgroup يبقى هذه
+
+27
+00:03:18,450 --> 00:03:24,310
+اللي وحدها بتعطيني مين بتعطيني انه في of y لكل
+
+28
+00:03:24,310 --> 00:03:34,850
+inverse اللي في of y inverse موجودة في كي بارطيب
+
+29
+00:03:34,850 --> 00:03:42,770
+تعالى ناخد في of x y inverse الفي همومورفزم يبقى
+
+30
+00:03:42,770 --> 00:03:53,400
+هذا في of x في في of y inverseالـ Phi of X موجودة
+
+31
+00:03:53,400 --> 00:04:01,640
+في K و Phi of Y موجودة في K يبقى هذا معناته ان هذه
+
+32
+00:04:01,640 --> 00:04:09,020
+كلها موجودة في K بار يبقى بناء عليه أصبح أن Phi of
+
+33
+00:04:09,020 --> 00:04:17,630
+X و Phi of Y موجود في K باريبقى لو أخدنا في انفرس
+
+34
+00:04:17,630 --> 00:04:26,250
+للطرفين بصير XY انفرس موجودة في في انفرس of K بار
+
+35
+00:04:26,250 --> 00:04:33,030
+وبالتالي أصبحت في انفرس of K عبارة عن subgroup
+
+36
+00:04:33,030 --> 00:04:41,970
+يبقى thus وهكذا في انفرس of K بار is a subgroup من
+
+37
+00:04:41,970 --> 00:04:47,510
+Gباقي علينا أن نثبت النقطة الثامنة وهي خاصية ال
+
+38
+00:04:47,510 --> 00:04:57,630
+normality يبقى أفترض أن جي موجود في جي and ال X
+
+39
+00:04:57,630 --> 00:05:04,530
+موجود في في انفرس of كي بار then
+
+40
+00:05:09,250 --> 00:05:16,810
+هذه معناها ايه؟ معناها ان جي موجودة في جي جي
+
+41
+00:05:16,810 --> 00:05:27,140
+موجودة في جي and في of اكس موجودة في كيباطب لو
+
+42
+00:05:27,140 --> 00:05:35,000
+أخدت له في of g x g inverse يبقى هذه بدأ تساوي في
+
+43
+00:05:35,000 --> 00:05:43,900
+of g في في of x في في of g inverse ليش؟ لأن في
+
+44
+00:05:43,900 --> 00:05:50,000
+عبارة عن homomorphismيبقى هذا الكلام بده يساوي في
+
+45
+00:05:50,000 --> 00:06:05,000
+اف جي وهذا في اف اكس وهذا في اف جي الكل انفرز خلي
+
+46
+00:06:05,000 --> 00:06:11,020
+بالك هنا الان في اف جي هذا ال element وين موجود ال
+
+47
+00:06:11,020 --> 00:06:17,330
+element الأول هذا في اي groupفي جي و لا في جي بار
+
+48
+00:06:17,330 --> 00:06:25,610
+في جي بار يبقى هذا belongs to جي بار belongs to جي
+
+49
+00:06:25,610 --> 00:06:33,170
+بار و ال five of x موجودة في كي بار و هذه موجودة
+
+50
+00:06:33,170 --> 00:06:37,190
+في كي بار بالشكل اللي عندنا
+
+51
+00:06:40,100 --> 00:06:47,320
+طيب و هذه وين موجودة؟ موجودة كذلك في جي با طيب ال
+
+52
+00:06:47,320 --> 00:06:52,280
+K bar هذه أصلا normal subgroup معطاة مدام normal
+
+53
+00:06:52,280 --> 00:07:00,020
+subgroup إذا كل هذا الكلام ماله وين موجود؟موجود في
+
+54
+00:07:00,020 --> 00:07:09,160
+K bar بالشكل لأن هذا ليش؟ sense لإن ال K bar عبارة
+
+55
+00:07:09,160 --> 00:07:15,860
+عن subgroup من ال G bar مع طيابإذا بناء عليه أصبح
+
+56
+00:07:15,860 --> 00:07:24,520
+عنده إيه؟ اللي هو الـPhi of G X G inverse موجود في
+
+57
+00:07:24,520 --> 00:07:31,820
+الـK bar معنى هذا الكلام إن الـG X G inverse موجود
+
+58
+00:07:31,820 --> 00:07:39,830
+في الـPhi inverse of K barيبقى بناء عليه أصبح أن
+
+59
+00:07:39,830 --> 00:07:47,690
+الـ Phi inverse of K bar is a normal subgroup من G
+
+60
+00:07:47,690 --> 00:07:53,300
+وانتهينا من هذه النقطةيبقى ده مقتصر النقطة السابعة
+
+61
+00:07:53,300 --> 00:08:02,040
+والثامنة مرة ثانية بدأ نيجي للنقطة التاسعة النقطة
+
+62
+00:08:02,040 --> 00:08:09,540
+التاسعة بتقول لي ما يأتي لو كانت في is unto في is
+
+63
+00:08:09,540 --> 00:08:18,880
+unto والكرن للفي بده يساوي ال identity elementثم
+
+64
+00:08:18,880 --> 00:08:24,680
+فاي هو ايزو مورفزم من
+
+65
+00:08:24,680 --> 00:08:27,820
+الـG
+
+66
+00:08:27,820 --> 00:08:35,140
+إلى الـG بارأنا لكي أثبت في ايزو مورفزم بدي أثبت
+
+67
+00:08:35,140 --> 00:08:39,820
+ثلاثة شروط one to one وانتوا وخاصية ال
+
+68
+00:08:39,820 --> 00:08:45,820
+homomorphism بقوله كويسة انتوا هيوم اعطينيها تمام
+
+69
+00:08:45,820 --> 00:08:51,020
+الفي قلي عنها من البداية هي homomorphism مش بقاش
+
+70
+00:08:51,020 --> 00:08:56,540
+dial علي اثبات fight one to one يبقى باجي بقول if
+
+71
+00:08:56,540 --> 00:09:07,830
+we show thatاللي هو five is one to one then we
+
+72
+00:09:07,830 --> 00:09:11,650
+have the result
+
+73
+00:09:13,650 --> 00:09:17,910
+يبقى لو أثبت أنه في one to one بكون وصلت إلى
+
+74
+00:09:17,910 --> 00:09:23,670
+النتيجة إذا بدأ أروح أخد صورتين متساويتين لأنصرين
+
+75
+00:09:23,670 --> 00:09:29,870
+وأثبت أن أصلهم متساوين يبقى بناء عليه بالداجة أقول
+
+76
+00:09:29,870 --> 00:09:40,900
+له assume أنه في of X بده يساوي في of Yطبعا إذا
+
+77
+00:09:40,900 --> 00:09:45,500
+قررت أثبت ان ال X تساوي الفي بكون تم المطلوب عندنا
+
+78
+00:09:45,500 --> 00:09:49,780
+then الان
+
+79
+00:09:49,780 --> 00:09:57,620
+لو جيت قلت الفي of X في الفي of Y inverse يعني
+
+80
+00:09:57,620 --> 00:10:01,740
+ضربت الطرفين في معكوس هذا ال element مين بدي
+
+81
+00:10:01,740 --> 00:10:07,910
+اعطيني يا شباب؟الـ Identity تبع من؟ تبع الـ G bar
+
+82
+00:10:07,910 --> 00:10:15,850
+هذا معناه ان Phi of X في Phi of Y inverse سوى الـ
+
+83
+00:10:15,850 --> 00:10:22,540
+Identity تبع الـ G barفى همومورفزم إذا برجع هذا
+
+84
+00:10:22,540 --> 00:10:28,880
+الى اصل فى of x y inverse بدي ساوى ال identity
+
+85
+00:10:28,880 --> 00:10:33,760
+element تبع ال g bar شو تفسيركوا لهذا الكلام
+
+86
+00:10:33,760 --> 00:10:40,820
+تفسيرنا لهذا الكلام ان ال x y inverse موجودة وينفي
+
+87
+00:10:40,820 --> 00:10:46,980
+الـKernel للفاي طب الكرنل لفاي كده يعطينا ال
+
+88
+00:10:46,980 --> 00:10:54,000
+identity يبقى هذا معناته ان ال X Y inverse موجودة
+
+89
+00:10:54,000 --> 00:10:58,600
+في الست اللي مافيه إلا ال identity elements يبقى
+
+90
+00:10:58,600 --> 00:11:03,780
+ال X Y inverse مين بدها تساويالـ Identity يبقى
+
+91
+00:11:03,780 --> 00:11:08,900
+بناء عليه تصير الـ X يساوي مين الـ Y يعني ضربنا
+
+92
+00:11:08,900 --> 00:11:13,340
+الطرفين من جهة اليمين في مين في الـ Y بنوصل إلى إن
+
+93
+00:11:13,340 --> 00:11:21,720
+الـ X تساوي الـ Y يبقى فهي Phi is one to one and
+
+94
+00:11:21,720 --> 00:11:30,210
+hence ومن ثم الـ Phi is an isomorphismone to one
+
+95
+00:11:30,210 --> 00:11:34,090
+أثبتناه
+
+96
+00:11:34,090 --> 00:11:39,450
+يبقى صارت هذه homomorphism يبقى هذه النقطة التاسعة
+
+97
+00:11:39,450 --> 00:11:51,690
+من النظرية يوجد كرولري عليها كرولري كرولري
+
+98
+00:11:51,690 --> 00:11:57,110
+بتقول ما يأتي بتقولت
+
+99
+00:12:00,860 --> 00:12:11,200
+الـ Phi لت الـ Phi من G إلى G bar بـ
+
+100
+00:12:11,200 --> 00:12:21,960
+homomorphism homomorphism ثم الكيرن للـ Phi عبارة
+
+101
+00:12:21,960 --> 00:12:26,960
+عن normal subgroup
+
+102
+00:12:26,960 --> 00:12:28,520
+من جهة G
+
+103
+00:12:33,470 --> 00:12:38,550
+يبقى نظرية مرة تانية في من جي إلى جي بار عبارة عن
+
+104
+00:12:38,550 --> 00:12:43,590
+homomorphism زي المعطى في أول نقطة في النظرية
+
+105
+00:12:43,590 --> 00:12:49,610
+السابقة قال هو من ثم الكيرنل بدنا نثبت انه normal
+
+106
+00:12:49,610 --> 00:12:53,570
+subgroup من جي يبقى لو عندي homomorphism ايش ما
+
+107
+00:12:53,570 --> 00:12:57,570
+يكون شكله يكون يبقى الكيرنل لهذا ال homomorphism
+
+108
+00:12:57,570 --> 00:13:03,560
+عبارة عن normal subgroup من جي السؤال هوهذا انا
+
+109
+00:13:03,560 --> 00:13:07,180
+بدي اثبت انه normal subgroup يعني ايش بدي اثبت
+
+110
+00:13:07,180 --> 00:13:11,920
+subgroup اولا ثم normal اظن subgroup اثبتناها في
+
+111
+00:13:11,920 --> 00:13:16,420
+النقطة الرابعة من النظرية الاولى شك كان اثبت ان ال
+
+112
+00:13:16,420 --> 00:13:27,630
+kernel subgroup يبقى هنا وapproved that أثبتنا إن
+
+113
+00:13:27,630 --> 00:13:38,690
+الـ kernel للـ Phi is a subgroup من جيب جهد part 4
+
+114
+00:13:38,690 --> 00:13:45,190
+of the first
+
+115
+00:13:45,190 --> 00:13:49,310
+theorem من
+
+116
+00:13:49,310 --> 00:13:54,830
+النظرية الأولىيبقى ليش يظل عليه نصف باتمين بس
+
+117
+00:13:54,830 --> 00:14:02,790
+normality يبقى بده اروح اخد ال G موجودة في G and
+
+118
+00:14:02,790 --> 00:14:13,190
+ال X موجودة في كيرن ال 5أحاول أن أثبت أن جي إكس جي
+
+119
+00:14:13,190 --> 00:14:17,670
+انفرس موجودة في كيرنا للفاي إن أثبتنا بكون تم
+
+120
+00:14:17,670 --> 00:14:24,390
+المطلوب طيب هذه معناها إيش ان جي موجودة في جي ان
+
+121
+00:14:24,390 --> 00:14:30,590
+لما تبقى موجودة في الفاي يبقى بصير الفاي of إكس
+
+122
+00:14:30,590 --> 00:14:31,110
+هذا كده
+
+123
+00:14:34,090 --> 00:14:42,790
+طبع الجي با طيب الان بدي اخد ال جي اكس جي انفرس
+
+124
+00:14:42,790 --> 00:14:49,290
+واخد لهم ال في شكل اللي عندنا هذا وشوف هذه لوين
+
+125
+00:14:49,290 --> 00:14:57,450
+بدها توصلنا في همومورفزم يبقى هذا في of جي في في
+
+126
+00:14:57,450 --> 00:15:08,050
+of اكس في في of جي انفرسأو انشئته فاقوله فاي اف جي
+
+127
+00:15:08,050 --> 00:15:17,710
+فاي اف جي طب الفاي اف اكسي بقداش بال identity يبقى
+
+128
+00:15:17,710 --> 00:15:24,470
+هذا هو ال identity تبع ال جي بار وهذا الفاي اف جي
+
+129
+00:15:24,470 --> 00:15:32,920
+لكل inverseطيب هذا بده يعطينا في of g في في of g
+
+130
+00:15:32,920 --> 00:15:39,320
+الكل inverse مين كمان بيعطينا طيب في لما انأثرت
+
+131
+00:15:39,320 --> 00:15:43,740
+على حصل الضرب ال three elements اعطاني ال identity
+
+132
+00:15:43,740 --> 00:15:48,420
+element تبع ال g bar يبقى هذا ال element موجود
+
+133
+00:15:48,420 --> 00:15:57,480
+وين؟ موجود في ال kernel تبع من؟ تبع ال فييبقى الـ
+
+134
+00:15:57,480 --> 00:16:04,460
+G X G Inverse موجود في الـ Kernel لـ Phi يبقى أيش
+
+135
+00:16:04,460 --> 00:16:09,340
+اللي حصل؟ أخدت Element من G و Element من الـ
+
+136
+00:16:09,340 --> 00:16:13,820
+Kernel و أثبت أنه حصل ضرب Element تبع الـ G في
+
+137
+00:16:13,820 --> 00:16:19,360
+معكس Element تبع الـ G موجود في الـ Kernel يبقى
+
+138
+00:16:19,360 --> 00:16:26,040
+هذا معناهإن الـ Kernel للـ Phi is a normal
+
+139
+00:16:26,040 --> 00:16:33,240
+subgroup من G وهو المطلوب يبقى من الآن فصاعد أنا
+
+140
+00:16:33,240 --> 00:16:39,460
+يا شباب طيب بدأ نيجي ناخد مثال على هذه النظرية
+
+141
+00:16:39,460 --> 00:16:46,100
+والـ Crawlery والنظرية اللي جابلها معاهم بيقول
+
+142
+00:16:46,100 --> 00:16:46,740
+define
+
+143
+00:16:49,950 --> 00:17:02,370
+فانكشن فاي من زد تمانتاشر إلى زد تمانتاش باي فاي
+
+144
+00:17:02,370 --> 00:17:12,490
+او اكس يساوي تلاتة اكس النقطة الأولى show that
+
+145
+00:17:20,670 --> 00:17:23,430
+النقطة الثانية
+
+146
+00:17:27,500 --> 00:17:39,880
+الـ Kernel للـ Phi and show that وبيلنا ان الـ Phi
+
+147
+00:17:39,880 --> 00:17:51,920
+is a تلاتة تون تلاتة تون تلاتة
+
+148
+00:17:51,920 --> 00:17:53,800
+تون function
+
+149
+00:17:56,780 --> 00:18:09,020
+النقطة التالتة find في انفرس of ستة النقطة الرابعة
+
+150
+00:18:09,020 --> 00:18:15,520
+show that ان
+
+151
+00:18:15,520 --> 00:18:21,160
+الفي of ال subgroup generated by تلاتة هي ال
+
+152
+00:18:21,160 --> 00:18:27,160
+subgroup generated by تسعةالنقطة الخامسة والأخيرة
+
+153
+00:18:27,160 --> 00:18:36,460
+Find ال order لل one and ال order لل five of one
+
+154
+00:18:36,460 --> 00:18:39,700
+على
+
+155
+00:18:39,700 --> 00:18:40,280
+أي حال
+
+156
+00:18:43,590 --> 00:18:48,970
+هنجي لسؤال مرة تانية قال لي عرف ال function في من
+
+157
+00:18:48,970 --> 00:18:56,830
+z 18 إلى z 18 بالشكل اللي قدامك هذا في of x بده
+
+158
+00:18:56,830 --> 00:18:59,510
+يساوي تلاتة x
+
+159
+00:19:03,530 --> 00:19:09,250
+و من خلال هذه ال function بدنا نروح نثبت ان هذه ال
+
+160
+00:19:09,250 --> 00:19:15,110
+function عبارة عن ايش عبارة عن homomorphism هذا
+
+161
+00:19:15,110 --> 00:19:21,330
+المطلوب الأول المطلوب الثاني بدنا نجيب ال kernel
+
+162
+00:19:21,330 --> 00:19:28,000
+لهذه ال function و نبين ان هذه ال functionهي تلاتة
+
+163
+00:19:28,000 --> 00:19:35,000
+to one يعني تلاتة عناصر صورتهم ال identity element
+
+164
+00:19:35,000 --> 00:19:42,020
+او بيروحوا لعنصر واحد فقط الأمر الرابع بدنا نقدش
+
+165
+00:19:42,020 --> 00:19:48,160
+Phi inverse of ستة بدنا نثبت ان Phi of ال subgroup
+
+166
+00:19:48,160 --> 00:19:52,100
+generated by تلاتة هي ال subgroup generated by
+
+167
+00:19:52,100 --> 00:19:57,220
+تسعة بعدين بدنا نجيب ال order للواحدوالـ order للـ
+
+168
+00:19:57,220 --> 00:20:00,660
+five of واحد يبقى solution
+
+169
+00:20:03,560 --> 00:20:07,720
+أريد أن أثبت أن في هذه عبارة عن homomorphism يبقى
+
+170
+00:20:07,720 --> 00:20:15,180
+لذلك تذهب تأخذ في of X في Y والله X زائد Y X زائد
+
+171
+00:20:15,180 --> 00:20:19,480
+Y لأن الوضع اللي عليه عملية جامعة حسب التعريف
+
+172
+00:20:19,480 --> 00:20:25,800
+تلاتة في X زائد Y يبقى تلاتة X زائد تلاتة Y يبقى
+
+173
+00:20:25,800 --> 00:20:32,500
+في of X زائد في of Y لذلك كانت هذه homomorphism
+
+174
+00:20:32,900 --> 00:20:39,460
+يبقى هذه هي النقطة الأولى نذهب للنقطة الثانية
+
+175
+00:20:39,460 --> 00:20:46,520
+جاليهات للكيرنل يبقى باجي بقوله الكيرنل للفاي كل
+
+176
+00:20:46,520 --> 00:20:54,140
+ال X اللي موجودة في ال Z 18 بحيث ان في of X بدي
+
+177
+00:20:54,140 --> 00:21:00,770
+سوى ال identity element تبع ال Z 18 اللي همينيبقى
+
+178
+00:21:00,770 --> 00:21:07,490
+كل ال X الموجودة في الـ Z 18 بحيث ان Phi of X هي
+
+179
+00:21:07,490 --> 00:21:13,230
+عبارة عن تلاتة X يساوي Zero إذا لما نقول تلاتة X
+
+180
+00:21:13,230 --> 00:21:20,170
+يساوي Zero إذا X تساوي Zeroبس والله هذا مش real
+
+181
+00:21:20,170 --> 00:21:24,010
+number عادية انت بتشتغل في group وليس في real
+
+182
+00:21:24,010 --> 00:21:30,590
+number عادية اذا هذا بده يساوي zero لان التلاتة في
+
+183
+00:21:30,590 --> 00:21:35,890
+zero تساوي zeroوكمان ستة لإنه ستة في تلاتة
+
+184
+00:21:35,890 --> 00:21:41,870
+بتمانتاش فيه زد تمانتاش بزيرو وكمان زيادة على ذلك
+
+185
+00:21:41,870 --> 00:21:46,510
+اتناش لإنه تلاتة في اتناش ستة و تلاتين جدت تمانتاش
+
+186
+00:21:46,510 --> 00:21:52,250
+مرتين يبقى ال zero في غيرهملأ ماعنديش يبقى هذا
+
+187
+00:21:52,250 --> 00:21:58,170
+الكيرن للـ Phi يبقى يا شباب هدول تلت عناصر ايش
+
+188
+00:21:58,170 --> 00:22:02,710
+صورتهم؟ Zero ال identity و من هنا ال function هي
+
+189
+00:22:02,710 --> 00:22:11,550
+تلتة to one يبقى هذا بده يعطيلك ان ال Phi is a
+
+190
+00:22:11,550 --> 00:22:16,170
+تلتة to one function
+
+191
+00:22:18,390 --> 00:22:23,930
+خلصنا النقطة الثانية النقطة التالتة النقطة التالتة
+
+192
+00:22:23,930 --> 00:22:32,310
+بيقول فاين فاينفرس of ستةأول امبارح اخدنا النقطة
+
+193
+00:22:32,310 --> 00:22:37,470
+السادسة في النظرية الأولى بيجينا نقول انه في انفرس
+
+194
+00:22:37,470 --> 00:22:41,790
+لو كان في اف جي بده يساوي ال جي برايم النقطة
+
+195
+00:22:41,790 --> 00:22:47,570
+السادسة عندك يبقى في انفرس اف جي برايم هو ال جي في
+
+196
+00:22:47,570 --> 00:22:53,620
+ال kernelأو بلغتنا هنا الجامعة يبقى يقول جي زائد
+
+197
+00:22:53,620 --> 00:22:59,220
+ال kernel بس بدنا نعرف مين هي جي هذه يبقى احنا
+
+198
+00:22:59,220 --> 00:23:06,480
+عندنا الفاي inverse of ستة الفاي inverse of ستة
+
+199
+00:23:06,480 --> 00:23:14,320
+تعني اللي هو ال X زائد ال kernel للفاي تمام؟
+
+200
+00:23:15,590 --> 00:23:20,470
+طيب خلّي هذه المعلومة على شجة إحنا عندنا الـ Phi
+
+201
+00:23:20,470 --> 00:23:27,590
+inverse of 6 أبصر إيش تساوي؟ كويس؟ يبقى لو قلت
+
+202
+00:23:27,590 --> 00:23:34,450
+تساوي X على سبيل المثال إذا هذا بده يعطينا أن Phi
+
+203
+00:23:34,450 --> 00:23:42,830
+of X بده يساوي قداش 6 طب ال Phi of X مين هي؟ تلاتة
+
+204
+00:23:42,830 --> 00:23:49,180
+Xيبقى تلاتة X يسوى ستة إذا ال X بده يسوى قداش
+
+205
+00:23:49,180 --> 00:23:56,860
+اتنين يبقى بناء عليه صار عند ال Phi inverse of ستة
+
+206
+00:23:56,860 --> 00:24:02,820
+بده يسوى ال X اللي هو اللي اتنين زائد ال kernel ال
+
+207
+00:24:02,820 --> 00:24:08,000
+kernel حسبناه اللي هو Zero وستة واطناش يبقى
+
+208
+00:24:08,000 --> 00:24:15,890
+النتيجة اتنين و تمانية واربعتاشيبقى معناته في عندي
+
+209
+00:24:15,890 --> 00:24:21,030
+تلت عناصر كانت صورتهم ستة اللي هو main اللي هو
+
+210
+00:24:21,030 --> 00:24:25,090
+اتنين والتمانية والاربعتاش يبقى five of اتنين
+
+211
+00:24:25,090 --> 00:24:29,370
+يساوي ستة وfive of تمانية يساوي ستة وfive of
+
+212
+00:24:29,370 --> 00:24:35,320
+اربعتاش يساوي كمان ستة وبالتالي حسبنا له الهمامالـ
+
+213
+00:24:35,320 --> 00:24:39,720
+Phi inverse of 6 طبعا في بعض الطلاب ممكن يشتغل
+
+214
+00:24:39,720 --> 00:24:44,820
+غلط، يشتغل غلط كيف؟ يقول ليه؟ يبقى Phi inverse of
+
+215
+00:24:44,820 --> 00:24:50,920
+6 بدي أقول يساوي X إذا الستة تساوي Phi of X إذا
+
+216
+00:24:50,920 --> 00:24:55,240
+Phi of X هي تلاتة X يساوي ستة إذا ال X يساوي جداش
+
+217
+00:24:55,240 --> 00:25:01,830
+اتنين إذا Phi inverse of 6 يساوي اتنين، مظبوط؟يبقى
+
+218
+00:25:01,830 --> 00:25:05,990
+احنا استخدمنا التعريف اللي قال عليه في of x تلاتة
+
+219
+00:25:05,990 --> 00:25:11,130
+x للوصول الى مين الى الشكل المطلوب يبقى هذا النقطة
+
+220
+00:25:11,130 --> 00:25:17,230
+تالتة بنروح للنقطة الرابعة جالي اثبتلي ان في of ال
+
+221
+00:25:17,230 --> 00:25:21,830
+subgroup generated by تلاتة بده يساوي ال subgroup
+
+222
+00:25:21,830 --> 00:25:26,970
+generated by تسعة بقوله النقطة الرابعة كتالة
+
+223
+00:25:29,450 --> 00:25:33,350
+بقى ليه بقى لك كده احنا بدنا نروح نجيبله ال
+
+224
+00:25:33,350 --> 00:25:37,330
+subgroup generated by تلاتة مين هي يا جماعة؟ Zero
+
+225
+00:25:37,330 --> 00:25:45,170
+و تلاتة و ستة و تسعة و اتناش و خمستاشر يبقى هذا من
+
+226
+00:25:45,170 --> 00:25:50,570
+هذا ال subgroup اللي عندنا الان لما يقول لي five
+
+227
+00:25:50,570 --> 00:25:55,690
+of ال subgroup generated by تلاتة حسب التعريف اللي
+
+228
+00:25:55,690 --> 00:26:00,460
+احنا جايله انه يبقى تلاتةفي الـ subgroup generated
+
+229
+00:26:00,460 --> 00:26:05,360
+by تلاتة اللي هو الـ zero تلاتة و ستة وتسعة و
+
+230
+00:26:05,360 --> 00:26:12,480
+اتناش و خمستاشر تمام؟ طيب نشوف هذه مين بدها تعطينا
+
+231
+00:26:12,480 --> 00:26:18,350
+تلاتة في zero بقداشعلى الجامعة، ماشي، بس هذه ضرب
+
+232
+00:26:18,350 --> 00:26:23,930
+تلاتة في ايه؟ لما اقول لك تلاتة في زيرو يعني كأنه
+
+233
+00:26:23,930 --> 00:26:28,810
+.. كأنه تلاتة في مية المية هذا المقصود فيها، يبقى
+
+234
+00:26:28,810 --> 00:26:34,770
+zero الان لما انا اجي تلاتة في تلاتة بقداش؟ بتسعة،
+
+235
+00:26:34,770 --> 00:26:39,620
+طب تلاتة في ستة؟18 تقريبا تقريبا تقريبا تقريبا
+
+236
+00:26:39,620 --> 00:26:47,040
+تقريبا تقريبا
+
+237
+00:26:47,040 --> 00:26:50,460
+تقريبا
+
+238
+00:26:50,460 --> 00:26:52,500
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+239
+00:26:52,500 --> 00:26:52,940
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+240
+00:26:52,940 --> 00:26:53,040
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+241
+00:26:53,040 --> 00:26:55,120
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+242
+00:26:55,120 --> 00:27:02,400
+تقريبا تقريبا تقريالضرب كله هيجيب لي ال two
+
+243
+00:27:02,400 --> 00:27:07,720
+elements هدول يبقى هذه هي ال subgroup generated by
+
+244
+00:27:07,720 --> 00:27:13,540
+تسعة مافيش غيرها، ليش؟ لأنه لما أقول تسعة تربيع
+
+245
+00:27:13,540 --> 00:27:18,960
+يبقى بواحد و تمانين، واحد و تمانين على تمانتاش
+
+246
+00:27:18,960 --> 00:27:25,760
+فيها الخمسة، ولا لا؟ صح؟كيف؟ جامع تسعة وتسعة
+
+247
+00:27:25,760 --> 00:27:27,700
+تمانتاش جامع تسعة تمانتاش تسعة تمانتاش تسعة
+
+248
+00:27:27,700 --> 00:27:31,900
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+249
+00:27:31,900 --> 00:27:35,680
+تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة
+
+250
+00:27:35,680 --> 00:27:35,720
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+251
+00:27:35,720 --> 00:27:36,140
+تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة
+
+252
+00:27:36,140 --> 00:27:37,120
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+253
+00:27:37,120 --> 00:27:39,960
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+254
+00:27:39,960 --> 00:27:49,290
+تسعة تمانتاش تسعة تمانتاش تسالنقطة الخامسة بيقول
+
+255
+00:27:49,290 --> 00:27:52,990
+find the order لل one وال order لل five of one ال
+
+256
+00:27:52,990 --> 00:27:59,010
+one هذا وين موجودزي الـ 18 الـ one هذا موجود في
+
+257
+00:27:59,010 --> 00:28:03,970
+الـ z تمانتاش يبقى ال order لل one جداش تحت عملية
+
+258
+00:28:03,970 --> 00:28:09,510
+الجمل هو تمانتاش طيب نيجي للي بعده بدنا ال order
+
+259
+00:28:09,510 --> 00:28:14,090
+لل five of one السؤال هو ما علاقة ال order بال
+
+260
+00:28:14,090 --> 00:28:18,190
+five of one بيقسم يبقى ال order تبع ال five of one
+
+261
+00:28:18,190 --> 00:28:22,970
+بدي يقسم ال order تبع ال one يعني بدي يكون قاسم لل
+
+262
+00:28:22,970 --> 00:28:27,440
+تمانتاشيبقى ال order لل five of one يا واحد، يا
+
+263
+00:28:27,440 --> 00:28:33,260
+اتنين، يا تلاتة، يا ستة، يا تسعة، يا تبنتاش، واحد
+
+264
+00:28:33,260 --> 00:28:37,080
+من هدول طب واحد اللي هو بدي اعرف منه و بنقول له
+
+265
+00:28:37,080 --> 00:28:43,860
+بسيط جدا عندك انت ال five of one قداشه سوى تلاتة
+
+266
+00:28:43,860 --> 00:28:48,690
+في one اللي هو بتلاتةمش هيك التعريف تبع الفاي يبقى
+
+267
+00:28:48,690 --> 00:28:55,110
+التلاتة التلاتة وين موجودة كمان في Z 18 موجودة في
+
+268
+00:28:55,110 --> 00:29:01,870
+Z 18 يبقى هذا بدي اعطيك ان ال order للفاي of one
+
+269
+00:29:01,870 --> 00:29:06,990
+هو ال order لتلاتة هو قداش
+
+270
+00:29:09,110 --> 00:29:14,130
+القصة التي تضعها تدور بضعف ستة يبقى الـ order يسوى
+
+271
+00:29:14,130 --> 00:29:19,430
+كم؟ يسوى ستة لأنه ستة في تلاتة أو تلاتة أست ستة
+
+272
+00:29:19,430 --> 00:29:24,270
+تعني ستة في تلاتة اللي هو بقى داشر بطمنتاش اللي هو
+
+273
+00:29:24,270 --> 00:29:29,050
+ال identity element ال zero يبقى هذا هو أول رقم
+
+274
+00:29:29,050 --> 00:29:33,050
+بحطه قصة التلاتة بيطلع ال identity يبقى ال order
+
+275
+00:29:33,050 --> 00:29:39,800
+يسوى ستة وزي ما انت شايف الستة بتجسمينبتجسم الـ 18
+
+276
+00:29:39,800 --> 00:29:46,680
+يبقى هذا مثال على النظريتين في آن واحد بدنا نيجي
+
+277
+00:29:46,680 --> 00:29:55,560
+لكمان نظرية اسمها ال first theorem اللي
+
+278
+00:29:55,560 --> 00:30:03,040
+هي ال first isomorphism
+
+279
+00:30:03,040 --> 00:30:04,500
+theorem
+
+280
+00:30:08,360 --> 00:30:17,800
+النظرية هذه بتقول ما يأتي let الـ Phi be a group
+
+281
+00:30:17,800 --> 00:30:26,840
+homomorphism from G
+
+282
+00:30:26,840 --> 00:30:34,280
+to G bar then the mapping then
+
+283
+00:30:44,170 --> 00:30:56,170
+معرفة من G موديول الـ Kernel للـ Phi إلى إلى من؟
+
+284
+00:30:56,170 --> 00:31:06,450
+إلى الـ Phi of capital G كلها given by والمعطى
+
+285
+00:31:06,450 --> 00:31:15,460
+Bipsi of G في الـ kernel للـ Phi بدي ساوي الـ Phi
+
+286
+00:31:15,460 --> 00:31:26,520
+of G يبقى هذا كله بدي ساوي الـ Phi of G is an
+
+287
+00:31:26,520 --> 00:31:36,710
+isomorphism that is ان الـ Gموديول الكيرني للـ Phi
+
+288
+00:31:36,710 --> 00:31:42,410
+ايزو مورف اكلمين للـ Phi of capital G
+
+289
+00:32:39,840 --> 00:32:45,640
+طيب نرجع للنظرية مرة تانية النظرية
+
+290
+00:32:45,640 --> 00:32:54,840
+بتقول لي لو كان عندنا five a group homomorphism
+
+291
+00:32:54,840 --> 00:33:00,900
+from G ل G bar ماقلش G و G bar groups هدول لكن أنا
+
+292
+00:33:00,900 --> 00:33:05,400
+بفهم انه groups من خلال قللي group homomorphism
+
+293
+00:33:05,400 --> 00:33:09,900
+يعني مش function بين two sets، بين two groupsيبقى
+
+294
+00:33:09,900 --> 00:33:14,020
+لو قللت الـPhi بـA جروب همومورفزم من G لـG bar أو
+
+295
+00:33:14,020 --> 00:33:18,640
+قللت Phi بـA همومورفزم from the group G to the
+
+296
+00:33:18,640 --> 00:33:22,940
+group G bar اتنين نفس النص تمام؟ يبقى then the
+
+297
+00:33:22,940 --> 00:33:27,780
+mapping ابصى من الـG kernel Phi للـPhi of G معرفة
+
+298
+00:33:27,780 --> 00:33:33,760
+بـPhi of الـleft coset الجي في ال kernel للـPhi
+
+299
+00:33:33,760 --> 00:33:38,300
+بده يساوي Phi of G is an isomorphismيعني اتنين
+
+300
+00:33:38,300 --> 00:33:43,480
+هذول are isomorphic لبعض وهي ال function معرفة
+
+301
+00:33:43,480 --> 00:33:48,280
+عندنا بالشكل اللي عندنا هذا طبعا واضح ان جي في
+
+302
+00:33:48,280 --> 00:33:52,280
+الكيرن اللي هو left coset اذا موجود في ال group
+
+303
+00:33:52,280 --> 00:33:58,780
+هذه في of small جي موجود في في كابتل او في في of
+
+304
+00:33:58,780 --> 00:34:05,520
+جي كابتل لان جي small موجودة في جي كابتلسنثبت هذه
+
+305
+00:34:05,520 --> 00:34:10,780
+عبارة عن isomorphism بس كونها left cosets هذه يبقى
+
+306
+00:34:10,780 --> 00:34:15,780
+الخطوة الأولى نثبت أن هذه ال function معرفة يعني
+
+307
+00:34:15,780 --> 00:34:21,600
+هذا التعريف تعريف صحيح يبقى أول ما أبدأ أقول له if
+
+308
+00:34:21,600 --> 00:34:32,390
+psi is well defined يبقى معرفة تعريفا سليمامشان
+
+309
+00:34:32,390 --> 00:34:41,350
+هيك بروح أخد عنصرين متساويين أفترض أفترض
+
+310
+00:34:41,350 --> 00:34:50,670
+أن ال X في الكيرنل للفاي بدي يساوي ال Y في الكيرنل
+
+311
+00:34:50,670 --> 00:34:56,910
+للفاي إذا كنت أثبت أن فاي of X بدي يساوي فاي of Y
+
+312
+00:34:56,910 --> 00:35:01,290
+بتم المطلوب يبقى then
+
+313
+00:35:06,420 --> 00:35:13,420
+يبقى لو جيت هنا ضربت من جهة الشمال في Y inverse او
+
+314
+00:35:13,420 --> 00:35:18,340
+في X inverse سيان الاتنين نفس الشيء يبقى لو ضربت
+
+315
+00:35:18,340 --> 00:35:25,120
+في Y inverse بصير Y inverse X في كيرنل الفاي بده
+
+316
+00:35:25,120 --> 00:35:32,300
+يسوى كيرنل الفاي ايش تفسيرك لهذه العبارة؟ يبقى
+
+317
+00:35:32,300 --> 00:35:39,920
+thenاللي هو main Y inverse X موجود في كيرن الـ Phi
+
+318
+00:35:39,920 --> 00:35:47,760
+يعني معناه هذا الكلام أن Phi of Y inverse X بديه
+
+319
+00:35:47,760 --> 00:35:55,210
+ساوي الـ Identity element تبع الـ G barهذا معناه
+
+320
+00:35:55,210 --> 00:36:04,190
+ايه؟ معناه ان الـ Phi of Y inverse في الـ Phi of X
+
+321
+00:36:04,190 --> 00:36:09,830
+بدي سوى الـ Identity Element تبع الـ G bar هذا
+
+322
+00:36:09,830 --> 00:36:17,830
+معناه ان Phi of Y الكل inverse في الـ Phi of X بدي
+
+323
+00:36:17,830 --> 00:36:25,220
+سوى الـ Identity Element تبع الـ G barهذا معناه ان
+
+324
+00:36:25,220 --> 00:36:32,000
+اضرب من جهة الشمال في الـPhi Y يبقى Phi of X بده
+
+325
+00:36:32,000 --> 00:36:38,780
+يساوي Phi of Y جينا على هذه المعادلة ضربنا من جهة
+
+326
+00:36:38,780 --> 00:36:44,270
+الشمال في Phi of Yهذه بيصير الـ Identity تبع الـ G
+
+327
+00:36:44,270 --> 00:36:49,870
+bar مع الـ Phi of X بالـ Phi of X وهنا الـ Phi of
+
+328
+00:36:49,870 --> 00:36:53,990
+Y مع الـ Identity تبع الـ G bar بيعطينا من الـ Phi
+
+329
+00:36:53,990 --> 00:36:59,250
+Y يبقى أصبع عندي Phi of X بدي يسوي Phi of Y يبقى
+
+330
+00:36:59,250 --> 00:37:05,160
+بناء عليه الدالة معرفة تعريفا سالماأريد أن أثبت له
+
+331
+00:37:05,160 --> 00:37:10,760
+أن الـipsi is one to one يعني أنه يريد أن يذهب
+
+332
+00:37:10,760 --> 00:37:21,600
+ويأخذ صورتين متساويتين أعتبر ذلك الـipsi أو جي في
+
+333
+00:37:21,600 --> 00:37:29,100
+الكيرن اللالفايبدا تساوي .. والله خلّيها X X في ال
+
+334
+00:37:29,100 --> 00:37:35,340
+kernel لفاي بده يساوي A بصي في ال Y في ال kernel
+
+335
+00:37:35,340 --> 00:37:41,220
+لفاي إذا استطعنا إنه نثبت X في ال kernel تساوي Y
+
+336
+00:37:41,220 --> 00:37:45,860
+في ال kernel بيكون ال A بصي صارت معاها one to one
+
+337
+00:37:45,860 --> 00:37:55,640
+يبقى thenهذه معناها إن الـPhi of X دي ساوة الـPhi
+
+338
+00:37:55,640 --> 00:38:05,120
+of Y هذا معناه لو ضربت في معكوس الـPhi of Y يبقى
+
+339
+00:38:05,120 --> 00:38:12,620
+إيش بيصير عندي الـPhi of X في الـPhi of Y الكل
+
+340
+00:38:12,620 --> 00:38:17,600
+inverse بدي ساوة الـidentity element تبع الـG bar
+
+341
+00:38:18,390 --> 00:38:26,390
+أو اللي هو main هكذا يصبح XY inverse في الـA بدي
+
+342
+00:38:26,390 --> 00:38:33,130
+أضرب بدل A هي هضربناها من جهة من .. لأ بدي أضربها
+
+343
+00:38:33,130 --> 00:38:39,950
+من جهة الشمال وليس من جهة اليمين عشان تظبط معنات
+
+344
+00:38:39,950 --> 00:38:47,060
+هي بدي أضربهامن جهة الشمال يبقى بدى اخد الان في of
+
+345
+00:38:47,060 --> 00:38:53,680
+Y الكل inverse في في of X دي سوى ال identity
+
+346
+00:38:53,680 --> 00:38:59,940
+element تبع ال G bar هذا بده يعطينا هذه نقدر نزلها
+
+347
+00:38:59,940 --> 00:39:08,240
+جوا يبقى بصير فيPhi of Y inverse في Phi of X يسوى
+
+348
+00:39:08,240 --> 00:39:15,800
+الـ Identity Element تبع الـ G bar هذا معناته أن
+
+349
+00:39:15,800 --> 00:39:23,980
+Phi of Y inverse في X يسوى الـ Identity Element
+
+350
+00:39:23,980 --> 00:39:29,590
+تبع الـ G bar لأن Phi عبارة عن Homomorphismهذا
+
+351
+00:39:29,590 --> 00:39:37,130
+معناه إيه؟ معناته إن الـ Y inverse X موجودة في الـ
+
+352
+00:39:37,130 --> 00:39:41,530
+kernel تبع الـ Phi لأن الصورتة بتعطينا الـ
+
+353
+00:39:41,530 --> 00:39:46,040
+identity element تبع الـ G barما دام موجودة في الـ
+
+354
+00:39:46,040 --> 00:39:52,560
+Kernel يبقى بيصير Y inverse X في ال Kernel للـ Phi
+
+355
+00:39:52,560 --> 00:39:58,260
+بده يساوي ال Kernel للـ Phi نفسه لأن ال subgroup
+
+356
+00:39:58,260 --> 00:40:02,920
+لما أضربها ب element منها بتعطيني نفس ال subgroup
+
+357
+00:40:02,920 --> 00:40:09,280
+طيب نضرب الطرفين في Y يبقى X في ال Kernel للـ Phi
+
+358
+00:40:09,280 --> 00:40:17,020
+بده يساوي Yفي الـ Kern المهم للـ Phi وهو ال مطلوب
+
+359
+00:40:17,020 --> 00:40:26,520
+يبقى بنا نيجي لإبصي as all يبقى بالداجة أقوله احنا
+
+360
+00:40:26,520 --> 00:40:33,950
+عندنا الإبصي ما هو طابلاتالـ X موجودة في Phi of
+
+361
+00:40:33,950 --> 00:40:43,550
+capital G then الـ X بدها تساوي Phi of G for some
+
+362
+00:40:43,550 --> 00:40:50,510
+G اللي موجودة في G Capitalيبقى الـ X اللي أخدتها
+
+363
+00:40:50,510 --> 00:40:56,770
+بدها تساوي Phi of G Small هذه بقدر أقول حسب الـ
+
+364
+00:40:56,770 --> 00:41:03,770
+Definition هي Psi G في الـ Kern للـ Phi لذلك Psi
+
+365
+00:41:03,770 --> 00:41:10,370
+is Unto One to one وUnto معرفة ضال عندي أخر نقطة
+
+366
+00:41:10,370 --> 00:41:15,110
+Psi is Homomorphism
+
+367
+00:41:16,290 --> 00:41:21,350
+Homomorphism وبالتالي بيصير isomorphism تمام؟ يبقى
+
+368
+00:41:21,350 --> 00:41:28,170
+homomorphism بتاخد إبصي لحاصل ضرب عددين الأول two
+
+369
+00:41:28,170 --> 00:41:34,850
+elements X في الكرن اللال فيفي الـY في الـKernel
+
+370
+00:41:34,850 --> 00:41:40,090
+للـPhi مش عددين وإنما two elements موجودات في
+
+371
+00:41:40,090 --> 00:41:45,510
+الـFactor A group هذا الكلام بده يساوي بـPsi of
+
+372
+00:41:45,510 --> 00:41:50,290
+هذا الـLeft Cosetة وهذا الـLeft Cosetة وقبل شوية
+
+373
+00:41:50,290 --> 00:41:54,770
+قولنا الـKernel هي normal subgroup إذا بناء عليه
+
+374
+00:41:54,770 --> 00:42:02,590
+بصير الـXY في الـKernel للـPhiطيب بـ Psi لما تأثر
+
+375
+00:42:02,590 --> 00:42:08,130
+على هذا بتعطينا mean Phi of X في Y Phi
+
+376
+00:42:08,130 --> 00:42:16,090
+homomorphism يبقى Phi of X في Phi of Y Phi of X
+
+377
+00:42:16,090 --> 00:42:21,300
+هذه اللي هي عبارة عالمياًاللي هي Epsi للـ X في الـ
+
+378
+00:42:21,300 --> 00:42:27,300
+Kernel للـ Phi وهذه Epsi Y في الـ Kernel للـ Phi
+
+379
+00:42:27,300 --> 00:42:36,420
+يبقى دص وهكذا Epsi is an isomorphism يبقى بناءً
+
+380
+00:42:36,420 --> 00:42:41,660
+على Epsi اللي عرفناها هذه طلعت من الـ G موديو للـ
+
+381
+00:42:41,660 --> 00:42:46,800
+Kernelللـ Phi of G عبارة عن أيش؟ Isomorphism فى
+
+382
+00:42:46,800 --> 00:42:56,920
+نتيجة بسيطة عليها Krullery الكرولرة
+
+383
+00:42:56,920 --> 00:43:10,100
+بتقول ما ياتى if الـ Phi is a homomorphism from a
+
+384
+00:43:10,100 --> 00:43:11,420
+finite
+
+385
+00:43:14,140 --> 00:43:21,220
+فاي نايت اجروب
+
+386
+00:43:21,220 --> 00:43:32,900
+جي تو جي بار then then
+
+387
+00:43:32,900 --> 00:43:42,380
+ال order للفاي of جي ال order of five divides
+
+388
+00:44:04,160 --> 00:44:09,500
+الكتاب مش انبرهنه احنا بنحاول انبرهنها برضه ال
+
+389
+00:44:09,500 --> 00:44:14,280
+proof خلّي
+
+390
+00:44:14,280 --> 00:44:22,310
+برا كدهالآن الـ Phi of G هو subgroup من الـ G bar
+
+391
+00:44:22,310 --> 00:44:28,050
+ولا لا؟ يبقى
+
+392
+00:44:28,050 --> 00:44:31,290
+هي subgroup، يبقى ال order اللي بيكسب ال order لل
+
+393
+00:44:31,290 --> 00:44:37,630
+group يبقى هذا معناه ان ال order لل Phi of G
+
+394
+00:44:37,630 --> 00:44:43,810
+divide ال order لمن؟ ل G bar يبقى خلصنا من هذه
+
+395
+00:44:44,690 --> 00:44:49,790
+تمام؟ بدنا نيجي للتانية التانية بدي أحاول أستخدمها
+
+396
+00:44:49,790 --> 00:45:00,510
+من النظرية احنا from and from the previous
+
+397
+00:45:02,610 --> 00:45:08,730
+Theorem من الـ Previous Theorem عندك الـ order للـ
+
+398
+00:45:08,730 --> 00:45:17,610
+G موديول الكيرن للـ Phi بده يساوي ال order للـ Phi
+
+399
+00:45:17,610 --> 00:45:25,050
+of G مش هذه isomorphic لهذه إذا ال order لهذه بده
+
+400
+00:45:25,050 --> 00:45:30,510
+يساوي ال order لهذه هذا معناه إيه؟ هذه تعني ال
+
+401
+00:45:30,510 --> 00:45:36,880
+order تبع ال Gمقسوما على ال order تبع الكرنل للفاي
+
+402
+00:45:36,880 --> 00:45:45,480
+بدي ساوي ال order للفاي of G بالشكل اللي عندنا طيب
+
+403
+00:45:45,480 --> 00:45:52,040
+لو ضربناها بصير عندنا مين بصير عندنا ان ال order
+
+404
+00:45:52,040 --> 00:45:59,640
+لل Gبدي ساوي ال order للكرن للـ Phi في ال order
+
+405
+00:45:59,640 --> 00:46:08,960
+للـ Phi of G هذا معناه ان ال order للـ Phi of G
+
+406
+00:46:08,960 --> 00:46:13,020
+divide ال order لـ G وهو المطلوب
+
+407
+00:46:16,800 --> 00:46:21,100
+يبقى أحاول أن أثبت الكرولري من خلال main من خلال
+
+408
+00:46:21,100 --> 00:46:24,560
+النتيجة يوم الأربعاء ان شاء الله بتكون المحاضرة
+
+409
+00:46:24,560 --> 00:46:30,680
+الأخيرة التي بها ننهي هذا section وحنحاول نحل أكثر
+
+410
+00:46:30,680 --> 00:46:33,460
+من سؤال على شكل أمثلة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..21cbf2b0442a2e122cdd6fa6c39d0119170a8ee1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.srt
@@ -0,0 +1,1648 @@
+1
+00:00:21,080 --> 00:00:24,480
+بسم الله الرحمن الرحيم سأكمل ما ابتدأنا به المرة
+
+2
+00:00:24,480 --> 00:00:31,120
+الماضية وهي النظرية المكونة من تسع نقاط أو من تسع
+
+3
+00:00:31,120 --> 00:00:35,140
+نقاط وصلنا إلى السابع والثامنة، بدي أحاول أدمج
+
+4
+00:00:35,140 --> 00:00:41,260
+التنتين بنقطة واحدة، النقطة الواحدة تتلخظ في أني
+
+5
+00:00:41,260 --> 00:00:45,160
+بدي أثبت أن Phi inverse of K bar عبارة عن normal
+
+6
+00:00:45,160 --> 00:00:49,810
+subgroup من ال group G، إذا أثبت نقطتينالنقطة
+
+7
+00:00:49,810 --> 00:00:56,090
+الأولى بدى أحاول أثبت أول شيء أنه الـ Phi inverse
+
+8
+00:00:56,090 --> 00:01:04,810
+of K bar هذي is a subgroup من G لذلك بدنا نروح
+
+9
+00:01:04,810 --> 00:01:10,270
+نثبت هذي أنها subgroup من G كالتالي النقطة الأولى
+
+10
+00:01:10,270 --> 00:01:17,290
+بروح بقوله Phi inverse of K bar is non-empty
+
+11
+00:01:18,030 --> 00:01:27,430
+مانأمتى ليش since او بدل since نقول because ..
+
+12
+00:01:27,430 --> 00:01:27,970
+because
+
+13
+00:01:31,280 --> 00:01:36,060
+الـ Phi of الـ Identity G بدل ساوي الـ Identity
+
+14
+00:01:36,060 --> 00:01:42,240
+تبع الـ G bar معناه هذا الكلام أن الـ Identity تبع
+
+15
+00:01:42,240 --> 00:01:48,880
+الـ G بدل ساوي Phi Inverse of الـ Identity Element
+
+16
+00:01:48,880 --> 00:01:55,580
+تبع الـ G bar وهذا الـ Element موجود في الجروب
+
+17
+00:01:55,580 --> 00:02:01,820
+اللي عندنا هذاوهذا موجود في الـ Phi inverse of K
+
+18
+00:02:01,820 --> 00:02:08,540
+bar بالشكل اللي عندنا بعدين افترض
+
+19
+00:02:08,540 --> 00:02:16,740
+ان ال X و ال Y موجودة في Phi inverse of K bar يبقى
+
+20
+00:02:16,740 --> 00:02:25,720
+thenالـ X هذي بيبقى تسوى في في انفرس of K1 for
+
+21
+00:02:25,720 --> 00:02:34,630
+some K1 اللي موجودة في K barوالـ y بدأت ساوي في
+
+22
+00:02:34,630 --> 00:02:45,030
+انفرس of k2 for some k2 اللي موجودة وين في k bar
+
+23
+00:02:45,030 --> 00:02:52,530
+كذلك من النقطتين هدول مع بعض بقدر اقول إذا في of x
+
+24
+00:02:52,530 --> 00:03:02,090
+بدأت ساوي k1 اللي موجودة في k bar andفاي واي بدها
+
+25
+00:03:02,090 --> 00:03:12,190
+تساوي كتو اللي موجودة في ك بارطيب هذه موجودة في كي
+
+26
+00:03:12,190 --> 00:03:18,450
+بار وكي بار هذه عبارة عن normal subgroup يبقى هذه
+
+27
+00:03:18,450 --> 00:03:24,310
+اللي وحدها بتعطيني مين بتعطيني انه في of y لكل
+
+28
+00:03:24,310 --> 00:03:34,850
+inverse اللي في of y inverse موجودة في كي بارطيب
+
+29
+00:03:34,850 --> 00:03:42,770
+تعالى ناخد في of x y inverse الفي همومورفزم يبقى
+
+30
+00:03:42,770 --> 00:03:53,400
+هذا في of x في في of y inverseالـ Phi of X موجودة
+
+31
+00:03:53,400 --> 00:04:01,640
+في K و Phi of Y موجودة في K يبقى هذا معناته ان هذه
+
+32
+00:04:01,640 --> 00:04:09,020
+كلها موجودة في K بار يبقى بناء عليه أصبح أن Phi of
+
+33
+00:04:09,020 --> 00:04:17,630
+X و Phi of Y موجود في K باريبقى لو أخدنا في انفرس
+
+34
+00:04:17,630 --> 00:04:26,250
+للطرفين بصير XY انفرس موجودة في في انفرس of K بار
+
+35
+00:04:26,250 --> 00:04:33,030
+وبالتالي أصبحت في انفرس of K عبارة عن subgroup
+
+36
+00:04:33,030 --> 00:04:41,970
+يبقى thus وهكذا في انفرس of K بار is a subgroup من
+
+37
+00:04:41,970 --> 00:04:47,510
+Gباقي علينا أن نثبت النقطة الثامنة وهي خاصية ال
+
+38
+00:04:47,510 --> 00:04:57,630
+normality يبقى أفترض أن جي موجود في جي and ال X
+
+39
+00:04:57,630 --> 00:05:04,530
+موجود في في انفرس of كي بار then
+
+40
+00:05:09,250 --> 00:05:16,810
+هذه معناها ايه؟ معناها ان جي موجودة في جي جي
+
+41
+00:05:16,810 --> 00:05:27,140
+موجودة في جي and في of اكس موجودة في كيباطب لو
+
+42
+00:05:27,140 --> 00:05:35,000
+أخدت له في of g x g inverse يبقى هذه بدأ تساوي في
+
+43
+00:05:35,000 --> 00:05:43,900
+of g في في of x في في of g inverse ليش؟ لأن في
+
+44
+00:05:43,900 --> 00:05:50,000
+عبارة عن homomorphismيبقى هذا الكلام بده يساوي في
+
+45
+00:05:50,000 --> 00:06:05,000
+اف جي وهذا في اف اكس وهذا في اف جي الكل انفرز خلي
+
+46
+00:06:05,000 --> 00:06:11,020
+بالك هنا الان في اف جي هذا ال element وين موجود ال
+
+47
+00:06:11,020 --> 00:06:17,330
+element الأول هذا في اي groupفي جي و لا في جي بار
+
+48
+00:06:17,330 --> 00:06:25,610
+في جي بار يبقى هذا belongs to جي بار belongs to جي
+
+49
+00:06:25,610 --> 00:06:33,170
+بار و ال five of x موجودة في كي بار و هذه موجودة
+
+50
+00:06:33,170 --> 00:06:37,190
+في كي بار بالشكل اللي عندنا
+
+51
+00:06:40,100 --> 00:06:47,320
+طيب و هذه وين موجودة؟ موجودة كذلك في جي با طيب ال
+
+52
+00:06:47,320 --> 00:06:52,280
+K bar هذه أصلا normal subgroup معطاة مدام normal
+
+53
+00:06:52,280 --> 00:07:00,020
+subgroup إذا كل هذا الكلام ماله وين موجود؟موجود في
+
+54
+00:07:00,020 --> 00:07:09,160
+K bar بالشكل لأن هذا ليش؟ sense لإن ال K bar عبارة
+
+55
+00:07:09,160 --> 00:07:15,860
+عن subgroup من ال G bar مع طيابإذا بناء عليه أصبح
+
+56
+00:07:15,860 --> 00:07:24,520
+عنده إيه؟ اللي هو الـPhi of G X G inverse موجود في
+
+57
+00:07:24,520 --> 00:07:31,820
+الـK bar معنى هذا الكلام إن الـG X G inverse موجود
+
+58
+00:07:31,820 --> 00:07:39,830
+في الـPhi inverse of K barيبقى بناء عليه أصبح أن
+
+59
+00:07:39,830 --> 00:07:47,690
+الـ Phi inverse of K bar is a normal subgroup من G
+
+60
+00:07:47,690 --> 00:07:53,300
+وانتهينا من هذه النقطةيبقى ده مقتصر النقطة السابعة
+
+61
+00:07:53,300 --> 00:08:02,040
+والثامنة مرة ثانية بدأ نيجي للنقطة التاسعة النقطة
+
+62
+00:08:02,040 --> 00:08:09,540
+التاسعة بتقول لي ما يأتي لو كانت في is unto في is
+
+63
+00:08:09,540 --> 00:08:18,880
+unto والكرن للفي بده يساوي ال identity elementثم
+
+64
+00:08:18,880 --> 00:08:24,680
+فاي هو ايزو مورفزم من
+
+65
+00:08:24,680 --> 00:08:27,820
+الـG
+
+66
+00:08:27,820 --> 00:08:35,140
+إلى الـG بارأنا لكي أثبت في ايزو مورفزم بدي أثبت
+
+67
+00:08:35,140 --> 00:08:39,820
+ثلاثة شروط one to one وانتوا وخاصية ال
+
+68
+00:08:39,820 --> 00:08:45,820
+homomorphism بقوله كويسة انتوا هيوم اعطينيها تمام
+
+69
+00:08:45,820 --> 00:08:51,020
+الفي قلي عنها من البداية هي homomorphism مش بقاش
+
+70
+00:08:51,020 --> 00:08:56,540
+dial علي اثبات fight one to one يبقى باجي بقول if
+
+71
+00:08:56,540 --> 00:09:07,830
+we show thatاللي هو five is one to one then we
+
+72
+00:09:07,830 --> 00:09:11,650
+have the result
+
+73
+00:09:13,650 --> 00:09:17,910
+يبقى لو أثبت أنه في one to one بكون وصلت إلى
+
+74
+00:09:17,910 --> 00:09:23,670
+النتيجة إذا بدأ أروح أخد صورتين متساويتين لأنصرين
+
+75
+00:09:23,670 --> 00:09:29,870
+وأثبت أن أصلهم متساوين يبقى بناء عليه بالداجة أقول
+
+76
+00:09:29,870 --> 00:09:40,900
+له assume أنه في of X بده يساوي في of Yطبعا إذا
+
+77
+00:09:40,900 --> 00:09:45,500
+قررت أثبت ان ال X تساوي الفي بكون تم المطلوب عندنا
+
+78
+00:09:45,500 --> 00:09:49,780
+then الان
+
+79
+00:09:49,780 --> 00:09:57,620
+لو جيت قلت الفي of X في الفي of Y inverse يعني
+
+80
+00:09:57,620 --> 00:10:01,740
+ضربت الطرفين في معكوس هذا ال element مين بدي
+
+81
+00:10:01,740 --> 00:10:07,910
+اعطيني يا شباب؟الـ Identity تبع من؟ تبع الـ G bar
+
+82
+00:10:07,910 --> 00:10:15,850
+هذا معناه ان Phi of X في Phi of Y inverse سوى الـ
+
+83
+00:10:15,850 --> 00:10:22,540
+Identity تبع الـ G barفى همومورفزم إذا برجع هذا
+
+84
+00:10:22,540 --> 00:10:28,880
+الى اصل فى of x y inverse بدي ساوى ال identity
+
+85
+00:10:28,880 --> 00:10:33,760
+element تبع ال g bar شو تفسيركوا لهذا الكلام
+
+86
+00:10:33,760 --> 00:10:40,820
+تفسيرنا لهذا الكلام ان ال x y inverse موجودة وينفي
+
+87
+00:10:40,820 --> 00:10:46,980
+الـKernel للفاي طب الكرنل لفاي كده يعطينا ال
+
+88
+00:10:46,980 --> 00:10:54,000
+identity يبقى هذا معناته ان ال X Y inverse موجودة
+
+89
+00:10:54,000 --> 00:10:58,600
+في الست اللي مافيه إلا ال identity elements يبقى
+
+90
+00:10:58,600 --> 00:11:03,780
+ال X Y inverse مين بدها تساويالـ Identity يبقى
+
+91
+00:11:03,780 --> 00:11:08,900
+بناء عليه تصير الـ X يساوي مين الـ Y يعني ضربنا
+
+92
+00:11:08,900 --> 00:11:13,340
+الطرفين من جهة اليمين في مين في الـ Y بنوصل إلى إن
+
+93
+00:11:13,340 --> 00:11:21,720
+الـ X تساوي الـ Y يبقى فهي Phi is one to one and
+
+94
+00:11:21,720 --> 00:11:30,210
+hence ومن ثم الـ Phi is an isomorphismone to one
+
+95
+00:11:30,210 --> 00:11:34,090
+أثبتناه
+
+96
+00:11:34,090 --> 00:11:39,450
+يبقى صارت هذه homomorphism يبقى هذه النقطة التاسعة
+
+97
+00:11:39,450 --> 00:11:51,690
+من النظرية يوجد كرولري عليها كرولري كرولري
+
+98
+00:11:51,690 --> 00:11:57,110
+بتقول ما يأتي بتقولت
+
+99
+00:12:00,860 --> 00:12:11,200
+الـ Phi لت الـ Phi من G إلى G bar بـ
+
+100
+00:12:11,200 --> 00:12:21,960
+homomorphism homomorphism ثم الكيرن للـ Phi عبارة
+
+101
+00:12:21,960 --> 00:12:26,960
+عن normal subgroup
+
+102
+00:12:26,960 --> 00:12:28,520
+من جهة G
+
+103
+00:12:33,470 --> 00:12:38,550
+يبقى نظرية مرة تانية في من جي إلى جي بار عبارة عن
+
+104
+00:12:38,550 --> 00:12:43,590
+homomorphism زي المعطى في أول نقطة في النظرية
+
+105
+00:12:43,590 --> 00:12:49,610
+السابقة قال هو من ثم الكيرنل بدنا نثبت انه normal
+
+106
+00:12:49,610 --> 00:12:53,570
+subgroup من جي يبقى لو عندي homomorphism ايش ما
+
+107
+00:12:53,570 --> 00:12:57,570
+يكون شكله يكون يبقى الكيرنل لهذا ال homomorphism
+
+108
+00:12:57,570 --> 00:13:03,560
+عبارة عن normal subgroup من جي السؤال هوهذا انا
+
+109
+00:13:03,560 --> 00:13:07,180
+بدي اثبت انه normal subgroup يعني ايش بدي اثبت
+
+110
+00:13:07,180 --> 00:13:11,920
+subgroup اولا ثم normal اظن subgroup اثبتناها في
+
+111
+00:13:11,920 --> 00:13:16,420
+النقطة الرابعة من النظرية الاولى شك كان اثبت ان ال
+
+112
+00:13:16,420 --> 00:13:27,630
+kernel subgroup يبقى هنا وapproved that أثبتنا إن
+
+113
+00:13:27,630 --> 00:13:38,690
+الـ kernel للـ Phi is a subgroup من جيب جهد part 4
+
+114
+00:13:38,690 --> 00:13:45,190
+of the first
+
+115
+00:13:45,190 --> 00:13:49,310
+theorem من
+
+116
+00:13:49,310 --> 00:13:54,830
+النظرية الأولىيبقى ليش يظل عليه نصف باتمين بس
+
+117
+00:13:54,830 --> 00:14:02,790
+normality يبقى بده اروح اخد ال G موجودة في G and
+
+118
+00:14:02,790 --> 00:14:13,190
+ال X موجودة في كيرن ال 5أحاول أن أثبت أن جي إكس جي
+
+119
+00:14:13,190 --> 00:14:17,670
+انفرس موجودة في كيرنا للفاي إن أثبتنا بكون تم
+
+120
+00:14:17,670 --> 00:14:24,390
+المطلوب طيب هذه معناها إيش ان جي موجودة في جي ان
+
+121
+00:14:24,390 --> 00:14:30,590
+لما تبقى موجودة في الفاي يبقى بصير الفاي of إكس
+
+122
+00:14:30,590 --> 00:14:31,110
+هذا كده
+
+123
+00:14:34,090 --> 00:14:42,790
+طبع الجي با طيب الان بدي اخد ال جي اكس جي انفرس
+
+124
+00:14:42,790 --> 00:14:49,290
+واخد لهم ال في شكل اللي عندنا هذا وشوف هذه لوين
+
+125
+00:14:49,290 --> 00:14:57,450
+بدها توصلنا في همومورفزم يبقى هذا في of جي في في
+
+126
+00:14:57,450 --> 00:15:08,050
+of اكس في في of جي انفرسأو انشئته فاقوله فاي اف جي
+
+127
+00:15:08,050 --> 00:15:17,710
+فاي اف جي طب الفاي اف اكسي بقداش بال identity يبقى
+
+128
+00:15:17,710 --> 00:15:24,470
+هذا هو ال identity تبع ال جي بار وهذا الفاي اف جي
+
+129
+00:15:24,470 --> 00:15:32,920
+لكل inverseطيب هذا بده يعطينا في of g في في of g
+
+130
+00:15:32,920 --> 00:15:39,320
+الكل inverse مين كمان بيعطينا طيب في لما انأثرت
+
+131
+00:15:39,320 --> 00:15:43,740
+على حصل الضرب ال three elements اعطاني ال identity
+
+132
+00:15:43,740 --> 00:15:48,420
+element تبع ال g bar يبقى هذا ال element موجود
+
+133
+00:15:48,420 --> 00:15:57,480
+وين؟ موجود في ال kernel تبع من؟ تبع ال فييبقى الـ
+
+134
+00:15:57,480 --> 00:16:04,460
+G X G Inverse موجود في الـ Kernel لـ Phi يبقى أيش
+
+135
+00:16:04,460 --> 00:16:09,340
+اللي حصل؟ أخدت Element من G و Element من الـ
+
+136
+00:16:09,340 --> 00:16:13,820
+Kernel و أثبت أنه حصل ضرب Element تبع الـ G في
+
+137
+00:16:13,820 --> 00:16:19,360
+معكس Element تبع الـ G موجود في الـ Kernel يبقى
+
+138
+00:16:19,360 --> 00:16:26,040
+هذا معناهإن الـ Kernel للـ Phi is a normal
+
+139
+00:16:26,040 --> 00:16:33,240
+subgroup من G وهو المطلوب يبقى من الآن فصاعد أنا
+
+140
+00:16:33,240 --> 00:16:39,460
+يا شباب طيب بدأ نيجي ناخد مثال على هذه النظرية
+
+141
+00:16:39,460 --> 00:16:46,100
+والـ Crawlery والنظرية اللي جابلها معاهم بيقول
+
+142
+00:16:46,100 --> 00:16:46,740
+define
+
+143
+00:16:49,950 --> 00:17:02,370
+فانكشن فاي من زد تمانتاشر إلى زد تمانتاش باي فاي
+
+144
+00:17:02,370 --> 00:17:12,490
+او اكس يساوي تلاتة اكس النقطة الأولى show that
+
+145
+00:17:20,670 --> 00:17:23,430
+النقطة الثانية
+
+146
+00:17:27,500 --> 00:17:39,880
+الـ Kernel للـ Phi and show that وبيلنا ان الـ Phi
+
+147
+00:17:39,880 --> 00:17:51,920
+is a تلاتة تون تلاتة تون تلاتة
+
+148
+00:17:51,920 --> 00:17:53,800
+تون function
+
+149
+00:17:56,780 --> 00:18:09,020
+النقطة التالتة find في انفرس of ستة النقطة الرابعة
+
+150
+00:18:09,020 --> 00:18:15,520
+show that ان
+
+151
+00:18:15,520 --> 00:18:21,160
+الفي of ال subgroup generated by تلاتة هي ال
+
+152
+00:18:21,160 --> 00:18:27,160
+subgroup generated by تسعةالنقطة الخامسة والأخيرة
+
+153
+00:18:27,160 --> 00:18:36,460
+Find ال order لل one and ال order لل five of one
+
+154
+00:18:36,460 --> 00:18:39,700
+على
+
+155
+00:18:39,700 --> 00:18:40,280
+أي حال
+
+156
+00:18:43,590 --> 00:18:48,970
+هنجي لسؤال مرة تانية قال لي عرف ال function في من
+
+157
+00:18:48,970 --> 00:18:56,830
+z 18 إلى z 18 بالشكل اللي قدامك هذا في of x بده
+
+158
+00:18:56,830 --> 00:18:59,510
+يساوي تلاتة x
+
+159
+00:19:03,530 --> 00:19:09,250
+و من خلال هذه ال function بدنا نروح نثبت ان هذه ال
+
+160
+00:19:09,250 --> 00:19:15,110
+function عبارة عن ايش عبارة عن homomorphism هذا
+
+161
+00:19:15,110 --> 00:19:21,330
+المطلوب الأول المطلوب الثاني بدنا نجيب ال kernel
+
+162
+00:19:21,330 --> 00:19:28,000
+لهذه ال function و نبين ان هذه ال functionهي تلاتة
+
+163
+00:19:28,000 --> 00:19:35,000
+to one يعني تلاتة عناصر صورتهم ال identity element
+
+164
+00:19:35,000 --> 00:19:42,020
+او بيروحوا لعنصر واحد فقط الأمر الرابع بدنا نقدش
+
+165
+00:19:42,020 --> 00:19:48,160
+Phi inverse of ستة بدنا نثبت ان Phi of ال subgroup
+
+166
+00:19:48,160 --> 00:19:52,100
+generated by تلاتة هي ال subgroup generated by
+
+167
+00:19:52,100 --> 00:19:57,220
+تسعة بعدين بدنا نجيب ال order للواحدوالـ order للـ
+
+168
+00:19:57,220 --> 00:20:00,660
+five of واحد يبقى solution
+
+169
+00:20:03,560 --> 00:20:07,720
+أريد أن أثبت أن في هذه عبارة عن homomorphism يبقى
+
+170
+00:20:07,720 --> 00:20:15,180
+لذلك تذهب تأخذ في of X في Y والله X زائد Y X زائد
+
+171
+00:20:15,180 --> 00:20:19,480
+Y لأن الوضع اللي عليه عملية جامعة حسب التعريف
+
+172
+00:20:19,480 --> 00:20:25,800
+تلاتة في X زائد Y يبقى تلاتة X زائد تلاتة Y يبقى
+
+173
+00:20:25,800 --> 00:20:32,500
+في of X زائد في of Y لذلك كانت هذه homomorphism
+
+174
+00:20:32,900 --> 00:20:39,460
+يبقى هذه هي النقطة الأولى نذهب للنقطة الثانية
+
+175
+00:20:39,460 --> 00:20:46,520
+جاليهات للكيرنل يبقى باجي بقوله الكيرنل للفاي كل
+
+176
+00:20:46,520 --> 00:20:54,140
+ال X اللي موجودة في ال Z 18 بحيث ان في of X بدي
+
+177
+00:20:54,140 --> 00:21:00,770
+سوى ال identity element تبع ال Z 18 اللي همينيبقى
+
+178
+00:21:00,770 --> 00:21:07,490
+كل ال X الموجودة في الـ Z 18 بحيث ان Phi of X هي
+
+179
+00:21:07,490 --> 00:21:13,230
+عبارة عن تلاتة X يساوي Zero إذا لما نقول تلاتة X
+
+180
+00:21:13,230 --> 00:21:20,170
+يساوي Zero إذا X تساوي Zeroبس والله هذا مش real
+
+181
+00:21:20,170 --> 00:21:24,010
+number عادية انت بتشتغل في group وليس في real
+
+182
+00:21:24,010 --> 00:21:30,590
+number عادية اذا هذا بده يساوي zero لان التلاتة في
+
+183
+00:21:30,590 --> 00:21:35,890
+zero تساوي zeroوكمان ستة لإنه ستة في تلاتة
+
+184
+00:21:35,890 --> 00:21:41,870
+بتمانتاش فيه زد تمانتاش بزيرو وكمان زيادة على ذلك
+
+185
+00:21:41,870 --> 00:21:46,510
+اتناش لإنه تلاتة في اتناش ستة و تلاتين جدت تمانتاش
+
+186
+00:21:46,510 --> 00:21:52,250
+مرتين يبقى ال zero في غيرهملأ ماعنديش يبقى هذا
+
+187
+00:21:52,250 --> 00:21:58,170
+الكيرن للـ Phi يبقى يا شباب هدول تلت عناصر ايش
+
+188
+00:21:58,170 --> 00:22:02,710
+صورتهم؟ Zero ال identity و من هنا ال function هي
+
+189
+00:22:02,710 --> 00:22:11,550
+تلتة to one يبقى هذا بده يعطيلك ان ال Phi is a
+
+190
+00:22:11,550 --> 00:22:16,170
+تلتة to one function
+
+191
+00:22:18,390 --> 00:22:23,930
+خلصنا النقطة الثانية النقطة التالتة النقطة التالتة
+
+192
+00:22:23,930 --> 00:22:32,310
+بيقول فاين فاينفرس of ستةأول امبارح اخدنا النقطة
+
+193
+00:22:32,310 --> 00:22:37,470
+السادسة في النظرية الأولى بيجينا نقول انه في انفرس
+
+194
+00:22:37,470 --> 00:22:41,790
+لو كان في اف جي بده يساوي ال جي برايم النقطة
+
+195
+00:22:41,790 --> 00:22:47,570
+السادسة عندك يبقى في انفرس اف جي برايم هو ال جي في
+
+196
+00:22:47,570 --> 00:22:53,620
+ال kernelأو بلغتنا هنا الجامعة يبقى يقول جي زائد
+
+197
+00:22:53,620 --> 00:22:59,220
+ال kernel بس بدنا نعرف مين هي جي هذه يبقى احنا
+
+198
+00:22:59,220 --> 00:23:06,480
+عندنا الفاي inverse of ستة الفاي inverse of ستة
+
+199
+00:23:06,480 --> 00:23:14,320
+تعني اللي هو ال X زائد ال kernel للفاي تمام؟
+
+200
+00:23:15,590 --> 00:23:20,470
+طيب خلّي هذه المعلومة على شجة إحنا عندنا الـ Phi
+
+201
+00:23:20,470 --> 00:23:27,590
+inverse of 6 أبصر إيش تساوي؟ كويس؟ يبقى لو قلت
+
+202
+00:23:27,590 --> 00:23:34,450
+تساوي X على سبيل المثال إذا هذا بده يعطينا أن Phi
+
+203
+00:23:34,450 --> 00:23:42,830
+of X بده يساوي قداش 6 طب ال Phi of X مين هي؟ تلاتة
+
+204
+00:23:42,830 --> 00:23:49,180
+Xيبقى تلاتة X يسوى ستة إذا ال X بده يسوى قداش
+
+205
+00:23:49,180 --> 00:23:56,860
+اتنين يبقى بناء عليه صار عند ال Phi inverse of ستة
+
+206
+00:23:56,860 --> 00:24:02,820
+بده يسوى ال X اللي هو اللي اتنين زائد ال kernel ال
+
+207
+00:24:02,820 --> 00:24:08,000
+kernel حسبناه اللي هو Zero وستة واطناش يبقى
+
+208
+00:24:08,000 --> 00:24:15,890
+النتيجة اتنين و تمانية واربعتاشيبقى معناته في عندي
+
+209
+00:24:15,890 --> 00:24:21,030
+تلت عناصر كانت صورتهم ستة اللي هو main اللي هو
+
+210
+00:24:21,030 --> 00:24:25,090
+اتنين والتمانية والاربعتاش يبقى five of اتنين
+
+211
+00:24:25,090 --> 00:24:29,370
+يساوي ستة وfive of تمانية يساوي ستة وfive of
+
+212
+00:24:29,370 --> 00:24:35,320
+اربعتاش يساوي كمان ستة وبالتالي حسبنا له الهمامالـ
+
+213
+00:24:35,320 --> 00:24:39,720
+Phi inverse of 6 طبعا في بعض الطلاب ممكن يشتغل
+
+214
+00:24:39,720 --> 00:24:44,820
+غلط، يشتغل غلط كيف؟ يقول ليه؟ يبقى Phi inverse of
+
+215
+00:24:44,820 --> 00:24:50,920
+6 بدي أقول يساوي X إذا الستة تساوي Phi of X إذا
+
+216
+00:24:50,920 --> 00:24:55,240
+Phi of X هي تلاتة X يساوي ستة إذا ال X يساوي جداش
+
+217
+00:24:55,240 --> 00:25:01,830
+اتنين إذا Phi inverse of 6 يساوي اتنين، مظبوط؟يبقى
+
+218
+00:25:01,830 --> 00:25:05,990
+احنا استخدمنا التعريف اللي قال عليه في of x تلاتة
+
+219
+00:25:05,990 --> 00:25:11,130
+x للوصول الى مين الى الشكل المطلوب يبقى هذا النقطة
+
+220
+00:25:11,130 --> 00:25:17,230
+تالتة بنروح للنقطة الرابعة جالي اثبتلي ان في of ال
+
+221
+00:25:17,230 --> 00:25:21,830
+subgroup generated by تلاتة بده يساوي ال subgroup
+
+222
+00:25:21,830 --> 00:25:26,970
+generated by تسعة بقوله النقطة الرابعة كتالة
+
+223
+00:25:29,450 --> 00:25:33,350
+بقى ليه بقى لك كده احنا بدنا نروح نجيبله ال
+
+224
+00:25:33,350 --> 00:25:37,330
+subgroup generated by تلاتة مين هي يا جماعة؟ Zero
+
+225
+00:25:37,330 --> 00:25:45,170
+و تلاتة و ستة و تسعة و اتناش و خمستاشر يبقى هذا من
+
+226
+00:25:45,170 --> 00:25:50,570
+هذا ال subgroup اللي عندنا الان لما يقول لي five
+
+227
+00:25:50,570 --> 00:25:55,690
+of ال subgroup generated by تلاتة حسب التعريف اللي
+
+228
+00:25:55,690 --> 00:26:00,460
+احنا جايله انه يبقى تلاتةفي الـ subgroup generated
+
+229
+00:26:00,460 --> 00:26:05,360
+by تلاتة اللي هو الـ zero تلاتة و ستة وتسعة و
+
+230
+00:26:05,360 --> 00:26:12,480
+اتناش و خمستاشر تمام؟ طيب نشوف هذه مين بدها تعطينا
+
+231
+00:26:12,480 --> 00:26:18,350
+تلاتة في zero بقداشعلى الجامعة، ماشي، بس هذه ضرب
+
+232
+00:26:18,350 --> 00:26:23,930
+تلاتة في ايه؟ لما اقول لك تلاتة في زيرو يعني كأنه
+
+233
+00:26:23,930 --> 00:26:28,810
+.. كأنه تلاتة في مية المية هذا المقصود فيها، يبقى
+
+234
+00:26:28,810 --> 00:26:34,770
+zero الان لما انا اجي تلاتة في تلاتة بقداش؟ بتسعة،
+
+235
+00:26:34,770 --> 00:26:39,620
+طب تلاتة في ستة؟18 تقريبا تقريبا تقريبا تقريبا
+
+236
+00:26:39,620 --> 00:26:47,040
+تقريبا تقريبا
+
+237
+00:26:47,040 --> 00:26:50,460
+تقريبا
+
+238
+00:26:50,460 --> 00:26:52,500
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+239
+00:26:52,500 --> 00:26:52,940
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+240
+00:26:52,940 --> 00:26:53,040
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+241
+00:26:53,040 --> 00:26:53,040
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+242
+00:26:53,040 --> 00:26:55,120
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+243
+00:26:55,120 --> 00:27:02,400
+تقريبا تقريبا تقريالضرب كله هيجيب لي ال two
+
+244
+00:27:02,400 --> 00:27:07,720
+elements هدول يبقى هذه هي ال subgroup generated by
+
+245
+00:27:07,720 --> 00:27:13,540
+تسعة مافيش غيرها، ليش؟ لأنه لما أقول تسعة تربيع
+
+246
+00:27:13,540 --> 00:27:18,960
+يبقى بواحد و تمانين، واحد و تمانين على تمانتاش
+
+247
+00:27:18,960 --> 00:27:25,760
+فيها الخمسة، ولا لا؟ صح؟كيف؟ جامع تسعة وتسعة
+
+248
+00:27:25,760 --> 00:27:27,700
+تمانتاش جامع تسعة تمانتاش تسعة تمانتاش تسعة
+
+249
+00:27:27,700 --> 00:27:31,900
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+250
+00:27:31,900 --> 00:27:35,680
+تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة
+
+251
+00:27:35,680 --> 00:27:35,720
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+252
+00:27:35,720 --> 00:27:36,140
+تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة
+
+253
+00:27:36,140 --> 00:27:37,120
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+254
+00:27:37,120 --> 00:27:37,120
+تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة
+
+255
+00:27:37,120 --> 00:27:39,960
+تمانتاش تسعة تمانتاش تسعة تمانتاش تسعة تمانتاش
+
+256
+00:27:39,960 --> 00:27:49,290
+تسعة تمانتاش تسعة تمانتاش تسالنقطة الخامسة بيقول
+
+257
+00:27:49,290 --> 00:27:52,990
+find the order لل one وال order لل five of one ال
+
+258
+00:27:52,990 --> 00:27:59,010
+one هذا وين موجودزي الـ 18 الـ one هذا موجود في
+
+259
+00:27:59,010 --> 00:28:03,970
+الـ z تمانتاش يبقى ال order لل one جداش تحت عملية
+
+260
+00:28:03,970 --> 00:28:09,510
+الجمل هو تمانتاش طيب نيجي للي بعده بدنا ال order
+
+261
+00:28:09,510 --> 00:28:14,090
+لل five of one السؤال هو ما علاقة ال order بال
+
+262
+00:28:14,090 --> 00:28:18,190
+five of one بيقسم يبقى ال order تبع ال five of one
+
+263
+00:28:18,190 --> 00:28:22,970
+بدي يقسم ال order تبع ال one يعني بدي يكون قاسم لل
+
+264
+00:28:22,970 --> 00:28:27,440
+تمانتاشيبقى ال order لل five of one يا واحد، يا
+
+265
+00:28:27,440 --> 00:28:33,260
+اتنين، يا تلاتة، يا ستة، يا تسعة، يا تبنتاش، واحد
+
+266
+00:28:33,260 --> 00:28:37,080
+من هدول طب واحد اللي هو بدي اعرف منه و بنقول له
+
+267
+00:28:37,080 --> 00:28:43,860
+بسيط جدا عندك انت ال five of one قداشه سوى تلاتة
+
+268
+00:28:43,860 --> 00:28:48,690
+في one اللي هو بتلاتةمش هيك التعريف تبع الفاي يبقى
+
+269
+00:28:48,690 --> 00:28:55,110
+التلاتة التلاتة وين موجودة كمان في Z 18 موجودة في
+
+270
+00:28:55,110 --> 00:29:01,870
+Z 18 يبقى هذا بدي اعطيك ان ال order للفاي of one
+
+271
+00:29:01,870 --> 00:29:06,990
+هو ال order لتلاتة هو قداش
+
+272
+00:29:09,110 --> 00:29:14,130
+القصة التي تضعها تدور بضعف ستة يبقى الـ order يسوى
+
+273
+00:29:14,130 --> 00:29:19,430
+كم؟ يسوى ستة لأنه ستة في تلاتة أو تلاتة أست ستة
+
+274
+00:29:19,430 --> 00:29:24,270
+تعني ستة في تلاتة اللي هو بقى داشر بطمنتاش اللي هو
+
+275
+00:29:24,270 --> 00:29:29,050
+ال identity element ال zero يبقى هذا هو أول رقم
+
+276
+00:29:29,050 --> 00:29:33,050
+بحطه قصة التلاتة بيطلع ال identity يبقى ال order
+
+277
+00:29:33,050 --> 00:29:39,800
+يسوى ستة وزي ما انت شايف الستة بتجسمينبتجسم الـ 18
+
+278
+00:29:39,800 --> 00:29:46,680
+يبقى هذا مثال على النظريتين في آن واحد بدنا نيجي
+
+279
+00:29:46,680 --> 00:29:55,560
+لكمان نظرية اسمها ال first theorem اللي
+
+280
+00:29:55,560 --> 00:30:03,040
+هي ال first isomorphism
+
+281
+00:30:03,040 --> 00:30:04,500
+theorem
+
+282
+00:30:08,360 --> 00:30:17,800
+النظرية هذه بتقول ما يأتي let الـ Phi be a group
+
+283
+00:30:17,800 --> 00:30:26,840
+homomorphism from G
+
+284
+00:30:26,840 --> 00:30:34,280
+to G bar then the mapping then
+
+285
+00:30:44,170 --> 00:30:56,170
+معرفة من G موديول الـ Kernel للـ Phi إلى إلى من؟
+
+286
+00:30:56,170 --> 00:31:06,450
+إلى الـ Phi of capital G كلها given by والمعطى
+
+287
+00:31:06,450 --> 00:31:15,460
+Bipsi of G في الـ kernel للـ Phi بدي ساوي الـ Phi
+
+288
+00:31:15,460 --> 00:31:26,520
+of G يبقى هذا كله بدي ساوي الـ Phi of G is an
+
+289
+00:31:26,520 --> 00:31:36,710
+isomorphism that is ان الـ Gموديول الكيرني للـ Phi
+
+290
+00:31:36,710 --> 00:31:42,410
+ايزو مورف اكلمين للـ Phi of capital G
+
+291
+00:32:39,840 --> 00:32:45,640
+طيب نرجع للنظرية مرة تانية النظرية
+
+292
+00:32:45,640 --> 00:32:54,840
+بتقول لي لو كان عندنا five a group homomorphism
+
+293
+00:32:54,840 --> 00:33:00,900
+from G ل G bar ماقلش G و G bar groups هدول لكن أنا
+
+294
+00:33:00,900 --> 00:33:05,400
+بفهم انه groups من خلال قللي group homomorphism
+
+295
+00:33:05,400 --> 00:33:09,900
+يعني مش function بين two sets، بين two groupsيبقى
+
+296
+00:33:09,900 --> 00:33:14,020
+لو قللت الـPhi بـA جروب همومورفزم من G لـG bar أو
+
+297
+00:33:14,020 --> 00:33:18,640
+قللت Phi بـA همومورفزم from the group G to the
+
+298
+00:33:18,640 --> 00:33:22,940
+group G bar اتنين نفس النص تمام؟ يبقى then the
+
+299
+00:33:22,940 --> 00:33:27,780
+mapping ابصى من الـG kernel Phi للـPhi of G معرفة
+
+300
+00:33:27,780 --> 00:33:33,760
+بـPhi of الـleft coset الجي في ال kernel للـPhi
+
+301
+00:33:33,760 --> 00:33:38,300
+بده يساوي Phi of G is an isomorphismيعني اتنين
+
+302
+00:33:38,300 --> 00:33:43,480
+هذول are isomorphic لبعض وهي ال function معرفة
+
+303
+00:33:43,480 --> 00:33:48,280
+عندنا بالشكل اللي عندنا هذا طبعا واضح ان جي في
+
+304
+00:33:48,280 --> 00:33:52,280
+الكيرن اللي هو left coset اذا موجود في ال group
+
+305
+00:33:52,280 --> 00:33:58,780
+هذه في of small جي موجود في في كابتل او في في of
+
+306
+00:33:58,780 --> 00:34:05,520
+جي كابتل لان جي small موجودة في جي كابتلسنثبت هذه
+
+307
+00:34:05,520 --> 00:34:10,780
+عبارة عن isomorphism بس كونها left cosets هذه يبقى
+
+308
+00:34:10,780 --> 00:34:15,780
+الخطوة الأولى نثبت أن هذه ال function معرفة يعني
+
+309
+00:34:15,780 --> 00:34:21,600
+هذا التعريف تعريف صحيح يبقى أول ما أبدأ أقول له if
+
+310
+00:34:21,600 --> 00:34:32,390
+psi is well defined يبقى معرفة تعريفا سليمامشان
+
+311
+00:34:32,390 --> 00:34:41,350
+هيك بروح أخد عنصرين متساويين أفترض أفترض
+
+312
+00:34:41,350 --> 00:34:50,670
+أن ال X في الكيرنل للفاي بدي يساوي ال Y في الكيرنل
+
+313
+00:34:50,670 --> 00:34:56,910
+للفاي إذا كنت أثبت أن فاي of X بدي يساوي فاي of Y
+
+314
+00:34:56,910 --> 00:35:01,290
+بتم المطلوب يبقى then
+
+315
+00:35:06,420 --> 00:35:13,420
+يبقى لو جيت هنا ضربت من جهة الشمال في Y inverse او
+
+316
+00:35:13,420 --> 00:35:18,340
+في X inverse سيان الاتنين نفس الشيء يبقى لو ضربت
+
+317
+00:35:18,340 --> 00:35:25,120
+في Y inverse بصير Y inverse X في كيرنل الفاي بده
+
+318
+00:35:25,120 --> 00:35:32,300
+يسوى كيرنل الفاي ايش تفسيرك لهذه العبارة؟ يبقى
+
+319
+00:35:32,300 --> 00:35:39,920
+thenاللي هو main Y inverse X موجود في كيرن الـ Phi
+
+320
+00:35:39,920 --> 00:35:47,760
+يعني معناه هذا الكلام أن Phi of Y inverse X بديه
+
+321
+00:35:47,760 --> 00:35:55,210
+ساوي الـ Identity element تبع الـ G barهذا معناه
+
+322
+00:35:55,210 --> 00:36:04,190
+ايه؟ معناه ان الـ Phi of Y inverse في الـ Phi of X
+
+323
+00:36:04,190 --> 00:36:09,830
+بدي سوى الـ Identity Element تبع الـ G bar هذا
+
+324
+00:36:09,830 --> 00:36:17,830
+معناه ان Phi of Y الكل inverse في الـ Phi of X بدي
+
+325
+00:36:17,830 --> 00:36:25,220
+سوى الـ Identity Element تبع الـ G barهذا معناه ان
+
+326
+00:36:25,220 --> 00:36:32,000
+اضرب من جهة الشمال في الـPhi Y يبقى Phi of X بده
+
+327
+00:36:32,000 --> 00:36:38,780
+يساوي Phi of Y جينا على هذه المعادلة ضربنا من جهة
+
+328
+00:36:38,780 --> 00:36:44,270
+الشمال في Phi of Yهذه بيصير الـ Identity تبع الـ G
+
+329
+00:36:44,270 --> 00:36:49,870
+bar مع الـ Phi of X بالـ Phi of X وهنا الـ Phi of
+
+330
+00:36:49,870 --> 00:36:53,990
+Y مع الـ Identity تبع الـ G bar بيعطينا من الـ Phi
+
+331
+00:36:53,990 --> 00:36:59,250
+Y يبقى أصبع عندي Phi of X بدي يسوي Phi of Y يبقى
+
+332
+00:36:59,250 --> 00:37:05,160
+بناء عليه الدالة معرفة تعريفا سالماأريد أن أثبت له
+
+333
+00:37:05,160 --> 00:37:10,760
+أن الـipsi is one to one يعني أنه يريد أن يذهب
+
+334
+00:37:10,760 --> 00:37:21,600
+ويأخذ صورتين متساويتين أعتبر ذلك الـipsi أو جي في
+
+335
+00:37:21,600 --> 00:37:29,100
+الكيرن اللالفايبدا تساوي .. والله خلّيها X X في ال
+
+336
+00:37:29,100 --> 00:37:35,340
+kernel لفاي بده يساوي A بصي في ال Y في ال kernel
+
+337
+00:37:35,340 --> 00:37:41,220
+لفاي إذا استطعنا إنه نثبت X في ال kernel تساوي Y
+
+338
+00:37:41,220 --> 00:37:45,860
+في ال kernel بيكون ال A بصي صارت معاها one to one
+
+339
+00:37:45,860 --> 00:37:55,640
+يبقى thenهذه معناها إن الـPhi of X دي ساوة الـPhi
+
+340
+00:37:55,640 --> 00:38:05,120
+of Y هذا معناه لو ضربت في معكوس الـPhi of Y يبقى
+
+341
+00:38:05,120 --> 00:38:12,620
+إيش بيصير عندي الـPhi of X في الـPhi of Y الكل
+
+342
+00:38:12,620 --> 00:38:17,600
+inverse بدي ساوة الـidentity element تبع الـG bar
+
+343
+00:38:18,390 --> 00:38:26,390
+أو اللي هو main هكذا يصبح XY inverse في الـA بدي
+
+344
+00:38:26,390 --> 00:38:33,130
+أضرب بدل A هي هضربناها من جهة من .. لأ بدي أضربها
+
+345
+00:38:33,130 --> 00:38:39,950
+من جهة الشمال وليس من جهة اليمين عشان تظبط معنات
+
+346
+00:38:39,950 --> 00:38:47,060
+هي بدي أضربهامن جهة الشمال يبقى بدى اخد الان في of
+
+347
+00:38:47,060 --> 00:38:53,680
+Y الكل inverse في في of X دي سوى ال identity
+
+348
+00:38:53,680 --> 00:38:59,940
+element تبع ال G bar هذا بده يعطينا هذه نقدر نزلها
+
+349
+00:38:59,940 --> 00:39:08,240
+جوا يبقى بصير فيPhi of Y inverse في Phi of X يسوى
+
+350
+00:39:08,240 --> 00:39:15,800
+الـ Identity Element تبع الـ G bar هذا معناته أن
+
+351
+00:39:15,800 --> 00:39:23,980
+Phi of Y inverse في X يسوى الـ Identity Element
+
+352
+00:39:23,980 --> 00:39:29,590
+تبع الـ G bar لأن Phi عبارة عن Homomorphismهذا
+
+353
+00:39:29,590 --> 00:39:37,130
+معناه إيه؟ معناته إن الـ Y inverse X موجودة في الـ
+
+354
+00:39:37,130 --> 00:39:41,530
+kernel تبع الـ Phi لأن الصورتة بتعطينا الـ
+
+355
+00:39:41,530 --> 00:39:46,040
+identity element تبع الـ G barما دام موجودة في الـ
+
+356
+00:39:46,040 --> 00:39:52,560
+Kernel يبقى بيصير Y inverse X في ال Kernel للـ Phi
+
+357
+00:39:52,560 --> 00:39:58,260
+بده يساوي ال Kernel للـ Phi نفسه لأن ال subgroup
+
+358
+00:39:58,260 --> 00:40:02,920
+لما أضربها ب element منها بتعطيني نفس ال subgroup
+
+359
+00:40:02,920 --> 00:40:09,280
+طيب نضرب الطرفين في Y يبقى X في ال Kernel للـ Phi
+
+360
+00:40:09,280 --> 00:40:17,020
+بده يساوي Yفي الـ Kern المهم للـ Phi وهو ال مطلوب
+
+361
+00:40:17,020 --> 00:40:26,520
+يبقى بنا نيجي لإبصي as all يبقى بالداجة أقوله احنا
+
+362
+00:40:26,520 --> 00:40:33,950
+عندنا الإبصي ما هو طابلاتالـ X موجودة في Phi of
+
+363
+00:40:33,950 --> 00:40:43,550
+capital G then الـ X بدها تساوي Phi of G for some
+
+364
+00:40:43,550 --> 00:40:50,510
+G اللي موجودة في G Capitalيبقى الـ X اللي أخدتها
+
+365
+00:40:50,510 --> 00:40:56,770
+بدها تساوي Phi of G Small هذه بقدر أقول حسب الـ
+
+366
+00:40:56,770 --> 00:41:03,770
+Definition هي Psi G في الـ Kern للـ Phi لذلك Psi
+
+367
+00:41:03,770 --> 00:41:10,370
+is Unto One to one وUnto معرفة ضال عندي أخر نقطة
+
+368
+00:41:10,370 --> 00:41:15,110
+Psi is Homomorphism
+
+369
+00:41:16,290 --> 00:41:21,350
+Homomorphism وبالتالي بيصير isomorphism تمام؟ يبقى
+
+370
+00:41:21,350 --> 00:41:28,170
+homomorphism بتاخد إبصي لحاصل ضرب عددين الأول two
+
+371
+00:41:28,170 --> 00:41:34,850
+elements X في الكرن اللال فيفي الـY في الـKernel
+
+372
+00:41:34,850 --> 00:41:40,090
+للـPhi مش عددين وإنما two elements موجودات في
+
+373
+00:41:40,090 --> 00:41:45,510
+الـFactor A group هذا الكلام بده يساوي بـPsi of
+
+374
+00:41:45,510 --> 00:41:50,290
+هذا الـLeft Cosetة وهذا الـLeft Cosetة وقبل شوية
+
+375
+00:41:50,290 --> 00:41:54,770
+قولنا الـKernel هي normal subgroup إذا بناء عليه
+
+376
+00:41:54,770 --> 00:42:02,590
+بصير الـXY في الـKernel للـPhiطيب بـ Psi لما تأثر
+
+377
+00:42:02,590 --> 00:42:08,130
+على هذا بتعطينا mean Phi of X في Y Phi
+
+378
+00:42:08,130 --> 00:42:16,090
+homomorphism يبقى Phi of X في Phi of Y Phi of X
+
+379
+00:42:16,090 --> 00:42:21,300
+هذه اللي هي عبارة عالمياًاللي هي Epsi للـ X في الـ
+
+380
+00:42:21,300 --> 00:42:27,300
+Kernel للـ Phi وهذه Epsi Y في الـ Kernel للـ Phi
+
+381
+00:42:27,300 --> 00:42:36,420
+يبقى دص وهكذا Epsi is an isomorphism يبقى بناءً
+
+382
+00:42:36,420 --> 00:42:41,660
+على Epsi اللي عرفناها هذه طلعت من الـ G موديو للـ
+
+383
+00:42:41,660 --> 00:42:46,800
+Kernelللـ Phi of G عبارة عن أيش؟ Isomorphism فى
+
+384
+00:42:46,800 --> 00:42:56,920
+نتيجة بسيطة عليها Krullery الكرولرة
+
+385
+00:42:56,920 --> 00:43:10,100
+بتقول ما ياتى if الـ Phi is a homomorphism from a
+
+386
+00:43:10,100 --> 00:43:11,420
+finite
+
+387
+00:43:14,140 --> 00:43:21,220
+فاي نايت اجروب
+
+388
+00:43:21,220 --> 00:43:32,900
+جي تو جي بار then then
+
+389
+00:43:32,900 --> 00:43:42,380
+ال order للفاي of جي ال order of five divides
+
+390
+00:44:04,160 --> 00:44:09,500
+الكتاب مش انبرهنه احنا بنحاول انبرهنها برضه ال
+
+391
+00:44:09,500 --> 00:44:14,280
+proof خلّي
+
+392
+00:44:14,280 --> 00:44:22,310
+برا كدهالآن الـ Phi of G هو subgroup من الـ G bar
+
+393
+00:44:22,310 --> 00:44:28,050
+ولا لا؟ يبقى
+
+394
+00:44:28,050 --> 00:44:31,290
+هي subgroup، يبقى ال order اللي بيكسب ال order لل
+
+395
+00:44:31,290 --> 00:44:37,630
+group يبقى هذا معناه ان ال order لل Phi of G
+
+396
+00:44:37,630 --> 00:44:43,810
+divide ال order لمن؟ ل G bar يبقى خلصنا من هذه
+
+397
+00:44:44,690 --> 00:44:49,790
+تمام؟ بدنا نيجي للتانية التانية بدي أحاول أستخدمها
+
+398
+00:44:49,790 --> 00:45:00,510
+من النظرية احنا from and from the previous
+
+399
+00:45:02,610 --> 00:45:08,730
+Theorem من الـ Previous Theorem عندك الـ order للـ
+
+400
+00:45:08,730 --> 00:45:17,610
+G موديول الكيرن للـ Phi بده يساوي ال order للـ Phi
+
+401
+00:45:17,610 --> 00:45:25,050
+of G مش هذه isomorphic لهذه إذا ال order لهذه بده
+
+402
+00:45:25,050 --> 00:45:30,510
+يساوي ال order لهذه هذا معناه إيه؟ هذه تعني ال
+
+403
+00:45:30,510 --> 00:45:36,880
+order تبع ال Gمقسوما على ال order تبع الكرنل للفاي
+
+404
+00:45:36,880 --> 00:45:45,480
+بدي ساوي ال order للفاي of G بالشكل اللي عندنا طيب
+
+405
+00:45:45,480 --> 00:45:52,040
+لو ضربناها بصير عندنا مين بصير عندنا ان ال order
+
+406
+00:45:52,040 --> 00:45:59,640
+لل Gبدي ساوي ال order للكرن للـ Phi في ال order
+
+407
+00:45:59,640 --> 00:46:08,960
+للـ Phi of G هذا معناه ان ال order للـ Phi of G
+
+408
+00:46:08,960 --> 00:46:13,020
+divide ال order لـ G وهو المطلوب
+
+409
+00:46:16,800 --> 00:46:21,100
+يبقى أحاول أن أثبت الكرولري من خلال main من خلال
+
+410
+00:46:21,100 --> 00:46:24,560
+النتيجة يوم الأربعاء ان شاء الله بتكون المحاضرة
+
+411
+00:46:24,560 --> 00:46:30,680
+الأخيرة التي بها ننهي هذا section وحنحاول نحل أكثر
+
+412
+00:46:30,680 --> 00:46:33,460
+من سؤال على شكل أمثلة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c8b140aadd7ced00486e29697f32132559ddbf36
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8.srt
@@ -0,0 +1,1271 @@
+1
+00:00:21,160 --> 00:00:25,720
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا به في
+
+2
+00:00:25,720 --> 00:00:30,320
+المرحلة الصباحية وهو نهاية chapter cosets and
+
+3
+00:00:30,320 --> 00:00:34,180
+Lagrange theorem في الفترة الصباحية أعطينا أربع
+
+4
+00:00:34,180 --> 00:00:38,700
+examples على نظرية Lagrange  و أعطينا على ذلك بعض
+
+5
+00:00:38,700 --> 00:00:44,790
+الأمثلة الآن صح برضه حكينا أن عكس نظرية Lagrange
+
+6
+00:00:44,790 --> 00:00:49,590
+ليس صحيحا يعني لو عندي قواسم لل order  تبع ال group
+
+7
+00:00:49,590 --> 00:00:54,790
+ليس بالضرورة أن هذه القواسم تكون orders ل sub
+
+8
+00:00:54,790 --> 00:00:58,790
+group ومعطيك مثال في الكتاب ياريت تطلع عليه مثال
+
+9
+00:00:58,790 --> 00:01:02,680
+خمسة الآن في نظرية بعض اللي هي نظرية اللي قدامنا
+
+10
+00:01:02,680 --> 00:01:05,740
+هذه بيقول اللي قلت G be a group of order 2P
+
+11
+00:01:05,740 --> 00:01:09,960
+حيث P is a prime greater than two then الـ G
+
+12
+00:01:09,960 --> 00:01:16,040
+isomorphic لـ Z2P أو D2P طب ليش قال هذول التنتين 
+
+13
+00:01:16,040 --> 00:01:20,380
+فيهم نفس العدد من العناصر ولا بيختلفوا عن بعض Z
+
+14
+00:01:20,380 --> 00:01:24,820
+2P و D2P عدد عناصرهم كانت بعض ولا بيختلفوا
+
+15
+00:01:24,820 --> 00:01:29,580
+عن بعض هدول جت بعض على طول خاطر لأن D2P عدد
+
+16
+00:01:29,580 --> 00:01:33,820
+عناصرها 2P و Z2P عدد عناصرها 2P طب
+
+17
+00:01:33,820 --> 00:01:40,380
+ليش قال Z2P اللي هو D2P يعني ليش قال
+
+18
+00:01:40,380 --> 00:01:48,440
+اتنتين هدول مثلا ليش ما قال واحدة فيهم؟ ليش ما قال
+
+19
+00:01:48,440 --> 00:01:52,840
+Z2P لحالها بس؟ أو قال اللي هو D2P لحالها 
+
+20
+00:01:52,840 --> 00:01:54,780
+بس؟ ليش قال هذه أو هذه؟
+
+21
+00:01:58,360 --> 00:02:06,480
+هذا بقدر أفكر يقول ليش؟ مية لمية تمام هذا الآن 
+
+22
+00:02:06,480 --> 00:02:10,500
+عندي الـ cyclic group يبقى لو كانت G أصلية الـ
+
+23
+00:02:10,500 --> 00:02:15,490
+cyclic automatic هتكون isomorphic لمين؟ لـ Z2P
+
+24
+00:02:15,490 --> 00:02:20,850
+مباشرة لو كانت هذه ما هيش Cyclic إذا هتبقى
+
+25
+00:02:20,850 --> 00:02:25,290
+isomorphic لمين؟ لـ D2P لإن D2P not cyclic group
+
+26
+00:02:25,290 --> 00:02:29,070
+تمام يبقى لما نقل التنتين والتنتين اللي هما نفس الـ
+
+27
+00:02:29,070 --> 00:02:33,410
+order يبقى isomorphic لـ Z2P إذا كانت الـ G
+
+28
+00:02:33,410 --> 00:02:38,560
+Cyclic يبقى إجباري هتكون isomorphic لمين؟ لـ Z2
+
+29
+00:02:38,560 --> 00:02:43,060
+P وإذا ما كانتش Cyclic يبقى إجباري isomorphic لـ D2P
+
+30
+00:02:43,060 --> 00:02:46,080
+الحقيقة برهان طويل فـ آسفينكوا بدك تطلع عليه
+
+31
+00:02:46,080 --> 00:02:49,540
+ماعنديش مشكلة روح تطلع عليه من الكتاب بيبينش 
+
+32
+00:02:49,540 --> 00:02:54,700
+الكتاب طيب في عندي two definitions لاتنين لازماتنا 
+
+33
+00:02:54,700 --> 00:02:59,340
+دول التعريف الأول أخدناه قبل ذلك في exercise واحد
+
+34
+00:02:59,340 --> 00:03:03,320
+و ثلاثين من الشابتر تبع خمسة و حليته لكوا عليه 
+
+35
+00:03:03,320 --> 00:03:07,010
+اللوحين و أثبت أن ال stabilizer هو عبارة عن
+
+36
+00:03:07,010 --> 00:03:10,690
+subgroup كان السؤال يثبت أن ال stabilizer لل
+
+37
+00:03:10,690 --> 00:03:15,710
+element i مثلا هو عبارة عن subgroup يبقى بيقول
+
+38
+00:03:15,710 --> 00:03:22,650
+Let G be a group of permutation of a set S أي element i
+
+39
+00:03:22,650 --> 00:03:26,590
+موجود في S ال Stabilizer تبع الـ i الـ i هي the
+
+40
+00:03:26,590 --> 00:03:30,830
+subset of G consisting of all elements in G that
+
+41
+00:03:30,830 --> 00:03:35,370
+fix الـ i يعني ليه تثبت الـ i؟ يعني صورة الـ i بتكون
+
+42
+00:03:35,370 --> 00:03:42,520
+من؟ الـ i itself يبقى ال stabilizer للـ i يعني كل الـ
+
+43
+00:03:42,520 --> 00:03:47,480
+elements اللي فيه يعني كل ال permutations اللي
+
+44
+00:03:47,480 --> 00:03:51,520
+موجودة في G و صورة الـ i بتبقى الـ i نفسه لو قلت بدل
+
+45
+00:03:51,520 --> 00:03:55,400
+الـ i واحد يبقى صورة الـ واحد هي واحد لو قلت بدل الـ i
+
+46
+00:03:55,400 --> 00:03:59,720
+قلت عشرة يبقى صورة العشرة هي من؟ يبقى هي عشرة يعني
+
+47
+00:03:59,720 --> 00:04:04,540
+كل ال permutations اللي فيهم العدد i هذا يكون 
+
+48
+00:04:05,020 --> 00:04:10,260
+ثابتًا يعني بيعطيني نفس ال element صورته نفسه فقلنا
+
+49
+00:04:10,260 --> 00:04:16,360
+ال stabilizer للـ i اللي موجود في S لعلى G هو كل
+
+50
+00:04:16,360 --> 00:04:20,240
+الـ Φ يعني كل ال permutation اللي موجودة في G
+
+51
+00:04:20,240 --> 00:04:26,620
+بحيث أن صورة i هي من الـ i itself طبعًا ال stabilizer
+
+52
+00:04:26,620 --> 00:04:31,360
+is a subgroup و هذا أنا برهنته لكوا سابقا اللي هو
+
+53
+00:04:31,360 --> 00:04:34,040
+السؤال واحد و ثلاثين من شابتر الخمسة أنا حلته
+
+54
+00:04:34,040 --> 00:04:38,140
+قدامكوا على اللوح هنا طيب يسيبنا هذا جديد لكن في
+
+55
+00:04:38,140 --> 00:04:41,740
+شغل ما... طب ليش جايبينه؟ اه لأنه لازم أن في شغل
+
+56
+00:04:41,740 --> 00:04:46,900
+متعلق فيه و في نظرية مرتبطة فيه بعد قليل بعد ذلك
+
+57
+00:04:46,900 --> 00:04:51,220
+قال Let G be a group of permutations of a set
+
+58
+00:04:51,220 --> 00:04:55,340
+S بدنا نعرف تعريف جديد هذا ما شوفناهوش قبل هيك
+
+59
+00:04:55,340 --> 00:04:59,960
+التعريف بيقول لي كل s موجود في S بدنا نعرف حاجة الـ
+
+60
+00:04:59,960 --> 00:05:04,800
+orbit تبع الـ s ال orbit يعني بالعربي ايه؟ مدار مسار
+
+61
+00:05:04,800 --> 00:05:10,680
+كويس يبقى المدار تبع الـ s ده هو ال images of s هي
+
+62
+00:05:10,680 --> 00:05:15,760
+الصور العنصر s اللي عندنا هذه under all
+
+63
+00:05:15,760 --> 00:05:21,200
+permutations in G يعني يعني بالداخل العنصر s لو
+
+64
+00:05:21,200 --> 00:05:25,920
+قلت واحد و أنا عندي G هذه بطلع من ال permutations
+
+65
+00:05:25,920 --> 00:05:31,630
+اللي الواحد له صورة و بروح باخد هذه الصورة طلع ايش
+
+66
+00:05:31,630 --> 00:05:36,790
+بقوله بقول ال orbit لـ s كل ال Φ of s يعني صورة
+
+67
+00:05:36,790 --> 00:05:40,830
+main صورة هذا الـ s بحيث الـ Φ موجودة في G يعني
+
+68
+00:05:40,830 --> 00:05:43,930
+أنا بتطلع على كل ال permutations اللي موجودة في الـ
+
+69
+00:05:43,930 --> 00:05:50,370
+group قلت بدل ال orbit مثلا لتلاتة بجيب أطلع وين
+
+70
+00:05:50,370 --> 00:05:54,250
+تلاتة كانت موجودة في ال cycle بقول صورة التلاتة ايش
+
+71
+00:05:54,250 --> 00:05:58,310
+كانت كانت مثلا خمسة بقول خمسة صورة التلاتة كانت
+
+72
+00:05:58,310 --> 00:06:01,850
+واحد بقول واحد صورة التلاتة كانت كذا بقول كذا جمعت
+
+73
+00:06:01,850 --> 00:06:06,790
+هذول إذا هذول أرقام عادية تمام يبقى في هذه الحالة
+
+74
+00:06:06,790 --> 00:06:11,970
+ال orbit للـ s هو كل ال Φ of s يعني الصور الـ s
+
+75
+00:06:11,970 --> 00:06:15,590
+بحيث الـ Φ هي permutation موجود وين؟ موجود في G
+
+76
+00:06:15,590 --> 00:06:20,770
+يعني يا شباب احنا بدنا نطبق موضوع ال cosets اللي
+
+77
+00:06:20,770 --> 00:06:25,390
+درسناه قبل شوية على مين؟ على ال permutation group
+
+78
+00:06:25,390 --> 00:06:29,330
+هاي هذا اللي هو المقصود فيه ال stabilizer و ال
+
+79
+00:06:29,330 --> 00:06:33,610
+orbit الآن عدد العناصر في ال orbit هديله الرمز ال
+
+80
+00:06:33,610 --> 00:06:38,240
+orbit لـ s على G و حط الخطين اللي بقيتنا نسميهم order
+
+81
+00:06:38,240 --> 00:06:43,620
+لـ G طبعًا ال order درجة العادة أن نقوله group أو
+
+82
+00:06:43,620 --> 00:06:47,940
+sub group أو element بس هذا ال order ما قلناش sub
+
+83
+00:06:47,940 --> 00:06:52,240
+group ما قلناش حتى أقول ال order هذا مش order هذا
+
+84
+00:06:52,240 --> 00:06:56,520
+رقم يدل على عدد العناصر في الست اللي عندنا اللي هو
+
+85
+00:06:56,520 --> 00:07:01,780
+ال orbit لـ G بنعطي مثال من خلال هذا المثال بدي
+
+86
+00:07:01,780 --> 00:07:05,760
+أحسب ال stabilizer لأعداد مختلفة و بدي أحسب ال
+
+87
+00:07:05,760 --> 00:07:10,720
+order لـ الأعداد المختلفة نجي الأقل ال stabilizer
+
+88
+00:07:10,720 --> 00:07:16,800
+لمين؟ للواحد حسب التعريف تبع ال stabilizer كل الـ
+
+89
+00:07:16,800 --> 00:07:20,760
+permutations اللي فيهم الواحد fixed ايش يعني 
+
+90
+00:07:20,760 --> 00:07:25,000
+الواحد fixed يعني صورة الواحد بتعطيني مين؟ الواحد
+
+91
+00:07:25,000 --> 00:07:30,440
+itself أظن الـ identity permutation منهم صح الواحد
+
+92
+00:07:30,440 --> 00:07:33,400
+صورته واحد اتنين صورته اتنين تلاته صورته تلاته إذا
+
+93
+00:07:33,400 --> 00:07:39,600
+الواحد هذي منهم الآن الواحد صورته ايش؟ يبقى هذي الـ
+
+94
+00:07:39,600 --> 00:07:43,800
+permutation منها لأ لإن ما ثبتتش الواحد صار صورته
+
+95
+00:07:43,800 --> 00:07:46,820
+اتنين احنا بدور ال permutation اللي هو الواحد
+
+96
+00:07:46,820 --> 00:07:52,980
+صورته واحد هذي منهم لأ هذي منهم لأ هذي منهم لأ هذي
+
+97
+00:07:52,980 --> 00:07:58,320
+منهم لأ لماذا؟ مضروبة في بعض ضرب الواحد صارت تلاتة
+
+98
+00:07:58,320 --> 00:08:03,660
+هنا هذه منهم لا يبقى ما عنديش إلا الأخيرة اتنين
+
+99
+00:08:03,660 --> 00:08:08,540
+و أربعة و خمسة يعني كل ال permutation اللي بيظهر فيهم
+
+100
+00:08:08,540 --> 00:08:14,040
+الواحد انسى الموضوع ما هذا ال identity يبقى اتنين
+
+101
+00:08:14,040 --> 00:08:21,140
+أربعة خمسة ستة يبقى اتنين أربعة هنا خمسة ستة
+
+102
+00:08:21,140 --> 00:08:26,100
+بالشكل اللي عندنا هنا طب بدي أجيب ال orbit لمين؟
+
+103
+00:08:26,100 --> 00:08:32,960
+للواحد على G و يساوي بدي أجيب صورة الآن في ال
+
+104
+00:08:32,960 --> 00:08:38,320
+permutation الأولى ايش صورة الواحد؟ واحد itself هنا
+
+105
+00:08:38,320 --> 00:08:45,940
+صورة الواحد تلاتة صورة الواحد اتنين هنا صورة الواحد
+
+106
+00:08:45,940 --> 00:08:52,260
+أخدناها بكرر اش كمان مرة صورة الواحد تلاتة صورة
+
+107
+00:08:52,260 --> 00:08:59,280
+الواحد أربعة صورة الواحد أخدناها صورة الواحد أربعة
+
+108
+00:08:59,280 --> 00:09:05,360
+أخدناها صورة الواحد واحد يبقى خلصنا هاي المقصود
+
+109
+00:09:05,360 --> 00:09:10,540
+بال Orbit بجيب الصورة التالتة العنصر لو بده أجيب الـ
+
+110
+00:09:10,540 --> 00:09:18,620
+stabilizer على G لل element مثلا تلاتة طيب
+
+111
+00:09:18,620 --> 00:09:22,340
+هذه منهم صحيح لأن هذه ال identity الصورة التلاتة
+
+112
+00:09:22,340 --> 00:09:27,460
+بتلاتة يبقى هذه منهم نيجي الآن بدل ال stabilizer
+
+113
+00:09:27,460 --> 00:09:33,820
+على تلاتة تلاتة شو صورتها؟ يبقى fixed لأ التلاتة
+
+114
+00:09:33,820 --> 00:09:40,000
+fixed التلاتة تلاتة
+
+115
+00:09:40,000 --> 00:09:49,100
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+116
+00:09:49,100 --> 00:09:52,080
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+117
+00:09:52,080 --> 00:09:52,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+118
+00:09:52,180 --> 00:09:53,520
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+119
+00:09:53,520 --> 00:09:54,760
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+120
+00:09:54,760 --> 00:10:03,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة أريد أن أشاهد
+
+121
+00:10:03,700 --> 00:10:07,900
+صور العناصر التلاتة في الـ Permutations المختلفة
+
+122
+00:10:07,900 --> 00:10:13,840
+صورة التلاتة هنا كم؟ تلاتة يبقى تلاتة منهم لأنه
+
+123
+00:10:13,840 --> 00:10:22,880
+مقرر صورة التلاتة أربعة صورة التلاتة مكررة صورة
+
+124
+00:10:22,880 --> 00:10:30,140
+التلاتة خلصنا من هذا صورة التلاتة اتنين صورة
+
+125
+00:10:30,140 --> 00:10:36,110
+التلاتة أما أخدناها هايه صورة التلاتة اتنين أخدناها
+
+126
+00:10:36,110 --> 00:10:41,750
+هذه صورة الثلاث ثلاثة هي أخذناها في الأول يبقى
+
+127
+00:10:41,750 --> 00:10:46,770
+انتهينا من الشغل هذه تمام؟ في خمسة خذ ال orbit لل
+
+128
+00:10:46,770 --> 00:10:52,790
+stabilizer للخمسة مثلاً ال stabilizer على الخمسة
+
+129
+00:10:52,790 --> 00:10:59,390
+ويساوي طبعاً صورة الخمسة اللي هي الخمسة نيجي هنا
+
+130
+00:11:01,020 --> 00:11:07,900
+الستابلازر اللي هو الواحد اللي هو الواحد مش ال
+
+131
+00:11:07,900 --> 00:11:12,180
+orbit اللي هو الواحد طبعاً طيب الستابلازر مثبت على
+
+132
+00:11:12,180 --> 00:11:17,240
+الخمسة الخمسة ظاهرة هنا يبقى هنا الخمسة fixed يبقى
+
+133
+00:11:17,240 --> 00:11:24,410
+بأجي أقوله واحد اثنين ثلاثة أربعة وكمان هنا الخمسة
+
+134
+00:11:24,410 --> 00:11:29,490
+ستة يبقى أنسى هنا ظهرت لأ يبقى واحد ثلاثة اثنين
+
+135
+00:11:29,490 --> 00:11:36,290
+أربعة يبقى واحد ثلاثة اثنين أربعة خلصنا منها هنا
+
+136
+00:11:36,290 --> 00:11:40,750
+الخمسة صورتها ستة ماهي fixed الخمسة صورتها ستة
+
+137
+00:11:40,750 --> 00:11:45,690
+ما أعرف كده يبقى واحد أربعة اثنين ثلاثة يبقى واحد
+
+138
+00:11:45,690 --> 00:11:52,670
+أربعة اثنين ثلاثة خلصنا منها واحد أربعة اثنين ثلاثة
+
+139
+00:11:52,670 --> 00:11:58,650
+هنا ماهي fixed يبقى أنت هنا منها يبقى هذا ال
+
+140
+00:11:58,650 --> 00:12:06,910
+orbit لمين؟ ال stabilizer للخمسة بد ال orbit للخمسة
+
+141
+00:12:06,910 --> 00:12:14,360
+على ال group G كويس يعني بده صورة العدد خمسة صورة
+
+142
+00:12:14,360 --> 00:12:20,740
+خمسة هنا بخمسة itself طيب وصورة الخمسة هنا خمسة
+
+143
+00:12:20,740 --> 00:12:27,120
+itself صورة الخمسة هنا هي ستة صورة الخمسة خمسة
+
+144
+00:12:27,120 --> 00:12:32,060
+أخذناها صورة الخمسة ستة أخذناها صورة الخمسة ستة
+
+145
+00:12:32,060 --> 00:12:37,040
+أخذناها صورة الخمسة خمسة أخذناها صورة الخمسة ستة
+
+146
+00:12:37,040 --> 00:12:43,960
+أخذناها يبقى بس two elements تمام؟ يبقى عرفنا كيف
+
+147
+00:12:43,960 --> 00:12:48,840
+بنحسب ال orbit و ال stabilizer تمام؟ الحين بدنا
+
+148
+00:12:48,840 --> 00:12:51,860
+نجيب نظرية تربط ما بين ال order
+
+149
+00:12:59,360 --> 00:13:03,800
+هذا الموضوع النظرية التالية
+
+150
+00:13:21,170 --> 00:13:31,830
+يبقى هذه نظرية نصف على ما يلي ثيرم let
+
+151
+00:13:31,830 --> 00:13:36,630
+الـ G be
+
+152
+00:13:36,630 --> 00:13:44,650
+a finite group of
+
+153
+00:13:44,650 --> 00:13:52,200
+permutations of a set S of permutations
+
+154
+00:13:52,200 --> 00:13:59,680
+of a set capital
+
+155
+00:13:59,680 --> 00:14:03,480
+S then
+
+156
+00:14:03,480 --> 00:14:08,100
+for
+
+157
+00:14:08,100 --> 00:14:20,000
+then for any i اللي موجودة في capital S الشكل اللي 
+
+158
+00:14:20,000 --> 00:14:24,400
+عندنا هنا هو عدد
+
+159
+00:14:24,400 --> 00:14:29,500
+العناصر في ال orbit على بورت i على G
+
+160
+00:14:53,700 --> 00:15:16,560
+عظم أن هذا النحيا خلاص يبقى
+
+161
+00:15:16,560 --> 00:15:17,660
+مرة ثانية بقول
+
+162
+00:15:24,280 --> 00:15:28,700
+عندنا g finite group of permutations يعني لازلنا
+
+163
+00:15:28,700 --> 00:15:32,180
+في موضوع ال group of permutations وهذه ال
+
+164
+00:15:32,180 --> 00:15:37,360
+permutations على ست S أخذت أي element i موجود في S
+
+165
+00:15:37,360 --> 00:15:42,780
+من خلال هذا الكلام أثبت أن ال order لل G هو عبارة
+
+166
+00:15:42,780 --> 00:15:48,350
+عن عدد العناصر في ال orbit لل i على G مضروب في ال
+
+167
+00:15:48,350 --> 00:15:52,810
+order تبع من؟ تبع ال stabilizer قلت ال order لل
+
+168
+00:15:52,810 --> 00:15:56,230
+stabilizer لأن ال stabilizer ال subgroup لكن هذه
+
+169
+00:15:56,230 --> 00:16:02,690
+ماهي subgroup طيب البرهان كان التالي احنا الآن
+
+170
+00:16:02,690 --> 00:16:04,650
+أقول
+
+171
+00:16:06,510 --> 00:16:13,530
+احنا بنعرف إن ال stabilizer لل i على G is a
+
+172
+00:16:13,530 --> 00:16:19,970
+subgroup من G هذا معناه إيش؟ معناه إن ال order لل
+
+173
+00:16:19,970 --> 00:16:30,000
+stabilizer على G لل i يقسم ال order ل G يعني معنى
+
+174
+00:16:30,000 --> 00:16:36,360
+هذا الكلام أن ال order ل G مقسوم على ال order لل
+
+175
+00:16:36,360 --> 00:16:45,060
+stabilizer على i لل G هذا كله بدي يساوي the number
+
+176
+00:16:45,060 --> 00:16:50,600
+of left cosets
+
+177
+00:16:52,010 --> 00:17:05,750
+of the stabilizer ل i على G مرة
+
+178
+00:17:05,750 --> 00:17:11,490
+ثانية احنا عارفين أن ال stabilizer هو subgroup من G
+
+179
+00:17:11,490 --> 00:17:16,370
+و قلنا لك هذا السؤال 31 من شهدر خمسة وقبل ذلك
+
+180
+00:17:16,370 --> 00:17:19,990
+أثبتناه إذا ال stabilizer هو subgroup من G حسب
+
+181
+00:17:19,990 --> 00:17:25,170
+نظرية Lagrange ال order لل stabilizer بده يقسم من
+
+182
+00:17:25,170 --> 00:17:26,750
+ال order لل G
+
+183
+00:17:30,470 --> 00:17:36,990
+يبقى ال order ل ال stabilizer بده يقسم ال order ل
+
+184
+00:17:36,990 --> 00:17:41,970
+ال g لما ال order ل ال h بده يقسم ال order ل ال g
+
+185
+00:17:41,970 --> 00:17:45,670
+يبقى لو قسمت ال order ل ال g على ال order ل ال h
+
+186
+00:17:45,670 --> 00:17:52,290
+بيعطيني عدد ال left distinct اللي هو cosets of h
+
+187
+00:17:52,290 --> 00:17:57,710
+in g يبقى هذا بدي يعطيني the number of left
+
+188
+00:17:57,710 --> 00:17:59,170
+distinct
+
+189
+00:18:01,470 --> 00:18:05,890
+cosets of the stabilizer تبع ال h in g يبقى هذا
+
+190
+00:18:05,890 --> 00:18:09,910
+بيعطيني عدد ال left cosets اللي ولا واحدة فيهم
+
+191
+00:18:09,910 --> 00:18:17,510
+مالها زي الثانية طيب كويس الآن أنا لو قدرت أثبت أن
+
+192
+00:18:17,510 --> 00:18:22,890
+هذا الرقم اللي عندي هو عدد عناصر في ال orbit بتما
+
+193
+00:18:22,890 --> 00:18:29,260
+المطلوب يعني لو أثبت إنه عدد اللي هو الرقم اللي
+
+194
+00:18:29,260 --> 00:18:37,380
+عندنا هذا عدد ال left cosets اللي عندي من ال
+
+195
+00:18:37,380 --> 00:18:42,820
+stabilizer في ال group G أثبته إنه يساوي اللي هو
+
+196
+00:18:42,820 --> 00:18:46,780
+عدد العناصر اللي موجودة في ال orbit باسم المطابق
+
+197
+00:18:46,780 --> 00:18:50,320
+بيبقى أشيل هذا و أضع عدد العناصر بنظر بضاربة تبذل
+
+198
+00:18:50,320 --> 00:18:55,790
+يكون برهان هذا الكلام عشان أثبت أن هذا العدد يساوي
+
+199
+00:18:55,790 --> 00:19:00,340
+هذا العدد يعني معناه بدي أعرف function من ال left
+
+200
+00:19:00,340 --> 00:19:05,080
+cosets للصور اللي عندنا هذه إذا ال function هذه
+
+201
+00:19:05,080 --> 00:19:09,600
+كنت أثبت إنها one to one and onto خلاص بصير
+
+202
+00:19:09,600 --> 00:19:14,360
+العدد قال بعض ولو وصلنا لإيه؟ وصلنا للمطلوب بسهولة
+
+203
+00:19:14,360 --> 00:19:20,680
+طبعاً احنا مر علينا جزء من نظرية مثل هذه قبل ذلك
+
+204
+00:19:20,680 --> 00:19:24,140
+بشأن نثبت أن ال order لهذا بدي يساوي ال order لهذا
+
+205
+00:19:24,140 --> 00:19:28,500
+عرفنا function يعني أخذنا نظرية في لف الكوسيطس أن
+
+206
+00:19:28,500 --> 00:19:35,300
+ال order لل H بدي يساوي ال order لل BH يعني عدد
+
+207
+00:19:35,300 --> 00:19:38,920
+عناصر يساوي عدد عناصر هنا عرفنا function فيه ما
+
+208
+00:19:38,920 --> 00:19:43,760
+بينهما و أثبتنا إنها one to one and onto يبقى الآن
+
+209
+00:19:43,760 --> 00:19:56,380
+أنا بدي أعمل نفس القصة define a function from the
+
+210
+00:19:56,380 --> 00:20:08,020
+set of all left-distinct left
+
+211
+00:20:08,020 --> 00:20:15,440
+-distinct cosets of stabilizer
+
+212
+00:20:18,540 --> 00:20:26,560
+ال i على G in G يبقى من هذه ال set to بدي مين؟
+
+213
+00:20:26,560 --> 00:20:35,700
+بديها ال set of elements في ال orbit لمن؟ to the
+
+214
+00:20:35,700 --> 00:20:47,480
+orbit على i لل G أو the set of numbers in the
+
+215
+00:20:47,480 --> 00:20:56,220
+orbit إلى مجموعة الأعداد اللي موجودة في ال orbit by
+
+216
+00:20:56,220 --> 00:20:59,400
+T
+
+217
+00:20:59,400 --> 00:21:06,750
+of أنا قلت left cosets و ال subgroup هي ال
+
+218
+00:21:06,750 --> 00:21:11,190
+stabilizer يبقى بدي آخذ element من G ال elements
+
+219
+00:21:11,190 --> 00:21:15,650
+اللي فيها كلهم permutations لأن ال G set of all
+
+220
+00:21:15,650 --> 00:21:21,550
+permutations يبقى بدي يكون ال element Φ مضروب في
+
+221
+00:21:21,550 --> 00:21:29,310
+ال stabilizer لمن؟ لل i على G هذه ال set اللي
+
+222
+00:21:29,310 --> 00:21:34,290
+عندنا عناصرها left coset من ال stabilizer يعني
+
+223
+00:21:34,290 --> 00:21:38,890
+element من G مضروب في ال stabilizer بدي أودي لل
+
+224
+00:21:38,890 --> 00:21:48,960
+set هذه يبقى T of كذا بدي يساوي Φ of i لأن ال
+
+225
+00:21:48,960 --> 00:21:54,220
+orbit عرفناها قبل قليل صور ال Φ of i حيث ال i
+
+226
+00:21:54,220 --> 00:21:59,420
+موجودة وين؟ موجودة في S طب أول شيء بنشوف هل هذه
+
+227
+00:21:59,420 --> 00:22:04,120
+فعلاً هي دالة ولا ماهي دالة وبعدين بشوف الحكاية
+
+228
+00:22:04,120 --> 00:22:12,380
+ال one to one and onto فبأجي بقوله الآن T is well
+
+229
+00:22:12,380 --> 00:22:18,460
+defined مشان أثبت حكاية الولد فاني بدي أمشي عكس ال
+
+230
+00:22:18,460 --> 00:22:25,080
+one to one يعني بدي آجي آخذ عنصرين متساويين و أثبت
+
+231
+00:22:25,080 --> 00:22:31,520
+أن صورتهم عليها بتكون متساويين الآن ماشي بدي آجي
+
+232
+00:22:31,520 --> 00:22:40,970
+أقوله assume إن α في ال stabilizer ل i على G
+
+233
+00:22:40,970 --> 00:22:50,670
+يساوي β في ال stabilizer ل i على G يعني
+
+234
+00:22:50,670 --> 00:22:57,970
+أفرض أن عندي two left cosets are equal يبقى then
+
+235
+00:23:05,810 --> 00:23:12,450
+معكوس ال α موجود في ال group of all
+
+236
+00:23:12,450 --> 00:23:13,550
+permutations
+
+237
+00:23:16,760 --> 00:23:23,420
+بصير عند ال stabilizer لل i على G بدل يساوي α
+
+238
+00:23:23,420 --> 00:23:31,100
+inverse مضروبة في β في ال stabilizer لل i على G
+
+239
+00:23:31,730 --> 00:23:35,690
+أضرب الطرفين في α inverse يصبح هنا ال identity
+
+240
+00:23:35,690 --> 00:23:39,810
+أضربها في ال stabilizer يصبح ال stabilizer أضرب
+
+241
+00:23:39,810 --> 00:23:43,430
+α inverse هنا يصبح α inverse β في ال
+
+242
+00:23:43,430 --> 00:23:48,890
+stabilizer طيب نرجع بالذاكرة قليلاً إلى ال left
+
+243
+00:23:48,890 --> 00:23:56,700
+cosets لما أقول H يساوي a H إيش يعني معناها عندما
+
+244
+00:23:56,700 --> 00:24:01,980
+أقول H يساوي a H ما يعني هذا بيحصل إذا كان ال a
+
+245
+00:24:01,980 --> 00:24:07,280
+موجود في H يبقى هذا معناه إن ال α inverse β
+
+246
+00:24:07,280 --> 00:24:13,600
+موجودة في ال stabilizer يبقى هذا معناه إن ال α
+
+247
+00:24:13,600 --> 00:24:22,900
+inverse β موجودة في ال stabilizer لل i على G ما دام
+
+248
+00:24:22,900 --> 00:24:28,000
+موجودة هنا يبقى ال α inverse بتأثيرها على i
+
+249
+00:24:28,000 --> 00:24:32,140
+نفسه
+
+250
+00:24:32,140 --> 00:24:37,680
+ما دام موجودة في ال stabilizer ما دام هذه 
+
+251
+00:24:37,680 --> 00:24:42,340
+موجودة في ال stabilizer هذا معناه أن alpha inverse
+
+252
+00:24:42,340 --> 00:24:51,180
+beta of I يساوي I طيب مادام Alpha يعني بدي أثر على
+
+253
+00:24:51,180 --> 00:24:56,180
+الطرفين بAlpha يبقى هذا إيش بيعطينا؟ بيعطينا أنه
+
+254
+00:24:56,180 --> 00:25:04,960
+Beta تأثيرها على I يساوي Alpha تأثيرها على I تمام؟
+
+255
+00:25:04,960 --> 00:25:09,900
+طيب إيش رأيك بدي أضرب ال stabilizer في الطرفين من
+
+256
+00:25:09,900 --> 00:25:19,570
+جهات اليمين؟ يعني هذا بيعطيك مين؟ بيعطيك أن بيتا في
+
+257
+00:25:19,570 --> 00:25:27,350
+ال stabilizer لل I على G بدها تساوي Alpha في ال
+
+258
+00:25:27,350 --> 00:25:37,580
+stabilizer ل I على G مصبوط هكذا؟ طيب أنا جاي أخدت
+
+259
+00:25:37,580 --> 00:25:43,520
+عنصرين متساوين لجيت .. احنا استنى .. استنى ..
