diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c2b88de5653f36be31793638be66a8f869697dc1
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_postprocess.srt
@@ -0,0 +1,2292 @@
+1
+00:00:00,000 --> 00:00:06,280
+بسم الله الرحمن الرحيم هذه المحاضرة الخامسة في
+
+2
+00:00:06,280 --> 00:00:11,920
+مساق رياضية مفاصلة لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:12,500 --> 00:00:19,280
+كلية الـ IT قسم الحوسبة المتنقلة اليوم سنحكي عن
+
+4
+00:00:19,280 --> 00:00:22,440
+سيكشن الثاني في شفتر أربعة اللي هو أربعة اتنين
+
+5
+00:00:22,440 --> 00:00:26,460
+اللي هو الـ integer representations أو اللي هو
+
+6
+00:00:26,460 --> 00:00:31,740
+اللي بنسمي اللي هي كيف نعبر عن الأعداد أو التعبير
+
+7
+00:00:31,740 --> 00:00:36,220
+عن الأعداد أو تمثيل الأعداد بأنظمة العد المختلفة
+
+8
+00:00:36,630 --> 00:00:41,930
+الان عشان ندخل لأنظمة العد خلنا في الأول نتذكر ايش
+
+9
+00:00:41,930 --> 00:00:44,530
+اللي حكيناه او بعض اللي حكيناها المرة الماضية في
+
+10
+00:00:44,530 --> 00:00:47,670
+المحاضرة الرابعة في ال congrance relation قولنا
+
+11
+00:00:47,670 --> 00:00:54,600
+ايه تطابق P مدله عشرة؟الـ A لو قسمت على عشرة و الـ
+
+12
+00:00:54,600 --> 00:00:59,160
+B لو قسمت على عشرة بيكون له نفس الـ Remainder و
+
+13
+00:00:59,160 --> 00:01:03,560
+الـ Remainder في هذه الحالة من سفر لعين تسعة أكبر
+
+14
+00:01:03,560 --> 00:01:06,480
+أو سوى سفر و أصغر strictly من عشرة يعني الـ
+
+15
+00:01:06,480 --> 00:01:09,680
+Remainder هيكون يا سفر يا واحد يا اتنين يا تلاتة
+
+16
+00:01:09,680 --> 00:01:12,660
+يا أربعة يا خمسة يا ستة يا سبعة يا تمانية يا تسعة
+
+17
+00:01:12,660 --> 00:01:18,480
+هدولة ال Remainders هم اللي احنا بنستخدمهم في نظام
+
+18
+00:01:18,480 --> 00:01:24,120
+العد العشريالان modulo عشرة يعني مقياس عشرة هذا
+
+19
+00:01:24,120 --> 00:01:29,910
+اللي هو اللي بده يعمله نظام العد العشرينأحنا كيف
+
+20
+00:01:29,910 --> 00:01:33,870
+كنا اللي هو نكتب اللي هو ال .. ال .. ال .. ال ..
+
+21
+00:01:33,870 --> 00:01:41,390
+في نظام العدل عشري 256 مثلا بتساوي اللي هو قداش
+
+22
+00:01:41,390 --> 00:01:45,710
+كمية فيها 200 و قداش فيها عشرات اللي هو خمسة و
+
+23
+00:01:45,710 --> 00:01:50,310
+قداش فيها أحد ستة فكنا نيجي نكتب اللي هو الست رقم
+
+24
+00:01:50,310 --> 00:01:54,450
+الأحد هيه ستة في عشر أقل سفر الخمسة في رقم الأقل
+
+25
+00:01:54,450 --> 00:01:58,110
+اللي هي العشرات خمسة في عشر أقل واحدوالتنين في
+
+26
+00:01:58,110 --> 00:02:02,850
+عشرة تربيع اللي هو رقم مين او خانة المنئات يعني
+
+27
+00:02:02,850 --> 00:02:07,370
+هذه الخانة اللي بيكون فيها العشرة أس سفر هذه
+
+28
+00:02:07,370 --> 00:02:11,190
+الخانة اللي بيكون فيها العشرة أس اتنى اقص واحد
+
+29
+00:02:11,190 --> 00:02:16,170
+وهذه الخانة الثالثة اللي العشرة اللي اتنين فيها
+
+30
+00:02:16,170 --> 00:02:21,460
+بيكون ضرب عشرة أس اتنينالان نجي لمثال اخر هذا احنا
+
+31
+00:02:21,460 --> 00:02:24,960
+النظام العد اللي احنا بنشتغل فيه عادة و بنتعلمه في
+
+32
+00:02:24,960 --> 00:02:29,520
+المدارس هو نظام العد العشرين الان اللي هي يعني
+
+33
+00:02:29,520 --> 00:02:33,700
+منزلة العدد هنا اللي هو ستة اللي هي منزلة العدد
+
+34
+00:02:33,700 --> 00:02:38,500
+هنا خمسين هذا منزلة العدد متين الان نجي لمثال اخر
+
+35
+00:02:38,500 --> 00:02:45,140
+ايه تطابق بيه مدل خمسة مدل خمسة اللي هي يعني لما
+
+36
+00:02:45,140 --> 00:02:49,440
+نقسم هذا على الخمسة تطلع remainderو هذا لما نقسمه
+
+37
+00:02:49,440 --> 00:02:52,380
+على خمسة بيطلع remainder عشان يكون المتطابقين لازم
+
+38
+00:02:52,380 --> 00:02:54,900
+ال remainder هان و ال remainder هيكون إيه شمالين
+
+39
+00:02:54,900 --> 00:02:58,400
+متساويين زي ما قلنا المرة الماضية ال remainder
+
+40
+00:02:58,400 --> 00:03:02,500
+عادة اللي هو عبارة عن سفر و واحد و اتنين و تلاتة و
+
+41
+00:03:02,500 --> 00:03:07,520
+أربعة لإن اللي هو الخمسة بيصير ال remainder له سفر
+
+42
+00:03:07,520 --> 00:03:12,780
+و هكذا يعني any integer is congruent modulo خمسة
+
+43
+00:03:12,780 --> 00:03:15,940
+to one of the following remaindersيعني أي عدد في
+
+44
+00:03:15,940 --> 00:03:20,460
+الدنيا هيكون بطابق واحد من هدولة ليش؟ لأن هذا لما
+
+45
+00:03:20,460 --> 00:03:24,140
+يكون ال remainder له سفر بيصير طابق السفر لما يكون
+
+46
+00:03:24,140 --> 00:03:26,720
+ال remainder له مع الخمسة واحد بطابق اللي هو
+
+47
+00:03:26,720 --> 00:03:30,700
+الواحد لو كان اللي هو ال remainder له اتنين بطابق
+
+48
+00:03:30,700 --> 00:03:34,320
+التنين لو كان ال remainder تلاتة بطابق التلاتةو لو
+
+49
+00:03:34,320 --> 00:03:37,540
+ال remainder لما نقسم ال a على خمسة طالع أربعة
+
+50
+00:03:37,540 --> 00:03:40,920
+بكون بطابق الأربعة إذا أي حدد في الدنيا ال
+
+51
+00:03:40,920 --> 00:03:43,640
+remainder اللي هو يا سفر يا واحد يا اتنين يا تلاتي
+
+52
+00:03:43,640 --> 00:03:48,560
+اربعة يعني بمعنى آخر ال a هيطابق واحد من هذولة
+
+53
+00:03:48,560 --> 00:03:53,120
+هذولة الآن من سفر لأربعة زي ما كان من سفر لعشرة هم
+
+54
+00:03:53,120 --> 00:03:57,460
+اللي هو ال digits تبعات اللي هي نظام العد العشري
+
+55
+00:03:57,460 --> 00:04:00,860
+هيكون في نظام العد الخماسي اللي هي ال digits سفر
+
+56
+00:04:00,860 --> 00:04:05,370
+وواحد واتنين وتلاتة واربعةيعني الآن لو بدنا الـ 56
+
+57
+00:04:05,370 --> 00:04:10,130
+نكتبها على صورة اللي هو نظام العد اللي هو الخمسة،
+
+58
+00:04:10,130 --> 00:04:13,990
+ده مش عشرة، هذه خمسة، هي الـ 56 في العشرة، بنكتبها
+
+59
+00:04:13,990 --> 00:04:18,910
+على صورة إيش؟ نظام عد عشرة، خمسين، هذه الآن الـ 56
+
+60
+00:04:18,910 --> 00:04:22,110
+في نظام العد العشري، اللي هي إحنا عادة إنت في نظام
+
+61
+00:04:22,110 --> 00:04:25,650
+العد العشري، بنكتبش لا عشرة ولا خمسة ولا كده ولا
+
+62
+00:04:25,650 --> 00:04:30,010
+كده، على طول بنكتب 56، لأنه متعارف عليه بين إنه
+
+63
+00:04:30,010 --> 00:04:35,190
+نقص نظام العد العشري،بدي احول ال 56 الى نظام العد
+
+64
+00:04:35,190 --> 00:04:44,870
+الخماسي شوف كيف الان ال 56 عندى اللى هي ال 56 فيها
+
+65
+00:04:44,870 --> 00:04:49,690
+الان خمسة في خمسة في خمسة و عشرين يعني خمسين و بضل
+
+66
+00:04:49,690 --> 00:04:54,990
+ستة الان الخمسين هذه اللى هي عبارة عن اتنين في
+
+67
+00:04:54,990 --> 00:04:57,910
+خمسة و عشرين يعني خمسة تربيع في اتنين بطلع خمسين
+
+68
+00:04:57,910 --> 00:05:01,710
+زائدالان بعد شوية هنقولكم طريقة الكتابة بس خليني
+
+69
+00:05:01,710 --> 00:05:05,610
+الان بس ناخد المثال عشان نشوف ايش اللي بنجزله في
+
+70
+00:05:05,610 --> 00:05:10,610
+نظام العد الخماسي زائد واحد في مين في خمسة أس واحد
+
+71
+00:05:10,610 --> 00:05:15,350
+زائد واحد في خمسة أس صفر اقدرنا نكتب ال 56 على هذه
+
+72
+00:05:15,350 --> 00:05:19,250
+الصورة يعني بدلنا نكتب العشرة بنكتب مين ونستخدم
+
+73
+00:05:19,250 --> 00:05:24,050
+بدلها الخمسة و بنسميه نظام العد الخماسيلاحظوا الآن
+
+74
+00:05:24,050 --> 00:05:30,150
+خانت اللي هي الأحد بالنسبة لهذه واحد خانت اللي هي
+
+75
+00:05:30,150 --> 00:05:33,050
+اللي كنا نسميها العشرات اللي هي اللي مضروبة في
+
+76
+00:05:33,050 --> 00:05:37,030
+عشرة هنا هنا بتكون مضروبة في خمسة بدلها خمسة أس
+
+77
+00:05:37,030 --> 00:05:37,870
+واحد واحد
+
+78
+00:05:40,870 --> 00:05:45,290
+الخانة الأولى مضروبة في خمسة أو السفر والخانة
+
+79
+00:05:45,290 --> 00:05:48,730
+الثانية مضروبة في خمسة أو السواعد والتانية مضروبة
+
+80
+00:05:48,730 --> 00:05:53,890
+في خمسة اياش اوس اتنين الان ندخل للنظام الات وطابق
+
+81
+00:05:53,890 --> 00:05:57,950
+ال بي ومدول اتنين اللى يقودنا للنظام العد الثنائي
+
+82
+00:05:58,270 --> 00:06:02,470
+الآن لما نقسم الـ A على الـ 2 يكون المتبقى يا سفر
+
+83
+00:06:02,470 --> 00:06:07,050
+يا إيش يا واحد بناء عليه هيكون عناصر الـ D أو الـ
+
+84
+00:06:07,050 --> 00:06:11,830
+digits تبعات نظام العد الثناني يا ثنائي يا سفر يا
+
+85
+00:06:11,830 --> 00:06:16,150
+واحد لو بدنا نيجي الآن الـ 56 نكتبها على صورة اللي
+
+86
+00:06:16,150 --> 00:06:22,290
+هو نظام عد A شمالهالـ 56 طبعاً اللي هي النظام لعدد
+
+87
+00:06:22,290 --> 00:06:27,670
+ثنائي معناته 2 أس 1 2 أس 1 2 أس 2 2 أس 3 2 أس 4 2
+
+88
+00:06:27,670 --> 00:06:32,410
+أس 5 إلى آخرين لو أجينا للـ 56 كيف بنكتبها على
+
+89
+00:06:32,410 --> 00:06:37,510
+صورة اللي هو نظام لعدد الثنائي الآن الـ 56 اللي هو
+
+90
+00:06:37,510 --> 00:06:44,620
+عندي 2 أس 5 32لو قلنا 2 أُس 6 بيصير 64 بيصير أكتر
+
+91
+00:06:44,620 --> 00:06:47,480
+منها دي إذا أنا ماقدرش استخدامها إذا بدي أخد 2 أُس
+
+92
+00:06:47,480 --> 00:06:55,740
+5 2 أُس 5 هي 32 في واحد بيصير 32 32 من 56 بيظل
+
+93
+00:06:55,740 --> 00:07:00,100
+اللي هو جداش 24 لذا دل فيه أرقامإذا بدنا ناخد
+
+94
+00:07:00,100 --> 00:07:06,020
+الخانة اللي بعدها 2 أس 4 2 أس 4 أيش 16 16 زائد 32
+
+95
+00:07:06,020 --> 00:07:14,340
+48 48 من 56 زاد 8 8 لحسن حظنا طلعت 2 أس 3 فعشان
+
+96
+00:07:14,340 --> 00:07:19,720
+كتبنا 1 في 2 أس 3 فطلعت هذا على بعض كلها 56 الآن
+
+97
+00:07:19,720 --> 00:07:25,920
+الخانات اللي بعدها لازم نكملهالأن هذه بتصبح خانة
+
+98
+00:07:25,920 --> 00:07:34,540
+0×2×2، 0×2×1، 0×2×0، ليش؟ على أساس أننا الآن نكتب
+
+99
+00:07:34,540 --> 00:07:45,240
+الرقم التالي الخانة 2×0،0، خانة 2×1،0، خانة 2×2،0،
+
+100
+00:07:45,240 --> 00:07:52,920
+خانة 2×3،1،خالت 2 أقصد 4 هو 1 خالت 2 أقصد 5 هو 1
+
+101
+00:07:52,920 --> 00:07:58,060
+فهذا الآن كتبنا العدد على صورة عدد في صورة نظام
+
+102
+00:07:58,060 --> 00:08:01,820
+العدد الثاني هذه 2 يا شباب و بنات مش اللي هو خمسة
+
+103
+00:08:01,820 --> 00:08:06,900
+اتنين هذه اه هذا نظام هذا العدد اللي هو واحد واحد
+
+104
+00:08:06,900 --> 00:08:12,620
+واحد تلت اصفاراللي هو بيمثل الرقم 56 هذا بنظام
+
+105
+00:08:12,620 --> 00:08:19,800
+العد الثنائي طيب الان نيجي لمثال آخر لسه احنا
+
+106
+00:08:19,800 --> 00:08:23,620
+بنشتغل شغل بدائي بعد شوية بيصير لعنا عملية
+
+107
+00:08:23,620 --> 00:08:28,710
+الحسابات أسن ان شاء اللهالان 965 في نظام العد
+
+108
+00:08:28,710 --> 00:08:32,530
+العشري هذه الخانة الأولى اللى هي في عشرة أقص سفر
+
+109
+00:08:32,530 --> 00:08:35,430
+هي اللى خمسة يعني عشرة أقص سفر يعني واحد يا جماعة
+
+110
+00:08:35,430 --> 00:08:38,750
+عشان هيك مكتبهاش عشرة أقص سفر مع قصود واحد وخمسة
+
+111
+00:08:38,750 --> 00:08:41,890
+أقص سفر واحد واتنين أقص سفر واحد عشان هيك الخانة
+
+112
+00:08:41,890 --> 00:08:47,030
+الأولى دايما قيمتها في كل أنظمة العد زي ما هي طيب
+
+113
+00:08:47,030 --> 00:08:50,990
+الان ستة اللى هي الخانة التانية اللى عبارة عن ستة
+
+114
+00:08:50,990 --> 00:08:54,690
+في عشرة أقص واحدتسعة اللي هي في الخانة التالتة
+
+115
+00:08:54,690 --> 00:08:59,430
+اللي هي تسعة في عشر عقل ساش اتنين هذه الآن قيمتها
+
+116
+00:08:59,430 --> 00:09:03,950
+اللي هي قيمة اللي هي اللي هي تسعة مية خمسة ستين
+
+117
+00:09:03,950 --> 00:09:07,390
+بالنظام العد العشر اللي احنا أصلا ما بنعرفه طيب
+
+118
+00:09:07,390 --> 00:09:10,810
+الان لو بدنا نيجي نحسب اتنين اربعة خمسة في نظام
+
+119
+00:09:10,810 --> 00:09:15,230
+العد الثماني كيف بنحسبها يا جماعة الخانة الأولى
+
+120
+00:09:15,230 --> 00:09:20,290
+اللي هي خمسة في تمانية قص سفر يعني خمسة زائد اربعة
+
+121
+00:09:20,290 --> 00:09:26,040
+في تمانية قص واحدالخانة الثانية الآن التالتة اللي
+
+122
+00:09:26,040 --> 00:09:29,980
+هي 2 في 8 أقصى 2 بالظبط زي ما كنا نعمل في اللي هو
+
+123
+00:09:29,980 --> 00:09:35,660
+النظام العد العشري زمان الان هي قيمته هذا بنحسبها
+
+124
+00:09:35,660 --> 00:09:40,960
+فبتطلع عندي هذه القيمة هي هذه الان كيف بدنا نحسبها
+
+125
+00:09:40,960 --> 00:09:47,480
+بنظام العد اللي هو يتمثل بنظام العد اللي هي العشري
+
+126
+00:09:47,480 --> 00:09:53,380
+هذه الرقم لو ضربناها في بعض هيطلع لنا 165في نظام
+
+127
+00:09:53,380 --> 00:09:59,120
+العد العشري إذا قيمة الـ 245 في الثماني هي 165 في
+
+128
+00:09:59,120 --> 00:10:02,920
+العشري وهينا حولناها من نظام العد الثماني اللي
+
+129
+00:10:02,920 --> 00:10:07,900
+مكتوب فيه هيه وضلعنا الرقم اللي طلع هذا الرقم اللي
+
+130
+00:10:07,900 --> 00:10:12,080
+طلع هذا اللي مجموعه عادي هو أعدادنا اللي احنا
+
+131
+00:10:12,080 --> 00:10:18,500
+بنتعامل معها اللي هي 165الان هذا نظام العد الثماني
+
+132
+00:10:18,500 --> 00:10:23,460
+لان فيه hexadecimal expansion اللي هو ايه ال
+
+133
+00:10:23,460 --> 00:10:27,860
+hexadecimal expansion هو نظام العد الست عشر هدول
+
+134
+00:10:27,860 --> 00:10:33,360
+النظام اللي بتعد بتهمكم انتوا في الحاسوبلأن ضام
+
+135
+00:10:33,360 --> 00:10:37,000
+العدل اللي هو في ال 16 ايش هيكون اللي هي الأرقام
+
+136
+00:10:37,000 --> 00:10:41,280
+اللي بنستخدمها ال digits اللي فيه سفر و واحد و
+
+137
+00:10:41,280 --> 00:10:45,640
+اتنين و تلاتة و اربع و خمسة و ستة و سبعة و تمانية
+
+138
+00:10:45,640 --> 00:10:48,420
+و تسعة و عشر و أحداشر لما أصل لخمسة عشر لأن
+
+139
+00:10:48,420 --> 00:10:53,120
+السبتاشر برجع السفرلكن احنا لو ده نيجي نكتب خمس
+
+140
+00:10:53,120 --> 00:10:57,480
+عشر واربع عشر بنصير نخربط اذا بدنا الرموز بعد
+
+141
+00:10:57,480 --> 00:11:01,540
+التسعة يعني بدنا نستخدم في الست عشر سفر واحد
+
+142
+00:11:01,540 --> 00:11:04,060
+واتنين وتلاتة واربعة وخمسة وستة وسبعة وتمانية
+
+143
+00:11:04,060 --> 00:11:09,480
+وتسعة بعد هيك بدنا نستخدم حروف أبجدية مين هي الـA
+
+144
+00:11:09,480 --> 00:11:12,800
+عشرة الـB عشرة الـB عشرة الـB عشرة الـC عشرة الـC
+
+145
+00:11:12,800 --> 00:11:14,780
+عشرة الـC عشرة الـC عشرة الـD عشرة الـD عشرة الـD
+
+146
+00:11:14,780 --> 00:11:15,900
+عشرة الـD عشرة الـD عشرة الـD عشرة الـD عشرة الـD
+
+147
+00:11:15,900 --> 00:11:21,790
+عشرة الـE عشرة الـE عشرةالان a,b,c,d,e و ال F 15
+
+148
+00:11:21,790 --> 00:11:25,690
+ماشي الحال و 16 طبعا ترجع السفر اذا هنستبدل
+
+149
+00:11:25,690 --> 00:11:35,870
+الاعداد من 10 ل 15 ب a,b,c,d,e,f على الترتيبهذا
+
+150
+00:11:35,870 --> 00:11:41,930
+الان عدد مكتوب بنظام العدد الست عشر كيف احسبه
+
+151
+00:11:41,930 --> 00:11:47,030
+بنسبة
+
+152
+00:11:47,030 --> 00:11:49,590
+للست عشر؟ اول حاجة
+
+153
+00:11:52,070 --> 00:11:56,090
+اللي هو جدّاش بيبني عرفه اللي هو بعد الـ A مباشرة
+
+154
+00:11:56,090 --> 00:12:00,870
+الـ A عشرة و الـ B 11 هي 11 في 16 أش سفر نكتبهش زي
+
+155
+00:12:00,870 --> 00:12:03,990
+ما احنا انتفجنا إذا هذا قيمته هو نفسه في أي ذاك
+
+156
+00:12:03,990 --> 00:12:09,770
+اللي هو B 11 زائد الآن Zero في 16 أس واحد هي Zero
+
+157
+00:12:09,770 --> 00:12:14,920
+في 16 زائدالتانى اللى هو مين E اللى هى اش قيمته
+
+158
+00:12:14,920 --> 00:12:19,380
+اربعة عشر فست عشر اش منزلته الخانة التالتة هذه
+
+159
+00:12:19,380 --> 00:12:24,200
+تربيع لان البعده ال A قيمته عشرة مضروب في الخانة
+
+160
+00:12:24,200 --> 00:12:28,820
+الرابعة اللى 16 أس 3زائد آخر واحد اللي هو في
+
+161
+00:12:28,820 --> 00:12:32,820
+الخانة الخامسة هي واحد، تنين، تلاتة، أربعة، خمسة،
+
+162
+00:12:32,820 --> 00:12:37,400
+اتنين في الخانة الخامسة ستة عشر أس أربعة يعني
+
+163
+00:12:37,400 --> 00:12:42,660
+الخانة الخامسة ماقص واحد إذا هذا الآن بنحسبه
+
+164
+00:12:42,660 --> 00:12:46,560
+بالحسبة العادية على آلة الحاسبة بطلعلنا الرقم هذا
+
+165
+00:12:46,560 --> 00:12:50,040
+هذا الرقم هو الرقم بالنظام العشري عشان هي كانت مش
+
+166
+00:12:50,040 --> 00:12:52,620
+كاتبله أنا عشرة عشان احنا متفقين مع بعض اللي
+
+167
+00:12:52,620 --> 00:12:56,760
+ماكنتبلهوشعشرة او اتنين او تلاتة يعني بنقصد بنظام
+
+168
+00:12:56,760 --> 00:13:00,820
+العد من العشري هي حولنا نظام العد الست عشري العد
+
+169
+00:13:00,820 --> 00:13:05,140
+من عد ست عشري الى نظام العد العشري نيجي الان
+
+170
+00:13:05,140 --> 00:13:09,420
+للنظرية اللى بتقولنا بتشرّعلنا لشغلنا ايش النظرية
+
+171
+00:13:09,420 --> 00:13:15,420
+بتقولbe an integer greater than 1 يعني بي عبارة عن
+
+172
+00:13:15,420 --> 00:13:20,200
+عدد أكبر من واحد then لو كان عندي n is a positive
+
+173
+00:13:20,200 --> 00:13:24,100
+integer يعني n كان عندي أي positive integer بقدر
+
+174
+00:13:24,100 --> 00:13:29,100
+أكتبره على صورة n بتساوي a k b k زائد a k minus
+
+175
+00:13:29,100 --> 00:13:33,160
+واحد b k minus واحد زائد لما أصل a واحد b زائد a
+
+176
+00:13:33,160 --> 00:13:36,000
+naught a naught هي ده في الواقع a naught ضرب b
+
+177
+00:13:36,000 --> 00:13:42,380
+والسفر الآن هذه بت هي اللي بتشرعلنا نظام العديعني
+
+178
+00:13:42,380 --> 00:13:46,760
+لو كان عندى الآن هذه الـ B هي اللى بنقصد فيها مرة
+
+179
+00:13:46,760 --> 00:13:50,540
+اتنين مرة خمسة مرة عشرة مرة كده كده الاخرى و ال A
+
+180
+00:13:50,540 --> 00:13:56,460
+note A1 A2 AK-1 لAK هي اللى بتمثل الاعداد اللى
+
+181
+00:13:56,460 --> 00:14:01,580
+بدنا نكتبها عندنا اللى هنا مثلا الخمسة او ستة واحد
+
+182
+00:14:01,980 --> 00:14:07,360
+والـ B هنا هي العشرة أو هنا مثلا اتنين A E A O
+
+183
+00:14:07,360 --> 00:14:12,280
+Zero A Zero B هذه هي اللي هي A نوت A واحد اللي عند
+
+184
+00:14:12,280 --> 00:14:16,580
+A كي في هذه الحالة الـ K اللي هي بتساوي عبارة عن
+
+185
+00:14:16,580 --> 00:14:21,410
+اللي هيالعدد اللى هو خمس طعش ده هو ستة عشر ناقص
+
+186
+00:14:21,410 --> 00:14:27,170
+واحد هدولة بيكونن هن من سفر لعند خمس طعش في حالة
+
+187
+00:14:27,170 --> 00:14:32,310
+الست عشر و هدولة اللى جوا هن الأعداد من سفر لعند
+
+188
+00:14:32,310 --> 00:14:38,340
+ست عشروالان ال B هو رقم 16 اللى هى بيمثلى اللى هو
+
+189
+00:14:38,340 --> 00:14:43,920
+نظام العد ال 16 واحد بيطبق على الأثناء هذا بيصير
+
+190
+00:14:43,920 --> 00:14:48,200
+ال B2 و هدولة بيصير العددين بس اللى هو ال 0 و ال 1
+
+191
+00:14:48,200 --> 00:14:55,400
+اذا هذه اللى هى بتشرعلى عملية اللى هو أنظمة العد
+
+192
+00:14:59,440 --> 00:15:06,980
+الان نكمل representations of integers نشوف عملية
+
+193
+00:15:06,980 --> 00:15:10,860
+تمثيل العدد بنحط أنظمة العدد اللي حكينا عليها
+
+194
+00:15:10,860 --> 00:15:18,400
+والان نشوف كيف نكتب العدد بنظام العدد الثنائي
+
+195
+00:15:18,400 --> 00:15:23,580
+الحسابات هتلاقوها مرتبة وسهلة أسهل من المقدمةو كيف
+
+196
+00:15:23,580 --> 00:15:29,540
+نحول من ثنائي إلى ثماني و إلى ستاش و العكس اللي هي
+
+197
+00:15:29,540 --> 00:15:33,420
+عملية التحويل احنا هنركز في أنظمة العد اللي عندنا
+
+198
+00:15:33,420 --> 00:15:38,300
+على نظام العد الثنائي نظام العد الثماني نظام العد
+
+199
+00:15:38,300 --> 00:15:41,820
+اللي هو الستاش بالاضافة للنظام العد اللي احنا
+
+200
+00:15:41,820 --> 00:15:44,380
+بنشتغل فيه عادة في المدارس اللي هو نظام العد
+
+201
+00:15:44,380 --> 00:15:53,000
+العشريالان بيناري اكسبرشن اكسبانشن نشوف كيف بدنا
+
+202
+00:15:53,000 --> 00:16:00,780
+ان نعمل اكسبانشن لبيناري اكسبرشن
+
+203
+00:16:00,780 --> 00:16:05,540
+او بيناري اكسبرشن
+
+204
+00:16:07,410 --> 00:16:10,210
+Example نشوف مرحلة الـ Example نفهم إيش نقول what
+
+205
+00:16:10,210 --> 00:16:14,310
+is the decimal expansion of the integer that has
+
+206
+00:16:14,310 --> 00:16:18,770
+اللي هو واحد سفر واحد سفر واحد واحد إلى آخره اتنين
+
+207
+00:16:18,770 --> 00:16:25,250
+as its binary expansion وقوللي أودد قيمة هذا العدد
+
+208
+00:16:25,250 --> 00:16:30,750
+هذا المكتوب بنظام العدد الثنائيمكتوب بنظام العد
+
+209
+00:16:30,750 --> 00:16:34,030
+الثنائي نظام العد الثنائي يا سفر يا واحد في
+
+210
+00:16:34,030 --> 00:16:38,370
+الخانات الآن الخانة الأولى اللى هي عبارة عن واحد
+
+211
+00:16:38,370 --> 00:16:42,350
+فى اتنين أقصى سفر الخانة التانية واحد فى اتنين
+
+212
+00:16:42,350 --> 00:16:47,010
+الخانة التالتة واحد فى اتنين تربيع الخانة الرابعة
+
+213
+00:16:47,010 --> 00:16:53,170
+واحد فى اتنين أقصى أربعةالخانة الخامسة واحد اثنين
+
+214
+00:16:53,170 --> 00:16:57,530
+اقصى اربعة اللي بعيدها سفر في اتنين اقصى خمسة اللي
+
+215
+00:16:57,530 --> 00:17:01,730
+بعيدها واحد في اتنين اقصى ستة وهكذا لما نصل لهدولة
+
+216
+00:17:01,730 --> 00:17:04,110
+لما نصل لاخر خانة اللي هي واحد في اتنين اقصى
+
+217
+00:17:04,110 --> 00:17:07,730
+تمانية عدهم هتلاقيه تسعة واحد اتنين تلاتة اربع
+
+218
+00:17:07,730 --> 00:17:11,870
+خمسة ستة سبعة تمانية تسعةاللي هي تسع خانات أخر
+
+219
+00:17:11,870 --> 00:17:15,270
+واحدة بتكون تمانية لإن أول واحدة بدأت من Zero فلما
+
+220
+00:17:15,270 --> 00:17:18,790
+نبدأ المصطلح من Zero لعين تمانية بيصير تسع أرقام
+
+221
+00:17:18,790 --> 00:17:22,570
+هي التسع أرقام الان لو جيت ضربت هدولة في بعض
+
+222
+00:17:22,570 --> 00:17:26,250
+وجماعتين هيطلع اني تلت مية و واحد و خمسين إذا هيك
+
+223
+00:17:26,250 --> 00:17:30,490
+بنحول من نظام العد الثنائي إلى نظام العد العشرين
+
+224
+00:17:30,900 --> 00:17:35,640
+الان بدنا نحكي على octal and hexadecimal
+
+225
+00:17:35,640 --> 00:17:40,460
+expansions ال octal اللي هو نظام العد الثماني ال
+
+226
+00:17:40,460 --> 00:17:44,020
+hexadecimal expansions اللي هو نظام العد اللي هو
+
+227
+00:17:44,020 --> 00:17:49,000
+اللي أساسه 16 ال octal هو نظام العد اللي أساسه
+
+228
+00:17:49,000 --> 00:17:52,820
+تمانية الان نشوف كيف يقول لي what is the decimal
+
+229
+00:17:52,820 --> 00:17:56,820
+expansion of the number with octal expansion يعني
+
+230
+00:17:56,820 --> 00:18:02,490
+بده يحولناالرقم هذا من نظام العد الثماني إلى نظام
+
+231
+00:18:02,490 --> 00:18:07,170
+العد العشري الحادى نشوف كيف يا جماعة الان سبعة صفر
+
+232
+00:18:07,170 --> 00:18:12,230
+واحد ستة الشغله صارت ليه سهلة ستة في تمانية أقل
+
+233
+00:18:12,230 --> 00:18:19,310
+سفرزاد واحد في تمان يقص واحد زاد سفر في تمان يقص
+
+234
+00:18:19,310 --> 00:18:24,330
+اتنين زاد سبعة في تمان يقص تلاتة ايّن الأرقام
+
+235
+00:18:24,330 --> 00:18:28,970
+نجمحل مع بعض نضرب هذه على القالة و نضرب هذه و نضرب
+
+236
+00:18:28,970 --> 00:18:32,890
+هذه و نجمحل لبعض بيطلع اني عندي تلت تالاف و خمسمية
+
+237
+00:18:32,890 --> 00:18:37,690
+و تمانية و تسعين بنظام العدمين العشرينناخد مثال
+
+238
+00:18:37,690 --> 00:18:41,350
+آخر بقول لي what is the decimal expansion of the
+
+239
+00:18:41,350 --> 00:18:45,150
+number with hexadecimal expansion؟ بده اللي هو هذا
+
+240
+00:18:45,150 --> 00:18:49,030
+الرقم اللي مكتوب بنظام العد الست عشر ال
+
+241
+00:18:49,030 --> 00:18:53,910
+hexadecimal نكتبه على صورة نظام عد مين اللي هو
+
+242
+00:18:53,910 --> 00:18:57,940
+العشر العادي اللي احنا بنعرفه رقمنا العاديخلّينا
+
+243
+00:18:57,940 --> 00:19:04,240
+ناخد الان P التي هي جداش P التي هي 11 احفظوهن A 10
+
+244
+00:19:04,240 --> 00:19:12,080
+B 11 C 12 D 13 E 14 و F 15 طيب P هدا في نظام مين
+
+245
+00:19:12,080 --> 00:19:18,280
+بنكتبهن ال 16 اللي بلزمنا 16 رقم 16 رقم من 0 ل 15
+
+246
+00:19:18,280 --> 00:19:22,960
+اذا و احنا جولنا من 10 ل 15 مش معقول نكتبهن زيك
+
+247
+00:19:22,960 --> 00:19:25,840
+بنصير خربط بيننا و بين الأعداد الأصلية فعشان
+
+248
+00:19:25,840 --> 00:19:33,680
+الكتبناها بالحروفطيب شوفوا الان B اللي هو ف16 أس 0
+
+249
+00:19:33,680 --> 00:19:37,000
+بيه ال 11 يعني هيها لحالها 11 تقعد لحالها قولنا
+
+250
+00:19:37,000 --> 00:19:42,480
+أول خانة في أي نظام عد تقعد منزلتها بقيمتها طيب
+
+251
+00:19:42,480 --> 00:19:53,140
+Zero ف16 أس 1 هيها E ف16 أس 2 A ف16 أس 3 اتنين ف16
+
+252
+00:19:53,140 --> 00:19:59,310
+أس 4ماشي ال A بيحط قيمة العشرة و ال E بتحط قيمة
+
+253
+00:19:59,310 --> 00:20:04,950
+الاربعتاش و بتحسب مع بعضبطلع عندك هذا الرقم الان
+
+254
+00:20:04,950 --> 00:20:09,150
+لو اجينا بس هال ملاحظة الان خلينا نشوفها each
+
+255
+00:20:09,150 --> 00:20:13,310
+hexadecimal digit can be represented using four
+
+256
+00:20:13,310 --> 00:20:19,510
+bits الان ايش ال bit ال bit اللي هي اللي منزلت او
+
+257
+00:20:19,510 --> 00:20:22,390
+اللي هي الاعداد اللي بنستخدمها في نظام العدد في
+
+258
+00:20:22,390 --> 00:20:26,430
+نائب منزلته الواحد سفر واحد سفر واحد واحد هذه كل
+
+259
+00:20:26,430 --> 00:20:31,950
+واحدة منهم بتسميها ايش bitهدولة بنسميهم ايش بيتز
+
+260
+00:20:31,950 --> 00:20:37,170
+الان بقوللي اي hexadecimal digit طبعا ال
+
+261
+00:20:37,170 --> 00:20:41,770
+hexadecimal digit يعني ايش ما هو نظام العد 16 لاحظ
+
+262
+00:20:41,770 --> 00:20:46,610
+نظام العد 16 هو عبارة عن 2 أس 4 ماشي الحال في
+
+263
+00:20:46,610 --> 00:20:51,120
+علاقة بينه وبين نظام العد الثنائي اللي هو 2ماشي
+
+264
+00:20:51,120 --> 00:20:55,400
+هداك اتنين اقصد اربعة في علافة بتروبطها بتقولك ان
+
+265
+00:20:55,400 --> 00:20:59,920
+كل اللي هو hexadecimal digit كل واحد من ال
+
+266
+00:20:59,920 --> 00:21:05,220
+hexadecimal digit بنقدر نكتبه على صورة اللي هو
+
+267
+00:21:05,220 --> 00:21:10,780
+اربعة bits هاي واحد تنين تلاتة اربعة يعني لو اجي
+
+268
+00:21:10,780 --> 00:21:16,720
+تاخد مثال ال E ال E اللي هي E عشرة B احداش C اتناش
+
+269
+00:21:16,720 --> 00:21:21,630
+D تلاتاش E اربعتاش ال E اربعتاش هذهالـ E هي قيمتها
+
+270
+00:21:21,630 --> 00:21:26,110
+14 و للضامن العدل السداسي هيا نكتبها على صورة 0 1
+
+271
+00:21:26,110 --> 00:21:30,890
+1 1 تعرفوا كيف تحسبوها سفر اللي هو سفر واحد اللي
+
+272
+00:21:30,890 --> 00:21:35,530
+هو في اتنين يعني اتنين و هاد في اتنين في اربعة هاي
+
+273
+00:21:35,530 --> 00:21:38,890
+اتنين و اربعة ستة هاد تمانية ستة و تمانية اربعة
+
+274
+00:21:38,890 --> 00:21:41,950
+اتاش اذا هذا صار كله على بعض و ليش اربعة اتاش اللي
+
+275
+00:21:41,950 --> 00:21:47,310
+هو Eإذاً هذا العدد الـ hexadecimal بقدر أكتبه على
+
+276
+00:21:47,310 --> 00:21:52,950
+صورة 01111 الآن بدي أخد الخمسة في نظام العدد الست
+
+277
+00:21:52,950 --> 00:21:58,050
+عشر برضه بقدر أكتبها على صورة أربع أرقام كيف؟ هاي
+
+278
+00:21:58,050 --> 00:22:01,750
+عند أول شي فردي، مدام فردي هذه اللي هنا فردية إذاً
+
+279
+00:22:01,750 --> 00:22:07,370
+أول عدد فيه واحدالان الابضال من الخمسة أربعة أربعة
+
+280
+00:22:07,370 --> 00:22:11,230
+هذا اتنين الأربعة دندا بيصير سفر وهذا هو الأربعة
+
+281
+00:22:11,230 --> 00:22:16,990
+الان هي عندك واحد زائد سفر في اتنين في اتنين بيطلع
+
+282
+00:22:16,990 --> 00:22:21,010
+سفر زائد واحد في أربعة باربعة وهذا سفر اللي هو في
+
+283
+00:22:21,010 --> 00:22:24,190
+اتنين قصة تلاتة اللي هي تمانية بيطلع سفر يعني هذا
+
+284
+00:22:24,190 --> 00:22:29,160
+العدد عبارة عن جداش خمسةولو جيت اخدت اي عدد من
+
+285
+00:22:29,160 --> 00:22:34,820
+الواحد للخمستعاش هتلاقيك بتقدر تكتبه على صورة اربع
+
+286
+00:22:34,820 --> 00:22:40,160
+ارقام اللي هو على صورة pets اربعة pets بنظام العد
+
+287
+00:22:40,160 --> 00:22:45,520
+الثنائيطيب الواحد كيف بدنا نكتبه على صورة الواحد
+
+288
+00:22:45,520 --> 00:22:49,020
+بالنظام العادى 16 واحد قيمته كيف بنا نكتبه هنا
+
+289
+00:22:49,020 --> 00:22:53,800
+واحد سفر سفر سفر و هكذا جربلي في باقى الأعداد من
+
+290
+00:22:53,800 --> 00:22:57,860
+واحد لخمس عشر او من سفر لخمس عشر شوف كيف نكتبها
+
+291
+00:22:57,860 --> 00:23:02,460
+على صورة أربعة bits طيب اللي هان بدنا نعرفها حاجة
+
+292
+00:23:02,460 --> 00:23:06,620
+اسمها bytes ال bytes هي عبارة عن تمانية bit يعني
+
+293
+00:23:06,620 --> 00:23:10,340
+هدولة و كمان كانت جنبهين أربعة بنسميهين byte كل
+
+294
+00:23:10,340 --> 00:23:14,280
+واحدة بنسميها إيش byteإذا الـ byte بتتكون من 8 bit
+
+295
+00:23:14,280 --> 00:23:20,740
+الآن بناء عليه اللي هو أي .. قولنا أي عدد .. أي
+
+296
+00:23:20,740 --> 00:23:23,480
+عدد لحاله اللي هو في ال .. في ال .. في ال
+
+297
+00:23:23,480 --> 00:23:28,840
+hexadecimal بكتبه على صورة 4 الآن عددين في ال ..
+
+298
+00:23:28,840 --> 00:23:34,300
+اللي هو رقم مكون من عددين في ال 16 بقدر أكتبه على
+
+299
+00:23:34,300 --> 00:23:39,950
+صورة byte يعني بقدر أكتب على صورة 4 و 4الخمسة هي
+
+300
+00:23:39,950 --> 00:23:45,470
+أربعته وهي الخمسة هي أربعته والإي هي أربعته إذا
+
+301
+00:23:45,470 --> 00:23:50,750
+عملية كتابة الرقم هذا سهل كيف بكتبها باجي بكتب هذا
+
+302
+00:23:50,750 --> 00:23:57,400
+بالاربعة bitsوهذا اربع بيت استبعوته و بحطهم جان
+
+303
+00:23:57,400 --> 00:24:02,920
+بعض بطلع عنده اللي هو الرقم هذا اللي بالنظام العد
+
+304
+00:24:02,920 --> 00:24:09,440
+16 بساوي اللي هو الرقم اللي اسمه byte بنظام العد
+
+305
+00:24:09,440 --> 00:24:16,260
+الثنائي طيب نيجي الآن ناخد اللي هو اللي هي
+
+306
+00:24:20,110 --> 00:24:24,930
+نحكي الآن عن الـ Base Conversion اللي هي عملية
+
+307
+00:24:24,930 --> 00:24:29,670
+التحويل من و إلى انتبهوا الآن لعملية التحويل عشان
+
+308
+00:24:29,670 --> 00:24:34,610
+ما تتغلبوش عشان الآن الحسابات تصير سهلة خالص في
+
+309
+00:24:34,610 --> 00:24:39,750
+عملية التحويل إلى نظام العدل اللي بدناها الان لو
+
+310
+00:24:39,750 --> 00:24:45,230
+جالنا find the octal expansion of اللي هي 1245 في
+
+311
+00:24:45,230 --> 00:24:49,440
+نظام العدل العشري هذا مكتوبفي نظام العدل عشري و
+
+312
+00:24:49,440 --> 00:24:54,400
+بدي حوله لل اوكتل كنا .. كنا من نظام ال اوكتل
+
+313
+00:24:54,400 --> 00:24:57,820
+للعشري او من ال binary للعشري او من اي اشي للعشري
+
+314
+00:24:57,820 --> 00:25:02,020
+سهل و قولنا كيف نحوله الان العكس .. العكس شوف كيف
+
+315
+00:25:02,020 --> 00:25:07,900
+هنلاجيه اسهل الان بمسك العدد اللي هو الف .. اللي
+
+316
+00:25:07,900 --> 00:25:11,240
+هو الف و متين و خمس و أربعين آسف فهذا مش مت .. الف
+
+317
+00:25:11,240 --> 00:25:13,640
+و متين و خمس و عشرين .. الف و متين و خمس و أربعين
+
+318
+00:25:14,230 --> 00:25:18,870
+أحولها لنظام العدمين الـ octal الثماني باجسمها على
+
+319
+00:25:18,870 --> 00:25:24,450
+تمانية بطلع عنده تمانية في 155 زي 5 هذا اللي هو
+
+320
+00:25:24,450 --> 00:25:29,570
+ناتج القسمة وهذا ال remainder انتبهوا اللي غامق
+
+321
+00:25:29,570 --> 00:25:33,360
+ناتج القسمة و اللي بالازرق هو ال remainderالان
+
+322
+00:25:33,360 --> 00:25:39,420
+نعيد العملية نقسم الـ 155 على 8 كمان مرة نقسم مين
+
+323
+00:25:39,420 --> 00:25:45,520
+اللي هو ناتج القسم اللي نتج في الأول 155 طلع 8 في
+
+324
+00:25:45,520 --> 00:25:50,180
+19 زائد remainder جديد اسمه تلاتةالان هذا الـ 19
+
+325
+00:25:50,180 --> 00:25:55,440
+اللي هو ناتج القسمة تبع الـ 155 على 8 بعمل نفس
+
+326
+00:25:55,440 --> 00:26:00,740
+الاشي هنا بجسم الـ 19 على 8 بتيجي 8 زائد 2 في 3
+
+327
+00:26:00,740 --> 00:26:05,960
+هذا ناتج القسمة برضه بعمله نفس الاشي باجي بقول 2
+
+328
+00:26:05,960 --> 00:26:10,160
+بساوة 8 بجسمه على 8 طبعا مافيش 8 مافيش فيه ولا 8
+
+329
+00:26:10,160 --> 00:26:15,310
+فبنكتبه على صورة 8 في 0 وال remainder هو 2يوم ما
+
+330
+00:26:15,310 --> 00:26:20,630
+نصل لهذه الخطوة بقى جاف يعني يوم ما نصل ان ناتج
+
+331
+00:26:20,630 --> 00:26:27,810
+القسمة طلع اللي هو سفر بقى جاف ماشي الحال طيب الان
+
+332
+00:26:27,810 --> 00:26:31,490
+ايش هذا ايش هو اللي عملته هذا انا تعالى نشوف مع
+
+333
+00:26:31,490 --> 00:26:36,810
+بعض الان ألف و متين و خمس و أربعين بساوي هذا زائد
+
+334
+00:26:36,810 --> 00:26:40,830
+هذا شايفينه هيد نجلتيه بقى الان الان المية و خمس و
+
+335
+00:26:40,830 --> 00:26:45,070
+خمسين هيهابدي أزيل الـ 155 و أعوض مكانها قيمة
+
+336
+00:26:45,070 --> 00:26:49,750
+تليادي زائدة دي أحوال تهيأني صار هاي الرقم وعكت
+
+337
+00:26:49,750 --> 00:26:54,010
+ضربهم في بعض بدلالة التمانية لإنه أنا بدور على
+
+338
+00:26:54,010 --> 00:26:57,690
+النظام العد الثماني الآن هذي بيصير تمانية ضرب
+
+339
+00:26:57,690 --> 00:27:03,490
+تمانية يعني تمانية تربيع في 19 هي الأولىو8×3 هي 2
+
+340
+00:27:03,490 --> 00:27:09,750
+زائد الخمسة ويساوي الان بدي أشيل ال 19 و أضع قيمة
+
+341
+00:27:09,750 --> 00:27:15,350
+هي ال 19 8×2 زائد 3 شيلت و أضعت قيمة ها هان اتيت
+
+342
+00:27:15,350 --> 00:27:20,530
+حسبتها صار 8 تربيع اللي هو مضروبة في 8 بيصير 8
+
+343
+00:27:20,530 --> 00:27:24,610
+تكعيبفى اتنين زائد تمانية تربيع برضه مضربة فى مين
+
+344
+00:27:24,610 --> 00:27:28,930
+فى تلاتة زائد تمانية فى تلاتة هيها زائد خمسة هيها
+
+345
+00:27:28,930 --> 00:27:33,390
+الآن هذا الناتج اللى طلع عندى تلاحظ من وين جبته من
+
+346
+00:27:33,390 --> 00:27:37,170
+اللى هو اللى عملته فى القسم هنا وفى الآخر عوضت فيه
+
+347
+00:27:37,530 --> 00:27:42,210
+إذا كتبت الرقم اللي عندي 1245 اللي تحته خط هذا
+
+348
+00:27:42,210 --> 00:27:47,110
+كتبته بالصورة هذه فصار هذا اللي هو خانة الأحد إذا
+
+349
+00:27:47,110 --> 00:27:51,710
+صح التعبير بنظام العد الثماني وهذه خانة اللي هي
+
+350
+00:27:51,710 --> 00:27:56,090
+اللي بنسميها العشرات اللي هي التمانيات يعني وهذه
+
+351
+00:27:56,090 --> 00:28:00,050
+خانة التمانيات تربيع وهذه خانة التمانيات تكعيد
+
+352
+00:28:00,050 --> 00:28:04,230
+يعني بيصير عندي العدد هذا بنظام العد الثنائي هو
+
+353
+00:28:04,230 --> 00:28:11,430
+عبارة عن هي الخمسةهى التلاتة هى التلاتة هى التنين
+
+354
+00:28:11,430 --> 00:28:16,410
+إذا صار عند العدد الأصلي ال 1245 نظام العد العشري
+
+355
+00:28:16,410 --> 00:28:20,390
+هى قيمته هتقولوا ليه و أحنا كل مرة بدنا نقعد نعمل
+
+356
+00:28:20,390 --> 00:28:24,410
+هيك و نعوض و مش عارف إيش و الله بتلخ منها هذا الآن
+
+357
+00:28:24,410 --> 00:28:29,370
+أنا شرعتلكم العملية شغل المكان كمانى ايه شغل
+
+358
+00:28:29,370 --> 00:28:33,690
+المكان الجسمة بتصور سهل هي اتجسمت و طلعت اللي هو
+
+359
+00:28:33,690 --> 00:28:39,340
+متبقى قسمة or remainderإيش هذا الرقم بيكون؟ هو
+
+360
+00:28:39,340 --> 00:28:44,380
+عبارة عن الـ remainders شوف الـ remainders انسى
+
+361
+00:28:44,380 --> 00:28:47,460
+هذه .. هذول الخطوات انساها إيه جاف العند الهن؟ شو
+
+362
+00:28:47,460 --> 00:28:51,160
+جفنا العند الهن؟ احنا بيصير أول remainder ال .. ال
+
+363
+00:28:51,160 --> 00:28:55,820
+.. ال .. ال .. ال .. وين جفنا؟ العند ال .. جسمنا
+
+364
+00:28:55,820 --> 00:29:01,100
+العند الهن مظبوط؟ هذه جسمنا العند الهن و هذه جسمنا
+
+365
+00:29:01,100 --> 00:29:03,520
+العند الهن و هذه العند الهن لما وصلنا لعند هذه أخر
+
+366
+00:29:03,520 --> 00:29:07,560
+واحدةماشي الحال .. باجي .. لو وين وصلنا هيها ..
+
+367
+00:29:07,560 --> 00:29:11,800
+لها باجي باخد أول .. أخر واحدة وصلتي لها هي اتنين
+
+368
+00:29:11,800 --> 00:29:15,620
+ال remainder اتنين الأزرق هيهم هي أول واحد ال
+
+369
+00:29:15,620 --> 00:29:18,200
+remainder اللي بعده التلاتة هيها باخد ال
+
+370
+00:29:18,200 --> 00:29:21,120
+remainders ال remainder اللي بعده تلاتة هيها ال
+
+371
+00:29:21,120 --> 00:29:25,060
+remainder اللي بعده هدون هي خمسةماشي الحال طيب
+
+372
+00:29:25,060 --> 00:29:27,800
+اللي .. اللي .. اللي .. اللي .. اللي شوية مضايق من
+
+373
+00:29:27,800 --> 00:29:31,540
+هذا يتبع معايا السؤال اللي بعده عشان يفهم بالظبط
+
+374
+00:29:31,540 --> 00:29:34,060
+اشي اللي بقول اللي عم بقول find the octal
+
+375
+00:29:34,060 --> 00:29:38,600
+expansion of هذا الرقم هذا بالنظام العد العشري بده
+
+376
+00:29:38,600 --> 00:29:44,160
+حوله لنظام العد الثماني الموضوع سهل يا جماعة هذا
+
+377
+00:29:44,160 --> 00:29:48,060
+لمين بده حوله لنظام العد الثماني إذا القسم على
+
+378
+00:29:48,060 --> 00:29:52,740
+تمانية باج الرقم الأصلي باج اسمه على تمانيةبظل
+
+379
+00:29:52,740 --> 00:29:57,860
+المتبقى واحد ناتج القسم هيوم ناتج القسم بقسمه على
+
+380
+00:29:57,860 --> 00:30:02,740
+تمانية هنا قسمت على تمانية طالع 192 والمتبقى 7
+
+381
+00:30:02,740 --> 00:30:09,100
+الان باجي بقسم ال 192 على تمانية بطلع ناتج القسم
+
+382
+00:30:09,100 --> 00:30:15,560
+24 المتبقى 0 ال 24 بقسمها على تمانيةبطلع الناتج
+
+383
+00:30:15,560 --> 00:30:19,660
+تلاتة و المتبقى سفر عندنا خلصنا مدام اللي هو ناتج
+
+384
+00:30:19,660 --> 00:30:22,580
+القسمة طلع أصغر من تمانية بكون وصلت للخطوة الأخيرة
+
+385
+00:30:22,580 --> 00:30:26,200
+ايش الخطوة الأخيرة اللي هو ناتج القسمة هذا تلاتة
+
+386
+00:30:26,200 --> 00:30:31,060
+بساوية تمانية ضرب سفر لأنه أصغر من تمانية زائد
+
+387
+00:30:31,060 --> 00:30:36,080
+تلاتة هنا بقف لأنه طلع عند ناتج القسمة جداش سفر
+
+388
+00:30:36,080 --> 00:30:39,520
+يعني تلاتة بساوية تمانية في سفر زائد تلاتة الآن
+
+389
+00:30:39,520 --> 00:30:44,490
+ايش نظام العد الثماني على طول زي ما قلناأخ .. أخ
+
+390
+00:30:44,490 --> 00:30:47,550
+.. و أنا وصلت تلاتة هو reminders هي reminders
+
+391
+00:30:47,550 --> 00:30:54,390
+تلاتة هيو اللي جابله سفر هيو كتبته هيو ال reminder
+
+392
+00:30:54,390 --> 00:30:58,350
+اللي جابله سفر هيو ال reminder اللي جابله سبعة هيو
+
+393
+00:30:58,350 --> 00:31:02,390
+ال reminder الأول هيو واحد اللي بده يبدأ بالعكس
+
+394
+00:31:02,390 --> 00:31:06,240
+ويحضر اللي بده بالعكس ويجي من هنا واحدومن هنا سبعة
+
+395
+00:31:06,240 --> 00:31:10,020
+اللي بعيدها ومن هنا سفر ومن هنا سفر ومن هنا سفر
+
+396
+00:31:10,020 --> 00:31:14,040
+اذا ما هي العملية قسمها وتاخد في الاخر الـ
+
+397
+00:31:14,040 --> 00:31:17,320
+remainders وترتبها بالترتيب اللي موجود بتطلع عندك
+
+398
+00:31:17,320 --> 00:31:21,380
+هذا نظام العد الثماني طيب الآن خلينا .. بدناش
+
+399
+00:31:21,380 --> 00:31:26,460
+ثماني بدنا ستاشه ال gate عمال لنا حاضر مثال لبعده
+
+400
+00:31:26,460 --> 00:31:32,130
+find the hexadecimal expansion of الرقم هذاماذا
+
+401
+00:31:32,130 --> 00:31:35,390
+يعني hexadecimal expansion؟ يعني بدنا نظام العد
+
+402
+00:31:35,390 --> 00:31:40,310
+الثماني لهذا الرقم ايش بسوي؟ بمسك الرقم اللي جوا و
+
+403
+00:31:40,310 --> 00:31:43,930
+بجسمه على اللي هو اللي بدي نظام عده مين نظام عده؟
+
+404
+00:31:43,930 --> 00:31:50,130
+ال 16 باجي بجسم ال 11070 ع 16 بطلع الناتج هذا
+
+405
+00:31:50,130 --> 00:31:53,990
+بالقالة يا جماعة بطلع الناتج هذا و بزيد 14 الآن
+
+406
+00:31:53,990 --> 00:31:59,890
+الناتج هذا بجسمه على 16 كمان مرة بطلع الناتج 43 و
+
+407
+00:31:59,890 --> 00:32:05,810
+بزيد 3ناتج القسمة برضه بجسمها 16 بطلع الناتج 2 و
+
+408
+00:32:05,810 --> 00:32:10,210
+بزيد 11 لما يطلع العدد أقل من 16 أقل من اللي بشتغل
+
+409
+00:32:10,210 --> 00:32:13,850
+عليه نظام العد برتاح بقول أخر خطوة عندي خلصتها
+
+410
+00:32:13,850 --> 00:32:19,100
+اللي هي 2 إيش هيساوي 16 في 0 زائد 2لأن ال maximum
+
+411
+00:32:19,100 --> 00:32:23,540
+على 16 مافيش هذا أصلا 16 فبطلع 16 ف0 زي 2 هنا بدف
+
+412
+00:32:23,540 --> 00:32:27,720
+بيصير عندي الآن أيش نظام العد اللي .. أيش .. أيش
+
+413
+00:32:27,720 --> 00:32:32,100
+اللي .. اللي .. اللي هو ال .. العدد بنظام العد ال
+
+414
+00:32:32,100 --> 00:32:36,740
+16 هي .. ال reminders .. ال reminders هي 2 هي أول
+
+415
+00:32:36,740 --> 00:32:45,740
+واحدة 11 هي اللي هو ال B تلاتة هي التلاتة 14 اللي
+
+416
+00:32:45,740 --> 00:32:50,980
+هي ال E إذا سهل الموضوعما هي الا عبارة عن اخد من
+
+417
+00:32:50,980 --> 00:32:55,660
+اللي هي reminders واصفها جانب بعض بالترتيب من
+
+418
+00:32:55,660 --> 00:32:59,620
+الشمال لليمين عندما انتهيت بيكون هذا نظام العدمين
+
+419
+00:32:59,620 --> 00:33:03,240
+ال 16 ويكون خارب طوق في اللي هو تبدأ من اليمين او
+
+420
+00:33:03,240 --> 00:33:08,640
+من الشمال من هنا من عند اخر ما وصلت بتبدأ من اللي
+
+421
+00:33:08,640 --> 00:33:15,300
+هو الشمال و بتتجه باتجاه اليمين طيب نجي لان بعدهم
+
+422
+00:33:15,650 --> 00:33:18,810
+سؤال آخر عشان نكبّت الفكرة find the binary
+
+423
+00:33:18,810 --> 00:33:23,030
+expansion of 120 اللي هو مكتوب بالعشرة إذا الأن
+
+424
+00:33:23,030 --> 00:33:27,170
+بدي أحول اللي هو من نظام عد عادي عشري إلى نظام
+
+425
+00:33:27,170 --> 00:33:31,790
+العد ثنائي برضه بنفس الطريقة بقسم ال 120 على 2
+
+426
+00:33:31,790 --> 00:33:36,570
+بتطلع 120 بالساوية 2 في 60 زي 0 الآن هي ناتج
+
+427
+00:33:36,570 --> 00:33:41,770
+القسمة 60 بقسمها على 2 بيصير 60 في 30 زي 10الان
+
+428
+00:33:41,770 --> 00:33:45,270
+طلع عندى تلاتين برضه تطول روحك في التلاتين نجسمها
+
+429
+00:33:45,270 --> 00:33:49,570
+على التنين برضه التنين مين هو نظام العدل اللى بدى
+
+430
+00:33:49,570 --> 00:33:54,410
+اشتغل عليه الان بيساوى 15 فى 2 طلع 15 الناتج و 0
+
+431
+00:33:54,410 --> 00:33:59,110
+remainder طبعا 15 مدام 15 اللى هو ناتج برضه و ده
+
+432
+00:33:59,110 --> 00:34:02,910
+جسمه 15 بيساوى 2 فى 7 زائد 1 يعني السابعة الان هى
+
+433
+00:34:02,910 --> 00:34:07,070
+الناتج السابعة بقى جسمها 2 برضه بيساوى 2 فى 3 زائد
+
+434
+00:34:07,070 --> 00:34:11,520
+1الان التلاتة برضه باقسمها بساوي تلاتة في اتنين
+
+435
+00:34:11,520 --> 00:34:15,200
+بساوي اتنين في واحد زائد واحد تلاتة باقسمها عمين
+
+436
+00:34:15,200 --> 00:34:18,000
+القسمة كلها ع اتنين ناتج القسمة ع اتنين و
+
+437
+00:34:18,000 --> 00:34:20,820
+remainder ناتج القسمة ع اتنين و remainder لما في
+
+438
+00:34:20,820 --> 00:34:25,660
+الاخر بصر ناتج القسمة واحد اللي هو اصغر من اتنين
+
+439
+00:34:25,660 --> 00:34:29,900
+على طول برتاح بقول اخر عنده وصلت الاخر خطوة الان
+
+440
+00:34:29,900 --> 00:34:34,870
+الواحد ايش بساوي اتنين في سفر زائد واحدالان الـ120
+
+441
+00:34:34,870 --> 00:34:39,590
+بنظام العد العشري هتساوي بنظام العد ثنائي ميالي
+
+442
+00:34:39,590 --> 00:34:46,630
+هاي واحد من اللي هو اليمين التاني واحد والتالت
+
+443
+00:34:46,630 --> 00:34:52,870
+واحد و الرابع واحد و الخامس صفر و السادس صفر و
+
+444
+00:34:52,870 --> 00:34:58,520
+السابع صفر هاي الان بنظام العد الثمانيالثنائي إذا
+
+445
+00:34:58,520 --> 00:35:03,400
+هذه هي طريقة تحويل الآن من نظام العد العشري إلى
+
+446
+00:35:03,400 --> 00:35:07,180
+أنظمة العد المختلفة وفي الأول احنا أخدنا اللي هو
+
+447
+00:35:07,180 --> 00:35:10,680
+العكس من التحويل من نظام العد الثنائي أو الثلاثي
+
+448
+00:35:10,680 --> 00:35:13,860
+أو الربيع أو الخماسي أو اللي هو أو السداسة أو
+
+449
+00:35:13,860 --> 00:35:19,620
+الثماني أو الست عشر للعد العشري أو هنا تبقوا ان
+
+450
+00:35:19,620 --> 00:35:28,570
+احنا خلصنا الاتجاهيننعود الآن لآخر دُزُق نحكي
+
+451
+00:35:28,570 --> 00:35:32,470
+فيه Conversion between binary, octal and
+
+452
+00:35:32,470 --> 00:35:38,770
+hexadecimal expansion نحن مركزين على تلت أنواع من
+
+453
+00:35:38,770 --> 00:35:43,250
+العدد العشري اللي نشتغل فيهالان العد الثنائي
+
+454
+00:35:43,250 --> 00:35:48,190
+والثماني ال octal و ال hexadecimal اللي هو الست
+
+455
+00:35:48,190 --> 00:35:53,570
+عشر حولنا من ال decimal هدول كلهم التلاتة و حولنا
+
+456
+00:35:53,570 --> 00:35:58,750
+بعدين من التلاتة اللي بنحكي عنها لمن لعشرين ضل
+
+457
+00:35:58,750 --> 00:36:03,950
+انحولهم بين بعض الان بدنا نشوف كيف نحول ال octal
+
+458
+00:36:04,660 --> 00:36:11,520
+وانحوّل الـ hexa إلى ash إلى binary ونشوف كيف اللي
+
+459
+00:36:11,520 --> 00:36:15,300
+أنا بقول find the octal and hexadecimal expansion
+
+460
+00:36:15,300 --> 00:36:20,660
+of هذه الرقم مكتوب بالاش مش بالتمانية هذه اتنين
+
+461
+00:36:20,660 --> 00:36:25,570
+آسف هذه اتنين من نظام العد الثنائيand the binary
+
+462
+00:36:25,570 --> 00:36:34,410
+expansion of 7,6,5,8,d,16 يعني بدنا نحول اشي من
+
+463
+00:36:34,410 --> 00:36:40,190
+الثنائي الى الثماني والست عشر ونحول اللي هو من
+
+464
+00:36:40,190 --> 00:36:44,650
+الثماني والست عشر الى اللي هو الثنائي خلينا اول
+
+465
+00:36:44,650 --> 00:36:48,990
+اشي نيجي هي الرقم اللي هو اللي هو هذا اللي هو
+
+466
+00:36:48,990 --> 00:36:56,240
+مكتوب بالنظام العدمين الثنائيالان لما بدحول لنظام
+
+467
+00:36:56,240 --> 00:37:02,360
+العد الثماني شوفوا يا جماعة الثنائي اتنين الثماني
+
+468
+00:37:02,360 --> 00:37:09,640
+اتنين او ثلاثة الان في الثماني باجي مادام ثماني
+
+469
+00:37:09,640 --> 00:37:17,280
+يعني اتنين او ثلاثة بجسم خنات الثنائيإلى تلت خنات
+
+470
+00:37:17,280 --> 00:37:21,140
+تلت خنات بعدد الأُس تبع التمانية التمانية هو عضار
+
+471
+00:37:21,140 --> 00:37:23,940
+عن اتنين أُس ثلاثة في علاقة بينهم مش مجالنا
+
+472
+00:37:23,940 --> 00:37:30,340
+لاستنتاج العلاقة أما كيف انحول من الثنائي للثماني
+
+473
+00:37:30,340 --> 00:37:36,280
+باجي بجسمهم الآن ببدأ عندي لأن سفر سفر واحد اخر
+
+474
+00:37:36,280 --> 00:37:42,070
+واحدة هيالان واحد واحد واحد هيها الان اللي بعدها
+
+475
+00:37:42,070 --> 00:37:46,790
+سفر واحد سفر واحد واحد واحد واحد واحد سفر من وين
+
+476
+00:37:46,790 --> 00:37:51,810
+جبت السفر الأخير هذا إذا كان هدول عددهم بيقبل جسم
+
+477
+00:37:51,810 --> 00:37:55,390
+على تلاتة خلاص بيسير اللي حالين بيطلع اللي حالين
+
+478
+00:37:55,390 --> 00:38:00,390
+إذا ناجس العدد بحط ايه سفر لإن العدد على السفر على
+
+479
+00:38:00,390 --> 00:38:04,790
+الشمال العدد بأثرشإذاً اللي عملته إيش يا جماعة
+
+480
+00:38:04,790 --> 00:38:09,050
+بيجيد قولت هاي أول مجموعة هايها التلاتة الأولانيات
+
+481
+00:38:09,050 --> 00:38:13,310
+بعدين هي التلاتة التانيات بعدين هي التلاتة
+
+482
+00:38:13,310 --> 00:38:17,330
+التالتات وهي التلاتة الرابعات والتلاتة الأخرات
+
+483
+00:38:17,330 --> 00:38:21,410
+اللي هي واحد واحد وإيش سفر هو بعد بالعكس الآن
+
+484
+00:38:21,410 --> 00:38:26,050
+كاتبلك سفر واحد سفر اللي هي سفر واحد واحد بعدين
+
+485
+00:38:26,050 --> 00:38:31,830
+واحد واحد واحد بعدين سفر واحد سفر ومكمل لعندهاإيه
+
+486
+00:38:31,830 --> 00:38:37,210
+دا اللي هي هذه جسمها إلى تلت خنات تلت خلات تعني
+
+487
+00:38:37,210 --> 00:38:43,050
+تلاتة bytes أو تلاتة bits ماشي كل تلت بتات مع بعض
+
+488
+00:38:43,050 --> 00:38:47,470
+الان لو خس علينا بتات من الشمال بضيف على الشمال
+
+489
+00:38:47,470 --> 00:38:51,090
+لإنه بضيف على الشمال أصفار لإن الأصفار اللي على
+
+490
+00:38:51,090 --> 00:38:54,650
+الشمال لا تؤثر في العدد بظل العدد زي ما هو زي ما
+
+491
+00:38:54,650 --> 00:38:59,100
+انتوا عارفين في العادي برضه بنفعهاالان هانا خسلنا
+
+492
+00:38:59,100 --> 00:39:03,780
+عدد فكتبنا صفر واحد واحد هذا ال bit التلك بتات
+
+493
+00:39:03,780 --> 00:39:07,660
+الأولى التلك بتات التانية هي التلك بتات التالتة
+
+494
+00:39:07,660 --> 00:39:12,960
+الاخرى خليهم بنفس الترتيب دير بالك الان جداش قيمته
+
+495
+00:39:12,960 --> 00:39:18,860
+هذا العدد هذا اتنين وهذا اللي هو واحد في منزلته
+
+496
+00:39:18,860 --> 00:39:23,520
+واحد هذا واحد في اتنين اذا واحد و اتنين تلاتة اذا
+
+497
+00:39:23,520 --> 00:39:27,840
+اول واحد قيمته تلاتة نيجي لالي بعدههذا اللي هو
+
+498
+00:39:27,840 --> 00:39:31,620
+واحد منزلته الأولى هذا المطمئنع اللي عدت تونية
+
+499
+00:39:31,620 --> 00:39:37,040
+جاعت بحسبهم واحد في اتنين قص واحد زائد اتنين قص
+
+500
+00:39:37,040 --> 00:39:42,460
+اتنين يعني واحد واتنين واربعة سبعة طيب نيجي للي
+
+501
+00:39:42,460 --> 00:39:48,940
+بعده سفر زائد اتنين زائد سفر اتنين ايه اللي بعده
+
+502
+00:39:49,330 --> 00:39:55,290
+هذا حسبناه اللي هو واحد واتنين واربعة سبعة هي جلة
+
+503
+00:39:55,290 --> 00:40:00,150
+اللي بعد والاخير صفر وصفر واربعة لأنها دخلت الصفر
+
+504
+00:40:00,150 --> 00:40:03,850
+اللي هو في اتنين وصفر دخلت الصفر في اتنين واس واحد
+
+505
+00:40:03,850 --> 00:40:07,990
+وهذا دخلت الواحد في اتنين واس اتنين يعني اربعة اذا
+
+506
+00:40:07,990 --> 00:40:12,310
+هاي الاعداد هذولة بشيل هذولة كل تلاتة و بحط مكانها
+
+507
+00:40:12,310 --> 00:40:18,540
+قيمتهابصير عندى هذا العدد بساوى اللى هو الآن بدأنا
+
+508
+00:40:18,540 --> 00:40:21,820
+من وين من الشمال هدولة من الشمال تلاتة اللى بعدها
+
+509
+00:40:21,820 --> 00:40:26,320
+سبعة اللى بعدها اتنين سبعة اربعة تلاتة سبعة اتنين
+
+510
+00:40:26,320 --> 00:40:31,680
+سبعة اربعة تمانية اذا هذا صار بساوى هذا باش بال
+
+511
+00:40:31,680 --> 00:40:36,440
+اللى هو من نظام العد الثماني نظام العد الثماني
+
+512
+00:40:36,440 --> 00:40:43,970
+قلنا اتنين أس تلاتة كل تلت بتاتبرقم من الثماني
+
+513
+00:40:43,970 --> 00:40:49,910
+الان في الـ hexadecimal كل أربع بالتات لأن الست
+
+514
+00:40:49,910 --> 00:40:55,430
+عبارة عن اتنين قصة أربعة فبصير عندي كل أربع بالتات
+
+515
+00:40:55,990 --> 00:41:01,990
+أب جداش اب واحد من الـ hexadecimal بناء عليه أنا
+
+516
+00:41:01,990 --> 00:41:07,550
+لو أعطاني هاي هذا الرقم في نظام العد الثنائي بدي
+
+517
+00:41:07,550 --> 00:41:11,350
+يعني أحوله للـ hexadecimal عشان أحوله للـ
+
+518
+00:41:11,350 --> 00:41:15,410
+hexadecimal بدي أجسمه لأربعات هاي الأربعة الأولى
+
+519
+00:41:15,410 --> 00:41:19,150
+وهي الأربعة الثانية وهي الأربعة الثالثة وهنا
+
+520
+00:41:19,150 --> 00:41:25,200
+الأربعة الأخيرة لها بيصير 11 و11 و0 و0نحسب الاربعة
+
+521
+00:41:25,200 --> 00:41:29,800
+هذه الاربعة هذه وعلى طول بدك تكتب العدد هذا سفر
+
+522
+00:41:29,800 --> 00:41:36,160
+وهذا سفر وهذا ايش اتنين plus اتنين يعني اربعة وهنا
+
+523
+00:41:36,160 --> 00:41:36,640
+تمانية
+
+524
+00:41:42,860 --> 00:41:47,080
+عشان تحفظوا على السريع هذا في اتنين هذا في واحد في
+
+525
+00:41:47,080 --> 00:41:52,280
+اتنين في اربعة في تمانية اذا سفر سفر اربعة و
+
+526
+00:41:52,280 --> 00:41:55,320
+تمانية اتناش اربعة تمانية اتناش اتناش اللي هو مين
+
+527
+00:41:55,320 --> 00:42:02,980
+هى ال C كتبته لان واحد و اتنين تلاتة و سفر تلاتة و
+
+528
+00:42:02,980 --> 00:42:08,190
+تمانية احداش اللي هو ال Bخلصنا هذا شفا و بنسير سفر
+
+529
+00:42:08,190 --> 00:42:12,630
+اتنين و اربعة ستة و تمانية اربعة اتاش هذا صار
+
+530
+00:42:12,630 --> 00:42:16,910
+اربعة اتاش اللي هو ال E لان هذا واحد و اتنين تلاتة
+
+531
+00:42:16,910 --> 00:42:20,170
+و الباقي الصفار يعني تلاتة ايه هذا اذا صار الان
+
+532
+00:42:20,170 --> 00:42:27,970
+التحويل من hexa من من تناء لhexa سهل اربعات و بنحط
+
+533
+00:42:27,970 --> 00:42:32,630
+مكان كل اربعة قيمتهافي التمانية نظام العد الثماني
+
+534
+00:42:32,630 --> 00:42:36,210
+تلتات وكل تلتة بنحط إيش قمت هذه التلتة الأول هذه
+
+535
+00:42:36,210 --> 00:42:38,390
+التلتة التانية هذه التلتة التالتة التلتة الرابعة
+
+536
+00:42:38,390 --> 00:42:41,490
+تلتة الخامسة وقلنا إذا خس علينا تلتات من الآخر
+
+537
+00:42:41,490 --> 00:42:44,850
+بنحط هناش أصفر لإنه بأثر ناش على العدل إذا هذا
+
+538
+00:42:44,850 --> 00:42:50,310
+عملية التحويل من الثنائي للثماني أو إلى الستة عشر
+
+539
+00:42:50,310 --> 00:42:56,090
+سهل وهيني جميعا عنهالان بدنا نحوّل العكس بدنا
+
+540
+00:42:56,090 --> 00:43:01,350
+نحوّل سبعة ستة خمسة للثماني برضه بدحوّلها ليش into
+
+541
+00:43:01,350 --> 00:43:06,510
+binary notation الان convert هذا ل binary notation
+
+542
+00:43:06,510 --> 00:43:11,810
+يعني بدحولها من نظام العد الثماني الى نظام العد من
+
+543
+00:43:11,810 --> 00:43:20,110
+الثنائي و قمر sale خالص الخمسة ايش بتساوي ثنائي
+
+544
+00:43:20,110 --> 00:43:21,550
+الخمسة
+
+545
+00:43:24,690 --> 00:43:28,730
+الخمسة عبارة عن واحد
+
+546
+00:43:38,990 --> 00:43:43,290
+الستة زوجي عبارة عن 2 زي 4
+
+547
+00:44:02,620 --> 00:44:08,140
+أسف هاي السبعة السبعة ايش قمتها واحد و اتنين و
+
+548
+00:44:08,140 --> 00:44:11,440
+اربعة واحد و اتنين تلاتة و اربعة سبعة عملتها ده
+
+549
+00:44:11,440 --> 00:44:15,620
+بالليل هاي حطيت مكان مين السبعة يعني باختصار اكيد
+
+550
+00:44:15,620 --> 00:44:20,740
+فانتوا الخمسة بحط قمتها في الثنائي و بعرف وجودها و
+
+551
+00:44:20,740 --> 00:44:25,700
+الستة بحط قمتها في الثنائي و السبعة بحط قمتها في
+
+552
+00:44:25,700 --> 00:44:31,870
+ايش في الثنائيبتطلع عندي اللي هي القيمة اللي أنا
+
+553
+00:44:31,870 --> 00:44:39,890
+بديها الان أكيد كلكم قال ال 16 انحولها لثنائي بنفس
+
+554
+00:44:39,890 --> 00:44:45,050
+الأسلوب يعني حوللي هذه للثنائي بتقوللي ال D بحط
+
+555
+00:44:45,050 --> 00:44:50,890
+قيمتها أربعة بالتالت ال 16 أربعة بالتالت كل واحدة
+
+556
+00:44:50,890 --> 00:44:54,730
+باربعةالـ D لها أربعة والـ 8 لها أربعة والـ A لها
+
+557
+00:44:54,730 --> 00:45:00,150
+أربعة الـ D اللي هي جداش الـ D الـ D اللي هي A B C
+
+558
+00:45:00,150 --> 00:45:04,970
+D يعني تلت عاش تلت عاش تلت عاش فردي مزام تلت عاش
+
+559
+00:45:04,970 --> 00:45:12,410
+فردي إذا أول خانة إيش بتطلع واحد واحد و سفر أو
+
+560
+00:45:12,410 --> 00:45:17,530
+أربعة خمسة وتمانية تلت عاش فعلا هيإذاً الـ D بتحط
+
+561
+00:45:17,530 --> 00:45:22,170
+قيمتها هي .. هي الآن التمانية .. التمانية زوجي
+
+562
+00:45:22,170 --> 00:45:25,950
+اللي هي اتنين وستلاتة يعني الأولى أنها صفر صفر صفر
+
+563
+00:45:25,950 --> 00:45:30,930
+و هي Aش التامنة لإنها تتنظر في واحد و تتنظر في
+
+564
+00:45:30,930 --> 00:45:33,950
+اتنين و تتنظر في أربعة و تتنظر في تمانية أكيد
+
+565
+00:45:33,950 --> 00:45:37,190
+التمانية اللي هي بس واحد و اللي قدامها تلات أصفار
+
+566
+00:45:37,190 --> 00:45:41,410
+إذاً هي التمانية الآن ال A اللي هي العشرةاللي هي
+
+567
+00:45:41,410 --> 00:45:44,270
+اتنين و تمانية يعني هي اتنين و هي تمانية و هدول
+
+568
+00:45:44,270 --> 00:45:51,230
+أسفار كتبناها هنا إذا نحولنا من اللي هو ستاشر اللي
+
+569
+00:45:51,230 --> 00:46:00,070
+هو hexa إلى إيش إلى binaryكيف كل دي و اي و تمانية
+
+570
+00:46:00,070 --> 00:46:05,930
+و اي باربع بتات بقيمهن اللي قلناهن هيك بإحنا بنكون
+
+571
+00:46:05,930 --> 00:46:13,410
+أنهينا المحاضرة اللي هي الـ five أو هي عند ال
+
+572
+00:46:13,410 --> 00:46:18,150
+homework المطلوب لهذه المحاضرة وإلى لقاء آخر
+
+573
+00:46:18,150 --> 00:46:21,090
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c2b88de5653f36be31793638be66a8f869697dc1
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/3DujSeOVlEM_raw.srt
@@ -0,0 +1,2292 @@
+1
+00:00:00,000 --> 00:00:06,280
+بسم الله الرحمن الرحيم هذه المحاضرة الخامسة في
+
+2
+00:00:06,280 --> 00:00:11,920
+مساق رياضية مفاصلة لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:12,500 --> 00:00:19,280
+كلية الـ IT قسم الحوسبة المتنقلة اليوم سنحكي عن
+
+4
+00:00:19,280 --> 00:00:22,440
+سيكشن الثاني في شفتر أربعة اللي هو أربعة اتنين
+
+5
+00:00:22,440 --> 00:00:26,460
+اللي هو الـ integer representations أو اللي هو
+
+6
+00:00:26,460 --> 00:00:31,740
+اللي بنسمي اللي هي كيف نعبر عن الأعداد أو التعبير
+
+7
+00:00:31,740 --> 00:00:36,220
+عن الأعداد أو تمثيل الأعداد بأنظمة العد المختلفة
+
+8
+00:00:36,630 --> 00:00:41,930
+الان عشان ندخل لأنظمة العد خلنا في الأول نتذكر ايش
+
+9
+00:00:41,930 --> 00:00:44,530
+اللي حكيناه او بعض اللي حكيناها المرة الماضية في
+
+10
+00:00:44,530 --> 00:00:47,670
+المحاضرة الرابعة في ال congrance relation قولنا
+
+11
+00:00:47,670 --> 00:00:54,600
+ايه تطابق P مدله عشرة؟الـ A لو قسمت على عشرة و الـ
+
+12
+00:00:54,600 --> 00:00:59,160
+B لو قسمت على عشرة بيكون له نفس الـ Remainder و
+
+13
+00:00:59,160 --> 00:01:03,560
+الـ Remainder في هذه الحالة من سفر لعين تسعة أكبر
+
+14
+00:01:03,560 --> 00:01:06,480
+أو سوى سفر و أصغر strictly من عشرة يعني الـ
+
+15
+00:01:06,480 --> 00:01:09,680
+Remainder هيكون يا سفر يا واحد يا اتنين يا تلاتة
+
+16
+00:01:09,680 --> 00:01:12,660
+يا أربعة يا خمسة يا ستة يا سبعة يا تمانية يا تسعة
+
+17
+00:01:12,660 --> 00:01:18,480
+هدولة ال Remainders هم اللي احنا بنستخدمهم في نظام
+
+18
+00:01:18,480 --> 00:01:24,120
+العد العشريالان modulo عشرة يعني مقياس عشرة هذا
+
+19
+00:01:24,120 --> 00:01:29,910
+اللي هو اللي بده يعمله نظام العد العشرينأحنا كيف
+
+20
+00:01:29,910 --> 00:01:33,870
+كنا اللي هو نكتب اللي هو ال .. ال .. ال .. ال ..
+
+21
+00:01:33,870 --> 00:01:41,390
+في نظام العدل عشري 256 مثلا بتساوي اللي هو قداش
+
+22
+00:01:41,390 --> 00:01:45,710
+كمية فيها 200 و قداش فيها عشرات اللي هو خمسة و
+
+23
+00:01:45,710 --> 00:01:50,310
+قداش فيها أحد ستة فكنا نيجي نكتب اللي هو الست رقم
+
+24
+00:01:50,310 --> 00:01:54,450
+الأحد هيه ستة في عشر أقل سفر الخمسة في رقم الأقل
+
+25
+00:01:54,450 --> 00:01:58,110
+اللي هي العشرات خمسة في عشر أقل واحدوالتنين في
+
+26
+00:01:58,110 --> 00:02:02,850
+عشرة تربيع اللي هو رقم مين او خانة المنئات يعني
+
+27
+00:02:02,850 --> 00:02:07,370
+هذه الخانة اللي بيكون فيها العشرة أس سفر هذه
+
+28
+00:02:07,370 --> 00:02:11,190
+الخانة اللي بيكون فيها العشرة أس اتنى اقص واحد
+
+29
+00:02:11,190 --> 00:02:16,170
+وهذه الخانة الثالثة اللي العشرة اللي اتنين فيها
+
+30
+00:02:16,170 --> 00:02:21,460
+بيكون ضرب عشرة أس اتنينالان نجي لمثال اخر هذا احنا
+
+31
+00:02:21,460 --> 00:02:24,960
+النظام العد اللي احنا بنشتغل فيه عادة و بنتعلمه في
+
+32
+00:02:24,960 --> 00:02:29,520
+المدارس هو نظام العد العشرين الان اللي هي يعني
+
+33
+00:02:29,520 --> 00:02:33,700
+منزلة العدد هنا اللي هو ستة اللي هي منزلة العدد
+
+34
+00:02:33,700 --> 00:02:38,500
+هنا خمسين هذا منزلة العدد متين الان نجي لمثال اخر
+
+35
+00:02:38,500 --> 00:02:45,140
+ايه تطابق بيه مدل خمسة مدل خمسة اللي هي يعني لما
+
+36
+00:02:45,140 --> 00:02:49,440
+نقسم هذا على الخمسة تطلع remainderو هذا لما نقسمه
+
+37
+00:02:49,440 --> 00:02:52,380
+على خمسة بيطلع remainder عشان يكون المتطابقين لازم
+
+38
+00:02:52,380 --> 00:02:54,900
+ال remainder هان و ال remainder هيكون إيه شمالين
+
+39
+00:02:54,900 --> 00:02:58,400
+متساويين زي ما قلنا المرة الماضية ال remainder
+
+40
+00:02:58,400 --> 00:03:02,500
+عادة اللي هو عبارة عن سفر و واحد و اتنين و تلاتة و
+
+41
+00:03:02,500 --> 00:03:07,520
+أربعة لإن اللي هو الخمسة بيصير ال remainder له سفر
+
+42
+00:03:07,520 --> 00:03:12,780
+و هكذا يعني any integer is congruent modulo خمسة
+
+43
+00:03:12,780 --> 00:03:15,940
+to one of the following remaindersيعني أي عدد في
+
+44
+00:03:15,940 --> 00:03:20,460
+الدنيا هيكون بطابق واحد من هدولة ليش؟ لأن هذا لما
+
+45
+00:03:20,460 --> 00:03:24,140
+يكون ال remainder له سفر بيصير طابق السفر لما يكون
+
+46
+00:03:24,140 --> 00:03:26,720
+ال remainder له مع الخمسة واحد بطابق اللي هو
+
+47
+00:03:26,720 --> 00:03:30,700
+الواحد لو كان اللي هو ال remainder له اتنين بطابق
+
+48
+00:03:30,700 --> 00:03:34,320
+التنين لو كان ال remainder تلاتة بطابق التلاتةو لو
+
+49
+00:03:34,320 --> 00:03:37,540
+ال remainder لما نقسم ال a على خمسة طالع أربعة
+
+50
+00:03:37,540 --> 00:03:40,920
+بكون بطابق الأربعة إذا أي حدد في الدنيا ال
+
+51
+00:03:40,920 --> 00:03:43,640
+remainder اللي هو يا سفر يا واحد يا اتنين يا تلاتي
+
+52
+00:03:43,640 --> 00:03:48,560
+اربعة يعني بمعنى آخر ال a هيطابق واحد من هذولة
+
+53
+00:03:48,560 --> 00:03:53,120
+هذولة الآن من سفر لأربعة زي ما كان من سفر لعشرة هم
+
+54
+00:03:53,120 --> 00:03:57,460
+اللي هو ال digits تبعات اللي هي نظام العد العشري
+
+55
+00:03:57,460 --> 00:04:00,860
+هيكون في نظام العد الخماسي اللي هي ال digits سفر
+
+56
+00:04:00,860 --> 00:04:05,370
+وواحد واتنين وتلاتة واربعةيعني الآن لو بدنا الـ 56
+
+57
+00:04:05,370 --> 00:04:10,130
+نكتبها على صورة اللي هو نظام العد اللي هو الخمسة،
+
+58
+00:04:10,130 --> 00:04:13,990
+ده مش عشرة، هذه خمسة، هي الـ 56 في العشرة، بنكتبها
+
+59
+00:04:13,990 --> 00:04:18,910
+على صورة إيش؟ نظام عد عشرة، خمسين، هذه الآن الـ 56
+
+60
+00:04:18,910 --> 00:04:22,110
+في نظام العد العشري، اللي هي إحنا عادة إنت في نظام
+
+61
+00:04:22,110 --> 00:04:25,650
+العد العشري، بنكتبش لا عشرة ولا خمسة ولا كده ولا
+
+62
+00:04:25,650 --> 00:04:30,010
+كده، على طول بنكتب 56، لأنه متعارف عليه بين إنه
+
+63
+00:04:30,010 --> 00:04:35,190
+نقص نظام العد العشري،بدي احول ال 56 الى نظام العد
+
+64
+00:04:35,190 --> 00:04:44,870
+الخماسي شوف كيف الان ال 56 عندى اللى هي ال 56 فيها
+
+65
+00:04:44,870 --> 00:04:49,690
+الان خمسة في خمسة في خمسة و عشرين يعني خمسين و بضل
+
+66
+00:04:49,690 --> 00:04:54,990
+ستة الان الخمسين هذه اللى هي عبارة عن اتنين في
+
+67
+00:04:54,990 --> 00:04:57,910
+خمسة و عشرين يعني خمسة تربيع في اتنين بطلع خمسين
+
+68
+00:04:57,910 --> 00:05:01,710
+زائدالان بعد شوية هنقولكم طريقة الكتابة بس خليني
+
+69
+00:05:01,710 --> 00:05:05,610
+الان بس ناخد المثال عشان نشوف ايش اللي بنجزله في
+
+70
+00:05:05,610 --> 00:05:10,610
+نظام العد الخماسي زائد واحد في مين في خمسة أس واحد
+
+71
+00:05:10,610 --> 00:05:15,350
+زائد واحد في خمسة أس صفر اقدرنا نكتب ال 56 على هذه
+
+72
+00:05:15,350 --> 00:05:19,250
+الصورة يعني بدلنا نكتب العشرة بنكتب مين ونستخدم
+
+73
+00:05:19,250 --> 00:05:24,050
+بدلها الخمسة و بنسميه نظام العد الخماسيلاحظوا الآن
+
+74
+00:05:24,050 --> 00:05:30,150
+خانت اللي هي الأحد بالنسبة لهذه واحد خانت اللي هي
+
+75
+00:05:30,150 --> 00:05:33,050
+اللي كنا نسميها العشرات اللي هي اللي مضروبة في
+
+76
+00:05:33,050 --> 00:05:37,030
+عشرة هنا هنا بتكون مضروبة في خمسة بدلها خمسة أس
+
+77
+00:05:37,030 --> 00:05:37,870
+واحد واحد
+
+78
+00:05:40,870 --> 00:05:45,290
+الخانة الأولى مضروبة في خمسة أو السفر والخانة
+
+79
+00:05:45,290 --> 00:05:48,730
+الثانية مضروبة في خمسة أو السواعد والتانية مضروبة
+
+80
+00:05:48,730 --> 00:05:53,890
+في خمسة اياش اوس اتنين الان ندخل للنظام الات وطابق
+
+81
+00:05:53,890 --> 00:05:57,950
+ال بي ومدول اتنين اللى يقودنا للنظام العد الثنائي
+
+82
+00:05:58,270 --> 00:06:02,470
+الآن لما نقسم الـ A على الـ 2 يكون المتبقى يا سفر
+
+83
+00:06:02,470 --> 00:06:07,050
+يا إيش يا واحد بناء عليه هيكون عناصر الـ D أو الـ
+
+84
+00:06:07,050 --> 00:06:11,830
+digits تبعات نظام العد الثناني يا ثنائي يا سفر يا
+
+85
+00:06:11,830 --> 00:06:16,150
+واحد لو بدنا نيجي الآن الـ 56 نكتبها على صورة اللي
+
+86
+00:06:16,150 --> 00:06:22,290
+هو نظام عد A شمالهالـ 56 طبعاً اللي هي النظام لعدد
+
+87
+00:06:22,290 --> 00:06:27,670
+ثنائي معناته 2 أس 1 2 أس 1 2 أس 2 2 أس 3 2 أس 4 2
+
+88
+00:06:27,670 --> 00:06:32,410
+أس 5 إلى آخرين لو أجينا للـ 56 كيف بنكتبها على
+
+89
+00:06:32,410 --> 00:06:37,510
+صورة اللي هو نظام لعدد الثنائي الآن الـ 56 اللي هو
+
+90
+00:06:37,510 --> 00:06:44,620
+عندي 2 أس 5 32لو قلنا 2 أُس 6 بيصير 64 بيصير أكتر
+
+91
+00:06:44,620 --> 00:06:47,480
+منها دي إذا أنا ماقدرش استخدامها إذا بدي أخد 2 أُس
+
+92
+00:06:47,480 --> 00:06:55,740
+5 2 أُس 5 هي 32 في واحد بيصير 32 32 من 56 بيظل
+
+93
+00:06:55,740 --> 00:07:00,100
+اللي هو جداش 24 لذا دل فيه أرقامإذا بدنا ناخد
+
+94
+00:07:00,100 --> 00:07:06,020
+الخانة اللي بعدها 2 أس 4 2 أس 4 أيش 16 16 زائد 32
+
+95
+00:07:06,020 --> 00:07:14,340
+48 48 من 56 زاد 8 8 لحسن حظنا طلعت 2 أس 3 فعشان
+
+96
+00:07:14,340 --> 00:07:19,720
+كتبنا 1 في 2 أس 3 فطلعت هذا على بعض كلها 56 الآن
+
+97
+00:07:19,720 --> 00:07:25,920
+الخانات اللي بعدها لازم نكملهالأن هذه بتصبح خانة
+
+98
+00:07:25,920 --> 00:07:34,540
+0×2×2، 0×2×1، 0×2×0، ليش؟ على أساس أننا الآن نكتب
+
+99
+00:07:34,540 --> 00:07:45,240
+الرقم التالي الخانة 2×0،0، خانة 2×1،0، خانة 2×2،0،
+
+100
+00:07:45,240 --> 00:07:52,920
+خانة 2×3،1،خالت 2 أقصد 4 هو 1 خالت 2 أقصد 5 هو 1
+
+101
+00:07:52,920 --> 00:07:58,060
+فهذا الآن كتبنا العدد على صورة عدد في صورة نظام
+
+102
+00:07:58,060 --> 00:08:01,820
+العدد الثاني هذه 2 يا شباب و بنات مش اللي هو خمسة
+
+103
+00:08:01,820 --> 00:08:06,900
+اتنين هذه اه هذا نظام هذا العدد اللي هو واحد واحد
+
+104
+00:08:06,900 --> 00:08:12,620
+واحد تلت اصفاراللي هو بيمثل الرقم 56 هذا بنظام
+
+105
+00:08:12,620 --> 00:08:19,800
+العد الثنائي طيب الان نيجي لمثال آخر لسه احنا
+
+106
+00:08:19,800 --> 00:08:23,620
+بنشتغل شغل بدائي بعد شوية بيصير لعنا عملية
+
+107
+00:08:23,620 --> 00:08:28,710
+الحسابات أسن ان شاء اللهالان 965 في نظام العد
+
+108
+00:08:28,710 --> 00:08:32,530
+العشري هذه الخانة الأولى اللى هي في عشرة أقص سفر
+
+109
+00:08:32,530 --> 00:08:35,430
+هي اللى خمسة يعني عشرة أقص سفر يعني واحد يا جماعة
+
+110
+00:08:35,430 --> 00:08:38,750
+عشان هيك مكتبهاش عشرة أقص سفر مع قصود واحد وخمسة
+
+111
+00:08:38,750 --> 00:08:41,890
+أقص سفر واحد واتنين أقص سفر واحد عشان هيك الخانة
+
+112
+00:08:41,890 --> 00:08:47,030
+الأولى دايما قيمتها في كل أنظمة العد زي ما هي طيب
+
+113
+00:08:47,030 --> 00:08:50,990
+الان ستة اللى هي الخانة التانية اللى عبارة عن ستة
+
+114
+00:08:50,990 --> 00:08:54,690
+في عشرة أقص واحدتسعة اللي هي في الخانة التالتة
+
+115
+00:08:54,690 --> 00:08:59,430
+اللي هي تسعة في عشر عقل ساش اتنين هذه الآن قيمتها
+
+116
+00:08:59,430 --> 00:09:03,950
+اللي هي قيمة اللي هي اللي هي تسعة مية خمسة ستين
+
+117
+00:09:03,950 --> 00:09:07,390
+بالنظام العد العشر اللي احنا أصلا ما بنعرفه طيب
+
+118
+00:09:07,390 --> 00:09:10,810
+الان لو بدنا نيجي نحسب اتنين اربعة خمسة في نظام
+
+119
+00:09:10,810 --> 00:09:15,230
+العد الثماني كيف بنحسبها يا جماعة الخانة الأولى
+
+120
+00:09:15,230 --> 00:09:20,290
+اللي هي خمسة في تمانية قص سفر يعني خمسة زائد اربعة
+
+121
+00:09:20,290 --> 00:09:26,040
+في تمانية قص واحدالخانة الثانية الآن التالتة اللي
+
+122
+00:09:26,040 --> 00:09:29,980
+هي 2 في 8 أقصى 2 بالظبط زي ما كنا نعمل في اللي هو
+
+123
+00:09:29,980 --> 00:09:35,660
+النظام العد العشري زمان الان هي قيمته هذا بنحسبها
+
+124
+00:09:35,660 --> 00:09:40,960
+فبتطلع عندي هذه القيمة هي هذه الان كيف بدنا نحسبها
+
+125
+00:09:40,960 --> 00:09:47,480
+بنظام العد اللي هو يتمثل بنظام العد اللي هي العشري
+
+126
+00:09:47,480 --> 00:09:53,380
+هذه الرقم لو ضربناها في بعض هيطلع لنا 165في نظام
+
+127
+00:09:53,380 --> 00:09:59,120
+العد العشري إذا قيمة الـ 245 في الثماني هي 165 في
+
+128
+00:09:59,120 --> 00:10:02,920
+العشري وهينا حولناها من نظام العد الثماني اللي
+
+129
+00:10:02,920 --> 00:10:07,900
+مكتوب فيه هيه وضلعنا الرقم اللي طلع هذا الرقم اللي
+
+130
+00:10:07,900 --> 00:10:12,080
+طلع هذا اللي مجموعه عادي هو أعدادنا اللي احنا
+
+131
+00:10:12,080 --> 00:10:18,500
+بنتعامل معها اللي هي 165الان هذا نظام العد الثماني
+
+132
+00:10:18,500 --> 00:10:23,460
+لان فيه hexadecimal expansion اللي هو ايه ال
+
+133
+00:10:23,460 --> 00:10:27,860
+hexadecimal expansion هو نظام العد الست عشر هدول
+
+134
+00:10:27,860 --> 00:10:33,360
+النظام اللي بتعد بتهمكم انتوا في الحاسوبلأن ضام
+
+135
+00:10:33,360 --> 00:10:37,000
+العدل اللي هو في ال 16 ايش هيكون اللي هي الأرقام
+
+136
+00:10:37,000 --> 00:10:41,280
+اللي بنستخدمها ال digits اللي فيه سفر و واحد و
+
+137
+00:10:41,280 --> 00:10:45,640
+اتنين و تلاتة و اربع و خمسة و ستة و سبعة و تمانية
+
+138
+00:10:45,640 --> 00:10:48,420
+و تسعة و عشر و أحداشر لما أصل لخمسة عشر لأن
+
+139
+00:10:48,420 --> 00:10:53,120
+السبتاشر برجع السفرلكن احنا لو ده نيجي نكتب خمس
+
+140
+00:10:53,120 --> 00:10:57,480
+عشر واربع عشر بنصير نخربط اذا بدنا الرموز بعد
+
+141
+00:10:57,480 --> 00:11:01,540
+التسعة يعني بدنا نستخدم في الست عشر سفر واحد
+
+142
+00:11:01,540 --> 00:11:04,060
+واتنين وتلاتة واربعة وخمسة وستة وسبعة وتمانية
+
+143
+00:11:04,060 --> 00:11:09,480
+وتسعة بعد هيك بدنا نستخدم حروف أبجدية مين هي الـA
+
+144
+00:11:09,480 --> 00:11:12,800
+عشرة الـB عشرة الـB عشرة الـB عشرة الـC عشرة الـC
+
+145
+00:11:12,800 --> 00:11:14,780
+عشرة الـC عشرة الـC عشرة الـD عشرة الـD عشرة الـD
+
+146
+00:11:14,780 --> 00:11:15,900
+عشرة الـD عشرة الـD عشرة الـD عشرة الـD عشرة الـD
+
+147
+00:11:15,900 --> 00:11:21,790
+عشرة الـE عشرة الـE عشرةالان a,b,c,d,e و ال F 15
+
+148
+00:11:21,790 --> 00:11:25,690
+ماشي الحال و 16 طبعا ترجع السفر اذا هنستبدل
+
+149
+00:11:25,690 --> 00:11:35,870
+الاعداد من 10 ل 15 ب a,b,c,d,e,f على الترتيبهذا
+
+150
+00:11:35,870 --> 00:11:41,930
+الان عدد مكتوب بنظام العدد الست عشر كيف احسبه
+
+151
+00:11:41,930 --> 00:11:47,030
+بنسبة
+
+152
+00:11:47,030 --> 00:11:49,590
+للست عشر؟ اول حاجة
+
+153
+00:11:52,070 --> 00:11:56,090
+اللي هو جدّاش بيبني عرفه اللي هو بعد الـ A مباشرة
+
+154
+00:11:56,090 --> 00:12:00,870
+الـ A عشرة و الـ B 11 هي 11 في 16 أش سفر نكتبهش زي
+
+155
+00:12:00,870 --> 00:12:03,990
+ما احنا انتفجنا إذا هذا قيمته هو نفسه في أي ذاك
+
+156
+00:12:03,990 --> 00:12:09,770
+اللي هو B 11 زائد الآن Zero في 16 أس واحد هي Zero
+
+157
+00:12:09,770 --> 00:12:14,920
+في 16 زائدالتانى اللى هو مين E اللى هى اش قيمته
+
+158
+00:12:14,920 --> 00:12:19,380
+اربعة عشر فست عشر اش منزلته الخانة التالتة هذه
+
+159
+00:12:19,380 --> 00:12:24,200
+تربيع لان البعده ال A قيمته عشرة مضروب في الخانة
+
+160
+00:12:24,200 --> 00:12:28,820
+الرابعة اللى 16 أس 3زائد آخر واحد اللي هو في
+
+161
+00:12:28,820 --> 00:12:32,820
+الخانة الخامسة هي واحد، تنين، تلاتة، أربعة، خمسة،
+
+162
+00:12:32,820 --> 00:12:37,400
+اتنين في الخانة الخامسة ستة عشر أس أربعة يعني
+
+163
+00:12:37,400 --> 00:12:42,660
+الخانة الخامسة ماقص واحد إذا هذا الآن بنحسبه
+
+164
+00:12:42,660 --> 00:12:46,560
+بالحسبة العادية على آلة الحاسبة بطلعلنا الرقم هذا
+
+165
+00:12:46,560 --> 00:12:50,040
+هذا الرقم هو الرقم بالنظام العشري عشان هي كانت مش
+
+166
+00:12:50,040 --> 00:12:52,620
+كاتبله أنا عشرة عشان احنا متفقين مع بعض اللي
+
+167
+00:12:52,620 --> 00:12:56,760
+ماكنتبلهوشعشرة او اتنين او تلاتة يعني بنقصد بنظام
+
+168
+00:12:56,760 --> 00:13:00,820
+العد من العشري هي حولنا نظام العد الست عشري العد
+
+169
+00:13:00,820 --> 00:13:05,140
+من عد ست عشري الى نظام العد العشري نيجي الان
+
+170
+00:13:05,140 --> 00:13:09,420
+للنظرية اللى بتقولنا بتشرّعلنا لشغلنا ايش النظرية
+
+171
+00:13:09,420 --> 00:13:15,420
+بتقولbe an integer greater than 1 يعني بي عبارة عن
+
+172
+00:13:15,420 --> 00:13:20,200
+عدد أكبر من واحد then لو كان عندي n is a positive
+
+173
+00:13:20,200 --> 00:13:24,100
+integer يعني n كان عندي أي positive integer بقدر
+
+174
+00:13:24,100 --> 00:13:29,100
+أكتبره على صورة n بتساوي a k b k زائد a k minus
+
+175
+00:13:29,100 --> 00:13:33,160
+واحد b k minus واحد زائد لما أصل a واحد b زائد a
+
+176
+00:13:33,160 --> 00:13:36,000
+naught a naught هي ده في الواقع a naught ضرب b
+
+177
+00:13:36,000 --> 00:13:42,380
+والسفر الآن هذه بت هي اللي بتشرعلنا نظام العديعني
+
+178
+00:13:42,380 --> 00:13:46,760
+لو كان عندى الآن هذه الـ B هي اللى بنقصد فيها مرة
+
+179
+00:13:46,760 --> 00:13:50,540
+اتنين مرة خمسة مرة عشرة مرة كده كده الاخرى و ال A
+
+180
+00:13:50,540 --> 00:13:56,460
+note A1 A2 AK-1 لAK هي اللى بتمثل الاعداد اللى
+
+181
+00:13:56,460 --> 00:14:01,580
+بدنا نكتبها عندنا اللى هنا مثلا الخمسة او ستة واحد
+
+182
+00:14:01,980 --> 00:14:07,360
+والـ B هنا هي العشرة أو هنا مثلا اتنين A E A O
+
+183
+00:14:07,360 --> 00:14:12,280
+Zero A Zero B هذه هي اللي هي A نوت A واحد اللي عند
+
+184
+00:14:12,280 --> 00:14:16,580
+A كي في هذه الحالة الـ K اللي هي بتساوي عبارة عن
+
+185
+00:14:16,580 --> 00:14:21,410
+اللي هيالعدد اللى هو خمس طعش ده هو ستة عشر ناقص
+
+186
+00:14:21,410 --> 00:14:27,170
+واحد هدولة بيكونن هن من سفر لعند خمس طعش في حالة
+
+187
+00:14:27,170 --> 00:14:32,310
+الست عشر و هدولة اللى جوا هن الأعداد من سفر لعند
+
+188
+00:14:32,310 --> 00:14:38,340
+ست عشروالان ال B هو رقم 16 اللى هى بيمثلى اللى هو
+
+189
+00:14:38,340 --> 00:14:43,920
+نظام العد ال 16 واحد بيطبق على الأثناء هذا بيصير
+
+190
+00:14:43,920 --> 00:14:48,200
+ال B2 و هدولة بيصير العددين بس اللى هو ال 0 و ال 1
+
+191
+00:14:48,200 --> 00:14:55,400
+اذا هذه اللى هى بتشرعلى عملية اللى هو أنظمة العد
+
+192
+00:14:59,440 --> 00:15:06,980
+الان نكمل representations of integers نشوف عملية
+
+193
+00:15:06,980 --> 00:15:10,860
+تمثيل العدد بنحط أنظمة العدد اللي حكينا عليها
+
+194
+00:15:10,860 --> 00:15:18,400
+والان نشوف كيف نكتب العدد بنظام العدد الثنائي
+
+195
+00:15:18,400 --> 00:15:23,580
+الحسابات هتلاقوها مرتبة وسهلة أسهل من المقدمةو كيف
+
+196
+00:15:23,580 --> 00:15:29,540
+نحول من ثنائي إلى ثماني و إلى ستاش و العكس اللي هي
+
+197
+00:15:29,540 --> 00:15:33,420
+عملية التحويل احنا هنركز في أنظمة العد اللي عندنا
+
+198
+00:15:33,420 --> 00:15:38,300
+على نظام العد الثنائي نظام العد الثماني نظام العد
+
+199
+00:15:38,300 --> 00:15:41,820
+اللي هو الستاش بالاضافة للنظام العد اللي احنا
+
+200
+00:15:41,820 --> 00:15:44,380
+بنشتغل فيه عادة في المدارس اللي هو نظام العد
+
+201
+00:15:44,380 --> 00:15:53,000
+العشريالان بيناري اكسبرشن اكسبانشن نشوف كيف بدنا
+
+202
+00:15:53,000 --> 00:16:00,780
+ان نعمل اكسبانشن لبيناري اكسبرشن
+
+203
+00:16:00,780 --> 00:16:05,540
+او بيناري اكسبرشن
+
+204
+00:16:07,410 --> 00:16:10,210
+Example نشوف مرحلة الـ Example نفهم إيش نقول what
+
+205
+00:16:10,210 --> 00:16:14,310
+is the decimal expansion of the integer that has
+
+206
+00:16:14,310 --> 00:16:18,770
+اللي هو واحد سفر واحد سفر واحد واحد إلى آخره اتنين
+
+207
+00:16:18,770 --> 00:16:25,250
+as its binary expansion وقوللي أودد قيمة هذا العدد
+
+208
+00:16:25,250 --> 00:16:30,750
+هذا المكتوب بنظام العدد الثنائيمكتوب بنظام العد
+
+209
+00:16:30,750 --> 00:16:34,030
+الثنائي نظام العد الثنائي يا سفر يا واحد في
+
+210
+00:16:34,030 --> 00:16:38,370
+الخانات الآن الخانة الأولى اللى هي عبارة عن واحد
+
+211
+00:16:38,370 --> 00:16:42,350
+فى اتنين أقصى سفر الخانة التانية واحد فى اتنين
+
+212
+00:16:42,350 --> 00:16:47,010
+الخانة التالتة واحد فى اتنين تربيع الخانة الرابعة
+
+213
+00:16:47,010 --> 00:16:53,170
+واحد فى اتنين أقصى أربعةالخانة الخامسة واحد اثنين
+
+214
+00:16:53,170 --> 00:16:57,530
+اقصى اربعة اللي بعيدها سفر في اتنين اقصى خمسة اللي
+
+215
+00:16:57,530 --> 00:17:01,730
+بعيدها واحد في اتنين اقصى ستة وهكذا لما نصل لهدولة
+
+216
+00:17:01,730 --> 00:17:04,110
+لما نصل لاخر خانة اللي هي واحد في اتنين اقصى
+
+217
+00:17:04,110 --> 00:17:07,730
+تمانية عدهم هتلاقيه تسعة واحد اتنين تلاتة اربع
+
+218
+00:17:07,730 --> 00:17:11,870
+خمسة ستة سبعة تمانية تسعةاللي هي تسع خانات أخر
+
+219
+00:17:11,870 --> 00:17:15,270
+واحدة بتكون تمانية لإن أول واحدة بدأت من Zero فلما
+
+220
+00:17:15,270 --> 00:17:18,790
+نبدأ المصطلح من Zero لعين تمانية بيصير تسع أرقام
+
+221
+00:17:18,790 --> 00:17:22,570
+هي التسع أرقام الان لو جيت ضربت هدولة في بعض
+
+222
+00:17:22,570 --> 00:17:26,250
+وجماعتين هيطلع اني تلت مية و واحد و خمسين إذا هيك
+
+223
+00:17:26,250 --> 00:17:30,490
+بنحول من نظام العد الثنائي إلى نظام العد العشرين
+
+224
+00:17:30,900 --> 00:17:35,640
+الان بدنا نحكي على octal and hexadecimal
+
+225
+00:17:35,640 --> 00:17:40,460
+expansions ال octal اللي هو نظام العد الثماني ال
+
+226
+00:17:40,460 --> 00:17:44,020
+hexadecimal expansions اللي هو نظام العد اللي هو
+
+227
+00:17:44,020 --> 00:17:49,000
+اللي أساسه 16 ال octal هو نظام العد اللي أساسه
+
+228
+00:17:49,000 --> 00:17:52,820
+تمانية الان نشوف كيف يقول لي what is the decimal
+
+229
+00:17:52,820 --> 00:17:56,820
+expansion of the number with octal expansion يعني
+
+230
+00:17:56,820 --> 00:18:02,490
+بده يحولناالرقم هذا من نظام العد الثماني إلى نظام
+
+231
+00:18:02,490 --> 00:18:07,170
+العد العشري الحادى نشوف كيف يا جماعة الان سبعة صفر
+
+232
+00:18:07,170 --> 00:18:12,230
+واحد ستة الشغله صارت ليه سهلة ستة في تمانية أقل
+
+233
+00:18:12,230 --> 00:18:19,310
+سفرزاد واحد في تمان يقص واحد زاد سفر في تمان يقص
+
+234
+00:18:19,310 --> 00:18:24,330
+اتنين زاد سبعة في تمان يقص تلاتة ايّن الأرقام
+
+235
+00:18:24,330 --> 00:18:28,970
+نجمحل مع بعض نضرب هذه على القالة و نضرب هذه و نضرب
+
+236
+00:18:28,970 --> 00:18:32,890
+هذه و نجمحل لبعض بيطلع اني عندي تلت تالاف و خمسمية
+
+237
+00:18:32,890 --> 00:18:37,690
+و تمانية و تسعين بنظام العدمين العشرينناخد مثال
+
+238
+00:18:37,690 --> 00:18:41,350
+آخر بقول لي what is the decimal expansion of the
+
+239
+00:18:41,350 --> 00:18:45,150
+number with hexadecimal expansion؟ بده اللي هو هذا
+
+240
+00:18:45,150 --> 00:18:49,030
+الرقم اللي مكتوب بنظام العد الست عشر ال
+
+241
+00:18:49,030 --> 00:18:53,910
+hexadecimal نكتبه على صورة نظام عد مين اللي هو
+
+242
+00:18:53,910 --> 00:18:57,940
+العشر العادي اللي احنا بنعرفه رقمنا العاديخلّينا
+
+243
+00:18:57,940 --> 00:19:04,240
+ناخد الان P التي هي جداش P التي هي 11 احفظوهن A 10
+
+244
+00:19:04,240 --> 00:19:12,080
+B 11 C 12 D 13 E 14 و F 15 طيب P هدا في نظام مين
+
+245
+00:19:12,080 --> 00:19:18,280
+بنكتبهن ال 16 اللي بلزمنا 16 رقم 16 رقم من 0 ل 15
+
+246
+00:19:18,280 --> 00:19:22,960
+اذا و احنا جولنا من 10 ل 15 مش معقول نكتبهن زيك
+
+247
+00:19:22,960 --> 00:19:25,840
+بنصير خربط بيننا و بين الأعداد الأصلية فعشان
+
+248
+00:19:25,840 --> 00:19:33,680
+الكتبناها بالحروفطيب شوفوا الان B اللي هو ف16 أس 0
+
+249
+00:19:33,680 --> 00:19:37,000
+بيه ال 11 يعني هيها لحالها 11 تقعد لحالها قولنا
+
+250
+00:19:37,000 --> 00:19:42,480
+أول خانة في أي نظام عد تقعد منزلتها بقيمتها طيب
+
+251
+00:19:42,480 --> 00:19:53,140
+Zero ف16 أس 1 هيها E ف16 أس 2 A ف16 أس 3 اتنين ف16
+
+252
+00:19:53,140 --> 00:19:59,310
+أس 4ماشي ال A بيحط قيمة العشرة و ال E بتحط قيمة
+
+253
+00:19:59,310 --> 00:20:04,950
+الاربعتاش و بتحسب مع بعضبطلع عندك هذا الرقم الان
+
+254
+00:20:04,950 --> 00:20:09,150
+لو اجينا بس هال ملاحظة الان خلينا نشوفها each
+
+255
+00:20:09,150 --> 00:20:13,310
+hexadecimal digit can be represented using four
+
+256
+00:20:13,310 --> 00:20:19,510
+bits الان ايش ال bit ال bit اللي هي اللي منزلت او
+
+257
+00:20:19,510 --> 00:20:22,390
+اللي هي الاعداد اللي بنستخدمها في نظام العدد في
+
+258
+00:20:22,390 --> 00:20:26,430
+نائب منزلته الواحد سفر واحد سفر واحد واحد هذه كل
+
+259
+00:20:26,430 --> 00:20:31,950
+واحدة منهم بتسميها ايش bitهدولة بنسميهم ايش بيتز
+
+260
+00:20:31,950 --> 00:20:37,170
+الان بقوللي اي hexadecimal digit طبعا ال
+
+261
+00:20:37,170 --> 00:20:41,770
+hexadecimal digit يعني ايش ما هو نظام العد 16 لاحظ
+
+262
+00:20:41,770 --> 00:20:46,610
+نظام العد 16 هو عبارة عن 2 أس 4 ماشي الحال في
+
+263
+00:20:46,610 --> 00:20:51,120
+علاقة بينه وبين نظام العد الثنائي اللي هو 2ماشي
+
+264
+00:20:51,120 --> 00:20:55,400
+هداك اتنين اقصد اربعة في علافة بتروبطها بتقولك ان
+
+265
+00:20:55,400 --> 00:20:59,920
+كل اللي هو hexadecimal digit كل واحد من ال
+
+266
+00:20:59,920 --> 00:21:05,220
+hexadecimal digit بنقدر نكتبه على صورة اللي هو
+
+267
+00:21:05,220 --> 00:21:10,780
+اربعة bits هاي واحد تنين تلاتة اربعة يعني لو اجي
+
+268
+00:21:10,780 --> 00:21:16,720
+تاخد مثال ال E ال E اللي هي E عشرة B احداش C اتناش
+
+269
+00:21:16,720 --> 00:21:21,630
+D تلاتاش E اربعتاش ال E اربعتاش هذهالـ E هي قيمتها
+
+270
+00:21:21,630 --> 00:21:26,110
+14 و للضامن العدل السداسي هيا نكتبها على صورة 0 1
+
+271
+00:21:26,110 --> 00:21:30,890
+1 1 تعرفوا كيف تحسبوها سفر اللي هو سفر واحد اللي
+
+272
+00:21:30,890 --> 00:21:35,530
+هو في اتنين يعني اتنين و هاد في اتنين في اربعة هاي
+
+273
+00:21:35,530 --> 00:21:38,890
+اتنين و اربعة ستة هاد تمانية ستة و تمانية اربعة
+
+274
+00:21:38,890 --> 00:21:41,950
+اتاش اذا هذا صار كله على بعض و ليش اربعة اتاش اللي
+
+275
+00:21:41,950 --> 00:21:47,310
+هو Eإذاً هذا العدد الـ hexadecimal بقدر أكتبه على
+
+276
+00:21:47,310 --> 00:21:52,950
+صورة 01111 الآن بدي أخد الخمسة في نظام العدد الست
+
+277
+00:21:52,950 --> 00:21:58,050
+عشر برضه بقدر أكتبها على صورة أربع أرقام كيف؟ هاي
+
+278
+00:21:58,050 --> 00:22:01,750
+عند أول شي فردي، مدام فردي هذه اللي هنا فردية إذاً
+
+279
+00:22:01,750 --> 00:22:07,370
+أول عدد فيه واحدالان الابضال من الخمسة أربعة أربعة
+
+280
+00:22:07,370 --> 00:22:11,230
+هذا اتنين الأربعة دندا بيصير سفر وهذا هو الأربعة
+
+281
+00:22:11,230 --> 00:22:16,990
+الان هي عندك واحد زائد سفر في اتنين في اتنين بيطلع
+
+282
+00:22:16,990 --> 00:22:21,010
+سفر زائد واحد في أربعة باربعة وهذا سفر اللي هو في
+
+283
+00:22:21,010 --> 00:22:24,190
+اتنين قصة تلاتة اللي هي تمانية بيطلع سفر يعني هذا
+
+284
+00:22:24,190 --> 00:22:29,160
+العدد عبارة عن جداش خمسةولو جيت اخدت اي عدد من
+
+285
+00:22:29,160 --> 00:22:34,820
+الواحد للخمستعاش هتلاقيك بتقدر تكتبه على صورة اربع
+
+286
+00:22:34,820 --> 00:22:40,160
+ارقام اللي هو على صورة pets اربعة pets بنظام العد
+
+287
+00:22:40,160 --> 00:22:45,520
+الثنائيطيب الواحد كيف بدنا نكتبه على صورة الواحد
+
+288
+00:22:45,520 --> 00:22:49,020
+بالنظام العادى 16 واحد قيمته كيف بنا نكتبه هنا
+
+289
+00:22:49,020 --> 00:22:53,800
+واحد سفر سفر سفر و هكذا جربلي في باقى الأعداد من
+
+290
+00:22:53,800 --> 00:22:57,860
+واحد لخمس عشر او من سفر لخمس عشر شوف كيف نكتبها
+
+291
+00:22:57,860 --> 00:23:02,460
+على صورة أربعة bits طيب اللي هان بدنا نعرفها حاجة
+
+292
+00:23:02,460 --> 00:23:06,620
+اسمها bytes ال bytes هي عبارة عن تمانية bit يعني
+
+293
+00:23:06,620 --> 00:23:10,340
+هدولة و كمان كانت جنبهين أربعة بنسميهين byte كل
+
+294
+00:23:10,340 --> 00:23:14,280
+واحدة بنسميها إيش byteإذا الـ byte بتتكون من 8 bit
+
+295
+00:23:14,280 --> 00:23:20,740
+الآن بناء عليه اللي هو أي .. قولنا أي عدد .. أي
+
+296
+00:23:20,740 --> 00:23:23,480
+عدد لحاله اللي هو في ال .. في ال .. في ال
+
+297
+00:23:23,480 --> 00:23:28,840
+hexadecimal بكتبه على صورة 4 الآن عددين في ال ..
+
+298
+00:23:28,840 --> 00:23:34,300
+اللي هو رقم مكون من عددين في ال 16 بقدر أكتبه على
+
+299
+00:23:34,300 --> 00:23:39,950
+صورة byte يعني بقدر أكتب على صورة 4 و 4الخمسة هي
+
+300
+00:23:39,950 --> 00:23:45,470
+أربعته وهي الخمسة هي أربعته والإي هي أربعته إذا
+
+301
+00:23:45,470 --> 00:23:50,750
+عملية كتابة الرقم هذا سهل كيف بكتبها باجي بكتب هذا
+
+302
+00:23:50,750 --> 00:23:57,400
+بالاربعة bitsوهذا اربع بيت استبعوته و بحطهم جان
+
+303
+00:23:57,400 --> 00:24:02,920
+بعض بطلع عنده اللي هو الرقم هذا اللي بالنظام العد
+
+304
+00:24:02,920 --> 00:24:09,440
+16 بساوي اللي هو الرقم اللي اسمه byte بنظام العد
+
+305
+00:24:09,440 --> 00:24:16,260
+الثنائي طيب نيجي الآن ناخد اللي هو اللي هي
+
+306
+00:24:20,110 --> 00:24:24,930
+نحكي الآن عن الـ Base Conversion اللي هي عملية
+
+307
+00:24:24,930 --> 00:24:29,670
+التحويل من و إلى انتبهوا الآن لعملية التحويل عشان
+
+308
+00:24:29,670 --> 00:24:34,610
+ما تتغلبوش عشان الآن الحسابات تصير سهلة خالص في
+
+309
+00:24:34,610 --> 00:24:39,750
+عملية التحويل إلى نظام العدل اللي بدناها الان لو
+
+310
+00:24:39,750 --> 00:24:45,230
+جالنا find the octal expansion of اللي هي 1245 في
+
+311
+00:24:45,230 --> 00:24:49,440
+نظام العدل العشري هذا مكتوبفي نظام العدل عشري و
+
+312
+00:24:49,440 --> 00:24:54,400
+بدي حوله لل اوكتل كنا .. كنا من نظام ال اوكتل
+
+313
+00:24:54,400 --> 00:24:57,820
+للعشري او من ال binary للعشري او من اي اشي للعشري
+
+314
+00:24:57,820 --> 00:25:02,020
+سهل و قولنا كيف نحوله الان العكس .. العكس شوف كيف
+
+315
+00:25:02,020 --> 00:25:07,900
+هنلاجيه اسهل الان بمسك العدد اللي هو الف .. اللي
+
+316
+00:25:07,900 --> 00:25:11,240
+هو الف و متين و خمس و أربعين آسف فهذا مش مت .. الف
+
+317
+00:25:11,240 --> 00:25:13,640
+و متين و خمس و عشرين .. الف و متين و خمس و أربعين
+
+318
+00:25:14,230 --> 00:25:18,870
+أحولها لنظام العدمين الـ octal الثماني باجسمها على
+
+319
+00:25:18,870 --> 00:25:24,450
+تمانية بطلع عنده تمانية في 155 زي 5 هذا اللي هو
+
+320
+00:25:24,450 --> 00:25:29,570
+ناتج القسمة وهذا ال remainder انتبهوا اللي غامق
+
+321
+00:25:29,570 --> 00:25:33,360
+ناتج القسمة و اللي بالازرق هو ال remainderالان
+
+322
+00:25:33,360 --> 00:25:39,420
+نعيد العملية نقسم الـ 155 على 8 كمان مرة نقسم مين
+
+323
+00:25:39,420 --> 00:25:45,520
+اللي هو ناتج القسم اللي نتج في الأول 155 طلع 8 في
+
+324
+00:25:45,520 --> 00:25:50,180
+19 زائد remainder جديد اسمه تلاتةالان هذا الـ 19
+
+325
+00:25:50,180 --> 00:25:55,440
+اللي هو ناتج القسمة تبع الـ 155 على 8 بعمل نفس
+
+326
+00:25:55,440 --> 00:26:00,740
+الاشي هنا بجسم الـ 19 على 8 بتيجي 8 زائد 2 في 3
+
+327
+00:26:00,740 --> 00:26:05,960
+هذا ناتج القسمة برضه بعمله نفس الاشي باجي بقول 2
+
+328
+00:26:05,960 --> 00:26:10,160
+بساوة 8 بجسمه على 8 طبعا مافيش 8 مافيش فيه ولا 8
+
+329
+00:26:10,160 --> 00:26:15,310
+فبنكتبه على صورة 8 في 0 وال remainder هو 2يوم ما
+
+330
+00:26:15,310 --> 00:26:20,630
+نصل لهذه الخطوة بقى جاف يعني يوم ما نصل ان ناتج
+
+331
+00:26:20,630 --> 00:26:27,810
+القسمة طلع اللي هو سفر بقى جاف ماشي الحال طيب الان
+
+332
+00:26:27,810 --> 00:26:31,490
+ايش هذا ايش هو اللي عملته هذا انا تعالى نشوف مع
+
+333
+00:26:31,490 --> 00:26:36,810
+بعض الان ألف و متين و خمس و أربعين بساوي هذا زائد
+
+334
+00:26:36,810 --> 00:26:40,830
+هذا شايفينه هيد نجلتيه بقى الان الان المية و خمس و
+
+335
+00:26:40,830 --> 00:26:45,070
+خمسين هيهابدي أزيل الـ 155 و أعوض مكانها قيمة
+
+336
+00:26:45,070 --> 00:26:49,750
+تليادي زائدة دي أحوال تهيأني صار هاي الرقم وعكت
+
+337
+00:26:49,750 --> 00:26:54,010
+ضربهم في بعض بدلالة التمانية لإنه أنا بدور على
+
+338
+00:26:54,010 --> 00:26:57,690
+النظام العد الثماني الآن هذي بيصير تمانية ضرب
+
+339
+00:26:57,690 --> 00:27:03,490
+تمانية يعني تمانية تربيع في 19 هي الأولىو8×3 هي 2
+
+340
+00:27:03,490 --> 00:27:09,750
+زائد الخمسة ويساوي الان بدي أشيل ال 19 و أضع قيمة
+
+341
+00:27:09,750 --> 00:27:15,350
+هي ال 19 8×2 زائد 3 شيلت و أضعت قيمة ها هان اتيت
+
+342
+00:27:15,350 --> 00:27:20,530
+حسبتها صار 8 تربيع اللي هو مضروبة في 8 بيصير 8
+
+343
+00:27:20,530 --> 00:27:24,610
+تكعيبفى اتنين زائد تمانية تربيع برضه مضربة فى مين
+
+344
+00:27:24,610 --> 00:27:28,930
+فى تلاتة زائد تمانية فى تلاتة هيها زائد خمسة هيها
+
+345
+00:27:28,930 --> 00:27:33,390
+الآن هذا الناتج اللى طلع عندى تلاحظ من وين جبته من
+
+346
+00:27:33,390 --> 00:27:37,170
+اللى هو اللى عملته فى القسم هنا وفى الآخر عوضت فيه
+
+347
+00:27:37,530 --> 00:27:42,210
+إذا كتبت الرقم اللي عندي 1245 اللي تحته خط هذا
+
+348
+00:27:42,210 --> 00:27:47,110
+كتبته بالصورة هذه فصار هذا اللي هو خانة الأحد إذا
+
+349
+00:27:47,110 --> 00:27:51,710
+صح التعبير بنظام العد الثماني وهذه خانة اللي هي
+
+350
+00:27:51,710 --> 00:27:56,090
+اللي بنسميها العشرات اللي هي التمانيات يعني وهذه
+
+351
+00:27:56,090 --> 00:28:00,050
+خانة التمانيات تربيع وهذه خانة التمانيات تكعيد
+
+352
+00:28:00,050 --> 00:28:04,230
+يعني بيصير عندي العدد هذا بنظام العد الثنائي هو
+
+353
+00:28:04,230 --> 00:28:11,430
+عبارة عن هي الخمسةهى التلاتة هى التلاتة هى التنين
+
+354
+00:28:11,430 --> 00:28:16,410
+إذا صار عند العدد الأصلي ال 1245 نظام العد العشري
+
+355
+00:28:16,410 --> 00:28:20,390
+هى قيمته هتقولوا ليه و أحنا كل مرة بدنا نقعد نعمل
+
+356
+00:28:20,390 --> 00:28:24,410
+هيك و نعوض و مش عارف إيش و الله بتلخ منها هذا الآن
+
+357
+00:28:24,410 --> 00:28:29,370
+أنا شرعتلكم العملية شغل المكان كمانى ايه شغل
+
+358
+00:28:29,370 --> 00:28:33,690
+المكان الجسمة بتصور سهل هي اتجسمت و طلعت اللي هو
+
+359
+00:28:33,690 --> 00:28:39,340
+متبقى قسمة or remainderإيش هذا الرقم بيكون؟ هو
+
+360
+00:28:39,340 --> 00:28:44,380
+عبارة عن الـ remainders شوف الـ remainders انسى
+
+361
+00:28:44,380 --> 00:28:47,460
+هذه .. هذول الخطوات انساها إيه جاف العند الهن؟ شو
+
+362
+00:28:47,460 --> 00:28:51,160
+جفنا العند الهن؟ احنا بيصير أول remainder ال .. ال
+
+363
+00:28:51,160 --> 00:28:55,820
+.. ال .. ال .. ال .. وين جفنا؟ العند ال .. جسمنا
+
+364
+00:28:55,820 --> 00:29:01,100
+العند الهن مظبوط؟ هذه جسمنا العند الهن و هذه جسمنا
+
+365
+00:29:01,100 --> 00:29:03,520
+العند الهن و هذه العند الهن لما وصلنا لعند هذه أخر
+
+366
+00:29:03,520 --> 00:29:07,560
+واحدةماشي الحال .. باجي .. لو وين وصلنا هيها ..
+
+367
+00:29:07,560 --> 00:29:11,800
+لها باجي باخد أول .. أخر واحدة وصلتي لها هي اتنين
+
+368
+00:29:11,800 --> 00:29:15,620
+ال remainder اتنين الأزرق هيهم هي أول واحد ال
+
+369
+00:29:15,620 --> 00:29:18,200
+remainder اللي بعده التلاتة هيها باخد ال
+
+370
+00:29:18,200 --> 00:29:21,120
+remainders ال remainder اللي بعده تلاتة هيها ال
+
+371
+00:29:21,120 --> 00:29:25,060
+remainder اللي بعده هدون هي خمسةماشي الحال طيب
+
+372
+00:29:25,060 --> 00:29:27,800
+اللي .. اللي .. اللي .. اللي .. اللي شوية مضايق من
+
+373
+00:29:27,800 --> 00:29:31,540
+هذا يتبع معايا السؤال اللي بعده عشان يفهم بالظبط
+
+374
+00:29:31,540 --> 00:29:34,060
+اشي اللي بقول اللي عم بقول find the octal
+
+375
+00:29:34,060 --> 00:29:38,600
+expansion of هذا الرقم هذا بالنظام العد العشري بده
+
+376
+00:29:38,600 --> 00:29:44,160
+حوله لنظام العد الثماني الموضوع سهل يا جماعة هذا
+
+377
+00:29:44,160 --> 00:29:48,060
+لمين بده حوله لنظام العد الثماني إذا القسم على
+
+378
+00:29:48,060 --> 00:29:52,740
+تمانية باج الرقم الأصلي باج اسمه على تمانيةبظل
+
+379
+00:29:52,740 --> 00:29:57,860
+المتبقى واحد ناتج القسم هيوم ناتج القسم بقسمه على
+
+380
+00:29:57,860 --> 00:30:02,740
+تمانية هنا قسمت على تمانية طالع 192 والمتبقى 7
+
+381
+00:30:02,740 --> 00:30:09,100
+الان باجي بقسم ال 192 على تمانية بطلع ناتج القسم
+
+382
+00:30:09,100 --> 00:30:15,560
+24 المتبقى 0 ال 24 بقسمها على تمانيةبطلع الناتج
+
+383
+00:30:15,560 --> 00:30:19,660
+تلاتة و المتبقى سفر عندنا خلصنا مدام اللي هو ناتج
+
+384
+00:30:19,660 --> 00:30:22,580
+القسمة طلع أصغر من تمانية بكون وصلت للخطوة الأخيرة
+
+385
+00:30:22,580 --> 00:30:26,200
+ايش الخطوة الأخيرة اللي هو ناتج القسمة هذا تلاتة
+
+386
+00:30:26,200 --> 00:30:31,060
+بساوية تمانية ضرب سفر لأنه أصغر من تمانية زائد
+
+387
+00:30:31,060 --> 00:30:36,080
+تلاتة هنا بقف لأنه طلع عند ناتج القسمة جداش سفر
+
+388
+00:30:36,080 --> 00:30:39,520
+يعني تلاتة بساوية تمانية في سفر زائد تلاتة الآن
+
+389
+00:30:39,520 --> 00:30:44,490
+ايش نظام العد الثماني على طول زي ما قلناأخ .. أخ
+
+390
+00:30:44,490 --> 00:30:47,550
+.. و أنا وصلت تلاتة هو reminders هي reminders
+
+391
+00:30:47,550 --> 00:30:54,390
+تلاتة هيو اللي جابله سفر هيو كتبته هيو ال reminder
+
+392
+00:30:54,390 --> 00:30:58,350
+اللي جابله سفر هيو ال reminder اللي جابله سبعة هيو
+
+393
+00:30:58,350 --> 00:31:02,390
+ال reminder الأول هيو واحد اللي بده يبدأ بالعكس
+
+394
+00:31:02,390 --> 00:31:06,240
+ويحضر اللي بده بالعكس ويجي من هنا واحدومن هنا سبعة
+
+395
+00:31:06,240 --> 00:31:10,020
+اللي بعيدها ومن هنا سفر ومن هنا سفر ومن هنا سفر
+
+396
+00:31:10,020 --> 00:31:14,040
+اذا ما هي العملية قسمها وتاخد في الاخر الـ
+
+397
+00:31:14,040 --> 00:31:17,320
+remainders وترتبها بالترتيب اللي موجود بتطلع عندك
+
+398
+00:31:17,320 --> 00:31:21,380
+هذا نظام العد الثماني طيب الآن خلينا .. بدناش
+
+399
+00:31:21,380 --> 00:31:26,460
+ثماني بدنا ستاشه ال gate عمال لنا حاضر مثال لبعده
+
+400
+00:31:26,460 --> 00:31:32,130
+find the hexadecimal expansion of الرقم هذاماذا
+
+401
+00:31:32,130 --> 00:31:35,390
+يعني hexadecimal expansion؟ يعني بدنا نظام العد
+
+402
+00:31:35,390 --> 00:31:40,310
+الثماني لهذا الرقم ايش بسوي؟ بمسك الرقم اللي جوا و
+
+403
+00:31:40,310 --> 00:31:43,930
+بجسمه على اللي هو اللي بدي نظام عده مين نظام عده؟
+
+404
+00:31:43,930 --> 00:31:50,130
+ال 16 باجي بجسم ال 11070 ع 16 بطلع الناتج هذا
+
+405
+00:31:50,130 --> 00:31:53,990
+بالقالة يا جماعة بطلع الناتج هذا و بزيد 14 الآن
+
+406
+00:31:53,990 --> 00:31:59,890
+الناتج هذا بجسمه على 16 كمان مرة بطلع الناتج 43 و
+
+407
+00:31:59,890 --> 00:32:05,810
+بزيد 3ناتج القسمة برضه بجسمها 16 بطلع الناتج 2 و
+
+408
+00:32:05,810 --> 00:32:10,210
+بزيد 11 لما يطلع العدد أقل من 16 أقل من اللي بشتغل
+
+409
+00:32:10,210 --> 00:32:13,850
+عليه نظام العد برتاح بقول أخر خطوة عندي خلصتها
+
+410
+00:32:13,850 --> 00:32:19,100
+اللي هي 2 إيش هيساوي 16 في 0 زائد 2لأن ال maximum
+
+411
+00:32:19,100 --> 00:32:23,540
+على 16 مافيش هذا أصلا 16 فبطلع 16 ف0 زي 2 هنا بدف
+
+412
+00:32:23,540 --> 00:32:27,720
+بيصير عندي الآن أيش نظام العد اللي .. أيش .. أيش
+
+413
+00:32:27,720 --> 00:32:32,100
+اللي .. اللي .. اللي هو ال .. العدد بنظام العد ال
+
+414
+00:32:32,100 --> 00:32:36,740
+16 هي .. ال reminders .. ال reminders هي 2 هي أول
+
+415
+00:32:36,740 --> 00:32:45,740
+واحدة 11 هي اللي هو ال B تلاتة هي التلاتة 14 اللي
+
+416
+00:32:45,740 --> 00:32:50,980
+هي ال E إذا سهل الموضوعما هي الا عبارة عن اخد من
+
+417
+00:32:50,980 --> 00:32:55,660
+اللي هي reminders واصفها جانب بعض بالترتيب من
+
+418
+00:32:55,660 --> 00:32:59,620
+الشمال لليمين عندما انتهيت بيكون هذا نظام العدمين
+
+419
+00:32:59,620 --> 00:33:03,240
+ال 16 ويكون خارب طوق في اللي هو تبدأ من اليمين او
+
+420
+00:33:03,240 --> 00:33:08,640
+من الشمال من هنا من عند اخر ما وصلت بتبدأ من اللي
+
+421
+00:33:08,640 --> 00:33:15,300
+هو الشمال و بتتجه باتجاه اليمين طيب نجي لان بعدهم
+
+422
+00:33:15,650 --> 00:33:18,810
+سؤال آخر عشان نكبّت الفكرة find the binary
+
+423
+00:33:18,810 --> 00:33:23,030
+expansion of 120 اللي هو مكتوب بالعشرة إذا الأن
+
+424
+00:33:23,030 --> 00:33:27,170
+بدي أحول اللي هو من نظام عد عادي عشري إلى نظام
+
+425
+00:33:27,170 --> 00:33:31,790
+العد ثنائي برضه بنفس الطريقة بقسم ال 120 على 2
+
+426
+00:33:31,790 --> 00:33:36,570
+بتطلع 120 بالساوية 2 في 60 زي 0 الآن هي ناتج
+
+427
+00:33:36,570 --> 00:33:41,770
+القسمة 60 بقسمها على 2 بيصير 60 في 30 زي 10الان
+
+428
+00:33:41,770 --> 00:33:45,270
+طلع عندى تلاتين برضه تطول روحك في التلاتين نجسمها
+
+429
+00:33:45,270 --> 00:33:49,570
+على التنين برضه التنين مين هو نظام العدل اللى بدى
+
+430
+00:33:49,570 --> 00:33:54,410
+اشتغل عليه الان بيساوى 15 فى 2 طلع 15 الناتج و 0
+
+431
+00:33:54,410 --> 00:33:59,110
+remainder طبعا 15 مدام 15 اللى هو ناتج برضه و ده
+
+432
+00:33:59,110 --> 00:34:02,910
+جسمه 15 بيساوى 2 فى 7 زائد 1 يعني السابعة الان هى
+
+433
+00:34:02,910 --> 00:34:07,070
+الناتج السابعة بقى جسمها 2 برضه بيساوى 2 فى 3 زائد
+
+434
+00:34:07,070 --> 00:34:11,520
+1الان التلاتة برضه باقسمها بساوي تلاتة في اتنين
+
+435
+00:34:11,520 --> 00:34:15,200
+بساوي اتنين في واحد زائد واحد تلاتة باقسمها عمين
+
+436
+00:34:15,200 --> 00:34:18,000
+القسمة كلها ع اتنين ناتج القسمة ع اتنين و
+
+437
+00:34:18,000 --> 00:34:20,820
+remainder ناتج القسمة ع اتنين و remainder لما في
+
+438
+00:34:20,820 --> 00:34:25,660
+الاخر بصر ناتج القسمة واحد اللي هو اصغر من اتنين
+
+439
+00:34:25,660 --> 00:34:29,900
+على طول برتاح بقول اخر عنده وصلت الاخر خطوة الان
+
+440
+00:34:29,900 --> 00:34:34,870
+الواحد ايش بساوي اتنين في سفر زائد واحدالان الـ120
+
+441
+00:34:34,870 --> 00:34:39,590
+بنظام العد العشري هتساوي بنظام العد ثنائي ميالي
+
+442
+00:34:39,590 --> 00:34:46,630
+هاي واحد من اللي هو اليمين التاني واحد والتالت
+
+443
+00:34:46,630 --> 00:34:52,870
+واحد و الرابع واحد و الخامس صفر و السادس صفر و
+
+444
+00:34:52,870 --> 00:34:58,520
+السابع صفر هاي الان بنظام العد الثمانيالثنائي إذا
+
+445
+00:34:58,520 --> 00:35:03,400
+هذه هي طريقة تحويل الآن من نظام العد العشري إلى
+
+446
+00:35:03,400 --> 00:35:07,180
+أنظمة العد المختلفة وفي الأول احنا أخدنا اللي هو
+
+447
+00:35:07,180 --> 00:35:10,680
+العكس من التحويل من نظام العد الثنائي أو الثلاثي
+
+448
+00:35:10,680 --> 00:35:13,860
+أو الربيع أو الخماسي أو اللي هو أو السداسة أو
+
+449
+00:35:13,860 --> 00:35:19,620
+الثماني أو الست عشر للعد العشري أو هنا تبقوا ان
+
+450
+00:35:19,620 --> 00:35:28,570
+احنا خلصنا الاتجاهيننعود الآن لآخر دُزُق نحكي
+
+451
+00:35:28,570 --> 00:35:32,470
+فيه Conversion between binary, octal and
+
+452
+00:35:32,470 --> 00:35:38,770
+hexadecimal expansion نحن مركزين على تلت أنواع من
+
+453
+00:35:38,770 --> 00:35:43,250
+العدد العشري اللي نشتغل فيهالان العد الثنائي
+
+454
+00:35:43,250 --> 00:35:48,190
+والثماني ال octal و ال hexadecimal اللي هو الست
+
+455
+00:35:48,190 --> 00:35:53,570
+عشر حولنا من ال decimal هدول كلهم التلاتة و حولنا
+
+456
+00:35:53,570 --> 00:35:58,750
+بعدين من التلاتة اللي بنحكي عنها لمن لعشرين ضل
+
+457
+00:35:58,750 --> 00:36:03,950
+انحولهم بين بعض الان بدنا نشوف كيف نحول ال octal
+
+458
+00:36:04,660 --> 00:36:11,520
+وانحوّل الـ hexa إلى ash إلى binary ونشوف كيف اللي
+
+459
+00:36:11,520 --> 00:36:15,300
+أنا بقول find the octal and hexadecimal expansion
+
+460
+00:36:15,300 --> 00:36:20,660
+of هذه الرقم مكتوب بالاش مش بالتمانية هذه اتنين
+
+461
+00:36:20,660 --> 00:36:25,570
+آسف هذه اتنين من نظام العد الثنائيand the binary
+
+462
+00:36:25,570 --> 00:36:34,410
+expansion of 7,6,5,8,d,16 يعني بدنا نحول اشي من
+
+463
+00:36:34,410 --> 00:36:40,190
+الثنائي الى الثماني والست عشر ونحول اللي هو من
+
+464
+00:36:40,190 --> 00:36:44,650
+الثماني والست عشر الى اللي هو الثنائي خلينا اول
+
+465
+00:36:44,650 --> 00:36:48,990
+اشي نيجي هي الرقم اللي هو اللي هو هذا اللي هو
+
+466
+00:36:48,990 --> 00:36:56,240
+مكتوب بالنظام العدمين الثنائيالان لما بدحول لنظام
+
+467
+00:36:56,240 --> 00:37:02,360
+العد الثماني شوفوا يا جماعة الثنائي اتنين الثماني
+
+468
+00:37:02,360 --> 00:37:09,640
+اتنين او ثلاثة الان في الثماني باجي مادام ثماني
+
+469
+00:37:09,640 --> 00:37:17,280
+يعني اتنين او ثلاثة بجسم خنات الثنائيإلى تلت خنات
+
+470
+00:37:17,280 --> 00:37:21,140
+تلت خنات بعدد الأُس تبع التمانية التمانية هو عضار
+
+471
+00:37:21,140 --> 00:37:23,940
+عن اتنين أُس ثلاثة في علاقة بينهم مش مجالنا
+
+472
+00:37:23,940 --> 00:37:30,340
+لاستنتاج العلاقة أما كيف انحول من الثنائي للثماني
+
+473
+00:37:30,340 --> 00:37:36,280
+باجي بجسمهم الآن ببدأ عندي لأن سفر سفر واحد اخر
+
+474
+00:37:36,280 --> 00:37:42,070
+واحدة هيالان واحد واحد واحد هيها الان اللي بعدها
+
+475
+00:37:42,070 --> 00:37:46,790
+سفر واحد سفر واحد واحد واحد واحد واحد سفر من وين
+
+476
+00:37:46,790 --> 00:37:51,810
+جبت السفر الأخير هذا إذا كان هدول عددهم بيقبل جسم
+
+477
+00:37:51,810 --> 00:37:55,390
+على تلاتة خلاص بيسير اللي حالين بيطلع اللي حالين
+
+478
+00:37:55,390 --> 00:38:00,390
+إذا ناجس العدد بحط ايه سفر لإن العدد على السفر على
+
+479
+00:38:00,390 --> 00:38:04,790
+الشمال العدد بأثرشإذاً اللي عملته إيش يا جماعة
+
+480
+00:38:04,790 --> 00:38:09,050
+بيجيد قولت هاي أول مجموعة هايها التلاتة الأولانيات
+
+481
+00:38:09,050 --> 00:38:13,310
+بعدين هي التلاتة التانيات بعدين هي التلاتة
+
+482
+00:38:13,310 --> 00:38:17,330
+التالتات وهي التلاتة الرابعات والتلاتة الأخرات
+
+483
+00:38:17,330 --> 00:38:21,410
+اللي هي واحد واحد وإيش سفر هو بعد بالعكس الآن
+
+484
+00:38:21,410 --> 00:38:26,050
+كاتبلك سفر واحد سفر اللي هي سفر واحد واحد بعدين
+
+485
+00:38:26,050 --> 00:38:31,830
+واحد واحد واحد بعدين سفر واحد سفر ومكمل لعندهاإيه
+
+486
+00:38:31,830 --> 00:38:37,210
+دا اللي هي هذه جسمها إلى تلت خنات تلت خلات تعني
+
+487
+00:38:37,210 --> 00:38:43,050
+تلاتة bytes أو تلاتة bits ماشي كل تلت بتات مع بعض
+
+488
+00:38:43,050 --> 00:38:47,470
+الان لو خس علينا بتات من الشمال بضيف على الشمال
+
+489
+00:38:47,470 --> 00:38:51,090
+لإنه بضيف على الشمال أصفار لإن الأصفار اللي على
+
+490
+00:38:51,090 --> 00:38:54,650
+الشمال لا تؤثر في العدد بظل العدد زي ما هو زي ما
+
+491
+00:38:54,650 --> 00:38:59,100
+انتوا عارفين في العادي برضه بنفعهاالان هانا خسلنا
+
+492
+00:38:59,100 --> 00:39:03,780
+عدد فكتبنا صفر واحد واحد هذا ال bit التلك بتات
+
+493
+00:39:03,780 --> 00:39:07,660
+الأولى التلك بتات التانية هي التلك بتات التالتة
+
+494
+00:39:07,660 --> 00:39:12,960
+الاخرى خليهم بنفس الترتيب دير بالك الان جداش قيمته
+
+495
+00:39:12,960 --> 00:39:18,860
+هذا العدد هذا اتنين وهذا اللي هو واحد في منزلته
+
+496
+00:39:18,860 --> 00:39:23,520
+واحد هذا واحد في اتنين اذا واحد و اتنين تلاتة اذا
+
+497
+00:39:23,520 --> 00:39:27,840
+اول واحد قيمته تلاتة نيجي لالي بعدههذا اللي هو
+
+498
+00:39:27,840 --> 00:39:31,620
+واحد منزلته الأولى هذا المطمئنع اللي عدت تونية
+
+499
+00:39:31,620 --> 00:39:37,040
+جاعت بحسبهم واحد في اتنين قص واحد زائد اتنين قص
+
+500
+00:39:37,040 --> 00:39:42,460
+اتنين يعني واحد واتنين واربعة سبعة طيب نيجي للي
+
+501
+00:39:42,460 --> 00:39:48,940
+بعده سفر زائد اتنين زائد سفر اتنين ايه اللي بعده
+
+502
+00:39:49,330 --> 00:39:55,290
+هذا حسبناه اللي هو واحد واتنين واربعة سبعة هي جلة
+
+503
+00:39:55,290 --> 00:40:00,150
+اللي بعد والاخير صفر وصفر واربعة لأنها دخلت الصفر
+
+504
+00:40:00,150 --> 00:40:03,850
+اللي هو في اتنين وصفر دخلت الصفر في اتنين واس واحد
+
+505
+00:40:03,850 --> 00:40:07,990
+وهذا دخلت الواحد في اتنين واس اتنين يعني اربعة اذا
+
+506
+00:40:07,990 --> 00:40:12,310
+هاي الاعداد هذولة بشيل هذولة كل تلاتة و بحط مكانها
+
+507
+00:40:12,310 --> 00:40:18,540
+قيمتهابصير عندى هذا العدد بساوى اللى هو الآن بدأنا
+
+508
+00:40:18,540 --> 00:40:21,820
+من وين من الشمال هدولة من الشمال تلاتة اللى بعدها
+
+509
+00:40:21,820 --> 00:40:26,320
+سبعة اللى بعدها اتنين سبعة اربعة تلاتة سبعة اتنين
+
+510
+00:40:26,320 --> 00:40:31,680
+سبعة اربعة تمانية اذا هذا صار بساوى هذا باش بال
+
+511
+00:40:31,680 --> 00:40:36,440
+اللى هو من نظام العد الثماني نظام العد الثماني
+
+512
+00:40:36,440 --> 00:40:43,970
+قلنا اتنين أس تلاتة كل تلت بتاتبرقم من الثماني
+
+513
+00:40:43,970 --> 00:40:49,910
+الان في الـ hexadecimal كل أربع بالتات لأن الست
+
+514
+00:40:49,910 --> 00:40:55,430
+عبارة عن اتنين قصة أربعة فبصير عندي كل أربع بالتات
+
+515
+00:40:55,990 --> 00:41:01,990
+أب جداش اب واحد من الـ hexadecimal بناء عليه أنا
+
+516
+00:41:01,990 --> 00:41:07,550
+لو أعطاني هاي هذا الرقم في نظام العد الثنائي بدي
+
+517
+00:41:07,550 --> 00:41:11,350
+يعني أحوله للـ hexadecimal عشان أحوله للـ
+
+518
+00:41:11,350 --> 00:41:15,410
+hexadecimal بدي أجسمه لأربعات هاي الأربعة الأولى
+
+519
+00:41:15,410 --> 00:41:19,150
+وهي الأربعة الثانية وهي الأربعة الثالثة وهنا
+
+520
+00:41:19,150 --> 00:41:25,200
+الأربعة الأخيرة لها بيصير 11 و11 و0 و0نحسب الاربعة
+
+521
+00:41:25,200 --> 00:41:29,800
+هذه الاربعة هذه وعلى طول بدك تكتب العدد هذا سفر
+
+522
+00:41:29,800 --> 00:41:36,160
+وهذا سفر وهذا ايش اتنين plus اتنين يعني اربعة وهنا
+
+523
+00:41:36,160 --> 00:41:36,640
+تمانية
+
+524
+00:41:42,860 --> 00:41:47,080
+عشان تحفظوا على السريع هذا في اتنين هذا في واحد في
+
+525
+00:41:47,080 --> 00:41:52,280
+اتنين في اربعة في تمانية اذا سفر سفر اربعة و
+
+526
+00:41:52,280 --> 00:41:55,320
+تمانية اتناش اربعة تمانية اتناش اتناش اللي هو مين
+
+527
+00:41:55,320 --> 00:42:02,980
+هى ال C كتبته لان واحد و اتنين تلاتة و سفر تلاتة و
+
+528
+00:42:02,980 --> 00:42:08,190
+تمانية احداش اللي هو ال Bخلصنا هذا شفا و بنسير سفر
+
+529
+00:42:08,190 --> 00:42:12,630
+اتنين و اربعة ستة و تمانية اربعة اتاش هذا صار
+
+530
+00:42:12,630 --> 00:42:16,910
+اربعة اتاش اللي هو ال E لان هذا واحد و اتنين تلاتة
+
+531
+00:42:16,910 --> 00:42:20,170
+و الباقي الصفار يعني تلاتة ايه هذا اذا صار الان
+
+532
+00:42:20,170 --> 00:42:27,970
+التحويل من hexa من من تناء لhexa سهل اربعات و بنحط
+
+533
+00:42:27,970 --> 00:42:32,630
+مكان كل اربعة قيمتهافي التمانية نظام العد الثماني
+
+534
+00:42:32,630 --> 00:42:36,210
+تلتات وكل تلتة بنحط إيش قمت هذه التلتة الأول هذه
+
+535
+00:42:36,210 --> 00:42:38,390
+التلتة التانية هذه التلتة التالتة التلتة الرابعة
+
+536
+00:42:38,390 --> 00:42:41,490
+تلتة الخامسة وقلنا إذا خس علينا تلتات من الآخر
+
+537
+00:42:41,490 --> 00:42:44,850
+بنحط هناش أصفر لإنه بأثر ناش على العدل إذا هذا
+
+538
+00:42:44,850 --> 00:42:50,310
+عملية التحويل من الثنائي للثماني أو إلى الستة عشر
+
+539
+00:42:50,310 --> 00:42:56,090
+سهل وهيني جميعا عنهالان بدنا نحوّل العكس بدنا
+
+540
+00:42:56,090 --> 00:43:01,350
+نحوّل سبعة ستة خمسة للثماني برضه بدحوّلها ليش into
+
+541
+00:43:01,350 --> 00:43:06,510
+binary notation الان convert هذا ل binary notation
+
+542
+00:43:06,510 --> 00:43:11,810
+يعني بدحولها من نظام العد الثماني الى نظام العد من
+
+543
+00:43:11,810 --> 00:43:20,110
+الثنائي و قمر sale خالص الخمسة ايش بتساوي ثنائي
+
+544
+00:43:20,110 --> 00:43:21,550
+الخمسة
+
+545
+00:43:24,690 --> 00:43:28,730
+الخمسة عبارة عن واحد
+
+546
+00:43:38,990 --> 00:43:43,290
+الستة زوجي عبارة عن 2 زي 4
+
+547
+00:44:02,620 --> 00:44:08,140
+أسف هاي السبعة السبعة ايش قمتها واحد و اتنين و
+
+548
+00:44:08,140 --> 00:44:11,440
+اربعة واحد و اتنين تلاتة و اربعة سبعة عملتها ده
+
+549
+00:44:11,440 --> 00:44:15,620
+بالليل هاي حطيت مكان مين السبعة يعني باختصار اكيد
+
+550
+00:44:15,620 --> 00:44:20,740
+فانتوا الخمسة بحط قمتها في الثنائي و بعرف وجودها و
+
+551
+00:44:20,740 --> 00:44:25,700
+الستة بحط قمتها في الثنائي و السبعة بحط قمتها في
+
+552
+00:44:25,700 --> 00:44:31,870
+ايش في الثنائيبتطلع عندي اللي هي القيمة اللي أنا
+
+553
+00:44:31,870 --> 00:44:39,890
+بديها الان أكيد كلكم قال ال 16 انحولها لثنائي بنفس
+
+554
+00:44:39,890 --> 00:44:45,050
+الأسلوب يعني حوللي هذه للثنائي بتقوللي ال D بحط
+
+555
+00:44:45,050 --> 00:44:50,890
+قيمتها أربعة بالتالت ال 16 أربعة بالتالت كل واحدة
+
+556
+00:44:50,890 --> 00:44:54,730
+باربعةالـ D لها أربعة والـ 8 لها أربعة والـ A لها
+
+557
+00:44:54,730 --> 00:45:00,150
+أربعة الـ D اللي هي جداش الـ D الـ D اللي هي A B C
+
+558
+00:45:00,150 --> 00:45:04,970
+D يعني تلت عاش تلت عاش تلت عاش فردي مزام تلت عاش
+
+559
+00:45:04,970 --> 00:45:12,410
+فردي إذا أول خانة إيش بتطلع واحد واحد و سفر أو
+
+560
+00:45:12,410 --> 00:45:17,530
+أربعة خمسة وتمانية تلت عاش فعلا هيإذاً الـ D بتحط
+
+561
+00:45:17,530 --> 00:45:22,170
+قيمتها هي .. هي الآن التمانية .. التمانية زوجي
+
+562
+00:45:22,170 --> 00:45:25,950
+اللي هي اتنين وستلاتة يعني الأولى أنها صفر صفر صفر
+
+563
+00:45:25,950 --> 00:45:30,930
+و هي Aش التامنة لإنها تتنظر في واحد و تتنظر في
+
+564
+00:45:30,930 --> 00:45:33,950
+اتنين و تتنظر في أربعة و تتنظر في تمانية أكيد
+
+565
+00:45:33,950 --> 00:45:37,190
+التمانية اللي هي بس واحد و اللي قدامها تلات أصفار
+
+566
+00:45:37,190 --> 00:45:41,410
+إذاً هي التمانية الآن ال A اللي هي العشرةاللي هي
+
+567
+00:45:41,410 --> 00:45:44,270
+اتنين و تمانية يعني هي اتنين و هي تمانية و هدول
+
+568
+00:45:44,270 --> 00:45:51,230
+أسفار كتبناها هنا إذا نحولنا من اللي هو ستاشر اللي
+
+569
+00:45:51,230 --> 00:46:00,070
+هو hexa إلى إيش إلى binaryكيف كل دي و اي و تمانية
+
+570
+00:46:00,070 --> 00:46:05,930
+و اي باربع بتات بقيمهن اللي قلناهن هيك بإحنا بنكون
+
+571
+00:46:05,930 --> 00:46:13,410
+أنهينا المحاضرة اللي هي الـ five أو هي عند ال
+
+572
+00:46:13,410 --> 00:46:18,150
+homework المطلوب لهذه المحاضرة وإلى لقاء آخر
+
+573
+00:46:18,150 --> 00:46:21,090
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q.srt
new file mode 100644
index 0000000000000000000000000000000000000000..90a4be7bd3f612e084d3001b9d051e545fed2c36
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q.srt
@@ -0,0 +1,995 @@
+1
+00:00:00,000 --> 00:00:06,040
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثالثة بعد
+
+2
+00:00:06,040 --> 00:00:14,360
+حالة التوارق لمساق رياضيات منفصلة لطلاب وطالبات 
+
+3
+00:00:14,360 --> 00:00:18,880
+الجامعة الإسلامية كلية تكنولوجيا المعلومات في قسم
+
+4
+00:00:18,880 --> 00:00:25,940
+الحوسبة المتنقلة تحدثنا المرة الماضية عن إيجاد
+
+5
+00:00:25,940 --> 00:00:30,960
+المعكوس الضربي للمصفوفة. اليوم بدنا نوظف هذه
+
+6
+00:00:30,960 --> 00:00:40,440
+المعلومات في حل system of linear equations يعني
+
+7
+00:00:40,440 --> 00:00:47,360
+بدنا نوظف المعلومة في حل معادلات خطية معادلتين
+
+8
+00:00:47,360 --> 00:00:54,100
+خطيتين بمجهولين أو ثلاث معادلات خطية بثلاثة مجاهيل
+
+9
+00:00:54,860 --> 00:00:59,280
+لو جينا نتطلع في البداية اللي كان عندنا معادلة
+
+10
+00:00:59,280 --> 00:01:03,820
+خطية اللي هي ax بتساوي b هذه المعادلة الخطية
+
+11
+00:01:03,820 --> 00:01:08,660
+وفرضنا أن الـ a لا تساوي صفر وطلب منها طبعا a عبارة
+
+12
+00:01:08,660 --> 00:01:12,580
+عن عدد و b عبارة عن عدد و x عبارة عن مجهول طبعا
+
+13
+00:01:12,580 --> 00:01:16,040
+هذه زي ما أنتم عارفين زي ما أخذناها سابقا في
+
+14
+00:01:16,040 --> 00:01:22,060
+الإعدادية أنه بنجسم الجهتين على ال a بتطلع عندي x
+
+15
+00:01:22,060 --> 00:01:28,300
+بتساوي b على a أو بمعنى آخر x بتساوي a inverse في b
+
+16
+00:01:28,300 --> 00:01:34,640
+حيث a لا تساوي صفر. هذه طبعا معلومات سابقة بس عشان
+
+17
+00:01:34,640 --> 00:01:38,960
+نعرف أن في عندنا هذه معادلة خطية في مجهول واحد
+
+18
+00:01:38,960 --> 00:01:45,520
+الآن لو كان في عندنا معطينا معادلتين خطيتين يعني
+
+19
+00:01:45,520 --> 00:01:50,020
+درجة اللي هو المتغير هذا واحد ودرجة المتغير هذا
+
+20
+00:01:50,020 --> 00:01:54,850
+واحد برضه. الآن لو كان عندنا هذه معادلة خطية في
+
+21
+00:01:54,850 --> 00:01:57,990
+مجهولين، هذه المجهول الأول وهذه المجهول الثاني
+
+22
+00:01:57,990 --> 00:02:02,030
+والمعادلة الثانية برضه معادلة خطية في نفس
+
+23
+00:02:02,030 --> 00:02:07,550
+المجهولين اللي فوق. بسيرة أنه الآن إمكانية نحكي عن
+
+24
+00:02:07,550 --> 00:02:12,930
+الحلول المشتركة. يعني بمعنى آخر إيجاد X1 و X2 اللي
+
+25
+00:02:12,930 --> 00:02:17,850
+بتحقق المعادلة الأولى وبتحقق المعادلة الثانية في
+
+26
+00:02:17,850 --> 00:02:23,030
+نفس الوقت. طبعا زمان احنا كنا في الإعدادية نجي نضرب
+
+27
+00:02:23,030 --> 00:02:30,270
+نوحّد اللي هو معامل اللي هو الـ X1 هنا و X1 هنا و
+
+28
+00:02:30,270 --> 00:02:33,890
+بعدين نطرح المعادلتين من بعض بيطلع عندي قيمة X2 و
+
+29
+00:02:33,890 --> 00:02:39,510
+بعدين نعوض عن X1 بيطلع عندي X1 بنكون جبنا قيمة X1 و
+
+30
+00:02:39,510 --> 00:02:43,390
+قيمة X2. طبعا مش هذا اللي بدنا إياه اليوم. بدنا
+
+31
+00:02:43,390 --> 00:02:47,050
+نوظّف اللي هو معلوماتنا في الـ matrices أو في
+
+32
+00:02:47,050 --> 00:02:52,710
+المصفوفات لحل اللي هو نظام من اللي هو المعادلات
+
+33
+00:02:52,710 --> 00:02:57,970
+الخطية في مجهولين. نشوف هذه اللي عندنا الآن هذا
+
+34
+00:02:57,970 --> 00:03:00,930
+النظام بدي أحله عن طريق الـ matrices نشوف إيش بدي
+
+35
+00:03:00,930 --> 00:03:07,580
+أسوي. في عندنا اللي هو أول شغلة اللي هي بدنا اللي هو
+
+36
+00:03:07,580 --> 00:03:13,360
+نحكي عن حاجة اسمها اللي هي مصفوفة العوامل وحاجة
+
+37
+00:03:13,360 --> 00:03:17,720
+اسمها مصفوفة المجهول وحاجة اسمها مصفوفة الحدود
+
+38
+00:03:17,720 --> 00:03:24,440
+المطلقة. المطلقة. فخلينا احنا نيجي اللي هو نستخدم
+
+39
+00:03:24,440 --> 00:03:30,340
+المصفوفات في اللي هو إيجاد الحلول. اطلعوا من دي الآن
+
+40
+00:03:30,340 --> 00:03:35,100
+أول شيء بنجي بنطلع كيف بدنا نوجد اللي هي المصوفة
+
+41
+00:03:35,100 --> 00:03:40,280
+اللي هي تبعت اللي هي مين مصفوفة عوامل اللي عندي
+
+42
+00:03:40,280 --> 00:03:47,240
+خليني أوجد هذه المصوفة. كيف نوجد مصفوفة العوامل هي
+
+43
+00:03:47,240 --> 00:03:52,320
+مصفوفة العوامل. طبعا مصفوفة العوامل هيكون درجتها اللي
+
+44
+00:03:52,320 --> 00:03:57,250
+هو عدد المجهول اثنين وعدد المعادلات اثنين. يعني عدد
+
+45
+00:03:57,250 --> 00:04:00,870
+المجهول ضرب عدد المعادلات يعني عبارة عن مصفوفة
+
+46
+00:04:00,870 --> 00:04:05,170
+مربعة اثنين في اثنين. كيف بنجيبها؟ بنجعل المجهول
+
+47
+00:04:05,170 --> 00:04:10,710
+الأول معامله اثنين هيّه. المجهول الثاني x اثنين
+
+48
+00:04:10,710 --> 00:04:14,190
+معامله ثلاثة هيّه. خلصنا من المعادلة الأولى نجي
+
+49
+00:04:14,190 --> 00:04:18,810
+للمعادلة الثانية. المعامل واحد هنا، المعامل الثاني
+
+50
+00:04:18,810 --> 00:04:22,910
+إيش؟ سالب اثنين. صارت هذه المصفوفة جاهزة هي مصفوفة
+
+51
+00:04:22,910 --> 00:04:27,470
+العوامل أو عوامل اللي هي من المجهول اللي في
+
+52
+00:04:27,470 --> 00:04:32,190
+المعادلة. الآن المصفوفة الثانية هي مصفوفة عمود عمود
+
+53
+00:04:32,190 --> 00:04:36,610
+هيكون اللي هو درجتها عدد أسطورها بعدد المجهول
+
+54
+00:04:36,610 --> 00:04:41,630
+وطبعا عمود واحد فبتصير عندي مجهولين يعني
+
+55
+00:04:41,630 --> 00:04:46,560
+درجتها اثنين في واحد. الآن هذا بنسميها مصفوفة
+
+56
+00:04:46,560 --> 00:04:50,980
+المجاهيل اللي احنا بنبحث عنها اللي بدنا نوجد قيمة
+
+57
+00:04:50,980 --> 00:04:55,920
+X1 و X2 تساوي إيش؟ تساوي اللي هي مصفوفة العمود
+
+58
+00:04:55,920 --> 00:05:00,960
+المكونة من اللي هو الحد المطلق للمعادلة الأولى و
+
+59
+00:05:00,960 --> 00:05:04,940
+الحد المطلق للمعادلة الثانية يعني خمسة وسالب واحد
+
+60
+00:05:05,450 --> 00:05:10,550
+الآن هذه المصفوفة بعد ما كتبناها على صورة a مصفوفة
+
+61
+00:05:10,550 --> 00:05:14,450
+في x مصفوفة بيساوي بي مصفوفة صارت على صورة مصفوفة
+
+62
+00:05:14,450 --> 00:05:20,090
+ax بتساوي ax بتساوي b. الآن هذه بيكون نقدر نحلها و
+
+63
+00:05:20,090 --> 00:05:25,970
+نوجد حلها إذا كان هذا الـ a inverse له موجود. إذا
+
+64
+00:05:25,970 --> 00:05:29,530
+الـ A inverse فيه موجود هين بنقدر نحلها عن طريق الـ
+
+65
+00:05:29,530 --> 00:05:33,990
+matrices. مش موجود ما أقدرش أحكي عن الحلول بطريقة الـ
+
+66
+00:05:33,990 --> 00:05:38,090
+matrices. ده نشوف كده الآن إذا كان الـ A inverse
+
+67
+00:05:38,090 --> 00:05:43,150
+موجود معناته أنه بقدر أضرب هنا في A inverse وهنا
+
+68
+00:05:43,150 --> 00:05:46,490
+في A inverse. لما أضرب الـ A inverse في الـ A بتطلع
+
+69
+00:05:46,490 --> 00:05:50,210
+المصفوفة اللي هو الـ identity. الـ identity لما تضرب
+
+70
+00:05:50,210 --> 00:05:54,870
+في X هش بتطلع عندي X. وهنا اللي ضربناه a inverse
+
+71
+00:05:54,870 --> 00:05:58,550
+بيصير a inverse في b بيصير x اللي هي مصفوفة
+
+72
+00:05:58,550 --> 00:06:03,370
+المجهول بتساوي الـ a inverse لمصفوفة اللي هي
+
+73
+00:06:03,370 --> 00:06:09,290
+العوامل مضروبة في b اللي هي مصفوفة اللي هي الحد
+
+74
+00:06:09,290 --> 00:06:13,430
+المطلق. يعني وكأنه من الآن وطالع الأمر سهل إيش
+
+75
+00:06:13,430 --> 00:06:18,830
+بنسوي؟ بنجي بنحدد مصفوفة المجهول أي مصفوفة عوامل
+
+76
+00:06:18,830 --> 00:06:23,530
+المجهول اللي هي الحد هذا والحد هذا والحد هذا والحد
+
+77
+00:06:23,530 --> 00:06:29,920
+هذا اللي هي عوامل المجهول. مصفوفة العوامل ضرب مصفوفة
+
+78
+00:06:29,920 --> 00:06:33,820
+المجهول بيساوي مصفوفة الحدود المطلقة زي ما احنا
+
+79
+00:06:33,820 --> 00:06:38,500
+شايفين. بعد هيك بنجي بنقول هذه المصفوفة بنجيب لها
+
+80
+00:06:38,500 --> 00:06:42,700
+الـ A inverse بنضربها في هذه بتطلع اللي هي X واحد و
+
+81
+00:06:42,700 --> 00:06:47,500
+X اثنين. يعني بتطلع X إيش بتساوي؟ A inverse في B. خلي
+
+82
+00:06:47,500 --> 00:06:53,060
+نشوف هذا الآن الكلام عمليا في اللي هو الـ
+
+83
+00:06:54,530 --> 00:06:58,670
+صار عندي اللي هي الـ matrix form أو صورة التحويل
+
+84
+00:06:58,670 --> 00:07:03,830
+المعادلات الخطية إلى صورة مصفوفات هي الـ a وهي الـ x
+
+85
+00:07:03,830 --> 00:07:09,550
+وهي مين الـ b. قلنا الحل هيكون x هذا كله بيساوي a
+
+86
+00:07:09,550 --> 00:07:13,650
+inverse في الـ b. هنا نوجد الـ a inverse هي الـ a هيها
+
+87
+00:07:13,650 --> 00:07:18,560
+قدامنا. عشان نجد الـ a inverse بلزم من المحدد زي ما
+
+88
+00:07:18,560 --> 00:07:21,860
+أنتم عارفين اثنين في ناقص اثنين بتطلع ناقص أربعة
+
+89
+00:07:21,860 --> 00:07:25,900
+ناقص أربعة ناقص أربعة إيش بيساوي؟ ناقص أربعة آسف
+
+90
+00:07:25,900 --> 00:07:29,660
+ناقص ثلاثة بتطلع ناقص سبعة. إذا قيمة المحدد له
+
+91
+00:07:29,660 --> 00:07:34,740
+سالب سبعة. إذا الآن الـ a inverse سهل إيجاده بس بيجي
+
+92
+00:07:34,740 --> 00:07:38,600
+بنغير هذا العنصر مكان هذا وهذا العنصر وهذا
+
+93
+00:07:38,600 --> 00:07:44,380
+بنعمله سالب وبنضربهم في مين؟ في مقلوب اللي هي مين؟
+
+94
+00:07:44,380 --> 00:07:48,440
+اللي هي سالب سبعة يعني بنضربهم في واحد على اللي
+
+95
+00:07:48,440 --> 00:07:54,020
+هي واحد على السبعة. زي ما قلنا إيش عندنا؟ صار عندنا الـ a
+
+96
+00:07:54,020 --> 00:07:58,810
+inverse إيش بيساوي؟ الـ a inverse هيّه ناقص واحد على
+
+97
+00:07:58,810 --> 00:08:03,150
+سبعة في قيمة المصفوفة هذه لما بدلنا هذا مكان هذا
+
+98
+00:08:03,150 --> 00:08:07,690
+وجينا غيرنا إشارة هذول فصار عندي سبعة في اثنين في
+
+99
+00:08:07,690 --> 00:08:12,470
+ثلاثة في واحد في ناقص اثنين. لما دخلنا الناقص جوا صار
+
+100
+00:08:12,470 --> 00:08:15,390
+عندي الآن x إيش بتساوي؟ بتساوي الـ a inverse هنا
+
+101
+00:08:15,390 --> 00:08:19,650
+وجدناها هيها كلها مضروبة في مين؟ في الـ B. مين الـ
+
+102
+00:08:19,650 --> 00:08:23,150
+B؟ اللي هي المصفوفة هذه هي الـ B. لأن ضربنا هذه
+
+103
+00:08:23,150 --> 00:08:25,370
+المصفوفة في هذه المصفوفة زي ما بتعرفوا الضرب
+
+104
+00:08:25,370 --> 00:08:29,370
+العادي بيطلع عندي اللي هي القيمة هذه المصفوفة اللي
+
+105
+00:08:29,370 --> 00:08:33,030
+طلعت عندي. لأن هذه المصفوفة لما نضرب السبعة فيها
+
+106
+00:08:33,030 --> 00:08:37,460
+بيطلع عندي 1 1 1. إذا X طلعت عدد D اللي هي المصفوفة
+
+107
+00:08:37,460 --> 00:08:42,160
+هذه. X واحد X اثنين مش حتساوي واحد واحد يعني X واحد
+
+108
+00:08:42,160 --> 00:08:46,260
+طلعت واحد و X اثنين طلعت واحد. و X اثنين طلعت واحد
+
+109
+00:08:46,260 --> 00:08:47,100
+و X اثنين طلعت واحد. و X اثنين طلعت واحد. و X اثنين
+
+110
+00:08:47,100 --> 00:08:47,180
+طلعت واحد. و X اثنين طلعت واحد. و X اثنين طلعت واحد
+
+111
+00:08:47,180 --> 00:08:48,480
+و X اثنين طلعت واحد. و X اثنين طلعت واحد. و X اثنين
+
+112
+00:08:48,480 --> 00:08:51,360
+طلعت واحد. و X اثنين طلعت واحد. و X اثنين طلعت واحد
+
+113
+00:08:51,360 --> 00:08:55,240
+و X اثنين طلعت واحد. و X اثنين طلعت واحد. و X اثنين
+
+114
+00:08:55,240 --> 00:09:01,320
+طلعت واحد. و X اثنين طلعت واحد. الآن المصفوفة اللي
+
+115
+00:09:01,320 --> 00:09:05,220
+قبل بشوية اللي هي المعادلتين الخطيتين طلع عندهم
+
+116
+00:09:05,220 --> 00:09:10,860
+الحل الوحيد اللي هو كان X1 بيساوي واحد و X2 بيساوي
+
+117
+00:09:10,860 --> 00:09:14,780
+واحد. ذاك حل وحيد. الآن ممكن المصفوفة اللي هي
+
+118
+00:09:14,780 --> 00:09:19,280
+معادلتين خطيتين يطلع لهم عدد لا نهائي من الحلول متى
+
+119
+00:09:19,280 --> 00:09:22,580
+بيطلع لهم عدد لا نهائي من الحلول زي المعادلة هذه
+
+120
+00:09:22,580 --> 00:09:28,040
+وبنسمي الـ equations are consistent. ماشي لكن لهم
+
+121
+00:09:28,040 --> 00:09:32,800
+infinite number of solutions. ليش؟ لاحظ إن هذه 2x1
+
+122
+00:09:32,800 --> 00:09:38,240
+زي 3x2 بيساوي 5 هذه بيساوي 4x1 زي 6x2 بيساوي 10
+
+123
+00:09:38,240 --> 00:09:42,580
+لاحظ هذه هي نفسها اللي فوق بس مضروبة هذه في إيه؟
+
+124
+00:09:42,580 --> 00:09:45,720
+في 2. يعني أنا ما عنديش معادلتين في الواقع أنا عندي
+
+125
+00:09:45,720 --> 00:09:49,500
+معادلة واحدة. وما دام عندي معادلة واحدة يعني مجهولين 
+
+126
+00:09:49,500 --> 00:09:52,840
+اللي هو معادلة واحدة في المجهولين عشان هيك لو
+
+127
+00:09:52,840 --> 00:09:57,520
+أعطيته X1 مثلا صفر تطلع X2، X2 بيساوي خمسة على تلاتة
+
+128
+00:09:57,520 --> 00:10:03,180
+لو أعطيته X1 مثلا بنص بيصير هادي عبارة عن واحد
+
+129
+00:10:03,180 --> 00:10:07,840
+بتنجلهانة بيصير أربعة X2 بيساوي أربعة على تلاتة بتعطي
+
+130
+00:10:07,840 --> 00:10:11,800
+X1  جد ما بدك من القيام هيطلعلك عدد لانهائي، إذا من
+
+131
+00:10:11,800 --> 00:10:17,000
+إيش من الحلول، بس للمعرفة بدي تعرفه إنه في النظام
+
+132
+00:10:17,000 --> 00:10:21,040
+الأولاني لما كانت A inverse موجودة اللي هو كان
+
+133
+00:10:21,040 --> 00:10:25,760
+عندي one solution، الآن لما inverse مش موجودة لإيه
+
+134
+00:10:25,760 --> 00:10:29,780
+inverse، لإنه ليش مش موجودة لو جيت أخدت اللي هي
+
+135
+00:10:29,780 --> 00:10:34,120
+المصفوفة تبعت العوامل هيطلع تنين وتلاتة أو أربعة 
+
+136
+00:10:34,120 --> 00:10:40,420
+أو ستة، هذه ليست لديها inverse، لما
+
+137
+00:10:40,420 --> 00:10:45,360
+يكون لديها inverse، يعني إذا لم يكن لديها inverse 
+
+138
+00:10:45,360 --> 00:10:45,780
+يعني إذا لم يكن لديها inverse 
+
+139
+00:10:45,780 --> 00:10:46,180
+يعني إذا لم أكن لديها inverse 
+
+140
+00:10:46,180 --> 00:10:46,640
+أكن لديها inverse 
+
+141
+00:10:46,640 --> 00:10:46,740
+لديها inverse
+
+142
+00:10:46,740 --> 00:10:46,780
+inverse
+
+143
+00:10:46,780 --> 00:10:50,260
+يعني إذا لم أكن لديها inverse 
+
+144
+00:10:50,260 --> 00:10:53,820
+لديها
+
+145
+00:10:55,630 --> 00:11:01,690
+لكن لو جينا لحالة أخرى ممكن اللي هو في حالة اللي
+
+146
+00:11:01,690 --> 00:11:05,210
+هي برضه يطلع ال a-inverse does not exist تطلع عندي
+
+147
+00:11:05,210 --> 00:11:11,970
+مافيش solution، لنين للمعادلات الأنية، لاحظوا في
+
+148
+00:11:11,970 --> 00:11:18,670
+المعادلة التانية 2x1 زي 3x2 بساوة 5، 4x1 زي 6x2
+
+149
+00:11:18,670 --> 00:11:26,470
+بساوة 9، الآن هذه المعادلة مافيش إلها إيش المعادلتين
+
+150
+00:11:26,470 --> 00:11:33,730
+مافيش إلها حلول، لو لاحظته تجي ال a inverse اللي هي
+
+151
+00:11:33,730 --> 00:11:40,950
+المعكوس الضربي لمصفوفة العوامل 2×6 ب 12 ناقص 12 صفر
+
+152
+00:11:40,950 --> 00:11:44,310
+إذا ال a inverse does not exist، does not exist، لكن
+
+153
+00:11:44,310 --> 00:11:48,950
+مش زي اللي فوق لو طلعنا على هذه هتكون هذه دربناها
+
+154
+00:11:48,950 --> 00:11:52,790
+وكأنه في اتنين بساوية دي اشي هنا تسعة، فالآن هذه
+
+155
+00:11:52,790 --> 00:11:57,090
+تسعة مش عشرة عشان هيك لو اجيت اعطيت اللي هو ضربت
+
+156
+00:11:57,090 --> 00:12:02,050
+هذه مثلا في اتنين، لو ضربت هذه في اتنين وجيت حلات
+
+157
+00:12:02,050 --> 00:12:05,090
+مع بعض المعادلة إنه ماعرفش نحلم بال matrices زي ما
+
+158
+00:12:05,090 --> 00:12:08,470
+قلنا وضربنا هدف اتنين بيصير أربع اكس واحد ستة اكس
+
+159
+00:12:08,470 --> 00:12:12,790
+اتنين بيساوي عشرة، و جيت طرحت مع بعض طرحت من بعض
+
+160
+00:12:12,790 --> 00:12:17,270
+هيطلع هذا صفر هنا صفر هيروح مع بعض، جرب لحالك و
+
+161
+00:12:17,270 --> 00:12:21,670
+هيطلع هنا عشرة ناقص تسعة اللي هي عبارة عن واحد
+
+162
+00:12:21,670 --> 00:12:25,390
+بيساوي اللي طلع هنا صفر، يعني صفر بيطلع بيساوي واحد
+
+163
+00:12:25,390 --> 00:12:28,670
+أو بيساوي سالب واحد وهذا مستحيل، عشان هيك بنسميه
+
+164
+00:12:28,670 --> 00:12:34,380
+inconsistent، إذا للعلم يا شباب ويا بنات إنه في حالة
+
+165
+00:12:34,380 --> 00:12:37,240
+ال a inverse does not exist احنا ما نقدر نحل
+
+166
+00:12:37,240 --> 00:12:45,160
+بواسطة
+
+167
+00:12:45,160 --> 00:12:49,090
+ال matrices لأنها مش هتظبط، لكن عندما تكون a inverse
+
+168
+00:12:49,090 --> 00:12:52,390
+لا توجد عندي حالتين حالة بس، الحالة الأولى اللي هي
+
+169
+00:12:52,390 --> 00:12:55,470
+عندي infinite number of solutions يعني عدد لانهاية
+
+170
+00:12:55,470 --> 00:12:59,790
+من الحلول، الحالة التانية has no solution يعني
+
+171
+00:12:59,790 --> 00:13:04,330
+للمعلومات المعادلتين الأنية بيكون لها unique
+
+172
+00:13:04,330 --> 00:13:08,090
+solution اللي هو حل وحيد وهذا الحالة اللي احنا
+
+173
+00:13:08,090 --> 00:13:11,310
+بنعرف نحلها لإنه بيكون ال a inverse exist لإنه
+
+174
+00:13:11,310 --> 00:13:15,930
+determinant بتطلع بساويش صفر، الحالة الثانية a
+
+175
+00:13:15,930 --> 00:13:19,150
+inverse does not exist بيكون يا إما عدد لانهائي من
+
+176
+00:13:19,150 --> 00:13:23,730
+الحلول يا إما مالهاش حلول، وهذه طبعا زي ما قلنا
+
+177
+00:13:23,730 --> 00:13:27,530
+احنا ما بنعرف نحلها بواسطة أو بتنحلش بواسطة ال
+
+178
+00:13:27,530 --> 00:13:31,230
+matrices وبتكون حالة أصلا سهلة الحل بالطرق العادية
+
+179
+00:13:31,230 --> 00:13:38,050
+الآن يا جماعة بدنا نحكي عن اللي هو ال system of
+
+180
+00:13:38,050 --> 00:13:42,610
+three equations in three variables يعني عبارة عن
+
+181
+00:13:42,610 --> 00:13:50,430
+نظام من المعادلات الأنية عدد المعادلات تلاتة وعدد
+
+182
+00:13:50,430 --> 00:13:55,910
+المجاهيل تلاتة، بدنا نودد اللي هو الحل عن طريق اللي
+
+183
+00:13:55,910 --> 00:13:59,610
+هو مين ال matrices، وهنا بتصير خلينا نقول أهمية ال
+
+184
+00:13:59,610 --> 00:14:04,730
+matrices في الحل، كل ما كثرت عدد المجاهيل وكل ما
+
+185
+00:14:04,730 --> 00:14:08,890
+كثرت عدد اللي هي المعادلات المقابلة بيصير العملية
+
+186
+00:14:08,890 --> 00:14:14,730
+اللي اتعلمناها في الاعدادية صعبة اللي هو ان نحلها
+
+187
+00:14:14,730 --> 00:14:18,850
+التلاتة مع بعض بيصير اللي هو موضوع الحل بواسطة
+
+188
+00:14:18,850 --> 00:14:24,870
+اللي هو الان زي ما قلنا عندي اللي هو هذه صارت عندي
+
+189
+00:14:24,870 --> 00:14:28,610
+تلت معادلات في تلت مجهيل، خلينا نشوف كيف بده نحلها
+
+190
+00:14:30,040 --> 00:14:35,180
+نفس الحل بالنسبة للمجهولين بالظبط، بنيجي بنحدد
+
+191
+00:14:35,180 --> 00:14:39,040
+مصفوفة العوامل، مصفوفة العوامل اسمها ايه؟ ايش
+
+192
+00:14:39,040 --> 00:14:42,860
+هتكون؟ اللي هي واحد سالب اتنين واحد، هي واحد سالب
+
+193
+00:14:42,860 --> 00:14:47,180
+اتنين واحد، التانية اتنين واحد سالب واحد، اتنين واحد
+
+194
+00:14:47,180 --> 00:14:50,640
+سالب واحد، اللي بعدها تلاتة سالب واحد اتنين تلاتة
+
+195
+00:14:50,640 --> 00:14:54,100
+سالب واحد ايش اتنين، هذه مصفوفة العوامل، نيجي
+
+196
+00:14:54,100 --> 00:14:58,990
+لمصفوفة المجاهيل اللي قلنا بنرسم عمود، هذه المجهول
+
+197
+00:14:58,990 --> 00:15:02,190
+الأول طبعا كنا بنكون احنا مرتبين ايش المعادلات
+
+198
+00:15:02,190 --> 00:15:05,330
+بالظبط، هذا المجهول الأول المجهول التاني المجهول
+
+199
+00:15:05,330 --> 00:15:08,190
+التالت، المجهول الأول المجهول التاني المجهول التالت
+
+200
+00:15:08,190 --> 00:15:10,990
+المجهول الأول المجهول التاني المجهول التالت وهنا
+
+201
+00:15:10,990 --> 00:15:14,030
+الحدود المطلقة بعد ما نرتبهم، ديروا بالكم إذا أول
+
+202
+00:15:14,030 --> 00:15:19,470
+شغلة بنعملها هي ترتيب المعادلات حسب مين المجهول
+
+203
+00:15:19,470 --> 00:15:22,590
+المجهول الأول المجهول التاني المجهول التالت وعلى
+
+204
+00:15:22,590 --> 00:15:25,570
+الجهة التانية لحد المطلق ونفسي الأشي في التاني و
+
+205
+00:15:25,570 --> 00:15:28,450
+نفسي الأشي في التالتة وإلا بيكون كل شغلنا مش
+
+206
+00:15:28,450 --> 00:15:33,790
+مظبوط، طيب هاي بعد مرتبناها نحطينا المصوفة العوامل
+
+207
+00:15:33,790 --> 00:15:38,230
+المعادلة الأخيرة تلاتة سلب واحد اتنين هذه زي ما
+
+208
+00:15:38,230 --> 00:15:42,550
+قولنا ايش مالها مصوفة المجاهيل بنفس الترتيب الأفقي
+
+209
+00:15:42,550 --> 00:15:46,190
+X واحد X اتنين X تلاتة بنخلي ايش بس على صورة ايش
+
+210
+00:15:46,190 --> 00:15:49,560
+عمود، وبنجي على العمود اللي على جباله بالظبط بنفس
+
+211
+00:15:49,560 --> 00:15:53,160
+الترتيب تلاتة وخمسة وإياش واطمعاش، صارت المعادلة
+
+212
+00:15:53,160 --> 00:15:57,780
+الآن جاهزة على صورة Ax بتساوي إياش B، هذه A وهذه X
+
+213
+00:15:57,780 --> 00:16:02,720
+وهذه B، إذن الحل وأنا مغمض عينيا بتطلع على ال A إذا
+
+214
+00:16:02,720 --> 00:16:06,360
+كانت ال A، A اللي هي inverse على طول بيصير ال X
+
+215
+00:16:06,360 --> 00:16:11,780
+بتساوي A inverse في B، هو الحل، X بتساوي A inverse في
+
+216
+00:16:11,780 --> 00:16:16,360
+B، بضل علي بس أن أوجد ال A inverse زي ما أوجدناها
+
+217
+00:16:16,360 --> 00:16:22,300
+المرة الماضية في المحاضرة السابقة وبنضربها في B
+
+218
+00:16:22,300 --> 00:16:27,380
+بتطلع لي اللي هي مصفوفة من الأعداد عجبال مصوفة
+
+219
+00:16:27,380 --> 00:16:30,500
+المجاهيل اللي بيكون زي ما عملنا قبل بشوية بالظبط
+
+220
+00:16:30,500 --> 00:16:35,430
+بتطلع اللي هو الحق، إذا زي ما قلنا X هتطلع بتساوي A
+
+221
+00:16:35,430 --> 00:16:39,390
+inverse في B، فال A inverse هي ال inverse لهذه وال
+
+222
+00:16:39,390 --> 00:16:44,270
+B هيها B اللي هي تلاتة أو خمسة أو اتناش مظبوط
+
+223
+00:16:44,270 --> 00:16:47,370
+فبيصير عند هذه اللي هي تلاتة أو خمسة أو اتناش و
+
+224
+00:16:47,370 --> 00:16:50,850
+بنضرب ال A inverse فيها اللي بتطلع ال X اللي هي ال
+
+225
+00:16:50,850 --> 00:16:54,990
+X واحد وال X اتنين اللي هي ال X تلاتة لنشوف كيف
+
+226
+00:16:54,990 --> 00:16:58,980
+اللي هو بدنا نطلعه، إذا زي ما اتعلمنا المرة الماضية
+
+227
+00:16:58,980 --> 00:17:01,380
+بنوجد الـ A-Inverse، الـ A-Inverse بنوجد الـ
+
+228
+00:17:01,380 --> 00:17:05,060
+determinant للـ A باللي جيله عبارة عن عشرة بكون
+
+229
+00:17:05,060 --> 00:17:08,760
+واحد على عشرة في الـ Adjoint بنكون أوجدنا الـ
+
+230
+00:17:08,760 --> 00:17:12,420
+Adjoint وجهزنا زي ما اتعلمتوا كيف توجدوه، الآن طلع
+
+231
+00:17:12,420 --> 00:17:15,690
+عندي الـ A-Inverse بتطلع ال X اللي هي عبارة عن مين
+
+232
+00:17:15,690 --> 00:17:18,550
+ال X، X واحد X اتنين X تلاتة، أيش بتساوي زي ما قلنا
+
+233
+00:17:18,550 --> 00:17:23,490
+A inverse في B، هي ال A inverse وهي مين المصفوفة B
+
+234
+00:17:23,490 --> 00:17:27,070
+اللي هي مصفوفة الحدود المطلقة بنضرب هادي الآن في
+
+235
+00:17:27,070 --> 00:17:31,170
+هادي، بطلع عندي اللي هو تلاتين عشرة عشرين ونضرب في
+
+236
+00:17:31,170 --> 00:17:34,130
+واحدة على العشر اللي برا هذا، بطلع عندي تلاتة واحد
+
+237
+00:17:34,130 --> 00:17:39,300
+اتنين فبكون عندي X واحد بيساوي تلاتة، X2 بيساوي واحد
+
+238
+00:17:39,300 --> 00:17:44,220
+وX3 بيساوي ايش بيساوي اتنين، إذا يا شباب ويا بنات
+
+239
+00:17:44,220 --> 00:17:48,980
+عندي مادامة ال A inverse موجودة إذا الحل بيكون
+
+240
+00:17:48,980 --> 00:17:54,540
+وحيد وهي الحل طلع عندي في هذه الحالة X1 ثلاثة وX2
+
+241
+00:17:54,540 --> 00:18:00,920
+واحد وX3 اتنين، هذه هي حلول المعادلات أو ال system
+
+242
+00:18:00,920 --> 00:18:05,200
+of equations اللي عددهم جديش يا جماعة اللي عددهم
+
+243
+00:18:05,200 --> 00:18:10,930
+تلت معادلات بتلت مجهيل، الآن يا جماعة خلصنا المحاضرة
+
+244
+00:18:10,930 --> 00:18:16,530
+الثالثة هي محاضرة بسيطة واضحة، مطلوب منكم تحلوا اللي
+
+245
+00:18:16,530 --> 00:18:18,810
+هو عندي solve the following equations using
+
+246
+00:18:18,810 --> 00:18:27,310
+inverse matrix، بدي تحلوا A وD بس، A وD اجبولياهم
+
+247
+00:18:27,310 --> 00:18:32,170
+اللي هو محلولات المرة القادمة زي ما بنعمل في كل
+
+248
+00:18:32,170 --> 00:18:36,810
+واجب، والسلام عليكم ورحمة الله وبركاته وإلى لقاء
+
+249
+00:18:36,810 --> 00:18:37,350
+آخر
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a3fd217848b0bf37c16459ed5b5f29a97a3c005
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_postprocess.srt
@@ -0,0 +1,996 @@
+1
+00:00:00,000 --> 00:00:06,040
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثالثة بعد
+
+2
+00:00:06,040 --> 00:00:14,360
+حالة التوارق لمساق رياضيات منفاصلة لطلاب وطالبات
+
+3
+00:00:14,360 --> 00:00:18,880
+الجامعة الإسلامية كلية technology المعلومات في قسم
+
+4
+00:00:18,880 --> 00:00:25,940
+الحوصفة المتنقلة تحدثنا المرة الماضية عن إيجاد
+
+5
+00:00:25,940 --> 00:00:30,960
+المعكوس الضربي للمصفوفةاليوم بدنا نوظف هذه
+
+6
+00:00:30,960 --> 00:00:40,440
+المعلومات في حل system of linear equations يعني
+
+7
+00:00:40,440 --> 00:00:47,360
+بدنا نوظف المعلومة في حل معادلات آنية معادلتين
+
+8
+00:00:47,360 --> 00:00:54,100
+آنيتين بمجهولين أو ثلاث معادلات آنية بثلاثة مجاهين
+
+9
+00:00:54,860 --> 00:00:59,280
+لو جينا اتطلعنا في البداية اللي كان عندنا معادلة
+
+10
+00:00:59,280 --> 00:01:03,820
+خطية اللي هي ax بتساوي b هذه المعادلة الخطية
+
+11
+00:01:03,820 --> 00:01:08,660
+وفرضنا ان ال a لا تساوي سفر وطلب منها طبعا a عبارة
+
+12
+00:01:08,660 --> 00:01:12,580
+عن عدد و b عبارة عن عدد و x عبارة عن مجهول طبعا
+
+13
+00:01:12,580 --> 00:01:16,040
+هذه زي ما انتوا عارفين زي ما أخدناها سابق في
+
+14
+00:01:16,040 --> 00:01:22,060
+الاعدادية انه بنجسم الجهتين على ال a بتطلع عندي x
+
+15
+00:01:22,060 --> 00:01:28,300
+بتساوي b على aأو بمعنى آخر x بتساوي a inverse في b
+
+16
+00:01:28,300 --> 00:01:34,640
+حيث a لا تساوي صفر هذه طبعا معلومات سابقة بس عشان
+
+17
+00:01:34,640 --> 00:01:38,960
+نعرف ان في عندنا هذه معادلة خطية في مجهول واحد
+
+18
+00:01:38,960 --> 00:01:45,520
+الان لو كان في عندنا معاطينا معادلتين خطيتين يعني
+
+19
+00:01:45,520 --> 00:01:50,020
+درجة اللي هو المتغير هذا واحد ودرجة المتغير هذا
+
+20
+00:01:50,020 --> 00:01:54,850
+واحد برضه الان لو كان عندنا هذه معادلةخطية في
+
+21
+00:01:54,850 --> 00:01:57,990
+مجهولين هذه المجهول الأول وهذه المجهول الثاني
+
+22
+00:01:57,990 --> 00:02:02,030
+والمعادلة الثانية برضه معادلة خطية في نفس
+
+23
+00:02:02,030 --> 00:02:07,550
+المجهولين اللي فوق بسيرة أنه الأن إمكانية نحكي عن
+
+24
+00:02:07,550 --> 00:02:12,930
+الحلول المشتركة يعني بمعنى آخر إيجاد X1 و X2 اللي
+
+25
+00:02:12,930 --> 00:02:17,850
+بتحقق المعادلة الأولى و بتحقق المعادلة الثانية في
+
+26
+00:02:17,850 --> 00:02:23,030
+نفس الوقتطبعا زمان احنا كنا في الاعدادية نجي نضرب
+
+27
+00:02:23,030 --> 00:02:30,270
+نوحد اللي هو معامل اللي هو ال X1 هنا و X1 هنا و
+
+28
+00:02:30,270 --> 00:02:33,890
+بعدين نطرح المعادلتين من بعض بطلع عنده قيمة X2 و
+
+29
+00:02:33,890 --> 00:02:39,510
+بعدين نعوض عن X1 بطلع عند X1 بنكون جيبنا قيمة X1 و
+
+30
+00:02:39,510 --> 00:02:43,390
+قيمة X2 طبعا مش هذا اللي بدنا يالي يوم اليوم بدنا
+
+31
+00:02:43,390 --> 00:02:47,050
+نوظفاللي هو معلوماتنا في ال matrices أو في
+
+32
+00:02:47,050 --> 00:02:52,710
+المصففات لحل اللي هو نظام من اللي هو المعادلات
+
+33
+00:02:52,710 --> 00:02:57,970
+الآنية في مجهولين نشوف هذه اللي عندنا الآن هذا
+
+34
+00:02:57,970 --> 00:03:00,930
+النظام بدي أحله عن طريق ال matrices نشوف إيش بدي
+
+35
+00:03:00,930 --> 00:03:07,580
+أسويفي عندنا اللي هو أول شغلة اللي هي بدنا اللي هو
+
+36
+00:03:07,580 --> 00:03:13,360
+نحكي عن حاجة اسمها اللي هي مصفوفة العوامل وحاجة
+
+37
+00:03:13,360 --> 00:03:17,720
+اسمها مصفوفة المجهيل وحاجة اسمها مصفوفة الحدود
+
+38
+00:03:17,720 --> 00:03:24,440
+المطلقة المطلقة فخلينا احنا نيجي اللي هو نستخدم
+
+39
+00:03:24,440 --> 00:03:30,340
+المصفوفات في اللي هو إيجاد الحلول اطلعوا من ديالان
+
+40
+00:03:30,340 --> 00:03:35,100
+اول اشي بنجي بنطلع كيف بدنا نوجد اللى هى المصوفة
+
+41
+00:03:35,100 --> 00:03:40,280
+اللى هى تبعت اللى هى مين مصوفة عوامل اللى عندى
+
+42
+00:03:40,280 --> 00:03:47,240
+خلينى اوجد هذه المصوفة كيف نوجد مصوفة العوامل هى
+
+43
+00:03:47,240 --> 00:03:52,320
+مصوفة العوامل طبعا مصوفة العوامل هيكون درجتها اللى
+
+44
+00:03:52,320 --> 00:03:57,250
+هو عدد المجهيل اتنينوعدد المعادلات اتنين يعني عدد
+
+45
+00:03:57,250 --> 00:04:00,870
+المجهول ضرب عدد المعادلات يعني عبارة عن مصفوفة
+
+46
+00:04:00,870 --> 00:04:05,170
+مربعة اتنين في اتنين كيف بنجيبها بنجعل المجهول
+
+47
+00:04:05,170 --> 00:04:10,710
+الاول معامله اتنين هيه المجهول التاني x اتنين
+
+48
+00:04:10,710 --> 00:04:14,190
+معامله تلاتة هيه خلصنا من المعادلة الاولى نجي
+
+49
+00:04:14,190 --> 00:04:18,810
+للمعادلة التانيةالمعامل واحد هنا المعامل التاني
+
+50
+00:04:18,810 --> 00:04:22,910
+ايش سالب اتنين صارت هذه المصفوفة جاهزة هي مصفوفة
+
+51
+00:04:22,910 --> 00:04:27,470
+العوامل او عوامل اللي هي من المجهيل اللي في
+
+52
+00:04:27,470 --> 00:04:32,190
+المعادلة الآن المصفوفة التانية هي مصفوفة عمود عمود
+
+53
+00:04:32,190 --> 00:04:36,610
+هيكون اللي هو درجتها عدد أسطورها بعدد المجهيل
+
+54
+00:04:36,610 --> 00:04:41,630
+وطبعا عمود واحد فبتصير عندي مجهول مجهولين يعني
+
+55
+00:04:41,630 --> 00:04:46,560
+درجتها اتنين في واحدالان هذا بنسميها مصفوفة
+
+56
+00:04:46,560 --> 00:04:50,980
+المجاهيل اللي احنا بنبحث عنها اللي بدنا نوجد قيمة
+
+57
+00:04:50,980 --> 00:04:55,920
+X1 و X2 تساوي ايش؟ تساوي اللي هي مصفوفة العمود
+
+58
+00:04:55,920 --> 00:05:00,960
+المكونة منه اللي هو الحد المطلق للمعادلة الأولى و
+
+59
+00:05:00,960 --> 00:05:04,940
+الحد المطلق للمعادلة الثانية يعني خمسة و سالب واحد
+
+60
+00:05:05,450 --> 00:05:10,550
+الان هذه المصفوفة بعد ما كتبناها على صورة a مصفوفة
+
+61
+00:05:10,550 --> 00:05:14,450
+في x مصفوفة بيساوي بي مصفوفة صارت على صورة مصفوفة
+
+62
+00:05:14,450 --> 00:05:20,090
+ax بتساوي ax بتساوي b الان هذه بيكون نقدر نحلها و
+
+63
+00:05:20,090 --> 00:05:25,970
+نودد حالها إذا كان هذا ال a inverse له موجودإذا
+
+64
+00:05:25,970 --> 00:05:29,530
+الـ A inverse فيه موجود هين بنقدر نحلها عن طريق ال
+
+65
+00:05:29,530 --> 00:05:33,990
+matrices مش موجود مقدرش أحكي عن الحلول بطريقة ال
+
+66
+00:05:33,990 --> 00:05:38,090
+matrices ده نشوف كده الان إذا كان ال A inverse
+
+67
+00:05:38,090 --> 00:05:43,150
+موجود معناته أنه بقدر أضرب هنا في A inverse و هنا
+
+68
+00:05:43,150 --> 00:05:46,490
+في A inverse لما أضرب ال A inverse في ال A بتطلع
+
+69
+00:05:46,490 --> 00:05:50,210
+المصفوف اللي هو ال identity ال identity لما تضرب
+
+70
+00:05:50,210 --> 00:05:54,870
+في X هش بتطلع عنده Xوهنا اللي ضربناه a inverse
+
+71
+00:05:54,870 --> 00:05:58,550
+بيصير a inverse في b بيصير x اللي هي مصفوفة
+
+72
+00:05:58,550 --> 00:06:03,370
+المجهيل بتساوي ال a inverse لمصفوفة اللي هي
+
+73
+00:06:03,370 --> 00:06:09,290
+العوامل مضروبة في b اللي هي مصفوفة اللي هي الحد
+
+74
+00:06:09,290 --> 00:06:13,430
+المطلق يعني و كأنه من الأن و طالع الأمر سهل ايش
+
+75
+00:06:13,430 --> 00:06:18,830
+بنسوي بنيجي بنحدد مصفوفة المجهيل اي مصفوفة عوامل
+
+76
+00:06:18,830 --> 00:06:23,530
+المجهيل اللي هيالحد هذا والحد هذا والحد هذا والحد
+
+77
+00:06:23,530 --> 00:06:29,920
+هذا اللي هيعوامل المجهيل مصفوفة العوامل ضرب مصفوفة
+
+78
+00:06:29,920 --> 00:06:33,820
+المجهيل بساوي مصفوفة الحدود المطلقة زي ما احنا
+
+79
+00:06:33,820 --> 00:06:38,500
+شايفين بعد هيك بنيجي بنقول هذه المصفوفة بنجيبلها
+
+80
+00:06:38,500 --> 00:06:42,700
+ال A inverse بنضربها في هذه بتطلع اللي هي X واحد و
+
+81
+00:06:42,700 --> 00:06:47,500
+X اتنين يعني بتطلع X ايش بتساوي A inverse في B خلي
+
+82
+00:06:47,500 --> 00:06:53,060
+نشوف هذا الآن الكلام عمليا في اللي هو ال
+
+83
+00:06:54,530 --> 00:06:58,670
+صار عندى اللى هى ال matrix form أو صورة التحويل
+
+84
+00:06:58,670 --> 00:07:03,830
+المعادلات الآنية إلى صورة مصففات هى ال a و هى ال x
+
+85
+00:07:03,830 --> 00:07:09,550
+و هى مين ال b قلنا الحل هيكون x هذا كله بساوي a
+
+86
+00:07:09,550 --> 00:07:13,650
+inverse في ال b هنا نوجد ال a inverse هى ال a هيها
+
+87
+00:07:13,650 --> 00:07:18,560
+قدامناعشان نجد ال a inverse بلزم من المحدد زي ما
+
+88
+00:07:18,560 --> 00:07:21,860
+انتوا عارفين اتنين في ناقص اتنين بتطلع ناقص اربعة
+
+89
+00:07:21,860 --> 00:07:25,900
+ناقص اربعة ناقص اربعة ايش بيساوي ناقص اربعة اسف
+
+90
+00:07:25,900 --> 00:07:29,660
+ناقص ثلاثة بتطلع ناقص سبعة اذا قيمة المحدد ليه
+
+91
+00:07:29,660 --> 00:07:34,740
+سالب سبعة اذا الان ال a inverse سهل ايجاده بس بيجي
+
+92
+00:07:34,740 --> 00:07:38,600
+بنغير هذا العنصر مكان هذا و هذا العنصر و هذا
+
+93
+00:07:38,600 --> 00:07:44,380
+بنعمله سالبوبنضربهم في مين في مقلوب اللي هي مين
+
+94
+00:07:44,380 --> 00:07:48,440
+اللي هي نقل السبعة يعني بنضربهم في واحد على اللي
+
+95
+00:07:48,440 --> 00:07:54,020
+هي واحد على السبعة زي ما قلنا ايش عند صار عند ال a
+
+96
+00:07:54,020 --> 00:07:58,810
+inverse ايش بيساوي ال a inverse هيهنقص واحد على
+
+97
+00:07:58,810 --> 00:08:03,150
+سبعة في قيمة المصفوفة هذه لما نبدلنا هذا مكان هذا
+
+98
+00:08:03,150 --> 00:08:07,690
+و جينا غيرنا إشارة هذولة فصار عندي سبع في اتنين في
+
+99
+00:08:07,690 --> 00:08:12,470
+تلاتة في واحد في نقص اتنين لما دخلنا النقص جوا صار
+
+100
+00:08:12,470 --> 00:08:15,390
+عندى الآن x ايش بساوي بساوى ال a inverse هنا
+
+101
+00:08:15,390 --> 00:08:19,650
+وجدناها هيها كلهامضروبة في مين؟ في الـ B مين الـ
+
+102
+00:08:19,650 --> 00:08:23,150
+B؟ اللي هي المصفوفة هذه هي الـ B لأن ضربنا هذه
+
+103
+00:08:23,150 --> 00:08:25,370
+المصفوفة في هذه المصفوفة زي ما بتعرفوا الضرب
+
+104
+00:08:25,370 --> 00:08:29,370
+العادي بطلع عندي اللي هي القيمة هذه المصفوفة اللي
+
+105
+00:08:29,370 --> 00:08:33,030
+طلعت عندي لأن هذه المصفوفة لما نضرب السبع فيها
+
+106
+00:08:33,030 --> 00:08:37,460
+بطلع عندي 1 1 1إذا X طلعت عدد D اللي هي المصفوفة
+
+107
+00:08:37,460 --> 00:08:42,160
+هذه X واحد X اتنين مش هتساوي واحد واحد يعني X واحد
+
+108
+00:08:42,160 --> 00:08:46,260
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+109
+00:08:46,260 --> 00:08:47,100
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+110
+00:08:47,100 --> 00:08:47,180
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+111
+00:08:47,180 --> 00:08:48,480
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+112
+00:08:48,480 --> 00:08:51,360
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+113
+00:08:51,360 --> 00:08:55,240
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+114
+00:08:55,240 --> 00:09:01,320
+طلعت واحد و X اتنين طلعت واحد والان المصفوف اللى
+
+115
+00:09:01,320 --> 00:09:05,220
+قبل بشوية اللى هى المعادلتين الأنياتين طلع عندهم
+
+116
+00:09:05,220 --> 00:09:10,860
+الحل الوحيد اللى هو كان X1 بيساو واحد و X2 بيساو
+
+117
+00:09:10,860 --> 00:09:14,780
+واحد هذاك حل وحيد الان ممكن المصفوف اللى هى
+
+118
+00:09:14,780 --> 00:09:19,280
+معادلتين أنياتين يطلعلهم عدد لانهاء من الحلول متى
+
+119
+00:09:19,280 --> 00:09:22,580
+بيطلعلهم عدد لانهاء من الحلول زى المعادلة هذه
+
+120
+00:09:22,580 --> 00:09:28,040
+وبنسمي ال equations are consistentماشي لكن إلهم
+
+121
+00:09:28,040 --> 00:09:32,800
+infinite number of solutions ليش؟ لاحظ إن هذه 2x1
+
+122
+00:09:32,800 --> 00:09:38,240
+زي 3x2 بيساوي 5 هذه بيساوي 4x1 زي 6x2 بيساوي 10
+
+123
+00:09:38,240 --> 00:09:42,580
+لاحظ هذه هي نفسها اللي فوق بس مضروبة هذه في إيه؟
+
+124
+00:09:42,580 --> 00:09:45,720
+في 2 يعني أنا ماعنديش معادلتين في الواقع أنا عندي
+
+125
+00:09:45,720 --> 00:09:49,500
+معادلة واحدةوما دام عندي معادلة واحدة يعني مجهولين
+
+126
+00:09:49,500 --> 00:09:52,840
+اللي هو معادلة واحدة في المجهولين عشان هيك لو
+
+127
+00:09:52,840 --> 00:09:57,520
+أعطيته X1 مثلا سفر تطلع X2 X2 بيساوي خمسة ع تلاتة
+
+128
+00:09:57,520 --> 00:10:03,180
+لو أعطيته X1 مثلا بنص بيصير هادي عبارة عن واحد
+
+129
+00:10:03,180 --> 00:10:07,840
+تنجلهانة بيصير أربعة X2 بيساوي أربعة تلاتة بتعطي
+
+130
+00:10:07,840 --> 00:10:11,800
+X1 جد ما بدك من القيام هيطلعلك عدد لانهائي إذا من
+
+131
+00:10:11,800 --> 00:10:17,000
+إيش من الحلول بس للمعرفة بدي تعرفهإنه في النظام
+
+132
+00:10:17,000 --> 00:10:21,040
+الأولاني لما كانت A inverse موجودة اللى هو كان
+
+133
+00:10:21,040 --> 00:10:25,760
+عندى one solution الآن لما inverse مش موجودة لإيه
+
+134
+00:10:25,760 --> 00:10:29,780
+inverse لإنه ليش مش موجودة لو جيت أخدت اللى هى
+
+135
+00:10:29,780 --> 00:10:34,120
+المصفوفة تبعت العوامل هيطلع تنين و تلاتة أو أربعة
+
+136
+00:10:34,120 --> 00:10:40,420
+أو ستةهذه ليست لديها inverse لما
+
+137
+00:10:40,420 --> 00:10:45,360
+يكون لديها inverse يعني إذا لم يكن لديها inverse
+
+138
+00:10:45,360 --> 00:10:45,780
+يعني إذا لم يكن لديها inverse يعني إذا لم يكن
+
+139
+00:10:45,780 --> 00:10:46,180
+inverse يعني إذا لم أكن لديها inverse يعني إذا لم
+
+140
+00:10:46,180 --> 00:10:46,640
+أكن لديها inverse يعني إذا لم أكن لديها inverse
+
+141
+00:10:46,640 --> 00:10:46,740
+لديها inverse يعني إذا لم أكن لديها inverse يعني
+
+142
+00:10:46,740 --> 00:10:46,780
+inverse يعني إذا لم أكن لديها inverse يعني إذا لم
+
+143
+00:10:46,780 --> 00:10:50,260
+يعني إذا لم أكن لديها inverse يعني إذا لم أكن
+
+144
+00:10:50,260 --> 00:10:53,820
+لديها
+
+145
+00:10:55,630 --> 00:11:01,690
+لكن لو جينا لحالة أخرى ممكن اللي هو في حالة اللي
+
+146
+00:11:01,690 --> 00:11:05,210
+هي برضه يطلع ال a-inverse does not exist تطلع عندي
+
+147
+00:11:05,210 --> 00:11:11,970
+مافيش solution لنين للمعادلات الأنية لاحظوا في
+
+148
+00:11:11,970 --> 00:11:18,670
+المعادلة التانية 2x1 زي 3x2 بساوة 5 4x1 زي 6x2
+
+149
+00:11:18,670 --> 00:11:26,470
+بساوة 9الان هذه المعادلة مافيش إلها إيش المعادلتين
+
+150
+00:11:26,470 --> 00:11:33,730
+مافيش إلها حلول لو لاحظته تجي ال a inverse اللي هي
+
+151
+00:11:33,730 --> 00:11:40,950
+المعكوس الضربي لمصفوفة العوامل 2×6 ب12 ناقص 12 سفر
+
+152
+00:11:40,950 --> 00:11:44,310
+إذا ال a inverse does not exist does not exist لكن
+
+153
+00:11:44,310 --> 00:11:48,950
+مش زي اللي فوق لو طلعنا على هذههتكون هذه دربناها
+
+154
+00:11:48,950 --> 00:11:52,790
+وكأنه في اتنين بساوية دي اشي هنا تسعة فالان هذه
+
+155
+00:11:52,790 --> 00:11:57,090
+تسعة مش عشرة عشان هيك لو اجيت اعطيت اللي هو ضربت
+
+156
+00:11:57,090 --> 00:12:02,050
+هذه مثلا في اتنين لو ضربت هذه في اتنينو جيت حلات
+
+157
+00:12:02,050 --> 00:12:05,090
+مع بعض المعادلة انه ماعرفش نحلم بال matrices زي ما
+
+158
+00:12:05,090 --> 00:12:08,470
+قلنا و ضربنا هدف اتنين بيصير اربع اكس واحد ستة اكس
+
+159
+00:12:08,470 --> 00:12:12,790
+اتنين بيساوي عشرة و جيت طرحت مع بعض طرحت من بعض
+
+160
+00:12:12,790 --> 00:12:17,270
+هيطلع هذا سفر هنا سفر هيروح مع بعض جرب لحالك و
+
+161
+00:12:17,270 --> 00:12:21,670
+هيطلع هنا عشرة ناقص تسعة اللي هي عبارة عن واحد
+
+162
+00:12:21,670 --> 00:12:25,390
+بساوي اللي طلع هنا سفر يعني سفر بيطلع بساوي واحد
+
+163
+00:12:25,390 --> 00:12:28,670
+او بساوي سالب واحد وهذا مستحيل عشان هيك بنسميه
+
+164
+00:12:28,670 --> 00:12:34,380
+inconsistentإذا للعلم يا شباب و يا بدا أنه في حالة
+
+165
+00:12:34,380 --> 00:12:37,240
+ال a inverse does not exist احنا ما نقدر نحل
+
+166
+00:12:37,240 --> 00:12:45,160
+بواسطة
+
+167
+00:12:45,160 --> 00:12:49,090
+ال matrices لأنها مش هتظبطلكن عندما تكون a inverse
+
+168
+00:12:49,090 --> 00:12:52,390
+لا توجد عندى حالتين حالة بس الحالة الأولى اللى هي
+
+169
+00:12:52,390 --> 00:12:55,470
+عندى infinite number of solutions يعني عدد لانهية
+
+170
+00:12:55,470 --> 00:12:59,790
+من الحلول الحالة التانية has no solution يعني
+
+171
+00:12:59,790 --> 00:13:04,330
+للمعلومات المعادلتين الأنيتين بيكون لها unique
+
+172
+00:13:04,330 --> 00:13:08,090
+solution اللى هو حل وحيد وهذا الحالة اللى احنا
+
+173
+00:13:08,090 --> 00:13:11,310
+بنعرف انحلها لإنه بيكون ال a inverse exist لإنه
+
+174
+00:13:11,310 --> 00:13:15,930
+determinant بتطلع بسويش سفرالحالة الثانية a
+
+175
+00:13:15,930 --> 00:13:19,150
+inverse does not exist بيكون يا إما عدد لنهائي من
+
+176
+00:13:19,150 --> 00:13:23,730
+الحلول يا إما مالهاش حلول وهذه طبعا زي ما قلنا
+
+177
+00:13:23,730 --> 00:13:27,530
+احنا ما بنعرف الحلها بواسطة أو بتنحلش بواسطة ال
+
+178
+00:13:27,530 --> 00:13:31,230
+matrices وبتكون حالة أصلا سهلة الحل بالطرق العادية
+
+179
+00:13:31,230 --> 00:13:38,050
+الآن يا جماعة بدنا نحكي عن اللي هو ال system of
+
+180
+00:13:38,050 --> 00:13:42,610
+three equations in three variables يعني عبارة عن
+
+181
+00:13:42,610 --> 00:13:50,430
+نظاممن المعادلات الآنية عدد المعادلات تلاتة وعدد
+
+182
+00:13:50,430 --> 00:13:55,910
+المجاهيل تلاتة بدنا نودد اللي هو الحل عن طريق اللي
+
+183
+00:13:55,910 --> 00:13:59,610
+هو مين ال matrices وهنا بتصير خلينا نقول أهمية ال
+
+184
+00:13:59,610 --> 00:14:04,730
+matrices في الحل كل ما كثرت عدد المجاهيلو كل ما
+
+185
+00:14:04,730 --> 00:14:08,890
+كثرت عدد اللي هي المعادلات المقابلة بيصير العملية
+
+186
+00:14:08,890 --> 00:14:14,730
+اللي اتعلمناها في الاعدادية صعبة اللي هو ان نحلها
+
+187
+00:14:14,730 --> 00:14:18,850
+التلاتة مع بعض بيصير اللي هو موضوع الحل بواسطة
+
+188
+00:14:18,850 --> 00:14:24,870
+اللي هو الان زي ما قلنا عندي اللي هو هذه صارت عندي
+
+189
+00:14:24,870 --> 00:14:28,610
+تلت معادلات في تلت مجهيل خلينا نشوف كيف بده نحلها
+
+190
+00:14:30,040 --> 00:14:35,180
+النفس الحل بالنسبة للمجهولين بالظبط بنيجي بنحدد
+
+191
+00:14:35,180 --> 00:14:39,040
+مصفوفة العوامل مصفوفة العوامل اسمها ايه؟ ايش
+
+192
+00:14:39,040 --> 00:14:42,860
+هتكون؟ اللي هي واحد سالب اتنين واحد هي واحد سالب
+
+193
+00:14:42,860 --> 00:14:47,180
+اتنين واحد التانية اتنين واحد سالب واحد اتنين واحد
+
+194
+00:14:47,180 --> 00:14:50,640
+سالب واحد اللي بعدها تلاتة سالب واحد اتنين تلاتة
+
+195
+00:14:50,640 --> 00:14:54,100
+سالب واحد ايش اتنين هذه مصفوفة العوامل نيجي
+
+196
+00:14:54,100 --> 00:14:58,990
+لمصفوفة المجاهي اللي قلنا بنرسم عمودهذه المجهول
+
+197
+00:14:58,990 --> 00:15:02,190
+الأول طبعا كنا بنكون احنا مرتبين ايش المعادلات
+
+198
+00:15:02,190 --> 00:15:05,330
+بالظبط هذا المجهول الأول المجهول التاني المجهول
+
+199
+00:15:05,330 --> 00:15:08,190
+التالت المجهول الأول المجهول التاني المجهول التالت
+
+200
+00:15:08,190 --> 00:15:10,990
+المجهول الأول المجهول التاني المجهول التالت وهنا
+
+201
+00:15:10,990 --> 00:15:14,030
+الحدود المطلقة بعد ما نرتبهم ديروا بالكم إذا أول
+
+202
+00:15:14,030 --> 00:15:19,470
+شغلة بنعملها هي ترتيب المعادلات حسب مين المجهول
+
+203
+00:15:19,470 --> 00:15:22,590
+المجهول الأول المجهول التاني المجهول التالت وعلى
+
+204
+00:15:22,590 --> 00:15:25,570
+الجهة التانية لحد المطلقو نفسي الأشي في التاني و
+
+205
+00:15:25,570 --> 00:15:28,450
+نفسي الأشي في التالتة و إلا بيكون كل شغلنا مش
+
+206
+00:15:28,450 --> 00:15:33,790
+مظبوط طيب هاي بعد مرتبناها نحطينا المصوفة العوامل
+
+207
+00:15:33,790 --> 00:15:38,230
+المعادلة الأخيرة تلاتة سلب واحد اتنين هذه زي ما
+
+208
+00:15:38,230 --> 00:15:42,550
+قولنا اش مالها مصوفة المجاهيل بنفس الترتيب الأفقي
+
+209
+00:15:42,550 --> 00:15:46,190
+X واحد X اتنين X تلاتة بنخلي اش بس على صورة اش
+
+210
+00:15:46,190 --> 00:15:49,560
+عمولوبنجي على العمود اللي على جباله بالظبط بنفس
+
+211
+00:15:49,560 --> 00:15:53,160
+الترتيب تلاتة وخمسة وإياش واطمعاش صارت المعادلة
+
+212
+00:15:53,160 --> 00:15:57,780
+الآن جاهزة على صورة Ax بتساوي إياش B هذه A وهذه X
+
+213
+00:15:57,780 --> 00:16:02,720
+وهذه B إذن الحل وانا مغمض عينيا بتطلع على ال A إذا
+
+214
+00:16:02,720 --> 00:16:06,360
+كانت ال A A اللي هي inverse على طول بيصير ال X
+
+215
+00:16:06,360 --> 00:16:11,780
+بتساوي A inverse في B هو الحلX بتساوي A inverse في
+
+216
+00:16:11,780 --> 00:16:16,360
+B بضل علي بس أن أوجد ال A inverse زي ما أوجدناها
+
+217
+00:16:16,360 --> 00:16:22,300
+المرة الماضية في المحاضرة السابقة و بنضربها في B
+
+218
+00:16:22,300 --> 00:16:27,380
+بتطلع لي اللي هي مصوفة من الأعداد عجبال مصوفة
+
+219
+00:16:27,380 --> 00:16:30,500
+المجاهي اللي بيكون زي ما عملنا قبل بشوية بالظبط
+
+220
+00:16:30,500 --> 00:16:35,430
+بتطلع اللي هو الحقإذا زي ما قلنا X هتطلع بتساوي A
+
+221
+00:16:35,430 --> 00:16:39,390
+inverse في B فال A inverse هي ال inverse لهذه و ال
+
+222
+00:16:39,390 --> 00:16:44,270
+B هيها B اللي هي تلاتة أو خمسة أو اتناش مظبوط
+
+223
+00:16:44,270 --> 00:16:47,370
+فبصير عند هذه اللي هي تلاتة أو خمسة او اتناش و
+
+224
+00:16:47,370 --> 00:16:50,850
+بنضرب ال A inverse فيها اللي بتطلع ال X اللي هي ال
+
+225
+00:16:50,850 --> 00:16:54,990
+X واحد وال X اتنين اللي هي ال X تلاتة لنشوف كيف
+
+226
+00:16:54,990 --> 00:16:58,980
+اللي هو بدنا نطلعهإذا زي ما اتعلمنا المرة الماضية
+
+227
+00:16:58,980 --> 00:17:01,380
+بنوجد الـ A-Inverse الـ A-Inverse بنوجد الـ
+
+228
+00:17:01,380 --> 00:17:05,060
+determinant للـ A باللي جيله عبارة عن عشرة بكون
+
+229
+00:17:05,060 --> 00:17:08,760
+واحد على عشرة في الـ Adjoint بنكون أوجدنا الـ
+
+230
+00:17:08,760 --> 00:17:12,420
+Adjoint وجهزنا زي ما اتعلمتوا كيف توجدوه الآن طلع
+
+231
+00:17:12,420 --> 00:17:15,690
+عندي الـ A-Inverseبتطلع ال X اللي هي عبارة عن مين
+
+232
+00:17:15,690 --> 00:17:18,550
+ال X X واحد X اتنين X تلاتة أيش بتساوي زي ما قلنا
+
+233
+00:17:18,550 --> 00:17:23,490
+A inverse في B هي ال A inverse وهي مين المصفوفة B
+
+234
+00:17:23,490 --> 00:17:27,070
+اللي هي مصفوفة الحدود المطلقة بنضرب هادي الآن في
+
+235
+00:17:27,070 --> 00:17:31,170
+هادي بطلع عندي اللي هو تلاتين عشرة عشرين ونضرب في
+
+236
+00:17:31,170 --> 00:17:34,130
+واحدة العشر اللي برا هذا بطلع عندي تلاتة واحد
+
+237
+00:17:34,130 --> 00:17:39,300
+اتنين فبكون عندي X واحد بساوي تلاتةX2 بيساوي واحد
+
+238
+00:17:39,300 --> 00:17:44,220
+و X3 بيساوي ايش بيساوي اتنين اذا يا شباب و يا بنات
+
+239
+00:17:44,220 --> 00:17:48,980
+عندي مادامة ال A inverse موجودة اذا الحل بيكون
+
+240
+00:17:48,980 --> 00:17:54,540
+وحيد وهي الحل طلع عندي في هذه الحالة X1 ثلاثة و X2
+
+241
+00:17:54,540 --> 00:18:00,920
+واحد و X3 اتنين هذه هي حلول المعادلات او ال system
+
+242
+00:18:00,920 --> 00:18:05,200
+of equations اللي عددهم جديش يا جماعة اللي عددهم
+
+243
+00:18:05,200 --> 00:18:10,930
+تلت معادلات بتلت مجهيلالان يا جماعة خلصنا المحاضرة
+
+244
+00:18:10,930 --> 00:18:16,530
+الثالثة هي محاضرة بسيطة واضحةمطلوب منكم تحلوا اللي
+
+245
+00:18:16,530 --> 00:18:18,810
+هو عندي solve the following equations using
+
+246
+00:18:18,810 --> 00:18:27,310
+inverse matrix بدي تحلوا A و D بس A و D اجبولياهم
+
+247
+00:18:27,310 --> 00:18:32,170
+اللي هو محلولات المرة القادمة زي ما بنعمل في كل
+
+248
+00:18:32,170 --> 00:18:36,810
+واجب والسلام عليكم ورحمة الله وبركاته وإلى لقاء
+
+249
+00:18:36,810 --> 00:18:37,350
+آخر
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9e1aee2b91342e7779a8f01fad336aa0117dc556
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2880, "start": 0.0, "end": 28.8, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة الثالثة بعد حالة التوارق لمساق رياضيات منفاصلة لطلاب وطالبات الجامعة الإسلامية كلية technology المعلومات في قسم الحوصفة المتنقلة تحدثنا المرة الماضية عن إيجاد المعكوس الضربي للمصفوفة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 6024, 104, 6027, 12984, 3660, 39182, 11331, 6027, 3660, 16712, 2407, 9640, 4587, 32767, 3794, 995, 4587, 12602, 1829, 46958, 1829, 9307, 9154, 5172, 33546, 37977, 5296, 9566, 15040, 3555, 4032, 9566, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 2899, 9673, 30241, 20498, 9307, 8978, 12174, 38251, 21542, 2407, 9381, 5172, 3660, 9673, 2655, 1863, 4587, 37977, 6055, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632, 18871, 11933, 1829, 7435, 18513, 9673, 3615, 4117, 41779, 6024, 114, 2288, 21292, 5296, 19528, 9381, 5172, 38688, 3660], "avg_logprob": 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"probability": 0.904296875}, {"start": 705.49, "end": 706.09, "word": " طلعنا", "probability": 0.8759765625}, {"start": 706.09, "end": 706.31, "word": " على", "probability": 0.88232421875}, {"start": 706.31, "end": 706.73, "word": " هذه", "probability": 0.76025390625}], "temperature": 1.0}, {"id": 31, "seek": 72085, "start": 707.43, "end": 720.85, "text": "هتكون هذه دربناها وكأنه في اتنين بساوية دي اشي هنا تسعة فالان هذه تسعة مش عشرة عشان هيك لو اجيت اعطيت اللي هو ضربت هذه مثلا في اتنين لو ضربت هذه في اتنين", "tokens": [3224, 2655, 30544, 29538, 11778, 25513, 8315, 11296, 4032, 4117, 33456, 3224, 8978, 1975, 2655, 1863, 9957, 4724, 3794, 995, 2407, 10632, 11778, 1829, 1975, 8592, 1829, 34105, 6055, 3794, 27884, 6156, 6027, 7649, 29538, 6055, 3794, 27884, 37893, 6225, 8592, 25720, 6225, 8592, 7649, 39896, 4117, 45164, 1975, 7435, 36081, 1975, 3615, 9566, 36081, 13672, 1829, 31439, 48812, 25513, 2655, 29538, 50113, 15040, 8978, 1975, 2655, 1863, 9957, 45164, 48812, 25513, 2655, 29538, 8978, 1975, 2655, 1863, 9957], "avg_logprob": -0.24179687444120646, "compression_ratio": 1.916083916083916, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 707.43, "end": 707.97, "word": "هتكون", "probability": 0.5381266276041666}, {"start": 707.97, "end": 708.31, "word": " هذه", "probability": 0.47119140625}, {"start": 708.31, "end": 708.95, "word": " دربناها", "probability": 0.76422119140625}, {"start": 708.95, "end": 709.39, "word": " وكأنه", "probability": 0.7408447265625}, {"start": 709.39, "end": 709.51, "word": " في", "probability": 0.51123046875}, {"start": 709.51, "end": 709.99, "word": " اتنين", "probability": 0.8153076171875}, {"start": 709.99, "end": 710.53, "word": " بساوية", "probability": 0.694482421875}, {"start": 710.53, "end": 710.83, "word": " دي", "probability": 0.60693359375}, {"start": 710.83, "end": 711.01, "word": " اشي", "probability": 0.5491129557291666}, {"start": 711.01, "end": 711.15, "word": " هنا", "probability": 0.4658203125}, {"start": 711.15, "end": 711.63, "word": " تسعة", "probability": 0.9547526041666666}, {"start": 711.63, "end": 712.55, "word": " فالان", "probability": 0.8927408854166666}, {"start": 712.55, "end": 712.79, "word": " هذه", "probability": 0.85302734375}, {"start": 712.79, "end": 713.13, "word": " تسعة", "probability": 0.9742838541666666}, {"start": 713.13, "end": 713.35, "word": " مش", "probability": 0.986328125}, {"start": 713.35, "end": 713.85, "word": " عشرة", "probability": 0.9435221354166666}, {"start": 713.85, "end": 714.35, "word": " عشان", "probability": 0.90966796875}, {"start": 714.35, "end": 714.61, "word": " هيك", "probability": 0.8798828125}, {"start": 714.61, "end": 714.79, "word": " لو", "probability": 0.765625}, {"start": 714.79, "end": 715.29, "word": " اجيت", "probability": 0.77490234375}, {"start": 715.29, "end": 716.27, "word": " اعطيت", "probability": 0.974853515625}, {"start": 716.27, "end": 716.53, "word": " اللي", "probability": 0.799560546875}, {"start": 716.53, "end": 716.67, "word": " هو", "probability": 0.7822265625}, {"start": 716.67, "end": 717.09, "word": " ضربت", "probability": 0.9119466145833334}, {"start": 717.09, "end": 717.33, "word": " هذه", "probability": 0.9384765625}, {"start": 717.33, "end": 717.75, "word": " مثلا", "probability": 0.796630859375}, {"start": 717.75, "end": 717.93, "word": " في", "probability": 0.89892578125}, {"start": 717.93, "end": 718.55, "word": " اتنين", "probability": 0.9835205078125}, {"start": 718.55, "end": 719.83, "word": " لو", "probability": 0.78857421875}, {"start": 719.83, "end": 720.17, "word": " ضربت", "probability": 0.9920247395833334}, {"start": 720.17, "end": 720.33, "word": " هذه", "probability": 0.94482421875}, {"start": 720.33, "end": 720.47, "word": " في", "probability": 0.916015625}, {"start": 720.47, "end": 720.85, "word": " اتنين", "probability": 0.98828125}], "temperature": 1.0}, {"id": 32, "seek": 74925, "start": 721.27, "end": 749.25, "text": "و جيت حلات مع بعض المعادلة انه ماعرفش نحلم بال matrices زي ما قلنا و ضربنا هدف اتنين بيصير اربع اكس واحد ستة اكس اتنين بيساوي عشرة و جيت طرحت مع بعض طرحت من بعض هيطلع هذا سفر هنا سفر هيروح مع بعض جرب لحالك و هيطلع هنا عشرة ناقص تسعة اللي هي عبارة عن واحد بساوي اللي طلع هنا سفر يعني سفر بيطلع بساوي واحد او بساوي سالب واحد وهذا مستحيل عشان هيك بنسميه inconsistent", "tokens": [2407, 10874, 36081, 11331, 1211, 9307, 20449, 45030, 11242, 9673, 3615, 18513, 37977, 16472, 3224, 19446, 3615, 28480, 8592, 8717, 5016, 19528, 20666, 32284, 30767, 1829, 19446, 12174, 1211, 8315, 4032, 48812, 25513, 8315, 8032, 3215, 5172, 1975, 2655, 1863, 9957, 4724, 1829, 9381, 13546, 1975, 25513, 3615, 1975, 4117, 3794, 36764, 24401, 8608, 2655, 3660, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 4724, 1829, 3794, 995, 45865, 6225, 8592, 25720, 4032, 10874, 36081, 23032, 2288, 33753, 20449, 45030, 11242, 23032, 2288, 33753, 9154, 45030, 11242, 39896, 9566, 1211, 3615, 23758, 8608, 5172, 2288, 34105, 8608, 5172, 2288, 39896, 32887, 5016, 20449, 45030, 11242, 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726.05, "word": " هدف", "probability": 0.6956380208333334}, {"start": 726.05, "end": 726.45, "word": " اتنين", "probability": 0.877685546875}, {"start": 726.45, "end": 727.01, "word": " بيصير", "probability": 0.767578125}, {"start": 727.01, "end": 727.31, "word": " اربع", "probability": 0.6585286458333334}, {"start": 727.31, "end": 727.51, "word": " اكس", "probability": 0.7906901041666666}, {"start": 727.51, "end": 727.89, "word": " واحد", "probability": 0.9677734375}, {"start": 727.89, "end": 728.27, "word": " ستة", "probability": 0.7591145833333334}, {"start": 728.27, "end": 728.47, "word": " اكس", "probability": 0.9757486979166666}, {"start": 728.47, "end": 728.75, "word": " اتنين", "probability": 0.967041015625}, {"start": 728.75, "end": 729.07, "word": " بيساوي", "probability": 0.748681640625}, {"start": 729.07, "end": 729.49, "word": " عشرة", "probability": 0.97119140625}, {"start": 729.49, "end": 730.23, "word": " و", "probability": 0.6845703125}, {"start": 730.23, "end": 730.39, "word": " جيت", "probability": 0.89208984375}, {"start": 730.39, "end": 730.75, "word": " طرحت", "probability": 0.9138997395833334}, {"start": 730.75, "end": 730.99, "word": " مع", "probability": 0.345458984375}, {"start": 730.99, "end": 731.53, "word": " بعض", "probability": 0.99658203125}, {"start": 731.53, "end": 732.19, "word": " طرحت", "probability": 0.9295247395833334}, {"start": 732.19, "end": 732.39, "word": " من", "probability": 0.61083984375}, {"start": 732.39, "end": 732.79, "word": " بعض", "probability": 0.99365234375}, {"start": 732.79, "end": 733.55, "word": " هيطلع", "probability": 0.81378173828125}, {"start": 733.55, "end": 733.77, "word": " هذا", "probability": 0.52880859375}, {"start": 733.77, "end": 734.21, "word": " سفر", "probability": 0.92431640625}, {"start": 734.21, "end": 734.67, "word": " هنا", "probability": 0.38427734375}, {"start": 734.67, "end": 734.99, "word": " سفر", "probability": 0.9905598958333334}, {"start": 734.99, "end": 735.33, "word": " هيروح", "probability": 0.935546875}, {"start": 735.33, "end": 735.47, "word": " مع", "probability": 0.7890625}, {"start": 735.47, "end": 735.81, "word": " بعض", "probability": 0.997314453125}, {"start": 735.81, "end": 736.17, "word": " جرب", "probability": 0.752685546875}, {"start": 736.17, "end": 736.75, "word": " لحالك", "probability": 0.9805908203125}, {"start": 736.75, "end": 737.27, "word": " و", "probability": 0.92138671875}, {"start": 737.27, "end": 737.77, "word": " هيطلع", "probability": 0.9224853515625}, {"start": 737.77, "end": 738.05, "word": " هنا", "probability": 0.95703125}, {"start": 738.05, "end": 738.59, "word": " عشرة", "probability": 0.9493815104166666}, {"start": 738.59, "end": 739.49, "word": " ناقص", "probability": 0.86181640625}, {"start": 739.49, "end": 739.99, "word": " تسعة", "probability": 0.9811197916666666}, {"start": 739.99, "end": 740.43, "word": " اللي", "probability": 0.934814453125}, {"start": 740.43, "end": 740.69, "word": " هي", "probability": 0.83056640625}, {"start": 740.69, "end": 741.05, "word": " عبارة", "probability": 0.99169921875}, {"start": 741.05, "end": 741.23, "word": " عن", "probability": 0.98486328125}, {"start": 741.23, "end": 741.67, "word": " واحد", "probability": 0.994140625}, {"start": 741.67, "end": 742.17, "word": " بساوي", "probability": 0.9305419921875}, {"start": 742.17, "end": 742.31, "word": " اللي", "probability": 0.96728515625}, {"start": 742.31, "end": 742.59, "word": " طلع", "probability": 0.97265625}, {"start": 742.59, "end": 742.89, "word": " هنا", "probability": 0.95751953125}, {"start": 742.89, "end": 743.25, "word": " سفر", "probability": 0.9833984375}, {"start": 743.25, "end": 743.89, "word": " يعني", "probability": 0.967041015625}, {"start": 743.89, "end": 744.27, "word": " سفر", "probability": 0.9866536458333334}, {"start": 744.27, "end": 744.61, "word": " بيطلع", "probability": 0.88896484375}, {"start": 744.61, "end": 745.01, "word": " بساوي", "probability": 0.947021484375}, {"start": 745.01, "end": 745.39, "word": " واحد", "probability": 0.989990234375}, {"start": 745.39, "end": 745.55, "word": " او", "probability": 0.8486328125}, {"start": 745.55, "end": 745.83, "word": " بساوي", "probability": 0.8690185546875}, {"start": 745.83, "end": 746.15, "word": " سالب", "probability": 0.8382161458333334}, {"start": 746.15, "end": 746.37, "word": " واحد", "probability": 0.9892578125}, {"start": 746.37, "end": 746.61, "word": " وهذا", "probability": 0.743896484375}, {"start": 746.61, "end": 747.21, "word": " مستحيل", "probability": 0.99169921875}, {"start": 747.21, "end": 747.85, "word": " عشان", "probability": 0.9664713541666666}, {"start": 747.85, "end": 748.03, "word": " هيك", "probability": 0.925048828125}, {"start": 748.03, "end": 748.67, "word": " بنسميه", "probability": 0.76611328125}, {"start": 748.67, "end": 749.25, "word": " inconsistent", "probability": 0.82568359375}], "temperature": 1.0}, {"id": 33, "seek": 76674, "start": 750.18, "end": 766.74, "text": "إذا للعلم يا شباب و يا بدا أنه في حالة ال a inverse does not exist احنا ما نقدر نحل بواسطة ال matrices لأنها مش هتظبط", "tokens": [28814, 15730, 24976, 3615, 19528, 35186, 13412, 3555, 16758, 4032, 35186, 4724, 28259, 14739, 3224, 8978, 11331, 6027, 3660, 2423, 257, 17340, 775, 406, 2514, 1975, 5016, 8315, 19446, 8717, 28543, 2288, 8717, 5016, 1211, 4724, 14407, 3794, 9566, 3660, 2423, 32284, 5296, 33456, 11296, 37893, 8032, 2655, 19913, 3555, 9566], "avg_logprob": -0.41616585793403477, "compression_ratio": 1.2836879432624113, "no_speech_prob": 0.0, "words": [{"start": 750.18, "end": 750.5, "word": "إذا", "probability": 0.5662841796875}, {"start": 750.5, "end": 751.16, "word": " للعلم", "probability": 0.671142578125}, {"start": 751.16, "end": 751.38, "word": " يا", "probability": 0.79443359375}, {"start": 751.38, "end": 751.88, "word": " شباب", "probability": 0.9814453125}, {"start": 751.88, "end": 751.98, "word": " و", "probability": 0.95068359375}, {"start": 751.98, "end": 752.1, "word": " يا", "probability": 0.490234375}, {"start": 752.1, "end": 752.4, "word": " بدا", "probability": 0.4515380859375}, {"start": 752.4, "end": 753.72, "word": " أنه", "probability": 0.577880859375}, {"start": 753.72, "end": 753.96, "word": " في", "probability": 0.8564453125}, {"start": 753.96, "end": 754.38, "word": " حالة", "probability": 0.99609375}, {"start": 754.38, "end": 754.48, "word": " ال", "probability": 0.498291015625}, {"start": 754.48, "end": 754.58, "word": " a", "probability": 0.369384765625}, {"start": 754.58, "end": 754.92, "word": " inverse", "probability": 0.5673828125}, {"start": 754.92, "end": 755.12, "word": " does", "probability": 0.50048828125}, {"start": 755.12, "end": 755.36, "word": " not", "probability": 0.96337890625}, {"start": 755.36, "end": 755.8, "word": " exist", "probability": 0.95654296875}, {"start": 755.8, "end": 756.22, "word": " احنا", "probability": 0.7644856770833334}, {"start": 756.22, "end": 756.4, "word": " ما", "probability": 0.3671875}, {"start": 756.4, "end": 756.7, "word": " نقدر", "probability": 0.5869954427083334}, {"start": 756.7, "end": 757.24, "word": " نحل", "probability": 0.9256184895833334}, {"start": 757.24, "end": 765.16, "word": " بواسطة", "probability": 0.6668212890625}, {"start": 765.16, "end": 765.16, "word": " ال", "probability": 0.6787109375}, {"start": 765.16, "end": 765.6, "word": " matrices", "probability": 0.955078125}, {"start": 765.6, "end": 765.96, "word": " لأنها", "probability": 0.6643880208333334}, {"start": 765.96, "end": 766.06, "word": " مش", "probability": 0.468994140625}, {"start": 766.06, "end": 766.74, "word": " هتظبط", "probability": 0.866796875}], "temperature": 1.0}, {"id": 34, "seek": 79375, "start": 767.47, "end": 793.75, "text": "لكن عندما تكون a inverse لا توجد عندى حالتين حالة بس الحالة الأولى اللى هي عندى infinite number of solutions يعني عدد لانهية من الحلول الحالة التانية has no solution يعني للمعلومات المعادلتين الأنيتين بيكون لها unique solution اللى هو حل وحيد وهذا الحالة اللى احنا بنعرف انحلها لإنه بيكون ال a inverse exist لإنه determinant بتطلع بسويش سفر", "tokens": [1211, 19452, 43242, 15042, 6055, 30544, 257, 17340, 20193, 6055, 29245, 3215, 43242, 7578, 11331, 6027, 2655, 9957, 11331, 6027, 3660, 4724, 3794, 21542, 6027, 3660, 16247, 12610, 7578, 13672, 7578, 39896, 43242, 7578, 13785, 1230, 295, 6547, 37495, 22653, 6225, 3215, 3215, 5296, 7649, 3224, 10632, 9154, 21542, 1211, 12610, 21542, 6027, 3660, 16712, 7649, 10632, 575, 572, 3827, 37495, 22653, 5296, 19528, 30241, 20498, 9307, 9673, 3615, 18513, 1211, 2655, 9957, 16247, 22653, 2655, 9957, 4724, 1829, 30544, 5296, 11296, 3845, 3827, 13672, 7578, 31439, 11331, 1211, 4032, 5016, 25708, 37037, 15730, 21542, 6027, 3660, 13672, 7578, 1975, 5016, 8315, 44945, 3615, 28480, 16472, 5016, 1211, 11296, 5296, 28814, 1863, 3224, 4724, 1829, 30544, 2423, 257, 17340, 2514, 5296, 28814, 1863, 3224, 41296, 39894, 9566, 1211, 3615, 4724, 3794, 45865, 8592, 8608, 5172, 2288], "avg_logprob": 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{"start": 770.87, "end": 771.45, "word": " الحالة", "probability": 0.7504069010416666}, {"start": 771.45, "end": 771.89, "word": " الأولى", "probability": 0.8888346354166666}, {"start": 771.89, "end": 772.03, "word": " اللى", "probability": 0.76123046875}, {"start": 772.03, "end": 772.39, "word": " هي", "probability": 0.47802734375}, {"start": 772.39, "end": 773.13, "word": " عندى", "probability": 0.766357421875}, {"start": 773.13, "end": 773.43, "word": " infinite", "probability": 0.6689453125}, {"start": 773.43, "end": 773.85, "word": " number", "probability": 0.970703125}, {"start": 773.85, "end": 774.03, "word": " of", "probability": 0.9501953125}, {"start": 774.03, "end": 774.55, "word": " solutions", "probability": 0.88330078125}, {"start": 774.55, "end": 774.85, "word": " يعني", "probability": 0.866455078125}, {"start": 774.85, "end": 775.13, "word": " عدد", "probability": 0.9716796875}, {"start": 775.13, "end": 775.47, "word": " لانهية", "probability": 0.5418701171875}, 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0.6975504557291666}, {"start": 783.53, "end": 783.83, "word": " لها", "probability": 0.46044921875}, {"start": 783.83, "end": 784.33, "word": " unique", "probability": 0.55810546875}, {"start": 784.33, "end": 784.99, "word": " solution", "probability": 0.95556640625}, {"start": 784.99, "end": 785.69, "word": " اللى", "probability": 0.9169921875}, {"start": 785.69, "end": 785.83, "word": " هو", "probability": 0.85107421875}, {"start": 785.83, "end": 786.07, "word": " حل", "probability": 0.882568359375}, {"start": 786.07, "end": 786.45, "word": " وحيد", "probability": 0.87255859375}, {"start": 786.45, "end": 786.81, "word": " وهذا", "probability": 0.6634521484375}, {"start": 786.81, "end": 787.79, "word": " الحالة", "probability": 0.9527994791666666}, {"start": 787.79, "end": 787.91, "word": " اللى", "probability": 0.994140625}, {"start": 787.91, "end": 788.09, "word": " احنا", "probability": 0.7889811197916666}, {"start": 788.09, "end": 788.51, "word": " بنعرف", "probability": 0.86572265625}, {"start": 788.51, "end": 788.91, "word": " انحلها", "probability": 0.83489990234375}, {"start": 788.91, "end": 789.31, "word": " لإنه", "probability": 0.79669189453125}, {"start": 789.31, "end": 789.57, "word": " بيكون", "probability": 0.7183430989583334}, {"start": 789.57, "end": 789.71, "word": " ال", "probability": 0.71728515625}, {"start": 789.71, "end": 789.87, "word": " a", "probability": 0.78564453125}, {"start": 789.87, "end": 790.21, "word": " inverse", "probability": 0.53125}, {"start": 790.21, "end": 790.87, "word": " exist", "probability": 0.5810546875}, {"start": 790.87, "end": 791.31, "word": " لإنه", "probability": 0.7652587890625}, {"start": 791.31, "end": 791.77, "word": " determinant", "probability": 0.24658203125}, {"start": 791.77, "end": 792.25, "word": " بتطلع", "probability": 0.890380859375}, {"start": 792.25, "end": 792.85, "word": " بسويش", "probability": 0.8489990234375}, {"start": 792.85, "end": 793.75, "word": " سفر", "probability": 0.8375651041666666}], "temperature": 1.0}, {"id": 35, "seek": 82329, "start": 794.47, "end": 823.29, "text": "الحالة الثانية a inverse does not exist بيكون يا إما عدد لنهائي من الحلول يا إما مالهاش حلول وهذه طبعا زي ما قلنا احنا ما بنعرف الحلها بواسطة أو بتنحلش بواسطة ال matrices وبتكون حالة أصلا سهلة الحل بالطرق العادية الآن يا جماعة بدنا نحكي عن اللي هو ال system of three equations in three variables يعني عبارة عن نظام", "tokens": [6027, 5016, 6027, 3660, 6024, 104, 7649, 10632, 257, 17340, 775, 406, 2514, 4724, 1829, 30544, 35186, 11933, 15042, 6225, 3215, 3215, 5296, 1863, 3224, 16373, 1829, 9154, 21542, 1211, 12610, 35186, 11933, 15042, 3714, 6027, 3224, 33599, 11331, 1211, 12610, 37037, 24192, 23032, 3555, 3615, 995, 30767, 1829, 19446, 12174, 1211, 8315, 1975, 5016, 8315, 19446, 44945, 3615, 28480, 21542, 1211, 11296, 4724, 14407, 3794, 9566, 3660, 34051, 39894, 1863, 5016, 1211, 8592, 4724, 14407, 3794, 9566, 3660, 2423, 32284, 4032, 3555, 2655, 30544, 11331, 6027, 3660, 5551, 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{"start": 802.73, "end": 803.05, "word": " طبعا", "probability": 0.9559326171875}, {"start": 803.05, "end": 803.23, "word": " زي", "probability": 0.725341796875}, {"start": 803.23, "end": 803.35, "word": " ما", "probability": 0.9736328125}, {"start": 803.35, "end": 803.73, "word": " قلنا", "probability": 0.90673828125}, {"start": 803.73, "end": 804.17, "word": " احنا", "probability": 0.8062337239583334}, {"start": 804.17, "end": 804.35, "word": " ما", "probability": 0.462646484375}, {"start": 804.35, "end": 804.57, "word": " بنعرف", "probability": 0.7063802083333334}, {"start": 804.57, "end": 805.07, "word": " الحلها", "probability": 0.5817464192708334}, {"start": 805.07, "end": 805.71, "word": " بواسطة", "probability": 0.9109375}, {"start": 805.71, "end": 806.23, "word": " أو", "probability": 0.65966796875}, {"start": 806.23, "end": 807.01, "word": " بتنحلش", "probability": 0.8609375}, {"start": 807.01, "end": 807.43, "word": " بواسطة", "probability": 0.91640625}, {"start": 807.43, 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813.73, "end": 814.05, "word": " بدنا", "probability": 0.77197265625}, {"start": 814.05, "end": 814.55, "word": " نحكي", "probability": 0.9906005859375}, {"start": 814.55, "end": 814.85, "word": " عن", "probability": 0.98291015625}, {"start": 814.85, "end": 815.23, "word": " اللي", "probability": 0.841796875}, {"start": 815.23, "end": 815.69, "word": " هو", "probability": 0.99072265625}, {"start": 815.69, "end": 816.67, "word": " ال", "probability": 0.76708984375}, {"start": 816.67, "end": 817.53, "word": " system", "probability": 0.8876953125}, {"start": 817.53, "end": 818.05, "word": " of", "probability": 0.96435546875}, {"start": 818.05, "end": 818.59, "word": " three", "probability": 0.82470703125}, {"start": 818.59, "end": 819.63, "word": " equations", "probability": 0.921875}, {"start": 819.63, "end": 820.15, "word": " in", "probability": 0.890625}, {"start": 820.15, "end": 820.63, "word": " three", "probability": 0.92041015625}, {"start": 820.63, "end": 821.31, "word": " variables", "probability": 0.943359375}, {"start": 821.31, "end": 821.91, "word": " يعني", "probability": 0.9375}, {"start": 821.91, "end": 822.39, "word": " عبارة", "probability": 0.9974365234375}, {"start": 822.39, "end": 822.61, "word": " عن", "probability": 0.9951171875}, {"start": 822.61, "end": 823.29, "word": " نظام", "probability": 0.9978841145833334}], "temperature": 1.0}, {"id": 36, "seek": 84323, "start": 823.87, "end": 843.23, "text": "من المعادلات الآنية عدد المعادلات تلاتة وعدد المجاهيل تلاتة بدنا نودد اللي هو الحل عن طريق اللي هو مين ال matrices وهنا بتصير خلينا نقول أهمية ال matrices في الحل كل ما كثرت عدد المجاهيل", "tokens": [27842, 9673, 3615, 18513, 1211, 9307, 6024, 48506, 10632, 6225, 3215, 3215, 9673, 3615, 18513, 1211, 9307, 6055, 1211, 9307, 3660, 4032, 22488, 3215, 9673, 7435, 40294, 26895, 6055, 1211, 9307, 3660, 47525, 8315, 8717, 23328, 3215, 13672, 1829, 31439, 21542, 1211, 18871, 23032, 16572, 4587, 13672, 1829, 31439, 3714, 9957, 2423, 32284, 37037, 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{"start": 831.15, "end": 831.93, "word": " تلاتة", "probability": 0.980224609375}, {"start": 831.93, "end": 832.69, "word": " بدنا", "probability": 0.710693359375}, {"start": 832.69, "end": 833.17, "word": " نودد", "probability": 0.7906901041666666}, {"start": 833.17, "end": 833.39, "word": " اللي", "probability": 0.814697265625}, {"start": 833.39, "end": 833.79, "word": " هو", "probability": 0.98779296875}, {"start": 833.79, "end": 834.71, "word": " الحل", "probability": 0.98388671875}, {"start": 834.71, "end": 835.09, "word": " عن", "probability": 0.9736328125}, {"start": 835.09, "end": 835.71, "word": " طريق", "probability": 0.9943033854166666}, {"start": 835.71, "end": 835.91, "word": " اللي", "probability": 0.6549072265625}, {"start": 835.91, "end": 836.05, "word": " هو", "probability": 0.97509765625}, {"start": 836.05, "end": 836.29, "word": " مين", "probability": 0.5528564453125}, {"start": 836.29, "end": 836.41, "word": " ال", "probability": 0.91357421875}, {"start": 836.41, 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"probability": 0.80712890625}, {"start": 1096.27, "end": 1096.53, "word": " اللي", "probability": 0.41546630859375}, {"start": 1096.53, "end": 1096.77, "word": " هو", "probability": 0.9375}, {"start": 1096.77, "end": 1097.09, "word": " عندي", "probability": 0.6307373046875}, {"start": 1097.09, "end": 1097.35, "word": " solve", "probability": 0.5771484375}, {"start": 1097.35, "end": 1097.53, "word": " the", "probability": 0.87353515625}, {"start": 1097.53, "end": 1097.83, "word": " following", "probability": 0.84521484375}, {"start": 1097.83, "end": 1098.41, "word": " equations", "probability": 0.90673828125}, {"start": 1098.41, "end": 1098.81, "word": " using", "probability": 0.8984375}, {"start": 1098.81, "end": 1099.19, "word": " inverse", "probability": 0.76708984375}, {"start": 1099.19, "end": 1099.77, "word": " matrix", "probability": 0.91943359375}, {"start": 1099.77, "end": 1100.47, "word": " بدي", "probability": 0.572509765625}, {"start": 1100.47, "end": 1101.05, "word": " تحلوا", "probability": 0.746826171875}, {"start": 1101.05, "end": 1101.49, "word": " A", "probability": 0.49072265625}, {"start": 1101.49, "end": 1102.63, "word": " و", "probability": 0.93310546875}, {"start": 1102.63, "end": 1102.89, "word": " D", "probability": 0.5185546875}, {"start": 1102.89, "end": 1103.57, "word": " بس", "probability": 0.904052734375}, {"start": 1103.57, "end": 1104.75, "word": " A", "probability": 0.72998046875}, {"start": 1104.75, "end": 1105.31, "word": " و", "probability": 0.9912109375}, {"start": 1105.31, "end": 1105.57, "word": " D", "probability": 0.82421875}, {"start": 1105.57, "end": 1107.31, "word": " اجبولياهم", "probability": 0.5892537434895834}, {"start": 1107.31, "end": 1107.81, "word": " اللي", "probability": 0.966552734375}, {"start": 1107.81, "end": 1108.17, "word": " هو", "probability": 0.90625}, {"start": 1108.17, "end": 1109.49, "word": " محلولات", "probability": 0.92880859375}, {"start": 1109.49, "end": 1109.95, "word": " المرة", "probability": 0.96533203125}, {"start": 1109.95, "end": 1110.59, "word": " القادمة", "probability": 0.9913736979166666}, {"start": 1110.59, "end": 1110.99, "word": " زي", "probability": 0.948486328125}, {"start": 1110.99, "end": 1111.09, "word": " ما", "probability": 0.9736328125}, {"start": 1111.09, "end": 1111.63, "word": " بنعمل", "probability": 0.96337890625}, {"start": 1111.63, "end": 1111.81, "word": " في", "probability": 0.908203125}, {"start": 1111.81, "end": 1112.17, "word": " كل", "probability": 0.9853515625}, {"start": 1112.17, "end": 1112.79, "word": " واجب", "probability": 0.98974609375}, {"start": 1112.79, "end": 1113.53, "word": " والسلام", "probability": 0.9212239583333334}, {"start": 1113.53, "end": 1113.97, "word": " عليكم", "probability": 0.931884765625}, {"start": 1113.97, "end": 1114.35, "word": " ورحمة", "probability": 0.9840087890625}, {"start": 1114.35, "end": 1114.63, "word": " الله", "probability": 0.9619140625}, {"start": 1114.63, "end": 1115.47, "word": " وبركاته", "probability": 0.990234375}, {"start": 1115.47, "end": 1116.29, "word": " وإلى", "probability": 0.91015625}, {"start": 1116.29, "end": 1116.81, "word": " لقاء", "probability": 0.96728515625}, {"start": 1116.81, "end": 1117.35, "word": " آخر", "probability": 0.896484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1117.55325, "duration_after_vad": 1109.3897187500006}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..316e31cfa825be5171bc1aee175eafcb5771c993
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/CAdAQZRQd_Q_raw.srt
@@ -0,0 +1,1016 @@
+1
+00:00:00,000 --> 00:00:06,040
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثالثة بعد
+
+2
+00:00:06,040 --> 00:00:14,360
+حالة التوارق لمساق رياضيات منفاصلة لطلاب وطالبات
+
+3
+00:00:14,360 --> 00:00:18,880
+الجامعة الإسلامية كلية technology المعلومات في قسم
+
+4
+00:00:18,880 --> 00:00:25,940
+الحوصفة المتنقلة تحدثنا المرة الماضية عن إيجاد
+
+5
+00:00:25,940 --> 00:00:30,960
+المعكوس الضربي للمصفوفةاليوم بدنا نوظف هذه
+
+6
+00:00:30,960 --> 00:00:40,440
+المعلومات في حل system of linear equations يعني
+
+7
+00:00:40,440 --> 00:00:47,360
+بدنا نوظف المعلومة في حل معادلات آنية معادلتين
+
+8
+00:00:47,360 --> 00:00:54,100
+آنيتين بمجهولين أو ثلاث معادلات آنية بثلاثة مجاهين
+
+9
+00:00:54,860 --> 00:00:59,280
+لو جينا اتطلعنا في البداية اللي كان عندنا معادلة
+
+10
+00:00:59,280 --> 00:01:03,820
+خطية اللي هي ax بتساوي b هذه المعادلة الخطية
+
+11
+00:01:03,820 --> 00:01:08,660
+وفرضنا ان ال a لا تساوي سفر وطلب منها طبعا a عبارة
+
+12
+00:01:08,660 --> 00:01:12,580
+عن عدد و b عبارة عن عدد و x عبارة عن مجهول طبعا
+
+13
+00:01:12,580 --> 00:01:16,040
+هذه زي ما انتوا عارفين زي ما أخدناها سابق في
+
+14
+00:01:16,040 --> 00:01:22,060
+الاعدادية انه بنجسم الجهتين على ال a بتطلع عندي x
+
+15
+00:01:22,060 --> 00:01:28,300
+بتساوي b على aأو بمعنى آخر x بتساوي a inverse في b
+
+16
+00:01:28,300 --> 00:01:34,640
+حيث a لا تساوي صفر هذه طبعا معلومات سابقة بس عشان
+
+17
+00:01:34,640 --> 00:01:38,960
+نعرف ان في عندنا هذه معادلة خطية في مجهول واحد
+
+18
+00:01:38,960 --> 00:01:45,520
+الان لو كان في عندنا معاطينا معادلتين خطيتين يعني
+
+19
+00:01:45,520 --> 00:01:50,020
+درجة اللي هو المتغير هذا واحد ودرجة المتغير هذا
+
+20
+00:01:50,020 --> 00:01:54,850
+واحد برضه الان لو كان عندنا هذه معادلةخطية في
+
+21
+00:01:54,850 --> 00:01:57,990
+مجهولين هذه المجهول الأول وهذه المجهول الثاني
+
+22
+00:01:57,990 --> 00:02:02,030
+والمعادلة الثانية برضه معادلة خطية في نفس
+
+23
+00:02:02,030 --> 00:02:07,550
+المجهولين اللي فوق بسيرة أنه الأن إمكانية نحكي عن
+
+24
+00:02:07,550 --> 00:02:12,930
+الحلول المشتركة يعني بمعنى آخر إيجاد X1 و X2 اللي
+
+25
+00:02:12,930 --> 00:02:17,850
+بتحقق المعادلة الأولى و بتحقق المعادلة الثانية في
+
+26
+00:02:17,850 --> 00:02:23,030
+نفس الوقتطبعا زمان احنا كنا في الاعدادية نجي نضرب
+
+27
+00:02:23,030 --> 00:02:30,270
+نوحد اللي هو معامل اللي هو ال X1 هنا و X1 هنا و
+
+28
+00:02:30,270 --> 00:02:33,890
+بعدين نطرح المعادلتين من بعض بطلع عنده قيمة X2 و
+
+29
+00:02:33,890 --> 00:02:39,510
+بعدين نعوض عن X1 بطلع عند X1 بنكون جيبنا قيمة X1 و
+
+30
+00:02:39,510 --> 00:02:43,390
+قيمة X2 طبعا مش هذا اللي بدنا يالي يوم اليوم بدنا
+
+31
+00:02:43,390 --> 00:02:47,050
+نوظفاللي هو معلوماتنا في ال matrices أو في
+
+32
+00:02:47,050 --> 00:02:52,710
+المصففات لحل اللي هو نظام من اللي هو المعادلات
+
+33
+00:02:52,710 --> 00:02:57,970
+الآنية في مجهولين نشوف هذه اللي عندنا الآن هذا
+
+34
+00:02:57,970 --> 00:03:00,930
+النظام بدي أحله عن طريق ال matrices نشوف إيش بدي
+
+35
+00:03:00,930 --> 00:03:07,580
+أسويفي عندنا اللي هو أول شغلة اللي هي بدنا اللي هو
+
+36
+00:03:07,580 --> 00:03:13,360
+نحكي عن حاجة اسمها اللي هي مصفوفة العوامل وحاجة
+
+37
+00:03:13,360 --> 00:03:17,720
+اسمها مصفوفة المجهيل وحاجة اسمها مصفوفة الحدود
+
+38
+00:03:17,720 --> 00:03:24,440
+المطلقة المطلقة فخلينا احنا نيجي اللي هو نستخدم
+
+39
+00:03:24,440 --> 00:03:30,340
+المصفوفات في اللي هو إيجاد الحلول اطلعوا من ديالان
+
+40
+00:03:30,340 --> 00:03:35,100
+اول اشي بنجي بنطلع كيف بدنا نوجد اللى هى المصوفة
+
+41
+00:03:35,100 --> 00:03:40,280
+اللى هى تبعت اللى هى مين مصوفة عوامل اللى عندى
+
+42
+00:03:40,280 --> 00:03:47,240
+خلينى اوجد هذه المصوفة كيف نوجد مصوفة العوامل هى
+
+43
+00:03:47,240 --> 00:03:52,320
+مصوفة العوامل طبعا مصوفة العوامل هيكون درجتها اللى
+
+44
+00:03:52,320 --> 00:03:57,250
+هو عدد المجهيل اتنينوعدد المعادلات اتنين يعني عدد
+
+45
+00:03:57,250 --> 00:04:00,870
+المجهول ضرب عدد المعادلات يعني عبارة عن مصفوفة
+
+46
+00:04:00,870 --> 00:04:05,170
+مربعة اتنين في اتنين كيف بنجيبها بنجعل المجهول
+
+47
+00:04:05,170 --> 00:04:10,710
+الاول معامله اتنين هيه المجهول التاني x اتنين
+
+48
+00:04:10,710 --> 00:04:14,190
+معامله تلاتة هيه خلصنا من المعادلة الاولى نجي
+
+49
+00:04:14,190 --> 00:04:18,810
+للمعادلة التانيةالمعامل واحد هنا المعامل التاني
+
+50
+00:04:18,810 --> 00:04:22,910
+ايش سالب اتنين صارت هذه المصفوفة جاهزة هي مصفوفة
+
+51
+00:04:22,910 --> 00:04:27,470
+العوامل او عوامل اللي هي من المجهيل اللي في
+
+52
+00:04:27,470 --> 00:04:32,190
+المعادلة الآن المصفوفة التانية هي مصفوفة عمود عمود
+
+53
+00:04:32,190 --> 00:04:36,610
+هيكون اللي هو درجتها عدد أسطورها بعدد المجهيل
+
+54
+00:04:36,610 --> 00:04:41,630
+وطبعا عمود واحد فبتصير عندي مجهول مجهولين يعني
+
+55
+00:04:41,630 --> 00:04:46,560
+درجتها اتنين في واحدالان هذا بنسميها مصفوفة
+
+56
+00:04:46,560 --> 00:04:50,980
+المجاهيل اللي احنا بنبحث عنها اللي بدنا نوجد قيمة
+
+57
+00:04:50,980 --> 00:04:55,920
+X1 و X2 تساوي ايش؟ تساوي اللي هي مصفوفة العمود
+
+58
+00:04:55,920 --> 00:05:00,960
+المكونة منه اللي هو الحد المطلق للمعادلة الأولى و
+
+59
+00:05:00,960 --> 00:05:04,940
+الحد المطلق للمعادلة الثانية يعني خمسة و سالب واحد
+
+60
+00:05:05,450 --> 00:05:10,550
+الان هذه المصفوفة بعد ما كتبناها على صورة a مصفوفة
+
+61
+00:05:10,550 --> 00:05:14,450
+في x مصفوفة بيساوي بي مصفوفة صارت على صورة مصفوفة
+
+62
+00:05:14,450 --> 00:05:20,090
+ax بتساوي ax بتساوي b الان هذه بيكون نقدر نحلها و
+
+63
+00:05:20,090 --> 00:05:25,970
+نودد حالها إذا كان هذا ال a inverse له موجودإذا
+
+64
+00:05:25,970 --> 00:05:29,530
+الـ A inverse فيه موجود هين بنقدر نحلها عن طريق ال
+
+65
+00:05:29,530 --> 00:05:33,990
+matrices مش موجود مقدرش أحكي عن الحلول بطريقة ال
+
+66
+00:05:33,990 --> 00:05:38,090
+matrices ده نشوف كده الان إذا كان ال A inverse
+
+67
+00:05:38,090 --> 00:05:43,150
+موجود معناته أنه بقدر أضرب هنا في A inverse و هنا
+
+68
+00:05:43,150 --> 00:05:46,490
+في A inverse لما أضرب ال A inverse في ال A بتطلع
+
+69
+00:05:46,490 --> 00:05:50,210
+المصفوف اللي هو ال identity ال identity لما تضرب
+
+70
+00:05:50,210 --> 00:05:54,870
+في X هش بتطلع عنده Xوهنا اللي ضربناه a inverse
+
+71
+00:05:54,870 --> 00:05:58,550
+بيصير a inverse في b بيصير x اللي هي مصفوفة
+
+72
+00:05:58,550 --> 00:06:03,370
+المجهيل بتساوي ال a inverse لمصفوفة اللي هي
+
+73
+00:06:03,370 --> 00:06:09,290
+العوامل مضروبة في b اللي هي مصفوفة اللي هي الحد
+
+74
+00:06:09,290 --> 00:06:13,430
+المطلق يعني و كأنه من الأن و طالع الأمر سهل ايش
+
+75
+00:06:13,430 --> 00:06:18,830
+بنسوي بنيجي بنحدد مصفوفة المجهيل اي مصفوفة عوامل
+
+76
+00:06:18,830 --> 00:06:23,530
+المجهيل اللي هيالحد هذا والحد هذا والحد هذا والحد
+
+77
+00:06:23,530 --> 00:06:29,920
+هذا اللي هيعوامل المجهيل مصفوفة العوامل ضرب مصفوفة
+
+78
+00:06:29,920 --> 00:06:33,820
+المجهيل بساوي مصفوفة الحدود المطلقة زي ما احنا
+
+79
+00:06:33,820 --> 00:06:38,500
+شايفين بعد هيك بنيجي بنقول هذه المصفوفة بنجيبلها
+
+80
+00:06:38,500 --> 00:06:42,700
+ال A inverse بنضربها في هذه بتطلع اللي هي X واحد و
+
+81
+00:06:42,700 --> 00:06:47,500
+X اتنين يعني بتطلع X ايش بتساوي A inverse في B خلي
+
+82
+00:06:47,500 --> 00:06:53,060
+نشوف هذا الآن الكلام عمليا في اللي هو ال
+
+83
+00:06:54,530 --> 00:06:58,670
+صار عندى اللى هى ال matrix form أو صورة التحويل
+
+84
+00:06:58,670 --> 00:07:03,830
+المعادلات الآنية إلى صورة مصففات هى ال a و هى ال x
+
+85
+00:07:03,830 --> 00:07:09,550
+و هى مين ال b قلنا الحل هيكون x هذا كله بساوي a
+
+86
+00:07:09,550 --> 00:07:13,650
+inverse في ال b هنا نوجد ال a inverse هى ال a هيها
+
+87
+00:07:13,650 --> 00:07:18,560
+قدامناعشان نجد ال a inverse بلزم من المحدد زي ما
+
+88
+00:07:18,560 --> 00:07:21,860
+انتوا عارفين اتنين في ناقص اتنين بتطلع ناقص اربعة
+
+89
+00:07:21,860 --> 00:07:25,900
+ناقص اربعة ناقص اربعة ايش بيساوي ناقص اربعة اسف
+
+90
+00:07:25,900 --> 00:07:29,660
+ناقص ثلاثة بتطلع ناقص سبعة اذا قيمة المحدد ليه
+
+91
+00:07:29,660 --> 00:07:34,740
+سالب سبعة اذا الان ال a inverse سهل ايجاده بس بيجي
+
+92
+00:07:34,740 --> 00:07:38,600
+بنغير هذا العنصر مكان هذا و هذا العنصر و هذا
+
+93
+00:07:38,600 --> 00:07:44,380
+بنعمله سالبوبنضربهم في مين في مقلوب اللي هي مين
+
+94
+00:07:44,380 --> 00:07:48,440
+اللي هي نقل السبعة يعني بنضربهم في واحد على اللي
+
+95
+00:07:48,440 --> 00:07:54,020
+هي واحد على السبعة زي ما قلنا ايش عند صار عند ال a
+
+96
+00:07:54,020 --> 00:07:58,810
+inverse ايش بيساوي ال a inverse هيهنقص واحد على
+
+97
+00:07:58,810 --> 00:08:03,150
+سبعة في قيمة المصفوفة هذه لما نبدلنا هذا مكان هذا
+
+98
+00:08:03,150 --> 00:08:07,690
+و جينا غيرنا إشارة هذولة فصار عندي سبع في اتنين في
+
+99
+00:08:07,690 --> 00:08:12,470
+تلاتة في واحد في نقص اتنين لما دخلنا النقص جوا صار
+
+100
+00:08:12,470 --> 00:08:15,390
+عندى الآن x ايش بساوي بساوى ال a inverse هنا
+
+101
+00:08:15,390 --> 00:08:19,650
+وجدناها هيها كلهامضروبة في مين؟ في الـ B مين الـ
+
+102
+00:08:19,650 --> 00:08:23,150
+B؟ اللي هي المصفوفة هذه هي الـ B لأن ضربنا هذه
+
+103
+00:08:23,150 --> 00:08:25,370
+المصفوفة في هذه المصفوفة زي ما بتعرفوا الضرب
+
+104
+00:08:25,370 --> 00:08:29,370
+العادي بطلع عندي اللي هي القيمة هذه المصفوفة اللي
+
+105
+00:08:29,370 --> 00:08:33,030
+طلعت عندي لأن هذه المصفوفة لما نضرب السبع فيها
+
+106
+00:08:33,030 --> 00:08:37,460
+بطلع عندي 1 1 1إذا X طلعت عدد D اللي هي المصفوفة
+
+107
+00:08:37,460 --> 00:08:42,160
+هذه X واحد X اتنين مش هتساوي واحد واحد يعني X واحد
+
+108
+00:08:42,160 --> 00:08:46,260
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+109
+00:08:46,260 --> 00:08:47,100
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+110
+00:08:47,100 --> 00:08:47,180
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+111
+00:08:47,180 --> 00:08:48,480
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+112
+00:08:48,480 --> 00:08:51,360
+طلعت واحد و X اتنين طلعت واحد و X اتنين طلعت واحد
+
+113
+00:08:51,360 --> 00:08:55,240
+و X اتنين طلعت واحد و X اتنين طلعت واحد و X اتنين
+
+114
+00:08:55,240 --> 00:09:01,320
+طلعت واحد و X اتنين طلعت واحد والان المصفوف اللى
+
+115
+00:09:01,320 --> 00:09:05,220
+قبل بشوية اللى هى المعادلتين الأنياتين طلع عندهم
+
+116
+00:09:05,220 --> 00:09:10,860
+الحل الوحيد اللى هو كان X1 بيساو واحد و X2 بيساو
+
+117
+00:09:10,860 --> 00:09:14,780
+واحد هذاك حل وحيد الان ممكن المصفوف اللى هى
+
+118
+00:09:14,780 --> 00:09:19,280
+معادلتين أنياتين يطلعلهم عدد لانهاء من الحلول متى
+
+119
+00:09:19,280 --> 00:09:22,580
+بيطلعلهم عدد لانهاء من الحلول زى المعادلة هذه
+
+120
+00:09:22,580 --> 00:09:28,040
+وبنسمي ال equations are consistentماشي لكن إلهم
+
+121
+00:09:28,040 --> 00:09:32,800
+infinite number of solutions ليش؟ لاحظ إن هذه 2x1
+
+122
+00:09:32,800 --> 00:09:38,240
+زي 3x2 بيساوي 5 هذه بيساوي 4x1 زي 6x2 بيساوي 10
+
+123
+00:09:38,240 --> 00:09:42,580
+لاحظ هذه هي نفسها اللي فوق بس مضروبة هذه في إيه؟
+
+124
+00:09:42,580 --> 00:09:45,720
+في 2 يعني أنا ماعنديش معادلتين في الواقع أنا عندي
+
+125
+00:09:45,720 --> 00:09:49,500
+معادلة واحدةوما دام عندي معادلة واحدة يعني مجهولين
+
+126
+00:09:49,500 --> 00:09:52,840
+اللي هو معادلة واحدة في المجهولين عشان هيك لو
+
+127
+00:09:52,840 --> 00:09:57,520
+أعطيته X1 مثلا سفر تطلع X2 X2 بيساوي خمسة ع تلاتة
+
+128
+00:09:57,520 --> 00:10:03,180
+لو أعطيته X1 مثلا بنص بيصير هادي عبارة عن واحد
+
+129
+00:10:03,180 --> 00:10:07,840
+تنجلهانة بيصير أربعة X2 بيساوي أربعة تلاتة بتعطي
+
+130
+00:10:07,840 --> 00:10:11,800
+X1 جد ما بدك من القيام هيطلعلك عدد لانهائي إذا من
+
+131
+00:10:11,800 --> 00:10:17,000
+إيش من الحلول بس للمعرفة بدي تعرفهإنه في النظام
+
+132
+00:10:17,000 --> 00:10:21,040
+الأولاني لما كانت A inverse موجودة اللى هو كان
+
+133
+00:10:21,040 --> 00:10:25,760
+عندى one solution الآن لما inverse مش موجودة لإيه
+
+134
+00:10:25,760 --> 00:10:29,780
+inverse لإنه ليش مش موجودة لو جيت أخدت اللى هى
+
+135
+00:10:29,780 --> 00:10:34,120
+المصفوفة تبعت العوامل هيطلع تنين و تلاتة أو أربعة
+
+136
+00:10:34,120 --> 00:10:40,420
+أو ستةهذه ليست لديها inverse لما
+
+137
+00:10:40,420 --> 00:10:45,360
+يكون لديها inverse يعني إذا لم يكن لديها inverse
+
+138
+00:10:45,360 --> 00:10:45,780
+يعني إذا لم يكن لديها inverse يعني إذا لم يكن
+
+139
+00:10:45,780 --> 00:10:45,780
+لديها inverse يعني إذا لم يكن لديها inverse يعني
+
+140
+00:10:45,780 --> 00:10:45,780
+إذا لم يكن لديها inverse يعني إذا لم يكن لديها
+
+141
+00:10:45,780 --> 00:10:46,180
+inverse يعني إذا لم أكن لديها inverse يعني إذا لم
+
+142
+00:10:46,180 --> 00:10:46,640
+أكن لديها inverse يعني إذا لم أكن لديها inverse
+
+143
+00:10:46,640 --> 00:10:46,640
+يعني إذا لم أكن لديها inverse يعني إذا لم أكن
+
+144
+00:10:46,640 --> 00:10:46,740
+لديها inverse يعني إذا لم أكن لديها inverse يعني
+
+145
+00:10:46,740 --> 00:10:46,740
+إذا لم أكن لديها inverse يعني إذا لم أكن لديها
+
+146
+00:10:46,740 --> 00:10:46,780
+inverse يعني إذا لم أكن لديها inverse يعني إذا لم
+
+147
+00:10:46,780 --> 00:10:46,780
+أكن لديها inverse يعني إذا لم أكن لديها inverse
+
+148
+00:10:46,780 --> 00:10:50,260
+يعني إذا لم أكن لديها inverse يعني إذا لم أكن
+
+149
+00:10:50,260 --> 00:10:53,820
+لديها
+
+150
+00:10:55,630 --> 00:11:01,690
+لكن لو جينا لحالة أخرى ممكن اللي هو في حالة اللي
+
+151
+00:11:01,690 --> 00:11:05,210
+هي برضه يطلع ال a-inverse does not exist تطلع عندي
+
+152
+00:11:05,210 --> 00:11:11,970
+مافيش solution لنين للمعادلات الأنية لاحظوا في
+
+153
+00:11:11,970 --> 00:11:18,670
+المعادلة التانية 2x1 زي 3x2 بساوة 5 4x1 زي 6x2
+
+154
+00:11:18,670 --> 00:11:26,470
+بساوة 9الان هذه المعادلة مافيش إلها إيش المعادلتين
+
+155
+00:11:26,470 --> 00:11:33,730
+مافيش إلها حلول لو لاحظته تجي ال a inverse اللي هي
+
+156
+00:11:33,730 --> 00:11:40,950
+المعكوس الضربي لمصفوفة العوامل 2×6 ب12 ناقص 12 سفر
+
+157
+00:11:40,950 --> 00:11:44,310
+إذا ال a inverse does not exist does not exist لكن
+
+158
+00:11:44,310 --> 00:11:48,950
+مش زي اللي فوق لو طلعنا على هذههتكون هذه دربناها
+
+159
+00:11:48,950 --> 00:11:52,790
+وكأنه في اتنين بساوية دي اشي هنا تسعة فالان هذه
+
+160
+00:11:52,790 --> 00:11:57,090
+تسعة مش عشرة عشان هيك لو اجيت اعطيت اللي هو ضربت
+
+161
+00:11:57,090 --> 00:12:02,050
+هذه مثلا في اتنين لو ضربت هذه في اتنينو جيت حلات
+
+162
+00:12:02,050 --> 00:12:05,090
+مع بعض المعادلة انه ماعرفش نحلم بال matrices زي ما
+
+163
+00:12:05,090 --> 00:12:08,470
+قلنا و ضربنا هدف اتنين بيصير اربع اكس واحد ستة اكس
+
+164
+00:12:08,470 --> 00:12:12,790
+اتنين بيساوي عشرة و جيت طرحت مع بعض طرحت من بعض
+
+165
+00:12:12,790 --> 00:12:17,270
+هيطلع هذا سفر هنا سفر هيروح مع بعض جرب لحالك و
+
+166
+00:12:17,270 --> 00:12:21,670
+هيطلع هنا عشرة ناقص تسعة اللي هي عبارة عن واحد
+
+167
+00:12:21,670 --> 00:12:25,390
+بساوي اللي طلع هنا سفر يعني سفر بيطلع بساوي واحد
+
+168
+00:12:25,390 --> 00:12:28,670
+او بساوي سالب واحد وهذا مستحيل عشان هيك بنسميه
+
+169
+00:12:28,670 --> 00:12:34,380
+inconsistentإذا للعلم يا شباب و يا بدا أنه في حالة
+
+170
+00:12:34,380 --> 00:12:37,240
+ال a inverse does not exist احنا ما نقدر نحل
+
+171
+00:12:37,240 --> 00:12:45,160
+بواسطة
+
+172
+00:12:45,160 --> 00:12:49,090
+ال matrices لأنها مش هتظبطلكن عندما تكون a inverse
+
+173
+00:12:49,090 --> 00:12:52,390
+لا توجد عندى حالتين حالة بس الحالة الأولى اللى هي
+
+174
+00:12:52,390 --> 00:12:55,470
+عندى infinite number of solutions يعني عدد لانهية
+
+175
+00:12:55,470 --> 00:12:59,790
+من الحلول الحالة التانية has no solution يعني
+
+176
+00:12:59,790 --> 00:13:04,330
+للمعلومات المعادلتين الأنيتين بيكون لها unique
+
+177
+00:13:04,330 --> 00:13:08,090
+solution اللى هو حل وحيد وهذا الحالة اللى احنا
+
+178
+00:13:08,090 --> 00:13:11,310
+بنعرف انحلها لإنه بيكون ال a inverse exist لإنه
+
+179
+00:13:11,310 --> 00:13:15,930
+determinant بتطلع بسويش سفرالحالة الثانية a
+
+180
+00:13:15,930 --> 00:13:19,150
+inverse does not exist بيكون يا إما عدد لنهائي من
+
+181
+00:13:19,150 --> 00:13:23,730
+الحلول يا إما مالهاش حلول وهذه طبعا زي ما قلنا
+
+182
+00:13:23,730 --> 00:13:27,530
+احنا ما بنعرف الحلها بواسطة أو بتنحلش بواسطة ال
+
+183
+00:13:27,530 --> 00:13:31,230
+matrices وبتكون حالة أصلا سهلة الحل بالطرق العادية
+
+184
+00:13:31,230 --> 00:13:38,050
+الآن يا جماعة بدنا نحكي عن اللي هو ال system of
+
+185
+00:13:38,050 --> 00:13:42,610
+three equations in three variables يعني عبارة عن
+
+186
+00:13:42,610 --> 00:13:50,430
+نظاممن المعادلات الآنية عدد المعادلات تلاتة وعدد
+
+187
+00:13:50,430 --> 00:13:55,910
+المجاهيل تلاتة بدنا نودد اللي هو الحل عن طريق اللي
+
+188
+00:13:55,910 --> 00:13:59,610
+هو مين ال matrices وهنا بتصير خلينا نقول أهمية ال
+
+189
+00:13:59,610 --> 00:14:04,730
+matrices في الحل كل ما كثرت عدد المجاهيلو كل ما
+
+190
+00:14:04,730 --> 00:14:08,890
+كثرت عدد اللي هي المعادلات المقابلة بيصير العملية
+
+191
+00:14:08,890 --> 00:14:14,730
+اللي اتعلمناها في الاعدادية صعبة اللي هو ان نحلها
+
+192
+00:14:14,730 --> 00:14:18,850
+التلاتة مع بعض بيصير اللي هو موضوع الحل بواسطة
+
+193
+00:14:18,850 --> 00:14:24,870
+اللي هو الان زي ما قلنا عندي اللي هو هذه صارت عندي
+
+194
+00:14:24,870 --> 00:14:28,610
+تلت معادلات في تلت مجهيل خلينا نشوف كيف بده نحلها
+
+195
+00:14:30,040 --> 00:14:35,180
+النفس الحل بالنسبة للمجهولين بالظبط بنيجي بنحدد
+
+196
+00:14:35,180 --> 00:14:39,040
+مصفوفة العوامل مصفوفة العوامل اسمها ايه؟ ايش
+
+197
+00:14:39,040 --> 00:14:42,860
+هتكون؟ اللي هي واحد سالب اتنين واحد هي واحد سالب
+
+198
+00:14:42,860 --> 00:14:47,180
+اتنين واحد التانية اتنين واحد سالب واحد اتنين واحد
+
+199
+00:14:47,180 --> 00:14:50,640
+سالب واحد اللي بعدها تلاتة سالب واحد اتنين تلاتة
+
+200
+00:14:50,640 --> 00:14:54,100
+سالب واحد ايش اتنين هذه مصفوفة العوامل نيجي
+
+201
+00:14:54,100 --> 00:14:58,990
+لمصفوفة المجاهي اللي قلنا بنرسم عمودهذه المجهول
+
+202
+00:14:58,990 --> 00:15:02,190
+الأول طبعا كنا بنكون احنا مرتبين ايش المعادلات
+
+203
+00:15:02,190 --> 00:15:05,330
+بالظبط هذا المجهول الأول المجهول التاني المجهول
+
+204
+00:15:05,330 --> 00:15:08,190
+التالت المجهول الأول المجهول التاني المجهول التالت
+
+205
+00:15:08,190 --> 00:15:10,990
+المجهول الأول المجهول التاني المجهول التالت وهنا
+
+206
+00:15:10,990 --> 00:15:14,030
+الحدود المطلقة بعد ما نرتبهم ديروا بالكم إذا أول
+
+207
+00:15:14,030 --> 00:15:19,470
+شغلة بنعملها هي ترتيب المعادلات حسب مين المجهول
+
+208
+00:15:19,470 --> 00:15:22,590
+المجهول الأول المجهول التاني المجهول التالت وعلى
+
+209
+00:15:22,590 --> 00:15:25,570
+الجهة التانية لحد المطلقو نفسي الأشي في التاني و
+
+210
+00:15:25,570 --> 00:15:28,450
+نفسي الأشي في التالتة و إلا بيكون كل شغلنا مش
+
+211
+00:15:28,450 --> 00:15:33,790
+مظبوط طيب هاي بعد مرتبناها نحطينا المصوفة العوامل
+
+212
+00:15:33,790 --> 00:15:38,230
+المعادلة الأخيرة تلاتة سلب واحد اتنين هذه زي ما
+
+213
+00:15:38,230 --> 00:15:42,550
+قولنا اش مالها مصوفة المجاهيل بنفس الترتيب الأفقي
+
+214
+00:15:42,550 --> 00:15:46,190
+X واحد X اتنين X تلاتة بنخلي اش بس على صورة اش
+
+215
+00:15:46,190 --> 00:15:49,560
+عمولوبنجي على العمود اللي على جباله بالظبط بنفس
+
+216
+00:15:49,560 --> 00:15:53,160
+الترتيب تلاتة وخمسة وإياش واطمعاش صارت المعادلة
+
+217
+00:15:53,160 --> 00:15:57,780
+الآن جاهزة على صورة Ax بتساوي إياش B هذه A وهذه X
+
+218
+00:15:57,780 --> 00:16:02,720
+وهذه B إذن الحل وانا مغمض عينيا بتطلع على ال A إذا
+
+219
+00:16:02,720 --> 00:16:06,360
+كانت ال A A اللي هي inverse على طول بيصير ال X
+
+220
+00:16:06,360 --> 00:16:11,780
+بتساوي A inverse في B هو الحلX بتساوي A inverse في
+
+221
+00:16:11,780 --> 00:16:16,360
+B بضل علي بس أن أوجد ال A inverse زي ما أوجدناها
+
+222
+00:16:16,360 --> 00:16:22,300
+المرة الماضية في المحاضرة السابقة و بنضربها في B
+
+223
+00:16:22,300 --> 00:16:27,380
+بتطلع لي اللي هي مصوفة من الأعداد عجبال مصوفة
+
+224
+00:16:27,380 --> 00:16:30,500
+المجاهي اللي بيكون زي ما عملنا قبل بشوية بالظبط
+
+225
+00:16:30,500 --> 00:16:35,430
+بتطلع اللي هو الحقإذا زي ما قلنا X هتطلع بتساوي A
+
+226
+00:16:35,430 --> 00:16:39,390
+inverse في B فال A inverse هي ال inverse لهذه و ال
+
+227
+00:16:39,390 --> 00:16:44,270
+B هيها B اللي هي تلاتة أو خمسة أو اتناش مظبوط
+
+228
+00:16:44,270 --> 00:16:47,370
+فبصير عند هذه اللي هي تلاتة أو خمسة او اتناش و
+
+229
+00:16:47,370 --> 00:16:50,850
+بنضرب ال A inverse فيها اللي بتطلع ال X اللي هي ال
+
+230
+00:16:50,850 --> 00:16:54,990
+X واحد وال X اتنين اللي هي ال X تلاتة لنشوف كيف
+
+231
+00:16:54,990 --> 00:16:58,980
+اللي هو بدنا نطلعهإذا زي ما اتعلمنا المرة الماضية
+
+232
+00:16:58,980 --> 00:17:01,380
+بنوجد الـ A-Inverse الـ A-Inverse بنوجد الـ
+
+233
+00:17:01,380 --> 00:17:05,060
+determinant للـ A باللي جيله عبارة عن عشرة بكون
+
+234
+00:17:05,060 --> 00:17:08,760
+واحد على عشرة في الـ Adjoint بنكون أوجدنا الـ
+
+235
+00:17:08,760 --> 00:17:12,420
+Adjoint وجهزنا زي ما اتعلمتوا كيف توجدوه الآن طلع
+
+236
+00:17:12,420 --> 00:17:15,690
+عندي الـ A-Inverseبتطلع ال X اللي هي عبارة عن مين
+
+237
+00:17:15,690 --> 00:17:18,550
+ال X X واحد X اتنين X تلاتة أيش بتساوي زي ما قلنا
+
+238
+00:17:18,550 --> 00:17:23,490
+A inverse في B هي ال A inverse وهي مين المصفوفة B
+
+239
+00:17:23,490 --> 00:17:27,070
+اللي هي مصفوفة الحدود المطلقة بنضرب هادي الآن في
+
+240
+00:17:27,070 --> 00:17:31,170
+هادي بطلع عندي اللي هو تلاتين عشرة عشرين ونضرب في
+
+241
+00:17:31,170 --> 00:17:34,130
+واحدة العشر اللي برا هذا بطلع عندي تلاتة واحد
+
+242
+00:17:34,130 --> 00:17:39,300
+اتنين فبكون عندي X واحد بساوي تلاتةX2 بيساوي واحد
+
+243
+00:17:39,300 --> 00:17:44,220
+و X3 بيساوي ايش بيساوي اتنين اذا يا شباب و يا بنات
+
+244
+00:17:44,220 --> 00:17:48,980
+عندي مادامة ال A inverse موجودة اذا الحل بيكون
+
+245
+00:17:48,980 --> 00:17:54,540
+وحيد وهي الحل طلع عندي في هذه الحالة X1 ثلاثة و X2
+
+246
+00:17:54,540 --> 00:18:00,920
+واحد و X3 اتنين هذه هي حلول المعادلات او ال system
+
+247
+00:18:00,920 --> 00:18:05,200
+of equations اللي عددهم جديش يا جماعة اللي عددهم
+
+248
+00:18:05,200 --> 00:18:10,930
+تلت معادلات بتلت مجهيلالان يا جماعة خلصنا المحاضرة
+
+249
+00:18:10,930 --> 00:18:16,530
+الثالثة هي محاضرة بسيطة واضحةمطلوب منكم تحلوا اللي
+
+250
+00:18:16,530 --> 00:18:18,810
+هو عندي solve the following equations using
+
+251
+00:18:18,810 --> 00:18:27,310
+inverse matrix بدي تحلوا A و D بس A و D اجبولياهم
+
+252
+00:18:27,310 --> 00:18:32,170
+اللي هو محلولات المرة القادمة زي ما بنعمل في كل
+
+253
+00:18:32,170 --> 00:18:36,810
+واجب والسلام عليكم ورحمة الله وبركاته وإلى لقاء
+
+254
+00:18:36,810 --> 00:18:37,350
+آخر
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c87b2d010ee4ff6533d3844cb19450ea20a0ccf2
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8.srt
@@ -0,0 +1,1959 @@
+1
+00:00:01,570 --> 00:00:06,970
+بسم الله الرحمن الرحيم هذه هي المحاضرة السابعة
+
+2
+00:00:06,970 --> 00:00:11,750
+مساق غياضيات منفصلة لطلاب وطالبات الجامعة
+
+3
+00:00:11,750 --> 00:00:18,030
+الإسلامية كلية  technology  الآمعلومات قسم الحوسبة
+
+4
+00:00:18,030 --> 00:00:22,090
+المتنقلة المحاضرة اليوم إن شاء الله هنستكمل فيها
+
+5
+00:00:22,090 --> 00:00:26,110
+الحديث عن الـ greatest common divisor أو العامل 
+
+6
+00:00:26,110 --> 00:00:31,460
+المشترك الأعلى بين عددين اليوم بدنا نعرف كيف نوجد
+
+7
+00:00:31,460 --> 00:00:35,420
+الـ greatest common divisor باستخدام حاجة اسمها
+
+8
+00:00:35,420 --> 00:00:43,560
+الـ prime factorization أو عن طريق تحليل العدد
+
+9
+00:00:43,560 --> 00:00:50,080
+إلى عوامله الأولية عن طريق العوامل الأولية كيف
+
+10
+00:00:50,080 --> 00:00:54,080
+نجد الـ greatest common divisor كما يلي تابعوا معايا
+
+11
+00:00:54,080 --> 00:00:58,060
+الآن نفترض أن الـ prime factorization للعدد a والـ b
+
+12
+00:00:58,060 --> 00:01:01,400
+هي كما يلي ماذا يعني الـ prime factorization يعني
+
+13
+00:01:01,400 --> 00:01:05,180
+نحلل العدد a إلى عوامله الأولية يطلع اللي عندي
+
+14
+00:01:05,180 --> 00:01:11,580
+العدد a عبارة عن b1<sup>a1</sup> b2<sup>a2</sup> ... b<sub>n</sub><sup>a<sub>n</sub></sup>  وبنأن حللنا b يطلع
+
+15
+00:01:11,580 --> 00:01:15,500
+على صورة b<sub>1</sub><sup>b<sub>1</sub></sup> b<sub>2</sub><sup>b<sub>2</sub></sup> ... b<sub>n</sub><sup>b<sub>n</sub></sup>
+
+16
+00:01:15,500 --> 00:01:19,860
+حيث الـ a<sub>1</sub> والـ b<sub>1</sub> والـ b<sub> </sub>
+
+17
+00:01:19,860 --> 00:01:22,900
+<sub>2</sub> والـ b<sub>n</sub> والـ a<sub>1</sub> والـ a<sub>2</sub> والـ a<sub>n</sub>
+
+18
+00:01:22,900 --> 00:01:27,620
+عبارة عن integers أكبر أو يساوي صفر بينما الـ b<sub> </sub>
+
+19
+00:01:27,620 --> 00:01:31,020
+<sub>1</sub> والـ b<sub>n</sub> عبارة عن الـ primes لأن بعد ما حللنا
+
+20
+00:01:31,020 --> 00:01:34,260
+هنا على الصورة هذه بيكون الـ greatest common divisor
+
+21
+00:01:34,260 --> 00:01:39,020
+بين الـ a والـ b هو عبارة عن b<sub>1</sub><sup>الـ minimum بين</sup>
+
+22
+00:01:39,020 --> 00:01:47,800
+a<sub>1</sub> والـ b<sub>1</sub> الـ b<sub>2</sub><sup>الـ minimum بين a<sub>2</sub> والـ b<sub>2</sub></sup> لما أصل عند
+
+23
+00:01:47,800 --> 00:01:53,840
+الـ b<sub>n</sub><sup>الـ minimum بين a<sub>n</sub> والـ b<sub>n</sub></sup> بهذه الطريقة بنكون
+
+24
+00:01:53,840 --> 00:01:58,420
+احنا حللنا أو وجدنا الـ greatest common divisor أو
+
+25
+00:01:58,420 --> 00:02:03,360
+العامل المشترك الأعلى بين العددين a والـ b بهذه
+
+26
+00:02:03,360 --> 00:02:08,000
+الطريقة والآن إن شاء الله هناخد example عملي على
+
+27
+00:02:08,000 --> 00:02:12,640
+هذه اللي هي الطريقة نجي الآن هذا الكلام عمليا ل
+
+28
+00:02:12,640 --> 00:02:13,880
+GMS شوفوا 
+
+29
+00:02:20,500 --> 00:02:24,240
+العامل المشترك الأعلى هو greatest common divisor
+
+30
+00:02:29,620 --> 00:02:35,840
+العامل المشترك الأعلى بين الـ 120 والـ 500 راح نوجد
+
+31
+00:02:35,840 --> 00:02:39,480
+الأعلى إيش بيشتغلوا؟ باقي الـ 120 بيستخدع راتورة
+
+32
+00:02:39,480 --> 00:02:43,440
+عاملها الأولية على اثنين باقي الـ 60 يطلع 
+
+33
+00:02:43,440 --> 00:02:47,120
+على اثنين يطلع الـ 30 على اثنين يطلع الـ 15 الـ 15
+
+34
+00:02:47,120 --> 00:02:54,050
+على ثلاثة يطلع خمسة وهي خمسة فبيصير التحليل إلى 
+
+35
+00:02:54,050 --> 00:02:58,310
+120 إلى primes هو عبارة عن اثنين في ثلاثة في خمسة
+
+36
+00:02:58,310 --> 00:03:01,850
+في خمسة نفس الشيء باقي الـ 500 برغم تحليلها
+
+37
+00:03:01,850 --> 00:03:05,730
+العوامل الأولية بنفس الطريقة بلاقيها عبارة عن 
+
+38
+00:03:05,730 --> 00:03:08,070
+الأول اثنين في 250 بعدين إذا فيها اثنين
+
+39
+00:03:08,070 --> 00:03:12,110
+ثلاثة على خمسة على خمسة وهكذا يطلع عندي اثنين تربيع
+
+40
+00:03:12,110 --> 00:03:16,060
+في خمسة تكعيب إن كتبت على الصورة هذه الـ prime
+
+41
+00:03:16,060 --> 00:03:19,380
+factorization الـ prime factorization الـ prime factorization
+
+42
+00:03:19,380 --> 00:03:19,880
+الـ prime factorization الـ prime factorization الـ prime
+
+43
+00:03:19,880 --> 00:03:21,880
+factorization الـ prime factorization الـ prime factorization
+
+44
+00:03:21,880 --> 00:03:24,460
+الـ prime factorization الـ prime factorization الـ prime
+
+45
+00:03:24,460 --> 00:03:28,220
+factorization الـ prime factorization الـ prime factorization
+
+46
+00:03:28,220 --> 00:03:30,380
+الـ prime factorization الـ prime factorization الـ prime
+
+47
+00:03:30,380 --> 00:03:33,480
+factorization الـ prime فهي الـ minimum بين ثلاثة واثنين
+
+48
+00:03:33,480 --> 00:03:38,120
+وقص هنا واحد وهنا فيش ثلاثة يعني وكأنه ثلاثة قص
+
+49
+00:03:38,120 --> 00:03:41,280
+صفر لما ثلاثة وصفر يعني بواحد لما ينضرب بواحد هنا
+
+50
+00:03:41,280 --> 00:03:44,720
+ثلاثة وصفر مش هيأثر هيظل العدد زي ما هو فبنكتب
+
+51
+00:03:44,720 --> 00:03:47,100
+ثلاثة قص الـ minimum واحد وصفر
+
+52
+00:03:50,450 --> 00:03:54,050
+الـ خمسة الـ minimum بين الأس اللي أنا والأس اللي
+
+53
+00:03:54,050 --> 00:03:58,450
+هو واحد وثلاثة بيصير الـ minimum بين ثلاثة واثنين
+
+54
+00:03:58,450 --> 00:04:03,750
+واحد بين ثلاثة واثنين اثنين بيصير اثنين أس اثنين
+
+55
+00:04:03,750 --> 00:04:07,390
+مضروبة في ثلاثة قص في الـ minimum بين واحد وصفر الـ
+
+56
+00:04:07,390 --> 00:04:10,590
+minimum بين واحد وصفر طبعًا صفر تصبح ثلاثة قص صفر
+
+57
+00:04:10,590 --> 00:04:13,390
+في الـ الآن الـ minimum بين واحد وثلاثة اللي هي إيش
+
+58
+00:04:13,390 --> 00:04:17,510
+واحد فتصبح خمسة قص واحد إذا بيصير الجواب عندي
+
+59
+00:04:17,510 --> 00:04:21,210
+اثنين تربيع يعني أربعة ثلاثة قص صفر يعني واحد
+
+60
+00:04:21,210 --> 00:04:25,210
+أقول لكم في حالة اللي عامل الـ greatest common divisor
+
+61
+00:04:25,540 --> 00:04:32,000
+اللي هو العامل المشترك الأعلى لو أنا ما حطيتش
+
+62
+00:04:32,000 --> 00:04:36,260
+الثلاثة بنفع يعني الثلاثة مش موجودة في الجهتين
+
+63
+00:04:36,260 --> 00:04:41,860
+انساه وما تكتبهاش وهذه نشيلها بنفع لأنه في الآخر
+
+64
+00:04:41,860 --> 00:04:45,380
+هتطلع ثلاثة أقل صفر طيب اثنين أقل أربعة في خمسة
+
+65
+00:04:45,380 --> 00:04:49,840
+بتطلع مجدهش ومن عشرين ندي لها المثال الثاني اللي
+
+66
+00:04:49,840 --> 00:04:53,970
+هو أوجد المضاعف الـ greatest common divisor بين الـ
+
+67
+00:04:53,970 --> 00:05:01,690
+2400 والـ 6300 بعد الـ 2400 بحللها عواملها
+
+68
+00:05:01,690 --> 00:05:06,990
+الأولية بلاقيها عبارة عن اثنين أس خمسة في ثلاثة في
+
+69
+00:05:06,990 --> 00:05:13,310
+خمسة تربيع وقولنا كيف بالحل الآن الـ 6300 بحللها
+
+70
+00:05:13,310 --> 00:05:16,250
+عواملها الأولية تطلع اثنين تربيع اثنين تربيع في
+
+71
+00:05:16,250 --> 00:05:21,040
+ثلاثة تربيع في خمسة تربيع في سبعة الآن على طول الـ
+
+72
+00:05:21,040 --> 00:05:25,300
+greatest common divisor اللي هو الموضوع العام
+
+73
+00:05:25,300 --> 00:05:29,940
+للمشترك الأعلى مادام هي الـ تمام موجودة هنا وموجودة
+
+74
+00:05:29,940 --> 00:05:32,940
+هنا بكتبها اثنين الـ minimum خمسة واثنين الثلاثة
+
+75
+00:05:32,940 --> 00:05:35,900
+موجودة هنا وموجودة هنا بكتب ثلاثة الـ minimum واحد و
+
+76
+00:05:35,900 --> 00:05:39,800
+اثنين الخمسة موجودة هنا وموجودة هنا خمسة أس
+
+77
+00:05:39,800 --> 00:05:42,700
+الـ minimum اثنين واثنين لأن هنا الأس اثنين وهنا الأس
+
+78
+00:05:42,700 --> 00:05:46,800
+اثنين السبعة مش موجودة هنا خلاص فانساها يعني لو
+
+79
+00:05:46,800 --> 00:05:49,880
+حاطيتها زي اللي فوق وعملت الـ minimum بين الأس صفر و
+
+80
+00:05:49,880 --> 00:05:52,260
+الواحد ما هو هيطلع صفر يعني معناته هيطلع واحد
+
+81
+00:05:52,260 --> 00:05:56,710
+الجواب وده خلاص ليش أغلب حالي إذا بأخد مين اللي
+
+82
+00:05:56,710 --> 00:06:01,850
+موجودة في الجهتين الاثنين قص الأصغر بيصير اثنين
+
+83
+00:06:01,850 --> 00:06:05,270
+قص اثنين ثلاثة قص الأصغر اللي هو واحد ثلاثة قص
+
+84
+00:06:05,270 --> 00:06:08,250
+واحد الخمسة قص اثنين قص الأصغر اللي هو خمسة قص
+
+85
+00:06:08,250 --> 00:06:11,810
+اثنين السبعة مش موجودة لغيرها نخلص بانساها بيصير
+
+86
+00:06:11,810 --> 00:06:16,070
+هذا هو المضاعف العامل المشترك الأعلى اللي هو
+
+87
+00:06:16,070 --> 00:06:19,190
+greatest common divisor باجي بحسبها بلاقيها إيش
+
+88
+00:06:19,190 --> 00:06:23,310
+بتساوي بتساوي 300 إذا الموضوع سهل طيب
+
+89
+00:06:29,490 --> 00:06:35,530
+العامل المشترك الأعلى اللي نسميه least common 
+
+90
+00:06:35,530 --> 00:06:43,710
+multiple أو المضاعف المشترك الأصغر المضاعف المشترك
+
+91
+00:06:43,710 --> 00:06:50,130
+الأقل أو الأصغر أو البسيط تعريفه كمان يعني the
+
+92
+00:06:50,130 --> 00:06:53,230
+least common multiple of the positive integers a
+
+93
+00:06:53,230 --> 00:06:57,090
+and b is the smallest positive integer هو عبارة عن
+
+94
+00:06:57,090 --> 00:07:01,390
+أصغر positive integer that is divisible by both a
+
+95
+00:07:01,390 --> 00:07:07,750
+and b يعني أصغر اللي هو مضاعف .. أصغر اللي هو
+
+96
+00:07:07,750 --> 00:07:13,010
+positive integer اللي هو divisible by a يعني اللي
+
+97
+00:07:13,010 --> 00:07:19,620
+هو a بتقسمه وb بتقسمه يعني بمعنى آخر بيكون أصغر
+
+98
+00:07:19,620 --> 00:07:26,760
+مضاعف للـ a وللـ b وبنرمزه بـ lcm بالـ a والـ b إذا
+
+99
+00:07:26,760 --> 00:07:32,280
+عشان نرمز لأصغر مضاعف بين a وb بدنا نجيب مضاعفات
+
+100
+00:07:32,280 --> 00:07:34,020
+الـ a ومضاعفات الـ b
+
+101
+00:07:39,360 --> 00:07:43,220
+مضاعفات الـ a عددها لا نهائي مضاعفات الـ b عددها
+
+102
+00:07:43,220 --> 00:07:49,020
+لا نهائي بنجيب أولها وبنشوف كيف نسوي لنوجد find least
+
+103
+00:07:49,020 --> 00:07:52,260
+common multiple بين ستة وعشرة نوجد المضاعف
+
+104
+00:07:52,260 --> 00:07:55,360
+المشترك الأصغر بين الستة والعشرة إيش بيجيب نوجد
+
+105
+00:07:55,360 --> 00:07:59,620
+لأن هذه طريقة بدائية بعد شوية هنجد الموضوع سهل
+
+106
+00:07:59,620 --> 00:08:04,760
+مضاعفات الستة إيش مضاعفات المضاعفات
+
+107
+00:08:23,040 --> 00:08:24,440
+6 12 18 24 30 36 ...