+
+260
+00:25:43,520 --> 00:25:50,630
+استنى شوية، لا لا لا استناشي لسا وأنا احنا أثبتنا
+
+261
+00:25:50,630 --> 00:25:57,850
+أن الـ Beta I بدها تساوي Alpha I وهو المطلوب
+
+262
+00:25:57,850 --> 00:26:03,250
+انتهينا من الشغل يعني يبقى T is well defined بداجي
+
+263
+00:26:03,250 --> 00:26:08,890
+الآن T is one to one يبقى بدي أعمل العملية العكسية
+
+264
+00:26:08,890 --> 00:26:15,330
+بدي أخد صورتين متساويتين وأثبت أن أصلهم متساوي
+
+265
+00:26:15,330 --> 00:26:18,310
+يبقى بداجي أقول Assume
+
+266
+00:26:20,190 --> 00:26:30,330
+أن T of Alpha في الـ Stabilizer لـ I على G بده
+
+267
+00:26:30,330 --> 00:26:37,550
+يساوي T of Beta في الـ Stabilizer على I لـ Main لـ
+
+268
+00:26:37,550 --> 00:26:39,850
+G itself بشكل عام
+
+269
+00:26:42,820 --> 00:26:47,620
+يبقى معنى هذا الكلام هذا الصورة اللي هو Alpha I
+
+270
+00:26:47,620 --> 00:26:56,120
+بدها تساوي Beta I حسب التعريف اللي احنا قايله طبعا
+
+271
+00:26:56,120 --> 00:27:01,740
+ما دام حسب التعريف الحين أنا بدي أثبت أن ال Alpha
+
+272
+00:27:01,740 --> 00:27:04,580
+في ال stabilizer بدها تساوي Beta في ال stabilizer
+
+273
+00:27:04,580 --> 00:27:09,040
+معناته هذه لو جيت ضربت كل واحدة فيهم ال stabilizer
+
+274
+00:27:09,040 --> 00:27:15,840
+هتطلع القيمتان متساويتان يبقى هذا معناته أنه Alpha
+
+275
+00:27:15,840 --> 00:27:23,680
+في ال stabilizer على I لجيه بدها تساوي Beta في ال
+
+276
+00:27:23,680 --> 00:27:30,220
+stabilizer على I لمين لجيه وهو المطلوب يبقى T سارة
+
+277
+00:27:30,220 --> 00:27:40,160
+تشير one to one الآن بدنا نثبت أن T is onto كويس
+
+278
+00:27:41,580 --> 00:27:47,020
+الآن بدي آجي على ال orbit مش هذه موجودة في ال
+
+279
+00:27:47,020 --> 00:27:52,240
+orbit يبقى بدي افترض أن عندي عنصر موجود في ال
+
+280
+00:27:52,240 --> 00:28:00,240
+orbit يبقى let ال X موجود في ال orbit على I ل G
+
+281
+00:28:00,240 --> 00:28:10,630
+then ال X هذا بدي أساويه Phi of I صح؟ يبقى الـ x hat
+
+282
+00:28:10,630 --> 00:28:18,610
+of I of I for some I
+
+283
+00:28:18,610 --> 00:28:25,930
+اللي موجودة في
+
+284
+00:28:25,930 --> 00:28:34,640
+capital S لأنه قال في نص النظرية قال لأي
+
+285
+00:28:34,640 --> 00:28:40,080
+ست له كامتل S يبقى ال I موجود وين في كامتل S طيب
+
+286
+00:28:40,080 --> 00:28:48,800
+ال Phi of I أليس تهيأ T ل Phi في ال stabilizer على
+
+287
+00:28:48,800 --> 00:28:56,750
+I ل G نعم يبقى سارة T is one to one and onto يبقى
+
+288
+00:28:56,750 --> 00:29:06,090
+هنا سارة T is one to one and onto بدأ من one to
+
+289
+00:29:06,090 --> 00:29:10,630
+one and onto يبقى عدد العناصر عدد ال left cosets
+
+290
+00:29:10,630 --> 00:29:17,550
+يبقى عدد العناصر في ال orbit يبقى هذا يعطينا مين
+
+291
+00:29:18,540 --> 00:29:29,560
+the number of left cosets
+
+292
+00:29:29,560 --> 00:29:44,020
+of the stabilizer لل I على G in G equal to equal
+
+293
+00:29:44,020 --> 00:29:46,640
+to the number
+
+294
+00:29:49,250 --> 00:30:00,230
+of equal to the number of elements in the orbit of
+
+295
+00:30:00,230 --> 00:30:03,130
+I على G
+
+296
+00:30:09,860 --> 00:30:12,940
+أن ال order اللي لجيه على ال order اللي لسه
+
+297
+00:30:12,940 --> 00:30:18,140
+بالإضافة بتساوي عدد من عدد ال left cosets هنا the
+
+298
+00:30:18,140 --> 00:30:25,420
+number of elements in اللي هو that is يعني أن that
+
+299
+00:30:25,420 --> 00:30:34,680
+is اللي هو العدد تبع ال orbit لل I على G هذه
+
+300
+00:30:34,680 --> 00:30:40,160
+المقصود فيها يعني صار إيش عدد ال left cosets اللي
+
+301
+00:30:40,160 --> 00:30:46,160
+ولا واحدة زي التانية يساوي من يساوي العدد تبع
+
+302
+00:30:46,160 --> 00:30:51,360
+العناصر هنا إذا بقدر أشيل هذه وأكتب القيمة
+
+303
+00:30:51,360 --> 00:30:57,620
+بتاعتها سميلي هذه star اللي بتقدر تقولي الصواب اسم
+
+304
+00:30:57,620 --> 00:31:08,860
+تت يوت in a star we get ال order لل G على ال order
+
+305
+00:31:08,860 --> 00:31:17,000
+لل stabilizer ل I على G بيساوي عدد العناصر أو عدد
+
+306
+00:31:17,000 --> 00:31:23,920
+ال elements في ال orbit تبع ال I على G لو ضربنا ضرب
+
+307
+00:31:23,920 --> 00:31:31,560
+تبادلي بصير ال order لل G بيساوي عدد العناصر في
+
+308
+00:31:31,560 --> 00:31:39,900
+ال orbit لل I على G في ال order لل stabilizer لل I
+
+309
+00:31:39,900 --> 00:31:42,320
+على G وهو المطلوب
+
+310
+00:31:44,870 --> 00:31:48,970
+دائما وأبدا لما نقول لك بدي عدل العناصر في الست
+
+311
+00:31:48,970 --> 00:31:53,370
+الأولى يساوي عدل العناصر في الستات التانية بتروح
+
+312
+00:31:53,370 --> 00:31:57,330
+تتعرف function ما بين اتين اتين و تثبت أن هذه one
+
+313
+00:31:57,330 --> 00:32:03,110
+to one and onto إذا أثبتتها بيكون هك تمام لحد هيك
+
+314
+00:32:03,110 --> 00:32:07,810
+بيكون انتهينا من الجزء النظري تبع هذا section طبعا
+
+315
+00:32:07,810 --> 00:32:11,940
+في شغل الموضوع اللي بدنا نشيها اللي هو دوران المكعب
+
+316
+00:32:11,940 --> 00:32:15,800
+وما إلى ذلك امسح هناك فيها لحد هنا stop يوم
+
+317
+00:32:15,800 --> 00:32:20,560
+الأثنين بنناقش بعض المسائل على هذا ال section إن
+
+318
+00:32:20,560 --> 00:32:22,120
+شاء الله تبارك وتعالى
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a2bb1d0f4ab579608be4f7435e4b841673274bbf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_postprocess.srt
@@ -0,0 +1,1824 @@
+1
+00:00:21,700 --> 00:00:26,740
+بسم الله الرحمن الرحيم عودة على بدء المرة الماضية
+
+2
+00:00:27,120 --> 00:00:31,700
+عطينا تعريف للـ isomorphism وعطينا بعض الأمثلة على
+
+3
+00:00:31,700 --> 00:00:37,640
+ال isomorphism ثم برهننا نظرية وهي أي group
+
+4
+00:00:37,640 --> 00:00:41,680
+isomorphic إلى ال group of permutations وعطينا
+
+5
+00:00:41,680 --> 00:00:46,920
+علامة ذلك مثلا واحدة المرة الماضية ووصلنا إلى خواص
+
+6
+00:00:46,920 --> 00:00:51,280
+ال isomorphism يبقى أنا كاتب عنوان properties of
+
+7
+00:00:51,280 --> 00:00:57,970
+isomorphism بخواص التشكل النمطيهنقسم هذه الخواص
+
+8
+00:00:57,970 --> 00:01:03,350
+إلى جزءين الجزء الأول الخواص حين يعمل ال
+
+9
+00:01:03,350 --> 00:01:08,970
+isomorphism على عناصر ال group والخاصية التانية
+
+10
+00:01:08,970 --> 00:01:13,170
+حينما يعمل isomorphism على الشكل العام لل group
+
+11
+00:01:13,170 --> 00:01:17,630
+وبالتالي هيكون عندنا نظريتين هذه النظرية الأولى
+
+12
+00:01:17,630 --> 00:01:22,890
+مكونة من سبع نقاط والنظرية الثانية مكونة من أربع
+
+13
+00:01:22,890 --> 00:01:28,320
+نقاط ان شاء الله تعالىنبدأ بالنظرية الأولى وهي الـ
+
+14
+00:01:28,320 --> 00:01:33,160
+properties of isomorphism acting on elements يبقى
+
+15
+00:01:33,160 --> 00:01:39,600
+خواص ال isomorphism إن كان يعمل عالميا على العناصر
+
+16
+00:01:39,600 --> 00:01:43,990
+اللي موجودة في ال groupبقول يفترض أن الـ Phi عبارة
+
+17
+00:01:43,990 --> 00:01:48,250
+عن isomorphism من الآن فالساعدة هختصر كلمة
+
+18
+00:01:48,250 --> 00:01:53,770
+isomorphism إلى ISO اللي هي أول تلت حروف من كلمة
+
+19
+00:01:53,770 --> 00:01:59,290
+isomorphism يبقى Phi isomorphism من ال group G on
+
+20
+00:01:59,290 --> 00:02:04,970
+to G bar يبقى one to one و on to و يختم خاصية اللي
+
+21
+00:02:04,970 --> 00:02:08,310
+هو ال isomorphism بالإضافة إلى أن ال Phi عبارة عن
+
+22
+00:02:08,310 --> 00:02:15,150
+functionيبقى then phi of EG يساوي ال EG bar يعني
+
+23
+00:02:15,150 --> 00:02:19,610
+فيه لما تأثر على ال identity element تبع ال group
+
+24
+00:02:19,610 --> 00:02:25,450
+G هتخلي صورته مين ال identity تبع ال group G bar
+
+25
+00:02:25,450 --> 00:02:29,070
+يعني صورة ال identity في ال group الأولى هو ال
+
+26
+00:02:29,070 --> 00:02:34,910
+identity تبع ال group الثانيالنقطة الثانية لو أخدت
+
+27
+00:02:34,910 --> 00:02:40,570
+أي عدد صحيح موجب أو سالب أو صفر موجود في z و أخدت
+
+28
+00:02:40,570 --> 00:02:45,510
+أي element a موجود في g ففاي لم تثر على a to the
+
+29
+00:02:45,510 --> 00:02:51,340
+power n بدي يسوي فاي of a كله to the power nلاحظوا
+
+30
+00:02:51,340 --> 00:02:56,440
+ان ال a انها دي موجودة في g لإن a موجودة في g بس
+
+31
+00:02:56,440 --> 00:03:02,000
+ال fi of a موجودة في جي بار يبقى هذا element موجود
+
+32
+00:03:02,000 --> 00:03:07,620
+في جي بار النقطة الثالثة فرعان a و b موجودة في g
+
+33
+00:03:07,620 --> 00:03:13,660
+ال a بيبدوا يسووا بي اي بي اي فندلوا fi of a في fi
+
+34
+00:03:13,660 --> 00:03:19,950
+of b وسووا fi of b في fi of a بمعنى آخرلو كان هذا
+
+35
+00:03:19,950 --> 00:03:24,430
+الكلام لأي two elements لو كانت الـG أبيليان يبقى
+
+36
+00:03:24,430 --> 00:03:28,990
+الـG bar بتصير أبيليان كذلك هذا معنى ال two
+
+37
+00:03:28,990 --> 00:03:33,690
+elements لو بتطورهم على مجموع العناصر كلها النقطة
+
+38
+00:03:33,690 --> 00:03:38,440
+الرابعةالـ G بدا تساوي ال group generated by A
+
+39
+00:03:38,440 --> 00:03:44,000
+فاندو ألف الجي بار generated by Phi of A يعني يا
+
+40
+00:03:44,000 --> 00:03:48,280
+شباب ال generator في ال group الأولى الصورة بتبقى
+
+41
+00:03:48,280 --> 00:03:54,080
+generator لمين؟ لل group A الثانيةيبقى انا عندي A
+
+42
+00:03:54,080 --> 00:03:59,140
+هو generator لل group G صارت صوته Phi of A هي
+
+43
+00:03:59,140 --> 00:04:04,560
+generator لمين؟ لل group G bar النقطة الخامسة ال
+
+44
+00:04:04,560 --> 00:04:09,220
+order ل A بدو يساوي ال order لل Phi of A ال order
+
+45
+00:04:09,220 --> 00:04:13,820
+لل element A اللي موجود في ال group G يساوي ال
+
+46
+00:04:13,820 --> 00:04:18,340
+order للصورة تبع هذه ال element اللي موجود وين؟ في
+
+47
+00:04:18,340 --> 00:04:22,010
+ال group G barواذا بتذكروا المرة الماضية لما
+
+48
+00:04:22,010 --> 00:04:26,630
+تكلمنا عن معنى ال isomorphism قلنا الخواص جميعها
+
+49
+00:04:26,630 --> 00:04:30,150
+اللي موجودة على ال group الأولى هي نفس الخواص اللي
+
+50
+00:04:30,150 --> 00:04:34,350
+موجودة على ال group الثانية ومن هنا فال order لل a
+
+51
+00:04:34,350 --> 00:04:40,660
+هو ال order لل phi of a بالضبط تماماالنقطة السادسة
+
+52
+00:04:40,660 --> 00:04:45,240
+فوريا هي fixed integer k يعني لو أخدت عدد صحيح
+
+53
+00:04:45,240 --> 00:04:51,060
+سميته k و fixed element b in g وكانت عند المعادلة
+
+54
+00:04:51,060 --> 00:04:57,400
+xk تساوي b يبقى هذه المعادلة لها نفس العدد من
+
+55
+00:04:57,400 --> 00:05:01,860
+الحلول مثل حل المعادلة x to the power k بده يسوى
+
+56
+00:05:01,860 --> 00:05:07,940
+five of b in g bar الأولانية في g والتانية وين؟بـG
+
+57
+00:05:07,940 --> 00:05:12,420
+bar حلول المعادلة لو كان عشرة حلول إذا المعادلة
+
+58
+00:05:12,420 --> 00:05:17,480
+الثانية لها عشرة حلول بالضبط تماما النقطة السادسة
+
+59
+00:05:17,480 --> 00:05:21,920
+السابعة والاخيرة لو كانت الـG finite يبقى ال order
+
+60
+00:05:21,920 --> 00:05:25,880
+اللي G بده يسوي من؟ ال order اللي G bar طب لو
+
+61
+00:05:25,880 --> 00:05:31,620
+كانوا اتنين N finiteيبقى ال order للأولى يساوي ال
+
+62
+00:05:31,620 --> 00:05:36,680
+order للتانية يساوي in finite لكن المشكلة تبقى لو
+
+63
+00:05:36,680 --> 00:05:41,640
+كانوا finite هل العدد هنا هو نفس العدد هنا الإجابة
+
+64
+00:05:41,640 --> 00:05:47,410
+نعم لماذا هذا ما سنعرفه بعد قليليبقى بعد أن فهمنا
+
+65
+00:05:47,410 --> 00:05:52,070
+هذه النقاط السابعة نريد أن نبرهن على صحة هذه
+
+66
+00:05:52,070 --> 00:05:58,270
+النقاط ونبدأ بالنقطة الأولى بدي أثبت أن صورة ال
+
+67
+00:05:58,270 --> 00:06:02,430
+identity element اللي موجود في G هو ال identity
+
+68
+00:06:02,430 --> 00:06:07,860
+element اللي موجود وينمش يعني هيك، إيش رأيك في
+
+69
+00:06:07,860 --> 00:06:13,120
+هالشغلة؟ لو جيت أخدت ال identity تبع ال G و ضربته
+
+70
+00:06:13,120 --> 00:06:18,100
+في ال identity تبع ال G، شو بيعطيني هذا؟ ال
+
+71
+00:06:18,100 --> 00:06:23,720
+identity تبع ال G هو نفسهطب ايش رايك بدي اثر في
+
+72
+00:06:23,720 --> 00:06:30,160
+على الطرفين مدام انصرين متساويين هذا يعني ان في of
+
+73
+00:06:30,160 --> 00:06:35,080
+ال identity تبع ال G في ال identity تبع ال G بدي
+
+74
+00:06:35,080 --> 00:06:41,780
+ساوي ال في of ال identity تبع ال G الآن احنا جالين
+
+75
+00:06:41,780 --> 00:06:47,150
+في عبارة عن ايش؟Isomorphism إذا بقدر أدخل الـ Phi
+
+76
+00:06:47,150 --> 00:06:52,130
+على كل element من هذه ال elements يبقى هذا بده
+
+77
+00:06:52,130 --> 00:06:57,850
+يعطينا أن Phi of ال identity تبع ال G في Phi of ال
+
+78
+00:06:57,850 --> 00:07:03,730
+identity تبع ال G بده سوى Phi of ال identity تبع
+
+79
+00:07:03,730 --> 00:07:08,910
+ال G ليش؟ لأن Phi عبارة عن Isomorphism وبالتالي
+
+80
+00:07:08,910 --> 00:07:14,440
+دخلت ال Phi على كل element من ال two elementsطب في
+
+81
+00:07:14,440 --> 00:07:19,460
+او في عنصر موجود وين هذا في اي groupفى جى بار طب
+
+82
+00:07:19,460 --> 00:07:23,140
+جى بار ايش قلنا عليها group العنصر معناته ايه له
+
+83
+00:07:23,140 --> 00:07:27,700
+معكوس معناته هذا العنصر اللى هو معكوس فى جى بار
+
+84
+00:07:27,700 --> 00:07:32,920
+بيدروح اضرب الطرفين فى هذا المعكوس يبقى لو روحت
+
+85
+00:07:32,920 --> 00:07:36,820
+ضربت الطرفين فى هذا المعكوس بيصير في of ال
+
+86
+00:07:36,820 --> 00:07:42,860
+identity تبع الجى فى في of ال identity تبع الجى فى
+
+87
+00:07:42,860 --> 00:07:49,290
+في of ال identity تبع الجى بس الكل inverseبدي ساوي
+
+88
+00:07:49,290 --> 00:07:53,830
+الـ Phi of ال identity تبع ال G في Phi of ال
+
+89
+00:07:53,830 --> 00:08:01,190
+identity تبع ال G لكل inverse يبقى ضاربت المعادلة
+
+90
+00:08:01,190 --> 00:08:06,010
+اللي عندنا هذه من جهتي اليمين في ال element Phi of
+
+91
+00:08:06,010 --> 00:08:11,590
+G inverse طب ال element هذا في هذا مش هذا ال
+
+92
+00:08:11,590 --> 00:08:16,970
+element و معكوسه؟ قدش بيعطيني؟تبع مين؟ تبع الـ G
+
+93
+00:08:16,970 --> 00:08:25,110
+bar في الـ Phi of EG بيعطيني مين؟ لا بيعطيني Phi
+
+94
+00:08:25,110 --> 00:08:30,810
+of EG دغلي لإن Phi of EG element في G barويعني هذا
+
+95
+00:08:30,810 --> 00:08:35,590
+بدي يعطيني مين؟ بدي يعطيني الـPhi of ال identity
+
+96
+00:08:35,590 --> 00:08:40,550
+تبع الـG في ال identity element تبع الـG bar وهذا
+
+97
+00:08:40,550 --> 00:08:45,410
+بدي يعطيني ال identity element تبع مين؟ تبع الـG
+
+98
+00:08:45,410 --> 00:08:51,220
+barطب هذا element في G bar لأن صورة ال identity
+
+99
+00:08:51,220 --> 00:08:55,340
+element تبع ال G و هذا ال identity element تبع ال
+
+100
+00:08:55,340 --> 00:09:01,640
+G bar حصل ضربهما شو بيعطيني ال phi of EG نفسه لأن
+
+101
+00:09:01,640 --> 00:09:04,660
+ال identity element اضرب في أي عنصر في ال group
+
+102
+00:09:04,660 --> 00:09:10,650
+بيعطيني نفس العنصر إذا بناء عليه هذا بده يعطينيإن
+
+103
+00:09:10,650 --> 00:09:17,570
+الـ Phi of الـ EG بدرساوي الـ Identity Element تبع
+
+104
+00:09:17,570 --> 00:09:24,170
+الـ G bar أظن و هو المطلوب يبقى هاي أثبتنا له أن
+
+105
+00:09:24,170 --> 00:09:28,130
+صوت الـ Identity Element تبع الـ G هو الـ Identity
+
+106
+00:09:28,130 --> 00:09:34,110
+Element تبع الـ G bar طيب، كويس نيجي للنقطة
+
+107
+00:09:34,110 --> 00:09:39,930
+الثانيةالنقطة الثانية بيقول for any n belongs to z
+
+108
+00:09:39,930 --> 00:09:45,930
+وما قالليش positive integer قاللي n موجود في z إذا
+
+109
+00:09:45,930 --> 00:09:51,630
+احتمال n أن يكون zero واحتمال أن يكون عدد موجب
+
+110
+00:09:51,630 --> 00:09:56,910
+واحتمال أن يكون عدد سالم مش كل احتمالات واردة إذا
+
+111
+00:09:56,910 --> 00:10:02,230
+لازم أدرس كل هذه الاحتمالات على العلاقة اللي عندنا
+
+112
+00:10:02,230 --> 00:10:07,040
+هذهيبقى انا بدي اثبت صحيحة في حالة ان السالبة و ان
+
+113
+00:10:07,040 --> 00:10:12,380
+الموجبة و ان الصفرية كل احتمالات لازم ادرسها حتى
+
+114
+00:10:12,380 --> 00:10:18,640
+تبقى العلاقة عندى صحيحة على طول بعد ذلك الانباجي
+
+115
+00:10:18,640 --> 00:10:26,220
+بيقولوا لو كانت الان تساوي zero thenماذا يحصل هنا
+
+116
+00:10:26,220 --> 00:10:34,840
+يا عزيزي؟ فاي او ا زرع يسوى فاي او ا زرع كله زرع
+
+117
+00:10:34,840 --> 00:10:41,780
+هذا يريد ان يعطينا اذا ازرع عبارة عن مين؟ تبع الجي
+
+118
+00:10:41,780 --> 00:10:46,680
+يبقى هذا يريد ان يعطينا ال five entity element تبع
+
+119
+00:10:46,680 --> 00:10:48,500
+الجي وهذا يريد ان يعطينا مين؟
+
+120
+00:10:54,190 --> 00:10:58,150
+النقطة الأولى اللى عندنا هذا بالضبط تماما يبقى
+
+121
+00:10:58,150 --> 00:11:03,350
+معناته ال statement صحيحة في حالة n تساوي zero
+
+122
+00:11:03,350 --> 00:11:12,640
+يبقى هذا بده يعطينا in the statement hallيبقى
+
+123
+00:11:12,640 --> 00:11:17,600
+الجملة اللى عندنا هذه مالها صحيحة في حالة n تساوي
+
+124
+00:11:17,600 --> 00:11:22,640
+zero طب لو كانت ال n تساوي واحد then
+
+125
+00:11:32,890 --> 00:11:38,630
+يبقى الجملة الصحيحة في حالة الان تساوي واحد هذا
+
+126
+00:11:38,630 --> 00:11:43,130
+سيعطينا ان ال statement صحيح في حالة الان تساوي
+
+127
+00:11:43,130 --> 00:11:48,240
+واحدالان بدي استخدم ال induction بدي افترض انها
+
+128
+00:11:48,240 --> 00:11:53,780
+صحيحة في حالة n تساوي k الموجبة و اثبت انها صحيحة
+
+129
+00:11:53,780 --> 00:11:59,180
+في حالة n تساوي k زائد واحد يبقى بداجي اقول له
+
+130
+00:11:59,180 --> 00:12:08,240
+assume that ان five a to the power k بتساوي five
+
+131
+00:12:08,240 --> 00:12:16,200
+of a كله to the power kوالـ K هذي أكبر منين؟ من
+
+132
+00:12:16,200 --> 00:12:22,440
+الواحد، لأن الواحد استخدمناها، حُطها على طول طيب،
+
+133
+00:12:22,440 --> 00:12:30,160
+بدأ أروح أقول الـ M Phi of K plus one ويساوي يبقى
+
+134
+00:12:30,160 --> 00:12:38,120
+هذه بقدر تبع Phi of K في A أس واحد، لو جمعته، نجمع
+
+135
+00:12:38,120 --> 00:12:40,520
+الأسس جامعه، يبقى صحيحة
+
+136
+00:12:45,990 --> 00:12:57,130
+فاي عبارة عن isomorphism لإن فاي
+
+137
+00:12:57,130 --> 00:13:00,370
+عبارة عن isomorphism لإن فاي عبارة عن isomorphism
+
+138
+00:13:00,370 --> 00:13:05,750
+لإن فاي عبارة عن isomorphism لإن
+
+139
+00:13:05,750 --> 00:13:13,670
+فاي عبارة عن isomorphismيبقى بقدر اكتب هذه في of a
+
+140
+00:13:13,670 --> 00:13:20,590
+كله to the power كيف في of a من وين من الفرض اللي
+
+141
+00:13:20,590 --> 00:13:32,540
+فوق اللي عندنا هذايبقى هذا الكلام from above
+
+142
+00:13:32,540 --> 00:13:40,940
+assumption من الفرض اللي فرضنايبقى صارت العبارة
+
+143
+00:13:40,940 --> 00:13:47,180
+صحيحة فرض صحتها عند n تساوي k و أثبت صحتها عند n
+
+144
+00:13:47,180 --> 00:13:53,400
+تساوي k plus one إذا العبارة صحيحة لكل ال n اللي
+
+145
+00:13:53,400 --> 00:14:00,300
+أكبر من أو تساوي zero يبقى هنا so the statement
+
+146
+00:14:02,650 --> 00:14:10,110
+hold صحيحة for all ان اللي أكبر من أو تساوي zero
+
+147
+00:14:10,110 --> 00:14:15,410
+ايش ضايل عندى اقل من ال zero يبقى باجي بقوله بعد
+
+148
+00:14:15,410 --> 00:14:21,150
+ما أخدنا FN و هنا لو كانت N تساوي K يبقى بدياجي
+
+149
+00:14:21,150 --> 00:14:29,620
+ياخد لو كانت N أقل من ال zero thenالـ N تساوي
+
+150
+00:14:29,620 --> 00:14:38,100
+الناقص M والـ M أكبر من الـ Zeroيبقى انا فارض ان
+
+151
+00:14:38,100 --> 00:14:44,340
+ان تساوي ناقص M و M أكبر من ال zero مسبوقة بإشارة
+
+152
+00:14:44,340 --> 00:14:48,840
+سالب إذا هذه السالبة على طول يبقى مضمون كلامي صحيح
+
+153
+00:14:48,840 --> 00:14:55,240
+مية المية يبقى لو كانت ال M الآن موجبة أكبر من ال
+
+154
+00:14:55,240 --> 00:14:59,580
+zero ضربت في إشارة سالب مش بيصير اللي هي ان يبقى
+
+155
+00:14:59,580 --> 00:15:05,620
+مضمون هيك ان سالبة مائة في المائة تماميبقى بدك تحط
+
+156
+00:15:05,620 --> 00:15:10,940
+في دماغك ان M موجبة سوقت بإشارة سالبة وصارت ايه؟
+
+157
+00:15:10,940 --> 00:15:17,860
+سالبة يبقى هذا بده يعطيلك ان ال N زائد ال M قداش
+
+158
+00:15:17,860 --> 00:15:23,860
+بده ساوي زيرو نجلناها على شجة تانية ساوي زيرو طيب
+
+159
+00:15:23,860 --> 00:15:32,620
+الان لو جيت أخدت A N زائد ال M مش بده ساوي ال A أو
+
+160
+00:15:32,620 --> 00:15:43,420
+ال Zeroفح؟ تمام؟ طيب، أليس تهادي A N في A M بده
+
+161
+00:15:43,420 --> 00:15:50,840
+يساوي ال identity element تبع ال G؟ مظبوط؟ طيب،
+
+162
+00:15:50,840 --> 00:15:55,930
+إيش رأيك؟ بده يأثر على الطرفين بـ Fiلأن في ايزو
+
+163
+00:15:55,930 --> 00:16:04,630
+مورفزم هذا بدي يعطيك ان في of a n في a m بدي سوى
+
+164
+00:16:04,630 --> 00:16:11,010
+في of ال identity element تبع ال G الان في ايزو
+
+165
+00:16:11,010 --> 00:16:18,910
+مورفزم معناه هذا الكلام ان في of a n في في of a m
+
+166
+00:16:18,910 --> 00:16:25,890
+بدي سوى ال identity element تبع ال G بقىطب الام
+
+167
+00:16:25,890 --> 00:16:31,320
+موجبه الله سالمه بقىطب و احنا اثبتنا ان هذه
+
+168
+00:16:31,320 --> 00:16:37,040
+الصحيحة لـK الموجبة اذا بالنسبة لإن بقدر اكتب في
+
+169
+00:16:37,040 --> 00:16:46,560
+of A لكل أس M مظبوط يبقى هذا بده يعطيلك ان في of A
+
+170
+00:16:46,560 --> 00:16:54,860
+N في في of A كل أس M بده سوى ال identity element
+
+171
+00:16:54,860 --> 00:17:03,390
+تبع الـG barليش هذا؟ هذا الكلام from the .. حطها
+
+172
+00:17:03,390 --> 00:17:12,330
+ليه بين قوسين؟ above approved since ال M greater
+
+173
+00:17:12,330 --> 00:17:19,300
+than zeroيعني نظرا لإن ال M أكبر من ال zero جدرت
+
+174
+00:17:19,300 --> 00:17:25,520
+أرفع الأس من هنا على A و أحطه على Phi of A كله لكن
+
+175
+00:17:25,520 --> 00:17:31,380
+تبع ال N لسه مش جادر، كويس؟ إيش رأيك؟ بدي أضرب فيه
+
+176
+00:17:31,380 --> 00:17:43,060
+معكوس هذا العنصريبقى هذا يعطيك ان في ام في في ام
+
+177
+00:17:43,060 --> 00:17:51,320
+في في ام في في ام في ام في ام في ام في ام في ام في
+
+178
+00:17:51,320 --> 00:17:51,520
+ام في ام في ام في ام في ام في ام في ام في ام في ام
+
+179
+00:17:51,520 --> 00:17:52,300
+في ام في ام في ام في ام في ام في ام في ام في ام في
+
+180
+00:17:52,300 --> 00:17:52,400
+ام في ام في ام في ام في ام في ام في ام في ام في ام
+
+181
+00:17:52,400 --> 00:18:01,860
+ام في ام في ام في ام في ام في ام في ام في ام في ام
+
+182
+00:18:01,860 --> 00:18:03,940
+في ام
+
+183
+00:18:05,750 --> 00:18:11,830
+طب ايش رأيك في العنصر هذا و هذا؟ مش واحد معكس
+
+184
+00:18:11,830 --> 00:18:16,670
+الثاني؟ اذا هذا بيعطيني ال identity element تبع
+
+185
+00:18:16,670 --> 00:18:23,290
+من؟ ال G bar بيقدروا في Phi of An يبقى هذا بيقدر
+
+186
+00:18:23,290 --> 00:18:30,730
+يعطيني Phi of An بيقدر يساويهذا أُس مُركّب
+
+187
+00:18:30,730 --> 00:18:35,030
+باعتباره يبقى تضرب الأسس في بعضها في ال identity
+
+188
+00:18:35,030 --> 00:18:42,470
+بطلع نفس ال main نفس ال element يبقى هذا Phi of L
+
+189
+00:18:42,470 --> 00:18:52,050
+ناقص Mتمام طيب ناقص M هي مين عندنا هنا N يبقى بده
+
+190
+00:18:52,050 --> 00:18:58,310
+يشيلها و اكتب بدلها N يبقى هذا بده يعطينا Phi of A
+
+191
+00:18:58,310 --> 00:19:06,370
+N بده يساوي Phi of A كله to the power N وهو المقوم
+
+192
+00:19:07,110 --> 00:19:12,670
+إذا أثبتنا هذه الخاصية رقم اتنين لإن Zero ان بواحد
+
+193
+00:19:12,670 --> 00:19:18,530
+وان عدد موجب وان عدد سالب إذا صحيحة لكل الان اللي
+
+194
+00:19:18,530 --> 00:19:27,850
+موجودة في Z يبقى هنا Suh Phi of A N بدرساوي Phi of
+
+195
+00:19:27,850 --> 00:19:34,430
+A كله to the power N لكل ان اللي موجود في Z بلا
+
+196
+00:19:34,430 --> 00:19:39,600
+استثناءحد بيحب يسألني سؤال هنا في النقطة الثانية
+
+197
+00:19:39,600 --> 00:19:46,720
+قبل أن نذهب إلى الثالثة حد بيحب يسألني سؤالتقرأ
+
+198
+00:19:46,720 --> 00:19:50,860
+زين مرة علينا شغل زي هيك مرة و فصلناها بهذا
+
+199
+00:19:50,860 --> 00:19:56,140
+التفصيل و بال induction من حد ما يقولك N في Z بدك
+
+200
+00:19:56,140 --> 00:20:01,880
+تسوي التفصيل هذا كله لكن لو جلك N موجودة في N
+
+201
+00:20:01,880 --> 00:20:06,100
+capital يعني set of natural number يبقى بكفيني ال
+
+202
+00:20:06,100 --> 00:20:09,920
+zero او حتى ال zero مش لازم ليه بكفيني ال واحد و
+
+203
+00:20:09,920 --> 00:20:15,390
+ال K خلاص اللي هو الجزء الأول من ال proofنعود
+
+204
+00:20:15,390 --> 00:20:21,830
+للنقطة الثالثة النقطة التالتة بيقول for any a وb
+
+205
+00:20:21,830 --> 00:20:26,750
+اللي موجود في جي a بيبقى بيبقى بي بيبقى a بيبقى a
+
+206
+00:20:26,750 --> 00:20:27,010
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+207
+00:20:27,010 --> 00:20:28,170
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+208
+00:20:28,170 --> 00:20:29,750
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+209
+00:20:29,750 --> 00:20:33,550
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+210
+00:20:33,550 --> 00:20:39,320
+بيبقى a بيبقى a بيبقى a بيA وB اللي موجودة في جيب
+
+211
+00:20:39,320 --> 00:20:49,000
+ال A بيبدوا يسووا بي A F and ألف تأثير الفاي على
+
+212
+00:20:49,000 --> 00:20:56,060
+الأولى بيبدوا يسووا تأثير الفاي على الثانىمش هدول
+
+213
+00:20:56,060 --> 00:21:00,640
+عنصرين متساويين وعندي isomorphism إذا تأثير الـ
+
+214
+00:21:00,640 --> 00:21:03,480
+Phi على ال element الأول هو نفس تأثير ال Phi
+
+215
+00:21:03,480 --> 00:21:07,500
+عالميا على ال element التاني لإنه one two and and
+
+216
+00:21:07,500 --> 00:21:14,110
+on two طيب الكلام هذا صحيح if and only ifالـ Phi
+
+217
+00:21:14,110 --> 00:21:18,470
+هذه عبارة عن ايزو مورفزم إذا بده فك هذي و فك هذي
+
+218
+00:21:18,470 --> 00:21:26,070
+إذا الـ Phi of A في Phi of B بده يساوي ده فك هذي
+
+219
+00:21:26,070 --> 00:21:35,590
+يبقى Phi of B في Phi of A طبعا يبقى إيه صارت عندنا
+
+220
+00:21:35,590 --> 00:21:40,550
+بالشكل هذا و هو المطلوب يبقى و هو المطلوب نجي
+
+221
+00:21:40,550 --> 00:21:42,350
+للنقطة الرابعة
+
+222
+00:21:44,760 --> 00:21:52,100
+بنمسح الشجة دي كلها طب وش بتستنوا يالا مافيش وقت
+
+223
+00:21:52,100 --> 00:21:55,560
+مش هنجي للشجة دي يعني خلصنا نقطة تالتة بنروح
+
+224
+00:21:55,560 --> 00:22:00,820
+للرابع الان بدنا نجي للنقطة الرابع واضح انه جيه
+
+225
+00:22:01,880 --> 00:22:07,040
+بيقول هي ال group generated by a أو ال group
+
+226
+00:22:07,040 --> 00:22:12,780
+generated by a if and only if ال g bar هي ال group
+
+227
+00:22:12,780 --> 00:22:19,740
+generated by phi of a وكأنه بمعنى آخر بيقول صورة
+
+228
+00:22:19,910 --> 00:22:26,750
+الجنريتر في جيه هو جنريتر لمين لجيه بار بعبارة
+
+229
+00:22:26,750 --> 00:22:33,830
+أخرى بيقول الجنريتر تبع لجروب جيه صورته هو
+
+230
+00:22:33,830 --> 00:22:38,710
+الجنريتر لمين لجروب جيه بار معناه ان انا بقول هذا
+
+231
+00:22:38,710 --> 00:22:43,090
+من ناحية الفهملكن احنا بدنا نروح نبرهن انا عندي
+
+232
+00:22:43,090 --> 00:22:48,010
+عبارتين مربوطات ب F and only F يبقى البرهام بده
+
+233
+00:22:48,010 --> 00:22:55,350
+يصير في اتجاهينه يبقى بده اجي اقوله assume افترض
+
+234
+00:22:55,350 --> 00:23:00,710
+العبارة الاولى ان G هو ال cyclic group generated
+
+235
+00:23:00,710 --> 00:23:07,320
+by Aماذا بدنا نثبت؟ بدنا نثبت ان جي بار هي ال
+
+236
+00:23:07,320 --> 00:23:12,880
+group generated by phi of a بمعنى أخر لو رجعت إلى
+
+237
+00:23:12,880 --> 00:23:19,240
+مبادئ الرياضيات وقدرت اثبت ان جي بار subset من ال
+
+238
+00:23:19,240 --> 00:23:23,920
+subgroup generated by phi of aو بعد ذلك استطعت أن
+
+239
+00:23:23,920 --> 00:23:29,220
+أثبت أن الـ subgroup من الـ G بار يبقى اتنين are
+
+240
+00:23:29,220 --> 00:23:33,080
+equal يبقى هذه السراتجية في البرهان بدأت تحدث
+
+241
+00:23:33,080 --> 00:23:38,820
+بالشكل اللي عندنا هذا طيب نمشي الآن انا بدأ أثبت
+
+242
+00:23:38,820 --> 00:23:45,280
+الاتنين هذول are equal كويس؟ الآن اسيوم فرضنا هذا
+
+243
+00:23:45,280 --> 00:23:54,460
+الآن ال A موجودة في جيهذا معناته ان الـ Phi of A
+
+244
+00:23:54,460 --> 00:24:03,000
+موجود في الـ G bar تمام ال Phi A موجود في الـ G
+
+245
+00:24:03,000 --> 00:24:10,480
+bar هذا معناته ان ال sub group generated by Phi of
+
+246
+00:24:10,480 --> 00:24:16,280
+A subset من الـ G bar صح ولا لاهذا ال element
+
+247
+00:24:16,280 --> 00:24:21,380
+موجود في ايه؟ يبقى صورته موجودة في جي بار مادام ال
+
+248
+00:24:21,380 --> 00:24:25,380
+element هذا موجود في جي بار يبقى هيكوّل ليه
+
+249
+00:24:25,380 --> 00:24:30,560
+subgroup generated by phi of a يمكن قد الجي بار
+
+250
+00:24:30,560 --> 00:24:35,420
+بالكامل ويمكن أقل شوية لكن عنها مازيدش بالمرة،
+
+251
+00:24:35,420 --> 00:24:38,280
+مظبوط؟ يبقى هذا معناه
+
+252
+00:24:45,310 --> 00:24:51,570
+العلاقة هذه رقم star الان
+
+253
+00:24:51,570 --> 00:24:57,390
+ناخد العملية العكسية افترض
+
+254
+00:24:57,390 --> 00:25:06,780
+ان بي موجودة في جي بارالان فاي is onto يبقى بي
+
+255
+00:25:06,780 --> 00:25:14,520
+اللي موجودة في جي بار الها أصل في جي يبقى هنا
+
+256
+00:25:14,520 --> 00:25:24,780
+since بما أن الفاي is onto ال بي هذه لازم تسوي لي
+
+257
+00:25:24,780 --> 00:25:34,470
+فاي of ا كيبقى الـP اللي أخدته في G أنا فرض من؟
+
+258
+00:25:34,470 --> 00:25:39,790
+فرض هذه هيك بالشكل هذا يعني فرضها الـCyclic group
+
+259
+00:25:39,790 --> 00:25:44,230
+generated by A إذا الـElement P يبدو يسوي
+
+260
+00:25:44,230 --> 00:25:49,070
+الـElement موجود هنا إيه شكل الـElement؟ شكله A
+
+261
+00:25:49,070 --> 00:25:54,130
+أُس K يبقى الـElement P اللي موجود في G برصوته Phi
+
+262
+00:25:54,130 --> 00:26:01,530
+of AKطيب لما اقول fi of a k ال k هادي positive ولا
+
+263
+00:26:01,530 --> 00:26:05,410
+negative ولا zero؟ positive و negative و zero
+
+264
+00:26:05,410 --> 00:26:15,270
+معقول؟ طلع هنا0 ممكن 1,2,3,4 لغاية ال N يبقى لا
+
+265
+00:26:15,270 --> 00:26:21,610
+يمكن تبقى negative بالمرة على الإطلاع حتى لو كانت
+
+266
+00:26:21,610 --> 00:26:29,010
+negative فهذه بدها تساوي 5 of A كله to the power K
+
+267
+00:26:29,010 --> 00:26:36,850
+from part 2طبعا نيجاتيب مش ممكن لكن احنا بقول حتى
+
+268
+00:26:36,850 --> 00:26:42,630
+لو كانت يبقى هذه صحيحة بقدر احط ال K من ال A إلى
+
+269
+00:26:42,630 --> 00:26:49,090
+ال Phi of A K كلها هذا طيب هذا ال element موجود في
+
+270
+00:26:49,090 --> 00:26:54,780
+ال subgroup generated by Phi of A ولا لا صح؟سكت
+
+271
+00:26:54,780 --> 00:26:59,540
+الشعب شخصيات السيكليك جروب شبتر أربع يبقى ال
+
+272
+00:26:59,540 --> 00:27:03,740
+element اللي موجود في السيكليك جروب generated by a
+
+273
+00:27:03,740 --> 00:27:08,380
+بيكون a أس رقم يبقى ال sub group generated by five
+
+274
+00:27:08,380 --> 00:27:14,740
+of a بيكون five of a أس رقم صحيح موجر يبقى معنى
+
+275
+00:27:14,740 --> 00:27:20,660
+هذا الكلام أن ال b تساوي هذه وهذه وإن موجودةهذه
+
+276
+00:27:20,660 --> 00:27:26,760
+موجودة في الـ subgroup generated by phi of a طب
+
+277
+00:27:26,760 --> 00:27:33,090
+اتطلع اخدنا بيه وين موجودةفي جي بار وين لقينا بيه
+
+278
+00:27:33,090 --> 00:27:37,810
+موجودة في five of a sub group generated by five of
+
+279
+00:27:37,810 --> 00:27:43,970
+a يبقى معنى هذا الكلام ان جي بار هذي ال subset من
+
+280
+00:27:43,970 --> 00:27:48,950
+ال sub group generated by five of a وهذه اللي هي
+
+281
+00:27:48,950 --> 00:27:53,370
+double star اتطلعلي في ال star و اتطلعلي في ال
+
+282
+00:27:53,370 --> 00:27:58,350
+double star ايش بنستنتج يبقى باجي بقوله هنا from
+
+283
+00:28:06,130 --> 00:28:13,010
+G bar بيساوي ال sub group generated by Phi of A
+
+284
+00:28:13,010 --> 00:28:16,870
+نمشي
+
+285
+00:28:16,870 --> 00:28:25,170
+العملية العكسية يبقى باجي بقوله conversely assume
+
+286
+00:28:25,170 --> 00:28:27,510
+that
+
+287
+00:28:28,610 --> 00:28:34,710
+الـ G bar هي الـ sub group generated by Phi of A
+
+288
+00:28:34,710 --> 00:28:38,850
+مرة
+
+289
+00:28:38,850 --> 00:28:44,870
+ثانية احنا اثبتنا الاتجاه افرضنا الاتجاه الأول و
+
+290
+00:28:44,870 --> 00:28:48,750
+اثبتنا الاتجاه الثاني الآن بدي افترض الاتجاه
+
+291
+00:28:48,750 --> 00:28:55,540
+الثاني و بدي احاول اثبت من الاتجاه الأولطب كويس
+
+292
+00:28:55,540 --> 00:29:01,120
+انا فرض ان جي بارتو ساوي في of a بدي احاول اثبت ان
+
+293
+00:29:01,120 --> 00:29:07,060
+الجي هي ال sub group generated by a اللي صورته من؟
+
+294
+00:29:07,060 --> 00:29:15,300
+صورته في of a طب كويس الان لو جيت اخد العنصر اللي
+
+295
+00:29:15,300 --> 00:29:19,340
+موجود في جي مين ما يكون يكون يبقى لو جيت يقولش لك
+
+296
+00:29:19,340 --> 00:29:23,660
+little a belongs to g then
+
+297
+00:29:26,000 --> 00:29:32,660
+الـ A K موجود في G ولا لا؟ لأنه جي جروب اضربه نفسه
+
+298
+00:29:32,660 --> 00:29:35,600
+ان شاء الله مليون مرة بيكون موجود فيه G لإن G
+
+299
+00:29:35,600 --> 00:29:40,660
+closed under the operation يبقى A K موجود فيه G
+
+300
+00:29:40,660 --> 00:29:48,980
+طيب، الآن لو جيت أخدت هذا بدي أخدلك إنه الـ Phi أو
+
+301
+00:29:48,980 --> 00:29:52,800
+في الأول أستنى، أستنى، لحظة شوية، لحظة شوية والله
+
+302
+00:29:52,800 --> 00:29:59,630
+يا شباباستعجلنا احنا هذه a موجودة في جيب تمام يبقى
+
+303
+00:29:59,630 --> 00:30:05,890
+معنى هذا الكلام ان ال sub group generated by a sub
+
+304
+00:30:05,890 --> 00:30:12,570
+set من جيب صح ولا لا يبقى هذه ال sub set من من جيب
+
+305
+00:30:12,570 --> 00:30:19,550
+وهذه النقطة الأولى اللى بدى أسميها شرطة واحدةتمام
+
+306
+00:30:19,550 --> 00:30:23,970
+يبقى انا صار sub group by subset من دى لان بدي
+
+307
+00:30:23,970 --> 00:30:31,210
+اعمل العملية العكسية يبقى بداتي اقول let ال a
+
+308
+00:30:31,210 --> 00:30:37,990
+belongs to g then ال
+
+309
+00:30:37,990 --> 00:30:43,630
+a k belongs to g تمام
+
+310
+00:30:44,690 --> 00:30:51,890
+طيب هذا معناه ايش ان الـ Phi of A K وين موجودة يا
+
+311
+00:30:51,890 --> 00:30:59,310
+شباب جي بار جي بار طب و جي بار مين هي subgroup
+
+312
+00:30:59,310 --> 00:31:08,170
+generated by Phi of A معناه هذا الكلام ان Phi of A
+
+313
+00:31:08,170 --> 00:31:12,270
+K بده يساوي هنا Phi
+
+314
+00:31:15,180 --> 00:31:25,420
+هذا فاى بيساوي فاى of a اللي هو كله to the power k
+
+315
+00:31:25,420 --> 00:31:33,060
+هذا من أين جبتها؟ من الخاصية الرقم اتنين يبقى هذه
+
+316
+00:31:33,060 --> 00:31:42,430
+from اللي هو الخاصية الرقم اتنينطيب، الآن صار عندي
+
+317
+00:31:42,430 --> 00:31:49,870
+مين؟ صار عندي Phi of A K بدي ساوي Phi of A كله to
+
+318
+00:31:49,870 --> 00:31:55,770
+the power K طيب، هذا يعتبر element وين موجود؟
+
+319
+00:31:55,770 --> 00:32:02,530
+موجود، فاهمين؟ هذا كله element موجود في ال
+
+320
+00:32:02,530 --> 00:32:10,650
+subgroup generated by Phi of Aلحظة شوية ا ك موجودة
+
+321
+00:32:10,650 --> 00:32:15,090
+في جي فاي او ا ك موجودة في بي بار جي بار احنا
+
+322
+00:32:15,090 --> 00:32:23,350
+فرضينها تساوي هيك اه طيب طيب
+
+323
+00:32:23,350 --> 00:32:28,830
+هذه العبارة لحظة شوية شباب هذه بدي اشيها ا موجودة
+
+324
+00:32:28,830 --> 00:32:40,670
+في جي ا موجودة في جيهذا بده يعطيني ان في او ا
+
+325
+00:32:40,670 --> 00:32:45,670
+موجودة
+
+326
+00:32:45,670 --> 00:32:54,390
+في جي بار تمام و جي بار هي اللتي تساوي من تساوي في
+
+327
+00:32:54,390 --> 00:33:01,930
+او ا طيب
+
+328
+00:33:01,930 --> 00:33:08,650
+يبقى أصبحت عنديبس بديش اخليها يا طيب هذا خط A
+
+329
+00:33:08,650 --> 00:33:14,550
+موجود في G يبقى Phi of A موجود في G bar تمام موجود
+
+330
+00:33:14,550 --> 00:33:25,470
+في G bar يبقى Phi of A بدها تساوي استنشف
+
+331
+00:33:25,470 --> 00:33:30,330
+بدي اخد خليلي HDB مشان مايصيرش بس لبس في الموضوع
+
+332
+00:33:30,330 --> 00:33:37,090
+HDB و HDBيبقى بدا افترض ان بي موجود في جي يبقى في
+
+333
+00:33:37,090 --> 00:33:46,170
+of بي موجود في جي بار في of a هذا بده يعطيني ان في
+
+334
+00:33:46,170 --> 00:33:58,820
+of بي بده يساوي في of a كله to the power of kفاي
+
+335
+00:33:58,820 --> 00:34:06,420
+او اي كله to the power k هذا اللي هو بده يساوي فاي
+
+336
+00:34:06,420 --> 00:34:16,240
+او اي to the power k طبعا فاي ايزو مورفزل يعني
+
+337
+00:34:16,240 --> 00:34:24,940
+الفاي ايش is one to one يبقى هنا but فاي is one to
+
+338
+00:34:24,940 --> 00:34:31,390
+oneما دام one to one صورتين متساويتين يبقى أصلهم
+
+339
+00:34:31,390 --> 00:34:37,510
+مش بده يكون متساوي يبقى five is one to one هذا بده
+
+340
+00:34:37,510 --> 00:34:46,190
+يعطيلك انه بي بدها تساوي a to the power k مدام a
+
+341
+00:34:46,190 --> 00:34:50,550
+to the power k يبقى ال a to the power k موجودة في
+
+342
+00:34:50,550 --> 00:34:55,780
+ال sub group generated by aممتاز اذا اخدنا بي
+
+343
+00:34:55,780 --> 00:35:01,160
+موجود في جي اثبتنا ان بي موجود في subgroup
+
+344
+00:35:01,160 --> 00:35:07,680
+generated by a هذا معناه ان جي is a subset
+
+345
+00:35:07,680 --> 00:35:14,700
+milligroup generated by a اطلعلي للأولى واطلعلي
+
+346
+00:35:14,700 --> 00:35:20,630
+للتانية هذه هياللي هو التانية بالشكل اللي عندنا
+
+347
+00:35:20,630 --> 00:35:26,130
+هنا يبقى بقدر أقول الآن
+
+348
+00:35:26,130 --> 00:35:35,030
+بقدر
+
+349
+00:35:35,030 --> 00:35:43,290
+أقول from اللي هو ال star الأولى ال star التانية
+
+350
+00:35:43,290 --> 00:35:52,100
+we haveإن الـ G بيكون ساوية لـ group generated by
+
+351
+00:35:52,100 --> 00:35:55,940
+A يبقى
+
+352
+00:35:55,940 --> 00:36:01,560
+هي أثبتنا A اللي هو النظرية يعني يبقى بناء عليه
+
+353
+00:36:01,560 --> 00:36:04,960
+الـ G بيكون ساوية لـ subgroup generated by A if
+
+354
+00:36:04,960 --> 00:36:08,340
+and only if الـ G برثة والsubgroup generated by
+
+355
+00:36:08,340 --> 00:36:12,680
+Phi of A بيبقى تفهيمي من الآن فصاعداإن ال
+
+356
+00:36:12,680 --> 00:36:17,540
+generator لجروب الأولى الصورة هتولد أو يكون
+
+357
+00:36:17,540 --> 00:36:22,840
+generator لمين؟ للجروب الثاني يبقى هذا النقطة
+
+358
+00:36:22,840 --> 00:36:29,390
+الرابعة بدنا نروح للنقطة الخامسةالنقطة الخامسة
+
+359
+00:36:29,390 --> 00:36:34,350
+بتقول ان ال order ل a بده يسوى ال order ل fi of a
+
+360
+00:36:34,350 --> 00:36:39,870
+لكل ال a اللي موجود في جيه يبقى بقى داجي اقول له
+
+361
+00:36:39,870 --> 00:36:50,390
+assume ان ال order ل a بده يسوى m and ال m is
+
+362
+00:36:50,390 --> 00:36:53,750
+finite and
+
+363
+00:36:55,110 --> 00:37:07,890
+الـ Order لـ Phi of A بدل سوء الـ N مثلا مرة
+
+364
+00:37:07,890 --> 00:37:12,350
+تانية مطلوب أني أثبت أن الـ Order لـ A بدل سوء الـ
+
+365
+00:37:12,350 --> 00:37:18,850
+Order لـ Phi A في حالة إذا كان Phi isomorphismيبقى
+
+366
+00:37:18,850 --> 00:37:22,650
+باجي بقول افترض ان ال order ليه يسوى m و ال m
+
+367
+00:37:22,650 --> 00:37:27,670
+finite لان ال order قد يكون infinite يبقى انا بدأ
+
+368
+00:37:27,670 --> 00:37:32,790
+اخد حالة ال finite ال m is finite واخدت ال order
+
+369
+00:37:32,790 --> 00:37:37,950
+لفا يو فيه يسوى ال n ايش بدى اثبت ان ال m بدها
+
+370
+00:37:37,950 --> 00:37:44,630
+ساوى ال n اذا جدت اثبت ان ال m اقل من او يسوى ال n
+
+371
+00:37:44,630 --> 00:37:51,000
+و ال n اقل من او يسوى ال mاريكل بلغة مبادئ
+
+372
+00:37:51,000 --> 00:38:00,480
+الرياضية كويس بأجي بقوله consider خدلي الـPhi of A
+
+373
+00:38:00,480 --> 00:38:12,160
+كله اسم يساوي هذا عبارة عن Phi of A M من أين جبت
+
+374
+00:38:12,160 --> 00:38:18,040
+المعلومة هذه؟من part two من الجزء الأول يبقى هذه
+
+375
+00:38:18,040 --> 00:38:27,980
+from part two هذا الكلام يساوي five of أنا فضل ال
+
+376
+00:38:27,980 --> 00:38:36,280
+m هو الأردر تبع ال a يبقى a أس m مابجداش a أس m a
+
+377
+00:38:36,280 --> 00:38:43,790
+أس m بمين؟بالـ Identity تبع من؟ تبع الـ G وليس الـ
+
+378
+00:38:43,790 --> 00:38:49,490
+G bar يبقى الـ Identity element تبع الـ G هذا كله
+
+379
+00:38:49,490 --> 00:38:54,790
+يسوى الـ Identity element تبع الـ G bar طيب، أنا
+
+380
+00:38:54,790 --> 00:39:01,530
+فرض ان ال order لـ Phi of A يسوى الـ N لجيت رقم
+
+381
+00:39:01,530 --> 00:39:06,870
+تاني رفعته للـ M ساوة الـ Identity شو العلاقة ما
+
+382
+00:39:06,870 --> 00:39:14,940
+بين الـ N و الـ M؟يبقى ال N أقل من M لإن ال N أصغر
+
+383
+00:39:14,940 --> 00:39:20,480
+عدد صحيح موجه بارفع أسل وبيعطينا ال identity يبقى
+
+384
+00:39:20,480 --> 00:39:27,200
+هنا هذا بده يعطينا إن ال N أقل من أو يساوي ال M
+
+385
+00:39:27,200 --> 00:39:36,100
+وهذا اعتبر هالي هنا Star أغششك أكتر؟ لو كان عندك
+
+386
+00:39:36,100 --> 00:39:42,420
+ال order لإيه هو Nو لو وجدت M وضعته أس سوى ال
+
+387
+00:39:42,420 --> 00:39:49,640
+identity يبقى لازم ال N تقسم ال M دائما و أبدا
+
+388
+00:39:49,640 --> 00:39:55,700
+يعني ال order لل element أقل أس بحطه للعدد بيعطيني
+
+389
+00:39:55,700 --> 00:40:00,720
+ال identity لو لجيت عدد غيره وضعته أس اللي يعطاني
+
+390
+00:40:00,720 --> 00:40:04,080
+ال identity يبقى ال order لل element هذا يقسم
+
+391
+00:40:04,080 --> 00:40:09,330
+الرقم الجديدانا عارف ان هناك شبتر اربع بس انا
+
+392
+00:40:09,330 --> 00:40:13,630
+بتذكره بتذكير لانها بتلزمنا كتير و احنا بنحل مسائل
+
+393
+00:40:13,630 --> 00:40:19,470
+هذه طيب يبقى ال N اقل من او يساوي من اقل من او
+
+394
+00:40:19,470 --> 00:40:25,510
+يساوي ال M الان بدنا نعمل العملية العكسية بدي اثبت
+
+395
+00:40:25,510 --> 00:40:32,380
+ان ال M اقل من او يساوي ال Mانا فارض هنا ال order
+
+396
+00:40:32,380 --> 00:40:38,880
+ل ال a يسوى ال m و ال m is finite افترض ان ال n is
+
+397
+00:40:38,880 --> 00:40:50,420
+finite يبقى هنا if ال n is finite if
+
+398
+00:40:50,420 --> 00:40:59,930
+ال n is finite then بدي اخد fi of a أس nيبقى من
+
+399
+00:40:59,930 --> 00:41:07,340
+part two هذا في of a كله to the power nطب انا افرض
+
+400
+00:41:07,340 --> 00:41:11,500
+ان ال order له كله بده يساوي ال N يبقى هذا مين بده
+
+401
+00:41:11,500 --> 00:41:17,120
+يساوي؟ بده يساوي ال identity element تبع مين؟ تبع
+
+402
+00:41:17,120 --> 00:41:23,320
+ال G bar ال identity element تبع ال G bar اللي هو
+
+403
+00:41:23,320 --> 00:41:28,920
+عبارة عن مين؟ عبارة عن صورة ال identity element
+
+404
+00:41:28,920 --> 00:41:34,020
+تبع ال Gهذا الكلام من وين؟ من part one من النقطة
+
+405
+00:41:34,020 --> 00:41:40,740
+الأولى طيب في one to one ولا لا؟لو كانت five one
+
+406
+00:41:40,740 --> 00:41:46,180
+one to one و الصورتين متساويتين يبقى الأصل متساوي
+
+407
+00:41:46,180 --> 00:41:53,020
+يبقى هذا بده يعطينا أن الان بده يساوي ال identity
+
+408
+00:41:53,020 --> 00:42:00,000
+since five is one to one نظرة لأن five is one to
+
+409
+00:42:00,000 --> 00:42:06,010
+oneطيب يبقى ايه؟ لجيت أس حتة طولة اعطانا ال
+
+410
+00:42:06,010 --> 00:42:13,630
+identity وانا فرض ال order ليه قداش؟ M يبقاش علاقة
+
+411
+00:42:13,630 --> 00:42:22,370
+M ب N أصغر منه بتقسمه كذلك يبقى باجي بقوله so ال M
+
+412
+00:42:22,370 --> 00:42:30,080
+أقل من أو تساوي ال N وهذه double star الثانيةيبقى
+
+413
+00:42:30,080 --> 00:42:34,900
+انا اثبتله في الحالة الأولى ان ان اقل من او تساوي
+
+414
+00:42:34,900 --> 00:42:40,220
+ام و اثبتله ان الام اقل من او تساوي ان من الاتنين
+
+415
+00:42:40,220 --> 00:42:44,800
+مع بعض هدول يبقى الاتنين are equal يبقى باجي بقوله
+
+416
+00:42:44,800 --> 00:42:54,490
+هنا fromstar and double star ال N بدها تساوي ال M
+
+417
+00:42:54,490 --> 00:43:00,250
+هذا معناه ان ال order لل element A بده يساوي ال
+
+418
+00:43:00,250 --> 00:43:05,770
+order لل Phi of A لكل ال element A اللي belongs ل
+
+419
+00:43:05,770 --> 00:43:11,350
+group main ل group G وهو المطلوب حد بده يسألي سؤال
+
+420
+00:43:11,350 --> 00:43:18,930
+في هذه النقطة الخامسة كذلك اهالنقطة السادسة
+
+421
+00:43:18,930 --> 00:43:22,830
+والسبعة على السريع في ثلاث دقائق ان شاء الله
+
+422
+00:43:32,770 --> 00:43:35,470
+النقطة الصعبة بالنسبة لي هي اذا قمت باستخدام انتجر
+
+423
+00:43:35,470 --> 00:43:38,050
+K وقمت باستخدام جروب Element P موجود في الـ
+
+424
+00:43:38,050 --> 00:43:46,210
+Equation يبقى بداجي اقوله افترض ان A اللي موجود في
+
+425
+00:43:46,210 --> 00:43:56,890
+G is a solution of ال X to the power K بدو يساوي
+
+426
+00:43:56,890 --> 00:44:04,650
+ال Bما دام انا افرض حل هذه المعادلة اذا تحقق هذه
+
+427
+00:44:04,650 --> 00:44:09,630
+المعادلة يبقى بصيلة ان a to the power of k بده
+
+428
+00:44:09,630 --> 00:44:16,110
+يساوي من؟ بده يساوي بي الان اثرلي على الطرفين بفاي
+
+429
+00:44:16,110 --> 00:44:23,980
+يبقى فاي of a كي بده يساوي فاي of بيمن الجزء اتنين
+
+430
+00:44:23,980 --> 00:44:29,580
+من النظرية يبقى phi of a كله to the power k بده
+
+431
+00:44:29,580 --> 00:44:35,540
+يساوي phi of v شوفلي هذا الجزء الثاني ولا لأ هو
+
+432
+00:44:35,540 --> 00:44:42,760
+هذايبقى فاي of a حققت لمين المعادلة الثانية يبقى
+
+433
+00:44:42,760 --> 00:44:48,000
+فاي of a عبارة عن solution يبقى هذا بده يقين ان
+
+434
+00:44:48,000 --> 00:44:55,880
+فاي of a is a solution of x to the power k بده
+
+435
+00:44:55,880 --> 00:45:05,660
+يسوي فاي of bمعناته اي solution للمعادلة يبقى
+
+436
+00:45:05,660 --> 00:45:15,860
+هنا sir any solution of the equation x to the
+
+437
+00:45:15,860 --> 00:45:20,500
+power k is corresponding
+
+438
+00:45:38,700 --> 00:45:46,740
+وهو المطلوبيعني أي حل للمعادلة الأولى سنجد نظيرة
+
+439
+00:45:46,740 --> 00:45:51,680
+له Phi of A حل من للمعادلة التانية وبالتالي عدد
+
+440
+00:45:51,680 --> 00:45:55,580
+الحلول للمعادلة الأولى يسوى عدد الحلول للمعادلة
+
+441
+00:45:55,580 --> 00:45:58,300
+التانية سبعة تحصيل حاصل
+
+442
+00:46:13,270 --> 00:46:17,730
+ذن ال order اللي اجيبه دي ساو ال order اللي اجيبه
+
+443
+00:46:17,730 --> 00:46:28,120
+ليش؟ because five is one to one and untoيبقى عدد
+
+444
+00:46:28,120 --> 00:46:31,880
+العناصر هنا بيكون جد عدد عدد عدد عدد عدد عدد عدد
+
+445
+00:46:31,880 --> 00:46:34,380
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+446
+00:46:34,380 --> 00:46:38,280
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+447
+00:46:38,280 --> 00:46:38,820
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+448
+00:46:38,820 --> 00:46:40,460
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+449
+00:46:40,460 --> 00:46:41,940
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+450
+00:46:41,940 --> 00:46:45,420
+عدد عدد
+
+451
+00:46:49,600 --> 00:46:53,300
+يبقى من بابا ولا مالة نهاية جد المالة نهاية يعني
+
+452
+00:46:53,300 --> 00:47:05,260
+يبقى if g is finite also if ال g is infinite then
+
+453
+00:47:05,260 --> 00:47:16,620
+ال g bar is infinite because برضه ال five is one
+
+454
+00:47:16,620 --> 00:47:18,880
+to one and unto
+
+455
+00:47:23,720 --> 00:47:29,800
+طيب لا يزال في خاصية أخيرة للمرة القادمة ان شاء
+
+456
+00:47:29,800 --> 00:47:31,060
+الله يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..20938c94dfec1b847c9d723276ecb28f4e1c7671
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_raw.json
@@ -0,0 +1 @@
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{"start": 452.83, "end": 452.83, "word": " 1", "probability": 0.96240234375}, {"start": 452.83, "end": 452.83, "word": " 1", "probability": 0.9609375}, {"start": 452.83, "end": 452.83, "word": " 1", "probability": 0.9609375}, {"start": 452.83, "end": 454.03, "word": " 1", "probability": 0.96044921875}, {"start": 454.03, "end": 459.93, "word": " 1", "probability": 0.95947265625}, {"start": 459.93, "end": 459.93, "word": " 1", "probability": 0.95849609375}, {"start": 459.93, "end": 459.93, "word": " 1", "probability": 0.95703125}, {"start": 459.93, "end": 459.93, "word": " 1", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 19, "seek": 48529, "start": 460.03, "end": 485.29, "text": "عبارة عن مجموعة تحت عملية ضرب المصوفات احنا بنعرف ان عملية ضرب المصوفات لأي أنواع المصوفات عبارة عن associative binary operation يعني لو ضرت مصوفتين اتنين في اتنين في بعض بيطلع نفس النظام له اتنين في اتنين غير هيك عملية الضرب عملية ادماجية يبقى باجي بقوله solution و", "tokens": [3615, 3555, 9640, 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matrix multiplication is an associative binary operation", "tokens": [15869, 300, 5296, 3555, 1863, 3615, 28480, 16472, 2423, 8141, 27290, 307, 364, 4180, 1166, 17434, 6916], "avg_logprob": -0.2899305505885018, "compression_ratio": 0.9888888888888889, "no_speech_prob": 0.0, "words": [{"start": 489.51, "end": 490.03, "word": "know", "probability": 0.11181640625}, {"start": 490.03, "end": 490.91, "word": " that", "probability": 0.939453125}, {"start": 490.91, "end": 493.21, "word": " لبنعرف", "probability": 0.747607421875}, {"start": 493.21, "end": 493.93, "word": " ان", "probability": 0.71484375}, {"start": 493.93, "end": 494.19, "word": " ال", "probability": 0.87353515625}, {"start": 494.19, "end": 495.07, "word": " matrix", "probability": 0.87451171875}, {"start": 495.07, "end": 498.35, "word": " multiplication", "probability": 0.8515625}, {"start": 498.35, "end": 503.47, "word": " is", "probability": 0.9267578125}, {"start": 503.47, "end": 505.41, "word": " an", "probability": 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واحدة", "probability": 0.8621419270833334}, {"start": 534.09, "end": 534.95, "word": " طبعا", "probability": 0.783477783203125}, {"start": 534.95, "end": 535.95, "word": " كيف", "probability": 0.8291015625}, {"start": 535.95, "end": 536.37, "word": " عنصر", "probability": 0.9899088541666666}, {"start": 536.37, "end": 536.75, "word": " واحدة", "probability": 0.9833984375}, {"start": 536.75, "end": 537.17, "word": " بحيث", "probability": 0.939208984375}, {"start": 537.17, "end": 537.41, "word": " هذا", "probability": 0.9052734375}, {"start": 537.41, "end": 537.91, "word": " العنصر", "probability": 0.905029296875}, {"start": 537.91, "end": 538.17, "word": " لو", "probability": 0.97265625}, {"start": 538.17, "end": 538.79, "word": " ضربته", "probability": 0.94677734375}, {"start": 538.79, "end": 538.99, "word": " في", "probability": 0.95361328125}, {"start": 538.99, "end": 539.25, "word": " أي", "probability": 0.5498046875}, {"start": 539.25, "end": 539.69, "word": " مصوفة", "probability": 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544.83, "end": 545.49, "word": " هعطيها", "probability": 0.935546875}, {"start": 545.49, "end": 546.25, "word": " رمز", "probability": 0.9921875}], "temperature": 1.0}, {"id": 22, "seek": 57213, "start": 546.53, "end": 572.13, "text": "و روح اطلع شو شكل هذا الرمز فبجي بقول assume افترض ان ال B بي بي بي is the identity element طبعا يا شباب ال B هنا مالها", "tokens": [2407, 12602, 2407, 5016, 1975, 9566, 1211, 3615, 13412, 2407, 13412, 28820, 23758, 34892, 2304, 11622, 6156, 3555, 7435, 1829, 4724, 39648, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 363, 4724, 1829, 4724, 1829, 4724, 1829, 307, 264, 6575, 4478, 23032, 3555, 3615, 995, 35186, 13412, 3555, 16758, 2423, 363, 34105, 3714, 6027, 11296], "avg_logprob": -0.24446023106575013, "compression_ratio": 1.316546762589928, "no_speech_prob": 0.0, "words": [{"start": 546.53, "end": 546.83, "word": "و", "probability": 0.486328125}, {"start": 546.83, "end": 547.09, "word": " روح", "probability": 0.6785074869791666}, {"start": 547.09, "end": 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"end": 1058.51, "word": " التعريف", "probability": 0.983154296875}, {"start": 1058.51, "end": 1058.87, "word": " الأول", "probability": 0.86181640625}, {"start": 1058.87, "end": 1059.43, "word": " التعريف", "probability": 0.9268798828125}, {"start": 1059.43, "end": 1059.89, "word": " الثاني", "probability": 0.9620361328125}, {"start": 1059.89, "end": 1060.47, "word": " بدنا", "probability": 0.843505859375}, {"start": 1060.47, "end": 1060.73, "word": " ال", "probability": 0.8056640625}, {"start": 1060.73, "end": 1061.31, "word": " order", "probability": 0.97607421875}, {"start": 1061.31, "end": 1062.77, "word": " للعنصر", "probability": 0.89765625}, {"start": 1062.77, "end": 1062.97, "word": " اللي", "probability": 0.971923828125}, {"start": 1062.97, "end": 1063.37, "word": " موجود", "probability": 0.9923502604166666}, {"start": 1063.37, "end": 1063.53, "word": " في", "probability": 0.9169921875}, {"start": 1063.53, "end": 1063.65, "word": " ال", "probability": 0.91552734375}, {"start": 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"probability": 0.767578125}, {"start": 1083.25, "end": 1083.41, "word": " ال", "probability": 0.97900390625}, {"start": 1083.41, "end": 1084.09, "word": " identity", "probability": 0.91357421875}, {"start": 1084.09, "end": 1085.15, "word": " يبقى", "probability": 0.9771728515625}, {"start": 1085.15, "end": 1085.33, "word": " ال", "probability": 0.97998046875}, {"start": 1085.33, "end": 1085.71, "word": " n", "probability": 0.5712890625}, {"start": 1085.71, "end": 1086.31, "word": " هذه", "probability": 0.6376953125}, {"start": 1086.31, "end": 1087.37, "word": " بقول", "probability": 0.6702880859375}, {"start": 1087.37, "end": 1087.81, "word": " عليها", "probability": 0.97900390625}, {"start": 1087.81, "end": 1088.07, "word": " هي", "probability": 0.75048828125}, {"start": 1088.07, "end": 1088.27, "word": " ال", "probability": 0.88671875}, {"start": 1088.27, "end": 1088.67, "word": " order", "probability": 0.98291015625}, {"start": 1088.67, "end": 1089.31, "word": " لمين", 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في الـ subgroup يمكن أن تثبت أن الـ H هي subgroup من هنا", "tokens": [6027, 39184, 389, 39896, 2423, 39184, 1422, 17377, 9154, 34105, 7251, 43020, 14739, 6055, 12984, 3555, 2655, 14739, 2423, 39184, 389, 39896, 1422, 17377, 34051, 7251, 43020, 14739, 6055, 12984, 3555, 2655, 14739, 2423, 39184, 389, 32239, 3794, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 1422, 17377, 7251, 43020, 14739, 6055, 12984, 3555, 2655, 14739, 2423, 39184, 389, 39896, 1422, 17377, 9154, 34105], "avg_logprob": -0.45507811987772584, "compression_ratio": 2.3564356435643563, "no_speech_prob": 0.0, "words": [{"start": 1283.5, "end": 1284.1, "word": "الـ", "probability": 0.4725341796875}, {"start": 1284.1, "end": 1284.34, "word": " H", "probability": 0.65771484375}, {"start": 1284.34, "end": 1284.88, "word": " هي", "probability": 0.485107421875}, {"start": 1284.88, "end": 1285.04, "word": " الـ", "probability": 0.373291015625}, {"start": 1285.04, "end": 1285.94, "word": " subgroup", "probability": 0.776611328125}, 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هذه", "probability": 0.4462890625}, {"start": 2265.24, "end": 2265.48, "word": " ال", "probability": 0.35888671875}, {"start": 2265.48, "end": 2265.78, "word": " sub", "probability": 0.7470703125}, {"start": 2265.78, "end": 2266.32, "word": " group", "probability": 0.5078125}, {"start": 2266.32, "end": 2267.22, "word": " الأن", "probability": 0.53741455078125}, {"start": 2267.22, "end": 2267.68, "word": " أنا", "probability": 0.7919921875}, {"start": 2267.68, "end": 2268.7, "word": " أدعي", "probability": 0.9285888671875}, {"start": 2268.7, "end": 2269.28, "word": " أن", "probability": 0.6962890625}, {"start": 2269.28, "end": 2269.74, "word": " هذه", "probability": 0.873046875}, {"start": 2269.74, "end": 2270.3, "word": " non", "probability": 0.64013671875}, {"start": 2270.3, "end": 2271.72, "word": "-empty", "probability": 0.7271321614583334}, {"start": 2271.72, "end": 2272.4, "word": " non", "probability": 0.35888671875}, {"start": 2272.4, "end": 2272.88, "word": "-empty", "probability": 0.9130859375}, {"start": 2272.88, "end": 2273.64, "word": " ليش؟", "probability": 0.88427734375}, {"start": 2273.64, "end": 2273.86, "word": " لأن", "probability": 0.7021484375}, {"start": 2273.86, "end": 2274.1, "word": " على", "probability": 0.68603515625}, {"start": 2274.1, "end": 2274.6, "word": " الأقل", "probability": 0.9602864583333334}, {"start": 2274.6, "end": 2274.96, "word": " فيها", "probability": 0.984619140625}, {"start": 2274.96, "end": 2275.36, "word": " من؟", "probability": 0.5391845703125}], "temperature": 1.0}, {"id": 90, "seek": 229573, "start": 2275.83, "end": 2295.73, "text": "مصفوفة الوحدة المحددة تبعها يساوي واحد صحيح يبقى باجي بقوله النقطة الأولى ال special linear group of two by two matrices over R is non empty السبب because", "tokens": [2304, 9381, 5172, 38688, 3660, 2423, 2407, 24401, 3660, 9673, 24401, 41891, 6055, 3555, 3615, 11296, 7251, 3794, 995, 45865, 36764, 24401, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 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"probability": 0.8365885416666666}, {"start": 2281.77, "end": 2282.35, "word": " بقوله", "probability": 0.646484375}, {"start": 2282.35, "end": 2283.07, "word": " النقطة", "probability": 0.9383138020833334}, {"start": 2283.07, "end": 2284.23, "word": " الأولى", "probability": 0.9327799479166666}, {"start": 2284.23, "end": 2284.61, "word": " ال", "probability": 0.70166015625}, {"start": 2284.61, "end": 2285.25, "word": " special", "probability": 0.689453125}, {"start": 2285.25, "end": 2286.05, "word": " linear", "probability": 0.8623046875}, {"start": 2286.05, "end": 2286.57, "word": " group", "probability": 0.94677734375}, {"start": 2286.57, "end": 2286.89, "word": " of", "probability": 0.94873046875}, {"start": 2286.89, "end": 2287.15, "word": " two", "probability": 0.77978515625}, {"start": 2287.15, "end": 2287.39, "word": " by", "probability": 0.9208984375}, {"start": 2287.39, "end": 2287.67, "word": " two", "probability": 0.943359375}, {"start": 2287.67, "end": 2288.25, "word": " matrices", "probability": 0.96630859375}, {"start": 2288.25, "end": 2288.93, "word": " over", "probability": 0.841796875}, {"start": 2288.93, "end": 2289.37, "word": " R", "probability": 0.9287109375}, {"start": 2289.37, "end": 2290.31, "word": " is", "probability": 0.86865234375}, {"start": 2290.31, "end": 2291.11, "word": " non", "probability": 0.65673828125}, {"start": 2291.11, "end": 2292.07, "word": " empty", "probability": 0.497802734375}, {"start": 2292.07, "end": 2294.63, "word": " السبب", "probability": 0.990234375}, {"start": 2294.63, "end": 2295.73, "word": " because", "probability": 0.5927734375}], "temperature": 1.0}, {"id": 91, "seek": 232023, "start": 2297.33, "end": 2320.23, "text": "اللي هو واحد زيرو زيرو واحد موجودة في ال special linear group of two by two matrices over R since ال determinant لواحد زيرو زيرو واحد بده يساوي من الواحد", "tokens": [6027, 20292, 31439, 36764, 24401, 30767, 13546, 2407, 30767, 13546, 2407, 36764, 24401, 3714, 29245, 23328, 3660, 8978, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 1670, 2423, 41296, 5296, 14407, 24401, 30767, 13546, 2407, 30767, 13546, 2407, 36764, 24401, 47525, 3224, 7251, 3794, 995, 45865, 9154, 2423, 14407, 24401], "avg_logprob": -0.23307292025398324, "compression_ratio": 1.5068493150684932, "no_speech_prob": 0.0, "words": [{"start": 2297.33, "end": 2297.87, "word": "اللي", "probability": 0.551025390625}, {"start": 2297.87, "end": 2298.19, "word": " هو", "probability": 0.970703125}, {"start": 2298.19, "end": 2298.93, "word": " واحد", "probability": 0.6396484375}, {"start": 2298.93, "end": 2299.51, "word": " زيرو", "probability": 0.6516927083333334}, {"start": 2299.51, "end": 2300.07, "word": " زيرو", "probability": 0.92919921875}, {"start": 2300.07, "end": 2300.59, "word": " واحد", "probability": 0.98046875}, {"start": 2300.59, "end": 2302.11, "word": " موجودة", "probability": 0.9263916015625}, {"start": 2302.11, "end": 2302.33, "word": " في", "probability": 0.91259765625}, {"start": 2302.33, "end": 2302.53, "word": " ال", "probability": 0.90283203125}, {"start": 2302.53, "end": 2303.27, "word": " special", "probability": 0.488525390625}, {"start": 2303.27, "end": 2304.11, "word": " linear", "probability": 0.8564453125}, {"start": 2304.11, "end": 2304.77, "word": " group", "probability": 0.95703125}, {"start": 2304.77, "end": 2305.03, "word": " of", "probability": 0.9287109375}, {"start": 2305.03, "end": 2305.29, "word": " two", "probability": 0.875}, {"start": 2305.29, "end": 2305.53, "word": " by", "probability": 0.9140625}, {"start": 2305.53, "end": 2305.81, "word": " two", "probability": 0.94873046875}, {"start": 2305.81, "end": 2306.41, "word": " matrices", "probability": 0.95947265625}, {"start": 2306.41, "end": 2307.23, "word": " over", "probability": 0.892578125}, {"start": 2307.23, "end": 2307.85, "word": " R", "probability": 0.94775390625}, {"start": 2307.85, "end": 2309.31, "word": " since", "probability": 0.5439453125}, {"start": 2309.31, "end": 2314.75, "word": " ال", "probability": 0.5146484375}, {"start": 2314.75, "end": 2315.75, "word": " determinant", "probability": 0.67822265625}, {"start": 2315.75, "end": 2317.15, "word": " لواحد", "probability": 0.77685546875}, {"start": 2317.15, "end": 2317.69, "word": " زيرو", "probability": 0.951171875}, {"start": 2317.69, "end": 2318.09, "word": " زيرو", "probability": 0.97998046875}, {"start": 2318.09, "end": 2318.47, "word": " واحد", "probability": 0.985107421875}, {"start": 2318.47, "end": 2318.79, "word": " بده", "probability": 0.4085693359375}, {"start": 2318.79, "end": 2319.11, "word": " يساوي", "probability": 0.76171875}, {"start": 2319.11, "end": 2319.31, "word": " من", "probability": 0.666015625}, {"start": 2319.31, "end": 2320.23, "word": " الواحد", "probability": 0.9303385416666666}], "temperature": 1.0}, {"id": 92, "seek": 234565, "start": 2321.29, "end": 2345.65, "text": "بعد ذلك اختار مصففين موجودة في ال special لت ال a و ال b موجودة في ال special linear group of two by two matrices over R ثم كم محدد الأولى يا شباب؟ واحد و كم محدد التانية؟", "tokens": [3555, 22488, 29910, 23275, 1975, 46456, 9640, 3714, 9381, 5172, 5172, 9957, 3714, 29245, 23328, 3660, 8978, 2423, 2121, 5296, 2655, 2423, 257, 4032, 2423, 272, 3714, 29245, 23328, 3660, 8978, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 38637, 2304, 9122, 2304, 3714, 24401, 3215, 16247, 12610, 7578, 35186, 13412, 3555, 16758, 22807, 36764, 24401, 4032, 9122, 2304, 3714, 24401, 3215, 16712, 7649, 10632, 22807], "avg_logprob": -0.3455357053450176, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 2321.29, "end": 2321.71, "word": "بعد", "probability": 0.5924072265625}, {"start": 2321.71, "end": 2321.91, "word": " ذلك", "probability": 0.7161865234375}, {"start": 2321.91, "end": 2323.11, "word": " اختار", "probability": 0.4176839192708333}, {"start": 2323.11, "end": 2324.35, "word": " مصففين", "probability": 0.67431640625}, {"start": 2324.35, "end": 2325.09, 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يساوي واحد ان كنت اثبت واحد معناته حصل الضرب هذا موجود وام موجود في ال special وبالتالي ال special صارت sub group من ال main group من ال group الأساسي اللي هي ال general linear group على اي حال", "tokens": [1829, 3794, 995, 45865, 36764, 24401, 23032, 3555, 1975, 8315, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 42963, 12610, 7578, 8978, 20449, 4117, 41779, 6024, 104, 7649, 10632, 3714, 29245, 23328, 3660, 8978, 2423, 2121, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 3714, 24401, 3215, 42963, 12610, 7578, 8978, 20449, 4117, 41779, 6024, 104, 7649, 10632, 7251, 3794, 995, 45865, 36764, 24401, 16472, 9122, 29399, 1975, 12984, 3555, 2655, 36764, 24401, 20449, 8315, 47395, 11331, 36520, 6024, 114, 25513, 23758, 3714, 29245, 23328, 4032, 10943, 3714, 29245, 23328, 8978, 2423, 2121, 46599, 6027, 2655, 6027, 1829, 2423, 2121, 20328, 9640, 2655, 1422, 1594, 9154, 2423, 2135, 1594, 9154, 2423, 1594, 16247, 3794, 32277, 1829, 13672, 1829, 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"end": 2370.19, "word": " sub", "probability": 0.59033203125}, {"start": 2370.19, "end": 2370.53, "word": " group", "probability": 0.45166015625}, {"start": 2370.53, "end": 2370.73, "word": " من", "probability": 0.97265625}, {"start": 2370.73, "end": 2370.91, "word": " ال", "probability": 0.81494140625}, {"start": 2370.91, "end": 2371.11, "word": " main", "probability": 0.66015625}, {"start": 2371.11, "end": 2371.71, "word": " group", "probability": 0.5654296875}, {"start": 2371.71, "end": 2371.71, "word": " من", "probability": 0.315185546875}, {"start": 2371.71, "end": 2371.89, "word": " ال", "probability": 0.6865234375}, {"start": 2371.89, "end": 2372.59, "word": " group", "probability": 0.90185546875}, {"start": 2372.59, "end": 2373.57, "word": " الأساسي", "probability": 0.7852783203125}, {"start": 2373.57, "end": 2373.75, "word": " اللي", "probability": 0.80224609375}, {"start": 2373.75, "end": 2373.85, "word": " هي", "probability": 0.4189453125}, {"start": 2373.85, "end": 2373.99, "word": " ال", "probability": 0.8955078125}, {"start": 2373.99, "end": 2374.37, "word": " general", "probability": 0.89990234375}, {"start": 2374.37, "end": 2374.83, "word": " linear", "probability": 0.51806640625}, {"start": 2374.83, "end": 2375.37, "word": " group", "probability": 0.98095703125}, {"start": 2375.37, "end": 2376.19, "word": " على", "probability": 0.92578125}, {"start": 2376.19, "end": 2376.41, "word": " اي", "probability": 0.736328125}, {"start": 2376.41, "end": 2376.71, "word": " حال", "probability": 0.993408203125}], "temperature": 1.0}, {"id": 94, "seek": 240654, "start": 2377.1, "end": 2406.54, "text": "لو جيت قلتلك بالله قداش ال determinant لل A B inverse ورجعنا بذاكرة الى الوراء الى الجبري الخاطى يبقى هذا بدي يعطينا ال determinant ل A في ال determinant لل B inverse طب انا ال determinant لل B inverse ماهواش عندي ماعرفوش لكن بنقدر نعرفه قداشه ساوي", "tokens": [1211, 2407, 10874, 36081, 12174, 1211, 2655, 23275, 4724, 6027, 43761, 12174, 3215, 33599, 2423, 41296, 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"word": " قداش", "probability": 0.8997395833333334}, {"start": 2380.3, "end": 2380.58, "word": " ال", "probability": 0.94091796875}, {"start": 2380.58, "end": 2381.72, "word": " determinant", "probability": 0.9208984375}, {"start": 2381.72, "end": 2382.4, "word": " لل", "probability": 0.81884765625}, {"start": 2382.4, "end": 2383.22, "word": " A", "probability": 0.246826171875}, {"start": 2383.22, "end": 2383.84, "word": " B", "probability": 0.21826171875}, {"start": 2383.84, "end": 2384.64, "word": " inverse", "probability": 0.7734375}, {"start": 2384.64, "end": 2386.46, "word": " ورجعنا", "probability": 0.9217529296875}, {"start": 2386.46, "end": 2387.32, "word": " بذاكرة", "probability": 0.809326171875}, {"start": 2387.32, "end": 2387.58, "word": " الى", "probability": 0.658447265625}, {"start": 2387.58, "end": 2388.14, "word": " الوراء", "probability": 0.91015625}, {"start": 2388.14, "end": 2388.44, "word": " الى", "probability": 0.796142578125}, {"start": 2388.44, "end": 2389.0, "word": " الجبري", "probability": 0.7900390625}, {"start": 2389.0, "end": 2389.98, "word": " الخاطى", "probability": 0.6818033854166666}, {"start": 2389.98, "end": 2391.0, "word": " يبقى", "probability": 0.9666748046875}, {"start": 2391.0, "end": 2391.34, "word": " هذا", "probability": 0.82958984375}, {"start": 2391.34, "end": 2391.82, "word": " بدي", "probability": 0.617919921875}, {"start": 2391.82, "end": 2392.28, "word": " يعطينا", "probability": 0.95849609375}, {"start": 2392.28, "end": 2392.42, "word": " ال", "probability": 0.8466796875}, {"start": 2392.42, "end": 2393.18, "word": " determinant", "probability": 0.97021484375}, {"start": 2393.18, "end": 2393.78, "word": " ل", "probability": 0.64404296875}, {"start": 2393.78, "end": 2394.28, "word": " A", "probability": 0.5703125}, {"start": 2394.28, "end": 2394.86, "word": " في", "probability": 0.49365234375}, {"start": 2394.86, "end": 2394.98, "word": " ال", "probability": 0.609375}, {"start": 2394.98, "end": 2395.88, "word": " 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"probability": 0.89404296875}, {"start": 2402.8, "end": 2403.82, "word": " ماعرفوش", "probability": 0.809716796875}, {"start": 2403.82, "end": 2404.8, "word": " لكن", "probability": 0.74267578125}, {"start": 2404.8, "end": 2405.34, "word": " بنقدر", "probability": 0.817138671875}, {"start": 2405.34, "end": 2405.72, "word": " نعرفه", "probability": 0.85980224609375}, {"start": 2405.72, "end": 2406.16, "word": " قداشه", "probability": 0.8463134765625}, {"start": 2406.16, "end": 2406.54, "word": " ساوي", "probability": 0.9562174479166666}], "temperature": 1.0}, {"id": 95, "seek": 243475, "start": 2407.15, "end": 2434.75, "text": "1 على determinant ل a من أين جبتها اه لو ضربنا المصوفة في معكس بيعطينا مصوفة من الواحدة الواحدة جداش محدد مصوفة الواحدة واحد ال determinant لل بي بي انفرس يساوي واحد يبقى صار ال determinant ل بي في ال determinant ل بي انفرس يساوي واحد اذا ال determinant ل بي انفرس يساوي واحد على ال determinant ل بي", "tokens": [16, 15844, 41296, 5296, 257, 9154, 5551, 9957, 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"probability": 0.8883463541666666}, {"start": 2415.65, "end": 2416.23, "word": " بيعطينا", "probability": 0.7888671875}, {"start": 2416.23, "end": 2416.75, "word": " مصوفة", "probability": 0.953857421875}, {"start": 2416.75, "end": 2417.09, "word": " من", "probability": 0.65234375}, {"start": 2417.09, "end": 2418.37, "word": " الواحدة", "probability": 0.7940673828125}, {"start": 2418.37, "end": 2418.37, "word": " الواحدة", "probability": 0.76324462890625}, {"start": 2418.37, "end": 2418.71, "word": " جداش", "probability": 0.5801595052083334}, {"start": 2418.71, "end": 2419.13, "word": " محدد", "probability": 0.9742838541666666}, {"start": 2419.13, "end": 2419.57, "word": " مصوفة", "probability": 0.9237060546875}, {"start": 2419.57, "end": 2420.07, "word": " الواحدة", "probability": 0.9779052734375}, {"start": 2420.07, "end": 2420.87, "word": " واحد", "probability": 0.905517578125}, {"start": 2420.87, "end": 2421.55, "word": " ال", "probability": 0.7666015625}, {"start": 2421.55, "end": 2422.13, "word": " determinant", "probability": 0.88232421875}, {"start": 2422.13, "end": 2422.53, "word": " لل", "probability": 0.53125}, {"start": 2422.53, "end": 2422.77, "word": " بي", "probability": 0.72412109375}, {"start": 2422.77, "end": 2423.05, "word": " بي", "probability": 0.7154541015625}, {"start": 2423.05, "end": 2423.57, "word": " انفرس", "probability": 0.782470703125}, {"start": 2423.57, "end": 2424.05, "word": " يساوي", "probability": 0.873779296875}, {"start": 2424.05, "end": 2424.51, "word": " واحد", "probability": 0.9794921875}, {"start": 2424.51, "end": 2424.77, "word": " يبقى", "probability": 0.9276123046875}, {"start": 2424.77, "end": 2424.99, "word": " صار", "probability": 0.72412109375}, {"start": 2424.99, "end": 2425.09, "word": " ال", "probability": 0.857421875}, {"start": 2425.09, "end": 2425.79, "word": " determinant", "probability": 0.96435546875}, {"start": 2425.79, "end": 2426.29, "word": " ل", "probability": 0.8876953125}, {"start": 2426.29, "end": 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2430.65, "word": " ل", "probability": 0.90966796875}, {"start": 2430.65, "end": 2430.83, "word": " بي", "probability": 0.900390625}, {"start": 2430.83, "end": 2431.19, "word": " انفرس", "probability": 0.9862060546875}, {"start": 2431.19, "end": 2431.61, "word": " يساوي", "probability": 0.984130859375}, {"start": 2431.61, "end": 2432.09, "word": " واحد", "probability": 0.99072265625}, {"start": 2432.09, "end": 2432.43, "word": " على", "probability": 0.93798828125}, {"start": 2432.43, "end": 2432.63, "word": " ال", "probability": 0.89013671875}, {"start": 2432.63, "end": 2433.47, "word": " determinant", "probability": 0.9697265625}, {"start": 2433.47, "end": 2434.29, "word": " ل", "probability": 0.9638671875}, {"start": 2434.29, "end": 2434.75, "word": " بي", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 96, "seek": 246388, "start": 2435.08, "end": 2463.88, "text": "إذا هذا الكلام بدي يساوي determinant للـA في واحد على determinant للـB الان determinant للـA بواحد و هذا واحد على واحد يبقى النتيجة كدهش؟ النتيجة واحدة صحيح ايش تفسيرك لهذا الكلام؟ ان ال A B inverse belong لل special linear group", "tokens": [28814, 15730, 23758, 2423, 28820, 10943, 4724, 16254, 7251, 3794, 995, 45865, 41296, 24976, 39184, 32, 8978, 36764, 24401, 15844, 41296, 24976, 39184, 33, 2423, 7649, 41296, 24976, 39184, 32, 4724, 14407, 24401, 4032, 23758, 36764, 24401, 15844, 36764, 24401, 7251, 3555, 4587, 7578, 28239, 31371, 7435, 3660, 9122, 3215, 3224, 8592, 22807, 28239, 31371, 7435, 3660, 36764, 24401, 3660, 20328, 5016, 1829, 5016, 1975, 1829, 8592, 6055, 36178, 13546, 4117, 46740, 15730, 2423, 28820, 10943, 22807, 16472, 2423, 316, 363, 17340, 5784, 24976, 2121, 8213, 1594], "avg_logprob": -0.27414771474220534, "compression_ratio": 1.7715736040609138, "no_speech_prob": 0.0, "words": [{"start": 2435.08, "end": 2435.56, "word": "إذا", "probability": 0.59130859375}, {"start": 2435.56, "end": 2436.08, "word": " هذا", "probability": 0.732421875}, {"start": 2436.08, "end": 2436.92, 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" للقطر", "probability": 0.8943684895833334}, {"start": 2693.55, "end": 2694.31, "word": " الثانوي", "probability": 0.7808837890625}, {"start": 2694.31, "end": 2694.81, "word": " كل", "probability": 0.97314453125}, {"start": 2694.81, "end": 2695.59, "word": " عناصره", "probability": 0.91455078125}, {"start": 2695.59, "end": 2696.81, "word": " أسفارا", "probability": 0.886328125}], "temperature": 1.0}, {"id": 106, "seek": 272604, "start": 2697.06, "end": 2726.04, "text": "يبقى هدول لايمكن في أي يوم من الأيام أن يكون أسفارا لكن هدول أسفارة على طول الخطب بيقول لي شوفلي بالله الإتش هذي ممكن تكون subgroup والله ممكن ما تكونش subgroup السؤال هو هل هذي non-empty تقدر تجيبولي عنصر فيها identity matrix الرئيسي واحد واحد لايسوي أسفارة والباقى أسفارة يبقى لقرب", "tokens": [1829, 3555, 4587, 7578, 8032, 3215, 12610, 20193, 32640, 19452, 8978, 36632, 7251, 20498, 9154, 16247, 1829, 10943, 14739, 7251, 30544, 5551, 3794, 5172, 9640, 995, 44381, 8032, 3215, 12610, 5551, 3794, 5172, 9640, 3660, 15844, 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0.70068359375}, {"start": 2958.76, "end": 2959.04, "word": " عندنا", "probability": 0.7353515625}, {"start": 2959.04, "end": 2959.74, "word": " تحققت", "probability": 0.8927734375}, {"start": 2959.74, "end": 2960.44, "word": " الخاصيتين", "probability": 0.95458984375}, {"start": 2960.44, "end": 2961.04, "word": " الأثنين", "probability": 0.81988525390625}, {"start": 2961.04, "end": 2961.46, "word": " أو", "probability": 0.873046875}, {"start": 2961.46, "end": 2962.16, "word": " المعطيات", "probability": 0.83203125}, {"start": 2962.16, "end": 2962.56, "word": " الأثنين", "probability": 0.9415283203125}, {"start": 2962.56, "end": 2962.82, "word": " تبع", "probability": 0.8387044270833334}, {"start": 2962.82, "end": 2963.48, "word": " النظرية", "probability": 0.8914794921875}, {"start": 2963.48, "end": 2964.18, "word": " يبقى", "probability": 0.92529296875}, {"start": 2964.18, "end": 2964.54, "word": " بناء", "probability": 0.899169921875}, {"start": 2964.54, "end": 2965.1, "word": " عليه", "probability": 0.93310546875}, {"start": 2965.1, "end": 2966.36, "word": " المصوفة", "probability": 0.83319091796875}, {"start": 2966.36, "end": 2967.04, "word": " الموطنة", "probability": 0.71630859375}, {"start": 2967.04, "end": 2967.22, "word": " هي", "probability": 0.64404296875}, {"start": 2967.22, "end": 2968.18, "word": " subgroup", "probability": 0.5887451171875}, {"start": 2968.18, "end": 2968.46, "word": " من", "probability": 0.9306640625}, {"start": 2968.46, "end": 2968.68, "word": " ال", "probability": 0.8369140625}, {"start": 2968.68, "end": 2969.12, "word": " general", "probability": 0.64697265625}, {"start": 2969.12, "end": 2969.84, "word": " linear", "probability": 0.9072265625}, {"start": 2969.84, "end": 2970.4, "word": " a", "probability": 0.1597900390625}, {"start": 2970.4, "end": 2970.82, "word": " group", "probability": 0.8291015625}, {"start": 2970.82, "end": 2971.76, "word": " يبقى", "probability": 0.98291015625}, {"start": 2971.76, "end": 2972.14, "word": " هنا", "probability": 0.978515625}, {"start": 2972.14, "end": 2972.5, "word": " by", "probability": 0.418701171875}], "temperature": 1.0}, {"id": 117, "seek": 299061, "start": 2979.83, "end": 2990.61, "text": "بالنظرية السابقة الـ H is a subgroup من ال general linear group of two by two matrices over R", "tokens": [3555, 6027, 1863, 19913, 2288, 10632, 21136, 16758, 28671, 2423, 39184, 389, 307, 257, 1422, 17377, 9154, 2423, 2674, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497], "avg_logprob": -0.3526400862068966, "compression_ratio": 1.0952380952380953, "no_speech_prob": 0.0, "words": [{"start": 2979.83, "end": 2980.79, "word": "بالنظرية", "probability": 0.8122151692708334}, {"start": 2980.79, "end": 2981.75, "word": " السابقة", "probability": 0.98828125}, {"start": 2981.75, "end": 2982.65, "word": " الـ", "probability": 0.4510498046875}, {"start": 2982.65, "end": 2983.01, "word": " H", "probability": 0.76904296875}, {"start": 2983.01, "end": 2983.45, "word": " is", "probability": 0.07208251953125}, {"start": 2983.45, "end": 2983.89, "word": " a", "probability": 0.9365234375}, {"start": 2983.89, "end": 2984.75, "word": " subgroup", "probability": 0.8359375}, {"start": 2984.75, "end": 2985.33, "word": " من", "probability": 0.8994140625}, {"start": 2985.33, "end": 2985.53, "word": " ال", "probability": 0.92236328125}, {"start": 2985.53, "end": 2985.91, "word": " general", "probability": 0.418701171875}, {"start": 2985.91, "end": 2986.39, "word": " linear", "probability": 0.78759765625}, {"start": 2986.39, "end": 2986.87, "word": " group", "probability": 0.96533203125}, {"start": 2986.87, "end": 2987.13, "word": " of", "probability": 0.95166015625}, {"start": 2987.13, "end": 2987.37, "word": " two", "probability": 0.57861328125}, {"start": 2987.37, "end": 2987.61, "word": " by", "probability": 0.9033203125}, {"start": 2987.61, "end": 2987.91, "word": " two", "probability": 0.9443359375}, {"start": 2987.91, "end": 2988.69, "word": " matrices", "probability": 0.9619140625}, {"start": 2988.69, "end": 2990.01, "word": " over", "probability": 0.8212890625}, {"start": 2990.01, "end": 2990.61, "word": " R", "probability": 0.97998046875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2991.89125, "duration_after_vad": 2883.391249999985}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fbaa518fafadebe96d0ef648f3c8b2566d1d0a1d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8.srt
@@ -0,0 +1,1279 @@
+1
+00:00:20,650 --> 00:00:24,970
+بسم الله الرحمن الرحيم المرة التي فاتت بدأنا في
+
+2
+00:00:24,970 --> 00:00:30,070
+chapter 8 الذي هو ال external direct product عرفنا
+
+3
+00:00:30,070 --> 00:00:34,010
+ال external direct product  وأخذنا على ذلك بعض 
+
+4
+00:00:34,010 --> 00:00:38,950
+الأمثلة ثم ذهبنا إلى أول نظرية على ال external
+
+5
+00:00:38,950 --> 00:00:44,030
+direct product وهو تحديد ال order لل element
+
+6
+00:00:44,030 --> 00:00:47,790
+المكون من ال external direct product بين two
+
+7
+00:00:47,790 --> 00:00:53,560
+groups أو أكثر فأقول النظرية بتقول أنه لو كان عندي
+
+8
+00:00:53,560 --> 00:00:58,720
+group G و group H عملنا ال external direct product
+
+9
+00:00:58,720 --> 00:01:03,280
+ما بين ال G و ال H يبقى أي element في ال external
+
+10
+00:01:03,280 --> 00:01:07,200
+direct product ال order له يساوي least common
+
+11
+00:01:07,200 --> 00:01:11,200
+multiple لمن؟ لل order للمركبة الأولى و order
+
+12
+00:01:11,200 --> 00:01:16,580
+المركبة الثانية هذا يعطينا ال order لل element
+
+13
+00:01:16,580 --> 00:01:21,090
+الذي موجود في ال external direct product طبعا هناخد
+
+14
+00:01:21,090 --> 00:01:28,550
+بعض الأمثلة على ذلك ونبدأ بالمثال الأول يبقى
+
+15
+00:01:28,550 --> 00:01:36,770
+example one يقول
+
+16
+00:01:36,770 --> 00:01:41,410
+find نمر
+
+17
+00:01:41,410 --> 00:01:52,970
+بـ .. نمر بـ ال order لستة و ثمانية نمر بـ
+
+18
+00:01:52,970 --> 00:02:02,990
+ال order لخمسة وخمسة كذلك كل هذا in the group in the
+
+19
+00:02:02,990 --> 00:02:10,890
+group في ال group الذي عندنا ليه Z8 external
+
+20
+00:02:10,890 --> 00:02:14,890
+product مع من؟ مع Z12
+
+21
+00:02:27,920 --> 00:02:32,840
+خلي بالك هنا جاء لي يشوف لقداش الأرض لل element 6
+
+22
+00:02:32,840 --> 00:02:38,600
+و8 الذي موجود في ال external direct product Z8 مع
+
+23
+00:02:38,600 --> 00:02:43,700
+من؟ مع Z12 واضح أن ال component الأول الذي هي 6
+
+24
+00:02:43,700 --> 00:02:49,280
+تكون مع من؟ في ال group الذي هي Z8 وال component
+
+25
+00:02:49,280 --> 00:02:54,380
+الثاني الذي هي 8 تكون موجودة في ال group Z12 إذا
+
+26
+00:02:54,380 --> 00:03:01,870
+أنا بدي أروح أدور على ال order لمن؟ لستة وثمانية
+
+27
+00:03:01,870 --> 00:03:06,930
+يبقى هو ال least common multiple لل order تبع
+
+28
+00:03:06,930 --> 00:03:12,150
+الستة وال order تبع الثمانية وكل واحد في ال
+
+29
+00:03:12,150 --> 00:03:19,620
+group تبعه الآن بدي أجي لستة يبقى هذا الكلام بدي
+
+30
+00:03:19,620 --> 00:03:24,340
+يساوي ال least common multiple لمن؟ لأبصر من؟ بدي
+
+31
+00:03:24,340 --> 00:03:32,080
+ال order لستة في من؟ في Z ثمانية يلا بدي ال order
+
+32
+00:03:32,080 --> 00:03:37,380
+لستة في Z ثمانية طبعا Z ثمانية صفر واحد اثنين
+
+33
+00:03:37,380 --> 00:03:42,340
+ثلاثة لغاية ثمانية أيوة كده إيش؟ أربعة ممتاز جدا
+
+34
+00:03:42,340 --> 00:03:48,410
+يبقى ال order لستة هو أربعة هذا وين؟ في Z الثمانية
+
+35
+00:03:48,410 --> 00:03:52,090
+لأن الأربعة في الستة 24 هي مضاعفات
+
+36
+00:03:52,090 --> 00:03:58,170
+الثمانية وهو أول أس بضربه في ستة يعطينا من؟
+
+37
+00:03:58,170 --> 00:04:02,950
+يعطينا صفر لأن ال identity element بدي أجي لل
+
+38
+00:04:02,950 --> 00:04:09,180
+order ثمانية في الاثناشر اضربه بثلاثة لأن ثلاثة في
+
+39
+00:04:09,180 --> 00:04:14,680
+ثمانية 24 مضاعفات اثناشر يبقى ال least
+
+40
+00:04:14,680 --> 00:04:18,280
+common multiple للأربعة والثلاثة الذي هو الاثناشر
+
+41
+00:04:18,280 --> 00:04:23,120
+وبالتالي ال order لستة وثمانية عبارة عن اثناشر
+
+42
+00:04:23,120 --> 00:04:29,220
+بمعنى ستة وثمانية لو حطيتها للأس اثناشر هذا الذي
+
+43
+00:04:29,220 --> 00:04:34,620
+تعطينا من؟ ال identity element وهو أول رقم بحطه ك
+
+44
+00:04:34,620 --> 00:04:38,940
+أس لستة وثمانية يعطينا الـ Main الـ Identity الـ
+
+45
+00:04:38,940 --> 00:04:43,260
+Main الآن أنا أخذت الـ 6 و 8 are not relative
+
+46
+00:04:43,260 --> 00:04:48,200
+prime لل 8 و 12 يعني ال 6 ماهي relative prime مع
+
+47
+00:04:48,200 --> 00:04:54,120
+ال 8 وال 8 ماهي relative prime مع Main مع ال 12
+
+48
+00:04:54,120 --> 00:04:55,180
+تعال نشوف ال B
+
+49
+00:05:03,720 --> 00:05:07,440
+الخامسة الأولى تختلف عن الخامسة الثانية لأن
+
+50
+00:05:07,440 --> 00:05:11,620
+الخامسة الأولى موجودة في Z8 والخامسة الثانية
+
+51
+00:05:11,620 --> 00:05:17,500
+موجودة في Z12 يبقى هذا ال least common multiple لل
+
+52
+00:05:17,500 --> 00:05:23,780
+order بتابع الخامسة وال order كذلك بتبع الخمسة يبقى
+
+53
+00:05:23,780 --> 00:05:28,640
+least common multiple ليه؟ الآن الخمسة element
+
+54
+00:05:28,640 --> 00:05:35,440
+موجود في Z ثمانية لقداش ال order إله؟ أي رقم في Z
+
+55
+00:05:35,440 --> 00:05:40,260
+ثمانية relatively prime مع ثمانية ال order إله لقداش؟
+
+56
+00:05:40,260 --> 00:05:48,420
+ثمانية وهو generator يبقى هذا برضه لقداش؟ ثمانية الآن
+
+57
+00:05:48,420 --> 00:05:52,940
+الخمسة الثانية relatively prime مع من؟ مع الاثناشر
+
+58
+00:05:52,940 --> 00:05:58,620
+يبقى ال order لها كذلك يساوي كده؟ يساوي الاثناشر
+
+59
+00:05:58,620 --> 00:06:03,140
+يبقى أنا بدي least common multiple لثمانية ولا
+
+60
+00:06:03,140 --> 00:06:09,820
+اثناشر الذي هو كده؟ اثناشر ولا ستة عشر ال least common
+
+61
+00:06:09,820 --> 00:06:14,740
+multiple يعني لا ثمانية ولا ستة عشر ولا اثناشر كمان
+
+62
+00:06:17,520 --> 00:06:23,380
+يبقى ال order لهذا ال element يساوي 24 بمعنى خمسة
+
+63
+00:06:23,380 --> 00:06:27,980
+وخمسة لو بدأت أحط له أس واحد اثنين ثلاثة لن أصل
+
+64
+00:06:27,980 --> 00:06:33,020
+إلى ال zero zero إلا بعد ما أوصل للأس الذي هو لقداش؟
+
+65
+00:06:33,020 --> 00:06:37,620
+الذي هو 24 طيب هذا يعتبر من الأمثلة
+
+66
+00:06:37,620 --> 00:06:43,980
+البسيطة جدا انتجلي شوية يبقى بدنا نروح لل example
+
+67
+00:06:43,980 --> 00:06:50,180
+two example two يقول لي ماتي how many number of
+
+68
+00:06:50,180 --> 00:07:03,380
+elements how many number of elements of
+
+69
+00:07:03,380 --> 00:07:17,990
+order of order five in the group في ال group الذي
+
+70
+00:07:17,990 --> 00:07:25,630
+هي Main الذي هي Z خمسة وعشرين external product
+
+71
+00:07:25,630 --> 00:07:30,170
+product مع Main مع Z خمسة
+
+72
+00:07:45,850 --> 00:07:51,450
+خلي بالك إيش بقول؟ بقول هات لي عدد العناصر التي
+
+73
+00:07:51,450 --> 00:07:56,050
+موجودة في ال group Z خمسة وعشرين كسنة ذاك product
+
+74
+00:07:56,050 --> 00:08:00,470
+مع Z خمسة والتي ال order إلها بيكون يساوي كده؟
+
+75
+00:08:00,470 --> 00:08:04,430
+يساوي خمسة، جاب المبدأ ال group هذه كام عنصر فيها
+
+76
+00:08:04,430 --> 00:08:10,110
+يا شباب؟ كده؟ مائة وخمسة وعشرون الذي هو ال order
+
+77
+00:08:10,110 --> 00:08:13,840
+للأولى ضرب ال order للثانية يعطيني كام عنصر؟ يبقى
+
+78
+00:08:13,840 --> 00:08:17,240
+أنا عندي في هذه ال group مائة وخمسة وعشرون عنصر
+
+79
+00:08:17,240 --> 00:08:22,540
+بدي أدور لقداش عدد العناصر في هذه ال group التي ال
+
+80
+00:08:22,540 --> 00:08:27,560
+order لهم بدي يساوي كدهش؟ بدي يساوي خمسة يبقى بداجي
+
+81
+00:08:27,560 --> 00:08:36,930
+أقوله assume افترض assume أن ال a وال b التي
+
+82
+00:08:36,930 --> 00:08:41,350
+موجودة في ال Z خمسة وعشرين external direct
+
+83
+00:08:41,350 --> 00:08:53,010
+product مع Z خمسة has order خمسة that is in ال
+
+84
+00:08:53,010 --> 00:09:00,720
+order لل a وال b بده يساوي كده؟ بده يساوي خمسة طب
+
+85
+00:09:00,720 --> 00:09:05,260
+ال order لهذا يعني من؟ least common multiple يبقى
+
+86
+00:09:05,260 --> 00:09:14,840
+هذا يعني أن ال order لل a وال b بده يساوي خمسة
+
+87
+00:09:14,840 --> 00:09:20,780
+الذي هو least common multiple لل order تبع ال a وال
+
+88
+00:09:20,780 --> 00:09:23,480
+order تبع ال b
+
+89
+00:09:25,940 --> 00:09:29,760
+أنا افترض أن عنصر A وB موجود في ال external
+
+90
+00:09:29,760 --> 00:09:35,880
+product ال order له يساوي خمسة من هذا الكلام دول
+
+91
+00:09:35,880 --> 00:09:42,500
+هطلع كم عدد أو كم عنصر على شكل A وB ال order لهم
+
+92
+00:09:42,500 --> 00:09:47,360
+يساوي خمسة بس في معلومة هيها بدي استفيد منها أن
+
+93
+00:09:47,360 --> 00:09:51,500
+الخمسة هي ال least common multiple لل order بتابع
+
+94
+00:09:51,500 --> 00:09:58,040
+ال A وال order بتابع ال B خمسة وواحد وواحد و
+
+95
+00:09:58,040 --> 00:10:03,500
+خمسة طب وخمسة وخمسة يعني
+
+96
+00:10:03,500 --> 00:10:08,480
+كتر والحين طيب على أي حال هنجي نشوف الحالات
+
+97
+00:10:08,480 --> 00:10:18,860
+الممكنة في هذا الموضوع يبقى هنا we have
+
+98
+00:10:18,860 --> 00:10:21,760
+the following
+
+99
+00:10:30,470 --> 00:10:36,050
+Possibilities يبقى فيه عندنا الاحتمالات الممكنة
+
+100
+00:10:36,050 --> 00:10:42,430
+التالية الاحتمال الأول أن ال order لل A بده يساوي
+
+101
+00:10:42,430 --> 00:10:51,270
+خمسة and ال order لل B بده يساوي خمسة ليش؟ هذا
+
+102
+00:10:51,270 --> 00:10:55,700
+يعطينا أن ال least common multiple يساوي خمسة that
+
+103
+00:10:55,700 --> 00:11:01,780
+is يعني أنه ال least common multiple للخمسة أو
+
+104
+00:11:01,780 --> 00:11:06,020
+خمسة الذي هو بده يساوي خمسة يعني ممكن يكون إذا بدي
+
+105
+00:11:06,020 --> 00:11:11,820
+أدور كم عنصر ال order الذي يساوي خمسة وين؟ في ال
+
+106
+00:11:11,820 --> 00:11:19,530
+group الأولى يعني كم واحد بيطلعون؟ أربعة ممتازين هنا
+
+107
+00:11:19,530 --> 00:11:25,290
+حد يقدر يعرفهم سهلة هذول؟ يلا جيب لي واحد بس
+
+108
+00:11:25,290 --> 00:11:30,490
+وأنا بجيب لكم الثالث كده؟ خمسة
+
+109
+00:11:30,490 --> 00:11:39,130
+وعشرة وخمسة عشر وعشرين في غيرهم؟ يبقى هنا we have
+
+110
+00:11:39,130 --> 00:11:42,470
+four
+
+111
+00:11:42,470 --> 00:11:44,030
+possibilities
+
+112
+00:11:46,450 --> 00:11:50,590
+والله have a choices خليها أسألكم في الكتابة شوية
+
+113
+00:11:50,590 --> 00:12:02,770
+we have four choices for a أربع خيارات لل a that
+
+114
+00:12:02,770 --> 00:12:11,050
+is الذي هم خمسة وعشرة وخمسة عشر وعشرين أي واحد من
+
+115
+00:12:11,050 --> 00:12:17,960
+عناصر هذول ال order الذي يساوي خمسة طيب الآن نحتاج
+
+116
+00:12:17,960 --> 00:12:22,680
+أن نصل إلى 10 ال order الذي يبدو يساوي خمسة بهذه
+
+117
+00:12:22,680 --> 00:12:27,660
+موجود وين؟ في ال Z خمسة كم element ال order الذي
+
+118
+00:12:27,660 --> 00:12:34,640
+يساوي خمسة؟ بس واحد الواحد
+
+119
+00:12:34,640 --> 00:12:43,310
+في غيره؟ طب واثنين كيف اثنين؟ لأ هذا prime يبقى كل
+
+120
+00:12:43,310 --> 00:12:47,410
+رقم فيها relatively prime مع الخمسة يعني كلهم ال
+
+121
+00:12:47,410 --> 00:12:51,690
+order له كل واحد فيهم يساوي خمسة صحيح ولا لا؟ لكن
+
+122
+00:12:51,690 --> 00:12:54,610
+لو ما كانت prime بيجي القلاب الذي تقوله بس كونه
+
+123
+00:12:54,610 --> 00:12:59,410
+prime automatic على طول الخط يبقى we have برضه
+
+124
+00:12:59,410 --> 00:13:06,320
+four choices for B الذي هم الواحد والاثنين والثلاثة
+
+125
+00:13:06,320 --> 00:13:10,640
+والأربعة فيهم كل واحد ال order الذي يساوي خمسة 
+
+126
+00:13:10,640 --> 00:13:16,020
+هاي that is الواحد والاثنين والثلاثة والأربعة طب
+
+127
+00:13:16,020 --> 00:13:20,460
+هدول اللي ما بدي أكون منهم order pair جدوش بيطلعوا
+
+128
+00:13:20,460 --> 00:13:25,260
+ستة عشر لإنه هذا هاخده مع الأربعة هدول يبقى يصير
+
+129
+00:13:25,260 --> 00:13:29,400
+أربعة والثاني أربعة والثالث أربعة والرابع أربعة من
+
+130
+00:13:29,400 --> 00:13:41,540
+الاثنين هدول بقول there are 16 elements of
+
+131
+00:13:41,540 --> 00:13:51,040
+order خمسة in Z خمسة وعشرون external direct
+
+132
+00:13:51,040 --> 00:13:58,260
+product ل Z خمسة طيب كويس هي أخدنا من الحالة
+
+133
+00:13:58,260 --> 00:14:03,910
+الأولى طيب الحالة الثانية ممكن يكون ال order لـ A
+
+134
+00:14:03,910 --> 00:14:10,130
+بده يساوي واحد و ال order لـ B بده يساوي خمسة يعني
+
+135
+00:14:10,130 --> 00:14:17,990
+that is ال least common multiple للواحد والخمسة
+
+136
+00:14:17,990 --> 00:14:23,110
+اللي هو خمسة إذا ممكن يبقى لما يكون ال order لـ A
+
+137
+00:14:23,110 --> 00:14:29,680
+يساوي واحد كم عنصر بيصير عندي كم خيار واحد في
+
+138
+00:14:29,680 --> 00:14:33,560
+شرط إجباري اللي هو ال identity element يبقى هنا
+
+139
+00:14:33,560 --> 00:14:41,660
+ماجي بقول if ال order لـ A بدّه يساوي واحد we have
+
+140
+00:14:41,660 --> 00:14:49,220
+one choice one choice for A اللي هو ال identity
+
+141
+00:14:49,220 --> 00:14:56,540
+element if ال order لـ B بدّه يساوي خمسة we have
+
+142
+00:14:56,540 --> 00:15:04,360
+كذاش؟ برضه أربعة choices for A و هذا as above كما
+
+143
+00:15:04,360 --> 00:15:12,240
+هو من فوق هذا بيعطيك كم عنصر ال order pair كم واحد
+
+144
+00:15:12,240 --> 00:15:17,600
+أربعة لأن هذا ال identity مع ال element الأول و ال
+
+145
+00:15:17,600 --> 00:15:20,200
+identity مع الثاني و ال identity مع الثالث و ال
+
+146
+00:15:20,200 --> 00:15:24,720
+identity مع الرابع يبقى أربعة عناصر هذا بيعطيني
+
+147
+00:15:24,720 --> 00:15:35,280
+there are اللي هو four elements of order خمسة هذا
+
+148
+00:15:35,280 --> 00:15:42,160
+بيعطيني أربعة طب الحالة الثالثة لو كان ال order لل
+
+149
+00:15:42,160 --> 00:15:48,540
+A بدّه يساوي خمسة and ال order لل B بدّه يساوي واحد
+
+150
+00:15:48,540 --> 00:15:56,080
+يبقى that is إن ال least common multiple للخمسة
+
+151
+00:15:56,080 --> 00:16:00,500
+والواحد هو يساوي خمسة طيب يبقى ال element الأول
+
+152
+00:16:00,500 --> 00:16:07,460
+بيعطيني كم خيار أربعة والثاني واحد يبقى هنا we
+
+153
+00:16:07,460 --> 00:16:15,620
+have four choices for
+
+154
+00:16:15,620 --> 00:16:28,850
+A الآن الثاني we have one choice for B من الاثنين
+
+155
+00:16:28,850 --> 00:16:38,850
+هدول بنجي نقوله we have four elements of
+
+156
+00:16:38,850 --> 00:16:46,210
+order five في غير هيك إذا
+
+157
+00:16:49,190 --> 00:17:03,270
+number of elements of order خمسة is الأولاني
+
+158
+00:17:03,270 --> 00:17:08,550
+جابتلي قداش ستة عشر والثاني جابتلي أربعة والثالث
+
+159
+00:17:08,550 --> 00:17:15,260
+جابتلي أربعة يبقى أربعة وعشرون elements يبقى من
+
+160
+00:17:15,260 --> 00:17:20,960
+المئة وعشرين بلاقي أربعة وعشرون element ال order
+
+161
+00:17:20,960 --> 00:17:28,840
+لهم يساوي خمسة يبقى
+
+162
+00:17:28,840 --> 00:17:36,480
+هذا المثال سهل عليه الحساب بعد ذلك اللي هو حساب كم
+
+163
+00:17:36,480 --> 00:17:42,130
+element يحمل نفس ال order في ال group الواحدة نعطي
+
+164
+00:17:42,130 --> 00:17:47,710
+مثال آخر ونتجلي شوية بدل ما بدي ال elements اللي
+
+165
+00:17:47,710 --> 00:17:52,770
+بيحملوا نفس ال order بدي ال cyclic subgroups اللي
+
+166
+00:17:52,770 --> 00:17:59,510
+بيحملوا نفس ال order وهذا موضوع المثال رقم ثلاثة
+
+167
+00:17:59,510 --> 00:18:06,130
+يبقى example ثلاثة example
+
+168
+00:18:06,130 --> 00:18:13,280
+ثلاثة بيقولي how many cyclic subgroups how many
+
+169
+00:18:13,280 --> 00:18:29,040
+cyclic subgroups
+
+170
+00:18:29,040 --> 00:18:34,400
+of order عشرة
+
+171
+00:18:34,400 --> 00:18:40,120
+in Z مئة
+
+172
+00:18:41,540 --> 00:18:49,140
+External Direct Product مع Z خمسة وعشرين هو Cyclic
+
+173
+00:18:49,140 --> 00:18:54,340
+Subgroup من أرض العشرة في Z مئة كثير نصف Cyclic
+
+174
+00:18:54,340 --> 00:19:01,500
+Subgroup ل Z مئة مع Z خمسة وعشرين
+
+175
+00:19:07,790 --> 00:19:12,410
+بقول ليش how many cyclic subgroups of order عشرة
+
+176
+00:19:12,410 --> 00:19:18,650
+in اللي هو Z مئة external product مع Z خمسة وعشرين
+
+177
+00:19:18,650 --> 00:19:25,230
+هذه ال group كم element فيها شباب كذاش الألفين
+
+178
+00:19:25,230 --> 00:19:30,910
+وخمسمية عنصر طبعا مئة في خمسة وعشرين ألفين وخمسماية
+
+179
+00:19:30,910 --> 00:19:35,410
+عنصر الآن بقول لي how many cyclic subgroups of
+
+180
+00:19:35,410 --> 00:19:40,180
+order عشرة يعني بدي كل ال subgroup اللي فهمش إلا
+
+181
+00:19:40,180 --> 00:19:46,280
+عشرة عناصر تمام ال order اللي يساوي عشرة بقول كويس
+
+182
+00:19:46,280 --> 00:19:52,100
+خليني أدور أنا لنص cyclic subgroup إذا خليني أدور
+
+183
+00:19:52,100 --> 00:19:56,940
+مين هم ال elements اللي ال order اللي يساوي عشرة
+
+184
+00:19:56,940 --> 00:20:01,360
+ال elements اللي ال order اللي يساوي عشرة كل واحد
+
+185
+00:20:01,360 --> 00:20:07,470
+هيجيبلي cyclic subgroup مظبوط يبقى هنا firstly
+
+186
+00:20:07,470 --> 00:20:18,170
+أولاً firstly we shall find بدنا نحاول نجد the
+
+187
+00:20:18,170 --> 00:20:26,990
+elements of اللي هو Z مئة external like a product
+
+188
+00:20:26,990 --> 00:20:38,560
+مع Z خمسة وعشرين with order عشرة لذلك حاجة أقوله
+
+189
+00:20:38,560 --> 00:20:48,580
+assume افترض أن ال G و ال H موجودة في ال Z مئة
+
+190
+00:20:48,580 --> 00:20:56,160
+stenotypic product مع Z خمسة وعشرين such that
+
+191
+00:20:56,160 --> 00:21:03,920
+بحيث أن ال order لل G و ال H بدّه يساوي عشرة
+
+192
+00:21:09,300 --> 00:21:13,440
+قال لي هاتلي ال cyclic subgroups أنا روحت قول له
+
+193
+00:21:13,440 --> 00:21:17,820
+بدي أجيب ال elements اللي ال order اللي لهم يساوي
+
+194
+00:21:17,820 --> 00:21:23,660
+عشرة لأن كل ال elements هدول هم اللي بيجيبولي من
+
+195
+00:21:23,660 --> 00:21:27,820
+ال cyclic subgroups أو هم اللي بيولولي كل ال
+
+196
+00:21:27,820 --> 00:21:35,120
+cyclic subgroups في هذه الحالة طيب
+
+197
+00:21:35,880 --> 00:21:45,860
+الآن هذا الكلام بده يساوي ال least common multiple
+
+198
+00:21:45,860 --> 00:21:52,340
+لل order بتاع ال G و ال order بتاع ال H
+
+199
+00:21:58,220 --> 00:22:01,740
+موجود في ال group اللي عندنا ال order اللي يساوي
+
+200
+00:22:01,740 --> 00:22:06,120
+عشرة وبيدّور أدور على ال list common multiples
+
+201
+00:22:06,120 --> 00:22:13,040
+اللي هو بيعطيني عشرة يبقى في عندنا عدة حالات خمسة
+
+202
+00:22:13,040 --> 00:22:21,760
+نشوف خمسة ولا أكثر يبقى هروح بقول له we have the
+
+203
+00:22:21,760 --> 00:22:26,040
+following cases
+
+204
+00:22:28,360 --> 00:22:38,440
+الحالة الأولى ال order لل G ممكن يكون عشرة and ال
+
+205
+00:22:38,440 --> 00:22:48,260
+order لل H ممكن يكون واحد أو خمسة صح ال order لل G
+
+206
+00:22:48,260 --> 00:22:52,880
+ممكن يكون عشرة و ال order لل H ممكن يكون واحد أو
+
+207
+00:22:52,880 --> 00:22:56,980
+خمسة يعني لو كان هذا عشرة أو هذا واحد لجرس ال
+
+208
+00:22:56,980 --> 00:23:02,180
+common divisor يساوي عشرة لو كان هذا عشرة أو هذا
+
+209
+00:23:02,180 --> 00:23:07,600
+خمسة لجرس ال common divisor يساوي عشرة
+
+210
+00:23:18,170 --> 00:23:23,830
+هل العشرة بتقسم الخمسة والعشرين؟ إذا لا يمكن تلاقي
+
+211
+00:23:23,830 --> 00:23:30,010
+element order له يساوي عشرة عندما تعمل على مطب ولا
+
+212
+00:23:30,010 --> 00:23:34,310
+تقع فيه مطب والحين ستقع فيه مطب بعد قليل إن شاء
+
+213
+00:23:34,310 --> 00:23:38,870
+الله ونشلك منه إن شاء الله بحيث ال element اللي
+
+214
+00:23:38,870 --> 00:23:42,710
+بدك تأخده ال order هذا بدّه يقسم ال order لل group
+
+215
+00:23:42,710 --> 00:23:46,290
+طبق ال algorithmic theorem و النتائج اللي عليها
+
+216
+00:23:46,290 --> 00:23:49,670
+أنا لما أخذت ال order اللي جيه اللي هو عشرة على
+
+217
+00:23:49,670 --> 00:23:56,210
+عشرة بتقسم المئة الآن أخذت هذه واحد أو خمسة بتقسم
+
+218
+00:23:56,210 --> 00:24:01,490
+من الخمسة والعشرين بس لو أخذت هذه بعشرة لا يمكن تقسم
+
+219
+00:24:01,490 --> 00:24:07,370
+من الخمسة والعشرين وبالتالي لا يمكن ألاقي order لبيه
+
+220
+00:24:07,370 --> 00:24:14,860
+يساوي من يساوي عشرة نرجع لهنا ال order لـ G يساوي
+
+221
+00:24:14,860 --> 00:24:23,620
+عشرة كويس الآن هذا بيجيب لي حسب chapter 4 unique
+
+222
+00:24:23,620 --> 00:24:29,720
+cyclic subgroup of order عشرة صحيح ولا لا يبقى هنا
+
+223
+00:24:29,720 --> 00:24:39,320
+ال order لل G بدّه يساوي عشرة gives you أو give a
+
+224
+00:24:39,320 --> 00:24:46,180
+unique cyclic subgroup
+
+225
+00:24:46,180 --> 00:24:50,080
+of
+
+226
+00:24:50,080 --> 00:24:58,180
+order عشرة that is مين هي هذه نرجع ل chapter أربعة
+
+227
+00:24:58,180 --> 00:25:03,040
+بنجي نقول بتروح تأخذ المئة اللي عندك على العشرة
+
+228
+00:25:05,100 --> 00:25:10,180
+عشرة يعني عشرة
+
+229
+00:25:10,180 --> 00:25:14,260
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+230
+00:25:14,260 --> 00:25:14,360
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+231
+00:25:14,360 --> 00:25:18,340
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+232
+00:25:18,340 --> 00:25:18,520
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+233
+00:25:18,520 --> 00:25:21,040
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+234
+00:25:21,040 --> 00:25:22,420
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+235
+00:25:22,420 --> 00:25:25,560
+عشرة عشرة
+
+236
+00:25:33,140 --> 00:25:37,720
+يعني ال order ليه عشرة في العشرة هي ال order ليه
+
+237
+00:25:37,720 --> 00:25:44,160
+عشرة مظبوط يبقى حالي أجي أربع عناصر فقط بيقول لي من؟
+
+238
+00:25:44,160 --> 00:25:54,860
+بيقول لي هذه ال group يبقى this group has four
+
+239
+00:25:54,860 --> 00:25:59,380
+generators four
+
+240
+00:25:59,380 --> 00:26:08,350
+generators ليش؟ that is اللي هو ال order ليه عشرة
+
+241
+00:26:08,350 --> 00:26:13,110
+أو ال phi عشرة اللي هو قداش يساوي اللي هو يساوي
+
+242
+00:26:13,110 --> 00:26:19,650
+أربعة طيب كويس يعني معناه هذا الكلام عندي أربع
+
+243
+00:26:19,650 --> 00:26:25,050
+خيارات لهذه ال subgroup مظبوط طيب تعال نشوف
+
+244
+00:26:25,050 --> 00:26:30,070
+الثاني هذا هذا بتعطيني خيار واحد وهذه بتعطيني كم
+
+245
+00:26:30,070 --> 00:26:36,170
+خيار أربع خيارات يعني خمس خيارات طيب بدي أجيب و
+
+246
+00:26:36,170 --> 00:26:43,990
+أقول له and ال order لل each بدّه يساوي واحد or خمسة
+
+247
+00:26:43,990 --> 00:26:49,090
+gives one
+
+248
+00:26:49,090 --> 00:26:54,690
+a choice for
+
+249
+00:26:56,370 --> 00:27:04,630
+order of each يساوي واحد and four choices وأربع
+
+250
+00:27:04,630 --> 00:27:15,210
+خيارات for order of each يساوي خمسة that is and we 
+
+251
+00:27:15,210 --> 00:27:20,910
+have خمسة
+
+252
+00:27:20,910 --> 00:27:25,610
+choices for each
+
+253
+00:27:27,270 --> 00:27:32,650
+طيب يبقى كام element في هذه حلبة سيارة؟ أربعة
+
+254
+00:27:32,650 --> 00:27:40,830
+لإيه؟ وخمسة لبيه يبقى عشرين عنصر يبقى هنا so the
+
+255
+00:27:40,830 --> 00:27:49,610
+element اللي قلنا عليه a g وh the element elements
+
+256
+00:27:49,610 --> 00:27:53,330
+also
+
+257
+00:27:53,330 --> 00:27:54,450
+دور
+
+258
+00:27:56,480 --> 00:28:11,240
+we have اللي هو عشرين element of order عشرة n اللي 
+
+259
+00:28:11,240 --> 00:28:19,740
+هو زد مية external product لزد خمسة و عشرين يبقى
+
+260
+00:28:19,740 --> 00:28:25,710
+الحالة الأولى هذه جبتلي جدار جبتلي عشرين answer
+
+261
+00:28:25,710 --> 00:28:33,210
+الآن الحالة الثانية لو كان ال order لل G بده يساوي
+
+262
+00:28:33,210 --> 00:28:40,110
+اثنين and ال order لل H بده يساوي خمسة هل هذا
+
+263
+00:28:40,110 --> 00:28:45,070
+الكلام ممكن؟ نعم لأن اثنين بتقسم المية و ال H
+
+264
+00:28:45,070 --> 00:28:50,310
+بتقسم مين؟ بتقسم الخمسة بالضبط تمام الآن شباب
+
+265
+00:28:50,310 --> 00:28:56,800
+اثنين بتقسم المية صح؟ يبقى في عندي unique cyclic
+
+266
+00:28:56,800 --> 00:29:05,240
+subgroup يبقى implies we have اللي هو unique
+
+267
+00:29:05,240 --> 00:29:17,720
+cyclic subgroup اللي هي من ال 100 على ال 2 اللي هي
+
+268
+00:29:17,720 --> 00:29:22,840
+الخمسين الخمسين كم عنصر فيها؟ دي اثنين ال order
+
+269
+00:29:22,840 --> 00:29:26,920
+يساوي اثنين الخمسين والمية بالزيرو يبقى ما عندناش
+
+270
+00:29:26,920 --> 00:29:32,660
+إلا زيرو وخمسين يبقى we have a unique cyclic
+
+271
+00:29:32,660 --> 00:29:38,660
+subgroup اللي هي subgroup واحدة وهذه ما فيهاش إلا
+
+272
+00:29:38,660 --> 00:29:43,340
+element واحد اللي هو الخمسين ال order اللي يساوي 
+
+273
+00:29:43,340 --> 00:29:49,840
+كده اثنين يعني ما عنديش إلا element واحد فقط لغيره
+
+274
+00:29:49,840 --> 00:30:05,380
+يبقى so we have one element only of order اثنين
+
+275
+00:30:07,650 --> 00:30:16,550
+نأتي إذا ال order لل H بده يساوي كده؟ خمسة يعني عندي
+
+276
+00:30:16,550 --> 00:30:23,170
+كم خيار؟ أربعة هم أيهم الخمسة عشر أو خمسة عشر يبقى
+
+277
+00:30:23,170 --> 00:30:34,650
+we have four choices for اللي هو ال H من الاتنين
+
+278
+00:30:34,650 --> 00:30:42,420
+هذول كده يكون عندي كم زوج مركب؟ حشرة؟ واحد وهنا
+
+279
+00:30:42,420 --> 00:30:46,200
+أربعة يبقى الواحد مع الأول مع الثاني مع الرابع
+
+280
+00:30:46,200 --> 00:30:53,300
+يبقى أربعة عناصر يبقى هذا بدي يعطيني we have four
+
+281
+00:30:53,300 --> 00:30:59,280
+elements of order
+
+282
+00:31:16,180 --> 00:31:21,720
+الحالة الثالثة لو كان ال order ل G خمسة و ال order
+
+283
+00:31:21,720 --> 00:31:22,860
+ل H و اثنين
+
+284
+00:31:28,040 --> 00:31:32,060
+منفعش يعني ال order لا تساوي اثنين اثنين لا تقسم
+
+285
+00:31:32,060 --> 00:31:36,140
+الخمسة والعشرين يبقى هذه الحالة غير موجودة مثل ما
+
+286
+00:31:36,140 --> 00:31:39,900
+واحد فيكم قلي قبل شوية عشرة وعشرة عشرة وعشرة انسى
+
+287
+00:31:39,900 --> 00:31:44,480
+الموضوع يبقى هذا انسى إذا لا يوجد عندي إلا هاتين
+
+288
+00:31:44,480 --> 00:31:53,660
+الحالتين مصدقة؟ يبقى هنا the number
+
+289
+00:31:53,660 --> 00:32:07,390
+of elements of order عشرة in z ميكس synodic product
+
+290
+00:32:07,390 --> 00:32:14,770
+مع z خمسة وعشرين is طلع هناك عشرين وجاني كمان
+
+291
+00:32:14,770 --> 00:32:18,830
+أربعة يبقى أربعة وعشرين element
+
+292
+00:32:23,390 --> 00:32:27,830
+يبقى فيه عندي أربعة وعشرين element ال order يساوي
+
+293
+00:32:27,830 --> 00:32:34,770
+عشرة يبقى عندي أربعة وعشرين cyclic subgroup of
+
+294
+00:32:34,770 --> 00:32:42,750
+order عشرة ردوا علي بس أنا طالع عندي أربعة وعشرين
+
+295
+00:32:42,750 --> 00:32:51,720
+عنصر ال order يساوي عشرة صح؟ مظبوط 24 السؤال هو هل
+
+296
+00:32:51,720 --> 00:32:57,280
+هذا يعني أنه عندي 24 cyclic subgroup of order عشرة
+
+297
+00:32:57,280 --> 00:33:08,780
+24
+
+298
+00:33:08,780 --> 00:33:14,170
+يعني عددهم طيب خلينا نسأل السؤال التالي الحلم يكون
+
+299
+00:33:14,170 --> 00:33:18,890
+عندي generator ال generator هذا مش بولد نفس ال
+
+300
+00:33:18,890 --> 00:33:24,450
+subgroup هدول فيهم generators وفيهم بعضهم معكوسات
+
+301
+00:33:24,450 --> 00:33:29,990
+ستين صحيح ولا لأ طيب كم generator في الواحدة
+
+302
+00:33:29,990 --> 00:33:34,830
+أربعة هي تبصها كتبناها في عندي أربعة generators
+
+303
+00:33:34,830 --> 00:33:40,580
+هي والله نسيته يبقى أنا في عندي أربعة يعني الأربعة
+
+304
+00:33:40,580 --> 00:33:45,640
+هدول بيجيبولي نفس ال subgroup يبقى بالدقة بدك
+
+305
+00:33:45,640 --> 00:33:49,980
+تجسم الأربعة والعشرين على عدد ال generators بيعطيك
+
+306
+00:33:49,980 --> 00:33:55,280
+بالضبط قداش عدد ال cyclic subgroups of order أربعة
+
+307
+00:33:55,870 --> 00:33:59,950
+لأن أي واحدة ال order لها يساوي عشرة فيها أربع
+
+308
+00:33:59,950 --> 00:34:04,490
+generators كل واحد فيهم ال order له يساوي عشرة
+
+309
+00:34:04,490 --> 00:34:09,550
+وبيجيب لنفس ال subgroup مظبوط إذا عدد ال cyclic
+
+310
+00:34:09,550 --> 00:34:13,890
+subgroups بدي يساوي عدد ال elements مجسوم على مين
+
+311
+00:34:13,890 --> 00:34:25,330
+على عدد ال generators يبقى هنا number of cyclic
+
+312
+00:34:29,010 --> 00:34:40,450
+subgroups of order عشرة in z مية extend that
+
+313
+00:34:40,450 --> 00:34:50,180
+product to z خمسة وعشرين بنقسم ال 24 على عدد ال
+
+314
+00:34:50,180 --> 00:34:57,340
+generators اللي هو أربعة يبقى ستة cyclic subgroups
+
+315
+00:34:57,340 --> 00:34:59,220
+فقط نغير
+
+316
+00:35:04,780 --> 00:35:11,920
+يبقى ال 2500 element اللي هم عناصر ال group هدول
+
+317
+00:35:11,920 --> 00:35:16,500
+بلاقي بس منهم اللي هو ال 6 elements بيجيبولي ال
+
+318
+00:35:16,500 --> 00:35:20,220
+cyclic subgroup ال order اللي يساوي قدامهم ال
+
+319
+00:35:20,220 --> 00:35:24,060
+order يساوي عشرة و بنكمل إن شاء الله في المحاضرة
+
+320
+00:35:24,060 --> 00:35:25,360
+القادمة
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0988e2a3409ce67f375733b7ef89e7a78ebeccfc
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_postprocess.srt
@@ -0,0 +1,1280 @@
+1
+00:00:20,650 --> 00:00:24,970
+بسم الله الرحمن الرحيم المرة اللى فاترة بدأنا في
+
+2
+00:00:24,970 --> 00:00:30,070
+chapter 8 اللى هو ال external direct product عرفنا
+
+3
+00:00:30,070 --> 00:00:34,010
+ال external direct product و أخذنا على ذلك بعض
+
+4
+00:00:34,010 --> 00:00:38,950
+الأمثلة ثم ذهبنا إلى أول نظرية على ال external
+
+5
+00:00:38,950 --> 00:00:44,030
+direct product وهو تحديد ال order لل element
+
+6
+00:00:44,030 --> 00:00:47,790
+المكون من ال external direct product بين two
+
+7
+00:00:47,790 --> 00:00:53,560
+groups أو أكثرفأقول النظرية بتقول أنه لو كان عندي
+
+8
+00:00:53,560 --> 00:00:58,720
+group G و group H عملنا ال external direct product
+
+9
+00:00:58,720 --> 00:01:03,280
+ما بين ال G و ال H يبقى أي element في ال external
+
+10
+00:01:03,280 --> 00:01:07,200
+direct product ال order له يسوي least common
+
+11
+00:01:07,200 --> 00:01:11,200
+multiple لمن ال order للمركبة الأولى و order
+
+12
+00:01:11,200 --> 00:01:16,580
+المركبة الثانية هذا بيعطينا ال order لل element
+
+13
+00:01:16,580 --> 00:01:21,090
+اللي موجود في ال external direct productطبعا هناخد
+
+14
+00:01:21,090 --> 00:01:28,550
+بعض الأمثلة على ذلك ونبدأ بالمثال الأول يبقى
+
+15
+00:01:28,550 --> 00:01:36,770
+example one يقول
+
+16
+00:01:36,770 --> 00:01:41,410
+find نمر
+
+17
+00:01:41,410 --> 00:01:52,970
+ايه نبدأ ال order لست و تمانيةنمر ب .. نمر ب ال
+
+18
+00:01:52,970 --> 00:02:02,990
+order لخمسة و خمسة كذلك كل هذا in the group in the
+
+19
+00:02:02,990 --> 00:02:10,890
+group في ال group اللي عندنا ليه z8 external
+
+20
+00:02:10,890 --> 00:02:14,890
+product مع مين مع z12
+
+21
+00:02:27,920 --> 00:02:32,840
+خلّى بلاك هنا جالى يشوف لقداش الارض لل element 6
+
+22
+00:02:32,840 --> 00:02:38,600
+و8 ايه اللى موجود في الاكسيدين نضايق افرادك z8 مع
+
+23
+00:02:38,600 --> 00:02:43,700
+مين مع z12 واضح ان ال component الاول اللى هى 6
+
+24
+00:02:43,700 --> 00:02:49,280
+بتكون مع مين في ال group اللى هى z8 و ال component
+
+25
+00:02:49,280 --> 00:02:54,380
+التانى اللى هى 8 بتكون موجودة في ال group z12 اذا
+
+26
+00:02:54,380 --> 00:03:01,870
+انا بدى اروحأدور على ال order لمين لستة و تمانية
+
+27
+00:03:01,870 --> 00:03:06,930
+يبقى هو ال least common multiple لل order تبع
+
+28
+00:03:06,930 --> 00:03:12,150
+الستة و ال order تبع التمانية و كل واحد في ال
+
+29
+00:03:12,150 --> 00:03:19,620
+group تبعه الآن بدي أجي لستةيبقى هذا الكلام بدي
+
+30
+00:03:19,620 --> 00:03:24,340
+يساوي ال least common multiple لمن؟ لأبصر من؟ بدي
+
+31
+00:03:24,340 --> 00:03:32,080
+ال order لستة في من؟ في z تمانية يلا بدي ال order
+
+32
+00:03:32,080 --> 00:03:37,380
+لستة في z تمانية طبعا z تمانية zero واحد اتنين
+
+33
+00:03:37,380 --> 00:03:42,340
+تلاتة لغاية تمانية ايوة كده اش؟ اربعة ممتاز جدا
+
+34
+00:03:42,340 --> 00:03:48,410
+يبقى ال order لستة هو اربعةهذا وين في زي التمانية
+
+35
+00:03:48,410 --> 00:03:52,090
+لإن الأربع في الستة باربع وعشرين هي مضاعفات
+
+36
+00:03:52,090 --> 00:03:58,170
+التمانية وهو أول أس بضربه في ستة بيعطينا مين
+
+37
+00:03:58,170 --> 00:04:02,950
+بيعطينا zero لإن ال identity element بدي أجيل ال
+
+38
+00:04:02,950 --> 00:04:09,180
+order تمانية في الأتناشبرضه تلاتة لان تلاتة في
+
+39
+00:04:09,180 --> 00:04:14,680
+تمانية باربعة وعشرين مضاعفات اتناش يبقى ال least
+
+40
+00:04:14,680 --> 00:04:18,280
+common multiple للاربعة والتلاتة اللي هو الاتناش
+
+41
+00:04:18,280 --> 00:04:23,120
+وبالتالي ال order لستة و تمانية عبارة عن اتناش
+
+42
+00:04:23,120 --> 00:04:29,220
+بمعنى ستة و تمانية لو حطيتها لل أس اتناش هذا اللي
+
+43
+00:04:29,220 --> 00:04:34,620
+بتعطينا من ال identity element وهو اول رقم بحطه ك
+
+44
+00:04:34,620 --> 00:04:38,940
+أس لستة و تمانيةبيعطينا الـ Main الـ Identity الـ
+
+45
+00:04:38,940 --> 00:04:43,260
+Main الان انا اخدت الـ 6 و 8 are not relative
+
+46
+00:04:43,260 --> 00:04:48,200
+prime لل 8 و 12 يعني ال 6 ماهياش relative prime مع
+
+47
+00:04:48,200 --> 00:04:54,120
+ال 8 وال 8 ماهياش relative prime مع Main مع ال 12
+
+48
+00:04:54,120 --> 00:04:55,180
+تعالى نشوف ال B
+
+49
+00:05:03,720 --> 00:05:07,440
+الخامسة الأولى تختلف عن الخامسة التانية لأن
+
+50
+00:05:07,440 --> 00:05:11,620
+الخامسة الأولى موجودة في Z8 و الخامسة التانية
+
+51
+00:05:11,620 --> 00:05:17,500
+موجودة في Z12 يبقى هذا ال lease common multiple لل
+
+52
+00:05:17,500 --> 00:05:23,780
+order بتابع الخامسةوال order كذلك بتبع الخمسة يبقى
+
+53
+00:05:23,780 --> 00:05:28,640
+least common multiple ليه؟ الآن الخمسة element
+
+54
+00:05:28,640 --> 00:05:35,440
+موجود في z تمانية جداش ال order إله؟ أي رقم في z
+
+55
+00:05:35,440 --> 00:05:40,260
+تمانية relatively prime مع تمانية ال order إله جد
+
+56
+00:05:40,260 --> 00:05:48,420
+تمانية وهو generator يبقى هذا برضه جداش تمانيةالان
+
+57
+00:05:48,420 --> 00:05:52,940
+الخمسة التانية relatively prime مع مين مع الاطناش
+
+58
+00:05:52,940 --> 00:05:58,620
+يبقى ال order لها كذلك يساوي كده؟ يساوي الاطناش
+
+59
+00:05:58,620 --> 00:06:03,140
+يبقى انا بدي least common multiple لتمانية ولا
+
+60
+00:06:03,140 --> 00:06:09,820
+اتناش اللي هو كده؟ اتناش ولا ستاش ال least common
+
+61
+00:06:09,820 --> 00:06:14,740
+multiple يعني لا تمانية ولا ستاش ولا اتناش كمان
+
+62
+00:06:17,520 --> 00:06:23,380
+يبقى ال order لهذا ال element يساوي 24 بمعنى خمسة
+
+63
+00:06:23,380 --> 00:06:27,980
+وخمسة لو بدأت أحط له أس واحد اتنين تلاتة لن أصل
+
+64
+00:06:27,980 --> 00:06:33,020
+إلى ال zero zero إلا بعد ما أوصل للأس اللي هو جداش
+
+65
+00:06:33,020 --> 00:06:37,620
+اللي هو أربعة وعشرين طيب هذا يعتبر من الأمثلة
+
+66
+00:06:37,620 --> 00:06:43,980
+البسيطة جدا انتجلي شويةيبقى بدنا نروح لل example
+
+67
+00:06:43,980 --> 00:06:50,180
+two example two بيقول لي ماتي how many number of
+
+68
+00:06:50,180 --> 00:07:03,380
+elements how many number of elements of
+
+69
+00:07:03,380 --> 00:07:17,990
+order of order fivein the group في ال group اللي
+
+70
+00:07:17,990 --> 00:07:25,630
+هي main اللي هي z خمسة وعشرين external product
+
+71
+00:07:25,630 --> 00:07:30,170
+product مع main مع z خمسة
+
+72
+00:07:45,850 --> 00:07:51,450
+خلّي ملاك اش بقول بقول هاتلي عدد العناصر اللي
+
+73
+00:07:51,450 --> 00:07:56,050
+موجودة في ال group z خمسة وعشرين كسنة ذاك product
+
+74
+00:07:56,050 --> 00:08:00,470
+مع z خمسة و اللي ال order إلها بيكون يسوى كده؟
+
+75
+00:08:00,470 --> 00:08:04,430
+يسوى خمسة، جاب المبدأ ال group هذه كام عنصر فيها
+
+76
+00:08:04,430 --> 00:08:10,110
+يا شباب؟ كده؟ مية و خمسة و عشرين اللي هو ال order
+
+77
+00:08:10,110 --> 00:08:13,840
+للأولى ضرب ال order للتانية بيعطيني كام عنصريبقى
+
+78
+00:08:13,840 --> 00:08:17,240
+انا عندى في هذى ال group مية و خمسة و عشرين عنصر
+
+79
+00:08:17,240 --> 00:08:22,540
+بدى ادور قداش عدد العناصر في هذى ال group اللى ال
+
+80
+00:08:22,540 --> 00:08:27,560
+order لهم بدى يساوي كدهش بدى يساوي خمسة يبقى بداجى
+
+81
+00:08:27,560 --> 00:08:36,930
+اقوله assume افترضassume ان ال a و ال b اللي
+
+82
+00:08:36,930 --> 00:08:41,350
+موجودة في ال z خمسة و عشرين external direct
+
+83
+00:08:41,350 --> 00:08:53,010
+product مع z خمسة has order خمسة that is in ال
+
+84
+00:08:53,010 --> 00:09:00,720
+order لل a و ال b بده يساوي كده؟ بده يساوي خمسةطب
+
+85
+00:09:00,720 --> 00:09:05,260
+ال order لهذا يعني مين؟ least common multiple يبقى
+
+86
+00:09:05,260 --> 00:09:14,840
+هذا يعني ان ال order لل a و ال b بده يساوي خمسة
+
+87
+00:09:14,840 --> 00:09:20,780
+اللي هو least common multiple لل order تبع ال a و
+
+88
+00:09:20,780 --> 00:09:23,480
+ال order تبع ال b
+
+89
+00:09:25,940 --> 00:09:29,760
+أنا افترض ان عنصر A وB موجود في الـ external
+
+90
+00:09:29,760 --> 00:09:35,880
+product ال order له يساوي خمسة من هذا الكلام دول
+
+91
+00:09:35,880 --> 00:09:42,500
+هطلع اكم عدد او اكم عنصر على شكل A وB ال order لهم
+
+92
+00:09:42,500 --> 00:09:47,360
+يساوي خمسة بس في معلومة هيها بدي استفيد منها ان
+
+93
+00:09:47,360 --> 00:09:51,500
+الخمسة هي ال least common multiple لل order بتابع
+
+94
+00:09:51,500 --> 00:09:58,040
+ال A و ال order بتابع ال Bخمسة و واحد و واحد و
+
+95
+00:09:58,040 --> 00:10:03,500
+خمسة طب و خمسة و خمسة يعني
+
+96
+00:10:03,500 --> 00:10:08,480
+كتر والحين طيب على أي حال هنجي نشوف الحالات
+
+97
+00:10:08,480 --> 00:10:18,860
+الممكنة في هذا الموضوع يبقى هنا we have
+
+98
+00:10:18,860 --> 00:10:21,760
+the following
+
+99
+00:10:30,470 --> 00:10:36,050
+Possibilities يبقى فيه عنا الاحتمالات الممكنة
+
+100
+00:10:36,050 --> 00:10:42,430
+التالية الاحتمال الأول ان ال order لل A بده يساوي
+
+101
+00:10:42,430 --> 00:10:51,270
+خمسة and ال order لل B بده يساوي خمسة ليش؟ هذا
+
+102
+00:10:51,270 --> 00:10:55,700
+بيعطينا ان ال least common multiple يساوي خمسةthat
+
+103
+00:10:55,700 --> 00:11:01,780
+is يعني انه ال list common multiple ل الخمسة او
+
+104
+00:11:01,780 --> 00:11:06,020
+خمسة اللي هو بده يسوي خمسة يعني ممكن يكون اذا بدي
+
+105
+00:11:06,020 --> 00:11:11,820
+ادور كم عنصر ال order اللي يسوي خمسة وين في ال
+
+106
+00:11:11,820 --> 00:11:19,530
+group الأولى يعني كم واحد بيطلعوناربع ممتازين هنا
+
+107
+00:11:19,530 --> 00:11:25,290
+حد بيقدر يعرفهم سهلات هدول يالا جيبولي واحد بس
+
+108
+00:11:25,290 --> 00:11:30,490
+وانا بجيبلكوا التالت كده؟ خمسة
+
+109
+00:11:30,490 --> 00:11:39,130
+وعشر وخمستاشر وعشرين في غيرهم يبقى هنا we have
+
+110
+00:11:39,130 --> 00:11:42,470
+four
+
+111
+00:11:42,470 --> 00:11:44,030
+possibilities
+
+112
+00:11:46,450 --> 00:11:50,590
+والله have a choices خليها أسالكوا في الكتابة شوية
+
+113
+00:11:50,590 --> 00:12:02,770
+we have four choices for a أربع خيارات لل a that
+
+114
+00:12:02,770 --> 00:12:11,050
+is اللي هما خمسة وعشرة وخمستاشر وعشرين أي واحد من
+
+115
+00:12:11,050 --> 00:12:17,960
+عناصر هدول ال order اللي بيسوي خمسة طيبالان نحتاج
+
+116
+00:12:17,960 --> 00:12:22,680
+ان نصل الى 10 ال order اللى يبدو يسوى خمسة بي هذا
+
+117
+00:12:22,680 --> 00:12:27,660
+موجود وين في ال z خمسة اكم element ال order اللى
+
+118
+00:12:27,660 --> 00:12:34,640
+يسوى خمسة بس واحد الواحد
+
+119
+00:12:34,640 --> 00:12:43,310
+في غيره طب و اتنين كيف اتنين لأ هذا primeيبقى كل
+
+120
+00:12:43,310 --> 00:12:47,410
+رقم فيها relatively prime مع الخمسة يعني كلهم ال
+
+121
+00:12:47,410 --> 00:12:51,690
+order له كل واحد فيهم يسوى خمسة صحيح ولا لا؟ لكن
+
+122
+00:12:51,690 --> 00:12:54,610
+لو ماكنتش prime بيجي القلاب اللي بتقوله بس كونه
+
+123
+00:12:54,610 --> 00:12:59,410
+prime automatic على طول الخط يبقى we have برضه
+
+124
+00:12:59,410 --> 00:13:06,320
+four choices for Bاللي هم الواحد والاتنين والتلاتة
+
+125
+00:13:06,320 --> 00:13:10,640
+والاربعة في شرم كل واحد ال order اللي يساوي خمسة
+
+126
+00:13:10,640 --> 00:13:16,020
+هاي that is الواحد والاتنين والتلاتة والاربعة طب
+
+127
+00:13:16,020 --> 00:13:20,460
+هدول اللي مابدي اكوّن منهم order pair جدوش بطلعوا
+
+128
+00:13:20,460 --> 00:13:25,260
+ستة عشر لإنه هذا هاخده مع الأربعة هدول يبقى يصار
+
+129
+00:13:25,260 --> 00:13:29,400
+أربعة والتاني أربعة والتالت أربعة والربعة أربعة من
+
+130
+00:13:29,400 --> 00:13:41,540
+الاتنين هدول بقول there is16 element of
+
+131
+00:13:41,540 --> 00:13:51,040
+order خمسة in z خمسة و عشرين external direct
+
+132
+00:13:51,040 --> 00:13:58,260
+product ل z خمسة طيب كويس هي أخدنا من الحالة
+
+133
+00:13:58,260 --> 00:14:03,910
+الأولى طيب الحالة الثانيةممكن يكون ال order ل a
+
+134
+00:14:03,910 --> 00:14:10,130
+بده يساوي واحد و ال order ل b بده يساوي خمسة يعني
+
+135
+00:14:10,130 --> 00:14:17,990
+that is ال least common multiple لل واحد و الخمسة
+
+136
+00:14:17,990 --> 00:14:23,110
+اللي هو خمسة إذا ممكن يبقى لما يكون ال order ل a
+
+137
+00:14:23,110 --> 00:14:29,680
+يساوي واحد أكم أنصر بيصير عندي أكم خيارواحد في
+
+138
+00:14:29,680 --> 00:14:33,560
+شريره إجباري اللي هو ال identity element يبقى هنا
+
+139
+00:14:33,560 --> 00:14:41,660
+ماجي بقول if ال order ل A بديه يسوي واحد we have
+
+140
+00:14:41,660 --> 00:14:49,220
+one choice one choice for A اللي هو ال identity
+
+141
+00:14:49,220 --> 00:14:56,540
+element if ال order ل B بديه يسوي خمسة we have
+
+142
+00:14:56,540 --> 00:15:04,360
+كدهش؟برضه اربعة choices for a و هذا as above كما
+
+143
+00:15:04,360 --> 00:15:12,240
+هو من فوق هذا بيعطيك كمانصر ال order pair كم واحد
+
+144
+00:15:12,240 --> 00:15:17,600
+اربعة لان هذا ال identity مع ال element الأول و ال
+
+145
+00:15:17,600 --> 00:15:20,200
+identity مع التاني و ال identity مع التالت و ال
+
+146
+00:15:20,200 --> 00:15:24,720
+identity مع الرابع يبقى اربعة عناصر هذا بيعطيني
+
+147
+00:15:24,720 --> 00:15:35,280
+there isاللي هو four elements of order خمسة هذا
+
+148
+00:15:35,280 --> 00:15:42,160
+بيعطيني أربعة طب الحالة التالتة لو كان ال order لل
+
+149
+00:15:42,160 --> 00:15:48,540
+a بده يساوي خمسة and ال order لل b بده يساوي واحد
+
+150
+00:15:48,540 --> 00:15:56,080
+يبقى that isإن ال least common multiple للخمسة
+
+151
+00:15:56,080 --> 00:16:00,500
+والواحد هو يساوي خمسة طيب يبقى ال element الأول
+
+152
+00:16:00,500 --> 00:16:07,460
+بيعطيني كام خيار أربعة والتاني واحد يبقى هنا we
+
+153
+00:16:07,460 --> 00:16:15,620
+have four choices for
+
+154
+00:16:15,620 --> 00:16:28,850
+a الآن التانيwe have one choice for B من الاتنين
+
+155
+00:16:28,850 --> 00:16:38,850
+هذول بنجي نقوله we have four elements of
+
+156
+00:16:38,850 --> 00:16:46,210
+order five فى غير هيك اذا
+
+157
+00:16:49,190 --> 00:17:03,270
+number of elements of order خمسة is الأولاني
+
+158
+00:17:03,270 --> 00:17:08,550
+جابتلي قداش ستة عشر والتاني جابتلي أربعة والتاله
+
+159
+00:17:08,550 --> 00:17:15,260
+جابتلي أربعة يبقى أربعة وعشرين elementsيبقى من
+
+160
+00:17:15,260 --> 00:17:20,960
+المائة وعشرين بلقى أربعة وعشرين element ال order
+
+161
+00:17:20,960 --> 00:17:28,840
+لهم يساوي خمسة يبقى
+
+162
+00:17:28,840 --> 00:17:36,480
+هذا المثال سهل عليه حساب بعد ذلك اللي هو حساب كم
+
+163
+00:17:36,480 --> 00:17:42,130
+element يحمل نفس ال order في ال group الواحدةنعطي
+
+164
+00:17:42,130 --> 00:17:47,710
+مثال آخر ونتجلي شوية بدل ما بدي ال elements اللي
+
+165
+00:17:47,710 --> 00:17:52,770
+بيحملوا نفس ال order بدي ال cyclic subgroups اللي
+
+166
+00:17:52,770 --> 00:17:59,510
+بيحملوا نفس ال order وهذا موضوع المثال رقم تلاتة
+
+167
+00:17:59,510 --> 00:18:06,130
+يبقى example تلاتة example
+
+168
+00:18:06,130 --> 00:18:13,280
+تلاتة بيقولي how many cyclic subgroups howmany
+
+169
+00:18:13,280 --> 00:18:29,040
+cyclic subgroups
+
+170
+00:18:29,040 --> 00:18:34,400
+of order عشرة
+
+171
+00:18:34,400 --> 00:18:40,120
+in زد مية
+
+172
+00:18:41,540 --> 00:18:49,140
+External Direct Product مع Z خمسة وعشرين هو Cyclic
+
+173
+00:18:49,140 --> 00:18:54,340
+Subgroup من أرض العشرة في Z مية كتير نصف Cyclic
+
+174
+00:18:54,340 --> 00:19:01,500
+Subgroup ل Z مية مع Z خمسة وعشرين
+
+175
+00:19:07,790 --> 00:19:12,410
+بقول ليش how many cyclic subgroups of order عشرة
+
+176
+00:19:12,410 --> 00:19:18,650
+in اللي هو z مية external product مع z خمسة وعشرين
+
+177
+00:19:18,650 --> 00:19:25,230
+هذه ال group كم element فيها شباب كدهش الفين
+
+178
+00:19:25,230 --> 00:19:30,910
+وخمسمية عنصر طبعا مية في خمسة وعشرين الفين وخمسمية
+
+179
+00:19:30,910 --> 00:19:35,410
+عنصر الان بقول لي how many cyclic subgroups of
+
+180
+00:19:35,410 --> 00:19:40,180
+order عشرةيعني بدى كل ال subgroup اللى فهمش الا
+
+181
+00:19:40,180 --> 00:19:46,280
+عشرة عناصر تمام ال order اللى يساوي عشرة بقول كويس
+
+182
+00:19:46,280 --> 00:19:52,100
+خلينى ادور انا لنص cyclic subgroup اذا خلينى ادور
+
+183
+00:19:52,100 --> 00:19:56,940
+مين هم ال elements اللى ال order اللى يساوي عشرة
+
+184
+00:19:56,940 --> 00:20:01,360
+ال elements اللى ال order اللى يساوي عشرة كل واحد
+
+185
+00:20:01,360 --> 00:20:07,470
+هيجيبلي cyclic subgroup مظبوطيبقى هنا firstly
+
+186
+00:20:07,470 --> 00:20:18,170
+أولاً firstly we shall find بدنا نحاول نجد the
+
+187
+00:20:18,170 --> 00:20:26,990
+elements of اللي هو z مية external like a product
+
+188
+00:20:26,990 --> 00:20:38,560
+مع z خمسة وعشرين with orderعشرة لذلك حاجة اقوله
+
+189
+00:20:38,560 --> 00:20:48,580
+assume افترض ان ال G و ال H موجودة في ال Z مية
+
+190
+00:20:48,580 --> 00:20:56,160
+stenotypic product مع Z خمسة و عشرين such that
+
+191
+00:20:56,160 --> 00:21:03,920
+بحيث ان ال order لل G و ال H بده يسوى عشر
+
+192
+00:21:09,300 --> 00:21:13,440
+قال لي هاتلي ال cyclic subgroups انا روحت قولله
+
+193
+00:21:13,440 --> 00:21:17,820
+بدي اجيب ال elements اللي ال order اللي لهم يساوي
+
+194
+00:21:17,820 --> 00:21:23,660
+عشرة لان كل ال elements هدول هم اللي بيجيبولي من
+
+195
+00:21:23,660 --> 00:21:27,820
+ال cyclic subgroups او هم اللي بيولولي كل ال
+
+196
+00:21:27,820 --> 00:21:35,120
+cyclic subgroups في هذه الحالة طيب
+
+197
+00:21:35,880 --> 00:21:45,860
+الان هذا الكلام بده يساوي ال least common multiple
+
+198
+00:21:45,860 --> 00:21:52,340
+لل order بتبع ال G و ال order بتبع ال H
+
+199
+00:21:58,220 --> 00:22:01,740
+موجود فى ال group اللى عندنا ال order اللى يساوي
+
+200
+00:22:01,740 --> 00:22:06,120
+عشرة و بيدروح ادور على ال list common multiples
+
+201
+00:22:06,120 --> 00:22:13,040
+اللى هو بيعطينى عشرة يبقى فى عندنا عدة حالات خمسة
+
+202
+00:22:13,040 --> 00:22:21,760
+نشوف خمسة ولا اكتر يبقى هروح بقوله we have the
+
+203
+00:22:21,760 --> 00:22:26,040
+following cases
+
+204
+00:22:28,360 --> 00:22:38,440
+الحالة الأولى ال order لل G ممكن يكون عشرة and ال
+
+205
+00:22:38,440 --> 00:22:48,260
+order لل H ممكن يكون واحد او خمسة صح ال order لل G
+
+206
+00:22:48,260 --> 00:22:52,880
+ممكن يكون عشرة و ال order لل H ممكن يكون واحد او
+
+207
+00:22:52,880 --> 00:22:56,980
+خمسة يعنيلو كان هذا عشرة او هذا واحد لجرس ال
+
+208
+00:22:56,980 --> 00:23:02,180
+common divisor يساوي عشرة لو كان هذا عشرة او هذا
+
+209
+00:23:02,180 --> 00:23:07,600
+خمسة لجرس ال common divisor يساوي عشرة
+
+210
+00:23:18,170 --> 00:23:23,830
+هل العشرة بتقسم الخمسة وعشرين ؟ إذا لا يمكن تلاقي
+
+211
+00:23:23,830 --> 00:23:30,010
+element order له يساوي عشرةعندما تعمل على مطب و لا
+
+212
+00:23:30,010 --> 00:23:34,310
+تقع فيه مطب و الحين ستقع فيه مطب بعد قليل ان شاء
+
+213
+00:23:34,310 --> 00:23:38,870
+الله و نشلك منه ان شاء الله بحيث ال element اللى
+
+214
+00:23:38,870 --> 00:23:42,710
+بدك تاخده ال order هذا بده يقسم ال order لل group
+
+215
+00:23:42,710 --> 00:23:46,290
+طبق ال algorithmic theorem و النتائج اللى عليها
+
+216
+00:23:46,290 --> 00:23:49,670
+انا لما أخدت ال order اللى جيه اللى هو عشرة على
+
+217
+00:23:49,670 --> 00:23:56,210
+عشرة بتقسم الميةالان اخذت هذه واحد او خمسة بتقسم
+
+218
+00:23:56,210 --> 00:24:01,490
+من الخمسة وعشرين بس لو اخذت هذه بعشرة لا يمكن تقسم
+
+219
+00:24:01,490 --> 00:24:07,370
+من الخمسة وعشرين وبالتالي لا يمكن الاقي order لبيه
+
+220
+00:24:07,370 --> 00:24:14,860
+يسوى من يساوي عشرنرجع لهنا ال order ل جي يساوي
+
+221
+00:24:14,860 --> 00:24:23,620
+عشرة كويس الان هذا بيجيبلي حسب chapter 4 unique
+
+222
+00:24:23,620 --> 00:24:29,720
+cyclic subgroup of order عشرة صحيح ولا لا يبقى هنا
+
+223
+00:24:29,720 --> 00:24:39,320
+ال order لل جي بدى يساوي عشرة gives you او give a
+
+224
+00:24:39,320 --> 00:24:46,180
+uniquecyclic subgroup
+
+225
+00:24:46,180 --> 00:24:50,080
+of
+
+226
+00:24:50,080 --> 00:24:58,180
+order عشرة that is مين هي هذه نرجع ل chapter أربعة
+
+227
+00:24:58,180 --> 00:25:03,040
+بجينا نقول بتروح تاخد المية اللي عندك على العشرة
+
+228
+00:25:05,100 --> 00:25:10,180
+عشرة يعني عشرة
+
+229
+00:25:10,180 --> 00:25:14,260
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+230
+00:25:14,260 --> 00:25:14,360
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+231
+00:25:14,360 --> 00:25:18,340
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+232
+00:25:18,340 --> 00:25:18,520
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+233
+00:25:18,520 --> 00:25:21,040
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+234
+00:25:21,040 --> 00:25:22,420
+عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة عشرة
+
+235
+00:25:22,420 --> 00:25:25,560
+عشرة عشرة
+
+236
+00:25:33,140 --> 00:25:37,720
+يعني ال order ليه عشرة في العشرة هي ال order ليه
+
+237
+00:25:37,720 --> 00:25:44,160
+عشرة مظبوط يبقى حالي أجي أربع أنصار فقط بولولي من؟
+
+238
+00:25:44,160 --> 00:25:54,860
+بولولي هذه ال group يبقى this group has four
+
+239
+00:25:54,860 --> 00:25:59,380
+generators four
+
+240
+00:25:59,380 --> 00:26:08,350
+generators ليش؟ that isاللي هو ال order ليه عشرة
+
+241
+00:26:08,350 --> 00:26:13,110
+أو ال five عشرة اللي هو قداش يساوي اللي هو يساوي
+
+242
+00:26:13,110 --> 00:26:19,650
+أربعة طيب كويس يعني معناه هذا الكلام عندي أربع
+
+243
+00:26:19,650 --> 00:26:25,050
+خيارات لهذه ال subgroup مظبوط طيب تعالى نشوف
+
+244
+00:26:25,050 --> 00:26:30,070
+التاني هذا هذا بتعطيني خيار واحدو هذه بتعطيني كام
+
+245
+00:26:30,070 --> 00:26:36,170
+خيار اربع خيارات يعني خمس خيارات طيب بدي اجيب و
+
+246
+00:26:36,170 --> 00:26:43,990
+اقوله and ال order لل each بدي ساوي واحد or خمسة
+
+247
+00:26:43,990 --> 00:26:49,090
+gives one
+
+248
+00:26:49,090 --> 00:26:54,690
+a choice for
+
+249
+00:26:56,370 --> 00:27:04,630
+order of each يساوي واحد and four choices واربع
+
+250
+00:27:04,630 --> 00:27:15,210
+خيارات for order of each يساوي خمسة that is and we
+
+251
+00:27:15,210 --> 00:27:20,910
+have خمسة
+
+252
+00:27:20,910 --> 00:27:25,610
+choices for each
+
+253
+00:27:27,270 --> 00:27:32,650
+طيب يبقى كام element في هذه حلبة سيارة؟ أربعة
+
+254
+00:27:32,650 --> 00:27:40,830
+لإيه؟ وخمسة لبيه يبقى عشرين أنصار يبقى هنا so the
+
+255
+00:27:40,830 --> 00:27:49,610
+element اللي قلنا عليه a g وh the element element
+
+256
+00:27:49,610 --> 00:27:53,330
+also
+
+257
+00:27:53,330 --> 00:27:54,450
+دور
+
+258
+00:27:56,480 --> 00:28:11,240
+we have اللي هو عشرين element of order عشرة n اللي
+
+259
+00:28:11,240 --> 00:28:19,740
+هو زد مية external product لزد خمسة و عشرين يبقى
+
+260
+00:28:19,740 --> 00:28:25,710
+الحالة الأولى هذه جبتلي جدارجبتلي عشرين answer
+
+261
+00:28:25,710 --> 00:28:33,210
+الان الحالة الثانية لو كان ال order لل G بده يساوي
+
+262
+00:28:33,210 --> 00:28:40,110
+اتنين and ال order لل H بده يساوي خمسة هل هذا
+
+263
+00:28:40,110 --> 00:28:45,070
+الكلام ممكن؟ نعم لإن اتنين بتقسم المية و ال H
+
+264
+00:28:45,070 --> 00:28:50,310
+بتقسم مين؟ بتقسم الخمسة بالضبط تمام الان شباب
+
+265
+00:28:50,310 --> 00:28:56,800
+اتنين بتقسم الميةصح؟ يبقى في عندي unique cyclic
+
+266
+00:28:56,800 --> 00:29:05,240
+subgroup يبقى implies we have اللي هو unique
+
+267
+00:29:05,240 --> 00:29:17,720
+cyclic subgroup اللي هي من ال 100 على ال 2 اللي هي
+
+268
+00:29:17,720 --> 00:29:22,840
+الخمسينالخمسين اكم انصر فيها دى اتنين ال order
+
+269
+00:29:22,840 --> 00:29:26,920
+يساوي اتنين الخمسين والمية بالزيرو يبقى ماعناشي
+
+270
+00:29:26,920 --> 00:29:32,660
+الا زيرو وخمسين يبقى we have a unique cyclic
+
+271
+00:29:32,660 --> 00:29:38,660
+subgroup اللى هى subgroup واحدةوهذه مافيهاش الا
+
+272
+00:29:38,660 --> 00:29:43,340
+element واحد اللى هو الخمسين ال order اللى يساوي
+
+273
+00:29:43,340 --> 00:29:49,840
+كده اتنين يعني ماعنديش الا element واحد فقط لغيره
+
+274
+00:29:49,840 --> 00:30:05,380
+يبقى so we have one element only of order اتنين
+
+275
+00:30:07,650 --> 00:30:16,550
+نجي اف ال order لل H بده يساوي كده؟ خمسة يعني عندى
+
+276
+00:30:16,550 --> 00:30:23,170
+كم خيار؟ اربع هم ايهم الخمسة عشر او خمستاشر يبقى
+
+277
+00:30:23,170 --> 00:30:34,650
+we have four choices for اللي هو ال H من الاتنين
+
+278
+00:30:34,650 --> 00:30:42,420
+هذول كده يكون عندىكم زوج مركب؟ حشرة؟ واحد و هنا
+
+279
+00:30:42,420 --> 00:30:46,200
+اربعة يبقى الواحد مع الاول مع التاني مع الرابع
+
+280
+00:30:46,200 --> 00:30:53,300
+يبقى اربعة عناصر يبقى هذا بدي يعطيني we have four
+
+281
+00:30:53,300 --> 00:30:59,280
+elements of order
+
+282
+00:31:16,180 --> 00:31:21,720
+الحالة التالتة لو كان ال order ل G خمسة و ال order
+
+283
+00:31:21,720 --> 00:31:22,860
+ل H و اتنين
+
+284
+00:31:28,040 --> 00:31:32,060
+منفعش يعني الارض لاتش يساوي اتنين اتنين لا تقسم
+
+285
+00:31:32,060 --> 00:31:36,140
+الخمسة وعشرين يبقى هذه الحالة غير موجودة مثل ما
+
+286
+00:31:36,140 --> 00:31:39,900
+واحد فيكوا قلي قبل شوية عشرة وعشرة عشرة وعشرة انسى
+
+287
+00:31:39,900 --> 00:31:44,480
+الموضوع يبقى هذا انسى إذا لا يوجد عندي إلا هاتين
+
+288
+00:31:44,480 --> 00:31:53,660
+الحالتين مصدوق؟ يبقى هنا the number
+
+289
+00:31:53,660 --> 00:32:07,390
+of elementsof order عشرة in z ميكس synodic product
+
+290
+00:32:07,390 --> 00:32:14,770
+مع z خمسة وعشرين is طلع هناك عشرين وجاني كمان
+
+291
+00:32:14,770 --> 00:32:18,830
+اربعة يبقى اربعة وعشرين element
+
+292
+00:32:23,390 --> 00:32:27,830
+يبقى فيه عندى اربع وعشرين element ال order يساوي
+
+293
+00:32:27,830 --> 00:32:34,770
+عشرة يبقى عندى اربع وعشرين cyclic subgroup of
+
+294
+00:32:34,770 --> 00:32:42,750
+order عشرة ردوا علي بس انا طالع عندى اربع وعشرين
+
+295
+00:32:42,750 --> 00:32:51,720
+عنصر ال order يساوي عشرة صح؟مظبوط 24 السؤال هو هل
+
+296
+00:32:51,720 --> 00:32:57,280
+هذا يعني انه عندي 24 cyclic subgroup of order عشرة
+
+297
+00:32:57,280 --> 00:33:08,780
+24
+
+298
+00:33:08,780 --> 00:33:14,170
+يعني عددهم طيب خلينا نسأل السؤال التاليالحلم يكون
+
+299
+00:33:14,170 --> 00:33:18,890
+عندي generator ال generator هذا مش بولد نفس ال
+
+300
+00:33:18,890 --> 00:33:24,450
+subgroup هدول فيهم generators و فيهم بعضهم معكوا
+
+301
+00:33:24,450 --> 00:33:29,990
+ستين صحيح ولا لأ طيب أكم generator في الواحدة
+
+302
+00:33:29,990 --> 00:33:34,830
+أربعة هاي تبصها كتبناها في عندي أربعة generators
+
+303
+00:33:34,830 --> 00:33:40,580
+هاي والله نسيتهيبقى انا في عندى اربعة يعني الاربعة
+
+304
+00:33:40,580 --> 00:33:45,640
+هدول بيجيبولي main نفس ال subgroup يبقى بالدقة بدك
+
+305
+00:33:45,640 --> 00:33:49,980
+تجسم الاربعة وعشرين على عدد ال generators بيعطيك
+
+306
+00:33:49,980 --> 00:33:55,280
+بالضبط قداش عدد ال cyclic subgroups of order اربعة
+
+307
+00:33:55,870 --> 00:33:59,950
+لأن اي واحدة ال order لها يساوي عشرة فيها اربع
+
+308
+00:33:59,950 --> 00:34:04,490
+generators كل واحد فيهم ال order له يساوي عشرة
+
+309
+00:34:04,490 --> 00:34:09,550
+وبيجيب لنفس ال subgroup مظبوط اذا عدد ال cyclic
+
+310
+00:34:09,550 --> 00:34:13,890
+subgroups بدي يساوي عدد ال elements مجسوم على مين
+
+311
+00:34:13,890 --> 00:34:25,330
+على عدد ال generators يبقى هنا number of cyclic
+
+312
+00:34:29,010 --> 00:34:40,450
+subgroups of order عشرة in z مية extend that
+
+313
+00:34:40,450 --> 00:34:50,180
+product to z خمسة وعشرينبنقسم ال 24 على عدد ال
+
+314
+00:34:50,180 --> 00:34:57,340
+generators اللي هو أربعة يبقى ستة cyclic subgroups
+
+315
+00:34:57,340 --> 00:34:59,220
+فقط نغير
+
+316
+00:35:04,780 --> 00:35:11,920
+يبقى ال 2500 element اللي هم عناصر ال group هدول
+
+317
+00:35:11,920 --> 00:35:16,500
+بلاقي بس منهم اللي هو ال 6 elements بيجيبولي ال
+
+318
+00:35:16,500 --> 00:35:20,220
+cyclic subgroup ال order اللي يساوي قدامهم ال
+
+319
+00:35:20,220 --> 00:35:24,060
+order يساوي عشرة و بنكمل ان شاء الله في المحاضرة
+
+320
+00:35:24,060 --> 00:35:25,360
+القادمة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..14a807b800243a1d3c460d80593dd5ddd70901d8
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/zMwkCWnM9Z8_raw.json
@@ -0,0 +1 @@
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{"start": 70.14, "end": 70.62, "word": " الأولى", "probability": 0.9918619791666666}, {"start": 70.62, "end": 70.7, "word": " و", "probability": 0.8466796875}, {"start": 70.7, "end": 71.2, "word": " order", "probability": 0.55908203125}, {"start": 71.2, "end": 72.3, "word": " المركبة", "probability": 0.8644205729166666}, {"start": 72.3, "end": 73.02, "word": " الثانية", "probability": 0.9378662109375}, {"start": 73.02, "end": 73.66, "word": " هذا", "probability": 0.88037109375}, {"start": 73.66, "end": 74.24, "word": " بيعطينا", "probability": 0.85107421875}, {"start": 74.24, "end": 74.62, "word": " ال", "probability": 0.485595703125}, {"start": 74.62, "end": 75.66, "word": " order", "probability": 0.93603515625}, {"start": 75.66, "end": 76.04, "word": " لل", "probability": 0.431640625}, {"start": 76.04, "end": 76.58, "word": " element", "probability": 0.95556640625}, {"start": 76.58, "end": 76.84, "word": " اللي", "probability": 0.778564453125}, {"start": 76.84, "end": 77.22, "word": " موجود", "probability": 0.9752604166666666}, {"start": 77.22, "end": 77.34, "word": " في", "probability": 0.94873046875}, {"start": 77.34, "end": 77.46, "word": " ال", "probability": 0.58935546875}, {"start": 77.46, "end": 77.94, "word": " external", "probability": 0.759765625}, {"start": 77.94, "end": 78.62, "word": " direct", "probability": 0.85302734375}, {"start": 78.62, "end": 79.2, "word": " product", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 3, "seek": 10837, "start": 79.71, "end": 108.37, "text": "طبعا هناخد بعض الأمثلة على ذلك ونبدأ بالمثال الأول يبقى example one يقول find نمر ايه نبدأ ال order لست و تمانية", "tokens": [9566, 3555, 3615, 995, 8032, 1863, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 15844, 29910, 23275, 4032, 1863, 44510, 10721, 20666, 2304, 12984, 6027, 16247, 12610, 7251, 3555, 4587, 7578, 1365, 472, 7251, 39648, 915, 8717, 29973, 1975, 1829, 3224, 8717, 44510, 10721, 2423, 1668, 5296, 14851, 4032, 46811, 7649, 10632], "avg_logprob": -0.2446933939771832, "compression_ratio": 1.3430656934306568, "no_speech_prob": 0.0, "words": [{"start": 79.71, "end": 80.45, "word": "طبعا", "probability": 0.81878662109375}, {"start": 80.45, "end": 81.09, "word": " هناخد", "probability": 0.793212890625}, {"start": 81.09, "end": 81.47, "word": " بعض", "probability": 0.93505859375}, {"start": 81.47, "end": 82.23, "word": " الأمثلة", "probability": 0.961669921875}, {"start": 82.23, "end": 82.67, "word": " على", "probability": 0.75244140625}, {"start": 82.67, "end": 83.75, "word": " ذلك", "probability": 0.974365234375}, {"start": 83.75, "end": 84.81, "word": " ونبدأ", "probability": 0.867431640625}, {"start": 84.81, "end": 86.07, "word": " بالمثال", "probability": 0.979736328125}, {"start": 86.07, "end": 87.39, "word": " الأول", "probability": 0.956787109375}, {"start": 87.39, "end": 88.55, "word": " يبقى", "probability": 0.659423828125}, {"start": 88.55, "end": 89.07, "word": " example", "probability": 0.88427734375}, {"start": 89.07, "end": 90.39, "word": " one", "probability": 0.732421875}, {"start": 90.39, "end": 96.77, "word": " يقول", "probability": 0.7919921875}, {"start": 96.77, "end": 97.69, "word": " find", "probability": 0.8837890625}, {"start": 97.69, "end": 101.41, "word": " نمر", "probability": 0.665283203125}, {"start": 101.41, "end": 102.77, "word": " ايه", "probability": 0.6778157552083334}, {"start": 102.77, "end": 104.19, "word": " نبدأ", "probability": 0.61767578125}, {"start": 104.19, "end": 104.51, "word": " ال", "probability": 0.6318359375}, {"start": 104.51, "end": 105.17, "word": " order", "probability": 0.94482421875}, {"start": 105.17, "end": 106.35, "word": " لست", "probability": 0.6439208984375}, {"start": 106.35, "end": 107.29, "word": " و", "probability": 0.77294921875}, {"start": 107.29, "end": 108.37, "word": " تمانية", "probability": 0.9308268229166666}], "temperature": 1.0}, {"id": 4, "seek": 13488, "start": 108.89, "end": 134.89, "text": "نمر ب .. نمر ب ال order لخمسة و خمسة كذلك كل هذا in the group in the group في ال group اللي عندنا ليه z8 external product مع مين مع z12", "tokens": [1863, 29973, 4724, 4386, 8717, 29973, 4724, 2423, 1668, 5296, 9778, 2304, 3794, 3660, 4032, 16490, 2304, 3794, 3660, 9122, 8848, 23275, 28242, 23758, 294, 264, 1594, 294, 264, 1594, 8978, 2423, 1594, 13672, 1829, 43242, 8315, 32239, 3224, 710, 23, 8320, 1674, 20449, 3714, 9957, 20449, 710, 4762], "avg_logprob": -0.2806249976158142, "compression_ratio": 1.355072463768116, "no_speech_prob": 0.0, "words": [{"start": 108.89, "end": 109.45, "word": "نمر", "probability": 0.4986572265625}, {"start": 109.45, "end": 109.85, "word": " ب", "probability": 0.32763671875}, {"start": 109.85, "end": 110.27, "word": " ..", "probability": 0.215576171875}, {"start": 110.27, "end": 111.63, "word": " نمر", "probability": 0.970947265625}, {"start": 111.63, "end": 112.13, "word": " ب", "probability": 0.9853515625}, {"start": 112.13, "end": 112.97, "word": " ال", "probability": 0.5205078125}, {"start": 112.97, "end": 113.69, "word": " order", "probability": 0.96533203125}, {"start": 113.69, "end": 115.61, "word": " لخمسة", "probability": 0.87314453125}, {"start": 115.61, "end": 115.83, "word": " و", "probability": 0.994140625}, {"start": 115.83, "end": 116.95, "word": " خمسة", "probability": 0.907470703125}, {"start": 116.95, "end": 117.87, "word": " كذلك", "probability": 0.9396158854166666}, {"start": 117.87, "end": 118.25, "word": " كل", "probability": 0.9599609375}, {"start": 118.25, "end": 118.83, "word": " هذا", "probability": 0.91064453125}, {"start": 118.83, "end": 120.11, "word": " in", "probability": 0.90625}, {"start": 120.11, "end": 120.41, "word": " the", "probability": 0.892578125}, {"start": 120.41, "end": 120.97, "word": " group", "probability": 0.98486328125}, {"start": 120.97, "end": 121.89, "word": " in", "probability": 0.62255859375}, {"start": 121.89, "end": 122.99, "word": " the", "probability": 0.86328125}, {"start": 122.99, "end": 124.61, "word": " group", "probability": 0.97900390625}, {"start": 124.61, "end": 125.79, "word": " في", "probability": 0.65966796875}, {"start": 125.79, "end": 125.95, "word": " ال", "probability": 0.85693359375}, {"start": 125.95, "end": 126.55, "word": " group", "probability": 0.98681640625}, {"start": 126.55, "end": 126.97, "word": " اللي", "probability": 0.8857421875}, {"start": 126.97, "end": 127.41, "word": " عندنا", "probability": 0.990478515625}, {"start": 127.41, "end": 127.67, "word": " ليه", "probability": 0.58837890625}, {"start": 127.67, "end": 128.69, "word": " z8", "probability": 0.4017333984375}, {"start": 128.69, "end": 130.89, "word": " external", "probability": 0.75634765625}, {"start": 130.89, "end": 131.39, "word": " product", "probability": 0.84423828125}, {"start": 131.39, "end": 132.19, "word": " مع", "probability": 0.7373046875}, {"start": 132.19, "end": 132.55, "word": " مين", "probability": 0.5986328125}, {"start": 132.55, "end": 133.33, "word": " مع", 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مين", "probability": 0.513671875}, {"start": 158.98, "end": 159.6, "word": " مع", "probability": 0.87451171875}, {"start": 159.6, "end": 160.82, "word": " z12", "probability": 0.96044921875}, {"start": 160.82, "end": 161.7, "word": " واضح", "probability": 0.9777018229166666}, {"start": 161.7, "end": 161.86, "word": " ان", "probability": 0.85595703125}, {"start": 161.86, "end": 161.98, "word": " ال", "probability": 0.8583984375}, {"start": 161.98, "end": 162.44, "word": " component", "probability": 0.9248046875}, {"start": 162.44, "end": 162.96, "word": " الاول", "probability": 0.79052734375}, {"start": 162.96, "end": 163.12, "word": " اللى", "probability": 0.749755859375}, {"start": 163.12, "end": 163.26, "word": " هى", "probability": 0.6356201171875}, {"start": 163.26, "end": 163.7, "word": " 6", "probability": 0.453125}, {"start": 163.7, "end": 164.2, "word": " بتكون", "probability": 0.94482421875}, {"start": 164.2, "end": 164.42, "word": " مع", "probability": 0.98486328125}, {"start": 164.42, "end": 164.86, "word": " مين", "probability": 0.943603515625}, {"start": 164.86, "end": 165.7, "word": " في", "probability": 0.74072265625}, {"start": 165.7, "end": 165.96, "word": " ال", "probability": 0.71484375}, {"start": 165.96, "end": 166.3, "word": " group", "probability": 0.96044921875}, {"start": 166.3, "end": 166.6, "word": " اللى", "probability": 0.834716796875}, {"start": 166.6, "end": 166.84, "word": " هى", "probability": 0.92333984375}, {"start": 166.84, "end": 167.8, "word": " z8", "probability": 0.953857421875}, {"start": 167.8, "end": 168.68, "word": " و", "probability": 0.493408203125}, {"start": 168.68, "end": 168.82, "word": " ال", "probability": 0.78125}, {"start": 168.82, "end": 169.28, "word": " component", "probability": 0.98388671875}, {"start": 169.28, "end": 169.7, "word": " التانى", "probability": 0.9051106770833334}, {"start": 169.7, "end": 169.86, "word": " اللى", "probability": 0.945068359375}, {"start": 169.86, "end": 169.98, "word": " هى", "probability": 0.927001953125}, {"start": 169.98, "end": 170.46, "word": " 8", "probability": 0.93896484375}, {"start": 170.46, "end": 171.06, "word": " بتكون", "probability": 0.943603515625}, {"start": 171.06, "end": 171.6, "word": " موجودة", "probability": 0.9317626953125}, {"start": 171.6, "end": 171.74, "word": " في", "probability": 0.8466796875}, {"start": 171.74, "end": 171.9, "word": " ال", "probability": 0.701171875}, {"start": 171.9, "end": 172.36, "word": " group", "probability": 0.93212890625}, {"start": 172.36, "end": 173.82, "word": " z12", "probability": 0.974365234375}, {"start": 173.82, "end": 174.38, "word": " اذا", "probability": 0.860595703125}, {"start": 174.38, "end": 175.32, "word": " انا", "probability": 0.911376953125}, {"start": 175.32, "end": 175.66, "word": " بدى", "probability": 0.8076171875}, {"start": 175.66, "end": 176.18, "word": " اروح", "probability": 0.9562174479166666}], "temperature": 1.0}, {"id": 6, "seek": 19707, "start": 176.49, "end": 197.07, "text": "أدور على ال order لمين لستة و تمانية يبقى هو ال least common multiple لل order تبع الستة و ال order تبع التمانية و كل واحد في ال group تبعه الآن بدي أجي لستة", "tokens": [10721, 3215, 13063, 15844, 2423, 1668, 32767, 9957, 5296, 14851, 3660, 4032, 46811, 7649, 10632, 7251, 3555, 4587, 7578, 31439, 2423, 1935, 2689, 3866, 24976, 1668, 6055, 3555, 3615, 21136, 2655, 3660, 4032, 2423, 1668, 6055, 3555, 3615, 16712, 2304, 7649, 10632, 4032, 28242, 36764, 24401, 8978, 2423, 1594, 6055, 3555, 3615, 3224, 6024, 48506, 4724, 16254, 5551, 7435, 1829, 5296, 14851, 3660], "avg_logprob": -0.2042236311826855, "compression_ratio": 1.5612903225806452, "no_speech_prob": 0.0, "words": [{"start": 176.49, "end": 177.33, "word": "أدور", "probability": 0.7325032552083334}, {"start": 177.33, "end": 177.99, "word": " على", "probability": 0.8955078125}, {"start": 177.99, "end": 178.23, "word": " ال", "probability": 0.85693359375}, {"start": 178.23, "end": 178.81, "word": " order", "probability": 0.9365234375}, {"start": 178.81, "end": 179.57, "word": " لمين", "probability": 0.816650390625}, {"start": 179.57, "end": 180.87, "word": " لستة", "probability": 0.6473795572916666}, {"start": 180.87, "end": 181.09, "word": " و", "probability": 0.6650390625}, {"start": 181.09, "end": 181.87, "word": " تمانية", "probability": 0.9767252604166666}, {"start": 181.87, "end": 182.65, "word": " يبقى", "probability": 0.70086669921875}, {"start": 182.65, "end": 182.89, "word": " هو", "probability": 0.96484375}, {"start": 182.89, "end": 183.11, "word": " ال", "probability": 0.7978515625}, {"start": 183.11, "end": 183.55, "word": " least", "probability": 0.98046875}, {"start": 183.55, "end": 184.13, "word": " common", "probability": 0.95849609375}, {"start": 184.13, "end": 185.15, "word": " multiple", "probability": 0.89013671875}, {"start": 185.15, "end": 185.87, "word": " لل", "probability": 0.86669921875}, {"start": 185.87, "end": 186.45, "word": " order", "probability": 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"end": 192.59, "word": " group", "probability": 0.99169921875}, {"start": 192.59, "end": 193.49, "word": " تبعه", "probability": 0.80615234375}, {"start": 193.49, "end": 194.39, "word": " الآن", "probability": 0.58514404296875}, {"start": 194.39, "end": 194.75, "word": " بدي", "probability": 0.739013671875}, {"start": 194.75, "end": 195.53, "word": " أجي", "probability": 0.74755859375}, {"start": 195.53, "end": 197.07, "word": " لستة", "probability": 0.7692057291666666}], "temperature": 1.0}, {"id": 7, "seek": 22606, "start": 197.94, "end": 226.06, "text": "يبقى هذا الكلام بدي يساوي ال least common multiple لمن؟ لأبصر من؟ بدي ال order لستة في من؟ في z تمانية يلا بدي ال order لستة في z تمانية طبعا z تمانية zero واحد اتنين تلاتة لغاية تمانية ايوة كده اش؟ اربعة ممتاز جدا يبقى ال order لستة هو اربعة", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 4724, 16254, 7251, 3794, 995, 45865, 2423, 1935, 2689, 3866, 5296, 27842, 22807, 5296, 10721, 3555, 9381, 2288, 9154, 22807, 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element بدي أجيل ال order تمانية في الأتناش", "tokens": [3224, 15730, 4032, 9957, 8978, 30767, 1829, 16712, 2304, 7649, 10632, 5296, 28814, 1863, 16247, 25513, 3615, 8978, 21136, 2655, 3660, 4724, 9640, 3555, 3615, 4032, 3615, 46309, 9957, 39896, 3714, 11242, 45761, 5172, 9307, 16712, 2304, 7649, 10632, 37037, 2407, 5551, 12610, 5551, 3794, 4724, 11242, 25513, 3224, 8978, 8608, 2655, 3660, 4724, 40228, 9566, 1829, 8315, 3714, 9957, 4724, 40228, 9566, 1829, 8315, 4018, 5296, 28814, 1863, 2423, 6575, 4478, 4724, 16254, 5551, 7435, 26895, 2423, 1668, 46811, 7649, 10632, 8978, 16247, 2655, 1863, 33599], "avg_logprob": -0.3332741494205865, "compression_ratio": 1.7514124293785311, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 226.31, "end": 226.75, "word": "هذا", "probability": 0.5103759765625}, {"start": 226.75, "end": 227.19, "word": " وين", "probability": 0.511749267578125}, {"start": 227.19, "end": 227.53, "word": " في", "probability": 0.53369140625}, {"start": 227.53, 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{"start": 506.22, "end": 507.04, "word": " يبقى", "probability": 0.9498291015625}, {"start": 507.04, "end": 507.56, "word": " بداجى", "probability": 0.7506510416666666}, {"start": 507.56, "end": 508.26, "word": " اقوله", "probability": 0.796875}, {"start": 508.26, "end": 509.1, "word": " assume", "probability": 0.64501953125}, {"start": 509.1, "end": 510.42, "word": " افترض", "probability": 0.956298828125}], "temperature": 1.0}, {"id": 19, "seek": 53957, "start": 511.41, "end": 539.57, "text": "assume ان ال a و ال b اللي موجودة في ال z خمسة و عشرين external direct product مع z خمسة has order خمسة that is in ال order لل a و ال b بده يساوي كده؟ بده يساوي خمسة", "tokens": [640, 2540, 16472, 2423, 257, 4032, 2423, 272, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 710, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 8320, 2047, 1674, 20449, 710, 16490, 2304, 3794, 3660, 575, 1668, 16490, 2304, 3794, 3660, 300, 307, 294, 2423, 1668, 24976, 257, 4032, 2423, 272, 47525, 3224, 7251, 3794, 995, 45865, 9122, 3215, 3224, 22807, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660], "avg_logprob": -0.21643926350163742, "compression_ratio": 1.5592105263157894, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 511.41, "end": 512.21, "word": "assume", "probability": 0.7237548828125}, {"start": 512.21, "end": 512.99, "word": " ان", "probability": 0.6572265625}, {"start": 512.99, "end": 514.47, "word": " ال", "probability": 0.77734375}, {"start": 514.47, "end": 514.87, "word": " a", "probability": 0.379638671875}, {"start": 514.87, "end": 515.55, "word": " و", "probability": 0.58837890625}, {"start": 515.55, "end": 515.79, "word": " ال", "probability": 0.8955078125}, {"start": 515.79, "end": 516.11, "word": " b", "probability": 0.939453125}, {"start": 516.11, "end": 516.93, "word": " اللي", "probability": 0.72119140625}, {"start": 516.93, "end": 517.77, "word": " موجودة", "probability": 0.96875}, {"start": 517.77, "end": 518.05, "word": " في", "probability": 0.91552734375}, {"start": 518.05, "end": 518.25, "word": " ال", "probability": 0.650390625}, {"start": 518.25, "end": 518.51, "word": " z", "probability": 0.71826171875}, {"start": 518.51, "end": 519.27, "word": " خمسة", "probability": 0.9481201171875}, {"start": 519.27, "end": 519.35, "word": " و", "probability": 0.9560546875}, {"start": 519.35, "end": 519.97, "word": " عشرين", "probability": 0.8318684895833334}, {"start": 519.97, "end": 520.85, "word": " external", "probability": 0.673828125}, {"start": 520.85, "end": 521.35, "word": " direct", "probability": 0.308349609375}, {"start": 521.35, "end": 522.07, "word": " product", "probability": 0.96435546875}, {"start": 522.07, "end": 522.59, "word": " مع", "probability": 0.8310546875}, {"start": 522.59, "end": 523.03, "word": " z", "probability": 0.77490234375}, {"start": 523.03, "end": 523.89, "word": " خمسة", "probability": 0.983154296875}, {"start": 523.89, "end": 525.25, "word": " has", "probability": 0.71240234375}, {"start": 525.25, "end": 526.67, "word": " order", "probability": 0.96484375}, {"start": 526.67, "end": 529.09, "word": " خمسة", "probability": 0.9942626953125}, {"start": 529.09, "end": 529.33, "word": " that", "probability": 0.87109375}, {"start": 529.33, "end": 530.49, "word": " is", "probability": 0.97021484375}, {"start": 530.49, "end": 532.13, "word": " in", "probability": 0.1534423828125}, {"start": 532.13, "end": 533.01, "word": " ال", "probability": 0.82275390625}, {"start": 533.01, "end": 533.73, "word": " order", "probability": 0.97607421875}, {"start": 533.73, "end": 534.59, "word": " لل", "probability": 0.69482421875}, {"start": 534.59, "end": 535.03, "word": " a", "probability": 0.951171875}, {"start": 535.03, "end": 535.29, "word": " و", "probability": 0.947265625}, {"start": 535.29, "end": 535.57, "word": " ال", "probability": 0.62109375}, {"start": 535.57, "end": 535.93, "word": " b", "probability": 0.98779296875}, {"start": 535.93, "end": 536.69, "word": " بده", "probability": 0.5003662109375}, {"start": 536.69, "end": 537.03, "word": " يساوي", "probability": 0.8291015625}, {"start": 537.03, "end": 537.77, "word": " كده؟", "probability": 0.72808837890625}, {"start": 537.77, "end": 538.31, "word": " بده", "probability": 0.9326171875}, {"start": 538.31, "end": 538.85, "word": " يساوي", "probability": 0.98583984375}, {"start": 538.85, "end": 539.57, "word": " خمسة", "probability": 0.9913330078125}], "temperature": 1.0}, {"id": 20, "seek": 56348, "start": 540.44, "end": 563.48, "text": "طب ال order لهذا يعني مين؟ least common multiple يبقى هذا يعني ان ال order لل a و ال b بده يساوي خمسة اللي هو least common multiple لل order تبع ال a و ال order تبع ال b", "tokens": [9566, 3555, 2423, 1668, 46740, 15730, 37495, 22653, 3714, 9957, 22807, 1935, 2689, 3866, 7251, 3555, 4587, 7578, 23758, 37495, 22653, 16472, 2423, 1668, 24976, 257, 4032, 2423, 272, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 1935, 2689, 3866, 24976, 1668, 6055, 3555, 3615, 2423, 257, 4032, 2423, 1668, 6055, 3555, 3615, 2423, 272], "avg_logprob": -0.23040471506900476, "compression_ratio": 1.7, "no_speech_prob": 0.0, "words": [{"start": 540.44, "end": 540.72, "word": "طب", "probability": 0.607666015625}, {"start": 540.72, "end": 540.88, "word": " ال", "probability": 0.92333984375}, {"start": 540.88, "end": 541.24, "word": " order", "probability": 0.966796875}, {"start": 541.24, "end": 541.7, "word": " لهذا", "probability": 0.806640625}, {"start": 541.7, "end": 542.08, "word": " يعني", "probability": 0.929931640625}, {"start": 542.08, "end": 542.8, "word": " مين؟", "probability": 0.5555013020833334}, {"start": 542.8, "end": 543.3, "word": " least", "probability": 0.451904296875}, {"start": 543.3, "end": 543.64, "word": " common", "probability": 0.9560546875}, {"start": 543.64, "end": 544.24, "word": " multiple", "probability": 0.921875}, {"start": 544.24, "end": 545.26, "word": " يبقى", "probability": 0.8939208984375}, {"start": 545.26, "end": 545.74, "word": " هذا", "probability": 0.93896484375}, {"start": 545.74, "end": 546.88, "word": " يعني", "probability": 0.939208984375}, {"start": 546.88, "end": 547.36, "word": " ان", "probability": 0.61962890625}, {"start": 547.36, "end": 547.98, "word": " ال", "probability": 0.8173828125}, {"start": 547.98, "end": 549.76, "word": " order", "probability": 0.978515625}, {"start": 549.76, "end": 550.62, "word": " لل", "probability": 0.53857421875}, {"start": 550.62, "end": 551.16, "word": " a", "probability": 0.53955078125}, {"start": 551.16, "end": 551.46, "word": " و", "probability": 0.54931640625}, {"start": 551.46, "end": 551.8, "word": " ال", "probability": 0.307373046875}, {"start": 551.8, "end": 552.14, "word": " b", "probability": 0.9765625}, {"start": 552.14, "end": 553.12, "word": " بده", "probability": 0.567626953125}, {"start": 553.12, "end": 553.66, "word": " يساوي", "probability": 0.9249267578125}, {"start": 553.66, "end": 554.84, "word": " خمسة", "probability": 0.911376953125}, {"start": 554.84, "end": 555.38, "word": " اللي", "probability": 0.9296875}, {"start": 555.38, "end": 555.54, "word": " هو", "probability": 0.90283203125}, {"start": 555.54, "end": 556.1, "word": " least", "probability": 0.87939453125}, {"start": 556.1, "end": 556.64, "word": " common", "probability": 0.92919921875}, {"start": 556.64, "end": 557.48, "word": " multiple", "probability": 0.86962890625}, {"start": 557.48, "end": 558.2, "word": " لل", "probability": 0.8681640625}, {"start": 558.2, "end": 558.88, "word": " order", "probability": 0.97412109375}, {"start": 558.88, "end": 559.52, "word": " تبع", "probability": 0.9607747395833334}, {"start": 559.52, "end": 559.84, "word": " ال", "probability": 0.94677734375}, {"start": 559.84, "end": 560.28, "word": " a", "probability": 0.96875}, {"start": 560.28, "end": 560.78, "word": " و", "probability": 0.95166015625}, {"start": 560.78, "end": 560.94, "word": " ال", "probability": 0.4580078125}, {"start": 560.94, "end": 561.54, "word": " order", "probability": 0.96142578125}, {"start": 561.54, "end": 562.06, "word": " تبع", "probability": 0.9576822916666666}, {"start": 562.06, "end": 562.3, "word": " ال", "probability": 0.60546875}, {"start": 562.3, "end": 563.48, "word": " b", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 21, "seek": 59428, "start": 565.94, "end": 594.28, "text": "أنا افترض ان عنصر A وB موجود في الـ external product ال order له يساوي خمسة من هذا الكلام دول هطلع اكم عدد او اكم عنصر على شكل A وB ال order لهم يساوي خمسة بس في معلومة هيها بدي استفيد منها ان الخمسة هي ال least common multiple لل order بتابع ال A و ال order بتابع ال B", "tokens": [10721, 8315, 1975, 5172, 2655, 43042, 16472, 18871, 9381, 2288, 316, 4032, 33, 3714, 29245, 23328, 8978, 2423, 39184, 8320, 1674, 2423, 1668, 46740, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 9154, 23758, 2423, 28820, 10943, 11778, 12610, 8032, 9566, 1211, 3615, 1975, 24793, 6225, 3215, 3215, 1975, 2407, 1975, 24793, 18871, 9381, 2288, 15844, 13412, 28820, 316, 4032, 33, 2423, 1668, 5296, 16095, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 4724, 3794, 8978, 20449, 1211, 20498, 3660, 39896, 11296, 4724, 16254, 44713, 5172, 25708, 9154, 11296, 16472, 33962, 2304, 3794, 3660, 39896, 2423, 1935, 2689, 3866, 24976, 1668, 39894, 16758, 3615, 2423, 316, 4032, 2423, 1668, 39894, 16758, 3615, 2423, 363], "avg_logprob": -0.2910326211348824, "compression_ratio": 1.7605042016806722, "no_speech_prob": 0.34033203125, "words": [{"start": 565.94, "end": 566.52, "word": "أنا", "probability": 0.32171630859375}, {"start": 566.52, "end": 566.9, "word": " افترض", "probability": 0.820068359375}, {"start": 566.9, "end": 567.18, "word": " ان", "probability": 0.5634765625}, {"start": 567.18, "end": 567.92, "word": " عنصر", "probability": 0.7708333333333334}, {"start": 567.92, "end": 568.14, "word": " A", "probability": 0.3115234375}, {"start": 568.14, "end": 568.58, "word": " وB", "probability": 0.8095703125}, {"start": 568.58, "end": 569.1, "word": " موجود", "probability": 0.8427734375}, {"start": 569.1, "end": 569.26, "word": " في", "probability": 0.75048828125}, {"start": 569.26, "end": 569.34, "word": " الـ", "probability": 0.504150390625}, {"start": 569.34, "end": 569.76, "word": " external", "probability": 0.1822509765625}, {"start": 569.76, "end": 570.34, "word": " product", "probability": 0.6728515625}, {"start": 570.34, "end": 571.32, "word": " ال", "probability": 0.21630859375}, {"start": 571.32, "end": 571.8, "word": " order", "probability": 0.394775390625}, {"start": 571.8, "end": 572.26, "word": " له", "probability": 0.293212890625}, {"start": 572.26, "end": 573.24, "word": " يساوي", "probability": 0.8177490234375}, {"start": 573.24, "end": 573.96, "word": " خمسة", "probability": 0.919677734375}, {"start": 573.96, "end": 574.68, "word": " من", "probability": 0.69091796875}, {"start": 574.68, "end": 575.2, "word": " هذا", "probability": 0.853515625}, {"start": 575.2, "end": 575.68, "word": " الكلام", "probability": 0.8938802083333334}, {"start": 575.68, "end": 575.88, "word": " دول", "probability": 0.3580322265625}, {"start": 575.88, "end": 576.78, "word": " هطلع", "probability": 0.7994384765625}, {"start": 576.78, "end": 577.54, "word": " اكم", "probability": 0.650634765625}, {"start": 577.54, "end": 578.16, "word": " عدد", "probability": 0.9352213541666666}, {"start": 578.16, "end": 578.42, "word": " او", "probability": 0.928466796875}, {"start": 578.42, "end": 578.86, "word": " اكم", "probability": 0.92578125}, {"start": 578.86, "end": 579.4, "word": " عنصر", "probability": 0.9855143229166666}, {"start": 579.4, "end": 579.64, "word": " على", "probability": 0.8876953125}, {"start": 579.64, "end": 580.16, "word": " شكل", "probability": 0.912841796875}, {"start": 580.16, "end": 580.5, "word": " A", "probability": 0.85302734375}, {"start": 580.5, "end": 580.94, "word": " وB", "probability": 0.943603515625}, {"start": 580.94, "end": 581.56, "word": " ال", "probability": 0.81591796875}, {"start": 581.56, "end": 582.0, "word": " order", "probability": 0.96728515625}, {"start": 582.0, "end": 582.5, "word": " لهم", "probability": 0.6326904296875}, {"start": 582.5, "end": 582.98, "word": " يساوي", "probability": 0.9794921875}, {"start": 582.98, "end": 583.5, "word": " خمسة", "probability": 0.9910888671875}, {"start": 583.5, "end": 584.12, "word": " بس", "probability": 0.821044921875}, {"start": 584.12, "end": 584.28, "word": " في", "probability": 0.77392578125}, {"start": 584.28, "end": 584.9, "word": " معلومة", "probability": 0.9635009765625}, {"start": 584.9, "end": 585.26, "word": " هيها", "probability": 0.5654296875}, {"start": 585.26, "end": 585.52, "word": " بدي", "probability": 0.63623046875}, {"start": 585.52, "end": 586.26, "word": " استفيد", "probability": 0.9357096354166666}, {"start": 586.26, "end": 586.74, "word": " منها", "probability": 0.994873046875}, {"start": 586.74, "end": 587.36, "word": " ان", "probability": 0.77587890625}, {"start": 587.36, "end": 588.2, "word": " الخمسة", "probability": 0.9580078125}, {"start": 588.2, "end": 588.42, "word": " هي", "probability": 0.9052734375}, {"start": 588.42, "end": 588.64, "word": " ال", "probability": 0.6455078125}, {"start": 588.64, "end": 588.92, "word": " least", "probability": 0.4091796875}, {"start": 588.92, "end": 589.28, "word": " common", "probability": 0.91357421875}, {"start": 589.28, "end": 589.92, "word": " multiple", "probability": 0.91162109375}, {"start": 589.92, "end": 590.56, "word": " لل", "probability": 0.62890625}, {"start": 590.56, "end": 590.96, "word": " order", "probability": 0.923828125}, {"start": 590.96, "end": 591.5, "word": " بتابع", "probability": 0.83642578125}, {"start": 591.5, "end": 591.7, "word": " ال", "probability": 0.875}, {"start": 591.7, "end": 591.98, "word": " A", "probability": 0.8828125}, {"start": 591.98, "end": 592.16, "word": " و", "probability": 0.6923828125}, {"start": 592.16, "end": 592.32, "word": " ال", "probability": 0.1959228515625}, {"start": 592.32, "end": 592.86, "word": " order", "probability": 0.94384765625}, {"start": 592.86, "end": 593.78, "word": " بتابع", "probability": 0.9759114583333334}, {"start": 593.78, "end": 594.08, "word": " ال", "probability": 0.95458984375}, {"start": 594.08, "end": 594.28, "word": " B", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 22, "seek": 62176, "start": 596.32, "end": 621.76, "text": "خمسة و واحد و واحد و خمسة طب و خمسة و خمسة يعني كتر والحين طيب على أي حال هنجي نشوف الحالات الممكنة في هذا الموضوع يبقى هنا we have the following", "tokens": [9778, 2304, 3794, 3660, 4032, 36764, 24401, 4032, 36764, 24401, 4032, 16490, 2304, 3794, 3660, 23032, 3555, 4032, 16490, 2304, 3794, 3660, 4032, 16490, 2304, 3794, 3660, 37495, 22653, 9122, 2655, 2288, 16070, 5016, 9957, 23032, 1829, 3555, 15844, 36632, 11331, 6027, 8032, 1863, 7435, 1829, 8717, 8592, 38688, 21542, 6027, 9307, 9673, 43020, 3660, 8978, 23758, 9673, 2407, 11242, 45367, 7251, 3555, 4587, 7578, 34105, 321, 362, 264, 3480], "avg_logprob": -0.1360035194477565, "compression_ratio": 1.5548387096774194, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 596.32, "end": 597.24, "word": "خمسة", "probability": 0.8968505859375}, {"start": 597.24, "end": 597.32, "word": " و", "probability": 0.81689453125}, {"start": 597.32, "end": 597.58, "word": " واحد", "probability": 0.83251953125}, {"start": 597.58, "end": 597.7, "word": " و", "probability": 0.9521484375}, {"start": 597.7, "end": 597.92, "word": " واحد", "probability": 0.949462890625}, {"start": 597.92, "end": 598.04, "word": " و", "probability": 0.9970703125}, {"start": 598.04, "end": 598.32, "word": " خمسة", "probability": 0.9560546875}, {"start": 598.32, "end": 598.52, "word": " طب", "probability": 0.8466796875}, {"start": 598.52, "end": 598.62, "word": " و", "probability": 0.9912109375}, {"start": 598.62, "end": 598.92, "word": " خمسة", "probability": 0.9559326171875}, {"start": 598.92, "end": 598.98, "word": " و", "probability": 0.99462890625}, {"start": 598.98, "end": 599.8, "word": " خمسة", "probability": 0.9786376953125}, {"start": 599.8, "end": 603.5, "word": " يعني", "probability": 0.6580810546875}, {"start": 603.5, "end": 603.86, "word": " كتر", "probability": 0.9314778645833334}, {"start": 603.86, "end": 604.36, "word": " والحين", "probability": 0.5546061197916666}, {"start": 604.36, "end": 605.68, "word": " طيب", "probability": 0.8963216145833334}, {"start": 605.68, "end": 606.26, "word": " على", "probability": 0.849609375}, {"start": 606.26, "end": 606.44, "word": " أي", "probability": 0.60888671875}, {"start": 606.44, "end": 606.82, "word": " حال", "probability": 0.99755859375}, {"start": 606.82, "end": 607.24, "word": " هنجي", "probability": 0.7042236328125}, {"start": 607.24, "end": 607.6, "word": " نشوف", "probability": 0.9951171875}, {"start": 607.6, "end": 608.48, "word": " الحالات", "probability": 0.9840494791666666}, {"start": 608.48, "end": 609.8, "word": " الممكنة", "probability": 0.9884440104166666}, {"start": 609.8, "end": 610.22, "word": " في", "probability": 0.9599609375}, {"start": 610.22, "end": 611.04, "word": " هذا", "probability": 0.966796875}, {"start": 611.04, "end": 611.9, "word": " الموضوع", "probability": 0.99853515625}, {"start": 611.9, "end": 613.02, "word": " يبقى", "probability": 0.9581298828125}, {"start": 613.02, "end": 613.92, "word": " هنا", "probability": 0.9931640625}, {"start": 613.92, "end": 614.48, "word": " we", "probability": 0.751953125}, {"start": 614.48, "end": 618.86, "word": " have", "probability": 0.65966796875}, {"start": 618.86, "end": 620.3, "word": " the", "probability": 0.904296875}, {"start": 620.3, "end": 621.76, "word": " following", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 23, "seek": 65475, "start": 630.47, "end": 654.75, "text": "Possibilities يبقى فيه عنا الاحتمالات الممكنة التالية الاحتمال الأول ان ال order لل A بده يساوي خمسة and ال order لل B بده يساوي خمسة ليش؟ هذا بيعطينا ان ال least common multiple يساوي خمسة", "tokens": [47, 772, 8261, 7251, 3555, 4587, 7578, 8978, 3224, 6225, 8315, 42963, 33753, 2304, 6027, 9307, 9673, 43020, 3660, 16712, 6027, 10632, 42963, 33753, 2304, 6027, 16247, 12610, 16472, 2423, 1668, 24976, 316, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 293, 2423, 1668, 24976, 363, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 32239, 8592, 22807, 23758, 4724, 40228, 9566, 1829, 8315, 16472, 2423, 1935, 2689, 3866, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660], "avg_logprob": -0.2527006172839506, "compression_ratio": 1.6685393258426966, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 630.47, "end": 631.63, "word": "Possibilities", "probability": 0.504150390625}, {"start": 631.63, "end": 632.79, "word": " يبقى", "probability": 0.9005126953125}, {"start": 632.79, "end": 633.07, "word": " فيه", "probability": 0.338134765625}, {"start": 633.07, "end": 633.47, "word": " عنا", "probability": 0.56640625}, {"start": 633.47, "end": 635.17, "word": " الاحتمالات", "probability": 0.919140625}, {"start": 635.17, "end": 636.05, "word": " الممكنة", "probability": 0.9817708333333334}, {"start": 636.05, "end": 636.73, "word": " التالية", "probability": 0.9772135416666666}, {"start": 636.73, "end": 638.15, "word": " الاحتمال", "probability": 0.9832763671875}, {"start": 638.15, "end": 638.93, "word": " الأول", "probability": 0.818359375}, {"start": 638.93, "end": 639.41, "word": " ان", "probability": 0.65185546875}, {"start": 639.41, "end": 639.69, "word": " ال", "probability": 0.80224609375}, {"start": 639.69, "end": 640.19, "word": " order", "probability": 0.94091796875}, {"start": 640.19, "end": 640.65, "word": " لل", "probability": 0.69189453125}, {"start": 640.65, "end": 641.11, "word": " A", "probability": 0.302001953125}, {"start": 641.11, "end": 641.87, "word": " بده", "probability": 0.3231201171875}, {"start": 641.87, "end": 642.43, "word": " يساوي", "probability": 0.8343505859375}, {"start": 642.43, "end": 643.57, "word": " خمسة", "probability": 0.8853759765625}, {"start": 643.57, "end": 644.47, "word": " and", "probability": 0.65087890625}, {"start": 644.47, "end": 645.21, "word": " ال", "probability": 0.7392578125}, {"start": 645.21, "end": 645.77, "word": " order", "probability": 0.962890625}, {"start": 645.77, "end": 646.35, "word": " لل", "probability": 0.9150390625}, {"start": 646.35, "end": 646.71, "word": " B", "probability": 0.80126953125}, {"start": 646.71, "end": 647.31, "word": " بده", "probability": 0.93994140625}, {"start": 647.31, "end": 647.67, "word": " يساوي", "probability": 0.98779296875}, {"start": 647.67, "end": 648.51, "word": " خمسة", "probability": 0.99267578125}, {"start": 648.51, "end": 650.91, "word": " ليش؟", "probability": 0.6599934895833334}, {"start": 650.91, "end": 651.27, "word": " هذا", "probability": 0.85400390625}, {"start": 651.27, "end": 651.87, "word": " بيعطينا", "probability": 0.903515625}, {"start": 651.87, "end": 652.07, "word": " ان", "probability": 0.79345703125}, {"start": 652.07, "end": 652.25, "word": " ال", "probability": 0.8154296875}, {"start": 652.25, "end": 652.49, "word": " least", "probability": 0.487060546875}, {"start": 652.49, "end": 652.83, "word": " common", "probability": 0.9345703125}, {"start": 652.83, "end": 653.33, "word": " multiple", "probability": 0.95654296875}, {"start": 653.33, "end": 654.13, "word": " يساوي", "probability": 0.7667236328125}, {"start": 654.13, "end": 654.75, "word": " خمسة", "probability": 0.987060546875}], "temperature": 1.0}, {"id": 24, "seek": 67722, "start": 655.12, "end": 677.22, "text": "that is يعني انه ال list common multiple ل الخمسة او خمسة اللي هو بده يسوي خمسة يعني ممكن يكون اذا بدي ادور كم عنصر ال order اللي يسوي خمسة وين في ال group الأولى يعني كم واحد بيطلعون", "tokens": [6780, 307, 37495, 22653, 16472, 3224, 2423, 1329, 2689, 3866, 5296, 33962, 2304, 3794, 3660, 1975, 2407, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 47525, 3224, 7251, 3794, 45865, 16490, 2304, 3794, 3660, 37495, 22653, 3714, 43020, 7251, 30544, 1975, 15730, 4724, 16254, 1975, 3215, 13063, 9122, 2304, 18871, 9381, 2288, 2423, 1668, 13672, 1829, 7251, 3794, 45865, 16490, 2304, 3794, 3660, 4032, 9957, 8978, 2423, 1594, 16247, 12610, 7578, 37495, 22653, 9122, 2304, 36764, 24401, 4724, 1829, 9566, 1211, 3615, 11536], "avg_logprob": -0.21573795216629305, "compression_ratio": 1.6610169491525424, "no_speech_prob": 0.0, "words": [{"start": 655.12, "end": 655.7, "word": "that", "probability": 0.63232421875}, {"start": 655.7, "end": 656.16, "word": " is", "probability": 0.8857421875}, {"start": 656.16, "end": 657.3, "word": " يعني", "probability": 0.87109375}, {"start": 657.3, "end": 658.68, "word": " انه", "probability": 0.417724609375}, {"start": 658.68, "end": 659.0, "word": " ال", "probability": 0.859375}, {"start": 659.0, "end": 659.36, "word": " list", "probability": 0.697265625}, {"start": 659.36, "end": 659.82, "word": " common", "probability": 0.921875}, {"start": 659.82, "end": 660.5, "word": " multiple", "probability": 0.91015625}, {"start": 660.5, "end": 660.78, "word": " ل", "probability": 0.458740234375}, {"start": 660.78, "end": 661.58, "word": " الخمسة", "probability": 0.9288330078125}, {"start": 661.58, "end": 661.78, "word": " او", "probability": 0.7489013671875}, {"start": 661.78, "end": 662.28, "word": " خمسة", "probability": 0.9085693359375}, {"start": 662.28, "end": 662.4, "word": " اللي", "probability": 0.58148193359375}, {"start": 662.4, "end": 662.5, "word": " هو", "probability": 0.9560546875}, {"start": 662.5, "end": 662.74, "word": " بده", "probability": 0.643798828125}, {"start": 662.74, "end": 663.08, "word": " يسوي", "probability": 0.83349609375}, {"start": 663.08, "end": 663.52, "word": " خمسة", "probability": 0.970703125}, {"start": 663.52, "end": 663.86, "word": " يعني", "probability": 0.880859375}, {"start": 663.86, "end": 664.32, "word": " ممكن", "probability": 0.987548828125}, {"start": 664.32, "end": 664.74, "word": " يكون", "probability": 0.989013671875}, {"start": 664.74, "end": 665.72, "word": " اذا", "probability": 0.7958984375}, {"start": 665.72, "end": 666.02, "word": " بدي", "probability": 0.678955078125}, {"start": 666.02, "end": 666.46, "word": " ادور", "probability": 0.9275716145833334}, {"start": 666.46, "end": 667.0, "word": " كم", "probability": 0.6829833984375}, {"start": 667.0, "end": 667.94, "word": " عنصر", "probability": 0.8673502604166666}, {"start": 667.94, "end": 668.54, "word": " ال", "probability": 0.9384765625}, {"start": 668.54, "end": 669.08, "word": " order", "probability": 0.974609375}, {"start": 669.08, "end": 669.46, "word": " اللي", "probability": 0.83349609375}, {"start": 669.46, "end": 670.04, "word": " يسوي", "probability": 0.7734375}, {"start": 670.04, "end": 670.6, "word": " خمسة", "probability": 0.96044921875}, {"start": 670.6, "end": 670.94, "word": " وين", "probability": 0.770263671875}, {"start": 670.94, "end": 671.6, "word": " في", "probability": 0.442138671875}, {"start": 671.6, "end": 671.82, "word": " ال", "probability": 0.705078125}, {"start": 671.82, "end": 672.28, "word": " group", "probability": 0.982421875}, {"start": 672.28, "end": 673.88, "word": " الأولى", "probability": 0.9052734375}, {"start": 673.88, "end": 676.06, "word": " يعني", "probability": 0.944580078125}, {"start": 676.06, "end": 676.34, "word": " كم", "probability": 0.81787109375}, {"start": 676.34, "end": 676.64, "word": " واحد", "probability": 0.990234375}, {"start": 676.64, "end": 677.22, "word": " بيطلعون", "probability": 0.8688151041666666}], "temperature": 1.0}, {"id": 25, "seek": 70403, "start": 677.99, "end": 704.03, "text": "اربع ممتازين هنا حد بيقدر يعرفهم سهلات هدول يالا جيبولي واحد بس وانا بجيبلكوا التالت كده؟ خمسة وعشر وخمستاشر وعشرين في غيرهم يبقى هنا we have four possibilities", "tokens": [9640, 3555, 3615, 3714, 2304, 2655, 31377, 9957, 34105, 11331, 3215, 4724, 1829, 28543, 2288, 37495, 28480, 16095, 8608, 3224, 1211, 9307, 8032, 3215, 12610, 7251, 6027, 995, 10874, 1829, 3555, 12610, 1829, 36764, 24401, 4724, 3794, 4032, 7649, 995, 4724, 7435, 1829, 3555, 23275, 14407, 16712, 6027, 2655, 9122, 3215, 3224, 22807, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 4032, 9778, 2304, 14851, 33599, 2288, 4032, 3615, 46309, 9957, 8978, 32771, 13546, 16095, 7251, 3555, 4587, 7578, 34105, 321, 362, 1451, 12178], "avg_logprob": -0.19587052968286334, "compression_ratio": 1.5168539325842696, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 677.99, "end": 678.69, "word": "اربع", "probability": 0.7450358072916666}, {"start": 678.69, "end": 679.41, "word": " ممتازين", "probability": 0.875390625}, {"start": 679.41, "end": 679.53, "word": " هنا", "probability": 0.11627197265625}, {"start": 679.53, "end": 679.77, "word": " حد", "probability": 0.88330078125}, {"start": 679.77, "end": 680.09, "word": " بيقدر", "probability": 0.964111328125}, {"start": 680.09, "end": 680.75, "word": " يعرفهم", "probability": 0.984375}, {"start": 680.75, "end": 682.33, "word": " سهلات", "probability": 0.8856201171875}, {"start": 682.33, "end": 683.01, "word": " هدول", "probability": 0.92529296875}, {"start": 683.01, "end": 684.33, "word": " يالا", "probability": 0.6285807291666666}, {"start": 684.33, "end": 684.75, "word": " جيبولي", "probability": 0.95517578125}, {"start": 684.75, "end": 685.05, "word": " واحد", "probability": 0.992431640625}, {"start": 685.05, "end": 685.29, "word": " بس", "probability": 0.8935546875}, {"start": 685.29, "end": 685.45, "word": " وانا", "probability": 0.68408203125}, {"start": 685.45, "end": 686.05, "word": " بجيبلكوا", "probability": 0.9111328125}, {"start": 686.05, "end": 686.29, "word": " التالت", "probability": 0.9059244791666666}, {"start": 686.29, "end": 687.29, "word": " كده؟", "probability": 0.71875}, {"start": 687.29, "end": 690.49, "word": " خمسة", "probability": 0.75244140625}, {"start": 690.49, "end": 692.11, "word": " وعشر", "probability": 0.7286783854166666}, {"start": 692.11, "end": 693.71, "word": " وخمستاشر", "probability": 0.8102213541666666}, {"start": 693.71, "end": 694.39, "word": " وعشرين", "probability": 0.928466796875}, {"start": 694.39, "end": 694.59, "word": " في", "probability": 0.7880859375}, {"start": 694.59, "end": 695.13, "word": " غيرهم", "probability": 0.9811197916666666}, {"start": 695.13, "end": 696.45, "word": " يبقى", "probability": 0.945068359375}, {"start": 696.45, "end": 696.95, "word": " هنا", "probability": 0.98828125}, {"start": 696.95, "end": 698.09, "word": " we", "probability": 0.60693359375}, {"start": 698.09, "end": 699.13, "word": " have", "probability": 0.9716796875}, {"start": 699.13, "end": 702.47, "word": " four", "probability": 0.90380859375}, {"start": 702.47, "end": 704.03, "word": " possibilities", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 26, "seek": 73507, "start": 706.45, "end": 735.07, "text": "والله have a choices خليها أسالكوا في الكتابة شوية we have four choices for a أربع خيارات لل a that is اللي هما خمسة وعشرة وخمستاشر وعشرين أي واحد من عناصر هدول ال order اللي بيسوي خمسة طيب", "tokens": [2407, 6027, 43761, 362, 257, 7994, 16490, 20292, 11296, 5551, 3794, 6027, 4117, 14407, 8978, 33251, 2655, 16758, 3660, 13412, 2407, 10632, 321, 362, 1451, 7994, 337, 257, 5551, 25513, 3615, 16490, 1829, 9640, 9307, 24976, 257, 300, 307, 13672, 1829, 8032, 15042, 16490, 2304, 3794, 3660, 4032, 3615, 8592, 25720, 4032, 9778, 2304, 14851, 33599, 2288, 4032, 3615, 46309, 9957, 36632, 36764, 24401, 9154, 18871, 33546, 2288, 8032, 3215, 12610, 2423, 1668, 13672, 1829, 4724, 1829, 3794, 45865, 16490, 2304, 3794, 3660, 23032, 1829, 3555], "avg_logprob": -0.26005747743036556, "compression_ratio": 1.5828877005347595, "no_speech_prob": 0.0, "words": [{"start": 706.45, "end": 706.93, "word": "والله", "probability": 0.718017578125}, {"start": 706.93, "end": 707.33, "word": " have", "probability": 0.1285400390625}, {"start": 707.33, "end": 707.51, "word": " a", "probability": 0.481689453125}, {"start": 707.51, "end": 708.21, "word": " choices", "probability": 0.5732421875}, {"start": 708.21, "end": 708.87, "word": " خليها", "probability": 0.472412109375}, {"start": 708.87, "end": 709.39, "word": " أسالكوا", "probability": 0.660205078125}, {"start": 709.39, "end": 709.53, "word": " في", "probability": 0.83935546875}, {"start": 709.53, "end": 710.05, "word": " الكتابة", "probability": 0.990234375}, {"start": 710.05, "end": 710.59, "word": " شوية", "probability": 0.8898111979166666}, {"start": 710.59, "end": 711.55, "word": " we", "probability": 0.49609375}, {"start": 711.55, "end": 712.29, "word": " have", "probability": 0.9755859375}, {"start": 712.29, "end": 713.59, "word": " four", "probability": 0.7646484375}, {"start": 713.59, "end": 714.57, "word": " choices", "probability": 0.92724609375}, {"start": 714.57, "end": 717.15, "word": " for", "probability": 0.91162109375}, {"start": 717.15, "end": 718.53, "word": " a", "probability": 0.61865234375}, {"start": 718.53, "end": 719.71, "word": " أربع", "probability": 0.8509114583333334}, {"start": 719.71, "end": 720.67, "word": " خيارات", "probability": 0.9949951171875}, {"start": 720.67, "end": 721.43, "word": " لل", "probability": 0.79931640625}, {"start": 721.43, "end": 721.85, "word": " a", "probability": 0.79052734375}, {"start": 721.85, "end": 722.77, "word": " that", "probability": 0.8310546875}, {"start": 722.77, "end": 723.29, "word": " is", "probability": 0.96435546875}, {"start": 723.29, "end": 724.63, "word": " اللي", "probability": 0.95556640625}, {"start": 724.63, "end": 725.11, "word": " هما", "probability": 0.73583984375}, {"start": 725.11, "end": 726.29, "word": " خمسة", "probability": 0.962890625}, {"start": 726.29, "end": 727.57, "word": " وعشرة", "probability": 0.66583251953125}, {"start": 727.57, "end": 728.77, "word": " وخمستاشر", "probability": 0.8463541666666666}, {"start": 728.77, "end": 729.51, "word": " وعشرين", "probability": 0.9151611328125}, {"start": 729.51, "end": 730.29, "word": " أي", "probability": 0.65087890625}, {"start": 730.29, "end": 730.81, "word": " واحد", "probability": 0.992431640625}, {"start": 730.81, "end": 731.05, "word": " من", "probability": 0.99609375}, {"start": 731.05, "end": 731.63, "word": " عناصر", "probability": 0.98828125}, {"start": 731.63, "end": 731.97, "word": " هدول", "probability": 0.72705078125}, {"start": 731.97, "end": 732.11, "word": " ال", "probability": 0.91796875}, {"start": 732.11, "end": 732.47, "word": " order", "probability": 0.97265625}, {"start": 732.47, "end": 732.73, "word": " اللي", "probability": 0.6121826171875}, {"start": 732.73, "end": 733.27, "word": " بيسوي", "probability": 0.6864013671875}, {"start": 733.27, "end": 734.15, "word": " خمسة", "probability": 0.98046875}, {"start": 734.15, "end": 735.07, "word": " طيب", "probability": 0.9348958333333334}], "temperature": 1.0}, {"id": 27, "seek": 76174, "start": 736.2, "end": 761.74, "text": "الان نحتاج ان نصل الى 10 ال order اللى يبدو يسوى خمسة بي هذا موجود وين في ال z خمسة اكم element ال order اللى يسوى خمسة بس واحد الواحد في غيره طب و اتنين كيف اتنين لأ هذا prime", "tokens": [6027, 7649, 8717, 33753, 26108, 16472, 8717, 36520, 2423, 7578, 1266, 2423, 1668, 13672, 7578, 7251, 44510, 2407, 7251, 3794, 2407, 7578, 16490, 2304, 3794, 3660, 4724, 1829, 23758, 3714, 29245, 23328, 4032, 9957, 8978, 2423, 710, 16490, 2304, 3794, 3660, 1975, 24793, 4478, 2423, 1668, 13672, 7578, 7251, 3794, 2407, 7578, 16490, 2304, 3794, 3660, 4724, 3794, 36764, 24401, 2423, 14407, 24401, 8978, 32771, 13546, 3224, 23032, 3555, 4032, 1975, 2655, 1863, 9957, 9122, 33911, 1975, 2655, 1863, 9957, 5296, 10721, 23758, 5835], "avg_logprob": -0.36985294398139507, "compression_ratio": 1.7142857142857142, "no_speech_prob": 0.0, "words": [{"start": 736.2, "end": 736.82, "word": "الان", "probability": 0.68701171875}, {"start": 736.82, "end": 737.96, "word": " نحتاج", "probability": 0.4892578125}, 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761.74, "word": " prime", "probability": 0.578125}], "temperature": 1.0}, {"id": 28, "seek": 78239, "start": 762.41, "end": 782.39, "text": "يبقى كل رقم فيها relatively prime مع الخمسة يعني كلهم ال order له كل واحد فيهم يسوى خمسة صحيح ولا لا؟ لكن لو ماكنتش prime بيجي القلاب اللي بتقوله بس كونه prime automatic على طول الخط يبقى we have برضه four choices for B", "tokens": [1829, 3555, 4587, 7578, 28242, 12602, 4587, 2304, 8978, 11296, 7226, 5835, 20449, 33962, 2304, 3794, 3660, 37495, 22653, 28242, 16095, 2423, 1668, 46740, 28242, 36764, 24401, 8978, 16095, 7251, 3794, 2407, 7578, 16490, 2304, 3794, 3660, 20328, 5016, 1829, 5016, 49429, 20193, 22807, 44381, 45164, 19446, 19452, 2655, 8592, 5835, 4724, 1829, 7435, 1829, 25062, 15040, 3555, 13672, 1829, 39894, 39648, 3224, 4724, 3794, 9122, 11536, 3224, 5835, 12509, 15844, 23032, 12610, 33962, 9566, 7251, 3555, 4587, 7578, 321, 362, 4724, 43042, 3224, 1451, 7994, 337, 363], "avg_logprob": -0.22155898742461472, "compression_ratio": 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خمسة", "probability": 0.8905029296875}, {"start": 828.3, "end": 828.4, "word": " و", "probability": 0.9658203125}, {"start": 828.4, "end": 829.14, "word": " عشرين", "probability": 0.7353515625}, {"start": 829.14, "end": 830.4, "word": " external", "probability": 0.833984375}, {"start": 830.4, "end": 831.04, "word": " direct", "probability": 0.673828125}, {"start": 831.04, "end": 831.8, "word": " product", "probability": 0.95849609375}, {"start": 831.8, "end": 832.16, "word": " ل", "probability": 0.900390625}, {"start": 832.16, "end": 832.46, "word": " z", "probability": 0.459228515625}, {"start": 832.46, "end": 833.84, "word": " خمسة", "probability": 0.9652099609375}, {"start": 833.84, "end": 835.56, "word": " طيب", "probability": 0.7874348958333334}, {"start": 835.56, "end": 836.06, "word": " كويس", "probability": 0.9630533854166666}, {"start": 836.06, "end": 836.66, "word": " هي", "probability": 0.439453125}, {"start": 836.66, "end": 837.12, "word": " أخدنا", "probability": 0.8680419921875}, {"start": 837.12, "end": 837.28, "word": " من", "probability": 0.95751953125}, {"start": 837.28, "end": 838.26, "word": " الحالة", "probability": 0.9171549479166666}, {"start": 838.26, "end": 839.16, "word": " الأولى", "probability": 0.96044921875}, {"start": 839.16, "end": 839.7, "word": " طيب", "probability": 0.9161783854166666}, {"start": 839.7, "end": 840.36, "word": " الحالة", "probability": 0.9685872395833334}, {"start": 840.36, "end": 841.08, "word": " الثانية", "probability": 0.9749755859375}], "temperature": 1.0}, {"id": 31, "seek": 86831, "start": 841.45, "end": 868.31, "text": "ممكن يكون ال order ل a بده يساوي واحد و ال order ل b بده يساوي خمسة يعني that is ال least common multiple لل واحد و الخمسة اللي هو خمسة إذا ممكن يبقى لما يكون ال order ل a يساوي واحد أكم أنصر بيصير عندي أكم خيار", "tokens": [2304, 43020, 7251, 30544, 2423, 1668, 5296, 257, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 4032, 2423, 1668, 5296, 272, 47525, 3224, 7251, 3794, 995, 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925.52, "text": "برضه اربعة choices for a و هذا as above كما هو من فوق هذا بيعطيك كمانصر ال order pair كم واحد اربعة لان هذا ال identity مع ال element الأول و ال identity مع التاني و ال identity مع التالت و ال identity مع الرابع يبقى اربعة عناصر هذا بيعطيني there is", "tokens": [3555, 43042, 3224, 1975, 25513, 27884, 7994, 337, 257, 4032, 23758, 382, 3673, 9122, 15042, 31439, 9154, 6156, 30543, 23758, 4724, 40228, 9566, 1829, 4117, 9122, 2304, 7649, 9381, 2288, 2423, 1668, 6119, 9122, 2304, 36764, 24401, 1975, 25513, 27884, 5296, 7649, 23758, 2423, 6575, 20449, 2423, 4478, 16247, 12610, 4032, 2423, 6575, 20449, 16712, 7649, 1829, 4032, 2423, 6575, 20449, 16712, 6027, 2655, 4032, 2423, 6575, 20449, 34892, 16758, 3615, 7251, 3555, 4587, 7578, 1975, 25513, 27884, 18871, 33546, 2288, 23758, 4724, 40228, 9566, 1829, 22653, 456, 307], "avg_logprob": -0.23472222520245445, "compression_ratio": 1.917948717948718, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 898.0, "end": 898.72, 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924.72, "end": 925.0, "word": " there", "probability": 0.90771484375}, {"start": 925.0, "end": 925.52, "word": " is", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 34, "seek": 95112, "start": 926.76, "end": 951.12, "text": "اللي هو four elements of order خمسة هذا بيعطيني أربعة طب الحالة التالتة لو كان ال order لل a بده يساوي خمسة and ال order لل b بده يساوي واحد يبقى that is", "tokens": [6027, 20292, 31439, 1451, 4959, 295, 1668, 16490, 2304, 3794, 3660, 23758, 4724, 1829, 3615, 9566, 1829, 22653, 5551, 25513, 27884, 23032, 3555, 21542, 6027, 3660, 16712, 6027, 2655, 3660, 45164, 25961, 2423, 1668, 24976, 257, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 293, 2423, 1668, 24976, 272, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 7251, 3555, 4587, 7578, 300, 307], "avg_logprob": -0.19850851685711832, "compression_ratio": 1.5096774193548388, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 926.76, "end": 927.1, "word": "اللي", "probability": 0.35693359375}, {"start": 927.1, "end": 927.34, "word": " هو", "probability": 0.9580078125}, {"start": 927.34, "end": 927.9, "word": " four", "probability": 0.77783203125}, {"start": 927.9, "end": 929.04, "word": " elements", "probability": 0.90625}, {"start": 929.04, "end": 931.14, "word": " of", "probability": 0.93115234375}, {"start": 931.14, "end": 933.0, "word": " order", "probability": 0.943359375}, {"start": 933.0, "end": 934.9, "word": " خمسة", "probability": 0.9703369140625}, {"start": 934.9, "end": 935.28, "word": " هذا", "probability": 0.51708984375}, {"start": 935.28, "end": 935.8, "word": " بيعطيني", "probability": 0.7288411458333334}, {"start": 935.8, "end": 936.22, "word": " أربعة", "probability": 0.8478190104166666}, {"start": 936.22, "end": 936.8, "word": " طب", "probability": 0.694091796875}, {"start": 936.8, "end": 937.34, "word": " الحالة", "probability": 0.8697916666666666}, {"start": 937.34, "end": 938.34, "word": " التالتة", "probability": 0.957275390625}, {"start": 938.34, "end": 939.92, "word": " لو", "probability": 0.85986328125}, {"start": 939.92, "end": 940.6, "word": " كان", "probability": 0.99267578125}, {"start": 940.6, "end": 941.0, "word": " ال", "probability": 0.888671875}, {"start": 941.0, "end": 941.6, "word": " order", "probability": 0.9755859375}, {"start": 941.6, "end": 942.16, "word": " لل", "probability": 0.76025390625}, {"start": 942.16, "end": 942.62, "word": " a", "probability": 0.35791015625}, {"start": 942.62, "end": 943.42, "word": " بده", "probability": 0.43896484375}, {"start": 943.42, "end": 943.92, "word": " يساوي", "probability": 0.83953857421875}, {"start": 943.92, "end": 944.92, "word": " خمسة", "probability": 0.986572265625}, {"start": 944.92, "end": 945.6, "word": " and", "probability": 0.76171875}, {"start": 945.6, "end": 945.84, "word": " ال", "probability": 0.85400390625}, {"start": 945.84, "end": 946.4, "word": " order", "probability": 0.96875}, {"start": 946.4, "end": 946.84, "word": " لل", "probability": 0.92138671875}, {"start": 946.84, "end": 947.02, "word": " b", "probability": 0.7587890625}, {"start": 947.02, "end": 947.38, "word": " بده", "probability": 0.923583984375}, {"start": 947.38, "end": 947.7, "word": " يساوي", "probability": 0.983642578125}, {"start": 947.7, "end": 948.54, "word": " واحد", "probability": 0.980224609375}, {"start": 948.54, "end": 950.2, "word": " يبقى", "probability": 0.9581298828125}, {"start": 950.2, "end": 950.48, "word": " that", "probability": 0.8603515625}, {"start": 950.48, "end": 951.12, "word": " is", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 35, "seek": 97970, "start": 952.42, "end": 979.7, "text": "إن ال least common multiple للخمسة والواحد هو يساوي خمسة طيب يبقى ال element الأول بيعطيني كام خيار أربعة والتاني واحد يبقى هنا we have four choices for a الآن التاني", "tokens": [28814, 1863, 2423, 1935, 2689, 3866, 24976, 9778, 2304, 3794, 3660, 16070, 14407, 24401, 31439, 7251, 3794, 995, 45865, 16490, 2304, 3794, 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957.0, "word": " هو", "probability": 0.8115234375}, {"start": 957.0, "end": 957.68, "word": " يساوي", "probability": 0.88134765625}, {"start": 957.68, "end": 958.6, "word": " خمسة", "probability": 0.958740234375}, {"start": 958.6, "end": 959.4, "word": " طيب", "probability": 0.768798828125}, {"start": 959.4, "end": 959.66, "word": " يبقى", "probability": 0.94482421875}, {"start": 959.66, "end": 959.8, "word": " ال", "probability": 0.90478515625}, {"start": 959.8, "end": 960.14, "word": " element", "probability": 0.94970703125}, {"start": 960.14, "end": 960.5, "word": " الأول", "probability": 0.943603515625}, {"start": 960.5, "end": 961.04, "word": " بيعطيني", "probability": 0.751318359375}, {"start": 961.04, "end": 961.3, "word": " كام", "probability": 0.7392578125}, {"start": 961.3, "end": 962.0, "word": " خيار", "probability": 0.9884440104166666}, {"start": 962.0, "end": 963.26, "word": " أربعة", "probability": 0.6551920572916666}, {"start": 963.26, "end": 964.28, "word": " والتاني", "probability": 0.8133544921875}, {"start": 964.28, "end": 964.68, "word": " واحد", "probability": 0.9189453125}, {"start": 964.68, "end": 965.98, "word": " يبقى", "probability": 0.9805908203125}, {"start": 965.98, "end": 966.52, "word": " هنا", "probability": 0.9892578125}, {"start": 966.52, "end": 967.46, "word": " we", "probability": 0.51416015625}, {"start": 967.46, "end": 969.14, "word": " have", "probability": 0.9677734375}, {"start": 969.14, "end": 970.76, "word": " four", "probability": 0.8857421875}, {"start": 970.76, "end": 972.3, "word": " choices", "probability": 0.91357421875}, {"start": 972.3, "end": 975.62, "word": " for", "probability": 0.408447265625}, {"start": 975.62, "end": 976.88, "word": " a", "probability": 0.58544921875}, {"start": 976.88, "end": 978.64, "word": " الآن", "probability": 0.679931640625}, {"start": 978.64, "end": 979.7, "word": " التاني", "probability": 0.9625651041666666}], "temperature": 1.0}, {"id": 36, "seek": 100621, "start": 979.85, "end": 1006.21, "text": "we have one choice for B من الاتنين هذول بنجي نقوله we have four elements of order five فى غير هيك اذا", "tokens": [826, 362, 472, 3922, 337, 363, 9154, 2423, 9307, 1863, 9957, 8032, 8848, 12610, 44945, 7435, 1829, 8717, 39648, 3224, 321, 362, 1451, 4959, 295, 1668, 1732, 6156, 7578, 32771, 13546, 39896, 4117, 1975, 15730], "avg_logprob": -0.366970482799742, "compression_ratio": 1.115702479338843, "no_speech_prob": 0.0, "words": [{"start": 979.85, "end": 980.33, "word": "we", "probability": 0.29443359375}, {"start": 980.33, "end": 980.91, "word": " have", "probability": 0.9677734375}, {"start": 980.91, "end": 981.51, "word": " one", "probability": 0.61962890625}, {"start": 981.51, "end": 982.33, "word": " choice", "probability": 0.9208984375}, {"start": 982.33, "end": 984.47, "word": " for", "probability": 0.8564453125}, {"start": 984.47, "end": 986.53, "word": " B", "probability": 0.422607421875}, {"start": 986.53, "end": 988.31, "word": " من", "probability": 0.8447265625}, {"start": 988.31, "end": 988.85, "word": " الاتنين", "probability": 0.766937255859375}, {"start": 988.85, "end": 989.53, "word": " هذول", "probability": 0.7032877604166666}, {"start": 989.53, "end": 990.41, "word": " بنجي", "probability": 0.6446940104166666}, {"start": 990.41, "end": 991.01, "word": " نقوله", "probability": 0.7295735677083334}, {"start": 991.01, "end": 991.17, "word": " we", "probability": 0.75048828125}, {"start": 991.17, "end": 991.99, "word": " have", "probability": 0.9736328125}, {"start": 991.99, "end": 993.81, "word": " four", "probability": 0.9072265625}, {"start": 993.81, "end": 995.73, "word": " elements", "probability": 0.90673828125}, {"start": 995.73, "end": 998.85, "word": " of", "probability": 0.96484375}, {"start": 998.85, "end": 1000.63, "word": " order", "probability": 0.96240234375}, {"start": 1000.63, "end": 1002.41, "word": " five", "probability": 0.84033203125}, {"start": 1002.41, "end": 1003.41, "word": " فى", "probability": 0.57080078125}, {"start": 1003.41, "end": 1003.65, "word": " غير", "probability": 0.973388671875}, {"start": 1003.65, "end": 1004.17, "word": " هيك", "probability": 0.962890625}, {"start": 1004.17, "end": 1006.21, "word": " اذا", "probability": 0.4766845703125}], "temperature": 1.0}, {"id": 37, "seek": 103357, "start": 1009.19, "end": 1033.57, "text": "number of elements of order خمسة is الأولاني جابتلي قداش ستة عشر والتاني جابتلي أربعة والتاله جابتلي أربعة يبقى أربعة وعشرين elements", "tokens": [41261, 295, 4959, 295, 1668, 16490, 2304, 3794, 3660, 307, 16247, 12610, 7649, 1829, 10874, 16758, 2655, 20292, 12174, 3215, 33599, 8608, 2655, 3660, 6225, 46309, 16070, 2655, 7649, 1829, 10874, 16758, 2655, 20292, 5551, 25513, 27884, 16070, 2655, 6027, 3224, 10874, 16758, 2655, 20292, 5551, 25513, 27884, 7251, 3555, 4587, 7578, 5551, 25513, 27884, 4032, 3615, 46309, 9957, 4959], "avg_logprob": -0.2110655776789931, "compression_ratio": 1.618320610687023, "no_speech_prob": 0.0, "words": [{"start": 1009.19, "end": 1010.59, "word": "number", "probability": 0.83203125}, {"start": 1010.59, "end": 1011.99, "word": " of", "probability": 0.9521484375}, {"start": 1011.99, "end": 1014.03, "word": " elements", "probability": 0.88818359375}, {"start": 1014.03, "end": 1016.51, "word": " of", "probability": 0.92236328125}, {"start": 1016.51, "end": 1018.51, "word": " order", "probability": 0.95751953125}, {"start": 1018.51, "end": 1020.85, "word": " خمسة", "probability": 0.9525146484375}, {"start": 1020.85, "end": 1021.77, "word": " is", "probability": 0.6806640625}, {"start": 1021.77, "end": 1023.27, "word": " الأولاني", "probability": 0.77392578125}, {"start": 1023.27, "end": 1023.71, "word": " جابتلي", "probability": 0.7239990234375}, {"start": 1023.71, "end": 1024.19, "word": " قداش", "probability": 0.6954752604166666}, {"start": 1024.19, "end": 1024.79, "word": " ستة", "probability": 0.6465657552083334}, {"start": 1024.79, "end": 1025.17, "word": " عشر", "probability": 0.6993408203125}, {"start": 1025.17, "end": 1026.25, "word": " والتاني", "probability": 0.7967529296875}, {"start": 1026.25, "end": 1026.89, "word": " جابتلي", "probability": 0.9625244140625}, {"start": 1026.89, "end": 1027.47, "word": " أربعة", "probability": 0.7648111979166666}, {"start": 1027.47, "end": 1028.55, "word": " والتاله", "probability": 0.741119384765625}, {"start": 1028.55, "end": 1029.25, "word": " جابتلي", "probability": 0.9744873046875}, {"start": 1029.25, "end": 1029.91, "word": " أربعة", "probability": 0.8859049479166666}, {"start": 1029.91, "end": 1030.83, "word": " يبقى", "probability": 0.972900390625}, {"start": 1030.83, "end": 1031.49, "word": " أربعة", "probability": 0.8282877604166666}, {"start": 1031.49, "end": 1032.79, "word": " وعشرين", "probability": 0.90380859375}, {"start": 1032.79, "end": 1033.57, "word": " elements", "probability": 0.82373046875}], "temperature": 1.0}, {"id": 38, "seek": 106104, "start": 1034.66, "end": 1061.04, "text": "يبقى من المائة وعشرين بلقى أربعة وعشرين element ال order لهم يساوي خمسة يبقى هذا المثال سهل عليه حساب بعد ذلك اللي هو حساب كم element يحمل نفس ال order في ال group الواحدة", "tokens": [1829, 3555, 4587, 7578, 9154, 9673, 16373, 3660, 4032, 3615, 46309, 9957, 4724, 1211, 4587, 7578, 5551, 25513, 27884, 4032, 3615, 46309, 9957, 4478, 2423, 1668, 5296, 16095, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 23758, 9673, 12984, 6027, 8608, 3224, 1211, 47356, 11331, 3794, 16758, 39182, 29910, 23275, 13672, 1829, 31439, 11331, 3794, 16758, 9122, 2304, 4478, 7251, 35571, 1211, 8717, 36178, 2423, 1668, 8978, 2423, 1594, 2423, 14407, 24401, 3660], "avg_logprob": -0.20152243073934165, "compression_ratio": 1.627906976744186, "no_speech_prob": 0.0, "words": [{"start": 1034.66, "end": 1035.1, "word": "يبقى", "probability": 0.717529296875}, {"start": 1035.1, "end": 1035.26, "word": " من", "probability": 0.82568359375}, {"start": 1035.26, "end": 1035.74, "word": " المائة", "probability": 0.5230305989583334}, {"start": 1035.74, "end": 1036.68, "word": " وعشرين", "probability": 0.877197265625}, {"start": 1036.68, "end": 1037.66, "word": " بلقى", "probability": 0.63702392578125}, {"start": 1037.66, "end": 1038.12, "word": " أربعة", "probability": 0.7176106770833334}, {"start": 1038.12, "end": 1038.86, "word": " وعشرين", "probability": 0.8863525390625}, {"start": 1038.86, "end": 1039.54, "word": " element", "probability": 0.54443359375}, {"start": 1039.54, "end": 1040.32, "word": " ال", "probability": 0.361083984375}, {"start": 1040.32, "end": 1040.96, "word": " order", "probability": 0.94921875}, {"start": 1040.96, "end": 1041.62, "word": " لهم", "probability": 0.56817626953125}, {"start": 1041.62, "end": 1042.6, "word": " يساوي", "probability": 0.951416015625}, {"start": 1042.6, "end": 1044.56, "word": " خمسة", "probability": 0.9814453125}, {"start": 1044.56, "end": 1048.84, "word": " يبقى", "probability": 0.9278564453125}, {"start": 1048.84, "end": 1049.12, "word": " 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"probability": 0.98876953125}, {"start": 1057.74, "end": 1058.1, "word": " نفس", "probability": 0.989990234375}, {"start": 1058.1, "end": 1058.3, "word": " ال", "probability": 0.96923828125}, {"start": 1058.3, "end": 1058.72, "word": " order", "probability": 0.95751953125}, {"start": 1058.72, "end": 1058.98, "word": " في", "probability": 0.93798828125}, {"start": 1058.98, "end": 1059.1, "word": " ال", "probability": 0.69580078125}, {"start": 1059.1, "end": 1059.66, "word": " group", "probability": 0.984375}, {"start": 1059.66, "end": 1061.04, "word": " الواحدة", "probability": 0.9189453125}], "temperature": 1.0}, {"id": 39, "seek": 109110, "start": 1061.59, "end": 1091.11, "text": "نعطي مثال آخر ونتجلي شوية بدل ما بدي ال elements اللي بيحملوا نفس ال order بدي ال cyclic subgroups اللي بيحملوا نفس ال order وهذا موضوع المثال رقم تلاتة يبقى example تلاتة example تلاتة بيقولي how many cyclic subgroups how", "tokens": [1863, 3615, 9566, 1829, 50113, 6027, 19753, 34740, 4032, 29399, 7435, 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0.9609375}, {"start": 1186.28, "end": 1186.98, "word": " خلينى", "probability": 0.8651123046875}, {"start": 1186.98, "end": 1187.68, "word": " ادور", "probability": 0.7613932291666666}, {"start": 1187.68, "end": 1188.06, "word": " انا", "probability": 0.844482421875}, {"start": 1188.06, "end": 1188.64, "word": " لنص", "probability": 0.9187825520833334}, {"start": 1188.64, "end": 1189.26, "word": " cyclic", "probability": 0.53369140625}, {"start": 1189.26, "end": 1190.2, "word": " subgroup", "probability": 0.7470703125}, {"start": 1190.2, "end": 1190.86, "word": " اذا", "probability": 0.7261962890625}, {"start": 1190.86, "end": 1191.52, "word": " خلينى", "probability": 0.9632568359375}, {"start": 1191.52, "end": 1192.1, "word": " ادور", "probability": 0.9337565104166666}, {"start": 1192.1, "end": 1192.56, "word": " مين", "probability": 0.885986328125}, {"start": 1192.56, "end": 1193.08, "word": " هم", "probability": 0.90234375}, {"start": 1193.08, "end": 1193.34, "word": " ال", "probability": 0.96337890625}, {"start": 1193.34, "end": 1194.2, "word": " elements", "probability": 0.89599609375}, {"start": 1194.2, "end": 1194.68, "word": " اللى", "probability": 0.948486328125}, {"start": 1194.68, "end": 1194.82, "word": " ال", "probability": 0.91015625}, {"start": 1194.82, "end": 1195.32, "word": " order", "probability": 0.9775390625}, {"start": 1195.32, "end": 1195.6, "word": " اللى", "probability": 0.796630859375}, {"start": 1195.6, "end": 1196.16, "word": " يساوي", "probability": 0.87109375}, {"start": 1196.16, "end": 1196.94, "word": " عشرة", "probability": 0.9523111979166666}, {"start": 1196.94, "end": 1197.44, "word": " ال", "probability": 0.93212890625}, {"start": 1197.44, "end": 1197.92, "word": " elements", "probability": 0.90380859375}, {"start": 1197.92, "end": 1198.2, "word": " اللى", "probability": 0.980712890625}, {"start": 1198.2, "end": 1198.36, "word": " ال", "probability": 0.9384765625}, {"start": 1198.36, "end": 1198.82, "word": " order", "probability": 0.9755859375}, {"start": 1198.82, "end": 1199.14, "word": " اللى", "probability": 0.8974609375}, {"start": 1199.14, "end": 1199.92, "word": " يساوي", "probability": 0.9566650390625}, {"start": 1199.92, "end": 1200.52, "word": " عشرة", "probability": 0.9833984375}, {"start": 1200.52, "end": 1200.94, "word": " كل", "probability": 0.955078125}, {"start": 1200.94, "end": 1201.36, "word": " واحد", "probability": 0.996337890625}, {"start": 1201.36, "end": 1202.28, "word": " هيجيبلي", "probability": 0.769775390625}, {"start": 1202.28, "end": 1203.1, "word": " cyclic", "probability": 0.826171875}, {"start": 1203.1, "end": 1203.8, "word": " subgroup", "probability": 0.965087890625}, {"start": 1203.8, "end": 1204.52, "word": " مظبوط", "probability": 0.90078125}], "temperature": 1.0}, {"id": 44, "seek": 123373, "start": 1204.87, "end": 1233.73, "text": "يبقى هنا firstly أولاً firstly we shall find بدنا نحاول نجد the elements of اللي هو z مية external like a product مع z خمسة وعشرين with order", "tokens": [1829, 3555, 4587, 7578, 34105, 27376, 5551, 12610, 995, 14111, 27376, 321, 4393, 915, 47525, 8315, 8717, 5016, 995, 12610, 8717, 7435, 3215, 264, 4959, 295, 13672, 1829, 31439, 710, 3714, 10632, 8320, 411, 257, 1674, 20449, 710, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 365, 1668], "avg_logprob": -0.2962372351665886, "compression_ratio": 1.2077922077922079, "no_speech_prob": 0.0, "words": [{"start": 1204.87, "end": 1205.59, "word": "يبقى", "probability": 0.7867431640625}, {"start": 1205.59, "end": 1206.13, "word": " هنا", "probability": 0.96533203125}, {"start": 1206.13, "end": 1207.47, "word": " firstly", "probability": 0.318359375}, {"start": 1207.47, "end": 1209.69, "word": " أولاً", "probability": 0.65899658203125}, {"start": 1209.69, "end": 1210.41, "word": " firstly", "probability": 0.34130859375}, {"start": 1210.41, "end": 1211.81, "word": " we", "probability": 0.8037109375}, {"start": 1211.81, "end": 1213.55, "word": " shall", "probability": 0.95751953125}, {"start": 1213.55, "end": 1215.55, "word": " find", "probability": 0.95068359375}, {"start": 1215.55, "end": 1215.89, "word": " بدنا", "probability": 0.6597900390625}, {"start": 1215.89, "end": 1216.47, "word": " نحاول", "probability": 0.9940185546875}, {"start": 1216.47, "end": 1217.29, "word": " نجد", "probability": 0.8095703125}, {"start": 1217.29, "end": 1218.17, "word": " the", "probability": 0.62109375}, {"start": 1218.17, "end": 1219.95, "word": " elements", "probability": 0.85888671875}, {"start": 1219.95, "end": 1221.95, "word": " of", "probability": 0.97119140625}, {"start": 1221.95, "end": 1223.13, "word": " اللي", "probability": 0.811279296875}, {"start": 1223.13, "end": 1223.39, "word": " هو", "probability": 0.970703125}, {"start": 1223.39, "end": 1223.79, "word": " z", "probability": 0.7080078125}, {"start": 1223.79, "end": 1224.83, "word": " مية", "probability": 0.738525390625}, {"start": 1224.83, "end": 1225.91, "word": " external", "probability": 0.421630859375}, {"start": 1225.91, "end": 1226.31, "word": " like", "probability": 0.2373046875}, {"start": 1226.31, "end": 1226.49, "word": " a", "probability": 0.4287109375}, {"start": 1226.49, "end": 1226.99, "word": " product", "probability": 0.966796875}, {"start": 1226.99, "end": 1227.81, "word": " مع", "probability": 0.89892578125}, {"start": 1227.81, "end": 1228.33, "word": " z", "probability": 0.9208984375}, {"start": 1228.33, "end": 1229.51, "word": " خمسة", "probability": 0.969482421875}, {"start": 1229.51, "end": 1230.41, "word": " وعشرين", "probability": 0.872802734375}, {"start": 1230.41, "end": 1231.67, "word": " with", "probability": 0.93896484375}, {"start": 1231.67, "end": 1233.73, "word": " order", "probability": 0.943359375}], "temperature": 1.0}, {"id": 45, "seek": 126392, "start": 1234.66, "end": 1263.92, "text": "عشرة لذلك حاجة اقوله assume افترض ان ال G و ال H موجودة في ال Z مية stenotypic product مع Z خمسة و عشرين such that بحيث ان ال order لل G و ال H بده يسوى عشر", "tokens": [3615, 8592, 25720, 5296, 8848, 23275, 11331, 26108, 3660, 1975, 39648, 3224, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 460, 4032, 2423, 389, 3714, 29245, 23328, 3660, 8978, 2423, 1176, 3714, 10632, 28031, 6737, 37509, 1674, 20449, 1176, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 1270, 300, 4724, 5016, 1829, 12984, 16472, 2423, 1668, 24976, 460, 4032, 2423, 389, 47525, 3224, 7251, 3794, 2407, 7578, 6225, 46309], "avg_logprob": -0.3106883937034054, "compression_ratio": 1.4036144578313252, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1234.66, "end": 1235.32, "word": "عشرة", "probability": 0.604248046875}, {"start": 1235.32, "end": 1237.4, "word": " لذلك", "probability": 0.83056640625}, {"start": 1237.4, "end": 1237.76, "word": " حاجة", "probability": 0.740478515625}, {"start": 1237.76, "end": 1238.56, "word": " اقوله", "probability": 0.62451171875}, {"start": 1238.56, "end": 1239.44, "word": " assume", "probability": 0.477294921875}, {"start": 1239.44, "end": 1241.68, "word": " افترض", "probability": 0.9385986328125}, {"start": 1241.68, "end": 1242.28, "word": " ان", "probability": 0.970703125}, {"start": 1242.28, "end": 1242.62, "word": " ال", "probability": 0.83056640625}, {"start": 1242.62, "end": 1242.92, "word": " G", "probability": 0.23681640625}, {"start": 1242.92, "end": 1243.66, "word": " و", "probability": 0.68212890625}, {"start": 1243.66, "end": 1243.9, "word": " ال", "probability": 0.82958984375}, {"start": 1243.9, "end": 1244.3, "word": " H", "probability": 0.96240234375}, {"start": 1244.3, "end": 1246.06, "word": " موجودة", "probability": 0.976318359375}, {"start": 1246.06, "end": 1246.88, "word": " في", "probability": 0.94482421875}, {"start": 1246.88, "end": 1247.54, "word": " ال", "probability": 0.859375}, {"start": 1247.54, "end": 1247.74, "word": " Z", "probability": 0.69189453125}, {"start": 1247.74, "end": 1248.58, "word": " مية", "probability": 0.5687255859375}, {"start": 1248.58, "end": 1250.4, "word": " stenotypic", "probability": 0.4053955078125}, {"start": 1250.4, "end": 1250.98, "word": " product", "probability": 0.96484375}, {"start": 1250.98, "end": 1251.82, "word": " مع", "probability": 0.7734375}, {"start": 1251.82, "end": 1252.64, "word": " Z", "probability": 0.87646484375}, {"start": 1252.64, "end": 1253.68, "word": " خمسة", "probability": 0.947265625}, {"start": 1253.68, "end": 1253.76, "word": " و", "probability": 0.984375}, {"start": 1253.76, "end": 1254.44, "word": " عشرين", "probability": 0.8543294270833334}, {"start": 1254.44, "end": 1255.42, "word": " such", "probability": 0.8984375}, {"start": 1255.42, "end": 1256.16, "word": " that", "probability": 0.9248046875}, {"start": 1256.16, "end": 1257.46, "word": " بحيث", "probability": 0.9862060546875}, {"start": 1257.46, "end": 1257.96, "word": " ان", "probability": 0.85986328125}, {"start": 1257.96, "end": 1259.16, "word": " ال", "probability": 0.93115234375}, {"start": 1259.16, "end": 1259.86, "word": " order", "probability": 0.98291015625}, {"start": 1259.86, "end": 1260.88, "word": " لل", "probability": 0.5390625}, {"start": 1260.88, "end": 1261.36, "word": " G", "probability": 0.91650390625}, {"start": 1261.36, "end": 1261.9, "word": " و", "probability": 0.86865234375}, {"start": 1261.9, "end": 1262.14, "word": " ال", "probability": 0.6748046875}, {"start": 1262.14, "end": 1262.56, "word": " H", "probability": 0.98046875}, {"start": 1262.56, "end": 1263.18, "word": " بده", "probability": 0.4271240234375}, {"start": 1263.18, "end": 1263.58, "word": " يسوى", "probability": 0.8243408203125}, {"start": 1263.58, "end": 1263.92, "word": " عشر", "probability": 0.8095703125}], "temperature": 1.0}, {"id": 46, "seek": 129511, "start": 1269.3, "end": 1295.12, "text": "قال لي هاتلي ال cyclic subgroups انا روحت قولله بدي اجيب ال elements اللي ال order اللي لهم يساوي عشرة لان كل ال elements هدول هم اللي بيجيبولي من ال cyclic subgroups او هم اللي بيولولي كل ال cyclic subgroups في هذه الحالة طيب", "tokens": [4587, 6027, 32239, 8032, 9307, 20292, 2423, 38154, 1050, 1422, 17377, 82, 1975, 8315, 12602, 2407, 33753, 12174, 12610, 43761, 4724, 16254, 1975, 7435, 1829, 3555, 2423, 4959, 13672, 1829, 2423, 1668, 13672, 1829, 5296, 16095, 7251, 3794, 995, 45865, 6225, 8592, 25720, 5296, 7649, 28242, 2423, 4959, 8032, 3215, 12610, 8032, 2304, 13672, 1829, 4724, 1829, 7435, 1829, 3555, 12610, 1829, 9154, 2423, 38154, 1050, 1422, 17377, 82, 1975, 2407, 8032, 2304, 13672, 1829, 4724, 1829, 12610, 12610, 1829, 28242, 2423, 38154, 1050, 1422, 17377, 82, 8978, 29538, 21542, 6027, 3660, 23032, 1829, 3555], "avg_logprob": -0.22086588044961294, "compression_ratio": 1.9162011173184357, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1269.3, "end": 1269.76, "word": "قال", "probability": 0.5467529296875}, {"start": 1269.76, "end": 1269.88, "word": " لي", "probability": 0.5615234375}, {"start": 1269.88, "end": 