+
+108
+00:08:34,800 --> 00:08:41,340
+لأن من المضاعفات المشتركة هي 6 لا 12 لا 18 لا 20
+
+109
+00:08:41,340 --> 00:08:47,260
+لا 24 لا 30 هذه وهذه أول واحد بنجد له مشترك
+
+110
+00:08:47,260 --> 00:08:50,440
+بين المضاعفات هو اللي بسميه least common multiple
+
+111
+00:08:50,440 --> 00:08:55,430
+بين 6 و10 يساوي 30 هذا الكلام يعني خلّيني أقول
+
+112
+00:08:55,430 --> 00:08:59,790
+مرهق شوية فإن احنا لو كانت الأعداد كبيرة بنقعد ده
+
+113
+00:08:59,790 --> 00:09:03,890
+هو نضاعف العدد ونضعف العدد يمكن يلتقي بعد عدد كبير
+
+114
+00:09:03,890 --> 00:09:08,450
+فبتغلب إذا في طريقة أكيد أسهل اللي هي طريقة مشابهة
+
+115
+00:09:08,450 --> 00:09:13,030
+لطريقة الـ greatest common divisor اللي هي عن طريق الـ
+
+116
+00:09:13,030 --> 00:09:17,370
+prime factorization إذا الـ least common multiple
+
+117
+00:09:17,370 --> 00:09:20,950
+can also be computed from the prime factorization
+
+118
+00:09:20,950 --> 00:09:24,110
+يعني ممكن إيجاد اللي هو الـ least common multiple
+
+119
+00:09:24,110 --> 00:09:27,050
+بواسطه الـ prime factorization نوجد الـ prime
+
+120
+00:09:27,050 --> 00:09:29,330
+factorization للأول والـ prime factorization
+
+121
+00:09:29,330 --> 00:09:32,310
+للثاني وبنقول الـ least common multiple بين الـ a و
+
+122
+00:09:32,310 --> 00:09:36,310
+الـ b بيساوي b<sub>1</sub> مش الـ minimum الآن بيجيب الـ
+
+123
+00:09:36,310 --> 00:09:40,910
+maximum بين a<sub>1</sub> وb<sub>1</sub> وb<sub>2</sub> بيساوي الـ
+
+124
+00:09:40,910 --> 00:09:44,540
+maximum بين a<sub>2</sub> وb<sub>2</sub> والـ b<sub>m</sub> الـ maximum
+
+125
+00:09:44,540 --> 00:09:48,840
+بين الـ a<sub>n</sub> والـ b<sub>m</sub> خلّينا نشوف هذا الكلام عمليًا و
+
+126
+00:09:48,840 --> 00:09:53,160
+حساسا عليكم كمان غير هذا سأسهل عليكم الآن ال 120
+
+127
+00:09:53,160 --> 00:09:57,860
+قبل قليل حللناها 2×3 في ثلاثة في خمسة والـ 500
+
+128
+00:09:57,860 --> 00:10:00,220
+اتنين تربيعي في خمسة تكعيب الآن الـ least common
+
+129
+00:10:00,220 --> 00:10:04,160
+multiple بين الـ 120 والـ 500 إيش بيساوي؟ اتنين
+
+130
+00:10:04,160 --> 00:10:07,400
+بمسك واحدة اتنين الـ maximum تلاتة واتنين بس هنا
+
+131
+00:10:07,400 --> 00:10:11,680
+لازم تحطهم كلهم مش زي قبل إن اللي ما فيش موجودة هنا
+
+132
+00:10:11,680 --> 00:10:15,880
+ما بحطهاش لأ هنا لازم تحطهم كلهم الاتنين والتلاتة
+
+133
+00:10:15,880 --> 00:10:18,840
+حتى لو مش ظاهرة هنا ولو إيش ظاهر هنا بدك تحطه
+
+134
+00:10:18,840 --> 00:10:22,690
+برضه اللي هو تلاتة في الـ maximum بين الواحد والاثنين
+
+135
+00:10:22,690 --> 00:10:27,260
+خمسة في الـ maximum بين الواحد والتلاتة الآن الظاهر غير
+
+136
+00:10:27,260 --> 00:10:29,780
+هذه الظاهر هي الظاهر التلاتة والخمسة وال
+
+137
+00:10:29,780 --> 00:10:31,040
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+138
+00:10:31,040 --> 00:10:32,520
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+139
+00:10:32,520 --> 00:10:36,520
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+140
+00:10:36,520 --> 00:10:40,240
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+141
+00:10:40,240 --> 00:10:44,000
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+142
+00:10:44,000 --> 00:10:44,020
+الخمسة والخمسة والخمسة والخمسة والخمسة والخمسة
+
+143
+00:10:44,020 --> 00:10:46,940
+الخمسة والخمسة والخمسة والخمسة 
+
+144
+00:10:55,050 --> 00:10:59,250
+طيب في علاقة بين اللي هو الـ least common multiple
+
+145
+00:10:59,250 --> 00:11:02,550
+والـ greatest common divisor هذه العلاقة بتريحنا
+
+146
+00:11:02,550 --> 00:11:07,810
+بتخلينا نوجد واحدة منهم والتانية نوجدها منها يعني
+
+147
+00:11:07,810 --> 00:11:13,530
+الآن العلاقة عبر نظرية خامسة بتقول كمالي let a and
+
+148
+00:11:13,530 --> 00:11:17,190
+b positive integers then لو كانت a و b عبارة عن
+
+149
+00:11:17,190 --> 00:11:21,430
+positive integers then الـ a في الـ b بتساوي الـ greatest
+
+150
+00:11:21,430 --> 00:11:24,770
+common divisor في الـ a والـ b وفي الـ least common
+
+151
+00:11:24,770 --> 00:11:28,090
+multiple بين الـ a والـ b يعني بيقول دائما دائما
+
+152
+00:11:28,090 --> 00:11:31,730
+دائما لو جبت الـ least common multiple وضربته في
+
+153
+00:11:31,730 --> 00:11:34,310
+الـ greatest common divisor هيطلع إيش اللي بيساوي الـ
+
+154
+00:11:34,310 --> 00:11:38,970
+a في الـ b عشان هي كأرياح لنا بكفى بنودد الـ greatest
+
+155
+00:11:38,970 --> 00:11:42,690
+common divisor بين الـ A والـ B وبنودد الـ least
+
+156
+00:11:42,690 --> 00:11:45,670
+common multiple كيف بنقول؟ A في B على الـ greatest
+
+157
+00:11:45,670 --> 00:11:48,610
+common divisor إذا ما فيش داعي إنه نودد هنا ونودد
+
+158
+00:11:48,610 --> 00:11:50,630
+هناك مع إنه الجهتين لو أوددت اللي هو الـ
+
+159
+00:11:50,630 --> 00:11:54,950
+factorization بيصير سهل تودي للتانين لكن اللي حابب
+
+160
+00:11:54,950 --> 00:11:59,330
+الطريقة الأخرى بيدي بيقول فرغبنا إنه بدوا الـ least
+
+161
+00:11:59,330 --> 00:12:03,170
+common multiple بين الـ 125 زي اللي فوق إيش بيساوي؟
+
+162
+00:12:03,290 --> 00:12:07,250
+كتب الـ 2400 على صورة الـ prime factorization ال
+
+163
+00:12:07,250 --> 00:12:08,770
+الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+164
+00:12:08,770 --> 00:12:10,290
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+165
+00:12:10,290 --> 00:12:11,650
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+166
+00:12:11,650 --> 00:12:16,590
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+167
+00:12:16,590 --> 00:12:16,950
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+168
+00:12:16,950 --> 00:12:17,950
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+169
+00:12:17,950 --> 00:12:18,670
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+170
+00:12:18,670 --> 00:12:20,230
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+171
+00:12:20,230 --> 00:12:20,590
+الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+172
+00:12:20,590 --> 00:12:24,470
+الـ الـ 
+
+173
+00:12:30,770 --> 00:12:35,750
+الـ least common multiple للـ 2400 والـ 6300
+
+174
+00:12:35,750 --> 00:12:40,510
+أول شيء بدي أوجد الـ greatest common divisor أوجدته
+
+175
+00:12:40,510 --> 00:12:43,970
+هنا قبل شوية إيش كان أوجدناه؟ الـ 2400 سواء
+
+176
+00:12:43,970 --> 00:12:47,590
+اتنين وخمسة في تلاتة في خمسة تربيع والـ 6300
+
+177
+00:12:47,590 --> 00:12:50,050
+سواء اتنين تربيع في تلاتة تربيع في خمسة تربيع في
+
+178
+00:12:50,050 --> 00:12:53,610
+سبعة الآن الـ greatest common divisor بين الجهتين سواء
+
+179
+00:12:53,610 --> 00:12:58,090
+اتنين الـ minimum بين اتنين وخمسة
+
+180
+00:13:00,080 --> 00:13:04,700
+التلاتة بين الواحدة والتانية والخمسة بين التنين
+
+181
+00:13:04,700 --> 00:13:09,000
+والتنين والسبعة لا يوجد داعي لأن أنا مجرد common
+
+182
+00:13:09,000 --> 00:13:15,120
+divisor لو مرتبل أفضل عنه لكتب السبعة عشان آخذ الـ
+
+183
+00:13:15,120 --> 00:13:19,900
+maximum لأن هذي بيصير اتنين قصر لصغير اتنين تلاتة
+
+184
+00:13:19,900 --> 00:13:20,680
+لصغير واحد
+
+185
+00:13:27,940 --> 00:13:35,940
+الـ least common multiple للـ 2400 والـ 6300 بيساوي اللي هو
+
+186
+00:13:35,940 --> 00:13:40,260
+حاصل ضرب الرقمين اللي هو A في B مقسوم عليه على
+
+187
+00:13:40,260 --> 00:13:44,200
+الـ 300 بطلع هذا بقى إذن هذه طريقة أخرى لإيجاد
+
+188
+00:13:44,200 --> 00:13:47,880
+least common multiple إذا أنت بتكشف وجودها مباشرة
+
+189
+00:13:47,880 --> 00:13:52,340
+من هذا ولو قدرتها مباشرة من هنا برضه اللي هو صحيح
+
+190
+00:13:52,340 --> 00:13:59,180
+الآن احنا في حاجة اسمها لدينا الـ Euclidean Algorithm
+
+191
+00:13:59,180 --> 00:14:03,820
+الـ Euclidean Algorithm بدنا نقصص الـ Euclidean Algorithm
+
+192
+00:14:03,820 --> 00:14:09,280
+نوجد الـ greatest common اللي هو divisor مش دائما
+
+193
+00:14:09,860 --> 00:14:13,580
+موضوع الـ greatest common divisor اللي هو إن التحليل
+
+194
+00:14:13,580 --> 00:14:18,620
+لو كانت الأرقام كبيرة برضه بتغلب لكن برضه هناخد
+
+195
+00:14:18,620 --> 00:14:25,060
+طريقة أخرى لإيجاد الـ greatest common divisor بالعددين
+
+196
+00:14:25,060 --> 00:14:31,000
+لو أعطونا A و B عددين هذه طريقة أخرى العددين A و B
+
+197
+00:14:31,000 --> 00:14:34,820
+ووجدنا بالله الـ greatest common divisor ده كله ماشي
+
+198
+00:14:35,320 --> 00:14:39,420
+أنا بدي أقول أكتب الـ A على طول الـ BQ زائد الـ R يعني
+
+199
+00:14:39,420 --> 00:14:44,460
+بدي أقسم الـ A على الـ B يطلع عندي A بيساوي BQ زائد الـ R
+
+200
+00:14:44,460 --> 00:14:50,100
+باقي لأن هذه اللي ما بتقولك ريحها دائما دائما
+
+201
+00:14:50,100 --> 00:14:54,060
+العامل المشترك الأعلى بين الـ A والـ B بيساوي العامل
+
+202
+00:14:54,060 --> 00:14:59,160
+المشترك الأعلى بين الـ B اللي مقسوم عليه وإيش؟ وباقي
+
+203
+00:14:59,550 --> 00:15:03,570
+دائما العامل المشترك الأعلى بين الـ A والـ B حيث هو
+
+204
+00:15:03,570 --> 00:15:07,810
+بين الـ B والـ Q والـ R هذه اللي هي اللي تعاملنا اللي
+
+205
+00:15:07,810 --> 00:15:13,210
+موجودة هي اللي بتشرع لنا الآن طريقة إيجاد greatest
+
+206
+00:15:13,210 --> 00:15:17,710
+common divisor بهذه الطريقة هذه بنسميها اللي هي عن
+
+207
+00:15:17,710 --> 00:15:23,510
+طريق الـ Euclidean Algorithm أو الخوارزمية القسمة Hence,
+
+208
+00:15:23,630 --> 00:15:26,550
+the Euclidean Algorithm is an efficient method for
+
+209
+00:15:26,550 --> 00:15:30,430
+computing the greatest common divisor of two integers
+
+210
+00:15:48,480 --> 00:15:50,680
+باقي الـ 287 عامل عامل عامل عامل عامل عامل عامل
+
+211
+00:15:50,680 --> 00:15:52,520
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+212
+00:15:52,520 --> 00:15:53,000
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+213
+00:15:53,000 --> 00:15:54,500
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+214
+00:15:54,500 --> 00:15:55,280
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+215
+00:15:55,280 --> 00:15:55,520
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+216
+00:15:55,520 --> 00:15:56,740
+عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+217
+00:15:56,740 --> 00:16:01,180
+عامل عامل
+
+218
+00:16:01,180 --> 00:16:08,020
+عامل عامل
+
+219
+00:16:08,020 --> 00:16:12,670
+طيب إيش يعني؟ أكمل أكملك بقسم الآن 91 مع
+
+220
+00:16:12,670 --> 00:16:16,290
+الـ 14 لما قسمت الـ 91 مع الـ 14
+
+221
+00:16:16,290 --> 00:16:20,250
+فالـ 91 صار 14 في 6 زائد 7 أطبق
+
+222
+00:16:20,250 --> 00:16:27,330
+الآن هذه الخاصية على الـ 91 والـ 14 العامل المشترك
+
+223
+00:16:27,330 --> 00:16:31,490
+الأعلى بين الـ 91 والـ 14 بيساوي العامل المشترك الأعلى
+
+224
+00:16:31,490 --> 00:16:35,550
+بين المقسوم عليه والـ remainder الـ 14 والـ 7 ماشي
+
+225
+00:16:35,550 --> 00:16:39,450
+الحال طيب إيش يعني؟ بجيبها الـ greatest بقولك إيش يعني؟
+
+226
+00:16:39,450 --> 00:16:44,830
+خذ الـ 14 والـ 7 هذه الـ 14 والـ 7 في 2 زائد 0 عندها أنا
+
+227
+00:16:44,830 --> 00:16:48,920
+بنهيل لأنه بيصير العامل المشترك الأعلى اللي هو بين
+
+228
+00:16:48,920 --> 00:16:54,120
+الـ 14 والـ 7 اللي هو عارفينه مين؟ 7 يعني
+
+229
+00:16:54,120 --> 00:16:57,840
+الآن من هذا بيصير عندي العامل المشترك الأعلى بين
+
+230
+00:16:57,840 --> 00:17:02,240
+الـ 14 بيساوي 7 بيصير عندي بضل أوجد هذا
+
+231
+00:17:02,240 --> 00:17:07,820
+بيخليني أستنتج ما يعني إنه بضل أوجد 287 على 91 ثم
+
+232
+00:17:07,820 --> 00:17:12,160
+ناتج القسمة على المتبقي ثم ناتج القسمة على المتبقي
+
+233
+00:17:12,160 --> 00:17:14,340
+ثم ناتج القسمة على المتبقي ثم ناتج القسمة على
+
+234
+00:17:14,340 --> 00:17:14,460
+المتبقي ثم ناتج القسمة على المتبقي ثم ناتج القسمة
+
+235
+00:17:14,460 --> 00:17:15,020
+على المتبقي ثم ناتج القسمة على المتبقي ثم ناتج
+
+236
+00:17:15,020 --> 00:17:15,760
+القسمة على المتبقي ثم ناتج القسمة على المتبقي ثم
+
+237
+00:17:15,760 --> 00:17:17,780
+ناتج القسمة على المتبقي ثم ناتج القسمة على المتبقي
+
+238
+00:17:17,780 --> 00:17:18,360
+ثم ناتج القسمة على المتبقي ثم ناتج القسمة على
+
+239
+00:17:18,360 --> 00:17:19,480
+المتبقي ثم ناتج القسمة على المتبقي ثم ناتج القسمة
+
+240
+00:17:19,480 --> 00:17:25,240
+على المتبقي ثم ناتج القسمة على المتبقي ثم ناتج
+
+241
+00:17:25,240 --> 00:17:28,690
+القسمة على المتبقي اللي هو هيكون إيش بيساوي؟ 7 من
+
+242
+00:17:28,690 --> 00:17:31,490
+وين جبته؟ هذا بناء على العلاقة هذه اللي أوجدناها
+
+243
+00:17:31,490 --> 00:17:33,270
+إن هذا بيساوي الـ greatest common divisor بين
+
+244
+00:17:33,270 --> 00:17:36,530
+الـ 14 والـ 7 بيساوي 7 يعني الآن شغل المثل
+
+245
+00:17:36,530 --> 00:17:40,990
+اللي بيوجد العامل المشترك العالمي للـ 287 والـ 91 إيش
+
+246
+00:17:40,990 --> 00:17:47,450
+بيساوي؟ بيجي بيقسم الـ 287 على الـ 91 اللي أنا بطلع
+
+247
+00:17:47,450 --> 00:17:51,270
+عنده ناتج قسمة ما هي 91 بطلع باقي بتقسم الـ 91 على
+
+248
+00:17:51,270 --> 00:17:56,020
+الباقي اللي هو بيطلع ناتج قسمة وباقي بيبقى تعمل
+
+249
+00:17:56,020 --> 00:18:00,900
+هذه لما تصل في الآخر باقي بيساوي صفر أول باقي
+
+250
+00:18:00,900 --> 00:18:05,400
+قبل الباقي صفر بيكون هو الـ Greatest Common
+
+251
+00:18:05,400 --> 00:18:12,700
+Divisor بين العددين اللي بدأت فيهم طيب الآن ال
+
+252
+00:18:12,700 --> 00:18:16,820
+Greatest Common Divisor بنقدر نكتبه على صورة اللي
+
+253
+00:18:16,820 --> 00:18:23,540
+هو الآن linear combinations بين اللي هم العددين تبع
+
+254
+00:18:23,540 --> 00:18:27,980
+اللوحي المفروض مفروض فمانعي بزواد سفينة بتقول
+
+255
+00:18:27,980 --> 00:18:33,180
+مانعي if a and b are positive integers then there
+
+256
+00:18:33,180 --> 00:18:37,080
+exist integers s and t for example جريتكم مبادرة
+
+257
+00:18:37,080 --> 00:18:38,580
+ومعينة a وb بساوية
+
+258
+00:18:42,440 --> 00:18:46,800
+يعني الآن إذا كانت a و b عبارة عن أعداد التي يجب
+
+259
+00:18:46,800 --> 00:18:51,920
+أن تنتجها بقدر ألاقي s و t عبارة عن أعداد صحيحة
+
+260
+00:18:51,920 --> 00:18:55,520
+لحيث أن ال greatest common divisor بين a و b
+
+261
+00:18:55,520 --> 00:19:00,440
+بيساوي عبارة عن s a زائد t b هذا بيسميها linear
+
+262
+00:19:00,440 --> 00:19:01,480
+combination
+
+263
+00:19:06,340 --> 00:19:09,880
+العامل المشترك اللي على بين الـA و الـB يعني كان D
+
+264
+00:19:09,880 --> 00:19:13,620
+written as a linear combination بين الـA و الـB
+
+265
+00:19:13,620 --> 00:19:16,700
+الآن هذا اللي هي by bezout theorem اللي قلته قبل
+
+266
+00:19:16,700 --> 00:19:20,380
+شوية the greatest common divisor of integers A and
+
+267
+00:19:20,380 --> 00:19:24,880
+D كان D expressed ممكن التعبير عنه on the form S A
+
+268
+00:19:24,880 --> 00:19:39,510
+زائد T B where S and T are integers هذا هو عامل
+
+269
+00:19:39,510 --> 00:19:43,730
+المشترك الأعلى بين الـ 6 والـ 14 بساوية هو ناقص 2
+
+270
+00:19:43,730 --> 00:19:47,650
+في 6 زائد 1 في 14 كيف أكتب بين هؤلاء؟ من أين أجيب
+
+271
+00:19:47,650 --> 00:19:52,010
+الـ 1 ونقص 2؟ من أين أجيب الـ 2؟ من أين أجيب الـ
+
+272
+00:19:52,010 --> 00:19:58,880
+2؟ من أين أجيب الـ 2؟ من أين أجيب الـ 2؟ add a
+
+273
+00:19:58,880 --> 00:20:02,560
+linear combination of these two non-valid integers
+
+274
+00:20:02,560 --> 00:20:06,900
+صلوا على النبي عليه الصلاة والسلام الآن finding
+
+275
+00:20:06,900 --> 00:20:10,840
+the greatest common divider add a linear
+
+276
+00:20:10,840 --> 00:20:15,560
+combination بدنا نوجد اللي هو العامل المشترك
+
+277
+00:20:15,560 --> 00:20:19,640
+الأعلى نكتبه على صورة linear combinations of
+
+278
+00:20:19,640 --> 00:20:22,540
+العددين اللي بدنا نوجد اللي هي العامل المشترك
+
+279
+00:20:22,540 --> 00:20:29,370
+الأعلى Express الـ 252 وال198 اللي هي ال address
+
+280
+00:20:29,370 --> 00:20:31,950
+from the device you're building Express الـ 18
+
+281
+00:20:31,950 --> 00:20:36,230
+طبعاً هيطلع Express هذا as a linear combination of
+
+282
+00:20:36,230 --> 00:20:41,310
+ال 252 و198 يعني أننا بدنا نكتب ال 252 و198 على
+
+283
+00:20:41,310 --> 00:20:46,170
+صورة إن هو حاط ال S في هذا زائد ال T في هذا بيساوي
+
+284
+00:20:46,170 --> 00:20:49,030
+إيه؟ إيش؟ طنان طاحته في الواقع الطريقة اللي
+
+285
+00:20:49,030 --> 00:20:53,310
+هنقولها .. هنقولها الآن هتضرب عصفرين بحجم إيش دي؟
+
+286
+00:20:53,310 --> 00:20:59,190
+هتيجي أول إشي توجدك ال 252 عندي اللي هو ال 252
+
+287
+00:20:59,190 --> 00:21:06,450
+هتوجده و في نفس الوجد ال 252 شايفين هذه و ال 198
+
+288
+00:21:06,450 --> 00:21:11,340
+هتيجي توجد العامل المشترك الأعلى بينهمو هتكتب لك
+
+289
+00:21:11,340 --> 00:21:19,820
+إياه في نفس الوقت كيف نشوف كيف شغل المكان الموضوع
+
+290
+00:21:19,820 --> 00:21:27,920
+بس مجرد أن نقسم ال 252 على 198 فالآن 252 على 198
+
+291
+00:21:27,920 --> 00:21:32,520
+بيطلع واحد و المتبقي 54 زي ما عملنا قبل شوية الآن
+
+292
+00:21:32,520 --> 00:21:40,380
+ال 198 بقسمه على المتبقي 198 بتساوي 3 في 54 زائد 36
+
+293
+00:21:40,380 --> 00:21:45,320
+ماشي الحال اللي عملته فوق بعمله كمان تحت بادي خلصت
+
+294
+00:21:45,320 --> 00:21:50,920
+من 198 بادي لل 54 اللي هو ناتج القسم هام مضربه في
+
+295
+00:21:50,920 --> 00:21:56,000
+مين في المتبقي بقى دي اسمه على المتبقي 36 54 بتساوي
+
+296
+00:21:56,000 --> 00:22:02,280
+1 في 36 زائد ال remainder 18 درد 36 و18 36 بتساوي
+
+297
+00:22:02,280 --> 00:22:06,720
+2 في 18 لما أصل مافيش remainder على طول بيكون هذا
+
+298
+00:22:06,720 --> 00:22:11,340
+زي ما قلنا قبل بشويه ال 18 هو هيكون يطلع ل greatest
+
+299
+00:22:11,340 --> 00:22:16,640
+common divisors بين 252 و198 إذا أنا بهذا الطريقة
+
+300
+00:22:16,640 --> 00:22:19,380
+فعلاً أوجدت اللي هو greatest common divisors يعني
+
+301
+00:22:19,380 --> 00:22:22,980
+بلزمنيش يعطيه لي هذا أصلاً هو بلزمنيش هذا أنا
+
+302
+00:22:22,980 --> 00:22:26,260
+هاعرفه أصلاً اللي أنا أوجدت العامل المشترك العالمي
+
+303
+00:22:26,260 --> 00:22:31,500
+بين 252 و198 إيش بيساوي أول متبقي بعد ما أصل
+
+304
+00:22:31,500 --> 00:22:36,210
+للمتبقي بيساوي 0 طيب مش هذا اللي بدنا ياه مدى عارفينه
+
+305
+00:22:36,210 --> 00:22:40,270
+من الأول اه بدنا نكتب اللي هو ال 18 as a linear
+
+306
+00:22:40,270 --> 00:22:47,550
+combination من 252 و198 العملية عملية رجوع لما
+
+307
+00:22:47,550 --> 00:22:53,810
+أصلها دي كده لأن 18 هي بتساوي هادي و بنجي لهادي
+
+308
+00:22:53,810 --> 00:22:59,210
+هان إلى ناقص 1 في 36 ايه سويه ال 18 أخ أسوأ
+
+309
+00:22:59,210 --> 00:23:05,160
+العالم المشترك بسوء 54 ناقص 1 في 36 ببدأ من عند
+
+310
+00:23:05,160 --> 00:23:08,780
+أول متبقي مش سفر اللي هو ال greatest-common divisor و
+
+311
+00:23:08,780 --> 00:23:14,360
+ببدأ أرجع سيرة 18 بيساوي 54 ناقص 1 في 36 أنا بدي
+
+312
+00:23:14,360 --> 00:23:20,320
+18 في دلالة 100 252 و 198 يعني لا بدي ال 36 ولا
+
+313
+00:23:20,320 --> 00:23:26,180
+بدي ال 54 الأربعة ماتضربش خليها زي هذا الآن عند ال
+
+314
+00:23:26,180 --> 00:23:33,770
+36 هذه هيها من هنا بتساوي 198 ناقص 3 في 54 إذا الـ
+
+315
+00:23:33,770 --> 00:23:37,610
+36 هذه من أين بتجيبها من الخطوة اللي جابلها أضالة
+
+316
+00:23:37,610 --> 00:23:43,290
+عن 198 ناقص ثلاثة في خمسة أربعة وخمسين الآن قيمة
+
+317
+00:23:43,290 --> 00:23:47,990
+الـ 36 هذه خليها زي ما هي وما تصبهاش بتعودها مكان
+
+318
+00:23:47,990 --> 00:23:51,830
+مين الـ 36 بصير الـ 18 بتساوي اربعة وخمسين زي ما
+
+319
+00:23:51,830 --> 00:23:56,430
+هي وما تصبهاش ناقص 1 ماشي الآن هذا الواحد مضروب
+
+320
+00:23:56,430 --> 00:24:01,290
+في الـ 36 مين الـ 36 هين هذا كله اللي هو 198 ناقص
+
+321
+00:24:01,290 --> 00:24:04,910
+ثلاثة في اربعة وخمسين تضرب إيش؟ لأنه أنا بدي احنا
+
+322
+00:24:04,910 --> 00:24:11,830
+في الآخر بدلالة 198 وال252 الآن هذه 54 ناقص 1
+
+323
+00:24:11,830 --> 00:24:19,130
+في 198 هي الواحد في 198 هيها الآن عند 54 واحدة وفي
+
+324
+00:24:19,130 --> 00:24:22,880
+عندي ناقص 1 في ناقص 3 في اربعة وخمسين بيصير
+
+325
+00:24:22,880 --> 00:24:26,300
+ناقص في ناقص بتزيد بيصير 1 في 3 في 3
+
+326
+00:24:26,300 --> 00:24:29,140
+بيصير 3 في اربعة وخمسين وفي عندي 1 اربعة
+
+327
+00:24:29,140 --> 00:24:33,040
+وخمسين بيصير 4 اربعة من اربعة وخمسين يعني
+
+328
+00:24:33,040 --> 00:24:38,940
+1 في ناقص 1 في ناقص 3 تطلع 3 3
+
+329
+00:24:38,940 --> 00:24:41,680
+مضروبة في مين في 4 وخمسين 1 في 4 وخمسين
+
+330
+00:24:41,680 --> 00:24:45,260
+بيصير 4 في 4 وخمسين لأنه بيصير من الـ 4
+
+331
+00:24:45,260 --> 00:24:48,960
+وخمسين لو سميناها دي اللي هو اللي هو س بيصير هنا
+
+332
+00:24:48,960 --> 00:24:51,720
+3 س وهنا س بيصير الـ 4 س مين الـ س
+
+333
+00:24:51,720 --> 00:24:55,060
+بيقولنا أنا 4 وخمسين فبيصير 4 في 4 وخمسين
+
+334
+00:24:55,060 --> 00:24:58,480
+ناقص 1 في 198 تضرب هنش لانه بدي
+
+335
+00:24:58,480 --> 00:25:02,330
+إياه إن أنا الآن الاربعة و خمسين لا أريد أن أقوم
+
+336
+00:25:02,330 --> 00:25:04,050
+باستخدامها أنا أريد أن أقوم باستخدام الاربعة و
+
+337
+00:25:04,050 --> 00:25:10,130
+خمسين الاربعة
+
+338
+00:25:10,130 --> 00:25:16,290
+و خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+339
+00:25:16,290 --> 00:25:16,550
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+340
+00:25:16,550 --> 00:25:18,150
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+341
+00:25:18,150 --> 00:25:18,270
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+342
+00:25:18,270 --> 00:25:26,030
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+343
+00:25:26,030 --> 00:25:30,570
+خمسين الاربعة وهذه الآن بدي أضعها في مكان الـ 54
+
+344
+00:25:30,570 --> 00:25:31,870
+لإنها ليست موجودة في الـ 54 لأنها ليست موجودة في
+
+345
+00:25:31,870 --> 00:25:33,370
+الـ 54 لإنها ليست موجودة في الـ 54 لإنها ليست
+
+346
+00:25:33,370 --> 00:25:34,310
+موجودة في الـ 54 لإنها ليست موجودة في الـ 54 لإنها
+
+347
+00:25:34,310 --> 00:25:36,210
+ليست موجودة في الـ 54 لإنها ليست موجودة في الـ 54
+
+348
+00:25:36,210 --> 00:25:36,590
+لإنها ليست موجودة في الـ 54 لإنها ليست موجودة في
+
+349
+00:25:36,590 --> 00:25:40,550
+الـ 54 لإنها ليست موجودة في الـ 54 لإنها ليست
+
+350
+00:25:40,550 --> 00:25:45,590
+موجودة في الـ 54 لإنها ليست موجودة في الـ 54 لإنها
+
+351
+00:25:45,590 --> 00:25:48,070
+ليست موجودة في الـ 54 لإنها ليست موجودة في الـ 54
+
+352
+00:25:48,070 --> 00:25:51,230
+لإنها 
+
+353
+00:25:51,230 --> 00:25:55,160
+ليست موجودة في الـ 4 في ناقص 1 ناقص 4
+
+354
+00:25:55,160 --> 00:26:01,140
+س وفي كمان ناقص س ناقص 5 س من الـ س
+
+355
+00:26:01,140 --> 00:26:05,880
+الـ 198 يعني عندي ناقص 4 من
+
+356
+00:26:05,880 --> 00:26:09,260
+الـ 198ات وعندي ناقص 1 من
+
+357
+00:26:09,260 --> 00:26:13,040
+الـ 198ات بيصير ناقص 4 وناقص
+
+358
+00:26:13,040 --> 00:26:15,980
+1 من 1 بيصير ناقص 5 في 198
+
+359
+00:26:15,980 --> 00:26:21,720
+وتسعين ماذا إذا قمت باستخدام الوصول لقمة 18 أكتبها
+
+360
+00:26:21,720 --> 00:26:25,360
+على صورة linear combination 4 في 252 ناقص 5 في 198
+
+361
+00:26:25,360 --> 00:26:28,820
+و خمسين ناقص 5 في 198 اللي هو
+
+362
+00:26:28,820 --> 00:26:32,620
+طالبه فبيصير عندي اللي هي 18 بتساوي هادي في
+
+363
+00:26:32,620 --> 00:26:37,220
+هادي فهو ال linear combination بين اللي هو الـ 252
+
+364
+00:26:37,220 --> 00:26:40,900
+و 198 في الـ 252 و 198 يعني ال S
+
+365
+00:26:40,900 --> 00:26:44,990
+عبارة عن 4 و ال T عبارة عن ناقص 5 إذا هذه
+
+366
+00:26:44,990 --> 00:26:48,210
+ضربت فيها عصفرين بحجم الـ Euclidean algorithm أو
+
+367
+00:26:48,210 --> 00:26:53,710
+خوارزميتا وقسمها إن أنا ضليت أن أقسم 252 على 198 لما
+
+368
+00:26:53,710 --> 00:26:56,950
+أصلت لل remainder zero أول remainder مش zero بكل
+
+369
+00:26:56,950 --> 00:27:01,190
+هو العامل المشترك الأعلى بينهم هذا بقدر أرجع أرجع
+
+370
+00:27:01,190 --> 00:27:04,490
+زي ما أرجع نهان لما أوصل إنه عبارة عن linear
+
+371
+00:27:04,490 --> 00:27:12,190
+combination بين 198 و252 وهو المخلوق طيب الآن بعض
+
+372
+00:27:12,190 --> 00:27:17,190
+النتائج على بيزوت فيورين Consequences of Bezout's
+
+373
+00:27:17,190 --> 00:27:20,930
+theorem الآن عندي اللي هو ال .. ال .. ال .. ال ..
+
+374
+00:27:20,930 --> 00:27:24,210
+Bezout's theorem إيش بتقول .. النتيجة الأولى بتقول if
+
+375
+00:27:24,210 --> 00:27:27,130
+a و b and c are positive integers such that 
+
+376
+00:27:27,130 --> 00:27:30,510
+لجريسكم ال divisor بين ال a و ال b بيساوي واحد and a
+
+377
+00:27:30,510 --> 00:27:34,910
+بتقسم ال bc then a بتقسم ال c باختصار بقول لو  عرض
+
+378
+00:27:34,910 --> 00:27:39,120
+عليك اللي a بتقسم ال b في c هل بتقدر تقول ال A
+
+379
+00:27:39,120 --> 00:27:43,580
+بتقسم ال B أو ال A بتقسم ال C؟ ليس شرطا متى بتقدر 
+
+380
+00:27:43,580 --> 00:27:47,200
+تقول لما يكون العامل المشترك الأعلى بين ال A و ال
+
+381
+00:27:47,200 --> 00:27:50,680
+B واحد مدام العامل المشترك الأعلى بين ال A و ال B
+
+382
+00:27:50,680 --> 00:27:56,120
+واحد يعني فش ذنهن عوامل مشتركة يعني الآن لما ال A
+
+383
+00:27:56,120 --> 00:27:59,850
+بتقسم ال B في ال C الـ A و الـ B لا يوجد بينهما عوامل
+
+384
+00:27:59,850 --> 00:28:03,090
+إذاً الـ M الـ A هتكون تجسم مين؟ هتجسم اللي بيطلع
+
+385
+00:28:03,090 --> 00:28:07,490
+للـ C كيف جسمت الـ B في الـ C إذاً لازم تجسمين الـ
+
+386
+00:28:07,490 --> 00:28:13,230
+C يعني مثلا عندك خمسة تجسم التلاتة في خمسة عشر
+
+387
+00:28:14,960 --> 00:28:18,400
+الخامسة و التلاتة ما فيش بينهما عوامل مشتركة الـ B ثلاثة إذا
+
+388
+00:28:18,400 --> 00:28:21,580
+الخامسة لازم تكسب مين؟ اللي بتظل C اللي هي قلناها
+
+389
+00:28:21,580 --> 00:28:26,980
+خمسة عشر اللي هي هذه خلينا أمور سريعة على الظهور
+
+390
+00:28:26,980 --> 00:28:31,300
+عسى ما تكونوا عندكم فكرة على كيف تبرهن الآن العامل
+
+391
+00:28:31,300 --> 00:28:34,060
+المشترك الأعلى بين الـ A و الـ B مقترضين واحد
+
+392
+00:28:34,060 --> 00:28:38,560
+مقترض أن الـ A تكسب مين؟ الـ B في الـ C مدام العامل
+
+393
+00:28:38,560 --> 00:28:41,380
+المشترك الأعلى بين الـ A و الـ B بيساوي واحد حسب
+
+394
+00:28:41,380 --> 00:28:45,960
+النظرية اللي جابت قليلبنكتب الواحد as a linear
+
+395
+00:28:45,960 --> 00:28:49,320
+combination بين ال A و ال B يعني بقدر اكتب الواحد
+
+396
+00:28:49,320 --> 00:28:55,700
+على صورة S في A زي ما عملنا قبل بشوية الآن S A حيث
+
+397
+00:28:55,700 --> 00:28:59,320
+S عبارة عن integer و T عبارة عن integer ضربنا
+
+398
+00:28:59,320 --> 00:29:07,160
+الجهتين في C هذهاس اي في سي زائد ت في بي في سي
+
+399
+00:29:07,160 --> 00:29:13,200
+بيساوي كداش بيساوي اللي هو عبارة عن سي إذا صارت
+
+400
+00:29:13,200 --> 00:29:17,340
+عندي اس اي سي زائد ت بي سي بيساوي سي لما ضربنا الطرف
+
+401
+00:29:17,340 --> 00:29:21,640
+اليمين في سي طيب خلي هدف الداكرة الآن عندي ال a
+
+402
+00:29:21,640 --> 00:29:26,540
+بتكسب ال bc معطينيها فوق ال a بتكسب ال bc الآن أكيد
+
+403
+00:29:26,540 --> 00:29:30,280
+اللي هو ال a هتكسب ال t في b في c مدام أنت بتكسب 
+
+404
+00:29:30,280 --> 00:29:35,420
+ال bc لحالها يعني مدام ال A بتكسب مثلا خمسة الخمسة
+
+405
+00:29:35,420 --> 00:29:39,100
+بتكسب خمسة في تلاتة إذا أكيد ال A بتكسب خمسة في
+
+406
+00:29:39,100 --> 00:29:45,400
+تلاتة في عشرة أكيد إذا ال A بتكسب T في C وعندي ال
+
+407
+00:29:45,400 --> 00:29:48,960
+A بتكسب ال S في A في C لأن ال A هي إذا ال A عامل
+
+408
+00:29:48,960 --> 00:29:52,360
+من العوامل هذه مدام ال A بتكسب هذه و ال A بتكسب
+
+409
+00:29:52,360 --> 00:29:56,680
+هذه إذا حسب نظرية سابقة ال A هتكسب مجموعهم اللي هو
+
+410
+00:29:56,680 --> 00:30:02,330
+SAC زي TBC مجموعهم هذا ايش اسمه C يعني ال A هتكسب
+
+411
+00:30:02,330 --> 00:30:07,490
+ال C إذا هيك أبوكول أثبتنا أنه لو A تكسب ال B و ال
+
+412
+00:30:07,490 --> 00:30:10,730
+C و المشتركة اللي عالة بين ال B و ال A واحد إذا ال
+
+413
+00:30:10,730 --> 00:30:16,910
+A تكسب ال C طيب الآن احنا نيجي اللي هو النظرية
+
+414
+00:30:16,910 --> 00:30:21,390
+اللي بعدها النظرية اللي بعدها أو اللمّة اللي بعدها
+
+415
+00:30:21,390 --> 00:30:25,590
+اللي بتقول التعميم يعني if B is a prime and B
+
+416
+00:30:25,590 --> 00:30:31,180
+بتكسب ال A واحد then بتقسم ال E I for some I بقول
+
+417
+00:30:31,180 --> 00:30:34,540
+يعني لو كانت عندي ال B عبارة عن إبراهيم يعني كتلة
+
+418
+00:30:34,540 --> 00:30:38,100
+واحدة بتقسم ال A واحد في ال A اتنين في ال A تلاتة
+
+419
+00:30:38,100 --> 00:30:43,660
+في ال A N إذا لازم ال B تقسم من واحدة من هدولة على
+
+420
+00:30:43,660 --> 00:30:46,120
+الأقل واحدة لو كنت تقسمت اتنين و كنت تقسمت تلاتة
+
+421
+00:30:46,120 --> 00:30:49,840
+يعني لو تلاتة بتقسم خمسة في ستة عشر في خمسة و
+
+422
+00:30:49,840 --> 00:30:53,900
+عشرين في خمسة و تلاتين في طمنتاش في كده إذا أكيد
+
+423
+00:30:53,900 --> 00:30:56,480
+التلاتة دي بتقسم واحدة من هنا و لتكون مثلا اللي
+
+424
+00:30:56,480 --> 00:31:00,550
+قلتها A اش طمنتاش إذا لما الـ prime بيكسب ال a1, a2
+
+425
+00:31:00,550 --> 00:31:05,030
+and an لازم ال prime بيكسب واحد من هذولة لأنه أصلا
+
+426
+00:31:05,030 --> 00:31:09,190
+هو كتلة واحدة مش هتلاقوه مفرّج بين تلتين لازم يكون
+
+427
+00:31:09,190 --> 00:31:12,310
+في هذه كله أو في هذه كله أو في هذه كله أو في كل
+
+428
+00:31:12,310 --> 00:31:16,270
+واحدة كله إذا ال b بتكسب ai for some i for some i
+
+429
+00:31:16,270 --> 00:31:18,590
+ممكن تكون واحدة و تلتين و تلتين إذا على الأقل
+
+430
+00:31:18,590 --> 00:31:23,150
+واحدة بتكسب طيب هذه اللي هي النظرية ال أو اللمّة
+
+431
+00:31:23,150 --> 00:31:28,350
+عبارة عن لمّة تلت الآن بدنا نجي لآخر issue في
+
+432
+00:31:28,350 --> 00:31:32,590
+المحاضرة اليوم اللي هو dividing congruences by an
+
+433
+00:31:32,590 --> 00:31:38,970
+integer يعني عملية اللي هي قسمة التطابق بواسطة
+
+434
+00:31:38,970 --> 00:31:42,550
+عدد صحيح يعني dividing both of a valid congruences
+
+435
+00:31:42,550 --> 00:31:47,770
+يعني لو كان عندي AC تطابق BC مدله M مدله M لو كان
+
+436
+00:31:47,770 --> 00:31:51,730
+هذه التطابقة صحيحة يعني ايش صحيحة يعني الطرف تكسب
+
+437
+00:31:51,730 --> 00:31:57,760
+ال AC نقص BC لو كانت هذه صحيحة مش شرط انه تقدر تقول
+
+438
+00:31:57,760 --> 00:32:02,100
+by an integer اللي هو does not always produce a
+
+439
+00:32:02,100 --> 00:32:05,960
+valid congruent يعني مش شرط انه اللي هو لو جسمنا
+
+440
+00:32:05,960 --> 00:32:09,440
+هدول الجهتين ع C نيجي نقول والله اذا A تطابق B
+
+441
+00:32:09,440 --> 00:32:14,580
+modulo M يعني لو كانت AC تطابق BC modulo M ليس شرط
+
+442
+00:32:14,580 --> 00:32:19,760
+انه يطلع ال A تطابق B modulo B modulo M هذه القسمة
+
+443
+00:32:19,760 --> 00:32:24,020
+أو الاقتصاد مش زي المعادلات العادية هذه القسمة مش
+
+444
+00:32:24,020 --> 00:32:26,600
+زي المعادلات العادية بتيجي تقول شيل ال C و شيل ال C
+
+445
+00:32:26,600 --> 00:32:30,560
+بيصير ايه تطابق ال D مدله M هذه مثال مثلا عند 2
+
+446
+00:32:30,560 --> 00:32:35,660
+فعشرة تطابق 3 فعشرة مدل 5 صحيح هذا ولا لا لأن 2
+
+447
+00:32:35,660 --> 00:32:39,380
+فعشرة 20 ثلاثة فعشرة تلاتين تلاتين ناقص عشرين عشرة
+
+448
+00:32:39,380 --> 00:32:44,140
+الخمسة بتقسم العشرة إذا فعلا هذه المتطابقة صحيحة لو
+
+449
+00:32:44,140 --> 00:32:46,840
+أتي واحد وقال لي خلّينا نختصر العشرة مع العشرة
+
+450
+00:32:46,840 --> 00:32:49,620
+بيصير عندي اتنين متطابق التلاتة من الخمسة صح ولا
+
+451
+00:32:49,620 --> 00:32:55,060
+غلط هذا غلط مش صحيح لأن الخمسة لا تقسم تلاتة نقص
+
+452
+00:32:55,060 --> 00:33:00,720
+اتنين لأن هيك معناته متطابقة عشان تكون هذه صحيحة
+
+453
+00:33:00,720 --> 00:33:03,320
+لازم الخمسة تقسم تلاتة نقص اتنين لكن الخمسة لا
+
+454
+00:33:03,320 --> 00:33:06,860
+تقسم تلاتة نقص اتنين لأن الخمسة لا تقسم الواحد إذا
+
+455
+00:33:06,860 --> 00:33:11,720
+ما نفعش نيجي اللي هو نختصر عشرة مع العشرة طب ها
+
+456
+00:33:11,720 --> 00:33:16,970
+كيفاش نسويهو يقول لك الاختصار كما يعني أو يشرّع لك
+
+457
+00:33:16,970 --> 00:33:21,410
+الاختصار بما يعني but divided by any integer
+
+458
+00:33:21,410 --> 00:33:27,110
+relative to the prime to the modulus does produce
+
+459
+00:33:27,110 --> 00:33:30,670
+a valid congruent ايش يعني هذا؟ ايش بتقول؟ بقول ما
+
+460
+00:33:30,670 --> 00:33:34,690
+يعني بقول الفيون السابع بتقول لك لو كانت M بي a
+
+461
+00:33:34,690 --> 00:33:39,350
+positive integer and A will be a C integer such
+
+462
+00:33:39,350 --> 00:33:44,000
+that A في C يتطابق بيه C مدله M لو فرضنا هذا A C
+
+463
+00:33:44,000 --> 00:33:48,200
+تطابق ال B و B C مدله M و ال greatest common
+
+464
+00:33:48,200 --> 00:33:53,200
+divisor بين ال C و ال M بيساوي واحد بين ال C و ال M
+
+465
+00:33:53,200 --> 00:33:57,940
+بساوي واحد هيعطينا ان ال A تطابق ال B مدله ال
+
+466
+00:33:57,940 --> 00:34:04,520
+M يعني بقول لك تقدر تعمل الاختصار C تروح مع ال C إذا
+
+467
+00:34:04,520 --> 00:34:07,480
+كان العامل المشترك الأعلى بين ال C و ال M ايش
+
+468
+00:34:07,480 --> 00:34:12,920
+بيساوي بيساوي واحد إذا عامل المشترك الأعلى بين الـ c
+
+469
+00:34:12,920 --> 00:34:16,420
+و ال m بيساوي واحد بين ال c و ال m بيساوي واحد
+
+470
+00:34:16,420 --> 00:34:23,200
+بيخليك تختصر هذه مع هذه يعني لو كان الآن خمسة في
+
+471
+00:34:23,200 --> 00:34:31,340
+اللي هو اتنين تطابق اللي هو خمسة في تلاتة اللي هو
+
+472
+00:34:31,340 --> 00:34:38,320
+modulo خمسة في اتنين تطابق اللي هو خمسة في اتنين
+
+473
+00:34:38,320 --> 00:34:39,460
+تطابق اللي هو 
+
+474
+00:34:46,680 --> 00:34:50,120
+العامل المشترك الأعلى بين الـ C و الـ M بيساوي واحد
+
+475
+00:34:50,120 --> 00:34:54,660
+بيكون عند الـ A تطابق الـ B modulo M اللي هو بكل
+
+476
+00:34:54,660 --> 00:34:58,720
+بساطة اقتصاد كما قلنا في مثال لو أخدنا خمسة مثلا في
+
+477
+00:34:58,720 --> 00:35:02,020
+اتنين تطابق اللي هو اتنين في اتنين modulo ثلاثة
+
+478
+00:35:12,570 --> 00:35:22,690
+الآن هذه هي قسم المشروع عندي A C تطابق B C mod M
+
+479
+00:35:22,690 --> 00:35:26,330
+معناته الطرف تكسب ال A C ناقص ال B C ناخد ال C
+
+480
+00:35:26,330 --> 00:35:29,830
+عامل مشترك بالضبط اللي هي الطرف تكسب ال C في ال A
+
+481
+00:35:29,830 --> 00:35:34,450
+ناقص B و قلنا بما انه اللي هي العامل المشترك الأعلى
+
+482
+00:35:34,450 --> 00:35:37,470
+بين ال M و ال C بيساوي واحد إذا الطرف تكسب ال A
+
+483
+00:35:37,470 --> 00:35:41,670
+ناقص B عن ال M اللي هي تطابق ال B mod M وهكذا
+
+484
+00:35:41,670 --> 00:35:46,550
+شرطنا ان ال A C تطابق ال B C mod M
+
+485
+00:35:49,450 --> 00:35:53,290
+إن نعمل نقوم بالاقتصاد لما نقول عامل مشترك الاعلى
+
+486
+00:35:53,290 --> 00:35:56,790
+بين ال C و ال M بيساوي واحد لكن غير هيك لا نكون
+
+487
+00:35:56,790 --> 00:36:02,590
+حاضرين في اللي هو الاقتصاد و هذه هي ال homework
+
+488
+00:36:02,590 --> 00:36:08,570
+اللي مطلوب تحلوها السؤال الأول و الثاني و الثالث و إن
+
+489
+00:36:08,570 --> 00:36:12,970
+شاء الله إلى لقاء آخر في محاضرة أخرى السلام عليكم
+
+490
+00:36:12,970 --> 00:36:13,470
+و رحمة الله 
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..8c862932bdb4db166b1c5cc65890aef31109d73a
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2763, "start": 1.57, "end": 27.63, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة السابعة مساق غياضيات منفصلة لطلاب و طالبات الجامعة الإسلامية كلية technology الأمعلومات قسم الحوسبة المتنقلة المحاضرة اليوم ان شاء الله هنستكمل فيها الحديث عن ال greatest common divisor أو العامل المشترك الأعلى", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 21136, 16758, 27884, 47524, 995, 4587, 32771, 1829, 46958, 1829, 9307, 9154, 5172, 36520, 3660, 5296, 9566, 15040, 3555, 4032, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 9122, 20292, 3660, 2899, 16247, 2304, 30241, 20498, 9307, 12174, 38251, 21542, 2407, 35457, 3660, 9673, 2655, 1863, 4587, 37977, 9673, 5016, 46958, 25720, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 14851, 24793, 1211, 8978, 11296, 21542, 16254, 12984, 18871, 2423, 6636, 2689, 25974, 284, 34051, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942], "avg_logprob": -0.12928185454354837, "compression_ratio": 1.7298387096774193, "no_speech_prob": 5.781650543212891e-06, "words": [{"start": 1.57, "end": 1.95, "word": "بسم", "probability": 0.876220703125}, {"start": 1.95, "end": 2.21, "word": " الله", "probability": 0.95458984375}, {"start": 2.21, "end": 2.67, "word": " الرحمن", "probability": 0.97265625}, {"start": 2.67, "end": 3.27, "word": " الرحيم", "probability": 0.9947916666666666}, {"start": 3.27, "end": 4.65, "word": " هذه", "probability": 0.69287109375}, {"start": 4.65, "end": 4.91, "word": " هي", "probability": 0.60595703125}, {"start": 4.91, "end": 5.73, "word": " المحاضرة", "probability": 0.98486328125}, {"start": 5.73, "end": 6.97, "word": " السابعة", "probability": 0.9376627604166666}, {"start": 6.97, "end": 7.81, "word": " مساق", "probability": 0.9192708333333334}, {"start": 7.81, "end": 9.25, "word": " غياضيات", "probability": 0.7864990234375}, {"start": 9.25, "end": 9.95, "word": " منفصلة", "probability": 0.9345703125}, {"start": 9.95, "end": 10.61, "word": " لطلاب", "probability": 0.941650390625}, {"start": 10.61, "end": 10.75, "word": " و", "probability": 0.99169921875}, {"start": 10.75, "end": 11.33, "word": " طالبات", "probability": 0.921142578125}, {"start": 11.33, "end": 11.75, "word": " الجامعة", "probability": 0.9856770833333334}, {"start": 11.75, "end": 12.53, "word": " الإسلامية", "probability": 0.97021484375}, {"start": 12.53, "end": 14.43, "word": " كلية", "probability": 0.6455891927083334}, {"start": 14.43, "end": 15.05, "word": " technology", "probability": 0.64599609375}, {"start": 15.05, "end": 16.33, "word": " الأمعلومات", "probability": 0.768505859375}, {"start": 16.33, "end": 17.35, "word": " قسم", "probability": 0.92626953125}, {"start": 17.35, "end": 18.03, "word": " الحوسبة", "probability": 0.79376220703125}, {"start": 18.03, "end": 18.85, "word": " المتنقلة", "probability": 0.9935546875}, {"start": 18.85, "end": 20.13, "word": " المحاضرة", "probability": 0.989501953125}, {"start": 20.13, "end": 20.49, "word": " اليوم", "probability": 0.94775390625}, {"start": 20.49, "end": 20.65, "word": " ان", "probability": 0.67626953125}, {"start": 20.65, "end": 20.91, "word": " شاء", "probability": 0.98388671875}, {"start": 20.91, "end": 20.99, "word": " الله", "probability": 0.96044921875}, {"start": 20.99, "end": 21.79, "word": " هنستكمل", "probability": 0.9234375}, {"start": 21.79, "end": 22.09, "word": " فيها", "probability": 0.97509765625}, {"start": 22.09, "end": 22.73, "word": " الحديث", "probability": 0.9641927083333334}, {"start": 22.73, "end": 22.93, "word": " عن", "probability": 0.9921875}, {"start": 22.93, "end": 23.07, "word": " ال", "probability": 0.52880859375}, {"start": 23.07, "end": 23.43, "word": " greatest", "probability": 0.9560546875}, {"start": 23.43, "end": 23.77, "word": " common", "probability": 0.64111328125}, {"start": 23.77, "end": 24.65, "word": " divisor", "probability": 0.865478515625}, {"start": 24.65, "end": 25.53, 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هنا على الصورة هذه بيكون الـ grades common divisor بين ال A و ال B هو عبارة عن B1 أس ال minimum بين A1 و B1 ال B2 أس ال minimum بين A2 و B2", "tokens": [1211, 33456, 39182, 19446, 11331, 1211, 1211, 8315, 34105, 15844, 31767, 13063, 3660, 29538, 4724, 1829, 30544, 2423, 39184, 18041, 2689, 25974, 284, 49374, 2423, 316, 4032, 2423, 363, 31439, 6225, 3555, 9640, 3660, 18871, 363, 16, 5551, 3794, 2423, 7285, 49374, 316, 16, 4032, 363, 16, 2423, 363, 17, 5551, 3794, 2423, 7285, 49374, 316, 17, 4032, 363, 17], "avg_logprob": -0.20978483020282182, "compression_ratio": 1.474025974025974, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 89.7, "end": 90.1, "word": "لأن", "probability": 0.6796875}, {"start": 90.1, "end": 90.36, "word": " بعد", "probability": 0.94921875}, {"start": 90.36, "end": 90.5, "word": " ما", "probability": 0.91796875}, {"start": 90.5, "end": 91.02, "word": " حللنا", "probability": 0.965087890625}, {"start": 91.02, "end": 91.18, "word": " هنا", "probability": 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divisor", "probability": 0.94140625}], "temperature": 1.0}, {"id": 8, "seek": 17070, "start": 149.62, "end": 170.7, "text": "العامل المشترك الأعلى بين الـ120 والـ500 راجلهم أعلى ايش بيشتغلوا؟ باقي الـ120 بيستخدع راتورة عاملها الأولية على اتنين باقي السنة بيطلع الـ60 على اتنين بيطلع الـ30 على اتنين بيطلع الـ15 الـ15 اتنية تراثية تطلع خمسة وهي خمسة فبيصير", "tokens": [6027, 3615, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 49374, 2423, 39184, 28829, 16070, 39184, 7526, 12602, 26108, 1211, 16095, 5551, 3615, 23942, 1975, 1829, 8592, 4724, 1829, 8592, 2655, 17082, 1211, 14407, 22807, 4724, 995, 38436, 2423, 39184, 28829, 4724, 1829, 14851, 9778, 3215, 3615, 12602, 9307, 13063, 3660, 6225, 10943, 1211, 11296, 16247, 12610, 10632, 15844, 1975, 2655, 1863, 9957, 4724, 995, 38436, 21136, 1863, 3660, 4724, 1829, 9566, 1211, 3615, 2423, 39184, 4550, 15844, 1975, 2655, 1863, 9957, 4724, 1829, 9566, 1211, 3615, 2423, 39184, 3446, 15844, 1975, 2655, 1863, 9957, 4724, 1829, 9566, 1211, 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common multiple أو المضاعف المشترك البسيط المضاعف المشترك الأقل أو الأصغر أو البسيط", "tokens": [6027, 3615, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 13672, 1829, 8717, 38251, 1829, 3224, 1935, 2689, 3866, 34051, 9673, 11242, 45761, 5172, 9673, 8592, 2655, 31747, 29739, 3794, 1829, 9566, 9673, 11242, 45761, 5172, 9673, 8592, 2655, 31747, 16247, 4587, 1211, 34051, 16247, 9381, 17082, 2288, 34051, 29739, 3794, 1829, 9566], "avg_logprob": -0.29886363744735717, "compression_ratio": 1.6299212598425197, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 389.49, "end": 390.89, "word": "العامل", "probability": 0.461090087890625}, {"start": 390.89, "end": 391.43, "word": " المشترك", "probability": 0.9775390625}, {"start": 391.43, "end": 391.95, "word": " الأعلى", "probability": 0.93310546875}, {"start": 391.95, "end": 392.49, "word": " اللي", "probability": 0.4501800537109375}, {"start": 392.49, "end": 394.81, "word": " نسميه", "probability": 0.557952880859375}, 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في", "probability": 0.92138671875}, {"start": 769.33, "end": 769.61, "word": " خمسة", "probability": 0.947265625}, {"start": 769.61, "end": 769.89, "word": " تربية", "probability": 0.8914388020833334}, {"start": 769.89, "end": 770.05, "word": " في", "probability": 0.8916015625}, {"start": 770.05, "end": 770.47, "word": " سبعة", "probability": 0.9348958333333334}, {"start": 770.47, "end": 771.21, "word": " الان", "probability": 0.5185546875}, {"start": 771.21, "end": 771.61, "word": " لgrades", "probability": 0.435546875}, {"start": 771.61, "end": 771.87, "word": " كومن", "probability": 0.96337890625}, {"start": 771.87, "end": 772.33, "word": " divisor", "probability": 0.829345703125}, {"start": 772.33, "end": 772.57, "word": " بين", "probability": 0.93310546875}, {"start": 772.57, "end": 773.25, "word": " الجهتين", "probability": 0.92578125}, {"start": 773.25, "end": 773.61, "word": " سواء", "probability": 0.94091796875}, {"start": 773.61, "end": 773.91, "word": " اتنين", 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84928, "start": 828.66, "end": 849.28, "text": "و لو قدرتها مباشرة من هنا برضه اللي هو صحيح الان احنا في حاجة اسمها لدينا الكلوديان algorithm الكلوديان algorithm بدنا نقصص للكلوديان algorithm ندد ال greatest common اللي هو divisor مش دايما", "tokens": [2407, 45164, 12174, 3215, 43500, 11296, 3714, 3555, 33599, 25720, 9154, 34105, 4724, 43042, 3224, 13672, 1829, 31439, 20328, 5016, 1829, 5016, 2423, 7649, 1975, 5016, 8315, 8978, 11331, 26108, 3660, 24525, 2304, 11296, 5296, 16254, 8315, 2423, 28820, 2407, 16254, 7649, 9284, 2423, 28820, 2407, 16254, 7649, 9284, 47525, 8315, 8717, 4587, 9381, 9381, 24976, 28820, 2407, 16254, 7649, 9284, 8717, 3215, 3215, 2423, 6636, 2689, 13672, 1829, 31439, 25974, 284, 37893, 11778, 47302, 15042], "avg_logprob": -0.33340098176683697, "compression_ratio": 1.7257142857142858, "no_speech_prob": 0.0, "words": [{"start": 828.66, "end": 828.88, "word": "و", "probability": 0.5205078125}, {"start": 828.88, "end": 829.04, "word": " لو", "probability": 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2170.37, "word": " في", "probability": 0.970703125}, {"start": 2170.37, "end": 2171.01, "word": " محاضرة", "probability": 0.98193359375}, {"start": 2171.01, "end": 2172.25, "word": " أخرى", "probability": 0.9557291666666666}, {"start": 2172.25, "end": 2172.67, "word": " السلام", "probability": 0.888671875}, {"start": 2172.67, "end": 2172.97, "word": " عليكم", "probability": 0.9267578125}, {"start": 2172.97, "end": 2173.25, "word": " ورحمة", "probability": 0.8489990234375}, {"start": 2173.25, "end": 2173.47, "word": " الله", "probability": 0.94140625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2173.71275, "duration_after_vad": 2146.3981249999943}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4121cd56537047831e49e7bf9994cef0254cac67
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/DhXhLQehnj8_raw.srt
@@ -0,0 +1,1980 @@
+1
+00:00:01,570 --> 00:00:06,970
+بسم الله الرحمن الرحيم هذه هي المحاضرة السابعة
+
+2
+00:00:06,970 --> 00:00:11,750
+مساق غياضيات منفصلة لطلاب و طالبات الجامعة
+
+3
+00:00:11,750 --> 00:00:18,030
+الإسلامية كلية technology الأمعلومات قسم الحوسبة
+
+4
+00:00:18,030 --> 00:00:22,090
+المتنقلة المحاضرة اليوم ان شاء الله هنستكمل فيها
+
+5
+00:00:22,090 --> 00:00:26,110
+الحديث عن ال greatest common divisor أو العامل
+
+6
+00:00:26,110 --> 00:00:31,460
+المشترك الأعلىبين عددين اليوم بدنا نعرف كيف نودي
+
+7
+00:00:31,460 --> 00:00:35,420
+الـ greatest common divisor باستخدام حاجة اسمها
+
+8
+00:00:35,420 --> 00:00:43,560
+الـ prime factorization أو عن طريق تحليل العدد
+
+9
+00:00:43,560 --> 00:00:50,080
+إلى عوام الأوليةعن طريق العوامل للعدد الأولية كيف
+
+10
+00:00:50,080 --> 00:00:54,080
+نجد ال grace command divisor كما يليه تابعوا معايا
+
+11
+00:00:54,080 --> 00:00:58,060
+الان نفترض ان ال prime factorization للعدد a والb
+
+12
+00:00:58,060 --> 00:01:01,400
+هي كما يليه ايش يعني ال prime factorization يعني
+
+13
+00:01:01,400 --> 00:01:05,180
+بنحلل العدد a إلى عوامله الأولية طلع اللي عندي
+
+14
+00:01:05,180 --> 00:01:11,580
+العدد a عبارة عن b1 a1 b2 a2بن ان وحللنا بي طلع
+
+15
+00:01:11,580 --> 00:01:15,500
+على صورة بي واحد اص بي واحد بي اتنين اص بي اتنين
+
+16
+00:01:15,500 --> 00:01:19,860
+بي ان نص بي ان حيث ال a واحد و ال b واحد و ال b
+
+17
+00:01:19,860 --> 00:01:22,900
+اتنين و ال b ان و ال a واحد و ال a اتنين و ال a ان
+
+18
+00:01:22,900 --> 00:01:27,620
+عبارة عن integers اكبر او يساوي سفر بينما ال b
+
+19
+00:01:27,620 --> 00:01:31,020
+واحد و ال b ان عبارة عن ال primesلأن بعد ما حللنا
+
+20
+00:01:31,020 --> 00:01:34,260
+هنا على الصورة هذه بيكون الـ grades common divisor
+
+21
+00:01:34,260 --> 00:01:39,020
+بين ال A و ال B هو عبارة عن B1 أس ال minimum بين
+
+22
+00:01:39,020 --> 00:01:47,800
+A1 و B1 ال B2 أس ال minimum بين A2 و B2لما أصل عند
+
+23
+00:01:47,800 --> 00:01:53,840
+ال BN أُس ال minimum بين AN وBN بهذه الطريقة بنكون
+
+24
+00:01:53,840 --> 00:01:58,420
+احنا حللنا او جدنا ال greatest common divisor او
+
+25
+00:01:58,420 --> 00:02:03,360
+العامل المشترك الأعلى بين العددين A وB بهذه
+
+26
+00:02:03,360 --> 00:02:08,000
+الطريقة والان ان شاء الله هناخد example عملي على
+
+27
+00:02:08,000 --> 00:02:12,640
+هذه اللي هي الطريقة نيجي الان هذا الكلام عمليا ل
+
+28
+00:02:12,640 --> 00:02:13,880
+GMS شوفوا
+
+29
+00:02:20,500 --> 00:02:24,240
+العام المشترك الأعلى هو greatest common divisor
+
+30
+00:02:29,620 --> 00:02:35,840
+العامل المشترك الأعلى بين الـ120 والـ500 راجلهم
+
+31
+00:02:35,840 --> 00:02:39,480
+أعلى ايش بيشتغلوا؟ باقي الـ120 بيستخدع راتورة
+
+32
+00:02:39,480 --> 00:02:43,440
+عاملها الأولية على اتنين باقي السنة بيطلع الـ60
+
+33
+00:02:43,440 --> 00:02:47,120
+على اتنين بيطلع الـ30 على اتنين بيطلع الـ15 الـ15
+
+34
+00:02:47,120 --> 00:02:54,050
+اتنية تراثية تطلع خمسة وهي خمسة فبيصيرالتحليل الى
+
+35
+00:02:54,050 --> 00:02:58,310
+120 الى brines هو عبارة عن اتنين في تلاتة في تلاتة
+
+36
+00:02:58,310 --> 00:03:01,850
+في خمسة نفس الشيء باقي الخمسمية برغم تحليلها
+
+37
+00:03:01,850 --> 00:03:05,730
+العوامل الأولية بنفس الطريقة بلاقيها عبارة عن
+
+38
+00:03:05,730 --> 00:03:08,070
+الأول اتنين في سمعة اتنين بعدين اذا فيها ثلاثة
+
+39
+00:03:08,070 --> 00:03:12,110
+ثلاثة على خمسة على خمسة وهكذا بطلع عند اتنين ترجية
+
+40
+00:03:12,110 --> 00:03:16,060
+في خمسة تكريمإن كتبت على الصورة هذا البرايم
+
+41
+00:03:16,060 --> 00:03:19,380
+فكتوريزيشن البرايم فكتوريزيشن البرايم فكتوريزيشن
+
+42
+00:03:19,380 --> 00:03:19,880
+البرايم فكتوريزيشن البرايم فكتوريزيشن البرايم
+
+43
+00:03:19,880 --> 00:03:21,880
+فكتوريزيشن البرايم فكتوريزيشن البرايم فكتوريزيشن
+
+44
+00:03:21,880 --> 00:03:24,460
+البرايم فكتوريزيشن البرايم فكتوريزيشن البرايم
+
+45
+00:03:24,460 --> 00:03:28,220
+فكتوريزيشن البرايم فكتوريزيشن البرايم فكتوريزيشن
+
+46
+00:03:28,220 --> 00:03:30,380
+البرايم فكتوريزيشن البرايم فكتوريزيشن البرايم
+
+47
+00:03:30,380 --> 00:03:33,480
+فكتوريزيشن البرايم فهي minimum بين تلاتة واثنين
+
+48
+00:03:33,480 --> 00:03:38,120
+وقص هنا واحد وهنا فيش تلاتة يعني و كأنه تلاتة قص
+
+49
+00:03:38,120 --> 00:03:41,280
+سفر لما تلاتة و سفر يعني بواحد لما ينضرب واحد هنا
+
+50
+00:03:41,280 --> 00:03:44,720
+تلاتة و سفر مش هيأثر هيظل العدد زي ما هو فبنكتب
+
+51
+00:03:44,720 --> 00:03:47,100
+تلاتة قص minimum واحد و سفر
+
+52
+00:03:50,450 --> 00:03:54,050
+الخامسة ال minimum بين الأُس اللي أنا و الأُس اللي
+
+53
+00:03:54,050 --> 00:03:58,450
+هو واحد و ثلاثة بيصير ال minimum بين ثلاثة و اتنين
+
+54
+00:03:58,450 --> 00:04:03,750
+واحد بين ثلاثة و اتنين اتنين بيصير اتنين أس اتنين
+
+55
+00:04:03,750 --> 00:04:07,390
+مضروبةفي تلاتة اقص في ال minimum بين واحد و سفر ال
+
+56
+00:04:07,390 --> 00:04:10,590
+minimum بين واحد و سفر طبعا سفر تصبح تلاتة اقص سفر
+
+57
+00:04:10,590 --> 00:04:13,390
+في الان ال minimum بين واحد و تلاتة اللي هي ايش
+
+58
+00:04:13,390 --> 00:04:17,510
+واحد فتصبح خمسة اقص واحد اذا بيصير الجواب عندي
+
+59
+00:04:17,510 --> 00:04:21,210
+اتنين تربيع يعني اربعة تلاتة اقص سفر يعني واحد
+
+60
+00:04:21,210 --> 00:04:25,210
+اقولكم في حالة اللي عامل ال greats common divisor
+
+61
+00:04:25,540 --> 00:04:32,000
+اللي هو العامل المشترك الأعلى لو أنا ماحطيتش
+
+62
+00:04:32,000 --> 00:04:36,260
+التلاتة بنفع يعني التلاتة مش موجودة في الجهتين
+
+63
+00:04:36,260 --> 00:04:41,860
+انساه وما تكتبهاش وهذه نشيلها بنفع لإنه في الأخر
+
+64
+00:04:41,860 --> 00:04:45,380
+هتطلع تلاتة أقل صفر طيب اتنين أقل أربعة في خمسة
+
+65
+00:04:45,380 --> 00:04:49,840
+بتطلع مجدهش ومن عشرين ندي لها المثال الثاني اللي
+
+66
+00:04:49,840 --> 00:04:53,970
+هو أوجد المضاع ال greatest common divisorبين ال
+
+67
+00:04:53,970 --> 00:05:01,690
+2400 و ال 6300 بعد ال 2400 بحللها ال عواملها
+
+68
+00:05:01,690 --> 00:05:06,990
+الأولية بلاجيها عبارة عن اتنين اص خمسة في تلاتة في
+
+69
+00:05:06,990 --> 00:05:13,310
+خمسة تربيع و قولنا كيف بالحلل الان ال 6300 بحللها
+
+70
+00:05:13,310 --> 00:05:16,250
+العواملها الأولية تطلع اتنين تربيع اتنين تربيع في
+
+71
+00:05:16,250 --> 00:05:21,040
+تلاتة تربيع في خمسة تربيع في سبعةالان على طول ال
+
+72
+00:05:21,040 --> 00:05:25,300
+greatest common divisor اللى هو الموضوع العام
+
+73
+00:05:25,300 --> 00:05:29,940
+للمشترك الأعلى مادى هي ال تمام موجودة هنا و موجودة
+
+74
+00:05:29,940 --> 00:05:32,940
+هنا بكتبها اتنين minimum خمسة و اتنين التلاتة
+
+75
+00:05:32,940 --> 00:05:35,900
+موجودة هنا و موجودة هنا بكتب تلاتة minimum واحد و
+
+76
+00:05:35,900 --> 00:05:39,800
+اتنينالخامسة موجودة هنا و موجودة هنا خمسة أس
+
+77
+00:05:39,800 --> 00:05:42,700
+minimum تنين و اتنين لأن هنا الأس تنين و هنا الأس
+
+78
+00:05:42,700 --> 00:05:46,800
+تنين السبعة مش موجودة هنا خلاص فانساها يعني لو
+
+79
+00:05:46,800 --> 00:05:49,880
+حاطيتها زي اللي فوق و عملت minimum بين الأس سفر و
+
+80
+00:05:49,880 --> 00:05:52,260
+الواحد ما هو هيطلع سفر يعني معناته هيطلع واحد
+
+81
+00:05:52,260 --> 00:05:56,710
+الجواب و ده خلاص ليش أغلب حالي اذا بأخد ميناللي
+
+82
+00:05:56,710 --> 00:06:01,850
+موجودة في الجهتين الاتنين القص الأصغر بيصير اتنين
+
+83
+00:06:01,850 --> 00:06:05,270
+اقص اتنين تلاتة القص الأصغر اللي هو واحد تلاتة اقص
+
+84
+00:06:05,270 --> 00:06:08,250
+واحد الخمسة اقص اتنين القص الأصغر اللي هو خمسة اقص
+
+85
+00:06:08,250 --> 00:06:11,810
+اتنين السبعة مش موجودة لغيرها نخلص بانساها بيصير
+
+86
+00:06:11,810 --> 00:06:16,070
+هذا هو المضاء العامل المشترك الأعلى اللي هو
+
+87
+00:06:16,070 --> 00:06:19,190
+greatest common divisor باجي بحسبها بلاجيها ايش
+
+88
+00:06:19,190 --> 00:06:23,310
+بتساوي بتساوي تلات مية اذا الموضوع سهل طيب
+
+89
+00:06:29,490 --> 00:06:35,530
+العامل المشترك الأعلى اللي نسميه least common
+
+90
+00:06:35,530 --> 00:06:43,710
+multiple أو المضاعف المشترك البسيط المضاعف المشترك
+
+91
+00:06:43,710 --> 00:06:50,130
+الأقل أو الأصغر أو البسيطتعريفه كمان يعني the
+
+92
+00:06:50,130 --> 00:06:53,230
+least common multiple of the positive integers a
+
+93
+00:06:53,230 --> 00:06:57,090
+and b is the smallest positive integer هو عبارة عن
+
+94
+00:06:57,090 --> 00:07:01,390
+أصغر positive انتجار that is divisible by both a
+
+95
+00:07:01,390 --> 00:07:07,750
+and b يعني أصغر اللي هو مضاعف .. أصغر اللي هو
+
+96
+00:07:07,750 --> 00:07:13,010
+positive انتجار اللي هو divisible by a يعني اللي
+
+97
+00:07:13,010 --> 00:07:19,620
+هو a بتقسمه و b بتقسمهيعني بمعنى آخر بيكون أصغر
+
+98
+00:07:19,620 --> 00:07:26,760
+مضاعف لل A و لل B و بنرمزه ب D كمومة بال A و B إذا
+
+99
+00:07:26,760 --> 00:07:32,280
+عشان نرمز أصغر مضاعف بين A و B بدنا نجيب مضاعفات
+
+100
+00:07:32,280 --> 00:07:34,020
+ال A و مضاعفات ال B
+
+101
+00:07:39,360 --> 00:07:43,220
+مضاعفات الـ a عددها لنهائي مضاعفات ال b عددها
+
+102
+00:07:43,220 --> 00:07:49,020
+لنهائي بنجيب أولها و بنشوف كيف نسوي لان find least
+
+103
+00:07:49,020 --> 00:07:52,260
+common multiple بين ستة و عشرة اوجز المضاعف
+
+104
+00:07:52,260 --> 00:07:55,360
+المشترك البسيط بين الستة و العشرة ايش بيجيب اوجز
+
+105
+00:07:55,360 --> 00:07:59,620
+لان هذه طريقة بدائية بعد شوية هلاج الموضوع السالب
+
+106
+00:07:59,620 --> 00:08:04,760
+مضاعفات الستة ايش مضاعفات المضاعفات
+
+107
+00:08:23,040 --> 00:08:24,440
+6x12x18x24x30x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x36x
+
+108
+00:08:34,800 --> 00:08:41,340
+لأن من المضاعفات المشتركة هي 6 لا 12 لا 14 لا 14
+
+109
+00:08:41,340 --> 00:08:47,260
+لا 24 لا 30 هاي هان و هان أول واحد بجابله مشترك
+
+110
+00:08:47,260 --> 00:08:50,440
+بين المضاعفات هو اللي بسميه least common multiple
+
+111
+00:08:50,440 --> 00:08:55,430
+بين 6 و 10 يساوي 30هذا الكلام يعني خلّيني أقول
+
+112
+00:08:55,430 --> 00:08:59,790
+مرهق شوية فإن احنا لو كانت الأعداد كبيرة بنقعد ده
+
+113
+00:08:59,790 --> 00:09:03,890
+هو نضاعف العدد وضعف العدد يمكن يلتجلب بعد عدد كبير
+
+114
+00:09:03,890 --> 00:09:08,450
+فبتغلب إذا في طريقة أكيد أسهل اللي هي طريقة مشابهة
+
+115
+00:09:08,450 --> 00:09:13,030
+لطريقة ال grade-sum divisor اللي هي عن طريق ال
+
+116
+00:09:13,030 --> 00:09:17,370
+bride factorizationإذا الـ least common multiple
+
+117
+00:09:17,370 --> 00:09:20,950
+can also be computed from the prime factorization
+
+118
+00:09:20,950 --> 00:09:24,110
+يعني ممكن إيجاد اللي هو ال least common multiple
+
+119
+00:09:24,110 --> 00:09:27,050
+بواصفة ال prime factorization بودع ال prime
+
+120
+00:09:27,050 --> 00:09:29,330
+factorization للأول و ال prime factorization
+
+121
+00:09:29,330 --> 00:09:32,310
+للثاني و بقول ال least common multiple بين ال a و
+
+122
+00:09:32,310 --> 00:09:36,310
+ال b بيسوء ال b واحد مش ال minimum الآن بيجيب ال
+
+123
+00:09:36,310 --> 00:09:40,910
+maximum بين a واحد و b واحد و b اتنين بيسوء ال
+
+124
+00:09:40,910 --> 00:09:44,540
+maximum بين a اتنين و b اتنينو ال DM الماكسومون
+
+125
+00:09:44,540 --> 00:09:48,840
+بين ال AN و ال BM خلّينا نشوف هذا الكلام عمليا و
+
+126
+00:09:48,840 --> 00:09:53,160
+حساسا عليكم كمانغير هذا سأسهل عليكم الان ال 120
+
+127
+00:09:53,160 --> 00:09:57,860
+قبل قليل حللناها 2×3 في ثلاثة في خمسة و الخمس مائة
+
+128
+00:09:57,860 --> 00:10:00,220
+اتنين تربيعي في خمسة تكعيد الان ال least common
+
+129
+00:10:00,220 --> 00:10:04,160
+multiple بين ال 120 و الخمس مائة ايش بيساوي اتنين
+
+130
+00:10:04,160 --> 00:10:07,400
+بمسك واحدة اتنين ال maximum تلاتة و اتنين بس هنا
+
+131
+00:10:07,400 --> 00:10:11,680
+لازم تحطهم كلهم مش زي قبل ان اللي مافيش موجودة هنا
+
+132
+00:10:11,680 --> 00:10:15,880
+مابحطهاش لأ هنا لازم تحطهم كلهم التنين و التلاتة
+
+133
+00:10:15,880 --> 00:10:18,840
+حتى لو مش ظاهرة هنا و لو ايش ظاهر هنا بدك تحطه
+
+134
+00:10:18,840 --> 00:10:22,690
+برضهاللي هو تلاتة في ال maximum بين الواحد والزفر
+
+135
+00:10:22,690 --> 00:10:27,260
+خمسة في ال maximum بين الواحد والتلاتةالأنظار غير
+
+136
+00:10:27,260 --> 00:10:29,780
+هذه الانظارات هي الانظارات الثلاثة و الخمسة و
+
+137
+00:10:29,780 --> 00:10:31,040
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+138
+00:10:31,040 --> 00:10:31,040
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+139
+00:10:31,040 --> 00:10:32,520
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+140
+00:10:32,520 --> 00:10:36,520
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+141
+00:10:36,520 --> 00:10:40,240
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+142
+00:10:40,240 --> 00:10:44,000
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+143
+00:10:44,000 --> 00:10:44,020
+الخمسة و الخمسة و الخمسة و الخمسة و الخمسة و
+
+144
+00:10:44,020 --> 00:10:46,940
+الخمسة و الخمسة و الخمسة و الخمسة
+
+145
+00:10:55,050 --> 00:10:59,250
+طيب في علاقة بين اللي هو ال least common multiple
+
+146
+00:10:59,250 --> 00:11:02,550
+و ال great common divisor هذه العلاقة بتريحنا
+
+147
+00:11:02,550 --> 00:11:07,810
+بتخلينا نوجد واحدة منهم والتانية نوجدها منهايعني
+
+148
+00:11:07,810 --> 00:11:13,530
+الآن العلاقة عبر نظرية خامسة بتقول كمالي let a and
+
+149
+00:11:13,530 --> 00:11:17,190
+b positive integers then لو كانت a و b عبارة عن
+
+150
+00:11:17,190 --> 00:11:21,430
+positive integers then ال a في b بتساوي ال grades
+
+151
+00:11:21,430 --> 00:11:24,770
+common divisor في ال a و ال b و في ال least common
+
+152
+00:11:24,770 --> 00:11:28,090
+multiple بين ال a و ال b يعني بيقول دائما دائما
+
+153
+00:11:28,090 --> 00:11:31,730
+دائما لو جبت ال least common multiple و ضربته في
+
+154
+00:11:31,730 --> 00:11:34,310
+ال grades common divisor هيقلع أيش اللي بيساوي ال
+
+155
+00:11:34,310 --> 00:11:38,970
+a في bعشان هي كأرياح لنا بكفى بنودد ال grade
+
+156
+00:11:38,970 --> 00:11:42,690
+common divisor بين ال A و ال B و بنودد ال least
+
+157
+00:11:42,690 --> 00:11:45,670
+common multiple كيف بنقول A في B على ال grade
+
+158
+00:11:45,670 --> 00:11:48,610
+common divisor إذا مافيش داعي إنه نودد هنا و نودد
+
+159
+00:11:48,610 --> 00:11:50,630
+هناك مع إنه الجهتين لو أوددت اللي هو ال
+
+160
+00:11:50,630 --> 00:11:54,950
+factorization بصير سهل تودي للتانين لكن اللي حابب
+
+161
+00:11:54,950 --> 00:11:59,330
+الطريقة أخرى بيدي بقول فرغبنا إنه بدوا least
+
+162
+00:11:59,330 --> 00:12:03,170
+common multiple بين ال 125 زي اللي فوق إيش بيسوي؟
+
+163
+00:12:03,290 --> 00:12:07,250
+كتب الـ 2400 على صورة الـ prime factorization ال
+
+164
+00:12:07,250 --> 00:12:08,770
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+165
+00:12:08,770 --> 00:12:10,290
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+166
+00:12:10,290 --> 00:12:10,290
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+167
+00:12:10,290 --> 00:12:11,650
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+168
+00:12:11,650 --> 00:12:16,590
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+169
+00:12:16,590 --> 00:12:16,950
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+170
+00:12:16,950 --> 00:12:17,950
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+171
+00:12:17,950 --> 00:12:18,670
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+172
+00:12:18,670 --> 00:12:20,230
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+173
+00:12:20,230 --> 00:12:20,590
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+174
+00:12:20,590 --> 00:12:20,590
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+175
+00:12:20,590 --> 00:12:20,590
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+176
+00:12:20,590 --> 00:12:24,470
+.. ال ..
+
+177
+00:12:30,770 --> 00:12:35,750
+الليست كومن موطن للألفين واربعمية وستلاف وتلاتمية
+
+178
+00:12:35,750 --> 00:12:40,510
+اول اشي بدي اوضب ل grades كومن ال divisor اوضبت
+
+179
+00:12:40,510 --> 00:12:43,970
+هنا قبل شوية ايش كان اوضبناه الفين واربعمية سواء
+
+180
+00:12:43,970 --> 00:12:47,590
+اتنين وخمسة في تلاتة في خمسة تربيع وستلاف تلاتمية
+
+181
+00:12:47,590 --> 00:12:50,050
+سواء اتنين تربية في تلاتة تربية في خمسة تربية في
+
+182
+00:12:50,050 --> 00:12:53,610
+سبعة الان لgrades كومن divisor بين الجهتين سواء
+
+183
+00:12:53,610 --> 00:12:58,090
+اتنين أسل ومينومان بين اتنين وخمسة
+
+184
+00:13:00,080 --> 00:13:04,700
+التلاتة بين الواحد والتانية والخمسة بين التنين
+
+185
+00:13:04,700 --> 00:13:09,000
+والتنين والسبعة لايوجد داعي لان انا مجرد command
+
+186
+00:13:09,000 --> 00:13:15,120
+divisor لو مرتبل افضل عنه لكتب السبعة عشان اخد ال
+
+187
+00:13:15,120 --> 00:13:19,900
+maximum لان هذي بيصير اتنين قصر لصغير اتنين تلاتة
+
+188
+00:13:19,900 --> 00:13:20,680
+لصغير واحد
+
+189
+00:13:27,940 --> 00:13:35,940
+الليست كوغل مارتدل بالـ 2400 و 6300 بساوية اللي هو
+
+190
+00:13:35,940 --> 00:13:40,260
+حاصل ضرب الرقمين اللي هو A في B مجسوم عالميا على
+
+191
+00:13:40,260 --> 00:13:44,200
+الـ 300 بطلح هذا بقى إذن هذه طريقة أخرى لإيجاد
+
+192
+00:13:44,200 --> 00:13:47,880
+least common multiple إذا أنت بتكاشف وجودها مباشرة
+
+193
+00:13:47,880 --> 00:13:52,340
+من هذاو لو قدرتها مباشرة من هنا برضه اللي هو صحيح
+
+194
+00:13:52,340 --> 00:13:59,180
+الان احنا في حاجة اسمها لدينا الكلوديان algorithm
+
+195
+00:13:59,180 --> 00:14:03,820
+الكلوديان algorithm بدنا نقصص للكلوديان algorithm
+
+196
+00:14:03,820 --> 00:14:09,280
+ندد ال greatest common اللي هو divisor مش دايما
+
+197
+00:14:09,860 --> 00:14:13,580
+موضوع ال grade common divisor اللي هو ان التحليل
+
+198
+00:14:13,580 --> 00:14:18,620
+لو كانت الأرقام كبيرة برضه بتغلب لكن برضه هناخد
+
+199
+00:14:18,620 --> 00:14:25,060
+طريقة أخرى لإيجاد ال grade common divisor بالعددين
+
+200
+00:14:25,060 --> 00:14:31,000
+لو أعطونا a و b عددين هذا طريقة أخرى العددين a و b
+
+201
+00:14:31,000 --> 00:14:34,820
+و جدني بالله ال grade common divisor ده كله ماشي
+
+202
+00:14:35,320 --> 00:14:39,420
+أنا بدي أدى اكتب ال A على طول ال BQ زي ال R يعني
+
+203
+00:14:39,420 --> 00:14:44,460
+بدي اكسم ال A على ال B نطلع عند A بيساو BQ زي ال R
+
+204
+00:14:44,460 --> 00:14:50,100
+رمضة لأن هذه اللي مابتقولك ريحها دائما دائما
+
+205
+00:14:50,100 --> 00:14:54,060
+العامل المشترك الأعلى بين ال A و ال B بيساو العامل
+
+206
+00:14:54,060 --> 00:14:59,160
+المشترك الأعلى بين ال B اللي مقسوم عليه اش و رمضة
+
+207
+00:14:59,550 --> 00:15:03,570
+دائما العالم المشترك الأعلى بين الـA والـB حيث هو
+
+208
+00:15:03,570 --> 00:15:07,810
+بين الـD والـE والـR هذه اللي هي اللي تعاملنا اللي
+
+209
+00:15:07,810 --> 00:15:13,210
+موجودة هي اللي بتشرع لنا الآن طريقة إيجاد greatest
+
+210
+00:15:13,210 --> 00:15:17,710
+common divisor بهذه الطريقة هذه بنسميها اللي هي عن
+
+211
+00:15:17,710 --> 00:15:23,510
+طريق الـGluten Algorithm أو الخوارزية القسمةHence,
+
+212
+00:15:23,630 --> 00:15:26,550
+the Occlusion Algorithm is an efficient method for
+
+213
+00:15:26,550 --> 00:15:30,430
+computing the Great School Divisor of two integers
+
+214
+00:15:48,480 --> 00:15:50,680
+باكسيم الـ 287 عامل عامل عامل عامل عامل عامل عامل
+
+215
+00:15:50,680 --> 00:15:52,520
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+216
+00:15:52,520 --> 00:15:53,000
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+217
+00:15:53,000 --> 00:15:54,500
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+218
+00:15:54,500 --> 00:15:55,280
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+219
+00:15:55,280 --> 00:15:55,520
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+220
+00:15:55,520 --> 00:15:56,740
+عامل عامل عامل عامل عامل عامل عامل عامل عامل عامل
+
+221
+00:15:56,740 --> 00:16:01,180
+عامل عامل
+
+222
+00:16:01,180 --> 00:16:08,020
+عامل عامل
+
+223
+00:16:08,020 --> 00:16:12,670
+عطيب اش يعني اكمل اكملك بقسم الان واحد وتسعين مع
+
+224
+00:16:12,670 --> 00:16:16,290
+الاربعتاش لما قسمت الواحد وتسعين مع الاربعتاش
+
+225
+00:16:16,290 --> 00:16:20,250
+فالواحد تسعين سوى اربعتاش في ستة زائد سبعةبطبق
+
+226
+00:16:20,250 --> 00:16:27,330
+الآن هذه الخاصية على الـ 91 والـ 14 عامل المشترك
+
+227
+00:16:27,330 --> 00:16:31,490
+الأعلى بين الـ 91 والـ 14 ساوي عامل المشترك الأعلى
+
+228
+00:16:31,490 --> 00:16:35,550
+بين المقسوم عليه والـ remainder الـ 14 والـ 7 ماشي
+
+229
+00:16:35,550 --> 00:16:39,450
+الحال طيب إيش يعني؟ بجيبها ال gate بقولك إيش يعني؟
+
+230
+00:16:39,450 --> 00:16:44,830
+خد ال 14 وال7 هذي ال 14 وال7 في 2 زي 2 0 عندها أنا
+
+231
+00:16:44,830 --> 00:16:48,920
+بنهيلأنه بيصير العام المشترك الأعلى اللى هو بين
+
+232
+00:16:48,920 --> 00:16:54,120
+الاربعتاش والسبعتاش اللى هو عارفينه مين سبعة يعني
+
+233
+00:16:54,120 --> 00:16:57,840
+الآن من هذا بيصير عندي العام المشترك الأعلى بين
+
+234
+00:16:57,840 --> 00:17:02,240
+الاربعتاش بتساوي سبعة بيصير عندي بضل أجسم هذا
+
+235
+00:17:02,240 --> 00:17:07,820
+بيخليني أستنتج ما يعني أنه بضل أجسم270 على 91 ثم
+
+236
+00:17:07,820 --> 00:17:12,160
+ناتج القسم على المتبقى ثم ناتج القسم على المتبقى
+
+237
+00:17:12,160 --> 00:17:14,340
+ثم ناتج القسم على المتبقى ثم ناتج القسم على
+
+238
+00:17:14,340 --> 00:17:14,460
+المتبقى ثم ناتج القسم على المتبقى ثم ناتج القسم
+
+239
+00:17:14,460 --> 00:17:15,020
+على المتبقى ثم ناتج القسم على المتبقى ثم ناتج
+
+240
+00:17:15,020 --> 00:17:15,760
+القسم على المتبقى ثم ناتج القسم على المتبقى ثم
+
+241
+00:17:15,760 --> 00:17:17,780
+ناتج القسم على المتبقى ثم ناتج القسم على المتبقى
+
+242
+00:17:17,780 --> 00:17:18,360
+ثم ناتج القسم على المتبقى ثم ناتج القسم على
+
+243
+00:17:18,360 --> 00:17:19,480
+المتبقى ثم ناتج القسم على المتبقى ثم ناتج القسم
+
+244
+00:17:19,480 --> 00:17:25,240
+على المتبقى ثم ناتج القسم على المتبقى ثم ناتج
+
+245
+00:17:25,240 --> 00:17:28,690
+القسم على المتبقاللي هو هيكون ايش بيساوي سبعة من
+
+246
+00:17:28,690 --> 00:17:31,490
+وين جيبته هذا بناء على العلاقة هذه اللي اودبناها
+
+247
+00:17:31,490 --> 00:17:33,270
+انه هذا بيساوي ال grade from the divisor بين
+
+248
+00:17:33,270 --> 00:17:36,530
+الاربعتاش السبعة بيساوي سبعة يعني الآن شغل المثل
+
+249
+00:17:36,530 --> 00:17:40,990
+اللي بيوجد العامل المشترك العالمي ال 287 و 91 ايش
+
+250
+00:17:40,990 --> 00:17:47,450
+بيساوي بيجي بيجسم ال 287 على ال 91 اللي انا بطلع
+
+251
+00:17:47,450 --> 00:17:51,270
+عنده ناتج قسم ما هيه 91 بطلع متبقي بتجسم ال 91 على
+
+252
+00:17:51,270 --> 00:17:56,020
+المتبقياللي هو بيطلع ناتج قسمة ومتبقي بيبقى تعمل
+
+253
+00:17:56,020 --> 00:18:00,900
+هادي لما انتصل في الآخر متبقي بيساوي سفر أول متبقي
+
+254
+00:18:00,900 --> 00:18:05,400
+قبل المتبقي سفر بيكون هو ال Greatest Common
+
+255
+00:18:05,400 --> 00:18:12,700
+Divisor بين العددين اللي بدأت فيهم طيب الآن ال
+
+256
+00:18:12,700 --> 00:18:16,820
+Greatest Common Divisor بنقدر نكتبه على طورة اللي
+
+257
+00:18:16,820 --> 00:18:23,540
+هوالان linear combinations بين اللي هم العددين تبع
+
+258
+00:18:23,540 --> 00:18:27,980
+اللوحي المفروض مفروض فمانعي بزواد سفينة بتقول
+
+259
+00:18:27,980 --> 00:18:33,180
+مانعي if a and b are positive integers then there
+
+260
+00:18:33,180 --> 00:18:37,080
+exist integers s and t for example جريتكم مبادرة
+
+261
+00:18:37,080 --> 00:18:38,580
+ومعينة a وb بساوية
+
+262
+00:18:42,440 --> 00:18:46,800
+يعني الآن إذا كانت a و b عبارة عن أعداد اللي يجب
+
+263
+00:18:46,800 --> 00:18:51,920
+أن تنتجها بقدر ألاقي s و t عبارة عن أعداد صحيحة
+
+264
+00:18:51,920 --> 00:18:55,520
+لحيث أن ال greatest common divisor بين a و b
+
+265
+00:18:55,520 --> 00:19:00,440
+بيساوي عبارة عن s a ذات t b هذا بيسميها linear
+
+266
+00:19:00,440 --> 00:19:01,480
+combination
+
+267
+00:19:06,340 --> 00:19:09,880
+العامل المشترك اللي على بين الـA و الـB يعني كان D
+
+268
+00:19:09,880 --> 00:19:13,620
+written as a linear combination بين الـA و الـB
+
+269
+00:19:13,620 --> 00:19:16,700
+الان هذا اللي هي by buzzard theorem اللي قلته قبل
+
+270
+00:19:16,700 --> 00:19:20,380
+شوية the greatest common divisor of integers A and
+
+271
+00:19:20,380 --> 00:19:24,880
+D كان D expressed ممكن التعبير عنه on the form S A
+
+272
+00:19:24,880 --> 00:19:39,510
+زي T B where S and T are integersهذا هو عامل
+
+273
+00:19:39,510 --> 00:19:43,730
+المشترك الأعلى بين الـ 6 والـ 14 بساوية هو نقص 2
+
+274
+00:19:43,730 --> 00:19:47,650
+في 6 زائد 1 في 14 كيف أكتب بين هؤلاء؟ من أين أجيب
+
+275
+00:19:47,650 --> 00:19:52,010
+الـ 1 ونقص 2؟ من أين أجيب الـ 2؟ من أين أجيب الـ
+
+276
+00:19:52,010 --> 00:19:58,880
+2؟ من أين أجيب الـ 2؟ من أين أجيب الـ 2؟add a
+
+277
+00:19:58,880 --> 00:20:02,560
+linear combination of these two non-valid integers
+
+278
+00:20:02,560 --> 00:20:06,900
+صلوا على النبي عليه الصلاة والسلام الان finding
+
+279
+00:20:06,900 --> 00:20:10,840
+the greatest common divider add a linear
+
+280
+00:20:10,840 --> 00:20:15,560
+combination بدنا نوجد اللي هو العامل المشترك
+
+281
+00:20:15,560 --> 00:20:19,640
+البسيط نكتب على صورة linear combinations of
+
+282
+00:20:19,640 --> 00:20:22,540
+العددين اللي بدنا نوجد اللي هي العامل المشترك
+
+283
+00:20:22,540 --> 00:20:29,370
+البسيطExpress الـ 252 وال198 اللي هي ال address
+
+284
+00:20:29,370 --> 00:20:31,950
+from the device you're building Express الـ 18
+
+285
+00:20:31,950 --> 00:20:36,230
+طبعاً هيطلع Express هذا as a linear combination of
+
+286
+00:20:36,230 --> 00:20:41,310
+ال 252 و198 يعني أننا بدنا نكتب ال 252 و198 على
+
+287
+00:20:41,310 --> 00:20:46,170
+طولإن هو حاط ال S في هذا زي ال T في هذا بيساوي
+
+288
+00:20:46,170 --> 00:20:49,030
+إيه؟ إيش؟ طنان طاحته في الواقع الطريقة اللي
+
+289
+00:20:49,030 --> 00:20:53,310
+هنقولها .. هنقولها الآن هتضرب عصفرين بحجم إيش دي؟
+
+290
+00:20:53,310 --> 00:20:59,190
+هتيجي أول إشي توجدك ال 252 عندي اللي هو ال 252
+
+291
+00:20:59,190 --> 00:21:06,450
+هتوجده و في نفس الوجد ال 252 شايفين هذه و ال 98
+
+292
+00:21:06,450 --> 00:21:11,340
+هتيجي توجد العامل المشترك الأعلى بينهمو هتكتب لك
+
+293
+00:21:11,340 --> 00:21:19,820
+إياه في نفس الوقت كيف نشوف كيف شغل المكان الموضوع
+
+294
+00:21:19,820 --> 00:21:27,920
+بس مجرد أن نقسم ال 252 على 198 فالان 252 على 198
+
+295
+00:21:27,920 --> 00:21:32,520
+بطلع واحد و المتبقي 54 زي ما عملنا قبل شوية الآن
+
+296
+00:21:32,520 --> 00:21:40,380
+ال 198 بقسمه على المتبقي198 بتساوة 3 فى 54 زائد 36
+
+297
+00:21:40,380 --> 00:21:45,320
+ماشي الحال اللى عملته فوق بعمله كمان تحت بادي خلصت
+
+298
+00:21:45,320 --> 00:21:50,920
+من 198 بادي لل 54 اللى هو ناتج القسم هام مضربه في
+
+299
+00:21:50,920 --> 00:21:56,000
+مين في المتبقى بقى دي اسمه على المتبقى 36 54 بساوة
+
+300
+00:21:56,000 --> 00:22:02,280
+31 فى 36 زائد ال remainder 18 درد 36 و18 36 بساوة
+
+301
+00:22:02,280 --> 00:22:06,720
+2 فى 18 لما أصل مافيش remainderعلى طول بيكون هذا
+
+302
+00:22:06,720 --> 00:22:11,340
+زي ما قلنا قبل بشويه ال 18 هو هيكون يطلع ل grades
+
+303
+00:22:11,340 --> 00:22:16,640
+and divisors بين 252 و198 اذا انا بهذا الطريقة
+
+304
+00:22:16,640 --> 00:22:19,380
+فعلا اوجدت اللي هو grades and divisors يعني
+
+305
+00:22:19,380 --> 00:22:22,980
+بلزمنيش يعطيه لي هذا اصلا هو بلزمنيش هذا انا
+
+306
+00:22:22,980 --> 00:22:26,260
+هاعرفه اصلا اللي انا اوجدت العام المشترك العالمي
+
+307
+00:22:26,260 --> 00:22:31,500
+بين 252 و198 ايش بيساوي اول متبقي بعد ما اصل
+
+308
+00:22:31,500 --> 00:22:36,210
+للمتبقي بساوي 0 طيبمش هذا اللي بدنا يامدى عارفينه
+
+309
+00:22:36,210 --> 00:22:40,270
+من الأول اه بدنا نكتب اللي هو ال 18 as a linear
+
+310
+00:22:40,270 --> 00:22:47,550
+combination من 252 و198 العملية عملية رجوع لما
+
+311
+00:22:47,550 --> 00:22:53,810
+أصلها دي كده لأن 18 هي بتساوي هادي و بنجي الهادي
+
+312
+00:22:53,810 --> 00:22:59,210
+هان إلى ناقص واحد في 36 ايه سويه ال 18 أخ أسوأ
+
+313
+00:22:59,210 --> 00:23:05,160
+العالم المشترك بسوء 54 ناقص واحد في 36ببدأ من عند
+
+314
+00:23:05,160 --> 00:23:08,780
+أول متبقى مش سفر اللي هو ال grade-common divisor و
+
+315
+00:23:08,780 --> 00:23:14,360
+ببدأ أرجع سيرة 18 بيساوي 54 ناقص 1 في 36 أنا بدي
+
+316
+00:23:14,360 --> 00:23:20,320
+18 في دلالة 100 252 و 198 يعني لا بدي ال 36 ولا
+
+317
+00:23:20,320 --> 00:23:26,180
+بدي ال 54 الاربع ماتضربش خليها زي هذا الان عند ال
+
+318
+00:23:26,180 --> 00:23:33,770
+36 هذه هيها من هنا بساوي 198 ناقص 3 في 54إذا الـ
+
+319
+00:23:33,770 --> 00:23:37,610
+36 هذه من أين بتجيبها من الخطوة اللي جابلها أضالة
+
+320
+00:23:37,610 --> 00:23:43,290
+عن 198 ناقص ثلاثة في خمسة أربعة وخمسين الان قيمة
+
+321
+00:23:43,290 --> 00:23:47,990
+الـ 36 هذه خليها زي ما هي وما تصبهاش بتعودها مكان
+
+322
+00:23:47,990 --> 00:23:51,830
+مين الـ 36 بصير الـ 18 بتساوي اربعة وخمسين زي ما
+
+323
+00:23:51,830 --> 00:23:56,430
+هي وما تصبهاش ناقص واحد ماشي الان هذا الواحد مضروب
+
+324
+00:23:56,430 --> 00:24:01,290
+في الـ 36 مين الـ 36 هين هذا كله اللي هو 198 ناقص
+
+325
+00:24:01,290 --> 00:24:04,910
+ثلاثة في اربعة وخمسينتضرب ايش؟ لأنه انا بدي احنا
+
+326
+00:24:04,910 --> 00:24:11,830
+في الاخر بدلالة 198 وال252 الان هذه 54 ناقص واحد
+
+327
+00:24:11,830 --> 00:24:19,130
+في 198 هي الواحد في 198 هيها الان عند 54 واحدة وفي
+
+328
+00:24:19,130 --> 00:24:22,880
+عندي ناقص واحدفي ناقص تلاتة في اربعة وخمسين بيصير
+
+329
+00:24:22,880 --> 00:24:26,300
+ناقص في ناقص اتزايد بيصير واحد في تلاتة في تلاتة
+
+330
+00:24:26,300 --> 00:24:29,140
+بيصير تلاتة في اربعة وخمسين وفي عند واحدة اربعة
+
+331
+00:24:29,140 --> 00:24:33,040
+وخمسين بيصير اربعة اربعة من اربعة وخمسين يعني
+
+332
+00:24:33,040 --> 00:24:38,940
+واحدةفي ناقص واحد في ناقص تلاتة تطلع تلاتة تلاتة
+
+333
+00:24:38,940 --> 00:24:41,680
+مضروبة في مين في اربع وخمسين واحد في اربع وخمسين
+
+334
+00:24:41,680 --> 00:24:45,260
+بيصير اربع في اربع وخمسين لأنه بيصير من الاربع
+
+335
+00:24:45,260 --> 00:24:48,960
+وخمسين لو سمناها دي اللي هو اللي هو سين بيصير هنا
+
+336
+00:24:48,960 --> 00:24:51,720
+تلاتة سين وهنا سين بيصير الاربع سين مين السين
+
+337
+00:24:51,720 --> 00:24:55,060
+بيقولنا انا اربع وخمسين فبيصير اربع في اربع وخمسين
+
+338
+00:24:55,060 --> 00:24:58,480
+ناقص واحد في مية وتمنية وتسعين تضرب هنش لانه بدي
+
+339
+00:24:58,480 --> 00:25:02,330
+اياه ان انا الانالاربعة و خمسين لا أريد أن أقوم
+
+340
+00:25:02,330 --> 00:25:04,050
+باستخدامها انا اريد ان اقوم باستخدام الاربعة و
+
+341
+00:25:04,050 --> 00:25:10,130
+خمسين الاربعة
+
+342
+00:25:10,130 --> 00:25:16,290
+و خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+343
+00:25:16,290 --> 00:25:16,550
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+344
+00:25:16,550 --> 00:25:16,550
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+345
+00:25:16,550 --> 00:25:18,150
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+346
+00:25:18,150 --> 00:25:18,270
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+347
+00:25:18,270 --> 00:25:26,030
+خمسين الاربعة و خمسين الاربعة و خمسين الاربعة و
+
+348
+00:25:26,030 --> 00:25:30,570
+خمسين الاربعة وهذه الآن بدي أضعها في مكان الـ 54
+
+349
+00:25:30,570 --> 00:25:31,870
+لإنها ليست موجودة في الـ 54 لأنها ليست موجودة في
+
+350
+00:25:31,870 --> 00:25:33,370
+الـ 54 لإنها ليست موجودة في الـ 54 لإنها ليست
+
+351
+00:25:33,370 --> 00:25:34,310
+موجودة في الـ 54 لإنها ليست موجودة في الـ 54 لإنها
+
+352
+00:25:34,310 --> 00:25:36,210
+ليست موجودة في الـ 54 لإنها ليست موجودة في الـ 54
+
+353
+00:25:36,210 --> 00:25:36,590
+لإنها ليست موجودة في الـ 54 لإنها ليست موجودة في
+
+354
+00:25:36,590 --> 00:25:40,550
+الـ 54 لإنها ليست موجودة في الـ 54 لإنها ليست
+
+355
+00:25:40,550 --> 00:25:45,590
+موجودة في الـ 54 لإنها ليست موجودة في الـ 54 لإنها
+
+356
+00:25:45,590 --> 00:25:48,070
+ليست موجودة في الـ 54 لإنها ليست موجودة في الـ 54
+
+357
+00:25:48,070 --> 00:25:51,230
+لإنها
+
+358
+00:25:51,230 --> 00:25:55,160
+ليست موجودة في الـأربعة في ناقص واحد ناقص أربعة
+
+359
+00:25:55,160 --> 00:26:01,140
+سين وفي كمان ناقص سين ناقص خمس سين من السين
+
+360
+00:26:01,140 --> 00:26:05,880
+المائية وتمانية وتسعين يعني عندي ناقص أربعة من
+
+361
+00:26:05,880 --> 00:26:09,260
+المائية وتمانية وتسعينات وعندي ناقص واحدة من
+
+362
+00:26:09,260 --> 00:26:13,040
+المائية وتمانية وتسعينات بيصير ناقص أربعة وناقص
+
+363
+00:26:13,040 --> 00:26:15,980
+واحدة من واحد بيصير ناقص خمسة في المائية وتمانية
+
+364
+00:26:15,980 --> 00:26:21,720
+وتسعينماذا اذا قمت باستخدام الوصول لقمة 18 اكتبها
+
+365
+00:26:21,720 --> 00:26:25,360
+على صورة linear combination اربعة في اتنين و اتنين
+
+366
+00:26:25,360 --> 00:26:28,820
+و خمسين ناقص خمسة في اتنين و اتنين و تسعين اللي هو
+
+367
+00:26:28,820 --> 00:26:32,620
+طالبه فبصير عندي اللي هي تمنتعش بالساوي هادي في
+
+368
+00:26:32,620 --> 00:26:37,220
+هادي فهو ال linear combination بين اللي هو الاتنين
+
+369
+00:26:37,220 --> 00:26:40,900
+و اتنين و خمسين في البين و تمنين و تسعين يعني ال S
+
+370
+00:26:40,900 --> 00:26:44,990
+عبارة عن اربعة و ال T عبارة عن ناقص خمسةإذا هذه
+
+371
+00:26:44,990 --> 00:26:48,210
+ضربت فيها عصفرين بحجم الـ Euclidean algorithm أو
+
+372
+00:26:48,210 --> 00:26:53,710
+خوارزميتا وقسمها إن أنا ضليت أن أقسم 252 ع 198 لما
+
+373
+00:26:53,710 --> 00:26:56,950
+أصلت لل remainder zero أول remainder مش zero بكل
+
+374
+00:26:56,950 --> 00:27:01,190
+هو العام المشترك الأعلى بينهم هذا بقدر أرجع ارجوع
+
+375
+00:27:01,190 --> 00:27:04,490
+زي ما أرجع نهان لما أوصل إنه عبارة عن linear
+
+376
+00:27:04,490 --> 00:27:12,190
+combination بين 198 و252 وهو المخلوق طيب الان بعض
+
+377
+00:27:12,190 --> 00:27:17,190
+النتائج على بيزوت فيورينConsequences of Biot's
+
+378
+00:27:17,190 --> 00:27:20,930
+theorem الان عندى اللى هو ال .. ال .. ال .. ال ..
+
+379
+00:27:20,930 --> 00:27:24,210
+Biot's theorem إيش بتقول .. اللمّة الأولى بتقول if
+
+380
+00:27:24,210 --> 00:27:27,130
+a و b and c are positive integers such that
+
+381
+00:27:27,130 --> 00:27:30,510
+لجريسكم ال divisor بين a و b بيساوة واحد and a
+
+382
+00:27:30,510 --> 00:27:34,910
+بتقسم ال bc then a بتقسم ال c باختصار بقول لو عرض
+
+383
+00:27:34,910 --> 00:27:39,120
+عليك اللي a بتقسم ال b في cهل بتقدر تقول ال A
+
+384
+00:27:39,120 --> 00:27:43,580
+بتقسم ال B أو ال A بتقسم ال C ؟ ليس شرطا متى بتقدر
+
+385
+00:27:43,580 --> 00:27:47,200
+تقول لما يكون العامل المشترك الأعلى بين ال A و ال
+
+386
+00:27:47,200 --> 00:27:50,680
+B واحد مدام العامل المشترك الأعلى بين ال A و ال B
+
+387
+00:27:50,680 --> 00:27:56,120
+واحد يعني فش ذنهن عوامل مشتركة يعني الآن لما ال A
+
+388
+00:27:56,120 --> 00:27:59,850
+بتقسم ال B في ال Cالـ A والـ B لا يوجد بين العوامل
+
+389
+00:27:59,850 --> 00:28:03,090
+إذاً الـ M الـ A هتكون تجسم مين؟ هتجسم اللي بطلع
+
+390
+00:28:03,090 --> 00:28:07,490
+للـ C كيف جسمت الـ B في الـ C إذاً لازم تجسمين الـ
+
+391
+00:28:07,490 --> 00:28:13,230
+C يعني مثلا عندك خمسة تجسم التلاتة في خمس عشر
+
+392
+00:28:14,960 --> 00:28:18,400
+الخامسة والتلاتة مافيش بين العوامل الـ B ثلاثة إذا
+
+393
+00:28:18,400 --> 00:28:21,580
+الخامسة لازم تكسب مين اللي بتظل C اللي هي جولناها
+
+394
+00:28:21,580 --> 00:28:26,980
+خمس عشر اللي هي هذه خلينا أمور سريعة على الظهار
+
+395
+00:28:26,980 --> 00:28:31,300
+عسى ما تكونوا عندكم فكرة على كيف تبرهن الآن العامل
+
+396
+00:28:31,300 --> 00:28:34,060
+المشترك الأعلى بين الـ A و الـ B مقترضين واحد
+
+397
+00:28:34,060 --> 00:28:38,560
+مقترض أن الـ A تكسب مين الـ B في الـ C مدام العامل
+
+398
+00:28:38,560 --> 00:28:41,380
+المشترك الأعلى بين الـ A و الـ B بساوء واحد حسب
+
+399
+00:28:41,380 --> 00:28:45,960
+النظرية اللي جابت قليلبنكتب الواحد as a linear
+
+400
+00:28:45,960 --> 00:28:49,320
+combination بين ال A و ال B يعني بقدر اكتب الواحد
+
+401
+00:28:49,320 --> 00:28:55,700
+على صورة S في A زي ما عملنا قبل بشوية الان S A حيث
+
+402
+00:28:55,700 --> 00:28:59,320
+S عبارة عن integer و T عبارة عن integer دربون
+
+403
+00:28:59,320 --> 00:29:07,160
+الجهتين في C هذهاس اي في سي زائد ت في بي في سي
+
+404
+00:29:07,160 --> 00:29:13,200
+بيساوي كداش بيساوي اللي هو عبارة عن سي إذا صارت
+
+405
+00:29:13,200 --> 00:29:17,340
+عندي اس اي سي زائد ت بي سي بيساوي سي لما ضربنا هدف
+
+406
+00:29:17,340 --> 00:29:21,640
+يمين في سي طيب خلي هدف الداكرة الان عندي ال a
+
+407
+00:29:21,640 --> 00:29:26,540
+بتكسب ال bc معطنيها فوق ال a بتكسب ال bc الان أكيد
+
+408
+00:29:26,540 --> 00:29:30,280
+اللي هو ال a هتكسب ال t في b في c مدام انت بتكسب
+
+409
+00:29:30,280 --> 00:29:35,420
+ال bc لحالهايعني مدام ال A بتكسب مثلا خمسة الخمسة
+
+410
+00:29:35,420 --> 00:29:39,100
+بتكسب خمسة في تلاتة اذا اكيد ال A بتكسب خمسة في
+
+411
+00:29:39,100 --> 00:29:45,400
+تلاتة في عشرة اكيد اذا ال A بتكسب T في C وعندي ال
+
+412
+00:29:45,400 --> 00:29:48,960
+A بتكسب ال S في A في C لان ال A هي اذا ال A عامل
+
+413
+00:29:48,960 --> 00:29:52,360
+من العوامل هذه مدام ال A بتكسب هذه و ال A بتكسب
+
+414
+00:29:52,360 --> 00:29:56,680
+هذه اذا حسب نظرية سابقة ال A هتكسب مجموحين اللي هو
+
+415
+00:29:56,680 --> 00:30:02,330
+SAC زي TBC مجموحين هذا ايش اسمه Cيعني ال A هتكسب
+
+416
+00:30:02,330 --> 00:30:07,490
+ال C إذا هيك أبوكول أثبتنا أنه لو A تكسب ال B و ال
+
+417
+00:30:07,490 --> 00:30:10,730
+C و المشتركة اللي عالة بين ال B و ال A واحد إذا ال
+
+418
+00:30:10,730 --> 00:30:16,910
+A تكسب ال C طيب الآن احنا نيجي اللي هو النظرية
+
+419
+00:30:16,910 --> 00:30:21,390
+اللي بعدها النظرية اللي بعدها أو اللملة اللي بعدها
+
+420
+00:30:21,390 --> 00:30:25,590
+اللي بتقول التعميم يعني if B is a prime and B
+
+421
+00:30:25,590 --> 00:30:31,180
+بتكسب ال A واحدthen بتقسم ال E I for some I بقول
+
+422
+00:30:31,180 --> 00:30:34,540
+يعني لو كانت عندي ال B عبارة عن إبراهيم يعني كتلة
+
+423
+00:30:34,540 --> 00:30:38,100
+واحدة بتقسم ال A واحد في ال A اتنين في ال A تلاتة
+
+424
+00:30:38,100 --> 00:30:43,660
+في ال A N إذا لازم ال B تقسم من واحدة من هدولة على
+
+425
+00:30:43,660 --> 00:30:46,120
+الأقل واحدة لو كنت تقسمت اتنين و كنت تقسمت تلاتة
+
+426
+00:30:46,120 --> 00:30:49,840
+يعني لو تلاتة بتقسم خمسة في ستة عشر في خمسة و
+
+427
+00:30:49,840 --> 00:30:53,900
+عشرين في خمسة و تلاتين في طمنتاش في كده إذا أكيد
+
+428
+00:30:53,900 --> 00:30:56,480
+التلاتة دي بتقسم واحدة من هنا و لتكون مثلا اللي
+
+429
+00:30:56,480 --> 00:31:00,550
+قلتها A اش طمنتاشإذا لما الـ prime بيكسب ال a1, a2
+
+430
+00:31:00,550 --> 00:31:05,030
+and an لازم ال prime بيكسب واحد من هذولة لأنه أصلا
+
+431
+00:31:05,030 --> 00:31:09,190
+هو كتلة واحدة مش هتلاقوه مفرّج بين تلتين لازم يكون
+
+432
+00:31:09,190 --> 00:31:12,310
+في هذه كله أو في هذه كله أو في هذه كله أو في كل
+
+433
+00:31:12,310 --> 00:31:16,270
+واحدة كله إذا ال b بتكسب ai for some i for some i
+
+434
+00:31:16,270 --> 00:31:18,590
+ممكن تكون واحدة و تلتين و تلتين إذا على الأقل
+
+435
+00:31:18,590 --> 00:31:23,150
+واحدة بتكسب طيب هذه اللي هي النظرية ال أو اللمّة
+
+436
+00:31:23,150 --> 00:31:28,350
+عبارة عن لمّة تلتالآن بدنا نجي لآخر issue في
+
+437
+00:31:28,350 --> 00:31:32,590
+المحاضرة اليوم اللي هو dividing concurrences by an
+
+438
+00:31:32,590 --> 00:31:38,970
+integer يعني عملية اللي هي قسمة التطابق بواسطة
+
+439
+00:31:38,970 --> 00:31:42,550
+انتجة يعني dividing both of a valid concurrences
+
+440
+00:31:42,550 --> 00:31:47,770
+يعني لو كان عندي AC تطابق BC مدله M مدله M لو كان
+
+441
+00:31:47,770 --> 00:31:51,730
+هذه التطابقة صحيحة يعني ايش صحيحة يعني الأمر تكسب
+
+442
+00:31:51,730 --> 00:31:57,760
+ال AC نقص BCلو كانت هذه صحيحة مش شرط انه تقدر تقول
+
+443
+00:31:57,760 --> 00:32:02,100
+by an integer اللي هو does not always produce a
+
+444
+00:32:02,100 --> 00:32:05,960
+valid congruent يعني مش شرط انه اللي هو لو جسمنا
+
+445
+00:32:05,960 --> 00:32:09,440
+هدول الجهتين ع C نيجي نقول والله اذا A تطابق B
+
+446
+00:32:09,440 --> 00:32:14,580
+modulo M يعني لو كانت AC تطابق BC modulo M ليس شرط
+
+447
+00:32:14,580 --> 00:32:19,760
+انه يطلع ال A تطابق B modulo B modulo Mهذه القسمة
+
+448
+00:32:19,760 --> 00:32:24,020
+أو الاقتصاد مش زي المعادلات العادية هذه القسمة مش
+
+449
+00:32:24,020 --> 00:32:26,600
+زي المعادلات العادية تيجي تقول شيل ال C و شيل ال C
+
+450
+00:32:26,600 --> 00:32:30,560
+بيصير ايه تطابق ال D مدله M هذه مثال مثلا عند 2
+
+451
+00:32:30,560 --> 00:32:35,660
+فعشرة تطابق 3 فعشرة مدل 5 صحيح هذا ولا لا لأن 2
+
+452
+00:32:35,660 --> 00:32:39,380
+فعشرة 20 ثلاثة فعشرة تلاتين تلاتين ناقص عشرين عشرة
+
+453
+00:32:39,380 --> 00:32:44,140
+الخمسة بتقسم العشرة إذا فعلا هذه المتطابقة صحيحةلو
+
+454
+00:32:44,140 --> 00:32:46,840
+أتي واحد وقال لي خلّينا نختصر العشرة مع العشرة
+
+455
+00:32:46,840 --> 00:32:49,620
+بيصير عندى اتنين متطابق التلاتة من الخمسة صح ولا
+
+456
+00:32:49,620 --> 00:32:55,060
+ضلع هذا ضلع مش صحيح لأن الخمسة لا تقسم تلاتة نقص
+
+457
+00:32:55,060 --> 00:33:00,720
+اتنين لأن هيك معناته متطابقة عشان تكون هذه صحيحة
+
+458
+00:33:00,720 --> 00:33:03,320
+لازم الخمسة تقسم تلاتة نقص اتنين لكن الخمسة لا
+
+459
+00:33:03,320 --> 00:33:06,860
+تقسم تلاتة نقص اتنين لأن الخمسة لا تقسم الواحد اذا
+
+460
+00:33:06,860 --> 00:33:11,720
+مانفعش نيجي اللي هو نختصر عشرة مع العشرة طب ها
+
+461
+00:33:11,720 --> 00:33:16,970
+كيفش نسويهو يقول لك الاختصار كما يعني او يشرّع لك
+
+462
+00:33:16,970 --> 00:33:21,410
+الاختصار بما يعني but divided by any integer
+
+463
+00:33:21,410 --> 00:33:27,110
+relative to the prime to the modulus does produce
+
+464
+00:33:27,110 --> 00:33:30,670
+a valid congruent ايش يعني هذا؟ ايش بتقول؟ بقول ما
+
+465
+00:33:30,670 --> 00:33:34,690
+يعني بقول الفيون السابع بتقول لك لو كانت M بي a
+
+466
+00:33:34,690 --> 00:33:39,350
+positive integer and A will be a C integer such
+
+467
+00:33:39,350 --> 00:33:44,000
+thatA في C يتطابق بيه C مدله M لو فرضنا هذا A C
+
+468
+00:33:44,000 --> 00:33:48,200
+تطابق ال B و B C مدله M و ال greatest common
+
+469
+00:33:48,200 --> 00:33:53,200
+divisor بين ال C و ال M بساوي واحد بين ال C و ال M
+
+470
+00:33:53,200 --> 00:33:57,940
+بساوي واحد هيعطينا ان ال A تطابق ال B ماله مدله ال
+
+471
+00:33:57,940 --> 00:34:04,520
+M يعني بقولك تقدر تعمل الاختصار C تروح مع ال C إذا
+
+472
+00:34:04,520 --> 00:34:07,480
+كان العامل المشترك الأعلى بين ال C و ال M ايش
+
+473
+00:34:07,480 --> 00:34:12,920
+بساوي بساوي واحدإذا عامل المشترك الأعلى بين الـ c
+
+474
+00:34:12,920 --> 00:34:16,420
+و ال m بساوة واحد بين ال c و ال m بساوة واحد
+
+475
+00:34:16,420 --> 00:34:23,200
+بحججلك تختصر هذه مع هذه يعني لو كان الآن خمسة في
+
+476
+00:34:23,200 --> 00:34:31,340
+اللي هو اتنين تطابق اللي هو خمسة في تلاتة اللي هو
+
+477
+00:34:31,340 --> 00:34:38,320
+modulo خمسة في اتنين تطابق اللي هو خمسة في اتنين
+
+478
+00:34:38,320 --> 00:34:39,460
+تطابق اللي هو
+
+479
+00:34:46,680 --> 00:34:50,120
+العامل المشترك الأعلى بين الـ C و الـ M بسوء واحد
+
+480
+00:34:50,120 --> 00:34:54,660
+يكون عند الـ A تطابق الـ B modulo M اللي هو بكل
+
+481
+00:34:54,660 --> 00:34:58,720
+سولة اقتصاد كما قلنا في مثال لو أخدنا خمسة مثلا في
+
+482
+00:34:58,720 --> 00:35:02,020
+اتنين تطابق اللي هو اتنين في اتنين modulo ثلاثة
+
+483
+00:35:12,570 --> 00:35:22,690
+الان هذه هي قسم المشروععندي A C تطابق B C mod M
+
+484
+00:35:22,690 --> 00:35:26,330
+معناته الامر تكسب ال A C minus ال B C ناخد ال C
+
+485
+00:35:26,330 --> 00:35:29,830
+عام المشترك بالسير اللي هي الامر تكسب ال C في ال A
+
+486
+00:35:29,830 --> 00:35:34,450
+minus B وقلنا بما انه اللي هي العام المشترك الأعلى
+
+487
+00:35:34,450 --> 00:35:37,470
+بين ال M و ال C لساوة واحد اذا الامر تكسب ال A
+
+488
+00:35:37,470 --> 00:35:41,670
+minus B عن ال M اللي هي تطابق ال B mod M وهكذا
+
+489
+00:35:41,670 --> 00:35:46,550
+شرعنا ان ال A C تطابق ال B C mod M
+
+490
+00:35:49,450 --> 00:35:53,290
+إن نعمل نقوم بالاقتصاد لما نقول عامل مشترك الاعلى
+
+491
+00:35:53,290 --> 00:35:56,790
+بين ال C و ال M بساوة واحد لكن غير هيك لأ نكون
+
+492
+00:35:56,790 --> 00:36:02,590
+حاضرين في اللي هو الاقتصاد وهذه هي ال homework
+
+493
+00:36:02,590 --> 00:36:08,570
+اللي مطلوب تحلوها السؤال الأول والثاني والتالت وإن
+
+494
+00:36:08,570 --> 00:36:12,970
+شاء الله إلى لقاء آخر في محاضرة أخرى السلام عليكم
+
+495
+00:36:12,970 --> 00:36:13,470
+ورحمة الله
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops.srt
new file mode 100644
index 0000000000000000000000000000000000000000..eb26090d2ead2e5e6e0e37bd12351c5faa748552
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops.srt
@@ -0,0 +1,1887 @@
+1
+00:00:00,000 --> 00:00:07,980
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثانية بعد
+
+2
+00:00:07,980 --> 00:00:18,940
+الطوارئ وهي لطلاب وطالبات الحوسبة المتنقلة لمساق 
+
+3
+00:00:18,940 --> 00:00:25,220
+رياضيات منفصلة لطلاب وطالبات كلية technology
+
+4
+00:00:25,220 --> 00:00:32,700
+المعلومات بالجامعة الإسلامية فرع الجنوب المحاضرة
+
+5
+00:00:32,700 --> 00:00:37,800
+اليوم هي بعنوان matrix determinant أو محدد
+
+6
+00:00:37,800 --> 00:00:42,920
+المصفوفة في هذه المحاضرة إن شاء الله هنتعرف على
+
+7
+00:00:42,920 --> 00:00:49,210
+شغلتين.. هنعرف شغلتين أساسيتين هي كيف نجد محدد
+
+8
+00:00:49,210 --> 00:00:56,270
+المصفوفة والأمر الآخر هو كيف نجد المعكوس الضربي
+
+9
+00:00:56,270 --> 00:01:02,630
+للمصفوفة في حال وجود هذا المعكوس دعونا الآن نتعرف
+
+10
+00:01:02,630 --> 00:01:08,370
+على محدد المصفوفة أو الـ matrix determinant الـ
+
+11
+00:01:08,370 --> 00:01:13,150
+Matrix Determinant أو محدد المصفوفة هو محدد
+
+12
+00:01:13,150 --> 00:01:20,110
+لمصفوفة مربعة يعني مصفوفة درجتها 2×2 أو 3×3 أو 4×4 
+
+13
+00:01:20,110 --> 00:01:25,510
+أو N×N بصورة عامة أحنا الآن هنتعرف في البداية شو
+
+14
+00:01:25,510 --> 00:01:30,710
+معناتها أو ما هو محدد المصفوفة the determinant of
+
+15
+00:01:30,710 --> 00:01:37,550
+المصفوفة اللي هي المكونة من اللي هو أو من الدرجة
+
+16
+00:01:37,550 --> 00:01:43,360
+اثنين في اثنين اللي هي A,B,C,D اللي أمامنا تعريف
+
+17
+00:01:43,360 --> 00:01:49,660
+محدد المصفوفة أو the determinant of the matrix هو
+
+18
+00:01:49,660 --> 00:01:54,200
+كمالي طبعًا بنرمز له بالرمز اللي هو column هنا و
+
+19
+00:01:54,200 --> 00:01:57,840
+column هنا أو اللي هو عمود من هنا و عمود من هنا و
+
+20
+00:01:57,840 --> 00:02:02,280
+بينهم مكتوبة نفس المصفوفة العادية نوجد المحدد بيجي
+
+21
+00:02:02,280 --> 00:02:07,560
+بنضرب عناصر القطر الرئيسي ناقص عناصر القطر الثانوي
+
+22
+00:02:07,560 --> 00:02:11,260
+يعني بمعنى آخر محدد المصفوفة عبارة عن رقم هيطلع اللي
+
+23
+00:02:11,260 --> 00:02:16,680
+هو A في D ناقص B في C هذا محدد المصفوفة اللي هي من
+
+24
+00:02:16,680 --> 00:02:22,540
+الدرجة 2 في 2 بالاستعانة بمحدد المصفوفة من الدرجة 2
+
+25
+00:02:22,540 --> 00:02:29,240
+في 2 هنعرف محدد المصفوفة لما تكون درجة المصفوفة 3 في
+
+26
+00:02:29,240 --> 00:02:33,860
+3 هي أمامنا مصفوفة 3 في 3 وهي عناصرها موجودة جوا
+
+27
+00:02:33,860 --> 00:02:40,880
+بدنا نحدد اللي هو شو محددها أو نوجد شو محددها الآن
+
+28
+00:02:40,880 --> 00:02:43,760
+الـ determinant هي الـ determinant اللي هو عمود
+
+29
+00:02:43,760 --> 00:02:46,740
+دنهان عمود دنهان أو عصام دنهان أو عصام دنهان ال
+
+30
+00:02:46,740 --> 00:02:51,820
+determinant هذا هيساوي اللي هو بنيجي يا بنستخدم
+
+31
+00:02:51,820 --> 00:02:58,260
+عناصر اللي هو عناصر الصف العمود أو عناصر الصف في
+
+32
+00:02:58,260 --> 00:03:01,820
+إيجاد المحدد إيش بيعني؟ شوفوا إيش بيعني خلينا
+
+33
+00:03:01,820 --> 00:03:06,500
+نستخدم اللي هو عناصر من العمود الأول فبكون عندي
+
+34
+00:03:06,500 --> 00:03:14,100
+اللي هو محدد المصفوفة هذه بيساوي A في اللي هو محدد
+
+35
+00:03:14,100 --> 00:03:21,130
+من الدرجة الثانية ناقص الآن موجب ناقص ناقص D في محدد
+
+36
+00:03:21,130 --> 00:03:26,030
+المصفوفة من الدرجة الثانية G في محدد المصفوفة
+
+37
+00:03:26,030 --> 00:03:30,270
+أيضًا من الدرجات الثانية بنبدأ بموجب سالب موجب ولو
+
+38
+00:03:30,270 --> 00:03:33,330
+أخذنا السطر الثاني برضه هنبدأ بموجب سالب موجب
+
+39
+00:03:33,330 --> 00:03:36,390
+خلينا نبدأ في العمود اللي عندنا الآن العمود اللي
+
+40
+00:03:36,390 --> 00:03:40,380
+عندنا بقولنا A و بادي بدورة المحدد اللي بدور بالـ A
+
+41
+00:03:40,380 --> 00:03:45,020
+فيه بشطب هذا السطر اللي فيه الـ A و بشطب هذا
+
+42
+00:03:45,020 --> 00:03:50,340
+العمود اللي فيه الـ A بيظل اللي هو المحدد هذا اللي
+
+43
+00:03:50,340 --> 00:03:54,960
+هو الـ E و الـ F و الـ H و الـ I إذا هذا بيساوي الـ
+
+44
+00:03:54,960 --> 00:03:59,980
+A في المحدد اللي نتج بعد تشطيب اللي هو الصف و
+
+45
+00:03:59,980 --> 00:04:05,250
+العمود اللي بيحتوي A نفس الشيء بالنسبة لـ D بنشطب
+
+46
+00:04:05,250 --> 00:04:09,550
+بالسطر و بنشطب بالعمود اللي هي فيه بيظل B و C و
+
+47
+00:04:09,550 --> 00:04:13,790
+H و I B و C و H و I إذا ناقص D في اللي هو
+
+48
+00:04:13,790 --> 00:04:14,070
+هذا
+
+49
+00:04:17,090 --> 00:04:23,010
+بنقص D ومن ثم زائد G بنشطب اللي هو السطر و
+
+50
+00:04:23,010 --> 00:04:26,390
+العمود اللي فيه بيظل B و C بس أنا بخطأ يعني بس
+
+51
+00:04:26,390 --> 00:04:30,590
+موجود اللي هي B و C هذه B و هذه C و بيظل من
+
+52
+00:04:30,590 --> 00:04:36,190
+كمان لما نشطب هذا و هذا بيظل كمان E و F هذه الآن
+
+53
+00:04:36,190 --> 00:04:40,630
+هي اللي ناتج هو عبارة عن محدد المصفوفة اللي فوق كيف
+
+54
+00:04:40,630 --> 00:04:43,850
+بنوجد هنا زي ما وجدنا اللي فوق هذه عبارة عن EI
+
+55
+00:04:43,850 --> 00:04:48,550
+ناقص H في F اللي بيطلع منه نضربه في الـ A ونفس الشيء
+
+56
+00:04:48,550 --> 00:04:54,310
+قلبك يعني الآن نأخذ مثال عددي على اللي حكينا find
+
+57
+00:04:54,310 --> 00:04:57,490
+the determinant of هي عندنا المصفوفة هذه بدنا نوجد
+
+58
+00:04:57,490 --> 00:05:02,110
+إيش مالها بدنا نوجد محدد هذه المصفوفة ده نشوف كيف
+
+59
+00:05:02,110 --> 00:05:05,590
+نوجد حد محدد المصفوفة بدأ استخدم اللي هو العمود
+
+60
+00:05:05,590 --> 00:05:10,360
+الأول إذا 1 في المحدد
+
+61
+00:05:10,360 --> 00:05:15,420
+الثانوي تبعها ناقص 1 في المحدد الثانوي تبعها
+
+62
+00:05:15,420 --> 00:05:19,180
+2 في المحدد الثانوي اللي تبعها إيش مقصود
+
+63
+00:05:19,180 --> 00:05:23,220
+بالمحدد الثانوي اللي حكيناها قبل شوية كيف هو نجي
+
+64
+00:05:23,220 --> 00:05:27,720
+1 في اللي هو بنشطب بسطر و بنشطب بإيش العمود اللي
+
+65
+00:05:27,720 --> 00:05:31,660
+هو فيه المحدد اللي بيظل بنسميه المحدد الثانوي لمين
+
+66
+00:05:31,660 --> 00:05:36,840
+للواحد بيصير 1 في ناقص 1 4 في 5 بعد ما
+
+67
+00:05:36,840 --> 00:05:43,040
+شطبنا السطر هذا و العمود هذا ناقص الآن 1 هذا
+
+68
+00:05:43,040 --> 00:05:49,540
+الثاني 1 و بشطب سطره و بشطب عموده بيضل المحدد
+
+69
+00:05:49,540 --> 00:05:52,400
+الثانوي اللي هو 2 و 3 و 4 و 5 هي
+
+70
+00:05:52,400 --> 00:05:56,320
+2 و 3 و 4 و 5 زائد ضل اللي هو العنصر
+
+71
+00:05:56,320 --> 00:06:00,380
+الأخير 2 بشطب هذا السطر و هذا العمود بيصير عند
+
+72
+00:06:00,380 --> 00:06:05,460
+2 في اللي هو المحدد الثانوي اللي عندنا اللي هو
+
+73
+00:06:05,460 --> 00:06:09,160
+اللي أمامنا هذا 2 3 0 ناقص 1 بكمل
+
+74
+00:06:09,160 --> 00:06:13,220
+الآن عشان أوجد القيمة هذه الآن 1 مضروبة بفتح
+
+75
+00:06:13,220 --> 00:06:19,980
+قوس الآن جداش قيمة هذا 0 في 5 ناقص ناقص 4
+
+76
+00:06:19,980 --> 00:06:26,990
+في 1 يعني زائد 4 في 1 اللي هو 1 يعني بمعنى
+
+77
+00:06:26,990 --> 00:06:34,530
+آخر أها 0 خلصنا من هذا القطر الرئيسي و بنضرب
+
+78
+00:06:34,530 --> 00:06:37,090
+هذا القطر الثانوي بيطلع عندي ناقص 1 في 4
+
+79
+00:06:37,090 --> 00:06:40,370
+بناقص 4 و ناقص الأصلي بيصير ناقص ناقص 4
+
+80
+00:06:40,370 --> 00:06:43,910
+بنجي للثاني بنفس الأسلوب ناقص 1 هذا اللي من أصل
+
+81
+00:06:43,910 --> 00:06:48,330
+الموضوع و بنجي بنضرب الرئيسي 2 في 5 بيطلع
+
+82
+00:06:48,330 --> 00:06:52,740
+بـ 10 ناقص 4 في 3 اللي هي 12 خلصنا من
+
+83
+00:06:52,740 --> 00:06:55,900
+هذه 2 و بنفتح قوس المحدد 2 في ناقص 1
+
+84
+00:07:22,220 --> 00:07:27,160
+إذا هذا هو عبارة عن محدد هذه المصفوفة يعني الأمر
+
+85
+00:07:27,160 --> 00:07:29,860
+سهل إيجاد المحدد 
+
+86
+00:07:33,440 --> 00:07:37,780
+عندي لاحظ ولما احنا أوجدنا اللي هو محدد المصفوفة
+
+87
+00:07:37,780 --> 00:07:41,200
+من الدرجة الثانية ما لزمناش لغير هذا نوجده لحاله
+
+88
+00:07:41,200 --> 00:07:46,120
+لكن لما أوجدنا محدد لمصفوفة من 3 في 3 طلع
+
+89
+00:07:46,120 --> 00:07:51,820
+لزمنا نوجد محددات ثانوية 3 1 2 3 يعني
+
+90
+00:07:51,820 --> 00:07:55,770
+بدرجة المحدد ولو كان في عندنا matrix 4 في
+
+91
+00:07:55,770 --> 00:07:59,670
+4 بنعمل بنفس الأسلوب بس اللي بيطلع إن عندنا
+
+92
+00:07:59,670 --> 00:08:04,410
+المحددات الثانوية اللي هي 3 في 3 بنعمل محدد
+
+93
+00:08:04,410 --> 00:08:09,950
+زي ما عملنا مع مين مع اللي هو هذا السؤال الآن
+
+94
+00:08:09,950 --> 00:08:14,290
+وهكذا بصورة عامة الآن احنا يعني هنشتغل شغلنا بس
+
+95
+00:08:14,290 --> 00:08:16,710
+على المحددات اللي وهين اللي هي من الدرجة 3 في
+
+96
+00:08:16,710 --> 00:08:21,640
+3 أو 2 في 2 الآن بدنا نعرف حاجة اسمها
+
+97
+00:08:21,640 --> 00:08:25,320
+the inverse of a matrix اللي هو الهدف الثاني من
+
+98
+00:08:25,320 --> 00:08:27,760
+هذه المحاضرة الهدف الثاني من هذه المحاضرة الهدف
+
+99
+00:08:27,760 --> 00:08:28,060
+الثاني من هذه المحاضرة الهدف الثاني من هذه
+
+100
+00:08:28,060 --> 00:08:28,740
+المحاضرة الهدف الثاني من هذه المحاضرة الهدف الثاني
+
+101
+00:08:28,740 --> 00:08:29,620
+من هذه المحاضرة الهدف الثاني من هذه المحاضرة الهدف
+
+102
+00:08:29,620 --> 00:08:29,860
+الثاني من هذه المحاضرة الهدف الثاني من هذه
+
+103
+00:08:29,860 --> 00:08:30,440
+المحاضرة الهدف الثاني من هذه المحاضرة الهدف الثاني
+
+104
+00:08:30,440 --> 00:08:34,700
+من هذه المحاضرة الهدف الثاني من هذه المحاضرة الهدف
+
+105
+00:08:34,700 --> 00:08:38,500
+الثاني من هذه المحاضرة الهدف الثاني من هذه
+
+106
+00:08:38,500 --> 00:08:43,620
+المحاضرة الهدف الثاني من هذه المحاضرة الهدف الثاني
+
+107
+00:08:43,620 --> 00:08:48,420
+من 2×2، 3×3، 4×4، 5×5 الأخرى
+
+108
+00:08:51,710 --> 00:08:57,750
+non-singular يعني بمعنى آخر اللي هي اللي بنسميها
+
+109
+00:08:57,750 --> 00:09:02,850
+المصفوفة اللي بيكون محددها مش صفر لما يكون محددها
+
+110
+00:09:02,850 --> 00:09:07,030
+مش صفر بنضمن اللي هو بعد شوية هتشوف التعريف أنه في
+
+111
+00:09:07,030 --> 00:09:11,430
+لها معكوس ضربي إذا المصفوفة اللي بتكون non
+
+112
+00:09:11,430 --> 00:09:17,080
+-singular هي المصفوفة اللي محددها لا يساوي صفر الآن
+
+113
+00:09:17,080 --> 00:09:23,340
+لو وجدنا الـ matrix B ضربناها في A بيساوي I لأ طبعًا
+
+114
+00:09:23,340 --> 00:09:25,180
+هذه المصفوفة الـ A اللي أخدت اللي هي الـ non
+
+115
+00:09:25,180 --> 00:09:29,840
+singular اللي هي اللي بمعنى آخر محددها مش صفر لو
+
+116
+00:09:29,840 --> 00:09:33,840
+وجدنا مصفوفة ثانية اسمها B وضربناها فيها طلعت عند
+
+117
+00:09:33,840 --> 00:09:37,330
+الـ identity وضربناها من الجهة الثانية B في A
+
+118
+00:09:37,330 --> 00:09:41,750
+برضه طلعت عند الـ identity بنسمي المصفوفة B في هذه
+
+119
+00:09:41,750 --> 00:09:46,370
+الحالة هي عبارة عن الـ inverse للـ A بنرمز لها من
+
+120
+00:09:46,370 --> 00:09:52,750
+الرمز A inverse أو اللي هو المعكوس الضربي للمصفوفة
+
+121
+00:09:52,750 --> 00:09:57,890
+A إذا المعكوس الضربي للمصفوفة A هو الـ matrix اللي
+
+122
+00:09:57,890 --> 00:10:01,410
+لو ضربناه في المصفوفة الأصلية من اليمين أو اليسار
+
+123
+00:10:01,410 --> 00:10:06,630
+بيطلع للـ identity matrix يعني مثل لو أديت جربت هذه
+
+124
+00:10:06,630 --> 00:10:10,170
+المصفوفة زي ما اتعلمنا الضرب وضربنا هذه المصفوفة
+
+125
+00:10:10,170 --> 00:10:14,030
+فيها هنلاقي هذه المصفوفة في هذه المصفوفة إيش بتساوي
+
+126
+00:10:14,030 --> 00:10:18,850
+بساوي الـ identity بناء عليه بنقول هذه المصفوفة أو
+
+127
+00:10:18,850 --> 00:10:23,130
+حتى هذه يعني لو سمعنا .. بنقول هذه هي عبارة عن الـ
+
+128
+00:10:23,130 --> 00:10:27,250
+inverse لهذه يعني هذه المعكوس الضربي لهذه، و أيضا 
+
+129
+00:10:27,250 --> 00:10:31,190
+هذه هتكون هي المعكوس الضربي لمين؟ للثانية الآن
+
+130
+00:10:31,190 --> 00:10:34,790
+عملية الضرب احنا اتعلمناها فيش ده in a  ده هذا
+
+131
+00:10:34,790 --> 00:10:37,190
+معناته اللي هو المعكوس الضربي المعكوس الضربي
+
+132
+00:10:37,190 --> 00:10:40,350
+المصفوفة اللي أمامنا هذه هي المصفوفة اللي لو
+
+133
+00:10:40,350 --> 00:10:43,830
+ضربناها من اليمين ومن اليسار بتساوي الـ identity طب
+
+134
+00:10:43,830 --> 00:10:46,630
+كيف بدنا نوجدها هذه المصفوفة اللي هي المعكوس
+
+135
+00:10:46,630 --> 00:10:51,870
+الضربي الآن؟ في البداية خلينا نيجي لطريقة بداية
+
+136
+00:10:51,870 --> 00:10:57,010
+لإيجادها ونشوف جداش بتغلبنا، ومن ثم بنتعلم قاعدة
+
+137
+00:10:57,010 --> 00:11:02,190
+كيف نوجد اللي هي المعكوس الضربي للمصفوفة بكل سهولة
+
+138
+00:11:02,190 --> 00:11:11,190
+الآن لو أخذنا المصفوفة 8 -10 -3 -4 هذه المصفوفة من
+
+139
+00:11:11,190 --> 00:11:15,650
+الدرجة 2x2 لو بدنا نوجد الـ inverse لها أو نوجد
+
+140
+00:11:15,650 --> 00:11:19,730
+المعكوس الضربي لها، نفترض أن المعكوس الضربي لها
+
+141
+00:11:19,730 --> 00:11:25,390
+عبارة عن a,b,c,d ماشي الحال، وأقول لأ عشان تكون هذه
+
+142
+00:11:25,390 --> 00:11:29,870
+معكوس ضربي لازم أضرب هذه في هذه يطلع من عندي اللي هو
+
+143
+00:11:29,870 --> 00:11:35,190
+الـ identity matrix 1 1 0 0 صار عندي هاي قيمتين مضربات
+
+144
+00:11:35,190 --> 00:11:39,370
+في بعض لازم يساون هدول عشان تطلع هذه عبارة عن
+
+145
+00:11:39,370 --> 00:11:47,060
+المعكوس الضربي لها ماشي الحال الآن الآن نضرب هذه في
+
+146
+00:11:47,060 --> 00:11:50,800
+هذه المصفوفة، نضرب ضرب عادي اضرب ثمانية في 
+
+147
+00:11:50,800 --> 00:11:55,820
+a في c بتطلع عندي ثمانية a ناقص عشرة في c نضرب 
+
+148
+00:11:55,820 --> 00:12:02,450
+هذه المصفوفة وبنضرب هذا اللي هو السطر في هذا العمود
+
+149
+00:12:02,450 --> 00:12:05,830
+بتطلع عند هذه قيمة زي ما اتعلمنا قبلين، وبنضرب هذا
+
+150
+00:12:05,830 --> 00:12:09,010
+السطر في هذا العمود بتطلع عند هذه القيمة، وبنضرب
+
+151
+00:12:09,010 --> 00:12:12,870
+هذا السطر في هذا العمود بتطلع عند هذه القيمة طبعا
+
+152
+00:12:12,870 --> 00:12:15,710
+كيف؟ خلنا أضرب الأخيرة هذا عشان تكون في الصورة كيف
+
+153
+00:12:15,710 --> 00:12:20,230
+تضرب ناقص ثلاثة في b في c ناقص ثلاثة b زائد أربعة
+
+154
+00:12:20,230 --> 00:12:23,730
+في d في c زائد أربعة d هذا كله لازم يساوي واحد، و
+
+155
+00:12:23,730 --> 00:12:27,900
+صفر و صفر و واحد صار عندي هذا المقدار اللي هو اللي
+
+156
+00:12:27,900 --> 00:12:32,240
+هو المصفوفة هذه بتساوي هذا المصفوفة عشان يطلع إن
+
+157
+00:12:32,240 --> 00:12:37,760
+هذا هو المعكوس الضربي لهذا طيب، بادي كل مساواة
+
+158
+00:12:37,760 --> 00:12:42,140
+مصفوفتين معناته إن هذا المقدار بساوي واحد، وهذا
+
+159
+00:12:42,140 --> 00:12:45,700
+المقدار بساوي صفر، وهذا المقدار بساوي صفر، وهذا
+
+160
+00:12:45,700 --> 00:12:49,880
+المقدار بساوي واحد هي عندي هذول هذه اللي ناتجة من
+
+161
+00:12:49,880 --> 00:12:54,560
+هذا، وهذه ناتجة من هذا، وهذه المعادلة ناتجة من هذا
+
+162
+00:12:55,560 --> 00:13:00,620
+هذه المعادلة هي ناقص ثلاثة b زائد أربعة d بساوي واحد
+
+163
+00:13:00,620 --> 00:13:04,520
+ناتجة من اللي فوق لأن صار عندي أنا معادلتي أربع
+
+164
+00:13:04,520 --> 00:13:10,020
+معادلات في نفس الوقت آنية الآن خلينا نحل المعادلة
+
+165
+00:13:10,020 --> 00:13:14,500
+هذه مع المعادلة هذه، حلها عادي بالمعادلات الآنيّة
+
+166
+00:13:14,500 --> 00:13:17,440
+اللي احنا بنعرفها اللي أخذناها في ثاني إعدادي أو
+
+167
+00:13:17,440 --> 00:13:23,610
+ثالث إعدادي بنحلها بنوجد قيمة الـ A و الـ C لأن
+
+168
+00:13:23,610 --> 00:13:28,510
+معادلتين فيه مجهولين فتطلع A، وتطلع قيمة C طلعت
+
+169
+00:13:28,510 --> 00:13:33,430
+عندي A اثنين، وتطلعت عندي C بساوي واحد ونص، الأهم
+
+170
+00:13:33,430 --> 00:13:38,370
+الحل هذول نفس الشيء هيطلع عندي معادلتين أنيتين مع
+
+171
+00:13:38,370 --> 00:13:43,260
+بعض هيطلع عندي B بساوي خمسة، و D بساوي أربعة هذه
+
+172
+00:13:43,260 --> 00:13:47,600
+اللي هي شايفين احنا جداش اتغلبنا في الإيجاد، واحنا
+
+173
+00:13:47,600 --> 00:13:50,660
+قاعدين اللي هو يمكن بعضكم ناسي كيف المعادلات
+
+174
+00:13:50,660 --> 00:13:54,480
+الآنية وكيف حلول المعادلات الآنية، وبدنا نتعلمها
+
+175
+00:13:54,480 --> 00:13:59,060
+عشان نوجد من الـ a inverse الآن احنا مش هنظل نشتغل
+
+176
+00:13:59,060 --> 00:14:02,980
+هيك يعني هذا بس عشان إن أنت تشوف جداش اللي هو هذا
+
+177
+00:14:02,980 --> 00:14:07,900
+هيغلب لو أنا أجيت وجدت بطرق العادية هذه عشان أوجد
+
+178
+00:14:07,900 --> 00:14:12,130
+الـ inverse الآن لو كانت بصفوفة ثلاثة في ثلاثة تقول
+
+179
+00:14:12,130 --> 00:14:16,810
+هيصير عندنا بدل ما هنا في عندي اللي هو عبارة عن
+
+180
+00:14:16,810 --> 00:14:20,870
+أربع معادلات هيطلع عندي عبارة عن تسعة معادلات، ايش
+
+181
+00:14:20,870 --> 00:14:24,330
+التسعة معادلات في تسعة مجهول ومش عارف ايش طبعا
+
+182
+00:14:24,330 --> 00:14:28,950
+هتغلبوا فكورة غلبة كبيرة، عشان هيك بدنا نريحكم وهي
+
+183
+00:14:28,950 --> 00:14:34,050
+في عندنا الطريقة finding the inverse of two by two
+
+184
+00:14:34,050 --> 00:14:39,450
+matrices نشوف كيف بنوجد اللي هو الـ inverse لـ two
+
+185
+00:14:39,450 --> 00:14:46,350
+by two matrices هذا هو الجزء الأول من المحاضرة
+
+186
+00:14:46,350 --> 00:14:50,210
+والجزء
+
+187
+00:14:50,210 --> 00:14:55,690
+الثاني من المحاضرة هي finding inverse of 2x2
+
+188
+00:14:55,690 --> 00:15:00,270
+matrices أو إيجاد المعاكوس الضربي للمصفوفة، وخلّينا
+
+189
+00:15:00,270 --> 00:15:04,490
+نوقف عندنا ونعمل المحاضرة على جزءين، و الله يعطيكوا
+
+190
+00:15:04,490 --> 00:15:08,390
+العافية نكمل الآن الجزء الثاني من المحاضرة
+
+191
+00:15:15,680 --> 00:15:19,100
+المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة
+
+192
+00:15:19,100 --> 00:15:22,240
+المعكوس
+
+193
+00:15:22,240 --> 00:15:27,300
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+194
+00:15:27,300 --> 00:15:28,780
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+195
+00:15:28,780 --> 00:15:28,880
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+196
+00:15:28,880 --> 00:15:28,980
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+197
+00:15:28,980 --> 00:15:29,180
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+198
+00:15:29,180 --> 00:15:32,220
+الضربي للمصفوفة المعكوس الضربي للمصفوفة هذه
+
+199
+00:15:32,220 --> 00:15:36,380
+المصفوفة بدنا نشوف كيف نوجد اللي هو المعكوس الضربي
+
+200
+00:15:36,380 --> 00:15:40,100
+للمصفوفة قبل ما نوجد المعكوس الضربي للمصفوفة لازم
+
+201
+00:15:40,100 --> 00:15:44,000
+نعرف الشيء لأن المصفوفة عشان يكون لها معكوس ضربي
+
+202
+00:15:44,000 --> 00:15:49,160
+لازم يكون الـ determinant لها ما بيساوي صفر يعني
+
+203
+00:15:49,160 --> 00:15:54,660
+المصفوفة اللي محددها صفر ليس لها معكوس ضربي إذن
+
+204
+00:15:54,660 --> 00:16:00,410
+الآن احنا أول شغلة بنعملها عشان نجد اللي هو المعكوس
+
+205
+00:16:00,410 --> 00:16:05,250
+الضربي للمصفوفة اللي عندنا اللي أمامنا هذه إنه بنشوف
+
+206
+00:16:05,250 --> 00:16:11,150
+اللي هو الـ determinant لها إذا AD ناقص BC مش صفر
+
+207
+00:16:11,150 --> 00:16:15,630
+معناته إحنا جاهزين لإن نجد اللي هو المعكوس الضربي
+
+208
+00:16:15,630 --> 00:16:19,780
+للمصفوفة شوفوا خلّينا نشوف كيف اللي هو نوجدها
+
+209
+00:16:19,780 --> 00:16:23,100
+العملية سهلة جدا في حالة المصفوفة اثنين باثنين
+
+210
+00:16:23,100 --> 00:16:27,440
+بنيجي لعناصر القطر الثانوي بنبدلها مع بعض يعني
+
+211
+00:16:27,440 --> 00:16:32,140
+بيصير الـ D هنا والـ A هنا، الأساسي الرئيسي العناصر
+
+212
+00:16:32,140 --> 00:16:37,020
+القطر الثانوي بس بنغير إشارتها هذه بيصير ناقصي
+
+213
+00:16:37,020 --> 00:16:42,780
+ناقص بي اللي بيطلع هذا بنضربه في واحد على المحدد
+
+214
+00:16:43,270 --> 00:16:49,130
+النتيجة اللي طلع بكون هو مين؟ هو عبارة عن المعكوس
+
+215
+00:16:49,130 --> 00:16:55,110
+الضربي للمصفوفة a,b,c,d واضح إن الأمر سهل جدا عن
+
+216
+00:16:55,110 --> 00:16:58,550
+المثال اللي حكيناه قبل بشوية اللي استخدمنا الطرق
+
+217
+00:16:58,550 --> 00:17:02,870
+الأولية فيه وكانت اللي هي بتستلزم نعرف معادلة
+
+218
+00:17:02,870 --> 00:17:06,210
+آنية ومعادلة آنية واحنا طبعا فيه ممكن نكون
+
+219
+00:17:06,210 --> 00:17:12,310
+جزء ناسي الأمر نشوف الآن مثال عددي لاللي بنحكي عن
+
+220
+00:17:12,310 --> 00:17:18,190
+الإيجاد عن طريق المثال العددي إذا كانت الـ A هي
+
+221
+00:17:18,190 --> 00:17:23,410
+المصفوفة اللي أمامنا هذه المعكوس الضربي لها هو
+
+222
+00:17:23,410 --> 00:17:28,410
+عبارة عن الـ DA بعد ما بدلنا عناصر القطر الثانوي
+
+223
+00:17:28,410 --> 00:17:35,970
+مع بعض أسف في الرئيسي وغيرنا عناصر قطر الثانوي بس
+
+224
+00:17:35,970 --> 00:17:39,630
+إشارتها وضربناها في واحد على قيمة الـ determinant
+
+225
+00:17:39,630 --> 00:17:44,890
+طلع عنده اللي هو الـ A inverse أو المعكوس الضربي
+
+226
+00:17:44,890 --> 00:17:49,470
+للمصفوفة نشوف مثال عددي الآن نطلع لـ Find the
+
+227
+00:17:49,470 --> 00:17:53,810
+inverse of A هي الـ A عندي الآن هي المصفوفة دي بس
+
+228
+00:17:53,810 --> 00:17:57,830
+ايش بده نوجد الآن يا شباب ويا بنات الآن بس بده
+
+229
+00:17:57,830 --> 00:18:01,930
+نجي نضرب نوجد محدد المصفوفة ايش المحدد؟ اثنين في
+
+230
+00:18:01,930 --> 00:18:07,130
+ناقص عشرة هي ناقص اللي هو ناقص أربعة في أربعة هي
+
+231
+00:18:07,130 --> 00:18:13,440
+ناقص عشرين أو زائد ستة عشر بيظل ايه؟ شماله ناقص
+
+232
+00:18:13,440 --> 00:18:17,700
+أربعة إذا المحدد بيساوي ناقص أربعة إذا مدام المحدد
+
+233
+00:18:17,700 --> 00:18:22,020
+مش صفر إذا المعاكوس الضربي موجود على طول المعاكوس
+
+234
+00:18:22,020 --> 00:18:25,560
+الضربي inverse ايه بيساوي واحد على قيمة الـ
+
+235
+00:18:25,560 --> 00:18:29,900
+determinant هي ناقص أربعة وبنيجي لمصفوفتنا هذه بس
+
+236
+00:18:29,900 --> 00:18:33,000
+بنبدل الناقص عشرة مع الاثنين هنا بدلناها صارت
+
+237
+00:18:33,000 --> 00:18:37,180
+ناقص عشرة وهي اثنين، وبنبدل إشارة ناقص أربعة بيصير
+
+238
+00:18:37,180 --> 00:18:41,330
+أربعة بنبدل إشارة الأربعة بيصير ناقص أربعة هذا الآن
+
+239
+00:18:41,330 --> 00:18:44,650
+هو عبارة عن مين؟ عن اللي هو الـ A inverse أو
+
+240
+00:18:44,650 --> 00:18:50,030
+المعكوس الضربي للمصفوفة A يساوي بنضرب هذه طبعا هذا
+
+241
+00:18:50,030 --> 00:18:54,030
+الضرب عملية الضرب تدخل على كل عنصر من عناصر الـ
+
+242
+00:18:54,030 --> 00:18:58,150
+matrix فبيصير ناقص عشرة في ناقص ربع عبارة عن خمسة
+
+243
+00:18:58,150 --> 00:19:02,910
+على اثنين ناقص أربعة في ناقص ربع عبارة عن واحد اللي
+
+244
+00:19:02,910 --> 00:19:06,610
+هو ناقص ربع في أربعة بيطلع ناقص واحد ناقص ربع في
+
+245
+00:19:06,610 --> 00:19:10,950
+اثنين بيطلع ناقص نص إذن هذه هي عبارة عن المعكوس
+
+246
+00:19:10,950 --> 00:19:14,550
+الضربي لو أنت في الدار لأ جيت وقولت والله بدي
+
+247
+00:19:14,550 --> 00:19:18,990
+أشوف كلامنا صح ولا لأ اضرب لهدي في هدي هتلاقي بيطلع
+
+248
+00:19:18,990 --> 00:19:23,090
+عبارة عن الـ identity matrix إذن عملية الإيجاد اللي
+
+249
+00:19:23,090 --> 00:19:26,250
+هو المعكوس الضربي سهلة لأن المصفوفة اثنين في اثنين
+
+250
+00:19:26,700 --> 00:19:33,640
+الآن معكم الآن الجزء من الـ homework لهذه المحاضرة
+
+251
+00:19:33,640 --> 00:19:37,660
+بدكم تحلوا يا جماعة هذا السؤال هذا في ال homework
+
+252
+00:19:37,660 --> 00:19:42,020
+find the inverse of a و b و c حيث a هيها و b هيها
+
+253
+00:19:42,020 --> 00:19:46,420
+و c هي ده بنتظر منكم اللي هو حل هذا في ال homework
+
+254
+00:19:46,420 --> 00:19:52,550
+طبعا جاي لاحقا كمان شغلة كيف بدنا نجد ما هو find
+
+255
+00:19:52,550 --> 00:19:58,210
+the inverse of a 3x3 matrix كيف بدنا نجد ما هو
+
+256
+00:19:58,210 --> 00:20:03,650
+المعكوس الضربي لمصفوفة من الدرجة تلاتة في تلاتة
+
+257
+00:20:03,650 --> 00:20:10,260
+شوفوا علي خلينا نطلع هنا أربع خطوات أربع خطوات اللي
+
+258
+00:20:10,260 --> 00:20:14,540
+هو احنا باختصار خلّينا نقولها أول شيء بتوجد حاجة
+
+259
+00:20:14,540 --> 00:20:19,180
+اسمها اللي هي ال matrix of minor determinants
+
+260
+00:20:19,180 --> 00:20:24,000
+حاجات هنقول ايش الان بنغير اشارات اللي هي كل
+
+261
+00:20:24,000 --> 00:20:30,100
+العناصر ما عدا عناصر القطر الرئيسي وعناصر قطر مين
+
+262
+00:20:30,100 --> 00:20:35,350
+الثانوي الان اللي بعدها اللي بيطلع عندنا اللي
+
+263
+00:20:35,350 --> 00:20:39,390
+بنعمله بناخده ل Transpose اللي هو مدور المصفوفة و
+
+264
+00:20:39,390 --> 00:20:42,650
+بعدين اللي بيطلع بنضربه في واحد على ال determinant
+
+265
+00:20:42,650 --> 00:20:46,890
+بيطلع عندنا اللي هو المعكوس الضربي نشوف هذا يمكن
+
+266
+00:20:46,890 --> 00:20:50,610
+الكلام النظري شوية مش واضح خلينا نشوف كيف عمليا
+
+267
+00:20:50,930 --> 00:20:55,050
+نوجد الكوبيا قبل ما نحكي عن ما هو نوجد ال inverse
+
+268
+00:20:55,050 --> 00:20:59,070
+بس عساس ان هو توضيح ايش هو ال matrix of minor
+
+269
+00:20:59,070 --> 00:21:02,430
+determinants الان بدنا نعرف شو معناته ال minor
+
+270
+00:21:02,430 --> 00:21:05,630
+determinants اللي هي المحددات الثانوية حكيتها قبل
+
+271
+00:21:05,630 --> 00:21:10,540
+بشوية في الجزء الأول من المحاضرة الان يعني بدي اشوف
+
+272
+00:21:10,540 --> 00:21:13,700
+ايش ال minor determinant للخمسة اللي بالنسبة
+
+273
+00:21:13,700 --> 00:21:18,380
+للعنصر خمسة هذا مفترض انه محدد أو matrix بدنا ال
+
+274
+00:21:18,380 --> 00:21:21,400
+minor determinant للخمسة ال minor determinant أو
+
+275
+00:21:21,400 --> 00:21:24,620
+اللي هو المحدد الثانوي باختصار يا جماعة بتيجي
+
+276
+00:21:24,620 --> 00:21:28,600
+بالشط بالصف اللي هي فيه و العمود اللي هي فيه بطلع
+
+277
+00:21:28,600 --> 00:21:32,200
+عند المحدد المحدد اللي بطلع هذا هو اللي بنسميه ال
+
+278
+00:21:32,200 --> 00:21:36,350
+minor determinant لمن؟ للخمسة الان واحد يقول اللي
+
+279
+00:21:36,350 --> 00:21:39,550
+بدي ال minor determinant لمناقس ثلاثة بقول له حاضر
+
+280
+00:21:39,550 --> 00:21:44,870
+شط بالسطر و شط بالعمود بطلع عندي اللي هو اللي ضال
+
+281
+00:21:44,870 --> 00:21:49,710
+هذا عبارة عن محدد المحدد هذا بكون هو ال minor
+
+282
+00:21:49,710 --> 00:21:53,510
+determinant لمناقس ثلاثة واحد قال لأ بدي للتمانية
+
+283
+00:21:53,510 --> 00:21:58,530
+بقول له حاضر هي للتمانية شط بعموده و شط بصفه اللي
+
+284
+00:21:58,530 --> 00:22:03,030
+بضل هو عبارة عن ال minor determinant لمن للتمانية
+
+285
+00:22:03,370 --> 00:22:09,450
+أو المحدد الثانوي للعنصر من تمانية لو كان ليه بدي
+
+286
+00:22:09,450 --> 00:22:12,730
+أوجدت قيمته بقول اه سهل ايجادها واحد في تلاتة
+
+287
+00:22:12,730 --> 00:22:17,690
+بتلاتة تلاتة ناقص ناقص أربعة يعني واحد زائد أربعة
+
+288
+00:22:17,690 --> 00:22:21,670
+يعني خمسة آسف تلاتة زائد أربعة يعني سبعة اللي هو
+
+289
+00:22:21,670 --> 00:22:27,010
+تلاتة زائد أربعة يعني سبعة هذا قيمة من ال minor
+
+290
+00:22:27,010 --> 00:22:30,980
+determinant of تمانية يعني المحدد الثانوي لمين؟
+
+291
+00:22:30,980 --> 00:22:36,140
+لتمانية هذا الكلام قدمناه عشان نستخدمه مباعد بشوية
+
+292
+00:22:36,140 --> 00:22:42,600
+في اللي هو إيجاد ال inverse للمصفوفة شوفوا ..
+
+293
+00:22:42,600 --> 00:22:45,420
+شوفوا صلى الله عليه وسلم بعتقد الأمور إن شاء الله
+
+294
+00:22:45,420 --> 00:22:49,440
+هتكون واضحة جدا الان ال determinant أم ال matrix
+
+295
+00:22:49,440 --> 00:22:54,000
+أم المصفوفة أم المطلوب إيجاد ال inverse لهذه
+
+296
+00:22:54,000 --> 00:23:00,880
+المصفوفة عندنا أربع خطوات عشان نوجد اللي هو ال .. ال
+
+297
+00:23:00,880 --> 00:23:04,880
+.. ال .. ال .. ال inverse لهذه المصفوفة أربع خطوات
+
+298
+00:23:04,880 --> 00:23:07,900
+الخطوة الأولى أكيد كلكم حيقول بدنا نجد ال
+
+299
+00:23:07,900 --> 00:23:11,600
+determinant يعني بدنا نتأكد أو شيء make sure انه
+
+300
+00:23:11,600 --> 00:23:14,320
+non-singular ايش يعني non-singular يعني
+
+301
+00:23:14,320 --> 00:23:17,300
+determinant له مش صفر لو حسبتوا ال determinant له
+
+302
+00:23:17,300 --> 00:23:20,060
+زي ما أخدناه في الطريقة الأولى لإيش نضيع الوجد في
+
+303
+00:23:20,060 --> 00:23:23,800
+حساباتها لإن حسبناها قبل هيك بتحسبوها هتلاقوا ال
+
+304
+00:23:23,800 --> 00:23:28,520
+determinant لهذه ال M ايش طالع عندنا -156 يعني مش
+
+305
+00:23:28,520 --> 00:23:32,800
+صفر مزا مش مش صفر إذا الان تأكدنا إنه non
+
+306
+00:23:32,800 --> 00:23:37,120
+singular هذه طبعا في الآخر اللي هي بستخدمها اللي
+
+307
+00:23:37,120 --> 00:23:42,300
+هي قيمة ال determinant نجي للخطوات اللي بدنا نصل
+
+308
+00:23:42,300 --> 00:23:46,640
+فيها لل inverse الخطوة الأولى اللي هو find the
+
+309
+00:23:46,640 --> 00:23:49,840
+matrix of minor determinants يعني بدأ أوجد ال
+
+310
+00:23:49,840 --> 00:23:53,800
+matrix اللي بجيبه من مين من minor determinants
+
+311
+00:23:54,610 --> 00:23:58,350
+بتنشوف بنوجد اول شيء للتلاتة شيء ال minor
+
+312
+00:23:58,350 --> 00:24:03,670
+determinant للتلاتة الان هاي التلاتة شطبنا السطر
+
+313
+00:24:03,670 --> 00:24:08,590
+شطبنا العمود ضل عندي هذا هذا قداش قيمته ناقص
+
+314
+00:24:08,590 --> 00:24:12,850
+اتنين في ناقص اتنين يعني اربعة ناقص خمسة وعشرين
+
+315
+00:24:12,850 --> 00:24:16,570
+اربعة ناقص خمسة وعشرين قداش بطلع ناقص واحد وعشرين
+
+316
+00:24:16,570 --> 00:24:20,450
+إذا بكتب الناقص واحد وعشرين هذا خلصنا من العنصر
+
+317
+00:24:20,450 --> 00:24:24,690
+الأول نجي للعنصر الثاني اللي هو بده أوجد ال minor
+
+318
+00:24:24,690 --> 00:24:29,770
+determinant لمن يا شباب للسبعة خلصنا من التلاتة
+
+319
+00:24:29,770 --> 00:24:33,850
+نجي للسبعة طب السبعة كيف نفس الشيء بنشطب السطر و
+
+320
+00:24:33,850 --> 00:24:36,930
+بنشطب العمود و بنحسب ال minor determinant اللي هو
+
+321
+00:24:36,930 --> 00:24:40,990
+واحد في ناقص اتنين بيطلع ناقص اتنين ناقص اللي
+
+322
+00:24:40,990 --> 00:24:47,070
+بيصير زائد خمستاشر اتنين نقص اتنين زائد خمستاعش
+
+323
+00:24:47,070 --> 00:24:53,050
+بيطلع قداش عبارة عن تلات عشرة خلصنا من السبعة بنوجد
+
+324
+00:24:53,050 --> 00:24:56,870
+ال minor determinant لمن الان للتنين ثاني تشوف ال
+
+325
+00:24:56,870 --> 00:24:58,510
+minor determinant للتنين
+
+326
+00:25:02,080 --> 00:25:08,660
+وشط بالعمود طلع الـ Minor Determinant أي المحدد 
+
+327
+00:25:08,660 --> 00:25:15,680
+الثانوي للعنصر 2 المحدد الثانوي للعنصر 2 خمسة زائد
+
+328
+00:25:15,680 --> 00:25:20,020
+اللي هي بصير ناقص ستة خمسة ناقص ستة بطلع ناقص واحد
+
+329
+00:25:20,020 --> 00:25:26,780
+نتأكد الكلام صحيح خلصنا من السطر الأول كله و نبدأ
+
+330
+00:25:26,780 --> 00:25:31,540
+بالواحد وهي نفس القصة وهي السطر وهي العمود وهي
+
+331
+00:25:31,540 --> 00:25:35,760
+السطر وهي minor determinant بنوجد قيمته سبعة في
+
+332
+00:25:35,760 --> 00:25:40,680
+ناقص اتنين ناقص اربعة عشر ناقص عشرة يعني عبارة عن
+
+333
+00:25:40,680 --> 00:25:45,680
+ناقص اربع وعشرين خلصنا اللي هو الواحد بنجي لمين
+
+334
+00:25:45,680 --> 00:25:49,600
+الان ناقص اتنين خليني نشوف يا شباب ناقص اتنين بنفس
+
+335
+00:25:49,600 --> 00:25:53,180
+الاسلوب هاي ال minor determinant اللي هو تلاتة في
+
+336
+00:25:53,180 --> 00:25:57,300
+ناقص اتنين ناقص ستة ناقص ستة وزاية ستة بطلع كده
+
+337
+00:25:57,300 --> 00:26:02,440
+صفر طيب خلصنا اللي هو اللي ناقص اتنين بنطلع لمين
+
+338
+00:26:02,440 --> 00:26:08,550
+الان للخمسة دلال الخمسة المحددة
+
+339
+00:26:08,550 --> 00:26:13,900
+الثانوية للخمسة بنشطب سطر الخمسة و عمود الخمسة بطلع
+
+340
+00:26:13,900 --> 00:26:18,640
+عند المحدد بحسب قيمة المحدد خمسة عشر زائد واحد و
+
+341
+00:26:18,640 --> 00:26:23,500
+عشرين بطلع اللي هو عبارة عن ستة و تلاتين خلصنا هذه
+
+342
+00:26:23,500 --> 00:26:27,420
+بنيجي للسطر الثالث اللي هو عبارة عن مين ناقص تلاتة
+
+343
+00:26:27,420 --> 00:26:31,500
+بنفس الاسلوب هي محددها محددها من وجود قيمته بتطلع
+
+344
+00:26:31,500 --> 00:26:35,880
+تسعة و تلاتين خلصنا من ناقص تلاتة بنيجي للخمسة
+
+345
+00:26:35,880 --> 00:26:40,280
+اللي هو خمسة محددها قداش بطلع بنحسبه بطلع تلت عشرة
+
+346
+00:26:40,810 --> 00:26:43,910
+بنفس الاسلوب اللي قبلت الان خلصنا من الخنصة ده
+
+347
+00:26:43,910 --> 00:26:48,110
+اللي عندي نقص اتنين هي محددها بنحسب محددها هدف
+
+348
+00:26:48,110 --> 00:26:50,050
+هدف نقص هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+349
+00:26:50,050 --> 00:26:54,290
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+350
+00:26:54,290 --> 00:26:55,550
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+351
+00:26:55,550 --> 00:26:55,570
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+352
+00:26:55,570 --> 00:27:05,830
+هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+353
+00:27:05,830 --> 00:27:11,840
+هلعناصر المصفوفة يعني هذا عبارة عن محدد ثانوي
+
+354
+00:27:11,840 --> 00:27:16,780
+للتلاتة هذا عبارة عن محدد ثانوي للسبعة هذا المحدد
+
+355
+00:27:16,780 --> 00:27:20,120
+الثانوي للتانين زي ما حكينا و البجيات نفس الشيء
+
+356
+00:27:20,120 --> 00:27:25,620
+إذا هذه أول خطوة نجي للخطوة الثانية الآن الخطوة
+
+357
+00:27:25,620 --> 00:27:31,600
+الثانية بنيجي بنحدد عناصر القطر الرئيسي و عناصر
+
+358
+00:27:31,600 --> 00:27:36,660
+القطر الثانوي واللي بضلنا بنقلب إشارتين بس اللي هو
+
+359
+00:27:36,660 --> 00:27:40,380
+alternate the sign of the minor which don't lie on
+
+360
+00:27:40,380 --> 00:27:44,440
+the diagonals يعني اللي هي الآن هي عندك اللي هي
+
+361
+00:27:44,440 --> 00:27:47,460
+اللي مش على القطر الرئيسي أو القطر الثانوي بدنا
+
+362
+00:27:47,460 --> 00:27:51,560
+نغير إشارتين بيصير هذا 24 وهذا 13 وهذا ناقص 13 وهذا
+
+363
+00:27:51,560 --> 00:27:58,080
+ايش سالب 36 خلينا نشوفها فعلا هيها سالب 13 سالب 36
+
+364
+00:27:58,080 --> 00:28:04,640
+سالب 13 24 الخطوة الثانية نجي للخطوة الثالثة الخطوة
+
+365
+00:28:04,640 --> 00:28:09,440
+الثالثة هذا الان اللي بطلع اللي طلع في الخطوة
+
+366
+00:28:09,440 --> 00:28:13,120
+الثانية بدنا نجيبله transpose يعني بدي أجيبله ايش
+
+367
+00:28:13,120 --> 00:28:18,540
+مدور هذه المصفوفة مدورها اللي هو السطر بيصير عمود
+
+368
+00:28:18,540 --> 00:28:21,700
+السطر بيصير عمود السطر بيصير عمود بيكون أوجدنا مين
+
+369
+00:28:21,700 --> 00:28:27,580
+ل Transpose هاي عندي السطر الأول صار عمود السطر
+
+370
+00:28:27,580 --> 00:28:32,350
+الثاني صار عمود السطر الثالث صار العمود الثالث هذا
+
+371
+00:28:32,350 --> 00:28:36,850
+اللي هو ايش بنسميه ل Transpose بالمناسبة هذا اللي
+
+372
+00:28:36,850 --> 00:28:40,730
+طلع في الخطوة الثالثة اللي هو ل Transpose هذا بعد
+
+373
+00:28:40,730 --> 00:28:47,690
+شوية هنسميه هي ال Adjoint ل Matrix M يعني لو طلب
+
+374
+00:28:47,690 --> 00:28:52,550
+عندي ال Adjoint ل Matrix M بيجيب بعمل تلت خطوات
+
+375
+00:28:52,550 --> 00:28:57,150
+نجد ال Matrix اللي هو تبع ال minor determinants
+
+376
+00:28:57,400 --> 00:29:01,980
+بنغير إشارات اللي هي العناصر كلها معدة عناصر اللي
+
+377
+00:29:01,980 --> 00:29:05,640
+هو القطر الثانوي والقطر الرئيسي وبعدين بناخدها لل
+
+378
+00:29:05,640 --> 00:29:10,240
+Transverse هذا اللي بنسمي الـ Adjunct الـ Adjoint 
+
+379
+00:29:10,240 --> 00:29:14,600
+للمصفوفة الان بدي انا الـ inverse الـ inverse في
+
+380
+00:29:14,600 --> 00:29:18,960
+الشتّال منها ايش طالت الخطوة الأخيرة Divide By
+
+381
+00:29:18,960 --> 00:29:23,600
+Determinant بنجسم هذا بإيش بالـ determinant للـ M
+
+382
+00:29:23,600 --> 00:29:27,500
+يعني الآن بنضرب هذا المقدار في واحد على الـ minus
+
+383
+00:29:27,500 --> 00:29:32,160
+ستة وخمسين بيطلع مين هو الـ M inverse بساوي ناقص
+
+384
+00:29:32,160 --> 00:29:36,540
+واحد على مئة وستة وخمسين في هذا اللي هو المصفوفة
+
+385
+00:29:36,540 --> 00:29:41,740
+اللي بيطلع عندي هذا الـ M inverse هو الان عبارة عن
+
+386
+00:29:41,740 --> 00:29:46,740
+اللي هي الـ inverse للمصفوفة اللي عندنا الان بتصور
+
+387
+00:29:46,740 --> 00:29:52,640
+الأمور واضحة الخطوة الأولى الخطوة الثانية الخطوة
+
+388
+00:29:52,640 --> 00:29:56,860
+الثالثة الخطوة الرابعة وكون حصلنا عالميا على الـ M
+
+389
+00:29:56,860 --> 00:30:02,040
+inverse أو المعكوس الضربي للمصفوفة M نجي ناخد مثال
+
+390
+00:30:02,040 --> 00:30:07,300
+ثاني هي عندي المثال ايه هو هي عندي بنوجد f inverse له
+
+391
+00:30:07,300 --> 00:30:12,240
+example واحد find a inverse هي الـ matrix A وهي أول
+
+392
+00:30:12,240 --> 00:30:15,680
+خطوة بنعملها ايش بنوجد اللي هو الـ determinant له
+
+393
+00:30:15,680 --> 00:30:19,420
+اوجدنا الـ determinant زي ما بنوجد دائما بيطلع عندي
+
+394
+00:30:19,420 --> 00:30:23,560
+determinant عبارة عن 32 يعني مش صفر يعني فعلا فيش
+
+395
+00:30:23,560 --> 00:30:28,400
+عندنا ايش اللي هو في عندنا اللي هو inverse
+
+396
+00:30:28,400 --> 00:30:33,790
+للمصفوفة طيب الخطوة الأولى اللي هي بعد ما وجدنا هذه
+
+397
+00:30:33,790 --> 00:30:37,430
+طبعا خطوة رئيسية هناخدها لاحقا الان الخطوات
+
+398
+00:30:37,430 --> 00:30:40,750
+الأربعة الخطوة الأولى اللي هو الـ matrix of minors
+
+399
+00:30:40,750 --> 00:30:45,410
+نجد الـ matrix of minors للواحد بنشطب اللي هو السطر
+
+400
+00:30:45,410 --> 00:30:47,690
+و العمود بيطلع الـ determinant هذا هي الـ determinant
+
+401
+00:30:47,690 --> 00:30:52,210
+للصفر هي الـ determinant للتلاتة تدرب لحالك هي ال
+
+402
+00:30:52,210 --> 00:30:54,910
+determinant أولاد سبعة أو أولاد تلاتة هاي كلها
+
+403
+00:30:54,910 --> 00:30:59,370
+هدول مين هنا اللي هي الـ matrix of minors أو
+
+404
+00:30:59,370 --> 00:31:03,130
+determinant الـ matrix of minor determinants
+
+405
+00:31:03,130 --> 00:31:10,950
+المفهوم اللي هو مصفوفة مصفوفة اللي هي المحددات
+
+406
+00:31:10,950 --> 00:31:17,090
+الثانوية هي قيمة هذا هي وقيمة هذا هي وقيمة هذا هي
+
+407
+00:31:17,090 --> 00:31:17,730
+وقيمة هذا هي وقيمة هذا هي وقيمة هذا هي و قيمة
+
+408
+00:31:17,730 --> 00:31:19,630
+هذا هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا هي و
+
+409
+00:31:19,630 --> 00:31:20,710
+قيمة هذا هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا
+
+410
+00:31:20,710 --> 00:31:24,290
+هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا هي و
+
+411
+00:31:24,290 --> 00:31:27,950
+قيمة هذا هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا
+
+412
+00:31:27,950 --> 00:31:28,550
+هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا هي و
+
+413
+00:31:28,550 --> 00:31:33,590
+قيمة هذا هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا
+
+414
+00:31:33,590 --> 00:31:38,410
+هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا هي و
+
+415
+00:31:38,410 --> 00:31:41,030
+قيمة هذا هي وقيمة هذا هي وقيمة هذا هي وقيمة هذا
+
+416
+00:31:41,030 --> 00:31:42,200
+هي وقيمة هذا هي وقيمة هذا هي وهيتطلع على اللي
+
+417
+00:31:42,200 --> 00:31:45,280
+قبل عشان ما تنساش الناقص تمانية و تلاتين هي صارت
+
+418
+00:31:45,280 --> 00:31:47,460
+ناقص تمانية و تلاتين هذي صارت ستة هذي صارت ناقص
+
+419
+00:31:47,460 --> 00:31:51,980
+اتنين هذي صارت اتنين و عشرين مظبوط طيب الخطوة
+
+420
+00:31:51,980 --> 00:31:55,600
+الثالثة ايش هذا اللي طبعا اللي بنسميه cofactor
+
+421
+00:31:55,600 --> 00:31:59,380
+matrix يعني اللي بنغير إشارات من ال .. ال .. ال ..
+
+422
+00:31:59,380 --> 00:32:06,570
+الـ matrix معدة أنصر الأقطار اللي موجودة الخطوة
+
+423
+00:32:06,570 --> 00:32:09,390
+الثالثة هي ان نجيب الـ Transpose نجيب اللي هو مدور
+
+424
+00:32:09,390 --> 00:32:12,870
+المصفوفة لـ Transpose اللي هو بيصير هذا السطر هي
+
+425
+00:32:12,870 --> 00:32:19,330
+عمود وهذا السطر هي عمود وهذا السطر هي عمود هذا
+
+426
+00:32:19,330 --> 00:32:24,210
+الـ Transpose هو اللي بنسميه الـ Adjoint لـ ميلة A
+
+427
+00:32:24,210 --> 00:32:27,870
+اللي حكيته قبل بشوية بيصير عندي الآن اللي هي
+
+428
+00:32:27,870 --> 00:32:31,890
+الخطوة الأخيرة الرابعة الـ A inverse بساوي 1 على 32
+
+429
+00:32:31,890 --> 00:32:35,550
+اللي هي قيمة الـ Determinant مضروبة في هذا ال
+
+430
+00:32:35,550 --> 00:32:38,010
+matrix اللي .. اللي .. اللي .. اللي هو الـ CT
+
+431
+00:32:38,010 --> 00:32:42,610
+سميناها وبيطلع عندي اللي هي القيمة اللي أمامي هذا
+
+432
+00:32:42,610 --> 00:32:46,230
+اللي بنسميه اللي هو الـ inverse أو المعكوس اللي
+
+433
+00:32:46,230 --> 00:32:51,510
+ضربنا مين يا جماعة لما مصوفة لو مثال آخر جالي find
+
+434
+00:32:51,510 --> 00:32:55,050
+A inverse الآن بدا نوجد الـ A inverse بالصورة اللي
+
+435
+00:32:55,050 --> 00:32:59,170
+حكينا عنها قبل بشوية اللي هو هي الـ A والـ A
+
+436
+00:32:59,170 --> 00:33:01,790
+inverse ايش بساوي واحد على الـ determinant في ال
+
+437
+00:33:01,790 --> 00:33:06,200
+adjoint ايش الـ adjoint بدنا نوجده اللي قلنا عنه قبل
+
+438
+00:33:06,200 --> 00:33:08,780
+بشوية وايش الـ determinant اللي أنتو عارفينه ال
+
+439
+00:33:08,780 --> 00:33:13,740
+determinant لهذا بساوي قيمة المحدد هذا وهيطلع لنا
+
+440
+00:33:13,740 --> 00:33:17,980
+القيمة عبارة عن قداش خمسة لو جربت أنت توجدها لحالك
+
+441
+00:33:17,980 --> 00:33:22,100
+نيجي لمين لايه نوجد الـ adjoint لايه عشان نوجد ال
+
+442
+00:33:22,100 --> 00:33:25,700
+adjoint اول شي بدنا نوجد مين الـ minors هذا ال
+
+443
+00:33:25,700 --> 00:33:29,360
+minors هذا اللي هو قيمة الـ determinant للعنصر
+
+444
+00:33:29,360 --> 00:33:32,950
+الأول determinant الثانوي وهذا للعنصر الثاني وهذا
+
+445
+00:33:32,950 --> 00:33:36,650
+للعنصر الثالث زي ما وجدنا قبل قليل والتفاصيل لكم
+
+446
+00:33:36,650 --> 00:33:41,180
+الحسابات وجدنا الـ Minors بعد ما نجد الـ Minors
+
+447
+00:33:41,180 --> 00:33:45,680
+بنجد الـ Co-Factor ماهو الـ Co-Factor؟ بنحدد هي
+
+448
+00:33:45,680 --> 00:33:49,860
+القطر الرئيسي وهي القطر الثانوي ومن هدول بنغير
+
+449
+00:33:49,860 --> 00:33:56,140
+إشاراتين هذا بيصير 25 هذا بيصير 4 هذا بيصير 5 وهذا
+
+450
+00:33:56,140 --> 00:34:01,180
+بيصير 18 هي اللي هو الـ Co-Factor عملية تغيير
+
+451
+00:34:01,180 --> 00:34:06,020
+الإشارات للعناصر غير عناصر القطر الثاني والقطر
+
+452
+00:34:06,020 --> 00:34:11,100
+الرئيسي الان الـ Cofactor اللي هو C أوجدناه ضال
+
+453
+00:34:11,100 --> 00:34:14,880
+عندنا نوجد مين الـ Adjoint الـ Adjoint مين هو ال
+
+454
+00:34:14,880 --> 00:34:18,980
+Transpose لهذا هي أوجدناه الـ Transpose سهل ال
+
+455
+00:34:18,980 --> 00:34:24,180
+Transpose كلكم بعرفها هي بيصير عمود سطر بيصير
+
+456
+00:34:24,180 --> 00:34:28,120
+عمود سطر بيصير عمود خلصنا الـ Adjoint بدنا نوجد ال
+
+457
+00:34:28,120 --> 00:34:31,100
+A-Inverse الـ A-Inverse ايش هي؟ واحد على قيمة ال
+
+458
+00:34:31,100 --> 00:34:34,570
+determinant اللي أوجدناه قبل و شوية اللي هو مضروب
+
+459
+00:34:34,570 --> 00:34:37,630
+في الـ Adjoint اللي هو عبارة عن واحد على خمسة اللي
+
+460
+00:34:37,630 --> 00:34:41,530
+هو الـ determinant خمسة مضروب في الـ Adjoint اللي هو
+
+461
+00:34:41,530 --> 00:34:46,810
+هاي الـ Adjoint هيك فبكون احنا أوجدنا الـ A inverse
+
+462
+00:34:46,810 --> 00:34:52,070
+لمين ل الـ matrix اللي الـ determinant له مش صفر
+
+463
+00:34:52,070 --> 00:34:57,060
+الان عندك الجزء الثاني من الواجباللي هو ال
+
+464
+00:34:57,060 --> 00:35:00,540
+question هو ان انا الـ a هيو وهي الـ a inverse
+
+465
+00:35:00,540 --> 00:35:03,760
+بالسوية واحدة الـ determinant في الـ adjoint او جدل
+
+466
+00:35:03,760 --> 00:35:07,820
+الـ a inverse او جدلي هذا الكلام بالتفصيل او جدل ال
+
+467
+00:35:07,820 --> 00:35:10,760
+determinant وبعدين او جدل الـ adjoint زي ما احنا
+
+468
+00:35:10,760 --> 00:35:14,600
+قلنا اللي قبل وهيطلع عندك الجواب a inverse
+
+469
+00:35:14,600 --> 00:35:19,990
+بالسوية كده انا بدي منك التفاصيل في الواجبالان
+
+470
+00:35:19,990 --> 00:35:24,190
+المرة القادمة ان شاء الله بنكمل وبندخل على الـ
+
+471
+00:35:24,190 --> 00:35:27,830
+solving linear equations using inverse matrix
+
+472
+00:35:27,830 --> 00:35:32,330
+والسلام عليكم ورحمة الله وبركاته وإلى لقاء آخر
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f0108b29f72f06d73f0389df36d9fa190abfaec6
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_postprocess.srt
@@ -0,0 +1,1888 @@
+1
+00:00:00,000 --> 00:00:07,980
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثانية بعد
+
+2
+00:00:07,980 --> 00:00:18,940
+الطوارئ وهي لطلاب وطالبات الحوسبة المتنقلة لمساق
+
+3
+00:00:18,940 --> 00:00:25,220
+رياضيات منفصلة طلبت وطالبات كلية technology
+
+4
+00:00:25,220 --> 00:00:32,700
+المعلوماتبالجامعة الإسلامية فرع الجنوب المحاضرة
+
+5
+00:00:32,700 --> 00:00:37,800
+اليوم هي بعنوان matrix determinant أو محدد
+
+6
+00:00:37,800 --> 00:00:42,920
+المصفوفة في هذه المحاضرة ان شاء الله هنتعرف على
+
+7
+00:00:42,920 --> 00:00:49,210
+شغلتين .. هنعرف شغلتين أساسيتينهي كيف نجد محدد
+
+8
+00:00:49,210 --> 00:00:56,270
+المصفوفة والأمر الآخر هو كيف نجد المعكوس الضربي
+
+9
+00:00:56,270 --> 00:01:02,630
+للمصفوفة في حال وجود هذا المعكوس دعونا الآن نتعرف
+
+10
+00:01:02,630 --> 00:01:08,370
+على محدد المصفوفة أو ال matrix determinantالـ
+
+11
+00:01:08,370 --> 00:01:13,150
+Matrix Determinant أو محدد المصفوفة هو محدد
+
+12
+00:01:13,150 --> 00:01:20,110
+لمصفوفة مربعة يعني مصفوفة درجتها 2×2 أو 3×3 أو 4×4
+
+13
+00:01:20,110 --> 00:01:25,510
+أو N×N بصورة عامةأحنا الآن هنتعرف في البداية شو
+
+14
+00:01:25,510 --> 00:01:30,710
+معنات أو ما هو محدد المصفوفة the determinant of
+
+15
+00:01:30,710 --> 00:01:37,550
+المصفوفة اللي هي المكوّنة من اللي هو او من الدرجة
+
+16
+00:01:37,550 --> 00:01:43,360
+اتنين في اتنين اللي هي A,B,C,D اللي أمامناتعريف
+
+17
+00:01:43,360 --> 00:01:49,660
+محدد المصوفة أو the determinant of the matrix هو
+
+18
+00:01:49,660 --> 00:01:54,200
+كمالي طبعا بنرمزله بالرامز اللي هو column هنا و
+
+19
+00:01:54,200 --> 00:01:57,840
+column هنا أو اللي هو عمود من هنا و عمود من هنا و
+
+20
+00:01:57,840 --> 00:02:02,280
+بينهم مكتوبة نفس المصوفة العادية نود المحدد بيجي
+
+21
+00:02:02,280 --> 00:02:07,560
+بنضرب عناصر القطر الرئيسي ناقص عناصر القطر التانوي
+
+22
+00:02:07,560 --> 00:02:11,260
+يعني بمعنى أخر محدد المصوفة عبارة عن رقم هيطلعاللي
+
+23
+00:02:11,260 --> 00:02:16,680
+هو A في D نقص بي في C هذا محدد المصوفة اللي هي من
+
+24
+00:02:16,680 --> 00:02:22,540
+الدرجة 2 في 2 بالاستعانة بمحدد المصوفة من الدرجة 2
+
+25
+00:02:22,540 --> 00:02:29,240
+في 2 هنعرف محدد المصوفة لما تكون درجة المصوفة 3 في
+
+26
+00:02:29,240 --> 00:02:33,860
+3 هي أمامنا مصوفة 3 في 3 وهي عناصرها موجودة جوا
+
+27
+00:02:33,860 --> 00:02:40,880
+بدنا نحدد اللي هو شو محددها او نوجد شو محددهاالأن
+
+28
+00:02:40,880 --> 00:02:43,760
+الـ determinant هي الـ determinant اللي هو عمود
+
+29
+00:02:43,760 --> 00:02:46,740
+دنهان عمود دنهان أو عصام دنهان أو عصام دنهان ال
+
+30
+00:02:46,740 --> 00:02:51,820
+determinant هذا هيساوي اللي هو بنيجي يا بنستخدم
+
+31
+00:02:51,820 --> 00:02:58,260
+عواقب اللي هو عناصر الصف العمود أو عناصر الصف في
+
+32
+00:02:58,260 --> 00:03:01,820
+إيجاد المحدد إيش بيعني؟ شوفوا إيش بيعني خلينا
+
+33
+00:03:01,820 --> 00:03:06,500
+نستخدم اللي هو عناصر من العمود الأولفبكون عندى
+
+34
+00:03:06,500 --> 00:03:14,100
+اللى هو محدد المصفوفة هذه بساوي a في اللى هو محدد
+
+35
+00:03:14,100 --> 00:03:21,130
+من الدرجة الثانية ناقص الان موجب ناقصنقص D في محدد
+
+36
+00:03:21,130 --> 00:03:26,030
+المصفوفة من الدرجة الثانية جي في محدد المصفوفة
+
+37
+00:03:26,030 --> 00:03:30,270
+أيضا من الدرجات الثانية بنبدأ بموجب سالب موجب و لو
+
+38
+00:03:30,270 --> 00:03:33,330
+أخدنا السطر الفجاني برضه هنبدأ بموجب سالب موجب
+
+39
+00:03:33,330 --> 00:03:36,390
+خلينا نبدأ في العمود اللي عندنا الآن العمود اللي
+
+40
+00:03:36,390 --> 00:03:40,380
+عندنا بقولناA و بادي بدوجة المحدد اللي بدور بالـ A
+
+41
+00:03:40,380 --> 00:03:45,020
+فيه بشطب هذا السطر اللي فيه الـ A و بشطب هذا
+
+42
+00:03:45,020 --> 00:03:50,340
+العمود اللي فيه الـ A بظل اللي هو المحدد هذا اللي
+
+43
+00:03:50,340 --> 00:03:54,960
+هو الـ E و الـ F و الـ H و الـ I إذا هذا بساوي الـ
+
+44
+00:03:54,960 --> 00:03:59,980
+A في المحدد اللي نتج بعد تشطيب اللي هو الصف و
+
+45
+00:03:59,980 --> 00:04:05,250
+العمود اللي بحتوي Aنفس الشيء بالنسبة لـ D بنشط
+
+46
+00:04:05,250 --> 00:04:09,550
+بالسطر و بنشط بالعمود اللي هي فيه بيظل بي و سي و
+
+47
+00:04:09,550 --> 00:04:13,790
+اتش و اي بي و سي و اتش و اي اذا ناقص دي في اللي هو
+
+48
+00:04:13,790 --> 00:04:14,070
+هذا
+
+49
+00:04:17,090 --> 00:04:23,010
+بنقص دي ومن ثم زائد جي بنشطب اللي هو السطر و
+
+50
+00:04:23,010 --> 00:04:26,390
+العمود اللي فيه بيظل بي و سي بس أنا بخطأ يعني بس
+
+51
+00:04:26,390 --> 00:04:30,590
+موجود اللي هي بي و سي هذه بي و هذه سي و بظل من
+
+52
+00:04:30,590 --> 00:04:36,190
+كمان لما نشطب هذا و هذا بظل كمان اي و افهذه الان
+
+53
+00:04:36,190 --> 00:04:40,630
+هي اللى ناتج هو عبارة عن محدد المصوفة اللى فوق كيف
+
+54
+00:04:40,630 --> 00:04:43,850
+بنوجد هنا زى ما وجدنا اللى فوق هذه عبارة عن EI
+
+55
+00:04:43,850 --> 00:04:48,550
+ناقص H في F اللى بيطلع منه ضربه في الـA ونفس الاشي
+
+56
+00:04:48,550 --> 00:04:54,310
+قلبك يعنىالان ناخد مثال عددي على اللى حكينا find
+
+57
+00:04:54,310 --> 00:04:57,490
+the determinant of هي عندنا المصفوفة هذه بدنا نوجد
+
+58
+00:04:57,490 --> 00:05:02,110
+ايش مالها بدنا نوجد محدد هذه المصفوفة ده نشوف كيف
+
+59
+00:05:02,110 --> 00:05:05,590
+نوجد حد محدد المصفوفة بدأ استخدم اللى هو العمود
+
+60
+00:05:05,590 --> 00:05:10,360
+الاول اذا modab سالب modab يعني واحدفي المحدد
+
+61
+00:05:10,360 --> 00:05:15,420
+الثانوي تبعها نقص واحد في المحدد الثانوي تبعها
+
+62
+00:05:15,420 --> 00:05:19,180
+اتنين في المحدد الثانوي اللي تبعها ايش مقصود
+
+63
+00:05:19,180 --> 00:05:23,220
+بالمحدد الثانوي اللي حكيناها قبل بشوية كيف هو نجي
+
+64
+00:05:23,220 --> 00:05:27,720
+واحد في اللي هو بنشط بسطر و بنشط بإيش العمود اللي
+
+65
+00:05:27,720 --> 00:05:31,660
+هو فيه المحدد اللي بيظل بنسميه المحدد الثانوي لمين
+
+66
+00:05:31,660 --> 00:05:36,840
+للواحد بيصير واحد في نقص واحد اربعة في خمسةبعد ما
+
+67
+00:05:36,840 --> 00:05:43,040
+شطبنا السطر هذا و العمود هذا ناقص الان واحد هذا
+
+68
+00:05:43,040 --> 00:05:49,540
+الثاني واحد و بشطب سطره و بشطب عموده بضل المحدد
+
+69
+00:05:49,540 --> 00:05:52,400
+الثانوي اللي هو اتنين و تلاتة واربعة وخمسة هي
+
+70
+00:05:52,400 --> 00:05:56,320
+اتنين و تلاتة واربعة وخمسة زائد ضل اللي هو العمصر
+
+71
+00:05:56,320 --> 00:06:00,380
+الأخير اتنين بشطب هذا السطر و هذا العمود بيصير عند
+
+72
+00:06:00,380 --> 00:06:05,460
+اتنين في اللي هو المحدد الثانوي اللي عندنااللي هو
+
+73
+00:06:05,460 --> 00:06:09,160
+اللي أمامنا هذا اتنين تلاتة سفر ناقص واحد بكمل
+
+74
+00:06:09,160 --> 00:06:13,220
+الآن عشان اوجد القيمة هذه الان واحد مضروبة بفتح
+
+75
+00:06:13,220 --> 00:06:19,980
+قوس الان جداش قيمة هذا سفر في خمسة ناقص ناقص أربعة
+
+76
+00:06:19,980 --> 00:06:26,990
+في واحد يعني زائد أربعة في إق اللي هو1 يعني بمعنى
+
+77
+00:06:26,990 --> 00:06:34,530
+اخر اهاي سفر خلصنا من هذا القطر الرئيسي و بنضرب
+
+78
+00:06:34,530 --> 00:06:37,090
+هذا القطر الثانوي بطلع عندى ناقص واحد في اربعة
+
+79
+00:06:37,090 --> 00:06:40,370
+بناقص اربعة و ناقص الاصلي بيصير ناقص ناقص اربعة
+
+80
+00:06:40,370 --> 00:06:43,910
+بنجي للثاني بنفس الاسلوب ناقص واحد هذا اللي من أصل
+
+81
+00:06:43,910 --> 00:06:48,330
+الموضوع و بنجي بنضرب الرئيسي اتنين في خمسة بيطلع
+
+82
+00:06:48,330 --> 00:06:52,740
+بعشرة ناقص اربعة في تلاتة اللي هي اتناشرخلصنا من
+
+83
+00:06:52,740 --> 00:06:55,900
+هذه اتنين و بنفتح جثم المحدد اتنين فى نقص واحد
+
+84
+00:07:22,220 --> 00:07:27,160
+إذا هذا هو عبارة عن محدد هذه المصفوفة يعني الأمر
+
+85
+00:07:27,160 --> 00:07:29,860
+سهل إيجاد المحدد
+
+86
+00:07:33,440 --> 00:07:37,780
+عندي لاحظ و لما احنا اوجدنا اللى هو محدد المصوفة
+
+87
+00:07:37,780 --> 00:07:41,200
+من الدرجة الثانية ما لازمش لغير هذا نوجده لحاله
+
+88
+00:07:41,200 --> 00:07:46,120
+لكن لما اوجدنا محدد لمصوفة من تلاتة في تلاتة طلق
+
+89
+00:07:46,120 --> 00:07:51,820
+لزمن اكم محدد ثانوي تلاتة واحد اتنين تلاتة يعني
+
+90
+00:07:51,820 --> 00:07:55,770
+بدرجة المحددو لو كان في عندنا matrix أربعة في
+
+91
+00:07:55,770 --> 00:07:59,670
+أربعة بنعمل بنفس الأسلوب بس اللي بطلع إن عندنا
+
+92
+00:07:59,670 --> 00:08:04,410
+المحددات الثانوية اللي هي تلاتة في تلاتة بنعمل محن
+
+93
+00:08:04,410 --> 00:08:09,950
+زي ما عملنا مع مين مع اللي هو هذا السؤال الان
+
+94
+00:08:09,950 --> 00:08:14,290
+وهكذا بصورة عامة الان احنا يعني هنشتغل شغلنا بس
+
+95
+00:08:14,290 --> 00:08:16,710
+على المحددات اللي وهين اللي هي من الدرجة تلاتة في
+
+96
+00:08:16,710 --> 00:08:21,640
+تلاتة أو اتنين في اتنينالان بدنا نعرف حاجة اسمها
+
+97
+00:08:21,640 --> 00:08:25,320
+the inverse of a matrix اللي هو الهدف التاني من
+
+98
+00:08:25,320 --> 00:08:27,760
+هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف
+
+99
+00:08:27,760 --> 00:08:28,060
+التاني من هذه المحاضرة الهدف التاني من هذه
+
+100
+00:08:28,060 --> 00:08:28,740
+المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني
+
+101
+00:08:28,740 --> 00:08:29,620
+من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف
+
+102
+00:08:29,620 --> 00:08:29,860
+التاني من هذه المحاضرة الهدف التاني من هذه
+
+103
+00:08:29,860 --> 00:08:30,440
+المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني
+
+104
+00:08:30,440 --> 00:08:34,700
+من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف
+
+105
+00:08:34,700 --> 00:08:38,500
+التاني من هذه المحاضرة الهدف التاني من هذه
+
+106
+00:08:38,500 --> 00:08:43,620
+المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني
+
+107
+00:08:43,620 --> 00:08:48,420
+من2×2، 3×3، 4×4، 5×5 الاخرى
+
+108
+00:08:51,710 --> 00:08:57,750
+non-singular يعني بمعنى آخر اللي هي اللي بنسميها
+
+109
+00:08:57,750 --> 00:09:02,850
+المصهوفة اللي بيكون محددها مش سفر لما يكون محددها
+
+110
+00:09:02,850 --> 00:09:07,030
+مش سفر بنضمن اللي هو بعد شوية هتشوف التعريف أنه في
+
+111
+00:09:07,030 --> 00:09:11,430
+إلها معكوس ضربي إذا المصهوفة اللي بتكون non
+
+112
+00:09:11,430 --> 00:09:17,080
+-singular هي المصهوفة اللي محددها لا يساوي سفرالان
+
+113
+00:09:17,080 --> 00:09:23,340
+لو وجدنا ال matrix B دربناها في A بساوي I لأ طبعا
+
+114
+00:09:23,340 --> 00:09:25,180
+هذه المصفوفة ال A اللي أخدت اللي هي ال non
+
+115
+00:09:25,180 --> 00:09:29,840
+singular اللي هي اللي بمعنى أخر محددها مش سفر لو
+
+116
+00:09:29,840 --> 00:09:33,840
+وجدنا مصفوفة تانية اسمها B ودربناها فيها طلعت عند
+
+117
+00:09:33,840 --> 00:09:37,330
+ال identityوضربناها من الجهة الثانية بي في إيه
+
+118
+00:09:37,330 --> 00:09:41,750
+برضه طلعت عند ال identity بنسمي المصفوفة بي في هذه
+
+119
+00:09:41,750 --> 00:09:46,370
+الحالة هي عبارة عن ال inverse للإيه بنرمزلها من
+
+120
+00:09:46,370 --> 00:09:52,750
+الرمز A inverse أو اللي هو المعكوس الضربي للمصفوفة
+
+121
+00:09:52,750 --> 00:09:57,890
+A إذا المعكوس الضربي للمصفوفة A هو ال matrix اللي
+
+122
+00:09:57,890 --> 00:10:01,410
+لو ضربناه في المصفوفة الأصلية من اليمين أو اليسار
+
+123
+00:10:01,410 --> 00:10:06,630
+بطلع لل identity matrixيعني مثل لو اديت جربت هذه
+
+124
+00:10:06,630 --> 00:10:10,170
+المصوفة زي ما اتعلمنا الضرب و ضربنا هذه المصوفة
+
+125
+00:10:10,170 --> 00:10:14,030
+فيها هنلاقي هذه المصوفة في هذه المصوفة ايش بتساوي
+
+126
+00:10:14,030 --> 00:10:18,850
+بساوي ال identity بناء عليه بنقول هذه المصوفة او
+
+127
+00:10:18,850 --> 00:10:23,130
+حتى هذه يعني لو سمعنا .. بنقول هذه هي عبارة عن ال
+
+128
+00:10:23,130 --> 00:10:27,250
+inverse لهذه يعني هذه المعكوس الضربي لهذه و ايضا
+
+129
+00:10:27,250 --> 00:10:31,190
+هذه هتكون هي المعكوس الضربي لمين؟ للثانية الآن
+
+130
+00:10:31,190 --> 00:10:34,790
+عملية الضرب احنا اتعلمناها فيش ده in a دههذا
+
+131
+00:10:34,790 --> 00:10:37,190
+معناته اللي هو المعكوس الضربي المعكوس الضربي
+
+132
+00:10:37,190 --> 00:10:40,350
+المصفوفة اللي أمامنا هذه هي المصفوفة اللي لو
+
+133
+00:10:40,350 --> 00:10:43,830
+ضربناها من اليمين ومن اليسار بتساوي ال identity طب
+
+134
+00:10:43,830 --> 00:10:46,630
+كيف بدنا نوجدها هذه المصفوفة اللي هي المعكوس
+
+135
+00:10:46,630 --> 00:10:51,870
+الضربي الآن في البداية خلينا نيجي لطريقة بداية
+
+136
+00:10:51,870 --> 00:10:57,010
+لإيجادها ونشوف جداش بتغلبنا ومن ثم بنتعلم قاعدة
+
+137
+00:10:57,010 --> 00:11:02,190
+كيف نوجد اللي هيالمعكوس الضربي للمصفوفة بكل سهولة
+
+138
+00:11:02,190 --> 00:11:11,190
+الان لو اخدنا المصفوفة 8-10-3-4 هذه المصفوفة من
+
+139
+00:11:11,190 --> 00:11:15,650
+الدرجة 2x2 لو بدنا نوجد ال inverse لها او نوجد
+
+140
+00:11:15,650 --> 00:11:19,730
+المعكوس الضربي لها نفترض ان المعكوس الضربي لها
+
+141
+00:11:19,730 --> 00:11:25,390
+عبارة عن a,b,c,dماشي الحال و أقول لأ عشان تكون هذه
+
+142
+00:11:25,390 --> 00:11:29,870
+معكوس ضربى لازم أضرب هذه فهذه يطلع من عندى اللى هو
+
+143
+00:11:29,870 --> 00:11:35,190
+ال identity matrix 1100 صار عندى هاي قيمتين مضربات
+
+144
+00:11:35,190 --> 00:11:39,370
+في بعض لازم يساون هدولة عشان تطلع هذه عبارة عن
+
+145
+00:11:39,370 --> 00:11:47,060
+المعكوس الضربى لهاماشي الحال الان الان نضرب هذه في
+
+146
+00:11:47,060 --> 00:11:50,800
+هذه المصفوفة نضرب ضرب عادي اضرب تمانية في نقص عشرة
+
+147
+00:11:50,800 --> 00:11:55,820
+في a في c بتطلع عندى تمانية a نقص عشرة في c نضرب
+
+148
+00:11:55,820 --> 00:12:02,450
+هذه المصفوفةوبنضرب هذا اللي هو السطر في هذا العمود
+
+149
+00:12:02,450 --> 00:12:05,830
+بتطلع عند هذه قيمة زي ما اتعلمنا قبلين و بنضرب هذا
+
+150
+00:12:05,830 --> 00:12:09,010
+السطر في هذا العمود بتطلع عند هذه القيمة و بنضرب
+
+151
+00:12:09,010 --> 00:12:12,870
+هذا السطر في هذا العمود بتطلع عند هذه القيمة طبعا
+
+152
+00:12:12,870 --> 00:12:15,710
+كيف؟ خلنا أضرب الأخيرة هذا عشان تكون في الصورة كيف
+
+153
+00:12:15,710 --> 00:12:20,230
+تضرب ناقص ثلاثة في B ب C ناقص ثلاثة بيه زائد أربعة
+
+154
+00:12:20,230 --> 00:12:23,730
+في D ب C زائد أربعة D هذا كله لازم يساوي واحد و
+
+155
+00:12:23,730 --> 00:12:27,900
+سفر و سفر و واحدصار عندى هذا المقدار اللى هو اللى
+
+156
+00:12:27,900 --> 00:12:32,240
+هو المصفوفة هذه بتساوي هذا المصفوفة عشان يطلع ان
+
+157
+00:12:32,240 --> 00:12:37,760
+هذا هو المعكوس الضرب لهذا طيب بادي كل مساواة
+
+158
+00:12:37,760 --> 00:12:42,140
+مصفوفتين معناته ان هذا المقدار بساوي واحد و هذا
+
+159
+00:12:42,140 --> 00:12:45,700
+المقدار بساوي سفر و هذا المقدار بساوي سفر و هذا
+
+160
+00:12:45,700 --> 00:12:49,880
+المقدار بساوي واحد هى عندى هذولة هذه اللى ناتجة من
+
+161
+00:12:49,880 --> 00:12:54,560
+هذا و هذه ناتجة من هذا و هذه المعادلة ناتجة من هذا
+
+162
+00:12:55,560 --> 00:13:00,620
+هذه المعادلة هي نقص تلاتة بيزاد أربع دي بسواحد
+
+163
+00:13:00,620 --> 00:13:04,520
+ناتجا من اللي فوق لأن صار عندي انا معادلتي اربع
+
+164
+00:13:04,520 --> 00:13:10,020
+معادلات في نفس الوقت انية الان خلينا نحل المعادلة
+
+165
+00:13:10,020 --> 00:13:14,500
+هذه مع المعادلة هذه حلها عادي بالمعادلات الانية
+
+166
+00:13:14,500 --> 00:13:17,440
+اللي احنا بنعرفها اللي اخدناها في تاني اعدادي او
+
+167
+00:13:17,440 --> 00:13:23,610
+تالت اعدادي بنحلهابنوجد قيمة الـ A و الـ C لأن
+
+168
+00:13:23,610 --> 00:13:28,510
+معادلتين فيه مجهولين فتطلع A و تطلع قيمة C طلعت
+
+169
+00:13:28,510 --> 00:13:33,430
+عندي A اتنين و تطلعت عندي C بساوين واحد و نص الأهم
+
+170
+00:13:33,430 --> 00:13:38,370
+الحل هذول نفس الأشي هيطلع عندي معادلتين أنيتين مع
+
+171
+00:13:38,370 --> 00:13:43,260
+بعض هيطلع عندي B بساوين خمسة و D بساوين أربعةهذه
+
+172
+00:13:43,260 --> 00:13:47,600
+اللي هي شايفين احنا جداش اتغلبنا في الإيجاد و احنا
+
+173
+00:13:47,600 --> 00:13:50,660
+جاعدين اللي هو يمكن بعضكم ناسي كيف المعادلات
+
+174
+00:13:50,660 --> 00:13:54,480
+الآنية و كيف حلول المعادلات الآنية و بدنا نتعلمها
+
+175
+00:13:54,480 --> 00:13:59,060
+عشان نوجد من ال a inverse الان احنا مش هنظل نشتغل
+
+176
+00:13:59,060 --> 00:14:02,980
+هيك يعني هذا بس عشان ان انت تشوف جداش اللي هو هذا
+
+177
+00:14:02,980 --> 00:14:07,900
+هيغلب لو انا اجيت اوجدت بطرق العادية هذه عشان اوجد
+
+178
+00:14:07,900 --> 00:14:12,130
+ال inverse الان لو كانت بصفوفة تلاتة في تلاتةتقول
+
+179
+00:14:12,130 --> 00:14:16,810
+هيصير عندنابدل ما هنا في عندى اللى هو عبارة عن
+
+180
+00:14:16,810 --> 00:14:20,870
+اربع معادلات هيطلع عندى عبارة عن تسعة معادلات ايش
+
+181
+00:14:20,870 --> 00:14:24,330
+التسعة معادلات في تسعة مجهيل ومش عارف ايش طبعا
+
+182
+00:14:24,330 --> 00:14:28,950
+هتغلبوا فكورة غلبة كبيرة عشان هيك بدنا نريحكم وهي
+
+183
+00:14:28,950 --> 00:14:34,050
+في عندنا الطريقة finding the inverse of two by two
+
+184
+00:14:34,050 --> 00:14:39,450
+matrices نشوف كيف بنوجد اللى هو ال inverse ل two
+
+185
+00:14:39,450 --> 00:14:46,350
+by two matricesهذا هو الجزء الأول من المحاضرة
+
+186
+00:14:46,350 --> 00:14:50,210
+والجزء
+
+187
+00:14:50,210 --> 00:14:55,690
+التاني من المحاضرة هي finding inverse of 2x2
+
+188
+00:14:55,690 --> 00:15:00,270
+matrices أو إيجاد المعاكوس الضربي للمصفوفة وخلّينا
+
+189
+00:15:00,270 --> 00:15:04,490
+نوقف عندنا ونعمل المحاضرة على جزءين و الله يعطيكوا
+
+190
+00:15:04,490 --> 00:15:08,390
+العافية نكمل الآن الجزء الثاني من المحاضرة
+
+191
+00:15:15,680 --> 00:15:19,100
+المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة
+
+192
+00:15:19,100 --> 00:15:22,240
+المعكوس
+
+193
+00:15:22,240 --> 00:15:27,300
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+194
+00:15:27,300 --> 00:15:28,780
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+195
+00:15:28,780 --> 00:15:28,880
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+196
+00:15:28,880 --> 00:15:28,980
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+197
+00:15:28,980 --> 00:15:29,180
+الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس
+
+198
+00:15:29,180 --> 00:15:32,220
+الضربي للمصفوفة المعكوس الضربي للمصفوفةهذه
+
+199
+00:15:32,220 --> 00:15:36,380
+المصفوفة بدنا نشوف كيف نودد اللي هو المعكوس الضربي
+
+200
+00:15:36,380 --> 00:15:40,100
+للمصفوفة قبل ما نودد المعكوس الضربي للمصفوف لازم
+
+201
+00:15:40,100 --> 00:15:44,000
+نعرف الشيء لأن المصفوفة عشان يكون لها معكوس ضربي
+
+202
+00:15:44,000 --> 00:15:49,160
+لازم يكون ال determinant لها ما بيساوي سفر يعني
+
+203
+00:15:49,160 --> 00:15:54,660
+المصفوفة اللي محددها سفر ليس لها معكوس ضربي إذن
+
+204
+00:15:54,660 --> 00:16:00,410
+الآن احناأول شغلة بنعملها عشان نجد اللي هو المعكوس
+
+205
+00:16:00,410 --> 00:16:05,250
+الضرب للمصفوفة اللي عنا اللي أمامنا هذه انه بنشوف
+
+206
+00:16:05,250 --> 00:16:11,150
+اللي هو ال determinant لها إذا AD ناقص BC مش سفر
+
+207
+00:16:11,150 --> 00:16:15,630
+معناته إحنا جاهزين لإن نجد اللي هو المعكوس الضرب
+
+208
+00:16:15,630 --> 00:16:19,780
+للمصفوفةشوفوا خلّينا نشوف كيف اللي هو نوجدها
+
+209
+00:16:19,780 --> 00:16:23,100
+العملية سهلة جدا في حالة المصوفة اتنين باتنين
+
+210
+00:16:23,100 --> 00:16:27,440
+بنيجي عناصر القطر الثانوي بنبدلها مع بعض يعني
+
+211
+00:16:27,440 --> 00:16:32,140
+بيصير الـD هنا والـA هنا الاسف الرئيسي العناصر
+
+212
+00:16:32,140 --> 00:16:37,020
+القطر الثانوي بس بنغير إشارتها هذه بيصير ناقصي
+
+213
+00:16:37,020 --> 00:16:42,780
+ناقص بي اللي بطلع هذا بنضربه في واحد على المحدد
+
+214
+00:16:43,270 --> 00:16:49,130
+النتيجة اللى طلع بكون هو مين هو عبارة عن المعكوس
+
+215
+00:16:49,130 --> 00:16:55,110
+الضربي للمصوفة a,b,c,d واضح ان الأمر سهل جدا عن
+
+216
+00:16:55,110 --> 00:16:58,550
+المثال اللى حكيناه قبل بشوية اللى استخدمنا الطرق
+
+217
+00:16:58,550 --> 00:17:02,870
+الأولية فيه وكانت اللى هى بتستلزم نعرف معادلة
+
+218
+00:17:02,870 --> 00:17:06,210
+اتقانية ومعادلة اتقانية واحنا طبعا فيه ممكن نكون
+
+219
+00:17:06,210 --> 00:17:12,310
+جزء ناسي الأمر نشوف الآن مثال عددي لاللي بنحكي عن
+
+220
+00:17:12,310 --> 00:17:18,190
+الإيجادعن طريق المثال العددي إذا كانت الـ A هي
+
+221
+00:17:18,190 --> 00:17:23,410
+المصوفة اللي أمامنا هذه المعكوس الضربي لها هو
+
+222
+00:17:23,410 --> 00:17:28,410
+عبارة عن الـ DA بعد ما بدلنا عناصر القطر التانوي
+
+223
+00:17:28,410 --> 00:17:35,970
+مع بعضأسف في الرئيسي وغيرنا عناصر قطر الثانوي بس
+
+224
+00:17:35,970 --> 00:17:39,630
+إشارتها وضربناها في واحد على قيمة ال determinant
+
+225
+00:17:39,630 --> 00:17:44,890
+طلع عنده اللي هو ال A inverse أو المعكوس الضربي
+
+226
+00:17:44,890 --> 00:17:49,470
+للمصفوفة نشوف مثال عدديالان نطلع لـ Find the
+
+227
+00:17:49,470 --> 00:17:53,810
+inverse of A هي الـ A عندي الان هي المصوفة دي بس
+
+228
+00:17:53,810 --> 00:17:57,830
+ايش بده اودد الان يا شباب و يا بنات الان بس بده
+
+229
+00:17:57,830 --> 00:18:01,930
+ادى اضرب اودد محدد المصوفة ايش المحدد اتنين في
+
+230
+00:18:01,930 --> 00:18:07,130
+ناقص عشرة هي ناقص اللي هو ناقص اربعة في اربعة هي
+
+231
+00:18:07,130 --> 00:18:13,440
+ناقص عشرينأو زائد ستة عشر بيظل إيه شماله ناقص
+
+232
+00:18:13,440 --> 00:18:17,700
+أربعة إذا المحدد بيساوي ناقص أربعة إذا مدام المحدد
+
+233
+00:18:17,700 --> 00:18:22,020
+مش سفر إذا المعاكوس الضربي مودون على طول المعاكوس
+
+234
+00:18:22,020 --> 00:18:25,560
+الضربي inverse إيه بيساوي واحد على قيمة ال
+
+235
+00:18:25,560 --> 00:18:29,900
+determinant هي ناقص أربعة وبنيجي لمصفوفتنا هذه بس
+
+236
+00:18:29,900 --> 00:18:33,000
+بنبدل الناقص عشرة مع الإتنين هينا بدلناها صارت
+
+237
+00:18:33,000 --> 00:18:37,180
+ناقص عشرة وهي اتنين و بنبدل إشارة ناقص أربعة بيصير
+
+238
+00:18:37,180 --> 00:18:41,330
+أربعة بنبدل إشارة الأربعة بيصير ناقص أربعةهذا الآن
+
+239
+00:18:41,330 --> 00:18:44,650
+هو عبارة عن مين؟ عن اللي هو الـ A inverse أو
+
+240
+00:18:44,650 --> 00:18:50,030
+المعكوس الضربي للمصفوف A Y ساوي بنضرب هذه طبعا هذا
+
+241
+00:18:50,030 --> 00:18:54,030
+الضرب عملية الضرب تدخل على كل عنصر من عناصر ال
+
+242
+00:18:54,030 --> 00:18:58,150
+matrix فبصير ناقص عشرة في ناقص ربع عبارة عن خمسة
+
+243
+00:18:58,150 --> 00:19:02,910
+على اتنين ناقص أربعة في ناقص ربع عبارة عن واحداللي
+
+244
+00:19:02,910 --> 00:19:06,610
+هو ناقص ربع في أربعة بيطلع ناقص واحد ناقص ربع في
+
+245
+00:19:06,610 --> 00:19:10,950
+اتنين بيطلع ناقص نص إذن هذه هي عبارة عن المعقوس
+
+246
+00:19:10,950 --> 00:19:14,550
+الضربي لو أنت في الدار لأ جيت و قولت والله بدأ
+
+247
+00:19:14,550 --> 00:19:18,990
+أشوف كلامنا صح ولا لأ اضرب لهدي فهدي هتلاقي بيطلع
+
+248
+00:19:18,990 --> 00:19:23,090
+عبارة عن ال identity matrix إذن عملية الإيجاد اللي
+
+249
+00:19:23,090 --> 00:19:26,250
+هو المعقوس الضربي سهلة لأن المصوفة اتنين في اتنين
+
+250
+00:19:26,700 --> 00:19:33,640
+الان معاكم الان الجزء من ال homework لهذه المحاضرة
+
+251
+00:19:33,640 --> 00:19:37,660
+بدكم تحلوا يا جماعة هذا السؤال هذا في ال homework
+
+252
+00:19:37,660 --> 00:19:42,020
+find the inverse of a و b و c حيث a هيها و b هيها
+
+253
+00:19:42,020 --> 00:19:46,420
+و c هي ده بنتظر منكم اللي هو حل هذا في ال homework
+
+254
+00:19:46,420 --> 00:19:52,550
+طبعا جاي لاحقا كمان شغلةكيف بدنا نجد ما هو find
+
+255
+00:19:52,550 --> 00:19:58,210
+the inverse of a 3x3 matrix كيف بدنا نجد ما هو
+
+256
+00:19:58,210 --> 00:20:03,650
+المعكوس الضربي لمصفوفة من الدرجة تلاتة في تلاتة
+
+257
+00:20:03,650 --> 00:20:10,260
+شوفوا علي خلينا نطلع هنا أربع خطواتأربع خطوات اللى
+
+258
+00:20:10,260 --> 00:20:14,540
+هو احنا باختصار خلّينا نقولها اول اشي بتوجد حاجة
+
+259
+00:20:14,540 --> 00:20:19,180
+اسمها اللى هى ال matrix of minor determinants
+
+260
+00:20:19,180 --> 00:20:24,000
+حاجات هنقول اشيه الان بنغير اشارات اللى هى كل
+
+261
+00:20:24,000 --> 00:20:30,100
+العناصر ما عدا عناصر القطر الرئيسى وعناصر قطر مين
+
+262
+00:20:30,100 --> 00:20:35,350
+التانويالان اللى بعدها اللى بيطلع عندنا اللى
+
+263
+00:20:35,350 --> 00:20:39,390
+بنعمله بناخده ل Transpose اللى هو مدور المصفوفة و
+
+264
+00:20:39,390 --> 00:20:42,650
+بعدين اللى بيطلع بنضربه فى واحد على ال determinant
+
+265
+00:20:42,650 --> 00:20:46,890
+بيطلع عندنا اللى هو المعكوس الضربى نشوف هذا يمكن
+
+266
+00:20:46,890 --> 00:20:50,610
+الكلام النظري شوية مش واضح خلينا نشوف كيف عمليا
+
+267
+00:20:50,930 --> 00:20:55,050
+نوجد الكوبيا قبل ما نحكي عن ما هو نوجد ال inverse
+
+268
+00:20:55,050 --> 00:20:59,070
+بس عساس ان هو توضيح ايش هو ال matrix of minor
+
+269
+00:20:59,070 --> 00:21:02,430
+determinants الان بدنا نعرف شو معناته ال minor
+
+270
+00:21:02,430 --> 00:21:05,630
+determinants اللي هي المحددات الثانوية حكيتها قبل
+
+271
+00:21:05,630 --> 00:21:10,540
+بشوية في الجزء الأول من المحاضرةالان يعني بدي اشوف
+
+272
+00:21:10,540 --> 00:21:13,700
+ايش ال minor determinant للخمسة اللي بالنسبة
+
+273
+00:21:13,700 --> 00:21:18,380
+للعنصر خمسة هذا مفترض انه محدد او matrix بدنا ال
+
+274
+00:21:18,380 --> 00:21:21,400
+minor determinant للخمسة ال minor determinant او
+
+275
+00:21:21,400 --> 00:21:24,620
+اللي هو المحدد الثانوي باختصار يا جماعة بتيجي
+
+276
+00:21:24,620 --> 00:21:28,600
+بالشط بالصف اللي هي فيه و العمود اللي هي فيه بطلع
+
+277
+00:21:28,600 --> 00:21:32,200
+عند المحدد المحدد اللي بطلع هذا هو اللي بنسميه ال
+
+278
+00:21:32,200 --> 00:21:36,350
+minor determinant لمن؟ للخمسةالان واحد يقول اللى
+
+279
+00:21:36,350 --> 00:21:39,550
+بدى ال minor determinant لمناقس ثلاثة بقول له حاضر
+
+280
+00:21:39,550 --> 00:21:44,870
+شط بالسطر و شط بالعمود بطلع عندى اللى هو اللى ضال
+
+281
+00:21:44,870 --> 00:21:49,710
+هذا عبارة عن محدد المحدد هذا بكون هو ال minor
+
+282
+00:21:49,710 --> 00:21:53,510
+determinant لمناقس ثلاثة واحد قال لأ بدي للتمانية
+
+283
+00:21:53,510 --> 00:21:58,530
+بقول له حاضر هى للتمانية شط بعموده و شط بصفه اللى
+
+284
+00:21:58,530 --> 00:22:03,030
+بضل هو عبارة عن ال minor determinant لمن للتمانية
+
+285
+00:22:03,370 --> 00:22:09,450
+أو المحدد الثانوي للعنصر من تمانية لو كان ليه بدي
+
+286
+00:22:09,450 --> 00:22:12,730
+اوديت قيمته بقول اه سهل ايجادها واحد في تلاتة
+
+287
+00:22:12,730 --> 00:22:17,690
+بتلاتة تلاتة ناقص ناقص أربعة يعني واحد زائد أربعة
+
+288
+00:22:17,690 --> 00:22:21,670
+يعني خمسة آسف تلاتة زائد أربعة يعني سابعة اللي هو
+
+289
+00:22:21,670 --> 00:22:27,010
+تلاتة زائد أربعة يعني سبعة هذا قيمة من ال minor
+
+290
+00:22:27,010 --> 00:22:30,980
+determinant of تمانيةيعني المحدد الثانوي لمين؟
+
+291
+00:22:30,980 --> 00:22:36,140
+لتمانية هذا الكلام قدمناله عشان نستخدم مباعد بشوية
+
+292
+00:22:36,140 --> 00:22:42,600
+في اللي هو إيجاد ال inverse للمصفوفة شوفوا ..