1270.22, "word": " هاتلي", "probability": 0.6131184895833334}, {"start": 1270.22, "end": 1270.38, "word": " ال", "probability": 0.86474609375}, {"start": 1270.38, "end": 1270.82, "word": " cyclic", "probability": 0.614013671875}, {"start": 1270.82, "end": 1271.72, "word": " subgroups", "probability": 0.77783203125}, {"start": 1271.72, "end": 1272.48, "word": " انا", "probability": 0.65869140625}, {"start": 1272.48, "end": 1272.84, "word": " روحت", "probability": 0.9459635416666666}, {"start": 1272.84, "end": 1273.44, "word": " قولله", "probability": 0.6935221354166666}, {"start": 1273.44, "end": 1274.24, "word": " بدي", "probability": 0.64501953125}, {"start": 1274.24, "end": 1274.62, "word": " اجيب", "probability": 0.9100341796875}, {"start": 1274.62, "end": 1274.84, "word": " ال", "probability": 0.95654296875}, {"start": 1274.84, "end": 1275.54, "word": " elements", "probability": 0.896484375}, {"start": 1275.54, "end": 1276.06, "word": " اللي", "probability": 0.89208984375}, {"start": 1276.06, "end": 1276.22, "word": " ال", "probability": 0.88818359375}, {"start": 1276.22, "end": 1276.72, "word": " order", "probability": 0.9755859375}, {"start": 1276.72, "end": 1277.04, "word": " اللي", "probability": 0.64501953125}, {"start": 1277.04, "end": 1277.24, "word": " لهم", "probability": 0.6527099609375}, {"start": 1277.24, "end": 1277.82, "word": " يساوي", "probability": 0.81201171875}, {"start": 1277.82, "end": 1278.56, "word": " عشرة", "probability": 0.9287109375}, {"start": 1278.56, "end": 1279.4, "word": " لان", "probability": 0.6727294921875}, {"start": 1279.4, "end": 1279.94, "word": " كل", "probability": 0.90283203125}, {"start": 1279.94, "end": 1280.24, "word": " ال", "probability": 0.94140625}, {"start": 1280.24, "end": 1280.92, "word": " elements", "probability": 0.9072265625}, {"start": 1280.92, "end": 1281.62, "word": " هدول", "probability": 0.8209635416666666}, {"start": 1281.62, "end": 1282.48, "word": " هم", "probability": 0.94384765625}, {"start": 1282.48, "end": 1282.74, "word": " اللي", "probability": 0.986328125}, {"start": 1282.74, "end": 1283.36, "word": " بيجيبولي", "probability": 0.9580775669642857}, {"start": 1283.36, "end": 1283.66, "word": " من", "probability": 0.3935546875}, {"start": 1283.66, "end": 1284.1, "word": " ال", "probability": 0.755859375}, {"start": 1284.1, "end": 1284.7, "word": " cyclic", "probability": 0.83544921875}, {"start": 1284.7, "end": 1285.58, "word": " subgroups", "probability": 0.8943684895833334}, {"start": 1285.58, "end": 1286.04, "word": " او", "probability": 0.92822265625}, {"start": 1286.04, "end": 1286.32, "word": " هم", "probability": 0.973876953125}, {"start": 1286.32, "end": 1286.48, "word": " اللي", "probability": 0.993408203125}, {"start": 1286.48, "end": 1287.22, "word": " بيولولي", "probability": 0.8166015625}, {"start": 1287.22, "end": 1287.6, "word": " كل", "probability": 0.9638671875}, {"start": 1287.6, "end": 1287.82, "word": " ال", "probability": 0.96142578125}, {"start": 1287.82, "end": 1288.4, "word": " cyclic", "probability": 0.900634765625}, {"start": 1288.4, "end": 1289.42, "word": " subgroups", "probability": 0.9640299479166666}, {"start": 1289.42, "end": 1289.8, "word": " في", "probability": 0.8525390625}, {"start": 1289.8, "end": 1290.32, "word": " هذه", "probability": 0.9638671875}, {"start": 1290.32, "end": 1292.7, "word": " الحالة", "probability": 0.9768880208333334}, {"start": 1292.7, "end": 1295.12, "word": " طيب", "probability": 0.9479166666666666}], "temperature": 1.0}, {"id": 47, "seek": 131234, "start": 1295.88, "end": 1312.34, "text": "الان هذا الكلام بده يساوي ال least common multiple لل order بتبع ال G و ال order بتبع ال H", "tokens": [6027, 7649, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 2423, 1935, 2689, 3866, 24976, 1668, 39894, 3555, 3615, 2423, 460, 4032, 2423, 1668, 39894, 3555, 3615, 2423, 389], "avg_logprob": -0.3205566452816129, "compression_ratio": 1.2871287128712872, "no_speech_prob": 0.0, "words": [{"start": 1295.88, "end": 1296.48, "word": "الان", "probability": 0.730712890625}, {"start": 1296.48, "end": 1296.86, "word": " هذا", "probability": 0.78271484375}, {"start": 1296.86, "end": 1297.56, "word": " الكلام", "probability": 0.93115234375}, {"start": 1297.56, "end": 1298.36, "word": " بده", "probability": 0.3359375}, {"start": 1298.36, "end": 1299.14, "word": " يساوي", "probability": 0.9571533203125}, {"start": 1299.14, "end": 1300.04, "word": " ال", "probability": 0.68603515625}, {"start": 1300.04, "end": 1300.46, "word": " least", "probability": 0.890625}, {"start": 1300.46, "end": 1301.02, "word": " common", "probability": 0.93310546875}, {"start": 1301.02, "end": 1305.86, "word": " multiple", "probability": 0.89013671875}, {"start": 1305.86, "end": 1306.66, "word": " لل", "probability": 0.73486328125}, {"start": 1306.66, "end": 1307.24, "word": " order", "probability": 0.91357421875}, {"start": 1307.24, "end": 1307.88, "word": " بتبع", "probability": 0.7615559895833334}, {"start": 1307.88, "end": 1308.12, "word": " ال", "probability": 0.8837890625}, {"start": 1308.12, "end": 1308.4, "word": " G", "probability": 0.248046875}, {"start": 1308.4, "end": 1309.04, "word": " و", "probability": 0.4580078125}, {"start": 1309.04, "end": 1309.26, "word": " ال", "probability": 0.464599609375}, {"start": 1309.26, "end": 1309.82, "word": " order", "probability": 0.9609375}, {"start": 1309.82, "end": 1310.58, "word": " بتبع", "probability": 0.9700520833333334}, {"start": 1310.58, "end": 1311.94, "word": " ال", "probability": 0.84716796875}, {"start": 1311.94, "end": 1312.34, "word": " H", "probability": 0.85009765625}], "temperature": 1.0}, {"id": 48, "seek": 134604, "start": 1318.22, "end": 1346.04, "text": "موجود فى ال group اللى عندنا ال order اللى يساوي عشرة و بيدروح ادور على ال list common multiples اللى هو بيعطينى عشرة يبقى فى عندنا عدة حالات خمسة نشوف خمسة ولا اكتر يبقى هروح بقوله we have the following cases", "tokens": [2304, 29245, 23328, 6156, 7578, 2423, 1594, 13672, 7578, 43242, 8315, 2423, 1668, 13672, 7578, 7251, 3794, 995, 45865, 6225, 8592, 25720, 4032, 4724, 25708, 32887, 5016, 1975, 3215, 13063, 15844, 2423, 1329, 2689, 46099, 13672, 7578, 31439, 4724, 40228, 9566, 9957, 7578, 6225, 8592, 25720, 7251, 3555, 4587, 7578, 6156, 7578, 43242, 8315, 6225, 41891, 11331, 6027, 9307, 16490, 2304, 3794, 3660, 8717, 8592, 38688, 16490, 2304, 3794, 3660, 49429, 1975, 4117, 2655, 2288, 7251, 3555, 4587, 7578, 8032, 32887, 5016, 4724, 39648, 3224, 321, 362, 264, 3480, 3331], "avg_logprob": -0.2063873623098646, "compression_ratio": 1.63, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1318.22, "end": 1318.86, "word": "موجود", "probability": 0.7259928385416666}, {"start": 1318.86, "end": 1319.04, "word": " فى", "probability": 0.570068359375}, {"start": 1319.04, "end": 1319.14, "word": " ال", "probability": 0.53857421875}, {"start": 1319.14, "end": 1319.44, "word": " group", "probability": 0.78662109375}, {"start": 1319.44, "end": 1319.68, "word": " اللى", "probability": 0.956787109375}, {"start": 1319.68, "end": 1319.98, "word": " عندنا", "probability": 0.939697265625}, {"start": 1319.98, "end": 1320.1, "word": " ال", "probability": 0.7548828125}, {"start": 1320.1, "end": 1320.58, "word": " order", "probability": 0.970703125}, {"start": 1320.58, "end": 1320.94, "word": " اللى", "probability": 0.71826171875}, {"start": 1320.94, "end": 1321.74, "word": " يساوي", "probability": 0.89501953125}, {"start": 1321.74, "end": 1322.72, "word": " عشرة", "probability": 0.8860677083333334}, {"start": 1322.72, "end": 1323.32, "word": " و", "probability": 0.72265625}, {"start": 1323.32, "end": 1323.82, "word": " بيدروح", "probability": 0.6207275390625}, {"start": 1323.82, "end": 1324.24, "word": " ادور", "probability": 0.7744140625}, {"start": 1324.24, "end": 1324.5, "word": " على", "probability": 0.75830078125}, {"start": 1324.5, "end": 1324.66, "word": " ال", "probability": 0.6943359375}, {"start": 1324.66, "end": 1324.96, "word": " list", "probability": 0.673828125}, {"start": 1324.96, "end": 1325.34, "word": " common", "probability": 0.54541015625}, {"start": 1325.34, "end": 1326.12, "word": " multiples", "probability": 0.95556640625}, {"start": 1326.12, "end": 1327.22, "word": " اللى", "probability": 0.965576171875}, {"start": 1327.22, "end": 1327.58, "word": " هو", "probability": 0.666015625}, {"start": 1327.58, "end": 1328.46, "word": " بيعطينى", "probability": 0.79150390625}, {"start": 1328.46, "end": 1329.02, "word": " عشرة", "probability": 0.90380859375}, {"start": 1329.02, "end": 1329.82, "word": " يبقى", "probability": 0.9736328125}, {"start": 1329.82, "end": 1329.98, "word": " فى", "probability": 0.88232421875}, {"start": 1329.98, "end": 1330.38, "word": " عندنا", "probability": 0.903564453125}, {"start": 1330.38, "end": 1330.76, "word": " عدة", "probability": 0.975830078125}, {"start": 1330.76, "end": 1331.66, "word": " حالات", "probability": 0.9943033854166666}, {"start": 1331.66, "end": 1333.04, "word": " خمسة", "probability": 0.94775390625}, {"start": 1333.04, "end": 1333.66, "word": " نشوف", "probability": 0.8740234375}, {"start": 1333.66, "end": 1334.48, "word": " خمسة", "probability": 0.81494140625}, {"start": 1334.48, "end": 1334.64, "word": " ولا", "probability": 0.84814453125}, {"start": 1334.64, "end": 1335.16, "word": " اكتر", "probability": 0.91796875}, {"start": 1335.16, "end": 1336.64, "word": " يبقى", "probability": 0.977783203125}, {"start": 1336.64, "end": 1337.26, "word": " هروح", "probability": 0.8719075520833334}, {"start": 1337.26, "end": 1338.22, "word": " بقوله", "probability": 0.8564453125}, {"start": 1338.22, "end": 1338.66, "word": " we", "probability": 0.75048828125}, {"start": 1338.66, "end": 1340.04, "word": " have", "probability": 0.97314453125}, {"start": 1340.04, "end": 1341.76, "word": " the", "probability": 0.86474609375}, {"start": 1341.76, "end": 1343.2, "word": " following", "probability": 0.89794921875}, {"start": 1343.2, "end": 1346.04, "word": " cases", "probability": 0.91552734375}], "temperature": 1.0}, {"id": 49, "seek": 137370, "start": 1348.36, "end": 1373.7, "text": "الحالة الأولى ال order لل G ممكن يكون عشرة and ال order لل H ممكن يكون واحد او خمسة صح ال order لل G ممكن يكون عشرة و ال order لل H ممكن يكون واحد او خمسة يعني", "tokens": [6027, 5016, 6027, 3660, 16247, 12610, 7578, 2423, 1668, 24976, 460, 3714, 43020, 7251, 30544, 6225, 8592, 25720, 293, 2423, 1668, 24976, 389, 3714, 43020, 7251, 30544, 36764, 24401, 1975, 2407, 16490, 2304, 3794, 3660, 20328, 5016, 2423, 1668, 24976, 460, 3714, 43020, 7251, 30544, 6225, 8592, 25720, 4032, 2423, 1668, 24976, 389, 3714, 43020, 7251, 30544, 36764, 24401, 1975, 2407, 16490, 2304, 3794, 3660, 37495, 22653], "avg_logprob": -0.1284466922721442, "compression_ratio": 2.2882882882882885, "no_speech_prob": 0.0, "words": [{"start": 1348.36, "end": 1348.96, "word": "الحالة", "probability": 0.89990234375}, {"start": 1348.96, "end": 1349.84, "word": " الأولى", "probability": 0.9371744791666666}, {"start": 1349.84, "end": 1352.14, "word": " ال", "probability": 0.703125}, {"start": 1352.14, "end": 1352.66, "word": " order", "probability": 0.91455078125}, {"start": 1352.66, "end": 1353.72, "word": " لل", "probability": 0.60400390625}, {"start": 1353.72, "end": 1354.08, "word": " G", "probability": 0.372802734375}, {"start": 1354.08, "end": 1354.96, "word": " ممكن", "probability": 0.969482421875}, {"start": 1354.96, "end": 1355.46, "word": " يكون", "probability": 0.984619140625}, {"start": 1355.46, "end": 1356.28, "word": " عشرة", "probability": 0.9259440104166666}, {"start": 1356.28, "end": 1357.56, "word": " and", "probability": 0.7275390625}, {"start": 1357.56, "end": 1358.44, "word": " ال", "probability": 0.73681640625}, {"start": 1358.44, "end": 1359.04, "word": " order", "probability": 0.98046875}, {"start": 1359.04, "end": 1359.36, "word": " لل", "probability": 0.9423828125}, {"start": 1359.36, "end": 1359.78, "word": " H", "probability": 0.90966796875}, {"start": 1359.78, "end": 1360.64, "word": " ممكن", "probability": 0.9814453125}, {"start": 1360.64, "end": 1361.02, "word": " يكون", "probability": 0.98779296875}, {"start": 1361.02, "end": 1361.52, "word": " واحد", "probability": 0.94287109375}, {"start": 1361.52, "end": 1361.84, "word": " او", "probability": 0.7408447265625}, {"start": 1361.84, "end": 1362.78, "word": " خمسة", "probability": 0.9698486328125}, {"start": 1362.78, "end": 1365.48, "word": " صح", "probability": 0.78125}, {"start": 1365.48, "end": 1367.32, "word": " ال", "probability": 0.6943359375}, {"start": 1367.32, "end": 1367.74, "word": " order", "probability": 0.9833984375}, {"start": 1367.74, "end": 1367.98, "word": " لل", "probability": 0.398193359375}, {"start": 1367.98, "end": 1368.26, "word": " G", "probability": 0.953125}, {"start": 1368.26, "end": 1368.82, "word": " ممكن", "probability": 0.982177734375}, {"start": 1368.82, "end": 1369.18, "word": " يكون", "probability": 0.982666015625}, {"start": 1369.18, "end": 1369.86, "word": " عشرة", "probability": 0.9539388020833334}, {"start": 1369.86, "end": 1370.48, "word": " و", "probability": 0.75537109375}, {"start": 1370.48, "end": 1370.62, "word": " ال", "probability": 0.88427734375}, {"start": 1370.62, "end": 1371.14, "word": " order", "probability": 0.9794921875}, {"start": 1371.14, "end": 1371.46, "word": " لل", "probability": 0.9375}, {"start": 1371.46, "end": 1371.76, "word": " H", "probability": 0.96923828125}, {"start": 1371.76, "end": 1372.16, "word": " ممكن", "probability": 0.966796875}, {"start": 1372.16, "end": 1372.44, "word": " يكون", "probability": 0.98681640625}, {"start": 1372.44, "end": 1372.76, "word": " واحد", "probability": 0.9443359375}, {"start": 1372.76, "end": 1372.88, "word": " او", "probability": 0.971435546875}, {"start": 1372.88, "end": 1373.28, "word": " خمسة", "probability": 0.9952392578125}, {"start": 1373.28, "end": 1373.7, "word": " يعني", "probability": 0.857421875}], "temperature": 1.0}, {"id": 50, "seek": 138760, "start": 1374.06, "end": 1387.6, "text": "لو كان هذا عشرة او هذا واحد لجرس ال common divisor يساوي عشرة لو كان هذا عشرة او هذا خمسة لجرس ال common divisor يساوي عشرة", "tokens": [1211, 2407, 25961, 23758, 6225, 8592, 25720, 1975, 2407, 23758, 36764, 24401, 5296, 7435, 2288, 3794, 2423, 2689, 25974, 284, 7251, 3794, 995, 45865, 6225, 8592, 25720, 45164, 25961, 23758, 6225, 8592, 25720, 1975, 2407, 23758, 16490, 2304, 3794, 3660, 5296, 7435, 2288, 3794, 2423, 2689, 25974, 284, 7251, 3794, 995, 45865, 6225, 8592, 25720], "avg_logprob": -0.20996093483907835, "compression_ratio": 1.9696969696969697, "no_speech_prob": 0.0, "words": [{"start": 1374.06, "end": 1374.48, "word": "لو", "probability": 0.775634765625}, {"start": 1374.48, "end": 1374.76, "word": " كان", "probability": 0.96923828125}, {"start": 1374.76, "end": 1375.12, "word": " هذا", "probability": 0.88134765625}, {"start": 1375.12, "end": 1375.64, "word": " عشرة", "probability": 0.802734375}, {"start": 1375.64, "end": 1375.78, "word": " او", "probability": 0.802978515625}, {"start": 1375.78, "end": 1376.06, "word": " هذا", "probability": 0.92822265625}, {"start": 1376.06, "end": 1376.46, "word": " واحد", "probability": 0.927490234375}, {"start": 1376.46, "end": 1376.86, "word": " لجرس", "probability": 0.5159912109375}, {"start": 1376.86, "end": 1376.98, "word": " ال", "probability": 0.62158203125}, {"start": 1376.98, "end": 1377.3, "word": " common", "probability": 0.91943359375}, {"start": 1377.3, "end": 1377.88, "word": " divisor", "probability": 0.90185546875}, {"start": 1377.88, "end": 1378.9, "word": " يساوي", "probability": 0.7586669921875}, {"start": 1378.9, "end": 1379.76, "word": " عشرة", "probability": 0.8704427083333334}, {"start": 1379.76, "end": 1380.48, "word": " لو", "probability": 0.4599609375}, {"start": 1380.48, "end": 1380.98, "word": " كان", "probability": 0.9853515625}, {"start": 1380.98, "end": 1381.26, "word": " هذا", "probability": 0.9384765625}, {"start": 1381.26, "end": 1381.8, "word": " عشرة", "probability": 0.8935546875}, {"start": 1381.8, "end": 1381.96, "word": " او", "probability": 0.841796875}, {"start": 1381.96, "end": 1382.18, "word": " هذا", "probability": 0.92529296875}, {"start": 1382.18, "end": 1382.74, "word": " خمسة", "probability": 0.9671630859375}, {"start": 1382.74, "end": 1383.16, "word": " لجرس", "probability": 0.989990234375}, {"start": 1383.16, "end": 1383.34, "word": " ال", "probability": 0.9453125}, {"start": 1383.34, "end": 1383.62, "word": " common", "probability": 0.96728515625}, {"start": 1383.62, "end": 1384.26, "word": " divisor", "probability": 0.936767578125}, {"start": 1384.26, "end": 1386.88, "word": " يساوي", "probability": 0.950439453125}, {"start": 1386.88, "end": 1387.6, "word": " عشرة", "probability": 0.9308268229166666}], "temperature": 1.0}, {"id": 51, "seek": 140625, "start": 1398.17, "end": 1406.25, "text": "هل العشرة بتقسم الخمسة وعشرين ؟ إذا لا يمكن تلاقي element order له يساوي عشرة", "tokens": [3224, 1211, 18863, 8592, 25720, 39894, 4587, 38251, 33962, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 45520, 11933, 15730, 20193, 7251, 43020, 6055, 15040, 38436, 4478, 1668, 46740, 7251, 3794, 995, 45865, 6225, 8592, 25720], "avg_logprob": -0.3489583233992259, "compression_ratio": 1.2075471698113207, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1398.17, "end": 1399.17, "word": "هل", "probability": 0.386474609375}, {"start": 1399.17, "end": 1399.97, "word": " العشرة", "probability": 0.8142903645833334}, {"start": 1399.97, "end": 1400.61, "word": " بتقسم", "probability": 0.8536783854166666}, {"start": 1400.61, "end": 1401.19, "word": " الخمسة", "probability": 0.84228515625}, {"start": 1401.19, "end": 1401.91, "word": " وعشرين", "probability": 0.900390625}, {"start": 1401.91, "end": 1402.29, "word": " ؟", "probability": 0.27734375}, {"start": 1402.29, "end": 1402.69, "word": " إذا", "probability": 0.771728515625}, {"start": 1402.69, "end": 1402.93, "word": " لا", "probability": 0.361572265625}, {"start": 1402.93, "end": 1403.35, "word": " يمكن", "probability": 0.899169921875}, {"start": 1403.35, "end": 1403.83, "word": " تلاقي", "probability": 0.6698404947916666}, {"start": 1403.83, "end": 1404.25, "word": " element", "probability": 0.6748046875}, {"start": 1404.25, "end": 1404.93, "word": " order", "probability": 0.413818359375}, {"start": 1404.93, "end": 1405.23, "word": " له", "probability": 0.2734375}, {"start": 1405.23, "end": 1405.75, "word": " يساوي", "probability": 0.8951416015625}, {"start": 1405.75, "end": 1406.25, "word": " عشرة", "probability": 0.9166666666666666}], "temperature": 1.0}, {"id": 52, "seek": 143247, "start": 1408.25, "end": 1432.47, "text": "عندما تعمل على مطب و لا تقع فيه مطب و الحين ستقع فيه مطب بعد قليل ان شاء الله و نشلك منه ان شاء الله بحيث ال element اللى بدك تاخده ال order هذا بده يقسم ال order لل group طبق ال algorithmic theorem و النتائج اللى عليها انا لما أخدت ال order اللى جيه اللى هو عشرة على عشرة بتقسم المية", "tokens": [3615, 41260, 15042, 6055, 25957, 1211, 15844, 3714, 9566, 3555, 4032, 20193, 6055, 4587, 3615, 8978, 3224, 3714, 9566, 3555, 4032, 21542, 9957, 8608, 2655, 4587, 3615, 8978, 3224, 3714, 9566, 3555, 39182, 12174, 20292, 1211, 16472, 13412, 16606, 21984, 4032, 8717, 8592, 23275, 9154, 3224, 16472, 13412, 16606, 21984, 4724, 5016, 1829, 12984, 2423, 4478, 13672, 7578, 47525, 4117, 6055, 47283, 3215, 3224, 2423, 1668, 23758, 47525, 3224, 7251, 4587, 38251, 2423, 1668, 24976, 1594, 23032, 3555, 4587, 2423, 9284, 299, 20904, 4032, 28239, 2655, 16373, 7435, 13672, 7578, 25894, 11296, 1975, 8315, 5296, 15042, 5551, 9778, 3215, 2655, 2423, 1668, 13672, 7578, 10874, 1829, 3224, 13672, 7578, 31439, 6225, 8592, 25720, 15844, 6225, 8592, 25720, 39894, 4587, 38251, 9673, 10632], "avg_logprob": -0.30614838222178015, "compression_ratio": 1.8857142857142857, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1408.2499999999998, "end": 1408.9299999999998, "word": "عندما", "probability": 0.4431966145833333}, {"start": 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"word": " a", "probability": 0.7236328125}, {"start": 1610.61, "end": 1611.33, "word": " choice", "probability": 0.951171875}, {"start": 1611.33, "end": 1614.69, "word": " for", "probability": 0.59814453125}], "temperature": 1.0}, {"id": 60, "seek": 164561, "start": 1616.37, "end": 1645.61, "text": "order of each يساوي واحد and four choices واربع خيارات for order of each يساوي خمسة that is and we have خمسة choices for each", "tokens": [4687, 295, 1184, 7251, 3794, 995, 45865, 36764, 24401, 293, 1451, 7994, 4032, 9640, 3555, 3615, 16490, 1829, 9640, 9307, 337, 1668, 295, 1184, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 300, 307, 293, 321, 362, 16490, 2304, 3794, 3660, 7994, 337, 1184], "avg_logprob": -0.3401041719648573, "compression_ratio": 1.3859649122807018, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1616.37, "end": 1617.45, "word": "order", "probability": 0.05816650390625}, {"start": 1617.45, "end": 1617.77, "word": " of", "probability": 0.31982421875}, {"start": 1617.77, "end": 1618.23, "word": " each", "probability": 0.701171875}, {"start": 1618.23, "end": 1618.85, "word": " يساوي", "probability": 0.625213623046875}, {"start": 1618.85, "end": 1619.45, "word": " واحد", "probability": 0.96142578125}, {"start": 1619.45, "end": 1620.67, "word": " and", "probability": 0.442626953125}, {"start": 1620.67, "end": 1621.99, "word": " four", "probability": 0.8212890625}, {"start": 1621.99, "end": 1623.05, "word": " choices", "probability": 0.88037109375}, {"start": 1623.05, "end": 1624.63, "word": " واربع", "probability": 0.74700927734375}, {"start": 1624.63, "end": 1625.63, "word": " خيارات", "probability": 0.9798583984375}, {"start": 1625.63, "end": 1626.73, "word": " for", "probability": 0.85986328125}, {"start": 1626.73, "end": 1627.93, "word": " order", "probability": 0.91015625}, {"start": 1627.93, "end": 1628.27, "word": " of", "probability": 0.8876953125}, {"start": 1628.27, "end": 1628.79, "word": " each", "probability": 0.96337890625}, {"start": 1628.79, "end": 1630.09, "word": " يساوي", "probability": 0.74066162109375}, {"start": 1630.09, "end": 1630.99, "word": " خمسة", "probability": 0.932373046875}, {"start": 1630.99, "end": 1631.93, "word": " that", "probability": 0.4580078125}, {"start": 1631.93, "end": 1633.19, "word": " is", "probability": 0.9248046875}, {"start": 1633.19, "end": 1634.19, "word": " and", "probability": 0.10504150390625}, {"start": 1634.19, "end": 1635.21, "word": " we", "probability": 0.78076171875}, {"start": 1635.21, "end": 1637.17, "word": " have", "probability": 0.97216796875}, {"start": 1637.17, "end": 1640.91, "word": " خمسة", "probability": 0.8670654296875}, {"start": 1640.91, "end": 1641.71, "word": " choices", "probability": 0.75341796875}, {"start": 1641.71, "end": 1644.11, "word": " for", "probability": 0.951171875}, {"start": 1644.11, "end": 1645.61, "word": " each", "probability": 0.95703125}], "temperature": 1.0}, {"id": 61, "seek": 167445, "start": 1647.27, "end": 1674.45, "text": "طيب يبقى كام element في هذه حلبة سيارة؟ أربعة لإيه؟ وخمسة لبيه يبقى عشرين أنصار يبقى هنا so the element اللي قلنا عليه a g وh the element element also دور", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 9122, 10943, 4478, 8978, 29538, 11331, 46152, 3660, 8608, 1829, 9640, 3660, 22807, 5551, 25513, 27884, 5296, 28814, 1829, 3224, 22807, 4032, 9778, 2304, 3794, 3660, 5296, 21292, 3224, 7251, 3555, 4587, 7578, 6225, 46309, 9957, 14739, 9381, 9640, 7251, 3555, 4587, 7578, 34105, 370, 264, 4478, 13672, 1829, 12174, 1211, 8315, 47356, 257, 290, 4032, 71, 264, 4478, 4478, 611, 11778, 13063], "avg_logprob": -0.2601232285230932, "compression_ratio": 1.4873417721518987, "no_speech_prob": 0.0, "words": [{"start": 1647.27, "end": 1647.65, "word": "طيب", "probability": 0.72314453125}, {"start": 1647.65, "end": 1648.09, "word": " يبقى", "probability": 0.9500732421875}, {"start": 1648.09, "end": 1648.41, "word": " كام", "probability": 0.7685546875}, {"start": 1648.41, "end": 1648.81, "word": " element", "probability": 0.80859375}, {"start": 1648.81, "end": 1649.05, "word": " في", "probability": 0.86669921875}, {"start": 1649.05, "end": 1649.33, "word": " هذه", "probability": 0.966796875}, {"start": 1649.33, "end": 1649.91, "word": " حلبة", "probability": 0.7516276041666666}, {"start": 1649.91, "end": 1651.03, "word": " سيارة؟", "probability": 0.807568359375}, {"start": 1651.03, "end": 1652.65, "word": " أربعة", "probability": 0.79296875}, {"start": 1652.65, "end": 1653.49, "word": " لإيه؟", "probability": 0.7735107421875}, {"start": 1653.49, "end": 1654.39, "word": " وخمسة", "probability": 0.93740234375}, {"start": 1654.39, "end": 1654.65, "word": " لبيه", "probability": 0.8567708333333334}, {"start": 1654.65, "end": 1654.87, "word": " يبقى", "probability": 0.84539794921875}, {"start": 1654.87, "end": 1655.53, "word": " عشرين", "probability": 0.9700520833333334}, {"start": 1655.53, "end": 1656.23, "word": " أنصار", "probability": 0.8914388020833334}, {"start": 1656.23, "end": 1657.25, "word": " يبقى", "probability": 0.936279296875}, {"start": 1657.25, "end": 1657.71, "word": " هنا", "probability": 0.98779296875}, {"start": 1657.71, "end": 1658.79, "word": " so", "probability": 0.1820068359375}, {"start": 1658.79, "end": 1660.83, "word": " the", "probability": 0.62841796875}, {"start": 1660.83, "end": 1662.15, "word": " element", "probability": 0.9423828125}, {"start": 1662.15, "end": 1662.37, "word": " اللي", "probability": 0.932861328125}, {"start": 1662.37, "end": 1662.77, "word": " قلنا", "probability": 0.9059244791666666}, {"start": 1662.77, "end": 1663.23, "word": " عليه", "probability": 0.9345703125}, {"start": 1663.23, "end": 1663.59, "word": " a", "probability": 0.45556640625}, {"start": 1663.59, "end": 1663.77, "word": " g", "probability": 0.387939453125}, {"start": 1663.77, "end": 1664.33, "word": " وh", "probability": 0.658935546875}, {"start": 1664.33, "end": 1665.25, "word": " the", "probability": 0.61083984375}, {"start": 1665.25, "end": 1667.01, "word": " element", "probability": 0.9599609375}, {"start": 1667.01, "end": 1669.61, "word": " element", "probability": 0.68359375}, {"start": 1669.61, "end": 1673.33, "word": " also", "probability": 0.57763671875}, {"start": 1673.33, "end": 1674.45, "word": " دور", "probability": 0.9296875}], "temperature": 1.0}, {"id": 62, "seek": 170296, "start": 1676.48, "end": 1702.96, "text": "we have اللي هو عشرين element of order عشرة n اللي هو زد مية external product لزد خمسة و عشرين يبقى الحالة الأولى هذه جبتلي جدار", "tokens": [826, 362, 13672, 1829, 31439, 6225, 46309, 9957, 4478, 295, 1668, 6225, 8592, 25720, 297, 13672, 1829, 31439, 30767, 3215, 3714, 10632, 8320, 1674, 5296, 11622, 3215, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 7251, 3555, 4587, 7578, 21542, 6027, 3660, 16247, 12610, 7578, 29538, 10874, 3555, 2655, 20292, 10874, 3215, 9640], "avg_logprob": -0.2826967531884158, "compression_ratio": 1.3829787234042554, "no_speech_prob": 0.0, "words": [{"start": 1676.48, "end": 1676.94, "word": "we", "probability": 0.1158447265625}, {"start": 1676.94, "end": 1677.94, "word": " have", "probability": 0.96240234375}, {"start": 1677.94, "end": 1679.86, "word": " اللي", "probability": 0.51702880859375}, {"start": 1679.86, "end": 1680.14, "word": " هو", "probability": 0.96337890625}, {"start": 1680.14, "end": 1681.12, "word": " عشرين", "probability": 0.95556640625}, {"start": 1681.12, "end": 1682.32, "word": " element", "probability": 0.6826171875}, {"start": 1682.32, "end": 1684.98, "word": " of", "probability": 0.958984375}, {"start": 1684.98, "end": 1686.84, "word": " order", "probability": 0.96826171875}, {"start": 1686.84, "end": 1689.22, "word": " عشرة", "probability": 0.8592122395833334}, {"start": 1689.22, "end": 1690.14, "word": " n", "probability": 0.296875}, {"start": 1690.14, "end": 1691.24, "word": " اللي", "probability": 0.93115234375}, {"start": 1691.24, "end": 1691.52, "word": " هو", "probability": 0.96240234375}, {"start": 1691.52, "end": 1692.06, "word": " زد", "probability": 0.544921875}, {"start": 1692.06, "end": 1692.78, "word": " مية", "probability": 0.870361328125}, {"start": 1692.78, "end": 1694.12, "word": " external", "probability": 0.80078125}, {"start": 1694.12, "end": 1694.44, "word": " product", "probability": 0.51708984375}, {"start": 1694.44, "end": 1696.46, "word": " لزد", "probability": 0.7036946614583334}, {"start": 1696.46, "end": 1697.16, "word": " خمسة", "probability": 0.9193115234375}, {"start": 1697.16, "end": 1697.32, "word": " و", "probability": 0.87158203125}, {"start": 1697.32, "end": 1698.34, "word": " عشرين", "probability": 0.8024088541666666}, {"start": 1698.34, "end": 1699.74, "word": " يبقى", "probability": 0.947998046875}, {"start": 1699.74, "end": 1700.26, "word": " الحالة", "probability": 0.9597981770833334}, {"start": 1700.26, "end": 1700.76, "word": " الأولى", "probability": 0.9534505208333334}, {"start": 1700.76, "end": 1701.18, "word": " هذه", "probability": 0.299560546875}, {"start": 1701.18, "end": 1702.34, "word": " جبتلي", "probability": 0.782470703125}, {"start": 1702.34, "end": 1702.96, "word": " جدار", "probability": 0.708251953125}], "temperature": 1.0}, {"id": 63, "seek": 173255, "start": 1703.43, "end": 1732.55, "text": "جبتلي عشرين answer الان الحالة الثانية لو كان ال order لل G بده يساوي اتنين and ال order لل H بده يساوي خمسة هل هذا الكلام ممكن؟ نعم لإن اتنين بتقسم المية و ال H بتقسم مين؟ بتقسم الخمسة بالضبط تمام الان شباب اتنين بتقسم المية", "tokens": [7435, 3555, 2655, 20292, 6225, 46309, 9957, 1867, 2423, 7649, 21542, 6027, 3660, 6024, 104, 7649, 10632, 45164, 25961, 2423, 1668, 24976, 460, 47525, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 293, 2423, 1668, 24976, 389, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 8032, 1211, 23758, 2423, 28820, 10943, 3714, 43020, 22807, 8717, 25957, 5296, 28814, 1863, 1975, 2655, 1863, 9957, 39894, 4587, 38251, 9673, 10632, 4032, 2423, 389, 39894, 4587, 38251, 3714, 9957, 22807, 39894, 4587, 38251, 33962, 2304, 3794, 3660, 20666, 11242, 3555, 9566, 46811, 10943, 2423, 7649, 13412, 3555, 16758, 1975, 2655, 1863, 9957, 39894, 4587, 38251, 9673, 10632], "avg_logprob": -0.18026621074036317, "compression_ratio": 2.0372340425531914, "no_speech_prob": 0.0, "words": [{"start": 1703.43, "end": 1704.09, "word": "جبتلي", "probability": 0.7734375}, {"start": 1704.09, "end": 1704.97, "word": " عشرين", "probability": 0.92138671875}, {"start": 1704.97, "end": 1705.71, "word": " answer", "probability": 0.7392578125}, {"start": 1705.71, "end": 1706.73, "word": " الان", "probability": 0.55322265625}, {"start": 1706.73, "end": 1707.43, "word": " الحالة", "probability": 0.8841145833333334}, {"start": 1707.43, "end": 1708.09, "word": " الثانية", "probability": 0.9566650390625}, {"start": 1708.09, "end": 1709.67, "word": " لو", "probability": 0.88232421875}, {"start": 1709.67, "end": 1710.15, "word": " كان", "probability": 0.9833984375}, {"start": 1710.15, "end": 1710.39, "word": " ال", "probability": 0.85888671875}, {"start": 1710.39, "end": 1710.91, "word": " order", "probability": 0.97412109375}, {"start": 1710.91, "end": 1711.39, "word": " لل", "probability": 0.607421875}, {"start": 1711.39, "end": 1711.87, "word": " G", "probability": 0.49658203125}, {"start": 1711.87, "end": 1712.63, "word": " بده", "probability": 0.3365478515625}, {"start": 1712.63, "end": 1713.21, "word": " يساوي", "probability": 0.91748046875}, {"start": 1713.21, "end": 1713.89, "word": " اتنين", "probability": 0.9588623046875}, {"start": 1713.89, "end": 1714.87, "word": " and", "probability": 0.84130859375}, {"start": 1714.87, "end": 1715.63, "word": " ال", "probability": 0.927734375}, {"start": 1715.63, "end": 1716.21, "word": " order", "probability": 0.98291015625}, {"start": 1716.21, "end": 1716.65, "word": " لل", "probability": 0.912109375}, {"start": 1716.65, "end": 1717.13, "word": " H", "probability": 0.89306640625}, {"start": 1717.13, "end": 1717.61, "word": " بده", "probability": 0.926025390625}, {"start": 1717.61, "end": 1718.05, "word": " يساوي", "probability": 0.984619140625}, {"start": 1718.05, "end": 1718.83, "word": " خمسة", "probability": 0.9716796875}, {"start": 1718.83, "end": 1719.85, "word": " هل", "probability": 0.940185546875}, {"start": 1719.85, "end": 1720.11, "word": " هذا", "probability": 0.97509765625}, {"start": 1720.11, "end": 1720.51, "word": " الكلام", "probability": 0.8811848958333334}, {"start": 1720.51, "end": 1721.65, "word": " ممكن؟", "probability": 0.7770182291666666}, {"start": 1721.65, "end": 1722.21, "word": " نعم", "probability": 0.96630859375}, {"start": 1722.21, "end": 1722.57, "word": " لإن", "probability": 0.7508951822916666}, {"start": 1722.57, "end": 1722.99, "word": " اتنين", "probability": 0.9088134765625}, {"start": 1722.99, "end": 1723.49, "word": " بتقسم", "probability": 0.803955078125}, {"start": 1723.49, "end": 1724.03, "word": " المية", "probability": 0.81005859375}, {"start": 1724.03, "end": 1724.63, "word": " و", "probability": 0.8544921875}, {"start": 1724.63, "end": 1724.81, "word": " ال", "probability": 0.806640625}, {"start": 1724.81, "end": 1725.07, "word": " H", "probability": 0.91015625}, {"start": 1725.07, "end": 1725.65, "word": " بتقسم", "probability": 0.9715169270833334}, {"start": 1725.65, "end": 1726.37, "word": " مين؟", "probability": 0.4007975260416667}, {"start": 1726.37, "end": 1726.83, "word": " بتقسم", "probability": 0.91064453125}, {"start": 1726.83, "end": 1727.57, "word": " الخمسة", "probability": 0.9901123046875}, {"start": 1727.57, "end": 1728.15, "word": " بالضبط", "probability": 0.900390625}, {"start": 1728.15, "end": 1728.63, "word": " تمام", "probability": 0.97021484375}, {"start": 1728.63, "end": 1729.83, "word": " الان", "probability": 0.6444091796875}, {"start": 1729.83, "end": 1730.31, "word": " شباب", "probability": 0.9322916666666666}, {"start": 1730.31, "end": 1731.13, "word": " اتنين", "probability": 0.9613037109375}, {"start": 1731.13, "end": 1731.95, "word": " بتقسم", "probability": 0.9754231770833334}, {"start": 1731.95, "end": 1732.55, "word": " المية", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 64, "seek": 175902, "start": 1733.04, "end": 1759.02, "text": "صح؟ يبقى في عندي unique cyclic subgroup يبقى implies we have اللي هو unique cyclic subgroup اللي هي من ال 100 على ال 2 اللي هي الخمسين", "tokens": [9381, 5016, 22807, 7251, 3555, 4587, 7578, 8978, 18871, 16254, 3845, 38154, 1050, 1422, 17377, 7251, 3555, 4587, 7578, 18779, 321, 362, 13672, 1829, 31439, 3845, 38154, 1050, 1422, 17377, 13672, 1829, 39896, 9154, 2423, 2319, 15844, 2423, 568, 13672, 1829, 39896, 33962, 2304, 3794, 9957], "avg_logprob": -0.19032579533597258, "compression_ratio": 1.434108527131783, "no_speech_prob": 0.0, "words": [{"start": 1733.04, "end": 1733.8, "word": "صح؟", "probability": 0.7010091145833334}, {"start": 1733.8, "end": 1734.84, "word": " يبقى", "probability": 0.96240234375}, {"start": 1734.84, "end": 1734.98, "word": " في", "probability": 0.91845703125}, {"start": 1734.98, "end": 1735.38, "word": " عندي", "probability": 0.6668701171875}, {"start": 1735.38, "end": 1735.84, "word": " unique", "probability": 0.86279296875}, {"start": 1735.84, "end": 1736.8, "word": " cyclic", "probability": 0.91015625}, {"start": 1736.8, "end": 1737.62, "word": " subgroup", "probability": 0.82861328125}, {"start": 1737.62, "end": 1738.88, "word": " يبقى", "probability": 0.957275390625}, {"start": 1738.88, "end": 1739.94, "word": " implies", "probability": 0.91650390625}, {"start": 1739.94, "end": 1740.36, "word": " we", "probability": 0.9326171875}, {"start": 1740.36, "end": 1741.42, "word": " have", "probability": 0.97509765625}, {"start": 1741.42, "end": 1743.3, "word": " اللي", "probability": 0.92919921875}, {"start": 1743.3, "end": 1743.68, "word": " هو", "probability": 0.98095703125}, {"start": 1743.68, "end": 1745.24, "word": " unique", "probability": 0.81689453125}, {"start": 1745.24, "end": 1747.5, "word": " cyclic", "probability": 0.91357421875}, {"start": 1747.5, "end": 1749.92, "word": " subgroup", "probability": 0.961181640625}, {"start": 1749.92, "end": 1752.38, "word": " اللي", "probability": 0.962158203125}, {"start": 1752.38, "end": 1752.58, "word": " هي", "probability": 0.8857421875}, {"start": 1752.58, "end": 1752.84, "word": " من", "probability": 0.53759765625}, {"start": 1752.84, "end": 1753.14, "word": " ال", "probability": 0.364501953125}, {"start": 1753.14, "end": 1754.56, "word": " 100", "probability": 0.68994140625}, {"start": 1754.56, "end": 1755.52, "word": " على", "probability": 0.4892578125}, {"start": 1755.52, "end": 1755.84, "word": " ال", "probability": 0.62939453125}, {"start": 1755.84, "end": 1756.4, "word": " 2", "probability": 0.8798828125}, {"start": 1756.4, "end": 1757.28, "word": " اللي", "probability": 0.9384765625}, {"start": 1757.28, "end": 1757.72, "word": " هي", "probability": 0.84765625}, {"start": 1757.72, "end": 1759.02, "word": " الخمسين", "probability": 0.8173828125}], "temperature": 1.0}, {"id": 65, "seek": 177678, "start": 1759.32, "end": 1776.78, "text": "الخمسين اكم انصر فيها دى اتنين ال order يساوي اتنين الخمسين والمية بالزيرو يبقى ماعناشي الا زيرو وخمسين يبقى we have a unique cyclic subgroup اللى هى subgroup واحدة", "tokens": [6027, 9778, 2304, 3794, 9957, 1975, 24793, 16472, 9381, 2288, 8978, 11296, 11778, 7578, 1975, 2655, 1863, 9957, 2423, 1668, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 33962, 2304, 3794, 9957, 16070, 2304, 10632, 20666, 11622, 13546, 2407, 7251, 3555, 4587, 7578, 19446, 3615, 1863, 33599, 1829, 42963, 30767, 13546, 2407, 4032, 9778, 2304, 3794, 9957, 7251, 3555, 4587, 7578, 321, 362, 257, 3845, 38154, 1050, 1422, 17377, 13672, 7578, 8032, 7578, 1422, 17377, 36764, 24401, 3660], "avg_logprob": -0.24901107444038875, "compression_ratio": 1.5757575757575757, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1759.32, "end": 1760.0, "word": "الخمسين", "probability": 0.8708984375}, {"start": 1760.0, "end": 1760.24, "word": " اكم", "probability": 0.25811767578125}, {"start": 1760.24, "end": 1760.68, "word": " انصر", "probability": 0.7941080729166666}, {"start": 1760.68, "end": 1761.04, "word": " فيها", "probability": 0.7841796875}, {"start": 1761.04, "end": 1761.82, "word": " دى", "probability": 0.516845703125}, {"start": 1761.82, "end": 1762.4, "word": " اتنين", "probability": 0.81439208984375}, {"start": 1762.4, "end": 1762.54, "word": " ال", "probability": 0.71630859375}, {"start": 1762.54, "end": 1762.84, "word": " order", "probability": 0.908203125}, {"start": 1762.84, "end": 1763.58, "word": " يساوي", "probability": 0.9154052734375}, {"start": 1763.58, "end": 1764.2, "word": " اتنين", "probability": 0.969482421875}, {"start": 1764.2, "end": 1765.24, "word": " الخمسين", "probability": 0.865966796875}, {"start": 1765.24, "end": 1765.64, "word": " والمية", "probability": 0.8294270833333334}, {"start": 1765.64, "end": 1766.16, "word": " بالزيرو", "probability": 0.731689453125}, {"start": 1766.16, "end": 1766.36, "word": " يبقى", "probability": 0.9166259765625}, {"start": 1766.36, "end": 1766.92, "word": " ماعناشي", "probability": 0.712646484375}, {"start": 1766.92, "end": 1767.08, "word": " الا", "probability": 0.79052734375}, {"start": 1767.08, "end": 1767.64, "word": " زيرو", "probability": 0.8136393229166666}, {"start": 1767.64, "end": 1768.76, "word": " وخمسين", "probability": 0.9208984375}, {"start": 1768.76, "end": 1769.6, "word": " يبقى", "probability": 0.9678955078125}, {"start": 1769.6, "end": 1769.74, "word": " we", "probability": 0.35205078125}, {"start": 1769.74, "end": 1770.3, "word": " have", "probability": 0.97216796875}, {"start": 1770.3, "end": 1771.26, "word": " a", "probability": 0.87451171875}, {"start": 1771.26, "end": 1772.06, "word": " unique", "probability": 0.7236328125}, {"start": 1772.06, "end": 1772.66, "word": " cyclic", "probability": 0.881591796875}, {"start": 1772.66, "end": 1773.52, "word": " subgroup", "probability": 0.712158203125}, {"start": 1773.52, "end": 1774.0, "word": " اللى", "probability": 0.797119140625}, {"start": 1774.0, "end": 1774.26, "word": " هى", "probability": 0.8955078125}, {"start": 1774.26, "end": 1776.28, "word": " subgroup", "probability": 0.726806640625}, {"start": 1776.28, "end": 1776.78, "word": " واحدة", "probability": 0.962890625}], "temperature": 1.0}, {"id": 66, "seek": 180538, "start": 1777.02, "end": 1805.38, "text": "وهذه مافيهاش الا element واحد اللى هو الخمسين ال order اللى يساوي كده اتنين يعني ماعنديش الا element واحد فقط لغيره يبقى so we have one element only of order اتنين", "tokens": [2407, 3224, 24192, 19446, 41185, 3224, 33599, 42963, 4478, 36764, 24401, 13672, 7578, 31439, 33962, 2304, 3794, 9957, 2423, 1668, 13672, 7578, 7251, 3794, 995, 45865, 9122, 3215, 3224, 1975, 2655, 1863, 9957, 37495, 22653, 19446, 3615, 1863, 16254, 8592, 42963, 4478, 36764, 24401, 6156, 47432, 5296, 17082, 13546, 3224, 7251, 3555, 4587, 7578, 370, 321, 362, 472, 4478, 787, 295, 1668, 1975, 2655, 1863, 9957], "avg_logprob": -0.217117543095973, "compression_ratio": 1.6, "no_speech_prob": 0.0, "words": [{"start": 1777.02, "end": 1777.46, "word": "وهذه", "probability": 0.6082356770833334}, {"start": 1777.46, "end": 1778.2, "word": " مافيهاش", "probability": 0.78558349609375}, {"start": 1778.2, "end": 1778.66, "word": " الا", "probability": 0.57080078125}, {"start": 1778.66, "end": 1779.44, "word": " element", "probability": 0.82421875}, {"start": 1779.44, "end": 1780.3, "word": " واحد", "probability": 0.994140625}, {"start": 1780.3, "end": 1780.8, "word": " اللى", "probability": 0.6597900390625}, {"start": 1780.8, "end": 1780.92, "word": " هو", "probability": 0.9609375}, {"start": 1780.92, "end": 1781.74, "word": " الخمسين", "probability": 0.9141845703125}, {"start": 1781.74, "end": 1782.24, "word": " ال", "probability": 0.74853515625}, {"start": 1782.24, "end": 1782.66, "word": " order", "probability": 0.96240234375}, {"start": 1782.66, "end": 1782.9, "word": " اللى", "probability": 0.765625}, {"start": 1782.9, "end": 1783.34, "word": " يساوي", "probability": 0.7899169921875}, {"start": 1783.34, "end": 1783.84, "word": " كده", "probability": 0.7854817708333334}, {"start": 1783.84, "end": 1784.72, "word": " اتنين", "probability": 0.8082275390625}, {"start": 1784.72, "end": 1784.94, "word": " يعني", "probability": 0.712158203125}, {"start": 1784.94, "end": 1785.76, "word": " ماعنديش", "probability": 0.95185546875}, {"start": 1785.76, "end": 1786.38, "word": " الا", "probability": 0.8232421875}, {"start": 1786.38, "end": 1787.02, "word": " element", "probability": 0.96337890625}, {"start": 1787.02, "end": 1787.58, "word": " واحد", "probability": 0.995849609375}, {"start": 1787.58, "end": 1788.26, "word": " فقط", "probability": 0.9794921875}, {"start": 1788.26, "end": 1789.84, "word": " لغيره", "probability": 0.75201416015625}, {"start": 1789.84, "end": 1791.22, "word": " يبقى", "probability": 0.79949951171875}, {"start": 1791.22, "end": 1792.8, "word": " so", "probability": 0.29345703125}, {"start": 1792.8, "end": 1793.86, "word": " we", "probability": 0.947265625}, {"start": 1793.86, "end": 1795.52, "word": " have", "probability": 0.96044921875}, {"start": 1795.52, "end": 1796.82, "word": " one", "probability": 0.919921875}, {"start": 1796.82, "end": 1798.18, "word": " element", "probability": 0.96875}, {"start": 1798.18, "end": 1800.4, "word": " only", "probability": 0.87744140625}, {"start": 1800.4, "end": 1802.54, "word": " of", "probability": 0.97265625}, {"start": 1802.54, "end": 1804.2, "word": " order", "probability": 0.9638671875}, {"start": 1804.2, "end": 1805.38, "word": " اتنين", "probability": 0.960693359375}], "temperature": 1.0}, {"id": 67, "seek": 183639, "start": 1807.65, "end": 1836.39, "text": "نجي اف ال order لل H بده يساوي كده؟ خمسة يعني عندى كم خيار؟ اربع هم ايهم الخمسة عشر او خمستاشر يبقى we have four choices for اللي هو ال H من الاتنين هذول كده يكون عندى", "tokens": [1863, 7435, 1829, 1975, 5172, 2423, 1668, 24976, 389, 47525, 3224, 7251, 3794, 995, 45865, 9122, 3215, 3224, 22807, 16490, 2304, 3794, 3660, 37495, 22653, 43242, 7578, 9122, 2304, 16490, 1829, 9640, 22807, 1975, 25513, 3615, 8032, 2304, 1975, 1829, 16095, 33962, 2304, 3794, 3660, 6225, 46309, 1975, 2407, 16490, 2304, 14851, 33599, 2288, 7251, 3555, 4587, 7578, 321, 362, 1451, 7994, 337, 13672, 1829, 31439, 2423, 389, 9154, 2423, 9307, 1863, 9957, 8032, 8848, 12610, 9122, 3215, 3224, 7251, 30544, 43242, 7578], "avg_logprob": -0.3554687368727866, "compression_ratio": 1.5310734463276836, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1807.65, "end": 1808.23, "word": "نجي", "probability": 0.4165852864583333}, {"start": 1808.23, "end": 1809.19, "word": " اف", "probability": 0.49981689453125}, {"start": 1809.19, "end": 1810.83, "word": " ال", "probability": 0.58447265625}, {"start": 1810.83, "end": 1811.49, "word": " order", "probability": 0.95849609375}, {"start": 1811.49, "end": 1812.63, "word": " لل", "probability": 0.58642578125}, {"start": 1812.63, "end": 1813.19, "word": " H", "probability": 0.457275390625}, {"start": 1813.19, "end": 1813.89, "word": " بده", "probability": 0.3681640625}, {"start": 1813.89, "end": 1814.29, "word": " يساوي", "probability": 0.9127197265625}, {"start": 1814.29, "end": 1814.91, "word": " كده؟", "probability": 0.70440673828125}, {"start": 1814.91, "end": 1815.53, "word": " خمسة", "probability": 0.9400634765625}, {"start": 1815.53, "end": 1816.19, "word": " يعني", "probability": 0.862548828125}, {"start": 1816.19, "end": 1816.55, "word": " عندى", "probability": 0.462890625}, {"start": 1816.55, "end": 1816.71, "word": " كم", "probability": 0.845947265625}, {"start": 1816.71, "end": 1817.97, "word": " خيار؟", "probability": 0.943603515625}, {"start": 1817.97, "end": 1818.99, "word": " اربع", "probability": 0.7600911458333334}, {"start": 1818.99, "end": 1819.39, "word": " هم", "probability": 0.792236328125}, {"start": 1819.39, "end": 1819.73, "word": " ايهم", "probability": 0.6116536458333334}, {"start": 1819.73, "end": 1820.35, "word": " الخمسة", "probability": 0.9122314453125}, {"start": 1820.35, "end": 1820.65, "word": " عشر", "probability": 0.6044921875}, {"start": 1820.65, "end": 1820.75, "word": " او", "probability": 0.68798828125}, {"start": 1820.75, "end": 1821.27, "word": " خمستاشر", "probability": 0.7104736328125}, {"start": 1821.27, "end": 1823.17, "word": " يبقى", "probability": 0.8453369140625}, {"start": 1823.17, "end": 1823.63, "word": " we", "probability": 0.63330078125}, {"start": 1823.63, "end": 1825.37, "word": " have", "probability": 0.94775390625}, {"start": 1825.37, "end": 1826.95, "word": " four", "probability": 0.78515625}, {"start": 1826.95, "end": 1828.69, "word": " choices", "probability": 0.7587890625}, {"start": 1828.69, "end": 1830.59, "word": " for", "probability": 0.837890625}, {"start": 1830.59, "end": 1832.03, "word": " اللي", "probability": 0.5592041015625}, {"start": 1832.03, "end": 1832.51, "word": " هو", "probability": 0.92919921875}, {"start": 1832.51, "end": 1832.93, "word": " ال", "probability": 0.966796875}, {"start": 1832.93, "end": 1833.29, "word": " H", "probability": 0.900390625}, {"start": 1833.29, "end": 1834.03, "word": " من", "probability": 0.84765625}, {"start": 1834.03, "end": 1834.65, "word": " الاتنين", "probability": 0.80755615234375}, {"start": 1834.65, "end": 1835.05, "word": " هذول", "probability": 0.9075520833333334}, {"start": 1835.05, "end": 1835.37, "word": " كده", "probability": 0.9192708333333334}, {"start": 1835.37, "end": 1835.75, "word": " يكون", "probability": 0.625}, {"start": 1835.75, "end": 1836.39, "word": " عندى", "probability": 0.849365234375}], "temperature": 1.0}, {"id": 68, "seek": 185928, "start": 1837.48, "end": 1859.28, "text": "كم زوج مركب؟ حشرة؟ واحد و هنا اربعة يبقى الواحد مع الاول مع التاني مع الرابع يبقى اربعة عناصر يبقى هذا بدي يعطيني we have four elements of order", "tokens": [24793, 30767, 29245, 3714, 31747, 3555, 22807, 11331, 8592, 25720, 22807, 36764, 24401, 4032, 34105, 1975, 25513, 27884, 7251, 3555, 4587, 7578, 2423, 14407, 24401, 20449, 42963, 12610, 20449, 16712, 7649, 1829, 20449, 34892, 16758, 3615, 7251, 3555, 4587, 7578, 1975, 25513, 27884, 18871, 33546, 2288, 7251, 3555, 4587, 7578, 23758, 4724, 16254, 37495, 9566, 9957, 1829, 321, 362, 1451, 4959, 295, 1668], "avg_logprob": -0.22155762277543545, "compression_ratio": 1.525974025974026, "no_speech_prob": 0.0, "words": [{"start": 1837.48, "end": 1837.78, "word": "كم", "probability": 0.362060546875}, {"start": 1837.78, "end": 1838.08, "word": " زوج", "probability": 0.9697265625}, {"start": 1838.08, "end": 1838.98, "word": " مركب؟", "probability": 0.85888671875}, {"start": 1838.98, "end": 1839.98, "word": " حشرة؟", "probability": 0.49615478515625}, {"start": 1839.98, "end": 1841.96, "word": " واحد", "probability": 0.947021484375}, {"start": 1841.96, "end": 1842.1, 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2423, 1668, 7251, 3794, 995, 45865, 6225, 8592, 25720, 4032, 44945, 24793, 1211, 16472, 13412, 16606, 21984, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007], "avg_logprob": -0.24657011849851143, "compression_ratio": 1.6197916666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2104.78, "end": 2105.22, "word": "يبقى", "probability": 0.7391357421875}, {"start": 2105.22, "end": 2105.34, "word": " ال", "probability": 0.56640625}, {"start": 2105.34, "end": 2106.46, "word": " 2500", "probability": 0.78125}, {"start": 2106.46, "end": 2109.36, "word": " element", "probability": 0.587890625}, {"start": 2109.36, "end": 2110.2, "word": " اللي", "probability": 0.80859375}, {"start": 2110.2, "end": 2110.46, "word": " هم", "probability": 0.813232421875}, {"start": 2110.46, "end": 2111.12, "word": " عناصر", "probability": 0.9625651041666666}, {"start": 2111.12, "end": 2111.26, "word": " ال", "probability": 0.78857421875}, {"start": 2111.26, "end": 2111.54, "word": " group", "probability": 0.95068359375}, {"start": 2111.54, "end": 2111.92, "word": " هدول", "probability": 0.8924153645833334}, {"start": 2111.92, "end": 2112.34, "word": " بلاقي", "probability": 0.7887369791666666}, {"start": 2112.34, "end": 2112.68, "word": " بس", "probability": 0.887451171875}, {"start": 2112.68, "end": 2113.3, "word": " منهم", "probability": 0.991455078125}, {"start": 2113.3, "end": 2113.84, "word": " اللي", "probability": 0.9619140625}, {"start": 2113.84, "end": 2113.98, "word": " هو", "probability": 0.68701171875}, {"start": 2113.98, "end": 2114.18, "word": " ال", "probability": 0.85205078125}, {"start": 2114.18, "end": 2114.58, "word": " 6", "probability": 0.61083984375}, {"start": 2114.58, "end": 2115.42, "word": " elements", "probability": 0.83984375}, {"start": 2115.42, "end": 2116.36, "word": " بيجيبولي", "probability": 0.83837890625}, {"start": 2116.36, "end": 2116.5, "word": " ال", "probability": 0.9287109375}, {"start": 2116.5, "end": 2116.96, "word": " cyclic", 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/Slls50l_wck_raw.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/Slls50l_wck_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..38c829b254f5c1555964a9aad57d9be17e833eda
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/Slls50l_wck_raw.srt
@@ -0,0 +1,2800 @@
+1
+00:00:20,640 --> 00:00:25,560
+بسم الله الرحمن الرحيم محاضرتنا اليوم هي
+
+2
+00:00:25,560 --> 00:00:30,440
+introduction to hemostasis and coagulation هي the
+
+3
+00:00:30,440 --> 00:00:36,360
+first lecture in this course نقدم من خلاله لمادة
+
+4
+00:00:36,360 --> 00:00:40,040
+جديدة مادة ال hemostasis and coagulation طبعا
+
+5
+00:00:40,040 --> 00:00:44,260
+hemostasis as a definition هي عبارة عن كلمة
+
+6
+00:00:44,260 --> 00:00:48,580
+لاتينية معناها hemostasis
+
+7
+00:00:49,810 --> 00:00:55,570
+هي blood و stasis هي بتعني arresting or stagnation
+
+8
+00:00:55,570 --> 00:00:59,730
+of the blood within blood vessels and once this
+
+9
+00:00:59,730 --> 00:01:05,650
+process occur we ensure two things بنأكد حصول
+
+10
+00:01:05,650 --> 00:01:09,930
+شغلتيه الشغلة الأولانية prevention of spontaneous
+
+11
+00:01:09,930 --> 00:01:17,180
+blood loss الشغلة التانيةبصير فيه stopping لل
+
+12
+00:01:17,180 --> 00:01:21,920
+hemorrhage وبالتالي بيرجع الدم إلى موضع الأساسي
+
+13
+00:01:21,920 --> 00:01:27,900
+وهو الوعاء الدموي وبالتالي بصير فيه prevention of
+
+14
+00:01:27,900 --> 00:01:33,200
+leakage or of hemorrhage outside the blood vessels
+
+15
+00:01:33,200 --> 00:01:39,680
+فيه طبعا في معظم الأحيان هذه العملية بتعني أن الدم
+
+16
+00:01:40,000 --> 00:01:44,560
+يطلع عليه تحول، بينتقل من الحالة السائلة إلى حالة
+
+17
+00:01:44,560 --> 00:01:48,440
+صلبة، ثم بيرجع مرة تانية إلى الحالة السائلة once
+
+18
+00:01:48,440 --> 00:01:53,240
+enter the blood vessels خارج ال blood vessels،
+
+19
+00:01:53,240 --> 00:01:57,140
+خارج ال blood vessels؟ لأ، لما بطلع، بيصير في
+
+20
+00:01:57,140 --> 00:02:01,300
+blood leakage، بطلع بره لوعده، ماببقى يتسرق ويتجمع
+
+21
+00:02:01,300 --> 00:02:04,300
+ويتجمع ويتجمع، لغاية ما يعمل hematoma، وبالتالي
+
+22
+00:02:04,300 --> 00:02:07,200
+بتحول إلى solid، وهذا بتعمل pressure على ال blood
+
+23
+00:02:07,200 --> 00:02:12,410
+vesselsطبعا عشان نمنع هذا بدوا يصير تجلط و نسد
+
+24
+00:02:12,410 --> 00:02:16,650
+الوعاء الدموي و قولنا بيتكون two plug واحدة
+
+25
+00:02:16,650 --> 00:02:19,170
+بيسموها primary و hemostatic plug و secondary
+
+26
+00:02:19,170 --> 00:02:27,050
+محصلة هذا الكلام تحويل الدم من سائل إلى سلطة طبعا
+
+27
+00:02:27,050 --> 00:02:31,490
+بعد ذلك يرجع عملية الدم و سريانه في الوعاء الدموي
+
+28
+00:02:31,490 --> 00:02:35,670
+as a fluid portion يبقى ال function of hemostasis
+
+29
+00:02:35,670 --> 00:02:42,630
+بتشمل أربع نقطةTesting of bleeding نمرة كنين
+
+30
+00:02:42,630 --> 00:02:48,150
+Keeping the blood in its fluidity status نمرة
+
+31
+00:02:48,150 --> 00:02:54,530
+تلاتة Repairing and reestablishingالدم يتجلط من
+
+32
+00:02:54,530 --> 00:02:58,150
+خلال الوعاء الدموي لما برجع الدم مرة تانية على
+
+33
+00:02:58,150 --> 00:03:04,250
+الوعاء الدموي نحن نأكد أن الدم متجلط لأنه طول ما
+
+34
+00:03:04,250 --> 00:03:09,270
+هو ماشي في الوعاء الدموي و لا يجب أن يتجلط مش لازم
+
+35
+00:03:09,270 --> 00:03:13,990
+يتجلط مش لازم يتجلط إذا كان ال blood vessels
+
+36
+00:03:13,990 --> 00:03:20,910
+healthy or intact نمرا أربعة بيصير في removing بعد
+
+37
+00:03:20,910 --> 00:03:26,270
+ذلكللـ Hemostatic blood وبالتالي بيصير فيه
+
+38
+00:03:26,270 --> 00:03:33,090
+repairing و healing لل blood vessels وفسروها
+
+39
+00:03:33,090 --> 00:03:37,970
+تلت مراحل أساسية سمنها Primary وSecondary
+
+40
+00:03:37,970 --> 00:03:45,170
+وTertiary Hemostatic process ماشي؟primary بيتكون
+
+41
+00:03:45,170 --> 00:03:48,950
+من خلالها ال primary hemostatic blood ثم ال
+
+42
+00:03:48,950 --> 00:03:52,750
+secondary بيتكون من خلالها secondary hemostatic
+
+43
+00:03:52,750 --> 00:03:58,430
+blood وبتتكون ال solid blood ثم بعد ذلك بنذيب
+
+44
+00:03:58,430 --> 00:04:01,650
+الزوائد من خلال ال fibromatic process وبالتالي
+
+45
+00:04:01,650 --> 00:04:08,930
+بيصير في removing ال excess of clot
+
+46
+00:04:12,650 --> 00:04:18,070
+طبعا إذا كان أي خلل صار في ذلك معناته صار فيه خلل
+
+47
+00:04:18,070 --> 00:04:22,710
+في ال balance وقولنا ال balance هو عبارة عن
+
+48
+00:04:22,710 --> 00:04:28,350
+constant condition internal condition في داخل
+
+49
+00:04:28,350 --> 00:04:32,830
+الجسم ما بين شغلتين هو عبارة عن balance ما بين
+
+50
+00:04:32,830 --> 00:04:37,470
+شغلتين bleeding constant أي خلل إما هيحدث bleeding
+
+51
+00:04:37,470 --> 00:04:42,970
+و إما هيحدث air through processو طبعا زي ما انتوا
+
+52
+00:04:42,970 --> 00:04:48,210
+شايفين الصورة بتؤكد انه في ميزان و الميزان هذا
+
+53
+00:04:48,210 --> 00:04:53,930
+توازن موجود بين ال bleeding و بين ال thrombosis
+
+54
+00:04:53,930 --> 00:04:58,370
+and without this balance the individual may
+
+55
+00:04:58,370 --> 00:05:02,550
+experience either thrombosis or bleeding طبعا ال
+
+56
+00:05:02,550 --> 00:05:07,230
+bleeding بيحدث لما بيحدث ال bleeding بيعني انه صار
+
+57
+00:05:07,230 --> 00:05:13,020
+في اما poor clot formationor excessive fibrolysis
+
+58
+00:05:13,020 --> 00:05:18,720
+إما poor clot formation الجلطة اللي تكونت ما تكونت
+
+59
+00:05:18,720 --> 00:05:25,500
+صح تكونت ضعيفة أو تكونت بطيئة or excessive
+
+60
+00:05:25,500 --> 00:05:30,180
+fibrolysis لما جينا ندوب ال excess of clot دوّبنا
+
+61
+00:05:30,180 --> 00:05:35,670
+بزيادة وبالتالي صار في bleedingأو ممكن يصير
+
+62
+00:05:35,670 --> 00:05:40,750
+ثرمبوسس، وثرمبوسس بيصير إذا كان فيه uncontrolled
+
+63
+00:05:40,750 --> 00:05:48,070
+formation للثرمبل in the vascular system and this
+
+64
+00:05:48,070 --> 00:05:53,250
+will occlude، أُكلود من الـocclusion بمعنى انسداد،
+
+65
+00:05:53,250 --> 00:05:58,790
+أُكلود the blood flow
+
+66
+00:06:00,890 --> 00:06:04,470
+وبالتالي بيصير فيه ischemia أو بيسموها debrieving
+
+67
+00:06:04,470 --> 00:06:09,410
+of oxygen supply لأن ال blood إيش وظيفته الأساسية
+
+68
+00:06:09,410 --> 00:06:13,990
+وبالتالي بيصير فيه ischemia وإذا صار فيه ischemia
+
+69
+00:06:13,990 --> 00:06:20,210
+بيصير فيه infarction بيصير في إيش؟ infarction طبعا
+
+70
+00:06:20,210 --> 00:06:24,130
+الكلام هذا ممكن يصير في
+
+71
+00:06:25,320 --> 00:06:29,020
+حالات مرضية متعددة على سجل مثال الـ bleeding بنشوف
+
+72
+00:06:29,020 --> 00:06:31,900
+في حالات الهموفيليا و بيسموا حالات ال bleeding
+
+73
+00:06:31,900 --> 00:06:38,180
+hypo-coagulable status شو بيسموها؟ hypo-coagulable
+
+74
+00:06:38,180 --> 00:06:43,440
+من coagulation status و بيصير في bleeding و أشهر
+
+75
+00:06:43,440 --> 00:06:46,700
+مثال على ذلك هو مرض الهموفيليا و كلكم بتعرفوا أن
+
+76
+00:06:46,700 --> 00:06:53,740
+الهموفيليا هو عبارة عن reduction or absenceof
+
+77
+00:06:53,740 --> 00:06:58,860
+coagulation factor 8 طبعا
+
+78
+00:06:58,860 --> 00:07:05,380
+كمان ممكن يصير في bleeding في حالات ال DIC و DIC
+
+79
+00:07:05,380 --> 00:07:09,340
+بتعرف في اختصار ل disseminated intravascular
+
+80
+00:07:09,340 --> 00:07:14,820
+coagulopathyهو في حالات ال liver disease او
+
+81
+00:07:14,820 --> 00:07:19,740
+failure لأنه في ال liver كمان بيصير فيه formation
+
+82
+00:07:19,740 --> 00:07:23,640
+and synthesis of coagulation factor وبالتالي يوم
+
+83
+00:07:23,640 --> 00:07:26,840
+ما يصير في liver failure يعني مافيش coagulation
+
+84
+00:07:26,840 --> 00:07:34,280
+factor and synthesis وهذه كلها بتعمل حالات امثلة
+
+85
+00:07:34,280 --> 00:07:37,880
+لحالات على ال bleeding ال
+
+86
+00:07:39,790 --> 00:07:45,430
+بالمقابل طبعا ال fibrolysis ال
+
+87
+00:07:45,430 --> 00:07:48,230
+coagulation ممكن يصير في حالات مرضية متعددة
+
+88
+00:07:48,230 --> 00:07:54,250
+بالاضافة إلى ذلك ال coagulation promotion بيصير و
+
+89
+00:07:54,250 --> 00:08:00,330
+في حالات visual injury that initiate fibrolysis in
+
+90
+00:08:00,330 --> 00:08:08,430
+a defect manner أوبصير فيه خلل في عملية التجلط عدم
+
+91
+00:08:08,430 --> 00:08:12,590
+حدوث عملية التجلط حدوثها بكميات كبيرة او in
+
+92
+00:08:12,590 --> 00:08:16,090
+advance فبصير في عملية ال thrombosis طبعا زي ما
+
+93
+00:08:16,090 --> 00:08:20,170
+اتفقنا بعد عملية ال thrombosis في fibrolysis و ال
+
+94
+00:08:20,170 --> 00:08:24,130
+fibrolysis بيتخلى لها عملية اللي هو tissue plasmid
+
+95
+00:08:24,130 --> 00:08:27,430
+activator
+
+96
+00:08:27,430 --> 00:08:34,000
+وهذا عبارة عن مادة بتعني بتنشطالـ Fibromytic
+
+97
+00:08:34,000 --> 00:08:37,320
+Process و هذه كلها عبارة عن المراحل اللي هنجيها ان
+
+98
+00:08:37,320 --> 00:08:42,920
+شاء الله بالتفصيل الممكن فنشوف
+
+99
+00:08:42,920 --> 00:08:49,560
+إيش دور ال Coagulation في ال Hemostasis طبعا ال
+
+100
+00:08:49,560 --> 00:08:57,560
+Coagulation هي عبارة عن عملية بيتم فيها سد
+
+101
+00:08:57,560 --> 00:09:02,520
+الجرح اللي صار في الوعاء الدموييعني بيصير فيه
+
+102
+00:09:02,520 --> 00:09:06,480
+blood formation ل blood vessel injury وبالتالي
+
+103
+00:09:06,480 --> 00:09:10,680
+بيصير فيه blood formation لل injured blood vessels
+
+104
+00:09:10,680 --> 00:09:17,800
+بيتخللها وجود عدة عوامل بيقوم بهذه العملية عدة
+
+105
+00:09:17,800 --> 00:09:21,780
+عوامل منها ال plasma protein و ال platelet و ال
+
+106
+00:09:21,780 --> 00:09:26,720
+calcium و عدة عوامل محصلة هذه العملية fiber and
+
+107
+00:09:26,720 --> 00:09:31,680
+clot formation وبالتالي فيه blood formationأيضًا
+
+108
+00:09:31,680 --> 00:09:36,180
+الـ Platelet هي هذه العملية تتعامل مع مصادر
+
+109
+00:09:36,180 --> 00:09:42,700
+الحرارة والتنين يكونوا الـ Clot Formation اللي
+
+110
+00:09:42,700 --> 00:09:48,180
+بنحكي عنهاهو ان من الحوامل .. من الحاجات الأساسية
+
+111
+00:09:48,180 --> 00:09:52,920
+يا شباب ان حوامل التجلد بتمشي في ال blood بتسير في
+
+112
+00:09:52,920 --> 00:09:57,620
+ال blood in their inert form in their inert form
+
+113
+00:09:57,620 --> 00:10:02,220
+لكن مطلوب منها ان once a blood vessel is injured
+
+114
+00:10:02,220 --> 00:10:07,000
+مطلوب منها to be active يعني لازم تكون موجودة في
+
+115
+00:10:07,000 --> 00:10:11,240
+البداية في الوضع اللي هي الطبيعي على .. بتكون
+
+116
+00:10:11,240 --> 00:10:14,460
+خاملة و يوم ما يسير فيه مزيع شو بتتحول؟
+
+117
+00:10:16,760 --> 00:10:21,860
+هذه العوامل هذه الـ platelet أو عوامل التجلد غالبا
+
+118
+00:10:21,860 --> 00:10:26,100
+هي عبارة عن enzyme و
+
+119
+00:10:26,100 --> 00:10:30,300
+معظم ال coordination factors are called serine
+
+120
+00:10:30,300 --> 00:10:39,900
+proteases و serine proteases بتعنيإن هؤلاء أنزين
+
+121
+00:10:39,900 --> 00:10:44,900
+يمتلكون أمينواسيد سيريني في مواقعهم الانزينية
+
+122
+00:10:44,900 --> 00:10:53,060
+ساموها سيريني بروتييز لأنها في سيرين أمينواسيد ويل
+
+123
+00:10:53,060 --> 00:11:02,620
+في مواقع الانزينية تبعها البروتييز باشي
+
+124
+00:11:02,620 --> 00:11:04,500
+نشوف ال mechanism of hemostasis
+
+125
+00:11:10,300 --> 00:11:14,820
+والميكانيزم كانت تالية يا شباب بدنا نعرف أنه في
+
+126
+00:11:14,820 --> 00:11:20,060
+وعاء دموي تعرض إلى مزعج ثم ستمت عمليات أو خطوات
+
+127
+00:11:20,060 --> 00:11:25,420
+تلت ذلك خطوات معينة هذه الخطوات أدت في النهاية إلى
+
+128
+00:11:25,420 --> 00:11:31,540
+إيه؟ إلى كما تكون الجفر لكن بدنا نحط في عيد اعتذار
+
+129
+00:11:31,540 --> 00:11:36,100
+أن الوعاء الدموي هذا مش وعاء خامل وإنما هو عبارة
+
+130
+00:11:36,100 --> 00:11:41,960
+عن خلايا حيةعندها صفات حيوية، من أهم صفات اللعاء
+
+131
+00:11:41,960 --> 00:11:46,840
+قدامه، أنه has physical and chemical، اللي هو
+
+132
+00:11:46,840 --> 00:11:55,260
+changes في حدوث المزع، بعد حدوث المزع، وأول حدث
+
+133
+00:11:55,260 --> 00:12:00,610
+بيتم بعد حدوث المزع، بيصير في vasoconstrictionبصير
+
+134
+00:12:00,610 --> 00:12:06,910
+فيها Vasoconstriction انقباض بأول خطوات ال
+
+135
+00:12:06,910 --> 00:12:11,430
+mechanism of hemostasis انه هذا الوعاء الدموي
+
+136
+00:12:11,430 --> 00:12:16,650
+بيتعرض او بيعمل Vasoconstriction و ال
+
+137
+00:12:16,650 --> 00:12:20,450
+Vasoconstriction يعني انقباض للوعاء الدموي هدفه
+
+138
+00:12:20,450 --> 00:12:26,930
+الأساسي انه نقلل من عملية او من ال volume of blood
+
+139
+00:12:27,320 --> 00:12:33,740
+في المنطقة المصابة .طبعا كل ما قلل كمية الدم في
+
+140
+00:12:33,740 --> 00:12:39,820
+منطقة الحدث، كل ما سهل التحكم فيه مظبوط، بيسهل
+
+141
+00:12:39,820 --> 00:12:44,920
+التحكم في هذه العملية، يعني أول خطوة بيصير في
+
+142
+00:12:44,920 --> 00:12:47,520
+Vasoconstriction، and this is usually under
+
+143
+00:12:47,520 --> 00:12:53,800
+neurochemical effect، وبيتم عملية اللي هو ال
+
+144
+00:12:53,800 --> 00:12:57,940
+Vasoconstriction، وبالتالي هدفها تقديل كمية الدم
+
+145
+00:12:57,940 --> 00:13:02,110
+اللي موجودة في هذا المنطقةالعادة التانية يا شباب
+
+146
+00:13:02,110 --> 00:13:06,630
+أنه بيصيط .. بي .. بتيجي ال platelet، ال platelet
+
+147
+00:13:06,630 --> 00:13:10,350
+بتخش على الخط و بيصير لها adherence and
+
+148
+00:13:10,350 --> 00:13:16,550
+aggregation و عشان تتخيلوا العملية بالظبط كلنا
+
+149
+00:13:16,550 --> 00:13:21,120
+بنعرف .. بدنا نتخيل رعاية دمه و فيه دمالوعي الدموي
+
+150
+00:13:21,120 --> 00:13:26,960
+في جلبه في الدم في الدم في cellular elements لأن
+
+151
+00:13:26,960 --> 00:13:30,180
+موضوعنا أساسي أننا نحكي عن ال platelets وهي عبارة
+
+152
+00:13:30,180 --> 00:13:34,060
+عن cellular elements cellular elements هي عبارة عن
+
+153
+00:13:34,060 --> 00:13:38,060
+خلايا وقت بيسيزوا وقت بيسيزوا platelets ال
+
+154
+00:13:38,060 --> 00:13:44,300
+platelets و الخلايا الأخرى بتمشي بتسير في الدم في
+
+155
+00:13:44,300 --> 00:13:50,840
+وسط الوعي الدموي ماتجيش على أطرافالـ Platelet هي
+
+156
+00:13:50,840 --> 00:13:55,060
+الوحيدة اللى ممكن تنزل إياه على الوعاء قدامه
+
+157
+00:13:55,060 --> 00:14:01,160
+والوعاء قدامه طول ما هو انت اكتشفها ال Platelet
+
+158
+00:14:01,160 --> 00:14:09,080
+بتمشي عليه دهرجة بتمشي عليه دهرجة بيشبهوها بال
+
+159
+00:14:09,080 --> 00:14:14,560
+ping pong ball movement بتعرفوا كرة بتنسى الطاولة
+
+160
+00:14:14,560 --> 00:14:20,610
+كيف بتمشي؟ بتمشي تنصب من واحد إلى التانىفالـ
+
+161
+00:14:20,610 --> 00:14:25,430
+Platelet لما تيجي بتنزل على الوعاء الدموي بيسللها
+
+162
+00:14:25,430 --> 00:14:30,210
+Repelling بتروح على الوسط وسط الوعاء الدموي ثم
+
+163
+00:14:30,210 --> 00:14:34,870
+بتنزل تاني على الوعاء الدموي فبيسللها Repelling
+
+164
+00:14:34,870 --> 00:14:39,090
+مرة تانية وال Repelling أمر طبيعي جدا لأنه في
+
+165
+00:14:39,090 --> 00:14:43,850
+Negative Charge في الجهتين صح؟ لازال في Negative
+
+166
+00:14:43,850 --> 00:14:50,990
+Charge في Repellingالوعاء الدموي على سطحه خلايا
+
+167
+00:14:50,990 --> 00:14:55,490
+ابيثيلية بتفرز
+
+168
+00:14:55,490 --> 00:14:59,050
+باستمرار بروستا سايكلين اللي بتحمل نيجاتيب اتشار
+
+169
+00:14:59,050 --> 00:15:05,790
+وبالتالي التنتين بيحملوا نيجاتيب اتشارفبصير في
+
+170
+00:15:05,790 --> 00:15:10,130
+continuous air continuous repelling يبقى بشبهوا ال
+
+171
+00:15:10,130 --> 00:15:14,310
+platelet اللي ماشية في الوعاء الدموي بشبهوا حركتها
+
+172
+00:15:14,310 --> 00:15:19,610
+بانها it rolls it rolling down على الوعاء الدموي
+
+173
+00:15:19,610 --> 00:15:24,750
+وبيشبهوها بال ping pong بال movement وبالتالي في
+
+174
+00:15:24,750 --> 00:15:28,470
+continuous repelling ليش للي platelet لكن once
+
+175
+00:15:28,470 --> 00:15:34,420
+blood vessel is injuredماتمصافي مازال يبطل فيه
+
+176
+00:15:34,420 --> 00:15:36,740
+negative charge على ال blood vessels وبالتالي ال
+
+177
+00:15:36,740 --> 00:15:40,520
+plate بتقاش بيصير اللي هي adherence بيصير اللي هي
+
+178
+00:15:40,520 --> 00:15:44,540
+adherence بيصير اللي هي adhesion على ال plate على
+
+179
+00:15:44,540 --> 00:15:49,610
+ال blood vessels فبأول خطوةالبلاد الهيموستاتيكية
+
+180
+00:15:49,610 --> 00:15:52,710
+تعمل في البرامج الهيموستاتيكية البرامج
+
+181
+00:15:52,710 --> 00:15:54,250
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+182
+00:15:54,250 --> 00:15:57,210
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+183
+00:15:57,210 --> 00:16:02,310
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+184
+00:16:02,310 --> 00:16:03,870
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+185
+00:16:03,870 --> 00:16:04,690
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+186
+00:16:04,690 --> 00:16:04,990
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+187
+00:16:04,990 --> 00:16:05,530
+الهيموستاكية البرامج الهيموستاكية البرامج
+
+188
+00:16:05,530 --> 00:16:11,650
+الهيموستاكية البرامج الهيموستاكية البرمن خلال ال
+
+189
+00:16:11,650 --> 00:16:15,590
+adherence و ال aggregation و بلا بلا لكنها still
+
+190
+00:16:15,590 --> 00:16:22,610
+هذه ال plug هشة و ضعيفةتحتاج إلى تقوى عشان هيك
+
+191
+00:16:22,610 --> 00:16:26,810
+الـSecondary Hemostatic Plug بيخش على الخط و بيخش
+
+192
+00:16:26,810 --> 00:16:29,630
+من خلال Coagulation Factors تتنشط الـCoagulation
+
+193
+00:16:29,630 --> 00:16:34,150
+Factors على سطح الـPlatelet يبقى الـPlatelet لما
+
+194
+00:16:34,150 --> 00:16:39,290
+إجت و لزجت على الوعاء الدموي شكلت سطح جديد هذا
+
+195
+00:16:39,290 --> 00:16:43,110
+السطح suitable for Coagulation Factor Activation
+
+196
+00:16:43,110 --> 00:16:46,470
+فتتنشط الـCoagulation Factor على سطح الـPlatelet و
+
+197
+00:16:46,470 --> 00:16:50,370
+بيصير فيه another plugهي الـ Secondary Hemostatic
+
+198
+00:16:50,370 --> 00:16:56,970
+Plug which enforce the Primary Hemostatic Plug أو
+
+199
+00:16:56,970 --> 00:17:01,570
+بيسموها Solid Plug تتكون
+
+200
+00:17:01,570 --> 00:17:09,190
+وبيقوها لكن السدادات اللي تكونت أو عملية البناء
+
+201
+00:17:09,190 --> 00:17:14,670
+اللي تمت هي عبارة عن عملية بناء عشوائية
+
+202
+00:17:17,300 --> 00:17:21,180
+في urgent process ايش urgent process؟ في حالة
+
+203
+00:17:21,180 --> 00:17:24,260
+عاجلة، ايش الحالة العاجلة؟ مزعج في الوعي الدموي،
+
+204
+00:17:24,260 --> 00:17:29,140
+سبب تسرط، فبالتالي الجسم automatically بيبني سدة
+
+205
+00:17:29,140 --> 00:17:34,180
+في هذا الوعي الدموي، المرحلة التي تلي بناء السدة
+
+206
+00:17:34,180 --> 00:17:41,360
+بيسموها fibrinolysis وهي عملية بناء .. عملية هدم
+
+207
+00:17:41,360 --> 00:17:52,190
+زوائد اللي صارت في ال ..Hemostatic Blood ما هي
+
+208
+00:17:52,190 --> 00:17:58,230
+Normal Hemostatic Component Normal Hemostatic
+
+209
+00:17:58,230 --> 00:18:07,510
+Component لأن Hemostatic Blood Hemostasis Normal
+
+210
+00:18:07,510 --> 00:18:11,850
+Blood Hemostatic Components تتكون من سبع عوامل سبع
+
+211
+00:18:11,850 --> 00:18:18,100
+عوامل بغض النظر عن موجودةالواحدة لكنها تتكون من
+
+212
+00:18:18,100 --> 00:18:23,940
+سبع عوامل نحددهم هم كالقاتل نمرة واحد blood
+
+213
+00:18:23,940 --> 00:18:31,900
+vessels نمرة اتنين platelet نمرة تلاتة coagulation
+
+214
+00:18:31,900 --> 00:18:40,540
+factor نمرة اربعة fibrolytic factor نمرة خمسة
+
+215
+00:18:40,540 --> 00:18:43,100
+complement
+
+216
+00:18:44,360 --> 00:18:53,040
+نمره 6 كاينين سيستم نمره 7 regulators for all
+
+217
+00:18:53,040 --> 00:19:00,020
+these system أكم واحد يعني سبعة عوامل أساسية
+
+218
+00:19:00,020 --> 00:19:07,480
+نعيدهم مرة تانية blood vessels نمره
+
+219
+00:19:07,480 --> 00:19:15,740
+2 platelet نمره 3 coagulation factorنمر أربعة،
+
+220
+00:19:15,740 --> 00:19:23,040
+Fibrelytic factor، نمر خمسة، Complement، نمر ستة،
+
+221
+00:19:23,040 --> 00:19:28,820
+Kinetic system، نمر سبعة، Regulators for all these
+
+222
+00:19:28,820 --> 00:19:36,280
+systems، Regulators or Controller for all these
+
+223
+00:19:36,280 --> 00:19:37,280
+systems
+
+224
+00:19:40,030 --> 00:19:44,790
+أولا، سنذهب، كما تشاهدون، إلى الـTissue Factors،
+
+225
+00:19:44,790 --> 00:19:52,830
+ثم الـTropocytic Factors، ثم الـHumoral Factors،
+
+226
+00:19:52,830 --> 00:19:57,130
+وهي الـPlasma Factors بمجموحة
+
+227
+00:20:00,300 --> 00:20:03,300
+ماشي يا شباب، هنتطلق إن شاء الله في محاضرات قادمة
+
+228
+00:20:03,300 --> 00:20:07,720
+لكل عامل من هذه العوامل بالتفصيل ودوره في الـ
+
+229
+00:20:07,720 --> 00:20:16,260
+Hemostasis ودوره في الـ Hemostatic Process ماشي؟
+
+230
+00:20:16,260 --> 00:20:21,380
+نجي الآن نحكي على ال effectiveness or failure of
+
+231
+00:20:21,380 --> 00:20:27,400
+Hemostatic Process لابد من وجود عواملبتؤثر في نجاح
+
+232
+00:20:27,400 --> 00:20:32,840
+أو فشل عملية الـ Anesthesia وإجراله إنه في ست
+
+233
+00:20:32,840 --> 00:20:38,820
+عوامل أساسية بتلعب دور كبير في نجاح أو فشل هذه
+
+234
+00:20:38,820 --> 00:20:45,140
+العملية أول هذه العوامل هو الـ Time and degree of
+
+235
+00:20:45,140 --> 00:20:51,640
+injury نوعها ودرجة الإصابة طبيعي كل ما
+
+236
+00:20:56,570 --> 00:21:01,890
+أكبر كل ما كان ال control على هذه الإصابة بتكون
+
+237
+00:21:01,890 --> 00:21:06,430
+صعبة وبالتالي ال process الهيموستاتيكي بتكون أصعب
+
+238
+00:21:06,430 --> 00:21:11,910
+نمرا اتنين ال size and ability of a blood vessel
+
+239
+00:21:11,910 --> 00:21:16,490
+to contractلأنه احنا قلنا من وظيفة normal function
+
+240
+00:21:16,490 --> 00:21:18,610
+أو blood vessel أنه أول حاجة بعملها
+
+241
+00:21:18,610 --> 00:21:22,410
+vasoconstriction، ماشي؟ طبعا ال vasoconstriction
+
+242
+00:21:22,410 --> 00:21:27,310
+هذا كلكم بتعرفه اللي بيتحكم في خلطة في ال Anatomy
+
+243
+00:21:27,310 --> 00:21:31,250
+أنه في عوامل كثيرة تتحكم في blood pressure و blood
+
+244
+00:21:31,250 --> 00:21:37,430
+flow، صح؟ حناتطرنا خلها إن شاء الله جداقدرة الوعاق
+
+245
+00:21:37,430 --> 00:21:41,110
+قدامه على انه يقوم بالcontract مهم جدا، طب هو في
+
+246
+00:21:41,110 --> 00:21:44,210
+قوية دموية لا تستطيع تقوم بالcontract نعم، او تقوم
+
+247
+00:21:44,210 --> 00:21:46,790
+بالcontract ببطء، او تقوم بالcontract بشكل مفيد
+
+248
+00:21:47,820 --> 00:21:51,140
+طبعاً كل ما الإنسان كبرت كل ما صار كان .. كان فيه
+
+249
+00:21:51,140 --> 00:21:54,380
+atherosclerotic blood vessels مش راح يقدر يعمل
+
+250
+00:21:54,380 --> 00:21:58,480
+contraction زي الخلق ماشي؟ لأنه كل ما صار فيه
+
+251
+00:21:58,480 --> 00:22:02,560
+atherosclerosis في ال blood vessels كل ما صار more
+
+252
+00:22:02,560 --> 00:22:07,340
+solid و كل ما قلت مروده ال elasticity تبعته و كل
+
+253
+00:22:07,340 --> 00:22:11,020
+ما قلت الإياش ال contractility of the blood
+
+254
+00:22:11,020 --> 00:22:14,860
+vessels و احنا قلنا أول خطوة من خطوات ال
+
+255
+00:22:14,860 --> 00:22:20,570
+hemostasis أنه يصير فيه إياشنبرة ثانية pressure
+
+256
+00:22:20,570 --> 00:22:23,170
+within blood vessels كل ما زاد pressure كل ما كانت
+
+257
+00:22:23,170 --> 00:22:28,770
+العملية أسحب، صح؟ and of course the ceramic tissue
+
+258
+00:22:28,770 --> 00:22:35,990
+pressure نمرة أربعة availability and activity of
+
+259
+00:22:35,990 --> 00:22:40,250
+platelets، من هنا نحكي على أياش؟ على عوامل تجلط،
+
+260
+00:22:40,250 --> 00:22:43,090
+platelets وما ينطبق على platelets ينطبق على
+
+261
+00:22:43,090 --> 00:22:49,840
+calculation factor، صح؟نبغى خمسة او ستة ال absence
+
+262
+00:22:49,840 --> 00:22:55,800
+of inhibitors اتفقنا على انه لأ في عامل سابع مجبوط
+
+263
+00:22:55,800 --> 00:22:59,920
+قولنا ال controller و ال regulators طب مافيش
+
+264
+00:22:59,920 --> 00:23:06,380
+controller factors يعني مابيصير bleeding على طول
+
+265
+00:23:06,380 --> 00:23:09,660
+يعني مابيصير clotting على طول صح؟ و هذه طبعا
+
+266
+00:23:09,660 --> 00:23:17,030
+عمليات مرضيةإن بس فيه ست عوامل أساسية بتأثر في
+
+267
+00:23:17,030 --> 00:23:23,390
+نجاح أو فشل عملية الـ Mastersلنبدأ نشوف، هذه طبعا
+
+268
+00:23:23,390 --> 00:23:29,230
+slide بتؤكد على أن الـ hemostatic component has to
+
+269
+00:23:29,230 --> 00:23:32,670
+be present in blood vessels in their inert form
+
+270
+00:23:32,670 --> 00:23:37,670
+متفقين في الوضع الطبيعي، كل هذه العوامل لازم تكون
+
+271
+00:23:37,670 --> 00:23:41,430
+خاملة، لازم تكون إيه؟ خاملة، لأن إذا كانت active
+
+272
+00:23:41,430 --> 00:23:44,970
+على طول، في clot formation على طول، صح؟ فبالتالي
+
+273
+00:23:44,970 --> 00:23:50,120
+لابد من أنها تكون خاملةهو انه مطلوب منها following
+
+274
+00:23:50,120 --> 00:23:56,280
+injury بعد الإصابة تتنشر بعد الإصابة بعد ال injury
+
+275
+00:23:56,280 --> 00:24:02,780
+انه يصير في optimal functioning or activation هذه
+
+276
+00:24:02,780 --> 00:24:06,280
+صورة ل blood vessels هذه صورة ل blood vessels زي
+
+277
+00:24:06,280 --> 00:24:09,760
+ما انت شايفين blood vessels is lining is lining by
+
+278
+00:24:09,760 --> 00:24:14,320
+عياش by normal epithelial cells normal epithelial
+
+279
+00:24:14,320 --> 00:24:24,320
+cellsو بيغلف هذه الطبقة وهي طبقة داخلية بتفصل الدم
+
+280
+00:24:24,320 --> 00:24:30,260
+عن باقي الوعاء الدموي Normal
+
+281
+00:24:30,260 --> 00:24:33,820
+epithelial cells مهم جدا و اللي هو ضايف متعدد احنا
+
+282
+00:24:33,820 --> 00:24:41,580
+بتضرر ناخدها الآن بيحيط بهذه الطبقة طبقتين و اننا
+
+283
+00:24:41,580 --> 00:24:45,810
+هنجي لل structure of blood vesselsماشي يبقى فيه
+
+284
+00:24:45,810 --> 00:24:50,110
+endothelial cells هي مبطن عن الوعاء الدموي وفي
+
+285
+00:24:50,110 --> 00:24:55,870
+طبقتين وراها بيسموها subendothelial layer بيكونوا
+
+286
+00:24:55,870 --> 00:25:03,230
+ما يسمى بال subendothelial cells or layers و طول
+
+287
+00:25:03,230 --> 00:25:06,630
+ما الوعاء الدموي فيه normal blood normal بيكون فيه
+
+288
+00:25:06,630 --> 00:25:09,310
+normal blood flow مظبوط؟
+
+289
+00:25:10,920 --> 00:25:14,660
+هنشوف الآن ان شاء الله ال structure طبعا هذه صورة
+
+290
+00:25:14,660 --> 00:25:18,160
+أخرى بتبين لنا انه فيه صار مزع في الوعاء الدمو
+
+291
+00:25:18,160 --> 00:25:22,540
+يهدهو وزع مزع في الوعاء الدمو وأول ما صار فيه
+
+292
+00:25:22,540 --> 00:25:29,420
+injury صار فيه platelet أدهيرة تدهية
+
+293
+00:25:29,420 --> 00:25:34,480
+عملت جلطة أو سكرت الوعاء المزع سكرته الموعق المزع
+
+294
+00:25:34,480 --> 00:25:38,680
+وزي ما تلاحظين اللذي اشترك في تكوين هذه العملية
+
+295
+00:25:38,680 --> 00:25:50,140
+شغلتينThrombocytes and Coagulation طبعا
+
+296
+00:25:50,140 --> 00:25:53,380
+احنا سكرنا المزع اللي صار وبالتالي رجعنا الواحد
+
+297
+00:25:53,380 --> 00:26:02,040
+دموي لها Normal blood flow طبعا
+
+298
+00:26:02,040 --> 00:26:10,860
+هذا بيقودنا اليها وبيذكرنا بمقولة virtueأو ما يسمى
+
+299
+00:26:10,860 --> 00:26:17,080
+بالـ Virtuo Law Virtuo هذا عبارة عن عالم كان
+
+300
+00:26:17,080 --> 00:26:25,900
+موجود في الـ 1640 تقريبا و جال إنه عملية الـ
+
+301
+00:26:25,900 --> 00:26:34,120
+Hemostasis normally بتتأثر بتلت حاجات أساسية تلاتة
+
+302
+00:26:34,120 --> 00:26:36,320
+different components
+
+303
+00:26:38,840 --> 00:26:43,840
+ماشي بيسمى نظريته virtue theory or law أو بيسموها
+
+304
+00:26:43,840 --> 00:26:49,760
+triad، triad جاي من ثلاثة، ثلاثي،
+
+305
+00:26:49,760 --> 00:26:54,140
+ثلاثي virtue، ايش بيقول ثلاثي virtue؟ بيقول انه في
+
+306
+00:26:54,140 --> 00:26:56,920
+تلاتة different component، اول component سماه ده
+
+307
+00:26:56,920 --> 00:27:02,820
+extravascular componentوال extravascular يعني
+
+308
+00:27:02,820 --> 00:27:09,640
+الطبقة الخارجية المغلفة لمن؟ لل endothelial cells
+
+309
+00:27:09,640 --> 00:27:14,960
+للطبقة الداخلية مهمة هذه طبقة مهمة جدا لإن فيها
+
+310
+00:27:14,960 --> 00:27:19,760
+smooth muscle و فيها كلها gene non elastic fibers
+
+311
+00:27:19,760 --> 00:27:22,700
+شو بتعمل هذه؟ هي اللتي
+
+312
+00:27:28,000 --> 00:27:32,580
+وبالتالي تتحكم في ال blood flow و blood pressure
+
+313
+00:27:32,580 --> 00:27:39,420
+within blood vessels ماشي يا شباب؟ يبقى هي it
+
+314
+00:27:39,420 --> 00:27:45,140
+provides the back pressure وقتين وين؟ in the
+
+315
+00:27:45,140 --> 00:27:48,460
+injured .. on the injured blood vessels يوم ما
+
+316
+00:27:48,460 --> 00:27:53,340
+يصير في المذبح، مين اللي داعم؟طبقة الخارجية طبقات
+
+317
+00:27:53,340 --> 00:27:57,320
+الخارجية طب لو كانت هذه non healthy and cannot
+
+318
+00:27:57,320 --> 00:28:04,360
+contract مش بيصير في توسع الفتحة مع المزيد توسع
+
+319
+00:28:04,360 --> 00:28:11,220
+الفتحة للا توسع طبقة
+
+320
+00:28:11,220 --> 00:28:14,000
+التانية او ال component التاني وهو ال bascular
+
+321
+00:28:14,000 --> 00:28:18,950
+componentوالـ vascular component يعني الوعاء الدمو
+
+322
+00:28:18,950 --> 00:28:24,790
+itself is it healthy is it intact or not وهذا
+
+323
+00:28:24,790 --> 00:28:28,470
+بيعتمد على size of the smooth muscles a presence
+
+324
+00:28:28,470 --> 00:28:34,330
+and integrity of the vascular or blood vessels
+
+325
+00:28:34,330 --> 00:28:39,390
+integrity of the blood vessels integrity of blood
+
+326
+00:28:39,390 --> 00:28:43,270
+vessels بتعتمد على ال integrity of endothelial
+
+327
+00:28:43,270 --> 00:28:44,650
+cells lining the
+
+328
+00:28:48,270 --> 00:28:55,030
+بالنسبة لهذا العمل التاني وهو عبارة عن وظائف عدة
+
+329
+00:28:55,030 --> 00:28:59,730
+لأنها عبارة عن Multifunctional Layer سنتعرف عليها
+
+330
+00:28:59,730 --> 00:29:06,010
+ثم Intramuscular Component وهذا يحكي على مكونات
+
+331
+00:29:06,010 --> 00:29:10,950
+الدم يعني أنا بقول عشان يحصل في جلطة لازم يكون في
+
+332
+00:29:10,950 --> 00:29:15,260
+Platelet Coagulation Factorمظبوط؟ طب لو مافيش في
+
+333
+00:29:15,260 --> 00:29:18,600
+الدم platelet او coagulation factor مش هيصير
+
+334
+00:29:18,600 --> 00:29:23,700
+فبالتالي هي عامل مهم من عوامل ال hemostesis يبقى
+
+335
+00:29:23,700 --> 00:29:28,060
+تلت عوامل حكى عنهم virtue الأولاني هو عبارة عن
+
+336
+00:29:28,060 --> 00:29:32,680
+extravascular component والتاني هو عبارة عن
+
+337
+00:29:32,680 --> 00:29:37,500
+vascular والتالت هو عبارة عن intravascular وهي ال
+
+338
+00:29:37,500 --> 00:29:42,460
+triad موجود أي هو بيحكي على three component
+
+339
+00:29:44,010 --> 00:29:45,030
+تغيّر عملية عملية عملية عملية عملية عملية عملية
+
+340
+00:29:45,030 --> 00:29:50,210
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+341
+00:29:50,210 --> 00:29:53,650
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+342
+00:29:53,650 --> 00:29:53,890
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+343
+00:29:53,890 --> 00:29:53,910
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+344
+00:29:53,910 --> 00:29:54,110
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+345
+00:29:54,110 --> 00:29:54,370
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+346
+00:29:54,370 --> 00:29:54,370
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+347
+00:29:54,370 --> 00:29:54,690
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+348
+00:29:54,690 --> 00:30:01,970
+عملية عملية
+
+349
+00:30:05,150 --> 00:30:10,630
+متفقين على إنه عملية الهيموستاسيس بيتتم على تلت
+
+350
+00:30:10,630 --> 00:30:13,210
+مراحل أساسية، اتفقنا على إنه فيه Primary
+
+351
+00:30:13,210 --> 00:30:16,650
+Hemostatic، Plague Formation، ثم Secondary
+
+352
+00:30:16,650 --> 00:30:20,110
+Hemostatic و Plague Formation، ثم Fibrinolysis،
+
+353
+00:30:20,110 --> 00:30:24,590
+صح؟ طبعا بيسموا ال Fibrinolysis tertiary، ل
+
+354
+00:30:24,590 --> 00:30:27,570
+Primary و Secondary، و ليش؟ و tertiary
+
+355
+00:30:36,200 --> 00:30:43,020
+تفاصيلة نبدأ بالـ Primary Hemostasis واتفقنا على
+
+356
+00:30:43,020 --> 00:30:47,360
+إنه it involves الـ platelets and blood vessels
+
+357
+00:30:47,360 --> 00:30:52,760
+يبقى ال function of blood vessels and platelets هم
+
+358
+00:30:52,760 --> 00:30:58,240
+اللي بيقوموا بهذه العملية ماشي؟ platelets or
+
+359
+00:30:59,650 --> 00:31:04,710
+Indothelial platelet phase بيسموها Indothelial
+
+360
+00:31:04,710 --> 00:31:07,970
+platelet phase لإنه بيصير فيه interaction ما بين
+
+361
+00:31:07,970 --> 00:31:12,410
+ال platelet و ال Indothelial في هذه المرحلة و طبعا
+
+362
+00:31:12,410 --> 00:31:17,250
+بيصير فيه platelet adhesion و aggregation و بتتكون
+
+363
+00:31:17,250 --> 00:31:21,510
+زي ما اتفقنا ل primary hemostatic blood و هذه
+
+364
+00:31:21,510 --> 00:31:29,360
+العملية بتاخد من 3 إلى 5 دقائق من 3 إلى 5دقائق
+
+365
+00:31:29,360 --> 00:31:36,920
+بياليها secondary hemostasis وتكوين ما يسمى بال
+
+366
+00:31:36,920 --> 00:31:43,540
+solid plug أو secondary hemostatic plug وبرضه هذه
+
+367
+00:31:43,540 --> 00:31:49,340
+العملية بتاخد من خمسة إلى عشر دقائق من خمسة إلى
+
+368
+00:31:49,340 --> 00:31:55,060
+عشر دقائق يتكون من خلالها ال fibrin clot أو
+
+369
+00:31:55,060 --> 00:32:01,670
+secondary hemostatic clotأو الـ Solid Blood
+
+370
+00:32:01,670 --> 00:32:08,030
+-Auriculot which is usually reinforced بتقوي
+
+371
+00:32:08,030 --> 00:32:13,790
+السدادة الهشة اللي هي الـ Primary Hemostatic Blood
+
+372
+00:32:13,790 --> 00:32:18,810
+بعد ذلك طبعا بيصير عملية الـ Fibrinolysis وهي
+
+373
+00:32:18,810 --> 00:32:28,060
+الترشري وهذه بتاخد من 48 إلى 72 ساعةبيصير في عملية
+
+374
+00:32:28,060 --> 00:32:34,360
+repairing and healing للـ blood vessels وبالتالي
+
+375
+00:32:34,360 --> 00:32:40,420
+برجع ال blood vessels intact and smooth وبالتالي
+
+376
+00:32:40,420 --> 00:32:47,540
+بيصير normal blood vessels ماشي يا شباب نحكي في ال
+
+377
+00:32:47,540 --> 00:32:52,840
+primary hemostasis اتفقنا على انه بيصير في it's a
+
+378
+00:32:52,840 --> 00:32:55,020
+result of three way interaction between
+
+379
+00:32:57,660 --> 00:32:59,860
+الـ blood vessel أو الـ vascular wall و الـ
+
+380
+00:32:59,860 --> 00:33:05,860
+platelet و ال plasma coagulation ما يحفظ هذه
+
+381
+00:33:05,860 --> 00:33:13,620
+العملية حاجتين أمر واحد small injury in blood
+
+382
+00:33:13,620 --> 00:33:19,880
+vessels و كتير بيصيرفي كل لحظة من لحظات حياتنا
+
+383
+00:33:19,880 --> 00:33:25,280
+ممكن يصير injured blood vessels وبالتالي بيصير فيه
+
+384
+00:33:25,280 --> 00:33:30,610
+normal hemostasis وبيسكرها الجراحةالحاجة التانية
+
+385
+00:33:30,610 --> 00:33:34,230
+يا شباب، إذا صار فيه damage للـ blood، للـ
+
+386
+00:33:34,230 --> 00:33:38,230
+endothelial cells، damage للـ endothelial cells
+
+387
+00:33:38,230 --> 00:33:41,830
+المبطنة للوعاء الدموي، يوم ما يصير فيه damage
+
+388
+00:33:41,830 --> 00:33:46,170
+بيسموها اللي هو .. بيصير فيه حاجة بيسموها plasma
+
+389
+00:33:46,170 --> 00:33:49,510
+coordination factor disquamation، بتطلع من الـ
+
+390
+00:33:49,510 --> 00:33:52,970
+endothelial cell عوامل تجلط،
+
+391
+00:33:56,050 --> 00:33:58,830
+طبعا من أشهر هذه العوامل و هو ال brand factor اللي
+
+392
+00:33:58,830 --> 00:34:05,350
+هنحكي عليه الآن ان شاء الله وبالتالي
+
+393
+00:34:05,350 --> 00:34:12,610
+ال primary hemostasis بيتضمن أربع نقاط أساسية
+
+394
+00:34:12,610 --> 00:34:20,530
+بتشمل نشاط أو وظيفة لل blood vessels و هي ال
+
+395
+00:34:20,530 --> 00:34:24,310
+vasoconstriction ثم وظيفة
+
+396
+00:34:27,240 --> 00:34:32,960
+الـ Platelet بتمر أثناء نشاطها في تلت وظائف أساسية
+
+397
+00:34:32,960 --> 00:34:37,780
+تعمل أول شي Adhesion ثم Aggregation ويوم ما يصير
+
+398
+00:34:37,780 --> 00:34:43,000
+في Adhesion و Aggregation تتنشط لـ Platelet فبتعمل
+
+399
+00:34:43,000 --> 00:34:47,340
+Degranulation شو بتعمل؟ Degranulation فبتعمل ما
+
+400
+00:34:47,340 --> 00:34:51,420
+يسمى بال Platelet Secretion يبقى المراحل هي
+
+401
+00:34:51,420 --> 00:34:56,910
+Adhesionand aggregation ثم degranulation وطبعا
+
+402
+00:34:56,910 --> 00:35:04,790
+بنوع من التفصيل في خطوة محزوفة هان هي الخطوة
+
+403
+00:35:04,790 --> 00:35:07,490
+التانية انه بعد ما يصير فيه platelet adhesion
+
+404
+00:35:07,490 --> 00:35:11,150
+بيصير فيه change in shape بيتغير شكل الخلية يعني
+
+405
+00:35:11,150 --> 00:35:16,690
+ايه خلية؟ ال platelet بيتغير شكلها وبالتالي بيصير
+
+406
+00:35:16,690 --> 00:35:19,370
+فيه change in shape ثم platelet aggregation and
+
+407
+00:35:19,370 --> 00:35:27,580
+platelet secretionماشي يا شبان Platelet
+
+408
+00:35:27,580 --> 00:35:32,880
+secretion يعني فرز ال .. اه بتفرز ماء محتوياتها ..
+
+409
+00:35:32,880 --> 00:35:35,740
+محتوياتها عندنا هنشوف ال structure لما نيجي لل
+
+410
+00:35:35,740 --> 00:35:38,740
+Platelet او Platelet و هنعرف انه في نوعين من ال
+
+411
+00:35:38,740 --> 00:35:43,160
+granules موجود فيها و كلهم بيحتوي على enzymes و
+
+412
+00:35:43,160 --> 00:35:47,100
+coordination factors و عوامل متعددة اخرى
+
+413
+00:35:50,770 --> 00:35:56,010
+ماشي يا شباب طب نبدأ الآن احنا هي كبنقول قدّمنا لل
+
+414
+00:35:56,010 --> 00:36:01,510
+Hemostatic Process حكينا في المراحل المختلفة حكينا
+
+415
+00:36:01,510 --> 00:36:08,190
+في العوامل المختلفة لل Hemostasis ثم حكينا في
+
+416
+00:36:08,190 --> 00:36:12,890
+عوامل نجاح وفشل هذه العملية العوامل التي تؤثر فيها
+
+417
+00:36:15,030 --> 00:36:18,790
+بدنا نبدأ الآن نحكي في عوام ال component
+
+418
+00:36:18,790 --> 00:36:21,210
+hemostatic component واحد واحد hemostatic
+
+419
+00:36:21,210 --> 00:36:25,070
+component واحد واحد وقلنا أول هذه ال hemostatic
+
+420
+00:36:25,070 --> 00:36:29,350
+component هو إيش blood vessels هو إيش blood
+
+421
+00:36:29,350 --> 00:36:32,950
+vessels عشان هيك بدنا نشوف دور ال blood vessels في
+
+422
+00:36:32,950 --> 00:36:36,790
+ال hemostasis بشكل عام طبعا كلكم بتعرفوا الدورة
+
+423
+00:36:36,790 --> 00:36:42,030
+الدموية بتعرفوا أن الدم يمشي في أوعية دموية فصلوها
+
+424
+00:36:42,030 --> 00:36:43,730
+إلى arteries
+
+425
+00:36:48,350 --> 00:36:51,490
+تعرف ان الدورة الدموية وظيفة الدم بيطلع من القلب
+
+426
+00:36:51,490 --> 00:36:56,050
+وعال رياتين بيحمل ال oxygen هاشي ثم بنتقل الى
+
+427
+00:36:56,050 --> 00:37:00,830
+tissue و هناك بيوزع ال oxygen و برجع تاني حامل
+
+428
+00:37:00,830 --> 00:37:03,770
+ثاني اكسيد الكربون مرة تانية على القلب ثم الرياتين
+
+429
+00:37:03,770 --> 00:37:10,570
+ثم بيصيرله oxygenation ثم ال tissue وواها كذا يبقى
+
+430
+00:37:10,570 --> 00:37:15,850
+بيمشي في أوعية دموية مفصلة كارتي و فيه و هاش و كده
+
+431
+00:37:16,630 --> 00:37:21,810
+الـ hemostasis mainly بيصير في ال arteries و ال
+
+432
+00:37:21,810 --> 00:37:31,690
+vein arteries و vein عشان و هذه الأوعيه الدموية زي
+
+433
+00:37:31,690 --> 00:37:36,370
+ما قلنا لازم نضمن في هذه الأوعيه الدموية تصير ..
+
+434
+00:37:36,370 --> 00:37:40,750
+to occur optimal hemostatic process لازم يصير في
+
+435
+00:37:40,750 --> 00:37:42,890
+normal contraction
+
+436
+00:37:44,590 --> 00:37:47,270
+لأن من وظيفة الواعي الدموي هو الوظيفة انه بعمل
+
+437
+00:37:47,270 --> 00:37:51,810
+narrowing or contraction لل blood vessels او
+
+438
+00:37:51,810 --> 00:37:57,660
+vasoconstrictionوVasodilatation يبقى بيعمل لازم
+
+439
+00:37:57,660 --> 00:38:01,420
+يكون فيه Normal function للـ blood vessels أول
+
+440
+00:38:01,420 --> 00:38:05,100
+حاجة بيعملها هو Vasoconstriction وVasodilatation
+
+441
+00:38:05,100 --> 00:38:08,740
+وقولنا هدول العمليتين continuous Vasoconstriction
+
+442
+00:38:08,740 --> 00:38:12,300
+وVasodilatation usually control blood flow rate
+
+443
+00:38:12,300 --> 00:38:15,920
+سرعيان الدم سرعة سرعيان الدم في الوعي الدموي and
+
+444
+00:38:15,920 --> 00:38:22,600
+blood pressure and blood pressure هذه حاجة الحاجة
+
+445
+00:38:22,600 --> 00:38:26,410
+التانيةالواضح هو أن هذا الشخص يفرس الكثير من
+
+446
+00:38:26,410 --> 00:38:32,150
+المادات ويمكنه إطلاق الكثير من المادات، من أين؟ من
+
+447
+00:38:32,150 --> 00:38:36,590
+الـendothelial layer ومن الـsubendothelial layer،
+
+448
+00:38:36,590 --> 00:38:42,730
+ماشي؟ ماذا تفعل؟ أيضًا تشارك بالطبية الطبيعية
+
+449
+00:38:42,730 --> 00:38:49,730
+وتمنع الاضطراب في التطبيق اللوحي، ماشي؟ بطبق
+
+450
+00:38:49,730 --> 00:38:55,740
+باستمرارإن يكون فيه Normal Blood Flowوالـ Normal
+
+451
+00:38:55,740 --> 00:38:58,580
+Blood Vessels أو الـ Healthy Blood Vessels أو الـ
+
+452
+00:38:58,580 --> 00:39:02,500
+Intact Blood Vessels فيه Prevention .. Continuous
+
+453
+00:39:02,500 --> 00:39:06,180
+Prevention للياش؟ لـ Clot Formation دائما الدم
+
+454
+00:39:06,180 --> 00:39:12,320
+ممشي بصفة سائلة ممشي بيهاش؟ بصفة سائلة ماشي؟ مين
+
+455
+00:39:12,320 --> 00:39:15,820
+بيساعد في ال fluidity continuous fluidity of the
+
+456
+00:39:15,820 --> 00:39:18,960
+blood؟ لازم يكون فيه Normal Blood Vessels بيفرز
+
+457
+00:39:18,960 --> 00:39:24,490
+باستمرار مواد بتحافظ على ال fluidityof the blood
+
+458
+00:39:24,490 --> 00:39:29,750
+vessels مما يتكوّن لـ blood vessels كانوا بيتكوّن
+
+459
+00:39:29,750 --> 00:39:35,130
+من تلاتة layers، تلت طبقات، خطوف الاناطومية ده،
+
+460
+00:39:35,130 --> 00:39:43,330
+تلت طبقات، معقول، تلت طبقات، طبقة الأولانية،
+
+461
+00:39:43,330 --> 00:39:52,390
+بيسموها Tunica Intima، Tunica Intimaماشي تونيكا
+
+462
+00:39:52,390 --> 00:39:57,310
+بمعنى طبقة layer Intima هي الطبقة الملامسة لل
+
+463
+00:39:57,310 --> 00:40:05,010
+blood ملامسة لمين للدم و غالبا بتتكون من ال
+
+464
+00:40:05,010 --> 00:40:11,170
+endothelial layer وهذه
+
+465
+00:40:11,170 --> 00:40:14,950
+ال layer هي عبارة عن thin layer زي ما قلنا بتفصل
+
+466
+00:40:14,950 --> 00:40:22,560
+الدمعن باقي الوعاء الدموي لأنه هي الطبق الملامس
+
+467
+00:40:22,560 --> 00:40:28,040
+على مين وهذه أهم طبقة طبعا كله مهم بس هذه مهمة جدا
+
+468
+00:40:28,040 --> 00:40:33,900
+لأنها التي تحافظ على ال fluidity of blood ماشي؟ هي
+
+469
+00:40:33,900 --> 00:40:38,720
+اللي بتحافظ على أنه يصير في continuous fluidity of
+
+470
+00:40:38,720 --> 00:40:41,360
+blood ماشي يا شباب؟
+
+471
+00:40:43,970 --> 00:40:49,530
+وهي تقوم بتكوين تبقية الـVessel من الـLumen وهي
+
+472
+00:40:49,530 --> 00:40:53,530
+عبارة عن Basement Membrane بيتكوّن من عبارة من
+
+473
+00:40:53,530 --> 00:40:54,010
+عبارة من عبارة من عبارة من عبارة من عبارة من عبارة
+
+474
+00:40:54,010 --> 00:40:54,250
+من عبارة من عبارة من عبارة من عبارة من عبارة من
+
+475
+00:40:54,250 --> 00:40:55,570
+عبارة من عبارة من عبارة من عبارة من عبارة من عبارة
+
+476
+00:40:55,570 --> 00:40:58,870
+من عبارة من عبارة من عبارة من عبارة من عبارة من
+
+477
+00:40:58,870 --> 00:40:59,310
+عبارة من عبارة من عبارة من عبارة من عبارة من عبارة
+
+478
+00:40:59,310 --> 00:40:59,530
+من عبارة من عبارة من عبارة من عبارة من عبارة من
+
+479
+00:40:59,530 --> 00:41:11,710
+عبارة من عبارة
+
+480
+00:41:11,710 --> 00:41:16,980
+من عبالـ Basement Membrane بيتكون بإيش من Thin
+
+481
+00:41:16,980 --> 00:41:20,660
+Layer أو Spongy Connective Tissue بيفرز باستمرار
+
+482
+00:41:20,660 --> 00:41:25,860
+اللي هو Elastic Collagen يبقى مقوية هي عبارة عن
+
+483
+00:41:25,860 --> 00:41:31,580
+طبقة ضعيفة طبقة من الخلايا الاندوثيلية أو
+
+484
+00:41:31,580 --> 00:41:35,580
+الابيثيلية ولكنها مقوة بالـ Basement Membrane
+
+485
+00:41:35,580 --> 00:41:43,130
+الطبقة التانية بيسموها Tonica Intermediaوهذه لازم
+
+486
+00:41:43,130 --> 00:41:46,490
+يكون فيها muscle smooth muscle لأن هي ال smooth
+
+487
+00:41:46,490 --> 00:41:50,430
+muscle هي اللي بتحافظ على contractility of blood
+
+488
+00:41:50,430 --> 00:41:55,650
+vessels ماشي؟ and usually function under
+
+489
+00:41:55,650 --> 00:42:01,430
+involuntary control involuntary
+
+490
+00:42:01,430 --> 00:42:05,390
+action بمعنى في .. في .. في .. بس بالظبط
+
+491
+00:42:05,390 --> 00:42:10,450
+parasympathetic ولا sympathetic parasympathetic
+
+492
+00:42:12,500 --> 00:42:18,280
+المرة تلاتة تحتوي على connective tissue which
+
+493
+00:42:18,280 --> 00:42:22,300
+produce collagen fiber whose elasticity is reduced
+
+494
+00:42:22,300 --> 00:42:27,320
+by hypertension طبيعي كل ما زاد الضغط كل ما قلت ال
+
+495
+00:42:27,320 --> 00:42:33,740
+elasticity زاد الشد اخر طبقة هي Tunica Adventita
+
+496
+00:42:33,740 --> 00:42:38,520
+او Adventisha حسب اللفظ
+
+497
+00:42:40,370 --> 00:42:43,690
+وهي الطبقة التي تغلف الطبقة التانية اللي الـ
+
+498
+00:42:43,690 --> 00:42:49,990
+Intermediate وهي بتحتوي على connective tissue اللي
+
+499
+00:42:49,990 --> 00:42:57,930
+بتتكوّن منها Elastic and elastic collagen fiber
+
+500
+00:42:57,930 --> 00:43:01,470
+وهي
+
+501
+00:43:01,470 --> 00:43:07,530
+طبقة قوية أنه بتمنع الـ Ballooning BalloonBallon
+
+502
+00:43:07,530 --> 00:43:12,690
+إيش يعني؟ بلون Balloning of vessel إنتفاخ إنتفاخ
+
+503
+00:43:12,690 --> 00:43:19,270
+ناشي و أكتر إيش بيصير إنتفاخات إذا كان في high
+
+504
+00:43:19,270 --> 00:43:23,550
+systolic blood pressure high systolic blood
+
+505
+00:43:23,550 --> 00:43:28,970
+pressure تعرفوا ال blood pressure يقاس by systolic
+
+506
+00:43:28,970 --> 00:43:30,110
+tone
+
+507
+00:43:36,450 --> 00:43:40,810
+وبقى Sostelic مش رقمين طبعا إذا صار فيه ballooning
+
+508
+00:43:40,810 --> 00:43:45,670
+بيصير حاجة بيسموها aneurysm aneurysm بمعنى أنه
+
+509
+00:43:45,670 --> 00:43:52,810
+بيصير فيه ضعف نتيجة وجود ضعف في بعض مناطق ال blood
+
+510
+00:43:52,810 --> 00:44:01,940
+vessels البنطقة الخارجية بقل اللي هو ال ..الـ
+
+511
+00:44:01,940 --> 00:44:04,460
+pressure و في نفس الوعاء بتتضعف فبصير فيها
+
+512
+00:44:04,460 --> 00:44:09,320
+ballooning و ممكن تعمل aneurysm بمعنى تشققات في
+
+513
+00:44:09,320 --> 00:44:15,680
+الوعاء الدموي تشققات في الوعاء الدموي و التشقق
+
+514
+00:44:15,680 --> 00:44:18,940
+ممكن يؤدي لانفجار الوعاء الدموي كتير سمعتوا انه
+
+515
+00:44:18,940 --> 00:44:24,160
+ممكن الوعاء الدموي يصير فيه انفجر فتحات فتحات
+
+516
+00:44:24,160 --> 00:44:29,440
+ماتجعنش على أساس aneurysm ضعف في بعض المناطق أدى
+
+517
+00:44:29,440 --> 00:44:37,220
+الى انفجارالمنطقة هذه نتيجة وجود ضغط عالي للدم في
+
+518
+00:44:37,220 --> 00:44:45,030
+الواعي الدموي ماشي يا شبابهذه هي ال anatomy أو
+
+519
+00:44:45,030 --> 00:44:50,930
+blood vessels تلات طبقات واحدة سبوها Tonica Intima
+
+520
+00:44:50,930 --> 00:44:54,710
+وواحدة Tonica Media وواحدة Tonica Intermedia
+
+521
+00:44:54,710 --> 00:44:59,250
+وتالتة Tonica Adventita وكل واحدة لها وظيفة معينة
+
+522
+00:44:59,250 --> 00:45:04,030
+الأولانية مهمة جدا لأنه متحافظ على ال fluidity
+
+523
+00:45:04,030 --> 00:45:07,810
+التانية داعمة التالتة برضه بتعمل back pressure
+
+524
+00:45:07,810 --> 00:45:16,660
+ومتحافظ على قوامالوعاء الدموي ك intact one طيب
+
+525
+00:45:16,660 --> 00:45:22,320
+what is the normal function of blood vessels؟
+
+526
+00:45:22,320 --> 00:45:29,540
+كانوا ال normal vessels usually
+
+527
+00:45:29,540 --> 00:45:36,120
+provide unimpeded movement of blood to area of
+
+528
+00:45:36,120 --> 00:45:42,350
+need لطول ما فيوعاء دموي عنده القدرة على ال
+
+529
+00:45:42,350 --> 00:45:45,770
+contraction كل ما بيصير فيه contraction بيصير فيه
+
+530
+00:45:45,770 --> 00:45:51,630
+قوة دافعة للدم في داخل الوعاء الدموي فبي .. بي ..
+
+531
+00:45:51,630 --> 00:45:56,350
+بيستمرار نتيجة حركة الوعاء الدموي باستمرار ماشي
+
+532
+00:45:56,350 --> 00:46:02,050
+بيؤدي هذا إلى دفع الدم باستمرار كمان إلى كل مناطق
+
+533
+00:46:02,050 --> 00:46:07,110
+الجسم اللي احنا بنيهالكن هذا التحرك عادةً تتجه إلى
+
+534
+00:46:07,110 --> 00:46:14,250
+نيرو كيميكال إفكت يعني في عصاب لازم في إشارة عصبية
+
+535
+00:46:14,250 --> 00:46:18,610
+لازم تيجي للوعاء الدموي عشان يصير في continuous
+
+536
+00:46:18,610 --> 00:46:24,890
+movement layer طبعا إشارة عصبية مصحوبة chemical
+
+537
+00:46:24,890 --> 00:46:34,390
+substance release ماشي؟
+
+538
+00:46:35,850 --> 00:46:39,130
+اندوثيليال هذا السبب ان مجلد اندوثيليال هو مجلد
+
+539
+00:46:39,130 --> 00:46:45,230
+كرتيكال وهو كرتيكال لجزء من جذب الدم يدفع تدفع
+
+540
+00:46:45,230 --> 00:46:46,590
+تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع
+
+541
+00:46:46,590 --> 00:46:50,750
+تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع
+
+542
+00:46:50,750 --> 00:46:51,230
+تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع
+
+543
+00:46:51,230 --> 00:46:53,410
+تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع تدفع
+
+544
+00:46:53,410 --> 00:46:59,150
+تدف
+
+545
+00:47:03,950 --> 00:47:07,390
+الـ endothelial function اللي هي الطبقة الداخلية،
+
+546
+00:47:07,390 --> 00:47:14,410
+قالوا وظائفها متعددة، هالسنت وظائف، ما بين صفات
+
+547
+00:47:14,410 --> 00:47:17,610
+وظائف، نمرا واحدة هي بتشكل physical barrier، هي
+
+548
+00:47:17,610 --> 00:47:21,550
+الحامل، هي الحاضنة، لمين؟ للبلاد، physical barrier
+
+549
+00:47:21,550 --> 00:47:25,710
+لمين؟ عزيزي، ما بين الدول؟ نعم، نمرا اتنين،
+
+550
+00:47:25,710 --> 00:47:32,510
+cellular regulation، blood flow and vascular tone،
+
+551
+00:47:32,510 --> 00:47:41,590
+تعرفوا؟tone معناته إيش؟ نغمة، أحسنت، نغمة ليش؟
+
+552
+00:47:41,590 --> 00:47:44,950
+نغمة جاية من إيش؟ من حركة الدم في لوحة الدمام،
+
+553
+00:47:44,950 --> 00:47:48,010
+vascular tone بيسموها، و هذه اللي غالبا الطبيب
+
+554
+00:47:48,010 --> 00:47:52,690
+بسمعها أثناء ما بحط السماعة و بشوف ال tone of
+
+555
+00:47:52,690 --> 00:47:53,870
+blood pressure
+
+556
+00:47:56,310 --> 00:47:59,450
+طبعا من صفات هذه الطبقة يا شباب، الطبقة
+
+557
+00:47:59,450 --> 00:48:04,470
+الاندوثيلية المبطنة للوعاء الدموي، من صفاتها إنها
+
+558
+00:48:04,470 --> 00:48:08,450
+antithromboticalية، ماذا يعني antithrombotic؟ أو
+
+559
+00:48:08,450 --> 00:48:16,430
+بيسموها non-thrombogenic، antithrombotic، تمقنعة،
+
+560
+00:48:16,430 --> 00:48:22,010
+تمنع التجلد، تمنع تجلد الدمشته، وقلنا إنها بتحافظ
+
+561
+00:48:22,010 --> 00:48:29,860
+على ال fluidity أووبالتالي بيتمنع حدوث التجلد
+
+562
+00:48:29,860 --> 00:48:36,260
+للدم، but once activated يوم ما تنمزع، بتتنشط،
+
+563
+00:48:36,260 --> 00:48:41,400
+فبتتحول from ant-thrombotic إلى thrombotic أو pro
+
+564
+00:48:41,400 --> 00:48:48,030
+-thromboticماشي تتحول from non-thrombogenic إلى
+
+565
+00:48:48,030 --> 00:48:52,630
+thrombogenic يعني بيصير قابلة لإن هيش تعمل تجارب و
+
+566
+00:48:52,630 --> 00:48:56,110
+هذا وضع طبيعي جدا يا شباب لإن طب و قلتلكوا انا يوم
+
+567
+00:48:56,110 --> 00:48:59,930
+ما تكون healthy بيصير فيه continuous release to
+
+568
+00:48:59,930 --> 00:49:04,410
+chemical substance أشهرها لبروستا سايكلين وأشهرها
+
+569
+00:49:04,410 --> 00:49:07,050
+ليش؟ لبروستا سايكلين هذا
+
+570
+00:49:09,880 --> 00:49:13,680
+بعمل continuous .. ساعدنا هنشوف وظيفته بعمل
+
+571
+00:49:13,680 --> 00:49:16,620
+continuous vasodilatation و بعمل inhibition لل
+
+572
+00:49:16,620 --> 00:49:21,830
+platelet aggregation and adherenceماشى، و في نفس
+
+573
+00:49:21,830 --> 00:49:25,930
+ال project بيعمل .. بيشكل او بي .. بيشكل negative
+
+574
+00:49:25,930 --> 00:49:29,690
+charge فبيعمل continuous repelling لمين؟ طب لما
+
+575
+00:49:29,690 --> 00:49:32,690
+يصير في المزيد، هدى المادة بتكون موجودة؟ أو بتانى
+
+576
+00:49:32,690 --> 00:49:37,170
+شو بيصير؟ العكس، بيصير ايه؟ العكس، فبتانى يصير في
+
+577
+00:49:37,170 --> 00:49:41,740
+adhesion و aggregationكمان بتلعب دور كبير في ال
+
+578
+00:49:41,740 --> 00:49:45,480
+flow distribution، بتوزيع السواق في داخل الوعي
+
+579
+00:49:45,480 --> 00:49:49,300
+الدموي، بتلعب دور كبير في .. في داخل الجسم، بتلعب
+
+580
+00:49:49,300 --> 00:49:53,560
+دور كبير في ال inflammation، by releasing certain
+
+581
+00:49:53,560 --> 00:49:57,580
+inflammatory cytokine، بتلعب دور كبير في ال
+
+582
+00:49:57,580 --> 00:50:03,280
+healing و repairingهو مجرد process لأنه تفرز بعض
+
+583
+00:50:03,280 --> 00:50:08,880
+الـ Growth Factors وهنا سنشاهد أنه له دور حيوي جدا
+
+584
+00:50:08,880 --> 00:50:12,860
+في الهيموستيسيه، له دور أيه؟ حيوي جدا في
+
+585
+00:50:12,860 --> 00:50:17,580
+الهيموستيسيه، احنا ان شاء الله هنركز على آخر هذه
+
+586
+00:50:17,580 --> 00:50:24,860
+الوظائف وهو الـ Hemostatic Function طيب، نشوف ما
+
+587
+00:50:24,860 --> 00:50:29,140
+هي ال Mediators، Chemical Mediators that are
+
+588
+00:50:29,140 --> 00:50:33,890
+releasedاحنا قلنا من وظائفها إنها non-thrombogenic
+
+589
+00:50:33,890 --> 00:50:39,710
+ولكن لما تنمزع أو تتنشر تصير thrombogenic وبالتالي
+
+590
+00:50:39,710 --> 00:50:43,210
+هذه العملية بتتم من خلال ال release of certain
+
+591
+00:50:43,210 --> 00:50:48,230
+chemical substance ماشي؟ ومن هذا المطلق بيكون
+
+592
+00:50:48,230 --> 00:50:51,370
+عندها القدرة إنها تفرز نوعين من ال chemical
+
+593
+00:50:51,370 --> 00:50:57,670
+substance إشي بيمنع التجلط وإشي بيساعد فيه التجلط،
+
+594
+00:50:57,670 --> 00:51:04,570
+نظمود؟المواد اللي بتلعب دور كبير في منع التجلط as
+
+595
+00:51:04,570 --> 00:51:08,130
+non-thrombogenic mediator المواد الأخرى، يعني اما
+
+596
+00:51:08,130 --> 00:51:11,770
+واحد prostate cyclin وهو نوع من الـprostaglandin،
+
+597
+00:51:11,770 --> 00:51:19,630
+مظبوط؟ شو وظيفته؟ بعمل vascular relaxation and
+
+598
+00:51:19,630 --> 00:51:22,070
+inhibit platelet adherence and aggregation
+
+599
+00:51:22,070 --> 00:51:30,410
+الحاجتين، ماشي؟ طبعا إذا كان في relaxationيعني
+
+600
+00:51:30,410 --> 00:51:34,690
+بيقلل ال blood pressure و بيقلل ال .. ال via ال ..
+
+601
+00:51:34,690 --> 00:51:38,390
+ال construction، مظبوط؟ وهذا بالتالي ال blood
+
+602
+00:51:38,390 --> 00:51:41,790
+pressure .. ال blood بمشي باشر، ال flow rate بيكون
+
+603
+00:51:41,790 --> 00:51:46,570
+مرتفع، نمرا اتنين انهيبت ال platelet adherence
+
+604
+00:51:46,570 --> 00:51:51,690
+segregation يعني انهيبت ال platelet function،ماشي؟
+
+605
+00:51:51,690 --> 00:51:58,690
+بمنع ال platelet functionactivation في منطقات على
+
+606
+00:51:58,690 --> 00:52:02,070
+blood vessels وإذا اتنشطت البلاتلت يعني عملت جلطة
+
+607
+00:52:02,070 --> 00:52:06,630
+يعني عملت ايش؟ جلطة نبر اتنين الـ nitric oxide
+
+608
+00:52:06,630 --> 00:52:14,610
+وطبعا هذا multifunctional من مضاعفه حاجتين
+
+609
+00:52:14,610 --> 00:52:18,990
+أساسيتين الحاجة الأولانية انه بعضه زي ال
+
+610
+00:52:18,990 --> 00:52:23,480
+prostacyclinبيمنع أول شي بيعمل platelet ..