+
+293
+00:22:42,600 --> 00:22:45,420
+شوفوا صلى الله عليه وسلم بعتقد الأمور ان شاء الله
+
+294
+00:22:45,420 --> 00:22:49,440
+هتكون واضحة جدا الان ال determinant ام ال matrix
+
+295
+00:22:49,440 --> 00:22:54,000
+ام المصفوفة ام المطلوب إيجاد ال inverse لهذه
+
+296
+00:22:54,000 --> 00:23:00,880
+المصفوفةعنا أربع خطوات عشان نوجد اللي هوال .. ال
+
+297
+00:23:00,880 --> 00:23:04,880
+.. ال .. ال .. ال inverse لهذه المصوفة أربع خطوات
+
+298
+00:23:04,880 --> 00:23:07,900
+الخطوة الأولى أكيد كلكم حيقول بدنا نجد ال
+
+299
+00:23:07,900 --> 00:23:11,600
+determinant يعني بدنا نتأكد أو اشي make sure انه
+
+300
+00:23:11,600 --> 00:23:14,320
+non-singular ايش يعني non-singular يعني
+
+301
+00:23:14,320 --> 00:23:17,300
+determinant له مش صفر لو حسبتوا ال determinant له
+
+302
+00:23:17,300 --> 00:23:20,060
+زي ما أخدناه في الطريقة الأولى لإيش نضيع الوجد في
+
+303
+00:23:20,060 --> 00:23:23,800
+حساباتها لإن حسبناها قبل هيك بتحسبوها هتلاقوا ال
+
+304
+00:23:23,800 --> 00:23:28,520
+determinant لهذه ال M إيش طالع عندنا-156 يعني مش
+
+305
+00:23:28,520 --> 00:23:32,800
+سفر مزا مش مش سفر إذا الأن اتأكدنا إنه non
+
+306
+00:23:32,800 --> 00:23:37,120
+singular هذه طبعا في الآخر اللي هي بستخدمها اللي
+
+307
+00:23:37,120 --> 00:23:42,300
+هي قيمة ال determinant نجي للخطوات اللي بدنا نصل
+
+308
+00:23:42,300 --> 00:23:46,640
+فيها لل inverse الخطوة الأولى اللي هو find the
+
+309
+00:23:46,640 --> 00:23:49,840
+matrix of minor determinants يعني بدأ أوجد ال
+
+310
+00:23:49,840 --> 00:23:53,800
+matrix اللي بجيبه من مين من minor determinants
+
+311
+00:23:54,610 --> 00:23:58,350
+بتنشوف بنوجد اول اشي للتلاتة اشي ال minor
+
+312
+00:23:58,350 --> 00:24:03,670
+determinant للتلاتة الان هاي التلاتة شطبنا السطر
+
+313
+00:24:03,670 --> 00:24:08,590
+شطبنا العمود ضال عندى هذا هذا قداش قيمته ناقص
+
+314
+00:24:08,590 --> 00:24:12,850
+اتنين فى ناقص اتنين يعني اربعة ناقص خمسة وعشرين
+
+315
+00:24:12,850 --> 00:24:16,570
+اربعة ناقص خمسة وعشرين قداش بطلع ناقص واحد وعشرين
+
+316
+00:24:16,570 --> 00:24:20,450
+اذا بكتب الناقص واحد وعشرين هذاخلصنا من العنصر
+
+317
+00:24:20,450 --> 00:24:24,690
+الأول نجي للعنصر الثاني اللى هو بده اودد ال minor
+
+318
+00:24:24,690 --> 00:24:29,770
+determinant لمن يا شباب للسبعة خلصنا من التلاتة
+
+319
+00:24:29,770 --> 00:24:33,850
+نجي للسبعة طب السبعة كيف نفس الاشي بنشطب السطر و
+
+320
+00:24:33,850 --> 00:24:36,930
+بنشطب العمود و بنحسب ال minor determinant اللى هو
+
+321
+00:24:36,930 --> 00:24:40,990
+واحد في ناقص اتنين بيطلع ناقص اتنين ناقص اللى
+
+322
+00:24:40,990 --> 00:24:47,070
+بيصير زائد خمستاشر اتنيننقص اتنين زائد خمستاعش
+
+323
+00:24:47,070 --> 00:24:53,050
+بيطلع قداش عبارة عن تلات طعش خلصنا من السبعة بنوجد
+
+324
+00:24:53,050 --> 00:24:56,870
+ال minor determinant لمن الان للتنين تاني تشوف ال
+
+325
+00:24:56,870 --> 00:24:58,510
+minor determinant للتنين
+
+326
+00:25:02,080 --> 00:25:08,660
+وشط بالعمود طلع الـ Minor Determinant أي المحدد
+
+327
+00:25:08,660 --> 00:25:15,680
+الثانوي للعنصر 2 المحدد الثانوي للعنصر 2 خمسة زائد
+
+328
+00:25:15,680 --> 00:25:20,020
+اللي هي بصير ناقص ستة خمسة ناقص ستة بطلع ناقص واحد
+
+329
+00:25:20,020 --> 00:25:26,780
+نتأكد الكلام صحيحخلّصنا من السطر الأول كله و نبدأ
+
+330
+00:25:26,780 --> 00:25:31,540
+بالواحد وهي نفس القصة وهي السطر وهي العمود وهي
+
+331
+00:25:31,540 --> 00:25:35,760
+السطر وهي minor determinantبنودد قيمته سبعة في
+
+332
+00:25:35,760 --> 00:25:40,680
+ناقص اتنين ناقص اربعة عشر ناقص عشرة يعني عبارة عن
+
+333
+00:25:40,680 --> 00:25:45,680
+ناقص اربع وعشرين خلصنا اللي هو الواحد بنجي لمين
+
+334
+00:25:45,680 --> 00:25:49,600
+الان ناقص اتنين خليني نشوف يا شباب ناقص اتنين بنفس
+
+335
+00:25:49,600 --> 00:25:53,180
+الأسلوب هاي ال minor determinant اللي هو تلاتة في
+
+336
+00:25:53,180 --> 00:25:57,300
+ناقص اتنين ناقص ستة ناقص ستة وزاية ستة بطلع كده
+
+337
+00:25:57,300 --> 00:26:02,440
+سفر طيب خلصنا اللي هو اللي ناقص اتنين بنطلع لمين
+
+338
+00:26:02,440 --> 00:26:08,550
+الان للخمسة دلالخمسة المحددة
+
+339
+00:26:08,550 --> 00:26:13,900
+الثانوية للخمسةبنشطب سطر الخمسة و عمود الخمسة بطلع
+
+340
+00:26:13,900 --> 00:26:18,640
+عند المحدد بحسب قيمة المحدد خمس طعش زائد واحد و
+
+341
+00:26:18,640 --> 00:26:23,500
+عشرين بطلع اللي هو عبارة عن ستة و تلاتين خلصنا هذه
+
+342
+00:26:23,500 --> 00:26:27,420
+بنيجي للسطر الثالث اللي هو عبارة عن مين ناقص تلاتة
+
+343
+00:26:27,420 --> 00:26:31,500
+بنفس الأسلوب هي محددها محددها من وجود قيمته بتطلع
+
+344
+00:26:31,500 --> 00:26:35,880
+تسعة و تلاتين خلصنا من ناقص تلاتة بنيجي للخمسة
+
+345
+00:26:35,880 --> 00:26:40,280
+اللي هو خمسة محددها جداش بطلع بنحسبه بطلع تلت عش
+
+346
+00:26:40,810 --> 00:26:43,910
+بنفس الاسلوب اللي قبلت الان خلصنا من الخنصة ده
+
+347
+00:26:43,910 --> 00:26:48,110
+المين عندى نقص اتنين هى محددها بنحسب محددها هدف
+
+348
+00:26:48,110 --> 00:26:50,050
+هدف نقص هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+349
+00:26:50,050 --> 00:26:54,290
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+350
+00:26:54,290 --> 00:26:55,550
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+351
+00:26:55,550 --> 00:26:55,570
+هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+352
+00:26:55,570 --> 00:27:05,830
+هدف هدف هدف هدف هدف هدف هدف هدف هدف
+
+353
+00:27:05,830 --> 00:27:11,840
+هلعناصر المصفوفة يعني هذا عبارة عن محدد ثانوي
+
+354
+00:27:11,840 --> 00:27:16,780
+للتلاتة هذا عبارة عن محدد ثانوي للسبعة هذا المحدد
+
+355
+00:27:16,780 --> 00:27:20,120
+الثانوي للتانين زي ما حكينا و البجيات نفس الشيء
+
+356
+00:27:20,120 --> 00:27:25,620
+إذا هذه أول خطوة نجي للخطوة الثانية الآن الخطوة
+
+357
+00:27:25,620 --> 00:27:31,600
+الثانية بنيجي بنحدد عناصر القطر الرئيسي و عناصر
+
+358
+00:27:31,600 --> 00:27:36,660
+القطر الثانويواللي بضلنا بنقلب إشارتين بس اللي هو
+
+359
+00:27:36,660 --> 00:27:40,380
+alternate the sign of the minor which don't lie on
+
+360
+00:27:40,380 --> 00:27:44,440
+the diagonals يعني اللي هي الآن هي عندك اللي هي
+
+361
+00:27:44,440 --> 00:27:47,460
+اللي مش على القطر الرئيسي أو القطر الثانوي بدنا
+
+362
+00:27:47,460 --> 00:27:51,560
+نغير إشارتين بيصير هذا 24 وهذا 13 وهذا نقص 13 وهذا
+
+363
+00:27:51,560 --> 00:27:58,080
+إيش سالب 36 خلينا نشوفها فعلا هيها سالب 13 سالب 36
+
+364
+00:27:58,080 --> 00:28:04,640
+سالب 13 24الخطوة الثانية نجي للخطوة الثالثة الخطوة
+
+365
+00:28:04,640 --> 00:28:09,440
+الثالثة هذا الآن اللي بطلع اللي طلع في الخطوة
+
+366
+00:28:09,440 --> 00:28:13,120
+الثانية بدنا نجيبله transpose يعني بدي أجيبله إيش
+
+367
+00:28:13,120 --> 00:28:18,540
+مدور هذه المصفوفة مدورها اللي هو السطر بيصير عمود
+
+368
+00:28:18,540 --> 00:28:21,700
+السطر بيصير عمود السطر بيصير عمود بيكون أوجدنا مين
+
+369
+00:28:21,700 --> 00:28:27,580
+ل Transpose هاي عندي السطر الأول صار عمود السطر
+
+370
+00:28:27,580 --> 00:28:32,350
+الثاني صار عمودالسطر الثالث صار العمود الثالث هذا
+
+371
+00:28:32,350 --> 00:28:36,850
+اللي هو ايش بنسميه ل Transpose بالمناسبة هذا اللي
+
+372
+00:28:36,850 --> 00:28:40,730
+طلع في الخطوة الثالثة اللي هو ل Transpose هذا بعد
+
+373
+00:28:40,730 --> 00:28:47,690
+شوية هنسميه هي ال Adjoint ل Matrix M يعني لو طلب
+
+374
+00:28:47,690 --> 00:28:52,550
+عندي ال Adjoint ل Matrix M بيجيب بعمل تلت خطوات
+
+375
+00:28:52,550 --> 00:28:57,150
+نجد ال Matrix اللي هو تبع ال minor determinants
+
+376
+00:28:57,400 --> 00:29:01,980
+بنغير إشارات اللي هي العناصر كلها معدع عناصر اللي
+
+377
+00:29:01,980 --> 00:29:05,640
+هو القطر الثانوي والقطر الرئيسي وبعدين بناخدها لل
+
+378
+00:29:05,640 --> 00:29:10,240
+Transverse هذا اللي بنسمي الـ Adjunctالـ Adjoint
+
+379
+00:29:10,240 --> 00:29:14,600
+للمصفوفة الان بدي انا ال inverse ال inverse في
+
+380
+00:29:14,600 --> 00:29:18,960
+الشثّال منها ايش طالت الخطوة الأخيرة Divide By
+
+381
+00:29:18,960 --> 00:29:23,600
+Determinant بنجسم هذا بإيش بال determinant لل M
+
+382
+00:29:23,600 --> 00:29:27,500
+يعني الآن بنضرب هذا المقدار في واحد على ال minus
+
+383
+00:29:27,500 --> 00:29:32,160
+ستة وخمسين بيطلع مين هو ال M inverse بسوى ناقص
+
+384
+00:29:32,160 --> 00:29:36,540
+واحد على مية وستة وخمسين في هذا اللي هو المصفوفة
+
+385
+00:29:36,540 --> 00:29:41,740
+اللي بيطلع عندى هذا ال M inverseهو الان عبارة عن
+
+386
+00:29:41,740 --> 00:29:46,740
+اللي هي ال inverse للمصوفة اللي عندنا الان بتصور
+
+387
+00:29:46,740 --> 00:29:52,640
+الأمور واضحة الخطوة الأولى الخطوة التانية الخطوة
+
+388
+00:29:52,640 --> 00:29:56,860
+التالتة الخطوة الرابعة وكون حصلنا عالميا على ال M
+
+389
+00:29:56,860 --> 00:30:02,040
+inverse أو المعكوس الضربي للمصوفة M نجي ناخد مثال
+
+390
+00:30:02,040 --> 00:30:07,300
+تاني هي عندي المثال ايهوهي عندى بنوجد f inverse له
+
+391
+00:30:07,300 --> 00:30:12,240
+example واحد find a inverse هى ال matrix A وهى أول
+
+392
+00:30:12,240 --> 00:30:15,680
+خطوة بنعملها ايش بنوجد اللى هو ال determinant له
+
+393
+00:30:15,680 --> 00:30:19,420
+اوجدنا ال determinant زى ما بنوجد دايما بطلع عندى
+
+394
+00:30:19,420 --> 00:30:23,560
+determinant عبارة عن 32 يعنى مش سفر يعنى فعلا فش
+
+395
+00:30:23,560 --> 00:30:28,400
+عندنا ايش اللى هو في عندنا اللى هو inverse
+
+396
+00:30:28,400 --> 00:30:33,790
+للمصفوفةطيب الخطوة الأولى اللى هى بعد ما وجدنا هذه
+
+397
+00:30:33,790 --> 00:30:37,430
+طبعا خطوة رئيسية هناخدها لاحقا الان الخطوات
+
+398
+00:30:37,430 --> 00:30:40,750
+الأربعة الخطوة الأولى اللى هو ال matrix of minors
+
+399
+00:30:40,750 --> 00:30:45,410
+نجد ال matrix of minors للواحد بنشطب اللى هو السطر
+
+400
+00:30:45,410 --> 00:30:47,690
+و العمود بطلع ال determinant هذا هى ال determinant
+
+401
+00:30:47,690 --> 00:30:52,210
+للسفر هى ال determinant للتلاتة تدرب لحالك هى ال
+
+402
+00:30:52,210 --> 00:30:54,910
+determinantأولاد سبعة أو أولاد تلاتة هاي كل ان
+
+403
+00:30:54,910 --> 00:30:59,370
+هدولة مين هنا اللي هي ال matrix of minors أو
+
+404
+00:30:59,370 --> 00:31:03,130
+determinant ال matrix of minor determinants
+
+405
+00:31:03,130 --> 00:31:10,950
+المفهوم اللي هو مصفوفة مصفوفة اللي هي المحددات
+
+406
+00:31:10,950 --> 00:31:17,090
+الثانويةهي قيمة هذا هي و قيمة هذا هي و قيمة هذا هي
+
+407
+00:31:17,090 --> 00:31:17,730
+و قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة
+
+408
+00:31:17,730 --> 00:31:19,630
+هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و
+
+409
+00:31:19,630 --> 00:31:20,710
+قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا
+
+410
+00:31:20,710 --> 00:31:24,290
+هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و
+
+411
+00:31:24,290 --> 00:31:27,950
+قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا
+
+412
+00:31:27,950 --> 00:31:28,550
+هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و
+
+413
+00:31:28,550 --> 00:31:33,590
+قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا
+
+414
+00:31:33,590 --> 00:31:38,410
+هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و
+
+415
+00:31:38,410 --> 00:31:41,030
+قيمة هذا هي و قيمة هذا هي و قيمة هذا هي و قيمة هذا
+
+416
+00:31:41,030 --> 00:31:42,200
+هي و قيمة هذا هي و قيمة هذا هي وهيتطلع على اللي
+
+417
+00:31:42,200 --> 00:31:45,280
+قبل عشان ما تنساش الناقص تمنع و تلاتين هي صارت
+
+418
+00:31:45,280 --> 00:31:47,460
+ناقص تمنع و تلاتين هذي صارت ستة هذي صارت ناقص
+
+419
+00:31:47,460 --> 00:31:51,980
+اتنين هذي صارت اتنين و عشرين مظبوط طيب الخطوة
+
+420
+00:31:51,980 --> 00:31:55,600
+الثالثة اشي هذا اللي طبعا اللي بنسميه cofactor
+
+421
+00:31:55,600 --> 00:31:59,380
+matrix يعني اللي بنغير إشارات من ال .. ال .. ال ..
+
+422
+00:31:59,380 --> 00:32:06,570
+ال matrix معدة أنصر الأقطار اللي موجودةالخطوة
+
+423
+00:32:06,570 --> 00:32:09,390
+التالتة هي ان نجيب الـ Transpose نجيب اللي هو مدور
+
+424
+00:32:09,390 --> 00:32:12,870
+المصوفة لـ Transpose اللي هو بيصير هذا السطر هي
+
+425
+00:32:12,870 --> 00:32:19,330
+عمود و هذا السطر هي عمود و هذا السطر هي عمود هذا
+
+426
+00:32:19,330 --> 00:32:24,210
+ال Transpose هو اللي بنسميه الـ Adjoint لميلة A
+
+427
+00:32:24,210 --> 00:32:27,870
+اللي حكيته قبل بشوية بيصير عندى الآن اللي هي
+
+428
+00:32:27,870 --> 00:32:31,890
+الخطوة الأخيرة الرابعة الـ A inverse بسوء 1 على 32
+
+429
+00:32:31,890 --> 00:32:35,550
+اللي هي قيمة الـ Determinantمضروبة في هذا ال
+
+430
+00:32:35,550 --> 00:32:38,010
+matrix اللي .. اللي .. اللي .. اللي هو ال CT
+
+431
+00:32:38,010 --> 00:32:42,610
+سمناها وبطلع عندى اللى هي القيمة اللى أمامى هذا
+
+432
+00:32:42,610 --> 00:32:46,230
+اللى بنسميه اللى هو ال inverse أو المعقوس اللى
+
+433
+00:32:46,230 --> 00:32:51,510
+ضربنا مين يا جماعة لما صوفة لو مثال آخر جالي find
+
+434
+00:32:51,510 --> 00:32:55,050
+A inverse الآن بدا نوجد ال A inverse بالصورة اللى
+
+435
+00:32:55,050 --> 00:32:59,170
+حكينا عنها قبل بشوية اللى هو هى ال A و ال A
+
+436
+00:32:59,170 --> 00:33:01,790
+inverse إيش بساوي واحد على ال determinant في ال
+
+437
+00:33:01,790 --> 00:33:06,200
+adjointإيش ال adjoint بدنا نوجده اللي قلنا عنه قبل
+
+438
+00:33:06,200 --> 00:33:08,780
+بشوية و إيش ال determinant اللي أنتوا عارفينه ال
+
+439
+00:33:08,780 --> 00:33:13,740
+determinant لهذا بساوي قيمة المحدد هذا و هيطلع لنا
+
+440
+00:33:13,740 --> 00:33:17,980
+القيمة عبارة عن قداش خمسة لو جربت أنت توجدها لحدك
+
+441
+00:33:17,980 --> 00:33:22,100
+نيجي لمين لإيه نوجد ال adjoint لإيه عشان نوجد ال
+
+442
+00:33:22,100 --> 00:33:25,700
+adjoint أول إشي بدنا نوجد مين ال minors هذا ال
+
+443
+00:33:25,700 --> 00:33:29,360
+minors هذا اللي هو قيمة ال determinant للعنصر
+
+444
+00:33:29,360 --> 00:33:32,950
+الأول determinant الثانويوهذا للعنصر التاني وهذا
+
+445
+00:33:32,950 --> 00:33:36,650
+للعنصر الثالث زي ما وجدنا قبل قليل والتفاصيل لكم
+
+446
+00:33:36,650 --> 00:33:41,180
+الحساباتوجدنا الـ Minors بعد ما نجد الـ Minors
+
+447
+00:33:41,180 --> 00:33:45,680
+بنجد الـ Co-Factor ماهو الـ Co-Factor؟ بنحدد هى
+
+448
+00:33:45,680 --> 00:33:49,860
+القطر الرئيسي وهى القطر الثانوي ومن هدولة بنغير
+
+449
+00:33:49,860 --> 00:33:56,140
+إشاراتين هذا بيصير 25 هذا بيصير 4 هذا بيصير 5 وهذا
+
+450
+00:33:56,140 --> 00:34:01,180
+بيصير 18 هى اللي هو الـ Co-Factor عملية تغيير
+
+451
+00:34:01,180 --> 00:34:06,020
+الإشارات للعناصر غير عناصر القطر التانوي والقطر
+
+452
+00:34:06,020 --> 00:34:11,100
+الرئيسيالان الـ Cofactor اللى هو C أوددناه ضال
+
+453
+00:34:11,100 --> 00:34:14,880
+عندنا نودد مين ال Adjoint ال Adjoint مين هو ال
+
+454
+00:34:14,880 --> 00:34:18,980
+Transpose لهذا هى أوددناه ال Transpose سهل ال
+
+455
+00:34:18,980 --> 00:34:24,180
+Transpose كلكم بعرفها هيه بيصير عمود سطر بيصير
+
+456
+00:34:24,180 --> 00:34:28,120
+عمود سطر بيصير عمود خلصنا ال Adjoint بدنا نودد ال
+
+457
+00:34:28,120 --> 00:34:31,100
+A-Inverse ال A-Inverse إيش هى؟ واحد عقيمة ال
+
+458
+00:34:31,100 --> 00:34:34,570
+determinant اللى أوددناه قبل و شويةاللي هو مضروب
+
+459
+00:34:34,570 --> 00:34:37,630
+في الـ Adjoint اللي هو عبارة عن واحدة لخمسة اللي
+
+460
+00:34:37,630 --> 00:34:41,530
+هو ال determinant خمسة مضروب في ال Adjoint اللي هو
+
+461
+00:34:41,530 --> 00:34:46,810
+هاي ال Adjoint هيك فبكون احنا اوددنا ال A inverse
+
+462
+00:34:46,810 --> 00:34:52,070
+لمين ل ال matrix اللي ال determinant له مش سفر
+
+463
+00:34:52,070 --> 00:34:57,060
+الان عندك الجزء الثاني من الوادياللي هو ال
+
+464
+00:34:57,060 --> 00:35:00,540
+question هو ان انا ال a هيو و هي ال a inverse
+
+465
+00:35:00,540 --> 00:35:03,760
+بالسوية واحدة ال determinant في ال adjoint او جدل
+
+466
+00:35:03,760 --> 00:35:07,820
+ال a inverse او جدلي هذا الكلام بالتفصيل او جدل ال
+
+467
+00:35:07,820 --> 00:35:10,760
+determinant و بعدين او جدل ال adjoint زي ما احنا
+
+468
+00:35:10,760 --> 00:35:14,600
+قلنا اللي قبل و هيطلع عندك الجواب a inverse
+
+469
+00:35:14,600 --> 00:35:19,990
+بالسوية كده انا بدي منك التفاصيل في الواجبالان
+
+470
+00:35:19,990 --> 00:35:24,190
+المرة القادمة ان شاء الله بنكمل و بندخل على الهو
+
+471
+00:35:24,190 --> 00:35:27,830
+solving linear equations using inverse matrix
+
+472
+00:35:27,830 --> 00:35:32,330
+والسلام عليكم ورحمة الله وبركاته وإلى لقاء آخر
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..de981d21a8cc9bea104c527280c6a78888c61f2f
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/OYaf6xTTops_raw.json
@@ -0,0 +1 @@
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"word": " N×N", "probability": 0.7898763020833334}, {"start": 81.15, "end": 81.73, "word": " بصورة", "probability": 0.990966796875}, {"start": 81.73, "end": 82.25, "word": " عامة", "probability": 0.99853515625}], "temperature": 1.0}, {"id": 5, "seek": 10235, "start": 82.69, "end": 102.35, "text": "أحنا الآن هنتعرف في البداية شو معنات أو ما هو محدد المصفوفة the determinant of المصفوفة اللي هي المكوّنة من اللي هو او من الدرجة اتنين في اتنين اللي هي A,B,C,D اللي أمامنا", "tokens": [10721, 5016, 8315, 6024, 48506, 8032, 29399, 3615, 28480, 8978, 29739, 28259, 10632, 13412, 2407, 20449, 8315, 2655, 34051, 19446, 31439, 3714, 24401, 3215, 9673, 9381, 5172, 38688, 3660, 264, 41296, 295, 9673, 9381, 5172, 38688, 3660, 13672, 1829, 39896, 9673, 4117, 2407, 11703, 1863, 3660, 9154, 13672, 1829, 31439, 1975, 2407, 9154, 32748, 47341, 3660, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 13672, 1829, 39896, 316, 11, 33, 11, 34, 11, 35, 13672, 1829, 5551, 2304, 10943, 8315], "avg_logprob": 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"word": " المصفوفة", "probability": 0.962109375}, {"start": 89.09, "end": 89.39, "word": " the", "probability": 0.1951904296875}, {"start": 89.39, "end": 89.93, "word": " determinant", "probability": 0.83203125}, {"start": 89.93, "end": 90.71, "word": " of", "probability": 0.97607421875}, {"start": 90.71, "end": 91.87, "word": " المصفوفة", "probability": 0.98583984375}, {"start": 91.87, "end": 92.31, "word": " اللي", "probability": 0.72314453125}, {"start": 92.31, "end": 92.69, "word": " هي", "probability": 0.79931640625}, {"start": 92.69, "end": 95.33, "word": " المكوّنة", "probability": 0.797607421875}, {"start": 95.33, "end": 95.63, "word": " من", "probability": 0.904296875}, {"start": 95.63, "end": 96.09, "word": " اللي", "probability": 0.595703125}, {"start": 96.09, "end": 96.31, "word": " هو", "probability": 0.98681640625}, {"start": 96.31, "end": 96.65, "word": " او", "probability": 0.72216796875}, {"start": 96.65, "end": 96.95, "word": " من", "probability": 0.97216796875}, {"start": 96.95, "end": 97.55, "word": " الدرجة", "probability": 0.955078125}, {"start": 97.55, "end": 97.99, "word": " اتنين", "probability": 0.8756103515625}, {"start": 97.99, "end": 98.13, "word": " في", "probability": 0.75537109375}, {"start": 98.13, "end": 98.65, "word": " اتنين", "probability": 0.98583984375}, {"start": 98.65, "end": 99.51, "word": " اللي", "probability": 0.95458984375}, {"start": 99.51, "end": 99.99, "word": " هي", "probability": 0.91845703125}, {"start": 99.99, "end": 100.51, "word": " A", "probability": 0.325927734375}, {"start": 100.51, "end": 100.73, "word": ",B", "probability": 0.69677734375}, {"start": 100.73, "end": 101.15, "word": ",C", "probability": 0.987060546875}, {"start": 101.15, "end": 101.41, "word": ",D", "probability": 0.988037109375}, {"start": 101.41, "end": 101.79, "word": " اللي", "probability": 0.885009765625}, {"start": 101.79, "end": 102.35, "word": " أمامنا", "probability": 0.9188232421875}], "temperature": 1.0}, {"id": 6, "seek": 13063, "start": 102.7, "end": 130.64, "text": "تعريف محدد المصوفة أو the determinant of the matrix هو كمالي طبعا بنرمزله بالرامز اللي هو column هنا و column هنا أو اللي هو عمود من هنا و عمود من هنا و بينهم مكتوبة نفس المصوفة العادية نود المحدد بيجي بنضرب عناصر القطر الرئيسي ناقص عناصر القطر التانوي يعني بمعنى أخر محدد المصوفة عبارة عن رقم هيطلع", "tokens": [2655, 3615, 16572, 5172, 3714, 24401, 3215, 9673, 9381, 38688, 3660, 34051, 264, 41296, 295, 264, 8141, 31439, 9122, 2304, 6027, 1829, 23032, 3555, 3615, 995, 44945, 2288, 2304, 11622, 43761, 20666, 2288, 10943, 11622, 13672, 1829, 31439, 7738, 34105, 4032, 7738, 34105, 34051, 13672, 1829, 31439, 6225, 2304, 23328, 9154, 34105, 4032, 6225, 2304, 23328, 9154, 34105, 4032, 49374, 16095, 3714, 4117, 2655, 37746, 3660, 8717, 36178, 9673, 9381, 38688, 3660, 18863, 18513, 10632, 8717, 23328, 9673, 24401, 3215, 4724, 1829, 7435, 1829, 44945, 11242, 25513, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 8717, 995, 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47306, "start": 453.44, "end": 473.06, "text": "عندي لاحظ و لما احنا اوجدنا اللى هو محدد المصوفة من الدرجة الثانية ما لازمش لغير هذا نوجده لحاله لكن لما اوجدنا محدد لمصوفة من تلاتة في تلاتة طلق لزمن اكم محدد ثانوي تلاتة واحد اتنين تلاتة يعني بدرجة المحدد", "tokens": [3615, 1863, 16254, 20193, 5016, 19913, 4032, 5296, 15042, 1975, 5016, 8315, 1975, 29245, 3215, 8315, 13672, 7578, 31439, 3714, 24401, 3215, 9673, 9381, 38688, 3660, 9154, 32748, 47341, 3660, 6024, 104, 7649, 10632, 19446, 5296, 31377, 2304, 8592, 5296, 17082, 13546, 23758, 8717, 29245, 3215, 3224, 5296, 5016, 6027, 3224, 44381, 5296, 15042, 1975, 29245, 3215, 8315, 3714, 24401, 3215, 32767, 9381, 38688, 3660, 9154, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 23032, 1211, 4587, 5296, 11622, 27842, 1975, 24793, 3714, 24401, 3215, 38637, 7649, 45865, 6055, 1211, 9307, 3660, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 37495, 22653, 47525, 47341, 3660, 9673, 24401, 3215], "avg_logprob": -0.1907087042927742, "compression_ratio": 2.1686046511627906, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 453.44, "end": 454.36, "word": "عندي", "probability": 0.68505859375}, {"start": 454.36, "end": 454.78, "word": " لاحظ", "probability": 0.9256184895833334}, {"start": 454.78, "end": 454.88, "word": " و", "probability": 0.5703125}, {"start": 454.88, "end": 455.08, "word": " لما", "probability": 0.740478515625}, {"start": 455.08, "end": 455.46, "word": " احنا", "probability": 0.7435709635416666}, {"start": 455.46, "end": 456.26, "word": " اوجدنا", "probability": 0.759033203125}, {"start": 456.26, "end": 456.46, "word": " اللى", "probability": 0.4571533203125}, {"start": 456.46, "end": 456.68, "word": " هو", "probability": 0.9326171875}, {"start": 456.68, "end": 457.16, "word": " محدد", "probability": 0.9806315104166666}, {"start": 457.16, "end": 457.78, "word": " المصوفة", "probability": 0.803466796875}, {"start": 457.78, "end": 458.0, "word": " من", "probability": 0.986328125}, {"start": 458.0, "end": 458.66, "word": " الدرجة", "probability": 0.9495442708333334}, {"start": 458.66, "end": 459.1, "word": " الثانية", "probability": 0.9342041015625}, {"start": 459.1, "end": 459.3, "word": " ما", "probability": 0.59716796875}, {"start": 459.3, "end": 459.76, "word": " لازمش", "probability": 0.758392333984375}, {"start": 459.76, "end": 460.06, "word": " لغير", "probability": 0.747802734375}, {"start": 460.06, "end": 460.28, "word": " هذا", "probability": 0.93115234375}, {"start": 460.28, "end": 460.72, "word": " نوجده", "probability": 0.8675537109375}, {"start": 460.72, "end": 461.2, "word": " لحاله", "probability": 0.95751953125}, {"start": 461.2, "end": 461.78, "word": " لكن", "probability": 0.734375}, {"start": 461.78, "end": 462.06, "word": " لما", "probability": 0.966064453125}, {"start": 462.06, "end": 462.7, "word": " اوجدنا", "probability": 0.92822265625}, {"start": 462.7, "end": 463.22, "word": " محدد", "probability": 0.98681640625}, {"start": 463.22, "end": 464.26, "word": " لمصوفة", "probability": 0.85137939453125}, {"start": 464.26, "end": 464.8, "word": " من", "probability": 0.96240234375}, {"start": 464.8, "end": 465.32, "word": " تلاتة", "probability": 0.8795166015625}, {"start": 465.32, "end": 465.4, "word": " في", "probability": 0.62890625}, {"start": 465.4, "end": 465.82, "word": " تلاتة", "probability": 0.96240234375}, {"start": 465.82, "end": 466.12, "word": " طلق", "probability": 0.542236328125}, {"start": 466.12, "end": 466.6, "word": " لزمن", "probability": 0.8819986979166666}, {"start": 466.6, "end": 466.96, "word": " اكم", "probability": 0.7138671875}, {"start": 466.96, "end": 468.92, "word": " محدد", "probability": 0.8870442708333334}, {"start": 468.92, "end": 469.38, "word": " ثانوي", "probability": 0.9793294270833334}, {"start": 469.38, "end": 469.92, "word": " تلاتة", "probability": 0.9228515625}, {"start": 469.92, "end": 470.26, "word": " واحد", "probability": 0.7454833984375}, {"start": 470.26, "end": 470.66, "word": " اتنين", "probability": 0.8580322265625}, {"start": 470.66, "end": 471.3, "word": " تلاتة", "probability": 0.97119140625}, {"start": 471.3, "end": 471.82, "word": " يعني", "probability": 0.91259765625}, {"start": 471.82, "end": 472.36, "word": " بدرجة", "probability": 0.8984375}, {"start": 472.36, "end": 473.06, "word": " المحدد", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 23, "seek": 49831, "start": 473.27, "end": 498.31, "text": "و لو كان في عندنا matrix أربعة في أربعة بنعمل بنفس الأسلوب بس اللي بطلع إن عندنا المحددات الثانوية اللي هي تلاتة في تلاتة بنعمل محن زي ما عملنا مع مين مع اللي هو هذا السؤال الان وهكذا بصورة عامة الان احنا يعني هنشتغل شغلنا بس على المحددات اللي وهين اللي هي من الدرجة تلاتة في تلاتة أو اتنين في اتنين", "tokens": [2407, 45164, 25961, 8978, 43242, 8315, 8141, 5551, 25513, 27884, 8978, 5551, 25513, 27884, 44945, 25957, 1211, 44945, 36178, 16247, 3794, 1211, 37746, 4724, 3794, 13672, 1829, 4724, 9566, 1211, 3615, 36145, 43242, 8315, 9673, 24401, 3215, 9307, 6024, 104, 7649, 2407, 10632, 13672, 1829, 39896, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 44945, 25957, 1211, 3714, 5016, 1863, 30767, 1829, 19446, 6225, 42213, 8315, 20449, 3714, 9957, 20449, 13672, 1829, 31439, 23758, 21136, 33604, 6027, 2423, 7649, 37037, 4117, 15730, 4724, 9381, 13063, 3660, 6225, 10943, 3660, 2423, 7649, 1975, 5016, 8315, 37495, 22653, 8032, 1863, 8592, 2655, 17082, 1211, 13412, 17082, 1211, 8315, 4724, 3794, 15844, 9673, 24401, 3215, 9307, 13672, 1829, 37037, 9957, 13672, 1829, 39896, 9154, 32748, 47341, 3660, 6055, 1211, 9307, 3660, 8978, 6055, 1211, 9307, 3660, 34051, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957], "avg_logprob": -0.12403016912526098, "compression_ratio": 2.1893004115226335, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 473.27, "end": 473.45, "word": "و", "probability": 0.67138671875}, {"start": 473.45, "end": 473.67, "word": " لو", "probability": 0.73388671875}, {"start": 473.67, "end": 473.95, "word": " كان", "probability": 0.9775390625}, {"start": 473.95, "end": 474.13, "word": " في", "probability": 0.7900390625}, {"start": 474.13, "end": 474.63, "word": " عندنا", "probability": 0.78955078125}, {"start": 474.63, "end": 475.09, "word": " matrix", "probability": 0.74609375}, {"start": 475.09, "end": 475.61, "word": " أربعة", "probability": 0.638427734375}, {"start": 475.61, "end": 475.77, "word": " في", "probability": 0.515625}, {"start": 475.77, "end": 476.11, "word": " أربعة", "probability": 0.9684244791666666}, {"start": 476.11, "end": 476.55, "word": " بنعمل", "probability": 0.8273111979166666}, {"start": 476.55, "end": 477.11, "word": " بنفس", "probability": 0.986328125}, {"start": 477.11, "end": 477.93, "word": " الأسلوب", "probability": 0.9022216796875}, {"start": 477.93, "end": 478.51, "word": " بس", "probability": 0.941162109375}, {"start": 478.51, "end": 478.69, "word": " اللي", "probability": 0.919921875}, {"start": 478.69, "end": 479.09, "word": " بطلع", "probability": 0.81884765625}, {"start": 479.09, "end": 479.25, "word": " إن", "probability": 0.51806640625}, {"start": 479.25, "end": 479.67, "word": " عندنا", "probability": 0.978515625}, {"start": 479.67, "end": 480.41, "word": " المحددات", "probability": 0.9742431640625}, {"start": 480.41, "end": 481.19, "word": " الثانوية", "probability": 0.95048828125}, {"start": 481.19, "end": 481.49, "word": " اللي", "probability": 0.88623046875}, {"start": 481.49, "end": 481.73, "word": " هي", "probability": 0.91748046875}, {"start": 481.73, "end": 482.25, "word": " تلاتة", "probability": 0.9471435546875}, {"start": 482.25, "end": 482.37, "word": " في", "probability": 0.96533203125}, {"start": 482.37, "end": 482.91, "word": " تلاتة", "probability": 0.9869384765625}, {"start": 482.91, "end": 483.97, "word": " بنعمل", "probability": 0.9166666666666666}, {"start": 483.97, "end": 484.41, "word": " محن", "probability": 0.87109375}, {"start": 484.41, "end": 484.67, "word": " زي", "probability": 0.971923828125}, {"start": 484.67, "end": 484.79, "word": " ما", "probability": 0.98046875}, {"start": 484.79, "end": 485.21, "word": " عملنا", "probability": 0.9794921875}, {"start": 485.21, "end": 485.41, "word": " مع", "probability": 0.98779296875}, {"start": 485.41, "end": 485.87, "word": " مين", "probability": 0.7666015625}, {"start": 485.87, "end": 486.37, "word": " مع", "probability": 0.73193359375}, {"start": 486.37, "end": 486.63, "word": " اللي", "probability": 0.943603515625}, {"start": 486.63, "end": 486.95, "word": " هو", "probability": 0.97412109375}, {"start": 486.95, "end": 487.53, "word": " هذا", "probability": 0.94921875}, {"start": 487.53, "end": 489.01, "word": " السؤال", "probability": 0.9925130208333334}, {"start": 489.01, "end": 489.95, "word": " الان", "probability": 0.65478515625}, {"start": 489.95, "end": 491.15, "word": " وهكذا", "probability": 0.8096516927083334}, {"start": 491.15, "end": 491.57, "word": " بصورة", "probability": 0.994384765625}, {"start": 491.57, "end": 491.93, "word": " عامة", "probability": 0.998046875}, {"start": 491.93, "end": 492.31, "word": " الان", "probability": 0.8251953125}, {"start": 492.31, "end": 492.65, "word": " احنا", "probability": 0.89794921875}, {"start": 492.65, "end": 492.97, "word": " يعني", "probability": 0.873291015625}, {"start": 492.97, "end": 493.69, "word": " هنشتغل", "probability": 0.9676920572916666}, {"start": 493.69, "end": 494.11, "word": " شغلنا", "probability": 0.9930419921875}, {"start": 494.11, "end": 494.29, "word": " بس", "probability": 0.95556640625}, {"start": 494.29, "end": 494.37, "word": " على", "probability": 0.481689453125}, {"start": 494.37, "end": 494.95, "word": " المحددات", "probability": 0.991943359375}, {"start": 494.95, "end": 495.13, "word": " اللي", "probability": 0.9833984375}, {"start": 495.13, "end": 495.45, "word": " وهين", "probability": 0.525634765625}, {"start": 495.45, "end": 495.63, "word": " اللي", "probability": 0.979248046875}, {"start": 495.63, "end": 495.79, "word": " هي", "probability": 0.78662109375}, {"start": 495.79, "end": 495.93, "word": " من", "probability": 0.98388671875}, {"start": 495.93, "end": 496.33, "word": " الدرجة", "probability": 0.9181315104166666}, {"start": 496.33, "end": 496.63, "word": " تلاتة", "probability": 0.941650390625}, {"start": 496.63, "end": 496.71, "word": " في", "probability": 0.96923828125}, {"start": 496.71, "end": 497.09, "word": " تلاتة", "probability": 0.9898681640625}, {"start": 497.09, "end": 497.27, "word": " أو", "probability": 0.5498046875}, {"start": 497.27, "end": 497.71, "word": " اتنين", "probability": 0.95703125}, {"start": 497.71, "end": 497.95, "word": " في", "probability": 0.98193359375}, {"start": 497.95, "end": 498.31, "word": " اتنين", "probability": 0.9881591796875}], "temperature": 1.0}, {"id": 24, "seek": 52362, "start": 498.92, "end": 523.62, "text": "الان بدنا نعرف حاجة اسمها the inverse of a matrix اللي هو الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من هذه المحاضرة الهدف التاني من", "tokens": [6027, 7649, 47525, 8315, 8717, 3615, 28480, 11331, 26108, 3660, 24525, 2304, 11296, 264, 17340, 295, 257, 8141, 13672, 1829, 31439, 2423, 3224, 3215, 5172, 16712, 7649, 1829, 9154, 29538, 9673, 5016, 46958, 25720, 2423, 3224, 3215, 5172, 16712, 7649, 1829, 9154, 29538, 9673, 5016, 46958, 25720, 2423, 3224, 3215, 5172, 16712, 7649, 1829, 9154, 29538, 9673, 5016, 46958, 25720, 2423, 3224, 3215, 5172, 16712, 7649, 1829, 9154, 29538, 9673, 5016, 46958, 25720, 2423, 3224, 3215, 5172, 16712, 7649, 1829, 9154, 29538, 9673, 5016, 46958, 25720, 2423, 3224, 3215, 5172, 16712, 7649, 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"probability": 0.81591796875}, {"start": 499.4, "end": 499.74, "word": " بدنا", "probability": 0.693359375}, {"start": 499.74, "end": 500.34, "word": " نعرف", "probability": 0.95458984375}, {"start": 500.34, "end": 501.0, "word": " حاجة", "probability": 0.9305013020833334}, {"start": 501.0, "end": 501.64, "word": " اسمها", "probability": 0.9669596354166666}, {"start": 501.64, "end": 502.18, "word": " the", "probability": 0.318359375}, {"start": 502.18, "end": 502.78, "word": " inverse", "probability": 0.9033203125}, {"start": 502.78, "end": 503.12, "word": " of", "probability": 0.96337890625}, {"start": 503.12, "end": 503.32, "word": " a", "probability": 0.89306640625}, {"start": 503.32, "end": 503.68, "word": " matrix", "probability": 0.9443359375}, {"start": 503.68, "end": 503.9, "word": " اللي", "probability": 0.625244140625}, {"start": 503.9, "end": 504.0, "word": " هو", "probability": 0.876953125}, {"start": 504.0, "end": 504.4, "word": " الهدف", "probability": 0.9844970703125}, {"start": 504.4, "end": 505.0, "word": " التاني", "probability": 0.89794921875}, {"start": 505.0, "end": 505.32, "word": " من", "probability": 0.9248046875}, {"start": 505.32, "end": 505.98, "word": " هذه", "probability": 0.34228515625}, {"start": 505.98, "end": 507.14, "word": " المحاضرة", "probability": 0.9849853515625}, {"start": 507.14, "end": 507.7, "word": " الهدف", "probability": 0.6644287109375}, {"start": 507.7, "end": 507.7, "word": " التاني", "probability": 0.92138671875}, {"start": 507.7, "end": 507.7, "word": " من", "probability": 0.77490234375}, {"start": 507.7, "end": 507.7, "word": " هذه", "probability": 0.88671875}, {"start": 507.7, "end": 507.7, "word": " المحاضرة", "probability": 0.9937744140625}, {"start": 507.7, "end": 507.76, "word": " الهدف", "probability": 0.8355712890625}, {"start": 507.76, "end": 507.76, "word": " التاني", "probability": 0.9801432291666666}, {"start": 507.76, "end": 507.76, "word": " من", "probability": 0.90283203125}, {"start": 507.76, "end": 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"word": " الهدف", "probability": 0.9385986328125}, {"start": 508.74, "end": 508.74, "word": " التاني", "probability": 0.9855143229166666}, {"start": 508.74, "end": 508.74, "word": " من", "probability": 0.9140625}, {"start": 508.74, "end": 508.74, "word": " هذه", "probability": 0.96435546875}, {"start": 508.74, "end": 508.74, "word": " المحاضرة", "probability": 0.99609375}, {"start": 508.74, "end": 509.48, "word": " الهدف", "probability": 0.9443359375}, {"start": 509.48, "end": 509.48, "word": " التاني", "probability": 0.9864908854166666}, {"start": 509.48, "end": 509.62, "word": " من", "probability": 0.9248046875}, {"start": 509.62, "end": 509.62, "word": " هذه", "probability": 0.96728515625}, {"start": 509.62, "end": 509.62, "word": " المحاضرة", "probability": 0.9964599609375}, {"start": 509.62, "end": 509.62, "word": " الهدف", "probability": 0.95263671875}, {"start": 509.62, "end": 509.62, "word": " التاني", "probability": 0.9879557291666666}, {"start": 509.62, "end": 509.66, "word": 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0.9562174479166666}, {"start": 514.94, "end": 515.42, "word": " من", "probability": 0.99267578125}, {"start": 515.42, "end": 515.84, "word": " هذه", "probability": 0.98193359375}, {"start": 515.84, "end": 516.46, "word": " المحاضرة", "probability": 0.99658203125}, {"start": 516.46, "end": 517.78, "word": " الهدف", "probability": 0.9912109375}, {"start": 517.78, "end": 517.82, "word": " التاني", "probability": 0.94189453125}, {"start": 517.82, "end": 518.26, "word": " من", "probability": 0.99365234375}, {"start": 518.26, "end": 518.5, "word": " هذه", "probability": 0.9814453125}, {"start": 518.5, "end": 519.5, "word": " المحاضرة", "probability": 0.996337890625}, {"start": 519.5, "end": 520.58, "word": " الهدف", "probability": 0.9923095703125}, {"start": 520.58, "end": 520.58, "word": " التاني", "probability": 0.9239908854166666}, {"start": 520.58, "end": 520.58, "word": " من", "probability": 0.99365234375}, {"start": 520.58, "end": 520.64, "word": " هذه", "probability": 0.98095703125}, {"start": 520.64, "end": 523.3, "word": " المحاضرة", "probability": 0.99609375}, {"start": 523.3, "end": 523.46, "word": " الهدف", "probability": 0.9925537109375}, {"start": 523.46, "end": 523.62, "word": " التاني", "probability": 0.8743489583333334}, {"start": 523.62, "end": 523.62, "word": " من", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 25, "seek": 52841, "start": 523.9, "end": 528.42, "text": "2×2، 3×3، 4×4، 5×5 الاخرى", "tokens": [17, 37550, 17, 12399, 805, 37550, 18, 12399, 1017, 37550, 19, 12399, 1025, 37550, 20, 2423, 47283, 2288, 7578], "avg_logprob": -0.45234375149011613, "compression_ratio": 0.8444444444444444, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 523.9, "end": 525.06, "word": "2×2،", "probability": 0.37139129638671875}, {"start": 525.06, "end": 525.96, "word": " 3×3،", "probability": 0.959228515625}, {"start": 525.96, "end": 526.7, "word": " 4×4،", "probability": 0.9759521484375}, {"start": 526.7, "end": 527.4, "word": " 5×5", "probability": 0.9894205729166666}, {"start": 527.4, "end": 528.42, "word": " الاخرى", "probability": 0.62518310546875}], "temperature": 1.0}, {"id": 26, "seek": 55591, "start": 531.71, "end": 555.91, "text": "non-singular يعني بمعنى آخر اللي هي اللي بنسميها المصهوفة اللي بيكون محددها مش سفر لما يكون محددها مش سفر بنضمن اللي هو بعد شوية هتشوف التعريف أنه في إلها معكوس ضربي إذا المصهوفة اللي بتكون non-singular هي المصهوفة اللي محددها لا يساوي سفر", "tokens": [30092, 12, 82, 278, 1040, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 13672, 1829, 39896, 13672, 1829, 44945, 38251, 1829, 11296, 9673, 9381, 3224, 38688, 3660, 13672, 1829, 4724, 1829, 30544, 3714, 24401, 3215, 11296, 37893, 8608, 5172, 2288, 5296, 15042, 7251, 30544, 3714, 24401, 3215, 11296, 37893, 8608, 5172, 2288, 44945, 11242, 27842, 13672, 1829, 31439, 39182, 13412, 2407, 10632, 8032, 2655, 8592, 38688, 16712, 3615, 16572, 5172, 14739, 3224, 8978, 11933, 1211, 11296, 20449, 4117, 41779, 48812, 2288, 21292, 11933, 15730, 9673, 9381, 3224, 38688, 3660, 13672, 1829, 39894, 30544, 2107, 12, 82, 278, 1040, 39896, 9673, 9381, 3224, 38688, 3660, 13672, 1829, 3714, 24401, 3215, 11296, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.1282552145421505, "compression_ratio": 2.1020408163265305, "no_speech_prob": 3.159046173095703e-06, "words": [{"start": 531.71, "end": 532.09, "word": "non", "probability": 0.332763671875}, {"start": 532.09, "end": 532.99, "word": "-singular", "probability": 0.77642822265625}, {"start": 532.99, "end": 534.99, "word": " يعني", "probability": 0.760986328125}, {"start": 534.99, "end": 535.47, "word": " بمعنى", "probability": 0.96923828125}, {"start": 535.47, "end": 535.95, "word": " آخر", "probability": 0.761962890625}, {"start": 535.95, "end": 536.41, "word": " اللي", "probability": 0.797119140625}, {"start": 536.41, "end": 536.61, "word": " هي", "probability": 0.67919921875}, {"start": 536.61, "end": 536.83, "word": " اللي", "probability": 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0.994140625}, {"start": 543.45, "end": 544.37, "word": " بنضمن", "probability": 0.9715169270833334}, {"start": 544.37, "end": 544.73, "word": " اللي", "probability": 0.974853515625}, {"start": 544.73, "end": 544.91, "word": " هو", "probability": 0.98095703125}, {"start": 544.91, "end": 545.11, "word": " بعد", "probability": 0.884765625}, {"start": 545.11, "end": 545.35, "word": " شوية", "probability": 0.8585611979166666}, {"start": 545.35, "end": 545.63, "word": " هتشوف", "probability": 0.9852294921875}, {"start": 545.63, "end": 546.17, "word": " التعريف", "probability": 0.98291015625}, {"start": 546.17, "end": 546.79, "word": " أنه", "probability": 0.630126953125}, {"start": 546.79, "end": 547.03, "word": " في", "probability": 0.93310546875}, {"start": 547.03, "end": 547.73, "word": " إلها", "probability": 0.7706705729166666}, {"start": 547.73, "end": 548.57, "word": " معكوس", "probability": 0.84033203125}, {"start": 548.57, "end": 549.09, "word": " ضربي", "probability": 0.7688802083333334}, {"start": 549.09, "end": 549.89, "word": " إذا", "probability": 0.63623046875}, {"start": 549.89, "end": 550.61, "word": " المصهوفة", "probability": 0.97099609375}, {"start": 550.61, "end": 550.71, "word": " اللي", "probability": 0.989013671875}, {"start": 550.71, "end": 551.15, "word": " بتكون", "probability": 0.95068359375}, {"start": 551.15, "end": 551.43, "word": " non", "probability": 0.94482421875}, {"start": 551.43, "end": 552.03, "word": "-singular", "probability": 0.8917236328125}, {"start": 552.03, "end": 552.25, "word": " هي", "probability": 0.9267578125}, {"start": 552.25, "end": 553.29, "word": " المصهوفة", "probability": 0.98798828125}, {"start": 553.29, "end": 553.69, "word": " اللي", "probability": 0.938232421875}, {"start": 553.69, "end": 554.67, "word": " محددها", "probability": 0.9888916015625}, {"start": 554.67, "end": 554.89, "word": " لا", "probability": 0.85595703125}, {"start": 554.89, "end": 555.51, "word": " يساوي", "probability": 0.92529296875}, {"start": 555.51, "end": 555.91, "word": " سفر", "probability": 0.9801432291666666}], "temperature": 1.0}, {"id": 27, "seek": 57460, "start": 556.4, "end": 574.6, "text": "الان لو وجدنا ال matrix B دربناها في A بساوي I لأ طبعا هذه المصفوفة ال A اللي أخدت اللي هي ال non singular اللي هي اللي بمعنى أخر محددها مش سفر لو وجدنا مصفوفة تانية اسمها B ودربناها فيها طلعت عند ال identity", "tokens": [6027, 7649, 45164, 49610, 3215, 8315, 2423, 8141, 363, 11778, 25513, 8315, 11296, 8978, 316, 4724, 3794, 995, 45865, 286, 5296, 10721, 23032, 3555, 3615, 995, 29538, 9673, 9381, 5172, 38688, 3660, 2423, 316, 13672, 1829, 5551, 9778, 3215, 2655, 13672, 1829, 39896, 2423, 2107, 20010, 13672, 1829, 39896, 13672, 1829, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 3714, 24401, 3215, 11296, 37893, 8608, 5172, 2288, 45164, 49610, 3215, 8315, 3714, 9381, 5172, 38688, 3660, 6055, 7649, 10632, 24525, 2304, 11296, 363, 4032, 3215, 25513, 8315, 11296, 8978, 11296, 23032, 1211, 34268, 43242, 2423, 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"probability": 0.888671875}, {"start": 561.88, "end": 563.06, "word": " لأ", "probability": 0.5667724609375}, {"start": 563.06, "end": 563.34, "word": " طبعا", "probability": 0.798980712890625}, {"start": 563.34, "end": 563.48, "word": " هذه", "probability": 0.53173828125}, {"start": 563.48, "end": 563.96, "word": " المصفوفة", "probability": 0.7938720703125}, {"start": 563.96, "end": 564.06, "word": " ال", "probability": 0.34326171875}, {"start": 564.06, "end": 564.16, "word": " A", "probability": 0.433349609375}, {"start": 564.16, "end": 564.28, "word": " اللي", "probability": 0.753173828125}, {"start": 564.28, "end": 564.58, "word": " أخدت", "probability": 0.8961181640625}, {"start": 564.58, "end": 564.7, "word": " اللي", "probability": 0.544921875}, {"start": 564.7, "end": 564.9, "word": " هي", "probability": 0.89990234375}, {"start": 564.9, "end": 565.0, "word": " ال", "probability": 0.517578125}, {"start": 565.0, "end": 565.18, "word": " non", "probability": 0.72607421875}, {"start": 565.18, "end": 565.64, "word": " singular", "probability": 0.64306640625}, {"start": 565.64, "end": 566.04, "word": " اللي", "probability": 0.956298828125}, {"start": 566.04, "end": 566.24, "word": " هي", "probability": 0.7919921875}, {"start": 566.24, "end": 566.52, "word": " اللي", "probability": 0.806396484375}, {"start": 566.52, "end": 567.06, "word": " بمعنى", "probability": 0.98271484375}, {"start": 567.06, "end": 567.5, "word": " أخر", "probability": 0.7298583984375}, {"start": 567.5, "end": 568.68, "word": " محددها", "probability": 0.9305419921875}, {"start": 568.68, "end": 568.88, "word": " مش", "probability": 0.9541015625}, {"start": 568.88, "end": 569.34, "word": " سفر", "probability": 0.8640950520833334}, {"start": 569.34, "end": 569.84, "word": " لو", "probability": 0.76171875}, {"start": 569.84, "end": 570.28, "word": " وجدنا", "probability": 0.7477213541666666}, {"start": 570.28, "end": 570.76, "word": " مصفوفة", "probability": 0.97294921875}, {"start": 570.76, 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المعكوس الضربي للمصفوفة A هو ال matrix اللي لو ضربناه في المصفوفة الأصلية من اليمين أو اليسار بطلع لل identity matrix", "tokens": [2407, 11242, 25513, 8315, 11296, 9154, 25724, 3224, 3660, 6024, 104, 7649, 10632, 4724, 1829, 8978, 11933, 1829, 3224, 4724, 43042, 3224, 23032, 1211, 34268, 43242, 2423, 6575, 44945, 38251, 1829, 9673, 9381, 5172, 38688, 3660, 4724, 1829, 8978, 29538, 21542, 6027, 3660, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 17340, 24976, 28814, 1829, 3224, 44945, 2288, 2304, 11622, 1211, 11296, 9154, 34892, 2304, 11622, 316, 17340, 34051, 13672, 1829, 31439, 9673, 3615, 4117, 41779, 6024, 114, 2288, 21292, 5296, 19528, 9381, 5172, 38688, 3660, 316, 11933, 15730, 9673, 3615, 4117, 41779, 6024, 114, 2288, 21292, 5296, 19528, 9381, 5172, 38688, 3660, 316, 31439, 2423, 8141, 13672, 1829, 45164, 48812, 25513, 8315, 3224, 8978, 9673, 9381, 5172, 38688, 3660, 16247, 9381, 20292, 3660, 9154, 45595, 2304, 9957, 34051, 45595, 3794, 9640, 4724, 9566, 1211, 3615, 24976, 6575, 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"seek": 88129, "start": 853.55, "end": 881.29, "text": "بدل ما هنا في عندى اللى هو عبارة عن اربع معادلات هيطلع عندى عبارة عن تسعة معادلات ايش التسعة معادلات في تسعة مجهيل ومش عارف ايش طبعا هتغلبوا فكورة غلبة كبيرة عشان هيك بدنا نريحكم وهي في عندنا الطريقة finding the inverse of two by two matrices نشوف كيف بنوجد اللى هو ال inverse ل two by two matrices", "tokens": [3555, 3215, 1211, 19446, 34105, 8978, 43242, 7578, 13672, 7578, 31439, 6225, 3555, 9640, 3660, 18871, 1975, 25513, 3615, 20449, 18513, 1211, 9307, 8032, 1829, 9566, 1211, 3615, 43242, 7578, 6225, 3555, 9640, 3660, 18871, 6055, 3794, 27884, 20449, 18513, 1211, 9307, 1975, 1829, 8592, 16712, 3794, 27884, 20449, 18513, 1211, 9307, 8978, 6055, 3794, 27884, 3714, 7435, 3224, 26895, 4032, 2304, 8592, 6225, 9640, 5172, 1975, 1829, 8592, 23032, 3555, 3615, 995, 8032, 2655, 17082, 46152, 14407, 6156, 4117, 13063, 3660, 32771, 46152, 3660, 9122, 3555, 48923, 6225, 8592, 7649, 39896, 4117, 47525, 8315, 8717, 16572, 5016, 24793, 37037, 1829, 8978, 43242, 8315, 41950, 16572, 28671, 5006, 264, 17340, 295, 732, 538, 732, 32284, 8717, 8592, 38688, 9122, 33911, 44945, 29245, 3215, 13672, 7578, 31439, 2423, 17340, 5296, 732, 538, 732, 32284], "avg_logprob": -0.24813432835820895, "compression_ratio": 1.9834710743801653, "no_speech_prob": 1.3232231140136719e-05, "words": [{"start": 853.55, "end": 854.13, "word": "بدل", "probability": 0.6766764322916666}, {"start": 854.13, "end": 854.29, "word": " ما", "probability": 0.6748046875}, {"start": 854.29, "end": 854.61, "word": " هنا", "probability": 0.05914306640625}, {"start": 854.61, "end": 854.83, "word": " في", "probability": 0.72265625}, {"start": 854.83, "end": 855.45, "word": " عندى", "probability": 0.600830078125}, {"start": 855.45, "end": 855.75, "word": " اللى", "probability": 0.4776611328125}, {"start": 855.75, "end": 856.11, "word": " هو", "probability": 0.638671875}, {"start": 856.11, "end": 856.63, "word": " عبارة", "probability": 0.92236328125}, {"start": 856.63, "end": 856.81, "word": " عن", "probability": 0.9873046875}, {"start": 856.81, "end": 857.21, "word": " اربع", "probability": 0.7123209635416666}, {"start": 857.21, "end": 857.79, "word": " معادلات", "probability": 0.9774169921875}, {"start": 857.79, "end": 858.41, "word": " هيطلع", "probability": 0.6885498046875}, {"start": 858.41, "end": 858.83, "word": " عندى", "probability": 0.891357421875}, {"start": 858.83, "end": 859.33, "word": " عبارة", "probability": 0.976318359375}, {"start": 859.33, "end": 859.51, "word": " عن", "probability": 0.97021484375}, {"start": 859.51, "end": 859.83, "word": " تسعة", "probability": 0.89208984375}, {"start": 859.83, "end": 860.53, "word": " معادلات", "probability": 0.9835205078125}, {"start": 860.53, "end": 860.87, "word": " ايش", "probability": 0.6547037760416666}, {"start": 860.87, "end": 861.41, "word": " التسعة", "probability": 0.756103515625}, {"start": 861.41, "end": 862.05, "word": " معادلات", "probability": 0.9637451171875}, {"start": 862.05, 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866.55, "end": 866.91, "word": " هيك", "probability": 0.97509765625}, {"start": 866.91, "end": 867.39, "word": " بدنا", "probability": 0.709228515625}, {"start": 867.39, "end": 868.21, "word": " نريحكم", "probability": 0.965087890625}, {"start": 868.21, "end": 868.95, "word": " وهي", "probability": 0.6158447265625}, {"start": 868.95, "end": 869.15, "word": " في", "probability": 0.7763671875}, {"start": 869.15, "end": 869.71, "word": " عندنا", "probability": 0.870849609375}, {"start": 869.71, "end": 870.83, "word": " الطريقة", "probability": 0.9611002604166666}, {"start": 870.83, "end": 871.73, "word": " finding", "probability": 0.4306640625}, {"start": 871.73, "end": 872.15, "word": " the", "probability": 0.77978515625}, {"start": 872.15, "end": 872.65, "word": " inverse", "probability": 0.88330078125}, {"start": 872.65, "end": 872.93, "word": " of", "probability": 0.96826171875}, {"start": 872.93, "end": 873.23, "word": " two", "probability": 0.59326171875}, {"start": 873.23, "end": 873.49, "word": " by", "probability": 0.89697265625}, {"start": 873.49, "end": 874.05, "word": " two", "probability": 0.94287109375}, {"start": 874.05, "end": 875.27, "word": " matrices", "probability": 0.97119140625}, {"start": 875.27, "end": 876.33, "word": " نشوف", "probability": 0.7486165364583334}, {"start": 876.33, "end": 876.57, "word": " كيف", "probability": 0.936279296875}, {"start": 876.57, "end": 877.31, "word": " بنوجد", "probability": 0.5949300130208334}, {"start": 877.31, "end": 877.71, "word": " اللى", "probability": 0.901611328125}, {"start": 877.71, "end": 877.97, "word": " هو", "probability": 0.9580078125}, {"start": 877.97, "end": 878.17, "word": " ال", "probability": 0.93017578125}, {"start": 878.17, "end": 878.71, "word": " inverse", "probability": 0.8173828125}, {"start": 878.71, "end": 879.21, "word": " ل", "probability": 0.87890625}, {"start": 879.21, "end": 879.45, "word": " two", "probability": 0.73193359375}, {"start": 879.45, "end": 879.73, "word": " by", 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890.61, "word": " من", "probability": 0.779296875}, {"start": 890.61, "end": 891.09, "word": " المحاضرة", "probability": 0.9583740234375}, {"start": 891.09, "end": 892.01, "word": " هي", "probability": 0.1868896484375}, {"start": 892.01, "end": 894.43, "word": " finding", "probability": 0.43310546875}, {"start": 894.43, "end": 895.01, "word": " inverse", "probability": 0.74072265625}, {"start": 895.01, "end": 895.19, "word": " of", "probability": 0.96435546875}, {"start": 895.19, "end": 895.69, "word": " 2x2", "probability": 0.6961263020833334}, {"start": 895.69, "end": 896.23, "word": " matrices", "probability": 0.953125}, {"start": 896.23, "end": 896.47, "word": " أو", "probability": 0.25439453125}, {"start": 896.47, "end": 896.89, "word": " إيجاد", "probability": 0.9425048828125}, {"start": 896.89, "end": 897.33, "word": " المعاكوس", "probability": 0.7603515625}, {"start": 897.33, "end": 897.87, "word": " الضربي", "probability": 0.83154296875}, {"start": 897.87, "end": 899.37, "word": " للمصفوفة", "probability": 0.9308268229166666}, {"start": 899.37, "end": 900.27, "word": " وخلّينا", "probability": 0.676513671875}, {"start": 900.27, "end": 900.67, "word": " نوقف", "probability": 0.8634440104166666}, {"start": 900.67, "end": 901.27, "word": " عندنا", "probability": 0.927978515625}, {"start": 901.27, "end": 902.01, "word": " ونعمل", "probability": 0.94677734375}, {"start": 902.01, "end": 902.61, "word": " المحاضرة", "probability": 0.9830322265625}, {"start": 902.61, "end": 902.91, "word": " على", "probability": 0.8056640625}, {"start": 902.91, "end": 903.77, "word": " جزءين", "probability": 0.9027099609375}, {"start": 903.77, "end": 903.89, "word": " و", "probability": 0.311279296875}, {"start": 903.89, "end": 904.09, "word": " الله", "probability": 0.52587890625}, {"start": 904.09, "end": 904.49, "word": " يعطيكوا", "probability": 0.8560546875}, {"start": 904.49, "end": 905.67, "word": " العافية", "probability": 0.8577473958333334}, {"start": 905.67, "end": 906.49, "word": " نكمل", "probability": 0.8987630208333334}, {"start": 906.49, "end": 906.81, "word": " الآن", "probability": 0.791748046875}, {"start": 906.81, "end": 907.17, "word": " الجزء", "probability": 0.9625651041666666}, {"start": 907.17, "end": 907.57, "word": " الثاني", "probability": 0.9239501953125}, {"start": 907.57, "end": 907.75, "word": " من", "probability": 0.986328125}, {"start": 907.75, "end": 908.39, "word": " المحاضرة", "probability": 0.997314453125}], "temperature": 1.0}, {"id": 42, "seek": 93122, "start": 915.68, "end": 931.22, "text": "المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة المعكوس الضربي للمصفوفة", "tokens": [45340, 3615, 4117, 41779, 6024, 114, 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إذن", "probability": 0.86328125}, {"start": 1162.01, "end": 1162.43, "word": " عملية", "probability": 0.9637044270833334}, {"start": 1162.43, "end": 1162.93, "word": " الإيجاد", "probability": 0.926513671875}, {"start": 1162.93, "end": 1163.09, "word": " اللي", "probability": 0.978515625}, {"start": 1163.09, "end": 1163.19, "word": " هو", "probability": 0.9716796875}, {"start": 1163.19, "end": 1163.61, "word": " المعقوس", "probability": 0.950439453125}, {"start": 1163.61, "end": 1163.95, "word": " الضربي", "probability": 0.9666748046875}, {"start": 1163.95, "end": 1164.39, "word": " سهلة", "probability": 0.8836263020833334}, {"start": 1164.39, "end": 1164.83, "word": " لأن", "probability": 0.580810546875}, {"start": 1164.83, "end": 1165.29, "word": " المصوفة", "probability": 0.645556640625}, {"start": 1165.29, "end": 1165.71, "word": " اتنين", "probability": 0.9112548828125}, {"start": 1165.71, "end": 1165.89, "word": " في", "probability": 0.96435546875}, {"start": 1165.89, "end": 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اللى هو احنا باختصار خلّينا نقولها اول اشي بتوجد حاجة اسمها اللى هى ال matrix of minor determinants حاجات هنقول اشيه الان بنغير اشارات اللى هى كل العناصر ما عدا عناصر القطر الرئيسى وعناصر قطر مين التانوي", "tokens": [10721, 25513, 3615, 16490, 9566, 2407, 9307, 13672, 7578, 31439, 1975, 5016, 8315, 4724, 47283, 2655, 9381, 9640, 16490, 1211, 11703, 9957, 995, 8717, 39648, 11296, 1975, 12610, 1975, 8592, 1829, 39894, 29245, 3215, 11331, 26108, 3660, 24525, 2304, 11296, 13672, 7578, 8032, 7578, 2423, 8141, 295, 6696, 15957, 1719, 11331, 26108, 9307, 8032, 1863, 39648, 1975, 8592, 1829, 3224, 2423, 7649, 44945, 17082, 13546, 1975, 8592, 9640, 9307, 13672, 7578, 8032, 7578, 28242, 18863, 1863, 33546, 2288, 19446, 6225, 28259, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 7578, 4032, 3615, 1863, 33546, 2288, 12174, 9566, 2288, 3714, 9957, 16712, 7649, 45865], "avg_logprob": -0.21241155224588681, "compression_ratio": 1.7298578199052133, "no_speech_prob": 0.0, "words": 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0.9851888020833334}, {"start": 1214.54, "end": 1215.12, "word": " اسمها", "probability": 0.9654947916666666}, {"start": 1215.12, "end": 1215.78, "word": " اللى", "probability": 0.843017578125}, {"start": 1215.78, "end": 1216.26, "word": " هى", "probability": 0.793212890625}, {"start": 1216.26, "end": 1216.78, "word": " ال", "probability": 0.83984375}, {"start": 1216.78, "end": 1217.32, "word": " matrix", "probability": 0.86474609375}, {"start": 1217.32, "end": 1217.76, "word": " of", "probability": 0.96875}, {"start": 1217.76, "end": 1218.2, "word": " minor", "probability": 0.98583984375}, {"start": 1218.2, "end": 1219.18, "word": " determinants", "probability": 0.90771484375}, {"start": 1219.18, "end": 1219.62, "word": " حاجات", "probability": 0.3935953776041667}, {"start": 1219.62, "end": 1219.96, "word": " هنقول", "probability": 0.9140625}, {"start": 1219.96, "end": 1220.56, "word": " اشيه", "probability": 0.670166015625}, {"start": 1220.56, "end": 1221.46, "word": " الان", "probability": 0.6588134765625}, {"start": 1221.46, "end": 1222.18, "word": " بنغير", "probability": 0.8740234375}, {"start": 1222.18, "end": 1222.96, "word": " اشارات", "probability": 0.8624267578125}, {"start": 1222.96, "end": 1223.3, "word": " اللى", "probability": 0.953857421875}, {"start": 1223.3, "end": 1223.64, "word": " هى", "probability": 0.95703125}, {"start": 1223.64, "end": 1224.0, "word": " كل", "probability": 0.958984375}, {"start": 1224.0, "end": 1224.7, "word": " العناصر", "probability": 0.9344482421875}, {"start": 1224.7, "end": 1224.96, "word": " ما", "probability": 0.59619140625}, {"start": 1224.96, "end": 1225.38, "word": " عدا", "probability": 0.5726318359375}, {"start": 1225.38, "end": 1226.54, "word": " عناصر", "probability": 0.9147135416666666}, {"start": 1226.54, "end": 1227.12, "word": " القطر", "probability": 0.9129231770833334}, {"start": 1227.12, "end": 1228.2, "word": " الرئيسى", "probability": 0.94140625}, {"start": 1228.2, "end": 1229.16, "word": " وعناصر", "probability": 0.92490234375}, {"start": 1229.16, "end": 1229.54, "word": " قطر", "probability": 0.8958333333333334}, {"start": 1229.54, "end": 1230.1, "word": " مين", "probability": 0.6934814453125}, {"start": 1230.1, "end": 1231.16, "word": " التانوي", "probability": 0.7882486979166666}], "temperature": 1.0}, {"id": 56, "seek": 125060, "start": 1231.67, "end": 1250.61, "text": "الان اللى بعدها اللى بيطلع عندنا اللى بنعمله بناخده ل Transpose اللى هو مدور المصفوفة و بعدين اللى بيطلع بنضربه فى واحد على ال determinant بيطلع عندنا اللى هو المعكوس الضربى نشوف هذا يمكن الكلام النظري شوية مش واضح خلينا نشوف كيف عمليا", "tokens": [6027, 7649, 13672, 7578, 39182, 11296, 13672, 7578, 4724, 1829, 9566, 1211, 3615, 43242, 8315, 13672, 7578, 44945, 25957, 43761, 44945, 47283, 3215, 3224, 5296, 6531, 43501, 13672, 7578, 31439, 3714, 3215, 13063, 9673, 9381, 5172, 38688, 3660, 4032, 39182, 9957, 13672, 7578, 4724, 1829, 9566, 1211, 3615, 44945, 11242, 25513, 3224, 6156, 7578, 36764, 24401, 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1235.35, "word": " اللى", "probability": 0.9755859375}, {"start": 1235.35, "end": 1236.17, "word": " بنعمله", "probability": 0.8561197916666666}, {"start": 1236.17, "end": 1236.67, "word": " بناخده", "probability": 0.76055908203125}, {"start": 1236.67, "end": 1236.77, "word": " ل", "probability": 0.91845703125}, {"start": 1236.77, "end": 1237.45, "word": " Transpose", "probability": 0.674072265625}, {"start": 1237.45, "end": 1237.61, "word": " اللى", "probability": 0.959716796875}, {"start": 1237.61, "end": 1237.77, "word": " هو", "probability": 0.8466796875}, {"start": 1237.77, "end": 1238.19, "word": " مدور", "probability": 0.9602864583333334}, {"start": 1238.19, "end": 1238.95, "word": " المصفوفة", "probability": 0.89111328125}, {"start": 1238.95, "end": 1239.39, "word": " و", "probability": 0.59033203125}, {"start": 1239.39, "end": 1239.83, "word": " بعدين", "probability": 0.89404296875}, {"start": 1239.83, "end": 1240.03, "word": " اللى", "probability": 0.984619140625}, {"start": 1240.03, "end": 1240.43, "word": " بيطلع", "probability": 0.94208984375}, {"start": 1240.43, "end": 1241.29, "word": " بنضربه", "probability": 0.8328857421875}, {"start": 1241.29, "end": 1241.47, "word": " فى", "probability": 0.6710205078125}, {"start": 1241.47, "end": 1241.83, "word": " واحد", "probability": 0.98388671875}, {"start": 1241.83, "end": 1242.05, "word": " على", "probability": 0.873046875}, {"start": 1242.05, "end": 1242.17, "word": " ال", "probability": 0.91162109375}, {"start": 1242.17, "end": 1242.65, "word": " determinant", "probability": 0.85546875}, {"start": 1242.65, "end": 1243.35, "word": " بيطلع", "probability": 0.8763671875}, {"start": 1243.35, "end": 1243.77, "word": " عندنا", "probability": 0.962646484375}, {"start": 1243.77, "end": 1243.97, "word": " اللى", "probability": 0.98779296875}, {"start": 1243.97, "end": 1244.17, "word": " هو", "probability": 0.787109375}, {"start": 1244.17, "end": 1244.95, "word": " المعكوس", "probability": 0.79248046875}, {"start": 1244.95, "end": 1245.71, "word": " الضربى", "probability": 0.726806640625}, {"start": 1245.71, "end": 1246.47, "word": " نشوف", "probability": 0.7958984375}, {"start": 1246.47, "end": 1246.63, "word": " هذا", "probability": 0.62890625}, {"start": 1246.63, "end": 1246.89, "word": " يمكن", "probability": 0.7349853515625}, {"start": 1246.89, "end": 1247.35, "word": " الكلام", "probability": 0.96142578125}, {"start": 1247.35, "end": 1247.85, "word": " النظري", "probability": 0.85888671875}, {"start": 1247.85, "end": 1248.23, "word": " شوية", "probability": 0.8937174479166666}, {"start": 1248.23, "end": 1248.41, "word": " مش", "probability": 0.9853515625}, {"start": 1248.41, "end": 1248.79, "word": " واضح", "probability": 0.97705078125}, {"start": 1248.79, "end": 1249.23, "word": " خلينا", "probability": 0.7369384765625}, {"start": 1249.23, "end": 1249.53, "word": " نشوف", "probability": 0.9970703125}, {"start": 1249.53, "end": 1249.81, "word": " كيف", "probability": 0.96923828125}, {"start": 1249.81, "end": 1250.61, "word": " عمليا", "probability": 0.877685546875}], "temperature": 1.0}, {"id": 57, "seek": 126808, "start": 1250.93, "end": 1268.09, "text": "نوجد الكوبيا قبل ما نحكي عن ما هو نوجد ال inverse بس عساس ان هو توضيح ايش هو ال matrix of minor determinants الان بدنا نعرف شو معناته ال minor determinants اللي هي المحددات الثانوية حكيتها قبل بشوية في الجزء الأول من المحاضرة", "tokens": [1863, 29245, 3215, 33251, 2407, 21292, 995, 12174, 36150, 19446, 8717, 5016, 4117, 1829, 18871, 19446, 31439, 8717, 29245, 3215, 2423, 17340, 4724, 3794, 6225, 3794, 32277, 16472, 31439, 33427, 11242, 1829, 5016, 1975, 1829, 8592, 31439, 2423, 8141, 295, 6696, 15957, 1719, 2423, 7649, 47525, 8315, 8717, 3615, 28480, 13412, 2407, 20449, 8315, 47395, 2423, 6696, 15957, 1719, 13672, 1829, 39896, 9673, 24401, 3215, 9307, 6024, 104, 7649, 2407, 10632, 11331, 4117, 36081, 11296, 12174, 36150, 4724, 8592, 2407, 10632, 8978, 25724, 11622, 38207, 16247, 12610, 9154, 9673, 5016, 46958, 25720], "avg_logprob": -0.26579300818904755, "compression_ratio": 1.7342995169082125, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1250.93, "end": 1251.45, "word": "نوجد", "probability": 0.4598388671875}, {"start": 1251.45, "end": 1252.11, "word": " الكوبيا", "probability": 0.73602294921875}, {"start": 1252.11, "end": 1252.67, "word": " قبل", "probability": 0.667724609375}, {"start": 1252.67, "end": 1252.79, "word": " ما", "probability": 0.6435546875}, {"start": 1252.79, "end": 1253.17, "word": " نحكي", "probability": 0.82073974609375}, {"start": 1253.17, "end": 1253.41, "word": " عن", "probability": 0.93408203125}, {"start": 1253.41, "end": 1253.63, "word": " ما", "probability": 0.22216796875}, {"start": 1253.63, "end": 1253.99, "word": " هو", "probability": 0.92919921875}, {"start": 1253.99, "end": 1254.55, "word": " نوجد", "probability": 0.8536783854166666}, {"start": 1254.55, "end": 1254.67, "word": " ال", "probability": 0.8486328125}, {"start": 1254.67, "end": 1255.05, "word": " inverse", "probability": 0.5048828125}, {"start": 1255.05, "end": 1255.37, "word": " بس", "probability": 0.782958984375}, {"start": 1255.37, "end": 1255.71, "word": " عساس", "probability": 0.7041015625}, {"start": 1255.71, "end": 1255.83, "word": " ان", "probability": 0.337158203125}, {"start": 1255.83, "end": 1256.03, "word": " هو", "probability": 0.50341796875}, {"start": 1256.03, "end": 1256.67, "word": " توضيح", "probability": 0.945068359375}, {"start": 1256.67, "end": 1257.31, "word": " ايش", "probability": 0.7843424479166666}, {"start": 1257.31, "end": 1257.65, "word": " هو", "probability": 0.91943359375}, {"start": 1257.65, "end": 1257.91, "word": " ال", "probability": 0.8662109375}, {"start": 1257.91, "end": 1258.41, "word": " matrix", "probability": 0.93798828125}, {"start": 1258.41, "end": 1258.71, "word": " of", "probability": 0.9365234375}, {"start": 1258.71, "end": 1259.07, "word": " minor", "probability": 0.9853515625}, {"start": 1259.07, "end": 1259.99, "word": " determinants", "probability": 0.93212890625}, {"start": 1259.99, "end": 1260.97, "word": " الان", "probability": 0.640380859375}, {"start": 1260.97, "end": 1261.19, "word": " بدنا", "probability": 0.5513916015625}, {"start": 1261.19, "end": 1261.45, "word": " نعرف", "probability": 0.9680989583333334}, {"start": 1261.45, "end": 1261.71, "word": " شو", "probability": 0.753173828125}, {"start": 1261.71, "end": 1262.07, "word": " معناته", "probability": 0.77197265625}, {"start": 1262.07, "end": 1262.19, "word": " ال", "probability": 0.6279296875}, {"start": 1262.19, "end": 1262.43, "word": " minor", "probability": 0.96630859375}, {"start": 1262.43, "end": 1263.27, "word": " determinants", "probability": 0.966064453125}, {"start": 1263.27, "end": 1263.59, "word": " اللي", "probability": 0.856689453125}, {"start": 1263.59, "end": 1263.79, "word": " هي", "probability": 0.86572265625}, {"start": 1263.79, "end": 1264.53, "word": " المحددات", "probability": 0.9776611328125}, {"start": 1264.53, "end": 1264.95, "word": " الثانوية", "probability": 0.88994140625}, {"start": 1264.95, "end": 1265.37, "word": " حكيتها", "probability": 0.921142578125}, {"start": 1265.37, "end": 1265.63, "word": " قبل", "probability": 0.7822265625}, {"start": 1265.63, "end": 1266.07, "word": " بشوية", "probability": 0.77679443359375}, {"start": 1266.07, "end": 1266.63, "word": " في", "probability": 0.935546875}, {"start": 1266.63, "end": 1267.03, "word": " الجزء", "probability": 0.9322916666666666}, {"start": 1267.03, "end": 1267.33, "word": " الأول", "probability": 0.80126953125}, {"start": 1267.33, "end": 1267.51, "word": " من", "probability": 0.93798828125}, {"start": 1267.51, "end": 1268.09, "word": " المحاضرة", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 58, "seek": 129461, "start": 1268.32, "end": 1294.62, "text": "الان يعني بدي اشوف ايش ال minor determinant للخمسة اللي بالنسبة للعنصر خمسة هذا مفترض انه محدد او matrix بدنا ال minor determinant للخمسة ال minor determinant او اللي هو المحدد الثانوي باختصار يا جماعة بتيجي بالشط بالصف اللي هي فيه و العمود اللي هي فيه بطلع عند المحدد المحدد اللي بطلع هذا هو اللي بنسميه ال minor determinant لمن؟ للخمسة", "tokens": [6027, 7649, 37495, 22653, 4724, 16254, 1975, 8592, 38688, 1975, 1829, 8592, 2423, 6696, 41296, 24976, 9778, 2304, 3794, 3660, 13672, 1829, 20666, 1863, 35457, 3660, 24976, 3615, 1863, 9381, 2288, 16490, 2304, 3794, 3660, 23758, 3714, 5172, 2655, 43042, 16472, 3224, 3714, 24401, 3215, 1975, 2407, 8141, 47525, 8315, 2423, 6696, 41296, 24976, 9778, 2304, 3794, 3660, 2423, 6696, 41296, 1975, 2407, 13672, 1829, 31439, 9673, 24401, 3215, 6024, 104, 7649, 45865, 4724, 47283, 2655, 9381, 9640, 35186, 10874, 15042, 27884, 39894, 1829, 7435, 1829, 20666, 8592, 9566, 20666, 9381, 5172, 13672, 1829, 39896, 8978, 3224, 4032, 18863, 2304, 23328, 13672, 1829, 39896, 8978, 3224, 4724, 9566, 1211, 3615, 43242, 9673, 24401, 3215, 9673, 24401, 3215, 13672, 1829, 4724, 9566, 1211, 3615, 23758, 31439, 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0.8837890625}, {"start": 1287.42, "end": 1288.02, "word": " فيه", "probability": 0.989990234375}, {"start": 1288.02, "end": 1288.6, "word": " بطلع", "probability": 0.8011474609375}, {"start": 1288.6, "end": 1288.84, "word": " عند", "probability": 0.96533203125}, {"start": 1288.84, "end": 1289.38, "word": " المحدد", "probability": 0.9921875}, {"start": 1289.38, "end": 1289.94, "word": " المحدد", "probability": 0.9597981770833334}, {"start": 1289.94, "end": 1290.06, "word": " اللي", "probability": 0.985107421875}, {"start": 1290.06, "end": 1290.46, "word": " بطلع", "probability": 0.9322509765625}, {"start": 1290.46, "end": 1290.86, "word": " هذا", "probability": 0.68212890625}, {"start": 1290.86, "end": 1291.2, "word": " هو", "probability": 0.98681640625}, {"start": 1291.2, "end": 1291.38, "word": " اللي", "probability": 0.989501953125}, {"start": 1291.38, "end": 1292.12, "word": " بنسميه", "probability": 0.9158935546875}, {"start": 1292.12, "end": 1292.2, "word": " ال", "probability": 0.54052734375}, {"start": 1292.2, "end": 1292.52, "word": " minor", "probability": 0.98828125}, {"start": 1292.52, "end": 1293.1, "word": " determinant", "probability": 0.8837890625}, {"start": 1293.1, "end": 1293.88, "word": " لمن؟", "probability": 0.6507161458333334}, {"start": 1293.88, "end": 1294.62, "word": " للخمسة", "probability": 0.95400390625}], "temperature": 1.0}, {"id": 59, "seek": 132303, "start": 1294.95, "end": 1323.03, "text": "الان واحد يقول اللى بدى ال minor determinant لمناقس ثلاثة بقول له حاضر شط بالسطر و شط بالعمود بطلع عندى اللى هو اللى ضال هذا عبارة عن محدد المحدد هذا بكون هو ال minor determinant لمناقس ثلاثة واحد قال لأ بدي للتمانية بقول له حاضر هى للتمانية شط بعموده و شط بصفه اللى بضل هو عبارة عن ال minor determinant لمن للتمانية", "tokens": [6027, 7649, 36764, 24401, 7251, 39648, 13672, 7578, 47525, 7578, 2423, 6696, 41296, 5296, 27842, 995, 4587, 3794, 38637, 1211, 5718, 104, 3660, 4724, 39648, 46740, 11331, 46958, 2288, 13412, 9566, 20666, 3794, 9566, 2288, 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matrix ام المصفوفة ام المطلوب إيجاد ال inverse لهذه المصفوفة", "tokens": [40228, 22653, 9673, 24401, 3215, 6024, 104, 7649, 45865, 32767, 9957, 22807, 5296, 39237, 7649, 10632, 23758, 2423, 28820, 10943, 12174, 40448, 8315, 43761, 6225, 8592, 7649, 8717, 14851, 9778, 40448, 3714, 3555, 995, 22488, 4724, 8592, 2407, 10632, 8978, 13672, 1829, 31439, 11933, 1829, 7435, 18513, 2423, 17340, 5296, 19528, 9381, 5172, 38688, 3660, 13412, 38688, 14407, 4386, 13412, 38688, 14407, 20328, 23942, 21984, 47356, 46952, 19528, 4724, 34268, 28543, 16247, 2304, 13063, 16472, 13412, 16606, 21984, 8032, 2655, 30544, 4032, 46958, 5016, 3660, 10874, 28259, 2423, 7649, 2423, 41296, 1975, 2304, 2423, 8141, 1975, 2304, 9673, 9381, 5172, 38688, 3660, 1975, 2304, 9673, 9566, 1211, 37746, 11933, 1829, 7435, 18513, 2423, 17340, 46740, 24192, 9673, 9381, 5172, 38688, 3660], "avg_logprob": -0.19595287544805495, "compression_ratio": 1.8685258964143425, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 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0.9404296875}, {"start": 1367.54, "end": 1368.08, "word": " determinant", "probability": 0.9697265625}, {"start": 1368.08, "end": 1368.52, "word": " ام", "probability": 0.6346435546875}, {"start": 1368.52, "end": 1368.88, "word": " ال", "probability": 0.64453125}, {"start": 1368.88, "end": 1369.44, "word": " matrix", "probability": 0.73876953125}, {"start": 1369.44, "end": 1369.82, "word": " ام", "probability": 0.881103515625}, {"start": 1369.82, "end": 1370.82, "word": " المصفوفة", "probability": 0.95556640625}, {"start": 1370.82, "end": 1371.04, "word": " ام", "probability": 0.96826171875}, {"start": 1371.04, "end": 1372.14, "word": " المطلوب", "probability": 0.9837646484375}, {"start": 1372.14, "end": 1372.9, "word": " إيجاد", "probability": 0.956787109375}, {"start": 1372.9, "end": 1373.08, "word": " ال", "probability": 0.986328125}, {"start": 1373.08, "end": 1373.52, "word": " inverse", "probability": 0.9541015625}, {"start": 1373.52, "end": 1374.0, "word": " لهذه", "probability": 0.754638671875}, {"start": 1374.0, "end": 1374.62, "word": " المصفوفة", "probability": 0.985546875}], "temperature": 1.0}, {"id": 62, "seek": 137882, "start": 1375.06, "end": 1378.82, "text": "عنا أربع خطوات عشان نوجد اللي هو", "tokens": [3615, 8315, 5551, 25513, 3615, 16490, 9566, 2407, 9307, 6225, 8592, 7649, 8717, 2407, 7435, 3215, 13672, 1829, 31439], "avg_logprob": -0.15507812798023224, "compression_ratio": 0.9508196721311475, "no_speech_prob": 0.0, "words": [{"start": 1375.06, "end": 1375.72, "word": "عنا", "probability": 0.6993408203125}, {"start": 1375.72, "end": 1376.4, "word": " أربع", "probability": 0.8544921875}, {"start": 1376.4, "end": 1377.2, "word": " خطوات", "probability": 0.99072265625}, {"start": 1377.2, "end": 1377.76, "word": " عشان", "probability": 0.94970703125}, {"start": 1377.76, "end": 1378.26, "word": " نوجد", "probability": 0.755859375}, {"start": 1378.26, "end": 1378.54, "word": " اللي", "probability": 0.961669921875}, {"start": 1378.54, "end": 1378.82, "word": " هو", "probability": 0.994140625}], "temperature": 1.0}, {"id": 63, "seek": 140588, "start": 1379.92, "end": 1405.88, "text": "ال .. ال .. ال .. ال .. ال inverse لهذه المصوفة أربع خطوات الخطوة الأولى أكيد كلكم حيقول بدنا نجد ال determinant يعني بدنا نتأكد أو اشي make sure انه non-singular ايش يعني non-singular يعني determinant له مش صفر لو حسبتوا ال determinant له زي ما أخدناه في الطريقة الأولى لإيش نضيع الوجد في حساباتها لإن حسبناها قبل هيك بتحسبوها هتلاقوا ال determinant لهذه ال M إيش طالع عندنا", "tokens": [6027, 4386, 2423, 4386, 2423, 4386, 2423, 4386, 2423, 17340, 46740, 24192, 9673, 9381, 38688, 3660, 5551, 25513, 3615, 16490, 9566, 2407, 9307, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 5551, 4117, 25708, 28242, 24793, 11331, 1829, 39648, 47525, 8315, 8717, 7435, 3215, 2423, 41296, 37495, 22653, 47525, 8315, 8717, 2655, 10721, 4117, 3215, 34051, 1975, 8592, 1829, 652, 988, 16472, 3224, 2107, 12, 82, 278, 1040, 1975, 1829, 8592, 37495, 22653, 2107, 12, 82, 278, 1040, 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{"start": 1403.68, "end": 1403.8, "word": " ال", "probability": 0.96630859375}, {"start": 1403.8, "end": 1404.4, "word": " determinant", "probability": 0.982421875}, {"start": 1404.4, "end": 1404.9, "word": " لهذه", "probability": 0.97412109375}, {"start": 1404.9, "end": 1405.0, "word": " ال", "probability": 0.63525390625}, {"start": 1405.0, "end": 1405.12, "word": " M", "probability": 0.62109375}, {"start": 1405.12, "end": 1405.3, "word": " إيش", "probability": 0.7345377604166666}, {"start": 1405.3, "end": 1405.54, "word": " طالع", "probability": 0.9637044270833334}, {"start": 1405.54, "end": 1405.88, "word": " عندنا", "probability": 0.862060546875}], "temperature": 1.0}, {"id": 64, "seek": 143380, "start": 1407.1, "end": 1433.8, "text": "-156 يعني مش سفر مزا مش مش سفر إذا الأن اتأكدنا إنه non singular هذه طبعا في الآخر اللي هي بستخدمها اللي هي قيمة ال determinant نجي للخطوات اللي بدنا نصل فيها لل inverse الخطوة الأولى اللي هو find the matrix of minor determinants يعني بدأ أوجد ال 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{"start": 2014.77, "end": 2015.13, "word": " قليل", "probability": 0.7919108072916666}, {"start": 2015.13, "end": 2016.03, "word": " والتفاصيل", "probability": 0.9126953125}, {"start": 2016.03, "end": 2016.65, "word": " لكم", "probability": 0.78173828125}, {"start": 2016.65, "end": 2017.59, "word": " الحسابات", "probability": 0.77227783203125}], "temperature": 1.0}, {"id": 90, "seek": 204680, "start": 2018.5, "end": 2046.8, "text": "وجدنا الـ Minors بعد ما نجد الـ Minors بنجد الـ Co-Factor ماهو الـ Co-Factor؟ بنحدد هى القطر الرئيسي وهى القطر الثانوي ومن هدولة بنغير إشاراتين هذا بيصير 25 هذا بيصير 4 هذا بيصير 5 وهذا بيصير 18 هى اللي هو الـ Co-Factor عملية تغيير الإشارات للعناصر غير عناصر القطر التانوي والقطر الرئيسي", "tokens": [29245, 3215, 8315, 2423, 39184, 2829, 830, 39182, 19446, 8717, 7435, 3215, 2423, 39184, 2829, 830, 44945, 7435, 3215, 2423, 39184, 3066, 12, 37, 15104, 19446, 3224, 2407, 2423, 39184, 3066, 12, 37, 15104, 22807, 44945, 24401, 3215, 8032, 7578, 25062, 9566, 2288, 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"probability": 0.669921875}, {"start": 2037.52, "end": 2038.6, "word": " هى", "probability": 0.4638671875}, {"start": 2038.6, "end": 2038.98, "word": " اللي", "probability": 0.635009765625}, {"start": 2038.98, "end": 2039.3, "word": " هو", "probability": 0.95068359375}, {"start": 2039.3, "end": 2039.62, "word": " الـ", "probability": 0.746826171875}, {"start": 2039.62, "end": 2039.76, "word": " Co", "probability": 0.9423828125}, {"start": 2039.76, "end": 2040.1, "word": "-Factor", "probability": 0.958984375}, {"start": 2040.1, "end": 2040.56, "word": " عملية", "probability": 0.9588216145833334}, {"start": 2040.56, "end": 2041.18, "word": " تغيير", "probability": 0.9775390625}, {"start": 2041.18, "end": 2042.02, "word": " الإشارات", "probability": 0.994384765625}, {"start": 2042.02, "end": 2043.16, "word": " للعناصر", "probability": 0.9119140625}, {"start": 2043.16, "end": 2043.62, "word": " غير", "probability": 0.933837890625}, {"start": 2043.62, "end": 2044.3, "word": " عناصر", 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Adjoint اللي هو هاي ال Adjoint هيك فبكون احنا اوددنا ال A inverse لمين ل ال matrix اللي ال determinant له مش سفر الان عندك الجزء الثاني من الوادي", "tokens": [6027, 20292, 31439, 3714, 11242, 32887, 3555, 8978, 2423, 39184, 1999, 48613, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 3660, 5296, 9778, 2304, 3794, 3660, 13672, 1829, 31439, 2423, 41296, 16490, 2304, 3794, 3660, 3714, 11242, 32887, 3555, 8978, 2423, 1999, 48613, 13672, 1829, 31439, 8032, 47302, 2423, 1999, 48613, 39896, 4117, 6156, 3555, 30544, 1975, 5016, 8315, 1975, 23328, 3215, 8315, 2423, 316, 17340, 32767, 9957, 5296, 2423, 8141, 13672, 1829, 2423, 41296, 46740, 37893, 8608, 5172, 2288, 2423, 7649, 43242, 4117, 25724, 11622, 38207, 6024, 104, 7649, 1829, 9154, 2423, 14407, 16254], "avg_logprob": -0.2058354613124108, "compression_ratio": 1.8955223880597014, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2073.51, "end": 2073.95, "word": "اللي", "probability": 0.4500732421875}, {"start": 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2083.23, "word": " Adjoint", "probability": 0.85498046875}, {"start": 2083.23, "end": 2083.89, "word": " هيك", "probability": 0.918701171875}, {"start": 2083.89, "end": 2084.25, "word": " فبكون", "probability": 0.5511881510416666}, {"start": 2084.25, "end": 2084.57, "word": " احنا", "probability": 0.9013671875}, {"start": 2084.57, "end": 2085.31, "word": " اوددنا", "probability": 0.7374267578125}, {"start": 2085.31, "end": 2085.71, "word": " ال", "probability": 0.95458984375}, {"start": 2085.71, "end": 2086.09, "word": " A", "probability": 0.59765625}, {"start": 2086.09, "end": 2086.81, "word": " inverse", "probability": 0.63720703125}, {"start": 2086.81, "end": 2087.53, "word": " لمين", "probability": 0.79296875}, {"start": 2087.53, "end": 2088.21, "word": " ل", "probability": 0.7822265625}, {"start": 2088.21, "end": 2088.65, "word": " ال", "probability": 0.457763671875}, {"start": 2088.65, "end": 2089.25, "word": " matrix", "probability": 0.88427734375}, {"start": 2089.25, "end": 2089.87, "word": " اللي", "probability": 0.9560546875}, {"start": 2089.87, "end": 2090.07, "word": " ال", "probability": 0.92626953125}, {"start": 2090.07, "end": 2090.45, "word": " determinant", "probability": 0.96484375}, {"start": 2090.45, "end": 2091.07, "word": " له", "probability": 0.6318359375}, {"start": 2091.07, "end": 2091.65, "word": " مش", "probability": 0.96630859375}, {"start": 2091.65, "end": 2092.07, "word": " سفر", "probability": 0.9013671875}, {"start": 2092.07, "end": 2092.99, "word": " الان", "probability": 0.6639404296875}, {"start": 2092.99, "end": 2093.73, "word": " عندك", "probability": 0.98828125}, {"start": 2093.73, "end": 2094.53, "word": " الجزء", "probability": 0.8518880208333334}, {"start": 2094.53, "end": 2094.97, "word": " الثاني", "probability": 0.93212890625}, {"start": 2094.97, "end": 2095.15, "word": " من", "probability": 0.9765625}, {"start": 2095.15, "end": 2095.59, "word": " الوادي", "probability": 0.9088541666666666}], "temperature": 1.0}, {"id": 93, "seek": 211836, "start": 2096.48, "end": 2118.36, "text": "اللي هو ال question هو ان انا ال a هيو و هي ال a inverse بالسوية واحدة ال determinant في ال adjoint او جدل ال a inverse او جدلي هذا الكلام بالتفصيل او جدل ال determinant و بعدين او جدل ال adjoint زي ما احنا قلنا اللي قبل و هيطلع عندك الجواب a inverse بالسوية كده انا بدي منك التفاصيل في الواجب", "tokens": [6027, 20292, 31439, 2423, 1168, 31439, 16472, 1975, 8315, 2423, 257, 39896, 2407, 4032, 39896, 2423, 257, 17340, 20666, 3794, 2407, 10632, 36764, 24401, 3660, 2423, 41296, 8978, 2423, 614, 48613, 1975, 2407, 10874, 3215, 1211, 2423, 257, 17340, 1975, 2407, 10874, 3215, 20292, 23758, 2423, 28820, 10943, 20666, 2655, 5172, 9381, 26895, 1975, 2407, 10874, 3215, 1211, 2423, 41296, 4032, 39182, 9957, 1975, 2407, 10874, 3215, 1211, 2423, 614, 48613, 30767, 1829, 19446, 1975, 5016, 8315, 12174, 1211, 8315, 13672, 1829, 12174, 36150, 4032, 39896, 9566, 1211, 3615, 43242, 4117, 25724, 14407, 3555, 257, 17340, 20666, 3794, 2407, 10632, 9122, 3215, 3224, 1975, 8315, 4724, 16254, 9154, 4117, 16712, 5172, 33546, 26895, 8978, 2423, 2407, 26108, 3555], "avg_logprob": -0.2313550405141686, "compression_ratio": 2.1013824884792625, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2096.48, "end": 2096.8, "word": "اللي", "probability": 0.434051513671875}, {"start": 2096.8, "end": 2096.96, "word": " هو", "probability": 0.8779296875}, {"start": 2096.96, "end": 2097.06, "word": " ال", "probability": 0.646484375}, {"start": 2097.06, "end": 2097.36, "word": " question", "probability": 0.74267578125}, {"start": 2097.36, "end": 2097.66, "word": " هو", "probability": 0.351806640625}, {"start": 2097.66, "end": 2097.78, "word": " ان", "probability": 0.316650390625}, {"start": 2097.78, "end": 2098.02, "word": " انا", "probability": 0.443603515625}, {"start": 2098.02, "end": 2098.24, "word": " ال", "probability": 0.5576171875}, {"start": 2098.24, "end": 2098.4, "word": " a", "probability": 0.48046875}, {"start": 2098.4, "end": 2098.94, "word": " هيو", "probability": 0.576904296875}, {"start": 2098.94, "end": 2099.44, "word": " و", "probability": 0.54541015625}, {"start": 2099.44, "end": 2099.66, "word": " هي", "probability": 0.8525390625}, {"start": 2099.66, "end": 2099.84, "word": " ال", "probability": 0.88916015625}, {"start": 2099.84, "end": 2100.02, "word": " a", "probability": 0.9189453125}, {"start": 2100.02, "end": 2100.54, "word": " inverse", "probability": 0.8056640625}, {"start": 2100.54, "end": 2101.0, "word": " بالسوية", "probability": 0.52587890625}, {"start": 2101.0, "end": 2101.32, "word": " واحدة", "probability": 0.8821614583333334}, {"start": 2101.32, "end": 2101.38, "word": " ال", "probability": 0.39013671875}, {"start": 2101.38, "end": 2101.74, "word": " determinant", "probability": 0.94970703125}, {"start": 2101.74, "end": 2102.04, "word": " في", "probability": 0.703125}, {"start": 2102.04, "end": 2102.06, "word": " ال", "probability": 0.9560546875}, {"start": 2102.06, "end": 2102.5, "word": " adjoint", "probability": 0.719970703125}, {"start": 2102.5, "end": 2103.3, "word": " او", "probability": 0.815185546875}, {"start": 2103.3, "end": 2103.76, "word": " جدل", "probability": 0.5890706380208334}, {"start": 2103.76, "end": 2103.88, "word": " ال", "probability": 0.7734375}, {"start": 2103.88, "end": 2104.06, "word": " a", "probability": 0.95703125}, {"start": 2104.06, "end": 2104.64, "word": " inverse", "probability": 0.845703125}, {"start": 2104.64, "end": 2105.08, "word": " او", "probability": 0.956298828125}, {"start": 2105.08, "end": 2105.42, "word": " جدلي", "probability": 0.9264322916666666}, {"start": 2105.42, "end": 2105.72, "word": " هذا", "probability": 0.884765625}, {"start": 2105.72, "end": 2106.14, "word": " الكلام", "probability": 0.9646809895833334}, {"start": 2106.14, "end": 2106.94, "word": " بالتفصيل", "probability": 0.966015625}, {"start": 2106.94, "end": 2107.5, "word": " او", "probability": 0.7161865234375}, {"start": 2107.5, "end": 2107.74, "word": " جدل", "probability": 0.96484375}, {"start": 2107.74, "end": 2107.82, "word": " ال", "probability": 0.962890625}, {"start": 2107.82, "end": 2108.26, "word": " determinant", "probability": 0.9521484375}, {"start": 2108.26, "end": 2108.48, "word": " و", "probability": 0.619140625}, {"start": 2108.48, "end": 2108.84, "word": " بعدين", "probability": 0.887451171875}, {"start": 2108.84, "end": 2108.98, "word": " او", "probability": 0.98828125}, {"start": 2108.98, "end": 2109.3, "word": " جدل", "probability": 0.9856770833333334}, {"start": 2109.3, "end": 2109.36, "word": " ال", "probability": 0.982421875}, {"start": 2109.36, "end": 2109.84, "word": " adjoint", "probability": 0.885009765625}, {"start": 2109.84, "end": 2110.28, "word": " زي", "probability": 0.882080078125}, {"start": 2110.28, "end": 2110.42, "word": " ما", "probability": 0.96630859375}, {"start": 2110.42, "end": 2110.76, "word": " احنا", "probability": 0.9638671875}, {"start": 2110.76, "end": 2111.28, "word": " قلنا", "probability": 0.9010416666666666}, {"start": 2111.28, "end": 2112.48, "word": " اللي", "probability": 0.634521484375}, {"start": 2112.48, "end": 2112.86, "word": " قبل", "probability": 0.90869140625}, {"start": 2112.86, "end": 2113.06, "word": " و", "probability": 0.8876953125}, {"start": 2113.06, "end": 2113.48, "word": " هيطلع", "probability": 0.8946533203125}, {"start": 2113.48, "end": 2113.74, "word": " عندك", "probability": 0.99560546875}, {"start": 2113.74, "end": 2114.14, "word": " الجواب", "probability": 0.9187825520833334}, {"start": 2114.14, "end": 2114.28, "word": " a", "probability": 0.89697265625}, {"start": 2114.28, "end": 2114.6, "word": " inverse", "probability": 0.8291015625}, {"start": 2114.6, "end": 2115.0, "word": " بالسوية", "probability": 0.9654541015625}, {"start": 2115.0, "end": 2115.26, "word": " كده", "probability": 0.84228515625}, {"start": 2115.26, "end": 2115.5, "word": " انا", "probability": 0.8466796875}, {"start": 2115.5, "end": 2115.76, "word": " بدي", "probability": 0.65625}, {"start": 2115.76, "end": 2116.28, "word": " منك", "probability": 0.97314453125}, {"start": 2116.28, "end": 2117.14, "word": " التفاصيل", "probability": 0.9864501953125}, {"start": 2117.14, "end": 2117.44, "word": " في", "probability": 0.9833984375}, {"start": 2117.44, "end": 2118.36, "word": " الواجب", "probability": 0.9713134765625}], "temperature": 1.0}, {"id": 94, "seek": 213233, "start": 2119.23, "end": 2132.33, "text": "الان المرة القادمة ان شاء الله بنكمل و بندخل على الهو solving linear equations using inverse matrix والسلام عليكم ورحمة الله وبركاته وإلى لقاء آخر", "tokens": [6027, 7649, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 4032, 44945, 3215, 9778, 1211, 15844, 2423, 3224, 2407, 12606, 8213, 11787, 1228, 17340, 8141, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224, 4032, 28814, 23942, 5296, 4587, 16606, 19753, 34740], "avg_logprob": -0.24115565925274254, "compression_ratio": 1.4339622641509433, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2119.23, "end": 2119.99, "word": "الان", "probability": 0.637451171875}, {"start": 2119.99, "end": 2120.73, "word": " المرة", "probability": 0.6156005859375}, {"start": 2120.73, "end": 2121.25, "word": " القادمة", "probability": 0.9715169270833334}, {"start": 2121.25, "end": 2121.37, "word": " ان", "probability": 0.190185546875}, {"start": 2121.37, "end": 2121.55, "word": " شاء", "probability": 0.977294921875}, {"start": 2121.55, "end": 2121.73, "word": " الله", "probability": 0.9423828125}, {"start": 2121.73, "end": 2122.39, "word": " بنكمل", "probability": 0.8636067708333334}, {"start": 2122.39, "end": 2122.45, "word": " و", "probability": 0.775390625}, {"start": 2122.45, "end": 2122.95, "word": " بندخل", "probability": 0.90771484375}, {"start": 2122.95, "end": 2123.31, "word": " على", "probability": 0.76416015625}, {"start": 2123.31, "end": 2124.19, "word": " الهو", "probability": 0.4966634114583333}, {"start": 2124.19, "end": 2124.47, "word": " solving", "probability": 0.420166015625}, {"start": 2124.47, "end": 2124.99, "word": " linear", "probability": 0.81689453125}, {"start": 2124.99, "end": 2126.05, "word": " equations", "probability": 0.92333984375}, {"start": 2126.05, "end": 2126.59, "word": " using", "probability": 0.83935546875}, {"start": 2126.59, "end": 2127.19, "word": " inverse", "probability": 0.849609375}, {"start": 2127.19, "end": 2127.83, "word": " matrix", "probability": 0.9013671875}, {"start": 2127.83, "end": 2129.15, "word": " والسلام", "probability": 0.7591959635416666}, {"start": 2129.15, "end": 2129.55, "word": " عليكم", "probability": 0.936279296875}, {"start": 2129.55, "end": 2129.97, "word": " ورحمة", "probability": 0.947998046875}, {"start": 2129.97, "end": 2130.19, "word": " الله", "probability": 0.96044921875}, {"start": 2130.19, "end": 2130.85, "word": " وبركاته", "probability": 0.991015625}, {"start": 2130.85, "end": 2131.25, "word": " وإلى", "probability": 0.79833984375}, {"start": 2131.25, "end": 2131.73, "word": " لقاء", "probability": 0.8927408854166666}, {"start": 2131.73, "end": 2132.33, "word": " آخر", "probability": 0.86572265625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2135.12125, "duration_after_vad": 2116.1503437499987}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fc45d0d6f576a05a9863d66ef0e23a86f8273d7c
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co.srt
@@ -0,0 +1,1367 @@
+1
+00:00:00,000 --> 00:00:04,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,180 --> 00:00:07,720
+والصلاة والسلام على سيد المرسلين سيدنا محمد على 
+
+3
+00:00:07,720 --> 00:00:14,600
+آله وصحبه أجمعين هذه هي المحاضرة الرابعة في مساق 
+
+4
+00:00:14,600 --> 00:00:18,960
+قياضيات منفصلة لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:18,960 --> 00:00:28,290
+كلية ال IT قسم الحوسبة المتنقلة المحاضرة اليوم هي 
+
+6
+00:00:28,290 --> 00:00:34,090
+المحاضرة الأولى أيضا في chapter 4 وهو المعنون ب
+
+7
+00:00:34,090 --> 00:00:39,210
+number theory and cryptography اللي هي بنقصد فيها
+
+8
+00:00:39,210 --> 00:00:44,010
+نظرية الأعداد والتشفير والتشفير هو عبارة عن تطبيق 
+
+9
+00:00:44,010 --> 00:00:50,230
+على نظرية الأعداد. ال section الأول اللي هنتحدث عنه
+
+10
+00:00:50,230 --> 00:00:53,910
+اليوم اللي هو divisibility and modular arithmetic 
+
+11
+00:00:54,520 --> 00:01:02,080
+اللي هو شو معناه القسمة أو قابلية القسمة وحنشوف
+
+12
+00:01:02,080 --> 00:01:05,920
+دالتين واحدة دالة اسمها المد وواحدة دالة اسمها
+
+13
+00:01:05,920 --> 00:01:12,840
+div  ونشوف إيش اللي بنقصد فيهم. الآن نحكي أول شيء عن
+
+14
+00:01:12,840 --> 00:01:18,380
+ال division. الآن ال division اللي هي القسمة نشوف
+
+15
+00:01:18,380 --> 00:01:24,020
+شو معناه ال a divides b؟ إيش معناه أنه عدد يقسم
+
+16
+00:01:24,020 --> 00:01:30,720
+عدد آخر اسمه b؟ طبعا حديثنا كله بيصب في اللي هو في
+
+17
+00:01:30,720 --> 00:01:33,860
+ال integers يعني احنا كل الأعداد اللي بنتناولها
+
+18
+00:01:33,860 --> 00:01:39,190
+اليوم هي عبارة عن أعداد صحيحة. الآن بنقول if a and b
+
+19
+00:01:39,190 --> 00:01:42,590
+are integers يعني لو كان عندي a و b عبارة عن أعداد
+
+20
+00:01:42,590 --> 00:01:46,870
+صحيحة with a لا تساوي صفر. مدام قال with a لا تساوي
+
+21
+00:01:46,870 --> 00:01:53,230
+صفر شكلنا هنقسم على a لأن القسمة على a مرفوضة فعشان
+
+22
+00:01:53,230 --> 00:01:58,120
+هيك مفترضين أن a لا تساوي صفر. الآن بيقول then a
+
+23
+00:01:58,120 --> 00:02:03,140
+divides b يعني بيقول أن a تقسم b. شو معنى a تقسم b؟
+
+24
+00:02:03,140 --> 00:02:07,700
+اللي هو if there exists an integer c such that ال
+
+25
+00:02:07,700 --> 00:02:13,440
+b بتساوي ال a في c. في هذه الحالة بيقول a divides b.
+
+26
+00:02:13,730 --> 00:02:18,310
+يعني إكترنا نكتب b على صورة a في integer آخر أو
+
+27
+00:02:18,310 --> 00:02:23,090
+في عدد صحيح آخر. زي ما نقول ستة بتساوي اثنين في ثلاثة.
+
+28
+00:02:23,090 --> 00:02:29,150
+فبتكون الاثنين تقسم من الستة. يعني بمعنى آخر a
+
+29
+00:02:29,150 --> 00:02:35,630
+divides b اللي هو a is a factor of b يعني a عامل
+
+30
+00:02:35,630 --> 00:02:41,660
+من عوامل b أو divisor of b أو قاسم من قواسم الـ b.
+
+31
+00:02:41,660 --> 00:02:46,160
+إذا لما نقول a divides b بنقصد أنه a عامل من عوامل
+
+32
+00:02:46,160 --> 00:02:52,900
+b وبنقصد a قاسم من قواسم الـ b أو بنقصد b عبارة عن
+
+33
+00:02:53,170 --> 00:02:58,210
+من مضاعفات الـ a. يعني b is multiple of a. كل
+
+34
+00:02:58,210 --> 00:03:04,230
+التعبير الثلاثة دول a قاسم من قاسم الـ b أو a عامل 
+
+35
+00:03:04,230 --> 00:03:09,010
+من عوامل الـ b أو b من مضاعفات الـ a كلها المقصود
+
+36
+00:03:09,010 --> 00:03:16,380
+فيها أن a divides b. ما هي الـ notation تبعتها؟ نقول
+
+37
+00:03:16,380 --> 00:03:20,660
+a divides b وهي a وهي عصره بينهم b. شكل العصره هي 
+
+38
+00:03:20,660 --> 00:03:26,720
+شبه عمودية يعني a divides b denotes that a divides
+
+39
+00:03:26,720 --> 00:03:32,420
+b أو a تقسم b. الآن قلنا أن a تقسم b معناه أن ال
+
+40
+00:03:32,420 --> 00:03:35,740
+a عامل من عامل b. يعني لو جينا قسمنا ال b على ال a
+
+41
+00:03:35,740 --> 00:03:40,190
+هتطلع integer. يعني الآن لما نقول a تقسم b بنعني أنه
+
+42
+00:03:40,190 --> 00:03:45,650
+على طول العدد b على العدد a. فده معناه يعني بيقول لك
+
+43
+00:03:45,650 --> 00:03:49,890
+b على العدد a هيطلع إيش مالو؟ انتجر زي ما هنا هاي مش
+
+44
+00:03:49,890 --> 00:03:53,970
+هاد معناه a تقسم b. يعني الآن b على a هتطلع ال c
+
+45
+00:03:53,970 --> 00:03:58,330
+يعني integer. إذا من الآن وطالع مجرد نقول a تقسم b
+
+46
+00:03:58,330 --> 00:04:02,110
+معناه ال b على ال a هو عبارة عن عدد صحيح. طب لو
+
+47
+00:04:02,110 --> 00:04:05,850
+بدنا نقول a does not divide b نرمز بالرمزية ده a
+
+48
+00:04:05,850 --> 00:04:10,030
+وهي الشحطة الأولى وهي فجهها شحطة ثانية. يعني a does
+
+49
+00:04:10,030 --> 00:04:15,810
+not divide b يعني a لا تقسم ال b. ناخذ أمثلة عددية
+
+50
+00:04:15,810 --> 00:04:19,830
+الآن المثال الأول determine whether الثلاثة بتقسم
+
+51
+00:04:19,830 --> 00:04:23,940
+السبعة و whether الثلاثة بتقسم 11. لإن احنا
+
+52
+00:04:23,940 --> 00:04:26,800
+على طول الحد ما نشوف على طول الثلاثة ما بتقسمش السبعة
+
+53
+00:04:26,800 --> 00:04:31,640
+ليش؟ لأن السبعة على الثلاثة مش عدد صحيح. إذا الثلاثة
+
+54
+00:04:31,640 --> 00:04:35,780
+does not divide بيه. إذا أكيد ال solution هنقوله
+
+55
+00:04:35,780 --> 00:04:40,020
+الثلاثة لا تقسم السبعة because اللي هو السبعة على
+
+56
+00:04:40,020 --> 00:04:44,520
+الثلاثة ليست عدد صحيح. لأن ثلاثة بتقسم 12. كلكم قلتم
+
+57
+00:04:44,520 --> 00:04:47,660
+هل جيت 12 على ثلاثة؟ أربعة. يعني الثلاثة لازم تقسم من
+
+58
+00:04:47,660 --> 00:04:52,080
+12. إذا أكيد ثلاثة بتقسم 12 لأن 12 على ثلاثة هي عبارة
+
+59
+00:04:52,080 --> 00:04:56,600
+عن إيش؟ طلعت الأربعة. أو بمعنى آخر 12 بتساوي 3 في 4.
+
+60
+00:04:56,600 --> 00:05:01,720
+زي ما عملنا في ال a ال b بتساوي a في c. إذا الثلاثة 
+
+61
+00:05:01,720 --> 00:05:06,460
+تقسم من 12. إذا الكلام سهل. طيب نيجي لخواص ال
+
+62
+00:05:06,460 --> 00:05:11,200
+divisibility أو خواص قابلية ال a أو خواص القسمة.
+
+63
+00:05:11,200 --> 00:05:16,530
+نشوف. اللي قال لو كان عند a وb وc عبارة عن integers 
+
+64
+00:05:16,530 --> 00:05:21,330
+أعداد صحيحة والـ a لا تساوي صفر لأن شكل اللي هنقسم
+
+65
+00:05:21,330 --> 00:05:24,470
+على الـ a عشان يجي الـ a لا تساوي الصفر. الآن بقول
+
+66
+00:05:24,470 --> 00:05:30,130
+لي لو a بتجسم الـ b والـ a بتجسم ال c أكيد ال a
+
+67
+00:05:30,130 --> 00:05:34,850
+هتجسم ال b زائد ال c. كلام منطقي. خد مثلا اثنين
+
+68
+00:05:34,850 --> 00:05:39,910
+بتجسم الستة واثنين بتجسم العشرة. إذا اثنين بتجسم
+
+69
+00:05:39,910 --> 00:05:43,110
+الستة زائد العشرة اللي هي الستة عشر. أكيد اثنين بتجسم
+
+70
+00:05:43,110 --> 00:05:47,210
+الستة عشر. إذا دائما ال a بتجسم ال b و ال a بتجسم ال
+
+71
+00:05:47,210 --> 00:05:53,110
+c. هذول بخزن المعلومة بتعطينا أن ال a بتجسم ال b
+
+72
+00:05:53,110 --> 00:05:58,700
+زائد ال c. هنروح لبعد من هيك بعد شوية. الآن a بتجسم ال
+
+73
+00:05:58,700 --> 00:06:04,280
+b. أكيد ال a هتجسم ال b في خمسة وال b في ستة وال
+
+74
+00:06:04,280 --> 00:06:08,180
+b في سبعة وال b في ثمانية. يعني أكيد ال a بتجسم ال
+
+75
+00:06:08,180 --> 00:06:13,780
+b في c لكل integer c. 100 مثال نستطيع أن نقولها. يعني
+
+76
+00:06:13,780 --> 00:06:18,460
+اثنين بتقسم الستة أكيد اثنين بتقسم الستة في ثلاثة
+
+77
+00:06:18,460 --> 00:06:21,540
+اللي هي 18. اثنين بتقسم الستة في خمسة في 30.
+
+78
+00:06:21,540 --> 00:06:25,840
+اثنين بتقسم الستة في مليون. إذا اثنين هتقسم ال b في
+
+79
+00:06:25,840 --> 00:06:34,640
+c اللي هو في حال اثنين بتقسم ال b. الآن الخاصية هذه
+
+80
+00:06:34,640 --> 00:06:38,380
+الثالثة اللي بنسميها خاصية التعدي. ال a بتجسم ال b
+
+81
+00:06:38,380 --> 00:06:42,240
+و ال b بتجسم ال c. مع بعض هدول لازم يعطلنا ال a
+
+82
+00:06:42,240 --> 00:06:47,460
+بتجسم ال c. هذا الكلام سهل برضه لإن ال a بتجسم ال
+
+83
+00:06:47,460 --> 00:06:52,660
+... خلنا نقول ال 2 بتجسم ال 6 وال 6 بتجسم ال 24.
+
+84
+00:06:52,660 --> 00:06:59,040
+إذا أكيد ال 2 بتجسم ال 24. الثلاثة بتجسم الستة
+
+85
+00:06:59,040 --> 00:07:03,240
+والستة بتجسم ال 18. إذا الثلاثة بتجسم من
+
+86
+00:07:03,240 --> 00:07:09,960
+ال 18. إذا خاصية التعدي متحققة أيضا. لأن نتيجة
+
+87
+00:07:09,960 --> 00:07:14,840
+للنظرية اللي فوق اللي هو طبعا هذه كان البرهان
+
+88
+00:07:14,840 --> 00:07:19,220
+المطلوب لكن احنا لسبب الظروف الآن أعطيناكم إياها
+
+89
+00:07:19,220 --> 00:07:22,820
+بدون برهان وهنا حكينا أمثلة عددية عليها. المهم نفهم
+
+90
+00:07:22,820 --> 00:07:27,160
+إيش اللي هو الخاصية دي. نيجي لل Corollary أو النتيجة
+
+91
+00:07:27,160 --> 00:07:31,420
+لل theorem اللي عندنا. بقول لو كان a و b و c عبارة
+
+92
+00:07:31,420 --> 00:07:35,820
+عن أعداد صحيحة وال a لا تساوي c يعني if a and b
+
+93
+00:07:35,820 --> 00:07:40,120
+and c are integers وال a لا تساوي صفر such that
+
+94
+00:07:40,120 --> 00:07:44,300
+ال a divides ال b وال a divides ال c يعني ال a
+
+95
+00:07:44,300 --> 00:07:48,990
+بتقسم ال b وال a بتقسم ال c. إذا الـ a هتقسم مش بس
+
+96
+00:07:48,990 --> 00:07:52,690
+الـ b زائد الـ c لأ هتقسم أي linear combination 
+
+97
+00:07:52,690 --> 00:07:57,610
+بينهم. يعني هندمج هذه وهذه مع بعض ونحصل أن الـ a
+
+98
+00:07:57,610 --> 00:08:04,090
+بتقسم الـ b m زائد الـ c n لكل m و n. إيش ال linear
+
+99
+00:08:04,090 --> 00:08:07,790
+combination هذا؟ بنسميه ال b m زائد ال c n عبارة عن
+
+100
+00:08:07,790 --> 00:08:12,010
+linear combination بين الـ b ومين؟ والـ c. إذا
+
+101
+00:08:12,010 --> 00:08:15,550
+بنقول ما يلي يا جماعة إنه لو الـ a بتقسم الـ b و
+
+102
+00:08:15,550 --> 00:08:19,810
+الـ a بتقسم الـ c حيكون عند الـ a بتقسم أي linear
+
+103
+00:08:19,810 --> 00:08:23,970
+combination b m زائد مين؟ c m where m and n 
+
+104
+00:08:23,970 --> 00:08:28,670
+integers. يعني ناخذ مثال عند الـ 3 بتقسم 12 والـ 3
+
+105
+00:08:28,670 --> 00:08:34,570
+بتقسم الـ 15. أكيد الـ 3 بتقسم 12 في m زائد 15 في n
+
+106
+00:08:34,570 --> 00:08:39,520
+لكل ال integers m و n. أنت جرب حط أي integers بيجي
+
+107
+00:08:39,520 --> 00:08:43,540
+على بالك m و n هتلاقي الثلاثة بتجسم 12 m زائد 15
+
+108
+00:08:43,540 --> 00:08:44,540
+m. ناخذ مثلا
+
+109
+00:08:54,500 --> 00:08:57,240
+الثلاثة بتجسم 78. أكيد لأن الثمانية
+
+110
+00:08:57,240 --> 00:09:01,540
+و7 و15 وجرب أعداد زي ما بدك هتلاقي مدام
+
+111
+00:09:01,540 --> 00:09:04,360
+الثلاثة بتجسم 12 والثلاثة بتجسم 15
+
+112
+00:09:04,360 --> 00:09:07,200
+الثلاثة هتجسم أي linear combination بين 12
+
+113
+00:09:07,200 --> 00:09:10,700
+و15. إيش linear combination يعني؟ 12 في m
+
+114
+00:09:10,700 --> 00:09:17,220
+زائد 15 في m لكل integers m. طيب الآن نيجي ل
+
+115
+00:09:17,220 --> 00:09:21,340
+division algorithm أو اللي بنسميها خوارزمية القسمة.
+
+116
+00:09:21,340 --> 00:09:25,600
+خوارزمية القسمة مش غريبة علينا بنعرفها بنعرفها من
+
+117
+00:09:25,600 --> 00:09:30,600
+و احنا صغار. الآن لو قلت لك قسم لي العشرة على الخمسة
+
+118
+00:09:30,600 --> 00:09:34,080
+هتقول لي العشرة على الخمسة بيساوي اثنين. بقول لك في متبقي
+
+119
+00:09:34,080 --> 00:09:38,580
+قسم هتقول لي لا. يعني وكأنه العشرة لما قسمناها على خمسة
+
+120
+00:09:38,580 --> 00:09:42,240
+طلعت ناتج قسمة اثنين ولا يوجد متبقي قسمة يعني
+
+121
+00:09:42,240 --> 00:09:47,080
+متبقي القسمة صفر. لكن لو قلت لك قسم 11 على خمسة على
+
+122
+00:09:47,080 --> 00:09:51,000
+خمسة هتقول 11 على خمسة بيساوي اثنين وبيزيد واحد.
+
+123
+00:09:51,000 --> 00:09:56,880
+هذا الواحد هو متبقي القسمة والاثنين هي ناتج القسمة.
+
+124
+00:09:56,880 --> 00:09:59,880
+هذا اللي بتقوله بالظبط ال division algorithm. when
+
+125
+00:09:59,880 --> 00:10:03,220
+an integer is divided by a positive integer there
+
+126
+00:10:03,220 --> 00:10:06,900
+is a quotient and remainder يعني في ذاتها قسمة وفي 
+
+127
+00:10:06,900 --> 00:10:12,560
+متبقي قسمة لما نقسم اللي هو العدد على positive number
+
+128
+00:10:12,560 --> 00:10:17,980
+دي اللي هو مقسوم عليه this is traditionally called
+
+129
+00:10:17,980 --> 00:10:22,780
+the division algorithm أو خوارزمية القسمة وخلّينا
+
+130
+00:10:22,780 --> 00:10:27,620
+نشوف إيش خوارزمية القسمة أو نظرية الخوارزمية
+
+131
+00:10:27,620 --> 00:10:31,320
+القسمة بتقول بقى يعني صلوا على النبي عليه الصلاة
+
+132
+00:10:31,320 --> 00:10:35,400
+والسلام if a is an integer and d is a positive
+
+133
+00:10:35,400 --> 00:10:38,940
+integer يعني a أي انتجر سالم موجبة بالإبداكية حتى 
+
+134
+00:10:38,940 --> 00:10:42,560
+لو كان صفر مش فارغة هقلناه و ال d positive integer
+
+135
+00:10:42,560 --> 00:10:47,340
+أكبر من صفر لما نقسم ال a على ال d هيطلع ناتج قسمة
+
+136
+00:10:47,340 --> 00:10:54,550
+بدي أسميه Q والمتبقي اللي هو بدي أسميه R بعد ذلك
+
+137
+00:10:54,550 --> 00:10:58,790
+يوجد
+
+138
+00:10:58,790 --> 00:11:05,370
+ناتج قسمة واحد Q ومتبقي واحد R بحيث أن R أكبر أو يساوي صفر
+
+139
+00:11:05,370 --> 00:11:13,050
+وصغر من D دائماً عندما تقسم ال A على ال D يعني
+
+140
+00:11:13,050 --> 00:11:17,750
+11 على خمسة و تقول 11 على خمسة بيطلع اثنين و بضال
+
+141
+00:11:17,750 --> 00:11:22,290
+واحد الواحد هذا سبناه ليش سبناه لأنه أصلاً هو أكبر أو
+
+142
+00:11:22,290 --> 00:11:25,650
+يساوي صفر و أصغر من المقسوم عليه اللي هي الخمسة
+
+143
+00:11:25,650 --> 00:11:29,450
+فدائماً ال remainder بيكون أكبر أو يساوي صفر و أصغر
+
+144
+00:11:29,450 --> 00:11:35,160
+من المقسوم عليه ال D إذاً لما نقعد نقسم ال A على ال
+
+145
+00:11:35,160 --> 00:11:40,920
+D بيطلع لنا ناتج قسمة اسمه Q وفيه remainder اسمه R
+
+146
+00:11:40,920 --> 00:11:45,700
+عشان هيك بنقول A بتساوي D في Q زائد R زي ما قولنا
+
+147
+00:11:45,700 --> 00:11:53,020
+ل 11 بساوي ال 5 في 2 ب 10 زائد ال 1 ال 1 هو ال
+
+148
+00:11:53,020 --> 00:11:58,060
+remainder وال 2 هو ناتج القسمة هو الخمسة اللي
+
+149
+00:11:58,060 --> 00:12:04,040
+قسمنا عليها إذاً الآن الـ A بيتساوى DQ زائد الـ R حيث
+
+150
+00:12:04,040 --> 00:12:10,160
+الـ A هو المقسوم والـ D المقسوم عليه والـ Q ناتج
+
+151
+00:12:10,160 --> 00:12:15,140
+القسمة والـ R هو المتبقي D is called the divisor
+
+152
+00:12:15,870 --> 00:12:19,670
+الآن المقسوم عليه A is called the dividend اللي هو
+
+153
+00:12:19,670 --> 00:12:24,690
+المقسوم و Q is called the quotient ناتج القسمة و R
+
+154
+00:12:24,690 --> 00:12:29,370
+is called the remainder من هذا الحديث الآن بدنا
+
+155
+00:12:29,370 --> 00:12:34,580
+نستقي مع بعض دالتين نعرفن كما يلي definitions of
+
+156
+00:12:34,580 --> 00:12:38,300
+functions واحدة اسمها div واحدة اسمها mod بدنا
+
+157
+00:12:38,300 --> 00:12:42,980
+نصطلح مع بعض شو معناه أن احنا بنقول ايه div دي
+
+158
+00:12:42,980 --> 00:12:47,360
+اللي بنقصد فيها أنه لما جينا قسمنا ال a على ال d
+
+159
+00:12:48,000 --> 00:12:52,640
+طلع عندي ناتج قسمة ناتج القسمة هذا اللي بتسميه a
+
+160
+00:12:52,640 --> 00:12:59,060
+ضاض d بقصد فيه ناتج قسمة a على d هذا ناتج القسمة
+
+161
+00:12:59,060 --> 00:13:06,200
+طيب أهم ال d إيش بقصد فيه هو المتبقي من ناتج قسمة a
+
+162
+00:13:06,200 --> 00:13:11,460
+على d إذا a ضاض d مقصود فيه لما أقسم a على d
+
+163
+00:13:11,460 --> 00:13:15,650
+بيطلع اللي هي ناتج القسمة لما أقسم الـ a على d
+
+164
+00:13:15,650 --> 00:13:19,170
+بيطلع عندي remainder فبقصد ال a mod ال d هو عبارة
+
+165
+00:13:19,170 --> 00:13:22,710
+عن مين المتبقي أو ال remainder اتفقنا علينا دول
+
+166
+00:13:22,710 --> 00:13:29,150
+الدالتين يللا خلينا نشوف أمثلة عددية طيب احنا نشوف
+
+167
+00:13:29,150 --> 00:13:35,190
+أمثلة عددية المثال العددي لل division algorithm هو ما
+
+168
+00:13:35,190 --> 00:13:38,610
+يعني what are the quotient and remainder when 101
+
+169
+00:13:38,610 --> 00:13:45,250
+is divided by 11 بنشوف إيش اللي هو الناتج القسمة
+
+170
+00:13:45,250 --> 00:13:50,410
+ومتبقي القسمة لما نقسم 101 على 11 أكيد كلكم كان
+
+171
+00:13:50,410 --> 00:13:56,870
+101 على 11 في 99 و بيظهر بينهم قد إيش بزيادة 2 فاكيد
+
+172
+00:13:56,870 --> 00:14:02,600
+اللي هو هيكون عندي 101 بيساوي 11 اللي هو ضرب تسعة
+
+173
+00:14:02,600 --> 00:14:08,040
+زائد اثنين تسعة هذا هو ناتج القسمة والاثنين هو
+
+174
+00:14:08,040 --> 00:14:12,480
+متبقي القسمة عشان هيك بنكتبهم بالطريقة اللي اتفقنا
+
+175
+00:14:12,480 --> 00:14:16,860
+عليها قبل شوية اللي هو بيصير عندي اللي هو عندي
+
+176
+00:14:16,860 --> 00:14:24,760
+المتبقي القسمة اللي هو 2 فبنكتب 101 mod 11 بما أن في
+
+177
+00:14:24,760 --> 00:14:30,560
+متبقي القسمة لما نقسم 101 ل 11 بيطلع 2 وبنكتب 101
+
+178
+00:14:30,560 --> 00:14:34,740
+mod 11 معناته الدالة هذه بتعني أنه لما نقسم 101
+
+179
+00:14:34,740 --> 00:14:40,720
+ل 11 بيكون ناتج القسمة 100 اللي هو 9 زي ما شفنا
+
+180
+00:14:40,720 --> 00:14:42,740
+اللي عاملينه احنا هنا في ال division
+
+181
+00:14:46,330 --> 00:14:52,950
+السؤال الثاني هو what are the quotient and
+
+182
+00:14:52,950 --> 00:14:59,090
+remainder when -11 is divided by 3 ناقص 11 ناقص 11 ناقص
+
+183
+00:14:59,090 --> 00:15:05,190
+11 ناقص 11 ناقص
+
+184
+00:15:05,190 --> 00:15:07,770
+11 ناقص 11 ناقص 11 ناقص 11 ناقص 11 ناقص 11 ناقص 11 ناقص
+
+185
+00:15:07,770 --> 00:15:12,600
+11 ناقص 11 ناقص 11 ناقص 11 ناقص 11 ناقص 11 في هذه الحالة
+
+186
+00:15:12,600 --> 00:15:16,720
+بيصير ناقص 11 بيساوي ثلاثة في ناقص أربعة زائد واحد
+
+187
+00:15:16,720 --> 00:15:19,900
+لما نقسم الناقص ماحدش يقول ناقص ثلاثة لأنه بيصير
+
+188
+00:15:19,900 --> 00:15:23,020
+ثلاثة في ناقص ثلاثة بيساوي ناقص تسعة ناقص تسعة
+
+189
+00:15:23,020 --> 00:15:26,520
+بيصير ناقص أحد عشر بيساوي ناقص تسعة ناقص اثنين و ال
+
+190
+00:15:26,520 --> 00:15:29,920
+remainder لازم المتبقي يكون إيه شماله أكبر من صفر
+
+191
+00:15:29,920 --> 00:15:33,420
+و أصغر من ثلاثة لأن احنا لما نقدر نقسم أي عدد على
+
+192
+00:15:33,420 --> 00:15:40,830
+ال remainder بيطلع أنه عدد صحيح لو زاد عن اللي هو
+
+193
+00:15:40,830 --> 00:15:44,490
+.. لو ال remainder طلع بالسالب لأ احنا ما بنقبلش
+
+194
+00:15:44,490 --> 00:15:48,130
+بنوحد الكلام كله مع بعض كلنا نقسم زي بعض و طلعنا
+
+195
+00:15:48,130 --> 00:15:51,810
+remainder زي بعض و ناتج قسمنا زي بعض عشان هيك
+
+196
+00:15:51,810 --> 00:15:55,650
+بنطلب ال remainder يكون بين الصفر و بين الثلاثة زي
+
+197
+00:15:55,650 --> 00:16:00,230
+ما كنا نعمل زمان في قسمة الأعداد الصحيحة على بعض
+
+198
+00:16:00,230 --> 00:16:04,090
+الآن هذا بيصير ناقص 11 بيساوي ثلاثة في ناقص 4 زائد من
+
+199
+00:16:04,090 --> 00:16:08,980
+1 الآن هذا اللي هو الواحد هو عبارة عن ال remainder
+
+200
+00:16:08,980 --> 00:16:13,880
+عشان هيك بنقول الواحد اللي هو بيساوي ناقص أحد عشر mod
+
+201
+00:16:13,880 --> 00:16:19,620
+ثلاثة نقول إن دالة المد هذه تعني قسمة ناقص أحد عشر ع
+
+202
+00:16:19,620 --> 00:16:24,380
+ثلاثة بيطلع متبقي القسمة بيساوي واحد يعني هذه تدل
+
+203
+00:16:24,380 --> 00:16:30,390
+على متبقي القسمة الآن اللي هو ناقص 11 ضاض 3 تعني
+
+204
+00:16:30,390 --> 00:16:34,610
+اللي هو ناتج قسمة ناقص 11 على 3 اللي هو إيش طلع
+
+205
+00:16:34,610 --> 00:16:40,030
+عندي ناقص 4 و هيك بنوجد اللي هو ناتج القسمة و
+
+206
+00:16:40,030 --> 00:16:47,990
+بنوجد مين اللي هو متبقي القسمة الآن إن دخلنا على
+
+207
+00:16:47,990 --> 00:16:52,510
+حاجة اسمها ال congruence relation أو اللي هي علاقة
+
+208
+00:16:52,510 --> 00:16:56,690
+التطابق الآن إيش اللي بنقصد فيها علاقة التطابق؟
+
+209
+00:16:56,690 --> 00:17:00,110
+خلينا نشوف إيش اللي هو تعريف علاقة التطابق دي، إيش
+
+210
+00:17:00,110 --> 00:17:03,670
+معناه الـcongruence؟ لو كان عندي A وB عبارة عن
+
+211
+00:17:03,670 --> 00:17:07,050
+أعداد صحيحة integers and M is a positive integer
+
+212
+00:17:07,050 --> 00:17:12,420
+والـ M إيش ماله؟ عدد صحيح موجب بنقول أن a is
+
+213
+00:17:12,420 --> 00:17:17,180
+congruent to b modulo m يعني a تطابق b modulo m
+
+214
+00:17:17,180 --> 00:17:23,200
+يعني a تطابق b اللي هو بالنسبة للمقياس m إذا حققت
+
+215
+00:17:23,200 --> 00:17:29,060
+مالي ال m تقسم ال b ناقص a أو تقسم ال a ناقص b
+
+216
+00:17:29,060 --> 00:17:33,420
+في هذه الحالة بنقول a تطابق ال b modulo m وبنرمز
+
+217
+00:17:33,420 --> 00:17:37,790
+لها بالرمز اللي عندي a is congruent to B modulo M
+
+218
+00:17:37,790 --> 00:17:46,650
+نعني بها أن M تقسم اللي هو ال A ناقص B تقسم ال A
+
+219
+00:17:46,650 --> 00:17:52,030
+ناقص B هذا معناه أن A تطابق ال B modulo M الآن
+
+220
+00:17:52,030 --> 00:17:57,510
+هذه على بعضها بنسميها is a congruence أو بنسميها
+
+221
+00:17:57,510 --> 00:18:03,870
+تطابقة و ال M هو ال modulus أو هو مقياس التطابق
+
+222
+00:18:03,870 --> 00:18:08,180
+بنسميه الآن اللي اللي اللي اللي اللي اللي اللي اللي
+
+223
+00:18:08,180 --> 00:18:08,440
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+224
+00:18:08,440 --> 00:18:09,560
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+225
+00:18:09,560 --> 00:18:10,360
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+226
+00:18:10,360 --> 00:18:10,480
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+227
+00:18:10,480 --> 00:18:12,300
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+228
+00:18:12,300 --> 00:18:12,320
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+229
+00:18:12,320 --> 00:18:13,660
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+230
+00:18:13,660 --> 00:18:14,520
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+231
+00:18:14,520 --> 00:18:16,420
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+232
+00:18:16,420 --> 00:18:17,660
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+233
+00:18:17,660 --> 00:18:24,600
+يكون المتطابقتين إذا كان ال a و ال b
+
+234
+00:18:24,600 --> 00:18:28,740
+اللي هي نفس ال remainder لو قسمناها على ال m يعني
+
+235
+00:18:28,740 --> 00:18:33,260
+لو قسمنا ال b على ال m هنلاقي اللي هو ناتج القسمة
+
+236
+00:18:33,260 --> 00:18:39,660
+b على m R1 و ناتج قسمة a على m R2 في حالة ما يكون
+
+237
+00:18:39,660 --> 00:18:44,980
+المتطابقتين لازم ال R1 إيش يساوي R2 عشان هيك two
+
+238
+00:18:44,980 --> 00:18:49,390
+integers are congruent modulo m if and only if they
+
+239
+00:18:49,390 --> 00:18:53,690
+have the same remainder when divided by m
+
+240
+00:18:53,690 --> 00:18:59,810
+لو كانت ال a لا تطابق ال b بنرمز ال a لا تطابق ال b
+
+241
+00:18:59,810 --> 00:19:03,430
+modulo m وهذا ماذا بتحدث؟ بتحدث لما نلاقي ال m لا
+
+242
+00:19:03,430 --> 00:19:08,430
+تقسم ال a ناقص b أو لما نلاقي ال remainder لل b
+
+243
+00:19:08,430 --> 00:19:13,250
+لما نقسمها على m يختلف عن ال remainder لل a لما
+
+244
+00:19:13,250 --> 00:19:18,910
+نقسمها على m طيب خلينا نشوف احنا مثال أو
+
+245
+00:19:18,910 --> 00:19:23,510
+أمثلة عددية نشوف المثال العددي بيقول determine
+
+246
+00:19:23,510 --> 00:19:27,670
+whether ال 17 is congruent to 5 ولا لأ أو بعدين
+
+247
+00:19:27,670 --> 00:19:31,630
+modulo 6 طبعاً and whether ال 24 and ال 14 are
+
+248
+00:19:31,630 --> 00:19:35,030
+congruent modulo 6 الآن بده يشوف السبعة عشر والخمسة
+
+249
+00:19:35,030 --> 00:19:39,830
+هل المتطابقتين modulo 6 قلنا أحد أمرين ابني جي
+
+250
+00:19:39,830 --> 00:19:44,810
+بنقول السبعة عشر ناقص خمسة بيطلع اثنا عشر الستة بتقسم 
+
+251
+00:19:44,810 --> 00:19:49,390
+إذن إذا السبعة عشر بتقسم الخمسة modulo 6 الآن طريقة
+
+252
+00:19:49,390 --> 00:19:53,910
+أخرى اللي هي أنه بنجيب نجسم السبعة عشر على الستة
+
+253
+00:19:53,910 --> 00:19:58,410
+المتبقي جدّيش خمسة هو نفس المتبقي لما الخمسة نجسمها 
+
+254
+00:19:58,410 --> 00:20:01,250
+على الستة لأن المتبقي بيطلع خمسة ونتج القسم صفر
+
+255
+00:20:01,250 --> 00:20:07,160
+طبيعي إذن الآن السبعة عشر تطابق خمسة modulo ستة لأن أحد
+
+256
+00:20:07,160 --> 00:20:12,540
+سببين يا إما الستة بتقسم حاصل طرحين يا إما هذا لما 
+
+257
+00:20:12,540 --> 00:20:16,180
+نقسم على هذا وهذا لما نقسم على هذا بيعطي نفس
+
+258
+00:20:16,180 --> 00:20:21,520
+النتيجة نفس اللي هو ال remainder طيب الآن يجي نحكم
+
+259
+00:20:21,520 --> 00:20:24,240
+على مين؟ على الرابعة والعشرين والرابعة عشر هل congruent
+
+260
+00:20:24,240 --> 00:20:27,100
+modulo ستة ولا لأ؟ أكيد كلكم قالوا الرابعة والعشرون نقص
+
+261
+00:20:27,100 --> 00:20:30,900
+الرابعة عشر بتساوي عشرة الستة بتقسمش العشرة إذن
+
+262
+00:20:30,900 --> 00:20:35,580
+الرابعة والعشرون لا تطابق الرابعة عشر modulo ستة أو
+
+263
+00:20:35,580 --> 00:20:40,080
+مقياس ستة الآن لو أحد قال لا ما هو أنا بتطلع لها
+
+264
+00:20:40,080 --> 00:20:44,080
+نظرة أخرى الرابعة والعشرون لو جسمناها على الستة بتطلع
+
+265
+00:20:44,080 --> 00:20:47,560
+ال remainder صفر لأنه تقبل القسمة عليها لكن الرابعة
+
+266
+00:20:47,560 --> 00:20:49,920
+عشر لما نجسمها على الستة بتطلع عندي remainder
+
+267
+00:20:49,920 --> 00:20:52,260
+اثنين إذن ال remainder هنا وال remainder هنا
+
+268
+00:20:52,260 --> 00:20:56,320
+مختلفات إذن they are not Congruent أحد الأمرين اللي
+
+269
+00:20:56,320 --> 00:21:02,220
+بتشتغلوه هو صحيح ندى الآن نشوف أخذنا شغلتين الآن
+
+270
+00:21:02,220 --> 00:21:07,310
+أخذنا اللي هو إيه؟ تطابق الـ P modulo M اللي هو و
+
+271
+00:21:07,310 --> 00:21:11,230
+الـ a mod m بتساوي b بدنا نشوف العلاقة the
+
+272
+00:21:11,230 --> 00:21:14,450
+relation between أو the relationship between mod m
+
+273
+00:21:14,450 --> 00:21:20,130
+and mod m notations يعني هذه اللي بالغامق هذه اللي
+
+274
+00:21:20,130 --> 00:21:25,350
+بنقصد فيها دالة a mod m اللي هي نقصدنا فيها دالة
+
+275
+00:21:25,350 --> 00:21:30,350
+لما عرفنا هي وال dive الآن a تطابق b mod m اللي
+
+276
+00:21:30,350 --> 00:21:35,560
+هي علاقة بين اللي هي integers a و b قلنا إيش هذا
+
+277
+00:21:35,560 --> 00:21:40,100
+بتعني؟ بتعني أن a تطابق b modulo m اللي هي معناتها
+
+278
+00:21:40,100 --> 00:21:45,480
+أن m بتجسم ال a minus b أو بمعنى آخر قلنا معناتها
+
+279
+00:21:45,480 --> 00:21:52,300
+أن المتبقي القسمة من a على m هو نفس متبقي القسمة
+
+280
+00:21:52,300 --> 00:21:57,650
+من b على m بينما هذه يا جماعة اللي بتعني a mod m
+
+281
+00:21:57,650 --> 00:22:04,790
+أنه لما نجسم ال a على m متبقي القسمة بساوي b ماشي
+
+282
+00:22:04,790 --> 00:22:09,870
+إذن لما نقول a mod m بساوي b يعني متبقي قسمة a على
+
+283
+00:22:09,870 --> 00:22:15,430
+m بساوي b أما هنا a تطابق b mod m أنه متبقي القسمة
+
+284
+00:22:15,430 --> 00:22:23,690
+a على m هو نفسه متبقي القسمة b لما نقسمه على m الآن
+
+285
+00:22:23,690 --> 00:22:27,050
+هذا الكلام حكيته أنا it وطبق me the relation on
+
+286
+00:22:27,050 --> 00:22:30,110
+the six integers هذه علاقة على الستة integers بينما
+
+287
+00:22:30,110 --> 00:22:33,370
+هذه عبارة عن دالة اتفاقنا عليها اللي هي the
+
+288
+00:22:33,370 --> 00:22:37,230
+notation denotes the function أو a function
+
+289
+00:22:37,230 --> 00:22:40,870
+العلاقة بين التنتين الآن هنشوف that the
+
+290
+00:22:40,870 --> 00:22:44,550
+relationship between these two is made clear in
+
+291
+00:22:44,550 --> 00:22:47,950
+this theorem هتكون واضحة من خلال هذه النظرية اللي
+
+292
+00:22:47,950 --> 00:22:51,230
+أمامنا شوفوا يا جماعة صلى الله عليه الصلاة والسلام
+
+293
+00:22:51,600 --> 00:22:56,700
+لو كان عندي a و b integers و m positive integers
+
+294
+00:22:56,700 --> 00:23:03,700
+احنا ال a تطابق b modulo m هي تكافئ تماما يعني if
+
+295
+00:23:03,700 --> 00:23:09,620
+and only if هذه على بعضها هذه تكافئ تماما أن نقول
+
+296
+00:23:09,620 --> 00:23:17,760
+a mod m بساوي b mod m لأن بي mod ام إيش بتعني؟ أن متبقي
+
+297
+00:23:17,760 --> 00:23:22,600
+قسمة ال b على m يساوي متبقي قسمة ال a على m لأن
+
+298
+00:23:22,600 --> 00:23:25,800
+هذه بتعني متبقي قسمة ال a على m وهذه بتعني متبقي
+
+299
+00:23:25,800 --> 00:23:29,860
+قسمة ال b على m هذه معناتها مساواة يعني متبقي
+
+300
+00:23:29,860 --> 00:23:33,760
+قسمة هذه على هذه بساوي متبقي قسمة هذه على هذه هو
+
+301
+00:23:33,760 --> 00:23:38,910
+بالضبط هذا اللي هو A تطابق B mod M يعني متطابق قسمة
+
+302
+00:23:38,910 --> 00:23:44,750
+A على M اللي هو نفسه متطابق قسمة B على M وكأنه هذا
+
+303
+00:23:44,750 --> 00:23:51,070
+التعبير هو هذا التعبير ولكن بصورة أخرى ماشي الحال؟
+
+304
+00:23:51,070 --> 00:23:58,070
+طيب الآن إذا هذا بكافة اللي هو هذه الكلمتين بخزن
+
+305
+00:23:58,070 --> 00:24:02,820
+هذول اللي عندنا أو كافاته خلينا نشوف مثال الآن الـ
+
+306
+00:24:02,820 --> 00:24:09,780
+31 و 351 متطابقتين ليش؟ لأن 351 ناقص 31 تطلع 320
+
+307
+00:24:09,780 --> 00:24:14,340
+العشرة بتجسمها إذن فعلاً متطابقتين بالنسبة للمقياس
+
+308
+00:24:14,340 --> 00:24:20,600
+عشرة الآن طيب الآن إني جيت نشوف اللي هو ال .. ال ..
+
+309
+00:24:20,600 --> 00:24:25,380
+ال .. نظرة أخرى لهذه أن هذا وهذول اللي هي نفس ال
+
+310
+00:24:25,380 --> 00:24:30,320
+remainder لما نجسمها للعشرة هذا هو الآن 31 لما
+
+311
+00:24:30,320 --> 00:24:35,160
+تجسمها على عشرة بيطلع متبقي واحد 351 لما تجسمها
+
+312
+00:24:35,160 --> 00:24:39,580
+على عشرة بيطلع متبقي واحد إذن هذا بيساوي هذا يعني
+
+313
+00:24:39,580 --> 00:24:44,640
+اللي هي التطابقات وبالمناسبة التطابقات اللي هو
+
+314
+00:24:44,640 --> 00:24:49,300
+موضوع ال congruences هذه هي أصلاً لودادتنا أو
+
+315
+00:24:49,300 --> 00:24:54,900
+خلينا نقول اللي بتعلمنا كيف أو قدام هنعرف أنظمة
+
+316
+00:24:54,900 --> 00:24:59,020
+العد من خلالها نظام العد الثاني نظام العد الثلاثي
+
+317
+00:24:59,020 --> 00:25:03,200
+الرباعي الخماسي العشاري اللي بنتعامل فيه أو الست عشري
+
+318
+00:25:03,200 --> 00:25:07,580
+أو الثمانية اللي بدنا إياه اللي هو النظام العد اللي
+
+319
+00:25:07,580 --> 00:25:11,800
+هو اللي بتبع من المقياس يعني مقياس عشرة بنصير مجول
+
+320
+00:25:11,800 --> 00:25:15,240
+عن نظام العد العشاري مقياس اثنين بنصير مجول عن
+
+321
+00:25:15,240 --> 00:25:19,440
+نظام العد الاثنين وهكذا وإن شاء الله هنجيه قدام
+
+322
+00:25:19,780 --> 00:25:24,780
+الآن بيكون هيك احنا خلصنا اللي هو اللي بدنا إياه في
+
+323
+00:25:24,780 --> 00:25:28,540
+هذا ال section وعندي ال homework التالي بدنا إياه
+
+324
+00:25:28,540 --> 00:25:32,580
+تجيبوليه ببعتلكم عن واتس بظبط إيش اللي بدنا إياه الآن
+
+325
+00:25:32,580 --> 00:25:36,920
+السؤال الأول بيقول لي 31 تطابق ماذا modulo سبعة هل
+
+326
+00:25:36,920 --> 00:25:40,140
+بالطابق الخامسة، بالطابق ال 211؟ يمكن الطابق
+
+327
+00:25:40,140 --> 00:25:42,720
+واحدة، اثنتين، ثلاث، كل واحدة من هناك تشوف مين
+
+328
+00:25:42,720 --> 00:25:46,420
+بالطابق ال 31 modulo السبعة وتحط اللي تحتها خط
+
+329
+00:25:46,420 --> 00:25:51,430
+وتقول لي ليش بالطابقها والثاني لماذا بالطبق عشرة؟
+
+330
+00:25:51,430 --> 00:25:55,430
+find اللي هو عشرة ضايف ثلاثة عشر ضايف ثلاثة قد إيش
+
+331
+00:25:55,430 --> 00:25:59,890
+قيمته 101 ضايف ثلاثة وعشرين برضه نفس الشيء وبعدين
+
+332
+00:25:59,890 --> 00:26:04,170
+أوجد عشرة modulo ثلاثة الآخر هذول إيجاد زي ما شرحنا
+
+333
+00:26:04,170 --> 00:26:07,530
+قبل شوية الآن question الثالث which of the
+
+334
+00:26:07,530 --> 00:26:09,710
+following divides the positive integer a؟ يعني
+
+335
+00:26:09,710 --> 00:26:15,070
+عندي في positive integer a مين من هذول divides
+
+336
+00:26:15,070 --> 00:26:19,950
+which of the following divides the positive
+
+337
+00:26:19,950 --> 00:26:25,510
+integer a إيه أو خلينا نقول which of the following
+
+338
+00:26:25,510 --> 00:26:52,400
+أو a divides which of the following a divides
+
+339
+00:26:52,400 --> 00:26:57,500
+which of the following يعني مش هنا اللي بدنا نوجد
+
+340
+00:26:57,500 --> 00:27:02,920
+منه هل ال a بتجسم هذول ولا لأ؟ a بتجسم مين منهم بدك
+
+341
+00:27:02,920 --> 00:27:07,360
+تحددها وهيك بكون خلصنا ال section الأول وإلى
+
+342
+00:27:07,360 --> 00:27:11,840
+لقاء آخر والسلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4ad0ad01c1d05314e1ec58727b9a070f83421317
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_postprocess.srt
@@ -0,0 +1,1368 @@
+1
+00:00:00,000 --> 00:00:04,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,180 --> 00:00:07,720
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:07,720 --> 00:00:14,600
+آله وصحبه أجمعين هذه هي المحاضرة الرابعة في مساق
+
+4
+00:00:14,600 --> 00:00:18,960
+قياضيات منفصلة لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:18,960 --> 00:00:28,290
+كلية ال IT قسم الحوسبة المتنقلةالمحاضرة اليوم هي
+
+6
+00:00:28,290 --> 00:00:34,090
+المحاضرة الأولى أيضا في chapter 4 وهو المعنوان ب
+
+7
+00:00:34,090 --> 00:00:39,210
+number theory and cryptography اللي هي بنقصد فيها
+
+8
+00:00:39,210 --> 00:00:44,010
+نظرية الأعداد والترميز والترميز هو عبارة عن تطبيق
+
+9
+00:00:44,010 --> 00:00:50,230
+على نظرية الأعداد ال section الأول اللي هنتحدث عنه
+
+10
+00:00:50,230 --> 00:00:53,910
+اليوم اللي هو divisibility and modular arithmetic
+
+11
+00:00:54,520 --> 00:01:02,080
+اللي هو شو معناته القسمة أو قابلية القسمة وحنشوف
+
+12
+00:01:02,080 --> 00:01:05,920
+دالتين واحدة دالة اسمها المد وواحدة دالة اسمها
+
+13
+00:01:05,920 --> 00:01:12,840
+dive ونشوف إيش اللي بنقصد فيهمالان نحكي اول شيء عن
+
+14
+00:01:12,840 --> 00:01:18,380
+ال division الان ال division اللي هي القسمة نشوف
+
+15
+00:01:18,380 --> 00:01:24,020
+شو معناته ال a divides b ايش معناته انه عدد يقسم
+
+16
+00:01:24,020 --> 00:01:30,720
+عدد اخر اسمه b طبعا حديثنا كله بصب بس اللي هو في
+
+17
+00:01:30,720 --> 00:01:33,860
+ال integers يعني احنا كل الاعداد اللي بنتناولها
+
+18
+00:01:33,860 --> 00:01:39,190
+اليوم هي عبارة عن اعداد صحيحةالان بنقول if a and b
+
+19
+00:01:39,190 --> 00:01:42,590
+are integers يعني لو كان عندي a و b عبارة عن أعداد
+
+20
+00:01:42,590 --> 00:01:46,870
+صحيحة with a لا تساوي سفر مدام قال with a لا تساوي
+
+21
+00:01:46,870 --> 00:01:53,230
+سفر شكلنا هنقسم على a لأن القسم على a مرفوض فعشان
+
+22
+00:01:53,230 --> 00:01:58,120
+هيك مفترضين ان a لا تساوي سفرالان بيقول then a
+
+23
+00:01:58,120 --> 00:02:03,140
+divides b يعني بيقول ان a تقسم b شو معنى a تقسم b
+
+24
+00:02:03,140 --> 00:02:07,700
+اللي هو if there exists an integer c such that ال
+
+25
+00:02:07,700 --> 00:02:13,440
+b بتساوي ال a في c في هذه الحالة بيقول a divides b
+
+26
+00:02:13,730 --> 00:02:18,310
+يعني اكترنا نكتب بي على صورة a في integer اخر او
+
+27
+00:02:18,310 --> 00:02:23,090
+في عدد صحيح اخر زي ما نقول ستة بتساوي اتنين فتلاتة
+
+28
+00:02:23,090 --> 00:02:29,150
+فبتكون التنين تقسم من الستة يعني بمعنى اخر a
+
+29
+00:02:29,150 --> 00:02:35,630
+divides b اللي هو a is a factor of b يعني a عامل
+
+30
+00:02:35,630 --> 00:02:41,660
+من عوامل bأو divisor of B أو قاسم من قواسم الـ B
+
+31
+00:02:41,660 --> 00:02:46,160
+إذا لما نقول A divides B بنقصد أنه A عامل من عوامل
+
+32
+00:02:46,160 --> 00:02:52,900
+B وبنقصد A قاسم من قواسم ال B أو بنقصد B عبارة عن
+
+33
+00:02:53,170 --> 00:02:58,210
+من مضاعفات الـ A يعني B is multiple of A كل
+
+34
+00:02:58,210 --> 00:03:04,230
+التعبير الثلاثة دول A قاسم من قاسم الـ B أو A عامل
+
+35
+00:03:04,230 --> 00:03:09,010
+من عوامل الـ B أو B من مضاعفات الـ A كلها المقصود
+
+36
+00:03:09,010 --> 00:03:16,380
+فيها أن A divides Bما هي الـ notation تبعتها؟ نقول
+
+37
+00:03:16,380 --> 00:03:20,660
+a divides b وهي a وهي عصرها بينهم b شكل العصرها هي
+
+38
+00:03:20,660 --> 00:03:26,720
+شبه عمودية يعني a divides b denotes that a divides
+
+39
+00:03:26,720 --> 00:03:32,420
+b أو a تقسم بي الان قلنا ان a تقسم بي معناته ان ال
+
+40
+00:03:32,420 --> 00:03:35,740
+a عامل من عامل بي يعني لو جينا جسمنا ال b على ال a
+
+41
+00:03:35,740 --> 00:03:40,190
+هتطلع integerيعني الآن لما نقول a تقسم b بنعني انه
+
+42
+00:03:40,190 --> 00:03:45,650
+على طول العدد b على العدد a فده مائل يعني بيقولك
+
+43
+00:03:45,650 --> 00:03:49,890
+بي على العدد a هيطلع اشمال و انتجر زي مهنا هاي مش
+
+44
+00:03:49,890 --> 00:03:53,970
+هاد معناه a تقسم b يعني الان b على a هتطلع ال c
+
+45
+00:03:53,970 --> 00:03:58,330
+يعني انتجر إذا من الآن و طالع مجرد نقول a تقسم b
+
+46
+00:03:58,330 --> 00:04:02,110
+معناته ال b على ال a هو عبارة عن عدد صحيحطب لو
+
+47
+00:04:02,110 --> 00:04:05,850
+بدنا نقول a does not divide b نرمز بالرمزية ده a
+
+48
+00:04:05,850 --> 00:04:10,030
+وهي الشحطة الأولى وهي فجهها شحطة تانية يعني a does
+
+49
+00:04:10,030 --> 00:04:15,810
+not divide b يعني a لا تقسم ال b ناخد أمثل عددية
+
+50
+00:04:15,810 --> 00:04:19,830
+الان المثال الأول determine whether التلاتة بتقسم
+
+51
+00:04:19,830 --> 00:04:23,940
+السابعة and whether التلاتة بتقسم أطنعاشلأ احنا
+
+52
+00:04:23,940 --> 00:04:26,800
+على طول الحد ما نشوف على طول التلاتة متقسمش السبعة
+
+53
+00:04:26,800 --> 00:04:31,640
+ليش لأن السبعة على التلاتة مش عدد صحيح اذا التلاتة
+
+54
+00:04:31,640 --> 00:04:35,780
+does not divide بيه اذا اكيد ال solution هنقوله
+
+55
+00:04:35,780 --> 00:04:40,020
+التلاتة لا تقسم السبعة because اللي هو السبعة على
+
+56
+00:04:40,020 --> 00:04:44,520
+التلاتة ليست عدد صحيحلأن تلاتة بتقسم 12 كلكم قال
+
+57
+00:04:44,520 --> 00:04:47,660
+هل جيت 12 ع تلاتة أربعة يعني التلاتة لازم تقسم من
+
+58
+00:04:47,660 --> 00:04:52,080
+12 إذا أكيد تلاتة بتقسم 12 لأن 12 ع تلاتة هي عبارة
+
+59
+00:04:52,080 --> 00:04:56,600
+عن إيش طلعت الأربعة أو بمعنى أخر 12 بتساوي 3 في 4
+
+60
+00:04:56,600 --> 00:05:01,720
+زي ما عملنا في ال A ال B بتساوي A في C إذا التلاتة
+
+61
+00:05:01,720 --> 00:05:06,460
+تقسم من 12 إذا الكلام سهل طيب نيجي لخواص ال
+
+62
+00:05:06,460 --> 00:05:11,200
+divisibility أو خواص قابلية ال A أو خواص القسمة
+
+63
+00:05:11,200 --> 00:05:16,530
+نشوفاللي قال لو كان عند A وB وC عبارة عن integers
+
+64
+00:05:16,530 --> 00:05:21,330
+أعداد صحيحة والـ A لا تساوي سفر لأن شكل اللي هنقسم
+
+65
+00:05:21,330 --> 00:05:24,470
+على الـ A عشان يجي الـ A لا تساوي السفر الآن بقول
+
+66
+00:05:24,470 --> 00:05:30,130
+لي لو A بتجسم الـ Bوالـ a بتجسم ال c أكيد ال a
+
+67
+00:05:30,130 --> 00:05:34,850
+هتجسم ال b زائد ال c كلام منطقي خد مثلا اتنين
+
+68
+00:05:34,850 --> 00:05:39,910
+بتجسم الستة و اتنين بتجسم العشرة اذا اتنين بتجسم
+
+69
+00:05:39,910 --> 00:05:43,110
+الستة زاد العشرة اللي هي الست عشر اكيد اتنين بتجسم
+
+70
+00:05:43,110 --> 00:05:47,210
+الست عشر اذا دائما ال a بتجسم ال b و ال a بتجسم ال
+
+71
+00:05:47,210 --> 00:05:53,110
+c هذولة بخزن المعلومة بتعطينا ان ال a بتجسم ال b
+
+72
+00:05:53,110 --> 00:05:58,700
+زاد ال cهنروح لبعد من هيك بعد شوية الان a بتجسم ال
+
+73
+00:05:58,700 --> 00:06:04,280
+b أكيد ال a هتجسم ال b في خمسة و ال b في ستة و ال
+
+74
+00:06:04,280 --> 00:06:08,180
+b في سبعة و ال b في تمانية يعني أكيد ال a بتجسم ال
+
+75
+00:06:08,180 --> 00:06:13,780
+b في c لكل انتجار cو100 مثال نستطيع أن نقولها يعني
+
+76
+00:06:13,780 --> 00:06:18,460
+اتنين بتقسم الستة اكيد اتنين بتقسم الستة في تلاتة
+
+77
+00:06:18,460 --> 00:06:21,540
+اللي هي 18 اتنين بتقسم الستة في خمسة في تلاتين
+
+78
+00:06:21,540 --> 00:06:25,840
+اتنين بتقسم الستة في مليون اذا اتنين هتقسم ال B في
+
+79
+00:06:25,840 --> 00:06:34,640
+C اللي هو في حال اتنين بتقسم ال Bالان الخاصية هذه
+
+80
+00:06:34,640 --> 00:06:38,380
+التلاتة اللى بنسميها خاصية التحدي ال A بتجسم ال B
+
+81
+00:06:38,380 --> 00:06:42,240
+و ال B بتجسم ال C مع بعض هدولة لازم يعطلنا ال A
+
+82
+00:06:42,240 --> 00:06:47,460
+بتجسم ال C هذا الكلام سهل برضه لإن ال A بتجسم ال
+
+83
+00:06:47,460 --> 00:06:52,660
+.. خلنا نقول ال 2 بتجسم ال 6 و ال 6 بتجسم ال 24
+
+84
+00:06:52,660 --> 00:06:59,040
+إذا أكيد ال 2 بتجسم ال 24التلاتة بتجسم الستة
+
+85
+00:06:59,040 --> 00:07:03,240
+والستة بتجسم التمنتاش اذا التلاتة بتجسم من
+
+86
+00:07:03,240 --> 00:07:09,960
+التمنتاش اذا خاصية التعد متحققة ايضا لان نتيجة
+
+87
+00:07:09,960 --> 00:07:14,840
+للنظرية اللي فوق اللي هو طبعا هذه كان البرهان
+
+88
+00:07:14,840 --> 00:07:19,220
+المطلوب لكن احنا لسبب الظروف الآن اعطيناكم بيها
+
+89
+00:07:19,220 --> 00:07:22,820
+بدون برهان وهنا حكينا امثلة عددية عليها المهم نفهم
+
+90
+00:07:22,820 --> 00:07:27,160
+ايش اللي هو الخواصة دي نيجي لل Corollaryأو النتيجة
+
+91
+00:07:27,160 --> 00:07:31,420
+للtheorem اللي عندنا بقول لو كان a و b و c عبارة
+
+92
+00:07:31,420 --> 00:07:35,820
+عن أعداد صحيحة و ال a لا يساوي c يعني ال f a and b
+
+93
+00:07:35,820 --> 00:07:40,120
+and c are integers و ال a لا تساوي سفر such that
+
+94
+00:07:40,120 --> 00:07:44,300
+ال a divides ال b و ال a divides ال c يعني ال a
+
+95
+00:07:44,300 --> 00:07:48,990
+بتقسم ال b و ال a بتقسم ال cإذا الـ A هتقسم مش بس
+
+96
+00:07:48,990 --> 00:07:52,690
+الـ B زائد الـ C لأ هتقسم أي linear combination
+
+97
+00:07:52,690 --> 00:07:57,610
+بينهم يعني هندمج هذه و هذه مع بعض و نحصل ان الـ A
+
+98
+00:07:57,610 --> 00:08:04,090
+بتقسم الـ B M زائد الـ C N لكل M و N ايش ال linear
+
+99
+00:08:04,090 --> 00:08:07,790
+combination هذا بنسميه ال M B زائد ال N C عبارة عن
+
+100
+00:08:07,790 --> 00:08:12,010
+linear combination بين الـ B و مين و الـ C إذا
+
+101
+00:08:12,010 --> 00:08:15,550
+بنقول ما ياليا يا جماعةإنه لو الـ A بتقسم الـ B و
+
+102
+00:08:15,550 --> 00:08:19,810
+الـ A بتقسم الـ C حيكون عند الـ A بتقسم أي Linear
+
+103
+00:08:19,810 --> 00:08:23,970
+combination M B زائد مين M C where M and N
+
+104
+00:08:23,970 --> 00:08:28,670
+integers يعني ناخد مثال عند الـ 3 بتقسم 12 و الـ 3
+
+105
+00:08:28,670 --> 00:08:34,570
+بتقسم الـ 15 أكيد الـ 3 بتقسم 12 في M زائد 15 في N
+
+106
+00:08:34,570 --> 00:08:39,520
+لكل ال integers M و Nانت جرب حط اي integers بيجي
+
+107
+00:08:39,520 --> 00:08:43,540
+على بالك ام و ان هتلاقي التلاتة بتجسم 12 ام زاد 15
+
+108
+00:08:43,540 --> 00:08:44,540
+ام ناخد مثلًا
+
+109
+00:08:54,500 --> 00:08:57,240
+التلاتة بتجسم التمانية وسبعين اكيد لان التمانية
+
+110
+00:08:57,240 --> 00:09:01,540
+وسبعة وخمسة عشر وجرب اعداد زي ما بدك هتلاقي مادامة
+
+111
+00:09:01,540 --> 00:09:04,360
+التلاتة بتجسم اتناش والتلاتة بتجسم الخمسة عشر
+
+112
+00:09:04,360 --> 00:09:07,200
+التلاتة هتجسم اي linear combination بين اتناش
+
+113
+00:09:07,200 --> 00:09:10,700
+وخمسة عشر ايش linear combination يعني اتناش فئام
+
+114
+00:09:10,700 --> 00:09:17,220
+زي خمسة عشر فئام لكل integers oneطيب الان نجي ل
+
+115
+00:09:17,220 --> 00:09:21,340
+division algorithm او اللي بنسميها خوارزمية القسمة
+
+116
+00:09:21,340 --> 00:09:25,600
+خوارزمية القسمة مش غريبة علينا بنعرفها بنعرفها من
+
+117
+00:09:25,600 --> 00:09:30,600
+و احنا صغار الان لو جلك اجسملي العشر على الخمسة
+
+118
+00:09:30,600 --> 00:09:34,080
+هتقولي العشر على الخمسة بيساو اتنين بقولك في متبقى
+
+119
+00:09:34,080 --> 00:09:38,580
+جسم هتقولي لايعني و كأنه العشر لما جسمت على خمسة
+
+120
+00:09:38,580 --> 00:09:42,240
+طلعت ناتج قسم اتنين ولا يودد متبقى قسمها يعني
+
+121
+00:09:42,240 --> 00:09:47,080
+متبقى القسمها سفر لكن لو قلتلك ديبل 11 على خمس على
+
+122
+00:09:47,080 --> 00:09:51,000
+خمسة هتقول 11 على خمسة بيساوي اتنين و بيزيد واحد
+
+123
+00:09:51,000 --> 00:09:56,880
+هذا الواحد هو متبقى قسمهاوالاتنين هي ناتج القسمة
+
+124
+00:09:56,880 --> 00:09:59,880
+هذا اللي بتقوله بالظبط ال division algorithm when
+
+125
+00:09:59,880 --> 00:10:03,220
+an integer is divided by a positive integer there
+
+126
+00:10:03,220 --> 00:10:06,900
+is a quotient and remainder يعني في ذاتج قسمة وفي
+
+127
+00:10:06,900 --> 00:10:12,560
+متبقى قسمة لما نجسم اللي هوعدد على positive number
+
+128
+00:10:12,560 --> 00:10:17,980
+دي اللي هو مقسوم عليه this is traditionally called
+
+129
+00:10:17,980 --> 00:10:22,780
+the division algorithm أو خوارزمية القسمة وخلّينا
+
+130
+00:10:22,780 --> 00:10:27,620
+نشوف إيش خوارزمية القسمة أو نظرية الخوارزمية
+
+131
+00:10:27,620 --> 00:10:31,320
+القسمةبتقول بقى يعني صلوا على النبي عليه الصلاة
+
+132
+00:10:31,320 --> 00:10:35,400
+والسلام if a is an integer and d is a positive
+
+133
+00:10:35,400 --> 00:10:38,940
+integer يعني a أي انتجر سالم موجة بالإبداكية حتى
+
+134
+00:10:38,940 --> 00:10:42,560
+لو كان سفر مش فارجة هقلناه و ال d positive integer
+
+135
+00:10:42,560 --> 00:10:47,340
+أكبر من سفر لما نجسم ال a على ال d هيطلع ناتج قسمة
+
+136
+00:10:47,340 --> 00:10:54,550
+بدي أسميه Q والمتبقى اللي هو بدي أسميه Rبعد ذلك
+
+137
+00:10:54,550 --> 00:10:58,790
+يوجد
+
+138
+00:10:58,790 --> 00:11:05,370
+ناتج قسم واحد Q ومتبقى واحد R بحيث ان R أكبر وسوء
+
+139
+00:11:05,370 --> 00:11:13,050
+سفر وأصغر من D دائما عندما تقسم ال A على ال Dيعني
+
+140
+00:11:13,050 --> 00:11:17,750
+11 على خمسة و تقول 11 على خمسة بطلع اتنين و بضال
+
+141
+00:11:17,750 --> 00:11:22,290
+واحد الواحد هذا سبته ليش سبته لأنه أصلا هو أكبر أو
+
+142
+00:11:22,290 --> 00:11:25,650
+يساوي سفر و أصغر من المقسوم عليه اللي هي الخمسة
+
+143
+00:11:25,650 --> 00:11:29,450
+فدائما ال remainder بكون أكبر أو يساوي سفر و أصغر
+
+144
+00:11:29,450 --> 00:11:35,160
+من المقسوم عليه ال Dإذاً لما نقعد يقسم ال A على ال
+
+145
+00:11:35,160 --> 00:11:40,920
+D بطلع لناتج قسمة اسمه Q وفيه remainder اسمه HR
+
+146
+00:11:40,920 --> 00:11:45,700
+عشان هيك بنقول A بتساوي D في Q زايد R زي ما قولنا
+
+147
+00:11:45,700 --> 00:11:53,020
+ل 11 بساوي ال 5 في 2 ب10 زايد ال 1 ال 1 هو ال
+
+148
+00:11:53,020 --> 00:11:58,060
+remainder وال 2 هو ناتج القسمة هو الخمسة اللي
+
+149
+00:11:58,060 --> 00:12:04,040
+قسمنا عليها إذاً الآنالـ A بيتساوى DQ زي الـ R حيث
+
+150
+00:12:04,040 --> 00:12:10,160
+الـ A هو المقسوم والـ D المقسوم عليه والـ Q ناتج
+
+151
+00:12:10,160 --> 00:12:15,140
+القسمة والـ R هو المتبقي D is called the divisor
+
+152
+00:12:15,870 --> 00:12:19,670
+الان المقصوم عليه A is called the dividend اللي هو
+
+153
+00:12:19,670 --> 00:12:24,690
+المقصوم و Q is called the quotient ناتج القسمة و R
+
+154
+00:12:24,690 --> 00:12:29,370
+is called the remainder من هذا الحديث الان بدنا
+
+155
+00:12:29,370 --> 00:12:34,580
+نستقي مع بعض دالتينانعرفن كما يالي definitions of
+
+156
+00:12:34,580 --> 00:12:38,300
+functions واحدة اسمها dive واحدة اسمها mud بدنا
+
+157
+00:12:38,300 --> 00:12:42,980
+نصطلح مع بعض شو معناته ان احنا بنقول ايه dive دي
+
+158
+00:12:42,980 --> 00:12:47,360
+اللي بنقصد فيها انه لما جينا قسمنا ال a على ال d
+
+159
+00:12:48,000 --> 00:12:52,640
+طلع عندى ناتج قسمة ناتج القسمة هذا اللى بتسميه a
+
+160
+00:12:52,640 --> 00:12:59,060
+ضايف d بقصد فيه ناتج قسمة a على d هذا ناتج القسمة
+
+161
+00:12:59,060 --> 00:13:06,200
+طب اهم ال d ايش بقصد فيه هو المتبقي من ناتج قسمة a
+
+162
+00:13:06,200 --> 00:13:11,460
+على d اذا a ضايف d مقصود فيه لما اقسم a على d
+
+163
+00:13:11,460 --> 00:13:15,650
+بتطلع اللى هى ناتج القسمةلما أقسم الـ a على d
+
+164
+00:13:15,650 --> 00:13:19,170
+بيطلع عندي remainder فبقصد ال a مو ال d هو عبارة
+
+165
+00:13:19,170 --> 00:13:22,710
+عن مين المتبقي او ال remainder اتفجن علينا دول
+
+166
+00:13:22,710 --> 00:13:29,150
+الدالتين يللا خلينا نشوف أمثل عددية طيب احنا نشوف
+
+167
+00:13:29,150 --> 00:13:35,190
+أمثل عددية المثل العدد لل division algorithm هو ما
+
+168
+00:13:35,190 --> 00:13:38,610
+يعني what are the quotient and remainder when 101
+
+169
+00:13:38,610 --> 00:13:45,250
+is divided by 111بنشوف ايش اللي هو الناتج القسمة
+
+170
+00:13:45,250 --> 00:13:50,410
+ومتبقى القسمة لما نجسم 101 على 11 اكيد كلكم كان
+
+171
+00:13:50,410 --> 00:13:56,870
+101 على 11 في 99 و بظهر بينهم قداش بزيادة 2 فاكيد
+
+172
+00:13:56,870 --> 00:14:02,600
+اللي هو هيكون عند 101 بساوة 11اللي هو ضرب تسعة
+
+173
+00:14:02,600 --> 00:14:08,040
+زائد اتنين تسعة هذا هو ناتج القسمة والتنين هو
+
+174
+00:14:08,040 --> 00:14:12,480
+متبقي القسمة عشان هيك بنكتبهم بالطريقة اللي اتفجنا
+
+175
+00:14:12,480 --> 00:14:16,860
+عليها قبل بشوية اللي هو بيصير عندي اللي هو عندي
+
+176
+00:14:16,860 --> 00:14:24,760
+المتبقيالقسمة اللي هو 2 فبنكتب 101 مد 11 بما أن في
+
+177
+00:14:24,760 --> 00:14:30,560
+متبقى القسمة لما نقسم 101 ل11 بيطلع 2 وبنكتب 101
+
+178
+00:14:30,560 --> 00:14:34,740
+ضايف 11 معناته الدالة هذه بتعني أنه لما نقسم 101
+
+179
+00:14:34,740 --> 00:14:40,720
+ل11 بيكون ناتج القسمة 100 اللي هو 9 زي ما شفنا
+
+180
+00:14:40,720 --> 00:14:42,740
+اللي عاملينه احنا هنا في ال division
+
+181
+00:14:46,330 --> 00:14:52,950
+السؤال الثاني هو what are the quotient and
+
+182
+00:14:52,950 --> 00:14:59,090
+remainder نقص 11 is divided by 3 نقص 11 نقص 11 نقص
+
+183
+00:14:59,090 --> 00:15:05,190
+11 نقص 11 نقص
+
+184
+00:15:05,190 --> 00:15:07,770
+11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11 نقص
+
+185
+00:15:07,770 --> 00:15:12,600
+11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11في هذه الحالة
+
+186
+00:15:12,600 --> 00:15:16,720
+بيصير نقص 11 بيساوي تلاتة فى ناقص أربعة زايد واحد
+
+187
+00:15:16,720 --> 00:15:19,900
+لما نقسم الناقص ماحدش يقول ناقص تلاتة لأنه بيصير
+
+188
+00:15:19,900 --> 00:15:23,020
+تلاتة فى ناقص تلاتة بيساوي ناقص تسعة ناقص تسعة
+
+189
+00:15:23,020 --> 00:15:26,520
+بيصير ناقص احداش بيساوي ناقص تسعة ناقص اتنين و ال
+
+190
+00:15:26,520 --> 00:15:29,920
+remainder لازم التفاجن يكون ايه شماله اكبر من سفر
+
+191
+00:15:29,920 --> 00:15:33,420
+و اصغر من تلاتة لأن احنا لما نقدر نقسم اي عدد على
+
+192
+00:15:33,420 --> 00:15:40,830
+ال remainder بيطلع انه عدد صحيحلو زاد عن اللي هو
+
+193
+00:15:40,830 --> 00:15:44,490
+.. لو ال remainder طلع بالسالب لأ احنا مابنقش
+
+194
+00:15:44,490 --> 00:15:48,130
+بنوحد الكلام كله مع بعض كلنا نجسم زي بعض و طلعنا
+
+195
+00:15:48,130 --> 00:15:51,810
+remainder زي بعض و ناتج قسمتنا زي بعض عشان هيك
+
+196
+00:15:51,810 --> 00:15:55,650
+بنطلب ال remainder يكون بين السفر و بين التلتة زي
+
+197
+00:15:55,650 --> 00:16:00,230
+ما كنا نعمل زمان في قسمة الأعداد الصحيحة على بعض
+
+198
+00:16:00,230 --> 00:16:04,090
+الان هذا بيصير نقص 11 بيساوي تلتة في نقص 4 زائد من
+
+199
+00:16:04,090 --> 00:16:08,980
+1الان هذا اللي هو الواحد هو عبارة عن ال remainder
+
+200
+00:16:08,980 --> 00:16:13,880
+عشان هيك بنقول الواحد اللي هو بساوي ناقص أحداش مدت
+
+201
+00:16:13,880 --> 00:16:19,620
+تلاتة نقولنا دالة المد هذه تعني قسمة ناقص أحداش ع
+
+202
+00:16:19,620 --> 00:16:24,380
+تلاتة بطلع متبقى القسمة بساوى واحد يعني هذه تدل
+
+203
+00:16:24,380 --> 00:16:30,390
+على متبقى القسمةالان اللى هو ناقص 11 ضايف 3 تعني
+
+204
+00:16:30,390 --> 00:16:34,610
+اللى هو ناتج قسمة ناقص 11 على 3 اللى هو ايش طلع
+
+205
+00:16:34,610 --> 00:16:40,030
+عندى ناقص 4 و هيك بنوجد اللى هو ناتج القسمة و
+
+206
+00:16:40,030 --> 00:16:47,990
+بنوجد مين اللى هو متبقي القسمة الان ان دخلنا على
+
+207
+00:16:47,990 --> 00:16:52,510
+حاجة اسمها ال congrance relation او اللى هي علاقة
+
+208
+00:16:52,510 --> 00:16:56,690
+التطابقالان ايش اللى بنقصد فيها علاقة التطابق؟
+
+209
+00:16:56,690 --> 00:17:00,110
+خلينا نشوف ايش اللى هو تعريف علاقة التطابق دي، ايش
+
+210
+00:17:00,110 --> 00:17:03,670
+معناه الـcongruence؟ لو كان عند A وB عبارة عن
+
+211
+00:17:03,670 --> 00:17:07,050
+أعداد صحيحة integers and M is a positive integer
+
+212
+00:17:07,050 --> 00:17:12,420
+والـ M إيش ماله؟ عدد صحيح موجببنقول أن a is
+
+213
+00:17:12,420 --> 00:17:17,180
+congruent to b modulo m يعني a تطابق b modulo m
+
+214
+00:17:17,180 --> 00:17:23,200
+يعني a تطابق b اللي هو بالنسبة للمقياس m إذا حققت
+
+215
+00:17:23,200 --> 00:17:29,060
+مالي ال m تقسم ال b minus a أو تقسم ال a minus b
+
+216
+00:17:29,060 --> 00:17:33,420
+في هذه الحالة بنقول a تطابق ال b modulo m وبنرمز
+
+217
+00:17:33,420 --> 00:17:37,790
+لها بالرمز اللي عندي ais congruent to B modulo M
+
+218
+00:17:37,790 --> 00:17:46,650
+نعني بها أن M تقسم اللي هو ال A ناقص B تقسم ال A
+
+219
+00:17:46,650 --> 00:17:52,030
+ناقص B هذا معناته أن A تطابق ال B modulo M الان
+
+220
+00:17:52,030 --> 00:17:57,510
+هذه ع بعضها بنسميها is a congruence أو بنسميها
+
+221
+00:17:57,510 --> 00:18:03,870
+تطابقة و ال M هو ال modulus أو هو مقياس التطابق
+
+222
+00:18:03,870 --> 00:18:08,180
+بنسميهالان اللى اللى اللى اللى اللى اللى اللى اللى
+
+223
+00:18:08,180 --> 00:18:08,440
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+224
+00:18:08,440 --> 00:18:09,560
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+225
+00:18:09,560 --> 00:18:10,360
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+226
+00:18:10,360 --> 00:18:10,480
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+227
+00:18:10,480 --> 00:18:12,300
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+228
+00:18:12,300 --> 00:18:12,320
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+229
+00:18:12,320 --> 00:18:13,660
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+230
+00:18:13,660 --> 00:18:14,520
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+231
+00:18:14,520 --> 00:18:16,420
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+232
+00:18:16,420 --> 00:18:17,660
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+233
+00:18:17,660 --> 00:18:24,600
+اللى اللى اللىيكون المتطابقتين إذا كان ال a و ال b
+
+234
+00:18:24,600 --> 00:18:28,740
+اللي هى نفس ال remainder لو قسمناها على ال m يعني
+
+235
+00:18:28,740 --> 00:18:33,260
+لو قسمنا ال b على ال m هنلاقي اللي هو ناتج القسمة
+
+236
+00:18:33,260 --> 00:18:39,660
+b على m R1 و ناتج قسمة a على m R2 في حالة ما يكون
+
+237
+00:18:39,660 --> 00:18:44,980
+المتطابقتين لازم ال R1 ايش يساوي R2 عشان هيك two
+
+238
+00:18:44,980 --> 00:18:49,390
+integers are congruent modulo mif and only if they
+
+239
+00:18:49,390 --> 00:18:53,690
+have the same remainder when divided by main by m
+
+240
+00:18:53,690 --> 00:18:59,810
+لو كانت ال a لاتطابق ال b بنرمز ال a لاتطابق ال b
+
+241
+00:18:59,810 --> 00:19:03,430
+modulo m وهذا ماذا بتحدث؟ بتحدث لما نلاقي ال m لا
+
+242
+00:19:03,430 --> 00:19:08,430
+تقسم ال a minus b أو لما نلاقي ال remainder لل b
+
+243
+00:19:08,430 --> 00:19:13,250
+لما نقسمها على m يختلف عن ال remainder لل a لما
+
+244
+00:19:13,250 --> 00:19:18,910
+نقسمها على mainعلى أمن طيب خلينا نشوف احنا مثال او
+
+245
+00:19:18,910 --> 00:19:23,510
+امثلة عددية نشوف المثال العددي بيقول determine
+
+246
+00:19:23,510 --> 00:19:27,670
+whether ال 17 is congruent to 5 ولا لأو بعدين
+
+247
+00:19:27,670 --> 00:19:31,630
+modulo 6 طبعا and whether ال 24 and ال 14 are
+
+248
+00:19:31,630 --> 00:19:35,030
+congruent modulo 6 الآن بده يشوف السبعتاش والخمسة
+
+249
+00:19:35,030 --> 00:19:39,830
+هل المتطابقتين modulo 6 قلنا أحد أمرين ابني جي
+
+250
+00:19:39,830 --> 00:19:44,810
+بنقول السبعتاش ناقص خمسة بطلع اتناش الستة بتقسم
+
+251
+00:19:44,810 --> 00:19:49,390
+اتناش اذا السبعتاش بتقسم الخمسة modulo 6الان طريقة
+
+252
+00:19:49,390 --> 00:19:53,910
+اخرى اللى هى انه بنجيب نجسم السبعتاش على الستة
+
+253
+00:19:53,910 --> 00:19:58,410
+المتبقى جديش خمسة هو نفس المتبقى لما الخمسة نجسمها
+
+254
+00:19:58,410 --> 00:20:01,250
+على الستة لإن المتبقى بيطلع خمسة ونتج القسم صفر
+
+255
+00:20:01,250 --> 00:20:07,160
+طبيعى اذا الان السبعتاش تطابق خمسة مدله ستةلأن أحد
+
+256
+00:20:07,160 --> 00:20:12,540
+سببين يا إما ستة بتقسم حصل طرحين يا إما هذا لما
+
+257
+00:20:12,540 --> 00:20:16,180
+نقسم على هذا و هذا لما نقسم على هذا بيعطي نفس
+
+258
+00:20:16,180 --> 00:20:21,520
+نتيجة نفس اللي هو ال remainder طيب الآن يجي نحكم
+
+259
+00:20:21,520 --> 00:20:24,240
+على مين الاربع عشرين و الاربعة عشر هال congrant
+
+260
+00:20:24,240 --> 00:20:27,100
+بدوله ستة ولا لأ أكيد كلكم قال اربعة عشرين نقص
+
+261
+00:20:27,100 --> 00:20:30,900
+اربعة عشر بتساوي عشرة الستة بتقسمش العشرةإذا
+
+262
+00:20:30,900 --> 00:20:35,580
+الأربعة عشرين لاتطابق الاربعة عشر مدلو ستة أو
+
+263
+00:20:35,580 --> 00:20:40,080
+مقياس ستة الان لو أحد قال لا ما هو أنا بتطلع لها
+
+264
+00:20:40,080 --> 00:20:44,080
+نظرة أخرى الأربعة عشرين لو جسمناها على الستة بتطلع
+
+265
+00:20:44,080 --> 00:20:47,560
+ال remainder صفر لأنه تقبل قسم عليها لكن الأربعة
+
+266
+00:20:47,560 --> 00:20:49,920
+عشر لما نجسمها على الستة بتطلع عندي remainder
+
+267
+00:20:49,920 --> 00:20:52,260
+اتنين إذا ال remainder هنا و ال remainder هنا
+
+268
+00:20:52,260 --> 00:20:56,320
+مختلفات إذا they are notCongruent أحد الأمرين اللي
+
+269
+00:20:56,320 --> 00:21:02,220
+بتشتغلوه هو صحيح ندى الأن نشوف أخدنا شغلتين الأن
+
+270
+00:21:02,220 --> 00:21:07,310
+أخدنا اللى هو ايه تطابق الـ P modulo Mاللي هو و
+
+271
+00:21:07,310 --> 00:21:11,230
+الـ a mod m بتساوي b بدنا نشوف العلاقة the
+
+272
+00:21:11,230 --> 00:21:14,450
+relation between او the relationship between mod m
+
+273
+00:21:14,450 --> 00:21:20,130
+and mod m notations يعني هذه اللي بالغامج هذه اللي
+
+274
+00:21:20,130 --> 00:21:25,350
+بنقصد فيها دالة a mod m اللي هي نصدنا فيها دالة
+
+275
+00:21:25,350 --> 00:21:30,350
+لما نعرفنا هي و ال dive الآن a تطابق b mod m اللي
+
+276
+00:21:30,350 --> 00:21:35,560
+هي علاقة بين اللي هي integers a و bقلنا ايش هذا
+
+277
+00:21:35,560 --> 00:21:40,100
+بتعني؟ بتعني ان a تطابق b modulo m اللي هي معناتها
+
+278
+00:21:40,100 --> 00:21:45,480
+ان m بتجسم ال a minus b او بمعنى اخر قلنا معناتها
+
+279
+00:21:45,480 --> 00:21:52,300
+ان المتبقى القسمة من a على m هو نفس متبقى القسمة
+
+280
+00:21:52,300 --> 00:21:57,650
+من b على mبينما هذه يا جماعة اللى بتعني a مد ام
+
+281
+00:21:57,650 --> 00:22:04,790
+انه لما نجسم ال a على m متبقى القسمة بساوة b ماشي
+
+282
+00:22:04,790 --> 00:22:09,870
+اذا لما نقول a مد ام بساوة b يعني متبقى قسمة a على
+
+283
+00:22:09,870 --> 00:22:15,430
+m بساوة b اما هنا a تطابق b مد ام انه متبقى القسمة
+
+284
+00:22:15,430 --> 00:22:23,690
+a على m هو نفسه متبقى القسمة b لما نقسمه على mالان
+
+285
+00:22:23,690 --> 00:22:27,050
+هذا الكلام حكيته انا it وطبق me the relation on
+
+286
+00:22:27,050 --> 00:22:30,110
+the six integers هذه علاقة على الست الفنتجرز بينما
+
+287
+00:22:30,110 --> 00:22:33,370
+هذه عبارة عن دالة اتفاقنا عليها اللي هي the
+
+288
+00:22:33,370 --> 00:22:37,230
+notation denotes the function او a function
+
+289
+00:22:37,230 --> 00:22:40,870
+العلاقة بين التنتين الآن هنشوف that the
+
+290
+00:22:40,870 --> 00:22:44,550
+relationship between these two is made clear in
+
+291
+00:22:44,550 --> 00:22:47,950
+this theorem هتكون واضحة من خلال هذه النظرية اللي
+
+292
+00:22:47,950 --> 00:22:51,230
+أمامنا شوفوا يا جماعة صلى الله عليه الصلاة والسلام
+
+293
+00:22:51,600 --> 00:22:56,700
+لو كان عندي a و b integers و m positive integers
+
+294
+00:22:56,700 --> 00:23:03,700
+احنا ال a تطابق b مدله m هي تكافئ تماما يعني if
+
+295
+00:23:03,700 --> 00:23:09,620
+and only if هذه على بعضها هذه تكافئ تماما ان نقول
+
+296
+00:23:09,620 --> 00:23:17,760
+a مد m بساوي b مد mلأن بي مض ام ايش بتعني ان متبقى
+
+297
+00:23:17,760 --> 00:23:22,600
+قسمة ال بي على ام يساوي متبقى قسمة ال ا على ام لان
+
+298
+00:23:22,600 --> 00:23:25,800
+هذه بتعني متبقى قسمة ال ا على ام وهذه بتعني متبقى
+
+299
+00:23:25,800 --> 00:23:29,860
+قسمة ال بي على ام هذه معناته مساواة يعني متبقى
+
+300
+00:23:29,860 --> 00:23:33,760
+قسمة هذه على هذه بساوي متبقى قسمة هذه على هذه هو
+
+301
+00:23:33,760 --> 00:23:38,910
+بالظبط هذااللي هو A تطابق B mod M يعني متطابق قسمة
+
+302
+00:23:38,910 --> 00:23:44,750
+A على M اللي هو نفسه متطابق قسمة B على M وكأنه هذا
+
+303
+00:23:44,750 --> 00:23:51,070
+التعبير هو هذا التعبير ولكن بصورة أخرى ماشي الحال؟
+
+304
+00:23:51,070 --> 00:23:58,070
+طيب الآن إذا هذا بكافة اللي هو هذه الكلمتين بخزن
+
+305
+00:23:58,070 --> 00:24:02,820
+هذولة اللي عندنا أو كفاتة خلينا نشوف مثالالان الـ
+
+306
+00:24:02,820 --> 00:24:09,780
+31 و 351 متطابقات ليش لأن 351 ناقص 31 تطلع 320
+
+307
+00:24:09,780 --> 00:24:14,340
+العشرة بتجسمها إذا فعلا متطابقتين بالنسبة للمقياس
+
+308
+00:24:14,340 --> 00:24:20,600
+عشرة الان طيب الان اني جي نشوف اللي هو ال .. ال ..
+
+309
+00:24:20,600 --> 00:24:25,380
+ال .. نظرة أخرى لهذه ان هذا و هدولة اللي هي نفس ال
+
+310
+00:24:25,380 --> 00:24:30,320
+remainder لما نجسمها للعشرة هذا هو الان31 لما
+
+311
+00:24:30,320 --> 00:24:35,160
+تجسمها على عشرة بيطلع متبقي واحد 351 لما تجسمها
+
+312
+00:24:35,160 --> 00:24:39,580
+على عشرة بيطلع متبقي واحد إذا هذا بيساوي هذا يعني
+
+313
+00:24:39,580 --> 00:24:44,640
+اللي هي التطابقات و بالمناسبة التطابقات اللي هو
+
+314
+00:24:44,640 --> 00:24:49,300
+موضوع ال concurrences هذه هي أصلا لأودادتنا أو
+
+315
+00:24:49,300 --> 00:24:54,900
+خلينا نقول اللي بتعلمنا كيف أو قدام هنعرف أنظمة
+
+316
+00:24:54,900 --> 00:24:59,020
+العد من خلالهانظام العد الثاني نظام العد الثلاثي
+
+317
+00:24:59,020 --> 00:25:03,200
+الرباعي الخماسي العشاري اللي بنتعامل فيه أو الستعش
+
+318
+00:25:03,200 --> 00:25:07,580
+أو التمانية اللي بدنا يه اللي هو النظام العد اللي
+
+319
+00:25:07,580 --> 00:25:11,800
+هو اللي بتبع من المقياس يعني مقياس عشرة بنصير مجول
+
+320
+00:25:11,800 --> 00:25:15,240
+عن نظام العد العشاري مقياس اتنين بنصير مجول عن
+
+321
+00:25:15,240 --> 00:25:19,440
+نظام العد الاتنين وهكذا وان شاء الله هنجيه قدام
+
+322
+00:25:19,780 --> 00:25:24,780
+الان بيكون هيك احنا خلصنا اللي هو اللي بدناياه في
+
+323
+00:25:24,780 --> 00:25:28,540
+هذا ال section وعندي ال homework التالي بدياه
+
+324
+00:25:28,540 --> 00:25:32,580
+تجيبوليه ببعتلكم عن واتس بظبط إيش اللي بدياه الآن
+
+325
+00:25:32,580 --> 00:25:36,920
+السؤال الأول بيقوللي 31 تطابق ماذا مدل سبعة هل
+
+326
+00:25:36,920 --> 00:25:40,140
+بالطابق الخامسة، بالطابق ال 211؟ يمكن الطابق
+
+327
+00:25:40,140 --> 00:25:42,720
+واحدة، تمتين، تلاتة، كل واحدة من هناك تشوف مين
+
+328
+00:25:42,720 --> 00:25:46,420
+بالطابق ال 31 مدل السبعة وتحط اللي تحتها خط
+
+329
+00:25:46,420 --> 00:25:51,430
+وتقوللي ليش بالطابقهاوالثاني لماذا بالطبق عشر؟
+
+330
+00:25:51,430 --> 00:25:55,430
+find اللي هو عشرة ضايف تلاتة عشرة ضايف تلاتة قدش
+
+331
+00:25:55,430 --> 00:25:59,890
+قيمته 101 ضايف تلاتة وعشرين برضه نفس الاشي و بعدين
+
+332
+00:25:59,890 --> 00:26:04,170
+اجدل عشرة موت تلاتة الاخر هدولة إيجاد زي ما شرحنا
+
+333
+00:26:04,170 --> 00:26:07,530
+قبل شوية الان question الثالث which of the
+
+334
+00:26:07,530 --> 00:26:09,710
+following divides the positive integer a؟ يعني
+
+335
+00:26:09,710 --> 00:26:15,070
+عندي في positive integer aمين من هدولة divides
+
+336
+00:26:15,070 --> 00:26:19,950
+which of the following divides the positive
+
+337
+00:26:19,950 --> 00:26:25,510
+integer ايه او خلينا نقول which of the following
+
+338
+00:26:25,510 --> 00:26:52,400
+او a divides which of the followingA divides
+
+339
+00:26:52,400 --> 00:26:57,500
+which of the followingيعني مش هنا اللي بدني اجيز
+
+340
+00:26:57,500 --> 00:27:02,920
+منه هل ال ا بتجسم هدول ولا لأ ا بتجسم مين منهم بدك
+
+341
+00:27:02,920 --> 00:27:07,360
+تحددها و هيك بكون خلصنا ال section الأول و إلى
+
+342
+00:27:07,360 --> 00:27:11,840
+لقاء آخر والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..deff5aa28397b30a7bfcbbf1801cb57150ef9eaa
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.json
@@ -0,0 +1 @@
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بي", "probability": 0.924072265625}, {"start": 213.76, "end": 214.02, "word": " يعني", "probability": 0.927978515625}, {"start": 214.02, "end": 214.18, "word": " لو", "probability": 0.89208984375}, {"start": 214.18, "end": 214.5, "word": " جينا", "probability": 0.7960611979166666}, {"start": 214.5, "end": 215.02, "word": " جسمنا", "probability": 0.8074544270833334}, {"start": 215.02, "end": 215.12, "word": " ال", "probability": 0.6591796875}, {"start": 215.12, "end": 215.24, "word": " b", "probability": 0.6220703125}, {"start": 215.24, "end": 215.42, "word": " على", "probability": 0.4638671875}, {"start": 215.42, "end": 215.62, "word": " ال", "probability": 0.9033203125}, {"start": 215.62, "end": 215.74, "word": " a", "probability": 0.958984375}, {"start": 215.74, "end": 216.24, "word": " هتطلع", "probability": 0.940625}, {"start": 216.24, "end": 216.68, "word": " integer", "probability": 0.7734375}], "temperature": 1.0}, {"id": 11, "seek": 24145, "start": 217.11, "end": 241.45, "text": "يعني الآن لما نقول a تقسم b بنعني انه على طول العدد b على العدد a فده مائل يعني بيقولك بي على العدد a هيطلع اشمال و انتجر زي مهنا هاي مش هاد معناه a تقسم b يعني الان b على a هتطلع ال c يعني انتجر إذا من الآن و طالع مجرد نقول a تقسم b معناته ال b على ال a هو عبارة عن عدد صحيح", "tokens": [40228, 22653, 6024, 48506, 5296, 15042, 8717, 39648, 257, 6055, 4587, 38251, 272, 44945, 3615, 22653, 16472, 3224, 15844, 23032, 12610, 18863, 3215, 3215, 272, 15844, 18863, 3215, 3215, 257, 6156, 3215, 3224, 3714, 16373, 1211, 37495, 22653, 4724, 1829, 39648, 4117, 4724, 1829, 15844, 18863, 3215, 3215, 257, 39896, 9566, 1211, 3615, 1975, 8592, 2304, 6027, 4032, 16472, 2655, 7435, 2288, 30767, 1829, 3714, 3224, 8315, 8032, 47302, 37893, 8032, 18513, 20449, 8315, 3224, 257, 6055, 4587, 38251, 272, 37495, 22653, 2423, 7649, 272, 15844, 257, 8032, 2655, 9566, 1211, 3615, 2423, 269, 37495, 22653, 16472, 2655, 7435, 2288, 11933, 15730, 9154, 6024, 48506, 4032, 23032, 6027, 3615, 3714, 7435, 2288, 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يعني a does not divide b يعني a لا تقسم ال b ناخد أمثل عددية الان المثال الأول determine whether التلاتة بتقسم السابعة and whether التلاتة بتقسم أطنعاش", "tokens": [9566, 3555, 45164, 47525, 8315, 8717, 39648, 257, 775, 406, 9845, 272, 8717, 2288, 2304, 11622, 20666, 2288, 2304, 11622, 10632, 11778, 3224, 257, 37037, 1829, 25124, 5016, 9566, 3660, 16247, 12610, 7578, 37037, 1829, 6156, 7435, 3224, 11296, 13412, 5016, 9566, 3660, 6055, 7649, 10632, 37495, 22653, 257, 775, 406, 9845, 272, 37495, 22653, 257, 20193, 6055, 4587, 38251, 2423, 272, 8717, 47283, 3215, 5551, 2304, 12984, 1211, 6225, 3215, 3215, 10632, 2423, 7649, 9673, 12984, 6027, 16247, 12610, 6997, 1968, 16712, 1211, 9307, 3660, 39894, 4587, 38251, 21136, 16758, 27884, 293, 1968, 16712, 1211, 9307, 3660, 39894, 4587, 38251, 5551, 9566, 1863, 3615, 33599], "avg_logprob": -0.2169976568667688, "compression_ratio": 1.8823529411764706, "no_speech_prob": 0.0, "words": [{"start": 241.61, "end": 241.97, "word": "طب", "probability": 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"probability": 0.9713541666666666}, {"start": 643.34, "end": 643.56, "word": " لما", "probability": 0.9404296875}, {"start": 643.56, "end": 644.0, "word": " نجسم", "probability": 0.9674479166666666}, {"start": 644.0, "end": 644.16, "word": " ال", "probability": 0.96337890625}, {"start": 644.16, "end": 644.38, "word": " a", "probability": 0.9189453125}, {"start": 644.38, "end": 644.58, "word": " على", "probability": 0.78466796875}, {"start": 644.58, "end": 644.78, "word": " ال", "probability": 0.9345703125}, {"start": 644.78, "end": 645.04, "word": " d", "probability": 0.896484375}, {"start": 645.04, "end": 646.34, "word": " هيطلع", "probability": 0.9051513671875}, {"start": 646.34, "end": 646.76, "word": " ناتج", "probability": 0.9845377604166666}, {"start": 646.76, "end": 647.34, "word": " قسمة", "probability": 0.9599609375}, {"start": 647.34, "end": 648.02, "word": " بدي", "probability": 0.40234375}, {"start": 648.02, "end": 648.56, "word": " أسميه", "probability": 0.92041015625}, {"start": 648.56, "end": 648.82, "word": " Q", "probability": 0.56298828125}, {"start": 648.82, "end": 650.52, "word": " والمتبقى", "probability": 0.8642578125}, {"start": 650.52, "end": 650.76, "word": " اللي", "probability": 0.9326171875}, {"start": 650.76, "end": 651.18, "word": " هو", "probability": 0.98876953125}, {"start": 651.18, "end": 651.94, "word": " بدي", "probability": 0.8916015625}, {"start": 651.94, "end": 652.54, "word": " أسميه", "probability": 0.97509765625}, {"start": 652.54, "end": 653.28, "word": " R", "probability": 0.320068359375}], "temperature": 1.0}, {"id": 31, "seek": 67207, "start": 653.63, "end": 672.07, "text": "بعد ذلك يوجد ناتج قسم واحد Q ومتبقى واحد R بحيث ان R أكبر وسوء سفر وأصغر من D دائما عندما تقسم ال A على ال D", "tokens": [3555, 22488, 29910, 23275, 7251, 29245, 3215, 8717, 9307, 7435, 12174, 38251, 36764, 24401, 1249, 4032, 2304, 2655, 3555, 4587, 7578, 36764, 24401, 497, 4724, 5016, 1829, 12984, 16472, 497, 5551, 4117, 26890, 4032, 3794, 2407, 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{"start": 1147.97, "end": 1148.43, "word": " b", "probability": 0.86767578125}, {"start": 1148.43, "end": 1149.43, "word": " لما", "probability": 0.889404296875}, {"start": 1149.43, "end": 1149.97, "word": " نقسمها", "probability": 0.9864501953125}, {"start": 1149.97, "end": 1150.15, "word": " على", "probability": 0.8701171875}, {"start": 1150.15, "end": 1150.47, "word": " m", "probability": 0.6396484375}, {"start": 1150.47, "end": 1151.59, "word": " يختلف", "probability": 0.9812825520833334}, {"start": 1151.59, "end": 1151.89, "word": " عن", "probability": 0.98486328125}, {"start": 1151.89, "end": 1152.05, "word": " ال", "probability": 0.90185546875}, {"start": 1152.05, "end": 1152.41, "word": " remainder", "probability": 0.9697265625}, {"start": 1152.41, "end": 1152.77, "word": " لل", "probability": 0.94482421875}, {"start": 1152.77, "end": 1152.99, "word": " a", "probability": 0.92333984375}, {"start": 1152.99, "end": 1153.25, "word": " لما", "probability": 0.972900390625}, {"start": 1153.25, "end": 1153.87, "word": " نقسمها", "probability": 0.9935302734375}, {"start": 1153.87, "end": 1154.09, "word": " على", "probability": 0.94140625}, {"start": 1154.09, "end": 1154.47, "word": " main", "probability": 0.74658203125}], "temperature": 1.0}, {"id": 53, "seek": 116641, "start": 1154.89, "end": 1166.41, "text": "على أمن طيب خلينا نشوف احنا مثال او امثلة عددية نشوف المثال العددي بيقول determine whether ال 17 is congruent to 5 ولا لأ", "tokens": [3615, 23942, 5551, 27842, 23032, 1829, 3555, 16490, 1211, 9957, 995, 8717, 8592, 38688, 1975, 5016, 8315, 50113, 6027, 1975, 2407, 1975, 2304, 12984, 37977, 6225, 3215, 3215, 10632, 8717, 8592, 38688, 9673, 12984, 6027, 18863, 3215, 16254, 4724, 1829, 39648, 6997, 1968, 2423, 3282, 307, 8882, 19226, 281, 1025, 49429, 5296, 10721], "avg_logprob": -0.27893517745865715, "compression_ratio": 1.3169014084507042, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 1154.89, "end": 1155.25, "word": "على", "probability": 0.615478515625}, {"start": 1155.25, "end": 1155.61, "word": " أمن", "probability": 0.617431640625}, {"start": 1155.61, "end": 1156.41, "word": " طيب", "probability": 0.7200927734375}, {"start": 1156.41, "end": 1156.95, "word": " خلينا", "probability": 0.6220703125}, {"start": 1156.95, "end": 1157.45, "word": " نشوف", "probability": 0.9866536458333334}, {"start": 1157.45, "end": 1157.95, "word": " احنا", "probability": 0.91845703125}, {"start": 1157.95, "end": 1158.65, "word": " مثال", "probability": 0.99169921875}, {"start": 1158.65, "end": 1158.91, "word": " او", "probability": 0.8037109375}, {"start": 1158.91, "end": 1159.49, "word": " امثلة", "probability": 0.83856201171875}, {"start": 1159.49, "end": 1160.37, "word": " عددية", "probability": 0.9609375}, {"start": 1160.37, "end": 1161.81, "word": " نشوف", "probability": 0.92578125}, {"start": 1161.81, "end": 1162.27, "word": " المثال", "probability": 0.92431640625}, {"start": 1162.27, "end": 1162.77, "word": " العددي", "probability": 0.8055013020833334}, {"start": 1162.77, "end": 1163.07, "word": " بيقول", "probability": 0.7218424479166666}, {"start": 1163.07, "end": 1163.51, "word": " determine", "probability": 0.2034912109375}, {"start": 1163.51, "end": 1163.99, "word": " whether", "probability": 0.68408203125}, {"start": 1163.99, "end": 1164.17, "word": " ال", "probability": 0.397705078125}, {"start": 1164.17, "end": 1164.65, "word": " 17", "probability": 0.6142578125}, {"start": 1164.65, "end": 1164.89, "word": " is", "probability": 0.93798828125}, {"start": 1164.89, "end": 1165.39, "word": " congruent", "probability": 0.959716796875}, {"start": 1165.39, "end": 1165.53, "word": " to", "probability": 0.64111328125}, {"start": 1165.53, "end": 1165.81, "word": " 5", "probability": 0.89208984375}, {"start": 1165.81, "end": 1166.09, "word": " ولا", "probability": 0.86328125}, {"start": 1166.09, "end": 1166.41, "word": " لأ", "probability": 0.86328125}], "temperature": 1.0}, {"id": 54, "seek": 118801, "start": 1167.01, "end": 1188.01, "text": "و بعدين modulo 6 طبعا and whether ال 24 and ال 14 are congruent modulo 6 الآن بده يشوف السبعتاش والخمسة هل المتطابقتين modulo 6 قلنا أحد أمرين ابني جي بنقول السبعتاش ناقص خمسة بطلع اتناش الستة بتقسم اتناش اذا السبعتاش بتقسم الخمسة modulo 6", "tokens": [2407, 39182, 9957, 1072, 13455, 1386, 23032, 3555, 3615, 995, 293, 1968, 2423, 4022, 293, 2423, 3499, 366, 8882, 19226, 1072, 13455, 1386, 6024, 48506, 47525, 3224, 7251, 8592, 38688, 21136, 3555, 34268, 33599, 16070, 9778, 2304, 3794, 3660, 8032, 1211, 9673, 2655, 9566, 16758, 38149, 9957, 1072, 13455, 1386, 12174, 1211, 8315, 5551, 24401, 5551, 29973, 9957, 48127, 22653, 10874, 1829, 44945, 39648, 21136, 3555, 34268, 33599, 8717, 995, 4587, 9381, 16490, 2304, 3794, 3660, 4724, 9566, 1211, 3615, 1975, 2655, 1863, 33599, 21136, 2655, 3660, 39894, 4587, 38251, 1975, 2655, 1863, 33599, 1975, 15730, 21136, 3555, 34268, 33599, 39894, 4587, 38251, 33962, 2304, 3794, 3660, 1072, 13455, 1386], 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المتطابقتين", "probability": 0.9353841145833334}, {"start": 1176.67, "end": 1177.07, "word": " modulo", "probability": 0.920166015625}, {"start": 1177.07, "end": 1177.47, "word": " 6", "probability": 0.96826171875}, {"start": 1177.47, "end": 1178.39, "word": " قلنا", "probability": 0.66357421875}, {"start": 1178.39, "end": 1178.71, "word": " أحد", "probability": 0.830078125}, {"start": 1178.71, "end": 1179.23, "word": " أمرين", "probability": 0.8795572916666666}, {"start": 1179.23, "end": 1179.63, "word": " ابني", "probability": 0.5633544921875}, {"start": 1179.63, "end": 1179.83, "word": " جي", "probability": 0.754638671875}, {"start": 1179.83, "end": 1180.19, "word": " بنقول", "probability": 0.9443359375}, {"start": 1180.19, "end": 1181.23, "word": " السبعتاش", "probability": 0.8262939453125}, {"start": 1181.23, "end": 1181.75, "word": " ناقص", "probability": 0.9700927734375}, {"start": 1181.75, "end": 1182.33, "word": " خمسة", "probability": 0.97509765625}, {"start": 1182.33, "end": 1182.91, "word": " بطلع", "probability": 0.84161376953125}, {"start": 1182.91, "end": 1183.43, "word": " اتناش", "probability": 0.78656005859375}, {"start": 1183.43, "end": 1184.43, "word": " الستة", "probability": 0.77734375}, {"start": 1184.43, "end": 1184.81, "word": " بتقسم", "probability": 0.8430989583333334}, {"start": 1184.81, "end": 1185.21, "word": " اتناش", "probability": 0.9427490234375}, {"start": 1185.21, "end": 1185.43, "word": " اذا", "probability": 0.6624755859375}, {"start": 1185.43, "end": 1186.15, "word": " السبعتاش", "probability": 0.9447021484375}, {"start": 1186.15, "end": 1186.63, "word": " بتقسم", "probability": 0.9619140625}, {"start": 1186.63, "end": 1187.31, "word": " الخمسة", "probability": 0.9873046875}, {"start": 1187.31, "end": 1187.71, "word": " modulo", "probability": 0.9501953125}, {"start": 1187.71, "end": 1188.01, "word": " 6", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 55, "seek": 120573, "start": 1188.59, "end": 1205.73, "text": "الان طريقة اخرى اللى هى انه بنجيب نجسم السبعتاش على الستة المتبقى جديش خمسة هو نفس المتبقى لما الخمسة نجسمها على الستة لإن المتبقى بيطلع خمسة ونتج القسم صفر طبيعى اذا الان السبعتاش تطابق خمسة مدله ستة", "tokens": [6027, 7649, 23032, 16572, 28671, 1975, 34740, 7578, 13672, 7578, 8032, 7578, 16472, 3224, 44945, 7435, 1829, 3555, 8717, 7435, 38251, 21136, 3555, 34268, 33599, 15844, 21136, 2655, 3660, 9673, 2655, 3555, 4587, 7578, 10874, 16254, 8592, 16490, 2304, 3794, 3660, 31439, 8717, 36178, 9673, 2655, 3555, 4587, 7578, 5296, 15042, 33962, 2304, 3794, 3660, 8717, 7435, 38251, 11296, 15844, 21136, 2655, 3660, 5296, 28814, 1863, 9673, 2655, 3555, 4587, 7578, 4724, 1829, 9566, 1211, 3615, 16490, 2304, 3794, 3660, 4032, 29399, 7435, 25062, 38251, 20328, 5172, 2288, 23032, 21292, 3615, 7578, 1975, 15730, 2423, 7649, 21136, 3555, 34268, 33599, 6055, 9566, 16758, 4587, 16490, 2304, 3794, 3660, 3714, 3215, 43761, 8608, 2655, 3660], "avg_logprob": -0.22038043607836183, "compression_ratio": 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{"start": 1193.91, "end": 1194.99, "word": " المتبقى", "probability": 0.8728515625}, {"start": 1194.99, "end": 1195.41, "word": " جديش", "probability": 0.76953125}, {"start": 1195.41, "end": 1195.93, "word": " خمسة", "probability": 0.8997802734375}, {"start": 1195.93, "end": 1196.37, "word": " هو", "probability": 0.81396484375}, {"start": 1196.37, "end": 1196.67, "word": " نفس", "probability": 0.98583984375}, {"start": 1196.67, "end": 1197.37, "word": " المتبقى", "probability": 0.97861328125}, {"start": 1197.37, "end": 1197.57, "word": " لما", "probability": 0.9150390625}, {"start": 1197.57, "end": 1198.03, "word": " الخمسة", "probability": 0.8819580078125}, {"start": 1198.03, "end": 1198.41, "word": " نجسمها", "probability": 0.9796142578125}, {"start": 1198.41, "end": 1198.55, "word": " على", "probability": 0.91015625}, {"start": 1198.55, "end": 1198.89, "word": " الستة", "probability": 0.8927408854166666}, {"start": 1198.89, "end": 1199.09, "word": " لإن", "probability": 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خمسة", "probability": 0.9656982421875}, {"start": 1204.91, "end": 1205.19, "word": " مدله", "probability": 0.653076171875}, {"start": 1205.19, "end": 1205.73, "word": " ستة", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 56, "seek": 123020, "start": 1206.0, "end": 1230.2, "text": "لأن أحد سببين يا إما ستة بتقسم حصل طرحين يا إما هذا لما نقسم على هذا و هذا لما نقسم على هذا بيعطي نفس نتيجة نفس اللي هو ال remainder طيب الآن يجي نحكم على مين الاربع عشرين و الاربعة عشر هال congrant بدوله ستة ولا لأ أكيد كلكم قال اربعة عشرين نقص اربعة عشر بتساوي عشرة الستة بتقسمش العشرة", "tokens": [1211, 33456, 5551, 24401, 8608, 3555, 3555, 9957, 35186, 11933, 15042, 8608, 2655, 3660, 39894, 4587, 38251, 11331, 9381, 1211, 23032, 2288, 5016, 9957, 35186, 11933, 15042, 23758, 5296, 15042, 8717, 4587, 38251, 15844, 23758, 4032, 23758, 5296, 15042, 8717, 4587, 38251, 15844, 23758, 4724, 40228, 9566, 1829, 8717, 36178, 8717, 31371, 7435, 3660, 8717, 36178, 13672, 1829, 31439, 2423, 29837, 23032, 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integers و m positive integers احنا ال a تطابق b مدله m هي تكافئ تماما يعني if and only if هذه على بعضها هذه تكافئ تماما ان نقول a مد m بساوي b مد m", "tokens": [1211, 2407, 25961, 43242, 1829, 257, 4032, 272, 41674, 4032, 275, 3353, 41674, 1975, 5016, 8315, 2423, 257, 6055, 9566, 16758, 4587, 272, 3714, 3215, 43761, 275, 39896, 6055, 4117, 31845, 19986, 46811, 10943, 995, 37495, 22653, 498, 293, 787, 498, 29538, 15844, 45030, 11242, 11296, 29538, 6055, 4117, 31845, 19986, 46811, 10943, 995, 16472, 8717, 39648, 257, 3714, 3215, 275, 4724, 3794, 995, 45865, 272, 3714, 3215, 275], "avg_logprob": -0.21685267644269127, "compression_ratio": 1.5246913580246915, "no_speech_prob": 0.0, "words": [{"start": 1371.6, "end": 1371.98, "word": "لو", "probability": 0.88134765625}, {"start": 1371.98, "end": 1372.16, "word": " كان", "probability": 0.9541015625}, {"start": 1372.16, "end": 1372.62, "word": " عندي", "probability": 0.5560302734375}, {"start": 1372.62, "end": 1372.9, "word": " a", 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1562.51, "word": " هدولة", "probability": 0.62823486328125}, {"start": 1562.51, "end": 1562.93, "word": " إيجاد", "probability": 0.78173828125}, {"start": 1562.93, "end": 1563.07, "word": " زي", "probability": 0.737060546875}, {"start": 1563.07, "end": 1563.29, "word": " ما", "probability": 0.9345703125}, {"start": 1563.29, "end": 1564.17, "word": " شرحنا", "probability": 0.973388671875}, {"start": 1564.17, "end": 1564.41, "word": " قبل", "probability": 0.983154296875}, {"start": 1564.41, "end": 1564.85, "word": " شوية", "probability": 0.9480794270833334}, {"start": 1564.85, "end": 1565.49, "word": " الان", "probability": 0.7568359375}, {"start": 1565.49, "end": 1566.29, "word": " question", "probability": 0.278076171875}, {"start": 1566.29, "end": 1566.89, "word": " الثالث", "probability": 0.8447265625}, {"start": 1566.89, "end": 1567.15, "word": " which", "probability": 0.8955078125}, {"start": 1567.15, "end": 1567.37, "word": " of", "probability": 0.97216796875}, {"start": 1567.37, "end": 1567.53, "word": " the", "probability": 0.9326171875}, {"start": 1567.53, "end": 1567.87, "word": " following", "probability": 0.83447265625}, {"start": 1567.87, "end": 1568.39, "word": " divides", "probability": 0.90234375}, {"start": 1568.39, "end": 1568.59, "word": " the", "probability": 0.84423828125}, {"start": 1568.59, "end": 1568.87, "word": " positive", "probability": 0.916015625}, {"start": 1568.87, "end": 1569.27, "word": " integer", "probability": 0.86376953125}, {"start": 1569.27, "end": 1569.61, "word": " a؟", "probability": 0.551513671875}, {"start": 1569.61, "end": 1569.71, "word": " يعني", "probability": 0.91796875}, {"start": 1569.71, "end": 1570.03, "word": " عندي", "probability": 0.652587890625}, {"start": 1570.03, "end": 1570.19, "word": " في", "probability": 0.86474609375}, {"start": 1570.19, "end": 1570.99, "word": " positive", "probability": 0.78369140625}, {"start": 1570.99, "end": 1571.53, "word": " integer", "probability": 0.958984375}, {"start": 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"probability": 0.99072265625}, {"start": 1582.55, "end": 1584.61, "word": " which", "probability": 0.76318359375}, {"start": 1584.61, "end": 1584.83, "word": " of", "probability": 0.97998046875}, {"start": 1584.83, "end": 1585.01, "word": " the", "probability": 0.927734375}, {"start": 1585.01, "end": 1585.51, "word": " following", "probability": 0.85986328125}, {"start": 1585.51, "end": 1586.31, "word": " او", "probability": 0.898681640625}, {"start": 1586.31, "end": 1586.65, "word": " a", "probability": 0.1885986328125}, {"start": 1586.65, "end": 1587.25, "word": " divides", "probability": 0.69091796875}, {"start": 1587.25, "end": 1587.57, "word": " which", "probability": 0.9619140625}, {"start": 1587.57, "end": 1587.77, "word": " of", "probability": 0.98291015625}, {"start": 1587.77, "end": 1587.89, "word": " the", "probability": 0.931640625}, {"start": 1587.89, "end": 1588.23, "word": " following", "probability": 0.890625}], "temperature": 1.0}, {"id": 72, "seek": 161440, "start": 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22653, 37893, 34105, 13672, 1829, 47525, 22653, 1975, 7435, 1829, 11622, 9154, 3224, 8032, 1211, 2423, 1975, 39894, 7435, 38251, 8032, 3215, 12610, 49429, 5296, 10721, 1975, 39894, 7435, 38251, 3714, 9957, 9154, 16095, 47525, 4117, 6055, 24401, 3215, 11296, 4032, 39896, 4117, 4724, 30544, 16490, 1211, 9381, 8315, 2423, 3541, 16247, 12610, 4032, 30731, 5296, 4587, 16606, 19753, 34740, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.30884740104923003, "compression_ratio": 1.6201117318435754, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1615.34, "end": 1616.12, "word": "يعني", "probability": 0.4931640625}, {"start": 1616.12, "end": 1616.6, "word": " مش", "probability": 0.6025390625}, {"start": 1616.6, "end": 1616.84, "word": " هنا", "probability": 0.29345703125}, {"start": 1616.84, "end": 1616.98, "word": " اللي", "probability": 0.81591796875}, {"start": 1616.98, "end": 1617.24, "word": " بدني", "probability": 0.581787109375}, {"start": 1617.24, "end": 1617.5, "word": " اجيز", "probability": 0.530517578125}, {"start": 1617.5, "end": 1617.7, "word": " منه", "probability": 0.6920166015625}, {"start": 1617.7, "end": 1617.98, "word": " هل", "probability": 0.575439453125}, {"start": 1617.98, "end": 1618.14, "word": " ال", "probability": 0.87255859375}, {"start": 1618.14, "end": 1618.32, "word": " ا", "probability": 0.343994140625}, {"start": 1618.32, "end": 1618.9, "word": " بتجسم", "probability": 0.6907552083333334}, {"start": 1618.9, "end": 1619.76, "word": " هدول", "probability": 0.8194986979166666}, {"start": 1619.76, "end": 1619.94, "word": " ولا", "probability": 0.386474609375}, {"start": 1619.94, "end": 1620.42, "word": " لأ", "probability": 0.8818359375}, {"start": 1620.42, "end": 1621.32, "word": " ا", "probability": 0.75390625}, {"start": 1621.32, "end": 1621.94, "word": " بتجسم", "probability": 0.7897135416666666}, {"start": 1621.94, "end": 1622.16, "word": " مين", 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0.86669921875}, {"start": 1627.36, "end": 1627.84, "word": " لقاء", "probability": 0.9661458333333334}, {"start": 1627.84, "end": 1628.32, "word": " آخر", "probability": 0.7919921875}, {"start": 1628.32, "end": 1628.88, "word": " والسلام", "probability": 0.88671875}, {"start": 1628.88, "end": 1629.38, "word": " عليكم", "probability": 0.9443359375}, {"start": 1629.38, "end": 1629.88, "word": " ورحمة", "probability": 0.901123046875}, {"start": 1629.88, "end": 1630.26, "word": " الله", "probability": 0.97119140625}, {"start": 1630.26, "end": 1631.84, "word": " وبركاته", "probability": 0.980078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1632.804, "duration_after_vad": 1620.1359687499978}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4ad0ad01c1d05314e1ec58727b9a070f83421317
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/RKNNpQx48co_raw.srt
@@ -0,0 +1,1368 @@
+1
+00:00:00,000 --> 00:00:04,180
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,180 --> 00:00:07,720
+والصلاة والسلام على سيد المرسلين سيدنا محمد على
+
+3
+00:00:07,720 --> 00:00:14,600
+آله وصحبه أجمعين هذه هي المحاضرة الرابعة في مساق
+
+4
+00:00:14,600 --> 00:00:18,960
+قياضيات منفصلة لطلاب وطالبات الجامعة الإسلامية
+
+5
+00:00:18,960 --> 00:00:28,290
+كلية ال IT قسم الحوسبة المتنقلةالمحاضرة اليوم هي
+
+6
+00:00:28,290 --> 00:00:34,090
+المحاضرة الأولى أيضا في chapter 4 وهو المعنوان ب
+
+7
+00:00:34,090 --> 00:00:39,210
+number theory and cryptography اللي هي بنقصد فيها
+
+8
+00:00:39,210 --> 00:00:44,010
+نظرية الأعداد والترميز والترميز هو عبارة عن تطبيق
+
+9
+00:00:44,010 --> 00:00:50,230
+على نظرية الأعداد ال section الأول اللي هنتحدث عنه
+
+10
+00:00:50,230 --> 00:00:53,910
+اليوم اللي هو divisibility and modular arithmetic
+
+11
+00:00:54,520 --> 00:01:02,080
+اللي هو شو معناته القسمة أو قابلية القسمة وحنشوف
+
+12
+00:01:02,080 --> 00:01:05,920
+دالتين واحدة دالة اسمها المد وواحدة دالة اسمها
+
+13
+00:01:05,920 --> 00:01:12,840
+dive ونشوف إيش اللي بنقصد فيهمالان نحكي اول شيء عن
+
+14
+00:01:12,840 --> 00:01:18,380
+ال division الان ال division اللي هي القسمة نشوف
+
+15
+00:01:18,380 --> 00:01:24,020
+شو معناته ال a divides b ايش معناته انه عدد يقسم
+
+16
+00:01:24,020 --> 00:01:30,720
+عدد اخر اسمه b طبعا حديثنا كله بصب بس اللي هو في
+
+17
+00:01:30,720 --> 00:01:33,860
+ال integers يعني احنا كل الاعداد اللي بنتناولها
+
+18
+00:01:33,860 --> 00:01:39,190
+اليوم هي عبارة عن اعداد صحيحةالان بنقول if a and b
+
+19
+00:01:39,190 --> 00:01:42,590
+are integers يعني لو كان عندي a و b عبارة عن أعداد
+
+20
+00:01:42,590 --> 00:01:46,870
+صحيحة with a لا تساوي سفر مدام قال with a لا تساوي
+
+21
+00:01:46,870 --> 00:01:53,230
+سفر شكلنا هنقسم على a لأن القسم على a مرفوض فعشان
+
+22
+00:01:53,230 --> 00:01:58,120
+هيك مفترضين ان a لا تساوي سفرالان بيقول then a
+
+23
+00:01:58,120 --> 00:02:03,140
+divides b يعني بيقول ان a تقسم b شو معنى a تقسم b
+
+24
+00:02:03,140 --> 00:02:07,700
+اللي هو if there exists an integer c such that ال
+
+25
+00:02:07,700 --> 00:02:13,440
+b بتساوي ال a في c في هذه الحالة بيقول a divides b
+
+26
+00:02:13,730 --> 00:02:18,310
+يعني اكترنا نكتب بي على صورة a في integer اخر او
+
+27
+00:02:18,310 --> 00:02:23,090
+في عدد صحيح اخر زي ما نقول ستة بتساوي اتنين فتلاتة
+
+28
+00:02:23,090 --> 00:02:29,150
+فبتكون التنين تقسم من الستة يعني بمعنى اخر a
+
+29
+00:02:29,150 --> 00:02:35,630
+divides b اللي هو a is a factor of b يعني a عامل
+
+30
+00:02:35,630 --> 00:02:41,660
+من عوامل bأو divisor of B أو قاسم من قواسم الـ B
+
+31
+00:02:41,660 --> 00:02:46,160
+إذا لما نقول A divides B بنقصد أنه A عامل من عوامل
+
+32
+00:02:46,160 --> 00:02:52,900
+B وبنقصد A قاسم من قواسم ال B أو بنقصد B عبارة عن
+
+33
+00:02:53,170 --> 00:02:58,210
+من مضاعفات الـ A يعني B is multiple of A كل
+
+34
+00:02:58,210 --> 00:03:04,230
+التعبير الثلاثة دول A قاسم من قاسم الـ B أو A عامل
+
+35
+00:03:04,230 --> 00:03:09,010
+من عوامل الـ B أو B من مضاعفات الـ A كلها المقصود
+
+36
+00:03:09,010 --> 00:03:16,380
+فيها أن A divides Bما هي الـ notation تبعتها؟ نقول
+
+37
+00:03:16,380 --> 00:03:20,660
+a divides b وهي a وهي عصرها بينهم b شكل العصرها هي
+
+38
+00:03:20,660 --> 00:03:26,720
+شبه عمودية يعني a divides b denotes that a divides
+
+39
+00:03:26,720 --> 00:03:32,420
+b أو a تقسم بي الان قلنا ان a تقسم بي معناته ان ال
+
+40
+00:03:32,420 --> 00:03:35,740
+a عامل من عامل بي يعني لو جينا جسمنا ال b على ال a
+
+41
+00:03:35,740 --> 00:03:40,190
+هتطلع integerيعني الآن لما نقول a تقسم b بنعني انه
+
+42
+00:03:40,190 --> 00:03:45,650
+على طول العدد b على العدد a فده مائل يعني بيقولك
+
+43
+00:03:45,650 --> 00:03:49,890
+بي على العدد a هيطلع اشمال و انتجر زي مهنا هاي مش
+
+44
+00:03:49,890 --> 00:03:53,970
+هاد معناه a تقسم b يعني الان b على a هتطلع ال c
+
+45
+00:03:53,970 --> 00:03:58,330
+يعني انتجر إذا من الآن و طالع مجرد نقول a تقسم b
+
+46
+00:03:58,330 --> 00:04:02,110
+معناته ال b على ال a هو عبارة عن عدد صحيحطب لو
+
+47
+00:04:02,110 --> 00:04:05,850
+بدنا نقول a does not divide b نرمز بالرمزية ده a
+
+48
+00:04:05,850 --> 00:04:10,030
+وهي الشحطة الأولى وهي فجهها شحطة تانية يعني a does
+
+49
+00:04:10,030 --> 00:04:15,810
+not divide b يعني a لا تقسم ال b ناخد أمثل عددية
+
+50
+00:04:15,810 --> 00:04:19,830
+الان المثال الأول determine whether التلاتة بتقسم
+
+51
+00:04:19,830 --> 00:04:23,940
+السابعة and whether التلاتة بتقسم أطنعاشلأ احنا
+
+52
+00:04:23,940 --> 00:04:26,800
+على طول الحد ما نشوف على طول التلاتة متقسمش السبعة
+
+53
+00:04:26,800 --> 00:04:31,640
+ليش لأن السبعة على التلاتة مش عدد صحيح اذا التلاتة
+
+54
+00:04:31,640 --> 00:04:35,780
+does not divide بيه اذا اكيد ال solution هنقوله
+
+55
+00:04:35,780 --> 00:04:40,020
+التلاتة لا تقسم السبعة because اللي هو السبعة على
+
+56
+00:04:40,020 --> 00:04:44,520
+التلاتة ليست عدد صحيحلأن تلاتة بتقسم 12 كلكم قال
+
+57
+00:04:44,520 --> 00:04:47,660
+هل جيت 12 ع تلاتة أربعة يعني التلاتة لازم تقسم من
+
+58
+00:04:47,660 --> 00:04:52,080
+12 إذا أكيد تلاتة بتقسم 12 لأن 12 ع تلاتة هي عبارة
+
+59
+00:04:52,080 --> 00:04:56,600
+عن إيش طلعت الأربعة أو بمعنى أخر 12 بتساوي 3 في 4
+
+60
+00:04:56,600 --> 00:05:01,720
+زي ما عملنا في ال A ال B بتساوي A في C إذا التلاتة
+
+61
+00:05:01,720 --> 00:05:06,460
+تقسم من 12 إذا الكلام سهل طيب نيجي لخواص ال
+
+62
+00:05:06,460 --> 00:05:11,200
+divisibility أو خواص قابلية ال A أو خواص القسمة
+
+63
+00:05:11,200 --> 00:05:16,530
+نشوفاللي قال لو كان عند A وB وC عبارة عن integers
+
+64
+00:05:16,530 --> 00:05:21,330
+أعداد صحيحة والـ A لا تساوي سفر لأن شكل اللي هنقسم
+
+65
+00:05:21,330 --> 00:05:24,470
+على الـ A عشان يجي الـ A لا تساوي السفر الآن بقول
+
+66
+00:05:24,470 --> 00:05:30,130
+لي لو A بتجسم الـ Bوالـ a بتجسم ال c أكيد ال a
+
+67
+00:05:30,130 --> 00:05:34,850
+هتجسم ال b زائد ال c كلام منطقي خد مثلا اتنين
+
+68
+00:05:34,850 --> 00:05:39,910
+بتجسم الستة و اتنين بتجسم العشرة اذا اتنين بتجسم
+
+69
+00:05:39,910 --> 00:05:43,110
+الستة زاد العشرة اللي هي الست عشر اكيد اتنين بتجسم
+
+70
+00:05:43,110 --> 00:05:47,210
+الست عشر اذا دائما ال a بتجسم ال b و ال a بتجسم ال
+
+71
+00:05:47,210 --> 00:05:53,110
+c هذولة بخزن المعلومة بتعطينا ان ال a بتجسم ال b
+
+72
+00:05:53,110 --> 00:05:58,700
+زاد ال cهنروح لبعد من هيك بعد شوية الان a بتجسم ال
+
+73
+00:05:58,700 --> 00:06:04,280
+b أكيد ال a هتجسم ال b في خمسة و ال b في ستة و ال
+
+74
+00:06:04,280 --> 00:06:08,180
+b في سبعة و ال b في تمانية يعني أكيد ال a بتجسم ال
+
+75
+00:06:08,180 --> 00:06:13,780
+b في c لكل انتجار cو100 مثال نستطيع أن نقولها يعني
+
+76
+00:06:13,780 --> 00:06:18,460
+اتنين بتقسم الستة اكيد اتنين بتقسم الستة في تلاتة
+
+77
+00:06:18,460 --> 00:06:21,540
+اللي هي 18 اتنين بتقسم الستة في خمسة في تلاتين
+
+78
+00:06:21,540 --> 00:06:25,840
+اتنين بتقسم الستة في مليون اذا اتنين هتقسم ال B في
+
+79
+00:06:25,840 --> 00:06:34,640
+C اللي هو في حال اتنين بتقسم ال Bالان الخاصية هذه
+
+80
+00:06:34,640 --> 00:06:38,380
+التلاتة اللى بنسميها خاصية التحدي ال A بتجسم ال B
+
+81
+00:06:38,380 --> 00:06:42,240
+و ال B بتجسم ال C مع بعض هدولة لازم يعطلنا ال A
+
+82
+00:06:42,240 --> 00:06:47,460
+بتجسم ال C هذا الكلام سهل برضه لإن ال A بتجسم ال
+
+83
+00:06:47,460 --> 00:06:52,660
+.. خلنا نقول ال 2 بتجسم ال 6 و ال 6 بتجسم ال 24
+
+84
+00:06:52,660 --> 00:06:59,040
+إذا أكيد ال 2 بتجسم ال 24التلاتة بتجسم الستة
+
+85
+00:06:59,040 --> 00:07:03,240
+والستة بتجسم التمنتاش اذا التلاتة بتجسم من
+
+86
+00:07:03,240 --> 00:07:09,960
+التمنتاش اذا خاصية التعد متحققة ايضا لان نتيجة
+
+87
+00:07:09,960 --> 00:07:14,840
+للنظرية اللي فوق اللي هو طبعا هذه كان البرهان
+
+88
+00:07:14,840 --> 00:07:19,220
+المطلوب لكن احنا لسبب الظروف الآن اعطيناكم بيها
+
+89
+00:07:19,220 --> 00:07:22,820
+بدون برهان وهنا حكينا امثلة عددية عليها المهم نفهم
+
+90
+00:07:22,820 --> 00:07:27,160
+ايش اللي هو الخواصة دي نيجي لل Corollaryأو النتيجة
+
+91
+00:07:27,160 --> 00:07:31,420
+للtheorem اللي عندنا بقول لو كان a و b و c عبارة
+
+92
+00:07:31,420 --> 00:07:35,820
+عن أعداد صحيحة و ال a لا يساوي c يعني ال f a and b
+
+93
+00:07:35,820 --> 00:07:40,120
+and c are integers و ال a لا تساوي سفر such that
+
+94
+00:07:40,120 --> 00:07:44,300
+ال a divides ال b و ال a divides ال c يعني ال a
+
+95
+00:07:44,300 --> 00:07:48,990
+بتقسم ال b و ال a بتقسم ال cإذا الـ A هتقسم مش بس
+
+96
+00:07:48,990 --> 00:07:52,690
+الـ B زائد الـ C لأ هتقسم أي linear combination
+
+97
+00:07:52,690 --> 00:07:57,610
+بينهم يعني هندمج هذه و هذه مع بعض و نحصل ان الـ A
+
+98
+00:07:57,610 --> 00:08:04,090
+بتقسم الـ B M زائد الـ C N لكل M و N ايش ال linear
+
+99
+00:08:04,090 --> 00:08:07,790
+combination هذا بنسميه ال M B زائد ال N C عبارة عن
+
+100
+00:08:07,790 --> 00:08:12,010
+linear combination بين الـ B و مين و الـ C إذا
+
+101
+00:08:12,010 --> 00:08:15,550
+بنقول ما ياليا يا جماعةإنه لو الـ A بتقسم الـ B و
+
+102
+00:08:15,550 --> 00:08:19,810
+الـ A بتقسم الـ C حيكون عند الـ A بتقسم أي Linear
+
+103
+00:08:19,810 --> 00:08:23,970
+combination M B زائد مين M C where M and N
+
+104
+00:08:23,970 --> 00:08:28,670
+integers يعني ناخد مثال عند الـ 3 بتقسم 12 و الـ 3
+
+105
+00:08:28,670 --> 00:08:34,570
+بتقسم الـ 15 أكيد الـ 3 بتقسم 12 في M زائد 15 في N
+
+106
+00:08:34,570 --> 00:08:39,520
+لكل ال integers M و Nانت جرب حط اي integers بيجي
+
+107
+00:08:39,520 --> 00:08:43,540
+على بالك ام و ان هتلاقي التلاتة بتجسم 12 ام زاد 15
+
+108
+00:08:43,540 --> 00:08:44,540
+ام ناخد مثلًا
+
+109
+00:08:54,500 --> 00:08:57,240
+التلاتة بتجسم التمانية وسبعين اكيد لان التمانية
+
+110
+00:08:57,240 --> 00:09:01,540
+وسبعة وخمسة عشر وجرب اعداد زي ما بدك هتلاقي مادامة
+
+111
+00:09:01,540 --> 00:09:04,360
+التلاتة بتجسم اتناش والتلاتة بتجسم الخمسة عشر
+
+112
+00:09:04,360 --> 00:09:07,200
+التلاتة هتجسم اي linear combination بين اتناش
+
+113
+00:09:07,200 --> 00:09:10,700
+وخمسة عشر ايش linear combination يعني اتناش فئام
+
+114
+00:09:10,700 --> 00:09:17,220
+زي خمسة عشر فئام لكل integers oneطيب الان نجي ل
+
+115
+00:09:17,220 --> 00:09:21,340
+division algorithm او اللي بنسميها خوارزمية القسمة
+
+116
+00:09:21,340 --> 00:09:25,600
+خوارزمية القسمة مش غريبة علينا بنعرفها بنعرفها من
+
+117
+00:09:25,600 --> 00:09:30,600
+و احنا صغار الان لو جلك اجسملي العشر على الخمسة
+
+118
+00:09:30,600 --> 00:09:34,080
+هتقولي العشر على الخمسة بيساو اتنين بقولك في متبقى
+
+119
+00:09:34,080 --> 00:09:38,580
+جسم هتقولي لايعني و كأنه العشر لما جسمت على خمسة
+
+120
+00:09:38,580 --> 00:09:42,240
+طلعت ناتج قسم اتنين ولا يودد متبقى قسمها يعني
+
+121
+00:09:42,240 --> 00:09:47,080
+متبقى القسمها سفر لكن لو قلتلك ديبل 11 على خمس على
+
+122
+00:09:47,080 --> 00:09:51,000
+خمسة هتقول 11 على خمسة بيساوي اتنين و بيزيد واحد
+
+123
+00:09:51,000 --> 00:09:56,880
+هذا الواحد هو متبقى قسمهاوالاتنين هي ناتج القسمة
+
+124
+00:09:56,880 --> 00:09:59,880
+هذا اللي بتقوله بالظبط ال division algorithm when
+
+125
+00:09:59,880 --> 00:10:03,220
+an integer is divided by a positive integer there
+
+126
+00:10:03,220 --> 00:10:06,900
+is a quotient and remainder يعني في ذاتج قسمة وفي
+
+127
+00:10:06,900 --> 00:10:12,560
+متبقى قسمة لما نجسم اللي هوعدد على positive number
+
+128
+00:10:12,560 --> 00:10:17,980
+دي اللي هو مقسوم عليه this is traditionally called
+
+129
+00:10:17,980 --> 00:10:22,780
+the division algorithm أو خوارزمية القسمة وخلّينا
+
+130
+00:10:22,780 --> 00:10:27,620
+نشوف إيش خوارزمية القسمة أو نظرية الخوارزمية
+
+131
+00:10:27,620 --> 00:10:31,320
+القسمةبتقول بقى يعني صلوا على النبي عليه الصلاة
+
+132
+00:10:31,320 --> 00:10:35,400
+والسلام if a is an integer and d is a positive
+
+133
+00:10:35,400 --> 00:10:38,940
+integer يعني a أي انتجر سالم موجة بالإبداكية حتى
+
+134
+00:10:38,940 --> 00:10:42,560
+لو كان سفر مش فارجة هقلناه و ال d positive integer
+
+135
+00:10:42,560 --> 00:10:47,340
+أكبر من سفر لما نجسم ال a على ال d هيطلع ناتج قسمة
+
+136
+00:10:47,340 --> 00:10:54,550
+بدي أسميه Q والمتبقى اللي هو بدي أسميه Rبعد ذلك
+
+137
+00:10:54,550 --> 00:10:58,790
+يوجد
+
+138
+00:10:58,790 --> 00:11:05,370
+ناتج قسم واحد Q ومتبقى واحد R بحيث ان R أكبر وسوء
+
+139
+00:11:05,370 --> 00:11:13,050
+سفر وأصغر من D دائما عندما تقسم ال A على ال Dيعني
+
+140
+00:11:13,050 --> 00:11:17,750
+11 على خمسة و تقول 11 على خمسة بطلع اتنين و بضال
+
+141
+00:11:17,750 --> 00:11:22,290
+واحد الواحد هذا سبته ليش سبته لأنه أصلا هو أكبر أو
+
+142
+00:11:22,290 --> 00:11:25,650
+يساوي سفر و أصغر من المقسوم عليه اللي هي الخمسة
+
+143
+00:11:25,650 --> 00:11:29,450
+فدائما ال remainder بكون أكبر أو يساوي سفر و أصغر
+
+144
+00:11:29,450 --> 00:11:35,160
+من المقسوم عليه ال Dإذاً لما نقعد يقسم ال A على ال
+
+145
+00:11:35,160 --> 00:11:40,920
+D بطلع لناتج قسمة اسمه Q وفيه remainder اسمه HR
+
+146
+00:11:40,920 --> 00:11:45,700
+عشان هيك بنقول A بتساوي D في Q زايد R زي ما قولنا
+
+147
+00:11:45,700 --> 00:11:53,020
+ل 11 بساوي ال 5 في 2 ب10 زايد ال 1 ال 1 هو ال
+
+148
+00:11:53,020 --> 00:11:58,060
+remainder وال 2 هو ناتج القسمة هو الخمسة اللي
+
+149
+00:11:58,060 --> 00:12:04,040
+قسمنا عليها إذاً الآنالـ A بيتساوى DQ زي الـ R حيث
+
+150
+00:12:04,040 --> 00:12:10,160
+الـ A هو المقسوم والـ D المقسوم عليه والـ Q ناتج
+
+151
+00:12:10,160 --> 00:12:15,140
+القسمة والـ R هو المتبقي D is called the divisor
+
+152
+00:12:15,870 --> 00:12:19,670
+الان المقصوم عليه A is called the dividend اللي هو
+
+153
+00:12:19,670 --> 00:12:24,690
+المقصوم و Q is called the quotient ناتج القسمة و R
+
+154
+00:12:24,690 --> 00:12:29,370
+is called the remainder من هذا الحديث الان بدنا
+
+155
+00:12:29,370 --> 00:12:34,580
+نستقي مع بعض دالتينانعرفن كما يالي definitions of
+
+156
+00:12:34,580 --> 00:12:38,300
+functions واحدة اسمها dive واحدة اسمها mud بدنا
+
+157
+00:12:38,300 --> 00:12:42,980
+نصطلح مع بعض شو معناته ان احنا بنقول ايه dive دي
+
+158
+00:12:42,980 --> 00:12:47,360
+اللي بنقصد فيها انه لما جينا قسمنا ال a على ال d
+
+159
+00:12:48,000 --> 00:12:52,640
+طلع عندى ناتج قسمة ناتج القسمة هذا اللى بتسميه a
+
+160
+00:12:52,640 --> 00:12:59,060
+ضايف d بقصد فيه ناتج قسمة a على d هذا ناتج القسمة
+
+161
+00:12:59,060 --> 00:13:06,200
+طب اهم ال d ايش بقصد فيه هو المتبقي من ناتج قسمة a
+
+162
+00:13:06,200 --> 00:13:11,460
+على d اذا a ضايف d مقصود فيه لما اقسم a على d
+
+163
+00:13:11,460 --> 00:13:15,650
+بتطلع اللى هى ناتج القسمةلما أقسم الـ a على d
+
+164
+00:13:15,650 --> 00:13:19,170
+بيطلع عندي remainder فبقصد ال a مو ال d هو عبارة
+
+165
+00:13:19,170 --> 00:13:22,710
+عن مين المتبقي او ال remainder اتفجن علينا دول
+
+166
+00:13:22,710 --> 00:13:29,150
+الدالتين يللا خلينا نشوف أمثل عددية طيب احنا نشوف
+
+167
+00:13:29,150 --> 00:13:35,190
+أمثل عددية المثل العدد لل division algorithm هو ما
+
+168
+00:13:35,190 --> 00:13:38,610
+يعني what are the quotient and remainder when 101
+
+169
+00:13:38,610 --> 00:13:45,250
+is divided by 111بنشوف ايش اللي هو الناتج القسمة
+
+170
+00:13:45,250 --> 00:13:50,410
+ومتبقى القسمة لما نجسم 101 على 11 اكيد كلكم كان
+
+171
+00:13:50,410 --> 00:13:56,870
+101 على 11 في 99 و بظهر بينهم قداش بزيادة 2 فاكيد
+
+172
+00:13:56,870 --> 00:14:02,600
+اللي هو هيكون عند 101 بساوة 11اللي هو ضرب تسعة
+
+173
+00:14:02,600 --> 00:14:08,040
+زائد اتنين تسعة هذا هو ناتج القسمة والتنين هو
+
+174
+00:14:08,040 --> 00:14:12,480
+متبقي القسمة عشان هيك بنكتبهم بالطريقة اللي اتفجنا
+
+175
+00:14:12,480 --> 00:14:16,860
+عليها قبل بشوية اللي هو بيصير عندي اللي هو عندي
+
+176
+00:14:16,860 --> 00:14:24,760
+المتبقيالقسمة اللي هو 2 فبنكتب 101 مد 11 بما أن في
+
+177
+00:14:24,760 --> 00:14:30,560
+متبقى القسمة لما نقسم 101 ل11 بيطلع 2 وبنكتب 101
+
+178
+00:14:30,560 --> 00:14:34,740
+ضايف 11 معناته الدالة هذه بتعني أنه لما نقسم 101
+
+179
+00:14:34,740 --> 00:14:40,720
+ل11 بيكون ناتج القسمة 100 اللي هو 9 زي ما شفنا
+
+180
+00:14:40,720 --> 00:14:42,740
+اللي عاملينه احنا هنا في ال division
+
+181
+00:14:46,330 --> 00:14:52,950
+السؤال الثاني هو what are the quotient and
+
+182
+00:14:52,950 --> 00:14:59,090
+remainder نقص 11 is divided by 3 نقص 11 نقص 11 نقص
+
+183
+00:14:59,090 --> 00:15:05,190
+11 نقص 11 نقص
+
+184
+00:15:05,190 --> 00:15:07,770
+11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11 نقص
+
+185
+00:15:07,770 --> 00:15:12,600
+11 نقص 11 نقص 11 نقص 11 نقص 11 نقص 11في هذه الحالة
+
+186
+00:15:12,600 --> 00:15:16,720
+بيصير نقص 11 بيساوي تلاتة فى ناقص أربعة زايد واحد
+
+187
+00:15:16,720 --> 00:15:19,900
+لما نقسم الناقص ماحدش يقول ناقص تلاتة لأنه بيصير
+
+188
+00:15:19,900 --> 00:15:23,020
+تلاتة فى ناقص تلاتة بيساوي ناقص تسعة ناقص تسعة
+
+189
+00:15:23,020 --> 00:15:26,520
+بيصير ناقص احداش بيساوي ناقص تسعة ناقص اتنين و ال
+
+190
+00:15:26,520 --> 00:15:29,920
+remainder لازم التفاجن يكون ايه شماله اكبر من سفر
+
+191
+00:15:29,920 --> 00:15:33,420
+و اصغر من تلاتة لأن احنا لما نقدر نقسم اي عدد على
+
+192
+00:15:33,420 --> 00:15:40,830
+ال remainder بيطلع انه عدد صحيحلو زاد عن اللي هو
+
+193
+00:15:40,830 --> 00:15:44,490
+.. لو ال remainder طلع بالسالب لأ احنا مابنقش
+
+194
+00:15:44,490 --> 00:15:48,130
+بنوحد الكلام كله مع بعض كلنا نجسم زي بعض و طلعنا
+
+195
+00:15:48,130 --> 00:15:51,810
+remainder زي بعض و ناتج قسمتنا زي بعض عشان هيك
+
+196
+00:15:51,810 --> 00:15:55,650
+بنطلب ال remainder يكون بين السفر و بين التلتة زي
+
+197
+00:15:55,650 --> 00:16:00,230
+ما كنا نعمل زمان في قسمة الأعداد الصحيحة على بعض
+
+198
+00:16:00,230 --> 00:16:04,090
+الان هذا بيصير نقص 11 بيساوي تلتة في نقص 4 زائد من
+
+199
+00:16:04,090 --> 00:16:08,980
+1الان هذا اللي هو الواحد هو عبارة عن ال remainder
+
+200
+00:16:08,980 --> 00:16:13,880
+عشان هيك بنقول الواحد اللي هو بساوي ناقص أحداش مدت
+
+201
+00:16:13,880 --> 00:16:19,620
+تلاتة نقولنا دالة المد هذه تعني قسمة ناقص أحداش ع
+
+202
+00:16:19,620 --> 00:16:24,380
+تلاتة بطلع متبقى القسمة بساوى واحد يعني هذه تدل
+
+203
+00:16:24,380 --> 00:16:30,390
+على متبقى القسمةالان اللى هو ناقص 11 ضايف 3 تعني
+
+204
+00:16:30,390 --> 00:16:34,610
+اللى هو ناتج قسمة ناقص 11 على 3 اللى هو ايش طلع
+
+205
+00:16:34,610 --> 00:16:40,030
+عندى ناقص 4 و هيك بنوجد اللى هو ناتج القسمة و
+
+206
+00:16:40,030 --> 00:16:47,990
+بنوجد مين اللى هو متبقي القسمة الان ان دخلنا على
+
+207
+00:16:47,990 --> 00:16:52,510
+حاجة اسمها ال congrance relation او اللى هي علاقة
+
+208
+00:16:52,510 --> 00:16:56,690
+التطابقالان ايش اللى بنقصد فيها علاقة التطابق؟
+
+209
+00:16:56,690 --> 00:17:00,110
+خلينا نشوف ايش اللى هو تعريف علاقة التطابق دي، ايش
+
+210
+00:17:00,110 --> 00:17:03,670
+معناه الـcongruence؟ لو كان عند A وB عبارة عن
+
+211
+00:17:03,670 --> 00:17:07,050
+أعداد صحيحة integers and M is a positive integer
+
+212
+00:17:07,050 --> 00:17:12,420
+والـ M إيش ماله؟ عدد صحيح موجببنقول أن a is
+
+213
+00:17:12,420 --> 00:17:17,180
+congruent to b modulo m يعني a تطابق b modulo m
+
+214
+00:17:17,180 --> 00:17:23,200
+يعني a تطابق b اللي هو بالنسبة للمقياس m إذا حققت
+
+215
+00:17:23,200 --> 00:17:29,060
+مالي ال m تقسم ال b minus a أو تقسم ال a minus b
+
+216
+00:17:29,060 --> 00:17:33,420
+في هذه الحالة بنقول a تطابق ال b modulo m وبنرمز
+
+217
+00:17:33,420 --> 00:17:37,790
+لها بالرمز اللي عندي ais congruent to B modulo M
+
+218
+00:17:37,790 --> 00:17:46,650
+نعني بها أن M تقسم اللي هو ال A ناقص B تقسم ال A
+
+219
+00:17:46,650 --> 00:17:52,030
+ناقص B هذا معناته أن A تطابق ال B modulo M الان
+
+220
+00:17:52,030 --> 00:17:57,510
+هذه ع بعضها بنسميها is a congruence أو بنسميها
+
+221
+00:17:57,510 --> 00:18:03,870
+تطابقة و ال M هو ال modulus أو هو مقياس التطابق
+
+222
+00:18:03,870 --> 00:18:08,180
+بنسميهالان اللى اللى اللى اللى اللى اللى اللى اللى
+
+223
+00:18:08,180 --> 00:18:08,440
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+224
+00:18:08,440 --> 00:18:09,560
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+225
+00:18:09,560 --> 00:18:10,360
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+226
+00:18:10,360 --> 00:18:10,480
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+227
+00:18:10,480 --> 00:18:12,300
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+228
+00:18:12,300 --> 00:18:12,320
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+229
+00:18:12,320 --> 00:18:13,660
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+230
+00:18:13,660 --> 00:18:14,520
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+231
+00:18:14,520 --> 00:18:16,420
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+232
+00:18:16,420 --> 00:18:17,660
+اللى اللى اللى اللى اللى اللى اللى اللى اللى اللى
+
+233
+00:18:17,660 --> 00:18:24,600
+اللى اللى اللىيكون المتطابقتين إذا كان ال a و ال b
+
+234
+00:18:24,600 --> 00:18:28,740
+اللي هى نفس ال remainder لو قسمناها على ال m يعني
+
+235
+00:18:28,740 --> 00:18:33,260
+لو قسمنا ال b على ال m هنلاقي اللي هو ناتج القسمة
+
+236
+00:18:33,260 --> 00:18:39,660
+b على m R1 و ناتج قسمة a على m R2 في حالة ما يكون
+
+237
+00:18:39,660 --> 00:18:44,980
+المتطابقتين لازم ال R1 ايش يساوي R2 عشان هيك two
+
+238
+00:18:44,980 --> 00:18:49,390
+integers are congruent modulo mif and only if they
+
+239
+00:18:49,390 --> 00:18:53,690
+have the same remainder when divided by main by m
+
+240
+00:18:53,690 --> 00:18:59,810
+لو كانت ال a لاتطابق ال b بنرمز ال a لاتطابق ال b
+
+241
+00:18:59,810 --> 00:19:03,430
+modulo m وهذا ماذا بتحدث؟ بتحدث لما نلاقي ال m لا
+
+242
+00:19:03,430 --> 00:19:08,430
+تقسم ال a minus b أو لما نلاقي ال remainder لل b
+
+243
+00:19:08,430 --> 00:19:13,250
+لما نقسمها على m يختلف عن ال remainder لل a لما
+
+244
+00:19:13,250 --> 00:19:18,910
+نقسمها على mainعلى أمن طيب خلينا نشوف احنا مثال او
+
+245
+00:19:18,910 --> 00:19:23,510
+امثلة عددية نشوف المثال العددي بيقول determine
+
+246
+00:19:23,510 --> 00:19:27,670
+whether ال 17 is congruent to 5 ولا لأو بعدين
+
+247
+00:19:27,670 --> 00:19:31,630
+modulo 6 طبعا and whether ال 24 and ال 14 are
+
+248
+00:19:31,630 --> 00:19:35,030
+congruent modulo 6 الآن بده يشوف السبعتاش والخمسة
+
+249
+00:19:35,030 --> 00:19:39,830
+هل المتطابقتين modulo 6 قلنا أحد أمرين ابني جي
+
+250
+00:19:39,830 --> 00:19:44,810
+بنقول السبعتاش ناقص خمسة بطلع اتناش الستة بتقسم
+
+251
+00:19:44,810 --> 00:19:49,390
+اتناش اذا السبعتاش بتقسم الخمسة modulo 6الان طريقة
+
+252
+00:19:49,390 --> 00:19:53,910
+اخرى اللى هى انه بنجيب نجسم السبعتاش على الستة
+
+253
+00:19:53,910 --> 00:19:58,410
+المتبقى جديش خمسة هو نفس المتبقى لما الخمسة نجسمها
+
+254
+00:19:58,410 --> 00:20:01,250
+على الستة لإن المتبقى بيطلع خمسة ونتج القسم صفر
+
+255
+00:20:01,250 --> 00:20:07,160
+طبيعى اذا الان السبعتاش تطابق خمسة مدله ستةلأن أحد
+
+256
+00:20:07,160 --> 00:20:12,540
+سببين يا إما ستة بتقسم حصل طرحين يا إما هذا لما
+
+257
+00:20:12,540 --> 00:20:16,180
+نقسم على هذا و هذا لما نقسم على هذا بيعطي نفس
+
+258
+00:20:16,180 --> 00:20:21,520
+نتيجة نفس اللي هو ال remainder طيب الآن يجي نحكم
+
+259
+00:20:21,520 --> 00:20:24,240
+على مين الاربع عشرين و الاربعة عشر هال congrant
+
+260
+00:20:24,240 --> 00:20:27,100
+بدوله ستة ولا لأ أكيد كلكم قال اربعة عشرين نقص
+
+261
+00:20:27,100 --> 00:20:30,900
+اربعة عشر بتساوي عشرة الستة بتقسمش العشرةإذا
+
+262
+00:20:30,900 --> 00:20:35,580
+الأربعة عشرين لاتطابق الاربعة عشر مدلو ستة أو
+
+263
+00:20:35,580 --> 00:20:40,080
+مقياس ستة الان لو أحد قال لا ما هو أنا بتطلع لها
+
+264
+00:20:40,080 --> 00:20:44,080
+نظرة أخرى الأربعة عشرين لو جسمناها على الستة بتطلع
+
+265
+00:20:44,080 --> 00:20:47,560
+ال remainder صفر لأنه تقبل قسم عليها لكن الأربعة
+
+266
+00:20:47,560 --> 00:20:49,920
+عشر لما نجسمها على الستة بتطلع عندي remainder
+
+267
+00:20:49,920 --> 00:20:52,260
+اتنين إذا ال remainder هنا و ال remainder هنا
+
+268
+00:20:52,260 --> 00:20:56,320
+مختلفات إذا they are notCongruent أحد الأمرين اللي
+
+269
+00:20:56,320 --> 00:21:02,220
+بتشتغلوه هو صحيح ندى الأن نشوف أخدنا شغلتين الأن
+
+270
+00:21:02,220 --> 00:21:07,310
+أخدنا اللى هو ايه تطابق الـ P modulo Mاللي هو و
+
+271
+00:21:07,310 --> 00:21:11,230
+الـ a mod m بتساوي b بدنا نشوف العلاقة the
+
+272
+00:21:11,230 --> 00:21:14,450
+relation between او the relationship between mod m
+
+273
+00:21:14,450 --> 00:21:20,130
+and mod m notations يعني هذه اللي بالغامج هذه اللي
+
+274
+00:21:20,130 --> 00:21:25,350
+بنقصد فيها دالة a mod m اللي هي نصدنا فيها دالة
+
+275
+00:21:25,350 --> 00:21:30,350
+لما نعرفنا هي و ال dive الآن a تطابق b mod m اللي
+
+276
+00:21:30,350 --> 00:21:35,560
+هي علاقة بين اللي هي integers a و bقلنا ايش هذا
+
+277
+00:21:35,560 --> 00:21:40,100
+بتعني؟ بتعني ان a تطابق b modulo m اللي هي معناتها
+
+278
+00:21:40,100 --> 00:21:45,480
+ان m بتجسم ال a minus b او بمعنى اخر قلنا معناتها
+
+279
+00:21:45,480 --> 00:21:52,300
+ان المتبقى القسمة من a على m هو نفس متبقى القسمة
+
+280
+00:21:52,300 --> 00:21:57,650
+من b على mبينما هذه يا جماعة اللى بتعني a مد ام
+
+281
+00:21:57,650 --> 00:22:04,790
+انه لما نجسم ال a على m متبقى القسمة بساوة b ماشي
+
+282
+00:22:04,790 --> 00:22:09,870
+اذا لما نقول a مد ام بساوة b يعني متبقى قسمة a على
+
+283
+00:22:09,870 --> 00:22:15,430
+m بساوة b اما هنا a تطابق b مد ام انه متبقى القسمة
+
+284
+00:22:15,430 --> 00:22:23,690
+a على m هو نفسه متبقى القسمة b لما نقسمه على mالان
+
+285
+00:22:23,690 --> 00:22:27,050
+هذا الكلام حكيته انا it وطبق me the relation on
+
+286
+00:22:27,050 --> 00:22:30,110
+the six integers هذه علاقة على الست الفنتجرز بينما
+
+287
+00:22:30,110 --> 00:22:33,370
+هذه عبارة عن دالة اتفاقنا عليها اللي هي the
+
+288
+00:22:33,370 --> 00:22:37,230
+notation denotes the function او a function
+
+289
+00:22:37,230 --> 00:22:40,870
+العلاقة بين التنتين الآن هنشوف that the
+
+290
+00:22:40,870 --> 00:22:44,550
+relationship between these two is made clear in
+
+291
+00:22:44,550 --> 00:22:47,950
+this theorem هتكون واضحة من خلال هذه النظرية اللي
+
+292
+00:22:47,950 --> 00:22:51,230
+أمامنا شوفوا يا جماعة صلى الله عليه الصلاة والسلام
+
+293
+00:22:51,600 --> 00:22:56,700
+لو كان عندي a و b integers و m positive integers
+
+294
+00:22:56,700 --> 00:23:03,700
+احنا ال a تطابق b مدله m هي تكافئ تماما يعني if
+
+295
+00:23:03,700 --> 00:23:09,620
+and only if هذه على بعضها هذه تكافئ تماما ان نقول
+
+296
+00:23:09,620 --> 00:23:17,760
+a مد m بساوي b مد mلأن بي مض ام ايش بتعني ان متبقى
+
+297
+00:23:17,760 --> 00:23:22,600
+قسمة ال بي على ام يساوي متبقى قسمة ال ا على ام لان
+
+298
+00:23:22,600 --> 00:23:25,800
+هذه بتعني متبقى قسمة ال ا على ام وهذه بتعني متبقى
+
+299
+00:23:25,800 --> 00:23:29,860
+قسمة ال بي على ام هذه معناته مساواة يعني متبقى
+
+300
+00:23:29,860 --> 00:23:33,760
+قسمة هذه على هذه بساوي متبقى قسمة هذه على هذه هو
+
+301
+00:23:33,760 --> 00:23:38,910
+بالظبط هذااللي هو A تطابق B mod M يعني متطابق قسمة
+
+302
+00:23:38,910 --> 00:23:44,750
+A على M اللي هو نفسه متطابق قسمة B على M وكأنه هذا
+
+303
+00:23:44,750 --> 00:23:51,070
+التعبير هو هذا التعبير ولكن بصورة أخرى ماشي الحال؟
+
+304
+00:23:51,070 --> 00:23:58,070
+طيب الآن إذا هذا بكافة اللي هو هذه الكلمتين بخزن
+
+305
+00:23:58,070 --> 00:24:02,820
+هذولة اللي عندنا أو كفاتة خلينا نشوف مثالالان الـ
+
+306
+00:24:02,820 --> 00:24:09,780
+31 و 351 متطابقات ليش لأن 351 ناقص 31 تطلع 320
+
+307
+00:24:09,780 --> 00:24:14,340
+العشرة بتجسمها إذا فعلا متطابقتين بالنسبة للمقياس
+
+308
+00:24:14,340 --> 00:24:20,600
+عشرة الان طيب الان اني جي نشوف اللي هو ال .. ال ..