+
+611
+00:52:23,480 --> 00:52:29,000
+vascular relaxation، نمرة اتنين بيمنع platelet
+
+612
+00:52:29,000 --> 00:52:33,120
+adhesion and degradation،
+
+613
+00:52:33,120 --> 00:52:37,680
+نمرة تلاتة بيشارك
+
+614
+00:52:37,680 --> 00:52:44,850
+في نشاطالـ Natural Occuring Inhibitors اللي هو
+
+615
+00:52:44,850 --> 00:52:47,510
+عبارة عن الـ Anticoagulant الطبيعية اللي موجودة في
+
+616
+00:52:47,510 --> 00:52:51,430
+الجسم و منها الـ Protein C، حنجيهم بالتفصيل إن شاء
+
+617
+00:52:51,430 --> 00:52:55,590
+الله قدام، و الـ Antithrombin 3 هدولة
+
+618
+00:52:55,590 --> 00:52:59,390
+Anticoagulant، يعني إذا اتمشطوا، إيش بيعملوا؟
+
+619
+00:52:59,390 --> 00:53:03,250
+بيبنعوا الـ Coagulation، صح؟ كيف بيبنعوا الـ
+
+620
+00:53:03,250 --> 00:53:05,430
+Coagulation؟ من خلال Prevention of Thrombin
+
+621
+00:53:05,430 --> 00:53:11,000
+Formation Thrombin إيش بيعمل لو اتكون؟بشتغلها الـ
+
+622
+00:53:11,000 --> 00:53:16,020
+Fibrinogen و بيحوله لمين؟ يعني بيعمل Clot فبالتالي
+
+623
+00:53:16,020 --> 00:53:22,700
+شو بيصير؟ بيصير من خلال هذا الميكانزم Inhibition
+
+624
+00:53:22,700 --> 00:53:26,640
+لل Coagulation Inhibition لل Coagulation عيدها
+
+625
+00:53:26,640 --> 00:53:33,440
+تاني، بينشط، بيشارك في نشاطية ال protein C و ال
+
+626
+00:53:33,440 --> 00:53:38,370
+Antithrombin 3و هدول عبارة عن Anti-coagulation لما
+
+627
+00:53:38,370 --> 00:53:42,890
+ماتنشطوش بيعملوا Anti-coagulation يعني ضد التجرمة
+
+628
+00:53:42,890 --> 00:53:46,490
+كيف؟ جانوا بيعملوا Inhibition لـ Thrombin
+
+629
+00:53:46,490 --> 00:53:49,570
+Formation وThrombin هو عبارة عن Coagulation Factor
+
+630
+00:53:49,570 --> 00:53:54,290
+نشر بيشتغل على الفيبرانج و بيحوله لمين؟ وبالتالي
+
+631
+00:53:54,290 --> 00:53:59,390
+بيعمل Clot يبقى هذا بيعمل Inhibition لClot ماشي؟
+
+632
+00:53:59,390 --> 00:54:03,910
+نمرة تلاتة Endothelium Derailed Hyperpolarizing
+
+633
+00:54:03,910 --> 00:54:10,770
+Factorبرضه بعمل Vascular Relaxation الوحيد اللى
+
+634
+00:54:10,770 --> 00:54:13,470
+بعمل Vasoconstriction اللى هو المادة الرابعة اللى
+
+635
+00:54:13,470 --> 00:54:17,730
+Indothelin-1 Indothelin-1 بتعمل ايهاش؟
+
+636
+00:54:17,730 --> 00:54:22,690
+Vasoconstriction ماشي؟
+
+637
+00:54:22,690 --> 00:54:28,080
+فهذه العربي اللى بتبنى التجنبلكن قلنا يوم ما يصير
+
+638
+00:54:28,080 --> 00:54:34,220
+فيه مزع بدنا إيه؟ انت تشتغل كمحفظة للتجلط وبالتالي
+
+639
+00:54:34,220 --> 00:54:40,120
+لابد من وجود برضه عوامل تساعد في عملية التجلط من
+
+640
+00:54:40,120 --> 00:54:43,360
+أشهر heart issue factor يا شباب and this is
+
+641
+00:54:43,360 --> 00:54:46,280
+released following endothelial injury غالبا مش
+
+642
+00:54:46,280 --> 00:54:52,860
+موجود في الطبقةملامسة للدم وانما موجود في ال sub
+
+643
+00:54:52,860 --> 00:54:56,320
+-endothelia اللى هي في يوم ما يحصل مزي على ال
+
+644
+00:54:56,320 --> 00:54:59,440
+endothelia اللى مين بيصير in direct contact with
+
+645
+00:54:59,440 --> 00:55:03,500
+blood ال sub-endothelia فى هاتيشوفاكتور بتنشط
+
+646
+00:55:03,500 --> 00:55:09,820
+العوامل التجمد نمرا اتنين ال vom-valerian factor
+
+647
+00:55:09,820 --> 00:55:14,160
+برضه بيطلع من ال endothelia اللى هي ال vom
+
+648
+00:55:14,160 --> 00:55:19,520
+-valerian factorالـ Von Willebrand طبعا اسم عالم
+
+649
+00:55:19,520 --> 00:55:24,440
+ألماني هو الاكتشاف في الـ W تلت في زياش V Von
+
+650
+00:55:24,440 --> 00:55:30,290
+Willebrand مشي Von Willebrand factorهذا يخزن في
+
+651
+00:55:30,290 --> 00:55:34,370
+الـ endothelial layer فيوم تنمزع هو بيطلع، بيطلع
+
+652
+00:55:34,370 --> 00:55:37,730
+برا، فبصير on direct contact with there و with
+
+653
+00:55:37,730 --> 00:55:41,590
+blood. شو بيعمل؟ قالوا هو اللي بيساعد في تلزيط ال
+
+654
+00:55:41,590 --> 00:55:44,810
+adhesion of platelet و there و with blood vessels
+
+655
+00:55:44,810 --> 00:55:50,710
+هو اللي بيساعد فيه في ال adherence of platelet to
+
+656
+00:55:50,710 --> 00:55:56,650
+the injured blood vesselsنبرة 3 بعضه بيطلع من الـ
+
+657
+00:55:56,650 --> 00:56:01,350
+endothelial layer هي عبارة عن مادة بيسموها
+
+658
+00:56:01,350 --> 00:56:05,250
+Plasminogen Activator Inhibitor Plasminogen
+
+659
+00:56:05,250 --> 00:56:11,270
+Activator Inhibitor والـ Plasminogen شبه هو عبارة
+
+660
+00:56:11,270 --> 00:56:18,470
+عن substrate of fibrinolysis fibrinolysis حكينا
+
+661
+00:56:18,470 --> 00:56:23,420
+عليها قبل أيه؟ إيش هي؟مرحلة التالتة اللى بتدور
+
+662
+00:56:23,420 --> 00:56:28,180
+مظبوط مرحلة التالتة الـ Plasmalogen هو برهان
+
+663
+00:56:28,180 --> 00:56:33,560
+substrate ال substrate بتتحول بيعتبر ال raw enzyme
+
+664
+00:56:33,560 --> 00:56:39,540
+بيتحول الى enzyme by the activator فى activator
+
+665
+00:56:39,540 --> 00:56:45,670
+بتنشطه بتحوله لمين؟ لبلازمينماشي ال endothelial
+
+666
+00:56:45,670 --> 00:56:53,530
+cell بتفرز ال inhibitor تبعت ال activator يعني
+
+667
+00:56:53,530 --> 00:56:59,610
+بتمنع ال fibrolysis فليش بصير؟ ليش عكس ال
+
+668
+00:56:59,610 --> 00:57:03,990
+bleeding؟ مش عارف طبعا مافهوم؟
+
+669
+00:57:03,990 --> 00:57:10,230
+هي بتفرز ال inhibitor لل activator of fibrolysis
+
+670
+00:57:10,230 --> 00:57:15,150
+ماشي؟يعني ماشي بتفرز البلازم من جين اكتيفتر
+
+671
+00:57:15,150 --> 00:57:19,530
+انتجار؟ اه، اش هو ده؟ برنامج الهيبوتر ده مين؟
+
+672
+00:57:19,530 --> 00:57:23,730
+للاكتفيتر للاكتفيتر للاكتفيتر of الفيبرونامج هذا
+
+673
+00:57:23,730 --> 00:57:26,910
+بيشتغل على الفيبرونامج؟ بيشتغل في الفيبرونامج،
+
+674
+00:57:26,910 --> 00:57:32,470
+بحق، عجيب برضه، ونشوف فضعه افضل يبقى مهم، مهمة جدا
+
+675
+00:57:32,470 --> 00:57:36,710
+هذه الطبقة طبعا مهمة جدا، لإن هو اشتغل اقرذتلي
+
+676
+00:57:36,710 --> 00:57:45,750
+مواد كيميائية أو مواد بتلعب فياتجاهين ماشي اتجاه
+
+677
+00:57:45,750 --> 00:57:51,330
+ال fluidity اللي هو المانع تكون الجلطة وهذا الكلام
+
+678
+00:57:51,330 --> 00:57:58,970
+احنا بدناه in healthy or normal condition و افرزت
+
+679
+00:57:58,970 --> 00:58:04,350
+مواد تعمل جلطة وسموها procoagulant substance وكتير
+
+680
+00:58:04,350 --> 00:58:10,010
+عشان لما يصير فيه blood injury بزر injury لما يصير
+
+681
+00:58:10,010 --> 00:58:11,410
+فيه مزعج المفروض
+
+682
+00:58:16,180 --> 00:58:20,600
+بتفرز مواد في الحالتين في حالة ال normal و ال
+
+683
+00:58:20,600 --> 00:58:25,240
+abnormal condition طبعا بالاضافة لذلك يا شباب
+
+684
+00:58:25,240 --> 00:58:28,240
+اتفقنا على ان هذه الطبقة اللي هي ال endothelial
+
+685
+00:58:28,240 --> 00:58:35,340
+cell كمان بتلعب دور كبير في ال repairing ناشي من
+
+686
+00:58:35,340 --> 00:58:41,410
+خلال ايش افراز certain growth factor orبعض الـ
+
+687
+00:58:41,410 --> 00:58:45,210
+cytokines مثل الـ growth factor البريطالي والفيبرو
+
+688
+00:58:45,210 --> 00:58:48,830
+بلاست الgrowth factors سمعتوا فيهم طبعا حكينا فيهم
+
+689
+00:58:48,830 --> 00:58:54,010
+قبل هيك في ال hematology ثم ال transforming growth
+
+690
+00:58:54,010 --> 00:58:58,130
+factor beta هذا عبارة عن hematory يعمل modulation
+
+691
+00:58:58,130 --> 00:59:03,530
+للvascular repair ثم Epidermal growth factor and
+
+692
+00:59:03,530 --> 00:59:10,400
+endothelial cell growth factor ماشي يا شبابطبعا
+
+693
+00:59:10,400 --> 00:59:14,800
+احنا هنقف هنا و
+
+694
+00:59:14,800 --> 00:59:19,300
+نكمل ان شاء الله المحاضرة القادمة في ال mechanism
+
+695
+00:59:19,300 --> 00:59:25,940
+of action او ال mode of action لكل مادة من هذه
+
+696
+00:59:25,940 --> 00:59:30,300
+المواد اللي بتفرزها ال endothelial cell ماشي؟
+
+697
+00:59:30,300 --> 00:59:33,760
+هنشوف كيف ال nitric oxide بتكون و كيف بيشتغل ال
+
+698
+00:59:33,760 --> 00:59:39,410
+prostacyclin كيف بتكون و كيف بيشتغلو هنتطرق ل ال
+
+699
+00:59:39,410 --> 00:59:43,890
+mechanisms that are involved in this process،
+
+700
+00:59:43,890 --> 00:59:50,050
+مفهوم يا شباب؟ حد يدّي سؤال؟ يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/_AmxJpfA97Q_raw.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/_AmxJpfA97Q_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f3308460e4e347912d45088491c16f4d116e6f20
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/_AmxJpfA97Q_raw.srt
@@ -0,0 +1,2476 @@
+1
+00:00:20,810 --> 00:00:23,670
+أعوذ بالله بالصلاة والسلام بسم الله الرحمن الرحيم،
+
+2
+00:00:23,670 --> 00:00:28,770
+اليوم ان شاء الله هنحكي في secondary hemostasis،
+
+3
+00:00:28,770 --> 00:00:32,310
+مرة فترة كنا بنحكي في محاضراتنا السابقة عن primary
+
+4
+00:00:32,310 --> 00:00:36,330
+hemostasis ويتطرقنا ل ال components of primary
+
+5
+00:00:36,330 --> 00:00:39,550
+hemostasis اللي هم ال plateletsو ال blood results،
+
+6
+00:00:39,550 --> 00:00:42,890
+مظبوط؟ اليوم احنا هنحكي في ال secondary hemostasis
+
+7
+00:00:42,890 --> 00:00:49,890
+و طبعا ال major role لل coagulation factors في ال
+
+8
+00:00:49,890 --> 00:00:50,830
+secondary hemostasis
+
+9
+00:00:55,380 --> 00:00:57,520
+بنتعرف على different characteristic features,
+
+10
+00:00:57,680 --> 00:01:02,220
+properties, structure يعني كل الصفات فيزيائية و
+
+11
+00:01:02,220 --> 00:01:06,860
+كيميائية منها قدر الإمكان عشان لما نحكي عن ال
+
+12
+00:01:06,860 --> 00:01:10,620
+coagulation factors لفلاني تكون عارف انت what is
+
+13
+00:01:10,620 --> 00:01:15,880
+it؟ شو بيعمل؟ و هكذا، ماشي؟ فمحاضرتنا اليوم مقدمة
+
+14
+00:01:18,380 --> 00:01:22,880
+مطلب دي Coagulation Factors أو System دلوقت ال
+
+15
+00:01:22,880 --> 00:01:30,420
+System بيتكون من 14 جليكو بروتين Substance أو
+
+16
+00:01:30,420 --> 00:01:36,900
+Factors ماشي؟ دي are 14 Coagulation Factors Most
+
+17
+00:01:36,900 --> 00:01:43,660
+of them إن لم يكن يعني الأغلبية العظمى إن لم يكن
+
+18
+00:01:43,660 --> 00:01:44,380
+كلهم
+
+19
+00:01:46,820 --> 00:01:53,780
+سيريني بروتييزي مادة واحد مادة واحد اللي هو factor
+
+20
+00:01:53,780 --> 00:02:01,100
+13 سيريني بروتييزي طبعا بروتييزي يعني انزين صح؟ و
+
+21
+00:02:01,100 --> 00:02:10,260
+سيرين يعني ان ال active sites تبع طوال الظبط عند
+
+22
+00:02:10,260 --> 00:02:10,940
+السيرين
+
+23
+00:02:15,860 --> 00:02:20,840
+يشتركوا مع بعض في الشغل and they are activating in
+
+24
+00:02:20,840 --> 00:02:26,900
+a cascade manner بمعنى واحد بنشت التاني و التاني
+
+25
+00:02:26,900 --> 00:02:32,620
+بنشت التالت و التالت بنشت الثالث و هكذا لغاية ما
+
+26
+00:02:32,620 --> 00:02:37,660
+نصل في النهاية الى ال final product وهو fibrin مش
+
+27
+00:02:37,660 --> 00:02:40,600
+محصلة تكوين جلطة مش هم بيعملوا جلطة
+
+28
+00:02:43,200 --> 00:02:48,280
+فاكتور من واحد عددهم من واحد لتلتار فاكتور ستة مش
+
+29
+00:02:48,280 --> 00:02:54,140
+موجود وفي اتنين ماعطوهم مش أرقام عطوهم أسماء فقط و
+
+30
+00:02:54,140 --> 00:03:01,540
+أسماء العائلات اللتي يعني
+
+31
+00:03:01,540 --> 00:03:08,480
+أسماء أفضل مش للعائلات أسماء و ليس أرقام الأولان
+
+32
+00:03:08,480 --> 00:03:09,600
+يسمو precategory
+
+33
+00:03:11,950 --> 00:03:14,490
+والتالي اسمه high molecular weight kyaninogen
+
+34
+00:03:14,490 --> 00:03:18,950
+precalicrate وhigh molecular weight kyaninogen
+
+35
+00:03:18,950 --> 00:03:23,310
+مامرروش عليكمه قبل هيك؟ اه precalicrate and high
+
+36
+00:03:23,310 --> 00:03:29,210
+molecular weight kyaninogen أي Pk اختصار ل
+
+37
+00:03:29,210 --> 00:03:34,250
+precalicrate والتاني
+
+38
+00:03:34,250 --> 00:03:37,610
+high molecular weight
+
+39
+00:03:42,870 --> 00:03:49,630
+كاينينوجيني و هنتعرف على دورهم مش هقولهم ده ماشي
+
+40
+00:03:49,630 --> 00:03:52,570
+شباب؟ they are usually circulating in their
+
+41
+00:03:52,570 --> 00:03:56,490
+inactive form بيمشوا في إيهاش؟ في ال blood
+
+42
+00:03:56,490 --> 00:04:00,610
+circulation in their inactive form و بما أنهم
+
+43
+00:04:00,610 --> 00:04:05,190
+enzyme they are circulating as zymogen لإن ال
+
+44
+00:04:05,190 --> 00:04:08,490
+precursor of enzyme هو عبارة عن إيهاش؟فأقول عن
+
+45
+00:04:08,490 --> 00:04:11,890
+Zymogen ولا لأ؟ فبالتالي they are acting .. they
+
+46
+00:04:11,890 --> 00:04:17,170
+are circulating as Zymogen and they are usually
+
+47
+00:04:17,170 --> 00:04:24,710
+designated by a roman numeral letters يعني أطناب
+
+48
+00:04:24,710 --> 00:04:30,510
+يعطوهم أيه؟ أرقام رومانية وبرضه في نفس الوجود اللي
+
+49
+00:04:30,510 --> 00:04:35,670
+هم أسماء على سبيل المثال ال fibrogen ال fibrinogen
+
+50
+00:04:35,670 --> 00:04:42,350
+اللي هو رقم واحداسمه Fibrinogen نقطة تانية ان الـ
+
+51
+00:04:42,350 --> 00:04:48,170
+active form once زيوموجين is transformed to enzyme
+
+52
+00:04:48,170 --> 00:04:55,270
+it's designated by letter A رمزا
+
+53
+00:04:55,270 --> 00:05:02,350
+إلى active فبينكون هو عبارة عن ايش؟ عن active طبعا
+
+54
+00:05:02,350 --> 00:05:06,330
+أمثلة كثيرة هنشوفها ان شاء الله many of them are
+
+55
+00:05:06,330 --> 00:05:12,160
+cofactorsو يمثل على ذلك اللي هو ال calcium و
+
+56
+00:05:12,160 --> 00:05:13,400
+placid factor 3
+
+57
+00:05:17,690 --> 00:05:21,370
+أقول قاعدة لازم ناخدها في نفس الوقت بأن كل واحد من
+
+58
+00:05:21,370 --> 00:05:25,010
+هذه العناصر must be present in its quantitative,
+
+59
+00:05:25,490 --> 00:05:28,650
+normal, quantitative and qualitative معنى، يعني
+
+60
+00:05:28,650 --> 00:05:32,050
+لازم يكون concentration طبيعي و لازم يكون بيشتغل
+
+61
+00:05:32,050 --> 00:05:35,710
+طبيعي، لازم يكون concentration طبيعي و الشغل لازم
+
+62
+00:05:35,710 --> 00:05:39,930
+يهيش، functioning is يهيش، also طبيعي، final
+
+63
+00:05:39,930 --> 00:05:43,290
+product لكون هذه ال calculation factor is final
+
+64
+00:05:43,290 --> 00:05:49,060
+formation و بيكون في النهاية مش workبمعنى شبكة من
+
+65
+00:05:49,060 --> 00:05:55,780
+إيش؟ من الجلطة of clot مكونها الأساسي هو إيش؟ هو
+
+66
+00:05:55,780 --> 00:06:03,640
+ال fibre هذا دورهم هان بيسموه secondary hemostasis
+
+67
+00:06:03,640 --> 00:06:08,460
+وطبعا في بعد ذلك slow contraction and lysis for
+
+68
+00:06:08,460 --> 00:06:13,860
+the clot بيمتمثل بالإيش؟ بال tertiary hemostasis
+
+69
+00:06:13,860 --> 00:06:18,960
+أو بال fibreأحنا معنيين الأن نبدأ بالsecondary ثم
+
+70
+00:06:18,960 --> 00:06:22,920
+ننتقل إلى إيش إلى بعد هيك ال tertiary و يبنوها طبع
+
+71
+00:06:22,920 --> 00:06:26,300
+التلاتة ال primary والsecondary و إيش ال tertiary
+
+72
+00:06:26,300 --> 00:06:33,120
+ال slide هذه أسباب أو الشريحة هذه بتمثل ال
+
+73
+00:06:33,120 --> 00:06:36,820
+coagulation factors and their inhibitors او ال
+
+74
+00:06:36,820 --> 00:06:40,320
+inhibitors ال coagulation factors and inhibitors
+
+75
+00:06:40,320 --> 00:06:45,220
+كل هوا من اللي بتشترك في عملية ال hemostasisماشي؟
+
+76
+00:06:45,220 --> 00:06:47,860
+طبعا احنا بنعرف ان في Procoagulant وفي
+
+77
+00:06:47,860 --> 00:06:52,120
+Anticoagulant صح؟ فاللي من هاله فوق هم عبارة عن
+
+78
+00:06:52,120 --> 00:06:56,020
+Procoagulant ومن هاله تحت هم عبارة عن
+
+79
+00:06:56,020 --> 00:06:59,680
+Anticoagulant بتضم different characteristic
+
+80
+00:06:59,680 --> 00:07:02,860
+feature for each فهي على سبيل المثال molecular
+
+81
+00:07:02,860 --> 00:07:09,420
+weight جداش في number of peptides وهل ال nature of
+
+82
+00:07:09,420 --> 00:07:10,940
+body
+
+83
+00:07:12,790 --> 00:07:17,010
+هل هي covalent ولا non-covalent bonds ثم ال
+
+84
+00:07:17,010 --> 00:07:21,190
+concentration، plasma concentration and whether
+
+85
+00:07:21,190 --> 00:07:25,010
+the coagulation factor is vitamin K dependent or
+
+86
+00:07:25,010 --> 00:07:29,890
+not وهذه برضه من النقاط المهمة and what is its
+
+87
+00:07:29,890 --> 00:07:35,090
+function ماشي؟ what is its function؟ الاصل أنه
+
+88
+00:07:35,090 --> 00:07:39,450
+نعرف هذه الحلول كلها، هنعرفه ونحفظه تماما من كتب
+
+89
+00:07:39,450 --> 00:07:44,140
+مانكررطبعا هذا للحفظ معناه يعني انا بعطيكم ال
+
+90
+00:07:44,140 --> 00:07:47,860
+molecular weight ديش ياكم تعرفوه مش تعرفوه ديش
+
+91
+00:07:47,860 --> 00:07:54,340
+تحفظوها و ال bonds number of peptides sorry and
+
+92
+00:07:54,340 --> 00:07:57,800
+the covalent bonding ما دول دالك لأ مطلوب منكوا و
+
+93
+00:07:57,800 --> 00:08:01,000
+مطلوب منكوا حفظها ماشي عشان بقى؟
+
+94
+00:08:05,580 --> 00:08:09,300
+هذه الموقع بتبين Coagulation Factors
+
+95
+00:08:09,300 --> 00:08:12,420
+Classification، فيه different classification
+
+96
+00:08:12,420 --> 00:08:17,180
+موجودة في ال literature، لكن هذه من الحاجات most
+
+97
+00:08:17,180 --> 00:08:21,060
+commonly used، وهي ال classification of these
+
+98
+00:08:21,060 --> 00:08:25,300
+factors according to the location، والموقع وين في
+
+99
+00:08:25,300 --> 00:08:28,850
+ال coagulation cascading mechanismكلنا بنعرف أن ال
+
+100
+00:08:28,850 --> 00:08:32,850
+coagulation cascade أنه بينقسم إلى تلت أجزاء
+
+101
+00:08:32,850 --> 00:08:38,830
+Intrinsic و Extrinsic و Common ماشي فتفصلين ال
+
+102
+00:08:38,830 --> 00:08:42,690
+coagulation factors whether it's in intrinsic أو
+
+103
+00:08:42,690 --> 00:08:47,610
+extrinsic أو common وكمان بيفين إذا كان هو
+
+104
+00:08:47,610 --> 00:08:53,850
+substrate أو enzyme أو cofactor ماشي substrate أو
+
+105
+00:08:53,850 --> 00:09:00,340
+enzyme أو إيش أو cofactorماشي يا شباب، فطبعا من
+
+106
+00:09:00,340 --> 00:09:03,240
+خلال دراستنا ال coagulation factors برضه هنعرف
+
+107
+00:09:03,240 --> 00:09:09,320
+بالظبط التفصيلة المختلفة لهذه العوامل ونبدأ بأول
+
+108
+00:09:09,320 --> 00:09:14,180
+واحد، نبدأ بإيش؟ بأول واحد، وهو ال fibrinogen،
+
+109
+00:09:14,180 --> 00:09:21,520
+factor one وهو إيش؟ ال fibrinogen وطبعا
+
+110
+00:09:21,520 --> 00:09:27,080
+fibrinogen يعني fibrinzymogenصح؟ إيش يعني fibrin
+
+111
+00:09:27,080 --> 00:09:32,140
+enzyme؟ ال precursor للfibrin طبعا شباب ال
+
+112
+00:09:32,140 --> 00:09:37,040
+fibrinogen mostly is a substrate هو عبارة عن
+
+113
+00:09:37,040 --> 00:09:40,600
+substrate و ليس أنزايم وبالتالي هذه الجملة أنا
+
+114
+00:09:40,600 --> 00:09:44,680
+بعتبرها يعني غير مقبولة لأنه مدام ما بيتحورش
+
+115
+00:09:44,680 --> 00:09:50,480
+لأنزايم معناته مش إيهاش أو ال fibrin لما يصير هو
+
+116
+00:09:50,480 --> 00:09:57,170
+عبارة عن مش أنزايم وبالتالي مشلكن جهة العادة انه
+
+117
+00:09:57,170 --> 00:10:04,510
+عشان نفهم قلنا انه لما بتحول بتحول للإزرع و
+
+118
+00:10:04,510 --> 00:10:07,710
+باعتبروا ما ده هو سواء من هذا خلنا نطلع على ال
+
+119
+00:10:07,710 --> 00:10:14,830
+structure باعتبروا ما ده هو عبارة عن coiled coiled
+
+120
+00:10:14,830 --> 00:10:21,330
+ايش coiled؟ ملفوف
+
+121
+00:10:21,330 --> 00:10:29,690
+لأفلامstructure بيتكون من تلاتة polypeptide chain
+
+122
+00:10:29,690 --> 00:10:36,210
+موجودين
+
+123
+00:10:36,210 --> 00:10:42,110
+in duplicate بمعنى pairs وموجودين
+
+124
+00:10:42,110 --> 00:10:46,390
+in mirror manner عيب
+
+125
+00:10:46,390 --> 00:10:50,710
+تاني عشان هيك بيسموه triplicate of duplicate
+
+126
+00:10:50,710 --> 00:10:56,390
+structureماشي triplicate لمين؟ لتالتة polypeptides
+
+127
+00:10:56,390 --> 00:11:04,670
+and of duplicate ل .. لإيه؟ ل mirror .. لجزئين
+
+128
+00:11:04,670 --> 00:11:11,410
+يبقى هو coil زي ما انتوا شايفين هيه أبرا عن coil
+
+129
+00:11:11,410 --> 00:11:15,930
+structure بيتكوّن من إيه؟ من three polypeptides
+
+130
+00:11:15,930 --> 00:11:20,350
+هدا هي واحدة اللون اللي ماخدة اللون اللي بنفسها G
+
+131
+00:11:20,350 --> 00:11:25,650
+Alphaوالتانية Beta اللي مخدة اللون الأخضر و Gamma
+
+132
+00:11:25,650 --> 00:11:30,810
+اللي تحت مخدة اللون ال pink مالفوفينها and they
+
+133
+00:11:30,810 --> 00:11:35,470
+are present in a narrow image بمعنى ان في تلاتها و
+
+134
+00:11:35,470 --> 00:11:41,390
+تلاتها المفروض يا شباب عشان هي نعتبرهم pairs they
+
+135
+00:11:41,390 --> 00:11:46,330
+are pairs تلاتها و تلاتها and they are connected
+
+136
+00:11:46,330 --> 00:11:52,270
+in by a disalphide bondشايفين هذه مربوطين في الـ
+
+137
+00:11:52,270 --> 00:11:56,870
+air في الـ disulfide point Forming three domain
+
+138
+00:11:56,870 --> 00:12:04,730
+بيكونوا تلاتة domain إذا بتطلعوا هذه عندي المربعات
+
+139
+00:12:04,730 --> 00:12:10,610
+هذه في عندي hand دي domain مربع الأول يعني وكمان
+
+140
+00:12:10,610 --> 00:12:17,390
+hand دي domain وفي المصفي E domain في المصفي هذا
+
+141
+00:12:17,390 --> 00:12:22,510
+هو مربع هذا الكبيرهو عبارة عن إيه؟ E-domain يبقى
+
+142
+00:12:22,510 --> 00:12:27,470
+فعل E-domain باسك في إيه؟ في اتنين D-domain كل
+
+143
+00:12:27,470 --> 00:12:33,190
+واحد في إيه؟ في طرف أو في جهة ماشي؟ يبقى التلاتة
+
+144
+00:12:33,190 --> 00:12:36,670
+ال polypeptide جزين من التلاتة polypeptide
+
+145
+00:12:36,670 --> 00:12:43,400
+structure أو chain مربوطين هناكby disulfide bond و
+
+146
+00:12:43,400 --> 00:12:47,720
+بيكونوا تلاتة different domain تلاتة different
+
+147
+00:12:47,720 --> 00:12:53,160
+domain ماشي؟ and this is a substrate substrate
+
+148
+00:12:53,160 --> 00:12:58,480
+معناته فيه enzyme بده يشتغل عليه صح؟ بيشتغل عليه
+
+149
+00:12:58,480 --> 00:13:03,820
+two enzyme مش واحد اتنين من ال enzyme ماشي يا
+
+150
+00:13:03,820 --> 00:13:06,660
+شباب؟ فاكرين انتوا في ال coagulation cascade
+
+151
+00:13:06,660 --> 00:13:09,140
+mechanism الفابرينكيل بتكون؟
+
+152
+00:13:12,250 --> 00:13:21,450
+بتكوّل لما ثرنبيل يحفظ الفيرنوجين يتحول لين لفيرن
+
+153
+00:13:21,450 --> 00:13:29,250
+وواسطة بين ثرنبيل صح يبقى ثرنبيل this is the major
+
+154
+00:13:29,250 --> 00:13:36,650
+role بيجي بيشغل على هذا ال structureو بيحولوا إلى
+
+155
+00:13:36,650 --> 00:13:43,430
+fibrin شو بيعمل؟ بيعمل قطع في ال polypeptide Alpha
+
+156
+00:13:43,430 --> 00:13:47,770
+و Beta شو بيعملوا هنا القطع؟ في ال polypeptide
+
+157
+00:13:47,770 --> 00:13:52,330
+Alpha و Beta طلعوا دي هنا يا شباب، تحت، مواقع
+
+158
+00:13:52,330 --> 00:13:59,150
+العمل عليه، فوق إجا نسرنبل و قطع هي Alpha و Beta،
+
+159
+00:13:59,150 --> 00:14:04,450
+شايفين؟ مجبوطوالداني حاجة بيسموها فيبرينو بيبتايد
+
+160
+00:14:04,450 --> 00:14:11,590
+a and b إيش بيسموها؟ فيبرينو بيبتايد a and b ماشي
+
+161
+00:14:11,590 --> 00:14:17,470
+يا شباب؟ لما بنقطع هذا جزء من الـfibrinogen بتحول
+
+162
+00:14:17,470 --> 00:14:21,370
+الموليكيول لـfibrin بتحول الموليكيول لإيش؟
+
+163
+00:14:21,370 --> 00:14:27,270
+لـfibrin فيبرينو بيبتايد a and b لما ينقطعوا by
+
+164
+00:14:27,270 --> 00:14:32,580
+the influence of thrombin actionيجي الخروم بنقطة
+
+165
+00:14:32,580 --> 00:14:38,380
+هن و هن فبطلّع فيبرينو بطاية A قبلي لما بطلعوا من
+
+166
+00:14:38,380 --> 00:14:42,860
+الموليكيوم بتحول الفيبرينوجين إلى ايه؟ إلى فيبرينو
+
+167
+00:14:42,860 --> 00:14:49,640
+الموقع التاني اللي بتم الشغل عليه هو من قبل إنزايم
+
+168
+00:14:49,640 --> 00:14:55,760
+تاني وهو البلازمين سمعنا بالبلازمين صح؟ سمعنا ولا
+
+169
+00:14:55,760 --> 00:15:00,240
+لا؟ هو من البلازمين 100% جا من البلازمين طلعوا
+
+170
+00:15:00,240 --> 00:15:08,310
+ميكانيزمة شدهجاي من البلازمينوجين 100
+
+171
+00:15:08,310 --> 00:15:15,930
+% بيروح بتحول الى بلازمين وهذا إنظام على مين
+
+172
+00:15:15,930 --> 00:15:24,390
+بيشتغل هذا؟ على ال fibrin 100% هذا هو ال tertiary
+
+173
+00:15:24,390 --> 00:15:29,870
+hemostasis بس بيشتغل على ال fibrin لبلازمين وعلى
+
+174
+00:15:29,870 --> 00:15:35,890
+ال fibrinogenعشان هيك نسميها fibrinogen ماشي؟ و
+
+175
+00:15:35,890 --> 00:15:41,850
+بيحولوا ليش يا شباب؟ ايش بيحولوا؟ fiber
+
+176
+00:15:41,850 --> 00:15:47,370
+degradation product 100% الـ phytofibrin فبعمل
+
+177
+00:15:47,370 --> 00:15:50,850
+إذابه و أنا ماعملش إذابه و من قطع الblasemen
+
+178
+00:15:50,850 --> 00:15:54,130
+جالبتها في المواقع الحالية هذا أيه؟ شايفينها؟ هذا
+
+179
+00:15:54,130 --> 00:16:00,560
+موقع و هذا موقع شايفين الردق؟ الخطين؟انتبه عليه
+
+180
+00:16:00,560 --> 00:16:07,520
+على اللوح خط هذا و خط هذا وبالتالي قطع في موقعين
+
+181
+00:16:07,520 --> 00:16:12,460
+ايش محصلة؟ لما يقطع هذا و هذا شباب بيشيل هذا و
+
+182
+00:16:12,460 --> 00:16:18,000
+بيشيل هذا جزء يعني بيشيل ال D domain و بيخل ال E
+
+183
+00:16:18,000 --> 00:16:21,380
+domain فبصير عندنا في ال products هذه ال product
+
+184
+00:16:21,380 --> 00:16:25,020
+ال fire degradation product أكام نوع من ال
+
+185
+00:16:25,020 --> 00:16:25,420
+fragment
+
+186
+00:16:29,230 --> 00:16:35,990
+إن دي fragment و دي fragments و إي fragments و في
+
+187
+00:16:35,990 --> 00:16:38,850
+كمان fragments اسمها X هناخدها ان شاء الله التفسير
+
+188
+00:16:38,850 --> 00:16:45,930
+ماشي و X و Y X و Y بعدين هنجي بالتفسير كتب التم
+
+189
+00:16:45,930 --> 00:16:49,470
+العملية مفهوم يا شباب يبدأ هو ربطة في موقعين
+
+190
+00:16:49,470 --> 00:16:56,070
+الموقع هذا و الموقع هذا اللي بنشال من خلالهم ال D
+
+191
+00:16:56,070 --> 00:17:00,400
+domain و بيدينا D fragmentsوبما أنه عندنا 2D
+
+192
+00:17:00,400 --> 00:17:04,820
+فبتكون حاجة بيسموها DD Diamer سمعتوا فيها؟ DD
+
+193
+00:17:04,820 --> 00:17:10,220
+Diamerization لإنه بيصير فيه Diamerization للـD
+
+194
+00:17:10,220 --> 00:17:14,720
+domain اللي موجودة وبالتالي بيكون DD Diamer مفهوم
+
+195
+00:17:14,720 --> 00:17:17,640
+يا شباب؟ يبقى في موقعين بنشغل عليه هو عبارة عن
+
+196
+00:17:17,640 --> 00:17:22,040
+Substrate الموقع الأولاني هو عبارة عن الـ Crumble
+
+197
+00:17:22,040 --> 00:17:29,470
+لما بيجي بقطع Alpha و Beta وبيبتعد A وBوالباقي الـ
+
+198
+00:17:29,470 --> 00:17:35,610
+Fibrin ثم الموقع التاني هو إيه؟ الـ Plasmin اللي
+
+199
+00:17:35,610 --> 00:17:41,250
+بيقطع الـD domain عن الـE domain، عن الـE domain،
+
+200
+00:17:41,250 --> 00:17:46,370
+مفهوم أشي بقى؟ طيب، بيجي نكمل إيش موجود، إيش مكتوب
+
+201
+00:17:46,370 --> 00:17:49,970
+منه صفات، الملك اللي قبله طبعه كستمر اللي قلناها
+
+202
+00:17:49,970 --> 00:17:55,930
+اسمه Fibrin1، الملك اللي قبله طبعه 340 كدو ال half
+
+203
+00:17:55,930 --> 00:17:58,850
+-life تبعكي من أربع لستية مهمة جدا ال half-life
+
+204
+00:17:58,850 --> 00:18:05,870
+ايه ده؟ ليش؟ في ال hemostasis غير ال hemostasis ال
+
+205
+00:18:05,870 --> 00:18:14,450
+bleeding و الطريق مشي
+
+206
+00:18:14,450 --> 00:18:20,390
+كتير يعني specific بس هو دي مهمة صحية ليش؟ لإنه في
+
+207
+00:18:20,390 --> 00:18:24,190
+حاجتين، الحاجة الأولانيةلأنه indication لبعض
+
+208
+00:18:24,190 --> 00:18:26,850
+الأمراض في بعض ال inflammatory reaction بزيد ال
+
+209
+00:18:26,850 --> 00:18:30,450
+fibrinogen في حالة الectopic pregnancy بزيد ال
+
+210
+00:18:30,450 --> 00:18:36,830
+fibrinogen الحاجة التانية ال fibrinogen هو عبارة
+
+211
+00:18:36,830 --> 00:18:39,830
+عن واحد من ال coagulation factors ممكن ينغطى لناس
+
+212
+00:18:39,830 --> 00:18:44,410
+ماعندهمش فرقة، صح؟ فبالتالي لما يكون عندى عينة دم
+
+213
+00:18:44,410 --> 00:18:49,730
+من عمرها بعرف انه ضايل فيها fibrinogen ولا لا؟ ولا
+
+214
+00:18:49,730 --> 00:18:54,570
+لا؟لما يكون عندى وحدة دم على سبيل المثال بتطلع على
+
+215
+00:18:54,570 --> 00:18:56,930
+عمرها وعرف ان هو الله ضايق في عندها fiber and gel
+
+216
+00:18:56,930 --> 00:19:00,510
+ولا لأ فبالتالي بقدر أنجل منها ولا بقدرش أنجل يعني
+
+217
+00:19:00,510 --> 00:19:03,890
+بقدر أنجل في fiber and gel من وحدة عمرها فوق
+
+218
+00:19:03,890 --> 00:19:10,850
+الستية أكيد لأ نظبط بيكون خلص ال fiber طيب it's a
+
+219
+00:19:10,850 --> 00:19:16,490
+glycoprotein and it's found in alpha granules or
+
+220
+00:19:16,490 --> 00:19:21,010
+platelets مش قولنا موجودهو بعض العناس الأخرى
+
+221
+00:19:21,010 --> 00:19:28,990
+فاكتور خمسة فاكتور تمانية و فاكتور تلاتة عشوائية
+
+222
+00:19:28,990 --> 00:19:32,650
+فاكتور تلاتة عشوائية فاكتور تلاتة عشوائية فاكتور
+
+223
+00:19:32,650 --> 00:19:34,570
+تلاتة عشوائية فاكتور تلاتة عشوائية فاكتور تلاتة
+
+224
+00:19:34,570 --> 00:19:37,890
+عشوائية فاكتور تلاتة عشوائية فاكتور تلاتة عشوائية
+
+225
+00:19:37,890 --> 00:19:37,890
+فاكتور تلاتة عشوائية فاكتور تلاتة عشوائية فاكتور
+
+226
+00:19:37,890 --> 00:19:38,150
+تلاتة عشوائية فاكتور تلاتة عشوائية فاكتور تلاتة
+
+227
+00:19:38,150 --> 00:19:41,190
+عشوائية فاكتور تلاتة عشوائية
+
+228
+00:19:42,980 --> 00:19:48,140
+وهو الوضع الرئيسي للترنبيل
+
+229
+00:19:48,140 --> 00:19:53,800
+وهو أيضًا وضع البوليبلازام مافهومش بقى؟ يبقى عرفنا
+
+230
+00:19:53,800 --> 00:19:57,020
+هل جيتها الفيبرينوجين، مع المادة جيدة عناش، على
+
+231
+00:19:57,020 --> 00:20:04,120
+الفيبرينوجين ولا لأ؟ نشوف التاني، الـcoagulation
+
+232
+00:20:04,120 --> 00:20:06,380
+factor التاني هو مين؟
+
+233
+00:20:16,260 --> 00:20:19,460
+هو ثرومبن ثرومبن ثرومبن ثرومبن ثرومبن ثرومبن
+
+234
+00:20:19,460 --> 00:20:27,200
+ثرومبن ثرومبن ثرومبن ثرومبن ثرومبن ثرومبن ثرومبن
+
+235
+00:20:27,200 --> 00:20:31,740
+ثرومبن
+
+236
+00:20:31,740 --> 00:20:41,980
+ثرومبن ثرومبن
+
+237
+00:20:44,430 --> 00:20:49,250
+2 ل 4 تية يعني أقل من تية ال mean plasma
+
+238
+00:20:49,250 --> 00:20:53,150
+concentration هي عبارة عن 10 milligram per
+
+239
+00:20:53,150 --> 00:20:58,110
+deciliter وهذه كمية مقارنة بالفيبرانجين كثيرة ولا
+
+240
+00:20:58,110 --> 00:21:04,910
+جليلة قليلة لكنها كمية كبيرة جدا لأنه احنا نحتاج
+
+241
+00:21:04,910 --> 00:21:10,370
+فقط تخيلوا كده أهميته one drop one drop of
+
+242
+00:21:10,370 --> 00:21:17,570
+thrombinكفيلة بإنها اتجلت لبلاسمة اللى موجودة في
+
+243
+00:21:17,570 --> 00:21:24,330
+جسمك كلها within minutes within years within
+
+244
+00:21:24,330 --> 00:21:31,890
+minutes strong procoagulant هو أبو الكل ماشي و
+
+245
+00:21:31,890 --> 00:21:36,610
+بيقولوا شوفوا مقدش أهميته بيقولوا ان هو عبارة عن
+
+246
+00:21:36,610 --> 00:21:44,250
+the father of coagulation factorsليش؟ لو هو بيشتغل
+
+247
+00:21:44,250 --> 00:21:50,490
+على تلتاشر substrate، كم واحد؟ تلتاشر substrate،
+
+248
+00:21:50,490 --> 00:21:56,510
+ويله خمسة cofactor، تلتاشر substrate ويله خمسة
+
+249
+00:21:56,510 --> 00:22:01,790
+cofactor، ماشي؟It's a big .. it's a major .. has a
+
+250
+00:22:01,790 --> 00:22:06,030
+major role في الإياش و واحد بتفاعل مع تلتاشر أنصر
+
+251
+00:22:06,030 --> 00:22:09,530
+ما دا إيش كتير كويس والسبب في ذلك يا شباب قالوا
+
+252
+00:22:09,530 --> 00:22:13,230
+إنه لما بتكون هو الأنصر الوحيد اللي can be
+
+253
+00:22:13,230 --> 00:22:18,830
+liberated بمعنى بيتحرر من إياش من الfather
+
+254
+00:22:18,830 --> 00:22:24,970
+molecule و once liberated it can diffuse ماشي؟في
+
+255
+00:22:24,970 --> 00:22:28,650
+المنطقة التي تسمى كـ Coagulation لأن أين نتكوّن
+
+256
+00:22:28,650 --> 00:22:33,750
+الثرمبين؟ في الوضع الطبيعي لأنه يتكوّن في الوضع
+
+257
+00:22:33,750 --> 00:22:34,530
+الطبيعي لأنه يتكوّن في الوضع الطبيعي لأنه يتكوّن
+
+258
+00:22:34,530 --> 00:22:35,570
+في الوضع الطبيعي لأنه يتكوّن في الوضع الطبيعي لأنه
+
+259
+00:22:35,570 --> 00:22:36,430
+يتكوّن في الوضع الطبيعي لأنه يتكوّن في الوضع
+
+260
+00:22:36,430 --> 00:22:40,170
+الطبيعي لأنه يتكوّن في الوضع الطبيعي لأنه يتكوّن
+
+261
+00:22:40,170 --> 00:22:45,270
+في الوضع الطبيعي لأنه يتكوّن في الوضع الطبيعي لأنه
+
+262
+00:22:45,270 --> 00:22:50,310
+يتكوّن
+
+263
+00:22:50,310 --> 00:22:54,330
+في الوضع الطبيعي لأنه
+
+264
+00:22:54,330 --> 00:22:57,560
+يمفهوم الـ thrombin خلّيني أتعرف شوية على ال
+
+265
+00:22:57,560 --> 00:23:02,840
+structure of thrombin ماشي ال structure of
+
+266
+00:23:02,840 --> 00:23:06,340
+thrombin و طبعا ال structure of thrombin بيتكون من
+
+267
+00:23:06,340 --> 00:23:11,700
+هياش من خلال معرفتنا بال structure أو pro thrombin
+
+268
+00:23:11,700 --> 00:23:15,820
+الزامج بتاع ال thrombin قولنا pro thrombin و زي ما
+
+269
+00:23:15,820 --> 00:23:19,580
+انتوا شايفين هو عبارة عن single chain بيتكون من
+
+270
+00:23:19,580 --> 00:23:27,580
+تلت مناطق أساسية ماشيتلقى مناطق أساسية 1.2 و 1.3
+
+271
+00:23:27,580 --> 00:23:34,960
+ماشي يا شباب تبقوا عليّ و افهموا لأنه من خلال
+
+272
+00:23:34,960 --> 00:23:38,320
+فهمكوا لتكوين ال thrombin بتعرفوا كيف بشتغل
+
+273
+00:23:38,320 --> 00:23:45,220
+المنطقة الأولانية منطقة بيسموها اللي هو ال gla
+
+274
+00:23:45,220 --> 00:23:51,200
+portion gla اختصار ل glutamic acid residue
+
+275
+00:23:51,200 --> 00:23:57,890
+glutamic acid residueهذه اختصار لمين؟ Glutamic
+
+276
+00:23:57,890 --> 00:24:04,570
+acid تتحول
+
+277
+00:24:04,570 --> 00:24:10,490
+من glutamic acid ل glutamate للملح
+
+278
+00:24:10,490 --> 00:24:16,510
+يعني by the action of vitamin K طيب
+
+279
+00:24:16,510 --> 00:24:23,030
+كتير مهم هذا الموضوع؟مهم ليش؟ لأنه قالوا vitamin K
+
+280
+00:24:23,030 --> 00:24:30,310
+is necessary for this process ليش؟ in order to
+
+281
+00:24:30,310 --> 00:24:35,990
+enable the coagulation factor عشان اتمكن ال
+
+282
+00:24:35,990 --> 00:24:40,190
+coagulation factor from bounding with the
+
+283
+00:24:40,190 --> 00:24:44,520
+phospholipid membrane برتبطالـ Coagulation factor
+
+284
+00:24:44,520 --> 00:24:46,900
+لما بيجي .. احنا مشكلنا في ال .. في ال primary
+
+285
+00:24:46,900 --> 00:24:50,600
+hemostasis أنه البليطلة بتوفر سطح .. مظبوط سطح
+
+286
+00:24:50,600 --> 00:24:56,520
+معركة .. ساحة معركة .. باشي .. بتنشط على سطحها ..
+
+287
+00:24:56,520 --> 00:24:59,200
+ال coagulation cascade mechanism .. coagulation
+
+288
+00:24:59,200 --> 00:25:01,760
+cascade mechanism .. بيجي ال coagulation factor
+
+289
+00:25:01,760 --> 00:25:06,040
+عشان يتنشط بيغرز حر و في مين؟ في ال phospholipid
+
+290
+00:25:06,040 --> 00:25:10,640
+membraneلازم يغرز حاله .. يعني بده يرتبط بالـ
+
+291
+00:25:10,640 --> 00:25:12,520
+phospholipid membrane، في وجود ال calcium
+
+292
+00:25:12,520 --> 00:25:18,230
+طبعا،ماشي يا شباب؟ فشو بيعمل هذا؟قالوا هذا اللي
+
+293
+00:25:18,230 --> 00:25:21,790
+بيمكن العنصر هذا من إيهاش الارتباط بال
+
+294
+00:25:21,790 --> 00:25:25,970
+phospholipid membrane يوم ما يرتبط بيشتغل يعني هو
+
+295
+00:25:25,970 --> 00:25:29,790
+أيه؟ زي ما شفنا ليه بالأتلت؟ يوم ما نسكت، اتنشطت،
+
+296
+00:25:29,790 --> 00:25:34,070
+وهذا يوم ما يرتبط، ليه؟ بده يتنشط ويتحول
+
+297
+00:25:34,070 --> 00:25:40,250
+لthrombin، بده يتنشط ويتحول ل .. مفهومش بقى؟ طب
+
+298
+00:25:40,250 --> 00:25:45,740
+مين اللي بيخليه يرتبط؟ اللي Glutamateماشي اللي هي
+
+299
+00:25:45,740 --> 00:25:49,180
+في الأساس هي عبارة عن إيش؟ Glutamic acid مينحولها
+
+300
+00:25:49,180 --> 00:25:52,560
+to vitamin K عشان إيه بيسموا العنصر هذا vitamin K
+
+301
+00:25:52,560 --> 00:25:56,860
+dependent؟ بمعنى يعتمد في تصنيعه إلى إيش؟ إلى
+
+302
+00:25:56,860 --> 00:26:03,100
+vitamin K ليش؟ لإنه بيروح و هو مزود العنصر بإيش؟
+
+303
+00:26:03,100 --> 00:26:08,540
+بأداء تربط اللي هي لجلاء ل glutamate residue اللي
+
+304
+00:26:08,540 --> 00:26:13,100
+موجودة في إيش؟ في التركيبة تبعة العنصروكانوا في
+
+305
+00:26:13,100 --> 00:26:21,100
+عند البروتروم من عشرة residues في التركيب عشرة
+
+306
+00:26:21,100 --> 00:26:24,600
+أجزاء اه في repeated sequence of ايه عشرة؟ of
+
+307
+00:26:24,600 --> 00:26:28,060
+glutamic acid عشرة glutamic acid كلهم بتحولوا له
+
+308
+00:26:28,060 --> 00:26:32,520
+glutamine فبربط و بفرد حاله بقعد ماشي بفرد حاله
+
+309
+00:26:32,520 --> 00:26:34,480
+على ايه عشرة؟ على الفشفة اللي في ال membrane و
+
+310
+00:26:34,480 --> 00:26:38,410
+بقعدمفروض يا شباب؟ وكل الـVitamin K dependent اللي
+
+311
+00:26:38,410 --> 00:26:41,310
+زيه هو نفس الحكاية بكتسبه هذه الخاصية من
+
+312
+00:26:41,310 --> 00:26:44,690
+الـVitamin K إنه بيحول لglutamic لglutamate
+
+313
+00:26:44,690 --> 00:26:49,950
+وبالتالي بيمكن العنصر من الارتباط بالـphospholipid
+
+314
+00:26:49,950 --> 00:26:54,470
+membrane، مفروض؟ الجزء التالع يا شباب، كانوا فيه
+
+315
+00:26:54,470 --> 00:27:01,350
+two cringles و الـcringle بالعربي أنا مش عارف اش
+
+316
+00:27:01,350 --> 00:27:04,610
+تعرف معناتها، لكن هي منحنة بالشكل
+
+317
+00:27:09,770 --> 00:27:14,530
+ماشى؟ مالهاش ترجمة عارفى؟ عربي، ماشى؟ اسم أكرج،
+
+318
+00:27:14,530 --> 00:27:18,730
+منحنى، ماشى؟ إمبعاج، في مين؟ في ال structure of
+
+319
+00:27:18,730 --> 00:27:23,570
+إيش؟ of the molecule في أغلب ال molecule بيكون
+
+320
+00:27:23,570 --> 00:27:28,250
+فيها ال active site مخبّى، مبعوش، جوا فى الداخل،
+
+321
+00:27:28,250 --> 00:27:32,400
+في ال zymogen formماشي؟ وكلكم بتعرفوا أنه يوم ما
+
+322
+00:27:32,400 --> 00:27:35,440
+بدنا نحوّل ال zymogen ل enzyme هذا الكلام اللي
+
+323
+00:27:35,440 --> 00:27:38,600
+أخدته في ال biochemistry بيتعرض ال zymogen إلى
+
+324
+00:27:38,600 --> 00:27:44,040
+إيش؟ إلى عملية قطعة مش هيك أخدته؟ cleavage صح؟
+
+325
+00:27:44,040 --> 00:27:48,280
+فإيش بيبين؟ ال active site فبتحول ل enzyme بتحول ل
+
+326
+00:27:48,280 --> 00:27:53,460
+إيه؟ لكن هو طول ما هي ال active site مخبية بشتغل؟
+
+327
+00:27:54,250 --> 00:27:58,350
+عشان انا أخلّيه يشتغل، بدي أبينها، بدي أظهرها،
+
+328
+00:27:58,350 --> 00:28:02,530
+فبروحوا أنا بقاطة، في أقلب العناصر، بيكون الـ
+
+329
+00:28:02,530 --> 00:28:05,110
+active site في هذه المنطقة، لكن في هذا غير صنع، مش
+
+330
+00:28:05,110 --> 00:28:08,510
+في هذه المنطقة، ومش عارفين إيش دورهم، لغاية الآن
+
+331
+00:28:08,510 --> 00:28:11,810
+الـkringle، ماعرف، has unknown function، has
+
+332
+00:28:11,810 --> 00:28:17,170
+unknown function، لكن هم موجودين، طب واللي بعدها،
+
+333
+00:28:17,170 --> 00:28:20,690
+جزء اللي بعدها، جالوا في هذه المنطقة، في الـ
+
+334
+00:28:20,690 --> 00:28:21,210
+Catalytic
+
+335
+00:28:24,680 --> 00:28:29,900
+Catalytic sites يبقى
+
+336
+00:28:29,900 --> 00:28:36,140
+هون موجودة Catalytic sites وزي أي زيموجين قلنا
+
+337
+00:28:36,140 --> 00:28:40,760
+عشان يتحول لإنزايم بده قطع لبرومبين عشان يتحول
+
+338
+00:28:40,760 --> 00:28:47,400
+لثرومبين يحتاج إلى قطعين مش قطع واحد يحتاج يحتاج
+
+339
+00:28:47,400 --> 00:28:52,240
+إلى قطعين هالجيت بورجيك ماشي؟ وبقطع جالو بنقطع عند
+
+340
+00:28:52,240 --> 00:28:54,040
+التلاتمية
+
+341
+00:28:55,360 --> 00:29:00,640
+وعشرين amino acids عند الـ bond هذه وعند مين؟ عند
+
+342
+00:29:00,640 --> 00:29:08,420
+الـ 271 يعني بالأكتر في الموقعين وبالتالي في عندنا
+
+343
+00:29:08,420 --> 00:29:11,580
+intermediates وبالتالي إيش في عندنا intermediates
+
+344
+00:29:11,580 --> 00:29:17,380
+وإذا عرفنا إن كل ال molecule هو عبارة عن يعني
+
+345
+00:29:17,380 --> 00:29:21,140
+المراجع مختلفة الصحية في مراجع جلد 608 amino acids
+
+346
+00:29:22,470 --> 00:29:28,190
+وفي مراجعة قالت لأ هو خمسمية وتسعين خمسمية تمانية
+
+347
+00:29:28,190 --> 00:29:32,610
+وتسعين amino acids whatever ماشي يعني في حدود
+
+348
+00:29:32,610 --> 00:29:37,590
+ستمائة amino acids كل المركب لما بنقطع القطعة
+
+349
+00:29:37,590 --> 00:29:41,670
+الأولى بنقطع انت 320 يعني من النص تقريبا من اياش
+
+350
+00:29:41,670 --> 00:29:46,410
+تقريبا من النص وبدينا عصرية بدينا intermediate
+
+351
+00:29:46,410 --> 00:29:49,430
+forms اللي قلنا عنها بدينا الميزو
+
+352
+00:29:57,770 --> 00:30:07,150
+Thrombin ماشي زائد حاجة بيسموها fragment one و two
+
+353
+00:30:07,150 --> 00:30:17,730
+بيجي بنقطة منها في الأول ماشي نوات ينقطع يعني نوات
+
+354
+00:30:17,730 --> 00:30:20,030
+ينقطع بيعطينا ميزو ثرومبين اه بيعطينا ميزو ثرومبين
+
+355
+00:30:20,030 --> 00:30:24,910
+و بيعطينا fragment واحد و اتنينطبعا بعد ذلك بتحول
+
+356
+00:30:24,910 --> 00:30:31,510
+اللى ال thrombin بأنواع مختلفة اللى هى Alpha و
+
+357
+00:30:31,510 --> 00:30:37,470
+Beta و Gamma ماشي المختلفة بس عشان تفهموا نقطة
+
+358
+00:30:37,470 --> 00:30:44,030
+معينة شباب مدي أرسم الكورسين القطع بتمها عند 320
+
+359
+00:30:44,030 --> 00:30:49,050
+فبالتالي القطع الأولانى بيكون بالشكل هذا هذا هو
+
+360
+00:30:49,050 --> 00:30:54,280
+شكف هادي كله تجه هذاماشي؟ ثم الشكفة التانية هدا هي
+
+361
+00:30:54,280 --> 00:31:01,500
+271 و 320 وهذا ال catalytic صح؟ صح مظبوط، هدا هي
+
+362
+00:31:01,500 --> 00:31:06,680
+الشكفة التانية القطع التاني بتمعنى 171 وفي ندفة
+
+363
+00:31:06,680 --> 00:31:13,780
+هادي، di-sulphate bond فبتحول المولوكيوم إلى،
+
+364
+00:31:13,780 --> 00:31:22,210
+ماشي؟ هادي، ثم نقطع من هنا، تبدللأنه مربوطة فبصير
+
+365
+00:31:22,210 --> 00:31:27,690
+إن الموليكيول بدل ما هو one chain صاريح two chains
+
+366
+00:31:27,690 --> 00:31:33,130
+واحدة كبيرة و بيسموها heavy والتانية صغيرة وشو
+
+367
+00:31:33,130 --> 00:31:39,250
+بيسموها light الكبيرة حوالي 29.59 أمين و أسل
+
+368
+00:31:39,250 --> 00:31:44,510
+والصغيرة حوالي 49 أمين و أسل و بيكون حاجة بيسموها
+
+369
+00:31:44,510 --> 00:31:45,570
+alpha thrombin
+
+370
+00:31:50,250 --> 00:31:53,290
+which is the active and mature thrombin active and
+
+371
+00:31:53,290 --> 00:31:57,850
+mature thrombin هو اللي بيشتغل المفهوم شباب و طبعا
+
+372
+00:31:57,850 --> 00:32:00,330
+هاي الوزانة اللي شايفينها هاي ال alpha thrombin
+
+373
+00:32:00,330 --> 00:32:06,850
+ممكن نقطع كمان قطعة و يدينا ال beta thrombin و
+
+374
+00:32:06,850 --> 00:32:11,950
+كمان هي قطعة ال beta domain أو chain ل beta 1 ل
+
+375
+00:32:11,950 --> 00:32:19,250
+beta 2 كمان beta 2 ممكن تنقطع و تدينا 4 أو 5 ماشي؟
+
+376
+00:32:19,680 --> 00:32:23,600
+هو يدّينا دا اللي هو النوع التاني التالت الوجامة
+
+377
+00:32:23,600 --> 00:32:27,560
+ثرمبين بغض النظرية اللي بيتكونوا انترو انفيدو لكن
+
+378
+00:32:27,560 --> 00:32:33,540
+المهم ال MV هو ال alpha-thrombin فهمتوا يا شباب؟
+
+379
+00:32:33,540 --> 00:32:38,400
+يبقى هو عبارة عن single chain لكن لما صار انزايم
+
+380
+00:32:38,400 --> 00:32:42,940
+تحول إلى double chain واحدة heavy واحدة light ال
+
+381
+00:32:42,940 --> 00:32:46,040
+heavy هي اللي فيها ال catalytic sites يعني هي اللي
+
+382
+00:32:46,040 --> 00:32:51,740
+فيها الشغل هي اللي فيها الشغلمفهومة يا شباب؟ حد
+
+383
+00:32:51,740 --> 00:32:58,320
+عنده سؤال؟ طيب، نشوف إيش فيه، فيه معلومات مكتوبة
+
+384
+00:32:58,320 --> 00:33:02,920
+الـmost molecular weight تبعه 71.6، صغير
+
+385
+00:33:02,920 --> 00:33:06,960
+بالنسبالها الـfibrinogen، الـsubstrate، إشي كتير،
+
+386
+00:33:06,960 --> 00:33:10,180
+عشان هيك بنقطع، فيه أكتر من موقع، نمرة 2 الـhalf
+
+387
+00:33:10,180 --> 00:33:14,180
+-life تبعته 2 ل4، هناك جد إيه؟ نمرة 3 المolecular
+
+388
+00:33:14,180 --> 00:33:17,340
+weight لـplasma concentration 10 ملي جرام، هناك جد
+
+389
+00:33:17,340 --> 00:33:18,500
+إيه؟ 300
+
+390
+00:33:24,380 --> 00:33:30,560
+it's vitamin cation it's
+
+391
+00:33:30,560 --> 00:33:35,980
+glycoprotein وهي موجود في ال alpha granule of
+
+392
+00:33:35,980 --> 00:33:43,220
+platelet and it has a mirror image of alpha و beta
+
+393
+00:33:43,220 --> 00:33:48,610
+و gammaعلى الأشكال التلاتة، هلاقيهم تقريبا متشابع،
+
+394
+00:33:48,610 --> 00:33:53,030
+mirror image يعني لكن كل ما هناك نو فيه قواطع
+
+395
+00:33:53,030 --> 00:33:58,950
+جديدة طبعا these polypeptided chains are linked
+
+396
+00:33:58,950 --> 00:34:01,970
+together by a disulfide bond وهي ال disulfide bond
+
+397
+00:34:01,970 --> 00:34:09,110
+اللي هي ال bridges، ماشي؟ تفهم علي؟ and it's
+
+398
+00:34:09,110 --> 00:34:17,060
+primarily substrate for trumpetطبيعي and it's a
+
+399
+00:34:17,060 --> 00:34:22,140
+substrate for the plasma قدامها نشوف أنه بيعمل ال
+
+400
+00:34:22,140 --> 00:34:25,240
+plasma برضه بيشتغل عليه و بيعمله cultivation و
+
+401
+00:34:25,240 --> 00:34:30,800
+بيعمل challenge بينه بينه حد ليه ليه جرميكاليزم؟
+
+402
+00:34:30,800 --> 00:34:34,420
+it's a series of proteins كل سلوكة بعدها اللي هو
+
+403
+00:34:34,420 --> 00:34:37,660
+factor 13 هو transglutaminase حد ياخده الطرف
+
+404
+00:34:37,660 --> 00:34:40,400
+السليماني المفهوم أشبه .. حد عنده سؤال
+
+405
+00:34:44,500 --> 00:34:47,620
+معلومات كافية عن Trumpet يعني المحاضرة الجاية لما
+
+406
+00:34:47,620 --> 00:34:50,980
+أجي عن ال cascade أحكي عن ال cascade مش راح نعيد
+
+407
+00:34:50,980 --> 00:34:55,400
+السفات تبعته لإننا نعرف إيش يعني Trumpet real هو
+
+408
+00:34:55,400 --> 00:34:58,720
+الأساس هو ال big هو اللي بيشتغل كل مكان وزي ما
+
+409
+00:34:58,720 --> 00:35:05,180
+اتفقنا ال diffuse liberate and diffuse ماشي فتالت
+
+410
+00:35:05,180 --> 00:35:11,260
+هو عبارة عن tissue factor factor رقم تلاتة هو ايش؟
+
+411
+00:35:11,260 --> 00:35:16,200
+tissue factorAlso known as tissue factor and
+
+412
+00:35:16,200 --> 00:35:22,160
+synonymous with tissue thromboplastin سمعتوا بالـ
+
+413
+00:35:22,160 --> 00:35:26,080
+tissue thromboplastin؟ ماحكلكوش أستاذ واقل عن هذا
+
+414
+00:35:26,080 --> 00:35:30,260
+في المعمل؟ لسه مقدمة طيب، ال tissue thromboplastin
+
+415
+00:35:30,260 --> 00:35:34,760
+هو أبداً ال agent of إيش؟ of prothrombin time يا
+
+416
+00:35:34,760 --> 00:35:38,180
+شباب، فحص مهم جدا، هتاخدوه بالتفاصيل الممالية،
+
+417
+00:35:38,180 --> 00:35:41,220
+هتشتغلوه في المعمل، إن شاء الله، هو الزمن المطلوب
+
+418
+00:35:41,220 --> 00:35:41,960
+لقياس
+
+419
+00:35:44,990 --> 00:35:48,530
+الزمن، قياس الزمن المطلوب لحدوث جلطة، قياس الزمن
+
+420
+00:35:48,530 --> 00:35:56,030
+المطلوب لحدوث جلطة by the extrinsic pathway المهم،
+
+421
+00:35:56,030 --> 00:35:59,490
+هذا عبارة عن هداك ال-thromboplastin عبارة عن crude
+
+422
+00:35:59,490 --> 00:36:05,730
+mixture، crude بمعنى مش .. مش صافي، ماشي؟ شو عبارة
+
+423
+00:36:05,730 --> 00:36:07,650
+عن إيه؟ قالوا عبارة عن tissue factor مع
+
+424
+00:36:07,650 --> 00:36:11,170
+phosphoricate، tissue factor مع إيه؟ وكأننا لما
+
+425
+00:36:11,170 --> 00:36:17,150
+بنحكي على factor تلاتة، بنحكي علشانعلى اللى هو ال
+
+426
+00:36:17,150 --> 00:36:19,910
+phospholipid membrane كنا حاكين عنه هذا of
+
+427
+00:36:19,910 --> 00:36:22,670
+platelets او تشوف ال factor اللى بيطلع من ال blood
+
+428
+00:36:22,670 --> 00:36:27,490
+vessels ماشي نفس ال structure بقولك اللى بيبقى 44
+
+429
+00:36:27,490 --> 00:36:31,890
+كده ده طبعا كلنا بنعرف ان شباب هذا ممنوع يكون في
+
+430
+00:36:31,890 --> 00:36:38,070
+الدم ولا لأ ليش لأ ده بيغلق الجلد بنشط مين؟ بنشط
+
+431
+00:36:38,880 --> 00:36:41,960
+الـ Extrinsic Pathway of Coagulation Cascade
+
+432
+00:36:41,960 --> 00:36:45,540
+Mechanism، وحنشوف المحاضرة الجاية في هذا الكلام.
+
+433
+00:36:46,980 --> 00:36:52,680
+Its half-life نقدرش نحكي عنها لأنه إنساليبل، مش
+
+434
+00:36:52,680 --> 00:36:56,580
+موجود في البلازمة، مظبوط؟ لا يدوج في البلازمة، ولا
+
+435
+00:36:56,580 --> 00:36:59,160
+لا يدوج ولا لا يوجد في البلازمة. من البلازمة،
+
+436
+00:36:59,160 --> 00:37:04,600
+concentration non-circulating and its lipoprotein
+
+437
+00:37:04,600 --> 00:37:07,620
+and usually constitutive lipoprotein of
+
+438
+00:37:07,620 --> 00:37:11,370
+subendotheliumهو موجود في الـ sub-endothelia
+
+439
+00:37:11,370 --> 00:37:14,010
+layer، مش في الـ endothelia، في الـ sub
+
+440
+00:37:14,010 --> 00:37:18,430
+-endothelia، عشان هيك يوم ما تصير مزعج، بتطلع And
+
+441
+00:37:18,430 --> 00:37:23,590
+it's pro-coagulant، بمعنى بيعمل جلطة ولا لا؟
+
+442
+00:37:23,590 --> 00:37:30,210
+Calcium, يا شباب، اللي هو factor رقم أربعة And
+
+443
+00:37:30,210 --> 00:37:36,950
+it's an essential mineralوالـ 40 دالتون و الـ half
+
+444
+00:37:36,950 --> 00:37:41,270
+-life not available موجود على طول الـmini plasma
+
+445
+00:37:41,270 --> 00:37:44,150
+concentration 8 ل 10 ميلي جرام per deciliter
+
+446
+00:37:44,150 --> 00:37:52,050
+واحفظوه شباب الكالشيوم مطلوب لكل خطوات الـ
+
+447
+00:37:52,050 --> 00:37:56,950
+coagulation cascade ميكانيزة بعد البدايات
+
+448
+00:37:56,950 --> 00:38:03,060
+والنهايات احفظوه حاجة بالشكل هذافي كل الخطوات
+
+449
+00:38:03,060 --> 00:38:09,700
+موجود ومطلوب مع ذا بدايات اللي هو الـ Coagulation
+
+450
+00:38:09,700 --> 00:38:16,680
+Cascade Mechanism and The End اللي هو عملية تحويل
+
+451
+00:38:16,680 --> 00:38:20,580
+الـ Fibrin جلّا Fibrin ماشي، هذه مش مطلوب فيها الـ
+
+452
+00:38:20,580 --> 00:38:28,020
+Calcium لكنه مطلوب وبشدة في بعض المواقع زي على
+
+453
+00:38:28,020 --> 00:38:33,040
+سبيل المثال Activation of Factor Xو activation of
+
+454
+00:38:33,040 --> 00:38:37,460
+air فاكتور 13 وهذه مواقع حساسة جدا في ال
+
+455
+00:38:37,460 --> 00:38:43,260
+coagulation ماشي
+
+456
+00:38:43,260 --> 00:38:54,320
+خمسة فاكتور خمسة socially known as labile factor
+
+457
+00:38:54,320 --> 00:38:58,000
+او proaxillary
+
+458
+00:39:02,870 --> 00:39:07,010
+و في يوم من الأيام كانوا يقرؤوا factor 6 كانوا
+
+459
+00:39:07,010 --> 00:39:11,470
+بسبب .. بفكروا إيش؟ factor 6 لكن بعد فترة رجوا أنه
+
+460
+00:39:11,470 --> 00:39:16,350
+مافيش factor 6 فيه إيش؟ فقط خمسة and it's a
+
+461
+00:39:16,350 --> 00:39:24,110
+substrate for thrombin اللي هو name إيه يا شباب؟
+
+462
+00:39:24,110 --> 00:39:29,370
+صح؟ مش thrombin جامل بقى thrombin؟ مية في الميات
+
+463
+00:39:29,370 --> 00:39:34,150
+يعني ال pro thrombin رقم اتنينو ال active form
+
+464
+00:39:34,150 --> 00:39:39,470
+يعني ايه؟ يعني 2A هو عبارة عن substrate for
+
+465
+00:39:39,470 --> 00:39:45,110
+thrombin and factor 10A و
+
+466
+00:39:45,110 --> 00:39:50,190
+هنشوف كيف بتتم الحكاية أنا
+
+467
+00:39:50,190 --> 00:39:55,070
+تهزم weight of 330 kilo و ال half-life تبعته من نص
+
+468
+00:39:55,070 --> 00:39:59,830
+لواحد و نص يوم عمالها بتقل ال layer و طبيعي لإنه
+
+469
+00:39:59,830 --> 00:40:05,680
+labile، labile يعني بتكسر بسرعةبظبط؟ اه and ال
+
+470
+00:40:05,680 --> 00:40:08,460
+concentration بلاحظ ما ال concentration واحد
+
+471
+00:40:08,460 --> 00:40:12,160
+milligram بدينا بال تلت مية لأ بدينا تلت مية
+
+472
+00:40:12,160 --> 00:40:18,800
+لاربعمية ثم عشر ثلاثة
+
+473
+00:40:18,800 --> 00:40:25,620
+مش موجود في الدم اربعة calcium وخمسة
+
+474
+00:40:25,620 --> 00:40:30,480
+واحد سهل لأ؟ و ال half life نفس الحكاية برضه
+
+475
+00:40:30,480 --> 00:40:37,640
+بالترتيبجالو انه 25% من هذا المراكم موجود في
+
+476
+00:40:37,640 --> 00:40:40,760
+الـAlpha granules of platelets من 20% ل 25%
+
+477
+00:40:40,760 --> 00:40:45,480
+الصحيح، حسب المراجع المختلفة جالو around 20 to 25
+
+478
+00:40:45,480 --> 00:40:51,020
+persons يعني بين جسيم ربع كمية هذا المراكم موجود
+
+479
+00:40:51,020 --> 00:40:54,700
+في الـplatelet مخزون وين؟ في الـplatelet وهذا شيء
+
+480
+00:40:54,700 --> 00:41:00,340
+جيد جدا لأنه الـplatelet أول ما بتصل الجريحو
+
+481
+00:41:00,340 --> 00:41:04,280
+بتتنشط و بتطلع النياز، يعني على طول، مظبوط، و
+
+482
+00:41:04,280 --> 00:41:07,620
+الأحلى ما في الموضوع أنه انه receptor على سطح مين؟
+
+483
+00:41:07,620 --> 00:41:13,980
+لـ Platelet، ماشي؟ و بيشترك في تكوين Complex،
+
+484
+00:41:13,980 --> 00:41:19,520
+شوفوا الأهمية اللي تبعته، بيشترك في تكوين Complex
+
+485
+00:41:19,520 --> 00:41:24,680
+على سطح لـPlatelet، فجيت خلاص، مش لازمنا نغرز حد
+
+486
+00:41:24,680 --> 00:41:30,630
+في الهياش؟في الـ Phospholipid من مريمه هو already
+
+487
+00:41:30,630 --> 00:41:33,050
+موجود ال factor خمسة وهو عبارة عن calculation
+
+488
+00:41:33,050 --> 00:41:38,730
+factor مظبوط موجود وقاعد على سطح ال platelet لأنه
+
+489
+00:41:38,730 --> 00:41:43,290
+فيه له receptor صح؟ شو يمل؟ كانوا كوّن complex
+
+490
+00:41:43,290 --> 00:41:48,750
+بيتكوّن هذا ال complex من factor عشرة A و factor
+
+491
+00:41:48,750 --> 00:41:56,080
+خمسة لكن في صورته نشطة Aماشي لأن الـThrombin بنشط
+
+492
+00:41:56,080 --> 00:42:01,920
+خمسة و تمانية و بيحولهم لخمسة A و تمانية A ثم ال
+
+493
+00:42:01,920 --> 00:42:08,180
+Calcium و Phospholipid فهو احنا قاعدين على سطح مين
+
+494
+00:42:08,180 --> 00:42:12,360
+اللي هو عبارة عن Phospholipid membrane، مجبوط؟
+
+495
+00:42:12,360 --> 00:42:17,480
+بيكونوا Complex بيسموه Pro-thrombinase Complex
+
+496
+00:42:26,400 --> 00:42:29,760
+ماشي بعملها ده؟ قالوا أخينا هذا هو زي ما انتم
+
+497
+00:42:29,760 --> 00:42:37,660
+لاحظينه يا شباب هو عبارة عن Quaternary Complex
+
+498
+00:42:37,660 --> 00:42:43,420
+Structure كل
+
+499
+00:42:43,420 --> 00:42:47,860
+ال Complex اللي بتتكون فيه داخل اللي هو ال
+
+500
+00:42:47,860 --> 00:42:51,860
+Hemostatic Mechanism يعني عبارة عن Quaternary
+
+501
+00:42:51,860 --> 00:42:56,670
+Structure Molecules رباعي ماشي بشتغل بيه علاجعلى
+
+502
+00:42:56,670 --> 00:43:00,890
+هيئة الربعية شو بيقول هذا ال program بنقل complex؟
+
+503
+00:43:00,890 --> 00:43:13,830
+بيحول ال factor 2 إلى 2A من
+
+504
+00:43:13,830 --> 00:43:20,250
+الأساس في الموضوع عشرة اللي اللحظه عشرة هو النشط
+
+505
+00:43:20,250 --> 00:43:25,860
+خمسة is a cofactor الكالسيوم cofactorوال
+
+506
+00:43:25,860 --> 00:43:29,500
+phospholipid membrane هي أبدا قاعدة برضه تعتبر
+
+507
+00:43:29,500 --> 00:43:33,820
+cofactor، يبقى من ال enzyme في هذه الشلة؟ العشرة،
+
+508
+00:43:33,820 --> 00:43:38,420
+عشرة ايه؟ بدوا يشتغلوا و يغطى على مين؟ على اتنين و
+
+509
+00:43:38,420 --> 00:43:41,120
+يحولوا لمين؟ اتنين ايه؟ مية فالمية، اتنين ايه يعني
+
+510
+00:43:41,120 --> 00:43:45,480
+ايش؟ عشرة اكتر، يعني ثرومبين، ثرومبين، صح؟ يعني
+
+511
+00:43:45,480 --> 00:43:49,580
+يحول البروثرومبين إلى ايه؟ إلى ثرومبين، ماشي يا
+
+512
+00:43:49,580 --> 00:43:59,200
+شباب؟جاله غياب هذا العنصر اللي هو factor V أو ما
+
+513
+00:43:59,200 --> 00:44:04,300
+يُعرف بالـ labile factor أو الـ Proaxilarin كل هذه
+
+514
+00:44:04,300 --> 00:44:12,740
+أسماء لخمسة بيعمل مرض بيسموها Orange Disease أو
+
+515
+00:44:12,740 --> 00:44:20,080
+Parahemophilia أو Parahemophilia وطبعا كلنا عارفين
+
+516
+00:44:20,080 --> 00:44:25,140
+أنهالـ hemophilia هي برا من برض نظيف صح؟ bleeding؟
+
+517
+00:44:25,140 --> 00:44:28,860
+مظبوط و البرا hemophilia نظيف يعني غياب خمسة بيعمل
+
+518
+00:44:28,860 --> 00:44:33,580
+نظيف بيعمل إيه؟ bleeding بيعمل bleeding و بساطة
+
+519
+00:44:33,580 --> 00:44:36,760
+عشان بيعمل bleeding لإنه ما تكونش ال complex هذا و
+
+520
+00:44:36,760 --> 00:44:39,320
+إذا ما تكونش ال complex هذا يعني مش بس خمسة اللي
+
+521
+00:44:39,320 --> 00:44:49,180
+بيغيب كله فاهمين عليا؟ اللي بعده ستة
+
+522
+00:44:49,180 --> 00:44:56,400
+مش موجودسبعة موجودة طبعا كله بعد هيك موجود also
+
+523
+00:44:56,400 --> 00:45:02,140
+known as stable factor اذاك لباين و هذا stable
+
+524
+00:45:02,140 --> 00:45:06,800
+factor and it's customary called factor seven
+
+525
+00:45:06,800 --> 00:45:12,020
+بقولك ان الوقت تبقى خمسين كيلو دالتون و ال half
+
+526
+00:45:12,020 --> 00:45:16,640
+-life تبعته hours بطرنا نحكي على أيام أخر واحد
+
+527
+00:45:16,640 --> 00:45:17,460
+حكينا عليه يوم
+
+528
+00:45:21,040 --> 00:45:28,640
+وهذا hours، من خمسة لتمانية hours، ساعات، وهو أقل
+
+529
+00:45:28,640 --> 00:45:37,860
+العوامل عمرا، أقل العوامل عمرا، half-life، قليلة
+
+530
+00:45:37,860 --> 00:45:43,700
+جدا، و ال plasma concentration قليلة، 0.05
+
+531
+00:45:43,700 --> 00:45:50,570
+milligramفي أقل، بس هذا برضه من العناصر القليلة، 0
+
+532
+00:45:50,570 --> 00:45:55,330
+.05 milligram per deciliter and it's one of the
+
+533
+00:45:55,330 --> 00:45:59,030
+vitamin K dependent coagulation factors، يعني بتمد
+
+534
+00:45:59,030 --> 00:46:04,790
+على vitamin K، والوحيد في ال coagulation factors
+
+535
+00:46:05,460 --> 00:46:12,900
+التي عادةً تتحول إلى زيموجين وإنزايم زيموجين لكن
+
+536
+00:46:12,900 --> 00:46:20,900
+الشكل الإنزايمي منه هو الـ traces الشكل الإنزايمي
+
+537
+00:46:20,900 --> 00:46:28,870
+قليل جدا لأنه يخوف يخوف واحد يعش يعملبلوفي لـ
+
+538
+00:46:28,870 --> 00:46:32,250
+blood circulation in its active form لكنه موجود
+
+539
+00:46:32,250 --> 00:46:38,510
+بكميات قليلة جدا and it's also a serine protease
+
+540
+00:46:38,510 --> 00:46:41,930
+ماشي
+
+541
+00:46:41,930 --> 00:46:47,790
+يا شباب طبعا ال factor 7 هتشوف دوره مهم جدا في
+
+542
+00:46:47,790 --> 00:46:51,770
+تنشيط ال extrinsic pathway of the coagulation
+
+543
+00:46:51,770 --> 00:46:59,770
+cascade mechanism تمانى يا شبابيسموه Anti
+
+544
+00:46:59,770 --> 00:47:03,650
+-Hemophilic Factor تبع الهموفيليا، مظبوط، Anti
+
+545
+00:47:03,650 --> 00:47:11,610
+-Hemophilic Factor و الملوك الهموبيت تبعه 330 كيلو
+
+546
+00:47:11,610 --> 00:47:17,430
+دالتون ال half-life تبعته hours برضه، من 8 إلى 12
+
+547
+00:47:17,430 --> 00:47:26,250
+ساعة، it's very labileوالمشكلة بتكسر بسرعة ومشكلة
+
+548
+00:47:26,250 --> 00:47:29,890
+انه it cannot circulates in its free form وانما
+
+549
+00:47:29,890 --> 00:47:33,290
+دايما مربوط بإيش؟ بالvolatile gram factor
+
+550
+00:47:33,290 --> 00:47:37,230
+فvolatile gram factor بيحمي بالظبط protect factor
+
+551
+00:47:37,230 --> 00:47:42,570
+تمانية from protein degradation فبيحمي دايما مربوط
+
+552
+00:47:42,570 --> 00:47:48,330
+بيه؟ بالvolatile gram factor وبالتالي يا شباب
+
+553
+00:47:48,330 --> 00:47:52,870
+تخيلوا هنا لازم ناخد فعلا اعتبار قاعدة لإنه لفاري
+
+554
+00:47:52,870 --> 00:47:59,550
+لفاريالناس اللي عندهم vom-lebran disease ماعندهم
+
+555
+00:47:59,550 --> 00:48:03,870
+مش factor اتبعه وبالتالي بيكون عندهم بالاضافة لل
+
+556
+00:48:03,870 --> 00:48:07,710
+vom-lebran disease Hemophilia بينما الناس اللي
+
+557
+00:48:07,710 --> 00:48:12,270
+عندهم Hemophilia بيكونش عندهم vom-lebran disease
+
+558
+00:48:12,270 --> 00:48:18,150
+يبقى مين بيعتمد على التاني؟ تمانية بيعتمد على vom
+
+559
+00:48:18,150 --> 00:48:20,250
+-lebran factor الحاجة التالية اللي بدنا ناخدها
+
+560
+00:48:20,250 --> 00:48:22,330
+فيها الاتبار انه they both
+
+561
+00:48:26,490 --> 00:48:31,630
+بمعنى in different area فfactor تمانية بتصنع في ال
+
+562
+00:48:31,630 --> 00:48:36,930
+liver و ال volume بتصنع في اكتر من موقع ال planet
+
+563
+00:48:36,930 --> 00:48:41,270
+من خلال ال mega karyocyte و موجود في ال
+
+564
+00:48:41,270 --> 00:48:45,630
+endothelial cell في مخازنه اللي سمناها المرة اللي
+
+565
+00:48:45,630 --> 00:48:50,790
+فاتت ايش سمناها
+
+566
+00:48:51,510 --> 00:49:00,970
+Pallid Places موجود
+
+567
+00:49:00,970 --> 00:49:06,970
+في الاندوثيلين وموجود في ال platelets Alpha
+
+568
+00:49:06,970 --> 00:49:15,630
+granules of platelets وبالتالي هذا هو موجود في
+
+569
+00:49:15,630 --> 00:49:19,570
+موقع ايه طبعا
+
+570
+00:49:19,570 --> 00:49:23,810
+فاكتور تمانيةمع ال Von Willebrand بيكون المغلقب
+
+571
+00:49:23,810 --> 00:49:28,210
+الأساسي اللي احنا شايفينه Von Willebrand مع factor
+
+572
+00:49:28,210 --> 00:49:33,910
+8 وزي ما انتوا شايفين ال Von Willebrand أكبر بكثير
+
+573
+00:49:33,910 --> 00:49:39,850
+حجما من factor 8 في بعض المراجع بنقول انه 90% من
+
+574
+00:49:39,850 --> 00:49:44,470
+ال structure هو عبارة عن Von Willebrand وال10%
+
+575
+00:49:44,470 --> 00:49:53,200
+بشكل ده factor 9 فاهم مشوف ايش كمان مكتوبPlasma
+
+576
+00:49:53,200 --> 00:49:58,840
+concentration 0.01 توقعنا نحكي على 0.5 يعني هذا
+
+577
+00:49:58,840 --> 00:50:04,460
+أقل من إيش من سبعة تمانية أقل من سبعة ال troubles
+
+578
+00:50:04,460 --> 00:50:09,160
+in plasma زياتير و بيمر طبعا احنا قاعدين بنقول
+
+579
+00:50:09,160 --> 00:50:13,540
+مربوط في مين؟ في الوحو دي برنامج and it's a
+
+580
+00:50:13,540 --> 00:50:18,890
+thrombin substrate factor تمانيةإنه 100% بنشطه لـ
+
+581
+00:50:18,890 --> 00:50:22,990
+Thrombin فبالتالي بيشتغل عليه صح؟ Thrombin
+
+582
+00:50:22,990 --> 00:50:28,570
+substrate and it is also a core factor في Complex
+
+583
+00:50:28,570 --> 00:50:34,190
+تاني بيسموه تنيز Complex ونشوف مما يتكون التنيز
+
+584
+00:50:34,190 --> 00:50:44,310
+شباب شوفنا هذا مظبوط؟ شوفنا هذا التنيز يتكوّن من
+
+585
+00:50:44,310 --> 00:50:44,790
+القادة
+
+586
+00:50:47,510 --> 00:50:58,570
+بيتكون من factor 9A مع تمانية برضه A مع الكارسيوم
+
+587
+00:50:58,570 --> 00:51:05,550
+والفسفوليبيت و برضه قوة T النارى و برضه A و ال ash
+
+588
+00:51:05,550 --> 00:51:13,770
+بيعمل بيحول ash عشرة الى عشرة E
+
+589
+00:51:16,970 --> 00:51:26,650
+و بيسموه تنيز لإنه بيشتغل علياش Complex تنيز
+
+590
+00:51:26,650 --> 00:51:30,770
+Complex ماشي يا شباب يبقى two complexes و التنيل
+
+591
+00:51:30,770 --> 00:51:34,210
+quaternary ماشي واحد تنيز و واحد Prothrombosis
+
+592
+00:51:34,210 --> 00:51:40,810
+واحد تنيز و واحد Prothrombosis مفهوم يا شباب؟
+
+593
+00:51:40,810 --> 00:51:46,820
+ماشي؟ايوة عشرة تحول إلى عشرة الانزيم هنا factor
+
+594
+00:51:46,820 --> 00:51:50,480
+تسعة طبعا الانزيم في هذه الحالة factor تسعة مية في
+
+595
+00:51:50,480 --> 00:51:55,500
+المية كلام لإن هو تمانية cofactor و ال calcium
+
+596
+00:51:55,500 --> 00:51:59,560
+another cofactor و ال phospholipid و بره ال
+
+597
+00:51:59,560 --> 00:52:05,400
+substrate أو قاعدة ماشي
+
+598
+00:52:05,400 --> 00:52:12,500
+Christmas factor او ما يسمى factor تسعة
+
+599
+00:52:16,570 --> 00:52:23,710
+وهو ايش؟ غيابه بيعمل Hemophilia اسمها Hemophilia-B
+
+600
+00:52:23,710 --> 00:52:27,530
+لإنه التمانية بيعمل Hemophilia بيسموها Hemophilia
+
+601
+00:52:27,530 --> 00:52:33,310
+-A ونقل الوقت تبعه 57 كيلو دالتون صغير و ال half
+
+602
+00:52:33,310 --> 00:52:39,070
+-life تبعته أيام من واحد لتلت أيام ماشي يعني more
+
+603
+00:52:39,070 --> 00:52:43,470
+stable than التمانية مظبوط انا ال bleeding plasma
+
+604
+00:52:43,470 --> 00:52:48,560
+concentrationهي عبارة عن point تلاتة milligram
+
+605
+00:52:48,560 --> 00:52:57,880
+activated by tissue factor factor 7a complex يعني
+
+606
+00:52:57,880 --> 00:53:08,520
+بنشط تسعة بنشطه tissue factor 7a complex و بنشط
+
+607
+00:53:08,520 --> 00:53:15,870
+تسعة بنشط إحدى عشر يوم ما يتنشط بنشط إحدى عشرهو
+
+608
+00:53:15,870 --> 00:53:23,330
+بتنشط ب 11 و ده هو بتنشط ب 11 اه sorry هو بتنشط ب
+
+609
+00:53:23,330 --> 00:53:28,090
+11 بتنشط 9 و 9 بتنشط 10 او هكذا هو بتنشط بال
+
+610
+00:53:28,090 --> 00:53:32,710
+complex بال extrinsic pathway و بتنشط ال 9A .. ال
+
+611
+00:53:32,710 --> 00:53:37,090
+11A بالإياج بال intrinsic pathway هاني جيبها
+
+612
+00:53:37,090 --> 00:53:41,110
+التنين ماشي؟ حسب المشكلة it's a vitamin K that
+
+613
+00:53:41,110 --> 00:53:43,210
+build up a coagulation factor and it's green
+
+614
+00:53:43,210 --> 00:53:44,110
+proteins
+
+615
+00:53:48,030 --> 00:53:57,310
+محدد شوية؟ محدد؟ طيب انا عارف اني انا اتخمتكم من
+
+616
+00:53:57,310 --> 00:54:03,130
+جهة نجا فهاد المراجعة ان شاء الله بنكمل باقي ال
+
+617
+00:54:03,130 --> 00:54:06,870
+coagulation factors و نتعرف على ال complexes of
+
+618
+00:54:06,870 --> 00:54:13,110
+coagulation factors و ننهي المحاضرة بإذن الله
+
+619
+00:54:13,110 --> 00:54:15,890
+يعطيكوا العافية شباب
+
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/lSWVO6saxpo.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/lSWVO6saxpo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..471bcbc3bd87a2277117b887855e403bf786a383
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/lSWVO6saxpo.srt
@@ -0,0 +1,2527 @@
+1
+00:00:20,820 --> 00:00:26,260
+عوض بالله مش طالع جيم بسم الله الرحمن الرحيم اليوم
+
+2
+00:00:26,260 --> 00:00:30,160
+إن شاء الله هنحكي على ال vitamin K و علاقته بال
+
+3
+00:00:30,160 --> 00:00:35,600
+coagulation طبعًا احنا في موضوع سابق كنا تطرّقنا إلى
+
+4
+00:00:35,600 --> 00:00:40,120
+هذه المعلومة و عرفنا أن vitamin K هو عبارة عن
+
+5
+00:00:40,120 --> 00:00:45,280
+cofactor بيَلعب دور كبير في عملية ال carboxylation
+
+6
+00:00:45,280 --> 00:00:46,300
+لمين؟
+
+7
+00:00:50,840 --> 00:00:57,020
+فاكرين هما؟ هما 2 و 7 و 9 و 10 و protein C و
+
+8
+00:00:57,020 --> 00:01:02,500
+protein S و protein Z اللي هنتعرف عليه ماشي؟ يبقى
+
+9
+00:01:02,500 --> 00:01:06,740
+هو عبارة عن ايه؟ هو عبارة عن cofactor وشوفنا في
+
+10
+00:01:06,740 --> 00:01:13,790
+برضه موضوع ثابت أن ال vitamin K في وجوده وفي وجود
+
+11
+00:01:13,790 --> 00:01:16,810
+ثاني أكسيد الكربون بيشتغل Carboxylase enzyme زي ما
+
+12
+00:01:16,810 --> 00:01:20,430
+هنِتعرف بالظبط في تلك التفاصيل وبيضيف Carboxyl
+
+13
+00:01:20,430 --> 00:01:25,450
+group لـ ال coagulation factors شو بتعمل؟ بتأهلها
+
+14
+00:01:25,450 --> 00:01:32,930
+للارتباط مع ال calcium اللي بيساعد في غرزها
+
+15
+00:01:32,930 --> 00:01:37,970
+وارتباطها مع ال phospholipid membrane هو في الأساس
+
+16
+00:01:37,970 --> 00:01:44,200
+بيساعد أو بيؤهل الـ Coagulation factor على الارتباط
+
+17
+00:01:44,200 --> 00:01:48,860
+بالكالشيوم على إيه؟ الارتباط بالكالشيوم وعملية
+
+18
+00:01:48,860 --> 00:01:54,720
+الارتباط بالكالشيوم محتاجة فيه أكتر من موقع في هذه
+
+19
+00:01:54,720 --> 00:02:00,320
+المحاضرة إن شاء الله هنبدأ نشوف دور ال vitamin K
+
+20
+00:02:00,320 --> 00:02:07,080
+في ال Coagulation وإن كان له أدوار في مواقع أخرى و
+
+21
+00:02:07,080 --> 00:02:09,200
+issues ال vitamin K
+
+22
+00:02:13,480 --> 00:02:19,820
+خلّيني أبدأ المحاضرة ماشي two vitamin K و أبرز
+
+23
+00:02:19,820 --> 00:02:24,460
+مفاتيحه سولي بال compound موجودة شباب طبعًا necessary
+
+24
+00:02:24,460 --> 00:02:28,520
+for the synthesis of several required blood
+
+25
+00:02:28,520 --> 00:02:35,880
+clotting factors وموجودة على شاكلتين الأولانية
+
+26
+00:02:35,880 --> 00:02:44,320
+موجودة كمصدر أو من مصدر نباتي من مصدر نباتي ويسمى
+
+27
+00:02:44,320 --> 00:02:51,960
+Phylloquinone أو بيسموه vitamin K1 vitamin ايش K1 و
+
+28
+00:02:51,960 --> 00:02:56,100
+ازاي ما تشوفوا ال structure تبعه هو natural form
+
+29
+00:02:56,100 --> 00:03:02,760
+موجود في أكثر من نوع من النباتات وبيشكل المصدر
+
+30
+00:03:02,760 --> 00:03:07,980
+الأساسي للإنسان يشكل المصدر الأساسي للإنسان
+
+31
+00:03:14,110 --> 00:03:17,590
+المصدر الثاني من مصادر ال vitamin K وهو المصدر
+
+32
+00:03:17,590 --> 00:03:25,810
+الحيواني وهو أبرز vitamin K2 أو بيسموه Menaquinone
+
+33
+00:03:25,810 --> 00:03:33,570
+طبعًا يُوَلّد ال vitamin K ويُصنع في ال human gut من
+
+34
+00:03:33,570 --> 00:03:38,170
+خلال البكتيريا ال normal flora يُصنع بكميات كبيرة
+
+35
+00:03:38,170 --> 00:03:44,310
+لكن احنا فقط نستخدم كمية قليلة منه ليش؟ ده يُصْدَر في
+
+36
+00:03:44,310 --> 00:03:48,030
+مكان الانتصاص بالظبط بعيد عن مواقع انتصاص ال
+
+37
+00:03:48,030 --> 00:03:53,050
+vitamin K في جسم الإنسان، يبقى فيه مصدرين، مصدر
+
+38
+00:03:53,050 --> 00:03:58,730
+نباتي ومصدر حيواني، وتخيلوا تشوفوا الشكل اللي
+
+39
+00:03:58,730 --> 00:04:03,970
+عاليه شكل مختلف، لكنه the same vitamin K مصدر
+
+40
+00:04:03,970 --> 00:04:07,410
+النباتي اللي موجود في الأكل يا شباب انتبهوا هي
+
+41
+00:04:07,410 --> 00:04:13,830
+مجموعة من المأكولات mostly found in green leafy
+
+42
+00:04:13,830 --> 00:04:18,730
+vegetables كل المأكولات الخضراء كل الحاجة لونها
+
+43
+00:04:18,730 --> 00:04:22,090
+خضراء موجود فيها vitamin K موجود فيه طبعًا مصدر
+
+44
+00:04:22,090 --> 00:04:26,890
+حيواني في ال product في ال meat في ال eggs وهكذا
+
+45
+00:04:27,750 --> 00:04:32,790
+من أغنى المصادر النباتية وجود ال vitamin K في ال
+
+46
+00:04:32,790 --> 00:04:33,910
+Brussels sprout
+
+47
+00:04:42,110 --> 00:04:46,910
+لكن صغير، حبة صغيرة، ملفوف عن نهار جد، مظبوط، لكن
+
+48
+00:04:46,910 --> 00:04:50,810
+هذا عذرًا عن حبة صغيرة، إنما زي الملفوف، وطبعًا
+
+49
+00:04:50,810 --> 00:04:55,890
+بتخرّط و بنسلج بهذه الطريقة، لأسف شديد مش موجودة
+
+50
+00:04:55,890 --> 00:04:59,650
+هنا في البلاد، ماشي؟ كمية ال vitamin K في أعلى
+
+51
+00:04:59,650 --> 00:05:07,330
+حاجة، 460 microgram في الـ .. الـ .. cooked Brussels
+
+52
+00:05:10,430 --> 00:05:16,790
+حوالي 460 microgram النوع الثاني الـ بروكلي سمعتوا
+
+53
+00:05:16,790 --> 00:05:20,690
+فيه بروكلي موجود عندنا في غزة صنع الزهرة لكن
+
+54
+00:05:20,690 --> 00:05:25,210
+الخضرة مش البيضة مظبوط الزهرة الخضراء هو برام
+
+55
+00:05:25,210 --> 00:05:31,870
+بروكلي غني جدًا فيه 248 microgram كل كوباية منه ثم ال
+
+56
+00:05:31,870 --> 00:05:35,330
+cauliflower اللي هو الظهر على البيضة الـ chromium
+
+57
+00:05:35,330 --> 00:05:40,770
+مظبوط برضه فيه كمية عالية ثم ال Swiss chard اللي
+
+58
+00:05:40,770 --> 00:05:46,110
+هو السلق أنت عارفه السبانخ والسلق مظبوط السبانخ
+
+59
+00:05:46,110 --> 00:05:50,910
+اللي هو Spanish مظبوط بس Swiss chard هو السلق
+
+60
+00:05:50,910 --> 00:05:57,410
+ماشي الـ برضه فيه نسبة عالية ثم ال beef اللحوم
+
+61
+00:05:57,410 --> 00:06:03,460
+البقرية ثم ال pork اللحوم الخنزير ثم ال eggs فيها
+
+62
+00:06:03,460 --> 00:06:10,160
+أقل كميات فيها حوالي خمسة وعشرين micro gram لكل
+
+63
+00:06:10,160 --> 00:06:16,160
+egg وزنها 11 gram ماشي؟ هي حوالي خمسة وعشرين
+
+64
+00:06:16,160 --> 00:06:22,630
+microgram تأثيره طبعًا كلنا بنعرف أنه ال
+
+65
+00:06:22,630 --> 00:06:28,070
+vitamin K بيَلعب as essential cofactor لنهي لل
+
+66
+00:06:28,070 --> 00:06:32,650
+carboxylase enzyme شو بيعمل؟ بيعمل carboxylation
+
+67
+00:06:32,650 --> 00:06:37,030
+لل vitamin K dependant coagulation factors، ماشي؟
+
+68
+00:06:37,030 --> 00:06:40,750
+يعني بيضيف carboxyl له وبالتالي هذه البروتينات
+
+69
+00:06:40,750 --> 00:06:44,710
+مهمة في مواقع مختلفة، ماشي؟
+
+70
+00:06:47,600 --> 00:06:51,860
+ما هي هذه المواقع؟ جعلتنا واحد كواجوليشن صح؟ سنشوف
+
+71
+00:06:51,860 --> 00:06:58,060
+وحضرتنا علاقتها بالكواجوليشن ثم Bone mineralization
+
+72
+00:06:58,060 --> 00:07:03,620
+عملية بناء العظم مظبوط ثم ال cell growth طبعًا لما
+
+73
+00:07:03,620 --> 00:07:07,760
+تتأهل هذه البروتينات في الارتباط بالكالسيوم بِتَلْعَب
+
+74
+00:07:07,760 --> 00:07:10,420
+وظيفة وبالتالي ممكن نستغلها في
+
+75
+00:07:14,330 --> 00:07:19,210
+طبعًا هذه الصورة زي ما أنتو شايفين Glutamic acid
+
+76
+00:07:19,210 --> 00:07:23,390
+residue موجودة في نهايات ال coagulation factor
+
+77
+00:07:23,390 --> 00:07:28,330
+تتحول لـ γ-Carboxyglutamic acid residue by addition of
+
+78
+00:07:28,330 --> 00:07:35,410
+carboxylic group إلى glutamate إلى glutamate
+
+79
+00:07:35,410 --> 00:07:40,450
+وهذه الصورة هي ال peptide الأخرى هي عبارة عن
+
+80
+00:07:40,450 --> 00:07:45,990
+glutamate في وجود الـ γ-glutamyl
+
+81
+00:07:45,990 --> 00:07:51,930
+Carboxylase وطبعًا في وجود CO2 و Oxygen بنضيف
+
+82
+00:07:51,930 --> 00:07:58,050
+Carboxyl group ثانية شايفين أصلًا إضافة ال Carboxyl
+
+83
+00:07:58,050 --> 00:08:03,050
+group عملت زي bucket عملت زي جيبه شو عملت الجيبة
+
+84
+00:08:03,050 --> 00:08:08,990
+ها دي؟ حَلّت الماء بالبروتين في إن ال calcium يرتبط
+
+85
+00:08:08,990 --> 00:08:10,230
+ماشي إنّها ترتبط
+
+86
+00:08:15,110 --> 00:08:20,390
+مُسْتَطِيع ال protein هذا إنه يغرز حاله فيها في ال
+
+87
+00:08:20,390 --> 00:08:22,930
+cell في ال phospholipid membrane في ال
+
+88
+00:08:22,930 --> 00:08:27,570
+phospholipid membrane of platelet يعني بدون
+
+89
+00:08:27,570 --> 00:08:31,990
+الكالسيوم مقدرش عشان هيك فاكرين قولنا ال
+
+90
+00:08:31,990 --> 00:08:37,610
+coagulation cascade كل خطواته تحتاج إلى الكالسيوم
+
+91
+00:08:50,780 --> 00:08:55,280
+هي عبارة عن عملية تحويل الدم from liquid to solid
+
+92
+00:08:55,280 --> 00:09:01,500
+بنمر في عدة خطوات in a cascade manner محصلتها
+
+93
+00:09:01,500 --> 00:09:05,200
+تصنيع ثرمبين بيشتغلوا على الـ fibrinogen وبيحولوا
+
+94
+00:09:05,200 --> 00:09:12,560
+إلى الـ fibrin 100% في
+
+95
+00:09:12,560 --> 00:09:19,400
+العوامل اللي الـ Coagulation Factors هذه المختلفة
+
+96
+00:09:19,400 --> 00:09:22,540
+عملنا لها Classification ولجينا أنه في مجموعة
+
+97
+00:09:22,540 --> 00:09:26,820
+منها سميناها كوايتا من كي دي بيبدأ الـ Coagulation
+
+98
+00:09:26,820 --> 00:09:31,400
+Factors ماشي وقولنا there are certain factors
+
+99
+00:09:34,490 --> 00:09:37,910
+تعتمد على vitamin K في تصنيعها، these factors
+
+100
+00:09:37,910 --> 00:09:42,030
+require calcium for their activation، بتحتاج إلى
+
+101
+00:09:42,030 --> 00:09:46,550
+calcium، عشان هيك احنا بدنا نشطها، عشان هيك بدنا
+
+102
+00:09:46,550 --> 00:09:51,090
+نأهلها للعمل، ماشي؟ يعني هي تُصَنّع في ال liver بشكل
+
+103
+00:09:51,090 --> 00:09:56,730
+طبيعي، لكن في غياب ال vitamin K بتشتغلش، ليش؟ بسبب
+
+104
+00:09:56,730 --> 00:10:00,870
+عدم carboxylation، ليه؟ وبالتالي بتقدرش ترتبط
+
+105
+00:10:00,870 --> 00:10:05,350
+بالكالشيوم، وبالتالي بتشتغلش ماذا يفعل الكالسيوم؟
+
+106
+00:10:05,350 --> 00:10:10,690
+الكالسيوم يمكنه فقط الارتباط بعد عملية carboxylation
+
+107
+00:10:10,690 --> 00:10:20,310
+100% وتحويل ال Glutamic acid إلى γ-Carboxyglutamic acid
+
+108
+00:10:20,310 --> 00:10:30,390
+γ-Carboxyglutamic acid تغيير لماذا نحتاجها؟ هي محتاجة لتهيير
+
+109
+00:10:30,390 --> 00:10:38,490
+الـ calcium وليس تهيير ماشي طبعًا في هذه العملية
+
+110
+00:10:38,490 --> 00:10:44,690
+ال vitamin K يعمل as a cofactor اللي هو دور مهم
+
+111
+00:10:44,690 --> 00:10:48,630
+جدًا في جسم الإنسان ولأنه موجود بكميات قليلة جدًا
+
+112
+00:10:48,630 --> 00:10:54,170
+وُجِدَ أن ال vitamin K is reutilized is continuously
+
+113
+00:10:54,170 --> 00:10:59,550
+reutilized يُعاد استخدامه وبالتالي بيمر في دائرة
+
+114
+00:10:59,550 --> 00:11:07,210
+يُستَغَلّ ماشي ولا يُستهلك وبالتالي لا يستهلك يُستَغَلّ ولا
+
+115
+00:11:07,210 --> 00:11:13,770
+يُستهلك ماشي يُعاد استغلاله باستمرار وهذا الكلام
+
+116
+00:11:13,770 --> 00:11:21,130
+كله بيصنع في موجود على هيئة بيسموها ال vitamin K
+
+117
+00:11:21,130 --> 00:11:27,570
+cycle ماشي العوامل التي تحتاج ال vitamin K في
+
+118
+00:11:27,570 --> 00:11:34,410
+2 و 7 و 9 و 10 و protein C و S و protein Z
+
+119
+00:11:34,410 --> 00:11:44,830
+ماشي نعرفهم كلهم و protein Z و protein Z و C و S
+
+120
+00:11:44,830 --> 00:11:53,230
+ماشي
+
+121
+00:11:53,230 --> 00:11:55,530
+ماني مكتوبة طبعًا ايش دورها
+
+122
+00:12:05,620 --> 00:12:11,300
+inactivated form of factor X factor X
+
+123
+00:12:11,300 --> 00:12:14,800
+inactivation
+
+124
+00:12:14,800 --> 00:12:24,980
+of factor X نشط طبعًا إذا صار في inactivation ل
+
+125
+00:12:24,980 --> 00:12:33,860
+X شو بيصير؟ كل الساكن، كل الكسكين بيجي، كل ده؟ 
+
+126
+00:12:33,860 --> 00:12:34,720
+ليش؟
+
+127
+00:12:37,570 --> 00:12:42,770
+اللي بروثرومبينيز كومبليكس وبالتالي اليوم طبعا إله 
+
+128
+00:12:42,770 --> 00:12:46,870
+أدوار أخرى ظهرت على الخط لكن إحنا مش ما مش يعني مش
+
+129
+00:12:46,870 --> 00:12:54,190
+مش عنوان محاضرة لما تضطرنا ناخدها معناه ده ال
+
+130
+00:12:54,190 --> 00:12:56,990
+combination cascade mechanism وكنا عارفين إن ده
+
+131
+00:12:56,990 --> 00:13:05,740
+intrinsic و extrinsic و الـ vitamin K تحتل مواقع
+
+132
+00:13:05,740 --> 00:13:12,980
+مهمة جدا في الكاسكيت ولا لأ تحتل مواقع مهمة جدا
+
+133
+00:13:12,980 --> 00:13:19,400
+لأنه قتل قيابها أو عدم عملها يعني وقف الكاسكيت
+
+134
+00:13:19,400 --> 00:13:24,920
+كاملا بيفكا
+
+135
+00:13:24,920 --> 00:13:29,440
+هو عبارة عن مصطلح جديد سمعتوا فيه؟ ما سمعتوش فيه
+
+136
+00:13:29,440 --> 00:13:36,960
+بيفكا هو اختصار protein induced مكتوبة دا هي في
+
+137
+00:13:36,960 --> 00:13:45,200
+آخر السطرين by vitamin K absence or antagonist
+
+138
+00:13:45,200 --> 00:13:53,500
+يعني في غياب الـ vitamin K أو في وجود إيش المضاد له
+
+139
+00:13:53,500 --> 00:14:01,860
+مظبوط antagonist أو المحبط له ماشي إشي هذه أو
+
+140
+00:14:01,860 --> 00:14:05,500
+البروتينات التي تتصنع في غياب الـ Vitamin K، يعني
+
+141
+00:14:05,500 --> 00:14:10,100
+الـ Vitamin K هذه البروتينات هي Vitamin K
+
+142
+00:14:10,100 --> 00:14:14,990
+-dependent coagulation factors تصنع في غياب الـ
+
+143
+00:14:14,990 --> 00:14:18,230
+vitamin K يعني لو إحنا ما عندناش vitamin K الـ liver
+
+144
+00:14:18,230 --> 00:14:21,350
+بيشتغل و بيصنع لنا coordination factors هو إن إيه
+
+145
+00:14:21,350 --> 00:14:25,430
+سواء بدها vitamin K أو لا بدهاش vitamin K فتطلع
+
+146
+00:14:25,430 --> 00:14:31,250
+العوامل لكن بدون تأهيل أنا ما بقولش بدون تصنيع ولا
+
+147
+00:14:31,250 --> 00:14:39,910
+بدون نشاط بدون تأهيل بالظبط لأن vitamin K غايب
+
+148
+00:14:39,910 --> 00:14:45,970
+فما يصيرش carboxylation وبالتالي لا تستطيع أن ترتبط
+
+149
+00:14:45,970 --> 00:14:57,390
+بالكالسيوم ومن هذا المطلق لا تتنشط لا تتنشط مفهوم
+
+150
+00:14:57,390 --> 00:15:02,810
+يا شباب؟ يبقى لا تعمل تطلع الـ blood circulation
+
+151
+00:15:02,810 --> 00:15:09,070
+لكنها لا تعمل inert و بتبقى inert مفهوم؟ طيب في
+
+152
+00:15:09,070 --> 00:15:11,590
+هذه الحالة المريض اللي منها منوعة بس اللي عنده
+
+153
+00:15:11,590 --> 00:15:12,030
+تجلب
+
+154
+00:15:20,970 --> 00:15:25,110
+مش اللي صار؟ فيتامين ك مش موجود أو غايب فيتامين ك
+
+155
+00:15:25,110 --> 00:15:31,270
+مش موجود اه غايب أو موجود مضاده يعني هتاك ماشي
+
+156
+00:15:31,270 --> 00:15:37,410
+ما عندوش دور طيب كيف نعرف إن المريض هذا عنده فيتامين
+
+157
+00:15:37,410 --> 00:15:42,630
+ك ولا ما عندوش مريض طبعا هذه حالة من الحالات اللي
+
+158
+00:15:42,630 --> 00:15:48,570
+قد تكون مرضية أو قد تكون induced يعني إحنا عملناها
+
+159
+00:15:48,570 --> 00:15:54,060
+مظلوم؟ كيف نعرف إنه عنده بيبكة وموجودش تركيزها؟ لما
+
+160
+00:15:54,060 --> 00:15:58,660
+تيجي تجيسها، كيف بدك تجيسها؟ بدك تعرف صفاتها، من
+
+161
+00:15:58,660 --> 00:16:01,880
+صفاتها إن هذه العوامل اللي هتستطيع أن ترتبط
+
+162
+00:16:01,880 --> 00:16:07,460
+بالكالسيوم، صح؟ ثم حاجة تانية، مثلها الـ adsorption
+
+163
+00:16:07,460 --> 00:16:14,740
+على الـ aluminium hydroxide أو الـ barium salts، إيش
+
+164
+00:16:14,740 --> 00:16:21,320
+هدولة؟ aluminium hydroxide أو الـ barium salts طبعا
+
+165
+00:16:21,320 --> 00:16:24,340
+إحنا هذه عبارة عن مواد نستخدمها في الـ
+
+166
+00:16:24,340 --> 00:16:29,100
+Electrophoresis خدتوا Electrophoresis؟ نية في
+
+167
+00:16:29,100 --> 00:16:34,120
+المية شو بيصير؟ Electrophoresis هي عبارة عن وسيلة
+
+168
+00:16:34,120 --> 00:16:38,420
+من وسائل فصل للمواد فيوم ما نيجي نفصلها إذا
+
+169
+00:16:38,420 --> 00:16:43,120
+استخدمنا الـ aluminium hydroxide والـ barium salts مش راح
+
+170
+00:16:43,120 --> 00:16:48,300
+تقطط نفسها فلازم تستخدم حاجة تانية بمعنى آخر بدك
+
+171
+00:16:48,300 --> 00:16:55,130
+تدور على إيش تاني تقيس فيه أو تتعرف فيه على هذه
+
+172
+00:16:55,130 --> 00:16:58,130
+المواد فمن الصفات التانية .. من الحاجات التانية
+
+173
+00:16:58,130 --> 00:17:04,110
+اللي لجوها أحد وسائل القياس يعني قالوا هذه العوامل
+
+174
+00:17:04,110 --> 00:17:13,130
+تستطيع أن تتنشط by بإضافة venom سم .. سم حية ماشي
+
+175
+00:17:13,130 --> 00:17:18,710
+من نوع الـ Echocarnitas من عائلة Echocarnitas
+
+176
+00:17:20,440 --> 00:17:26,140
+ماشي أخدوا السم وعملوا منه فحص سموه Acrin time شو
+
+177
+00:17:26,140 --> 00:17:32,560
+سموه Acrin time هاي Acrin طبعا Acrin جاية اختصار من
+
+178
+00:17:32,560 --> 00:17:39,540
+Echis carinatas Echis أخدوا منها الـ E والـ Carin من
+
+179
+00:17:39,540 --> 00:17:45,160
+الـ carinatas المفهوم مش هبقى هو عبارة عن فحص سهل جدا
+
+180
+00:17:45,160 --> 00:17:51,950
+استخدامه ماشي كل ما هناك إنه إحنا بنجيبه بلازم عشان
+
+181
+00:17:51,950 --> 00:17:55,770
+نعرف إنه فيها بيفكة ولا لأ و بنضيف عليها الـ Acrin
+
+182
+00:17:55,770 --> 00:18:02,390
+اللي هو الـ Venom و بنقيس زمن التجلد زي الـ BT
+
+183
+00:18:02,390 --> 00:18:07,910
+اشتغلتوا BT بتقولوا بالظبط زي الـ BT لإنه شو بعمل
+
+184
+00:18:07,910 --> 00:18:13,690
+الـ Acrin عنده القدرة إنه ينشط تنشيط مباشر لعوامل
+
+185
+00:18:13,690 --> 00:18:20,320
+التجلد اللي ما بتشتغلش اللي هي الـ بيفكة ماشي؟ طب لما
+
+186
+00:18:20,320 --> 00:18:25,480
+ينشطها تصبح exaggeration فالـ plasma اللي أنت جاي الطش
+
+187
+00:18:25,480 --> 00:18:28,580
+تلعب عليها تتجلط ولا تتجلطش؟ تتجلط ببساطة مقاس
+
+188
+00:18:28,580 --> 00:18:33,180
+الزمن المطلوب ولو لها حسبه معينة بتعرف من خلالها
+
+189
+00:18:33,180 --> 00:18:42,860
+المفكرة مفهوم يا شباب؟ نتطلق الآن لـ vitamin K
+
+190
+00:18:42,860 --> 00:18:47,880
+cycle اتفقنا على إن vitamin K دي الـ
+
+191
+00:18:51,100 --> 00:18:56,140
+and not consumed وسمينا عملية de-utilization
+
+192
+00:18:56,140 --> 00:19:05,220
+vitamin K cycle و أشرح لكم إياها ببساطة
+
+193
+00:19:05,220 --> 00:19:09,280
+من خلال اللي كنا صفقنا على إن الـ vitamin K موجود
+
+194
+00:19:09,280 --> 00:19:14,960
+في جسم الإنسان شوان كان حيواني ولا نباتي هو أبدا
+
+195
+00:19:14,960 --> 00:19:21,630
+vitamin K يتحول هذا Vitamin K إلى الـ Reduced Form
+
+196
+00:19:21,630 --> 00:19:31,530
+عشان يشتغل يختزل By Reductase Enzyme و بيسموه الـ
+
+197
+00:19:31,530 --> 00:19:40,230
+Enzyme Quinone Reductase هدنا هنشوف فبتحول إلى
+
+198
+00:19:40,230 --> 00:19:43,890
+Vitamin 
+
+199
+00:19:43,890 --> 00:19:44,570
+K
+
+200
+00:19:47,360 --> 00:19:52,980
+Reduced Form of Vitamin K يبقى بيختزل ولما بنختزل
+
+201
+00:19:52,980 --> 00:20:01,480
+عنصر بنضيف له إيش؟ H2 مظبوط 100% Vitamin K H2 أو
+
+202
+00:20:01,480 --> 00:20:08,120
+اللي هو Reduced Form of Vitamin K This Form هو
+
+203
+00:20:08,120 --> 00:20:11,160
+اللي بيشتغل، الـ active هو اللي بيشتغل هو اللي
+
+204
+00:20:11,160 --> 00:20:16,880
+بيشتغل هذا الـ factor في وجوده الشباب ماشي في وجوده
+
+205
+00:20:16,880 --> 00:20:21,620
+شايفين التفاعل كيف صار الـ vitamin K dependent
+
+206
+00:20:21,620 --> 00:20:26,500
+coagulation factors بيصير فيه carboxylation للـ
+
+207
+00:20:26,500 --> 00:20:32,180
+glutamic acid residue ماشي و بيصير جامعة
+
+208
+00:20:32,180 --> 00:20:37,480
+carboxylation لهذه العوامل طبعا في وجود الـ
+
+209
+00:20:37,480 --> 00:20:43,000
+carboxylase enzyme و CO2 الأكسر ماذا يحصل؟ الـ
+
+210
+00:20:43,000 --> 00:20:47,540
+Coagulation Factors يحصل لها Carboxylation لكن الـ
+
+211
+00:20:47,540 --> 00:20:54,960
+Vitamin K بيتأكسد، هو كان مختزن وإيش؟ واتأكسد،
+
+212
+00:20:54,960 --> 00:21:00,860
+ماشي يا شباب؟ فبيتحول إلى Vitamin K Epoxide،
+
+213
+00:21:00,860 --> 00:21:06,260
+Vitamin K Epoxide، هذا لا يعمل، لا نستفيد منه
+
+214
+00:21:07,340 --> 00:21:13,720
+وبالتالي عشان نعيد استغلاله، بدنا نعيد اختزاله،
+
+215
+00:21:13,720 --> 00:21:20,980
+صح؟ بدنا نعيد اختزاله، فبيختزل بواسطة إنزايم اسمه
+
+216
+00:21:20,980 --> 00:21:26,640
+Epoxide Reductase Enzyme برجع مرة تانية الـ vitamin
+
+217
+00:21:26,640 --> 00:21:32,620
+عشان ك إيه؟ عشان يختزل ثم بيخش في التفاعل،
+
+218
+00:21:32,620 --> 00:21:39,480
+بيتأكسد، بيعاد اختزاله، و بيختزل، وهكذا، بتأكسد،
+
+219
+00:21:39,480 --> 00:21:42,420
+بعد ما يخش في التفاعل، وهكذا، بتضل الـ cycle
+
+220
+00:21:42,420 --> 00:21:49,780
+شرّال، المفهوم شباب؟ وطبعا
+
+221
+00:21:50,870 --> 00:21:54,450
+سمعتوا أنتو بالـ warfarin أو الـ antagonist وعبارة
+
+222
+00:21:54,450 --> 00:21:58,790
+عن انت warfarin سمعتوا فيها أولى اسم التجار ياله
+
+223
+00:21:58,790 --> 00:22:04,170
+Coumadin بيعمل inhibition للـ epoxide reductase
+
+224
+00:22:04,170 --> 00:22:12,510
+enzyme بشكل أساسي بشكل إيه؟ أساسي وهي المعادلات
+
+225
+00:22:12,510 --> 00:22:18,560
+المتعلقة ماشي؟ شايفين الـ Enzyme؟ الشيء اللي .. الـ
+
+226
+00:22:18,560 --> 00:22:23,140
+Vitamin الشيء اللي بقى؟ هي موجود في شكل أساسي كـ
+
+227
+00:22:23,140 --> 00:22:31,360
+Vitamin K بيسموه quinone Vitamin K quinone أو
+
+228
+00:22:31,360 --> 00:22:40,890
+quinone form of Vitamin K بيختزن وبيتحول الـ KH2 و
+
+229
+00:22:40,890 --> 00:22:46,850
+لاحظوا من خلال اختزاله بيتم طبعا في بواسطة إنزايم
+
+230
+00:22:46,850 --> 00:22:51,510
+اسمه quinone reductase الناد بتحول الناد بي بتحول
+
+231
+00:22:51,510 --> 00:22:55,310
+الناد بي اتش الناد بي اتش بتحول الناد بي لأنه إحنا
+
+232
+00:22:55,310 --> 00:23:00,690
+بنضيف ناخد الهيدروجين ولا اه وطبعا في إنزايم تاني
+
+233
+00:23:00,690 --> 00:23:09,130
+بيبقوا بنفس الدور اسمه diethiol إنزايم ماشي وإيه
+
+234
+00:23:10,300 --> 00:23:16,920
+بيروحوا وفاكك أو كاسر الـ reduced link اللي موجودة
+
+235
+00:23:16,920 --> 00:23:24,160
+هنا RSH بيحولها إلى RSRS وبياخد الـ hydrogen اللي
+
+236
+00:23:24,160 --> 00:23:28,300
+موجود فيها المهم الـ enzyme الـ vitamin sorry بيتحول
+
+237
+00:23:28,300 --> 00:23:33,240
+من quinone form إلى hydroquinone hydro يعني في
+
+238
+00:23:33,240 --> 00:23:38,120
+hydrogen أتفناله تابعين معايا؟ أبو إسماعيل؟
+
+239
+00:23:41,230 --> 00:23:45,010
+هذه الشكلة هو الشغالة هو الـ cofactor الأساسي في
+
+240
+00:23:45,010 --> 00:23:49,730
+وجوده الـ peptide اللي هي جالو glutamic acid residue
+
+241
+00:23:49,730 --> 00:23:57,490
+تتحول لـ glutamate ولاحظوا إيش موجود CO2 و Oxygen و
+
+242
+00:23:57,490 --> 00:24:02,310
+Carboxylase enzyme أو بيسموه Epoxidase ليش
+
+243
+00:24:02,310 --> 00:24:08,840
+Epoxidase؟ لأن الـ Vitamin K بتتحول لـ Epoxide ماشي
+
+244
+00:24:08,840 --> 00:24:14,400
+هايوم تحول تأكسد الـ Vitamin K إلى Vitamin K23
+
+245
+00:24:14,400 --> 00:24:21,820
+إبوكسايد وعبارة عن شكل من أشكال الـ Vitamin K
+
+246
+00:24:21,820 --> 00:24:27,760
+المتأكسد مش المختزن، ماشي طبعا تأكسد معناه إنتهى
+
+247
+00:24:27,760 --> 00:24:34,150
+الموضوع بطل اشتغل بعد اه والـ coagulation factors
+
+248
+00:24:34,150 --> 00:24:38,090
+تحولت لـ glutamic acid إلى glutamate هي أضفنا كمان
+
+249
+00:24:38,090 --> 00:24:44,630
+carboxyl group الهجامة carboxylation مظبوط؟ مظبوط
+
+250
+00:24:44,630 --> 00:24:49,750
+يا رجل طبعا هذا الـ epoxide form should be reduced
+
+251
+00:24:49,750 --> 00:24:54,630
+مرة ثانية فبنرجع للي بيكونهم ماشي بواسطة epoxide
+
+252
+00:24:54,630 --> 00:25:01,490
+reductase وهذا مرة ثانية بيصير له ايش اشتغلوا الـ
+
+253
+00:25:01,490 --> 00:25:07,950
+reduction لا فهمة يا شباب، الناس عندهم سؤال يجيبوا و
+
+254
+00:25:07,950 --> 00:25:13,610
+يختزل ثم يدخلوا ككوفاكتور ويتأكسد ويختزلوا مرة
+
+255
+00:25:13,610 --> 00:25:17,110
+ثانية ومرة ثانية ولا ننسى أن الـ warfarin يأتي و
+
+256
+00:25:17,110 --> 00:25:21,450
+يشتغل ويشتغل ويشتغل ويشتغل ويشتغل ويشتغل و
+
+257
+00:25:21,450 --> 00:25:25,820
+يشتغل ويشتغل  وبالتالي يمنع عليه epoxide
+
+258
+00:25:25,820 --> 00:25:29,840
+reductase وبالتالي يمنع اختزال الـ vitamin K مرة
+
+259
+00:25:29,840 --> 00:25:38,100
+ثانية بيمنع اختزال الـ vitamin K حد عنده شوية طبعا
+
+260
+00:25:38,100 --> 00:25:51,020
+هذه  مُفصّلة بشكل تفصيلي ماشي وهذا
+
+261
+00:25:51,020 --> 00:26:00,320
+الملخص احنا ما بنعش نحكي في biochemistry لل
+
+262
+00:26:00,320 --> 00:26:08,820
+cycle حد عنده سؤال فيها؟ ما حدش طيب الـ coumarin and
+
+263
+00:26:08,820 --> 00:26:13,900
+warfarin are anticoagulants that antagonize the
+
+264
+00:26:13,900 --> 00:26:18,760
+action of vitamin K اتفقنا كمان أن الـ warfarin أو
+
+265
+00:26:18,760 --> 00:26:19,620
+الـ coumarin
+
+266
+00:26:22,940 --> 00:26:26,480
+اللي بيدخل تحتها الـ warfarin بتشتغل ك
+
+267
+00:26:26,480 --> 00:26:30,400
+anticoagulant، شو بتعمل؟ بتشتغل as anti
+
+268
+00:26:30,400 --> 00:26:34,700
+-antagonized for the vitamin K، وبالتالي بتمنع 
+
+269
+00:26:34,700 --> 00:26:42,380
+عادة اختزاله، شو بيعمل؟ يعني الـ warfarin بيتدخل في
+
+270
+00:26:42,380 --> 00:26:47,350
+عمل الـ diaphorase-Catalyzed Quinone Reductase
+
+271
+00:26:47,350 --> 00:26:51,170
+Activity اللي هو عبارة عن الانزيم الأولاني اللي
+
+272
+00:26:51,170 --> 00:26:56,630
+لازم عشان تحويل الـ vitamin K لـ vitamin K  هيدروكسيد ماشي
+
+273
+00:26:56,630 --> 00:27:05,050
+هان أول مرة اه فاهمين عليا؟ كمان بيشتغلها الـ
+
+274
+00:27:05,050 --> 00:27:10,830
+Epoxide Reductase بس إذا بتلاحظوا هان هو بيشتغل
+
+275
+00:27:10,830 --> 00:27:17,560
+على الانزيم الفجاني لكن في تحت كمان NADPH
+
+276
+00:27:17,560 --> 00:27:21,920
+يتحول NADPH و
+
+277
+00:27:21,920 --> 00:27:25,420
+يمنع
+
+278
+00:27:25,420 --> 00:27:29,220
+إعادة اختزاله NADPH الـ coumarin reductase هو
+
+279
+00:27:29,220 --> 00:27:36,240
+عائلة
+
+280
+00:27:36,240 --> 00:27:41,520
+الكيومارين كما تلاحظون يا شباب عائلة كبيرة جدا
+
+281
+00:27:41,520 --> 00:27:43,360
+بتضم حوالي خمس عشر
+
+282
+00:27:46,460 --> 00:27:51,540
+وهذه المركبات بتختلف من مكان لمكان، كل شركة من
+
+283
+00:27:51,540 --> 00:27:54,600
+الشركات بتطلع إنها مركبة، وتعتبر warfarin،
+
+284
+00:27:54,600 --> 00:27:59,540
+لأن كلهم war، ماشي؟ عشان هيك الدواء بيختلف من دولة
+
+285
+00:27:59,540 --> 00:28:04,540
+لدولة، الدواء كمان بيختلف من دولة لدولة، عشان هيك
+
+286
+00:28:04,540 --> 00:28:07,100
+لو واحد اتصل في جريبه في الخليج وقال له بعطلي
+
+287
+00:28:07,100 --> 00:28:09,980
+مثلا warfarin، الـ warfarin اللي رجع من الخليج
+
+288
+00:28:09,980 --> 00:28:12,360
+بيختلف عن الـ warfarin اللي عنده، بيختلف عن الـ
+
+289
+00:28:12,360 --> 00:28:15,960
+warfarin اللي في المقلب في مصر ماشي؟ ومن هذا
+
+290
+00:28:15,960 --> 00:28:19,720
+المطلب دائما بننصح الناس هدول اللي بيغيروا في
+
+291
+00:28:19,720 --> 00:28:23,660
+الدواء أنه كل ما يغير الدواء يعمل standardization
+
+292
+00:28:23,660 --> 00:28:30,900
+لنفس، كيف؟ ايه الـ test أو الفحص؟ أنا والفحص ايه؟
+
+293
+00:28:30,900 --> 00:28:34,800
+فعلا المحالي اللي متعرضة يشوفه ويتحسن؟ مش متعرض
+
+294
+00:28:34,800 --> 00:28:39,620
+يتحسن ولا لأ؟ احنا كده بنديس الـ .. الـ warfarin
+
+295
+00:28:39,620 --> 00:28:40,340
+effect
+
+296
+00:28:42,860 --> 00:28:47,520
+100% بنعمل فحص الـ PT، الـ PT هو برنامج فحص بنقيس من
+
+297
+00:28:47,520 --> 00:28:54,140
+خلاله أي ذراع من الذراع الأزرق، the extrinsic
+
+298
+00:28:54,140 --> 00:28:57,780
+pathway of coagulation cascade mechanism، ايش
+
+299
+00:28:57,780 --> 00:29:00,280
+بنقيس من خلاله؟ ايش موجود في هذه العوالم؟
+
+300
+00:29:11,900 --> 00:29:13,080
+يعني عدوا معاه
+
+301
+00:29:20,750 --> 00:29:26,150
+الخطوات التنسيقية تشتغل على عشرة أ  على طول مش قولنا
+
+302
+00:29:26,150 --> 00:29:32,410
+التنين pathway بيجتمعوا عند عشرة أ تحويل عشرة أ لعشرين
+
+303
+00:29:32,410 --> 00:29:37,990
+مظبوط عشرة أ عشرة ناس فبنشتغل عشرة أ إلى عشرة  أ لكن
+
+304
+00:29:37,990 --> 00:29:42,510
+عشرة أ بعد هيك على مين بيشتغل بيكد يكون
+
+305
+00:29:42,510 --> 00:29:45,850
+البروترومبينيز اللي هو البروثرومبين المشط
+
+306
+00:29:49,560 --> 00:29:53,440
+البروترومبينيش كومبليكس عبارة عن ايش؟ عشرة أ؟
+
+307
+00:29:53,440 --> 00:29:58,380
+وخمسة
+
+308
+00:29:58,380 --> 00:30:04,200
+أ؟ وفي وجود الكالسيوم والفوسفوليبيد ماشي؟ بدو يشتغل
+
+309
+00:30:04,200 --> 00:30:09,780
+على مين؟ ويحولوا لأولى؟ طبعا كام factor عدينا؟ ده
+
+310
+00:30:09,780 --> 00:30:15,720
+الواحد البروترومبين بدو يشتغل على مين؟ ريتهم ثانية
+
+311
+00:30:15,720 --> 00:30:17,500
+عادة؟ سبعة؟
+
+312
+00:30:22,350 --> 00:30:25,630
+ماشي وتلاتة اذا بدك تقعد تفشخفه في البيت واتنين و
+
+313
+00:30:25,630 --> 00:30:31,630
+واحد، اتنين وواحد، ماشي طيب الـ program in time
+
+314
+00:30:31,630 --> 00:30:35,410
+بيقيس كل هذه العوامل، طب ليش سموه program؟ ليش
+
+315
+00:30:35,410 --> 00:30:40,290
+مسموهش باسم factor عشرة أو factor خمسة أو factor
+
+316
+00:30:40,290 --> 00:30:47,130
+واحد، واحد أكبر واحد، كثير كمية، ليش؟
+
+317
+00:30:49,310 --> 00:30:51,950
+احنا اتفقنا على أنه بيغش الـ extrinsic كله، والـ
+
+318
+00:30:51,950 --> 00:30:55,330
+extrinsic في كل هذه العوامل، ليه سموه باسم
+
+319
+00:30:55,330 --> 00:31:01,790
+Protrombin؟ ما جالوش مثلا باسم tissue factor أو
+
+320
+00:31:01,790 --> 00:31:03,970
+باسم factor 7 أو whatever
+
+321
+00:31:07,200 --> 00:31:11,860
+لأ، احنا لسنا دا هذه النقطة بشكل أساسي بس بشكل
+
+322
+00:31:11,860 --> 00:31:16,540
+أساسي هذه معلومة سابقة اخذناها يوم اتعرفنا على الـ
+
+323
+00:31:16,540 --> 00:31:19,740
+characteristic feature لكل الـ coagulation factors
+
+324
+00:31:19,740 --> 00:31:26,720
+وعرفنا كل واحد فاكتور اتنين شباب يلا أكتر life
+
+325
+00:31:26,720 --> 00:31:33,160
+span في الـ coagulation factors بي summit حوالي 72
+
+326
+00:31:33,160 --> 00:31:36,360
+ساعة، من 72 لـ 96 ساعة
+
+327
+00:31:40,600 --> 00:31:44,920
+لأ وهذه عوامل تجارب ثانية بالساعات يعني عقلها ستة
+
+328
+00:31:44,920 --> 00:31:49,340
+وتلاتين ساعة اللي هو factor عشرة ثم factor تسعة
+
+329
+00:31:49,340 --> 00:31:54,540
+وأربع وعشرين ثم factor سبعة أقل الـ half-life لمين
+
+330
+00:31:54,540 --> 00:32:01,800
+لـ factor سبعة لأنه قلنا سبعة قليل ماشي وعندنا
+
+331
+00:32:01,800 --> 00:32:04,680
+هنربط هذا الموضوع طب يا شباب نرجع مرة ثانية لل
+
+332
+00:32:04,680 --> 00:32:08,600
+cycle ما زال هيك وخلينا نقعد فترة في هذا الموضوع
+
+333
+00:32:08,600 --> 00:32:10,200
+احنا
+
+334
+00:32:14,010 --> 00:32:22,990
+ماشي احنا عشان نشوف تأثير الـ warfarin بنقيس الـ
+
+335
+00:32:22,990 --> 00:32:26,870
+coagulation factors اللي في الـ extrinsic pathway
+
+336
+00:32:26,870 --> 00:32:33,150
+يعني أنا بنشط من خلال فحص الـ PT كل أوامر التجلط
+
+337
+00:32:33,150 --> 00:32:39,390
+اللي موجودة في الـ extrinsic القياس هذا بيسموه
+
+338
+00:32:39,390 --> 00:32:44,780
+دائرة  indirect ولا ايه دائرة indirect؟ لأن المدرسة
+
+339
+00:32:44,780 --> 00:32:52,680
+مابتوجهش لجهة للورفل؟ مش بشكل مباشر لإيش؟ للورفل؟
+
+340
+00:32:52,680 --> 00:32:57,320
+للورفل، احنا مابتوجهش للورفل، ماشي؟ احنا بنشوف
+
+341
+00:32:57,320 --> 00:33:03,480
+تأثيره على حاجة عشان نشوف الـ effect تبعه، طيب في
+
+342
+00:33:03,480 --> 00:33:06,480
+تأثير مباشر للورفل؟
+
+343
+00:33:08,400 --> 00:33:12,520
+وين بيشتغل الورفة؟ طلع وين بيشتغل الورفة؟ في الـ ..
+
+344
+00:33:12,520 --> 00:33:15,280
+في الـ .. في الـ .. في الـ .. في الـ vitamin K cycle
+
+345
+00:33:15,280 --> 00:33:21,220
+صح مش بيوقفها؟ طيب ايش ممكن أقيس في الـ cycle عشان
+
+346
+00:33:21,220 --> 00:33:25,280
+أسمي الـ measurement direct؟
+
+347
+00:33:25,280 --> 00:33:30,580
+vitamin K epoxide أو vitamin K epoxide هيا ده H2؟ لأ H2 و
+
+348
+00:33:30,580 --> 00:33:32,260
+vitamin K بنفسها
+
+349
+00:33:34,520 --> 00:33:42,040
+مش مشكلة الـ epoxide هو تحويل air تحويل الـ vitamin
+
+350
+00:33:42,040 --> 00:33:49,320
+K hydroquinone إلى الـ epoxide يعني تحت تأثير الـ warfarin الـ
+
+351
+00:33:49,320 --> 00:33:55,640
+vitamin K المختزن يتأكسد يبقى كل ما زاد المتأكسد كل
+
+352
+00:33:55,640 --> 00:34:03,020
+ما زاد الـ effect of air of warfarin عشان هيك كان
+
+353
+00:34:03,020 --> 00:34:10,640
+التفكير أنه احنا لو قيصنا الـ epoxide form بنقيس الـ
+
+354
+00:34:10,640 --> 00:34:17,020
+effect of warfarin directly، ماشي؟
+
+355
+00:34:17,020 --> 00:34:23,140
+وبينما بفحص الـ PT أنا بدي أشتغل الـ coagulation
+
+356
+00:34:23,140 --> 00:34:27,800
+cascade عشان أشوف الـ coagulation cascade تأثر ولا لم
+
+357
+00:34:27,800 --> 00:34:35,930
+يتأثر مفهوم عليا؟ وهي قياس غير مباشر ومن عيوب هذا
+
+358
+00:34:35,930 --> 00:34:42,190
+الفحص أنه لازم أنا يوم ما أعطي warfarin أستنى أقل
+
+359
+00:34:42,190 --> 00:34:47,990
+شيء 72 ساعة عشان أحصل على الـ effect of warfarin، مظبوط؟ ليش 72 ساعة؟ لأن الـ half-life
+
+360
+00:34:47,990 --> 00:34:52,470
+تبع الـ prothrombin أو الثرومبين النشط 72 ساعة يعني
+
+361
+00:34:59,820 --> 00:35:04,300
+ما ينفعش الدكتور يكتب علاج warfarin ويطلع فحص PT
+
+362
+00:35:04,300 --> 00:35:12,300
+على طول، لازم نستنى لینه سبعين ساعة عشان نشوف الـ
+
+363
+00:35:12,300 --> 00:35:17,360
+effect of warfarin على المرضى، ماشي؟ بينما بالقياس
+
+364
+00:35:17,360 --> 00:35:21,440
+هذا لـ vitamin K epoxide، بقت ساعة أنا باخد نتيجة
+
+365
+00:35:23,460 --> 00:35:27,060
+باقي ساعة باخد نتيجة، لكن للأسف الشديد وكانت
+
+366
+00:35:27,060 --> 00:35:34,140
+العملية سهلة جدا، يعني لو عملوا biosensor يبينوا
+
+367
+00:35:34,140 --> 00:35:38,520
+من خلاله هذا المركب بتعرفوا الـ biosensor؟ بتعرفوا
+
+368
+00:35:38,520 --> 00:35:43,080
+فحص السكر اللي .. الـ glucometer اللي بيقيسوا فيه
+
+369
+00:35:43,080 --> 00:35:47,920
+السكر في البيوت؟ هو برضه biosensor لو بيقيس بيقيسه
+
+370
+00:35:47,920 --> 00:35:50,480
+بياخدوا one drop of blood وبيحطوه على شريحة و
+
+371
+00:35:50,480 --> 00:35:54,940
+بيقيسوه جوا مظبوط 100% بنفس الطريقة ممكن نقيس الـ
+
+372
+00:35:54,940 --> 00:36:01,680
+epoxide form ونشوف زاد ولا نقص ماشي زاد ولا نقص
+
+373
+00:36:02,190 --> 00:36:06,050
+وبالتالي بنعمل direct measurement وفي نفس الوقت
+
+374
+00:36:06,050 --> 00:36:12,110
+نستغني عن فترة 72 ساعة اللي بدنا نستنى، مظبوط؟ لأن 
+
+376
+00:36:12,110 --> 00:36:15,770
+هذا عبارة عن direct measurement لمين؟ للـ war front
+
+377
+00:36:15,770 --> 00:36:21,710
+effect للـ war front effect للأساس شديد طبعا هذا
+
+378
+00:36:21,710 --> 00:36:30,850
+الكلام من فترة طويلة انعمل لكن الـ companies و شركات
+
+379
+00:36:30,850 --> 00:36:36,390
+الأدوية لأن شركات الأدوية لو بدنا نعمل هيك بتخسر
+
+380
+00:36:36,390 --> 00:36:41,410
+كتير في الـ warfarin، مع أنه رخيص كعلاج، رخيص، إلا
+
+381
+00:36:41,410 --> 00:36:45,810
+أنه بيتباع بكمية رهيبة جدا في العالم، وبالتالي هم
+
+382
+00:36:45,810 --> 00:36:49,310
+مش معنين يستعملوا عن صناعة تياشر، تصنيع الـ
+
+383
+00:36:49,310 --> 00:36:50,070
+warfarin أكثر.