+
+309
+00:24:20,600 --> 00:24:25,380
+ال .. نظرة أخرى لهذه ان هذا و هدولة اللي هي نفس ال
+
+310
+00:24:25,380 --> 00:24:30,320
+remainder لما نجسمها للعشرة هذا هو الان31 لما
+
+311
+00:24:30,320 --> 00:24:35,160
+تجسمها على عشرة بيطلع متبقي واحد 351 لما تجسمها
+
+312
+00:24:35,160 --> 00:24:39,580
+على عشرة بيطلع متبقي واحد إذا هذا بيساوي هذا يعني
+
+313
+00:24:39,580 --> 00:24:44,640
+اللي هي التطابقات و بالمناسبة التطابقات اللي هو
+
+314
+00:24:44,640 --> 00:24:49,300
+موضوع ال concurrences هذه هي أصلا لأودادتنا أو
+
+315
+00:24:49,300 --> 00:24:54,900
+خلينا نقول اللي بتعلمنا كيف أو قدام هنعرف أنظمة
+
+316
+00:24:54,900 --> 00:24:59,020
+العد من خلالهانظام العد الثاني نظام العد الثلاثي
+
+317
+00:24:59,020 --> 00:25:03,200
+الرباعي الخماسي العشاري اللي بنتعامل فيه أو الستعش
+
+318
+00:25:03,200 --> 00:25:07,580
+أو التمانية اللي بدنا يه اللي هو النظام العد اللي
+
+319
+00:25:07,580 --> 00:25:11,800
+هو اللي بتبع من المقياس يعني مقياس عشرة بنصير مجول
+
+320
+00:25:11,800 --> 00:25:15,240
+عن نظام العد العشاري مقياس اتنين بنصير مجول عن
+
+321
+00:25:15,240 --> 00:25:19,440
+نظام العد الاتنين وهكذا وان شاء الله هنجيه قدام
+
+322
+00:25:19,780 --> 00:25:24,780
+الان بيكون هيك احنا خلصنا اللي هو اللي بدناياه في
+
+323
+00:25:24,780 --> 00:25:28,540
+هذا ال section وعندي ال homework التالي بدياه
+
+324
+00:25:28,540 --> 00:25:32,580
+تجيبوليه ببعتلكم عن واتس بظبط إيش اللي بدياه الآن
+
+325
+00:25:32,580 --> 00:25:36,920
+السؤال الأول بيقوللي 31 تطابق ماذا مدل سبعة هل
+
+326
+00:25:36,920 --> 00:25:40,140
+بالطابق الخامسة، بالطابق ال 211؟ يمكن الطابق
+
+327
+00:25:40,140 --> 00:25:42,720
+واحدة، تمتين، تلاتة، كل واحدة من هناك تشوف مين
+
+328
+00:25:42,720 --> 00:25:46,420
+بالطابق ال 31 مدل السبعة وتحط اللي تحتها خط
+
+329
+00:25:46,420 --> 00:25:51,430
+وتقوللي ليش بالطابقهاوالثاني لماذا بالطبق عشر؟
+
+330
+00:25:51,430 --> 00:25:55,430
+find اللي هو عشرة ضايف تلاتة عشرة ضايف تلاتة قدش
+
+331
+00:25:55,430 --> 00:25:59,890
+قيمته 101 ضايف تلاتة وعشرين برضه نفس الاشي و بعدين
+
+332
+00:25:59,890 --> 00:26:04,170
+اجدل عشرة موت تلاتة الاخر هدولة إيجاد زي ما شرحنا
+
+333
+00:26:04,170 --> 00:26:07,530
+قبل شوية الان question الثالث which of the
+
+334
+00:26:07,530 --> 00:26:09,710
+following divides the positive integer a؟ يعني
+
+335
+00:26:09,710 --> 00:26:15,070
+عندي في positive integer aمين من هدولة divides
+
+336
+00:26:15,070 --> 00:26:19,950
+which of the following divides the positive
+
+337
+00:26:19,950 --> 00:26:25,510
+integer ايه او خلينا نقول which of the following
+
+338
+00:26:25,510 --> 00:26:52,400
+او a divides which of the followingA divides
+
+339
+00:26:52,400 --> 00:26:57,500
+which of the followingيعني مش هنا اللي بدني اجيز
+
+340
+00:26:57,500 --> 00:27:02,920
+منه هل ال ا بتجسم هدول ولا لأ ا بتجسم مين منهم بدك
+
+341
+00:27:02,920 --> 00:27:07,360
+تحددها و هيك بكون خلصنا ال section الأول و إلى
+
+342
+00:27:07,360 --> 00:27:11,840
+لقاء آخر والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6ed5188fbaea7405c34e9e1e6978d5e912fa2f22
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c.srt
@@ -0,0 +1,1763 @@
+1
+00:00:01,080 --> 00:00:07,140
+بسم الله الرحمن الرحيم هذه المحاضرة السادسة لمساق
+
+2
+00:00:07,140 --> 00:00:11,660
+رياضيات منفصلة لطلاب وطالبات الجامعة الإسلامية
+
+3
+00:00:11,660 --> 00:00:16,040
+كلية  Information Technology المعلومات قسم الحوسبة المتلقلة
+
+4
+00:00:16,620 --> 00:00:21,700
+اليوم إن شاء الله هنشرح اللي هو جزء من section
+
+5
+00:00:21,700 --> 00:00:26,820
+أربعة تلاتة اللي هنحكي فيه عن ال-primes الأعداد
+
+6
+00:00:26,820 --> 00:00:32,160
+الأولية and greatest common divisors هنحكي مقدمة
+
+7
+00:00:32,160 --> 00:00:35,560
+بسيطة عن اللي هو greatest common divisors اللي هو
+
+8
+00:00:35,560 --> 00:00:41,720
+عبارة عن العامل المشترك الأعلى بعد ما نتحدث عن
+
+9
+00:00:41,720 --> 00:00:46,880
+اللي هو موضوع الأعداد الأولية الآن نشوف شو معناه
+
+10
+00:00:46,880 --> 00:00:50,100
+الـprimes الـprimes هي الأعداد الأولية اللي احنا
+
+11
+00:00:50,100 --> 00:00:53,420
+أخذناها في اللي هو الثاني في الأعداد دي
+
+12
+00:00:53,420 --> 00:00:58,100
+واستعملناها بعد ذلك الآن شو هو العدد الأولي a
+
+13
+00:00:58,100 --> 00:01:04,660
+positive integer بيه عدد اللي هو الصحيح الموجب بيه
+
+14
+00:01:04,660 --> 00:01:08,400
+اللي أكبر من واحد بنسميه عدد أولي is called the
+
+15
+00:01:08,400 --> 00:01:15,720
+prime إذا بس مالوش divisor أو عامل إلا نفسه يعني
+
+16
+00:01:15,720 --> 00:01:19,960
+بمعنى آخر بنقول عن العدد .. والواحد طبعا .. بنقول
+
+17
+00:01:19,960 --> 00:01:25,970
+عن العدد B اللي هو إن عدد أولي إذا كان the only
+
+18
+00:01:25,970 --> 00:01:32,510
+divisor of B are one and B يعني الأعداد القواسم
+
+19
+00:01:32,510 --> 00:01:39,990
+للعدد B فقط هما عددان العدد نفسه والعدد واحد طبعا
+
+20
+00:01:39,990 --> 00:01:47,090
+و B هو أكبر من واحد بمعنى آخر العدد الأولي هو عدد
+
+21
+00:01:47,090 --> 00:01:56,960
+صحيح موجب له قاسمان مختلفان فقط الواحد والعدد نفسه
+
+22
+00:01:56,960 --> 00:02:01,560
+العدد اللي بيكونش أولي a positive integer that is
+
+23
+00:02:01,560 --> 00:02:05,460
+greater than one and is not prime بنسمي أيش ماله
+
+24
+00:02:05,800 --> 00:02:11,480
+اللي هو composite أو عدد غير أولي إلا نيجي ناخد
+
+25
+00:02:11,480 --> 00:02:16,160
+مثال انتجار سبعة is prime because it's only
+
+26
+00:02:16,160 --> 00:02:21,980
+positive factors are واحد وسبعة وزي تلاتة والتلاتة
+
+27
+00:02:21,980 --> 00:02:27,120
+عدد أول لأن الواحد والثلاثة هما بس قواصمه والاثنين
+
+28
+00:02:27,120 --> 00:02:31,180
+عدد أولي الأربعة لا مش عدد أولي لأن الأربعة في
+
+29
+00:02:31,180 --> 00:02:36,660
+عندنا اللي هو الاثنين والأربعة بقسمله والاثنين غير
+
+30
+00:02:36,660 --> 00:02:41,080
+اللي هو الأربعة but تسعة is composite زي ما هو
+
+31
+00:02:41,080 --> 00:02:45,300
+حاكين because it is divisible by ثلاثة واحدة شرط
+
+32
+00:02:45,300 --> 00:02:50,260
+أن يكون عدد أولي أنه بس له قاسمين مختلفين الواحد
+
+33
+00:02:50,260 --> 00:02:51,360
+والعدد نفسه
+
+34
+00:02:59,120 --> 00:03:06,200
+النظرية الأساسية للحساب
+
+35
+00:03:06,200 --> 00:03:11,170
+تقول ما يلي Every positive integer greater than
+
+36
+00:03:11,170 --> 00:03:15,510
+one can be written uniquely as a prime or the
+
+37
+00:03:15,510 --> 00:03:19,590
+product of two or more primes where the prime
+
+38
+00:03:19,590 --> 00:03:23,010
+factors are written in order of non-decreasing
+
+39
+00:03:23,010 --> 00:03:27,870
+size يعني النظرية بتقولنا أن أي عدد positive أكبر
+
+40
+00:03:27,870 --> 00:03:33,210
+من واحد بنقدر نكتبه بطريقة وحيدة على صورة a
+
+41
+00:03:33,210 --> 00:03:37,290
+product of primes يعني حاصل ضرب إيش primes وده كان
+
+42
+00:03:37,290 --> 00:03:43,390
+الـprime بكون نفسه بيه الآن اللي هو هذه الطريقة
+
+43
+00:03:43,390 --> 00:03:48,390
+وحيدة وبنقدر نرتب اللي هي حاصل الضرب من الصغيرة
+
+44
+00:03:48,390 --> 00:03:53,410
+لكبيرة لما نصل لأكبر عامل إيش اللي بقوله نجي نشوف
+
+45
+00:03:53,410 --> 00:03:58,730
+مثال يعني الآن مية المية هذا لو جينا اللي هو بدنا
+
+46
+00:03:58,730 --> 00:04:05,370
+نفككه إلى عوامله الأولية يعني إلى حاصل ضرب أعداد
+
+47
+00:04:05,370 --> 00:04:10,310
+أولية المية لو جسمناها على اثنين بتطلع خمسين اثنين
+
+48
+00:04:10,310 --> 00:04:12,990
+الخمسين لو جسمناها على اثنين بتطلع خمسة وعشرين
+
+49
+00:04:12,990 --> 00:04:15,930
+الخمسة والعشرين لو جسمناها على خمسة بتطلع خمسة
+
+50
+00:04:15,930 --> 00:04:19,590
+الخمسة لما نجسمها على خمسة بتطلع واحد إذا مين
+
+51
+00:04:19,590 --> 00:04:23,510
+عوامل العدد مية اللي هو اثنين في اثنين في خمسة في
+
+52
+00:04:23,510 --> 00:04:27,210
+خمسة يعني كتبناها على حصة على صورة إيش يا جماعة
+
+53
+00:04:27,210 --> 00:04:33,220
+حاصل ضرب اللي هي أعداد أولية الآن هدول الأوليين
+
+54
+00:04:33,220 --> 00:04:36,020
+هدول اثنين واثنين مقررات زي ما بتعرفوا مكتبها
+
+55
+00:04:36,020 --> 00:04:40,280
+اثنين أقصى اثنين في خمسة أقصى اثنين الصورة هذه هي
+
+56
+00:04:40,280 --> 00:04:44,260
+الصورة الوحيدة لكتابة المية as a product of a
+
+57
+00:04:44,260 --> 00:04:47,960
+prime of power of primes يعني إيش power of primes
+
+58
+00:04:47,960 --> 00:04:52,460
+يعني برايم مرفوع لأقصه وهذا البرايم مرفوع لأقصه
+
+59
+00:04:52,710 --> 00:04:56,390
+فصار عندي اللي هو المية مضروبة في صورة حاصل ضرب
+
+60
+00:04:56,390 --> 00:05:00,970
+اللي هي power of primes أو حاصل ضرب إيش primes و
+
+61
+00:05:00,970 --> 00:05:05,390
+هذه الصورة الوحيدة من الـ .. طبعا الوحيدة إننا نتفق
+
+62
+00:05:05,390 --> 00:05:10,310
+مع بعض إن اللي هو بدنا اللي هو نكتب من الصغير إلى
+
+63
+00:05:10,310 --> 00:05:13,970
+الأكبر يعني الـprime اثنين وبعدين اثنين وبعدين
+
+64
+00:05:13,970 --> 00:05:17,050
+الخمسة وبعدين الخمسة هي المقصود من الصغير إلى
+
+65
+00:05:17,050 --> 00:05:21,490
+الأكبر وطبعا وده تكرر نكتبه نفسه الآن 641 لو
+
+66
+00:05:21,490 --> 00:05:25,530
+جربنا نشوف هذا 641 بيقسم على حاجة ما بيقسمش ولا على
+
+67
+00:05:25,530 --> 00:05:28,930
+حاجة إلا غير على نفسه على الواحد عشان هي .. طبعا
+
+68
+00:05:28,930 --> 00:05:32,170
+هناخد كيف نوجد الـprimes كمان شوية أو نثبت إنه
+
+69
+00:05:32,170 --> 00:05:37,890
+prime أو لا الآن 641 سوى 641 اللي هو لأنه نفسه
+
+70
+00:05:37,890 --> 00:05:43,860
+كتلة واحدة الـprime هو كتلة واحدة لا تتجزأ الآن 999
+
+71
+00:05:43,860 --> 00:05:48,120
+نجي اللي هو بدنا نحاول نجزقه لعوامله الأولية لو
+
+72
+00:05:48,120 --> 00:05:51,760
+قسمنا على ثلاثة بالذي اللي بيطلع ثلاث مية وثلاثة وثلاثين
+
+73
+00:05:51,760 --> 00:05:54,920
+وثلاثين ثلاث مية وثلاثة وثلاثين لو قسمنا على ثلاثة
+
+74
+00:05:54,920 --> 00:05:58,420
+بيطلع مية وأحد عشر يعني قسمنا كمان مرة على ثلاثة
+
+75
+00:05:58,420 --> 00:06:03,900
+اللي .. اه .. لو قسمنا على ثلاثة بيطلع إيش اللي هو
+
+76
+00:06:03,900 --> 00:06:10,840
+عبارة عن قداش سبعة وثلاثين ثلاثة على ثلاثة بيطلع ثلاثة
+
+77
+00:06:10,840 --> 00:06:14,580
+مئة وثلاثة وثلاثين ثلاثة بيطلع مئة وأحد عشر على مئة
+
+78
+00:06:14,580 --> 00:06:18,460
+وأحد عشر بيطلع ثلاثة في سبعة وثلاثين اللي هي اللي
+
+79
+00:06:18,460 --> 00:06:22,280
+هي المئة وأحد عشر الآن بيصير عندي هذا العدد اللي
+
+80
+00:06:22,280 --> 00:06:25,840
+كتبناه على صورة product of primes حصل ضرب primes
+
+81
+00:06:25,840 --> 00:06:29,060
+أو على صورة اللي هو product of power of primes
+
+82
+00:06:29,060 --> 00:06:33,160
+يعني ثلاثة اتكررت قداش اثنين ثلاثة في سبعة وثلاثين
+
+83
+00:06:33,160 --> 00:06:37,210
+زي ما اتعودنا على الكتابة احنا عادة الألف وأربع
+
+84
+00:06:37,210 --> 00:06:39,930
+وعشرين اللي هو برضه هنكتبه على صورة product of
+
+85
+00:06:39,930 --> 00:06:43,090
+وprimes و صورة واحدة مش غيرها أصلا اللي هنبنيه جهة
+
+86
+00:06:43,090 --> 00:06:46,170
+أكيد هدول جسم يقبل جسمها دلنا نجسم نجسم نجسم نجسم
+
+87
+00:06:46,170 --> 00:06:46,830
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+88
+00:06:46,830 --> 00:06:48,090
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+89
+00:06:48,090 --> 00:06:48,290
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+90
+00:06:48,290 --> 00:06:48,310
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+91
+00:06:48,310 --> 00:06:59,080
+نجسم نجسم نجسم نجسم نجسم نجسم أو على صورة power of
+
+92
+00:06:59,080 --> 00:07:03,300
+برايم وهذه الصورة صورة إيش وحيدة إذا نفهم شو معناه
+
+93
+00:07:03,300 --> 00:07:05,440
+if a positive integer greater than one can be
+
+94
+00:07:05,440 --> 00:07:11,710
+written uniquely as a product of إيش of primes نيجي
+
+95
+00:07:11,710 --> 00:07:20,150
+الآن كيف نبحث عن اللي هو الـprimes أو مسألة
+
+96
+00:07:20,150 --> 00:07:26,210
+قديمة حتى يعني اللي هو الحل اللي موجود هو حل قديم
+
+97
+00:07:26,210 --> 00:07:31,250
+حل the sieve of Eratosthenes
+
+98
+00:07:31,250 --> 00:07:35,990
+اللي هو إراتوستينس اللي هو نشوف إيش اللي هو البحث
+
+99
+00:07:35,990 --> 00:07:42,390
+كيف بحث إراتوستينس في مسألة إيجاد الأعداد الأولية
+
+100
+00:07:42,390 --> 00:07:47,390
+من واحد إلى مئة الآن هذا بقول لك sieve of إراتوستينس
+
+101
+00:07:47,390 --> 00:07:52,050
+can be used to find all primes not exceeding a
+
+102
+00:07:52,050 --> 00:07:56,490
+specified positive integer بقول لك يعني احنا لو بدنا
+
+103
+00:07:56,490 --> 00:08:01,770
+نيجي نبحث عن الأعداد الأولية من الـ .. اللي اللي من
+
+104
+00:08:01,770 --> 00:08:07,890
+واحد لعند خمسمية إيش بنسوي؟ من واحد لعشرين إيش
+
+105
+00:08:07,890 --> 00:08:11,670
+بنسوي؟ من واحد لثلاثين إيش بنسوي؟ الآن بقول لي for
+
+106
+00:08:11,670 --> 00:08:15,450
+example بده يبحث beginning with the list of integers
+
+107
+00:08:15,450 --> 00:08:19,890
+between واحد ومئة يريد أن يبحث عن الأعداد الأولية
+
+108
+00:08:20,210 --> 00:08:23,570
+اللي من الأعداد من واحد لمئة .. من واحد لمئة في
+
+109
+00:08:23,570 --> 00:08:28,690
+عندنا مائة عدد الآن هذول المائة عدد بدنا نبحث مين
+
+110
+00:08:28,690 --> 00:08:32,350
+فيهم اللي هو إبراهيم شوفوا الطريقة الحلوة الجميلة
+
+111
+00:08:32,350 --> 00:08:36,910
+هذه طريقة قديمة من أيام إراتوستينس اللي هو بيقول
+
+112
+00:08:37,760 --> 00:08:41,460
+delete all integers other than اثنين divisible by
+
+113
+00:08:41,460 --> 00:08:46,660
+اثنين إيش تسوي أول حاجة بقول لك كل الأعداد اللي
+
+114
+00:08:46,660 --> 00:08:52,820
+بتقسم على اثنين لعنده مئة اللي هو شطة بقى يعني
+
+115
+00:08:52,820 --> 00:08:57,200
+اكتب الأعداد من واحد لمئة وبده شطة مضاعفة يعني
+
+116
+00:08:57,200 --> 00:09:06,470
+اثنين ومضاعفاته يعني 2×3×6 و 2×4×8 و 2×5×10
+
+117
+00:09:06,470 --> 00:09:12,450
+و 2×6×12 بظلي اللي هي كل الأعداد اللي هي مضاعفات 2
+
+118
+00:09:12,450 --> 00:09:17,580
+مشطبها من اللي استهال الآن بعد هيك بشطب كل الأعداد
+
+119
+00:09:17,580 --> 00:09:20,600
+اللي هي delete all the integers other than ثلاثة
+
+120
+00:09:20,600 --> 00:09:23,900
+divisible by ثلاثة بشطب كل الأعداد طبعا سيب
+
+121
+00:09:23,900 --> 00:09:29,280
+الثلاثة لأنه prime سيب .. شطب كل المضاعفات الثلاثة
+
+122
+00:09:29,280 --> 00:09:33,560
+شطب الست وشطب التسعة وشطب الاثنا عشر و و و الآخر
+
+123
+00:09:33,560 --> 00:09:36,960
+يه طبعا في شيء اللي بشطبهن تكون شطبتهن نور على نور
+
+124
+00:09:36,960 --> 00:09:40,080
+أصلًا مديش إيه أنا طبعا المضاعفات هي مش هيكون الـ
+
+125
+00:09:40,080 --> 00:09:44,820
+prime أكيد delete all the integers other than خمسة 
+
+126
+00:09:44,820 --> 00:09:50,040
+or divisible by خمسة الآن شطب على كل الأعداد
+
+127
+00:09:50,040 --> 00:09:55,240
+مضاعفات من الخمسة الآن شطبت على مضاعفات الخمسة
+
+128
+00:09:55,240 --> 00:09:58,820
+اللي هي عشرة وخمسة عشر وعشرين إلى آخر ما
+
+129
+00:09:58,820 --> 00:10:03,960
+تصل إلى المئة الآن بعدها شطب على كل الأعداد اللي
+
+130
+00:10:03,960 --> 00:10:10,280
+هي مضاعفات العدد من سبعة الآن وكأنه بيقول لي تعال
+
+131
+00:10:10,280 --> 00:10:15,220
+من الأعداد الأقل من عشرة وشوف الـprimes اللي فيها
+
+132
+00:10:15,220 --> 00:10:20,480
+اللي هي الاثنين والثلاثة والخمسة والسبعة وشطب 
+
+133
+00:10:20,480 --> 00:10:25,420
+مضاعفاتها الآن بعد ما تشطب مضاعفاتها بقول لك since
+
+134
+00:10:25,420 --> 00:10:28,320
+all the remaining integers are not divisible by
+
+135
+00:10:28,320 --> 00:10:32,240
+any of the previous integers other than the واحد
+
+136
+00:10:32,240 --> 00:10:37,400
+primes are بقول لك أنا بكفلك أنه يظل المتبقيات مين
+
+137
+00:10:37,400 --> 00:10:44,020
+هم اللي هم الـprimes ليش؟ لأن أنت أصلاً لما تيجي
+
+138
+00:10:44,020 --> 00:10:48,220
+تشطب اللي هي كل مضاعفات الاثنين ومضاعفات الثلاثة
+
+139
+00:10:48,220 --> 00:10:52,440
+ومضاعفات الخمسة ومضاعفات السبعة لو بدك تيجي للرقم
+
+140
+00:10:52,440 --> 00:10:58,900
+100 الرقم 100 إذا بده يكون اللي هو في اللي هو 
+
+141
+00:10:58,900 --> 00:11:06,930
+قواسم الآن القواسم اللي هتكون لازم يكون واحد من يا 
+
+142
+00:11:06,930 --> 00:11:10,790
+إثنين يا ثلاثة يا خمسة يا سبعة موجودة في هذه
+
+143
+00:11:10,790 --> 00:11:15,410
+القواسم لأنه لو بده يكون ما يكونش ولا واحد من هدول
+
+144
+00:11:15,410 --> 00:11:19,010
+الـprimes في القواسم معناته مين بده يكون اللي هو
+
+145
+00:11:19,010 --> 00:11:25,150
+منهن اللي هو الـ11 أو الـ13 طب ما هو الـ11 لو بده
+
+146
+00:11:25,150 --> 00:11:29,880
+يقسم الـ100 أو الـ13 بده يقسم الـ100 لازم يكون في
+
+147
+00:11:29,880 --> 00:11:33,600
+رقم أصغر منه بيقسمها لأن لو كل الأرقام اللي بدأت
+
+148
+00:11:33,600 --> 00:11:37,440
+تقسم اللي هو الـ100 من الـPrimes عبارة عن اللي
+
+149
+00:11:37,440 --> 00:11:42,200
+هو أكبر من اللي هو السبعة اللي هي أكبر من الـ11
+
+150
+00:11:42,200 --> 00:11:45,700
+يعني بيصير 11 في اللي أكبر منه أكثر من 100
+
+151
+00:11:45,700 --> 00:11:50,280
+يتجاوزوا يعني يعني الأعداد ال ... ال ... الـcomposite
+
+152
+00:11:50,280 --> 00:11:56,600
+الفيلمية غصبًا عنها هتطلع اللي هي مضاعفات اللي هي 
+
+153
+00:11:56,600 --> 00:12:00,980
+الاثنين والثلاثة والخمسة والسبعة لازم نلاقيها
+
+154
+00:12:00,980 --> 00:12:06,120
+للأسباب اللي حكيته طيب نيجي الآن نشوف هذا الكلام
+
+155
+00:12:06,120 --> 00:12:11,120
+عمليًا أدري إيش سوى هيحط اللي هي الأعداد من واحد
+
+156
+00:12:11,120 --> 00:12:16,860
+لمئة هذه طريقة إراتوستينس وهذه الأعداد من واحد لمئة
+
+157
+00:12:16,860 --> 00:12:18,820
+وهذه الأعداد من واحد لمئة وهذه الأعداد من واحد
+
+158
+00:12:18,820 --> 00:12:23,360
+لمئة أول شيء قال خلينا نجي لمضاعفات من الاثنين هي
+
+159
+00:12:23,360 --> 00:12:26,680
+الاربعة وهي الستة وهي الثمانية وهي العشرة وهي
+
+160
+00:12:26,680 --> 00:12:28,720
+اثنا عشر وهي الاربعة عشر وهي الستة عشر وهي
+
+161
+00:12:28,720 --> 00:12:33,300
+الثمانية عشر ولما كمل لوين لمئة لما اجى ل ... ل ... ل
+
+162
+00:12:33,300 --> 00:12:34,680
+... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل
+
+163
+00:12:34,680 --> 00:12:35,600
+... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل
+
+164
+00:12:35,600 --> 00:12:35,620
+... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل ... ل
+
+165
+00:12:35,620 --> 00:12:39,050
+... ل ... ل ... ل ... ل ... ل ... ل مضاعفات الثلاثة
+
+166
+00:12:39,050 --> 00:12:41,870
+اللي عليها خط اللي هي مضاعفات الاثنين نسيبها الآن
+
+167
+00:12:41,870 --> 00:12:46,350
+حطينا كمان خط لمضاعفات مين الثلاثة وهيوش الطبهين
+
+168
+00:12:46,350 --> 00:12:51,670
+كمان مرة طبعًا دخل شيء جديد هاي 32 مضاعفات ال ...
+
+169
+00:12:51,670 --> 00:12:56,380
+آسف الـ33 مضاعفات مين الثلاثة ما كانت شان، إذًا
+
+170
+00:12:56,380 --> 00:12:59,480
+هذا تشطب كمان، بخط واحد، اللي بخط، اللي بخطين ولا
+
+171
+00:12:59,480 --> 00:13:02,600
+بالأربعة؟ في الآخر إشمال، اللي هين بده ينشل، اللي
+
+172
+00:13:02,600 --> 00:13:05,780
+هين composite صار، اللي هين مضاعفات إثنين أو
+
+173
+00:13:05,780 --> 00:13:08,240
+مضاعفات ثلاثة أو مضاعفات الأربعة أو مضاعفات
+
+174
+00:13:08,240 --> 00:13:22,090
+الخمسة، مش primes الآن نشطب مضاعفات الخمسة خمسة
+
+175
+00:13:22,090 --> 00:13:22,890
+مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة
+
+176
+00:13:22,890 --> 00:13:26,670
+مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة
+
+177
+00:13:26,670 --> 00:13:36,090
+مضاعفات الخمسة مضاعفات الخمسة خمسة عشر عشرين وهكذا
+
+178
+00:13:36,090 --> 00:13:42,210
+نجي لمضاعفات من السبعة هذه السبعة سبناها شطبنا
+
+179
+00:13:42,210 --> 00:13:45,810
+مضاعفها أربعة عشر بعدين الواحد والعشرين بعدين
+
+180
+00:13:45,810 --> 00:13:49,690
+الأخرين طبعًا في أعداد الآن فيها خط فيها خطين و
+
+181
+00:13:49,690 --> 00:13:53,450
+فيها ثلاثة وفيها أربعة اللي فيها خط معناته بس بتكسب
+
+182
+00:13:53,450 --> 00:13:57,230
+واحد من هدول الأربعة الـprimes خطين بتكسبين اثنين
+
+183
+00:13:57,230 --> 00:14:01,770
+يعني تكررت مرتين ثلاث خطوط معناته بتكسبين ثلاثة
+
+184
+00:14:01,770 --> 00:14:05,290
+أربعة خطوط معناته بتكسب أربعة الآن هيك بكون خلصنا
+
+185
+00:14:05,290 --> 00:14:10,700
+على كل الأعداد اللي هي اللي مش prime ليش؟ زي ما
+
+186
+00:14:10,700 --> 00:14:16,760
+قلنا لأنه لو بده يكون قاسم قواصم المئة فيها قواصم
+
+187
+00:14:16,760 --> 00:14:21,720
+بده يكون فيها قاسمين بي و كيو وهدول بي و كيو حاصل
+
+188
+00:14:21,720 --> 00:14:26,620
+ضربها المئة لازم يكون في واحد منهم على الأقل اللي
+
+189
+00:14:26,620 --> 00:14:30,160
+هو من المضاعفات ... اللي هو أقل من ... من مين؟ من
+
+190
+00:14:30,160 --> 00:14:34,180
+العشرة لأنه لو اثنين أكثر من عشرة بيصير اللي هو ب
+
+191
+00:14:34,180 --> 00:14:38,960
+و cube ونط من مين؟ المئة عشان هيك لازم يكون اللي
+
+192
+00:14:38,960 --> 00:14:44,220
+هو البحث في الأعداد الأولية اللي أقل من الجذر
+
+193
+00:14:44,220 --> 00:14:49,470
+المئة اللي هنا عشرة ورمينا مضاعفات بكفينا أن نقول
+
+194
+00:14:49,470 --> 00:14:54,090
+اللي بيظل هو Primes إذا هذه الطريقة عشان نوجد
+
+195
+00:14:54,090 --> 00:14:59,950
+الأعداد الأولية لأعداد الأولية من واحد لعند اللي
+
+196
+00:14:59,950 --> 00:15:03,930
+هو خمسين مثلًا إيش بسوي باجي باخد الجذر التربيعي
+
+197
+00:15:03,930 --> 00:15:09,150
+للخمسين اللي هو أو اللي هي يعني الأعداد الأقل من
+
+198
+00:15:09,150 --> 00:15:13,030
+جذر التربيعي وبأخد مضاعفات وب ... اللي هي الأعداد
+
+199
+00:15:13,030 --> 00:15:15,250
+الأولية الأقل من جذر ... يعني نقول تسعة وأربعين من
+
+200
+00:15:15,250 --> 00:15:17,770
+واحد لتسعة وأربعين بناخد تسعة وأربعين جذر ومين
+
+201
+00:15:17,770 --> 00:15:22,290
+السبعة بأخد الآن الأعداد اللي هي الأولية اثنين
+
+202
+00:15:22,290 --> 00:15:27,150
+وثلاثة وخمسة وسبعة وبشطب مضاعفات من واحد لتسعة
+
+203
+00:15:27,150 --> 00:15:30,490
+وأربعين اللي بيظهر يكون أولي طب نقول من واحد لخمسة
+
+204
+00:15:30,490 --> 00:15:34,370
+وعشرين أو من واحد لستة وثلاثين الأعداد الأولية من
+
+205
+00:15:34,370 --> 00:15:37,550
+واحد لستة وثلاثين إيش بسوي باجي باخد جذر التربيع
+
+206
+00:15:37,550 --> 00:15:40,390
+لستة وثلاثين بيطلع ستة بأخد الأعداد الأولية الأقل
+
+207
+00:15:40,390 --> 00:15:44,430
+من ستة فتطلع اثنين وثلاثة وخمسة كل مضاعفات اثنين
+
+208
+00:15:44,430 --> 00:15:46,950
+وثلاثة وخمسة بشطبهم من الأعداد من واحد لستة و
+
+209
+00:15:46,950 --> 00:15:51,370
+ثلاثين اللي بيضل عنده prime وهكذا هيك شغل المكان
+
+210
+00:15:51,370 --> 00:15:58,910
+طيب الآن تكملة اللي أنا بقوله برضه بحث أرصده في
+
+211
+00:15:58,910 --> 00:16:03,510
+اللي هو معرفة العدد إنه prime ولا مش الـprime بقول
+
+212
+00:16:03,510 --> 00:16:09,790
+ليه؟ لسبب بسيط بقول لي لو كان n composite if n is
+
+213
+00:16:09,790 --> 00:16:15,050
+composite number يعني عدد غير أولي إذا العدد مدام
+
+214
+00:16:15,050 --> 00:16:19,710
+غير أولي إذا n له عاملين مختلفين يعني n بنقدر نكتب
+
+215
+00:16:19,710 --> 00:16:23,890
+على صورة a في b حيث الـa والـb ولا واحد فيه واحد
+
+216
+00:16:24,650 --> 00:16:28,630
+عشان هو اللي هو composite يعني حللنا إلى اللي هو
+
+217
+00:16:28,630 --> 00:16:35,250
+عددين حاصل ضربهما بساوي n اللي هو ولا واحد لا الـa
+
+218
+00:16:35,250 --> 00:16:42,470
+ولا الـb لا بساوي الـn طيب احنا فرضنا إنه n
+
+219
+00:16:42,470 --> 00:16:45,570
+composite مدام إن composite ده نقدر نكتبه على صورة
+
+220
+00:16:45,570 --> 00:16:51,890
+a في b الآن أكيد الـA نفسه أصغر أو يساوي جذر الـn الآن
+
+221
+00:16:51,890 --> 00:16:56,610
+والـB أصغر أو يساوي جذر الـn واحد منهم أكيد أصغر
+
+222
+00:16:56,610 --> 00:17:01,250
+أو يساوي جذر الـn ليش؟ لأن لو الاثنين هدول بدهم
+
+223
+00:17:01,250 --> 00:17:06,750
+يكون أكبر من جذر الـn بيصير حاصل ضربهما أكبر من الـn
+
+224
+00:17:06,750 --> 00:17:12,110
+إذا لازم على الأقل من واحد من القواسم يكون أصغر من
+
+225
+00:17:12,110 --> 00:17:19,180
+مين أصغر أو يساوي جذر الـn بناء عليه ثم N لديه
+
+226
+00:17:19,180 --> 00:17:25,120
+مقارنة أسفل أو متساوي لجذر الـN يعني الـN لما
+
+227
+00:17:25,120 --> 00:17:29,620
+يكون Uncomposite لازم تلاقي عامل من عوامله أصغر أو
+
+228
+00:17:29,620 --> 00:17:36,500
+يساوي جذر الـN عشان هيك إذا كانت if N مالوش prime
+
+229
+00:17:36,500 --> 00:17:40,340
+divisor 
+
+230
+00:17:40,340 --> 00:17:45,580
+less than or equal to general N إذا N مالوش prime
+
+231
+00:17:45,580 --> 00:17:54,450
+divisor إذا N مالوش prime divisor أي إذا كان N اللي
+
+232
+00:17:54,450 --> 00:17:58,490
+هو composite لازم يكون له prime divisor من هدول
+
+233
+00:17:58,490 --> 00:18:02,930
+الاثنين يكون أصغر من جذر الـN طب لو ما لقيناش ولا
+
+234
+00:18:02,930 --> 00:18:09,530
+prime divisor للـN أصغر من اللي هو يساوي جذر الـN
+
+235
+00:18:09,530 --> 00:18:13,070
+معناته الـN كلّه كتلة واحدة مستحيل يكون يشملّه
+
+236
+00:18:13,070 --> 00:18:18,990
+كتلتين بناء على إنه إذا كان uncomposite فهو يكون
+
+237
+00:18:18,990 --> 00:18:22,290
+اللي هو حاصل ضربه a في b واحد من هدول على
+
+238
+00:18:22,290 --> 00:18:26,990
+الأقل يكون اللي هو a شماله الـprime اللي هو يكون
+
+239
+00:18:26,990 --> 00:18:32,890
+اللي هو أصغر من مين أو يساوي جذر الـn عشان هيك عشان
+
+240
+00:18:32,890 --> 00:18:38,990
+هذا الكلام to prove that N is prime it is enough
+
+241
+00:18:38,990 --> 00:18:42,290
+to show that every integer I أصغر أشهر وجدر الـN
+
+242
+00:18:42,290 --> 00:18:46,490
+does not divide N يعني عشان نثبت أن N اللي هو
+
+243
+00:18:46,490 --> 00:18:52,320
+prime بكفيني أخد الجذر التربيعي للـn وأجي أخد كل
+
+244
+00:18:52,320 --> 00:18:56,240
+الأعداد الـI الأصغر يساوي جذر الـn إذا كان هدول
+
+245
+00:18:56,240 --> 00:19:00,700
+الأعداد الـI أصغر يساوي جذر الـn ولا واحد منهم
+
+246
+00:19:00,700 --> 00:19:07,260
+بيقسم الـn معناته صارت الـn إيه شماله prime لأنه
+
+247
+00:19:07,260 --> 00:19:13,900
+لو بده يكون اللي هولأنه لو بده يكون فيه ما يكونش
+
+248
+00:19:13,900 --> 00:19:18,680
+ولا واحد فيهم اللي هو بيقسم الـn مستحيل تكون n
+
+249
+00:19:18,680 --> 00:19:25,850
+شماله اللي هي composite لأنه سيصبح قواسمها كلها
+
+250
+00:19:25,850 --> 00:19:31,210
+أكبر من جذر الـn فإذا 
+
+251
+00:19:31,210 --> 00:19:34,190
+حصل الضرب هذا أكبر من جذر الأن وهذا أكبر من جذر
+
+252
+00:19:34,190 --> 00:19:38,210
+الآن سيصبح حصل ضرب أكبر من مين؟ من أن عشان هيك و
+
+253
+00:19:38,210 --> 00:19:43,890
+أنت مغمض عشان تثبت اللي هو العدد إن برايم بتجيب كل 
+
+254
+00:19:43,890 --> 00:19:47,650
+الأعداد بتاخدوا الجذر التربيعي له بعد ما تاخد الجذر
+
+255
+00:19:47,650 --> 00:19:50,910
+التربيعي إيه؟ لو بتيجي بتاخد كل الأعداد اللي أصغر
+
+256
+00:19:50,910 --> 00:19:55,690
+أو يساوي الجذر التربيعي بتفحصها بتقسم العدد اللي هو
+
+257
+00:19:55,690 --> 00:20:00,470
+اللي هو مش prime بتقسموش وأنت مغمض قول prime نشوف
+
+258
+00:20:00,470 --> 00:20:07,670
+هذا عمليا الآن مثال determine which of 37, 59, 161
+
+259
+00:20:07,670 --> 00:20:12,830
+is prime ولا لأ؟ كيف بدي احدد الـ 37 Prime ولا لا؟
+
+260
+00:20:12,830 --> 00:20:18,010
+باجي باخد له الجذر التربيعي طلع 6.08 ماشي الحال ايش؟
+
+261
+00:20:18,010 --> 00:20:22,190
+بده في الكسور باجي من ال 6 نازل الآن باجي
+
+262
+00:20:22,190 --> 00:20:27,830
+للأعداد من ال 6 نازل باجي مين هي الأعداد ال
+
+263
+00:20:27,830 --> 00:20:31,910
+prime باخدها مين ال primes اللي أصغر من ال 6
+
+264
+00:20:31,910 --> 00:20:37,930
+الاثنين والثلاثة والخمسة لا اثنين ولا ثلاثة ولا خمسة
+
+265
+00:20:37,930 --> 00:20:42,050
+بيدفع بجسم من مين الـ 37؟ إذا وأنا مغمض بقول الـ
+
+266
+00:20:42,050 --> 00:20:46,950
+37 ايش ماله؟ is prime اللي ماوضحتلوش هذا يجي للمثال
+
+267
+00:20:46,950 --> 00:20:51,250
+اللي بعده باجي ال 59 ايش بعمل؟ باخد الجذر التربيعي
+
+268
+00:20:51,250 --> 00:20:55,470
+طلع سبعة وشوية انسى الشوية هذه الآن سبعة بشوف
+
+269
+00:20:55,470 --> 00:20:59,010
+الأعداد ال primes اللي أقل أو تساوي سبعة مين هي؟
+
+270
+00:20:59,600 --> 00:21:04,380
+التي هي الاثنين والثلاثة والخمسة والسبعة هي الأعداد
+
+271
+00:21:04,380 --> 00:21:09,000
+اللي هي اللي أصغر أو يساوي من سبعة هذه اللي بدأت
+
+272
+00:21:09,000 --> 00:21:13,620
+تحصلي إن هذا التسعة والخمسين composite أو prime باجي
+
+273
+00:21:13,620 --> 00:21:16,340
+الاثنين من عمو من التسعة والخمسين لأ ثلاثة من التسعة
+
+274
+00:21:16,340 --> 00:21:19,180
+وخمسين لأ الخمسة من التسعة وخمسين لأ السبعة من
+
+275
+00:21:19,180 --> 00:21:24,080
+التسعة وخمسين لأ إذا على طول بحكم أن تسعة وخمسين
+
+276
+00:21:24,080 --> 00:21:29,920
+is ايش prime الآن نيجي للمية وواحد وستين بدي أشوف
+
+277
+00:21:29,920 --> 00:21:32,280
+الـ prime ولا مش الـ prime باجي باخده الجذر
+
+278
+00:21:32,280 --> 00:21:37,420
+التربيعي للـ 161 لجيته 12.610 من مين بده أفحص الآن؟
+
+279
+00:21:37,420 --> 00:21:40,740
+بده أفحص الأقل أو يساوي 12 من الـ primes اللي هي
+
+280
+00:21:40,740 --> 00:21:45,440
+الاثنين والثلاثة والخمسة والسبعة والاحدى عشرة في
+
+281
+00:21:45,440 --> 00:21:50,540
+primes أقل من 12 أقل أو يساوي 12 غير هدولة لأ بمسك
+
+282
+00:21:50,540 --> 00:21:55,720
+الاثنين بيكسب 161 لأ الثلاثة بتكسب 161 لأ الخمسة
+
+283
+00:21:55,720 --> 00:22:02,490
+بتكسب 161 لأ الآن دل السابعة والاحدى عشرة لو جربت
+
+284
+00:22:02,490 --> 00:22:06,950
+الاحدى عشرة هتلاقي الاحدى عشرة برضه بتكسبش لكن لو جربت
+
+285
+00:22:06,950 --> 00:22:11,930
+السبعة على 161 هتلاقيها بتجسم مدام السبعة جسمت إذا
+
+286
+00:22:11,930 --> 00:22:16,770
+على طول كومبوزات لكن لو كمان السبعة ما جسمتش بكون
+
+287
+00:22:16,770 --> 00:22:21,310
+كلهين ما جسمنش لو كلهين ما جسمنش زي اللي فوق بنقول
+
+288
+00:22:21,310 --> 00:22:26,430
+عن 161 prime لكن هنا لحسن أو سوء حظنا السبعة جسمت
+
+289
+00:22:26,430 --> 00:22:32,280
+161 معنى صار تقصار 161 is prime إذاً هذه الطريقة
+
+290
+00:22:32,280 --> 00:22:36,020
+كيف نعرف إنه العدد prime ولا مش prime أو إحدى
+
+291
+00:22:36,020 --> 00:22:40,280
+الطرق اللي بتعرفنا كيف إنه هذا العدد prime أو مش
+
+292
+00:22:40,280 --> 00:22:44,640
+prime الآن السؤال بيسأله زمان بيقول لي هل عدد اللي
+
+293
+00:22:44,640 --> 00:22:48,320
+هي الprime finite ولا infinite؟ طبعا احنا بنعرف إن
+
+294
+00:22:48,320 --> 00:22:51,620
+العدد الصحيح لملا نهاية واحد واثنين وثلاثة أو
+
+295
+00:22:51,620 --> 00:22:54,600
+أربعة وخمسة إلى ملا نهاية بيقولي ال prime منها
+
+296
+00:22:54,600 --> 00:22:58,560
+finite ولا infinite؟ اللي هو نظرية اقليدس بيقول لك
+
+297
+00:22:58,560 --> 00:23:03,300
+there are infinitely many primes يعني يوجد عدد
+
+298
+00:23:03,300 --> 00:23:09,100
+لا نهائي من الأعداد الأولية ماشي الحال هذا الكلام
+
+299
+00:23:09,100 --> 00:23:13,840
+مثبت وهي الإثبات لكن احنا لضيق الوقت مش هنطلبكم
+
+300
+00:23:13,840 --> 00:23:19,700
+بإثبات النظرية طيب الآن في نوع من أنواع ال primes
+
+301
+00:23:19,700 --> 00:23:25,790
+اللي هو بنسميها Mersini Primes الآن مرسيني برايم
+
+302
+00:23:25,790 --> 00:23:30,730
+عرفة كما هي ليه وقول لـ definition prime numbers
+
+303
+00:23:30,730 --> 00:23:34,270
+of the form 2 to the b minus 1 where b is prime
+
+304
+00:23:34,270 --> 00:23:37,610
+are called Mersini Primes يعني الأعداد اللي على
+
+305
+00:23:37,610 --> 00:23:42,930
+الصورة هذه الصورة هذه الـ B هذا prime الأعداد
+
+306
+00:23:42,930 --> 00:23:48,290
+الصورة 2 أس B minus 1 إذا كانت prime بنسميها
+
+307
+00:23:48,290 --> 00:23:52,970
+مرسيني prime عالم اسمه مرسيني في القرن الخامس أو
+
+308
+00:23:52,970 --> 00:23:57,450
+السادس عشر ده السادس عشر الآن الأعداد الصورة 2
+
+309
+00:23:57,450 --> 00:24:02,330
+أس B minus 1 حيث B is prime إذا كان هذا كله prime
+
+310
+00:24:02,330 --> 00:24:07,590
+بيطلع اللي هو هذا مرسيني prime يعني وكأن دا في حكيه
+
+311
+00:24:07,590 --> 00:24:11,290
+معناته إنه ممكن هذا بالرغم من B ما يطلعش كله على
+
+312
+00:24:11,290 --> 00:24:16,630
+بعضه هي في أول أشهر نشوف اثنين أس اثنين ناقص واحد
+
+313
+00:24:16,630 --> 00:24:19,110
+اثنين prime اثنين أس اثنين ناقص واحد ثلاثة prime
+
+314
+00:24:19,110 --> 00:24:22,710
+اثنين أس ثلاثة ثلاثة prime ناقص واحد بتطلع سبعة
+
+315
+00:24:22,710 --> 00:24:25,830
+prime اثنين أس خمسة ناقص واحد بتطلع سبعة وثلاثين
+
+316
+00:24:25,830 --> 00:24:28,990
+prime اثنين أس سبعة ناقص واحد بتطلع مية وسبعة وعشرين
+
+317
+00:24:28,990 --> 00:24:33,030
+prime عشان ايه ككلنا دول اسمهم مرسين اش
+
+318
+00:24:33,030 --> 00:24:38,130
+prime لكن هي على سبيل المثال اثنين أس احد عشر ناقص
+
+319
+00:24:38,130 --> 00:24:42,930
+واحد بالرغم من احد عشر انه prime هيو إلا انه 2
+
+320
+00:24:42,930 --> 00:24:49,090
+ناقص 11 ناقص واحد بيطلع 2047 وهذا مش prime عشان يك
+
+321
+00:24:49,090 --> 00:24:53,850
+بنقول عنه is not mercenary prime because 2047
+
+322
+00:24:53,850 --> 00:24:57,850
+هتلاقيه 2047 في 23 في 89 طبعا هذا
+
+323
+00:24:57,850 --> 00:25:01,390
+بتقدر تثبته انتم بطريقتنا اللي قبل بشوية كيف
+
+324
+00:25:01,390 --> 00:25:05,490
+تاخدوا الجذر التربيعي وبتبدأ لكل الأعداد اللي أقل
+
+325
+00:25:05,490 --> 00:25:09,290
+أو يساوي الجذر التربيعي تفحصها هتلاقي اللي هو واحد
+
+326
+00:25:09,290 --> 00:25:12,750
+منهم اللي هو الثلاثة وعشرين هتلاقي بيقسم هذا واللي
+
+327
+00:25:12,750 --> 00:25:16,690
+اللي قبلها بيقسمش عشان هي كبكون ايش is not إبراهيم
+
+328
+00:25:16,690 --> 00:25:23,450
+إذا هذا مثال على مرسين اللي هو على اللي هو is not
+
+329
+00:25:23,450 --> 00:25:29,080
+مرسين إبراهيم بالرغم من ان ال B هذا is إبراهيم بقول
+
+330
+00:25:29,080 --> 00:25:35,720
+لي as of mind يعني في ال 2014 يعني قبل ال 2014
+
+331
+00:25:35,720 --> 00:25:40,260
+ماكانش معروف في الدنيا إلا 48 مرسيني برايمز 48
+
+332
+00:25:40,260 --> 00:25:45,120
+واحد من ال form هذه اللي هو يشمل مرسيني برايمز
+
+333
+00:25:45,120 --> 00:25:49,740
+ماكانش معروف إلا 48 واحد أكبرهم كان اللي هو هذا
+
+334
+00:25:49,740 --> 00:25:54,400
+العدد اللي هو هذا طبعا هذا خيالي العدد which has
+
+335
+00:25:54,400 --> 00:25:58,630
+nearly 17 million decimal digits الآن ليش الأعداد
+
+336
+00:25:58,630 --> 00:26:01,470
+هذه احنا بندور على أعداد الأولية الكبيرة الأعداد
+
+337
+00:26:01,470 --> 00:26:05,630
+الأولية الكبيرة يا جماعة هذه تستخدم في اللي هي
+
+338
+00:26:05,630 --> 00:26:11,710
+نظرية الترميز اللي لو أسعفنا الوجد هناخد مقدمة
+
+339
+00:26:11,710 --> 00:26:18,690
+عنها طيب الآن عملية إنتاج اللي هو primes يعني بدنا
+
+340
+00:26:18,690 --> 00:26:23,570
+ننتج primes زي ما قلنا في اللي هو عملية ايجاد اللي
+
+341
+00:26:23,570 --> 00:26:27,250
+هي ال primes اللي بتكون very large الناس يعني خلنا
+
+342
+00:26:27,250 --> 00:26:32,010
+نقول بتبحث فيها لأنها بتلزمهم لكن الأمور مش دائما
+
+343
+00:26:32,010 --> 00:26:36,830
+بهذه السهولة الآن بس يعني خلنا نقول مثلا finding
+
+344
+00:26:36,830 --> 00:26:41,070
+large primes with hundreds of digits is important
+
+345
+00:26:41,070 --> 00:26:45,010
+and cryptography زي ما قلنا في الترميز اللي هو مهم
+
+346
+00:26:45,470 --> 00:26:52,350
+عشان هيك بدوا يحاولوا يدوروا على دوال f of n هل
+
+347
+00:26:52,350 --> 00:26:57,510
+نستطيع نجد دوال تكون دائما f of n is prime؟ طبعا
+
+348
+00:26:57,510 --> 00:27:01,510
+الموضوع ليس موضوع سهل أو كانوا يعتقدوا مثلا f of n
+
+349
+00:27:01,510 --> 00:27:06,550
+بحيث أن تربيع ناقص n زائد 41 اللي هو طلعوا على هذه
+
+350
+00:27:06,550 --> 00:27:11,870
+اللي هو لجوا إن الأعداد من واحد لعند أربعين لو
+
+351
+00:27:11,870 --> 00:27:15,050
+حطينا عن أنب واحد أو أنب اثنين أو أنب أربعين
+
+352
+00:27:15,050 --> 00:27:19,070
+هتلاقي اللي هي primes إنه بيطلع دائما ايش primes
+
+353
+00:27:19,070 --> 00:27:22,930
+لكن لو أخذنا عند الواحد والأربعين افف واحد والأربعين
+
+354
+00:27:22,930 --> 00:27:26,010
+بيطلع اللي هو واحد وأربعين تربيع ناقص واحد وأربعين
+
+355
+00:27:26,010 --> 00:27:28,390
+زائد واحد وأربعين بروحن مع بعض وبيظل واحد وأربعين
+
+356
+00:27:28,390 --> 00:27:32,130
+تربيع مش primes هاي مثال إنه يطلع حاجة ده اللي
+
+357
+00:27:32,130 --> 00:27:37,920
+بتجيبش دائما ايش primes الآن بشكل أكبر يقول لي هناك
+
+358
+00:27:37,920 --> 00:27:41,660
+لا بولنوميال فش بولنوميال كثيرة حدود يعني with
+
+359
+00:27:41,660 --> 00:27:46,160
+integer coefficients such that F of N is prime for
+
+360
+00:27:46,160 --> 00:27:49,960
+all positive integers N يعني هذا معلومة بس يعني
+
+361
+00:27:49,960 --> 00:27:56,720
+للمعرفة إنه لو أخدنا F of N عبارة عن بولنوميال كل
+
+362
+00:27:56,720 --> 00:28:02,510
+عواملها integers مستحيل نجيها F of n تطلع دائما
+
+363
+00:28:02,510 --> 00:28:08,630
+ال primes يعني حاولوا في بعض الدول لكن اللي هي مش
+
+364
+00:28:08,630 --> 00:28:12,950
+ذابطة اللي هي بالنسبالي ان نقول polynomial وكل ال
+
+365
+00:28:12,950 --> 00:28:17,250
+integers انها تكون تطلع لنا دائما is prime يعني
+
+366
+00:28:17,250 --> 00:28:20,170
+F of n تطلع عبارة عن قانون يطلع لنا ال prime لأ
+
+367
+00:28:20,170 --> 00:28:25,660
+لأ لأ مش عارفين الآن هذه المعلومات اللي هي حول اللي
+
+368
+00:28:25,660 --> 00:28:29,080
+هو ال prime يبقى كون هي خلصنا الحديث عن ال prime
+
+369
+00:28:29,080 --> 00:28:33,040
+بدنا نحكي بس اللي هو نظرة سريعة على ال greatest
+
+370
+00:28:33,040 --> 00:28:41,600
+common divisors أو اللي هو المضاعف المشترك العامل
+
+371
+00:28:41,600 --> 00:28:46,460
+المشترك الأعلى العامل المشترك الأعلى ال greatest
+
+372
+00:28:46,460 --> 00:28:50,850
+common divisor الآن بدنا نعرف let a و let b
+
+373
+00:28:50,850 --> 00:28:55,870
+بأعداد صحيحة not both zero
+
+374
+00:29:02,370 --> 00:29:08,630
+لأن السفر كل الدنيا بتقسمه، فلما نتحدث عن العوام
+
+375
+00:29:08,630 --> 00:29:11,810
+المشتركة بينهم لأن كل أعداد الدنيا العوامل المشتركة 
+
+376
+00:29:11,810 --> 00:29:14,450
+بين السفر والسفر عشان هيك ما يوجد حاجة اسمها
+
+377
+00:29:14,450 --> 00:29:16,570
+greatest common divisor أو عوام مشتركة أعلى بين
+
+378
+00:29:16,570 --> 00:29:21,270
+السفر والسفر عشان هيك فرضين احنا A وB اللي هي ليس 
+
+379
+00:29:21,270 --> 00:29:26,570
+الواحد منهم على الأقل مش سفر The largest integer D
+
+380
+00:29:26,570 --> 00:29:29,430
+such that D بتقسم A وD بتقسم B is called the
+
+381
+00:29:29,430 --> 00:29:33,470
+greatest common divisor of A and B يعني أكبر عامل 
+
+382
+00:29:33,470 --> 00:29:38,750
+مشترك يعني بيقسم اللي هو الـ A و الـ B بنسميه
+
+383
+00:29:38,750 --> 00:29:42,330
+greatest common divisor يعني باجي لقاسم العدد A و
+
+384
+00:29:42,330 --> 00:29:46,650
+لقاسم العدد B و بشوف القاسم المشتركة بينهم أكبر
+
+385
+00:29:46,650 --> 00:29:49,650
+واحد في القاسم المشتركة هو اللي بسميه greatest
+
+386
+00:29:49,650 --> 00:29:53,870
+common divisor و برمزله بالرمز greatest common
+
+387
+00:29:53,870 --> 00:29:58,540
+divisor  A و B الآن السؤال الأول what is the
+
+388
+00:29:58,540 --> 00:30:03,220
+greatest common divisor of 24 and 36؟ بدي أوجد
+
+389
+00:30:03,220 --> 00:30:11,200
+العامل المشترك اللي هو الأعلى بين 24 و 36 باختصار
+
+390
+00:30:11,200 --> 00:30:18,310
+الطريقة البدائية بجيب عوامل 24 و 36 باخد العامل
+
+391
+00:30:18,310 --> 00:30:21,810
+المشتركة بينهم أكبر واحد بينهم يكون العامل المشترك
+
+392
+00:30:21,810 --> 00:30:26,770
+اللي هي الأعلى طبعا هذا الكلام متعب خصوصا لما تكون
+
+393
+00:30:26,770 --> 00:30:30,610
+العدد كبيرة لكن احنا لإن لسه في بداية الموضوع لإن
+
+394
+00:30:30,610 --> 00:30:35,530
+solutions divisors of 24 يعني عوامل العدد 24 أو
+
+395
+00:30:35,530 --> 00:30:41,550
+قواسم العدد 24 هي 1 و 2 و 3 و 4 و 6 و 8 و 12 و 24
+
+396
+00:30:42,380 --> 00:30:50,680
+الآن ندخل لقواسم العدد 36 ونشوف 
+
+397
+00:30:50,680 --> 00:30:54,440
+القواسم المشتركة بينهم ال common divisors بينهم
+
+398
+00:30:54,440 --> 00:30:58,860
+common divisors of 24 and 36 وقواسم مشتركة بينهم 
+
+399
+00:30:58,860 --> 00:31:03,000
+الواحد والتاني والتلاتة والاربعة والستة والاثناش
+
+400
+00:31:03,000 --> 00:31:06,890
+هي المشترك بين الجهتين الآن الـ greatest common
+
+401
+00:31:06,890 --> 00:31:11,250
+divisor يعني العامل المشترك الأعلى هيطلع مين بيساوي 
+
+402
+00:31:11,250 --> 00:31:14,950
+الـ 12 طيب نجي لمثال آخر what is the greatest
+
+403
+00:31:14,950 --> 00:31:19,310
+common divisor of 17 and 22 الـ 17 طبعا عارفينه
+
+404
+00:31:19,310 --> 00:31:24,570
+أنه عدد أولي مين قواصمه بس الواحد والسبعة عشر ال 22 
+
+405
+00:31:24,570 --> 00:31:29,290
+مين قواصمه بس الواحد والاثنين والاحد عشر والاثنين
+
+406
+00:31:29,290 --> 00:31:35,250
+وعشرين القواسم المشتركة بين الجهتين بس الواحد عشان 
+
+407
+00:31:35,250 --> 00:31:38,730
+هيك لـ Greatest common divisor بينهم بيساوي ايه 
+
+408
+00:31:38,730 --> 00:31:50,130
+ايش واحد الآن بس
+
+409
+00:31:50,130 --> 00:31:59,000
+في شغلة حابين نعرفها بنقول عن العددين العددين 17 و
+
+410
+00:31:59,000 --> 00:32:02,220
+22 لما يكون العام المشترك الأعلى بينهم واحد
+
+411
+00:32:02,220 --> 00:32:07,160
+بنسميهم ايه شمالهم relatively prime relatively
+
+412
+00:32:07,160 --> 00:32:10,980
+prime يعني العام المشترك الأعلى بينهم 17 و 2
+
+413
+00:32:10,980 --> 00:32:15,240
+بيساوي واحد بنسميهم relatively prime لو كان عندي
+
+414
+00:32:15,240 --> 00:32:19,770
+بدل ما هن عددين تلات أعداد بنقول عنهم relatively
+
+415
+00:32:19,770 --> 00:32:23,870
+prime in pairs relatively prime in pairs يعني لو
+
+416
+00:32:23,870 --> 00:32:30,460
+كان عندي 17 و 22 و 13 مثلاماشي بنقول عنه ان
+
+417
+00:32:30,460 --> 00:32:33,740
+relatively prime in pairs إذا كان العامل المشترك
+
+418
+00:32:33,740 --> 00:32:37,540
+الأعلى بين كل اثنتين بيساوي واحد يعني التلاتة عشر
+
+419
+00:32:37,540 --> 00:32:41,140
+والسبعة عشر واحد والتلاتة عشر واتنين وعشرين واحد واتنين
+
+420
+00:32:41,140 --> 00:32:45,280
+وعشرين وسبعة عشر واحد العامل المشترك الأعلى فبنسميه
+
+421
+00:32:45,280 --> 00:32:48,880
+relatively prime in pairs عشان هيك السبعة عشر واتنين
+
+422
+00:32:48,880 --> 00:32:53,480
+وعشرين والتلاتة عشر relatively prime in pairs لكن لو
+
+423
+00:32:53,480 --> 00:32:57,080
+جينا قولنا لو بدنا نشوف سبعة عشر واتنين وعشرين
+
+424
+00:32:57,080 --> 00:33:09,050
+وخمسة وثلاثين هل relative الـ 17 و 22 و 33 هل
+
+425
+00:33:09,050 --> 00:33:13,060
+relative الـ prime in pairs الـ 33 مع 17 العامل
+
+426
+00:33:13,060 --> 00:33:16,580
+المشترك الأعلى بينهم واحد والـ 17 مع 22 العامل
+
+427
+00:33:16,580 --> 00:33:20,480
+المشترك الأعلى بينهم واحد لكن الـ 22 والـ 33
+
+428
+00:33:20,480 --> 00:33:25,160
+العامل المشترك الأعلى بينهم مين؟ 11 عشان هيك
+
+429
+00:33:25,160 --> 00:33:31,980
+نقول هدولة اللي هي الـ 17 و 22 و33 are not
+
+430
+00:33:31,980 --> 00:33:36,800
+relatively prime in pairs يعني مش كل اثنتين اثنتين
+
+431
+00:33:36,800 --> 00:33:40,750
+اثنتين relative prime عشان هذا انا شرحته عشان ال
+
+432
+00:33:40,750 --> 00:33:46,840
+homework اللي بيكون معاكم هذه الأسئلة ستكون معكم
+
+433
+00:33:46,840 --> 00:33:51,460
+homework من ضمن أنك تبحث عن الـ20 و 37 و 91
+
+434
+00:33:51,460 --> 00:33:54,120
+relative prime and pairs و لا لأ يعني تبحث عن
+
+435
+00:33:54,120 --> 00:33:57,280
+الـ20 و 37 ما هي العامة المشتركة الأعلى و هذه ما
+
+436
+00:33:57,280 --> 00:33:59,600
+هي العامة المشتركة الأعلى و بين هذه و هذه ما هي
+
+437
+00:33:59,600 --> 00:34:01,620
+العامة المشتركة الأعلى إذا كان كلهم العامة
+
+438
+00:34:01,620 --> 00:34:04,160
+المشتركة الأعلى بينهم in pairs واحد بنقول relative
+
+439
+00:34:04,160 --> 00:34:07,820
+prime and pairs إذا لأ بنقول are not relatively
+
+440
+00:34:07,820 --> 00:34:11,260
+prime and pairs و السلام عليكم و رحمة الله و بركاته
+
+441
+00:34:11,260 --> 00:34:13,760
+هذا ال homework طبعا تسلموا ليها 
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8db1366f6b9df7e869a5a213feffdc48808df0e0
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_postprocess.srt
@@ -0,0 +1,1764 @@
+1
+00:00:01,080 --> 00:00:07,140
+بسم الله الرحمن الرحيم هذه المحاضرة السادسة لمساق
+
+2
+00:00:07,140 --> 00:00:11,660
+رياضيات منفصلة لطلاب و طالبات الجامعة الإسلامية
+
+3
+00:00:11,660 --> 00:00:16,040
+كلية technology المعلومات قسم الحوسبة المتلقلة
+
+4
+00:00:16,620 --> 00:00:21,700
+اليوم ان شاء الله هنشرح اللي هو جزء من section
+
+5
+00:00:21,700 --> 00:00:26,820
+أربعة تلاتة اللي هنحكي فيه عن ال primes الأعداد
+
+6
+00:00:26,820 --> 00:00:32,160
+الأولية and greatest common divisors هنحكي مقدمة
+
+7
+00:00:32,160 --> 00:00:35,560
+بسيطة عن اللي هو greatest common divisors اللي هو
+
+8
+00:00:35,560 --> 00:00:41,720
+عبارة عن العامل المشترك الأعلى بعد ما نتحدث عن
+
+9
+00:00:41,720 --> 00:00:46,880
+اللي هو موضوع الأعداد الأوليةالان نشوف شو معناه
+
+10
+00:00:46,880 --> 00:00:50,100
+الـprimes الـprimes هي الأعداد الأولية اللي احنا
+
+11
+00:00:50,100 --> 00:00:53,420
+اخدناها في اللي هو الثاني في الاعداد دي
+
+12
+00:00:53,420 --> 00:00:58,100
+واستعملناها بعد ذلك الان شو هو العدد الأولي a
+
+13
+00:00:58,100 --> 00:01:04,660
+positive integer بيه عدد اللي هو الصحيح المودب بيه
+
+14
+00:01:04,660 --> 00:01:08,400
+اللي أكبر من واحد بنسميه عدد أولي is called the
+
+15
+00:01:08,400 --> 00:01:15,720
+primeإذا بس مالوش divisor أو عامل إلا نفسه يعني
+
+16
+00:01:15,720 --> 00:01:19,960
+بمعنى آخر بنقول عن العدد .. و الواحد طبعا .. بنقول
+
+17
+00:01:19,960 --> 00:01:25,970
+عن العدد B اللي هوإن عدد أولي إذا كان the only
+
+18
+00:01:25,970 --> 00:01:32,510
+divisor of B are one and B يعني الأعداد القواسم
+
+19
+00:01:32,510 --> 00:01:39,990
+للعدد B فقط هما عددان العدد نفسه والعدد واحد طبعا
+
+20
+00:01:39,990 --> 00:01:47,090
+و B هو أكبر من واحد بمعنى آخر العدد الأولي هو عدد
+
+21
+00:01:47,090 --> 00:01:56,960
+صحيح موجبله قاسمان مختلفان فقط الواحد والعدد نفسه
+
+22
+00:01:56,960 --> 00:02:01,560
+العدد اللي بيكونش أولي a positive integer that is
+
+23
+00:02:01,560 --> 00:02:05,460
+greater than one and is not prime بنسمي أيش ماله
+
+24
+00:02:05,800 --> 00:02:11,480
+اللي هو composite أو عدد غير أولى إلا نيجي ناخد
+
+25
+00:02:11,480 --> 00:02:16,160
+مثال انتجار سبعة is prime because it's only
+
+26
+00:02:16,160 --> 00:02:21,980
+positive factors are واحد وسبعة وزي تلاتة والتلاتة
+
+27
+00:02:21,980 --> 00:02:27,120
+عدد أول لإن الواحدوالتلاتة هما بس قواصمه والتنين
+
+28
+00:02:27,120 --> 00:02:31,180
+عدد أولي الأربعة لأ مش عدد أولي لإن الأربعة في
+
+29
+00:02:31,180 --> 00:02:36,660
+عندنا اللي هو التنين والاربعة بقسمله والتنين غير
+
+30
+00:02:36,660 --> 00:02:41,080
+اللي هو الأربعة but تسعة is composite زي ما هو
+
+31
+00:02:41,080 --> 00:02:45,300
+حاكيين because it is divisible by تلاتة واحدة شرط
+
+32
+00:02:45,300 --> 00:02:50,260
+ان يكون عدد أولي انه بس له قاصمين مختلفين الواحد
+
+33
+00:02:50,260 --> 00:02:51,360
+والعدد نفسه
+
+34
+00:02:59,120 --> 00:03:06,200
+النظرية الأساسية للحساب
+
+35
+00:03:06,200 --> 00:03:11,170
+تقول ما يليهEvery positive integer greater than
+
+36
+00:03:11,170 --> 00:03:15,510
+one can be written uniquely as a prime or the
+
+37
+00:03:15,510 --> 00:03:19,590
+product of two or more primes where the prime
+
+38
+00:03:19,590 --> 00:03:23,010
+factors are written in order of non decreasing
+
+39
+00:03:23,010 --> 00:03:27,870
+size يعني النظرية بتقولنا أن أي عددpositive أكبر
+
+40
+00:03:27,870 --> 00:03:33,210
+من واحد بنقدر نكتبه بطريقة وحيدة على صورة a
+
+41
+00:03:33,210 --> 00:03:37,290
+product of primes يعني حاصل ضرب إيش primes وده كان
+
+42
+00:03:37,290 --> 00:03:43,390
+الprime بكون نفسه بيه الآن اللي هو هذه الطريقة
+
+43
+00:03:43,390 --> 00:03:48,390
+وحيدة وبنقدر نرتب اللي هي حاصل الضرب من الصغيرة
+
+44
+00:03:48,390 --> 00:03:53,410
+لكتيرة لما نصل لأكبر عامل إيش اللي بقوله نجي نشوف
+
+45
+00:03:53,410 --> 00:03:58,730
+مثال يعني الآن ميةالمية هذا لو جينا اللي هو بدنا
+
+46
+00:03:58,730 --> 00:04:05,370
+نفسثه إلى عوامله الأوليةيعني إلى حاصل ضرب أعداد
+
+47
+00:04:05,370 --> 00:04:10,310
+أولية المية لو جسمناها على اتنين بتطلع خمسين اتنين
+
+48
+00:04:10,310 --> 00:04:12,990
+الخمسين لو جسمناها على اتنين بتطلع خمسة وعشرين
+
+49
+00:04:12,990 --> 00:04:15,930
+الخمسة وعشرين لو جسمناها على خمسة بتطلع خمسة
+
+50
+00:04:15,930 --> 00:04:19,590
+الخمسة لما نجسمها على خمسة بتطلع واحد اذا مين
+
+51
+00:04:19,590 --> 00:04:23,510
+عوامل العدد مية اللي هو اتنين في اتنين في خمسة في
+
+52
+00:04:23,510 --> 00:04:27,210
+خمسة يعني كتبناها على حصة على صورة ايش يا جماعة
+
+53
+00:04:27,210 --> 00:04:33,220
+حاصل ضرب اللي هي أعداد أوليةالان هددين الأوليين
+
+54
+00:04:33,220 --> 00:04:36,020
+هدولة اتنين و اتنين مقررات زي ما بتعرفوا مكتبها
+
+55
+00:04:36,020 --> 00:04:40,280
+اتنين أقصى اتنين في خمسة أقصى اتنين الصورة هذه هي
+
+56
+00:04:40,280 --> 00:04:44,260
+الصورة الوحيدة لكتابة المية as a product of a
+
+57
+00:04:44,260 --> 00:04:47,960
+prime of power of primes يعني ايش power of primes
+
+58
+00:04:47,960 --> 00:04:52,460
+يعني برايم مرفوع لأقصه وهذا البرايم مرفوع لأقصه
+
+59
+00:04:52,710 --> 00:04:56,390
+فصار عندى اللى هو المية مضروبة فى صورة حاصل ضرب
+
+60
+00:04:56,390 --> 00:05:00,970
+اللى هى power of primes او حاصل ضرب ايش primes و
+
+61
+00:05:00,970 --> 00:05:05,390
+هذه الصورة الوحيدة من ال .. طبعا الوحيدة اننا نتفق
+
+62
+00:05:05,390 --> 00:05:10,310
+مع بعض انه اللى هو بدنا اللى هو نكتب من الصغير الى
+
+63
+00:05:10,310 --> 00:05:13,970
+الأكبر يعنى ال prime اتنين و بعدين اتنين و بعدين
+
+64
+00:05:13,970 --> 00:05:17,050
+الخمسة و بعدين الخمسة هى المقصود من الصغير الى
+
+65
+00:05:17,050 --> 00:05:21,490
+الأكبر و طبعا و ده تكرر نكتبه نفسهالان 641 لو
+
+66
+00:05:21,490 --> 00:05:25,530
+جربنا نشوف هذا 641 بيقسم على حاجة مابيقسمش ولا على
+
+67
+00:05:25,530 --> 00:05:28,930
+حاجة إلا غير على نفسه على الواحد عشان هي .. طبعا
+
+68
+00:05:28,930 --> 00:05:32,170
+هناخد كيف نوجد ال primes كمان شوية أو نثبت انه
+
+69
+00:05:32,170 --> 00:05:37,890
+prime او لأ الان 641 سوى 641 اللي هو لإن هو نفسه
+
+70
+00:05:37,890 --> 00:05:43,860
+كتلة واحدة ال prime هو كتلة واحدة لا تتجزأالان 999
+
+71
+00:05:43,860 --> 00:05:48,120
+نجي اللى هو بدنا نحاول نجزقها لعواملها الأولية لو
+
+72
+00:05:48,120 --> 00:05:51,760
+قسمنا على تلاتة بالذى اللى بيطلع تلت مية و تلتة و
+
+73
+00:05:51,760 --> 00:05:54,920
+تلتين تلت مية و تلتة و تلتين لو قسمنا على تلتة
+
+74
+00:05:54,920 --> 00:05:58,420
+بيطلع مية و احداش يعني قسمنا كمان مرة على تلتة
+
+75
+00:05:58,420 --> 00:06:03,900
+اللى .. اه .. لو قسمنا على تلتة بيطلع ايش اللى هو
+
+76
+00:06:03,900 --> 00:06:10,840
+عبارة عن قداش سبعة و تلتينتلاتة ع تلاتة بيطلع تلات
+
+77
+00:06:10,840 --> 00:06:14,580
+مية و تلاتة و تلاتين تلاتة بيطلع مية و أحداش ع مية
+
+78
+00:06:14,580 --> 00:06:18,460
+و أحداش بيطلع تلاتة فى سبعة و تلاتين اللى هى اللى
+
+79
+00:06:18,460 --> 00:06:22,280
+هى المية و أحداش الان بيصير عندي هذا العدد اللى
+
+80
+00:06:22,280 --> 00:06:25,840
+كتبناه على صورة product of primes حصل ضرب primes
+
+81
+00:06:25,840 --> 00:06:29,060
+او على صورة اللى هو product of power of primes
+
+82
+00:06:29,060 --> 00:06:33,160
+يعني تلاتة اتكررت جديش از تلاتة فى سبعة و تلاتين
+
+83
+00:06:33,160 --> 00:06:37,210
+زى ما اتعودنا على الكتابة احنا عادةالألف واربع
+
+84
+00:06:37,210 --> 00:06:39,930
+وعشرين اللي هو برضه هنكتبه على صورة product of
+
+85
+00:06:39,930 --> 00:06:43,090
+وprimes وصورة واحدة مش غيرها أصلا اللي هنبنيه جهة
+
+86
+00:06:43,090 --> 00:06:46,170
+أكيد هدب جسم يقبل جسمها دلنا نجسم نجسم نجسم نجسم
+
+87
+00:06:46,170 --> 00:06:46,830
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+88
+00:06:46,830 --> 00:06:48,090
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+89
+00:06:48,090 --> 00:06:48,290
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+90
+00:06:48,290 --> 00:06:48,310
+نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم نجسم
+
+91
+00:06:48,310 --> 00:06:59,080
+نجسم نجسم نجسم نجسم نجسم نجسم نأو على صورة باور of
+
+92
+00:06:59,080 --> 00:07:03,300
+برايم وهذه الصورة صورة إيش وحيدة إذا نفهم شو معناه
+
+93
+00:07:03,300 --> 00:07:05,440
+if a positive integer greater than one can be
+
+94
+00:07:05,440 --> 00:07:11,710
+written uniquely as a product of إيش of برايمنيجي
+
+95
+00:07:11,710 --> 00:07:20,150
+الان كيف نبحث عن اللي هو ال Ibrahim's او مسألة
+
+96
+00:07:20,150 --> 00:07:26,210
+قديمة حتى يعني اللي هو الحل اللي موجود هو حل قديم
+
+97
+00:07:26,210 --> 00:07:31,250
+حل the thief of erastothenes
+
+98
+00:07:31,250 --> 00:07:35,990
+اللي هو أرستوطاليساللي هو نشوف إيش اللي هو البحث
+
+99
+00:07:35,990 --> 00:07:42,390
+كيف بحث أرستو طاليس في مسألة إيجاد الأعداد الأولية
+
+100
+00:07:42,390 --> 00:07:47,390
+من واحد إلى مية الان هذا بقولك بسيف of أرستو طاليس
+
+101
+00:07:47,390 --> 00:07:52,050
+can be used to find all primes not exceeding a
+
+102
+00:07:52,050 --> 00:07:56,490
+specified positive integer بقولك يعني احنا لو بدنا
+
+103
+00:07:56,490 --> 00:08:01,770
+نيجي نبحث عن الأعداد الأولية من ال .. اللياللي من
+
+104
+00:08:01,770 --> 00:08:07,890
+واحد لعند خمسمية ايش بنسوي؟ من واحد لعشرين ايش
+
+105
+00:08:07,890 --> 00:08:11,670
+بنسوي؟ من واحد لتلاتين ايش بنسوي؟ الان بقولي for
+
+106
+00:08:11,670 --> 00:08:15,450
+example بده يبحث being with the list of integers
+
+107
+00:08:15,450 --> 00:08:19,890
+between واحدة ومية يريد ان يبحث عن الأعداد الأولية
+
+108
+00:08:20,210 --> 00:08:23,570
+اللي من الأعداد من واحد لمية .. من واحد لمية في
+
+109
+00:08:23,570 --> 00:08:28,690
+عندنا مائة عدد الان هذول المائة عدد بدنا نبحث مين
+
+110
+00:08:28,690 --> 00:08:32,350
+فيهم اللي هو إبراهيم شوفوا الطريقة الحلوة الجميلة
+
+111
+00:08:32,350 --> 00:08:36,910
+هذا طريقة خديمة من أيام رستو طاليس اللي هو بيقول
+
+112
+00:08:37,760 --> 00:08:41,460
+delete all integers other than two divisible by
+
+113
+00:08:41,460 --> 00:08:46,660
+اتنين ايش تسوي اول حاجة بقولك كل الاعداد اللى
+
+114
+00:08:46,660 --> 00:08:52,820
+بتقسم على اتنين لعنده مية اللى هو شطة بقى يعني
+
+115
+00:08:52,820 --> 00:08:57,200
+اكتب الاعداد من واحد لمية وبده شطة مضاعفة يعني
+
+116
+00:08:57,200 --> 00:09:06,470
+اتنينو مضاعفاته يعني 2x3x6 و 2x4x8 و 2x5x10
+
+117
+00:09:06,470 --> 00:09:12,450
+و 2x6x12 بظلي اللي هي كل الأعداد اللي هي مضاعفات 2
+
+118
+00:09:12,450 --> 00:09:17,580
+مشطبها من اللي أستهالان بعد هيك بشطب كل الأعداد
+
+119
+00:09:17,580 --> 00:09:20,600
+اللي هي delete all the integers other than تلاتة
+
+120
+00:09:20,600 --> 00:09:23,900
+divisible by تلاتة بشطب كل الأعداد طبعا سيب
+
+121
+00:09:23,900 --> 00:09:29,280
+التلاتة لانه prime سيب .. شطب كل المضاعفات التلاتة
+
+122
+00:09:29,280 --> 00:09:33,560
+شطب الست و شطب التسعة و شطب الاطنعاش و و و الاخر
+
+123
+00:09:33,560 --> 00:09:36,960
+يه طبعا فيشي اللي بشطبهن تكون شطبتهن نور ع نور
+
+124
+00:09:36,960 --> 00:09:40,080
+اصلا مديش ايه انا طبعا المضاعفات هي مش هيكون ال
+
+125
+00:09:40,080 --> 00:09:44,820
+prime اكيدdelete all the integers other than خمسة
+
+126
+00:09:44,820 --> 00:09:50,040
+or divisible by خمسة الان شطب على كل الأعداد
+
+127
+00:09:50,040 --> 00:09:55,240
+مضاعفات من الخمسة الان شطبت على مضاعفات الخمسة
+
+128
+00:09:55,240 --> 00:09:58,820
+اللي هي عشرة وخمس تعاشر وخمسة وعشرين إلى خير لما
+
+129
+00:09:58,820 --> 00:10:03,960
+تسلمي إلى المية الان بعدها شطب على كل الأعداد اللي
+
+130
+00:10:03,960 --> 00:10:10,280
+هي مضاعفات العدد من سبعة الان وكأنه بيقول ليتعال
+
+131
+00:10:10,280 --> 00:10:15,220
+من الأعداد الأقل من عشرة وشوف الـprimes اللي فيها
+
+132
+00:10:15,220 --> 00:10:20,480
+اللي هي التنين والتلاتة والخمسة والسبعة وشطبل
+
+133
+00:10:20,480 --> 00:10:25,420
+مضاعفاتهاالان بعد ما تشطب مضاعفاتها بقول لك since
+
+134
+00:10:25,420 --> 00:10:28,320
+all the remaining integers are not divisible by
+
+135
+00:10:28,320 --> 00:10:32,240
+any of the previous integers other than واحد the
+
+136
+00:10:32,240 --> 00:10:37,400
+primes are بقول لك انا بكفلك انه يظل المتبقيات مين
+
+137
+00:10:37,400 --> 00:10:44,020
+هم اللي هم ال primesليش؟ لأن أنت أصلاً لما تيجي
+
+138
+00:10:44,020 --> 00:10:48,220
+تشطق اللي هي كل مضاعفات التنين ومضاعفات التلتة
+
+139
+00:10:48,220 --> 00:10:52,440
+ومضاعفات الخمسة ومضاعفات السبعة لو بدك تيجي للرقم
+
+140
+00:10:52,440 --> 00:10:58,900
+100 الرقم 100 إذا بده يكون اللي هو في اللي هو
+
+141
+00:10:58,900 --> 00:11:06,930
+قواسمالان القواسم اللى هتكون لازم يكون واحد من يا
+
+142
+00:11:06,930 --> 00:11:10,790
+اتنين يا تلاتة يا خمسة يا سبعة موجودة في هذه
+
+143
+00:11:10,790 --> 00:11:15,410
+القواسم لإنه لو بده يكون مايكونش ولا واحد من هدول
+
+144
+00:11:15,410 --> 00:11:19,010
+ال primes في القواسم معناته مين بده يكون اللى هو
+
+145
+00:11:19,010 --> 00:11:25,150
+منهن اللى هو ال 11 او ال 13 طب ما هو ال 11 لو بده
+
+146
+00:11:25,150 --> 00:11:29,880
+يجسم ال 100 او ال 13 بده يجسم ال 100لازم يكون في
+
+147
+00:11:29,880 --> 00:11:33,600
+رقم أصغر منه بيقسمها لأن لو كل الأرقام اللي بدأت
+
+148
+00:11:33,600 --> 00:11:37,440
+تقسم اللي هو الـ 100 من الـ Primes عبارة عن اللي
+
+149
+00:11:37,440 --> 00:11:42,200
+هو أكبر من اللي هو السبعة اللي هي أكبر من ال 11
+
+150
+00:11:42,200 --> 00:11:45,700
+يعني بيصير 11 في اللي أكبر منه أكتر من 100
+
+151
+00:11:45,700 --> 00:11:50,280
+اتجاوزوا يعنييعني الأعقام ال .. ال .. ال composite
+
+152
+00:11:50,280 --> 00:11:56,600
+الفلمية غصبًا عنها هتطلع اللي هي مضاعفات اللي هي
+
+153
+00:11:56,600 --> 00:12:00,980
+الاتنين والتلاتة والخمسة والسبعة لازم نلاقيها
+
+154
+00:12:00,980 --> 00:12:06,120
+للسباب اللي حكيته طيب نيجي الآن نشوف هذا الكلام
+
+155
+00:12:06,120 --> 00:12:11,120
+عمليًا ادري ايش سوىهيحط اللي هي الاعداد من واحد
+
+156
+00:12:11,120 --> 00:12:16,860
+لمية هذه طريقة ارستور وهذه الاعداد من واحد لمية
+
+157
+00:12:16,860 --> 00:12:18,820
+وهذه الاعداد من واحد لمية وهذه الاعداد من واحد
+
+158
+00:12:18,820 --> 00:12:23,360
+لمية اول اشي قال خلينا نيدي لمضاعفات من الاتنين هي
+
+159
+00:12:23,360 --> 00:12:26,680
+الاربعة و هي الستة و هي التمانية و هي العشرة و هي
+
+160
+00:12:26,680 --> 00:12:28,720
+اتناشر و هي الاربعتاشر و هي الستة عشر و هي
+
+161
+00:12:28,720 --> 00:12:33,300
+الطمنتاشر و لمّا كمل لوين لمية لما اجى ل .. ل .. ل
+
+162
+00:12:33,300 --> 00:12:34,680
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+163
+00:12:34,680 --> 00:12:35,600
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+164
+00:12:35,600 --> 00:12:35,620
+.. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل .. ل
+
+165
+00:12:35,620 --> 00:12:39,050
+.. ل .. ل .. ل .. ل .. ل .. ل ..مضاعفات التلاتة
+
+166
+00:12:39,050 --> 00:12:41,870
+اللي عليها خط اللي هي مضاعفات التنية نسيبها الآن
+
+167
+00:12:41,870 --> 00:12:46,350
+حطينا كمان خط لمضاعفات مين التلاتة وهيوش الطبهين
+
+168
+00:12:46,350 --> 00:12:51,670
+كمان مرة طبعا دخل اشي جديد هاي 32 مضاعفات ال ..
+
+169
+00:12:51,670 --> 00:12:56,380
+آسف الـ 33 مضاعفات مينالتلاتة ما كانت شان، إذاً
+
+170
+00:12:56,380 --> 00:12:59,480
+هذا تشطّب كمان، بخط واحد، اللي بخط، اللي بخطين ولا
+
+171
+00:12:59,480 --> 00:13:02,600
+بالاربعة؟ في الآخر إشمال، اللي هين بده ينشل، اللي
+
+172
+00:13:02,600 --> 00:13:05,780
+هين composite صار، اللي هين مضاعفات اتنين أو
+
+173
+00:13:05,780 --> 00:13:08,240
+مضاعفات تلاتة أو مضاعفات الأربعة أو مضاعفات
+
+174
+00:13:08,240 --> 00:13:22,090
+الخمسة، مش primesالان نشطب مضاعفات الخمسة خمسة
+
+175
+00:13:22,090 --> 00:13:22,890
+مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة
+
+176
+00:13:22,890 --> 00:13:26,670
+مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة
+
+177
+00:13:26,670 --> 00:13:36,090
+مضاعفات الخمسة مضاعفات الخمسةخمس طعش عشرين و هكذا
+
+178
+00:13:36,090 --> 00:13:42,210
+نجي لمضاعفات من السبعة هذه السبعة سبناها شطبنا
+
+179
+00:13:42,210 --> 00:13:45,810
+مضاعفها لاربعة طعش بعدين الواحد و عشرين بعدين
+
+180
+00:13:45,810 --> 00:13:49,690
+الاخرين طبعا في أعداد الآن فيها خط فيها خطين و
+
+181
+00:13:49,690 --> 00:13:53,450
+فيها تلاتة و فيه أربعةاللي فيها خط معناته بس بتكسب
+
+182
+00:13:53,450 --> 00:13:57,230
+واحد من هدول الاربعة الprimes خطين بتكسبين اتنين
+
+183
+00:13:57,230 --> 00:14:01,770
+يعني اتكررت مرتين تلت خطوط معناته بتكسبين تلاتة
+
+184
+00:14:01,770 --> 00:14:05,290
+اربع خطوط معناته بتكسب اربعة الآن هيك بكون خلصنا
+
+185
+00:14:05,290 --> 00:14:10,700
+على كل الأعداد اللي هي اللي مش primeليش؟ زي ما
+
+186
+00:14:10,700 --> 00:14:16,760
+قلنا لإنه لو بده يكون قاسم قواصم المية فيها قواصم
+
+187
+00:14:16,760 --> 00:14:21,720
+بده يكون فيها قاسمين بي و كيو و هدول بي و كيو حاصل
+
+188
+00:14:21,720 --> 00:14:26,620
+ضربها الميةلازم يكون في واحد منهم على الأقل اللي
+
+189
+00:14:26,620 --> 00:14:30,160
+هو من المضاعفات .. اللي هو أجل من .. من مين؟ من
+
+190
+00:14:30,160 --> 00:14:34,180
+العشرة لأنه لو اتنين أكثر من عشرة بيصير اللي هو ب
+
+191
+00:14:34,180 --> 00:14:38,960
+و cube و نط من مين؟ المية عشان هيك لازم يكون اللي
+
+192
+00:14:38,960 --> 00:14:44,220
+هو البحث في الأعداد الأولية اللي أجل من الجدر
+
+193
+00:14:44,220 --> 00:14:49,470
+المية اللي هنا عشرةو رمينا مضاعفات بكفينا ان نقول
+
+194
+00:14:49,470 --> 00:14:54,090
+اللي بيظل هو Libraims اذا هذه الطريقة عشان نوجد
+
+195
+00:14:54,090 --> 00:14:59,950
+الأعداد الأولية لأعداد الأولية من واحد لعند اللي
+
+196
+00:14:59,950 --> 00:15:03,930
+هو خمسين مثلا ايش بسوي باجي باخد الجدر التربيعي
+
+197
+00:15:03,930 --> 00:15:09,150
+للخمسيناللي هو أو اللي هي يعني الأعداد الأقل من
+
+198
+00:15:09,150 --> 00:15:13,030
+جدر التربيعي وباخد مضاعفات وب .. اللي هي الأعداد
+
+199
+00:15:13,030 --> 00:15:15,250
+الأولية الأقل من جدر .. يعني نقول تسعة واربعين من
+
+200
+00:15:15,250 --> 00:15:17,770
+واحد لتسعة واربعين بناخد تسعة واربعين جدر ومين
+
+201
+00:15:17,770 --> 00:15:22,290
+السبعة باخد الآن الأعداد اللي هي الأولية اتنين
+
+202
+00:15:22,290 --> 00:15:27,150
+وتلاتة وخمسة وسبعة وبشطب مضاعفات من واحد لتسعة
+
+203
+00:15:27,150 --> 00:15:30,490
+واربعين اللي بظهر يكون أولين طب نقول من واحد لخمسة
+
+204
+00:15:30,490 --> 00:15:34,370
+وعشرين او من واحد لستة وتلاتين الأعدادالأولية من
+
+205
+00:15:34,370 --> 00:15:37,550
+واحد لست و تلاتين ايش بسوي باجي باخد جذر التربيع
+
+206
+00:15:37,550 --> 00:15:40,390
+لست و تلاتين بطلع ستة باخد الأعداد الأولية الأقل
+
+207
+00:15:40,390 --> 00:15:44,430
+من ستة فتطلع اتنين و تلاتة و خمسة كل مضاعفات اتنين
+
+208
+00:15:44,430 --> 00:15:46,950
+و تلاتة و خمسة بشطبهم من الأعداد من واحد لست و
+
+209
+00:15:46,950 --> 00:15:51,370
+تلاتين اللي بيضل عنده prime و هكذا هيك شغل المكان
+
+210
+00:15:51,370 --> 00:15:58,910
+طيب الآن تكملة اللي انا بقولي برضه بحث أرصده في
+
+211
+00:15:58,910 --> 00:16:03,510
+اللي هو معنفة العدد انه prime ولا مش ال primeبقول
+
+212
+00:16:03,510 --> 00:16:09,790
+ليه؟ لسبب بسيط بقول لي لو كان n composite if n is
+
+213
+00:16:09,790 --> 00:16:15,050
+composite number يعني عدد غير أولي إذا العدد مدام
+
+214
+00:16:15,050 --> 00:16:19,710
+غير أولي إذا n له عاملين مختلفين يعني n بنقدر نكتب
+
+215
+00:16:19,710 --> 00:16:23,890
+على صورة a في b حيث ال a و ال b ولا واحد فيه واحد
+
+216
+00:16:24,650 --> 00:16:28,630
+عشان هو اللي هو composite يعني حللنا إلى اللي هو
+
+217
+00:16:28,630 --> 00:16:35,250
+عددين حاصل ضربهم بساوي n اللي هو ولا واحد لا ال a
+
+218
+00:16:35,250 --> 00:16:42,470
+ولا ال b لا بساوي ال n طيب احنا فرضنا انه n
+
+219
+00:16:42,470 --> 00:16:45,570
+composite مدام ان composite ده نقدر نكتب على صورة
+
+220
+00:16:45,570 --> 00:16:51,890
+a في bالأن أكيد ال A نفسه أصغر أو يساوي جدر الأن
+
+221
+00:16:51,890 --> 00:16:56,610
+وال B أصغر أو يساوي جدر الأن واحد منهم أكيد أصغر
+
+222
+00:16:56,610 --> 00:17:01,250
+أو يساوي جدر الأن ليش؟ لأن لو الاتنين هدولة بدهم
+
+223
+00:17:01,250 --> 00:17:06,750
+يكون أكبر من جدر الأن بصير حاصل ضربهم أكبر من الأن
+
+224
+00:17:06,750 --> 00:17:12,110
+إذا لازم على الأقل من واحد من القواسم يكون أصغر من
+
+225
+00:17:12,110 --> 00:17:19,180
+مين أصغر أو يساوي جدر الأنبناء عليه ثم N لديه
+
+226
+00:17:19,180 --> 00:17:25,120
+مقارنة أسفل أو متساوي لجذر الـ N يعني الـ N لما
+
+227
+00:17:25,120 --> 00:17:29,620
+يكون Uncomposite لازم تلاقي عامل من عوامله أصغر أو
+
+228
+00:17:29,620 --> 00:17:36,500
+يساوي جذر الـ Nعشان هيك إذا كانت if N مالوش prime
+
+229
+00:17:36,500 --> 00:17:40,340
+divisor
+
+230
+00:17:40,340 --> 00:17:45,580
+less than or equal to general N إذا N مالوش prime
+
+231
+00:17:45,580 --> 00:17:54,450
+divisor إذا N مالوش prime divisorأي إذا كان N اللي
+
+232
+00:17:54,450 --> 00:17:58,490
+هو composite لازم يكون له prime divisor من هدول
+
+233
+00:17:58,490 --> 00:18:02,930
+الاتنين يكون أصغر من جدر ال N طب لو مالجيناش ولا
+
+234
+00:18:02,930 --> 00:18:09,530
+prime divisor لل N أصغر من اللي هو يساوي جدر ال N
+
+235
+00:18:09,530 --> 00:18:13,070
+معناته ال N كله كتلة واحدة مستحيل يكون يشمله
+
+236
+00:18:13,070 --> 00:18:18,990
+كتلتينبناء على انه اذا كان uncomposite فهو يكون
+
+237
+00:18:18,990 --> 00:18:22,290
+اللي هو حاصل ضربه ايه في بي واحد من هدولة على
+
+238
+00:18:22,290 --> 00:18:26,990
+الأقل يكون اللي هو ايه شماله الـprime اللي هو يكون
+
+239
+00:18:26,990 --> 00:18:32,890
+اللي هو اصغر من مين او يساوي جدر الأنعشان هيك عشان
+
+240
+00:18:32,890 --> 00:18:38,990
+هذا الكلام to prove that N is prime it is enough
+
+241
+00:18:38,990 --> 00:18:42,290
+to show that every integer I أصغر أشهر وجدر ال N
+
+242
+00:18:42,290 --> 00:18:46,490
+does not divide N يعني عشان نثبت أن N اللي هو
+
+243
+00:18:46,490 --> 00:18:52,320
+primeبكفيني اخد الجدر التربيعي للان واجي اخد كل
+
+244
+00:18:52,320 --> 00:18:56,240
+الاعداد ال I الأصغر يساوي جدر الان اذا كان هدول
+
+245
+00:18:56,240 --> 00:19:00,700
+الاعداد ال I أصغر يساوي جدر الان ولا واحد منهم
+
+246
+00:19:00,700 --> 00:19:07,260
+بيقسم الان معناته صارت الان إيه شمالها prime لأنه
+
+247
+00:19:07,260 --> 00:19:13,900
+لو بده يكون اللي هولأنه لو بده يكون فيه ما يكونش
+
+248
+00:19:13,900 --> 00:19:18,680
+ولا واحد فيهم اللي هو بيقسم الان مستحيل تكون ان
+
+249
+00:19:18,680 --> 00:19:25,850
+أشمالها اللي هي compositeلأنه سيصبح قواسمها كلها
+
+250
+00:19:25,850 --> 00:19:31,210
+أكبر من جدر الأن فإذا
+
+251
+00:19:31,210 --> 00:19:34,190
+حصل الضرب هذا أكبر من جدر الأن و هذا أكبر من جدر
+
+252
+00:19:34,190 --> 00:19:38,210
+الأن سيصبح حصل ضرب أكبر من مين من أن عشان هيك و
+
+253
+00:19:38,210 --> 00:19:43,890
+أنت مغمض عشان تثبت اللي هو العدد أن برايم بتجيب كل
+
+254
+00:19:43,890 --> 00:19:47,650
+الأعداء تاخدوا الجدر التربيعي لهبعد ما تاخد الجدر
+
+255
+00:19:47,650 --> 00:19:50,910
+التربيعي إيه لو بتيجي بتاخد كل الأعداد اللي أصغر
+
+256
+00:19:50,910 --> 00:19:55,690
+أو يسوى الجدر التربيعي بتفحصها بتقسم العدد هيو
+
+257
+00:19:55,690 --> 00:20:00,470
+اللي هو مش prime بتقسموش و أنت مغمض قول prime نشوف
+
+258
+00:20:00,470 --> 00:20:07,670
+هذا عمليا الآن مثال determine which of 37, 59, 161
+
+259
+00:20:07,670 --> 00:20:12,830
+is prime ولا لأكيف بدي احدد الـ 37 Prime ولا لا
+
+260
+00:20:12,830 --> 00:20:18,010
+باجي باخدله الجدر التربيعي طلع 6.08 ماشي الحال ايش
+
+261
+00:20:18,010 --> 00:20:22,190
+بده في الكسور باجي من ال 6 و نازل الان باجي
+
+262
+00:20:22,190 --> 00:20:27,830
+للأعداد من ال 6 و نازل باجي مين هي الأعداد ال
+
+263
+00:20:27,830 --> 00:20:31,910
+prime باخدها مين ال primes اللي أصغر من ال 6
+
+264
+00:20:31,910 --> 00:20:37,930
+التنين والتلاتة والخمسةلا تنين ولا تلاتة ولا خمسة
+
+265
+00:20:37,930 --> 00:20:42,050
+بيدفع بجسم من مين الـ 37 إذا و أنا مغمض بقول الـ
+
+266
+00:20:42,050 --> 00:20:46,950
+37 إيش ماله is prime اللي ماوضحتلوش هذه يجي للمثال
+
+267
+00:20:46,950 --> 00:20:51,250
+اللي بعده باجي ال 59 إيش بعمل باخد الجدر التربيع
+
+268
+00:20:51,250 --> 00:20:55,470
+طلع سبعة و شوية انسى الشوية هذه الان سبعة بشوف
+
+269
+00:20:55,470 --> 00:20:59,010
+الأعداد ال primes اللي أقل أو تساوي سبعة مين هي
+
+270
+00:20:59,600 --> 00:21:04,380
+التي هي التنين والتلاتة والخمسة والسبعة هي الأعداد
+
+271
+00:21:04,380 --> 00:21:09,000
+اللي هي اللي أصغر أو يساوي من سبعة هذه اللي بدأت
+
+272
+00:21:09,000 --> 00:21:13,620
+تحصلي أن هذا التسعة وخمسين composite أو prime باجي
+
+273
+00:21:13,620 --> 00:21:16,340
+التنين من عمو من التسعة وخمسين لأ تلاتة من التسعة
+
+274
+00:21:16,340 --> 00:21:19,180
+وخمسين لأ الخمسة من التسعة وخمسين لأ السابعة من
+
+275
+00:21:19,180 --> 00:21:24,080
+التسعة وخمسين لأ إذا على طول بحكم أن تسعة وخمسين
+
+276
+00:21:24,080 --> 00:21:29,920
+is إيش prime الآن نيجي للمية وواحد وستينبدي أشوف
+
+277
+00:21:29,920 --> 00:21:32,280
+الـ prime ولا مش الـ prime باجي باخده الجدر
+
+278
+00:21:32,280 --> 00:21:37,420
+التربيعي للـ 161 لجيته 12610 من مين بده أفحص الآن؟
+
+279
+00:21:37,420 --> 00:21:40,740
+بده أفحص الأقل أو يسوء 12 من الـ primes اللي هي
+
+280
+00:21:40,740 --> 00:21:45,440
+التنين والتلاتة والخمسة والسبعة والإحدى عشرة فى
+
+281
+00:21:45,440 --> 00:21:50,540
+primes أقل من 12 أقل أو يسوء 12 غير هدولة لأ بمسك
+
+282
+00:21:50,540 --> 00:21:55,720
+التنين بيكسب 161 لأ التلاتة بتكسب 161 لأ الخمسة
+
+283
+00:21:55,720 --> 00:22:02,490
+بتكسب 161 لأالان دل السابعة و الاحداشر لو جربت
+
+284
+00:22:02,490 --> 00:22:06,950
+الاحداشر هتلاقي الاحداشر برضه بتكسبشلكن لو جربت
+
+285
+00:22:06,950 --> 00:22:11,930
+السبعة على 161 هتلاقيها بتجسم مدام السبعة جسمت اذا
+
+286
+00:22:11,930 --> 00:22:16,770
+على طول كومبوزات لكن لو كمان السبعة ما جسمتش بكون
+
+287
+00:22:16,770 --> 00:22:21,310
+كلهين ما جسمنش لو كلهين ما جسمنش زي اللي فوق بنقول
+
+288
+00:22:21,310 --> 00:22:26,430
+عن 161 prime لكن هنا لحسن او سوء حظنا السبعة جسمت
+
+289
+00:22:26,430 --> 00:22:32,280
+161 معنى صار تقصار 161 is primeإذاً هذه الطريقة
+
+290
+00:22:32,280 --> 00:22:36,020
+كيف نعرف إنه العدد prime ولا مش prime أو إحدى
+
+291
+00:22:36,020 --> 00:22:40,280
+الطرق اللي بتعرفنا كيف إنه هذا العدد prime أو مش
+
+292
+00:22:40,280 --> 00:22:44,640
+prime الآن السؤال بيسأله زمان بيقول لي هل عدد اللي
+
+293
+00:22:44,640 --> 00:22:48,320
+هي الprime finite ولا infinite؟ طبعا احنا بنعرف إن
+
+294
+00:22:48,320 --> 00:22:51,620
+العدد الصحيح لملا نهاية واحد واتنين وتلاتة أو
+
+295
+00:22:51,620 --> 00:22:54,600
+أربعة وخمسة إلى ملا نهاية بيقولي ال prime منها
+
+296
+00:22:54,600 --> 00:22:58,560
+finite ولا infinite؟اللي هو نظرية قليدس بيقول لك
+
+297
+00:22:58,560 --> 00:23:03,300
+there are infinitely many primes يعني يوجد عدد
+
+298
+00:23:03,300 --> 00:23:09,100
+لانهائي من الأعداد الأولية ماشي الحال هذا الكلام
+
+299
+00:23:09,100 --> 00:23:13,840
+مثبت وهي الإثبات لكن احنا لضيق الوقت مش هنطلبكم
+
+300
+00:23:13,840 --> 00:23:19,700
+بإثبات النظرية طيب الان في نوع من أنواع ال primes
+
+301
+00:23:19,700 --> 00:23:25,790
+اللي هو بنسميها Mersini Primesالان مرسيني برايم
+
+302
+00:23:25,790 --> 00:23:30,730
+عرفة كما هي ليه وقول لـ definition prime numbers
+
+303
+00:23:30,730 --> 00:23:34,270
+of the form 2 to the b minus 1 where b is prime
+
+304
+00:23:34,270 --> 00:23:37,610
+are called Mersini Primes يعني الأعداد اللي على
+
+305
+00:23:37,610 --> 00:23:42,930
+الصورة هذهالعصورة هذه الـ B هذا prime الأعداد
+
+306
+00:23:42,930 --> 00:23:48,290
+العصورة 2 أُس B minus 1 إذا كانت prime بنسميها
+
+307
+00:23:48,290 --> 00:23:52,970
+ميرسيني prime عالم اسمه ميرسيني في القرن الخامس أو
+
+308
+00:23:52,970 --> 00:23:57,450
+السادس عشر ده السادس عشر الآن الأعداد العصورة 2
+
+309
+00:23:57,450 --> 00:24:02,330
+أُس B minus 1 حيث B is prime إذا كان هذا كله prime
+
+310
+00:24:02,330 --> 00:24:07,590
+بطلع اللي هو هذا ميرسيني primeيعني وكأن دا في حكيه
+
+311
+00:24:07,590 --> 00:24:11,290
+معناته أنه ممكن هذا بالرغم من B' ما يطلعش كله على
+
+312
+00:24:11,290 --> 00:24:16,630
+بعضههي في أول أشهر نشوف اتنين أس اتنين ناقص واحد
+
+313
+00:24:16,630 --> 00:24:19,110
+اتنين برايم اتنين أس اتنين ناقص واحد تلاتة برايم
+
+314
+00:24:19,110 --> 00:24:22,710
+اتنين أس تلاتة تلاتة برايم ناقص واحد بتطلع سبعة
+
+315
+00:24:22,710 --> 00:24:25,830
+برايم اتنين أس خمسة ناقص واحد بتطلع سبعة و تلاتين
+
+316
+00:24:25,830 --> 00:24:28,990
+برايم اتنين أس سبعة ناقص واحد بتطلع مية و سبعة و
+
+317
+00:24:28,990 --> 00:24:33,030
+عشرين برايم عشان أيه ككلنا دول اسمهم مرسين Ash
+
+318
+00:24:33,030 --> 00:24:38,130
+برايم لكن هي على سبيل المثال اتنين أس احداش ناقص
+
+319
+00:24:38,130 --> 00:24:42,930
+واحد بالرغم من احداش انه برايمprime هيو الا انه 2
+
+320
+00:24:42,930 --> 00:24:49,090
+نقص 11 نقص واحد بيطلع 2047 وهذا مش prime عشان يك
+
+321
+00:24:49,090 --> 00:24:53,850
+بنقول عنه is not mercenary prime because 2047
+
+322
+00:24:53,850 --> 00:24:57,850
+هتلاقيه تقلط وعشرين في تسعة و تمانين طبعا هذا
+
+323
+00:24:57,850 --> 00:25:01,390
+بتقدر تثبته انتوا بطريقتنا اللي قبل بشوية كيف
+
+324
+00:25:01,390 --> 00:25:05,490
+تاخدوا الجدر التربيعي و بتبدأ لكل الأعداد اللي أقل
+
+325
+00:25:05,490 --> 00:25:09,290
+أو يساوي الجدر التربيعي تفحصهاهتلاقي اللي هو واحد
+
+326
+00:25:09,290 --> 00:25:12,750
+منهم اللي هو التلاتة و عشرين هتلاقي بيقسم هدى و
+
+327
+00:25:12,750 --> 00:25:16,690
+اللي قبلها بيقسمش عشان هي كبكون إيش is not إبراهيم
+
+328
+00:25:16,690 --> 00:25:23,450
+إذا هذا مثال على مرسين اللي هو على اللي هو is not
+
+329
+00:25:23,450 --> 00:25:29,080
+مرسين إبراهيم بالرغم من أن ال B هدى is إبراهيمبقول
+
+330
+00:25:29,080 --> 00:25:35,720
+لي as of mind يعني في ال 2014 يعني قبل ال 2014
+
+331
+00:25:35,720 --> 00:25:40,260
+ماكانش معروف في الدنيا لغير 48 مرسيني برايمز 48
+
+332
+00:25:40,260 --> 00:25:45,120
+واحد من ال form هذه اللي هو يشمل مرسيني برايمز
+
+333
+00:25:45,120 --> 00:25:49,740
+ماكانش معروف إلا 48 واحد أكبرهم كان اللي هو هذا
+
+334
+00:25:49,740 --> 00:25:54,400
+العدد اللي هو هذا طبعا هذا خيالي العدد which has
+
+335
+00:25:54,400 --> 00:25:58,630
+nearly 17 million decimal digitsالان ليش الاعداد
+
+336
+00:25:58,630 --> 00:26:01,470
+هذه احنا بندور على اعداد الاولية الكبيرة الاعداد
+
+337
+00:26:01,470 --> 00:26:05,630
+الاولية الكبيرة يا جماعة هذه تستخدم في اللي هي
+
+338
+00:26:05,630 --> 00:26:11,710
+نظرية الترميز اللي لو أسعفنا الوجد هناخد مقدمة
+
+339
+00:26:11,710 --> 00:26:18,690
+عنها طيب الان عملية إنتاج اللي هو primes يعني بدنا
+
+340
+00:26:18,690 --> 00:26:23,570
+ننتج primesزي ما قلنا في اللي هو عملية إيجاد اللي
+
+341
+00:26:23,570 --> 00:26:27,250
+هي الـprimes اللي بتكون very large الناس يعني خلنا
+
+342
+00:26:27,250 --> 00:26:32,010
+نقول بتبحث فيها لأنها بتلزمهم لكن الأمور مش دايما
+
+343
+00:26:32,010 --> 00:26:36,830
+بهذه السهولة الان بس يعني خلنا نقول مثلا finding
+
+344
+00:26:36,830 --> 00:26:41,070
+large primes with hundreds of digits is important
+
+345
+00:26:41,070 --> 00:26:45,010
+and كربوتографي زي ما قلنا في الترميز اللي هو مهم
+
+346
+00:26:45,470 --> 00:26:52,350
+عشان هيك بدوا يحاولوا يدوروا على دوال f of n هل
+
+347
+00:26:52,350 --> 00:26:57,510
+نستطيع نجد دوال تكون دائما f of n is prime؟ طبعا
+
+348
+00:26:57,510 --> 00:27:01,510
+الموضوع ليس موضوع سهل أو كانوا يعتقدوا مثلا f of n
+
+349
+00:27:01,510 --> 00:27:06,550
+بسوا أن تربيع نقص n زائد 41 اللي هو طلعوا على هذه
+
+350
+00:27:06,550 --> 00:27:11,870
+اللي هو لجوا أن الأعداد من واحد لعند أربعينلو
+
+351
+00:27:11,870 --> 00:27:15,050
+حطينا عن أنب واحد أو أنب اتنين أو أنب اربعين
+
+352
+00:27:15,050 --> 00:27:19,070
+هتلاقي اللي هي برايمز انه بطلع دايما ايش برايمز
+
+353
+00:27:19,070 --> 00:27:22,930
+لكن لو أخدنا عند الواحد واربعين أفف واحد واربعين
+
+354
+00:27:22,930 --> 00:27:26,010
+بطلع اللي هو واحد واربعين تربيع ناقص واحد واربعين
+
+355
+00:27:26,010 --> 00:27:28,390
+زاد واحد واربعين بروحن مع بعض و بظل واحد واربعين
+
+356
+00:27:28,390 --> 00:27:32,130
+تربيع مش برايمز هاي مثال انه يطلع حاجة ده اللي
+
+357
+00:27:32,130 --> 00:27:37,920
+بتجيبش دايما ايش برايمزالآن بشكل أكبر يقول لي هناك
+
+358
+00:27:37,920 --> 00:27:41,660
+لا بولنوميال فش بولنوميال كثيرة حدود يعني with
+
+359
+00:27:41,660 --> 00:27:46,160
+integer coefficients such that F of N is prime for
+
+360
+00:27:46,160 --> 00:27:49,960
+all positive integers N يعني هذا معلومة بس يعني
+
+361
+00:27:49,960 --> 00:27:56,720
+للمعرفة أنه لو أخدنا F of N عبارة عن بولنوميال كل
+
+362
+00:27:56,720 --> 00:28:02,510
+عواملها integersمستحيل نجيها off of n تطلع دايما
+
+363
+00:28:02,510 --> 00:28:08,630
+الprimes يعني حاولوا في بعض الدول لكن اللي هي مش
+
+364
+00:28:08,630 --> 00:28:12,950
+ذابطة اللي هي بالنسبالي ان نقول polynomial وكل ال
+
+365
+00:28:12,950 --> 00:28:17,250
+integers انها تكون تطلع لنا دايما is prime يعني
+
+366
+00:28:17,250 --> 00:28:20,170
+off of n تطلع عبارة عن قانون يطلع لنا ال prime لأ
+
+367
+00:28:20,170 --> 00:28:25,660
+لأ لأ مش عارفينالآن هذه المعلومات اللي هي حول اللي
+
+368
+00:28:25,660 --> 00:28:29,080
+هو الـ prime يبقى كون هي خلصنا الحديث عن ال prime
+
+369
+00:28:29,080 --> 00:28:33,040
+بدنا نحكي بس اللي هو نظرة سريعة على ال greatest
+
+370
+00:28:33,040 --> 00:28:41,600
+common divisors أو اللي هو المضاعف المشترك العامل
+
+371
+00:28:41,600 --> 00:28:46,460
+المشترك الأعلى العامل المشترك الأعلى ال greatest
+
+372
+00:28:46,460 --> 00:28:50,850
+common divisorالان بدنا نعرف let a و let b
+
+373
+00:28:50,850 --> 00:28:55,870
+بإنتجارات صحيحة not both zero
+
+374
+00:29:02,370 --> 00:29:08,630
+لأن السفر كل الدنيا بتقسمه، فلمّا نتحدث عن العوام
+
+375
+00:29:08,630 --> 00:29:11,810
+المشتركة بينهم لأن كل أعداد الدنيا العوام المشتركة
+
+376
+00:29:11,810 --> 00:29:14,450
+بين السفر والسفر عشان هيك ما يوجد حاجة اسمها
+
+377
+00:29:14,450 --> 00:29:16,570
+greatest common divisor أو عوام مشتركة أعلى بين
+
+378
+00:29:16,570 --> 00:29:21,270
+السفر والسفر عشان هيك فرضين احنا A وB اللي هي ليس
+
+379
+00:29:21,270 --> 00:29:26,570
+الواحد منهم على الأقل مش سفر The largest integer D
+
+380
+00:29:26,570 --> 00:29:29,430
+such that D بتقسم A وD بتقسم B is called the
+
+381
+00:29:29,430 --> 00:29:33,470
+greatest common divisor of A and Bيعني أكبر عامل
+
+382
+00:29:33,470 --> 00:29:38,750
+مشترك يعني بيجسم اللي هو الـ A و الـ B بنسميه
+
+383
+00:29:38,750 --> 00:29:42,330
+greatest common divisor يعني باجي لقاسم العدد A و
+
+384
+00:29:42,330 --> 00:29:46,650
+لقاسم العدد B و بشوف القاسم المشتركة بينهم أكبر
+
+385
+00:29:46,650 --> 00:29:49,650
+واحد في القاسم المشتركة هو اللي بسميه greatest
+
+386
+00:29:49,650 --> 00:29:53,870
+common divisor و برمزله بالرمز greatest common
+
+387
+00:29:53,870 --> 00:29:58,540
+divisor A و Bالان السؤال الأول what is the
+
+388
+00:29:58,540 --> 00:30:03,220
+greatest common divisor of 24 and 36؟ بدي أوجد
+
+389
+00:30:03,220 --> 00:30:11,200
+العامل المشترك اللي هو الأعلى بين 24 و 36 باختصار
+
+390
+00:30:11,200 --> 00:30:18,310
+الطريقة البدائية بجيب عوامل 24 و 36باخد العامل
+
+391
+00:30:18,310 --> 00:30:21,810
+المشتركة بينهم أكبر واحد بينهم يكون العامل المشترك
+
+392
+00:30:21,810 --> 00:30:26,770
+اللي هي الأعلى طبعا هذا الكلام متعب خصوصا لما تكون
+
+393
+00:30:26,770 --> 00:30:30,610
+العدد كبيرة لكن احنا لان لسه في بداية الموضوع لان
+
+394
+00:30:30,610 --> 00:30:35,530
+solutions divisors of 24 يعني عوامل العدد 24 أو
+
+395
+00:30:35,530 --> 00:30:41,550
+قواصم العدد 24 هي 1 و 2 و 3 و 4 و 6 و 8 و 12 و 24
+
+396
+00:30:42,380 --> 00:30:50,680
+الان ندخل لقواسم العدد 36 ونشوف
+
+397
+00:30:50,680 --> 00:30:54,440
+القواسم المشتركة بينهم ال common divisors بينهم
+
+398
+00:30:54,440 --> 00:30:58,860
+common divisors of 24 and 36 وقواسم مشتركة بينهم
+
+399
+00:30:58,860 --> 00:31:03,000
+الواحد والتاني والتلاتة والاربعة والستة والاطناش
+
+400
+00:31:03,000 --> 00:31:06,890
+هي المشترك بين الجهتينالان الـ greatest common
+
+401
+00:31:06,890 --> 00:31:11,250
+divisor يعني العامل المشترك الأعلى هيطلع مين بساوي
+
+402
+00:31:11,250 --> 00:31:14,950
+الـ 12 طيب نجي لمثال أخر what is the greatest
+
+403
+00:31:14,950 --> 00:31:19,310
+common divisor of 17 and 22 الـ 17 طبعا عارفينه
+
+404
+00:31:19,310 --> 00:31:24,570
+أنه عدد أولي مين قواصمه بس الواحد والسبعتاش ال 22
+
+405
+00:31:24,570 --> 00:31:29,290
+مين قواصمه بس الواحد والتنين والإحداش والتنين
+
+406
+00:31:29,290 --> 00:31:35,250
+وعشرينالقواسم المشتركة بين الجهتين بس الواحد عشان
+
+407
+00:31:35,250 --> 00:31:38,730
+هيك لـ Greatest common divisor بينهم بساوي الهو
+
+408
+00:31:38,730 --> 00:31:50,130
+ايش واحد الان بس
+
+409
+00:31:50,130 --> 00:31:59,000
+في شغلة حابين نعرفهابنقول عن العددين العددين 17 و
+
+410
+00:31:59,000 --> 00:32:02,220
+22 لما يكون العام المشترك الأعلى بينهم واحد
+
+411
+00:32:02,220 --> 00:32:07,160
+بنسميهم إيه شمالهم relatively prime relatively
+
+412
+00:32:07,160 --> 00:32:10,980
+prime يعني العام المشترك الأعلى بينهم 17 و 2
+
+413
+00:32:10,980 --> 00:32:15,240
+بيساوي واحد بنسميهم relatively prime لو كان عندي
+
+414
+00:32:15,240 --> 00:32:19,770
+بدل ما هن عددين تلت أعدادبنقول عنهم relatively
+
+415
+00:32:19,770 --> 00:32:23,870
+prime in pairs relatively prime in pairs يعني لو
+
+416
+00:32:23,870 --> 00:32:30,460
+كان عندي 17 و 22 و 13 مثلاماشي مقول عنه ان
+
+417
+00:32:30,460 --> 00:32:33,740
+relatively prime in pairs إذا كان العامل المشترك
+
+418
+00:32:33,740 --> 00:32:37,540
+الأعلى بين كل تنتين بساوي واحد يعني التلتاش
+
+419
+00:32:37,540 --> 00:32:41,140
+والسبعتاش واحد والتلتاش واتنين وعشرين واحد واتنين
+
+420
+00:32:41,140 --> 00:32:45,280
+وعشرين وسبعتاش واحد العامل المشترك الأعلى فبنسميه
+
+421
+00:32:45,280 --> 00:32:48,880
+relatively prime in pairs عشان هيك السبعتاش واتنين
+
+422
+00:32:48,880 --> 00:32:53,480
+وعشرين والتلتاش relatively prime in pairs لكن لو
+
+423
+00:32:53,480 --> 00:32:57,080
+جينا قولنا لو بدنا نشوف سبعتاش واتنين وعشرين
+
+424
+00:32:57,080 --> 00:33:09,050
+وخمستاشهل relative الـ 17 و 22 و 33 هل
+
+425
+00:33:09,050 --> 00:33:13,060
+relative الـ prime in pairsالـ 33 مع 17 العامل
+
+426
+00:33:13,060 --> 00:33:16,580
+المشترك الأعلى بينهم واحد والـ 17 مع 22 العامل
+
+427
+00:33:16,580 --> 00:33:20,480
+المشترك الأعلى بينهم واحد لكن الـ 22 والـ 13
+
+428
+00:33:20,480 --> 00:33:25,160
+العامل المشترك الأعلى بينهم مين؟ 11 عشان هي كما
+
+429
+00:33:25,160 --> 00:33:31,980
+نقول هدولة اللي هي الـ 17 و 22 و33 are not
+
+430
+00:33:31,980 --> 00:33:36,800
+relatively prime in pairs يعني مش كل تنتين تنتين
+
+431
+00:33:36,800 --> 00:33:40,750
+تنتين relative primeعشان هذا انا شرحته عشان ال
+
+432
+00:33:40,750 --> 00:33:46,840
+homework اللي بيكون معاكمهذه الأسئلة ستكون معكم
+
+433
+00:33:46,840 --> 00:33:51,460
+homework من ضمن أنك تبحث عن الـ20 و 37 و 91
+
+434
+00:33:51,460 --> 00:33:54,120
+relative prime and pairs و لا لأ يعني تبحث عن
+
+435
+00:33:54,120 --> 00:33:57,280
+الـ20 و 37 ما هي العامة المشتركة الأعلى و هذه ما
+
+436
+00:33:57,280 --> 00:33:59,600
+هي العامة المشتركة الأعلى و بين هذه و هذه ما هي
+
+437
+00:33:59,600 --> 00:34:01,620
+العامة المشتركة الأعلى إذا كان كلهم العامة
+
+438
+00:34:01,620 --> 00:34:04,160
+المشتركة الأعلى بينهم in pairs واحد بنقول relative
+
+439
+00:34:04,160 --> 00:34:07,820
+prime and pairs إذا لأ بنقول are not relatively
+
+440
+00:34:07,820 --> 00:34:11,260
+prime and pairsو السلام عليكم و رحمة الله و بركاته
+
+441
+00:34:11,260 --> 00:34:13,760
+هذا ال homework طبعا تسلموا ليها
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d7aeb662fc732877e08e4cf65065e75c7c7c717
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/SGeMpwv7S4c_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1604, "start": 1.08, "end": 16.04, "text": "بسم الله الرحمن الرحيم هذه المحاضرة السادسة لمساق رياضيات منفصلة لطلاب و طالبات الجامعة الإسلامية كلية technology المعلومات قسم الحوسبة المتلقلة", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 9673, 5016, 46958, 25720, 21136, 18513, 3794, 3660, 32767, 3794, 995, 4587, 12602, 1829, 46958, 1829, 9307, 9154, 5172, 36520, 3660, 5296, 9566, 15040, 3555, 4032, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 2899, 9673, 30241, 20498, 9307, 12174, 38251, 21542, 2407, 35457, 3660, 9673, 2655, 1211, 4587, 37977], "avg_logprob": -0.1015624985324614, "compression_ratio": 1.6125, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1.08, "end": 1.44, "word": "بسم", "probability": 0.851318359375}, {"start": 1.44, "end": 1.66, "word": " الله", "probability": 0.95068359375}, {"start": 1.66, "end": 2.16, "word": " الرحمن", "probability": 0.9695638020833334}, {"start": 2.16, "end": 2.76, "word": " الرحيم", "probability": 0.9954427083333334}, {"start": 2.76, "end": 3.1, "word": " هذه", "probability": 0.77099609375}, {"start": 3.1, "end": 3.84, "word": " المحاضرة", "probability": 0.879638671875}, {"start": 3.84, "end": 5.16, "word": " السادسة", "probability": 0.936279296875}, {"start": 5.16, "end": 7.14, "word": " لمساق", "probability": 0.908203125}, {"start": 7.14, "end": 8.0, "word": " رياضيات", "probability": 0.980859375}, {"start": 8.0, "end": 8.82, "word": " منفصلة", "probability": 0.95947265625}, {"start": 8.82, "end": 9.92, "word": " لطلاب", "probability": 0.8603515625}, {"start": 9.92, "end": 10.04, "word": " و", "probability": 0.9912109375}, {"start": 10.04, "end": 10.62, "word": " طالبات", "probability": 0.8936767578125}, {"start": 10.62, "end": 11.02, "word": " الجامعة", "probability": 0.9894205729166666}, {"start": 11.02, "end": 11.66, "word": " الإسلامية", "probability": 0.966552734375}, {"start": 11.66, "end": 12.1, "word": " كلية", "probability": 0.7294921875}, {"start": 12.1, "end": 12.68, "word": " technology", "probability": 0.38720703125}, {"start": 12.68, "end": 13.74, "word": " المعلومات", "probability": 0.9388427734375}, {"start": 13.74, "end": 14.18, "word": " قسم", "probability": 0.940673828125}, {"start": 14.18, "end": 14.98, "word": " الحوسبة", "probability": 0.8807373046875}, {"start": 14.98, "end": 16.04, "word": " المتلقلة", "probability": 0.955859375}], "temperature": 1.0}, {"id": 2, "seek": 4418, "start": 16.62, "end": 44.18, "text": "اليوم ان شاء الله هنشرح اللي هو جزء من section أربعة تلاتة اللي هنحكي فيه عن ال primes الأعداد الأولية and greatest common divisors هنحكي مقدمة بسيطة عن اللي هو greatest common divisors اللي هو عبارة عن العامل المشترك الأعلى بعد ما نتحدث عن اللي هو موضوع الأعداد الأولية", "tokens": [6027, 1829, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 46309, 5016, 13672, 1829, 31439, 10874, 11622, 38207, 9154, 3541, 5551, 25513, 27884, 6055, 1211, 9307, 3660, 13672, 1829, 8032, 1863, 5016, 4117, 1829, 8978, 3224, 18871, 2423, 2886, 279, 16247, 22488, 18513, 16247, 12610, 10632, 293, 6636, 2689, 25974, 830, 8032, 1863, 5016, 4117, 1829, 3714, 28543, 46007, 4724, 3794, 1829, 9566, 3660, 18871, 13672, 1829, 31439, 6636, 2689, 25974, 830, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 18863, 10943, 1211, 9673, 8592, 2655, 31747, 16247, 3615, 23942, 39182, 19446, 8717, 2655, 24401, 12984, 18871, 13672, 1829, 31439, 3714, 2407, 11242, 45367, 16247, 22488, 18513, 16247, 12610, 10632], "avg_logprob": -0.09730113839561289, "compression_ratio": 1.92, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 16.62, "end": 17.1, "word": "اليوم", "probability": 0.9381510416666666}, {"start": 17.1, "end": 17.28, "word": " ان", "probability": 0.51708984375}, {"start": 17.28, "end": 17.54, "word": " شاء", "probability": 0.950927734375}, {"start": 17.54, "end": 17.68, "word": " الله", "probability": 0.94921875}, {"start": 17.68, "end": 18.44, "word": " هنشرح", "probability": 0.928466796875}, {"start": 18.44, "end": 18.76, "word": " اللي", "probability": 0.6832275390625}, {"start": 18.76, "end": 19.22, "word": " هو", "probability": 0.96875}, {"start": 19.22, "end": 21.02, "word": " جزء", "probability": 0.9716796875}, {"start": 21.02, "end": 21.3, "word": " من", "probability": 0.98876953125}, {"start": 21.3, "end": 21.7, "word": " section", "probability": 0.673828125}, {"start": 21.7, "end": 22.2, "word": " أربعة", "probability": 0.6750081380208334}, {"start": 22.2, "end": 22.9, "word": " تلاتة", "probability": 0.8953857421875}, {"start": 22.9, "end": 24.14, "word": " اللي", "probability": 0.965087890625}, {"start": 24.14, "end": 24.84, "word": " هنحكي", "probability": 0.9361328125}, {"start": 24.84, "end": 25.16, "word": " فيه", "probability": 0.977294921875}, {"start": 25.16, "end": 25.38, "word": " عن", "probability": 0.9912109375}, {"start": 25.38, "end": 25.58, "word": " ال", "probability": 0.87841796875}, {"start": 25.58, "end": 26.22, "word": " primes", "probability": 0.5196533203125}, {"start": 26.22, "end": 26.82, "word": " الأعداد", "probability": 0.9401041666666666}, {"start": 26.82, "end": 27.58, "word": " الأولية", "probability": 0.9739583333333334}, {"start": 27.58, "end": 28.12, "word": " and", "probability": 0.77783203125}, {"start": 28.12, "end": 28.9, "word": " greatest", "probability": 0.91162109375}, {"start": 28.9, "end": 29.42, "word": " common", "probability": 0.93798828125}, {"start": 29.42, "end": 30.04, "word": " divisors", "probability": 0.982421875}, {"start": 30.04, "end": 31.22, "word": " هنحكي", "probability": 0.88984375}, {"start": 31.22, "end": 32.16, "word": " مقدمة", "probability": 0.9713541666666666}, {"start": 32.16, "end": 32.76, "word": " بسيطة", "probability": 0.9947265625}, {"start": 32.76, "end": 32.96, "word": " عن", "probability": 0.9814453125}, {"start": 32.96, "end": 33.16, "word": " اللي", "probability": 0.97021484375}, {"start": 33.16, "end": 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0.892578125}, {"start": 40.6, "end": 41.34, "word": " نتحدث", "probability": 0.9849853515625}, {"start": 41.34, "end": 41.72, "word": " عن", "probability": 0.99072265625}, {"start": 41.72, "end": 41.98, "word": " اللي", "probability": 0.87353515625}, {"start": 41.98, "end": 42.14, "word": " هو", "probability": 0.98974609375}, {"start": 42.14, "end": 42.56, "word": " موضوع", "probability": 0.9884033203125}, {"start": 42.56, "end": 43.3, "word": " الأعداد", "probability": 0.97265625}, {"start": 43.3, "end": 44.18, "word": " الأولية", "probability": 0.9837239583333334}], "temperature": 1.0}, {"id": 3, "seek": 6878, "start": 44.8, "end": 68.78, "text": "الان نشوف شو معناه الـprimes الـprimes هي الأعداد الأولية اللي احنا اخدناها في اللي هو الثاني في الاعداد دي واستعملناها بعد ذلك الان شو هو العدد الأولي a positive integer بيه عدد اللي هو الصحيح المودب بيه اللي أكبر من واحد بنسميه عدد أولي is called the prime", "tokens": [6027, 7649, 8717, 8592, 38688, 13412, 2407, 20449, 8315, 3224, 2423, 39184, 1424, 1532, 2423, 39184, 1424, 1532, 39896, 16247, 22488, 18513, 16247, 12610, 10632, 13672, 1829, 1975, 5016, 8315, 1975, 9778, 3215, 8315, 11296, 8978, 13672, 1829, 31439, 6024, 104, 7649, 1829, 8978, 42963, 22488, 18513, 11778, 1829, 36764, 14851, 25957, 1211, 8315, 11296, 39182, 29910, 23275, 2423, 7649, 13412, 2407, 31439, 18863, 3215, 3215, 16247, 12610, 1829, 257, 3353, 24922, 4724, 1829, 3224, 6225, 3215, 3215, 13672, 1829, 31439, 31767, 5016, 1829, 5016, 9673, 23328, 3555, 4724, 1829, 3224, 13672, 1829, 5551, 4117, 26890, 9154, 36764, 24401, 44945, 38251, 1829, 3224, 6225, 3215, 3215, 5551, 12610, 1829, 307, 1219, 264, 5835], "avg_logprob": -0.26233552683863726, "compression_ratio": 1.8888888888888888, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 44.8, "end": 45.52, "word": "الان", "probability": 0.28070068359375}, {"start": 45.52, "end": 46.04, "word": " نشوف", "probability": 0.6112467447916666}, {"start": 46.04, "end": 46.34, "word": " شو", 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65.52, "end": 65.88, "word": " واحد", "probability": 0.95654296875}, {"start": 65.88, "end": 66.72, "word": " بنسميه", "probability": 0.9464111328125}, {"start": 66.72, "end": 67.08, "word": " عدد", "probability": 0.99365234375}, {"start": 67.08, "end": 67.64, "word": " أولي", "probability": 0.896484375}, {"start": 67.64, "end": 67.9, "word": " is", "probability": 0.74365234375}, {"start": 67.9, "end": 68.2, "word": " called", "probability": 0.93994140625}, {"start": 68.2, "end": 68.4, "word": " the", "probability": 0.30615234375}, {"start": 68.4, "end": 68.78, "word": " prime", "probability": 0.87939453125}], "temperature": 1.0}, {"id": 4, "seek": 8240, "start": 69.46, "end": 82.4, "text": "إذا بس مالوش divisor أو عامل إلا نفسه يعني بمعنى آخر بنقول عن العدد .. و الواحد طبعا .. بنقول عن العدد B اللي هو", "tokens": [28814, 15730, 4724, 3794, 3714, 6027, 2407, 8592, 25974, 284, 34051, 6225, 10943, 1211, 11933, 15040, 8717, 36178, 3224, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 44945, 39648, 18871, 18863, 3215, 3215, 4386, 4032, 2423, 14407, 24401, 23032, 3555, 3615, 995, 4386, 44945, 39648, 18871, 18863, 3215, 3215, 363, 13672, 1829, 31439], "avg_logprob": -0.23181817531585694, "compression_ratio": 1.4351145038167938, "no_speech_prob": 3.600120544433594e-05, "words": [{"start": 69.46, "end": 70.36, "word": "إذا", "probability": 0.84765625}, {"start": 70.36, "end": 71.16, "word": " بس", "probability": 0.905029296875}, {"start": 71.16, "end": 72.1, "word": " مالوش", "probability": 0.83843994140625}, {"start": 72.1, "end": 73.04, "word": " divisor", "probability": 0.756103515625}, {"start": 73.04, "end": 73.32, "word": " أو", "probability": 0.88916015625}, {"start": 73.32, "end": 73.94, "word": " عامل", "probability": 0.9973958333333334}, {"start": 73.94, "end": 74.26, "word": " إلا", "probability": 0.932861328125}, {"start": 74.26, "end": 75.08, "word": " نفسه", "probability": 0.9973958333333334}, {"start": 75.08, "end": 75.72, "word": " يعني", "probability": 0.71142578125}, {"start": 75.72, "end": 76.2, "word": " بمعنى", "probability": 0.9861328125}, {"start": 76.2, "end": 76.54, "word": " آخر", "probability": 0.8681640625}, {"start": 76.54, "end": 77.0, "word": " بنقول", "probability": 0.6986083984375}, {"start": 77.0, "end": 77.28, "word": " عن", "probability": 0.98291015625}, {"start": 77.28, "end": 77.86, "word": " العدد", "probability": 0.9378255208333334}, {"start": 77.86, "end": 78.0, "word": " ..", "probability": 0.341552734375}, {"start": 78.0, "end": 78.2, "word": " و", "probability": 0.2205810546875}, {"start": 78.2, "end": 78.6, "word": " الواحد", "probability": 0.6772867838541666}, {"start": 78.6, "end": 79.1, "word": " طبعا", "probability": 0.9710693359375}, {"start": 79.1, "end": 79.48, "word": " ..", "probability": 0.24560546875}, {"start": 79.48, "end": 79.96, "word": " بنقول", "probability": 0.92822265625}, {"start": 79.96, "end": 80.22, "word": " عن", "probability": 0.9873046875}, {"start": 80.22, "end": 80.92, "word": " العدد", "probability": 0.96240234375}, {"start": 80.92, "end": 81.28, "word": " B", "probability": 0.281982421875}, {"start": 81.28, "end": 82.08, "word": " اللي", "probability": 0.92041015625}, {"start": 82.08, "end": 82.4, "word": " هو", "probability": 0.990234375}], "temperature": 1.0}, {"id": 5, "seek": 10857, "start": 82.97, "end": 108.57, "text": "إن عدد أولي إذا كان the only divisor of B are one and B يعني الأعداد القواسم للعدد B فقط هما عددان العدد نفسه والعدد واحد طبعا و B هو أكبر من واحد بمعنى آخر العدد الأولي هو عدد صحيح موجب", "tokens": [28814, 1863, 6225, 3215, 3215, 5551, 12610, 1829, 11933, 15730, 25961, 264, 787, 25974, 284, 295, 363, 366, 472, 293, 363, 37495, 22653, 16247, 22488, 18513, 25062, 14407, 38251, 24976, 22488, 3215, 363, 6156, 47432, 8032, 15042, 6225, 3215, 3215, 7649, 18863, 3215, 3215, 8717, 36178, 3224, 16070, 22488, 3215, 36764, 24401, 23032, 3555, 3615, 995, 4032, 363, 31439, 5551, 4117, 26890, 9154, 36764, 24401, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 18863, 3215, 3215, 16247, 12610, 1829, 31439, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555], "avg_logprob": -0.13541666385200288, "compression_ratio": 1.6117021276595744, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 82.97, "end": 83.39, "word": "إن", "probability": 0.7470703125}, {"start": 83.39, "end": 83.89, "word": " عدد", "probability": 0.9446614583333334}, {"start": 83.89, "end": 84.45, "word": " أولي", "probability": 0.77978515625}, {"start": 84.45, "end": 84.85, "word": " إذا", "probability": 0.880859375}, {"start": 84.85, "end": 85.17, "word": " كان", "probability": 0.9931640625}, {"start": 85.17, "end": 85.39, "word": " the", "probability": 0.42724609375}, {"start": 85.39, "end": 85.97, "word": " only", "probability": 0.91455078125}, {"start": 85.97, "end": 86.85, "word": " divisor", "probability": 0.932373046875}, {"start": 86.85, "end": 87.13, "word": " of", "probability": 0.9736328125}, {"start": 87.13, "end": 87.53, "word": " B", "probability": 0.444580078125}, {"start": 87.53, "end": 88.47, "word": " are", "probability": 0.73681640625}, {"start": 88.47, "end": 88.85, "word": " one", "probability": 0.548828125}, {"start": 88.85, "end": 89.19, "word": " and", "probability": 0.9609375}, {"start": 89.19, "end": 89.47, "word": " B", "probability": 0.6806640625}, {"start": 89.47, "end": 89.87, "word": " يعني", "probability": 0.890869140625}, {"start": 89.87, "end": 91.27, "word": " الأعداد", "probability": 0.95068359375}, {"start": 91.27, "end": 92.51, "word": " القواسم", "probability": 0.8409830729166666}, {"start": 92.51, "end": 93.25, "word": " للعدد", "probability": 0.8857421875}, {"start": 93.25, "end": 93.51, "word": " B", "probability": 0.5419921875}, {"start": 93.51, "end": 94.17, "word": " فقط", "probability": 0.99169921875}, {"start": 94.17, "end": 95.01, "word": " هما", "probability": 0.92041015625}, {"start": 95.01, "end": 95.85, "word": " عددان", "probability": 0.971435546875}, {"start": 95.85, "end": 96.93, "word": " العدد", "probability": 0.9514973958333334}, {"start": 96.93, "end": 97.53, "word": " نفسه", "probability": 0.9977213541666666}, {"start": 97.53, "end": 98.55, "word": " والعدد", "probability": 0.8994140625}, {"start": 98.55, "end": 99.25, "word": " واحد", "probability": 0.98388671875}, {"start": 99.25, "end": 99.99, "word": " طبعا", "probability": 0.9180908203125}, {"start": 99.99, "end": 100.11, "word": " و", "probability": 0.50048828125}, {"start": 100.11, "end": 100.35, "word": " B", "probability": 0.4208984375}, {"start": 100.35, "end": 101.63, "word": " هو", "probability": 0.41357421875}, {"start": 101.63, "end": 102.29, "word": " أكبر", "probability": 0.93212890625}, {"start": 102.29, "end": 102.43, "word": " من", "probability": 0.9814453125}, {"start": 102.43, "end": 102.79, "word": " واحد", "probability": 0.97998046875}, {"start": 102.79, "end": 103.23, "word": " بمعنى", "probability": 0.94921875}, {"start": 103.23, "end": 103.67, "word": " آخر", "probability": 0.81689453125}, {"start": 103.67, "end": 104.99, "word": " العدد", "probability": 0.97314453125}, {"start": 104.99, "end": 105.81, "word": " الأولي", "probability": 0.9005533854166666}, {"start": 105.81, "end": 106.09, "word": " هو", "probability": 0.97412109375}, {"start": 106.09, "end": 107.09, "word": " عدد", "probability": 0.9930013020833334}, {"start": 107.09, "end": 107.95, "word": " صحيح", "probability": 0.997314453125}, {"start": 107.95, "end": 108.57, "word": " موجب", "probability": 0.9765625}], "temperature": 1.0}, {"id": 6, "seek": 12546, "start": 109.64, "end": 125.46, "text": "له قاسمان مختلفان فقط الواحد والعدد نفسه العدد اللي بيكونش أولي a positive integer that is greater than one and is not prime بنسمي أيش ماله", "tokens": [43761, 12174, 32277, 2304, 7649, 3714, 46456, 46538, 7649, 6156, 47432, 2423, 14407, 24401, 16070, 22488, 3215, 8717, 36178, 3224, 18863, 3215, 3215, 13672, 1829, 4724, 1829, 30544, 8592, 5551, 12610, 1829, 257, 3353, 24922, 300, 307, 5044, 813, 472, 293, 307, 406, 5835, 44945, 38251, 1829, 36632, 8592, 3714, 6027, 3224], "avg_logprob": -0.16730542677753377, "compression_ratio": 1.3421052631578947, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 109.64, "end": 110.14, "word": "له", "probability": 0.74755859375}, {"start": 110.14, "end": 111.6, "word": " قاسمان", "probability": 0.798583984375}, {"start": 111.6, "end": 112.94, "word": " مختلفان", "probability": 0.9423828125}, {"start": 112.94, "end": 113.7, "word": " فقط", "probability": 0.977783203125}, {"start": 113.7, "end": 115.18, "word": " الواحد", "probability": 0.94677734375}, {"start": 115.18, "end": 116.22, "word": " والعدد", "probability": 0.9420572916666666}, {"start": 116.22, "end": 116.96, "word": " نفسه", "probability": 0.9879557291666666}, {"start": 116.96, "end": 118.14, "word": " العدد", "probability": 0.9029947916666666}, {"start": 118.14, "end": 118.28, "word": " اللي", "probability": 0.91796875}, {"start": 118.28, "end": 118.92, "word": " بيكونش", "probability": 0.782958984375}, {"start": 118.92, "end": 119.58, "word": " أولي", "probability": 0.78125}, {"start": 119.58, "end": 120.06, "word": " a", "probability": 0.66748046875}, {"start": 120.06, "end": 120.5, "word": " positive", "probability": 0.90625}, {"start": 120.5, "end": 120.96, "word": " integer", "probability": 0.89794921875}, {"start": 120.96, "end": 121.3, "word": " that", "probability": 0.8427734375}, {"start": 121.3, "end": 121.56, "word": " is", "probability": 0.94677734375}, {"start": 121.56, "end": 121.86, "word": " greater", "probability": 0.88916015625}, {"start": 121.86, "end": 122.22, "word": " than", "probability": 0.96630859375}, {"start": 122.22, "end": 122.48, "word": " one", "probability": 0.80810546875}, {"start": 122.48, "end": 122.74, "word": " and", "probability": 0.91552734375}, {"start": 122.74, "end": 122.96, "word": " is", "probability": 0.87109375}, {"start": 122.96, "end": 123.32, "word": " not", "probability": 0.95703125}, {"start": 123.32, "end": 123.92, "word": " prime", "probability": 0.8095703125}, {"start": 123.92, "end": 124.66, "word": " بنسمي", "probability": 0.8357747395833334}, {"start": 124.66, "end": 124.94, "word": " أيش", "probability": 0.5450439453125}, {"start": 124.94, "end": 125.46, "word": " ماله", "probability": 0.8367513020833334}], "temperature": 1.0}, {"id": 7, "seek": 14380, "start": 125.8, "end": 143.8, "text": "اللي هو composite أو عدد غير أولى إلا نيجي ناخد مثال انتجار سبعة is prime because it's only positive factors are واحد وسبعة وزي تلاتة والتلاتة عدد أول لإن الواحد", "tokens": [6027, 20292, 31439, 25557, 34051, 6225, 3215, 3215, 32771, 13546, 5551, 12610, 7578, 11933, 15040, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 50113, 6027, 16472, 2655, 7435, 9640, 8608, 3555, 27884, 307, 5835, 570, 309, 311, 787, 3353, 6771, 366, 36764, 24401, 4032, 35457, 27884, 4032, 11622, 1829, 6055, 1211, 9307, 3660, 16070, 2655, 1211, 9307, 3660, 6225, 3215, 3215, 5551, 12610, 5296, 28814, 1863, 2423, 14407, 24401], "avg_logprob": -0.2463768115942029, "compression_ratio": 1.4269005847953216, "no_speech_prob": 2.384185791015625e-06, "words": [{"start": 125.8, "end": 126.16, "word": "اللي", "probability": 0.4168701171875}, {"start": 126.16, "end": 126.62, "word": " هو", "probability": 0.947265625}, {"start": 126.62, "end": 127.32, "word": " composite", "probability": 0.6484375}, {"start": 127.32, "end": 127.9, "word": " أو", "probability": 0.38232421875}, {"start": 127.9, "end": 128.48, "word": " عدد", "probability": 0.9755859375}, {"start": 128.48, "end": 129.02, "word": " غير", "probability": 0.99169921875}, {"start": 129.02, "end": 129.8, "word": " أولى", "probability": 0.7801106770833334}, {"start": 129.8, "end": 130.46, "word": " إلا", "probability": 0.3382568359375}, {"start": 130.46, "end": 131.02, "word": " نيجي", "probability": 0.682220458984375}, {"start": 131.02, "end": 131.48, "word": " ناخد", "probability": 0.98193359375}, {"start": 131.48, "end": 132.04, "word": " مثال", "probability": 0.975830078125}, {"start": 132.04, "end": 133.06, "word": " انتجار", "probability": 0.7752685546875}, {"start": 133.06, "end": 133.58, "word": " سبعة", "probability": 0.8603515625}, {"start": 133.58, "end": 134.02, "word": " is", "probability": 0.8857421875}, {"start": 134.02, "end": 134.6, "word": " prime", "probability": 0.80810546875}, {"start": 134.6, "end": 135.28, "word": " because", "probability": 0.7685546875}, {"start": 135.28, "end": 135.72, "word": " it's", "probability": 0.680908203125}, {"start": 135.72, "end": 136.16, "word": " only", "probability": 0.89697265625}, {"start": 136.16, "end": 137.12, "word": " positive", "probability": 0.900390625}, {"start": 137.12, "end": 137.96, "word": " factors", "probability": 0.96142578125}, {"start": 137.96, "end": 138.26, "word": " are", "probability": 0.93505859375}, {"start": 138.26, "end": 138.74, "word": " واحد", "probability": 0.96923828125}, {"start": 138.74, "end": 139.58, "word": " وسبعة", "probability": 0.8380533854166666}, {"start": 139.58, "end": 140.54, "word": " وزي", "probability": 0.8509114583333334}, {"start": 140.54, "end": 141.2, "word": " تلاتة", "probability": 0.7698974609375}, {"start": 141.2, "end": 141.98, "word": " والتلاتة", "probability": 0.854248046875}, {"start": 141.98, "end": 142.4, "word": " عدد", "probability": 0.9873046875}, {"start": 142.4, "end": 142.7, "word": " أول", "probability": 0.948974609375}, {"start": 142.7, "end": 143.12, "word": " لإن", "probability": 0.7722981770833334}, {"start": 143.12, "end": 143.8, "word": " الواحد", "probability": 0.8800455729166666}], "temperature": 1.0}, {"id": 8, "seek": 17136, "start": 144.18, "end": 171.36, "text": "والتلاتة هما بس قواصمه والتنين عدد أولي الأربعة لأ مش عدد أولي لإن الأربعة في عندنا اللي هو التنين والاربعة بقسمله والتنين غير اللي هو الأربعة but تسعة is composite زي ما هو حاكيين because it is divisible by تلاتة واحدة شرط ان يكون عدد أولي انه بس له قاصمين مختلفين الواحد والعدد نفسه", "tokens": [2407, 6027, 2655, 1211, 9307, 3660, 8032, 15042, 4724, 3794, 12174, 2407, 33546, 2304, 3224, 16070, 2655, 1863, 9957, 6225, 3215, 3215, 5551, 12610, 1829, 16247, 25513, 27884, 5296, 10721, 37893, 6225, 3215, 3215, 5551, 12610, 1829, 5296, 28814, 1863, 16247, 25513, 27884, 8978, 43242, 8315, 13672, 1829, 31439, 16712, 1863, 9957, 16070, 9640, 3555, 27884, 4724, 4587, 38251, 43761, 16070, 2655, 1863, 9957, 32771, 13546, 13672, 1829, 31439, 16247, 25513, 27884, 457, 6055, 3794, 27884, 307, 25557, 30767, 1829, 19446, 31439, 11331, 995, 4117, 1829, 9957, 570, 309, 307, 25974, 964, 538, 6055, 1211, 9307, 3660, 36764, 24401, 3660, 13412, 2288, 9566, 16472, 7251, 30544, 6225, 3215, 3215, 5551, 12610, 1829, 16472, 3224, 4724, 3794, 46740, 12174, 33546, 2304, 9957, 3714, 46456, 46538, 9957, 2423, 14407, 24401, 16070, 22488, 3215, 8717, 36178, 3224], "avg_logprob": -0.14270832980120624, "compression_ratio": 1.9631147540983607, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 144.18, "end": 145.3, "word": "والتلاتة", "probability": 0.9144694010416666}, {"start": 145.3, "end": 145.74, "word": " هما", "probability": 0.834228515625}, {"start": 145.74, "end": 146.04, "word": " بس", "probability": 0.89404296875}, {"start": 146.04, "end": 146.6, "word": " قواصمه", "probability": 0.76337890625}, {"start": 146.6, "end": 147.12, "word": " والتنين", "probability": 0.852294921875}, {"start": 147.12, "end": 147.5, "word": " عدد", "probability": 0.98095703125}, {"start": 147.5, "end": 147.94, "word": " أولي", "probability": 0.8473307291666666}, {"start": 147.94, "end": 148.46, "word": " الأربعة", "probability": 0.923828125}, {"start": 148.46, "end": 148.94, "word": " لأ", "probability": 0.935546875}, {"start": 148.94, "end": 149.1, "word": " مش", "probability": 0.98095703125}, {"start": 149.1, "end": 149.4, "word": " عدد", "probability": 0.9899088541666666}, {"start": 149.4, "end": 149.8, "word": " أولي", "probability": 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"temperature": 1.0}, {"id": 21, "seek": 45269, "start": 431.15, "end": 452.69, "text": "نيجي الان كيف نبحث عن اللي هو ال Ibrahim's او مسألة قديمة حتى يعني اللي هو الحل اللي موجود هو حل قديم حل the thief of erastothenes اللي هو أرستوطاليس", "tokens": [1863, 1829, 7435, 1829, 2423, 7649, 9122, 33911, 8717, 49628, 12984, 18871, 13672, 1829, 31439, 2423, 286, 38837, 311, 1975, 2407, 47524, 10721, 37977, 12174, 16254, 46007, 11331, 49975, 37495, 22653, 13672, 1829, 31439, 21542, 1211, 13672, 1829, 3714, 29245, 23328, 31439, 11331, 1211, 12174, 16254, 2304, 11331, 1211, 264, 23176, 295, 1189, 33869, 19096, 279, 13672, 1829, 31439, 5551, 2288, 14851, 2407, 9566, 6027, 1829, 3794], "avg_logprob": -0.28975184787722197, "compression_ratio": 1.515923566878981, "no_speech_prob": 0.0, "words": [{"start": 431.15, "end": 431.71, "word": "نيجي", "probability": 0.676025390625}, {"start": 431.71, "end": 432.29, "word": " الان", "probability": 0.6458740234375}, {"start": 432.29, "end": 433.15, "word": " كيف", "probability": 0.98193359375}, {"start": 433.15, "end": 433.87, "word": " نبحث", "probability": 0.9905598958333334}, {"start": 433.87, "end": 434.27, "word": " عن", "probability": 0.98681640625}, {"start": 434.27, "end": 434.55, "word": " اللي", "probability": 0.7978515625}, {"start": 434.55, "end": 434.95, "word": " هو", "probability": 0.98388671875}, {"start": 434.95, "end": 437.11, "word": " ال", "probability": 0.53173828125}, {"start": 437.11, "end": 437.93, "word": " Ibrahim's", "probability": 0.40948486328125}, {"start": 437.93, "end": 438.43, "word": " او", "probability": 0.6988525390625}, {"start": 438.43, "end": 440.15, "word": " مسألة", "probability": 0.9547526041666666}, {"start": 440.15, "end": 441.13, "word": " قديمة", "probability": 0.86865234375}, {"start": 441.13, "end": 443.35, "word": " حتى", "probability": 0.842041015625}, {"start": 443.35, "end": 443.67, "word": " يعني", "probability": 0.65380859375}, {"start": 443.67, "end": 443.93, "word": " اللي", "probability": 0.914306640625}, {"start": 443.93, "end": 444.11, "word": " هو", "probability": 0.873046875}, {"start": 444.11, "end": 444.51, "word": " الحل", "probability": 0.94677734375}, {"start": 444.51, "end": 444.65, "word": " اللي", "probability": 0.9189453125}, {"start": 444.65, "end": 445.05, "word": " موجود", "probability": 0.9847005208333334}, {"start": 445.05, "end": 445.21, "word": " هو", "probability": 0.68798828125}, {"start": 445.21, "end": 445.59, "word": " حل", "probability": 0.9541015625}, {"start": 445.59, "end": 446.21, "word": " قديم", "probability": 0.9871419270833334}, {"start": 446.21, "end": 446.63, "word": " حل", "probability": 0.884765625}, {"start": 446.63, "end": 446.99, "word": " the", "probability": 0.4853515625}, {"start": 446.99, "end": 447.29, "word": " thief", "probability": 0.71142578125}, {"start": 447.29, "end": 447.55, "word": " of", "probability": 0.82421875}, {"start": 447.55, "end": 451.25, "word": " erastothenes", "probability": 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463.39, "word": " إلى", "probability": 0.64111328125}, {"start": 463.39, "end": 463.83, "word": " مية", "probability": 0.731689453125}, {"start": 463.83, "end": 464.57, "word": " الان", "probability": 0.60455322265625}, {"start": 464.57, "end": 464.87, "word": " هذا", "probability": 0.84033203125}, {"start": 464.87, "end": 465.33, "word": " بقولك", "probability": 0.9002278645833334}, {"start": 465.33, "end": 466.09, "word": " بسيف", "probability": 0.3564860026041667}, {"start": 466.09, "end": 466.45, "word": " of", "probability": 0.81005859375}, {"start": 466.45, "end": 466.83, "word": " أرستو", "probability": 0.80975341796875}, {"start": 466.83, "end": 467.39, "word": " طاليس", "probability": 0.9942626953125}, {"start": 467.39, "end": 467.67, "word": " can", "probability": 0.87353515625}, {"start": 467.67, "end": 467.97, "word": " be", "probability": 0.96484375}, {"start": 467.97, "end": 468.39, "word": " used", "probability": 0.91845703125}, {"start": 468.39, "end": 468.63, "word": " to", "probability": 0.98095703125}, {"start": 468.63, "end": 469.19, "word": " find", "probability": 0.90869140625}, {"start": 469.19, "end": 469.95, "word": " all", "probability": 0.8798828125}, {"start": 469.95, "end": 470.57, "word": " primes", "probability": 0.6102294921875}, {"start": 470.57, "end": 470.97, "word": " not", "probability": 0.94677734375}, {"start": 470.97, "end": 471.85, "word": " exceeding", "probability": 0.941650390625}, {"start": 471.85, "end": 472.05, "word": " a", "probability": 0.951171875}, {"start": 472.05, "end": 473.25, "word": " specified", "probability": 0.59716796875}, {"start": 473.25, "end": 473.83, "word": " positive", "probability": 0.90966796875}, {"start": 473.83, "end": 474.23, "word": " integer", "probability": 0.9130859375}, {"start": 474.23, "end": 475.11, "word": " بقولك", "probability": 0.9430338541666666}, {"start": 475.11, "end": 475.45, "word": " يعني", "probability": 0.9013671875}, {"start": 475.45, "end": 475.81, "word": " احنا", "probability": 0.8468424479166666}, {"start": 475.81, "end": 475.99, "word": " لو", "probability": 0.98828125}, {"start": 475.99, "end": 476.49, "word": " بدنا", "probability": 0.987548828125}, {"start": 476.49, "end": 477.23, "word": " نيجي", "probability": 0.9669189453125}, {"start": 477.23, "end": 477.95, "word": " نبحث", "probability": 0.9777018229166666}, {"start": 477.95, "end": 478.13, "word": " عن", "probability": 0.994140625}, {"start": 478.13, "end": 478.67, "word": " الأعداد", "probability": 0.9679361979166666}, {"start": 478.67, "end": 479.31, "word": " الأولية", "probability": 0.98583984375}, {"start": 479.31, "end": 479.61, "word": " من", "probability": 0.98876953125}, {"start": 479.61, "end": 480.07, "word": " ال", "probability": 0.55908203125}, {"start": 480.07, "end": 480.13, "word": " ..", "probability": 0.64892578125}, {"start": 480.13, "end": 480.49, "word": " اللي", "probability": 0.740966796875}], "temperature": 1.0}, {"id": 23, "seek": 49989, "start": 480.75, "end": 499.89, "text": "اللي من واحد لعند خمسمية ايش بنسوي؟ من واحد لعشرين ايش بنسوي؟ من واحد لتلاتين ايش بنسوي؟ الان بقولي for example بده يبحث being with the list of integers between واحدة ومية يريد ان يبحث عن الأعداد الأولية", "tokens": [6027, 20292, 9154, 36764, 24401, 5296, 3615, 41260, 16490, 2304, 38251, 10632, 1975, 1829, 8592, 44945, 3794, 45865, 22807, 9154, 36764, 24401, 5296, 3615, 8592, 16572, 1863, 1975, 1829, 8592, 44945, 3794, 45865, 22807, 9154, 36764, 24401, 5296, 2655, 1211, 9307, 9957, 1975, 1829, 8592, 44945, 3794, 45865, 22807, 2423, 7649, 4724, 39648, 1829, 337, 1365, 47525, 3224, 7251, 49628, 12984, 885, 365, 264, 1329, 295, 41674, 1296, 36764, 24401, 3660, 4032, 2304, 10632, 7251, 16572, 3215, 16472, 7251, 49628, 12984, 18871, 16247, 22488, 18513, 16247, 12610, 10632], "avg_logprob": -0.16388694489939828, "compression_ratio": 1.7814207650273224, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 480.75, "end": 481.45, "word": "اللي", "probability": 0.76025390625}, {"start": 481.45, "end": 481.77, "word": " من", "probability": 0.962890625}, {"start": 481.77, "end": 483.03, "word": " واحد", "probability": 0.804931640625}, {"start": 483.03, "end": 483.95, "word": " لعند", "probability": 0.8859049479166666}, {"start": 483.95, "end": 484.91, "word": " خمسمية", "probability": 0.9354248046875}, {"start": 484.91, "end": 485.77, "word": " ايش", "probability": 0.6753743489583334}, {"start": 485.77, "end": 486.59, "word": " بنسوي؟", "probability": 0.818359375}, {"start": 486.59, "end": 486.77, "word": " من", "probability": 0.876953125}, {"start": 486.77, "end": 487.15, "word": " واحد", "probability": 0.9853515625}, {"start": 487.15, "end": 487.69, "word": " لعشرين", "probability": 0.82392578125}, {"start": 487.69, "end": 487.89, "word": " ايش", "probability": 0.9373372395833334}, {"start": 487.89, "end": 488.43, "word": " بنسوي؟", "probability": 0.9486083984375}, {"start": 488.43, "end": 488.55, "word": " من", "probability": 0.9716796875}, {"start": 488.55, "end": 488.83, "word": " واحد", "probability": 0.988037109375}, {"start": 488.83, "end": 489.37, "word": " لتلاتين", "probability": 0.9185546875}, {"start": 489.37, "end": 489.59, "word": " ايش", "probability": 0.9490559895833334}, {"start": 489.59, "end": 490.69, "word": " بنسوي؟", "probability": 0.95751953125}, {"start": 490.69, "end": 491.09, "word": " الان", "probability": 0.69189453125}, {"start": 491.09, "end": 491.49, "word": " بقولي", "probability": 0.6707356770833334}, {"start": 491.49, "end": 491.67, "word": " for", "probability": 0.91064453125}, {"start": 491.67, "end": 492.41, "word": " example", "probability": 0.97021484375}, {"start": 492.41, "end": 492.87, "word": " بده", "probability": 0.682373046875}, {"start": 492.87, "end": 493.37, "word": " يبحث", "probability": 0.9905598958333334}, {"start": 493.37, "end": 493.75, "word": " being", "probability": 0.66064453125}, {"start": 493.75, "end": 494.23, "word": " with", "probability": 0.93896484375}, {"start": 494.23, "end": 494.41, "word": " the", "probability": 0.74072265625}, {"start": 494.41, "end": 494.75, "word": " list", "probability": 0.908203125}, {"start": 494.75, "end": 494.97, "word": " of", "probability": 0.9765625}, {"start": 494.97, "end": 495.45, "word": " integers", "probability": 0.94287109375}, {"start": 495.45, "end": 495.95, "word": " between", "probability": 0.87939453125}, {"start": 495.95, "end": 496.35, "word": " واحدة", "probability": 0.8577473958333334}, {"start": 496.35, "end": 496.79, "word": " ومية", "probability": 0.77392578125}, {"start": 496.79, "end": 497.75, "word": " يريد", "probability": 0.8600260416666666}, {"start": 497.75, "end": 497.89, "word": " ان", "probability": 0.71337890625}, {"start": 497.89, "end": 498.37, "word": " يبحث", "probability": 0.9920247395833334}, {"start": 498.37, "end": 498.57, "word": " عن", "probability": 0.99365234375}, {"start": 498.57, "end": 499.09, "word": " الأعداد", "probability": 0.801513671875}, {"start": 499.09, "end": 499.89, "word": " الأولية", "probability": 0.8937174479166666}], "temperature": 1.0}, {"id": 24, "seek": 51691, "start": 500.21, "end": 516.91, "text": "اللي من الأعداد من واحد لمية .. من واحد لمية في عندنا مائة عدد الان هذول المائة عدد بدنا نبحث مين فيهم اللي هو إبراهيم شوفوا الطريقة الحلوة الجميلة هذا طريقة خديمة من أيام رستو طاليس اللي هو بيقول", "tokens": [6027, 20292, 9154, 16247, 22488, 18513, 9154, 36764, 24401, 5296, 2304, 10632, 4386, 9154, 36764, 24401, 5296, 2304, 10632, 8978, 43242, 8315, 3714, 16373, 3660, 6225, 3215, 3215, 2423, 7649, 8032, 8848, 12610, 9673, 16373, 3660, 6225, 3215, 3215, 47525, 8315, 8717, 49628, 12984, 3714, 9957, 8978, 16095, 13672, 1829, 31439, 11933, 3555, 23557, 3224, 32640, 13412, 38688, 14407, 41950, 16572, 28671, 21542, 1211, 2407, 3660, 25724, 2304, 26895, 3660, 23758, 23032, 16572, 28671, 16490, 16254, 46007, 9154, 36632, 10943, 12602, 14851, 2407, 23032, 6027, 1829, 3794, 13672, 1829, 31439, 4724, 1829, 39648], "avg_logprob": 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0.71826171875}, {"start": 503.57, "end": 504.39, "word": " عندنا", "probability": 0.83544921875}, {"start": 504.39, "end": 505.29, "word": " مائة", "probability": 0.8056640625}, {"start": 505.29, "end": 505.77, "word": " عدد", "probability": 0.9557291666666666}, {"start": 505.77, "end": 506.23, "word": " الان", "probability": 0.5743408203125}, {"start": 506.23, "end": 506.51, "word": " هذول", "probability": 0.7615559895833334}, {"start": 506.51, "end": 506.77, "word": " المائة", "probability": 0.7137044270833334}, {"start": 506.77, "end": 507.13, "word": " عدد", "probability": 0.9890950520833334}, {"start": 507.13, "end": 507.77, "word": " بدنا", "probability": 0.81201171875}, {"start": 507.77, "end": 508.19, "word": " نبحث", "probability": 0.9851888020833334}, {"start": 508.19, "end": 508.69, "word": " مين", "probability": 0.956787109375}, {"start": 508.69, "end": 509.53, "word": " فيهم", "probability": 0.75244140625}, {"start": 509.53, "end": 509.77, "word": " اللي", "probability": 0.8388671875}, {"start": 509.77, "end": 510.09, "word": " هو", "probability": 0.98779296875}, {"start": 510.09, "end": 510.61, "word": " إبراهيم", "probability": 0.88525390625}, {"start": 510.61, "end": 510.97, "word": " شوفوا", "probability": 0.755859375}, {"start": 510.97, "end": 511.31, "word": " الطريقة", "probability": 0.9749348958333334}, {"start": 511.31, "end": 511.69, "word": " الحلوة", "probability": 0.97021484375}, {"start": 511.69, "end": 512.35, "word": " الجميلة", "probability": 0.984619140625}, {"start": 512.35, "end": 513.13, "word": " هذا", "probability": 0.53857421875}, {"start": 513.13, "end": 513.51, "word": " طريقة", "probability": 0.98828125}, {"start": 513.51, "end": 514.03, "word": " خديمة", "probability": 0.8017578125}, {"start": 514.03, "end": 514.33, "word": " من", "probability": 0.97509765625}, {"start": 514.33, "end": 514.69, "word": " أيام", "probability": 0.856201171875}, {"start": 514.69, "end": 515.51, "word": " رستو", "probability": 0.6985677083333334}, {"start": 515.51, "end": 516.05, "word": " طاليس", "probability": 0.8670654296875}, {"start": 516.05, "end": 516.53, "word": " اللي", "probability": 0.97216796875}, {"start": 516.53, "end": 516.63, "word": " هو", "probability": 0.9853515625}, {"start": 516.63, "end": 516.91, "word": " بيقول", "probability": 0.94189453125}], "temperature": 1.0}, {"id": 25, "seek": 53764, "start": 517.76, "end": 537.64, "text": "delete all integers other than two divisible by اتنين ايش تسوي اول حاجة بقولك كل الاعداد اللى بتقسم على اتنين لعنده مية اللى هو شطة بقى يعني اكتب الاعداد من واحد لمية وبده شطة مضاعفة يعني اتنين", "tokens": [18105, 3498, 439, 41674, 661, 813, 732, 25974, 964, 538, 1975, 2655, 1863, 9957, 1975, 1829, 8592, 6055, 3794, 45865, 1975, 12610, 11331, 26108, 3660, 4724, 39648, 4117, 28242, 42963, 22488, 18513, 13672, 7578, 39894, 4587, 38251, 15844, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 3224, 3714, 10632, 13672, 7578, 31439, 13412, 9566, 3660, 4724, 4587, 7578, 37495, 22653, 1975, 4117, 2655, 3555, 42963, 22488, 18513, 9154, 36764, 24401, 5296, 2304, 10632, 4032, 44510, 3224, 13412, 9566, 3660, 3714, 11242, 45761, 5172, 3660, 37495, 22653, 1975, 2655, 1863, 9957], "avg_logprob": -0.18611111094554264, "compression_ratio": 1.631578947368421, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 517.76, "end": 518.56, "word": "delete", "probability": 0.6417236328125}, {"start": 518.56, "end": 518.84, "word": " all", "probability": 0.9013671875}, {"start": 518.84, "end": 519.42, "word": " integers", "probability": 0.9453125}, {"start": 519.42, "end": 519.78, "word": " other", "probability": 0.8623046875}, {"start": 519.78, "end": 520.28, "word": " than", "probability": 0.9423828125}, {"start": 520.28, "end": 520.6, "word": " two", "probability": 0.6513671875}, {"start": 520.6, "end": 521.18, "word": " divisible", "probability": 0.873291015625}, {"start": 521.18, "end": 521.46, "word": " by", "probability": 0.97900390625}, {"start": 521.46, "end": 521.82, "word": " اتنين", "probability": 0.83612060546875}, {"start": 521.82, "end": 522.16, "word": " ايش", "probability": 0.684326171875}, {"start": 522.16, "end": 522.5, "word": " تسوي", "probability": 0.8932291666666666}, {"start": 522.5, "end": 522.74, "word": " اول", "probability": 0.858154296875}, {"start": 522.74, "end": 523.46, "word": " حاجة", "probability": 0.9630533854166666}, {"start": 523.46, "end": 524.28, "word": " بقولك", "probability": 0.8284505208333334}, {"start": 524.28, "end": 525.18, "word": " كل", "probability": 0.89208984375}, {"start": 525.18, "end": 526.2, "word": " الاعداد", "probability": 0.8795572916666666}, {"start": 526.2, "end": 526.66, "word": " اللى", "probability": 0.759033203125}, {"start": 526.66, "end": 527.08, "word": " بتقسم", "probability": 0.98486328125}, {"start": 527.08, "end": 527.32, "word": " على", "probability": 0.8740234375}, {"start": 527.32, "end": 527.96, "word": " اتنين", "probability": 0.9727783203125}, {"start": 527.96, "end": 528.72, "word": " لعنده", "probability": 0.6650390625}, {"start": 528.72, "end": 529.06, "word": " مية", "probability": 0.893310546875}, {"start": 529.06, "end": 529.72, "word": " اللى", "probability": 0.93505859375}, {"start": 529.72, "end": 530.36, "word": " هو", "probability": 0.841796875}, {"start": 530.36, "end": 531.96, "word": " شطة", "probability": 0.6476236979166666}, {"start": 531.96, "end": 532.32, "word": " بقى", "probability": 0.767578125}, {"start": 532.32, "end": 532.82, "word": " يعني", "probability": 0.840576171875}, {"start": 532.82, "end": 533.1, "word": " اكتب", "probability": 0.971923828125}, {"start": 533.1, "end": 534.06, "word": " الاعداد", "probability": 0.93408203125}, {"start": 534.06, "end": 534.2, "word": " من", "probability": 0.96826171875}, {"start": 534.2, "end": 534.42, "word": " واحد", "probability": 0.982666015625}, {"start": 534.42, "end": 534.72, "word": " لمية", "probability": 0.9319661458333334}, {"start": 534.72, "end": 534.96, "word": " وبده", "probability": 0.6119791666666666}, {"start": 534.96, "end": 535.6, "word": " شطة", "probability": 0.98193359375}, {"start": 535.6, "end": 536.7, "word": " مضاعفة", "probability": 0.86708984375}, {"start": 536.7, "end": 537.2, "word": " يعني", "probability": 0.8857421875}, {"start": 537.2, "end": 537.64, "word": " اتنين", "probability": 0.9390869140625}], "temperature": 1.0}, {"id": 26, "seek": 55380, "start": 537.99, "end": 553.81, "text": "و مضاعفاته يعني 2x3x6 و 2x4x8 و 2x5x10 و 2x6x12 بظلي اللي هي كل الأعداد اللي هي مضاعفات 2 مشطبها من اللي أسته", "tokens": [2407, 3714, 11242, 45761, 5172, 9307, 3224, 37495, 22653, 568, 87, 18, 87, 21, 4032, 568, 87, 19, 87, 23, 4032, 568, 87, 20, 87, 3279, 4032, 568, 87, 21, 87, 4762, 4724, 19913, 20292, 13672, 1829, 39896, 28242, 16247, 22488, 18513, 13672, 1829, 39896, 3714, 11242, 45761, 5172, 9307, 568, 37893, 9566, 3555, 11296, 9154, 13672, 1829, 5551, 3794, 47395], "avg_logprob": -0.29158265456076593, "compression_ratio": 1.4661016949152543, "no_speech_prob": 1.2516975402832031e-06, "words": [{"start": 537.99, "end": 538.27, "word": "و", "probability": 0.3681640625}, {"start": 538.27, "end": 538.97, "word": " مضاعفاته", "probability": 0.8819986979166666}, {"start": 538.97, "end": 539.15, "word": " يعني", "probability": 0.71240234375}, {"start": 539.15, "end": 540.07, "word": " 2x3x6", "probability": 0.5396697998046875}, {"start": 540.07, "end": 540.73, "word": " و", "probability": 0.1734619140625}, {"start": 540.73, "end": 542.59, "word": " 2x4x8", "probability": 0.92001953125}, {"start": 542.59, "end": 543.45, "word": " و", "probability": 0.39013671875}, {"start": 543.45, "end": 546.47, "word": " 2x5x10", "probability": 0.845654296875}, {"start": 546.47, "end": 546.63, "word": " و", "probability": 0.85693359375}, {"start": 546.63, "end": 548.77, "word": " 2x6x12", "probability": 0.97841796875}, {"start": 548.77, "end": 549.57, "word": " بظلي", "probability": 0.4512532552083333}, {"start": 549.57, "end": 549.73, "word": " اللي", "probability": 0.7119140625}, {"start": 549.73, "end": 549.95, "word": " هي", "probability": 0.8125}, {"start": 549.95, "end": 550.31, "word": " كل", "probability": 0.888671875}, {"start": 550.31, "end": 551.09, "word": " الأعداد", "probability": 0.9026692708333334}, {"start": 551.09, "end": 551.41, "word": " اللي", "probability": 0.961669921875}, {"start": 551.41, "end": 551.63, "word": " هي", "probability": 0.9052734375}, {"start": 551.63, "end": 552.21, "word": " مضاعفات", "probability": 0.98046875}, {"start": 552.21, "end": 552.45, "word": " 2", "probability": 0.90185546875}, {"start": 552.45, "end": 553.09, "word": " مشطبها", "probability": 0.89208984375}, {"start": 553.09, "end": 553.29, "word": " من", "probability": 0.98046875}, {"start": 553.29, "end": 553.55, "word": " اللي", "probability": 0.775634765625}, {"start": 553.55, "end": 553.81, "word": " أسته", "probability": 0.4515787760416667}], "temperature": 1.0}, {"id": 27, "seek": 58084, "start": 554.46, "end": 580.84, "text": "الان بعد هيك بشطب كل الأعداد اللي هي delete all the integers other than تلاتة divisible by تلاتة بشطب كل الأعداد طبعا سيب التلاتة لانه prime سيب .. شطب كل المضاعفات التلاتة شطب الست و شطب التسعة و شطب الاطنعاش و و و الاخر يه طبعا فيشي اللي بشطبهن تكون شطبتهن نور ع نور اصلا مديش ايه انا طبعا المضاعفات هي مش هيكون ال prime اكيد", "tokens": [6027, 7649, 39182, 39896, 4117, 4724, 8592, 9566, 3555, 28242, 16247, 22488, 18513, 13672, 1829, 39896, 12097, 439, 264, 41674, 661, 813, 6055, 1211, 9307, 3660, 25974, 964, 538, 6055, 1211, 9307, 3660, 4724, 8592, 9566, 3555, 28242, 16247, 22488, 18513, 23032, 3555, 3615, 995, 8608, 1829, 3555, 16712, 1211, 9307, 3660, 5296, 7649, 3224, 5835, 8608, 1829, 3555, 4386, 13412, 9566, 3555, 28242, 9673, 11242, 45761, 5172, 9307, 16712, 1211, 9307, 3660, 13412, 9566, 3555, 2423, 14851, 4032, 13412, 9566, 3555, 16712, 3794, 27884, 4032, 13412, 9566, 3555, 2423, 41193, 1863, 3615, 33599, 4032, 4032, 4032, 2423, 47283, 2288, 7251, 3224, 23032, 3555, 3615, 995, 8978, 8592, 1829, 13672, 1829, 4724, 8592, 9566, 3555, 3224, 1863, 6055, 30544, 13412, 9566, 3555, 47395, 1863, 8717, 13063, 6225, 8717, 13063, 1975, 9381, 15040, 3714, 16254, 8592, 1975, 1829, 3224, 1975, 8315, 23032, 3555, 3615, 995, 9673, 11242, 45761, 5172, 9307, 39896, 37893, 39896, 30544, 2423, 5835, 1975, 4117, 25708], "avg_logprob": -0.2604166674164106, "compression_ratio": 2.057471264367816, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 554.46, "end": 554.96, "word": "الان", "probability": 0.5655517578125}, {"start": 554.96, "end": 555.5, "word": " بعد", "probability": 0.44873046875}, {"start": 555.5, "end": 555.8, "word": " هيك", "probability": 0.51953125}, {"start": 555.8, "end": 556.32, "word": " بشطب", "probability": 0.7786865234375}, {"start": 556.32, "end": 556.68, "word": " كل", "probability": 0.94140625}, {"start": 556.68, "end": 557.58, "word": " الأعداد", "probability": 0.8050130208333334}, {"start": 557.58, "end": 557.88, "word": " اللي", "probability": 0.633056640625}, {"start": 557.88, "end": 558.1, "word": " هي", "probability": 0.82373046875}, {"start": 558.1, "end": 558.46, "word": " delete", "probability": 0.94140625}, {"start": 558.46, "end": 558.72, "word": " all", "probability": 0.91845703125}, {"start": 558.72, "end": 558.86, "word": " the", "probability": 0.4892578125}, {"start": 558.86, "end": 559.28, "word": " integers", "probability": 0.9423828125}, {"start": 559.28, "end": 559.64, "word": " other", "probability": 0.837890625}, {"start": 559.64, "end": 560.0, "word": " than", "probability": 0.9501953125}, {"start": 560.0, "end": 560.6, "word": " تلاتة", "probability": 0.865966796875}, {"start": 560.6, "end": 561.52, "word": " divisible", "probability": 0.8486328125}, {"start": 561.52, "end": 561.76, "word": " by", "probability": 0.9755859375}, {"start": 561.76, "end": 562.12, "word": " تلاتة", "probability": 0.955322265625}, {"start": 562.12, "end": 562.6, "word": " بشطب", "probability": 0.9044189453125}, {"start": 562.6, "end": 562.88, "word": " كل", "probability": 0.97265625}, {"start": 562.88, "end": 563.42, "word": " الأعداد", "probability": 0.9661458333333334}, {"start": 563.42, "end": 563.66, "word": " طبعا", "probability": 0.8743896484375}, {"start": 563.66, "end": 563.9, "word": " سيب", "probability": 0.92919921875}, {"start": 563.9, "end": 564.28, "word": " التلاتة", "probability": 0.9168701171875}, {"start": 564.28, "end": 564.52, "word": " لانه", "probability": 0.7599283854166666}, {"start": 564.52, "end": 564.82, "word": " prime", "probability": 0.76953125}, {"start": 564.82, "end": 565.72, "word": " سيب", "probability": 0.8349609375}, {"start": 565.72, "end": 566.0, "word": " ..", "probability": 0.46630859375}, {"start": 566.0, "end": 567.4, "word": " شطب", "probability": 0.8409830729166666}, {"start": 567.4, "end": 567.8, "word": " كل", "probability": 0.990234375}, {"start": 567.8, "end": 568.62, "word": " المضاعفات", "probability": 0.88779296875}, {"start": 568.62, "end": 569.28, "word": " التلاتة", "probability": 0.9852294921875}, {"start": 569.28, "end": 570.02, "word": " شطب", "probability": 0.9715169270833334}, {"start": 570.02, "end": 570.44, "word": " الست", "probability": 0.712158203125}, {"start": 570.44, "end": 570.62, "word": " و", "probability": 0.82275390625}, {"start": 570.62, "end": 571.06, "word": " شطب", "probability": 0.81982421875}, {"start": 571.06, "end": 571.58, "word": " التسعة", "probability": 0.97265625}, {"start": 571.58, "end": 571.7, "word": " و", "probability": 0.9833984375}, {"start": 571.7, "end": 572.12, "word": " شطب", "probability": 0.9571940104166666}, {"start": 572.12, "end": 572.68, "word": " الاطنعاش", "probability": 0.673974609375}, {"start": 572.68, "end": 572.82, "word": " و", "probability": 0.81298828125}, {"start": 572.82, "end": 573.08, "word": " و", "probability": 0.50390625}, {"start": 573.08, "end": 573.14, "word": " و", "probability": 0.3291015625}, {"start": 573.14, "end": 573.56, "word": " الاخر", "probability": 0.7965494791666666}, {"start": 573.56, "end": 573.76, "word": " يه", "probability": 0.459991455078125}, {"start": 573.76, "end": 574.22, "word": " طبعا", "probability": 0.9686279296875}, {"start": 574.22, "end": 574.6, "word": " فيشي", "probability": 0.4661865234375}, {"start": 574.6, "end": 574.68, "word": " اللي", "probability": 0.73974609375}, {"start": 574.68, "end": 575.26, "word": " بشطبهن", "probability": 0.6219685872395834}, {"start": 575.26, "end": 575.48, "word": " تكون", "probability": 0.677490234375}, {"start": 575.48, "end": 576.24, "word": " شطبتهن", "probability": 0.91015625}, {"start": 576.24, "end": 576.72, "word": " نور", "probability": 0.92919921875}, {"start": 576.72, "end": 576.8, "word": " ع", "probability": 0.27490234375}, {"start": 576.8, "end": 576.96, "word": " نور", "probability": 0.9775390625}, {"start": 576.96, "end": 577.18, "word": " اصلا", "probability": 0.8147786458333334}, {"start": 577.18, "end": 577.52, "word": " مديش", "probability": 0.6897786458333334}, {"start": 577.52, "end": 577.68, "word": " ايه", "probability": 0.5546061197916666}, {"start": 577.68, "end": 577.96, "word": " انا", "probability": 0.932861328125}, {"start": 577.96, "end": 578.64, "word": " طبعا", "probability": 0.97705078125}, {"start": 578.64, "end": 579.38, "word": " المضاعفات", "probability": 0.99560546875}, {"start": 579.38, "end": 579.46, "word": " هي", "probability": 0.24462890625}, {"start": 579.46, "end": 579.58, "word": " مش", "probability": 0.990234375}, {"start": 579.58, "end": 579.98, "word": " هيكون", "probability": 0.943115234375}, {"start": 579.98, "end": 580.08, "word": " ال", "probability": 0.72998046875}, {"start": 580.08, "end": 580.36, "word": " prime", "probability": 0.77392578125}, {"start": 580.36, "end": 580.84, "word": " اكيد", "probability": 0.8841145833333334}], "temperature": 1.0}, {"id": 28, "seek": 60912, "start": 581.02, "end": 609.12, "text": "delete all the integers other than خمسة or divisible by خمسة الان شطب على كل الأعداد مضاعفات من الخمسة الان شطبت على مضاعفات الخمسة اللي هي عشرة وخمس تعاشر وخمسة وعشرين إلى خير لما تسلمي إلى المية الان بعدها شطب على كل الأعداد اللي هي مضاعفات العدد من سبعة الان وكأنه بيقول لي", "tokens": [18105, 3498, 439, 264, 41674, 661, 813, 16490, 2304, 3794, 3660, 420, 25974, 964, 538, 16490, 2304, 3794, 3660, 2423, 7649, 13412, 9566, 3555, 15844, 28242, 16247, 22488, 18513, 3714, 11242, 45761, 5172, 9307, 9154, 33962, 2304, 3794, 3660, 2423, 7649, 13412, 9566, 3555, 2655, 15844, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 13672, 1829, 39896, 6225, 8592, 25720, 4032, 9778, 2304, 3794, 37279, 33599, 2288, 4032, 9778, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 30731, 16490, 13546, 5296, 15042, 6055, 3794, 19528, 1829, 30731, 9673, 10632, 2423, 7649, 39182, 11296, 13412, 9566, 3555, 15844, 28242, 16247, 22488, 18513, 13672, 1829, 39896, 3714, 11242, 45761, 5172, 9307, 18863, 3215, 3215, 9154, 8608, 3555, 27884, 2423, 7649, 4032, 4117, 33456, 3224, 4724, 1829, 39648, 32239], "avg_logprob": -0.1898375986598608, "compression_ratio": 2.1009174311926606, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 581.02, "end": 582.32, "word": "delete", "probability": 0.682373046875}, {"start": 582.32, "end": 582.84, "word": " all", "probability": 0.8349609375}, {"start": 582.84, "end": 583.04, "word": " the", "probability": 0.348876953125}, {"start": 583.04, "end": 583.52, "word": " integers", "probability": 0.9501953125}, {"start": 583.52, "end": 583.88, "word": " other", "probability": 0.82421875}, {"start": 583.88, "end": 584.22, "word": " than", "probability": 0.94580078125}, {"start": 584.22, "end": 584.82, "word": " خمسة", "probability": 0.8497314453125}, {"start": 584.82, "end": 585.52, "word": " or", "probability": 0.453857421875}, {"start": 585.52, "end": 586.32, "word": " divisible", "probability": 0.88427734375}, {"start": 586.32, "end": 586.54, "word": " by", "probability": 0.9755859375}, 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"probability": 0.8720703125}, {"start": 605.34, "end": 605.72, "word": " من", "probability": 0.99169921875}, {"start": 605.72, "end": 606.28, "word": " سبعة", "probability": 0.9583333333333334}, {"start": 606.28, "end": 607.56, "word": " الان", "probability": 0.9580078125}, {"start": 607.56, "end": 608.54, "word": " وكأنه", "probability": 0.9156494140625}, {"start": 608.54, "end": 608.9, "word": " بيقول", "probability": 0.7967122395833334}, {"start": 608.9, "end": 609.12, "word": " لي", "probability": 0.3671875}], "temperature": 1.0}, {"id": 29, "seek": 62154, "start": 609.56, "end": 621.54, "text": "تعال من الأعداد الأقل من عشرة وشوف الـprimes اللي فيها اللي هي التنين والتلاتة والخمسة والسبعة وشطبل مضاعفاتها", "tokens": [2655, 3615, 6027, 9154, 16247, 22488, 18513, 16247, 4587, 1211, 9154, 6225, 8592, 25720, 4032, 8592, 38688, 2423, 39184, 1424, 1532, 13672, 1829, 8978, 11296, 13672, 1829, 39896, 16712, 1863, 9957, 16070, 2655, 1211, 9307, 3660, 16070, 9778, 2304, 3794, 3660, 16070, 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بدك تيجي للرقم 100 الرقم 100 إذا بده يكون اللي هو في اللي هو قواسم", "tokens": [20292, 8592, 22807, 5296, 33456, 14739, 2655, 5551, 9381, 15040, 14111, 5296, 15042, 6055, 1829, 7435, 1829, 6055, 8592, 9566, 4587, 13672, 1829, 39896, 28242, 3714, 11242, 45761, 5172, 9307, 16712, 1863, 9957, 4032, 2304, 11242, 45761, 5172, 9307, 16712, 1211, 2655, 3660, 4032, 2304, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 4032, 2304, 11242, 45761, 5172, 9307, 21136, 3555, 27884, 45164, 47525, 4117, 6055, 1829, 7435, 1829, 24976, 2288, 4587, 2304, 2319, 34892, 4587, 2304, 2319, 11933, 15730, 47525, 3224, 7251, 30544, 13672, 1829, 31439, 8978, 13672, 1829, 31439, 12174, 14407, 38251], "avg_logprob": -0.1697368439875151, "compression_ratio": 1.9936305732484076, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 640.08, "end": 641.48, "word": "ليش؟", "probability": 0.6918131510416666}, {"start": 641.48, "end": 641.9, "word": " لأن", "probability": 0.8466796875}, {"start": 641.9, "end": 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{"start": 789.06, "end": 789.5, "word": " primes", "probability": 0.6304931640625}], "temperature": 1.0}, {"id": 38, "seek": 81347, "start": 790.07, "end": 813.47, "text": "الان نشطب مضاعفات الخمسة خمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة مضاعفات الخمسة", "tokens": [6027, 7649, 8717, 8592, 9566, 3555, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 16490, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660, 3714, 11242, 45761, 5172, 9307, 33962, 2304, 3794, 3660], "avg_logprob": -0.215692938507899, "compression_ratio": 4.711864406779661, 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عشرين بعدين الاخرين طبعا في أعداد الآن فيها خط فيها خطين و فيها تلاتة و فيه أربعة", "tokens": [9778, 2304, 3794, 23032, 3615, 8592, 6225, 46309, 9957, 4032, 8032, 4117, 15730, 8717, 7435, 1829, 5296, 2304, 11242, 45761, 5172, 9307, 9154, 21136, 3555, 27884, 29538, 21136, 3555, 27884, 8608, 3555, 8315, 11296, 13412, 9566, 3555, 8315, 3714, 11242, 45761, 5172, 11296, 5296, 9640, 3555, 27884, 23032, 3615, 8592, 39182, 9957, 2423, 14407, 24401, 4032, 6225, 46309, 9957, 39182, 9957, 2423, 47283, 2288, 9957, 23032, 3555, 3615, 995, 8978, 5551, 22488, 18513, 6024, 48506, 8978, 11296, 16490, 9566, 8978, 11296, 16490, 9566, 9957, 4032, 8978, 11296, 6055, 1211, 9307, 3660, 4032, 8978, 3224, 5551, 25513, 27884], "avg_logprob": -0.29846939079615536, "compression_ratio": 2.0559006211180124, "no_speech_prob": 9.179115295410156e-06, "words": [{"start": 813.51, "end": 814.13, "word": "خمس", "probability": 0.6699015299479166}, {"start": 814.13, "end": 814.59, "word": " طعش", "probability": 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بتكسبين اتنين يعني اتكررت مرتين تلت خطوط معناته بتكسبين تلاتة اربع خطوط معناته بتكسب اربعة الآن هيك بكون خلصنا على كل الأعداد اللي هي اللي مش prime", "tokens": [6027, 20292, 8978, 11296, 16490, 9566, 20449, 8315, 47395, 4724, 3794, 39894, 4117, 35457, 36764, 24401, 9154, 8032, 3215, 12610, 2423, 9640, 3555, 27884, 2423, 1424, 1532, 16490, 9566, 9957, 39894, 4117, 35457, 9957, 1975, 2655, 1863, 9957, 37495, 22653, 1975, 2655, 37983, 43500, 3714, 43500, 9957, 6055, 1211, 2655, 16490, 9566, 2407, 9566, 20449, 8315, 47395, 39894, 4117, 35457, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 3615, 16490, 9566, 2407, 9566, 20449, 8315, 47395, 39894, 4117, 35457, 1975, 25513, 27884, 6024, 48506, 39896, 4117, 4724, 30544, 16490, 1211, 9381, 8315, 15844, 28242, 16247, 22488, 18513, 13672, 1829, 39896, 13672, 1829, 37893, 5835], "avg_logprob": -0.2500000060177766, "compression_ratio": 1.9840425531914894, "no_speech_prob": 0.0, "words": [{"start": 831.09, "end": 831.49, "word": "اللي", "probability": 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"start": 1163.29, "end": 1185.89, "text": "لأنه سيصبح قواسمها كلها أكبر من جدر الأن فإذا حصل الضرب هذا أكبر من جدر الأن و هذا أكبر من جدر الأن سيصبح حصل ضرب أكبر من مين من أن عشان هيك و أنت مغمض عشان تثبت اللي هو العدد أن برايم بتجيب كل الأعداء تاخدوا الجدر التربيعي له", "tokens": [1211, 33456, 3224, 8608, 1829, 9381, 49628, 12174, 14407, 38251, 11296, 28242, 11296, 5551, 4117, 26890, 9154, 10874, 3215, 2288, 16247, 1863, 6156, 28814, 15730, 11331, 36520, 6024, 114, 25513, 23758, 5551, 4117, 26890, 9154, 10874, 3215, 2288, 16247, 1863, 4032, 23758, 5551, 4117, 26890, 9154, 10874, 3215, 2288, 16247, 1863, 8608, 1829, 9381, 49628, 11331, 36520, 48812, 25513, 5551, 4117, 26890, 9154, 3714, 9957, 9154, 14739, 6225, 8592, 7649, 39896, 4117, 4032, 14739, 2655, 3714, 17082, 2304, 11242, 6225, 8592, 7649, 6055, 12984, 3555, 2655, 13672, 1829, 31439, 18863, 3215, 3215, 14739, 4724, 23557, 32640, 39894, 7435, 1829, 3555, 28242, 16247, 22488, 16606, 6055, 47283, 3215, 14407, 25724, 3215, 2288, 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"probability": 0.9312744140625}, {"start": 1184.87, "end": 1185.13, "word": " الجدر", "probability": 0.8025716145833334}, {"start": 1185.13, "end": 1185.65, "word": " التربيعي", "probability": 0.819140625}, {"start": 1185.65, "end": 1185.89, "word": " له", "probability": 0.72705078125}], "temperature": 1.0}, {"id": 57, "seek": 120877, "start": 1186.55, "end": 1208.77, "text": "بعد ما تاخد الجدر التربيعي إيه لو بتيجي بتاخد كل الأعداد اللي أصغر أو يسوى الجدر التربيعي بتفحصها بتقسم العدد هيو اللي هو مش prime بتقسموش و أنت مغمض قول prime نشوف هذا عمليا الآن مثال determine which of 37, 59, 161 is prime ولا لأ", "tokens": [3555, 22488, 19446, 6055, 47283, 3215, 25724, 3215, 2288, 16712, 2288, 21292, 3615, 1829, 11933, 1829, 3224, 45164, 39894, 1829, 7435, 1829, 39894, 47283, 3215, 28242, 16247, 22488, 18513, 13672, 1829, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 2407, 7578, 25724, 3215, 2288, 16712, 2288, 21292, 3615, 1829, 39894, 5172, 5016, 9381, 11296, 39894, 4587, 38251, 18863, 3215, 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الكلام مثبت وهي الإثبات لكن احنا لضيق الوقت مش هنطلبكم بإثبات النظرية طيب الان في نوع من أنواع ال primes اللي هو بنسميها Mersini Primes", "tokens": [6027, 20292, 31439, 8717, 19913, 2288, 10632, 12174, 20292, 3215, 3794, 4724, 1829, 39648, 5296, 4117, 456, 366, 36227, 867, 582, 1532, 37495, 22653, 7251, 29245, 3215, 6225, 3215, 3215, 5296, 7649, 3224, 16373, 1829, 9154, 16247, 22488, 18513, 16247, 12610, 10632, 3714, 33599, 1829, 21542, 6027, 23758, 2423, 28820, 10943, 3714, 12984, 3555, 2655, 37037, 1829, 33688, 12984, 3555, 9307, 44381, 1975, 5016, 8315, 5296, 11242, 1829, 4587, 2423, 30543, 2655, 37893, 8032, 1863, 9566, 46152, 24793, 4724, 28814, 12984, 3555, 9307, 28239, 19913, 2288, 10632, 23032, 1829, 3555, 2423, 7649, 8978, 8717, 45367, 9154, 14739, 14407, 3615, 2423, 582, 1532, 13672, 1829, 31439, 44945, 38251, 1829, 11296, 376, 433, 3812, 2114, 1532], "avg_logprob": -0.1862771723581397, "compression_ratio": 1.6761133603238867, "no_speech_prob": 5.960464477539063e-08, "words": 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" في", "probability": 0.78515625}, {"start": 1397.48, "end": 1398.16, "word": " نوع", "probability": 0.982177734375}, {"start": 1398.16, "end": 1398.36, "word": " من", "probability": 0.99169921875}, {"start": 1398.36, "end": 1398.9, "word": " أنواع", "probability": 0.9337565104166666}, {"start": 1398.9, "end": 1399.02, "word": " ال", "probability": 0.9052734375}, {"start": 1399.02, "end": 1399.7, "word": " primes", "probability": 0.61712646484375}, {"start": 1399.7, "end": 1400.4, "word": " اللي", "probability": 0.93994140625}, {"start": 1400.4, "end": 1400.56, "word": " هو", "probability": 0.94287109375}, {"start": 1400.56, "end": 1401.18, "word": " بنسميها", "probability": 0.935546875}, {"start": 1401.18, "end": 1401.78, "word": " Mersini", "probability": 0.6086832682291666}, {"start": 1401.78, "end": 1402.36, "word": " Primes", "probability": 0.689208984375}], "temperature": 1.0}, {"id": 66, "seek": 141851, "start": 1403.83, "end": 1418.51, "text": "الان مرسيني برايم عرفة كما هي ليه وقول لـ definition prime numbers of the form 2 to the b minus 1 where b is prime are called Mersini Primes يعني الأعداد اللي على الصورة هذه", "tokens": [6027, 7649, 3714, 2288, 3794, 9957, 1829, 4724, 23557, 32640, 6225, 28480, 3660, 9122, 15042, 39896, 32239, 3224, 4032, 39648, 5296, 39184, 7123, 5835, 3547, 295, 264, 1254, 568, 281, 264, 272, 3175, 502, 689, 272, 307, 5835, 366, 1219, 376, 433, 3812, 2114, 1532, 37495, 22653, 16247, 22488, 18513, 13672, 1829, 15844, 31767, 13063, 3660, 29538], "avg_logprob": -0.39035560807277414, "compression_ratio": 1.3016759776536313, "no_speech_prob": 0.0, "words": [{"start": 1403.83, "end": 1404.59, "word": "الان", "probability": 0.733642578125}, {"start": 1404.59, "end": 1405.35, "word": " مرسيني", "probability": 0.649609375}, {"start": 1405.35, "end": 1405.79, "word": " برايم", "probability": 0.6419270833333334}, {"start": 1405.79, "end": 1407.17, "word": " عرفة", "probability": 0.6285807291666666}, {"start": 1407.17, "end": 1407.41, "word": " 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1554.76, "word": " nearly", "probability": 0.95263671875}, {"start": 1554.76, "end": 1555.28, "word": " 17", "probability": 0.923828125}, {"start": 1555.28, "end": 1555.72, "word": " million", "probability": 0.568359375}, {"start": 1555.72, "end": 1556.16, "word": " decimal", "probability": 0.96142578125}, {"start": 1556.16, "end": 1556.88, "word": " digits", "probability": 0.95703125}], "temperature": 1.0}, {"id": 73, "seek": 157973, "start": 1557.43, "end": 1579.73, "text": "الان ليش الاعداد هذه احنا بندور على اعداد الاولية الكبيرة الاعداد الاولية الكبيرة يا جماعة هذه تستخدم في اللي هي نظرية الترميز اللي لو أسعفنا الوجد هناخد مقدمة عنها طيب الان عملية إنتاج اللي هو primes يعني بدنا ننتج primes", "tokens": [6027, 7649, 32239, 8592, 42963, 22488, 18513, 29538, 1975, 5016, 8315, 44945, 3215, 13063, 15844, 1975, 22488, 18513, 42963, 12610, 10632, 33251, 3555, 48923, 42963, 22488, 18513, 42963, 12610, 10632, 33251, 3555, 48923, 35186, 10874, 15042, 27884, 29538, 6055, 14851, 9778, 40448, 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0.96337890625}, {"start": 1564.89, "end": 1565.21, "word": " اللي", "probability": 0.826904296875}, {"start": 1565.21, "end": 1565.63, "word": " هي", "probability": 0.91357421875}, {"start": 1565.63, "end": 1566.87, "word": " نظرية", "probability": 0.8858642578125}, {"start": 1566.87, "end": 1567.61, "word": " الترميز", "probability": 0.94521484375}, {"start": 1567.61, "end": 1568.31, "word": " اللي", "probability": 0.948974609375}, {"start": 1568.31, "end": 1568.55, "word": " لو", "probability": 0.9931640625}, {"start": 1568.55, "end": 1569.09, "word": " أسعفنا", "probability": 0.82060546875}, {"start": 1569.09, "end": 1569.49, "word": " الوجد", "probability": 0.7513020833333334}, {"start": 1569.49, "end": 1570.67, "word": " هناخد", "probability": 0.914306640625}, {"start": 1570.67, "end": 1571.71, "word": " مقدمة", "probability": 0.9801432291666666}, {"start": 1571.71, "end": 1572.37, "word": " عنها", "probability": 0.991455078125}, {"start": 1572.37, "end": 1573.97, "word": " طيب", 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عملية إيجاد اللي هي الـprimes اللي بتكون very large الناس يعني خلنا نقول بتبحث فيها لأنها بتلزمهم لكن الأمور مش دايما بهذه السهولة الان بس يعني خلنا نقول مثلا finding large primes with hundreds of digits is important and كربوتографي زي ما قلنا في الترميز اللي هو مهم", "tokens": [11622, 1829, 19446, 12174, 1211, 8315, 8978, 13672, 1829, 31439, 6225, 42213, 10632, 11933, 1829, 7435, 18513, 13672, 1829, 39896, 2423, 39184, 1424, 1532, 13672, 1829, 39894, 30544, 588, 2416, 2423, 8315, 3794, 37495, 22653, 16490, 1211, 8315, 8717, 39648, 39894, 49628, 12984, 8978, 11296, 5296, 33456, 11296, 39894, 1211, 11622, 2304, 16095, 44381, 16247, 2304, 13063, 37893, 11778, 47302, 15042, 39627, 24192, 21136, 3224, 12610, 3660, 2423, 7649, 4724, 3794, 37495, 22653, 16490, 1211, 8315, 8717, 39648, 50113, 15040, 5006, 2416, 582, 1532, 365, 6779, 295, 27011, 307, 1021, 293, 9122, 25513, 35473, 29046, 1829, 30767, 1829, 19446, 12174, 1211, 8315, 8978, 16712, 2288, 2304, 1829, 11622, 13672, 1829, 31439, 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"text": "لأن السفر كل الدنيا بتقسمه، فلمّا نتحدث عن العوام المشتركة بينهم لأن كل أعداد الدنيا العوام المشتركة بين السفر والسفر عشان هيك ما يوجد حاجة اسمها greatest common divisor أو عوام مشتركة أعلى بين السفر والسفر عشان هيك فرضين احنا A وB اللي هي ليس الواحد منهم على الأقل مش سفر The largest integer D such that D بتقسم A وD بتقسم B is called the greatest common divisor of A and B", "tokens": [1211, 33456, 21136, 5172, 2288, 28242, 32748, 22653, 995, 39894, 4587, 38251, 3224, 12399, 6156, 19528, 11703, 995, 8717, 2655, 24401, 12984, 18871, 18863, 2407, 10943, 9673, 8592, 2655, 31747, 3660, 49374, 16095, 5296, 33456, 28242, 5551, 22488, 18513, 32748, 22653, 995, 18863, 2407, 10943, 9673, 8592, 2655, 31747, 3660, 49374, 21136, 5172, 2288, 16070, 3794, 5172, 2288, 6225, 8592, 7649, 39896, 4117, 19446, 7251, 29245, 3215, 11331, 26108, 3660, 24525, 2304, 11296, 6636, 2689, 25974, 284, 34051, 6225, 2407, 10943, 37893, 2655, 31747, 3660, 5551, 3615, 23942, 49374, 21136, 5172, 2288, 16070, 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"word": " the", "probability": 0.76416015625}, {"start": 1769.43, "end": 1769.77, "word": " greatest", "probability": 0.921875}, {"start": 1769.77, "end": 1770.11, "word": " common", "probability": 0.90234375}, {"start": 1770.11, "end": 1770.65, "word": " divisor", "probability": 0.962890625}, {"start": 1770.65, "end": 1770.79, "word": " of", "probability": 0.97021484375}, {"start": 1770.79, "end": 1770.93, "word": " A", "probability": 0.9873046875}, {"start": 1770.93, "end": 1771.11, "word": " and", "probability": 0.8134765625}, {"start": 1771.11, "end": 1771.31, "word": " B", "probability": 0.99560546875}], "temperature": 1.0}, {"id": 82, "seek": 179521, "start": 1771.79, "end": 1795.21, "text": "يعني أكبر عامل مشترك يعني بيجسم اللي هو الـ A و الـ B بنسميه greatest common divisor يعني باجي لقاسم العدد A و لقاسم العدد B و بشوف القاسم المشتركة بينهم أكبر واحد في القاسم المشتركة هو اللي بسميه greatest common divisor و برمزله بالرمز greatest common divisor A و B", "tokens": [40228, 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2025.28, "end": 2025.86, "word": " الأسئلة", "probability": 0.9361572265625}, {"start": 2025.86, "end": 2026.46, "word": " ستكون", "probability": 0.6617838541666666}, {"start": 2026.46, "end": 2026.84, "word": " معكم", "probability": 0.5177001953125}, {"start": 2026.84, "end": 2027.2, "word": " homework", "probability": 0.75}, {"start": 2027.2, "end": 2027.6, "word": " من", "probability": 0.693359375}, {"start": 2027.6, "end": 2027.88, "word": " ضمن", "probability": 0.956298828125}, {"start": 2027.88, "end": 2028.5, "word": " أنك", "probability": 0.341064453125}, {"start": 2028.5, "end": 2029.48, "word": " تبحث", "probability": 0.658203125}, {"start": 2029.48, "end": 2030.0, "word": " عن", "probability": 0.802734375}, {"start": 2030.0, "end": 2030.34, "word": " الـ20", "probability": 0.4439290364583333}, {"start": 2030.34, "end": 2030.5, "word": " و", "probability": 0.38330078125}, {"start": 2030.5, "end": 2030.8, "word": " 37", "probability": 0.4267578125}, {"start": 2030.8, "end": 2031.16, "word": " و", "probability": 0.82958984375}, {"start": 2031.16, "end": 2031.46, "word": " 91", "probability": 0.96484375}, {"start": 2031.46, "end": 2032.32, "word": " relative", "probability": 0.51123046875}, {"start": 2032.32, "end": 2032.8, "word": " prime", "probability": 0.80419921875}, {"start": 2032.8, "end": 2033.0, "word": " and", "probability": 0.2342529296875}, {"start": 2033.0, "end": 2033.2, "word": " pairs", "probability": 0.88720703125}, {"start": 2033.2, "end": 2033.32, "word": " و", "probability": 0.1636962890625}, {"start": 2033.32, "end": 2033.42, "word": " لا", "probability": 0.97607421875}, {"start": 2033.42, "end": 2033.64, "word": " لأ", "probability": 0.650146484375}, {"start": 2033.64, "end": 2033.8, "word": " يعني", "probability": 0.71435546875}, {"start": 2033.8, "end": 2034.08, "word": " تبحث", "probability": 0.7815755208333334}, {"start": 2034.08, "end": 2034.12, "word": " عن", "probability": 0.95458984375}, {"start": 2034.12, "end": 2034.38, "word": " الـ20", "probability": 0.74560546875}, {"start": 2034.38, "end": 2034.52, "word": " و", "probability": 0.9794921875}, {"start": 2034.52, "end": 2034.84, "word": " 37", "probability": 0.9404296875}, {"start": 2034.84, "end": 2035.8, "word": " ما", "probability": 0.1239013671875}, {"start": 2035.8, "end": 2035.88, "word": " هي", "probability": 0.301513671875}, {"start": 2035.88, "end": 2036.04, "word": " العامة", "probability": 0.7420247395833334}, {"start": 2036.04, "end": 2036.46, "word": " المشتركة", "probability": 0.9751953125}, {"start": 2036.46, "end": 2036.74, "word": " الأعلى", "probability": 0.9835611979166666}, {"start": 2036.74, "end": 2036.88, "word": " و", "probability": 0.73193359375}, {"start": 2036.88, "end": 2037.1, "word": " هذه", "probability": 0.276123046875}, {"start": 2037.1, "end": 2037.28, "word": " ما", "probability": 0.7705078125}, {"start": 2037.28, "end": 2037.28, "word": " هي", "probability": 0.9345703125}, {"start": 2037.28, "end": 2037.44, "word": " العامة", "probability": 0.9689127604166666}, {"start": 2037.44, "end": 2037.88, "word": " المشتركة", "probability": 0.9888671875}, {"start": 2037.88, "end": 2038.28, "word": " الأعلى", "probability": 0.9925130208333334}, {"start": 2038.28, "end": 2038.72, "word": " و", "probability": 0.8896484375}, {"start": 2038.72, "end": 2038.92, "word": " بين", "probability": 0.80029296875}, {"start": 2038.92, "end": 2039.18, "word": " هذه", "probability": 0.830078125}, {"start": 2039.18, "end": 2039.26, "word": " و", "probability": 0.86767578125}, {"start": 2039.26, "end": 2039.44, "word": " هذه", "probability": 0.8427734375}, {"start": 2039.44, "end": 2039.6, "word": " ما", "probability": 0.90576171875}, {"start": 2039.6, "end": 2039.6, "word": " هي", "probability": 0.845703125}, {"start": 2039.6, "end": 2039.78, "word": " العامة", "probability": 0.9772135416666666}, {"start": 2039.78, "end": 2040.2, "word": " المشتركة", "probability": 0.99521484375}, {"start": 2040.2, "end": 2040.44, "word": " الأعلى", "probability": 0.9842122395833334}, {"start": 2040.44, "end": 2040.68, "word": " إذا", "probability": 0.886962890625}, {"start": 2040.68, "end": 2040.88, "word": " كان", "probability": 0.951171875}, {"start": 2040.88, "end": 2041.3, "word": " كلهم", "probability": 0.63623046875}, {"start": 2041.3, "end": 2041.62, "word": " العامة", "probability": 0.9475911458333334}, {"start": 2041.62, "end": 2042.1, "word": " المشتركة", "probability": 0.99541015625}, {"start": 2042.1, "end": 2042.38, "word": " الأعلى", "probability": 0.9842122395833334}, {"start": 2042.38, "end": 2042.8, "word": " بينهم", "probability": 0.8623046875}, {"start": 2042.8, "end": 2043.0, "word": " in", "probability": 0.241943359375}, {"start": 2043.0, "end": 2043.22, "word": " pairs", "probability": 0.935546875}, {"start": 2043.22, "end": 2043.54, "word": " واحد", "probability": 0.965087890625}, {"start": 2043.54, "end": 2043.84, "word": " بنقول", "probability": 0.58087158203125}, {"start": 2043.84, "end": 2044.16, "word": " relative", "probability": 0.485595703125}, {"start": 2044.16, "end": 2044.56, "word": " prime", "probability": 0.95458984375}, {"start": 2044.56, "end": 2044.72, "word": " and", "probability": 0.875}, {"start": 2044.72, "end": 2044.96, "word": " pairs", "probability": 0.8984375}, {"start": 2044.96, "end": 2045.66, "word": " إذا", "probability": 0.95458984375}, {"start": 2045.66, "end": 2045.92, "word": " لأ", "probability": 0.837158203125}, {"start": 2045.92, "end": 2046.54, "word": " بنقول", "probability": 0.882568359375}, {"start": 2046.54, "end": 2047.1, "word": " are", "probability": 0.79736328125}, {"start": 2047.1, "end": 2047.4, "word": " not", "probability": 0.962890625}, {"start": 2047.4, "end": 2047.82, "word": " relatively", "probability": 0.469482421875}, {"start": 2047.82, "end": 2048.2, "word": " prime", "probability": 0.9228515625}, {"start": 2048.2, "end": 2048.42, "word": " and", "probability": 0.95263671875}, {"start": 2048.42, "end": 2048.66, "word": " pairs", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 95, "seek": 205376, "start": 2048.86, "end": 2053.76, "text": "و السلام عليكم و رحمة الله و بركاته هذا ال homework طبعا تسلموا ليها", "tokens": [2407, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 4032, 4724, 31747, 9307, 3224, 23758, 2423, 14578, 23032, 3555, 3615, 995, 6055, 3794, 19528, 14407, 32239, 11296], "avg_logprob": -0.18345904966880536, "compression_ratio": 1.2234042553191489, "no_speech_prob": 0.0, "words": [{"start": 2048.86, "end": 2049.22, "word": "و", "probability": 0.79296875}, {"start": 2049.22, "end": 2049.56, "word": " السلام", "probability": 0.892822265625}, {"start": 2049.56, "end": 2050.0, "word": " عليكم", "probability": 0.94970703125}, {"start": 2050.0, "end": 2050.12, "word": " و", "probability": 0.9775390625}, {"start": 2050.12, "end": 2050.4, "word": " رحمة", "probability": 0.8380533854166666}, {"start": 2050.4, "end": 2050.58, "word": " الله", "probability": 0.96435546875}, {"start": 2050.58, "end": 2050.72, "word": " و", "probability": 0.98388671875}, {"start": 2050.72, "end": 2051.26, "word": " بركاته", "probability": 0.8724365234375}, {"start": 2051.26, "end": 2051.6, "word": " هذا", "probability": 0.611328125}, {"start": 2051.6, "end": 2051.84, "word": " ال", "probability": 0.91552734375}, {"start": 2051.84, "end": 2052.16, "word": " homework", "probability": 0.71826171875}, {"start": 2052.16, "end": 2052.76, "word": " طبعا", "probability": 0.9256591796875}, {"start": 2052.76, "end": 2053.5, "word": " تسلموا", "probability": 0.76171875}, {"start": 2053.5, "end": 2053.76, "word": " ليها", "probability": 0.7109375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2057.89175, "duration_after_vad": 2029.9349999999945}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e057d5fb099def18b7571c8ca97a8e6d25965978
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s.srt
@@ -0,0 +1,2371 @@
+1
+00:00:00,760 --> 00:00:05,260
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثامنة
+
+2
+00:00:05,260 --> 00:00:10,040
+مساق رياضيات منفصلة طلاب وطالبات الجامعة
+
+3
+00:00:10,040 --> 00:00:15,020
+الإسلامية قسم الحوسبة المتنقلة كلية العلوم وكلية
+
+4
+00:00:15,020 --> 00:00:19,240
+تكنولوجيا المعلومات المحاضرة اليوم إن شاء الله 
+
+5
+00:00:19,240 --> 00:00:23,460
+هنحكي عن اللي هو Section 4.4 اللي هو solving
+
+6
+00:00:23,460 --> 00:00:29,770
+congruences أو حل التطابقات هنحل .. هنحكي عن شغلتين
+
+7
+00:00:29,770 --> 00:00:34,150
+في حل التطابقات أول شيء حل تطابق خطية لحالها و
+
+8
+00:00:34,150 --> 00:00:38,810
+بعدين حل system of linear congruences أو اللي هي
+
+9
+00:00:38,810 --> 00:00:44,590
+تطابقات آنية في آن واحد لمجموعة من التطابقات و
+
+10
+00:00:44,590 --> 00:00:48,200
+هنشوف كيف اللي هو نستخدم ال chinese remainder
+
+11
+00:00:48,200 --> 00:00:53,500
+theorem والـ back substitution method يعني 
+
+12
+00:00:53,500 --> 00:00:58,260
+طريقتين هنحل فيهم التطابقات الأنية في البداية
+
+13
+00:00:58,260 --> 00:01:02,380
+خليني نتعرف شو معناه الـ Linear congruences
+
+14
+00:01:02,380 --> 00:01:06,660
+congruences شيء مشابه لللي هي الـ Linear equations
+
+15
+00:01:06,660 --> 00:01:11,080
+ولكن بتظهر بدل علامة المساواة بتظهر علامة اللي 
+
+16
+00:01:11,080 --> 00:01:15,180
+هي التطابق وبتظهر اللي هو المقياس بالضبط ايش
+
+17
+00:01:15,180 --> 00:01:19,040
+بنقول؟ بنقول a congruence of the form اللي هي Ax
+
+18
+00:01:19,040 --> 00:01:22,960
+طابق B modulo M هذه اللي هي بنسميها Linear
+
+19
+00:01:22,960 --> 00:01:27,800
+congruences لأن X عبارة عن أس واحد وعندي الـ a والـ
+
+20
+00:01:27,800 --> 00:01:31,500
+b بتكون أعداد معطية والـ m عدد معطي والمطلوب اللي
+
+21
+00:01:31,500 --> 00:01:35,840
+هو إيجاد قيمة المجهول x هذه بنسميها اللي هي linear
+
+22
+00:01:35,840 --> 00:01:40,760
+congruences حل الـ linear congruences هو كما يلي
+
+23
+00:01:40,760 --> 00:01:45,660
+اللي هو بنقصد في حل الـ congruence ax طابق b
+
+24
+00:01:45,660 --> 00:01:49,520
+modulo m هي إيجاد كل قيم x اللي هي بتحقق اللي هي
+
+25
+00:01:49,520 --> 00:01:54,050
+التطابق اللي عندي الآن قبل ما نشوف كيف نحل 
+
+26
+00:01:54,050 --> 00:01:58,750
+التطابقات الخطية خلينا نتطلع بس على شغلة اللي هي
+
+27
+00:01:58,750 --> 00:02:03,490
+بتلزمنا في حل التطابقات اللي هو بنقول عن an
+
+28
+00:02:03,490 --> 00:02:08,010
+integer a bar such that a bar في a طابق الواحد
+
+29
+00:02:08,010 --> 00:02:12,070
+modulo m بنسمي في هذه الحالة اللي هو الـ a bar هو
+
+30
+00:02:12,070 --> 00:02:17,080
+عبارة عن الـ inverse للـ a modulo m إذاً العدد اللي
+
+31
+00:02:17,080 --> 00:02:21,140
+بنجيبه لما نضربه في الـ A يطابق الواحد modulo M
+
+32
+00:02:21,140 --> 00:02:26,140
+بنقول عنه هذا A bar اللي هو عبارة عن الـ inverse للـ
+
+33
+00:02:26,140 --> 00:02:30,680
+A الـ inverse of A modulo M خلينا نتطلع على مثال
+
+34
+00:02:30,680 --> 00:02:35,460
+بسيط الآن بقول لي عندي خمسة هي inverse of تلاتة 
+
+35
+00:02:35,460 --> 00:02:40,430
+modulo سبعة الخمسة هي inverse للتلاتة modulo سبعة
+
+36
+00:02:40,430 --> 00:02:44,630
+يعني الخمسة معكوس التلاتة بالنسبة للمقياس السبعة
+
+37
+00:02:44,630 --> 00:02:48,730
+لأن لو ضربنا الخمسة في التلاتة بخمستعش الخمستعش
+
+38
+00:02:48,730 --> 00:02:52,990
+دائماً طابق الواحد modulo سبعة عارفين ايش معنى تطابق
+
+39
+00:02:52,990 --> 00:02:57,050
+الواحد modulo سبعة يعني الخمستعش لو شيلنا مضاعفات
+
+40
+00:02:57,050 --> 00:03:01,340
+السبعة منها هنلاقي بضل المتبقي بس واحد ماشي الحل
+
+41
+00:03:01,340 --> 00:03:07,040
+فعشان يكون 15 طابق الواحد modulo سبعة الآن عند الـ
+
+42
+00:03:07,040 --> 00:03:11,820
+linear congruencies هتنستخدمها هنستخدم في إيجاد 
+
+43
+00:03:11,820 --> 00:03:16,240
+قيمة الـ X فيها اللي هو الـ inverse تبع العنصر
+
+44
+00:03:16,240 --> 00:03:21,400
+هنستعين فيه لإيجاد اللي هو الحل في الأول خلينا
+
+45
+00:03:21,400 --> 00:03:25,580
+نشوف هالنظرية اللي بتشرّع لنا اللي هو اللي هي إن
+
+46
+00:03:25,580 --> 00:03:31,860
+يكون فيه الـ congruence حل أو اللي مالهاش بس قبل ما
+
+47
+00:03:31,860 --> 00:03:37,980
+ناخد نظرية بتشرّع لنا إن العدد له اللي هو inverse
+
+48
+00:03:37,980 --> 00:03:42,080
+ولا مالقوش تقولنا نظرية if a and m are relatively
+
+49
+00:03:42,080 --> 00:03:47,630
+prime integers إذا كان الـ a والـ m العدد ومقياسه
+
+50
+00:03:47,630 --> 00:03:51,050
+are relatively prime integers and M أكبر من واحد
+
+51
+00:03:51,050 --> 00:03:55,350
+then an inverse of A modulo M exists يعني دائماً 
+
+52
+00:03:55,350 --> 00:03:58,510
+دوم لما يكون العامل المشترك بين الـ A والـ M
+
+53
+00:03:58,510 --> 00:04:02,050
+بساوي واحد بتضمن وجود اللي هو inverse للـ A
+
+54
+00:04:02,050 --> 00:04:08,160
+modulo M ماشي الحال خلينا نشوف مثالنا هنا
+
+55
+00:04:08,160 --> 00:04:11,220
+الخمسة
+
+56
+00:04:11,220 --> 00:04:14,980
+is an inverse of تلاتة modulo M modulo السبعة هذه
+
+57
+00:04:14,980 --> 00:04:20,620
+وجدناها احنا قبل شوية نلاحظ إن اللي هو الخمسة والـ
+
+58
+00:04:20,620 --> 00:04:25,840
+لي هي التلاتة اللي بدنا نوجد لها inverse هي
+
+59
+00:04:25,840 --> 00:04:31,020
+والسبعة ايه شمالها relatively prime الآن this
+
+60
+00:04:31,020 --> 00:04:38,040
+اللي هو inverse is unique unique بس ايه شماله؟
+
+61
+00:04:38,040 --> 00:04:41,400
+modulo سبعة يعني وحيد بالنسبة لمقياس سبعة، ايش يعني؟
+
+62
+00:04:41,570 --> 00:04:46,150
+يعني اللي هو من واحد لعند سبعة مافيش غير inverse
+
+63
+00:04:46,150 --> 00:04:50,130
+واحد للتلاتة modulo اللي هو سبعة اللي هو مين لجناه
+
+64
+00:04:50,130 --> 00:04:55,250
+خمسة لكن في غيره بعد السبعة كل الأعداد اللي هي لما
+
+65
+00:04:55,250 --> 00:05:00,290
+نضيف لها نضيف مضاعفات السبعة على الخمسة بتطلع برضه
+
+66
+00:05:00,290 --> 00:05:04,470
+ايش عبارة عن inverse ايش يعني؟ يعني الخمسة لجناه
+
+67
+00:05:04,470 --> 00:05:09,120
+اللي هو inverse للتلاتة modulo سبعة الآن لو ضفنا على
+
+68
+00:05:09,120 --> 00:05:12,100
+السبعة الخمسة كمان سبعة بصير اتناشر برضه inverse
+
+69
+00:05:12,100 --> 00:05:16,220
+للتلاتة التسعة اتعش برضه inverse للتلاتة لو طرحنا
+
+70
+00:05:16,220 --> 00:05:19,700
+سبعة من الخمسة نقص اتنين برضه inverse لمين للتلاتة
+
+71
+00:05:19,700 --> 00:05:26,310
+modulo سبعة إذا نقصد احنا الـ uniqueness بعنوان هذا
+
+72
+00:05:26,310 --> 00:05:28,750
+يعني أنه يوجد inverse واحد  
+
+73
+00:05:28,750 --> 00:05:35,590
+A bar أقل من M وهو inverse لـ A modulo M وكل inverse آخر
+
+74
+00:05:35,590 --> 00:05:44,910
+لـ A modulo M بيكون طابق لـ A bar modulo M الـ 12 والـ نقص 2
+
+75
+00:05:44,910 --> 00:05:50,970
+والـ 19 وكل هذول برضه بيكونوا inverse للتلاتة
+
+76
+00:05:50,970 --> 00:05:55,630
+modulo 7 لأن اللي هنا كلهم بطابقوا من الخمسة اللي
+
+77
+00:05:55,630 --> 00:05:57,490
+لجيناها modulo 7
+
+78
+00:06:03,840 --> 00:06:08,520
+طيب شوف خلونا نجد كيف نجد الـ inverse اللي هو للعدد
+
+79
+00:06:08,520 --> 00:06:13,360
+لأي عدد بدنا إياه بالنسبة لقياس معين الـ Euclidean
+
+80
+00:06:13,360 --> 00:06:15,760
+algorithm اللي هي خوارزمية القسمة الأوروبية
+
+81
+00:06:15,760 --> 00:06:19,400
+coefficients اللي هو بتعطينا gives us a systematic
+
+82
+00:06:19,400 --> 00:06:24,120
+approach to find اللي هو ايش to find inverse كيف؟
+
+83
+00:06:24,290 --> 00:06:27,810
+اللي هو .. اللي هو كمالي ابني يجيب .. يطلب إن هو
+
+84
+00:06:27,810 --> 00:06:31,650
+فيلم تلقى find an inverse of 3 modulo 7 العدد
+
+85
+00:06:31,650 --> 00:06:36,250
+عشان إن صغير سهل إن نعملهم .. نوددهم زي قبل ما
+
+86
+00:06:36,250 --> 00:06:40,510
+شوية بالتحذير أو كده بس ما ينفعش بالتحذير الآن بدنا
+
+87
+00:06:40,510 --> 00:06:43,470
+نودي الطريقة .. نلاقي طريقة لإيجادها الطريقة عن
+
+88
+00:06:43,470 --> 00:06:46,050
+طريقة الـ Euclidean القسمة أول حاجة نعمل مشترك اللي
+
+89
+00:06:46,050 --> 00:06:49,440
+على بين 3 و 7 بيساوي واحد إذا مضمون من النظرية اللي
+
+90
+00:06:49,440 --> 00:06:52,620
+هي واحد إن نلاقي inverse للتلاتة modulo منين سبعة
+
+91
+00:06:52,620 --> 00:06:55,940
+يعني الـ inverse modulo of تلاتة modulo سبعة exist
+
+92
+00:06:55,940 --> 00:06:59,920
+always خلينا نشوف كيف بدنا نوجده الآن بتيجي السبعة
+
+93
+00:06:59,920 --> 00:07:02,140
+بتيجي اسمها التلاتة سبعة بيساوي 2 في تلاتة 
+
+94
+00:07:02,140 --> 00:07:06,860
+والمتبقي ايش واحد الآن جهزة الآن الواحد هو عبارة
+
+95
+00:07:06,860 --> 00:07:10,800
+عن العامل المشترك الأعلى بين التلاتة والسبعة هذا
+
+96
+00:07:10,800 --> 00:07:14,130
+عارفينه احنا من قبل اللي هي الطريقة الآن واحد بقت
+
+97
+00:07:14,130 --> 00:07:16,550
+وع صورة Linear combination من التنين اللي هي
+
+98
+00:07:16,550 --> 00:07:19,950
+بيزوتز كوفيه عن طريق اللي هو ايه اللي هي بيزوتز
+
+99
+00:07:19,950 --> 00:07:23,430
+كوفيه coefficients بيصير عند الواحد بيساوي بنجلها
+
+100
+00:07:23,430 --> 00:07:26,950
+ده بيصير نقص اتنين في تلاتة زائد واحد في سبعة الآن
+
+101
+00:07:26,950 --> 00:07:30,310
+أنا مين اللي بده اوجدله اللي هو الـ inverse التلاتة
+
+102
+00:07:30,310 --> 00:07:35,110
+modulo مين modulo السبعة معامل التلاتة في هذا الـ
+
+103
+00:07:35,110 --> 00:07:38,990
+linear combination اللي هو نقص اتنين هو اللي هيطلع
+
+104
+00:07:38,990 --> 00:07:45,830
+لنا اللي هو مين الإنفرس المطلوب and see that نقص
+
+105
+00:07:45,830 --> 00:07:49,310
+اتنين and واحد هي الـ Bezout coefficients اللي
+
+106
+00:07:49,310 --> 00:07:54,530
+معامل التلاتة هو عبارة عن نقص اتنين هو اللي هيكون
+
+107
+00:07:54,530 --> 00:07:59,170
+inverse of تلاتة modulo مين modulo سبعة إذا الأمر سهل 
+
+108
+00:07:59,170 --> 00:08:04,530
+عشان نوجد الـ inverse بس بنيجي اللي هو بنكتب الـ ..
+
+109
+00:08:04,530 --> 00:08:07,970
+بناخد .. بنكتب الـ .. الواحد اللي هو المشترك الأعلى
+
+110
+00:08:07,970 --> 00:08:11,480
+بينهمأزالينا الـ combination بين التلاتة والسبعة
+
+111
+00:08:11,480 --> 00:08:15,260
+كيف هذا بطريقة اللي هو الـ division algorithm اللي
+
+112
+00:08:15,260 --> 00:08:21,160
+اتعلمناها وبكون معامل اللي هو التلاتة هو عبارة عن
+
+113
+00:08:21,160 --> 00:08:26,750
+الـ inverse للتلاتة modulo السبعة الآن اللي جينا نقص
+
+114
+00:08:26,750 --> 00:08:30,530
+اتنين إذا بلاقي البجيهات كلها اللي بدك تضيف على
+
+115
+00:08:30,530 --> 00:08:34,190
+السبعة على نقص اتنين سبعة بيطلع الخمسة اضيف عليه
+
+116
+00:08:34,190 --> 00:08:37,370
+كمان سبعة بيطلع اتناشر اضيف عليه كمان سبعة بيطلع
+
+117
+00:08:37,370 --> 00:08:41,730
+تسعة عشر لو طرحت منه سبعة بيطلع نقص تسعة كل هذول
+
+118
+00:08:41,860 --> 00:08:47,860
+هو عبارة عن Inverses اللي هي التلاتة modulo سبعة
+
+119
+00:08:47,860 --> 00:08:52,680
+لكن واحد منهم الـ unique هو الخمسة اللي من الواحد
+
+120
+00:08:52,680 --> 00:08:57,400
+لعند مين لعند السبعة زي ما حكينا قبل شوية الآن
+
+121
+00:08:57,400 --> 00:09:02,510
+ناخد مثال على أعداد كبيرة نشوف كيف نوجده ناخد
+
+122
+00:09:02,510 --> 00:09:06,150
+المثال الثاني هذا find an inverse of 101 modulo
+
+123
+00:09:06,150 --> 00:09:12,370
+4620 نشوف الآن ايش اللي بنسويه الطريقة كمالي
+
+124
+00:09:12,370 --> 00:09:17,930
+باجي بقسم هذا على 101 بطريقة الـ Euclidean اللي هو الـ division
+
+125
+00:09:17,930 --> 00:09:22,550
+algorithm لما أصل في الآخر للمتبقي صفر بيكون أول
+
+126
+00:09:22,550 --> 00:09:25,870
+واحد قبل المتبقي صفر هو الـ greatest common divisor
+
+127
+00:09:25,870 --> 00:09:29,520
+زي ما قلنا قبل هيك، بنّه بتجيب اللي هو الـ grades
+
+128
+00:09:29,520 --> 00:09:32,540
+common divisor as a linear combination of الاثنين
+
+129
+00:09:32,540 --> 00:09:36,680
+وبكون المعامل الـ 101 هو الـ inverse المطلوب، خلّينا 
+
+130
+00:09:36,680 --> 00:09:40,540
+نشوف الكلام هذا عمليًا الآن، أولًا استخدم الـ
+
+131
+00:09:40,540 --> 00:09:43,480
+Euclidean algorithm to show that الـ greatest common divisor
+
+132
+00:09:43,480 --> 00:09:46,860
+بين هذول العددين بيساوي واحد، ايش بنسوي؟ بنقسم هذا
+
+133
+00:09:46,860 --> 00:09:53,160
+على هذا، جسمنا على 101، حصل قسم 45، المتبقي 75، باجي جسم
+
+134
+00:09:53,160 --> 00:10:00,220
+101 على 75، بيطلع المتبقي 26، بعاود الـ 75 بنفس الطريقة
+
+135
+00:10:00,220 --> 00:10:05,500
+على الـ 26، بيطلع المتبقي 23، الـ 26 مع الـ 23، بضل المتبقي
+
+136
+00:10:05,500 --> 00:10:09,260
+3، الـ 23 مع الـ 3، بضل المتبقي 2، هذا عارفين، عشان هيك
+
+137
+00:10:09,260 --> 00:10:12,910
+أنا من السرعة، اللي هي التلاتة مع الاتنين، بطلع 
+
+138
+00:10:12,910 --> 00:10:17,250
+المتبقي واحد، الاتنين اللي هو مع اللي هو الواحد
+
+139
+00:10:17,250 --> 00:10:22,010
+اللي هو بضلّش متبقي، فبكون أول واحد قبل اللي هو ما ضلّش
+
+140
+00:10:22,010 --> 00:10:25,130
+متبقي، هو ده العام المشترك الأعلى بين العددين اللي
+
+141
+00:10:25,130 --> 00:10:29,150
+هو 4621، الآن بده
+
+142
+00:10:29,150 --> 00:10:32,470
+مش هنا، أنا مش غرضي بس أوجد العام المشترك الأعلى
+
+143
+00:10:32,470 --> 00:10:36,480
+بين الواحد، لأ، غرضي أن أكتب الواحد، بالرجوع زي ما كنا
+
+144
+00:10:36,480 --> 00:10:40,160
+نرجع قبل هيك، أزلنا الـ combination من الـ 4621
+
+145
+00:10:40,160 --> 00:10:44,200
+والـ 101، وعارفين الطريقة احنا، واحد بتساوي تلاتة ناقص
+
+146
+00:10:44,200 --> 00:10:48,900
+واحد في واحد في اتنين، الآن الاتنين هنا بجيبه من
+
+147
+00:10:48,900 --> 00:10:54,850
+هنا، بجيبه هذا ناقص هذا، وبعوّض عنهم، وبافردها الآن
+
+148
+00:10:54,850 --> 00:10:58,030
+اللي بيطلع عندي هو، 4621 ناقص 13 في 
+
+149
+00:10:58,030 --> 00:11:01,330
+8 في 3، بتجيب الآن قيمة من التلاتة، بشيل
+
+150
+00:11:01,330 --> 00:11:05,330
+التلاتة، وبجيب قيمة تهيئتها، وبنعوّضها، وبضلّ باستمر
+
+151
+00:11:05,330 --> 00:11:08,890
+كل شغل بتجيبها من اللي جابلها، لما نقصل في الآخر
+
+152
+00:11:08,890 --> 00:11:12,970
+لآخر لينا الـ combination، بيطلع واحد، بسّوء ناقص تلاتة
+
+153
+00:11:12,970 --> 00:11:16,610
+35 في 4621 زائد 1601 في 101، لاحظ أنا أنا قدرت أكتب الواحد
+
+154
+00:11:16,610 --> 00:11:21,510
+بأزالي بالـ Bézout، الـ Bézout الـ coefficient سيها مقصّ
+
+155
+00:11:21,510 --> 00:11:25,170
+35 و 1601 لـ 4621 و 101، يعني واحد لينا
+
+156
+00:11:25,170 --> 00:11:32,150
+combination من هذا ومن هذا، بيكون معامل الـ 101
+
+157
+00:11:32,150 --> 00:11:36,750
+اللي هو 1601 هو اللي is an inverse of 101 mod
+
+158
+00:11:36,750 --> 00:11:42,810
+4621، ولو جيت أنت تتأكد من كلامك، اضرب الـ 1601 في الـ
+
+159
+00:11:42,810 --> 00:11:50,670
+101، هتلاقي بيطلع الرقم هذا، هذا الرقم لو جسمته على
+
+160
+00:11:50,670 --> 00:11:55,530
+4621، هيطلع المتبقي واحد، يعني هذا يطابق الواحد mod
+
+161
+00:11:55,530 --> 00:11:58,990
+4621، إذا فعلاً هذا عبارة عن الـ inverse لهذا mod
+
+162
+00:11:58,990 --> 00:12:05,050
+4621، حسب ما عرفنا قبل بشوية، هكذا فإننا وجدنا
+
+163
+00:12:05,050 --> 00:12:11,070
+الانفرس لأعداد أو أرقام كبيرة، الآن بدنا نستخدم
+
+164
+00:12:11,070 --> 00:12:16,290
+الانفرس لإيجاد الـ linear congruences، بدنا نستخدم
+
+165
+00:12:16,290 --> 00:12:20,850
+الانفرس في إيجاد الـ linear congruences، ايش الفكرة؟
+
+166
+00:12:20,850 --> 00:12:26,210
+نشوف كيف نستخدم الانفرس في إيجاد الـ linear congruences، ايش الفكرة؟
+
+167
+00:12:26,210 --> 00:12:29,530
+نشوف كده ايش الفكرة في استخدام الانفرس، نستطيع
+
+168
+00:12:29,530 --> 00:12:32,950
+تحسين الانفرس Ax، ويطابق بـ mod By multiplying
+
+169
+00:12:32,950 --> 00:12:37,210
+both sides by A bar، الـ A bar اللي هي من الـ inverse
+
+170
+00:12:37,210 --> 00:12:41,050
+لو ضربناها من الجهتين في A bar، فبيصير A bar في A في
+
+171
+00:12:41,050 --> 00:12:46,230
+X بيساوي A bar في B، لأن A في A bar في X، الـ A في A
+
+172
+00:12:46,230 --> 00:12:49,670
+bar ما هي بطابق الواحد، يعني وكأننا بنكون شيلنا
+
+173
+00:12:49,670 --> 00:12:52,970
+الـ A في الـ A bar، وصار في عندي الواحد لحاله، يعني
+
+174
+00:12:52,970 --> 00:12:57,230
+صارت الـ X قاعدة لحالها، يعني صارت الـ X بتساوي A bar
+
+175
+00:12:57,230 --> 00:13:05,110
+في B modulo M، هي الحل، بتنشوف كيف، What are the
+
+176
+00:13:05,110 --> 00:13:07,990
+solutions of the congruence 3x يطابق 4
+
+177
+00:13:07,990 --> 00:13:09,430
+mod 7؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟يطابق
+
+178
+00:13:09,430 --> 00:13:10,390
+4 mod 7؟ يطابق
+
+179
+00:13:10,390 --> 00:13:11,290
+4 mod 7؟ يطابق
+
+180
+00:13:11,290 --> 00:13:13,050
+4 mod 7؟ يطابق
+
+181
+00:13:13,050 --> 00:13:16,630
+4 mod 7؟ يطابق
+
+182
+00:13:16,630 --> 00:13:24,030
+4 mod 7؟ يطابق
+
+183
+00:13:24,030 --> 00:13:29,440
+4، الآن واضح إنه اللي هو صار عندي الواحد هو الـ
+
+184
+00:13:29,440 --> 00:13:32,040
+greatest common divisor بين التلاتة وبين السبعة
+
+185
+00:13:32,040 --> 00:13:36,500
+وبيساوي 7 ناقص 2 في 3، يعني طلع عندي ناقص
+
+186
+00:13:36,500 --> 00:13:40,680
+2 هو الـ inverse للي هو التلاتة modulo 7
+
+187
+00:13:40,680 --> 00:13:45,560
+زي ما احنا اتعلمنا الآن، بضرب الجهتين في ناقص 3
+
+188
+00:13:45,560 --> 00:13:48,880
+اضرب هنا في ناقص 3 وهنا في ناقص 2 اللي هو
+
+189
+00:13:48,880 --> 00:13:52,330
+الـ inverse، ناقص 2 في ناقص 2 بيصير عبارة عن
+
+190
+00:13:52,330 --> 00:13:55,910
+ناقص 2 في 3 يطابق ناقص 2 في 4 mod
+
+191
+00:13:55,910 --> 00:13:59,990
+7، الآن ايش هذه عبارة عن ناقص 6 يطابق ناقص
+
+192
+00:13:59,990 --> 00:14:04,110
+8 mod 7، الـ ناقص 6 هي الواحد، هي تطابق
+
+193
+00:14:04,110 --> 00:14:07,350
+الواحد، لإنه هي ناقص 2، ناقص 3 الـ inverse وهذا
+
+194
+00:14:07,350 --> 00:14:11,480
+الفكرة أصلًا، الآن ناقص 6 يطابق الواحد mod 7، لأن
+
+195
+00:14:11,480 --> 00:14:15,140
+ناقص 6 ناقص 1 تصبح ناقص 7، السبعة تجسم ناقص
+
+196
+00:14:15,140 --> 00:14:18,660
+7، إذا فعلاً كلامنا صحيح، إذا ناقص 6 بيصير
+
+197
+00:14:18,660 --> 00:14:22,260
+مكانها اللي هي عبارة عن 1، لأن الواحد يطابق ناقص
+
+198
+00:14:22,260 --> 00:14:27,360
+6، فبيصير عند الـ X يطابق ناقص 8 mod 7
+
+199
+00:14:27,360 --> 00:14:34,500
+الآن ناقص 8 اللي هي شيله، ضفّوله 7، بيصير عندّه
+
+200
+00:14:34,500 --> 00:14:38,880
+اللي هو ناقص 1، لو ضفّنوله 7، بتصير 6، 
+
+201
+00:14:38,880 --> 00:14:42,660
+طب مش اللي بيسويه بالإضافات، بالإضافات، ما هو إضافات
+
+202
+00:14:42,660 --> 00:14:47,460
+الـ 7، أي إضافة للسبعة تطابق صفر mod 7، كيف
+
+203
+00:14:47,460 --> 00:14:50,580
+يعني؟ ايش اللي بقوله؟ ده نشوف، لإن هذه الـ ناقص
+
+204
+00:14:50,580 --> 00:14:55,800
+8 يطابق الـ 6 mod 7، ايش عرفك الـ 6؟
+
+205
+00:14:55,800 --> 00:15:00,980
+ضفت على الـ 7 على الـ ناقص، الآن ضفت اللي هي مضاعفات
+
+206
+00:15:00,980 --> 00:15:04,920
+الـ 7، 7 و 7، 14، 14 ناقص 8
+
+207
+00:15:04,920 --> 00:15:08,180
+بتطلع 6، عشان هيك طلعت 6، طب بتطلع هذا الكلام
+
+208
+00:15:08,180 --> 00:15:13,060
+صحيح؟ اه، مضمون، ليش؟ تعال، 7 بتجسم ناقص 8،
+
+209
+00:15:13,060 --> 00:15:17,120
+ناقص 6، اللي ناقص 14، الـ 7 بتجسم مين؟ ناقص
+
+210
+00:15:17,120 --> 00:15:21,720
+14، يعني دائماً دائماً لو كان عندي 3، خلينا
+
+211
+00:15:21,720 --> 00:15:26,120
+نقول 3، 3 لو ضفّنلها 7، بيصير 10، الـ 10
+
+212
+00:15:26,120 --> 00:15:30,400
+يطابق الـ 3 mod 7، اللي هو ضفّنلها كمان 7
+
+213
+00:15:30,400 --> 00:15:35,420
+اللي هي 17، و 17 يطابق الـ 3 mod
+
+214
+00:15:35,420 --> 00:15:41,990
+7، يعني دائماً يا جماعة، الآن العدد لو ضفّت له جد ما
+
+215
+00:15:41,990 --> 00:15:47,110
+ضفته من المقياس بظلّ يطابق نفسه، يعني لو كان عندنا في
+
+216
+00:15:47,110 --> 00:15:51,170
+الأصل 5، وضفّنلها 7، بيصير 12، ويطابق 5
+
+217
+00:15:51,170 --> 00:15:54,730
+وضفّنلها كمان 7، بيصير 19، ويطابق 5، ولو
+
+218
+00:15:54,730 --> 00:15:58,270
+طرحت منه 7، برضه بتظلّ المتطابقات، عشان هيك هذه
+
+219
+00:15:58,270 --> 00:16:03,930
+بتساعدنا كثير بعد شوية في حلّ المتطابقات، إذا صار
+
+220
+00:16:03,930 --> 00:16:08,810
+عند الـ X يطابق الـ 6 mod مين؟ mod 7، ومنه بيكون
+
+221
+00:16:08,810 --> 00:16:12,410
+الـ solutions are the integers اللي هي مدام x يطابق
+
+222
+00:16:12,410 --> 00:16:17,110
+الـ 6، إذا صار عند الـ 6، واللي هو ضفّله 7، اللي
+
+223
+00:16:17,110 --> 00:16:22,230
+هي 7 بيصير 6 و 7 اللي هي 13، ضفّله
+
+224
+00:16:22,230 --> 00:16:26,270
+كمان 7 بيصير اللي هو 13 و 7، 20، اطرح
+
+225
+00:16:26,270 --> 00:16:29,970
+منه 7، من الـ 6 بتطلع ناقص 1، اطرح منه كمان
+
+226
+00:16:29,970 --> 00:16:33,030
+7، ناقص 8، اطرح منه كمان 7 بيصير ناقص 15
+
+227
+00:16:33,030 --> 00:16:38,170
+إذا كل دولة اللي هنحلّ الـ x يطابق الـ 7، أو حلّ
+
+228
+00:16:38,170 --> 00:16:40,650
+الـ x يطابق الـ 6 modulo 7
+
+229
+00:16:43,670 --> 00:16:47,670
+الآن بعد شوية هتلاقيني بقى أريحكم في الحل هذا، يعني
+
+230
+00:16:47,670 --> 00:16:50,730
+بدون حتى ما نستخدم اللي هو الـ inverses وكده
+
+231
+00:16:50,730 --> 00:16:55,410
+هتلاقيني باستخدم اللي هو طريقة اللي هي بتعتمد على
+
+232
+00:16:55,410 --> 00:17:01,270
+مضاعفات السبعة، بنضيف أو نطرح، وبنخلي الـ X لحاله، و
+
+233
+00:17:01,270 --> 00:17:04,950
+الباقي هان لحاله، فبتكون الحلول سهلة بعد شوية إن
+
+234
+00:17:04,950 --> 00:17:08,450
+شاء الله، هنشوف هذه الطريقة في الـ Chinese remainder
+
+235
+00:17:08,450 --> 00:17:13,750
+theorem، اللي هو نثبت هذه الطريقة اللي أخذناها الآن
+
+236
+00:17:13,750 --> 00:17:17,510
+إن شاء الله، وبعد شوية نشوف الـ Chinese remainder
+
+237
+00:17:17,510 --> 00:17:22,010
+يعني، خلّينا نجي لـ Chinese remainder theorem، أو
+
+238
+00:17:22,010 --> 00:17:28,570
+نظرية الباقي الصينية، المشهورة في بعض المثال كانت
+
+239
+00:17:28,570 --> 00:17:34,470
+تطرح قديمًا، أحد المثال هو أحد العلماء الصينيين، Sun
+
+240
+00:17:34,470 --> 00:17:40,210
+Tzu، states the following، بيقول اللي بدي عدد اللي هو
+
+241
+00:17:40,210 --> 00:17:46,370
+يقبل القسمة على 3، والمتبقي له 2، وهو نفسه لو
+
+242
+00:17:46,370 --> 00:17:50,510
+قسمته على 5، المتبقي 3، وهو نفسه لو قسمته
+
+243
+00:17:50,510 --> 00:17:54,510
+على 7، المتبقي 2، بيقول ايش هذا العدد؟
+
+244
+00:17:54,510 --> 00:18:02,610
+الآن طبعًا اللي هو الفكرة الآن ايش هي؟ إن احنا بنحول
+
+245
+00:18:02,610 --> 00:18:08,130
+اللي هي الحديث هذا إلى تطابقات، ايش علاقة الموضوع
+
+246
+00:18:08,130 --> 00:18:13,080
+بالتطابقات؟ احنا بنقول دائماً إن العدد دائماً يطابق
+
+247
+00:18:13,080 --> 00:18:19,020
+اللي هو المتبقي له لو قسمناه على عدد ما، يعني الآن
+
+248
+00:18:19,020 --> 00:18:24,320
+لو أجينا قسمنا عدد على اللي هو 3، وكان المتبقي
+
+249
+00:18:24,320 --> 00:18:28,060
+2، معناته صار العدد يطابق الـ 2 mod 3
+
+250
+00:18:28,060 --> 00:18:33,540
+عشان هي فرضنا، نفرض إن العدد اسمه X، هذا الـ X إذا 
+
+251
+00:18:33,540 --> 00:18:38,020
+قسمته على ثلاثة  هيظل اثنان عشان هيك اختارت له
+
+252
+00:18:38,020 --> 00:18:43,280
+التطابق X تطابق اثنين مدولة ثلاثة بس هو قال طب أنا 
+
+253
+00:18:43,280 --> 00:18:48,280
+بدي العدد نفسه يقبل ما يلي أنه لو اجيت قسمته على
+
+254
+00:18:48,280 --> 00:18:53,130
+خمسة يظل المتبقي ثلاثة ما دام يقبل اللي بدك تقسمه
+
+255
+00:18:53,130 --> 00:18:57,670
+على الـ X تقسمه على خمسة و يظل ثلاثة معناته هذا الـ
+
+256
+00:18:57,670 --> 00:19:03,190
+X حيطابق المتبقي له الثلاثة مقياس مين؟ مقياس الخمسة
+
+257
+00:19:03,190 --> 00:19:07,250
+اللي قسمته عليه لأ و طلب كمان أكثر من هيك قال لأ بدي
+
+258
+00:19:07,250 --> 00:19:12,590
+نفس العدد اللي هو لو قسمته على سبعة يظل المتبقي
+
+259
+00:19:12,590 --> 00:19:18,280
+اثنان ترجمها برضه لصورة المتطابق احنا نقول الـ X
+
+260
+00:19:18,280 --> 00:19:22,340
+بيطابق المتبقي modulo المقسوم عليه اللي هو مين؟
+
+261
+00:19:22,340 --> 00:19:26,940
+السبعة عشان هيك قال اللي هي الـ X اللي أنتو
+
+262
+00:19:26,940 --> 00:19:31,580
+طلبتوها يا جماعة اللي لو قسمناها ثلاثة بيظل اثنان و
+
+263
+00:19:31,580 --> 00:19:35,300
+قسمناها خمسة بيظل ثلاثة و قسمناها سبعة بيظل اثنان
+
+264
+00:19:35,300 --> 00:19:39,240
+نحن نترجمها إلى اللي هو system of linear
+
+265
+00:19:39,240 --> 00:19:42,940
+congruences اللي هو X وطابق اثنين modulo ثلاثة X
+
+266
+00:19:42,940 --> 00:19:45,860
+وطابق الثلاثة modulo خمسة X وطابق الاثنين modulo
+
+267
+00:19:45,860 --> 00:19:50,280
+سبعة يعني X وطابق اللي هو المتبقي modulo المقسوم
+
+268
+00:19:50,280 --> 00:19:54,340
+عليه لما نقسم X على ثلاثة X تطابق اللي هو الثلاثة
+
+269
+00:19:54,340 --> 00:19:57,700
+المتبقية لما نقسم X على خمسة X تطابق اللي هي
+
+270
+00:19:57,700 --> 00:20:01,200
+المتبقي اثنان لما نقسمها على سبعة فاتحولت إلى
+
+271
+00:20:01,200 --> 00:20:05,300
+تطابقات اللي هي ده تنحل في نفس الوقت عشان هي كانت
+
+272
+00:20:05,300 --> 00:20:10,420
+نسميها system of linear congruences وهذه اللي هي
+
+273
+00:20:10,420 --> 00:20:13,560
+اللي بيحلها عادة اسمها الـ Chinese remainder
+
+274
+00:20:13,560 --> 00:20:18,100
+theorem اللي الآن احنا هندرس إيه اللي هو كيف اللي
+
+275
+00:20:18,100 --> 00:20:23,320
+هي إيش النظرية بتقول متى بيكون حل و كيف بنحل اللي
+
+276
+00:20:23,320 --> 00:20:28,860
+هو التطابقات The Chinese remainder theorem بتقول ما
+
+277
+00:20:28,860 --> 00:20:35,920
+يلي بالضبط Theorem 2 بتقول let M1, M2, Mn be
+
+278
+00:20:35,920 --> 00:20:39,240
+pairwise relatively prime positive integers
+
+279
+00:20:39,240 --> 00:20:43,620
+greater than one يعني هدول M1 و M2, Mn كلهم
+
+280
+00:20:43,620 --> 00:20:46,300
+positive integer أكبر من واحد و relatively prime
+
+281
+00:20:46,570 --> 00:20:50,510
+ونفترض a1 و a2 و aN are arbitrary integers، then
+
+282
+00:20:50,510 --> 00:20:56,310
+the system X تطابق الـ a1 a1 عدد، X تطابق الـ a2 a2
+
+283
+00:20:56,310 --> 00:21:01,050
+عدد، X تطابق الـ aN aN عدد، طبعاً هذه مدولة M1 و
+
+284
+00:21:01,050 --> 00:21:05,150
+هذه مدولة M2 ومدولة MN لو كان في عندي system of
+
+285
+00:21:05,150 --> 00:21:09,790
+linear congruences بالشكل هذا و كلهم المجهول فيهم
+
+286
+00:21:09,790 --> 00:21:15,490
+X و الـ M1 و الـ M2 و الـ MN كلهم relatively prime
+
+287
+00:21:15,490 --> 00:21:19,210
+بتقولك الـ Chinese remainder theorem إذا يوجد حل
+
+288
+00:21:19,210 --> 00:21:22,950
+مشترك وحيد لهذه المجموعات اللي هو has a unique
+
+289
+00:21:22,950 --> 00:21:29,040
+solution modulo M اللي هو Mم1 م2 في مين؟ في Mn يعني
+
+290
+00:21:29,040 --> 00:21:32,140
+بتقولك الآن اللي هي chinese remainder theorem لو
+
+291
+00:21:32,140 --> 00:21:36,580
+كان عندك فيه system من اللي هو الـ linear
+
+292
+00:21:36,580 --> 00:21:40,360
+congruences هذه تطابق أي واحد مدولة m واحد والـ X
+
+293
+00:21:40,360 --> 00:21:45,060
+تطابق اثنين مدولة m اثنين تطابق en modulo mn هذه
+
+294
+00:21:45,060 --> 00:21:50,840
+بيكون solution unique لها مدولة m بس بشرط أن m1 و
+
+295
+00:21:50,840 --> 00:21:54,820
+m2 و mn يكون in pair wise relatively prime يعني كل
+
+296
+00:21:54,820 --> 00:21:58,420
+اثنتين مع بعض العامل المشترك الأعلى بينهم بيساوي
+
+297
+00:21:58,420 --> 00:22:02,610
+واحد that is there is a solution x زي ما بقول x
+
+298
+00:22:02,610 --> 00:22:06,410
+أكبر أو يساوي صفر أو أصغر من M يعني لأنه مدولة M يعني
+
+299
+00:22:06,410 --> 00:22:10,110
+من عند الصفر لعند الـ M أو من عند الواحد لعند الـ M
+
+300
+00:22:10,110 --> 00:22:14,390
+نفسها أو من الصفر لعند الـ M ناقص واحد and all
+
+301
+00:22:14,390 --> 00:22:17,230
+other solutions are congruent مدولة M to this
+
+302
+00:22:17,230 --> 00:22:20,710
+solution يعني أي solution ثاني هتلاقيه هيلاقيه
+
+303
+00:22:20,710 --> 00:22:25,530
+اللي هو العدد اللي لاجيناه زائد اللي هو مضاعفات من
+
+304
+00:22:25,530 --> 00:22:30,780
+الـ M يعني يطابق الـ M اللي هو Modulo .. يطابق الـ ..
+
+305
+00:22:30,780 --> 00:22:37,300
+الـ .. الـ X Modulo اللي هي الـ M الآن نشوف كيف بدنا
+
+306
+00:22:37,300 --> 00:22:40,660
+نستخدم الـ Chinese remainder theorem to find a
+
+307
+00:22:40,660 --> 00:22:45,600
+solution الآن تركز معايا هذه الـ .. الـ .. الـ ..