+
+384
+00:36:58,890 --> 00:37:02,610
+خمسة و عشرين مراكب من الـ Q-marine وهي كل شركة
+
+385
+00:37:02,610 --> 00:37:07,290
+بتختار واحد من هذه المراكبات الـ warfare واحد منها
+
+386
+00:37:07,290 --> 00:37:10,930
+أو الـ commodity الاسم التجاري وهي زي ما أنتم
+
+387
+00:37:10,930 --> 00:37:15,550
+شايفين تأثيره هي بيمنع تحويل الـ epoxide form إلى
+
+388
+00:37:15,550 --> 00:37:19,810
+reduced form وبالتالي بيوقف الـ reaction ولا لا؟
+
+389
+00:37:19,810 --> 00:37:27,430
+وبالتالي منه carboxylation صح؟ ماشي؟ لكن الـ
+
+390
+00:37:27,430 --> 00:37:33,860
+warfarin من عيوبه إنه ما له تأثير على أي جلطة سابقة،
+
+391
+00:37:33,860 --> 00:37:39,300
+هو يمنع الجلطات المستقبلية، ولكن لا، لو فيه جلطة
+
+392
+00:37:39,300 --> 00:37:46,120
+قديمة، ما له أي تأثير على هذه الجلطة، ومش بس هيك،
+
+393
+00:37:46,120 --> 00:37:53,580
+هذه الصورة تبين أن الـ inactivation of warfarin طبعا
+
+394
+00:37:53,580 --> 00:37:56,680
+كنا بنعرف أن الـ liver هو الـ detoxifying agent اللي
+
+395
+00:37:56,680 --> 00:38:03,280
+موجود في الجسم بيخلصنا من الـ drugs من خلال أيه؟ الـ
+
+396
+00:38:03,280 --> 00:38:13,420
+cytochrome بيعملوا activation وبيخلصنا منه وهي 
+
+397
+00:38:13,420 --> 00:38:16,160
+الـ half-life يا شباب زي ما قلت اتنين وسبعة وتسعة
+
+398
+00:38:16,160 --> 00:38:20,020
+وعشرة اتنين يديش 72 ساعة
+
+399
+00:38:23,120 --> 00:38:30,740
+هو 924 عشان هيك الـ peak anticoagulant effect بعد
+
+400
+00:38:30,740 --> 00:38:37,440
+77 لـ 96 يعني زي ما قلت لكم ما بنفع نفحص الـ prothrombin بين
+
+401
+00:38:37,440 --> 00:38:47,720
+طاقم إلا بعد 72 ساعة طيب مكتشف ممكن نعطي warfarin
+
+402
+00:38:48,160 --> 00:38:53,260
+ولا أي مرضى، لأن هو بينعطى as a prophylactic and
+
+403
+00:38:53,260 --> 00:38:59,580
+as a treatment of what؟ of venous thromboembolism
+
+404
+00:38:59,580 --> 00:39:03,200
+disease الناس اللي بيسرع عندهم deep venous
+
+405
+00:39:03,200 --> 00:39:10,320
+thrombosis، وبعدين embolism، بياخدوا warfarin كمان في
+
+406
+00:39:10,320 --> 00:39:16,980
+حالات الـ atrial fibrillation atrial من atrium، إيش
+
+407
+00:39:16,980 --> 00:39:23,940
+atrium؟ وذين وذين والبطاية في القلب مشغطوه ventricle
+
+408
+00:39:23,940 --> 00:39:32,100
+yes and valvular stenosis valvular من valve
+
+409
+00:39:32,100 --> 00:39:41,700
+stenosis ديق ده ديق ثم heart valve replacement ناس
+
+410
+00:39:41,700 --> 00:39:45,480
+اللي عندهم إيه؟ عشان تغيير مغيرين صباب
+
+411
+00:39:55,080 --> 00:40:01,860
+ليش لازم نتابع الـ warfarin as a drug؟ ليش لازم
+
+412
+00:40:01,860 --> 00:40:08,540
+نتابعه؟ قالوا لأن الـ warfarin as a drug has a
+
+413
+00:40:08,540 --> 00:40:13,040
+narrow therapeutic range إيش يعني narrow
+
+414
+00:40:13,040 --> 00:40:16,220
+therapeutic range؟ يعني
+
+415
+00:40:18,300 --> 00:40:25,180
+اللعب في أي قدوز، أي جرعة من جرعات الـ warfarin، بدينا
+
+416
+00:40:25,180 --> 00:40:29,620
+إيهاش؟ بدينا تأثيرات سلبية، وبالتالي إيهاش؟ الـ
+
+417
+00:40:29,620 --> 00:40:33,460
+therapeutic range، يعني مش لازم أزيد كتير أو أقلل
+
+418
+00:40:33,460 --> 00:40:34,180
+كتير منهاش
+
+419
+00:40:41,540 --> 00:40:50,080
+طب ليش لو لعبنا في الـ dose بيأثر وإذا قلق 100%
+
+420
+00:40:50,080 --> 00:40:53,580
+يعني يا بيصير نلعب في الـ balance أو في الـ hemostasis
+
+421
+00:40:53,580 --> 00:40:56,720
+وبالتالي إما بيصير bleeding وإما بيصير عنده إياش
+
+422
+00:40:56,720 --> 00:41:00,280
+thrombosis
+
+423
+00:41:00,280 --> 00:41:05,380
+طب كيف نعمل monitoring للـ Prothrombin؟ اتفقنا على
+
+424
+00:41:05,380 --> 00:41:06,060
+أنه بنعمل
+
+425
+00:41:09,770 --> 00:41:13,810
+كيف بنعمل Monitoring للـ warfarin؟ اتفقنا على أنه
+
+426
+00:41:13,810 --> 00:41:21,450
+بنعمل Prothrombin Time صح؟ 100% بعد 72 ساعة بعد 72
+
+427
+00:41:21,450 --> 00:41:29,750
+ساعة طيب المهم إيش
+
+428
+00:41:29,750 --> 00:41:32,970
+اللي
+
+429
+00:41:32,970 --> 00:41:37,310
+بنعمله في الـ Prothrombin Time؟ أنتم اشتغلتوا بيتي
+
+430
+00:41:37,310 --> 00:41:38,170
+إيش عملتوا؟
+
+431
+00:42:03,390 --> 00:42:08,970
+جمعنا الـ plasma معينات healthy صحية
+
+432
+00:42:11,450 --> 00:42:18,030
+عشان اعملنا كيف؟ عملنا العينة وقررنا إيش حطيته؟
+
+433
+00:42:18,030 --> 00:42:27,150
+في ريجا إيش الـ oranges؟ كالشيان؟ لحاله؟ لا العينة
+
+434
+00:42:27,150 --> 00:42:32,510
+جت كالسم من مخلوطة مخلوطة إيه؟ thromboplastin في
+
+435
+00:42:32,510 --> 00:42:40,710
+ريجا إيش الـ reagent؟ هو المفروض من الـ رابط أو الـ فواني اه
+
+436
+00:42:40,710 --> 00:42:46,930
+إيش هو هذا اللي أنت ماخده من حياتك؟ IMR ولا
+
+437
+00:42:46,930 --> 00:42:56,770
+INR؟ ماشي
+
+438
+00:42:56,770 --> 00:43:00,250
+أنتم خجبتوا الـ vial ها دي واخدتوا منها؟
+
+439
+00:43:04,420 --> 00:43:08,540
+برد النظر، جبته بلازمة وحطيته عليها reagents وقصته 
+
+440
+00:43:08,540 --> 00:43:13,460
+الزمن المطلوب لعمل جلطة، إيش الـ reagent؟ هو
+
+441
+00:43:13,460 --> 00:43:22,660
+إما brain phospholipid أو thromboplastin، صح؟
+
+442
+00:43:22,660 --> 00:43:24,680
+هو brain tissue
+
+443
+00:43:34,480 --> 00:43:40,300
+معناه نضيفه وبمجرد ما نضيفه نقيص الزمن لكن الأسف
+
+444
+00:43:40,300 --> 00:43:47,000
+الشديد وجدوا أنه النتائج متمايزة بين المختبرات حتى
+
+445
+00:43:47,000 --> 00:43:49,400
+في الدولة الواحدة .. أنا حتى في الدولة الواحدة
+
+446
+00:43:49,400 --> 00:43:56,760
+والسبب في ذلك إيش؟ 100% هو أن استخدام الـ
+
+447
+00:43:56,760 --> 00:44:03,120
+reagents الـ reagents اللي بيوزع مختلف مختلف في
+
+448
+00:44:03,120 --> 00:44:10,060
+إيش؟ في مصدر الـ tissue factor اللي هو بقى بره الـ
+
+449
+00:44:10,060 --> 00:44:13,680
+tissue factor و الـ tissue factor موجود وين؟ في الـ
+
+450
+00:44:13,680 --> 00:44:18,600
+brain وفي الـ lung وفي الـ uterus أو placenta
+
+451
+00:44:18,600 --> 00:44:23,200
+بكمية كبيرة يعني الشركة عشان تصنعلي tissue factor
+
+452
+00:44:23,200 --> 00:44:24,040
+بدها إيش؟
+
+453
+00:44:26,920 --> 00:44:31,200
+المصدر الحيواني صح في الأول هو الأصل أنهم يعتمدوا
+
+454
+00:44:31,200 --> 00:44:35,820
+على الإنسان يعني بنتشه فاكتور من مين؟ من الإنسان بس
+
+455
+00:44:35,820 --> 00:44:39,900
+صعب جدا الحصول عليه من الإنسان فبدوا يدوروا على
+
+456
+00:44:39,900 --> 00:44:45,460
+مصادر مختلفة ففي مصادر مختلفة سواء كان horses,
+
+457
+00:44:46,160 --> 00:44:49,460
+rabbits,  borgs أو pigs
+
+458
+00:44:56,720 --> 00:45:02,620
+بدأت النتائج تختلف والسبب في ذلك حساسية الـ reagent
+
+459
+00:45:02,620 --> 00:45:09,780
+مختلفة حساسية الـ reagent مختلفة فبالتالي النتائج
+
+460
+00:45:09,780 --> 00:45:14,640
+كانت تطلع مختلفة فحاولوا يحلوا هذه المشكلة فإيش
+
+461
+00:45:14,640 --> 00:45:20,940
+عملوا؟ قالوا خلّيني أشوف الـ ratio لكن الـ ratio ما
+
+462
+00:45:20,940 --> 00:45:26,530
+حلتش المشكلة ليش ما حلتش المشكلة؟ لأن كل ما عملنا
+
+463
+00:45:26,530 --> 00:45:31,550
+هو قسمنا على ثابت صح ratio إيش الـ PT ratio؟ هي
+
+464
+00:45:31,550 --> 00:45:33,610
+عبارة عن الـ patient PT على
+
+465
+00:45:43,910 --> 00:45:47,790
+بحل المشكلة هيك، بحلش المشكلة، وكأنك قسمتها على
+
+466
+00:45:47,790 --> 00:45:52,010
+إيه؟ على ثابت، وبالتالي ما حلش المشكلة، فكانوا
+
+467
+00:45:52,010 --> 00:45:57,050
+فكروا في طريقة أخرى ليه تقبض الـ variation
+
+468
+00:45:57,050 --> 00:46:02,330
+فاستخدموا ما يسمى بالـ INR International Normalized
+
+469
+00:46:02,330 --> 00:46:08,270
+Ratio وهي عبارة عن الـ ratio، PT ratio للقوة إيش؟
+
+470
+00:46:08,270 --> 00:46:11,210
+ISI، اختصار لإيش ISI؟
+
+471
+00:46:16,880 --> 00:46:21,380
+International Sensitivity Index هو بره الـ
+
+472
+00:46:21,380 --> 00:46:32,200
+index ناشي أعطاني الـ variation of sensitivity اللي
+
+473
+00:46:32,200 --> 00:46:37,360
+موجودة في الـ reagent أو في الـ different reagent
+
+474
+00:46:37,360 --> 00:46:42,140
+يعني يوم تستخدم كذا بيطلع عندك كذا يوم تستخدم كذا
+
+475
+00:46:42,140 --> 00:46:47,610
+استخدم الـ ISI كذا وبعد كذا ارتبت أن هي عشان هي
+
+476
+00:46:47,610 --> 00:46:51,710
+دايما في كل شركة بتعمل الـ standardization للـ agent
+
+477
+00:46:51,710 --> 00:46:56,550
+تبعها وبتحسبلك الـ ISI وبتديلك هي للاستخدام،
+
+478
+00:46:56,550 --> 00:47:00,670
+مفهوم عليها؟ وبالتالي أنت لو استخدمت أي kit في أي
+
+479
+00:47:00,670 --> 00:47:05,090
+دولة من دول العالم، مدام استخدمت هذه الـ formula
+
+480
+00:47:06,390 --> 00:47:13,210
+ضاعت الـ variation عشان هي كان الأصل أنه نستخدم الـ
+
+481
+00:47:13,210 --> 00:47:26,270
+INR في تقييمنا لمن؟ للـ PT بس طبعا الـ PT تبعت الـ
+
+482
+00:47:26,270 --> 00:47:30,090
+patient normal person
+
+483
+00:47:33,880 --> 00:47:38,680
+يكون ماشي على warfarin drug عشان أستخدم هذه الفرقة
+
+484
+00:47:38,680 --> 00:47:43,640
+PT العادي اللي بنعمله prerequisite وإن كان يعني
+
+485
+00:47:43,640 --> 00:47:49,980
+كله بيطلع بهذه النتيجة ماشي إيش الـ prothrombin
+
+486
+00:47:49,980 --> 00:47:55,740
+time وبره time required for blood to coagulate
+
+487
+00:47:55,740 --> 00:48:04,240
+ماشي and it's called PT وهي تعمل من خلال مزيج
+
+488
+00:48:04,240 --> 00:48:08,400
+تضع مزيج من مين؟ من الـ calcium مع الـ thromboplastin
+
+489
+00:48:08,400 --> 00:48:14,200
+على الـ plasma وتبدأ تفحص أو تعدى الزمن المطلوب وها
+
+490
+00:48:14,200 --> 00:48:26,260
+الـ ratio PT ratio هي مرفيشة PT على control PT الـ
+
+491
+00:48:26,260 --> 00:48:30,300
+factors influencing the dose
+
+492
+00:48:33,350 --> 00:48:39,050
+response في عدة عوامل منها
+
+493
+00:48:39,050 --> 00:48:47,270
+الـ inaccurate lab testing طبيعي جدا يا شباب كل
+
+494
+00:48:47,270 --> 00:48:51,790
+مريض بيروح على طبيب بيروح على الطبيب عشان يتابع الـ
+
+495
+00:48:51,790 --> 00:48:56,150
+warfarin ولازم يتابع الطبيب معين ويفضل أن يكون
+
+496
+00:48:56,150 --> 00:48:57,690
+طبيب واحد مش كل مرة يغيروا
+
+497
+00:49:00,960 --> 00:49:07,380
+بناء على نتيجة المختبر الدكتور الطبيب يا إما بيزود
+
+498
+00:49:07,380 --> 00:49:11,760
+الجرعة يا إما بيعيش ويقلل الجرعة طب لو كانت نتيجتك
+
+499
+00:49:11,760 --> 00:49:16,900
+غلط، شو بيصير؟ مشكلة، مشكلة، مشكلة، مشكلة، مشكلة،
+
+500
+00:49:16,900 --> 00:49:19,340
+مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، 
+
+501
+00:49:19,340 --> 00:49:25,800
+مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة،
+
+502
+00:49:25,800 --> 00:49:26,860
+مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة،
+
+503
+00:49:26,860 --> 00:49:27,320
+مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة، مشكلة،
+
+504
+00:49:27,320 --> 00:49:34,680
+مش patient complaints عدم أو ضعف شكوى المريض وما
+
+505
+00:49:34,680 --> 00:49:39,620
+أكثرها هذه أنه في كثير من المرضى بتكون بقى بتشكيش
+
+506
+00:49:39,620 --> 00:49:45,660
+بيكون خاش في مرحلة خطر دون أن يشكي دون أن 
+
+507
+00:49:45,660 --> 00:49:50,200
+أن يشكي كثير وهذه ممكن ببساطة المرضى دي اللي
+
+508
+00:49:50,200 --> 00:49:52,200
+بياخدوه كومودين أو warfarin
+
+509
+00:49:55,920 --> 00:50:00,740
+لما يفرش أسنانه أو صرت معه رعفة أو صرت معه أقل
+
+510
+00:50:00,740 --> 00:50:05,180
+ضربة صرت يتعلم في جسمه المفروض على طول يراجع طبيب
+
+511
+00:50:05,180 --> 00:50:10,600
+لكن هو ما بيراجع الطبيب إلا لما بيسيهاش دولة تلاتة
+
+512
+00:50:10,600 --> 00:50:17,540
+concurrent medication الأدوية المتداخلة ممنوح مريض
+
+513
+00:50:17,540 --> 00:50:19,760
+بياخد كومودين أن ياخد أي دواء 
+
+514
+00:50:22,400 --> 00:50:26,000
+يستشير طبيبه لأنه في كثير من اللاجئين تعمل
+
+515
+00:50:26,000 --> 00:50:33,580
+potentiation أو تعمل inhibition لـ warfarin effect
+
+516
+00:50:33,580 --> 00:50:40,220
+وبالتالي الـ potentiation أو الـ inhibition هيأثر
+
+517
+00:50:40,220 --> 00:50:42,820
+على الدوز ولا لا؟ هيأثر على الـ effect of warfarin
+
+518
+00:50:42,820 --> 00:50:46,000
+ولا لا؟ وبالتالي المريض ممكن يخش في إما bleeding
+
+519
+00:50:46,000 --> 00:50:47,840
+وإما thrombosis
+
+520
+00:50:49,830 --> 00:50:56,230
+levels of dietary vitamin K نسبة الـ vitamin K في 
+
+521
+00:50:56,230 --> 00:51:02,130
+الأكل ماشي لما مريض يكون أكل ثابت وبياخد جرعة
+
+522
+00:51:02,130 --> 00:51:10,190
+و warfarin تأثير يكون ثابت لكن يوم ما ياكل غذاء غني بالـ
+
+523
+00:51:10,190 --> 00:51:17,640
+vitamin K على سبيل المثال عندنا في بلادنا أكل أكثر
+
+524
+00:51:17,640 --> 00:51:23,080
+أكلتين كانوا يأزونا هو الإبلوخية والزهرة،
+
+525
+00:51:23,080 --> 00:51:27,840
+الكورونا، ماشي؟ تنتن فيهم كمية كبيرة من إيش؟ من الـ
+
+526
+00:51:27,840 --> 00:51:34,780
+vitamin K طبعًا أكلة الإبلوخية، ماشي؟ في
+
+527
+00:51:34,780 --> 00:51:39,780
+نص الأشبوع كفيلة منها تغير أو تأثر على الوقف لمدة
+
+528
+00:51:39,780 --> 00:51:39,960
+شهور
+
+529
+00:51:48,360 --> 00:51:52,000
+في هذه الحالة في كثير من الأمور طبيب لما يروح
+
+530
+00:51:52,000 --> 00:51:58,140
+للمريض إليه بنتيجة مختلفة automatically بيسأله
+
+531
+00:51:58,140 --> 00:52:02,720
+كنت الأسبوع عادي والجواب المتعرف عليه عند المرضى
+
+532
+00:52:02,720 --> 00:52:07,120
+أنه والله أنا ما أنا فاكر إيش أفطرت الصبح صح؟
+
+533
+00:52:07,120 --> 00:52:15,060
+فبالتالي لاوضة من أنه يا شي يكون فيه صدق ومعلومات
+
+534
+00:52:15,850 --> 00:52:24,170
+ياخدها الطبيب تكون معلومات قيمة، يعني
+
+535
+00:52:24,170 --> 00:52:27,190
+هو احنا مشكلتنا أنه في كميات الأكل اللي بناخدها،
+
+536
+00:52:27,190 --> 00:52:31,570
+بناكل كميات كبيرة جدًا، صح؟ فبالتالي بيكون تأثيرها
+
+537
+00:52:31,570 --> 00:52:34,730
+سلبي، الـ adverse reaction عليها على الـ core frame
+
+538
+00:52:34,730 --> 00:52:36,790
+يكون عالي جدًا أو سلمي جدًا
+
+539
+00:52:39,600 --> 00:52:43,560
+السبب الرابع الخامس الـ alcohol والحمد لله مش
+
+540
+00:52:43,560 --> 00:52:47,080
+موجود في بلادنا اللي هو المشروبات الكحولية يعني
+
+541
+00:52:47,080 --> 00:52:51,580
+إليها تأثير سلبي علي الـ warfarin لأنه بتأثر على الـ
+
+542
+00:52:51,580 --> 00:52:57,060
+liver بشكل أساسي ثم الـ hepatic dysfunction مصنع
+
+543
+00:52:57,060 --> 00:53:00,920
+بالظبط مصنع الـ coagulation factor ما يصنع الـ
+
+544
+00:53:00,920 --> 00:53:05,880
+coagulation factor ماشي لـ all notion المصنع مضروب
+
+545
+00:53:05,880 --> 00:53:08,300
+بشكل .. بصنع في coagulation factor
+
+546
+00:53:12,280 --> 00:53:17,040
+التي تؤثر على الـ warfarin فيفر من الأشياء التي تؤثر
+
+547
+00:53:17,040 --> 00:53:24,880
+أيضًا على الـ warfarin طبعًا دورة الترابية هذه طبعًا
+
+548
+00:53:24,880 --> 00:53:31,660
+معلومات طبيب ممكن يعني
+
+549
+00:53:31,660 --> 00:53:37,380
+دور الطبيب الـ venous embolism بيعطي المريض و
+
+550
+00:53:37,380 --> 00:53:40,720
+الـ warfarin من 3 إلى 6 شهور الـ acute myocardial
+
+551
+00:53:40,720 --> 00:53:49,330
+infarction حوالي 14 يوم من حد ما بيخش المستشفى و
+
+552
+00:53:49,330 --> 00:53:54,890
+بيبدأ أو أول ما بيبدأ يتحرك بعد الـ AMI الـ mitral
+
+553
+00:53:54,890 --> 00:54:00,130
+valve disease هو الـ replacement بياخد العلاج على
+
+554
+00:54:00,130 --> 00:54:10,330
+طول العمر الـ bioprosthetic heart valve هو اللي
+
+555
+00:54:10,330 --> 00:54:19,050
+بيستبدل صمام صناعي لكن بيولوجي المصدر ويقعد بياخده
+
+556
+00:54:19,050 --> 00:54:23,430
+لقد تلت شهر شهور لأتري الـ fabulation الأمور كله
+
+557
+00:54:23,430 --> 00:54:27,410
+prevention of cerebral embolism من تلاتة إلى ست
+
+558
+00:54:27,410 --> 00:54:36,250
+شهور هل كنت في موقع جنبي أو بواسطة رمضان؟ كنت أجل
+
+559
+00:54:36,250 --> 00:54:42,790
+هذا الجواب لأخر محاضرة في عندنا محاضرة بتقطعنا بالـ
+
+560
+00:54:42,790 --> 00:54:45,350
+anticoagulation وهنحكي على الـ warfarin وكيفية
+
+561
+00:54:45,350 --> 00:54:49,490
+استخدامة وإيش أثره الجانبية وإن شاء الله
+
+562
+00:54:49,490 --> 00:54:55,450
+Contraindication and therapeutic precautions نبغى
+
+563
+00:54:55,450 --> 00:54:58,990
+واحد يعني ماكنتش مش لازم يتاخد الـ warfarin نبغى
+
+564
+00:54:58,990 --> 00:55:04,600
+واحد إذا في المريض عنده حساسية للـ warfarin نبر
+
+565
+00:55:04,600 --> 00:55:07,940
+اتنين condition of risk hemorrhage واحد عنده
+
+566
+00:55:07,940 --> 00:55:19,120
+إمكانية أو خطر حدوث نزيف hemorrhagic tendency and
+
+567
+00:55:19,120 --> 00:55:23,300
+inadequate laboratory technique في بعض المرات يوم
+
+568
+00:55:23,300 --> 00:55:28,490
+تطلع نتائج مش مظبوطة بدك توقف العلاج لغاية ما تتأكد
+
+569
+00:55:28,490 --> 00:55:32,690
+من نتيجة طبعًا الطبيب هو الأحساس ثم protein C و
+
+570
+00:55:32,690 --> 00:55:36,490
+protein S deficiency الناس اللي عندهم deficiency
+
+571
+00:55:36,490 --> 00:55:45,270
+في protein C أو S شو معناه هذا الكلام؟ واحد عندهم
+
+572
+00:55:45,270 --> 00:55:54,410
+deficiency في protein C أو S طيب
+
+573
+00:55:54,410 --> 00:56:04,140
+واش يعني؟ الناس هدول يا شباب كل ما هناك بحكي
+
+574
+00:56:04,140 --> 00:56:07,420
+على إنسان عنده deficiency في protein C أو S
+
+575
+00:56:07,420 --> 00:56:14,460
+protein C أو S هم عبارة عن إيه؟ anticoagulant صح؟
+
+576
+00:56:14,460 --> 00:56:20,360
+anticoagulant مظبوط واحنا متفقين إن الإنسان في
+
+577
+00:56:20,360 --> 00:56:28,240
+الجسم عنده hemostatic balance بين مين ومين بين الـ
+
+578
+00:56:28,240 --> 00:56:34,000
+anticoagulant وبين
+
+579
+00:56:34,000 --> 00:56:42,740
+الـ pro coagulant، مظبوط؟
+
+580
+00:56:42,740 --> 00:56:46,880
+طب واحد عنده الـ anticoagulant قليل، شو بيصير في
+
+581
+00:56:46,880 --> 00:56:51,000
+الميزان؟ الـ pro coagulant بيزيد
+
+582
+00:56:58,380 --> 00:57:07,100
+مش هيك بيصير الميزان؟ على حساب مين؟ هي كفة الميزان
+
+583
+00:57:07,100 --> 00:57:12,360
+ولا لا؟ هذا بيقل وهذا
+
+584
+00:57:12,360 --> 00:57:20,440
+بيزيد فبتغلب الميزان، مظبوط؟ طيب لما تيجي تحطي
+
+585
+00:57:20,440 --> 00:57:26,120
+warfarin، الـ warfarin عبارة عن إيش؟ anticoagulant
+
+586
+00:57:26,120 --> 00:57:35,760
+ولا لأ؟ يعني إيش بده يشيل؟ الميزان بنزل لكن أنا في
+
+587
+00:57:35,760 --> 00:57:39,940
+هذا الحلقة إيش عملت؟ عوضت نقص في الـ anticoagulant
+
+588
+00:57:39,940 --> 00:57:49,320
+لكن إيش عوضت نقص؟ إيش عملت؟ anticoagulant مش
+
+589
+00:57:49,320 --> 00:57:56,200
+موجود يعني في pro coagulant effect حطيت كمان
+
+590
+00:57:56,200 --> 00:58:00,380
+anticoagulant يعني زودت الـ pro coagulant effect
+
+591
+00:58:00,380 --> 00:58:04,120
+صح؟
+
+592
+00:58:04,120 --> 00:58:09,100
+تبقى نية واحد ما عندهوش anticoagulant صح؟ شو صار في
+
+593
+00:58:09,100 --> 00:58:12,620
+الـ pro coagulant؟ زاد زاد زاد طيب أعطيته كمان
+
+594
+00:58:12,620 --> 00:58:16,980
+anticoagulant شو صار في الـ pro coagulant؟ هتجلب
+
+595
+00:58:16,980 --> 00:58:20,360
+هتجلب الـ pro coagulant؟ أنا مش عارف اتجلب عنك
+
+596
+00:58:20,360 --> 00:58:22,660
+بتجلب الـ pro coagulant
+
+597
+00:58:48,370 --> 00:58:50,570
+ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي
+
+598
+00:58:50,570 --> 00:58:50,670
+ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي
+
+599
+00:58:50,670 --> 00:58:51,010
+ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي
+
+600
+00:58:51,010 --> 00:58:51,130
+ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي
+
+601
+00:58:51,130 --> 00:58:53,390
+ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي ماشي
+
+602
+00:58:53,390 --> 00:58:56,850
+ماشي ماشي ماشي ماشي ماشي هذا منزل لتحت أكثر أو لا؟
+
+603
+00:58:56,850 --> 00:59:01,850
+فمريض من هالنوع بيصير عنده جلطات متكررة، ماشي؟ أول
+
+604
+00:59:01,850 --> 00:59:05,850
+ما تديه، إذا ما عندهوش protein C أو protein S وتديه
+
+605
+00:59:05,850 --> 00:59:11,610
+warfarin، بيخش فيه جلطة، بيخش فيه إيش؟ فيه جلطة،
+
+606
+00:59:11,610 --> 00:59:17,490
+ليش؟ لأنه زودت الخلل الموجود في التوازن عند
+
+607
+00:59:17,490 --> 00:59:25,310
+المريض، مفهوم يا شباب؟ فالناس ممنوعة تاخد warfarin ما
+
+608
+00:59:25,310 --> 00:59:31,030
+لم يكون الميزان مظبوط، وقت ما الـ K-Deficiency نفس
+
+609
+00:59:31,030 --> 00:59:34,510
+الحكاية،
+
+610
+00:59:34,510 --> 00:59:38,620
+الـ intramuscular Injection هذه عبارة عن Contra
+
+611
+00:59:38,620 --> 00:59:43,800
+Indication لجوا أن الـ Vitamin K بيعمل ألم فظيع
+
+612
+00:59:43,800 --> 00:59:49,020
+جدا عند الناس لما يتاخد intramuscular وFibrosis،
+
+613
+00:59:49,020 --> 00:59:53,580
+ماشي؟ فبالتالي لا يفضل أن يتاخد intramuscular،
+
+614
+00:59:53,580 --> 00:59:59,660
+مفهوم يا شباب؟ حددوا شوية؟ طبعًا الـ Side Effect
+
+615
+00:59:59,660 --> 01:00:08,650
+تبعه إيه؟ Hemorrhage و Skin Necrosis لأنه لما بيصير
+
+616
+01:00:08,650 --> 01:00:13,530
+فيه هنا ممكن يعمل skin necrosis multiple clot
+
+617
+01:00:13,530 --> 01:00:17,950
+formation محصلة عن skin necrosis purple toe
+
+618
+01:00:17,950 --> 01:00:26,170
+syndrome purple إيش يعني؟ مية في المية، toe، أصبع
+
+619
+01:00:26,170 --> 01:00:32,350
+رزق كبير، syndrome بيصير فيه إيش؟ لونه؟ بنفس أو
+
+620
+01:00:32,350 --> 01:00:37,420
+أسود بنفسجي or whatever بنتجة كثرة الأفضل هذا
+
+621
+01:00:37,420 --> 01:00:43,120
+الموضوع micro embolization برضه من هنا ثم
+
+622
+01:00:43,120 --> 01:00:48,240
+teratogenicity teratogenicity وهي عبارة عن سندروم
+
+623
+01:00:48,240 --> 01:00:55,900
+يعني agranulocytosis ثم leukopenia وdiarrhea ونوزيا
+
+624
+01:00:55,900 --> 01:01:00,900
+وانوركسيا teratogenicity
+
+625
+01:01:00,900 --> 01:01:07,140
+هي عبارة عن سندروم بيكون فيه أكثر من حالة من الحالات 
+
+626
+01:01:07,140 --> 01:01:10,680
+ماشي
+
+627
+01:01:10,680 --> 01:01:14,420
+عند
+
+628
+01:01:14,420 --> 01:01:23,740
+المتغير العلاج من نوع لنوع ماشي شوفت مش قولنا 
+
+629
+01:01:23,740 --> 01:01:26,980
+اتفقنا على أنه في حوالي 25 نوع من العلاج يوم
+
+630
+01:01:26,980 --> 01:01:33,920
+أتغيره لازم المريض يعمل I&R جديدة، ولازم عندها 
+
+631
+01:01:34,310 --> 01:01:39,410
+الطبيب يبدأ معاه جرعة اتنين ملي جرام ويبدأ يزيد
+
+632
+01:01:39,410 --> 01:01:43,550
+الجرعة slowly لغاية ما يعرف الـ optimal dose
+
+633
+01:01:43,550 --> 01:01:49,310
+المناسبة للمريض، ماشي شباب؟ 
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/s9StxN7sbug_raw.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/s9StxN7sbug_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..450262b1bbb21ba60f953fba334e6687cbe1611b
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/s9StxN7sbug_raw.srt
@@ -0,0 +1,1548 @@
+1
+00:00:20,790 --> 00:00:26,270
+بسم الله الرحمن الرحيم طيب اليوم هنستكمل ان شاء
+
+2
+00:00:26,270 --> 00:00:29,050
+الله محاضرة vitamin K دي efficiency او vitamin K
+
+3
+00:00:29,050 --> 00:00:33,110
+and coagulation وصلنا لهذه ال slide وهي vitamin K
+
+4
+00:00:33,110 --> 00:00:35,910
+دي efficiency وان vitamin K دي efficiency ممكن
+
+5
+00:00:35,910 --> 00:00:43,270
+ينتج نتيجة عدة حالات في عدة حالات منها انه نقص ال
+
+6
+00:00:43,270 --> 00:00:45,770
+vitamin في الأكل اللي بتاكل، بتاكل أكل مافيش فيه
+
+7
+00:00:45,770 --> 00:00:54,720
+vitamin اوإنه في disorders بتقلل من امتصاص ال
+
+8
+00:00:54,720 --> 00:01:00,520
+vitamin أو في drugs بتتاخد بتعمل interaction مع ال
+
+9
+00:01:00,520 --> 00:01:06,580
+vitamin K وبالتالي بتمنع امتصاصه بتزود او بتقلل
+
+10
+00:01:06,580 --> 00:01:09,800
+دول ال vitamin K يعني في بعض الليالات بتعمل
+
+11
+00:01:09,800 --> 00:01:13,360
+potentiation وفي بعض الليالات بتعمل inhibition لل
+
+12
+00:01:13,360 --> 00:01:16,590
+vitamin K actionمنها على سبيل المثال الـ
+
+13
+00:01:16,590 --> 00:01:22,810
+Anticomposants و ال Antibiotics طبعا سبب آخر و
+
+14
+00:01:22,810 --> 00:01:26,910
+أخير هو ال use of Clomarine Warfarin كلنا عرفنا من
+
+15
+00:01:26,910 --> 00:01:30,990
+المحاضرة السابقة أن ال Warfarin هو أبرع ال Vitamin
+
+16
+00:01:30,990 --> 00:01:35,650
+K Antagonist Vitamin K Antagonist وبالتالي بعمل
+
+17
+00:01:35,650 --> 00:01:42,370
+Inhibition or Vitamin K Deficiency statesما هي
+
+18
+00:01:42,370 --> 00:01:46,490
+المظاهر المرضية لهذا النقص؟ طبعا كلنا بنعرف أنه
+
+19
+00:01:46,490 --> 00:01:49,990
+ممكن يصير فيه bleeding، ليش؟ Vitamin K، عارفين
+
+20
+00:01:49,990 --> 00:01:55,710
+دوره، بيساعد في activation of certain coagulation
+
+21
+00:01:55,710 --> 00:02:00,710
+أو Vitamin K، مظبوط؟ 100% وبالتالي مافيش
+
+22
+00:02:00,710 --> 00:02:05,770
+coagulation factorsعندها القدرة ان تتنشر، يعني في
+
+23
+00:02:05,770 --> 00:02:10,070
+bleeding صح؟ 100% في نوزي bleeding، في gum
+
+24
+00:02:10,070 --> 00:02:15,150
+bleeding، في stomach bleeding، في urine، في blood
+
+25
+00:02:15,150 --> 00:02:19,650
+أو stool، في blood، في terriplag stool، terriplag
+
+26
+00:02:19,650 --> 00:02:23,250
+stool هو برعن حالة مرضية تصيب غالبا المناطق
+
+27
+00:02:23,250 --> 00:02:27,290
+الاستوائية ويصير فيها إسهال شديد، مصحوب بدم شديد،
+
+28
+00:02:27,290 --> 00:02:36,430
+إسهال شديد، مصحوب ب .. بدم شديدطبعا في كمان يصير
+
+29
+00:02:36,430 --> 00:02:42,710
+فيه extremely heavy menstrual bleeding يعني ال X
+
+30
+00:02:42,710 --> 00:02:47,610
+بتطول على ال 6 بتقعد فترة طويلة and in infants في
+
+31
+00:02:47,610 --> 00:02:54,050
+خوف أنه يصير فيه intra cranial hemorrhage
+
+32
+00:02:54,050 --> 00:03:01,880
+in infants الأطفال newborn غالباare brought to
+
+33
+00:03:01,880 --> 00:03:06,920
+vitamin K deficiency يعني غالبا اطفال بيولدوا و
+
+34
+00:03:06,920 --> 00:03:13,180
+عندهم ايش عندهم vitamin K deficiency او بعد ولادة
+
+35
+00:03:13,180 --> 00:03:19,500
+من الأسباب لذلك هي القاتل نمر واحد ان ال vitamin K
+
+36
+00:03:19,500 --> 00:03:22,720
+هو أبرعان و ال limit و أبرعان فاتي sorry بال
+
+37
+00:03:22,720 --> 00:03:26,620
+substance مظبوط they cannot cross the placenta
+
+38
+00:03:26,620 --> 00:03:32,450
+وبالتالي بيسروا من الأم للطفلبسلوش نبرة اتنين
+
+39
+00:03:32,450 --> 00:03:38,770
+Coagulation factor وبالذات Pro-thrombin Synthesis
+
+40
+00:03:38,770 --> 00:03:42,370
+في ال liver هي عبارة عن عملية غير نادجة premature
+
+41
+00:03:42,370 --> 00:03:49,110
+process عشان هيك معظم الأطفال الحديثي الولادة ال
+
+42
+00:03:49,110 --> 00:03:54,650
+normal value بتاعة ال coagulation factors are less
+
+43
+00:03:54,650 --> 00:03:57,850
+than others are less than others بتوصل لغاية fifty
+
+44
+00:03:57,850 --> 00:04:03,560
+percentالنسبة، ماشي؟ يبقى في عندنا قلة في إنتاج ال
+
+45
+00:04:03,560 --> 00:04:07,780
+coagulation factors عند إيش؟ عند الأطفال، يبقى فيش
+
+46
+00:04:07,780 --> 00:04:12,020
+vitamin K وفيش coagulation factors، ماشي؟ هذه كلها
+
+47
+00:04:12,020 --> 00:04:16,660
+عوامل عبارة عن إيش؟ايبار عن عوامل بتؤدي الى
+
+48
+00:04:16,660 --> 00:04:20,400
+vitamin K deficiency نمرة تلاتة الطفل بنولد و ال
+
+49
+00:04:20,400 --> 00:04:24,680
+gut تبقى أستراليكا ال gut الأرمعاد تبقى أستراليكا
+
+50
+00:04:24,680 --> 00:04:29,860
+يعني في ميناكوينون بتصنع ميناكوينون هو يبقى اللي
+
+51
+00:04:29,860 --> 00:04:38,440
+بدأت مظهور يعني كمان هذا سبب أخر أنه يصير فيه سبب
+
+52
+00:04:38,440 --> 00:04:41,760
+خامس أو رابع ال breast milk
+
+53
+00:04:46,090 --> 00:04:49,910
+ماشي؟ مافيش فيه vitamin K عشان هيك الناس اللي
+
+54
+00:04:49,910 --> 00:04:54,510
+بتطول و هي بتعتمد فقط على حليب صدرها للأم اللي طول
+
+55
+00:04:54,510 --> 00:04:58,030
+هي أمر عن .. هي خاطئة دول أن تدري لإن مافيش
+
+56
+00:04:58,030 --> 00:05:01,630
+vitamin .. بتمنع طفلها أو بتحلم طفلها من إيش؟ من
+
+57
+00:05:01,630 --> 00:05:05,770
+ال vitamin K اللي هو أصلا محتاجه .. اللي هو أصلا
+
+58
+00:05:05,770 --> 00:05:13,770
+محتاجه طبعا كنتيجة لهذه الأسباب كلها Hemorrhagecan
+
+59
+00:05:13,770 --> 00:05:19,450
+be seen in infants و بيسمو هذه الحالة vitamin K
+
+60
+00:05:19,450 --> 00:05:26,790
+deficiency bleeding disease و هذا الكلام بنشوفه
+
+61
+00:05:26,790 --> 00:05:29,650
+غضبا اما في ال breast feeding of children الناس
+
+62
+00:05:29,650 --> 00:05:35,410
+اللي بيعتمدوا على اللي هو حليب الأم او في المهالة
+
+63
+00:05:35,410 --> 00:05:39,550
+absorption او في ال liver disorders يكون الطفل
+
+64
+00:05:39,550 --> 00:05:45,020
+عنده هذه الشيءطبعا كلكوا عشان تكونوا بس جديش
+
+65
+00:05:45,020 --> 00:05:50,380
+تكونوا عندكوا فكرة على كمية ال bottom key المطلوبة
+
+66
+00:05:50,380 --> 00:05:56,680
+للإنسان في اليوم ماشي؟ يعني لو في كل يوم تخيلوا
+
+67
+00:05:56,680 --> 00:06:02,340
+الأضلتة دهي الأضلتة على سبيل مثال الشباب اللي زيكم
+
+68
+00:06:02,340 --> 00:06:08,640
+بيحتاج إلى مائة وعشرين مايكرو جرام في اليوم120
+
+69
+00:06:08,640 --> 00:06:14,980
+microgram عرفنا من أين ممكن نحصله صح في مال بتحتاج
+
+70
+00:06:14,980 --> 00:06:23,600
+أقل في مال بتحتاج أقل طيب
+
+71
+00:06:23,600 --> 00:06:27,800
+prevention and treatment ال vitamin K بنعطيه
+
+72
+00:06:27,800 --> 00:06:32,380
+orally ماشي لإنه قلنا انترا ماسكولر و vitamin K
+
+73
+00:06:32,380 --> 00:06:39,970
+الwarfarin is a contradictoryال vitamin K بنحطها
+
+74
+00:06:39,970 --> 00:06:45,170
+orally في بعض الأحيان مافيش good absorption
+
+75
+00:06:45,170 --> 00:06:52,050
+فبيعطوه by injection و الأمبولات بتاعة ال vitamin
+
+76
+00:06:52,050 --> 00:06:56,090
+K في ال emergency room كثيرة لإن أي إنسان بيخش ب
+
+77
+00:06:56,090 --> 00:07:03,850
+bleeding بيفكروا يعطوه إيهVitamin K. The dose is
+
+78
+00:07:03,850 --> 00:07:11,250
+altered or extra vitamin K is given في بعض الحالات
+
+79
+00:07:11,250 --> 00:07:16,890
+اللي يكون عندها mal absorption خلل في امتصاص ال
+
+80
+00:07:16,890 --> 00:07:22,190
+vitamin شو بيعملوا؟ بيعطوا injection و بيزودوا
+
+81
+00:07:22,190 --> 00:07:27,530
+الجرع عشان يعوضوا النقص ال layer اللي موجود في بعض
+
+82
+00:07:27,530 --> 00:07:35,890
+الأحيانبعض المرضى تعانى من liver disease وبالتالي
+
+83
+00:07:35,890 --> 00:07:43,830
+في vitamin K deficiency و vitamin K injectionلحاله
+
+84
+00:07:43,830 --> 00:07:48,970
+لا يكفي في هذه الظرر ال vitamin K لحاله لا يكفي
+
+85
+00:07:48,970 --> 00:07:53,790
+ففي إيش بيفكروا بالظبط بيعملوله blood transfusion
+
+86
+00:07:53,790 --> 00:07:57,910
+على أساس يعيشوا أو يعطوا coagulation factor
+
+87
+00:07:57,910 --> 00:08:00,890
+already يعني جاهزة for activity
+
+88
+00:08:04,560 --> 00:08:09,260
+اليوم منظمة الصحة العالمية أوصت بإن كل طفل بيولد
+
+89
+00:08:09,260 --> 00:08:13,960
+بما انه عنده هذه الظروف لازم ياخد vitamin K عند
+
+90
+00:08:13,960 --> 00:08:16,980
+الولادة عشان هيك معظم الأطفال عند الولادة بياخدوا
+
+91
+00:08:16,980 --> 00:08:20,100
+إبرة وهذه الإبرة هي عبارة عن vitamin K عبارة عن
+
+92
+00:08:20,100 --> 00:08:23,880
+هاش و vitamin K لإن زي ما قلتلكم بنخاف من intra
+
+93
+00:08:23,880 --> 00:08:27,800
+cranial bleeding عند هاش الأطفال الحاجة التانية
+
+94
+00:08:27,800 --> 00:08:32,340
+اللي بيوصوا فيها لإن معظم الحليب اليوم صار مدعم
+
+95
+00:08:32,340 --> 00:08:41,750
+بهاشبال vitamin K، حد عنده سؤال؟ طبعا الان نقدر
+
+96
+00:08:41,750 --> 00:08:52,110
+نجاوب انه وين ممكن نحصل على ال vitamin، هنا two
+
+97
+00:08:52,110 --> 00:08:57,930
+ways we get vitamin K نباتات وعن طرح ال bacterium
+
+98
+00:08:57,930 --> 00:09:01,610
+اللي بتكون في النار 100% يعني نباتي و حيواني، خيلك
+
+99
+00:09:01,610 --> 00:09:08,630
+منه و منك منهبدنا good source for vitamin K برسلز
+
+100
+00:09:08,630 --> 00:09:16,110
+برسلز ماشي بروكلي بروكلي الزهرة الكعب الطفل ماشي
+
+101
+00:09:16,110 --> 00:09:21,070
+what types of chemical reaction does vitamin K 100
+
+102
+00:09:21,070 --> 00:09:24,890
+% بيعمل carboxylation طبعا بيعمل 100% على vitamin
+
+103
+00:09:24,890 --> 00:09:30,190
+K cycle صح طبعا anticoagulant بيعمل inhibition
+
+104
+00:09:30,190 --> 00:09:35,300
+لvitamin K 100%name sign of vitamin k deficiency
+
+105
+00:09:35,300 --> 00:09:41,500
+really صح summer يا شباب طبعا احنا ممكن نلخص ان ال
+
+106
+00:09:41,500 --> 00:09:45,440
+vitamin k is a fat soluble نفس المحاضرة كلها عدينا
+
+107
+00:09:45,440 --> 00:09:50,920
+عليها حد عنده سؤال حد عنده سؤال طيب استكمال
+
+108
+00:09:50,920 --> 00:09:55,760
+الموضوع اليوم هنحكي في الجزء التاني من المادة
+
+109
+00:09:55,760 --> 00:09:59,800
+اليوم هنبدأ نحكي في الجزء التاني من المادة وهو
+
+110
+00:09:59,800 --> 00:10:04,170
+bleeding disordersوهو disorder طبعا ال disorder يا
+
+111
+00:10:04,170 --> 00:10:09,830
+شباب بتقسم إلى جزئين هنحكي في bleeding disorders و
+
+112
+00:10:09,830 --> 00:10:13,010
+هنحكي في thrombotic disorders يعني هنحكي في
+
+113
+00:10:13,010 --> 00:10:14,370
+bleeding و thrombosis
+
+114
+00:10:19,020 --> 00:10:24,660
+هي مقسمة إلى أمراضها، مقسم إلى جزء إيه؟ إما
+
+115
+00:10:24,660 --> 00:10:29,440
+hereditary وإما acquired disease، إما hereditary
+
+116
+00:10:29,440 --> 00:10:33,060
+وإما acquired disease هندرس different disease
+
+117
+00:10:33,060 --> 00:10:39,080
+associated with the defective mechanisms اللي
+
+118
+00:10:39,080 --> 00:10:42,960
+اتعلمناها، ميكانيزمات اللي اتعلمناها، يوم ما يصير
+
+119
+00:10:42,960 --> 00:10:47,550
+فيها defect، معناته إيش؟ معناته حالة مرضىطبعا نشوف
+
+120
+00:10:47,550 --> 00:10:50,870
+إيش الموضوع و نبدأ بال Vascular و Platelet
+
+121
+00:10:50,870 --> 00:10:55,590
+Disorder و
+
+122
+00:10:55,590 --> 00:10:59,690
+قبل ما نبدأ في الموضوع خلّونا نتعرف على بعض
+
+123
+00:10:59,690 --> 00:11:04,430
+المصطلحات المتعلقة بالأمراض، لما بحكي على
+
+124
+00:11:04,430 --> 00:11:08,650
+symptoms، بدي أحكي على مصطلح، أكون عارف هذا
+
+125
+00:11:08,650 --> 00:11:16,670
+المصطلح، نبدأ ورا حد بتاشي، مصطلح بتاشيماشي او في
+
+126
+00:11:16,670 --> 00:11:22,730
+بعض ال دول
+
+127
+00:11:22,730 --> 00:11:29,330
+بتنفذوا بتاكياي بتاكياي وان كنت انا مش كتير بفضل
+
+128
+00:11:29,330 --> 00:11:35,110
+هذا المصطلح هو عبارة عن بتاشي ماشي دول ببساطة
+
+129
+00:11:35,110 --> 00:11:41,510
+بتاشي هو عبارة عن شباب مدموة pinpoint size or
+
+130
+00:11:41,510 --> 00:11:46,940
+pinhead size bleeding under the skinماشي، إيش
+
+131
+00:11:46,940 --> 00:11:52,940
+يعني؟ يعني بيصير نقطة حمراء صغيرة نازمة برا ..
+
+132
+00:11:52,940 --> 00:11:58,140
+بحاجة براس ليه؟ الدبوس تحت الجلب و يمكن كتير
+
+133
+00:11:58,140 --> 00:12:03,480
+تلاحظوها، تشوفوها ولا بتشوفواش؟ كتير تلاحظوا انه
+
+134
+00:12:03,480 --> 00:12:10,560
+مرات بيكون فياش pinpoint ندبة يعني، ندبة إشي أكبر
+
+135
+00:12:11,120 --> 00:12:16,080
+Perpera مصطلح آخر وهو hemorrhage under the skin
+
+136
+00:12:16,080 --> 00:12:24,660
+لكن بيختلف varying in color and duration بيختلف
+
+137
+00:12:24,660 --> 00:12:31,920
+ماشي من حالة إلى حالة بوقت ال .. بالوقت و بالعياش
+
+138
+00:12:31,920 --> 00:12:38,460
+و باللون، ماشي؟يبدأ هو عبارة عن نزيف تحت الجل لكن
+
+139
+00:12:38,460 --> 00:12:46,440
+ب .. it's a varying picture نمرا تلاتة ايكوموزز
+
+140
+00:12:46,440 --> 00:12:52,740
+ايكوموزز هو عبارة عن purple .. purple patch patch
+
+141
+00:12:52,740 --> 00:12:56,500
+معناته ايش؟ هي النادبلة اللي هو حكى عليها لطا
+
+142
+00:12:56,500 --> 00:13:05,100
+ماشي؟ patch كبيرة يعني نزيفوصارله diffusion وين؟
+
+143
+00:13:05,100 --> 00:13:09,800
+under the skin بيصير فيه extravasation of blood
+
+144
+00:13:09,800 --> 00:13:17,540
+into the skin يعني بيمد تحت الجلد larger than
+
+145
+00:13:17,540 --> 00:13:20,760
+بتاشي أكتر من أيش ال pinpoint اللي طبعاك هنا
+
+146
+00:13:20,760 --> 00:13:26,080
+عليها؟ Echemosis هو عبارة عن bleeding وفشلleading
+
+147
+00:13:26,080 --> 00:13:30,040
+وصارله diffusion ماشى طبعا ال diffusion بيختلف
+
+148
+00:13:30,040 --> 00:13:34,620
+حجمها من منطقة الى منطقة هذه كتير بتشوفوها شباب
+
+149
+00:13:34,620 --> 00:13:39,200
+يوم بتعمل ت .. تسحب عيلة الدم من ايه؟ من زميلك ايش
+
+150
+00:13:39,200 --> 00:13:44,020
+بتعمله؟ امتو امتو بالظبط بيكون فيه صار ecomosis
+
+151
+00:13:44,020 --> 00:13:48,920
+وطلع دم برا ال blood vessels وصارله diffusion
+
+152
+00:13:48,920 --> 00:13:50,580
+extravascular
+
+153
+00:13:54,430 --> 00:14:00,010
+هو عبارة عن nose bleeding بيسموها إيه؟ Epistaxis
+
+154
+00:14:00,010 --> 00:14:06,950
+ماشي Minorrhagia مانعتها excessive menses
+
+155
+00:14:06,950 --> 00:14:12,830
+Minorrhagia مانعتها إيه؟ Excessive menses ثم
+
+156
+00:14:12,830 --> 00:14:19,670
+Hematuria من الإسم blood urine Hemarthrosis
+
+157
+00:14:21,210 --> 00:14:26,610
+البلد لكن في الـ joints ماشي and hematemesis
+
+158
+00:14:26,610 --> 00:14:37,690
+spitting البلدش يعني يبصق او ياش اه بالظبط ثم ا
+
+159
+00:14:37,690 --> 00:14:42,450
+sorry vomiting hematemesis hemoptysis هو ال
+
+160
+00:14:42,450 --> 00:14:47,430
+spitting انه لما ييجي يبزق بتلاقي ياش خلّى دم ثم
+
+161
+00:14:47,430 --> 00:14:52,470
+ميلينا والميليناهى عبارة عن blood in a .. in a
+
+162
+00:14:52,470 --> 00:14:56,270
+stool يعني فيه gastrointestinal bleeding نزل فيهاش
+
+163
+00:14:56,270 --> 00:15:01,710
+فى الستول وعمل ما يسمى بال occult blood خاتون ماشى
+
+164
+00:15:01,710 --> 00:15:06,690
+اللى هو الدم المخفي فى البرازق الدم المخفي فيهاش
+
+165
+00:15:06,690 --> 00:15:13,350
+فى الستول ماشى دى مصطلحات هنفترق اليها أثناء شرحنا
+
+166
+00:15:13,350 --> 00:15:17,240
+كثيراطبعا قبل ما نبدأ كلنا بنعرف أنه في homostatic
+
+167
+00:15:17,240 --> 00:15:21,800
+balance between coagulation and fibrolysis أو
+
+168
+00:15:21,800 --> 00:15:31,250
+coagulation factors بأنواع and inhibitorsمظبوط في
+
+169
+00:15:31,250 --> 00:15:35,810
+palance يوم ما يصير فيه bleeding مين اللي رجحت
+
+170
+00:15:35,810 --> 00:15:42,190
+كفته او ال inhibitors ماشي fibromyalgia او اياش او
+
+171
+00:15:42,190 --> 00:15:45,450
+ال inhibitors وبالتالي presence of inhibitors زي
+
+172
+00:15:45,450 --> 00:15:49,750
+ال warfarin او ال heparin ماشي او في بعض الحالات
+
+173
+00:15:49,750 --> 00:15:54,270
+المرضية زي القلو او ال auto antibodyto certain
+
+174
+00:15:54,270 --> 00:15:58,950
+factors بيسموهم inhibitors، شو بيعملوا؟ بيعملوا
+
+175
+00:15:58,950 --> 00:16:03,830
+blocking لل inhibitors فبيصير فيه bleeding، ماشي؟
+
+176
+00:16:03,830 --> 00:16:10,490
+O2 or اللوم antibody دخل ل certain coagulation
+
+177
+00:16:10,490 --> 00:16:15,290
+factor، ماشي؟ وعمل بيسموهم inhibitors ال antibody
+
+178
+00:16:15,290 --> 00:16:20,220
+هدولعمل انهيبش ل ال factors و بالتالي صار فيه
+
+179
+00:16:20,220 --> 00:16:24,700
+bleeding و أشهرها طبعا مرض ال hemophilia بيسموه
+
+180
+00:16:24,700 --> 00:16:29,800
+acquired hemophilia ليش؟ صار فيه antibody لمين؟ ال
+
+181
+00:16:29,800 --> 00:16:34,140
+coordination factor قسموا ال bleeding disorders
+
+182
+00:16:34,140 --> 00:16:42,120
+إلى أربع different area طبعا الشباب احنا ممكن نقسم
+
+183
+00:16:42,120 --> 00:16:50,630
+ال bleeding disorders إلى أكتر من هناماشى، ليش؟
+
+184
+00:16:50,630 --> 00:16:56,410
+احنا من بداية الفصل قولنا ال hemostatic components
+
+185
+00:16:56,410 --> 00:17:01,570
+كام واحد، جبل بليتليتش فيه
+
+186
+00:17:12,280 --> 00:17:15,840
+وشيبونا الكوينم الكمني ما تضلك وخشوا على الخط أجيت
+
+187
+00:17:15,840 --> 00:17:22,860
+هدول العوامل المختلفة كل خلل في كل عامل من العوامل
+
+188
+00:17:22,860 --> 00:17:27,980
+ممكن يأدي إما إلى thrombosis أو إلى إيه؟ إلى
+
+189
+00:17:27,980 --> 00:17:33,780
+bleeding وبالتالي التقسيمة سهلة ماشي؟ لكن أنا شفت
+
+190
+00:17:33,780 --> 00:17:39,180
+أن هذه التقسيمة هي أفضل تقسيمة لتقسيم هذه الأمراض
+
+191
+00:17:39,180 --> 00:17:45,180
+و ..اتقسموا إلى ال major component vascular
+
+192
+00:17:45,180 --> 00:17:51,840
+abnormality ثم platelet disorders ثم coagulation
+
+193
+00:17:51,840 --> 00:17:55,940
+factor disorders ولمّا بقول bleeding يعني إيش صار
+
+194
+00:17:55,940 --> 00:18:05,080
+صار قلة مظبوط ثم الرابع تقدروا
+
+195
+00:18:05,080 --> 00:18:10,500
+تسموه miscellaneous الرابعيعرفين ايش يعني
+
+196
+00:18:10,500 --> 00:18:15,980
+miscellaneous؟ اخر او من اخر و تفريقات ماشي
+
+197
+00:18:15,980 --> 00:18:20,220
+miscellaneous فحطيتلكم مثال عليه اللي هو ال DIC
+
+198
+00:18:20,220 --> 00:18:25,000
+لأنه لا بقدر احطه تحت hereditary ولا acquired ماشي
+
+199
+00:18:25,000 --> 00:18:33,260
+فحطيته يعني مختلف مفهوم يا شباب ونبدأ بأول هذه ال
+
+200
+00:18:33,260 --> 00:18:37,930
+component وهي ال blood vessels or vasculardefect
+
+201
+00:18:37,930 --> 00:18:45,490
+بتؤدي الى bleeding بتؤدي الى bleeding يعني it
+
+202
+00:18:45,490 --> 00:18:51,850
+begins with bleeding episodes in the presence of
+
+203
+00:18:51,850 --> 00:19:00,990
+laboratory normal laboratory coagulation test وهذا
+
+204
+00:19:00,990 --> 00:19:04,610
+وضع طبيعي جدا يا شباب في blood vesselsالـ
+
+205
+00:19:04,610 --> 00:19:07,990
+hemostatic tests are normal، إيش الـ hemostatic
+
+206
+00:19:07,990 --> 00:19:12,450
+tests؟ الـ BTU طب و لما ما أتخدتهم ال BT و ال BTT،
+
+207
+00:19:12,450 --> 00:19:20,730
+إيش بندرس من خلالهم؟ برضه
+
+208
+00:19:20,730 --> 00:19:24,890
+مافهمتش، ندرس من خلالهم ال coagulation cascade،
+
+209
+00:19:24,890 --> 00:19:29,540
+صح؟ يعني تدرس من خلال ال coagulation cascadeو
+
+210
+00:19:29,540 --> 00:19:31,420
+بالتالي blood vessels اللي دخلت في الموضوع و
+
+211
+00:19:31,420 --> 00:19:36,780
+بالتالي Hemostatic tests are normal مانو مش دخلت
+
+212
+00:19:36,780 --> 00:19:40,480
+يعني حتى لو خرجت blood vessels ال Hemostatic
+
+213
+00:19:40,480 --> 00:19:48,300
+laboratory tests of correlation are normal قسمهم
+
+214
+00:19:48,300 --> 00:19:55,220
+إلى Hereditary و Acquired و في الغرب ال symptoms
+
+215
+00:19:55,220 --> 00:19:59,250
+اللي بتتعلق بال blood vessels are superficialبحكي
+
+216
+00:19:59,250 --> 00:20:06,230
+على blood vessels and usually these are diagnosed
+
+217
+00:20:06,230 --> 00:20:15,210
+by exclusion بتروح و أنت مدور على الفعصار و عاملها
+
+218
+00:20:15,210 --> 00:20:18,470
+واحد ورا التاني، ده كلهم normal، معناته ميدنال
+
+219
+00:20:18,470 --> 00:20:24,470
+بيجي by exclusion after you rolling out the
+
+220
+00:20:24,470 --> 00:20:29,410
+platelet ثم coagulationهما fiber analytic
+
+221
+00:20:29,410 --> 00:20:34,670
+components ماشي بيضال ال air بيضال ال blood
+
+222
+00:20:34,670 --> 00:20:44,210
+vessels و ال defect ماشي vascular disease اتفقنا
+
+223
+00:20:44,210 --> 00:20:48,310
+على انه ال platelet و ال hemostatic tests are
+
+224
+00:20:48,310 --> 00:20:53,110
+normal و ال platelet function test such as
+
+225
+00:20:53,110 --> 00:20:57,330
+breeding time و بعض الفحوصات الأخرى اللي بتتعلق ب
+
+226
+00:20:58,030 --> 00:21:02,990
+هذا الموضوع
+
+227
+00:21:02,990 --> 00:21:07,470
+بالذات bleeding time بيصير لها prolongation، بيصير
+
+228
+00:21:07,470 --> 00:21:10,470
+لها إيش؟ prolongation، ليه يا شباب ال bleeding
+
+229
+00:21:10,470 --> 00:21:14,670
+time؟ لأنه ال platelet لما بدها تيجي تشتغل، بتشتغل
+
+230
+00:21:14,670 --> 00:21:17,950
+على مين؟ع ال blood vessels؟ ع ال blood vessels لما
+
+231
+00:21:17,950 --> 00:21:20,830
+يكون فيه خلل في ال blood vessels تأثر البليتلت
+
+232
+00:21:20,830 --> 00:21:25,090
+تتأثر، تلاقيش إشي تايم تمسك فيه، مظبوط؟ وبالتالي
+
+233
+00:21:25,090 --> 00:21:27,670
+الخلل مش في البليتلت، الخلل في المكان اللي بدها
+
+234
+00:21:27,670 --> 00:21:32,650
+تمسك فيه البليتلت، ماشي؟ إلا إنه تتأثر، إلا إنه
+
+235
+00:21:32,650 --> 00:21:36,990
+البليتلت، فالفحص بيصير له prolongation، لكن إنتوا
+
+236
+00:21:36,990 --> 00:21:40,030
+اشتغلتوا ال bleeding طبعا، وحنافته إن شاء الله هو
+
+237
+00:21:40,030 --> 00:21:43,710
+طبعا insensitive، non-sensitive، مظبوط؟
+
+238
+00:21:49,860 --> 00:21:55,320
+Inherited نبدأ من inherited وجاله فيه مجموعة من
+
+239
+00:21:55,320 --> 00:22:00,340
+الأمراض الوراثية لكنها rare لكنها rare disease
+
+240
+00:22:00,340 --> 00:22:06,480
+بينما ال bleeding is a common symptoms فيها
+
+241
+00:22:06,480 --> 00:22:11,860
+Hemostasis tests are not necessary for diagnosis
+
+242
+00:22:11,860 --> 00:22:15,200
+يبقى هى hereditary they are rare
+
+243
+00:22:18,570 --> 00:22:22,770
+الوحيد اللى بنشوفه هو ال bleeding لو عملنا فحصات
+
+244
+00:22:22,770 --> 00:22:28,690
+hemostatic test بتكون ايه؟ بتكون اول هذه الأمراضة
+
+245
+00:22:28,690 --> 00:22:34,530
+شبهها حاجة بتتعلق بال connected tissue disease
+
+246
+00:22:34,530 --> 00:22:36,390
+defect في ال connected tissue
+
+247
+00:22:42,450 --> 00:22:46,910
+بنكتب blood vessels نحنا بنحكي على blood vessels
+
+248
+00:22:46,910 --> 00:22:54,350
+فأي طبقة من ال blood vessels في الانتما
+
+249
+00:22:54,350 --> 00:22:59,630
+طبقة
+
+250
+00:22:59,630 --> 00:23:05,330
+التالتة طبقة
+
+251
+00:23:05,330 --> 00:23:08,450
+التالتة
+
+252
+00:23:08,450 --> 00:23:15,220
+ماشيطبقة تالتة تانية فيها كلاجن وسموك مصر وخفيف من
+
+253
+00:23:15,220 --> 00:23:18,880
+ال connective tissue لكن ال connective tissue اللى
+
+254
+00:23:18,880 --> 00:23:22,780
+بنشوفها فى الطبقة التالتة وهى طبقة داعمة وهى طبقة
+
+255
+00:23:22,780 --> 00:23:26,880
+ايه؟ داعمة للواعي الدموي وبالتالي الواعي الدموي
+
+256
+00:23:26,880 --> 00:23:30,560
+دون ايه؟ this connective tissue شو بيصير فيه؟
+
+257
+00:23:30,560 --> 00:23:31,160
+fragile
+
+258
+00:23:38,310 --> 00:23:42,610
+عشان هي بيسموه defects, affects, ability to
+
+259
+00:23:42,610 --> 00:23:48,230
+support, to support visceral wall، ماشي؟ هي عبارة
+
+260
+00:23:48,230 --> 00:23:52,930
+عن خلل في الطبقة الدائمة لمين؟ بالوعي الدماغ، من
+
+261
+00:23:52,930 --> 00:23:56,770
+أشهر الأمراض هو Ehlers-Danlos Syndrome، بتنين هدول
+
+262
+00:23:56,770 --> 00:24:03,020
+علماء، Ehlers-Danlos Syndromeجالوا هذا المرض بيصير
+
+263
+00:24:03,020 --> 00:24:09,500
+فيه lack في ال structural tissue which support the
+
+264
+00:24:09,500 --> 00:24:16,260
+blood vessels وهي ال collagen substance فبصير في
+
+265
+00:24:16,260 --> 00:24:21,800
+skin elasticity and fragility ماشي؟ ويمكن شفته في
+
+266
+00:24:21,800 --> 00:24:28,860
+كثير من البسلسلات او في التليفزيون بعض الصور لبعض
+
+267
+00:24:28,860 --> 00:24:33,000
+ال ..ال .. ال .. ال .. ال human beings اللي عندهم
+
+268
+00:24:33,000 --> 00:24:37,000
+قوة خارقة بتقولي، ماشي؟ هي عبارة عن abnormality يا
+
+269
+00:24:37,000 --> 00:24:40,820
+شباب، كانوا يجيبوا بعض الصور لبعض الناس اللي ممكن
+
+270
+00:24:40,820 --> 00:24:46,000
+تشبك skin تلتين و أربعين صنطي عن إدراعها، صح؟ أو
+
+271
+00:24:46,000 --> 00:24:52,330
+يلف إيده تلتر بألفات و يسيبها ترجع مرة تانيةهذا
+
+272
+00:24:52,330 --> 00:24:56,890
+عبارة عن حالات مرضية ناجحة عن خلل أو نقص في
+
+273
+00:24:56,890 --> 00:25:01,370
+الكلاجن، ناجحة عن إيش؟ نقص في الكلاجن، فبصير
+
+274
+00:25:01,370 --> 00:25:08,430
+elastic، بالظبط الجرد عنده، ال skin بصير إيش؟
+
+275
+00:25:08,430 --> 00:25:14,990
+elastic، لكنها fragile، سهل جدا أن هي تنبزج، بصير
+
+276
+00:25:14,990 --> 00:25:20,230
+في hyper mobility of jointshyper mobility of
+
+277
+00:25:20,230 --> 00:25:24,270
+joints بمعنى .. زي ما قلت قبله باشي أو بيجيب رجله
+
+278
+00:25:24,270 --> 00:25:28,130
+من ورا و بخشش أقل ده من الحركات البهلوانية الغريبة
+
+279
+00:25:28,130 --> 00:25:31,690
+جدا اللي ممكن تشوفها و لن تصدق انه انسان طبيعي
+
+280
+00:25:31,690 --> 00:25:36,630
+ممكن يعملها بظبط او بيصير فيه طبعا evidence of
+
+281
+00:25:36,630 --> 00:25:46,710
+bleeding and bruising بمعنى في scarring في علامات
+
+282
+00:25:49,630 --> 00:25:54,150
+في ال skin طبعا ال skin يوم تنمزج يا شباب و تيجي
+
+283
+00:25:54,150 --> 00:26:01,190
+تلحن تاني بيضال معلم صح تلاقي الجلد مشطط كتير ماشي
+
+284
+00:26:01,190 --> 00:26:07,330
+صار في scars multiple scars ليش لإنه لإنه بالظبط
+
+285
+00:26:07,330 --> 00:26:13,010
+زي اللي في دك بالظبط ماشي ليش لإنه أصلا المزعق و
+
+286
+00:26:13,010 --> 00:26:19,010
+لما إجا عمله healing مرة تانية صار في علامةThe
+
+287
+00:26:19,010 --> 00:26:25,270
+most serious is deficient of type 3 collagen و هذا
+
+288
+00:26:25,270 --> 00:26:29,230
+موجود في blood vessels هذا النوع من ال collagen
+
+289
+00:26:29,230 --> 00:26:35,440
+موجود في blood vessels بيؤدي إلى acuteand severe
+
+290
+00:26:35,440 --> 00:26:41,500
+internal bleeding and sudden death في كثير من
+
+291
+00:26:41,500 --> 00:26:47,900
+الأحيان بتلاقي صار نزيف داخلي عند المريض و توفى
+
+292
+00:26:47,900 --> 00:26:55,240
+فجأة و توفى ايش؟ فجأة طيب استقبالنا للموضوع قولنا
+
+293
+00:26:55,240 --> 00:26:59,180
+الناس هدول بيكونوا عندهم نقص في ال collagen رقم 3
+
+294
+00:27:01,390 --> 00:27:04,470
+وهذا النوع من الكلاجين بيكون موجود في blood
+
+295
+00:27:04,470 --> 00:27:09,190
+vessels وبالتالي سهل جدا الناس دول اللي ما عندهمش
+
+296
+00:27:09,190 --> 00:27:14,310
+كلاجين بيصير في عندهم internal bleeding and sudden
+
+297
+00:27:14,310 --> 00:27:18,470
+death Internal bleeding occurs and sudden death
+
+298
+00:27:18,470 --> 00:27:23,650
+نوع تاني من الأمراض اللي بتتعلق بال blood vessels
+
+299
+00:27:23,650 --> 00:27:26,450
+حاجة بيسموها pseudoxanthoma elastica
+
+300
+00:27:26,450 --> 00:27:33,620
+pseudoxanthoma elasticaو هدا المرضة عكس التاني شو
+
+301
+00:27:33,620 --> 00:27:36,120
+بيصير؟ هو عبارة عن autosoma hereditary طبعا
+
+302
+00:27:36,120 --> 00:27:39,860
+hereditary disease autosoma recessive trait بيصير
+
+303
+00:27:39,860 --> 00:27:44,640
+في lack of skin elasticity عكس اللي جابله عكس اللي
+
+304
+00:27:44,640 --> 00:27:49,140
+جابله و إيش صار فيها؟ صار في calcification لل skin
+
+305
+00:27:49,140 --> 00:27:54,280
+calcification يعني ضم elastic يعني تيبشت يعني صارت
+
+306
+00:27:54,280 --> 00:27:59,520
+سهلة الكسر صارت air سهلة الكسر some connective
+
+307
+00:27:59,520 --> 00:28:05,810
+tissuecalcified وبالتالي bruising and bleeding
+
+308
+00:28:05,810 --> 00:28:12,970
+evidence can ensue مرض اخر اسمه hereditary
+
+309
+00:28:12,970 --> 00:28:19,450
+hemorrhagic telangiectasia hereditary hemorrhagic
+
+310
+00:28:19,450 --> 00:28:23,190
+telangiectasia وهو عبارة عن مرض بيصير فيه خلل في
+
+311
+00:28:23,190 --> 00:28:27,650
+ال angiogenesis process ايش ال angiogenesis
+
+312
+00:28:27,650 --> 00:28:33,510
+process هي عبارة عن عملية بنائيالوعاء الدموي عملية
+
+313
+00:28:33,510 --> 00:28:39,550
+بناء الوعاء الدموي وهذه العملية يحصل فيها خلل
+
+314
+00:28:39,550 --> 00:28:43,770
+بتؤدي إلى ما يسمى بال Telangiectasias
+
+315
+00:28:43,770 --> 00:28:49,150
+Telangiectasias وهي عبارة عن فستولة عبارة عن فتحات
+
+316
+00:28:49,150 --> 00:28:52,970
+عبارة عن إيش فتحات في الوعاء الدموي Vessels
+
+317
+00:28:52,970 --> 00:29:00,680
+involved cannot contract normallyand collapse
+
+318
+00:29:00,680 --> 00:29:06,700
+easily and collapse easily طبعا مرضى من هذا النوع
+
+319
+00:29:06,700 --> 00:29:11,360
+بيصير في عندهم tiny area و bleeding pinpoint
+
+320
+00:29:11,360 --> 00:29:16,500
+lesions و tiny area و bleeding و ممكن نشوف ال
+
+321
+00:29:16,500 --> 00:29:22,000
+lesion في ال face في ال hands في ال feet في مناطق
+
+322
+00:29:22,000 --> 00:29:27,600
+مختلفة لكنه هذا مرض ممكن يصير في أي عمر من الأعمار
+
+323
+00:29:28,430 --> 00:29:31,790
+أي عملية خلل في الانجيوجينيس بتعدي لإيش
+
+324
+00:29:31,790 --> 00:29:36,650
+تلانجيبتازياز وفي نفس الوقت بنشوفها بوضوع
+
+325
+00:29:36,650 --> 00:29:41,250
+physically ماشي كان بي diagnose by physical
+
+326
+00:29:41,250 --> 00:29:48,530
+appearance بتلاقي الواحد بيكون في عنده scars كثيرة
+
+327
+00:29:48,530 --> 00:29:52,730
+نوع
+
+328
+00:29:52,730 --> 00:29:55,890
+تاني من الأمراض اسمه Kasachmeritsin
+
+329
+00:29:57,860 --> 00:30:03,100
+أو بيسموه Hemangioma و هذا ال Hemangioma بالعربي
+
+330
+00:30:03,100 --> 00:30:08,460
+بيسموه الواحمة عشان سمعته بالواحمة؟ ايوة تطبع في
+
+331
+00:30:08,460 --> 00:30:12,320
+أماكن مختلفة من الجسم الواحمة دي عبارة عن benign
+
+332
+00:30:12,320 --> 00:30:18,340
+tumor عبارة عن ايه؟ benign tumor of vascular
+
+333
+00:30:18,340 --> 00:30:23,280
+tissue وين جا في blood vessels، vascular tissue
+
+334
+00:30:24,410 --> 00:30:29,370
+grow rapidly to a giant proportion و بيبدأ يكبر،
+
+335
+00:30:29,370 --> 00:30:36,550
+يكبر، يكبر، بيبدأ صغير، بنولد الطفل غالبا بالوحمة
+
+336
+00:30:36,550 --> 00:30:40,510
+اللي احنا بنحكي عليها، فبيكون حاجبها صغير، لكن
+
+337
+00:30:40,510 --> 00:30:47,660
+ممكن هذه الحاجب يكبرطبعا هذه الوحمة بتكون full of
+
+338
+00:30:47,660 --> 00:30:53,440
+small blood vessels او capillary ماشي full of
+
+339
+00:30:53,440 --> 00:30:58,200
+وبالتالي اقل ضربة فيها شو بتعمل؟ بتعمل bleeding
+
+340
+00:30:58,200 --> 00:31:02,500
+بتعمل إيه؟ bleeding it should be removed if
+
+341
+00:31:02,500 --> 00:31:08,330
+applicable إذا كانت موجودة في منطقةممكن الجراح
+
+342
+00:31:08,330 --> 00:31:12,250
+يصللها، لازم يشيلها، لكن في الاسف الشديد في بعض
+
+343
+00:31:12,250 --> 00:31:17,150
+المناطق، بتكون حساسة لاستطيع أن يصللها الجراح،
+
+344
+00:31:17,150 --> 00:31:21,030
+فبالتالي بتعمل مشاكل كثيرة محمور عادية، عادية من
+
+345
+00:31:21,030 --> 00:31:25,950
+شوفها .. ايه احنا اتعودنا ان نشوفها في الإيد، في
+
+346
+00:31:25,950 --> 00:31:29,930
+الغاص، فوق
+
+347
+00:31:29,930 --> 00:31:35,000
+العين يعني في الحاجبة ممكنالمهم هذه وحمد لونها
+
+348
+00:31:35,000 --> 00:31:38,800
+أحمر شباب عشان تتميزوا بينها وجنة الشامة العادية
+
+349
+00:31:38,800 --> 00:31:42,900
+التنتين benign tumor لكن هذه لونها أحمر ال can
+
+350
+00:31:42,900 --> 00:31:51,860
+grow هذه أسود الشامة العادية طبعا ببقى اني بحكي
+
+351
+00:31:51,860 --> 00:31:59,620
+على benign tumor أشوف تكون أحمر منين؟ لأ لأ مش هي
+
+352
+00:31:59,620 --> 00:32:00,500
+.. مش هي اللي بحكي عنها
+
+353
+00:32:09,540 --> 00:32:12,380
+لأ لأ انا هنجت بشوفها بس مش .. لأ مش اللي اللي
+
+354
+00:32:12,380 --> 00:32:17,040
+بحكي عليها دي بتكون لونها حمراء لإنه full of blood
+
+355
+00:32:17,040 --> 00:32:20,520
+vessels full of blood vessels اللي بدها surgeon
+
+356
+00:32:20,520 --> 00:32:26,360
+بدها vascular surgeon يشيلها يعني جراح أو عيادة
+
+357
+00:32:26,360 --> 00:32:30,580
+موية ماشي؟ ماشي و بالتالي صعب جدا لإنه mechanical
+
+358
+00:32:30,580 --> 00:32:34,660
+injury أي لعب فيها هتؤدي ل bleeding و ممكن يكون
+
+359
+00:32:34,660 --> 00:32:37,180
+uncontrollable ممكن ماتحكمش فيه
+
+360
+00:32:41,090 --> 00:32:45,050
+طبعا هذه ببساطة شباب بتؤثر على ال neighboring
+
+361
+00:32:45,050 --> 00:32:50,990
+tissue وممكن تؤدي الى localized DIC نعرف ال DIC
+
+362
+00:32:50,990 --> 00:32:59,670
+ديسميتر وطبعا بيؤدي الى thrombocytopenia وبعض
+
+363
+00:32:59,670 --> 00:33:05,190
+العوامل التجلط بتستهلك عند المريض وهذا كله بيؤدي
+
+364
+00:33:05,190 --> 00:33:08,950
+إلى bleeding بيؤدي إلى bleeding
+
+365
+00:33:14,120 --> 00:33:19,660
+Tumor composed of many blood vessels أو بيسموه
+
+366
+00:33:19,660 --> 00:33:28,040
+blood filled tumor مليانة بالدم استكملنا للموضوع
+
+367
+00:33:28,040 --> 00:33:33,000
+ال hemangioma بيسموها بعض المرات ال cavernous
+
+368
+00:33:33,000 --> 00:33:39,770
+hemangioma هو عبارة عن Legionmay swell and bleed
+
+369
+00:33:39,770 --> 00:33:44,530
+.شناد الأطفال اللي عندهم هذه الحاجات لما قلتلكوا
+
+370
+00:33:44,530 --> 00:33:48,570
+should be removed if applicable لكن إذا ماقدرناش
+
+371
+00:33:48,570 --> 00:33:55,670
+نفحها لازم يحذر الطفل ومن يعامله أن أي حركة أي لعب
+
+372
+00:33:55,670 --> 00:34:02,470
+دفش للطفل ممكن يؤدي إلى نزيف لتحمض عقبها.Tumor
+
+373
+00:34:02,470 --> 00:34:08,340
+sites may form clotsPneumolized RBCs and Vessel
+
+374
+00:34:08,340 --> 00:34:12,000
+Obstruction ممكن تؤدي إلى جلطة متسكّر الهوية
+
+375
+00:34:12,000 --> 00:34:17,900
+الدموية المجاورة للموضوع Present since birth تيجي
+
+376
+00:34:17,900 --> 00:34:23,940
+مع عياش مع ولادة وال treatment هو surgical removal
+
+377
+00:34:23,940 --> 00:34:29,000
+تشيل عياش من جراحها if possible زي ما قلتلكوا إذا
+
+378
+00:34:29,000 --> 00:34:34,680
+كان الجراح يستطيع أن يصل إلى هذا المكانأو ماجدرش
+
+379
+00:34:34,680 --> 00:34:39,780
+localized radiotherapy تعرف العلاج من إشعاع ماشي
+
+380
+00:34:39,780 --> 00:34:46,900
+لمنطقة إيهاش الهيمانجيومة with injection of anti
+
+381
+00:34:46,900 --> 00:34:50,200
+.. of fibrinolytic inhibitors fibrinolytic يعني
+
+382
+00:34:50,200 --> 00:34:55,440
+antifibrinolysis ماشي عشان مايصارش إيهاش مايصارش
+
+383
+00:34:55,440 --> 00:34:59,000
+إيهاش بفوش
+
+384
+00:34:59,000 --> 00:34:59,300
+بقى
+
+385
+00:35:03,770 --> 00:35:07,490
+مرة جاى ان شاء الله بنكمل عشان نمشي مغايش مع
+
+386
+00:35:07,490 --> 00:35:10,850
+التعليبات خلصنا ال hereditary type مرة جاى بنحكي
+
+387
+00:35:10,850 --> 00:35:13,010
+في ال acquired type او blood vessels
+
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..61674dcbcb7434a1a1b78eba709de3ac9475d626
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo.srt
@@ -0,0 +1,1899 @@
+1
+00:00:21,330 --> 00:00:26,670
+بسم الله الرحمن الرحيم اليوم إن شاء الله هنحكي في
+
+2
+00:00:26,670 --> 00:00:31,470
+الـ clotting factor في الشيانسي or abnormalities أو 
+
+3
+00:00:31,470 --> 00:00:34,850
+ما يسمى بالـ disorders of secondary hemostasis لما 
+
+4
+00:00:34,850 --> 00:00:38,170
+كنا نحكي المرة اللي فاتت كنا نحكي على platelet
+
+5
+00:00:38,170 --> 00:00:42,170
+disorders و blood vessel disorders وقلت لكم عبارة 
+
+6
+00:00:42,170 --> 00:00:45,810
+عن primary hemostasis عبارة عن primary hemostasis
+
+7
+00:00:45,810 --> 00:00:48,370
+اليوم إن شاء الله هنحكي في ما يتعلق بالـ secondary
+
+8
+00:00:48,370 --> 00:00:51,530
+hemostasis  وإحنا بنعرف أن الـ coordination factors
+
+9
+00:00:51,530 --> 00:00:54,490
+هم اللي بيقوموا بالـ secondary hemostasis mostly
+
+10
+00:00:54,490 --> 00:00:59,850
+they are hereditary in their nature يعني معظم
+
+11
+00:00:59,850 --> 00:01:06,240
+الأمراض they are hereditary types and usually
+
+12
+00:01:06,240 --> 00:01:09,980
+associated either by failure of coagulation factor
+
+13
+00:01:09,980 --> 00:01:16,140
+to function normally or is associated with the
+
+14
+00:01:16,140 --> 00:01:18,960
+absence of the coagulation factor وبالتالي كان دي 
+
+15
+00:01:18,960 --> 00:01:23,020
+يعني differentiated إلى إما quantitative أو
+
+16
+00:01:23,020 --> 00:01:32,530
+qualitative defect طيب معظم هذه غياب هذه العوامل
+
+17
+00:01:32,530 --> 00:01:38,390
+بيؤدي لغياب تكوين الـ fibre clot مظبوط معظم الـ
+
+18
+00:01:38,390 --> 00:01:42,870
+coagulation factors غيابها بيعمل deficiency في الـ
+
+19
+00:01:42,870 --> 00:01:46,890
+fibre formation مع ده مجموعة أخدناها سابقا، 
+
+20
+00:01:46,890 --> 00:01:52,070
+تفكرينها؟ اللي غيابها بيعمل prolongation للـ
+
+21
+00:01:52,070 --> 00:01:54,430
+hemostatic test لكن ما بيبقى ماشي bleeding الـ
+
+22
+00:01:54,430 --> 00:01:59,190
+contact phase الـ contact phase 100% لبناء الـ
+
+23
+00:01:59,190 --> 00:02:05,310
+screening Test usually is measured by the time
+
+24
+00:02:05,310 --> 00:02:09,310
+required for a clot formation وبالتالي
+
+25
+00:02:09,310 --> 00:02:18,270
+prolongation of the time بيعني غياب أو عدم اللي هو
+
+26
+00:02:18,270 --> 00:02:21,710
+قيام الـ coordination factor بالـ test المطلوب أو 
+
+27
+00:02:21,710 --> 00:02:23,250
+بالـ function المطلوبة
+
+28
+00:02:27,790 --> 00:02:30,670
+زي ما اتفقنا can be differentiated either الـ
+
+29
+00:02:30,670 --> 00:02:33,690
+quantitative و الـ qualitative و عشان أفرق بين الـ
+
+30
+00:02:33,690 --> 00:02:36,350
+quantitative و الـ qualitative test لأن زي ما
+
+31
+00:02:36,350 --> 00:02:40,570
+قلت لكم إحنا بنقيس quantitative أو بنقيس زمن بنقيس
+
+32
+00:02:40,570 --> 00:02:45,390
+زمن لكن الزمن ما بيميزليش ما بيفرقليش ما بين
+
+33
+00:02:45,390 --> 00:02:49,470
+quantitative و qualitative عشان أقول أن هذا المرض
+
+34
+00:02:49,470 --> 00:02:54,590
+quantitative أو qualitative I should have to use
+
+35
+00:02:54,590 --> 00:02:58,420
+immunological testing إيش يعني؟ يعني أدور على الـ
+
+36
+00:02:58,420 --> 00:03:02,320
+antigen إيش هو الـ antigen هذه المرة؟ هو عبارة عن
+
+37
+00:03:02,320 --> 00:03:05,620
+coagulation factor بعتبر الـ coagulation factor
+
+38
+00:03:05,620 --> 00:03:11,320
+antigen و بحط الـ antibody المناسب إليه إذا صار
+
+39
+00:03:11,320 --> 00:03:14,880
+agglutination معناته الـ antigen موجود يعني الـ
+
+40
+00:03:14,880 --> 00:03:19,140
+factor موجود ماشي وإذا كان ما صارش agglutination
+
+41
+00:03:19,140 --> 00:03:24,480
+معناته الـ antigen غايب وبالتالي الـ function غايبة
+
+42
+00:03:24,480 --> 00:03:32,440
+إذا كان إعطاني agglutination وفي bleeding معناته
+
+43
+00:03:32,440 --> 00:03:36,540
+الـ antigen موجود يعني الـ factor موجود لكنه لا يعمل
+
+44
+00:03:36,540 --> 00:03:43,120
+بغض النظر بسمه هذه الحالة CRM positive CRM
+
+45
+00:03:43,120 --> 00:03:47,000
+positive بمعنى أنه cross-reacting material
+
+46
+00:03:47,000 --> 00:03:50,040
+positive إيش الـ cross-reacting material؟ هي عبارة
+
+47
+00:03:50,040 --> 00:03:53,220
+عن antibody reaction انتيجين إيش؟ antibody
+
+48
+00:03:53,220 --> 00:03:56,360
+reaction if there is no protein
+
+49
+00:04:00,210 --> 00:04:02,710
+والتجارية التجارية التجارية التجارية التجارية
+
+50
+00:04:02,710 --> 00:04:02,870
+التجارية التجارية التجارية التجارية التجارية
+
+51
+00:04:02,870 --> 00:04:04,570
+التجارية التجارية التجارية التجارية التجارية
+
+52
+00:04:04,570 --> 00:04:11,870
+التجارية التجارية التجارية التجارية التجارية
+
+53
+00:04:11,870 --> 00:04:12,710
+التجارية التجارية التجارية التجارية التجارية
+
+54
+00:04:12,710 --> 00:04:15,230
+التجارية التجارية التجارية التجارية التجارية
+
+55
+00:04:15,230 --> 00:04:15,610
+التجارية التجارية التجارية التجارية التجارية
+
+56
+00:04:15,610 --> 00:04:17,370
+التجارية التجارية التجارية التجارية التجارية
+
+57
+00:04:17,370 --> 00:04:18,730
+التجارية التجارية التجارية التجارية التجارية
+
+58
+00:04:18,730 --> 00:04:24,370
+التجارية التجارية التجارية التجارية التجارية
+
+59
+00:04:24,370 --> 00:04:25,730
+التج
+
+60
+00:04:27,400 --> 00:04:30,480
+يقسموا هذه العوامل التي هي qualitative و
+
+61
+00:04:30,480 --> 00:04:35,760
+quantitative إلى مصطلحين جديدين وهو CRM positive و
+
+62
+00:04:35,760 --> 00:04:40,700
+CRM negative طبعا إحنا يا شباب هنتطرق إلى بعض أهم
+
+63
+00:04:40,700 --> 00:04:47,940
+الأمثلة في الـ coagulation factor disorders و أهم
+
+64
+00:04:47,940 --> 00:04:50,560
+الأمثلة بتتمثل في المرض كثير مشهور هو الـ
+
+65
+00:04:50,560 --> 00:04:51,140
+hemophilia
+
+66
+00:04:55,680 --> 00:04:58,460
+هو بالمناسبة الـ von Willebrand disease is more common
+
+67
+00:04:58,460 --> 00:05:05,440
+than hemophilia von Willebrand disease و الـ
+
+68
+00:05:05,440 --> 00:05:09,220
+hemophilia بأنواعها فبنعرف أن الـ hemophilia في
+
+69
+00:05:09,220 --> 00:05:14,720
+منها hemophilia A إذا كان factor 8 deficient و
+
+70
+00:05:14,720 --> 00:05:17,920
+hemophilia B إذا كان factor 9 deficient
+
+71
+00:05:24,860 --> 00:05:28,160
+ثم الـ von Willebrand يا عزيزي إحنا بنتطرق إليه وإن 
+
+72
+00:05:28,160 --> 00:05:33,960
+شاء الله برضه هنمر في others وناخد مثال عن DIC في
+
+73
+00:05:33,960 --> 00:05:39,100
+الـ others و نبدأ في هذه العواء لهذا المرض لكن قبل
+
+74
+00:05:39,100 --> 00:05:43,100
+ما نبدأ نبدأ أذكركم في محاضرة سابقة
+
+75
+00:05:46,460 --> 00:05:50,840
+اللي بيحدث نتيجة لـ platelet disorders is
+
+76
+00:05:50,840 --> 00:05:57,740
+superficial وبالتالي بنشوف بتاشي و Ecchymosis على
+
+77
+00:05:57,740 --> 00:06:03,580
+وين؟ على الـ skin بينما الـ bleeding اللي بينتج من
+
+78
+00:06:03,580 --> 00:06:09,320
+coagulation factor هو عبارة عن ديب ماشي وبالتالي
+
+79
+00:06:09,320 --> 00:06:14,400
+ممكن ما نشوفش على الـ skin زي ما هذا هو موجود
+
+80
+00:06:15,570 --> 00:06:20,450
+Bleeding موجود في الـ joints، في الرقبة، لكن مش
+
+81
+00:06:20,450 --> 00:06:23,910
+مبينش، صح؟ طب كيف بتلاقيها بيصير فيه swallowing في
+
+82
+00:06:23,910 --> 00:06:27,490
+الرقبة؟ وشوفنا مناظر المحاضرة اللي فاتت عن هذا 
+
+83
+00:06:27,490 --> 00:06:33,270
+الموضوع، مظبوط؟ طيب What is Hemophilia؟ نبدأ في الـ
+
+84
+00:06:33,270 --> 00:06:36,870
+Hemophilia زي ما اتفقنا Hemophilia هو عبارة عن مرض
+
+85
+00:06:36,870 --> 00:06:43,950
+وراثي بأنواع مختلفة ناتج على نقص في factor 8 إذا
+
+86
+00:06:43,950 --> 00:06:49,350
+كانت Hemophilia A أو 9 إذا كانت A و Hemophilia B
+
+87
+00:06:49,350 --> 00:06:55,550
+وانتبهوا على الجدول القادم اللي بيفرق لي ما بين
+
+88
+00:06:55,550 --> 00:07:00,590
+Hemophilia A و B متفقين
+
+89
+00:07:00,590 --> 00:07:05,990
+أن ده هو الجدول Hemophilia A factor 8 deficiency و
+
+90
+00:07:05,990 --> 00:07:12,370
+Hemophilia B Factor 9 Deficiency Inheritance Both
+
+91
+00:07:12,370 --> 00:07:15,490
+are inherited as X-linked recessive diseases
+
+92
+00:07:15,490 --> 00:07:20,910
+الـ X-linked recessive يعني بنشوفهم في مين؟ في
+
+93
+00:07:20,910 --> 00:07:25,550
+الذكور الـ
+
+94
+00:07:25,550 --> 00:07:30,670
+incidence بشكل عام يا شباب الـ Hemophilia A أكثر من 
+
+95
+00:07:30,670 --> 00:07:36,120
+Hemophilia B بحوالي خمسة إلى ست مرات خمسة إلى ست
+
+96
+00:07:36,120 --> 00:07:41,060
+أضعاف الـ hemophilia B يعني الـ incidence هي واحد إلى
+
+97
+00:07:41,060 --> 00:07:46,160
+عشرة آلاف واحد في كل عشر آلاف لكن بعد في كل خمسين
+
+98
+00:07:46,160 --> 00:07:53,240
+ألف which means أنه في حوالي خمس أضعاف صح؟ طيب الـ
+
+99
+00:07:53,240 --> 00:07:57,240
+severity يعني بتعتمد على الـ concentration of
+
+100
+00:07:57,240 --> 00:08:02,520
+coagulation factor الـ concentration of إيش؟ of
+
+101
+00:08:02,520 --> 00:08:09,220
+coagulation factor وجدنا أنه بتعرفوا أنتم أن الـ
+
+102
+00:08:09,220 --> 00:08:11,360
+normal concentration أو الـ concentration of
+
+103
+00:08:11,360 --> 00:08:19,840
+coagulation factors has أما normal range نبدأ نحكي
+
+104
+00:08:19,840 --> 00:08:27,420
+في اتفاقنا على أن الـ normal range للـ
+
+105
+00:08:27,420 --> 00:08:31,200
+coagulation factor بيساوي قد إيش يا شباب
+
+106
+00:08:34,310 --> 00:08:40,730
+أنه بيساوي الخمسين إلى مئة وخمسين في المئة
+
+107
+00:08:40,730 --> 00:08:47,290
+calculation factors
+
+108
+00:08:47,290 --> 00:08:50,170
+نسبته من خمسين إلى مئة وخمسين في المئة عارفين إيش
+
+109
+00:08:50,170 --> 00:08:53,910
+يعني هذا؟ يعني أنه لو كان لو قسنا على سبيل
+
+110
+00:08:53,910 --> 00:09:01,570
+المثال BT وعطانا normal time معناته الـ activity
+
+111
+00:09:01,570 --> 00:09:10,550
+مئة في المئة أو مظبوط؟ إيه الثاني؟ لو عملنا BTE و
+
+112
+00:09:10,550 --> 00:09:21,070
+أعطانا normal time قد إيش الـ normal time؟ أحسنت
+
+113
+00:09:21,070 --> 00:09:26,410
+من عشر إلى ثلاث عشر second مظبوط؟ لو أعطانا الـ BTE
+
+114
+00:09:26,410 --> 00:09:29,990
+normal time معناته الـ concentration أو الـ activity
+
+115
+00:09:29,990 --> 00:09:36,540
+قد إيش؟ من 100 ل 150% بس طبعا معظم الناس تكتب 100%
+
+116
+00:09:36,540 --> 00:09:41,580
+أنا بتخاف تكتب 150% لأن معظم الناس ما بتعرفش إيش يعني
+
+117
+00:09:41,580 --> 00:09:46,620
+150% هأقول الـ normal range لغاية 150% يعني بعضيا
+
+118
+00:09:46,620 --> 00:09:50,560
+إحنا اتعلمنا اتعودنا نقول أنه 100% عن الـ top
+
+119
+00:09:50,560 --> 00:09:55,340
+يعني إيش؟ الـ top لكن 150% يعني شيء كثير خالص
+
+120
+00:09:55,340 --> 00:10:01,060
+مظبوط؟ طيب اتعلمنا في المقابل أن في حاجة اسمها
+
+121
+00:10:07,030 --> 00:10:12,070
+هناك حاجة اسمها hemostatic level وعرفناها
+
+122
+00:10:12,070 --> 00:10:20,430
+سابقا هي عبارة عن القيمة المطلوبة من الـ factor
+
+123
+00:10:20,430 --> 00:10:24,270
+لإحداث
+
+124
+00:10:24,270 --> 00:10:30,550
+normal hemostasis، مظبوط؟ القيمة المطلوبة من الـ
+
+125
+00:10:30,550 --> 00:10:35,970
+coagulation factors عشان يعمل normal hemostasis، 
+
+126
+00:10:35,970 --> 00:10:40,600
+مظبوط؟ طيب القيمة المطلوبة من الـ factor عشان يعمل
+
+127
+00:10:40,600 --> 00:10:46,440
+normal hemostasis الأصل حسب الجدول هذا خلينا نشوفه
+
+128
+00:10:46,440 --> 00:10:52,800
+قداش أقصى نسبة 25؟ قداش أقصى نسبة 25؟ معناته هي
+
+129
+00:10:52,800 --> 00:11:01,520
+النسبة المطلوبة من 25 فما فوق، من 25 فما فوق بيصيرش
+
+130
+00:11:01,520 --> 00:11:05,010
+فيها bleeding؟ آه، بيصيرش فيها bleeding ماشي؟ يعني في
+
+131
+00:11:05,010 --> 00:11:10,550
+normal hemostasis؟ نعم، normal وهذا بفسر لي الأطفال
+
+132
+00:11:10,550 --> 00:11:15,270
+لما بنولدوا، متفقين احنا إنه الـ coagulation factor
+
+133
+00:11:15,270 --> 00:11:19,770
+لسه ما يكونش متكون تمامًا، صح؟ صح، هو بالتالي بتكون كمّيته
+
+134
+00:11:19,770 --> 00:11:24,310
+قليلة، ومع ذلك بس ليش عندهم bleeding؟ ليش؟ لأنه
+
+135
+00:11:24,310 --> 00:11:27,690
+عندهم hemostatic level ما عندهمش normal range، عندهم
+
+136
+00:11:27,690 --> 00:11:31,630
+إيش؟ hemostatic level، ما عندهمش إيش؟ normal range، و
+
+137
+00:11:31,630 --> 00:11:37,490
+بالتالي ما فيش bleeding. طيب according to this figure
+
+138
+00:11:37,490 --> 00:11:42,970
+إيش بيقول؟ صنّفوا أمراض الـ hemophilia إلى ثلاث أنواع
+
+139
+00:11:42,970 --> 00:11:50,150
+قالوا mild و moderate و severe، صح؟ والـ mild قالوا
+
+140
+00:11:50,150 --> 00:11:57,800
+من 5 لـ 25%، والـ moderate من 1 لـ 5، والـ Severe أقل
+
+141
+00:11:57,800 --> 00:12:01,300
+من 1%، تخيلوا لما الواحد يكون عنده Coagulation
+
+142
+00:12:01,300 --> 00:12:04,520
+Factor أقل من 1%، يبدأ يصير عنده يشبه الـ Severe
+
+143
+00:12:04,520 --> 00:12:09,100
+أرجع الناس اللي عندهم Severe mostly إما 1% or less
+
+144
+00:12:09,100 --> 00:12:13,600
+مرات بيكون Undetectable، Undetectable إيش يعني؟
+
+145
+00:12:13,600 --> 00:12:18,820
+ما نقدرش نميّزه، نسبته قليلة جدًا جدًا جدًا، صح؟ فهو هذا
+
+146
+00:12:18,820 --> 00:12:22,040
+الـ Severe، وغالبا هذا الناس اللي بيصير عندهم
+
+147
+00:12:22,040 --> 00:12:26,630
+Spontaneous Bleeding، المدرّف من 1% لـ 5%، ثم المعارض
+
+148
+00:12:26,630 --> 00:12:30,710
+من خمسة لخمسة وعشرين بالمئة، ماشي؟ وده التصنيف
+
+149
+00:12:30,710 --> 00:12:32,590
+موجودة على... على كل أنواع الـ hemophilia
+
+150
+00:12:32,590 --> 00:12:38,470
+hemophilia A, hemophilia B, hemophilia H, Z طبعًا
+
+151
+00:12:38,470 --> 00:12:41,390
+مضاعفات الـ hemophilia بشكل عام بناخدها يا شباب هي
+
+152
+00:12:41,390 --> 00:12:46,410
+عبارة عن... عبارة عن soft tissue bleeding وهي
+
+153
+00:12:46,410 --> 00:12:47,550
+عبارة عن D بقى
+
+154
+00:12:54,140 --> 00:12:57,580
+الهموفيليا A وB X-linked، هموفيليا A وB X-linked
+
+155
+00:12:57,580 --> 00:12:57,980
+هموفيليا A وB X-linked، هموفيليا A وB X-linked
+
+156
+00:12:57,980 --> 00:12:59,040
+هموفيليا A وB X-linked، هموفيليا A وB X-linked
+
+157
+00:12:59,040 --> 00:12:59,760
+هموفيليا A وB X-linked، هموفيليا A وB X-linked
+
+158
+00:12:59,760 --> 00:13:04,960
+هموفيليا A وB X-linked، هموفيليا A وB X-linked
+
+159
+00:13:04,960 --> 00:13:10,800
+هموفيليا A وB X-linked، شوفنا الجذور كيف
+
+160
+00:13:10,800 --> 00:13:14,600
+صنفنا إياها، و30% من الحالات هي عبارة عن new
+
+161
+00:13:14,600 --> 00:13:19,440
+mutation، يعني ممكن أشوف حالات جديدة بتظهر في بعض
+
+162
+00:13:19,440 --> 00:13:23,820
+العائلات اللي ما فيش عندها medical history لمين؟
+
+163
+00:13:23,820 --> 00:13:29,900
+للهيموفيليك، لأكوين، مش أكوين، أكوين ده حاجة ثانية،
+
+164
+00:13:29,900 --> 00:13:32,000
+مش هي عبارة عن hereditary لإن فيها mutation
+
+165
+00:13:37,370 --> 00:13:40,670
+بالنسبة للجين المسؤول، هموفيليا A الجينات
+
+166
+00:13:40,670 --> 00:13:42,870
+هموفيليا A، الجين مسؤول عن factor ثمانية، موجودة
+
+167
+00:13:42,870 --> 00:13:48,850
+على X-chromosome وعطرفه يا شباب في الـ XQ28Q
+
+168
+00:13:48,850 --> 00:13:54,230
+يعني في الـ long arm 28 في الآخر، أو بيسمّوه XQTER
+
+169
+00:13:54,230 --> 00:13:56,170
+Terminal
+
+170
+00:13:58,210 --> 00:14:02,310
+طبعًا تقريبًا جامب in telomeric region بيحتوي على 26
+
+171
+00:14:02,310 --> 00:14:09,390
+exon، 25 intron طوله 186 كيلو باوند وهي المشهورة
+
+172
+00:14:09,390 --> 00:14:14,890
+messenger RNA حوالي 8.8 كيلو باوند، شايفين كده إيش
+
+173
+00:14:14,890 --> 00:14:22,310
+بنترجمه اللي بيحتوي على 2351 amino acids وفيه leader
+
+174
+00:14:22,310 --> 00:14:24,850
+sequence حوالي 19
+
+175
+00:14:30,560 --> 00:14:36,140
+ماشي أو تعمل sequence تعرف بالضبط كل شِقفة قداش
+
+176
+00:14:36,140 --> 00:14:41,040
+طولها وقداش بدايات الـ gene ماشي بالضبط هدول الحاجات
+
+177
+00:14:41,040 --> 00:14:44,760
+اللي بتنفعها، وبالتالي الـ so ده الـ real protein، الـ
+
+178
+00:14:44,760 --> 00:14:50,520
+protein نفسه بيتكوّن من 2332 amino acids، تشيل الـ
+
+179
+00:14:50,520 --> 00:14:55,720
+leader sequence، بده اللي هيبقى الطول الحقيقية، تفرّعوا
+
+180
+00:14:55,720 --> 00:14:57,760
+معانا؟ بخطوات دي في الورق ده مظبوط
+
+181
+00:15:01,480 --> 00:15:05,560
+الـ Genetic... انتبهوا عليها يا شباب، تقسيم الـ...
+
+182
+00:15:05,560 --> 00:15:10,200
+الـ hemophilia من ناحية وراثية قسموها إلى جزء إيه؟
+
+183
+00:15:10,200 --> 00:15:14,340
+50% منهم severe، 50% منهم هي
+
+184
+00:15:14,340 --> 00:15:18,100
+severe، بمعنى إنه لو قسمنا الـ coagulation factor
+
+185
+00:15:18,100 --> 00:15:22,360
+عندهم، هنلاقيه undetectable، هنلاقيه undetectable
+
+186
+00:15:22,360 --> 00:15:25,300
+دلوقتي قداش؟ 50%... دلوقتي 50%
+
+187
+00:15:25,300 --> 00:15:30,740
+التانية الـ 50% التانية، 5% منهم بيكونوا
+
+188
+00:15:30,740 --> 00:15:34,480
+mild qualitative
+
+189
+00:15:34,480 --> 00:15:39,220
+sorry، CRM positive، والخمسة والأربعين CRM negative
+
+190
+00:15:39,220 --> 00:15:44,220
+لكن فيه variability في الـ concentration of the
+
+191
+00:15:44,220 --> 00:15:47,700
+factor، عيد ثاني، 50%
+
+192
+00:15:48,880 --> 00:15:53,360
+Quantitative، طبعًا Undetectable، Severe، وخمسين في
+
+193
+00:15:53,360 --> 00:15:57,780
+المئة اللي هو الجزء الثاني، 5% منهم
+
+194
+00:15:57,780 --> 00:16:01,480
+qualitative، يعني positive، وخمسة وأربعين في المئة
+
+195
+00:16:01,480 --> 00:16:07,700
+quantitative، لكن with variable concentration، with
+
+196
+00:16:07,700 --> 00:16:14,240
+variable concentration، عشان
+
+197
+00:16:14,240 --> 00:16:18,670
+أشخص Hemophilia، يا شباب detection of Hemophilia لما
+
+198
+00:16:18,670 --> 00:16:21,170
+واحد بيدور على الـ family history، احنا متفقين على
+
+199
+00:16:21,170 --> 00:16:23,990
+إن هو genetic disease، وبالتالي لازم أدور على إنه
+
+200
+00:16:23,990 --> 00:16:28,550
+في أفراد في العائلة عندهم هموفيليا ولا لأ؟ ماشي، صحيح
+
+201
+00:16:28,550 --> 00:16:34,750
+فيه طبعًا حالات جديدة، لكن الثلثين عندهم family
+
+202
+00:16:34,750 --> 00:16:40,230
+history، مظاهر symptoms أكيد المريض بيجي بيعاني من
+
+203
+00:16:40,230 --> 00:16:44,870
+bleeding، bruising، يعني bleeding with circumcision
+
+204
+00:16:45,980 --> 00:16:50,740
+circumcision، معناته تهور لإن احنا بنتكلم عن المرض
+
+205
+00:16:50,740 --> 00:16:57,740
+موجود في الذكور، والذكر أول تحدي بيواجهه إيه؟ يوم
+
+206
+00:16:57,740 --> 00:17:02,900
+يطهّره، بيصير في عنده bleeding مش راضي يجف، مش راضي
+
+207
+00:17:02,900 --> 00:17:06,400
+إيش يجف؟ عشان هيك الأطفال هدول بيتشخصوا في العام
+
+208
+00:17:06,400 --> 00:17:11,740
+الأول من عمرهم، في العام الأول من عمرهم، muscle
+
+209
+00:17:11,740 --> 00:17:18,130
+joints or soft tissue bleeding is also seen، لكن في
+
+210
+00:17:18,130 --> 00:17:22,870
+أعمار متقدمة بعد، ليش؟ ليش في أعمار متقدمة بعد ما
+
+211
+00:17:22,870 --> 00:17:29,230
+يكبر ويتعرّض لإيش؟ لتحديات أخرى، طبيعة عمل، طبيعة
+
+212
+00:17:29,230 --> 00:17:32,630
+رياضة، دفشة، طبيعة... يعني حاجات من النوعية اللي
+
+213
+00:17:32,630 --> 00:17:37,030
+بتؤدي إلى المخاطر والنزيف، فبنشوف عنده soft tissue
+
+214
+00:17:37,030 --> 00:17:42,310
+bleeding أو deep bleeding، من التحديات اللي بنخاف
+
+215
+00:17:42,310 --> 00:17:46,660
+منها لمريض الـ hemophilia، نلاقيه محتاج يعمل إيه؟
+
+216
+00:17:46,660 --> 00:17:55,720
+عملية surgery or dental work or trauma or accident
+
+217
+00:17:55,720 --> 00:18:04,560
+وهذول الشباب، هدول المرضى مش لازم يعني يعملوا في
+
+218
+00:18:04,560 --> 00:18:13,460
+أعمال شاقة، المفروض إنه حتى في المدارس العامة على
+
+219
+00:18:13,460 --> 00:18:17,200
+المدارس إنه هذا الطفل عنده Hemophilia، ممنوع يعيش،
+
+220
+00:18:17,200 --> 00:18:20,540
+ممنوع يتيندرام، ممنوع يتنطنط، ممنوع ي... يعني
+
+221
+00:18:20,540 --> 00:18:24,420
+يتعرضوا لـ strenuous exercise، هذه كلها الحاجات
+
+222
+00:18:24,420 --> 00:18:28,740
+لازم ما يتعمّق فيها، يعني أنا بعرف حالة على سبيل
+
+223
+00:18:28,740 --> 00:18:33,140
+المثال، راجل يعني طبيعي جدًا، لكن هو بسوق سيارة و
+
+224
+00:18:33,140 --> 00:18:38,840
+بنشرت السيارة، فنزل يعمل الـ puncher وجاء الـ jack،
+
+225
+00:18:38,840 --> 00:18:43,850
+بتعرف الـ jack إيش بيعمل؟ مات على المطرح يعني ما لحقش
+
+226
+00:18:43,850 --> 00:18:51,170
+يسعفوه، اندوسيفيريا هموفيليا، فاهمين عليها؟ وهذا بيعتبر
+
+227
+00:18:51,170 --> 00:18:55,570
+من الأعمال الشاقة، إنك تغير بنشر عمل شاقة
+
+228
+00:18:55,570 --> 00:18:59,870
+بالنسبة لي، مظبوط، فيعرّض له accident، الـ damage إلى
+
+229
+00:18:59,870 --> 00:19:06,950
+حياته، فالأصل يكون فيه ملاحظة، طيب كيف نشخصهم by
+
+230
+00:19:06,950 --> 00:19:13,830
+laboratory؟ لتبّه لل... معلومات القاطعة، انتبهوا
+
+231
+00:19:13,830 --> 00:19:18,670
+عليها، الـ hemostatic
+
+232
+00:19:18,670 --> 00:19:23,110
+test عادة، hemostatic disease بتتشخص بـ hemostatic
+
+233
+00:19:23,110 --> 00:19:26,550
+test، وأشهر hemostatic test اللي اليوم بتتشخص
+
+234
+00:19:26,550 --> 00:19:31,400
+بـ hemostatic test، اللي بنستخدمه إنه الـ BT بيقيس الـ extrinsic
+
+235
+00:19:31,400 --> 00:19:35,480
+بينما الـ BTT بيقيس الـ intrinsic، الـ factor 8 و9 و
+
+236
+00:19:35,480 --> 00:19:38,140
+11، مولودين في الـ intrinsic ولا الـ extrinsic؟ في الـ
+
+237
+00:19:38,140 --> 00:19:42,140
+intrinsic، وهي في المئة؟ آه، بالتالي الخلل بنشوفه
+
+238
+00:19:42,140 --> 00:19:45,860
+عند مريض الـ hemophilia في الـ BTT ولا الـ BT؟ في الـ
+
+239
+00:19:45,860 --> 00:19:50,580
+BTT، والـ BT بيكون
+
+240
+00:19:50,580 --> 00:19:56,340
+normal، والـ BT بيكون إيه؟ بيكون normal، ماشي يا
+
+241
+00:19:56,340 --> 00:20:04,400
+شباب؟ لأ، اللي بيصير في أغلب الأحيان إنه أنت بتعمل
+
+242
+00:20:04,400 --> 00:20:10,420
+هذه الفحوصات وبتبدأ تفرّق، وبعد مرات بتطلعش الحكاية
+
+243
+00:20:10,420 --> 00:20:14,800
+من أول مرة، إنك تشوف إنه تاخد التنين واحد normal واحد
+
+244
+00:20:14,800 --> 00:20:21,780
+abnormal، ماشي؟ فبتضطر تعمل فحوصات أخرى إضافية
+
+245
+00:20:21,780 --> 00:20:26,260
+بتضطر تعمل إيه؟ فحوصات أخرى إضافية، هنشوفها منها
+
+246
+00:20:26,260 --> 00:20:30,990
+thrombin time، في أغلب الأحيان thrombin time بيكون
+
+247
+00:20:30,990 --> 00:20:37,350
+normal ولا abnormal؟ 100% لإن ما فيش فاكتور عشرة نشط
+
+248
+00:20:37,350 --> 00:20:41,990
+اثنين، مجبور ثم الـ fibrinogen في الغالب بيكون
+
+249
+00:20:41,990 --> 00:20:50,410
+normal ولا abnormal؟ مستهلك نهر وهاكذا، في فحوصات
+
+250
+00:20:50,410 --> 00:20:56,260
+أخرى ممكن كمان تضاف منها دي دايا، مثلًا منها الـ FDBs
+
+251
+00:20:56,260 --> 00:21:01,780
+تعرفونهم طبعا، منها الـ antithrombin 3، هذه كلها
+
+252
+00:21:01,780 --> 00:21:07,140
+فحصات ممكن تنعمل، وطبعا القائمة تطول لبيت ما تصل
+
+253
+00:21:07,140 --> 00:21:11,540
+لتشخيص حقيقي لمرضى، كل هذه فحصات و hemostasis؟
+
+254
+00:21:11,540 --> 00:21:17,160
+نعم، مظبوط؟ طيب، degree of severity يا شباب
+
+255
+00:21:17,160 --> 00:21:23,000
+لهيموفيليا بشكل عام شرحتلكوا يا قولتلكوا normal range
+
+256
+00:21:23,000 --> 00:21:29,560
+للدين من خمسين لجدين 150 من خمسين لجدين 150 في الـ
+
+257
+00:21:29,560 --> 00:21:35,640
+hemophilia الـ classification هتكون كالقاتل قولنا
+
+258
+00:21:35,640 --> 00:21:38,960
+الـ mild من خمسة لخمسة وعشرين أنا ممكن أقول من خمسة
+
+259
+00:21:38,960 --> 00:21:44,400
+لخمسين عشان أوصل لـ hemostatic air levelالـ mild هو
+
+260
+00:21:44,400 --> 00:21:47,840
+من خمسة لخمسين ثم الـ moderate والـ severe زي بعد
+
+261
+00:21:47,840 --> 00:21:54,900
+من واحد لخمسة ثم من أقل من آخر أقل من آخر طيب
+
+262
+00:21:54,900 --> 00:21:58,340
+هيموفيليا أيه يا شباب prevalence of hemophilia أيه
+
+263
+00:21:58,340 --> 00:22:03,600
+اتفقنا أنه خمسة إلى ست أضعاف hemophilia بها الـ
+
+264
+00:22:03,600 --> 00:22:06,560
+incidence اللي شفناها دي كان مرة واحد لعشر تلات
+
+265
+00:22:06,560 --> 00:22:12,380
+واحد في كل أنا أقول واحد في خمس تلاتة هناك كانت الـ
+
+266
+00:22:12,380 --> 00:22:17,300
+100 لـ 50 ألف وأنا 30 ألف لو لاحظتوا النسبة واحدة
+
+267
+00:22:17,300 --> 00:22:25,820
+مظبوط هنا 5 أضعاف فأنا 6 أضعاف 100 أخد من 100 طيب
+
+268
+00:22:25,820 --> 00:22:31,040
+مظاهر الـ hemophilia المرضية كلنا بنعرف الـ types of
+
+269
+00:22:31,040 --> 00:22:34,800
+bleeding هي عبارة عن joint bleeding هي عبارة عن
+
+270
+00:22:34,800 --> 00:22:39,300
+إيش؟ joint bleeding وهي أشهرها joint bleeding
+
+271
+00:22:39,300 --> 00:22:45,930
+تعمل hemarthrosis ماشي ثم muscle hemorrhage المرة
+
+272
+00:22:45,930 --> 00:22:50,790
+اللي فاتت أنا أرجيتكوا صورة واحد إيش الفخد كله إيش
+
+273
+00:22:50,790 --> 00:22:55,650
+عنده bleeding صح هذا عبارة عن hemophilic patient
+
+274
+00:22:55,650 --> 00:23:00,730
+صار فيه muscle bleeding شو صار؟ muscle bleeding or
+
+275
+00:23:00,730 --> 00:23:06,570
+soft tissue bleeding طبعا sometimes bleeding is
+
+276
+00:23:06,570 --> 00:23:09,610
+life threatening condition وبالتالي ممكن مايهاش
+
+277
+00:23:09,610 --> 00:23:15,080
+مايضحكش هي في أنواع أخرى من الـ bleeding وهذا صورة
+
+278
+00:23:15,080 --> 00:23:18,860
+واضحة ومعبرة جدا للهمارثروسيش، شايفين كده الشرق
+
+279
+00:23:18,860 --> 00:23:24,640
+بقى يا شباب؟ كل هذا bleeding،
+
+280
+00:23:24,640 --> 00:23:30,710
+هذا مش مصدر، هذا جوانب شايفين كده الـ bleeding صار
+
+281
+00:23:30,710 --> 00:23:34,450
+في الرقبة؟ شايفين الرقبة هدي طبعته؟ طبعا واحد من
+
+282
+00:23:34,450 --> 00:23:37,350
+هالنوع شايفين المفصل هان في طفل قاعد طب ما هيش
+
+283
+00:23:37,350 --> 00:23:39,730
+الحالة يا دكتور؟ أنا مش هانعرف الـ bleeding جورج
+
+284
+00:23:39,730 --> 00:23:42,870
+كده كيف؟ ما هيش الحالة في الحال إزاي؟ خلاص مضارب
+
+285
+00:23:42,870 --> 00:23:46,030
+مريضة؟ المريض هدي طبعا المفروض أنه يتغير المفصل
+
+286
+00:23:46,030 --> 00:23:52,410
+لأن بعد فترة المفصل بيصير فيه تليف وبيصير فش حركة
+
+287
+00:23:53,160 --> 00:23:56,380
+في المفصل وإذا ما فيش حركة في المفصل إيش الفائدة
+
+288
+00:23:56,380 --> 00:24:01,900
+منها صح فبقى بيصير ثابت عشان يرجع يعيش ثانوية ميدك
+
+289
+00:24:01,900 --> 00:24:08,720
+تقياش ميدك تغيير مفصل طبعا شباب لما كل عشان نأخر
+
+290
+00:24:08,720 --> 00:24:12,080
+هذه العملية يعني هتسير هتسير مع الزمن ده نعمل نعمل
+
+291
+00:24:12,080 --> 00:24:17,200
+نعمل لكن عشان نأخرها الأصل أنه نقلل عدد مرات
+
+292
+00:24:17,200 --> 00:24:22,560
+النزيف لإن كل ما زاد النزيف كل ما خربت الرجل أكثر
+
+293
+00:24:23,010 --> 00:24:33,330
+المريض بيتقلم عند المشاكل؟ مفصل وسابق، تلاقي، بطل
+
+294
+00:24:33,330 --> 00:24:38,170
+زي الـ .. زي الـ .. البرغ المصدق، بطل يعيش، يتحرك،
+
+295
+00:24:38,170 --> 00:24:41,930
+بتقلم ولا ما تقلمش؟ طبعا متقلم شكل فظيع جدا، مش
+
+296
+00:24:41,930 --> 00:24:46,230
+متقلم، ووصل لمرحلة بيقولك بيثبت المفصل، يثبت،
+
+297
+00:24:46,230 --> 00:24:47,930
+فبالتالي لابد من تغيير المفصل
+
+298
+00:24:53,270 --> 00:24:56,970
+طيب other types طبعا الـ joint bleeding من مظاهرها
+
+299
+00:24:56,970 --> 00:25:02,690
+الشباب أنه أول شيء بتبدأ tingling or bubbling إيش
+
+300
+00:25:02,690 --> 00:25:09,210
+يعني؟ لأ لأ لأ لأ هي tingling بتعرفوا النمنمة؟
+
+301
+00:25:11,660 --> 00:25:19,140
+and warmth طبيعي
+
+302
+00:25:19,140 --> 00:25:23,360
+جدا مفصل خربان شو بده يصير inflammation مظبوط شو
+
+303
+00:25:23,360 --> 00:25:27,680
+بده يصير حرارة and pain مظهر inflammation ولا لا
+
+304
+00:25:27,680 --> 00:25:33,860
+and unusual limb position إيش يعني يعني بياخد وضع
+
+305
+00:25:33,860 --> 00:25:36,340
+ثابت أو غير طبيعي unusual
+
+306
+00:25:40,350 --> 00:25:46,530
+طبعا يا شباب من المشاكل المميّطة، أنواع النظيفة
+
+307
+00:25:46,530 --> 00:25:49,910
+المميّطة، يوم ما يشير في الـ head، bleeding
+
+308
+00:25:56,350 --> 00:25:59,090
+الـ bleeding يعني احنا مش حابين نخش فيها إنما
+
+309
+00:25:59,090 --> 00:26:02,150
+هاريمة و هالـ life threatening neck and throat
+
+310
+00:26:02,150 --> 00:26:07,190
+بتبدأ تنفق الراجب تنفق تنفق المحاصلة إيش؟ asphyxia
+
+311
+00:26:07,190 --> 00:26:10,650
+بالظبط وبموت ولا بموت إيش؟ فبالتالي لازم ينتهي
+
+312
+00:26:10,650 --> 00:26:14,750
+abdominal gastro intestinal bleeding يعني نزيف
+
+313
+00:26:14,750 --> 00:26:19,690
+داخلي في المعدة في المرضى بالتحجور ماشي وفي
+
+314
+00:26:19,690 --> 00:26:23,270
+المرضى بدك تنجولله دم باستمرار إلى أن يقف ياش
+
+315
+00:26:23,270 --> 00:26:31,430
+النزيف ثم ليو بسوسيز اللي هو اللي .. اللي زي ما
+
+316
+00:26:31,430 --> 00:26:33,970
+قلتلكوا الـ softshell muscle أو الـ muscle اللي
+
+317
+00:26:33,970 --> 00:26:37,810
+موجودة في هذه المنطقة هي عبارة عن .. يسموها الـ ..
+
+318
+00:26:37,810 --> 00:26:43,570
+الـ .. الـ .. منطقة الـ buttocks أرضية وطبعا هذه مؤلمة
+
+319
+00:26:43,570 --> 00:26:50,410
+جدا بتعمل back pain وبتعمل abdominal pain وبتعمل
+
+320
+00:26:50,410 --> 00:26:53,870
+thigh tingling وlumpness وكل الشيء
+
+321
+00:26:56,910 --> 00:27:00,130
+أنواع أخرى من نزيف ممكن يصير نزيف من الـ mouth ومن
+
+322
+00:27:00,130 --> 00:27:06,070
+الـ nose ومن الـ scrapes or اللي هو بيسموها minor
+
+323
+00:27:06,070 --> 00:27:15,050
+scratches اللي هي الكشطات أو السحاجات ممكن يصيره
+
+324
+00:27:15,050 --> 00:27:19,090
+إن كان يعني قليل كمان منه regia عند الـ female
+
+325
+00:27:33,720 --> 00:27:38,180
+Arthritis, Chronic Pain, Muscle Atrophy,
+
+326
+00:27:38,900 --> 00:27:42,900
+Compartment Syndrome و Neurological Impairment
+
+327
+00:27:42,900 --> 00:27:51,080
+كلها عبارة عن مظاهر ليه نظيف ومظلم فاهمين شباب؟ حد
+
+328
+00:27:51,080 --> 00:27:57,660
+عنده سؤال؟ نشوف بعض المعلومات العامة عن الـ هيموفيليا
+
+329
+00:27:57,660 --> 00:28:01,060
+بشكل عام، من المعلومات العامة، كلنا بنعرف نمر
+
+330
+00:28:01,060 --> 00:28:05,540
+واحد، يعني يعتبروها summary، أن هناك مرتبط بين
+
+331
+00:28:05,540 --> 00:28:09,440
+الـ factor concentration وبين الـ bleeding، صح؟ كل
+
+332
+00:28:09,440 --> 00:28:11,940
+ما جاب كان factor concentration كل ما زاد في
+
+333
+00:28:11,940 --> 00:28:16,480
+الـ 100%، وإن spontaneous bleeding بنشوفها في الناس
+
+334
+00:28:16,480 --> 00:28:17,760
+اللي عندهم severe hemophilia
+
+335
+00:28:20,950 --> 00:28:25,590
+فعنده ممكن يصير عنده spontaneous bleeding في أي
+
+336
+00:28:25,590 --> 00:28:33,990
+لحظة من اللحظة وإن males are affected لأنه no X
+
+337
+00:28:33,990 --> 00:28:37,730
+-laying process كمان
+
+338
+00:28:37,730 --> 00:28:42,110
+اتفقنا على إنه في new mutation طولت الحلقات ننجي
+
+339
+00:28:42,110 --> 00:28:45,550
+عن الـ new mutation وبالتالي مش شرط دائما يكون في
+
+340
+00:28:45,550 --> 00:28:52,590
+medical history من الحاجات اللي كمان موجودة أنه
+
+341
+00:28:52,590 --> 00:28:57,750
+غالبا المرضى الميل يشخصه في العام الأول من إيش من
+
+342
+00:28:57,750 --> 00:29:03,790
+همهم أنه فيه circumcision ماشي لكن لو ما صارش
+
+343
+00:29:03,790 --> 00:29:10,750
+بتزيد إمكانية احتمالية أنه يصير عنده bleeding بعد
+
+344
+00:29:10,750 --> 00:29:13,770
+سن المراهقة أو لما بيصل سن المراهقة ليه؟
+
+345
+00:29:21,340 --> 00:29:25,780
+أولا هذه التحديات بنشوفها .. زي ما شفناش في السنة
+
+346
+00:29:25,780 --> 00:29:29,580
+الأولى بكون المريض غالبا عنده minor hemophilia
+
+347
+00:29:29,580 --> 00:29:36,760
+minor hemophilia طيب كيف نعالج مرضى الـ hemophilia؟
+
+348
+00:29:36,760 --> 00:29:40,460
+غالبا نعالج مرضى .. أي مريض عنده نقص في شغلة معينة
+
+349
+00:29:40,460 --> 00:29:44,300
+بنحاول نعوضه هده الشرطة، مظبوط؟ هذا مريض
+
+350
+00:29:44,300 --> 00:29:48,160
+hemophilia اللي عنده نقص في factor 8 أو 9، ماشي،
+
+351
+00:29:48,160 --> 00:29:51,820
+بدنا نديه هذا الـ factor والفترة يا شباب موجود أما
+
+352
+00:29:51,820 --> 00:29:59,260
+على شكل dried powder موجود في بال وبينبع بيحضر من
+
+353
+00:29:59,260 --> 00:30:06,260
+pool دي plasma ماشي أو موجود في الـ plasma تاخده
+
+354
+00:30:06,260 --> 00:30:10,360
+على شكل أما cryo وحناخده إن شاء الله قدها أو أما
+
+355
+00:30:10,360 --> 00:30:15,320
+fresh frozen plasma وفيه فترة فاهمين عليا؟ بينعطى
+
+356
+00:30:15,320 --> 00:30:19,820
+on demand مش عارفاني بالمالية ماشي مش كل يوم
+
+357
+00:30:19,820 --> 00:30:24,520
+ياخدله حبة بنعطى on demand بمعنى يوم ما يصير نزيف
+
+358
+00:30:24,520 --> 00:30:30,540
+يوم ما ياكل ما يصير نزيف أو إذا بده يتعرض إلى تحدي
+
+359
+00:30:30,540 --> 00:30:35,100
+واحد بده يعمل عملية جراحية على سبيل المثال بدنا
+
+360
+00:30:35,100 --> 00:30:39,840
+نضبط الـ factor أنه قبل ما ياكل يخش العملية الجراحية
+
+361
+00:30:39,840 --> 00:30:45,440
+فبيجي ع المستشفى بيقول أنا يوم كذا عندي عملية ماشي
+
+362
+00:30:45,940 --> 00:30:49,660
+فبنجب العملية بيومين تلاتة بتدو ياكل الـ factor
+
+363
+00:30:49,660 --> 00:30:55,260
+بيظبط فع نسبة الـ coagulation factor طبعا هذا الكلام
+
+364
+00:30:55,260 --> 00:31:00,440
+بنعطيه للناس اللي عندهم اللي هو حاجة للـ factor في
+
+365
+00:31:00,440 --> 00:31:04,820
+ناس عندهم mild المرض بيكون mild فبيعطوهم بعض
+
+366
+00:31:04,820 --> 00:31:09,540
+الأدوية بيعطوهم مش لا factor ولا هدف بيعطوهم بعض
+
+367
+00:31:09,540 --> 00:31:12,600
+الأدوية وهي من أشهر الأدوية اللي بتلعب دوري كثير
+
+368
+00:31:12,600 --> 00:31:15,480
+كويس في المياه الـ disease هو الـ DDAVP أو
+
+369
+00:31:15,480 --> 00:31:20,540
+Desmopressin أو بيسموه Stigmate الاسم التجاري وهذا
+
+370
+00:31:20,540 --> 00:31:27,740
+ببساطة شمال هو عبارة عن drug شو بيعمل؟ بيطلع الـ
+
+371
+00:31:27,740 --> 00:31:34,020
+von Willebrand من مخازنه، وين موجودة مخازنه؟ الـ 100 طب
+
+372
+00:31:34,020 --> 00:31:39,020
+لما يطلع الـ von Willebrand من مخازنه شو بيعمل؟ الـ 100
+
+373
+00:31:39,020 --> 00:31:42,940
+في الـ 100 هو بالتالي بيحافظ عليه ولا بيحافظش عليه؟
+
+374
+00:31:42,940 --> 00:31:47,480
+هو بالتالي بيحميه من التكسر 100% فمريض عنده الـ
+
+375
+00:31:47,480 --> 00:31:53,340
+factor قليل لو طلعنا bodyguard له باستمرار يحميه 
+
+376
+00:31:53,340 --> 00:31:56,880
+من التكسر، بنحافظ على الـ concentration ولا لا؟ لا
+
+377
+00:31:56,880 --> 00:32:05,840
+حزارة Anti-fibrillitic agents مضادات الـ Fibrolysis
+
+378
+00:32:07,580 --> 00:32:10,360
+زي الـ Amicar، وده عبارة عن الـ drug موجود الآن
+
+379
+00:32:10,360 --> 00:32:15,760
+بانعطفه لكل حالات النزيف، بما فيهم الـ post-partum 
+
+380
+00:32:15,760 --> 00:32:22,380
+bleeding، يعني الستات اللي بيلدوا، طبعا مريض الـ
+
+381
+00:32:22,380 --> 00:32:26,720
+hemophilia لابد من أنه ي... قبل ما يصل للمستشفى
+
+382
+00:32:26,720 --> 00:32:31,400
+يعملوله supportive treatment و تبدأ من القاعدة يعني
+
+383
+00:32:31,400 --> 00:32:36,660
+مريض وجعه و بده ينزل أول شغلة تعمله icing تحط إيش؟
+
+384
+00:32:36,660 --> 00:32:44,940
+تنهج على... على المكان عشان إيش؟ عشان تقلل من تصريف 
+
+385
+00:32:44,940 --> 00:32:49,740
+الدم إلى منطقة الجارية، مظبوط؟ نعمل basic
+
+386
+00:32:49,740 --> 00:32:51,380
+restriction، صح؟
+
+387
+00:32:54,200 --> 00:33:02,380
+الحركة شو بتعمل؟ سبب النزيف and arresting ومن بعد
+
+388
+00:33:02,380 --> 00:33:06,340
+هيك بروح المستشفى و بدهم يركبوله أول شي IV 
+
+389
+00:33:06,340 --> 00:33:09,820
+وبيعطوه
+
+390
+00:33:09,820 --> 00:33:15,880
+ intravenous infusion infusion و بدهم الـ factor
+
+391
+00:33:15,880 --> 00:33:23,380
+على شكل محلول ماشي، ووجدوا أنه
+
+392
+00:33:26,470 --> 00:33:34,250
+كل واحد اللى هو كل factor بيحتوي على عشرين إلى
+
+393
+00:33:34,250 --> 00:33:40,090
+خمسين في المئة unit الـ
+
+394
+00:33:40,090 --> 00:33:45,190
+factor بنعطى من عشرين إلى خمسين في المئة unit لكل 
+
+395
+00:33:45,190 --> 00:33:49,250
+kilogram من وزن المريض، الـ half-life تبعته من
+
+396
+00:33:49,250 --> 00:33:53,290
+ثمانية لعشرة، وجاله كل واحدة ترفع factor ثمانية
+
+397
+00:33:53,290 --> 00:33:58,490
+level 2%، كل واحدة بترفع factor ثمانية
+
+398
+00:33:58,490 --> 00:34:02,410
+level 2%، طبعا بنلاقيها إنطبق على ثمانية، إنطبق على 
+
+399
+00:34:02,410 --> 00:34:08,590
+تسعة، بس كل ما في الأمر أنه الـ units هناك من عشرين
+
+400
+00:34:08,590 --> 00:34:12,650
+لخمسين، هن من عشرين لمية، half life أكثر من اثنا عشر
+
+401
+00:34:12,650 --> 00:34:18,110
+لأربع وعشر ساعة، لكن كل واحدة بترفع نسبة الـ factor
+
+402
+00:34:18,110 --> 00:34:24,030
+تسعة بنسبة واحد في المئة مش اثنين في المئة، حد عنده سؤال؟
+
+403
+00:34:24,030 --> 00:34:24,390
+شباب
+
+404
+00:34:47,070 --> 00:34:50,870
+اللي هو زي ما قلتلكوا الـ vial بيجي بتحضر على شكل 
+
+405
+00:34:50,870 --> 00:34:55,730
+dried powder في الـ vialات بتنحلوا و بتنحطوا في
+
+406
+00:34:55,730 --> 00:34:59,070
+المحلول و بتنحطوا للمريض، تبدو هذه نواحي تنغيضية
+
+407
+00:34:59,070 --> 00:35:03,910
+prophylactic treatment بتنحطها للناس اللي عندهم
+
+408
+00:35:03,910 --> 00:35:13,730
+mild disease، فجاتوهم DDAVB و بالتالي بنزود اللي هو
+
+409
+00:35:15,060 --> 00:35:23,660
+الـ  وهبل براند ده هو الـ DDVB الأول استعيمت نفسه هذا
+
+410
+00:35:23,660 --> 00:35:27,780
+كيف بنقطع، احنا مش كتير معنين فيه لإنه برضه معلومات
+
+411
+00:35:27,780 --> 00:35:35,000
+طبية بحتة أو تمرضية، هذا الـ Amicar من مضاعفات مرض
+
+412
+00:35:35,000 --> 00:35:38,900
+الـ hemophilia، مريض بيتعرض الى نقل
+
+413
+00:35:50,940 --> 00:36:00,820
+هي بطاقة A وB وC وHIV وقائمة تطوط CMV وHTV وهكذا
+
+414
+00:36:00,820 --> 00:36:06,240
+طب
+
+415
+00:36:06,240 --> 00:36:14,780
+من المضاعفات الأخرى التي تحدث هو
+
+416
+00:36:21,830 --> 00:36:28,510
+وهي بتسمى Inhibitors And
+
+417
+00:36:28,510 --> 00:36:35,930
+this antibody can be either O2 or Allo Antibody
+
+418
+00:36:35,930 --> 00:36:40,470
+ماشي؟ إيش يعني O2 Antibody؟ يعني Antibody من نفس
+
+419
+00:36:40,470 --> 00:36:46,350
+الجسم لنفس الـ factor تبعه Or Allo يعني Antibody هو
+
+420
+00:36:46,350 --> 00:36:54,030
+بيكونها لكل factor بيجي من برة، مفهوم عليا either
+
+421
+00:36:54,030 --> 00:36:59,410
+auto or allo وبالتالي أول ما يخش الـ factor أو أول
+
+422
+00:36:59,410 --> 00:37:03,050
+ما يشوف الـ factor هذا الـ antibody شو بيعمله؟ وإيش
+
+423
+00:37:03,050 --> 00:37:08,810
+بيعمل؟ بيعمله blocking يعني... يعني inhibition
+
+424
+00:37:08,810 --> 00:37:14,790
+يعني عشان هيك إيش سموهم؟ inhibitors الناس اللي
+
+425
+00:37:14,790 --> 00:37:20,670
+بيصير عندهم هذا الشيء غالبا
+
+426
+00:37:23,250 --> 00:37:29,950
+بيفرقوهم عن الـ traditional hemophilia فبيحطوهم تحت 
+
+427
+00:37:29,950 --> 00:37:33,570
+category بيسموه acquired hemophilia acquired
+
+428
+00:37:33,570 --> 00:37:37,970
+hemophilia عشان هيك الناس اللي بيكونوا inhibitors
+
+429
+00:37:37,970 --> 00:37:43,270
+أو اللي عندهم inhibitors عندهم acquired hemophilia
+
+430
+00:37:43,270 --> 00:37:49,030
+عندهم إيه؟ acquired hemophilia مش traditional or
+
+431
+00:37:49,030 --> 00:37:49,590
+hereditary
+
+432
+00:37:53,040 --> 00:37:58,840
+برد اكتسبه المريض اكتسابا، أما هو كون antibody
+
+433
+00:37:58,840 --> 00:38:04,440
+لاحقا للـ factor، و أما كون antibody لـ factor اصلا مش
+
+434
+00:38:04,440 --> 00:38:08,720
+موجود عنده، لما يخش بيعتبره كـ antigen و مبدعيش
+
+435
+00:38:08,720 --> 00:38:13,380
+تتكون بالنسبة في الـ hemophilia إيه؟ بنشوفها
+
+436
+00:38:13,380 --> 00:38:18,600
+بالنسبة أكثر بكثير من الـ hemophilia B، بقالوا الـ
+
+437
+00:38:18,600 --> 00:38:21,740
+prevalence من 20 ل 30% من حالات الـ hemophilia
+
+438
+00:38:37,320 --> 00:38:43,380
+لأ هي مجرد ما يكون Antibody بيصير أكبر لما هي مش
+
+439
+00:38:43,380 --> 00:38:48,420
+hereditary يعني مش شيء مكتسب... موروث، وإنما شيء ما
+
+440
+00:38:48,420 --> 00:38:53,000
+إيه؟ مكتسب طيب،
+
+441
+00:38:53,000 --> 00:38:59,160
+الأمراض اللي بيعمل Hepatitis A وB وC HIV
+
+442
+00:38:59,160 --> 00:39:05,900
+و
+
+443
+00:39:05,900 --> 00:39:12,270
+...المعلومات المتبقية هذه أنا مش حابب أخش فيها، هذه
+
+444
+00:39:12,270 --> 00:39:18,890
+يعني معلومات عامة بتحكي على الـ site social issue
+
+445
+00:39:18,890 --> 00:39:23,370
+يعني كيفية التعامل مع الـ hemophilia من ناحية نفسية
+
+446
+00:39:23,370 --> 00:39:30,490
+من ناحية اجتماعية، من ناحية تمريضية، كل هذه الأمور
+
+447
+00:39:30,490 --> 00:39:37,510
+ثم هدول، هذا بيسموه الـ hemophilia team فريق الـ
+
+448
+00:39:37,510 --> 00:39:41,630
+hemophilia لازم يتكون من هذه الناس، لازم يكون مريض
+
+449
+00:39:41,630 --> 00:39:47,490
+أو عائلة، صح؟ إيه؟ لازم يكون مريض، طبيب hematology
+
+450
+00:39:47,490 --> 00:39:56,110
+شخص، ثم nurse طبق، ثم social worker لما مريض الـ
+
+451
+00:39:56,110 --> 00:40:00,840
+hemophilia هو مريض بيمارس حياته طبيعيًا جدًا جدًا جدًا
+
+452
+00:40:00,840 --> 00:40:04,900
+كل ما في الأمر أنه عنده هالنقطة هالي اللي ممكن يتعرض له
+
+453
+00:40:04,900 --> 00:40:08,320
+لنزيـفة أي لحظة من اللحظات، وبالتالي دائمًا بيحس حاله
+
+454
+00:40:08,320 --> 00:40:12,120
+في خطر دائم، مريض من هالنور من هالنور قد يتعرض
+
+455
+00:40:12,120 --> 00:40:16,480
+لضغوط نفسية، ده الطبيعي، فبدنا social worker ثم
+
+456
+00:40:16,480 --> 00:40:21,680
+physical therapist علاج طبيعي، طب ما احنا عارفين
+
+457
+00:40:21,680 --> 00:40:28,080
+وقولنا المفصل بيغرب إذا خير به، حركته بتثبت، مظبوط؟
+
+458
+00:40:28,080 --> 00:40:32,220
+فبده دائمًا إياه علاج طبيعي عشان إياه نلين
+
+459
+00:40:32,220 --> 00:40:37,940
+المفاصل، Otopedist طبيب عظام، طبيعي لإنه طبيب عظام
+
+460
+00:40:37,940 --> 00:40:43,520
+لأنه ممكن نحتاج إلى تغيير مفصل صح؟ مبرر ماريكير
+
+461
+00:40:43,520 --> 00:40:50,060
+أكيد، و infectious disease هذا واحد بيتعرض لنقل دم أو
+
+462
+00:40:50,060 --> 00:40:54,490
+بلا فاكتور باستمرار، فينتقل يصير عنده infectious
+
+463
+00:40:54,490 --> 00:41:00,130
+disease وارد، ثم genetics وده مهم جدا، genetics ليه؟
+
+464
+00:41:00,130 --> 00:41:04,910
+لأنه بتعمل family بـ degree تشوف هنوء أه فبدا
+
+465
+00:41:04,910 --> 00:41:09,330
+consultation pharmacy لازم يكون في صيدلية في مركز
+
+466
+00:41:09,330 --> 00:41:15,170
+من هنوء، وبالتالي بدنا pharmacist ثم dental work
+
+467
+00:41:15,170 --> 00:41:18,450
+بدنا dentist and hepatologist
+
+468
+00:41:21,980 --> 00:41:29,960
+لأنه الكبد وارد جدًا يصير في عنده level of virus،
+
+469
+00:41:29,960 --> 00:41:34,120
+كيف يا بابا؟ مختبئ كده الآن؟ الـ hematologist إيش
+
+470
+00:41:34,120 --> 00:41:39,120
+معناته؟ شاب طبيب يعني دائمًا، وإنما كمان ممكن يكون 
+
+471
+00:41:39,120 --> 00:41:46,010
+مختص، طبعًا احنا الأساس في التشخيص، طبعًا involved 
+
+472
+00:41:46,010 --> 00:41:50,250
+hemophilia centers في العلاج هي، وفي الـ education
+
+473
+00:41:50,250 --> 00:41:53,410
+وفي الـ research وفي الـ out research يعني حاجات
+
+474
+00:41:53,410 --> 00:41:59,750
+كتيرة ممكن، وواحد هيشياكي فيها، حد عنده سؤال؟ no
+
+475
+00:41:59,750 --> 00:42:00,390
+question؟
diff --git a/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo_postprocess.srt b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a6ba5399a9c98fcf91af84100c9ef772eec2f47
--- /dev/null
+++ b/PL9fwy3NUQKwZk82_1AeatKVgXG0nDxlHE/u3nrVUvmemo_postprocess.srt
@@ -0,0 +1,1900 @@
+1
+00:00:21,330 --> 00:00:26,670
+بسم الله الرحمن الرحيم اليوم ان شاء الله هنحكي في
+
+2
+00:00:26,670 --> 00:00:31,470
+ال clotting factor في الشيانسي or abnormalities او
+
+3
+00:00:31,470 --> 00:00:34,850
+ما يسمى بال disorders of secondary hemostasis لما
+
+4
+00:00:34,850 --> 00:00:38,170
+كنا نحكي المرة اللى فاتركنا نحكي على platelet
+
+5
+00:00:38,170 --> 00:00:42,170
+disorders و blood vessel disorders و قولتوله عبارة
+
+6
+00:00:42,170 --> 00:00:45,810
+عن primary hemostasis عبارة عن primary hemostasis
+
+7
+00:00:45,810 --> 00:00:48,370
+اليوم ان شاء الله هنحكي في ما يتعلق بال secondary
+
+8
+00:00:48,370 --> 00:00:51,530
+hemostasis و احنا بنعرف ان ال coordination factors
+
+9
+00:00:51,530 --> 00:00:54,490
+هم اللي بيقوموا بال secondary hemostasis mostly
+
+10
+00:00:54,490 --> 00:00:59,850
+they are hereditary in their nature يعني معظم
+
+11
+00:00:59,850 --> 00:01:06,240
+الأمراض they are hereditary typesand usually
+
+12
+00:01:06,240 --> 00:01:09,980
+associated either by failure of coagulation factor
+
+13
+00:01:09,980 --> 00:01:16,140
+to function normally or is associated with the
+
+14
+00:01:16,140 --> 00:01:18,960
+absence of the coagulation factor وبتالي كان دي
+
+15
+00:01:18,960 --> 00:01:23,020
+يعني differentiated إلى إما quantitative أو
+
+16
+00:01:23,020 --> 00:01:32,530
+qualitative defect طيب معظم هذهغياب هذه العوامل
+
+17
+00:01:32,530 --> 00:01:38,390
+بيؤدي لغياب تكوين ال fibre clot مظبوط معظم ال
+
+18
+00:01:38,390 --> 00:01:42,870
+coagulation factors غيابها بيعمل deficiency في ال
+
+19
+00:01:42,870 --> 00:01:46,890
+fibre formation مع ده مجموعة أخدناها سابقا،
+
+20
+00:01:46,890 --> 00:01:52,070
+تفكرينها؟ اللي غيابها بيعمل prolongation لل
+
+21
+00:01:52,070 --> 00:01:54,430
+hemostatic test لكن ما بيبقى ماشي bleeding ال
+
+22
+00:01:54,430 --> 00:01:59,190
+contact phase ال contact phase 100% لبناء ال
+
+23
+00:01:59,190 --> 00:02:05,310
+screeningTest usually is measured by the time
+
+24
+00:02:05,310 --> 00:02:09,310
+required for a clot formation وبالتالي
+
+25
+00:02:09,310 --> 00:02:18,270
+prolongation of the time بيعني غياب أو عدم اللي هو
+
+26
+00:02:18,270 --> 00:02:21,710
+قيام ال coordination factor بال test المطلوب أو
+
+27
+00:02:21,710 --> 00:02:23,250
+بال function المطلوبة
+
+28
+00:02:27,790 --> 00:02:30,670
+زي ما اتفقنا can be differentiated either ال
+
+29
+00:02:30,670 --> 00:02:33,690
+quantitative و ال qualitative و عشان افرق بين ال
+
+30
+00:02:33,690 --> 00:02:36,350
+quantitative و ال qualitative test لأن زي ما
+
+31
+00:02:36,350 --> 00:02:40,570
+قلتلكوا احنا بنقيس quantitative او بنقيس زمن بنقيس
+
+32
+00:02:40,570 --> 00:02:45,390
+زمن لكن الزمن مابميزليش مابفرقليش ما بين
+
+33
+00:02:45,390 --> 00:02:49,470
+quantitative و qualitative عشان اقول ان هذا المرض
+
+34
+00:02:49,470 --> 00:02:54,590
+quantitative او qualitative I should have to use
+
+35
+00:02:54,590 --> 00:02:58,420
+immunological testingإيش يعني؟ يعني أدور على ال
+
+36
+00:02:58,420 --> 00:03:02,320
+antigen إيش هو ال antigen هذه المرة؟ هو عبارة عن
+
+37
+00:03:02,320 --> 00:03:05,620
+coagulation factor بعتبر ال coagulation factor
+
+38
+00:03:05,620 --> 00:03:11,320
+antigen و بحط ال antibody المناسب إليه إذا صار
+
+39
+00:03:11,320 --> 00:03:14,880
+agglutination معناته ال antigen موجود يعني ال
+
+40
+00:03:14,880 --> 00:03:19,140
+factor موجود ماشي و إذا كان ماصارش agglutination
+
+41
+00:03:19,140 --> 00:03:24,480
+معناته ال antigen غايب وبالتالي ال function غايبة
+
+42
+00:03:24,480 --> 00:03:32,440
+إذا كانإعطاني agglutination وفي bleeding معناته
+
+43
+00:03:32,440 --> 00:03:36,540
+الانتيجين موجود يعني ال factor موجود لكنه لا يعمل
+
+44
+00:03:36,540 --> 00:03:43,120
+بغض النظر بسمه هذه الحالة CRM positive CRM
+
+45
+00:03:43,120 --> 00:03:47,000
+positive بمعنى انه cross-reacting material
+
+46
+00:03:47,000 --> 00:03:50,040
+positive ايش ال cross-reacting material؟ هي عبارة
+
+47
+00:03:50,040 --> 00:03:53,220
+عن antibody reaction انتيجين ايش؟ antibody
+
+48
+00:03:53,220 --> 00:03:56,360
+reaction if there is no protein
+
+49
+00:04:00,210 --> 00:04:02,710
+والتجارة التجارية التجارية التجارية التجارية
+
+50
+00:04:02,710 --> 00:04:02,870
+التجارية التجارية التجارية التجارية التجارية
+
+51
+00:04:02,870 --> 00:04:04,570
+التجارية التجارية التجارية التجارية التجارية
+
+52
+00:04:04,570 --> 00:04:11,870
+التجارية التجارية التجارية التجارية التجارية
+
+53
+00:04:11,870 --> 00:04:12,710
+التجارية التجارية التجارية التجارية التجارية
+
+54
+00:04:12,710 --> 00:04:15,230
+التجارية التجارية التجارية التجارية التجارية
+
+55
+00:04:15,230 --> 00:04:15,610
+التجارية التجارية التجارية التجارية التجارية
+
+56
+00:04:15,610 --> 00:04:17,370
+التجارية التجارية التجارية التجارية التجارية
+
+57
+00:04:17,370 --> 00:04:18,730
+التجارية التجارية التجارية التجارية التجارية
+
+58
+00:04:18,730 --> 00:04:24,370
+التجارية التجارية التجارية التجارية التجارية
+
+59
+00:04:24,370 --> 00:04:25,730
+التج
+
+60
+00:04:27,400 --> 00:04:30,480
+يقسموا هذه العوامل التي هي qualitative و
+
+61
+00:04:30,480 --> 00:04:35,760
+quantitative إلى مصطلحين جديدين وهو CRM positive و
+
+62
+00:04:35,760 --> 00:04:40,700
+CRM negative طبعا احنا يا شباب هنتطلق إلى بعض أهم
+
+63
+00:04:40,700 --> 00:04:47,940
+الأمثلة في ال coagulation factor disorders و أهم
+
+64
+00:04:47,940 --> 00:04:50,560
+الأمثلة بتتمثل في المرض كتير مشهور هو ال
+
+65
+00:04:50,560 --> 00:04:51,140
+hemophilia
+
+66
+00:04:55,680 --> 00:04:58,460
+هو بالمناسبة ال vomliebrand disease is more common
+
+67
+00:04:58,460 --> 00:05:05,440
+than hemophilia vomliebrand disease و ال
+
+68
+00:05:05,440 --> 00:05:09,220
+hemophilia بأنواعها فبنعرف أن ال hemophilia في
+
+69
+00:05:09,220 --> 00:05:14,720
+منها hemophilia A إذا كان factor 8 deficient و
+
+70
+00:05:14,720 --> 00:05:17,920
+hemophilia B إذا كان factor 9 deficient
+
+71
+00:05:24,860 --> 00:05:28,160
+ثم ال family brand يا عزيزي احنا بتتطرق اليه و ان
+
+72
+00:05:28,160 --> 00:05:33,960
+شاء الله برضه هنمر في others و ناخد مثال عن DIC في
+
+73
+00:05:33,960 --> 00:05:39,100
+الothers و نبدأ في هذه العواء لهذا المرد لكن قبل
+
+74
+00:05:39,100 --> 00:05:43,100
+ما نبدأ بدأ اذكركم في محاضرة سابقة
+
+75
+00:05:46,460 --> 00:05:50,840
+اللي بيحدث نتيجة لـplatelet disorders is
+
+76
+00:05:50,840 --> 00:05:57,740
+superficial وبالتالي بنشوف بتاشي وEcomosis على
+
+77
+00:05:57,740 --> 00:06:03,580
+وين؟ على ال skin بينما ال bleeding اللي بينتج من
+
+78
+00:06:03,580 --> 00:06:09,320
+coagulation factor هو عبارة عن ديب ماشي و بالتالي
+
+79
+00:06:09,320 --> 00:06:14,400
+ممكن مانشوفش على ال skin زي ما هذا هو موجود
+
+80
+00:06:15,570 --> 00:06:20,450
+Bleeding موجود في ال joints، في الرقبة، لكن مش
+
+81
+00:06:20,450 --> 00:06:23,910
+مبينش، صح؟ طب كيف بتلاقيها بيصير فيه swallowing في
+
+82
+00:06:23,910 --> 00:06:27,490
+الرقبة؟ وشوفنا مناظر المحاضرة اللي فاتت عن هذا
+
+83
+00:06:27,490 --> 00:06:33,270
+الموضوع، مظبوط؟ طيب What is Hemophilia؟ نبدأ في ال
+
+84
+00:06:33,270 --> 00:06:36,870
+Hemophilia زي ما اتفقنا Hemophilia هو عبارة عن مرض
+
+85
+00:06:36,870 --> 00:06:43,950
+وراثي بأنواع مختلفةناتج على نقص في factor 8 إذا
+
+86
+00:06:43,950 --> 00:06:49,350
+كانت Hemophilia A أو 9 إذا كانت Air و Hemophilia B
+
+87
+00:06:49,350 --> 00:06:55,550
+وانتبهوا على الجدول القاتى اللي بيفرقلي ما بين
+
+88
+00:06:55,550 --> 00:07:00,590
+Hemophilia A و B ماتفقين
+
+89
+00:07:00,590 --> 00:07:05,990
+أن ده هو الجدول Hemophilia A factor 8 deficiencyو
+
+90
+00:07:05,990 --> 00:07:12,370
+Hemophilia B Factor 9 Deficiency Inheritance Both
+
+91
+00:07:12,370 --> 00:07:15,490
+are inherited as X-linked recessive diseases
+
+92
+00:07:15,490 --> 00:07:20,910
+التنتين X-linked recessive يعني بنشوفهم في مين؟ في
+
+93
+00:07:20,910 --> 00:07:25,550
+المال ال
+
+94
+00:07:25,550 --> 00:07:30,670
+incidence بشكل عام شباب ال Hemophilia A أكتر من
+
+95
+00:07:30,670 --> 00:07:36,120
+Hemophilia B بحوالي خمسة إلى ست مراتخمسة إلى ست
+
+96
+00:07:36,120 --> 00:07:41,060
+أضعاف الهموفيليا B يعني ال incidence هي واحد إلى
+
+97
+00:07:41,060 --> 00:07:46,160
+عشرة تلاف واحد في كل عشر تلاف لكن بعد في كل خمسين
+
+98
+00:07:46,160 --> 00:07:53,240
+ألف which means انه في حوالي خمس أضعاف صح؟ طيب ال
+
+99
+00:07:53,240 --> 00:07:57,240
+severity يعني بتعتند على ال concentration of
+
+100
+00:07:57,240 --> 00:08:02,520
+coagulation factor ال concentration of ايش؟ of
+
+101
+00:08:02,520 --> 00:08:09,220
+coagulation factorو جالو انه بتعرفوا انتوا ان ال
+
+102
+00:08:09,220 --> 00:08:11,360
+normal concentration او ال concentration of
+
+103
+00:08:11,360 --> 00:08:19,840
+coagulation factors has اما normal range نبدأ نحكي
+
+104
+00:08:19,840 --> 00:08:27,420
+في اتفاقنا على ان ال normal range لل
+
+105
+00:08:27,420 --> 00:08:31,200
+coagulation factor بيساوي جديش يا شباب
+
+106
+00:08:34,310 --> 00:08:40,730
+انه بيساوي الخمسين الى مية وخمسين في المية
+
+107
+00:08:40,730 --> 00:08:47,290
+calculation factors
+
+108
+00:08:47,290 --> 00:08:50,170
+نسبته من خمسين الى مية وخمسين في المية عارفين ايش
+
+109
+00:08:50,170 --> 00:08:53,910
+بيعني هذا؟ بيعني انه لو كان لو قسنا على سبيل
+
+110
+00:08:53,910 --> 00:09:01,570
+المثال BT وعطانا normal time معناته ال activity
+
+111
+00:09:01,570 --> 00:09:10,550
+مية في المية اومصبوط؟ ايه التاني؟ لو عملنا BTE و
+
+112
+00:09:10,550 --> 00:09:21,070
+اتدانا normal time جديش ال normal time؟ احسنت
+
+113
+00:09:21,070 --> 00:09:26,410
+من عشر إلى تلتاشر second مصبوط؟ لو اتدانا ال BTE
+
+114
+00:09:26,410 --> 00:09:29,990
+normal time معناته ال concentration او ال activity
+
+115
+00:09:29,990 --> 00:09:36,540
+جديش؟من 100 ل 150% بس طبعا معظم الناس تكتب 100%
+
+116
+00:09:36,540 --> 00:09:41,580
+انا بتخاف تكتب 150% لأن معظم الناس بتعرفش ايش يعني
+
+117
+00:09:41,580 --> 00:09:46,620
+150% هقول ال normal range لغاية 150% يعني بعضيا
+
+118
+00:09:46,620 --> 00:09:50,560
+احنا اتعادلمنا اتعودنا نقول انه 100% عن ال top
+
+119
+00:09:50,560 --> 00:09:55,340
+يعني ايش؟ ال top لكن 150% يعني اشي كتير خالص
+
+120
+00:09:55,340 --> 00:10:01,060
+مظبوط؟ طيب اتعلمنا في المقابل ان في حاجة اسمها
+
+121
+00:10:07,030 --> 00:10:12,070
+هناك حاجة اسمها hemostatic level وعرفناها
+
+122
+00:10:12,070 --> 00:10:20,430
+سابقا هي عبارة عن القيمة المطلوبة من ال factor
+
+123
+00:10:20,430 --> 00:10:24,270
+لإحداث
+
+124
+00:10:24,270 --> 00:10:30,550
+normal hemostasis، مظبوط؟ القيمة المطلوبة من ال
+
+125
+00:10:30,550 --> 00:10:35,970
+coagulation factors عشان يعمل normal hemostasis،
+
+126
+00:10:35,970 --> 00:10:40,600
+مظبوط؟طيب القيمة المطلوبة من ال factor عشان يعمل
+
+127
+00:10:40,600 --> 00:10:46,440
+normal hemostasis الاصل حسب الجدول هذا خلينا نشوفه
+
+128
+00:10:46,440 --> 00:10:52,800
+قداش أقصى نسبة 25 قداش أقصى نسبة 25 معناته هي
+
+129
+00:10:52,800 --> 00:11:01,520
+النسبة المطلوبة من 25 فما فوق من 25 فما فوق بصيرش
+
+130
+00:11:01,520 --> 00:11:05,010
+فيها bleeding أه بصيرش فيها bleedingماشي؟ يعني في
+
+131
+00:11:05,010 --> 00:11:10,550
+normal hemostasis؟ نعم normal و هذا بفسرلي الأطفال
+
+132
+00:11:10,550 --> 00:11:15,270
+لما بنولدوا متفقين احنا انه ال coagulation factor
+
+133
+00:11:15,270 --> 00:11:19,770
+لسه مكونش متكون تماما صح؟ صح هو بالتالي بتكون كمته
+
+134
+00:11:19,770 --> 00:11:24,310
+قليلة و مع ذلك بس ليش عندهم bleeding ليش؟ لأنه
+
+135
+00:11:24,310 --> 00:11:27,690
+عندهم hemostatic level ماعندهمش normal range عندهم
+
+136
+00:11:27,690 --> 00:11:31,630
+ايش؟ hemostatic level ماعندهمش ايش؟ normal range و
+
+137
+00:11:31,630 --> 00:11:37,490
+بالتالي مافيش bleedingطيب according to this figure
+
+138
+00:11:37,490 --> 00:11:42,970
+ايش بيقول صنفوا أمراد ال hemophilia إلى تلت أنواع
+
+139
+00:11:42,970 --> 00:11:50,150
+جالوا mild و moderate و severe صح؟ و ال mild جالوا
+
+140
+00:11:50,150 --> 00:11:57,800
+من 5 ل 25% و ال moderate من 1 ل 5والـ Severe أقل
+
+141
+00:11:57,800 --> 00:12:01,300
+من 1% تخيلوا لما الواحد يكون عنده Coagulation
+
+142
+00:12:01,300 --> 00:12:04,520
+Factor أقل من 1% يبدأ يصير عنده يشبه الـ Severe
+
+143
+00:12:04,520 --> 00:12:09,100
+أرجع الناس اللي عندهم Severe mostly إما 1% or less
+
+144
+00:12:09,100 --> 00:12:13,600
+مرات بيكون Undetectable Undetectable إيش يعني؟
+
+145
+00:12:13,600 --> 00:12:18,820
+نقدرش نمجيزه نسبته قليلة جدا جدا جدا صح؟ فهو هذا
+
+146
+00:12:18,820 --> 00:12:22,040
+الـ Severe وغالبا هذا الناس اللي بيصير عندهم
+
+147
+00:12:22,040 --> 00:12:26,630
+Spontaneous Bleeding المدرّف من 1% ل 5%ثم المعارض
+
+148
+00:12:26,630 --> 00:12:30,710
+من خمسة لخمسة وعشرين فرميل، ماشي؟ وده التصنيفة
+
+149
+00:12:30,710 --> 00:12:32,590
+موجودة على .. على كل انواع ال hemophilia
+
+150
+00:12:32,590 --> 00:12:38,470
+hemophilia A, hemophilia B, hemophilia H, Z طبعا
+
+151
+00:12:38,470 --> 00:12:41,390
+مضاعفات ال hemophilia بشكل عام بناها يا شباب هي
+
+152
+00:12:41,390 --> 00:12:46,410
+عبارة عن .. عبارة عن soft tissue bleeding وهي
+
+153
+00:12:46,410 --> 00:12:47,550
+عبارة عن D بقى
+
+154
+00:12:54,140 --> 00:12:57,580
+الهموفيليا A وB X-linked هموفيليا A وB X-linked
+
+155
+00:12:57,580 --> 00:12:57,980
+هموفيليا A وB X-linked هموفيليا A وB X-linked
+
+156
+00:12:57,980 --> 00:12:59,040
+هموفيليا A وB X-linked هموفيليا A وB X-linked
+
+157
+00:12:59,040 --> 00:12:59,760
+هموفيليا A وB X-linked هموفيليا A وB X-linked
+
+158
+00:12:59,760 --> 00:13:04,960
+هموفيليا A وB X-linked هموفيليا A وB X-linked
+
+159
+00:13:04,960 --> 00:13:10,800
+هموفيليا A وB X-linked هموفوشوفنا الجدور كيف
+
+160
+00:13:10,800 --> 00:13:14,600
+صنفرنا إياها، و 30% من الحالات هي عبارة عن new
+
+161
+00:13:14,600 --> 00:13:19,440
+mutation يعني ممكن أشوف حالات جديدة بتظهر في بعض
+
+162
+00:13:19,440 --> 00:13:23,820
+العائلات اللي مافيش عندها medical history لمين
+
+163
+00:13:23,820 --> 00:13:29,900
+للهموفيك، لأكوين، مش أكوين، أكوين ده حاجة ثانية،
+
+164
+00:13:29,900 --> 00:13:32,000
+مش هي عبارة عن hereditary لإن فيها mutation
+
+165
+00:13:37,370 --> 00:13:40,670
+بالنسبة للجين المسؤول هيموفيلياية جناتيكوف
+
+166
+00:13:40,670 --> 00:13:42,870
+هيموفيلياية الجين مسؤول عن factor تمانية موجودة
+
+167
+00:13:42,870 --> 00:13:48,850
+على X-chromosome وعطرفها شباب في ال XQ28Q
+
+168
+00:13:48,850 --> 00:13:54,230
+يعني في ال long R 28 في الآخر أو بيسموه XQTER
+
+169
+00:13:54,230 --> 00:13:56,170
+Terminal
+
+170
+00:13:58,210 --> 00:14:02,310
+طبعا تقريبا جامب in telomeric region بيحتوي على 26
+
+171
+00:14:02,310 --> 00:14:09,390
+x 25 انترال طوله 186 كيلو باوندر وهي المشهور
+
+172
+00:14:09,390 --> 00:14:14,890
+messenger RNA حوالي 8.8 كيلو باوندر شايفون كده إيش
+
+173
+00:14:14,890 --> 00:14:22,310
+بنزل اللي بيحتوي على 2351 amino acids وفيه leader
+
+174
+00:14:22,310 --> 00:14:24,850
+sequence حوالي 19
+
+175
+00:14:30,560 --> 00:14:36,140
+ماشي او تعمل sequence تعرف بالظبط كل شكفة جداش
+
+176
+00:14:36,140 --> 00:14:41,040
+طولها و جداش بداك ال gene ماشي بالظبط هد الحاجات
+
+177
+00:14:41,040 --> 00:14:44,760
+اللي بتنفعها وبالتالي ال so ده ال real protein ال
+
+178
+00:14:44,760 --> 00:14:50,520
+protein نفسه بيتكوّن من 2332 amino acids تشيل ال
+
+179
+00:14:50,520 --> 00:14:55,720
+leader sequence بده اللي اش الطول الحقيقية تفرعين
+
+180
+00:14:55,720 --> 00:14:57,760
+معانا؟ بخطوها ده في الوراق ده مظبوط
+
+181
+00:15:01,480 --> 00:15:05,560
+الـ Genetic .. انتبهوا عليها يا شباب تقسيم ال ..