+
+308
+00:22:45,600 --> 00:22:49,740
+التطابقات اللي موجودة عندك بدك توجد الحل المشترك
+
+309
+00:22:49,740 --> 00:22:56,320
+بينهم أولاً نسمي m واحد capital m واحد اللي هي
+
+310
+00:22:56,320 --> 00:23:01,380
+عبارة عن حاصل الضرب هذا m على m واحد m اثنين
+
+311
+00:23:01,380 --> 00:23:06,140
+capital m اثنين capital بتساوي m على m اثنين
+
+312
+00:23:06,140 --> 00:23:09,380
+small m ثلاثة capital بتساوي m على m ثلاثة
+
+313
+00:23:09,380 --> 00:23:15,400
+small وهكذا لما نخلص على كل المعادلات إذا وكأن كل
+
+314
+00:23:15,400 --> 00:23:19,780
+معادلة .. كل تطابقة من هدول بجيبلهم M و M كبيرة
+
+315
+00:23:19,780 --> 00:23:25,220
+هذا هي .. هتلزمني بعد شوية ركز فيها بعد ما سميتها
+
+316
+00:23:25,220 --> 00:23:30,700
+بدي آجي أحل التطابقة التالية التطابقة اللي هي مايا
+
+317
+00:23:30,700 --> 00:23:37,760
+ليه M1 في Y1 تطابق الواحد مدولة مين؟ M1 مين M1 هذه
+
+318
+00:23:37,760 --> 00:23:44,960
+اللي هي تبعت هذه من M1 هذه اللي قسمتها على M1 small
+
+319
+00:23:44,960 --> 00:23:50,060
+M على M1 small إذا بعد ما قسمت هذه بحل التطابقات
+
+320
+00:23:50,060 --> 00:23:53,840
+التالية طبعاً التطابقات هدولة هيكون عددهن لأن قلت
+
+321
+00:23:53,840 --> 00:23:59,320
+Mk و Yk تطابق الواحد مدولة Mk حيث اللي هي Yk مجهول
+
+322
+00:23:59,320 --> 00:24:04,450
+هو اللي بتوجد من حل هذه والـ k هذه من واحد لعند n
+
+323
+00:24:04,450 --> 00:24:09,030
+بعدد مين؟ اللي هي التطابقات اللي موجودة في الأصل
+
+324
+00:24:09,030 --> 00:24:13,430
+إذا بدي الآن الخطوة اللي بعدها بعد ما سميت الـ mk
+
+325
+00:24:13,430 --> 00:24:19,010
+بالطريقة هذه بدي أحل التطابق mk في yk mk بتكون
+
+326
+00:24:19,010 --> 00:24:23,010
+معطية عدد أو جدناه و الـ yk هو المجهول اللي بده
+
+327
+00:24:23,010 --> 00:24:27,890
+يجده تطابق الواحد modulo mk بعد ما حل التطابق هذه
+
+328
+00:24:27,890 --> 00:24:31,230
+وجد الـ yk يعني أنا بدأ أوجد الـ y1 و الـ y2 لعند الـ
+
+329
+00:24:31,230 --> 00:24:36,350
+yn بعد موجودة هنا بقول the unique solution modulo
+
+330
+00:24:36,350 --> 00:24:39,950
+m is given by إذن هذا قانون حيطلع عليه إيش؟ اللي هو
+
+331
+00:24:39,950 --> 00:24:44,790
+الـ solution x بتساوي a1 m1 a1 هذا اللي أنا ظهرته الـ
+
+332
+00:24:44,790 --> 00:24:48,530
+M1 هذه مين؟ اللي هي من هنا الـ Y1 اللي هي اللي
+
+333
+00:24:48,530 --> 00:24:51,550
+بتغلبنا هذه اللي هي الـ solution اللي هنجدها الآن
+
+334
+00:24:51,550 --> 00:24:56,790
+زائد نفس الشيء لمين؟ للمعادلة الثانية A2 اللي هي في
+
+335
+00:24:56,790 --> 00:25:00,950
+A2 هنا طيب مضروبة في M2 M2 هذه اللي جبناها من هنا
+
+336
+00:25:01,280 --> 00:25:05,180
+الـ Y2 اللي جبناها من هنا لما أصل لآخر معادلة
+
+337
+00:25:05,180 --> 00:25:11,180
+اللي هي AN في MN تبعتها في YN تبعتها اللي حليتها
+
+338
+00:25:11,180 --> 00:25:15,860
+هنا فبتطلع هذه هي الـ X اللي أمامي هي عبارة عن الـ
+
+339
+00:25:15,860 --> 00:25:21,640
+solution الـ unique solution لأ الـ system هذا كله
+
+340
+00:25:21,640 --> 00:25:27,540
+مدولة مدولة m وحاصل الضرب الكلية الآن هي الثلاثة
+
+341
+00:25:27,540 --> 00:25:32,140
+خطوات اللي بدنا نختوها من أجل حل اللي هو system of
+
+342
+00:25:32,140 --> 00:25:36,500
+linear equations تسمية mk أول شيء وبعدين نحل هذه
+
+343
+00:25:36,500 --> 00:25:40,640
+التطابقة وبعدين نعوض في هذه بيكون خلصنا اللي هو
+
+344
+00:25:40,640 --> 00:25:44,260
+حلنا اللي هو سؤال الـ Chinese remainder theorem
+
+345
+00:25:44,260 --> 00:25:50,260
+والآن نيجي إلى اللي هو مثال عملي لتطبيقه خلّيني أنا
+
+346
+00:25:50,260 --> 00:25:53,040
+أشوف مثال عملي على اللي هو chinese remainder
+
+347
+00:25:53,040 --> 00:25:57,300
+theorem بقول consider the three congruences from
+
+348
+00:25:57,300 --> 00:26:01,460
+some two problem two problem اللي قبل شوية عرضناها
+
+349
+00:26:01,460 --> 00:26:05,380
+يعني X تطابق الاثنين مدولة ثلاثة X تطابق الثلاثة
+
+350
+00:26:05,380 --> 00:26:08,960
+مدولة خمسة X تطابق الاثنين مدولة سبعة الآن هذه
+
+351
+00:26:08,960 --> 00:26:14,700
+بتمثلي A1 هذه بتمثلي A2 هذه بتمثلي A3 اللي هحتاجين
+
+352
+00:26:14,700 --> 00:26:21,680
+بعد شوية هذه M1 هذه M2 هذه M3 خلّينا نشوف الآن بدنا
+
+353
+00:26:21,680 --> 00:26:26,200
+ناخد اللي هو الـ .. الـ M اللي هي حاصل ضرب ثلاثة في
+
+354
+00:26:26,200 --> 00:26:30,000
+خمسة في سبعة mات مع بعض يعني M هذه هي ثلاثة في
+
+355
+00:26:30,000 --> 00:26:33,160
+خمسة في سبعة اللي هي مئة وخمسة منها بدنا نحسب الـ
+
+356
+00:26:33,160 --> 00:26:35,980
+M واحد capital زي ما شوفنا قبل شوية M واحد capital
+
+357
+00:26:35,980 --> 00:26:39,460
+هي عبارة عن اللي هو المئة وخمسة بنجسمها على
+
+358
+00:26:39,460 --> 00:26:43,620
+الثلاثة بيطلع جداش خمسة وثلاثين M اثنين capital
+
+359
+00:26:43,620 --> 00:26:47,340
+هذه اللي هي المئة وخمسة مجسمة على الخمسة هذه اللي
+
+360
+00:26:47,340 --> 00:26:52,610
+هي بيطلع واحد وعشرين M3 هي 105 عالية 7 اللي هنا
+
+361
+00:26:52,610 --> 00:26:58,030
+بتطلع جداش 15 الآن نيجي للخطوة المركزية المهمة لأن
+
+362
+00:26:58,030 --> 00:27:01,430
+we solve the congruences التالية بدنا نحل المين
+
+363
+00:27:01,430 --> 00:27:06,550
+اللي هو M1 Y1 تطابق الواحد مدولة M1 الآن M1 جداش
+
+364
+00:27:06,550 --> 00:27:11,550
+أودتنا هي اللي هي عبارة عن 35 يصير 35 Y1 تطابق
+
+365
+00:27:11,550 --> 00:27:17,120
+الواحد مدولة ومين؟ M1 اللي هي جداش 3 بدنا نحل هذه الآن
+
+366
+00:27:17,120 --> 00:27:20,740
+طريقة الحل هذه ماعنش نقعد ندور على اللي هو الـ
+
+367
+00:27:20,740 --> 00:27:23,740
+inverse لهذا ومش عارف إيش لأ لأ لأ أسهل لكم كثير
+
+368
+00:27:23,740 --> 00:27:27,280
+كثير كثير اللي هو إيش؟ من نيجي بنشيل من خمسة و
+
+369
+00:27:27,280 --> 00:27:32,540
+ثلاثين كل مضاعفات من الثلاثة الآن بنشيل من هذه
+
+370
+00:27:32,540 --> 00:27:35,920
+اللي هو عبارة عن مضاعفات الثلاثة أقرب شيء للثلاثة
+
+371
+00:27:35,920 --> 00:27:39,640
+خمسة وثلاثين يعني على الثلاثة بتطلع اللي هي
+
+372
+00:27:39,640 --> 00:27:45,640
+المتبقي جداش اثنان لأنه بيصير 11 والمتبقي اللي هو 2
+
+373
+00:27:45,640 --> 00:27:50,000
+يعني بقسم 35 على 3 بيطلع اللي هو عدد مدولة المتبقي
+
+374
+00:27:50,000 --> 00:27:54,080
+المتبقي هو اللي بيبقى بيبقى بيضل لأن هذا الـ 35
+
+375
+00:27:54,080 --> 00:28:00,400
+بيصير يطابق المتبقي 32 مدولة مدولة اللي هي الثلاثة 
+
+376
+00:28:00,400 --> 00:28:04,220
+ماشي الحال إذا انطلقنا من 35 مضاعفات الثلاث اللي 
+
+377
+00:28:04,220 --> 00:28:10,180
+هي 33 اللي هي بيبقى الجداد 2 بيصير 2 Y1 تطابق الآن
+
+378
+00:28:10,180 --> 00:28:14,130
+الواحد  بيصير اثنين و أي واحد وطابق الواحد بس
+
+379
+00:28:14,130 --> 00:28:19,510
+عشان أنا بتدجسم بعد شوية بدي أحول الواحد لرقم زوجي
+
+380
+00:28:19,510 --> 00:28:24,430
+ايش أحول رقم زوجي؟ واحد بطابقه الآن بضيف له ثلاثة
+
+381
+00:28:24,430 --> 00:28:28,150
+أو بطرح منه ثلاثة بيصير اللي هو عدد زوجي طب بنفع
+
+382
+00:28:28,150 --> 00:28:31,470
+آه لأن لو ضفت له ثلاثة بيصير الأربعة الأربعة بتطابق
+
+383
+00:28:31,470 --> 00:28:38,010
+الواحد مدله مين مدله ثلاثة إذا أنت لها نوّهان ضيف زي
+
+384
+00:28:38,010 --> 00:28:42,310
+ما بدك من مضاعفات الثلاث أو اطرح مضاعفات الثلاث
+
+385
+00:28:42,310 --> 00:28:46,530
+للوصول للأعداد القليلة اللي بتقدر تستخدمها زي ما
+
+386
+00:28:46,530 --> 00:28:49,530
+بدك بظل نفس ال issue متطابق
+
+387
+00:28:58,270 --> 00:29:02,990
+بينفع تجسم إذا العامل المشترك الأعلى بين اللي بده
+
+388
+00:29:02,990 --> 00:29:06,390
+يجسمه وبين الثلاث ايش بيساوي واحد وهي العامل
+
+389
+00:29:06,390 --> 00:29:09,570
+المشترك الأعلى بين الثلاث وبين الواحد بين الـ 3 و
+
+390
+00:29:09,570 --> 00:29:12,530
+بين الـ 2 و 1 إذا أنا بقول شيء سهولة بقول على 2
+
+391
+00:29:12,530 --> 00:29:17,270
+بظهر Y1 على 2 بظهر 2 فبيصير Y1 تطابق الـ 2 مدلة 3
+
+392
+00:29:17,270 --> 00:29:21,650
+هي عبارة عن حل الـ congruence هذه شايفين مثلًا حل
+
+393
+00:29:21,650 --> 00:29:24,110
+الـ linear congruence أسهل من ما نقعد نودد ال
+
+394
+00:29:24,110 --> 00:29:27,870
+inverse زي ما قلنا قبل شوية نيجي الآن نعملها مع
+
+395
+00:29:27,870 --> 00:29:32,410
+الأولى و نعملها مع التالية باجي بقول M2 في Y2
+
+396
+00:29:32,410 --> 00:29:38,480
+تطابق الواحد مدلة M2 مين M2 هيها 21Y2 مين هي
+
+397
+00:29:38,480 --> 00:29:45,260
+المجهول الآن يصبح 21 Y2 تطابق الواحد مضله مين أما 
+
+398
+00:29:45,260 --> 00:29:49,460
+2 small هي هادي هيها هادي هي بيصير مضله خمسة الآن
+
+399
+00:29:49,460 --> 00:29:54,480
+نحلها لحسن حظنا هادي أصلًا لو شيلنا منها مضاعفات
+
+400
+00:29:54,480 --> 00:29:59,380
+الخمسة اللي هي عشرين بظل بس مين واحد فبتظل Y2
+
+401
+00:29:59,380 --> 00:30:03,720
+تطابق الواحد مضله خمسة يعني بس اشتغلت على هادي قلت
+
+402
+00:30:03,720 --> 00:30:09,010
+بما أن الواحد والعشرين تطابق الواحد اللي هو إذا صار
+
+403
+00:30:09,010 --> 00:30:12,870
+عندي الـ y .. ال 21 y2 تطابق ال y2 حطيت مكانها
+
+404
+00:30:12,870 --> 00:30:20,050
+يعني بمعنى آخر شلت مضاعفات ال 21 اللي هي عشرين ضلت
+
+405
+00:30:20,050 --> 00:30:24,670
+واحدة واحد صار y2 و هو اللي جاهز صار y2 تطابق
+
+406
+00:30:24,670 --> 00:30:27,230
+الواحد و دولة خمسة اللي ما استبعبش هذه خلينا اللي
+
+407
+00:30:27,230 --> 00:30:32,410
+بعدها الآن نعمل M3 Y3 تطابق الواحد يعني بعدد مين
+
+408
+00:30:32,410 --> 00:30:37,210
+التطابقات اللي موجودة الآن M3 اللي هي مين عبارة عن
+
+409
+00:30:37,210 --> 00:30:41,570
+أوجدناها اللي هي خمسة عشر يصير خمسة عشر Y3 المجهول
+
+410
+00:30:41,570 --> 00:30:46,550
+تطابق الواحد موضله مين موضله سبعة السبعة مين
+
+411
+00:30:46,550 --> 00:30:50,380
+السبعة اللي هي ال M3 اللي عندي طبعًا ليش أنت بتحل
+
+412
+00:30:50,380 --> 00:30:53,580
+هدولة .. هدولة في القانون .. هدولة حالهن .. هن
+
+413
+00:30:53,580 --> 00:30:57,220
+اللي بدنا نعوض من حالهن هنا بتطلع ليه اللي هو مين
+
+414
+00:30:57,220 --> 00:31:01,860
+اللي هي الحل العام حسب اللي هو مين الطريقة تبعت
+
+415
+00:31:01,860 --> 00:31:05,460
+Chinese remainder theorem إذا صار عندي الآن Y1 وY3
+
+416
+00:31:05,460 --> 00:31:08,980
+هذا آسف مش Y1 وY3 وطبعًا كل واحد مدله مين مدله سبعة
+
+417
+00:31:09,210 --> 00:31:14,310
+إذا صار هي عندي Y1 هنا و Y2 هنا و Y3 هنا دلت علي
+
+418
+00:31:14,310 --> 00:31:17,750
+العملية الأخيرة هي عملية التعويض بكون أوجدت الحل
+
+419
+00:31:17,750 --> 00:31:24,190
+النهائي X بتساوي A1 M1 Y1 A2 M2 Y2 زي A3 MY3 هي
+
+420
+00:31:24,190 --> 00:31:28,950
+قانوننا اللي هو قانون اللي هو بيجيب لحل ال system
+
+421
+00:31:28,950 --> 00:31:33,270
+كله بعد ما تأكدنا ال 3 وال5 وال7 اللي تيبل براين
+
+422
+00:31:33,270 --> 00:31:38,870
+بكون هذا هو حل ال system A1 مين هي؟ هي هالتنينام
+
+423
+00:31:38,870 --> 00:31:42,230
+واحد أو أوجدناها اللي هي خمسة وثلاثين Y واحد هم اللي
+
+424
+00:31:42,230 --> 00:31:45,410
+حللناها عشان خطر الاثنين فبيصير اثنين في خمسة و
+
+425
+00:31:45,410 --> 00:31:48,950
+ثلاثين في اثنين اثنين هي الاثنين اثنين لها ثلاثة
+
+426
+00:31:49,340 --> 00:31:53,260
+الآن مضروبة في مين في و ام اثنين اللي هي جديش واحد
+
+427
+00:31:53,260 --> 00:31:56,120
+و عشرين هاي واحد وعشرون في واي اثنين اللي هي
+
+428
+00:31:56,120 --> 00:32:00,220
+أوجدناها اللي هي واحد زاد ثلاثة هاي ثلاثة اللي
+
+429
+00:32:00,220 --> 00:32:04,960
+هي برضه جديش اثنين مضبوط هاي اثنين في مين في
+
+430
+00:32:04,960 --> 00:32:07,660
+خمسة عشر اللي هي ام ثلاثة في واي ثلاثة اللي هي
+
+431
+00:32:07,660 --> 00:32:13,260
+أوجدناها بتساوي واحد طلع عندي الرقم ثلاثة وثلاثين إذا
+
+432
+00:32:13,260 --> 00:32:20,560
+X بيثاور 233 لكن أنا بدخلي هذا العدد من أعداد
+
+433
+00:32:20,560 --> 00:32:26,400
+1 لعند 105 أو من 0 لعند 104 ماشي فبشيل منه كل
+
+434
+00:32:26,400 --> 00:32:32,010
+مضاعفات 105 مضاعفات الـ 105 مضاعفات الـ 210 مضاعفات
+
+435
+00:32:32,010 --> 00:32:36,250
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+436
+00:32:36,250 --> 00:32:37,490
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+437
+00:32:37,490 --> 00:32:40,030
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+438
+00:32:40,030 --> 00:32:42,170
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+439
+00:32:42,170 --> 00:32:44,150
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+440
+00:32:44,150 --> 00:32:50,580
+الـ 230 مضاعفات الـ 230 لكن .. لكن .. لكن عندي اللي
+
+441
+00:32:50,580 --> 00:32:54,620
+هو عدد لانهائي من الحلول اللي هي اللي متطابقات هن
+
+442
+00:32:54,620 --> 00:33:03,200
+زي الـ 233 و زي لما نزيد 105 لها بيصير 338 و لو 
+
+443
+00:33:03,200 --> 00:33:07,020
+طرحنا 105 و لو طرحنا 105 بيطلع عندك اللي هو كل
+
+444
+00:33:07,020 --> 00:33:11,770
+اللي بيطابق هنا الـ 23 مدلة 105 هي عبارة عن حلول
+
+445
+00:33:11,770 --> 00:33:16,610
+لهذا الـ System أو اختصارًا اختزالًا نختزل الحل في X
+
+446
+00:33:16,610 --> 00:33:21,230
+تو تطابق الـ 23 مدلة 105 و اللي بده يوجد الأرقام زي
+
+447
+00:33:21,230 --> 00:33:26,790
+ما بده بيوجدها بضيف 105ات و يطرح 105ات بكون we have
+
+448
+00:33:26,790 --> 00:33:30,070
+shown that 23 is the smallest positive integer
+
+449
+00:33:30,070 --> 00:33:34,950
+that is simultaneous solution اللي هو يعني هو 23
+
+450
+00:33:34,950 --> 00:33:39,870
+هو عبارة عن أصغر عدد بيجسم اللي هما ايش اللي هي
+
+451
+00:33:39,870 --> 00:33:42,890
+الثلاث و المتبقي اثنين و بيجسم الخمسة و المتبقي
+
+452
+00:33:42,890 --> 00:33:46,430
+ثلاثة و بيجسم السبعة و المتبقي جديش اثنين أو هو
+
+453
+00:33:46,430 --> 00:33:50,370
+عبارة عن الحل العام لهذا ال system of linear
+
+454
+00:33:50,370 --> 00:33:55,510
+equations طيب نيجي الآن إلى اللي هو طريقة ثانية لحل
+
+455
+00:33:55,510 --> 00:33:59,450
+اللي هي المعادلات التطابقات الهالية حاجة اسمها
+
+456
+00:33:59,450 --> 00:34:04,820
+الـ back substitution نشوف كيف بدنا نحل الآن بدنا نحل
+
+457
+00:34:04,820 --> 00:34:11,420
+اللي هو system of linear congruences باستخدام حاجة
+
+458
+00:34:11,420 --> 00:34:14,800
+اسمها ال back substitution الـ back substitution
+
+459
+00:34:14,800 --> 00:34:19,420
+اللي هي بتعتمد أنه بنحول ال linear congruences إلى
+
+460
+00:34:19,420 --> 00:34:23,400
+معادلات ومن ثم بنبدأ نعوض ونرجع و نرجع لما نصل
+
+461
+00:34:23,400 --> 00:34:26,480
+لحل النهائي نشوف كيف برضه اللي هو إن شاء الله
+
+462
+00:34:26,480 --> 00:34:29,970
+الطريقة سهلة لو تابعوا معايا هتلاقوا حالكم تعرفوا
+
+463
+00:34:29,970 --> 00:34:33,530
+تحلو إن شاء الله example use the method of back
+
+464
+00:34:33,530 --> 00:34:37,470
+substitution to find all integers x such that أوجد
+
+465
+00:34:37,470 --> 00:34:41,630
+كل الأعداد x التي تحقق x وطابق الواحد مدلة خمسة أو
+
+466
+00:34:41,630 --> 00:34:45,230
+x وطابق الاثنين مدلة خمسة وفي نفس الوقت x وطابق
+
+467
+00:34:45,230 --> 00:34:48,770
+الثلاثة مدلة سبعة يعني بدنا نحل العاملة هذه اللي هو
+
+468
+00:34:48,770 --> 00:34:54,590
+ال system of linear congruences شوفوا الأول نبدأ
+
+469
+00:34:54,590 --> 00:34:57,770
+في الأولى الآن x تطابق الواحد من دول الخمسة الغرض
+
+470
+00:34:57,770 --> 00:35:01,030
+إيجاد قيمة x يا جماعة since x تطابق الواحد من دول
+
+471
+00:35:01,030 --> 00:35:04,570
+الخمسة إذا حسب المفهوم اللي هو التطابق بتكون
+
+472
+00:35:04,570 --> 00:35:07,970
+الخمسة بتجسم ال x ناقص واحد ايش معناه الخمسة
+
+473
+00:35:07,970 --> 00:35:10,930
+بتجسم ال x ناقص واحد يعني ال x ناقص واحد بتساوي
+
+474
+00:35:10,930 --> 00:35:15,110
+خمسة في some integer mean T يعني x ناقص واحد بتساوي
+
+475
+00:35:15,110 --> 00:35:20,890
+خمسة في T اللي هو حيث T عدد صحيح ماشي الآن so بس
+
+476
+00:35:20,890 --> 00:35:24,760
+بتدنجل الواحد هنا بيصير x بتساوي خمسة زائد ايش زائد
+
+477
+00:35:24,760 --> 00:35:28,480
+T الآن صارت عندي خمسة بالساوية X بالساوية خمسة
+
+478
+00:35:28,480 --> 00:35:32,180
+زائد T بتعوض عن قيمة X هنا لأن ده وجود الحل
+
+479
+00:35:32,180 --> 00:35:36,360
+المشترك هذه حققت المعادلة الأولى أو التطابق الأولى
+
+480
+00:35:36,360 --> 00:35:41,140
+هذه حققت التطابق الأولى بتعوضها هنا عشان تحقق
+
+481
+00:35:41,140 --> 00:35:45,860
+التطابق الثانية طيب إذا عوضولي في هذه عن قيمة خمسة
+
+482
+00:35:45,860 --> 00:35:49,680
+T زائد واحد Substituting into X في التطابق اثنين
+
+483
+00:35:49,680 --> 00:35:54,500
+مدلة ستة هذه yields بنتجلي خمسة T زائد واحد مكان
+
+484
+00:35:54,500 --> 00:35:59,180
+ال X تطابق الاثنين مدلة ستة انجلي هذا على الجهة هذه
+
+485
+00:35:59,180 --> 00:36:03,440
+بيصير ليه خمسة T تطابق الواحد مدله ايش مدله ستة
+
+486
+00:36:03,440 --> 00:36:06,400
+لأنه اثنين ناقص واحد بيطلع واحد الآن زي ما عملنا
+
+487
+00:36:06,400 --> 00:36:10,040
+قبل بشوية بدي أشيل من هذه مضاعفات ال .. من مضاعفات
+
+488
+00:36:10,040 --> 00:36:17,640
+الستة -6-6-6
+
+489
+00:36:17,640 --> 00:36:22,160
+-6-6-6
+
+490
+00:36:22,160 --> 00:36:30,400
+-6-6-6-6-6-6
+
+491
+00:36:30,400 --> 00:36:32,760
+-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6
+
+492
+00:36:32,760 --> 00:36:32,780
+-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6
+
+493
+00:36:36,280 --> 00:36:39,300
+الآن ناقص واحد أنا ما بديش يامودب سالب بدي يامودب
+
+494
+00:36:39,300 --> 00:36:43,040
+الآن بضيف على الناقص واحد اللي هو ستة أو مضاعفات
+
+495
+00:36:43,040 --> 00:36:47,880
+الستة صح آه طبعًا انفجنا علي هذا الكلام أنه بيطلع
+
+496
+00:36:47,880 --> 00:36:51,820
+متطابق لما نضيف المضاعفات المقياس ستة وناقص واحد
+
+497
+00:36:51,820 --> 00:36:55,420
+بيطلع خمسة إذا T تطابق الخمسة modulo 6 إذا T
+
+498
+00:36:55,420 --> 00:37:01,340
+تبعتنا هادي الجنه بتحقق T بطابق الخمسة modulo 6
+
+499
+00:37:01,760 --> 00:37:06,860
+طيب هذه الآن بدي أكتبها على صورة معادلة زي ما عملت
+
+500
+00:37:06,860 --> 00:37:10,220
+في مين؟ في الـ X اللي فوق اللي أنصرت X اللي عندنا 
+
+501
+00:37:10,220 --> 00:37:15,280
+حققت هذه وهي حققت هذه بس خلّيني أكمل  T تطابق
+
+502
+00:37:15,280 --> 00:37:18,860
+الخمسة modulo ستة أيش معناته؟ يعني الستة بتجسم الـ
+
+503
+00:37:18,860 --> 00:37:22,240
+T ناقص خمسة يعني الـ T ناقص خمسة بالساوية ستة في
+
+504
+00:37:22,240 --> 00:37:26,180
+U مثلا أو T بتساوية ستة U زائد خمسة زي ما عملت فوق
+
+505
+00:37:26,180 --> 00:37:29,840
+بالظبط بدي أعمل في هذه بالطريقة اللي حكيت عنها فوق
+
+506
+00:37:29,870 --> 00:37:39,670
+بتجسم الـ 6 بـ T-5 إذا الـ T-5 بيساوي 6 في U نجلت
+
+507
+00:37:39,670 --> 00:37:43,410
+الخمسة هنا صارت T بيساوي 6 U زائد خمسة where U 
+
+508
+00:37:43,410 --> 00:37:47,410
+أشماله is an integer الـ T اللي طلعت عندي هنا بدي
+
+509
+00:37:47,410 --> 00:37:52,870
+أرد اللي هي أعوضها في اللي هي الـ T اللي عندي اللي
+
+510
+00:37:52,870 --> 00:37:57,470
+هي بدي أعوض substituting
+
+511
+00:37:57,470 --> 00:38:02,030
+this back into X بتساوي خمسة T زائد واحد لإن عندي
+
+512
+00:38:02,030 --> 00:38:05,790
+اللي هي ال X عندي جدش قيمة طلعت اللي بالأحمر هذه
+
+513
+00:38:05,790 --> 00:38:10,130
+خمسة T زائد واحد بعد ما وجدنا T اللي هي اللي صارت
+
+514
+00:38:10,130 --> 00:38:15,040
+تتحقق هذه التطابق اللي هي حققت التطابق هذه صار عندى
+
+515
+00:38:15,040 --> 00:38:21,480
+اعوض عن T بقيمتها 6U زائد خمسة هان بيصير X بتساوي
+
+516
+00:38:21,480 --> 00:38:25,600
+شيل ال T وحط 6U زائد خمسة بتطلع عبارة عن خمسة في
+
+517
+00:38:25,600 --> 00:38:29,080
+هذا المقدار زائد واحد اضربه جوا بيصير ثلاثين U
+
+518
+00:38:29,080 --> 00:38:32,540
+زائد خمسة وعشرين واحد بيطلع زائد إيه؟ ستة وعشرين إذا
+
+519
+00:38:32,540 --> 00:38:36,100
+صارت عندى X بتساوي ثلاثين U زائد ستة وعشرين صارت
+
+520
+00:38:36,100 --> 00:38:41,670
+هذه حققت هذه و حققت هذه دلنا نشوف كيف تتحقق هذه و
+
+521
+00:38:41,670 --> 00:38:46,510
+نكون أوجدنا الحل المشترك الآن الخطوة الثالثة مكررة
+
+522
+00:38:46,510 --> 00:38:53,230
+يعني مشابه للسابق insert this into X طابق 3 مدل 7
+
+523
+00:38:53,230 --> 00:38:57,810
+بعد ما عوضناها نعوضها نعوض الآن في الأخيرة X طابق
+
+524
+00:38:57,810 --> 00:39:01,470
+3 مدل 7 شيل اللي هي ال X هذه و حط قيمته اللي
+
+525
+00:39:01,470 --> 00:39:06,300
+أوجدناها هذه فوق بصير 30U زي 26 تطابق من التلاتة
+
+526
+00:39:06,300 --> 00:39:09,200
+مدرس سبعة بدنا نحل هذا زي ما حلنا اللي قبل solving
+
+527
+00:39:09,200 --> 00:39:15,500
+this بيعطيني الان الـ 26 من جلها بيصير ناقص 26 و في
+
+528
+00:39:15,500 --> 00:39:20,420
+عندي 3 بيصير ناقص 23 صارت 30 U تطابق ناقص 23 و دول
+
+529
+00:39:20,420 --> 00:39:24,440
+7 الان هذه بدنا نحلها بدنا نحلها لإيجاد ال inverse
+
+530
+00:39:24,440 --> 00:39:28,720
+زي ما قلنا شيل المضاعفات اللي هي السبعة أجرب اشي
+
+531
+00:39:28,720 --> 00:39:33,360
+30 على 7 بتطلع 4 في 7 ب 28 و بزيد 2 خلاص عند ال 2
+
+532
+00:39:33,360 --> 00:39:39,390
+إذا شيلت 28 بظل 2 U لان ناقص تلاتة و عشرين و نضيف
+
+533
+00:39:39,390 --> 00:39:47,870
+مضاعفات السبعة لكي نضيف أقرب رقم لكي نضغر قيمة
+
+534
+00:39:47,870 --> 00:39:48,650
+الرقم
+
+535
+00:39:53,690 --> 00:39:56,150
+21 من مضاعفات السبعة و 21 من مضاعفات السبعة و 21
+
+536
+00:39:56,150 --> 00:39:58,790
+من مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+537
+00:39:58,790 --> 00:40:02,090
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+538
+00:40:02,090 --> 00:40:03,350
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+539
+00:40:03,350 --> 00:40:04,010
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+540
+00:40:04,010 --> 00:40:06,330
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+541
+00:40:06,330 --> 00:40:07,370
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+542
+00:40:07,370 --> 00:40:08,890
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+543
+00:40:08,890 --> 00:40:10,670
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+544
+00:40:10,670 --> 00:40:13,530
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من مض
+
+545
+00:40:13,560 --> 00:40:17,700
+التلاتين يو حطينا اتنين يو اللي أنا عملت هيك عشان
+
+546
+00:40:17,700 --> 00:40:21,180
+أنا عارف إنه أنا بتخليها ده اللي هو طلع عند اتنين
+
+547
+00:40:21,180 --> 00:40:25,380
+بتخليها ده برضه بيطلع فيه زوجي عشان اللي هو اجسم
+
+548
+00:40:25,380 --> 00:40:29,760
+الجهتين على اتنين و يظل ال يو لحالها بنفع اه لان
+
+549
+00:40:29,760 --> 00:40:33,440
+أهم المشتركة الأعلى بين السبعة و اتنين واحد بنجسم
+
+550
+00:40:33,440 --> 00:40:36,000
+على اتنين بيطلع يو تطابق الناقص واحد مضول سبعة
+
+551
+00:40:36,000 --> 00:40:41,620
+الناقص واحد ضيفله سبعة بيصير اللي هو ستة بيصير due
+
+552
+00:40:41,620 --> 00:40:44,980
+تطابق الستة modulo من modulo سبعة احنا اضافة اللي
+
+553
+00:40:44,980 --> 00:40:51,560
+هو اضافة اللي هي مضاعفات او طرح مضاعفات العدد اللي
+
+554
+00:40:51,560 --> 00:40:56,420
+هو المقياس لأي من الطرفين طبعا منضيف سبعة you هنا
+
+555
+00:40:56,420 --> 00:41:00,820
+أو أربع طاش you ومش سبعة لحالها واما هنا منضيف
+
+556
+00:41:00,820 --> 00:41:06,320
+السبعة وكذا عسى انه يظل المتطابقات بتنطلع عند U
+
+557
+00:41:06,320 --> 00:41:09,220
+ترابق الستة مضلوا سبعة بنعمل هذه زي ما عملنا اللي
+
+558
+00:41:09,220 --> 00:41:12,820
+فوق اللي هو سبعة بتجسم ال U نقص ستة معناته اللي هو
+
+559
+00:41:12,820 --> 00:41:16,860
+ال U نقص ستة بساوية سبعة V يعني ال U بساوية سبعة V
+
+560
+00:41:16,860 --> 00:41:22,420
+زائد ستة where V is an integer الآن بدأ أعوض عن ال
+
+561
+00:41:22,420 --> 00:41:28,270
+U في من؟ في ال X هنابصير عند ال X بتساوي شيل ال U
+
+562
+00:41:28,270 --> 00:41:33,410
+وحط قيمتها اللي هي 7V زائد 6 بصير ال X بتساوي اللي
+
+563
+00:41:33,410 --> 00:41:38,850
+هي بدل 30U 30 في 7V زائد 6 زائد 26 وضربها بتطلع
+
+564
+00:41:38,850 --> 00:41:45,190
+210U زائد 30 في 6 ال 180 و 26 بتطلع 206 يعني
+
+565
+00:41:45,190 --> 00:41:50,950
+اتصلعت عندي الآن X بتساوي 210U زائد 206 وهذه طبعا
+
+566
+00:41:50,950 --> 00:41:56,530
+نتيجة الحل في الأولى وفي التانية وفي التالتة يعني
+
+567
+00:41:56,530 --> 00:42:00,830
+ال X اللي عند هذه حققت هذه وحققت هذه وحققت هذه
+
+568
+00:42:00,830 --> 00:42:05,030
+معناته ال X اللي طلعت هنا هي عبارة عن حل
+
+569
+00:42:05,030 --> 00:42:10,610
+المتطابقات كلها اللي هي التلاتة في نفس الوقت يعني
+
+570
+00:42:10,610 --> 00:42:15,010
+صارت عند X بتساوي 210 U زي 206 هي عبارة عن الحلول
+
+571
+00:42:15,010 --> 00:42:19,100
+حيث U is an integer الان هادى بنقدر نكتبها على صورة
+
+572
+00:42:19,100 --> 00:42:23,280
+ايش تطابقة اللى هى ايش أصل التطابقة X تطابق الـ
+
+573
+00:42:23,280 --> 00:42:30,840
+206 modulo 210 ايش عرفك هاي X ناقص 206 اللى هو 210
+
+574
+00:42:30,840 --> 00:42:39,320
+بتجسمها 210 بتجسم X ناقص 26 يعني X ناقص 26 بساوية
+
+575
+00:42:39,320 --> 00:42:43,540
+210 في some number سمينا U هو فعلا صارت عند X
+
+576
+00:42:43,540 --> 00:42:51,150
+بساوي 210 U زائد 206 إذا هذه x بتساوي 210 u زائد
+
+577
+00:42:51,150 --> 00:42:56,510
+206 هي نفس التعبير اللي بنقوله x تطابق ال 206
+
+578
+00:42:56,510 --> 00:43:03,440
+modulo 210 ليش لإن زي ما قلت X تطابق الـ 206 مده
+
+579
+00:43:03,440 --> 00:43:09,900
+210 معناته 210 تقسم ال X ناقص 206 وزي ما عملنا
+
+580
+00:43:09,900 --> 00:43:19,340
+بسير X ناقص 206 تساوي 210 في U التي تساوي 210 في U
+
+581
+00:43:19,340 --> 00:43:25,730
+زائد 206 إذا هذه هي هذا التعبير وهذا معناته أنه
+
+582
+00:43:25,730 --> 00:43:29,830
+اللي هي الأرقام مائتين وستة وبعدين ضيف كمان مائتين
+
+583
+00:43:29,830 --> 00:43:33,110
+وعشرة بيصير أربعمائة وست عشر وضيف كمان مائتين وعشرة
+
+584
+00:43:33,110 --> 00:43:37,150
+بيصير كده بيصير كده كلهين حلول مشتركة لهذه التطابق
+
+585
+00:43:37,150 --> 00:43:41,290
+وهذا حل اللي كلهين ولو لاحظت حتة تجي المائتين
+
+586
+00:43:41,290 --> 00:43:47,070
+وعشرة هي عبارة عن ستة في خمسة في سبعة ستة في خمسة
+
+587
+00:43:47,070 --> 00:43:50,490
+في تلاتين و تلاتة في سبعة في متين و عشرة إذا صار
+
+588
+00:43:50,490 --> 00:43:54,350
+عنده X وطابق متين و ستة مدله متين و عشرة و هيك
+
+589
+00:43:54,350 --> 00:43:58,010
+بيكون احنا حللنا اللي هي ال system of linear
+
+590
+00:43:58,010 --> 00:44:02,410
+equations بواسطة حاجة اسم ال back substitution و
+
+591
+00:44:02,410 --> 00:44:07,670
+هذا هو ال homework اللي مطلوب منكم حل السؤال الأول
+
+592
+00:44:07,670 --> 00:44:11,150
+و التاني و التالت بسلامونيه و إلى لقاء آخر السلام
+
+593
+00:44:11,150 --> 00:44:12,790
+عليكم و رحمة الله وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d180c9681a1baac28b2af616ea601c2210f9be21
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/TN1XRPbiL9s_postprocess.srt
@@ -0,0 +1,2372 @@
+1
+00:00:00,760 --> 00:00:05,260
+بسم الله الرحمن الرحيم هذه هي المحاضرة الثامنة
+
+2
+00:00:05,260 --> 00:00:10,040
+مساق رياضيات منفصلة طلاب و طالبات الجامعة
+
+3
+00:00:10,040 --> 00:00:15,020
+الإسلامية قسم الحوسبة المتنقلة كلية العلو و كلية
+
+4
+00:00:15,020 --> 00:00:19,240
+تكنولوجيا المعلومات المحاضرة اليوم ان شاء الله
+
+5
+00:00:19,240 --> 00:00:23,460
+هنحكي عن اللي هو section 4.4 اللي هو solving
+
+6
+00:00:23,460 --> 00:00:29,770
+congruences او حل التطابقاتهنحل .. هنحكي عن شغلتين
+
+7
+00:00:29,770 --> 00:00:34,150
+في حد التطابقات أول إشي حل تطابق خطية لحالها و
+
+8
+00:00:34,150 --> 00:00:38,810
+بعدين حل system of linear congruences أو اللي هي
+
+9
+00:00:38,810 --> 00:00:44,590
+تطابقات أنية في أن واحد لمجموعة من التطابقات و
+
+10
+00:00:44,590 --> 00:00:48,200
+هنشوف كيفاللي هو نستخدم ال chinese remainder
+
+11
+00:00:48,200 --> 00:00:53,500
+theorem و ال back اللي هو substitution method يعني
+
+12
+00:00:53,500 --> 00:00:58,260
+طريقتين هنحل فيهم التطابقات الأنية في البداية
+
+13
+00:00:58,260 --> 00:01:02,380
+خليني نتعرف شو معناه linear congruencesالـ Linear
+
+14
+00:01:02,380 --> 00:01:06,660
+congruences شيء مشابه لللي هي الـ Linear equations
+
+15
+00:01:06,660 --> 00:01:11,080
+ولكن بتظهر بدل عدد علامة المساواة بتظهر علامة اللي
+
+16
+00:01:11,080 --> 00:01:15,180
+هي التطابق وبتظهر اللي هو المقياس بالظبط ايش
+
+17
+00:01:15,180 --> 00:01:19,040
+بنقول؟ بنقول a congruence of the form اللي هي Ax
+
+18
+00:01:19,040 --> 00:01:22,960
+تطابق B modulo M هذه اللي هي بنسميها Linear
+
+19
+00:01:22,960 --> 00:01:27,800
+congruences لأن X عبارة عن أس واحدوعندي الـ a و ال
+
+20
+00:01:27,800 --> 00:01:31,500
+b بتكون عداد معطية و ال m عدد معطي و المطلوب اللي
+
+21
+00:01:31,500 --> 00:01:35,840
+هو إيجاد قيمة المجهول x هذه بنسميها اللي هي linear
+
+22
+00:01:35,840 --> 00:01:40,760
+congruences حل ال linear congruences هو كما يلي
+
+23
+00:01:40,760 --> 00:01:45,660
+اللي هو بنقصد في حل ال congruence ax تطابق b
+
+24
+00:01:45,660 --> 00:01:49,520
+modulo m هي إيجاد كل قيم x اللي هي بتحقق اللي هي
+
+25
+00:01:49,520 --> 00:01:54,050
+التطابق اللي عنديالان قبل ما نشوف كيف نحل
+
+26
+00:01:54,050 --> 00:01:58,750
+التطابقات الخطية خلّينا نتطلع بس على شغلة اللي هي
+
+27
+00:01:58,750 --> 00:02:03,490
+بتلزمنا في حل التطابقات اللي هو بنقول عن an
+
+28
+00:02:03,490 --> 00:02:08,010
+integer a bar such that a bar في a طابق الواحد
+
+29
+00:02:08,010 --> 00:02:12,070
+modulo m بنسمي في هذه الحالة اللي هو ال a bar هو
+
+30
+00:02:12,070 --> 00:02:17,080
+عبارة عن ال inverse لل a modulo mإذاً العدد اللي
+
+31
+00:02:17,080 --> 00:02:21,140
+بنجيبه لما نضربه في الـ A يطابق الواحد modulo M
+
+32
+00:02:21,140 --> 00:02:26,140
+بنقول عنه هذا A bar اللي هو عبارة عن ال inverse لل
+
+33
+00:02:26,140 --> 00:02:30,680
+A ال inverse of A modulo M خلينا نتطلع على مثال
+
+34
+00:02:30,680 --> 00:02:35,460
+بسيط الآن بقول لي عندي خمسة إزئان inverse of تلاتة
+
+35
+00:02:35,460 --> 00:02:40,430
+modulo سبعةالخامسة هي inverse للتلاتة مدل سبعة
+
+36
+00:02:40,430 --> 00:02:44,630
+يعني الخمسة معكوس التلاتة بالنسبة للمقياس السبعة
+
+37
+00:02:44,630 --> 00:02:48,730
+لأن لو ضربنا الخمسة في التلاتة بخمستعش الخمستعش
+
+38
+00:02:48,730 --> 00:02:52,990
+دائما تطابق الواحد مدل سبعة عارفين ايش معنى تطابق
+
+39
+00:02:52,990 --> 00:02:57,050
+الواحد مدل سبعة يعني الخمستعش لو شيلنا مضاعفات
+
+40
+00:02:57,050 --> 00:03:01,340
+السبعة منها هنلاقي بضل المتبقي بس واحدماشي الحل
+
+41
+00:03:01,340 --> 00:03:07,040
+فعشان يكون 15 طابق الواحد مدله سبعة الان عند ال
+
+42
+00:03:07,040 --> 00:03:11,820
+linear congruencies هتنستخدمها هنستخدم في إيجاد
+
+43
+00:03:11,820 --> 00:03:16,240
+قيمة ال X فيها اللي هو ال inverse تبع العنصر
+
+44
+00:03:16,240 --> 00:03:21,400
+هنستعين فيه لإيجاد اللي هو الحلفي الأول خلّينا
+
+45
+00:03:21,400 --> 00:03:25,580
+نشوف هالنظرية اللي بتشرّع لنا اللي هو اللي هي ان
+
+46
+00:03:25,580 --> 00:03:31,860
+يكون فيه ال congrance حل أو اللي مالهاش بس قبل ما
+
+47
+00:03:31,860 --> 00:03:37,980
+ناخد نظرية بتشرّع لنا انه العدد له اللي هو inverse
+
+48
+00:03:37,980 --> 00:03:42,080
+ولا مالقوش تقولنا نظرية if a and m are relatively
+
+49
+00:03:42,080 --> 00:03:47,630
+prime integers إذا كان ال a و ال mالعدد ومقياسه
+
+50
+00:03:47,630 --> 00:03:51,050
+are relatively prime integers and M أكبر من واحد
+
+51
+00:03:51,050 --> 00:03:55,350
+then an inverse of A modulo M exists يعني دائما
+
+52
+00:03:55,350 --> 00:03:58,510
+دوم لما يكون العالم مشترك على بين ال A و ال M
+
+53
+00:03:58,510 --> 00:04:02,050
+بساوة واحدة بتضمن وجود اللي هو inverse لل A
+
+54
+00:04:02,050 --> 00:04:08,160
+مدلومين modulo Mماشي الحال خلّينا نشوف مثالنا هنا
+
+55
+00:04:08,160 --> 00:04:11,220
+الخمسة
+
+56
+00:04:11,220 --> 00:04:14,980
+is an inverse of تلاتة مدل M مدل السبعة هذه
+
+57
+00:04:14,980 --> 00:04:20,620
+وجدناها احنا قبل و شوية نلاحظ انه اللي هو الخمسة و
+
+58
+00:04:20,620 --> 00:04:25,840
+اللي هيالتلاتة اللي بدنا نوجد لها inverse هي
+
+59
+00:04:25,840 --> 00:04:31,020
+والسبعة ايه شمالها relatively ابراهيم الان this
+
+60
+00:04:31,020 --> 00:04:38,040
+اللي هو inverse is unique unique بس ايه شماله؟
+
+61
+00:04:38,040 --> 00:04:41,400
+ودله سبعة يعني وحيد بالنسبة لمقياس سبعة، ايش يعني؟
+
+62
+00:04:41,570 --> 00:04:46,150
+يعني اللي هو من واحد لعند سبعة مافيش لغير inverse
+
+63
+00:04:46,150 --> 00:04:50,130
+واحد للتلاتة مدله اللي هو سبعة اللي هو مين لجناه
+
+64
+00:04:50,130 --> 00:04:55,250
+خمسة لكن في غيره بعد السبعة كل الأعداد اللي هي لما
+
+65
+00:04:55,250 --> 00:05:00,290
+نضيفها نضيف مضاعفات السبعة على الخمسة بتطلع برضه
+
+66
+00:05:00,290 --> 00:05:04,470
+إيش عبارة عن inverse إيش يعني؟ يعني الخمسة لجناه
+
+67
+00:05:04,470 --> 00:05:09,120
+اللي هو inverse للتلاتة مدله سبعةالان لو ضفنا على
+
+68
+00:05:09,120 --> 00:05:12,100
+السابعة الخمسة كمان سبعة بصير اتناش برضه inverse
+
+69
+00:05:12,100 --> 00:05:16,220
+للتلاتة التسعة اتعش برضه inverse للتلاتة لو طرحنا
+
+70
+00:05:16,220 --> 00:05:19,700
+سبعة من الخمسة نقص اتنين برضه inverse لمين للتلاتة
+
+71
+00:05:19,700 --> 00:05:26,310
+مدلوا سبعة اذا نقصد احنا ال uniqueness بعنماليهذا
+
+72
+00:05:26,310 --> 00:05:28,750
+يعني أنه يوجد كتابة عظيمة عظيمة عظيمة عظيمة عظيمة
+
+73
+00:05:28,750 --> 00:05:35,590
+A bar أقل من M وهو عدسة A مدلو M وكل عدسة آخرة
+
+74
+00:05:35,590 --> 00:05:44,910
+عدسة A مدلو M مقارنة بـ A bar مدلو Mالـ12 والنقص 2
+
+75
+00:05:44,910 --> 00:05:50,970
+والـ19 وكل هنا دولة برضه بيكون ال inverse للتلاتة
+
+76
+00:05:50,970 --> 00:05:55,630
+modulo 7 لإن اللي هنا كلهم بطابق من الخمسة اللي
+
+77
+00:05:55,630 --> 00:05:57,490
+لجيناها modulo 7
+
+78
+00:06:03,840 --> 00:06:08,520
+طيب شوف خلونا نجد كيف نجد ال inverse اللي هو للعدد
+
+79
+00:06:08,520 --> 00:06:13,360
+لأي عدد بدنيا بالنسبة لقياس معين ال Euclidean
+
+80
+00:06:13,360 --> 00:06:15,760
+algorithm اللي هي خورزمية القسمة و بذوذ
+
+81
+00:06:15,760 --> 00:06:19,400
+coefficients اللي هو بتعطينا gives us a systematic
+
+82
+00:06:19,400 --> 00:06:24,120
+approach to find اللي هو إيش to find inverse كيف؟
+
+83
+00:06:24,290 --> 00:06:27,810
+اللي هو .. اللي هو كمالي ابني يجيب .. يطلب إن هو
+
+84
+00:06:27,810 --> 00:06:31,650
+فيلم تلقى find an inverse of 3 modulo 7 العداد
+
+85
+00:06:31,650 --> 00:06:36,250
+عشان إن صغيرة سهل إنه نعملهم .. نوددهم زي قبل ما
+
+86
+00:06:36,250 --> 00:06:40,510
+شوية بالتحذير أو كده بس ماينفعش بالتحذير الآن بدنا
+
+87
+00:06:40,510 --> 00:06:43,470
+نودي الطريقة .. نلاقي طريقة لإيجادها الطريقة عن
+
+88
+00:06:43,470 --> 00:06:46,050
+طريقة charismatic القسمة أول حاجة نعمل مشترك اللي
+
+89
+00:06:46,050 --> 00:06:49,440
+على بين 3 و 7 بيساوي أحدإذا مضمون من النظرية اللي
+
+90
+00:06:49,440 --> 00:06:52,620
+هي واحد انه نلاقي inverse للتلاتة modulo منين سبعة
+
+91
+00:06:52,620 --> 00:06:55,940
+يعني ال inverse modulo of تلاتة modulo سبعة exist
+
+92
+00:06:55,940 --> 00:06:59,920
+always خلينا نشوف كيف بدنا نوجده الان بتيجي السبعة
+
+93
+00:06:59,920 --> 00:07:02,140
+بتيجي اسمها التلاتة سبعة بساوة اتنين في تلاتة
+
+94
+00:07:02,140 --> 00:07:06,860
+والمتبقى ايش واحد الان جهزة الان الواحد هو عبارة
+
+95
+00:07:06,860 --> 00:07:10,800
+عن العامل المشترك الأعلى بين التلاتة والسبعة هذا
+
+96
+00:07:10,800 --> 00:07:14,130
+عارفينه احنا من قبل اللي هي الطريقةالان واحد بقت
+
+97
+00:07:14,130 --> 00:07:16,550
+وع صورة Linear combination من التنين اللي هي
+
+98
+00:07:16,550 --> 00:07:19,950
+بيزوتز كوفيه عن طريق اللي هو ايه اللي هي بيزوتز
+
+99
+00:07:19,950 --> 00:07:23,430
+كوفيه coefficients بيصير عند الواحد بساوي بنجلها
+
+100
+00:07:23,430 --> 00:07:26,950
+ده بيصير نقص اتنين في تلاتة زائد واحد في سبعة الان
+
+101
+00:07:26,950 --> 00:07:30,310
+انا مين اللي بده اوجدله اللي هو ال inverse التلاتة
+
+102
+00:07:30,310 --> 00:07:35,110
+مدله مين مدله السبعة معامل التلاتة في هذا ال
+
+103
+00:07:35,110 --> 00:07:38,990
+linear combination اللي هو نقص اتنين هو اللي هيطلع
+
+104
+00:07:38,990 --> 00:07:45,830
+لنا اللي هو مينالإنفرس المطلوب and see that نقص
+
+105
+00:07:45,830 --> 00:07:49,310
+اتنين and واحد هي ال بيزوتز coefficients اللي
+
+106
+00:07:49,310 --> 00:07:54,530
+معامل التلاتة هو عبارة عن نقص اتنين هو اللي هيكون
+
+107
+00:07:54,530 --> 00:07:59,170
+inverse of تلاتة مدله مين مدله سبعة إذا الأمر سهل
+
+108
+00:07:59,170 --> 00:08:04,530
+عشان نوجد ال inverse بس بنيجي اللي هو بنكتب ال ..
+
+109
+00:08:04,530 --> 00:08:07,970
+بناخد .. بنكتب ال .. الواحد اللي هو المشترك الأعلى
+
+110
+00:08:07,970 --> 00:08:11,480
+بينهمأزالينا الـ combination بين التلاتة والسبعة
+
+111
+00:08:11,480 --> 00:08:15,260
+كيف هذا بطريقة اللي هو ال division algorithm اللي
+
+112
+00:08:15,260 --> 00:08:21,160
+اتعلمناها وبكون معامل اللي هو التلاتة هو عبارة عن
+
+113
+00:08:21,160 --> 00:08:26,750
+ال inverse للتلاتة مظلمين السبعةالان اللي جينا نقص
+
+114
+00:08:26,750 --> 00:08:30,530
+اتنين اذا بلاقي البجيهات كلها اللي لدك اضيف على
+
+115
+00:08:30,530 --> 00:08:34,190
+السبعة على نقص اتنين سبعة بيطلع الخمسة اضيف عليه
+
+116
+00:08:34,190 --> 00:08:37,370
+كمان سبعة بيطلع اتناشر اضيف عليه كمان سبعة بيطلع
+
+117
+00:08:37,370 --> 00:08:41,730
+تسعة عشر لو طرحت منه سبعة بيطلع نقص تسعة كل هذولة
+
+118
+00:08:41,860 --> 00:08:47,860
+هو عبارة عن Inverses اللي هي التلاتة مدلوا سبعة
+
+119
+00:08:47,860 --> 00:08:52,680
+لكن واحد منهم ال unique هو الخمسة اللي من الواحد
+
+120
+00:08:52,680 --> 00:08:57,400
+لعند مين لعند السبعة زي ما حكينا قبل بشوية الآن
+
+121
+00:08:57,400 --> 00:09:02,510
+ناخد مثال على أعداد كبيرة نشوف كيف نوجدهاناخد
+
+122
+00:09:02,510 --> 00:09:06,150
+المثال الثاني هذا find an inverse of 101 modulo
+
+123
+00:09:06,150 --> 00:09:12,370
+4620 تنشوف الآن ايش اللي بنسويه الطريقة كمالي
+
+124
+00:09:12,370 --> 00:09:17,930
+باجسم هذا على 101 بطريقة mean اللي هو ال division
+
+125
+00:09:17,930 --> 00:09:22,550
+algorithm لما أصل في الآخر للمتبقى صفر بيكون أول
+
+126
+00:09:22,550 --> 00:09:25,870
+واحد قبل المتبقى صفر هو ال greatest common divisor
+
+127
+00:09:25,870 --> 00:09:29,520
+زي ما قلنا قبل هيكوبنه بتجيب اللي هو الـ grades
+
+128
+00:09:29,520 --> 00:09:32,540
+common divisor as a linear combination of الاتنين
+
+129
+00:09:32,540 --> 00:09:36,680
+وبكون المعامل الـ 101 هو ال inverse المطلوب خلّينا
+
+130
+00:09:36,680 --> 00:09:40,540
+نشوف الكلام هذا عمليًا الان اولًا استخدم ال
+
+131
+00:09:40,540 --> 00:09:43,480
+algorithm to show that ال grades common divisor
+
+132
+00:09:43,480 --> 00:09:46,860
+بين هدول العددين بساوة واحد ايش بنسوي؟ بنقسم هذا
+
+133
+00:09:46,860 --> 00:09:53,160
+على هذا جسمنا على 101حصل قسم 45 المتبقى 75 باجسم
+
+134
+00:09:53,160 --> 00:10:00,220
+101 على 75 بطلع المتبقى 26 بعاود ال 75 نفس الطريقة
+
+135
+00:10:00,220 --> 00:10:05,500
+ع ال 26 بطلع المتبقى 23 ال 26 مع ال 23 بضل المتبقى
+
+136
+00:10:05,500 --> 00:10:09,260
+3 ال 23 مع ال 3 بضل المتبقى 2 هذا عارفين عشان هيك
+
+137
+00:10:09,260 --> 00:10:12,910
+أنا من السرعةالتي هي التلاتة مع الاتنين بطلالة
+
+138
+00:10:12,910 --> 00:10:17,250
+المتبقي واحد الاتنين اللي هو مع اللي هو الواحد
+
+139
+00:10:17,250 --> 00:10:22,010
+اللي هو بضلش متبقي فبكون أول واحد قبل اللي هو مضلش
+
+140
+00:10:22,010 --> 00:10:25,130
+متبقي هو ده العام المشترك الأعلى بين العددين اللي
+
+141
+00:10:25,130 --> 00:10:29,150
+هو أربعة آلاف وستمائة وعشرين ومية وواحد الان بده
+
+142
+00:10:29,150 --> 00:10:32,470
+مش هنا أنا مش غرضي بس أوجد العام المشترك الأعلى
+
+143
+00:10:32,470 --> 00:10:36,480
+بين الواحد لأ غرضي أن اكتب الواحدبرجوع زى ما كنا
+
+144
+00:10:36,480 --> 00:10:40,160
+نرجع قبل هيك أزلنا ال combination من الـ 426
+
+145
+00:10:40,160 --> 00:10:44,200
+وال101 وعارفين الطريقة احنا واحد بتساوي تلاتة ناقص
+
+146
+00:10:44,200 --> 00:10:48,900
+واحد في واحد في اتنين الان الاتنين هنا بجيبه من
+
+147
+00:10:48,900 --> 00:10:54,850
+هنا بجيبه هذا ناقص هذا و بعوض عنيهم و بافردهاالان
+
+148
+00:10:54,850 --> 00:10:58,030
+اللى بيطلع عندى هو و ناقص واحد تلاتة عشرين في
+
+149
+00:10:58,030 --> 00:11:01,330
+تمانية في تلاتة بتجيب الان قيمة من التلاتة بشيل
+
+150
+00:11:01,330 --> 00:11:05,330
+التلاتة و بجيب قيمة تهيأة و بنعوضها و بضل باستمر
+
+151
+00:11:05,330 --> 00:11:08,890
+كل شغل بتجيبها من اللي جابلها لما نقصل في الآخر
+
+152
+00:11:08,890 --> 00:11:12,970
+لآخر لينا ال combination بطلع واحد بسوء ناقص تلاتة
+
+153
+00:11:12,970 --> 00:11:16,610
+خمسة و تلاتين فاربعمائة تلاتة و ستمائية و عشرينزاد
+
+154
+00:11:16,610 --> 00:11:21,510
+1600 و 1 في 101 لاحظ انا انا قدرت اكتب الواحد
+
+155
+00:11:21,510 --> 00:11:25,170
+ازالي بال بيزوت ال بيزوت ال coefficient سيها مقص
+
+156
+00:11:25,170 --> 00:11:32,150
+35 و 1600 و 1 ل 4620 و 101 يعني واحد لينا
+
+157
+00:11:32,150 --> 00:11:36,750
+combination من هذا و من هذا بيكون معامل ال 101
+
+158
+00:11:36,750 --> 00:11:42,810
+اللي هو 1600 و 1 هو اللي is an inverse of 101 mod
+
+159
+00:11:42,810 --> 00:11:50,670
+4620و لو جيت انت تتأكد من كلامك اضرب ال 1601 في ال
+
+160
+00:11:50,670 --> 00:11:55,530
+101 هتلاقي بيطلع الرقم هذا هذا الرقم لو جسمته على
+
+161
+00:11:55,530 --> 00:11:58,990
+سبعة هيطلع المتبقي واحد يعني هذا يطابق الواحد مدله
+
+162
+00:11:58,990 --> 00:12:05,050
+سبعة اذا فعلا هذا عبارة عن ال inverse لهذا مدله
+
+163
+00:12:05,050 --> 00:12:11,070
+سبعة حسب ما عرفنا قبل بشويةهكذا فإننا وجدنا
+
+164
+00:12:11,070 --> 00:12:16,290
+الانفرس لأعداد أو أرقام كبيرة الآن بدنا نستخدم
+
+165
+00:12:16,290 --> 00:12:20,850
+الانفرس لإيجاد الـlinear congruences بدنا نستخدم
+
+166
+00:12:20,850 --> 00:12:26,210
+الانفرس في إيجاد الـlinear congruences إيش الفكرة؟
+
+167
+00:12:26,210 --> 00:12:29,530
+نشوف كده إيش الفكرة في استخدام الانفرس نستطيع
+
+168
+00:12:29,530 --> 00:12:32,950
+تحسين الانفرس Ax وطابق بيه مدلًا By multiplying
+
+169
+00:12:32,950 --> 00:12:37,210
+both sides by A barالـ A bar اللي هي من ال inverse
+
+170
+00:12:37,210 --> 00:12:41,050
+لو ضربناها من الجهتين في A bar فبصير A bar في A في
+
+171
+00:12:41,050 --> 00:12:46,230
+X بساوي A bar في B لأن A في A bar في X الـ A في A
+
+172
+00:12:46,230 --> 00:12:49,670
+bar ما هي بالطابق الواحد يعني و كأننا بنكون شيلنا
+
+173
+00:12:49,670 --> 00:12:52,970
+الـ A في الـ A bar و صار في عندي الواحد لحاله يعني
+
+174
+00:12:52,970 --> 00:12:57,230
+صارت ال X قاعدة لحالها يعني صارت ال X بتساوي A bar
+
+175
+00:12:57,230 --> 00:13:05,110
+في B modulo M هي الحل بتنشوف كيفWhat are the
+
+176
+00:13:05,110 --> 00:13:07,990
+solutions of the congruence 3x على طابق الأربعة
+
+177
+00:13:07,990 --> 00:13:09,430
+مدلوا ثلاثة؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟طابق
+
+178
+00:13:09,430 --> 00:13:10,390
+الأربعة مدلوا ثلاثة؟طابق الأربعة مدلوا ثلاثة؟طابق
+
+179
+00:13:10,390 --> 00:13:11,290
+الأربعة مدلوا ثلاثة؟طابق الأربعة مدلوا ثلاثة؟طابق
+
+180
+00:13:11,290 --> 00:13:13,050
+الأربعة مدلوا ثلاثة؟طابق الأربعة مدلوا ثلاثة؟طابق
+
+181
+00:13:13,050 --> 00:13:16,630
+الأربعة مدلوا ثلاثة؟طابق الأربعة مدلوا ثلاثة؟طابق
+
+182
+00:13:16,630 --> 00:13:24,030
+الأربعة مدلوا ثلاثة؟طابق الأربعة مدلوا ثلاثة؟طابق
+
+183
+00:13:24,030 --> 00:13:29,440
+الأربعةالان واضح انه اللي هو صار عندى الواحد هو ال
+
+184
+00:13:29,440 --> 00:13:32,040
+grade's common divisor بين التلاتة وبين السبعة
+
+185
+00:13:32,040 --> 00:13:36,500
+وبساوي سبعة ناقص اتنين في تلاتة يعني طلع عندى ناقص
+
+186
+00:13:36,500 --> 00:13:40,680
+اتنين هو ال inverse ل اللي هو التلاتة modulo سبعة
+
+187
+00:13:40,680 --> 00:13:45,560
+زي ما احنا اتعلمنا الان بضرب الجهتين في ناقص تلاتة
+
+188
+00:13:45,560 --> 00:13:48,880
+اضرب هنا في ناقص تلاتة وهنا في ناقص اتنين اللي هو
+
+189
+00:13:48,880 --> 00:13:52,330
+ال inverseنقص اتنين في نقص اتنين بيصير عبارة عن
+
+190
+00:13:52,330 --> 00:13:55,910
+نقص اتنين في تلاتة تطابق نقص اتنين في أربعة مدلوا
+
+191
+00:13:55,910 --> 00:13:59,990
+سبعة الان ايش هذه عبارة عن نقص ستة تطابق نقص
+
+192
+00:13:59,990 --> 00:14:04,110
+تمانية مدلوا سبعة النقص الستة هي الواحد هي تطابق
+
+193
+00:14:04,110 --> 00:14:07,350
+الواحد لإنه هي نقص اتنين نقص تلاتة ال inverse وهذا
+
+194
+00:14:07,350 --> 00:14:11,480
+الفكرة أصلالأن ناقص ستة تطابق الواحد مدله سبعة لأن
+
+195
+00:14:11,480 --> 00:14:15,140
+ناقص ستة ناقص واحد تصبح ناقص سبعة السبعة تجسم ناقص
+
+196
+00:14:15,140 --> 00:14:18,660
+سبعة إذا فعلا كلامنا صحيح إذا ناقص ستة بيصير
+
+197
+00:14:18,660 --> 00:14:22,260
+مكانها اللي هي عبارة عن واحد لأن الواحد تطابق ناقص
+
+198
+00:14:22,260 --> 00:14:27,360
+ستة فبيصير عند ال X تطابق ناقص تمانية مدله سبعة
+
+199
+00:14:27,360 --> 00:14:34,500
+الآن ناقص تمانية اللي هي شيله ضفولها سبعةبصير عنده
+
+200
+00:14:34,500 --> 00:14:38,880
+اللي هو ناقص واحد لو دفنوله سبعتين بتصير اربعتاش
+
+201
+00:14:38,880 --> 00:14:42,660
+طب مش اللي بيسويه بالاضيف بالاضيف ما هو إضافات
+
+202
+00:14:42,660 --> 00:14:47,460
+السبعة أي إضافة للسبعة تطابق السفر مدل سبعةكيف
+
+203
+00:14:47,460 --> 00:14:50,580
+يعني؟ ايش اللي بقوله؟ ده نشوف لإن هذه الناقص
+
+204
+00:14:50,580 --> 00:14:55,800
+تمانية بالطبق من الستة مدرس سبعة ايش عرفك الستة؟
+
+205
+00:14:55,800 --> 00:15:00,980
+ضفت على السبعة على الناقص الآن ضفت اللي هي مضاعفات
+
+206
+00:15:00,980 --> 00:15:04,920
+السبعة سبعة وسبعة اربع طعش اربع طعش ناقص تمانية
+
+207
+00:15:04,920 --> 00:15:08,180
+بتطلع ستة عشان هيك طلعت ستة طب بتطلع هذا الكلام
+
+208
+00:15:08,180 --> 00:15:13,060
+صحيح؟ اه مضمون ليش؟تعالى سبعة بتجسم ناقص تمانية
+
+209
+00:15:13,060 --> 00:15:17,120
+ناقص ستة اللى ناقص اربعتاشر السبعة بتجسم مين ناقص
+
+210
+00:15:17,120 --> 00:15:21,720
+اربعتاشر يعنى دائما دائما لو كان عندى تلاتة اخلينا
+
+211
+00:15:21,720 --> 00:15:26,120
+نقول تلاتة تلاتة لو ضفتلها سبعة بيصير عشرة العشرة
+
+212
+00:15:26,120 --> 00:15:30,400
+تطابق التلاتة مدله سبعة اللى هو ضفلها كمان سبعة
+
+213
+00:15:30,400 --> 00:15:35,420
+اللى هى سبعة عشرة وسبعة سبعتاشر تطابق التلاتة مدله
+
+214
+00:15:35,420 --> 00:15:41,990
+سبعة يعنى دائما يا جماعة الان العددلو ضفته جد ما
+
+215
+00:15:41,990 --> 00:15:47,110
+ضفته من المقياس بظل طابق أسوأ يعني لو كان عنا في
+
+216
+00:15:47,110 --> 00:15:51,170
+الأصل خمسة وضفته لها سبعة بصير اتناشط وطابق خمسة
+
+217
+00:15:51,170 --> 00:15:54,730
+وضفته لها كمان سبعة بصير تسعتاش وطابق خمسة ولو
+
+218
+00:15:54,730 --> 00:15:58,270
+طرحت منه سبعة برضه بتظل المتطابقات عشان هيك هذه
+
+219
+00:15:58,270 --> 00:16:03,930
+بتساعدنا كتير بعد شوية في حل المتطابقات اذا صار
+
+220
+00:16:03,930 --> 00:16:08,810
+عند ال X تطابق الست مدله مين مدله سبعةومنه بيكون
+
+221
+00:16:08,810 --> 00:16:12,410
+ال solutions are the integers اللي هي مدام x وطابق
+
+222
+00:16:12,410 --> 00:16:17,110
+الستة إذا صار عند الستة و اللي هو ضيفله سبعة اللي
+
+223
+00:16:17,110 --> 00:16:22,230
+هي سبعة بيصير ستة و سبعة اللي هي تلت عشر ضيفله
+
+224
+00:16:22,230 --> 00:16:26,270
+كمان سبعة بيصير اللي هو تلت عشر و سبعة عشرين اطرح
+
+225
+00:16:26,270 --> 00:16:29,970
+منه سبعة من الستة بتطلع نقص واحد اطرح منه كمان
+
+226
+00:16:29,970 --> 00:16:33,030
+سبعة نقص تمانية اطرح منه كمان سبعة بيصير نقص خمس
+
+227
+00:16:33,030 --> 00:16:38,170
+عشر إذا كل دولة اللي هنحل الاكس بطابق السبعة أو حل
+
+228
+00:16:38,170 --> 00:16:40,650
+الاكس بطابق الستة modulo سبعة
+
+229
+00:16:43,670 --> 00:16:47,670
+الان بعد شوية هتلاقيني بقى اريحكم في الحل هذا يعني
+
+230
+00:16:47,670 --> 00:16:50,730
+بدون حتى ما نستخدم اللي هو ال inverses و كده
+
+231
+00:16:50,730 --> 00:16:55,410
+هتلاقوني باستخدم اللي هو طريقة اللي هي بتعتمد على
+
+232
+00:16:55,410 --> 00:17:01,270
+مضاعفات السبعة بنضيف او نطرح و بنخلي ال X لحاله و
+
+233
+00:17:01,270 --> 00:17:04,950
+الباقي هان لحاله فبتكون الحلول سهلة بعد شوية ان
+
+234
+00:17:04,950 --> 00:17:08,450
+شاء الله هنشوف هذه الطريقة في ال chinese remainder
+
+235
+00:17:08,450 --> 00:17:13,750
+theoremاللي هو نثبت هذه الطريقة اللي أخدناها الآن
+
+236
+00:17:13,750 --> 00:17:17,510
+ان شاء الله و بعد شوية نشوف ال chinese remandatory
+
+237
+00:17:17,510 --> 00:17:22,010
+يعنيخلّينا نجي لان لـ Chinese remainder theorem أو
+
+238
+00:17:22,010 --> 00:17:28,570
+نظرية البواق الصينية المشهورة في بعض المثال كانت
+
+239
+00:17:28,570 --> 00:17:34,470
+تطرح قديما أحد المثال هو أحد العلماء الصينيين سان
+
+240
+00:17:34,470 --> 00:17:40,210
+تسو أسكت the following بيقول اللي بدي عدد اللي هو
+
+241
+00:17:40,210 --> 00:17:46,370
+يقبل الجسم على تلاتة والمتبقي له اتنينو هو نفسه لو
+
+242
+00:17:46,370 --> 00:17:50,510
+قسمته على خمسة المتبقي تلاتة و هو نفسه لو قسمته
+
+243
+00:17:50,510 --> 00:17:54,510
+على سبعة المتبقي جديش اتنين بقول ايش هذا العدد
+
+244
+00:17:54,510 --> 00:18:02,610
+الان طبعا اللي هو الفكرة الان ايش هي ان احنا بنحول
+
+245
+00:18:02,610 --> 00:18:08,130
+اللي هي الحديث هذا الى تطابقات ايش علاقة الموضوع
+
+246
+00:18:08,130 --> 00:18:13,080
+بالتطابقاتأحنا بنقول دائما إن العدد دائما يطابق
+
+247
+00:18:13,080 --> 00:18:19,020
+اللي هو المتبق إله لو قسمناه على عدد ما يعني الآن
+
+248
+00:18:19,020 --> 00:18:24,320
+لو أجينا قسمنا عدد على اللي هو تلاتة وكان المتبق
+
+249
+00:18:24,320 --> 00:18:28,060
+اتنين معناته صار العدد يطابق التنين مدله تلاتة
+
+250
+00:18:28,060 --> 00:18:33,540
+عشان هي فرضنا نفرض إن العدد اسمه Xهذا ال X إذا
+
+251
+00:18:33,540 --> 00:18:38,020
+قسمته على تلاتة هيظل اتنين عشان هيك اختارت ليه
+
+252
+00:18:38,020 --> 00:18:43,280
+التطابق X تطابق اتنين مدله تلاتة بس هو قال طب انا
+
+253
+00:18:43,280 --> 00:18:48,280
+بدي العدد نفسه يقبل ما يلي انه لو اجيت قسمته على
+
+254
+00:18:48,280 --> 00:18:53,130
+خمسة يظل المتبقى تلاتةما دام يقبل اللي بدك تجسمه
+
+255
+00:18:53,130 --> 00:18:57,670
+على ال X تجسمه على خمسة و يظل تلاتة معناته هذا ال
+
+256
+00:18:57,670 --> 00:19:03,190
+X حيطابق المتبقق له التلاتة مقياس مين مقياس الخمسة
+
+257
+00:19:03,190 --> 00:19:07,250
+اللي جسمته عليه لأ و طلب كمان أكتر من هيجال لأ بدي
+
+258
+00:19:07,250 --> 00:19:12,590
+نفس العدد اللي هو لو قسمته على سبعة يظل المتبقى
+
+259
+00:19:12,590 --> 00:19:18,280
+اتنينترجمها برضه لصورة المتطابق احنا نقول ال X
+
+260
+00:19:18,280 --> 00:19:22,340
+بطابق المتبقي modulo المقسوم عليه اللي هو مين
+
+261
+00:19:22,340 --> 00:19:26,940
+السبعة عشان هيك قال اللي هي ال X اللي انتوا
+
+262
+00:19:26,940 --> 00:19:31,580
+طلبتوها يا جماعةاللي لو جسمناها تلاتة بيظل اتنين و
+
+263
+00:19:31,580 --> 00:19:35,300
+جسمناها خمسة بيظل تلاتة و جسمناها سبعة بيظل اتنين
+
+264
+00:19:35,300 --> 00:19:39,240
+نحن نترجمها إلى اللي هو system of linear
+
+265
+00:19:39,240 --> 00:19:42,940
+congruences اللي هو X وطابق اتنين modulo تلاتة X
+
+266
+00:19:42,940 --> 00:19:45,860
+وطابق التلاتة modulo خمسة X وطابق التنين modulo
+
+267
+00:19:45,860 --> 00:19:50,280
+سبعة يعني X وطابق اللي هو المتبقي modulo المقسوم
+
+268
+00:19:50,280 --> 00:19:54,340
+عليه لما نجسم X على تلاتةX تطابق اللي هو التلاتة
+
+269
+00:19:54,340 --> 00:19:57,700
+المتبقية لما نجسم X على خمسة X تطابق اللي هي
+
+270
+00:19:57,700 --> 00:20:01,200
+المتبقى اتنين لما نجسمها على سبعة فاتحولت إلى
+
+271
+00:20:01,200 --> 00:20:05,300
+تطابقات اللي هي ده تنحل في نفس الوقت عشان هي كانت
+
+272
+00:20:05,300 --> 00:20:10,420
+نسميها system of linear congruencesو هذه اللي هي
+
+273
+00:20:10,420 --> 00:20:13,560
+اللي بيحلها عادة اسمها ال chinese remainder
+
+274
+00:20:13,560 --> 00:20:18,100
+theorem اللي الآن احنا هندرس ايه اللي هو كيف اللي
+
+275
+00:20:18,100 --> 00:20:23,320
+هي ايش النظرية بتقول متى بيكون حل و كيف بنحل اللي
+
+276
+00:20:23,320 --> 00:20:28,860
+هو التطابقاتThe Chinese remainder theorem بتقول ما
+
+277
+00:20:28,860 --> 00:20:35,920
+يلي بالظبط Theorem 2 بتقول let M1, M2, Mn be
+
+278
+00:20:35,920 --> 00:20:39,240
+pairwise relatively prime positive integers
+
+279
+00:20:39,240 --> 00:20:43,620
+greater than one يعني هدول M1 و M2, Mn كلهم
+
+280
+00:20:43,620 --> 00:20:46,300
+positive integer أكبر من واحد و relatively prime
+
+281
+00:20:46,570 --> 00:20:50,510
+ونفترض a1 و a2 و aN are arbitrary integers، then
+
+282
+00:20:50,510 --> 00:20:56,310
+the system X تطابق ال a1 a1 عدد، X تطابق ال a2 a2
+
+283
+00:20:56,310 --> 00:21:01,050
+عدد، X تطابق ال aN aN عدد، طبعاً هذه مدولة M1 و
+
+284
+00:21:01,050 --> 00:21:05,150
+هذه مدولة M2 ومدولة MNلو كان في عندي system of
+
+285
+00:21:05,150 --> 00:21:09,790
+linear congruences بالشكل هذا و كلهم المجهول فيهم
+
+286
+00:21:09,790 --> 00:21:15,490
+X و ال M1 و ال M2 و ال MN كلهم relatively prime
+
+287
+00:21:15,490 --> 00:21:19,210
+بتقولك ال Chinese remainder theorem إذا يوجد حل
+
+288
+00:21:19,210 --> 00:21:22,950
+مشترك وحيد لهذه المجموعات اللي هو has a unique
+
+289
+00:21:22,950 --> 00:21:29,040
+solution modulo M اللي هو Mم1 م2 في مين في من يعني
+
+290
+00:21:29,040 --> 00:21:32,140
+بتقولك الآن اللي هي chinese remainder theorem لو
+
+291
+00:21:32,140 --> 00:21:36,580
+كان عندك فيه system من اللي هو ال linear
+
+292
+00:21:36,580 --> 00:21:40,360
+congruences هذه تطابق اي واحد مدل ام واحد وال X
+
+293
+00:21:40,360 --> 00:21:45,060
+تطابق اتنين مدل ام اتنينتطابق en modulo mn هذي
+
+294
+00:21:45,060 --> 00:21:50,840
+بيكون solution unique لها modulo m بس بشرط ان m1 و
+
+295
+00:21:50,840 --> 00:21:54,820
+m2 و mn يكون in pair wise relatively prime يعني كل
+
+296
+00:21:54,820 --> 00:21:58,420
+تنتين مع بعض العامل المشترك الأعلى بينهين بساوي
+
+297
+00:21:58,420 --> 00:22:02,610
+واحدthat is there is a solution x زي ما بقول x
+
+298
+00:22:02,610 --> 00:22:06,410
+أكبر أو سوى سفر أو أصغر من M يعني لأنه مدل M يعني
+
+299
+00:22:06,410 --> 00:22:10,110
+من عند السفر لعند ال M أو من عند ال واحد لعند ال M
+
+300
+00:22:10,110 --> 00:22:14,390
+نفسها أو من السفر لعند ال M ناقص واحد and all
+
+301
+00:22:14,390 --> 00:22:17,230
+other solutions are congruent مدل M to this
+
+302
+00:22:17,230 --> 00:22:20,710
+solution يعني أي solution تاني هتلاقيه هيلاقيه
+
+303
+00:22:20,710 --> 00:22:25,530
+اللي هو العدد اللي لاجيناه زائد اللي هو مضاعفات من
+
+304
+00:22:25,530 --> 00:22:30,780
+ال M يعني يطابق ال Mاللي هو Modulo .. طابق ال ..
+
+305
+00:22:30,780 --> 00:22:37,300
+ال .. ال X Modulo اللي هي ال M الان نشوف كيف بدنا
+
+306
+00:22:37,300 --> 00:22:40,660
+نستخدم ال Chinese remainder theorem to find a
+
+307
+00:22:40,660 --> 00:22:45,600
+solution الان تركز معايا هذه ال .. ال .. ال ..
+
+308
+00:22:45,600 --> 00:22:49,740
+التطابقات اللي موجودة عندك بدك توجد الحل المشترك
+
+309
+00:22:49,740 --> 00:22:56,320
+بينهمأولا نسمي ام واحد capital ام واحد اللي هي
+
+310
+00:22:56,320 --> 00:23:01,380
+عبارة عن حاصل الضرب هذا الام على ام واحد ام اتنين
+
+311
+00:23:01,380 --> 00:23:06,140
+capital ام اتنين capital بتساوي ام على ام اتنين
+
+312
+00:23:06,140 --> 00:23:09,380
+small ام تلاتة capital بتساوي ام على ام تلاتة
+
+313
+00:23:09,380 --> 00:23:15,400
+small وهكذا لما نخلص على كل المعادلاتأذا و كأن كل
+
+314
+00:23:15,400 --> 00:23:19,780
+معادلة .. كل تطابقة من هدول بجيبلهم M و M كبيرة
+
+315
+00:23:19,780 --> 00:23:25,220
+هذا هي .. هتلزمني بعد شوية ركز فيها بعد ما سميتها
+
+316
+00:23:25,220 --> 00:23:30,700
+بدي آجي أحل التطابقة التالية التطابقة اللي هي مايا
+
+317
+00:23:30,700 --> 00:23:37,760
+ليه M1 في Y1 تطابق الواحد مدل مين M1 مين M1 هذه
+
+318
+00:23:37,760 --> 00:23:44,960
+اللي هي تبعت هذهمن M1 هذه اللي جسمتها على M1 small
+
+319
+00:23:44,960 --> 00:23:50,060
+M على M1 small إذا بعد ما جسمت هذه بحل التطابقات
+
+320
+00:23:50,060 --> 00:23:53,840
+التالية طبعا التطابقات هدولة هيكون عددهن لإن قلت
+
+321
+00:23:53,840 --> 00:23:59,320
+MK وYK تطابق الواحد مضله MK حيث اللي هي YK مجهول
+
+322
+00:23:59,320 --> 00:24:04,450
+هو اللي بتدوجد من حل هذهوالـ k هذه من واحد لعند ان
+
+323
+00:24:04,450 --> 00:24:09,030
+بعدد مين اللي هي التطابقات اللي موجودة في الأصل
+
+324
+00:24:09,030 --> 00:24:13,430
+إذا بدي الآن الخطوة اللي بعدها بعد ما سميت ال mk
+
+325
+00:24:13,430 --> 00:24:19,010
+بالطريقة هذه بدي أحل التطابق mk في yk mk بتكون
+
+326
+00:24:19,010 --> 00:24:23,010
+معطية عدد أو جدناه و ال yk هو المجهول اللي بده
+
+327
+00:24:23,010 --> 00:24:27,890
+وجده تطابق الواحد modulo mkبعد ما حل التطابق هذه
+
+328
+00:24:27,890 --> 00:24:31,230
+اوجد ال yk يعني انا بدأ اوجد ال y1 و ال y2 لعند ال
+
+329
+00:24:31,230 --> 00:24:36,350
+yn بعد موجودة هنا بقول the unique solution modulo
+
+330
+00:24:36,350 --> 00:24:39,950
+m is given by إذن هذا قانون حيطلع عليه إيش اللي هو
+
+331
+00:24:39,950 --> 00:24:44,790
+ال solution x بتساوي a1 m1 a1 هذا اللي أنا ظهرتالـ
+
+332
+00:24:44,790 --> 00:24:48,530
+M1 هذه مين اللي هي من هنا الـ Y1 اللي هي اللي
+
+333
+00:24:48,530 --> 00:24:51,550
+بتغلبنا هذه اللي هي ال solution اللي هنجدها الان
+
+334
+00:24:51,550 --> 00:24:56,790
+زاد نفس الاشي لمين للمعادلة التانية A2 اللي هي في
+
+335
+00:24:56,790 --> 00:25:00,950
+A2 هنا طيب مضروبة في M2 M2 هذه اللي جيبناها من هنا
+
+336
+00:25:01,280 --> 00:25:05,180
+الـ Y2 اللي جيبناها من هنا لما أصل لآخر معادلة
+
+337
+00:25:05,180 --> 00:25:11,180
+اللي هي AN في MN تبعتها في YN تبعتها اللي حليتها
+
+338
+00:25:11,180 --> 00:25:15,860
+هنا فبتطلع هذه هي ال X اللي أمامي هي عبارة عن ال
+
+339
+00:25:15,860 --> 00:25:21,640
+solutionالـ unique solution لأ ال system هذا كله
+
+340
+00:25:21,640 --> 00:25:27,540
+مدلمين مدلؤمل وحاصل الدرب الكلية الآن هي التلات
+
+341
+00:25:27,540 --> 00:25:32,140
+خطوات اللي بدنا نختوها من أجل حل اللي هو system of
+
+342
+00:25:32,140 --> 00:25:36,500
+linear equations تسميت mk اول اشي و بعدين نحل هذه
+
+343
+00:25:36,500 --> 00:25:40,640
+التطابقه و بعدين نعوض في هذه بيكون خلصنااللي هو
+
+344
+00:25:40,640 --> 00:25:44,260
+حلنا اللي هو سؤال الـ Chinese remainder theorem
+
+345
+00:25:44,260 --> 00:25:50,260
+والآن نيجي إلى اللي هو مثال عملي لتطبيقهخلّيني انا
+
+346
+00:25:50,260 --> 00:25:53,040
+شوف مثال عملي على اللي هو chinese remainder
+
+347
+00:25:53,040 --> 00:25:57,300
+theorem بقول consider the three congruences from
+
+348
+00:25:57,300 --> 00:26:01,460
+some two problem two problem اللي قبل شوية عرضناها
+
+349
+00:26:01,460 --> 00:26:05,380
+يعني X تطابق التنين مدولة تلاتة X تطابق التلاتة
+
+350
+00:26:05,380 --> 00:26:08,960
+مدولة خمسة X تطابق التنين مدولة سبعة الان هذه
+
+351
+00:26:08,960 --> 00:26:14,700
+بتمثلي A1 هذه بتمثلي A2 هذه بتمثلي A3 اللي هحتاجين
+
+352
+00:26:14,700 --> 00:26:21,680
+بعد شوية هذه M1 هذه M2 هذه M3خلّينا نشوف الآن بدنا
+
+353
+00:26:21,680 --> 00:26:26,200
+ناخد اللي هو ال .. ال M اللي هي حاصل ضرب تلاتة في
+
+354
+00:26:26,200 --> 00:26:30,000
+خمسة في سبعة الأمات مع بعض يعني M هذه هي تلاتة في
+
+355
+00:26:30,000 --> 00:26:33,160
+خمسة في سبعة اللي هي مية و خمسة منها بدنا نحسب ال
+
+356
+00:26:33,160 --> 00:26:35,980
+M واحد capital زي ما شوفنا قبل شوية M واحد capital
+
+357
+00:26:35,980 --> 00:26:39,460
+هي عبارة عن اللي هو المية و خمسة بنجسمها على
+
+358
+00:26:39,460 --> 00:26:43,620
+التلاتة بيطلع جداش خمسة و تلاتين M اتنين capital
+
+359
+00:26:43,620 --> 00:26:47,340
+هذه اللي هي المية و خمسة مجسمة على الخمسة هذه اللي
+
+360
+00:26:47,340 --> 00:26:52,610
+هي بيطلع واحد و عشرينM3 هي 105 عالى 7 اللي هنا
+
+361
+00:26:52,610 --> 00:26:58,030
+بتطلع جداش 15 الآن نيجي للخطوة المركزية المهمة لأن
+
+362
+00:26:58,030 --> 00:27:01,430
+we solve the congruences التالية بدنا نحل المين
+
+363
+00:27:01,430 --> 00:27:06,550
+اللي هو M1 Y1 تطابق الواحد مدل M1 الان M1 جداش
+
+364
+00:27:06,550 --> 00:27:11,550
+اودتنا هي اللي هي عبارة عن 35 يصير 35 Y1 تطابق
+
+365
+00:27:11,550 --> 00:27:17,120
+الواحد مدل ومين M1 اللي هي جداش 3 بدنا نحل هذهالان
+
+366
+00:27:17,120 --> 00:27:20,740
+طريقة الحل هذه ماعنش نقعد ندور على اللي هو ال
+
+367
+00:27:20,740 --> 00:27:23,740
+inverse لهذا ومش عارف ايش لأ لأ لأ اسهلكم كتير
+
+368
+00:27:23,740 --> 00:27:27,280
+كتير كتير اللي هو ايش من نيجي بنشيل من خمسة و
+
+369
+00:27:27,280 --> 00:27:32,540
+تلاتين كل مضاعفات من التلاتة الان بنشيل من هذه
+
+370
+00:27:32,540 --> 00:27:35,920
+اللي هو عبارة عن مضاعفات التلاتة اقرب اشي للتلاتة
+
+371
+00:27:35,920 --> 00:27:39,640
+خمسة و تلاتين يعني على التلاتة بتطلع اللي هي
+
+372
+00:27:39,640 --> 00:27:45,640
+المتبقى جداش اتنينلأنه بيصير 11 والمتبقي اللي هو 2
+
+373
+00:27:45,640 --> 00:27:50,000
+يعني بقسم 35 على 3 بطلع اللي هو عدد مضل المتبقي
+
+374
+00:27:50,000 --> 00:27:54,080
+المتبقي هو اللي بيبقى بيبقى بضل لأن هذا ال 35
+
+375
+00:27:54,080 --> 00:28:00,400
+بيصير يطابق المتبقي 32 مظلمين مضلو اللي هي التلاتة
+
+376
+00:28:00,400 --> 00:28:04,220
+ماشي الحال إذا انشلنا من 35 مضاعفات التلاتة اللي
+
+377
+00:28:04,220 --> 00:28:10,180
+هي 33 اللي هي بيبقى الجداش 2 بيصير 2 Y1 تطابق الآن
+
+378
+00:28:10,180 --> 00:28:14,130
+الواحدانا بيصير اتنين و اي واحد وطابق الواحد بس
+
+379
+00:28:14,130 --> 00:28:19,510
+عشان انا بتدجسم بعد شوية بدي احول الواحد لرقم زوجي
+
+380
+00:28:19,510 --> 00:28:24,430
+ايش احول رقم زوجي؟ واحد بطابقه الان بضيفله تلاتة
+
+381
+00:28:24,430 --> 00:28:28,150
+او بطرح منه تلاتة بيصير اللي هو عدد زوجي طب بنفع
+
+382
+00:28:28,150 --> 00:28:31,470
+اه لان لو ضفتله تلاتة بيصير الأربعة الأربعة بتطابق
+
+383
+00:28:31,470 --> 00:28:38,010
+الواحد مدله مين مدله تلاتةإذا انت لها نوهان ضيف زي
+
+384
+00:28:38,010 --> 00:28:42,310
+ما بدك من مضاعفات التلاتة أو اطرح مضاعفات التلاتة
+
+385
+00:28:42,310 --> 00:28:46,530
+للوصول للأعداد القليلة اللي بتقدر تستخدمها زي ما
+
+386
+00:28:46,530 --> 00:28:49,530
+بدك بظله نفس ال issue متطابق
+
+387
+00:28:58,270 --> 00:29:02,990
+بينفع تجسم اذا العامل المشترك الاعلى بين اللي بده
+
+388
+00:29:02,990 --> 00:29:06,390
+جسمه وبين التلاتة ايش بيساوي واحد وهي العامل
+
+389
+00:29:06,390 --> 00:29:09,570
+المشترك الاعلى بين التلاتة وبين الواحدبين الـ 3 و
+
+390
+00:29:09,570 --> 00:29:12,530
+بين الـ 2 و 1 إذا أنا بقول شيء سهولة بقول على 2
+
+391
+00:29:12,530 --> 00:29:17,270
+بظهر Y1 على 2 بظهر 2 فبصير Y1 تطابق الـ 2 مدلة 3
+
+392
+00:29:17,270 --> 00:29:21,650
+هي عبارة عن حل الـ congrance هذه شايفين مثلًا حل
+
+393
+00:29:21,650 --> 00:29:24,110
+الـ linear congrance أسهل من ما نقعد نودد ال
+
+394
+00:29:24,110 --> 00:29:27,870
+inverse زي ما قلنا قبل شوية نيجي الآن نعملها مع
+
+395
+00:29:27,870 --> 00:29:32,410
+الأولى و نعملها مع التالية باجي بقول M2 في Y2
+
+396
+00:29:32,410 --> 00:29:38,480
+تطابق الواحد مدلة M2 مين M2 هيها 21Y2 مين هي
+
+397
+00:29:38,480 --> 00:29:45,260
+المجهول الان يصبح 21 Y2 تطابق الواحد مضله مين اما
+
+398
+00:29:45,260 --> 00:29:49,460
+2 small هي هادي هيها هادي هي بيصير مضله خمسة الان
+
+399
+00:29:49,460 --> 00:29:54,480
+نحل هادي لحسن حظنا هادي اصلا لو شيلنا منها مضعفات
+
+400
+00:29:54,480 --> 00:29:59,380
+الخمسة اللي هي عشرين بظل بس مين واحد فبتظل Y2
+
+401
+00:29:59,380 --> 00:30:03,720
+تطابق الواحد مضله خمسة يعني بس اشتغلت على هادي قلت
+
+402
+00:30:03,720 --> 00:30:09,010
+بما ان الواحد عشرين تطابق الواحداللي هو إذا صار
+
+403
+00:30:09,010 --> 00:30:12,870
+عندى الـ y .. ال 21 y2 تطابق ال y2 حطيت مكانها
+
+404
+00:30:12,870 --> 00:30:20,050
+يعني بمعنى أخر شلت مضاعفات ال 21 اللي هي عشرين ضلت
+
+405
+00:30:20,050 --> 00:30:24,670
+واحدة واحد صار y2 و هو اللي جاهز صار y2 تطابق
+
+406
+00:30:24,670 --> 00:30:27,230
+الواحد و دولة خمسة اللي ما استبعبش هذه خلينا اللي
+
+407
+00:30:27,230 --> 00:30:32,410
+بعدهاالان نعمل M3 Y3 تطابق الواحد يعني بعدد مين
+
+408
+00:30:32,410 --> 00:30:37,210
+التطابقات اللي موجودة الان M3 اللي هي مين عبارة عن
+
+409
+00:30:37,210 --> 00:30:41,570
+اوددناها اللي هي خمست عشر يصير خمست عشر Y3 المجهول
+
+410
+00:30:41,570 --> 00:30:46,550
+تطابق الواحد موضله مين موضله سبعة السبعة مين
+
+411
+00:30:46,550 --> 00:30:50,380
+السبعة اللي هي ال M3 اللي عندىطبعا ليش انت بتحل
+
+412
+00:30:50,380 --> 00:30:53,580
+هدولة .. هدولة في القانون .. هدولة حالهن .. هن
+
+413
+00:30:53,580 --> 00:30:57,220
+اللي بدنا نعوض من حالهن هنا بتطلع ليه اللي هو مين
+
+414
+00:30:57,220 --> 00:31:01,860
+اللي هي الحل العام حسب اللي هو مين الطريقة تبعت
+
+415
+00:31:01,860 --> 00:31:05,460
+Chinese remainder theorem إذا صار عندي الان Y1 وY3
+
+416
+00:31:05,460 --> 00:31:08,980
+هذا آسف مش Y1 وY3 وطبعا كل واحد مدله مين مدله سبعة
+
+417
+00:31:09,210 --> 00:31:14,310
+إذا صار هي عندي Y1 هنا و Y2 هنا و Y3 هنا دلت علي
+
+418
+00:31:14,310 --> 00:31:17,750
+العملية الأخيرة هي عملية التعويض بكون أوجدت الحل
+
+419
+00:31:17,750 --> 00:31:24,190
+النهائي X بتساوي A1 M1 Y1 A2 M2 Y2 زي A3 MY3 هي
+
+420
+00:31:24,190 --> 00:31:28,950
+قانوننا اللي هو قانون اللي هو بجيب لحل ال system
+
+421
+00:31:28,950 --> 00:31:33,270
+كله بعد ما اتأكدنا ال 3 وال5 وال7 اللي تيبل براين
+
+422
+00:31:33,270 --> 00:31:38,870
+بكون هذا هو حل ال system A1 مين هي؟ هي هالتنينام
+
+423
+00:31:38,870 --> 00:31:42,230
+واحد او جدناها اللي هي خمس و تلاتين Y واحد هم اللي
+
+424
+00:31:42,230 --> 00:31:45,410
+حللناها عشان خطر الاتنين فبصير اتنين في خمس و
+
+425
+00:31:45,410 --> 00:31:48,950
+تلاتين في اتنين اتنين هي الاتنين اتنين ليها تلاتة
+
+426
+00:31:49,340 --> 00:31:53,260
+الان مضروبة في مين في و ام اتنين اللي هي جديش واحد
+
+427
+00:31:53,260 --> 00:31:56,120
+و عشرين هاي واحد و عشرين في واي اتنين اللي هي
+
+428
+00:31:56,120 --> 00:32:00,220
+اوجدناها اللي هي واحد زاد اتلاتة هاي اتلاتة اللي
+
+429
+00:32:00,220 --> 00:32:04,960
+هي برضه جديش اتنين مظبوط هاي اتنين في مين في
+
+430
+00:32:04,960 --> 00:32:07,660
+خمستاشر اللي هي ام تلاتة في واي تلاتة اللي هي
+
+431
+00:32:07,660 --> 00:32:13,260
+اوجدناها بتساوي واحد طلع عند الرقم تلت و تلتينإذا
+
+432
+00:32:13,260 --> 00:32:20,560
+X بيثاور 233 لكن أنا بيدخلي هذا العدد من أعداد
+
+433
+00:32:20,560 --> 00:32:26,400
+1 لعند 105 أو من 0 لعند 104 ماشي فبشيل منه كل
+
+434
+00:32:26,400 --> 00:32:32,010
+مضاعفات 105مضاعفات الـ 105 مضاعفات الـ 210 مضاعفات
+
+435
+00:32:32,010 --> 00:32:36,250
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+436
+00:32:36,250 --> 00:32:37,490
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+437
+00:32:37,490 --> 00:32:40,030
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+438
+00:32:40,030 --> 00:32:42,170
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+439
+00:32:42,170 --> 00:32:44,150
+الـ 230 مضاعفات الـ 230 مضاعفات الـ 230 مضاعفات
+
+440
+00:32:44,150 --> 00:32:50,580
+الـ 230 مضاعفات الـ 230لكن .. لكن .. لكن عندى اللى
+
+441
+00:32:50,580 --> 00:32:54,620
+هو عدد لانهاء من الحلول اللى هى اللى متطابقات الهن
+
+442
+00:32:54,620 --> 00:33:03,200
+زى الـ 233 و زى لما نزيد 105 ليها بيصير 1728 و لو
+
+443
+00:33:03,200 --> 00:33:07,020
+ضارحنا 105 و لو ضارحنا 105 بيطلع عندك اللى هو كل
+
+444
+00:33:07,020 --> 00:33:11,770
+اللى بيطابق هنا الـ 23 مضلوا 105هي عبارة عن حلول
+
+445
+00:33:11,770 --> 00:33:16,610
+لهذا الـ System او اختصارا اختزالا نختزل الحل في X
+
+446
+00:33:16,610 --> 00:33:21,230
+تو طابق الـ 23 مدله 105 و اللي بده يوجد الأرقام زي
+
+447
+00:33:21,230 --> 00:33:26,790
+ما بده بوجدها بضيف 105ات و يطرح 150اتبكون we have
+
+448
+00:33:26,790 --> 00:33:30,070
+shown that 23 is the smallest positive integer
+
+449
+00:33:30,070 --> 00:33:34,950
+that is simultaneous solution اللي هو يعني هو 23
+
+450
+00:33:34,950 --> 00:33:39,870
+هو عبارة عن أصغر عدد بجسم اللي هما إيش اللي هي
+
+451
+00:33:39,870 --> 00:33:42,890
+التلاتة و المتبقى اتنين و بجسم الخمسة و المتبقى
+
+452
+00:33:42,890 --> 00:33:46,430
+تلاتة و بجسم السبعة و المتبقى جديش اتنين أو هو
+
+453
+00:33:46,430 --> 00:33:50,370
+عبارة عن الحل العام لهذا ال system of linear
+
+454
+00:33:50,370 --> 00:33:55,510
+equationsطيب نيجي الآن إلى اللي هو طريقة ثانية لحل
+
+455
+00:33:55,510 --> 00:33:59,450
+اللي هي المعادلات التطابقات الهالية حاجة اسمها
+
+456
+00:33:59,450 --> 00:34:04,820
+الباق substitution تنشوف كيف بدنا نحلالان بدنا نحل
+
+457
+00:34:04,820 --> 00:34:11,420
+اللي هو system of linear congruences باستخدام حاجة
+
+458
+00:34:11,420 --> 00:34:14,800
+اسمها ال back substitution ال back substitution
+
+459
+00:34:14,800 --> 00:34:19,420
+اللي هي بتعتمد انه بنحول ال linear congruences إلى
+
+460
+00:34:19,420 --> 00:34:23,400
+معادلات و من ثم بنبدأ نعوض و نرجع و نرجع لما نصل
+
+461
+00:34:23,400 --> 00:34:26,480
+لحل انهيط نشوف كيف برضه اللي هو ان شاء الله
+
+462
+00:34:26,480 --> 00:34:29,970
+الطريقةسهل لو تابعوا معايا هتلاقوا حالكم تعرفوا
+
+463
+00:34:29,970 --> 00:34:33,530
+تحلو ان شاء الله example use the method of back
+
+464
+00:34:33,530 --> 00:34:37,470
+substitution to find all integers x such that أوجد
+
+465
+00:34:37,470 --> 00:34:41,630
+كل الأعداد x التي تحقق x وطابق الواحد مدل خمسة او
+
+466
+00:34:41,630 --> 00:34:45,230
+x وطابق التانية مدل خمسة وفي نفس الوقت x وطابق
+
+467
+00:34:45,230 --> 00:34:48,770
+التلاتة مدل سبعة يعني بدنا نحل العاملة هذه اللي هو
+
+468
+00:34:48,770 --> 00:34:54,590
+ال system of linear congruences شوفوا الأولبنبدأ
+
+469
+00:34:54,590 --> 00:34:57,770
+في الأولى الان x تطابق الواحد من دول الخمسة الغرض
+
+470
+00:34:57,770 --> 00:35:01,030
+إيجاد قيمة x يا جماعة since x تطابق الواحد من دول
+
+471
+00:35:01,030 --> 00:35:04,570
+الخمسة إذا حسب المفهوم اللي هو التطابق بتكون
+
+472
+00:35:04,570 --> 00:35:07,970
+الخمسة بتجسم ال x minus واحد إيش معناته الخمسة
+
+473
+00:35:07,970 --> 00:35:10,930
+بتجسم ال x minus واحد يعني ال x minus واحد بتساوي
+
+474
+00:35:10,930 --> 00:35:15,110
+خمسة في sum integer mean T يعني x ناقص واحد بتساوي
+
+475
+00:35:15,110 --> 00:35:20,890
+خمسة في T اللي هو حيث T عدد صحيح ماشي الان so بس
+
+476
+00:35:20,890 --> 00:35:24,760
+بتدنجل الواحد هنا بيصير x بتساوي خمسة زائد إيشزاقة
+
+477
+00:35:24,760 --> 00:35:28,480
+T الآن صارت عندي خمسة بالساوية X بالساوية خمسة
+
+478
+00:35:28,480 --> 00:35:32,180
+زاقة T بتعوض عن قيمة X هنا لأن ده وجود الحل
+
+479
+00:35:32,180 --> 00:35:36,360
+المشترك هذه حققت المعادلة الأولى أو التطابق الأولى
+
+480
+00:35:36,360 --> 00:35:41,140
+هذه حققت التطابق الأولى بتعوضها هنا عشان تحقق
+
+481
+00:35:41,140 --> 00:35:45,860
+التطابق التانيةطيب إذا عوضولي في هذه عن قيمة خمسة
+
+482
+00:35:45,860 --> 00:35:49,680
+T زائد واحد Substituting into X في الطابق اتنين
+
+483
+00:35:49,680 --> 00:35:54,500
+مدله ستة هذه yields بنتجلي خمسة T زائد واحد مكان
+
+484
+00:35:54,500 --> 00:35:59,180
+ال X تطابق التنين مدله ستة انجلي هذا على الجهة هذه
+
+485
+00:35:59,180 --> 00:36:03,440
+بيصير ليه خمسة T تطابق الواحد مدله إياش مدله ستة
+
+486
+00:36:03,440 --> 00:36:06,400
+لأنه اتنين ناقص واحد بيطلع واحد الآن زي ما عملنا
+
+487
+00:36:06,400 --> 00:36:10,040
+قبل بشوية بدي أشيل من هذه مضاعفات ال .. من مضاعفات
+
+488
+00:36:10,040 --> 00:36:17,640
+الستة-6-6-6
+
+489
+00:36:17,640 --> 00:36:22,160
+-6-6-6
+
+490
+00:36:22,160 --> 00:36:30,400
+-6-6-6-6-6-6
+
+491
+00:36:30,400 --> 00:36:32,760
+-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6
+
+492
+00:36:32,760 --> 00:36:32,780
+-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6-6
+
+493
+00:36:36,280 --> 00:36:39,300
+الأن نقص واحد أنا ما بديش يامودب سالب بدي يامودب
+
+494
+00:36:39,300 --> 00:36:43,040
+الان بضيف على الناقص واحد اللي هو ستة او مضاعفات
+
+495
+00:36:43,040 --> 00:36:47,880
+الستة صح اه طبعا اتفجنا علي هذا الكلام انه بيطلع
+
+496
+00:36:47,880 --> 00:36:51,820
+متطابق لما نضيف المضاعفات المقياس ستة و ناقص واحد
+
+497
+00:36:51,820 --> 00:36:55,420
+بيطلع خمسة اذا T تطابق الخمسة modulo 6 اذا T
+
+498
+00:36:55,420 --> 00:37:01,340
+تبعتنا هادى الجنها بتحقق T بطابق الخمسة modulo 6
+
+499
+00:37:01,760 --> 00:37:06,860
+طيب هذه الأن بدي أكتبها على صورة معادلة زي ما عملت
+
+500
+00:37:06,860 --> 00:37:10,220
+في مين؟ في الـ X اللي فوق اللي أنصرت X اللي عندنا
+
+501
+00:37:10,220 --> 00:37:15,280
+حققت هذه وهي حققت هذه بس خلّيني أكمل T تطابق
+
+502
+00:37:15,280 --> 00:37:18,860
+الخمسة modulo ستة أيش معناته؟ يعني الستة بتجسم الـ
+
+503
+00:37:18,860 --> 00:37:22,240
+T minus خمسة يعني الـ T minus خمسة بالساوية ستة في
+
+504
+00:37:22,240 --> 00:37:26,180
+U مثلا أو T بتساوية ستة U زائد خمسة زي ما عملت فوق
+
+505
+00:37:26,180 --> 00:37:29,840
+بالظبط بدي أعمل في هذه بالطريقة اللي حكيت عنها فوق
+
+506
+00:37:29,870 --> 00:37:39,670
+بتجسم الـ 6 بـ T-5 إذا الـ T-5 بيساوي 6 في U نجلت
+
+507
+00:37:39,670 --> 00:37:43,410
+الخمسة هنا صارت T بيساوي 6 U زائد خمسة where U
+
+508
+00:37:43,410 --> 00:37:47,410
+أشماله is an integerالـ T اللي طلعت عندي هنا بدي
+
+509
+00:37:47,410 --> 00:37:52,870
+أرد اللي هي أعوضها في اللي هي الـ T اللي عندي اللي
+
+510
+00:37:52,870 --> 00:37:57,470
+هي بدي أعوض substituting
+
+511
+00:37:57,470 --> 00:38:02,030
+this back into X بتساوي خمسة T زائد واحد لإن عندي
+
+512
+00:38:02,030 --> 00:38:05,790
+اللي هي ال X عندي جدش قيمة طلعت اللي بالأحمر هذه
+
+513
+00:38:05,790 --> 00:38:10,130
+خمسة T زائد واحد بعد ما وجدنا T اللي هي اللي صارت
+
+514
+00:38:10,130 --> 00:38:15,040
+تتحقق هذه التطابق اللي هي حققت التطابق هذهصار عندى
+
+515
+00:38:15,040 --> 00:38:21,480
+اعوض عن T بقيمتها 6U زائد خمسة هان بيصير X بتساوي
+
+516
+00:38:21,480 --> 00:38:25,600
+شيل ال T وحط 6U زائد خمسة بتطلع عبارة عن خمسة في
+
+517
+00:38:25,600 --> 00:38:29,080
+هذا المقدار زائد واحد اضربه جوا بيصير تلاتين U
+
+518
+00:38:29,080 --> 00:38:32,540
+زائد خمسة عشرين واحد بيطلع زائد إيه؟ ستة عشرين إذا
+
+519
+00:38:32,540 --> 00:38:36,100
+صارت عندى X بتساوي تلاتين U زائد ستة وعشرين صارت
+
+520
+00:38:36,100 --> 00:38:41,670
+هذهحققت هذه و حققت هذه دلنا نشوف كيف تتحقق هذه و
+
+521
+00:38:41,670 --> 00:38:46,510
+نكون أوجدنا الحل المشترك الآن الخطوة الثالثة مكررة
+
+522
+00:38:46,510 --> 00:38:53,230
+يعني مشابه للسابق insert this into X طابق 3 مدل 7
+
+523
+00:38:53,230 --> 00:38:57,810
+بعد ما عوضناها نعوضها نعوض الآن في الأخيرة X طابق
+
+524
+00:38:57,810 --> 00:39:01,470
+3 مدل 7 شيل اللي هي ال X هذه و حط قيمته اللي
+
+525
+00:39:01,470 --> 00:39:06,300
+أوجدناها هذه فوقبصير 30U زي 26 تطابق من التلاتة
+
+526
+00:39:06,300 --> 00:39:09,200
+مدرس سبعة بدنا نحل هذا زي ما حلنا اللي قبل solving
+
+527
+00:39:09,200 --> 00:39:15,500
+thisبيعطيني الان الـ 26 من جلها بيصير ناقص 26 و في
+
+528
+00:39:15,500 --> 00:39:20,420
+عندي 3 بيصير ناقص 23 صارت 30 U تطابق ناقص 23 و دول
+
+529
+00:39:20,420 --> 00:39:24,440
+7 الان هذه بدنا نحلها بدنا نحلها لإيجاد ال inverse
+
+530
+00:39:24,440 --> 00:39:28,720
+زي ما قلنا شيل المضاعفات اللي هي السبعة أجرب اشي
+
+531
+00:39:28,720 --> 00:39:33,360
+30 على 7 بتطلع 4 في 7 ب28 و بزيد 2 خلاص عند ال 2
+
+532
+00:39:33,360 --> 00:39:39,390
+إذا شيلت 28 بظل 2 Uلان ناقص تلاتة و عشرين و نضيف
+
+533
+00:39:39,390 --> 00:39:47,870
+مضاعفات السبعة لكي نضيف أقرب رقم لكي نضغر قيمة
+
+534
+00:39:47,870 --> 00:39:48,650
+الرقم
+
+535
+00:39:53,690 --> 00:39:56,150
+21 من مضاعفات السبعة و 21 من مضاعفات السبعة و 21
+
+536
+00:39:56,150 --> 00:39:58,790
+من مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+537
+00:39:58,790 --> 00:40:02,090
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+538
+00:40:02,090 --> 00:40:03,350
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+539
+00:40:03,350 --> 00:40:04,010
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+540
+00:40:04,010 --> 00:40:06,330
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+541
+00:40:06,330 --> 00:40:07,370
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+542
+00:40:07,370 --> 00:40:08,890
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+543
+00:40:08,890 --> 00:40:10,670
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من
+
+544
+00:40:10,670 --> 00:40:13,530
+مضاعفات السبعة و 21 من مضاعفات السبعة و 21 من مض
+
+545
+00:40:13,560 --> 00:40:17,700
+التلاتين يو حطينا اتنين يو اللي انا عملت هيك عشان
+
+546
+00:40:17,700 --> 00:40:21,180
+انا عارف انه انا بتخليها ده اللي هو طلع عند اتنين
+
+547
+00:40:21,180 --> 00:40:25,380
+بتخليها ده برضه بيطلع فيه زوجي عشان اللي هو اجسم
+
+548
+00:40:25,380 --> 00:40:29,760
+الجهتين على اتنين و يظل ال يو لحالها بنفع اه لان
+
+549
+00:40:29,760 --> 00:40:33,440
+اهم المشتركة الأعلى بين السبعة و اتنين واحد بنجسم
+
+550
+00:40:33,440 --> 00:40:36,000
+على اتنين بيطلع يو تطابق الناقص واحد مضول سبعة
+
+551
+00:40:36,000 --> 00:40:41,620
+الناقص واحد ضيفله سبعةبيصير اللي هو ستة بيصير due
+
+552
+00:40:41,620 --> 00:40:44,980
+تطابق الستة modulo من modulo سبعة احنا اضافة اللي
+
+553
+00:40:44,980 --> 00:40:51,560
+هو اضافة اللي هي مضاعفات او طرح مضاعفات العدد اللي
+
+554
+00:40:51,560 --> 00:40:56,420
+هو المقياس لأي من الطرفين طبعا منضيف سبعة you هنا
+
+555
+00:40:56,420 --> 00:41:00,820
+او اربعتاش you ومش سبعة لحالها واما هنا منضيف
+
+556
+00:41:00,820 --> 00:41:06,320
+السبعة وكذا عسى انه يظل المتطابقاتبتنطلع عند U
+
+557
+00:41:06,320 --> 00:41:09,220
+ترابق الستة مضلوا سبعة بنعمل هذه زي ما عملنا اللي
+
+558
+00:41:09,220 --> 00:41:12,820
+فوق اللي هو سبعة بتجسم ال U نقص ستة معناته اللي هو
+
+559
+00:41:12,820 --> 00:41:16,860
+ال U نقص ستة بساوية سبعة V يعني ال U بساوية سبعة V
+
+560
+00:41:16,860 --> 00:41:22,420
+زائد ستة where V is an integer الآن بدأ أعوض عن ال
+
+561
+00:41:22,420 --> 00:41:28,270
+U في من؟ في ال X هنابصير عند ال X بتساوي شيل ال U
+
+562
+00:41:28,270 --> 00:41:33,410
+وحط قيمتها اللي هي 7V زائد 6 بصير ال X بتساوي اللي
+
+563
+00:41:33,410 --> 00:41:38,850
+هي بدل 30U 30 في 7V زائد 6 زائد 26 وضربها بتطلع
+
+564
+00:41:38,850 --> 00:41:45,190
+210U زائد 30 في 6 ال 180 و 26 بتطلع 206 يعني
+
+565
+00:41:45,190 --> 00:41:50,950
+اتصلعت عندي الآن X بتساوي 210U زائد 206 وهذه طبعا
+
+566
+00:41:50,950 --> 00:41:56,530
+نتيجة الحل في الأولىوفي التانية وفي التالتة يعني
+
+567
+00:41:56,530 --> 00:42:00,830
+ال X اللي عند هذه حققت هذه وحققت هذه وحققت هذه
+
+568
+00:42:00,830 --> 00:42:05,030
+معناته ال X اللي طلعت هنا هي عبارة عن حل
+
+569
+00:42:05,030 --> 00:42:10,610
+المتطابقات كلها اللي هي التلاتة في نفس الوقت يعني
+
+570
+00:42:10,610 --> 00:42:15,010
+صارت عند X بتساوي 210 U زي 206 هي عبارة عن الحلول
+
+571
+00:42:15,010 --> 00:42:19,100
+حيث U is an integerالان هادى بنقدر نكتبها على صورة
+
+572
+00:42:19,100 --> 00:42:23,280
+ايش تطابقة اللى هى ايش أصل التطابقة X تطابق الـ
+
+573
+00:42:23,280 --> 00:42:30,840
+206 modulo 210 ايش عرفك هاي X ناقص 206 اللى هو 210
+
+574
+00:42:30,840 --> 00:42:39,320
+بتجسمها 210 بتجسم X ناقص 26 يعني X ناقص 26 بساوية
+
+575
+00:42:39,320 --> 00:42:43,540
+210 في some number سمينا U هو فعلا صارت عند X
+
+576
+00:42:43,540 --> 00:42:51,150
+بساوية 210 U زائد 206إذا هذه x بتساوي 210 u زائد
+
+577
+00:42:51,150 --> 00:42:56,510
+206 هي نفس التعبير اللي بنقوله x تطابق ال 206
+
+578
+00:42:56,510 --> 00:43:03,440
+modulo 210 ليش لإن زي ما قلتX تطابق الـ 206 مده
+
+579
+00:43:03,440 --> 00:43:09,900
+210 معناته 210 تقسم ال X ناقص 206 وزي ما عملنا
+
+580
+00:43:09,900 --> 00:43:19,340
+بسير X ناقص 206 تساوي 210 في U التي تساوي 210 في U
+
+581
+00:43:19,340 --> 00:43:25,730
+زائد 206إذا هذه هي هذا التعبير وهذا معناته أنه
+
+582
+00:43:25,730 --> 00:43:29,830
+اللي هي الأرقام مائتين وستة وبعدين ضيف كمان مائتين
+
+583
+00:43:29,830 --> 00:43:33,110
+وعشرة بيصير اربعمية وست عشر وضيف كمان مائتين وعشرة
+
+584
+00:43:33,110 --> 00:43:37,150
+بيصير كده بيصير كده كلهين حلول مشتركة لهذه التطابق
+
+585
+00:43:37,150 --> 00:43:41,290
+وهذا حل اللي كلهين ولو لاحظت حتة تجي المائتين
+
+586
+00:43:41,290 --> 00:43:47,070
+وعشرة هي عبارة عنستة في خمسة في سبعة ستة في خمسة
+
+587
+00:43:47,070 --> 00:43:50,490
+في تلاتين و تلاتة في سبعة في متين و عشرة إذا صار
+
+588
+00:43:50,490 --> 00:43:54,350
+عنده X وطابق متين و ستة مدله متين و عشرة و هيك
+
+589
+00:43:54,350 --> 00:43:58,010
+بيكون احنا حللنا اللي هي ال system of linear
+
+590
+00:43:58,010 --> 00:44:02,410
+equations بواسطة حاجة اسم ال back substitution و
+
+591
+00:44:02,410 --> 00:44:07,670
+هذا هو ال homework اللي مطلوب منكم حل السؤال الأول
+
+592
+00:44:07,670 --> 00:44:11,150
+و التاني و التالت بسلامونيه و إلى لقاء آخر السلام
+
+593
+00:44:11,150 --> 00:44:12,790
+عليكم و رحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6cd915e71f926882189c8cbafa1d55f6dba86aeb
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w.srt
@@ -0,0 +1,2299 @@
+1
+00:00:01,230 --> 00:00:05,050
+بسم الله الرحمن الرحيم هذه هي المحاضرة التاسعة
+
+2
+00:00:05,050 --> 00:00:09,790
+مساق رياضيات مفاصلة لطلبة الجامعة الإسلامية قسم
+
+3
+00:00:09,790 --> 00:00:14,250
+الحوسبة المتنقلة كلية التكنولوجيا المعلومات اليوم
+
+4
+00:00:14,250 --> 00:00:20,000
+هيكون الحديث عن اللي هو طرق البرهان الرياضية نحكي 
+
+5
+00:00:20,000 --> 00:00:25,000
+طبعا هو نزيج من chapter 5 و باقي chapter 1-7
+
+6
+00:00:25,000 --> 00:00:28,620
+section 1-7 في chapter الأول اللي هو proof
+
+7
+00:00:28,620 --> 00:00:31,600
+techniques and mathematical induction اللي هي طرق
+
+8
+00:00:31,600 --> 00:00:37,720
+البرهان و اللي هي الاستقراء الرياضي الآن في بعض
+
+9
+00:00:37,720 --> 00:00:41,720
+الحقائق بس حابين نذكرها على السريع عسى أن تلزمنا
+
+10
+00:00:41,720 --> 00:00:46,210
+بعد شوية The product of two non-zero real numbers
+
+11
+00:00:46,210 --> 00:00:51,130
+is non-zero يعني لو ضربنا عددين حقيقية و لا واحد
+
+12
+00:00:51,130 --> 00:00:54,870
+فيهما صفر أكيد هيطلع مش صفر The square of a non-zero
+
+13
+00:00:54,870 --> 00:00:57,710
+real number is a positive real number اللي هو لو
+
+14
+00:00:57,710 --> 00:01:00,690
+كان عندي a real number بيكون a تربيع اللي هو
+
+15
+00:01:00,690 --> 00:01:04,600
+positive real number الآن الـ even integer is of
+
+16
+00:01:04,600 --> 00:01:09,020
+the form 2k لأن لو كان عندي اللي هو عدد زوجي بنقدر
+
+17
+00:01:09,020 --> 00:01:12,180
+نكتبه على صورة 2k for some k element in Z يعني
+
+18
+00:01:12,180 --> 00:01:16,300
+هذه صورة العدد الزوجي أما العدد الفردي the odd
+
+19
+00:01:16,300 --> 00:01:20,820
+integer is of the form 2k زائد 1 for some k
+
+20
+00:01:20,820 --> 00:01:28,560
+element in Z حاصل ضرب two even integers is even
+
+21
+00:01:28,560 --> 00:01:33,700
+وحاصل ضرب two odd integers is odd a real number is
+
+22
+00:01:33,700 --> 00:01:36,960
+a rational number if it is a common fraction that
+
+23
+00:01:36,960 --> 00:01:40,880
+is of the form M على N of integers M and N و N لا
+
+24
+00:01:40,880 --> 00:01:45,260
+تساوي صفر يعني بيقولي العدد النسبي هو العدد اللي
+
+25
+00:01:45,260 --> 00:01:49,240
+بنقدر نكتبه على صورة M على N حيث و M و N عدد صحيحة
+
+26
+00:01:52,650 --> 00:01:57,730
+الآن لا يساوي صفر a prime طبعا احنا عرفناه هو
+
+27
+00:01:57,730 --> 00:02:00,670
+عبارة عن positive integer أكبر من واحد اللي
+
+28
+00:02:00,670 --> 00:02:04,510
+بيقبل القسمة بس على اللي هو الواحد والـ p وطبعا هيكسب على
+
+29
+00:02:04,510 --> 00:02:11,340
+السالب واحد والسالب p الآن البرهان النظريات أو
+
+30
+00:02:11,340 --> 00:02:16,200
+اللي هي أنواع البرهان اللي هي فيه أنواع للبرهان
+
+31
+00:02:16,200 --> 00:02:20,720
+اليوم بدنا نحكي عن واحد منهم اسمه الـ Direct Proof
+
+32
+00:02:20,720 --> 00:02:25,280
+أو البرهان المباشر إذا اليوم بس هنحكي عن البرهان
+
+33
+00:02:25,280 --> 00:02:29,900
+المباشر اللي هي بذكركم في اللي هو ال implication
+
+34
+00:02:29,900 --> 00:02:34,310
+لما أخذنا ال implication بـ implies a Q قلنا هذه
+
+35
+00:02:34,310 --> 00:02:40,710
+اللي هي لو بدنا عشان نثبت صحتها لو كانت p صحيحة
+
+36
+00:02:40,710 --> 00:02:45,850
+عشان نثبت صحة الجملة كلها p implies q لازم نثبت
+
+37
+00:02:45,850 --> 00:02:49,790
+أن q شمالها صحيحة إذا ال direct proof هنا
+
+38
+00:02:49,790 --> 00:02:56,350
+بعتمد على ماذا؟ بعتمد على إنه لو نفترض صحة p و
+
+39
+00:02:56,350 --> 00:03:01,570
+بنبدأ اللي هو نستخدم اللي هو اللي هي كل الحقائق
+
+40
+00:03:01,570 --> 00:03:04,790
+اللي معناها و كل اللي هي المعطيات اللي معناها لما
+
+41
+00:03:04,790 --> 00:03:10,290
+نصلّي إلى صحة q إذاً an implication p implies q
+
+42
+00:03:10,290 --> 00:03:15,730
+can be proved by showing that if p is true then q
+
+43
+00:03:15,730 --> 00:03:20,730
+is also true إن ناخذ مثال Give a direct proof of
+
+44
+00:03:20,730 --> 00:03:24,290
+the theorem if n is odd then n تربيع is odd لأن
+
+45
+00:03:24,290 --> 00:03:28,130
+عندي نظرية أو عندي سؤال أو عندي المثال اللي هو
+
+46
+00:03:28,130 --> 00:03:33,170
+بيقول لي لو كانت n is odd اثبتلي أن n تربيع إيش
+
+47
+00:03:33,170 --> 00:03:37,290
+ماله is odd كيف بنثبت باستخدام ال directive proof
+
+48
+00:03:37,290 --> 00:03:41,230
+بنيجي بنفترض assume that the hypothesis p of this
+
+49
+00:03:41,230 --> 00:03:47,260
+implication is true يعني بنفترض أن هذا صحيح و بنبدأ
+
+50
+00:03:47,260 --> 00:03:52,160
+نستخدم هذه الحقيقة و حقائق معروفة للوصول إلى أن
+
+51
+00:03:52,160 --> 00:03:58,480
+n تربيع is odd then use the rules of inference and
+
+52
+00:03:58,480 --> 00:04:02,040
+known theorems to show that the conclusion must
+
+53
+00:04:02,040 --> 00:04:07,230
+be true اللي هو أن n تربيع is odd يعني الآن بنفترض
+
+54
+00:04:07,230 --> 00:04:12,190
+صحة n بنبدأ نستخدم هذه كمعطيات و بنستخدم اللي هو
+
+55
+00:04:12,190 --> 00:04:16,210
+أي حاجة احنا بنعرف أنها صحيحة و تم إثباتها في
+
+56
+00:04:16,210 --> 00:04:21,090
+إثبات أن n تربيع شمالها is odd الآن ناخد ناخد
+
+57
+00:04:21,090 --> 00:04:25,530
+نشوف نبرهن نبرهن هذا السؤال assume that n is odd
+
+58
+00:04:25,530 --> 00:04:29,190
+إيش معنى n is odd يا جماعة هذا الآن مثال على ال
+
+59
+00:04:29,190 --> 00:04:34,280
+direct proof زي ما قلنا assume that n is odd اللي
+
+60
+00:04:34,280 --> 00:04:38,440
+هو يعني and then n can be written as يعني and
+
+61
+00:04:38,440 --> 00:04:42,400
+يمكن كتابتها على صورة اثنين k زائد واحد حيث و k is
+
+62
+00:04:42,400 --> 00:04:47,480
+an integer ال n أنا بدي مين بدي n تربيع
+
+63
+00:04:47,480 --> 00:04:51,620
+نثبتها إذا ال n تربيع consequently ال n تربيع
+
+64
+00:04:51,620 --> 00:04:55,780
+إيش هتساوي هذا المقدار لكل تربيع اثنين k زائد واحد
+
+65
+00:04:55,780 --> 00:05:01,770
+لكل تربيع الآن باجي بربع هذا الطرف بيطلع عندي هو 4k
+
+66
+00:05:01,770 --> 00:05:06,750
+تربيع زي 4k زي 1 تعرفوا تربعوها مربع الأول زي مربع
+
+67
+00:05:06,750 --> 00:05:10,450
+الثاني زي الأول في الثاني في اثنين الآن هذا الرقم
+
+68
+00:05:10,450 --> 00:05:14,850
+اللي عندي أنا بدأ اكتبه على اثبات النقود طيب كيف
+
+69
+00:05:14,850 --> 00:05:18,330
+بتثبت نقود؟ خد للأربعة من هدول عامل مشترك أو
+
+70
+00:05:18,330 --> 00:05:21,670
+اثنين عامل مشترك بيصير عند اثنين في اثنين k تربيع زي 2k زائد 1 هذا عبارة عن عدد صحيح
+
+71
+00:05:21,670 --> 00:05:25,750
+لأن k صحيح و هذا k صحيح يعني بقدر اسمي هذا العدد كل
+
+72
+00:05:25,750 --> 00:05:29,930
+هم m بيصير عبارة عن اثنين m زائد 1 صار عندي العدد
+
+73
+00:05:29,930 --> 00:05:35,250
+هذا انكتب اللي هو n تربيع على صورة اثنين m
+
+74
+00:05:35,250 --> 00:05:37,930
+زائد 1 حيث m هو هذا العدد اثنين n التربيع
+
+75
+00:05:37,930 --> 00:05:41,490
+زائد اثنين is an integer يعني قدرت الآن n تربيع
+
+76
+00:05:41,490 --> 00:05:45,850
+اكتب على صورة اثنين m زائد 1 معناته أنه اثبتت
+
+77
+00:05:45,850 --> 00:05:49,270
+أنه لما كانت n odd إذا طلعت عندي n تربيع can be
+
+78
+00:05:49,270 --> 00:05:54,190
+written in this form it is odd هذا هو مثال على
+
+79
+00:05:58,790 --> 00:06:04,550
+البرهان المباشر مثال آخر عن البرهان المباشر بقول
+
+80
+00:06:04,550 --> 00:06:08,550
+show that the product of two rational numbers is a
+
+81
+00:06:08,550 --> 00:06:12,630
+rational number بدنا نثبت أن حاصل ضرب two rational
+
+82
+00:06:12,630 --> 00:06:17,230
+numbers شمالها يا جماعة is a rational number بدنا
+
+83
+00:06:17,230 --> 00:06:21,850
+نبرهن البرهان كما يلي assume that m و n are
+
+84
+00:06:21,850 --> 00:06:25,250
+rational numbers يعني بنفترض أن عندي في two
+
+85
+00:06:25,250 --> 00:06:29,990
+rational numbers S1 اسمه m و S2 اسمه n مدام m
+
+86
+00:06:29,990 --> 00:06:37,190
+ريشونال نمبر إذا m ممكن كتابته على صورة ألف على ب
+
+87
+00:06:37,190 --> 00:06:40,630
+حيث ال ب لا يساوي صفرا الألف و الباء أو ال a
+
+88
+00:06:40,630 --> 00:06:45,150
+و ال b عبارة عن أعداد صحيحة Similarly بنفس الأسلوب
+
+89
+00:06:45,150 --> 00:06:49,630
+ال n ريشنال نمبر إذا n ممكن كتابته على صورة x على
+
+90
+00:06:49,630 --> 00:06:53,510
+y يعني n ممكن كتابته على صورة x على y حيث برضه y
+
+91
+00:06:53,510 --> 00:06:58,420
+لا تساوي صفرا ال x شمالها و ال y أعداد صحيحة هدول
+
+92
+00:06:58,420 --> 00:07:00,740
+rational numbers from the definition of rational
+
+93
+00:07:00,740 --> 00:07:06,460
+numbers الآن مين بده هو أثبت إنه the product of
+
+94
+00:07:06,460 --> 00:07:10,140
+two rational numbers is rational يعني بدنا نودي
+
+95
+00:07:10,140 --> 00:07:15,880
+دلان m في n و نثبتها إن هي روش rational so m في n
+
+96
+00:07:15,880 --> 00:07:21,400
+بسيطة ال m هي a على b و ال n هي x على y ال n هذا
+
+97
+00:07:21,400 --> 00:07:24,380
+بتضربه في البسط بيصير a في x و المقام في المقام
+
+98
+00:07:24,380 --> 00:07:29,140
+بيصير على b في y إذا صار عند الرقم m في n عبارة عن
+
+99
+00:07:29,140 --> 00:07:32,320
+a في x عبارة عن Integer لأن هذا Integer و هذا
+
+100
+00:07:32,320 --> 00:07:36,110
+Integer و b في y Integer لأن هذا Integer و هذا Integer
+
+101
+00:07:36,110 --> 00:07:39,390
+وحاصل ضرب زي ما قلنا في الملاحظة الأولى مش هيكون
+
+102
+00:07:39,390 --> 00:07:44,210
+صفر لأنه ولا واحد فيهم صفر إذا صارت m في n مكتوبة
+
+103
+00:07:44,210 --> 00:07:48,350
+على صورة Integer على Integer و ال Integer اللي تحت مش صفر
+
+104
+00:07:48,350 --> 00:07:53,350
+إذا ال m في n عبارة عن rational number يعني الآن
+
+105
+00:07:53,350 --> 00:07:57,690
+صار ال product of two rational numbers is also a
+
+106
+00:07:57,690 --> 00:08:04,120
+rational number و هذا أيضا مثال آخر على اللي هو الـ
+
+107
+00:08:04,120 --> 00:08:08,180
+Direct Proof أو على البرهان المباشر الـ Direct
+
+108
+00:08:08,180 --> 00:08:14,080
+Proof More Examples اللي هو أمثلة أخرى على الـ
+
+109
+00:08:14,080 --> 00:08:18,570
+Direct Proof هتلاقوها برضه سهلة شوف الآن show that
+
+110
+00:08:18,570 --> 00:08:23,310
+ال example تلاتة the sum of two odd integers is
+
+111
+00:08:23,310 --> 00:08:28,930
+even يعني بدنا نقول أنه نثبت أنه مجموع اثنين odd
+
+112
+00:08:28,930 --> 00:08:34,230
+integers هيكون إيش ماله even Integer كيف؟ الآن مدام
+
+113
+00:08:34,230 --> 00:08:40,230
+اللي هو الاثنين عندي odd إذا بدنا نسميهم let n
+
+114
+00:08:40,230 --> 00:08:47,090
+بتساوي اثنين k زائد واحد و m إيش بتساوي اثنين j
+
+115
+00:08:47,090 --> 00:08:53,690
+زائد واحد ب odd integers ماشي الحال طيب الآن
+
+116
+00:08:53,690 --> 00:09:02,720
+مجموحا بدك تقول n زائد m إيش هيساوي؟ 2k و 2j و 1 زائد
+
+117
+00:09:02,720 --> 00:09:07,900
+واحد يعني هيصير عند ال n زائد m عبارة عن 2k زائد
+
+118
+00:09:07,900 --> 00:09:15,510
+2j زائد 2 إذا الآن خد الاثنين عامل مشترك فيهم بيصير
+
+119
+00:09:15,510 --> 00:09:20,390
+n زائد m اللي هو مجموع n زائد m بيساوي اثنين في
+
+120
+00:09:20,390 --> 00:09:25,710
+العامل المشترك k زائد j زائد 1 يعني ال n زائد m
+
+121
+00:09:25,710 --> 00:09:32,510
+كتبناه على صورة 2 زائد اللي هو اثنين m prime مثلا
+
+122
+00:09:32,510 --> 00:09:35,970
+اللي هو is even integer
+
+124
+00:09:44,650 --> 00:09:49,830
+لم يكتب المثال لكن سهل و أنا حكيته بالتفصيل لأن
+
+125
+00:09:49,830 --> 00:09:55,490
+جرب اكتب n زائد m مجموعن و خد اثنين عامل مشترك بيطلع 
+
+126
+00:09:55,490 --> 00:10:00,390
+إن N زائد M عن اثنين إذا عندي N زائد M زي ما قلنا 2K
+
+127
+00:10:00,390 --> 00:10:05,470
+زائد 1 زائد 2G زائد 1 اللي هو بسوء 2K زائد 2G زائد 
+
+128
+00:10:05,470 --> 00:10:09,350
+2 أخذنا 2 عامل مشترك من هذول كلهم وضل عندي K زائد
+
+129
+00:10:09,350 --> 00:10:13,210
+G زائد 1 وهذا عبارة عن اللي هو integer مضروب في 2
+
+130
+00:10:13,210 --> 00:10:16,770
+إذا صار الـ N زائد M is even هذه اللي هو مثال آخر
+
+131
+00:10:16,770 --> 00:10:20,020
+على الـ direct proof الآن المثال الأخير على direct
+
+132
+00:10:20,020 --> 00:10:24,340
+proof if M and N are both perfect squares يعني
+
+133
+00:10:24,340 --> 00:10:28,520
+مربعات كاملة M و N إيش معناه مربع كامل يعني الـ M
+
+134
+00:10:28,520 --> 00:10:32,880
+بنقدر نكتبه على صورة B تربيع أو الـ N بنقدر نكتبه
+
+135
+00:10:32,880 --> 00:10:36,950
+على صورة B تربيع بقول إذا n في m برضه is also a
+
+136
+00:10:36,950 --> 00:10:40,150
+perfect square ده نشوف الآن الآن بدنا نفترض أن ن
+
+137
+00:10:40,150 --> 00:10:43,770
+assume that m and n are perfect squares يعني m و n
+
+138
+00:10:43,770 --> 00:10:47,870
+عبارة عن مربعات كاملة إيش يعني؟ يعني m بنقدر نكتبه
+
+139
+00:10:47,870 --> 00:10:51,870
+على صورة S تربيع و n بتساوي عبارة عن T تربيع هذول
+
+140
+00:10:51,870 --> 00:10:55,550
+معناته أن m و n مربعات كاملة حيث S تساوي T element
+
+141
+00:10:55,550 --> 00:11:00,320
+تنتمي إذا بدنا نثبت أن M في N برضه مربع كامل اضرب M
+
+142
+00:11:00,320 --> 00:11:05,640
+في N بصير S تربيع في T تربيع اللي هو عبارة عن S في
+
+143
+00:11:05,640 --> 00:11:10,240
+T في الكل تربيع أو اللي هو زي ما أعمل S في S في T
+
+144
+00:11:10,240 --> 00:11:13,640
+في T أنتم عارفينه هذا الكلام سهل S في T اللي هو
+
+145
+00:11:13,640 --> 00:11:17,160
+في S في T اللي هو عبارة عن S في T لكل تربيع يعني M
+
+146
+00:11:17,160 --> 00:11:21,280
+في N كتبناه على صورة ST لكل تربيع ST عبارة عن رقم
+
+147
+00:11:21,280 --> 00:11:25,250
+Integer لأن هذا Integer و هذا Integer يعني MN كتبنا
+
+148
+00:11:25,250 --> 00:11:29,150
+على صورة Integer تربيع أو بمعنى آخر MN is also a
+
+149
+00:11:29,150 --> 00:11:33,610
+perfect square هيك بيكون إحنا اللي هو خلصنا الجزء
+
+150
+00:11:33,610 --> 00:11:38,230
+الأول اللي هو عبارة عن الـ direct proof اللي هو أو
+
+151
+00:11:38,230 --> 00:11:42,110
+البرهان المباشر بدنا الآن نيجي إلى طريقة ثانية من
+
+152
+00:11:42,110 --> 00:11:44,190
+طرق البرهان الرياضي
+
+153
+00:12:09,490 --> 00:12:13,110
+الآن نيجي لـ للنوع الثاني من أنواع البرهان اللي
+
+154
+00:12:13,110 --> 00:12:19,450
+هو بنا نسميه البرهان الـ indirect proof أو البرهان
+
+155
+00:12:19,450 --> 00:12:24,060
+غير المباشر بالظبط هنحكي الآن في البرهان غير مباشر
+
+156
+00:12:24,060 --> 00:12:28,200
+عن حاجة اسمها Contrapositive أو Contraposition هذه
+
+157
+00:12:28,200 --> 00:12:32,440
+طبعًا مش غريبة عليكم ممكن حكينا عنها في بداية الـ ..
+
+158
+00:12:32,440 --> 00:12:36,900
+المادة قلنا إن implication B implies Q is
+
+159
+00:12:36,900 --> 00:12:40,920
+equivalent هذه كلها لبعض is equivalent to
+
+160
+00:12:40,920 --> 00:12:44,620
+Contrapositive إليها إيش Contrapositive يعني not Q
+
+161
+00:12:44,620 --> 00:12:50,440
+implies not B يعني لو إحنا أثبتنا not Q implies not
+
+162
+00:12:50,440 --> 00:12:56,100
+B يكون أثبتنا بـ B implies Q يعني عشان نثبت الـ B
+
+163
+00:12:56,100 --> 00:13:02,720
+implies Q بنفترض عكس الـ Q إنها صحيحة و بنصل لعكس
+
+164
+00:13:02,720 --> 00:13:06,940
+الـ B إنها صحيحة إذا قدرنا نصل لهيك بكون إن إحنا
+
+165
+00:13:06,940 --> 00:13:12,620
+اللي هي أن تكون على بعضها دي كلها الـ B implies Q
+
+166
+00:13:12,620 --> 00:13:14,700
+اللي أثبتناها
+
+167
+00:13:17,480 --> 00:13:21,460
+أو اللي هو بنثبت إن not q implies not b زي ما قلنا
+
+168
+00:13:21,460 --> 00:13:25,860
+أو q is false implies اللي هو b is false فبكون
+
+169
+00:13:25,860 --> 00:13:29,940
+عنده اللي هو الـ contraposition اللي حكينا عنه إذا
+
+170
+00:13:29,940 --> 00:13:33,220
+باختصار الـ contraposition بنفترض اللي هو عكس الـ q
+
+171
+00:13:33,220 --> 00:13:37,620
+و بنصل لعكس الـ b أو بنفترض الـ q is false يعني عكس
+
+172
+00:13:37,620 --> 00:13:43,280
+الـ q بنفترض و بنصل لـ الـ b is false يعني عكس الـ b
+
+173
+00:13:43,280 --> 00:13:51,960
+طيب الآن نعود لمثال عملي للأمر المثال العملي يجيب on
+
+174
+00:13:51,960 --> 00:13:55,400
+indirect proof of the theorem اللي هي التالية إيش
+
+175
+00:13:55,400 --> 00:13:59,820
+اللي بده نثبت بده يثبت if ثلاثة زائد اثنين is odd
+
+176
+00:13:59,820 --> 00:14:03,940
+then n is odd كيف بدنا نثبتها الآن هذه؟ هذي بدنا
+
+177
+00:14:03,940 --> 00:14:07,500
+نثبتها بالـ indirect proof بالـ contraposition اللي
+
+178
+00:14:07,500 --> 00:14:11,340
+الآن بدنا نفترض عكس الـ n is odd يعني نقول نفترض
+
+179
+00:14:11,340 --> 00:14:16,080
+إن n is not odd ونصل لـ ثلاثة n زائد اثنين is not
+
+180
+00:14:16,080 --> 00:14:20,000
+odd إذا وصلنا لهيك بيكون إحنا أثبتنا الـ Contra ..
+
+181
+00:14:20,000 --> 00:14:23,380
+عملنا الـ Contraposition وبذلك الـ Contraposition
+
+182
+00:14:23,380 --> 00:14:28,940
+بكافئ أنه 3N زائد 2 is odd يؤدي إلى N is odd إذن
+
+183
+00:14:28,940 --> 00:14:33,360
+الآن اللي بدي أفعله بدي أفترض أن N is odd is not
+
+184
+00:14:33,360 --> 00:14:37,440
+true يعني بدي أفترض أن N is not odd يعني بدي أفترض
+
+185
+00:14:37,440 --> 00:14:41,700
+أن N is even و أوصلكم لهذه is not odd يعني بمعنى
+
+186
+00:14:41,700 --> 00:14:47,130
+آخر it is even هذا الآن اللي بدي أعمله خلّينا مع
+
+187
+00:14:47,130 --> 00:14:53,190
+بعض نشوف كيف نفترض الآن إن n is even مدام n is even
+
+188
+00:14:53,190 --> 00:14:56,610
+إذا n الآن بتساوي اثنين k where k is an integer زي
+
+189
+00:14:56,610 --> 00:15:00,450
+ما أنتم عارفين الآن بناء على ذلك ثلاثة n زائد
+
+190
+00:15:00,450 --> 00:15:04,600
+اثنين اللي هي المطلوبة بنعوض عن n باثنين k بصير
+
+191
+00:15:04,600 --> 00:15:08,060
+ثلاثة في اثنين k زائد اثنين يعني بمعنى آخر ستة k
+
+192
+00:15:08,060 --> 00:15:11,580
+زائد اثنين بناخد اثنين الآن عامل مشترك بيصير
+
+193
+00:15:11,580 --> 00:15:15,460
+اثنين في ثلاثة k زائد واحد يعني أقدر أكتب اللي هو
+
+194
+00:15:15,460 --> 00:15:20,860
+ثلاثة n زائد اثنين على صورة اثنين مثلا حيث نزلنا
+
+195
+00:15:20,860 --> 00:15:25,300
+Integer أو بمعنى آخر وصلنا إن ثلاثة n زائد اثنين
+
+196
+00:15:25,300 --> 00:15:32,100
+is even أثبتنا الـ Contraposition لذلك ثلاثة N زائد
+
+197
+00:15:32,100 --> 00:15:34,780
+اثنين يعني ليس غير غير غير غير غير غير غير غير غير
+
+198
+00:15:34,780 --> 00:15:37,240
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+199
+00:15:37,240 --> 00:15:38,440
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+200
+00:15:38,440 --> 00:15:38,580
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+201
+00:15:38,580 --> 00:15:39,140
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+202
+00:15:39,140 --> 00:15:39,200
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+203
+00:15:39,200 --> 00:15:39,520
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+204
+00:15:39,520 --> 00:15:39,960
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+205
+00:15:39,960 --> 00:15:43,900
+غير غير غير غير
+
+206
+00:15:43,900 --> 00:15:46,720
+غير
+
+207
+00:15:47,920 --> 00:15:52,160
+مُكافئ لهذا أنه أثبتنا أن n is not odd أو بمعنى آخر
+
+208
+00:15:52,160 --> 00:15:56,200
+even تؤدي إلى ثلاثة زائد n زائد اثنين is not odd
+
+209
+00:15:56,200 --> 00:16:00,320
+يعني even وهيك بيكون أثبتنا اللي هو بواسط البرهان
+
+210
+00:16:00,320 --> 00:16:04,880
+غير المباشر هذه الحقيقة وبيكون اللي هو أثبتنا
+
+211
+00:16:04,880 --> 00:16:09,060
+بواسط حاجة اسمها الـ contra positive اللي هناخد مثال
+
+212
+00:16:09,060 --> 00:16:12,860
+آخر على الـ Contrapositive let M N أو N element in
+
+213
+00:16:12,860 --> 00:16:16,840
+N show that if M زائد N أكبر من خمسين then M أكبر
+
+214
+00:16:16,840 --> 00:16:20,220
+من خمسة وعشرين أو N أكبر من خمسة وعشرين بقول لو كان
+
+215
+00:16:20,220 --> 00:16:24,160
+عندي M و N integers بحيث أن M زائد N أكبر من خمسين
+
+216
+00:16:24,160 --> 00:16:29,640
+لازم لازم يعطينا أن M أكبر من خمسة وعشرين أو N أكبر
+
+217
+00:16:29,640 --> 00:16:33,000
+من خمسة وعشرين الـ Contrapositive لها أنه إحنا
+
+218
+00:16:33,000 --> 00:16:37,320
+بفترض عكس الجملة هذه كلها على بعضها و بنصل لعكس
+
+219
+00:16:37,320 --> 00:16:41,480
+هذه يعني بدنا نفترض إيش معناه عكس M أكبر من 25 or
+
+220
+00:16:41,480 --> 00:16:48,380
+N أكبر من 25 إيش نفيه جملة or يعني M أكبر من 25
+
+221
+00:16:48,380 --> 00:16:54,460
+false and N أكبر من 25 false إيش يعني؟ يعني M
+
+222
+00:16:54,460 --> 00:17:01,240
+أصغر أو يساوي 25 and N أصغر أو يساوي 25 إذا
+
+223
+00:17:01,240 --> 00:17:05,780
+assume not q اللي هي هذه يعني بمعنى آخر assume أن
+
+224
+00:17:05,780 --> 00:17:10,720
+M أصغر أو يساوي 25 and N أصغر أو يساوي 25 بناء
+
+225
+00:17:10,720 --> 00:17:16,840
+على هذا الحديث M زائد N أصغر أو يساوي 25 زائد 25 يعني
+
+226
+00:17:16,840 --> 00:17:22,160
+M زائد N أصغر أو يساوي 50 مدام M زائد N أصغر أو يساوي
+
+227
+00:17:22,160 --> 00:17:27,120
+50 إذن هي عكس هذه اللي هي عكس M زائد N أكبر من 50
+
+228
+00:17:27,120 --> 00:17:34,270
+إذن وصلنا not Q not هذه أدت إلى not P اللي هي not هذه
+
+229
+00:17:34,270 --> 00:17:38,570
+وهذا هو الـ contrapositive فبنكون هيك إحنا أثبتنا
+
+230
+00:17:38,570 --> 00:17:42,690
+الـ example بواسطة إثبات الـ contrapositive أو
+
+231
+00:17:42,690 --> 00:17:47,630
+بواسطة الـ indirect approve الآن في سؤال بيقول لي
+
+232
+00:17:47,630 --> 00:17:54,090
+approve or disapprove يعني اثبت أو اللي هو اثبت
+
+233
+00:17:54,090 --> 00:17:58,950
+صحة أو اثبت عدم صحة that يعني بيقول الجملة التالية
+
+234
+00:17:58,950 --> 00:18:03,150
+صحيحة ولا مش صحيحة بقول that the product of two
+
+235
+00:18:03,150 --> 00:18:06,730
+irrational numbers is irrational بقول لي هل حاصل
+
+236
+00:18:06,730 --> 00:18:09,930
+ضرب two irrational numbers لازم يطلع irrational
+
+237
+00:18:09,930 --> 00:18:15,330
+عشان نثبت لازم نثبت لكل الحالات يعني نفترض إنه أي
+
+238
+00:18:15,330 --> 00:18:19,070
+اثنين irrational و نصل لهين irrational لو في حالة
+
+239
+00:18:19,070 --> 00:18:23,630
+واحدة بس يعني مثال واحد اللي هو هذا بنتناقش يعني لو
+
+240
+00:18:23,630 --> 00:18:28,440
+قدرنا نجيب اللي هو عددين irrational حاصل ضربهم مش
+
+241
+00:18:28,440 --> 00:18:32,040
+irrational بتكون هذه الجملة مش صحيحة وفي هذه
+
+242
+00:18:32,040 --> 00:18:35,540
+الحالة بنقول هذا العمل هو disapprove و الـ
+
+243
+00:18:35,540 --> 00:18:39,240
+disapprove بنجيب counter example يعني بنجيب مثال
+
+244
+00:18:39,240 --> 00:18:45,990
+عددي بنبين فيه إن هذه الجملة غير صحيحة الآن بيقول
+
+245
+00:18:45,990 --> 00:18:50,790
+إيش الجملة؟ إن الـ product of two irrational is
+
+246
+00:18:50,790 --> 00:18:54,590
+irrational أنا بقول هذا الكلام مش صحيح ليش؟ خد هي
+
+247
+00:18:54,590 --> 00:18:58,250
+مثال هي جذر الاثنين irrational إيش irrational؟
+
+248
+00:18:58,250 --> 00:19:01,570
+يعني عدد لا يمكن كتابته على صورة ألف على باء حيث
+
+249
+00:19:01,570 --> 00:19:06,700
+ألف و باء أعداد صحيحة و باء لا تساوي صفر جذر الاثنين مش
+
+250
+00:19:06,700 --> 00:19:09,940
+irrational وجذر الاثنين برضه مش irrational حاصل ضرب 
+
+251
+00:19:09,940 --> 00:19:15,860
+هنا بساوة 2 اللي هو rational إذا فعلاً لجينا مثال
+
+252
+00:19:15,860 --> 00:19:21,580
+يبين لإن حاصل ضرب 2 irrational ليس شرطًا إنه يطلع
+
+253
+00:19:21,580 --> 00:19:26,000
+irrational عشان هيك هذه الجملة مش صحيحة عشان هيك
+
+254
+00:19:26,000 --> 00:19:30,520
+بنسميها ده اسمه disproved  كيف؟ بنجيب
+
+255
+00:19:30,520 --> 00:19:35,860
+counter example بحقق الجزء اللي هو حاصل الضرب ما
+
+256
+00:19:35,860 --> 00:19:40,260
+يطلع شبيه المطلوب يعني هاي عندي two irrational is
+
+257
+00:19:40,260 --> 00:19:44,320
+irrational مش صحيح وهي مثل جذر الاثنين irrational
+
+258
+00:19:44,320 --> 00:19:48,500
+جذر الاثنين irrational وحاصل ضربه ما طلعش irrational
+
+259
+00:19:49,200 --> 00:19:52,280
+طلع rational number و هذا بقولك the product of two
+
+260
+00:19:52,280 --> 00:19:55,520
+irrational numbers يعني is not necessarily
+
+261
+00:19:55,520 --> 00:20:00,280
+irrational يعني need not to be irrational وهي مثال
+
+262
+00:20:00,280 --> 00:20:04,380
+نيجي للسؤال اللي بعده بقول prove that إذا كانت n
+
+263
+00:20:04,380 --> 00:20:08,400
+بتساوي a في b هذا بيعطينا a أصغر أو يساوي جذر ال n
+
+264
+00:20:08,400 --> 00:20:12,140
+or b أصغر أو يساوي جذر ال n حيث ال a و ال b عبارة
+
+265
+00:20:12,140 --> 00:20:16,440
+عن أعداد صحيحة موجبة كمان مرة بدنا نثبت أنه لو كان
+
+266
+00:20:16,440 --> 00:20:22,070
+n بتساوي a في b هذا سيعطينا أو a أصغر أو يساوي جذر
+
+267
+00:20:22,070 --> 00:20:25,850
+الآن أو b أصغر أو يساوي جذر الآن بدنا نثبت هذا عن
+
+268
+00:20:25,850 --> 00:20:28,710
+طريق مين اللي هو ال contraposition إيش بدنا نثبت
+
+269
+00:20:28,710 --> 00:20:33,570
+بدنا نفرض عكس المطلوب هايو بدنا نفرض عكس هذا ونصل 
+
+270
+00:20:33,570 --> 00:20:39,160
+لعكس هذا يعني بنفترض أنه a أصغر أو يساوي b or b أصغر
+
+271
+00:20:39,160 --> 00:20:43,200
+أو يساوي جذر الان هذه مش صحيحة كيف جملة هذه على
+
+272
+00:20:43,200 --> 00:20:48,840
+بعضها or مش صحيحة معناته a أكبر من جذر الان and b
+
+273
+00:20:48,840 --> 00:20:52,220
+أكبر من جذر الان لأنه لا في ال or اللي هو and زي ما
+
+274
+00:20:52,220 --> 00:20:56,640
+إحنا عارفين إذا الآن بنفترض عكس هذا يعني بنفترض
+
+275
+00:20:56,640 --> 00:21:00,780
+أنه a أكبر من جذر الان and b أكبر من جذر الان منه
+
+276
+00:21:00,780 --> 00:21:04,900
+بنصل ل a في b أكبر من جذر الان في جذر الان اللي هو
+
+277
+00:21:04,900 --> 00:21:08,050
+الـ n مدام a أكبر من الـ .. من الـ .. من الـ .. من ال a
+
+278
+00:21:08,050 --> 00:21:12,330
+b أكبر من ال n إذا يعني ال a b لا تساوي ال n مدام
+
+279
+00:21:12,330 --> 00:21:15,470
+a لا تساوي ال a b لا تساوي ال n معناه توصلنا لمين
+
+280
+00:21:15,470 --> 00:21:18,570
+إلى عكس هذا وهذا معناته أنه إحنا بال
+
+281
+00:21:18,570 --> 00:21:22,650
+contrapositive فرضنا عكس هذه ووصلنا لعكس هذه
+
+282
+00:21:22,650 --> 00:21:26,050
+فبتكون الجملة الأصلية هذه كلها على بعض صحيحة
+
+283
+00:21:26,050 --> 00:21:30,010
+وبنكون هذا أثبتناها الجملة عن طريق ال
+
+284
+00:21:30,010 --> 00:21:34,420
+contrapositive أو ال contraposition يعني أثبتنا fn
+
+285
+00:21:34,420 --> 00:21:38,600
+بيساوي a و a أصغر أو أصغر جذر الان أو b أصغر أو
+
+286
+00:21:38,600 --> 00:21:43,340
+أصغر جذر الان الآن في طريقة أخرى أخيرة أو قبل
+
+287
+00:21:43,340 --> 00:21:47,000
+الأخيرة بالبرهان الهي proof by contradiction
+
+288
+00:21:47,000 --> 00:21:51,370
+الإثبات عن طريق التناقض ما هو الإثبات عن طريق
+
+289
+00:21:51,370 --> 00:21:55,410
+التناقض؟ طبعًا هذه مهمة كمان اللي هي an important
+
+290
+00:21:55,410 --> 00:21:58,470
+implication يعني بدنا نثبت بيه implies a Q إيش
+
+291
+00:21:58,470 --> 00:22:05,490
+بنعمل؟ بنفترض عكس لـQ ونصل لتناقض بنصل لإيش
+
+292
+00:22:05,490 --> 00:22:10,770
+بناقض المُعطى أو بناقض حقيقة إحنا بنعرفها يعني
+
+293
+00:22:10,770 --> 00:22:13,990
+اللي هو proved by contradiction يتلخص فيما يلي
+
+294
+00:22:14,240 --> 00:22:23,880
+بنقول Assume B and Assume Not Q وبنصل لتناقض تشوف
+
+295
+00:22:23,880 --> 00:22:28,440
+كيف بنحصل على تناقض show that هي مثال if the
+
+296
+00:22:28,440 --> 00:22:31,820
+square of an integer number is odd then the
+
+297
+00:22:31,820 --> 00:22:38,970
+integer is odd بيقول إذا كان مربع اللي هي عدد is
+
+298
+00:22:38,970 --> 00:22:43,950
+odd اثبت انه العدد نفسه إيش is odd يعني لو كان n
+
+299
+00:22:43,950 --> 00:22:49,510
+تربيع odd هيعطينا الان is odd الآن assume that
+
+300
+00:22:49,510 --> 00:22:52,910
+hypothesis B of this implication is true نفترض
+
+301
+00:22:52,910 --> 00:22:56,290
+اللي هو ال hypothesis إيش ماله الفرضية أنها صحيحة
+
+302
+00:22:56,810 --> 00:23:01,570
+وبنفرض عكس المطلوب وبنقول and the conclusion if
+
+303
+00:23:01,570 --> 00:23:05,890
+you is false وبنفرض إن اللي هو المطلوب أو ال
+
+304
+00:23:05,890 --> 00:23:10,090
+conclusion مش صحيحة وبعدين then use rules of
+
+305
+00:23:10,090 --> 00:23:13,330
+inference and non-theorems to deduce contradiction
+
+306
+00:23:13,330 --> 00:23:17,330
+وبعدين نبدأ نستخدم اللي هو معلوماتنا من النظريات
+
+307
+00:23:17,330 --> 00:23:21,590
+ومن الحقائق للوصول إلى تناقض خلينا نشوف هذا الكلام
+
+308
+00:23:21,590 --> 00:23:26,140
+عمليًا الآن نفترض الان assume x تربيع is odd هذا
+
+309
+00:23:26,140 --> 00:23:29,880
+المعطى فرضناه المعطى زي ما هو بنصبهوش الان وإيش
+
+310
+00:23:29,880 --> 00:23:35,460
+بدنا نفرض بدنا نفرض إنه المطلوب غير متحقق يعني
+
+311
+00:23:35,460 --> 00:23:40,500
+بدنا نفرض إن x is not odd مدام x is not odd إذا x
+
+312
+00:23:40,500 --> 00:23:44,980
+أكيد even مدام .. لأن أي عدد في الدنيا يا even يا
+
+313
+00:23:44,980 --> 00:23:50,040
+إيش يقضي مدام X even إذا ال X تربيع لل even هيطلع
+
+314
+00:23:50,040 --> 00:23:54,640
+even لأن X even معناته على صورة 2N 2N لكل تربيع
+
+315
+00:23:54,640 --> 00:23:59,080
+معناته 4N تربيع يعني X تربيع 4N تربيع is even إذا
+
+316
+00:23:59,080 --> 00:24:03,480
+وصلنا لعكس mean اللي هو المطلوب يعني وصلنا ل X
+
+317
+00:24:03,480 --> 00:24:08,750
+تربيع is even و إحنا في الأصل عندي X تربيع is odd
+
+318
+00:24:08,750 --> 00:24:12,450
+صار عندي X تربيع is even و في نفس الوقت X تربيع is
+
+319
+00:24:12,450 --> 00:24:18,010
+odd وهذا اللي هو Contradiction لأن وصلنا ل X تربيع
+
+320
+00:24:18,010 --> 00:24:21,510
+is odd في الأصل و X تربيع is even يعني not odd
+
+321
+00:24:21,510 --> 00:24:25,150
+يعني وصلنا ل X تربيع is odd and not odd which is a
+
+322
+00:24:25,150 --> 00:24:31,480
+contradiction Therefore الفرضية الأولى إن فرضنا عكس
+
+323
+00:24:31,480 --> 00:24:35,820
+المطلوب مش صحيحة إذن لما ال X تربيع is odd لازم
+
+324
+00:24:35,820 --> 00:24:42,060
+تطلع ال X is odd هذا البرهان by contradiction الآن
+
+325
+00:24:42,060 --> 00:24:47,840
+نيجي ناخد مثال آخر المثال كمان بيقول let m و n
+
+326
+00:24:47,840 --> 00:24:51,540
+element in n show that if m زائد n أصغر من 90 then
+
+327
+00:24:51,540 --> 00:24:56,880
+m أصغر من 45 or n أصغر من 45 by contradiction كيف؟
+
+328
+00:24:56,880 --> 00:25:00,840
+بنفترض المعطوعة زي ما هو بنفترض أن m زائد n أصغر من
+
+329
+00:25:00,840 --> 00:25:06,580
+90 وبنفترض عكس المطلوب إذا by contradiction بنفترض
+
+330
+00:25:06,580 --> 00:25:11,020
+من عكس المطلوب مشابهة دير بالكم لـ Contraposition
+
+331
+00:25:11,020 --> 00:25:16,320
+بس هنا إحنا بنصل هذا اللي بنصل بعد خطوات إلى شيء
+
+332
+00:25:16,320 --> 00:25:21,780
+بناقض إما المطلوب أو المعطى بناقض المعطى أو بناقض
+
+333
+00:25:21,780 --> 00:25:26,090
+حقيقة بنعرفها أما في الـ Contraposition كنا نفترض
+
+334
+00:25:26,090 --> 00:25:29,390
+عكس هذا و نصل لعكس هذا في الـ Contraposition مش
+
+335
+00:25:29,390 --> 00:25:34,130
+شرط تصل لعكس هذا ممكن تصل لإيش بناقض إحنا حقيقة
+
+336
+00:25:34,130 --> 00:25:39,150
+بنعرفها وممكن تصل طبعًا لمين للّي هو بناقض المعطى
+
+337
+00:25:39,150 --> 00:25:42,150
+يعني بنكون اللي هو Contraposition و كأنها حالة
+
+338
+00:25:42,150 --> 00:25:46,720
+خاصة من Contradiction show that if M زيادة N أصغر
+
+339
+00:25:46,720 --> 00:25:50,080
+من تسعين then M أصغر من خمسة وأربعين or N أصغر من
+
+340
+00:25:50,080 --> 00:25:53,420
+خمسة وأربعين بدنا نفترض الأن suppose M زيادة N
+
+341
+00:25:53,420 --> 00:25:59,280
+أصغر من تسعين and suppose عكس هذا عكس هذا يعني
+
+342
+00:25:59,280 --> 00:26:03,000
+بدنا نفترض الأن assume M زيادة N أصغر من تسعين مش
+
+343
+00:26:03,000 --> 00:26:06,920
+تسعة وتمانين هذا تسعين طبعًا and بنفترض عكس هذا إيش
+
+344
+00:26:06,920 --> 00:26:11,380
+عكس هذا أن M أكبر أو يساوي خمسة وأربعين وفي نفس
+
+345
+00:26:11,380 --> 00:26:16,720
+الوقت لأنه نفي ال or andand n أكبر ويساوي 45 الآن
+
+346
+00:26:16,720 --> 00:26:21,360
+then m زائد n طبعًا إحنا ماخدين m زائد n أصغر من
+
+347
+00:26:21,360 --> 00:26:29,820
+تسعين من تسعين بس أنا غلط بس كتابة m زائد n الآن
+
+348
+00:26:29,820 --> 00:26:33,720
+بما أن هذه أكبر من 45 وهذه أكبر من 45 إذا حاصل
+
+349
+00:26:33,720 --> 00:26:38,210
+جمعهن أكبر أو يساوي 90 اللي صارت عندي M زائد N أكبر
+
+350
+00:26:38,210 --> 00:26:42,690
+ويساوي 90 و M زائد N أصغر من 90 إذا هذا
+
+351
+00:26:42,690 --> 00:26:46,830
+contradiction therefore اللي هو الفرضية اللي
+
+352
+00:26:46,830 --> 00:26:50,590
+فرضناها مش صحيحة يعني بمعنى آخر لما ال M زائد N
+
+353
+00:26:50,590 --> 00:26:54,390
+أصغر من 90 يعطينا ال M أصغر من 45 or
+
+354
+00:26:54,390 --> 00:27:00,110
+N أصغر من مين من 45 هذه تسعين برضه الآن
+
+355
+00:27:00,110 --> 00:27:03,910
+آخر جزء في المحاضرة هيكون أن ال mathematical
+
+356
+00:27:03,910 --> 00:27:08,830
+induction أو الاستقراء الرياضي هي طريقة للبرهان
+
+357
+00:27:08,830 --> 00:27:13,610
+لبرهان بعض الجمل المعينة اللي بتكون بدلالة اللي هي
+
+358
+00:27:13,610 --> 00:27:18,200
+ال natural numbers أو ال integers if we have a
+
+359
+00:27:18,200 --> 00:27:21,680
+propositional function P of N لو كان في عندنا اللي
+
+360
+00:27:21,680 --> 00:27:26,240
+هي جملة بتعتمد على اللي هي من على N اللي هي ال
+
+361
+00:27:26,240 --> 00:27:29,840
+natural number وبدنا نثبت أنه هذه الجملة P of N
+
+362
+00:27:29,840 --> 00:27:34,420
+صحيحة لكل natural number N طبعًا إحنا هنعتبر ال
+
+363
+00:27:34,420 --> 00:27:37,240
+natural number اللي هي عبارة عن واحد اثنين ثلاثة
+
+364
+00:27:37,240 --> 00:27:40,500
+أربعة إلى ما انتهى مش هنعتبر السفر فيها في كل
+
+365
+00:27:40,500 --> 00:27:46,320
+حديثنا اتفقنا نتفج عليك إن شاء الله الآن عشان نثبت
+
+366
+00:27:46,320 --> 00:27:49,240
+هذه اللي هي ال P of N أنها صحيحة على كل natural
+
+367
+00:27:49,240 --> 00:27:53,240
+number بنعمل ما يلي أول شيء بنثبت أنها صحيحة
+
+368
+00:27:53,240 --> 00:27:58,660
+الجملة عند الان بتساوي واحد يعني بنثبت P واحد is
+
+369
+00:27:58,660 --> 00:28:02,540
+true show that P واحد is true الخطوة الثانية هذه
+
+370
+00:28:02,540 --> 00:28:06,380
+اللي بنسميها ال basic step الخطوة الثانية بنفترض
+
+371
+00:28:06,380 --> 00:28:12,790
+أن ال P صحيحة عند number k وبنثبت أنها صحيحة عند
+
+372
+00:28:12,790 --> 00:28:18,010
+P k زائد واحد يعني بنفترض أنه P of K صحيحة
+
+373
+00:28:18,010 --> 00:28:23,050
+وبنثبت P of K زائد واحد لكل K element in N الـ N
+
+374
+00:28:23,050 --> 00:28:25,970
+هذا اللي بنسميها الـ P of K is true بنفرضها ده
+
+375
+00:28:25,970 --> 00:28:30,550
+بنسميها induction hypothesis اللي هي فرضية 
+
+376
+00:28:30,550 --> 00:28:36,190
+الاستقراء، ومنها بنثبت b<sub>k</sub> زائد واحد لو خلصنا هذا
+
+377
+00:28:36,190 --> 00:28:40,950
+الكلام هذه، وهذه كلها على بعض أثبتناها بنكون
+
+378
+00:28:40,950 --> 00:28:45,510
+أثبتنا اللي هو then b of n must be true for any n
+
+379
+00:28:45,510 --> 00:28:48,630
+element in N، هذه الطريقة بنسميها اللي هي ال
+
+380
+00:28:48,630 --> 00:28:53,290
+mathematical induction أو الاستقراء الرياضي بنثبت
+
+381
+00:28:53,290 --> 00:28:57,260
+الجملة صحيحة عند واحد، بعدين مفترض أن صحة الجملة عند
+
+382
+00:28:57,260 --> 00:29:01,560
+b<sub>k</sub>، ومنها بنثبت أن نثبت صحة b<sub>k</sub> عند b<sub>k</sub> زائد واحد
+
+383
+00:29:01,560 --> 00:29:05,600
+وبكون هي كأثبتنا أن هي صحيحة لكل n element in
+
+384
+00:29:05,600 --> 00:29:10,140
+وخلينا ناخد أمثلة عملية، وهي أول مثال عملي بقول
+
+385
+00:29:10,140 --> 00:29:13,420
+prove that 1 زائد 3 زائد 5 زائد 2
+
+386
+00:29:13,420 --> 00:29:17,800
+n ناقص 1 بيساوي n تربيع، صحيحة هذا المقدار لو
+
+387
+00:29:17,800 --> 00:29:21,120
+جمعته لبعض بيساوي دائماً n تربيع، صحيحة لكل n
+
+388
+00:29:21,120 --> 00:29:24,700
+element in، بندنا نثبت هذه اللاحظة، إن الجملة تعتمد
+
+389
+00:29:24,700 --> 00:29:27,500
+على مين؟ على الـ n اللي هي إيش؟ الـ natural numbers
+
+390
+00:29:27,500 --> 00:29:32,060
+إذا الـ mathematical induction بتظبط فيها طبعاً هذه
+
+391
+00:29:32,060 --> 00:29:36,620
+إيش معناتها هي؟ the sum of the first n odd integers
+
+392
+00:29:36,620 --> 00:29:40,600
+يعني أول n من الـ odd integers، 1 زائد 3 زائد
+
+393
+00:29:40,600 --> 00:29:43,540
+5 زائد 2 n ناقص 1، دول عدد n، لو جمعتها
+
+394
+00:29:43,540 --> 00:29:47,650
+لبعض هيطلع n بيساوي n تربيع، الـ n مش هو هذا
+
+395
+00:29:47,650 --> 00:29:51,970
+موضوعنا، موضوعنا بنثبت إن هذه صحيحة دائماً، الـ n مثال
+
+396
+00:29:51,970 --> 00:29:54,730
+عليها بس عشان نوضع عليها هذه اللي هي عبارة عن لو
+
+397
+00:29:54,730 --> 00:29:57,750
+جيت جمعت 1 زائد 3 اللي هو عددين فرديين اللي
+
+398
+00:29:57,750 --> 00:30:01,810
+هو 2 تربيع اللي هي 4، لو جيت جمعت العدد
+
+399
+00:30:01,810 --> 00:30:04,790
+الأول فردي، والثاني فردي، والثالث فردي هتطلع قداش؟
+
+400
+00:30:04,790 --> 00:30:10,170
+اللي هي 9 اللي هي 3 تربيع، أو 4 أعداد 1، 2، 3، 4
+
+401
+00:30:10,170 --> 00:30:13,450
+يعني 1 و 3 أو 5 و 7 اللي هو هيطلع
+
+402
+00:30:13,450 --> 00:30:19,150
+قيمتنا 16 يعني 4 تربيع، هذا بس مثال توضيحي لأن
+
+403
+00:30:19,150 --> 00:30:22,090
+نيجي لموضوعنا اللي هو برهان هذه by induction، الـ
+
+404
+00:30:22,090 --> 00:30:25,480
+proof، أول حاجة بدنا نثبت صحة الجملة هذه، الـ basic
+
+405
+00:30:25,480 --> 00:30:29,840
+step الأولى، بدنا نثبت صحة الجملة هذه صحيحة لمين؟
+
+406
+00:30:29,840 --> 00:30:34,920
+لـ n بتساوي 1، يعني لما نعوض هنا بـ n لازم يطلع
+
+407
+00:30:34,920 --> 00:30:38,820
+الطرف الأيسر هذا بيساوي الطرف الأيمن لو عوضنا هنا
+
+408
+00:30:38,820 --> 00:30:42,360
+بـ n، طبعاً لو عوضنا هنا بـ n واضح أنه بيطلع عندي 1
+
+409
+00:30:42,360 --> 00:30:47,740
+تربيع، يعني 1، طب نيجي نعوض هنا بـ n اللي هو لما إنه
+
+410
+00:30:47,740 --> 00:30:51,020
+بقى 1، بصير 2 في 1 اللي هي 2 ناقص 1
+
+411
+00:30:51,020 --> 00:30:54,060
+1، يعني ما فيش شيء بنجمعه إلا الـ 1 لحاله يعني
+
+412
+00:30:54,060 --> 00:30:57,980
+هذه بس اللي هو أول term اللي هو الـ 1، الـ n the
+
+413
+00:30:57,980 --> 00:31:01,320
+sum of the first odd number اللي هو 1 اللي هو
+
+414
+00:31:01,320 --> 00:31:05,280
+الطرف الأيسر هذا وهذا بيساوي 1 تربيع، والثانية
+
+415
+00:31:05,280 --> 00:31:09,210
+متساويين، مدام الثانية متساويين، إذا هذا الطرف بيساوي
+
+416
+00:31:09,210 --> 00:31:13,690
+هذا for n بتساوي 1، إذا الـ basic step بتحققت، إذا
+
+417
+00:31:13,690 --> 00:31:17,630
+صارت اللي هي الجملة دي صحيحة for n بتساوي 1
+
+418
+00:31:17,630 --> 00:31:22,130
+نيجي الآن نثبت إن افترض صحتها، الـ inductive step
+
+419
+00:31:22,130 --> 00:31:27,490
+بدنا نقول assume that this is true for n بتساوي k
+
+420
+00:31:27,490 --> 00:31:31,470
+إيش يعني؟ يعني بدنا نفرض صحة 1 زائد 3 زائد
+
+421
+00:31:31,470 --> 00:31:37,400
+5 زائد، ما دام للـ n k بنحط 2k-1 تساوي الـ k تربيع
+
+422
+00:31:37,400 --> 00:31:41,340
+يعني فرضنا صحة هذه الجملة عند n بتساوي k يعني
+
+423
+00:31:41,340 --> 00:31:45,700
+عوضنا أنا k و أنا k، الآن هذه صارت عندنا اللي هو
+
+424
+00:31:45,700 --> 00:31:51,460
+مفترضين صحتها، بدنا نثبت من خلالها إن الجملة صحيحة
+
+425
+00:31:51,460 --> 00:31:56,020
+now we prove that إن هذه صحيحة لـ k زائد 1، إيش
+
+426
+00:31:56,020 --> 00:32:00,280
+معناتها لـ k زائد 1؟ يعني لما ننشيل الـ n ونحط
+
+427
+00:32:00,280 --> 00:32:04,340
+مكانها k زائد 1، بتصير 1 زائد 3 زائد 5
+
+428
+00:32:04,340 --> 00:32:08,440
+زائد 2 اللي هو k ناقص 1 زائد اللي هو آخر
+
+429
+00:32:08,440 --> 00:32:12,620
+term هذا، مين اللي هو؟ 2 في k زائد 1 ناقص 1
+
+430
+00:32:12,620 --> 00:32:16,780
+يعني شيلت الـ n هذه وحطيت مكانها k زائد 1، إذا
+
+431
+00:32:16,780 --> 00:32:19,780
+كانت هذه مضايقاتكم سابقوها يعني أنا بقصد ونظل نجمع
+
+432
+00:32:19,780 --> 00:32:23,260
+1 زائد 3 زائد 5 زائد 7، لما نصل لآخر
+
+433
+00:32:23,260 --> 00:32:27,960
+term هذا اللي حطينا مكان الـ n اللي هو k زائد 1
+
+434
+00:32:27,960 --> 00:32:32,370
+شيلت الـ n هيها وحطيت k زائد 1، بتثبت إن هذا بيساوي
+
+435
+00:32:32,370 --> 00:32:36,530
+هذا المقدار لما أشيل الـ n هنا برضه أحط كمان إيش؟ k
+
+436
+00:32:36,530 --> 00:32:40,370
+زائد 1، فبصير k زائد 1 لكل تربيع، هذا الآن هو
+
+437
+00:32:40,370 --> 00:32:44,850
+اللي بدنا نثبته، لو أثبتته معناته وأثبتت صحة الجملة هذه
+
+438
+00:32:44,850 --> 00:32:48,550
+في حالة الـ n بتساوي k زائد 1، يلا نشوف مع بعض
+
+439
+00:32:48,550 --> 00:32:53,090
+طبعاً أكيد بنستعيني بهذه، أكيد تشوفوا الآن، ناخد الطرف
+
+440
+00:32:53,090 --> 00:32:57,870
+الأيمن هذا الآن، أول حاجة من هنا من induction
+
+441
+00:32:57,870 --> 00:33:02,130
+hypothesis، هيها هذه بيساوي k تربيع، يعني 1 زي
+
+442
+00:33:02,130 --> 00:33:06,230
+3 زي 5 زي 2 k ناقص 1 بيساوي k تربيع
+
+443
+00:33:06,230 --> 00:33:10,050
+بتعتمد على هدف الوصول من الطرف الأيسر هنا للطرف
+
+444
+00:33:10,050 --> 00:33:13,490
+الأيمن، ناخد الطرف الأيسر هذا ماشي الحال، هي الطرف
+
+445
+00:33:13,490 --> 00:33:17,130
+الأيسر هذا إيش هو؟ هو عبارة عن 1 زي 3 زي
+
+446
+00:33:17,130 --> 00:33:22,900
+2 k كده ناقص 1 زي مين؟ زي هذا، هذا بدخل هذه بيصير
+
+447
+00:33:22,900 --> 00:33:28,560
+2 k زائد 2 ناقص 1 زائد 2 ناقص 1
+
+448
+00:33:28,560 --> 00:33:32,440
+يعني 1، يعني بيصير هذا المقدار هو عبارة عن 2
+
+449
+00:33:32,440 --> 00:33:38,450
+k زائد 1، هذا لما نفكه بيصير 2 k زائد 1، طيب
+
+450
+00:33:38,450 --> 00:33:43,110
+الجزء الأول هذا كله هيو من هنا لهنا هيو ما تنسيها يا
+
+451
+00:33:43,110 --> 00:33:46,190
+في الـ induction hypothesis كتربيع، فبيصير هذه
+
+452
+00:33:46,190 --> 00:33:51,270
+k تربيع، مكان كل هذا المقدار بيضل كمان جنبه من 2
+
+453
+00:33:51,270 --> 00:33:56,030
+k زائد 1، هذا زائد هذا اللي هو مفكوك k زائد 1
+
+454
+00:33:56,030 --> 00:33:59,110
+لكل تربيع، زي ما أنتم عارفين يعني إيش اللي وصلنا
+
+455
+00:33:59,110 --> 00:34:06,290
+له؟ وصلنا لأن هذه اللي هي بتساوي هذه، يعني صار اللي
+
+456
+00:34:06,290 --> 00:34:11,390
+هي الجملة لما ثبتت هذه بتساوي هذه، صارت الجملة اللي
+
+457
+00:34:11,390 --> 00:34:16,590
+فوق صحيحة لـ k زائد 1، مدام خلصنا أطبطنا صحيحة لـ
+
+458
+00:34:16,590 --> 00:34:22,850
+k زائد 1، نكون اللي هو الـ conclusion اللي هي الـ
+
+459
+00:34:22,850 --> 00:34:26,170
+mathematical induction اكتملت، معناته إنه صارت هذه
+
+460
+00:34:26,170 --> 00:34:32,680
+الجملة صحيحة لكل element in، الذي لم يتابع جيداً في
+
+461
+00:34:32,680 --> 00:34:35,340
+هذا المثال يتابع في المثال اللي بعده برضه عن
+
+462
+00:34:35,340 --> 00:34:37,600
+الـ mathematical induction، الآن يستخدم
+
+463
+00:34:37,600 --> 00:34:41,240
+الـ mathematical induction لكي يثبت أن 1 زائد
+
+464
+00:34:41,240 --> 00:34:45,520
+2 زائد n يساوي n في n زائد 1 هذا كله مجسوم
+
+465
+00:34:45,520 --> 00:34:49,930
+على 2، لكل n element in، الآن بدنا نستخدم اللي
+
+466
+00:34:49,930 --> 00:34:53,190
+هو الـ mathematical induction اللي اتبعت هذا أكيد
+
+467
+00:34:53,190 --> 00:34:56,290
+الـ mathematical induction، ليش؟ لأنه بده يبقى اللي
+
+468
+00:34:56,290 --> 00:34:58,550
+هو لكل n element in n، يعني بدنا نتبع صحة الجملة
+
+469
+00:34:58,550 --> 00:35:03,630
+هذه لكل الـ natural numbers n، قولنا الـ natural
+
+470
+00:35:03,630 --> 00:35:08,120
+numbers بنقصد فيها من 1 إلى ما لا نهاية، نيجي أول
+
+471
+00:35:08,120 --> 00:35:11,400
+خطوة، أول خطوة زي ما اتفقنا بنثبت.. بنثبت صحة هذه
+
+472
+00:35:11,400 --> 00:35:15,340
+الجملة اللي سميتها 1، أنا بنثبت صحتها لـ n بتساوي
+
+473
+00:35:15,340 --> 00:35:19,520
+1، يعني لما نعوض في الطرف الأيسر بـ 1 لازم يطلع
+
+474
+00:35:19,520 --> 00:35:22,660
+لـ.. بيساوي الطرف الأيسر لما.. لأي من لما نعوض
+
+475
+00:35:22,660 --> 00:35:26,420
+فيه بـ 1، ده نجرب لـ basic step for n بتساوي
+
+476
+00:35:26,420 --> 00:35:31,780
+1، since الـ n لما نعوض هنا بـ 1 بيصير بس 1
+
+477
+00:35:31,780 --> 00:35:36,200
+يعني ما كنت جمعتش ولا شيء لسه، بيساوي 1 لأن الطرف
+
+478
+00:35:36,200 --> 00:35:40,380
+الأيمن هنا إيش هو؟ بيصير 1 في 1 زائد 1
+
+479
+00:35:40,380 --> 00:35:43,900
+1 زائد 1، 2 في 1 بـ 1، يعني 2 على
+
+480
+00:35:43,900 --> 00:35:49,270
+2 بيساوي 1، إذا بما إن هذا الطرف بيساوي 1
+
+481
+00:35:49,270 --> 00:35:53,450
+بيساوي اللي هو الطرف الأيسر، إذا صارت اللي هي 1
+
+482
+00:35:53,450 --> 00:35:57,110
+هذه الجملة 1، مقصود فيها الجملة دي كلها، صارت هذه
+
+483
+00:35:57,110 --> 00:36:01,910
+الجملة 1 is true for one بتساوي 1، رقمنا أنا
+
+484
+00:36:01,910 --> 00:36:05,850
+1، عشان إن أسهر يسهر سهل التعامل معها، إذا صارت
+
+485
+00:36:05,850 --> 00:36:09,030
+هذه عبارة عن صحيحة لـ n بتساوي 1، إذا الـ basic
+
+486
+00:36:09,030 --> 00:36:13,830
+step اتحققت، الآن بدنا نفترض صحة، بدنا نيجي إلى الـ
+
+487
+00:36:13,830 --> 00:36:17,960
+inductive step اللي هي inductive hypothesis اللي هي
+
+488
+00:36:17,960 --> 00:36:23,100
+فرضية الاستقراء اللي هي إيش بتقول؟ نفترض أن الجملة
+
+489
+00:36:23,100 --> 00:36:28,020
+صحيحة، assume that 1 is true for n بتساوي k
+
+490
+00:36:28,020 --> 00:36:32,200
+بدنا نفترض أن صحة الجملة هذه لـ n بتساوي k، مدام
+
+491
+00:36:32,200 --> 00:36:36,920
+فرضنا صحتها لـ n بتساوي k، إذا 1 زائد 2 لما
+
+492
+00:36:36,920 --> 00:36:41,810
+نصل عند k، هيها هتساوي هذه k يا دماغها مش k مش n
+
+493
+00:36:41,810 --> 00:36:47,470
+بتساوي k في k زائد 1، بتساوي k في k زائد 1
+
+494
+00:36:47,470 --> 00:36:51,790
+إذن مدام فرضت إن هذا صحيح على k، بشيل الـ n وبحط
+
+495
+00:36:51,790 --> 00:36:55,450
+مكانها k، وهذا اللي هي induction hypothesis الـ n
+
+496
+00:36:55,450 --> 00:37:02,110
+منها بدي أثبت، now we prove that 1 is true for n
+
+497
+00:37:02,110 --> 00:37:06,550
+إيش بتساوي k زائد 1؟ يعني بمعنى آخر إيش بدي أثبت؟
+
+498
+00:37:06,550 --> 00:37:12,720
+we prove that 1 زائد 2 زائد k زائد 1، ماشي الحال، إذا
+
+499
+00:37:12,720 --> 00:37:15,480
+1 زائد 2 لما نصل عند k زائد 1، لأنه
+
+500
+00:37:15,480 --> 00:37:18,760
+شيلت الـ n إشمالها k زائد 1، طبعاً الجاب اللي k 
+
+501
+00:37:18,760 --> 00:37:20,880
+زائد واحد هي الـ k زي ما احنا عارفين أنه بنجمع واحد
+
+502
+00:37:20,880 --> 00:37:23,890
+زائد اثنين زائد ثلاثة زائد أربعة إلخ نبدأ نثبت
+
+503
+00:37:23,890 --> 00:37:27,630
+بساوي مين؟ أشيل كل K و أضع مكانها K زائد واحد يعني
+
+504
+00:37:27,630 --> 00:37:31,690
+K زائد واحد في اللي هي برضه K زائد واحد زائد واحد
+
+505
+00:37:31,690 --> 00:37:34,850
+على اثنين يعني الآن أنا بدأ أثبت هذه الجملة
+
+506
+00:37:34,850 --> 00:37:38,990
+بالاستعانة بمين؟ بالـ induction hypothesis اللي 
+
+507
+00:37:38,990 --> 00:37:43,150
+فرضته هذا اللي هي دي K في K بساوي K في K زائد واحد
+
+508
+00:37:43,150 --> 00:37:46,910
+على اثنين دعونا نشوف كده الآن ناخد الطرف الأيمن
+
+509
+00:37:46,910 --> 00:37:52,010
+هذا proof بنثبت لهذه .. بنثبت لهذه هي عندنا أخدت
+
+510
+00:37:52,010 --> 00:37:56,750
+الطرف الأيسر هنا هي من هنا لهنا بدأ أشيل هذا من
+
+511
+00:37:56,750 --> 00:38:00,970
+هنا لهنا واحد زائد اثنين و أصل عند الـ K و أعوضها
+
+512
+00:38:00,970 --> 00:38:05,370
+من هذا اللي فرضته هذا معناه جنبها دي K حسب هنا
+
+513
+00:38:05,370 --> 00:38:10,050
+إيش هذي بيصير بدل هذه من هنا لهنا اللي هي K في K 
+
+514
+00:38:10,050 --> 00:38:13,830
+زائد واحد على اثنين بعوض عنها بيصير K في K زائد
+
+515
+00:38:13,830 --> 00:38:18,790
+واحد على اثنين زائد الأصلي هذه K زائد واحد الآن هنا
+
+516
+00:38:18,790 --> 00:38:21,670
+بدي أوحد المقامات هنا المقام اللي تحت واحد هنا
+
+517
+00:38:21,670 --> 00:38:26,310
+اثنين فلما أوحدهم بيصير كيف؟ K زائد واحد زائد
+
+518
+00:38:26,310 --> 00:38:30,790
+اللي هو مين؟ اثنين في K زائد واحد الكل على اثنين
+
+519
+00:38:30,790 --> 00:38:35,050
+عشان أوحد المقامات يساوي الآن هنا في عامل مشترك
+
+520
+00:38:35,050 --> 00:38:37,710
+بقدر آخذ الـ K زائد واحد إيش مالها؟ عامل مشترك
+
+521
+00:38:37,710 --> 00:38:41,510
+فباخد عامل مشترك من هنا اللي هي الـ K زائد واحد من
+
+522
+00:38:41,510 --> 00:38:45,290
+هنا بظل اللي هي الـ K و هنا بظل الاثنين فبصير مضروبة
+
+523
+00:38:45,290 --> 00:38:48,770
+في الـ K زائد الاثنين والكل مقسوم على اثنين هذه
+
+524
+00:38:48,770 --> 00:38:52,950
+بالضبط هي عبارة عن K زائد واحد مضروبة في الـ K زائد
+
+525
+00:38:52,950 --> 00:38:56,810
+اثنين هي عبارة عن K زائد واحد زائد واحد على اثنين
+
+526
+00:38:56,810 --> 00:39:02,330
+إذا صارت اللي هو هذا المقدار بساوي هذا المقدار يعني
+
+527
+00:39:02,330 --> 00:39:08,730
+أثبتت اللي هو هذه اللي هو أثبتت صحة واحد لمين؟ لأن
+
+528
+00:39:08,730 --> 00:39:12,610
+بتساوي K زائد واحد ومدام أثبتتها لـ K زائد واحد
+
+529
+00:39:12,610 --> 00:39:15,910
+معناته أنا اللي هو خلصت الـ induction hypothesis
+
+530
+00:39:15,910 --> 00:39:19,570
+معناته جملتيها دي صارت صحيحة لكل N element in N
+
+531
+00:39:19,570 --> 00:39:23,630
+يعني لو لخصنا إيش اللي سويناه؟ أثبتنا صحة هذه أول
+
+532
+00:39:23,630 --> 00:39:28,010
+شيء لأن بتساوي واحد وبعدين فرضنا صحتها لأن بتساوي
+
+533
+00:39:28,010 --> 00:39:33,240
+K ومنها أثبتنا صحتها لـ K زائد واحد وهذا كله على بعض
+
+534
+00:39:33,240 --> 00:39:35,920
+هو اللي بنسميه الـ mathematical induction أو
+
+535
+00:39:35,920 --> 00:39:40,240
+الاستقراء الرياضي وبكون هيك أثبتناها لكل N element 
+
+536
+00:39:40,240 --> 00:39:43,540
+in N ناخد مثال آخر شوفوا المثال صلوا على النبي
+
+537
+00:39:43,540 --> 00:39:46,600
+عليه الصلاة والسلام اللي بيقول show that N أصغر من
+
+538
+00:39:46,600 --> 00:39:51,320
+2N لكل N element in N طبعا عارفينها دي الآن كيف
+
+539
+00:39:51,320 --> 00:39:54,420
+نثبتها؟ برضه بنثبتها بـ Mathematical Induction
+
+540
+00:39:54,420 --> 00:39:58,880
+لأنه اللي هي جملة تعتمد على اللي هو الـ integers أو
+
+541
+00:39:58,880 --> 00:40:02,180
+الأعداد الطبيعية نشوف الـ proof أول حاجة الـ basic
+
+542
+00:40:02,180 --> 00:40:06,380
+step الـ basic step اللي هي P of واحد هذا سميناها
+
+543
+00:40:06,380 --> 00:40:10,600
+الجملة P of n يعني P of واحد يعني n عند n بتساوي
+
+544
+00:40:10,600 --> 00:40:15,400
+واحد هذه بتساوي واحد وهذه بتساوي اثنين صح؟ إذا
+
+545
+00:40:15,400 --> 00:40:19,160
+الواحد أصغر من اثنين إذا فعلا اللي هي n اللي هي
+
+546
+00:40:19,160 --> 00:40:23,700
+واحد أصغر من اثنين is true دائما يعني صارت الـ P
+
+547
+00:40:23,700 --> 00:40:27,660
+واحد is true لإن الواحد أصغر من اثنين في واحد اللي
+
+548
+00:40:27,660 --> 00:40:31,640
+هو بيساوي إيش؟ اثنين الـ Inductive step بدنا نفترض
+
+549
+00:40:31,640 --> 00:40:37,060
+الآن Assume that P of K is true وبدنا نثبت منها
+
+550
+00:40:37,060 --> 00:40:41,200
+إنها P K زائد واحد is true إذن الآن بدنا نفترض إن P
+
+551
+00:40:41,200 --> 00:40:47,440
+of K is true يعني نفترض صحة هذه الجملة عند K عند N
+
+552
+00:40:47,440 --> 00:40:52,240
+بساوي K مثلا مثلا هي عند K إذن K أصغر من 2K طيب،
+
+553
+00:40:52,240 --> 00:40:56,560
+لأن we need to show that P of K زائد واحد is true
+
+554
+00:40:56,560 --> 00:41:00,360
+يعني بدنا نثبت صحة الجملة عند K زائد واحد، إيش
+
+555
+00:41:00,360 --> 00:41:04,460
+يعني؟ بدنا نثبت صحة إن K زائد واحد هي أصغر من
+
+556
+00:41:04,460 --> 00:41:08,300
+اثنين في K زائد واحد، لو أثبتنا هذه، بيكون خلصنا
+
+557
+00:41:08,300 --> 00:41:12,890
+الـ induction hypothesis طيب الآن بدنا نثبت هذه الآن
+
+558
+00:41:12,890 --> 00:41:17,530
+بدي أستخدم أكيد هذه عند الـ K أصغر من الـ 2 K ماشي
+
+559
+00:41:17,530 --> 00:41:21,870
+الحال منها لو أضفت الآن واحد للجهتين بيصير K
+
+560
+00:41:21,870 --> 00:41:26,810
+زائد واحد أصغر من 2 K زائد واحد أكيد بتطلع صح
+
+561
+00:41:26,810 --> 00:41:32,080
+يعني الآن عند الـ K زائد واحد أصغر من 2 K زائد
+
+562
+00:41:32,080 --> 00:41:36,220
+اثنين أكيد لأن هذا زيادة عن هذا بواحد طيب من هدول
+
+563
+00:41:36,220 --> 00:41:41,740
+مع بعض التنتين بيصير 2 K زائد واحد هذه أصغر من
+
+564
+00:41:41,740 --> 00:41:45,800
+2 K اثنين في K زائد واحد أخدت اثنين إيه شمالها
+
+565
+00:41:45,800 --> 00:41:52,940
+عامل مشترك الآن أثبتت هذه من هذه وهذه أثبتها من فوق
+
+566
+00:41:52,940 --> 00:41:57,840
+التنتين مع بعض together بيصير عندي اللي هو K زائد
+
+567
+00:41:57,840 --> 00:42:01,700
+واحد أصغر من هذه وهذه بدورها أصغر من هذه إذا
+
+568
+00:42:01,700 --> 00:42:05,660
+بخاصية التعدي هذه أصغر من هذه يعني K زائد واحد أصغر
+
+569
+00:42:05,660 --> 00:42:09,600
+من اثنين في K زائد واحد وبهيك احنا بنكون أثبتنا
+
+570
+00:42:09,600 --> 00:42:14,000
+اللي هو صحة الجملة عند K زائد واحد اللي هي اللي
+
+571
+00:42:14,000 --> 00:42:19,040
+فوق هذه معناته إذا صارت صحيحة على كل element in ويا
+
+572
+00:42:19,040 --> 00:42:24,880
+سيدي هاي كمان اللي هو الآن بنصل للي هو عندي الـ
+
+573
+00:42:24,880 --> 00:42:29,600
+homework اللي بدنا إيّاه اللي هو للمحاضرة هذه كلها
+
+574
+00:42:29,600 --> 00:42:34,080
+على طرق البرهان اللي هو الـ direct proof أو الـ
+
+575
+00:42:34,080 --> 00:42:37,700
+indirect proof أو الـ mathematical induction وإلى
+
+576
+00:42:37,700 --> 00:42:41,600
+لقاء آخر السلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0569dc65620185356586d485c8b392016d0569fa
--- /dev/null
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اللي معناها لما نصلّمين إلى صحة Q إذاً an implication B implies Q can be proved by showing that if B is true then Q is also true", "tokens": [6027, 20292, 39896, 28242, 21542, 4587, 16373, 4587, 13672, 1829, 20449, 8315, 11296, 4032, 28820, 13672, 1829, 39896, 9673, 3615, 9566, 1829, 9307, 13672, 1829, 20449, 8315, 11296, 5296, 15042, 8717, 36520, 11703, 2304, 9957, 30731, 20328, 5016, 3660, 1249, 11933, 15730, 14111, 364, 37814, 363, 18779, 1249, 393, 312, 14617, 538, 4099, 300, 498, 363, 307, 2074, 550, 1249, 307, 611, 2074], "avg_logprob": -0.24938963586464524, "compression_ratio": 1.4736842105263157, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 179.61, "end": 180.11, "word": "اللي", "probability": 0.327362060546875}, {"start": 180.11, "end": 180.43, "word": " هي", "probability": 0.9091796875}, {"start": 180.43, "end": 180.79, "word": " كل", "probability": 0.90185546875}, {"start": 180.79, "end": 181.57, "word": " الحقائق", "probability": 0.9923095703125}, {"start": 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517.69, "end": 518.41, "word": " بدنا", "probability": 0.811279296875}, {"start": 518.41, "end": 519.21, "word": " نسميهم", "probability": 0.80303955078125}, {"start": 519.21, "end": 519.95, "word": " let", "probability": 0.7802734375}, {"start": 519.95, "end": 520.23, "word": " n", "probability": 0.75390625}, {"start": 520.23, "end": 520.93, "word": " بتساوي", "probability": 0.86962890625}, {"start": 520.93, "end": 521.81, "word": " اتنين", "probability": 0.86358642578125}, {"start": 521.81, "end": 522.33, "word": " k", "probability": 0.33251953125}, {"start": 522.33, "end": 522.93, "word": " زائد", "probability": 0.9471028645833334}, {"start": 522.93, "end": 523.47, "word": " واحد", "probability": 0.98779296875}, {"start": 523.47, "end": 524.05, "word": " و", "probability": 0.9541015625}, {"start": 524.05, "end": 524.29, "word": " m", "probability": 0.2384033203125}, {"start": 524.29, "end": 524.49, "word": " ايش", "probability": 0.8190104166666666}, {"start": 524.49, "end": 525.17, 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مجموحا", "probability": 0.905517578125}, {"start": 534.61, "end": 535.37, "word": " بدك", "probability": 0.7578125}, {"start": 535.37, "end": 535.85, "word": " تقول", "probability": 0.995849609375}, {"start": 535.85, "end": 536.27, "word": " n", "probability": 0.86572265625}, {"start": 536.27, "end": 536.87, "word": " زائد", "probability": 0.9713541666666666}, {"start": 536.87, "end": 537.29, "word": " m", "probability": 0.962890625}, {"start": 537.29, "end": 537.73, "word": " ايش", "probability": 0.8251953125}, {"start": 537.73, "end": 538.59, "word": " هيساوي؟", "probability": 0.87666015625}], "temperature": 1.0}, {"id": 25, "seek": 55046, "start": 539.02, "end": 550.46, "text": "2k و2j و1 زائد واحد يعني هيصير عند ال N زائد M عبارة عن 2k زائد 2j زائد 2", "tokens": [17, 74, 4032, 17, 73, 4032, 16, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 8032, 1829, 9381, 13546, 43242, 2423, 426, 30767, 16373, 3215, 376, 6225, 3555, 9640, 3660, 18871, 568, 74, 30767, 16373, 3215, 568, 73, 30767, 16373, 3215, 568], "avg_logprob": -0.2706473178806759, "compression_ratio": 1.380952380952381, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 539.02, "end": 539.92, "word": "2k", "probability": 0.4949951171875}, {"start": 539.92, "end": 541.02, "word": " و2j", "probability": 0.5707194010416666}, {"start": 541.02, "end": 542.14, "word": " و1", "probability": 0.6416015625}, {"start": 542.14, "end": 542.72, "word": " زائد", "probability": 0.6214599609375}, {"start": 542.72, "end": 543.12, "word": " واحد", "probability": 0.7239990234375}, {"start": 543.12, "end": 543.38, "word": " يعني", "probability": 0.761474609375}, {"start": 543.38, "end": 543.82, "word": " هيصير", "probability": 0.7166748046875}, {"start": 543.82, "end": 544.06, "word": " عند", "probability": 0.8515625}, {"start": 544.06, "end": 544.24, "word": " ال", "probability": 0.6455078125}, {"start": 544.24, "end": 544.38, "word": " N", "probability": 0.2305908203125}, {"start": 544.38, "end": 544.88, 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{"start": 564.15, "end": 564.93, "word": " يعني", "probability": 0.9189453125}, {"start": 564.93, "end": 565.09, "word": " ال", "probability": 0.88037109375}, {"start": 565.09, "end": 565.25, "word": " N", "probability": 0.8603515625}, {"start": 565.25, "end": 565.55, "word": " زائد", "probability": 0.9111328125}, {"start": 565.55, "end": 565.71, "word": " M", "probability": 0.99169921875}, {"start": 565.71, "end": 566.25, "word": " كتبناه", "probability": 0.93740234375}, {"start": 566.25, "end": 566.45, "word": " على", "probability": 0.90673828125}, {"start": 566.45, "end": 566.91, "word": " صورة", "probability": 0.9894205729166666}, {"start": 566.91, "end": 567.67, "word": " 2", "probability": 0.6328125}, {"start": 567.67, "end": 568.97, "word": " زائد", "probability": 0.9176432291666666}, {"start": 568.97, "end": 569.81, "word": " اللي", "probability": 0.6259765625}, {"start": 569.81, "end": 570.03, "word": " هو", "probability": 0.93212890625}, {"start": 570.03, "end": 570.81, 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656.38, "end": 683.26, "text": "إذا بدنا نثبت أن M في N برضه مربع كامل اضرب M في N بصير S تربيع في T تربيع اللي هو عبارة عن S في T في الكل تربيع أو اللي هو زي ما اعمل S في S في T في T انتوا عارفينه هذا الكلام سهل S في T اللي هو في S في T اللي هو عبارة عن S في T لكل تربيع يعني M في N كتبناه على صورة ST لكل تربيع ST عبارة عن رقم انتجار لأن هذا انتجار و هذا انتجار", "tokens": [28814, 15730, 47525, 8315, 8717, 12984, 3555, 2655, 14739, 376, 8978, 426, 4724, 43042, 3224, 3714, 25513, 3615, 9122, 10943, 1211, 1975, 11242, 25513, 376, 8978, 426, 4724, 9381, 13546, 318, 6055, 2288, 21292, 3615, 8978, 314, 6055, 2288, 21292, 3615, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 318, 8978, 314, 8978, 2423, 28820, 6055, 2288, 21292, 3615, 34051, 13672, 1829, 31439, 30767, 1829, 19446, 1975, 25957, 1211, 318, 8978, 318, 8978, 314, 8978, 314, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 3224, 23758, 2423, 28820, 10943, 8608, 3224, 1211, 318, 8978, 314, 13672, 1829, 31439, 8978, 318, 8978, 314, 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{"start": 985.72, "end": 986.32, "word": " يعطينا", "probability": 0.9749755859375}, {"start": 986.32, "end": 986.5, "word": " أن", "probability": 0.86865234375}, {"start": 986.5, "end": 986.86, "word": " M", "probability": 0.89013671875}, {"start": 986.86, "end": 987.22, "word": " أكبر", "probability": 0.9811197916666666}, {"start": 987.22, "end": 987.32, "word": " من", "probability": 0.99560546875}, {"start": 987.32, "end": 987.58, "word": " خمس", "probability": 0.9689127604166666}, {"start": 987.58, "end": 988.16, "word": " وعشرين", "probability": 0.9874267578125}, {"start": 988.16, "end": 988.68, "word": " أو", "probability": 0.9306640625}, {"start": 988.68, "end": 989.22, "word": " N", "probability": 0.95703125}, {"start": 989.22, "end": 989.64, "word": " أكبر", "probability": 0.9847005208333334}, {"start": 989.64, "end": 989.76, "word": " من", "probability": 0.998046875}, {"start": 989.76, "end": 990.02, "word": " خمس", "probability": 0.99462890625}, {"start": 990.02, "end": 990.54, "word": " وعشرين", "probability": 0.9920654296875}], "temperature": 1.0}, {"id": 45, "seek": 100626, "start": 990.9, "end": 1006.26, "text": "الـ Contrapositive لها أنه احنا بنفترض عكس الجملة هذه كلها على بعضها و بنصل لعكس هذه يعني بدنا نفترض ايش معناه عكس M أكبر من 25 or N أكبر من 25 ايش نفيه جملة or يعني M", "tokens": [6027, 39184, 4839, 4007, 329, 2187, 5296, 11296, 14739, 3224, 1975, 5016, 8315, 44945, 5172, 2655, 43042, 6225, 4117, 3794, 25724, 2304, 37977, 29538, 28242, 11296, 15844, 45030, 11242, 11296, 4032, 44945, 36520, 5296, 3615, 4117, 3794, 29538, 37495, 22653, 47525, 8315, 8717, 5172, 2655, 43042, 1975, 1829, 8592, 20449, 8315, 3224, 6225, 4117, 3794, 376, 5551, 4117, 26890, 9154, 3552, 420, 426, 5551, 4117, 26890, 9154, 3552, 1975, 1829, 8592, 8717, 41185, 3224, 10874, 2304, 37977, 420, 37495, 22653, 376], "avg_logprob": -0.2076981683693281, "compression_ratio": 1.6153846153846154, "no_speech_prob": 9.47713851928711e-06, "words": [{"start": 990.9, "end": 991.16, "word": "الـ", "probability": 0.742431640625}, {"start": 991.16, "end": 991.94, "word": " Contrapositive", "probability": 0.8616943359375}, {"start": 991.94, "end": 992.42, "word": " لها", "probability": 0.59075927734375}, {"start": 992.42, "end": 992.84, "word": " أنه", "probability": 0.45745849609375}, {"start": 992.84, "end": 993.0, "word": " احنا", "probability": 0.795654296875}, {"start": 993.0, "end": 993.52, "word": " بنفترض", "probability": 0.95751953125}, {"start": 993.52, "end": 993.88, "word": " عكس", "probability": 0.9881184895833334}, {"start": 993.88, "end": 994.28, "word": " الجملة", "probability": 0.96337890625}, {"start": 994.28, "end": 994.58, "word": " هذه", "probability": 0.75048828125}, {"start": 994.58, "end": 995.12, "word": " كلها", "probability": 0.96240234375}, {"start": 995.12, "end": 995.32, "word": " على", "probability": 0.439208984375}, {"start": 995.32, "end": 995.92, "word": " بعضها", "probability": 0.9986979166666666}, {"start": 995.92, "end": 996.38, "word": " و", "probability": 0.51904296875}, {"start": 996.38, "end": 996.8, "word": " بنصل", "probability": 0.873046875}, {"start": 996.8, "end": 997.32, "word": " لعكس", "probability": 0.9547119140625}, {"start": 997.32, "end": 997.68, "word": " هذه", "probability": 0.81982421875}, {"start": 997.68, "end": 998.36, "word": " يعني", "probability": 0.885009765625}, {"start": 998.36, "end": 998.66, "word": " بدنا", "probability": 0.9111328125}, {"start": 998.66, "end": 999.2, "word": " نفترض", "probability": 0.9951171875}, {"start": 999.2, "end": 999.44, "word": " ايش", "probability": 0.7770182291666666}, {"start": 999.44, "end": 999.76, "word": " معناه", "probability": 0.837890625}, {"start": 999.76, "end": 1000.22, "word": " عكس", "probability": 0.9827473958333334}, {"start": 1000.22, "end": 1000.4, "word": " M", "probability": 0.70654296875}, {"start": 1000.4, "end": 1000.7, "word": " أكبر", "probability": 0.8883463541666666}, {"start": 1000.7, "end": 1000.76, "word": " من", "probability": 0.9365234375}, {"start": 1000.76, "end": 1001.14, "word": " 25", "probability": 0.97216796875}, {"start": 1001.14, "end": 1001.48, "word": " or", "probability": 0.1539306640625}, {"start": 1001.48, "end": 1001.7, "word": " N", "probability": 0.63427734375}, {"start": 1001.7, "end": 1002.0, "word": " أكبر", "probability": 0.97900390625}, {"start": 1002.0, "end": 1002.1, "word": " من", "probability": 0.99560546875}, {"start": 1002.1, "end": 1002.68, "word": " 25", "probability": 0.98583984375}, {"start": 1002.68, "end": 1003.72, "word": " ايش", "probability": 0.818359375}, {"start": 1003.72, "end": 1004.2, "word": " نفيه", "probability": 0.6853841145833334}, {"start": 1004.2, "end": 1004.6, "word": " جملة", "probability": 0.90283203125}, {"start": 1004.6, "end": 1005.1, "word": " or", "probability": 0.72705078125}, {"start": 1005.1, "end": 1005.8, "word": " يعني", "probability": 0.869873046875}, {"start": 1005.8, "end": 1006.26, "word": " M", "probability": 0.70703125}], "temperature": 1.0}, {"id": 46, "seek": 103196, "start": 1007.18, "end": 1031.96, "text": "أكبر من 25 false and أن أكبر من 25 false إيش يعني؟ يعني أم أصغر أو يساوي 25 and أن أصغر أو يساوي 25 إذا assume not q اللي هي هذه يعني بمعنى آخر assume أن أم أصغر أو يساوي 25 and أن أصغر أو يساوي 25 بناء على هذا الحديث", "tokens": [10721, 4117, 26890, 9154, 3552, 7908, 293, 14739, 5551, 4117, 26890, 9154, 3552, 7908, 11933, 1829, 8592, 37495, 22653, 22807, 37495, 22653, 5551, 2304, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 293, 14739, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 11933, 15730, 6552, 406, 9505, 13672, 1829, 39896, 29538, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 19753, 34740, 6552, 14739, 5551, 2304, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 293, 14739, 5551, 9381, 17082, 2288, 34051, 7251, 3794, 995, 45865, 3552, 44945, 16606, 15844, 23758, 21542, 16254, 12984], "avg_logprob": -0.1707589249221646, "compression_ratio": 2.067484662576687, "no_speech_prob": 8.106231689453125e-06, "words": [{"start": 1007.18, "end": 1007.68, "word": "أكبر", "probability": 0.71826171875}, {"start": 1007.68, "end": 1007.8, "word": " من", "probability": 0.99072265625}, {"start": 1007.8, "end": 1008.38, "word": " 25", "probability": 0.828125}, {"start": 1008.38, "end": 1009.14, "word": " false", "probability": 0.307861328125}, {"start": 1009.14, "end": 1010.18, "word": " and", "probability": 0.83203125}, {"start": 1010.18, "end": 1010.8, "word": " أن", "probability": 0.346923828125}, {"start": 1010.8, "end": 1011.2, "word": " أكبر", "probability": 0.9890950520833334}, {"start": 1011.2, "end": 1011.3, "word": " من", "probability": 0.9951171875}, {"start": 1011.3, "end": 1011.94, "word": " 25", "probability": 0.986328125}, {"start": 1011.94, "end": 1012.52, "word": " false", "probability": 0.84033203125}, {"start": 1012.52, "end": 1012.86, "word": " إيش", "probability": 0.728759765625}, {"start": 1012.86, "end": 1013.52, "word": " يعني؟", "probability": 0.7256673177083334}, {"start": 1013.52, "end": 1014.08, "word": " يعني", "probability": 0.918212890625}, {"start": 1014.08, "end": 1014.46, "word": " أم", "probability": 0.5552978515625}, {"start": 1014.46, "end": 1015.0, "word": " أصغر", "probability": 0.99267578125}, {"start": 1015.0, "end": 1015.16, "word": " أو", "probability": 0.9580078125}, {"start": 1015.16, "end": 1015.58, "word": " يساوي", "probability": 0.9720458984375}, {"start": 1015.58, "end": 1016.24, "word": " 25", "probability": 0.83349609375}, {"start": 1016.24, "end": 1017.48, "word": " and", "probability": 0.74560546875}, {"start": 1017.48, "end": 1017.88, "word": " أن", "probability": 0.86376953125}, {"start": 1017.88, "end": 1018.54, "word": " أصغر", "probability": 0.9964599609375}, {"start": 1018.54, "end": 1018.72, "word": " أو", "probability": 0.9677734375}, {"start": 1018.72, "end": 1019.38, "word": " يساوي", "probability": 0.9931640625}, {"start": 1019.38, "end": 1020.32, "word": " 25", "probability": 0.9833984375}, {"start": 1020.32, "end": 1021.24, "word": " إذا", "probability": 0.8046875}, {"start": 1021.24, "end": 1021.94, "word": " assume", "probability": 0.281982421875}, {"start": 1021.94, "end": 1022.3, "word": " not", "probability": 0.63134765625}, {"start": 1022.3, "end": 1022.7, "word": " q", "probability": 0.4462890625}, {"start": 1022.7, "end": 1022.92, "word": " اللي", "probability": 0.775634765625}, {"start": 1022.92, "end": 1023.16, "word": " هي", "probability": 0.79736328125}, {"start": 1023.16, "end": 1023.6, "word": " هذه", "probability": 0.78125}, {"start": 1023.6, "end": 1024.28, "word": " يعني", "probability": 0.929443359375}, {"start": 1024.28, "end": 1024.72, "word": " بمعنى", "probability": 0.99150390625}, {"start": 1024.72, "end": 1025.06, "word": " آخر", "probability": 0.804443359375}, {"start": 1025.06, "end": 1025.54, "word": " assume", "probability": 0.7431640625}, {"start": 1025.54, "end": 1025.78, "word": " أن", "probability": 0.90625}, {"start": 1025.78, "end": 1026.08, "word": " أم", "probability": 0.83447265625}, {"start": 1026.08, "end": 1026.38, "word": " أصغر", "probability": 0.9931640625}, {"start": 1026.38, "end": 1026.46, "word": " أو", "probability": 0.94677734375}, {"start": 1026.46, "end": 1026.6, "word": " يساوي", "probability": 0.986328125}, {"start": 1026.6, "end": 1027.18, "word": " 25", "probability": 0.9755859375}, {"start": 1027.18, "end": 1028.14, "word": " and", "probability": 0.9296875}, {"start": 1028.14, "end": 1028.4, "word": " أن", "probability": 0.97607421875}, {"start": 1028.4, "end": 1028.96, "word": " أصغر", "probability": 0.9967041015625}, {"start": 1028.96, "end": 1029.18, "word": " أو", "probability": 0.97802734375}, {"start": 1029.18, "end": 1029.6, "word": " يساوي", "probability": 0.992431640625}, {"start": 1029.6, "end": 1030.3, "word": " 25", "probability": 0.986328125}, {"start": 1030.3, "end": 1030.72, "word": " بناء", "probability": 0.94384765625}, {"start": 1030.72, "end": 1031.02, "word": " على", "probability": 0.76025390625}, {"start": 1031.02, "end": 1031.34, "word": " هذا", "probability": 0.95263671875}, {"start": 1031.34, "end": 1031.96, "word": " الحديث", "probability": 0.7529296875}], "temperature": 1.0}, {"id": 47, "seek": 105048, "start": 1032.36, "end": 1050.48, "text": "M زائد N أصغر أو سوى 25 زائد 25 يعني M زائد N أصغر أو سوى 50 مدام M زائد N أصغر أو سوى 50 إذن هي عكس هذه اللي هي عكس M زائد N أكبر من 50 إذن وصلنا نط Q نط هذه", "tokens": [44, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 3552, 30767, 16373, 3215, 3552, 37495, 22653, 376, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 2625, 3714, 3215, 10943, 376, 30767, 16373, 3215, 426, 5551, 9381, 17082, 2288, 34051, 8608, 2407, 7578, 2625, 11933, 8848, 1863, 39896, 6225, 4117, 3794, 29538, 13672, 1829, 39896, 6225, 4117, 3794, 376, 30767, 16373, 3215, 426, 5551, 4117, 26890, 9154, 2625, 11933, 8848, 1863, 4032, 36520, 8315, 8717, 9566, 1249, 8717, 9566, 29538], "avg_logprob": -0.21519885754043405, "compression_ratio": 2.0, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1032.36, "end": 1032.62, "word": "M", "probability": 0.29833984375}, {"start": 1032.62, "end": 1033.02, "word": " زائد", "probability": 0.4358164469401042}, {"start": 1033.02, "end": 1033.22, "word": " N", "probability": 0.91357421875}, {"start": 1033.22, "end": 1033.88, "word": " أصغر", "probability": 0.853271484375}, {"start": 1033.88, "end": 1033.98, "word": " أو", "probability": 0.845703125}, {"start": 1033.98, "end": 1034.26, "word": " سوى", "probability": 0.7869466145833334}, {"start": 1034.26, "end": 1034.78, "word": " 25", "probability": 0.82666015625}, {"start": 1034.78, "end": 1035.24, "word": " زائد", "probability": 0.6560872395833334}, {"start": 1035.24, "end": 1035.78, "word": " 25", "probability": 0.953125}, {"start": 1035.78, "end": 1036.84, "word": " يعني", "probability": 0.630859375}, {"start": 1036.84, "end": 1037.06, "word": " M", "probability": 0.86328125}, {"start": 1037.06, "end": 1037.38, "word": " زائد", "probability": 0.93408203125}, {"start": 1037.38, "end": 1037.56, "word": " N", "probability": 0.9658203125}, {"start": 1037.56, "end": 1038.02, "word": " أصغر", "probability": 0.9722900390625}, {"start": 1038.02, "end": 1038.16, "word": " أو", "probability": 0.8974609375}, {"start": 1038.16, "end": 1038.5, "word": " سوى", "probability": 0.9306640625}, {"start": 1038.5, "end": 1039.58, "word": " 50", "probability": 0.438720703125}, {"start": 1039.58, "end": 1040.78, "word": " مدام", "probability": 0.6800130208333334}, {"start": 1040.78, "end": 1041.04, "word": " M", "probability": 0.48876953125}, {"start": 1041.04, "end": 1041.54, "word": " زائد", "probability": 0.8743489583333334}, {"start": 1041.54, "end": 1041.66, "word": " N", "probability": 0.97607421875}, {"start": 1041.66, "end": 1041.96, "word": " أصغر", "probability": 0.9619140625}, {"start": 1041.96, "end": 1042.04, "word": " أو", "probability": 0.88623046875}, {"start": 1042.04, "end": 1042.16, "word": " سوى", "probability": 0.9303385416666666}, {"start": 1042.16, "end": 1042.62, "word": " 50", "probability": 0.96533203125}, {"start": 1042.62, "end": 1042.98, "word": " إذن", "probability": 0.6189778645833334}, {"start": 1042.98, "end": 1043.16, "word": " هي", "probability": 0.4814453125}, {"start": 1043.16, "end": 1043.62, "word": " عكس", "probability": 0.99365234375}, {"start": 1043.62, "end": 1044.04, "word": " هذه", "probability": 0.69384765625}, {"start": 1044.04, "end": 1044.9, "word": " اللي", "probability": 0.70458984375}, {"start": 1044.9, "end": 1045.1, "word": " هي", "probability": 0.80078125}, {"start": 1045.1, "end": 1045.56, "word": " عكس", "probability": 0.998046875}, {"start": 1045.56, "end": 1045.76, "word": " M", "probability": 0.9306640625}, {"start": 1045.76, "end": 1046.08, "word": " زائد", "probability": 0.9178059895833334}, {"start": 1046.08, "end": 1046.26, "word": " N", "probability": 0.9912109375}, {"start": 1046.26, "end": 1046.58, "word": " أكبر", "probability": 0.9669596354166666}, {"start": 1046.58, "end": 1046.7, "word": " من", "probability": 0.9775390625}, {"start": 1046.7, "end": 1047.12, "word": " 50", "probability": 0.94677734375}, {"start": 1047.12, "end": 1047.42, "word": " إذن", "probability": 0.7884928385416666}, {"start": 1047.42, "end": 1047.94, "word": " وصلنا", "probability": 0.97412109375}, {"start": 1047.94, "end": 1049.16, "word": " نط", "probability": 0.74658203125}, {"start": 1049.16, "end": 1049.54, "word": " Q", "probability": 0.8173828125}, {"start": 1049.54, "end": 1050.02, "word": " نط", "probability": 0.928466796875}, {"start": 1050.02, "end": 1050.48, "word": " هذه", "probability": 0.82666015625}], "temperature": 1.0}, {"id": 48, "seek": 107999, "start": 1050.85, "end": 1079.99, "text": "أدت إلى نط بي اللي هي نط هذه وهذا هو ال contrapositive فبنكون هيك احنا أثبتنا ال example بواسطة إثبات ال contrapositive أو بواسطة ال indirect approve الان في سؤال بيقولي approve or disapprove يعني اثبت او اللي هو اثبت صحة او اثبت عدم صحة that يعني بيقول الجملة التالية صحيحة ولا مش صحيحة", "tokens": [10721, 3215, 2655, 30731, 8717, 9566, 4724, 1829, 13672, 1829, 39896, 8717, 9566, 29538, 37037, 15730, 31439, 2423, 660, 4007, 329, 2187, 6156, 3555, 1863, 30544, 39896, 4117, 1975, 5016, 8315, 5551, 12984, 3555, 2655, 8315, 2423, 1365, 4724, 14407, 3794, 9566, 3660, 11933, 12984, 3555, 9307, 2423, 660, 4007, 329, 2187, 34051, 4724, 14407, 3794, 9566, 3660, 2423, 19523, 18827, 2423, 7649, 8978, 8608, 33604, 6027, 4724, 1829, 39648, 1829, 18827, 420, 4518, 32467, 37495, 22653, 1975, 12984, 3555, 2655, 1975, 2407, 13672, 1829, 31439, 1975, 12984, 3555, 2655, 20328, 5016, 3660, 1975, 2407, 1975, 12984, 3555, 2655, 6225, 40448, 20328, 5016, 3660, 300, 37495, 22653, 4724, 1829, 39648, 25724, 2304, 37977, 16712, 6027, 10632, 20328, 5016, 1829, 5016, 3660, 49429, 37893, 20328, 5016, 1829, 5016, 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"end": 1077.89, "word": " يعني", "probability": 0.965576171875}, {"start": 1077.89, "end": 1078.17, "word": " بيقول", "probability": 0.953125}, {"start": 1078.17, "end": 1078.57, "word": " الجملة", "probability": 0.8798828125}, {"start": 1078.57, "end": 1078.95, "word": " التالية", "probability": 0.99267578125}, {"start": 1078.95, "end": 1079.37, "word": " صحيحة", "probability": 0.96884765625}, {"start": 1079.37, "end": 1079.47, "word": " ولا", "probability": 0.552734375}, {"start": 1079.47, "end": 1079.61, "word": " مش", "probability": 0.98583984375}, {"start": 1079.61, "end": 1079.99, "word": " صحيحة", "probability": 0.98759765625}], "temperature": 1.0}, {"id": 49, "seek": 110465, "start": 1080.77, "end": 1104.65, "text": "بقول that the product of two irrational numbers is irrational بقول لي هل حاصل ضرب two irrational numbers لازم يطلع irrational عشان نثبت لازم نثبت لكل الحالات يعني نفترض انه اي اتنين irrational و نصل الهين irrational لو في حالة واحدة بس يعني مثال واحد اللي هو هذا بنتقش يعني لو جدرنا نجيب", "tokens": [3555, 39648, 300, 264, 1674, 295, 732, 39914, 3547, 307, 39914, 4724, 39648, 32239, 8032, 1211, 11331, 33546, 1211, 48812, 25513, 732, 39914, 3547, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 39914, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 5296, 31377, 2304, 8717, 12984, 3555, 2655, 5296, 28820, 21542, 6027, 9307, 37495, 22653, 8717, 5172, 2655, 43042, 16472, 3224, 1975, 1829, 1975, 2655, 1863, 9957, 39914, 4032, 8717, 36520, 2423, 3224, 9957, 39914, 45164, 8978, 11331, 6027, 3660, 36764, 24401, 3660, 4724, 3794, 37495, 22653, 50113, 6027, 36764, 24401, 13672, 1829, 31439, 23758, 4724, 29399, 4587, 8592, 37495, 22653, 45164, 10874, 3215, 2288, 8315, 8717, 7435, 1829, 3555], "avg_logprob": -0.127723623853211, "compression_ratio": 1.86784140969163, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1080.77, "end": 1081.29, "word": "بقول", "probability": 0.77734375}, {"start": 1081.29, "end": 1082.05, "word": " that", "probability": 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"word": " لو", "probability": 0.974609375}, {"start": 1098.37, "end": 1098.59, "word": " في", "probability": 0.82421875}, {"start": 1098.59, "end": 1099.07, "word": " حالة", "probability": 0.994140625}, {"start": 1099.07, "end": 1099.51, "word": " واحدة", "probability": 0.9734700520833334}, {"start": 1099.51, "end": 1099.87, "word": " بس", "probability": 0.9921875}, {"start": 1099.87, "end": 1100.25, "word": " يعني", "probability": 0.955078125}, {"start": 1100.25, "end": 1100.67, "word": " مثال", "probability": 0.98095703125}, {"start": 1100.67, "end": 1101.27, "word": " واحد", "probability": 0.995361328125}, {"start": 1101.27, "end": 1101.93, "word": " اللي", "probability": 0.973388671875}, {"start": 1101.93, "end": 1102.15, "word": " هو", "probability": 0.98046875}, {"start": 1102.15, "end": 1102.49, "word": " هذا", "probability": 0.87890625}, {"start": 1102.49, "end": 1103.21, "word": " بنتقش", "probability": 0.62213134765625}, {"start": 1103.21, "end": 1103.43, "word": " يعني", "probability": 0.966064453125}, {"start": 1103.43, "end": 1103.63, "word": " لو", "probability": 0.98046875}, {"start": 1103.63, "end": 1104.09, "word": " جدرنا", "probability": 0.9591064453125}, {"start": 1104.09, "end": 1104.65, "word": " نجيب", "probability": 0.9959716796875}], "temperature": 1.0}, {"id": 50, "seek": 111982, "start": 1104.8, "end": 1119.82, "text": "اللي هو عددين irrational حاصر ضربهم مش irrational بتكون هذه الجملة مش صحيحة وفي هذه الحالة بنقول هذا العمل هو disapprove و ال disapprove بنجيب counter example يعني بنجيب مثال عددي", "tokens": [6027, 20292, 31439, 6225, 3215, 3215, 9957, 39914, 11331, 33546, 2288, 48812, 25513, 16095, 37893, 39914, 39894, 30544, 29538, 25724, 2304, 37977, 37893, 20328, 5016, 1829, 5016, 3660, 4032, 41185, 29538, 21542, 6027, 3660, 44945, 39648, 23758, 18863, 42213, 31439, 4518, 32467, 4032, 2423, 4518, 32467, 44945, 7435, 1829, 3555, 5682, 1365, 37495, 22653, 44945, 7435, 1829, 3555, 50113, 6027, 6225, 3215, 16254], "avg_logprob": 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{"start": 1329.15, "end": 1330.01, "word": " بنعرفها", "probability": 0.961181640625}, {"start": 1330.01, "end": 1330.77, "word": " يعني", "probability": 0.95166015625}, {"start": 1330.77, "end": 1331.13, "word": " اللي", "probability": 0.93212890625}, {"start": 1331.13, "end": 1331.31, "word": " هو", "probability": 0.97705078125}, {"start": 1331.31, "end": 1331.61, "word": " proved", "probability": 0.30126953125}, {"start": 1331.61, "end": 1331.81, "word": " by", "probability": 0.9814453125}, {"start": 1331.81, "end": 1332.37, "word": " contradiction", "probability": 0.919921875}, {"start": 1332.37, "end": 1333.17, "word": " يتلخص", "probability": 0.8595703125}, {"start": 1333.17, "end": 1333.53, "word": " فيما", "probability": 0.788818359375}, {"start": 1333.53, "end": 1333.99, "word": " يليه", "probability": 0.93359375}], "temperature": 1.0}, {"id": 60, "seek": 135544, "start": 1334.24, "end": 1355.44, "text": "بنقول Assume B and Assume Not Q وبنصل لتناقض تشوف كيف بنحصل على تناقض show that هي مثال if the square of an integer number is odd then the integer is odd بيقول إذا كان مربع", "tokens": [3555, 1863, 39648, 6281, 2540, 363, 293, 6281, 2540, 1726, 1249, 46599, 1863, 36520, 5296, 2655, 8315, 4587, 11242, 6055, 8592, 38688, 9122, 33911, 44945, 5016, 36520, 15844, 6055, 8315, 4587, 11242, 855, 300, 39896, 50113, 6027, 498, 264, 3732, 295, 364, 24922, 1230, 307, 7401, 550, 264, 24922, 307, 7401, 4724, 1829, 39648, 11933, 15730, 25961, 3714, 25513, 3615], "avg_logprob": -0.2797131264796022, "compression_ratio": 1.3470588235294119, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 1334.24, "end": 1335.16, "word": "بنقول", "probability": 0.5641276041666666}, {"start": 1335.16, "end": 1336.06, "word": " Assume", "probability": 0.634033203125}, {"start": 1336.06, "end": 1338.02, "word": " B", "probability": 0.388671875}, {"start": 1338.02, "end": 1338.8, "word": " and", "probability": 0.8349609375}, {"start": 1338.8, "end": 1339.64, "word": " Assume", 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هي", "probability": 0.2109375}, {"start": 1347.4, "end": 1347.92, "word": " مثال", "probability": 0.93017578125}, {"start": 1347.92, "end": 1348.18, "word": " if", "probability": 0.5380859375}, {"start": 1348.18, "end": 1348.44, "word": " the", "probability": 0.89208984375}, {"start": 1348.44, "end": 1348.84, "word": " square", "probability": 0.89111328125}, {"start": 1348.84, "end": 1349.02, "word": " of", "probability": 0.966796875}, {"start": 1349.02, "end": 1349.22, "word": " an", "probability": 0.71337890625}, {"start": 1349.22, "end": 1349.64, "word": " integer", "probability": 0.9443359375}, {"start": 1349.64, "end": 1350.3, "word": " number", "probability": 0.94482421875}, {"start": 1350.3, "end": 1350.6, "word": " is", "probability": 0.94677734375}, {"start": 1350.6, "end": 1350.96, "word": " odd", "probability": 0.85205078125}, {"start": 1350.96, "end": 1351.62, "word": " then", "probability": 0.71923828125}, {"start": 1351.62, "end": 1351.82, "word": " the", "probability": 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odd", "probability": 0.79296875}, {"start": 1364.87, "end": 1366.09, "word": " هيعطينا", "probability": 0.91220703125}, {"start": 1366.09, "end": 1366.65, "word": " الان", "probability": 0.5660400390625}, {"start": 1366.65, "end": 1367.35, "word": " is", "probability": 0.8623046875}, {"start": 1367.35, "end": 1367.85, "word": " odd", "probability": 0.876953125}, {"start": 1367.85, "end": 1368.61, "word": " الان", "probability": 0.6676025390625}, {"start": 1368.61, "end": 1369.15, "word": " assume", "probability": 0.6953125}, {"start": 1369.15, "end": 1369.51, "word": " that", "probability": 0.91357421875}, {"start": 1369.51, "end": 1370.19, "word": " hypothesis", "probability": 0.346435546875}, {"start": 1370.19, "end": 1370.61, "word": " B", "probability": 0.52685546875}, {"start": 1370.61, "end": 1370.87, "word": " of", "probability": 0.927734375}, {"start": 1370.87, "end": 1371.13, "word": " this", "probability": 0.94970703125}, {"start": 1371.13, "end": 1371.85, "word": " 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{"start": 1462.13, "end": 1462.51, "word": " وصلنا", "probability": 0.9869791666666666}, {"start": 1462.51, "end": 1462.59, "word": " ل", "probability": 0.7568359375}, {"start": 1462.59, "end": 1462.69, "word": " X", "probability": 0.88916015625}, {"start": 1462.69, "end": 1463.15, "word": " تربيع", "probability": 0.981201171875}, {"start": 1463.15, "end": 1463.35, "word": " is", "probability": 0.94091796875}, {"start": 1463.35, "end": 1463.59, "word": " odd", "probability": 0.896484375}, {"start": 1463.59, "end": 1463.81, "word": " and", "probability": 0.82373046875}, {"start": 1463.81, "end": 1464.07, "word": " not", "probability": 0.95654296875}, {"start": 1464.07, "end": 1464.35, "word": " odd", "probability": 0.921875}, {"start": 1464.35, "end": 1464.67, "word": " which", "probability": 0.7490234375}, {"start": 1464.67, "end": 1465.03, "word": " is", "probability": 0.9638671875}, {"start": 1465.03, "end": 1465.15, "word": " a", "probability": 0.86376953125}, {"start": 1465.15, "end": 1465.67, "word": " contradiction", "probability": 0.8125}], "temperature": 1.0}, {"id": 66, "seek": 148510, "start": 1466.1, "end": 1485.1, "text": "Therefore الفرضية الأولى إن فرضنا عكس المطلوب مش صحيحة إذن لما ال X تربيع is odd لازم تطلع ال X is odd هذا المرهان by contradiction الآن نيجي ناخد مثال آخر المثال كماني", "tokens": [9077, 845, 27188, 43042, 10632, 16247, 12610, 7578, 36145, 6156, 43042, 8315, 6225, 4117, 3794, 9673, 9566, 1211, 37746, 37893, 20328, 5016, 1829, 5016, 3660, 11933, 8848, 1863, 5296, 15042, 2423, 1783, 6055, 25513, 40228, 307, 7401, 5296, 31377, 2304, 6055, 9566, 1211, 3615, 2423, 1783, 307, 7401, 23758, 9673, 2288, 3224, 7649, 538, 34937, 6024, 48506, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 50113, 6027, 19753, 34740, 9673, 12984, 6027, 9122, 2304, 7649, 1829], "avg_logprob": -0.19346217771894053, "compression_ratio": 1.488888888888889, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1466.1, "end": 1467.14, "word": "Therefore", 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"probability": 0.7783203125}, {"start": 1473.94, "end": 1474.36, "word": " تربيع", "probability": 0.7374674479166666}, {"start": 1474.36, "end": 1474.54, "word": " is", "probability": 0.09698486328125}, {"start": 1474.54, "end": 1474.76, "word": " odd", "probability": 0.7119140625}, {"start": 1474.76, "end": 1475.82, "word": " لازم", "probability": 0.9837239583333334}, {"start": 1475.82, "end": 1476.62, "word": " تطلع", "probability": 0.986083984375}, {"start": 1476.62, "end": 1476.9, "word": " ال", "probability": 0.94287109375}, {"start": 1476.9, "end": 1477.38, "word": " X", "probability": 0.98974609375}, {"start": 1477.38, "end": 1478.12, "word": " is", "probability": 0.86962890625}, {"start": 1478.12, "end": 1478.38, "word": " odd", "probability": 0.9619140625}, {"start": 1478.38, "end": 1478.72, "word": " هذا", "probability": 0.86669921875}, {"start": 1478.72, "end": 1479.4, "word": " المرهان", "probability": 0.8046875}, {"start": 1479.4, "end": 1479.84, "word": " by", 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by contradiction بنفترض من عكس المطلوب", "tokens": [3555, 39648, 718, 275, 4032, 297, 4478, 294, 297, 855, 300, 498, 275, 30767, 18513, 297, 5551, 9381, 17082, 2288, 9154, 4289, 550, 275, 5551, 9381, 17082, 2288, 9154, 6905, 420, 297, 5551, 9381, 17082, 2288, 9154, 6905, 538, 34937, 9122, 33911, 22807, 44945, 5172, 2655, 43042, 9673, 3615, 9566, 2407, 27884, 30767, 1829, 19446, 31439, 44945, 5172, 2655, 43042, 14739, 275, 30767, 18513, 297, 5551, 9381, 17082, 2288, 9154, 4289, 46599, 1863, 5172, 2655, 43042, 6225, 4117, 3794, 9673, 9566, 1211, 37746, 11933, 15730, 538, 34937, 44945, 5172, 2655, 43042, 9154, 6225, 4117, 3794, 9673, 9566, 1211, 37746], "avg_logprob": -0.1807812497019768, "compression_ratio": 1.8021390374331552, "no_speech_prob": 0.0, "words": [{"start": 1486.4, "end": 1486.8, "word": "بقول", "probability": 0.6820068359375}, {"start": 1486.8, "end": 1487.08, "word": " let", "probability": 0.152099609375}, {"start": 1487.08, "end": 1487.38, "word": " m", "probability": 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1490.86, "word": " من", "probability": 0.98583984375}, {"start": 1490.86, "end": 1491.3, "word": " 90", "probability": 0.7626953125}, {"start": 1491.3, "end": 1491.54, "word": " then", "probability": 0.56201171875}, {"start": 1491.54, "end": 1491.9, "word": " m", "probability": 0.90576171875}, {"start": 1491.9, "end": 1492.2, "word": " أصغر", "probability": 0.982666015625}, {"start": 1492.2, "end": 1492.28, "word": " من", "probability": 0.986328125}, {"start": 1492.28, "end": 1492.84, "word": " 45", "probability": 0.9619140625}, {"start": 1492.84, "end": 1493.24, "word": " or", "probability": 0.65771484375}, {"start": 1493.24, "end": 1493.52, "word": " n", "probability": 0.94677734375}, {"start": 1493.52, "end": 1493.92, "word": " أصغر", "probability": 0.9915771484375}, {"start": 1493.92, "end": 1494.0, "word": " من", "probability": 0.994140625}, {"start": 1494.0, "end": 1494.66, "word": " 45", "probability": 0.96875}, {"start": 1494.66, "end": 1495.3, "word": " by", "probability": 0.469482421875}, {"start": 1495.3, "end": 1496.0, "word": " contradiction", "probability": 0.884765625}, {"start": 1496.0, "end": 1496.88, "word": " كيف؟", "probability": 0.7801920572916666}, {"start": 1496.88, "end": 1497.62, "word": " بنفترض", "probability": 0.917236328125}, {"start": 1497.62, "end": 1498.34, "word": " المعطوعة", "probability": 0.72802734375}, {"start": 1498.34, "end": 1498.58, "word": " زي", "probability": 0.9833984375}, {"start": 1498.58, "end": 1498.66, "word": " ما", "probability": 0.98681640625}, {"start": 1498.66, "end": 1498.88, "word": " هو", "probability": 0.99267578125}, {"start": 1498.88, "end": 1499.54, "word": " بنفترض", "probability": 0.84637451171875}, {"start": 1499.54, "end": 1499.68, "word": " أن", "probability": 0.65087890625}, {"start": 1499.68, "end": 1499.92, "word": " m", "probability": 0.46240234375}, {"start": 1499.92, "end": 1500.22, "word": " زاد", "probability": 0.967041015625}, {"start": 1500.22, "end": 1500.4, "word": " n", "probability": 0.91943359375}, {"start": 1500.4, "end": 1500.7, "word": " أصغر", "probability": 0.992431640625}, {"start": 1500.7, "end": 1500.84, "word": " من", "probability": 0.99560546875}, {"start": 1500.84, "end": 1501.32, "word": " 90", "probability": 0.96533203125}, {"start": 1501.32, "end": 1502.98, "word": " وبنفترض", "probability": 0.885693359375}, {"start": 1502.98, "end": 1503.66, "word": " عكس", "probability": 0.9923502604166666}, {"start": 1503.66, "end": 1504.76, "word": " المطلوب", "probability": 0.989501953125}, {"start": 1504.76, "end": 1505.1, "word": " إذا", "probability": 0.5726318359375}, {"start": 1505.1, "end": 1505.3, "word": " by", "probability": 0.8974609375}, {"start": 1505.3, "end": 1505.92, "word": " contradiction", "probability": 0.875}, {"start": 1505.92, "end": 1506.58, "word": " بنفترض", "probability": 0.9493408203125}, {"start": 1506.58, "end": 1506.86, "word": " من", "probability": 0.701171875}, {"start": 1506.86, "end": 1507.56, "word": " عكس", 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{"start": 1593.72, "end": 1594.18, "word": " جمحن", "probability": 0.66619873046875}, {"start": 1594.18, "end": 1594.56, "word": " أكبر", "probability": 0.9832356770833334}, {"start": 1594.56, "end": 1594.86, "word": " ويساوي", "probability": 0.96240234375}, {"start": 1594.86, "end": 1595.34, "word": " 45", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 72, "seek": 161859, "start": 1596.19, "end": 1618.59, "text": "اللي صارت عندي M زاد N أكبر وسوء وخمسة واربعين و M زاد N أصغر من تسعين إذا هذا contradiction therefore اللي هو الفرضية اللي فرضناها مش صحيحة يعني بمعنى أخر لما ال M زاد N أصغر من تسعين يعطينا ال M أصغر من خمسة واربعين or N أصغر من مين من خمسة واربعين هذه تسعين برضه", "tokens": [6027, 20292, 20328, 9640, 2655, 18871, 16254, 376, 30767, 18513, 426, 5551, 4117, 26890, 4032, 3794, 2407, 38207, 4032, 9778, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 4032, 376, 30767, 18513, 426, 5551, 9381, 17082, 2288, 9154, 6055, 3794, 3615, 9957, 11933, 15730, 23758, 34937, 4412, 13672, 1829, 31439, 27188, 43042, 10632, 13672, 1829, 6156, 43042, 8315, 11296, 37893, 20328, 5016, 1829, 5016, 3660, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 5296, 15042, 2423, 376, 30767, 18513, 426, 5551, 9381, 17082, 2288, 9154, 6055, 3794, 3615, 9957, 37495, 9566, 1829, 8315, 2423, 376, 5551, 9381, 17082, 2288, 9154, 16490, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 420, 426, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 9154, 16490, 2304, 3794, 3660, 4032, 9640, 3555, 3615, 9957, 29538, 6055, 3794, 3615, 9957, 4724, 43042, 3224], "avg_logprob": -0.15681612923525381, "compression_ratio": 2.09478672985782, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 1596.19, "end": 1596.45, "word": "اللي", "probability": 0.517578125}, {"start": 1596.45, "end": 1596.97, "word": " صارت", "probability": 0.7841796875}, {"start": 1596.97, "end": 1597.19, "word": " عندي", "probability": 0.7381591796875}, {"start": 1597.19, "end": 1597.37, "word": " M", 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صحيحة", "probability": 0.9890625}, {"start": 1608.31, "end": 1608.85, "word": " يعني", "probability": 0.887939453125}, {"start": 1608.85, "end": 1609.21, "word": " بمعنى", "probability": 0.9875}, {"start": 1609.21, "end": 1609.51, "word": " أخر", "probability": 0.7479248046875}, {"start": 1609.51, "end": 1609.79, "word": " لما", "probability": 0.8818359375}, {"start": 1609.79, "end": 1609.93, "word": " ال", "probability": 0.74609375}, {"start": 1609.93, "end": 1610.07, "word": " M", "probability": 0.931640625}, {"start": 1610.07, "end": 1610.37, "word": " زاد", "probability": 0.975341796875}, {"start": 1610.37, "end": 1610.59, "word": " N", "probability": 0.98828125}, {"start": 1610.59, "end": 1611.03, "word": " أصغر", "probability": 0.9918212890625}, {"start": 1611.03, "end": 1611.15, "word": " من", "probability": 0.99560546875}, {"start": 1611.15, "end": 1611.77, "word": " تسعين", "probability": 0.9915771484375}, {"start": 1611.77, "end": 1612.69, "word": " يعطينا", "probability": 0.9669189453125}, {"start": 1612.69, "end": 1612.83, "word": " ال", "probability": 0.8466796875}, {"start": 1612.83, "end": 1612.97, "word": " M", "probability": 0.9384765625}, {"start": 1612.97, "end": 1613.23, "word": " أصغر", "probability": 0.9937744140625}, {"start": 1613.23, "end": 1613.31, "word": " من", "probability": 0.994140625}, {"start": 1613.31, "end": 1613.63, "word": " خمسة", "probability": 0.92626953125}, {"start": 1613.63, "end": 1614.07, "word": " واربعين", "probability": 0.970703125}, {"start": 1614.07, "end": 1614.39, "word": " or", "probability": 0.395751953125}, {"start": 1614.39, "end": 1614.67, "word": " N", "probability": 0.64208984375}, {"start": 1614.67, "end": 1615.25, "word": " أصغر", "probability": 0.9925537109375}, {"start": 1615.25, "end": 1615.47, "word": " من", "probability": 0.9970703125}, {"start": 1615.47, "end": 1615.95, "word": " مين", "probability": 0.6990966796875}, {"start": 1615.95, "end": 1616.57, "word": " من", "probability": 0.9697265625}, {"start": 1616.57, "end": 1617.23, "word": " خمسة", "probability": 0.99365234375}, {"start": 1617.23, "end": 1617.63, "word": " واربعين", "probability": 0.9884765625}, {"start": 1617.63, "end": 1617.81, "word": " هذه", "probability": 0.3505859375}, {"start": 1617.81, "end": 1618.21, "word": " تسعين", "probability": 0.9842529296875}, {"start": 1618.21, "end": 1618.59, "word": " برضه", "probability": 0.9874674479166666}], "temperature": 1.0}, {"id": 73, "seek": 163565, "start": 1619.25, "end": 1635.65, "text": "الان اخر جزء في المحاضرة هيكون ان ال mathematical induction او الاستقراء الرياضي هي طريقة للبرهان لبرهان بعض الجمل المعينة اللي بتكون بدلالة اللي هي ال natural numbers او ال integers", "tokens": [6027, 7649, 1975, 34740, 10874, 11622, 38207, 8978, 9673, 5016, 46958, 25720, 39896, 30544, 16472, 2423, 18894, 33371, 1975, 2407, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 39896, 23032, 16572, 28671, 24976, 26890, 3224, 7649, 5296, 26890, 3224, 7649, 45030, 11242, 25724, 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"probability": 0.595703125}, {"start": 1623.91, "end": 1624.71, "word": " induction", "probability": 0.98193359375}, {"start": 1624.71, "end": 1625.47, "word": " او", "probability": 0.845947265625}, {"start": 1625.47, "end": 1626.19, "word": " الاستقراء", "probability": 0.93896484375}, {"start": 1626.19, "end": 1626.91, "word": " الرياضي", "probability": 0.9295654296875}, {"start": 1626.91, "end": 1627.39, "word": " هي", "probability": 0.87060546875}, {"start": 1627.39, "end": 1627.91, "word": " طريقة", "probability": 0.990234375}, {"start": 1627.91, "end": 1628.83, "word": " للبرهان", "probability": 0.9342041015625}, {"start": 1628.83, "end": 1629.55, "word": " لبرهان", "probability": 0.878173828125}, {"start": 1629.55, "end": 1629.89, "word": " بعض", "probability": 0.9580078125}, {"start": 1629.89, "end": 1630.49, "word": " الجمل", "probability": 0.700439453125}, {"start": 1630.49, "end": 1631.57, "word": " المعينة", "probability": 0.9791259765625}, {"start": 1631.57, "end": 1631.83, 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خلصنا هذا الكلام هذه و هذه كلها على بعض أثبتناها بنكون أثبتنا اللي هو then b of n must be true for any n element in N هذا الطريقة بنسميها اللي هي ال mathematical induction أو الاستقراء الرياضي بنثبت الجملة صحيحة عند واحد", "tokens": [6027, 20292, 39896, 6156, 43042, 10632, 42963, 14851, 4587, 2288, 16606, 257, 4032, 27842, 11296, 44945, 12984, 3555, 2655, 272, 74, 30767, 16373, 3215, 36764, 24401, 45164, 16490, 1211, 9381, 8315, 23758, 2423, 28820, 10943, 29538, 4032, 29538, 28242, 11296, 15844, 45030, 11242, 5551, 12984, 3555, 2655, 8315, 11296, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 13672, 1829, 31439, 550, 272, 295, 297, 1633, 312, 2074, 337, 604, 297, 4478, 294, 426, 23758, 41950, 16572, 28671, 44945, 38251, 1829, 11296, 13672, 1829, 39896, 2423, 18894, 33371, 34051, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 44945, 12984, 3555, 2655, 25724, 2304, 37977, 20328, 5016, 1829, 5016, 3660, 43242, 36764, 24401], "avg_logprob": -0.13595145754516125, 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بالاستعانة بمين بال induction hypothesis اللي فرضته هذا اللي هي دي K في K بساوة K في K زائد واحد على اتنين دعونا نشوف كده الآن ناخد الطرف الأيمن هذا proof", "tokens": [3555, 3215, 10721, 5551, 12984, 3555, 2655, 4724, 3794, 995, 2407, 3660, 3714, 9957, 5551, 8592, 26895, 28242, 591, 4032, 5551, 11242, 3615, 3714, 41361, 11296, 591, 30767, 16373, 3215, 36764, 24401, 37495, 22653, 591, 30767, 16373, 3215, 36764, 24401, 8978, 13672, 1829, 39896, 4724, 43042, 3224, 591, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 37495, 22653, 6024, 48506, 41850, 47525, 10721, 5551, 12984, 3555, 2655, 29538, 25724, 2304, 37977, 20666, 995, 14851, 3615, 7649, 3660, 4724, 2304, 9957, 20666, 33371, 17291, 13672, 1829, 6156, 43042, 47395, 23758, 13672, 1829, 39896, 11778, 1829, 591, 8978, 591, 4724, 3794, 995, 2407, 3660, 591, 8978, 591, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 11778, 3615, 2407, 8315, 8717, 8592, 38688, 9122, 3215, 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إيش هذي بيصير بدل هذه من هنا لهنا اللي هي K في K زائد واحد على اتنين بعوض عنها بيصير K في K زائد واحد على اتنين زائد الأصلي هذه K زائد واحد", "tokens": [1863, 32887, 5172, 46740, 24192, 4386, 8717, 32887, 5172, 46740, 24192, 39896, 43242, 8315, 5551, 9778, 3215, 2655, 41950, 28480, 16247, 1829, 3794, 2288, 34105, 39896, 9154, 34105, 46740, 8315, 47525, 10721, 5551, 8592, 26895, 23758, 9154, 34105, 46740, 8315, 36764, 24401, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 4032, 5551, 2655, 4587, 1211, 43242, 2423, 591, 4032, 5551, 3615, 2407, 11242, 11296, 9154, 23758, 13672, 1829, 6156, 43042, 47395, 23758, 20449, 8315, 3224, 10874, 1863, 18871, 11296, 11778, 1829, 591, 11331, 35457, 34105, 11933, 1829, 8592, 8032, 8848, 1829, 4724, 1829, 9381, 13546, 47525, 1211, 29538, 9154, 34105, 46740, 8315, 13672, 1829, 39896, 591, 8978, 591, 30767, 16373, 3215, 36764, 24401, 15844, 1975, 2655, 1863, 9957, 45030, 2407, 11242, 18871, 11296, 4724, 1829, 9381, 13546, 591, 8978, 591, 30767, 16373, 3215, 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المقدار يعني أثبتت اللي هو هذه اللي هو أثبتت صحة واحد لمين لان بتساوي K زائد واحد ومدام أثبتتها لK زائد واحد معناته أنا اللي هو خلصت ال induction hypothesis معناته جملتيها دي صارت صحيحة لكل N element in N يعني لو لخصنا أيش اللي سوناه أثبتنا صحة هذه أول إشي لان بتساوي واحد و بعدين فرضنا صحتها لان بتساوي K", "tokens": [3555, 3794, 995, 45865, 23758, 9673, 28543, 9640, 37495, 22653, 5551, 12984, 3555, 2655, 2655, 13672, 1829, 31439, 29538, 13672, 1829, 31439, 5551, 12984, 3555, 2655, 2655, 20328, 5016, 3660, 36764, 24401, 32767, 9957, 5296, 7649, 39894, 3794, 995, 45865, 591, 30767, 16373, 3215, 36764, 24401, 4032, 2304, 3215, 10943, 5551, 12984, 3555, 2655, 2655, 11296, 5296, 42, 30767, 16373, 3215, 36764, 24401, 20449, 8315, 47395, 41850, 13672, 1829, 31439, 16490, 1211, 9381, 2655, 2423, 33371, 17291, 20449, 8315, 47395, 10874, 42213, 31371, 11296, 11778, 1829, 20328, 9640, 2655, 20328, 5016, 1829, 5016, 3660, 5296, 28820, 426, 4478, 294, 426, 37495, 22653, 45164, 5296, 9778, 9381, 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"probability": 0.9619140625}, {"start": 2360.25, "end": 2360.45, "word": " لو", "probability": 0.9755859375}, {"start": 2360.45, "end": 2361.01, "word": " لخصنا", "probability": 0.95166015625}, {"start": 2361.01, "end": 2361.17, "word": " أيش", "probability": 0.66845703125}, {"start": 2361.17, "end": 2361.31, "word": " اللي", "probability": 0.991943359375}, {"start": 2361.31, "end": 2362.15, "word": " سوناه", "probability": 0.8668212890625}, {"start": 2362.15, "end": 2362.75, "word": " أثبتنا", "probability": 0.99189453125}, {"start": 2362.75, "end": 2363.19, "word": " صحة", "probability": 0.9033203125}, {"start": 2363.19, "end": 2363.39, "word": " هذه", "probability": 0.60302734375}, {"start": 2363.39, "end": 2363.63, "word": " أول", "probability": 0.869873046875}, {"start": 2363.63, "end": 2363.91, "word": " إشي", "probability": 0.6449381510416666}, {"start": 2363.91, "end": 2364.11, "word": " لان", "probability": 0.88818359375}, {"start": 2364.11, "end": 2364.53, "word": " بتساوي", "probability": 0.9840087890625}, {"start": 2364.53, "end": 2364.97, "word": " واحد", "probability": 0.9873046875}, {"start": 2364.97, "end": 2365.41, "word": " و", "probability": 0.71630859375}, {"start": 2365.41, "end": 2365.85, "word": " بعدين", "probability": 0.8203125}, {"start": 2365.85, "end": 2366.55, "word": " فرضنا", "probability": 0.9928385416666666}, {"start": 2366.55, "end": 2367.15, "word": " صحتها", "probability": 0.8251139322916666}, {"start": 2367.15, "end": 2367.43, "word": " لان", "probability": 0.943603515625}, {"start": 2367.43, "end": 2368.01, "word": " بتساوي", "probability": 0.9903564453125}, {"start": 2368.01, "end": 2368.27, "word": " K", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 106, "seek": 239000, "start": 2368.54, "end": 2390.0, "text": "ومنها أثبتنا صحتها ل K زائد واحد وهذا كله على بعض هو اللي بنسميه ال mathematical induction أو الاستقراء الرياضي وبكون هيك أثبتناها لكل N element in N ناخد مثال أخر شوفوا المثال صلوا على النبي عليه الصلاة والسلام اللي بيقول show that N أصغر من 2N لكل N element in N طبعا عارفينها دي", "tokens": [20498, 1863, 11296, 5551, 12984, 3555, 2655, 8315, 20328, 33753, 11296, 5296, 591, 30767, 16373, 3215, 36764, 24401, 37037, 15730, 28242, 3224, 15844, 45030, 11242, 31439, 13672, 1829, 44945, 38251, 1829, 3224, 2423, 18894, 33371, 34051, 42963, 14851, 4587, 2288, 16606, 2423, 16572, 46958, 1829, 46599, 30544, 39896, 4117, 5551, 12984, 3555, 2655, 8315, 11296, 5296, 28820, 426, 4478, 294, 426, 8717, 47283, 3215, 50113, 6027, 5551, 34740, 13412, 38688, 14407, 9673, 12984, 6027, 20328, 1211, 14407, 15844, 28239, 21292, 47356, 31767, 15040, 3660, 16070, 3794, 37440, 13672, 1829, 4724, 1829, 39648, 855, 300, 426, 5551, 9381, 17082, 2288, 9154, 568, 45, 5296, 28820, 426, 4478, 294, 426, 23032, 3555, 3615, 995, 6225, 9640, 5172, 9957, 11296, 11778, 1829], "avg_logprob": -0.16380207911133765, "compression_ratio": 1.696629213483146, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2368.54, 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{"start": 2379.04, "end": 2379.4, "word": " N", "probability": 0.291259765625}, {"start": 2379.4, "end": 2380.24, "word": " element", "probability": 0.85693359375}, {"start": 2380.24, "end": 2380.5, "word": " in", "probability": 0.78125}, {"start": 2380.5, "end": 2380.66, "word": " N", "probability": 0.931640625}, {"start": 2380.66, "end": 2381.38, "word": " ناخد", "probability": 0.9606119791666666}, {"start": 2381.38, "end": 2381.68, "word": " مثال", "probability": 0.99462890625}, {"start": 2381.68, "end": 2382.02, "word": " أخر", "probability": 0.704833984375}, {"start": 2382.02, "end": 2382.66, "word": " شوفوا", "probability": 0.8294270833333334}, {"start": 2382.66, "end": 2382.96, "word": " المثال", "probability": 0.9073893229166666}, {"start": 2382.96, "end": 2383.28, "word": " صلوا", "probability": 0.7303059895833334}, {"start": 2383.28, "end": 2383.36, "word": " على", "probability": 0.63818359375}, {"start": 2383.36, "end": 2383.54, "word": " النبي", "probability": 0.919677734375}, {"start": 2383.54, "end": 2383.7, "word": " عليه", "probability": 0.77587890625}, {"start": 2383.7, "end": 2384.02, "word": " الصلاة", "probability": 0.95458984375}, {"start": 2384.02, "end": 2384.36, "word": " والسلام", "probability": 0.9591471354166666}, {"start": 2384.36, "end": 2384.92, "word": " اللي", "probability": 0.974365234375}, {"start": 2384.92, "end": 2385.22, "word": " بيقول", "probability": 0.7340494791666666}, {"start": 2385.22, "end": 2385.48, "word": " show", "probability": 0.42431640625}, {"start": 2385.48, "end": 2385.86, "word": " that", "probability": 0.8916015625}, {"start": 2385.86, "end": 2386.12, "word": " N", "probability": 0.55078125}, {"start": 2386.12, "end": 2386.48, "word": " أصغر", "probability": 0.967041015625}, {"start": 2386.48, "end": 2386.6, "word": " من", "probability": 0.98486328125}, {"start": 2386.6, "end": 2387.82, "word": " 2N", "probability": 0.65625}, {"start": 2387.82, "end": 2388.2, "word": " لكل", "probability": 0.94287109375}, {"start": 2388.2, "end": 2388.46, "word": " N", "probability": 0.9677734375}, {"start": 2388.46, "end": 2388.76, "word": " element", "probability": 0.95947265625}, {"start": 2388.76, "end": 2388.94, "word": " in", "probability": 0.92041015625}, {"start": 2388.94, "end": 2389.06, "word": " N", "probability": 0.98486328125}, {"start": 2389.06, "end": 2389.32, "word": " طبعا", "probability": 0.9376220703125}, {"start": 2389.32, "end": 2389.8, "word": " عارفينها", "probability": 0.847216796875}, {"start": 2389.8, "end": 2390.0, "word": " دي", "probability": 0.923095703125}], "temperature": 1.0}, {"id": 107, "seek": 240258, "start": 2390.76, "end": 2402.58, "text": "الان كيف نرتبطها؟ برضه بنرتبطها بـ Mathematical Induction لأنه اللي هي جملة تعتمد على اللي هو ال integers أو الأعداد الطبيعية نشوف ال proof أول حاجة ال basic step", "tokens": [6027, 7649, 9122, 33911, 8717, 43500, 3555, 9566, 11296, 22807, 4724, 43042, 3224, 44945, 43500, 3555, 9566, 11296, 4724, 39184, 15776, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..607cfde0ad8e40ce11aa0082a78eb710329369a4
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/ahIgPhYJp3w_raw.srt
@@ -0,0 +1,2304 @@
+1
+00:00:01,230 --> 00:00:05,050
+بسم الله الرحمن الرحيم هذه هي المحاضرة التاسعة
+
+2
+00:00:05,050 --> 00:00:09,790
+مساق رياضيات مفاصلة لطلبات الجامعة الإسلامية قسم
+
+3
+00:00:09,790 --> 00:00:14,250
+الحوثف المتنقلة كلي التكنولوجيا المعلومات اليوم
+
+4
+00:00:14,250 --> 00:00:20,000
+هيكون الحديث عن اللي هو طرق البرهان الرياضيهنحكي
+
+5
+00:00:20,000 --> 00:00:25,000
+طبعا هو نزيج من chapter 5 و باقي chapter 1-7
+
+6
+00:00:25,000 --> 00:00:28,620
+section 1-7 في chapter الأول اللي هو proof
+
+7
+00:00:28,620 --> 00:00:31,600
+techniques and mathematical induction اللي هي طرق
+
+8
+00:00:31,600 --> 00:00:37,720
+البرهان و اللي هي الاستقرار الرياضي الان في بعض
+
+9
+00:00:37,720 --> 00:00:41,720
+الحقائق بس حابين نذكرها على السريع عسى انه تلزمنا
+
+10
+00:00:41,720 --> 00:00:46,210
+بعد شويةThe product of the non-zero real numbers
+
+11
+00:00:46,210 --> 00:00:51,130
+is non-zero يعني لو ضربنا عددين حقيقية و لا واحد
+
+12
+00:00:51,130 --> 00:00:54,870
+فين صفر أكيد هيطلع مش صفار The square of non-zero
+
+13
+00:00:54,870 --> 00:00:57,710
+real numbers is a positive real number اللي هو لو
+
+14
+00:00:57,710 --> 00:01:00,690
+كان عندي a real number بيكون a تربيع اللي هو
+
+15
+00:01:00,690 --> 00:01:04,600
+positive real numberالأن الـ even integer is of
+
+16
+00:01:04,600 --> 00:01:09,020
+the form 2k لأن لو كان عندي اللي هو عدد زوجي بنقدر
+
+17
+00:01:09,020 --> 00:01:12,180
+نكتبه على صورة 2k for some k element in and يعني
+
+18
+00:01:12,180 --> 00:01:16,300
+هذه صورة العدد الزوجي أما العدد الفردي the odd
+
+19
+00:01:16,300 --> 00:01:20,820
+integer is on the form 2k زائد 1 for some k
+
+20
+00:01:20,820 --> 00:01:28,560
+element in andحاصل ضرب two even integers is even
+
+21
+00:01:28,560 --> 00:01:33,700
+وحاصل ضرب two odd integers is odd a real number is
+
+22
+00:01:33,700 --> 00:01:36,960
+a rational number if it is a common fraction that
+
+23
+00:01:36,960 --> 00:01:40,880
+is on the form M على N of integers M and N و N لا
+
+24
+00:01:40,880 --> 00:01:45,260
+تساوي سفر يعني بيقولي العدد النسبي هو العدد اللي
+
+25
+00:01:45,260 --> 00:01:49,240
+بنقدر نكتبه على صورة M على N حيث و M و N عدد صحيحة
+
+26
+00:01:52,650 --> 00:01:57,730
+الأن لا يساوي سفر a prime طبعا احنا اعرفناه هو
+
+27
+00:01:57,730 --> 00:02:00,670
+عبارة عن positive integer بي أكبر من واحد اللي
+
+28
+00:02:00,670 --> 00:02:04,510
+بيكسب بس على اللي هو الواحد والبي وطبعا هيكسب على
+
+29
+00:02:04,510 --> 00:02:11,340
+السالب واحد والسالب بيالأن البرهان النظريات أو
+
+30
+00:02:11,340 --> 00:02:16,200
+اللي هي الأنواع البرهين اللي هي فيه أنواع للبرهين
+
+31
+00:02:16,200 --> 00:02:20,720
+اليوم بدنا نحكي عن واحد منهم اسمه الـ Direct Proof
+
+32
+00:02:20,720 --> 00:02:25,280
+أو البرهان المباشر إذا اليوم بس هنحكي عن البرهان
+
+33
+00:02:25,280 --> 00:02:29,900
+المباشر اللي هي بذكركم في اللي هو ال implication
+
+34
+00:02:29,900 --> 00:02:34,310
+لما أخدنا ال implication بـ implies a Qقلنا هذه
+
+35
+00:02:34,310 --> 00:02:40,710
+اللي هي لو بدنا عشان نثبت صحتها لو كانت بيه صحيحة
+
+36
+00:02:40,710 --> 00:02:45,850
+عشان نثبت صحة الجملة كلها بيه implies q لازم نثبت
+
+37
+00:02:45,850 --> 00:02:49,790
+ان q إيه شمالها صحيحة إذا ال direct proof هنا
+
+38
+00:02:49,790 --> 00:02:56,350
+بعتمد على ماذا؟ بعتمد على إنه لو نفترض صحة بيه و
+
+39
+00:02:56,350 --> 00:03:01,570
+بنبدأ اللي هو نستخدم اللي هواللي هي كل الحقائق
+
+40
+00:03:01,570 --> 00:03:04,790
+اللي معناها وكل اللي هي المعطيات اللي معناها لما
+
+41
+00:03:04,790 --> 00:03:10,290
+نصلّمين إلى صحة Q إذاً an implication B implies Q
+
+42
+00:03:10,290 --> 00:03:15,730
+can be proved by showing that if B is true then Q
+
+43
+00:03:15,730 --> 00:03:20,730
+is also trueإن ناخد مثال Give a direct proof of
+
+44
+00:03:20,730 --> 00:03:24,290
+the theorem if N is odd then N تربيع is odd لأن
+
+45
+00:03:24,290 --> 00:03:28,130
+عندي نظرية أو عندي سؤال أو عندي المثال اللي هو
+
+46
+00:03:28,130 --> 00:03:33,170
+بقول لي لو كانت N is odd اثبتلي أن N تربيع إيش
+
+47
+00:03:33,170 --> 00:03:37,290
+ماله is odd كيف بنثبت استخدام ال directive proof
+
+48
+00:03:37,290 --> 00:03:41,230
+بنيجي بنفترض assume that the hypothesis B of this
+
+49
+00:03:41,230 --> 00:03:47,260
+implication is true يعني بنفترض أن هذا صحيحوبنبدأ
+
+50
+00:03:47,260 --> 00:03:52,160
+نستخدم هذه الحقيقة وحقائق معروفة للوصول إلى أن
+
+51
+00:03:52,160 --> 00:03:58,480
+تربيع is odd then use the rules of inference and
+
+52
+00:03:58,480 --> 00:04:02,040
+non-theorems to show that the conclusion you must
+
+53
+00:04:02,040 --> 00:04:07,230
+be true اللي هو أن تربيع is oddيعني الآن بنفترض
+
+54
+00:04:07,230 --> 00:04:12,190
+صحة أن بنبدأ نستخدم هذه كمعطيات و بنستخدم اللي هو
+
+55
+00:04:12,190 --> 00:04:16,210
+أي حاجة احنا بنعرف أنها صحيحة و تم إثباتها في
+
+56
+00:04:16,210 --> 00:04:21,090
+إثبات أن تربيع إيه شماله is odd الان ناخد ناخد
+
+57
+00:04:21,090 --> 00:04:25,530
+نشوف نبرهن نبرهن هذا السؤال assume that n is odd
+
+58
+00:04:25,530 --> 00:04:29,190
+إيش معناة n is odd يا جماعة هذا الان مثال على ال
+
+59
+00:04:29,190 --> 00:04:34,280
+direct proof زي ما قلنا assume that n is oddاللي
+
+60
+00:04:34,280 --> 00:04:38,440
+هو يعني and then and can be written as يعني and
+
+61
+00:04:38,440 --> 00:04:42,400
+يمكن كتبتها على صورة اتنين كزائد واحد حيث وk is
+
+62
+00:04:42,400 --> 00:04:47,480
+and إيش integer ال and أنا بدي مين بدي and تربيع
+
+63
+00:04:47,480 --> 00:04:51,620
+نتبتها إذا ال and تربيع consequently ال and تربيع
+
+64
+00:04:51,620 --> 00:04:55,780
+إيش هتساوي هذا المقدار لكل تربيع اتنين كزائد واحد
+
+65
+00:04:55,780 --> 00:05:01,770
+لكل تربيعالان باجي بربع هذا الطرف بطلع عندى هو 4k
+
+66
+00:05:01,770 --> 00:05:06,750
+تربيع زي 4k زي 1 تعرفوا تربعوها مربع الأول زي مربع
+
+67
+00:05:06,750 --> 00:05:10,450
+الثاني زي الأول في الثاني في اتنين الان هذا الرقم
+
+68
+00:05:10,450 --> 00:05:14,850
+اللى عندى انا بدأ اكتبه على اثبات النقودطب كيف
+
+69
+00:05:14,850 --> 00:05:18,330
+بتبتد نقود؟ خد للأربعة من هدولة عامل مشترك أو
+
+70
+00:05:18,330 --> 00:05:21,670
+اتنين عامل مشترك بيصير عند اتنين في اتنين كتر
+
+71
+00:05:21,670 --> 00:05:25,750
+تربيع زي اتنين K زائد واحد هذا عبارة عن عدد صحيح
+
+72
+00:05:25,750 --> 00:05:29,930
+لأن K صحيح و هذا K صحيح يعني بقدر اسم هذا العدد كل
+
+73
+00:05:29,930 --> 00:05:35,250
+ام بيصير عبارة عن اتنين ام زائد واحدصار عندى العدد
+
+74
+00:05:35,250 --> 00:05:37,930
+هذا انكتب اللى هو الان تربيع على صورة اتنين ام
+
+75
+00:05:37,930 --> 00:05:41,490
+زائد واحد حيث ام هو هذا العدد اتنين ان التربيع
+
+76
+00:05:41,490 --> 00:05:45,850
+زائد اتنين is an integer يعني اجدرت الان تربيع
+
+77
+00:05:45,850 --> 00:05:49,270
+اكتب على صورة اتنين ام زائد واحد معناته انه اثبتت
+
+78
+00:05:49,270 --> 00:05:54,190
+انه لما كانت unod اذا طلعت عندى الان تربيع can be
+
+79
+00:05:54,190 --> 00:05:58,790
+written in this form it is odd هذا هو مثال على
+
+80
+00:05:58,790 --> 00:06:04,550
+البرهان المباشرمثال آخر عن البرهان المباشر بقول
+
+81
+00:06:04,550 --> 00:06:08,550
+show that the product of two rational numbers is a
+
+82
+00:06:08,550 --> 00:06:12,630
+rational number بدنا نثبت أن حاصل ضرب two rational
+
+83
+00:06:12,630 --> 00:06:17,230
+numbers أشمل يا جماعة is a rational number بدنا
+
+84
+00:06:17,230 --> 00:06:21,850
+نبرهن البرهان كما يلي assume that M و N are
+
+85
+00:06:21,850 --> 00:06:25,250
+rational numbers يعني بنفترض أن عندي في two
+
+86
+00:06:25,250 --> 00:06:29,990
+rational numbers S1 اسمه M و S1 اسمه Nمدام M
+
+87
+00:06:29,990 --> 00:06:37,190
+ريشونال نمبر إذا M ممكن كتابته على صورة ألف على با
+
+88
+00:06:37,190 --> 00:06:40,630
+حيث ال با لا يساوي سفره الألف والبا أو ال إيه
+
+89
+00:06:40,630 --> 00:06:45,150
+والبي عبارة عن أعداد صحيحة Similarly بنفس الأسلوب
+
+90
+00:06:45,150 --> 00:06:49,630
+ال N ريشونال نمبر إذا N ممكن كتابته على صورة X على
+
+91
+00:06:49,630 --> 00:06:53,510
+Y يعني N ممكن كتابته على صورة X على Y حيثه برضه Y
+
+92
+00:06:53,510 --> 00:06:58,420
+لا تساوي سفره ال X أشماله والY أعداد صحيحةهدولة
+
+93
+00:06:58,420 --> 00:07:00,740
+rational numbers from the definition of rational
+
+94
+00:07:00,740 --> 00:07:06,460
+numbers الان مين بده هو اثبت انه the product of
+
+95
+00:07:06,460 --> 00:07:10,140
+two rational numbers is rational يعني بدنا نودي
+
+96
+00:07:10,140 --> 00:07:15,880
+دلان m في n و نثبتها انها روش rational so m في n
+
+97
+00:07:15,880 --> 00:07:21,400
+بسيطالـ M هي A على B والـ N هي X على Y الـ N هذا
+
+98
+00:07:21,400 --> 00:07:24,380
+بص تضربه في البص بيصير A في X والمقام في المقام
+
+99
+00:07:24,380 --> 00:07:29,140
+بيصير على B في Y إذا صار عند الرقم M في N عبارة عن
+
+100
+00:07:29,140 --> 00:07:32,320
+A في X عبارة عن Integer لأن هذا Integer وهذا
+
+101
+00:07:32,320 --> 00:07:36,110
+Integerو B في Y انتجر لأن هذا انتجر وهذا انتجر
+
+102
+00:07:36,110 --> 00:07:39,390
+وحاصل درب زي ما قلنا في الملاحظة الأولى مش هيكون
+
+103
+00:07:39,390 --> 00:07:44,210
+صفر لأنه ولا واحد فيه صفر إذا صارت M في N مكتوبة
+
+104
+00:07:44,210 --> 00:07:48,350
+على صورة انتجر على انتجر والانتجر اللي تحت مش صفر
+
+105
+00:07:48,350 --> 00:07:53,350
+إذا ال M في N عبارة عن rational number يعني الآن
+
+106
+00:07:53,350 --> 00:07:57,690
+صار ال product of two rational numbers is also a
+
+107
+00:07:57,690 --> 00:08:04,120
+rational number وهذا أيضا مثال آخرعلى اللي هو الـ
+
+108
+00:08:04,120 --> 00:08:08,180
+Direct Proof أو على البران المباشر الـ Direct
+
+109
+00:08:08,180 --> 00:08:14,080
+Proof More Examples اللي هو أمثلة أخرى على الـ
+
+110
+00:08:14,080 --> 00:08:18,570
+Direct Proof هتلاقوها برضه سهلةشوف الآن show that
+
+111
+00:08:18,570 --> 00:08:23,310
+ال example تلاتة the sum of two odd integers is
+
+112
+00:08:23,310 --> 00:08:28,930
+even يعني بدنا نقول أنه نثبت أنه مجموع اتنين odd
+
+113
+00:08:28,930 --> 00:08:34,230
+integers هيكون أيش معله even انتجار كيف؟الان مدام
+
+114
+00:08:34,230 --> 00:08:40,230
+اللي هو الاتنين عندى odd إذا بدنا نسميهم let n
+
+115
+00:08:40,230 --> 00:08:47,090
+بتساوي اتنين k زائد واحد و m ايش بتساوي اتنين j
+
+116
+00:08:47,090 --> 00:08:53,690
+زائد واحد ب odd integers ماشي الحال طيب الان
+
+117
+00:08:53,690 --> 00:09:02,720
+مجموحا بدك تقول n زائد m ايش هيساوي؟2k و2j و1 زائد
+
+118
+00:09:02,720 --> 00:09:07,900
+واحد يعني هيصير عند ال N زائد M عبارة عن 2k زائد
+
+119
+00:09:07,900 --> 00:09:15,510
+2j زائد 2أذا الان خد الاتنين عامل مشترك فيهم بيصير
+
+120
+00:09:15,510 --> 00:09:20,390
+N زائد M اللي هو مجموح N زائد M بيساوي اتنين في
+
+121
+00:09:20,390 --> 00:09:25,710
+العامل المشترك K زائد J زائد 1 يعني ال N زائد M
+
+122
+00:09:25,710 --> 00:09:32,510
+كتبناه على صورة 2 زائد اللي هو اتنين M prime مثلا
+
+123
+00:09:32,510 --> 00:09:35,970
+اللي هو is even integer
+
+124
+00:09:44,650 --> 00:09:49,830
+مش مكتوب المثال لكن سهل و انا حكيته بالتفصيل لان
+
+125
+00:09:49,830 --> 00:09:55,490
+جرب اكتب ان زائد ام مجمحن و خد اتنين عن مشترك بطلع
+
+126
+00:09:55,490 --> 00:10:00,390
+ان زائد ام عن اتنينإذا عندي N زائد M زي ما قلنا 2K
+
+127
+00:10:00,390 --> 00:10:05,470
+زائد 1 زائد 2G زائد 1 اللي هو بسوء 2K زائد 2G زائد
+
+128
+00:10:05,470 --> 00:10:09,350
+2 أخدنا 2 عامل مشترك من هدولة كلهم وضل عندي K زائد
+
+129
+00:10:09,350 --> 00:10:13,210
+G زائد 1 وهذا عبارة عن اللي هو integer مضروف في 2
+
+130
+00:10:13,210 --> 00:10:16,770
+إذا صار ال N زائد M is even هذه اللي هو مثال آخر
+
+131
+00:10:16,770 --> 00:10:20,020
+على ال direct proofالان المثال الأخير على direct
+
+132
+00:10:20,020 --> 00:10:24,340
+proof if M and N are both perfect squares يعني
+
+133
+00:10:24,340 --> 00:10:28,520
+مربعات كاملة M و N ايش معناه مربع كامل يعني ال M
+
+134
+00:10:28,520 --> 00:10:32,880
+بنقدر نكتبه على صورة B تربيع او ال N بنقدر نكتبه
+
+135
+00:10:32,880 --> 00:10:36,950
+على صورة B تربيعبقول إذا n في m برضه is also a
+
+136
+00:10:36,950 --> 00:10:40,150
+perfect square ده نشوف الان الان بدنا نفترض أن ن
+
+137
+00:10:40,150 --> 00:10:43,770
+assume that m and n are perfect squares يعني m و n
+
+138
+00:10:43,770 --> 00:10:47,870
+عبارة عن مربعات كاملة إيش يعني؟ يعني m بنقدر نكتبه
+
+139
+00:10:47,870 --> 00:10:51,870
+على صورة S تربيع و n بتساوي عبارة عن T تربيع هدولة
+
+140
+00:10:51,870 --> 00:10:55,550
+معناته أن m و n مربعات كاملة حيث أسوة T element
+
+141
+00:10:55,550 --> 00:11:00,320
+تنزلإذا بدنا نثبت أن M في N برضه مربع كامل اضرب M
+
+142
+00:11:00,320 --> 00:11:05,640
+في N بصير S تربيع في T تربيع اللي هو عبارة عن S في
+
+143
+00:11:05,640 --> 00:11:10,240
+T في الكل تربيع أو اللي هو زي ما اعمل S في S في T
+
+144
+00:11:10,240 --> 00:11:13,640
+في T انتوا عارفينه هذا الكلام سهل S في T اللي هو
+
+145
+00:11:13,640 --> 00:11:17,160
+في S في T اللي هو عبارة عن S في T لكل تربيع يعني M
+
+146
+00:11:17,160 --> 00:11:21,280
+في N كتبناه على صورة ST لكل تربيع ST عبارة عن رقم
+
+147
+00:11:21,280 --> 00:11:25,250
+انتجار لأن هذا انتجار و هذا انتجاريعني MN كتبنا
+
+148
+00:11:25,250 --> 00:11:29,150
+على صورة integer تربيع أو بمعنى آخر MN is also a
+
+149
+00:11:29,150 --> 00:11:33,610
+perfect square هيك بيكون احنا اللي هو خلصنا الجزء
+
+150
+00:11:33,610 --> 00:11:38,230
+الأول اللي هو عبارة عن ال direct proof اللي هو أو
+
+151
+00:11:38,230 --> 00:11:42,110
+البرهان المباشر بدنا الآن نيجي إلى طريقة ثانية من
+
+152
+00:11:42,110 --> 00:11:44,190
+طرق البرهان الرياضي
+
+153
+00:12:09,490 --> 00:12:13,110
+الان نيجي لان للنوع الثاني من أنواع البرهان اللي
+
+154
+00:12:13,110 --> 00:12:19,450
+هو بنا نسميه البرهان ال indirect proof او البرهان
+
+155
+00:12:19,450 --> 00:12:24,060
+غير المباشربالظبط هنحكي الآن في البرهان غير مباشر
+
+156
+00:12:24,060 --> 00:12:28,200
+عن حاجة اسمها Contrapositive أو Contraposition هذه
+
+157
+00:12:28,200 --> 00:12:32,440
+طبعا مش غريبة عليكم ممكن حكينا عنها في بداية ال ..