+
+182
+00:15:05,560 --> 00:15:10,200
+ال hemophilia من ناحية ورثية قسموها إلى جزء ايه؟
+
+183
+00:15:10,200 --> 00:15:14,340
+خمسين في المية منهم severe خمسين في المية منهم هي
+
+184
+00:15:14,340 --> 00:15:18,100
+severe بمعنى انه لو قسمنا ال coagulation factor
+
+185
+00:15:18,100 --> 00:15:22,360
+عندهم، هنلاجيه undetectable هنلاجيه undetectable
+
+186
+00:15:22,360 --> 00:15:25,300
+دل جداش؟ خمسين في المية .. دل خمسين في المية
+
+187
+00:15:25,300 --> 00:15:30,740
+التانية الخمسين في المية التانية، خمسة منهمبيكونوا
+
+188
+00:15:30,740 --> 00:15:34,480
+mild qualitative
+
+189
+00:15:34,480 --> 00:15:39,220
+sorry CRM positive والخمسة واربعين CRM negative
+
+190
+00:15:39,220 --> 00:15:44,220
+لكن الفيه variability في ال concentration of the
+
+191
+00:15:44,220 --> 00:15:47,700
+age of the factory عيد تاني خمسين في المية
+
+192
+00:15:48,880 --> 00:15:53,360
+Quantitative طبعا Undetectable Severe وخمسين في
+
+193
+00:15:53,360 --> 00:15:57,780
+المية اللى هو الجزء التانى خمسة في المية منهم
+
+194
+00:15:57,780 --> 00:16:01,480
+qualitative يعني positive وخمسة واربعين في المية
+
+195
+00:16:01,480 --> 00:16:07,700
+quantitative لكن with variable concentration with
+
+196
+00:16:07,700 --> 00:16:14,240
+variable concentration عشان
+
+197
+00:16:14,240 --> 00:16:18,670
+اشخص Hemophilia شباب detection of Hemophiliaلما
+
+198
+00:16:18,670 --> 00:16:21,170
+واحد بيدور على ال family history احنا متفقين على
+
+199
+00:16:21,170 --> 00:16:23,990
+ان هو genetic disease وبالتالي لازم ادور على انه
+
+200
+00:16:23,990 --> 00:16:28,550
+في افراد في العائلة عندهم نوفيلة ولا لأ ماشي صحيح
+
+201
+00:16:28,550 --> 00:16:34,750
+في طولة الحالات جديدة لكن التلتين عندهم family
+
+202
+00:16:34,750 --> 00:16:40,230
+history مظروف symptoms أكيد المريض بيجي بيعاني من
+
+203
+00:16:40,230 --> 00:16:44,870
+bleeding bruising يعني bleeding with circumcision
+
+204
+00:16:45,980 --> 00:16:50,740
+circumcision معناتها تهور لإن احنا بتقولنا المرض
+
+205
+00:16:50,740 --> 00:16:57,740
+موجود في الميل والميل أول تحدي بيواجهه اتهو يوم
+
+206
+00:16:57,740 --> 00:17:02,900
+يطهره بيصير في عنده bleeding مش راضي يجف مش راضي
+
+207
+00:17:02,900 --> 00:17:06,400
+إيش يجف عشان هيك الأطفال هدول يشخصوا في العام
+
+208
+00:17:06,400 --> 00:17:11,740
+الأول من عمرهم في العام الأول من عمرهم muscle
+
+209
+00:17:11,740 --> 00:17:18,130
+joints or soft tissue bleedingis also seen لكن في
+
+210
+00:17:18,130 --> 00:17:22,870
+أعمار متقدمة بعد ليش؟ ليش في أعمار متقدمة بعد ما
+
+211
+00:17:22,870 --> 00:17:29,230
+يكبر ويتعرض لإيش؟ لتحديات أخرى طبيعة عمل طبيعة
+
+212
+00:17:29,230 --> 00:17:32,630
+رياضة دفشة طبيعة .. يعني حاجات منها النوعية اللي
+
+213
+00:17:32,630 --> 00:17:37,030
+بتؤدي إلى المخاطر والنزيفة فبنشوف عنده soft tissue
+
+214
+00:17:37,030 --> 00:17:42,310
+bleeding أو deep bleeding من التحديات اللي بخاف
+
+215
+00:17:42,310 --> 00:17:46,660
+منها مريض ال hemophilia نلاقوا حد حاجتهلعمل اي
+
+216
+00:17:46,660 --> 00:17:55,720
+عملية surgery or dental work or trauma or accident
+
+217
+00:17:55,720 --> 00:18:04,560
+و هدول الشباب هدول المرضى مش لازم يعني يعملوا في
+
+218
+00:18:04,560 --> 00:18:13,460
+أعمال شاقة المفروض انه حتى في المدارس العامة على
+
+219
+00:18:13,460 --> 00:18:17,200
+المدارسإنه هذا الطفل عنده Hemophilia ممنوع يعيش،
+
+220
+00:18:17,200 --> 00:18:20,540
+ممنوع يتيندرام، ممنوع يتنطنط، ممنوع ي .. يعني
+
+221
+00:18:20,540 --> 00:18:24,420
+يتعرضوا ل Australia's exercise، هذه كلها الحاجات
+
+222
+00:18:24,420 --> 00:18:28,740
+لازماش يتعمق فيها يعني أنا بعرف حالة على سبيل
+
+223
+00:18:28,740 --> 00:18:33,140
+المثال، راجل يعني طبيعي جدا، لكن هو بسوق سيارة و
+
+224
+00:18:33,140 --> 00:18:38,840
+بنشرت السيارة، فنزل يعمل ال puncher و جاء ال jack،
+
+225
+00:18:38,840 --> 00:18:43,850
+بتعرف ال jack إيش بيعمل؟مات على المطرح يعني مالحوش
+
+226
+00:18:43,850 --> 00:18:51,170
+يسعفوه اندوسيفيريا مفيلة فاهمين عليها؟ وهذا بيعتبر
+
+227
+00:18:51,170 --> 00:18:55,570
+من الأعمال الشاقة انك اتغير بنشر عمل شاقة
+
+228
+00:18:55,570 --> 00:18:59,870
+بالنسبالي مظبوط فيعرض له accident ال damage إلى
+
+229
+00:18:59,870 --> 00:19:06,950
+حياته فالأصل يكون فيه ملاحظة طيب كيف نشخصهم by
+
+230
+00:19:06,950 --> 00:19:13,830
+laboratory؟ لتبه لل ..معلومات القاتية، انتبهوا
+
+231
+00:19:13,830 --> 00:19:18,670
+عليها، الهيموستاتيك
+
+232
+00:19:18,670 --> 00:19:23,110
+تست عادة، hemostatic disease بتشخص بهيموستاتيك
+
+233
+00:19:23,110 --> 00:19:26,550
+تست، و أشهر hemostatic test اللي اليوم بتشخص
+
+234
+00:19:26,550 --> 00:19:31,400
+بهيموستاتيك بتستواخدته ان ال BT بيقيس ال extrinsic
+
+235
+00:19:31,400 --> 00:19:35,480
+بينما ال BTT بيقيس ال extrinsic ال factor 8 و 9 و
+
+236
+00:19:35,480 --> 00:19:38,140
+11 مولودين في ال intrinsic ولا ال extrinsic؟ في ال
+
+237
+00:19:38,140 --> 00:19:42,140
+intrinsic و هي في الميه؟ اه بالتالي الخلل بنشوفه
+
+238
+00:19:42,140 --> 00:19:45,860
+عند مريض ال hemophilia في ال BTT ولا ال BT؟ في ال
+
+239
+00:19:45,860 --> 00:19:50,580
+BTT و ال BT بيكون
+
+240
+00:19:50,580 --> 00:19:56,340
+normal و ال BT بيكون ايه؟ بيكون normal ماشي يا
+
+241
+00:19:56,340 --> 00:20:04,400
+شباب؟لأ اللى بيصير في أغلب الأحيان أنه أنت بتعمل
+
+242
+00:20:04,400 --> 00:20:10,420
+هذه الفحوصات و بتبدأ تفرق وبعد مرات بتطلعش الحكاية
+
+243
+00:20:10,420 --> 00:20:14,800
+من أول مرة انكاش أنه تاخد التنين واحد normal واحد
+
+244
+00:20:14,800 --> 00:20:21,780
+abnormal ماشي؟ فبتضطر تعمل فحوصات أخرى إضافية
+
+245
+00:20:21,780 --> 00:20:26,260
+بتضطر تعمل إيه؟ فحوصات أخرى إضافية هنشوفها منها
+
+246
+00:20:26,260 --> 00:20:30,990
+tropical timeفي أغلب الأحيان thrombin time بيكون
+
+247
+00:20:30,990 --> 00:20:37,350
+normal ولا abnormal؟ 100% لأنه مصلش لفكتور عشر نشط
+
+248
+00:20:37,350 --> 00:20:41,990
+اتنين مجبور ثم ال fibrinogen في الغالب بيكون
+
+249
+00:20:41,990 --> 00:20:50,410
+normal ولا abnormal؟ مستهلك نهر وها كذا في فحوصات
+
+250
+00:20:50,410 --> 00:20:56,260
+أخرى ممكن كمان تضاف منها دي دايا مثلامنها ال FDBs
+
+251
+00:20:56,260 --> 00:21:01,780
+تعرفونهم طبعا، منها ال antithrombin 3، هذه كلها
+
+252
+00:21:01,780 --> 00:21:07,140
+فحصات ممكن تنعمل، و طبعا القائمة تطول لبيت ما تصل
+
+253
+00:21:07,140 --> 00:21:11,540
+لتشخيص حقيقي لمرضى، كل هذه فحصات و hemostasis؟
+
+254
+00:21:11,540 --> 00:21:17,160
+نعم، مظبوط؟ طيب، degree of severity يا شباب
+
+255
+00:21:17,160 --> 00:21:23,000
+لهموفيليابشكل عام شرحتلكوا يا قولتلكوا normal rain
+
+256
+00:21:23,000 --> 00:21:29,560
+لدين من خمسين لجدين 150 من خمسين لجدين 150 في ال
+
+257
+00:21:29,560 --> 00:21:35,640
+hemophilia ال classification هتكون كالقاتل قولنا
+
+258
+00:21:35,640 --> 00:21:38,960
+ال mild من خمسة لخمس عشرين انا ممكن اقول من خمسة
+
+259
+00:21:38,960 --> 00:21:44,400
+لخمسين عشان اصل لل hemostatic air levelالـ mild هو
+
+260
+00:21:44,400 --> 00:21:47,840
+من خمسة لخمسين ثم ال moderate و ال severe زي بعد
+
+261
+00:21:47,840 --> 00:21:54,900
+من واحد لخمسة ثم من اقل من اخر اقل من اخر طيب
+
+262
+00:21:54,900 --> 00:21:58,340
+هموفيليا ايه يا شباب prevalence of hemophilia ايه
+
+263
+00:21:58,340 --> 00:22:03,600
+اتفقنا انه خمسة الى ست اضعاف hemophilia بها ال
+
+264
+00:22:03,600 --> 00:22:06,560
+incidence اللي شفناها دي كان مرة واحد لعشر تلات
+
+265
+00:22:06,560 --> 00:22:12,380
+واحد في كل انا اقول واحد في خمس تلاتو هناك كانت ال
+
+266
+00:22:12,380 --> 00:22:17,300
+100 ل 50 ألف و أنا 30 ألف لو لاحظته النسبة واحدة
+
+267
+00:22:17,300 --> 00:22:25,820
+مظبوط هنا 5 أدعى فانا 6 أدعى 100 أخد من 100 طيب
+
+268
+00:22:25,820 --> 00:22:31,040
+مظاهر ال hemophilia المرضية كلنا بنعرف ال types of
+
+269
+00:22:31,040 --> 00:22:34,800
+bleeding هي عبارة عن joint bleeding هي عبارة عن
+
+270
+00:22:34,800 --> 00:22:39,300
+ايش؟ joint bleeding و هي أشهرها joint bleeding
+
+271
+00:22:39,300 --> 00:22:45,930
+تعمل hemarthrosisماشى ثم muscle hemorrhage المرة
+
+272
+00:22:45,930 --> 00:22:50,790
+اللى فاتت انا مرجيتكوا صورة واحد ايش الفخد كله ايش
+
+273
+00:22:50,790 --> 00:22:55,650
+عنده bleeding صح هذا عبارة عن hemophilic patient
+
+274
+00:22:55,650 --> 00:23:00,730
+صار فيه muscle bleeding شو صار؟ muscle bleeding or
+
+275
+00:23:00,730 --> 00:23:06,570
+soft tissue bleeding طبعا sometimes bleeding is
+
+276
+00:23:06,570 --> 00:23:09,610
+life threatening condition وبالتالي ممكن مايهاش
+
+277
+00:23:09,610 --> 00:23:15,080
+مايضحكشو هي في أنواع أخرى من ال bleeding وهذا صورة
+
+278
+00:23:15,080 --> 00:23:18,860
+واضحة ومعبرة جدا للهمار ثروسيش، شايفين كده الشرق
+
+279
+00:23:18,860 --> 00:23:24,640
+بقى يا شباب؟ كل هذا bleeding،
+
+280
+00:23:24,640 --> 00:23:30,710
+هذا مش مصدر، هذا جوانبشايفين كدش ال bleeding صار
+
+281
+00:23:30,710 --> 00:23:34,450
+فى الرقبة؟ شايفين الرقبة هدى طبعته؟ طبعا واحد من
+
+282
+00:23:34,450 --> 00:23:37,350
+هالنوع شايفين المفصل هان فى طفل قاعد طب ماهيش
+
+283
+00:23:37,350 --> 00:23:39,730
+الحالة يا دكتور؟ انا مش هان يعرف ال bleeding جورج
+
+284
+00:23:39,730 --> 00:23:42,870
+كده كيف؟ ماهيش الحالة في الحال ازاي؟ خلاص مضارب
+
+285
+00:23:42,870 --> 00:23:46,030
+مريضة؟ المريض هدى طبعا المفروض انه يتغير المفصل
+
+286
+00:23:46,030 --> 00:23:52,410
+لأن بعد فترة المفصل بيصير فى تليف و بيصير فش حركة
+
+287
+00:23:53,160 --> 00:23:56,380
+فى المفصل وإذا مافيش حركة فى المفصل إيش الفادة
+
+288
+00:23:56,380 --> 00:24:01,900
+منها صح فبقى بيصير ثابت عشان يرجع يعيش ثانوية ميدك
+
+289
+00:24:01,900 --> 00:24:08,720
+تقياش ميدك تغير مفصل طبعا شباب لما كل عشان نأخر
+
+290
+00:24:08,720 --> 00:24:12,080
+هذه العملية يعنى هتسير هتسير مع الزمن ده نعمل نعمل
+
+291
+00:24:12,080 --> 00:24:17,200
+نعمل لكن عشان نأخرها الأصل أنه نقلل عدد مرات
+
+292
+00:24:17,200 --> 00:24:22,560
+النزيل لإن كل ما زاد النزيل كل ما خربت الرجل أكتر
+
+293
+00:24:23,010 --> 00:24:33,330
+المريض بيتقلم عند المشاكل؟ مفصل و سابق، تلاقى، بطل
+
+294
+00:24:33,330 --> 00:24:38,170
+زي ال .. زي ال .. البرغ المصدق، بطل يعيش، يتحرك،
+
+295
+00:24:38,170 --> 00:24:41,930
+بتقلم ولا متقلمش؟ طبعا متقلم شكل فظيع جدا، مش
+
+296
+00:24:41,930 --> 00:24:46,230
+متقلم، ووصل لمرحلة بيقولك بيثبت المفصل، يثبت،
+
+297
+00:24:46,230 --> 00:24:47,930
+فبالتالي لابد من تغيير المفصل
+
+298
+00:24:53,270 --> 00:24:56,970
+طيب other types طبعا ال joint bleeding من مظاهرها
+
+299
+00:24:56,970 --> 00:25:02,690
+الشباب انه اول اشي بتبدأ tingling or bubbling ايش
+
+300
+00:25:02,690 --> 00:25:09,210
+يعني؟ لأ لأ لأ لأ هي tingling بتعرفوا النمنمة؟
+
+301
+00:25:11,660 --> 00:25:19,140
+and warmth طبيعى
+
+302
+00:25:19,140 --> 00:25:23,360
+جدا مفصل خربان شو بده يصير inflammation مظبوط شو
+
+303
+00:25:23,360 --> 00:25:27,680
+بده يصير حرارة and pain مظهر inflammation ولا لا
+
+304
+00:25:27,680 --> 00:25:33,860
+and unusual limb position ايش يعني يعني بياخد وضع
+
+305
+00:25:33,860 --> 00:25:36,340
+ثابت او غير طبيعى unusual
+
+306
+00:25:40,350 --> 00:25:46,530
+طبعا يا شباب من المشاكل المميطة، أنواع النظيفة
+
+307
+00:25:46,530 --> 00:25:49,910
+المميطة، يوم ما يشير في الhead، bleeding
+
+308
+00:25:56,350 --> 00:25:59,090
+ال bleeding يعني احنا مش حابين نخش فيها انما
+
+309
+00:25:59,090 --> 00:26:02,150
+هاريمة و هال life threatening neck and throat
+
+310
+00:26:02,150 --> 00:26:07,190
+بتبدأ تنفق الراجب تنفق تنفق المحاصلة ايش؟ asphyxia
+
+311
+00:26:07,190 --> 00:26:10,650
+بالظبط و بموت و لا بموت ايش؟ فبالتالي لازم ينتهي
+
+312
+00:26:10,650 --> 00:26:14,750
+abdominal gastro intestinal bleeding يعني نزيف
+
+313
+00:26:14,750 --> 00:26:19,690
+داخلي في المعدة في المرضى بالتحجور ماشي و في
+
+314
+00:26:19,690 --> 00:26:23,270
+المرضى بدك تنجولله دم باستمرار الى ان يقف ياش
+
+315
+00:26:23,270 --> 00:26:31,430
+النزيفثم ليو بسوسيز اللى هو اللى .. اللى زى ما
+
+316
+00:26:31,430 --> 00:26:33,970
+قلتلكوا ال softshell muscle او ال muscle اللى
+
+317
+00:26:33,970 --> 00:26:37,810
+موجودة فى هذه المنطقة هي عبارة عن .. يسموها ال ..
+
+318
+00:26:37,810 --> 00:26:43,570
+ال .. ال .. منطقة ال botox أرضية و طبعا هذه مؤلمة
+
+319
+00:26:43,570 --> 00:26:50,410
+جدا بتعمل back pain و بتعمل abdominal pain و بتعمل
+
+320
+00:26:50,410 --> 00:26:53,870
+thigh tingling و lumpness و كل الشيء
+
+321
+00:26:56,910 --> 00:27:00,130
+أنواع أخرى من نزيف ممكن يصير نزيف من ال mouth و من
+
+322
+00:27:00,130 --> 00:27:06,070
+ال nose و من الscrapes or اللي هو بيسموها minor
+
+323
+00:27:06,070 --> 00:27:15,050
+scratches اللي هي الكشطات أو السحاجات ممكن يصيره
+
+324
+00:27:15,050 --> 00:27:19,090
+أن كان يعني قليل كمان منه regia عند ال female
+
+325
+00:27:33,720 --> 00:27:38,180
+Arthritis, Chronic Pain, Muscle Atrophy,
+
+326
+00:27:38,900 --> 00:27:42,900
+Compartment Syndrome و Neurological Impairment
+
+327
+00:27:42,900 --> 00:27:51,080
+كلها عبارة عن مظاهر ليه نظيف و مظلم فهم شباب؟ حد
+
+328
+00:27:51,080 --> 00:27:57,660
+عنده سؤال؟نشوف بعض المعلومات العامة عن الهيموفيليا
+
+329
+00:27:57,660 --> 00:28:01,060
+بشكل عام، من المعلومات العامة، كلنا بنعرف نمر
+
+330
+00:28:01,060 --> 00:28:05,540
+واحد، يعني يعتبروها summary، أن هناك مرتبط بين
+
+331
+00:28:05,540 --> 00:28:09,440
+الـfactor concentration وبين ال bleeding، صح؟ كل
+
+332
+00:28:09,440 --> 00:28:11,940
+ما جالب كان factor concentration كل ما زاد في
+
+333
+00:28:11,940 --> 00:28:16,480
+الـ100%، وإن spontaneous bleeding بنشوفها في الناس
+
+334
+00:28:16,480 --> 00:28:17,760
+اللي عندهم severe hemophilia
+
+335
+00:28:20,950 --> 00:28:25,590
+فعنده ممكن يصير عنده spontaneous bleeding في أي
+
+336
+00:28:25,590 --> 00:28:33,990
+لحظة من اللحظة وإن ال males are affected لأنه no X
+
+337
+00:28:33,990 --> 00:28:37,730
+-laying process كمان
+
+338
+00:28:37,730 --> 00:28:42,110
+اتفقنا على إنه في new mutation طولت الحلقات ننجي
+
+339
+00:28:42,110 --> 00:28:45,550
+عن ال new mutation وبالتالي مش شرط دايما يكون في
+
+340
+00:28:45,550 --> 00:28:52,590
+medical historyمن الحاجات اللي كمان موجودة انه
+
+341
+00:28:52,590 --> 00:28:57,750
+غالبا المرضى الميل يشخصه في العام الأول من اياش من
+
+342
+00:28:57,750 --> 00:29:03,790
+همهم انه فيه circumcision ماشي لكن لو ما صارش
+
+343
+00:29:03,790 --> 00:29:10,750
+بتزيد امكانية احتمالية انه يصير عنده bleeding بعد
+
+344
+00:29:10,750 --> 00:29:13,770
+سن المراحقة او لما بيصل سن المراحقة ليه؟
+
+345
+00:29:21,340 --> 00:29:25,780
+أولا هذه التحديات بنشوفها .. زي ما شوفناش في السنة
+
+346
+00:29:25,780 --> 00:29:29,580
+الأولى بكون المريض غالبا عنده minor hemophilia
+
+347
+00:29:29,580 --> 00:29:36,760
+minor hemophilia طيب كيف نعالج مرضى ال hemophilia؟
+
+348
+00:29:36,760 --> 00:29:40,460
+غالبا نعالج مرضى .. أي مريض عنده نقص في شغلة معينة
+
+349
+00:29:40,460 --> 00:29:44,300
+بنحاول نعوده هده الشرطة، مظبوط؟ هذا مريض
+
+350
+00:29:44,300 --> 00:29:48,160
+hemophilia اللي عنده نقص في factor 8 أو 9، ماشي،
+
+351
+00:29:48,160 --> 00:29:51,820
+بدنا نديه هذا ال factorوالفترة يا شباب موجود اما
+
+352
+00:29:51,820 --> 00:29:59,260
+على شكل dried powder موجود في بال وبينبع بيحضر من
+
+353
+00:29:59,260 --> 00:30:06,260
+pool دي plasma ماشي او موجود في ال plasma تاخده
+
+354
+00:30:06,260 --> 00:30:10,360
+على شكل اما cryo وحناخده ان شاء الله قدها واما
+
+355
+00:30:10,360 --> 00:30:15,320
+fresh frozen plasma وفيه فترة فاهمين عليا؟ بينعطى
+
+356
+00:30:15,320 --> 00:30:19,820
+on demand مش عارفاني بالماليانماشي مش كل يوم
+
+357
+00:30:19,820 --> 00:30:24,520
+ياخدله حبة بنعطى on demand بمعنى يوم مايصير نظيف
+
+358
+00:30:24,520 --> 00:30:30,540
+يوم ماياش مايصير نظيف او اذا بده يتعرض الى تحدي
+
+359
+00:30:30,540 --> 00:30:35,100
+واحد بده يعمل عملية جراحية على سبيل المثال بدنا
+
+360
+00:30:35,100 --> 00:30:39,840
+نظبط ال factor انه قبل ماياش يخش العملية الجراحية
+
+361
+00:30:39,840 --> 00:30:45,440
+فبيجي ع المستشفى بيقول انا يوم كذا عندي عملية ماشي
+
+362
+00:30:45,940 --> 00:30:49,660
+فبنجب العملية بيومين تلاتة بتدو ياش ال factor
+
+363
+00:30:49,660 --> 00:30:55,260
+بيظبر فع نسبة ال coagration factor طبعا هذا الكلام
+
+364
+00:30:55,260 --> 00:31:00,440
+بنعطيه للناس اللي عندهم اللي هو حاجة لل factor في
+
+365
+00:31:00,440 --> 00:31:04,820
+ناس عندهم mild المرض بيكون mild فبيعطوهم بعض
+
+366
+00:31:04,820 --> 00:31:09,540
+الأدويات بيعطوهم مش لا factor ولا هدف بيعطوهم بعض
+
+367
+00:31:09,540 --> 00:31:12,600
+الأدويةوهي من أشهر الأدوية اللي بتلعب دوري كتير
+
+368
+00:31:12,600 --> 00:31:15,480
+كويس في المياه ال disease هو ال DDBB او
+
+369
+00:31:15,480 --> 00:31:20,540
+Desmopressin او بيسموه Stigmate الاسم التجارى وهذا
+
+370
+00:31:20,540 --> 00:31:27,740
+ببساطة شمال هو عبارة عن drug شو بيعمل؟ بيطلع ال
+
+371
+00:31:27,740 --> 00:31:34,020
+vom Libran من مخازنه، وين موجودة مخازنه؟ ال 100 طب
+
+372
+00:31:34,020 --> 00:31:39,020
+لما يطلع ال vom Libran من مخازنه شو بيعمل؟ ال 100
+
+373
+00:31:39,020 --> 00:31:42,940
+في ال 100هو بالتالي بيحافظ عليه ولا بيحافظش عليه؟
+
+374
+00:31:42,940 --> 00:31:47,480
+هو بالتالي بيحميه من التكسر 100% فمريض عنده ال
+
+375
+00:31:47,480 --> 00:31:53,340
+factor قليل لو طلعنا bodyguard له باستمرار يحميه
+
+376
+00:31:53,340 --> 00:31:56,880
+من التكسر، بنحافظ على ال concentration ولا لا؟ لا
+
+377
+00:31:56,880 --> 00:32:05,840
+حزارة Anti-fibrillitic agents مضادات ال fibrolysis
+
+378
+00:32:07,580 --> 00:32:10,360
+زي ال Amicar، وده عبارة عن ال drug موجود الآن
+
+379
+00:32:10,360 --> 00:32:15,760
+بانعطفه لكل حالات نزيل، بما فيهم ال post-partum
+
+380
+00:32:15,760 --> 00:32:22,380
+bleeding، يعني الستات اللي بيلدواطبعا مريض ال
+
+381
+00:32:22,380 --> 00:32:26,720
+hemophilia لابد من انه ي .. قبل ما يصل للمستشفى
+
+382
+00:32:26,720 --> 00:32:31,400
+يعملوله supportive treatment و تبدأ من القادة يعني
+
+383
+00:32:31,400 --> 00:32:36,660
+مريض وجعه و بده ينزل أول شغلة تعمله icing تحط إيش
+
+384
+00:32:36,660 --> 00:32:44,940
+تنهج على .. على المكان عشان إيش؟ عشان تقلل من مصود
+
+385
+00:32:44,940 --> 00:32:49,740
+الدم إلى منطقة الجارية، مظبوط؟ نعمل basic
+
+386
+00:32:49,740 --> 00:32:51,380
+restriction، صح؟
+
+387
+00:32:54,200 --> 00:33:02,380
+الحركة شو بتعمل؟ سبب النزيل and arresting ومن بعد
+
+388
+00:33:02,380 --> 00:33:06,340
+هيك بروح المستشفى و بدهوا بركبوله اول نمسك IV
+
+389
+00:33:06,340 --> 00:33:09,820
+وبيعطوا
+
+390
+00:33:09,820 --> 00:33:15,880
+infusion intravenous infusion و بدهوا ال factor
+
+391
+00:33:15,880 --> 00:33:23,380
+على شكل محلول ماشي ووجدوا انه
+
+392
+00:33:26,470 --> 00:33:34,250
+كل واحدة اللى هو كل factor بيحتوي على عشرين الى
+
+393
+00:33:34,250 --> 00:33:40,090
+خمسين في المية unit ال
+
+394
+00:33:40,090 --> 00:33:45,190
+factor بنعطى من عشرين الى خمسين في المية unit لكل
+
+395
+00:33:45,190 --> 00:33:49,250
+kilogram من وزن المريض ال half-life تبعته من
+
+396
+00:33:49,250 --> 00:33:53,290
+تمانية لعشرة وجاله كل واحدة ترفع factor تمانية
+
+397
+00:33:53,290 --> 00:33:58,490
+level نين في الميةكل واحدة بترفع factor تمانية
+
+398
+00:33:58,490 --> 00:34:02,410
+level 2% طبعا نبناها انطبق على تمانية انطبق على
+
+399
+00:34:02,410 --> 00:34:08,590
+تسعة بس كل ما هناك انه ال units هناك من عشرين
+
+400
+00:34:08,590 --> 00:34:12,650
+لخمسين هن من عشرين لمية half life اكتر اتناشر
+
+401
+00:34:12,650 --> 00:34:18,110
+لاربع وعشر ساعة لكن كل واحدة بترفع نسبة ال factor
+
+402
+00:34:18,110 --> 00:34:24,030
+تسعة بنسبة واحد فالمية مش اتنين فالمية حد انت ساعة
+
+403
+00:34:24,030 --> 00:34:24,390
+شباب
+
+404
+00:34:47,070 --> 00:34:50,870
+اللي هو زي ما قلتلكوا ال vial بيجي بتحضر على شكل
+
+405
+00:34:50,870 --> 00:34:55,730
+dried powder في ال vialات بتنحلوا و بتنحطوا في
+
+406
+00:34:55,730 --> 00:34:59,070
+المحلول و بتنحطوا للمريض تبدو هذه نواحي تنغيضية
+
+407
+00:34:59,070 --> 00:35:03,910
+prophylactic treatment بتنحطها للناس اللي عندهم
+
+408
+00:35:03,910 --> 00:35:13,730
+mild disease فجاتوهم DDAVB و بالتالي بنزود اللي هو
+
+409
+00:35:15,060 --> 00:35:23,660
+الوهبل براند ده هو ال DDVB الاول استعيمت نفسه هذا
+
+410
+00:35:23,660 --> 00:35:27,780
+كيف بنقطع احنا مش كتير معنين فيه لإنه برضه معلومات
+
+411
+00:35:27,780 --> 00:35:35,000
+طبية بحتة او طمرضية هذا ال Amicar من مضاعفات مرض
+
+412
+00:35:35,000 --> 00:35:38,900
+ال hemophilia مريض بيتعرض الى نقل
+
+413
+00:35:50,940 --> 00:36:00,820
+هي بطاقة A وB وC وHIV وقائمة تطوط CMV وHTV وهكذا
+
+414
+00:36:00,820 --> 00:36:06,240
+طب
+
+415
+00:36:06,240 --> 00:36:14,780
+من المضاعفات الأخرى التي تحدث هو
+
+416
+00:36:21,830 --> 00:36:28,510
+وهي بتسمى Inhibitors And
+
+417
+00:36:28,510 --> 00:36:35,930
+this antibody can be either O2 or Allo Antibody
+
+418
+00:36:35,930 --> 00:36:40,470
+ماشي؟ إيش يعني O2 Antibody؟ يعني Antibody من نفس
+
+419
+00:36:40,470 --> 00:36:46,350
+الجسم لنفس ال factor تبعه Or Allo يعني Antibody هو
+
+420
+00:36:46,350 --> 00:36:54,030
+بيكونها لكل factor بيجي من بقىمفهوم عليا either
+
+421
+00:36:54,030 --> 00:36:59,410
+auto or allo وبالتالي أول ما يخش ال factor أو أول
+
+422
+00:36:59,410 --> 00:37:03,050
+ما يشوف ال factor هذا ال antibody شو بيعمله؟ وإيش
+
+423
+00:37:03,050 --> 00:37:08,810
+بيعمل؟ بيعمله blocking يعني .. يعني inhibition
+
+424
+00:37:08,810 --> 00:37:14,790
+يعني عشان هيك إيش سموهم؟ inhibitors الناس اللي
+
+425
+00:37:14,790 --> 00:37:20,670
+بيصير عندهم هذا الاشي غالبا
+
+426
+00:37:23,250 --> 00:37:29,950
+بيفرقوهم عن ال traditional hemophilia فبيحطوهم تحت
+
+427
+00:37:29,950 --> 00:37:33,570
+category بيسموه acquired hemophilia acquired
+
+428
+00:37:33,570 --> 00:37:37,970
+hemophilia عشان هيك الناس اللي بيكونوا inhibitors
+
+429
+00:37:37,970 --> 00:37:43,270
+او اللي عندهم inhibitors عندهم acquired hemophilia
+
+430
+00:37:43,270 --> 00:37:49,030
+عندهم ايه؟ acquired hemophilia مش traditional or
+
+431
+00:37:49,030 --> 00:37:49,590
+hereditary
+
+432
+00:37:53,040 --> 00:37:58,840
+برد اكتسبه المريض اكتسابا اما هو كون antibody
+
+433
+00:37:58,840 --> 00:38:04,440
+لاحقا لل factor واما كون antibody ل factor اصلا مش
+
+434
+00:38:04,440 --> 00:38:08,720
+موجود عنده لما يخش بيعتبره ك antigen و مبدعيش
+
+435
+00:38:08,720 --> 00:38:13,380
+تتكون بالنسبة في ال hemophilia ايه؟ بنشوفها
+
+436
+00:38:13,380 --> 00:38:18,600
+بالنسبة اكتر بكثير من ال hemophilia B بقالوا ال
+
+437
+00:38:18,600 --> 00:38:21,740
+prevalence من 20 ل 30% من حالات ال hemophilia
+
+438
+00:38:37,320 --> 00:38:43,380
+لأ هي مجرد ما يكون Antibody بصير أكبر لما هي مش
+
+439
+00:38:43,380 --> 00:38:48,420
+hereditary يعني مش شيء مكتسع .. مورّط وانما شيء ما
+
+440
+00:38:48,420 --> 00:38:53,000
+إيه؟ مكتسع طيب،
+
+441
+00:38:53,000 --> 00:38:59,160
+الأمراض اللي بيعمل Hepatitis A وB وC HIV
+
+442
+00:38:59,160 --> 00:39:05,900
+و
+
+443
+00:39:05,900 --> 00:39:12,270
+..المعلومات المتبقية هذه أنا مش حابب أخش فيها هذه
+
+444
+00:39:12,270 --> 00:39:18,890
+يعني معلومات عامة بتحكي على ال site social issue
+
+445
+00:39:18,890 --> 00:39:23,370
+يعني كيفية تعمل على ال hemophilia من ناحية نفسية
+
+446
+00:39:23,370 --> 00:39:30,490
+من ناحية اجتماعية من ناحية تمريضية كل هذه الأمور
+
+447
+00:39:30,490 --> 00:39:37,510
+ثم هدولهذا بيسموه ال hemophilia team فريق ال
+
+448
+00:39:37,510 --> 00:39:41,630
+hemophilia لازم يتكون من هذه الناس لازم يكون مريض
+
+449
+00:39:41,630 --> 00:39:47,490
+او عائلة صح؟ ايه؟ لازم يكون مريض طبيب hematology
+
+450
+00:39:47,490 --> 00:39:56,110
+شخص ثم nurse طبق ثم social worker لما مريض ال
+
+451
+00:39:56,110 --> 00:40:00,840
+hemophilia هو مريضبيمارس حياته طبيعيا جدا جدا جدا
+
+452
+00:40:00,840 --> 00:40:04,900
+كل ما هناك انه عنده هالنقطة هالى اللى ممكن يتعرضه
+
+453
+00:40:04,900 --> 00:40:08,320
+لنزيفة اي لحظة من اللحظات وبالتالي دايما بيحس حاله
+
+454
+00:40:08,320 --> 00:40:12,120
+في خطر دائم مريض من هالنور من هالنور قد يتعرض
+
+455
+00:40:12,120 --> 00:40:16,480
+لضغوط نفسية ده الطبيعى فبدنا social worker ثم
+
+456
+00:40:16,480 --> 00:40:21,680
+physical therapist علاج طبيعى طب ما احنا عارفين تا
+
+457
+00:40:21,680 --> 00:40:28,080
+وقولنا المفصل بغربواذا خير بيهاش حركته بتثبت مظبوط
+
+458
+00:40:28,080 --> 00:40:32,220
+فبده دايما إيهاش علاج طبيعي عشان إيهاش نلين
+
+459
+00:40:32,220 --> 00:40:37,940
+المفاصل Otopedist طبيب عظام طبيعي لإنه طبيب عظام
+
+460
+00:40:37,940 --> 00:40:43,520
+لإنه ممكن نحتاج إلى تغيير مفصل صح؟ مبرر ماريكير
+
+461
+00:40:43,520 --> 00:40:50,060
+أكيد وinfectious disease هذا واحد بتعرض لنقل دم أو
+
+462
+00:40:50,060 --> 00:40:54,490
+بلاءفاكتور باستمرار فانتقل يصير عنده infectious
+
+463
+00:40:54,490 --> 00:41:00,130
+disease وارد ثم genetics وده مهم جدا genetics ليه؟
+
+464
+00:41:00,130 --> 00:41:04,910
+لأنه بتعمل family ب degree تشوف هنوء اه فبدا
+
+465
+00:41:04,910 --> 00:41:09,330
+consultation pharmacy لازم يكون في صدرية في مركز
+
+466
+00:41:09,330 --> 00:41:15,170
+من هنوء وبالتالي بدنا pharmacist ثم dental work
+
+467
+00:41:15,170 --> 00:41:18,450
+بدنا dentist and hepatologist
+
+468
+00:41:21,980 --> 00:41:29,960
+لأنه الكبد وارد جدا يصير في عنده level of virus،
+
+469
+00:41:29,960 --> 00:41:34,120
+كيف يا بابا؟ مختبئ كده الان؟ ال hematologist ايش
+
+470
+00:41:34,120 --> 00:41:39,120
+معناته؟ شاب طبيب يعني دائما وانما كمان ممكن يكون
+
+471
+00:41:39,120 --> 00:41:46,010
+مخصائي، طبعا احنا الأساس في التشخيصطبعا involved
+
+472
+00:41:46,010 --> 00:41:50,250
+hemophilia centers في العلاج هي و في ال education
+
+473
+00:41:50,250 --> 00:41:53,410
+و في ال research و في ال out research يعني حاجات
+
+474
+00:41:53,410 --> 00:41:59,750
+كتيرة ممكن و حد هيشياكى فيها، حد عنده سؤال؟ no
+
+475
+00:41:59,750 --> 00:42:00,390
+question؟
+
diff --git a/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/63Bbug1nURs.srt b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/63Bbug1nURs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b9505d1621ffa96440bd996a5e20cae6c590be62
--- /dev/null
+++ b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/63Bbug1nURs.srt
@@ -0,0 +1,1687 @@
+1
+00:00:20,870 --> 00:00:23,610
+أعوذ بالله السميع العليم من الشيطان الرجيم بسم 
+
+2
+00:00:23,610 --> 00:00:26,950
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة 
+
+3
+00:00:26,950 --> 00:00:30,930
+والسلام على رسولنا الكريم وبعد طبعا يا أخوات في 
+
+4
+00:00:30,930 --> 00:00:36,150
+المحاضرة السابقة احنا تحدثنا عن يعني المظاهر أو 
+
+5
+00:00:36,150 --> 00:00:40,370
+خصائص أو التوازن والتناسق الموجود في النظم 
+
+6
+00:00:40,370 --> 00:00:45,010
+الإسلامية وقلنا تظهر شمولية النظم الإسلامية في 
+
+7
+00:00:45,010 --> 00:00:52,690
+توازن وتناسق بحيث يعني ركزت على كل هذه الجوانب قلنا 
+
+8
+00:00:52,690 --> 00:00:57,530
+يا أخوات يعني توازن بين حياة الأفراد وحياة المجتمع 
+
+9
+00:00:57,530 --> 00:01:02,190
+شرحنا ذلك وبيّنا وضربنا الأمثلة الكثيرة توازن بين 
+
+10
+00:01:02,190 --> 00:01:06,520
+متطلبات الروح ورغبات الجسد توازن بين الواقعية 
+
+11
+00:01:06,520 --> 00:01:10,220
+والمثالية توازن بين الاهتمام بشؤون الدنيا وشؤون 
+
+12
+00:01:10,220 --> 00:01:15,280
+الآخرة وقلنا قول الله سبحانه وتعالى وابتغي فيما 
+
+13
+00:01:15,280 --> 00:01:20,780
+أتيك الله الدار الآخرة ولا تنسى نصيبك من الدنيا 
+
+14
+00:01:20,780 --> 00:01:25,200
+وقلنا ما أتيك الله يعني كل شيء الوقت الصحة الفراغ 
+
+15
+00:01:25,200 --> 00:01:32,730
+النشاط الشباب المال كل شيء يجب أن يوجه باتجاه 
+
+16
+00:01:32,730 --> 00:01:37,470
+الآخرة لكن الجزء الثاني من الآية أوضح ولا تنسى 
+
+17
+00:01:37,470 --> 00:01:43,250
+نصيبك من الدنيا يعني زي ما بقول أخونا الكريم يعني 
+
+18
+00:01:43,250 --> 00:01:48,770
+خذ راحتك ولازم تعيش دنياتك بأريحية وتعيش دنياتك 
+
+19
+00:01:48,770 --> 00:01:56,750
+كما هو في الوضع الطبيعي لأن في ناس يا أخوات يعني قد 
+
+20
+00:01:56,750 --> 00:02:00,770
+تكون العبادة تغلب على حياته اليومية وعلى حياته 
+
+21
+00:02:00,770 --> 00:02:06,590
+الشخصية وقد يعني مثلا لا يعمل بحجة أنه يعني يبذل 
+
+22
+00:02:06,590 --> 00:02:11,810
+الجهد والوقت في طاعة الله ومن أجل الآخرة، ليس هذا 
+
+23
+00:02:11,810 --> 00:02:16,930
+الفهم الصحيح للإسلام الفهم الصحيح للإسلام يعني يبين 
+
+24
+00:02:16,930 --> 00:02:21,590
+التوازن بين الدنيا والآخرة التوازن في كل هذه 
+
+25
+00:02:21,590 --> 00:02:25,210
+المجالات اللي احنا درسناها توازن بين الإسراف 
+
+26
+00:02:25,210 --> 00:02:30,330
+والتقشف يعني مش معناته الكلام إن أنا إيمانياتي 
+
+27
+00:02:30,330 --> 00:02:34,450
+عالية وعايز أكون من السعداء في الآخرة أروح أنفق 
+
+28
+00:02:34,450 --> 00:02:39,530
+مالي كله وبعد هيك أروح أتكفف في الناس أو أنفق مالي 
+
+29
+00:02:39,530 --> 00:02:44,620
+على الفقراء والمساكين وأهل بيتي أولى إذا قال لك يجب 
+
+30
+00:02:44,620 --> 00:02:49,560
+أن يكون توازن بين الإنفاق الذي يتقرب به إلى الله 
+
+31
+00:02:49,560 --> 00:02:55,880
+الإنفاق الذي فيه سبيل الله ويتقرب به إلى الله لازم 
+
+32
+00:02:55,880 --> 00:02:59,300
+يكون فيه توازن ما أروحش أنفق مال وأتكفف في الناس 
+
+33
+00:02:59,300 --> 00:03:04,480
+والذين إذا أنفقوا لم يسرفوا ولم يقتروا وكان بين 
+
+34
+00:03:04,480 --> 00:03:11,610
+ذلك قوامة توازن بين حقوق الله وحقوق النفس القصة 
+
+35
+00:03:11,610 --> 00:03:15,470
+المشهورة لما سمع النبي صلى الله عليه وسلم الثلاثة 
+
+36
+00:03:15,470 --> 00:03:20,210
+نفر واحد بيقول أنا لا أتزوج النساء أبدا يعني سأمضي 
+
+37
+00:03:20,210 --> 00:03:25,330
+وأفرغ أوقاتي كلها للعبادة واحد بيقولك إيه أنا 
+
+38
+00:03:25,330 --> 00:03:31,150
+أصوم ولا أفطر والثالث يقول وإنا أقوم الليل ولا 
+
+39
+00:03:31,150 --> 00:03:38,340
+أرقد فقال لهم النبي صلى الله عليه وسلم أما وإني أما 
+
+40
+00:03:38,340 --> 00:03:44,300
+والله إني لأخشاكم لله وأتقاكم إليه ولكني أصوم 
+
+41
+00:03:44,300 --> 00:03:50,240
+وأفطر وأصلّي وأرقد وأتزوج النساء وهذه سنتي فمن رغب 
+
+42
+00:03:50,240 --> 00:03:56,820
+عن سنتي فليس مني إذن يا أخوات يعني هذه كل مظاهر من 
+
+43
+00:03:56,820 --> 00:04:02,400
+مظاهر التوازن أيضًا النظم الإسلامية فيها توازن في 
+
+44
+00:04:02,400 --> 00:04:09,370
+معالجتها وتنظيمها لكل جوانب الحياة يعني في شتى 
+
+45
+00:04:09,370 --> 00:04:15,850
+المجالات وشتى النواحي النظم الإسلامية يعني تشير أو 
+
+46
+00:04:15,850 --> 00:04:22,750
+تدل على التوازن أيضا بتوازن بينها وتوازن في كل 
+
+47
+00:04:22,750 --> 00:04:28,030
+المتقابلات يعني كل الأمور المتقابلة لا تتعارض وإنما 
+
+48
+00:04:28,030 --> 00:04:35,710
+تسير بتوازن وتناسق إلى غير ذلك اليوم سنتحدث في 
+
+49
+00:04:35,710 --> 00:04:40,510
+خاصية جديدة الخاصية الرابعة هي العموم والعالمية زي 
+
+50
+00:04:40,510 --> 00:04:44,090
+ما أنتم شايفين يا أخوات يعني لو قلنا ما المقصود 
+
+51
+00:04:44,090 --> 00:04:47,750
+بالعموم والعالمية فضلاً 
+
+52
+00:04:50,320 --> 00:04:53,780
+يعني عبارة عن أن النظم الإسلامية لا تختص بجيل دون 
+
+53
+00:04:53,780 --> 00:04:59,880
+جيل أو طائفة دون طائفة؟ تمام 
+
+54
+00:04:59,880 --> 00:05:07,120
+العموم والعالمية يعني أن النظم الإسلامية لا تختص 
+
+55
+00:05:07,120 --> 00:05:12,640
+بقوم دون قوم ولا بجيل دون جيل يعني ما بتنظم أحوال 
+
+56
+00:05:12,640 --> 00:05:19,810
+قوم معين أو بتنظم أحوال جيل معين أو بيئة معينة أو 
+
+57
+00:05:19,810 --> 00:05:24,570
+مكان معين لأ النظم الإسلامية يعني هذه الخاصية 
+
+58
+00:05:24,570 --> 00:05:29,330
+أنتم ملاحظين الخصائص أخوات اللي اتعرضنا لها من 
+
+59
+00:05:29,330 --> 00:05:35,420
+البداية لحد تلقاه بتلاقيها مترابطة بتلاقيها بتكمل 
+
+60
+00:05:35,420 --> 00:05:40,800
+بعضها بعضا، بتلاقيها متشابكة مع بعضها البعض، يعني 
+
+61
+00:05:40,800 --> 00:05:45,640
+مثلا العموم العالمية متشابكة مع الشمول والتوازن، 
+
+62
+00:05:45,640 --> 00:05:49,400
+إذا العموم العالمية المقصودة بها أنها لا تختصّ قوم 
+
+63
+00:05:49,400 --> 00:05:54,960
+دون قوم ولا بجيل دون جيل ولا بجنس دون جنس ولا 
+
+64
+00:05:54,960 --> 00:05:59,640
+بإقليم دون إقليم ولا طبقة دون طبقة يعني ما راحتش 
+
+65
+00:05:59,640 --> 00:06:04,360
+النظم الإسلامية تنظم طبقة أو تعتني بطبقة الأغنياء 
+
+66
+00:06:04,360 --> 00:06:10,700
+وتترك الفقراء أو العلماء وتترك طبقة العمال وإنما 
+
+67
+00:06:10,700 --> 00:06:17,840
+جاءت عامة أي بمعنى لكل الأقوام لكل الأجناس ولكل 
+
+68
+00:06:17,840 --> 00:06:23,750
+المستويات فلماذا تميزت النظم الإسلامية بالعموم 
+
+69
+00:06:23,750 --> 00:06:29,310
+والعالمية؟ لماذا تميزت النظم الإسلامية بالعموم 
+
+70
+00:06:29,310 --> 00:06:35,750
+والعالمية؟ لأن الرسول صلى الله عليه وسلم قُتل 
+
+71
+00:06:35,750 --> 00:06:40,370
+للعالم كافة، فيقول سبحانه وتعالى ما أرسلناك إلا كافة 
+
+72
+00:06:40,370 --> 00:06:43,950
+للناس، بمعنى أنه قُتل بدستور كامل شامل، ليس لفئة 
+
+73
+00:06:43,950 --> 00:06:47,990
+العرب أو لفئة أو قبيلة من الناس، إنما قُتل للناس 
+
+74
+00:06:47,990 --> 00:06:54,180
+كافة تمام يعني ليش اجت النظم الإسلامية أخوات؟ لماذا 
+
+75
+00:06:54,180 --> 00:06:58,420
+تميزت النظم الإسلامية بالعموم والعالمية؟ قال لك 
+
+76
+00:06:58,420 --> 00:07:03,800
+لأنها لا تختص بقوم دون قوم أو بشيل دون شيل أو جنس 
+
+77
+00:07:03,800 --> 00:07:08,780
+أو طبقة أو قلين بل هي نظم ذات صبغة عالمية لا يحدها 
+
+78
+00:07:08,780 --> 00:07:15,630
+أو يقيدها شيء كمان لتكون للعالمين دستورا ليش أشهد 
+
+79
+00:07:15,630 --> 00:07:20,690
+النظم الإسلامية يعني عامة لتكون للعالمين دستورا 
+
+80
+00:07:20,690 --> 00:07:27,170
+ومنهج حياة وأسلوب حياة وكمان علشان تنظر الناس 
+
+81
+00:07:27,170 --> 00:07:34,060
+جميعا نظرة إخاء ومساواة جاءت النظم الإسلامية تدل 
+
+82
+00:07:34,060 --> 00:07:38,960
+على العموم العالمية لأنها تؤكد على وحدة الأصل فيما 
+
+83
+00:07:38,960 --> 00:07:44,670
+بينهم وصلة القربى والرحم يا أيها الناس التقوى ربكم 
+
+84
+00:07:44,670 --> 00:07:50,170
+الذي خلقكم من نفس واحدة وخلق منها زوجها وبث منهما 
+
+85
+00:07:50,170 --> 00:07:54,490
+رجالا كثيرا ونساء يعني الخلق جميعا في الأصل 
+
+86
+00:07:54,490 --> 00:08:00,350
+مخلوقين من أب واحد ومن أم واحدة تربطهم العلاقات، 
+
+87
+00:08:00,350 --> 00:08:07,600
+تربطهم المصالح المختلفة إذا بهذا المنهج النظم 
+
+88
+00:08:07,600 --> 00:08:14,100
+الإسلامية تشجع وتحث على توطيد العلاقة بين الناس 
+
+89
+00:08:14,100 --> 00:08:20,580
+على اختلافهم يا أيها الناس إن خلقناكم من ذكر وأنثى 
+
+90
+00:08:20,580 --> 00:08:27,560
+وجعلناكم قبائل شعوبا وقبائلا لتعرفوا أن أقربكم عند 
+
+91
+00:08:27,560 --> 00:08:32,530
+الله أتقاكم والنبي صلى الله عليه وسلم يقول يبعث 
+
+92
+00:08:32,530 --> 00:08:38,290
+للرسول أو النبي إلى قوم أو إلى فئة ولكن يبعثه 
+
+93
+00:08:38,290 --> 00:08:44,650
+للعالمين كافة للناس كافة بشيرا ونذيرا الآن أخوات 
+
+94
+00:08:44,650 --> 00:08:52,450
+صار في التباس بين مفهوم العموم والعالمية ومفهوم 
+
+95
+00:08:52,450 --> 00:09:00,470
+العولمة كثير في ناس بيظنوا أنه يعني في اتحاد في هذا 
+
+96
+00:09:00,470 --> 00:09:06,630
+أو هذان المفهومين وطبعا كلام هذا لا يستقيم يعني في 
+
+97
+00:09:06,630 --> 00:09:10,790
+فرق كبير بين العموم والعالمية اللي أشارت إليه النظم 
+
+98
+00:09:10,790 --> 00:09:13,950
+الإسلامية والتي امتازت بها النظم الإسلامية وبين 
+
+99
+00:09:13,950 --> 00:09:19,300
+العولمة إيش عايزة تحكي؟ إن العولمة بتدرس تجمع جميع 
+
+100
+00:09:19,300 --> 00:09:25,720
+الأنظمة في هذا التسيطرة على العالم تختص بتاعة 
+
+101
+00:09:25,720 --> 00:09:30,940
+معينة أو في قوة معينة ممكن كمان تفضل تفضل العولمة 
+
+102
+00:09:30,940 --> 00:09:34,840
+هي أتت لتوحيد النظم الأساسية في الكون للناس مع 
+
+103
+00:09:34,840 --> 00:09:38,660
+الاحتفاظ بخصوصية كل بلد وكل مكان العالمية عالمية 
+
+104
+00:09:38,660 --> 00:09:41,660
+عالمية ما أنتِ بحكي العالمية لكن العولمة هي بتحكي 
+
+105
+00:09:41,660 --> 00:09:45,460
+لانفتاح العام بدون حفاظ على خصوصية المكان في الشوق 
+
+106
+00:09:59,850 --> 00:10:04,830
+العالمية مصدرها اللي هو النظم الإسلامية والعولمة 
+
+107
+00:10:04,830 --> 00:10:09,060
+مصدرها اللي هي النظم الوضعية الآن يا أخوات كلامكم 
+
+108
+00:10:09,060 --> 00:10:13,700
+اللي حكيتوه كله جميل لكن خلّينا يعني نضفي مزيدا من 
+
+109
+00:10:13,700 --> 00:10:18,940
+الإيضاح على الفرق بين العموم والعالمية من جهة وبين 
+
+110
+00:10:18,940 --> 00:10:24,260
+العولمة من جهة أخرى احنا قاعدين حتى هذا الكلام أو 
+
+111
+00:10:24,260 --> 00:10:29,480
+هذه المبادئ يعني تفهم من الخصائص التي تم دراستها 
+
+112
+00:10:29,480 --> 00:10:36,590
+الخصائص اللي درسناها بينت وأوضحت إن هذه النظم 
+
+113
+00:10:36,590 --> 00:10:43,050
+الإسلامية صالحة لكل زمان ولكل مكان ولكل شخص و
+
+114
+00:10:43,050 --> 00:10:48,150
+لكل زمن وللعادات والتقاليد واختلاف الأجناس و 
+
+115
+00:10:48,150 --> 00:10:51,790
+اختلاف الألوان واختلاف الطبائع واختلاف العادات 
+
+116
+00:10:52,820 --> 00:10:58,000
+النظم الإسلامية جاءت شاملة تنظم حياة الفرد وحياة 
+
+117
+00:10:58,000 --> 00:11:01,840
+المجتمع وحياة الطفل وحياة المرأة وحياة المؤسسة 
+
+118
+00:11:01,840 --> 00:11:10,620
+وحياة المجتمع جاءت تعتمد الأشياء 
+
+119
+00:11:10,620 --> 00:11:15,240
+الحسنة والعادات والأعراف التي تتماشى مع النظم 
+
+120
+00:11:15,240 --> 00:11:20,750
+الإسلامية ولا تتصادم معها أقرتها واعتمدتها راعت 
+
+121
+00:11:20,750 --> 00:11:26,250
+عادات الناس راعت ثقافة الناس راعت مبادئ الناس اللي 
+
+122
+00:11:26,250 --> 00:11:31,650
+بتمسك بها مادامت لا تتصادم مع القواعد الشرعية 
+
+123
+00:11:31,650 --> 00:11:37,490
+أقرتها تعاملت مع الروح تعاملت مع الجسد صح؟ اللي 
+
+124
+00:11:37,490 --> 00:11:41,270
+درسناها قبلها تتعامل مع الروح تتعامل مع الجسد 
+
+125
+00:11:41,270 --> 00:11:46,130
+بتنظر إلى الأمور نظرة مجردة لكن تتعامل مع الجسد 
+
+126
+00:11:46,130 --> 00:11:52,410
+ومع الضمير، مش هاي هاي الميزات والخصائص اللي درسناها
+
+127
+00:11:52,410 --> 00:11:58,230
+فيما سبق، يعني ما بتيجيش تلغي أعراف الناس وتقيد 
+
+128
+00:11:58,230 --> 00:12:03,470
+حرياتهم وتجبرهم على نمط معين سواء سياسي أو اجتماعي
+
+129
+00:12:03,470 --> 00:12:07,930
+أو اقتصادي أو أخلاقي أو كذا، مادام هذه الأمور لا
+
+130
+00:12:07,930 --> 00:12:13,690
+تتصادم مع الشريعة، اعتمدتها وأقرتها واعتبرتها مشروعيا
+
+131
+00:12:13,690 --> 00:12:16,110
+وإيه لكم الخيار، أنتم أحرار
+
+132
+00:12:19,170 --> 00:12:24,230
+الرجل يلبس باكستاني، يلبس جلبية، يلبس بنطلون، يلبس
+
+133
+00:12:24,230 --> 00:12:29,350
+جميص، هو حر ما دام يتحرك في دائرات المباح، هو حر
+
+134
+00:12:29,350 --> 00:12:34,290
+هذا يرجع إلى العادات والتقاليد والأعراف في الناس
+
+135
+00:12:34,290 --> 00:12:38,710
+اللي هم بتشنجهم، بيقول لك لبس السنة الجلبية و بس أو
+
+136
+00:12:38,710 --> 00:12:43,530
+الباكستاني و بس، ما الدليل على ذلك؟ كل هذه الأنواع من
+
+137
+00:12:43,530 --> 00:12:47,610
+اللباس مُعتَبَرة ومُقَرَّة شرعًا، والأمر يرجع إلى
+
+138
+00:12:47,610 --> 00:12:51,890
+الأعراف، الأعراف اللي بتحدد، فالإسلام أقر الأعراف
+
+139
+00:12:51,890 --> 00:12:58,750
+إلا أن تتناقض مع قواعد الشريعة، هذا ما يتعلق بالنظم
+
+140
+00:12:58,750 --> 00:13:05,690
+الإسلامية من جهة، أما العولمة، بدا تلغي كل حاجة من
+
+141
+00:13:05,690 --> 00:13:11,270
+عداد وتقاليد وأعراف اجتماعية وأعراف اقتصادية و
+
+142
+00:13:11,270 --> 00:13:19,030
+أعراف سياسية وأعراف أخلاقية، بدا تلغي كل شيء عند
+
+143
+00:13:19,030 --> 00:13:24,290
+الإنسان وتمشيه على إطار معين، على نمط معين، على
+
+144
+00:13:24,290 --> 00:13:29,960
+عداد معينة، على تقاليد معينة، تقاليد مين؟ تقاليد
+
+145
+00:13:29,960 --> 00:13:34,220
+الولايات المتحدة الأمريكية، تقاليد الأمريكان عشان
+
+146
+00:13:34,220 --> 00:13:39,900
+نحن نكون عصريين، لابد أن نستخدم أسلوب America في
+
+147
+00:13:39,900 --> 00:13:45,320
+تنصيب الحاكم، لابد لنا أن نستخدم الديمقراطية، لابد 
+
+148
+00:13:45,320 --> 00:13:49,760
+لنا أن نستخدم، نعتمد العادات والتقاليد المجتمعية
+
+149
+00:13:49,760 --> 00:13:56,850
+هيك عاوزين العالم كله يصير، عاوزين يجعل العالم يسير
+
+150
+00:13:56,850 --> 00:14:05,180
+على مشروع أو هدف أو نمط حياة، يعني مصوخ أو موجه
+
+151
+00:14:05,180 --> 00:14:11,160
+باتجاه المجتمع الأمريكي، بسيئاته وحسناته طبعًا، نحن
+
+152
+00:14:11,160 --> 00:14:15,400
+ما بنرفض هذا الكلام جملة وتفصيلاً، نحن كيف عشان
+
+153
+00:14:15,400 --> 00:14:20,920
+نكون موضوعيين وعشان نعمل بمقتضى التوازن الموجود
+
+154
+00:14:20,920 --> 00:14:24,140
+عندنا في شريعتنا وفي النظم الإسلامية، بنقول ما
+
+155
+00:14:24,140 --> 00:14:29,260
+يتوافق من مبادئكم وأفكاركم، ما يتوافق مع الإسلام
+
+156
+00:14:29,260 --> 00:14:36,400
+فأهلاً وسهلاً، وما لا يتوافق مع الإسلام، ما بدناش نكون
+
+157
+00:14:36,400 --> 00:14:42,800
+عصريين وبدناش نركب سلم للعولمة، ما بدناها ما دام
+
+158
+00:14:42,800 --> 00:14:46,060
+تتعارض مع ديننا ومع أخلاقنا ومع مبادئنا ومع 
+
+159
+00:14:46,060 --> 00:14:51,200
+عاداتنا ومع تقاليدنا ومع أعرافنا، ما بدناها، لكن
+
+160
+00:14:51,200 --> 00:14:56,700
+للأسف اليوم في العالم العربي يظنون أن كل ما يصلح
+
+161
+00:14:56,700 --> 00:15:00,640
+في أمريكا يصلح للعالم العربي، يصلح للعالم الإسلامي
+
+162
+00:15:02,120 --> 00:15:06,380
+عاوزين يطبقوا التجربة الأمريكية في كل شيء؟ طب يا
+
+163
+00:15:06,380 --> 00:15:09,940
+عم، الناس دي عندهم إمكانيات، عندهم عادات، عندهم
+
+164
+00:15:09,940 --> 00:15:14,320
+تقاليد، فيه تميّز، فيه اختلاف بيننا وبينهم، بلاش 
+
+165
+00:15:14,320 --> 00:15:18,080
+هذا الكلام، ممكن يتصادم مع مبادئ شريعتنا ومبادئ 
+
+166
+00:15:18,080 --> 00:15:23,220
+النظم الإسلامية في الإسلام، إذا جاك يا أخوات،
+
+167
+00:15:23,220 --> 00:15:29,360
+مفهوم العولمة هي الحالة التي تقوم فيها عملية تغيير
+
+168
+00:15:29,360 --> 00:15:35,520
+الأنماط والنظم الاقتصادية والثقافية والاجتماعية
+
+169
+00:15:35,520 --> 00:15:40,080
+ومجموعة القيم والعداد السائدة وإزالة الفروق
+
+170
+00:15:40,080 --> 00:15:45,990
+الدينية والقومية والوطنية في إطار تدويل النظام
+
+171
+00:15:45,990 --> 00:15:49,530
+الرأسمالي الحديث وفق الرؤية الأمريكية المهيمنة
+
+172
+00:15:49,530 --> 00:15:54,590
+والتي تزعم أنها سيدة الكون وحامية النظام العالمي
+
+173
+00:15:54,590 --> 00:16:04,490
+الجديد، هذا مفهوم العولمة بالمقارنة، يتبين لنا إيش
+
+174
+00:16:04,490 --> 00:16:11,330
+أوجه الاختلاف وأوجه الاتفاق بين العموم والعالمية
+
+175
+00:16:11,330 --> 00:16:29,040
+وبين مفهوم العولمة، تفضلي يعني
+
+176
+00:16:29,040 --> 00:16:34,160
+أختكم بتقول أن العموم، العالمية، النظم الإسلامية
+
+177
+00:16:34,160 --> 00:16:40,380
+يعني صالحة لكل العالم، ليش صالحة لكل العالم؟ بتحترم
+
+178
+00:16:40,380 --> 00:16:47,480
+يعني عاداتهم وتقاليدهم، ما لم تتعارض التي تتعارض مع
+
+179
+00:16:47,480 --> 00:16:52,360
+الشرع بتلغيها، والتي لا تتعارض مع الشرع تبقي عليها
+
+180
+00:16:52,360 --> 00:16:57,120
+حتى الإسلام يا أخوتي، عندما جاء الإسلام وجد العرب
+
+181
+00:16:57,120 --> 00:17:03,120
+في الجاهلية ما كانوا يعني شرًّا محدّدًا، كانوا عندهم أشياء
+
+182
+00:17:03,120 --> 00:17:07,700
+مثل إيش؟ كان عندهم كرم، أختكم بتقول كان عندهم كرم
+
+183
+00:17:07,700 --> 00:17:13,380
+كان عندهم شجاعة، كان عندهم نخوة، كان عندهم إكرام 
+
+184
+00:17:13,380 --> 00:17:18,510
+الضيف، على سبيل هذا طبعًا في العادات والتقاليد حتى في
+
+185
+00:17:18,510 --> 00:17:23,390
+سبيل التشريع، على سبيل التشريع كان عندهم تشريعات في
+
+186
+00:17:23,390 --> 00:17:28,230
+الجاهلية سائدة، اعتمدها القرآن الكريم واعتمدت تشريع
+
+187
+00:17:28,230 --> 00:17:38,910
+الإسلامية، مثل الدية، ديات المقتول مائة ناقة، هذه
+
+188
+00:17:38,910 --> 00:17:42,030
+الدية تشريع جاهلي، في الجاهلية كانوا ماشيين عليه
+
+189
+00:17:43,360 --> 00:17:48,020
+واعتمدته الشريعة الإسلامية وأقرته وأثبتته وتحول
+
+190
+00:17:48,020 --> 00:17:54,980
+الحكم إلى حكم شرعي بالنص، وأصبح دية المقتول خطأً، 
+
+191
+00:17:54,980 --> 00:18:02,530
+مائة من القبل، 100 ناقة، 100 من القبل، إذا بنقول شوفوا
+
+192
+00:18:02,530 --> 00:18:06,510
+كيف الشريعة الإسلامية يعني لم تتناقض مع الأعراف، لم
+
+193
+00:18:06,510 --> 00:18:12,670
+تتناقض مع العادات، احترمت التوجهات الإنسان، إنما
+
+194
+00:18:12,670 --> 00:18:16,790
+غيّرت عقيدة الإنسان، العقيدة مش فيها اجتهاد، مش فيها
+
+195
+00:18:16,790 --> 00:18:21,230
+زيادة ولا نقص، العقيدة لازم تأخذ كما هي، لكن العادات
+
+196
+00:18:21,230 --> 00:18:27,320
+والتقاليد والأعراف فيها مرونة، فيها مرونة، ما دام
+
+197
+00:18:27,320 --> 00:18:32,280
+المجتمع أقرها ولا تتصادم مع الدين فأهلاً وسهلاً،
+
+198
+00:18:32,280 --> 00:18:38,060
+لكن العولمة ما فيش عندها هذه المراعاة، بيقول لك إيه؟
+
+199
+00:18:38,060 --> 00:18:46,220
+تغيير، تغيير، تغيير، كل الأنماط والنظم الاقتصادية
+
+200
+00:18:47,100 --> 00:18:50,860
+يعني بدهم إياها نتعامل بالربا عشان نكون عصريين
+
+201
+00:18:50,860 --> 00:18:56,680
+والثقافية، ثقافة المجتمع، الثقافة اللي بيغلب عليها
+
+202
+00:18:56,680 --> 00:18:59,980
+الطبيعة الإسلامية ما بدهم إياها، بدهم الثقافة
+
+203
+00:18:59,980 --> 00:19:05,040
+المتحللة من الأخلاق، الثقافة المتحللة من الآداب
+
+204
+00:19:05,040 --> 00:19:07,540
+العامة والاجتماعية
+
+205
+00:19:09,740 --> 00:19:15,600
+تفكك أسر، يعني تفكك أسر، عدم احترام، الزواج عندهم
+
+206
+00:19:15,600 --> 00:19:20,440
+غير منظم، الطلاق غير منظم، يعني ممكن على سبيل
+
+207
+00:19:20,440 --> 00:19:25,460
+المثال، ممنوع الرجل يطلق زوجته، ممنوع الرجل يطلق
+
+208
+00:19:25,460 --> 00:19:30,760
+زوجته، يعني الزوجة مش برا عليه، عندهم عادات و
+
+209
+00:19:30,760 --> 00:19:34,600
+تقاليد، يعني مثلًا لو جاء الرجل وبده يدخل بيته،
+
+210
+00:19:34,600 --> 00:19:40,560
+لازم يستأذن، قد تكون زوجته يعني قدت بصاحبها،
+
+211
+00:19:40,560 --> 00:19:45,120
+لازم يستأذن عليهم ويقول وانقل لكم، ارجعوا، فارجعوا،
+
+212
+00:19:45,120 --> 00:19:48,880
+وإذا قالت لي ارجع يعني كمان ساعتين بترجع البيت،
+
+213
+00:19:48,880 --> 00:19:53,000
+بمشي الحال، هاي الثقافة، هاي المجتمع، مش هيك بدهم
+
+214
+00:19:53,000 --> 00:19:57,230
+إيانا نسير يا إخوان؟ يقبضوا مصادرنا الثقافية عشان
+
+215
+00:19:57,230 --> 00:20:02,430
+نكون عصريين، ومجموعة القيم والعادات السائدة وإزالة
+
+216
+00:20:02,430 --> 00:20:09,610
+الفروق الدينية، يعني الشيوعي والإسلامي والمجوسي
+
+217
+00:20:09,610 --> 00:20:17,250
+والوثني وكل عندهم فيه نظر لهذه الثقافة وهذه العالَم
+
+218
+00:20:17,250 --> 00:20:22,730
+السواء، طب هذا بتصدم مع ديننا ولا بتصدمش؟ تصدم أكيد
+
+219
+00:20:23,280 --> 00:20:27,980
+بتصادم، يعني نحن لو اجا واحد غير مسلم بدي تزوّج
+
+220
+00:20:27,980 --> 00:20:34,000
+بنت المسلمة، هالدين ناق بيسمح له؟ آه لا يجوز تزويج
+
+221
+00:20:34,000 --> 00:20:38,500
+بنات المسلمين من النصارى والمشركين وأهل الكتاب لا
+
+222
+00:20:38,500 --> 00:20:44,120
+يجوز يا إخوان، إذا أسلم خلاص صار مسلم، لكن اللي لم
+
+223
+00:20:44,120 --> 00:20:51,640
+يسلم ممنوع إن يتزوج، هذا مش موجود في العولمة، الشيعة أو
+
+224
+00:20:51,640 --> 00:20:56,520
+الشيوعي يتزوج من مسلمة أو يخش الإسلام ويرتد بكرة
+
+225
+00:20:56,520 --> 00:21:01,560
+وبعده يصير نصراني وبعده يصير إسلامي، هذا عندهم
+
+226
+00:21:01,560 --> 00:21:07,020
+ديمقراطية، هذا يؤدي إلى تدمير الحياة بالنسبة لنا،
+
+227
+00:21:07,020 --> 00:21:13,180
+لكن عندهم هذا أمر مشروع، وإزالة الفروق الدينية
+
+228
+00:21:13,180 --> 00:21:19,300
+والقومية والوطنية في إطار تدويل النظام الرأسمالي
+
+229
+00:21:19,300 --> 00:21:24,380
+الحديث، كل هذا التغيير وهذا النمط يا أخوات وفق رؤية
+
+230
+00:21:24,380 --> 00:21:34,470
+مين؟ الإله، يعني هم نصبوا أنفسهم آلهة لكي يرغبوا أو
+
+231
+00:21:34,470 --> 00:21:41,370
+يشبّعوا الدول المختلفة، حتى اليوم نجد أن أمريكا تبتز 
+
+232
+00:21:41,370 --> 00:21:46,270
+بعض الدول، تبتز بعض الدول ماليًا، يا إما تسيلوا على
+
+233
+00:21:46,270 --> 00:21:51,230
+هذا النمط العولمة، يا إما ما فيش مساعدات، يا إما
+
+234
+00:21:51,230 --> 00:21:54,430
+تطبقوا الديمقراطية، يا إما ما فيش معاملات اقتصادية
+
+235
+00:21:54,430 --> 00:21:59,890
+معاكم، يعني هم بيلجأوا إلى تطبيق العولمة بالضغط
+
+236
+00:22:00,740 --> 00:22:06,420
+المالي والاقتصادي والكذا إلى غير ذلك، وفق الرؤية
+
+237
+00:22:06,420 --> 00:22:11,940
+الأمريكية المهيمنة، والتي تزعم أنها سيدة الكون
+
+238
+00:22:11,940 --> 00:22:18,140
+وحامية النظام العالمي، السخيف طبعًا يا أخوات، لا يمكن
+
+239
+00:22:18,140 --> 00:22:23,750
+في يوم من الأيام، يعني نطبق هذه العولمة في مجتمعنا
+
+240
+00:22:23,750 --> 00:22:29,090
+أو في عاداتنا وفي حياتنا المسلمة، ولكن عشان نعمل
+
+241
+00:22:29,090 --> 00:22:32,370
+بمقتضى النظم الإسلامية اللي عندنا، بنقول لهم بناخد
+
+242
+00:22:32,370 --> 00:22:38,650
+منكم ما يتوافق ولا يتعارض مع ديننا ونظام الإسلام 
+
+243
+00:22:38,650 --> 00:22:46,590
+عندنا، وما يتعارض لا نريده، يعني مردود عليكم، لا نقول
+
+244
+00:22:46,590 --> 00:22:52,410
+إنه شرًّا محدّدًا، نرميها التجربة كلها بحذافيرها، ممكن تكون
+
+245
+00:22:52,410 --> 00:22:56,230
+عندهم أشياء اقتصادية تتوافق مع النظم الإسلامية أو
+
+246
+00:22:56,230 --> 00:22:59,430
+النظم الاقتصادية في الإسلام، أهلاً وسهلاً نعمل بها
+
+247
+00:22:59,430 --> 00:23:04,470
+استخدام الحاسوب، التكتيك الإداري، التكتيك المالي
+
+248
+00:23:04,470 --> 00:23:08,930
+الحسابات، ممكن نستخدمها، لكن ما تكونش نبقى نبتعد كل
+
+249
+00:23:08,930 --> 00:23:15,580
+البعيد عن الربا، ما هي الخاصية الجديدة؟ الخاصية
+
+250
+00:23:15,580 --> 00:23:21,920
+الخامسة، التكامل والترابط، أنتم ملاحظين؟ شايفين كيف؟ 
+
+251
+00:23:21,920 --> 00:23:26,760
+الشريعة الإسلامية الخصائص اللي ذكرناها من أول
+
+252
+00:23:26,760 --> 00:23:33,720
+خاصية إلى الآن نجد فيها علاقة بين كل خاصية والتي 
+
+253
+00:23:33,720 --> 00:23:41,500
+تليها أليس كذلك؟ بلى، أه في .. في .. في ترابط يعني
+
+254
+00:23:41,500 --> 00:23:46,520
+مافيش خاصية منفكة عن الخاصية الثانية إنما يعني
+
+255
+00:23:46,520 --> 00:23:51,840
+مثلا إحنا في روابط بيننا الآن، في روابط إحنا كلنا
+
+256
+00:23:51,840 --> 00:23:56,360
+من جنس الإنسان صح ولا؟ إحنا كلنا بربطنا الإسلام 
+
+257
+00:23:56,360 --> 00:24:01,580
+إحنا كلنا بتربطنا المحاضرة، النظم الإسلامية كلنا
+
+258
+00:24:01,580 --> 00:24:07,720
+بربطنا محاضرة التصوير، إذا بنقول يا أخوات في روابط
+
+259
+00:24:09,490 --> 00:24:14,670
+الخصائص، الخصائص النظم الإسلامية جميعها مترابطة و
+
+260
+00:24:14,670 --> 00:24:19,490
+متكاملة كأنه يعني كل خاصية بتكمل الثانية بتضفي
+
+261
+00:24:19,490 --> 00:24:24,850
+عليها مزيدا من التجميل والتحسين والإتقان والمنظر
+
+262
+00:24:24,850 --> 00:24:30,770
+والهيبة، أنا اليوم لما بدي أبني حيطة، وأجي في نص
+
+263
+00:24:30,770 --> 00:24:37,040
+الحيطة أترك مكان لبنة، ومهما أزملت الحيطة الجدار، و
+
+264
+00:24:37,040 --> 00:24:44,160
+مهما زينته وأطفيت عليه من التحسينات لكن في إيه؟ في 
+
+265
+00:24:44,160 --> 00:24:49,600
+لبنة ناقصة، ليس ممكن يتم  تلاحظ هذه اللبنة وهذا
+
+266
+00:24:49,600 --> 00:24:55,080
+النقص، أحيانًا كثيرة لما نعمل مثلا لو عملنا في البيت
+
+267
+00:24:55,080 --> 00:25:00,760
+أطعم وألذ أكلة عند أهل البيت بالإجماع يعني في 
+
+268
+00:25:00,760 --> 00:25:05,180
+إجماع من قبل أفراد الأسرة جميعًا بأن هذه الأكلة هي
+
+269
+00:25:05,180 --> 00:25:09,560
+المفضلة، ولكل واحدة منكم أنت تخيل ما هي الأكلة 
+
+270
+00:25:09,560 --> 00:25:13,060
+المفضلة لديها ولكن 
+
+271
+00:25:14,020 --> 00:25:22,420
+ولكن عندما أعددنا هذا الطعام وتكلفنا ودفعنا المال
+
+272
+00:25:22,420 --> 00:25:28,500
+الكثير، لكن لو نسيت ربط البيت، وضع الملح
+
+273
+00:25:32,860 --> 00:25:37,920
+نسيت وضع الملح على الطعام، كيف بنشعر بطعم الأكل؟
+
+274
+00:25:37,920 --> 00:25:42,440
+يعني الأكل مش ناقص، لا طهي ولا إتقان ولا في المواد
+
+275
+00:25:42,440 --> 00:25:47,060
+المشتركة المكونة لهذا الطعام كله جاهز وكامل و
+
+276
+00:25:47,060 --> 00:25:51,840
+تمام التمام، لكن نقص حاجة، عنصر واحد، لبنة واحدة
+
+277
+00:25:51,840 --> 00:25:55,960
+تخلفت من الجدار، إيش بيصير الأكل؟ والله لا نستطيع 
+
+278
+00:25:55,960 --> 00:26:02,030
+أن نتجرعه، أه ليش؟ لأنه خلاص إن خرم هذا النظام
+
+279
+00:26:02,030 --> 00:26:16,650
+وبالتالي نعني به أن كل خاصية مكملة ومتممة للأخرى 
+
+280
+00:26:17,190 --> 00:26:23,530
+مش بس هيك، ومترابطة معها، ولذلك ترابط العقد، و
+
+281
+00:26:23,530 --> 00:26:28,110
+ترابط، عندي مثالين، المثال الأول ترابط العقد الآن يا
+
+282
+00:26:28,110 --> 00:26:34,870
+أخوات، النظم الإسلامية عبارة عن عقد جميل زي ما أنا 
+
+283
+00:26:34,870 --> 00:26:39,750
+ضربتلكم مثال في أول المحاضرات زي السبحة، يعني هذه 
+
+284
+00:26:39,750 --> 00:26:45,030
+منظومة جميلة، منظومة جميلة ومعمولة بإتقان وإحكام
+
+285
+00:26:45,030 --> 00:26:51,150
+وبتناسق في الألوان، الآن العقد اللي إحنا بنلبسه لو
+
+286
+00:26:51,150 --> 00:26:55,070
+كان كل العقد حباته صغيرة، وبعدين جبنا حبة كبيرة جدًا
+
+287
+00:26:55,070 --> 00:27:01,650
+كده، إيش بتساوي في العقد؟ صحيح هي مكملة، مثلا لو كان
+
+288
+00:27:01,650 --> 00:27:08,950
+العقد مية حبة، هذه الحبة مكملة ومتممة لكن مترابطة
+
+289
+00:27:08,950 --> 00:27:15,470
+معاه، متناسقة معاه، بيطلع العقد إيه؟ مالوش منظر،
+
+290
+00:27:15,470 --> 00:27:23,370
+يفقد جماله، طب لو فقدت حبة بكاملها، بيتم إلى أطر، و
+
+291
+00:27:23,370 --> 00:27:28,480
+مكان فاضي في إلهاء أثر، ومكان فاضي، إذا جالك النظم
+
+292
+00:27:28,480 --> 00:27:35,080
+الإسلامي كعقد جميل، نظمت حباته ونصقت فيه، ترابط فيه،
+
+293
+00:27:35,080 --> 00:27:40,260
+إتقان فيه، إحكام فيه، تناسق في الحجم، في الألوان، في
+
+294
+00:27:40,260 --> 00:27:47,540
+الزخارف، فيه ترابط وفيه تكامل وفيه تناسق وفيه توازن 
+
+295
+00:27:47,540 --> 00:27:48,320
+وفيه شمول
+
+296
+00:27:50,990 --> 00:27:55,650
+هذا نعني بالتكامل والترابط، يعني على سبيل المثال
+
+297
+00:27:55,650 --> 00:28:03,670
+الإسلام أعطى المرأة نصف الرجل في الميراث، في
+
+298
+00:28:03,670 --> 00:28:09,930
+الميراث لو توفي المورث وترك ميراثًا، ترك ثروة أو
+
+299
+00:28:09,930 --> 00:28:15,110
+جينا نقسم للذكر مثل حظ الأنثيين، ابن ادى البنت كم
+
+300
+00:28:15,110 --> 00:28:25,480
+نصيب، والولد كمين نصيبين، وهذه قسمة في غاية العدل، لكن 
+
+301
+00:28:25,480 --> 00:28:32,480
+وكتيرش بتكون مفيدة ومؤثرة، وقسمة يعني متكاملة إذا
+
+302
+00:28:32,480 --> 00:28:39,760
+طبقنا النظام الإسلامي بكامله، لكن لو طبقنا نظام
+
+303
+00:28:39,760 --> 00:28:43,880
+الميراث، أعطينا المرأة نصف الرجل وماطبقناش باقي
+
+304
+00:28:43,880 --> 00:28:48,740
+الأنظمة الإسلامية، المرأة بتطلع مظلومة، والمرأة
+
+305
+00:28:48,740 --> 00:28:55,640
+بتطلع يعني إيه بتعيش في ضيق وفي عسر، لكن لما نقولك
+
+306
+00:28:55,640 --> 00:29:02,400
+مثلا المرأة مكفولة النفقة، مكفولة
+
+307
+00:29:02,400 --> 00:29:08,180
+النفقة لو كانت بنت لأبوها بيصرف عليها وإن كانت أختا
+
+308
+00:29:08,180 --> 00:29:14,820
+مالهاش أبو، أخوها بيصرف عليها، وإن كانت زوجة، زوجها
+
+309
+00:29:14,820 --> 00:29:19,960
+بيصرف عليها، وإن كانت أما ابنها بيصرف عليها، يعني في
+
+310
+00:29:19,960 --> 00:29:26,760
+كل مراحل الحياة مكفولة فقط سواء كانت طفلة أو بنتا
+
+311
+00:29:26,760 --> 00:29:34,340
+أو زوجة أو أما أو أختا، في كل مواصفات الفتاة البنت
+
+312
+00:29:34,960 --> 00:29:40,580
+مكفولة النفقة، إذا ماشينا على هذا النظام وأعطيناها
+
+313
+00:29:40,580 --> 00:29:46,360
+نصف الرجل، بتكون القسمة عادلة وبكون يعني هذا
+
+314
+00:29:46,360 --> 00:29:54,090
+التقسيم وهذا النظام هو الفعال حتى مثلا عكس النظام
+
+315
+00:29:54,090 --> 00:29:59,870
+العولمي، أدللكم على أن الرجل لو .. البنت لو أخدت
+
+316
+00:29:59,870 --> 00:30:06,570
+نصف الرجل هذه قسمة عادلة، مثلا على سبيل الزواج لو
+
+317
+00:30:06,570 --> 00:30:17,870
+توفي رجل وترك بنتين وولد، الولد بده ياخد نص التركة 
+
+318
+00:30:17,870 --> 00:30:25,430
+والبنات بدهم ياخدوا النص، يعني مثلا لو ترك الرجل هذا
+
+319
+00:30:25,430 --> 00:30:32,410
+عشرين ألف دينار، الولد كده ياخد؟ عشرة آلاف، طب 
+
+320
+00:30:32,410 --> 00:30:37,450
+والبنات كل واحدة منهم بدأ تاخد خمسة، إذا البنت كل
+
+321
+00:30:37,450 --> 00:30:41,930
+واحدة منهم أخدت خمسة آلاف دينار، والرجل أخذ عشرة
+
+322
+00:30:41,930 --> 00:30:48,350
+آلاف دينار، تعالوا نحسب مع بعض، العشرة آلاف دينار كده
+
+323
+00:30:48,350 --> 00:30:54,390
+يجهز البيت منهم الرجل؟ ثلاثة إيش ثلاثة ولا خمسة؟ 
+
+324
+00:30:54,390 --> 00:30:59,230
+كده، بده يدفع مهر منهم، كده بده يشتري سيارة، بده
+
+325
+00:30:59,230 --> 00:31:03,230
+يشتري عفش بيت، هيحط العشرة آلاف دينار ويروح يدين
+
+326
+00:31:03,230 --> 00:31:07,210
+كمان فوقهم عشرة آلاف دينار عشان يستطيع أن يتزوج
+
+327
+00:31:07,210 --> 00:31:13,800
+فقط، طب البنت أخدت الخمسة آلاف دينار في الجيبة هدول فيش
+
+328
+00:31:13,800 --> 00:31:18,420
+عليهم كلام، هدول في الجيبة فيش عليهم كلام، وإذا كانت
+
+329
+00:31:18,420 --> 00:31:24,220
+بنت أخوها بيصرف عليها، إذا بدت تتزوج يعني تقدم لها
+
+330
+00:31:24,220 --> 00:31:31,800
+الفتى المتأمل فيه المواصف أو المطابق للمواصفات
+
+331
+00:31:32,600 --> 00:31:38,600
+بيقولوله سبعة سبعة سبعة يعني سبعة مجبوض وسبعة 
+
+332
+00:31:38,600 --> 00:31:43,680
+متأخر وسبعة مافيش، بيت ولا خمسة خمسة خمسة، هذا يتبع
+
+333
+00:31:43,680 --> 00:31:48,580
+الأعراف، في أعراف ثلاثة ثلاثة ثلاثة، قرار مجلس الأمن
+
+334
+00:31:48,580 --> 00:31:57,720
+وفي خمسة خمسة خمسة، وفي تلت سبعات، هذا خلينا نقول 
+
+335
+00:31:57,720 --> 00:32:01,080
+يرجع إلى العادات والتقاليد والأعراف والمستويات
+
+336
+00:32:02,030 --> 00:32:09,580
+كويس؟ إذا البنت أخدت مهرا يعني لما الله سبحانه
+
+337
+00:32:09,580 --> 00:32:14,040
+وتعالى قسم بين الرجل والمرأة يعني هذه القسمة كانت
+
+338
+00:32:14,040 --> 00:32:21,080
+في غاية العدل، العدل المطلق يعني كافأة الرجل وزيادة
+
+339
+00:32:21,080 --> 00:32:27,320
+كمان، كافأة الرجل وزيادة، لكن وكتيرش إذا عملنا
+
+340
+00:32:27,320 --> 00:32:33,140
+بالنظم الإسلامية مجتمعة، أما أنا أعطيها نصف الميراث
+
+341
+00:32:33,140 --> 00:32:40,970
+وأقولها انفق عن نفسك، إذا تزوجت مالكش مهر، ما حرق
+
+342
+00:32:40,970 --> 00:32:47,970
+وقاتوا النساء صدقاتهن نحلة، يعني فيها الأمر يجب
+
+343
+00:32:47,970 --> 00:32:52,430
+المهر للمرأة المتزوجة، يجب المهر، يجب الشريعة أوجبت
+
+344
+00:32:52,430 --> 00:32:56,170
+لها المهر، لكن أنا إذا تزوجت المرأة قلت لها تزوجي
+
+345
+00:32:56,170 --> 00:33:03,250
+بلا مهر، وانفق على نفسك، بتطلع قسمة الميراث جائرة أو
+
+346
+00:33:03,250 --> 00:33:07,810
+لا تستقيم، بدناش نقول جائرة، لا تستقيم، لكن واكتشف
+
+347
+00:33:07,810 --> 00:33:12,210
+تستقيم وبتؤدي العدالة الموجودة فيها عند تطبيق
+
+348
+00:33:12,210 --> 00:33:17,570
+النظم الإسلامية وأحكام الشرقية مكتملة ومتناسقة
+
+349
+00:33:17,570 --> 00:33:23,810
+ومجتمعة، هذا هو الذي نعني به التكامل والترابط
+
+350
+00:33:33,390 --> 00:33:38,910
+شوف الشهادة، شهادة رجل بامرأتين، وفي الميراث وفي
+
+351
+00:33:38,910 --> 00:33:42,530
+الديّة كمان، ديّات المرأة، وفي حاجات كتير يعني في
+
+352
+00:33:42,530 --> 00:33:47,170
+الغالب يعني ديّات الـ .. الـ .. الـ .. ديّات المرأة على
+
+353
+00:33:47,170 --> 00:33:51,810
+النصف من ديّات الرجل، يعني شوف إحنا هذا الموضوع يا
+
+354
+00:33:51,810 --> 00:34:00,410
+أخوات هندرسه في قدام في الأسرة، فيه أشياء الشريعة أو
+
+355
+00:34:00,410 --> 00:34:04,670
+النظم الإسلامي فرقت فيها بين الرجل والمرأة، وفي
+
+356
+00:34:04,670 --> 00:34:09,690
+أشياء ساوت بين الرجل والمرأة، يعني هذه القاعدة اللي
+
+357
+00:34:09,690 --> 00:34:13,510
+إحنا بنحكيها ليس على الإطلاق، المساواة والتقييد ليس
+
+358
+00:34:13,510 --> 00:34:17,570
+على الإطلاق، لكن هناك في حالات هنتطرق إليها وندرسها
+
+359
+00:34:17,570 --> 00:34:23,240
+بالتفصيل في موضعه، في حالات في أشياء يعني جمعت
+
+360
+00:34:23,240 --> 00:34:28,460
+الشريعة ساوت بين الراجل والمرأة تمامًا، المرأة مثل
+
+361
+00:34:28,460 --> 00:34:34,530
+الراجل، وفي أشياء الشريعة جعلت المرأة على نصف من
+
+362
+00:34:34,530 --> 00:34:40,490
+الرجل، وزي ما حكيت ليس إنقاصًا ولا تفريطًا ولا ظلمًا 
+
+363
+00:34:40,490 --> 00:34:46,830
+للمرأة، ولكن هذا عين العدل وعين السعادة للمرأة، عين
+
+364
+00:34:46,830 --> 00:34:51,190
+السعادة للمرأة، ليش؟ لأن المرأة جُبلت يا أخوات على
+
+365
+00:34:51,190 --> 00:34:57,200
+صفات وطباع وكذا، والأحكام الشرعية والنظم الإسلامي
+
+366
+00:34:57,200 --> 00:35:04,620
+تتناسق مع فترة المرأة ومع ما جُبلت عليه، يعني ليش
+
+367
+00:35:04,620 --> 00:35:10,740
+الشريعة الإسلامية أوجبت الحضانة على المرأة؟ يعني 
+
+368
+00:35:10,740 --> 00:35:13,740
+الشريعة الإسلامية جعلت الحضانة من خصائص من؟ من
+
+369
+00:35:13,740 --> 00:35:20,640
+خصائص المرأة، ليش؟ لأن المرأة فطرت على حب طفلها
+
+370
+00:35:20,640 --> 00:35:25,120
+وتعلقها والحنان والعاطفة الجياشة، الراجل ما عندهوش
+
+371
+00:35:25,120 --> 00:35:28,960
+العاطفة الجياشة، يعني أنا مثلا لو سمعت ابني في
+
+372
+00:35:28,960 --> 00:35:37,350
+منتصف الليل يصرخ وكنت تعبان، قد أطنش، لكن المرأة الأم
+
+373
+00:35:37,350 --> 00:35:44,730
+الزوجة، ولا يمكن ولا يمكن تسمع طفلها يبكي ولا تعتني
+
+374
+00:35:44,730 --> 00:35:50,310
+.. لا يمكن حتى لو شعرت أنه .. لو شعرت أنه يعني
+
+375
+00:35:50,310 --> 00:35:55,850
+ساخن شوية ولا حاجة، لا يأتيها النوم أبدًا، ليش 
+
+376
+00:35:55,850 --> 00:36:00,930
+العاطفة؟ ولذلك يا أخوات يعني إن شاء الله تعالى
+
+377
+00:36:02,950 --> 00:36:09,050
+بنقول إن المرأة يعني مفتورة الأحكام المتعلقة 
+
+378
+00:36:09,050 --> 00:36:14,490
+بالمرأة متناسقة ومنسجمة مع فطرة المرأة ومع
+
+379
+00:36:14,490 --> 00:36:19,410
+عاداتها ومع تقاليدها ومع الجبلية التي هي مفتورة 
+
+380
+00:36:19,410 --> 00:36:25,030
+عليه من هنا كيف
+
+381
+00:36:25,030 --> 00:36:31,350
+يتحقق التكامل والترابط؟ كيف يتحقق التكامل والترابط؟
+
+382
+00:36:31,350 --> 00:36:37,550
+1- ضرورة تطبيق أنظمة الإسلام ككل متكامل كوحدة
+
+383
+00:36:37,550 --> 00:36:43,170
+واحدة أفتؤمنون ببعض الكتاب وتكفرون ببعض؟ إذا أردنا
+
+384
+00:36:43,170 --> 00:36:51,590
+أن تأتي هذه النظم أكلها لابد من أن تطبق كوحدة
+
+385
+00:36:51,590 --> 00:36:58,090
+واحدة متكاملة علشان تظهر النتائج والآثار المترتبة 
+
+386
+00:36:58,090 --> 00:37:05,360
+عليه. إثنين، عدم الأخذ بأنظمة الإسلام وتعليماته كافة 
+
+387
+00:37:05,360 --> 00:37:11,120
+يعتبر اتباعًا للشيطان ومنهجه ولذلك يقول سبحانه
+
+388
+00:37:11,120 --> 00:37:14,600
+وَلَا تَتَّبِعُوا خُطُوَّاتِ الشَّيْطَانِ إِنَّهُ 
+
+389
+00:37:14,600 --> 00:37:18,840
+لَكُمْ عَدُوٌ مُّبِينٌ كما وصفت الشريعة النصوص
+
+390
+00:37:18,840 --> 00:37:23,100
+الشّرعية فعل من يأخذون ببعض أنظمة الإسلام ويتركون
+
+391
+00:37:23,100 --> 00:37:29,580
+البعض الآخر أفتؤمنون ببعض الكتاب وتكفرون ببعض؟
+
+392
+00:37:31,530 --> 00:37:39,850
+واحذرهم أن يفتنوك عن بعض ما أنزل الله إليك وكمان
+
+393
+00:37:39,850 --> 00:37:44,890
+بيقول يجب العمل بالنظم الإسلامية ككل متكامل لا 
+
+394
+00:37:44,890 --> 00:37:53,350
+يُقبل تجزئة ولا مساومة مثاله عندما ساومت قريش النبي
+
+395
+00:37:53,350 --> 00:37:59,370
+صلى الله عليه وسلم قالت يا محمد إن أردت مالًا
+
+396
+00:37:59,370 --> 00:38:07,950
+جعلناك أغنى الناس، أعطيناك من الأموال ما تتميز
+
+397
+00:38:07,950 --> 00:38:14,320
+علينا جميعًا في الغنى والثراء وإن أردت نساء أو 
+
+398
+00:38:14,320 --> 00:38:22,140
+زواج، زوجناك أفضل بناتنا، بدنا نزوجك أجمل نساءنا، 
+
+399
+00:38:22,140 --> 00:38:28,140
+وإن أردت جهة وسلطانة وزارة ورتبة، جعلناك أميرًا
+
+400
+00:38:28,140 --> 00:38:33,480
+علينا، أمرناك علينا لكن يا محمد إيش اللي بدنا منك؟
+
+401
+00:38:33,480 --> 00:38:37,680
+بدنا نمشي معك في كل الإسلام اللي جئت به أنت
+
+402
+00:38:37,680 --> 00:38:41,500
+يعني هم ما برفضوا الإسلام ككل يا إخوان قالوا له بدنا
+
+403
+00:38:41,500 --> 00:38:47,260
+نمشي في كل تعاليم الإسلام إلا شغلة واحدة اترخص لنا
+
+404
+00:38:47,260 --> 00:38:55,420
+أن نعبد آلهتنا نطق على عبادة الآلهة الأصنام إيش
+
+405
+00:38:55,420 --> 00:39:02,560
+كان الرد؟ قالوا لهم والله لو وضعتم الشمس في يميني
+
+406
+00:39:02,560 --> 00:39:09,500
+والقمر في يساري على أن أترك هذا الدين ما تركته حتى 
+
+407
+00:39:09,500 --> 00:39:18,860
+أن أهلك دونه أو أن يظهره الله فيش ممكنية للمساومة
+
+408
+00:39:18,860 --> 00:39:26,060
+معاها لأن الدين كتلة واحدة ترابط وتكامل ازاي أنا
+
+409
+00:39:26,060 --> 00:39:31,970
+أشيل لبنة من هذا البنيان الشامخ والحادثة الشهيرة
+
+410
+00:39:31,970 --> 00:39:36,290
+بعد وفاة النبي صلى الله عليه وسلم ارتدت العرب عن
+
+411
+00:39:36,290 --> 00:39:41,150
+دفع الزكاة قالوا يا أبا بكر هذه الزكاة احنا كنا
+
+412
+00:39:41,150 --> 00:39:46,750
+ندفعها لمحمد عليه الصلاة والسلام ومحمد قد مات احنا 
+
+413
+00:39:46,750 --> 00:39:52,770
+بدناش ندفع زكاة بدنا نصوم ونصلي ونحج ونعمل كل شعائر
+
+414
+00:39:52,770 --> 00:40:02,570
+الإسلام ولكن الزكاة لأفجيش لهم جيشًا قال و الله لأ
+
+415
+00:40:02,570 --> 00:40:08,390
+قاتلنهم حتى يؤدوا زكاة كانوا يؤدونه لرسول الله
+
+416
+00:40:08,390 --> 00:40:15,820
+الحبل أو يعني صغير الماعز عناقالأقاتلنهم حتى 
+
+417
+00:40:15,820 --> 00:40:22,480
+يؤدونه رغم عن أنفهم وبالفعل يا أخوات قاتل المرتدين
+
+418
+00:40:22,480 --> 00:40:27,980
+وأخضعهم وأرجعهم إلى حضيرة الإسلام وطبق الإسلام ككل
+
+419
+00:40:27,980 --> 00:40:34,200
+متكامل وحدة متكاملة ومترابطة ومتناسقة من هنا يتضح
+
+420
+00:40:34,200 --> 00:40:39,480
+لنا أن النظم الإسلامية وحدة كاملة لا تقبل التجزئة
+
+421
+00:40:39,480 --> 00:40:45,620
+ولا تقبل المساومة ولا تقبل التفريط معا وسويًا حتى
+
+422
+00:40:45,620 --> 00:40:47,780
+المحاضرة القادمة إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/NxCXMcc4Y0Q_raw.srt b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/NxCXMcc4Y0Q_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1cbfbe87bf209d1d288e6104762658a0736a3a6c
--- /dev/null
+++ b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/NxCXMcc4Y0Q_raw.srt
@@ -0,0 +1,1652 @@
+1
+00:00:20,430 --> 00:00:23,250
+أعوذ بالله السماء العليم من الشيطان الرجيم بسم
+
+2
+00:00:23,250 --> 00:00:27,210
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:27,210 --> 00:00:31,230
+والسلام على رسولنا الكريم وبعد خوات الكريمات في
+
+4
+00:00:31,230 --> 00:00:36,110
+المحاضرة السابقة كنا تطرقنا إلى الخاصية السابعة
+
+5
+00:00:36,110 --> 00:00:40,790
+على و هي علم ثالية و الأخلاق ان شاء الله تعالى
+
+6
+00:00:40,790 --> 00:00:44,830
+اليوم هنتطرق إلى الخاصية الثامنة و الأخيرة و هي
+
+7
+00:00:44,830 --> 00:00:50,790
+الجزاءالأخروي طبعا يا أخوات يعني أي مشروع و أي
+
+8
+00:00:50,790 --> 00:00:55,650
+نظام و أي مؤسسة و أي جامعة و أي أسرة حتى الأسرة
+
+9
+00:00:55,650 --> 00:01:00,330
+لابد من أن يتوفر فيها الجزاء الدنيوي و الجزاء
+
+10
+00:01:00,330 --> 00:01:05,510
+الأخروي يعني هذا الجزاء بقسميه الجزاء الدنيوي و
+
+11
+00:01:05,510 --> 00:01:10,560
+الجزاء الأخروي يعتبر يعني سور أمانلأي مشروع سواء
+
+12
+00:01:10,560 --> 00:01:15,880
+مؤسسة أو زامعة أو عمل أو كذا طبعا النظم الإسلامية
+
+13
+00:01:15,880 --> 00:01:20,660
+أخوات تميزت عن غيرها من النظم بالجزاء الأخرى لكن
+
+14
+00:01:20,660 --> 00:01:26,580
+أنا عشان أبرز أهمية هذا الجزاء ومدى تأثيره في
+
+15
+00:01:26,580 --> 00:01:31,720
+النظميعني ال .. احنا في وقت سابق قولنا يا أخوات
+
+16
+00:01:31,720 --> 00:01:36,780
+انه ال .. ال .. الكتير من الناس يعني 95% من الناس
+
+17
+00:01:36,780 --> 00:01:40,920
+ايش اللي بيدري على الاستقامة و ايش اللي بيدري على
+
+18
+00:01:40,920 --> 00:01:47,030
+الانضباط؟ هل هوالعقوبة والزجر ولا الوازع الديني
+
+19
+00:01:47,030 --> 00:01:52,590
+المنبعث من الضمير ما يسمى بالضمير الإيمان يعني 95%
+
+20
+00:01:52,590 --> 00:01:57,110
+من الناس اللي بيردع وبيجعله مستقيم اللي هو ايه
+
+21
+00:01:57,110 --> 00:02:03,620
+الوازع الدينيالوازع الديني هل هو من قبيل الجزاء
+
+22
+00:02:03,620 --> 00:02:07,920
+الدنياوي ولا من قبيل الجزاء الأخرى؟ من قبيل الجزاء
+
+23
+00:02:07,920 --> 00:02:13,860
+الأخرى ولذلك النظم الغربية والنظم الوضعية لا تعرف
+
+24
+00:02:13,860 --> 00:02:18,060
+هذا النوع من الجزاء وبالتالي القصور بيكون واضح
+
+25
+00:02:18,060 --> 00:02:23,590
+والخلل في التطبيق واقع لكن النظم الإسلاميةجمعت بين
+
+26
+00:02:23,590 --> 00:02:28,970
+الأمرين ما أهملت الجزاء الدنيوي وما أهملت الجزاء
+
+27
+00:02:28,970 --> 00:02:33,050
+الأخروي بتعرفوا كتير من الشغلات اللي احنا بنقوم
+
+28
+00:02:33,050 --> 00:02:38,290
+فيها أصلا لا نلتفت إلى الجزاء الدنيوي صح ولا لا؟
+
+29
+00:02:38,890 --> 00:02:43,270
+أيوة أنا لما أساعد المسكين بدي أفتخر قدام الناس
+
+30
+00:02:43,270 --> 00:02:48,850
+بالعكس من قاتل اللي يقال عنه شجاع ايش بيصير فيه؟
+
+31
+00:02:48,850 --> 00:02:55,870
+اه قاتلت اللي يقال عنك شجاع و قد قيل فيسحبه فيأخذه
+
+32
+00:02:55,870 --> 00:03:00,850
+بيه فيسحبه فيطرحه على وجهه في النار ليش؟ لأنه عشاء
+
+33
+00:03:00,850 --> 00:03:07,590
+الجزاء الدنيوي اه او المنفقالمنفق بالليل والنهار
+
+34
+00:03:07,590 --> 00:03:13,070
+اللي يقال عنه إيه؟ سخي، منفق، كريم، وقد قيل، فيؤمر
+
+35
+00:03:13,070 --> 00:03:18,070
+به، فيُصحب، فيأخذ إلى إيه؟ إلى النار، والذي تعلم
+
+36
+00:03:18,070 --> 00:03:21,770
+القرآن وعلمه، ليش؟ اللي يقال عنه قارئ، ما شاء
+
+37
+00:03:21,770 --> 00:03:26,240
+الله، إيش هالصوت الجميل هذا؟ حُنجرة ذهبيةومافيش
+
+38
+00:03:26,240 --> 00:03:32,280
+إخلاص ومش لله بده الجزاء الدنيوي السمعة الصيط
+
+39
+00:03:32,280 --> 00:03:36,920
+الرياء طبعا انت حصلت عليها يعني حتى الجزاء الدنيوي
+
+40
+00:03:36,920 --> 00:03:41,600
+أحيان بإذا الإنسان طمع فيه بودي إيه إلى عاقبة
+
+41
+00:03:41,600 --> 00:03:46,000
+مجهولة لكن الجزاء الأخر ويا أخوتي الإخلاص فيه هناك
+
+42
+00:03:46,000 --> 00:03:50,740
+جنة فيه هناك نار هذا الجزاء اللي بيخلي الإنسان إيه
+
+43
+00:03:51,440 --> 00:03:56,560
+يستقيم بخلّي الإنسان يجود بماله، يجود بنفسه، يجود
+
+44
+00:03:56,560 --> 00:04:01,620
+بأبنائه في سبيل الله، صح ولا لا؟ صح، صح، صح، صح،
+
+45
+00:04:01,620 --> 00:04:01,620
+صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح،
+
+46
+00:04:01,620 --> 00:04:03,800
+صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح،
+
+47
+00:04:03,800 --> 00:04:03,820
+صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح،
+
+48
+00:04:03,820 --> 00:04:07,480
+صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح، صح،
+
+49
+00:04:07,480 --> 00:04:16,440
+صح، صح، صح، صح، صح، صح، صح
+
+50
+00:04:16,460 --> 00:04:20,260
+الجزاء الأخرى النظم الإسلامية الشاملة للجزاء
+
+51
+00:04:20,260 --> 00:04:25,140
+الأخروي وشاملة يعني شمعت بين الجزائين وابتغي فيما
+
+52
+00:04:25,140 --> 00:04:30,220
+أتاك الله الدار الأخرى ولا تنسى نصيبك من الدنيا
+
+53
+00:04:30,220 --> 00:04:35,640
+إذا يا أخوات الجزاء الأخروي يعني معزز وسياج أمان
+
+54
+00:04:35,640 --> 00:04:41,500
+لهذه الشريعة ويتمثل في الحلال والحرام
+
+55
+00:04:47,160 --> 00:04:55,260
+وبيدعو الناس إلى الاستقامة وطبعا يعني يوضح ذلك ما
+
+56
+00:04:55,260 --> 00:04:59,880
+ورد عن النبي صلى الله عليه وسلم جاء رجلان يختصما
+
+57
+00:04:59,880 --> 00:05:05,110
+عند رسول الله صلى الله عليه وسلمفيقول لهم النبي
+
+58
+00:05:05,110 --> 00:05:10,210
+صلى الله عليه و سلم ربما يكون أحدكم ألحن بحجته من
+
+59
+00:05:10,210 --> 00:05:15,810
+الآخر يعني أشطر يعني إلسانه طليق إلسانه يعني حلو
+
+60
+00:05:15,810 --> 00:05:19,930
+يستطيع الدبلجة و التنصيق و التقديم و التأكير
+
+61
+00:05:19,930 --> 00:05:25,090
+يستطيع عرض الحجة في ثوب جميل أيوة فيقول له النبي
+
+62
+00:05:25,090 --> 00:05:29,600
+صلى الله عليه و سلم ربما يكون أحدكم ألحنيعني أقوى
+
+63
+00:05:29,600 --> 00:05:34,340
+على العرض والصياغة والتقدير ألحن بحجته من أخيه
+
+64
+00:05:34,340 --> 00:05:40,640
+فأحكم له نحو ما أسمع فإنما أحكم له .. من حكمته له
+
+65
+00:05:40,640 --> 00:05:46,740
+بشيء من حق أخيه فإنما أحكم له إيه؟ بقطعة من النار
+
+66
+00:05:46,740 --> 00:05:49,880
+يعني شوف النبي صلى الله عليه استخدم على طول ذكرهم
+
+67
+00:05:49,880 --> 00:05:54,220
+بالجزاء الأخرى و بالفعل عندما سمعوا هذا الكلام من
+
+68
+00:05:54,220 --> 00:05:59,780
+النبي كلاهما قال لا أريد هذا الماللا أريد هذه
+
+69
+00:05:59,780 --> 00:06:05,260
+الأرض ليش يا أخوات؟ إذا هذا يظبط الإنسان ويظبط
+
+70
+00:06:05,260 --> 00:06:09,680
+السلوك وينظم النظم الإسلامية ويجعلها يعني متناسقة
+
+71
+00:06:09,680 --> 00:06:16,000
+شاملة مؤثرة ومن هنا تميزت النظم الإسلامية عن غيرها
+
+72
+00:06:16,000 --> 00:06:21,980
+في هذه النقطة وهذا المجال كما تميزت في خصائص سابقة
+
+73
+00:06:23,690 --> 00:06:28,870
+أما اليوم ان شاء الله سنتحدث في مصادر النظم
+
+74
+00:06:28,870 --> 00:06:33,390
+الإسلامية احنا في وقت سابق يا أخوات مش قلنا ان
+
+75
+00:06:33,390 --> 00:06:38,950
+الخاصية الأولى من خصائص النظم الإسلامية هي
+
+76
+00:06:38,950 --> 00:06:44,270
+الربانية ربانية المصدر وربانية الغاية طب ايش
+
+77
+00:06:44,270 --> 00:06:48,190
+المقصود بالربانية؟أنا من عند الله عز وجل أنا بدي
+
+78
+00:06:48,190 --> 00:06:52,250
+إجابات محددة، ده بديش إجابات جماعية، تفضلي هي من
+
+79
+00:06:52,250 --> 00:06:55,150
+عند الله عز وجل، هو الذي أنزلها على سيدنا محمد و
+
+80
+00:06:55,150 --> 00:07:03,320
+هو خالص كمان، ربانية، يعني مصدر، المصدر، تفضليأو
+
+81
+00:07:03,320 --> 00:07:10,560
+أي مصدر تمام ربانية المصدر يا أخوات يعني أصولها و
+
+82
+00:07:10,560 --> 00:07:15,820
+أسس تشريعاتها و أنظمتها هذه جاية من وين من عند
+
+83
+00:07:15,820 --> 00:07:20,520
+الله سواء كان من القرآن أو السنة أو الإجماع أو
+
+84
+00:07:20,520 --> 00:07:27,000
+القياس القرآن كلام الله سبحانه وتعالى السنة
+
+85
+00:07:28,520 --> 00:07:34,360
+أيضًا وما ينطق عن الهوى إنه إلا وحي يوحى الإجماع
+
+86
+00:07:34,360 --> 00:07:39,340
+مستنبط من القرآن القياس مستنبط من القرآن إذا هذه
+
+87
+00:07:39,340 --> 00:07:44,900
+المصادر الأربعة كلها أخوات عائدةالى الله سبحانه
+
+88
+00:07:44,900 --> 00:07:49,980
+وتعالى من هنا كانت ربانية المصدر طبعا الان لابد من
+
+89
+00:07:49,980 --> 00:07:57,340
+الترتيب والتنصيق بين هذه المصادر الان لو وجها سؤال
+
+90
+00:07:57,340 --> 00:08:03,300
+فقهى الى احدى كنه ايش ستتصرف كيف ستتصرف في ما
+
+91
+00:08:03,300 --> 00:08:09,080
+ستبحث نرجع للقرآن الكريم اول حاجة اتفضلي اول حاجة
+
+92
+00:08:09,080 --> 00:08:14,920
+عن القرآن الكريم تمامطبا و يافا علم قصيدت برضه و
+
+93
+00:08:14,920 --> 00:08:18,020
+دالك بتبقى عشان تشتغل عندهم على القياصةأيوة كلام
+
+94
+00:08:18,020 --> 00:08:26,480
+جميل أختكم بتقول لكي أراعي الترتيب من حيث الأحقية
+
+95
+00:08:26,480 --> 00:08:31,980
+والقوة والوضوح والتكليف أول حاجة أنا ببحث في
+
+96
+00:08:31,980 --> 00:08:36,980
+القرآن الكريم إذا عرض لي قضاء إذا عرضتلي مسألة
+
+97
+00:08:36,980 --> 00:08:41,120
+مابروحش أبحث في الشنة بروحش أبحث في القياس أو في
+
+98
+00:08:41,120 --> 00:08:47,260
+الإجماع أول شيء بروحعلى إلى كتاب الله ببحث فيه
+
+99
+00:08:47,260 --> 00:08:53,260
+كتاب الله المسألة في إله زواب نعمل به طب إذا لم
+
+100
+00:08:53,260 --> 00:08:58,960
+نجد فيه كتاب الله نتحول إلى السنة نبحث في سنة رسول
+
+101
+00:08:58,960 --> 00:09:03,520
+الله صلى الله عليه وسلم وجدنا مبتغانة وجدنا
+
+102
+00:09:03,520 --> 00:09:09,540
+الإجابة وجدنا المسألة نأخذ الحكم من السنة طب إذا
+
+103
+00:09:09,540 --> 00:09:16,740
+لم نجدبنروح على الإجماع إذا لم نجد المسألة فيها
+
+104
+00:09:16,740 --> 00:09:21,360
+إجماع من العلماء بنروح على القياس هل هي لها قرائن
+
+105
+00:09:21,360 --> 00:09:26,800
+لها أشياء تساويها العلة متحققة إذا في علة إذا
+
+106
+00:09:26,800 --> 00:09:31,100
+توفرت أركان القياس الأربعة المتمثلة في الأصل وحكم
+
+107
+00:09:31,100 --> 00:09:37,860
+الأصل والفرع والعلة أركان القياس أربعة أصل حكم
+
+108
+00:09:37,860 --> 00:09:45,390
+للأصلفرع إلا جامعة بين الأصلي والفرع إذا نقاط
+
+109
+00:09:45,390 --> 00:09:51,110
+بنقول وهذا يوضح هذا المبدأ وهذا التسلسل وهذا ترتيب
+
+110
+00:09:51,110 --> 00:09:56,030
+الأولويات النبي صلى الله عليه وسلم عندما بعث معاذا
+
+111
+00:09:56,030 --> 00:10:04,000
+بعث وين حاكما إلى اليمن قال له يا معاذبما تقضي يا
+
+112
+00:10:04,000 --> 00:10:09,340
+معاذي إذا أرضى لك قضاء بإيش بدك تحكم؟ كيف بدك
+
+113
+00:10:09,340 --> 00:10:14,740
+تحكم؟ قال بكتاب الله فقال له النبي صلى الله عليه
+
+114
+00:10:14,740 --> 00:10:20,040
+وسلم إيه اللي ماتجهد؟ قال فبسنة رسول الله صلى الله
+
+115
+00:10:20,040 --> 00:10:24,200
+عليه وسلم طب إيه اللي ماتجهد؟ قال له أجتهد رأي و
+
+116
+00:10:24,200 --> 00:10:30,340
+القياس و الإجماع نوع من أنواع الاجتهادفي هذا
+
+117
+00:10:30,340 --> 00:10:35,420
+الحديث أخوات يعني يبين لنا النبي ﷺ فإيه ماذا فعل
+
+118
+00:10:35,420 --> 00:10:40,220
+النبي ضرب على صدري و قال الحمد لله الذي وفق رسوله
+
+119
+00:10:40,220 --> 00:10:44,480
+رسول الله لما يرضي الله ورسوله يعني بمعنى الكلام
+
+120
+00:10:44,480 --> 00:10:49,020
+النبي أقر على هذا العمل و هذا الترتيب بين المصادر
+
+121
+00:10:49,020 --> 00:10:56,680
+التي تستقى منها النظم الإسلاميةطبعاً يعني مدام هذا
+
+122
+00:10:56,680 --> 00:11:01,180
+التنصيق وهذا الترتيب مراعا كان لزمان علينا أن نبدأ
+
+123
+00:11:01,180 --> 00:11:05,300
+بهذا الترتيب وهذا التنصيق فسنتحدث ان شاء الله
+
+124
+00:11:05,300 --> 00:11:10,940
+تعالى عن القرآن الكريم هذا الحديث الشيق يعني من
+
+125
+00:11:10,940 --> 00:11:17,260
+أروع الحديث الذي يمكن التحدث به في كلام الله
+
+126
+00:11:17,260 --> 00:11:21,820
+سبحانه وتعالى القرآن الكريم يعني لو قلنا يعني ما
+
+127
+00:11:21,820 --> 00:11:27,250
+هو تعريف القرآن الكريمالقرآن الكريم وطلاب الله عز
+
+128
+00:11:27,250 --> 00:11:30,590
+وجل أنه نزل على نبي محمد صلى الله عليه وسلم ووثق
+
+129
+00:11:30,590 --> 00:11:34,770
+الجنبي المعبد بالدراوات عليه المنطقود بالتواتر
+
+130
+00:11:34,770 --> 00:11:42,010
+تمامتمام القرآن الكريم أخوات كلام الله اللي عايزة
+
+131
+00:11:42,010 --> 00:11:46,950
+تتكلم مع الله سبحانه وتعالى ماذا تفعل تقرأ القرآن
+
+132
+00:11:46,950 --> 00:11:51,550
+التي تريد أن تجتمع مع الله سبحانه وتعالى ماذا تفعل
+
+133
+00:11:51,550 --> 00:11:57,630
+تسجد تقترب أقرب ما يكون العبد إلى الله وهو الساجد
+
+134
+00:11:57,630 --> 00:12:03,070
+من أراد أن يفرج الهم الذي أصابه فعليه بالقرآن من
+
+135
+00:12:03,070 --> 00:12:09,200
+أراد أن يشفى من المرض الذي ألم به فعليهبالقرآن من
+
+136
+00:12:09,200 --> 00:12:15,100
+أرادت أن يؤسر الله لها أمرها فعليها ايه بالقرآن
+
+137
+00:12:15,100 --> 00:12:19,880
+والله العظيم يا أخوات القرآن هذا أكبر نعمة امتنى
+
+138
+00:12:19,880 --> 00:12:25,880
+الله بها علينا القرآن مفرج القروب يعني معالج
+
+139
+00:12:25,880 --> 00:12:31,120
+للنفسيات القرآن يا أخوات انتوا طبعا اكيد في طالبات
+
+140
+00:12:31,120 --> 00:12:36,290
+معاهم دورات تلاوة صح ولا لاوبيعرفوا ما الفرق بين
+
+141
+00:12:36,290 --> 00:12:44,470
+اسم الحرف وصوت الحرفاسم الحرف ألف مثلا هذا اسمه أ
+
+142
+00:12:44,470 --> 00:12:54,350
+لف ألف لكن نطق الحرف أ صد هذا اسم الحرف لكن صوته
+
+143
+00:12:54,350 --> 00:13:00,370
+صح بتعرفوا يا أخوات في شي عجيب من تآلف الحروف و
+
+144
+00:13:00,370 --> 00:13:06,910
+تناسقها و اجتماعها و تنظيمها ايوة الآن يعني شوفوا
+
+145
+00:13:07,520 --> 00:13:13,200
+إنسان أو عالم غربي أسمع مرضى نفسيين قسمهم قسمين،
+
+146
+00:13:13,200 --> 00:13:19,840
+قسم أسمع القرآن والقسم الآخر أسمع موسيقى صاخبةفوجد
+
+147
+00:13:19,840 --> 00:13:24,280
+الناس اللي سمع القرآن يعني اتحسنت نفسيته ارتاحه
+
+148
+00:13:24,280 --> 00:13:28,400
+شعره بارتياح هذا كله ياخدهم بيعرفوش إيه الشيء ده
+
+149
+00:13:28,400 --> 00:13:32,480
+إيش معناه بيعرفوش لا يتكلمون ولا كلمة بالعربية
+
+150
+00:13:32,480 --> 00:13:36,920
+بيفهموش إيش معناها لكن مجرد الصوت التناسق في خروج
+
+151
+00:13:36,920 --> 00:13:44,150
+الأصوات والحروف هذا التناسق العجيب ريح نفسيتهلو
+
+152
+00:13:44,150 --> 00:13:50,110
+أنزلنا هذا القرآن على جبل لرأيته خاشعا متصدعا من
+
+153
+00:13:50,110 --> 00:13:54,490
+خشية الله فما بالكم الإنسان اللي عنده حسيس ووجدان
+
+154
+00:13:54,490 --> 00:14:01,910
+وشعور ويسمع ويعقل ويتكلمأيوة وننزله من القرآن ما
+
+155
+00:14:01,910 --> 00:14:09,130
+هو شفاء ورحمة للمؤمنين ولا يزيد الظالمين إلا خسارة
+
+156
+00:14:09,130 --> 00:14:14,510
+القرآن يا أخوات شفاء لما في الصدور شفاء للأسقام
+
+157
+00:14:14,510 --> 00:14:19,530
+شفاء من الاعتقادات الفاسدة القرآن يا أخوات نعمة
+
+158
+00:14:19,530 --> 00:14:26,070
+كبيرة عشان هيك بنقول القرآن كلام الله لا يضهيه
+
+159
+00:14:26,070 --> 00:14:31,540
+كلامولذلك الله سبحانه وتعالى اتحدى العرب قل لإن
+
+160
+00:14:31,540 --> 00:14:36,820
+جتمعت الإنس والجن على أن يأتوا بمثل هذا القرآن لا
+
+161
+00:14:36,820 --> 00:14:41,480
+يأتون بمثله و لو كان بعضهم لبعض يعني لو اجتمعوا مع
+
+162
+00:14:41,480 --> 00:14:45,920
+بعض و اتساعدوا و اتشاركوا و اظهروا مع بعض على أن
+
+163
+00:14:45,920 --> 00:14:53,660
+يأتوا بهذا القرآن لا يأتون بمثلهإذا بعد هذا التحدي
+
+164
+00:14:53,660 --> 00:15:01,160
+قال لهم فليأتوا بعشري صور من مثله ماجدروش و
+
+165
+00:15:01,160 --> 00:15:05,800
+بتعرفوا
+
+166
+00:15:05,800 --> 00:15:10,980
+العرب أغوات في الجاهلية قبل نزول القرآن الله
+
+167
+00:15:10,980 --> 00:15:17,680
+سبحانه وتعالى أوصلهمللقمة في اللغة إن أنزلناه
+
+168
+00:15:17,680 --> 00:15:22,540
+قرآنا عربيا لعلكم تعقلوا ابتعرفوا الله سبحانه
+
+169
+00:15:22,540 --> 00:15:28,940
+وتعالى أوصلهم إلى قمة الإتقان في اللغة يعني عصر
+
+170
+00:15:28,940 --> 00:15:34,180
+تنزل الوحي وعصر تنزل القرآن كان العرب بلغ العرب
+
+171
+00:15:34,920 --> 00:15:40,260
+أقوى شيء في اللغة ومع ذلك ومع قوتهم في اللغة
+
+172
+00:15:40,260 --> 00:15:48,440
+وإتقانهم للغة إلا أنه جاء القرآن معجزاً لهم بشهادة
+
+173
+00:15:48,440 --> 00:15:52,260
+الكافرين منهم الذين أبوا الدخول في الإسلام قالوا
+
+174
+00:15:52,260 --> 00:15:58,870
+إن له لا حلاوة وإن عليه لا طلاوة إلى آخرينإقرار،
+
+175
+00:15:58,870 --> 00:16:02,890
+إقرار، لكن العناد هو اللي منحهم، ليش هذه السواهد
+
+176
+00:16:02,890 --> 00:16:08,250
+كلها يا أخوات؟ هذا لأنه كلام الله، لأنه كلام الله،
+
+177
+00:16:08,250 --> 00:16:12,410
+لا يأتيه الباطل من بين يديه ولا من خلفه، كلام
+
+178
+00:16:12,410 --> 00:16:19,480
+الله، إذا القرآن الكريم كلام اللهالمنزل على سيدنا
+
+179
+00:16:19,480 --> 00:16:25,320
+محمد صلى الله عليه وسلم الكافرين او الكافرون قالوا
+
+180
+00:16:25,320 --> 00:16:31,320
+يا محمد اتي بقرآن غير هذا او بدله بدنا نؤمن ابك بس
+
+181
+00:16:31,320 --> 00:16:37,440
+بشرط جيب قرآن غير هذا او بدله فإيش الإجابة قل ما
+
+182
+00:16:37,440 --> 00:16:44,150
+يكون لي أن أبدله من تلقائي نفسي إن أنا إلا نثيرهه
+
+183
+00:16:44,150 --> 00:16:47,170
+يعني مش أنا اللي جبت القرآن هذا النبي عليه الصلاة
+
+184
+00:16:47,170 --> 00:16:52,330
+والسلام كان رجلا أميا لا يقرأ ولا يكتب ومع ذلك
+
+185
+00:16:52,330 --> 00:16:58,110
+سأقى يعني هذا بالكلام المعجز والمعجز اذا بنقول يا
+
+186
+00:16:58,110 --> 00:17:04,810
+أخواتالقرآن كلام الله تعالى المنزل على سيدنا محمد
+
+187
+00:17:04,810 --> 00:17:09,390
+صلى الله عليه وسلم بواسطة من جبريل عليه السلام
+
+188
+00:17:09,390 --> 00:17:15,570
+المعجز بلفظه ونظمه اللفظ يعني تنظيم الألفاظ اللي
+
+189
+00:17:15,570 --> 00:17:21,630
+حكينا عليه انا اديكم مثال سورة يوسف عليه السلام
+
+190
+00:17:21,630 --> 00:17:28,410
+بتعرفوا قصة يوسفلو جبت أكبر الأدباء و جبت أكبر
+
+191
+00:17:28,410 --> 00:17:33,570
+علماء اللغة و أهل البلاغة و الفصاحة قلتلهم احكولي
+
+192
+00:17:33,570 --> 00:17:41,190
+قصة مثل قصة يوسفهيحكوا لكن لابد من عشان يوضحوا
+
+193
+00:17:41,190 --> 00:17:46,190
+الفكرة لابد ان يتلفظوا بكلام في فحش وتفحش وإلا كيف
+
+194
+00:17:46,190 --> 00:17:50,110
+بيوصلوا الفكرة في الشمكانية مهما بلغ طب شوفوا
+
+195
+00:17:50,110 --> 00:17:55,510
+القرآن الكريم وهمت بيه وهم بها وإن كان قميصه قد من
+
+196
+00:17:55,510 --> 00:18:02,380
+قبل إن كان قميصه قد من دبروغلقت الأبواب وقالت
+
+197
+00:18:02,380 --> 00:18:09,000
+هيتلك كلام مافيه فحش مافيه تفحش كلام بدل كلام
+
+198
+00:18:09,000 --> 00:18:14,540
+بيفهمنا القصة بحذفيرها صح ولا لأ هذا كلام الله
+
+199
+00:18:14,540 --> 00:18:20,380
+كلام الله يا أخوات لا يمكن أن يستمل على ايوة أحيان
+
+200
+00:18:20,380 --> 00:18:23,680
+بستخدم التصريح أحيان التلميح أحيان الإشارة أحيان
+
+201
+00:18:23,680 --> 00:18:29,250
+هذا كلام اللههي السعادة فيه لما نقرأ الكلام هذا
+
+202
+00:18:29,250 --> 00:18:34,190
+عندما نقرأ القرآن نشعر والله يا أخوات انا اخدوها
+
+203
+00:18:34,190 --> 00:18:38,730
+مني نصيحة و جربوا هذا الكلام اللي بصيب هم او حزن
+
+204
+00:18:38,730 --> 00:18:45,710
+او نكد او غم تذهب تتوضأ مش ضرور سورة يوسف تتوضأ و
+
+205
+00:18:45,710 --> 00:18:50,150
+تقرأ من اين شاءت من القرآن تقرأ جزء القرآن بس و
+
+206
+00:18:50,150 --> 00:18:55,810
+بعد الجزء اذا تم معاها النكد والهم والزعل ترجعليه
+
+207
+00:18:56,330 --> 00:18:59,510
+هتنسى اصلا هامها و هتنسى .. بس ابنيه ليش الله
+
+208
+00:18:59,510 --> 00:19:04,710
+سبحانه وتعالى شعل هذا القرآن شفاء؟ شفاء للصدور،
+
+209
+00:19:04,710 --> 00:19:11,270
+ابتعرفوا شغل أخوان؟لما نقول لك تبت يد أبي لهبل
+
+210
+00:19:11,270 --> 00:19:16,110
+وتبق .. شوف الحكم هذا اللي في القلقلة، أيوة؟ البقى
+
+211
+00:19:16,110 --> 00:19:21,670
+الساكنة مش بنقلقلها، أبق، شوف جديش لما نقول أبق،
+
+212
+00:19:21,670 --> 00:19:26,330
+شوف ضيق، أه ضيق شديد، لكن الحكم هذا بعد الضيق اللي
+
+213
+00:19:26,330 --> 00:19:33,040
+يصير بيعمل فتحة وكأنه بنشرالحروف يـ .. أيوة شوف
+
+214
+00:19:33,040 --> 00:19:38,000
+المد كيف بيفتح الصدر أيوة بيفتح الصدر بتعرف أخد
+
+215
+00:19:38,000 --> 00:19:41,780
+قراء القرآن المهريين الله سبحانه وتعالى بيديهم
+
+216
+00:19:41,780 --> 00:19:46,240
+عمار كبيرة بعمره تسعين سنة ميت سنة مية وعشر ستين
+
+217
+00:19:46,240 --> 00:19:51,280
+إذا كنا نقرأ القرآن و نؤديه قراءة صحية بالأحكام
+
+218
+00:19:51,280 --> 00:19:56,630
+يعني عاكس على صحة الإنسانلأنه اه انا ممكن لما اجيب
+
+219
+00:19:56,630 --> 00:20:01,250
+الغنى فيه ضغط ابتسير هنا لما اجيب الإضغام فيه ضغط
+
+220
+00:20:01,250 --> 00:20:05,270
+ابتسير على بعض الغداد هذا الضغط على الغداد المد
+
+221
+00:20:05,270 --> 00:20:12,010
+هنا كله أثار صحية شوفوا عظمة التناسق الحروف عظمة
+
+222
+00:20:12,010 --> 00:20:16,730
+التناسق الحروف كيف؟ إذن يا أخوات حتى نعكس على صحة
+
+223
+00:20:16,730 --> 00:20:22,610
+الإنسان القراءة فبنقولكلام الله تعالى المنزل على
+
+224
+00:20:22,610 --> 00:20:27,390
+سيدنا محمد صلى الله عليه وسلم بواسطة مين؟ جبريل
+
+225
+00:20:27,390 --> 00:20:33,310
+عليه السلام المعجز بلفظه ونظمه في التآلف والتنسيق
+
+226
+00:20:33,310 --> 00:20:37,190
+والأصوات والحروف في النظم في اللفظ معجز بنفظه
+
+227
+00:20:37,190 --> 00:20:43,650
+ونظمه المتعبد بتجاهته لا أقول ألف لام ميم حرف ولكن
+
+228
+00:20:43,650 --> 00:20:50,020
+ألف حرفو لا من حرف و مين من حرف و كل حرف إله حسنة
+
+229
+00:20:50,020 --> 00:20:55,080
+و الحسنة إلى سبع أمتالها و الله يضاعفه لما يشاء
+
+230
+00:20:55,080 --> 00:20:59,240
+أيوة يعني كمان هذا القرآن لما نقرأ أول حاجة
+
+231
+00:20:59,240 --> 00:21:03,640
+بنستفيد بنعكس علينا و على صحتنا و على إزالة الهموم
+
+232
+00:21:03,640 --> 00:21:07,780
+و الغموم و الشفاء و بعدين في تعظيم لله في عبادة في
+
+233
+00:21:07,780 --> 00:21:14,400
+أجر في ثواب أيوةجانب روحي طبعاً وفيه كمان جانب
+
+234
+00:21:14,400 --> 00:21:19,720
+عقائدي وجانب أحكام القرآن تشريع القرآن يتعبد به
+
+235
+00:21:19,720 --> 00:21:24,960
+وكمان في نفس اللحظة القرآن تشريع شرع لنا كثير من
+
+236
+00:21:24,960 --> 00:21:29,500
+الأحكام نظّم حياتنا حياة الزوجين حياة الجيران حياة
+
+237
+00:21:29,500 --> 00:21:37,180
+الحكومة نظّم الحكومة للمجتمع المؤسسات نظّم صلاحيات
+
+238
+00:21:37,180 --> 00:21:42,950
+إذا القرآن منهج حياةليس فقط يعني يتعبد بتلاوته بس
+
+239
+00:21:42,950 --> 00:21:50,890
+لديها تشريع كمان اذا نقول للمتعبد بتلاوته المبدوء
+
+240
+00:21:50,890 --> 00:21:56,650
+بصورة الفاتحة والمختتم بصورة الناس هذا هو يا أخوات
+
+241
+00:21:56,650 --> 00:22:00,770
+تعريف القرآن الكريم ولو روحت انا اتحدث عن القرآن
+
+242
+00:22:00,770 --> 00:22:05,410
+الكريم عشرين محاضرة ما بعطي حقه اه والحديث جميل
+
+243
+00:22:05,410 --> 00:22:14,030
+جدا في هذا المجال ايوا كلام اللهإذا بتقول القرآن
+
+244
+00:22:14,030 --> 00:22:17,730
+الكريم أخوات هو المصدر الأول مصدر المصادر كل
+
+245
+00:22:17,730 --> 00:22:22,430
+المصادر يعني تعود وتقوب وترجع إلى المصدر الأساس
+
+246
+00:22:22,430 --> 00:22:28,390
+اللي هو كل الشريعة القرآن الكريم يا أيها الذين
+
+247
+00:22:28,390 --> 00:22:31,270
+آمنوا أطيعوا الله و أطيعوا الرسول و أقول الأمر
+
+248
+00:22:31,270 --> 00:22:37,230
+منكم فإن تنازعتم في شيء لمين تردوه فردوه إلى الله
+
+249
+00:22:38,670 --> 00:22:42,950
+والرسول وإلى الرسول إن كنتم إلى الله والرسول إن
+
+250
+00:22:42,950 --> 00:22:50,630
+كنتم تؤمنون بالله واليوم الآخر طبعا يا أخوات يعني
+
+251
+00:22:50,630 --> 00:22:56,750
+هناك أدت خصائص للقرآن الكريم أولا القرآن الكريم هو
+
+252
+00:22:56,750 --> 00:23:02,030
+كلام الله بلفظه ومعناه وليس كلام أي خلق من خلقه
+
+253
+00:23:02,030 --> 00:23:08,370
+إذا مذام كلام اللهعلى طول تظهر فيه صفات الله
+
+254
+00:23:15,730 --> 00:23:20,210
+تظهر فيه صفات الله سبحانه وتعالى، يظهر فيه الكمال،
+
+255
+00:23:20,210 --> 00:23:25,350
+يظهر فيه الإتقان، يظهر فيه العلم، الغيب، الحكمة،
+
+256
+00:23:25,350 --> 00:23:28,670
+كل شيء يظهر فيه مذامه كلام الله سبحانه وتعالى،
+
+257
+00:23:28,670 --> 00:23:34,070
+يظهر فيه صفات الله تعالى، اتنين، القرآن الكريم أو
+
+258
+00:23:34,070 --> 00:23:39,510
+كلام الله المنزل على رسول الله محمد صلى الله عليه
+
+259
+00:23:39,510 --> 00:23:46,080
+وسلم، والنبي إيش كان وظيفته؟مبلغا وهاديا ومنذرا
+
+260
+00:23:46,080 --> 00:23:52,520
+بهذا القرآن ويجادل بيه ويحتاج بيه لكن هل يمتلك
+
+261
+00:23:52,520 --> 00:23:57,620
+التغيير لا يمتلك تعرفوا يا أخوات القرآن الكريم
+
+262
+00:23:57,620 --> 00:24:04,360
+يعرض لنا قصة تدلل بالقطع أن النبي صلى الله عليه
+
+263
+00:24:04,360 --> 00:24:12,880
+وسلم ليس له أي دخل في القرآن الكريمالنبي عليه
+
+264
+00:24:12,880 --> 00:24:17,600
+الصلاة والسلامكما تعلمنا في بداية الإسلام كانت
+
+265
+00:24:17,600 --> 00:24:20,600
+القبلة وين؟ يعني اللي بدي صلي وين يصلي؟ على المسجد
+
+266
+00:24:20,600 --> 00:24:25,400
+الأقصى آه على المسجد الأقصى كان اللي بدي صلي يصلي
+
+267
+00:24:25,400 --> 00:24:30,780
+وين؟ يتجهي إلى المسجد الأقصى النبي صلى الله عليه
+
+268
+00:24:30,780 --> 00:24:36,820
+وسلم كان عنده أمنية يوجه وين؟ إلى مكة على ملة أبيه
+
+269
+00:24:36,820 --> 00:24:43,220
+إبراهيم وإسماعيل عليهما السلام يعني كان إرونية أنه
+
+270
+00:24:43,220 --> 00:24:50,230
+يوجه في الصلاة وين؟فلكن مش جادر اه مش جادر يعني في
+
+271
+00:24:50,230 --> 00:24:55,730
+نفس الأمر هو حابب يتوجه المسلمون الى الكعبة الى
+
+272
+00:24:55,730 --> 00:25:02,230
+بيت الله الحرام الى بلاد أجداده و أبائهفالله
+
+273
+00:25:02,230 --> 00:25:06,150
+سبحانه وتعالى بيقول في سورة البقرة قد نرى تقلب
+
+274
+00:25:06,150 --> 00:25:10,970
+وجهك في السماء والله احنا يا محمد نعلم ما يدور في
+
+275
+00:25:10,970 --> 00:25:17,450
+خاطرك نعلم أمنيتك نعلم قموحك قد نرى تقلب وجهك في
+
+276
+00:25:17,450 --> 00:25:24,770
+السماء فلنولينك قبلة ترضاها فولي وجهك شطرة المسجد
+
+277
+00:25:24,770 --> 00:25:32,310
+الحرام وحيث ما كنتم فولوا وجهكم شطرةطيب لو كان
+
+278
+00:25:32,310 --> 00:25:37,430
+شوفوا هذه القصة هذه القصة تبين ان النبي فقط مبلغ
+
+279
+00:25:37,430 --> 00:25:44,370
+تالي منذر مبشر بهذا القرآن وكمان يا أخوات النص
+
+280
+00:25:44,370 --> 00:25:50,790
+الواضح والذي ينص صراحة على ان النبي نذير فقط عندما
+
+281
+00:25:50,790 --> 00:25:57,070
+قالوا اتي بقرآن غير هذا او بدلهفقال الله سبحانه
+
+282
+00:25:57,070 --> 00:26:03,850
+وتعالى قل ما يكون
+
+283
+00:26:03,850 --> 00:26:12,450
+لي أن أبدله من تلقاء نفسي إن أنا إلا نذير إن أتبع
+
+284
+00:26:12,450 --> 00:26:19,810
+إلا ما يوحى إليا تمام إذا بيقول يا أخوات نزل
+
+285
+00:26:19,810 --> 00:26:26,290
+بالعربيةوهذه من نعم الله علينا أن القرآن جاء
+
+286
+00:26:26,290 --> 00:26:32,710
+يخاطبنا بلغتنا وانا قلتلكم مش عارف القصة عادي قبل
+
+287
+00:26:32,710 --> 00:26:37,190
+هيك عندما ذهبت إلى الحجز في سنة 2002 يعني قبل 11
+
+288
+00:26:37,190 --> 00:26:41,910
+سنة وجدت يا أخوات وناس أصحاب البشر السوداء
+
+289
+00:26:41,910 --> 00:26:48,450
+أثيوبيين أفارقة وفي دينهم المصاحف فجلست بجانبهم
+
+290
+00:26:48,450 --> 00:26:54,960
+ملايين من البشرفيتحدثون مع بعضهم البعض اللغة
+
+291
+00:26:54,960 --> 00:26:58,760
+الإنجليزية فاستهجنت واستغربت قلت يعني هل يُعقل
+
+292
+00:26:58,760 --> 00:27:04,540
+إنهم بيحكوا عربي؟ أيوة فقلت .. قلت لأحدهم حكيت
+
+293
+00:27:04,540 --> 00:27:09,060
+معاه مافهمش بفهمش ولا كلمة فهم إنه أنا طلبت منه
+
+294
+00:27:09,060 --> 00:27:13,920
+يقرأ القرآن أشرت عليه وقلته اقرأ ففهم بالإشارة مش
+
+295
+00:27:13,920 --> 00:27:18,630
+بالإبارةلأن عربي مافيش ولا حرف اقوله كيف حالك
+
+296
+00:27:18,630 --> 00:27:25,470
+بقولك I don't know مابعرف فقلته
+
+297
+00:27:25,470 --> 00:27:31,670
+اقرأ فاخد يقرأ القرآن يا أخوات بشكل رائع صحيح في
+
+298
+00:27:31,670 --> 00:27:36,940
+لقنة اللسانعُجمة اللسان موجودة؟ لكن بيقرأ القرآن
+
+299
+00:27:36,940 --> 00:27:42,240
+صح بيقرأ القرآن 100% ولا يستطيع أن ينطق بالعربية
+
+300
+00:27:42,240 --> 00:27:47,120
+كلمة واحدة طب كم هو عليهم شاق هذا التعلم و هذا
+
+301
+00:27:47,120 --> 00:27:52,600
+الحفظ؟ و هذا قصة الحفظ عندهم بيحفظوا الكلمة قوالب
+
+302
+00:27:52,600 --> 00:27:59,240
+بالصورة يعني يعني لما نكتب مثلا الله هى هم بيكتبوا
+
+303
+00:27:59,240 --> 00:28:04,890
+الله هذا الشكل الشكلوين ما يشوف هذا الشكل بيقولك
+
+304
+00:28:04,890 --> 00:28:10,190
+الله طب ايه .. قولله اكم حرف .. ايش الحروف .. وين
+
+305
+00:28:10,190 --> 00:28:15,970
+حرفي الليان .. بيفهمش الشكل .. هذا اسمه الله زي ما
+
+306
+00:28:15,970 --> 00:28:19,550
+بيصير عندنا في المدارس الابتدائية بيجيبوا الحمامة
+
+307
+00:28:19,550 --> 00:28:25,330
+.. بيجيبوا الحمامة .. صورة الحمامة و مكتوب هنا
+
+308
+00:28:25,330 --> 00:28:30,510
+حمامة و في الصفحه التانية بيجيبوا صورة الحمامة و
+
+309
+00:28:30,510 --> 00:28:34,930
+هنا فراخبقولّه اكتب، بنظر إلى الشكل، إيش؟ بقولّك
+
+310
+00:28:34,930 --> 00:28:38,910
+حمامة، لأنه خزانها في الذاكرة إيه؟ قالب واحد،
+
+311
+00:28:38,910 --> 00:28:43,070
+بفهمش إيش حروفة، اللي هي حيوان، هي طائر، هي ..