+
+158
+00:12:32,440 --> 00:12:36,900
+المادة قلنا ان implication B implies Q is
+
+159
+00:12:36,900 --> 00:12:40,920
+equivalent هذه كلها لبعض is equivalent to
+
+160
+00:12:40,920 --> 00:12:44,620
+Contrapositive إليها إيش Contrapositive يعني not Q
+
+161
+00:12:44,620 --> 00:12:50,440
+implies not B يعني لو أحنا أثبتناnot Q implies not
+
+162
+00:12:50,440 --> 00:12:56,100
+B يكون أثبتنا بـ B implies Q يعني عشان نثبت الـ B
+
+163
+00:12:56,100 --> 00:13:02,720
+implies Q بنفترض عكس الـ Q إنها صحيحة و بنصل لعكس
+
+164
+00:13:02,720 --> 00:13:06,940
+الـ B إنها صحيحة إذا قدرنا نصل لهيك بكون إن إحنا
+
+165
+00:13:06,940 --> 00:13:12,620
+اللي هي أن تكون على بعضها دي كلها الـ B implies Q
+
+166
+00:13:12,620 --> 00:13:14,700
+اللي أثبتناها
+
+167
+00:13:17,480 --> 00:13:21,460
+أو اللي هو بنثبت ان not q implies not b زي ما قلنا
+
+168
+00:13:21,460 --> 00:13:25,860
+او q is false implies اللي هو b is false فبكون
+
+169
+00:13:25,860 --> 00:13:29,940
+عنده اللي هو ال contraposition اللي حكينا عنه اذا
+
+170
+00:13:29,940 --> 00:13:33,220
+باختصار ال contraposition بنفترض اللي هو عكس ال q
+
+171
+00:13:33,220 --> 00:13:37,620
+و بنصل لعكس ال b او بنفترض ال q is false يعني عكس
+
+172
+00:13:37,620 --> 00:13:43,280
+ال q بنفترض و بنصل ل ال b is false يعني عكس ال b
+
+173
+00:13:43,280 --> 00:13:51,960
+طيبالان نعود لمثال عملي للأمرالمثال العامل يجيب on
+
+174
+00:13:51,960 --> 00:13:55,400
+indirect proof of the theorem اللي هي التالية ايش
+
+175
+00:13:55,400 --> 00:13:59,820
+اللي بده نثبت بده يثبت if تلاتة زائد اتنين is odd
+
+176
+00:13:59,820 --> 00:14:03,940
+then n is odd كيف بدنا نثبتها الآن هذه؟ هذي بدنا
+
+177
+00:14:03,940 --> 00:14:07,500
+نثبتها بال indirect proof بالcontraposition اللي
+
+178
+00:14:07,500 --> 00:14:11,340
+الآن بدنا نفترض عكس ال on is odd يعني نقول نفترض
+
+179
+00:14:11,340 --> 00:14:16,080
+ان on is not odd ونصل لتلاتة n زائد اتنين is not
+
+180
+00:14:16,080 --> 00:14:20,000
+oddإذا وصلنا لهك بيكون إحنا أثبتنا الـ Contra ..
+
+181
+00:14:20,000 --> 00:14:23,380
+عملنا الـ Contraposition وبذلك الـ Contraposition
+
+182
+00:14:23,380 --> 00:14:28,940
+بكافئ أنه 3N زاد 2 is odd يؤدي إلى N is odd إذن
+
+183
+00:14:28,940 --> 00:14:33,360
+الآن اللي بدي أفعله بدي أفترض أن N is odd is not
+
+184
+00:14:33,360 --> 00:14:37,440
+true يعني بدي أفترض أن N is not odd يعني بدي أفترض
+
+185
+00:14:37,440 --> 00:14:41,700
+أن N is even و أصلكم لهذه is not odd يعني بمعنى
+
+186
+00:14:41,700 --> 00:14:47,130
+آخر it is evenهذا الان اللي بدي أعمله خلّينا مع
+
+187
+00:14:47,130 --> 00:14:53,190
+بعض نشوف كيف نفترض الان ان is even مدام ان is even
+
+188
+00:14:53,190 --> 00:14:56,610
+اذا الان بتساوى اتنين k where k is an integer زي
+
+189
+00:14:56,610 --> 00:15:00,450
+ما انتوا عارفين الان بناء على ذلك تلاتة ان زائد
+
+190
+00:15:00,450 --> 00:15:04,600
+اتنين اللي هي المطلوبةبنعوض عن n بتنين k بصير
+
+191
+00:15:04,600 --> 00:15:08,060
+تلاتة في اتنين k زائد اتنين يعني بمعنى اخر ستة k
+
+192
+00:15:08,060 --> 00:15:11,580
+زائد اتنين بناخد اتنين الان عام المشترك بيصير
+
+193
+00:15:11,580 --> 00:15:15,460
+اتنين في تلاتة k زائد واحد يعني اقدر اكتب اللي هو
+
+194
+00:15:15,460 --> 00:15:20,860
+تلاتة n زائد اتنين على صورة اتنين مثلا حيث انزلنا
+
+195
+00:15:20,860 --> 00:15:25,300
+انتجار او بمعنى اخر وصلنا انه تلاتة n زائد اتنين
+
+196
+00:15:25,300 --> 00:15:32,100
+is evenأثبتنا الـ Contraposition لذلك تلاتة N زاد
+
+197
+00:15:32,100 --> 00:15:34,780
+اتنين يعني ليس غير غير غير غير غير غير غير غير غير
+
+198
+00:15:34,780 --> 00:15:37,240
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+199
+00:15:37,240 --> 00:15:38,440
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+200
+00:15:38,440 --> 00:15:38,580
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+201
+00:15:38,580 --> 00:15:39,140
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+202
+00:15:39,140 --> 00:15:39,200
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+203
+00:15:39,200 --> 00:15:39,520
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+204
+00:15:39,520 --> 00:15:39,960
+غير غير غير غير غير غير غير غير غير غير غير غير
+
+205
+00:15:39,960 --> 00:15:43,900
+غير غير غير غير
+
+206
+00:15:43,900 --> 00:15:46,720
+غير
+
+207
+00:15:47,920 --> 00:15:52,160
+مكافئ لهذا أنه أثبتنا أن is not odd أو بمعنى آخر
+
+208
+00:15:52,160 --> 00:15:56,200
+even تؤدي إلى تلاتة زائد أن زائد اتنين is not odd
+
+209
+00:15:56,200 --> 00:16:00,320
+يعني even وهيك بيكون أثبتنا اللي هو بواسط البرهان
+
+210
+00:16:00,320 --> 00:16:04,880
+غير المباشر هذه الحقيقة وبيكون اللي هو أثبتنا
+
+211
+00:16:04,880 --> 00:16:09,060
+بواسط حاجة اسمها الcontra positiveاللي هناخد مثال
+
+212
+00:16:09,060 --> 00:16:12,860
+آخر على الـ Contrapositive let M N أو N element in
+
+213
+00:16:12,860 --> 00:16:16,840
+N show that if M زيد N أكبر من خمسين then M أكبر
+
+214
+00:16:16,840 --> 00:16:20,220
+من خمس وعشرين أو N أكبر من خمس وعشرين بقول لو كان
+
+215
+00:16:20,220 --> 00:16:24,160
+عندي M وN integers بحيث أن M زيد N أكبر من خمسين
+
+216
+00:16:24,160 --> 00:16:29,640
+لازم لازم يعطينا أن M أكبر من خمس وعشرين أو N أكبر
+
+217
+00:16:29,640 --> 00:16:33,000
+من خمس وعشرينالـ Contrapositive لها أنه احنا
+
+218
+00:16:33,000 --> 00:16:37,320
+بنفترض عكس الجملة هذه كلها على بعضها و بنصل لعكس
+
+219
+00:16:37,320 --> 00:16:41,480
+هذه يعني بدنا نفترض ايش معناه عكس M أكبر من 25 or
+
+220
+00:16:41,480 --> 00:16:48,380
+N أكبر من 25 ايش نفيه جملة or يعني Mأكبر من 25
+
+221
+00:16:48,380 --> 00:16:54,460
+false and أن أكبر من 25 false إيش يعني؟ يعني أم
+
+222
+00:16:54,460 --> 00:17:01,240
+أصغر أو يساوي 25 and أن أصغر أو يساوي 25 إذا
+
+223
+00:17:01,240 --> 00:17:05,780
+assume not q اللي هي هذه يعني بمعنى آخر assume أن
+
+224
+00:17:05,780 --> 00:17:10,720
+أم أصغر أو يساوي 25 and أن أصغر أو يساوي 25 بناء
+
+225
+00:17:10,720 --> 00:17:16,840
+على هذا الحديثM زائد N أصغر أو سوى 25 زائد 25 يعني
+
+226
+00:17:16,840 --> 00:17:22,160
+M زائد N أصغر أو سوى 50 مدام M زائد N أصغر أو سوى
+
+227
+00:17:22,160 --> 00:17:27,120
+50 إذن هي عكس هذه اللي هي عكس M زائد N أكبر من 50
+
+228
+00:17:27,120 --> 00:17:34,270
+إذن وصلنا نط Q نط هذهأدت إلى نط بي اللي هي نط هذه
+
+229
+00:17:34,270 --> 00:17:38,570
+وهذا هو ال contrapositive فبنكون هيك احنا أثبتنا
+
+230
+00:17:38,570 --> 00:17:42,690
+ال example بواسطة إثبات ال contrapositive أو
+
+231
+00:17:42,690 --> 00:17:47,630
+بواسطة ال indirect approve الان في سؤال بيقولي
+
+232
+00:17:47,630 --> 00:17:54,090
+approve or disapprove يعني اثبت او اللي هو اثبت
+
+233
+00:17:54,090 --> 00:17:58,950
+صحة او اثبت عدم صحة that يعني بيقول الجملة التالية
+
+234
+00:17:58,950 --> 00:18:03,150
+صحيحة ولا مش صحيحةبقول that the product of two
+
+235
+00:18:03,150 --> 00:18:06,730
+irrational numbers is irrational بقول لي هل حاصل
+
+236
+00:18:06,730 --> 00:18:09,930
+ضرب two irrational numbers لازم يطلع irrational
+
+237
+00:18:09,930 --> 00:18:15,330
+عشان نثبت لازم نثبت لكل الحالات يعني نفترض انه اي
+
+238
+00:18:15,330 --> 00:18:19,070
+اتنين irrational و نصل الهين irrational لو في حالة
+
+239
+00:18:19,070 --> 00:18:23,630
+واحدة بس يعني مثال واحد اللي هو هذا بنتقش يعني لو
+
+240
+00:18:23,630 --> 00:18:28,440
+جدرنا نجيباللي هو عددين irrational حاصر ضربهم مش
+
+241
+00:18:28,440 --> 00:18:32,040
+irrational بتكون هذه الجملة مش صحيحة وفي هذه
+
+242
+00:18:32,040 --> 00:18:35,540
+الحالة بنقول هذا العمل هو disapprove و ال
+
+243
+00:18:35,540 --> 00:18:39,240
+disapprove بنجيب counter example يعني بنجيب مثال
+
+244
+00:18:39,240 --> 00:18:45,990
+عدديبنبين فيه ان هذه الجملة غير صحيحة الان بيقول
+
+245
+00:18:45,990 --> 00:18:50,790
+ايش الجملة؟ ان ال product of two irrational is
+
+246
+00:18:50,790 --> 00:18:54,590
+irrational انا بقول هذا الكلام مش صحيح ليش؟ خد هاي
+
+247
+00:18:54,590 --> 00:18:58,250
+مثال هاي جدر التنين irrational ايش irrational؟
+
+248
+00:18:58,250 --> 00:19:01,570
+يعني عدد لا يمكن كتابته على صورة ألف على با حيث
+
+249
+00:19:01,570 --> 00:19:06,700
+ألف وبا أعداد صحيحة وبلده ساوى سفرالجدر التنين مش
+
+250
+00:19:06,700 --> 00:19:09,940
+irrational وجدر التنين برضه مش irrational حاصل ضرب
+
+251
+00:19:09,940 --> 00:19:15,860
+هنا بساوة 2 اللي هو rational إذا فعلا لجينا مثال
+
+252
+00:19:15,860 --> 00:19:21,580
+يبين لإن حاصل ضرب 2 irrational ليس شرطا إنه يطلع
+
+253
+00:19:21,580 --> 00:19:26,000
+irrational عشان هيك هذه الجملة مش صحيحة عشان هيك
+
+254
+00:19:26,000 --> 00:19:30,520
+بنسميها ده اسمه disprovedisprove كيف؟ بنجيب
+
+255
+00:19:30,520 --> 00:19:35,860
+counter example بحقق الجزء اللي هو حاصل الضرب ما
+
+256
+00:19:35,860 --> 00:19:40,260
+يطلع شمين المطلوب يعني هاي عندى two irrational is
+
+257
+00:19:40,260 --> 00:19:44,320
+irrational مش صحيح وهي مثل جدر التنين irrational
+
+258
+00:19:44,320 --> 00:19:48,500
+جدر التنين irrational وحاصل ضرب ما طلعش irrational
+
+259
+00:19:49,200 --> 00:19:52,280
+طلع rational number و هذا بقولك the product of two
+
+260
+00:19:52,280 --> 00:19:55,520
+irrational numbers يعني is not necessarily
+
+261
+00:19:55,520 --> 00:20:00,280
+irrational يعني need not to be irrational وهي مثال
+
+262
+00:20:00,280 --> 00:20:04,380
+نيجي للسؤال اللي بعده بقول prove that إذا كانت n
+
+263
+00:20:04,380 --> 00:20:08,400
+بتساوي a في b هذا بيعطينا a أصغر أو ساوي جذر ال n
+
+264
+00:20:08,400 --> 00:20:12,140
+or b أصغر أو ساوي جذر ال n حيث ال a و ال b عبارة
+
+265
+00:20:12,140 --> 00:20:16,440
+عن أعداد صحيحة موجبة كمان مرة بدنا نثبت أنه لو كان
+
+266
+00:20:16,440 --> 00:20:22,070
+n بتساوي a في bهذا سيعطينا او a أصغر او ساوى جدر
+
+267
+00:20:22,070 --> 00:20:25,850
+الآن او b أصغر او ساوى جدر الآن بدا نثبت هذا عن
+
+268
+00:20:25,850 --> 00:20:28,710
+طريق مين اللي هو ال contraposition ايش بنا نثبت
+
+269
+00:20:28,710 --> 00:20:33,570
+بدا نفرض عكس المطلوب هايو بدا نفرض عكس هذا و نصل
+
+270
+00:20:33,570 --> 00:20:39,160
+لعكس هذايعني بنفترض أنه a أصغر أو يسوي b or b أصغر
+
+271
+00:20:39,160 --> 00:20:43,200
+أو يسوي جدر الان هذه مش صحيحة كيف جملة هذه على
+
+272
+00:20:43,200 --> 00:20:48,840
+بعضها or مش صحيحة معناته a أكبر من جدر الان and b
+
+273
+00:20:48,840 --> 00:20:52,220
+أكبر من جدر الان لأنه لا في الor اللي هو and زي ما
+
+274
+00:20:52,220 --> 00:20:56,640
+احنا عارفين إذا الأن بنفترض عكس هذا يعني بنفترض
+
+275
+00:20:56,640 --> 00:21:00,780
+أنه a أكبر من جدر الان and b أكبر من جدر الان منه
+
+276
+00:21:00,780 --> 00:21:04,900
+بنصل ل a في b أكبر من جدر الان في جدر الان اللي هو
+
+277
+00:21:04,900 --> 00:21:08,050
+الانمدام a أكبر من ال .. من ال .. من ال .. من ال a
+
+278
+00:21:08,050 --> 00:21:12,330
+b أكبر من ال n إذا يعني ال a b لا تساوي ال n مدام
+
+279
+00:21:12,330 --> 00:21:15,470
+a لا تساوي ال a b لا تساوي ال n معناه توصلنا لمين
+
+280
+00:21:15,470 --> 00:21:18,570
+إلى عكس هذا وهذا معناته أنه احنا بال
+
+281
+00:21:18,570 --> 00:21:22,650
+contrapositive فرضنا عكس هذه ووصلنا لعكس هذه
+
+282
+00:21:22,650 --> 00:21:26,050
+فبتكون الجملة الأصلية هذه كلها على بعض صحيحة
+
+283
+00:21:26,050 --> 00:21:30,010
+وبنكون هذا أثبتناها الجملة عن طريق ال
+
+284
+00:21:30,010 --> 00:21:34,420
+contrapositive أو ال contrapositionيعني أثبتنا fn
+
+285
+00:21:34,420 --> 00:21:38,600
+بيساوي a و a أصغر أو أصغر جدر الان او b أصغر أو
+
+286
+00:21:38,600 --> 00:21:43,340
+أصغر جدر الان الآن في طريقة أخرى أخيرة أو قبل
+
+287
+00:21:43,340 --> 00:21:47,000
+الأخيرة بالبرهان الهي proof by contradiction
+
+288
+00:21:47,000 --> 00:21:51,370
+الإثبات عن طريق التناقضما هو الإثبات عن طريق
+
+289
+00:21:51,370 --> 00:21:55,410
+التناقض؟ طبعاً هذه مهمة كمان اللي هي an important
+
+290
+00:21:55,410 --> 00:21:58,470
+implication يعني بدنا نثبت بيه implies a Q إيش
+
+291
+00:21:58,470 --> 00:22:05,490
+بنسوي؟ بنفترض عكس لـQ و بنصل لتناقض بنصل لإيش
+
+292
+00:22:05,490 --> 00:22:10,770
+بناقض المُعطَى أو بناقض حقيقة إحنا بنعرفها يعني
+
+293
+00:22:10,770 --> 00:22:13,990
+اللي هو proved by contradiction يتلخص فيما يليه
+
+294
+00:22:14,240 --> 00:22:23,880
+بنقول Assume B and Assume Not Q وبنصل لتناقض تشوف
+
+295
+00:22:23,880 --> 00:22:28,440
+كيف بنحصل على تناقض show that هي مثال if the
+
+296
+00:22:28,440 --> 00:22:31,820
+square of an integer number is odd then the
+
+297
+00:22:31,820 --> 00:22:38,970
+integer is odd بيقول إذا كان مربعاللي هي عدد is
+
+298
+00:22:38,970 --> 00:22:43,950
+odd اثبت انه العدد نفسه ايش is odd يعني لو كان n
+
+299
+00:22:43,950 --> 00:22:49,510
+تربيع odd هيعطينا الان is odd الان assume that
+
+300
+00:22:49,510 --> 00:22:52,910
+hypothesis B of this implication is true نفترض
+
+301
+00:22:52,910 --> 00:22:56,290
+اللي هو ال hypothesis ايش ماله الفرضية أنها صحيحة
+
+302
+00:22:56,810 --> 00:23:01,570
+وبنفرض عكس المطلوب وبنقول and the conclusion if
+
+303
+00:23:01,570 --> 00:23:05,890
+you is false وبنفرض إن اللي هو المطلوب أو ال
+
+304
+00:23:05,890 --> 00:23:10,090
+conclusion مش صحيحة وبعدين then use roles of
+
+305
+00:23:10,090 --> 00:23:13,330
+inference and non-theorems to deduce contradiction
+
+306
+00:23:13,330 --> 00:23:17,330
+وبعدين نبدأ نستخدم اللي هو معلوماتنا من النظريات
+
+307
+00:23:17,330 --> 00:23:21,590
+ومن الحقائق للوصول إلى تناقض خلينا نشوف هذا الكلام
+
+308
+00:23:21,590 --> 00:23:26,140
+عمليًاالان نفترض الان assume x تربيع is odd هذا
+
+309
+00:23:26,140 --> 00:23:29,880
+المعطى فرضناه المعطى زي ما هو بنصبهوش الان و إيش
+
+310
+00:23:29,880 --> 00:23:35,460
+بدنا نفرض بدنا نفرض إنه المطلوب غير متحقق يعني
+
+311
+00:23:35,460 --> 00:23:40,500
+بدنا نفرض إن x is not odd مدان x is not odd إذا x
+
+312
+00:23:40,500 --> 00:23:44,980
+أكيد evenمدام .. لأن أي عدد في الدنيا يا even يا
+
+313
+00:23:44,980 --> 00:23:50,040
+إيش يقض مدام X even إذا ال X تربيع لل even هيطلع
+
+314
+00:23:50,040 --> 00:23:54,640
+even لأن X even معناته على صورة 2N 2N لكل تربيع
+
+315
+00:23:54,640 --> 00:23:59,080
+معناته 4N تربيع يعني X تربيع 4N تربيع is even إذا
+
+316
+00:23:59,080 --> 00:24:03,480
+وصلنا لعكس mean اللي هو المطلوب يعني وصلنا ل X
+
+317
+00:24:03,480 --> 00:24:08,750
+تربيع is evenو احنا في الأصل عندي X تربيع is odd
+
+318
+00:24:08,750 --> 00:24:12,450
+صار عندي X تربيع is even و في نفس الوقت X تربيع is
+
+319
+00:24:12,450 --> 00:24:18,010
+odd وهذا اللي هو Contradiction لأن وصلنا ل X تربيع
+
+320
+00:24:18,010 --> 00:24:21,510
+is odd في الأصل و X تربيع is even يعني not odd
+
+321
+00:24:21,510 --> 00:24:25,150
+يعني وصلنا ل X تربيع is odd and not odd which is a
+
+322
+00:24:25,150 --> 00:24:31,480
+contradictionTherefore الفرضية الأولى إن فرضنا عكس
+
+323
+00:24:31,480 --> 00:24:35,820
+المطلوب مش صحيحة إذن لما ال X تربيع is odd لازم
+
+324
+00:24:35,820 --> 00:24:42,060
+تطلع ال X is odd هذا المرهان by contradiction الآن
+
+325
+00:24:42,060 --> 00:24:47,840
+نيجي ناخد مثال آخر المثال كمانيبقول let m و n
+
+326
+00:24:47,840 --> 00:24:51,540
+element in n show that if m زاد n أصغر من 90 then
+
+327
+00:24:51,540 --> 00:24:56,880
+m أصغر من 45 or n أصغر من 45 by contradiction كيف؟
+
+328
+00:24:56,880 --> 00:25:00,840
+بنفترض المعطوعة زي ما هو بنفترض أن m زاد n أصغر من
+
+329
+00:25:00,840 --> 00:25:06,580
+90 وبنفترض عكس المطلوب إذا by contradiction بنفترض
+
+330
+00:25:06,580 --> 00:25:11,020
+من عكس المطلوبمشابهة دير بالكم لـ Contraposition
+
+331
+00:25:11,020 --> 00:25:16,320
+بس هنا إحنا بنصل هذا اللي بنصل بعد خطوات إلى شيء
+
+332
+00:25:16,320 --> 00:25:21,780
+بناقض إما المطلوب أو المعطى بناقض المعطى أو بناقض
+
+333
+00:25:21,780 --> 00:25:26,090
+حقيقة بنعرفهاأما في الـ Contraposition كنا نفترض
+
+334
+00:25:26,090 --> 00:25:29,390
+عكس هذا و نصل لعكس هذا في الـ Contraposition مش
+
+335
+00:25:29,390 --> 00:25:34,130
+شرط تصل لعكس هذا ممكن تصل لإيش بناقض احنا حقيقة
+
+336
+00:25:34,130 --> 00:25:39,150
+بنعرفها و ممكن تصل طبعا لمين لاللي هو بناقض المعطى
+
+337
+00:25:39,150 --> 00:25:42,150
+يعني بنكون اللي هو Contraposition و كأنها حالة
+
+338
+00:25:42,150 --> 00:25:46,720
+خاصة من Contradictionshow that if M زيادة N أصغر
+
+339
+00:25:46,720 --> 00:25:50,080
+من تسعين then M أصغر من خمسة واربعين or N أصغر من
+
+340
+00:25:50,080 --> 00:25:53,420
+خمسة واربعين بدنا نفترض الأن suppose M زيادة N
+
+341
+00:25:53,420 --> 00:25:59,280
+أصغر من تسعين and suppose عكس هذا عكس هذا يعني
+
+342
+00:25:59,280 --> 00:26:03,000
+بدنا نفترض الأن assume M زيادة N أصغر من تسعين مش
+
+343
+00:26:03,000 --> 00:26:06,920
+تسعة وتمانين هذا تسعين طبعا and بنفترض عكس هذا إيش
+
+344
+00:26:06,920 --> 00:26:11,380
+عكس هذا أن M أكبر أو يساوي خمسة واربعين وفي نفس
+
+345
+00:26:11,380 --> 00:26:16,720
+الوقت لأنه نفي ال or andand n أكبر ويساوي 45 الان
+
+346
+00:26:16,720 --> 00:26:21,360
+then m زائد n طبعا احنا ماخدين m زائد n أصغر من
+
+347
+00:26:21,360 --> 00:26:29,820
+100 من 90 من 90 بس أنا غلط بس كتابة m زائد n الان
+
+348
+00:26:29,820 --> 00:26:33,720
+بما أن هذه أكبر من 45 وهذه أكبر من 45 إذا حاصل
+
+349
+00:26:33,720 --> 00:26:38,210
+جمحن أكبر ويساوي 45اللي صارت عندي M زاد N أكبر
+
+350
+00:26:38,210 --> 00:26:42,690
+وسوء وخمسة واربعين و M زاد N أصغر من تسعين إذا هذا
+
+351
+00:26:42,690 --> 00:26:46,830
+contradiction therefore اللي هو الفرضية اللي
+
+352
+00:26:46,830 --> 00:26:50,590
+فرضناها مش صحيحة يعني بمعنى أخر لما ال M زاد N
+
+353
+00:26:50,590 --> 00:26:54,390
+أصغر من تسعين يعطينا ال M أصغر من خمسة واربعين or
+
+354
+00:26:54,390 --> 00:27:00,110
+N أصغر من مين من خمسة واربعين هذه تسعين برضهالان
+
+355
+00:27:00,110 --> 00:27:03,910
+اخر جزء في المحاضرة هيكون ان ال mathematical
+
+356
+00:27:03,910 --> 00:27:08,830
+induction او الاستقراء الرياضي هي طريقة للبرهان
+
+357
+00:27:08,830 --> 00:27:13,610
+لبرهان بعض الجمل المعينة اللي بتكون بدلالة اللي هي
+
+358
+00:27:13,610 --> 00:27:18,200
+ال natural numbers او ال integersif we have a
+
+359
+00:27:18,200 --> 00:27:21,680
+propositional function P of N لو كان في عندنا اللي
+
+360
+00:27:21,680 --> 00:27:26,240
+هي جملة بتعتمد على اللي هي من على N اللي هي ال
+
+361
+00:27:26,240 --> 00:27:29,840
+natural number و بدنا نثبت أنه هذه الجملة P of N
+
+362
+00:27:29,840 --> 00:27:34,420
+صحيحة لكل natural number N طبعا احنا هنعتبر ال
+
+363
+00:27:34,420 --> 00:27:37,240
+natural number اللي هي عبارة عن واحد اتنين تلاتة
+
+364
+00:27:37,240 --> 00:27:40,500
+اربعة إلى مال انتهى مش هنعتبر السفر فيها في كل
+
+365
+00:27:40,500 --> 00:27:46,320
+حديثنا اتفجنا نتفج عليك ان شاء اللهالان عشان نثبت
+
+366
+00:27:46,320 --> 00:27:49,240
+هذه اللي هي ال بي of ان انها صحيحة على كل natural
+
+367
+00:27:49,240 --> 00:27:53,240
+number بنعمل ما يلي اول اشي بنثبت انها صحيحة
+
+368
+00:27:53,240 --> 00:27:58,660
+الجملة عند الان بتساوي واحد يعني بنثبت بي واحد is
+
+369
+00:27:58,660 --> 00:28:02,540
+true show that بي واحد is true الخطوة الثانية هذه
+
+370
+00:28:02,540 --> 00:28:06,380
+اللي بنسميها ال basic step الخطوة الثانية بنفترض
+
+371
+00:28:06,380 --> 00:28:12,790
+ان ال بي صحيحة عند number kوبنثبت أنها صحيحة عند
+
+372
+00:28:12,790 --> 00:28:18,010
+BK BK زائد واحد يعني بنفترض أنه B of K صحيحة
+
+373
+00:28:18,010 --> 00:28:23,050
+وبنثبت B of K زائد واحد لكل K element in N الـ N
+
+374
+00:28:23,050 --> 00:28:25,970
+هذا اللي بنسميها الـ B of K is true بنفرضها ده
+
+375
+00:28:25,970 --> 00:28:30,550
+بنسميها induction hypothesisاللي هي فرضية
+
+376
+00:28:30,550 --> 00:28:36,190
+الاستقراء a ومنها بنثبت bk زائد واحد لو خلصنا هذا
+
+377
+00:28:36,190 --> 00:28:40,950
+الكلام هذه و هذه كلها على بعض أثبتناها بنكون
+
+378
+00:28:40,950 --> 00:28:45,510
+أثبتنا اللي هو then b of n must be true for any n
+
+379
+00:28:45,510 --> 00:28:48,630
+element in N هذا الطريقة بنسميها اللي هي ال
+
+380
+00:28:48,630 --> 00:28:53,290
+mathematical induction أو الاستقراء الرياضي بنثبت
+
+381
+00:28:53,290 --> 00:28:57,260
+الجملة صحيحة عند واحدبعدين مفترض أن صحة الجملة عند
+
+382
+00:28:57,260 --> 00:29:01,560
+بك ومنها بنثبت أن نثبت صحة بك عند بك زائد واحد
+
+383
+00:29:01,560 --> 00:29:05,600
+وبكون هي كأثبتنا أن هي صحيحة لكل أن element ان
+
+384
+00:29:05,600 --> 00:29:10,140
+وخلّينا ناخد أمثلة عملية وهي أول مثال عملي بقول
+
+385
+00:29:10,140 --> 00:29:13,420
+prove that واحد زائد تلاتة زائد خمسة زائد اتنين
+
+386
+00:29:13,420 --> 00:29:17,800
+الناقص واحد بيساوي أن تربيع صحيحة هذا المقدار لو
+
+387
+00:29:17,800 --> 00:29:21,120
+جمعته لبعض بيساوي دايما أن تربيع صحيحة لكل أن
+
+388
+00:29:21,120 --> 00:29:24,700
+element انبندن اثبت هذه اللاحظة ان الجملة تعتمد
+
+389
+00:29:24,700 --> 00:29:27,500
+على مين على الان اللي هي ايش ال natural numbers
+
+390
+00:29:27,500 --> 00:29:32,060
+اذا ال mathematical induction بتظبط فيها طبعا هذه
+
+391
+00:29:32,060 --> 00:29:36,620
+ايش معناته هي the sum of the first n odd integers
+
+392
+00:29:36,620 --> 00:29:40,600
+يعني اول n من ال odd integers واحد زائد تلاتة زائد
+
+393
+00:29:40,600 --> 00:29:43,540
+خمس زائد اتنين ان نقص واحد دول عدد ان ان لو جمعتها
+
+394
+00:29:43,540 --> 00:29:47,650
+لبعض هيطلع ان بساوين ان تربيةالان مش هو هذا
+
+395
+00:29:47,650 --> 00:29:51,970
+موضوعنا موضوعنا بنثبت ان هذه صحيحة دائما الان مثال
+
+396
+00:29:51,970 --> 00:29:54,730
+عليها بس عشان نوضع عليها هذه اللي هي عبارة عن لو
+
+397
+00:29:54,730 --> 00:29:57,750
+جيت جمعت واحد زائد تلاتة اللي هو عددين فرديين اللي
+
+398
+00:29:57,750 --> 00:30:01,810
+هو اتنين تربيع اللي هي أربعة لو جيت جمعت العدد
+
+399
+00:30:01,810 --> 00:30:04,790
+الأول فردي والتاني الفردي والتالت فردي هتطلع قداش
+
+400
+00:30:04,790 --> 00:30:10,170
+اللي هي تسعة اللي هي تلتة تربيعأو 4 أعداد 1 2 3 4
+
+401
+00:30:10,170 --> 00:30:13,450
+يعني واحد و تلات أو خمسة و سبعة اللي هو هيطلع
+
+402
+00:30:13,450 --> 00:30:19,150
+قيمتنا 16 يعني أربعة تربية هذا بس مثال توضيحي لان
+
+403
+00:30:19,150 --> 00:30:22,090
+نيجي لموضوعنا اللي هو برهان هذه by induction ال
+
+404
+00:30:22,090 --> 00:30:25,480
+proofأول حاجة بدنا نثبت صحة الجملة هذه ال basic
+
+405
+00:30:25,480 --> 00:30:29,840
+step الأولى بدنا نثبت صحة الجملة هذه صحيحة لمين
+
+406
+00:30:29,840 --> 00:30:34,920
+لأن بتساوي واحد يعني لما نعوض هن بأن لازم يطلع
+
+407
+00:30:34,920 --> 00:30:38,820
+الطرف الأيصر هذا بيساوي الطرف الأيمن لو عوضنا هن
+
+408
+00:30:38,820 --> 00:30:42,360
+بأن طبعا لو عوضنا هن بأن واضح أنه بيطلع عندى واحد
+
+409
+00:30:42,360 --> 00:30:47,740
+تربع يعني واحدطب نيجي نعوض هنا بان اللي هو لما انه
+
+410
+00:30:47,740 --> 00:30:51,020
+بقى واحد بصير اتنين في واحد اللي هي اتنين نقص واحد
+
+411
+00:30:51,020 --> 00:30:54,060
+واحد يعني مافيش اشي بجموع الا الواحد لحاله يعني
+
+412
+00:30:54,060 --> 00:30:57,980
+هذه بس اللي هو اول term اللي هو الواحد الان the
+
+413
+00:30:57,980 --> 00:31:01,320
+sum of the first odd number اللي هو واحد اللي هو
+
+414
+00:31:01,320 --> 00:31:05,280
+الطرف الأيسر هذا وهذا بيساوي واحد تربيع والتانية
+
+415
+00:31:05,280 --> 00:31:09,210
+متساويين مدام التانية متساويينإذا هذا الطرف بيساوي
+
+416
+00:31:09,210 --> 00:31:13,690
+هذا for n بتساوي واحد إذا ال basic step بتحققت إذا
+
+417
+00:31:13,690 --> 00:31:17,630
+صارت اللي هي الجملة دي صحيحة for n بتساوي واحد
+
+418
+00:31:17,630 --> 00:31:22,130
+نيجي الآن نثبت إن افترض صحتها ال inductive step
+
+419
+00:31:22,130 --> 00:31:27,490
+بدنا نقول assume that this is true for n بتساوي K
+
+420
+00:31:27,490 --> 00:31:31,470
+إيش يعني؟ يعني بدنا نفرض صحة واحد زائد تلاتة زائد
+
+421
+00:31:31,470 --> 00:31:37,400
+خمسة زائد مادة لل N K بنحط2k-1 تساوي الـ k تربيع
+
+422
+00:31:37,400 --> 00:31:41,340
+يعني فرضنا صحة هذه الجملة عند n بتساوي k يعني
+
+423
+00:31:41,340 --> 00:31:45,700
+عوضنا أنا k و أنا k الآن هذه صارت عندنا اللي هو
+
+424
+00:31:45,700 --> 00:31:51,460
+مفترضين صحتها بدنا نثبت من خلالها أن الجملة صحيحة
+
+425
+00:31:51,460 --> 00:31:56,020
+now we prove thatإن هذه صحيحة لـ K زائد واحد إيش
+
+426
+00:31:56,020 --> 00:32:00,280
+معنات لـ K زائد واحد يعني لما ننشيل الان ونحط
+
+427
+00:32:00,280 --> 00:32:04,340
+مكانها K زائد واحد بتصير واحد زائد تلاتة زائد خمسة
+
+428
+00:32:04,340 --> 00:32:08,440
+زائد اتنين اللي هو K minus واحد زائد اللي هو آخر
+
+429
+00:32:08,440 --> 00:32:12,620
+term هذا ميناللي هو اتنين في K زائد واحد نقص واحد
+
+430
+00:32:12,620 --> 00:32:16,780
+يعني شيلت ال N هذه وحطيت مكانها K زائد واحد إذا
+
+431
+00:32:16,780 --> 00:32:19,780
+كانت هذه مضايقاتكم سابقوها يعني أنا بقصد ونظل نجمع
+
+432
+00:32:19,780 --> 00:32:23,260
+واحد زائد تلاتة زائد خمسة زائد سبعة لما نصل لآخر
+
+433
+00:32:23,260 --> 00:32:27,960
+term هذا اللي حطينا مكان ال N اللي هو K زائد واحد
+
+434
+00:32:27,960 --> 00:32:32,370
+شيلت ال N هيها وحطيت K زائد واحدبتثبت ان هذا بساوي
+
+435
+00:32:32,370 --> 00:32:36,530
+هذا المقدار لما اشير لان هنا برضه احط كمان ايش K
+
+436
+00:32:36,530 --> 00:32:40,370
+زائد واحد فبصير K زائد واحد لكل تربيع هذا الان هو
+
+437
+00:32:40,370 --> 00:32:44,850
+اللي بدكبته لو أثبتت معناته و أثبتت صحة الجملة هذه
+
+438
+00:32:44,850 --> 00:32:48,550
+في حالة الان بتساوي K زائد واحد يلا نشوف مع بعض
+
+439
+00:32:48,550 --> 00:32:53,090
+طبعا اكيد بنستعيني بهذه اكيد تشوف الاننأخد الطرف
+
+440
+00:32:53,090 --> 00:32:57,870
+الأيمن هذا الأن أول حاجة من هنا من induction
+
+441
+00:32:57,870 --> 00:33:02,130
+hypothesis هيها هذه بيساوي K تربيعي يعني واحد زي
+
+442
+00:33:02,130 --> 00:33:06,230
+تلتة زي خمسة زي اتنين K minus واحد بيساوي K تربيعي
+
+443
+00:33:06,230 --> 00:33:10,050
+بتعتمد على هدف الوصول من الطرف الأيسر هنا للطرف
+
+444
+00:33:10,050 --> 00:33:13,490
+الأيمن ناخد الطرف الأيسر هذا ماشي الحال هي الطرف
+
+445
+00:33:13,490 --> 00:33:17,130
+الأيسر هذا ايش هو؟ هو عبارة عن واحد زي تلت زي
+
+446
+00:33:17,130 --> 00:33:22,900
+اتنين كده نقص واحد زي مين زي هذا هذابدخل هذه بيصير
+
+447
+00:33:22,900 --> 00:33:28,560
+اتنين K زائد اتنين ناقص واحد زائد اتنين ناقص واحد
+
+448
+00:33:28,560 --> 00:33:32,440
+يعني واحد يعني بيصير هذا المقدر هو عبارة عن اتنين
+
+449
+00:33:32,440 --> 00:33:38,450
+K زائد واحد هذا لما فكه بيصير اتنين K زائد واحدطيب
+
+450
+00:33:38,450 --> 00:33:43,110
+الجزء الأول هذا كله هيو من هان لهان هيو ماتينايا
+
+451
+00:33:43,110 --> 00:33:46,190
+في ال induction hypothesis كتربيع فبيصير هذه
+
+452
+00:33:46,190 --> 00:33:51,270
+كتربيع مكان كل هذا المقدر بيضل كمان جنبه من اتنين
+
+453
+00:33:51,270 --> 00:33:56,030
+كزائد واحد هذا زائد هذا اللي هو مفقوق كزائد واحد
+
+454
+00:33:56,030 --> 00:33:59,110
+لكل تربيع زي ما انتوا عارفين يعني ايش اللي وصلنا
+
+455
+00:33:59,110 --> 00:34:06,290
+له وصلنا لأن هذهاللي هي بتساوي هذه يعني صار اللي
+
+456
+00:34:06,290 --> 00:34:11,390
+هي الجملة لما ثبتت هذه بتساوي هذه صارت الجملة اللي
+
+457
+00:34:11,390 --> 00:34:16,590
+فوق صحيحة ل K زائد واحد مدام خلصنا أطبطنا صحيحة ل
+
+458
+00:34:16,590 --> 00:34:22,850
+K زائد واحد نكون اللي هو ال conclusion اللي هي ال
+
+459
+00:34:22,850 --> 00:34:26,170
+mathematical induction اكتملت معناته أنه صارت هذه
+
+460
+00:34:26,170 --> 00:34:32,680
+الجملة صحيحة لكل element inالذي لم يتابع جيدًا في
+
+461
+00:34:32,680 --> 00:34:35,340
+هذا المثال يتابع في المثال اللي بعده برضه عن
+
+462
+00:34:35,340 --> 00:34:37,600
+الmathematical induction الان يستخدم
+
+463
+00:34:37,600 --> 00:34:41,240
+الmathematical induction لكي يثبت أن واحد زاد
+
+464
+00:34:41,240 --> 00:34:45,520
+اتنين زائد ان ساوي ان في ان زائد واحد هذا كله مجسم
+
+465
+00:34:45,520 --> 00:34:49,930
+على اتنين لكل ان element انالان بدنا نستخدم اللي
+
+466
+00:34:49,930 --> 00:34:53,190
+هو ال mathematical induction اللي اتبعت هذا اكيد
+
+467
+00:34:53,190 --> 00:34:56,290
+ال mathematical induction ليش؟ لأنه بده يبقى اللي
+
+468
+00:34:56,290 --> 00:34:58,550
+هو لكل n element in n يعني بدنا نتبع صحة الجملة
+
+469
+00:34:58,550 --> 00:35:03,630
+هذه لكل ال natural numbers n قولنا ال natural
+
+470
+00:35:03,630 --> 00:35:08,120
+numbers بنقصد فيها من واحد إلى مالة نهايةنيجي أول
+
+471
+00:35:08,120 --> 00:35:11,400
+خطوة أول خطوة زي ما اتفجناش بنثبت .. بنثبت صحة هذه
+
+472
+00:35:11,400 --> 00:35:15,340
+الجملة اللي سميتها واحد انا بتثبت صحتها لان بتساوي
+
+473
+00:35:15,340 --> 00:35:19,520
+واحد يعني لما نعود في الطرف الأيسر بواحد لازم يطلع
+
+474
+00:35:19,520 --> 00:35:22,660
+ل .. بيساوي الطرف الأيسر لما .. لأي من لما نعود
+
+475
+00:35:22,660 --> 00:35:26,420
+فيه بواحد ده نجرب لان basic step for ان بتساوي
+
+476
+00:35:26,420 --> 00:35:31,780
+واحدsince الان لما نعوض هنا بواحد بيصير بس واحد
+
+477
+00:35:31,780 --> 00:35:36,200
+يعني ماكنت جمعتش ولا شي لسه بيساوي واحد لأن الطرف
+
+478
+00:35:36,200 --> 00:35:40,380
+الأيمن هنا ايش هو بيصير واحد في واحد زائد واحد
+
+479
+00:35:40,380 --> 00:35:43,900
+واحد زائد واحد اتنين في واحد بواحد يعني اتنين على
+
+480
+00:35:43,900 --> 00:35:49,270
+اتنين يساوي واحد اذا بما ان هذا الطرفبساوي واحد
+
+481
+00:35:49,270 --> 00:35:53,450
+بساوي اللي هو الطرف الأيصر إذا صارت اللي هي واحد
+
+482
+00:35:53,450 --> 00:35:57,110
+هذه الجملة واحد مقصود فيها الجملة دي كلها صارت هذه
+
+483
+00:35:57,110 --> 00:36:01,910
+الجملة واحد is true for one بتساوي واحد رقمتها انا
+
+484
+00:36:01,910 --> 00:36:05,850
+واحد عساس ان أسهر يسهر سهل التعامل معها إذا صارت
+
+485
+00:36:05,850 --> 00:36:09,030
+هذه عبارة عن صحيحة لان بتساوي واحد إذا ال basic
+
+486
+00:36:09,030 --> 00:36:13,830
+step اتحققاتي الآن بدنا نفترض صحة بدنا نيجي إلى ال
+
+487
+00:36:13,830 --> 00:36:17,960
+inductive stepاللي هي inductive hypothesis اللي هي
+
+488
+00:36:17,960 --> 00:36:23,100
+فرضية الاستقرار اللي هي أش بتقول نفترض أن الجملة
+
+489
+00:36:23,100 --> 00:36:28,020
+صحيحة assume that واحد is true for أن بتساوي كي
+
+490
+00:36:28,020 --> 00:36:32,200
+بدنا نفترض أن صحة الجملة هذه لأن بتساوي كي مدام
+
+491
+00:36:32,200 --> 00:36:36,920
+فرضنا صحتها لأن بتساوي كي إذا واحد زائد اتنين لما
+
+492
+00:36:36,920 --> 00:36:41,810
+نقصل عند كيهيها هتساوي هذه K يا دماغها مش K مش N
+
+493
+00:36:41,810 --> 00:36:47,470
+بتساوي K في K زائد واحد بتساوي K في K زائد واحد
+
+494
+00:36:47,470 --> 00:36:51,790
+إذن مدام فرضت إن هذا صحيح على K بشيل ال N و بحط
+
+495
+00:36:51,790 --> 00:36:55,450
+مكانها K وهذا اللي هي induction hypothesis ال N
+
+496
+00:36:55,450 --> 00:37:02,110
+منها بدي أثبت now we prove that one is true for N
+
+497
+00:37:02,110 --> 00:37:06,550
+إيش بتساوي K زائد واحد يعني بمعنى أخر إيش بدي أثبت
+
+498
+00:37:06,550 --> 00:37:12,720
+we prove that1 زائد 2 زائد k زائد 1 ماشي الحال إذا
+
+499
+00:37:12,720 --> 00:37:15,480
+واحد زائد اتنين لما الأصل عند k زائد واحد لأنه
+
+500
+00:37:15,480 --> 00:37:18,760
+شيلت الان إشمالها k زائد واحد طبعا الجاب اللي k
+
+501
+00:37:18,760 --> 00:37:20,880
+زائد واحد هي ال k زي ما احنا عارفين أنه بنجمع واحد
+
+502
+00:37:20,880 --> 00:37:23,890
+زائد اتنين زائد تلت زائد أربعة الاخرينبدأ أثبت
+
+503
+00:37:23,890 --> 00:37:27,630
+بساوة مين أشيل كل K و أضع مكانها K زائد واحد يعني
+
+504
+00:37:27,630 --> 00:37:31,690
+K زائد واحد في اللي هي برضه K زائد واحد زائد واحد
+
+505
+00:37:31,690 --> 00:37:34,850
+على اتنين يعني الآن أنا بدأ أثبت هذه الجملة
+
+506
+00:37:34,850 --> 00:37:38,990
+بالاستعانة بمين بال induction hypothesis اللي
+
+507
+00:37:38,990 --> 00:37:43,150
+فرضته هذا اللي هي دي K في K بساوة K في K زائد واحد
+
+508
+00:37:43,150 --> 00:37:46,910
+على اتنين دعونا نشوف كده الآن ناخد الطرف الأيمن
+
+509
+00:37:46,910 --> 00:37:52,010
+هذا proofنروف لهذه .. نروف لهذه هي عندنا أخدت
+
+510
+00:37:52,010 --> 00:37:56,750
+الطرف الأيسر هنا هي من هنا لهنا بدأ أشيل هذا من
+
+511
+00:37:56,750 --> 00:38:00,970
+هنا لهنا واحد زائد اتنين و أتقل عند ال K و أعوضها
+
+512
+00:38:00,970 --> 00:38:05,370
+من هذا اللي فرضته هذا معناه جن عنها دي K حسب هنا
+
+513
+00:38:05,370 --> 00:38:10,050
+إيش هذي بيصير بدل هذه من هنا لهنا اللي هي K في K
+
+514
+00:38:10,050 --> 00:38:13,830
+زائد واحد على اتنين بعوض عنها بيصير K في K زائد
+
+515
+00:38:13,830 --> 00:38:18,790
+واحد على اتنين زائد الأصلي هذه K زائد واحدالان هنا
+
+516
+00:38:18,790 --> 00:38:21,670
+بده واحد المقامات هنا المقام اللي تحت واحد هنا
+
+517
+00:38:21,670 --> 00:38:26,310
+اتنين بل لما واحدهم بيصير كيف ك زائد واحد زائد
+
+518
+00:38:26,310 --> 00:38:30,790
+اللي هو مين اتنين في ك زائد واحد الكل على اتنين
+
+519
+00:38:30,790 --> 00:38:35,050
+عشان واحدة المقاماتو يساوي الان هنا في عامل مشترك
+
+520
+00:38:35,050 --> 00:38:37,710
+بقدر اخد ال K زائد واحد ايش ما لها عامل مشترك
+
+521
+00:38:37,710 --> 00:38:41,510
+فباخد عامل مشترك من هنا اللي هي ال K زائد واحد من
+
+522
+00:38:41,510 --> 00:38:45,290
+هنا بظل اللي هي ال K و هنا بظل التنين فبصير مضروبة
+
+523
+00:38:45,290 --> 00:38:48,770
+في ال K زائد التنين و الكل مكسوم على اتنين هذه
+
+524
+00:38:48,770 --> 00:38:52,950
+بالظبط هي عبارة عن K زائد واحد مضروبة في ال K زائد
+
+525
+00:38:52,950 --> 00:38:56,810
+اتنين هي عبارة عن K زائد واحد زائد واحد على اتنين
+
+526
+00:38:56,810 --> 00:39:02,330
+اذا صارت اللي هو هذا المقداربساوي هذا المقدار يعني
+
+527
+00:39:02,330 --> 00:39:08,730
+أثبتت اللي هو هذه اللي هو أثبتت صحة واحد لمين لان
+
+528
+00:39:08,730 --> 00:39:12,610
+بتساوي K زائد واحد ومدام أثبتتها لK زائد واحد
+
+529
+00:39:12,610 --> 00:39:15,910
+معناته أنا اللي هو خلصت ال induction hypothesis
+
+530
+00:39:15,910 --> 00:39:19,570
+معناته جملتيها دي صارت صحيحة لكل N element in N
+
+531
+00:39:19,570 --> 00:39:23,630
+يعني لو لخصنا أيش اللي سوناه أثبتنا صحة هذه أول
+
+532
+00:39:23,630 --> 00:39:28,010
+إشي لان بتساوي واحد و بعدين فرضنا صحتها لان بتساوي
+
+533
+00:39:28,010 --> 00:39:33,240
+Kومنها أثبتنا صحتها ل K زائد واحد وهذا كله على بعض
+
+534
+00:39:33,240 --> 00:39:35,920
+هو اللي بنسميه ال mathematical induction أو
+
+535
+00:39:35,920 --> 00:39:40,240
+الاستقراء الرياضي وبكون هيك أثبتناها لكل N element
+
+536
+00:39:40,240 --> 00:39:43,540
+in N ناخد مثال أخر شوفوا المثال صلوا على النبي
+
+537
+00:39:43,540 --> 00:39:46,600
+عليه الصلاة والسلام اللي بيقول show that N أصغر من
+
+538
+00:39:46,600 --> 00:39:51,320
+2N لكل N element in N طبعا عارفينها ديالان كيف
+
+539
+00:39:51,320 --> 00:39:54,420
+نرتبطها؟ برضه بنرتبطها بـ Mathematical Induction
+
+540
+00:39:54,420 --> 00:39:58,880
+لأنه اللي هي جملة تعتمد على اللي هو ال integers أو
+
+541
+00:39:58,880 --> 00:40:02,180
+الأعداد الطبيعية نشوف ال proof أول حاجة ال basic
+
+542
+00:40:02,180 --> 00:40:06,380
+stepال basic step اللي هي P of واحد هذا سمنها
+
+543
+00:40:06,380 --> 00:40:10,600
+الجملة P of n يعني P of واحد يعني n عند n بتساوي
+
+544
+00:40:10,600 --> 00:40:15,400
+واحد هذه بتساوي واحد وهذه بتساوي اتنين صح؟ اذا
+
+545
+00:40:15,400 --> 00:40:19,160
+الواحد اصغر من اتنين اذا فعلا اللي هي n اللي هي
+
+546
+00:40:19,160 --> 00:40:23,700
+واحد اصغر من اتنين is true دائما يعني صارت ال P
+
+547
+00:40:23,700 --> 00:40:27,660
+واحد is true لإن الواحد اصغر من اتنين في واحد اللي
+
+548
+00:40:27,660 --> 00:40:31,640
+هو بيساوي ايش اتنينالـ Inductive step بدنا نفترض
+
+549
+00:40:31,640 --> 00:40:37,060
+الآن Assume that B of K is true وبدنا نثبت منها
+
+550
+00:40:37,060 --> 00:40:41,200
+إنها BK زائد واحد is true إذن الآن بدنا نفترض إن B
+
+551
+00:40:41,200 --> 00:40:47,440
+of K is true يعني نفترض صحة هذه الجملة عند K عند N
+
+552
+00:40:47,440 --> 00:40:52,240
+بالساوية K مثلا مثلا هي عند K إذن K أصغر من 2Kطيب،
+
+553
+00:40:52,240 --> 00:40:56,560
+لأن we need to show that B of K زائد واحد is true
+
+554
+00:40:56,560 --> 00:41:00,360
+يعني بدنا نثبت صحة الجملة عند K زائد واحد، إيش
+
+555
+00:41:00,360 --> 00:41:04,460
+يعني؟ بدنا نثبت صحة إن K زائد واحد هي أصغر من
+
+556
+00:41:04,460 --> 00:41:08,300
+اتنين في K زائد واحد، لو أثبتنا هذه، بيكون خلصنا
+
+557
+00:41:08,300 --> 00:41:12,890
+ال induction hypothesisطيب الان بدنا نتبت هذه الان
+
+558
+00:41:12,890 --> 00:41:17,530
+بدي استخدم اكيد هذه عند ال K أصغر من ال 2 K ماشي
+
+559
+00:41:17,530 --> 00:41:21,870
+الحال منها لو ضفت الان واحد ده الجهتين بيصير K
+
+560
+00:41:21,870 --> 00:41:26,810
+زائد واحد أصغر من اتنين K زائد واحد اكيد بتطلع صح
+
+561
+00:41:26,810 --> 00:41:32,080
+يعنيالان عند ال K زائد واحد اصغر من اتنين K زائد
+
+562
+00:41:32,080 --> 00:41:36,220
+اتنين اكيد لان هذا زيادة عن هذا بواحد طيب من هدولة
+
+563
+00:41:36,220 --> 00:41:41,740
+مع بعض التنتين بيصير اتنين K زائد واحد هذه اصغر من
+
+564
+00:41:41,740 --> 00:41:45,800
+اتنين K اتنين في K زائد واحد اخدت اتنين ايه شمالها
+
+565
+00:41:45,800 --> 00:41:52,940
+عامل مشترك الان اثبتت هذهمن هذه وهذه أثبتها من فوق
+
+566
+00:41:52,940 --> 00:41:57,840
+التامتين مع بعض together بيصير عنده اللي هو k زائد
+
+567
+00:41:57,840 --> 00:42:01,700
+واحد أصغر من هذه وهذه بدورها أصغر من هذه إذا
+
+568
+00:42:01,700 --> 00:42:05,660
+بخاصية التعد هذه أصغر من هذه يعني k زائد واحد أصغر
+
+569
+00:42:05,660 --> 00:42:09,600
+من اتنين في k زائد واحد وبهيك احنا بنكون أثبتنا
+
+570
+00:42:09,600 --> 00:42:14,000
+اللي هو صحة الجملة عند k زائد واحد اللي هي اللي
+
+571
+00:42:14,000 --> 00:42:19,040
+فوق هذه معناته إذا صارت صحيح على كل element inويا
+
+572
+00:42:19,040 --> 00:42:24,880
+سيدي هاي كمان اللي هو الآن بنصل ل اللي هو عندي ال
+
+573
+00:42:24,880 --> 00:42:29,600
+homework اللي بدنا ياه اللي هو للمحاضرة هذه كلها
+
+574
+00:42:29,600 --> 00:42:34,080
+على طرق البرهان اللي هو ال direct proof أو ال
+
+575
+00:42:34,080 --> 00:42:37,700
+indirect proof أو ال mathematical induction وإلى
+
+576
+00:42:37,700 --> 00:42:41,600
+لقاء آخر السلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3eaa4e819035cc8faccb0b22d6952ba2a8672a8c
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA.srt
@@ -0,0 +1,1195 @@
+1
+00:00:00,000 --> 00:00:05,100
+بسم الله الرحمن الرحيم هذه هي المحاضرة الأولى
+
+2
+00:00:05,100 --> 00:00:11,520
+لمادة رياضيات منفصلة لطلاب وطالبات الجامعة
+
+3
+00:00:11,520 --> 00:00:16,680
+الإسلامية كلية  Technology المعلومات قسم الحوسبة
+
+4
+00:00:16,680 --> 00:00:24,200
+المتنقلة المحاضرة الأولى بعد حالة الطوارئ
+
+5
+00:00:26,540 --> 00:00:33,800
+عنوان المحاضرة الـ Matrices أو إكمال محاضرة
+
+6
+00:00:33,800 --> 00:00:39,300
+Matrices التي بدأناها سابقًا كنا عرفنا شو معناتها
+
+7
+00:00:39,300 --> 00:00:46,300
+Matrix وقلنا اللي هو شو معناتها أنه درجة الـ Matrix M
+
+8
+00:00:46,300 --> 00:00:53,050
+by N يعني عدد الصفوف M وعدد الأعمدة N وعرفنا أيضًا
+
+9
+00:00:53,050 --> 00:00:57,930
+اللي هو شو معناه تجمع two Matrices قبل هيك وقلنا
+
+10
+00:00:57,930 --> 00:01:02,170
+عشان نجمع اللي هو مصفوفتين لازم يكون المصفوفتين
+
+11
+00:01:02,170 --> 00:01:06,050
+نفس الدرجة يعني لو كانت المصفوفة الأولى ثلاثة في
+
+12
+00:01:06,050 --> 00:01:09,820
+ثلاثة بدها تكون المصفوفة الثانية اللي بنجمعها هيها
+
+13
+00:01:09,820 --> 00:01:12,740
+أيضًا ثلاثة في ثلاثة وعملية الجمع زي ما أنتم
+
+14
+00:01:12,740 --> 00:01:17,740
+عارفين كل Entry مع الـ Entry المقابل له بعد هيك
+
+15
+00:01:17,740 --> 00:01:21,980
+عرفنا عملية الضرب اللي هو two Matrices وقلنا عشان
+
+16
+00:01:21,980 --> 00:01:27,380
+نضرب الـ Matrix اللي درجته m by k لازم اللي هو يكون
+
+17
+00:01:27,380 --> 00:01:31,660
+الـ Matrix الثاني k by something يعني k by n يعني
+
+18
+00:01:31,660 --> 00:01:35,780
+عدد اللي هو الأعمدة في الـ Matrix الأول يساوي عدد
+
+19
+00:01:35,780 --> 00:01:39,640
+الصفوف في الـ Matrix الثاني عشان اللي هو اللي هو
+
+20
+00:01:39,640 --> 00:01:44,640
+تكون عملية الضرب بين a و b عملية معرفة وقلنا كيف
+
+21
+00:01:44,640 --> 00:01:48,560
+اللي هي عملية الضرب اللي هو مصفوفتين مع بعض و
+
+22
+00:01:48,560 --> 00:01:52,380
+قلنا عشان نضرب مصفوفتين هي المصفوفة هذه مثلًا من
+
+23
+00:01:52,380 --> 00:01:56,020
+الدرجة اللي هو هاي صفين ثلاثة أربعة من الدرجة
+
+24
+00:01:56,020 --> 00:02:01,560
+أربعة في ثلاثة يعني أربع مصفوف .. أربع صفوف و ثلاث
+
+25
+00:02:01,560 --> 00:02:07,020
+أعمدة بنضربها في مصفوفة ثانية ثلاث صفوف وعمودين
+
+26
+00:02:07,020 --> 00:02:10,960
+معناته عملية الضرب جائزة وبيصير عملية الضرب ميج
+
+27
+00:02:10,960 --> 00:02:15,000
+بنضرب الصف اللي هو الأول في العمود الأول بنضرب
+
+28
+00:02:15,000 --> 00:02:19,240
+واحد في اثنين زائد صفر في واحد زائد أربعة في ثلاثة
+
+29
+00:02:19,240 --> 00:02:23,380
+و اللي بيطلع عندي بيكون هو الـ Entry الأول عند ال
+
+30
+00:02:23,380 --> 00:02:28,440
+C11 بنفس الأسلوب اللي هو بناخد اللي هو
+
+31
+00:02:28,440 --> 00:02:33,350
+الصف الأول في العمود الثاني بنحصل على العنصر C12
+
+32
+00:02:33,350 --> 00:02:39,390
+وخلصنا من السطر الأول بنجي للسطر الثاني في العمود
+
+33
+00:02:39,390 --> 00:02:44,130
+الأول بنجيب أول واحد في السطر الثاني في حصل نتج
+
+34
+00:02:44,130 --> 00:02:49,450
+الضرب وهكذا لما نكمل اللي هو المصفوفة كامل اللي هي
+
+35
+00:02:49,450 --> 00:02:54,990
+عملية الضرب كما شرحناها سابقًا ما فيش داعي أننا
+
+36
+00:02:54,990 --> 00:03:00,450
+نعيدها وأخدنا أمثلة على ضرب مصفوفات وقلنا المصفوفة
+
+37
+00:03:00,450 --> 00:03:04,590
+A B ليس شرطًا أنها تساوي المصفوفة B A وهيعني مثال
+
+38
+00:03:04,590 --> 00:03:09,230
+على ذلك بعدين عرفنا شو معناتها مصفوفة الوحدة مصفوفة
+
+39
+00:03:09,230 --> 00:03:12,110
+الوحدة اللي بيكون عناصر القطر الرئيسي واحد واحد
+
+40
+00:03:12,110 --> 00:03:15,650
+والباقي عناصرها أصفار سواء مصفوفة الوحدة من درجة
+
+41
+00:03:15,650 --> 00:03:18,970
+اثنين في اثنين أو مصفوفة الوحدة من درجة ثلاثة في
+
+42
+00:03:18,970 --> 00:03:24,570
+ثلاثة بنفس الأسلوب عرفنا اللي هو مدور المصفوفة أو A
+
+43
+00:03:24,570 --> 00:03:29,230
+Transpose اللي هي عملية تحويل الصفوف إلى أعمدة و
+
+44
+00:03:29,230 --> 00:03:36,390
+قلنا كيف بنحولها سابقًا قلنا عملية ضرب A R المتكررة
+
+45
+00:03:36,390 --> 00:03:40,890
+A R معناته أنه ضربنا الـ Matrix في نفسه R من المرات
+
+46
+00:03:40,890 --> 00:03:44,810
+لما نقول A أو الصفر نعني البقية اللي هو المصفوفة
+
+47
+00:03:44,810 --> 00:03:50,320
+المصفوفة الوحدة اللي هي من الدرجة اللي هي النية حسب
+
+48
+00:03:50,320 --> 00:03:54,980
+اللي هي الـ A اللي بنحكي عنها عرفنا شو معناتها اللي
+
+49
+00:03:54,980 --> 00:04:02,000
+هو الـ Matrix يكون Symmetric وبعدين أجينا اللي هو
+
+50
+00:04:02,000 --> 00:04:06,220
+وصلنا للموضوع اللي احنا اليوم بدنا نفصل فيه و
+
+51
+00:04:06,220 --> 00:04:10,400
+حكينا برضه مقدمة فيه في المحاضرة قلنا اللي هو حاجة
+
+52
+00:04:10,400 --> 00:04:15,040
+اسمها Zero One Matrix هذه عبارة عن مصفوفة كل
+
+53
+00:04:15,040 --> 00:04:19,640
+عناصرها عبارة عن يا صفر يا واحد عناصر المصفوفة يا
+
+54
+00:04:19,640 --> 00:04:23,920
+صفر يا واحد في عندنا عملية بدنا نجريها بين
+
+55
+00:04:23,920 --> 00:04:27,780
+المصفوفات اسمها الـ Boolean Operations الـ Boolean
+
+56
+00:04:27,780 --> 00:04:33,220
+Operations بين اللي هي المصفوفتين هنعرفها بعد شوية
+
+57
+00:04:33,220 --> 00:04:39,570
+اللي هي أو عملية الضرب البولينية أول شيء بدنا نعرف
+
+58
+00:04:39,570 --> 00:04:44,010
+شو معناتها الـ Boolean Operation بين الصفر والواحد
+
+59
+00:04:44,010 --> 00:04:48,510
+اللي هما عناصر الـ 01 Matrix اللي احنا بدنا نجري
+
+60
+00:04:48,510 --> 00:04:53,870
+عليه عملية الـ Boolean Operation وبرضه ذكرناها في
+
+61
+00:04:53,870 --> 00:04:59,570
+المحاضرة قلنا عشان بدنا نعرف شو معناتها عمليتين الـ
+
+62
+00:04:59,570 --> 00:05:02,970
+Boolean Operations عندنا اللي هي الـ Meet والـ Join
+
+63
+00:05:03,390 --> 00:05:06,670
+وقلنا نتخيل الـ Meet والـ Join طبعًا الـ B1 والـ B2
+
+64
+00:05:06,670 --> 00:05:10,850
+هدول اللي بنعملهم Meet أو نعملهم Join هدول الـ B1
+
+65
+00:05:10,850 --> 00:05:15,610
+والـ B2 يا بياخد صفر يا بياخد ايش واحد فالآن عملية
+
+66
+00:05:15,610 --> 00:05:22,070
+الـ Meet اللي هي بتذكرنا وكأنه احنا قلنا أنه بنذكر
+
+67
+00:05:22,070 --> 00:05:26,890
+اللي هي عملية الـ And والـ Join عملية الـ Or و
+
+68
+00:05:26,890 --> 00:05:31,070
+بنتخيل أن الواحد هو عبارة عن الـ True والصفر
+
+69
+00:05:31,070 --> 00:05:36,030
+False فبكون اللي هي ال .. ال .. ال .. ال .. الجملة
+
+70
+00:05:36,030 --> 00:05:40,850
+اللي فيها الـ And True اللي هي في حال .. ال .. ال
+
+71
+00:05:40,850 --> 00:05:45,590
+.. في حالة واحدة لما يكون التمتين True يعني بكون
+
+72
+00:05:45,590 --> 00:05:49,210
+كلهم False في حالة اللي هي التمتين False أو أي
+
+73
+00:05:49,210 --> 00:05:53,470
+واحدة فيهم True فبيصير عندي الآن الواحد وواحد
+
+74
+00:05:53,470 --> 00:05:59,040
+الواحد Meet الواحد واحد والباقي الحالات كلها هيطلع
+
+75
+00:05:59,040 --> 00:06:05,040
+عندي صفر الـ Join اللي هو بتكون اللي هو False في
+
+76
+00:06:05,040 --> 00:06:09,560
+حالة واحدة لما نكون عندي التنتين False وباقي
+
+77
+00:06:09,560 --> 00:06:14,200
+الحالات ايش بتروا لكن الآن بعد شوية هعلمكم طريقة
+
+78
+00:06:14,200 --> 00:06:18,320
+اللي هو بتسهل عليكم اللي هو إيجاد الـ Join والـ
+
+79
+00:06:18,320 --> 00:06:23,560
+Meet بكل سهولة بس خليني الآن نيجي نعرف شو معناتها
+
+80
+00:06:23,560 --> 00:06:28,380
+الـ Join بين اللي هو two Matrices يعني عند الـ Matrix
+
+81
+00:06:28,380 --> 00:06:33,900
+A والـ Matrix B عشان نعملهم Join بين الـ A والـ B
+
+82
+00:06:33,900 --> 00:06:38,620
+لازم زي عملية الجمع يكون اللي هو الـ Order للإثنين
+
+83
+00:06:38,620 --> 00:06:42,600
+اللي هي نفس الـ Order يعني لو كان الـ A من الـ Order
+
+84
+00:06:42,600 --> 00:06:46,840
+m by n لازم يكون الـ B برضه من الـ Order m by
+
+85
+00:06:46,840 --> 00:06:51,170
+n يعني اللي هي نفس الدرجة كذلك عملية الـ Meet
+
+86
+00:06:51,170 --> 00:06:54,930
+برضه بين الـ A والـ B، A Meet B برضه لازم يكون
+
+87
+00:06:54,930 --> 00:07:00,970
+الإثنتين اللي هي بنفس الدرجة وعملية اللي هي الـ
+
+88
+00:07:00,970 --> 00:07:06,170
+Meet أو الـ Joined في روحة شبيهة بعملية الجمع يعني
+
+89
+00:07:06,170 --> 00:07:12,290
+كل بمعنى آخر أنه كل عنصر بنعمله Join مع العنصر
+
+90
+00:07:12,290 --> 00:07:16,250
+اللي مقابل له والـ Meet برضه نفس الشيء خليني أخد
+
+91
+00:07:16,250 --> 00:07:19,480
+مثال، تشوفوا الصلاة والنبي عليه الصلاة والسلام نجي
+
+92
+00:07:19,480 --> 00:07:23,400
+للمثال الأول بقول Find the Join and Meet of the 0
+
+93
+00:07:23,400 --> 00:07:28,440
+,1 Matrix 0,1 Matrices اللي أنا عندي لأن في عندي
+
+94
+00:07:28,440 --> 00:07:31,920
+مصفوفتين مصفوفة الأولى واضح من الدرجة واحدة اللي هي
+
+95
+00:07:31,920 --> 00:07:36,260
+2 في عدد الأعمدة ثلاثة اثنين في ثلاثة والثانية بيه
+
+96
+00:07:36,260 --> 00:07:38,660
+في اثنين في ثلاثة ايه ده من الاثنين من نفس الدرجة
+
+97
+00:07:38,660 --> 00:07:44,810
+إذا الخطوة الأولى نحو اتجاه أننا نعرف اللي هي
+
+98
+00:07:44,810 --> 00:07:50,730
+موجودة فخليني أنا بقول إذا Join of A and B ايه
+
+99
+00:07:50,730 --> 00:07:56,030
+Join بيه ايش بده بناخد كل الـ Entry مع اللي عاجبه
+
+100
+00:07:56,030 --> 00:08:00,280
+عند الواحد Or اللي هو Mean الصفر أو Join الصفر و
+
+101
+00:08:00,280 --> 00:08:04,920
+الصفر Or الواحد والواحد Or الصفر هي واحد Or الصفر و صفر
+
+102
+00:08:04,920 --> 00:08:10,680
+Or الواحد ونفس الشيء واحد Or الصفر هي وهنا صفر Or ال
+
+103
+00:08:10,680 --> 00:08:16,640
+واحد وهنا واحد Or الواحد وهنا صفر Or الصفر بدنا نعمل هنا
+
+104
+00:08:16,640 --> 00:08:22,220
+الـ Join هذه أريحكم الـ Join بس خد العدد الأكبر من
+
+105
+00:08:22,220 --> 00:08:26,100
+هنا واحد ولا صفر من العدد واحد مين الأكبر هنا؟
+
+106
+00:08:26,100 --> 00:08:29,720
+واحد مين الأكبر هنا؟ واحد مين الأكبر هنا؟ واحد،
+
+107
+00:08:29,720 --> 00:08:32,080
+مين الأكبر هنا؟ واحد مين الأكبر هنا؟ اللي هو
+
+108
+00:08:32,080 --> 00:08:36,660
+الصفر إذا الـ Join اللي هو بتاخد الأكبر فيهم،
+
+109
+00:08:36,660 --> 00:08:39,620
+الأكبر بين الواحد وبين الصفر أو بين الصفر والصفر
+
+110
+00:08:39,620 --> 00:08:43,480
+أو بين الواحد والواحد واضحة بتصور، نيجي الآن ال
+
+111
+00:08:43,480 --> 00:08:47,000
+Meet الـ Meet مين الأصغر؟ وأنت بتيجي ايه؟ الآن
+
+112
+00:08:47,000 --> 00:08:50,700
+معلش نستذكر True و False ومش عارف ايش مع أنه
+
+113
+00:08:50,700 --> 00:08:55,280
+سهل الـ True والـ False اللي بده أحد الطريقين اللي هو
+
+114
+00:08:55,280 --> 00:09:01,200
+أسهلكم الآن The Meet of A and B is A Meet B A Meet
+
+115
+00:09:01,200 --> 00:09:05,820
+B اللي هو بيجي الآن مع كل عنصر A Meet صفر صفر
+
+116
+00:09:05,820 --> 00:09:10,960
+Meet واحد واحد Meet صفر الآن نفس الشيء صفر Meet
+
+117
+00:09:10,960 --> 00:09:15,990
+واحد واحد Meet واحد And صفر Meet صفر هاي اللي هنا
+
+118
+00:09:15,990 --> 00:09:22,170
+اللي هي A Meet B الآن الـ A Meet B نيجي للواحد Or
+
+119
+00:09:22,170 --> 00:09:24,670
+صفر زي ما قلنا بتاخد الصغير بيطلع الصفر بتاخد
+
+120
+00:09:24,670 --> 00:09:27,370
+الصغير بيطلع الصفر بتاخد الصغير بيطلع الصفر بتاخد
+
+121
+00:09:27,370 --> 00:09:30,350
+الصغير بيطلع الصفر وهنا الصغير واحد اللي هو بين
+
+122
+00:09:30,350 --> 00:09:34,430
+الواحد والواحد والصغير هنا صفر أو صفر إذن هاي
+
+123
+00:09:34,430 --> 00:09:39,830
+معناها الـ Join بين two Matrices وهي معناتها الـ Meet
+
+124
+00:09:39,830 --> 00:09:46,100
+بين two Matrices الآن بدنا نعرف Boolean Product الـ
+
+125
+00:09:46,100 --> 00:09:49,800
+Boolean Product بين two Matrices صلوا على النبي
+
+126
+00:09:49,800 --> 00:09:53,500
+عليه الصلاة والسلام الآن الـ Boolean product بين
+
+127
+00:09:53,500 --> 00:09:59,780
+ال matrix A و ال matrix B بروح 
+
+128
+00:09:59,780 --> 00:10:05,060
+الطريقة العادية لكن بواسطة ال join و ال meet وكأنه
+
+129
+00:10:05,060 --> 00:10:11,810
+بده يصير عند ال meet بلعب دور الضرب و الـ join بلعب 
+
+130
+00:10:11,810 --> 00:10:16,310
+دور اللي هو إيش الجمع؟ اتخيل إنه أنت بتضرب two
+
+131
+00:10:16,310 --> 00:10:21,370
+matrices ضرب عادي بس بدل ما تحط عملية الضرب حط 
+
+132
+00:10:21,370 --> 00:10:25,930
+عملية الـ join و بدل ما تحط... آسف عملية ال meet و
+
+133
+00:10:25,930 --> 00:10:32,350
+بدل ما تحط عملية الجمع حط عملية مين؟ الـ join هذه
+
+134
+00:10:32,350 --> 00:10:35,850
+وما بيكونش ولا شيء جديد و زي الضرب العادي اللي
+
+135
+00:10:35,850 --> 00:10:42,570
+بنعرفه بالظبط لحتى إن عدد درجات الـ A هيكون N by
+
+136
+00:10:42,570 --> 00:10:48,990
+K Matrix لازم درجة الـ B يكون مقاسه اللي هو يبدأ 
+
+137
+00:10:48,990 --> 00:10:55,450
+بـ K by N Matrix يعني الاتنين والعدد الأولاني عدد
+
+138
+00:10:55,450 --> 00:11:00,360
+الأعمدة اللي فيه لازم يساوي عدد السطور اللي في مين؟
+
+139
+00:11:00,360 --> 00:11:05,460
+في الـ matrix اللي هو الثاني لتشوف مثال عملي
+
+140
+00:11:05,460 --> 00:11:09,900
+أمامنا هذه عند الـ A وهذه عند الـ B بيقول لي find
+
+141
+00:11:09,900 --> 00:11:13,920
+the Boolean product of A and B where إذا بدنا نوجد
+
+142
+00:11:13,920 --> 00:11:18,710
+اللي هو الـ Boolean product اللي هو بين الـ A و الـ
+
+143
+00:11:18,710 --> 00:11:22,630
+B ماشي يا جماعة؟ طيب الآن عشان وجود الـ Boolean
+
+144
+00:11:22,630 --> 00:11:25,590
+Product بمش بسأل حالنا أصلا يعني هذا هو Zero
+
+145
+00:11:25,590 --> 00:11:28,930
+Matrix وهذا Zero Matrix إذا بنحكي فعلا عن Boolean
+
+146
+00:11:28,930 --> 00:11:34,130
+Product طيب هل هذا درجته اللي هو واحد، اثنين،
+
+147
+00:11:34,130 --> 00:11:41,580
+ثلاثة صفوف عمودين؟ أه وهذا قداش؟ اللي هو درجته 
+
+148
+00:11:41,580 --> 00:11:45,860
+ثلاثة في اثنين وهذا درجته اثنين في ثلاثة إذا اللي
+
+149
+00:11:45,860 --> 00:11:50,560
+هو عملية الضرب إيه شمالها جائزة ومعرفة الـ Boolean
+
+150
+00:11:50,560 --> 00:11:55,080
+Product معرفة عملية الضرب في هذه الحالة نشوف كيف
+
+151
+00:11:55,080 --> 00:11:59,830
+نوجدها شوفوا عليها لأن بدي آجي زي ما قلنا بتخيل
+
+152
+00:11:59,830 --> 00:12:04,710
+حالنا إننا بنضرب ضرب عادي باجي على اللي هو بس اللي
+
+153
+00:12:04,710 --> 00:12:11,770
+هو بنغير عملية الضرب بـJoin وعملية اللي هي الجمع
+
+154
+00:12:11,770 --> 00:12:21,180
+بنبدل عملية الضرب بـmeet وعملية الجمع بـjoin بنشوف
+
+155
+00:12:21,180 --> 00:12:27,200
+كيف لأن نيجي هنا والسطر الأول بنيجي بنقول واحد
+
+156
+00:12:27,200 --> 00:12:30,240
+السطر الأول مع إيش؟ طبعا زي ما بنعمل في الضرب مع
+
+157
+00:12:30,240 --> 00:12:39,050
+العمود الأول واحد  وإيش مالهم؟ meet واحد Zero meet واحد و
+
+158
+00:12:39,050 --> 00:12:43,110
+بين الاتنين إيش مالهم؟ ال join هاي واحد meet الواحد و
+
+159
+00:12:43,110 --> 00:12:48,670
+Zero meet ال zero الآن خلصنا اللي هو السطر الأول مع
+
+160
+00:12:48,670 --> 00:12:52,430
+العمود الأول الآن السطر الأول مع مين؟ مع العمود
+
+161
+00:12:52,430 --> 00:13:00,490
+الثاني اللي هو واحد اللي هو and الواحد و Zero
+
+162
+00:13:00,490 --> 00:13:08,550
+and الواحد وبينهم عملية ال or وهذه meet وهذه join 
+
+163
+00:13:08,550 --> 00:13:14,610
+يمكن نقول and و or أسهل لكم الآن خلصنا من الجزء
+
+164
+00:13:14,610 --> 00:13:20,530
+الثاني نيجي للثالث واحد مع اللي هو ال zero واحد مع 
+
+165
+00:13:20,530 --> 00:13:24,850
+ال zero and و ال zero مع ال واحد and وبينهم إيش؟
+
+166
+00:13:24,850 --> 00:13:30,370
+or الآن بنعمل نفس الشيء السطر الثاني مع العمود
+
+167
+00:13:30,370 --> 00:13:34,050
+الأول السطر الثاني مع العمود الثاني السطر الثاني
+
+168
+00:13:34,050 --> 00:13:37,250
+مع العمود الثالث بيكون جبنا السطر الثاني في
+
+169
+00:13:37,250 --> 00:13:41,330
+المصفوفة الناتجة نيجي الآن نفس الشيء السطر الثالث
+
+170
+00:13:41,330 --> 00:13:45,570
+مع العمود الأول بتجيب ال entry هذا السطر الأول مع
+
+171
+00:13:45,570 --> 00:13:49,590
+هذا بتجيب ال entry اللي بعده وهكذا فبكون إحنا
+
+172
+00:13:49,590 --> 00:13:54,540
+حصلنا على ال job اللي هو ال boolean product الـ
+
+173
+00:13:54,540 --> 00:13:59,500
+Boolean product ندى الآن اللي هو على طول نحسب الآن
+
+174
+00:13:59,500 --> 00:14:05,260
+الـ... قلنا ال and إيش ماله؟ لصغير واحد والـ or هنا
+
+175
+00:14:05,260 --> 00:14:09,920
+لصغير صفر بينهم بدنا نأخذ الكبير ال join بده
+
+176
+00:14:09,920 --> 00:14:13,960
+الكبير هذا واحد وهذا صفر الكبير واحد ماشي الحال؟
+
+177
+00:14:13,960 --> 00:14:19,360
+على طول اللي بعده هنا واحد الصغير واحد والصغير هنا
+
+178
+00:14:19,360 --> 00:14:24,020
+صفر واحد ولا صفر الكبير هنا ال join كبير هذا ال or
+
+179
+00:14:24,020 --> 00:14:27,600
+كبير يعني بآخذ صغير هذه وصغير هذه مع كبير الكل
+
+180
+00:14:27,600 --> 00:14:31,860
+صغير هذه واحد وصغير هذه صفر كبير هنا الاثنين واحد
+
+181
+00:14:32,420 --> 00:14:36,240
+الآن صغير هذه صفر وصغير هذه صفر كبير هين إيش؟
+
+182
+00:14:36,240 --> 00:14:42,000
+هيُطلع صفر لأن هذه صغير هين صفر وهذه صغير هين صفر
+
+183
+00:14:42,000 --> 00:14:46,920
+إذا كبير هين الاثنين الاثنين لازم يطلع صفر لأن الصغير
+
+184
+00:14:46,920 --> 00:14:51,820
+هدول صفر وكبير هدول واحد الآن صار عندي صفر و
+
+185
+00:14:51,820 --> 00:14:56,180
+واحد كبير هين واحد طبعا نفس الشيء صغير هين صفر
+
+186
+00:14:56,180 --> 00:14:59,620
+هدول وهدول صغير هين واحد كبير الجهتين اللي
+
+187
+00:14:59,620 --> 00:15:04,730
+بيطلعين واحد الآن صغير هنا واحد صغير هنا صفر
+
+188
+00:15:04,730 --> 00:15:11,290
+كبير الجهتين واحد صغير هنا واحد وصغير هنا صفر
+
+189
+00:15:11,290 --> 00:15:16,770
+كبير هنا واحد فاهمين عليها؟ صغير هنا صفر وصغير
+
+190
+00:15:16,770 --> 00:15:21,990
+هنا صفر الصفر والصفر كبير هنا إيش؟ صفر واضح هذا
+
+191
+00:15:21,990 --> 00:15:24,370
+اللي هو ال boolean of product
+
+192
+00:15:26,860 --> 00:15:31,660
+الآن نأخذ مثال آخر لت إيه بتساوي إيه ال matrix
+
+193
+00:15:31,660 --> 00:15:35,040
+اللي أمامي هذا عبارة عن matrix ثلاثة في ثلاثة ويقول
+
+194
+00:15:35,040 --> 00:15:40,280
+لي find ما يليه ماشي ال matrices التالية بدي إيه؟
+
+195
+00:15:40,280 --> 00:15:44,740
+تربيع وإيه تكعيب وإيه أربعة وإيه خمسة وإيه n
+
+196
+00:15:45,300 --> 00:15:49,680
+إيش مقصود بالـ A تربيع؟ يعني A Boolean product مع A
+
+197
+00:15:49,680 --> 00:15:54,440
+A تكعيب Boolean product A مع A مع A ثلاث مرات يعني
+
+198
+00:15:54,440 --> 00:15:58,560
+A تربيع مع A نيجي نأخذ واحدة واحدة يا شباب ويا
+
+199
+00:15:58,560 --> 00:16:02,940
+بنات شوفوا صلوا على النبي عليه الصلاة والسلام عندي
+
+200
+00:16:02,940 --> 00:16:07,800
+الـ A الـ A تربيع بيساوي A اللي هو الـ Boolean
+
+201
+00:16:07,800 --> 00:16:12,570
+product مع الـ A A Boolean product مع الـ A اللي هو 
+
+202
+00:16:12,570 --> 00:16:17,050
+كما يلي بنجي بنحط الـ A هنا والـ A الثانية في
+
+203
+00:16:17,050 --> 00:16:22,910
+هذه الجهة الآن بنجي بناخد الصف مع مين؟ مع العمود
+
+204
+00:16:22,910 --> 00:16:28,250
+الآن الصغير الـ 0 والـ 0 اللي مع بعض صغير والكل
+
+205
+00:16:28,250 --> 00:16:32,430
+اللي يا كبير يعني الآن Zero مع Zero صغيرهم Zero
+
+206
+00:16:32,430 --> 00:16:36,890
+Zero مع واحد صغيرهم Zero واحد مع واحد صغيرهم واحد
+
+207
+00:16:36,890 --> 00:16:40,390
+إذا كبير الثلاثة اللي هي Zero و Zero و واحد اللي
+
+208
+00:16:40,390 --> 00:16:44,120
+هو هيطلع واحد طيب اللي ما... اللي ما... عارف اللي
+
+209
+00:16:44,120 --> 00:16:48,500
+ما... ماشي معه فادف ثانية الآن السطر الأول مع
+
+210
+00:16:48,500 --> 00:16:52,620
+العمود الثاني ماشي الآن السطر الأول Zero Zero
+
+211
+00:16:52,620 --> 00:16:56,360
+صغيرهن Zero Zero Zero صغيرهن Zero الواحد والواحد
+
+212
+00:16:56,360 --> 00:17:00,420
+صغيرهن الواحد الآن اكبير الثلاثة اللي طلع إن اللي 
+
+213
+00:17:00,420 --> 00:17:04,620
+عندي الصفر والصفر والواحد واحد فبيطلع عند إيش؟
+
+214
+00:17:04,620 --> 00:17:11,430
+اللي هو الناتج واحد لأن العمود هذا... آسف السطر هذا
+
+215
+00:17:11,430 --> 00:17:15,670
+الأول مع العمود الثالث الـ 0 والـ 1 صغيرهم Zero
+
+216
+00:17:15,670 --> 00:17:19,030
+الـ 0 والـ 0 صغيرهم Zero الـ 1 والـ 0 صغيرهم
+
+217
+00:17:19,030 --> 00:17:22,770
+Zero اللي هنطلع كله هذا Zero إذن كبيرهم إيش هيطلع؟
+
+218
+00:17:22,770 --> 00:17:27,550
+Zero بنفس الطريقة بناخد اللي هو السطر الثاني مع
+
+219
+00:17:27,550 --> 00:17:32,570
+العمود الأول واحد مع الـ 0 صغيرهن Zero Zero مع
+
+220
+00:17:32,570 --> 00:17:36,910
+الواحد صغيرهن Zero Zero مع الواحد صغيرهن Zero إذا
+
+221
+00:17:36,910 --> 00:17:40,970
+الثلاثة صغيرة هنا مش هيطلع اللي هو الـ Zero بنفس
+
+222
+00:17:40,970 --> 00:17:45,130
+الأسلوب بنطلع باقي اللي هي القيم فبكون عندي بيطلع
+
+223
+00:17:45,130 --> 00:17:48,950
+ال matrix هذا اللي أمامي لأن هذا الـ matrix اللي
+
+224
+00:17:48,950 --> 00:17:52,130
+أمامي هو الـ A تربيع بدي أوجد الـ A تكعيب الـ A
+
+225
+00:17:52,130 --> 00:17:55,350
+تكعيب إيش هتساوي؟ الـ A تربيع اللي طلع هذا هيو
+
+226
+00:17:55,350 --> 00:18:00,050
+جبناه الآن درق اللي هو Boolean product مع مين؟ مع الـ A
+
+227
+00:18:00,050 --> 00:18:04,190
+اللي هو الأصل هيو نيجي نضربهم مع بعض زي ما قلنا
+
+228
+00:18:04,190 --> 00:18:08,450
+قبل بشوية واحد و Zero صغير من Zero واحد واحد صغير
+
+229
+00:18:08,450 --> 00:18:13,090
+من واحد خلاص مدام طلع هنا واحد في الصغار واحد إذا
+
+230
+00:18:13,090 --> 00:18:17,780
+على طول الكبار هيطلع بينهم إيش؟ واحد ما كملش يعني لأن
+
+231
+00:18:17,780 --> 00:18:22,880
+هذا السطر مع العمود الثاني لأن واحد مع ال zero
+
+232
+00:18:22,880 --> 00:18:26,020
+zero واحد مع ال zero zero الصغير طبعا zero مع ال
+
+233
+00:18:26,020 --> 00:18:29,000
+zero zero ده نطلع كله نصفار ده هيطلع الكبير zero
+
+234
+00:18:29,000 --> 00:18:32,800
+لأن واحد مع الواحد طلع واحد مثلا واحد طلع واحد من
+
+235
+00:18:32,800 --> 00:18:36,260
+عملية اللي هو مين؟ صغيرهم هذا اللي اخذنا مين يا
+
+236
+00:18:36,260 --> 00:18:40,090
+جماعة؟ اللي اخذناه العمود السطر الأول مع العمود
+
+237
+00:18:40,090 --> 00:18:43,830
+الثالث واحد مع واحد لصغير واحد إذا ما يطلع الكبير
+
+238
+00:18:43,830 --> 00:18:45,770
+هنا إيش؟ ما يطلع من الباقي هيطلع الكبير هنا واحد
+
+239
+00:18:45,770 --> 00:18:50,110
+هاي واحد وبعدين بعمل السطر الثاني بنفس الأسلوب مع
+
+240
+00:18:50,110 --> 00:18:53,730
+العمود الأول والسطر الثاني بحصل على ال matrix اللي
+
+241
+00:18:53,730 --> 00:18:57,450
+أمامي اللي هو هذا هذا اللي طلع مين عندي؟ a تكعيب
+
+242
+00:18:57,450 --> 00:19:01,910
+تعال ال a تكعيب هذا بدي أضربه في ال a بيطلع مين؟ a
+
+243
+00:19:01,910 --> 00:19:04,810
+قوة أربعة يعني إيه؟ بدي a أربعة بيساوي a تكعيب اللي
+
+244
+00:19:04,810 --> 00:19:08,610
+طلعته من الخطوة هذه في a هايه a تكعيب وهيه ال a
+
+245
+00:19:09,070 --> 00:19:15,490
+لاحظ الآن واحد مع الـ 00 بالصغير، Zero مع السطر
+
+246
+00:19:15,490 --> 00:19:19,410
+الأول مع العمود الأول، نعيد نفس الكلام، واحد مع
+
+247
+00:19:19,410 --> 00:19:23,230
+الـ 00، Zero مع الواحد، Zero، واحد مع الواحد،
+
+248
+00:19:23,230 --> 00:19:27,290
+واحد، ده نطلع واحد، الآن اللي بعده، هذا السطر مع
+
+249
+00:19:27,290 --> 00:19:30,410
+هذا العمود، لاحظوا إنه هيتجي الواحد هذا مع الواحد،
+
+250
+00:19:30,410 --> 00:19:33,610
+ده هيطلع واحد منه، ده هيطلع الكل إيه شماله؟ واحد
+
+251
+00:19:33,810 --> 00:19:38,370
+نجي لهذا هيلتقي مع هذا مع الواحد مادام واحد التجهيز
+
+252
+00:19:38,370 --> 00:19:41,870
+مع الواحد إذا أصغر الواحدين واحد إذا الكبير
+
+253
+00:19:41,870 --> 00:19:46,750
+الناتج بيطلع إيش واحد إذا هذا كل واحد ده هجرب هذا
+
+254
+00:19:46,750 --> 00:19:50,530
+مع هذا برضه نفس الشيء واحد مع Zero Zero واحد مع
+
+255
+00:19:50,530 --> 00:19:53,150
+واحد واحد بزن طلع واحد على طول بيطلع إيش هذا عند
+
+256
+00:19:53,150 --> 00:19:57,070
+واحد بكمل عملية الضرب هيطلع عند الـ matrix الأمامي
+
+257
+00:19:57,070 --> 00:20:00,290
+هذا كل واحدات مع هذا اللي في النص Zero طيب شوف إيش
+
+258
+00:20:00,290 --> 00:20:05,350
+اللي .. إيش اللي بدنا هيتعال خد a5 a5 عبارة عن إيش
+
+259
+00:20:05,350 --> 00:20:15,990
+يا جماعة a5 هي a5 اللي عندك ماشي طيب a5 شوف
+
+260
+00:20:15,990 --> 00:20:21,670
+هي a5 a5 بسوء a4 في a a4 هي اللي جيبته منها هي a4
+
+261
+00:20:21,670 --> 00:20:26,610
+يا شباب ماشي هين حطيته هان وهي هذا الـ A الأصلي الـ
+
+262
+00:20:26,610 --> 00:20:31,310
+D اتضربت هلجيت الواحد مع ال zero اللي هو zero لأنه
+
+263
+00:20:31,310 --> 00:20:34,030
+لصغير بناخد واحد مع الواحد واحد مدام طلع واحد زي
+
+264
+00:20:34,030 --> 00:20:38,470
+ما قلنا بيطلع كبير الناتج واحد الآن تعالي مع هذا
+
+265
+00:20:38,470 --> 00:20:42,250
+السطر مع هذا هيلتقي أكيد واحد مع واحد مدام التقى
+
+266
+00:20:42,250 --> 00:20:45,370
+واحد مع واحد إذا أنا صغير هنا واحد إذا كبير الكل
+
+267
+00:20:45,370 --> 00:20:48,350
+بيصير إشارة هو بيصير واحد بيطلع الـ entry هذا واحد
+
+268
+00:20:48,760 --> 00:20:52,680
+الآن اللي مش فاهم عليا يعني يضرب ضرب واحدة واحدة
+
+269
+00:20:52,680 --> 00:20:57,020
+لكن بصور الكلام واضح الآن هذا السطر مع العمود اللي
+
+270
+00:20:57,020 --> 00:21:01,780
+هو الاش الأخير السطر هذا واحد مع الواحد واحد يعني
+
+271
+00:21:01,780 --> 00:21:06,640
+لأنه صغير واحد الآن ما كملش الضرب لإنه لما بدي أخد
+
+272
+00:21:06,640 --> 00:21:10,140
+كبير الناتج وعندي واحد طلع واحد إذا كبير الناتج
+
+273
+00:21:10,140 --> 00:21:15,420
+هييطلع إيش واحد الآن هذا بكمله مع هذا و بكمله مع هذا
+
+274
+00:21:15,420 --> 00:21:18,440
+و بكمله مع هذا بيطلع عندي الـ matrix الأمامي بيطلع
+
+275
+00:21:18,440 --> 00:21:23,760
+عندي A5 إيش بيساوي بيساوي واحد الآن بعد هيك لو جيت
+
+276
+00:21:23,760 --> 00:21:27,720
+ضربت جبت A6 يعني جبت الـ matrix الأصلي هذا و
+
+277
+00:21:27,720 --> 00:21:31,330
+ضربته في الـ هذا اللي طلع وحدات تقطعا الوحدات هيتجابل
+
+278
+00:21:31,330 --> 00:21:37,830
+مع الـ أصفار فهيعملن كل وحدات إذا الآن جرب A5 مع A و
+
+279
+00:21:37,830 --> 00:21:41,990
+ضربها بيطلع عندك A6 هيطلع واحد واحد واحد كل واحد و
+
+280
+00:21:41,990 --> 00:21:45,730
+هيظلوا يطلع عندك واحد اللي هو الـ matrix هذا على
+
+281
+00:21:45,730 --> 00:21:50,440
+طول بالشكل هذا هذه الآن اللي هي عملية الـ boolean
+
+282
+00:21:50,440 --> 00:21:54,920
+اللي هو operation أو ال .. ال .. الـ boolean
+
+283
+00:21:54,920 --> 00:21:59,560
+product اللي .. اللي هي زي ما قلنا في المحاضرة
+
+284
+00:21:59,560 --> 00:22:04,280
+اللي هي الـ boolean operation هي في الواقع الـ or و
+
+285
+00:22:04,280 --> 00:22:08,480
+الـ and بتعمل حاجة اسمها boolean algebra مش موضوعنا
+
+286
+00:22:08,480 --> 00:22:17,520
+لكن للي بدوا يعرف الآن انتهت الجزء الأول من محاضرة
+
+287
+00:22:17,520 --> 00:22:23,500
+الـ matrices ككل المطلوب
+
+288
+00:22:23,500 --> 00:22:27,460
+منكم أن يكون عند الـ matrix هذا الـ matrix B وهي الـ
+
+289
+00:22:27,460 --> 00:22:31,590
+matrix الـ identity matrix بدي توجدولي اللي هو الـ a
+
+290
+00:22:31,590 --> 00:22:35,490
+تربيع و الـ a تكعيب و الـ a n لكل n greater than or
+
+291
+00:22:35,490 --> 00:22:39,490
+equal to 3 و توجدولي الـ boolean الـ product بين الـ a و
+
+292
+00:22:39,490 --> 00:22:43,090
+الـ b و الـ boolean الـ product بين الـ a و الـ c و هذولة
+
+293
+00:22:43,090 --> 00:22:46,830
+اللي هي هذا السؤال بس هي السؤال هذا اللي هو الـ a و
+
+294
+00:22:46,830 --> 00:22:50,930
+الـ b و الـ i و هذولة و هذولة بدي توجدوليها و
+
+295
+00:22:50,930 --> 00:22:55,210
+تعملوليها و تكتبوليها في homework و زي الـ homework
+
+296
+00:22:55,210 --> 00:22:59,770
+اللي فات و تبعتوليه على اللي هو الـ whats او على الـ
+
+297
+00:22:59,770 --> 00:23:04,990
+model زي ما بدكم زي ما بتشوفوا مناسب و إن شاء الله
+
+298
+00:23:04,990 --> 00:23:10,470
+في لقاء آخر بينكمل اللي هو الـ determinants أو
+
+299
+00:23:10,470 --> 00:23:14,170
+المحددات والسلام عليكم ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5b47beced82370f52437f56c4be3e81fdcffe183
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_postprocess.srt
@@ -0,0 +1,1196 @@
+1
+00:00:00,000 --> 00:00:05,100
+بسم الله الرحمن الرحيم هذه هي المحاضرة الأولى
+
+2
+00:00:05,100 --> 00:00:11,520
+لمادة رياضيات منفصلة لطلاب وطالبات الجامعة
+
+3
+00:00:11,520 --> 00:00:16,680
+الإسلامية كلية technology المعلومات قسم الحوسبة
+
+4
+00:00:16,680 --> 00:00:24,200
+المتنقلة المحاضرة الأولى بعد حالة الطوارئ
+
+5
+00:00:26,540 --> 00:00:33,800
+عنوان المحاضرة الـ matrices أو اكمال محاضرة
+
+6
+00:00:33,800 --> 00:00:39,300
+matrices التي بدأناها سابقاً كنا عرفنا شو معنات
+
+7
+00:00:39,300 --> 00:00:46,300
+matrix وقلنا اللي هو شو معنات انه درجة ال matrix M
+
+8
+00:00:46,300 --> 00:00:53,050
+by N يعني عدد الصفوف M وعدد الأعمد Nوعرفنا أيضًا
+
+9
+00:00:53,050 --> 00:00:57,930
+اللي هو شو معناه تجمع two matrices قبل هيك وقلنا
+
+10
+00:00:57,930 --> 00:01:02,170
+عشان نجمع اللي هو مصفوفتين لازم يكون المصفوفتين
+
+11
+00:01:02,170 --> 00:01:06,050
+نفس الدرجة يعني لو كانت المصفوفة الأولى تلاتة في
+
+12
+00:01:06,050 --> 00:01:09,820
+تلاتة بدها تكون المصفوفة التانية اللي بنجمعهاهيها
+
+13
+00:01:09,820 --> 00:01:12,740
+أيضا تلاتة في تلاتة وعملية الجمع زي ما انتوا
+
+14
+00:01:12,740 --> 00:01:17,740
+عارفين كل entry مع ال entry المقابل لهم بعد هيك
+
+15
+00:01:17,740 --> 00:01:21,980
+عرفنا عملية الضرب اللي هو two matrices وقلنا عشان
+
+16
+00:01:21,980 --> 00:01:27,380
+نضرب ال matrix اللي درجتهm by k لازم اللي هو يكون
+
+17
+00:01:27,380 --> 00:01:31,660
+ال matrix التاني k by something يعني k by n يعني
+
+18
+00:01:31,660 --> 00:01:35,780
+عدد اللي هو الأعمدة في ال matrix الأول يساوي عدد
+
+19
+00:01:35,780 --> 00:01:39,640
+الصفوف في ال matrix التاني عساس اللي هو اللي هو
+
+20
+00:01:39,640 --> 00:01:44,640
+تكون عملية الضرب بين a وb عملية معرفةو قولنا كيف
+
+21
+00:01:44,640 --> 00:01:48,560
+اللي هي عملية الضرب اللي هو مصفوفتين مع بعض و
+
+22
+00:01:48,560 --> 00:01:52,380
+قولنا عشان نضرب مصفوفتين هي المصفوفة هذه مثلا من
+
+23
+00:01:52,380 --> 00:01:56,020
+الدرجة اللي هو هاي صف صفين تلاتة أربعة من الدرجة
+
+24
+00:01:56,020 --> 00:02:01,560
+أربعة في تلاتة يعني أربع مصفوف .. أربع صفوف و تلات
+
+25
+00:02:01,560 --> 00:02:07,020
+أعمدةبنضربها في مصفوفة تانية تلت صفوف و عمودين
+
+26
+00:02:07,020 --> 00:02:10,960
+معناته عملية الضرب جائزة و بيصير عملية الضرب ميج
+
+27
+00:02:10,960 --> 00:02:15,000
+بنضرب الصف اللي هو الأول في العمود الأول بنضرب
+
+28
+00:02:15,000 --> 00:02:19,240
+واحد في اتنين زائد سفر في واحد زائد أربعة في تلاتة
+
+29
+00:02:19,240 --> 00:02:23,380
+و اللي بيطلع عندى بيكون هو ال entry الأول عند ال
+
+30
+00:02:23,380 --> 00:02:28,440
+seminar c11 بنفس الأسلوب اللي هو بناخد اللي هو
+
+31
+00:02:28,440 --> 00:02:33,350
+الصف الأول في العمود الثاني بنحصل على العنصرC12
+
+32
+00:02:33,350 --> 00:02:39,390
+وخلصنا من السطر الأول بنجي للسطر الثاني في العمود
+
+33
+00:02:39,390 --> 00:02:44,130
+الأول بنجيب أول واحد في السطر الثاني في حصل نتج
+
+34
+00:02:44,130 --> 00:02:49,450
+الضرب وهكذا لما نكمل اللي هو المصفوفة كامل اللي هي
+
+35
+00:02:49,450 --> 00:02:54,990
+عملية الضرب كما شرحناها سابقا مافيش داعي أننا
+
+36
+00:02:54,990 --> 00:03:00,450
+نعيدهاواخدنا أمثلة على ضرب مصهوفات وقلنا المصهوفة
+
+37
+00:03:00,450 --> 00:03:04,590
+A B ليس شرطا أنها تساوي المصهوفة B A وهيعنى مثال
+
+38
+00:03:04,590 --> 00:03:09,230
+على ذلك بعدين عرفنا شو معنات مصهوفة الوحدة مصهوفة
+
+39
+00:03:09,230 --> 00:03:12,110
+الوحدة اللى بيكون عناصر القطر الرئيسى واحد واحد
+
+40
+00:03:12,110 --> 00:03:15,650
+والباقى عناصر الصفار سواء مصهوفة الوحدة من درجة
+
+41
+00:03:15,650 --> 00:03:18,970
+اتنين في اتنين او مصهوفة الوحدة من درجة تلاتة في
+
+42
+00:03:18,970 --> 00:03:24,570
+تلاتة بنفس الاسلوبعرفنا اللي هو مدور المصفوفة أو A
+
+43
+00:03:24,570 --> 00:03:29,230
+Transverse اللي هي عملية تحويل الصفوف إلى أعمدة و
+
+44
+00:03:29,230 --> 00:03:36,390
+قلنا كيف بنحولها سابقا قلنا عملية ضرب A R المتكررة
+
+45
+00:03:36,390 --> 00:03:40,890
+A R معناته أنه ضربنا ال matrix في نفسه R من المرات
+
+46
+00:03:40,890 --> 00:03:44,810
+لما نقول A أو السفر نعني البقية اللي هو المصوفة
+
+47
+00:03:44,810 --> 00:03:50,320
+المصوفة الوحدةاللي هي من الدرجة اللي هي النية حسب
+
+48
+00:03:50,320 --> 00:03:54,980
+اللي هي الـ A اللي بنحكي عنها عرفنا شو معناته اللي
+
+49
+00:03:54,980 --> 00:04:02,000
+هو ال matrix يكون symmetric و بعدين أجينا اللي هو
+
+50
+00:04:02,000 --> 00:04:06,220
+أوصلنا للموضوع اللي احنا اليوم بدنا نفصل فيه و
+
+51
+00:04:06,220 --> 00:04:10,400
+حكينا برضه مقدمة فيه في المحاضرة قلنا اللي هو حاجة
+
+52
+00:04:10,400 --> 00:04:15,040
+اسمها zero one matrix هذه عبارة عن مصفوفةكل
+
+53
+00:04:15,040 --> 00:04:19,640
+عناصرها عبارة عن يا سفر يا واحد عناصر المصفوفة يا
+
+54
+00:04:19,640 --> 00:04:23,920
+سفر يا واحد في عندنا عملية بدنا نجريها بين
+
+55
+00:04:23,920 --> 00:04:27,780
+المصفوفات اسمها الـ Boolean Operations الـ Boolean
+
+56
+00:04:27,780 --> 00:04:33,220
+Operations بين اللي هي المصفوفتين هنعرفها بعد شوية
+
+57
+00:04:33,220 --> 00:04:39,570
+اللي هي او عملية الضرب البولينيأول اشي بدنا نعرف
+
+58
+00:04:39,570 --> 00:04:44,010
+شو معنات الـ Boolean operation بين الصفر والواحد
+
+59
+00:04:44,010 --> 00:04:48,510
+اللي هما عناصر الـ 01 matrix اللي احنا بدنا نجري
+
+60
+00:04:48,510 --> 00:04:53,870
+عليه عملية الـ Boolean operation وبرضه ذكرناها في
+
+61
+00:04:53,870 --> 00:04:59,570
+المحاضرة قلنا عشان بدنا نعرف شو معنات عمليتين الـ
+
+62
+00:04:59,570 --> 00:05:02,970
+Boolean operations عندنا اللي هي ال meet وال joint
+
+63
+00:05:03,390 --> 00:05:06,670
+وقلنا نتخيل ال meet و ال join طبعا ال b1 و ال b2
+
+64
+00:05:06,670 --> 00:05:10,850
+هدول اللي بنعملهم meet او نعملهم joint هدول ال b1
+
+65
+00:05:10,850 --> 00:05:15,610
+و ال b2 يا بياخدن 0 يا بياخدن اياش 1 فالان عملية
+
+66
+00:05:15,610 --> 00:05:22,070
+ال meet اللي هي بتذكرنا و كأنه احنا قلنا انه بنذكر
+
+67
+00:05:22,070 --> 00:05:26,890
+اللي هي عملية ال and و ال joint عملية ال or و
+
+68
+00:05:26,890 --> 00:05:31,070
+بنتخيل ان الواحد هو عبارة عن ال true و ال zero
+
+69
+00:05:31,070 --> 00:05:36,030
+falseفبكون اللي هي ال .. ال .. ال .. ال .. الجملة
+
+70
+00:05:36,030 --> 00:05:40,850
+اللي فيها الـ and true اللي هي في حال .. ال .. ال
+
+71
+00:05:40,850 --> 00:05:45,590
+.. في حالة واحدة لما يكون التمتين true يعني بكون
+
+72
+00:05:45,590 --> 00:05:49,210
+كلهم false في حالة اللي هي التمتين false أو أي
+
+73
+00:05:49,210 --> 00:05:53,470
+واحدة فيهم true فبصير عندى الآن الواحد وواحد
+
+74
+00:05:53,470 --> 00:05:59,040
+الواحد ميت الواحد واحدو الباقى الحالات كلها هيطلع
+
+75
+00:05:59,040 --> 00:06:05,040
+عندى سفر ال joint اللى هو بتكون اللى هو false فى
+
+76
+00:06:05,040 --> 00:06:09,560
+حالة واحدة لما نكون عندى التنتين false وباقى
+
+77
+00:06:09,560 --> 00:06:14,200
+الحالات ايش اتروا لكن الان بعد شوية هعلمكم طريقة
+
+78
+00:06:14,200 --> 00:06:18,320
+اللى هو اتسهل عليكم اللى هو إيجاد ال joint و ال
+
+79
+00:06:18,320 --> 00:06:23,560
+meet بكل سهولة بس خلينى الان نيجي نعرف شو معناته
+
+80
+00:06:23,560 --> 00:06:28,380
+ال joinبين اللي هو two matrices يعني عند ال matrix
+
+81
+00:06:28,380 --> 00:06:33,900
+A و ال matrix B عشان نعملهم join بين ال A و ال B
+
+82
+00:06:33,900 --> 00:06:38,620
+لازم زي عملية الجمع يكون اللي هو ال order للإتنين
+
+83
+00:06:38,620 --> 00:06:42,600
+اللي هين نفس ال order يعني لو كان ال A من ال order
+
+84
+00:06:42,600 --> 00:06:46,840
+on by and لازم يكون ال B برضه من ال order on by
+
+85
+00:06:46,840 --> 00:06:51,170
+and يعني اللي هين نفس الدرجةكذلك عملية الـ meet
+
+86
+00:06:51,170 --> 00:06:54,930
+برضه بين الـ A والـ B، A ميت B برضه لازم يكون
+
+87
+00:06:54,930 --> 00:07:00,970
+الاتنتين اللي هن بنفس الدرجة وعملية اللي هى ال
+
+88
+00:07:00,970 --> 00:07:06,170
+meet أو ال joined في روحة شبيهة بعملية الجمع يعني
+
+89
+00:07:06,170 --> 00:07:12,290
+كل بمعنى آخر أنه كل عنصر بنعمله joined مع العنصر
+
+90
+00:07:12,290 --> 00:07:16,250
+اللي مقابل إله و ال meet برضه نفس الشيء خليني أخد
+
+91
+00:07:16,250 --> 00:07:19,480
+مثال، تشوفوا الصلاة والنبي عليه الصلاة والسلامنجي
+
+92
+00:07:19,480 --> 00:07:23,400
+للمثال الأول بقول find the join and meet of the 0
+
+93
+00:07:23,400 --> 00:07:28,440
+,1 matrix 0,1 matrices اللي أنا عندي لان في عندي
+
+94
+00:07:28,440 --> 00:07:31,920
+مصففتين مصفوفة الأولى واضح من الدرجة واحدة اللي هي
+
+95
+00:07:31,920 --> 00:07:36,260
+2 في عدد الأعناد تلاتة اتنين في تلاتة والتانية بيه
+
+96
+00:07:36,260 --> 00:07:38,660
+في اتنين في تلاتة ايه ده من التنين من نفس الدرجة
+
+97
+00:07:38,660 --> 00:07:44,810
+اذا الخطوة الأولى نحو اتجاه اننا نعرف الاللي هي
+
+98
+00:07:44,810 --> 00:07:50,730
+موجودة فخلّيني انا بقول اذا join of a and b ايه
+
+99
+00:07:50,730 --> 00:07:56,030
+join بيه ايش بده بناخد كل ال entry مع اللي عاجباله
+
+100
+00:07:56,030 --> 00:08:00,280
+عند الواحد or اللي هو mean ال zeroأو join الـ 0 و
+
+101
+00:08:00,280 --> 00:08:04,920
+الـ 0 or الـ 1 و الـ 1 or الـ 0 هى 1 or الـ 0 و 0
+
+102
+00:08:04,920 --> 00:08:10,680
+or الـ 1 و نفس الاشي 1 or الـ 0 هى و هنا 0 or الـ
+
+103
+00:08:10,680 --> 00:08:16,640
+1 و هنا 1 or الـ 1 و هنا 0 or الـ 0 بدنا نعمل هنا
+
+104
+00:08:16,640 --> 00:08:22,220
+الـ join هذه أريحكم الـ join بس خد العدد الأكبر من
+
+105
+00:08:22,220 --> 00:08:26,100
+هنا واحد ولا زيرو من العدد واحدمين الأكبر هنا؟
+
+106
+00:08:26,100 --> 00:08:29,720
+واحد، مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ واحد،
+
+107
+00:08:29,720 --> 00:08:32,080
+مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ اللي هو
+
+108
+00:08:32,080 --> 00:08:36,660
+السفر، إذا ال join اللي هو تاخد الأكبر فيهم،
+
+109
+00:08:36,660 --> 00:08:39,620
+الأكبر بين الواحد وبين السفر أو بين السفر والسفر
+
+110
+00:08:39,620 --> 00:08:43,480
+أو بين الواحد والواحد، واضحة بتصور، نيجي الآن ال
+
+111
+00:08:43,480 --> 00:08:47,000
+meet، ال meet مين الأصغر؟ وانت بتيجي ايه؟الان
+
+112
+00:08:47,000 --> 00:08:50,700
+مالعشنا نستذكر true و false و مش عارف ايش مع انه
+
+113
+00:08:50,700 --> 00:08:55,280
+سهل ال true و false اللي بده احد الطريقين اللي هو
+
+114
+00:08:55,280 --> 00:09:01,200
+اسهلكم الان the meet of a and b is a meet b a meet
+
+115
+00:09:01,200 --> 00:09:05,820
+b اللي هو بيجي الان مع كل عنصر a meet zero zero
+
+116
+00:09:05,820 --> 00:09:10,960
+meet one one meet zero الان نفس الاشي zero meet
+
+117
+00:09:10,960 --> 00:09:15,990
+one one meet oneand zero meet zero هاي اللي هنا
+
+118
+00:09:15,990 --> 00:09:22,170
+اللي هي a meet b الان ال a meet b نيجي للواحد or
+
+119
+00:09:22,170 --> 00:09:24,670
+zero زي ما قلنا بتاخد الصغير بطلع الصفر تاخد
+
+120
+00:09:24,670 --> 00:09:27,370
+الصغير بطلع الصفر تاخد الصغير بطلع الصفر تاخد
+
+121
+00:09:27,370 --> 00:09:30,350
+الصغير بطلع الصفر وهنا الصغير واحد اللي هو بين
+
+122
+00:09:30,350 --> 00:09:34,430
+الواحد والواحد والصغير هنا zero أو zero إذن هاي
+
+123
+00:09:34,430 --> 00:09:39,830
+معناة ال join بين two matrices وهي معناة ال meet
+
+124
+00:09:39,830 --> 00:09:46,100
+بين two matricesالان بدنا نعرف Boolean product الـ
+
+125
+00:09:46,100 --> 00:09:49,800
+Boolean product بين two matrices صلوا على النبي
+
+126
+00:09:49,800 --> 00:09:53,500
+عليه الصلاة والسلام الان الـ Boolean product بين
+
+127
+00:09:53,500 --> 00:09:59,780
+ال matrix A و ال matrix B بروح
+
+128
+00:09:59,780 --> 00:10:05,060
+الدرب العادى لكن بواسطة ال join و ال meet و كأنه
+
+129
+00:10:05,060 --> 00:10:11,810
+بده يصير عند ال meet بلعبدور الضرب و الـ join بلعب
+
+130
+00:10:11,810 --> 00:10:16,310
+دور اللي هو إيش الجمع اتخيل إنه أنت بتضرب two
+
+131
+00:10:16,310 --> 00:10:21,370
+matrices ضرب عادي بس بدل ما تحط عملية الضرب حط
+
+132
+00:10:21,370 --> 00:10:25,930
+عملية الـ join و بدل ما تحط .. آسف عملية الميت و
+
+133
+00:10:25,930 --> 00:10:32,350
+بدل ما تحط عملية الجمع حط عملية مين الـ joinهدى
+
+134
+00:10:32,350 --> 00:10:35,850
+وما بيكونش ولا إش جديد و زى الضرب العادى اللى
+
+135
+00:10:35,850 --> 00:10:42,570
+بنعرفه بالظبط لحتى أن عدد الدرجة الـ A هيكون N by
+
+136
+00:10:42,570 --> 00:10:48,990
+K Matrix لازم درجة الـ B يكون مقماله اللى هو يبدأ
+
+137
+00:10:48,990 --> 00:10:55,450
+بـ K by N Matrix يعني الاتنين والعدد الأولانى عدد
+
+138
+00:10:55,450 --> 00:11:00,360
+الأعمدة اللى فيهلازم يساوي عدد السطور اللي في مين
+
+139
+00:11:00,360 --> 00:11:05,460
+في الـ matrix اللي هو الثاني لتشوف مثال عملي
+
+140
+00:11:05,460 --> 00:11:09,900
+أمامنا هذه عند الـ A وهذه عند الـ B بيقول لي find
+
+141
+00:11:09,900 --> 00:11:13,920
+the Boolean product of A and B where إذا بدنا نوجد
+
+142
+00:11:13,920 --> 00:11:18,710
+اللي هو الـ Boolean productاللي هو بين الـ A و الـ
+
+143
+00:11:18,710 --> 00:11:22,630
+B ماشي يا جماعة طيب الآن عشان وجود الـ Boolean
+
+144
+00:11:22,630 --> 00:11:25,590
+Product بمش بسأل حالنا أصلا يعني هذا هو Zero
+
+145
+00:11:25,590 --> 00:11:28,930
+Matrix و هذا Zero Matrix إذا بنحكي فعلا عن Boolean
+
+146
+00:11:28,930 --> 00:11:34,130
+Product طيب هل هذا درجته اللي هو واحد، اتنين،
+
+147
+00:11:34,130 --> 00:11:41,580
+تلاتة صفوف عمودين؟ أه و هذا قداش؟اللي هو درجته
+
+148
+00:11:41,580 --> 00:11:45,860
+تلاتة في اتنين وهذا درجته اتنين في تلاتة اذا اللي
+
+149
+00:11:45,860 --> 00:11:50,560
+هو عملية الضرب ايه شمالها جائزة ومعرفة الـ Boolean
+
+150
+00:11:50,560 --> 00:11:55,080
+Product معرف عملية الضرب في هذه الحالة نشوف كيف
+
+151
+00:11:55,080 --> 00:11:59,830
+نوجدهاشوفوا عليها لأن بدي اجي زي ما قلنا بتخيل
+
+152
+00:11:59,830 --> 00:12:04,710
+حالنا اننا بنضرب ضرب عادي باجي على اللي هو بس اللي
+
+153
+00:12:04,710 --> 00:12:11,770
+هو بنغير عملية الضرب بـJoin وعملية اللي هي الجامع
+
+154
+00:12:11,770 --> 00:12:21,180
+ابنيتعملية الضرب بميت وعملية الجمع ب join بنشوف
+
+155
+00:12:21,180 --> 00:12:27,200
+كيف لأن نيجي هنا و السطر الأول بنيجي بنقول واحد
+
+156
+00:12:27,200 --> 00:12:30,240
+السطر الأول مع ايش طبعا زي ما بنعمل في الضرب مع
+
+157
+00:12:30,240 --> 00:12:39,050
+العمود الأول واحد اشمالهميت واحد Zero ميت واحد و
+
+158
+00:12:39,050 --> 00:12:43,110
+بين الاتنين ايش ماله ال join هاي واحد ميت الواحد و
+
+159
+00:12:43,110 --> 00:12:48,670
+Zero ميت ال zero الان خلصنا اللي هو السطر الأول مع
+
+160
+00:12:48,670 --> 00:12:52,430
+العمود الأول الان السطر الأول مع مين مع العمود
+
+161
+00:12:52,430 --> 00:13:00,490
+الأول التاني اللي هو واحد اللي هو and الواحدو Zero
+
+162
+00:13:00,490 --> 00:13:08,550
+and الواحد و بينهما عملية الار وهذه ميت وهذه جوين
+
+163
+00:13:08,550 --> 00:13:14,610
+امكن نقول أند و ار أسهل لكم الآن خلصنا من الجزء
+
+164
+00:13:14,610 --> 00:13:20,530
+الثاني نجي للثالث واحد مع اللي هو ال zero واحد مع
+
+165
+00:13:20,530 --> 00:13:24,850
+ال zero and و ال zero مع ال واحد and و بينهم ايش
+
+166
+00:13:24,850 --> 00:13:30,370
+ارالان بنعمل نفس الاشي السطر الثاني مع العمود
+
+167
+00:13:30,370 --> 00:13:34,050
+الأول السطر الثاني مع العمود الثاني السطر الثاني
+
+168
+00:13:34,050 --> 00:13:37,250
+مع العمود الثالث بيكون جيبنا السطر الثاني في
+
+169
+00:13:37,250 --> 00:13:41,330
+المصهوفة الناتجة نيجي الأن نفس الاشي السطر الثالث
+
+170
+00:13:41,330 --> 00:13:45,570
+مع العمود الأول بتجيب ال entry هذا السطر الأول مع
+
+171
+00:13:45,570 --> 00:13:49,590
+هذا بتجيب ال entry اللي بعده و هكذا فبكون احنا
+
+172
+00:13:49,590 --> 00:13:54,540
+حصلنا على ال job اللي هو ال boolean productالـ
+
+173
+00:13:54,540 --> 00:13:59,500
+Boolean product ندى الان اللى هو على طول نحسب الان
+
+174
+00:13:59,500 --> 00:14:05,260
+ال ال قولنا ال and ايش ماله لصغير واحد و ال هنا
+
+175
+00:14:05,260 --> 00:14:09,920
+لصغير سفر بينهم بدنا ناخد الكبير ال join بده
+
+176
+00:14:09,920 --> 00:14:13,960
+الكبير هذا واحد وهذا سفر الكبير واحد ماشي الحال
+
+177
+00:14:13,960 --> 00:14:19,360
+على طول اللى بعده هنا واحدالصغير واحد والصغير هنا
+
+178
+00:14:19,360 --> 00:14:24,020
+سفر واحد ولا سفر الكبير هنا ال join كبير هذا ال or
+
+179
+00:14:24,020 --> 00:14:27,600
+كبير يعني باخد صغير هذه وصغير هذه مع كبير الكل
+
+180
+00:14:27,600 --> 00:14:31,860
+صغير هذه واحد وصغير هذه سفر كبير هنا الاتنين واحد
+
+181
+00:14:32,420 --> 00:14:36,240
+الان صغير هذه سفر و صغير هذه سفر كبير هين ايش
+
+182
+00:14:36,240 --> 00:14:42,000
+هيطلع سفر لأن هذه صغير هين سفر و هذه صغير هين سفر
+
+183
+00:14:42,000 --> 00:14:46,920
+إذا كبير هين اتين اتين لازم يطلع سفر لأن الصغير
+
+184
+00:14:46,920 --> 00:14:51,820
+هدولة سفر و كبير هدولة واحد الان صار عندي سفر و
+
+185
+00:14:51,820 --> 00:14:56,180
+واحد كبير هين واحد طبعا نفس الاشي صغير هين سفر
+
+186
+00:14:56,180 --> 00:14:59,620
+هدول و هدولة صغير هين واحد كبير الجهتين اللي
+
+187
+00:14:59,620 --> 00:15:04,730
+بيطلعين واحدالان أصغير هنا واحد أصغير هنا سفر
+
+188
+00:15:04,730 --> 00:15:11,290
+أكبير الجهتين واحد أصغير هنا واحد و أصغير هنا سفر
+
+189
+00:15:11,290 --> 00:15:16,770
+أكبير هنا واحد فاهمين عليها أصغير هنا سفر و أصغير
+
+190
+00:15:16,770 --> 00:15:21,990
+هنا سفر السفر و السفر أكبير هنا إيش سفر واضح هذا
+
+191
+00:15:21,990 --> 00:15:24,370
+اللي هو ال boolean of product
+
+192
+00:15:26,860 --> 00:15:31,660
+الان ناخد مثال اخر لت ايه بتساوي ايه ال matrix
+
+193
+00:15:31,660 --> 00:15:35,040
+اللي امامي هذا عبارة عن matrix ثلاثة في ثلاثة وقول
+
+194
+00:15:35,040 --> 00:15:40,280
+لي find ما يليه ماشي ال matrices التالية بدي ايه
+
+195
+00:15:40,280 --> 00:15:44,740
+تربيع و ايه تكعيد و ايه اربعة و ايه خمسة و ايه n
+
+196
+00:15:45,300 --> 00:15:49,680
+ايش مقصود بالـ A تربيع يعني A Boolean product مع A
+
+197
+00:15:49,680 --> 00:15:54,440
+A تكعيب Boolean product A مع A مع A تلت مرات يعني
+
+198
+00:15:54,440 --> 00:15:58,560
+A تربيع مع A نيدي ناخد واحدة واحدة يا شباب و يا
+
+199
+00:15:58,560 --> 00:16:02,940
+بنات شوفوا صلوا على النبي عليه الصلاة والسلام عندي
+
+200
+00:16:02,940 --> 00:16:07,800
+ال A ال A تربيع بالساوية A اللي هو ال Boolean
+
+201
+00:16:07,800 --> 00:16:12,570
+product مع ال AA بولي انا product مع الـ A اللي هو
+
+202
+00:16:12,570 --> 00:16:17,050
+كما يلي بنيجي بنحط الـ A هنا و الـ A الثانية في
+
+203
+00:16:17,050 --> 00:16:22,910
+هذه الجهة الان بنيجي بناخد الصف مع مين مع العمود
+
+204
+00:16:22,910 --> 00:16:28,250
+الان الصغير الـ 0 و الـ 0 اللي مع بعض صغير و الكل
+
+205
+00:16:28,250 --> 00:16:32,430
+اللي يا كبيريعني الآن Zero مع Zero صغيرهم Zero
+
+206
+00:16:32,430 --> 00:16:36,890
+Zero مع واحد صغيرهم Zero واحد مع واحد صغيرهم واحد
+
+207
+00:16:36,890 --> 00:16:40,390
+اذا كبير التلاتة اللي هي Zero و Zero و واحد اللي
+
+208
+00:16:40,390 --> 00:16:44,120
+هو هيطلع واحدطيب اللي ما .. اللي ما .. عارف اللي
+
+209
+00:16:44,120 --> 00:16:48,500
+ما .. مامشيش معاه فادف تانية الان السطر الأول مع
+
+210
+00:16:48,500 --> 00:16:52,620
+العمود التاني ماشي الان السطر الأول Zero Zero
+
+211
+00:16:52,620 --> 00:16:56,360
+صغيرهن Zero Zero Zero صغيرهن Zero الواحد و الواحد
+
+212
+00:16:56,360 --> 00:17:00,420
+صغيرهن الواحد الان اكبير التلاتة اللي طلع ان اللي
+
+213
+00:17:00,420 --> 00:17:04,620
+عندي السفر و السفر و الواحد واحد فبطلع عند ايش
+
+214
+00:17:04,620 --> 00:17:11,430
+اللي هو الناتج واحد لأن العمود هذاأسف السطر هذا
+
+215
+00:17:11,430 --> 00:17:15,670
+الأول مع العمود التالت الـ 0 و الـ 1 صغيرهم Zero
+
+216
+00:17:15,670 --> 00:17:19,030
+الـ 0 و الـ 0 صغيرهم Zero الـ 1 و الـ 0 صغيرهم
+
+217
+00:17:19,030 --> 00:17:22,770
+Zero اللي هنطلع كله هذا Zero إذن كبيرهم إيش هيطلع
+
+218
+00:17:22,770 --> 00:17:27,550
+Zeroبنفس الطريقة بناخد اللي هو السطر الثاني مع
+
+219
+00:17:27,550 --> 00:17:32,570
+العمود الأول واحد مع الـ0 صغيرهن Zero Zero مع
+
+220
+00:17:32,570 --> 00:17:36,910
+الواحد صغيرهن Zero Zero مع الواحد صغيرهن Zero إذا
+
+221
+00:17:36,910 --> 00:17:40,970
+التلاتة صغيرة هنا مش هيطلع اللي هو الـ Zero بنفس
+
+222
+00:17:40,970 --> 00:17:45,130
+الأسلوب بنطلع باقي اللي هي القيم فبكون عندى بطلع
+
+223
+00:17:45,130 --> 00:17:48,950
+ال matrix هذا اللي أمامىلأن هذا الـ matrix اللي
+
+224
+00:17:48,950 --> 00:17:52,130
+أمامي هو الـ A تربيع بدي أوجد الـ A تكعيب الـ A
+
+225
+00:17:52,130 --> 00:17:55,350
+تكعيب إيش هتساوي الـ A تربيع اللي طلع هذا هيو
+
+226
+00:17:55,350 --> 00:18:00,050
+جبتهان درق اللي هو Boolean product مع مين مع الـ A
+
+227
+00:18:00,050 --> 00:18:04,190
+اللي هو الأصل هيو نيدي نضربهم مع بعض زي ما قلنا
+
+228
+00:18:04,190 --> 00:18:08,450
+قبل بشوية واحد و Zero صغير من Zero واحد واحد صغير
+
+229
+00:18:08,450 --> 00:18:13,090
+من واحد خلاص مدام طلع هنا واحد في الصغار واحد إذا
+
+230
+00:18:13,090 --> 00:18:17,780
+على طول الكبار هيطلع بينهن إيش واحدماكملش يعني لإن
+
+231
+00:18:17,780 --> 00:18:22,880
+هذا السطر مع العمود الثاني لإن واحد مع ال zero
+
+232
+00:18:22,880 --> 00:18:26,020
+zero واحد مع ال zero zero الصغير طبعا zero مع ال
+
+233
+00:18:26,020 --> 00:18:29,000
+zero zero ده نطلع كله نصفار ده هيطلع الكبير zero
+
+234
+00:18:29,000 --> 00:18:32,800
+لإن واحد مع الواحد طلع واحد مثلا واحد طلع واحد من
+
+235
+00:18:32,800 --> 00:18:36,260
+عملية اللي هو مين صغيرهم هذا اللي ماخدت مين يا
+
+236
+00:18:36,260 --> 00:18:40,090
+جماعة اللي ماخدتي العمود السطر الأولمع العمود
+
+237
+00:18:40,090 --> 00:18:43,830
+التالت واحد مع واحد لصغير واحد إذا ما يطلع الكبير
+
+238
+00:18:43,830 --> 00:18:45,770
+هنا إيش ما يطلع من الباقيت هيطلع الكبير هنا واحد
+
+239
+00:18:45,770 --> 00:18:50,110
+هاي واحد وبعدي بعمل السطر الثاني بنفس الأسلوب مع
+
+240
+00:18:50,110 --> 00:18:53,730
+العمود الأول والسطر الثاني بحصل على ال matrix اللي
+
+241
+00:18:53,730 --> 00:18:57,450
+أمامني اللي هو هذا هذا اللي طلع مين عندي a تكعيب
+
+242
+00:18:57,450 --> 00:19:01,910
+تعالي ال a تكعيب هذا بدي أضربه في ال a بطلع مين a
+
+243
+00:19:01,910 --> 00:19:04,810
+قصة أربعة يعني ايه بدي a أربعة بساوي a تكعيب اللي
+
+244
+00:19:04,810 --> 00:19:08,610
+طلعته من الخطوة هذه في a هايه a تكعيب وهيه ال a
+
+245
+00:19:09,070 --> 00:19:15,490
+لاحظ الآن واحد مع الـ 00 بالصغير، Zero مع السطر
+
+246
+00:19:15,490 --> 00:19:19,410
+الأول مع العمود الأول، نعيد نفس الكلام، واحد مع
+
+247
+00:19:19,410 --> 00:19:23,230
+الـ 00، Zero مع الواحد، Zero، واحد مع الواحد،
+
+248
+00:19:23,230 --> 00:19:27,290
+واحد، ده نطلع واحد، الآن اللي بعده، هذا السطر مع
+
+249
+00:19:27,290 --> 00:19:30,410
+هذا العمود، لاحظوا أنه هيتجي الواحد هذا مع الواحد،
+
+250
+00:19:30,410 --> 00:19:33,610
+ده هيطلع واحد منه، ده هيطلع الكل إيه شماله؟ واحد
+
+251
+00:19:33,810 --> 00:19:38,370
+نجي لهذا هيلتجي مع هذا مع الواحد مادام واحد التجه
+
+252
+00:19:38,370 --> 00:19:41,870
+مع الواحد إذا أصغير الواحدين واحد إذا الكبير
+
+253
+00:19:41,870 --> 00:19:46,750
+الناتج بيطلع إيش واحد إذا هذا كل واحد ده هجرب هذا
+
+254
+00:19:46,750 --> 00:19:50,530
+مع هذا برضه نفس الاشي واحد مع Zero Zero واحد مع
+
+255
+00:19:50,530 --> 00:19:53,150
+واحد واحد بزن طلع واحد على طول بيطلع إيش هذا عند
+
+256
+00:19:53,150 --> 00:19:57,070
+واحد بكمل عملية الدرب هيطلع عند ال matrix الأمامي
+
+257
+00:19:57,070 --> 00:20:00,290
+هذا كل واحدات مع هذا اللي في النص Zero طيب شوف إيش
+
+258
+00:20:00,290 --> 00:20:05,350
+اللي .. إيش اللي بدنا هيتعال خد a5 a5 عبارة عن ايش
+
+259
+00:20:05,350 --> 00:20:15,990
+يا جماعة a5 هي a5 اللي عندك ماشي طيب a5 شوف
+
+260
+00:20:15,990 --> 00:20:21,670
+هي a5 a5 بسوء a4 في a a4 هي اللي جيبته منها هي a4
+
+261
+00:20:21,670 --> 00:20:26,610
+يا شبابماشي هين حطيته هان وهي هذا الـ A الأصلي الـ
+
+262
+00:20:26,610 --> 00:20:31,310
+D اتضربت هلجيت الواحد مع ال zero اللي هو zero لأنه
+
+263
+00:20:31,310 --> 00:20:34,030
+لصغير بناخد واحد مع الواحد واحد مدام طلع واحد زي
+
+264
+00:20:34,030 --> 00:20:38,470
+ما قلنا بيطلع كبير الناتج واحد الان تعالي مع هذا
+
+265
+00:20:38,470 --> 00:20:42,250
+السطر مع هذا هيلتقي اكيد واحد مع واحد مدام التقى
+
+266
+00:20:42,250 --> 00:20:45,370
+واحد مع واحد اذا انا صغير هنا واحد اذا كبير الكل
+
+267
+00:20:45,370 --> 00:20:48,350
+بيصير اشمال هو بيصير واحد بيطلع ال entry هذا واحد
+
+268
+00:20:48,760 --> 00:20:52,680
+الان اللي مش فاهم عليا يعني يضرب ضرب واحدة واحدة
+
+269
+00:20:52,680 --> 00:20:57,020
+لكن بصور الكلام واضح الان هذا السطر مع العمود اللي
+
+270
+00:20:57,020 --> 00:21:01,780
+هو الاش الأخير السطر هذا واحد مع الواحد واحد يعني
+
+271
+00:21:01,780 --> 00:21:06,640
+لإنه صغير واحد الان ماكملش الضرب لإنه لما بدي أخد
+
+272
+00:21:06,640 --> 00:21:10,140
+كبير الناتج وعندي واحد طلع واحد إذا كبير الناتج
+
+273
+00:21:10,140 --> 00:21:15,420
+هيطلع اش واحدالان هذا بكمله مع هذا و بكمله مع هذا
+
+274
+00:21:15,420 --> 00:21:18,440
+و بكمله مع هذا بطلع عندي ال matrix الأمامي بطلع
+
+275
+00:21:18,440 --> 00:21:23,760
+عندي A5 ايش بساوي بساوي واحد الان بعد هيك لو جيت
+
+276
+00:21:23,760 --> 00:21:27,720
+ضربت جيبت A6 يعني جيبت ال matrix الأصلي هذا و
+
+277
+00:21:27,720 --> 00:21:31,330
+ضربته في ال هذا اللي طلع وحداتقطعا الوحدات هيتجابل
+
+278
+00:21:31,330 --> 00:21:37,830
+مع اللغات فهيعملن كل وحدات اذا الان جرب A5 مع A و
+
+279
+00:21:37,830 --> 00:21:41,990
+ضربها بيطلع عندك A6 هيطلع واحد واحد واحد كل واحد و
+
+280
+00:21:41,990 --> 00:21:45,730
+هيظلوا يطلع عندك واحد اللي هو ال matrix هذا على
+
+281
+00:21:45,730 --> 00:21:50,440
+طول بالشكل هذاهذه الآن اللي هي عملية ال boolean
+
+282
+00:21:50,440 --> 00:21:54,920
+اللي هو operation أو ال .. ال .. ال boolean
+
+283
+00:21:54,920 --> 00:21:59,560
+product اللي .. اللي هي زي ما قلنا في المحاضرة
+
+284
+00:21:59,560 --> 00:22:04,280
+اللي هي ال boolean operation هي في الواقع ال or و
+
+285
+00:22:04,280 --> 00:22:08,480
+ال and بتعمل حاجة اسمها boolean algebra مش موضوعنا
+
+286
+00:22:08,480 --> 00:22:17,520
+لكن للي بدوا يعرفالان انتهت الجزء الأول من محاضرة
+
+287
+00:22:17,520 --> 00:22:23,500
+الـ matrices ككل المطلوب
+
+288
+00:22:23,500 --> 00:22:27,460
+منكم ان يكون عند ال matrix هذا ال matrix B وهي ال
+
+289
+00:22:27,460 --> 00:22:31,590
+matrix ال identity matrixبدي توجدولي اللي هو ال a
+
+290
+00:22:31,590 --> 00:22:35,490
+تربيع و ال a تكعيب و ال a n لكل n greater than or
+
+291
+00:22:35,490 --> 00:22:39,490
+equal to 3 و توجدولي البولين ال product بين ال a و
+
+292
+00:22:39,490 --> 00:22:43,090
+ال b و البولين ال product بين ال a و ال c و هذولة
+
+293
+00:22:43,090 --> 00:22:46,830
+اللي هى هذا السؤال بس هى السؤال هذا اللي هو ال a و
+
+294
+00:22:46,830 --> 00:22:50,930
+ال b و ال i و هذولة و هذولة بدي توجدوليها و
+
+295
+00:22:50,930 --> 00:22:55,210
+تعملوليها و تكتبوليهافي homework و زي ال homework
+
+296
+00:22:55,210 --> 00:22:59,770
+اللي فات و تبعتوليه على اللي هو ال whats او على ال
+
+297
+00:22:59,770 --> 00:23:04,990
+model زي ما بدكم زي ما بتشوفوا مناسب و ان شاء الله
+
+298
+00:23:04,990 --> 00:23:10,470
+في لقاء اخر بينكمل اللي هو ال determinants او
+
+299
+00:23:10,470 --> 00:23:14,170
+المحددات والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..91302a822ffb6813a4b4786078ff1837f9e055a0
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.json
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واحد", "probability": 0.974609375}], "temperature": 1.0}, {"id": 22, "seek": 52579, "start": 504.8, "end": 525.8, "text": "مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ اللي هو السفر، إذا ال join اللي هو تاخد الأكبر فيهم، الأكبر بين الواحد وبين السفر أو بين السفر والسفر أو بين الواحد والواحد، واضحة بتصور، نيجي الآن ال meet، ال meet مين الأصغر؟ وانت بتيجي ايه؟", "tokens": [2304, 9957, 16247, 4117, 26890, 34105, 22807, 36764, 24401, 12399, 3714, 9957, 16247, 4117, 26890, 34105, 22807, 36764, 24401, 12399, 3714, 9957, 16247, 4117, 26890, 34105, 22807, 36764, 24401, 12399, 3714, 9957, 16247, 4117, 26890, 34105, 22807, 36764, 24401, 12399, 3714, 9957, 16247, 4117, 26890, 34105, 22807, 13672, 1829, 31439, 21136, 5172, 2288, 12399, 11933, 15730, 2423, 3917, 13672, 1829, 31439, 6055, 47283, 3215, 16247, 4117, 26890, 8978, 16095, 12399, 16247, 4117, 26890, 49374, 2423, 14407, 24401, 46599, 9957, 21136, 5172, 2288, 34051, 49374, 21136, 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"probability": 0.254638671875}, {"start": 544.9, "end": 545.82, "word": " zero", "probability": 0.76416015625}, {"start": 545.82, "end": 546.16, "word": " meet", "probability": 0.9765625}, {"start": 546.16, "end": 546.52, "word": " one", "probability": 0.95703125}, {"start": 546.52, "end": 547.26, "word": " one", "probability": 0.91943359375}, {"start": 547.26, "end": 547.82, "word": " meet", "probability": 0.9765625}, {"start": 547.82, "end": 548.34, "word": " zero", "probability": 0.9013671875}, {"start": 548.34, "end": 549.24, "word": " الان", "probability": 0.869140625}, {"start": 549.24, "end": 549.54, "word": " نفس", "probability": 0.994873046875}, {"start": 549.54, "end": 550.1, "word": " الاشي", "probability": 0.7676595052083334}, {"start": 550.1, "end": 550.64, "word": " zero", "probability": 0.76220703125}, {"start": 550.64, "end": 550.96, "word": " meet", "probability": 0.97412109375}, {"start": 550.96, "end": 551.3, "word": " one", "probability": 0.95361328125}, {"start": 551.3, "end": 552.0, "word": " one", "probability": 0.94482421875}, {"start": 552.0, "end": 552.28, "word": " meet", "probability": 0.9814453125}, {"start": 552.28, "end": 552.62, "word": " one", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 24, "seek": 58173, "start": 553.01, "end": 581.73, "text": "and zero meet zero هاي اللي هنا اللي هي a meet b الان ال a meet b نيجي للواحد or zero زي ما قلنا بتاخد الصغير بطلع الصفر تاخد الصغير بطلع الصفر تاخد الصغير بطلع الصفر تاخد الصغير بطلع الصفر وهنا الصغير واحد اللي هو بين الواحد والواحد والصغير هنا zero أو zero إذن هاي معناة ال join بين two matrices وهي معناة ال meet بين two matrices", "tokens": [474, 4018, 1677, 4018, 8032, 47302, 13672, 1829, 34105, 13672, 1829, 39896, 257, 1677, 272, 2423, 7649, 2423, 257, 1677, 272, 8717, 1829, 7435, 1829, 24976, 14407, 24401, 420, 4018, 30767, 1829, 19446, 12174, 1211, 8315, 39894, 47283, 3215, 31767, 17082, 13546, 4724, 9566, 1211, 3615, 31767, 5172, 2288, 6055, 47283, 3215, 31767, 17082, 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"probability": 0.7284749348958334}, {"start": 564.67, "end": 564.95, "word": " الصغير", "probability": 0.98876953125}, {"start": 564.95, "end": 565.23, "word": " بطلع", "probability": 0.94287109375}, {"start": 565.23, "end": 565.53, "word": " الصفر", "probability": 0.9794921875}, {"start": 565.53, "end": 565.85, "word": " تاخد", "probability": 0.8709309895833334}, {"start": 565.85, "end": 566.11, "word": " الصغير", "probability": 0.9928385416666666}, {"start": 566.11, "end": 566.37, "word": " بطلع", "probability": 0.974853515625}, {"start": 566.37, "end": 566.73, "word": " الصفر", "probability": 0.9876302083333334}, {"start": 566.73, "end": 567.37, "word": " تاخد", "probability": 0.9207356770833334}, {"start": 567.37, "end": 567.63, "word": " الصغير", "probability": 0.9905598958333334}, {"start": 567.63, "end": 567.89, "word": " بطلع", "probability": 0.9632568359375}, {"start": 567.89, "end": 568.25, "word": " الصفر", "probability": 0.9874674479166666}, {"start": 568.25, "end": 568.65, 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zero", "probability": 0.72802734375}, {"start": 573.81, "end": 574.15, "word": " إذن", "probability": 0.6759440104166666}, {"start": 574.15, "end": 574.43, "word": " هاي", "probability": 0.783203125}, {"start": 574.43, "end": 574.95, "word": " معناة", "probability": 0.783203125}, {"start": 574.95, "end": 575.13, "word": " ال", "probability": 0.85009765625}, {"start": 575.13, "end": 575.51, "word": " join", "probability": 0.70751953125}, {"start": 575.51, "end": 576.31, "word": " بين", "probability": 0.7822265625}, {"start": 576.31, "end": 576.57, "word": " two", "probability": 0.919921875}, {"start": 576.57, "end": 577.17, "word": " matrices", "probability": 0.94384765625}, {"start": 577.17, "end": 578.45, "word": " وهي", "probability": 0.7998046875}, {"start": 578.45, "end": 579.39, "word": " معناة", "probability": 0.9866536458333334}, {"start": 579.39, "end": 579.57, "word": " ال", "probability": 0.82666015625}, {"start": 579.57, "end": 579.83, "word": " meet", "probability": 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"word": " two", "probability": 0.6533203125}, {"start": 587.54, "end": 588.16, "word": " matrices", "probability": 0.931640625}, {"start": 588.16, "end": 589.38, "word": " صلوا", "probability": 0.8087565104166666}, {"start": 589.38, "end": 589.5, "word": " على", "probability": 0.59521484375}, {"start": 589.5, "end": 589.8, "word": " النبي", "probability": 0.978515625}, {"start": 589.8, "end": 590.08, "word": " عليه", "probability": 0.6787109375}, {"start": 590.08, "end": 590.52, "word": " الصلاة", "probability": 0.9606119791666666}, {"start": 590.52, "end": 591.04, "word": " والسلام", "probability": 0.9627278645833334}, {"start": 591.04, "end": 591.94, "word": " الان", "probability": 0.801025390625}, {"start": 591.94, "end": 592.26, "word": " الـ", "probability": 0.8837890625}, {"start": 592.26, "end": 592.56, "word": " Boolean", "probability": 0.90283203125}, {"start": 592.56, "end": 593.12, "word": " product", "probability": 0.93701171875}, {"start": 593.12, "end": 593.5, "word": " بين", "probability": 0.93798828125}, {"start": 593.5, "end": 593.94, "word": " ال", "probability": 0.89404296875}, {"start": 593.94, "end": 594.38, "word": " matrix", "probability": 0.568359375}, {"start": 594.38, "end": 594.72, "word": " A", "probability": 0.83984375}, {"start": 594.72, "end": 594.86, "word": " و", "probability": 0.748046875}, {"start": 594.86, "end": 594.94, "word": " ال", "probability": 0.61767578125}, {"start": 594.94, "end": 595.38, "word": " matrix", "probability": 0.95458984375}, {"start": 595.38, "end": 595.82, "word": " B", "probability": 0.97216796875}, {"start": 595.82, "end": 599.78, "word": " بروح", "probability": 0.9342447916666666}, {"start": 599.78, "end": 600.2, "word": " الدرب", "probability": 0.576416015625}, {"start": 600.2, "end": 600.92, "word": " العادى", "probability": 0.8683268229166666}, {"start": 600.92, "end": 601.6, "word": " لكن", "probability": 0.74853515625}, {"start": 601.6, "end": 602.4, "word": " بواسطة", "probability": 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"probability": 0.5657958984375}, {"start": 1021.04, "end": 1021.52, "word": " السفر", "probability": 0.798583984375}, {"start": 1021.52, "end": 1021.64, "word": " و", "probability": 0.76416015625}, {"start": 1021.64, "end": 1022.0, "word": " السفر", "probability": 0.9723307291666666}, {"start": 1022.0, "end": 1022.1, "word": " و", "probability": 0.96826171875}, {"start": 1022.1, "end": 1022.54, "word": " الواحد", "probability": 0.9876302083333334}, {"start": 1022.54, "end": 1023.28, "word": " واحد", "probability": 0.949462890625}, {"start": 1023.28, "end": 1024.08, "word": " فبطلع", "probability": 0.973828125}, {"start": 1024.08, "end": 1024.3, "word": " عند", "probability": 0.80419921875}, {"start": 1024.3, "end": 1024.62, "word": " ايش", "probability": 0.7212727864583334}, {"start": 1024.62, "end": 1024.74, "word": " اللي", "probability": 0.989501953125}, {"start": 1024.74, "end": 1024.9, "word": " هو", "probability": 0.986328125}, {"start": 1024.9, "end": 1025.48, "word": " الناتج", "probability": 0.822265625}, {"start": 1025.48, "end": 1026.12, "word": " واحد", "probability": 0.9560546875}, {"start": 1026.12, "end": 1026.72, "word": " لأن", "probability": 0.5035400390625}, {"start": 1026.72, "end": 1027.26, "word": " العمود", "probability": 0.9912109375}, {"start": 1027.26, "end": 1027.74, "word": " هذا", "probability": 0.857421875}], "temperature": 1.0}, {"id": 45, "seek": 104334, "start": 1029.93, "end": 1043.35, "text": "أسف السطر هذا الأول مع العمود التالت الـ 0 و الـ 1 صغيرهم Zero الـ 0 و الـ 0 صغيرهم Zero الـ 1 و الـ 0 صغيرهم Zero اللي هنطلع كله هذا Zero إذن كبيرهم إيش هيطلع Zero", "tokens": [10721, 3794, 5172, 21136, 9566, 2288, 23758, 16247, 12610, 20449, 18863, 2304, 23328, 16712, 6027, 2655, 2423, 39184, 1958, 4032, 2423, 39184, 502, 20328, 17082, 13546, 16095, 17182, 2423, 39184, 1958, 4032, 2423, 39184, 1958, 20328, 17082, 13546, 16095, 17182, 2423, 39184, 502, 4032, 2423, 39184, 1958, 20328, 17082, 13546, 16095, 17182, 13672, 1829, 8032, 1863, 9566, 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"word": " 0", "probability": 0.340087890625}, {"start": 1034.35, "end": 1034.51, "word": " و", "probability": 0.546875}, {"start": 1034.51, "end": 1034.59, "word": " الـ", "probability": 0.459716796875}, {"start": 1034.59, "end": 1034.71, "word": " 1", "probability": 0.7490234375}, {"start": 1034.71, "end": 1035.27, "word": " صغيرهم", "probability": 0.8653564453125}, {"start": 1035.27, "end": 1035.67, "word": " Zero", "probability": 0.10186767578125}, {"start": 1035.67, "end": 1036.09, "word": " الـ", "probability": 0.73388671875}, {"start": 1036.09, "end": 1036.31, "word": " 0", "probability": 0.45654296875}, {"start": 1036.31, "end": 1036.43, "word": " و", "probability": 0.71142578125}, {"start": 1036.43, "end": 1036.51, "word": " الـ", "probability": 0.878173828125}, {"start": 1036.51, "end": 1036.69, "word": " 0", "probability": 0.71484375}, {"start": 1036.69, "end": 1037.09, "word": " صغيرهم", "probability": 0.9945068359375}, {"start": 1037.09, "end": 1037.45, "word": " Zero", 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"probability": 0.90869140625}, {"start": 1041.27, "end": 1041.51, "word": " إذن", "probability": 0.4418131510416667}, {"start": 1041.51, "end": 1041.95, "word": " كبيرهم", "probability": 0.9168701171875}, {"start": 1041.95, "end": 1042.11, "word": " إيش", "probability": 0.748779296875}, {"start": 1042.11, "end": 1042.77, "word": " هيطلع", "probability": 0.782763671875}, {"start": 1042.77, "end": 1043.35, "word": " Zero", "probability": 0.94140625}], "temperature": 1.0}, {"id": 46, "seek": 106719, "start": 1043.95, "end": 1067.19, "text": "بنفس الطريقة بناخد اللي هو السطر الثاني مع العمود الأول واحد مع الـ0 صغيرهن Zero Zero مع الواحد صغيرهن Zero Zero مع الواحد صغيرهن Zero إذا التلاتة صغيرة هنا مش هيطلع اللي هو الـ Zero بنفس الأسلوب بنطلع باقي اللي هي القيم فبكون عندى بطلع ال matrix هذا اللي أمامى", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 44945, 47283, 3215, 13672, 1829, 31439, 21136, 9566, 2288, 6024, 104, 7649, 1829, 20449, 18863, 2304, 23328, 16247, 12610, 36764, 24401, 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"probability": 0.2083740234375}, {"start": 1358.47, "end": 1358.79, "word": " product", "probability": 0.90771484375}, {"start": 1358.79, "end": 1359.05, "word": " بين", "probability": 0.93603515625}, {"start": 1359.05, "end": 1359.23, "word": " ال", "probability": 0.90478515625}, {"start": 1359.23, "end": 1359.39, "word": " a", "probability": 0.94775390625}, {"start": 1359.39, "end": 1359.49, "word": " و", "probability": 0.89794921875}, {"start": 1359.49, "end": 1359.59, "word": " ال", "probability": 0.9248046875}, {"start": 1359.59, "end": 1359.75, "word": " b", "probability": 0.9697265625}, {"start": 1359.75, "end": 1359.93, "word": " و", "probability": 0.96728515625}, {"start": 1359.93, "end": 1360.37, "word": " البولين", "probability": 0.9716796875}, {"start": 1360.37, "end": 1360.51, "word": " ال", "probability": 0.98193359375}, {"start": 1360.51, "end": 1360.79, "word": " product", "probability": 0.98291015625}, {"start": 1360.79, "end": 1361.07, "word": " بين", "probability": 0.96240234375}, {"start": 1361.07, "end": 1361.25, "word": " ال", "probability": 0.97607421875}, {"start": 1361.25, "end": 1361.37, "word": " a", "probability": 0.97705078125}, {"start": 1361.37, "end": 1361.45, "word": " و", "probability": 0.984375}, {"start": 1361.45, "end": 1361.59, "word": " ال", "probability": 0.94482421875}, {"start": 1361.59, "end": 1361.87, "word": " c", "probability": 0.9833984375}, {"start": 1361.87, "end": 1362.45, "word": " و", "probability": 0.53955078125}, {"start": 1362.45, "end": 1363.09, "word": " هذولة", "probability": 0.8031005859375}, {"start": 1363.09, "end": 1363.31, "word": " اللي", "probability": 0.96142578125}, {"start": 1363.31, "end": 1363.59, "word": " هى", "probability": 0.5145263671875}, {"start": 1363.59, "end": 1364.15, "word": " هذا", "probability": 0.58935546875}, {"start": 1364.15, "end": 1364.57, "word": " السؤال", "probability": 0.9930013020833334}, {"start": 1364.57, "end": 1364.85, "word": " بس", "probability": 0.867431640625}, {"start": 1364.85, "end": 1365.03, "word": " هى", "probability": 0.854248046875}, {"start": 1365.03, "end": 1365.49, "word": " السؤال", "probability": 0.9931640625}, {"start": 1365.49, "end": 1365.79, "word": " هذا", "probability": 0.8671875}, {"start": 1365.79, "end": 1366.23, "word": " اللي", "probability": 0.720703125}, {"start": 1366.23, "end": 1366.41, "word": " هو", "probability": 0.8662109375}, {"start": 1366.41, "end": 1366.53, "word": " ال", "probability": 0.8984375}, {"start": 1366.53, "end": 1366.71, "word": " a", "probability": 0.97119140625}, {"start": 1366.71, "end": 1366.83, "word": " و", "probability": 0.96923828125}, {"start": 1366.83, "end": 1366.91, "word": " ال", "probability": 0.94482421875}, {"start": 1366.91, "end": 1367.13, "word": " b", "probability": 0.9853515625}, {"start": 1367.13, "end": 1367.33, "word": " و", "probability": 0.99609375}, {"start": 1367.33, "end": 1367.47, "word": " ال", "probability": 0.912109375}, {"start": 1367.47, "end": 1367.79, "word": " i", "probability": 0.5390625}, {"start": 1367.79, "end": 1368.35, "word": " و", "probability": 0.94775390625}, {"start": 1368.35, "end": 1369.05, "word": " هذولة", "probability": 0.9189453125}, {"start": 1369.05, "end": 1369.39, "word": " و", "probability": 0.6376953125}, {"start": 1369.39, "end": 1369.79, "word": " هذولة", "probability": 0.985595703125}, {"start": 1369.79, "end": 1370.01, "word": " بدي", "probability": 0.813232421875}, {"start": 1370.01, "end": 1370.77, "word": " توجدوليها", "probability": 0.81494140625}, {"start": 1370.77, "end": 1370.93, "word": " و", "probability": 0.68115234375}, {"start": 1370.93, "end": 1371.71, "word": " تعملوليها", "probability": 0.9227701822916666}, {"start": 1371.71, "end": 1371.83, "word": " و", "probability": 0.91259765625}, {"start": 1371.83, "end": 1372.55, "word": " تكتبوليها", "probability": 0.9802594866071429}], "temperature": 1.0}, {"id": 60, "seek": 139417, "start": 1373.07, "end": 1394.17, "text": "في homework و زي ال homework اللي فات و تبعتوليه على اللي هو ال whats او على ال model زي ما بدكم زي ما بتشوفوا مناسب و ان شاء الله في لقاء اخر بينكمل اللي هو ال determinants او المحددات والسلام عليكم ورحمة الله وبركاته", "tokens": [41185, 14578, 4032, 30767, 1829, 2423, 14578, 13672, 1829, 6156, 9307, 4032, 6055, 3555, 34268, 12610, 1829, 3224, 15844, 13672, 1829, 31439, 2423, 29625, 1975, 2407, 15844, 2423, 2316, 30767, 1829, 19446, 47525, 24793, 30767, 1829, 19446, 39894, 8592, 38688, 14407, 3714, 8315, 35457, 4032, 16472, 13412, 16606, 21984, 8978, 5296, 4587, 16606, 1975, 34740, 49374, 24793, 1211, 13672, 1829, 31439, 2423, 15957, 1719, 1975, 2407, 9673, 24401, 3215, 9307, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.15779432429130688, "compression_ratio": 1.778894472361809, "no_speech_prob": 4.118680953979492e-05, "words": [{"start": 1373.07, "end": 1373.31, "word": "في", "probability": 0.65576171875}, {"start": 1373.31, "end": 1373.97, "word": " homework", "probability": 0.431396484375}, {"start": 1373.97, "end": 1374.55, "word": " و", "probability": 0.8662109375}, {"start": 1374.55, "end": 1374.81, "word": " زي", "probability": 0.804931640625}, {"start": 1374.81, "end": 1374.93, "word": " ال", "probability": 0.98583984375}, {"start": 1374.93, "end": 1375.21, "word": " homework", "probability": 0.8564453125}, {"start": 1375.21, "end": 1375.47, "word": " اللي", "probability": 0.7626953125}, {"start": 1375.47, "end": 1375.95, "word": " فات", "probability": 0.9912109375}, {"start": 1375.95, "end": 1376.39, "word": " و", "probability": 0.595703125}, {"start": 1376.39, "end": 1377.37, "word": " تبعتوليه", "probability": 0.8129069010416666}, {"start": 1377.37, "end": 1378.23, "word": " على", "probability": 0.93359375}, {"start": 1378.23, "end": 1378.55, "word": " اللي", "probability": 0.87744140625}, {"start": 1378.55, "end": 1378.75, "word": " هو", "probability": 0.97412109375}, {"start": 1378.75, "end": 1378.87, "word": " ال", "probability": 0.97412109375}, {"start": 1378.87, "end": 1379.21, "word": " whats", "probability": 0.2412109375}, {"start": 1379.21, "end": 1379.55, "word": " او", "probability": 0.73876953125}, {"start": 1379.55, "end": 1379.67, "word": " على", "probability": 0.70849609375}, {"start": 1379.67, "end": 1379.77, "word": " ال", "probability": 0.79345703125}, {"start": 1379.77, "end": 1380.09, "word": " model", "probability": 0.8603515625}, {"start": 1380.09, "end": 1380.47, "word": " زي", "probability": 0.95654296875}, {"start": 1380.47, "end": 1380.57, "word": " ما", "probability": 0.91796875}, {"start": 1380.57, "end": 1381.07, "word": " بدكم", "probability": 0.92041015625}, {"start": 1381.07, "end": 1381.67, "word": " زي", "probability": 0.834228515625}, {"start": 1381.67, "end": 1381.77, "word": " ما", "probability": 0.93896484375}, {"start": 1381.77, "end": 1382.47, "word": " بتشوفوا", "probability": 0.93701171875}, {"start": 1382.47, "end": 1383.17, "word": " مناسب", "probability": 0.9601236979166666}, {"start": 1383.17, "end": 1384.17, "word": " و", "probability": 0.97509765625}, {"start": 1384.17, "end": 1384.45, "word": " ان", "probability": 0.818359375}, {"start": 1384.45, "end": 1384.67, "word": " شاء", "probability": 0.989501953125}, {"start": 1384.67, "end": 1384.99, "word": " الله", "probability": 0.9462890625}, {"start": 1384.99, "end": 1385.45, "word": " في", "probability": 0.83837890625}, {"start": 1385.45, "end": 1385.95, "word": " لقاء", "probability": 0.96337890625}, {"start": 1385.95, "end": 1386.55, "word": " اخر", "probability": 0.84423828125}, {"start": 1386.55, "end": 1387.71, "word": " بينكمل", "probability": 0.734375}, {"start": 1387.71, "end": 1388.09, "word": " اللي", "probability": 0.985595703125}, {"start": 1388.09, "end": 1388.43, "word": " هو", "probability": 0.9912109375}, {"start": 1388.43, "end": 1389.13, "word": " ال", "probability": 0.94189453125}, {"start": 1389.13, "end": 1389.97, "word": " determinants", "probability": 0.89404296875}, {"start": 1389.97, "end": 1390.47, "word": " او", "probability": 0.92578125}, {"start": 1390.47, "end": 1392.53, "word": " المحددات", "probability": 0.9862060546875}, {"start": 1392.53, "end": 1393.01, "word": " والسلام", "probability": 0.8860677083333334}, {"start": 1393.01, "end": 1393.35, "word": " عليكم", "probability": 0.93603515625}, {"start": 1393.35, "end": 1393.63, "word": " ورحمة", "probability": 0.82525634765625}, {"start": 1393.63, "end": 1393.81, "word": " الله", "probability": 0.9541015625}, {"start": 1393.81, "end": 1394.17, "word": " وبركاته", "probability": 0.9767578125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1394.1725, "duration_after_vad": 1384.1609687499997}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5b47beced82370f52437f56c4be3e81fdcffe183
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/h5dPgLG9XGA_raw.srt
@@ -0,0 +1,1196 @@
+1
+00:00:00,000 --> 00:00:05,100
+بسم الله الرحمن الرحيم هذه هي المحاضرة الأولى
+
+2
+00:00:05,100 --> 00:00:11,520
+لمادة رياضيات منفصلة لطلاب وطالبات الجامعة
+
+3
+00:00:11,520 --> 00:00:16,680
+الإسلامية كلية technology المعلومات قسم الحوسبة
+
+4
+00:00:16,680 --> 00:00:24,200
+المتنقلة المحاضرة الأولى بعد حالة الطوارئ
+
+5
+00:00:26,540 --> 00:00:33,800
+عنوان المحاضرة الـ matrices أو اكمال محاضرة
+
+6
+00:00:33,800 --> 00:00:39,300
+matrices التي بدأناها سابقاً كنا عرفنا شو معنات
+
+7
+00:00:39,300 --> 00:00:46,300
+matrix وقلنا اللي هو شو معنات انه درجة ال matrix M
+
+8
+00:00:46,300 --> 00:00:53,050
+by N يعني عدد الصفوف M وعدد الأعمد Nوعرفنا أيضًا
+
+9
+00:00:53,050 --> 00:00:57,930
+اللي هو شو معناه تجمع two matrices قبل هيك وقلنا
+
+10
+00:00:57,930 --> 00:01:02,170
+عشان نجمع اللي هو مصفوفتين لازم يكون المصفوفتين
+
+11
+00:01:02,170 --> 00:01:06,050
+نفس الدرجة يعني لو كانت المصفوفة الأولى تلاتة في
+
+12
+00:01:06,050 --> 00:01:09,820
+تلاتة بدها تكون المصفوفة التانية اللي بنجمعهاهيها
+
+13
+00:01:09,820 --> 00:01:12,740
+أيضا تلاتة في تلاتة وعملية الجمع زي ما انتوا
+
+14
+00:01:12,740 --> 00:01:17,740
+عارفين كل entry مع ال entry المقابل لهم بعد هيك
+
+15
+00:01:17,740 --> 00:01:21,980
+عرفنا عملية الضرب اللي هو two matrices وقلنا عشان
+
+16
+00:01:21,980 --> 00:01:27,380
+نضرب ال matrix اللي درجتهm by k لازم اللي هو يكون
+
+17
+00:01:27,380 --> 00:01:31,660
+ال matrix التاني k by something يعني k by n يعني
+
+18
+00:01:31,660 --> 00:01:35,780
+عدد اللي هو الأعمدة في ال matrix الأول يساوي عدد
+
+19
+00:01:35,780 --> 00:01:39,640
+الصفوف في ال matrix التاني عساس اللي هو اللي هو
+
+20
+00:01:39,640 --> 00:01:44,640
+تكون عملية الضرب بين a وb عملية معرفةو قولنا كيف
+
+21
+00:01:44,640 --> 00:01:48,560
+اللي هي عملية الضرب اللي هو مصفوفتين مع بعض و
+
+22
+00:01:48,560 --> 00:01:52,380
+قولنا عشان نضرب مصفوفتين هي المصفوفة هذه مثلا من
+
+23
+00:01:52,380 --> 00:01:56,020
+الدرجة اللي هو هاي صف صفين تلاتة أربعة من الدرجة
+
+24
+00:01:56,020 --> 00:02:01,560
+أربعة في تلاتة يعني أربع مصفوف .. أربع صفوف و تلات
+
+25
+00:02:01,560 --> 00:02:07,020
+أعمدةبنضربها في مصفوفة تانية تلت صفوف و عمودين
+
+26
+00:02:07,020 --> 00:02:10,960
+معناته عملية الضرب جائزة و بيصير عملية الضرب ميج
+
+27
+00:02:10,960 --> 00:02:15,000
+بنضرب الصف اللي هو الأول في العمود الأول بنضرب
+
+28
+00:02:15,000 --> 00:02:19,240
+واحد في اتنين زائد سفر في واحد زائد أربعة في تلاتة
+
+29
+00:02:19,240 --> 00:02:23,380
+و اللي بيطلع عندى بيكون هو ال entry الأول عند ال
+
+30
+00:02:23,380 --> 00:02:28,440
+seminar c11 بنفس الأسلوب اللي هو بناخد اللي هو
+
+31
+00:02:28,440 --> 00:02:33,350
+الصف الأول في العمود الثاني بنحصل على العنصرC12
+
+32
+00:02:33,350 --> 00:02:39,390
+وخلصنا من السطر الأول بنجي للسطر الثاني في العمود
+
+33
+00:02:39,390 --> 00:02:44,130
+الأول بنجيب أول واحد في السطر الثاني في حصل نتج
+
+34
+00:02:44,130 --> 00:02:49,450
+الضرب وهكذا لما نكمل اللي هو المصفوفة كامل اللي هي
+
+35
+00:02:49,450 --> 00:02:54,990
+عملية الضرب كما شرحناها سابقا مافيش داعي أننا
+
+36
+00:02:54,990 --> 00:03:00,450
+نعيدهاواخدنا أمثلة على ضرب مصهوفات وقلنا المصهوفة
+
+37
+00:03:00,450 --> 00:03:04,590
+A B ليس شرطا أنها تساوي المصهوفة B A وهيعنى مثال
+
+38
+00:03:04,590 --> 00:03:09,230
+على ذلك بعدين عرفنا شو معنات مصهوفة الوحدة مصهوفة
+
+39
+00:03:09,230 --> 00:03:12,110
+الوحدة اللى بيكون عناصر القطر الرئيسى واحد واحد
+
+40
+00:03:12,110 --> 00:03:15,650
+والباقى عناصر الصفار سواء مصهوفة الوحدة من درجة
+
+41
+00:03:15,650 --> 00:03:18,970
+اتنين في اتنين او مصهوفة الوحدة من درجة تلاتة في
+
+42
+00:03:18,970 --> 00:03:24,570
+تلاتة بنفس الاسلوبعرفنا اللي هو مدور المصفوفة أو A
+
+43
+00:03:24,570 --> 00:03:29,230
+Transverse اللي هي عملية تحويل الصفوف إلى أعمدة و
+
+44
+00:03:29,230 --> 00:03:36,390
+قلنا كيف بنحولها سابقا قلنا عملية ضرب A R المتكررة
+
+45
+00:03:36,390 --> 00:03:40,890
+A R معناته أنه ضربنا ال matrix في نفسه R من المرات
+
+46
+00:03:40,890 --> 00:03:44,810
+لما نقول A أو السفر نعني البقية اللي هو المصوفة
+
+47
+00:03:44,810 --> 00:03:50,320
+المصوفة الوحدةاللي هي من الدرجة اللي هي النية حسب
+
+48
+00:03:50,320 --> 00:03:54,980
+اللي هي الـ A اللي بنحكي عنها عرفنا شو معناته اللي
+
+49
+00:03:54,980 --> 00:04:02,000
+هو ال matrix يكون symmetric و بعدين أجينا اللي هو
+
+50
+00:04:02,000 --> 00:04:06,220
+أوصلنا للموضوع اللي احنا اليوم بدنا نفصل فيه و
+
+51
+00:04:06,220 --> 00:04:10,400
+حكينا برضه مقدمة فيه في المحاضرة قلنا اللي هو حاجة
+
+52
+00:04:10,400 --> 00:04:15,040
+اسمها zero one matrix هذه عبارة عن مصفوفةكل
+
+53
+00:04:15,040 --> 00:04:19,640
+عناصرها عبارة عن يا سفر يا واحد عناصر المصفوفة يا
+
+54
+00:04:19,640 --> 00:04:23,920
+سفر يا واحد في عندنا عملية بدنا نجريها بين
+
+55
+00:04:23,920 --> 00:04:27,780
+المصفوفات اسمها الـ Boolean Operations الـ Boolean
+
+56
+00:04:27,780 --> 00:04:33,220
+Operations بين اللي هي المصفوفتين هنعرفها بعد شوية
+
+57
+00:04:33,220 --> 00:04:39,570
+اللي هي او عملية الضرب البولينيأول اشي بدنا نعرف
+
+58
+00:04:39,570 --> 00:04:44,010
+شو معنات الـ Boolean operation بين الصفر والواحد
+
+59
+00:04:44,010 --> 00:04:48,510
+اللي هما عناصر الـ 01 matrix اللي احنا بدنا نجري
+
+60
+00:04:48,510 --> 00:04:53,870
+عليه عملية الـ Boolean operation وبرضه ذكرناها في
+
+61
+00:04:53,870 --> 00:04:59,570
+المحاضرة قلنا عشان بدنا نعرف شو معنات عمليتين الـ
+
+62
+00:04:59,570 --> 00:05:02,970
+Boolean operations عندنا اللي هي ال meet وال joint
+
+63
+00:05:03,390 --> 00:05:06,670
+وقلنا نتخيل ال meet و ال join طبعا ال b1 و ال b2
+
+64
+00:05:06,670 --> 00:05:10,850
+هدول اللي بنعملهم meet او نعملهم joint هدول ال b1
+
+65
+00:05:10,850 --> 00:05:15,610
+و ال b2 يا بياخدن 0 يا بياخدن اياش 1 فالان عملية
+
+66
+00:05:15,610 --> 00:05:22,070
+ال meet اللي هي بتذكرنا و كأنه احنا قلنا انه بنذكر
+
+67
+00:05:22,070 --> 00:05:26,890
+اللي هي عملية ال and و ال joint عملية ال or و
+
+68
+00:05:26,890 --> 00:05:31,070
+بنتخيل ان الواحد هو عبارة عن ال true و ال zero
+
+69
+00:05:31,070 --> 00:05:36,030
+falseفبكون اللي هي ال .. ال .. ال .. ال .. الجملة
+
+70
+00:05:36,030 --> 00:05:40,850
+اللي فيها الـ and true اللي هي في حال .. ال .. ال
+
+71
+00:05:40,850 --> 00:05:45,590
+.. في حالة واحدة لما يكون التمتين true يعني بكون
+
+72
+00:05:45,590 --> 00:05:49,210
+كلهم false في حالة اللي هي التمتين false أو أي
+
+73
+00:05:49,210 --> 00:05:53,470
+واحدة فيهم true فبصير عندى الآن الواحد وواحد
+
+74
+00:05:53,470 --> 00:05:59,040
+الواحد ميت الواحد واحدو الباقى الحالات كلها هيطلع
+
+75
+00:05:59,040 --> 00:06:05,040
+عندى سفر ال joint اللى هو بتكون اللى هو false فى
+
+76
+00:06:05,040 --> 00:06:09,560
+حالة واحدة لما نكون عندى التنتين false وباقى
+
+77
+00:06:09,560 --> 00:06:14,200
+الحالات ايش اتروا لكن الان بعد شوية هعلمكم طريقة
+
+78
+00:06:14,200 --> 00:06:18,320
+اللى هو اتسهل عليكم اللى هو إيجاد ال joint و ال
+
+79
+00:06:18,320 --> 00:06:23,560
+meet بكل سهولة بس خلينى الان نيجي نعرف شو معناته
+
+80
+00:06:23,560 --> 00:06:28,380
+ال joinبين اللي هو two matrices يعني عند ال matrix
+
+81
+00:06:28,380 --> 00:06:33,900
+A و ال matrix B عشان نعملهم join بين ال A و ال B
+
+82
+00:06:33,900 --> 00:06:38,620
+لازم زي عملية الجمع يكون اللي هو ال order للإتنين
+
+83
+00:06:38,620 --> 00:06:42,600
+اللي هين نفس ال order يعني لو كان ال A من ال order
+
+84
+00:06:42,600 --> 00:06:46,840
+on by and لازم يكون ال B برضه من ال order on by
+
+85
+00:06:46,840 --> 00:06:51,170
+and يعني اللي هين نفس الدرجةكذلك عملية الـ meet
+
+86
+00:06:51,170 --> 00:06:54,930
+برضه بين الـ A والـ B، A ميت B برضه لازم يكون
+
+87
+00:06:54,930 --> 00:07:00,970
+الاتنتين اللي هن بنفس الدرجة وعملية اللي هى ال
+
+88
+00:07:00,970 --> 00:07:06,170
+meet أو ال joined في روحة شبيهة بعملية الجمع يعني
+
+89
+00:07:06,170 --> 00:07:12,290
+كل بمعنى آخر أنه كل عنصر بنعمله joined مع العنصر
+
+90
+00:07:12,290 --> 00:07:16,250
+اللي مقابل إله و ال meet برضه نفس الشيء خليني أخد
+
+91
+00:07:16,250 --> 00:07:19,480
+مثال، تشوفوا الصلاة والنبي عليه الصلاة والسلامنجي
+
+92
+00:07:19,480 --> 00:07:23,400
+للمثال الأول بقول find the join and meet of the 0
+
+93
+00:07:23,400 --> 00:07:28,440
+,1 matrix 0,1 matrices اللي أنا عندي لان في عندي
+
+94
+00:07:28,440 --> 00:07:31,920
+مصففتين مصفوفة الأولى واضح من الدرجة واحدة اللي هي
+
+95
+00:07:31,920 --> 00:07:36,260
+2 في عدد الأعناد تلاتة اتنين في تلاتة والتانية بيه
+
+96
+00:07:36,260 --> 00:07:38,660
+في اتنين في تلاتة ايه ده من التنين من نفس الدرجة
+
+97
+00:07:38,660 --> 00:07:44,810
+اذا الخطوة الأولى نحو اتجاه اننا نعرف الاللي هي
+
+98
+00:07:44,810 --> 00:07:50,730
+موجودة فخلّيني انا بقول اذا join of a and b ايه
+
+99
+00:07:50,730 --> 00:07:56,030
+join بيه ايش بده بناخد كل ال entry مع اللي عاجباله
+
+100
+00:07:56,030 --> 00:08:00,280
+عند الواحد or اللي هو mean ال zeroأو join الـ 0 و
+
+101
+00:08:00,280 --> 00:08:04,920
+الـ 0 or الـ 1 و الـ 1 or الـ 0 هى 1 or الـ 0 و 0
+
+102
+00:08:04,920 --> 00:08:10,680
+or الـ 1 و نفس الاشي 1 or الـ 0 هى و هنا 0 or الـ
+
+103
+00:08:10,680 --> 00:08:16,640
+1 و هنا 1 or الـ 1 و هنا 0 or الـ 0 بدنا نعمل هنا
+
+104
+00:08:16,640 --> 00:08:22,220
+الـ join هذه أريحكم الـ join بس خد العدد الأكبر من
+
+105
+00:08:22,220 --> 00:08:26,100
+هنا واحد ولا زيرو من العدد واحدمين الأكبر هنا؟
+
+106
+00:08:26,100 --> 00:08:29,720
+واحد، مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ واحد،
+
+107
+00:08:29,720 --> 00:08:32,080
+مين الأكبر هنا؟ واحد، مين الأكبر هنا؟ اللي هو
+
+108
+00:08:32,080 --> 00:08:36,660
+السفر، إذا ال join اللي هو تاخد الأكبر فيهم،
+
+109
+00:08:36,660 --> 00:08:39,620
+الأكبر بين الواحد وبين السفر أو بين السفر والسفر
+
+110
+00:08:39,620 --> 00:08:43,480
+أو بين الواحد والواحد، واضحة بتصور، نيجي الآن ال
+
+111
+00:08:43,480 --> 00:08:47,000
+meet، ال meet مين الأصغر؟ وانت بتيجي ايه؟الان
+
+112
+00:08:47,000 --> 00:08:50,700
+مالعشنا نستذكر true و false و مش عارف ايش مع انه
+
+113
+00:08:50,700 --> 00:08:55,280
+سهل ال true و false اللي بده احد الطريقين اللي هو
+
+114
+00:08:55,280 --> 00:09:01,200
+اسهلكم الان the meet of a and b is a meet b a meet
+
+115
+00:09:01,200 --> 00:09:05,820
+b اللي هو بيجي الان مع كل عنصر a meet zero zero
+
+116
+00:09:05,820 --> 00:09:10,960
+meet one one meet zero الان نفس الاشي zero meet
+
+117
+00:09:10,960 --> 00:09:15,990
+one one meet oneand zero meet zero هاي اللي هنا
+
+118
+00:09:15,990 --> 00:09:22,170
+اللي هي a meet b الان ال a meet b نيجي للواحد or
+
+119
+00:09:22,170 --> 00:09:24,670
+zero زي ما قلنا بتاخد الصغير بطلع الصفر تاخد
+
+120
+00:09:24,670 --> 00:09:27,370
+الصغير بطلع الصفر تاخد الصغير بطلع الصفر تاخد
+
+121
+00:09:27,370 --> 00:09:30,350
+الصغير بطلع الصفر وهنا الصغير واحد اللي هو بين
+
+122
+00:09:30,350 --> 00:09:34,430
+الواحد والواحد والصغير هنا zero أو zero إذن هاي
+
+123
+00:09:34,430 --> 00:09:39,830
+معناة ال join بين two matrices وهي معناة ال meet
+
+124
+00:09:39,830 --> 00:09:46,100
+بين two matricesالان بدنا نعرف Boolean product الـ
+
+125
+00:09:46,100 --> 00:09:49,800
+Boolean product بين two matrices صلوا على النبي
+
+126
+00:09:49,800 --> 00:09:53,500
+عليه الصلاة والسلام الان الـ Boolean product بين
+
+127
+00:09:53,500 --> 00:09:59,780
+ال matrix A و ال matrix B بروح
+
+128
+00:09:59,780 --> 00:10:05,060
+الدرب العادى لكن بواسطة ال join و ال meet و كأنه
+
+129
+00:10:05,060 --> 00:10:11,810
+بده يصير عند ال meet بلعبدور الضرب و الـ join بلعب
+
+130
+00:10:11,810 --> 00:10:16,310
+دور اللي هو إيش الجمع اتخيل إنه أنت بتضرب two
+
+131
+00:10:16,310 --> 00:10:21,370
+matrices ضرب عادي بس بدل ما تحط عملية الضرب حط
+
+132
+00:10:21,370 --> 00:10:25,930
+عملية الـ join و بدل ما تحط .. آسف عملية الميت و
+
+133
+00:10:25,930 --> 00:10:32,350
+بدل ما تحط عملية الجمع حط عملية مين الـ joinهدى
+
+134
+00:10:32,350 --> 00:10:35,850
+وما بيكونش ولا إش جديد و زى الضرب العادى اللى
+
+135
+00:10:35,850 --> 00:10:42,570
+بنعرفه بالظبط لحتى أن عدد الدرجة الـ A هيكون N by
+
+136
+00:10:42,570 --> 00:10:48,990
+K Matrix لازم درجة الـ B يكون مقماله اللى هو يبدأ
+
+137
+00:10:48,990 --> 00:10:55,450
+بـ K by N Matrix يعني الاتنين والعدد الأولانى عدد
+
+138
+00:10:55,450 --> 00:11:00,360
+الأعمدة اللى فيهلازم يساوي عدد السطور اللي في مين
+
+139
+00:11:00,360 --> 00:11:05,460
+في الـ matrix اللي هو الثاني لتشوف مثال عملي
+
+140
+00:11:05,460 --> 00:11:09,900
+أمامنا هذه عند الـ A وهذه عند الـ B بيقول لي find
+
+141
+00:11:09,900 --> 00:11:13,920
+the Boolean product of A and B where إذا بدنا نوجد
+
+142
+00:11:13,920 --> 00:11:18,710
+اللي هو الـ Boolean productاللي هو بين الـ A و الـ
+
+143
+00:11:18,710 --> 00:11:22,630
+B ماشي يا جماعة طيب الآن عشان وجود الـ Boolean
+
+144
+00:11:22,630 --> 00:11:25,590
+Product بمش بسأل حالنا أصلا يعني هذا هو Zero
+
+145
+00:11:25,590 --> 00:11:28,930
+Matrix و هذا Zero Matrix إذا بنحكي فعلا عن Boolean
+
+146
+00:11:28,930 --> 00:11:34,130
+Product طيب هل هذا درجته اللي هو واحد، اتنين،
+
+147
+00:11:34,130 --> 00:11:41,580
+تلاتة صفوف عمودين؟ أه و هذا قداش؟اللي هو درجته
+
+148
+00:11:41,580 --> 00:11:45,860
+تلاتة في اتنين وهذا درجته اتنين في تلاتة اذا اللي
+
+149
+00:11:45,860 --> 00:11:50,560
+هو عملية الضرب ايه شمالها جائزة ومعرفة الـ Boolean
+
+150
+00:11:50,560 --> 00:11:55,080
+Product معرف عملية الضرب في هذه الحالة نشوف كيف
+
+151
+00:11:55,080 --> 00:11:59,830
+نوجدهاشوفوا عليها لأن بدي اجي زي ما قلنا بتخيل
+
+152
+00:11:59,830 --> 00:12:04,710
+حالنا اننا بنضرب ضرب عادي باجي على اللي هو بس اللي
+
+153
+00:12:04,710 --> 00:12:11,770
+هو بنغير عملية الضرب بـJoin وعملية اللي هي الجامع
+
+154
+00:12:11,770 --> 00:12:21,180
+ابنيتعملية الضرب بميت وعملية الجمع ب join بنشوف
+
+155
+00:12:21,180 --> 00:12:27,200
+كيف لأن نيجي هنا و السطر الأول بنيجي بنقول واحد
+
+156
+00:12:27,200 --> 00:12:30,240
+السطر الأول مع ايش طبعا زي ما بنعمل في الضرب مع
+
+157
+00:12:30,240 --> 00:12:39,050
+العمود الأول واحد اشمالهميت واحد Zero ميت واحد و
+
+158
+00:12:39,050 --> 00:12:43,110
+بين الاتنين ايش ماله ال join هاي واحد ميت الواحد و
+
+159
+00:12:43,110 --> 00:12:48,670
+Zero ميت ال zero الان خلصنا اللي هو السطر الأول مع
+
+160
+00:12:48,670 --> 00:12:52,430
+العمود الأول الان السطر الأول مع مين مع العمود
+
+161
+00:12:52,430 --> 00:13:00,490
+الأول التاني اللي هو واحد اللي هو and الواحدو Zero
+
+162
+00:13:00,490 --> 00:13:08,550
+and الواحد و بينهما عملية الار وهذه ميت وهذه جوين
+
+163
+00:13:08,550 --> 00:13:14,610
+امكن نقول أند و ار أسهل لكم الآن خلصنا من الجزء
+
+164
+00:13:14,610 --> 00:13:20,530
+الثاني نجي للثالث واحد مع اللي هو ال zero واحد مع
+
+165
+00:13:20,530 --> 00:13:24,850
+ال zero and و ال zero مع ال واحد and و بينهم ايش
+
+166
+00:13:24,850 --> 00:13:30,370
+ارالان بنعمل نفس الاشي السطر الثاني مع العمود
+
+167
+00:13:30,370 --> 00:13:34,050
+الأول السطر الثاني مع العمود الثاني السطر الثاني
+
+168
+00:13:34,050 --> 00:13:37,250
+مع العمود الثالث بيكون جيبنا السطر الثاني في
+
+169
+00:13:37,250 --> 00:13:41,330
+المصهوفة الناتجة نيجي الأن نفس الاشي السطر الثالث
+
+170
+00:13:41,330 --> 00:13:45,570
+مع العمود الأول بتجيب ال entry هذا السطر الأول مع
+
+171
+00:13:45,570 --> 00:13:49,590
+هذا بتجيب ال entry اللي بعده و هكذا فبكون احنا
+
+172
+00:13:49,590 --> 00:13:54,540
+حصلنا على ال job اللي هو ال boolean productالـ
+
+173
+00:13:54,540 --> 00:13:59,500
+Boolean product ندى الان اللى هو على طول نحسب الان
+
+174
+00:13:59,500 --> 00:14:05,260
+ال ال قولنا ال and ايش ماله لصغير واحد و ال هنا
+
+175
+00:14:05,260 --> 00:14:09,920
+لصغير سفر بينهم بدنا ناخد الكبير ال join بده
+
+176
+00:14:09,920 --> 00:14:13,960
+الكبير هذا واحد وهذا سفر الكبير واحد ماشي الحال
+
+177
+00:14:13,960 --> 00:14:19,360
+على طول اللى بعده هنا واحدالصغير واحد والصغير هنا
+
+178
+00:14:19,360 --> 00:14:24,020
+سفر واحد ولا سفر الكبير هنا ال join كبير هذا ال or
+
+179
+00:14:24,020 --> 00:14:27,600
+كبير يعني باخد صغير هذه وصغير هذه مع كبير الكل
+
+180
+00:14:27,600 --> 00:14:31,860
+صغير هذه واحد وصغير هذه سفر كبير هنا الاتنين واحد
+
+181
+00:14:32,420 --> 00:14:36,240
+الان صغير هذه سفر و صغير هذه سفر كبير هين ايش
+
+182
+00:14:36,240 --> 00:14:42,000
+هيطلع سفر لأن هذه صغير هين سفر و هذه صغير هين سفر
+
+183
+00:14:42,000 --> 00:14:46,920
+إذا كبير هين اتين اتين لازم يطلع سفر لأن الصغير
+
+184
+00:14:46,920 --> 00:14:51,820
+هدولة سفر و كبير هدولة واحد الان صار عندي سفر و
+
+185
+00:14:51,820 --> 00:14:56,180
+واحد كبير هين واحد طبعا نفس الاشي صغير هين سفر
+
+186
+00:14:56,180 --> 00:14:59,620
+هدول و هدولة صغير هين واحد كبير الجهتين اللي
+
+187
+00:14:59,620 --> 00:15:04,730
+بيطلعين واحدالان أصغير هنا واحد أصغير هنا سفر
+
+188
+00:15:04,730 --> 00:15:11,290
+أكبير الجهتين واحد أصغير هنا واحد و أصغير هنا سفر
+
+189
+00:15:11,290 --> 00:15:16,770
+أكبير هنا واحد فاهمين عليها أصغير هنا سفر و أصغير
+
+190
+00:15:16,770 --> 00:15:21,990
+هنا سفر السفر و السفر أكبير هنا إيش سفر واضح هذا
+
+191
+00:15:21,990 --> 00:15:24,370
+اللي هو ال boolean of product
+
+192
+00:15:26,860 --> 00:15:31,660
+الان ناخد مثال اخر لت ايه بتساوي ايه ال matrix
+
+193
+00:15:31,660 --> 00:15:35,040
+اللي امامي هذا عبارة عن matrix ثلاثة في ثلاثة وقول
+
+194
+00:15:35,040 --> 00:15:40,280
+لي find ما يليه ماشي ال matrices التالية بدي ايه
+
+195
+00:15:40,280 --> 00:15:44,740
+تربيع و ايه تكعيد و ايه اربعة و ايه خمسة و ايه n
+
+196
+00:15:45,300 --> 00:15:49,680
+ايش مقصود بالـ A تربيع يعني A Boolean product مع A
+
+197
+00:15:49,680 --> 00:15:54,440
+A تكعيب Boolean product A مع A مع A تلت مرات يعني
+
+198
+00:15:54,440 --> 00:15:58,560
+A تربيع مع A نيدي ناخد واحدة واحدة يا شباب و يا
+
+199
+00:15:58,560 --> 00:16:02,940
+بنات شوفوا صلوا على النبي عليه الصلاة والسلام عندي
+
+200
+00:16:02,940 --> 00:16:07,800
+ال A ال A تربيع بالساوية A اللي هو ال Boolean
+
+201
+00:16:07,800 --> 00:16:12,570
+product مع ال AA بولي انا product مع الـ A اللي هو
+
+202
+00:16:12,570 --> 00:16:17,050
+كما يلي بنيجي بنحط الـ A هنا و الـ A الثانية في
+
+203
+00:16:17,050 --> 00:16:22,910
+هذه الجهة الان بنيجي بناخد الصف مع مين مع العمود
+
+204
+00:16:22,910 --> 00:16:28,250
+الان الصغير الـ 0 و الـ 0 اللي مع بعض صغير و الكل
+
+205
+00:16:28,250 --> 00:16:32,430
+اللي يا كبيريعني الآن Zero مع Zero صغيرهم Zero
+
+206
+00:16:32,430 --> 00:16:36,890
+Zero مع واحد صغيرهم Zero واحد مع واحد صغيرهم واحد
+
+207
+00:16:36,890 --> 00:16:40,390
+اذا كبير التلاتة اللي هي Zero و Zero و واحد اللي
+
+208
+00:16:40,390 --> 00:16:44,120
+هو هيطلع واحدطيب اللي ما .. اللي ما .. عارف اللي
+
+209
+00:16:44,120 --> 00:16:48,500
+ما .. مامشيش معاه فادف تانية الان السطر الأول مع
+
+210
+00:16:48,500 --> 00:16:52,620
+العمود التاني ماشي الان السطر الأول Zero Zero
+
+211
+00:16:52,620 --> 00:16:56,360
+صغيرهن Zero Zero Zero صغيرهن Zero الواحد و الواحد
+
+212
+00:16:56,360 --> 00:17:00,420
+صغيرهن الواحد الان اكبير التلاتة اللي طلع ان اللي
+
+213
+00:17:00,420 --> 00:17:04,620
+عندي السفر و السفر و الواحد واحد فبطلع عند ايش
+
+214
+00:17:04,620 --> 00:17:11,430
+اللي هو الناتج واحد لأن العمود هذاأسف السطر هذا
+
+215
+00:17:11,430 --> 00:17:15,670
+الأول مع العمود التالت الـ 0 و الـ 1 صغيرهم Zero
+
+216
+00:17:15,670 --> 00:17:19,030
+الـ 0 و الـ 0 صغيرهم Zero الـ 1 و الـ 0 صغيرهم
+
+217
+00:17:19,030 --> 00:17:22,770
+Zero اللي هنطلع كله هذا Zero إذن كبيرهم إيش هيطلع
+
+218
+00:17:22,770 --> 00:17:27,550
+Zeroبنفس الطريقة بناخد اللي هو السطر الثاني مع
+
+219
+00:17:27,550 --> 00:17:32,570
+العمود الأول واحد مع الـ0 صغيرهن Zero Zero مع
+
+220
+00:17:32,570 --> 00:17:36,910
+الواحد صغيرهن Zero Zero مع الواحد صغيرهن Zero إذا
+
+221
+00:17:36,910 --> 00:17:40,970
+التلاتة صغيرة هنا مش هيطلع اللي هو الـ Zero بنفس
+
+222
+00:17:40,970 --> 00:17:45,130
+الأسلوب بنطلع باقي اللي هي القيم فبكون عندى بطلع
+
+223
+00:17:45,130 --> 00:17:48,950
+ال matrix هذا اللي أمامىلأن هذا الـ matrix اللي
+
+224
+00:17:48,950 --> 00:17:52,130
+أمامي هو الـ A تربيع بدي أوجد الـ A تكعيب الـ A
+
+225
+00:17:52,130 --> 00:17:55,350
+تكعيب إيش هتساوي الـ A تربيع اللي طلع هذا هيو
+
+226
+00:17:55,350 --> 00:18:00,050
+جبتهان درق اللي هو Boolean product مع مين مع الـ A
+
+227
+00:18:00,050 --> 00:18:04,190
+اللي هو الأصل هيو نيدي نضربهم مع بعض زي ما قلنا
+
+228
+00:18:04,190 --> 00:18:08,450
+قبل بشوية واحد و Zero صغير من Zero واحد واحد صغير
+
+229
+00:18:08,450 --> 00:18:13,090
+من واحد خلاص مدام طلع هنا واحد في الصغار واحد إذا
+
+230
+00:18:13,090 --> 00:18:17,780
+على طول الكبار هيطلع بينهن إيش واحدماكملش يعني لإن
+
+231
+00:18:17,780 --> 00:18:22,880
+هذا السطر مع العمود الثاني لإن واحد مع ال zero
+
+232
+00:18:22,880 --> 00:18:26,020
+zero واحد مع ال zero zero الصغير طبعا zero مع ال
+
+233
+00:18:26,020 --> 00:18:29,000
+zero zero ده نطلع كله نصفار ده هيطلع الكبير zero
+
+234
+00:18:29,000 --> 00:18:32,800
+لإن واحد مع الواحد طلع واحد مثلا واحد طلع واحد من
+
+235
+00:18:32,800 --> 00:18:36,260
+عملية اللي هو مين صغيرهم هذا اللي ماخدت مين يا
+
+236
+00:18:36,260 --> 00:18:40,090
+جماعة اللي ماخدتي العمود السطر الأولمع العمود
+
+237
+00:18:40,090 --> 00:18:43,830
+التالت واحد مع واحد لصغير واحد إذا ما يطلع الكبير
+
+238
+00:18:43,830 --> 00:18:45,770
+هنا إيش ما يطلع من الباقيت هيطلع الكبير هنا واحد
+
+239
+00:18:45,770 --> 00:18:50,110
+هاي واحد وبعدي بعمل السطر الثاني بنفس الأسلوب مع
+
+240
+00:18:50,110 --> 00:18:53,730
+العمود الأول والسطر الثاني بحصل على ال matrix اللي
+
+241
+00:18:53,730 --> 00:18:57,450
+أمامني اللي هو هذا هذا اللي طلع مين عندي a تكعيب
+
+242
+00:18:57,450 --> 00:19:01,910
+تعالي ال a تكعيب هذا بدي أضربه في ال a بطلع مين a
+
+243
+00:19:01,910 --> 00:19:04,810
+قصة أربعة يعني ايه بدي a أربعة بساوي a تكعيب اللي
+
+244
+00:19:04,810 --> 00:19:08,610
+طلعته من الخطوة هذه في a هايه a تكعيب وهيه ال a
+
+245
+00:19:09,070 --> 00:19:15,490
+لاحظ الآن واحد مع الـ 00 بالصغير، Zero مع السطر
+
+246
+00:19:15,490 --> 00:19:19,410
+الأول مع العمود الأول، نعيد نفس الكلام، واحد مع
+
+247
+00:19:19,410 --> 00:19:23,230
+الـ 00، Zero مع الواحد، Zero، واحد مع الواحد،
+
+248
+00:19:23,230 --> 00:19:27,290
+واحد، ده نطلع واحد، الآن اللي بعده، هذا السطر مع
+
+249
+00:19:27,290 --> 00:19:30,410
+هذا العمود، لاحظوا أنه هيتجي الواحد هذا مع الواحد،
+
+250
+00:19:30,410 --> 00:19:33,610
+ده هيطلع واحد منه، ده هيطلع الكل إيه شماله؟ واحد
+
+251
+00:19:33,810 --> 00:19:38,370
+نجي لهذا هيلتجي مع هذا مع الواحد مادام واحد التجه
+
+252
+00:19:38,370 --> 00:19:41,870
+مع الواحد إذا أصغير الواحدين واحد إذا الكبير
+
+253
+00:19:41,870 --> 00:19:46,750
+الناتج بيطلع إيش واحد إذا هذا كل واحد ده هجرب هذا
+
+254
+00:19:46,750 --> 00:19:50,530
+مع هذا برضه نفس الاشي واحد مع Zero Zero واحد مع
+
+255
+00:19:50,530 --> 00:19:53,150
+واحد واحد بزن طلع واحد على طول بيطلع إيش هذا عند
+
+256
+00:19:53,150 --> 00:19:57,070
+واحد بكمل عملية الدرب هيطلع عند ال matrix الأمامي
+
+257
+00:19:57,070 --> 00:20:00,290
+هذا كل واحدات مع هذا اللي في النص Zero طيب شوف إيش
+
+258
+00:20:00,290 --> 00:20:05,350
+اللي .. إيش اللي بدنا هيتعال خد a5 a5 عبارة عن ايش
+
+259
+00:20:05,350 --> 00:20:15,990
+يا جماعة a5 هي a5 اللي عندك ماشي طيب a5 شوف
+
+260
+00:20:15,990 --> 00:20:21,670
+هي a5 a5 بسوء a4 في a a4 هي اللي جيبته منها هي a4
+
+261
+00:20:21,670 --> 00:20:26,610
+يا شبابماشي هين حطيته هان وهي هذا الـ A الأصلي الـ
+
+262
+00:20:26,610 --> 00:20:31,310
+D اتضربت هلجيت الواحد مع ال zero اللي هو zero لأنه
+
+263
+00:20:31,310 --> 00:20:34,030
+لصغير بناخد واحد مع الواحد واحد مدام طلع واحد زي
+
+264
+00:20:34,030 --> 00:20:38,470
+ما قلنا بيطلع كبير الناتج واحد الان تعالي مع هذا
+
+265
+00:20:38,470 --> 00:20:42,250
+السطر مع هذا هيلتقي اكيد واحد مع واحد مدام التقى
+
+266
+00:20:42,250 --> 00:20:45,370
+واحد مع واحد اذا انا صغير هنا واحد اذا كبير الكل
+
+267
+00:20:45,370 --> 00:20:48,350
+بيصير اشمال هو بيصير واحد بيطلع ال entry هذا واحد
+
+268
+00:20:48,760 --> 00:20:52,680
+الان اللي مش فاهم عليا يعني يضرب ضرب واحدة واحدة
+
+269
+00:20:52,680 --> 00:20:57,020
+لكن بصور الكلام واضح الان هذا السطر مع العمود اللي
+
+270
+00:20:57,020 --> 00:21:01,780
+هو الاش الأخير السطر هذا واحد مع الواحد واحد يعني
+
+271
+00:21:01,780 --> 00:21:06,640
+لإنه صغير واحد الان ماكملش الضرب لإنه لما بدي أخد
+
+272
+00:21:06,640 --> 00:21:10,140
+كبير الناتج وعندي واحد طلع واحد إذا كبير الناتج
+
+273
+00:21:10,140 --> 00:21:15,420
+هيطلع اش واحدالان هذا بكمله مع هذا و بكمله مع هذا
+
+274
+00:21:15,420 --> 00:21:18,440
+و بكمله مع هذا بطلع عندي ال matrix الأمامي بطلع
+
+275
+00:21:18,440 --> 00:21:23,760
+عندي A5 ايش بساوي بساوي واحد الان بعد هيك لو جيت
+
+276
+00:21:23,760 --> 00:21:27,720
+ضربت جيبت A6 يعني جيبت ال matrix الأصلي هذا و
+
+277
+00:21:27,720 --> 00:21:31,330
+ضربته في ال هذا اللي طلع وحداتقطعا الوحدات هيتجابل
+
+278
+00:21:31,330 --> 00:21:37,830
+مع اللغات فهيعملن كل وحدات اذا الان جرب A5 مع A و
+
+279
+00:21:37,830 --> 00:21:41,990
+ضربها بيطلع عندك A6 هيطلع واحد واحد واحد كل واحد و
+
+280
+00:21:41,990 --> 00:21:45,730
+هيظلوا يطلع عندك واحد اللي هو ال matrix هذا على
+
+281
+00:21:45,730 --> 00:21:50,440
+طول بالشكل هذاهذه الآن اللي هي عملية ال boolean
+
+282
+00:21:50,440 --> 00:21:54,920
+اللي هو operation أو ال .. ال .. ال boolean
+
+283
+00:21:54,920 --> 00:21:59,560
+product اللي .. اللي هي زي ما قلنا في المحاضرة
+
+284
+00:21:59,560 --> 00:22:04,280
+اللي هي ال boolean operation هي في الواقع ال or و
+
+285
+00:22:04,280 --> 00:22:08,480
+ال and بتعمل حاجة اسمها boolean algebra مش موضوعنا
+
+286
+00:22:08,480 --> 00:22:17,520
+لكن للي بدوا يعرفالان انتهت الجزء الأول من محاضرة
+
+287
+00:22:17,520 --> 00:22:23,500
+الـ matrices ككل المطلوب
+
+288
+00:22:23,500 --> 00:22:27,460
+منكم ان يكون عند ال matrix هذا ال matrix B وهي ال
+
+289
+00:22:27,460 --> 00:22:31,590
+matrix ال identity matrixبدي توجدولي اللي هو ال a
+
+290
+00:22:31,590 --> 00:22:35,490
+تربيع و ال a تكعيب و ال a n لكل n greater than or
+
+291
+00:22:35,490 --> 00:22:39,490
+equal to 3 و توجدولي البولين ال product بين ال a و
+
+292
+00:22:39,490 --> 00:22:43,090
+ال b و البولين ال product بين ال a و ال c و هذولة
+
+293
+00:22:43,090 --> 00:22:46,830
+اللي هى هذا السؤال بس هى السؤال هذا اللي هو ال a و
+
+294
+00:22:46,830 --> 00:22:50,930
+ال b و ال i و هذولة و هذولة بدي توجدوليها و
+
+295
+00:22:50,930 --> 00:22:55,210
+تعملوليها و تكتبوليهافي homework و زي ال homework
+
+296
+00:22:55,210 --> 00:22:59,770
+اللي فات و تبعتوليه على اللي هو ال whats او على ال
+
+297
+00:22:59,770 --> 00:23:04,990
+model زي ما بدكم زي ما بتشوفوا مناسب و ان شاء الله
+
+298
+00:23:04,990 --> 00:23:10,470
+في لقاء اخر بينكمل اللي هو ال determinants او
+
+299
+00:23:10,470 --> 00:23:14,170
+المحددات والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c309ad1ad01222e5d575085793e8b6fae30192d
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g.srt
@@ -0,0 +1,1647 @@
+1
+00:00:00,720 --> 00:00:05,260
+بسم الله الرحمن الرحيم هذه هي المحاضرة الرقم 11
+
+2
+00:00:05,260 --> 00:00:12,280
+لمساق رياضيات من فصل لطلاب وطالبات الجامعة
+
+3
+00:00:12,280 --> 00:00:16,080
+الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة
+
+4
+00:00:16,080 --> 00:00:22,540
+المتنقلة بدأنا حديثنا في المحاضرة العاشرة السابقة
+
+5
+00:00:22,540 --> 00:00:27,700
+على اللي هو ال-graphs عرفنا شو معنى ال-graph قلنا
+
+6
+00:00:27,700 --> 00:00:33,160
+عبارة عن اللي هو set V اللي هي بتمثل vertices و A
+
+7
+00:00:33,160 --> 00:00:37,940
+بتمثل اللي هي عبارة عن الخطوط اللي بين اللي هي ال-
+
+8
+00:00:37,940 --> 00:00:46,300
+vertices وبعدين أخذنا اللي هو شو معنى ال-edge
+
+9
+00:00:46,300 --> 00:00:51,360
+اللي هو الخط وشو معنى اللي هو ال-neighborhood 
+
+10
+00:00:51,360 --> 00:00:55,700
+وبعدين اللي هو شو .. قلنا شو معنى أنه two edges تكون
+
+11
+00:00:55,700 --> 00:01:02,960
+adjacent وأيضا عرفنا اللي هو شو معنى ال-degree
+
+12
+00:01:02,960 --> 00:01:08,340
+لل-vertex و .. وقلنا ال-vertex اللي ال-degree له
+
+13
+00:01:08,340 --> 00:01:12,900
+zero قلنا isolated وأخذنا أمثلة على هيك لأمثلة
+
+14
+00:01:12,900 --> 00:01:18,300
+اللي أمامنا هذه وعلى ال-degree إلى آخره وانتقلنا
+
+15
+00:01:20,810 --> 00:01:24,030
+طبعا كنا حاكينا عن الـundirected graph بعدين
+
+16
+00:01:24,030 --> 00:01:28,650
+أخذنا أمثلة على كل هذه الموضوعات وجئنا أخذنا اللي
+
+17
+00:01:28,650 --> 00:01:33,270
+هو النظرية اللي بتقول دائما اللي هو المجموع اللي
+
+18
+00:01:33,270 --> 00:01:37,050
+هو ال-degree لل-vertices على كل ال-vertices اللي
+
+19
+00:01:37,050 --> 00:01:41,650
+في ال-V بتساوي 2 في حاصل ضرب اللي هو عدد الخطوط أو
+
+20
+00:01:41,650 --> 00:01:46,570
+عدد ال-edges اللي في الشكل وبعدين أخذنا أمثلة على
+
+21
+00:01:46,570 --> 00:01:51,570
+هيك وأخذنا بعد هيك شو معنى .. شو معنى اللي هو ال-
+
+22
+00:01:51,570 --> 00:01:54,690
+directed graph اللي بيكون .. قلنا بيسير اللي هو
+
+23
+00:01:54,690 --> 00:02:00,370
+الخط اللي هو directed from نقطة إلى نقطة أخرى
+
+24
+00:02:00,370 --> 00:02:05,990
+وأخذنا اللي هو أمثلة عليهم وأخذنا شو ال-degree اللي
+
+25
+00:02:05,990 --> 00:02:09,990
+هي الخارجة والـdegree الداخلة وأخذنا ال-homework
+
+26
+00:02:09,990 --> 00:02:13,690
+واليوم إن شاء الله بدنا نبدأ نحكي عن اللي هو
+
+27
+00:02:13,690 --> 00:02:18,210
+الموضوعات المكملة للي حكيناها اللي هي خلينا نحكي
+
+28
+00:02:18,210 --> 00:02:22,510
+عن حاجة اسمها subigraph subigraph يعني جزء من
+
+29
+00:02:22,510 --> 00:02:25,930
+ال-igraph جزء من ال-igraph طبيعى نشوف إيش عرفناه
+
+30
+00:02:26,460 --> 00:02:31,860
+بقول لو كان عندي graph g1 is a sub graph يعني هذا
+
+31
+00:02:31,860 --> 00:02:36,320
+g1 بنقول عنه sub graph من مين of another graph g
+
+32
+00:02:36,320 --> 00:02:41,040
+يعني g1 عبارة عن sub graph أو graph جزئي من ال-
+
+33
+00:02:41,040 --> 00:02:46,080
+graph g if and only if the vertex and edges sets
+
+34
+00:02:46,080 --> 00:02:49,730
+of g1 are respectively subsets of the vertex and
+
+35
+00:02:49,730 --> 00:02:53,730
+edges of G نحن نتفاجأ أن G يكون مكون من شغل ثاني
+
+36
+00:02:53,730 --> 00:02:59,270
+من vertices من vertices ومن خطوط إذا بنقول إن G1
+
+37
+00:02:59,270 --> 00:03:04,450
+sub graph من G إذا كان كل ال-vertices اللي في G1
+
+38
+00:03:04,450 --> 00:03:11,610
+موجودة في vertices في G في ال-V تبعته وكل الخطوط
+
+39
+00:03:11,610 --> 00:03:15,190
+الـedges اللي في الـ .. اللي في الـG1 اللي كنا
+
+40
+00:03:15,190 --> 00:03:20,070
+نسميها إيه هي عبارة عن خطوط موجودة في مين في الـG
+
+41
+00:03:20,070 --> 00:03:24,950
+الأصلية الآن نيجي نأخذ أمثلة اللي هي أمامنا هذه
+
+42
+00:03:24,950 --> 00:03:27,570
+عندي ال-graph G هذه وهذا ال-graph G هذه ال-
+
+43
+00:03:27,570 --> 00:03:31,290
+vertices كلها موجودة عندي وهذه الخطوط اللي بينها
+
+44
+00:03:31,290 --> 00:03:34,550
+اللي هي ال-edges اللي بينها اللي هنجي نطلعها
+
+45
+00:03:34,550 --> 00:03:42,870
+لهذا هذا V4 هي موجودة هنا V4V3 هيها جاي من هنا V7
+
+46
+00:03:42,870 --> 00:03:48,090
+هيها من هنا V6 هيها من هنا الخطوط اللي بينهم V7 و
+
+47
+00:03:48,090 --> 00:03:58,230
+V6 هي V7 و V6 موجود V6 و V3 هي موجود V4 و V3 هي V4
+
+48
+00:03:58,230 --> 00:04:04,770
+و V3 موجود إذا هذا ال-graph هو عبارة عن جزء من هذا
+
+49
+00:04:04,770 --> 00:04:08,510
+لأن الخطوط هذه موجودة في ال-graph الأصلي والـ
+
+50
+00:04:08,510 --> 00:04:12,530
+vertices موجودة في ال-graph الأصلي عشان هيك بنسمي
+
+51
+00:04:12,530 --> 00:04:17,150
+هذا sub graph من هذا نشوف ال-graph الثاني، لاحظوا
+
+52
+00:04:17,150 --> 00:04:25,280
+V2 هي موجودة V3 هي V3 V6
+
+53
+00:04:25,280 --> 00:04:33,000
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+54
+00:04:33,000 --> 00:04:33,140
+V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+55
+00:04:33,140 --> 00:04:34,080
+هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+56
+00:04:34,080 --> 00:04:34,920
+V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+57
+00:04:34,920 --> 00:04:47,760
+V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+58
+00:04:47,760 --> 00:04:53,380
+V7 الآن بدنا نأخذ اللي هو some special simple
+
+59
+00:04:53,380 --> 00:04:58,160
+graphs أو حاجة بنسميها complete graphs بدنا نرجع ل
+
+60
+00:04:58,160 --> 00:05:03,420
+اللي هو ال-graphs وبدنا نسمي بعض ال-graphs ليش
+
+61
+00:05:03,420 --> 00:05:09,820
+بنسميها complete graph بنسميه ونشوف ليش ال-graph
+
+62
+00:05:09,820 --> 00:05:14,340
+بنسميه complete بناخذ أنواع معينة خلينا نشوف إيش
+
+63
+00:05:14,340 --> 00:05:18,280
+المجولة for any positive integer n لو كان n عبارة
+
+64
+00:05:18,280 --> 00:05:20,840
+عن positive integer يعني واحد أو اثنين أو ثلاثة
+
+65
+00:05:20,840 --> 00:05:24,280
+أو أربعة إلى آخره هي the complete graph on n
+
+66
+00:05:24,280 --> 00:05:29,620
+vertices يعني لما نقول عن ال-graph اللي فيه n
+
+67
+00:05:29,620 --> 00:05:30,220
+vertices
+
+68
+00:05:33,500 --> 00:05:38,600
+يعني في كم رأس في N من الرؤوس بقول ده complete
+
+69
+00:05:38,600 --> 00:05:43,380
+graph on N vertices denote KN يعني الآن بدنا نسمي
+
+70
+00:05:43,380 --> 00:05:51,240
+ال-KN هذا يرمز إلى complete graph with n vertices
+
+71
+00:05:51,240 --> 00:05:57,700
+في إيش ماله n من الرؤوس طبعا شوفوا هذا كأن is a
+
+72
+00:05:57,700 --> 00:06:02,400
+graph with n vertices يعني هذا كأن عبارة عن graph
+
+73
+00:06:02,400 --> 00:06:06,760
+with n vertices every two of which are adjacent
+
+74
+00:06:06,760 --> 00:06:11,380
+يعني كل اثنين من ال-vertices adjacent متجاورتان
+
+75
+00:06:11,380 --> 00:06:14,420
+متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان
+
+76
+00:06:14,420 --> 00:06:15,000
+متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان
+
+77
+00:06:15,000 --> 00:06:19,260
+متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان متجاورتان
+
+78
+00:06:19,260 --> 00:06:23,500
+متجاورتان متجاورتان متجاورتان اهي عندي كأني في نقطتين
+
+79
+00:06:23,500 --> 00:06:29,260
+النقطتين هدول في التنتين بينها خط ما فيش أي نقطة
+
+80
+00:06:29,260 --> 00:06:34,440
+في داخل الكنتين ما فيش بينها وبين الباقيات خطوط
+
+81
+00:06:34,440 --> 00:06:42,900
+عشان هيك بنسمي هذا complete graph من النوع K2 نشوف
+
+82
+00:06:42,900 --> 00:06:50,440
+نوع آخر K3 K3 K3 أشمل فيه ثلاث رؤوس هذه رأس هذه
+
+83
+00:06:50,440 --> 00:06:55,960
+رأسان هذه ثلاثة لاحظت ثلاث رؤوس فعلا هذا وهذا بين
+
+84
+00:06:55,960 --> 00:06:59,860
+الخط وهذا وهذا بين الخط وهذا وهذا بين الخط يعني كل
+
+85
+00:06:59,860 --> 00:07:05,920
+الرؤوس are adjacent يعني ما لهن كل الرؤوس اللي هي
+
+86
+00:07:05,920 --> 00:07:09,380
+بينهن وبين بعض خطوط عشان هيك بنسميها ده Complete
+
+87
+00:07:09,380 --> 00:07:13,640
+Graph هذا النوع من ال-graphs اللي زي هيك اللي
+
+88
+00:07:13,640 --> 00:07:17,240
+كنتين كتلاتة اللي في عدد اللي هو اثنين أو عدد
+
+89
+00:07:17,240 --> 00:07:21,860
+ثلاثة أو بعد شوية أربعة أو خمسة أو ستة وبكون بخاصية
+
+90
+00:07:21,860 --> 00:07:28,320
+أنه كل اثنين كل نقطتين بين الخط بنسميه اللي هو
+
+91
+00:07:28,320 --> 00:07:32,990
+Complete Graph من النوع KN نجي لـ K أربعة K أربعة
+
+92
+00:07:32,990 --> 00:07:36,110
+اللي هو واحد اثنين ثلاثة أربعة فيها أربع عياش نقاط
+
+93
+00:07:36,110 --> 00:07:43,330
+الأربع نقاط كلهم بين هذه وهذه خط وبينها وبينها
+
+94
+00:07:43,330 --> 00:07:48,510
+دي خط وبينها وبينها دي خط يعني كل النقاط اللي هم
+
+95
+00:07:48,510 --> 00:07:52,970
+adjacent لبعض عشان هيك بنسميه graph إذا ال-
+
+96
+00:07:52,970 --> 00:07:58,890
+complete graph هو graph عادي كل نقطتين فيه adjacent
+
+97
+00:07:58,890 --> 00:08:03,590
+يعني كل نقطتين فيه graph حالة خاصة من هذول ال-
+
+98
+00:08:03,590 --> 00:08:08,850
+complete graph اللي هي عائلة من ال-graphs اسمها Kn
+
+99
+00:08:08,850 --> 00:08:14,890
+إيش ال-Kn هذه اللي هي عددها n من اللي هو ال-
+
+100
+00:08:14,890 --> 00:08:20,000
+vertices فيها؟ وبيعملين complete graph يعني كل
+
+101
+00:08:20,000 --> 00:08:25,820
+النقاط are adjacent ده نشوف اللي بعدها هذه K خمسة
+
+102
+00:08:25,820 --> 00:08:30,140
+مثلا بخمسة هذه عندي خمس نقاط واحدة اثنين ثلاثة
+
+103
+00:08:30,140 --> 00:08:32,900
+أربعة خمسة واضح أن كل النقاط كل واحدة بيطلع منها
+
+104
+00:08:32,900 --> 00:08:37,940
+أربع خطوط للآخرين فعشان هيك بنسميها complete graph
+
+105
+00:08:37,940 --> 00:08:43,680
+من النوع K لو واحد بده يرسم K6 بتقدر ترسمها بنفس
+
+106
+00:08:43,680 --> 00:08:48,060
+الاسم و K7 طبعا بتغلب شوية لكن بتظلها في نفس
+
+107
+00:08:48,060 --> 00:08:54,800
+النطاق هذه بنسميها complete graphs أو مثل على ال-
+
+108
+00:08:54,800 --> 00:09:00,240
+complete graphs اللي هي العائلة اللي سميناها Kn عند
+
+109
+00:09:00,240 --> 00:09:03,280
+K واحد برضه نعتبره complete ليش؟ لأن ال-complete
+
+110
+00:09:03,280 --> 00:09:07,740
+graph ما يكونش فيه نقطتين مش adjacent ما فيش فيه
+
+111
+00:09:07,740 --> 00:09:10,840
+نقطتين مش adjacent لأنه أصلا هي النقطة بس لحالها
+
+112
+00:09:10,840 --> 00:09:17,730
+عشان هيك بنسميها اللي هي برضه complete graph K1, K2,
+
+113
+00:09:17,850 --> 00:09:22,130
+K3, K4, K5 إلى آخره هي زمنته بتاعنا الآن بدنا نيجي
+
+114
+00:09:22,130 --> 00:09:26,810
+نوع ثاني لـ graphs حاجة اسمها ال-cycles ماشي إيش ال-
+
+115
+00:09:26,810 --> 00:09:31,850
+cycles اللي هي وال-wheels اه إيش نشوف إيش ال-
+
+116
+00:09:31,850 --> 00:09:37,900
+cycle وإيش ال-wheel الآن cycle cn ده نرمز له ببرنامج
+
+117
+00:09:37,900 --> 00:09:41,220
+cn بعد إذنكم يعني في عندي n أكبر أو تساوي ثلاثة يعني
+
+118
+00:09:41,220 --> 00:09:47,380
+عندي cycle c3 و c4 و c5 و c6 إلى ما لا نهاية
+
+119
+00:09:47,380 --> 00:09:51,900
+consists of n vertices يعني ال-cn هذه برضه بتحتوي
+
+120
+00:09:51,900 --> 00:09:57,860
+على إيه على n من ال-vertices ماذا نسميه Cycle لما
+
+121
+00:09:57,860 --> 00:10:02,960
+نكون تحقق ما يلي ال-CNN Consists Of N Vertices
+
+122
+00:10:02,960 --> 00:10:08,480
+V1 و V2 و VN And Edges والـEdges إيش ما لها V1 و
+
+123
+00:10:08,480 --> 00:10:13,890
+V2 يعني خط بين V1 و V2 وخط بين V2 و V3 وخط بين V3
+
+124
+00:10:13,890 --> 00:10:19,330
+و V4 لما أصل عند خط بين اللي هي النقطة الأخيرة VN
+
+125
+00:10:19,330 --> 00:10:25,430
+وبرجع لمين للـV1 وكأن إيش بسكر وبعمله cycle زي 
+
+126
+00:10:25,430 --> 00:10:30,190
+دائرة أو اللي هو دورة كاملة ماشي the cycles C3,
+
+127
+00:10:30,330 --> 00:10:38,350
+C4, C5, C6 are displaced انفجارا هي وهذه وهذه اللي
+
+128
+00:10:38,350 --> 00:10:46,690
+هي V1 V2 V2 V3 V3 V1 إذاً هذا cycle صار الآن هذا
+
+129
+00:10:46,690 --> 00:10:50,170
+ال graph complete  أه complete لأنه كل مغطين
+
+130
+00:10:50,170 --> 00:10:54,850
+adjacent يعني ال cycle ممكن تكون complete يعني
+
+131
+00:10:54,850 --> 00:10:59,730
+مثال على complete graph نجي للي بعدها C4 هي من عند
+
+132
+00:10:59,730 --> 00:11:03,010
+النقطة الأولى للتانية في خط و من التانية للتالتة و
+
+133
+00:11:03,010 --> 00:11:05,770
+من التالتة للرابعة و من الرابعة للأولى رجعت يعني
+
+134
+00:11:05,770 --> 00:11:10,190
+أقفلت الدائرة أو أقفلت اللي هي ال cycle هذا بنسميه
+
+135
+00:11:10,190 --> 00:11:13,590
+برضه cycle هل هذا complete؟ لا مش complete ليش مش
+
+136
+00:11:13,590 --> 00:11:16,850
+complete؟ لأن هذي و هذا النقطة they are not
+
+137
+00:11:16,850 --> 00:11:20,850
+adjacent لأنه مافيش بين الخط و هذي كمان و هذي إذا
+
+138
+00:11:20,850 --> 00:11:24,090
+هي في عند ال cycle ليس شرط أن تكون إيش مالها
+
+139
+00:11:24,090 --> 00:11:28,450
+complete اقرأ الآن نجي لـ C5 C5 بنفس الأسلوب فيها
+
+140
+00:11:28,450 --> 00:11:31,330
+خمس نقاط الخمس نقاط بتبدأ من عند النقطة الأولى و
+
+141
+00:11:31,330 --> 00:11:33,670
+بتبدأ للتانية أو للتالتة أو للرابعة أو للخامسة أو
+
+142
+00:11:33,670 --> 00:11:37,770
+للسادسة اللي الخمسة بترجع لمين للنقطة الأولى
+
+143
+00:11:37,770 --> 00:11:42,770
+فبتعمل ليه cycle اللي هي بتسكر اللي هي الدورة الآن
+
+144
+00:11:42,770 --> 00:11:47,890
+C6 بنفس الأسلوب فيها ست نقاط كل نقطة ال V1 بتروحها
+
+145
+00:11:47,890 --> 00:11:52,150
+V2 V2 تلاتة V3 أو V4 مافهمش معنات بتروح يعني بين
+
+146
+00:11:52,150 --> 00:12:02,610
+الخط V4 V5 V5 V6 V6 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+147
+00:12:02,610 --> 00:12:03,510
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+148
+00:12:03,510 --> 00:12:06,110
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+149
+00:12:06,110 --> 00:12:06,890
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+150
+00:12:06,890 --> 00:12:08,650
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+151
+00:12:08,650 --> 00:12:12,150
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+152
+00:12:12,150 --> 00:12:15,610
+V1 V1
+
+153
+00:12:15,980 --> 00:12:21,720
+when we add an additional vertex to cycle CN يعني
+
+154
+00:12:21,720 --> 00:12:29,280
+إيش بنجيب؟ بنجيب هي ال cycle و بنضيف لها نقطة إيش
+
+155
+00:12:29,280 --> 00:12:33,040
+النقطة دي مالها؟ نشوف إيش مالها we add an
+
+156
+00:12:33,040 --> 00:12:36,260
+additional vertex to cycle CN for N أكبر سواء
+
+157
+00:12:36,260 --> 00:12:41,940
+ثلاثة and connect this new vertex to each of the
+
+158
+00:12:41,940 --> 00:12:48,410
+vertices in CN by new edges إذا الآن ما هي إلا
+
+159
+00:12:48,410 --> 00:12:52,570
+cycle بنحط جواتها نقطة أو جنبها نقطة في المكان
+
+160
+00:12:52,570 --> 00:12:56,010
+المناسب جواتها أفضل يعني بتكون أحلى في الرسم و
+
+161
+00:12:56,010 --> 00:13:01,590
+بنوصل من النقطة هذه خطوط لكل أو edges لكل من ال
+
+162
+00:13:01,590 --> 00:13:05,390
+vertices اللي موجودة هذه النقطة هيعملنا اللي هو
+
+163
+00:13:05,390 --> 00:13:09,810
+edge وهي edge وهي edge مع كل النقاط هذه بنسميها
+
+164
+00:13:09,810 --> 00:13:16,510
+wheel W ثلاثة تبعا ل C ثلاثة الآن هذه complete أه
+
+165
+00:13:16,510 --> 00:13:19,590
+complete هذه واضح أنها complete لأنها مع الكل كل
+
+166
+00:13:19,590 --> 00:13:26,570
+النقاط مع الكل الآن هذه النقطة هي عندي اللي هو من
+
+167
+00:13:26,570 --> 00:13:31,630
+النقطة هذه حطينا و رسمنا لكل النقاط، مظبوط؟ هذه
+
+168
+00:13:31,630 --> 00:13:35,050
+عملت ل wheel هي نفسها اللي فوق بس عملنا لها نقطة و
+
+169
+00:13:35,050 --> 00:13:40,390
+نقطة وودينا لها اللي هي من لكل النقاط خطوط حسب تعريف
+
+170
+00:13:40,390 --> 00:13:44,370
+اللي عرفنا لمين لل wheel هل هذه complete؟ ليس شرطا
+
+171
+00:13:44,370 --> 00:13:47,410
+لأنه فيش بين النقطة هذه مثلا النقطة هذه خط مباشر
+
+172
+00:13:47,850 --> 00:13:51,270
+هذا لو خط من هنا إلى هنا وهذا من هنا إلى هنا لأن
+
+173
+00:13:51,270 --> 00:13:55,530
+لو كان هناك خط مباشر بينهم نسميه complete لو كان
+
+174
+00:13:55,530 --> 00:13:59,430
+هناك خطوط من الكل طبعا الآن نأتي لهذه اللي هي ال
+
+175
+00:13:59,430 --> 00:14:03,850
+wheel بنجيب ال C3 و بنحط نقطة في داخلها و بنوصل
+
+176
+00:14:03,850 --> 00:14:08,470
+بينهم كلهم اللي هي إيش بين النقطة هذه و بين كل
+
+177
+00:14:08,470 --> 00:14:12,030
+النقاط الأخرى بنوصل خطوط فبتعمل wheel هل ال wheel
+
+178
+00:14:12,030 --> 00:14:15,090
+complete ليس شرطًا لأن هو من هنا إلى هنا مثلا إيش
+
+179
+00:14:15,090 --> 00:14:19,810
+مافيش خط هكذا اللي بعدها الآن هذه اللي هي مين الشكل
+
+180
+00:14:19,810 --> 00:14:23,810
+السداسي في الشكل السداسي حطينا نقطة ووصلنا بين
+
+181
+00:14:23,810 --> 00:14:28,090
+النقطة و بين باقي النقاط فعملت ليش برضه wheel هاي
+
+182
+00:14:28,090 --> 00:14:32,850
+شكل السداسي عندي وهي النقطة و بدي اتوصل من الشكل
+
+183
+00:14:32,850 --> 00:14:37,350
+السداسي لكل النقاط شوفوها هتشتبه تطلعوش تقبلوا ليها
+
+184
+00:14:37,350 --> 00:14:40,310
+تقوليها مكعب لا هذا مقطب في المصف وطبعا هي بتظهر
+
+185
+00:14:40,310 --> 00:14:43,790
+لو اتنعانت هتشوفها مكعب لو اتنعانت في صورة أخرى
+
+186
+00:14:43,790 --> 00:14:47,070
+هتشوفها نقطة في الداخل و من الكل مش موضوعنا هذا بس
+
+187
+00:14:47,070 --> 00:14:51,930
+لكن عشان الخداع البصري طيب هذه اللي هي معنات ال
+
+188
+00:14:51,930 --> 00:14:58,050
+wheel الآن في حد اسمه بيبا ترايت بيبا بيبارتايت
+
+189
+00:14:58,410 --> 00:15:03,350
+graph بيبرتايت graph اللي هو يعني الـ Graph
+
+190
+00:15:03,350 --> 00:15:06,830
+الثنائي إيش ال graph الثنائي خلينا نشوف إيش بيقول
+
+191
+00:15:06,830 --> 00:15:11,030
+ال graph الثنائي a bipartite graph is a graph هو
+
+192
+00:15:11,030 --> 00:15:14,750
+عبارة عن graph whose vertices can be partitioned
+
+193
+00:15:14,750 --> 00:15:19,470
+into two disjoint sets V1 and V2 يعني ال بيبرتايت
+
+194
+00:15:19,470 --> 00:15:23,970
+graph أو اللي هو ال graph الثنائي بيقول هذا بتقدر
+
+195
+00:15:23,970 --> 00:15:32,640
+تعمل ال vertices إليه جزئين V1 و V2 هي V1 وهي V2 بس
+
+196
+00:15:32,640 --> 00:15:39,940
+تحت شرط معين كل Graphs ممكن تعملها V1 و V2 بقدر
+
+197
+00:15:39,940 --> 00:15:45,220
+أعمل V1 و V2 بيبقى partition sets يعني هذول اللي
+
+198
+00:15:45,220 --> 00:15:50,540
+بنسميهم هم اللي جزء من ال set الأصلي تبع ال
+
+199
+00:15:50,540 --> 00:15:56,440
+vertices in such a way بتجزئها بطريقة هي V1 و V2
+
+200
+00:15:56,440 --> 00:16:02,840
+بتجزئها بطريقة that every edge point joins a
+
+201
+00:16:02,840 --> 00:16:08,070
+vertex in V1 و V2 يعني الآن لما ناخد V1 وفيه اثنين
+
+202
+00:16:08,070 --> 00:16:16,590
+هتجزئلي اللي هي ال vertices إلى جزئين ابحث أنه كل
+
+203
+00:16:16,590 --> 00:16:22,730
+edge في الشكل بربط نقطة من هنا مع نقطة من هنا كل
+
+204
+00:16:22,730 --> 00:16:26,590
+edge في الشكل .. كل edge موجود هي edge بربط نقطة
+
+205
+00:16:26,590 --> 00:16:29,150
+من هنا مع نقطة من هنا ال edge الثاني هي بربط نقطة
+
+206
+00:16:29,150 --> 00:16:31,710
+من هنا مع نقطة من هنا ال edge الثالث من نقطة من
+
+207
+00:16:31,710 --> 00:16:33,830
+هنا مع نقطة من هنا ال edge الرابع من نقطة من هنا
+
+208
+00:16:33,830 --> 00:16:37,390
+مع نقطة من هنا كل الاتجاهات اللي موجودة الخطوط
+
+209
+00:16:37,390 --> 00:16:42,810
+بتكون واصلة بين نقطة من مجموعة ال vertices الأولى
+
+210
+00:16:42,810 --> 00:16:47,770
+ونقطة من مجموعة ال vertices الثانية يعني الآن لو
+
+211
+00:16:47,770 --> 00:16:52,290
+كان بين هذه وهذه لا بنفعش يكون اللي هو إيه شماله
+
+212
+00:16:52,680 --> 00:16:58,620
+عندي اللي هو بمسميهش عملة partition لأنه من هالهال
+
+213
+00:16:58,620 --> 00:17:02,920
+بيصير هذا النقطة في نفس ال .. نقطتين في نفس ال V
+
+214
+00:17:02,920 --> 00:17:08,420
+واحد لا لأن كل الخطوط بدها تكون جاية من ال
+
+215
+00:17:08,420 --> 00:17:13,080
+vertices الأولى مع ال vertices الثانية عشان هيك
+
+216
+00:17:13,080 --> 00:17:20,280
+بنسمي هذا bipartite graph أو graph ثنائي الآن هاي
+
+217
+00:17:20,280 --> 00:17:26,820
+واحد ثاني برضه ببرتاية graph آخر هي ال V1 الكبيرة
+
+218
+00:17:26,820 --> 00:17:31,920
+يعني بتحتوي على كل اللي هي ال vertices الجزء الأول
+
+219
+00:17:31,920 --> 00:17:35,980
+وهذه بتحتوي على ال vertices الجزء الثاني لاحظ أنه
+
+220
+00:17:35,980 --> 00:17:42,030
+كل خط موجود بربط بين نقطة بين هذه V1 و V2 كل خط
+
+221
+00:17:42,030 --> 00:17:47,670
+موجود بربط بين V2 و V1 كل خط موجود بين V1 و V2 و
+
+222
+00:17:47,670 --> 00:17:54,470
+هكذا هذا بنسميهم إشمالهم أمثل عبارة على bipartite
+
+223
+00:17:54,470 --> 00:17:58,330
+graphs نيجي لاخر واحدة طبعا هي الحالة من حالة
+
+224
+00:17:58,330 --> 00:18:05,600
+رسمها حالة هي هذه اللي هو ال V2 وهي هدمين الـ V1 هي
+
+225
+00:18:05,600 --> 00:18:12,920
+اللي هما ال V1 و ال V2 اللي جزءين ليه اللي جزءين
+
+226
+00:18:12,920 --> 00:18:18,460
+ليه اللي هو ال vertices اللي جزءين ابحث أن كل خط
+
+227
+00:18:18,460 --> 00:18:24,900
+موجود ياخد من نقطة في ال V1 إلى V2 أو من V2 ل V1 و
+
+228
+00:18:24,900 --> 00:18:29,700
+هكذا زي ما أنتم شايفين فهدول أمثلة على bipartite
+
+229
+00:18:29,700 --> 00:18:36,590
+graphs أو جرافات ثنائية الـ Complete bipartite
+
+230
+00:18:36,590 --> 00:18:41,310
+graph is a bipartite graph in which every vertex
+
+231
+00:18:41,310 --> 00:18:46,390
+in V1 is joined to every vertex in V2
+
+232
+00:18:49,970 --> 00:18:54,290
+عبارة عن بيبرتايته graph in which every vertex in
+
+233
+00:18:54,290 --> 00:18:58,870
+v1 كل ال vertex في ال v1 is joined to every vertex
+
+234
+00:18:58,870 --> 00:19:03,570
+in v2 ما قلناش أن كل ال vertices اللي في ال v1
+
+235
+00:19:03,570 --> 00:19:08,410
+بتتبط مع بعض و ال v2 اللي بتتبط مع بعض لا قلنا أن
+
+236
+00:19:08,410 --> 00:19:13,870
+كل vertex v1 بتتبط مع أيش مع اللي في ال .. مع
+
+237
+00:19:13,870 --> 00:19:19,030
+واحد من مين من v2 every vertex in v1 is joined to
+
+238
+00:19:19,030 --> 00:19:23,280
+everyjoin to every وليس مع واحد فقط to every واحد
+
+239
+00:19:23,280 --> 00:19:31,460
+في ذي اثنين الآن خلينا لو رجعنا الآن هذا مثلا نشوف
+
+240
+00:19:31,460 --> 00:19:35,240
+complete ولا لا هي هي هذا بيتبط مع هذا وبيتبط مع
+
+241
+00:19:35,240 --> 00:19:40,360
+هذا لكن بيتبطش مع اللي بعيد هذا إذا مش complete طب
+
+242
+00:19:40,360 --> 00:19:46,630
+الآن هذا هي وبيتبط مع هذا وبيتبط مع هذا وهذه
+
+243
+00:19:46,630 --> 00:19:52,150
+بتتبطش مع مين؟ مع هذا لو ربطناها مع هذا يعني لو
+
+244
+00:19:52,150 --> 00:19:58,850
+وصلنا هذا الخط هيك ووصلنا هذا الخط هيك ووصلنا هذا
+
+245
+00:19:58,850 --> 00:20:02,670
+خط واصل فبيصير عندي هذا complete يعني متى بيصير هذا
+
+246
+00:20:02,670 --> 00:20:07,290
+complete لما نهادي لأن هي وصلت مع حده ووصلت مع حده
+
+247
+00:20:07,290 --> 00:20:13,030
+ونوصل هذه مع حده ومش هيك كمان ونوصل هذه مع حده
+
+248
+00:20:13,030 --> 00:20:16,950
+بيصير ال graph اللي طلع عنده يشمله complete يعني
+
+249
+00:20:16,950 --> 00:20:20,490
+عشان يكون complete هذا بيكون كل واحدة من هدول
+
+250
+00:20:20,490 --> 00:20:26,950
+الاثنين بتتوصل مع كل واحدة من الثلاث يعني بينها 
+
+251
+00:20:26,950 --> 00:20:31,070
+وبين كل أحد من تلاتة خط واضح أننا نسميه complete
+
+252
+00:20:31,070 --> 00:20:35,200
+bipartite graph إذا زي ما قلنا الـ bipartite graph
+
+253
+00:20:35,200 --> 00:20:39,700
+بكون complete إذا كان هو bipartite graph وكل 
+
+254
+00:20:39,700 --> 00:20:46,140
+vertex في الـ V1 is joined to every vertex in V2
+
+255
+00:20:46,140 --> 00:20:48,420
+وكل vertex في الـ V1 is joined to every vertex in
+
+256
+00:20:48,420 --> 00:20:53,360
+V2 وكل vertex في الـ V1 is joined to every vertex
+
+257
+00:20:53,360 --> 00:20:53,540
+in V2 وكل vertex في الـ V1 is joined to every
+
+258
+00:20:53,540 --> 00:20:53,600
+to every vertex in V2 وكل vertex في الـ V1 is
+
+259
+00:20:53,600 --> 00:20:53,660
+joined to every vertex in V2 وكل vertex في الـ V1
+
+260
+00:20:53,660 --> 00:20:58,580
+vertex في الـ V1 is joined to every vertex in V2
+
+261
+00:20:58,580 --> 00:21:04,130
+وكل vertex في الـ V1 is اللي بيكون اللي هو ال .. ال
+
+262
+00:21:04,130 --> 00:21:08,930
+.. ال .. ال V1 في M من العناصر و ال V2 بيكون M من
+
+263
+00:21:08,930 --> 00:21:13,890
+ال .. N من العناصر يعني عند ال V1 ال vertices
+
+264
+00:21:13,890 --> 00:21:19,570
+عددهم M و ال V2 عددهم N و كان هذا bipartite graph
+
+265
+00:21:19,570 --> 00:21:24,370
+و في نفس الوقت complete بيكون اللي هو هاي شكله
+
+266
+00:21:24,370 --> 00:21:30,120
+اتنين و تلاتة الان هي عندي فوق اتنين وها تحت
+
+267
+00:21:30,120 --> 00:21:33,360
+ايش تلاتة زي ما عملناها قبل شوية هي الان هذه بدها
+
+268
+00:21:33,360 --> 00:21:39,020
+تروح للكل هي راحت للكل وهذه برضه راحت لإيش للكل
+
+269
+00:21:39,020 --> 00:21:44,150
+وطبعا هدولة اوتوماتيك راحلن مين لتنتين اللي فوق لأن
+
+270
+00:21:44,150 --> 00:21:47,290
+K ثلاثة ثلاثة هيكون عندنا ثلاثة هنا و ثلاثة وين
+
+271
+00:21:47,290 --> 00:21:50,730
+فوق لأن الاتنين الأولى خلينا نصطلح مع بعض اللي
+
+272
+00:21:50,730 --> 00:21:57,230
+بنرسمها فوق التلاتة التانية هذه بنرسمها تحت لأن
+
+273
+00:21:57,230 --> 00:22:00,650
+تلاتة و تلاتة هي تلاتة فوق و هي تلاتة تحت و بنوصل
+
+274
+00:22:00,650 --> 00:22:05,150
+من كل واحدة للكل ممنوع نوصل بين هدول اللي هنا مع
+
+275
+00:22:05,150 --> 00:22:10,110
+بعض لأ بيبطل ال bipartite أصلا ال bipartite أن
+
+276
+00:22:10,110 --> 00:22:16,810
+هدولة في جهة و هدولة في جهة و الخطوط بين هنا وبس
+
+277
+00:22:16,810 --> 00:22:23,850
+مافيش بين اللي هو عناصر اللي هي ال V2 مع بعضها
+
+278
+00:22:23,850 --> 00:22:28,590
+خطوط بيبطل بيبرتايد وهذا نفس الشيء طيب لإن نيجي
+
+279
+00:22:28,590 --> 00:22:32,670
+تلاتة و خمسة إذا تلاتة بنرسمها فوق وهذه خمسة تحت و
+
+280
+00:22:32,670 --> 00:22:38,950
+بنطلع من كل تلاتة خمس خطوط لخمس نقاط من كل تلاتة
+
+281
+00:22:38,950 --> 00:22:42,630
+خمس خطوط من كل تلاتة خمس خطوط يعني لو بدك تيجي
+
+282
+00:22:42,630 --> 00:22:47,210
+تحسب الخطوط الموجودة من هذه بتطلع منها خمس خطوط
+
+283
+00:22:47,210 --> 00:22:51,650
+خمس خطوط ومن هذه خمسة ومن هذه خمسة يعني خمسة عشر خط
+
+284
+00:22:52,480 --> 00:22:56,460
+ممكن أعد إن الـ 15 الخط بطريقة تانية إن هذه اطلع
+
+285
+00:22:56,460 --> 00:23:00,620
+منها تلات خطوط للي فوق عشان يصير complete وهذه اطلع
+
+286
+00:23:00,620 --> 00:23:03,360
+منها تلات خطوط للي فوق وهذه اطلع منها تلات خطوط
+
+287
+00:23:03,360 --> 00:23:07,880
+بيصير تلات خطوط في خمس نقاط بخمسة عشر هنا خمس نقاط
+
+288
+00:23:07,880 --> 00:23:11,220
+طالعين تلات نقاط طالعين الخمس خطوط تلاتة في خمسة بخمسة
+
+289
+00:23:11,220 --> 00:23:14,480
+عشر اذا بقدر أعد الخطوط من أعلى أو الخطوط من
+
+290
+00:23:14,480 --> 00:23:21,730
+أسفل زي ما وضحت الان اتنين و ستة هي نقطة نقطتين وهي
+
+291
+00:23:21,730 --> 00:23:25,090
+اللي هي ست نقطة تحت هيك التفاجنة الأولى بتطلع فوق
+
+292
+00:23:25,090 --> 00:23:30,190
+والتانية بتطلع تحتها تصلح بينها وبين بعض الان هذه
+
+293
+00:23:30,190 --> 00:23:34,970
+الاتنين النقطة الأولى بتطلع ستة تقريبا ست خطوط و هدى
+
+294
+00:23:34,970 --> 00:23:38,650
+بتطلع ست خطوط للنقاط اللي تحتها فبصير ستة و ستة
+
+295
+00:23:38,650 --> 00:23:42,670
+اتناش هدى بتطلع خطين و هدى خطين و هدى خطين كل
+
+296
+00:23:42,670 --> 00:23:45,670
+واحدة ست نقاط بتطلع كل واحدة خطين بيصير ستة في
+
+297
+00:23:45,670 --> 00:23:49,870
+اتنين باتناش ده بقدر أعد اللي هو من هنا أو من هنا
+
+298
+00:23:49,870 --> 00:23:53,270
+يعني هدولة بتطلعين اتناش خط و هدولة بتطلعين اتناش
+
+299
+00:23:53,270 --> 00:23:57,100
+خط يعني لو بدنا نحسب ال degree لهدولة ال degree
+
+300
+00:23:57,100 --> 00:24:00,980
+لهدولة اتناش و ال degree للي فوق برضه ايش اتناش
+
+301
+00:24:00,980 --> 00:24:06,280
+يعني مجموع ال degree مجموع ال degree لكل العناصر
+
+302
+00:24:06,280 --> 00:24:10,800
+لكل ال vertices اللي هنا هي أربعة و عشرين اللي هي
+
+303
+00:24:10,800 --> 00:24:13,920
+ضعف عدد الخطوط زي ما قلنا في النظرية اللي قلناها
+
+304
+00:24:13,920 --> 00:24:17,780
+المرة الماضية وهذا اللي هو sum of degree اللي
+
+305
+00:24:17,780 --> 00:24:22,970
+بحكيه الان how many edges does K3 و K6 contains في
+
+306
+00:24:22,970 --> 00:24:27,790
+الشرح قلته قبل شوية بيطلع من تلاتة ست خطوط فبصير
+
+307
+00:24:27,790 --> 00:24:33,410
+عندي كم خط تلاتة في ستة بتمانية عشر لأن الستة بيطلع
+
+308
+00:24:33,410 --> 00:24:36,490
+منها تلات خطوط كل واحدة ستة في تلاتة برضه بتمانية عشر
+
+309
+00:24:36,490 --> 00:24:41,310
+إذا ثمانية عشر ثمانية عشر خط اللي هو وكأنه ال degrees
+
+310
+00:24:41,310 --> 00:24:45,470
+لهدولة اللي هي كل واحدة ال degree اللي هي ستة من
+
+311
+00:24:45,470 --> 00:24:50,990
+النقاط التلاتة فبكون مجموع ال degrees للنقاط اللي
+
+312
+00:24:50,990 --> 00:24:56,610
+فوق 18 الان ال 6 اللي تحت ال degree لكل واحدة
+
+313
+00:24:56,610 --> 00:24:59,690
+تلاتة لإنه بيطلع منها تلات خطوط فبكون مجموع ال
+
+314
+00:24:59,690 --> 00:25:03,570
+degrees اللي تحت 18 يعني اللي تحت 18 و اللي فوق 18
+
+315
+00:25:03,570 --> 00:25:08,490
+بيطلع عن 36 36 هنا ضعف عدد الخطوط زي ما عكينا قبل
+
+316
+00:25:08,490 --> 00:25:14,120
+شوية هذا هي this complete bipartite graph has six
+
+317
+00:25:14,120 --> 00:25:17,100
+vertices يعني هذا الـ Complete bipartite الـ Graph
+
+318
+00:25:17,100 --> 00:25:21,860
+اللي قلنا عنه زي اللي توه له ستة vertices with
+
+319
+00:25:21,860 --> 00:25:25,280
+degree تلاتة يعني ستة vertices with degree تلاتة و
+
+320
+00:25:25,280 --> 00:25:28,660
+تلاتة vertices with degree ستة زي ما وضحت قبل و
+
+321
+00:25:28,660 --> 00:25:33,220
+شوية الان مجموع ال degree لكل ال V اللي هما الستة
+
+322
+00:25:33,220 --> 00:25:38,680
+والتلاتة ستة كل واحد degree تلاتة و تلاتة كل واحدة
+
+323
+00:25:38,680 --> 00:25:44,200
+degree ستة بتطلع ل 36 يعني اتنين في عدد الخطوط اللي
+
+324
+00:25:44,200 --> 00:25:48,380
+هو بيكون عدد الخطوط 18 خط لإن ال 36 زي ما أنتو
+
+325
+00:25:48,380 --> 00:25:53,600
+عارفين يعني مضاعف عدد الخطوط قلنا اذا الكل بيكون
+
+326
+00:25:53,600 --> 00:26:00,410
+عدد الخطوط عندنا 18 خط So that K36 has 18 edges
+
+327
+00:26:00,410 --> 00:26:04,570
+تقريبا 18 خط degree sequence نعرف حاجة اسمها
+
+328
+00:26:04,570 --> 00:26:10,800
+degree sequence نشوف ايش degree sequence  الشعر الله
+
+329
+00:26:10,800 --> 00:26:16,100
+سهل يعني suppose that D1 وD2 وDn are degree of the
+
+330
+00:26:16,100 --> 00:26:18,900
+vertices of a graph يعني في عندنا graph بيسيده
+
+331
+00:26:18,900 --> 00:26:22,580
+graph زي ال graph تبعت المرة الفاتة عندنا graph G
+
+332
+00:26:22,580 --> 00:26:27,200
+هذا ال graph جينا حسبنا اللي هي فيه N من ال
+
+333
+00:26:27,200 --> 00:26:31,020
+vertices حسبنا أول واحدة لجينا انها degree D1
+
+334
+00:26:31,020 --> 00:26:38,320
+التانية D2 التلاتة Dn عندما نرتبها تنازلي D1
+
+335
+00:26:38,320 --> 00:26:43,320
+أكبر سواء D2 أكبر سواء D3 أكبر سواء DN هذه الـ D1 وD2
+
+336
+00:26:43,320 --> 00:26:48,160
+وDN المرتبة اللي هي بشكل تنازلي
+
+337
+00:26:48,980 --> 00:26:55,540
+اللي هي طبعا دي واحد تمثل ال degree ل اللي هو نقطة
+
+338
+00:26:55,540 --> 00:26:58,520
+أولى هذه ال degree للتانية هذه ال degree للأخيرة
+
+339
+00:26:58,520 --> 00:27:03,760
+لما نرتبه تنازلي زي هيك بنسميه degree
+
+340
+00:27:03,760 --> 00:27:08,220
+sequence of G اللي هي degree sequence لمين لل G في
+
+341
+00:27:08,220 --> 00:27:11,620
+الواقع degree sequence لل G لأ هي في الواقع ال
+
+342
+00:27:11,620 --> 00:27:16,530
+degree sequence لل vertices تبعات ال G هذا اصطلاحا
+
+343
+00:27:16,530 --> 00:27:19,930
+مع بعض عشان لما نحكي عن ال degree sequence of G
+
+344
+00:27:19,930 --> 00:27:26,130
+نكون فاهمين انه بقصد انه بنجيب اللي هو ال degree
+
+345
+00:27:26,130 --> 00:27:31,910
+لكل لكل نقطة من النقاط و بعدين بنرتبها تصاعدي تنازلي
+
+346
+00:27:31,910 --> 00:27:37,050
+ده نشوف هاي عندي مثلا V1 V2 هاي الخطوط اللي بينهم
+
+347
+00:27:37,050 --> 00:27:43,440
+ال degree لل V1 هي 1 2 ال degree لل V2 هي واحد
+
+348
+00:27:43,440 --> 00:27:51,040
+اتنين تلاتة صح ال degree لل V3 هي واحد اتنين و هذا
+
+349
+00:27:51,040 --> 00:27:55,240
+زي ما .. ده فاكرين بنحسب ايش اتنين هي أربعة و هذه
+
+350
+00:27:55,240 --> 00:27:59,260
+ال degree اللي هي ايش واحد اذا في عندي .. هي في
+
+351
+00:27:59,260 --> 00:28:04,320
+عندي أربعة هذه ال V3 أربعة ال degree لها و V2
+
+352
+00:28:04,320 --> 00:28:11,620
+اتنين V2 تلاتة اسف هي واحد هي اتنين هي تلاتة هي اذا
+
+353
+00:28:11,620 --> 00:28:17,620
+V3 V2 ال degree degree V3 degree V2 أربعة تلاتة
+
+354
+00:28:17,620 --> 00:28:21,540
+بعدين الأجل من هنا ال degree ل V1 2 بعدين ال degree
+
+355
+00:28:21,540 --> 00:28:26,200
+ل V4 اللي هو واحد يعني بيصير عندي the degree
+
+356
+00:28:26,200 --> 00:28:29,600
+sequence of the pseudograph هذا اللي أمامنا is
+
+357
+00:28:29,600 --> 00:28:38,600
+degree V3 اللي هي أربعة degree V2 اللي هي تلاتة
+
+358
+00:28:38,600 --> 00:28:45,200
+degree V1 التي هي واحد اتنين degree V4 التي هي
+
+359
+00:28:45,200 --> 00:28:50,560
+واحد اذا هذه اللي هي مثال على الـ sequence degree
+
+360
+00:28:50,560 --> 00:28:55,960
+أو الـ degree sequence of this pseudograph الأمامي
+
+361
+00:28:55,960 --> 00:29:06,080
+الآن how many degree does a graph have if its
+
+362
+00:29:06,080 --> 00:29:09,920
+degree sequence is خمسة، اتنين، اتنين، اتنين،
+
+363
+00:29:09,920 --> 00:29:15,300
+اتنين، واحد draw such a graph بقول ليه الآن جداش ال
+
+364
+00:29:15,300 --> 00:29:19,160
+degree اللي هو جداش اللي هو how many edges جداش
+
+365
+00:29:19,160 --> 00:29:24,360
+عدد ال edges اللي في ال .. اللي .. اللي في الجراف
+
+366
+00:29:24,360 --> 00:29:28,160
+اللي عندي اللي ال degree لكله اللي ال degree
+
+367
+00:29:28,160 --> 00:29:33,840
+sequence اللي هو هي how many edges of a graph كم
+
+368
+00:29:33,840 --> 00:29:39,200
+خط في في الجراف إذا كانت ال degree sequence يعني ال
+
+369
+00:29:39,200 --> 00:29:44,820
+degree sequence شكلها بدها هي تجعلنا نعرف نرسم ال
+
+370
+00:29:44,820 --> 00:29:50,220
+graph هي اللي بتجعلنا نعرف جداش الخطوط اللي فيها
+
+371
+00:29:50,220 --> 00:29:56,100
+اللي أنا مقول is خمسة و اتنين و اتنين و اتنين و
+
+372
+00:29:56,100 --> 00:30:01,300
+اتنين و واحد أول حاجة بدي بتطلع هذول أكبر نقطة هذه
+
+373
+00:30:01,300 --> 00:30:05,200
+كل واحدة نقطة من النقاط لأنها بتمثل degree للنقاط
+
+374
+00:30:05,200 --> 00:30:10,920
+هذه نقطة نقطتين تلاتة أربعة خمسة ستة إذا ست نقاط
+
+375
+00:30:10,920 --> 00:30:16,280
+لما آتي أطلع ل degree النقطة هذه الأولى بقول ستة
+
+376
+00:30:16,280 --> 00:30:22,500
+طالع منها اللي هي degree لها خمسة ماشي إذا رايحة
+
+377
+00:30:22,500 --> 00:30:27,080
+لواحد لاتنين لتلاتة لاربعة لخمسة إذا في إليها إيه
+
+378
+00:30:27,080 --> 00:30:32,160
+شمالها طالع منها خمس خطوط التنين طالع منها خطين
+
+379
+00:30:33,030 --> 00:30:37,010
+التنين خطين .. التنين خطين .. التنين خطين ..
+
+380
+00:30:37,010 --> 00:30:42,650
+الواحد خطين .. إذا لما أحسب ال degree .. ال degree
+
+381
+00:30:42,650 --> 00:30:48,310
+الأولى خمسة جدّاش الأولى خمسة والثانية اثنين
+
+382
+00:30:48,310 --> 00:30:50,630
+والثانية اثنين والثانية اثنين والثانية اثنين واحدة
+
+383
+00:30:50,630 --> 00:30:54,390
+هذا مجموع ال degrees لمين؟ للنقاط اللي موجودة لأن
+
+384
+00:30:54,390 --> 00:30:57,530
+هي ال sequence لل degrees للنقاط كلها فكما
+
+385
+00:30:57,530 --> 00:31:01,090
+أعطينيها إذن أربعتاش واحنا اتفاجأنا الأربعتاش أيش
+
+386
+00:31:01,090 --> 00:31:05,410
+بيساوي إن اثنين ضعف الخطوط هذه نظرية خدناها المرة
+
+387
+00:31:05,410 --> 00:31:08,770
+الماضية اثنين ضعف الخطوط يعني عدد الخطوط أيش
+
+388
+00:31:08,770 --> 00:31:12,810
+بيساوي سبعة إذا ال edges اللي موجودة هي عبارة عن
+
+389
+00:31:12,810 --> 00:31:18,470
+سبعة ماشي سبعة الآن كيف بتدرسمها السبعة الآن باجي
+
+390
+00:31:18,470 --> 00:31:22,150
+للنقطة اللي هي اللي .. اللي هي عنده ست نقاط بحط
+
+391
+00:31:22,150 --> 00:31:26,570
+واحدة اثنتين ثلاث أربع خمسة وهي ست هي ست نقاط
+
+392
+00:31:26,570 --> 00:31:30,370
+ماشي ليش حطيتها هنا دي وماحطيتهاش هنا؟ لأن أنا
+
+393
+00:31:30,370 --> 00:31:33,210
+عارف هذا إن في نقطة من النقاط اللي هي طالع منها
+
+394
+00:31:33,210 --> 00:31:38,490
+جدّاش خمس خطوط يعني طالع منها دي خط هنا وهنا خط و
+
+395
+00:31:38,490 --> 00:31:43,520
+هنا خط وهنا خط يعني طالع لها لكل خطوط فهنا أسهل في
+
+396
+00:31:43,520 --> 00:31:47,560
+الرسم بس عشان سهولة الرسم يعني واحد ثاني ممكن يحط
+
+397
+00:31:47,560 --> 00:31:51,960
+هنا هنا ممكن يحطها ويقعد يرسم ويصل بينهم بنفع هنا
+
+398
+00:31:51,960 --> 00:31:55,580
+ممكن يحطها هنا ممكن يحطها يعني ممكن يكون الرسم صح
+
+399
+00:31:55,580 --> 00:32:00,880
+لكن شكلها مختلف من واحد لواحد بس بيكون أيش الصح إن
+
+400
+00:32:00,880 --> 00:32:05,510
+النهاردة طالع لها خمس خطوط هايين هاي الخمسة الآن
+
+401
+00:32:05,510 --> 00:32:09,750
+النقطة الثانية التانيات كلهم واحدة اثنتين ثلاثة
+
+402
+00:32:09,750 --> 00:32:13,690
+أربع كلهم شمال فين خطين خطين خطين يعني هذه الآن
+
+403
+00:32:13,690 --> 00:32:17,650
+بتطلع بينها خطين هيدي محدد وهذه خط هي هذه وهذه خط
+
+404
+00:32:17,650 --> 00:32:21,590
+وهذه وهذه خط وهذه وهذه خط وبنخلي واحدة بس بيطلع
+
+405
+00:32:21,590 --> 00:32:24,550
+منها خط اللي هو طالع علميا لهذا النقطة خاصة عنها
+
+406
+00:32:24,550 --> 00:32:28,730
+عشان نسينا الخمسة دولار فهذا بيكون اللي هو رسمنا ل
+
+407
+00:32:28,730 --> 00:32:34,110
+graph من وعرفنا جدّاش عدد الخطوط من خلال اللي هو
+
+408
+00:32:34,110 --> 00:32:40,300
+معرفة ال degree سيكوانس للـ vertices تبعات ال graph
+
+409
+00:32:40,300 --> 00:32:45,660
+وهي كما نكون احنا خلصنا المحاضرة رقم 11 وهي عندكم
+
+410
+00:32:45,660 --> 00:32:50,460
+ال homework المطلوب تحلو وتسلمونيها كالعادة إن
+
+411
+00:32:50,460 --> 00:32:53,700
+شاء الله وإلى لقاء آخر السلام عليكم ورحمة الله
+
+412
+00:32:53,700 --> 00:32:54,280
+وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7c63c882ef307f45fd1dceed3e63078adb47c1aa
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_postprocess.srt
@@ -0,0 +1,1648 @@
+1
+00:00:00,720 --> 00:00:05,260
+بسم الله الرحمن الرحيم هذه هي المحاضرة الرقم 11
+
+2
+00:00:05,260 --> 00:00:12,280
+لمساق رياضيات من فصلة لطلاب طالبات الجامعة
+
+3
+00:00:12,280 --> 00:00:16,080
+الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة
+
+4
+00:00:16,080 --> 00:00:22,540
+المتنقلة بدأنا حديثنا في المحاضرة العاشرة السابقة
+
+5
+00:00:22,540 --> 00:00:27,700
+على اللي هو ال graphsعرفنا شو معنات ال graph قلنا
+
+6
+00:00:27,700 --> 00:00:33,160
+عبارة عن اللي هو set V اللي هي بتمثل vertices و A
+
+7
+00:00:33,160 --> 00:00:37,940
+بتمثل اللي هي عبارة عن الخطوط اللي بين اللي هي ال
+
+8
+00:00:37,940 --> 00:00:46,300
+vertices و بعدين أخذنا اللي هو شو معنات ال edge
+
+9
+00:00:46,300 --> 00:00:51,360
+اللي هو الخط و شو معنات اللي هو ال neighborhoodو
+
+10
+00:00:51,360 --> 00:00:55,700
+بعدين اللي هو شو .. قلنا شو معنات انه two edgesكون
+
+11
+00:00:55,700 --> 00:01:02,960
+adjacent و أيضا عرفنا اللي هو شو معنات ال degree
+
+12
+00:01:02,960 --> 00:01:08,340
+لل vertex و .. و قلنا ال vertex اللي ال degree له
+
+13
+00:01:08,340 --> 00:01:12,900
+zero قلنا isolated و أخدنا أمثلة على هيك لأمثلة
+
+14
+00:01:12,900 --> 00:01:18,300
+اللي أمامنا هذه و على ال degree إلى أخره و انتقلنا
+
+15
+00:01:20,810 --> 00:01:24,030
+طبعا كنا حاكينا عن الـ undirected graph بعدين
+
+16
+00:01:24,030 --> 00:01:28,650
+أخدنا أمثلة على كل هذه الموضوعات وجينا أخدنا اللي
+
+17
+00:01:28,650 --> 00:01:33,270
+هو النظرية اللي بتقول دايما اللي هو المجموع اللي
+
+18
+00:01:33,270 --> 00:01:37,050
+هو ال degree لل vertices على كل ال vertices اللي
+
+19
+00:01:37,050 --> 00:01:41,650
+في ال V بتساوي 2 فحاصل ضرب اللي هو عدد الخطوط أو
+
+20
+00:01:41,650 --> 00:01:46,570
+عدد ال edges اللي في الشكلو بعدين أخدنا أمثلة على
+
+21
+00:01:46,570 --> 00:01:51,570
+هيك و أخدنا بعد هيك شو معنى .. شو معنات اللي هو ال
+
+22
+00:01:51,570 --> 00:01:54,690
+directed graph اللي بيكون .. قولنا بيسير اللي هو
+
+23
+00:01:54,690 --> 00:02:00,370
+الخط اللي هو directed from نقطة إلى نقطة أخرىو
+
+24
+00:02:00,370 --> 00:02:05,990
+أخدنا اللي هو أنثى عليهم و أخدنا شو ال degree اللي
+
+25
+00:02:05,990 --> 00:02:09,990
+هي الخارجة و ال degree الداخلة و أخدنا ال homework
+
+26
+00:02:09,990 --> 00:02:13,690
+و اليوم ان شاء الله بدنا نبدأ نحكي عن اللي هو
+
+27
+00:02:13,690 --> 00:02:18,210
+الموضوعات المكملة للي حكيناها اللي هي خلينا نحكي
+
+28
+00:02:18,210 --> 00:02:22,510
+عن حاجة اسمها subigraph subigraph يعني جزء من
+
+29
+00:02:22,510 --> 00:02:25,930
+الigraph جزء من الigraph طبيعى نشوف إيش يعرفناه
+
+30
+00:02:26,460 --> 00:02:31,860
+بقول لو كان عندى graph g1 is a sub graph يعني هذا
+
+31
+00:02:31,860 --> 00:02:36,320
+g1 بنقول عنه sub graph من مين of another graph g
+
+32
+00:02:36,320 --> 00:02:41,040
+يعني g1 عبارة عن sub graph او graph جزئي من ال
+
+33
+00:02:41,040 --> 00:02:46,080
+graph g if and only if the vertex and edges sits
+
+34
+00:02:46,080 --> 00:02:49,730
+of g1G1 are respectively subsets of the vertex and
+
+35
+00:02:49,730 --> 00:02:53,730
+edges of G نحن نتفاج أن G يكون مكوّن من شغل تاني
+
+36
+00:02:53,730 --> 00:02:59,270
+من vertices من vertices ومن خطوط إذا بنقول إن G1
+
+37
+00:02:59,270 --> 00:03:04,450
+sub graph من G إذا كان كل ال vertices اللي في G1
+
+38
+00:03:04,450 --> 00:03:11,610
+موجودة في vertices في G في ال V تبعتهمو كل الخطوط
+
+39
+00:03:11,610 --> 00:03:15,190
+الـ edges اللي في ال .. اللي في الـ G1 اللي كنا
+
+40
+00:03:15,190 --> 00:03:20,070
+نسميها إيه هي عبارة عن خطوط موجودة في مين في الـ G
+
+41
+00:03:20,070 --> 00:03:24,950
+الأصلية الآن نيجي ناخد أمثلة اللي هي أمامنا هاي
+
+42
+00:03:24,950 --> 00:03:27,570
+عندى ال graph G هاي و هذا ال graph G هاي ال
+
+43
+00:03:27,570 --> 00:03:31,290
+vertices كلها موجودة عندى و هاي الخطوط اللي بينها
+
+44
+00:03:31,290 --> 00:03:34,550
+اللي هي ال edges اللي بينها اللي هنوجينا نطلعنا
+
+45
+00:03:34,550 --> 00:03:42,870
+لهذا هذا V4 هي موجودة هنا V4V3 هيها جاي من هنا V7
+
+46
+00:03:42,870 --> 00:03:48,090
+هيها من هنا V6 هيها من هنا الخطوط اللي بينهم V7 و
+
+47
+00:03:48,090 --> 00:03:58,230
+V6 هي V7 و V6 موجود V6 و V3 هي موجود V4 و V3 هي V4
+
+48
+00:03:58,230 --> 00:04:04,770
+و V3 موجودإذا هذا ال graph هو عبارة عن جزء من هذا
+
+49
+00:04:04,770 --> 00:04:08,510
+لأن الخطوط هذه موجودة في ال graph الأصلي و ال
+
+50
+00:04:08,510 --> 00:04:12,530
+vertices موجودة في ال graph الأصلي عشان هيك بنسمي
+
+51
+00:04:12,530 --> 00:04:17,150
+هذا sub graph من هذا نشوف ال graph التاني، لاحظوا
+
+52
+00:04:17,150 --> 00:04:25,280
+V2 هي موجودةV3 هي V3 V6
+
+53
+00:04:25,280 --> 00:04:33,000
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+54
+00:04:33,000 --> 00:04:33,140
+V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7
+
+55
+00:04:33,140 --> 00:04:34,080
+هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+56
+00:04:34,080 --> 00:04:34,920
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+57
+00:04:34,920 --> 00:04:47,760
+V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+58
+00:04:47,760 --> 00:04:53,380
+V7الان بدنا ناخد اللي هو some special simple
+
+59
+00:04:53,380 --> 00:04:58,160
+graphs أو حاجة بنسميها complete graphs بدنا نرجع ل
+
+60
+00:04:58,160 --> 00:05:03,420
+اللي هو ال graphs و بدنا نسمي بعض ال graphs ليش
+
+61
+00:05:03,420 --> 00:05:09,820
+بنسميها complete graph بنسميه و نشوف ليش ال graph
+
+62
+00:05:09,820 --> 00:05:14,340
+بنسميه completeبناخد أنواع معينة خلّينا نشوف إيش
+
+63
+00:05:14,340 --> 00:05:18,280
+المجولة for any positive integer n لو كان n عبارة
+
+64
+00:05:18,280 --> 00:05:20,840
+عن positive integer يعني واحد ولا اتنين ولا تلاتة
+
+65
+00:05:20,840 --> 00:05:24,280
+ولا اربعة الاخر هي the complete graph on n
+
+66
+00:05:24,280 --> 00:05:29,620
+vertices يعني لما نقول عن ال graph اللي فيه n
+
+67
+00:05:29,620 --> 00:05:30,220
+vertices
+
+68
+00:05:33,500 --> 00:05:38,600
+يعني في أكم رأس في N من الرؤوس بقول ده complete
+
+69
+00:05:38,600 --> 00:05:43,380
+graph on N vertices denote KN يعني الآن بدنا نسمي
+
+70
+00:05:43,380 --> 00:05:51,240
+ال KN هذا يرمز إلى complete graphwith n vertices
+
+71
+00:05:51,240 --> 00:05:57,700
+فى ايش ماله ن من الرؤوس طبعا شوفوا هذا كأن is a
+
+72
+00:05:57,700 --> 00:06:02,400
+graph with n vertices يعني هذا كأن عبارة عن graph
+
+73
+00:06:02,400 --> 00:06:06,760
+with n vertices every two of which are adjacent
+
+74
+00:06:06,760 --> 00:06:11,380
+يعني كل اتنين من ال vertices adjacent اتجسنت
+
+75
+00:06:11,380 --> 00:06:14,420
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+76
+00:06:14,420 --> 00:06:15,000
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+77
+00:06:15,000 --> 00:06:19,260
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+78
+00:06:19,260 --> 00:06:23,500
+اتجسنت اتجسنت اتجسنت اهي عندى كتنين في نقطتين
+
+79
+00:06:23,500 --> 00:06:29,260
+النقطتين هدولة في التنتين بينها خط مافيش اي نقطة
+
+80
+00:06:29,260 --> 00:06:34,440
+في داخل الكتنين مافيش بينها وبين الباقيات خطوط
+
+81
+00:06:34,440 --> 00:06:42,900
+عشان هيك بنسمي هذا complete graphمن النوع K2 نشوف
+
+82
+00:06:42,900 --> 00:06:50,440
+نوع آخر K3 K3 K3 أشمل فيه تلات رؤوس هذه راس هذه
+
+83
+00:06:50,440 --> 00:06:55,960
+راسين هذه تلاتة لاحظت تلات رؤوس فعلا هذا وهذا بين
+
+84
+00:06:55,960 --> 00:06:59,860
+الخط وهذا وهذا بين الخط وهذا وهذا بين الخط يعني كل
+
+85
+00:06:59,860 --> 00:07:05,920
+الرؤوس are adjacentيعني ما لهن كل الرؤوس اللي هي
+
+86
+00:07:05,920 --> 00:07:09,380
+بينهن وبين بعض خطوط عشان هيك بنسميها ده Complete
+
+87
+00:07:09,380 --> 00:07:13,640
+Graph هذا النوع من ال graphs اللي زي هيك اللي
+
+88
+00:07:13,640 --> 00:07:17,240
+كتنين كتلاتة اللي في عدد اللي هو اتنين او عدد
+
+89
+00:07:17,240 --> 00:07:21,860
+تلاتة او بعد شوية اربع او خمس او ستة وبكون بخاصية
+
+90
+00:07:21,860 --> 00:07:28,320
+انه كل اتنين كل نقطتين بين الخط بنسميه اللي هو
+
+91
+00:07:28,320 --> 00:07:32,990
+Complete Graph من النوع KNنجي لكي أربعة كي أربعة
+
+92
+00:07:32,990 --> 00:07:36,110
+اللي هو واحد تنين تلاتة أربعة فيها أربع عياش نقاط
+
+93
+00:07:36,110 --> 00:07:43,330
+الأربع نقاط كلهم بين هذه و هذه خط و بينها و بينها
+
+94
+00:07:43,330 --> 00:07:48,510
+دي خط و بينها و بينها دي خط يعني كل النقاط اللي هم
+
+95
+00:07:48,510 --> 00:07:52,970
+adjacent لبعض عشان هيك بنسميه graph إذا ال
+
+96
+00:07:52,970 --> 00:07:58,890
+complete graphهو graph عادي كل نقطين فيه adjacent
+
+97
+00:07:58,890 --> 00:08:03,590
+يعني كل نقطين فيه graph حالة خاصة من هذول ال
+
+98
+00:08:03,590 --> 00:08:08,850
+complete graph اللي هي عائلة من ال graphs اسمها kn
+
+99
+00:08:08,850 --> 00:08:14,890
+ايش ال kn هذه اللي هي عددها n من اللي هو ال
+
+100
+00:08:14,890 --> 00:08:20,000
+vertices فيها؟و بيعملين complete graph يعني كل
+
+101
+00:08:20,000 --> 00:08:25,820
+النقاط are adjacent ده نشوف اللي بعدها هاي K خمسة
+
+102
+00:08:25,820 --> 00:08:30,140
+مثلا بخمسة هاي عندى خمس نقاط واحدة تنتهي من تلاتة
+
+103
+00:08:30,140 --> 00:08:32,900
+اربعة خمسة واضح ان كل النقاط كل واحدة بيطلع منها
+
+104
+00:08:32,900 --> 00:08:37,940
+اربع خطوط للاخرين فعشان هيك بنسميها complete graph
+
+105
+00:08:37,940 --> 00:08:43,680
+من النوع Kلو واحد بدى يرسم K6 بتقدر ترسمها بنفس
+
+106
+00:08:43,680 --> 00:08:48,060
+الاسم و K7 طبعا بتغلب شوية لكن بتظلها في نفس
+
+107
+00:08:48,060 --> 00:08:54,800
+النطاق هذه بنسميها complete graphs او مثل على ال
+
+108
+00:08:54,800 --> 00:09:00,240
+complete graphs اللي هي العائلة اللي سميناها KNعند
+
+109
+00:09:00,240 --> 00:09:03,280
+K واحد برضه نعتبره complete ليش؟ لأن الـ complete
+
+110
+00:09:03,280 --> 00:09:07,740
+graph مايكونش فيه نقطتين مش adjacent هانفيش فيه
+
+111
+00:09:07,740 --> 00:09:10,840
+نقطتين مش adjacent لأنه أصلا هي النقطة بس لحالها
+
+112
+00:09:10,840 --> 00:09:17,730
+عشانك بنسميها اللي هي برضه complete graphK1, K2,
+
+113
+00:09:17,850 --> 00:09:22,130
+K3, K4, K5 الاخر هي زمنته بتاعنا الان بدنا نيجي
+
+114
+00:09:22,130 --> 00:09:26,810
+نوع ثاني ل graphs حاجة اسمها ال cycles ماشي ايش ال
+
+115
+00:09:26,810 --> 00:09:31,850
+cycles اللي هي و ال wheels اه ايش تشوف ايش ال
+
+116
+00:09:31,850 --> 00:09:37,900
+cycle و ايش ال wheelالان cycle cn ده نرمزي لبرنامج
+
+117
+00:09:37,900 --> 00:09:41,220
+cn بعد اذنكم يعني في عندي n أكبر تساوي تلاتة يعني
+
+118
+00:09:41,220 --> 00:09:47,380
+عندي cycle c3 و c4 و c5 و c6 إلى ما لنهاية
+
+119
+00:09:47,380 --> 00:09:51,900
+consists of n vertices يعني ال cn هذه برضه بتحتوي
+
+120
+00:09:51,900 --> 00:09:57,860
+على ايه عشان n من ال verticesماذا نسميه Cycle لما
+
+121
+00:09:57,860 --> 00:10:02,960
+نكون تحقيق ما يليه الـ CNN Consists Of N Vertices
+
+122
+00:10:02,960 --> 00:10:08,480
+V1 و V2 و VN And Edges و الـ Edges ايش ما لها V1 و
+
+123
+00:10:08,480 --> 00:10:13,890
+V2 يعني خط بين V1 و V2 و خط بين V2 و V3و خط بين V3
+
+124
+00:10:13,890 --> 00:10:19,330
+و V4 لما أصل عند خط بين اللي هي النقطة الأخيرة VN
+
+125
+00:10:19,330 --> 00:10:25,430
+و برجع لمين لل V1 و كإن إيش بسكر و بعمله cycle زي
+
+126
+00:10:25,430 --> 00:10:30,190
+دائرة أو اللي هو دورة كاملة ماشي the cycles C3,
+
+127
+00:10:30,330 --> 00:10:38,350
+C4, C5, C6 are displaced انفجارا هى وهذه وهذهاللي
+
+128
+00:10:38,350 --> 00:10:46,690
+هي V1 V2 V2 V3 V3 V1 إذاً هذا cycle صار الآن هذا
+
+129
+00:10:46,690 --> 00:10:50,170
+ال graph complete أه complete لأنه كل مغطين
+
+130
+00:10:50,170 --> 00:10:54,850
+adjacent يعني ال cycle ممكن تكون complete يعني
+
+131
+00:10:54,850 --> 00:10:59,730
+مثال على complete graph نجي للي بعدها C4هي من عند
+
+132
+00:10:59,730 --> 00:11:03,010
+النقطة الأولى للتانية في خط و من التانية للتالتة و
+
+133
+00:11:03,010 --> 00:11:05,770
+من التالتة للرابعة و من الرابعة للأولى رجعت يعني
+
+134
+00:11:05,770 --> 00:11:10,190
+أقفلة الدائرة أو أقفلة اللي هي ال cycle هذا بنسميه
+
+135
+00:11:10,190 --> 00:11:13,590
+برضه cycle هل هذا complete؟ لأ مش complete ليش مش
+
+136
+00:11:13,590 --> 00:11:16,850
+complete؟ لأن هذي و هذا النقطة they are not
+
+137
+00:11:16,850 --> 00:11:20,850
+adjacent لأنه مافيش بين الخط و هذي كمان و هذي إذا
+
+138
+00:11:20,850 --> 00:11:24,090
+هي في عند ال cycle ليس شرط انها تكون إيش مالها
+
+139
+00:11:24,090 --> 00:11:28,450
+complete اقرأتالان نجي لـ C5 C5 بنفس الأسلوب فيها
+
+140
+00:11:28,450 --> 00:11:31,330
+خمس نقاط الخمس نقاط بتبدأ من عند النقطة الأولى و
+
+141
+00:11:31,330 --> 00:11:33,670
+بتبدأ للتانية أو للتالتة أو للربعة أو للخمسة أو
+
+142
+00:11:33,670 --> 00:11:37,770
+للسادسة اللي الخمسة بترجع لمين للنقطة الأولى
+
+143
+00:11:37,770 --> 00:11:42,770
+فبتعمل ليه cycle اللي هي بتسكر اللي هي الدورة الان
+
+144
+00:11:42,770 --> 00:11:47,890
+C6 بنفس الأسلوب فيها ست نقاط كل نقطة ال V1 بتروحها
+
+145
+00:11:47,890 --> 00:11:52,150
+V2 V2 تلاتة V3 او V4 مافهومش معنات بتروح يعني بين
+
+146
+00:11:52,150 --> 00:12:02,610
+الخطV4 V5 V5 V6 V6 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+147
+00:12:02,610 --> 00:12:03,510
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+148
+00:12:03,510 --> 00:12:06,110
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+149
+00:12:06,110 --> 00:12:06,890
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+150
+00:12:06,890 --> 00:12:08,650
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+151
+00:12:08,650 --> 00:12:12,150
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+152
+00:12:12,150 --> 00:12:15,610
+V1 V1
+
+153
+00:12:15,980 --> 00:12:21,720
+when we add an additional vertex to cycle CN يعني
+
+154
+00:12:21,720 --> 00:12:29,280
+ايش بنجيب؟ بنجيب هي ال cycle و بنضيف لها نقطة ايش
+
+155
+00:12:29,280 --> 00:12:33,040
+النقطة دي مالها؟ تنشوف ايش مالها we add an
+
+156
+00:12:33,040 --> 00:12:36,260
+additional vertex to cycle CN for N أكبر سواء
+
+157
+00:12:36,260 --> 00:12:41,940
+تلاتة and connect this new vertex to each of the
+
+158
+00:12:41,940 --> 00:12:48,410
+vertices in CN by new edgesإذا الآن ما هي إلا
+
+159
+00:12:48,410 --> 00:12:52,570
+cycle بنحط جواتها نقطة أو جنبها نقطة في المكان
+
+160
+00:12:52,570 --> 00:12:56,010
+المناسب جواتها أفضل يعني بتكون أحلى في الرسم و
+
+161
+00:12:56,010 --> 00:13:01,590
+بنوصل من النقطة هذه خطوط لكل او edges لكل من ال
+
+162
+00:13:01,590 --> 00:13:05,390
+vertices اللي موجودة هذه النقطة هيعملنا اللي هو
+
+163
+00:13:05,390 --> 00:13:09,810
+edge وهي edge وهي edge مع كل النقاط هذه بنسميها
+
+164
+00:13:09,810 --> 00:13:16,510
+wheel W تلاتة تبعا ل C تلاتةالان هذه complete اه
+
+165
+00:13:16,510 --> 00:13:19,590
+complete هذه واضح انها complete لان هي مع الكل كل
+
+166
+00:13:19,590 --> 00:13:26,570
+النقاط مع الكل الان هذه النقطة هي عندياللي هو من
+
+167
+00:13:26,570 --> 00:13:31,630
+النقطة هذه حطينا و رسمنا لكل النقاط، مظبوط؟ هذه
+
+168
+00:13:31,630 --> 00:13:35,050
+عملت ل wheel هي نفسها اللي فوق بس عملنا لها نقطة و
+
+169
+00:13:35,050 --> 00:13:40,390
+نقطة ودنا لها اللي هي من لكل النقاط خطوط حسب تعريف
+
+170
+00:13:40,390 --> 00:13:44,370
+اللي عرفنا لمين لل wheel هل هذه complete؟ ليس شرطا
+
+171
+00:13:44,370 --> 00:13:47,410
+لأنه فيش بين النقطة هذه مثلا النقطة هذه خط مباشر
+
+172
+00:13:47,850 --> 00:13:51,270
+هذا لو خط من هنا إلى هنا وهذا من هنا إلى هنا لأن
+
+173
+00:13:51,270 --> 00:13:55,530
+لو كان هناك خط مباشر بينهم نسميه complete لو كان
+
+174
+00:13:55,530 --> 00:13:59,430
+هناك خطوط من الكل طبعا الان نأتي لهذه اللي هي ال
+
+175
+00:13:59,430 --> 00:14:03,850
+wheel بنجيب ال C3 و بنحط نقطة في داخلها و بنوصل
+
+176
+00:14:03,850 --> 00:14:08,470
+بينهم كلهم اللي هي ايش بين النقطة هذه و بين كل
+
+177
+00:14:08,470 --> 00:14:12,030
+النقاط الأخرى بنوصل خطوط فبتعمل wheel هل ال wheel
+
+178
+00:14:12,030 --> 00:14:15,090
+complete ليس شطء لأن هو من هنا إلى هنا مثلا ايش
+
+179
+00:14:15,090 --> 00:14:19,810
+مافيش خطهكذا اللي بعدها الان هذه اللي هي مين الشكل
+
+180
+00:14:19,810 --> 00:14:23,810
+السداسي في الشكل السداسي حطينا نقطة ووصلنا بين
+
+181
+00:14:23,810 --> 00:14:28,090
+النقطة و بين باقى النقاط فعملت ليش برضه wheel هاي
+
+182
+00:14:28,090 --> 00:14:32,850
+شكل السداسي عندي وهي النقطة و بدي اتوصل من الشكل
+
+183
+00:14:32,850 --> 00:14:37,350
+السداسي لكل النقاط شوفوهاشتبتطلعوش تقبلوا ليها
+
+184
+00:14:37,350 --> 00:14:40,310
+تقوليها مكعب لأ هذا مقطب في المصف و طبعا هي بتظهر
+
+185
+00:14:40,310 --> 00:14:43,790
+لو اتنعانت هتشوفها مكعب لو اتنعانت في صورة أخرى
+
+186
+00:14:43,790 --> 00:14:47,070
+هتشوفها نقطة في الداخل و من الكل مش موضوعنا هذا بس
+
+187
+00:14:47,070 --> 00:14:51,930
+لكن عشان الخداع البصري طيب هذه اللي هي معنات ال
+
+188
+00:14:51,930 --> 00:14:58,050
+wheel الان في حد اسمه بيبا ترايت بيبا بيبارتايت
+
+189
+00:14:58,410 --> 00:15:03,350
+graph بيبرتايت graph اللي هو يعني الـ Graph
+
+190
+00:15:03,350 --> 00:15:06,830
+الثنائي ايش ال graph الثنائي خلينا نشوف ايش بيقول
+
+191
+00:15:06,830 --> 00:15:11,030
+ال graph الثنائي a bipartite graph is a graph هو
+
+192
+00:15:11,030 --> 00:15:14,750
+عبارة عن graph whose vertices can be partitioned
+
+193
+00:15:14,750 --> 00:15:19,470
+into two disjoint sets V1 and V2 يعني ال بيبرتايت
+
+194
+00:15:19,470 --> 00:15:23,970
+graph أو اللي هو ال graph الثنائي بيقول هذا بتقدر
+
+195
+00:15:23,970 --> 00:15:32,640
+تعمل ال vertices إليه جزئينV1 و V2 هي V1 وهي V2 بس
+
+196
+00:15:32,640 --> 00:15:39,940
+تحت شرط معين كل Graphs ممكن تعملها V1 و V2بقدر
+
+197
+00:15:39,940 --> 00:15:45,220
+اعمل V1 و V2 بيبقى partition sets يعني هذول اللي
+
+198
+00:15:45,220 --> 00:15:50,540
+بنسميهم هم اللي جزء من ال set الأصلي تبع ال
+
+199
+00:15:50,540 --> 00:15:56,440
+vertices in such a way بتجزئها بطريقة هي V1 و V2
+
+200
+00:15:56,440 --> 00:16:02,840
+بتجزئها بطريقة that every edge point joins a
+
+201
+00:16:02,840 --> 00:16:08,070
+vertex in V1 و V2 يعني الآن لما ناخد V1وفيه اتنين
+
+202
+00:16:08,070 --> 00:16:16,590
+هتجزئلي اللي هي ال vertices إلى جزئين ابحث انه كل
+
+203
+00:16:16,590 --> 00:16:22,730
+edge في الشكل بربط نقطة من هنا مع نقطة من هنا كل
+
+204
+00:16:22,730 --> 00:16:26,590
+edge في الشكل .. كل edge موجود هي edge بربط نقطة
+
+205
+00:16:26,590 --> 00:16:29,150
+من هنا مع نقطة من هنا ال edge التاني هي بربط نقطة
+
+206
+00:16:29,150 --> 00:16:31,710
+من هنا مع نقطة من هنا ال edge التالت من نقطة من
+
+207
+00:16:31,710 --> 00:16:33,830
+هنا مع نقطة من هنا ال edge الرابع من نقطة من هنا
+
+208
+00:16:33,830 --> 00:16:37,390
+مع نقطة من هناكل الاتجاهات اللي موجودة الخطوط
+
+209
+00:16:37,390 --> 00:16:42,810
+بتكون واصلة بين نقطة من مجموعة ال vertices الأولى
+
+210
+00:16:42,810 --> 00:16:47,770
+ونقطة من مجموعة ال vertices التانية يعني الآن لو
+
+211
+00:16:47,770 --> 00:16:52,290
+كان بين هذه وهذه لأ بنفعش يكون اللي هو ايه شماله
+
+212
+00:16:52,680 --> 00:16:58,620
+عندي اللي هو بمسميهش عملة partition لأنه من هالهال
+
+213
+00:16:58,620 --> 00:17:02,920
+بيصير هذا النقطة في نفس ال .. نقطتين في نفس ال V
+
+214
+00:17:02,920 --> 00:17:08,420
+واحد لأ لأن كل الخطوط بدها تكون جاية من ال
+
+215
+00:17:08,420 --> 00:17:13,080
+vertices الأولى مع ال vertices التانية عشان هيك
+
+216
+00:17:13,080 --> 00:17:20,280
+بنسمي هذا bipartite graph أو graph ثنائيالان هاي
+
+217
+00:17:20,280 --> 00:17:26,820
+واحد تاني برضه ببرتاية graph آخر هي ال V1 الكبيرة
+
+218
+00:17:26,820 --> 00:17:31,920
+يعني بتحتوي على كل اللي هي ال vertices الجزء الأول
+
+219
+00:17:31,920 --> 00:17:35,980
+وهذه بتحتوي على ال vertices الجزء الثاني لاحظ انه
+
+220
+00:17:35,980 --> 00:17:42,030
+كل خطموجود بربط بين نقطة بين هذه V1 و V2 كل خط
+
+221
+00:17:42,030 --> 00:17:47,670
+موجود بربط بين V2 و V1 كل خط موجود بين V1 و V2 و
+
+222
+00:17:47,670 --> 00:17:54,470
+هكذا هذا بنسميهم اشمالهم امثل عبارة على bipartite
+
+223
+00:17:54,470 --> 00:17:58,330
+graphs نيجي لاخر واحدة طبعا هي الحالة من حالة
+
+224
+00:17:58,330 --> 00:18:05,600
+رسمها حالة هي هذه اللي هو ال V2وهي هدمين الـ V1 هى
+
+225
+00:18:05,600 --> 00:18:12,920
+اللى هما ال V1 و ال V2 اللى جزءين ليه اللى جزءين
+
+226
+00:18:12,920 --> 00:18:18,460
+ليه اللى هو ال vertices الى جزءين ابحث ان كل خط
+
+227
+00:18:18,460 --> 00:18:24,900
+موجود ياخد من نقطة في ال V1 الى V2 او من V2 ل V1 و
+
+228
+00:18:24,900 --> 00:18:29,700
+هكذا زى ما انتوا شايفين فهدولة امثلة على bipartite
+
+229
+00:18:29,700 --> 00:18:36,590
+graphsأو جرافات ثنائية الـ Complete bipartite
+
+230
+00:18:36,590 --> 00:18:41,310
+graph is a bipartite graph in which every vertex
+
+231
+00:18:41,310 --> 00:18:46,390
+in V1 is joined to every vertex in V2
+
+232
+00:18:49,970 --> 00:18:54,290
+عبارة عن بيبرتايته graph in which every vertex in
+
+233
+00:18:54,290 --> 00:18:58,870
+v1 كل ال vertex في ال v1 is joined to every vertex
+
+234
+00:18:58,870 --> 00:19:03,570
+in v2 ماقلناش ان كل ال vertices اللي في ال v1
+
+235
+00:19:03,570 --> 00:19:08,410
+برتبط مع بعض و ال v2 اللي برتبط مع بعض لأ قلنا ان
+
+236
+00:19:08,410 --> 00:19:13,870
+كل vertex v1 برتبط مع اياش مع اللي في ال .. مع
+
+237
+00:19:13,870 --> 00:19:19,030
+واحد من مين من v2 every vertex in v1 is joined to
+
+238
+00:19:19,030 --> 00:19:23,280
+everyjoin to every وليس مع واحد فقط to every واحد
+
+239
+00:19:23,280 --> 00:19:31,460
+في ذي اتنى الان خلينا لو رجعنا الان هذا مثلا نشوف
+
+240
+00:19:31,460 --> 00:19:35,240
+complete ولا لأ هى هى هذا برتبط مع هذا وبرتبط مع
+
+241
+00:19:35,240 --> 00:19:40,360
+هذا لكن برتبطش مع اللي بعيد هذا اذا مش complete طب
+
+242
+00:19:40,360 --> 00:19:46,630
+الان هذا هى وبرتبط مع هذا وبرتبط مع هذاو هذه
+
+243
+00:19:46,630 --> 00:19:52,150
+بترتبطش مع مين؟ مع هذا لو ربطناها مع هذا يعني لو
+
+244
+00:19:52,150 --> 00:19:58,850
+وصلنا هذا الخط هيك و وصلنا هذا الخط هيكووصلنا هذا
+
+245
+00:19:58,850 --> 00:20:02,670
+خط واصل فبصير عندي هذا complete يعني متى بيصير هذا
+
+246
+00:20:02,670 --> 00:20:07,290
+complete لما نهادي لأن هي وصلت مع حده ووصلت مع حده
+
+247
+00:20:07,290 --> 00:20:13,030
+ونوصل هذه مع حده ومش هيك كمان ونوصل هذه مع حده
+
+248
+00:20:13,030 --> 00:20:16,950
+بيصير ال graph اللي طلع عنده يشمله complete يعني
+
+249
+00:20:16,950 --> 00:20:20,490
+عشان يكون complete هذا بيكون كل واحدة من هدولة
+
+250
+00:20:20,490 --> 00:20:26,950
+التنتين بتتوصل مع كل واحدة من التلاتةيعني بينها
+
+251
+00:20:26,950 --> 00:20:31,070
+وبين كل أحد من تلاتة خط واضح أننا نسميه complete
+
+252
+00:20:31,070 --> 00:20:35,200
+bipartiteigraphأذا زي ما قلنا الـ bipartite graph
+
+253
+00:20:35,200 --> 00:20:39,700
+بكون complete إذا كان هو bipartite graph وكل
+
+254
+00:20:39,700 --> 00:20:46,140
+vertex في الـ V1 is joined to every vertex in V2
+
+255
+00:20:46,140 --> 00:20:48,420
+وكل vertex في الـ V1 is joined to every vertex in
+
+256
+00:20:48,420 --> 00:20:53,360
+V2 وكل vertex في الـ V1 is joined to every vertex
+
+257
+00:20:53,360 --> 00:20:53,540
+in V2 وكل vertex في الـ V1 is joined to every
+
+258
+00:20:53,540 --> 00:20:53,600
+to every vertex in V2 وكل vertex في الـ V1 is
+
+259
+00:20:53,600 --> 00:20:53,660
+joined to every vertex in V2 وكل vertex في الـ V1
+
+260
+00:20:53,660 --> 00:20:58,580
+vertex في الـ V1 is joined to every vertex in V2
+
+261
+00:20:58,580 --> 00:21:04,130
+وكل vertex في الـ V1 isاللي بيكون اللي هو ال .. ال
+
+262
+00:21:04,130 --> 00:21:08,930
+.. ال .. ال V1 في M من العناصر و ال V2 بيكون M من
+
+263
+00:21:08,930 --> 00:21:13,890
+ال .. N من العناصر يعني عند ال V1 ال vertices
+
+264
+00:21:13,890 --> 00:21:19,570
+عددهم M و ال V2 عددهم N و كان هذا bipartite graph
+
+265
+00:21:19,570 --> 00:21:24,370
+و في نفس الوقت complete بيكون اللي هو هاي شكله
+
+266
+00:21:24,370 --> 00:21:30,120
+نيجيكتنين و تلاتة الان هي عندى فوق اتنين وها نتحت
+
+267
+00:21:30,120 --> 00:21:33,360
+ايش تلاتة زى ما عملناها قبل شوية هي الان هذه بدها
+
+268
+00:21:33,360 --> 00:21:39,020
+تروح للكل هي راحت للكل وهذه برضه راحت لإيش للكل
+
+269
+00:21:39,020 --> 00:21:44,150
+وطبعا هدولة اوتوماتيك راحلن مين لتنتين اللى فوقلأن
+
+270
+00:21:44,150 --> 00:21:47,290
+K ثلاثة ثلاثة هيكون عندنا ثلاثة هنا و ثلاثة وين
+
+271
+00:21:47,290 --> 00:21:50,730
+فوق لأن التنين الأولى خلّينا نصطلح مع بعض اللي
+
+272
+00:21:50,730 --> 00:21:57,230
+بنرسمها فوق التلاتة التانية هذه بنرسمها تحت لأن
+
+273
+00:21:57,230 --> 00:22:00,650
+تلاتة و تلاتة هي تلاتة فوق و هي تلاتة تحت و بنوصل
+
+274
+00:22:00,650 --> 00:22:05,150
+من كل واحدة للكل ممنوع نوصل بين هدول اللي هنا مع
+
+275
+00:22:05,150 --> 00:22:10,110
+بعض لأ بيبطل ال bipartite أصلا ال bipartite أن
+
+276
+00:22:10,110 --> 00:22:16,810
+هدولةفي جهة و هدولة في جهة و الخطوط بين هنا وبس
+
+277
+00:22:16,810 --> 00:22:23,850
+مافيش بين اللي هو عناصر اللي هي ال V2 مع بعضها
+
+278
+00:22:23,850 --> 00:22:28,590
+خطوط بيبطل بيبرتايد وهذا نفس الاشي طيب لإن نيجي
+
+279
+00:22:28,590 --> 00:22:32,670
+تلاتة و خمسة إذا تلاتة بنرسمها فوق وهذه خمسة تحت و
+
+280
+00:22:32,670 --> 00:22:38,950
+بنطلع من كل تلاتةخمس خطوط لخمس نقاط من كل تلاتة
+
+281
+00:22:38,950 --> 00:22:42,630
+خمس خطوط من كل تلاتة خمس خطوط يعني لو بدك تيجي
+
+282
+00:22:42,630 --> 00:22:47,210
+تحسب الخطوط الموجودة من هذه بتطلع منها خمس خطوط
+
+283
+00:22:47,210 --> 00:22:51,650
+خمس خطوط ومن هذه خمسة ومن هذه خمسة يعني خمستاشر خط
+
+284
+00:22:52,480 --> 00:22:56,460
+ممكن اعد ان الـ 15 الخط بطريقة تانية ان هذه اطلع
+
+285
+00:22:56,460 --> 00:23:00,620
+منها تلت خطوط للي فوق عشان يصير complete وهذه اطلع
+
+286
+00:23:00,620 --> 00:23:03,360
+منها تلت خطوط للي فوق وهذه اطلع منها تلت خطوط
+
+287
+00:23:03,360 --> 00:23:07,880
+بيصير تلت خطوط في خمس نقاط بخمس تعاشر هنا خمس نقاط
+
+288
+00:23:07,880 --> 00:23:11,220
+طالعين تلت نقاط طالع الخمس خطوط تلت في خمسة بخمس
+
+289
+00:23:11,220 --> 00:23:14,480
+تعاشر اذا بقدر اعد الخطوط من اعلى او الخطوط من
+
+290
+00:23:14,480 --> 00:23:21,730
+اسفل زي ما وضحتالان اتنين و ستة هي نقطة نقطتين وهي
+
+291
+00:23:21,730 --> 00:23:25,090
+اللي هي ست نقطة تحت هيك التفاجنة الأولى بتطلع فوق
+
+292
+00:23:25,090 --> 00:23:30,190
+والتانية بتطلع تحتها تصلح بينها وبين بعض الان هذه
+
+293
+00:23:30,190 --> 00:23:34,970
+التنتين النقطة الأولى بتطلع ستة تقريه ست خطوطو هدى
+
+294
+00:23:34,970 --> 00:23:38,650
+بتطلع ست خطوط للنقاط اللى تحتها فبصير ستة و ستة
+
+295
+00:23:38,650 --> 00:23:42,670
+اتناش هدى بتطلع خطين و هدى خطين و هدى خطين كل
+
+296
+00:23:42,670 --> 00:23:45,670
+واحدة ست نقاط بتطلع كل واحدة خطين بيصير ستة في
+
+297
+00:23:45,670 --> 00:23:49,870
+اتنين باتناش ده بقدر اعد اللى هو من هنا او من هنا
+
+298
+00:23:49,870 --> 00:23:53,270
+يعني هدولة بتطلعين اتناش خط و هدولة بتطلعين اتناش
+
+299
+00:23:53,270 --> 00:23:57,100
+خطيعني لو بدنا نحسب ال degree لهدولة ال degree
+
+300
+00:23:57,100 --> 00:24:00,980
+لهدولة اتناش و ال degree للي فوق برضه ايش اتناش
+
+301
+00:24:00,980 --> 00:24:06,280
+يعني مجموع ال degree مجموع ال degree لكل العناصر
+
+302
+00:24:06,280 --> 00:24:10,800
+لكل ال vertices اللي هان هي أربعة و عشرين اللي هي
+
+303
+00:24:10,800 --> 00:24:13,920
+ضائف عدد الخطوط زي ما قلنا في النظرية اللي قلناها
+
+304
+00:24:13,920 --> 00:24:17,780
+المرة الماضية وهذا اللي هو sum of degree اللي
+
+305
+00:24:17,780 --> 00:24:22,970
+بحكيهلأن how many edges does K3 و K6 contains في
+
+306
+00:24:22,970 --> 00:24:27,790
+الشرح قلته قبل شوية بيطلع من تلاتة ست خطوط فبصير
+
+307
+00:24:27,790 --> 00:24:33,410
+عندى أكم خط تلاتة في ستة بطمنتعش لأن الستة بيطلع
+
+308
+00:24:33,410 --> 00:24:36,490
+منها تلت خطوط كل واحدة ستة في تلاتة برضه بطمنتعش
+
+309
+00:24:36,490 --> 00:24:41,310
+اذا طمنتعش طمنتعشر خط اللي هو وكأنه ال degrees
+
+310
+00:24:41,310 --> 00:24:45,470
+لهدولة اللي هي كل واحدة ال degree اللي هي ستة من
+
+311
+00:24:45,470 --> 00:24:50,990
+النقاط التلاتةفبكون مجموع ال degrees للنقاط اللي
+
+312
+00:24:50,990 --> 00:24:56,610
+فوق 18 الان ال 6 اللي تحت ال degree لكل واحدة
+
+313
+00:24:56,610 --> 00:24:59,690
+تلاتة لإنه بيطلع بينها تلت خطوط فبكون مجموع ال
+
+314
+00:24:59,690 --> 00:25:03,570
+degrees اللي تحت 18 يعني اللي تحت 18 و اللي فوق 18
+
+315
+00:25:03,570 --> 00:25:08,490
+بيطلع عن 36 36 هنا ضعف عدد الخطوط زي ما عكينا قبل
+
+316
+00:25:08,490 --> 00:25:14,120
+شوية هذا هي this complete bipartiteGraph has six
+
+317
+00:25:14,120 --> 00:25:17,100
+vertices يعني هذا الـ Complete بيبرتايت الـ Graph
+
+318
+00:25:17,100 --> 00:25:21,860
+اللي قلنا عنه زي اللي توه له ستة vertices with
+
+319
+00:25:21,860 --> 00:25:25,280
+degree تلاتة يعني ستة vertices with degree تلاتة و
+
+320
+00:25:25,280 --> 00:25:28,660
+تلاتة vertices with degree ستة زي ما وضحت قبل و
+
+321
+00:25:28,660 --> 00:25:33,220
+شوية الان مدموع ال degree لكل ال V اللي هما الستة
+
+322
+00:25:33,220 --> 00:25:38,680
+والتلاتة ستةكل واحد ديجري تلاتة و تلاتة كل واحدة
+
+323
+00:25:38,680 --> 00:25:44,200
+ديجري ستة بتطلع ل 36 يعني اتنين في عدد الخطوط اللي
+
+324
+00:25:44,200 --> 00:25:48,380
+هو بيكون عدد الخطوط 18 خط لإن ال 36 زي ما انتوا
+
+325
+00:25:48,380 --> 00:25:53,600
+عارفين يعني مضاعف عدد الخطوط جولنا اذا الكل بيكون
+
+326
+00:25:53,600 --> 00:26:00,410
+عدد الخطوط عنا 18 خطSo that K36 has 18 edges
+
+327
+00:26:00,410 --> 00:26:04,570
+تقريبا 18 خط degree sequence نعرف حاجة اسمها
+
+328
+00:26:04,570 --> 00:26:10,800
+degree sequence نشوف ايش degree sequenceالشعر الله
+
+329
+00:26:10,800 --> 00:26:16,100
+سهل يعني suppose that D1 وD2 وDn are degree of the
+
+330
+00:26:16,100 --> 00:26:18,900
+vertices of a graph يعني في عندنا graph بيسيده
+
+331
+00:26:18,900 --> 00:26:22,580
+graph زي ال graph تبعت المرة الفاتة عندنا graph G
+
+332
+00:26:22,580 --> 00:26:27,200
+هذا ال graph جينا حسبنا اللي هي فيه N من ال
+
+333
+00:26:27,200 --> 00:26:31,020
+vertices حسبنا أول واحدة لجينا انها degree D1
+
+334
+00:26:31,020 --> 00:26:38,320
+التانية D2 التلاتة Dnعندما نرتب تساعد تنازلي D1
+
+335
+00:26:38,320 --> 00:26:43,320
+أكبر سوى D2 أكبر سوى D3 أكبر سوى DN هذه الـ D1 وD2
+
+336
+00:26:43,320 --> 00:26:48,160
+وDN المرتبة اللي هي بشكل تنازلي
+
+337
+00:26:48,980 --> 00:26:55,540
+اللي هي طبعا دي واحد تمثل ال degree ل اللي هو نقطة
+
+338
+00:26:55,540 --> 00:26:58,520
+أولى هذه ال degree لتانية هذه ال degree ل الأخيرة
+
+339
+00:26:58,520 --> 00:27:03,760
+لما نرتبه انتصار تنازل زي هيك بنسميه degree
+
+340
+00:27:03,760 --> 00:27:08,220
+sequence of G اللي هي degree sequence لمين لل G في
+
+341
+00:27:08,220 --> 00:27:11,620
+الواقع degree sequence لل G لأ هي في الواقع ال
+
+342
+00:27:11,620 --> 00:27:16,530
+degree sequence لل vertices تبعات ال Gهذا اصطلاحا
+
+343
+00:27:16,530 --> 00:27:19,930
+مع بعض عشان لما نحكي عن ال degree sequence of G
+
+344
+00:27:19,930 --> 00:27:26,130
+نكون فاهمين انه بقصد انه بنجيب اللي هو ال degree
+
+345
+00:27:26,130 --> 00:27:31,910
+لكل لكل نقطة من النقاط و بعدين بنرتبها تساق تنازلي
+
+346
+00:27:31,910 --> 00:27:37,050
+ده نشوف هاي عندي مثلا V1 V2 هاي الخطوط اللي بينهم
+
+347
+00:27:37,050 --> 00:27:43,440
+ال degree لل V1 هي 1 2ال degree لل V2 هي واحد
+
+348
+00:27:43,440 --> 00:27:51,040
+اتنين تلاتة صح ال degree لل V3 هي واحد اتنين و هذا
+
+349
+00:27:51,040 --> 00:27:55,240
+زي ما .. ده مفتكرين بنحسب ايش اتنين هي اربعة و هذه
+
+350
+00:27:55,240 --> 00:27:59,260
+ال degree اللي هي ايش واحد اذا في عندي .. هي في
+
+351
+00:27:59,260 --> 00:28:04,320
+عندي اربعة هذه ال V3 اربعة ال degree لها و V2
+
+352
+00:28:04,320 --> 00:28:11,620
+اتنين V2 تلاتة اسف هي واحد هي اتنين هي تلاتةهي اذا
+
+353
+00:28:11,620 --> 00:28:17,620
+V3 V2 ال degree degree V3 degree V2 أربعة تلاتة
+
+354
+00:28:17,620 --> 00:28:21,540
+بعدين الأجل من هنا ال degree ل V12 بعدين ال degree
+
+355
+00:28:21,540 --> 00:28:26,200
+ل V4 اللي هو واحد يعني بيصير عندي the degree
+
+356
+00:28:26,200 --> 00:28:29,600
+sequence of the pseudograph هذا اللي أمامنا is
+
+357
+00:28:29,600 --> 00:28:38,600
+degree V3 اللي هي أربعة degree V2 اللي هيتلاتة
+
+358
+00:28:38,600 --> 00:28:45,200
+degree v1 التي هي واحد اتنين degree v4 التي هي
+
+359
+00:28:45,200 --> 00:28:50,560
+واحدإذاً هذه اللي هي مثال على الـ sequence degree
+
+360
+00:28:50,560 --> 00:28:55,960
+أو الـ degree sequence of this pseudograph الأمامي
+
+361
+00:28:55,960 --> 00:29:06,080
+الآن how many degree does a graph have if its
+
+362
+00:29:06,080 --> 00:29:09,920
+degree sequence is خمسة، اتنين، اتنين، اتنين،
+
+363
+00:29:09,920 --> 00:29:15,300
+اتنين، واحدdraw such a graph بقول ليه الآن جداش ال
+
+364
+00:29:15,300 --> 00:29:19,160
+degree اللي هو جداش اللي هو how many edges جداش
+
+365
+00:29:19,160 --> 00:29:24,360
+عدد ال edges اللي في ال .. اللي .. اللي في الجراف
+
+366
+00:29:24,360 --> 00:29:28,160
+اللي عندى اللي ال degree لكله اللي ال degree
+
+367
+00:29:28,160 --> 00:29:33,840
+sequence اللي هو هي how many edges of a graph أكم
+
+368
+00:29:33,840 --> 00:29:39,200
+خط في في الجرافإذا كانت ال degree sequence يعني ال
+
+369
+00:29:39,200 --> 00:29:44,820
+degree sequence شكلها بدها هي تجعلنا نعرف نرسم ال
+
+370
+00:29:44,820 --> 00:29:50,220
+graph هي اللي بتجعلنا نعرف جداش الخطوط اللي فيها
+
+371
+00:29:50,220 --> 00:29:56,100
+اللي أنا مقول is خمسة و اتنين و اتنين و اتنين و
+
+372
+00:29:56,100 --> 00:30:01,300
+اتنين و واحد أول حاجة بدي بتطلع هذول أكب نقطة هذه
+
+373
+00:30:01,300 --> 00:30:05,200
+كل واحدة نقطة من النقاطلأنه بتمثل degree للنقاط
+
+374
+00:30:05,200 --> 00:30:10,920
+هذه نقطة نقطين تلاتة أربعة خمسة ستة إذا ست نقاط
+
+375
+00:30:10,920 --> 00:30:16,280
+لما أتي أطلع ل degree النقطة هذه الأولى بقول ست
+
+376
+00:30:16,280 --> 00:30:22,500
+طالع منها اللي هي degree لها خمسة ماشي إذا رايحة
+
+377
+00:30:22,500 --> 00:30:27,080
+لواحد لاتنين لتلاتة لاربعة لخمسة إذا في إليها إيه
+
+378
+00:30:27,080 --> 00:30:32,160
+شمالها طالع منها خمس خطوط التنين طالع منها خطين
+
+379
+00:30:33,030 --> 00:30:37,010
+التنين خطين .. التنين خطين .. التنين خطين ..
+
+380
+00:30:37,010 --> 00:30:42,650
+الواحد خطين .. إذا لما أحسب ال degree .. ال degree
+
+381
+00:30:42,650 --> 00:30:48,310
+الأولى خمسةجدّاش الأولى خمسة والتانية اتنين
+
+382
+00:30:48,310 --> 00:30:50,630
+والتانية اتنين والتانية اتنين والتانية اتنين واحدة
+
+383
+00:30:50,630 --> 00:30:54,390
+هذا مجموع ال degrees لمين للنقاط اللي موجودة لأن
+
+384
+00:30:54,390 --> 00:30:57,530
+هي ال sequence لل degrees للنقاط كلها فكما
+
+385
+00:30:57,530 --> 00:31:01,090
+أعطينيها إذن أربعتاش واحنا اتفاجنا الأربعتاش أيش
+
+386
+00:31:01,090 --> 00:31:05,410
+بيساوي ان اتنين ضعف الخطوط هذه نظرية خدناها المرة
+
+387
+00:31:05,410 --> 00:31:08,770
+الماضية اتنين ضعف الخطوط يعني عدد الخطوط أيش
+
+388
+00:31:08,770 --> 00:31:12,810
+بيساوي سبعة إذا ال edges اللي موجودة هي عبارة عن
+
+389
+00:31:12,810 --> 00:31:18,470
+سبعةماشي سبعة الان كيف بتدرسمها السبعة الان باجي
+
+390
+00:31:18,470 --> 00:31:22,150
+للنقطة اللي هي اللي .. اللي هي عنده ست نقاط بحط
+
+391
+00:31:22,150 --> 00:31:26,570
+واحدة تانتين تلاتة اربعة خمسة و هي ست هي ست نقاط
+
+392
+00:31:26,570 --> 00:31:30,370
+ماشي ليش حطيتها هنا دي و ماحطيتهاش هنا لإن انا
+
+393
+00:31:30,370 --> 00:31:33,210
+عارف هذا ان في نقطة من النقاط اللي هي طالع منها
+
+394
+00:31:33,210 --> 00:31:38,490
+جداش خمس خطوط يعني طالع منها دي خط هنا و هنا خط و
+
+395
+00:31:38,490 --> 00:31:43,520
+هنا خط و هنا خطيعني طالعلها لكل خطوط فهنا أسهل في
+
+396
+00:31:43,520 --> 00:31:47,560
+الرسم بس عشان سهولة الرسم يعني واحد تاني ممكن يحط
+
+397
+00:31:47,560 --> 00:31:51,960
+هنا هنا ممكن يحطها ويقعد يرسم ويوصل بينهم بنفع هنا
+
+398
+00:31:51,960 --> 00:31:55,580
+ممكن يحطها هنا ممكن يحطها يعني ممكن يكون الرسم صح
+
+399
+00:31:55,580 --> 00:32:00,880
+لكن شكلها مختلف من واحد لواحد بس بيكون ايش الصح ان
+
+400
+00:32:00,880 --> 00:32:05,510
+النهاردة طالعلها خمس خطوط هايين هاي الخمسةالان
+
+401
+00:32:05,510 --> 00:32:09,750
+النقطة التانية التانيات كلهم واحدة تلتين تلاتة
+
+402
+00:32:09,750 --> 00:32:13,690
+اربعة كلهم اشمال فين خطين خطين خطين يعني هذه الآن
+
+403
+00:32:13,690 --> 00:32:17,650
+بتطلع بينها خطين هيدي محدد وهذه خطوهي هذه وهذه خط
+
+404
+00:32:17,650 --> 00:32:21,590
+وهذه وهذه خط وهذه وهذه خط وبنخلي واحدة بس بيطلع
+
+405
+00:32:21,590 --> 00:32:24,550
+منها خط اللي هو طال علميا لهذا النقطة خاصة عنها
+
+406
+00:32:24,550 --> 00:32:28,730
+عشان نسينا الخمسة دولار فهذا بيكون اللي هو رسمنا ل
+
+407
+00:32:28,730 --> 00:32:34,110
+graph من وعرفنا جداش عدد الخطوط من خلال اللي هو
+
+408
+00:32:34,110 --> 00:32:40,300
+معرفة ال degreeسيكوانس للـ vertices تبعات ال graph
+
+409
+00:32:40,300 --> 00:32:45,660
+و هي كما نكون احنا خلصنا المحاضرة رقم 11 وهي عندكم
+
+410
+00:32:45,660 --> 00:32:50,460
+ال homework المطلوب تحلو و تسلمونيها كالعادة ان
+
+411
+00:32:50,460 --> 00:32:53,700
+شاء الله و إلى لقاء اخر السلام عليكم و رحمة الله
+
+412
+00:32:53,700 --> 00:32:54,280
+وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1183d04cab999b69887771769e10273c6a78811b
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2422, "start": 0.72, "end": 24.22, "text": "بسم الله الرحمن الرحيم هذه هي المحاضرة الرقم 11 لمساق رياضيات من فصلة لطلاب طالبات الجامعة الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة المتنقلة بدأنا حديثنا في المحاضرة العاشرة السابقة على اللي هو ال graphs", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 39896, 9673, 5016, 46958, 25720, 34892, 4587, 2304, 2975, 32767, 3794, 995, 4587, 12602, 1829, 46958, 1829, 9307, 9154, 6156, 9381, 37977, 5296, 9566, 15040, 3555, 23032, 6027, 3555, 9307, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 6055, 19452, 12610, 29245, 25528, 9673, 30241, 20498, 9307, 12174, 38251, 21542, 2407, 35457, 3660, 9673, 2655, 1863, 4587, 37977, 47525, 10721, 8315, 11331, 16254, 12984, 8315, 8978, 9673, 5016, 46958, 25720, 18863, 33599, 25720, 21136, 16758, 28671, 15844, 13672, 1829, 31439, 2423, 24877], "avg_logprob": -0.09624334773484697, "compression_ratio": 1.8571428571428572, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 0.72, "end": 1.04, "word": "بسم", "probability": 0.883544921875}, {"start": 1.04, "end": 1.28, "word": " الله", "probability": 0.9609375}, {"start": 1.28, "end": 1.76, "word": " الرحمن", "probability": 0.97509765625}, {"start": 1.76, "end": 2.32, "word": " الرحيم", "probability": 0.9951171875}, {"start": 2.32, "end": 3.42, "word": " هذه", "probability": 0.8095703125}, {"start": 3.42, "end": 3.68, "word": " هي", "probability": 0.5703125}, {"start": 3.68, "end": 4.22, "word": " المحاضرة", "probability": 0.9837646484375}, {"start": 4.22, "end": 4.66, "word": " الرقم", "probability": 0.9588216145833334}, {"start": 4.66, "end": 5.26, "word": " 11", "probability": 0.7900390625}, {"start": 5.26, "end": 7.02, "word": " لمساق", "probability": 0.88134765625}, {"start": 7.02, "end": 7.8, "word": " رياضيات", "probability": 0.972265625}, {"start": 7.8, "end": 7.94, "word": " من", "probability": 0.9833984375}, {"start": 7.94, "end": 9.26, "word": " فصلة", "probability": 0.6556803385416666}, {"start": 9.26, "end": 10.66, "word": " لطلاب", "probability": 0.927001953125}, {"start": 10.66, "end": 11.58, "word": " طالبات", "probability": 0.9024658203125}, {"start": 11.58, "end": 12.28, "word": " الجامعة", "probability": 0.9855143229166666}, {"start": 12.28, "end": 13.02, "word": " الإسلامية", "probability": 0.965576171875}, {"start": 13.02, "end": 13.58, "word": " كلية", "probability": 0.7335205078125}, {"start": 13.58, "end": 14.26, "word": " تكنولوجيا", "probability": 0.905859375}, {"start": 14.26, "end": 15.0, "word": " المعلومات", "probability": 0.93701171875}, {"start": 15.0, "end": 15.46, "word": " قسم", "probability": 0.97265625}, {"start": 15.46, "end": 16.08, "word": " الحوسبة", "probability": 0.863525390625}, {"start": 16.08, "end": 16.74, "word": " المتنقلة", "probability": 0.986328125}, {"start": 16.74, "end": 18.2, "word": " بدأنا", "probability": 0.96923828125}, {"start": 18.2, "end": 19.64, "word": " حديثنا", "probability": 0.9835205078125}, {"start": 19.64, "end": 20.34, "word": " في", "probability": 0.98388671875}, {"start": 20.34, "end": 21.4, "word": " المحاضرة", "probability": 0.993896484375}, {"start": 21.4, "end": 21.9, "word": " العاشرة", "probability": 0.9348958333333334}, {"start": 21.9, "end": 22.54, "word": " السابقة", "probability": 0.98876953125}, {"start": 22.54, "end": 23.0, "word": " على", "probability": 0.79638671875}, {"start": 23.0, "end": 23.32, "word": " اللي", "probability": 0.79931640625}, {"start": 23.32, "end": 23.56, "word": " هو", "probability": 0.986328125}, {"start": 23.56, "end": 23.7, "word": " ال", "probability": 0.4912109375}, {"start": 23.7, "end": 24.22, "word": " graphs", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 2, "seek": 5048, "start": 24.92, "end": 50.48, "text": "عرفنا شو معنات ال graph قلنا عبارة عن اللي هو set V اللي هي بتمثل vertices و A بتمثل اللي هي عبارة عن الخطوط اللي بين اللي هي ال vertices و بعدين أخذنا اللي هو شو معنات ال edge اللي هو الخط و شو معنات اللي هو ال neighborhood", "tokens": [3615, 28480, 8315, 13412, 2407, 20449, 8315, 2655, 2423, 4295, 12174, 1211, 8315, 6225, 3555, 9640, 3660, 18871, 13672, 1829, 31439, 992, 691, 13672, 1829, 39896, 39894, 2304, 12984, 1211, 32053, 4032, 316, 39894, 2304, 12984, 1211, 13672, 1829, 39896, 6225, 3555, 9640, 3660, 18871, 33962, 9566, 2407, 9566, 13672, 1829, 49374, 13672, 1829, 39896, 2423, 32053, 4032, 39182, 9957, 5551, 9778, 8848, 8315, 13672, 1829, 31439, 13412, 2407, 20449, 8315, 2655, 2423, 4691, 13672, 1829, 31439, 33962, 9566, 4032, 13412, 2407, 20449, 8315, 2655, 13672, 1829, 31439, 2423, 7630], "avg_logprob": -0.24072802328801418, "compression_ratio": 2.1183431952662723, "no_speech_prob": 0.0, "words": [{"start": 24.92, "end": 25.56, "word": "عرفنا", "probability": 0.7838541666666666}, {"start": 25.56, "end": 25.84, "word": " شو", "probability": 0.5576171875}, {"start": 25.84, "end": 26.42, "word": " معنات", "probability": 0.75732421875}, {"start": 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" الخط", "probability": 0.992919921875}, {"start": 47.12, "end": 47.8, "word": " و", "probability": 0.89111328125}, {"start": 47.8, "end": 48.2, "word": " شو", "probability": 0.7193603515625}, {"start": 48.2, "end": 48.94, "word": " معنات", "probability": 0.9658203125}, {"start": 48.94, "end": 49.28, "word": " اللي", "probability": 0.939453125}, {"start": 49.28, "end": 49.68, "word": " هو", "probability": 0.990234375}, {"start": 49.68, "end": 50.02, "word": " ال", "probability": 0.52783203125}, {"start": 50.02, "end": 50.48, "word": " neighborhood", "probability": 0.87744140625}], "temperature": 1.0}, {"id": 3, "seek": 7830, "start": 51.1, "end": 78.3, "text": "و بعدين اللي هو شو .. قلنا شو معنات انه two edgesكون adjacent و أيضا عرفنا اللي هو شو معنات ال degree لل vertex و .. و قلنا ال vertex اللي ال degree له zero قلنا isolated و أخدنا أمثلة على هيك لأمثلة اللي أمامنا هذه و على ال degree إلى أخره و انتقلنا", "tokens": [2407, 39182, 9957, 13672, 1829, 31439, 13412, 2407, 4386, 12174, 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حاكينا عن الـ undirected graph بعدين أخدنا أمثلة على كل هذه الموضوعات وجينا أخدنا اللي هو النظرية اللي بتقول دايما اللي هو المجموع اللي هو ال degree لل vertices على كل ال vertices اللي في ال V بتساوي 2 فحاصل ضرب اللي هو عدد الخطوط أو عدد ال edges اللي في الشكل", "tokens": [9566, 3555, 3615, 995, 9122, 8315, 11331, 995, 4117, 1829, 8315, 18871, 2423, 39184, 674, 11890, 292, 4295, 39182, 9957, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 15844, 28242, 29538, 9673, 2407, 11242, 45367, 9307, 49610, 1829, 8315, 5551, 9778, 3215, 8315, 13672, 1829, 31439, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 39648, 11778, 47302, 15042, 13672, 1829, 31439, 9673, 7435, 2304, 45367, 13672, 1829, 31439, 2423, 4314, 24976, 32053, 15844, 28242, 2423, 32053, 13672, 1829, 8978, 2423, 691, 39894, 3794, 995, 45865, 568, 6156, 5016, 33546, 1211, 48812, 25513, 13672, 1829, 31439, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 34051, 6225, 3215, 3215, 2423, 8819, 13672, 1829, 8978, 25124, 28820], 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"probability": 0.968505859375}, {"start": 97.05, "end": 97.17, "word": " في", "probability": 0.962890625}, {"start": 97.17, "end": 97.31, "word": " ال", "probability": 0.90087890625}, {"start": 97.31, "end": 97.53, "word": " V", "probability": 0.8681640625}, {"start": 97.53, "end": 98.25, "word": " بتساوي", "probability": 0.855224609375}, {"start": 98.25, "end": 99.15, "word": " 2", "probability": 0.56396484375}, {"start": 99.15, "end": 99.97, "word": " فحاصل", "probability": 0.68206787109375}, {"start": 99.97, "end": 100.29, "word": " ضرب", "probability": 0.97900390625}, {"start": 100.29, "end": 100.45, "word": " اللي", "probability": 0.950439453125}, {"start": 100.45, "end": 100.59, "word": " هو", "probability": 0.9267578125}, {"start": 100.59, "end": 100.87, "word": " عدد", "probability": 0.9892578125}, {"start": 100.87, "end": 101.45, "word": " الخطوط", "probability": 0.9869384765625}, {"start": 101.45, "end": 101.65, "word": " أو", "probability": 0.783203125}, {"start": 101.65, "end": 102.01, "word": " عدد", "probability": 0.9944661458333334}, {"start": 102.01, "end": 102.13, "word": " ال", "probability": 0.9765625}, {"start": 102.13, "end": 102.53, "word": " edges", "probability": 0.84765625}, {"start": 102.53, "end": 103.05, "word": " اللي", "probability": 0.987060546875}, {"start": 103.05, "end": 103.33, "word": " في", "probability": 0.98095703125}, {"start": 103.33, "end": 104.37, "word": " الشكل", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 5, "seek": 11903, "start": 104.79, "end": 119.03, "text": "و بعدين أخدنا أمثلة على هيك و أخدنا بعد هيك شو معنى .. شو معنات اللي هو ال directed graph اللي بيكون .. قولنا بيسير اللي هو الخط اللي هو directed from نقطة إلى نقطة أخرى", "tokens": [2407, 39182, 9957, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 15844, 39896, 4117, 4032, 5551, 9778, 3215, 8315, 39182, 39896, 4117, 13412, 2407, 20449, 1863, 7578, 4386, 13412, 2407, 20449, 8315, 2655, 13672, 1829, 31439, 2423, 12898, 4295, 13672, 1829, 4724, 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"probability": 0.5908203125}, {"start": 108.89, "end": 109.25, "word": " هيك", "probability": 0.927978515625}, {"start": 109.25, "end": 109.45, "word": " شو", "probability": 0.802490234375}, {"start": 109.45, "end": 109.77, "word": " معنى", "probability": 0.62890625}, {"start": 109.77, "end": 109.77, "word": " ..", "probability": 0.46533203125}, {"start": 109.77, "end": 110.67, "word": " شو", "probability": 0.891357421875}, {"start": 110.67, "end": 111.21, "word": " معنات", "probability": 0.8362630208333334}, {"start": 111.21, "end": 111.35, "word": " اللي", "probability": 0.77587890625}, {"start": 111.35, "end": 111.47, "word": " هو", "probability": 0.96337890625}, {"start": 111.47, "end": 111.57, "word": " ال", "probability": 0.7666015625}, {"start": 111.57, "end": 111.95, "word": " directed", "probability": 0.61328125}, {"start": 111.95, "end": 112.65, "word": " graph", "probability": 0.9716796875}, {"start": 112.65, "end": 112.89, "word": " اللي", "probability": 0.98388671875}, {"start": 112.89, "end": 113.31, "word": " بيكون", "probability": 0.955078125}, {"start": 113.31, "end": 113.41, "word": " ..", "probability": 0.255126953125}, {"start": 113.41, "end": 113.75, "word": " قولنا", "probability": 0.781005859375}, {"start": 113.75, "end": 114.25, "word": " بيسير", "probability": 0.881591796875}, {"start": 114.25, "end": 114.41, "word": " اللي", "probability": 0.94921875}, {"start": 114.41, "end": 114.69, "word": " هو", "probability": 0.96728515625}, {"start": 114.69, "end": 115.81, "word": " الخط", "probability": 0.96533203125}, {"start": 115.81, "end": 116.03, "word": " اللي", "probability": 0.988525390625}, {"start": 116.03, "end": 116.23, "word": " هو", "probability": 0.98291015625}, {"start": 116.23, "end": 116.75, "word": " directed", "probability": 0.88330078125}, {"start": 116.75, "end": 117.11, "word": " from", "probability": 0.9345703125}, {"start": 117.11, "end": 117.79, "word": " نقطة", "probability": 0.9778645833333334}, {"start": 117.79, "end": 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{"start": 387.66, "end": 388.4, "word": " مافيش", "probability": 0.7744140625}, {"start": 388.4, "end": 388.78, "word": " اي", "probability": 0.465576171875}, {"start": 388.78, "end": 389.26, "word": " نقطة", "probability": 0.9855143229166666}, {"start": 389.26, "end": 389.38, "word": " في", "probability": 0.60302734375}, {"start": 389.38, "end": 389.88, "word": " داخل", "probability": 0.9523111979166666}, {"start": 389.88, "end": 390.96, "word": " الكتنين", "probability": 0.81854248046875}, {"start": 390.96, "end": 391.88, "word": " مافيش", "probability": 0.9095052083333334}, {"start": 391.88, "end": 392.48, "word": " بينها", "probability": 0.9130859375}, {"start": 392.48, "end": 393.08, "word": " وبين", "probability": 0.87646484375}, {"start": 393.08, "end": 393.86, "word": " الباقيات", "probability": 0.64208984375}, {"start": 393.86, "end": 394.44, "word": " خطوط", "probability": 0.974365234375}, {"start": 394.44, "end": 395.02, "word": " عشان", "probability": 0.9168294270833334}, 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{"start": 480.43, "end": 480.91, "word": " graph", "probability": 0.68408203125}, {"start": 480.91, "end": 482.05, "word": " حالة", "probability": 0.8043619791666666}, {"start": 482.05, "end": 482.69, "word": " خاصة", "probability": 0.9814453125}, {"start": 482.69, "end": 482.89, "word": " من", "probability": 0.98291015625}, {"start": 482.89, "end": 483.43, "word": " هذول", "probability": 0.5713297526041666}, {"start": 483.43, "end": 483.59, "word": " ال", "probability": 0.379638671875}, {"start": 483.59, "end": 484.05, "word": " complete", "probability": 0.470458984375}, {"start": 484.05, "end": 484.65, "word": " graph", "probability": 0.87060546875}, {"start": 484.65, "end": 485.47, "word": " اللي", "probability": 0.8212890625}, {"start": 485.47, "end": 485.73, "word": " هي", "probability": 0.697265625}, {"start": 485.73, "end": 486.45, "word": " عائلة", "probability": 0.9962565104166666}, {"start": 486.45, "end": 486.99, "word": " من", "probability": 0.9453125}, {"start": 486.99, "end": 487.27, "word": " ال", "probability": 0.650390625}, {"start": 487.27, "end": 487.81, "word": " graphs", "probability": 0.8251953125}, {"start": 487.81, "end": 488.43, "word": " اسمها", "probability": 0.9503580729166666}, {"start": 488.43, "end": 488.85, "word": " kn", "probability": 0.320556640625}, {"start": 488.85, "end": 489.23, "word": " ايش", "probability": 0.7300618489583334}, {"start": 489.23, "end": 489.35, "word": " ال", "probability": 0.95751953125}, {"start": 489.35, "end": 489.69, "word": " kn", "probability": 0.5732421875}, {"start": 489.69, "end": 490.21, "word": " هذه", "probability": 0.71826171875}, {"start": 490.21, "end": 490.91, "word": " اللي", "probability": 0.97119140625}, {"start": 490.91, "end": 491.23, "word": " هي", "probability": 0.88525390625}, {"start": 491.23, "end": 492.45, "word": " عددها", "probability": 0.8580322265625}, {"start": 492.45, "end": 492.95, "word": " n", "probability": 0.51318359375}, {"start": 492.95, "end": 493.97, "word": " من", "probability": 0.958984375}, {"start": 493.97, "end": 494.49, "word": " اللي", "probability": 0.9189453125}, {"start": 494.49, "end": 494.77, "word": " هو", "probability": 0.93017578125}, {"start": 494.77, "end": 494.89, "word": " ال", "probability": 0.90771484375}, {"start": 494.89, "end": 495.37, "word": " vertices", "probability": 0.97509765625}, {"start": 495.37, "end": 496.11, "word": " فيها؟", "probability": 0.9581705729166666}], "temperature": 1.0}, {"id": 22, "seek": 51874, "start": 496.46, "end": 518.74, "text": "و بيعملين complete graph يعني كل النقاط are adjacent ده نشوف اللي بعدها هاي K خمسة مثلا بخمسة هاي عندى خمس نقاط واحدة تنتهي من تلاتة اربعة خمسة واضح ان كل النقاط كل واحدة بيطلع منها اربع خطوط للاخرين فعشان هيك بنسميها complete graph من النوع K", "tokens": [2407, 4724, 1829, 25957, 1211, 9957, 3566, 4295, 37495, 22653, 28242, 28239, 4587, 41193, 366, 24441, 11778, 3224, 8717, 8592, 38688, 13672, 1829, 39182, 11296, 8032, 47302, 591, 16490, 2304, 3794, 3660, 50113, 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499.72, "word": " يعني", "probability": 0.825439453125}, {"start": 499.72, "end": 500.0, "word": " كل", "probability": 0.87451171875}, {"start": 500.0, "end": 502.26, "word": " النقاط", "probability": 0.72509765625}, {"start": 502.26, "end": 502.68, "word": " are", "probability": 0.68505859375}, {"start": 502.68, "end": 503.46, "word": " adjacent", "probability": 0.96337890625}, {"start": 503.46, "end": 503.98, "word": " ده", "probability": 0.59716796875}, {"start": 503.98, "end": 504.24, "word": " نشوف", "probability": 0.8046061197916666}, {"start": 504.24, "end": 504.38, "word": " اللي", "probability": 0.929443359375}, {"start": 504.38, "end": 505.0, "word": " بعدها", "probability": 0.74462890625}, {"start": 505.0, "end": 505.32, "word": " هاي", "probability": 0.51177978515625}, {"start": 505.32, "end": 505.44, "word": " K", "probability": 0.74169921875}, {"start": 505.44, "end": 505.82, "word": " خمسة", "probability": 0.8345947265625}, {"start": 505.82, "end": 506.52, "word": " 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"end": 523.68, "word": " بنفس", "probability": 0.94140625}, {"start": 523.68, "end": 523.94, "word": " الاسم", "probability": 0.6016845703125}, {"start": 523.94, "end": 524.08, "word": " و", "probability": 0.5263671875}, {"start": 524.08, "end": 524.58, "word": " K7", "probability": 0.745849609375}, {"start": 524.58, "end": 524.94, "word": " طبعا", "probability": 0.801513671875}, {"start": 524.94, "end": 525.8, "word": " بتغلب", "probability": 0.7711588541666666}, {"start": 525.8, "end": 526.14, "word": " شوية", "probability": 0.8824869791666666}, {"start": 526.14, "end": 526.46, "word": " لكن", "probability": 0.8037109375}, {"start": 526.46, "end": 527.2, "word": " بتظلها", "probability": 0.7061767578125}, {"start": 527.2, "end": 527.68, "word": " في", "probability": 0.65576171875}, {"start": 527.68, "end": 528.06, "word": " نفس", "probability": 0.9970703125}, {"start": 528.06, "end": 528.84, "word": " النطاق", "probability": 0.96533203125}, {"start": 528.84, "end": 529.16, "word": " 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{"id": 25, "seek": 57347, "start": 556.43, "end": 573.47, "text": "K1, K2, K3, K4, K5 الاخر هي زمنته بتاعنا الان بدنا نيجي نوع ثاني ل graphs حاجة اسمها ال cycles ماشي ايش ال cycles اللي هي و ال wheels اه ايش تشوف ايش ال cycle و ايش ال wheel", "tokens": [42, 16, 11, 591, 17, 11, 591, 18, 11, 591, 19, 11, 591, 20, 2423, 47283, 2288, 39896, 30767, 27842, 47395, 39894, 45761, 8315, 2423, 7649, 47525, 8315, 8717, 1829, 7435, 1829, 8717, 45367, 38637, 7649, 1829, 5296, 24877, 11331, 26108, 3660, 24525, 2304, 11296, 2423, 17796, 3714, 33599, 1829, 1975, 1829, 8592, 2423, 17796, 13672, 1829, 39896, 4032, 2423, 10046, 1975, 3224, 1975, 1829, 8592, 6055, 8592, 38688, 1975, 1829, 8592, 2423, 6586, 4032, 1975, 1829, 8592, 2423, 5589], "avg_logprob": -0.32561728983749577, "compression_ratio": 1.5757575757575757, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 556.43, "end": 557.17, "word": "K1,", "probability": 0.465087890625}, {"start": 557.35, "end": 557.73, "word": " K2,", 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{"start": 591.02, "end": 591.34, "word": " برضه", "probability": 0.94091796875}, {"start": 591.34, "end": 591.9, "word": " بتحتوي", "probability": 0.7835286458333334}, {"start": 591.9, "end": 592.08, "word": " على", "probability": 0.73828125}, {"start": 592.08, "end": 592.28, "word": " ايه", "probability": 0.6822102864583334}, {"start": 592.28, "end": 592.94, "word": " عشان", "probability": 0.5612386067708334}, {"start": 592.94, "end": 593.22, "word": " n", "probability": 0.60009765625}, {"start": 593.22, "end": 593.44, "word": " من", "probability": 0.986328125}, {"start": 593.44, "end": 593.58, "word": " ال", "probability": 0.984375}, {"start": 593.58, "end": 594.08, "word": " vertices", "probability": 0.96484375}], "temperature": 1.0}, {"id": 27, "seek": 61224, "start": 594.82, "end": 612.24, "text": "ماذا نسميه Cycle لما نكون تحقيق ما يليه الـ CNN Consists Of N Vertices V1 و V2 و VN And Edges و الـ Edges ايش ما لها V1 و V2 يعني خط بين V1 و V2 و خط بين V2 و V3", "tokens": [2304, 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خط بين V3 و V4 لما أصل عند خط بين اللي هي النقطة الأخيرة VN و برجع لمين لل V1 و كإن إيش بسكر و بعمله cycle زي دائرة أو اللي هو دورة كاملة ماشي the cycles C3, C4, C5, C6 are displaced انفجارا هى وهذه وهذه", "tokens": [2407, 16490, 9566, 49374, 691, 18, 4032, 691, 19, 5296, 15042, 5551, 36520, 43242, 16490, 9566, 49374, 13672, 1829, 39896, 28239, 47432, 3660, 16247, 9778, 48923, 691, 45, 4032, 4724, 47341, 3615, 32767, 9957, 24976, 691, 16, 4032, 9122, 28814, 1863, 11933, 1829, 8592, 4724, 3794, 37983, 4032, 4724, 25957, 43761, 6586, 30767, 1829, 11778, 16373, 25720, 34051, 13672, 1829, 31439, 11778, 13063, 3660, 9122, 10943, 37977, 3714, 33599, 1829, 264, 17796, 383, 18, 11, 383, 19, 11, 383, 20, 11, 383, 21, 366, 33692, 16472, 5172, 7435, 9640, 995, 8032, 7578, 37037, 24192, 37037, 24192], "avg_logprob": -0.2931701129244775, "compression_ratio": 1.4722222222222223, "no_speech_prob": 7.748603820800781e-07, "words": [{"start": 612.59, "end": 612.95, "word": "و", "probability": 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"probability": 0.9111328125}, {"start": 1548.2, "end": 1548.38, "word": " انتوا", "probability": 0.8103841145833334}, {"start": 1548.38, "end": 1548.72, "word": " عارفين", "probability": 0.979736328125}, {"start": 1548.72, "end": 1549.16, "word": " يعني", "probability": 0.61669921875}, {"start": 1549.16, "end": 1550.4, "word": " مضاعف", "probability": 0.80767822265625}, {"start": 1550.4, "end": 1550.74, "word": " عدد", "probability": 0.9759114583333334}, {"start": 1550.74, "end": 1551.16, "word": " الخطوط", "probability": 0.98828125}, {"start": 1551.16, "end": 1551.52, "word": " جولنا", "probability": 0.5801595052083334}, {"start": 1551.52, "end": 1551.86, "word": " اذا", "probability": 0.6324462890625}, {"start": 1551.86, "end": 1552.9, "word": " الكل", "probability": 0.7027587890625}, {"start": 1552.9, "end": 1553.6, "word": " بيكون", "probability": 0.9195963541666666}, {"start": 1553.6, "end": 1553.88, "word": " عدد", "probability": 0.9930013020833334}, {"start": 1553.88, "end": 1554.28, "word": " الخطوط", "probability": 0.9912109375}, {"start": 1554.28, "end": 1554.5, "word": " عنا", "probability": 0.745361328125}, {"start": 1554.5, "end": 1554.98, "word": " 18", "probability": 0.8759765625}, {"start": 1554.98, "end": 1555.94, "word": " خط", "probability": 0.986572265625}], "temperature": 1.0}, {"id": 69, "seek": 156891, "start": 1556.55, "end": 1568.91, "text": "So that K36 has 18 edges تقريبا 18 خط degree sequence نعرف حاجة اسمها degree sequence نشوف ايش degree sequence", "tokens": [6455, 300, 591, 11309, 575, 2443, 8819, 6055, 4587, 16572, 3555, 995, 2443, 16490, 9566, 4314, 8310, 8717, 3615, 28480, 11331, 26108, 3660, 24525, 2304, 11296, 4314, 8310, 8717, 8592, 38688, 1975, 1829, 8592, 4314, 8310], "avg_logprob": -0.4400337870056565, "compression_ratio": 1.2432432432432432, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1556.55, "end": 1556.87, "word": "So", "probability": 0.280029296875}, {"start": 1556.87, "end": 1557.29, "word": " that", "probability": 0.8896484375}, {"start": 1557.29, "end": 1558.25, "word": " K36", "probability": 0.554443359375}, {"start": 1558.25, "end": 1558.77, "word": " has", "probability": 0.79931640625}, {"start": 1558.77, "end": 1559.63, "word": " 18", "probability": 0.8271484375}, {"start": 1559.63, "end": 1560.41, "word": " edges", "probability": 0.8486328125}, {"start": 1560.41, "end": 1560.75, "word": " تقريبا", "probability": 0.59549560546875}, {"start": 1560.75, "end": 1561.35, "word": " 18", "probability": 0.2435302734375}, {"start": 1561.35, "end": 1562.01, "word": " خط", "probability": 0.9765625}, {"start": 1562.01, "end": 1562.73, "word": " degree", "probability": 0.375}, {"start": 1562.73, "end": 1563.35, "word": " sequence", "probability": 0.9453125}, {"start": 1563.35, "end": 1563.91, "word": " نعرف", "probability": 0.6072591145833334}, {"start": 1563.91, "end": 1564.23, "word": " حاجة", "probability": 0.717041015625}, {"start": 1564.23, "end": 1564.57, "word": " اسمها", "probability": 0.8846028645833334}, {"start": 1564.57, "end": 1564.91, "word": " degree", "probability": 0.943359375}, {"start": 1564.91, "end": 1566.15, "word": " sequence", "probability": 0.9833984375}, {"start": 1566.15, "end": 1567.89, "word": " نشوف", "probability": 0.80908203125}, {"start": 1567.89, "end": 1568.07, "word": " ايش", "probability": 0.86083984375}, {"start": 1568.07, "end": 1568.37, "word": " degree", "probability": 0.7373046875}, {"start": 1568.37, "end": 1568.91, "word": " sequence", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 70, "seek": 159292, "start": 1570.2, "end": 1592.92, "text": "الشعر الله سهل يعني suppose that D1 وD2 وDn are degree of the vertices of a graph يعني في عندنا graph بيسيده graph زي ال graph تبعت المرة الفاتة عندنا graph G هذا ال graph جينا حسبنا اللي هي فيه N من ال vertices حسبنا أول واحدة لجينا انها degree D1 التانية D2 التلاتة Dn", "tokens": [6027, 8592, 3615, 2288, 21984, 8608, 3224, 1211, 37495, 22653, 7297, 300, 413, 16, 4032, 35, 17, 4032, 35, 77, 366, 4314, 295, 264, 32053, 295, 257, 4295, 37495, 22653, 8978, 43242, 8315, 4295, 4724, 1829, 3794, 25708, 3224, 4295, 30767, 1829, 2423, 4295, 6055, 3555, 34268, 9673, 25720, 27188, 9307, 3660, 43242, 8315, 4295, 460, 23758, 2423, 4295, 10874, 1829, 8315, 11331, 35457, 8315, 13672, 1829, 39896, 8978, 3224, 426, 9154, 2423, 32053, 11331, 35457, 8315, 5551, 12610, 36764, 24401, 3660, 5296, 7435, 1829, 8315, 16472, 11296, 4314, 413, 16, 16712, 7649, 10632, 413, 17, 16712, 1211, 9307, 3660, 413, 77], "avg_logprob": -0.2774575109620696, "compression_ratio": 1.7268722466960353, "no_speech_prob": 0.0, "words": [{"start": 1570.2, "end": 1570.62, "word": "الشعر", "probability": 0.684326171875}, {"start": 1570.62, "end": 1570.8, "word": " الله", "probability": 0.55712890625}, {"start": 1570.8, "end": 1571.14, "word": " سهل", "probability": 0.9772135416666666}, {"start": 1571.14, "end": 1571.34, "word": " يعني", "probability": 0.728271484375}, {"start": 1571.34, "end": 1571.82, "word": " suppose", "probability": 0.2369384765625}, {"start": 1571.82, "end": 1572.16, "word": " that", "probability": 0.58544921875}, {"start": 1572.16, "end": 1572.68, "word": " D1", "probability": 0.6444091796875}, {"start": 1572.68, "end": 1573.38, "word": " وD2", "probability": 0.845703125}, {"start": 1573.38, "end": 1574.08, "word": " وDn", "probability": 0.7870279947916666}, {"start": 1574.08, "end": 1574.5, "word": " are", "probability": 0.7578125}, {"start": 1574.5, "end": 1575.06, "word": " degree", "probability": 0.7939453125}, {"start": 1575.06, "end": 1575.92, "word": " of", "probability": 0.96923828125}, {"start": 1575.92, "end": 1576.1, "word": " the", "probability": 0.73974609375}, {"start": 1576.1, "end": 1576.78, "word": " vertices", "probability": 0.97021484375}, {"start": 1576.78, "end": 1577.02, "word": " of", "probability": 0.97119140625}, {"start": 1577.02, "end": 1577.2, "word": " a", "probability": 0.640625}, {"start": 1577.2, "end": 1577.34, "word": " graph", "probability": 0.9541015625}, {"start": 1577.34, "end": 1577.68, "word": " يعني", "probability": 0.860107421875}, {"start": 1577.68, "end": 1577.82, "word": " في", "probability": 0.81396484375}, {"start": 1577.82, "end": 1578.14, "word": " عندنا", "probability": 0.85009765625}, {"start": 1578.14, "end": 1578.44, "word": " graph", "probability": 0.8056640625}, {"start": 1578.44, "end": 1578.9, "word": " بيسيده", "probability": 0.5139892578125}, {"start": 1578.9, "end": 1579.12, "word": " graph", "probability": 0.82275390625}, {"start": 1579.12, "end": 1579.32, "word": " زي", "probability": 0.96484375}, {"start": 1579.32, "end": 1579.44, "word": " ال", "probability": 0.50390625}, {"start": 1579.44, "end": 1579.6, "word": " graph", "probability": 0.462158203125}, {"start": 1579.6, "end": 1580.06, "word": " تبعت", "probability": 0.5350748697916666}, {"start": 1580.06, "end": 1580.4, "word": " المرة", "probability": 0.884765625}, {"start": 1580.4, "end": 1580.86, "word": " الفاتة", "probability": 0.6709798177083334}, {"start": 1580.86, "end": 1581.76, "word": " عندنا", "probability": 0.832275390625}, {"start": 1581.76, "end": 1582.3, "word": " graph", "probability": 0.8740234375}, {"start": 1582.3, "end": 1582.58, "word": " G", "probability": 0.806640625}, {"start": 1582.58, "end": 1583.32, "word": " هذا", "probability": 0.7802734375}, {"start": 1583.32, "end": 1583.48, "word": " ال", "probability": 0.86083984375}, {"start": 1583.48, "end": 1583.94, "word": " graph", "probability": 0.75146484375}, {"start": 1583.94, "end": 1584.54, "word": " جينا", "probability": 0.8308919270833334}, {"start": 1584.54, "end": 1585.24, "word": " حسبنا", "probability": 0.98486328125}, {"start": 1585.24, "end": 1585.94, "word": " اللي", "probability": 0.90185546875}, {"start": 1585.94, "end": 1586.18, "word": " هي", "probability": 0.587890625}, {"start": 1586.18, "end": 1586.6, "word": " فيه", "probability": 0.719482421875}, {"start": 1586.6, "end": 1586.82, "word": " N", "probability": 0.438232421875}, {"start": 1586.82, "end": 1587.02, "word": " من", "probability": 0.9912109375}, {"start": 1587.02, "end": 1587.2, "word": " ال", "probability": 0.9794921875}, {"start": 1587.2, "end": 1587.68, "word": " vertices", "probability": 0.98046875}, {"start": 1587.68, "end": 1588.92, "word": " حسبنا", "probability": 0.9842122395833334}, {"start": 1588.92, "end": 1589.36, "word": " أول", "probability": 0.95263671875}, {"start": 1589.36, "end": 1589.78, "word": " واحدة", "probability": 0.9436848958333334}, {"start": 1589.78, "end": 1590.06, "word": " لجينا", "probability": 0.7716064453125}, {"start": 1590.06, "end": 1590.26, "word": " انها", "probability": 0.58984375}, {"start": 1590.26, "end": 1590.54, "word": " degree", "probability": 0.9462890625}, {"start": 1590.54, "end": 1591.02, "word": " D1", "probability": 0.90625}, {"start": 1591.02, "end": 1591.56, "word": " التانية", "probability": 0.7150065104166666}, {"start": 1591.56, "end": 1592.0, "word": " D2", "probability": 0.967041015625}, {"start": 1592.0, "end": 1592.54, "word": " التلاتة", "probability": 0.8228759765625}, {"start": 1592.54, "end": 1592.92, "word": " Dn", "probability": 0.800048828125}], "temperature": 1.0}, {"id": 71, "seek": 160816, "start": 1593.1, "end": 1608.16, "text": "عندما نرتب تساعد تنازلي D1 أكبر سوى D2 أكبر سوى D3 أكبر سوى DN هذه الـ D1 وD2 وDN المرتبة اللي هي بشكل تنازلي", "tokens": [3615, 41260, 15042, 8717, 2288, 2655, 3555, 6055, 3794, 995, 22488, 6055, 1863, 31377, 20292, 413, 16, 5551, 4117, 26890, 8608, 2407, 7578, 413, 17, 5551, 4117, 26890, 8608, 2407, 7578, 413, 18, 5551, 4117, 26890, 8608, 2407, 7578, 21500, 29538, 2423, 39184, 413, 16, 4032, 35, 17, 4032, 35, 45, 9673, 43500, 49401, 13672, 1829, 39896, 4724, 8592, 28820, 6055, 1863, 31377, 20292], "avg_logprob": -0.39615384615384613, "compression_ratio": 1.6306306306306306, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1593.1, "end": 1593.62, "word": "عندما", "probability": 0.32757568359375}, {"start": 1593.62, "end": 1594.22, "word": " نرتب", "probability": 0.64532470703125}, {"start": 1594.22, "end": 1595.2, "word": " تساعد", "probability": 0.6126708984375}, {"start": 1595.2, "end": 1597.22, "word": " تنازلي", "probability": 0.509521484375}, {"start": 1597.22, "end": 1598.32, "word": " D1", "probability": 0.41943359375}, {"start": 1598.32, "end": 1598.68, "word": " أكبر", "probability": 0.7838541666666666}, {"start": 1598.68, "end": 1598.86, "word": " سوى", "probability": 0.5576578776041666}, {"start": 1598.86, "end": 1599.24, "word": " D2", "probability": 0.96875}, {"start": 1599.24, "end": 1599.58, "word": " أكبر", "probability": 0.9055989583333334}, {"start": 1599.58, "end": 1599.8, "word": " سوى", "probability": 0.9479166666666666}, {"start": 1599.8, "end": 1600.14, "word": " D3", "probability": 0.9931640625}, {"start": 1600.14, "end": 1600.46, "word": " أكبر", "probability": 0.9471028645833334}, {"start": 1600.46, "end": 1600.72, "word": " سوى", "probability": 0.9461263020833334}, {"start": 1600.72, "end": 1601.04, "word": " DN", "probability": 0.41552734375}, {"start": 1601.04, "end": 1602.1, "word": " هذه", "probability": 0.253173828125}, {"start": 1602.1, "end": 1602.28, "word": " الـ", "probability": 0.5648193359375}, {"start": 1602.28, "end": 1602.68, "word": " D1", "probability": 0.82763671875}, {"start": 1602.68, "end": 1603.32, "word": " وD2", "probability": 0.82763671875}, {"start": 1603.32, "end": 1603.86, "word": " وDN", "probability": 0.8606770833333334}, {"start": 1603.86, "end": 1604.68, "word": " المرتبة", "probability": 0.9703776041666666}, {"start": 1604.68, "end": 1604.96, "word": " اللي", "probability": 0.5394287109375}, {"start": 1604.96, "end": 1605.26, "word": " هي", "probability": 0.82861328125}, {"start": 1605.26, "end": 1605.94, "word": " بشكل", "probability": 0.8694661458333334}, {"start": 1605.94, "end": 1608.16, "word": " تنازلي", "probability": 0.95703125}], "temperature": 1.0}, {"id": 72, "seek": 163518, "start": 1608.98, "end": 1635.18, "text": "اللي هي طبعا دي واحد تمثل ال degree ل اللي هو نقطة أولى هذه ال degree لتانية هذه ال degree ل الأخيرة لما نرتبه انتصار تنازل زي هيك بنسميه degree sequence of G اللي هي degree sequence لمين لل G في الواقع degree sequence لل G لأ هي في الواقع ال degree sequence لل vertices تبعات ال G", "tokens": [6027, 20292, 39896, 23032, 3555, 3615, 995, 11778, 1829, 36764, 24401, 46811, 12984, 1211, 2423, 4314, 5296, 13672, 1829, 31439, 8717, 47432, 3660, 5551, 12610, 7578, 29538, 2423, 4314, 5296, 2655, 7649, 10632, 29538, 2423, 4314, 5296, 16247, 9778, 48923, 5296, 15042, 8717, 43500, 3555, 3224, 16472, 2655, 9381, 9640, 6055, 1863, 31377, 1211, 30767, 1829, 39896, 4117, 44945, 38251, 1829, 3224, 4314, 8310, 295, 460, 13672, 1829, 39896, 4314, 8310, 32767, 9957, 24976, 460, 8978, 2423, 14407, 4587, 3615, 4314, 8310, 24976, 460, 5296, 10721, 39896, 8978, 2423, 14407, 4587, 3615, 2423, 4314, 8310, 24976, 32053, 6055, 3555, 3615, 9307, 2423, 460], "avg_logprob": -0.23106971812935975, "compression_ratio": 1.9952153110047848, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1608.98, "end": 1609.38, "word": "اللي", "probability": 0.260009765625}, {"start": 1609.38, "end": 1609.92, "word": " هي", "probability": 0.787109375}, {"start": 1609.92, "end": 1610.86, "word": " طبعا", "probability": 0.8935546875}, {"start": 1610.86, "end": 1610.98, "word": " دي", "probability": 0.7166748046875}, {"start": 1610.98, "end": 1611.22, "word": " واحد", "probability": 0.99072265625}, {"start": 1611.22, "end": 1612.16, "word": " تمثل", "probability": 0.9513346354166666}, {"start": 1612.16, "end": 1612.7, "word": " ال", "probability": 0.783203125}, {"start": 1612.7, "end": 1613.18, "word": " degree", "probability": 0.72900390625}, {"start": 1613.18, "end": 1614.26, "word": " ل", "probability": 0.8544921875}, {"start": 1614.26, "end": 1614.76, "word": " اللي", "probability": 0.5364990234375}, {"start": 1614.76, "end": 1615.06, "word": " 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هي واحد", "tokens": [2655, 1211, 9307, 3660, 4314, 371, 16, 38392, 39896, 36764, 24401, 1975, 2655, 1863, 9957, 4314, 371, 19, 38392, 39896, 36764, 24401], "avg_logprob": -0.28736412006875744, "compression_ratio": 1.380952380952381, "no_speech_prob": 0.0, "words": [{"start": 1717.62, "end": 1718.6, "word": "تلاتة", "probability": 0.771697998046875}, {"start": 1718.6, "end": 1719.18, "word": " degree", "probability": 0.8740234375}, {"start": 1719.18, "end": 1720.14, "word": " v1", "probability": 0.608154296875}, {"start": 1720.14, "end": 1720.7, "word": " التي", "probability": 0.0906982421875}, {"start": 1720.7, "end": 1720.9, "word": " هي", "probability": 0.904296875}, {"start": 1720.9, "end": 1721.38, "word": " واحد", "probability": 0.8984375}, {"start": 1721.38, "end": 1722.1, "word": " اتنين", "probability": 0.8616943359375}, {"start": 1722.1, "end": 1723.48, "word": " degree", "probability": 0.931640625}, {"start": 1723.48, "end": 1724.44, "word": " v4", "probability": 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of", "probability": 0.943359375}, {"start": 1771.84, "end": 1772.02, "word": " a", "probability": 0.97412109375}, {"start": 1772.02, "end": 1772.56, "word": " graph", "probability": 0.9619140625}, {"start": 1772.56, "end": 1773.84, "word": " أكم", "probability": 0.767333984375}, {"start": 1773.84, "end": 1774.44, "word": " خط", "probability": 0.981201171875}, {"start": 1774.44, "end": 1774.76, "word": " في", "probability": 0.9453125}, {"start": 1774.76, "end": 1775.06, "word": " في", "probability": 0.47802734375}, {"start": 1775.06, "end": 1775.68, "word": " الجراف", "probability": 0.9254557291666666}], "temperature": 1.0}, {"id": 79, "seek": 180284, "start": 1776.24, "end": 1802.84, "text": "إذا كانت ال degree sequence يعني ال degree sequence شكلها بدها هي تجعلنا نعرف نرسم ال graph هي اللي بتجعلنا نعرف جداش الخطوط اللي فيها اللي أنا مقول is خمسة و اتنين و اتنين و اتنين و اتنين و واحد أول حاجة بدي بتطلع هذول أكب نقطة هذه كل واحدة نقطة من النقاط", "tokens": [28814, 15730, 25961, 2655, 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0.7080078125}, {"start": 1923.2, "end": 1923.76, "word": " هاي", "probability": 0.6619873046875}, {"start": 1923.76, "end": 1924.28, "word": " الخمسة", "probability": 0.9810791015625}], "temperature": 1.0}, {"id": 85, "seek": 193561, "start": 1925.03, "end": 1935.61, "text": "الان النقطة التانية التانيات كلهم واحدة تلتين تلاتة اربعة كلهم اشمال فين خطين خطين خطين يعني هذه الآن بتطلع بينها خطين هيدي محدد وهذه خط", "tokens": [6027, 7649, 28239, 47432, 3660, 16712, 7649, 10632, 16712, 7649, 1829, 9307, 28242, 16095, 36764, 24401, 3660, 6055, 1211, 2655, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 28242, 16095, 1975, 8592, 2304, 6027, 8978, 1863, 16490, 9566, 9957, 16490, 9566, 9957, 16490, 9566, 9957, 37495, 22653, 29538, 6024, 48506, 39894, 9566, 1211, 3615, 49374, 11296, 16490, 9566, 9957, 39896, 16254, 3714, 24401, 3215, 37037, 24192, 16490, 9566], "avg_logprob": -0.3109148688938307, "compression_ratio": 1.878787878787879, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1925.03, "end": 1925.51, "word": "الان", "probability": 0.6597900390625}, {"start": 1925.51, "end": 1926.47, "word": " النقطة", "probability": 0.7526041666666666}, {"start": 1926.47, "end": 1927.11, "word": " التانية", "probability": 0.9715169270833334}, {"start": 1927.11, "end": 1927.97, "word": " التانيات", "probability": 0.80035400390625}, {"start": 1927.97, "end": 1928.61, "word": " كلهم", "probability": 0.605712890625}, {"start": 1928.61, "end": 1929.05, "word": " واحدة", "probability": 0.8932291666666666}, {"start": 1929.05, "end": 1929.39, "word": " تلتين", "probability": 0.824462890625}, {"start": 1929.39, "end": 1929.75, "word": " تلاتة", "probability": 0.7017822265625}, {"start": 1929.75, "end": 1930.01, "word": " اربعة", "probability": 0.763671875}, {"start": 1930.01, "end": 1930.33, "word": " كلهم", "probability": 0.90673828125}, {"start": 1930.33, "end": 1930.81, "word": " اشمال", "probability": 0.9078369140625}, {"start": 1930.81, "end": 1931.67, "word": " فين", "probability": 0.290771484375}, {"start": 1931.67, "end": 1932.11, "word": " خطين", "probability": 0.7500813802083334}, {"start": 1932.11, "end": 1932.51, "word": " خطين", "probability": 0.96484375}, {"start": 1932.51, "end": 1932.93, "word": " خطين", "probability": 0.9798177083333334}, {"start": 1932.93, "end": 1933.21, "word": " يعني", "probability": 0.86279296875}, {"start": 1933.21, "end": 1933.47, "word": " هذه", "probability": 0.5732421875}, {"start": 1933.47, "end": 1933.69, "word": " الآن", "probability": 0.56927490234375}, {"start": 1933.69, "end": 1933.95, "word": " بتطلع", "probability": 0.76708984375}, {"start": 1933.95, "end": 1934.15, "word": " بينها", "probability": 0.6962890625}, {"start": 1934.15, "end": 1934.49, "word": " خطين", "probability": 0.9773763020833334}, {"start": 1934.49, "end": 1934.83, "word": " هيدي", "probability": 0.60400390625}, {"start": 1934.83, "end": 1935.15, "word": " محدد", "probability": 0.673095703125}, {"start": 1935.15, "end": 1935.37, "word": " وهذه", "probability": 0.54150390625}, {"start": 1935.37, "end": 1935.61, "word": " خط", "probability": 0.91650390625}], "temperature": 1.0}, {"id": 86, "seek": 195533, "start": 1936.59, "end": 1955.33, "text": "وهي هذه وهذه خط وهذه وهذه خط وهذه وهذه خط وبنخلي واحدة بس بيطلع منها خط اللي هو طال علميا لهذا النقطة خاصة عنها عشان نسينا الخمسة دولار فهذا بيكون اللي هو رسمنا ل graph من وعرفنا جداش عدد الخطوط من خلال اللي هو معرفة ال degree", "tokens": [2407, 3224, 1829, 29538, 37037, 24192, 16490, 9566, 37037, 24192, 37037, 24192, 16490, 9566, 37037, 24192, 37037, 24192, 16490, 9566, 4032, 3555, 1863, 9778, 20292, 36764, 24401, 3660, 4724, 3794, 4724, 1829, 9566, 1211, 3615, 9154, 11296, 16490, 9566, 13672, 1829, 31439, 23032, 6027, 11203, 2304, 25528, 46740, 15730, 28239, 47432, 3660, 16490, 33546, 3660, 18871, 11296, 6225, 8592, 7649, 8717, 3794, 1829, 8315, 33962, 2304, 3794, 3660, 11778, 12610, 9640, 6156, 3224, 15730, 4724, 1829, 30544, 13672, 1829, 31439, 12602, 38251, 8315, 5296, 4295, 9154, 4032, 3615, 28480, 8315, 10874, 3215, 33599, 6225, 3215, 3215, 33962, 9566, 2407, 9566, 9154, 16490, 1211, 6027, 13672, 1829, 31439, 20449, 28480, 3660, 2423, 4314], "avg_logprob": -0.16772677624120122, "compression_ratio": 1.9362745098039216, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 1936.59, "end": 1936.97, "word": "وهي", "probability": 0.5533040364583334}, {"start": 1936.97, "end": 1937.07, "word": " هذه", "probability": 0.810546875}, {"start": 1937.07, "end": 1937.33, "word": " وهذه", "probability": 0.705078125}, {"start": 1937.33, "end": 1937.65, "word": " خط", "probability": 0.974365234375}, {"start": 1937.65, "end": 1938.03, "word": " وهذه", "probability": 0.852294921875}, {"start": 1938.03, "end": 1938.31, "word": " وهذه", "probability": 0.8837890625}, {"start": 1938.31, "end": 1938.67, "word": " خط", "probability": 0.990966796875}, {"start": 1938.67, "end": 1938.99, "word": " وهذه", "probability": 0.788330078125}, {"start": 1938.99, "end": 1939.27, "word": " وهذه", "probability": 0.851806640625}, {"start": 1939.27, "end": 1939.61, "word": " خط", "probability": 0.986572265625}, {"start": 1939.61, "end": 1940.61, "word": " وبنخلي", "probability": 0.75830078125}, {"start": 1940.61, "end": 1941.05, "word": " واحدة", "probability": 0.96435546875}, {"start": 1941.05, "end": 1941.25, "word": " بس", "probability": 0.954345703125}, {"start": 1941.25, "end": 1941.59, "word": " بيطلع", "probability": 0.773583984375}, {"start": 1941.59, "end": 1941.85, "word": " منها", "probability": 0.987060546875}, {"start": 1941.85, "end": 1942.21, "word": " خط", "probability": 0.994873046875}, {"start": 1942.21, "end": 1942.43, "word": " اللي", "probability": 0.886962890625}, {"start": 1942.43, "end": 1942.57, "word": " هو", "probability": 0.9619140625}, {"start": 1942.57, "end": 1942.81, "word": " طال", "probability": 0.917724609375}, {"start": 1942.81, "end": 1943.25, "word": " علميا", "probability": 0.74755859375}, {"start": 1943.25, "end": 1943.69, "word": " لهذا", "probability": 0.488525390625}, {"start": 1943.69, "end": 1944.03, "word": " النقطة", "probability": 0.970703125}, {"start": 1944.03, "end": 1944.25, "word": " خاصة", "probability": 0.7277018229166666}, {"start": 1944.25, "end": 1944.55, "word": " عنها", "probability": 0.829833984375}, {"start": 1944.55, "end": 1944.77, "word": " عشان", "probability": 0.92041015625}, {"start": 1944.77, "end": 1945.07, "word": " نسينا", "probability": 0.87744140625}, {"start": 1945.07, "end": 1945.53, "word": " الخمسة", "probability": 0.866943359375}, {"start": 1945.53, "end": 1945.87, "word": " دولار", "probability": 0.9816080729166666}, {"start": 1945.87, "end": 1946.69, "word": " فهذا", "probability": 0.9404296875}, {"start": 1946.69, "end": 1947.11, "word": " بيكون", "probability": 0.84033203125}, {"start": 1947.11, "end": 1947.29, "word": " اللي", "probability": 0.91796875}, {"start": 1947.29, "end": 1947.59, "word": " هو", "probability": 0.97998046875}, {"start": 1947.59, "end": 1948.57, "word": " رسمنا", "probability": 0.9654947916666666}, {"start": 1948.57, "end": 1948.73, "word": " ل", "probability": 0.389892578125}, {"start": 1948.73, "end": 1949.45, "word": " graph", "probability": 0.5361328125}, {"start": 1949.45, "end": 1950.63, "word": " من", "probability": 0.489501953125}, {"start": 1950.63, "end": 1951.35, "word": " وعرفنا", "probability": 0.9041748046875}, {"start": 1951.35, "end": 1951.79, "word": " جداش", "probability": 0.779296875}, {"start": 1951.79, "end": 1952.07, "word": " عدد", "probability": 0.9734700520833334}, {"start": 1952.07, "end": 1952.75, "word": " الخطوط", "probability": 0.9586181640625}, {"start": 1952.75, "end": 1953.15, "word": " من", "probability": 0.99169921875}, {"start": 1953.15, "end": 1953.71, "word": " خلال", "probability": 0.9871419270833334}, {"start": 1953.71, "end": 1953.93, "word": " اللي", "probability": 0.966064453125}, {"start": 1953.93, "end": 1954.11, "word": " هو", "probability": 0.98046875}, {"start": 1954.11, "end": 1954.67, "word": " معرفة", "probability": 0.9952799479166666}, {"start": 1954.67, "end": 1954.85, "word": " ال", "probability": 0.7763671875}, {"start": 1954.85, "end": 1955.33, "word": " degree", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 87, "seek": 197428, "start": 1956.78, "end": 1974.28, "text": "سيكوانس للـ vertices تبعات ال graph و هي كما نكون احنا خلصنا المحاضرة رقم 11 وهي عندكم ال homework المطلوب تحلو و تسلمونيها كالعادة ان شاء الله و إلى لقاء اخر السلام عليكم و رحمة الله وبركاته", "tokens": [3794, 1829, 4117, 2407, 7649, 3794, 24976, 39184, 32053, 6055, 3555, 3615, 9307, 2423, 4295, 4032, 39896, 9122, 15042, 8717, 30544, 1975, 5016, 8315, 16490, 1211, 9381, 8315, 9673, 5016, 46958, 25720, 12602, 4587, 2304, 2975, 37037, 1829, 43242, 24793, 2423, 14578, 9673, 9566, 1211, 37746, 6055, 5016, 1211, 2407, 4032, 6055, 3794, 19528, 11536, 1829, 11296, 9122, 6027, 3615, 18513, 3660, 16472, 13412, 16606, 21984, 4032, 30731, 5296, 4587, 16606, 1975, 34740, 21136, 37440, 25894, 24793, 4032, 12602, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.25674715502695605, "compression_ratio": 1.5603864734299517, "no_speech_prob": 3.2186508178710938e-06, "words": [{"start": 1956.78, "end": 1957.5, "word": "سيكوانس", "probability": 0.64422607421875}, {"start": 1957.5, "end": 1958.22, "word": " للـ", "probability": 0.4755859375}, {"start": 1958.22, "end": 1958.76, "word": " vertices", "probability": 0.8671875}, {"start": 1958.76, "end": 1959.7, "word": " تبعات", "probability": 0.8248291015625}, {"start": 1959.7, "end": 1959.84, "word": " ال", "probability": 0.412353515625}, {"start": 1959.84, "end": 1960.3, "word": " graph", "probability": 0.406494140625}, {"start": 1960.3, "end": 1961.62, "word": " و", "probability": 0.25634765625}, {"start": 1961.62, "end": 1961.82, "word": " هي", "probability": 0.6591796875}, {"start": 1961.82, "end": 1962.04, "word": " كما", "probability": 0.777099609375}, {"start": 1962.04, "end": 1962.26, "word": " نكون", "probability": 0.595947265625}, {"start": 1962.26, "end": 1962.58, "word": " احنا", "probability": 0.8074544270833334}, {"start": 1962.58, "end": 1963.3, "word": " خلصنا", "probability": 0.9736328125}, {"start": 1963.3, "end": 1963.78, "word": " المحاضرة", "probability": 0.9669189453125}, {"start": 1963.78, "end": 1964.06, "word": " رقم", "probability": 0.88916015625}, {"start": 1964.06, "end": 1964.36, "word": " 11", "probability": 0.67431640625}, {"start": 1964.36, "end": 1965.3, "word": " وهي", "probability": 0.6676025390625}, {"start": 1965.3, "end": 1965.66, "word": " عندكم", "probability": 0.830810546875}, {"start": 1965.66, "end": 1965.8, "word": " ال", "probability": 0.74951171875}, {"start": 1965.8, "end": 1966.4, "word": " homework", "probability": 0.65966796875}, {"start": 1966.4, "end": 1967.24, "word": " المطلوب", "probability": 0.9210205078125}, {"start": 1967.24, "end": 1967.84, "word": " تحلو", "probability": 0.91357421875}, {"start": 1967.84, "end": 1968.04, "word": " و", "probability": 0.5712890625}, {"start": 1968.04, "end": 1969.04, "word": " تسلمونيها", "probability": 0.8509928385416666}, {"start": 1969.04, "end": 1970.22, "word": " كالعادة", "probability": 0.9626953125}, {"start": 1970.22, "end": 1970.46, "word": " ان", "probability": 0.7021484375}, {"start": 1970.46, "end": 1970.76, "word": " شاء", "probability": 0.98291015625}, {"start": 1970.76, "end": 1970.94, "word": " الله", "probability": 0.94921875}, {"start": 1970.94, "end": 1971.22, "word": " و", "probability": 0.89990234375}, {"start": 1971.22, "end": 1971.42, "word": " إلى", "probability": 0.78515625}, {"start": 1971.42, "end": 1971.96, "word": " لقاء", "probability": 0.9554036458333334}, {"start": 1971.96, "end": 1972.5, "word": " اخر", "probability": 0.755615234375}, {"start": 1972.5, "end": 1972.96, "word": " السلام", "probability": 0.762939453125}, {"start": 1972.96, "end": 1973.28, "word": " عليكم", "probability": 0.919189453125}, {"start": 1973.28, "end": 1973.44, "word": " و", "probability": 0.95849609375}, {"start": 1973.44, "end": 1973.54, "word": " رحمة", "probability": 0.7395833333333334}, {"start": 1973.54, "end": 1973.7, "word": " الله", "probability": 0.92626953125}, {"start": 1973.7, "end": 1974.28, "word": " وبركاته", "probability": 0.88955078125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1974.18375, "duration_after_vad": 1956.9599999999966}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d591cbed08bb937461492a3e1abe8e5d5fc52e45
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/qLKU-bwDW9g_raw.srt
@@ -0,0 +1,1692 @@
+1
+00:00:00,720 --> 00:00:05,260
+بسم الله الرحمن الرحيم هذه هي المحاضرة الرقم 11
+
+2
+00:00:05,260 --> 00:00:12,280
+لمساق رياضيات من فصلة لطلاب طالبات الجامعة
+
+3
+00:00:12,280 --> 00:00:16,080
+الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة
+
+4
+00:00:16,080 --> 00:00:22,540
+المتنقلة بدأنا حديثنا في المحاضرة العاشرة السابقة
+
+5
+00:00:22,540 --> 00:00:27,700
+على اللي هو ال graphsعرفنا شو معنات ال graph قلنا
+
+6
+00:00:27,700 --> 00:00:33,160
+عبارة عن اللي هو set V اللي هي بتمثل vertices و A
+
+7
+00:00:33,160 --> 00:00:37,940
+بتمثل اللي هي عبارة عن الخطوط اللي بين اللي هي ال
+
+8
+00:00:37,940 --> 00:00:46,300
+vertices و بعدين أخذنا اللي هو شو معنات ال edge
+
+9
+00:00:46,300 --> 00:00:51,360
+اللي هو الخط و شو معنات اللي هو ال neighborhoodو
+
+10
+00:00:51,360 --> 00:00:55,700
+بعدين اللي هو شو .. قلنا شو معنات انه two edgesكون
+
+11
+00:00:55,700 --> 00:01:02,960
+adjacent و أيضا عرفنا اللي هو شو معنات ال degree
+
+12
+00:01:02,960 --> 00:01:08,340
+لل vertex و .. و قلنا ال vertex اللي ال degree له
+
+13
+00:01:08,340 --> 00:01:12,900
+zero قلنا isolated و أخدنا أمثلة على هيك لأمثلة
+
+14
+00:01:12,900 --> 00:01:18,300
+اللي أمامنا هذه و على ال degree إلى أخره و انتقلنا
+
+15
+00:01:20,810 --> 00:01:24,030
+طبعا كنا حاكينا عن الـ undirected graph بعدين
+
+16
+00:01:24,030 --> 00:01:28,650
+أخدنا أمثلة على كل هذه الموضوعات وجينا أخدنا اللي
+
+17
+00:01:28,650 --> 00:01:33,270
+هو النظرية اللي بتقول دايما اللي هو المجموع اللي
+
+18
+00:01:33,270 --> 00:01:37,050
+هو ال degree لل vertices على كل ال vertices اللي
+
+19
+00:01:37,050 --> 00:01:41,650
+في ال V بتساوي 2 فحاصل ضرب اللي هو عدد الخطوط أو
+
+20
+00:01:41,650 --> 00:01:46,570
+عدد ال edges اللي في الشكلو بعدين أخدنا أمثلة على
+
+21
+00:01:46,570 --> 00:01:51,570
+هيك و أخدنا بعد هيك شو معنى .. شو معنات اللي هو ال
+
+22
+00:01:51,570 --> 00:01:54,690
+directed graph اللي بيكون .. قولنا بيسير اللي هو
+
+23
+00:01:54,690 --> 00:02:00,370
+الخط اللي هو directed from نقطة إلى نقطة أخرىو
+
+24
+00:02:00,370 --> 00:02:05,990
+أخدنا اللي هو أنثى عليهم و أخدنا شو ال degree اللي
+
+25
+00:02:05,990 --> 00:02:09,990
+هي الخارجة و ال degree الداخلة و أخدنا ال homework
+
+26
+00:02:09,990 --> 00:02:13,690
+و اليوم ان شاء الله بدنا نبدأ نحكي عن اللي هو
+
+27
+00:02:13,690 --> 00:02:18,210
+الموضوعات المكملة للي حكيناها اللي هي خلينا نحكي
+
+28
+00:02:18,210 --> 00:02:22,510
+عن حاجة اسمها subigraph subigraph يعني جزء من
+
+29
+00:02:22,510 --> 00:02:25,930
+الigraph جزء من الigraph طبيعى نشوف إيش يعرفناه
+
+30
+00:02:26,460 --> 00:02:31,860
+بقول لو كان عندى graph g1 is a sub graph يعني هذا
+
+31
+00:02:31,860 --> 00:02:36,320
+g1 بنقول عنه sub graph من مين of another graph g
+
+32
+00:02:36,320 --> 00:02:41,040
+يعني g1 عبارة عن sub graph او graph جزئي من ال
+
+33
+00:02:41,040 --> 00:02:46,080
+graph g if and only if the vertex and edges sits
+
+34
+00:02:46,080 --> 00:02:49,730
+of g1G1 are respectively subsets of the vertex and
+
+35
+00:02:49,730 --> 00:02:53,730
+edges of G نحن نتفاج أن G يكون مكوّن من شغل تاني
+
+36
+00:02:53,730 --> 00:02:59,270
+من vertices من vertices ومن خطوط إذا بنقول إن G1
+
+37
+00:02:59,270 --> 00:03:04,450
+sub graph من G إذا كان كل ال vertices اللي في G1
+
+38
+00:03:04,450 --> 00:03:11,610
+موجودة في vertices في G في ال V تبعتهمو كل الخطوط
+
+39
+00:03:11,610 --> 00:03:15,190
+الـ edges اللي في ال .. اللي في الـ G1 اللي كنا
+
+40
+00:03:15,190 --> 00:03:20,070
+نسميها إيه هي عبارة عن خطوط موجودة في مين في الـ G
+
+41
+00:03:20,070 --> 00:03:24,950
+الأصلية الآن نيجي ناخد أمثلة اللي هي أمامنا هاي
+
+42
+00:03:24,950 --> 00:03:27,570
+عندى ال graph G هاي و هذا ال graph G هاي ال
+
+43
+00:03:27,570 --> 00:03:31,290
+vertices كلها موجودة عندى و هاي الخطوط اللي بينها
+
+44
+00:03:31,290 --> 00:03:34,550
+اللي هي ال edges اللي بينها اللي هنوجينا نطلعنا
+
+45
+00:03:34,550 --> 00:03:42,870
+لهذا هذا V4 هي موجودة هنا V4V3 هيها جاي من هنا V7
+
+46
+00:03:42,870 --> 00:03:48,090
+هيها من هنا V6 هيها من هنا الخطوط اللي بينهم V7 و
+
+47
+00:03:48,090 --> 00:03:58,230
+V6 هي V7 و V6 موجود V6 و V3 هي موجود V4 و V3 هي V4
+
+48
+00:03:58,230 --> 00:04:04,770
+و V3 موجودإذا هذا ال graph هو عبارة عن جزء من هذا
+
+49
+00:04:04,770 --> 00:04:08,510
+لأن الخطوط هذه موجودة في ال graph الأصلي و ال
+
+50
+00:04:08,510 --> 00:04:12,530
+vertices موجودة في ال graph الأصلي عشان هيك بنسمي
+
+51
+00:04:12,530 --> 00:04:17,150
+هذا sub graph من هذا نشوف ال graph التاني، لاحظوا
+
+52
+00:04:17,150 --> 00:04:25,280
+V2 هي موجودةV3 هي V3 V6
+
+53
+00:04:25,280 --> 00:04:33,000
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+54
+00:04:33,000 --> 00:04:33,140
+V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7
+
+55
+00:04:33,140 --> 00:04:33,140
+هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+56
+00:04:33,140 --> 00:04:33,140
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+57
+00:04:33,140 --> 00:04:33,140
+V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7
+
+58
+00:04:33,140 --> 00:04:34,080
+هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+59
+00:04:34,080 --> 00:04:34,920
+V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي V6 V7 هي
+
+60
+00:04:34,920 --> 00:04:47,760
+V6 V7 هي V6 V7 هي V6 V7 هي V6
+
+61
+00:04:47,760 --> 00:04:53,380
+V7الان بدنا ناخد اللي هو some special simple
+
+62
+00:04:53,380 --> 00:04:58,160
+graphs أو حاجة بنسميها complete graphs بدنا نرجع ل
+
+63
+00:04:58,160 --> 00:05:03,420
+اللي هو ال graphs و بدنا نسمي بعض ال graphs ليش
+
+64
+00:05:03,420 --> 00:05:09,820
+بنسميها complete graph بنسميه و نشوف ليش ال graph
+
+65
+00:05:09,820 --> 00:05:14,340
+بنسميه completeبناخد أنواع معينة خلّينا نشوف إيش
+
+66
+00:05:14,340 --> 00:05:18,280
+المجولة for any positive integer n لو كان n عبارة
+
+67
+00:05:18,280 --> 00:05:20,840
+عن positive integer يعني واحد ولا اتنين ولا تلاتة
+
+68
+00:05:20,840 --> 00:05:24,280
+ولا اربعة الاخر هي the complete graph on n
+
+69
+00:05:24,280 --> 00:05:29,620
+vertices يعني لما نقول عن ال graph اللي فيه n
+
+70
+00:05:29,620 --> 00:05:30,220
+vertices
+
+71
+00:05:33,500 --> 00:05:38,600
+يعني في أكم رأس في N من الرؤوس بقول ده complete
+
+72
+00:05:38,600 --> 00:05:43,380
+graph on N vertices denote KN يعني الآن بدنا نسمي
+
+73
+00:05:43,380 --> 00:05:51,240
+ال KN هذا يرمز إلى complete graphwith n vertices
+
+74
+00:05:51,240 --> 00:05:57,700
+فى ايش ماله ن من الرؤوس طبعا شوفوا هذا كأن is a
+
+75
+00:05:57,700 --> 00:06:02,400
+graph with n vertices يعني هذا كأن عبارة عن graph
+
+76
+00:06:02,400 --> 00:06:06,760
+with n vertices every two of which are adjacent
+
+77
+00:06:06,760 --> 00:06:11,380
+يعني كل اتنين من ال vertices adjacent اتجسنت
+
+78
+00:06:11,380 --> 00:06:14,420
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+79
+00:06:14,420 --> 00:06:15,000
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+80
+00:06:15,000 --> 00:06:19,260
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+81
+00:06:19,260 --> 00:06:19,260
+اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت اتجسنت
+
+82
+00:06:19,260 --> 00:06:23,500
+اتجسنت اتجسنت اتجسنت اهي عندى كتنين في نقطتين
+
+83
+00:06:23,500 --> 00:06:29,260
+النقطتين هدولة في التنتين بينها خط مافيش اي نقطة
+
+84
+00:06:29,260 --> 00:06:34,440
+في داخل الكتنين مافيش بينها وبين الباقيات خطوط
+
+85
+00:06:34,440 --> 00:06:42,900
+عشان هيك بنسمي هذا complete graphمن النوع K2 نشوف
+
+86
+00:06:42,900 --> 00:06:50,440
+نوع آخر K3 K3 K3 أشمل فيه تلات رؤوس هذه راس هذه
+
+87
+00:06:50,440 --> 00:06:55,960
+راسين هذه تلاتة لاحظت تلات رؤوس فعلا هذا وهذا بين
+
+88
+00:06:55,960 --> 00:06:59,860
+الخط وهذا وهذا بين الخط وهذا وهذا بين الخط يعني كل
+
+89
+00:06:59,860 --> 00:07:05,920
+الرؤوس are adjacentيعني ما لهن كل الرؤوس اللي هي
+
+90
+00:07:05,920 --> 00:07:09,380
+بينهن وبين بعض خطوط عشان هيك بنسميها ده Complete
+
+91
+00:07:09,380 --> 00:07:13,640
+Graph هذا النوع من ال graphs اللي زي هيك اللي
+
+92
+00:07:13,640 --> 00:07:17,240
+كتنين كتلاتة اللي في عدد اللي هو اتنين او عدد
+
+93
+00:07:17,240 --> 00:07:21,860
+تلاتة او بعد شوية اربع او خمس او ستة وبكون بخاصية
+
+94
+00:07:21,860 --> 00:07:28,320
+انه كل اتنين كل نقطتين بين الخط بنسميه اللي هو
+
+95
+00:07:28,320 --> 00:07:32,990
+Complete Graph من النوع KNنجي لكي أربعة كي أربعة
+
+96
+00:07:32,990 --> 00:07:36,110
+اللي هو واحد تنين تلاتة أربعة فيها أربع عياش نقاط
+
+97
+00:07:36,110 --> 00:07:43,330
+الأربع نقاط كلهم بين هذه و هذه خط و بينها و بينها
+
+98
+00:07:43,330 --> 00:07:48,510
+دي خط و بينها و بينها دي خط يعني كل النقاط اللي هم
+
+99
+00:07:48,510 --> 00:07:52,970
+adjacent لبعض عشان هيك بنسميه graph إذا ال
+
+100
+00:07:52,970 --> 00:07:58,890
+complete graphهو graph عادي كل نقطين فيه adjacent
+
+101
+00:07:58,890 --> 00:08:03,590
+يعني كل نقطين فيه graph حالة خاصة من هذول ال
+
+102
+00:08:03,590 --> 00:08:08,850
+complete graph اللي هي عائلة من ال graphs اسمها kn
+
+103
+00:08:08,850 --> 00:08:14,890
+ايش ال kn هذه اللي هي عددها n من اللي هو ال
+
+104
+00:08:14,890 --> 00:08:20,000
+vertices فيها؟و بيعملين complete graph يعني كل
+
+105
+00:08:20,000 --> 00:08:25,820
+النقاط are adjacent ده نشوف اللي بعدها هاي K خمسة
+
+106
+00:08:25,820 --> 00:08:30,140
+مثلا بخمسة هاي عندى خمس نقاط واحدة تنتهي من تلاتة
+
+107
+00:08:30,140 --> 00:08:32,900
+اربعة خمسة واضح ان كل النقاط كل واحدة بيطلع منها
+
+108
+00:08:32,900 --> 00:08:37,940
+اربع خطوط للاخرين فعشان هيك بنسميها complete graph
+
+109
+00:08:37,940 --> 00:08:43,680
+من النوع Kلو واحد بدى يرسم K6 بتقدر ترسمها بنفس
+
+110
+00:08:43,680 --> 00:08:48,060
+الاسم و K7 طبعا بتغلب شوية لكن بتظلها في نفس
+
+111
+00:08:48,060 --> 00:08:54,800
+النطاق هذه بنسميها complete graphs او مثل على ال
+
+112
+00:08:54,800 --> 00:09:00,240
+complete graphs اللي هي العائلة اللي سميناها KNعند
+
+113
+00:09:00,240 --> 00:09:03,280
+K واحد برضه نعتبره complete ليش؟ لأن الـ complete
+
+114
+00:09:03,280 --> 00:09:07,740
+graph مايكونش فيه نقطتين مش adjacent هانفيش فيه
+
+115
+00:09:07,740 --> 00:09:10,840
+نقطتين مش adjacent لأنه أصلا هي النقطة بس لحالها
+
+116
+00:09:10,840 --> 00:09:17,730
+عشانك بنسميها اللي هي برضه complete graphK1, K2,
+
+117
+00:09:17,850 --> 00:09:22,130
+K3, K4, K5 الاخر هي زمنته بتاعنا الان بدنا نيجي
+
+118
+00:09:22,130 --> 00:09:26,810
+نوع ثاني ل graphs حاجة اسمها ال cycles ماشي ايش ال
+
+119
+00:09:26,810 --> 00:09:31,850
+cycles اللي هي و ال wheels اه ايش تشوف ايش ال
+
+120
+00:09:31,850 --> 00:09:37,900
+cycle و ايش ال wheelالان cycle cn ده نرمزي لبرنامج
+
+121
+00:09:37,900 --> 00:09:41,220
+cn بعد اذنكم يعني في عندي n أكبر تساوي تلاتة يعني
+
+122
+00:09:41,220 --> 00:09:47,380
+عندي cycle c3 و c4 و c5 و c6 إلى ما لنهاية
+
+123
+00:09:47,380 --> 00:09:51,900
+consists of n vertices يعني ال cn هذه برضه بتحتوي
+
+124
+00:09:51,900 --> 00:09:57,860
+على ايه عشان n من ال verticesماذا نسميه Cycle لما
+
+125
+00:09:57,860 --> 00:10:02,960
+نكون تحقيق ما يليه الـ CNN Consists Of N Vertices
+
+126
+00:10:02,960 --> 00:10:08,480
+V1 و V2 و VN And Edges و الـ Edges ايش ما لها V1 و
+
+127
+00:10:08,480 --> 00:10:13,890
+V2 يعني خط بين V1 و V2 و خط بين V2 و V3و خط بين V3
+
+128
+00:10:13,890 --> 00:10:19,330
+و V4 لما أصل عند خط بين اللي هي النقطة الأخيرة VN
+
+129
+00:10:19,330 --> 00:10:25,430
+و برجع لمين لل V1 و كإن إيش بسكر و بعمله cycle زي
+
+130
+00:10:25,430 --> 00:10:30,190
+دائرة أو اللي هو دورة كاملة ماشي the cycles C3,
+
+131
+00:10:30,330 --> 00:10:38,350
+C4, C5, C6 are displaced انفجارا هى وهذه وهذهاللي
+
+132
+00:10:38,350 --> 00:10:46,690
+هي V1 V2 V2 V3 V3 V1 إذاً هذا cycle صار الآن هذا
+
+133
+00:10:46,690 --> 00:10:50,170
+ال graph complete أه complete لأنه كل مغطين
+
+134
+00:10:50,170 --> 00:10:54,850
+adjacent يعني ال cycle ممكن تكون complete يعني
+
+135
+00:10:54,850 --> 00:10:59,730
+مثال على complete graph نجي للي بعدها C4هي من عند
+
+136
+00:10:59,730 --> 00:11:03,010
+النقطة الأولى للتانية في خط و من التانية للتالتة و
+
+137
+00:11:03,010 --> 00:11:05,770
+من التالتة للرابعة و من الرابعة للأولى رجعت يعني
+
+138
+00:11:05,770 --> 00:11:10,190
+أقفلة الدائرة أو أقفلة اللي هي ال cycle هذا بنسميه
+
+139
+00:11:10,190 --> 00:11:13,590
+برضه cycle هل هذا complete؟ لأ مش complete ليش مش
+
+140
+00:11:13,590 --> 00:11:16,850
+complete؟ لأن هذي و هذا النقطة they are not
+
+141
+00:11:16,850 --> 00:11:20,850
+adjacent لأنه مافيش بين الخط و هذي كمان و هذي إذا
+
+142
+00:11:20,850 --> 00:11:24,090
+هي في عند ال cycle ليس شرط انها تكون إيش مالها
+
+143
+00:11:24,090 --> 00:11:28,450
+complete اقرأتالان نجي لـ C5 C5 بنفس الأسلوب فيها
+
+144
+00:11:28,450 --> 00:11:31,330
+خمس نقاط الخمس نقاط بتبدأ من عند النقطة الأولى و
+
+145
+00:11:31,330 --> 00:11:33,670
+بتبدأ للتانية أو للتالتة أو للربعة أو للخمسة أو
+
+146
+00:11:33,670 --> 00:11:37,770
+للسادسة اللي الخمسة بترجع لمين للنقطة الأولى
+
+147
+00:11:37,770 --> 00:11:42,770
+فبتعمل ليه cycle اللي هي بتسكر اللي هي الدورة الان
+
+148
+00:11:42,770 --> 00:11:47,890
+C6 بنفس الأسلوب فيها ست نقاط كل نقطة ال V1 بتروحها
+
+149
+00:11:47,890 --> 00:11:52,150
+V2 V2 تلاتة V3 او V4 مافهومش معنات بتروح يعني بين
+
+150
+00:11:52,150 --> 00:12:02,610
+الخطV4 V5 V5 V6 V6 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+151
+00:12:02,610 --> 00:12:03,510
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+152
+00:12:03,510 --> 00:12:06,110
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+153
+00:12:06,110 --> 00:12:06,890
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+154
+00:12:06,890 --> 00:12:08,650
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+155
+00:12:08,650 --> 00:12:08,650
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+156
+00:12:08,650 --> 00:12:12,150
+V1 V1 V1 V1 V1 V1 V1 V1 V1 V1
+
+157
+00:12:12,150 --> 00:12:15,610
+V1 V1
+
+158
+00:12:15,980 --> 00:12:21,720
+when we add an additional vertex to cycle CN يعني
+
+159
+00:12:21,720 --> 00:12:29,280
+ايش بنجيب؟ بنجيب هي ال cycle و بنضيف لها نقطة ايش
+
+160
+00:12:29,280 --> 00:12:33,040
+النقطة دي مالها؟ تنشوف ايش مالها we add an
+
+161
+00:12:33,040 --> 00:12:36,260
+additional vertex to cycle CN for N أكبر سواء
+
+162
+00:12:36,260 --> 00:12:41,940
+تلاتة and connect this new vertex to each of the
+
+163
+00:12:41,940 --> 00:12:48,410
+vertices in CN by new edgesإذا الآن ما هي إلا
+
+164
+00:12:48,410 --> 00:12:52,570
+cycle بنحط جواتها نقطة أو جنبها نقطة في المكان
+
+165
+00:12:52,570 --> 00:12:56,010
+المناسب جواتها أفضل يعني بتكون أحلى في الرسم و
+
+166
+00:12:56,010 --> 00:13:01,590
+بنوصل من النقطة هذه خطوط لكل او edges لكل من ال
+
+167
+00:13:01,590 --> 00:13:05,390
+vertices اللي موجودة هذه النقطة هيعملنا اللي هو
+
+168
+00:13:05,390 --> 00:13:09,810
+edge وهي edge وهي edge مع كل النقاط هذه بنسميها
+
+169
+00:13:09,810 --> 00:13:16,510
+wheel W تلاتة تبعا ل C تلاتةالان هذه complete اه
+
+170
+00:13:16,510 --> 00:13:19,590
+complete هذه واضح انها complete لان هي مع الكل كل
+
+171
+00:13:19,590 --> 00:13:26,570
+النقاط مع الكل الان هذه النقطة هي عندياللي هو من
+
+172
+00:13:26,570 --> 00:13:31,630
+النقطة هذه حطينا و رسمنا لكل النقاط، مظبوط؟ هذه
+
+173
+00:13:31,630 --> 00:13:35,050
+عملت ل wheel هي نفسها اللي فوق بس عملنا لها نقطة و
+
+174
+00:13:35,050 --> 00:13:40,390
+نقطة ودنا لها اللي هي من لكل النقاط خطوط حسب تعريف
+
+175
+00:13:40,390 --> 00:13:44,370
+اللي عرفنا لمين لل wheel هل هذه complete؟ ليس شرطا
+
+176
+00:13:44,370 --> 00:13:47,410
+لأنه فيش بين النقطة هذه مثلا النقطة هذه خط مباشر
+
+177
+00:13:47,850 --> 00:13:51,270
+هذا لو خط من هنا إلى هنا وهذا من هنا إلى هنا لأن
+
+178
+00:13:51,270 --> 00:13:55,530
+لو كان هناك خط مباشر بينهم نسميه complete لو كان
+
+179
+00:13:55,530 --> 00:13:59,430
+هناك خطوط من الكل طبعا الان نأتي لهذه اللي هي ال
+
+180
+00:13:59,430 --> 00:14:03,850
+wheel بنجيب ال C3 و بنحط نقطة في داخلها و بنوصل
+
+181
+00:14:03,850 --> 00:14:08,470
+بينهم كلهم اللي هي ايش بين النقطة هذه و بين كل
+
+182
+00:14:08,470 --> 00:14:12,030
+النقاط الأخرى بنوصل خطوط فبتعمل wheel هل ال wheel
+
+183
+00:14:12,030 --> 00:14:15,090
+complete ليس شطء لأن هو من هنا إلى هنا مثلا ايش
+
+184
+00:14:15,090 --> 00:14:19,810
+مافيش خطهكذا اللي بعدها الان هذه اللي هي مين الشكل
+
+185
+00:14:19,810 --> 00:14:23,810
+السداسي في الشكل السداسي حطينا نقطة ووصلنا بين
+
+186
+00:14:23,810 --> 00:14:28,090
+النقطة و بين باقى النقاط فعملت ليش برضه wheel هاي
+
+187
+00:14:28,090 --> 00:14:32,850
+شكل السداسي عندي وهي النقطة و بدي اتوصل من الشكل
+
+188
+00:14:32,850 --> 00:14:37,350
+السداسي لكل النقاط شوفوهاشتبتطلعوش تقبلوا ليها
+
+189
+00:14:37,350 --> 00:14:40,310
+تقوليها مكعب لأ هذا مقطب في المصف و طبعا هي بتظهر
+
+190
+00:14:40,310 --> 00:14:43,790
+لو اتنعانت هتشوفها مكعب لو اتنعانت في صورة أخرى
+
+191
+00:14:43,790 --> 00:14:47,070
+هتشوفها نقطة في الداخل و من الكل مش موضوعنا هذا بس
+
+192
+00:14:47,070 --> 00:14:51,930
+لكن عشان الخداع البصري طيب هذه اللي هي معنات ال
+
+193
+00:14:51,930 --> 00:14:58,050
+wheel الان في حد اسمه بيبا ترايت بيبا بيبارتايت
+
+194
+00:14:58,410 --> 00:15:03,350
+graph بيبرتايت graph اللي هو يعني الـ Graph
+
+195
+00:15:03,350 --> 00:15:06,830
+الثنائي ايش ال graph الثنائي خلينا نشوف ايش بيقول
+
+196
+00:15:06,830 --> 00:15:11,030
+ال graph الثنائي a bipartite graph is a graph هو
+
+197
+00:15:11,030 --> 00:15:14,750
+عبارة عن graph whose vertices can be partitioned
+
+198
+00:15:14,750 --> 00:15:19,470
+into two disjoint sets V1 and V2 يعني ال بيبرتايت
+
+199
+00:15:19,470 --> 00:15:23,970
+graph أو اللي هو ال graph الثنائي بيقول هذا بتقدر
+
+200
+00:15:23,970 --> 00:15:32,640
+تعمل ال vertices إليه جزئينV1 و V2 هي V1 وهي V2 بس
+
+201
+00:15:32,640 --> 00:15:39,940
+تحت شرط معين كل Graphs ممكن تعملها V1 و V2بقدر
+
+202
+00:15:39,940 --> 00:15:45,220
+اعمل V1 و V2 بيبقى partition sets يعني هذول اللي
+
+203
+00:15:45,220 --> 00:15:50,540
+بنسميهم هم اللي جزء من ال set الأصلي تبع ال
+
+204
+00:15:50,540 --> 00:15:56,440
+vertices in such a way بتجزئها بطريقة هي V1 و V2
+
+205
+00:15:56,440 --> 00:16:02,840
+بتجزئها بطريقة that every edge point joins a
+
+206
+00:16:02,840 --> 00:16:08,070
+vertex in V1 و V2 يعني الآن لما ناخد V1وفيه اتنين
+
+207
+00:16:08,070 --> 00:16:16,590
+هتجزئلي اللي هي ال vertices إلى جزئين ابحث انه كل
+
+208
+00:16:16,590 --> 00:16:22,730
+edge في الشكل بربط نقطة من هنا مع نقطة من هنا كل
+
+209
+00:16:22,730 --> 00:16:26,590
+edge في الشكل .. كل edge موجود هي edge بربط نقطة
+
+210
+00:16:26,590 --> 00:16:29,150
+من هنا مع نقطة من هنا ال edge التاني هي بربط نقطة
+
+211
+00:16:29,150 --> 00:16:31,710
+من هنا مع نقطة من هنا ال edge التالت من نقطة من
+
+212
+00:16:31,710 --> 00:16:33,830
+هنا مع نقطة من هنا ال edge الرابع من نقطة من هنا
+
+213
+00:16:33,830 --> 00:16:37,390
+مع نقطة من هناكل الاتجاهات اللي موجودة الخطوط
+
+214
+00:16:37,390 --> 00:16:42,810
+بتكون واصلة بين نقطة من مجموعة ال vertices الأولى
+
+215
+00:16:42,810 --> 00:16:47,770
+ونقطة من مجموعة ال vertices التانية يعني الآن لو
+
+216
+00:16:47,770 --> 00:16:52,290
+كان بين هذه وهذه لأ بنفعش يكون اللي هو ايه شماله
+
+217
+00:16:52,680 --> 00:16:58,620
+عندي اللي هو بمسميهش عملة partition لأنه من هالهال
+
+218
+00:16:58,620 --> 00:17:02,920
+بيصير هذا النقطة في نفس ال .. نقطتين في نفس ال V
+
+219
+00:17:02,920 --> 00:17:08,420
+واحد لأ لأن كل الخطوط بدها تكون جاية من ال
+
+220
+00:17:08,420 --> 00:17:13,080
+vertices الأولى مع ال vertices التانية عشان هيك
+
+221
+00:17:13,080 --> 00:17:20,280
+بنسمي هذا bipartite graph أو graph ثنائيالان هاي
+
+222
+00:17:20,280 --> 00:17:26,820
+واحد تاني برضه ببرتاية graph آخر هي ال V1 الكبيرة
+
+223
+00:17:26,820 --> 00:17:31,920
+يعني بتحتوي على كل اللي هي ال vertices الجزء الأول
+
+224
+00:17:31,920 --> 00:17:35,980
+وهذه بتحتوي على ال vertices الجزء الثاني لاحظ انه
+
+225
+00:17:35,980 --> 00:17:42,030
+كل خطموجود بربط بين نقطة بين هذه V1 و V2 كل خط
+
+226
+00:17:42,030 --> 00:17:47,670
+موجود بربط بين V2 و V1 كل خط موجود بين V1 و V2 و
+
+227
+00:17:47,670 --> 00:17:54,470
+هكذا هذا بنسميهم اشمالهم امثل عبارة على bipartite
+
+228
+00:17:54,470 --> 00:17:58,330
+graphs نيجي لاخر واحدة طبعا هي الحالة من حالة
+
+229
+00:17:58,330 --> 00:18:05,600
+رسمها حالة هي هذه اللي هو ال V2وهي هدمين الـ V1 هى
+
+230
+00:18:05,600 --> 00:18:12,920
+اللى هما ال V1 و ال V2 اللى جزءين ليه اللى جزءين
+
+231
+00:18:12,920 --> 00:18:18,460
+ليه اللى هو ال vertices الى جزءين ابحث ان كل خط
+
+232
+00:18:18,460 --> 00:18:24,900
+موجود ياخد من نقطة في ال V1 الى V2 او من V2 ل V1 و
+
+233
+00:18:24,900 --> 00:18:29,700
+هكذا زى ما انتوا شايفين فهدولة امثلة على bipartite
+
+234
+00:18:29,700 --> 00:18:36,590
+graphsأو جرافات ثنائية الـ Complete bipartite
+
+235
+00:18:36,590 --> 00:18:41,310
+graph is a bipartite graph in which every vertex
+
+236
+00:18:41,310 --> 00:18:46,390
+in V1 is joined to every vertex in V2
+
+237
+00:18:49,970 --> 00:18:54,290
+عبارة عن بيبرتايته graph in which every vertex in
+
+238
+00:18:54,290 --> 00:18:58,870
+v1 كل ال vertex في ال v1 is joined to every vertex
+
+239
+00:18:58,870 --> 00:19:03,570
+in v2 ماقلناش ان كل ال vertices اللي في ال v1
+
+240
+00:19:03,570 --> 00:19:08,410
+برتبط مع بعض و ال v2 اللي برتبط مع بعض لأ قلنا ان
+
+241
+00:19:08,410 --> 00:19:13,870
+كل vertex v1 برتبط مع اياش مع اللي في ال .. مع
+
+242
+00:19:13,870 --> 00:19:19,030
+واحد من مين من v2 every vertex in v1 is joined to
+
+243
+00:19:19,030 --> 00:19:23,280
+everyjoin to every وليس مع واحد فقط to every واحد
+
+244
+00:19:23,280 --> 00:19:31,460
+في ذي اتنى الان خلينا لو رجعنا الان هذا مثلا نشوف
+
+245
+00:19:31,460 --> 00:19:35,240
+complete ولا لأ هى هى هذا برتبط مع هذا وبرتبط مع
+
+246
+00:19:35,240 --> 00:19:40,360
+هذا لكن برتبطش مع اللي بعيد هذا اذا مش complete طب
+
+247
+00:19:40,360 --> 00:19:46,630
+الان هذا هى وبرتبط مع هذا وبرتبط مع هذاو هذه
+
+248
+00:19:46,630 --> 00:19:52,150
+بترتبطش مع مين؟ مع هذا لو ربطناها مع هذا يعني لو
+
+249
+00:19:52,150 --> 00:19:58,850
+وصلنا هذا الخط هيك و وصلنا هذا الخط هيكووصلنا هذا
+
+250
+00:19:58,850 --> 00:20:02,670
+خط واصل فبصير عندي هذا complete يعني متى بيصير هذا
+
+251
+00:20:02,670 --> 00:20:07,290
+complete لما نهادي لأن هي وصلت مع حده ووصلت مع حده
+
+252
+00:20:07,290 --> 00:20:13,030
+ونوصل هذه مع حده ومش هيك كمان ونوصل هذه مع حده
+
+253
+00:20:13,030 --> 00:20:16,950
+بيصير ال graph اللي طلع عنده يشمله complete يعني
+
+254
+00:20:16,950 --> 00:20:20,490
+عشان يكون complete هذا بيكون كل واحدة من هدولة
+
+255
+00:20:20,490 --> 00:20:26,950
+التنتين بتتوصل مع كل واحدة من التلاتةيعني بينها
+
+256
+00:20:26,950 --> 00:20:31,070
+وبين كل أحد من تلاتة خط واضح أننا نسميه complete
+
+257
+00:20:31,070 --> 00:20:35,200
+bipartiteigraphأذا زي ما قلنا الـ bipartite graph
+
+258
+00:20:35,200 --> 00:20:39,700
+بكون complete إذا كان هو bipartite graph وكل
+
+259
+00:20:39,700 --> 00:20:46,140
+vertex في الـ V1 is joined to every vertex in V2
+
+260
+00:20:46,140 --> 00:20:48,420
+وكل vertex في الـ V1 is joined to every vertex in
+
+261
+00:20:48,420 --> 00:20:53,360
+V2 وكل vertex في الـ V1 is joined to every vertex
+
+262
+00:20:53,360 --> 00:20:53,540
+in V2 وكل vertex في الـ V1 is joined to every
+
+263
+00:20:53,540 --> 00:20:53,540
+vertex in V2 وكل vertex في الـ V1 is joined to
+
+264
+00:20:53,540 --> 00:20:53,540
+every vertex in V2 وكل vertex في الـ V1 is joined
+
+265
+00:20:53,540 --> 00:20:53,600
+to every vertex in V2 وكل vertex في الـ V1 is
+
+266
+00:20:53,600 --> 00:20:53,660
+joined to every vertex in V2 وكل vertex في الـ V1
+
+267
+00:20:53,660 --> 00:20:53,660
+is joined to every vertex in V2 وكل vertex في الـ
+
+268
+00:20:53,660 --> 00:20:53,660
+V1 is joined to every vertex in V2 وكل vertex في
+
+269
+00:20:53,660 --> 00:20:53,660
+الـ V1 is joined to every vertex in V2 وكل vertex
+
+270
+00:20:53,660 --> 00:20:53,660
+في الـ V1 is joined to every vertex in V2 وكل
+
+271
+00:20:53,660 --> 00:20:58,580
+vertex في الـ V1 is joined to every vertex in V2
+
+272
+00:20:58,580 --> 00:21:04,130
+وكل vertex في الـ V1 isاللي بيكون اللي هو ال .. ال
+
+273
+00:21:04,130 --> 00:21:08,930
+.. ال .. ال V1 في M من العناصر و ال V2 بيكون M من
+
+274
+00:21:08,930 --> 00:21:13,890
+ال .. N من العناصر يعني عند ال V1 ال vertices
+
+275
+00:21:13,890 --> 00:21:19,570
+عددهم M و ال V2 عددهم N و كان هذا bipartite graph
+
+276
+00:21:19,570 --> 00:21:24,370
+و في نفس الوقت complete بيكون اللي هو هاي شكله
+
+277
+00:21:24,370 --> 00:21:30,120
+نيجيكتنين و تلاتة الان هي عندى فوق اتنين وها نتحت
+
+278
+00:21:30,120 --> 00:21:33,360
+ايش تلاتة زى ما عملناها قبل شوية هي الان هذه بدها
+
+279
+00:21:33,360 --> 00:21:39,020
+تروح للكل هي راحت للكل وهذه برضه راحت لإيش للكل
+
+280
+00:21:39,020 --> 00:21:44,150
+وطبعا هدولة اوتوماتيك راحلن مين لتنتين اللى فوقلأن
+
+281
+00:21:44,150 --> 00:21:47,290
+K ثلاثة ثلاثة هيكون عندنا ثلاثة هنا و ثلاثة وين
+
+282
+00:21:47,290 --> 00:21:50,730
+فوق لأن التنين الأولى خلّينا نصطلح مع بعض اللي
+
+283
+00:21:50,730 --> 00:21:57,230
+بنرسمها فوق التلاتة التانية هذه بنرسمها تحت لأن
+
+284
+00:21:57,230 --> 00:22:00,650
+تلاتة و تلاتة هي تلاتة فوق و هي تلاتة تحت و بنوصل
+
+285
+00:22:00,650 --> 00:22:05,150
+من كل واحدة للكل ممنوع نوصل بين هدول اللي هنا مع
+
+286
+00:22:05,150 --> 00:22:10,110
+بعض لأ بيبطل ال bipartite أصلا ال bipartite أن
+
+287
+00:22:10,110 --> 00:22:16,810
+هدولةفي جهة و هدولة في جهة و الخطوط بين هنا وبس
+
+288
+00:22:16,810 --> 00:22:23,850
+مافيش بين اللي هو عناصر اللي هي ال V2 مع بعضها
+
+289
+00:22:23,850 --> 00:22:28,590
+خطوط بيبطل بيبرتايد وهذا نفس الاشي طيب لإن نيجي
+
+290
+00:22:28,590 --> 00:22:32,670
+تلاتة و خمسة إذا تلاتة بنرسمها فوق وهذه خمسة تحت و
+
+291
+00:22:32,670 --> 00:22:38,950
+بنطلع من كل تلاتةخمس خطوط لخمس نقاط من كل تلاتة
+
+292
+00:22:38,950 --> 00:22:42,630
+خمس خطوط من كل تلاتة خمس خطوط يعني لو بدك تيجي
+
+293
+00:22:42,630 --> 00:22:47,210
+تحسب الخطوط الموجودة من هذه بتطلع منها خمس خطوط
+
+294
+00:22:47,210 --> 00:22:51,650
+خمس خطوط ومن هذه خمسة ومن هذه خمسة يعني خمستاشر خط
+
+295
+00:22:52,480 --> 00:22:56,460
+ممكن اعد ان الـ 15 الخط بطريقة تانية ان هذه اطلع
+
+296
+00:22:56,460 --> 00:23:00,620
+منها تلت خطوط للي فوق عشان يصير complete وهذه اطلع
+
+297
+00:23:00,620 --> 00:23:03,360
+منها تلت خطوط للي فوق وهذه اطلع منها تلت خطوط
+
+298
+00:23:03,360 --> 00:23:07,880
+بيصير تلت خطوط في خمس نقاط بخمس تعاشر هنا خمس نقاط
+
+299
+00:23:07,880 --> 00:23:11,220
+طالعين تلت نقاط طالع الخمس خطوط تلت في خمسة بخمس
+
+300
+00:23:11,220 --> 00:23:14,480
+تعاشر اذا بقدر اعد الخطوط من اعلى او الخطوط من
+
+301
+00:23:14,480 --> 00:23:21,730
+اسفل زي ما وضحتالان اتنين و ستة هي نقطة نقطتين وهي
+
+302
+00:23:21,730 --> 00:23:25,090
+اللي هي ست نقطة تحت هيك التفاجنة الأولى بتطلع فوق
+
+303
+00:23:25,090 --> 00:23:30,190
+والتانية بتطلع تحتها تصلح بينها وبين بعض الان هذه
+
+304
+00:23:30,190 --> 00:23:34,970
+التنتين النقطة الأولى بتطلع ستة تقريه ست خطوطو هدى
+
+305
+00:23:34,970 --> 00:23:38,650
+بتطلع ست خطوط للنقاط اللى تحتها فبصير ستة و ستة
+
+306
+00:23:38,650 --> 00:23:42,670
+اتناش هدى بتطلع خطين و هدى خطين و هدى خطين كل
+
+307
+00:23:42,670 --> 00:23:45,670
+واحدة ست نقاط بتطلع كل واحدة خطين بيصير ستة في
+
+308
+00:23:45,670 --> 00:23:49,870
+اتنين باتناش ده بقدر اعد اللى هو من هنا او من هنا
+
+309
+00:23:49,870 --> 00:23:53,270
+يعني هدولة بتطلعين اتناش خط و هدولة بتطلعين اتناش
+
+310
+00:23:53,270 --> 00:23:57,100
+خطيعني لو بدنا نحسب ال degree لهدولة ال degree
+
+311
+00:23:57,100 --> 00:24:00,980
+لهدولة اتناش و ال degree للي فوق برضه ايش اتناش
+
+312
+00:24:00,980 --> 00:24:06,280
+يعني مجموع ال degree مجموع ال degree لكل العناصر
+
+313
+00:24:06,280 --> 00:24:10,800
+لكل ال vertices اللي هان هي أربعة و عشرين اللي هي
+
+314
+00:24:10,800 --> 00:24:13,920
+ضائف عدد الخطوط زي ما قلنا في النظرية اللي قلناها
+
+315
+00:24:13,920 --> 00:24:17,780
+المرة الماضية وهذا اللي هو sum of degree اللي
+
+316
+00:24:17,780 --> 00:24:22,970
+بحكيهلأن how many edges does K3 و K6 contains في
+
+317
+00:24:22,970 --> 00:24:27,790
+الشرح قلته قبل شوية بيطلع من تلاتة ست خطوط فبصير
+
+318
+00:24:27,790 --> 00:24:33,410
+عندى أكم خط تلاتة في ستة بطمنتعش لأن الستة بيطلع
+
+319
+00:24:33,410 --> 00:24:36,490
+منها تلت خطوط كل واحدة ستة في تلاتة برضه بطمنتعش
+
+320
+00:24:36,490 --> 00:24:41,310
+اذا طمنتعش طمنتعشر خط اللي هو وكأنه ال degrees
+
+321
+00:24:41,310 --> 00:24:45,470
+لهدولة اللي هي كل واحدة ال degree اللي هي ستة من
+
+322
+00:24:45,470 --> 00:24:50,990
+النقاط التلاتةفبكون مجموع ال degrees للنقاط اللي
+
+323
+00:24:50,990 --> 00:24:56,610
+فوق 18 الان ال 6 اللي تحت ال degree لكل واحدة
+
+324
+00:24:56,610 --> 00:24:59,690
+تلاتة لإنه بيطلع بينها تلت خطوط فبكون مجموع ال
+
+325
+00:24:59,690 --> 00:25:03,570
+degrees اللي تحت 18 يعني اللي تحت 18 و اللي فوق 18
+
+326
+00:25:03,570 --> 00:25:08,490
+بيطلع عن 36 36 هنا ضعف عدد الخطوط زي ما عكينا قبل
+
+327
+00:25:08,490 --> 00:25:14,120
+شوية هذا هي this complete bipartiteGraph has six
+
+328
+00:25:14,120 --> 00:25:17,100
+vertices يعني هذا الـ Complete بيبرتايت الـ Graph
+
+329
+00:25:17,100 --> 00:25:21,860
+اللي قلنا عنه زي اللي توه له ستة vertices with
+
+330
+00:25:21,860 --> 00:25:25,280
+degree تلاتة يعني ستة vertices with degree تلاتة و
+
+331
+00:25:25,280 --> 00:25:28,660
+تلاتة vertices with degree ستة زي ما وضحت قبل و
+
+332
+00:25:28,660 --> 00:25:33,220
+شوية الان مدموع ال degree لكل ال V اللي هما الستة
+
+333
+00:25:33,220 --> 00:25:38,680
+والتلاتة ستةكل واحد ديجري تلاتة و تلاتة كل واحدة
+
+334
+00:25:38,680 --> 00:25:44,200
+ديجري ستة بتطلع ل 36 يعني اتنين في عدد الخطوط اللي
+
+335
+00:25:44,200 --> 00:25:48,380
+هو بيكون عدد الخطوط 18 خط لإن ال 36 زي ما انتوا
+
+336
+00:25:48,380 --> 00:25:53,600
+عارفين يعني مضاعف عدد الخطوط جولنا اذا الكل بيكون
+
+337
+00:25:53,600 --> 00:26:00,410
+عدد الخطوط عنا 18 خطSo that K36 has 18 edges
+
+338
+00:26:00,410 --> 00:26:04,570
+تقريبا 18 خط degree sequence نعرف حاجة اسمها
+
+339
+00:26:04,570 --> 00:26:10,800
+degree sequence نشوف ايش degree sequenceالشعر الله
+
+340
+00:26:10,800 --> 00:26:16,100
+سهل يعني suppose that D1 وD2 وDn are degree of the
+
+341
+00:26:16,100 --> 00:26:18,900
+vertices of a graph يعني في عندنا graph بيسيده
+
+342
+00:26:18,900 --> 00:26:22,580
+graph زي ال graph تبعت المرة الفاتة عندنا graph G
+
+343
+00:26:22,580 --> 00:26:27,200
+هذا ال graph جينا حسبنا اللي هي فيه N من ال
+
+344
+00:26:27,200 --> 00:26:31,020
+vertices حسبنا أول واحدة لجينا انها degree D1
+
+345
+00:26:31,020 --> 00:26:38,320
+التانية D2 التلاتة Dnعندما نرتب تساعد تنازلي D1
+
+346
+00:26:38,320 --> 00:26:43,320
+أكبر سوى D2 أكبر سوى D3 أكبر سوى DN هذه الـ D1 وD2
+
+347
+00:26:43,320 --> 00:26:48,160
+وDN المرتبة اللي هي بشكل تنازلي
+
+348
+00:26:48,980 --> 00:26:55,540
+اللي هي طبعا دي واحد تمثل ال degree ل اللي هو نقطة
+
+349
+00:26:55,540 --> 00:26:58,520
+أولى هذه ال degree لتانية هذه ال degree ل الأخيرة
+
+350
+00:26:58,520 --> 00:27:03,760
+لما نرتبه انتصار تنازل زي هيك بنسميه degree
+
+351
+00:27:03,760 --> 00:27:08,220
+sequence of G اللي هي degree sequence لمين لل G في
+
+352
+00:27:08,220 --> 00:27:11,620
+الواقع degree sequence لل G لأ هي في الواقع ال
+
+353
+00:27:11,620 --> 00:27:16,530
+degree sequence لل vertices تبعات ال Gهذا اصطلاحا
+
+354
+00:27:16,530 --> 00:27:19,930
+مع بعض عشان لما نحكي عن ال degree sequence of G
+
+355
+00:27:19,930 --> 00:27:26,130
+نكون فاهمين انه بقصد انه بنجيب اللي هو ال degree
+
+356
+00:27:26,130 --> 00:27:31,910
+لكل لكل نقطة من النقاط و بعدين بنرتبها تساق تنازلي
+
+357
+00:27:31,910 --> 00:27:37,050
+ده نشوف هاي عندي مثلا V1 V2 هاي الخطوط اللي بينهم
+
+358
+00:27:37,050 --> 00:27:43,440
+ال degree لل V1 هي 1 2ال degree لل V2 هي واحد
+
+359
+00:27:43,440 --> 00:27:51,040
+اتنين تلاتة صح ال degree لل V3 هي واحد اتنين و هذا
+
+360
+00:27:51,040 --> 00:27:55,240
+زي ما .. ده مفتكرين بنحسب ايش اتنين هي اربعة و هذه
+
+361
+00:27:55,240 --> 00:27:59,260
+ال degree اللي هي ايش واحد اذا في عندي .. هي في
+
+362
+00:27:59,260 --> 00:28:04,320
+عندي اربعة هذه ال V3 اربعة ال degree لها و V2
+
+363
+00:28:04,320 --> 00:28:11,620
+اتنين V2 تلاتة اسف هي واحد هي اتنين هي تلاتةهي اذا
+
+364
+00:28:11,620 --> 00:28:17,620
+V3 V2 ال degree degree V3 degree V2 أربعة تلاتة
+
+365
+00:28:17,620 --> 00:28:21,540
+بعدين الأجل من هنا ال degree ل V12 بعدين ال degree
+
+366
+00:28:21,540 --> 00:28:26,200
+ل V4 اللي هو واحد يعني بيصير عندي the degree
+
+367
+00:28:26,200 --> 00:28:29,600
+sequence of the pseudograph هذا اللي أمامنا is
+
+368
+00:28:29,600 --> 00:28:38,600
+degree V3 اللي هي أربعة degree V2 اللي هيتلاتة
+
+369
+00:28:38,600 --> 00:28:45,200
+degree v1 التي هي واحد اتنين degree v4 التي هي
+
+370
+00:28:45,200 --> 00:28:50,560
+واحدإذاً هذه اللي هي مثال على الـ sequence degree
+
+371
+00:28:50,560 --> 00:28:55,960
+أو الـ degree sequence of this pseudograph الأمامي
+
+372
+00:28:55,960 --> 00:29:06,080
+الآن how many degree does a graph have if its
+
+373
+00:29:06,080 --> 00:29:09,920
+degree sequence is خمسة، اتنين، اتنين، اتنين،
+
+374
+00:29:09,920 --> 00:29:15,300
+اتنين، واحدdraw such a graph بقول ليه الآن جداش ال
+
+375
+00:29:15,300 --> 00:29:19,160
+degree اللي هو جداش اللي هو how many edges جداش
+
+376
+00:29:19,160 --> 00:29:24,360
+عدد ال edges اللي في ال .. اللي .. اللي في الجراف
+
+377
+00:29:24,360 --> 00:29:28,160
+اللي عندى اللي ال degree لكله اللي ال degree
+
+378
+00:29:28,160 --> 00:29:33,840
+sequence اللي هو هي how many edges of a graph أكم
+
+379
+00:29:33,840 --> 00:29:39,200
+خط في في الجرافإذا كانت ال degree sequence يعني ال
+
+380
+00:29:39,200 --> 00:29:44,820
+degree sequence شكلها بدها هي تجعلنا نعرف نرسم ال
+
+381
+00:29:44,820 --> 00:29:50,220
+graph هي اللي بتجعلنا نعرف جداش الخطوط اللي فيها
+
+382
+00:29:50,220 --> 00:29:56,100
+اللي أنا مقول is خمسة و اتنين و اتنين و اتنين و
+
+383
+00:29:56,100 --> 00:30:01,300
+اتنين و واحد أول حاجة بدي بتطلع هذول أكب نقطة هذه
+
+384
+00:30:01,300 --> 00:30:05,200
+كل واحدة نقطة من النقاطلأنه بتمثل degree للنقاط
+
+385
+00:30:05,200 --> 00:30:10,920
+هذه نقطة نقطين تلاتة أربعة خمسة ستة إذا ست نقاط
+
+386
+00:30:10,920 --> 00:30:16,280
+لما أتي أطلع ل degree النقطة هذه الأولى بقول ست
+
+387
+00:30:16,280 --> 00:30:22,500
+طالع منها اللي هي degree لها خمسة ماشي إذا رايحة
+
+388
+00:30:22,500 --> 00:30:27,080
+لواحد لاتنين لتلاتة لاربعة لخمسة إذا في إليها إيه
+
+389
+00:30:27,080 --> 00:30:32,160
+شمالها طالع منها خمس خطوط التنين طالع منها خطين
+
+390
+00:30:33,030 --> 00:30:37,010
+التنين خطين .. التنين خطين .. التنين خطين ..
+
+391
+00:30:37,010 --> 00:30:42,650
+الواحد خطين .. إذا لما أحسب ال degree .. ال degree
+
+392
+00:30:42,650 --> 00:30:48,310
+الأولى خمسةجدّاش الأولى خمسة والتانية اتنين
+
+393
+00:30:48,310 --> 00:30:50,630
+والتانية اتنين والتانية اتنين والتانية اتنين واحدة
+
+394
+00:30:50,630 --> 00:30:54,390
+هذا مجموع ال degrees لمين للنقاط اللي موجودة لأن
+
+395
+00:30:54,390 --> 00:30:57,530
+هي ال sequence لل degrees للنقاط كلها فكما
+
+396
+00:30:57,530 --> 00:31:01,090
+أعطينيها إذن أربعتاش واحنا اتفاجنا الأربعتاش أيش
+
+397
+00:31:01,090 --> 00:31:05,410
+بيساوي ان اتنين ضعف الخطوط هذه نظرية خدناها المرة
+
+398
+00:31:05,410 --> 00:31:08,770
+الماضية اتنين ضعف الخطوط يعني عدد الخطوط أيش
+
+399
+00:31:08,770 --> 00:31:12,810
+بيساوي سبعة إذا ال edges اللي موجودة هي عبارة عن
+
+400
+00:31:12,810 --> 00:31:18,470
+سبعةماشي سبعة الان كيف بتدرسمها السبعة الان باجي
+
+401
+00:31:18,470 --> 00:31:22,150
+للنقطة اللي هي اللي .. اللي هي عنده ست نقاط بحط
+
+402
+00:31:22,150 --> 00:31:26,570
+واحدة تانتين تلاتة اربعة خمسة و هي ست هي ست نقاط
+
+403
+00:31:26,570 --> 00:31:30,370
+ماشي ليش حطيتها هنا دي و ماحطيتهاش هنا لإن انا
+
+404
+00:31:30,370 --> 00:31:33,210
+عارف هذا ان في نقطة من النقاط اللي هي طالع منها
+
+405
+00:31:33,210 --> 00:31:38,490
+جداش خمس خطوط يعني طالع منها دي خط هنا و هنا خط و
+
+406
+00:31:38,490 --> 00:31:43,520
+هنا خط و هنا خطيعني طالعلها لكل خطوط فهنا أسهل في
+
+407
+00:31:43,520 --> 00:31:47,560
+الرسم بس عشان سهولة الرسم يعني واحد تاني ممكن يحط
+
+408
+00:31:47,560 --> 00:31:51,960
+هنا هنا ممكن يحطها ويقعد يرسم ويوصل بينهم بنفع هنا
+
+409
+00:31:51,960 --> 00:31:55,580
+ممكن يحطها هنا ممكن يحطها يعني ممكن يكون الرسم صح
+
+410
+00:31:55,580 --> 00:32:00,880
+لكن شكلها مختلف من واحد لواحد بس بيكون ايش الصح ان
+
+411
+00:32:00,880 --> 00:32:05,510
+النهاردة طالعلها خمس خطوط هايين هاي الخمسةالان
+
+412
+00:32:05,510 --> 00:32:09,750
+النقطة التانية التانيات كلهم واحدة تلتين تلاتة
+
+413
+00:32:09,750 --> 00:32:13,690
+اربعة كلهم اشمال فين خطين خطين خطين يعني هذه الآن
+
+414
+00:32:13,690 --> 00:32:17,650
+بتطلع بينها خطين هيدي محدد وهذه خطوهي هذه وهذه خط
+
+415
+00:32:17,650 --> 00:32:21,590
+وهذه وهذه خط وهذه وهذه خط وبنخلي واحدة بس بيطلع
+
+416
+00:32:21,590 --> 00:32:24,550
+منها خط اللي هو طال علميا لهذا النقطة خاصة عنها
+
+417
+00:32:24,550 --> 00:32:28,730
+عشان نسينا الخمسة دولار فهذا بيكون اللي هو رسمنا ل
+
+418
+00:32:28,730 --> 00:32:34,110
+graph من وعرفنا جداش عدد الخطوط من خلال اللي هو
+
+419
+00:32:34,110 --> 00:32:40,300
+معرفة ال degreeسيكوانس للـ vertices تبعات ال graph
+
+420
+00:32:40,300 --> 00:32:45,660
+و هي كما نكون احنا خلصنا المحاضرة رقم 11 وهي عندكم
+
+421
+00:32:45,660 --> 00:32:50,460
+ال homework المطلوب تحلو و تسلمونيها كالعادة ان
+
+422
+00:32:50,460 --> 00:32:53,700
+شاء الله و إلى لقاء اخر السلام عليكم و رحمة الله
+
+423
+00:32:53,700 --> 00:32:54,280
+وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..34dec97256615bb980bd0ea236424f1b647f13f3
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4.srt
@@ -0,0 +1,1659 @@
+1
+00:00:00,930 --> 00:00:06,630
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم عشرة
+
+2
+00:00:06,630 --> 00:00:12,170
+لمساق رياضيات منفصلة لطلاب وطالبات الجامعة 
+
+3
+00:00:12,170 --> 00:00:17,470
+الإسلامية كلية تكنولوجيا المعلومات قسم الحوسبة
+
+4
+00:00:17,470 --> 00:00:22,690
+المتنقلة اليوم إن شاء الله هنبدأ في الفصل الأخير
+
+5
+00:00:22,690 --> 00:00:28,290
+في المادة اللي هو فصل عشرة تحت عنوان Graphs
+
+6
+00:00:30,140 --> 00:00:36,120
+هنجي اللي هو نعرف إيش هو معنى Graphs إيش معنى
+
+7
+00:00:36,120 --> 00:00:42,500
+الـ Graph؟ a graph هو باختصار is a pair of V و E of
+
+8
+00:00:42,500 --> 00:00:49,640
+V يعني هو عبارة عن زوج من V مجموعة و E مجموعة الآن
+
+9
+00:00:49,640 --> 00:00:54,820
+V إيش هي و E إيش هي؟ هنشوف إيش الآن بالتفصيل إيش
+
+10
+00:00:54,820 --> 00:00:59,760
+هي الـ V و إيش هي الـ E؟ V non-empty set اللي هي
+
+11
+00:00:59,760 --> 00:01:06,020
+مجموعة غير خالية and each element of the set E of E
+
+12
+00:01:06,020 --> 00:01:10,120
+is a set يعني كل element في الـ E عبارة عن set الـ
+
+13
+00:01:10,120 --> 00:01:14,420
+set هذه بس مكونة منها مكونة بس من عنصرين الـ set E
+
+14
+00:01:14,420 --> 00:01:19,720
+هذه عناصرها عناصرها عبارة عن مجموعات كل مجموعة
+
+15
+00:01:19,720 --> 00:01:24,760
+مكونة من عنصرين، هذول العنصرين من وين جايين؟ من الـ V
+
+16
+00:01:24,760 --> 00:01:31,480
+اللي هي كما مرة and each element of E is a set يعني
+
+17
+00:01:31,480 --> 00:01:34,840
+كل element في الـ E عبارة عن set of two distinct
+
+18
+00:01:34,840 --> 00:01:39,760
+elements من عنصرين مختلفين من وين؟ من الـ V of V
+
+19
+00:01:39,760 --> 00:01:46,040
+الآن هي الـ E مثلاً V1 و V2 موجودات عناصر في مين؟ في
+
+20
+00:01:46,040 --> 00:01:53,600
+V فالـ and E عناصرها عبارة عن الـ set المكونة من V1
+
+21
+00:01:53,600 --> 00:02:02,340
+و V2 أو اللي هو بنقول V1 join V2 هذا عنصر من عناصر
+
+22
+00:02:02,340 --> 00:02:07,140
+اللي هو الـ set E هل جيت تضحي الصورة أكثر؟ اصبروا
+
+23
+00:02:07,140 --> 00:02:13,240
+عليها، الـ elements of V called vertices يعني عناصر
+
+24
+00:02:13,240 --> 00:02:19,700
+الـ V هذه بنسميها vertices رؤوس يعني الآن كل عنصر من
+
+25
+00:02:19,700 --> 00:02:24,960
+عنصر الـ V بنسميه رأس، بعد شوية كل عنصر من عناصر الـ
+
+26
+00:02:24,960 --> 00:02:32,280
+E اللي هو بتكون من رأسين V1 و V2 بنسميه Edge أو خط
+
+27
+00:02:32,280 --> 00:02:40,870
+هذا اللي هو عنصر من عناصر الـ E، الآن الـ elements of
+
+28
+00:02:40,870 --> 00:02:48,570
+E عناصر الـ E is an unordered pairs يعني عناصر
+
+29
+00:02:48,570 --> 00:02:52,730
+الـ E عبارة عن أزواج غير مرتبة ما بنقولش عنها أزواج
+
+30
+00:02:52,730 --> 00:02:58,010
+مرتبة لأ of vertices إذن عناصر الـ E اللي هي عبارة
+
+31
+00:02:58,010 --> 00:03:06,080
+عن كل عنصر في الـ E عبارة عن زوج من العناصر اللي هي
+
+32
+00:03:06,080 --> 00:03:12,760
+من الـ vertices بنسميها إيش؟ Edge يعني عناصر الـ E هو
+
+33
+00:03:12,760 --> 00:03:16,700
+عبارة عنصر الـ E زي واحد من عناصر الـ E اللي هو الـ
+
+34
+00:03:16,700 --> 00:03:26,780
+Edge V1 V2 يعني V1 و V2 هذا عنصر من عناصر الـ E هذا
+
+35
+00:03:26,780 --> 00:03:32,160
+العنصر V1 و V2 بنسميه Edge يعني هيو إيش عبارة عن
+
+36
+00:03:32,160 --> 00:03:37,970
+حرف، هذا الحرف عنصر من عناصر الـ E، ومن أين جاءت اللي
+
+37
+00:03:37,970 --> 00:03:43,490
+هي اللي بيكون الحرف الـ V1 و V2 من الـ V اللي هي
+
+38
+00:03:43,490 --> 00:03:47,650
+الـ V تبع الرؤوس اللي عناصرها اللي هي عبارة عن إيش؟
+
+39
+00:03:47,650 --> 00:03:52,450
+عن vertices هتتضح الصورة اصبروا شوية، نيجي لبعض
+
+40
+00:03:52,450 --> 00:03:58,440
+التسميات، بقول لي لو كان E is an edge، E هذا عنصر من
+
+41
+00:03:58,440 --> 00:04:02,260
+عناصر الـ E، الكلام اللي قبله شوية كيف E شكله
+
+42
+00:04:02,260 --> 00:04:08,000
+عبارة عن V و W عبارة عن مجموعة فيها V و W هذول الـ
+
+43
+00:04:08,000 --> 00:04:14,800
+V و W الآن V بيكون و الـ W are elements in V
+
+44
+00:04:14,800 --> 00:04:20,830
+different elements in V، الآن E جمع الـ two vertices
+
+45
+00:04:20,830 --> 00:04:27,170
+V و W يعني الـ E بتربط الـ V مع الـ W و بتربط هنا
+
+46
+00:04:27,170 --> 00:04:34,590
+و بتكون إيش؟ الـ edge اللي بدنا إياها أو بنقول أنه Or the
+
+47
+00:04:34,590 --> 00:04:39,330
+vertices v and w are said to be incident with the
+
+48
+00:04:39,330 --> 00:04:45,730
+edge vw يعني اللي اللي هي الـ vertices v و w بحدثن
+
+49
+00:04:45,730 --> 00:04:52,410
+اللي هو الـ edge اللي هي vw مش هنظل نكتب هيك اللي
+
+50
+00:04:52,410 --> 00:04:59,290
+هو العنصر اللي في E بعد شوية خلاص هنسميه V or أو V
+
+51
+00:04:59,290 --> 00:05:03,950
+joined W أو زي ما احنا شايفين هو عبارة عن اللي هو
+
+52
+00:05:03,950 --> 00:05:10,150
+الـ edge هذا طيب نشوف الآن اللي هو ندخل كمان مرة
+
+53
+00:05:10,150 --> 00:05:15,350
+ناخد بعض التسميات، two vertices are adjacent يعني
+
+54
+00:05:15,350 --> 00:05:18,650
+بنقول عن two vertices راسين إنهم جانب بعض
+
+55
+00:05:18,650 --> 00:05:23,930
+متجاورين أو جايات ورا بعض or neighborhoods يعني
+
+56
+00:05:23,930 --> 00:05:29,990
+جيران، If they are the end vertices of an edge يعني
+
+57
+00:05:29,990 --> 00:05:32,630
+بتقول عن two vertices in an adjacent أو
+
+58
+00:05:32,630 --> 00:05:38,110
+neighborhood إذا كان الاتنين هدول بيكونوا من الـ edge
+
+59
+00:05:38,110 --> 00:05:43,460
+يعني الاتنين بيكونوا هذا الـ edge بنسميهم adjacent اللي
+
+60
+00:05:43,460 --> 00:05:46,480
+هو بتسمي اللي هو العنصرين في هذه الحالة إسمهم
+
+61
+00:05:46,480 --> 00:05:53,160
+عبارة عن adjacent اللي هي الـ الـ two vertices اللي
+
+62
+00:05:53,160 --> 00:05:57,780
+عندنا اللي هي two edges اتنين اللي هو two edges هي
+
+63
+00:05:57,780 --> 00:06:02,320
+edge و هدق هي edge بنقول عنهم adjacent متجاورتين
+
+64
+00:06:02,320 --> 00:06:06,440
+if they have a vertex in common إذا كان في عندهم
+
+65
+00:06:06,440 --> 00:06:12,310
+رأس مشترك يعني إذا الراس هذا طلع edge وهي edge مع
+
+66
+00:06:12,310 --> 00:06:15,390
+الرأس هذا وهذا الرأس نفسه طلع مع هذا الرأس edge
+
+67
+00:06:15,390 --> 00:06:20,790
+بنقول إن هذا الـ edge وهذا الـ edge adjacent هذا الـ
+
+68
+00:06:20,790 --> 00:06:24,490
+edge هو عناصر الـ E capital وهذا هو عناصر الـ E
+
+69
+00:06:24,490 --> 00:06:30,330
+capital والرؤوس هي عناصر من الـ V اللي سميناها اللي
+
+70
+00:06:30,330 --> 00:06:36,780
+هي الـ set، الـ graph عبارة عن V و عن E، الآن the
+
+71
+00:06:36,780 --> 00:06:40,840
+number of the edges that incident with a vertex v
+
+72
+00:06:40,840 --> 00:06:43,580
+is called the degree of the vertex إيش اللي بقوله
+
+73
+00:06:43,580 --> 00:06:48,580
+هذا؟ بقول لك الآن بدنا نعرف الـ degree لمين؟ للـ vertex
+
+74
+00:06:48,580 --> 00:06:51,840
+هذا أحد الأهداف اللي بدنا نعرفها اليوم إيش الـ
+
+75
+00:06:51,840 --> 00:06:57,660
+degree للـ vertex؟ هو عبارة عن عدد الـ edges اللي
+
+76
+00:06:57,660 --> 00:07:03,010
+بيطلع من الـ vertex يعني the number of edges that
+
+77
+00:07:03,010 --> 00:07:06,870
+incident with a vertex V is called the degree of
+
+78
+00:07:06,870 --> 00:07:11,510
+the vertex بتضح معي المثال الآن if إذا كان طلع
+
+79
+00:07:11,510 --> 00:07:14,410
+عندي الـ degree للـ V بعد شوية بنحسب يا جماعة بس
+
+80
+00:07:14,410 --> 00:07:18,430
+خليني نسمي بعض التسميات if الـ degree للـ V اللي هو
+
+81
+00:07:18,430 --> 00:07:23,970
+الـ degree للـ vertex درجة الـ vertex كانت odd أو even
+
+82
+00:07:23,970 --> 00:07:28,410
+بنقول we say that V is an odd أو even vertex إذا
+
+83
+00:07:28,410 --> 00:07:32,070
+لما نقول odd vertex أو even vertex معناته الـ
+
+84
+00:07:32,070 --> 00:07:38,350
+degree للـ vertex even أو odd، طيب الآن a vertex of
+
+85
+00:07:38,350 --> 00:07:42,970
+degree zero يعني الـ vertex اللي degree له zero is
+
+86
+00:07:42,970 --> 00:07:47,470
+called an isolated vertex يعني الـ degree له zero
+
+87
+00:07:47,470 --> 00:07:53,510
+يعني ما فيش بتطلعش منه ولا خط، ما فيش ولا خط بيروح منه
+
+88
+00:07:53,510 --> 00:07:57,210
+عشان هيك بنقول عنها النقطة إيه؟ الـ isolated
+
+89
+00:07:57,210 --> 00:08:02,490
+vertex يعني معزولة ما فيش فيها ولا خط طالع منها
+
+90
+00:08:02,490 --> 00:08:07,280
+الآن neighborhood of a vertex يعني الجوار تبع الـ
+
+91
+00:08:07,280 --> 00:08:11,300
+vertex بنسميه الـ neighborhood إيش جوار الـ vertex؟ كل اللي
+
+92
+00:08:11,300 --> 00:08:16,020
+هي النقاط اللي بتصنع مع الـ إيه؟ الـ edges تبعتها
+
+93
+00:08:16,020 --> 00:08:20,180
+هنشوف هذا الكلام كله هتلاقوه سهل، شوفوا الآن صلوا
+
+94
+00:08:20,180 --> 00:08:23,000
+على النبي عليه الصلاة والسلام، نجي الآن لحاجة اسمها
+
+95
+00:08:23,000 --> 00:08:26,460
+pseudograph الـ graph بيسموه pseudograph أو graph
+
+96
+00:08:26,460 --> 00:08:30,060
+زائف، إيش هذا الـ graph؟ هذا هو graph like a graph
+
+97
+00:08:30,060 --> 00:08:34,960
+بشبه لـ graph هو graph but it may contains loops يعني
+
+98
+00:08:34,960 --> 00:08:38,640
+ممكن تحتوي على إيش؟ على loop، أي loop يعني الـ loop
+
+99
+00:08:38,640 --> 00:08:43,920
+بيجي من النقطة و برجع للنقطة نفسها أو a multiple of
+
+100
+00:08:43,920 --> 00:08:47,040
+edges أو بيحتوي على multiple edges يعني هي من هذا
+
+101
+00:08:47,040 --> 00:08:53,160
+لهنا هي أول خط و برضه هي كمان خط من V2 لعند V1 الـ
+
+102
+00:08:53,160 --> 00:08:57,760
+graph اللي بيحتوي على اللي هو multiple edges يعني
+
+103
+00:08:57,760 --> 00:09:04,000
+أكثر من خط بين النقطتين أو اللي هو اللي هي loop خط
+
+104
+00:09:04,000 --> 00:09:08,980
+بيروح للنقطة و برجع لها بنسميه اللي هو pseudo graph
+
+105
+00:09:09,430 --> 00:09:13,650
+خلينا ناخد المثال هذا و نيجي نحسب اللي بدنا نحسبه
+
+106
+00:09:13,650 --> 00:09:21,370
+اللي هو الـ degree للـ V3 مثلاً للـ V3 ماشي الآن قبل
+
+107
+00:09:21,370 --> 00:09:25,290
+ما نحسب الـ degree للـ V3 خلينا نحسب الـ degree للـ
+
+108
+00:09:25,290 --> 00:09:32,230
+V1 إيش الـ degree للـ V1؟ إيش الخطوط اللي بتطلع
+
+109
+00:09:32,230 --> 00:09:37,820
+منها؟ هي اتنين فبيكون الـ degree للـ V واحد اتنين، طب
+
+110
+00:09:37,820 --> 00:09:42,320
+نيجي للـ V تلاتة الـ V تلاتة بيطلع هاي خط هاي خطين
+
+111
+00:09:42,320 --> 00:09:49,520
+ماشي لكن الـ V تلاتة اللي هو بيطلع خط منها in و خط
+
+112
+00:09:49,520 --> 00:09:55,120
+منها out، الـ Loop بنحسبه دائماً اتنين في الـ degree
+
+113
+00:09:55,120 --> 00:10:00,980
+يعني بنحسب واحد in و واحد out فبيصير عنده اتنين وهي
+
+114
+00:10:00,980 --> 00:10:04,800
+كمان خط وهي كمان خط فبيصير الـ degree للـ V3 إيش؟
+
+115
+00:10:04,800 --> 00:10:09,000
+بيساوي أربعة، الـ degree للـ V3 بيساوي أربعة because
+
+116
+00:10:09,000 --> 00:10:17,120
+it connected E3 لأنها بتعمل الـ edge E3 و بتعمل الـ
+
+117
+00:10:17,120 --> 00:10:23,500
+edge E4 و الـ edge E5 اللي هو under the loop E5
+
+118
+00:10:23,500 --> 00:10:29,680
+edge computed 2 واحد as in و واحد as out، ده الـ
+
+119
+00:10:29,680 --> 00:10:33,780
+loop بس اللي بنحسبه اتنين و الباقي بنحسبه إيش؟ واحد
+
+120
+00:10:33,780 --> 00:10:39,800
+واحد فبيصير الـ degree للـ V3 بعدد الخطوط اللي طالعة
+
+121
+00:10:40,370 --> 00:10:45,650
+اللي هي منها أو اللي داخلة إلها وهذا ينحسب اتنين في
+
+122
+00:10:45,650 --> 00:10:50,190
+حالة الـ loop، طيب نيجي الآن undirected graphs حاجة
+
+123
+00:10:50,190 --> 00:10:52,790
+اسمها undirected graphs أو الـ graphs اللي بتكون
+
+124
+00:10:52,790 --> 00:10:57,600
+إيه؟ غير متجهة، طيب غير متجهة جدًا بنعرف لأنه
+
+125
+00:10:57,600 --> 00:11:00,780
+هنأخذ الـ Directed Graph بعد شوية بنعرف شو معناه
+
+126
+00:11:00,780 --> 00:11:05,480
+Undirected Undirected يعني مش فارغة من A ل B أو من
+
+127
+00:11:05,480 --> 00:11:10,460
+B ل A مش مرتبة What are the degree and what are 
+
+128
+00:11:10,460 --> 00:11:13,640
+the neighborhoods of the vertices in the graph
+
+129
+00:11:13,640 --> 00:11:18,560
+Undirected؟ الآن بدنا نعرف إيش ال degree وإيش ال
+
+130
+00:11:18,560 --> 00:11:21,440
+neighborhoods للنقاط اللي موجودة عندي هدول ال
+
+131
+00:11:21,440 --> 00:11:26,700
+vertices اللي عندي ال degree لل vertices واللي هي
+
+132
+00:11:26,700 --> 00:11:30,220
+ال neighborhood لل vertices نيجي أول حاجة لل
+
+133
+00:11:30,220 --> 00:11:33,920
+degree للـ إيه ال degree للـ إيه يعني قداش .. إيش
+
+134
+00:11:33,920 --> 00:11:38,000
+الخطوط اللي طالعة منها هاي خط هاي اثنين إذا هذا
+
+135
+00:11:38,000 --> 00:11:42,240
+عندها ال degree إيش بتساوي اثنين طيب ال degree لل
+
+136
+00:11:42,240 --> 00:11:47,850
+B كلكم حقول هاي واحدة هي اثنين هي ثلاثة هي أربع
+
+137
+00:11:47,850 --> 00:11:52,070
+خطوط طالعين منها إذا ال degree لل B إيش أربعة لو
+
+138
+00:11:52,070 --> 00:11:56,230
+حد جالك ال degree لل C لل C هتقول هي واحد هي اثنين
+
+139
+00:11:56,230 --> 00:12:01,030
+هي ثلاثة هي أربعة لو جالك ال degree لل G هتقول لي
+
+140
+00:12:01,030 --> 00:12:05,110
+صفر عشان هيك بنسميها isolated معزولة في الشاشة
+
+141
+00:12:05,110 --> 00:12:09,310
+بتطلع منها طيب ال degree اللي الآن ال neighbor هد
+
+142
+00:12:09,310 --> 00:12:14,830
+ولمن؟ لل A جوار ال A جوار ال A اللي بيعمل الخطوط
+
+143
+00:12:14,830 --> 00:12:18,170
+معها جوار ال A اللي بيعمل الخطوط معها مين اللي
+
+144
+00:12:18,170 --> 00:12:22,470
+بيعمل الخط مع ال A؟ ال B وال F عشان هيك بنقول
+
+145
+00:12:22,470 --> 00:12:27,710
+جوار ال A هو ال B وال F نيجي الآن يا جماعة إيش
+
+146
+00:12:27,710 --> 00:12:31,350
+جوار ال B اللي بيعمل الخطوط مع ال B؟ إيش مين اللي
+
+147
+00:12:31,350 --> 00:12:38,820
+بيعمل الخطوط مع ال B؟ ال C وال E وال F والـ A هي
+
+148
+00:12:38,820 --> 00:12:44,980
+A وC وE وF هدول جوار من الـ B الآن جوار الـ D
+
+149
+00:12:44,980 --> 00:12:47,540
+اللي بيعمل الخطوط مع الـ D ما فيش حد بيعمل الخطوط
+
+150
+00:12:47,540 --> 00:12:51,340
+مع الـ D العالمين الـ C لكن لو جينا لجوار الـ G
+
+151
+00:12:51,340 --> 00:12:59,660
+هنلاقي ما فيش إيش فاي عشان هي كانت بنسميها isolated إيش
+
+152
+00:12:59,660 --> 00:13:06,640
+point اللي بيكونش إلها ولا جوار أو بتكونش عاملة أو
+
+153
+00:13:06,640 --> 00:13:10,240
+ال degree إلها بتساوي صفر مش ولا خط طالع منها أو
+
+154
+00:13:10,240 --> 00:13:14,140
+جاي نيجي الآن ناخد مثال آخر what are the degree
+
+155
+00:13:14,140 --> 00:13:17,820
+and what are the neighborhoods of the vertices in
+
+156
+00:13:17,820 --> 00:13:20,980
+the undirected graph خلينا هذا ال graph ال
+
+157
+00:13:20,980 --> 00:13:24,870
+undirected اللي غير متجه اللي يعني تفرجش من A لعند
+
+158
+00:13:24,870 --> 00:13:29,630
+B أو من B لعند A ما فيش اتجاه عندنا الآن نشوف اللي هو
+
+159
+00:13:29,630 --> 00:13:32,950
+يسأل سؤاله ال degree لل A إيش ال degree لل A هاي
+
+160
+00:13:32,950 --> 00:13:38,650
+واحد هاي اثنين هاي ثلاثة هاي أربعة ال degree لل A
+
+161
+00:13:38,650 --> 00:13:43,090
+نيجي لل degree لمين لل B ال degree لل B هاي واحد
+
+162
+00:13:43,090 --> 00:13:50,590
+هاي اثنين هاي ثلاثة هذه أربعة وقلنا ال loop نحسب
+
+163
+00:13:50,590 --> 00:13:56,790
+كأنه out وin اثنين يعني إيش بيصير ال degree ل ال
+
+164
+00:13:56,790 --> 00:14:02,910
+B 6 نيجي ال neighborhood لل A جوار ال A اللي هي
+
+165
+00:14:02,910 --> 00:14:07,930
+النقاط اللي بيصنع معها خطوط مين بيصنع معها
+
+166
+00:14:07,930 --> 00:14:16,640
+خطوط بيه؟ O D O E B D E نعود للـ neighborhood للـ B
+
+167
+00:14:16,640 --> 00:14:20,020
+ال neighborhood للـ B من يصنع الخطوط معاها الـ A
+
+168
+00:14:20,020 --> 00:14:29,020
+والـ E والـ A الـ D آسف والـ C ونفسه لأن هو بيصنع
+
+169
+00:14:29,020 --> 00:14:33,420
+خط مع نفسه إذا بده ينحط في neighborhood للـ B الـ
+
+170
+00:14:33,420 --> 00:14:38,520
+B لاحظ إنه لما يكون في داخل ال neighborhood للـ B
+
+171
+00:14:38,520 --> 00:14:43,470
+الـ B معناته إنه في Loop هي ال neighborhood للـ A
+
+172
+00:14:43,470 --> 00:14:47,210
+في الشيء A إذا ما في Loop ال neighborhood لل B فيه
+
+173
+00:14:47,210 --> 00:14:51,230
+B جواته إذا ما في Loop يعني فيه خط جاي منه لنفسه
+
+174
+00:14:51,230 --> 00:14:56,750
+طيب نيجي الآن اللي هو ناخد نحاول اللي هو أمثلة
+
+175
+00:14:56,750 --> 00:15:00,330
+بقدر الإمكان ومفاهيم زي ما بدنا طيب ال
+
+176
+00:15:00,330 --> 00:15:03,270
+neighborhood لل D neighborhood لل D من نفس الأسلوب
+
+177
+00:15:03,270 --> 00:15:05,730
+إيش ال neighborhood لل D اللي هو مين اللي مال
+
+178
+00:15:05,730 --> 00:15:12,100
+الخطوط معاه اللي هي ال B وال A وال E الـ B والـ A
+
+179
+00:15:12,100 --> 00:15:15,720
+والـ E هيها ال neighborhood للـ A الـ A هيها الـ
+
+180
+00:15:15,720 --> 00:15:22,610
+D وهي الـ B وهي الـ A الآن بتصور الصورة واضحة إنها
+
+181
+00:15:22,610 --> 00:15:27,770
+وصارت اللي هي الأمور واضحة تماما لتنشوف الآن graph
+
+182
+00:15:27,770 --> 00:15:31,530
+example الآن نرجع لل graph لأن زي ما اتفقنا ال
+
+183
+00:15:31,530 --> 00:15:36,210
+graph هو عبارة عن إيش عن V و E ال V هي إيش عبارة
+
+184
+00:15:36,210 --> 00:15:43,130
+عن vertices هاي V V1 V2 V3 V4 V5 V6 إذا مجموعة من
+
+185
+00:15:43,130 --> 00:15:48,380
+النقاط تسمى vertices أو تسمى رؤوس هذا الـ Graph
+
+186
+00:15:48,380 --> 00:15:53,100
+عبارة عن مجموعة V ومجموعة ثانية E الـ E هي خطوط
+
+187
+00:15:53,100 --> 00:15:58,360
+يعني هذه نقاط أو رؤوس وهذه خطوط هذا الـ Graph الـ
+
+188
+00:15:58,360 --> 00:16:03,780
+Graph عبارة عن مجموعة من ال vertices الرؤوس
+
+189
+00:16:03,780 --> 00:16:10,850
+ومجموعة أخرى من ال edges المصموعة من الرؤوس V إذا
+
+190
+00:16:10,850 --> 00:16:14,890
+نوضح إيش هو ال graph على بعضه ال graph هو عبارة عن
+
+191
+00:16:14,890 --> 00:16:19,210
+مجموعتين واحدة مجموعة الرؤوس والثانية مجموعة
+
+192
+00:16:19,210 --> 00:16:25,290
+الخطوط التي تكون من هذه الرؤوس بطريقة ما طيب ال NE
+
+193
+00:16:25,290 --> 00:16:30,890
+هيها V1 joined V4 اللي يعني باختصار V1 V4 الخط V1
+
+194
+00:16:30,890 --> 00:16:45,530
+V4 V1 V6 V1 V6 V2 V5 V2 V5 V4 V5 V4 V5 V5 V6 إذن هي
+
+195
+00:16:45,530 --> 00:16:50,310
+تعبيرا آخر عن مين عن الخطوط يعني ممكن واحد يكتب V1
+
+196
+00:16:50,310 --> 00:17:00,590
+V4 خلاص V1 V6 V2 V5 V4 V5 V5 V6 مش فارق الترتيب
+
+197
+00:17:00,590 --> 00:17:06,820
+هنا اه هنا مش فارق الترتيب ليش؟ لأن عندي اللي هو
+
+198
+00:17:06,820 --> 00:17:13,160
+ال هذا بنسمي undirected graph يعني graph غير متجه
+
+199
+00:17:13,160 --> 00:17:17,440
+يعني ما فرجش عندي v1 ل v4 و v4 ل v1 ما فيش اتجاهات
+
+200
+00:17:17,440 --> 00:17:22,940
+ماحدش حاجة به طيب الآن لو الآن note that بقول v3
+
+201
+00:17:22,940 --> 00:17:27,860
+is an isolated vertex زي ما عملنا قبل شوية ليش لأن
+
+202
+00:17:27,860 --> 00:17:32,800
+ال degree ل ال v3 ما فيش ولا إيش بيطلع منه اللي هو إيش
+
+203
+00:17:32,800 --> 00:17:38,520
+بيساوي؟ بيساوي صفر طيب، الآن ال vertex، بدنا نسميه
+
+204
+00:17:38,520 --> 00:17:44,000
+تسميه الآن a vertex is .. is .. اللي هو بنسميه a
+
+205
+00:17:44,000 --> 00:17:49,880
+vertex بنسميه is pendent if and only if it has
+
+206
+00:17:49,880 --> 00:17:54,240
+degree one يعني ال vertex اللي بيكون degree تبعته
+
+207
+00:17:54,240 --> 00:18:00,260
+واحد، بنسميه pendent ماشي V2 مثلا V2 is a pendant
+
+208
+00:18:00,260 --> 00:18:05,420
+ليش لأنه ما فيش لغير اللي هو خط واحد طالع منه لعند V
+
+209
+00:18:05,420 --> 00:18:08,140
+خمسة يعني ال adjacent له بس خمسة أو ال
+
+210
+00:18:08,140 --> 00:18:12,040
+neighborhood له ال V خمسة يعني هذا اللي هو ال
+
+211
+00:18:12,040 --> 00:18:16,420
+degree له بيساوي واحد مدام ال degree له بيساوي واحد
+
+212
+00:18:16,420 --> 00:18:24,630
+إذا على طول اللي هو بنسميه pendant طيب هنا في نظرية
+
+213
+00:18:24,630 --> 00:18:29,310
+hand shaking theorem بيقول ال sum of the degree
+
+214
+00:18:29,310 --> 00:18:34,150
+of the vertices of an undirected graph بسيده graph
+
+215
+00:18:34,150 --> 00:18:39,670
+is even number or equal to twice the number of
+
+216
+00:18:39,670 --> 00:18:44,690
+edges إيش اللي بيقوله بقول يا جماعة لو أنت جيت أخدت
+
+217
+00:18:44,690 --> 00:18:48,970
+ال graph اللي عندك كي عندك فيه graph graph V و V و
+
+218
+00:18:48,970 --> 00:18:53,570
+جيت لك كل ال vertices ال V وحسبت كل الرؤوس هنا
+
+219
+00:18:53,570 --> 00:18:58,770
+حسبت ال degree لكل رأس وجمعت كل ال degree تبعات
+
+220
+00:18:58,770 --> 00:19:01,510
+الرؤوس يعني الرأس الأول degree قداش الرأس الأول
+
+221
+00:19:01,510 --> 00:19:04,910
+ثاني degree قداش لما خلصت على كل الرؤوس عرفت
+
+222
+00:19:04,910 --> 00:19:09,610
+درجاتهم بجمع درجات الرؤوس بجمع درجات الرؤوس اللي
+
+223
+00:19:09,610 --> 00:19:14,770
+هي ال vertices بلاقيهم دائما دائما دائما بيساوي
+
+224
+00:19:14,770 --> 00:19:21,230
+اثنين في عدد ال edges في عدد عناصر من ال E عناصر
+
+225
+00:19:21,230 --> 00:19:26,970
+من ال E إيش هي خطوط يعني بمعنى آخر عدد مجموع
+
+226
+00:19:26,970 --> 00:19:34,550
+مجموع مجموع درجات ال vertices بيساوي ضعف عدد الخطوط
+
+227
+00:19:34,550 --> 00:19:38,870
+يعني لو ضربنا اثنين في عدد الخطوط عدد عناصر ال E
+
+228
+00:19:38,870 --> 00:19:46,830
+هلاقيهم دائما بيساوي إيش مجموع درجات ال vertices أو
+
+229
+00:19:46,830 --> 00:19:50,270
+أنت امسك مثال وجرب على اللي حكيناه وخلينا نجرب
+
+230
+00:19:50,270 --> 00:19:54,470
+على هذا المثال مثلا هاي في عندي اللي هو graph
+
+231
+00:19:54,470 --> 00:19:59,270
+undirected graph وهي ال vertices تبع عيوننا V1 V2
+
+232
+00:19:59,270 --> 00:20:05,110
+V3 V4 وهي اللي هي ال edges تبعاته أو الخطوط إيش
+
+233
+00:20:05,110 --> 00:20:09,730
+الخطوط اللي موجودة هيها واحد اثنين ثلاثة أربعة خمسة
+
+234
+00:20:09,730 --> 00:20:14,410
+ست خطوط V1 V2 طبعا هذا في ال degree بنحسب اثنين
+
+235
+00:20:14,410 --> 00:20:22,230
+لكن هو E بالساوية V1 V2 V2 V3 V1 V3 V3 V4 V4 V1 V3
+
+236
+00:20:22,230 --> 00:20:27,050
+V3 هي الخطوط قداش واحد اثنين آسف عناء ال edges
+
+237
+00:20:27,050 --> 00:20:32,470
+تبعات ال E واحد اثنين ثلاثة أربعة خمسة ستة الآن تعالى
+
+238
+00:20:32,470 --> 00:20:38,250
+احسب ال degree لكل واحد من هدول واجمعهم هتلاقيهم
+
+239
+00:20:38,250 --> 00:20:41,850
+اثنا عشر هاي واحد، هاي اثنين، هاي ثلاثة، هاي أربعة،
+
+240
+00:20:41,850 --> 00:20:46,850
+هاي خمسة، هاي ستة لازم لو أخدت ال degree لهذه زائد
+
+241
+00:20:46,850 --> 00:20:49,250
+ال degree لهذه زائد ال degree لهذه زائد ال degree
+
+242
+00:20:49,250 --> 00:20:54,710
+لهذه يطلع مجموع ال degrees اثنين في ستة حسب
+
+243
+00:20:54,710 --> 00:20:57,550
+القانون أنا اثنا عشر يعني هيطلع لنا اثنا عشر degree
+
+244
+00:20:57,550 --> 00:21:02,270
+مجموحين ده نشوف نجرب ال degree لل V واحد إيه واحد
+
+245
+00:21:02,270 --> 00:21:06,730
+هي اثنين هي ثلاثة طيب ال degree لل V اثنين واحد
+
+246
+00:21:06,730 --> 00:21:11,630
+اثنين ال degree لل V ثلاثة هي واحد هي اثنين هي
+
+247
+00:21:11,630 --> 00:21:16,310
+ثلاثة وال loop بنحسب اثنين أو two in هي خمسة وال
+
+248
+00:21:16,310 --> 00:21:20,770
+degree لل V4 قداش اثنين هي واحد هي اثنين اجمع ليه
+
+249
+00:21:20,770 --> 00:21:23,710
+هنا دولة ثلاثة واثنين خمسة وخمسة عشر واثنين
+
+250
+00:21:23,710 --> 00:21:29,500
+اثنا عشر فعلا اثنا عشر بيساوي ستة اللي هي عدد عناصر هدول 
+
+251
+00:21:29,500 --> 00:21:32,920
+في اثنين بطلع ايش اثنين عشر ايه ده ايه ده انها دي
+
+252
+00:21:32,920 --> 00:21:37,160
+hand shaking theorem هي كده هي تقول إذا ال
+
+253
+00:21:37,160 --> 00:21:40,980
+summation لل edge لل V هي هي هي بساوة اثنين في
+
+254
+00:21:40,980 --> 00:21:46,020
+اللي اثنين في ستة بساوة اثنين عشر الان sum of degree
+
+255
+00:21:46,020 --> 00:21:49,680
+اللي هو مثال عالي جايبه شوية بقول لي how many edges
+
+256
+00:21:50,490 --> 00:21:55,030
+كم edges يعني قد ايش عناصر الـ E are there in a
+
+257
+00:21:55,030 --> 00:22:00,540
+graph في الـ graph اللي ال vertices له عشرة each of
+
+258
+00:22:00,540 --> 00:22:04,320
+degree six يعني بيقول لي عندي .. عندي اللي هو
+
+259
+00:22:04,320 --> 00:22:09,920
+vertices عشر vertices عشر رؤوس كل راس منهم ال
+
+260
+00:22:09,920 --> 00:22:15,220
+degree له ستة مدام ال degree له ستة الان بيصير
+
+261
+00:22:15,220 --> 00:22:20,620
+اللي هم مجموع اللي هي ال vertices هدول مجموع ال
+
+262
+00:22:20,620 --> 00:22:26,020
+degrees له عشرة في ستة بستين مظبوط ستين اللي هم
+
+263
+00:22:26,020 --> 00:22:30,950
+بيساوون اثنين مضروبة في مين في عدد عناصر ال graph
+
+264
+00:22:30,950 --> 00:22:34,390
+إذا العدد عناصر ال edge إذا ال edge لازم يطلع ايه؟
+
+265
+00:22:34,390 --> 00:22:37,390
+اللي هي ستين على اثنين وهي ثلاثين شوف ايش
+
+266
+00:22:37,390 --> 00:22:40,770
+اللي بقوله because the sum of the degrees of the
+
+267
+00:22:40,770 --> 00:22:44,630
+vertices is ستة في عشرة يعني الان ال vertices عشرة
+
+268
+00:22:44,630 --> 00:22:48,650
+و كل واحد ال degree له ستة بيصير مجموعة degrees لل
+
+269
+00:22:48,650 --> 00:22:53,740
+vertices ستين it follows that اثنين في M M ايش هي
+
+270
+00:22:53,740 --> 00:22:58,580
+عبارة عن عدد عناصر ال E فرضناها اه اثنين M بساوي
+
+271
+00:22:58,580 --> 00:23:03,400
+ستين اللي هي where M is the number of edges ماشي
+
+272
+00:23:03,400 --> 00:23:06,220
+اللي انا مش اللي انا مش ال E هذا مش مظبوطة هيك
+
+273
+00:23:06,220 --> 00:23:11,570
+اثنين M بساوي ايش ستين حيث ال M ايش اللي هي عدد
+
+274
+00:23:11,570 --> 00:23:15,550
+عناصر لدك therefore M ايش بتساوي بتساوي ثلاثين
+
+275
+00:23:15,550 --> 00:23:20,050
+اللي هي عدد عناصر ال M is the number of edges اللي
+
+276
+00:23:20,050 --> 00:23:23,850
+هي عدد عناصر ال E هذه فش هذا مش مظبوطة اثنين M
+
+277
+00:23:23,850 --> 00:23:28,470
+بتساوي ستين هذه طبعا فش يساوي هنا هذه ال E اللي هي
+
+278
+00:23:28,470 --> 00:23:32,610
+عبارة عن ال M is the number of edge الان اذا ال M
+
+279
+00:23:32,610 --> 00:23:35,650
+ايش بتساوي ثلاثين او عدد عناصر ال edge هذه ايش
+
+280
+00:23:35,650 --> 00:23:41,430
+بتساوي ثلاثين الان نجي للـ Directed Graph يا جماعة
+
+281
+00:23:41,430 --> 00:23:45,980
+الـ Directed Graph اللي هو خلّيني اشوف Directed
+
+282
+00:23:45,980 --> 00:23:49,480
+Graph V of E Consists .. هو نفس ال graph اللي قبل
+
+283
+00:23:49,480 --> 00:23:53,060
+بشوية بس بده يصير احنا نأخذ بعين الاعتبار الاتجاه
+
+284
+00:23:53,060 --> 00:23:58,340
+.. الترتيب يعني اتجاه من وين طالع اللي هو ال .. ال
+
+285
+00:23:58,340 --> 00:24:01,560
+.. ال .. ال vertex و اين رايحه الخط من وين طالع و
+
+286
+00:24:01,560 --> 00:24:04,660
+من وين رايحه ده نشوف ايش اللي بقوله A Directed
+
+287
+00:24:04,660 --> 00:24:09,580
+Graph V of E يعني Graph V و E زي اللي قبل Consists
+
+288
+00:24:09,580 --> 00:24:14,580
+of a set of vertices V نفس الشيء and a set of each
+
+289
+00:24:14,580 --> 00:24:19,320
+E الان الاختلاف هيجي على ال E ال E ايش بدها تصير
+
+290
+00:24:19,320 --> 00:24:23,980
+which are ordered pairs of elements of V يعني
+
+291
+00:24:23,980 --> 00:24:30,080
+عناصر ال E الان لما نقول V1 V2 خلاص V1 V2 يعني هذا
+
+292
+00:24:30,080 --> 00:24:35,620
+مش V2 V1 يعني عند ال order مهم عشان هيك بنقول عنها
+
+293
+00:24:35,620 --> 00:24:39,220
+ايش معناه directed graph يعني ordered pairs
+
+294
+00:24:39,220 --> 00:24:45,600
+عناصرها نشوف كيف هي مثلًا V بتساوي A و B و C و D هذه
+
+295
+00:24:45,600 --> 00:24:49,200
+الـ V عبارة عن ايش يا جماعة؟ هي عبارة عن the set
+
+296
+00:24:49,200 --> 00:24:54,800
+of vertices الان الـ E تبعتنا اللي هي ال edges الـ
+
+297
+00:24:54,800 --> 00:25:01,000
+E ايش الـ E؟ هي A و B و مرتبة كتبها ordered pair
+
+298
+00:25:01,000 --> 00:25:04,320
+يعني بقصدي ال a و ال b و مش بال b و ال a ال a و ال
+
+299
+00:25:04,320 --> 00:25:08,280
+b معناته انه جاي السهم من a و رايح من بيه يعني هي
+
+300
+00:25:08,280 --> 00:25:12,700
+جاي من a و رايح ل b يعني هذه ال initial point وهذه
+
+301
+00:25:12,700 --> 00:25:17,340
+ال terminal point هيك بتنفهم يعني ال a هي نقطة
+
+302
+00:25:17,340 --> 00:25:23,320
+البداية و b نقطة النهاية c و b اللي هي جاي من c و
+
+303
+00:25:23,320 --> 00:25:27,640
+رايح ل b هذه c نقطة البداية و b نقطة النهاية D و B
+
+304
+00:25:27,640 --> 00:25:32,280
+هي من D إلى B نقطة البداية وهي نقطة النهاية دي ايه
+
+305
+00:25:32,280 --> 00:25:37,220
+نقطة البداية دي ونقطة النهاية ايه إذا الان الـ A
+
+306
+00:25:37,220 --> 00:25:42,640
+ordered pairs و الـ V هيها vertices مع بعض V و E
+
+307
+00:25:42,640 --> 00:25:48,770
+بنسميها directed graph يعني graph اللي هو ايش متجه
+
+308
+00:25:48,770 --> 00:25:54,070
+يعني الاتجاه فيه بالنسبة لنا اللي هو ضروري let u
+
+309
+00:25:54,070 --> 00:25:57,890
+,v directed graph خلّيني اخذ الان اللي هي التسميات
+
+310
+00:25:57,890 --> 00:26:01,990
+اللي قلتها قبل شوية انا let u,v be an edge of the
+
+311
+00:26:01,990 --> 00:26:05,730
+graph G يعني نفترض ان ال u و ال v هو عبارة عن edge
+
+312
+00:26:05,730 --> 00:26:10,510
+يعني عنصر من عناصر ال E النقطة البداية U الان بنقصد
+
+313
+00:26:10,510 --> 00:26:15,210
+U is called the initial vertex يعني نقطة البداية
+
+314
+00:26:15,210 --> 00:26:20,530
+يعني اللي بيطلع منها من الخط is the initial vertex
+
+315
+00:26:20,530 --> 00:26:27,560
+of U V is called the terminal or end vertex of U V
+
+316
+00:26:27,560 --> 00:26:31,400
+وبنسمي ال V اللي هي ال terminal او نقطة النهاية او
+
+317
+00:26:31,400 --> 00:26:34,760
+ال end لل vertex لذن يعني الخط بيطلع من U بيروح
+
+318
+00:26:34,760 --> 00:26:39,720
+لمين ل V لذن لما نقول U و V معناته U نقطة البداية
+
+319
+00:26:39,720 --> 00:26:46,990
+adjacent to V ماشي يعني اللي هي اللي هي بجنب بالجنب
+
+320
+00:26:46,990 --> 00:26:51,850
+رايح عليه بجنب V بس رايح على مين على V ال U
+
+321
+00:26:51,850 --> 00:26:57,830
+adjacent to V يعني ذاهبة الى مين الى V يعني بجوار
+
+322
+00:26:57,830 --> 00:27:03,210
+V ذاهبة اليها لكن الـ V بالنسبة للـ U adjacent from
+
+323
+00:27:03,210 --> 00:27:09,850
+U اللي هو جنبها خارجها منها اه يعني طالعة من U و
+
+324
+00:27:09,850 --> 00:27:16,330
+رايحة لمين لل V يعني adjacent from U اللي هو اللي
+
+325
+00:27:16,330 --> 00:27:27,100
+هي بجوار الى U وهذه بجوار من V او الى V طيب ايش
+
+326
+00:27:27,100 --> 00:27:30,720
+يعني بالاقتصاد هذه نقطة اللي هي البداية وهذه نقطة
+
+327
+00:27:30,720 --> 00:27:35,740
+النهاية بالنسبة ل ال H Definition بدنا نعرف الان
+
+328
+00:27:35,740 --> 00:27:42,000
+احنا عرفنا قبل ال degree لل vertex الان بدنا نعرف
+
+329
+00:27:42,000 --> 00:27:46,980
+انه صار في عندي اللي هو نقاط داخلة و نقاط خارجة
+
+330
+00:27:46,980 --> 00:27:51,340
+خطوط داخلة و خطوط خارجة يعني هذا الخط خارج من ال U
+
+331
+00:27:51,850 --> 00:27:56,130
+وداخل عالمين عن الـ V عشان هيك بنقول in a graph
+
+332
+00:27:56,130 --> 00:28:01,150
+with directed edges the n degree of a vertex V
+
+333
+00:28:01,150 --> 00:28:06,150
+بنعرف حاجة اسمها الـ n degree اللي هي الدرجة الى
+
+334
+00:28:06,150 --> 00:28:10,390
+of a vertex V اللي هي degree و ناقص بنكتبها n
+
+335
+00:28:10,390 --> 00:28:15,550
+degree V is the number of edges with V as their
+
+336
+00:28:15,550 --> 00:28:20,530
+terminal vertex يعني اللي هو لما نقول in V يعني
+
+337
+00:28:20,530 --> 00:28:24,550
+اللي داخل على ال V يعني ال V بدها تكون النقطة
+
+338
+00:28:24,550 --> 00:28:29,810
+النهائية ال terminal إذن degree in degree لل V
+
+339
+00:28:29,810 --> 00:28:37,030
+الداخلة على ال V عدد الخطوط الداخلة على ال V إذن
+
+340
+00:28:37,030 --> 00:28:43,000
+in degree عدد الخطوط الداخلة على ال V الان out
+
+341
+00:28:43,000 --> 00:28:49,660
+degree of V عدد الخطوط الخارجة اللي هو main من ال
+
+342
+00:28:49,660 --> 00:28:54,580
+V يعني بتكون ال V initial point الان out degree
+
+343
+00:28:54,580 --> 00:28:59,080
+الخارجة من V يعني بتكون ال V عبارة عن initial
+
+344
+00:28:59,080 --> 00:29:04,600
+point نأخذ مثال الان بقول find the in degree and
+
+345
+00:29:04,600 --> 00:29:09,870
+out degree of each vertex in the graph G with
+
+346
+00:29:09,870 --> 00:29:12,930
+directed edges shown in figure 2 هي الفيجور اللي
+
+347
+00:29:12,930 --> 00:29:18,530
+قلناها بدك تحسبه ال in degree نيجي لمن لال ايه
+
+348
+00:29:18,530 --> 00:29:22,670
+نشوف ال in degree اللي هي ايه شمالها الداخل على ال
+
+349
+00:29:22,670 --> 00:29:26,090
+ايه مين الخطوط الداخل على ال ايه هاي واحد هاي اول
+
+350
+00:29:26,090 --> 00:29:31,630
+خط اثنين اللي داخل على ال ايه هاي كمان خط في
+
+351
+00:29:31,630 --> 00:29:37,690
+غيرهم؟ لا طيب ال degree للـ B ال degree لل B ال
+
+352
+00:29:37,690 --> 00:29:41,510
+degree لل B الداخل على ال B مين الداخل على ال B
+
+353
+00:29:41,510 --> 00:29:45,390
+هاي هذا داخل على ال B وهي داخل على ال B في غيرهم
+
+354
+00:29:45,390 --> 00:29:50,930
+لا إذا اثنين ال degree لل C هاي اول واحد داخل على
+
+355
+00:29:50,930 --> 00:29:56,470
+ال C الان هاي كمان واحد داخل على ال C هاي كمان
+
+356
+00:29:56,470 --> 00:30:00,150
+واحد داخل على ال C إذا ثلاث خطوط إذا ال degree in C
+
+357
+00:30:00,150 --> 00:30:04,950
+ثلاثة الان او ال degree ال degree لل a اللي هي
+
+358
+00:30:04,950 --> 00:30:11,090
+الخارجة من ال a اه الخارجة من ال a اول ايش اللي
+
+359
+00:30:11,090 --> 00:30:16,010
+خارج من a هي نفسها خارج وهي كمان واحد خارج اثنين
+
+360
+00:30:16,010 --> 00:30:20,310
+وهي كمان واحد خارج ثلاثة وهي كمان واحد خارج ايش
+
+361
+00:30:20,310 --> 00:30:25,700
+اربعة إذا لاحظوا ان اللي في ال loop اللي في ال
+
+362
+00:30:25,700 --> 00:30:32,500
+loop بنحسب انه داخل و خارج لانه داخل على ال a و
+
+363
+00:30:32,500 --> 00:30:36,980
+خارج من ال a عشان هيك في العادي بنحسب برتين هنا
+
+364
+00:30:36,980 --> 00:30:41,660
+طبعا هينحسب في الداخل و في الخارج لانه فعلا من ال
+
+365
+00:30:41,660 --> 00:30:47,200
+a ل ال a بيطلع من ال a و بيدخل لل a و بنحسب داخل و
+
+366
+00:30:47,200 --> 00:30:52,670
+خارج ال degree لل B اللي هو ال out degree اللي خرجت
+
+367
+00:30:52,670 --> 00:30:56,090
+من ال B اللي خرجت من ال B وين اللي خرجت من ال B؟
+
+368
+00:30:56,090 --> 00:31:01,090
+هاي واحد، في غيره؟ لا، هاي واحد اللي خرجت من مين؟
+
+369
+00:31:01,090 --> 00:31:06,530
+من ال C الان اللي خرجت من ال C، هاي واحد، هاي
+
+370
+00:31:06,530 --> 00:31:11,210
+اثنين، في غيرهم؟ لا، هاي اللي خرجت من ايش؟ من ال C
+
+371
+00:31:11,210 --> 00:31:20,700
+طيب، نيجي الان لنظرية بتقول للنظرية الان لاحظوا انه
+
+372
+00:31:20,700 --> 00:31:25,340
+لو جينا كانت G عند theorem let G بيساوي V و E be
+
+373
+00:31:25,340 --> 00:31:29,180
+the graph with directed edges يعني نفترض انه اللي
+
+374
+00:31:29,180 --> 00:31:33,300
+هو هذا عبارة عن graph عناصر ال E عبارة عن ordered
+
+375
+00:31:33,300 --> 00:31:39,140
+pairs يعني directed edges then اللي هو لو جيت حسبت 
+
+376
+00:31:39,140 --> 00:31:44,580
+للـ in-degree يعني عدد الخطوط اللي داخلة اللي داخلة
+
+377
+00:31:47,340 --> 00:31:52,440
+الـ N هذه اللي داخلة على الـ V لكل النقاط وجمعتهم
+
+378
+00:31:52,440 --> 00:31:57,700
+هيكون إن هما نفس عدد الخطوط الخارجية طبيعي طبيعي
+
+379
+00:31:57,700 --> 00:32:02,580
+لأنه بتكون اللي هي مش بنحسب على كل النقاط إذا مش
+
+380
+00:32:02,580 --> 00:32:07,890
+داخلة في هذا الـ .. إذا داخلة في النقطة هذه إذا مش
+
+381
+00:32:07,890 --> 00:32:11,770
+داخلة في النقطة هذه داخلة في النقطة الثانية إذا مش
+
+382
+00:32:11,770 --> 00:32:14,350
+خارجة في النقطة هذه خارجة في النقطة الثانية وما ده
+
+383
+00:32:14,350 --> 00:32:19,030
+بنجمع على كل النقاط إذا حيكون هدول هنا عدد الخطوط
+
+384
+00:32:19,030 --> 00:32:23,840
+كلهم وهدول عدد الخطوط كلهم وعدد الخطوط كل إن هما
+
+385
+00:32:23,840 --> 00:32:29,740
+من عدد الخطوط اللي هو هذه فدائماً عدد الخطوط
+
+386
+00:32:29,740 --> 00:32:34,780
+المجموعة عدد الخطوط الداخلة بيساوي مجموعة عدد
+
+387
+00:32:34,780 --> 00:32:38,420
+الخطوط الخارجية لكل النقاط طبعاً بيساوي اللي هو
+
+388
+00:32:38,420 --> 00:32:42,820
+الخطوط هذه طبعاً هذه إيه هي مجموعة الخطوط اللي هي
+
+389
+00:32:42,820 --> 00:32:48,920
+out-degree اللي هي عدد الخطوط الخارجة out-degree
+
+390
+00:32:48,920 --> 00:32:52,800
+عدد الخطوط الخارجة مجمعة على كل النقاط وهذا عدد
+
+391
+00:32:52,800 --> 00:32:57,760
+الخطوط الداخلة على كل النقاط فبيطلع عندي هذه كل
+
+392
+00:32:57,760 --> 00:33:01,560
+الخطوط اللي عندي وهذه برضه كل الخطوط لأن اللي خارج
+
+393
+00:33:01,930 --> 00:33:06,190
+في نقطة بيكون داخل في نقطة فبتنجمع اللي بنجمع حن
+
+394
+00:33:06,190 --> 00:33:10,370
+بنجمع حن فبنجمع كله على هدول بنجمع كله فبيكون نفس
+
+395
+00:33:10,370 --> 00:33:14,770
+الشيء و بيطلع عدد الخطوط الداخلة وأنت إذا كان
+
+396
+00:33:14,770 --> 00:33:19,490
+يعني شاكة روح عدلي عدد الـ in-degree  و الـ 
+ 
+397
+00:33:19,490 --> 00:33:22,350
+in-degree و الـ in-degree و الـ in-degree و الـ in-degree
+
+398
+00:33:22,350 --> 00:33:25,960
+و الـ in-degree و الـ in-degree و اجمعهم هتلاقيهم
+
+399
+00:33:25,960 --> 00:33:29,660
+بيساوين الـ out-degree و الـ out-degree و الـ
+
+400
+00:33:29,660 --> 00:33:31,240
+out-degree و الـ out-degree و الـ out-degree 
+
+401
+00:33:31,240 --> 00:33:32,520
+و الـ out-degree و الـ out-degree و الـ 
+
+402
+00:33:32,520 --> 00:33:32,720
+out-degree و الـ out-degree و الـ
+
+403
+00:33:32,720 --> 00:33:32,960
+out-degree و الـ out-degree و الـ 
+
+404
+00:33:32,960 --> 00:33:33,000
+out-degree و الـ out-degree و الـ
+
+405
+00:33:33,000 --> 00:33:33,040
+out-degree و الـ out-degree و الـ
+
+406
+00:33:33,040 --> 00:33:33,520
+out-degree و الـ out-degree و الـ
+
+407
+00:33:33,520 --> 00:33:34,400
+out-degree و الـ out-degree و الـ
+
+408
+00:33:34,400 --> 00:33:39,180
+out-degree و الـ
+
+409
+00:33:39,180 --> 00:33:44,090
+out-degree وهنا بكون عندي بكون وصلنا للـ homework
+
+410
+00:33:44,090 --> 00:33:49,110
+للمحاضرة العاشرة هي السؤال الأول هي السؤال الأول a
+
+411
+00:33:49,110 --> 00:33:53,630
+و b وعلى الرسم هذه سخلات سلة وهي السؤال الثاني كله
+
+412
+00:33:53,630 --> 00:33:58,090
+زي اللي شرحته وهي السؤال الثالث في الهداك فائلا
+
+413
+00:33:58,090 --> 00:34:02,650
+عندي إذا تلت أسئلة وإن شاء الله بتحلون تعطونيا
+
+414
+00:34:02,650 --> 00:34:07,350
+كالعادة وإلى لقاء آخر والسلام عليكم ورحمة الله
+
+415
+00:34:07,350 --> 00:34:08,630
+وبركاته
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_postprocess.srt b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..725c1c26b1928e410440a52a46323d875a4b89b3
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_postprocess.srt
@@ -0,0 +1,1660 @@
+1
+00:00:00,930 --> 00:00:06,630
+بسم الله الرحمن الرحيم هذه هي المحاضرة رقم عشرة
+
+2
+00:00:06,630 --> 00:00:12,170
+لمساق رياضيات منفصلة طلاب و طالبات الجامعة
+
+3
+00:00:12,170 --> 00:00:17,470
+الإسلامية كلية تكنولوجيا المعلومات قسم الحوثبة
+
+4
+00:00:17,470 --> 00:00:22,690
+المتنقلة اليوم ان شاء الله هنبدأ في الشبطر الأخير
+
+5
+00:00:22,690 --> 00:00:28,290
+في المادة اللي هو شبطر عشرة تحت عنوانigraphs
+
+6
+00:00:30,140 --> 00:00:36,120
+هنجي اللي هو انعرف إيش هو معناة graphs إيش معناة
+
+7
+00:00:36,120 --> 00:00:42,500
+ال graph؟ a graph هو باختصار is a pair of V و E of
+
+8
+00:00:42,500 --> 00:00:49,640
+6 يعني هو عبارة عن زوج من V مجموعة و E مجموعة الآن
+
+9
+00:00:49,640 --> 00:00:54,820
+V إيش هي و E إيش هي؟ هنشوف إيش الآن بالتفصيل إيش
+
+10
+00:00:54,820 --> 00:00:59,760
+هي ال V و إيش هي ال EV non-empty set اللي هي
+
+11
+00:00:59,760 --> 00:01:06,020
+مجموعة غير خالية and each element of a set E of E
+
+12
+00:01:06,020 --> 00:01:10,120
+is a set يعني كل element في ال E عبارة عن set ال
+
+13
+00:01:10,120 --> 00:01:14,420
+set هذه بس مكون منها مكونة بس من عنصرين ال set E
+
+14
+00:01:14,420 --> 00:01:19,720
+هذه عناصرها عناصرها عبارة عن مجموعات كل مجموعة
+
+15
+00:01:19,720 --> 00:01:24,760
+مكونة من عنصرينهدول العنصرين من وين جيات من ال V
+
+16
+00:01:24,760 --> 00:01:31,480
+اللي هي كما مرة and each element of E a set يعني
+
+17
+00:01:31,480 --> 00:01:34,840
+كل element في ال E عبارة عن set of two distinct
+
+18
+00:01:34,840 --> 00:01:39,760
+elements من عنصرين مختلفات من وين من ال E of V
+
+19
+00:01:39,760 --> 00:01:46,040
+الآن هي ال E مثلا V1 و V2 موجودات عناصر في مين في
+
+20
+00:01:46,040 --> 00:01:53,600
+V فال and Eعناصرها عبارة عن الـ set المكونة من V1
+
+21
+00:01:53,600 --> 00:02:02,340
+و V2 أو اللي هو بنقول V1 join V2 هذا عنصر من عناصر
+
+22
+00:02:02,340 --> 00:02:07,140
+اللي هو الـ set E هلجيت تضحي الصورة أكثر اصبروا
+
+23
+00:02:07,140 --> 00:02:13,240
+عليها ال elements of V called vertices يعني عناصر
+
+24
+00:02:13,240 --> 00:02:19,700
+ال V هذه بنسميها vertices رؤوس يعنيالان كل عنصر من
+
+25
+00:02:19,700 --> 00:02:24,960
+عنصر ال V بنسميه رأس بعد شوية كل عنصر من عناصر ال
+
+26
+00:02:24,960 --> 00:02:32,280
+E اللي هو بتكون من رأسين V1 و V2 بنسميه Edge او خط
+
+27
+00:02:32,280 --> 00:02:40,870
+هذا اللي هو عنصر من عناصر ال Eالأن الـ elements of
+
+28
+00:02:40,870 --> 00:02:48,570
+E عناصر الـ E is an an unordered pairs يعني عناصر
+
+29
+00:02:48,570 --> 00:02:52,730
+الـ E عبارة عن أزواج مش مرتبة ما بنقولش عنها أزواج
+
+30
+00:02:52,730 --> 00:02:58,010
+مرتبة لأ of vertices إذن عناصر الـ E اللي هي عبارة
+
+31
+00:02:58,010 --> 00:03:06,080
+عن كل عنصر في الـ E عبارة عن زوجمن العناصر اللي هي
+
+32
+00:03:06,080 --> 00:03:12,760
+من ال vertices بنسميها إيش Edge يعني عناصر ال E هو
+
+33
+00:03:12,760 --> 00:03:16,700
+عبارة عنصر ال E زي واحد من عناصر ال E اللي هو ال
+
+34
+00:03:16,700 --> 00:03:26,780
+Edge V1 V2يعني V1 و V2 هذا عنصر من عناصر الـ E هذا
+
+35
+00:03:26,780 --> 00:03:32,160
+العنصر V1 و V2 بنسميه Edge يعني هيو إيش عبارة عن
+
+36
+00:03:32,160 --> 00:03:37,970
+حرف هذا الحرف عنصر من عناصر الـ Eومن أين جاءت اللي
+
+37
+00:03:37,970 --> 00:03:43,490
+هي اللي بيكون الحرف ال V1 و V2 من ال 6V اللي هي
+
+38
+00:03:43,490 --> 00:03:47,650
+الست تبع الرؤوس اللي عناصرها اللي هي عبارة عن ايش
+
+39
+00:03:47,650 --> 00:03:52,450
+عن vertices هتتضح الصورة اصبروا شوية نيجي لبعض
+
+40
+00:03:52,450 --> 00:03:58,440
+التسمياتبقول لي لو كان E is an edge E هذا عنصر من
+
+41
+00:03:58,440 --> 00:04:02,260
+عناصر الـ E الكابتن اللي قبله شوية كيف E شكله
+
+42
+00:04:02,260 --> 00:04:08,000
+عبارة عن V و W عبارة عن مجموعة فيها V و W هذولة ال
+
+43
+00:04:08,000 --> 00:04:14,800
+V و W الآن V بيكون و ال W are elements in V
+
+44
+00:04:14,800 --> 00:04:20,830
+different elements in Vالان E جمع الـ two vertices
+
+45
+00:04:20,830 --> 00:04:27,170
+V وW يعني الـ E بتربط الـ V مع الـ W وبتربط هنا
+
+46
+00:04:27,170 --> 00:04:34,590
+وبتكون إيش ال edge اللي بدنايا أو بنقول أنهOr the
+
+47
+00:04:34,590 --> 00:04:39,330
+vertices v and w are said to be incident with the
+
+48
+00:04:39,330 --> 00:04:45,730
+edged vw يعني اللي اللي هي ال vertices v و w بحدثن
+
+49
+00:04:45,730 --> 00:04:52,410
+اللي هو ال edge اللي هي vwمش هنظل نكتب هيكا اللي
+
+50
+00:04:52,410 --> 00:04:59,290
+هو العنصر اللي في E بعد شوية خلاص هنسميه V or أو V
+
+51
+00:04:59,290 --> 00:05:03,950
+joined W أو زي ما احنا شايفين هو عبارة عن اللي هو
+
+52
+00:05:03,950 --> 00:05:10,150
+ال edge هذاطيب نشوف الآن اللي هو ندخل كمان مرة
+
+53
+00:05:10,150 --> 00:05:15,350
+ناخد بعض التسميات two vertices are adjacent يعني
+
+54
+00:05:15,350 --> 00:05:18,650
+بنقول عن two vertices راسين إن هين جانب بعض
+
+55
+00:05:18,650 --> 00:05:23,930
+متجاورين أو جايات ورا بعض or neighborhoods يعني
+
+56
+00:05:23,930 --> 00:05:29,990
+جيرانIf they are the end vertices of an edge يعني
+
+57
+00:05:29,990 --> 00:05:32,630
+بتقول عن two vertices in an adjacent أو
+
+58
+00:05:32,630 --> 00:05:38,110
+neighborhood إذا كان الاتنين هدولة بكون من ال edge
+
+59
+00:05:38,110 --> 00:05:43,460
+يعني الاتنين بكون هذا ال edge بنسميهم adjacentاللي
+
+60
+00:05:43,460 --> 00:05:46,480
+هو بتسمي اللي هو العنصرين في هذه الحالة إشمالهم
+
+61
+00:05:46,480 --> 00:05:53,160
+عبارة عن adjacent اللي هي ال ال two vertices اللي
+
+62
+00:05:53,160 --> 00:05:57,780
+عندنا اللي هي two edges اتجين اللي هو two edges هي
+
+63
+00:05:57,780 --> 00:06:02,320
+edge و هدق هي edge بنقول عنهم adjacent متجاورتين
+
+64
+00:06:02,320 --> 00:06:06,440
+if they have a vertex in common إذا كان في عندهم
+
+65
+00:06:06,440 --> 00:06:12,310
+راس مشترك يعني إذا الراس هذاطلّع edge وهي edge مع
+
+66
+00:06:12,310 --> 00:06:15,390
+الرأس هذا وهذا الرأس نفسه طلّع مع هذا الرأس edge
+
+67
+00:06:15,390 --> 00:06:20,790
+بنقول إن هذا ال edge وهذا ال edge adjacent هذا ال
+
+68
+00:06:20,790 --> 00:06:24,490
+edge هو عناصر ال E capital وهذا هو عناصر ال E
+
+69
+00:06:24,490 --> 00:06:30,330
+capital والرؤوس هي عناصر من ال V اللي سمناها اللي
+
+70
+00:06:30,330 --> 00:06:36,780
+هي ال set ال graph عبارة عن V و عن Eالأن the
+
+71
+00:06:36,780 --> 00:06:40,840
+number of the edges that incident with a vertex v
+
+72
+00:06:40,840 --> 00:06:43,580
+is called the degree of the vertex ايش اللي بقوله
+
+73
+00:06:43,580 --> 00:06:48,580
+هذا؟ بقولك الآن بدنا نعرف ال degree لمن؟ لل vertex
+
+74
+00:06:48,580 --> 00:06:51,840
+هذا أحد الأهداف اللي بدنا نعرفها اليوم ايش ال
+
+75
+00:06:51,840 --> 00:06:57,660
+degree لل vertex؟ هو عبارة عن عدد ال edges اللي
+
+76
+00:06:57,660 --> 00:07:03,010
+بيطلع من ال vertexيعني the number of edges that
+
+77
+00:07:03,010 --> 00:07:06,870
+incident with a vertex V is called the degree of
+
+78
+00:07:06,870 --> 00:07:11,510
+the vertex بتضح معي المثال الان if إذا كان طلع
+
+79
+00:07:11,510 --> 00:07:14,410
+عندي ال degree لل V بعد شوية بنحسب يا جماعة بس
+
+80
+00:07:14,410 --> 00:07:18,430
+خليني نسمي بعض التسميات if ال degree لل V اللي هو
+
+81
+00:07:18,430 --> 00:07:23,970
+ال degree لل vertex درجة ال vertex كانت oddأو even
+
+82
+00:07:23,970 --> 00:07:28,410
+بنقول we say that V is an odd أو even vertex إذا
+
+83
+00:07:28,410 --> 00:07:32,070
+لما نقول odd vertex أو even vertex معناته ال
+
+84
+00:07:32,070 --> 00:07:38,350
+degree لل vertex even أو odd طيب الآن a vertex of
+
+85
+00:07:38,350 --> 00:07:42,970
+degree zero يعني ال vertex اللي degree له zero is
+
+86
+00:07:42,970 --> 00:07:47,470
+called an isolated vertexيعني الـ degree له zero
+
+87
+00:07:47,470 --> 00:07:53,510
+يعني مافيش بتطلعش منه ولا خط فيش ولا خط بروح منه
+
+88
+00:07:53,510 --> 00:07:57,210
+عشان هيك بنقول عنها النقطة إيه الشمال isolated
+
+89
+00:07:57,210 --> 00:08:02,490
+vertex يعني معزولة مافيش فيها ولا خط طالع منها
+
+90
+00:08:02,490 --> 00:08:07,280
+الان neighborhood of a vertexيعنى الجوار تبع ال
+
+91
+00:08:07,280 --> 00:08:11,300
+vertex بنسميه ال نوفي ايش جوار ال vertex كل اللى
+
+92
+00:08:11,300 --> 00:08:16,020
+هى النقاط اللى بتصنع مع ال ايه ال edges تبعتها
+
+93
+00:08:16,020 --> 00:08:20,180
+هنشوف هذا الكلام كله هتلاقوه سهل شوفوا الآن صلوا
+
+94
+00:08:20,180 --> 00:08:23,000
+على النبي عليه الصلاة والسلام نجى الان لحاجة اسمة
+
+95
+00:08:23,000 --> 00:08:26,460
+pseudograph ال graph بيسموه pseudograph او graph
+
+96
+00:08:26,460 --> 00:08:30,060
+زائف ايش هذا ال graph هذا هو graph like a graph
+
+97
+00:08:30,060 --> 00:08:34,960
+بشبه لgraph هو graphbut it may contains loops يعني
+
+98
+00:08:34,960 --> 00:08:38,640
+ممكن تحتوي على إيش؟ على loop، أي loop يعني ال loop
+
+99
+00:08:38,640 --> 00:08:43,920
+بيجي من النقطة و برجع للنقطة نفسهاأو a multiple of
+
+100
+00:08:43,920 --> 00:08:47,040
+edges أو بيحتوي على multiple edges يعني هي من هذا
+
+101
+00:08:47,040 --> 00:08:53,160
+لهنا هي أول خط وبرضه هي كمان خط من V2 لعند V1 ال
+
+102
+00:08:53,160 --> 00:08:57,760
+graph اللي بيحتوي على اللي هو multiple edges يعني
+
+103
+00:08:57,760 --> 00:09:04,000
+أكتر من خط بين النقطتين أو اللي هو اللي هي loop خط
+
+104
+00:09:04,000 --> 00:09:08,980
+بيروح للنقطة وبرجعلها بنسميه اللي هو pseudo graph
+
+105
+00:09:09,430 --> 00:09:13,650
+خلّينا ناخد المثال هذا و نيجي نحسب اللي بدنا نحسب
+
+106
+00:09:13,650 --> 00:09:21,370
+اللي هو ال degree لل V3 مثلا لل V3 ماشي الآن جبل
+
+107
+00:09:21,370 --> 00:09:25,290
+ما نحسب ال degree لل V3 خلّينا نحسب ال degree لل
+
+108
+00:09:25,290 --> 00:09:32,230
+V1 إيش ال degree لل V1؟ إيش الخطوط اللي بتطلع
+
+109
+00:09:32,230 --> 00:09:37,820
+منها؟هي اتنين فبكون ال degree لل V واحد اتنين طب
+
+110
+00:09:37,820 --> 00:09:42,320
+نيجي لل V تلاتة ال V تلاتة بطلع هاي خط هاي خطين
+
+111
+00:09:42,320 --> 00:09:49,520
+ماشي لكن ال V تلاتة اللي هو بطلع خط منها in و خط
+
+112
+00:09:49,520 --> 00:09:55,120
+منها outالـ Loop بنحسبه دايما اتنين في ال degree
+
+113
+00:09:55,120 --> 00:10:00,980
+يعني بنحسب واحد in و واحد out فبصير عنده اتنين وهي
+
+114
+00:10:00,980 --> 00:10:04,800
+كمان خط وهي كمان خط فبصير ال degree لل V3 ايش؟
+
+115
+00:10:04,800 --> 00:10:09,000
+بيساوي اربعة ال degree لل V3 بيساوي اربعة because
+
+116
+00:10:09,000 --> 00:10:17,120
+it connected E3لأنها بتعمل الـ edge E3 و بتعمل الـ
+
+117
+00:10:17,120 --> 00:10:23,500
+edge E4 و الـ edge E5 اللي هو under the loop E5
+
+118
+00:10:23,500 --> 00:10:29,680
+edge computed 2 واحد as in و واحد as out ده ال
+
+119
+00:10:29,680 --> 00:10:33,780
+loop بس اللي بنحسبه اتنين و الباقى بنحسبه ايش واحد
+
+120
+00:10:33,780 --> 00:10:39,800
+واحد فبصير ال degree للـ V3 بعدد الخطوط اللي طالعة
+
+121
+00:10:40,370 --> 00:10:45,650
+اللي هي منها أو اللي دخلة إلها وهذا ينحسب اتنين في
+
+122
+00:10:45,650 --> 00:10:50,190
+حالة ال loop طيب نيجي الآن undirected graphs حاجة
+
+123
+00:10:50,190 --> 00:10:52,790
+اسمها undirected graphs أو ال graphs اللي بتكون
+
+124
+00:10:52,790 --> 00:10:57,600
+إيه شمالها غير متجهة طيبغير متجنهة جدًا بنعرف لأنه
+
+125
+00:10:57,600 --> 00:11:00,780
+هناخد الـ Directed Graph بعد شوية بنعرف شو معناه
+
+126
+00:11:00,780 --> 00:11:05,480
+Undirected Undirected يعني مش فارجة من A ل B أو من
+
+127
+00:11:05,480 --> 00:11:10,460
+B ل A مش مرتبة What are the degree and what are
+
+128
+00:11:10,460 --> 00:11:13,640
+the neighborhoods of the vertices in the graph
+
+129
+00:11:13,640 --> 00:11:18,560
+Undirected؟ الآن بدنا نعرف إيش ال degreeو إيش ال
+
+130
+00:11:18,560 --> 00:11:21,440
+neighborhoods للنقاط اللي موجودة عندي هدول ال
+
+131
+00:11:21,440 --> 00:11:26,700
+vertices اللي عندي ال degree لل vertices و اللي هي
+
+132
+00:11:26,700 --> 00:11:30,220
+ال neighborhood لل vertices نيجي أول حاجة لل
+
+133
+00:11:30,220 --> 00:11:33,920
+degree لل إيه ال degree لل إيه يعني قداش .. إيش
+
+134
+00:11:33,920 --> 00:11:38,000
+الخطوط اللي طالعة منها هاي خط هاي اتنين إذا هذا
+
+135
+00:11:38,000 --> 00:11:42,240
+عندها ال degree إيش بتساوي اتنين طيب ال degree لل
+
+136
+00:11:42,240 --> 00:11:47,850
+بيه كلكم حقول هاي واحدهي اتنين هي تلاتة هي اربع
+
+137
+00:11:47,850 --> 00:11:52,070
+خطوط طالعين منها اذا ال degree لل بيه ايش اربعة لو
+
+138
+00:11:52,070 --> 00:11:56,230
+حد جالك ال degree لل C لل C هتقول هى واحد هى اتنين
+
+139
+00:11:56,230 --> 00:12:01,030
+هى تلاتة هى اربعة لو جالك ال degree لل G هتقوللي
+
+140
+00:12:01,030 --> 00:12:05,110
+سفر عشان هيك بنسميها isolated معزولة في الشاشة
+
+141
+00:12:05,110 --> 00:12:09,310
+بتطلع منها طيب ال degree اللي الان ال neighbor هد
+
+142
+00:12:09,310 --> 00:12:14,830
+لمن؟ لل A جوار ال Aجوار ال A اللي بيعمل الخطوط
+
+143
+00:12:14,830 --> 00:12:18,170
+معها جوار ال A اللي بيعمل الخطوط معها مين اللي
+
+144
+00:12:18,170 --> 00:12:22,470
+بيعمل الخط مع ال A؟ ال B و ال F عشان هيك بنقول
+
+145
+00:12:22,470 --> 00:12:27,710
+جوار ال A هو ال B و ال F نيجي الآن يا جماعة ايش
+
+146
+00:12:27,710 --> 00:12:31,350
+جوار ال B اللي بيعمل الخطوط مع ال B؟ ايش مين اللي
+
+147
+00:12:31,350 --> 00:12:38,820
+بيعمل الخطوط مع ال B؟ ال C و ال E و ال Fوالـ A هي
+
+148
+00:12:38,820 --> 00:12:44,980
+A وC وE وF هدولة جوار من الـ B الآن جوار الـ D
+
+149
+00:12:44,980 --> 00:12:47,540
+اللي بيعمل الخطوط مع الـ D مافيش حد بيعمل الخطوط
+
+150
+00:12:47,540 --> 00:12:51,340
+مع الـ D العالمين الـ C لكن لو جينا لجوار الـ G
+
+151
+00:12:51,340 --> 00:12:59,660
+هنلاقي فش إيش فاي عشان هي كانت بنسميها isolatedإيش
+
+152
+00:12:59,660 --> 00:13:06,640
+point اللي بيكونش إلها ولا جوار أو بتكونش عاملة أو
+
+153
+00:13:06,640 --> 00:13:10,240
+ال degree إلها بتساوي سفر مش ولا خط طالع منها أو
+
+154
+00:13:10,240 --> 00:13:14,140
+جاي نيجي الآن ناخد مثال آخر what are the degree
+
+155
+00:13:14,140 --> 00:13:17,820
+and what are the neighborhoods of the vertices in
+
+156
+00:13:17,820 --> 00:13:20,980
+the undirected graph خلينا هذا ال graph ال
+
+157
+00:13:20,980 --> 00:13:24,870
+undirected اللي غير متجهاللي يعني تفرجش من A لعند
+
+158
+00:13:24,870 --> 00:13:29,630
+B أو من B لعند A فاش اتجاه عندنا الان نشوف اللي هو
+
+159
+00:13:29,630 --> 00:13:32,950
+يسأل سؤاله ال degree لل A ايش ال degree لل A هاي
+
+160
+00:13:32,950 --> 00:13:38,650
+واحد هاي اتنين هاي تلاتة هاي اربعة ال degree لل A
+
+161
+00:13:38,650 --> 00:13:43,090
+نيجي لل degree لمين لل B ال degree لل B هاي واحد
+
+162
+00:13:43,090 --> 00:13:50,590
+هاي اتنين هاي تلاتةهذه أربعة وقلنا ال loop نحسب
+
+163
+00:13:50,590 --> 00:13:56,790
+جداش out وin اتنين يعني ايش بيصير ال degree ل ال
+
+164
+00:13:56,790 --> 00:14:02,910
+B6 نيجي ال neighborhood لل A جوار ال A اللي هي
+
+165
+00:14:02,910 --> 00:14:07,930
+النقاط اللي بيصنع المحين خطوط مين بيصنع المحين
+
+166
+00:14:07,930 --> 00:14:16,640
+خطوط بيه؟O D O E B D E نعود للـ neighborhood للـ B
+
+167
+00:14:16,640 --> 00:14:20,020
+ال neighborhood للـ B من يصنع الخطوط معاها الـ A
+
+168
+00:14:20,020 --> 00:14:29,020
+والـ E والـ A الـ D أسفوالـ C ونفسه لإن هو بيصنع
+
+169
+00:14:29,020 --> 00:14:33,420
+خط مع نفسه إذا بده ينحط في neighborhood للـ B الـ
+
+170
+00:14:33,420 --> 00:14:38,520
+B لاحظ إنه لما يكون في داخل ال neighborhood للـ B
+
+171
+00:14:38,520 --> 00:14:43,470
+الـ B معناته إنه في Loopهي الـ neighborhood للـ A
+
+172
+00:14:43,470 --> 00:14:47,210
+في الشيء A إذا مافيه Loop ال neighborhood لل B فيه
+
+173
+00:14:47,210 --> 00:14:51,230
+B جواته إذا مافيه Loop يعني فيه خط جاي منه لنفسه
+
+174
+00:14:51,230 --> 00:14:56,750
+طيب نيجي الآن اللي هو ناخد نحاول اللي هو أمثلة
+
+175
+00:14:56,750 --> 00:15:00,330
+بقدر الإمكان ومفاهيم زي ما بدنا طيب ال
+
+176
+00:15:00,330 --> 00:15:03,270
+neighborhood لل D neighborhood لل D من نفس الأسلوب
+
+177
+00:15:03,270 --> 00:15:05,730
+إيش ال neighborhood لل D اللي هو مين اللي مال
+
+178
+00:15:05,730 --> 00:15:12,100
+الخطوط معاه اللي هي ال B و ال A و ال Eالـ B والـ A
+
+179
+00:15:12,100 --> 00:15:15,720
+والـ E هيها الـ neighborhood للـ A الـ A هيها الـ
+
+180
+00:15:15,720 --> 00:15:22,610
+D وهي الـ B وهي الـ Aالان بتصور الصورة واضحة انها
+
+181
+00:15:22,610 --> 00:15:27,770
+وصارت اللي هي الأمور واضحة تماما لتنشوف الان graph
+
+182
+00:15:27,770 --> 00:15:31,530
+example الان نرجع لل graph لأن زي ما اتفجنا ال
+
+183
+00:15:31,530 --> 00:15:36,210
+graph هو عبارة عن ايش عن V و E ال V هي ايش عبارة
+
+184
+00:15:36,210 --> 00:15:43,130
+عن vertices هاي V V1 V2 V3 V4 V5 V6 اذا مجموعة من
+
+185
+00:15:43,130 --> 00:15:48,380
+النقاط تسمى vertices او تسمى رؤوسهذا الـ Graph
+
+186
+00:15:48,380 --> 00:15:53,100
+عبارة عن مجموعة V ومجموعة تانية E الـ E هي خطوط
+
+187
+00:15:53,100 --> 00:15:58,360
+يعني هذه نقاط أو رؤوس وهذه خطوط هذا الـ Graph الـ
+
+188
+00:15:58,360 --> 00:16:03,780
+Graph عبارة عن مجموعة من الـ vertices الرؤوس
+
+189
+00:16:03,780 --> 00:16:10,850
+ومجموعة أخرى من الـ edges المصموعة من الرؤوس Vإذا
+
+190
+00:16:10,850 --> 00:16:14,890
+نوضح إيش هو ال graph على بعضه ال graph هو عبارة عن
+
+191
+00:16:14,890 --> 00:16:19,210
+مجموعتين واحدة مجموعة الرؤوس والتانية مجموعة
+
+192
+00:16:19,210 --> 00:16:25,290
+الخطوط التي تكون من هذه الرؤوس بطريقة ما طيب ال NE
+
+193
+00:16:25,290 --> 00:16:30,890
+هيها V1 joined V4 اللي يعني باختصار V1 V4 الخط V1
+
+194
+00:16:30,890 --> 00:16:45,530
+V4 V1 V6 V1 V6V2 V5 V2 V5 V4 V5 V4 V5 V5 V6 إذن هي
+
+195
+00:16:45,530 --> 00:16:50,310
+تعبير آخر عن مين عن الخطوط يعني ممكن واحد يكتب V1
+
+196
+00:16:50,310 --> 00:17:00,590
+V4 خلاص V1 V6 V2 V5 V4 V5 V5 V6 مش فارق الترتيب
+
+197
+00:17:00,590 --> 00:17:06,820
+هنا اه هنا مش فارق الترتيب ليش؟لأنه عندى اللى هو
+
+198
+00:17:06,820 --> 00:17:13,160
+ال هذا بنسمي undirected graph يعني graph غير متجه
+
+199
+00:17:13,160 --> 00:17:17,440
+يعني مفرجش عندى v1 ل v4 و v4 ل v1 مافيش اتجاهات
+
+200
+00:17:17,440 --> 00:17:22,940
+ماحدش حاجة بيها طيب الان لو الان note that بقول v3
+
+201
+00:17:22,940 --> 00:17:27,860
+is an isolated vertex زى ما عملنا قبل شوية ليش لإن
+
+202
+00:17:27,860 --> 00:17:32,800
+ال degree ل ال v3 فش ولا إيش يطالع منهاللي هو إيش
+
+203
+00:17:32,800 --> 00:17:38,520
+بيساوي؟ بيساوي سفر طيب، الآن ال vertex، بدنا نسميه
+
+204
+00:17:38,520 --> 00:17:44,000
+تسميه الآن a vertex is .. is .. اللي هو بنسميه a
+
+205
+00:17:44,000 --> 00:17:49,880
+vertex بنسميه is pendent if and only if it has
+
+206
+00:17:49,880 --> 00:17:54,240
+degree one يعني ال vertex اللي بيكون degree تبعته
+
+207
+00:17:54,240 --> 00:18:00,260
+واحد، بنسميه pendentماشي V2 مثلا V2 is a pendant
+
+208
+00:18:00,260 --> 00:18:05,420
+ليش لأنه فش لغير اللي هو خط واحد طالع منه لعند V
+
+209
+00:18:05,420 --> 00:18:08,140
+أخمسة يعني ال adjacent له بس خمسة أو ال
+
+210
+00:18:08,140 --> 00:18:12,040
+neighborhood له ال V خمسة يعني هذا اللي هو ال
+
+211
+00:18:12,040 --> 00:18:16,420
+degree له بساوي واحد مدام ال degree له بساوي واحد
+
+212
+00:18:16,420 --> 00:18:24,630
+إذا على طول اللي هو بنسميه pendant طيبهنا في نظرية
+
+213
+00:18:24,630 --> 00:18:29,310
+hand shaking theorem بيقول الـ sum of the degree
+
+214
+00:18:29,310 --> 00:18:34,150
+of the vertices of an undirected graph بسيده graph
+
+215
+00:18:34,150 --> 00:18:39,670
+is even number or equal to twice the number of
+
+216
+00:18:39,670 --> 00:18:44,690
+edges ايش اللي بقوله بقول يا جماعة لو انت جيت اخدت
+
+217
+00:18:44,690 --> 00:18:48,970
+ال graph اللي عندك كي عندك فيه graph graph V و V و
+
+218
+00:18:48,970 --> 00:18:53,570
+جيت لك كل ال vertices ال Vو حسبت كل الرؤوس هنا
+
+219
+00:18:53,570 --> 00:18:58,770
+حسبت ال degree لكل رأس وجمعت كل ال degree تبعات
+
+220
+00:18:58,770 --> 00:19:01,510
+الرؤوس يعني الرأس الأول degree جديش الرأس الأول
+
+221
+00:19:01,510 --> 00:19:04,910
+تاني degree جديش لما خلصت على كل الرؤوس عرفت
+
+222
+00:19:04,910 --> 00:19:09,610
+درجاتهم بجمع درجات الرؤوس بجمع درجات الرؤوس اللي
+
+223
+00:19:09,610 --> 00:19:14,770
+هي ال vertices بلاجهن دائما دائما دائما بساود
+
+224
+00:19:14,770 --> 00:19:21,230
+اتنين في عدد ال edgesفي عدد عناصر من الـ E عناصر
+
+225
+00:19:21,230 --> 00:19:26,970
+من الـ E إيش هي خطوط يعني بمعنى آخر عدد مجموع
+
+226
+00:19:26,970 --> 00:19:34,550
+مجموع مجموع درجات ال vertices بساوي ضعف عدد الخطوط
+
+227
+00:19:34,550 --> 00:19:38,870
+يعني لو ضربنا اتنين في عدد الخطوط عدد عناصر الـ E
+
+228
+00:19:38,870 --> 00:19:46,830
+هلاجيهم دايما بساوين إيش مجموع درجات ال verticesأو
+
+229
+00:19:46,830 --> 00:19:50,270
+انت امسك مثال و جرب على اللي حكيناه و خلينا نجرب
+
+230
+00:19:50,270 --> 00:19:54,470
+على هذا المثال مثلا هاي في عندي اللي هو graph
+
+231
+00:19:54,470 --> 00:19:59,270
+undirected graph وهي ال vertices تبع عيوننا V1 V2
+
+232
+00:19:59,270 --> 00:20:05,110
+V3 V4 وهي اللي هي ال edges تبعاته أو الخطوطإيش
+
+233
+00:20:05,110 --> 00:20:09,730
+الخطوط اللي موجودة هيها واحد تنين تلاتة أربع خمسة
+
+234
+00:20:09,730 --> 00:20:14,410
+ست خطوط V1 V2 طبعا هذا في ال degree بنحسب اتنين
+
+235
+00:20:14,410 --> 00:20:22,230
+لكن هو E بالساوية V1 V2 V2 V3 V1 V3 V3 V4 V4 V1 V3
+
+236
+00:20:22,230 --> 00:20:27,050
+V3 هي الخطوط جداش واحد تنين آسف عناء ال edges
+
+237
+00:20:27,050 --> 00:20:32,470
+تبعات ال E واحد تنين تلاتة أربع خمسة ستةالان تعالى
+
+238
+00:20:32,470 --> 00:20:38,250
+احسب ال degree لكل واحد من هدولة وجمحن هتلاقيهين
+
+239
+00:20:38,250 --> 00:20:41,850
+اتناش هاي واحد، هاي اتنين، هاي تلاتة، هاي اربعة،
+
+240
+00:20:41,850 --> 00:20:46,850
+هاي خمسة، هاي ستةلازم لو أخدت ال degree لهذه زائد
+
+241
+00:20:46,850 --> 00:20:49,250
+ال degree لهذه زائد ال degree لهذه زائد ال degree
+
+242
+00:20:49,250 --> 00:20:54,710
+لهذه يطلع مجموع ال degrees اتنين في ستة حسب
+
+243
+00:20:54,710 --> 00:20:57,550
+القانون انا اتناشر يعني هيطلع لنا اتناشر degree
+
+244
+00:20:57,550 --> 00:21:02,270
+مجموحين ده نشوف نجرب ال degree لل V واحد ايه واحد
+
+245
+00:21:02,270 --> 00:21:06,730
+هي اتنين هي تلاتة طيب ال degree لل V اتنين واحد
+
+246
+00:21:06,730 --> 00:21:11,630
+اتنين ال degree لل V تلاتةهي واحد هي اتنين هي
+
+247
+00:21:11,630 --> 00:21:16,310
+تلاتة و ال loop بنحسب اتنين او two in هي خمسة و ال
+
+248
+00:21:16,310 --> 00:21:20,770
+degree لل V4 جديش اتنين هي واحد هي اتنين اجمع ليه
+
+249
+00:21:20,770 --> 00:21:23,710
+هنا دولة تلاتة و اتنين خمسة و خمسة عشرة و اتنين
+
+250
+00:21:23,710 --> 00:21:29,500
+اتناش فعلا اتناش بساوي ستةاللي هى عدد عناصر هدول
+
+251
+00:21:29,500 --> 00:21:32,920
+فى اتنين بطلع ايش اتن عاش ايه ده ايه ده انها دى
+
+252
+00:21:32,920 --> 00:21:37,160
+hand shaking theorem هي كده هى تقول اذا ال
+
+253
+00:21:37,160 --> 00:21:40,980
+summation لل edge لل V هي هى هى بساوة اتنين فى
+
+254
+00:21:40,980 --> 00:21:46,020
+اللى اتنين فستة بساوة اتن عاش الان sum of degree
+
+255
+00:21:46,020 --> 00:21:49,680
+اللى هو مثال عالى جبله شوية بقول لي how many edges
+
+256
+00:21:50,490 --> 00:21:55,030
+أكم edges يعني قداش عناصر الـ E are there in a
+
+257
+00:21:55,030 --> 00:22:00,540
+graph في الـ graph اللي ال vertices له عشرةeach of
+
+258
+00:22:00,540 --> 00:22:04,320
+degree six يعني بيقول لي عندي .. عندي اللي هو
+
+259
+00:22:04,320 --> 00:22:09,920
+vertices عشر vertices عشر رؤوس كل راس منهم ال
+
+260
+00:22:09,920 --> 00:22:15,220
+degree له ستة مدام ال degree له ستة الآن بيصير
+
+261
+00:22:15,220 --> 00:22:20,620
+اللي هم مجموع اللي هي ال vertices هدولة مجموع ال
+
+262
+00:22:20,620 --> 00:22:26,020
+degrees له عشرة في ستة بستين مظبوط ستين اللي هم
+
+263
+00:22:26,020 --> 00:22:30,950
+بيساوون اتنين مضروبة في مينفى عدد عناصر ال graph
+
+264
+00:22:30,950 --> 00:22:34,390
+إذا العدد عناصر ال edge إذا ال edge لازم يطلع ايه؟
+
+265
+00:22:34,390 --> 00:22:37,390
+اللى هى ستين على اتنين و هي ساعة و تلاتين شوف ايش
+
+266
+00:22:37,390 --> 00:22:40,770
+اللى بقوله because the sum of the degrees of the
+
+267
+00:22:40,770 --> 00:22:44,630
+vertices is ستة فى عشرة يعني الآن ال vertices عشرة
+
+268
+00:22:44,630 --> 00:22:48,650
+و كل واحد ال degree له ستة بيصير مجموعة degrees لل
+
+269
+00:22:48,650 --> 00:22:53,740
+vertices ستينit follows that اتنين في M M إيش هي
+
+270
+00:22:53,740 --> 00:22:58,580
+عبارة عن عدد عناصر ال E فرضناها اه اتنين M بساوي
+
+271
+00:22:58,580 --> 00:23:03,400
+ستين اللي هي where M is the number of edges ماشي
+
+272
+00:23:03,400 --> 00:23:06,220
+اللي أنا مش اللي انا مش ال E هذا مش مظبوطة هيك
+
+273
+00:23:06,220 --> 00:23:11,570
+اتنين M بساوي إيش ستين حيث ال M إيشاللي هي عدد
+
+274
+00:23:11,570 --> 00:23:15,550
+عناصر لدك therefore M ايش بتساوي بتساوي تلاتين
+
+275
+00:23:15,550 --> 00:23:20,050
+اللي هي عدد عناصر ال M is the number of edges اللي
+
+276
+00:23:20,050 --> 00:23:23,850
+هي عدد عناصر ال E هذه فش هذا مش مظبوطة اتنين M
+
+277
+00:23:23,850 --> 00:23:28,470
+بتساوي ستين هذه طبعا فش يساوي هان هذه ال E اللي هي
+
+278
+00:23:28,470 --> 00:23:32,610
+عبارة عن ال M is the number of edge الان اذا ال M
+
+279
+00:23:32,610 --> 00:23:35,650
+ايش بتساوي تلاتين او عدد عناصر ال edge هذه ايش
+
+280
+00:23:35,650 --> 00:23:41,430
+بتساوي تلاتينالان نجي للـ Directed Graph يا جماعة
+
+281
+00:23:41,430 --> 00:23:45,980
+الـ Directed Graphاللي هو خلّيني أشوف Directed
+
+282
+00:23:45,980 --> 00:23:49,480
+Graph V of E Consists .. هو نفس ال graph اللي قبل
+
+283
+00:23:49,480 --> 00:23:53,060
+بشوية بس بده يسير احنا نأخد بعين الاعتبار التجاه
+
+284
+00:23:53,060 --> 00:23:58,340
+.. الترتيب يعني اتجاه من وين طالع اللي هو ال .. ال
+
+285
+00:23:58,340 --> 00:24:01,560
+.. ال .. ال vertex و أين رايحه الخط من وين طالع و
+
+286
+00:24:01,560 --> 00:24:04,660
+من وين رايحه ده نشوف أشي اللي بقوله A Directed
+
+287
+00:24:04,660 --> 00:24:09,580
+Graph V of E يعني Graph V و E زي اللي قبل Consists
+
+288
+00:24:09,580 --> 00:24:14,580
+of a set of vertices V نفس الأشيand a set of each
+
+289
+00:24:14,580 --> 00:24:19,320
+E الآن الاختلاف هيجي على ال E ال E إيش بدها تصير
+
+290
+00:24:19,320 --> 00:24:23,980
+which are ordered pairs of elements of V يعني
+
+291
+00:24:23,980 --> 00:24:30,080
+عناصر ال E الآن لما نقول V1 V2 خلاص V1 V2 يعني هذا
+
+292
+00:24:30,080 --> 00:24:35,620
+مش V2 V1 يعني عند ال order مهم عشان هيك بنقول عنها
+
+293
+00:24:35,620 --> 00:24:39,220
+إيش معناه directed graph يعني ordered pairs
+
+294
+00:24:39,220 --> 00:24:45,600
+عناصرها نشوف كيفهي مثلًا V بتساوي A وB وC وD هذه
+
+295
+00:24:45,600 --> 00:24:49,200
+الـ V عبارة عن إيش يا جماعة؟ هي عبارة عن the set
+
+296
+00:24:49,200 --> 00:24:54,800
+of vertices الآن الـ E تبعتنا اللي هي ال edges الـ
+
+297
+00:24:54,800 --> 00:25:01,000
+E إيش الـ E؟ هي A وBو مرتبة كتبها ordered pair
+
+298
+00:25:01,000 --> 00:25:04,320
+يعني بقصود ال a و ال b و مش بال b و ال a ال a و ال
+
+299
+00:25:04,320 --> 00:25:08,280
+b معناته انه جاي السهم من a و رايح من بيه يعني هيه
+
+300
+00:25:08,280 --> 00:25:12,700
+جاي من a و رايح ل b يعني هذه ال initial point وهذه
+
+301
+00:25:12,700 --> 00:25:17,340
+ال terminal point هيك بتنفهم يعني ال a هي نقطة
+
+302
+00:25:17,340 --> 00:25:23,320
+البداية و b نقطة النهاية c و b اللي هي جاي من c و
+
+303
+00:25:23,320 --> 00:25:27,640
+رايح ل b هذه c نقطة البداية و b نقطة النهايةD وB
+
+304
+00:25:27,640 --> 00:25:32,280
+هي من D إلى B نقطة البداية وهي نقطة النهاية دي إيه
+
+305
+00:25:32,280 --> 00:25:37,220
+نقطة البداية دي ونقطة النهاية إيه إذا الأن الـ A
+
+306
+00:25:37,220 --> 00:25:42,640
+ordered pairs والـ V هيها vertices مع بعض V وE
+
+307
+00:25:42,640 --> 00:25:48,770
+بنسميها directed graphيعني graph اللي هو إيش متجه
+
+308
+00:25:48,770 --> 00:25:54,070
+يعني الاتجاه فيه بالنسبة إلنا اللي هو ضروري let u
+
+309
+00:25:54,070 --> 00:25:57,890
+,v directed graph خلّيني أخد الآن اللي هي التسميات
+
+310
+00:25:57,890 --> 00:26:01,990
+اللي قلتها قبل شوية أنا let u,v be an edge of the
+
+311
+00:26:01,990 --> 00:26:05,730
+graph G يعني نفترض إن ال u و ال v هو عبارة عن edge
+
+312
+00:26:05,730 --> 00:26:10,510
+يعني عنصر من عناصر ال Eالنقطة البداية U الان بنقصد
+
+313
+00:26:10,510 --> 00:26:15,210
+U is called the initial vertex يعني نقطة البداية
+
+314
+00:26:15,210 --> 00:26:20,530
+يعني اللي بيطلع منها من الخط is the initial vertex
+
+315
+00:26:20,530 --> 00:26:27,560
+of UVis called the terminal or end vertex of U V
+
+316
+00:26:27,560 --> 00:26:31,400
+وبنسمي ال V اللي هي ال terminal أو نقطة النهاية أو
+
+317
+00:26:31,400 --> 00:26:34,760
+ال end لل vertex لذن يعني الخط بيطلع من U بروح
+
+318
+00:26:34,760 --> 00:26:39,720
+لمين ل V لذن لما نقول U و V معناته U نقطة البداية
+
+319
+00:26:39,720 --> 00:26:46,990
+adjacent to Vماشي يعني اللي هي اللي هي بجنب بالجنب
+
+320
+00:26:46,990 --> 00:26:51,850
+رايح على بيه جنب V بس رايح على مين على V ال U
+
+321
+00:26:51,850 --> 00:26:57,830
+adjacent to V يعني ذاهبة إلى مين إلى V يعني بجوار
+
+322
+00:26:57,830 --> 00:27:03,210
+V ذاهبة إليهالكن الـ V بالنسبة للـ U adjacent from
+
+323
+00:27:03,210 --> 00:27:09,850
+U اللي هو جنبها خارجها منها اه يعني طالعة من U و
+
+324
+00:27:09,850 --> 00:27:16,330
+رايحة لمين لل V يعني adjacent from U اللي هو اللي
+
+325
+00:27:16,330 --> 00:27:27,100
+هي بجوار إلى U وهذه بجوار من Vأو الى V طيب ايش
+
+326
+00:27:27,100 --> 00:27:30,720
+يعني بالاقتصاد هذه نقطة اللي هي البداية وهذه نقطة
+
+327
+00:27:30,720 --> 00:27:35,740
+النهاية بالنسبة ل ال H Definition بدنا نعرف الآن
+
+328
+00:27:35,740 --> 00:27:42,000
+احنا عرفنا قبل ال degree لل vertex الآن بدنا نعرف
+
+329
+00:27:42,000 --> 00:27:46,980
+انه صار في عندى اللي هو نقاط داخلة و نقاط خارجة
+
+330
+00:27:46,980 --> 00:27:51,340
+خطوط داخلة و خطوط خارجة يعني هذا الخط خارج من ال U
+
+331
+00:27:51,850 --> 00:27:56,130
+وداخل العالمين عن الـ V عشان هيك بنقول in a graph
+
+332
+00:27:56,130 --> 00:28:01,150
+with directed edges the n degree of a vertex V
+
+333
+00:28:01,150 --> 00:28:06,150
+بنعرف حاجة اسمها الـ n degree اللي هي الدرجة الى
+
+334
+00:28:06,150 --> 00:28:10,390
+of a vertex V اللي هي degree وناقص بنكتبها n
+
+335
+00:28:10,390 --> 00:28:15,550
+degree V is the number of edges with V as their
+
+336
+00:28:15,550 --> 00:28:20,530
+terminal vertexيعني اللي هو لما نقول in V يعني
+
+337
+00:28:20,530 --> 00:28:24,550
+اللي داخل على ال V يعني ال V بدها تكون النقطة
+
+338
+00:28:24,550 --> 00:28:29,810
+النهائية ال terminal إذن degree in degree لل V
+
+339
+00:28:29,810 --> 00:28:37,030
+الداخلة على ال V عدد الخطوط الداخلة على ال V إذن
+
+340
+00:28:37,030 --> 00:28:43,000
+in degree عدد الخطوط الداخلة على ال Vالان out
+
+341
+00:28:43,000 --> 00:28:49,660
+degree of V عدد الخطوط الخارجة اللي هو main من ال
+
+342
+00:28:49,660 --> 00:28:54,580
+V يعني بتكون ال V initial point الان out degree
+
+343
+00:28:54,580 --> 00:28:59,080
+الخارجة من V يعني بتكون ال V عبارة عن initial
+
+344
+00:28:59,080 --> 00:29:04,600
+point ناخد مثال الان بقول find the in degree and
+
+345
+00:29:04,600 --> 00:29:09,870
+out degree of each vertex in the graph Gwith
+
+346
+00:29:09,870 --> 00:29:12,930
+directed edges shown in figure 2 هي الفيجور اللي
+
+347
+00:29:12,930 --> 00:29:18,530
+قلناها بدك تحسبه ال in degree نيجي لمن لال إيه
+
+348
+00:29:18,530 --> 00:29:22,670
+نشوف ال in degree اللي هي إيه شمالها الداخل على ال
+
+349
+00:29:22,670 --> 00:29:26,090
+إيه مين الخطوط الداخل على ال إيه هاي واحد هاي أول
+
+350
+00:29:26,090 --> 00:29:31,630
+خط اتنين اللي داخل على ال إيه هاي كمان خط في
+
+351
+00:29:31,630 --> 00:29:37,690
+غيرهم؟ لأ طيبالـ degree للـ B ال degree لل B ال
+
+352
+00:29:37,690 --> 00:29:41,510
+degree لل B الداخل على ال B مين الداخل على ال B
+
+353
+00:29:41,510 --> 00:29:45,390
+هاي هذا داخل على ال B وهي داخل على ال B في غيرهم
+
+354
+00:29:45,390 --> 00:29:50,930
+لأ إذا اتنين ال degree لل C هاي أول واحد داخل على
+
+355
+00:29:50,930 --> 00:29:56,470
+ال C الآن هاي كمان واحد داخل على ال C هاي كمان
+
+356
+00:29:56,470 --> 00:30:00,150
+واحد داخل على ال C إذا تلت خطوط إذا ال degree in C
+
+357
+00:30:00,150 --> 00:30:04,950
+تلاتةالان او ال degree ال degree لل a اللي هي
+
+358
+00:30:04,950 --> 00:30:11,090
+الخارجة من ال a اه الخارجة من ال a اول اش اللي
+
+359
+00:30:11,090 --> 00:30:16,010
+خارج من a هيه نفسه خارج وهي كمان واحد خارج اتنين
+
+360
+00:30:16,010 --> 00:30:20,310
+وهي كمان واحد خارج تلاتة وهي كمان واحد خارج ايش
+
+361
+00:30:20,310 --> 00:30:25,700
+اربعة اذا اللاحظوا ان اللي في ال loopاللي في ال
+
+362
+00:30:25,700 --> 00:30:32,500
+loop بنحسب أنه داخل و خارج لإن هو داخل على ال a و
+
+363
+00:30:32,500 --> 00:30:36,980
+خارج من ال a عشان هيك في العادى بنحسب برتين هنا
+
+364
+00:30:36,980 --> 00:30:41,660
+طبعا هينحسب في الداخل و في الخارج لإنه فعلا من ال
+
+365
+00:30:41,660 --> 00:30:47,200
+a ل ال a بطلع من ال a و بدخل لل a و بنحسب داخل و
+
+366
+00:30:47,200 --> 00:30:52,670
+خارجال degree لل B اللي هو ال out degree اللي خرجت
+
+367
+00:30:52,670 --> 00:30:56,090
+من ال B اللي خرجت من ال B وين اللي خرجت من ال B؟
+
+368
+00:30:56,090 --> 00:31:01,090
+هاي واحد، في غيره؟ لأ، هاي واحد اللي خرجت من مين؟
+
+369
+00:31:01,090 --> 00:31:06,530
+من ال C الآن اللي خرجت من ال C، هاي واحد، هاي
+
+370
+00:31:06,530 --> 00:31:11,210
+اتنين، في غيرهم؟ لأ، هاي اللي خرجت من إيش؟ من ال C
+
+371
+00:31:11,210 --> 00:31:20,700
+طيب، نيجي الآن لنظرية بتقول للنظريةالان ناحظوا انه
+
+372
+00:31:20,700 --> 00:31:25,340
+لو جينا كانت G عند theorem let G بيسوو V و E be
+
+373
+00:31:25,340 --> 00:31:29,180
+the graph with directed edges يعني نفترض انه اللي
+
+374
+00:31:29,180 --> 00:31:33,300
+هو هذا عبارة عن graph عناصر ال E عبارة عن ordered
+
+375
+00:31:33,300 --> 00:31:39,140
+pairs يعني directed edges then اللي هو لو جيت حسبت
+
+376
+00:31:39,140 --> 00:31:44,580
+لل indegree يعني عدد الخطوط اللي داخلة اللي داخلة
+
+377
+00:31:47,340 --> 00:31:52,440
+الـ N هذه اللي داخلة على الـ V لكل النقاط وجمعتهم
+
+378
+00:31:52,440 --> 00:31:57,700
+هيكون إن هما نفس عدد الخطوط الخارجية طبيعي طبيعي
+
+379
+00:31:57,700 --> 00:32:02,580
+لإنه بتكون اللي هي مش بنحسب على كل النقاط إذا مش
+
+380
+00:32:02,580 --> 00:32:07,890
+داخلة في هذا ال .. إذا داخلة في النقطة هذهإذا مش
+
+381
+00:32:07,890 --> 00:32:11,770
+داخلة في النقطة هذه داخلة في النقطة الثانية إذا مش
+
+382
+00:32:11,770 --> 00:32:14,350
+خارجة في النقطة هذه خارجة في النقطة الثانية وما ده
+
+383
+00:32:14,350 --> 00:32:19,030
+بنجمع على كل المقاط إذا حيكون هدولة هنا عدد الخطوط
+
+384
+00:32:19,030 --> 00:32:23,840
+كلهم وهدولة عدد الخطوط كلهموعدد الخطوط كل إن هما
+
+385
+00:32:23,840 --> 00:32:29,740
+من عدد الخطوط اللي هو هذه فدائما عدد الخطوط
+
+386
+00:32:29,740 --> 00:32:34,780
+المجموعة عدد الخطوط الداخلة بساوي مجموعة عدد
+
+387
+00:32:34,780 --> 00:32:38,420
+الخطوط الخارجية لكل النقاط طبعا بساوي اللي هو
+
+388
+00:32:38,420 --> 00:32:42,820
+الخطوط هذه طبعا هذه ايه هي مجموعة الخطوط اللي هي
+
+389
+00:32:42,820 --> 00:32:48,920
+degree outاللي هي عدد الخطوط الخارجة degree out
+
+390
+00:32:48,920 --> 00:32:52,800
+عدد الخطوط الخارجة مجموح على كل النقاط وهذا عدد
+
+391
+00:32:52,800 --> 00:32:57,760
+الخطوط الداخلة على كل النقاط فبطلع عندى هذه كل
+
+392
+00:32:57,760 --> 00:33:01,560
+الخطوط اللى عندى وهذه برضه كل الخطوط لأن اللى خارج
+
+393
+00:33:01,930 --> 00:33:06,190
+في نقطة بيكون داخل في نقطة فبتنجمع اللي بنجمع حان
+
+394
+00:33:06,190 --> 00:33:10,370
+بنجمع حان فبنجمع كله على هدولة بنجمع كله فبكون نفس
+
+395
+00:33:10,370 --> 00:33:14,770
+الاشي و بيطلع عدد الخطوط الداخلة و أنت إذا كان
+
+396
+00:33:14,770 --> 00:33:19,490
+يعني شاكك روح عدلي عدد ال degree انهان و degree
+
+397
+00:33:19,490 --> 00:33:22,350
+انهان و degree انهان و degree انهان و degree انهان
+
+398
+00:33:22,350 --> 00:33:25,960
+و degree انهان و degree انهانو اجمحهم هتلاقيهم
+
+399
+00:33:25,960 --> 00:33:29,660
+بساوين ال degree out و ال degree out و ال degree
+
+400
+00:33:29,660 --> 00:33:31,240
+out و ال degree out و ال degree out و ال degree
+
+401
+00:33:31,240 --> 00:33:32,520
+out و ال degree out و ال degree out و ال degree
+
+402
+00:33:32,520 --> 00:33:32,720
+out و ال degree out و ال degree out و ال degree
+
+403
+00:33:32,720 --> 00:33:32,960
+out و ال degree out و ال degree out و ال degree
+
+404
+00:33:32,960 --> 00:33:33,000
+out و ال degree out و ال degree out و ال degree
+
+405
+00:33:33,000 --> 00:33:33,040
+out و ال degree out و ال degree out و ال degree
+
+406
+00:33:33,040 --> 00:33:33,520
+out و ال degree out و ال degree out و ال degree
+
+407
+00:33:33,520 --> 00:33:34,400
+out و ال degree out و ال degree out و ال degree
+
+408
+00:33:34,400 --> 00:33:39,180
+out و ال
+
+409
+00:33:39,180 --> 00:33:44,090
+degree out ووهنا بكون عندى بكون وصلنا لل homework
+
+410
+00:33:44,090 --> 00:33:49,110
+للمحاضرة العاشرة هى السؤال الاول هى السؤال الاول a
+
+411
+00:33:49,110 --> 00:33:53,630
+و b وعلى الرسم هذه سخلات سلة وهى السؤال التانى كله
+
+412
+00:33:53,630 --> 00:33:58,090
+زى اللى شرحته وهى السؤال التالت في الهداك فائلا
+
+413
+00:33:58,090 --> 00:34:02,650
+عندى اذا تلت اسئلة وان شاء الله بتحلون تعطونيا
+
+414
+00:34:02,650 --> 00:34:07,350
+كالعادة والى لقاء اخر والسلام عليكم ورحمة الله
+
+415
+00:34:07,350 --> 00:34:08,630
+وبركاته
+
diff --git a/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_raw.json b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..63c83053e67fae31d29930cb50e71404e3340971
--- /dev/null
+++ b/PL9fwy3NUQKwY_stEoTlrdAvi6H_x0XBo-/tnhYkXvqDD4_raw.json
@@ -0,0 +1 @@
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182.33, "word": " عن", "probability": 0.9951171875}, {"start": 182.33, "end": 183.25, "word": " زوج", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 8, "seek": 19892, "start": 184.14, "end": 198.92, "text": "من العناصر اللي هي من ال vertices بنسميها إيش Edge يعني عناصر ال E هو عبارة عنصر ال E زي واحد من عناصر ال E اللي هو ال Edge V1 V2", "tokens": [27842, 18863, 1863, 33546, 2288, 13672, 1829, 39896, 9154, 2423, 32053, 44945, 38251, 1829, 11296, 11933, 1829, 8592, 19328, 37495, 22653, 18871, 33546, 2288, 2423, 462, 31439, 6225, 3555, 9640, 3660, 18871, 9381, 2288, 2423, 462, 30767, 1829, 36764, 24401, 9154, 18871, 33546, 2288, 2423, 462, 13672, 1829, 31439, 2423, 19328, 691, 16, 691, 17], "avg_logprob": -0.182059146463871, "compression_ratio": 1.5769230769230769, "no_speech_prob": 2.8014183044433594e-06, "words": [{"start": 184.14, "end": 184.52, "word": "من", "probability": 0.91845703125}, {"start": 184.52, "end": 185.56, "word": " العناصر", "probability": 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1340.62, "word": " ال", "probability": 0.9736328125}, {"start": 1340.62, "end": 1341.08, "word": " degrees", "probability": 0.8779296875}, {"start": 1341.08, "end": 1341.42, "word": " له", "probability": 0.77734375}, {"start": 1341.42, "end": 1341.82, "word": " عشرة", "probability": 0.9703776041666666}, {"start": 1341.82, "end": 1341.98, "word": " في", "probability": 0.8505859375}, {"start": 1341.98, "end": 1342.32, "word": " ستة", "probability": 0.9881184895833334}, {"start": 1342.32, "end": 1343.02, "word": " بستين", "probability": 0.9611002604166666}, {"start": 1343.02, "end": 1344.08, "word": " مظبوط", "probability": 0.847509765625}, {"start": 1344.08, "end": 1345.12, "word": " ستين", "probability": 0.9127604166666666}, {"start": 1345.12, "end": 1345.76, "word": " اللي", "probability": 0.991455078125}, {"start": 1345.76, "end": 1346.02, "word": " هم", "probability": 0.794921875}, {"start": 1346.02, "end": 1346.6, "word": " بيساوون", "probability": 0.7873942057291666}, {"start": 1346.6, "end": 1347.38, "word": " اتنين", "probability": 0.96044921875}, {"start": 1347.38, "end": 1348.28, "word": " مضروبة", "probability": 0.9639892578125}, {"start": 1348.28, "end": 1348.48, "word": " في", "probability": 0.927734375}, {"start": 1348.48, "end": 1348.86, "word": " مين", "probability": 0.8701171875}], "temperature": 1.0}, {"id": 61, "seek": 136997, "start": 1349.15, "end": 1369.97, "text": "فى عدد عناصر ال graph إذا العدد عناصر ال edge إذا ال edge لازم يطلع ايه؟ اللى هى ستين على اتنين و هي ساعة و تلاتين شوف ايش اللى بقوله because the sum of the degrees of the vertices is ستة فى عشرة يعني الآن ال vertices عشرة و كل واحد ال degree له ستة بيصير مجموعة degrees لل vertices ستين", "tokens": [5172, 7578, 6225, 3215, 3215, 18871, 33546, 2288, 2423, 4295, 11933, 15730, 18863, 3215, 3215, 18871, 33546, 2288, 2423, 4691, 11933, 15730, 2423, 4691, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 1975, 1829, 3224, 22807, 13672, 7578, 8032, 7578, 8608, 2655, 9957, 15844, 1975, 2655, 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إيش ستين حيث ال M إيش", "tokens": [270, 10002, 300, 1975, 2655, 1863, 9957, 8978, 376, 376, 11933, 1829, 8592, 39896, 6225, 3555, 9640, 3660, 18871, 6225, 3215, 3215, 18871, 33546, 2288, 2423, 462, 6156, 43042, 8315, 11296, 1975, 3224, 1975, 2655, 1863, 9957, 376, 4724, 3794, 995, 45865, 8608, 2655, 9957, 13672, 1829, 39896, 689, 376, 307, 264, 1230, 295, 8819, 3714, 33599, 1829, 13672, 1829, 41850, 37893, 13672, 1829, 1975, 8315, 37893, 2423, 462, 23758, 37893, 3714, 19913, 3555, 2407, 9566, 3660, 39896, 4117, 1975, 2655, 1863, 9957, 376, 4724, 3794, 995, 45865, 11933, 1829, 8592, 8608, 2655, 9957, 11331, 1829, 12984, 2423, 376, 11933, 1829, 8592], "avg_logprob": -0.21374393174949202, "compression_ratio": 1.719387755102041, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1370.48, "end": 1370.74, "word": "it", "probability": 0.340087890625}, {"start": 1370.74, "end": 1371.12, "word": " follows", "probability": 0.8447265625}, {"start": 1371.12, "end": 1371.66, "word": " 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0.513671875}, {"start": 1381.82, "end": 1382.12, "word": " number", "probability": 0.97412109375}, {"start": 1382.12, "end": 1382.36, "word": " of", "probability": 0.97900390625}, {"start": 1382.36, "end": 1382.72, "word": " edges", "probability": 0.88232421875}, {"start": 1382.72, "end": 1383.4, "word": " ماشي", "probability": 0.779296875}, {"start": 1383.4, "end": 1383.94, "word": " اللي", "probability": 0.7587890625}, {"start": 1383.94, "end": 1384.06, "word": " أنا", "probability": 0.44921875}, {"start": 1384.06, "end": 1384.28, "word": " مش", "probability": 0.9833984375}, {"start": 1384.28, "end": 1384.46, "word": " اللي", "probability": 0.6102294921875}, {"start": 1384.46, "end": 1384.72, "word": " انا", "probability": 0.6949462890625}, {"start": 1384.72, "end": 1385.02, "word": " مش", "probability": 0.9072265625}, {"start": 1385.02, "end": 1385.18, "word": " ال", "probability": 0.77490234375}, {"start": 1385.18, "end": 1385.28, "word": " E", "probability": 0.82861328125}, {"start": 1385.28, "end": 1385.46, "word": " هذا", "probability": 0.365234375}, {"start": 1385.46, "end": 1385.62, "word": " مش", "probability": 0.98876953125}, {"start": 1385.62, "end": 1386.08, "word": " مظبوطة", "probability": 0.8534342447916666}, {"start": 1386.08, "end": 1386.22, "word": " هيك", "probability": 0.786376953125}, {"start": 1386.22, "end": 1386.58, "word": " اتنين", "probability": 0.96923828125}, {"start": 1386.58, "end": 1386.74, "word": " M", "probability": 0.96337890625}, {"start": 1386.74, "end": 1387.14, "word": " بساوي", "probability": 0.973388671875}, {"start": 1387.14, "end": 1387.34, "word": " إيش", "probability": 0.7786458333333334}, {"start": 1387.34, "end": 1387.84, "word": " ستين", "probability": 0.9820963541666666}, {"start": 1387.84, "end": 1388.54, "word": " حيث", "probability": 0.9744466145833334}, {"start": 1388.54, "end": 1388.68, "word": " ال", "probability": 0.8486328125}, {"start": 1388.68, "end": 1388.96, "word": " M", "probability": 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"probability": 0.88720703125}, {"start": 1479.22, "end": 1479.96, "word": " عناصرها", "probability": 0.9771728515625}, {"start": 1479.96, "end": 1480.46, "word": " نشوف", "probability": 0.7325439453125}, {"start": 1480.46, "end": 1480.74, "word": " كيف", "probability": 0.982421875}], "temperature": 1.0}, {"id": 67, "seek": 149776, "start": 1481.3, "end": 1497.76, "text": "هي مثلًا V بتساوي A وB وC وD هذه الـ V عبارة عن إيش يا جماعة؟ هي عبارة عن the set of vertices الآن الـ E تبعتنا اللي هي ال edges الـ E إيش الـ E؟ هي A وB", "tokens": [3224, 1829, 50113, 1211, 14111, 995, 691, 39894, 3794, 995, 45865, 316, 4032, 33, 4032, 34, 4032, 35, 29538, 2423, 39184, 691, 6225, 3555, 9640, 3660, 18871, 11933, 1829, 8592, 35186, 10874, 15042, 27884, 22807, 39896, 6225, 3555, 9640, 3660, 18871, 264, 992, 295, 32053, 6024, 48506, 2423, 39184, 462, 6055, 3555, 34268, 8315, 13672, 1829, 39896, 2423, 8819, 2423, 39184, 462, 11933, 1829, 8592, 2423, 39184, 462, 22807, 39896, 316, 4032, 33], "avg_logprob": -0.21051520813961286, "compression_ratio": 1.4478527607361964, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 1481.3, "end": 1482.22, "word": "هي", "probability": 0.51513671875}, {"start": 1482.22, "end": 1482.72, "word": " مثلًا", "probability": 0.84014892578125}, {"start": 1482.72, "end": 1482.92, "word": " V", "probability": 0.6875}, {"start": 1482.92, "end": 1483.56, "word": " بتساوي", "probability": 0.7175750732421875}, {"start": 1483.56, "end": 1483.92, "word": " A", "probability": 0.7861328125}, {"start": 1483.92, "end": 1484.38, "word": " وB", "probability": 0.778076171875}, {"start": 1484.38, "end": 1484.84, "word": " وC", "probability": 0.868408203125}, {"start": 1484.84, "end": 1485.16, "word": " وD", "probability": 0.98291015625}, {"start": 1485.16, "end": 1485.6, "word": " هذه", "probability": 0.35791015625}, {"start": 1485.6, "end": 1485.82, "word": " الـ", "probability": 0.760986328125}, {"start": 1485.82, "end": 1485.96, "word": " V", 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2041.95, "word": " بتحلون", "probability": 0.900390625}, {"start": 2041.95, "end": 2042.65, "word": " تعطونيا", "probability": 0.7879638671875}, {"start": 2042.65, "end": 2044.53, "word": " كالعادة", "probability": 0.9142578125}, {"start": 2044.53, "end": 2045.13, "word": " والى", "probability": 0.77880859375}, {"start": 2045.13, "end": 2045.51, "word": " لقاء", "probability": 0.9611002604166666}, {"start": 2045.51, "end": 2045.83, "word": " اخر", "probability": 0.777099609375}, {"start": 2045.83, "end": 2046.29, "word": " والسلام", "probability": 0.92138671875}, {"start": 2046.29, "end": 2046.67, "word": " عليكم", "probability": 0.947265625}, {"start": 2046.67, "end": 2047.05, "word": " ورحمة", "probability": 0.9739990234375}, {"start": 2047.05, "end": 2047.35, "word": " الله", "probability": 0.96875}, {"start": 2047.35, "end": 2048.63, "word": " وبركاته", "probability": 0.983984375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2049.091375, "duration_after_vad": 2033.567499999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bf73a4f5e40bf5fa2417bd6624e8290f47fe9896
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0.srt
@@ -0,0 +1,1947 @@
+1
+00:00:00,000 --> 00:00:02,980
+طيب، بسم الله الرحمن الرحيم إحنا إن شاء الله راح 
+
+2
+00:00:02,980 --> 00:00:08,160
+نكمل شرح المادة طبعاً الـHematology زي ما حكيناها 
+
+3
+00:00:08,160 --> 00:00:12,660
+أخدنا المحاضرة السابقة عن موضوع الـBlood Film كيف 
+
+4
+00:00:12,660 --> 00:00:15,660
+نعمل Film وكيف نصبغاه إحنا طبعاً لما نصبغه الـFilm 
+
+5
+00:00:15,660 --> 00:00:19,320
+هيدور معانا أشكال الخلايا تحت نجهة بصورة هاي هاي
+
+6
+00:00:19,320 --> 00:00:22,400
+الصورة عندي زي ما تلاحظين عندي هنا الخلايا الحمرة
+
+7
+00:00:22,400 --> 00:00:26,670
+اللي تسمى Red Blood Cells طبعاً الـPink، ماشي؟ في عندي 
+
+8
+00:00:26,670 --> 00:00:29,610
+الخلايا طبعًا الأحمر، طبعًا لاحظوا عندي أن الخلايا 
+
+9
+00:00:29,610 --> 00:00:32,370
+الحمرة في الـ "Center" مسبوخ والـ "Edge" غير
+
+10
+00:00:32,370 --> 00:00:36,050
+مسبوخ، طبعًا هي بتظهر بالصورة هيك لأن طبعًا هي 
+
+11
+00:00:36,050 --> 00:00:40,770
+عبارة عن الـ "Discoid" كيف يعني الـ "Discoid"؟ الـ
+
+12
+00:00:40,770 --> 00:00:46,350
+"Disk" طبعًا من الأطراف كبيرة ومن الوسط "thin"
+
+13
+00:00:46,350 --> 00:00:49,750
+شوية، أخف شوية، سمكة، فبتالي بتظهر كأنه خفيف، 
+
+14
+00:00:49,750 --> 00:00:52,790
+همنها عن طبعًا، الخلايا الحمرة مليانة 
+
+15
+00:00:52,790 --> 00:00:56,130
+بالـHemoglobina، زي ما أحنا عارفين، عندها الخلايا 
+
+16
+00:00:56,130 --> 00:00:59,270
+البيضا خمس أنواع أساسيين، اللي هم، هذي إيه خلية؟
+
+17
+00:00:59,270 --> 00:01:03,150
+هذي Neutrophil، هذي خلية الـEosinophil، هذي خلية 
+
+18
+00:01:03,150 --> 00:01:06,590
+الـLymphocyte، الـMonocyte، والـBasophil، طبعًا، 
+
+19
+00:01:06,590 --> 00:01:10,830
+خلية الـMonocyte وLymphocyte، طبعًا، هي عبارة 
+
+20
+00:01:10,830 --> 00:01:15,410
+بيسموها Mononuclear، Mononuclear Lycoside، بينما 
+
+21
+00:01:15,410 --> 00:01:20,650
+الخلايا التلاتة الضايقين، اللي الـGranular هذه 
+
+22
+00:01:20,650 --> 00:01:24,590
+بيسموها Poly-Nuclear أو Granulocyte، طبعًا لأنها 
+
+23
+00:01:24,590 --> 00:01:29,010
+تحتوى على حبيبات الـNeutrophil حبيباتها نعم كتير 
+
+24
+00:01:29,010 --> 00:01:34,710
+وPink، يعني دوب ميزين إحنا الـEosinophil حبيباتها 
+
+25
+00:01:34,710 --> 00:01:38,210
+بيكون مرسوسة صح وبيكون لون أحمر الـBasophil
+
+26
+00:01:38,210 --> 00:01:40,890
+حبيباتها حجمها مختلفة، تتفاوت إيش كبير وإيش صغير 
+
+27
+00:01:40,890 --> 00:01:46,630
+ومبعترة ولونها أسود، تمام؟ 
+
+28
+00:01:46,630 --> 00:01:51,470
+هاي كمان مرة عندي هذه خلية الـ Band، هذا طبعًا اسمه 
+
+29
+00:01:51,470 --> 00:01:53,490
+بيسميه إحنا "Band Neutrophil" طبعًا "Band
+
+30
+00:01:53,490 --> 00:01:56,170
+Neutrophil" المرحلة مقبل الـ "Neutrophil" إحنا 
+
+31
+00:01:56,170 --> 00:02:00,090
+هندرس في عملية الـ "maturation" اللي هي تطور إنشاء
+
+32
+00:02:00,090 --> 00:02:03,850
+الخلايا كيف تنشأ الخلايا من الخلية الأم لـ "stem
+
+33
+00:02:03,850 --> 00:02:07,330
+cells" لعند ما توصل لخلية الـ "mature cells" فهذه 
+
+34
+00:02:07,330 --> 00:02:09,890
+المرحلتين هاي اللي مُتسبرة يعني "maturation"
+
+35
+00:02:09,890 --> 00:02:12,490
+"maturation" الـ "Band Neutrophil" تظهر عندي 
+
+36
+00:02:12,490 --> 00:02:16,800
+بالنسبة تقريبًا 5%، 3 إلى 5% في الـ Blood Film، 
+
+37
+00:02:16,800 --> 00:02:18,800
+يعني تظهر نوع من الظهورة في الـ Blood Film بنسبة
+
+38
+00:02:18,800 --> 00:02:22,800
+معينة، طبعا هذه خلية الـ Poly-Nuclear، طبعا نسميها 
+
+39
+00:02:22,800 --> 00:02:25,580
+Poly-Nuclear، طبعا إن هو أصلا مجزقة، صارت إن دي 
+
+40
+00:02:25,580 --> 00:02:28,340
+عبارة عن تلاتة Loops، هذا ما نسميه إحنا الـ "Jews"، 
+
+41
+00:02:28,340 --> 00:02:32,370
+وهذا ما نسميه Loops فمسميه three loops، طبعًا الـ 
+
+42
+00:02:32,370 --> 00:02:34,890
+Neutrophil شايفين الحبابات فيها كيف؟ يعني نعم، من 
+
+43
+00:02:34,890 --> 00:02:38,190
+وعنها الخليه هاي الـ Eosinophil، طبعًا لاحظينها الـ
+
+44
+00:02:38,190 --> 00:02:40,910
+Neutrophil تنتين دول؟ هذه الـ Eosinophil، الحباباتها 
+
+45
+00:02:40,910 --> 00:02:45,650
+مرصوصة كإنه حد صفطها تسيط، ولونه أحمر، وغالبًا 
+
+46
+00:02:45,650 --> 00:02:49,970
+النواة عبارة عن Bilobed، فيها جزئين غالب النواة
+
+47
+00:02:49,970 --> 00:02:56,570
+دكتور، بقى دستك، بس في mouse أو في مؤشر؟ كيف؟ في 
+
+48
+00:02:56,570 --> 00:03:00,200
+mouse أو مؤشر؟ هيبقى أشير أنا جاعد، هيبقى شايف الـ
+
+49
+00:03:00,200 --> 00:03:07,640
+mouse؟ لأ، مش شايفينه لأ مش واضح دكتور مش عارف إذا 
+
+50
+00:03:07,640 --> 00:03:12,040
+فيها آلية مش
+
+51
+00:03:12,040 --> 00:03:15,800
+شايفين ال mouse عندي؟ لأ، عشان مش عارفين ع أي صورة
+
+52
+00:03:15,800 --> 00:03:20,060
+بتحكي جاعد، ع أي صورة بتشرح طويل طيب، أنا ببنشت من 
+
+53
+00:03:20,060 --> 00:03:24,640
+الصورة العلوية على الشمال تمام، هذه ال band 
+
+54
+00:03:24,640 --> 00:03:30,110
+Neutrophil شايفينها؟ هذه Band Neutrophil هي برعن جزء 
+
+55
+00:03:30,110 --> 00:03:36,430
+واحد، إن هو فيها زي إيش؟ زي نحكي حدوث الحصان زمان 
+
+56
+00:03:36,430 --> 00:03:40,270
+أو زي حد السنين، هذه بيسميها Band Neutrophil، 
+
+57
+00:03:40,270 --> 00:03:48,320
+شفتوها؟ طبعا هذه فيها نعمة، لونها طبعا pink وطبعًا، 
+
+58
+00:03:48,320 --> 00:03:51,820
+زي ما حكينا، هذه نسبة تواجدها تقريبًا من، زي ما 
+
+59
+00:03:51,820 --> 00:03:56,540
+حكينا، من 3% لـ5%، من 3% لـ5%، ماشي؟ هالجهة اللي 
+
+60
+00:03:56,540 --> 00:04:00,200
+عندي خلية الجنبها، اللي هي المرحلة ما بعديها 
+
+61
+00:04:00,200 --> 00:04:04,660
+بيسموها، طبعًا، Segmented Neutrophil أو بيسموها 
+
+62
+00:04:04,660 --> 00:04:09,010
+Poly-Nuclear Neutrophil طبعًا، زي ما حكينا، الـ
+
+63
+00:04:09,010 --> 00:04:15,210
+Maturation، إن شاء الله، هندرسه في أحد المحاضرات، 
+
+64
+00:04:15,210 --> 00:04:17,410
+هيكون عندي من الـSegmented Neutrophil، الحبل ما 
+
+65
+00:04:17,410 --> 00:04:22,110
+يتطور، هجيت الجنب، اللي في الأعلى، أقصى، اليمين، 
+
+66
+00:04:22,110 --> 00:04:27,880
+هذي بيسميها إحنا Eosinophil، تمام؟ تمام الـEosinophil،
+
+67
+00:04:27,880 --> 00:04:30,780
+طب الـEosinophil، خلّيني أشوف ممكن فيه اندهانة، إذا 
+
+68
+00:04:30,780 --> 00:04:33,760
+بقدر أجيب الـpointer "بش روح تحت يا دكتور، كل 
+
+69
+00:04:33,760 --> 00:04:36,800
+slide لحال" "بش روحين؟ آه، هنخدم، إحنا الدباش مش 
+
+70
+00:04:36,800 --> 00:04:41,840
+مشكلة" "طبعا، في انديهاد الشمال، تحت، Basophil،
+
+71
+00:04:41,840 --> 00:04:46,380
+شايفين كيف هو بيبعت كبير ومبعترة، ومش ثابت الحجم؟"
+
+72
+00:04:46,380 --> 00:04:49,540
+"عندي هنا طبعا، هذه الـLymphocyte، اللي بالنص، 
+
+73
+00:04:49,540 --> 00:04:53,020
+تحت، وتحت أقصى اليمين، تحت، عبارة عن Monocyte"
+
+74
+00:04:53,020 --> 00:04:57,110
+"هنخدمه واحد وواحد، زي ما حكى محمد ونيشي هذه أول 
+
+75
+00:04:57,110 --> 00:05:00,990
+واحدة، بسميها إحنا هذه "Stab Neutrophil" أو "Band 
+
+76
+00:05:00,990 --> 00:05:05,120
+Neutrophil"، شايفين؟ عبارة عن جزء واحد، لسه ما أصارش 
+
+77
+00:05:05,120 --> 00:05:09,540
+فيه تقسيم النواة لعدة loops طبعًا، الحجم ها من 12 
+
+78
+00:05:09,540 --> 00:05:13,020
+إلى 16، الـCytoplasm فيها Pink الـGranules هي 
+
+79
+00:05:13,020 --> 00:05:15,840
+عبارة عن الـPrimary وSecondary Granules طبعًا، 
+
+80
+00:05:15,840 --> 00:05:19,560
+النواة عبارة عن Dark Peripheral وفيها الـChromatin، 
+
+81
+00:05:19,560 --> 00:05:22,080
+شايفين الـChromatin ها؟  Loose Chromatin، طبعًا 
+
+82
+00:05:22,080 --> 00:05:27,260
+الـChromatin هي تعتبر تجمع الـDNA وهي أحد المميزات 
+
+83
+00:05:27,260 --> 00:05:31,820
+التي تقدر تميزها نواة الخلايا طبعًا، البعدية زي ما 
+
+84
+00:05:31,820 --> 00:05:33,480
+أكيدها "Segmented Neutrophil" "Segmented
+
+85
+00:05:33,480 --> 00:05:36,300
+Neutrophil" هين شايفين الخلية؟ بيكون الخلية عبارة 
+
+86
+00:05:36,300 --> 00:05:39,460
+عن أكثر من اتنين لخمس loops شايفين؟ Two to five
+
+87
+00:05:39,460 --> 00:05:43,780
+loops الخلية، يعني لاحظين الخلية الفوق؟ عندي واحد، 
+
+88
+00:05:43,780 --> 00:05:46,740
+اتنين وممكن تلاتي ناجحة، تتبرها الخلية التحت عبارة 
+
+89
+00:05:46,740 --> 00:05:50,700
+عن اتنين loops طبعًا، زي نفس الـBand حجمها اتناشر 
+
+90
+00:05:50,700 --> 00:05:54,260
+لستة عشر مايكرون "Cytoplasm Pink" فيها Primary 
+
+91
+00:05:54,260 --> 00:05:58,640
+وSecondary Granules الـ"Nucleus Dark Purple Blue"
+
+92
+00:05:58,640 --> 00:06:01,370
+شايفين كيف Dark Purple Blue؟ والـ Chromatin dense 
+
+93
+00:06:01,370 --> 00:06:05,190
+تلاحظين أن في الجمعات الأزرق فيه كتير فيها، فتعتبر 
+
+94
+00:06:05,190 --> 00:06:11,250
+dense هذه خلية الـEosinophil أكبر شبه حجمها من 14 إلى 
+
+95
+00:06:11,250 --> 00:06:14,550
+16 مايكرون مليئة بالـ granules الـ granules حجمها 
+
+96
+00:06:14,550 --> 00:06:18,050
+كبير، لونها أحمر، وهتميز الإلها، أنا ممكن أميز أن 
+
+97
+00:06:18,050 --> 00:06:21,090
+اللون أحمر الـ granules وبيضع في النواة عبارة عن 
+
+98
+00:06:21,090 --> 00:06:25,290
+two loops عبارة عن two loops غالبا للنواة ولونها 
+
+99
+00:06:25,290 --> 00:06:29,890
+أزرقالنواء؟ النواة، الأنوية تتصرف الأزرق بشكل 
+
+100
+00:06:29,890 --> 00:06:33,650
+عام، وجود الـDNA يا محمد، ليش؟ بحكينا إحنا 
+
+101
+00:06:33,650 --> 00:06:37,490
+الـRight Stain أو الـLishman Stain فيها By Basic 
+
+102
+00:06:37,490 --> 00:06:42,290
+Stains، فيه جزء بصبغة لنواة، الـLishman أو New 
+
+103
+00:06:42,290 --> 00:06:45,970
+Methylene Blue، وفيه جزء بصبغة لـCytoplasm، اللي يزين 
+
+104
+00:06:45,970 --> 00:06:50,350
+Red، تمام؟ فالجزء بصبغة لنواة، بصبغة لـDNA أزرق، 
+
+105
+00:06:50,350 --> 00:06:58,350
+مر معناك سابقًا، تمام؟ طيب، هالجيت أنا عندي هذي 
+
+106
+00:06:58,350 --> 00:07:04,010
+حكينا الـEosinophil، البعدية الـBasophil الحجم 14–16
+
+107
+00:07:04,010 --> 00:07:06,590
+أكبر شوية من الـNeutrophil، الـCytoplasm طبعًا 
+
+108
+00:07:06,590 --> 00:07:10,930
+Pink، الـGranules Dark وBlue وطبعًا Obscure 
+
+109
+00:07:10,930 --> 00:07:14,430
+Nucleus، طبعًا نواة مش واضحة، مش جدًا ميزي حرف 
+
+110
+00:07:14,430 --> 00:07:19,370
+الـS، لأن الـGranules بغطاتيها كامل، والنواة Dark 
+
+111
+00:07:19,370 --> 00:07:22,110
+Blue أكيد، طبعًا التلاتة المرة السابقة، اللي هو 
+
+112
+00:07:22,110 --> 00:07:25,970
+الـNeutrophil والـ Eosinophil والـ Basophil نسميهم 
+
+113
+00:07:25,970 --> 00:07:29,710
+Granular Glycosides لأنهم فيها نواة محبقة حبيبات 
+
+114
+00:07:29,710 --> 00:07:33,410
+ونسميهم طبعًا إيه؟ Poly-Nuclear لأن النواة تبعتها 
+
+115
+00:07:33,410 --> 00:07:38,050
+مجزقة يعني زي الـ Nucleus 2 إلى 5 Lobe الـ Eosinophil
+
+116
+00:07:38,050 --> 00:07:41,070
+2 Lobe الـ Basophil طبعًا مش واضحة كتير لكن تكون 
+
+117
+00:07:41,070 --> 00:07:42,650
+مجزقة غالباً، تمام؟
+
+118
+00:07:46,580 --> 00:07:50,440
+عندي الـMononuclear اللي هي الـ"لمفو سايتس"
+
+119
+00:07:50,440 --> 00:07:53,400
+والـ"مونو سايتس" الـ"لمفو سايتس" كما تشاهدون، 
+
+120
+00:07:53,400 --> 00:07:58,360
+حجمها تختلف حسب نوع الخلايا، فعندي "صغير" "لمفو
+
+121
+00:07:58,360 --> 00:08:06,260
+سايتس" في التحت أسفل، إذا شايفين شايفين ولا لا؟ ‏-
+
+122
+00:08:06,260 --> 00:08:08,680
+أشوفك. ‏- أشوفك. ‏- لتحت كلمة كبيرة. ‏- آه، 
+
+123
+00:08:08,680 --> 00:08:09,020
+شايفين.