+
+312
+00:28:43,070 --> 00:28:47,290
+خلاص، هو بدي يحفظ حمامة، إذا هم بيحفظوا القرآن
+
+313
+00:28:47,290 --> 00:28:55,170
+يقعد قوالب، طب كم هو عليه مشاق هذا الأمر؟ما هذا
+
+314
+00:28:55,170 --> 00:29:01,570
+بيخلّينا نقول الحمد لله الذي جعل القرآن بلغتنا حتى
+
+315
+00:29:01,570 --> 00:29:07,510
+نقرأ حتى نتدبر أفلا يتدبرون القرآن أم على قلوب
+
+316
+00:29:07,510 --> 00:29:12,270
+أقفلوها أفلا يتدبرون القرآن و لو كان من عند غير
+
+317
+00:29:12,270 --> 00:29:18,090
+الله نوجدوا فيه اختلافا كثيرة صح ولاإذا بنقول يا
+
+318
+00:29:18,090 --> 00:29:22,670
+أخوات يعني جديش الله سبحانه وتعالى أكرمنا وجعل
+
+319
+00:29:22,670 --> 00:29:28,990
+القرآن بلغتنا إنه نزل بالعربية إن أنزلناه قرآنا
+
+320
+00:29:28,990 --> 00:29:36,010
+عربيا لعلكم تاكلون الخصية الرابعةيختلف القرآن
+
+321
+00:29:36,010 --> 00:29:40,230
+الكريم عن الأحاديث القدسية وإن كانت من كلام الله
+
+322
+00:29:40,230 --> 00:29:45,990
+لكن غير متعبد بتلاوتها، كلام غير معجز ويختلف عن
+
+323
+00:29:45,990 --> 00:29:49,830
+الأحاديث النبوية، الأحاديث النبوية صحيح إن هي إلا
+
+324
+00:29:49,830 --> 00:29:55,370
+وحي ومن الله، لكن اللفظ والتعبير من الرسول صلى
+
+325
+00:29:55,370 --> 00:30:00,730
+الله عليه وسلم ولا يتعبد بيها خمسة
+
+326
+00:30:01,880 --> 00:30:08,180
+ترجمة القرآن لا تُعتبر قرآنًا مهما بلغت من دقتها،
+
+327
+00:30:08,180 --> 00:30:14,500
+ليش؟ لأن الكلمة القرأنية تؤدي عدة .. لا يمكن
+
+328
+00:30:14,500 --> 00:30:20,560
+حسرها، لا يمكن يا أخوات حسر الدلالة، دلالة الألفاظ
+
+329
+00:30:20,560 --> 00:30:25,040
+في العربية، عشان هي .. يعني لا يمكن، يعني أقولكوا
+
+330
+00:30:25,040 --> 00:30:31,050
+مثال،الآن انا لو مان بدي اترجم الآية هذه و لا تجعل
+
+331
+00:30:31,050 --> 00:30:38,630
+يدك مغلولة إلى عنقك و لا تبسطها كل البسط بدي
+
+332
+00:30:38,630 --> 00:30:44,590
+اترجمها للانجليزية يعني بتقولك ماتخليش ايدك مربوطة
+
+333
+00:30:44,590 --> 00:30:50,710
+في عنقك و ماتخليها شبابها هي الترجمة الحرفية لكن
+
+334
+00:30:50,710 --> 00:30:54,730
+هذه الكلمة وين دللت في اللغة العربية؟ وين دللت؟
+
+335
+00:30:56,330 --> 00:31:00,450
+يعني ماتبخلش كتير أو ماتبسطش ايدك كتير في الانفق
+
+336
+00:31:00,450 --> 00:31:04,130
+وكمان يعني هل يمكن حصر المعنى على هذا المعنى اللي
+
+337
+00:31:04,130 --> 00:31:09,310
+قلناه في الشمكانية اللغة العربية حملة اوجه يعني
+
+338
+00:31:09,310 --> 00:31:18,700
+تستخدم في عبارات كثيرة وامور كثيرةولهذا لا يمكن
+
+339
+00:31:18,700 --> 00:31:24,380
+للترجمة أن ترتقي لتكون قرآنا أو حتى تبين كل ما جاء
+
+340
+00:31:24,380 --> 00:31:30,440
+به القرآن الكريم ستة أنه يشترط فيه التواتر أي
+
+341
+00:31:30,440 --> 00:31:34,940
+ينقله جامع عن جامع يستحيل تواطوهم على الكاتب يعني
+
+342
+00:31:34,940 --> 00:31:41,350
+القرآن هذا في حاجة مهمة بديكوا تعرفوهاالقرآن من
+
+343
+00:31:41,350 --> 00:31:46,690
+حيث الثبوت والدلالة القرآن من حيث الثبوت قطعي مائة
+
+344
+00:31:46,690 --> 00:31:51,650
+في المائة بتعرفوا لو واحد أو طالب أو طالبة شكت في
+
+345
+00:31:51,650 --> 00:31:57,700
+حرف من القرآن بتعرفوا عقيدتا إيش بيصير فيها؟أه صار
+
+346
+00:31:57,700 --> 00:32:02,740
+خلل كبير، خلل عقائدي كبير في عقيدتها، من ظنت أو
+
+347
+00:32:02,740 --> 00:32:08,680
+شكت في عدم ثبوت حرف واحد من القرآن، العقيدة انتهت،
+
+348
+00:32:08,680 --> 00:32:12,100
+خلل كبير في العقيدة، القرآن هذا ثابت من عند الله
+
+349
+00:32:12,100 --> 00:32:19,340
+بإيه؟ بقطع، لكن الدلالةدلالة آيات القرآن مقصومة
+
+350
+00:32:19,340 --> 00:32:26,320
+بعضها قطري أو بعضها ظنّي انما ثبوت يعني القرآن هدا
+
+351
+00:32:26,320 --> 00:32:31,540
+من وين ثابت من عند الله بقطع وصل إلينا بقطع زي ما
+
+352
+00:32:31,540 --> 00:32:37,520
+هو زي كما جاء من في رسول الله صلى الله عليه وسلم
+
+353
+00:32:37,520 --> 00:32:39,720
+إذا بنقول يا أخوات
+
+354
+00:32:44,570 --> 00:32:50,610
+في آية واحدة آية واحدة هي اللي ثبتت بشاهد واحد
+
+355
+00:32:50,610 --> 00:32:54,910
+اللي هو إن الله اشترع من المؤمنين أنفسهم وأموالهم
+
+356
+00:32:54,910 --> 00:33:01,850
+بأن لهم الجنة في سورة التوبة هذه رواها مين أو
+
+357
+00:33:01,850 --> 00:33:09,670
+قالها مين خزايمة وخزايمة يا أخوات شهدت رجلين بفعل
+
+358
+00:33:09,670 --> 00:33:14,560
+النبي صلى الله عليه وسلم اختصم النبي مع يهودياختصم
+
+359
+00:33:14,560 --> 00:33:20,220
+النبي مع يهودي فقال اليهودي من يشهد لك يا محمد صلى
+
+360
+00:33:20,220 --> 00:33:25,160
+الله عليه وسلم فقال يا خزايمة أنا أشهد له شهد
+
+361
+00:33:25,160 --> 00:33:29,080
+للنبي قال له يا خزايمة كيف تشهد و أنت لم تشهد يعني
+
+362
+00:33:29,080 --> 00:33:32,680
+كيف بدك تشهد حاجة أنت مشوفتهاش قال له يا رسول الله
+
+363
+00:33:32,680 --> 00:33:37,160
+صدقناك في أمر السماء بدناش نصدقك في أمر الدنيا
+
+364
+00:33:37,160 --> 00:33:44,270
+فقال اذهب يا خزايمة فإن شهادتك بشهادتينفالآية هذه
+
+365
+00:33:44,270 --> 00:33:47,650
+إن الله اشترع من المؤمنين أنفسهم وأموالهم إلى آخر
+
+366
+00:33:47,650 --> 00:33:51,890
+الآية ثبتت بفعل أو بشهادة خسايمة و بهيئة بكل
+
+367
+00:33:51,890 --> 00:33:56,870
+القرآن كله قطعي كله ثابت من عند الله سبحانه وتعالى
+
+368
+00:33:56,870 --> 00:33:58,650
+سابعة
+
+369
+00:34:00,840 --> 00:34:05,060
+ليس معنى كونه اه يمكن واحد يقول ليك يسمع كلمة
+
+370
+00:34:05,060 --> 00:34:11,440
+الإعجاز يكافر القرآن هذا معجز القرآن هذا صعب
+
+371
+00:34:11,440 --> 00:34:17,620
+القرآن هذا لا يمكن حفظه لا يمكن تدبره اه في ناس
+
+372
+00:34:17,620 --> 00:34:23,390
+كتير بتفكر الإعجازإشصار و أنا بقولكم يا أخوات
+
+373
+00:34:23,390 --> 00:34:29,210
+الإعجاز والتيسير بيمشوا مع بعض جنبا إلى جنب لا
+
+374
+00:34:29,210 --> 00:34:37,650
+يمكن لهم أن يتصادمان إنما يمشيان في خطين متوازين
+
+375
+00:34:37,650 --> 00:34:43,690
+كما أن القرآن كم هو القرآن في إعجاز كم هو في تيسير
+
+376
+00:34:43,690 --> 00:34:47,710
+بتعرفوا يا أخوات جربي
+
+377
+00:34:48,740 --> 00:34:53,440
+حاولي تحفظي صفحة واحدة من القرآن خمس دقائق بيتني
+
+378
+00:34:53,440 --> 00:34:58,380
+الصادق خمس دقائق ابتتكنيها بتسميها عن ظهر القلب
+
+379
+00:35:00,920 --> 00:35:05,280
+فبدي أديك صفحة من كتاب النظم الإسلامية صفحة واحدة
+
+380
+00:35:05,280 --> 00:35:11,000
+و بدي أديك أسبوع و تعالي سمعيها بعد أسبوع لابد أن
+
+381
+00:35:11,000 --> 00:35:15,300
+تقعي في أخطاء مافي إمكانية لابد أن تقعي في أخطاء
+
+382
+00:35:15,300 --> 00:35:20,880
+لكن صفحة القرآن خمس دقائق والله يا أخوات خمس دقائق
+
+383
+00:35:20,880 --> 00:35:25,280
+بيحفظها الإنسان و بسمعها كيف كأنه بينظر في القرآن
+
+384
+00:35:25,280 --> 00:35:32,150
+لما يسمعها بدون أي خلل بدون أي خطأليش؟ و لقد يسرنا
+
+385
+00:35:32,150 --> 00:35:37,250
+القرآن للذكري فهل من مدكر الله سبحانه وتعالى يسر
+
+386
+00:35:37,250 --> 00:35:41,650
+فهمه و يسر تدبره و يسر حفظه بتعرفوا أخدت تجربتي مع
+
+387
+00:35:41,650 --> 00:35:48,630
+القرآن الكريم تجربة فريدة بدأت في حفظ كتاب الله
+
+388
+00:35:48,630 --> 00:35:54,690
+سبحانه وتعالى بنصف صفحة كل ليلة بعد العشاء أقعد مع
+
+389
+00:35:54,690 --> 00:36:01,930
+القرآن الكريم نص ساعة أحفظ نصف صفحةأحفظ الجزئين
+
+390
+00:36:01,930 --> 00:36:09,980
+بعد هيككبرت للمساحة صرت صفحة احفظت جزء ايه بعد هيك
+
+391
+00:36:09,980 --> 00:36:14,200
+ثلاث صفحة الآن اللي عنده عضلات كمال الأجسام الناس
+
+392
+00:36:14,200 --> 00:36:17,780
+اللي بتنام عضلاتهم من يوم و ليلة بيعملوا العضلات و
+
+393
+00:36:17,780 --> 00:36:21,260
+الصيقان هذه الضخمة ولا بالتدريب شوية شوية و
+
+394
+00:36:21,260 --> 00:36:24,360
+الذاكرة تبعتي الإنسان يمكن واحدة تقولك والله أنا
+
+395
+00:36:24,360 --> 00:36:28,820
+حاولت أحفظ عملت كل مجهود ماقدرتش أحفظ إلا نص صفحة
+
+396
+00:36:28,820 --> 00:36:34,670
+في اليوم و أنا ماكنتش بتحفظ القرآن يا شيخ سيبكأيوة
+
+397
+00:36:34,670 --> 00:36:39,910
+وانا بقولك انك انت طبيعية مية في المية وانت زيك زي
+
+398
+00:36:39,910 --> 00:36:44,010
+الحافظين على المصحف زي العلماء زي القراء تماما
+
+399
+00:36:44,010 --> 00:36:48,690
+بتمام هم لما بدأوا كانوا زيك تماما اه ما هو ممكن
+
+400
+00:36:48,690 --> 00:36:52,410
+يكون يا أخوات يعني تيجي واحدة مثلا تاخدلها ساعة
+
+401
+00:36:52,410 --> 00:36:55,650
+ولا ساعتين ويدوها تحفظلها نصف صفحة يقولك طب انا
+
+402
+00:36:55,650 --> 00:36:59,930
+وقتش بتحفظ القرآن يا شيخ سيباوانا بقولك هذا مش
+
+403
+00:36:59,930 --> 00:37:04,130
+مرض، هذا مش قصور، هذا مش نقص، انت طبيعة مية في
+
+404
+00:37:04,130 --> 00:37:09,470
+المية، هيك الأمر في حقيقته احفظيلك بس جزء و جزءين
+
+405
+00:37:09,470 --> 00:37:13,750
+بهذه الشكلة، و بعد هيك كبري، كبري مع سافة الحفظ،
+
+406
+00:37:13,750 --> 00:37:19,460
+بيصير صفحةبعد هيك صفحتين بتعرف انتهى ايه بالمطاف
+
+407
+00:37:19,460 --> 00:37:24,080
+في الليلة بعد صلاة الإشع في ساعتين جديش أحفظ خمسة
+
+408
+00:37:24,080 --> 00:37:28,040
+ستة لو وصلت لسبع صفحات كل ليلة في ساعتين سبع صفحات
+
+409
+00:37:28,040 --> 00:37:32,940
+في ساعتين سبع صفحات أصبحت الذاكرة يا أخوات تالتهم
+
+410
+00:37:32,940 --> 00:37:38,060
+المعلومات التهاماليش فيه نية وفيه إخلاص وفيه إصرار
+
+411
+00:37:38,060 --> 00:37:43,920
+وفيه لله والممارسة و التجربة و التمرين أقول بقولي
+
+412
+00:37:43,920 --> 00:37:46,920
+هذا وأستغفر الله لي ولكم ان شاء الله تعالى في
+
+413
+00:37:46,920 --> 00:37:49,120
+المحاضرة اللي جاي يا أخوان نكمل
+
diff --git a/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/aAXflflP268_postprocess.srt b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/aAXflflP268_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b22fb213b7ad55b6ae30568a842d98c0dbcb2e4f
--- /dev/null
+++ b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/aAXflflP268_postprocess.srt
@@ -0,0 +1,1688 @@
+1
+00:00:20,470 --> 00:00:23,610
+أعوذ بالله السميع العليم من الشيطان الرجيم بسم
+
+2
+00:00:23,610 --> 00:00:28,250
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:28,250 --> 00:00:32,170
+والسلام على رسولنا الكريم وبعد أخوات الكريمات في
+
+4
+00:00:32,170 --> 00:00:38,370
+المحاضرة السابقة كنا قد بدأنا في توضيح وشرح مفهوم
+
+5
+00:00:38,370 --> 00:00:43,070
+الثبات والمرونة وكنا عمل مقصود بالثبات والمرونة
+
+6
+00:00:44,550 --> 00:00:49,350
+وقولنا الثبات يا أخوات هو الثبات الذي لا يؤدي إلى
+
+7
+00:00:49,350 --> 00:00:56,690
+الجمود والمرونة التي لا تؤدي إلى التسيب والسهولة
+
+8
+00:00:56,690 --> 00:01:02,530
+غير المحمودة أما الثبات والمرونة يعني بينهما علاقة
+
+9
+00:01:02,530 --> 00:01:08,260
+وارتباط وثيق جدا، لماذا؟لأن لو لحظة حتى في
+
+10
+00:01:08,260 --> 00:01:12,540
+المحاضرة السابقة ضربنا مثال وقولنا إنه يعني
+
+11
+00:01:12,540 --> 00:01:17,240
+التكليف بالصلاة هذا أمر ثابت لا يتغير لا بتغير
+
+12
+00:01:17,240 --> 00:01:23,840
+الزمان ولا بتغير المكان ولا بتغير الأشخاص ولكن في
+
+13
+00:01:23,840 --> 00:01:28,320
+التطبيق والأداء فيه نوع من المرونة يعني على سبيل
+
+14
+00:01:28,320 --> 00:01:31,820
+المثال إذا كان الإنسان مريضا ولا يستطيع أن يصلي
+
+15
+00:01:31,820 --> 00:01:36,970
+قائما يقولوا صلي جالسإذا كان الإنسان مريضا و لا
+
+16
+00:01:36,970 --> 00:01:43,050
+يستطيع الصيام والصيام من الثوابت بنقوله اقضي عندما
+
+17
+00:01:43,050 --> 00:01:49,810
+تصرف وتتعافى تستطيع قضاء هذه الفريضة وقولنا يا
+
+18
+00:01:49,810 --> 00:01:54,590
+أخوات يعني مجالات الثبات والمرونة يعني الثبات
+
+19
+00:01:54,590 --> 00:01:58,770
+والمرونة يدخل في جميع مجالات الإنسان في حياة
+
+20
+00:01:58,770 --> 00:02:03,910
+الإنسان بشتى جوانبها في حياته كل تفاصيلها في ثباته
+
+21
+00:02:03,910 --> 00:02:09,680
+في مرونةحتى الإنسان في معاملته مع أصحابه، إنسان
+
+22
+00:02:09,680 --> 00:02:14,060
+معاملته مع زوجتي، إنسان احتكاكه بالمجتمع، في هناك
+
+23
+00:02:14,060 --> 00:02:18,040
+ثوابت وفي هناك أمور فيها مرونة، يعني العلاقة أو
+
+24
+00:02:18,040 --> 00:02:23,600
+مجالات للإثبات والمرونة لا تقتصر على مجال معين أو
+
+25
+00:02:23,600 --> 00:02:28,060
+مسألة بحد ذاتها، إنما فيه مرونة، على سبيل المثال
+
+26
+00:02:28,060 --> 00:02:32,080
+الآن، بتقولوا كيف بدنا ناخد الحضور والغياب؟صحيح
+
+27
+00:02:32,080 --> 00:02:37,320
+الالتزام الطالب بحضور المحاضرة هذا من الثوابط، لكن
+
+28
+00:02:37,320 --> 00:02:41,860
+ليس من الثوابط الجامدة، والله في بعض المرونة، لكن
+
+29
+00:02:41,860 --> 00:02:47,350
+المرونة مش بشكلها الواسعلو تركنا المجال مفتوح ربما
+
+30
+00:02:47,350 --> 00:02:51,970
+لا يحضر المخاضرة إلا عدد خليل جدا وبالتالي بيكون
+
+31
+00:02:51,970 --> 00:02:56,950
+المرونة أدت إلى أشياء يعني تسيب أو عدم انضباط أو
+
+32
+00:02:56,950 --> 00:03:02,110
+كذا إذا لابد من الثبات والمرونة في جميع مجالات
+
+33
+00:03:02,110 --> 00:03:08,930
+الحياة على اختلافة وتنوحة أما لو جينا يعني نتطرق
+
+34
+00:03:08,930 --> 00:03:13,280
+لأهمية الثبات والمرونةالثبات يا أخوات يطمن
+
+35
+00:03:13,280 --> 00:03:17,240
+الاستقامة للمجتمع المسلم والوضوح وعدم التخبط
+
+36
+00:03:17,240 --> 00:03:22,080
+والمرونة ضرورية لاختلاف البيئات والظروف والأعراف
+
+37
+00:03:22,080 --> 00:03:27,490
+والعاداتأشياء كثيرة في المجتمع حتى يستقيم المجتمع
+
+38
+00:03:27,490 --> 00:03:34,110
+لابد أن تكون ثابتة الأعراف العادات الأخلاق الحميدة
+
+39
+00:03:34,110 --> 00:03:39,090
+لابد لها من ثبوت الإنسان دايما الأخوات بيحب الوضوع
+
+40
+00:03:39,090 --> 00:03:43,410
+ليش؟ لأن لو كان الأمر مشكلة عليه هذا يؤدي إلى
+
+41
+00:03:43,410 --> 00:03:49,780
+التخبط فلابد من الثباتعلاقة الإنسان بزميله لابد
+
+42
+00:03:49,780 --> 00:03:55,160
+لها من أمور ثابتة تستند إليها علاقة الرجل بأسرته
+
+43
+00:03:55,160 --> 00:04:00,820
+لابد أن يكون له أو لابد أن تكون ثابتة في هذه
+
+44
+00:04:00,820 --> 00:04:08,100
+المجال وهذا الإزاوي حتى يتحقق الإطمئنان ويتحقق
+
+45
+00:04:08,100 --> 00:04:14,990
+الوضوح وعدم التخبط أما المرونةطبعا يا أخوات العداد
+
+46
+00:04:14,990 --> 00:04:21,090
+تختلف، البيئات تختلف، الظروف تختلف، وبالتالي لابد
+
+47
+00:04:21,090 --> 00:04:25,290
+للإنسان أن يتأقلم، لازم يكون الإنسان مرن، ما يكون
+
+48
+00:04:25,290 --> 00:04:30,200
+جافوالمرونة يا أخوات قلنا قبل شوية يعني في جميع
+
+49
+00:04:30,200 --> 00:04:34,940
+مجالات الحياة لابد أن يستخدم الإنسان المرونة يعني
+
+50
+00:04:34,940 --> 00:04:40,060
+وخيره الأمور الوسط يعني ما نتسددش وما يكونش فيه
+
+51
+00:04:40,060 --> 00:04:46,060
+ثبات الذي يؤدي إلى التسنج والتطرف والشدة وما يكونش
+
+52
+00:04:46,060 --> 00:04:50,840
+فيه مرونة بحيث تؤدي إلى التسيبلذلك يقول سبحانه
+
+53
+00:04:50,840 --> 00:04:55,940
+وتعالى و كذلك جعلناكم أمة وسطة لتكونوا شهداء يعني
+
+54
+00:04:55,940 --> 00:05:03,220
+الوسط احنا ناس وسط في الخلقه وسط في الهيئة وسط في
+
+55
+00:05:03,220 --> 00:05:07,740
+الشريعة وسط في التكليف وسطية الاعتقاد وسطية
+
+56
+00:05:07,740 --> 00:05:13,630
+العبادة وسطية الأخلاق وسطية المعاملاتيعني النظم
+
+57
+00:05:13,630 --> 00:05:17,850
+الإسلامية تمتاز بالوساطية في كل شيء يعني في كل
+
+58
+00:05:17,850 --> 00:05:21,850
+مراحل وفي كل أقسام النظم الإسلامية سواء كانت
+
+59
+00:05:21,850 --> 00:05:26,190
+عقوبات، سواء كانت معاملات، سواء كانت يعني من قبيل
+
+60
+00:05:26,190 --> 00:05:31,410
+الاعتقاد، حتى الاعتقاد، اعتقادنا اعتقاد يعني وساطي
+
+61
+00:05:31,410 --> 00:05:35,970
+أيضا الثبات يلبي الرغبة في الاستقرار والاطمئنان
+
+62
+00:05:35,970 --> 00:05:40,050
+على المستقبل بالرغم من تغير الحكام والحكومات لأنها
+
+63
+00:05:40,050 --> 00:05:44,830
+محكومة بالمنهج الإسلاميالآن أنا مهمنيش من الحكومة
+
+64
+00:05:44,830 --> 00:05:48,490
+اللي تيجي، من القائد اللي يأتي، من السايمة اللي
+
+65
+00:05:48,490 --> 00:05:55,690
+يذهب، يتغير الرئيس، تتغير الحكومة، تتغير المؤسسة،
+
+66
+00:05:55,690 --> 00:05:58,990
+لكن في النهاية يا أخوتي، مدام هذه المؤسسات
+
+67
+00:05:58,990 --> 00:06:03,790
+المتغيرة، والحكام المتغيرين، والحكومات المتغيرة،
+
+68
+00:06:03,790 --> 00:06:08,330
+في النهاية، مدامها بتتغير وبتتحرك في إطار دائرة
+
+69
+00:06:08,330 --> 00:06:14,400
+الشرع، أنا بأقلق؟ أنا بكاف؟ما دام التغير هذا
+
+70
+00:06:14,400 --> 00:06:19,840
+الحاصل ما دام التغير في النهاية مضبوط أو موجود في
+
+71
+00:06:19,840 --> 00:06:24,660
+داخل دائرة الشرع دائرة النظم الإسلامية دائرة
+
+72
+00:06:24,660 --> 00:06:29,160
+الضابط الإسلامية هذا بيأثر علي في الشيء أنا يعني
+
+73
+00:06:29,160 --> 00:06:34,560
+أنا صاحب فكرة مش صاحب شخص يعني أفضل البشر على
+
+74
+00:06:34,560 --> 00:06:41,170
+الإطلاق سيدنا رسول الله صلى الله عليه وسلمعندما
+
+75
+00:06:41,170 --> 00:06:46,450
+توفي يا أخوات أبو بكر الصديق رضي الله تعالى عنهم
+
+76
+00:06:46,450 --> 00:06:53,430
+كان رجلا بكاء كان مايقدرش يصلي في الناس ليش؟ لأنه
+
+77
+00:06:53,430 --> 00:07:01,370
+رجل رقيق حساس على طول بيبكي شوفوا كيف المحن بتستع
+
+78
+00:07:01,370 --> 00:07:06,910
+الرجال و لكل يعني زمان ومناسبة إليها عادات أو
+
+79
+00:07:06,910 --> 00:07:11,460
+تقاليدها ومواصفات أو دوابطةفي حضرة رسول الله صلى
+
+80
+00:07:11,460 --> 00:07:15,880
+الله عليه وسلم كان أبو بكر رضي الله تعالى عنه رجل
+
+81
+00:07:15,880 --> 00:07:23,760
+بكاء رجل رقيق رجل حساس لكن عندما توفي النبي صلى
+
+82
+00:07:23,760 --> 00:07:27,720
+الله عليه وسلم تعرفوا فيه من الصحابة ماقدروش يجفع
+
+83
+00:07:27,720 --> 00:07:32,600
+أجليهم عمر رضي الله تعالى عنه الرجل الشديد القوي
+
+84
+00:07:32,600 --> 00:07:39,010
+في الحق عمر هوقول لأ صدق نفسيلا أصدقه ما تقولون
+
+85
+00:07:39,010 --> 00:07:44,650
+كانت يعني كسائقة خبر وفاة رسول الله نزل عليه
+
+86
+00:07:44,650 --> 00:07:52,810
+كسائقة لكن أبو بكر رضي الله تعالى عنه وقف وخطب في
+
+87
+00:07:52,810 --> 00:07:59,230
+الناس أيها الناس من كان يعبد محمدا فإن محمدا قد
+
+88
+00:07:59,230 --> 00:08:06,620
+مات ومن كان يعبد الله فإن الله حي لا يموتوقفاه في
+
+89
+00:08:06,620 --> 00:08:13,480
+عنفوان في قوة في إصرار .. ليش؟ لأنه احنا يعني نعم
+
+90
+00:08:13,480 --> 00:08:18,080
+الرسول صلى الله عليه وسلم قدوة واسوة ورسولنا
+
+91
+00:08:18,080 --> 00:08:23,780
+وشفينا وحبيبنا ومن أطاعني فقد أطاع الله يعني طاعة
+
+92
+00:08:23,780 --> 00:08:30,920
+واجبة حبه من حب الله حب وواجب لكن الإسلام لا ينحصر
+
+93
+00:08:30,920 --> 00:08:38,060
+في شخص ولا في حكومة ولا في عصروما أرسلناك إلا رحمة
+
+94
+00:08:38,060 --> 00:08:44,460
+للعالمين الإسلام هذا دين عالمي لا يموت بموت شخص
+
+95
+00:08:44,460 --> 00:08:50,460
+ولا ينتهي بانتهاء الزمن إنما هو على مر العصور وهذه
+
+96
+00:08:50,460 --> 00:08:55,860
+يعني النظم الإسلامي المستوحى من الإسلام من القرآن
+
+97
+00:08:55,860 --> 00:09:02,100
+من سنة النبي صلى الله عليه وسلمثابتة هذا الثبات
+
+98
+00:09:02,100 --> 00:09:07,740
+يجعل عند الإنسان إطمئنان واستقرار على المستقبل
+
+99
+00:09:07,740 --> 00:09:12,020
+مهما تغيرت الظروف والحكومات والأنظمة والمؤسسات
+
+100
+00:09:12,020 --> 00:09:18,660
+تلاتة التشابه الكبير بين النظم التي تنظم حياة
+
+101
+00:09:18,660 --> 00:09:22,880
+البشر والنظم التي تنظم حركة الكون من حيث الثبات
+
+102
+00:09:22,880 --> 00:09:27,500
+والمرورة يعني كالك النظم اللي بتنظم حياة الإنسان
+
+103
+00:09:28,600 --> 00:09:36,540
+بتشبه أو بتتشابه بقدر كبير جداً مع النظم التي تنظم
+
+104
+00:09:36,540 --> 00:09:44,880
+الكون كلها على سبيل المثال الآن الشمس يا أخوات
+
+105
+00:09:44,880 --> 00:09:51,420
+مرنة، بتمشي، بتتحرك، بتدور وكل في فلك يسبحون القمر
+
+106
+00:09:51,420 --> 00:09:58,000
+بتتحرك، الأرض بتتحرك، هذه المرونة لكن إيش الثبات؟
+
+107
+00:09:58,710 --> 00:10:06,110
+الثبات إنها بتتحرك في إطار معين، يعني ثابتة في هذا
+
+108
+00:10:06,110 --> 00:10:09,530
+المصار، بتعرفوا الشمس لو انحرفت عن مصارها إيش
+
+109
+00:10:09,530 --> 00:10:15,870
+بيصير؟ قد تحرق الأرض في لحظات، القمر لو خرج عن
+
+110
+00:10:15,870 --> 00:10:20,110
+مصاره، لتعرفوا عدد السنين أو الحساب، بنبطل نعرف
+
+111
+00:10:20,110 --> 00:10:24,940
+الأيام و نحسب الشهور و الساعاتإذن أخوات صحيح فيها
+
+112
+00:10:24,940 --> 00:10:29,360
+مرونة لكن في نفس الوقت فيها ثبات يعني النظام الكون
+
+113
+00:10:29,360 --> 00:10:34,580
+المجرة الشمسية تجتمل على الثبات والمرونة وهذا يعني
+
+114
+00:10:34,580 --> 00:10:41,350
+يظهرعظمة الله سبحانه وتعالى لأنه من الصانعاء
+
+115
+00:10:41,350 --> 00:10:45,830
+الصانعاء واحد والخالق واحد الله سبحانه وتعالى خلق
+
+116
+00:10:45,830 --> 00:10:52,030
+الإنسان وخلق الكون وأوجد نظاما ينظم أحوال الإنسان
+
+117
+00:10:52,030 --> 00:10:57,870
+يتشابه تماما مع النظام الذي ينظم حركة الأجرام
+
+118
+00:10:57,870 --> 00:11:03,530
+السماوية والكواكب والكون أربع
+
+119
+00:11:03,530 --> 00:11:09,620
+خاصية الثبات والمرونةتعتبر مقياسا وميزانا لأعمال
+
+120
+00:11:09,620 --> 00:11:16,160
+البشر ومشاعرهم وافكارهم وتصوراتهم يعني ايه في عندي
+
+121
+00:11:16,160 --> 00:11:22,260
+دايما العلماء بيوجدوا لهم مقياس انا مثلا لما بدي
+
+122
+00:11:22,260 --> 00:11:29,180
+أعمل مقابلة بدي وظيفة بدي أخت تشتغل مدرسة بحط
+
+123
+00:11:29,180 --> 00:11:33,640
+المقياس المطلوب و بعدين بجيب الناس بقدرجهم على
+
+124
+00:11:33,640 --> 00:11:38,490
+المقياس هذالو كان هذا المقياس خلال نتيجة المقابلة
+
+125
+00:11:38,490 --> 00:11:43,170
+تبتطلعش معبرة عن الواقع عن الحقيقة لكن لما نكون
+
+126
+00:11:43,170 --> 00:11:48,270
+المقياس دقيق تماما زي الميزان يا اخوان انا مثلا لو
+
+127
+00:11:48,270 --> 00:11:54,130
+روحت اشتريت شغل من ال supermarket من المحل التجاري
+
+128
+00:11:54,130 --> 00:11:57,790
+اشتريت شغل يعني من قبيل الموزولات يعني اللي بتتوزن
+
+129
+00:11:57,790 --> 00:12:04,520
+وكان الميزان طبع الراجل فيه خلالبصير فيه ظلم ..
+
+130
+00:12:04,520 --> 00:12:09,220
+بصير فيه ظلم .. بيصير يا إما بديني أكتر من حجي، يا
+
+131
+00:12:09,220 --> 00:12:17,580
+إما ينقص من حقي، وهنا بصير اختلال في المعاملة، لكن
+
+132
+00:12:17,580 --> 00:12:23,510
+عندما يكون الميزان دقيق ومتوفر .. وافقين منهبيصير
+
+133
+00:12:23,510 --> 00:12:27,750
+هذا الميزان مقياس حقيقي يعبر عن الواقع النظم
+
+134
+00:12:27,750 --> 00:12:32,970
+الإسلامية جالك تعتبر أو كثية الثبات والمرورة تعتبر
+
+135
+00:12:32,970 --> 00:12:38,850
+من قبيل المقياس اللي الإنسان بيقيص شخصيته أفعاله
+
+136
+00:12:38,850 --> 00:12:45,590
+أقوله عليها يعني بمثابة الميزان الذي يقاس عليه أو
+
+137
+00:12:45,590 --> 00:12:50,110
+به الأشياء ودائما احنا بنقول يا أخوات لازم شخصية
+
+138
+00:12:50,110 --> 00:12:57,510
+الإنسان المسلمحتى عندما يعني نسأل في فتاوة عن
+
+139
+00:12:57,510 --> 00:13:04,870
+اللباس عن الزينا عن الكذا دايما عملا بمنهج النبي
+
+140
+00:13:04,870 --> 00:13:09,050
+صلى الله عليه وسلم ماخوية ربينا أمرين إلا اختار
+
+141
+00:13:09,050 --> 00:13:14,390
+أيصر هما احنا بنختار للناس الأيصر في مرونة في
+
+142
+00:13:14,390 --> 00:13:19,150
+اللباس الشرعي للبنت للطالبة مادامها محققة فيه
+
+143
+00:13:19,150 --> 00:13:23,260
+الضوابط الشرعية في مرونةلكن هم ماشيش هتقولوا هذا
+
+144
+00:13:23,260 --> 00:13:28,200
+المنديل ألوانهم أبصر كيف .. هذا يعني .. يعني بتخلي
+
+145
+00:13:28,200 --> 00:13:32,640
+.. بتصعب الأمور على الناس مادام .. يعني في نوع من
+
+146
+00:13:32,640 --> 00:13:36,820
+المرونة لكن بشرط أخوات ليس المرونة التي تؤدي إلى
+
+147
+00:13:36,820 --> 00:13:41,350
+الاعتداء على الدوابط الشرعيةفي مرونة يعني في
+
+148
+00:13:41,350 --> 00:13:46,730
+نطاقها مرونة بما تسمل الكلمة من معنى وليست مرونة
+
+149
+00:13:46,730 --> 00:13:51,850
+المطلقة وكمان مش لازم تتشكد كلش حرام حرام حرام
+
+150
+00:13:51,850 --> 00:13:58,710
+حرام يعني انما بعثهم ميسيرين وليس منافرين مبشرين
+
+151
+00:13:58,710 --> 00:14:03,690
+وليس منافرين ولذلك يا أخوات بنقول خاصية الثبات
+
+152
+00:14:03,690 --> 00:14:07,910
+والمرونةتعتبر حتى المحاضرة اللي احنا بيصددها لو
+
+153
+00:14:07,910 --> 00:14:12,650
+تمنا من أول محاضرة لأخرى علمه بس مافيش يعني تغيير
+
+154
+00:14:12,650 --> 00:14:16,890
+جوه حتى في الأمور يعني في قواعد الترب يقولك لابد
+
+155
+00:14:16,890 --> 00:14:21,090
+من استخدام في المحاضرة أساليب، مناقشة تربوية،
+
+156
+00:14:21,090 --> 00:14:27,010
+تغيير جوه المحاضرة، كذا علشان إيه تكون يعني الأمثل
+
+157
+00:14:27,010 --> 00:14:28,210
+و الأفضل
+
+158
+00:14:31,370 --> 00:14:35,270
+أيجي اليوم ان شاء الله سنتحدث في خاصية جديدة من
+
+159
+00:14:35,270 --> 00:14:40,950
+خصائص النظم الإسلامية على وهي يعني خاصية الشمول
+
+160
+00:14:40,950 --> 00:14:46,010
+والتوازن طبعا الشمول والتوازن يا أخوات ماذا نقصد
+
+161
+00:14:46,010 --> 00:14:54,030
+بالشمول؟ مالمقصود بالشمول؟ اتفضلي نظر تعالج حياته
+
+162
+00:14:54,030 --> 00:15:00,350
+لكل واحد في الحياة يعني إنه شخص نظر التعالج كل شخص
+
+163
+00:15:00,350 --> 00:15:05,260
+في الحياةطبعاً هي زميلتكم بتقول يعني معنى الشمول
+
+164
+00:15:05,260 --> 00:15:12,120
+أنها .. أن هذا النظم يعني تعالج جوانب الحياة كلها
+
+165
+00:15:12,120 --> 00:15:17,180
+يعني بجميع أقسامها سواء كان عقيدة أو أخلاق أو
+
+166
+00:15:17,180 --> 00:15:23,800
+عبادات أو معاملات أو سياسة أو حكم يعني شاملة ل ..
+
+167
+00:15:23,800 --> 00:15:32,340
+بتنظيمها لجميع مجالات الحياة بتنوعها واختلافهاليه
+
+168
+00:15:32,340 --> 00:15:38,140
+يا أخوات؟ يعني من أين جاء هذا الشمون؟ الشمون هي ده
+
+169
+00:15:38,140 --> 00:15:46,220
+الـلأن مصدر هذه النظم مصدرها الله سبحانه وتعالى
+
+170
+00:15:46,220 --> 00:15:52,220
+الذي أحاط بكل شيء علم مدام الله سبحانه وتعالى أحاط
+
+171
+00:15:52,220 --> 00:15:56,160
+بكل شيء علم إذا أوجد من النظم ما يعالج جميع
+
+172
+00:15:56,160 --> 00:16:03,000
+المجالات وجميع الجوانب المختلفة للحياة سواء كانت
+
+173
+00:16:03,000 --> 00:16:09,310
+عقيدة أو أخلاق أو عباداتأو معاملات أو سياسة أو غير
+
+174
+00:16:09,310 --> 00:16:15,010
+ذلك ولذلك يقول سبحانه وتعالى وكل شيء أحصيناه فيه
+
+175
+00:16:15,010 --> 00:16:21,570
+إمام مبين وكمان يا أخوات الشمول يراعي حياة الفرد
+
+176
+00:16:21,570 --> 00:16:29,630
+بمراحله المختلفة يعني بلغت هذه النظم من الاعتناء
+
+177
+00:16:29,630 --> 00:16:35,410
+بشؤون الفرد بكافة المراحل حتى قبل أن يوجد على هذه
+
+178
+00:16:35,410 --> 00:16:41,710
+الأرضالطفل وهو في بطن أمه، تخيلوا يا أخوات لو توفي
+
+179
+00:16:41,710 --> 00:16:48,820
+والد هذا الطفل، بيرث من أبي ولا لا يرث؟يُنسب لأبيه
+
+180
+00:16:48,820 --> 00:16:53,860
+ولا لا يُنسب؟ يُنسب لأبيه ويرث لأبيه يعني بتكون
+
+181
+00:16:53,860 --> 00:16:58,940
+عنده أهلية ناقصة لكن إله أهلية أو إله كيان أو إله
+
+182
+00:16:58,940 --> 00:17:05,200
+اعتبار لا نقسم الميراث إلا بنزول هذا الطفل ننظر هل
+
+183
+00:17:05,200 --> 00:17:10,020
+هو يعني ذكراً أو أنثى قد يكون توأم قد يكون كذا
+
+184
+00:17:10,020 --> 00:17:14,520
+يعني بنحجز الميراث لا نقسم الميراث حتى يأتي هذا
+
+185
+00:17:14,520 --> 00:17:20,050
+والله يا أخوتي أنا بعرفأنا بعرف يعني حادثة وقعت
+
+186
+00:17:20,050 --> 00:17:23,230
+يعني
+
+187
+00:17:23,230 --> 00:17:31,670
+امرأة وهي حامل في الأسبوع الأول توفي عنها زوجها في
+
+188
+00:17:31,670 --> 00:17:35,750
+الأسبوع الأول توفي عنها زوجها وهي حامل في الأسبوع
+
+189
+00:17:35,750 --> 00:17:41,910
+الأول فماء مضى الأربعين يوما قالت لأهل الزوج
+
+190
+00:17:41,910 --> 00:17:48,380
+درباكم أنا حامللكي لا تتهم فيما بعد يعني من أين
+
+191
+00:17:48,380 --> 00:17:53,880
+جاءت بهذا الطفل قالت لهم أني حامل وبالفعل يعني
+
+192
+00:17:53,880 --> 00:18:00,300
+أنجبت ويعني نصبة إلى أبيه ويعني أخذ نصيبه من
+
+193
+00:18:00,300 --> 00:18:05,040
+الميراث شوفوا النظم الإسلامية اعتنت بالإنسان حتى
+
+194
+00:18:05,040 --> 00:18:12,460
+قبل ما جئواطب حتى إذا جاء طفلا وعلى المولود له
+
+195
+00:18:12,460 --> 00:18:19,200
+رزقهن وكسوتهن يعني جالتلك النفقة لابد أن .. يعني
+
+196
+00:18:19,200 --> 00:18:25,800
+كافلة له النفقة و التأديب و التوجيه علموا أبناءكم
+
+197
+00:18:25,800 --> 00:18:31,970
+الصلاة على سبع وضربهم عليها على عشريعني و أوجبت
+
+198
+00:18:31,970 --> 00:18:37,630
+هذه الأمور أوجبت التأديب كلكم راعن و كلكم مسئول عن
+
+199
+00:18:37,630 --> 00:18:43,150
+رعيته المرأة في بيت زوجها راعية راعية عن مين؟
+
+200
+00:18:43,150 --> 00:18:46,810
+راعية عن المال و راعية عن الأطفال و راعية عن البيت
+
+201
+00:18:46,810 --> 00:18:52,170
+إذا يا أخوات شوفوا النظام الإسلامي بيكفل للإنسان
+
+202
+00:18:52,170 --> 00:18:57,310
+في مراحله المختلفة العناية و التوجيه و التربية و
+
+203
+00:18:57,310 --> 00:19:04,440
+التأديب و التعليم إلى أنإلى أن حتى يموت حتى عندما
+
+204
+00:19:04,440 --> 00:19:09,180
+يموت الإنسان الله سبحانه وتعالى أوجب على المسلمين
+
+205
+00:19:09,180 --> 00:19:15,520
+تغسيل هذا الرجل وتكفينه وصلاة عليه ودفنه في مقابر
+
+206
+00:19:15,520 --> 00:19:22,100
+المسلمين يعني مجرد ما أن يتخلق هذا الإنسان على جته
+
+207
+00:19:22,100 --> 00:19:28,730
+واعتنت به النظم الإسلامية وهذه العناية مشت معاهفي
+
+208
+00:19:28,730 --> 00:19:34,550
+كل أطوار الحياة إلى أن عاد إلى الآخرة مرة أخرى لذن
+
+209
+00:19:34,550 --> 00:19:39,250
+بيقول يا أخوات هذا المقصود بالشمول تنظم شمولية
+
+210
+00:19:39,250 --> 00:19:49,610
+الإنسان في كل مراحله المختلفة ويقول
+
+211
+00:19:49,610 --> 00:19:53,510
+شهدة لها بعض اليهود في عصر النبي صلى الله عليه
+
+212
+00:19:53,510 --> 00:19:59,720
+وسلم بيقول أحد اليهود عجبالهذا الدين وعجبا لهذه
+
+213
+00:19:59,720 --> 00:20:04,320
+النظم وعجبا لهذه الشريعة يعني نبيكم عليه الصلاة
+
+214
+00:20:04,320 --> 00:20:11,380
+والسلام علمكم حتى دخول الخلاء حتى دخول الحمام
+
+215
+00:20:11,380 --> 00:20:15,180
+النبي عليه الصلاة والسلام علمنا النبي صلى الله
+
+216
+00:20:15,180 --> 00:20:21,530
+عليه وسلم علمنا كيف يأتي الرجل أهله ماذا يقولعند
+
+217
+00:20:21,530 --> 00:20:26,390
+زفافي، ماذا يقول في المصيبة؟ ماذا يقول في الفرح؟
+
+218
+00:20:26,390 --> 00:20:33,850
+ماذا يقول عندما يشاهد نفسه في المرأة؟ ما شاء الله،
+
+219
+00:20:33,850 --> 00:20:43,050
+لا قوة إلا بالله اللهم حسن خلقي كما حسنت خلقي حسن
+
+220
+00:20:43,050 --> 00:20:49,370
+خلقي كما حسنت خلقي كيف ننزع ملابسنا؟ وكيف نرتديها؟
+
+221
+00:20:49,370 --> 00:20:55,320
+فيه قليةكيف ننام؟ كيف نستيقظ؟ كيف نتحرك؟ حتى
+
+222
+00:20:55,320 --> 00:21:04,580
+انتعال الجزمة أو النقل له طريقة معينة ليش؟ اندلة
+
+223
+00:21:04,580 --> 00:21:10,360
+على شيء على ماذا يدل هذا التنظيم الشمولية على
+
+224
+00:21:10,360 --> 00:21:17,580
+شمولية النظم الإسلامية وهذه الشمولية لا يمكن لبشر
+
+225
+00:21:17,580 --> 00:21:25,790
+ما أن يحيط بهالأن البشر لا علم لهم، يفتقرون إلى
+
+226
+00:21:25,790 --> 00:21:31,090
+العلم، إلى الخبرة، إلى الإدقاء حتى خلي واحد يعمل
+
+227
+00:21:31,090 --> 00:21:36,570
+عملية جراحية، هل يعود لسابقه؟ لا يمكن، صنع الله
+
+228
+00:21:36,570 --> 00:21:42,410
+الذي أتقن كل شيء .. كل شيء .. شيءإذا هذا شمول
+
+229
+00:21:42,410 --> 00:21:48,070
+يعالج الجوانب المختلفة بقولنا مجالات الشمول يعالج
+
+230
+00:21:48,070 --> 00:21:53,050
+و بنظم الحياة الدنيا بيهيئ الإنسان و بيعد الإنسان
+
+231
+00:21:53,050 --> 00:22:01,230
+للآخرة بيعتني بالفرد بكافة مراحله يعتني بالمجتمع
+
+232
+00:22:01,230 --> 00:22:09,810
+بكافة مؤسساته لو شفنا يعني أو لاحظنا اللي هوتوازن
+
+233
+00:22:09,810 --> 00:22:17,050
+قلنا في شمول وفي توازن طبعا التوازن يا أخوات تظهر
+
+234
+00:22:17,050 --> 00:22:23,010
+شمولية النظم الإسلامية في توازن وتناسق يعني الشمول
+
+235
+00:22:23,010 --> 00:22:30,310
+الذي جاءت به وأحاط بكل شيء تنظيما واتقانا لحياة
+
+236
+00:22:30,310 --> 00:22:37,070
+البشر لحياة الناس للمجتمعات هذا الشمول متوازن
+
+237
+00:22:37,070 --> 00:22:38,690
+ومتناسق
+
+238
+00:22:40,090 --> 00:22:46,150
+يعني اضرب لكم مثل انا ممكن اجمع كل مقاعد هذه
+
+239
+00:22:46,150 --> 00:22:53,050
+القاعة اجمعها و اضح بعضها فوق بعض انا بتصرفي هذا
+
+240
+00:22:53,050 --> 00:22:59,950
+شامل لكن الشمول هذا مش متوازن ليش؟ اشترين كرسي
+
+241
+00:22:59,950 --> 00:23:04,710
+هناك و كرسي هنا انا لما اصلح أوراح الامتحان مافي
+
+242
+00:23:04,710 --> 00:23:10,350
+امكانية لازم كل ورقة من الأوراق تمر عليهافيش
+
+243
+00:23:10,350 --> 00:23:16,550
+إمكانية شمولية مطلقة لكن برضه في التصحيح لازم يكون
+
+244
+00:23:16,550 --> 00:23:22,710
+فيه توازن لازم يكون فيه تناسق بين الأوراق وبين
+
+245
+00:23:22,710 --> 00:23:28,010
+الطلبات توازن ميزان دقيق يعني مثلا أنا بجيب إجابة
+
+246
+00:23:28,010 --> 00:23:31,990
+نموذجية يعني المقياس اللي حكينا عليه قبل شوية
+
+247
+00:23:31,990 --> 00:23:38,190
+إجابة نموذجية مقياسوبحاول بالجهد البشري
+
+248
+00:23:38,190 --> 00:23:43,990
+بالإمكانيات البشرية اللي عندي بحاول أقيس الإجابات
+
+249
+00:23:43,990 --> 00:23:51,160
+على هذا الميزان بحيث تكون فيه تناسقوتوازن مع كل
+
+250
+00:23:51,160 --> 00:23:54,580
+الطالبات طبعا الأسئلة الموضوعية مافيش فيها هذا
+
+251
+00:23:54,580 --> 00:23:58,880
+الكلام يا بتاخد درجة الطالب يا إما بتفقد درجة لكن
+
+252
+00:23:58,880 --> 00:24:04,580
+في الأسئلة المقالية بنعمل إجابة نموذج إجابة يعتبر
+
+253
+00:24:04,580 --> 00:24:09,340
+مقياس أنثى و بنقيس عليه هذه الإجابات في توازن
+
+254
+00:24:09,340 --> 00:24:15,300
+وتناسق طبعا التوازن بين حياة الأفراد وحياة المجتمع
+
+255
+00:24:16,260 --> 00:24:20,300
+والفقاء بيقولوا المصلحة العامة مقدمة على المصلحة
+
+256
+00:24:20,300 --> 00:24:26,020
+الخاصة لكن حتى المصلحة أو حياة الفرد توازن بين
+
+257
+00:24:26,020 --> 00:24:32,860
+حياة الفرد بنفسها من ناحية وتوازن بين حياة الفرد
+
+258
+00:24:32,860 --> 00:24:39,240
+وحياة المجتمع أما التوازن بين حياة الفرد نفسه
+
+259
+00:24:39,240 --> 00:24:45,160
+يبينه قول النبي صلى الله عليه وسلم ما ملأ ابن آدم
+
+260
+00:24:45,160 --> 00:24:54,640
+وعاءشرًا من بطنه يعني الآن الأصل فينا في الطعام يا
+
+261
+00:24:54,640 --> 00:25:01,780
+أخوات لقيمات الأصل في الإنسان لقيمات يقمن بها
+
+262
+00:25:01,780 --> 00:25:09,580
+صلبهم لكن إن كان لابد آكلًا إن كان يريد أن يقتحم
+
+263
+00:25:09,580 --> 00:25:17,750
+أسوار الطعام فجلّك فثلثلطعامه و ثلث لشرابه و ثلث
+
+264
+00:25:17,750 --> 00:25:22,170
+لنفسه وهذا ايه هذا مش في الوضع الطبيعي في الوضع
+
+265
+00:25:22,170 --> 00:25:27,790
+الطبيعي لقيمات يقيمنا بيها شلبهم لكن في الوضع
+
+266
+00:25:27,790 --> 00:25:32,510
+الغير طبيعي فثلث و ثلث و ثلث لكن المراحز اليوم ان
+
+267
+00:25:32,510 --> 00:25:37,150
+احنا من البداية مش في الوضع الطبيعي في الوضع
+
+268
+00:25:37,150 --> 00:25:44,840
+الطبيعي عندنا ايهولا في نفس ولا للماء ولا غيره إذا
+
+269
+00:25:44,840 --> 00:25:51,520
+التوازن بين حياتي الأفراد هذا الجسم وهذا الجسد له
+
+270
+00:25:51,520 --> 00:25:59,820
+عليا حقه ويعني واسف أعطيه ساعات من الراحة أعطيه ما
+
+271
+00:25:59,820 --> 00:26:07,540
+يستحق من التنظيف والاعتناء توازن حتى في العبادة
+
+272
+00:26:07,540 --> 00:26:13,720
+نعم في العبادةعندما كانت زينب بنته رسول الله صلى
+
+273
+00:26:13,720 --> 00:26:17,540
+الله عليه وسلم شدت حبل بين الساريتين في المسجد
+
+274
+00:26:17,540 --> 00:26:22,290
+وتقوم الليلحتى إذا يعني شعرت بالتعب والارهاك
+
+275
+00:26:22,290 --> 00:26:29,250
+والنأس بتروح تتعلق بالحمل لكي تستعيد نشاطها فقال
+
+276
+00:26:29,250 --> 00:26:34,350
+للنبي صلى الله عليه وسلم يا زينب صلي ما شاء الله
+
+277
+00:26:34,350 --> 00:26:40,270
+لك أن تصلي ساعة و ساعة صلي ما شاء الله لك أن تصلي
+
+278
+00:26:40,270 --> 00:26:43,970
+الإنسان من هنا يصلي طاقته حتى في العبادة نعم في
+
+279
+00:26:43,970 --> 00:26:48,510
+العبادة نعم في العبادة في الطاقة نعم في الطاقة
+
+280
+00:26:49,870 --> 00:26:54,290
+توازن يا أخوات المرأة في بيتها لازم تكون متوازنة
+
+281
+00:26:54,290 --> 00:27:01,770
+تدلي ولايات حقهم تدلي الزوش حقهمتدّي البنات نصيبهم
+
+282
+00:27:01,770 --> 00:27:07,010
+تدّي البيت نصيبه من التنظيف والترتيب وكذا مش معناة
+
+283
+00:27:07,010 --> 00:27:10,910
+الكلام أنا بمنحها عن متابعة المستجدات والأخبار
+
+284
+00:27:10,910 --> 00:27:15,550
+والاطلاع ماذا يجري من حولها حتى في السياسة مفترض
+
+285
+00:27:15,550 --> 00:27:19,370
+المرأة تكون متوازنة يعني ماتركز على برامج المطبخ
+
+286
+00:27:19,370 --> 00:27:23,170
+وبرامج الأسرة وبرامج أبصر إجلال لازم المرأة
+
+287
+00:27:23,170 --> 00:27:28,930
+المسلمة تجيد فن السياسة أيضاليش؟ المرأة المتوازنة
+
+288
+00:27:28,930 --> 00:27:33,670
+مع نفسها بتعد أسرة متوازنة بتعد أسرة يعني نتيجة
+
+289
+00:27:33,670 --> 00:27:39,290
+هذا لإن المرأة يا أخوات يعني .. يعني تصرفات و
+
+290
+00:27:39,290 --> 00:27:45,490
+منهجها في الحياة هذا اسمه يعني تعليم بالقدوة و
+
+291
+00:27:45,490 --> 00:27:51,590
+التعليم بالقدوة يؤثر في نفس الطفل أكثر من التوجيه
+
+292
+00:27:51,590 --> 00:27:57,740
+باللسان و القول بألف مرةتعالوا مثلا انا لو اعطيتكم
+
+293
+00:27:57,740 --> 00:28:05,880
+عشر محاضرات عن سيرة احد الخلفاء هذه العشر محاضرات
+
+294
+00:28:05,880 --> 00:28:12,940
+لا تساوي مسلسل او حلقة من مسلسل تعالج هذا الموضوع
+
+295
+00:28:12,940 --> 00:28:18,960
+صح ولا؟ يعني هذا في اسلوب في وسيلة مختلفة والمرأة
+
+296
+00:28:18,960 --> 00:28:24,980
+في بيتها يعني الطفل يستقيم منها العاداتيستقي منها
+
+297
+00:28:24,980 --> 00:28:30,000
+سواء كانت العادات متوازنة أو سواء كانت العادات
+
+298
+00:28:30,000 --> 00:28:36,140
+يعني مائلة كل المائل ولذلك التوازن يا أخوات ينعكس
+
+299
+00:28:36,140 --> 00:28:42,180
+على حياة الفرد ابتداء وينعكس على أبناء الإنسان طب
+
+300
+00:28:42,180 --> 00:28:46,410
+ما هو إيش المجتمع؟المجتمع عبارة عن مجموعة من
+
+301
+00:28:46,410 --> 00:28:51,490
+الأفراد إذا تحقق التوازن في الفرد ينعكس ذلك على
+
+302
+00:28:51,490 --> 00:28:58,170
+المجتمع فيتحقق التوازن في المجتمع توازن بين
+
+303
+00:28:58,170 --> 00:29:05,490
+متطلبات الروح ورغبات الجسد والروح
+
+304
+00:29:05,490 --> 00:29:12,290
+تحتاج إلى الغذاء كما أن الأجساد والأبدان تحتاج إلى
+
+305
+00:29:12,290 --> 00:29:19,320
+الغذاءالجسد يحتاج إلى الغذاء والطعام والشراب، لكن
+
+306
+00:29:19,320 --> 00:29:26,160
+العقول تحتاج إلى التخذية، التخذية بماذا؟ بالقراءة،
+
+307
+00:29:26,160 --> 00:29:32,020
+بالتعلم، بالمطالعة، بالثقافة العامة، أنا بشخصيتي
+
+308
+00:29:32,780 --> 00:29:40,960
+ولمّا فكري ليش كلما ازدادت قراءة ومطالعة وثقافة
+
+309
+00:29:40,960 --> 00:29:49,080
+ينعكس ذلك على سعة الأفق في التفكير بصير عندي سعة
+
+310
+00:29:49,080 --> 00:29:53,980
+في التفكير يا أخوات هل يستوي الذين يعلمون والذين
+
+311
+00:29:53,980 --> 00:30:00,520
+لايعلمون؟ هل يستوي الأعمى والبصير؟ هل يستوي الظل
+
+312
+00:30:00,520 --> 00:30:07,150
+والحرور؟لا يستوون غذاء
+
+313
+00:30:07,150 --> 00:30:15,570
+الروح الغذاء الروحي أغذي نفسي بالطهات بالعبادات
+
+314
+00:30:15,570 --> 00:30:24,030
+بالتوحيد أغذي عقلي بالقراءة بالمطالعة بالثقافة لكي
+
+315
+00:30:24,030 --> 00:30:31,430
+امتلك يعني قدرة وسعة في التفكيرلأن يا أخوات جدّيش
+
+316
+00:30:31,430 --> 00:30:35,690
+الإنسان عنده ساعة في الإطلاع وفي العلم يستطيع أن
+
+317
+00:30:35,690 --> 00:30:42,750
+يصل إلى نتائج و أسس علمية صحيحة أي قضية أنا بترحى
+
+318
+00:30:42,750 --> 00:30:47,830
+للعلاج و للنقاش بتختلف فيها وجهات النظر لكن أكثر
+
+319
+00:30:47,830 --> 00:30:53,470
+أو أقرب وجهات النظر إلى الصواباللي هي بتصدر يعني
+
+320
+00:30:53,470 --> 00:30:59,530
+من الشخص الأكتر اتساع مداركه متسعة وعقله متفتح
+
+321
+00:30:59,530 --> 00:31:06,530
+مستنير ودايما بيغذي والإنسان لا يحكرانه صغيرة يعني
+
+322
+00:31:06,530 --> 00:31:12,670
+أي معلومة أي كتيب أي جريدة لابد للإنسان يتعامل
+
+323
+00:31:12,670 --> 00:31:17,410
+معاها يقرأ ما فيها من المعلومات فقد تنقذه في يوم
+
+324
+00:31:17,410 --> 00:31:25,010
+من الأيام من مصيبة كبيرةإذا جالك توازن بين متطلبات
+
+325
+00:31:25,010 --> 00:31:31,350
+الروح ورغبات الجسد النظم الإسلامية لم تأتي لتحرم
+
+326
+00:31:31,350 --> 00:31:38,310
+هذا الجسد و تعيشوا فيه شقاء لكن لابد أن يكون فيه
+
+327
+00:31:38,310 --> 00:31:43,470
+توازن يعني النبي صلى الله عليه وسلم في يوم من
+
+328
+00:31:43,470 --> 00:31:51,540
+الأيام استماع إلى ثلاثة نفس في المسجد أحدهموقول
+
+329
+00:31:51,540 --> 00:31:58,860
+إيه؟ والله لا أتزوج النساء أبدا أنا بديش أتزوج أنا
+
+330
+00:31:58,860 --> 00:32:04,220
+ان شاء الله تعالى عبادة أروح أجيبلي زوجة وامرأة
+
+331
+00:32:04,220 --> 00:32:09,060
+وروح وتعالى وتشغلنا عن العبادة لا أنا لن أتزوج
+
+332
+00:32:09,060 --> 00:32:16,620
+النساء والثاني يقول وانا أشوم الدهرة ولا أفطر خلاص
+
+333
+00:32:16,620 --> 00:32:23,130
+يوم يوم صيام عبادة تقرب إلى اللهوالثالث قال انا
+
+334
+00:32:23,130 --> 00:32:29,070
+اقوم الليل ولا ارقد ماعندي نوم في الليل خلاص جثة
+
+335
+00:32:29,070 --> 00:32:35,990
+نوم اشطبها من القاموس جثتهم ايه يعني يدنوا من الله
+
+336
+00:32:35,990 --> 00:32:43,190
+ويتقربوا الى الله ويبلغوا درجة المثالية فخرج عليه
+
+337
+00:32:43,190 --> 00:32:47,330
+من النبي صلى الله عليه وسلم وكان غضبان غضبة من هذا
+
+338
+00:32:47,330 --> 00:32:53,610
+الكلام فقال لهمأما وإني والله أتقاكم إلى الله
+
+339
+00:32:53,610 --> 00:33:04,210
+وأقربكم إليه وأدناكم إليه منزلة لكني أصوم وأفطر
+
+340
+00:33:04,210 --> 00:33:12,910
+وأقوم وأرقد وأتزوج النساء وهذه سنتي فمن رغب عن
+
+341
+00:33:12,910 --> 00:33:19,740
+سنتي فليس منيشايفين يا أخوات؟ هي في توازن أنا
+
+342
+00:33:19,740 --> 00:33:24,760
+توازن بين الجسد، هذا الجسد مفطور على حب الشهوات
+
+343
+00:33:24,760 --> 00:33:30,540
+وإشباع هذه الشهوات يعني الله سبحانه وتعالى مش هو
+
+344
+00:33:30,540 --> 00:33:34,420
+اللي خلق هذا الجسد ويعلم أن الجسد مفطور على
+
+345
+00:33:34,420 --> 00:33:39,640
+الشهوات، صح ولا؟ طب هل خلقه وأوضع فيه هذه الخاصية
+
+346
+00:33:39,640 --> 00:33:47,650
+وتركه؟ولا شرّع له ما يلبّي هذه الرغبات وما يسكت
+
+347
+00:33:47,650 --> 00:33:54,690
+هذه السهوات ولكن في الإطار الشرعي بالضوابط الشرعية
+
+348
+00:33:54,690 --> 00:34:02,070
+أباح له النكاح وحرّم عليه السفاهة نعم أباح له
+
+349
+00:34:02,070 --> 00:34:07,510
+التملؤ والثراء والمال وحرّم عليه الربا والصرقة
+
+350
+00:34:07,510 --> 00:34:16,630
+والغش وكذاليش؟ لكي يتحقق للإنسان كل ما يشد هذه
+
+351
+00:34:16,630 --> 00:34:24,250
+الشهوات ويحقق هذه الرغبات التوازن بين الواقعية
+
+352
+00:34:24,250 --> 00:34:32,870
+والمثالية إيش المقصود بالمثالية هنا؟ إيش المقصود
+
+353
+00:34:32,870 --> 00:34:36,670
+بالمثالية أخوات؟
+
+354
+00:34:36,670 --> 00:34:45,910
+المثالية في قسمينمثالية في مقدور البشر ومثالية لله
+
+355
+00:34:45,910 --> 00:34:52,690
+موصوف بها الله سبحانه وتعالى احنا بنطلبكم
+
+356
+00:34:52,690 --> 00:34:58,070
+بالمثالية اللي في مقدور البشر يعني مثلا المثالية
+
+357
+00:34:58,070 --> 00:35:06,660
+أن تحصلي على أعلى درجة على أخواتك فهي مثاليةان
+
+358
+00:35:06,660 --> 00:35:12,680
+تصلى الى في الأدب و الأخلاق الى المستوى اخر مستوى
+
+359
+00:35:12,680 --> 00:35:19,440
+لكن المستوى اللى فيه مقدور مين؟ مقدور البشر ان يصل
+
+360
+00:35:19,440 --> 00:35:25,600
+الانسان الى المثالية في الفاتحةمش معناة الكلام هذا
+
+361
+00:35:25,600 --> 00:35:29,760
+يؤدي إلى التشنج وكل كلمة بدي أتلفظ بها أنا بدي
+
+362
+00:35:29,760 --> 00:35:34,100
+أجيسها على الميزان و بتصلح ولا لا تصلح و بتؤذي ولا
+
+363
+00:35:34,100 --> 00:35:39,460
+لا تؤذي و كويسة ولا مش كويسة هذا بيوجهني في الشدة
+
+364
+00:35:39,460 --> 00:35:45,880
+و الحرج لكن أنا بطالب أو بأحرص على أن تكون الفاظي
+
+365
+00:35:45,880 --> 00:35:49,940
+قمة في المثالية اللي في مقدور البشر لكن لا يعني كل
+
+366
+00:35:49,940 --> 00:35:56,460
+كلام هيطلع هيكهذا ليس فيه مقدور إنسان لكن الهنات
+
+367
+00:35:56,460 --> 00:36:02,340
+تكون معدودة تكون قليلة الخطأ يكون قليل مايكونش خطأ
+
+368
+00:36:02,340 --> 00:36:09,220
+كبير هذه المثالية المثالية الوصول إلى أرفع مستوى
+
+369
+00:36:09,220 --> 00:36:15,040
+من الإتقان أرفع مستوى من الأخلاق أرفع مستوى من
+
+370
+00:36:15,040 --> 00:36:23,990
+الذي يسطر أو تتحقق فيه الضوابط الشرعيةأصل إلى أعلى
+
+371
+00:36:23,990 --> 00:36:29,610
+مستوى في التحصيل أصل إلى أعلى مستوى في النشاط في
+
+372
+00:36:29,610 --> 00:36:34,090
+مساعدة الوالدة في البيت مثالية
+
+373
+00:36:38,360 --> 00:36:42,960
+لازم نصل إليه طبعا النظم الإسلامي توازن بين
+
+374
+00:36:42,960 --> 00:36:47,860
+الواقعية و بين المثالية الواقعية مجبرة عليه
+
+375
+00:36:47,860 --> 00:36:51,560
+الإنسان واقع الإنسان الإنسان صاحب شهوات نعم
+
+376
+00:36:51,560 --> 00:36:56,340
+الإنسان مفتور على حب للتميز نعم مفتور على حب
+
+377
+00:36:56,340 --> 00:37:02,460
+السيطرة نعم هذا واقع واقع أنا ممكن مثلا أخد
+
+378
+00:37:02,460 --> 00:37:03,440
+أضربلكم مثال
+
+379
+00:37:07,110 --> 00:37:12,450
+المثالية في اللبس أو في الجلباب يكون الجلباب أخر
+
+380
+00:37:12,450 --> 00:37:20,570
+صيحة لو كان الجلباب أخر صيحة و طبعا ساتر من الجسد
+
+381
+00:37:20,570 --> 00:37:26,650
+و وفق الضوابط الإسلامية الشرعية هذا بيكون مثالي
+
+382
+00:37:26,650 --> 00:37:31,610
+هذا اللبس بيكون مثالي طب أنا مش قادر أجيب جلباب
+
+383
+00:37:31,610 --> 00:37:39,070
+أخر صيحةأنا ممكن أصل بالجلباب اللى عندي إلى
+
+384
+00:37:39,070 --> 00:37:43,330
+المثالية اللى بقدر أصل إليها الجلباب أولا دائما
+
+385
+00:37:43,330 --> 00:37:49,790
+يكون مقصود ونظيف تمام تمام مكوي منظره لائق كذا
+
+386
+00:37:49,790 --> 00:37:54,230
+بهذا الشكل بصل إلى المثالية ولا بصلش يعني مش
+
+387
+00:37:54,230 --> 00:37:58,630
+المثالية تعيشني في عالم من الخيال بدي إمكانيات
+
+388
+00:37:58,630 --> 00:38:03,630
+كبيرة عشان أكون مثالي أنا ممكن أكون مثالي بأفسط
+
+389
+00:38:03,630 --> 00:38:10,530
+الأموربأبسط الأمور زي المثال اللي ضربنا يعني ممكن
+
+390
+00:38:10,530 --> 00:38:15,430
+الإنسان يتميز على غيره لأ بكثرة لباس ولكن برضه
+
+391
+00:38:15,430 --> 00:38:19,010
+يعني الواقعية أنا بوزن بين الواقع اللي أنا بعيشه
+
+392
+00:38:19,010 --> 00:38:24,930
+وبين المثالية المنشودة وهناك أمثلة كثيرة لو بدنا
+
+393
+00:38:24,930 --> 00:38:29,410
+نضرب أمثلة يعني كل المحاضرة بنضرب أمثلة الموازنة
+
+394
+00:38:29,410 --> 00:38:37,980
+بين الواقعية وبين المثاليةبعد ذلك توازن بين
+
+395
+00:38:37,980 --> 00:38:46,360
+الاهتمام بشؤون الدنيا وشؤون الآخرة نعم صحيح هي
+
+396
+00:38:46,360 --> 00:38:51,560
+الحياة الآخرة دار الحيوان لو كانوا يعلمون لكن ليس
+
+397
+00:38:51,560 --> 00:38:55,300
+معناته الكلام صحيح أنا كل تصرفاتي في الدنيا يجب أن
+
+398
+00:38:55,300 --> 00:39:00,860
+تكون ممهدة وميسرة للآخرة السعيدة لكن ليس معناته
+
+399
+00:39:00,860 --> 00:39:06,590
+الكلام أنسى نفسيوأنقطع على الذكر و العبادة و لا
+
+400
+00:39:06,590 --> 00:39:10,910
+أخلط الناس ولا أندمس في المجتمع و كذا لكن الأخوات
+
+401
+00:39:10,910 --> 00:39:17,570
+بيقول التوازن بين الحياة الدنيا و شؤون الآخرة ولا
+
+402
+00:39:17,570 --> 00:39:23,770
+أدل ولا أزمل على هذا المفهوم
+
+403
+00:39:23,770 --> 00:39:29,550
+من قول الله تعالى وابتغي فيما آتاك الله الدار
+
+404
+00:39:29,550 --> 00:39:36,200
+الآخرةطب إيش المقصود بما أتاك الله؟
+
+405
+00:39:36,200 --> 00:39:43,940
+ما أتاك الله النعم عليه المال الصحة الفراخ العلم
+
+406
+00:39:43,940 --> 00:39:52,180
+الجهد وعدد وإن تعدوا نعمة الله لا تحصوها وابتغي في
+
+407
+00:39:52,180 --> 00:39:57,750
+ما أتاك الله الدار الأخرىلكن الجزء الثاني من اللي
+
+408
+00:39:57,750 --> 00:40:01,410
+قال و لا تنسى نصيبك من الدنيا تشوفوا هذا التوازن
+
+409
+00:40:01,410 --> 00:40:07,610
+الجميل اللي في الآية التوازن صحيح احنا كل هدفنا و
+
+410
+00:40:07,610 --> 00:40:10,470
+كل شغلنا الشغل في هذه الحياة الدنيا الوصول الى
+
+411
+00:40:10,470 --> 00:40:14,050
+الآخر السعيدة و النهاية المقبولة ان شاء الله و
+
+412
+00:40:14,050 --> 00:40:20,390
+تعالى لكن لا يعني ذلك انه انا هو دايما لازم
+
+413
+00:40:20,390 --> 00:40:26,470
+الإنسان يوازن بين حياته و بين أخرته يوازنحتى في
+
+414
+00:40:26,470 --> 00:40:31,410
+حياته الاقتصادية يعمل موازنة وزارة الداخلية اللي
+
+415
+00:40:31,410 --> 00:40:37,950
+في البيت طبعا لازم تعمل ايه موازنة بين الحياة
+
+416
+00:40:37,950 --> 00:40:41,150
+الدنيا و الحياة الآخر حتى في النواحي المالية
+
+417
+00:40:41,150 --> 00:40:48,150
+هنضطرقلها يعني بعد قليل لازم يكون في ايه موازنة
+
+418
+00:40:55,380 --> 00:41:00,340
+توازن بين الإسراف والتقطير والله سبحانه وتعالى
+
+419
+00:41:00,340 --> 00:41:05,240
+يقول و لا تجعل يدك مغلولة إلى عنقك ولا تبسطها كل
+
+420
+00:41:05,240 --> 00:41:10,000
+البسط فتقعد ملومة محصورة في المحاضرة الجاية ان شاء
+
+421
+00:41:10,000 --> 00:41:14,740
+الله سنكمل هذا المبدأ و نضرب عليه الأمثلة الكثيرة
+
+422
+00:41:14,740 --> 00:41:17,200
+بارك الله فيكم جزاكم الله كذلك
+
diff --git a/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/fI1U0RQ1UP4_raw.srt b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/fI1U0RQ1UP4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0419984159a41145a29ab3e56edb5e94f17bc401
--- /dev/null
+++ b/PL9fwy3NUQKwapW80A76o1gpc_SiZTlPz3/fI1U0RQ1UP4_raw.srt
@@ -0,0 +1,1664 @@
+1
+00:00:20,910 --> 00:00:23,950
+أعوذ بالله السميع العليم من الشيطان الرجيم بسم
+
+2
+00:00:23,950 --> 00:00:28,130
+الله الرحمن الرحيم الحمد لله رب العالمين والصلاة
+
+3
+00:00:28,130 --> 00:00:32,590
+والسلام على رسولنا الكريم أما بعده طبعا أخوات في
+
+4
+00:00:32,590 --> 00:00:37,630
+المحاضرة السابقة كنا قد انتهينا من الأمور التي فرق
+
+5
+00:00:37,630 --> 00:00:41,910
+أو المجالات التي فرق فيها الإسلام بين الرجل
+
+6
+00:00:41,910 --> 00:00:47,530
+والمرأةوتطرخنا إليها وشرحناها وضربنا الأمثلة
+
+7
+00:00:47,530 --> 00:00:53,110
+الكثيرة ثم يعني بياننا ما يجب على المرأة وما هي
+
+8
+00:00:53,110 --> 00:00:58,050
+الضوابط التي تنضبط بها المرأة عند العمل والمشي
+
+9
+00:00:58,050 --> 00:01:03,370
+والكلام إلى غير ذلك اليوم ان شاء الله سننتقل إلى
+
+10
+00:01:03,370 --> 00:01:10,370
+العنوان الجديد والمجال الجديد اللي هو نظام السياسة
+
+11
+00:01:10,370 --> 00:01:18,190
+والحكمطبعا يا أخوات يعني هذا للسياسة من الأمور
+
+12
+00:01:18,190 --> 00:01:25,210
+الضرورية للمجتمعات و للشعوب و للتجمعات و من هنا
+
+13
+00:01:25,210 --> 00:01:30,230
+يعني جاء تعريف السياسة في اللغة هي من ساسة الأمر
+
+14
+00:01:30,230 --> 00:01:34,330
+إذا قام به وهي القيام على الشق أو القيام على الشق
+
+15
+00:01:34,330 --> 00:01:40,140
+بما يصلحهأو بمعنى الأمر والنهي يعني على سبيل
+
+16
+00:01:40,140 --> 00:01:45,760
+المثال جاء في الحديث الشريف يعني كان بنو إسرائيل
+
+17
+00:01:45,760 --> 00:01:52,200
+تسوسهم أنبياءهم، إيش يعني تسوسهم أنبياءهم؟ إيش
+
+18
+00:01:52,200 --> 00:01:59,080
+يعني تتولى أمورهم؟ كيف تخودهم؟
+
+19
+00:02:02,530 --> 00:02:08,630
+تدبير يعني تقوم على تدبير شؤونهم وتتولى أمورهم
+
+20
+00:02:08,630 --> 00:02:13,870
+أيضا كمان السياسة في المعنى الثاني قد تاتي بمعنى
+
+21
+00:02:13,870 --> 00:02:19,430
+الأمر والنهي من قولنا سُستوا الرعية سياسة إذا
+
+22
+00:02:19,430 --> 00:02:24,570
+أمرتها ونهيتها وتكون بمعنى التأديب يعني سُستوا
+
+23
+00:02:24,570 --> 00:02:32,550
+الرعية أمرتها ونهيتها طبعا أخواتالإنسان يسوس بيته
+
+24
+00:02:32,550 --> 00:02:39,030
+يعني فيه إله سياسة بيطبقها في بيته لو قلنا يعني من
+
+25
+00:02:39,030 --> 00:02:45,050
+سسته البيت يعني يطبق أنظمة معينة أو قواعد أخلاقية
+
+26
+00:02:45,050 --> 00:02:49,970
+أو قواعد اقتصادية أو قواعد اجتماعية هذه الأنظمة
+
+27
+00:02:49,970 --> 00:02:55,610
+اللي بتدبر شؤون البيت وتسيس أمور البيت وتديه شؤون
+
+28
+00:02:55,610 --> 00:03:01,950
+البيت هذه اسمها إيه؟سياسة والسياسة قد يكون لها
+
+29
+00:03:01,950 --> 00:03:08,450
+طابع ديمقراطي طابع ديني وطابع أخلاقي وطابع اجتماعي
+
+30
+00:03:08,450 --> 00:03:13,570
+صح ولا لأ صح يعني في بعض البيوت مش انت كل حاجة أنا
+
+31
+00:03:13,570 --> 00:03:19,510
+بقولها صح بتقولي صح صح يعني في بعض البيوت السياسة
+
+32
+00:03:19,510 --> 00:03:24,230
+بتبعت البيت قائمة على إيش الانغلاق صح
+
+33
+00:03:25,590 --> 00:03:30,310
+في بعض البيوت سياستة قائمة على البعد الانفتاح
+
+34
+00:03:30,310 --> 00:03:35,390
+الاجتماعي في بعض البيوت سياستة الطابع السياسي
+
+35
+00:03:35,390 --> 00:03:39,970
+عندها في البيت الطابع اللي هو ايه الديني في هناك
+
+36
+00:03:39,970 --> 00:03:45,970
+بيوت الطابع السياسة طابع السياسي عندهم التحلل
+
+37
+00:03:45,970 --> 00:03:55,810
+والسقوط و الكذا طبعا هذه تتعلق برب البيتإذا كان رب
+
+38
+00:03:55,810 --> 00:04:01,150
+البيتي بتدفي ضاربا إيه الشيمة أهل البيتي؟ لأنه
+
+39
+00:04:01,150 --> 00:04:06,370
+سياسة خلاص هو ارتضى هذه السياسة ولذلك السياسة يا
+
+40
+00:04:06,370 --> 00:04:11,450
+أخوات يعني تدبير شؤون الأسرة تدبير شؤون الدولة
+
+41
+00:04:11,450 --> 00:04:16,270
+تدبير شؤون المؤسسة مش احنا بيقول سياسة الجامعة
+
+42
+00:04:16,270 --> 00:04:23,520
+الإسلاميةالسياسة المالية للجامعة الإسلامية السياسة
+
+43
+00:04:23,520 --> 00:04:27,780
+الأكاديمية السياسة الكذا يعني في أنظم أو لوائح
+
+44
+00:04:27,780 --> 00:04:34,420
+تنظم هذه المؤسسة المعنى الثالث تكون بمعنى التأديب
+
+45
+00:04:34,420 --> 00:04:40,180
+والتجربة واكتساب الخبرة مثل فلان مجرب قد ساسا
+
+46
+00:04:40,180 --> 00:04:46,840
+وسيسا عليه أي أدب و تأدب أما السياسة يا أخواتي
+
+47
+00:04:50,430 --> 00:04:57,070
+في الاصطلاح هي الرياسة و إدارة الحكم، من تقرأ هذه
+
+48
+00:04:57,070 --> 00:05:03,020
+الفكرة؟ تفضلياستياسة في الاستلاح من التعريف بمعنى
+
+49
+00:05:03,020 --> 00:05:06,420
+كلمة استياسة في لغنا لأنها تدل على تدل في بعض
+
+50
+00:05:06,420 --> 00:05:10,320
+معانيها على رياسة وردارة الحكم وهذا المعنى هو أصل
+
+51
+00:05:10,320 --> 00:05:13,560
+المعنى الاستلاحي المتعرف عليه بين العلماء ولما
+
+52
+00:05:13,560 --> 00:05:16,820
+استخدموا صحاب رسول الله صلى الله عليه وسلم كلمة
+
+53
+00:05:16,820 --> 00:05:20,200
+استياسة بهذا المعنى فقد كتب عمرو بن العاصلى أبي
+
+54
+00:05:20,200 --> 00:05:25,250
+موسى الأشعري رضي الله عنهمافقال اقولوا اني وشرته
+
+55
+00:05:25,250 --> 00:05:29,450
+وليه الخليفة المطلوب واضطرق اقدمى، انحسن السياسة،
+
+56
+00:05:29,450 --> 00:05:32,610
+انفسنا قلبية واجهنا معاوية وقهرة بديع على بلاد
+
+57
+00:05:32,610 --> 00:05:37,170
+الشام تفضل
+
+58
+00:05:38,660 --> 00:05:41,940
+هذا والعلماء في مفهوم سياسة تعريف مختلفة تبع
+
+59
+00:05:41,940 --> 00:05:46,280
+الإنفلاق في مدارسهم واتجاهاتهم وتفاوت عصورهم، ولكن
+
+60
+00:05:46,280 --> 00:05:50,000
+هذه التعريفات على اختلافها يمكن تقسمها إلى منهجين
+
+61
+00:05:50,000 --> 00:05:54,940
+رئيسيين، رئيسيين، الأول منهج علماء المسلمينوهو
+
+62
+00:05:54,940 --> 00:05:57,960
+يتميز باتفاقهم على أن السياسة في الإسلام هي تلك
+
+63
+00:05:57,960 --> 00:06:01,040
+السياسة التي تتفق بمبادئ الشريعة الإسلامية ونظامها
+
+64
+00:06:01,040 --> 00:06:04,740
+العام، وهي السياسة التي تدير جميع شغون البلاد
+
+65
+00:06:04,740 --> 00:06:09,180
+ويحكم لتحقيق مصلحة الأمة في دينها ودنياها وعاجلة
+
+66
+00:06:09,180 --> 00:06:13,480
+أمها واجلة، سالكة بسبب قلوب تلك الغاية كل وسيلة
+
+67
+00:06:13,480 --> 00:06:17,170
+وشريطة اللاتحيد عن أضمة الإسلام والتعاليمةتمام،
+
+68
+00:06:17,170 --> 00:06:23,370
+الآن السياسة يا أخوات في قسمين رئيسيين للنظرة أو
+
+69
+00:06:23,370 --> 00:06:28,530
+النظر لمفهوم السياسة، في النظرة الإسلامية وفي
+
+70
+00:06:28,530 --> 00:06:34,090
+النظرة غير الإسلامية، يعني النظرة للقوانين الوضعية
+
+71
+00:06:34,090 --> 00:06:39,660
+لمفهوم السياسةوفي عندنا نظرة الإسلاميين أو نظرة
+
+72
+00:06:39,660 --> 00:06:44,820
+المسلمين لمفهوم السياسة وعشان هيك يعني السياسة
+
+73
+00:06:44,820 --> 00:06:51,400
+تعرف ضمن خطين عريضين خط الأول السياسة في الاصطلاح
+
+74
+00:06:51,400 --> 00:06:57,160
+عند المسلمين والسياسة في الاصطلاح عند غير المسلمين
+
+75
+00:06:57,820 --> 00:07:01,000
+طبعاً يا أخوات فيه ضوابط لمفهوم السياسة عند
+
+76
+00:07:01,000 --> 00:07:05,480
+المسلمين، مهما كانت تعريفها، أنا اتطرق إلى تعريفات
+
+77
+00:07:05,480 --> 00:07:10,940
+متعددة، لكن في النهاية أي تعريف من هذه التعريفات
+
+78
+00:07:10,940 --> 00:07:16,660
+لابد أن ينسجن مع الإسلاميعني مثلا بحجة أن هذا أمر
+
+79
+00:07:16,660 --> 00:07:22,460
+سياسي أو هذا يعني من طبيعة السياسة وبحجة أنه أمر
+
+80
+00:07:22,460 --> 00:07:28,720
+سياسي يروح يعارض أو يصادم ضوابط الإسلام و تعاليم
+
+81
+00:07:28,720 --> 00:07:33,020
+الإسلام وشريعة الإسلام فهذا لا يعتبر سياسي، هذا
+
+82
+00:07:33,020 --> 00:07:39,830
+عمل غير مشروع يا أخوانهذا عمل غير مشروع انما يعني
+
+83
+00:07:39,830 --> 00:07:46,550
+من أحدث في أمرنا هذا ما ليس منه فهو رد لكن السياسة
+
+84
+00:07:46,550 --> 00:07:52,390
+فيها مرونةحسب الأوضاع، حسب الناس، حسب اختلاف
+
+85
+00:07:52,390 --> 00:07:56,570
+البيئات واختلاف الأشخاص واختلاف الأزمنة والمعادلة
+
+86
+00:07:56,570 --> 00:08:02,350
+الدولية وكذا ماشي أنا بدي أتحرك في هذا الأفق، لكن
+
+87
+00:08:02,350 --> 00:08:07,990
+في النهاية لا أتصادم مع نص من القرآن أو السنة أو
+
+88
+00:08:07,990 --> 00:08:14,600
+قاعدة فقهية أو أصوليةعشان هيك قال لك السياسة تتفق
+
+89
+00:08:14,600 --> 00:08:21,380
+ومبادئ الإسلامية ونظامها العام السياسة تدبير جميع
+
+90
+00:08:21,380 --> 00:08:25,640
+شؤون البلاد والحكم لتحقيق مصلحة الأمة في دينها
+
+91
+00:08:25,640 --> 00:08:30,440
+ودنياها إذا احنا لو استقرأنا الشريعة الإسلامية
+
+92
+00:08:30,440 --> 00:08:35,620
+والنصوص القرآنية والنبوية وتعاليم الإسلام ما جاءت
+
+93
+00:08:35,620 --> 00:08:41,150
+يا أخوات إلا لتحقيق مصلحةوأنا قلتلكم قبل هيك أي
+
+94
+00:08:41,150 --> 00:08:48,230
+أمر أي شخص أمرنا إبه الإسلام فيها مصلحة وأي نهي أي
+
+95
+00:08:48,230 --> 00:08:54,450
+مسألة أو أمر نهانا عنه الإسلام فيه مفسدة القيام به
+
+96
+00:08:54,450 --> 00:09:02,030
+مفسدة طيب تركه مصلحةتركوا مصلحة وعشان هيك الشريعة
+
+97
+00:09:02,030 --> 00:09:07,290
+جاءت لتحقق مصالح الأمة قالك إيه ده؟ السياسة بدها
+
+98
+00:09:07,290 --> 00:09:13,570
+جلبت المصالح للناس وما تتعرضش مع دينهم كانت من
+
+99
+00:09:13,570 --> 00:09:19,710
+الدين وكانت مشروعة وللأسف الشديد اليوم في تيار
+
+100
+00:09:19,710 --> 00:09:23,110
+بيدخل
+
+101
+00:09:23,110 --> 00:09:25,310
+للطعن في الإسلام من هذا المدخل
+
+102
+00:09:27,760 --> 00:09:32,380
+بقولك هو الإسلام فيه سياسة يا عم طبعا هذول
+
+103
+00:09:32,380 --> 00:09:36,120
+العلمانيين اللي بيقولوا هيك العلمانيين اللي بدهم
+
+104
+00:09:36,120 --> 00:09:40,940
+يضربوا الإسلام بيكيدوا للإسلام بقولك يا عم هو
+
+105
+00:09:40,940 --> 00:09:44,880
+الإسلام فيه سياسة والله يا مشايخ انتوا خربتوا
+
+106
+00:09:44,880 --> 00:09:51,300
+الدنيا خلطوا السياسة بالعبادة المسجد هو للعبادة
+
+107
+00:09:51,300 --> 00:09:57,670
+ولا للسياسة والحرب؟ بقولك لاأصحاب هذا الفكر
+
+108
+00:09:57,670 --> 00:10:02,330
+المنحرف والفهم الخاطئ للدين أنا متأكد أنه مش عندهم
+
+109
+00:10:02,330 --> 00:10:07,090
+فهم خاطئ والله يعلمون الحق كما يعلمون أبناءهم لكن
+
+110
+00:10:07,090 --> 00:10:11,510
+يستخدمون هذا الطريق لضرب الإسلام والمسلمين وقولك
+
+111
+00:10:11,510 --> 00:10:15,710
+يا مسايخ انتوا خليتوا الجوامع مش للعبادة الجوامع
+
+112
+00:10:15,710 --> 00:10:22,140
+للعبادة مساجد صلي ويروحيعني مش فاهمين أصلا إيش دور
+
+113
+00:10:22,140 --> 00:10:29,200
+المسجد المسجد يا أخوات دوره سياسي و دوره تعبدي و
+
+114
+00:10:29,200 --> 00:10:35,280
+دوره إجتماعي و دوره تعليمي و ثقافي كل الأعمال التي
+
+115
+00:10:35,280 --> 00:10:39,340
+لا تتنافى مع الشريعة تقام في المسجد كانوا بيعملوا
+
+116
+00:10:39,340 --> 00:10:46,560
+الإشهار قديمافي المسجد دروس علمية التعليم لأبناء
+
+117
+00:10:46,560 --> 00:10:51,400
+القرآن تدبير شؤون البلاد ارسال البعثات والجيوش
+
+118
+00:10:51,400 --> 00:10:56,000
+تنطلق من المساجد هي قصة اما بقولك انتوا يا مشايخ
+
+119
+00:10:56,000 --> 00:11:01,040
+ايش دخل السياسة في الدين الدين ايش والسياسة ايش
+
+120
+00:11:01,040 --> 00:11:06,160
+كيف انتوا خلطوا بين الدين والسياسةواحنا بنقول يا
+
+121
+00:11:06,160 --> 00:11:12,500
+أخوات الصواب السياسة من عنق الدين السياسة من جوهر
+
+122
+00:11:12,500 --> 00:11:21,510
+الدين وهي كما مرت الأخت قرأت قبل شويةالحسن السياسة
+
+123
+00:11:21,510 --> 00:11:28,470
+أو الحسن التدبير تدبير أمور الرعية هذه سياسة النبي
+
+124
+00:11:28,470 --> 00:11:32,070
+صلى الله عليه وسلم أقام دولة سياسية في المدينة
+
+125
+00:11:32,070 --> 00:11:37,010
+المنورة إلها علاقات مع جيرانها وإلها أحلاف وإلها
+
+126
+00:11:37,010 --> 00:11:43,830
+اقتصاد وإلها جيش وإلها دعوة دولة إسلامية دولة مش
+
+127
+00:11:43,830 --> 00:11:48,050
+كيان ولا مجموعة دولة إسلامية بما لها وما عليها
+
+128
+00:11:48,930 --> 00:11:53,870
+فبنقول يا أخوات يعني لابد أن نرد على أصحاب هذا
+
+129
+00:11:53,870 --> 00:11:57,970
+المدخل أو الفكر المنحرف اللي بيقولك إيه أنه لابد
+
+130
+00:11:57,970 --> 00:12:01,950
+أن نفصل بين الدين والسياسة وقلنا الفصل بين الدين
+
+131
+00:12:01,950 --> 00:12:07,570
+والسياسة اللي يواقع في أوروبا نتيجة يعني الفسق
+
+132
+00:12:07,570 --> 00:12:14,670
+وظلم الكنيسة والكهنةأه كان في ظلم وفسق واضح جدا،
+
+133
+00:12:14,670 --> 00:12:18,850
+لكن احنا شريعتنا تختلف، لا تتساوى مع هذا الظلم،
+
+134
+00:12:18,850 --> 00:12:25,170
+شريعتنا جاءت لتنقذ الناس، لتحقق المصالح للناس،
+
+135
+00:12:25,170 --> 00:12:33,320
+عشان هيك بنقول السياسة من عمق الدينولا سياسة بلا
+
+136
+00:12:33,320 --> 00:12:38,400
+دين لا يمكن أن تنفصل السياسة عن الدين وإذا انفصلت
+
+137
+00:12:38,400 --> 00:12:42,520
+السياسة عن الدين يا أخوات لم تحقق مصلحة لأن أحيان
+
+138
+00:12:42,520 --> 00:12:48,380
+احنا لو نظرنا في أوروبا من السياسات الإجرامية أن
+
+139
+00:12:48,380 --> 00:12:54,160
+تفتعل الحروب أن تفتعل المجازر عشان الدولة تدخش في
+
+140
+00:12:54,160 --> 00:12:59,940
+أحلاف وتخضع شعوب وتبيع أسلحة وكذا لكن هل هذه
+
+141
+00:12:59,940 --> 00:13:05,730
+السياسةفي الإسلام الإسلام يقول بهذه السياسة بالعكس
+
+142
+00:13:05,730 --> 00:13:12,070
+الإسلام وضع معايير وضوابط للسياسة عشان هيك جاءت
+
+143
+00:13:12,070 --> 00:13:17,090
+تعريفات مختلفة للسياسة في الإسلام على سبيل المثال
+
+144
+00:13:17,090 --> 00:13:22,510
+التعريف الأول السياسة هي أيوة من تقرا فضلي
+
+145
+00:13:23,940 --> 00:13:28,440
+السياسة هي ما كان فعلا يكون معاه الناس أقرب إلى
+
+146
+00:13:28,440 --> 00:13:32,280
+الصلاة وأبعد عن الفساد وإلا يضعه الرسول صلى الله
+
+147
+00:13:32,280 --> 00:13:38,880
+عليه وسلم ولا نزل به وحده تمام، هذا التعريف أشمل
+
+148
+00:13:38,880 --> 00:13:44,390
+التعريف وأضق التعريف وأفضل التعريفاتقال لك السياسة
+
+149
+00:13:44,390 --> 00:13:49,870
+هي ما كان فعلًا يكونوا معاه الناس أقرب إلى الصلاة
+
+150
+00:13:49,870 --> 00:13:56,550
+يعني أي فعل أي أمر أي قرار أي شيء يكون الناس مع
+
+151
+00:13:56,550 --> 00:14:01,690
+هذا القرار يا إما يتحقق صلاحهم يا إما يكونوا
+
+152
+00:14:01,690 --> 00:14:07,760
+قريبين من الصلاة وأبعد عن الفساديعني قريبين من
+
+153
+00:14:07,760 --> 00:14:11,260
+المصلحة و بعيدين عن المفسدة يعني هذا الرأي و هذا
+
+154
+00:14:11,260 --> 00:14:17,120
+القرار و هذا الفعل بدي يوديني للمصلحة و يقربني
+
+155
+00:14:17,120 --> 00:14:23,360
+للمصلحة و يبعدني عن المفسدة و مش شرط .. خلي بالك
+
+156
+00:14:23,360 --> 00:14:28,820
+.. و مش شرط يكون نزل إيه بوحي أو وردة في السنة و
+
+157
+00:14:28,820 --> 00:14:34,460
+القرآنمش شرط قد يكون الأمر مافيش فيه نص قرآني
+
+158
+00:14:34,460 --> 00:14:41,980
+ومافيش فيه وحي لكن قد يكون رأي إجماع من العلماء قد
+
+159
+00:14:41,980 --> 00:14:48,920
+يكون قياس قد يكون رأي اجتهادي بيحقق مصلحة الأمة
+
+160
+00:14:48,920 --> 00:14:56,490
+بيحقق مصلحة الأمةحتى الديمقراطية الديمقراطية اليوم
+
+161
+00:14:56,490 --> 00:15:02,490
+المعاصرة على شكلها المؤاصر لا أستطيع القول بأنها
+
+162
+00:15:02,490 --> 00:15:08,410
+مشروعة في ديننا بحذافيرها بهذا الشكل بهذا التنفيذ
+
+163
+00:15:08,410 --> 00:15:13,610
+بهذا الأداء لا يمكن القول أن نقول أن الديمقراطية
+
+164
+00:15:13,610 --> 00:15:22,290
+مشروعة في ديننالكن من المصلحة في هذا الزمن أن نعمل
+
+165
+00:15:22,290 --> 00:15:28,710
+بهذه الديمقراطية وأن نوجه هذه الديمقراطية في توجيه
+
+166
+00:15:28,710 --> 00:15:35,110
+سليم وتوجيه شرعي وتوجيه يحقق مصلحة وأن نضبط هذه
+
+167
+00:15:35,110 --> 00:15:39,450
+العملية الديمقراطية بقدر الإمكان بالضوابط الشرعية
+
+168
+00:15:39,450 --> 00:15:48,180
+يعني على سبيل المثال التجربة التركيةتوركيا ما يحدث
+
+169
+00:15:48,180 --> 00:15:53,540
+اليوم في توركيا لو قلنا ان الديمقراطية حرام وانتوا
+
+170
+00:15:53,540 --> 00:15:58,060
+أيها الأحزاب الإسلامية ماتشاركوش طبعا نظام علماني
+
+171
+00:15:58,060 --> 00:16:02,660
+اللي كان في توركيا بنسبة 100% بل عدو للإسلام
+
+172
+00:16:02,660 --> 00:16:07,420
+والمسلمين نقولهم انتوا أيها الأحزاب الإسلامية هذا
+
+173
+00:16:07,420 --> 00:16:12,380
+الديمقراطية حرام سياسة الديمقراطية حرام وماتخشوش
+
+174
+00:16:12,380 --> 00:16:15,500
+ماتفوتوش ماتشاركوش فيها
+
+175
+00:16:18,160 --> 00:16:21,860
+طب إيش بده يصير في تركيا؟ لكان فاز الحزب العلماني
+
+176
+00:16:21,860 --> 00:16:25,820
+و زاد العداء و زاد الانتقام من المسلمين لكن عندما
+
+177
+00:16:25,820 --> 00:16:32,300
+شارك الحزب الإسلامي في تركيا و حققوا نجاحا و فوزا
+
+178
+00:16:32,300 --> 00:16:38,840
+عظيما و أخذوا يغيروا المؤسسات أخذوا ينقوا الجيش من
+
+179
+00:16:38,840 --> 00:16:43,400
+العلمانيينتغيرت النظرة إلى بلاد الإسلام والمسلمين
+
+180
+00:16:43,400 --> 00:16:47,640
+وشوفنا كيف التحيز لصالح القضية الفلسطينية التحيز
+
+181
+00:16:47,640 --> 00:16:54,460
+للعرب للتحيز لصالح المسلمين وبدت تركيا تخطو خطوات
+
+182
+00:16:54,460 --> 00:16:59,520
+رظينة ومتناسقة وثابتة نحو التغيير والحمد لله اليوم
+
+183
+00:16:59,520 --> 00:17:03,740
+تركيا تعتبر قلعة إسلامية تدافع عن قضايا الإسلام
+
+184
+00:17:03,740 --> 00:17:07,020
+والمسلمين ولا نقول الديمقراطية حراب وخلّيكوا
+
+185
+00:17:07,020 --> 00:17:13,130
+نايمينإذن يا أخوات وإن كانت في أصل مشروعية التلاتة
+
+186
+00:17:13,130 --> 00:17:20,210
+جوز لكن اتخالها كوسيلة مش غاية كوسيلة للتغيير إلى
+
+187
+00:17:20,210 --> 00:17:27,490
+الأصل حتى لو على مدار السنين بقول فهي مشروعة لحاجة
+
+188
+00:17:27,490 --> 00:17:32,430
+لأن قالت وإن لم يضحو الرسول صلى الله عليه وسلم ولا
+
+189
+00:17:32,430 --> 00:17:39,350
+نزل به وحي لكن إن كان رأي اجتهادي ممن يصحمنهم
+
+190
+00:17:39,350 --> 00:17:44,390
+الاجتهاد فهو مُعتبر واحدة من قبيل السياسة التعريف
+
+191
+00:17:44,390 --> 00:17:51,510
+الثاني الناحية اللي هناك ايوة اتفضل ايه اصلاح
+
+192
+00:17:51,510 --> 00:17:54,770
+الخطوة عشان ما بيقولكوا ان مانيشي عاجل او اتاجر
+
+193
+00:17:55,530 --> 00:18:01,690
+أيوة إصلاح القلق بإرشادهم إلى الطريق المنجي هذا
+
+194
+00:18:01,690 --> 00:18:07,850
+الضابط الأخير أروع ما في التعريف في الآجل والعاجل
+
+195
+00:18:07,850 --> 00:18:13,910
+يعني بمعنى في الدنيا والآخرة وهذا ما تفتكر إليه
+
+196
+00:18:13,910 --> 00:18:18,900
+السياسة في النظوم الوضعيةالسياسة في النظم الوضعية
+
+197
+00:18:18,900 --> 00:18:24,480
+لا تعتني بالآخرة بالآجل هما بدهم الآجل حياة الدنيا
+
+198
+00:18:24,480 --> 00:18:30,220
+ثلاثة تفضلي حملي الكافة على مقتدى النظر الشرعي في
+
+199
+00:18:30,220 --> 00:18:35,260
+مصالحهم الأخروية والبنيوية راجعة إليها حملي الكافة
+
+200
+00:18:35,260 --> 00:18:38,440
+على مقتدى النظر الشرعي في مصالحهم الأخروية
+
+201
+00:18:38,440 --> 00:18:42,620
+والبنيوية حملي الكافة عارفين إيش معنات كلمة حمل
+
+202
+00:18:42,620 --> 00:18:51,420
+فرضأيوة الفرض الإجبار لإيه لأن النظام السياسي هو
+
+203
+00:18:51,420 --> 00:18:56,180
+اللي بيدير شؤون البلد يجيلي حزب يجيلي فريق يجيلي
+
+204
+00:18:56,180 --> 00:19:01,280
+شخص يقولك لأ أنا شايف هيك أنا مش شايف هيك صحبيطلعش
+
+205
+00:19:01,280 --> 00:19:06,220
+بيقدرش لازم يكون في نظام اي دولة اي بُقعة من الأرض
+
+206
+00:19:06,220 --> 00:19:10,360
+مافيش فيها سلطة مهيمة مافيش فيها نظام فهذا ايه
+
+207
+00:19:10,360 --> 00:19:14,380
+يعني هذا نظام فاشل ولا يمكن تحقيق الأمن ولا
+
+208
+00:19:14,380 --> 00:19:20,360
+المصالح لكن لما نكون في نظام سياسي قوي يحمل الناس
+
+209
+00:19:20,360 --> 00:19:25,620
+الكافة التزام بالقانون طب ليش احنا بنلتزم
+
+210
+00:19:25,620 --> 00:19:32,490
+بالقانون؟ ليش؟يعني لو ماكانش فينا جهاز شرطة مرورية
+
+211
+00:19:32,490 --> 00:19:37,370
+إيش بيصير في شوارعنا؟طيب تعالي السواجين يقولك اللي
+
+212
+00:19:37,370 --> 00:19:41,570
+احنا الشرطة هذه ب .. لكن غصب عنه يبقى يلتزم
+
+213
+00:19:41,570 --> 00:19:46,150
+بالقانون لأن كل واحد في دماغه قانون يختلف عن
+
+214
+00:19:46,150 --> 00:19:50,090
+الثاني لو بدنا نطرح كل واحد يطبق القانون اللي
+
+215
+00:19:50,090 --> 00:19:55,390
+بيعجبه خربت البلد لاتستقيم لكن لما نطبق قانون واحد
+
+216
+00:19:55,390 --> 00:20:00,370
+البلد بتمشي و بتتحقق المصلحة للجميع
+
+217
+00:20:02,170 --> 00:20:06,190
+لكن من هذه التعريفات كان فيها تعريف مختار يمكن
+
+218
+00:20:06,190 --> 00:20:11,260
+تلخيص مجاء في التعريفات الثلاثة في هذا التعريفمن
+
+219
+00:20:11,260 --> 00:20:27,720
+تقرأ التعريف المختار تفضليه الان
+
+220
+00:20:27,720 --> 00:20:35,740
+يا أخوات المنهج الثاني منهج عند غير المسلمين اه من
+
+221
+00:20:35,740 --> 00:20:40,590
+تقرأ الفقرة تفضليهالمنهج التاني، منهج غير
+
+222
+00:20:40,590 --> 00:20:44,230
+المسلمين، وهو منهج يفصل معنى السياسة في تنظيم
+
+223
+00:20:44,230 --> 00:20:47,690
+الشؤون الدنياوية للعباد، وفق القوانين والدساتير
+
+224
+00:20:47,690 --> 00:20:52,490
+التي يضحك مختصهم أو أهل الحل والعب أو من .. أو من
+
+225
+00:20:52,490 --> 00:20:56,590
+بيدهم مقاليد الحكم في البلاد، كما يتميت منهجهم
+
+226
+00:20:56,590 --> 00:21:00,530
+بأنه لا ينتسب أي قيد أو ضابط، دالك أن مفهوم
+
+227
+00:21:00,530 --> 00:21:05,070
+السياسة عندهم هو سلوك جميع السبل الموصلة إلى الحدد
+
+228
+00:21:05,070 --> 00:21:09,680
+الذي يسعى إليه الساترحتى وإن كانت سورة غير أخلاقية
+
+229
+00:21:09,680 --> 00:21:13,960
+وغير مشروعة وذلك بخلاف المنهج الإسلامي الذي يطبق
+
+230
+00:21:13,960 --> 00:21:18,520
+السياسة ويقيدها بقواعد الإسلام ومبادئها تمام شوف
+
+231
+00:21:18,520 --> 00:21:24,660
+هذا الضابط الآن السياسة في القوانين الوضعية مش
+
+232
+00:21:24,660 --> 00:21:29,360
+مشكلة تسلك أي طريق طريق أخلاقي طريق غير أخلاقي
+
+233
+00:21:29,360 --> 00:21:33,000
+المهم اتحقق سياسة البلد يعني مثلا إذا تشيلك الدول
+
+234
+00:21:33,000 --> 00:21:38,880
+الصناعية الثمانية الكبرىبتفرض قيود على الدول لإن
+
+235
+00:21:38,880 --> 00:21:48,500
+هما عندهم مفاتح القوة عندهم مفاتح يمسكونها بضابط
+
+236
+00:21:48,500 --> 00:21:53,080
+أو عجلة الاقتصاد العالمي الدول الصناعية الثمانية
+
+237
+00:21:53,080 --> 00:21:58,980
+بتفرض سياسات حتى لو كانت سياسات غير أخلاقية ممكن
+
+238
+00:21:58,980 --> 00:22:05,530
+الدولة اللي لها نفوطتوجد عداوة بين الدول تشعل حربا
+
+239
+00:22:05,530 --> 00:22:10,230
+ضروسا تزهق فيه آلاف بل ملايين الأروح ليش؟ عشان
+
+240
+00:22:10,230 --> 00:22:14,110
+تشغل مصانع الأسلحة اللي عندها طب هل هذه السياسة
+
+241
+00:22:14,110 --> 00:22:20,570
+تنسجم؟ إذا السياسة في الغرب أكت مبرقة من كل قيدهي
+
+242
+00:22:20,570 --> 00:22:25,150
+المهم اتحقق مصلحة المصلحة السياسية اللي رسمها
+
+243
+00:22:25,150 --> 00:22:30,030
+الرجال السياسة ايش الهدف السياسي اللي وضعه رجال
+
+244
+00:22:30,030 --> 00:22:35,270
+السياسة ايش هو مش مشكلة يتخذوا اي يسلكوا اي طريقة
+
+245
+00:22:35,270 --> 00:22:40,150
+من الطرق لكن في النهاية يتحقق لهم الهدف السياسي
+
+246
+00:22:40,150 --> 00:22:45,830
+لكن عندنا في الإسلامهذا الكلام مش موجود، أنا بحط
+
+247
+00:22:45,830 --> 00:22:50,710
+هدف سياسي لا يتعرض مع النص، لا يتعرض مع نظام
+
+248
+00:22:50,710 --> 00:22:54,590
+الأخلاق، ولا يتعرض مع النظام الاجتماعي، ولا يتعرض
+
+249
+00:22:54,590 --> 00:23:00,530
+مع القواعد الشرعية، لأن أي نظام بيخرج عن القواعد
+
+250
+00:23:00,530 --> 00:23:07,120
+الشرعية، لا يحقق مصلحةإنما المصلحة محصورة في نظام
+
+251
+00:23:07,120 --> 00:23:12,000
+الشريعة الإسلامية وعشان هيك يا أخوات لو نظرنا
+
+252
+00:23:12,000 --> 00:23:16,660
+للتعريفات اللي جاءت للسياسة في القوانين الوضعية
+
+253
+00:23:16,660 --> 00:23:22,800
+نجد أنها مبرقة من كل قيم كلام عام كلام عام وفاضفاض
+
+254
+00:23:22,800 --> 00:23:28,280
+يعني يحتمل كل شيء كلام غير مقين عشان احنا لما نعرف
+
+255
+00:23:28,280 --> 00:23:33,850
+شخصية بيكون في التعريف محترزاتعشان تضبط التعريف
+
+256
+00:23:33,850 --> 00:23:39,170
+تمنع دخول غير أجزاء المعرف فيه وبكون شامل لكل
+
+257
+00:23:39,170 --> 00:23:43,170
+أجزاء المعرف هنا تعريفات تبفطفط يعني على سبيل
+
+258
+00:23:43,170 --> 00:23:47,870
+المثال جاني التعريف الأول فن حكم المجتمعات
+
+259
+00:23:47,870 --> 00:23:54,070
+الإنسانية فن
+
+260
+00:23:54,070 --> 00:23:59,400
+حكم المجتمعات الإنسانيةشايفين كيف التعريف مأوسى أو
+
+261
+00:23:59,400 --> 00:24:05,160
+فضفاط كلام عام فن حكم المجتمعات الإنسانية طب كيف
+
+262
+00:24:05,160 --> 00:24:12,840
+أحكمها؟ طب بأي وسائل؟ بأي كيفية؟ أي فن هي ده الفن؟
+
+263
+00:24:12,840 --> 00:24:17,360
+كلك فن حكم المجتمعات الإنسانية التعريف التاني أو
+
+264
+00:24:17,360 --> 00:24:22,480
+فن الحكم طب إيش أهداف الحكم؟ وإيش وسائل الحكم؟
+
+265
+00:24:22,480 --> 00:24:28,040
+وإيش طبيعة الحكم؟مصطلحات فضفاضة حط تحتها أيش بدات
+
+266
+00:24:28,040 --> 00:24:35,960
+أو علم إدارة الدولة السياسة هي علم إدارة الدولة
+
+267
+00:24:35,960 --> 00:24:43,840
+وحط تحتها الإنوان هذا ما شئت من المعايير و من ..
+
+268
+00:24:43,840 --> 00:24:49,420
+طيب نيجي الأن لمقارنة بين تعريف السياسة عند
+
+269
+00:24:49,420 --> 00:24:57,090
+المسلمين و عند غيرهممقارنة يعني في نقاط التقاء و
+
+270
+00:24:57,090 --> 00:25:03,270
+نقاط افتراق واختلاف لو جينا للنقطة الأولى من حيث
+
+271
+00:25:03,270 --> 00:25:12,070
+مفهوم السياسة نجد أن علماء المسلمين و غيرهم يرون
+
+272
+00:25:12,070 --> 00:25:16,250
+أن السياسة هي تدبير شؤون البلاد و العباد على
+
+273
+00:25:16,250 --> 00:25:23,060
+اختلاف بينهم في كيفية ذلك إذا هذا في اتفاقيعني هذا
+
+274
+00:25:23,060 --> 00:25:28,280
+الـ band الأول فيه وجه اتفاق ووجه اختلاف ما أنت
+
+275
+00:25:28,280 --> 00:25:31,880
+تقول أنا أه وجه الاتفاق ووجه الخلاف اتفضلي وجه
+
+276
+00:25:31,880 --> 00:25:36,200
+الاتفاق أما كله تدبير شؤون البلاد و العباد أما وجه
+
+277
+00:25:36,200 --> 00:25:41,440
+الاختلاف يعني تشترك كله أو كله من السياسة في
+
+278
+00:25:41,440 --> 00:25:45,660
+المفهوم الإسلامي والسياسة في المفهوم الوظيفي أن كل
+
+279
+00:25:45,660 --> 00:25:50,500
+منهم يقوم على تدبير شؤون البلاد وهذا نقطة إيه؟
+
+280
+00:25:51,050 --> 00:25:56,590
+توافق واتفاق والتقاء يعني كما أن الشريعة الإسلامية
+
+281
+00:25:56,590 --> 00:25:59,750
+أو السياسة في الشريعة الإسلامية تعنى بتدبير شؤون
+
+282
+00:25:59,750 --> 00:26:05,450
+البلاد والعباد كمان السياسة في النظم الوضعية تعنى
+
+283
+00:26:05,450 --> 00:26:10,370
+بتدبير شؤون البلاد والعباد أما نقطة الاختلاف فهي
+
+284
+00:26:10,370 --> 00:26:15,120
+أن عند المسلمين تكون نقطة عالية الدين الإسلاميأه
+
+285
+00:26:15,120 --> 00:26:19,760
+على اختلاف بينهم في كيفية ذلك يعني الكيفية في
+
+286
+00:26:19,760 --> 00:26:23,940
+الشريعة الإسلامية مضبوطة بالقواعد الشرعية لكن
+
+287
+00:26:23,940 --> 00:26:28,300
+الكيفية في القوانين الوضعية غير مرتبطة بقيد مش
+
+288
+00:26:28,300 --> 00:26:36,980
+مضبوطة بقيد تمام اتنين ايه الأخوات اللي هناك؟ ليش
+
+289
+00:26:36,980 --> 00:26:41,660
+الباجين بدهم مش يشاركوا؟بتنوجح جديد ومشاركات يا
+
+290
+00:26:41,660 --> 00:26:47,340
+أخوان الأمر سهل ممكن تقرا أيه من ال slide نفسه اه
+
+291
+00:26:47,340 --> 00:26:54,380
+تفضلي حضرتك اللي هناك ايوة من حته القانون اللي
+
+292
+00:26:54,380 --> 00:26:58,380
+يحكم رجال السياسة ففي الإسلام الحكم هو الشرع الله
+
+293
+00:26:58,380 --> 00:27:01,920
+تعالى اما عشان غير المسلمين فالحكم هو القانون اللي
+
+294
+00:27:01,920 --> 00:27:06,580
+يدعم رجال السياسة أو الإسلام تمام الآن ايش
+
+295
+00:27:06,580 --> 00:27:16,400
+المرجعية؟مرجعية السياسة في الإسلام، إيش المرجعية؟
+
+296
+00:27:16,400 --> 00:27:17,580
+إيش الحاكم؟
+
+297
+00:27:20,150 --> 00:27:27,190
+شريعة الله هي الحاكمة على السياسة الشريعة
+
+298
+00:27:27,190 --> 00:27:31,590
+الإسلامية هي الحاكمة على السياسة يعني السياسة في
+
+299
+00:27:31,590 --> 00:27:36,250
+النهاية لابد و أن تتوافق مع الشريعة الإسلامية أما
+
+300
+00:27:36,250 --> 00:27:39,510
+في القوانين الوضعية إيش الحاكم؟ إيش الضابط؟ إيش
+
+301
+00:27:39,510 --> 00:27:44,670
+المرجية؟ قوانين
+
+302
+00:27:44,670 --> 00:27:51,330
+بتضحى رجال السياسةليش؟ رجال السياسة أنفسهم طب الآن
+
+303
+00:27:51,330 --> 00:27:56,670
+بتميز إلنا و يتضح إلنا الفرق فرق كبير جدا من
+
+304
+00:27:56,670 --> 00:28:02,550
+القانون الإلهي أو التشريع الإلهي أنا قلتلكم في أول
+
+305
+00:28:02,550 --> 00:28:10,170
+الفصلإن التشريع الإلهي أو الشريع الإسلامي تستمد
+
+306
+00:28:10,170 --> 00:28:17,290
+صفاته من صفات الموجد لها، المشرع، من صفات المشرع،
+
+307
+00:28:17,290 --> 00:28:21,790
+تستمد صفاته من صفات المشرع، العليم، الحليم،
+
+308
+00:28:21,790 --> 00:28:24,050
+الخبير، الكريم، العليم
+
+309
+00:28:26,820 --> 00:28:31,580
+في ما صنع لكن في القوانين الوضعية كمان تستمد
+
+310
+00:28:31,580 --> 00:28:37,260
+السياسة صفتها أو القوانين تستمد في القوانين في
+
+311
+00:28:37,260 --> 00:28:42,860
+الأنظمة الوضعية تستمد صفتها من واضح هذا القانون طب
+
+312
+00:28:42,860 --> 00:28:49,900
+مين واضح هذا القانون؟ بشر مثلنا مثله بشر الناقص
+
+313
+00:28:49,900 --> 00:28:55,000
+والهوى والجهل والتحيز والظلم والكذا إلى غير ذلك
+
+314
+00:28:57,500 --> 00:29:05,160
+تلاتة اتفضليه من حيث ان المسلمين يتحققوا مصلحة
+
+315
+00:29:05,160 --> 00:29:09,320
+الأمة عاجلة بما عاجلة أما غير المسلمين هي بحسب
+
+316
+00:29:09,320 --> 00:29:14,560
+أتراه كل جماعة على حد يعني كل جماعة حسب أهواء أهم
+
+317
+00:29:14,560 --> 00:29:20,740
+من أدبها أما في الإسلام هي عن طريق المصلحة العامة
+
+318
+00:29:20,740 --> 00:29:25,410
+يقول للناس سواء في الدنيا أو في المحلةتمام من حيثه
+
+319
+00:29:25,410 --> 00:29:29,210
+هدف السياسة في اللي عند المسلمين هو تحقيق مصالح
+
+320
+00:29:29,210 --> 00:29:33,370
+الأمة في العجل و الأجل حسب وفق ضابط معين، ضابط
+
+321
+00:29:33,370 --> 00:29:37,650
+اللي هو الشريعة الإسلامية و أنظمتها، لكن عند غير
+
+322
+00:29:37,650 --> 00:29:42,750
+المسلمين يا أخوات الهدف يختلف حسب وضع أيه؟ يعني
+
+323
+00:29:42,750 --> 00:29:47,530
+مثلا في إن النظام السياسي الديمقراطي في أوروبافي
+
+324
+00:29:47,530 --> 00:29:51,450
+عند النظام السياسي الاشتراكي النظام السياسي
+
+325
+00:29:51,450 --> 00:29:56,470
+الرئيسمالي صح ولا هم ارتضوا أن تكون السياسة تتجه
+
+326
+00:29:56,470 --> 00:30:00,510
+هذا الاتجاه حسب الجماعة اللي بتضاء حسب اختلاف
+
+327
+00:30:00,510 --> 00:30:05,410
+البيئات و الأعرف لكن عندنا نحن المسلمين لابد أن
+
+328
+00:30:05,410 --> 00:30:12,670
+ينسجم هدف السياسة مع الشريعة الإسلامية طبعا أخوات
+
+329
+00:30:14,670 --> 00:30:20,350
+في عندنا الببحث الثاني أهم قواعد النظام السياسي في
+
+330
+00:30:20,350 --> 00:30:24,670
+الإسلام زي ما أنتوا شايفين عندنا أربع قواعد للنظام
+
+331
+00:30:24,670 --> 00:30:27,910
+السياسي في الإسلام وهذه القواعد اللي بدنا نركز
+
+332
+00:30:27,910 --> 00:30:32,430
+عليها ان شاء الله تعالى و بدنا ندرسها بالتفصيل وهي
+
+333
+00:30:32,430 --> 00:30:36,070
+طبعا هذه القواعد هي المطالبة مننا في الامتحان فقط
+
+334
+00:30:36,070 --> 00:30:40,690
+يعني قاعدة الأولى الحاكمية لله العدل والمساواة
+
+335
+00:30:40,690 --> 00:30:47,190
+الشورى الطاعةهذه أربع قواعد أخوات احنا بدنا ندرسها
+
+336
+00:30:47,190 --> 00:30:51,710
+إن شاء الله تعالى، ما هو المقصود بالقواعد النظام
+
+337
+00:30:51,710 --> 00:30:56,350
+السياسي؟ تفضلي تلك المبادئ هو القواعد الأساسية
+
+338
+00:30:56,350 --> 00:31:01,730
+التي يبني عليها الإسلام دولته ويستلهم منها نظام
+
+339
+00:31:01,730 --> 00:31:05,870
+السياسي للحكومةتمام يعني يقصد بقواعد النظام
+
+340
+00:31:05,870 --> 00:31:09,550
+السياسي في الإسلام تلك المبادئ والثوابت الأساسية
+
+341
+00:31:09,550 --> 00:31:14,070
+التي يبني عليها الإسلام ودولته ويستلهم منها النظام
+
+342
+00:31:14,070 --> 00:31:18,970
+السياسي للحكم يعني الدولة مبنية أخوات على هذه
+
+343
+00:31:18,970 --> 00:31:24,150
+القواعد الأربعة وبنستلهم من هذه القواعد كمان إيه
+
+344
+00:31:24,150 --> 00:31:30,190
+النظام السياسي للحكم يعني إيش هو النظام السياسي
+
+345
+00:31:31,870 --> 00:31:37,150
+طبعا هناك اختلاف اجدش
+
+346
+00:31:37,150 --> 00:31:41,090
+هما القواعد تلاتة اربع اكثر من ذلك يعني هذا خلاف
+
+347
+00:31:41,090 --> 00:31:46,710
+احنا مش معنيين فيه بنجي للقاعدة الأولى القاعدة
+
+348
+00:31:46,710 --> 00:31:51,390
+الأولى الحاكمية لله ايش يعني الحاكمية لله؟
+
+349
+00:31:53,840 --> 00:31:57,240
+أيس المقصود بأن الحاكم هي لله؟ اتفضل يا عزيزي
+
+350
+00:31:57,240 --> 00:32:00,140
+بالله بإيه دي الأفكار في الشؤون يعني خالده و أنه
+
+351
+00:32:00,140 --> 00:32:03,600
+ممكن يتحكم و يحافظ في الشعر لهو و هو ممكن لا يكافر
+
+352
+00:32:03,600 --> 00:32:07,600
+الشرقية ولا يكافر .. لا يحافظ أنه يغير بغير ما
+
+353
+00:32:07,600 --> 00:32:14,170
+شغالأول عجب نقول حاكمية اسم مصدر من الفعل الماضي
+
+354
+00:32:14,170 --> 00:32:19,430
+حَكَمَ بمعنى قضى ومنه حَكَم بالأمر حُكما أي قضى به
+
+355
+00:32:19,430 --> 00:32:26,270
+ويقال حَكَم له وحَكَم عليه وحَكَم فيه الحاكمية
+
+356
+00:32:26,270 --> 00:32:31,900
+يعني اسم مصدر حاكمية من الفعل الماضي حَكَمَحكم
+
+357
+00:32:31,900 --> 00:32:39,600
+يحكم حكما حاكمية إذا بنقول اسم مصدر من الفعل الحكم
+
+358
+00:32:39,600 --> 00:32:46,700
+لإن الحاكمية يعني هذا المصدر يشتق منه يحكم وحاكم
+
+359
+00:32:46,700 --> 00:32:52,500
+ومحكوم يعني أي كلمة طبعا المصدر يا أخوات إله
+
+360
+00:32:52,500 --> 00:32:59,260
+اشتقاقات يعني ممكن المصدر يكون أو يشتق من المصدر
+
+361
+00:32:59,260 --> 00:33:07,570
+الفعل الأمرحكم حكمة يحكم وممكن نشتق منه اسم الفاعل
+
+362
+00:33:07,570 --> 00:33:15,550
+حاكم واسم المفعول حاكم حاكمية حاكمية
+
+363
+00:33:15,550 --> 00:33:21,490
+حاكمية حاكمية حاكمية
+
+364
+00:33:21,490 --> 00:33:27,250
+حاكمية حاكمية حاكمية حاكمية حاكمية حاكمية حاكمية
+
+365
+00:33:30,810 --> 00:33:36,670
+أنا لو قلت الحاكمية الراجل الذي يحكم زوجته هذا في
+
+366
+00:33:36,670 --> 00:33:43,470
+حاكمية المدرس اللي بيحكم طلابه في حاكمية الجامعة
+
+367
+00:33:43,470 --> 00:33:48,530
+اللي بتحكم طلابها المؤسسة اللي بتحكم موظفيها
+
+368
+00:33:48,530 --> 00:33:53,600
+الدولة اللي بتحكم جيشها صح ولا لا؟مش هذه حاكمية؟
+
+369
+00:33:53,600 --> 00:33:58,920
+لكن الحاكمية كلمة الحاكمية يعني جنس في التعريف
+
+370
+00:33:58,920 --> 00:34:05,420
+مصطلح فاطفات لكن لما أقول أنا الحاكمية لله أنا
+
+371
+00:34:05,420 --> 00:34:11,580
+أضافت الحاكمية لله يعني قصرت الحكم لله ولما كان
+
+372
+00:34:11,580 --> 00:34:17,020
+الحكم أو الحاكمية بمعنى القضاء والحكم وأقول القضاء
+
+373
+00:34:17,020 --> 00:34:25,170
+لله فقطالحكم لله فقط فلما أقول حاكمية لله أي أن
+
+374
+00:34:25,170 --> 00:34:31,870
+بيده القضاء في شؤون عباده وأنه صاحب الحكم فيهم وله
+
+375
+00:34:31,870 --> 00:34:38,330
+حق التشريع لهم وهو مصدر التشريع ولا يحق لهم ولا
+
+376
+00:34:38,330 --> 00:34:44,510
+لأحد منهم أن يشرع غير شرعه تعالىأو يأمر أحدًا
+
+377
+00:34:44,510 --> 00:34:51,210
+باتباع شرع غير شرع الله تعالى ويأتمر هو بشرع غير
+
+378
+00:34:51,210 --> 00:34:59,890
+شرع الله جل وعلا أما الأدلة التي جاءت تبين على أن
+
+379
+00:34:59,890 --> 00:35:04,310
+الحاكمية لله واحدة أخوات قوله تعالى
+
+380
+00:35:17,070 --> 00:35:23,050
+إن الحكم إلا لله يعني هذا قصر الأخوات لا يجوز لأحد
+
+381
+00:35:23,050 --> 00:35:27,890
+أن يحكم إلا الله سبحانه وتعالى نعم يريدون أن
+
+382
+00:35:27,890 --> 00:35:31,130
+يتحكموا إلى الترابوت وقد أمروا أن يكتبوا فيديو
+
+383
+00:35:31,130 --> 00:35:54,480
+يريد الشيطان أن يظهر لهم ظلالةيا أخوات
+
+384
+00:35:54,480 --> 00:36:00,850
+الحكم لمين التحكم؟ نحتكم إلى الله جميعًاحتى
+
+385
+00:36:00,850 --> 00:36:05,710
+السياسة لابد ان تحكم بمنهج الله ولابد ان تحكم
+
+386
+00:36:05,710 --> 00:36:10,810
+بشراء الله طبعا في مفهوم يقول السياسة كل شي جائز
+
+387
+00:36:10,810 --> 00:36:16,700
+فيها صح؟في ناس بيقولوا السياسة كل إشي جائز فيها
+
+388
+00:36:16,700 --> 00:36:22,100
+وممكن يقولك السياسة تياسة والسياسة كلمة سياسة يعني
+
+389
+00:36:22,100 --> 00:36:26,960
+رخصة بتديك رخصة افعل ولا اخرج مدام في إطار سياسة
+
+390
+00:36:26,960 --> 00:36:31,640
+الدولة افعل ما تجلجش طبعا هذا التعبيرات و هذا
+
+391
+00:36:31,640 --> 00:36:36,180
+المبادئ في السياسة في القوانين الوضعية كل شيء جائز
+
+392
+00:36:36,180 --> 00:36:42,670
+في السياسة عندهم لكن عندنا شايفين التقييدأه ثلاثة
+
+393
+00:36:52,440 --> 00:36:57,300
+العقوبة الشديدة يعني لو شفنا احنا الاية بالله فيها
+
+394
+00:36:57,300 --> 00:37:05,640
+عقوبة شديدة للذين يحتكمون لغير شرع الله ولغير منهج
+
+395
+00:37:05,640 --> 00:37:12,260
+الله فلا وربك لا يؤمنون نفى صفة الإيمان وأي عقوبة
+
+396
+00:37:12,260 --> 00:37:18,130
+أشد من نفي الإيمان على الرجلأنا لو قلت لواحد و
+
+397
+00:37:18,130 --> 00:37:22,250
+الله انت ماعندكش دين ايش بيسوي؟ كيف رد فعله بيكون؟
+
+398
+00:37:22,250 --> 00:37:27,510
+بيغضب، بيبسعل هذا إن لم يضربني اه تقول لوحد
+
+399
+00:37:27,510 --> 00:37:32,650
+ماعندكش دين؟ او انت مافيش عندك أمانة؟ ايش بيصير
+
+400
+00:37:32,650 --> 00:37:40,370
+فيه؟ اذا فلو ربك لا يؤمنون مهما فعلوا لا يؤمنون
+
+401
+00:37:40,370 --> 00:37:47,700
+إذا تحاكمواإلى غير حكم الله وإلى غير منهج الله حتى
+
+402
+00:37:47,700 --> 00:37:53,740
+يحكموك فيما ششر بينهم وماشي بس احنا نحتكم إلى شراء
+
+403
+00:37:53,740 --> 00:37:59,560
+الله وإذا طلعت النتيجة لاتسرنا أو مش بصالحنا نتمرد
+
+404
+00:37:59,560 --> 00:38:07,300
+أو نتجر لأ جالك لابد أن نرضى بحكم الله ونسلم
+
+405
+00:38:07,300 --> 00:38:09,060
+تسليمة
+
+406
+00:38:10,460 --> 00:38:17,200
+فلو ربك يؤمنون حتى يحكموك في ما سشر بينهم ثم لا
+
+407
+00:38:17,200 --> 00:38:26,160
+يجدوا في أنفسهم حرجا يعني زعل وضيق و قهر و غل و
+
+408
+00:38:26,160 --> 00:38:33,520
+حقد من الحكم و يسلموا .. ايش يقولوا سمعنا و قطعنا
+
+409
+00:38:33,520 --> 00:38:39,060
+بهيك يا أخوات ان شاء الله تعالىيعني بتكون السياسة
+
+410
+00:38:39,060 --> 00:38:43,340
+تسير في الإطار الشرعي وفق هذه الضوابط كمان هناك
+
+411
+00:38:43,340 --> 00:38:47,740
+الكثير من النصوص كذلك العقل السليم يقر أن الله
+
+412
+00:38:47,740 --> 00:38:54,340
+واحدة الذي له أن يسن التشريعات والقوانين و لا إله
+
+413
+00:38:54,340 --> 00:39:00,850
+إلا الله تقرر مبدأ الحاكمية للهو ان شاء الله تعالى
+
+414
+00:39:00,850 --> 00:39:04,330
+نكمل هذه القاعدة و نتطرق للقواعد الأخرى في
+
+415
+00:39:04,330 --> 00:39:07,610
+المحاضرة اللى جاية ان شاء الله تعالى بارك الله
+
+416
+00:39:07,610 --> 00:39:08,130
+فيكم
+