+
+124
+00:08:18,060 --> 00:08:24,180
+أه دكتور، شايفينها؟ مش فاهم عليكم إيش؟ شايفينها،
+
+125
+00:08:24,180 --> 00:08:28,080
+شايفينها تمام اللي تحت كلمة "chromatin dense" يا 
+
+126
+00:08:28,080 --> 00:08:30,800
+دكتور؟ اللي تحت كلمة «chromatin dense»، آه في ندخل
+
+127
+00:08:30,800 --> 00:08:33,200
+نخليتين، في صغيرة وفي كبيرة هذه بالطبع small
+
+128
+00:08:33,200 --> 00:08:35,820
+lymphocyte وlarge lymphocyte وفي بالنص
+
+129
+00:08:35,820 --> 00:08:39,060
+intermediate ال «small lymphocyte» حجمها، وهذه
+
+130
+00:08:39,060 --> 00:08:43,120
+النقطة أذكرها كويس ال «small lymphocyte» حجمها 7
+
+131
+00:08:43,120 --> 00:08:46,550
+على 9 مايكرون يعادل حجم الخلايا الحمراء، هل جئت؟
+
+132
+00:08:46,550 --> 00:08:50,250
+ممكن أنا أسحب من «محمد» وممكن أسحب من «معاد» 
+
+133
+00:08:50,250 --> 00:08:52,610
+الخلايا الحمراء عندهم مش شبهة بالحجم، ممكن حجم
+
+134
+00:08:52,610 --> 00:08:55,010
+الخلايا الحمراء عند «معاد» نوعًا ما، طبعًا إيه
+
+135
+00:08:55,010 --> 00:08:57,250
+الخلايا الحمراء حجمها تقريبًا من 7 إلى 9 مايكرون
+
+136
+00:08:57,250 --> 00:09:01,170
+يكون عند «معاد» مثلًا، أو بلاش هاي، ممكن أسحب وأنا
+
+137
+00:09:01,170 --> 00:09:03,150
+شوف تعرف إن الخلايا الحمراء هاي طبيعية أو مش طبيعية
+
+138
+00:09:03,150 --> 00:09:06,370
+حجمها بقارنها بحجم الـ«Lymphocytes» اللي اسمه
+
+139
+00:09:06,370 --> 00:09:08,910
+الـ«small Lymphocytes»، فالـ«small Lymphocytes» يعتبر كأنه عندي
+
+140
+00:09:08,910 --> 00:09:15,440
+Indicators لحجم الخلايا الحمراء عشان أقدر أقارن، طبعًا
+
+141
+00:09:15,440 --> 00:09:17,800
+الـCytoplasm، لاحظوا الـCytoplasm عنديها؟ أنه إيش
+
+142
+00:09:17,800 --> 00:09:20,840
+لون الـCytoplasm؟ الخلية اللي بالنص هذه، الداخل
+
+143
+00:09:20,840 --> 00:09:24,700
+المربع الـCytoplasm لونه إيش لاحظين؟ أزرق، سماوي،
+
+144
+00:09:24,700 --> 00:09:30,880
+شايفينه؟ شايفينه؟ آه، واللي طبعًا هو عبارة عن dark
+
+145
+00:09:30,880 --> 00:09:35,300
+blue لكن بتكون طبعًا مش زي الـChromatin، زي
+
+146
+00:09:35,300 --> 00:09:39,020
+الـNeutrophil بيكون dense الـChromatin، لكن أقل
+
+147
+00:09:39,020 --> 00:09:44,630
+التجمعات، تمام؟ هذه اسمها الـLymphocyte، الـ Slides
+
+148
+00:09:44,630 --> 00:09:47,030
+اللي بعتيها، اللي هي الـ Mono Slides، هاي خلية الـ
+
+149
+00:09:47,030 --> 00:09:50,150
+Mono Slides الموجودة عندي، أنا بحاول أشوف إذا في
+
+150
+00:09:50,150 --> 00:09:54,490
+عندي، أجيب، أقدر أجيب لكم جلم، بس مش عارف الـ… من
+
+151
+00:09:54,490 --> 00:09:57,870
+أين أجيب لكم إياها، على كل حاجة، مرة قد كنت أعمل على
+
+152
+00:09:57,870 --> 00:10:01,770
+الرسامة، ظنين؟ على الرسامة كنت أشتغل، آه، آه، من
+
+153
+00:10:01,770 --> 00:10:06,350
+المرة إيش عملت؟ أنا جبت، شو اسمه؟ خليني أشوف إذا
+
+154
+00:10:06,350 --> 00:10:06,630
+…
+
+155
+00:10:12,240 --> 00:10:18,440
+سيف، أبعد الكتب ولا لسه؟ الكتب إيش يا عزيزي؟ احنا
+
+156
+00:10:18,440 --> 00:10:26,980
+ممكن كتب بلجيات؟ ده بحكي لسيف عشان ألجهم، سيف
+
+157
+00:10:26,980 --> 00:10:32,120
+اعنوه النص واتبعه من سيفه، طيب شايفين ما هو فيك
+
+158
+00:10:32,120 --> 00:10:40,730
+حاليًا ولا لسه؟ ولا إيش اتحرك ولا إيش دعوة؟ فجأت
+
+159
+00:10:40,730 --> 00:10:44,230
+الدكتورة أنت، جيب لي إياها المعلومة بالراحة، طيب، خلّيني
+
+160
+00:10:44,230 --> 00:10:47,530
+أكمل، مش مشكلة، هلأ بنشوف المشكلة هذه، طيب، احنا
+
+161
+00:10:47,530 --> 00:10:53,490
+وجدت طبعًا، لحظة، عندي هان الـ… الـ… الـ… الـ…
+
+162
+00:10:53,490 --> 00:10:57,010
+الـMonocytes كيف حجمها؟ أكبر حجم تقريبًا، 14 لـ20
+
+163
+00:10:57,010 --> 00:11:00,110
+الـCytoplasm فيها، طبعًا الـ… الـLymphocytes،
+
+164
+00:11:00,110 --> 00:11:03,190
+الـCytoplasm فيه blue، إذاً سماوي، لكن في
+
+165
+00:11:03,190 --> 00:11:07,610
+الـMonocytes، grey-blue، يعني بيكون أزرق ما يميله
+
+166
+00:11:07,610 --> 00:11:11,150
+أي شيء لسكري، نوعًا ما، طبعًا الـGranules، ما فيش
+
+167
+00:11:11,150 --> 00:11:14,890
+فيها Granules، لكن ممكن يظهر بعد الـOrganelles
+
+168
+00:11:14,890 --> 00:11:18,470
+أحيانًا النواة Blue و Large و Irregular في
+
+169
+00:11:18,470 --> 00:11:21,950
+الـShape، ممكن يكون حالة في الـS طبعًا، شايفين كيف؟
+
+170
+00:11:21,950 --> 00:11:25,050
+طبعًا، زي ما حكينا هي تعتبر أكبر حجم الخلايا
+
+171
+00:11:25,050 --> 00:11:28,270
+البيضاء الموجودة، طبعًا شايفين التجمعات هذه جنبها،
+
+172
+00:11:28,270 --> 00:11:31,350
+اللي على اليمين؟ فيه تجمعات خلايا صغيرة، إيش هي؟
+
+173
+00:11:31,350 --> 00:11:32,070
+فعلاً إيش هي؟
+
+174
+00:11:56,890 --> 00:11:58,290
+هذه………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
+
+175
+00:12:06,150 --> 00:12:11,010
+تحكي سيد، صح؟ هذه اللي قبل شوية اللي… اللي قبل
+
+176
+00:12:11,010 --> 00:12:13,710
+شوية اللي هي الـ lymphocyte الـ small والـ هذا؟
+
+177
+00:12:13,710 --> 00:12:16,490
+لأ، لأ، هذه عبارة عن صفائح دموية، الـ platelets
+
+178
+00:12:16,490 --> 00:12:22,270
+آه، platelets، هي هذه الـ Mega… دكتور، معلش، بس،
+
+179
+00:12:22,270 --> 00:12:25,890
+هي هذه الـ Megakaryocyte اللي هي اللي عاملة… لأ،
+
+180
+00:12:25,890 --> 00:12:30,910
+لأ، الـ Megakaryocyte خلية فيها نواة وCytoplasm
+
+181
+00:12:30,910 --> 00:12:33,670
+وفيها… بيطلع منها الـPlatelets، الـPlatelets هي بقى
+
+182
+00:12:33,670 --> 00:12:39,110
+عن، نحكي، أجزاء من الـCytoplasm، ما نعتبرهاش خلايا
+
+183
+00:12:39,110 --> 00:12:41,850
+كاملة، لأن ما فيش فيها نواة، وبعدين، حجمها، لحظة،
+
+184
+00:12:41,850 --> 00:12:44,750
+حجمها أقل من حجم الخلايا الحمراء بكثير، Platelets،
+
+185
+00:12:44,750 --> 00:12:46,890
+الخلايا الحمراء حجمها، حكينا، من 7 إلى 9 مايكرون
+
+186
+00:12:46,890 --> 00:12:51,170
+بينما الـPlatelets حجمها تقريبًا 4 مايكرون، تمام؟
+
+187
+00:12:51,170 --> 00:12:54,690
+فحجمها أقل بكثير، بس طبعًا هي مجمعة مع بعض، مع بعض
+
+188
+00:12:54,690 --> 00:12:57,360
+لأن Platelets إيش وظيفته يا شباب؟ الـ Platelets
+
+189
+00:12:57,360 --> 00:13:01,180
+وظيفتها اللي هو الـ Clumping، تعمل الـ Clump اللي
+
+190
+00:13:01,180 --> 00:13:03,680
+بتتجمع مع بعض عشان تعمل تجارب الدم، تعمل تجارب الدم
+
+191
+00:13:03,680 --> 00:13:06,380
+وهنا جاياني في الـ slide عاملة الـ Clump، بيجمع
+
+192
+00:13:06,380 --> 00:13:09,180
+الخلايا الصفائح الدموية مع بعض، بعض هذه بيسميها
+
+193
+00:13:09,180 --> 00:13:13,160
+احنا Clump of Platelets، لو شفت في الـ block فلان
+
+194
+00:13:13,160 --> 00:13:18,640
+بكتبه في التقرير، تمام؟
+
+195
+00:13:18,640 --> 00:13:20,100
+معي يا شباب أنتم؟
+
+196
+00:13:23,580 --> 00:13:26,900
+طيب، الـ Abnormal Changes في الخلايا البيضاء، إيش
+
+197
+00:13:26,900 --> 00:13:30,800
+بيصير عندي؟ طبعًا، نجات كلها بقى برع الأشكال، بدنا
+
+198
+00:13:30,800 --> 00:13:36,620
+نركز فيها كويس، طبعًا، أول شغلة، في مصطلح بيسموه
+
+199
+00:13:36,620 --> 00:13:42,840
+«Left Shift» و «Right Shift»، «Left Shift» إنه أنا
+
+200
+00:13:42,840 --> 00:13:46,540
+بكون عندي Non-Segmented Neutrophil أكثر من 5%، كيف
+
+201
+00:13:46,540 --> 00:13:51,100
+يعني؟ يعني إنه أنا في الـ «maturation» هتمرّ على
+
+202
+00:13:51,100 --> 00:13:54,320
+الـ «maturation» هيكون عندي الـ «Neutrophil» هتمرّ
+
+203
+00:13:54,320 --> 00:14:02,040
+بعدد مراحل، بتبلش من الـ… تبلش من، نحكي الـ… الشيء
+
+204
+00:14:02,040 --> 00:14:04,820
+اسمه الـ «stem cells» اللي بتؤدي لـ«segmented
+
+205
+00:14:04,820 --> 00:14:08,280
+neutrophil»، لو شفت خلايا ما قبل الـ«band» أو
+
+206
+00:14:08,280 --> 00:14:12,680
+الـ«stab» 5%، بعتبر أنا عندي «left shift»، هيجيب
+
+207
+00:14:12,680 --> 00:14:16,100
+العكس، الـRight Shift إن أنا الـModulation زاد عن
+
+208
+00:14:16,100 --> 00:14:19,000
+حده، زاد عن حده، إن أنا الـNeutrophil عدد الـLoops
+
+209
+00:14:19,000 --> 00:14:23,240
+فيها 2 إلى 5، لو شفت خلايا الـNeutrophil 3% أكثر
+
+210
+00:14:23,240 --> 00:14:28,080
+من 5 Loops، بعتبر عندي Right Shift، تمام؟ طبعًا،
+
+211
+00:14:28,080 --> 00:14:31,120
+بتفيدني إيش Left Shift، Right Shift، تحديد حالات
+
+212
+00:14:31,120 --> 00:14:34,660
+مرضية، أنا Normal لازم أكونش في عندي Shift نهائيًا،
+
+213
+00:14:34,660 --> 00:14:38,730
+طيبToxic Granulation، طبعًا هذا كتير مصطلحات كتير
+
+214
+00:14:38,730 --> 00:14:42,510
+مُرَدة ومشوهة كتير، إنه أنا شايفين الخلايا النيتروفيل
+
+215
+00:14:42,510 --> 00:14:46,610
+اللي على اليمين الـgranules فيها، إيش لونها؟ –
+
+216
+00:14:46,610 --> 00:14:49,470
+أزرق – أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+217
+00:14:49,470 --> 00:14:49,550
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+218
+00:14:49,550 --> 00:14:50,150
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+219
+00:14:50,150 --> 00:14:58,010
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+220
+00:14:58,010 --> 00:15:04,310
+أزرق، طبعًا، فهذه بتدل على إنه فيه التهابات بكتيرية
+
+221
+00:15:04,310 --> 00:15:07,430
+وهذا دليل على… طبعًا، بيكون عندي خلايا Neutrophil
+
+222
+00:15:07,430 --> 00:15:12,090
+عالية، عددها بالإضافة إن الـ… الـGranules بتتغير
+
+223
+00:15:12,090 --> 00:15:14,090
+من شكلها، بيصير Toxic، طبعًا ليش بتتغير من
+
+224
+00:15:14,090 --> 00:15:17,130
+شكلها؟ لأن ده هتفرز في نظري، الـGranules فيه عندها
+
+225
+00:15:17,130 --> 00:15:20,450
+عدة أنواع، فيه Primary وSecondary وفيه من ضمن وظيفة
+
+226
+00:15:20,450 --> 00:15:23,770
+في الـGranules فرز مواد تقتل البكتيريا،
+
+227
+00:15:23,770 --> 00:15:27,190
+الـLysosomes فهذه دور جدًا في تغيير، وفرز المواد
+
+228
+00:15:27,190 --> 00:15:33,130
+تؤدي لتغيير شكلها، تمام؟ طبعًا، عندي فيه الـAll
+
+229
+00:15:33,130 --> 00:15:37,450
+Roots، الـAll Roots فيه عندي، شايفين العصاي داخل
+
+230
+00:15:37,450 --> 00:15:41,250
+الـ… شايفين الـSlides على اليمين؟ آه، آه، فيه
+
+231
+00:15:41,250 --> 00:15:44,030
+عصاي، فيه عصاي صغيرة هيك، طبعًا، اللي بيسموه
+
+232
+00:15:44,030 --> 00:15:47,490
+All Roots، All Roots، وفي عندك على الشمال برضه، في
+
+233
+00:15:47,490 --> 00:15:50,050
+عندي بعض الخلايا، طبعًا، هذه الخلايا عبارة عن
+
+234
+00:15:50,050 --> 00:15:53,090
+المراحل الأولية من الـNeutrophil، طبعًا، اللي هي
+
+235
+00:15:53,090 --> 00:15:57,520
+عبارة عن الـ… نحكي الـ… الـ… اللهم صلي الله عليه وسلم،
+
+236
+00:15:57,520 --> 00:16:00,440
+الـMetamyelocytes وMyelocytes، فعندي هنا أغلب
+
+237
+00:16:00,440 --> 00:16:04,720
+الخلايا هدول عبارة عن Myelocytes، تمام؟ لمرحلة ما،
+
+238
+00:16:04,720 --> 00:16:07,600
+طبعًا ما بتظهرش كثير، بيكون هذه في الـbone
+
+239
+00:16:07,600 --> 00:16:10,460
+marrow غالبًا إلا في حالات، نحكي سرطانية،
+
+240
+00:16:10,460 --> 00:16:13,180
+الـLeukemia أو إذا كان بيعاني حالات Leukemoid
+
+241
+00:16:13,180 --> 00:16:16,420
+Reaction تظهر عندي، بعدين هم بيظهر عندي اللي هي
+
+242
+00:16:16,420 --> 00:16:19,460
+طبعًا هذه الحالة اللي هي الـDohle bodies طبعًا تمُر معنا
+
+243
+00:16:19,460 --> 00:16:24,320
+بشكل تفصيل أكثر، الـDohle bodies وإيش أساسها وإيش سببها
+
+244
+00:16:24,320 --> 00:16:29,170
+و وين تظهر بأي حالة، طبعًا، مرة معناها بالصلاة على
+
+245
+00:16:29,170 --> 00:16:31,070
+الـHypersegmented، إيش هو يعني بالصلاة على
+
+246
+00:16:31,070 --> 00:16:35,250
+الـHypersegmented، يا شباب؟ Right Shift، بالظبط،
+
+247
+00:16:35,250 --> 00:16:36,770
+Right Shift، الـHypersegmented بيكون خلايا
+
+248
+00:16:36,770 --> 00:16:41,890
+Neutrophil الـSegmentation عالية، لاحظوا الـslide
+
+249
+00:16:41,890 --> 00:16:48,390
+على الشمال، كان محدّد فيها، عدّولي يا هون، سبعة،
+
+250
+00:16:48,390 --> 00:16:51,970
+بالضبط، سبعة Segmentation، فتعتبر Right Shift
+
+251
+00:16:51,970 --> 00:16:56,790
+يعني، ولاحظوا اليمين برضه نفس الحكاية، 2، 4، 6، 8،
+
+252
+00:16:56,790 --> 00:16:58,930
+فهذا يسموها hyper-segmented neutrophil
+
+253
+00:17:01,970 --> 00:17:07,210
+طبعًا، الخلايا الثانية دي خلايا حمرة الخلية فوق،
+
+254
+00:17:07,210 --> 00:17:09,870
+الـNeutrophilها دي ممكن تخربطكم شوية تفكروا هي
+
+255
+00:17:09,870 --> 00:17:13,730
+عبارة عن خلية إيش؟ Lymphocyte لأن Lymphocyte قريب
+
+256
+00:17:13,730 --> 00:17:16,690
+منها لكن هي دي خلية اللي هي الخلية الأولية الخلايا
+
+257
+00:17:16,690 --> 00:17:20,990
+الحمرة اللي هي بقى Nucleated RBC، Nucleated RBC
+
+258
+00:17:20,990 --> 00:17:25,030
+شباب، موضوع الخلايا يعني حاولوا تركزوا فيه كثير
+
+259
+00:17:25,030 --> 00:17:28,770
+لأنه من هالجهة كل مرة تلاقوا خلية درسوها صح عشان من
+
+260
+00:17:28,770 --> 00:17:31,520
+القدام شوية إن شاء الله ما تخربطوش كثير في تمييز بين
+
+261
+00:17:31,520 --> 00:17:33,800
+خلية وخلية، تمام؟
+
+262
+00:17:35,900 --> 00:17:39,060
+عندي مصطلح بيسموه «anisocytosis of neutrophil»
+
+263
+00:17:39,060 --> 00:17:42,480
+كلمة «anisocytosis» مصطلح له تعدد الحجم، كيف تعدد
+
+264
+00:17:42,480 --> 00:17:45,440
+الحجم؟ عندي حجم صغير وحجم كبير، طبعًا عندي خلايا
+
+265
+00:17:45,440 --> 00:17:48,960
+الـ «نيتروفيل»، عندي خمس خلايا، طلعوا الخلايا، احنا
+
+266
+00:17:48,960 --> 00:17:51,000
+الخلايا نفكروا عليها شغل، هل جئنا احنا نعتبره
+
+267
+00:17:51,000 --> 00:17:55,260
+الدائرة هاي ساعة، تمام؟ هل جئنا عند الساعة تقريبًا
+
+268
+00:17:55,260 --> 00:17:59,800
+عشرة، بين الساعة عشرة ومركز، في خلية، قارنوها مع
+
+269
+00:17:59,800 --> 00:18:02,680
+الخلية اللي عند الساعة خمسة، في فرق بين الحجم، صح
+
+270
+00:18:02,680 --> 00:18:06,960
+ولا لأ؟ أيه؟ هذا طبعًا تختلف حجم الـNeutrophil نسميها
+
+271
+00:18:06,960 --> 00:18:11,880
+Anisocytosis of Neutrophil فيه عندي الـvacuolation،
+
+272
+00:18:11,880 --> 00:18:14,840
+الـvacuolation طبعًا هي وجود زي الهواء أو فقعات
+
+273
+00:18:14,840 --> 00:18:19,360
+الهواء داخل الـNeutrophil أو الـBronchitis طبعًا عندي
+
+274
+00:18:19,360 --> 00:18:23,870
+أنا الـNeutrophil اللي هي اللي على اليمين لعظم ينظف
+
+275
+00:18:23,870 --> 00:18:26,550
+فيها لأن فيه فقعات هواء فيها والمرصد، طبعًا وجود
+
+276
+00:18:26,550 --> 00:18:30,330
+الـVacuolation بتدل على وجود Infections، الجهبات
+
+277
+00:18:30,330 --> 00:18:33,950
+لأن الـVacuolation عبارة عن بصيرة عندي حالة نشطة
+
+278
+00:18:33,950 --> 00:18:37,410
+Vacuolation هذه الحالة نشطة الـVacuolation، كما
+
+279
+00:18:37,410 --> 00:18:43,050
+حكينا، تؤدي إلى إن الـGranules تفرغ محتوياتها من
+
+280
+00:18:43,050 --> 00:18:46,110
+المواد وبتصبح الـGranules فارغة، فهذه عبارة عن
+
+281
+00:18:46,110 --> 00:18:50,010
+الـVacuolation طبعًا عندي الخليتين اللي بيقوموا
+
+282
+00:18:50,010 --> 00:18:53,510
+بعملية اللي بيحكي البلعمة أو الـPhagocytosis اللي
+
+283
+00:18:53,510 --> 00:19:01,750
+هي الـNeutrophil والـMonocyte دكتور، معلش، ممكن بس
+
+284
+00:19:01,750 --> 00:19:06,110
+عسريق، بس تشرحلي نهائيًا لأنه أنا ما .. يعني الـNet
+
+285
+00:19:06,110 --> 00:19:13,710
+عندي ما كانش كويس الو؟
+
+286
+00:19:14,100 --> 00:19:16,600
+تمام يا سعيد، تمام، بأحكيلك أنا الـVacuolation
+
+287
+00:19:16,600 --> 00:19:23,000
+طبعًا هي عبارة عن زي بقعات هواء داخل الخلايا
+
+288
+00:19:23,000 --> 00:19:27,400
+الـNeutrophilic، لأن السببها، السببها أنه في
+
+289
+00:19:27,400 --> 00:19:32,840
+اضطرابات تعمل سيئة عملية البلعمة للبكتيريا أو
+
+290
+00:19:32,840 --> 00:19:38,220
+للميكروبات المدخلة، طبعًا نتيجة البلعمة تضرر
+
+291
+00:19:38,220 --> 00:19:42,770
+اضطرابات البكتيريا والدكتور بس داخل خلية الـ
+
+292
+00:19:42,770 --> 00:19:45,970
+Neutrophil يعني؟ مش سامع زي الدكتور معاه تفضل
+
+293
+00:19:45,970 --> 00:19:49,230
+تقبيلاتك على سهيلة فأقولك بس داخل خلية الـ
+
+294
+00:19:49,230 --> 00:19:51,570
+Neutrophil بس ولا فيها خلايا .. الـNeutrophil و
+
+295
+00:19:51,570 --> 00:19:54,070
+الـMonocyte بس الـNeutrophil والـMonocyte ضمن
+
+296
+00:19:54,070 --> 00:19:57,070
+الخلايا المسؤولة على البلعمة خلية الـMonocyte هي
+
+297
+00:19:57,070 --> 00:20:00,350
+موجودة على اليمين، شايفينها؟ وخلية الـNeutrophil
+
+298
+00:20:00,350 --> 00:20:02,750
+موجودة على الشمال، شايفينهم؟
+
+299
+00:20:05,240 --> 00:20:08,360
+طبعًا، فيه عندي Degeneration of Nucleus طبعًا،
+
+300
+00:20:08,360 --> 00:20:11,640
+الـDegeneration of Nucleus العظيم إن هو طبعًا مش
+
+301
+00:20:11,640 --> 00:20:16,180
+طبيعي الشكل لها، عظيم النواة شكلها مش طبيعي طبعًا
+
+302
+00:20:16,180 --> 00:20:19,240
+لسه شكلها مش طبيعي النواة لأنه طبعًا صارت تغيرات على
+
+303
+00:20:19,240 --> 00:20:21,880
+النواة طبعًا ماذا بيصير Degeneration of nucleus في
+
+304
+00:20:21,880 --> 00:20:25,460
+حالة العين القادمة يعني أنا سحبت عينة بدل ما
+
+305
+00:20:25,460 --> 00:20:27,960
+أعملها Blood film مباشرة سنت عليها يوم وبعدين سحبت
+
+306
+00:20:27,960 --> 00:20:30,880
+لها Blood film طبعًا بيصير تغيرات على النواة بيصير
+
+307
+00:20:30,880 --> 00:20:34,000
+Degeneration of nucleus شايفين النواة كيف صارت؟ صارت
+
+308
+00:20:34,000 --> 00:20:37,420
+تغيرات فيها لأنها بتمشي شوية ويصير لها غامقة كثير
+
+309
+00:20:37,420 --> 00:20:40,480
+عندي الـDohle bodies الـDohle bodies شايفين
+
+310
+00:20:40,480 --> 00:20:46,970
+طبعًا الزوائد اللي في داخل الخلايا النيفي نقطة
+
+311
+00:20:46,970 --> 00:20:52,910
+درجة في نقطة درجة بيسموها Dohle bodies احنا
+
+312
+00:20:52,910 --> 00:20:56,490
+طبعًا خلصنا ما تبقى من المحاضرة خلوا يجوا معايا إن
+
+313
+00:20:56,490 --> 00:21:07,430
+شاء الله بدي أدخل للمحاضرة الثانية دكتور
+
+314
+00:21:07,430 --> 00:21:13,350
+أنت متابع المحاضرة ولا لأ؟ يعني في تسجيل؟ آه، لا تقلق،
+
+315
+00:21:13,350 --> 00:21:15,890
+أنا هنزلكم تسجيل إن شاء الله بالإضافة لتسجيل
+
+316
+00:21:15,890 --> 00:21:19,630
+المسابق اللي منزلكم يا أنا مش منزلها، بهاست عليه
+
+317
+00:21:19,630 --> 00:21:23,250
+عمود اللي مش ملاقيه تسجيل الجديد لأ، منزل، كله
+
+318
+00:21:23,250 --> 00:21:28,050
+فلس، تبعتني على الرابط لما أنزله إن شاء الله خير،
+
+319
+00:21:28,050 --> 00:21:31,830
+طيب، احنا هناخد الـWBC اللي طبعًا اللي نرجع كمان
+
+320
+00:21:31,830 --> 00:21:38,130
+مرة لموضوع الـWBC morphology هبعتلكم ملف ثاني إن
+
+321
+00:21:38,130 --> 00:21:44,800
+شاء الله هذا طبعًا أخذنا منه بعضه، هكمل لكم عليه على
+
+322
+00:21:44,800 --> 00:21:48,440
+السريع، طبعًا لأنه في بعض الـSlides مش موجودة كانت
+
+323
+00:21:48,440 --> 00:21:53,940
+هناك، أنا بس أنا هاخد بشوية بتفاصيل أكثر هلجيت
+
+324
+00:21:53,940 --> 00:21:56,280
+بالنسبة للموعد، كنتوا بتثبتوه عليك يا شباب، ولا
+
+325
+00:21:56,280 --> 00:22:01,040
+كيف؟ أنا شايف الصبح أحسن، والله الصبح أحسن يا
+
+326
+00:22:01,040 --> 00:22:04,220
+دكتور، بصراحة يعني أنا شايف المساء أحسن، عشان في
+
+327
+00:22:04,220 --> 00:22:08,780
+هالة قطع الـNet بقدر الواحد يدبر حاله أنا .. أنا ..
+
+328
+00:22:08,780 --> 00:22:11,480
+أنا المسألة بالنسبة لي أني بدي أنا واحد بيصحى الصبح،
+
+329
+00:22:11,480 --> 00:22:15,820
+بدرس المسألة، بطول، بطلع، بنزل، رابطة إيه؟ والله يا
+
+330
+00:22:15,820 --> 00:22:19,300
+محمد، أجيب نرجع للصبح أحسن، لأنه .. للمحاضرة الصبح
+
+331
+00:22:19,300 --> 00:22:21,760
+أحسن، بعدين اسمع، احنا الصبح ممكن نبلش متأخر
+
+332
+00:22:21,760 --> 00:22:26,180
+شوية، ممكن نبلش على الساعة إحدى عشرة، إذا حابين، عادي،
+
+333
+00:22:26,180 --> 00:22:28,780
+خلاص خليني على الساعة إحدى عشرة، بدل الصبح هبقى كتير،
+
+334
+00:22:28,780 --> 00:22:29,300
+بدر على عشرة
+
+335
+00:22:35,180 --> 00:22:37,200
+ظهر لكم شاشة بالنسبة للـWhite Blood Cells لأن الـ
+
+336
+00:22:37,200 --> 00:22:40,540
+Platelets Abnormal Morphology؟ ده أه، لأ بالتالي
+
+337
+00:22:40,540 --> 00:22:45,160
+وهناخد الـRBCs Morphology إن شاء الله ومدياكم
+
+338
+00:22:45,160 --> 00:22:48,080
+تدرسوهم كويس لأن المرة الجاية مدياكم تدرسوهم كويس
+
+339
+00:22:48,080 --> 00:22:57,260
+وزي الأسئلة بعد وإن شاء الله نجاوب عليها طيب طبعًا زي
+
+340
+00:22:57,260 --> 00:23:00,960
+ما حكينا في مصطلح بيسموه Platelets Satellitosis
+
+341
+00:23:01,270 --> 00:23:03,650
+Satellitosis يعني الـSatellite، الـSatellite يعني
+
+342
+00:23:03,650 --> 00:23:05,950
+اللي بيجي على سطح الخلايا، على سطح الشيء
+
+343
+00:23:05,950 --> 00:23:07,690
+الـSatellite عندنا، صح ولا لأ؟
+
+344
+00:23:07,690 --> 00:23:10,830
+فالـPlatelet Satellitosis، الـPlatelet Satellitosis عبارة عن
+
+345
+00:23:10,830 --> 00:23:13,890
+الصفائح الدموية موجودة على سطح الـNeutrophil طبعًا،
+
+346
+00:23:13,890 --> 00:23:16,150
+موجودة على سطح الـNeutrophil بسبب أنه بينتشر على
+
+347
+00:23:16,150 --> 00:23:21,210
+سطح الـNeutrophil ممكن أن تكون سببها الـEDTA طبعًا،
+
+348
+00:23:21,210 --> 00:23:22,970
+بتعمل Exchanges، هذه Exchanges تؤدي إلى
+
+349
+00:23:22,970 --> 00:23:26,470
+الـPlatelet Satellitosis، تمام؟
+
+350
+00:23:29,420 --> 00:23:32,880
+طبعًا هذه الحالة مش مرضية، هذه الحالة بيصير in
+
+351
+00:23:32,880 --> 00:23:36,740
+vitro ليس in vivo، بـPlatelet Satellitosis، طيب، شايفين
+
+352
+00:23:36,740 --> 00:23:44,780
+هالصورة هاي؟ واضحة جدا، واضحة جدا، بـPlatelet Satellitosis، هذه
+
+353
+00:23:44,780 --> 00:23:49,450
+بـPlatelet Satellitosis في عندي ال .. الـGiant Platelets
+
+354
+00:23:49,450 --> 00:23:53,370
+من اسمها، الـPlatelets بحكيلكم حجمها صغير، حجمها
+
+355
+00:23:53,370 --> 00:23:56,890
+تقريبًا هي Platelets، شايفين؟ أنتم شايفين الـMouse
+
+356
+00:23:56,890 --> 00:24:00,870
+للأسف الشديد، أه؟ جهاز كيف وصل لكم الـMouse أنا؟ لأ و
+
+357
+00:24:00,870 --> 00:24:06,150
+الله، طب .. طب دكتور بشر، بالنسبة لل .. ال .. ال
+
+358
+00:24:06,150 --> 00:24:09,730
+Satellitosis هذي قبل شوية، ليش بتصير الـSatellitosis هيك؟ ما
+
+359
+00:24:09,730 --> 00:24:14,510
+حكينا الـEDTA، هاي كتابتها، هاي سببها الـEDTA
+
+360
+00:24:14,510 --> 00:24:17,790
+بتعمل الـChanges، طبعًا هذه الـChanges تؤدي
+
+361
+00:24:17,790 --> 00:24:22,170
+لـPlatelet Satellitosis، فطبعًا هذه حالة in vitro و
+
+362
+00:24:22,170 --> 00:24:25,170
+لسه in vivo، طبعًا و نتيجة Platelet Satellitosis، أنا
+
+363
+00:24:25,170 --> 00:24:28,010
+ما بنعطي عدد Platelets في الـCBC، بيكون عددها
+
+364
+00:24:28,010 --> 00:24:34,240
+قليل، تمام؟ طيب، الـ… الـPlatelets الـGiant
+
+365
+00:24:34,240 --> 00:24:38,080
+Platelets من اسمها Giant يعني حجم كبير، Giant حجم
+
+366
+00:24:38,080 --> 00:24:43,440
+كبير، فـGiant Platelets، شايفين الصورة اللي بالنص،
+
+367
+00:24:43,440 --> 00:24:46,500
+فيه عندي خلية Lymphocytes على اليمين وعلى الشمال،
+
+368
+00:24:46,500 --> 00:24:51,240
+هذا عبارة عن Giant Platelets، شايفينها؟
+
+369
+00:24:51,240 --> 00:24:55,540
+أكبر من الـLymphocytes صحيح، أكبر من الـLymphocyte
+
+370
+00:24:55,540 --> 00:24:58,280
+هذا ما زالت الـPlatelets طبعًا، يكون أكبر من حجم
+
+371
+00:24:58,280 --> 00:24:59,880
+الخلايا الحمراء كمان طبعًا، حكينا إن الـ
+
+372
+00:24:59,880 --> 00:25:02,280
+Lymphocyte قريب حجمها من الخلايا الحمراء الصغيرة
+
+373
+00:25:02,280 --> 00:25:05,960
+طبعًا، هذه بيصير مدى، في حالة Increase Platelets
+
+374
+00:25:05,960 --> 00:25:09,100
+Turnover إنه أنا عندي نشاط في الصفائح، في إنتاج
+
+375
+00:25:09,100 --> 00:25:12,720
+الصفائح، فبالزيت أو في حالة المرض، بيسميها أنا الـ
+
+376
+00:25:12,720 --> 00:25:17,040
+MPD، الـ Myeloproliferative Disorders أو الـ
+
+377
+00:25:17,040 --> 00:25:20,460
+MDS، الـ Myelodysplastic Syndrome أو Syndrome
+
+378
+00:25:20,460 --> 00:25:24,680
+طبعًا، في الحالات المرضية هذه هتبقوا معجوبين كتير،
+
+379
+00:25:24,680 --> 00:25:29,640
+هتاخدوها بالنظري بشكل تفصيل كامل، تمام؟ لكن 
+
+380
+00:25:29,640 --> 00:25:33,360
+اتذكروها، الـ Platelet اسم بيصير في حالة Plateless 
+
+381
+00:25:33,360 --> 00:25:36,260
+turnover turn over يعني إيش؟ عندك نشاط زائد في
+
+382
+00:25:36,260 --> 00:25:39,420
+إنتاج الصفائح الدموية، لأي سبب من الأسباب أو في
+
+383
+00:25:39,420 --> 00:25:45,780
+الـ MPD Myeloproliferative disorder أو الـ MDS
+
+384
+00:25:45,780 --> 00:25:51,720
+Myelodysplastic syndrome، تمام؟ هي هن دي هن،
+
+385
+00:25:51,720 --> 00:25:54,440
+شايفين الخلايا هذه بيسموها بالنص الذرق جهنم 
+
+386
+00:25:54,440 --> 00:25:59,600
+Platelets، شايفينها؟ طبعا الخلايا كل اللي موجودة عندي 
+
+387
+00:25:59,600 --> 00:26:00,640
+هي أخبار عن الخلايا الحمرى
+
+388
+00:26:03,890 --> 00:26:05,990
+الخلايا الحمرى، هنأخد تفاصيل عنها فيما بعد إن شاء
+
+389
+00:26:05,990 --> 00:26:08,290
+الله مش مشكلة، مش هنحكيها لجد أنا فيه اندي Large
+
+390
+00:26:08,290 --> 00:26:12,130
+Platelets، طبعًا Large Platelets حجم أقل من حجم
+
+391
+00:26:12,130 --> 00:26:18,090
+الـ… الـGiant Platelets لكن أكبر من إيش؟ طبعًا من
+
+392
+00:26:18,090 --> 00:26:21,110
+الصفائح الدموية نفسها، فلاحظين انديها طبعًا حجم أقل
+
+393
+00:26:21,110 --> 00:26:23,910
+من الخلايا الحمرة كمان، فلاحظين انديها في اندي
+
+394
+00:26:23,910 --> 00:26:31,030
+الصورة، الصورة في اندي تلت خلايا جنبها زرقة تحت،
+
+395
+00:26:31,030 --> 00:26:38,360
+وبالنص في خلية حمرةوالمركز تحت شوية فيناهذه عبارة
+
+396
+00:26:38,360 --> 00:26:43,600
+عن Large Platelets طبعًا هذه أبناء المرض بيصير نفس
+
+397
+00:26:43,600 --> 00:26:48,400
+التلات حالات السابقة اللي تبعت الـ Giant Platelets
+
+398
+00:26:48,400 --> 00:26:54,240
+بيصير اللي هي Turnover بزيد أو الـ MPD أو الـ MDS
+
+399
+00:26:54,240 --> 00:26:58,260
+بالإضافة الحالات التالتة مرضية الميهيجلين أدومالي
+
+400
+00:26:58,260 --> 00:27:01,300
+والـ Gray Platelet Syndrome والـ Bernard-Soulier
+
+401
+00:27:01,300 --> 00:27:04,420
+Syndrome هذه حالات مرضية بالزير، بالزير تلات حالات
+
+402
+00:27:04,420 --> 00:27:06,000
+الأولى بالإضافة لتلات حالات التانية
+
+403
+00:27:10,750 --> 00:27:13,910
+فين دي؟ احنا طبعا ممكن نسحب عين الدم، عين الدم
+
+404
+00:27:13,910 --> 00:27:16,310
+طبعتنا حكينا في الـCBS، في الـHematology عبارة عن
+
+405
+00:27:16,310 --> 00:27:20,950
+عينة A.H.EDTA، يعني Holy Blood أحيانا أنا بسحب،
+
+406
+00:27:20,950 --> 00:27:23,770
+ماكانتش كمية الـanticoagulant كفاية للدم، بسحب دم
+
+407
+00:27:23,770 --> 00:27:27,930
+بزيادة، فبتؤدي إلى بعض الجلطات، أنا بسميها Micro
+
+408
+00:27:27,930 --> 00:27:31,890
+Clots، Micro Clots Micro Clots طبعا بتظهر معاي،
+
+409
+00:27:31,890 --> 00:27:35,060
+اللي هي عبارة عن الـFibrin strandsوفيها خلايا بيض
+
+410
+00:27:35,060 --> 00:27:38,000
+وفيها خلايا بلاتلس وممكن تكون فيها خلايا حمره
+
+411
+00:27:38,000 --> 00:27:40,420
+أحياناً، طبعا شايفين الزرق هذا اللي في ال
+
+412
+00:27:40,420 --> 00:27:43,740
+background، عبارة عن خيوط الزرق هذه، هذه عبارة عن
+
+413
+00:27:43,740 --> 00:27:47,040
+micro-clots، طبعا زي ما حكي هناإذاً micro
+
+414
+00:27:47,040 --> 00:27:49,520
+-clots في حالة إن كان عندى نسبة الـ ratio غلط
+
+415
+00:27:49,520 --> 00:27:53,280
+بالنسبة للـ anticoagulant أو إن أنا نتيجة إن طولت
+
+416
+00:27:53,280 --> 00:27:57,540
+كتير في عملية سحب دور من sections إن أنا بسحب الدم
+
+417
+00:27:57,540 --> 00:28:00,920
+طولت كتير أو ماعرفش أسحب صح هذه تؤدي إلى طبعا
+
+418
+00:28:00,920 --> 00:28:04,480
+التجلطات قبل ما الدم أنه طبعا أحنا حكينا الـ
+
+419
+00:28:04,480 --> 00:28:07,660
+EDTA الهدف منها منع التجلط كيف يمنع تجلط الشباب؟
+
+420
+00:28:07,660 --> 00:28:14,470
+إذا تذكروا في المقدمة مين بيحكيلي؟ تجلطفاكيف
+
+421
+00:28:14,470 --> 00:28:19,290
+الإيدة تتملأ تجلط الدم؟
+
+422
+00:28:19,290 --> 00:28:22,610
+أظن
+
+423
+00:28:22,610 --> 00:28:30,850
+فيها مادة الهيبارين؟ لأ، اسمعي، اسمعي،
+
+424
+00:28:30,850 --> 00:28:34,270
+الهيبارين نفس الإيدي دا، أبعد من الدنم وانا تجلط،
+
+425
+00:28:34,270 --> 00:28:37,570
+لكن كيف تملأ التجلط؟ عن طريق الـChelating
+
+426
+00:28:37,570 --> 00:28:44,680
+للكالسيون، صح، صح،الذكرته؟ الـ Chelating
+
+427
+00:28:44,680 --> 00:28:50,000
+للكالسيوم؟ صحيح، الإيه دي ده؟ والكالس بأجزالها
+
+428
+00:28:50,000 --> 00:28:54,000
+والسيطرية نفس الهدف إنه بتعملي Chelating
+
+429
+00:28:54,000 --> 00:28:57,900
+للكالسيوم، ترتبطلي مع الكالسيوم اللي هو مهم جدا في
+
+430
+00:28:57,900 --> 00:29:01,120
+تجلط، في عملية تجلط الدم، وبالتالي لازمنا أتجلط
+
+431
+00:29:01,120 --> 00:29:02,580
+الدم عن طريق Chelating للكالسيوم
+
+432
+00:29:06,710 --> 00:29:09,930
+الهيبرين بيرتبطلي مع الـ Antithrombin فبيمنع
+
+433
+00:29:09,930 --> 00:29:13,310
+الهيبرين يحولي الفيبرونجين لفيبرين فالهيبرين بيقلب
+
+434
+00:29:13,310 --> 00:29:15,870
+القليل شوية عنهم لكن كلهم يقدّوا نفس الغرض اللي هو
+
+435
+00:29:15,870 --> 00:29:20,790
+مانع تجاربه قدامأنا استخدمت الإيدة دا، كان الإيدة
+
+436
+00:29:20,790 --> 00:29:25,150
+نحكي بور قديم، كان الإيدة في مشكلة، أو إن أنا خلال
+
+437
+00:29:25,150 --> 00:29:28,550
+العملية تسحب، طولت، جيت أسحب من المعاد، المعاد ما
+
+438
+00:29:28,550 --> 00:29:31,890
+شاء الله إيده مليانة، مش عارف أتطلع للـVan، طولت و
+
+439
+00:29:31,890 --> 00:29:35,810
+أنا بسحب الـVan، صار عندي تجولوطة خفيفة هادية،
+
+440
+00:29:35,810 --> 00:29:38,990
+بتظهر لي تحت الـMicroscope، بتسليد عليها شكل، إيش
+
+441
+00:29:38,990 --> 00:29:43,290
+اسمها؟ Micro Clots، شايفينها؟ تمام، Micro Clots،
+
+442
+00:29:43,290 --> 00:29:49,480
+تمام، تمام، فين دي Platelets Clumps؟بلايست كلامز
+
+443
+00:29:49,480 --> 00:29:55,720
+اللي أحكيناها جمعات الصباح مع بعض، شايفين في الـ
+
+444
+00:29:55,720 --> 00:30:01,290
+slide عند الساعة تقريبا 11فيه تجميعات تتوقع لنقطة
+
+445
+00:30:01,290 --> 00:30:03,250
+صغيرة هي برعاية الـ Platelets Clumps والـ
+
+446
+00:30:03,250 --> 00:30:06,390
+Platelets Clumps سببها برضه in vitro وليس in vivo
+
+447
+00:30:06,390 --> 00:30:09,630
+مانعش تدخل في الحالات المرضية لكن سببها إن أنا
+
+448
+00:30:09,630 --> 00:30:13,210
+الإيديات اللي استخدمتها قديمة شوية ممكن تؤدي
+
+449
+00:30:13,210 --> 00:30:18,970
+لتجميع الصفائح طبعا أو ممكن تؤدي ل… أو ممكن عملية
+
+450
+00:30:18,970 --> 00:30:22,650
+سحب الدم إن أنا خلال عملية سحب الدم طولت طبعا
+
+451
+00:30:22,650 --> 00:30:25,790
+النقطة المهمة جدا في Platelets Clumps إن أنا لو
+
+452
+00:30:25,790 --> 00:30:29,570
+مشيت عين الـCBC وكان عندي عدد Platelets قليلفي
+
+453
+00:30:29,570 --> 00:30:32,230
+الحالة هاي، مش لازم نعتمد أنه والله عندي plates
+
+454
+00:30:32,230 --> 00:30:34,590
+قليل، أنه فيه مشكلة في الـplates، لأ، لازم نتأكد
+
+455
+00:30:34,590 --> 00:30:37,650
+أنه مشكلة خارجية، مش داخلية، فبعمل الـBlood Film،
+
+456
+00:30:37,650 --> 00:30:40,070
+لما شوفت الـBlood Film وشوفت الـplateless clumps،
+
+457
+00:30:40,070 --> 00:30:42,550
+بعرف أن الـplateless عددها ده مش قليل، عددها الصح
+
+458
+00:30:42,550 --> 00:30:44,250
+أعلى من هيك، تمام؟
+
+459
+00:30:50,650 --> 00:30:55,130
+طبعًا في عندي نحكي الـSmall Platelets الـSmall
+
+460
+00:30:55,130 --> 00:30:58,730
+Platelets بيكون حجم صغير كتير طبعًا جايبين الـ… في
+
+461
+00:30:58,730 --> 00:31:01,770
+المركز في عندي خلية همرة فيها Small Platelets
+
+462
+00:31:01,770 --> 00:31:05,290
+طبعًا هذه حالة مرضية وحيدة اللي هي الـWiskott
+
+463
+00:31:05,290 --> 00:31:07,770
+-Aldrich Syndrome طبعًا هذه الحالة المرضية بيكون
+
+464
+00:31:07,770 --> 00:31:10,570
+فيها Small Platelets أو يكون عدد Platelets قليل
+
+465
+00:31:10,570 --> 00:31:13,710
+شدنا الـThrombocytopenia طبعًا هذه الحالة المرضية بتصيب
+
+466
+00:31:13,710 --> 00:31:18,450
+الـ… طبعًا الـ… الـ… Platelets أكتر شيءأو الـ
+
+467
+00:31:18,450 --> 00:31:20,450
+Degranulation أو الـ Platelets، طبعاً الـ
+
+468
+00:31:20,450 --> 00:31:22,490
+Degranulation أو الـ Platelets بيكون عندي الـ
+
+469
+00:31:22,490 --> 00:31:25,030
+Platelets مش فيها أزرق، إذا حتشوف الـ Platelets
+
+470
+00:31:25,030 --> 00:31:28,630
+فيها زرق كتير، زرقة، بيكون لونها فاهي شوية، زي
+
+471
+00:31:28,630 --> 00:31:34,130
+عنديوانا المركز لتحت شويه بين المركز وبين الساعة
+
+472
+00:31:34,130 --> 00:31:38,830
+نحكي سبعة طبعا فيه دي خلية Platelets هذه طبعا
+
+473
+00:31:38,830 --> 00:31:43,170
+فاهية شويه طبعا تتواجد الـ… نحكي الـDegradation في
+
+474
+00:31:43,170 --> 00:31:46,150
+Platelets في حالات الـGrey Platelet Syndrome وهي
+
+475
+00:31:46,150 --> 00:31:48,150
+نفس الحالة اللي مرض معناها كان بظهر فيها إيه؟ إذا
+
+476
+00:31:48,150 --> 00:31:53,060
+بتذكروا، بظهر فيها الـLarge Plateletsبظهر فيها
+
+477
+00:31:53,060 --> 00:31:55,760
+كمان، بتظهر في حالات discharge of platelet
+
+478
+00:31:55,760 --> 00:31:59,680
+granules نتيجة طبعاً لوكيميا، نتيجة cardio
+
+479
+00:31:59,680 --> 00:32:02,540
+-pulmonary bypass، نتيجة hairy cells لوكيميا أو
+
+480
+00:32:02,540 --> 00:32:06,160
+discharge of platelet granules في حالة غور من
+
+481
+00:32:06,160 --> 00:32:10,000
+سيكشن، تقنية كان عندي غلط وإجتماعات الأسهم طبعاً
+
+482
+00:32:10,000 --> 00:32:13,360
+خلصنا هذه الواحدة الموية، هندخل على الخلايا
+
+483
+00:32:13,360 --> 00:32:18,040
+البيضاء طيب، يا شباب، احنا عشان أهدئ نسخة تجربية
+
+484
+00:32:18,600 --> 00:32:23,500
+فأنا بدي أوجب شويه، خلّيه يسجل اللي هدا عشان ما
+
+485
+00:32:23,500 --> 00:32:26,420
+بديش أفقد التسجيل، لإنه بعد كده بيعطيني أنه ضايق
+
+486
+00:32:26,420 --> 00:32:28,520
+الأقل من الـPK تقع، و بعد كده أخرجي عليكم إن شاء
+
+487
+00:32:28,520 --> 00:32:30,060
+الله، إتبعوا؟ فاليكم معايا إتبعوا 
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_postprocess.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9a9d2e9434a03e97044f3de69d2441270061785e
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_postprocess.srt
@@ -0,0 +1,1949 @@
+1
+00:00:00,000 --> 00:00:02,980
+طيب، بسم الله الرحمن الرحيم إحنا إن شاء الله راح
+
+2
+00:00:02,980 --> 00:00:08,160
+نكمل شرح المادة طبعاً الـHematology زي ما حكيناها
+
+3
+00:00:08,160 --> 00:00:12,660
+أخدنا المحاضرة السابقة عن موضوع الـBlood Film كيف
+
+4
+00:00:12,660 --> 00:00:15,660
+نعمل Film وكيف نصبغاه إحنا طبعاً لما نصبغه الـFilm
+
+5
+00:00:15,660 --> 00:00:19,320
+هيدور معانا أشكال الخلايا تحت نجهة بصورة هاي هاي
+
+6
+00:00:19,320 --> 00:00:22,400
+الصورة عندي زي ما تلاحظين عندي هنا الخلايا الحمرة
+
+7
+00:00:22,400 --> 00:00:26,670
+اللي تسمى Bullion طبعاً الـPink، ماشي؟في عندي
+
+8
+00:00:26,670 --> 00:00:29,610
+الخلايا طبعًا الأحمر، طبعًا لاحظوا عندي أن الخلايا
+
+9
+00:00:29,610 --> 00:00:32,370
+الحمرة في الـ «تولتين» مسبوخ والـ «تولت» غير
+
+10
+00:00:32,370 --> 00:00:36,050
+مسبوخ، طبعًا هي بتظهر بالصورة هيك لأن طبعًا هي
+
+11
+00:00:36,050 --> 00:00:40,770
+عبارة عن الـ «Discoid» كيف يعني الـ «Discoid»؟ الـ
+
+12
+00:00:40,770 --> 00:00:46,350
+«جولد» طبعًا من الأطراف الكبيرة ومن الوسط، «thin»
+
+13
+00:00:46,350 --> 00:00:49,750
+شوية، أخف شوية، سمكة، فبتالي بتظهر كأنه خفيف،
+
+14
+00:00:49,750 --> 00:00:52,790
+همنها عنطبعًا، الخلايا الحمرة مليانة
+
+15
+00:00:52,790 --> 00:00:56,130
+بالـHemoglobina، زي ما أحنا عارفين، عندها الخلايا
+
+16
+00:00:56,130 --> 00:00:59,270
+البيضا خمس أنواع أساسيين، اللي هم، هذي إيه خلية؟
+
+17
+00:00:59,270 --> 00:01:03,150
+هذي نيتروفيل، هذي خلية الإيزينوفيل، هذي خلية
+
+18
+00:01:03,150 --> 00:01:06,590
+الـLymphocyte، الـMonocyte، والبيزوفيل، طبعًا،
+
+19
+00:01:06,590 --> 00:01:10,830
+خلية الـMonocyte وLymphocyte، طبعًا، هي عبارة
+
+20
+00:01:10,830 --> 00:01:15,410
+بيسموها Mononuclear، Mononuclear Lycoside، بينما
+
+21
+00:01:15,410 --> 00:01:20,650
+الخلايا التلاتة الضايقين، اللي الـGranularهذه
+
+22
+00:01:20,650 --> 00:01:24,590
+بيسموها Poly-Nuclear أو Granulocyte، طبعاً لأنها
+
+23
+00:01:24,590 --> 00:01:29,010
+تحتوى على حبيبات الـNitrophil حبيباتها نعم كتير
+
+24
+00:01:29,010 --> 00:01:34,710
+وPink، يعني دوب ميزين احنا الـXenophil حبيباتها
+
+25
+00:01:34,710 --> 00:01:38,210
+بيكون مرسوسة صح وبيكون لون أحمر الـBisophil
+
+26
+00:01:38,210 --> 00:01:40,890
+حبيباتها حجمها مختلفة، تتفاوت إيش كبير وإيش صغير
+
+27
+00:01:40,890 --> 00:01:46,630
+ومبعترة ولونها أسود، تمام؟
+
+28
+00:01:46,630 --> 00:01:51,470
+هاي كمان مرة عنديهذه خلية الـ Band، هذا طبعًا اسمه
+
+29
+00:01:51,470 --> 00:01:53,490
+بيسميه أحنا «Band Neutrophil» طبعًا «Band
+
+30
+00:01:53,490 --> 00:01:56,170
+Neutrophil» المرحلة مقبل الـ «Neutrophil» أحنا
+
+31
+00:01:56,170 --> 00:02:00,090
+هندرس في عملية الـ «maturation» اللي هي تطور إنشاء
+
+32
+00:02:00,090 --> 00:02:03,850
+الخلايا كيف تنشأ الخلايا من الخلية الأم لـ «stem
+
+33
+00:02:03,850 --> 00:02:07,330
+cells» لعند ما توصل لخلية الـ «mature cells» فهذه
+
+34
+00:02:07,330 --> 00:02:09,890
+المرحلتين هاي اللي مُتسبرة يعني «maturation»
+
+35
+00:02:09,890 --> 00:02:12,490
+«maturation» الـ «Band Neutrophil» تظهر عندي
+
+36
+00:02:12,490 --> 00:02:16,800
+بالنسبة تقريبًا 5%، 3 إلى 5%في الـ Blood Film،
+
+37
+00:02:16,800 --> 00:02:18,800
+يعني تظهر نوع من الظهورة في الـ Blood Film بنسبة
+
+38
+00:02:18,800 --> 00:02:22,800
+معينة، طبعا هذه خلية الـ Poly-Nuclear، طبعا نسميها
+
+39
+00:02:22,800 --> 00:02:25,580
+Poly-Nuclear، طبعا إن هو أصلا مجزقة، صارت إن دي
+
+40
+00:02:25,580 --> 00:02:28,340
+عبارة عن تلاتة Loops، هذا ما نسميه إحنا الـ Jews،
+
+41
+00:02:28,340 --> 00:02:32,370
+وهذا ما نسميه Loopsفمسميه three loops، طبعًا الـ
+
+42
+00:02:32,370 --> 00:02:34,890
+Neutrophil شايفين الحبابات فيها كيف؟ يعني نعم، من
+
+43
+00:02:34,890 --> 00:02:38,190
+وعنها الخليه هاي الـ Xenophil، طبعًا لاحظينها الـ
+
+44
+00:02:38,190 --> 00:02:40,910
+Neutrophil تنتين دول؟ هذه الـ Xenophil، الحباباتها
+
+45
+00:02:40,910 --> 00:02:45,650
+مرصوصة كإنه حد صفطها تسيط، ولونه أحمر، وغالبًا
+
+46
+00:02:45,650 --> 00:02:49,970
+النواة عبارة عن Binublia، فيها جزئين غالب النواة
+
+47
+00:02:49,970 --> 00:02:56,570
+دكتور، بقى دستك، بس في mouse أو في مؤشر؟ كيف؟ في
+
+48
+00:02:56,570 --> 00:03:00,200
+mouse أو مؤشر؟هيبقى أشير أنا جاعد، هيبقى شايف الـ
+
+49
+00:03:00,200 --> 00:03:07,640
+mouse؟ لأ، مش شايفينه لأ مش واضح دكتور مش عارف إذا
+
+50
+00:03:07,640 --> 00:03:12,040
+فيها آلية مش
+
+51
+00:03:12,040 --> 00:03:15,800
+شايفين ال mouse عندي؟ لأ، عشان مش عارفين ع أي صورة
+
+52
+00:03:15,800 --> 00:03:20,060
+بتحكي جاعد، ع أي صورة بتشرح طويل طيب، أنا ببنشت من
+
+53
+00:03:20,060 --> 00:03:24,640
+الصورة العلوية على الشمال تمام، هذه ال band
+
+54
+00:03:24,640 --> 00:03:30,110
+نيتروفيل شايفينها؟هذه باند نيتروفيل هي برعن جزء
+
+55
+00:03:30,110 --> 00:03:36,430
+واحد، إن هو فيها زي إيش؟ زي نحكي حدوث الحصان زمان
+
+56
+00:03:36,430 --> 00:03:40,270
+أو زي حد السنين، هذه بيسميها باند نيتروفيل،
+
+57
+00:03:40,270 --> 00:03:48,320
+شفتوها؟ طبعا هذه فيها نعمة، لونها طبعا pinkوطبعًا،
+
+58
+00:03:48,320 --> 00:03:51,820
+زي ما حكينا، هذه نسبة تواجدها تقريبًا من، زي ما
+
+59
+00:03:51,820 --> 00:03:56,540
+حكينا، من 3% لـ5%، من 3% لـ5%، ماشي؟ هالجهة اللي
+
+60
+00:03:56,540 --> 00:04:00,200
+عندي خلية الجنبها، اللي هي المرحلة ما بعديها
+
+61
+00:04:00,200 --> 00:04:04,660
+بيسموها، طبعًا، Segmented Neutrophil أو بيسموها
+
+62
+00:04:04,660 --> 00:04:09,010
+Poly-Nuclear Neutrophilطبعًا، زي ما حكينا، الـ
+
+63
+00:04:09,010 --> 00:04:15,210
+Maturation، إن شاء الله، هندرسه في أحد المحاضرات،
+
+64
+00:04:15,210 --> 00:04:17,410
+هيكون عندي من الـSegmented Neutrophil، الحبل ما
+
+65
+00:04:17,410 --> 00:04:22,110
+يتطور، هجيت الجنب، اللي في الأعلى، أقصى، اليمين،
+
+66
+00:04:22,110 --> 00:04:27,880
+هذي بيسميها أحنا أزينوفيل، تمام؟ تمامالـXenophil،
+
+67
+00:04:27,880 --> 00:04:30,780
+طب الـXenophil، خلّيني أشوف ممكن فيه اندهانة، إذا
+
+68
+00:04:30,780 --> 00:04:33,760
+بقدر أجيب الـpointer «بش روح تحت يا دكتور، كل
+
+69
+00:04:33,760 --> 00:04:36,800
+slide لحال» «بش روحين؟ آه، هنخدم، إحنا الدباش مش
+
+70
+00:04:36,800 --> 00:04:41,840
+مشكلة» «طبعا، في انديهاد الشمال، تحت، بيزوفيل،
+
+71
+00:04:41,840 --> 00:04:46,380
+شايفين كيف هو بيبعت كبير ومبعترة، ومش ثابت الحجم؟»
+
+72
+00:04:46,380 --> 00:04:49,540
+«عندي هنا طبعا، هذه الـLymphocyte، اللي بالنص،
+
+73
+00:04:49,540 --> 00:04:53,020
+تحت، وتحت أقصى اليمين، تحت، إبارة عن Monocyte»
+
+74
+00:04:53,020 --> 00:04:57,110
+«هنخدمه واحد وواحد، زي ما حكى محمد ونيشيهذه أول
+
+75
+00:04:57,110 --> 00:05:00,990
+واحدة، بسميها إحنا هذه «Stab in Utrophil» أو «Bad
+
+76
+00:05:00,990 --> 00:05:05,120
+Utrophil»، شايفين؟ عبارة عنجزء واحد، لسه ما أصارش
+
+77
+00:05:05,120 --> 00:05:09,540
+فيه تقسيم النواة لعدة loops طبعًا، الحجم ها من 12
+
+78
+00:05:09,540 --> 00:05:13,020
+إلى 16، الـCytoplasm فيها Pink الـGranulars هي
+
+79
+00:05:13,020 --> 00:05:15,840
+عبارة عن الـPrimary وSecondary Granules طبعًا،
+
+80
+00:05:15,840 --> 00:05:19,560
+النواة عبارة عن Dark Peripher وفيها الـChromatin،
+
+81
+00:05:19,560 --> 00:05:22,080
+شايفين الـChromatin ها؟ Lens Chromatin، طبعًا
+
+82
+00:05:22,080 --> 00:05:27,260
+الـChromatin هي تعتبر تجمع الـDNA وهي أحد المميزات
+
+83
+00:05:27,260 --> 00:05:31,820
+التي تقدر تميزها نواة الخلاياطبعًا، البعدية زي ما
+
+84
+00:05:31,820 --> 00:05:33,480
+أكيدها «Segmented Neutrophil» «Segmented
+
+85
+00:05:33,480 --> 00:05:36,300
+Neutrophil» هين شايفين الخلية؟ بيكون الخلية عبارة
+
+86
+00:05:36,300 --> 00:05:39,460
+عن أكثر من اتنين لخمس loops شايفين؟ Two to five
+
+87
+00:05:39,460 --> 00:05:43,780
+loops الخلية، يعني لاحظين الخلية الفوق؟ عندي واحد،
+
+88
+00:05:43,780 --> 00:05:46,740
+اتنين وممكن تلاتي ناجحة، تتبرها الخلية التحت عبارة
+
+89
+00:05:46,740 --> 00:05:50,700
+عن اتنين loops طبعًا، زي نفس الـBand حجمها اتناشر
+
+90
+00:05:50,700 --> 00:05:54,260
+لستة عشر مايكرون «Cytoplasm Pink» فيها Primary
+
+91
+00:05:54,260 --> 00:05:58,640
+وSecondary Granules الـ«Nucleus Dark Purple Blue»
+
+92
+00:05:58,640 --> 00:06:01,370
+شايفين كيف Dark Purple Blue؟والـ Chromatin dense
+
+93
+00:06:01,370 --> 00:06:05,190
+تلاحظين أن في الجمعات الأزرق فيه كتير فيها، فتعتبر
+
+94
+00:06:05,190 --> 00:06:11,250
+dense هذه خلية الازينوفيل أكبر شبه حجمها من 14 إلى
+
+95
+00:06:11,250 --> 00:06:14,550
+16 مايكرون مليئة بالـ granules الـ granules حجمها
+
+96
+00:06:14,550 --> 00:06:18,050
+كبير، لونها أحمر، وهتميز الإلها، أنا ممكن أميز أن
+
+97
+00:06:18,050 --> 00:06:21,090
+اللون أحمر الـ granules وبيضع في النواة عبارة عن
+
+98
+00:06:21,090 --> 00:06:25,290
+two loops عبارة عن two loops غالبا للنواة ولونها
+
+99
+00:06:25,290 --> 00:06:29,890
+أزرقالنواء؟ النواء، الأنويات تتصرف الأزرق بشكل
+
+100
+00:06:29,890 --> 00:06:33,650
+عام، وجود الـDNA يا محمد، ليش؟ بحكينا احنا
+
+101
+00:06:33,650 --> 00:06:37,490
+الـRight Stain أو الـLishman Stain فيها By Basic
+
+102
+00:06:37,490 --> 00:06:42,290
+Stains، فيه جزء بصبغة لنواء، الـLishman أو New
+
+103
+00:06:42,290 --> 00:06:45,970
+Methyl Blue، وفيه جزء بصبغة لـCytoplasm، اللي يزين
+
+104
+00:06:45,970 --> 00:06:50,350
+Red، تمام؟ فالجزء بصبغة لنواء، بصبغة لـDNA أزرق،
+
+105
+00:06:50,350 --> 00:06:58,350
+مر معناك سابقًا، تمام؟طيب، هالجيت أنا عندي هذي
+
+106
+00:06:58,350 --> 00:07:04,010
+حكينا الـXenophil، البعدية الـBesophil الحجم 14–16
+
+107
+00:07:04,010 --> 00:07:06,590
+أكبر شوية من الـNitrophil، الـCytoplasm طبعًا
+
+108
+00:07:06,590 --> 00:07:10,930
+Pink، الـGranules Dark وBlue وطبعًا Obscure
+
+109
+00:07:10,930 --> 00:07:14,430
+Nucleus، طبعًا نواة مش واضحة، مش جدًا ميزي حرف
+
+110
+00:07:14,430 --> 00:07:19,370
+الـS، لأن الـGranules بغطاتيها كامل، والنواة Dark
+
+111
+00:07:19,370 --> 00:07:22,110
+Blue أكيد، طبعًا التلاتة المرة السابقة، اللي هو
+
+112
+00:07:22,110 --> 00:07:25,970
+الـNitrophilوالـ Ezinofil والـ Bezofil نسميهم
+
+113
+00:07:25,970 --> 00:07:29,710
+Granular Glycosides لأنهم فيها نواة محبقة حبيبات
+
+114
+00:07:29,710 --> 00:07:33,410
+ونسميهم طبعاً إيه؟ Poly-Nuclear لأن النواة تبعتها
+
+115
+00:07:33,410 --> 00:07:38,050
+مجزقة يعني زي الـ Nucleus 2 إلى 5 لوث الـ Ezinofil
+
+116
+00:07:38,050 --> 00:07:41,070
+2 لوث الـ Bezofil طبعاً مش واضحة كتير لكن تكون
+
+117
+00:07:41,070 --> 00:07:42,650
+مجزقة غالباً، تمام؟
+
+118
+00:07:46,580 --> 00:07:50,440
+عندي الـMononuclear اللي هي الـ«لمفو سايس»
+
+119
+00:07:50,440 --> 00:07:53,400
+والـ«مونو سايتس» الـ«لمفو سايتس» كما تشاهدون،
+
+120
+00:07:53,400 --> 00:07:58,360
+حجمها تختلف حسب نوع الخلايا، فعندي «صغير» «لمفو
+
+121
+00:07:58,360 --> 00:08:06,260
+سايتس» في التحت أسفل، إذا شايفين شايفين ولا لا؟ ‏-
+
+122
+00:08:06,260 --> 00:08:08,680
+أشوفك. ‏- أشوفك. ‏- لتحت كلمة كبيرة. ‏- آه،
+
+123
+00:08:08,680 --> 00:08:09,020
+شايفين.
+
+124
+00:08:18,060 --> 00:08:24,180
+أه دكتور، شايفينها؟ مش فاهم عليكم إيش؟ شايفينها،
+
+125
+00:08:24,180 --> 00:08:28,080
+شايفينها تمام اللي تحت كلمة «chromatin dense» يا
+
+126
+00:08:28,080 --> 00:08:30,800
+دكتور؟ اللي تحت كلمة «chromatin dense»، أه في ندخل
+
+127
+00:08:30,800 --> 00:08:33,200
+نخليتين، في صغيرة وفي كبيرة هذه بالطبع small
+
+128
+00:08:33,200 --> 00:08:35,820
+lymphocyte وlarge lymphocyte وفي بالنص
+
+129
+00:08:35,820 --> 00:08:39,060
+intermediate ال «small lymphocyte» حجمها، وهذه
+
+130
+00:08:39,060 --> 00:08:43,120
+النقطة أذكرها كويس ال «small lymphocyte» حجمها 7
+
+131
+00:08:43,120 --> 00:08:46,550
+على 9 مايكرون يعادل حجم الخلايا الحمراءهل جيت؟
+
+132
+00:08:46,550 --> 00:08:50,250
+ممكن أنا أسحب من «محمد» وممكن أسحب من «معاد»
+
+133
+00:08:50,250 --> 00:08:52,610
+الخلايا الحمرا عندهم مش شبهة بالحجم ممكن حجم
+
+134
+00:08:52,610 --> 00:08:55,010
+الخلايا الحمرا عند «معاد» نوعًا ما طبعًا إيه
+
+135
+00:08:55,010 --> 00:08:57,250
+الخلايا الحمرا حجمها تقريبًا من 7 إلى 7 مايكرون
+
+136
+00:08:57,250 --> 00:09:01,170
+يكون عند «معاد» مثلًا أو بلاش هاي ممكن أسحب وأنا
+
+137
+00:09:01,170 --> 00:09:03,150
+شوف تعرف إن الخلايا الحمرا هاي طبيعية أو مش طبيعية
+
+138
+00:09:03,150 --> 00:09:06,370
+حجمها بقارنها بحجم الـ«Lymphocytes» اللي اسمه
+
+139
+00:09:06,370 --> 00:09:08,910
+الـ«Lymphocytes» فالـ«Lymphocytes» يعتبر كأنه عندي
+
+140
+00:09:08,910 --> 00:09:15,440
+Indicators لحجم الخلايا الحمرا عشان أقدر أقارطبعًا
+
+141
+00:09:15,440 --> 00:09:17,800
+الـCytoplasm، لاحظوا الـCytoplasm عنديها؟ أنه إيش
+
+142
+00:09:17,800 --> 00:09:20,840
+لون الـCytoplasm؟ الخلية اللي بالنص هذه، الداخل
+
+143
+00:09:20,840 --> 00:09:24,700
+المربع الـCytoplasm لونه إيش لاحظين؟ أزرق، سماوي،
+
+144
+00:09:24,700 --> 00:09:30,880
+شايفينه؟ شايفينه؟ آه، واللي طبعًا هو عبارة عن dark
+
+145
+00:09:30,880 --> 00:09:35,300
+blue لكن بتكون طبعًا مش زي الـChromatin، زي
+
+146
+00:09:35,300 --> 00:09:39,020
+الـNitrophil بيكون dense الـChromatin، لكن أقل
+
+147
+00:09:39,020 --> 00:09:44,630
+التجمعات، تمام؟ هذه اسمها الـLymphocyteالـ Slides
+
+148
+00:09:44,630 --> 00:09:47,030
+اللي بعتيها، اللي هي الـ Mono Slides، هاي خلية الـ
+
+149
+00:09:47,030 --> 00:09:50,150
+Mono Slides الموجودة عندي، أنا بحاول أشوف إذا في
+
+150
+00:09:50,150 --> 00:09:54,490
+عندي، أجيب، أقدر أجيبكم جلم، بس مش عارف ال .. من
+
+151
+00:09:54,490 --> 00:09:57,870
+أين أجيبكم إياها، على كل حاجة. مرة قد كنت تعمل على
+
+152
+00:09:57,870 --> 00:10:01,770
+الرسامة، ظنين؟ على الرسامة كنت أشتغل، آه، آه، من
+
+153
+00:10:01,770 --> 00:10:06,350
+المرة إيش عملت؟ أنا جبت، شو اسمه؟ خليني أشوف إذا
+
+154
+00:10:06,350 --> 00:10:06,630
+..
+
+155
+00:10:12,240 --> 00:10:18,440
+سيف أبعد الكتب ولا لسه؟ الكتب ايش يا عزيزي؟ احنا
+
+156
+00:10:18,440 --> 00:10:26,980
+ممكن كتب بلجيات؟ ده بحكي لسيفة عشان ألجهم سيف
+
+157
+00:10:26,980 --> 00:10:32,120
+اعنوه النص و اتبعه من سيفه طيب شايفين ما هو فيك
+
+158
+00:10:32,120 --> 00:10:40,730
+حاليا ولا لسه؟ ولا ايش اتحرك ولا ايش دعوة؟فجأت
+
+159
+00:10:40,730 --> 00:10:44,230
+الدكتورة انت، جيبليها المعلومة بالراحة طيب، خلّيني
+
+160
+00:10:44,230 --> 00:10:47,530
+أكمل، مش مشكلة، هلأ بنشوف المشكلة هذه طيب، احنا
+
+161
+00:10:47,530 --> 00:10:53,490
+لقيت طبعا، لحظة عندي هان الـ… الـ… الـ… الـ…
+
+162
+00:10:53,490 --> 00:10:57,010
+الـMonocytes كيف حجمها؟ أكبر حجم تقرر، 14 لـ20
+
+163
+00:10:57,010 --> 00:11:00,110
+الـCytoplasm فيها، طبعا الـ… الـLymphocytes،
+
+164
+00:11:00,110 --> 00:11:03,190
+الـCytoplasm فيه blue أذاك سماوي، لكن في
+
+165
+00:11:03,190 --> 00:11:07,610
+الـMonocytes، grey، blueيعني بيكون أزرق ما يلقيه
+
+166
+00:11:07,610 --> 00:11:11,150
+أي شيء لسكري نوعًا ما طبعًا الـ Granules، ما فيش
+
+167
+00:11:11,150 --> 00:11:14,890
+فيها Granules لكن ممكن يظهر بعد الـOrgranules
+
+168
+00:11:14,890 --> 00:11:18,470
+أحيانًا النواء Blue و Large و Irregular في
+
+169
+00:11:18,470 --> 00:11:21,950
+الـShape ممكن يكون حالة في الـS طبعًا، شايفين كيف؟
+
+170
+00:11:21,950 --> 00:11:25,050
+طبعًا، زي ما حكينا هي تعتبر أكبر حجم الخلايا
+
+171
+00:11:25,050 --> 00:11:28,270
+البيضة موجودة طبعًا، شايفين الجمعات هذه جنبها،
+
+172
+00:11:28,270 --> 00:11:31,350
+اللي علي اليمين؟ فيه جمعات خلايا صغيرة، إيش هي؟
+
+173
+00:11:31,350 --> 00:11:32,070
+فعلاً إيش هي؟
+
+174
+00:11:56,890 --> 00:11:58,290
+هذه………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
+
+175
+00:12:06,150 --> 00:12:11,010
+تحكي سيد، صح؟ هذه اللي قبل شويه اللي .. اللي قبل
+
+176
+00:12:11,010 --> 00:12:13,710
+شويه اللي هي الـ lymphocyte الـ small و الـ هذا؟
+
+177
+00:12:13,710 --> 00:12:16,490
+لأ، لأ، هذه عبارة عن صفائح دموية، الـ platelets
+
+178
+00:12:16,490 --> 00:12:22,270
+آه، platelets، هي هذه الـ Mega .. دكتور، معلش، بس،
+
+179
+00:12:22,270 --> 00:12:25,890
+هي هذه الـ Megakaryocyte اللي هي اللي عاملة .. لأ،
+
+180
+00:12:25,890 --> 00:12:30,910
+لأ، الـ Megakaryocyte خليةفيها نواء وCytoplasm
+
+181
+00:12:30,910 --> 00:12:33,670
+وفيها… بيطلع منها الـPlatelets الـPlatelets هي بقى
+
+182
+00:12:33,670 --> 00:12:39,110
+عن، نحكي، ذوائط من الـCytoplasm ما نعتبرهاش خلايا
+
+183
+00:12:39,110 --> 00:12:41,850
+كاملة، لأن مافيش فيها أنوبيا وبعدين، حجمها، لحظة،
+
+184
+00:12:41,850 --> 00:12:44,750
+حجمها أقل من حجم الخلايا الحمراء بكتير Platelets،
+
+185
+00:12:44,750 --> 00:12:46,890
+الخلايا الحمراء حجمها، حكينا، من 7 إلى 7 مايكرون
+
+186
+00:12:46,890 --> 00:12:51,170
+بينما الـPlatelets حجمها تقريباً 4 مايكرون، تمام؟
+
+187
+00:12:51,170 --> 00:12:54,690
+فحجمها أقل بكتير، بس طبعاً هي مجمعة مع بعض، مع بعض
+
+188
+00:12:54,690 --> 00:12:57,360
+لأن Platelets إيش وظيفته يا شباب؟الـ Platelets
+
+189
+00:12:57,360 --> 00:13:01,180
+مظبتها اللي هو الـ Clumping تعمل الـ Clump اللي
+
+190
+00:13:01,180 --> 00:13:03,680
+بتتجمع بعض عشان تعمل تجارب الدم تبنع تجارب الدم
+
+191
+00:13:03,680 --> 00:13:06,380
+وهنا جاياني في ال slide عاملة الـ Clump بيجمع
+
+192
+00:13:06,380 --> 00:13:09,180
+الخلايا الصفايا الدموية مع بعض بعض هذه بيسميها
+
+193
+00:13:09,180 --> 00:13:13,160
+احنا Clump of Platelets لو شوفت في ال block فلان
+
+194
+00:13:13,160 --> 00:13:18,640
+بكتبه في التقرير، تمام؟
+
+195
+00:13:18,640 --> 00:13:20,100
+معاي يا شباب انتم؟
+
+196
+00:13:23,580 --> 00:13:26,900
+طيب، الـ Abnormal Changes في الخلايا البيضاء، إيش
+
+197
+00:13:26,900 --> 00:13:30,800
+بيصير عندي؟ طبعًا، نجات كلها بقى برع الأشكال، بدنا
+
+198
+00:13:30,800 --> 00:13:36,620
+نركز فيها كويس طبعًا، أول شغلة، في مصطلح بيسموه
+
+199
+00:13:36,620 --> 00:13:42,840
+«Left Shift» و «Right Shift» «Left Shift» إنه أنا
+
+200
+00:13:42,840 --> 00:13:46,540
+بكون عندي Non-Segmented Neutrophil أكتر من 5%، كيف
+
+201
+00:13:46,540 --> 00:13:51,100
+يعني؟يعني إنه أنا في الـ «maturation» هتمرب على
+
+202
+00:13:51,100 --> 00:13:54,320
+الـ «maturation» هكون عندي الـ «نيتروفيل» هتمرب
+
+203
+00:13:54,320 --> 00:14:02,040
+بعدد مراحل بتبلش من الـ… تبلش من، نحكي الـ… الشيء
+
+204
+00:14:02,040 --> 00:14:04,820
+اسمه الـ «stem cells» اللي بتوطني لـ«segmented
+
+205
+00:14:04,820 --> 00:14:08,280
+neutrophil» لو شوفت خلايا ما قبل الـ«band» أو
+
+206
+00:14:08,280 --> 00:14:12,680
+الـ«stab» 5%، بعتبر أنا عندي «left chip»هيجيب
+
+207
+00:14:12,680 --> 00:14:16,100
+العكس، الـRight Shift إن أنا الـModulation زاد عن
+
+208
+00:14:16,100 --> 00:14:19,000
+حده زاد عن حده، إن أنا الـNeutrophil عدد الـLoops
+
+209
+00:14:19,000 --> 00:14:23,240
+فيها 2 إلى 5، لو شفت خلائي الـNeutrophil 3% أكثر
+
+210
+00:14:23,240 --> 00:14:28,080
+من 5 Loops، بعتبر عندي Right Shift، تمام؟ طبعا،
+
+211
+00:14:28,080 --> 00:14:31,120
+بتفيدني إيش Left Shift، Right Shift، تحديد حالات
+
+212
+00:14:31,120 --> 00:14:34,660
+مرضية، أنا Normal لازم أكونش في عندي Shift نهائيا،
+
+213
+00:14:34,660 --> 00:14:38,730
+طيبToxic Granulation، طبعًا هذا كتير مصالح كتير
+
+214
+00:14:38,730 --> 00:14:42,510
+بُرد ومشوه كتير إنه أنا شايفين الخلايا النيتروفي
+
+215
+00:14:42,510 --> 00:14:46,610
+اللي على اليمين الـgranules فيها، إيش لونها؟ –
+
+216
+00:14:46,610 --> 00:14:49,470
+أزرق – أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+217
+00:14:49,470 --> 00:14:49,550
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+218
+00:14:49,550 --> 00:14:50,150
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+219
+00:14:50,150 --> 00:14:58,010
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+220
+00:14:58,010 --> 00:15:04,310
+أزرقطبعًا، فهذه بتدل على إنه فيه التهيبات بكتيرية
+
+221
+00:15:04,310 --> 00:15:07,430
+وهذا دليل على… طبعًا، بيكون عندي خلالي نتروفيل
+
+222
+00:15:07,430 --> 00:15:12,090
+عالية، عددها بالإضافة إن الـ… الـGranules بتتغير
+
+223
+00:15:12,090 --> 00:15:14,090
+من شكلها، بيصير توكسجالوش، طبعًا ليش بتتغير من
+
+224
+00:15:14,090 --> 00:15:17,130
+شكلها؟ لأن ده هتخضر في نظري، الـGranules فيه عنده
+
+225
+00:15:17,130 --> 00:15:20,450
+عدة أنواع، فيه Primary وSecondary وفيه من ضمن وضع
+
+226
+00:15:20,450 --> 00:15:23,770
+في الـGranules فرزل مواد تختلل بكتيريا،
+
+227
+00:15:23,770 --> 00:15:27,190
+الـIsocytes فهذه دور جدًا في تغيير، وفرز المواد
+
+228
+00:15:27,190 --> 00:15:33,130
+تؤدي لتغيير شكلها، تمام؟طبعًا، عندي فيه الـAll
+
+229
+00:15:33,130 --> 00:15:37,450
+Roots، الـAll Roots فيه عندي، شايفين العصاي داخل
+
+230
+00:15:37,450 --> 00:15:41,250
+الـ… شايفين الـSlides على اليمين؟ آه، آه، فيه
+
+231
+00:15:41,250 --> 00:15:44,030
+عصاي، فيه عصاي ذرج صغير هيك. طبعًا، اللي بيسموه
+
+232
+00:15:44,030 --> 00:15:47,490
+All Roots، All Roots، وفي عندك على الشمال برضه، في
+
+233
+00:15:47,490 --> 00:15:50,050
+عندي بعض الخلايا، طبعًا، هذه الخلايا عبارة عن
+
+234
+00:15:50,050 --> 00:15:53,090
+المراحل الأولية من الـNitrophil، طبعًا، اللي هي
+
+235
+00:15:53,090 --> 00:15:57,520
+عبارة عن ال… نحكي ال… ال…اللهم صلى الله عليه وسلم،
+
+236
+00:15:57,520 --> 00:16:00,440
+الـMeta-myrocytes وMyrocytes فعندي هنا أغلب
+
+237
+00:16:00,440 --> 00:16:04,720
+الخلايا هدول عبارة عن Myrocytes، تمام؟ لمرحلة ما،
+
+238
+00:16:04,720 --> 00:16:07,600
+طبعًا ما أخبر نشوريشن بكتير، بيكون هذه في الـbone
+
+239
+00:16:07,600 --> 00:16:10,460
+marrow غالبًا إلا في حالات، نحكي سرطانية،
+
+240
+00:16:10,460 --> 00:16:13,180
+الـLeukemia أو إذا كان بيعيندي حالات Leukemoid
+
+241
+00:16:13,180 --> 00:16:16,420
+Reaction تظهر عندى، بعدين هم بيظهر عندى اللي هي
+
+242
+00:16:16,420 --> 00:16:19,460
+طبعًا هذه الحالة اللي هي الـOroles طبعًا تمور معنا
+
+243
+00:16:19,460 --> 00:16:24,320
+بشكل تفصيل أكتر الـOroles وإيش أساسها وإيش سببها
+
+244
+00:16:24,320 --> 00:16:29,170
+ووين تظهر بأي حالةطبعًا، مرة معناها بالصلاة على
+
+245
+00:16:29,170 --> 00:16:31,070
+الـHyper-segmented،
+إيش هو يعني بالصلاة على
+
+246
+00:16:31,070 --> 00:16:35,250
+الـHyper-segmented، يا شباب؟ Right Shift. بالظبط،
+
+247
+00:16:35,250 --> 00:16:36,770
+Right Shift. الـHyper-segmented بيكون خلايا
+
+248
+00:16:36,770 --> 00:16:41,890
+نيدروفيل الـSegmentation عالية. لاحظوا الـslide
+
+249
+00:16:41,890 --> 00:16:48,390
+على الشمال، كان محد فيها،عدّولي يا هون، سبعة،
+
+250
+00:16:48,390 --> 00:16:51,970
+بالضبط، سبعة segmentation، فتعتبر right shift
+
+251
+00:16:51,970 --> 00:16:56,790
+يعني، ولاحظوا اليمين برضه نفس الحكاية، 2، 4، 6، 8،
+
+252
+00:16:56,790 --> 00:16:58,930
+فهذا يسموها hyper-segmented neutrophil
+
+253
+00:17:01,970 --> 00:17:07,210
+طبعًا، الخلايا التانية دي خلايا حمرة الخلية الفوق،
+
+254
+00:17:07,210 --> 00:17:09,870
+الـNitrophilها دي ممكن تخربطكم شوية تفكروا هي
+
+255
+00:17:09,870 --> 00:17:13,730
+عبارة عن خلية إيش؟ Lymphocyte لأن Lymphocyte قريب
+
+256
+00:17:13,730 --> 00:17:16,690
+منها لكن هي دي خلية اللي هي الخلية الأولية الخلاية
+
+257
+00:17:16,690 --> 00:17:20,990
+الحمرة اللي هي بقى Nucleated RBC، Nucleated RBC
+
+258
+00:17:20,990 --> 00:17:25,030
+شباب، موضوع الخلاية يعني حاولوا تركزوا فيه كتير
+
+259
+00:17:25,030 --> 00:17:28,770
+لإنه من هالجهة كل مراتينكم خلية درسوها صح عشان من
+
+260
+00:17:28,770 --> 00:17:31,520
+الجدام شوية إن شاء الله ماتخربطش كتيرفي تمييز بين
+
+261
+00:17:31,520 --> 00:17:33,800
+خلية وخلية، تمام؟
+
+262
+00:17:35,900 --> 00:17:39,060
+عندي مصالح بيسموه «anisocytosis of neutrophil»
+
+263
+00:17:39,060 --> 00:17:42,480
+كلمة «anisocytosis» مصالح له تعدد الحجم، كيف تعدد
+
+264
+00:17:42,480 --> 00:17:45,440
+الحجم؟ عندي حجم صغير وحجم كبير، طبعا عندي خلايا
+
+265
+00:17:45,440 --> 00:17:48,960
+الـ «نيتروفيل»، عندي خمس خلايا، طلعوا الخلية، احنا
+
+266
+00:17:48,960 --> 00:17:51,000
+الخلية تفكروا على شغل، هل جيتوا احنا نعتبره
+
+267
+00:17:51,000 --> 00:17:55,260
+الدائرة هاي ساعة، تمام؟ هل جيتوا عند الساعة تقريبا
+
+268
+00:17:55,260 --> 00:17:59,800
+عشرة، بين الساعة عشرة ومركز، في خلية، قارنوها مع
+
+269
+00:17:59,800 --> 00:18:02,680
+الخلية اللي عند الساعة خمسة، في فرق بين الحجم، صح
+
+270
+00:18:02,680 --> 00:18:06,960
+ولا لأ؟أيه؟ هذا طبعا تختلف حجم النيتروفيل نسميها
+
+271
+00:18:06,960 --> 00:18:11,880
+نيزو سي دوزيز of نيتروفيل فيه عندي ال vacuolation،
+
+272
+00:18:11,880 --> 00:18:14,840
+ال vacuolation طبعا هي وجود زي الهواء أو فقاعد
+
+273
+00:18:14,840 --> 00:18:19,360
+الهواء داخل النيتروفيل أو البرونسايتز طبعا عندي
+
+274
+00:18:19,360 --> 00:18:23,870
+أنا النيتروفيلاللي هي اللي على اليمين لعظم ينظف
+
+275
+00:18:23,870 --> 00:18:26,550
+فيها لأن فيه فخوعات هوا فيها والمرصد، طبعاً وجود
+
+276
+00:18:26,550 --> 00:18:30,330
+الـVacculation بتدل على وجود Infections، الجهبات
+
+277
+00:18:30,330 --> 00:18:33,950
+لأن الـVacculation عبارة عن بصير عندي حالة نشطة
+
+278
+00:18:33,950 --> 00:18:37,410
+Vapocytosis هذه الحالة نشطة الـVapocytosis، كما
+
+279
+00:18:37,410 --> 00:18:43,050
+حكينا، تؤدي إلى إن الـGranules تفضّي محتوياتها من
+
+280
+00:18:43,050 --> 00:18:46,110
+المواد وبتتقدر الـGranules فاضية، فهذه عبارة عن
+
+281
+00:18:46,110 --> 00:18:50,010
+الـVacculationطبعًا عندي الخليتين اللي بيقوموا
+
+282
+00:18:50,010 --> 00:18:53,510
+بعملية اللي بيحكي البلعنة أو الـ Bacocytation اللي
+
+283
+00:18:53,510 --> 00:19:01,750
+هي الـ نيتروفيل والـ Monocyte دكتور، معلش، ممكن بس
+
+284
+00:19:01,750 --> 00:19:06,110
+عسريق، بس تشرحلي نهادر لإنه أنا ما .. يعني الـ net
+
+285
+00:19:06,110 --> 00:19:13,710
+عندي ماكانش كويس الو؟
+
+286
+00:19:14,100 --> 00:19:16,600
+ماتك يا سعيد، ماتك، بأحكيلك أنا الـVacculation
+
+287
+00:19:16,600 --> 00:19:23,000
+طبعاً هي بره عن زي بقعات هواء داخل الخلايا
+
+288
+00:19:23,000 --> 00:19:27,400
+الديوتروفينية، لأن السببها، السببها أنه في
+
+289
+00:19:27,400 --> 00:19:32,840
+اندراجات تعمل سيئة عملية البلعمة للبكتيريا أو
+
+290
+00:19:32,840 --> 00:19:38,220
+للميكروهبينيات المدخل، طبعاً نتيجة البلعمة تضرر
+
+291
+00:19:38,220 --> 00:19:42,770
+اندراجات البكيوروالدكتور بس داخل خلية الـ
+
+292
+00:19:42,770 --> 00:19:45,970
+Neutrophil يعني؟ مش سامع زي دكتور معاه تفضل
+
+293
+00:19:45,970 --> 00:19:49,230
+تقبيلاتك على سهيلة فأقولك بس داخل خلية الـ
+
+294
+00:19:49,230 --> 00:19:51,570
+Neutrophil بس ولا فيها خلايا .. الـ Neutrophil و
+
+295
+00:19:51,570 --> 00:19:54,070
+الـ Monocyte بس الـ Neutrophil و الـ Monocyte ضمن
+
+296
+00:19:54,070 --> 00:19:57,070
+الخلايا المسؤولة على البلعمة خلية الـ Monocyte هي
+
+297
+00:19:57,070 --> 00:20:00,350
+موجودة على اليمين، شايفينها؟ وخلية الـ Neutrophil
+
+298
+00:20:00,350 --> 00:20:02,750
+موجودة على الشمال، شايفينهم؟
+
+299
+00:20:05,240 --> 00:20:08,360
+طبعًا، فيه عندي Degeneration of Nucleus طبعًا،
+
+300
+00:20:08,360 --> 00:20:11,640
+الـDegeneration of Nucleus العظيم إن هو طبعًا مش
+
+301
+00:20:11,640 --> 00:20:16,180
+طبيعي الشكل لها، عظيمًاالنواة شكلها مش طبيعي طبعاً
+
+302
+00:20:16,180 --> 00:20:19,240
+لسه شكلها مش طبيعي نواة لأنه طبعاً صارت تغيرات على
+
+303
+00:20:19,240 --> 00:20:21,880
+النواة طبعاً ماذا بيصير generation of nucleus في
+
+304
+00:20:21,880 --> 00:20:25,460
+حالة العين القادمة يعني أنا سحبت عينة بدل ما
+
+305
+00:20:25,460 --> 00:20:27,960
+أعملها blood film مباشرة سنت عليها يوم وبعدين سحبت
+
+306
+00:20:27,960 --> 00:20:30,880
+لها blood film طبعاً بيصير تغيرات على النواة بيصير
+
+307
+00:20:30,880 --> 00:20:34,000
+generation of nucleus سافين النواة كيف صارت؟ صارت
+
+308
+00:20:34,000 --> 00:20:37,420
+تغيرات فيها لإن بتمكن مشي شوية ويصير لها غامض كتير
+
+309
+00:20:37,420 --> 00:20:40,480
+عندي الـDohrybutyrate الـDohrybutyrate شايفين
+
+310
+00:20:40,480 --> 00:20:46,970
+طبعاً الزراعة اللي في داخل الغلايا النيفي نقطة
+
+311
+00:20:46,970 --> 00:20:52,910
+درجة في نقطة درجة بيسموها Dohil Buddels احنا
+
+312
+00:20:52,910 --> 00:20:56,490
+طبعا خلصنا ما تبقى من المحاضرة خلوا يجوا معايا ان
+
+313
+00:20:56,490 --> 00:21:07,430
+شاء الله بدي أدخل المحاضرة تانية دكتور
+
+314
+00:21:07,430 --> 00:21:13,350
+انت متجن المحاضرة ولا لأ؟يعني في تسجيل؟ آه، تقلقش،
+
+315
+00:21:13,350 --> 00:21:15,890
+أنا هنزلكم تسجيل إن شاء الله بالإضافة لتسجيل
+
+316
+00:21:15,890 --> 00:21:19,630
+المسبق اللي منزلكم يا أنا مش منزله، بهاست عليه
+
+317
+00:21:19,630 --> 00:21:23,250
+عمود اللي مش ملاقيه تسجيل الجديد لأ، منزل، كله
+
+318
+00:21:23,250 --> 00:21:28,050
+فلس، تبعتني على الرابط لما تنزله إن شاء الله خير،
+
+319
+00:21:28,050 --> 00:21:31,830
+طيب، احنا هناخد الـGET اللي طبعا اللي نرجع كمان
+
+320
+00:21:31,830 --> 00:21:38,130
+مرة لموضوع الـYPC morphology هبتعلكم ملف تاني إن
+
+321
+00:21:38,130 --> 00:21:44,800
+شاء اللههذا طبعا أخدنا منه بعضه، هكملكم عليه على
+
+322
+00:21:44,800 --> 00:21:48,440
+السريع، طبعا لإنه في بعض ال slides مش موجودة كانت
+
+323
+00:21:48,440 --> 00:21:53,940
+هناك، أنا بس أنا هاخد بشوية بتفاصيل أكتر هلجيت
+
+324
+00:21:53,940 --> 00:21:56,280
+بالنسبة للموعد، كنتوا بثبتوه عليك يا شباب، و لا
+
+325
+00:21:56,280 --> 00:22:01,040
+كيف؟ أنا شايف الصبح أحسن، والله الصبح أحسن يا
+
+326
+00:22:01,040 --> 00:22:04,220
+دكتور، بصراحة يعني أنا شايف المساء أحسن، عشان في
+
+327
+00:22:04,220 --> 00:22:08,780
+هالة قطع ال net بقدر الواحد يدبر حالهأنا .. أنا ..
+
+328
+00:22:08,780 --> 00:22:11,480
+أنا المسأ بالنسبالي أني بدي انا واحد بصحى الصوبة،
+
+329
+00:22:11,480 --> 00:22:15,820
+بدرس المسأ، بطول، بطلع، بنزل، رابطة أيه؟ والله يا
+
+330
+00:22:15,820 --> 00:22:19,300
+محمد، أجيب نرجع للصوبة أحسن، لإننا .. للمحب الصوبة
+
+331
+00:22:19,300 --> 00:22:21,760
+أحسن، بعدين اسمع، احنا الصوبة ممكن نبلس متأخر
+
+332
+00:22:21,760 --> 00:22:26,180
+شوية، ممكن نبلس على الإحدى عشرة، إذا حابين، عادي،
+
+333
+00:22:26,180 --> 00:22:28,780
+خلاص خليني على الإحدى عشرة، بلد الصوبة هبقى كتير،
+
+334
+00:22:28,780 --> 00:22:29,300
+بدر على عشرة
+
+335
+00:22:35,180 --> 00:22:37,200
+ظهر لكم شاشة بالنسبة للـ White Bases لأن الـ
+
+336
+00:22:37,200 --> 00:22:40,540
+Platelets أبنورمال مورفوليجي؟ ده أه، لأ بالتالي
+
+337
+00:22:40,540 --> 00:22:45,160
+وحناخد الـ RBCs مورفوليجي إن شاء الله ومدياكم
+
+338
+00:22:45,160 --> 00:22:48,080
+تدرسوهم كويس لإن المرة الجاية مدياكم تدرسوهم كويس
+
+339
+00:22:48,080 --> 00:22:57,260
+وزي السهر بعد وإن شاء الله نجاوب عليها طيب طبعا زي
+
+340
+00:22:57,260 --> 00:23:00,960
+ما حكينا في مصالح بسموه Platelets Citilism
+
+341
+00:23:01,270 --> 00:23:03,650
+Centralism يعني الـSatellite، الـSatellite يعني
+
+342
+00:23:03,650 --> 00:23:05,950
+اللي بيجي على سطح الخلايا، على سطح الإشي
+
+343
+00:23:05,950 --> 00:23:07,690
+الـSatellite عندنا، صح ولا لأ؟
+
+344
+00:23:07,690 --> 00:23:10,830
+فالـPlatyscentralism، الـPlatyscentralism عبارة عن
+
+345
+00:23:10,830 --> 00:23:13,890
+الصفائح دباوية موجودة على سطح الـNitrophil طبعا،
+
+346
+00:23:13,890 --> 00:23:16,150
+موجودة على سطح الـNitrophil بسبب أنه بينترجمت على
+
+347
+00:23:16,150 --> 00:23:21,210
+سطح الـNitrophil ممكن أن تكون سببها الـEdita طبعا،
+
+348
+00:23:21,210 --> 00:23:22,970
+بتعمل exchanges، هذه exchanges تؤدي إلى
+
+349
+00:23:22,970 --> 00:23:26,470
+الـPlatyscentralism، تمام؟
+
+350
+00:23:29,420 --> 00:23:32,880
+طبعا هذه الحالة مش مرضية، هذه الحالة بيصير in
+
+351
+00:23:32,880 --> 00:23:36,740
+vitro ليس in vivo، بلاي الـSentilism، طيب، شايفين
+
+352
+00:23:36,740 --> 00:23:44,780
+هالصورة هاي؟ واضحة جدا، واضحة جدا، البيتظارد، هذه
+
+353
+00:23:44,780 --> 00:23:49,450
+بلاي الـSentilismفي عندي ال .. ال giant plateless
+
+354
+00:23:49,450 --> 00:23:53,370
+من اسمها، ال plateless بحكيلكم حجمها صغير، حجمها
+
+355
+00:23:53,370 --> 00:23:56,890
+تقريبا هي plateless، شايفين؟ أنتم شايفين ال mouse
+
+356
+00:23:56,890 --> 00:24:00,870
+للأسف شديد، أه؟ جهاز كيف دوصلكم ال mouse أنا؟ لأ و
+
+357
+00:24:00,870 --> 00:24:06,150
+الله، طب .. طب دكتور بشر، بالنسبة لل .. ال .. ال
+
+358
+00:24:06,150 --> 00:24:09,730
+cytrism هذي قبل شوية، ليش بتصير ال cytrism هيك؟ما
+
+359
+00:24:09,730 --> 00:24:14,510
+حكينا الـEdita، هاي كتابت أنا، هاي سببها الـEdita
+
+360
+00:24:14,510 --> 00:24:17,790
+بتعملي الـChanges، طبعًا هذه الـChanges تؤدي
+
+361
+00:24:17,790 --> 00:24:22,170
+لـPlateless Italism، فطبعًا هذه حالة in vitro و
+
+362
+00:24:22,170 --> 00:24:25,170
+لسه in vivo، طبعًا و نتيجة Plateless Italism، أنا
+
+363
+00:24:25,170 --> 00:24:28,010
+مانعزي أعدّل Plateless في الـCBC، بيكون عددها
+
+364
+00:24:28,010 --> 00:24:34,240
+قليل، تمام؟ طيب، الـ… الـPlatelessالـGiant
+
+365
+00:24:34,240 --> 00:24:38,080
+Plateless من اسمها Giant يعني حجم كبير، Giant حجم
+
+366
+00:24:38,080 --> 00:24:43,440
+كبير، فـGiant Plateless، شايفين الصورة اللي بالنص،
+
+367
+00:24:43,440 --> 00:24:46,500
+فيه عندي خلية lymphocytes على اليمين وعلى الشمال،
+
+368
+00:24:46,500 --> 00:24:51,240
+هذا عبارة عن Giant Plateless، شايفينها؟
+
+369
+00:24:51,240 --> 00:24:55,540
+أكبر من الـLymphocytesصحيح، أكبر من الـ lymphocyte
+
+370
+00:24:55,540 --> 00:24:58,280
+هذا ما زلت الـ Plateless طبعًا، يكون أكبر من حجم
+
+371
+00:24:58,280 --> 00:24:59,880
+الخلايا الحامرة كمان طبعًا، حكينا إن الـ
+
+372
+00:24:59,880 --> 00:25:02,280
+lymphocyte قريب حجمها من الخلايا الحامرة الصغيرة
+
+373
+00:25:02,280 --> 00:25:05,960
+طبعًا، هذه بيصير مدى، في حالة increase plateless
+
+374
+00:25:05,960 --> 00:25:09,100
+turnover إنه أنا عندي نشاط في الصفائح، في إنتاج
+
+375
+00:25:09,100 --> 00:25:12,720
+الصفائح، فبالزيت أو في حالة المرض، بيسميها أنا الـ
+
+376
+00:25:12,720 --> 00:25:17,040
+MPD، الـ Myeloprophy Relative Disorders أو الـ
+
+377
+00:25:17,040 --> 00:25:20,460
+MDS، الـ Myelodysplastic Syndrome أو Syndrome
+
+378
+00:25:20,460 --> 00:25:24,680
+طبعًا، في الحالات المرضية هذههتبقوا معجوبين كتير،
+
+379
+00:25:24,680 --> 00:25:29,640
+هتاخدوها بالنظري بشكل تفصيل كامل، تمام؟ لكن
+
+380
+00:25:29,640 --> 00:25:33,360
+اتذكروها، الـ Platelism بيصير في حالة Plateless
+
+381
+00:25:33,360 --> 00:25:36,260
+turnover turn over يعني إيش؟ عندك نشاط زاهد في
+
+382
+00:25:36,260 --> 00:25:39,420
+إنتاج الصفائح الدموية، لأي سبب من الأسباب أو في
+
+383
+00:25:39,420 --> 00:25:45,780
+الـ MPD Myeloprophylactive disorder أو الـ MDS
+
+384
+00:25:45,780 --> 00:25:51,720
+Myelopnephelastic syndrome، تمام؟هي هن دي هن،
+
+385
+00:25:51,720 --> 00:25:54,440
+شايفين الخلايا هذه بيسموها بالنص الذرق جهنم
+
+386
+00:25:54,440 --> 00:25:59,600
+بلادلس، شايفينها؟ طبعا الخلايا كل اللي موجودة عندي
+
+387
+00:25:59,600 --> 00:26:00,640
+هي أخبار عن الخلايا الحمرة
+
+388
+00:26:03,890 --> 00:26:05,990
+الخلايا الحمرى، هنأخد تفاصيل عنها فيما بعد إن شاء
+
+389
+00:26:05,990 --> 00:26:08,290
+الله مش مشكلة، مش هنحكيها لجد أنا فيه اندي Large
+
+390
+00:26:08,290 --> 00:26:12,130
+Platelets، طبعًا Large Platelets حجم أقل من حجم
+
+391
+00:26:12,130 --> 00:26:18,090
+الـ… الـGiant Platelets لكن أكبر من إيش؟ طبعًا من
+
+392
+00:26:18,090 --> 00:26:21,110
+الصبائح دموية نفسها، فلاحظين انديها طبعًا حجم أقل
+
+393
+00:26:21,110 --> 00:26:23,910
+من الخلايا الحمرة كمان، فلاحظين انديها في اندي
+
+394
+00:26:23,910 --> 00:26:31,030
+الصورة، الصورة في اندي تلت خلايا جنبها زرقة تحت،
+
+395
+00:26:31,030 --> 00:26:38,360
+وبالنص في خلية حمرةوالمركز تحت شوية فيناهذه عبارة
+
+396
+00:26:38,360 --> 00:26:43,600
+عن Large Platelets طبعًا هذه أبناء المرض بيصير نفس
+
+397
+00:26:43,600 --> 00:26:48,400
+التلات حالات السابقة اللي تبعت الـ Giant Platelets
+
+398
+00:26:48,400 --> 00:26:54,240
+بيصير اللي هي Turnover بزيد أو الـ MPD أو الـ MDS
+
+399
+00:26:54,240 --> 00:26:58,260
+بالإضافة الحالات التالتة مرضية الميهيجلين أدومالي
+
+400
+00:26:58,260 --> 00:27:01,300
+والـ Gray Platelet Syndrome والـ Bernhardt-Sauer
+
+401
+00:27:01,300 --> 00:27:04,420
+Syndrome هذه حالات مرضية بالزير، بالزير تلات حالات
+
+402
+00:27:04,420 --> 00:27:06,000
+الأولى بالإضافة لتلات حالات التانية
+
+403
+00:27:10,750 --> 00:27:13,910
+فين دي؟ احنا طبعا ممكن نسحب عين الدم، عين الدم
+
+404
+00:27:13,910 --> 00:27:16,310
+طبعتنا حكينا في الـCBS، في الـHematology عبارة عن
+
+405
+00:27:16,310 --> 00:27:20,950
+عينة A.H.Edita، يعني Holy Blood أحيانا أنا بسحب،
+
+406
+00:27:20,950 --> 00:27:23,770
+ماكانتش كمية الـanticoagulant كفاية للدم، بسحب دم
+
+407
+00:27:23,770 --> 00:27:27,930
+بزيادة، فبتؤدي إلى بعض الجلطات، أنا بسميها Micro
+
+408
+00:27:27,930 --> 00:27:31,890
+Eclots، Micro Eclots Micro Eclots طبعا بتظهر معاي،
+
+409
+00:27:31,890 --> 00:27:35,060
+اللي هي عبارة عن الـFibrin strandsوفيها خلايا بيض
+
+410
+00:27:35,060 --> 00:27:38,000
+وفيها خلايا بلاتلس وممكن تكون فيها خلايا حمره
+
+411
+00:27:38,000 --> 00:27:40,420
+أحياناً، طبعا شايفين الزرق هذا اللي في ال
+
+412
+00:27:40,420 --> 00:27:43,740
+background، عبارة عن خيوط الزرق هذه، هذه عبارة عن
+
+413
+00:27:43,740 --> 00:27:47,040
+micro-ecloids، طبعا زي ما حكي هناإذاً micro
+
+414
+00:27:47,040 --> 00:27:49,520
+-closure في حالة إن كان عندى نسبة الـ ratio غلط
+
+415
+00:27:49,520 --> 00:27:53,280
+بالنسبة للـ anticoagulant أو إن أنا نتيجة إن طولت
+
+416
+00:27:53,280 --> 00:27:57,540
+كتير في عملية سحب دور من sections إن أنا بسحب الدم
+
+417
+00:27:57,540 --> 00:28:00,920
+طولت كتير أو ماعرفش أسحب صح هذه تؤدي إلى طبعا
+
+418
+00:28:00,920 --> 00:28:04,480
+التجلطات قبل ما الدم أنه طبعا أحنا حكينا الـ
+
+419
+00:28:04,480 --> 00:28:07,660
+Editor الهدف منها منع التجلط كيف يمنع تجلط الشباب؟
+
+420
+00:28:07,660 --> 00:28:14,470
+إذا تذكروا في المقدمة مين بيحكيلي؟ تجلطفاكيف
+
+421
+00:28:14,470 --> 00:28:19,290
+الإيدة تتملأ تجلط الدم؟
+
+422
+00:28:19,290 --> 00:28:22,610
+أظن
+
+423
+00:28:22,610 --> 00:28:30,850
+فيها مادة الهيبارين؟ لأ، اسمعي، اسمعي،
+
+424
+00:28:30,850 --> 00:28:34,270
+الهيبارين نفس الإيدي دا، أبعد من الدنم وانا تجلط،
+
+425
+00:28:34,270 --> 00:28:37,570
+لكن كيف تملأ التجلط؟ عن طريق الـChelating
+
+426
+00:28:37,570 --> 00:28:44,680
+للكالسيون، صح، صح،الذكرته؟ الـ Chelating
+
+427
+00:28:44,680 --> 00:28:50,000
+للكالسيوم؟ صحيح، الإيه دي ده؟ والكالس بأجزالها
+
+428
+00:28:50,000 --> 00:28:54,000
+والسيطرية نفس الهدف إنه بتعملي Chelating
+
+429
+00:28:54,000 --> 00:28:57,900
+للكالسيوم، ترتبطلي مع الكالسيوم اللي هو مهم جدا في
+
+430
+00:28:57,900 --> 00:29:01,120
+تجلط، في عملية تجلط الدم، وبالتالي لازمنا أتجلط
+
+431
+00:29:01,120 --> 00:29:02,580
+الدم عن طريق Chelating للكالسيوم
+
+432
+00:29:06,710 --> 00:29:09,930
+الهيبرين بيرتبطلي مع الـ Antithrombin فبيمنع
+
+433
+00:29:09,930 --> 00:29:13,310
+الهيبرين يحولي الفيبرونجين لفيبرين فالهيبرين بيقلب
+
+434
+00:29:13,310 --> 00:29:15,870
+القليل شوية عنهم لكن كلهم يقدّوا نفس الغرض اللي هو
+
+435
+00:29:15,870 --> 00:29:20,790
+مانع تجاربه قدامأنا استخدمت الإيدة دا، كان الإيدة
+
+436
+00:29:20,790 --> 00:29:25,150
+نحكي بور قديم، كان الإيدة في مشكلة، أو إن أنا خلال
+
+437
+00:29:25,150 --> 00:29:28,550
+العملية تسحب، طولت، جيت أسحب من المعاد، المعاد ما
+
+438
+00:29:28,550 --> 00:29:31,890
+شاء الله إيده مليانة، مش عارف أتطلع للـVan، طولت و
+
+439
+00:29:31,890 --> 00:29:35,810
+أنا بسحب الـVan، صار عندي تجولوطة خفيفة هادية،
+
+440
+00:29:35,810 --> 00:29:38,990
+بتظهر لي تحت الـMicroscope، بتسليد عليها شكل، إيش
+
+441
+00:29:38,990 --> 00:29:43,290
+اسمها؟ Micro Clots، شايفينها؟ تمام، Micro Clots،
+
+442
+00:29:43,290 --> 00:29:49,480
+تمام، تمام، فين دي Platelets Clumps؟بلايست كلامز
+
+443
+00:29:49,480 --> 00:29:55,720
+اللي أحكيناها جمعات الصباح مع بعض، شايفين في الـ
+
+444
+00:29:55,720 --> 00:30:01,290
+slide عند الساعة تقريبا 11فيه تجميعات تتوقع لنقطة
+
+445
+00:30:01,290 --> 00:30:03,250
+صغيرة هي برعاية الـ Platelets Clumps والـ
+
+446
+00:30:03,250 --> 00:30:06,390
+Platelets Clumps سببها برضه in vitro وليس in vivo
+
+447
+00:30:06,390 --> 00:30:09,630
+مانعش تدخل في الحالات المرضية لكن سببها إن أنا
+
+448
+00:30:09,630 --> 00:30:13,210
+الإيديات اللي استخدمتها قديمة شوية ممكن تؤدي
+
+449
+00:30:13,210 --> 00:30:18,970
+لتجميع الصفائح طبعا أو ممكن تؤدي ل… أو ممكن عملية
+
+450
+00:30:18,970 --> 00:30:22,650
+سحب الدم إن أنا خلال عملية سحب الدم طولت طبعا
+
+451
+00:30:22,650 --> 00:30:25,790
+النقطة المهمة جدا في Platelets Clumps إن أنا لو
+
+452
+00:30:25,790 --> 00:30:29,570
+مشيت عين الـCBC وكان عندي عدد Platelets قليلفي
+
+453
+00:30:29,570 --> 00:30:32,230
+الحالة هاي، مش لازم نعتمد أنه والله عندي plates
+
+454
+00:30:32,230 --> 00:30:34,590
+قليل، أنه فيه مشكلة في الـplates، لأ، لازم نتأكد
+
+455
+00:30:34,590 --> 00:30:37,650
+أنه مشكلة خارجية، مش داخلية، فبعمل الـBlood Film،
+
+456
+00:30:37,650 --> 00:30:40,070
+لما شوفت الـBlood Film وشوفت الـplateless clumps،
+
+457
+00:30:40,070 --> 00:30:42,550
+بعرف أن الـplateless عددها ده مش قليل، عددها الصح
+
+458
+00:30:42,550 --> 00:30:44,250
+أعلى من هيك، تمام؟
+
+459
+00:30:50,650 --> 00:30:55,130
+طبعًا في عندي نحكي الـSmall Platelets الـSmall
+
+460
+00:30:55,130 --> 00:30:58,730
+Platelets بيكون حجم صغير كتير طبعًا جايبين الـ… في
+
+461
+00:30:58,730 --> 00:31:01,770
+المركز في عندي خلية همرة فيها Small Platelets
+
+462
+00:31:01,770 --> 00:31:05,290
+طبعًا هذه حالة مرضية وحيدة اللي هي الـWiscott
+
+463
+00:31:05,290 --> 00:31:07,770
+-Aldrich Syndrome طبعًا هذه الحالة المرضية بيكون
+
+464
+00:31:07,770 --> 00:31:10,570
+فيها Small Platelets أو يكون عدد Platelets قليل
+
+465
+00:31:10,570 --> 00:31:13,710
+شدنا الـLicopenia طبعًا هذه الحالة المرضية بتصيب
+
+466
+00:31:13,710 --> 00:31:18,450
+الـ… طبعًا الـ… الـ… Platelets أكتر شيءأو الـ
+
+467
+00:31:18,450 --> 00:31:20,450
+Degranulation أو الـ Blateless، طبعاً الـ
+
+468
+00:31:20,450 --> 00:31:22,490
+Degranulation أو الـ Blateless بيكون عندي الـ
+
+469
+00:31:22,490 --> 00:31:25,030
+Blateless مش فيها أزرق، إذا حتشوف الـ Blateless
+
+470
+00:31:25,030 --> 00:31:28,630
+فيها زرق كتير، زرقة، بيكون لونها فاهي شوية، زي
+
+471
+00:31:28,630 --> 00:31:34,130
+عنديوانا المركز لتحت شويه بين المركز وبين الساعة
+
+472
+00:31:34,130 --> 00:31:38,830
+نحكي سبعة طبعا فيه دي خلية Platelets هذه طبعا
+
+473
+00:31:38,830 --> 00:31:43,170
+فاهية شويه طبعا تتواجد الـ… نحكي الـDegradation في
+
+474
+00:31:43,170 --> 00:31:46,150
+Platelets في حالات الـGrey Platelet Syndrome وهي
+
+475
+00:31:46,150 --> 00:31:48,150
+نفس الحالة اللي مرض معناها كان بظهر فيها إيه؟ إذا
+
+476
+00:31:48,150 --> 00:31:53,060
+بتذكروا، بظهر فيها الـLarge Plateletsبظهر فيها
+
+477
+00:31:53,060 --> 00:31:55,760
+كمان، بتظهر في حالات discharge of bloodless
+
+478
+00:31:55,760 --> 00:31:59,680
+granules نتيجة طبعاً لوكيميا، نتيجة cardio
+
+479
+00:31:59,680 --> 00:32:02,540
+-pulmonary bypass، نتيجة hairy cells لوكيميا أو
+
+480
+00:32:02,540 --> 00:32:06,160
+discharge of bloodless granules في حالة غور من
+
+481
+00:32:06,160 --> 00:32:10,000
+سيكشن، تقنية كان عندي غلط وإجتماعات الأسهم طبعاً
+
+482
+00:32:10,000 --> 00:32:13,360
+خلصنا هذه الواحدة الموية، هندخل على الخلايا
+
+483
+00:32:13,360 --> 00:32:18,040
+البيضاء طيب، يا شباب، احنا عشان أهدئ نسخة تجربية
+
+484
+00:32:18,600 --> 00:32:23,500
+فأنا بدي أوجب شويه، خلّيه يسجل اللي هدا عشان ما
+
+485
+00:32:23,500 --> 00:32:26,420
+بديش أفقد التسجيل، لإنه بعد كده بيعطيني أنه ضايق
+
+486
+00:32:26,420 --> 00:32:28,520
+الأقل من الـPK تقع، و بعد كده أخرجي عليكم إن شاء
+
+487
+00:32:28,520 --> 00:32:30,060
+الله، إتبعوا؟ فاليكم معايا إتبعوا
+
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.json b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6c902d207c1a74be870b266dab85630e6148ba77
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.json
@@ -0,0 +1 @@
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3215, 3224, 5551, 34740, 7435, 1829, 25894, 24793, 36145, 13412, 16606, 21984, 12399, 11933, 2655, 3555, 3615, 14407, 22807, 6156, 6027, 1829, 24793, 20449, 995, 25528, 11933, 2655, 3555, 3615, 14407], "avg_logprob": -0.42529763267153786, "compression_ratio": 1.7219251336898396, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1938.6, "end": 1939.0, "word": "فأنا", "probability": 0.7753092447916666}, {"start": 1939.0, "end": 1939.4, "word": " بدي", "probability": 0.802490234375}, {"start": 1939.4, "end": 1940.14, "word": " أوجب", "probability": 0.594482421875}, {"start": 1940.14, "end": 1941.22, "word": " شويه،", "probability": 0.67742919921875}, {"start": 1941.22, "end": 1941.82, "word": " خلّيه", "probability": 0.763525390625}, {"start": 1941.82, "end": 1942.88, "word": " يسجل", "probability": 0.9486083984375}, {"start": 1942.88, "end": 1943.08, "word": " اللي", "probability": 0.7227783203125}, {"start": 1943.08, "end": 1943.26, "word": " هدا", "probability": 0.463134765625}, {"start": 1943.26, "end": 1943.4, "word": " عشان", "probability": 0.83984375}, {"start": 1943.4, "end": 1943.5, "word": " ما", "probability": 0.267333984375}, {"start": 1943.5, "end": 1943.62, "word": " بديش", "probability": 0.7362467447916666}, {"start": 1943.62, "end": 1943.82, "word": " أفقد", "probability": 0.7223307291666666}, {"start": 1943.82, "end": 1944.34, "word": " التسجيل،", "probability": 0.87861328125}, {"start": 1944.34, "end": 1944.54, "word": " لإنه", "probability": 0.83209228515625}, {"start": 1944.54, "end": 1944.7, "word": " بعد", "probability": 0.79345703125}, {"start": 1944.7, "end": 1944.86, "word": " كده", "probability": 0.7788899739583334}, {"start": 1944.86, "end": 1945.3, "word": " بيعطيني", "probability": 0.8138671875}, {"start": 1945.3, "end": 1946.28, "word": " أنه", "probability": 0.4996337890625}, {"start": 1946.28, "end": 1946.42, "word": " ضايق", "probability": 0.7901204427083334}, {"start": 1946.42, "end": 1946.66, "word": " الأقل", "probability": 0.8233235677083334}, {"start": 1946.66, "end": 1946.76, "word": " من", "probability": 0.9609375}, {"start": 1946.76, "end": 1947.04, "word": " الـPK", "probability": 0.2841339111328125}, {"start": 1947.04, "end": 1947.62, "word": " تقع،", "probability": 0.449920654296875}, {"start": 1947.62, "end": 1947.7, "word": " و", "probability": 0.347412109375}, {"start": 1947.7, "end": 1947.78, "word": " بعد", "probability": 0.9052734375}, {"start": 1947.78, "end": 1947.88, "word": " كده", "probability": 0.756591796875}, {"start": 1947.88, "end": 1948.18, "word": " أخرجي", "probability": 0.70654296875}, {"start": 1948.18, "end": 1948.36, "word": " عليكم", "probability": 0.6741943359375}, {"start": 1948.36, "end": 1948.48, "word": " إن", "probability": 0.5869140625}, {"start": 1948.48, "end": 1948.52, "word": " شاء", "probability": 0.97314453125}, {"start": 1948.52, "end": 1948.7, "word": " الله،", "probability": 0.9033203125}, {"start": 1948.7, "end": 1948.96, "word": " إتبعوا؟", "probability": 0.69281005859375}, {"start": 1948.96, "end": 1949.26, "word": " فاليكم", "probability": 0.4737548828125}, {"start": 1949.26, "end": 1949.46, "word": " معايا", "probability": 0.8990885416666666}, {"start": 1949.46, "end": 1950.06, "word": " إتبعوا", "probability": 0.726416015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1952.70525, "duration_after_vad": 1869.4578437499943}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9a9d2e9434a03e97044f3de69d2441270061785e
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/P5bjrVb9pO0_raw.srt
@@ -0,0 +1,1949 @@
+1
+00:00:00,000 --> 00:00:02,980
+طيب، بسم الله الرحمن الرحيم إحنا إن شاء الله راح
+
+2
+00:00:02,980 --> 00:00:08,160
+نكمل شرح المادة طبعاً الـHematology زي ما حكيناها
+
+3
+00:00:08,160 --> 00:00:12,660
+أخدنا المحاضرة السابقة عن موضوع الـBlood Film كيف
+
+4
+00:00:12,660 --> 00:00:15,660
+نعمل Film وكيف نصبغاه إحنا طبعاً لما نصبغه الـFilm
+
+5
+00:00:15,660 --> 00:00:19,320
+هيدور معانا أشكال الخلايا تحت نجهة بصورة هاي هاي
+
+6
+00:00:19,320 --> 00:00:22,400
+الصورة عندي زي ما تلاحظين عندي هنا الخلايا الحمرة
+
+7
+00:00:22,400 --> 00:00:26,670
+اللي تسمى Bullion طبعاً الـPink، ماشي؟في عندي
+
+8
+00:00:26,670 --> 00:00:29,610
+الخلايا طبعًا الأحمر، طبعًا لاحظوا عندي أن الخلايا
+
+9
+00:00:29,610 --> 00:00:32,370
+الحمرة في الـ «تولتين» مسبوخ والـ «تولت» غير
+
+10
+00:00:32,370 --> 00:00:36,050
+مسبوخ، طبعًا هي بتظهر بالصورة هيك لأن طبعًا هي
+
+11
+00:00:36,050 --> 00:00:40,770
+عبارة عن الـ «Discoid» كيف يعني الـ «Discoid»؟ الـ
+
+12
+00:00:40,770 --> 00:00:46,350
+«جولد» طبعًا من الأطراف الكبيرة ومن الوسط، «thin»
+
+13
+00:00:46,350 --> 00:00:49,750
+شوية، أخف شوية، سمكة، فبتالي بتظهر كأنه خفيف،
+
+14
+00:00:49,750 --> 00:00:52,790
+همنها عنطبعًا، الخلايا الحمرة مليانة
+
+15
+00:00:52,790 --> 00:00:56,130
+بالـHemoglobina، زي ما أحنا عارفين، عندها الخلايا
+
+16
+00:00:56,130 --> 00:00:59,270
+البيضا خمس أنواع أساسيين، اللي هم، هذي إيه خلية؟
+
+17
+00:00:59,270 --> 00:01:03,150
+هذي نيتروفيل، هذي خلية الإيزينوفيل، هذي خلية
+
+18
+00:01:03,150 --> 00:01:06,590
+الـLymphocyte، الـMonocyte، والبيزوفيل، طبعًا،
+
+19
+00:01:06,590 --> 00:01:10,830
+خلية الـMonocyte وLymphocyte، طبعًا، هي عبارة
+
+20
+00:01:10,830 --> 00:01:15,410
+بيسموها Mononuclear، Mononuclear Lycoside، بينما
+
+21
+00:01:15,410 --> 00:01:20,650
+الخلايا التلاتة الضايقين، اللي الـGranularهذه
+
+22
+00:01:20,650 --> 00:01:24,590
+بيسموها Poly-Nuclear أو Granulocyte، طبعاً لأنها
+
+23
+00:01:24,590 --> 00:01:29,010
+تحتوى على حبيبات الـNitrophil حبيباتها نعم كتير
+
+24
+00:01:29,010 --> 00:01:34,710
+وPink، يعني دوب ميزين احنا الـXenophil حبيباتها
+
+25
+00:01:34,710 --> 00:01:38,210
+بيكون مرسوسة صح وبيكون لون أحمر الـBisophil
+
+26
+00:01:38,210 --> 00:01:40,890
+حبيباتها حجمها مختلفة، تتفاوت إيش كبير وإيش صغير
+
+27
+00:01:40,890 --> 00:01:46,630
+ومبعترة ولونها أسود، تمام؟
+
+28
+00:01:46,630 --> 00:01:51,470
+هاي كمان مرة عنديهذه خلية الـ Band، هذا طبعًا اسمه
+
+29
+00:01:51,470 --> 00:01:53,490
+بيسميه أحنا «Band Neutrophil» طبعًا «Band
+
+30
+00:01:53,490 --> 00:01:56,170
+Neutrophil» المرحلة مقبل الـ «Neutrophil» أحنا
+
+31
+00:01:56,170 --> 00:02:00,090
+هندرس في عملية الـ «maturation» اللي هي تطور إنشاء
+
+32
+00:02:00,090 --> 00:02:03,850
+الخلايا كيف تنشأ الخلايا من الخلية الأم لـ «stem
+
+33
+00:02:03,850 --> 00:02:07,330
+cells» لعند ما توصل لخلية الـ «mature cells» فهذه
+
+34
+00:02:07,330 --> 00:02:09,890
+المرحلتين هاي اللي مُتسبرة يعني «maturation»
+
+35
+00:02:09,890 --> 00:02:12,490
+«maturation» الـ «Band Neutrophil» تظهر عندي
+
+36
+00:02:12,490 --> 00:02:16,800
+بالنسبة تقريبًا 5%، 3 إلى 5%في الـ Blood Film،
+
+37
+00:02:16,800 --> 00:02:18,800
+يعني تظهر نوع من الظهورة في الـ Blood Film بنسبة
+
+38
+00:02:18,800 --> 00:02:22,800
+معينة، طبعا هذه خلية الـ Poly-Nuclear، طبعا نسميها
+
+39
+00:02:22,800 --> 00:02:25,580
+Poly-Nuclear، طبعا إن هو أصلا مجزقة، صارت إن دي
+
+40
+00:02:25,580 --> 00:02:28,340
+عبارة عن تلاتة Loops، هذا ما نسميه إحنا الـ Jews،
+
+41
+00:02:28,340 --> 00:02:32,370
+وهذا ما نسميه Loopsفمسميه three loops، طبعًا الـ
+
+42
+00:02:32,370 --> 00:02:34,890
+Neutrophil شايفين الحبابات فيها كيف؟ يعني نعم، من
+
+43
+00:02:34,890 --> 00:02:38,190
+وعنها الخليه هاي الـ Xenophil، طبعًا لاحظينها الـ
+
+44
+00:02:38,190 --> 00:02:40,910
+Neutrophil تنتين دول؟ هذه الـ Xenophil، الحباباتها
+
+45
+00:02:40,910 --> 00:02:45,650
+مرصوصة كإنه حد صفطها تسيط، ولونه أحمر، وغالبًا
+
+46
+00:02:45,650 --> 00:02:49,970
+النواة عبارة عن Binublia، فيها جزئين غالب النواة
+
+47
+00:02:49,970 --> 00:02:56,570
+دكتور، بقى دستك، بس في mouse أو في مؤشر؟ كيف؟ في
+
+48
+00:02:56,570 --> 00:03:00,200
+mouse أو مؤشر؟هيبقى أشير أنا جاعد، هيبقى شايف الـ
+
+49
+00:03:00,200 --> 00:03:07,640
+mouse؟ لأ، مش شايفينه لأ مش واضح دكتور مش عارف إذا
+
+50
+00:03:07,640 --> 00:03:12,040
+فيها آلية مش
+
+51
+00:03:12,040 --> 00:03:15,800
+شايفين ال mouse عندي؟ لأ، عشان مش عارفين ع أي صورة
+
+52
+00:03:15,800 --> 00:03:20,060
+بتحكي جاعد، ع أي صورة بتشرح طويل طيب، أنا ببنشت من
+
+53
+00:03:20,060 --> 00:03:24,640
+الصورة العلوية على الشمال تمام، هذه ال band
+
+54
+00:03:24,640 --> 00:03:30,110
+نيتروفيل شايفينها؟هذه باند نيتروفيل هي برعن جزء
+
+55
+00:03:30,110 --> 00:03:36,430
+واحد، إن هو فيها زي إيش؟ زي نحكي حدوث الحصان زمان
+
+56
+00:03:36,430 --> 00:03:40,270
+أو زي حد السنين، هذه بيسميها باند نيتروفيل،
+
+57
+00:03:40,270 --> 00:03:48,320
+شفتوها؟ طبعا هذه فيها نعمة، لونها طبعا pinkوطبعًا،
+
+58
+00:03:48,320 --> 00:03:51,820
+زي ما حكينا، هذه نسبة تواجدها تقريبًا من، زي ما
+
+59
+00:03:51,820 --> 00:03:56,540
+حكينا، من 3% لـ5%، من 3% لـ5%، ماشي؟ هالجهة اللي
+
+60
+00:03:56,540 --> 00:04:00,200
+عندي خلية الجنبها، اللي هي المرحلة ما بعديها
+
+61
+00:04:00,200 --> 00:04:04,660
+بيسموها، طبعًا، Segmented Neutrophil أو بيسموها
+
+62
+00:04:04,660 --> 00:04:09,010
+Poly-Nuclear Neutrophilطبعًا، زي ما حكينا، الـ
+
+63
+00:04:09,010 --> 00:04:15,210
+Maturation، إن شاء الله، هندرسه في أحد المحاضرات،
+
+64
+00:04:15,210 --> 00:04:17,410
+هيكون عندي من الـSegmented Neutrophil، الحبل ما
+
+65
+00:04:17,410 --> 00:04:22,110
+يتطور، هجيت الجنب، اللي في الأعلى، أقصى، اليمين،
+
+66
+00:04:22,110 --> 00:04:27,880
+هذي بيسميها أحنا أزينوفيل، تمام؟ تمامالـXenophil،
+
+67
+00:04:27,880 --> 00:04:30,780
+طب الـXenophil، خلّيني أشوف ممكن فيه اندهانة، إذا
+
+68
+00:04:30,780 --> 00:04:33,760
+بقدر أجيب الـpointer «بش روح تحت يا دكتور، كل
+
+69
+00:04:33,760 --> 00:04:36,800
+slide لحال» «بش روحين؟ آه، هنخدم، إحنا الدباش مش
+
+70
+00:04:36,800 --> 00:04:41,840
+مشكلة» «طبعا، في انديهاد الشمال، تحت، بيزوفيل،
+
+71
+00:04:41,840 --> 00:04:46,380
+شايفين كيف هو بيبعت كبير ومبعترة، ومش ثابت الحجم؟»
+
+72
+00:04:46,380 --> 00:04:49,540
+«عندي هنا طبعا، هذه الـLymphocyte، اللي بالنص،
+
+73
+00:04:49,540 --> 00:04:53,020
+تحت، وتحت أقصى اليمين، تحت، إبارة عن Monocyte»
+
+74
+00:04:53,020 --> 00:04:57,110
+«هنخدمه واحد وواحد، زي ما حكى محمد ونيشيهذه أول
+
+75
+00:04:57,110 --> 00:05:00,990
+واحدة، بسميها إحنا هذه «Stab in Utrophil» أو «Bad
+
+76
+00:05:00,990 --> 00:05:05,120
+Utrophil»، شايفين؟ عبارة عنجزء واحد، لسه ما أصارش
+
+77
+00:05:05,120 --> 00:05:09,540
+فيه تقسيم النواة لعدة loops طبعًا، الحجم ها من 12
+
+78
+00:05:09,540 --> 00:05:13,020
+إلى 16، الـCytoplasm فيها Pink الـGranulars هي
+
+79
+00:05:13,020 --> 00:05:15,840
+عبارة عن الـPrimary وSecondary Granules طبعًا،
+
+80
+00:05:15,840 --> 00:05:19,560
+النواة عبارة عن Dark Peripher وفيها الـChromatin،
+
+81
+00:05:19,560 --> 00:05:22,080
+شايفين الـChromatin ها؟ Lens Chromatin، طبعًا
+
+82
+00:05:22,080 --> 00:05:27,260
+الـChromatin هي تعتبر تجمع الـDNA وهي أحد المميزات
+
+83
+00:05:27,260 --> 00:05:31,820
+التي تقدر تميزها نواة الخلاياطبعًا، البعدية زي ما
+
+84
+00:05:31,820 --> 00:05:33,480
+أكيدها «Segmented Neutrophil» «Segmented
+
+85
+00:05:33,480 --> 00:05:36,300
+Neutrophil» هين شايفين الخلية؟ بيكون الخلية عبارة
+
+86
+00:05:36,300 --> 00:05:39,460
+عن أكثر من اتنين لخمس loops شايفين؟ Two to five
+
+87
+00:05:39,460 --> 00:05:43,780
+loops الخلية، يعني لاحظين الخلية الفوق؟ عندي واحد،
+
+88
+00:05:43,780 --> 00:05:46,740
+اتنين وممكن تلاتي ناجحة، تتبرها الخلية التحت عبارة
+
+89
+00:05:46,740 --> 00:05:50,700
+عن اتنين loops طبعًا، زي نفس الـBand حجمها اتناشر
+
+90
+00:05:50,700 --> 00:05:54,260
+لستة عشر مايكرون «Cytoplasm Pink» فيها Primary
+
+91
+00:05:54,260 --> 00:05:58,640
+وSecondary Granules الـ«Nucleus Dark Purple Blue»
+
+92
+00:05:58,640 --> 00:06:01,370
+شايفين كيف Dark Purple Blue؟والـ Chromatin dense
+
+93
+00:06:01,370 --> 00:06:05,190
+تلاحظين أن في الجمعات الأزرق فيه كتير فيها، فتعتبر
+
+94
+00:06:05,190 --> 00:06:11,250
+dense هذه خلية الازينوفيل أكبر شبه حجمها من 14 إلى
+
+95
+00:06:11,250 --> 00:06:14,550
+16 مايكرون مليئة بالـ granules الـ granules حجمها
+
+96
+00:06:14,550 --> 00:06:18,050
+كبير، لونها أحمر، وهتميز الإلها، أنا ممكن أميز أن
+
+97
+00:06:18,050 --> 00:06:21,090
+اللون أحمر الـ granules وبيضع في النواة عبارة عن
+
+98
+00:06:21,090 --> 00:06:25,290
+two loops عبارة عن two loops غالبا للنواة ولونها
+
+99
+00:06:25,290 --> 00:06:29,890
+أزرقالنواء؟ النواء، الأنويات تتصرف الأزرق بشكل
+
+100
+00:06:29,890 --> 00:06:33,650
+عام، وجود الـDNA يا محمد، ليش؟ بحكينا احنا
+
+101
+00:06:33,650 --> 00:06:37,490
+الـRight Stain أو الـLishman Stain فيها By Basic
+
+102
+00:06:37,490 --> 00:06:42,290
+Stains، فيه جزء بصبغة لنواء، الـLishman أو New
+
+103
+00:06:42,290 --> 00:06:45,970
+Methyl Blue، وفيه جزء بصبغة لـCytoplasm، اللي يزين
+
+104
+00:06:45,970 --> 00:06:50,350
+Red، تمام؟ فالجزء بصبغة لنواء، بصبغة لـDNA أزرق،
+
+105
+00:06:50,350 --> 00:06:58,350
+مر معناك سابقًا، تمام؟طيب، هالجيت أنا عندي هذي
+
+106
+00:06:58,350 --> 00:07:04,010
+حكينا الـXenophil، البعدية الـBesophil الحجم 14–16
+
+107
+00:07:04,010 --> 00:07:06,590
+أكبر شوية من الـNitrophil، الـCytoplasm طبعًا
+
+108
+00:07:06,590 --> 00:07:10,930
+Pink، الـGranules Dark وBlue وطبعًا Obscure
+
+109
+00:07:10,930 --> 00:07:14,430
+Nucleus، طبعًا نواة مش واضحة، مش جدًا ميزي حرف
+
+110
+00:07:14,430 --> 00:07:19,370
+الـS، لأن الـGranules بغطاتيها كامل، والنواة Dark
+
+111
+00:07:19,370 --> 00:07:22,110
+Blue أكيد، طبعًا التلاتة المرة السابقة، اللي هو
+
+112
+00:07:22,110 --> 00:07:25,970
+الـNitrophilوالـ Ezinofil والـ Bezofil نسميهم
+
+113
+00:07:25,970 --> 00:07:29,710
+Granular Glycosides لأنهم فيها نواة محبقة حبيبات
+
+114
+00:07:29,710 --> 00:07:33,410
+ونسميهم طبعاً إيه؟ Poly-Nuclear لأن النواة تبعتها
+
+115
+00:07:33,410 --> 00:07:38,050
+مجزقة يعني زي الـ Nucleus 2 إلى 5 لوث الـ Ezinofil
+
+116
+00:07:38,050 --> 00:07:41,070
+2 لوث الـ Bezofil طبعاً مش واضحة كتير لكن تكون
+
+117
+00:07:41,070 --> 00:07:42,650
+مجزقة غالباً، تمام؟
+
+118
+00:07:46,580 --> 00:07:50,440
+عندي الـMononuclear اللي هي الـ«لمفو سايس»
+
+119
+00:07:50,440 --> 00:07:53,400
+والـ«مونو سايتس» الـ«لمفو سايتس» كما تشاهدون،
+
+120
+00:07:53,400 --> 00:07:58,360
+حجمها تختلف حسب نوع الخلايا، فعندي «صغير» «لمفو
+
+121
+00:07:58,360 --> 00:08:06,260
+سايتس» في التحت أسفل، إذا شايفين شايفين ولا لا؟ ‏-
+
+122
+00:08:06,260 --> 00:08:08,680
+أشوفك. ‏- أشوفك. ‏- لتحت كلمة كبيرة. ‏- آه،
+
+123
+00:08:08,680 --> 00:08:09,020
+شايفين.
+
+124
+00:08:18,060 --> 00:08:24,180
+أه دكتور، شايفينها؟ مش فاهم عليكم إيش؟ شايفينها،
+
+125
+00:08:24,180 --> 00:08:28,080
+شايفينها تمام اللي تحت كلمة «chromatin dense» يا
+
+126
+00:08:28,080 --> 00:08:30,800
+دكتور؟ اللي تحت كلمة «chromatin dense»، أه في ندخل
+
+127
+00:08:30,800 --> 00:08:33,200
+نخليتين، في صغيرة وفي كبيرة هذه بالطبع small
+
+128
+00:08:33,200 --> 00:08:35,820
+lymphocyte وlarge lymphocyte وفي بالنص
+
+129
+00:08:35,820 --> 00:08:39,060
+intermediate ال «small lymphocyte» حجمها، وهذه
+
+130
+00:08:39,060 --> 00:08:43,120
+النقطة أذكرها كويس ال «small lymphocyte» حجمها 7
+
+131
+00:08:43,120 --> 00:08:46,550
+على 9 مايكرون يعادل حجم الخلايا الحمراءهل جيت؟
+
+132
+00:08:46,550 --> 00:08:50,250
+ممكن أنا أسحب من «محمد» وممكن أسحب من «معاد»
+
+133
+00:08:50,250 --> 00:08:52,610
+الخلايا الحمرا عندهم مش شبهة بالحجم ممكن حجم
+
+134
+00:08:52,610 --> 00:08:55,010
+الخلايا الحمرا عند «معاد» نوعًا ما طبعًا إيه
+
+135
+00:08:55,010 --> 00:08:57,250
+الخلايا الحمرا حجمها تقريبًا من 7 إلى 7 مايكرون
+
+136
+00:08:57,250 --> 00:09:01,170
+يكون عند «معاد» مثلًا أو بلاش هاي ممكن أسحب وأنا
+
+137
+00:09:01,170 --> 00:09:03,150
+شوف تعرف إن الخلايا الحمرا هاي طبيعية أو مش طبيعية
+
+138
+00:09:03,150 --> 00:09:06,370
+حجمها بقارنها بحجم الـ«Lymphocytes» اللي اسمه
+
+139
+00:09:06,370 --> 00:09:08,910
+الـ«Lymphocytes» فالـ«Lymphocytes» يعتبر كأنه عندي
+
+140
+00:09:08,910 --> 00:09:15,440
+Indicators لحجم الخلايا الحمرا عشان أقدر أقارطبعًا
+
+141
+00:09:15,440 --> 00:09:17,800
+الـCytoplasm، لاحظوا الـCytoplasm عنديها؟ أنه إيش
+
+142
+00:09:17,800 --> 00:09:20,840
+لون الـCytoplasm؟ الخلية اللي بالنص هذه، الداخل
+
+143
+00:09:20,840 --> 00:09:24,700
+المربع الـCytoplasm لونه إيش لاحظين؟ أزرق، سماوي،
+
+144
+00:09:24,700 --> 00:09:30,880
+شايفينه؟ شايفينه؟ آه، واللي طبعًا هو عبارة عن dark
+
+145
+00:09:30,880 --> 00:09:35,300
+blue لكن بتكون طبعًا مش زي الـChromatin، زي
+
+146
+00:09:35,300 --> 00:09:39,020
+الـNitrophil بيكون dense الـChromatin، لكن أقل
+
+147
+00:09:39,020 --> 00:09:44,630
+التجمعات، تمام؟ هذه اسمها الـLymphocyteالـ Slides
+
+148
+00:09:44,630 --> 00:09:47,030
+اللي بعتيها، اللي هي الـ Mono Slides، هاي خلية الـ
+
+149
+00:09:47,030 --> 00:09:50,150
+Mono Slides الموجودة عندي، أنا بحاول أشوف إذا في
+
+150
+00:09:50,150 --> 00:09:54,490
+عندي، أجيب، أقدر أجيبكم جلم، بس مش عارف ال .. من
+
+151
+00:09:54,490 --> 00:09:57,870
+أين أجيبكم إياها، على كل حاجة. مرة قد كنت تعمل على
+
+152
+00:09:57,870 --> 00:10:01,770
+الرسامة، ظنين؟ على الرسامة كنت أشتغل، آه، آه، من
+
+153
+00:10:01,770 --> 00:10:06,350
+المرة إيش عملت؟ أنا جبت، شو اسمه؟ خليني أشوف إذا
+
+154
+00:10:06,350 --> 00:10:06,630
+..
+
+155
+00:10:12,240 --> 00:10:18,440
+سيف أبعد الكتب ولا لسه؟ الكتب ايش يا عزيزي؟ احنا
+
+156
+00:10:18,440 --> 00:10:26,980
+ممكن كتب بلجيات؟ ده بحكي لسيفة عشان ألجهم سيف
+
+157
+00:10:26,980 --> 00:10:32,120
+اعنوه النص و اتبعه من سيفه طيب شايفين ما هو فيك
+
+158
+00:10:32,120 --> 00:10:40,730
+حاليا ولا لسه؟ ولا ايش اتحرك ولا ايش دعوة؟فجأت
+
+159
+00:10:40,730 --> 00:10:44,230
+الدكتورة انت، جيبليها المعلومة بالراحة طيب، خلّيني
+
+160
+00:10:44,230 --> 00:10:47,530
+أكمل، مش مشكلة، هلأ بنشوف المشكلة هذه طيب، احنا
+
+161
+00:10:47,530 --> 00:10:53,490
+لقيت طبعا، لحظة عندي هان الـ… الـ… الـ… الـ…
+
+162
+00:10:53,490 --> 00:10:57,010
+الـMonocytes كيف حجمها؟ أكبر حجم تقرر، 14 لـ20
+
+163
+00:10:57,010 --> 00:11:00,110
+الـCytoplasm فيها، طبعا الـ… الـLymphocytes،
+
+164
+00:11:00,110 --> 00:11:03,190
+الـCytoplasm فيه blue أذاك سماوي، لكن في
+
+165
+00:11:03,190 --> 00:11:07,610
+الـMonocytes، grey، blueيعني بيكون أزرق ما يلقيه
+
+166
+00:11:07,610 --> 00:11:11,150
+أي شيء لسكري نوعًا ما طبعًا الـ Granules، ما فيش
+
+167
+00:11:11,150 --> 00:11:14,890
+فيها Granules لكن ممكن يظهر بعد الـOrgranules
+
+168
+00:11:14,890 --> 00:11:18,470
+أحيانًا النواء Blue و Large و Irregular في
+
+169
+00:11:18,470 --> 00:11:21,950
+الـShape ممكن يكون حالة في الـS طبعًا، شايفين كيف؟
+
+170
+00:11:21,950 --> 00:11:25,050
+طبعًا، زي ما حكينا هي تعتبر أكبر حجم الخلايا
+
+171
+00:11:25,050 --> 00:11:28,270
+البيضة موجودة طبعًا، شايفين الجمعات هذه جنبها،
+
+172
+00:11:28,270 --> 00:11:31,350
+اللي علي اليمين؟ فيه جمعات خلايا صغيرة، إيش هي؟
+
+173
+00:11:31,350 --> 00:11:32,070
+فعلاً إيش هي؟
+
+174
+00:11:56,890 --> 00:11:58,290
+هذه………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………
+
+175
+00:12:06,150 --> 00:12:11,010
+تحكي سيد، صح؟ هذه اللي قبل شويه اللي .. اللي قبل
+
+176
+00:12:11,010 --> 00:12:13,710
+شويه اللي هي الـ lymphocyte الـ small و الـ هذا؟
+
+177
+00:12:13,710 --> 00:12:16,490
+لأ، لأ، هذه عبارة عن صفائح دموية، الـ platelets
+
+178
+00:12:16,490 --> 00:12:22,270
+آه، platelets، هي هذه الـ Mega .. دكتور، معلش، بس،
+
+179
+00:12:22,270 --> 00:12:25,890
+هي هذه الـ Megakaryocyte اللي هي اللي عاملة .. لأ،
+
+180
+00:12:25,890 --> 00:12:30,910
+لأ، الـ Megakaryocyte خليةفيها نواء وCytoplasm
+
+181
+00:12:30,910 --> 00:12:33,670
+وفيها… بيطلع منها الـPlatelets الـPlatelets هي بقى
+
+182
+00:12:33,670 --> 00:12:39,110
+عن، نحكي، ذوائط من الـCytoplasm ما نعتبرهاش خلايا
+
+183
+00:12:39,110 --> 00:12:41,850
+كاملة، لأن مافيش فيها أنوبيا وبعدين، حجمها، لحظة،
+
+184
+00:12:41,850 --> 00:12:44,750
+حجمها أقل من حجم الخلايا الحمراء بكتير Platelets،
+
+185
+00:12:44,750 --> 00:12:46,890
+الخلايا الحمراء حجمها، حكينا، من 7 إلى 7 مايكرون
+
+186
+00:12:46,890 --> 00:12:51,170
+بينما الـPlatelets حجمها تقريباً 4 مايكرون، تمام؟
+
+187
+00:12:51,170 --> 00:12:54,690
+فحجمها أقل بكتير، بس طبعاً هي مجمعة مع بعض، مع بعض
+
+188
+00:12:54,690 --> 00:12:57,360
+لأن Platelets إيش وظيفته يا شباب؟الـ Platelets
+
+189
+00:12:57,360 --> 00:13:01,180
+مظبتها اللي هو الـ Clumping تعمل الـ Clump اللي
+
+190
+00:13:01,180 --> 00:13:03,680
+بتتجمع بعض عشان تعمل تجارب الدم تبنع تجارب الدم
+
+191
+00:13:03,680 --> 00:13:06,380
+وهنا جاياني في ال slide عاملة الـ Clump بيجمع
+
+192
+00:13:06,380 --> 00:13:09,180
+الخلايا الصفايا الدموية مع بعض بعض هذه بيسميها
+
+193
+00:13:09,180 --> 00:13:13,160
+احنا Clump of Platelets لو شوفت في ال block فلان
+
+194
+00:13:13,160 --> 00:13:18,640
+بكتبه في التقرير، تمام؟
+
+195
+00:13:18,640 --> 00:13:20,100
+معاي يا شباب انتم؟
+
+196
+00:13:23,580 --> 00:13:26,900
+طيب، الـ Abnormal Changes في الخلايا البيضاء، إيش
+
+197
+00:13:26,900 --> 00:13:30,800
+بيصير عندي؟ طبعًا، نجات كلها بقى برع الأشكال، بدنا
+
+198
+00:13:30,800 --> 00:13:36,620
+نركز فيها كويس طبعًا، أول شغلة، في مصطلح بيسموه
+
+199
+00:13:36,620 --> 00:13:42,840
+«Left Shift» و «Right Shift» «Left Shift» إنه أنا
+
+200
+00:13:42,840 --> 00:13:46,540
+بكون عندي Non-Segmented Neutrophil أكتر من 5%، كيف
+
+201
+00:13:46,540 --> 00:13:51,100
+يعني؟يعني إنه أنا في الـ «maturation» هتمرب على
+
+202
+00:13:51,100 --> 00:13:54,320
+الـ «maturation» هكون عندي الـ «نيتروفيل» هتمرب
+
+203
+00:13:54,320 --> 00:14:02,040
+بعدد مراحل بتبلش من الـ… تبلش من، نحكي الـ… الشيء
+
+204
+00:14:02,040 --> 00:14:04,820
+اسمه الـ «stem cells» اللي بتوطني لـ«segmented
+
+205
+00:14:04,820 --> 00:14:08,280
+neutrophil» لو شوفت خلايا ما قبل الـ«band» أو
+
+206
+00:14:08,280 --> 00:14:12,680
+الـ«stab» 5%، بعتبر أنا عندي «left chip»هيجيب
+
+207
+00:14:12,680 --> 00:14:16,100
+العكس، الـRight Shift إن أنا الـModulation زاد عن
+
+208
+00:14:16,100 --> 00:14:19,000
+حده زاد عن حده، إن أنا الـNeutrophil عدد الـLoops
+
+209
+00:14:19,000 --> 00:14:23,240
+فيها 2 إلى 5، لو شفت خلائي الـNeutrophil 3% أكثر
+
+210
+00:14:23,240 --> 00:14:28,080
+من 5 Loops، بعتبر عندي Right Shift، تمام؟ طبعا،
+
+211
+00:14:28,080 --> 00:14:31,120
+بتفيدني إيش Left Shift، Right Shift، تحديد حالات
+
+212
+00:14:31,120 --> 00:14:34,660
+مرضية، أنا Normal لازم أكونش في عندي Shift نهائيا،
+
+213
+00:14:34,660 --> 00:14:38,730
+طيبToxic Granulation، طبعًا هذا كتير مصالح كتير
+
+214
+00:14:38,730 --> 00:14:42,510
+بُرد ومشوه كتير إنه أنا شايفين الخلايا النيتروفي
+
+215
+00:14:42,510 --> 00:14:46,610
+اللي على اليمين الـgranules فيها، إيش لونها؟ –
+
+216
+00:14:46,610 --> 00:14:49,470
+أزرق – أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+217
+00:14:49,470 --> 00:14:49,550
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+218
+00:14:49,550 --> 00:14:50,150
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+219
+00:14:50,150 --> 00:14:58,010
+أزرق، أزرق، أزرق، أزرق، أزرق، أزرق،
+
+220
+00:14:58,010 --> 00:15:04,310
+أزرقطبعًا، فهذه بتدل على إنه فيه التهيبات بكتيرية
+
+221
+00:15:04,310 --> 00:15:07,430
+وهذا دليل على… طبعًا، بيكون عندي خلالي نتروفيل
+
+222
+00:15:07,430 --> 00:15:12,090
+عالية، عددها بالإضافة إن الـ… الـGranules بتتغير
+
+223
+00:15:12,090 --> 00:15:14,090
+من شكلها، بيصير توكسجالوش، طبعًا ليش بتتغير من
+
+224
+00:15:14,090 --> 00:15:17,130
+شكلها؟ لأن ده هتخضر في نظري، الـGranules فيه عنده
+
+225
+00:15:17,130 --> 00:15:20,450
+عدة أنواع، فيه Primary وSecondary وفيه من ضمن وضع
+
+226
+00:15:20,450 --> 00:15:23,770
+في الـGranules فرزل مواد تختلل بكتيريا،
+
+227
+00:15:23,770 --> 00:15:27,190
+الـIsocytes فهذه دور جدًا في تغيير، وفرز المواد
+
+228
+00:15:27,190 --> 00:15:33,130
+تؤدي لتغيير شكلها، تمام؟طبعًا، عندي فيه الـAll
+
+229
+00:15:33,130 --> 00:15:37,450
+Roots، الـAll Roots فيه عندي، شايفين العصاي داخل
+
+230
+00:15:37,450 --> 00:15:41,250
+الـ… شايفين الـSlides على اليمين؟ آه، آه، فيه
+
+231
+00:15:41,250 --> 00:15:44,030
+عصاي، فيه عصاي ذرج صغير هيك. طبعًا، اللي بيسموه
+
+232
+00:15:44,030 --> 00:15:47,490
+All Roots، All Roots، وفي عندك على الشمال برضه، في
+
+233
+00:15:47,490 --> 00:15:50,050
+عندي بعض الخلايا، طبعًا، هذه الخلايا عبارة عن
+
+234
+00:15:50,050 --> 00:15:53,090
+المراحل الأولية من الـNitrophil، طبعًا، اللي هي
+
+235
+00:15:53,090 --> 00:15:57,520
+عبارة عن ال… نحكي ال… ال…اللهم صلى الله عليه وسلم،
+
+236
+00:15:57,520 --> 00:16:00,440
+الـMeta-myrocytes وMyrocytes فعندي هنا أغلب
+
+237
+00:16:00,440 --> 00:16:04,720
+الخلايا هدول عبارة عن Myrocytes، تمام؟ لمرحلة ما،
+
+238
+00:16:04,720 --> 00:16:07,600
+طبعًا ما أخبر نشوريشن بكتير، بيكون هذه في الـbone
+
+239
+00:16:07,600 --> 00:16:10,460
+marrow غالبًا إلا في حالات، نحكي سرطانية،
+
+240
+00:16:10,460 --> 00:16:13,180
+الـLeukemia أو إذا كان بيعيندي حالات Leukemoid
+
+241
+00:16:13,180 --> 00:16:16,420
+Reaction تظهر عندى، بعدين هم بيظهر عندى اللي هي
+
+242
+00:16:16,420 --> 00:16:19,460
+طبعًا هذه الحالة اللي هي الـOroles طبعًا تمور معنا
+
+243
+00:16:19,460 --> 00:16:24,320
+بشكل تفصيل أكتر الـOroles وإيش أساسها وإيش سببها
+
+244
+00:16:24,320 --> 00:16:29,170
+ووين تظهر بأي حالةطبعًا، مرة معناها بالصلاة على
+
+245
+00:16:29,170 --> 00:16:31,070
+الـHyper-segmented،
+إيش هو يعني بالصلاة على
+
+246
+00:16:31,070 --> 00:16:35,250
+الـHyper-segmented، يا شباب؟ Right Shift. بالظبط،
+
+247
+00:16:35,250 --> 00:16:36,770
+Right Shift. الـHyper-segmented بيكون خلايا
+
+248
+00:16:36,770 --> 00:16:41,890
+نيدروفيل الـSegmentation عالية. لاحظوا الـslide
+
+249
+00:16:41,890 --> 00:16:48,390
+على الشمال، كان محد فيها،عدّولي يا هون، سبعة،
+
+250
+00:16:48,390 --> 00:16:51,970
+بالضبط، سبعة segmentation، فتعتبر right shift
+
+251
+00:16:51,970 --> 00:16:56,790
+يعني، ولاحظوا اليمين برضه نفس الحكاية، 2، 4، 6، 8،
+
+252
+00:16:56,790 --> 00:16:58,930
+فهذا يسموها hyper-segmented neutrophil
+
+253
+00:17:01,970 --> 00:17:07,210
+طبعًا، الخلايا التانية دي خلايا حمرة الخلية الفوق،
+
+254
+00:17:07,210 --> 00:17:09,870
+الـNitrophilها دي ممكن تخربطكم شوية تفكروا هي
+
+255
+00:17:09,870 --> 00:17:13,730
+عبارة عن خلية إيش؟ Lymphocyte لأن Lymphocyte قريب
+
+256
+00:17:13,730 --> 00:17:16,690
+منها لكن هي دي خلية اللي هي الخلية الأولية الخلاية
+
+257
+00:17:16,690 --> 00:17:20,990
+الحمرة اللي هي بقى Nucleated RBC، Nucleated RBC
+
+258
+00:17:20,990 --> 00:17:25,030
+شباب، موضوع الخلاية يعني حاولوا تركزوا فيه كتير
+
+259
+00:17:25,030 --> 00:17:28,770
+لإنه من هالجهة كل مراتينكم خلية درسوها صح عشان من
+
+260
+00:17:28,770 --> 00:17:31,520
+الجدام شوية إن شاء الله ماتخربطش كتيرفي تمييز بين
+
+261
+00:17:31,520 --> 00:17:33,800
+خلية وخلية، تمام؟
+
+262
+00:17:35,900 --> 00:17:39,060
+عندي مصالح بيسموه «anisocytosis of neutrophil»
+
+263
+00:17:39,060 --> 00:17:42,480
+كلمة «anisocytosis» مصالح له تعدد الحجم، كيف تعدد
+
+264
+00:17:42,480 --> 00:17:45,440
+الحجم؟ عندي حجم صغير وحجم كبير، طبعا عندي خلايا
+
+265
+00:17:45,440 --> 00:17:48,960
+الـ «نيتروفيل»، عندي خمس خلايا، طلعوا الخلية، احنا
+
+266
+00:17:48,960 --> 00:17:51,000
+الخلية تفكروا على شغل، هل جيتوا احنا نعتبره
+
+267
+00:17:51,000 --> 00:17:55,260
+الدائرة هاي ساعة، تمام؟ هل جيتوا عند الساعة تقريبا
+
+268
+00:17:55,260 --> 00:17:59,800
+عشرة، بين الساعة عشرة ومركز، في خلية، قارنوها مع
+
+269
+00:17:59,800 --> 00:18:02,680
+الخلية اللي عند الساعة خمسة، في فرق بين الحجم، صح
+
+270
+00:18:02,680 --> 00:18:06,960
+ولا لأ؟أيه؟ هذا طبعا تختلف حجم النيتروفيل نسميها
+
+271
+00:18:06,960 --> 00:18:11,880
+نيزو سي دوزيز of نيتروفيل فيه عندي ال vacuolation،
+
+272
+00:18:11,880 --> 00:18:14,840
+ال vacuolation طبعا هي وجود زي الهواء أو فقاعد
+
+273
+00:18:14,840 --> 00:18:19,360
+الهواء داخل النيتروفيل أو البرونسايتز طبعا عندي
+
+274
+00:18:19,360 --> 00:18:23,870
+أنا النيتروفيلاللي هي اللي على اليمين لعظم ينظف
+
+275
+00:18:23,870 --> 00:18:26,550
+فيها لأن فيه فخوعات هوا فيها والمرصد، طبعاً وجود
+
+276
+00:18:26,550 --> 00:18:30,330
+الـVacculation بتدل على وجود Infections، الجهبات
+
+277
+00:18:30,330 --> 00:18:33,950
+لأن الـVacculation عبارة عن بصير عندي حالة نشطة
+
+278
+00:18:33,950 --> 00:18:37,410
+Vapocytosis هذه الحالة نشطة الـVapocytosis، كما
+
+279
+00:18:37,410 --> 00:18:43,050
+حكينا، تؤدي إلى إن الـGranules تفضّي محتوياتها من
+
+280
+00:18:43,050 --> 00:18:46,110
+المواد وبتتقدر الـGranules فاضية، فهذه عبارة عن
+
+281
+00:18:46,110 --> 00:18:50,010
+الـVacculationطبعًا عندي الخليتين اللي بيقوموا
+
+282
+00:18:50,010 --> 00:18:53,510
+بعملية اللي بيحكي البلعنة أو الـ Bacocytation اللي
+
+283
+00:18:53,510 --> 00:19:01,750
+هي الـ نيتروفيل والـ Monocyte دكتور، معلش، ممكن بس
+
+284
+00:19:01,750 --> 00:19:06,110
+عسريق، بس تشرحلي نهادر لإنه أنا ما .. يعني الـ net
+
+285
+00:19:06,110 --> 00:19:13,710
+عندي ماكانش كويس الو؟
+
+286
+00:19:14,100 --> 00:19:16,600
+ماتك يا سعيد، ماتك، بأحكيلك أنا الـVacculation
+
+287
+00:19:16,600 --> 00:19:23,000
+طبعاً هي بره عن زي بقعات هواء داخل الخلايا
+
+288
+00:19:23,000 --> 00:19:27,400
+الديوتروفينية، لأن السببها، السببها أنه في
+
+289
+00:19:27,400 --> 00:19:32,840
+اندراجات تعمل سيئة عملية البلعمة للبكتيريا أو
+
+290
+00:19:32,840 --> 00:19:38,220
+للميكروهبينيات المدخل، طبعاً نتيجة البلعمة تضرر
+
+291
+00:19:38,220 --> 00:19:42,770
+اندراجات البكيوروالدكتور بس داخل خلية الـ
+
+292
+00:19:42,770 --> 00:19:45,970
+Neutrophil يعني؟ مش سامع زي دكتور معاه تفضل
+
+293
+00:19:45,970 --> 00:19:49,230
+تقبيلاتك على سهيلة فأقولك بس داخل خلية الـ
+
+294
+00:19:49,230 --> 00:19:51,570
+Neutrophil بس ولا فيها خلايا .. الـ Neutrophil و
+
+295
+00:19:51,570 --> 00:19:54,070
+الـ Monocyte بس الـ Neutrophil و الـ Monocyte ضمن
+
+296
+00:19:54,070 --> 00:19:57,070
+الخلايا المسؤولة على البلعمة خلية الـ Monocyte هي
+
+297
+00:19:57,070 --> 00:20:00,350
+موجودة على اليمين، شايفينها؟ وخلية الـ Neutrophil
+
+298
+00:20:00,350 --> 00:20:02,750
+موجودة على الشمال، شايفينهم؟
+
+299
+00:20:05,240 --> 00:20:08,360
+طبعًا، فيه عندي Degeneration of Nucleus طبعًا،
+
+300
+00:20:08,360 --> 00:20:11,640
+الـDegeneration of Nucleus العظيم إن هو طبعًا مش
+
+301
+00:20:11,640 --> 00:20:16,180
+طبيعي الشكل لها، عظيمًاالنواة شكلها مش طبيعي طبعاً
+
+302
+00:20:16,180 --> 00:20:19,240
+لسه شكلها مش طبيعي نواة لأنه طبعاً صارت تغيرات على
+
+303
+00:20:19,240 --> 00:20:21,880
+النواة طبعاً ماذا بيصير generation of nucleus في
+
+304
+00:20:21,880 --> 00:20:25,460
+حالة العين القادمة يعني أنا سحبت عينة بدل ما
+
+305
+00:20:25,460 --> 00:20:27,960
+أعملها blood film مباشرة سنت عليها يوم وبعدين سحبت
+
+306
+00:20:27,960 --> 00:20:30,880
+لها blood film طبعاً بيصير تغيرات على النواة بيصير
+
+307
+00:20:30,880 --> 00:20:34,000
+generation of nucleus سافين النواة كيف صارت؟ صارت
+
+308
+00:20:34,000 --> 00:20:37,420
+تغيرات فيها لإن بتمكن مشي شوية ويصير لها غامض كتير
+
+309
+00:20:37,420 --> 00:20:40,480
+عندي الـDohrybutyrate الـDohrybutyrate شايفين
+
+310
+00:20:40,480 --> 00:20:46,970
+طبعاً الزراعة اللي في داخل الغلايا النيفي نقطة
+
+311
+00:20:46,970 --> 00:20:52,910
+درجة في نقطة درجة بيسموها Dohil Buddels احنا
+
+312
+00:20:52,910 --> 00:20:56,490
+طبعا خلصنا ما تبقى من المحاضرة خلوا يجوا معايا ان
+
+313
+00:20:56,490 --> 00:21:07,430
+شاء الله بدي أدخل المحاضرة تانية دكتور
+
+314
+00:21:07,430 --> 00:21:13,350
+انت متجن المحاضرة ولا لأ؟يعني في تسجيل؟ آه، تقلقش،
+
+315
+00:21:13,350 --> 00:21:15,890
+أنا هنزلكم تسجيل إن شاء الله بالإضافة لتسجيل
+
+316
+00:21:15,890 --> 00:21:19,630
+المسبق اللي منزلكم يا أنا مش منزله، بهاست عليه
+
+317
+00:21:19,630 --> 00:21:23,250
+عمود اللي مش ملاقيه تسجيل الجديد لأ، منزل، كله
+
+318
+00:21:23,250 --> 00:21:28,050
+فلس، تبعتني على الرابط لما تنزله إن شاء الله خير،
+
+319
+00:21:28,050 --> 00:21:31,830
+طيب، احنا هناخد الـGET اللي طبعا اللي نرجع كمان
+
+320
+00:21:31,830 --> 00:21:38,130
+مرة لموضوع الـYPC morphology هبتعلكم ملف تاني إن
+
+321
+00:21:38,130 --> 00:21:44,800
+شاء اللههذا طبعا أخدنا منه بعضه، هكملكم عليه على
+
+322
+00:21:44,800 --> 00:21:48,440
+السريع، طبعا لإنه في بعض ال slides مش موجودة كانت
+
+323
+00:21:48,440 --> 00:21:53,940
+هناك، أنا بس أنا هاخد بشوية بتفاصيل أكتر هلجيت
+
+324
+00:21:53,940 --> 00:21:56,280
+بالنسبة للموعد، كنتوا بثبتوه عليك يا شباب، و لا
+
+325
+00:21:56,280 --> 00:22:01,040
+كيف؟ أنا شايف الصبح أحسن، والله الصبح أحسن يا
+
+326
+00:22:01,040 --> 00:22:04,220
+دكتور، بصراحة يعني أنا شايف المساء أحسن، عشان في
+
+327
+00:22:04,220 --> 00:22:08,780
+هالة قطع ال net بقدر الواحد يدبر حالهأنا .. أنا ..
+
+328
+00:22:08,780 --> 00:22:11,480
+أنا المسأ بالنسبالي أني بدي انا واحد بصحى الصوبة،
+
+329
+00:22:11,480 --> 00:22:15,820
+بدرس المسأ، بطول، بطلع، بنزل، رابطة أيه؟ والله يا
+
+330
+00:22:15,820 --> 00:22:19,300
+محمد، أجيب نرجع للصوبة أحسن، لإننا .. للمحب الصوبة
+
+331
+00:22:19,300 --> 00:22:21,760
+أحسن، بعدين اسمع، احنا الصوبة ممكن نبلس متأخر
+
+332
+00:22:21,760 --> 00:22:26,180
+شوية، ممكن نبلس على الإحدى عشرة، إذا حابين، عادي،
+
+333
+00:22:26,180 --> 00:22:28,780
+خلاص خليني على الإحدى عشرة، بلد الصوبة هبقى كتير،
+
+334
+00:22:28,780 --> 00:22:29,300
+بدر على عشرة
+
+335
+00:22:35,180 --> 00:22:37,200
+ظهر لكم شاشة بالنسبة للـ White Bases لأن الـ
+
+336
+00:22:37,200 --> 00:22:40,540
+Platelets أبنورمال مورفوليجي؟ ده أه، لأ بالتالي
+
+337
+00:22:40,540 --> 00:22:45,160
+وحناخد الـ RBCs مورفوليجي إن شاء الله ومدياكم
+
+338
+00:22:45,160 --> 00:22:48,080
+تدرسوهم كويس لإن المرة الجاية مدياكم تدرسوهم كويس
+
+339
+00:22:48,080 --> 00:22:57,260
+وزي السهر بعد وإن شاء الله نجاوب عليها طيب طبعا زي
+
+340
+00:22:57,260 --> 00:23:00,960
+ما حكينا في مصالح بسموه Platelets Citilism
+
+341
+00:23:01,270 --> 00:23:03,650
+Centralism يعني الـSatellite، الـSatellite يعني
+
+342
+00:23:03,650 --> 00:23:05,950
+اللي بيجي على سطح الخلايا، على سطح الإشي
+
+343
+00:23:05,950 --> 00:23:07,690
+الـSatellite عندنا، صح ولا لأ؟
+
+344
+00:23:07,690 --> 00:23:10,830
+فالـPlatyscentralism، الـPlatyscentralism عبارة عن
+
+345
+00:23:10,830 --> 00:23:13,890
+الصفائح دباوية موجودة على سطح الـNitrophil طبعا،
+
+346
+00:23:13,890 --> 00:23:16,150
+موجودة على سطح الـNitrophil بسبب أنه بينترجمت على
+
+347
+00:23:16,150 --> 00:23:21,210
+سطح الـNitrophil ممكن أن تكون سببها الـEdita طبعا،
+
+348
+00:23:21,210 --> 00:23:22,970
+بتعمل exchanges، هذه exchanges تؤدي إلى
+
+349
+00:23:22,970 --> 00:23:26,470
+الـPlatyscentralism، تمام؟
+
+350
+00:23:29,420 --> 00:23:32,880
+طبعا هذه الحالة مش مرضية، هذه الحالة بيصير in
+
+351
+00:23:32,880 --> 00:23:36,740
+vitro ليس in vivo، بلاي الـSentilism، طيب، شايفين
+
+352
+00:23:36,740 --> 00:23:44,780
+هالصورة هاي؟ واضحة جدا، واضحة جدا، البيتظارد، هذه
+
+353
+00:23:44,780 --> 00:23:49,450
+بلاي الـSentilismفي عندي ال .. ال giant plateless
+
+354
+00:23:49,450 --> 00:23:53,370
+من اسمها، ال plateless بحكيلكم حجمها صغير، حجمها
+
+355
+00:23:53,370 --> 00:23:56,890
+تقريبا هي plateless، شايفين؟ أنتم شايفين ال mouse
+
+356
+00:23:56,890 --> 00:24:00,870
+للأسف شديد، أه؟ جهاز كيف دوصلكم ال mouse أنا؟ لأ و
+
+357
+00:24:00,870 --> 00:24:06,150
+الله، طب .. طب دكتور بشر، بالنسبة لل .. ال .. ال
+
+358
+00:24:06,150 --> 00:24:09,730
+cytrism هذي قبل شوية، ليش بتصير ال cytrism هيك؟ما
+
+359
+00:24:09,730 --> 00:24:14,510
+حكينا الـEdita، هاي كتابت أنا، هاي سببها الـEdita
+
+360
+00:24:14,510 --> 00:24:17,790
+بتعملي الـChanges، طبعًا هذه الـChanges تؤدي
+
+361
+00:24:17,790 --> 00:24:22,170
+لـPlateless Italism، فطبعًا هذه حالة in vitro و
+
+362
+00:24:22,170 --> 00:24:25,170
+لسه in vivo، طبعًا و نتيجة Plateless Italism، أنا
+
+363
+00:24:25,170 --> 00:24:28,010
+مانعزي أعدّل Plateless في الـCBC، بيكون عددها
+
+364
+00:24:28,010 --> 00:24:34,240
+قليل، تمام؟ طيب، الـ… الـPlatelessالـGiant
+
+365
+00:24:34,240 --> 00:24:38,080
+Plateless من اسمها Giant يعني حجم كبير، Giant حجم
+
+366
+00:24:38,080 --> 00:24:43,440
+كبير، فـGiant Plateless، شايفين الصورة اللي بالنص،
+
+367
+00:24:43,440 --> 00:24:46,500
+فيه عندي خلية lymphocytes على اليمين وعلى الشمال،
+
+368
+00:24:46,500 --> 00:24:51,240
+هذا عبارة عن Giant Plateless، شايفينها؟
+
+369
+00:24:51,240 --> 00:24:55,540
+أكبر من الـLymphocytesصحيح، أكبر من الـ lymphocyte
+
+370
+00:24:55,540 --> 00:24:58,280
+هذا ما زلت الـ Plateless طبعًا، يكون أكبر من حجم
+
+371
+00:24:58,280 --> 00:24:59,880
+الخلايا الحامرة كمان طبعًا، حكينا إن الـ
+
+372
+00:24:59,880 --> 00:25:02,280
+lymphocyte قريب حجمها من الخلايا الحامرة الصغيرة
+
+373
+00:25:02,280 --> 00:25:05,960
+طبعًا، هذه بيصير مدى، في حالة increase plateless
+
+374
+00:25:05,960 --> 00:25:09,100
+turnover إنه أنا عندي نشاط في الصفائح، في إنتاج
+
+375
+00:25:09,100 --> 00:25:12,720
+الصفائح، فبالزيت أو في حالة المرض، بيسميها أنا الـ
+
+376
+00:25:12,720 --> 00:25:17,040
+MPD، الـ Myeloprophy Relative Disorders أو الـ
+
+377
+00:25:17,040 --> 00:25:20,460
+MDS، الـ Myelodysplastic Syndrome أو Syndrome
+
+378
+00:25:20,460 --> 00:25:24,680
+طبعًا، في الحالات المرضية هذههتبقوا معجوبين كتير،
+
+379
+00:25:24,680 --> 00:25:29,640
+هتاخدوها بالنظري بشكل تفصيل كامل، تمام؟ لكن
+
+380
+00:25:29,640 --> 00:25:33,360
+اتذكروها، الـ Platelism بيصير في حالة Plateless
+
+381
+00:25:33,360 --> 00:25:36,260
+turnover turn over يعني إيش؟ عندك نشاط زاهد في
+
+382
+00:25:36,260 --> 00:25:39,420
+إنتاج الصفائح الدموية، لأي سبب من الأسباب أو في
+
+383
+00:25:39,420 --> 00:25:45,780
+الـ MPD Myeloprophylactive disorder أو الـ MDS
+
+384
+00:25:45,780 --> 00:25:51,720
+Myelopnephelastic syndrome، تمام؟هي هن دي هن،
+
+385
+00:25:51,720 --> 00:25:54,440
+شايفين الخلايا هذه بيسموها بالنص الذرق جهنم
+
+386
+00:25:54,440 --> 00:25:59,600
+بلادلس، شايفينها؟ طبعا الخلايا كل اللي موجودة عندي
+
+387
+00:25:59,600 --> 00:26:00,640
+هي أخبار عن الخلايا الحمرة
+
+388
+00:26:03,890 --> 00:26:05,990
+الخلايا الحمرى، هنأخد تفاصيل عنها فيما بعد إن شاء
+
+389
+00:26:05,990 --> 00:26:08,290
+الله مش مشكلة، مش هنحكيها لجد أنا فيه اندي Large
+
+390
+00:26:08,290 --> 00:26:12,130
+Platelets، طبعًا Large Platelets حجم أقل من حجم
+
+391
+00:26:12,130 --> 00:26:18,090
+الـ… الـGiant Platelets لكن أكبر من إيش؟ طبعًا من
+
+392
+00:26:18,090 --> 00:26:21,110
+الصبائح دموية نفسها، فلاحظين انديها طبعًا حجم أقل
+
+393
+00:26:21,110 --> 00:26:23,910
+من الخلايا الحمرة كمان، فلاحظين انديها في اندي
+
+394
+00:26:23,910 --> 00:26:31,030
+الصورة، الصورة في اندي تلت خلايا جنبها زرقة تحت،
+
+395
+00:26:31,030 --> 00:26:38,360
+وبالنص في خلية حمرةوالمركز تحت شوية فيناهذه عبارة
+
+396
+00:26:38,360 --> 00:26:43,600
+عن Large Platelets طبعًا هذه أبناء المرض بيصير نفس
+
+397
+00:26:43,600 --> 00:26:48,400
+التلات حالات السابقة اللي تبعت الـ Giant Platelets
+
+398
+00:26:48,400 --> 00:26:54,240
+بيصير اللي هي Turnover بزيد أو الـ MPD أو الـ MDS
+
+399
+00:26:54,240 --> 00:26:58,260
+بالإضافة الحالات التالتة مرضية الميهيجلين أدومالي
+
+400
+00:26:58,260 --> 00:27:01,300
+والـ Gray Platelet Syndrome والـ Bernhardt-Sauer
+
+401
+00:27:01,300 --> 00:27:04,420
+Syndrome هذه حالات مرضية بالزير، بالزير تلات حالات
+
+402
+00:27:04,420 --> 00:27:06,000
+الأولى بالإضافة لتلات حالات التانية
+
+403
+00:27:10,750 --> 00:27:13,910
+فين دي؟ احنا طبعا ممكن نسحب عين الدم، عين الدم
+
+404
+00:27:13,910 --> 00:27:16,310
+طبعتنا حكينا في الـCBS، في الـHematology عبارة عن
+
+405
+00:27:16,310 --> 00:27:20,950
+عينة A.H.Edita، يعني Holy Blood أحيانا أنا بسحب،
+
+406
+00:27:20,950 --> 00:27:23,770
+ماكانتش كمية الـanticoagulant كفاية للدم، بسحب دم
+
+407
+00:27:23,770 --> 00:27:27,930
+بزيادة، فبتؤدي إلى بعض الجلطات، أنا بسميها Micro
+
+408
+00:27:27,930 --> 00:27:31,890
+Eclots، Micro Eclots Micro Eclots طبعا بتظهر معاي،
+
+409
+00:27:31,890 --> 00:27:35,060
+اللي هي عبارة عن الـFibrin strandsوفيها خلايا بيض
+
+410
+00:27:35,060 --> 00:27:38,000
+وفيها خلايا بلاتلس وممكن تكون فيها خلايا حمره
+
+411
+00:27:38,000 --> 00:27:40,420
+أحياناً، طبعا شايفين الزرق هذا اللي في ال
+
+412
+00:27:40,420 --> 00:27:43,740
+background، عبارة عن خيوط الزرق هذه، هذه عبارة عن
+
+413
+00:27:43,740 --> 00:27:47,040
+micro-ecloids، طبعا زي ما حكي هناإذاً micro
+
+414
+00:27:47,040 --> 00:27:49,520
+-closure في حالة إن كان عندى نسبة الـ ratio غلط
+
+415
+00:27:49,520 --> 00:27:53,280
+بالنسبة للـ anticoagulant أو إن أنا نتيجة إن طولت
+
+416
+00:27:53,280 --> 00:27:57,540
+كتير في عملية سحب دور من sections إن أنا بسحب الدم
+
+417
+00:27:57,540 --> 00:28:00,920
+طولت كتير أو ماعرفش أسحب صح هذه تؤدي إلى طبعا
+
+418
+00:28:00,920 --> 00:28:04,480
+التجلطات قبل ما الدم أنه طبعا أحنا حكينا الـ
+
+419
+00:28:04,480 --> 00:28:07,660
+Editor الهدف منها منع التجلط كيف يمنع تجلط الشباب؟
+
+420
+00:28:07,660 --> 00:28:14,470
+إذا تذكروا في المقدمة مين بيحكيلي؟ تجلطفاكيف
+
+421
+00:28:14,470 --> 00:28:19,290
+الإيدة تتملأ تجلط الدم؟
+
+422
+00:28:19,290 --> 00:28:22,610
+أظن
+
+423
+00:28:22,610 --> 00:28:30,850
+فيها مادة الهيبارين؟ لأ، اسمعي، اسمعي،
+
+424
+00:28:30,850 --> 00:28:34,270
+الهيبارين نفس الإيدي دا، أبعد من الدنم وانا تجلط،
+
+425
+00:28:34,270 --> 00:28:37,570
+لكن كيف تملأ التجلط؟ عن طريق الـChelating
+
+426
+00:28:37,570 --> 00:28:44,680
+للكالسيون، صح، صح،الذكرته؟ الـ Chelating
+
+427
+00:28:44,680 --> 00:28:50,000
+للكالسيوم؟ صحيح، الإيه دي ده؟ والكالس بأجزالها
+
+428
+00:28:50,000 --> 00:28:54,000
+والسيطرية نفس الهدف إنه بتعملي Chelating
+
+429
+00:28:54,000 --> 00:28:57,900
+للكالسيوم، ترتبطلي مع الكالسيوم اللي هو مهم جدا في
+
+430
+00:28:57,900 --> 00:29:01,120
+تجلط، في عملية تجلط الدم، وبالتالي لازمنا أتجلط
+
+431
+00:29:01,120 --> 00:29:02,580
+الدم عن طريق Chelating للكالسيوم
+
+432
+00:29:06,710 --> 00:29:09,930
+الهيبرين بيرتبطلي مع الـ Antithrombin فبيمنع
+
+433
+00:29:09,930 --> 00:29:13,310
+الهيبرين يحولي الفيبرونجين لفيبرين فالهيبرين بيقلب
+
+434
+00:29:13,310 --> 00:29:15,870
+القليل شوية عنهم لكن كلهم يقدّوا نفس الغرض اللي هو
+
+435
+00:29:15,870 --> 00:29:20,790
+مانع تجاربه قدامأنا استخدمت الإيدة دا، كان الإيدة
+
+436
+00:29:20,790 --> 00:29:25,150
+نحكي بور قديم، كان الإيدة في مشكلة، أو إن أنا خلال
+
+437
+00:29:25,150 --> 00:29:28,550
+العملية تسحب، طولت، جيت أسحب من المعاد، المعاد ما
+
+438
+00:29:28,550 --> 00:29:31,890
+شاء الله إيده مليانة، مش عارف أتطلع للـVan، طولت و
+
+439
+00:29:31,890 --> 00:29:35,810
+أنا بسحب الـVan، صار عندي تجولوطة خفيفة هادية،
+
+440
+00:29:35,810 --> 00:29:38,990
+بتظهر لي تحت الـMicroscope، بتسليد عليها شكل، إيش
+
+441
+00:29:38,990 --> 00:29:43,290
+اسمها؟ Micro Clots، شايفينها؟ تمام، Micro Clots،
+
+442
+00:29:43,290 --> 00:29:49,480
+تمام، تمام، فين دي Platelets Clumps؟بلايست كلامز
+
+443
+00:29:49,480 --> 00:29:55,720
+اللي أحكيناها جمعات الصباح مع بعض، شايفين في الـ
+
+444
+00:29:55,720 --> 00:30:01,290
+slide عند الساعة تقريبا 11فيه تجميعات تتوقع لنقطة
+
+445
+00:30:01,290 --> 00:30:03,250
+صغيرة هي برعاية الـ Platelets Clumps والـ
+
+446
+00:30:03,250 --> 00:30:06,390
+Platelets Clumps سببها برضه in vitro وليس in vivo
+
+447
+00:30:06,390 --> 00:30:09,630
+مانعش تدخل في الحالات المرضية لكن سببها إن أنا
+
+448
+00:30:09,630 --> 00:30:13,210
+الإيديات اللي استخدمتها قديمة شوية ممكن تؤدي
+
+449
+00:30:13,210 --> 00:30:18,970
+لتجميع الصفائح طبعا أو ممكن تؤدي ل… أو ممكن عملية
+
+450
+00:30:18,970 --> 00:30:22,650
+سحب الدم إن أنا خلال عملية سحب الدم طولت طبعا
+
+451
+00:30:22,650 --> 00:30:25,790
+النقطة المهمة جدا في Platelets Clumps إن أنا لو
+
+452
+00:30:25,790 --> 00:30:29,570
+مشيت عين الـCBC وكان عندي عدد Platelets قليلفي
+
+453
+00:30:29,570 --> 00:30:32,230
+الحالة هاي، مش لازم نعتمد أنه والله عندي plates
+
+454
+00:30:32,230 --> 00:30:34,590
+قليل، أنه فيه مشكلة في الـplates، لأ، لازم نتأكد
+
+455
+00:30:34,590 --> 00:30:37,650
+أنه مشكلة خارجية، مش داخلية، فبعمل الـBlood Film،
+
+456
+00:30:37,650 --> 00:30:40,070
+لما شوفت الـBlood Film وشوفت الـplateless clumps،
+
+457
+00:30:40,070 --> 00:30:42,550
+بعرف أن الـplateless عددها ده مش قليل، عددها الصح
+
+458
+00:30:42,550 --> 00:30:44,250
+أعلى من هيك، تمام؟
+
+459
+00:30:50,650 --> 00:30:55,130
+طبعًا في عندي نحكي الـSmall Platelets الـSmall
+
+460
+00:30:55,130 --> 00:30:58,730
+Platelets بيكون حجم صغير كتير طبعًا جايبين الـ… في
+
+461
+00:30:58,730 --> 00:31:01,770
+المركز في عندي خلية همرة فيها Small Platelets
+
+462
+00:31:01,770 --> 00:31:05,290
+طبعًا هذه حالة مرضية وحيدة اللي هي الـWiscott
+
+463
+00:31:05,290 --> 00:31:07,770
+-Aldrich Syndrome طبعًا هذه الحالة المرضية بيكون
+
+464
+00:31:07,770 --> 00:31:10,570
+فيها Small Platelets أو يكون عدد Platelets قليل
+
+465
+00:31:10,570 --> 00:31:13,710
+شدنا الـLicopenia طبعًا هذه الحالة المرضية بتصيب
+
+466
+00:31:13,710 --> 00:31:18,450
+الـ… طبعًا الـ… الـ… Platelets أكتر شيءأو الـ
+
+467
+00:31:18,450 --> 00:31:20,450
+Degranulation أو الـ Blateless، طبعاً الـ
+
+468
+00:31:20,450 --> 00:31:22,490
+Degranulation أو الـ Blateless بيكون عندي الـ
+
+469
+00:31:22,490 --> 00:31:25,030
+Blateless مش فيها أزرق، إذا حتشوف الـ Blateless
+
+470
+00:31:25,030 --> 00:31:28,630
+فيها زرق كتير، زرقة، بيكون لونها فاهي شوية، زي
+
+471
+00:31:28,630 --> 00:31:34,130
+عنديوانا المركز لتحت شويه بين المركز وبين الساعة
+
+472
+00:31:34,130 --> 00:31:38,830
+نحكي سبعة طبعا فيه دي خلية Platelets هذه طبعا
+
+473
+00:31:38,830 --> 00:31:43,170
+فاهية شويه طبعا تتواجد الـ… نحكي الـDegradation في
+
+474
+00:31:43,170 --> 00:31:46,150
+Platelets في حالات الـGrey Platelet Syndrome وهي
+
+475
+00:31:46,150 --> 00:31:48,150
+نفس الحالة اللي مرض معناها كان بظهر فيها إيه؟ إذا
+
+476
+00:31:48,150 --> 00:31:53,060
+بتذكروا، بظهر فيها الـLarge Plateletsبظهر فيها
+
+477
+00:31:53,060 --> 00:31:55,760
+كمان، بتظهر في حالات discharge of bloodless
+
+478
+00:31:55,760 --> 00:31:59,680
+granules نتيجة طبعاً لوكيميا، نتيجة cardio
+
+479
+00:31:59,680 --> 00:32:02,540
+-pulmonary bypass، نتيجة hairy cells لوكيميا أو
+
+480
+00:32:02,540 --> 00:32:06,160
+discharge of bloodless granules في حالة غور من
+
+481
+00:32:06,160 --> 00:32:10,000
+سيكشن، تقنية كان عندي غلط وإجتماعات الأسهم طبعاً
+
+482
+00:32:10,000 --> 00:32:13,360
+خلصنا هذه الواحدة الموية، هندخل على الخلايا
+
+483
+00:32:13,360 --> 00:32:18,040
+البيضاء طيب، يا شباب، احنا عشان أهدئ نسخة تجربية
+
+484
+00:32:18,600 --> 00:32:23,500
+فأنا بدي أوجب شويه، خلّيه يسجل اللي هدا عشان ما
+
+485
+00:32:23,500 --> 00:32:26,420
+بديش أفقد التسجيل، لإنه بعد كده بيعطيني أنه ضايق
+
+486
+00:32:26,420 --> 00:32:28,520
+الأقل من الـPK تقع، و بعد كده أخرجي عليكم إن شاء
+
+487
+00:32:28,520 --> 00:32:30,060
+الله، إتبعوا؟ فاليكم معايا إتبعوا
+
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0564c4d875707d6a867784133c019b211e0d1c53
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0.srt
@@ -0,0 +1,2815 @@
+1
+00:00:00,000 --> 00:00:05,600
+بس دكتور بعد اسمك بس في نقطة أنا هنا في إنّي علامة
+
+2
+00:00:05,600 --> 00:00:08,720
+تسجيل بضغط عليها بيقول place as the host and give
+
+3
+00:00:08,720 --> 00:00:10,780
+you ده مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+4
+00:00:10,780 --> 00:00:11,880
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+5
+00:00:11,880 --> 00:00:12,560
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+6
+00:00:12,560 --> 00:00:12,960
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+7
+00:00:12,960 --> 00:00:15,760
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+8
+00:00:15,760 --> 00:00:18,260
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+9
+00:00:18,260 --> 00:00:23,880
+مش مش مش مش مش مش مش مش
+
+10
+00:00:23,880 --> 00:00:30,150
+مش مش مشعلم الدم طبعًا عملت، احنا أخذنا في المقاطعة
+
+11
+00:00:30,150 --> 00:00:33,950
+بعض المعامل اللي لها علاقة بعلم الدم وكان منها
+
+12
+00:00:33,950 --> 00:00:39,290
+طبعًا آخر معمل كنتوا بتذكروه أنه هيكون أول معمل في
+
+13
+00:00:39,290 --> 00:00:42,550
+الـ hematology صح ولا لأ؟ فعندنا آخر معمل هو كيف
+
+14
+00:00:42,550 --> 00:00:47,170
+نعمل الشريحة وكيف نصبغها، احنا طبعًا المعمل الحالي
+
+15
+00:00:47,170 --> 00:00:52,030
+هنعيد كيف نعمل شريحة، كيف نصبغها وكيف ثاني نقرأها
+
+16
+00:00:52,030 --> 00:00:55,190
+إن شاء الله، سواء كانت نوعية طبيعية أو غير طبيعية
+
+17
+00:00:55,190 --> 00:01:01,850
+طبعًا بالنسبة لي، نحكي الـ Outline تبع المعمل تبعنا،
+
+18
+00:01:01,850 --> 00:01:10,010
+خليني أنا أشاركم الشاشة، هل جئتم معي؟ في محمد،
+
+19
+00:01:10,010 --> 00:01:12,250
+تشوفون الشاشة حاليًا؟ شايفين الشاشة، تمام؟
+
+20
+00:01:20,380 --> 00:01:27,260
+واضح الشاشة عندكم يا شباب؟ واضح، كبّروها، عادل نقدر
+
+21
+00:01:27,260 --> 00:01:29,920
+نكبرها من عندنا نكبرها من عندكم، نكبرها من عندنا
+
+22
+00:01:29,920 --> 00:01:33,530
+اللي بتحبه، يعني أنا ما عنديش مشكلة، تمام،
+
+23
+00:01:33,530 --> 00:01:35,450
+تمام، طبعًا "العالم الزمزمري" بالنسبة لوعيد
+
+24
+00:01:35,450 --> 00:01:37,590
+المحاضرة إن شاء الله أنا حكيت لكم وحددّت لكم زي ما
+
+25
+00:01:37,590 --> 00:01:40,690
+اتفقنا، هكون الساعة 4 بعد العصر، إمّا السبت أو
+
+26
+00:01:40,690 --> 00:01:45,930
+الاثنين، حسب توزيع الجدول، أنا هوزّع جدول بينهم
+
+27
+00:01:45,930 --> 00:01:50,490
+وبين الشباب الثانيين طبعًا، بالنسبة للمراجع، طبعًا
+
+28
+00:01:50,490 --> 00:01:53,510
+فينا كتاب اسمه "Practical Hematology" لـ "باربرا"،
+
+29
+00:01:53,510 --> 00:01:57,550
+كتاب مهم جدا، إن شاء الله ممكن أنزّل لكم نسخة منه PDF
+
+30
+00:01:58,140 --> 00:02:02,900
+طبعًا فينا Color Atlas of Hematology هذا يحتوي
+
+31
+00:02:02,900 --> 00:02:07,320
+على صور كثيرة طبعًا أهم مرجع أو أكثر مرجع ممكن
+
+32
+00:02:07,320 --> 00:02:10,940
+تستفيد منه اللي هو الـ Internet الصور لأنّ إحنا
+
+33
+00:02:10,940 --> 00:02:14,460
+عملنا معمل عبارة عن خاصة في المعامل الأولى بركزلي
+
+34
+00:02:14,460 --> 00:02:17,300
+على موضوع شكل الخلايا الطبيعية وشكل الخلايا
+
+35
+00:02:17,300 --> 00:02:20,300
+الطبيعية وكيف نميز بين خلية طبيعية وخلية طبيعية في
+
+36
+00:02:20,300 --> 00:02:24,520
+حالة الطبيعية والأمراض، تمام؟ ‏- تمام ‏- طبعًا،
+
+37
+00:02:24,520 --> 00:02:27,270
+مراجعة ممكن نلتقطها طبعًا، احنا هنتذكر عن موضوع
+
+38
+00:02:27,270 --> 00:02:30,130
+المحاضرات للـ "سلايدات" اللي بنزّل لكم إياها على الـ
+
+39
+00:02:30,130 --> 00:02:34,610
+"موديول" إن شاء الله وطبعًا المجلد المراجعة طبعًا
+
+40
+00:02:34,610 --> 00:02:39,590
+طبعًا يعني كمراجع إفراداً أقول لكم في تنمية طبعًا
+
+41
+00:02:39,590 --> 00:02:45,200
+المادة أكثر بالنسبة لكم طبعًا المادة زي ما
+
+42
+00:02:45,200 --> 00:02:48,800
+حكيت لكم هي عبارة عن دراسة لمكونات الدم والخلايا
+
+43
+00:02:48,800 --> 00:02:51,920
+ودراسة الـ Hemoglobin وأنواع الـ Hemoglobin ودراسة
+
+44
+00:02:51,920 --> 00:02:55,840
+الأمراض المختلفة اللي لها علاقة بالدم زي الأنيميا
+
+45
+00:02:55,840 --> 00:03:01,320
+زي مثلًا مرض الثلاسيميا وأمراض أخرى طبعًا الهدف
+
+46
+00:03:01,320 --> 00:03:03,900
+منها زي ما حكينا الدراسة طبعًا أنتم هتاخدوا إن
+
+47
+00:03:03,900 --> 00:03:07,420
+شاء الله جزء نظري مع دكتور أحمد سلمي وهيثيركم
+
+48
+00:03:07,420 --> 00:03:11,640
+بنحكي المادة النظرية بشكل كبير جدا وأنا إن شاء
+
+49
+00:03:11,640 --> 00:03:14,840
+الله هنعطيكم جزء عملي بمثابة مع المادة النظرية
+
+50
+00:03:14,840 --> 00:03:18,420
+فهندرس الخلايا، هندرس تشخيص حالات الأنيميا، هندرس
+
+51
+00:03:18,420 --> 00:03:22,560
+اللوكيميا وهندرس طبعًا اللي هي تحضير الأفلام، الدم
+
+52
+00:03:22,560 --> 00:03:26,930
+وكيف نقدر نحكم عليها فعندنا طبعًا المعمل الأول اللي
+
+53
+00:03:26,930 --> 00:03:29,870
+هو "Slight Vibration and Staining" حكيت لكم إذا
+
+54
+00:03:29,870 --> 00:03:34,030
+بتذكروا إن هذا المعمل هو يعني كان آخر معمل في
+
+55
+00:03:34,030 --> 00:03:38,510
+المقدمة هيكون إن هو دا أول معمل في الـ Hematology
+
+56
+00:03:38,510 --> 00:03:42,550
+المعمل الثاني، هندرس طبعًا الخلايا البيضاء، كيف
+
+57
+00:03:42,550 --> 00:03:46,190
+نعمل differential بين صفائح دموية وإيش الـ… نحكي
+
+58
+00:03:46,190 --> 00:03:52,630
+الـ abnormal morphology فيها هنعمل برضه لندرس المعمل
+
+59
+00:03:52,630 --> 00:03:54,910
+الثالث الـ Abnormal Morphology في الخلايا الحمراء
+
+60
+00:03:54,910 --> 00:03:58,510
+وكيف نشخصها المعمل الرابع هيكون عندنا عن
+
+61
+00:03:58,510 --> 00:04:02,230
+Reticulocyte Count المعمل الخامس عن Sickle Cell
+
+62
+00:04:02,230 --> 00:04:06,350
+Anemia المعمل السادس هيكون عندنا عن الـ Hemoglobin
+
+63
+00:04:06,350 --> 00:04:09,990
+A2 طبعًا احنا كل دراستنا هتكون فترة حاليًا دراسة
+
+64
+00:04:09,990 --> 00:04:14,750
+نظرية لكن إن شاء الله في أول ما يصير فرصة لنا نروح
+
+65
+00:04:14,750 --> 00:04:19,270
+المعامل، نتغذّى كويس في ناحية النظرية، وندخل
+
+66
+00:04:19,270 --> 00:04:23,170
+العمل مباشرة، ونكون عندنا موضوع اللي إجراء تجربة
+
+67
+00:04:23,170 --> 00:04:27,190
+سهل جدا بإذن الله تعالى طبعًا المعمل السابع يكون
+
+68
+00:04:27,190 --> 00:04:32,470
+على الـ Feta-Hemoglobin المعمل الثامن عن الـ
+
+69
+00:04:32,470 --> 00:04:36,950
+Metamoglobin المعمل التاسع عن الـ G6PD Deficiency
+
+70
+00:04:36,950 --> 00:04:41,230
+اللي هو مرض الفول وعندنا المعمل العاشر عن الـ
+
+71
+00:04:41,230 --> 00:04:43,550
+Sacrosis السنة والمعمل الحادي عشر عن اسم الـ
+
+72
+00:04:43,550 --> 00:04:48,190
+Defragility طبعًا لأن المعمل رقم 12 طبعًا يعتبر
+
+73
+00:04:48,190 --> 00:04:52,170
+معمل مهم جدا هنُتكلم عن جهاز الـ CPC اللي بالتأكيد
+
+74
+00:04:52,170 --> 00:04:55,910
+اشتغلتم عليه في فترة المقدمة في المعمل المقدمة
+
+75
+00:04:55,910 --> 00:05:00,550
+أكيد احنا عملنا اه يا معاد، فضل اشتغلنا عليها و
+
+76
+00:05:00,550 --> 00:05:04,130
+أحكيها اه صحيح، اشتغلنا بتوعها ومشيتم عينات
+
+77
+00:05:04,130 --> 00:05:07,810
+عليها بس لنعرف احنا كيف مبدأه، على أي أساس بيشتغل،
+
+78
+00:05:07,810 --> 00:05:10,670
+العينة اللي بتمشيها في الجهاز، كيف بتروح، وأين
+
+79
+00:05:10,670 --> 00:05:14,330
+بتروح، إيش بيصير فيها، طب كيف بيقرأ الجهاز، كل هذا
+
+80
+00:05:14,330 --> 00:05:17,370
+ندرسه في معمل Automated Hematology Cell Counter
+
+81
+00:05:17,870 --> 00:05:21,830
+طبعًا، وآخر المعاملين، طبعًا هما آخر تلات معامل
+
+82
+00:05:21,830 --> 00:05:25,570
+دولة أكبر نظرية بحتة، يعني مش ناحية عملية المعامل
+
+83
+00:05:25,570 --> 00:05:29,350
+الأخرى، هذا ممكن تأخذوه في نظري أكثر، اللي هو "cell
+
+84
+00:05:29,350 --> 00:05:34,150
+maturation" وطبعًا تشخيص اللوكيميا، الآخر، طبعًا
+
+85
+00:05:34,150 --> 00:05:37,310
+المعامل هيكون عن أنواع اللوكيميا وكيف نشخصها،
+
+86
+00:05:37,310 --> 00:05:44,290
+الأخرين طبعًا، هذه بشكل أساسي بالنسبة لـ… نحكي
+
+87
+00:05:44,290 --> 00:05:48,580
+المعامل بتاعتنا هنوصل إن شاء الله، هتكون عندنا فرصة
+
+88
+00:05:48,580 --> 00:05:52,500
+لتنمية مهاراتنا في معمل الدم إن شاء الله، بدي أسأل
+
+89
+00:05:52,500 --> 00:05:59,760
+"سيف" دخل ولا لسه؟ لسه ما دخلش طب خلاص، يعني هذه
+
+90
+00:05:59,760 --> 00:06:04,280
+إن شاء الله مسجلة، هنحاول قدر المستطاع إن شاء الله
+
+91
+00:06:04,280 --> 00:06:08,140
+نوصل إلى "سيف" وزي ما السفّار، ممكن إن شاء الله شرش
+
+92
+00:06:08,140 --> 00:06:14,140
+باقي، هنروح لمعملنا حاليًا الأول طبعًا المعمل هذا أخذنا
+
+93
+00:06:14,140 --> 00:06:17,980
+.. إذا بتذكروا نفس المحاضرة تقريبًا يعني في ال ..
+
+94
+00:06:17,980 --> 00:06:24,920
+شو اسمه؟ المقدمة يعني دقيقة شباب، ده واقف بتزيل، بس
+
+95
+00:06:24,920 --> 00:06:30,000
+عشان التليفون من شغله شوف
+
+96
+00:06:30,000 --> 00:06:33,960
+سيف، إيش صار معه؟
+
+97
+00:06:38,130 --> 00:06:41,650
+وأنا معك. طيب، احنا هنكمل إن شاء الله أنا عملت
+
+98
+00:06:41,650 --> 00:06:46,210
+تكملة التسجيل إن شاء الله أنا هروح طبعًا هذه
+
+99
+00:06:46,210 --> 00:06:49,670
+بالنسبة للـ Outline للمادة هروح هنا زي ما حكينا
+
+100
+00:06:49,670 --> 00:06:53,970
+المعمل الأول المعمل
+
+101
+00:06:53,970 --> 00:06:57,930
+الأول الـ Blood اسمه، شايفين الـ Screen معايا، اه؟
+
+102
+00:06:57,930 --> 00:07:02,290
+طيب، طيب، احنا إن شاء الله، بس خليني أنا أعمل لكم
+
+103
+00:07:02,290 --> 00:07:05,470
+الـ…
+
+104
+00:07:05,470 --> 00:07:10,210
+طيب الـ Blood Smear، طبعًا، هذا المعمل أخذناه في،
+
+105
+00:07:10,210 --> 00:07:13,930
+زي ما حكينا في المقدمة، آخر معمل كان عندنا طبعًا،
+
+106
+00:07:13,930 --> 00:07:17,210
+إذا بتذكروا، قلنا إحنا عندنا تلات أنواع طرق في عمل
+
+107
+00:07:17,210 --> 00:07:21,490
+الـ Blood Smear إذا بتذكروا، عندي الـ Cover Glass
+
+108
+00:07:21,490 --> 00:07:24,770
+Smear واللي بيستخدموا فيها الـ Cover Slide، تمام؟
+
+109
+00:07:24,770 --> 00:07:29,550
+وبيُستخدم على Slide طبعًا، هذه الطريقة شوية تقنية
+
+110
+00:07:29,550 --> 00:07:32,670
+أو الـ practice بتاعها شوية صعبة نوعًا ما، عندي
+
+111
+00:07:32,670 --> 00:07:36,730
+الـ…–الكاميرات الصحيفة عنها آه يا معاد ما كانتش
+
+112
+00:07:36,730 --> 00:07:39,870
+تظبط معنا أساسًا ما كانتش تظبط معايا لأنها بتغلب
+
+113
+00:07:39,870 --> 00:07:43,890
+شوية كانت تظبط معايا بس كانت تظبط معايا كشر محمد
+
+114
+00:07:43,890 --> 00:07:46,190
+اللي هي الوجه … اللي هي الولادتين اللي هي
+
+115
+00:07:46,190 --> 00:07:48,610
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+116
+00:07:48,610 --> 00:07:48,630
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+117
+00:07:48,630 --> 00:07:48,750
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+118
+00:07:48,750 --> 00:07:48,770
+هي الولادتين اللي هي الولادتين اللي هي الولادتين
+
+119
+00:07:48,770 --> 00:07:49,270
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+120
+00:07:49,270 --> 00:07:55,110
+الولادتين اللي هي الولادتين
+
+121
+00:07:55,110 --> 00:07:57,730
+اللي هي ال
+
+122
+00:08:00,670 --> 00:08:03,990
+طبعًا هذه كانت تقصد معكم وإن شاء الله بس نروح على
+
+123
+00:08:03,990 --> 00:08:09,160
+المعامل هنعيد نعملها ونصبغ الـ slide ونقرأها عندي
+
+124
+00:08:09,160 --> 00:08:11,620
+نوع ثالث هو "Spun Smear" زي اللي تذكرت وقلت لكم هذا
+
+125
+00:08:11,620 --> 00:08:16,080
+عبارة عن استخدام جهاز خاص في الـ "سلايدات" وتحط 
+
+126
+00:08:16,080 --> 00:08:19,740
+عليه نقطة دم مع نحكي الـ "كيت" خاص طبعا الـ "كيت"
+
+127
+00:08:19,740 --> 00:08:24,020
+هذا بنحط عليه الـ "سلايد" مع نقطة الدم وهو بفردلي،
+
+128
+00:08:24,020 --> 00:08:27,400
+بعملي الـ "distribution" لفرد الخلايا متجانس 100%
+
+129
+00:08:27,400 --> 00:08:32,220
+طبعا "Spun Smear" كنا نستخدمها إحنا في عملية أنه
+
+130
+00:08:32,220 --> 00:08:35,460
+نقرأ الـ "differential" أو شيء خاصة في حالات في
+
+131
+00:08:35,460 --> 00:08:39,790
+الكيميابتوزع الخلايا بشكل متجانس طبعا في عندي
+
+132
+00:08:39,790 --> 00:08:43,070
+نوعين تانية يستخدموها في حالات خاصة اللي ما في قوة
+
+133
+00:08:43,070 --> 00:08:45,210
+تسمية وهذه في حالة إذا كان عندك بعض الحالات اللي
+
+134
+00:08:45,210 --> 00:08:49,010
+بيكون عندها الخلايا البيضا أقل من ألف كدهش نور
+
+135
+00:08:49,010 --> 00:08:56,170
+مريض لخلايا البيضا سعيد؟ 8000 كدهش؟ 8000 تقريبا من
+
+136
+00:08:56,170 --> 00:09:00,240
+4000 ل 11000 فبالحالة اللي كانت عندك Leukopenia إذا
+
+137
+00:09:00,240 --> 00:09:03,840
+بتذكروا Leukopenia هو نقص في خلايا البيضاء، الحال هي
+
+138
+00:09:03,840 --> 00:09:06,420
+أنا بستخدم الـ Buffy Smear، الـ Coat Smear، طبعا
+
+139
+00:09:06,420 --> 00:09:10,420
+باخد العينة، بـ Centerها و باخد من الـ Buffy Coat،
+
+140
+00:09:10,420 --> 00:09:13,540
+بحطها على الـ Blood Film و نفرضها، ممكن إن شاء الله
+
+141
+00:09:13,540 --> 00:09:17,820
+نعملها إحنا، في نوع اللي بيسموه الـ Thick Blood
+
+142
+00:09:17,820 --> 00:09:20,560
+Smear، هذا بيستخدمها في حالات، إن أنا دول بيشوف
+
+143
+00:09:20,560 --> 00:09:24,000
+حالات الـ Parasite، خاصة الملاريا طبعًا الـ Malaria
+
+144
+00:09:24,000 --> 00:09:27,600
+بنعرف أنه موجود داخل الخلايا الحمراء لو بنتخب الـ
+
+145
+00:09:27,600 --> 00:09:31,280
+Buffy Smear فبالتالي أنا مش هقدر أني أنا أشوف
+
+146
+00:09:31,280 --> 00:09:34,420
+الباراسايت لأنه هكون عدده قليل وصعب جدًا أني أميزها
+
+147
+00:09:34,420 --> 00:09:39,160
+لكن بالحالة بستخدم الـ Thick Smear بتقدر أني أتميز
+
+148
+00:09:39,160 --> 00:09:43,420
+الخلايا وتقدر أنه لو كان مثلًا نحكي عدد الباراسايت
+
+149
+00:09:43,420 --> 00:09:48,620
+قليلة بقدر أني أشخص الحالة الحقيقية، تمام؟ طبعًا
+
+150
+00:09:48,620 --> 00:09:51,440
+العينات المستخدمة إحنا في الـ Wedge Smear اللي هي
+
+151
+00:09:51,440 --> 00:09:54,920
+عينة الـ EDTA طبعًا هي العين الـ CBC نفسها لازم
+
+152
+00:09:54,920 --> 00:09:58,920
+تكون Fresh مستخدم خلال ساعتين إلى تلت ساعات طبعًا
+
+153
+00:09:58,920 --> 00:10:03,200
+– زي هذا يا دكتور – هذا لأ، هذا يعتبر Chemistry 
+
+154
+00:10:03,200 --> 00:10:05,960
+Tube هذا، مش EDTA أنا مش شايف، اللي هو اللي هو
+
+155
+00:10:05,960 --> 00:10:10,880
+أحمر الغطاية، محمد؟ – لأ، الفكرة مكتوبة على EDTA
+
+156
+00:10:10,880 --> 00:10:12,860
+– اللي هو EDTA صح، اللي هو غطاية غلط، اللي هو
+
+157
+00:10:12,860 --> 00:10:15,600
+غطاية غلط، لازم الغطاية يكون Purple – لأ، لأ، صح
+
+158
+00:10:15,600 --> 00:10:20,340
+كلامك، صح الغطايب محطوطة غلط، لأنه غالبًا يكون لونه
+
+159
+00:10:20,340 --> 00:10:23,500
+Purple أو أزرق، وغالبًا Purple، مكتوب على إيده ده
+
+160
+00:10:23,500 --> 00:10:28,880
+صحيح. طبعًا، لأ، فيه إن طبعًا، ليش أنا، ليش أنا
+
+161
+00:10:28,880 --> 00:10:33,940
+أول شي ب .. طبعًا بستخدم فرش اسمه blood، عشان
+
+162
+00:10:33,940 --> 00:10:37,340
+ما يصيحش عندي تغيرات في الخلايا الحمراء، يعني نقطة
+
+163
+00:10:37,340 --> 00:10:40,620
+مهمة. وهي وضرف تبعاته. بيصيح تغيرات في خلايا الدم
+
+164
+00:10:40,620 --> 00:10:43,260
+الحمراء، وبيصير زي عملية .. أنه بيصير زي
+
+165
+00:10:43,260 --> 00:10:46,950
+Crenated، بيصير زي أكيد إنها من شرية، وهذه، في
+
+166
+00:10:46,950 --> 00:10:50,010
+عندي بعض الحالات بيكون في أصلًا هي عبارة عن سموها
+
+167
+00:10:50,010 --> 00:10:52,830
+"Crenated" أو "Speculated" طبعًا اللي هي "Spar"
+
+168
+00:10:52,830 --> 00:10:55,830
+وطبعًا هذه الخلايا في حالات مرضية لكن هنا بيكون مش
+
+169
+00:10:55,830 --> 00:11:00,610
+مرضية سببها اللي هي درجة الحرارة أو الـ "old
+
+170
+00:11:00,610 --> 00:11:05,090
+Specimen"، تمام؟ طبعًا، متى بيصير هذه الحالات الـ
+
+171
+00:11:05,090 --> 00:11:07,150
+"Crenated"؟ تمحك هنا، في حالة إنه عندي
+
+172
+00:11:07,150 --> 00:11:11,510
+الـ Anticoagulant كميته أكثر من العينة، كيف يعني؟
+
+173
+00:11:11,780 --> 00:11:15,040
+إحنا بنعرف إحنا عندي مثلا الـ Tube EDTA
+
+174
+00:11:15,040 --> 00:11:18,480
+موجود معاك يا محمد، إيش مكتوب عليه كمية الدم؟
+
+175
+00:11:18,480 --> 00:11:22,540
+مكتوب إنك تحط مل 3 مل 3 مل، هتجيب لو حطيت
+
+176
+00:11:22,540 --> 00:11:25,880
+أقل من 3 مل، حطيت 1 مل، تسيطر عملية الـ
+
+177
+00:11:25,880 --> 00:11:28,140
+Ratio بين الـ Anticoagulant اللي هو الـ EDTA اللي
+
+178
+00:11:28,140 --> 00:11:31,960
+موجودة في الـ Tube، و الدم تختلف، فهذه تؤدي لغيرات
+
+179
+00:11:31,960 --> 00:11:36,700
+شكلية في الخلايا نفسها، تمام؟ في نقطة تانية تؤدي
+
+180
+00:11:36,700 --> 00:11:39,880
+لكرينية الـ…………………………………………………………
+
+181
+00:11:41,810 --> 00:11:45,830
+بينفع شجر المنتلات، هشوف عليه، يعني هو مش زي مثلًا
+
+182
+00:11:45,830 --> 00:11:49,410
+إذا معمل مثلًا إن شاء الله لنا نذهب، هنكون عملية
+
+183
+00:11:49,410 --> 00:11:53,090
+ال Ratio High مهم جدًا كتير بالنسبة للدم والـ
+
+184
+00:11:53,090 --> 00:11:56,570
+Atomic Aggregate بالنسبة للمعمل الـ Hematology،
+
+185
+00:11:56,570 --> 00:12:00,530
+هي مهمة، مهمة، يعني لكن مش، يعني بنقدر نتجاهلها،
+
+186
+00:12:00,530 --> 00:12:03,650
+لكن مش أنه نتجاهلها بشكل كبير، يعني كيف مثلًا، أنا
+
+187
+00:12:03,650 --> 00:12:07,850
+لو عند المطلوب إن أحط 3، وروح وحطيت 2.5،
+
+188
+00:12:07,850 --> 00:12:12,610
+بمشيها عادي عادي، لكن ما أحطش 1، ما أحطش 0.5 لأنه
+
+189
+00:12:12,610 --> 00:12:15,170
+مثلًا إن أحط 0.5، لو فرض أن أنا فيها 2 ml
+
+190
+00:12:15,170 --> 00:12:18,610
+وحطيت 0.5 ال Ratio بينهم هيختلف، هتؤدي لاختلاف حتى
+
+191
+00:12:18,610 --> 00:12:21,190
+في توزيع الخلايا وبالتالي، هتؤدي لاختلاف في حجم
+
+192
+00:12:21,190 --> 00:12:25,350
+الخلايا بالنسبة للـ Antibiotic لو تؤدي لاختلاف في
+
+193
+00:12:25,350 --> 00:12:28,250
+عملية القراءة في جهة الـ CBC ممكن فهذه النقطة مهم
+
+194
+00:12:28,250 --> 00:12:33,320
+جدا بالنسبة لل Ratio عندي السبب الثاني اللي يؤدي
+
+195
+00:12:33,320 --> 00:12:36,100
+لـ Crenated يعني أحد الأسباب اللي يؤدي لـ Crenated
+
+196
+00:12:36,100 --> 00:12:40,220
+طبعًا اللي بنسميها إحنا الحالات، مش مرضية هاي،
+
+197
+00:12:40,220 --> 00:12:43,080
+اللي هي Old Specimens في عندي بذلة بحكي عنها برضه
+
+198
+00:12:43,080 --> 00:12:45,780
+الحرارة، في حالة الحرارة تؤدي لـ Crenated دور
+
+199
+00:12:45,780 --> 00:12:48,560
+الـ Crenated، الثاني تلت أسباب تؤدي لدور
+
+200
+00:12:48,560 --> 00:12:55,720
+الـ Crenated طبعًا للحالات الـ Normal دكتور، آه محمد
+
+201
+00:12:55,720 --> 00:12:59,020
+– بعدين أتفضل على الـ slide اللي بتشرح عليها – تمام
+
+202
+00:13:02,780 --> 00:13:07,480
+الثلاث حالات اللي تؤدي للحالات الغير مرضية اللي هي
+
+203
+00:13:07,480 --> 00:13:14,360
+الحالات ال Normal هي بالضبط ال old blood
+
+204
+00:13:14,360 --> 00:13:20,280
+و ال Ratio تبقى هذا ال Ratio amount of blood blood
+
+205
+00:13:20,280 --> 00:13:24,380
+blood blood blood blood blood blood blood blood
+
+206
+00:13:24,380 --> 00:13:24,620
+blood blood blood blood blood blood blood blood
+
+207
+00:13:24,620 --> 00:13:26,860
+blood blood blood blood blood blood blood blood
+
+208
+00:13:26,860 --> 00:13:26,920
+blood blood blood blood blood blood blood blood
+
+209
+00:13:26,920 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+210
+00:13:27,320 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+211
+00:13:27,340 --> 00:13:29,510
+blood blood blood الـ Crenated بدأت بالحالة أن تكون
+
+212
+00:13:29,510 --> 00:13:33,550
+ملم فيها لأن هذه الحالة سببها مش مرضي طبعًا هذه
+
+213
+00:13:33,550 --> 00:13:36,410
+كيف تعرفها؟ هذه تعرفها إنه مثلًا أنا ما لاجي عامل
+
+214
+00:13:36,410 --> 00:13:40,090
+عصلاية هلاقي إنه عملية الـ Crenated مش مسك لكل RBC
+
+215
+00:13:40,090 --> 00:13:43,870
+هتلاقي بعض المناطق فيها Crenated وبعض المناطق لأ،
+
+216
+00:13:43,870 --> 00:13:46,930
+تمام؟ هتلاقي بعض الخلايا آه وبعض الخلايا لأ، في
+
+217
+00:13:46,930 --> 00:13:48,730
+الحياة المرضية لأ، بيكون معظم الخلايا فيها
+
+218
+00:13:48,730 --> 00:13:52,310
+Crenated في الحياة المرضية ليست بره، تمام؟ هل جيت
+
+219
+00:13:52,310 --> 00:13:56,390
+الحالات اللي نحكي الـ "normal" ويكون أصلًا سببها
+
+220
+00:13:56,390 --> 00:14:00,610
+نحكي خارجي، يعني مش مرضي، اللي هي زي ما حكينا ليه
+
+221
+00:14:00,610 --> 00:14:04,010
+الـ Ratio Anticoagulant للـ Old Displacement و الـ Warm
+
+222
+00:14:04,010 --> 00:14:11,970
+Environment، تمام؟ محمد
+
+223
+00:14:11,970 --> 00:14:17,790
+تمام؟ ما سمعت ناس آه
+
+224
+00:14:17,790 --> 00:14:26,180
+سامع دعوتي نرجع للـ slide، فيه عندك سؤال بهي؟
+
+225
+00:14:26,180 --> 00:14:33,260
+بس ما تغيرت الـ slide عندي، أنا
+
+226
+00:14:33,260 --> 00:14:41,260
+رجعت لها، ما تغيرش عندي، إيه الـ slide اللي قمت
+
+227
+00:14:41,260 --> 00:14:42,740
+بإيديك؟
+
+228
+00:14:49,920 --> 00:14:53,500
+محمد slide high؟ لا بتغير الشاشة عندك قاعدة كله
+
+229
+00:14:53,500 --> 00:14:59,440
+ثابت عند الكل طب ليش؟ هو عندك كمان ثابت عند ال
+
+230
+00:14:59,440 --> 00:15:06,080
+Outline كله موجود عند ال Outline عندك؟ آه كله كله
+
+231
+00:15:06,080 --> 00:15:09,060
+عند ال Outline الشاشة اللي واضحة عند ال Outline
+
+232
+00:15:09,060 --> 00:15:14,980
+أنا ومحمد نفس القصة طب هيك؟ أيوة هيك اتغيرت صحيح؟
+
+233
+00:15:14,980 --> 00:15:18,400
+هيك اتغيرت ناحية ال Practical Hematology تجيبني
+
+234
+00:15:18,400 --> 00:15:22,010
+على slide B now؟ أنواع الـ، شو اسمها؟ الاسمية،
+
+235
+00:15:22,010 --> 00:15:25,610
+شفتوها؟ آه تمام، تمام هاي الـ slide دلك يا محمد،
+
+236
+00:15:25,610 --> 00:15:29,890
+هاي؟ تمام، هاي، هاي، هاي قدام إيش سؤالك فيها يا
+
+237
+00:15:29,890 --> 00:15:33,110
+محمد؟
+
+238
+00:15:33,110 --> 00:15:41,310
+يا محمد؟
+
+239
+00:15:41,310 --> 00:15:44,950
+دكتورة
+
+240
+00:15:44,950 --> 00:15:50,370
+آه، معذرة عشان بقيتها في الـ Wedge بالـ Blood Smear
+
+241
+00:15:50,370 --> 00:15:56,350
+مكتوب "Collected to Mark of Tube"، إيش يعني؟ ليه؟
+
+242
+00:15:56,350 --> 00:16:00,390
+حكيناها الـ Ratio، يعني أنت بدك تسحب اللي عندك
+
+243
+00:16:00,390 --> 00:16:04,350
+علامة، في عندك علامة، آه، بدك تسحب اللي عندك علامة
+
+244
+00:16:04,350 --> 00:16:07,470
+أو تحط نفس الكمية ليه 3 ml زي ما موجود عند محمد 3
+
+245
+00:16:07,470 --> 00:16:12,510
+ml، في عندك الـ Department، أي Mark، يكون 3 ml أو
+
+246
+00:16:12,510 --> 00:16:17,350
+في Mark، يكون علامة، تمام، تمام، فهمت، فهمت طيب،
+
+247
+00:16:17,350 --> 00:16:23,390
+السمير إحنا؟ دخل سيف ولا لسه؟ آه دخل، هاي صوت
+
+248
+00:16:23,390 --> 00:16:29,030
+موجود إيه وإيه يا عم، معاكم هأفتح كاميرا غنيه،
+
+249
+00:16:29,030 --> 00:16:33,730
+بياخد أهلا، طيب، إحنا .. نسمي الشباب عشان وقت
+
+250
+00:16:33,730 --> 00:16:39,010
+وعمل وقت طبعا الـ Procedures أخذناها قبل ذلك، زي ما 
+
+251
+00:16:39,010 --> 00:16:43,540
+حكينا، ملحوظ على الـ «سلايد» إذا تذكرونه، نجيب
+
+252
+00:16:43,540 --> 00:16:48,060
+سلايد ثاني بزاوية ثلاثين إلى أربعين درجة، وبعدين
+
+253
+00:16:48,060 --> 00:16:54,100
+نفردها بطريقة طبعا سلسة، مش جيركي مانار، تمام؟
+
+254
+00:16:54,100 --> 00:16:59,890
+نخلي الـ«بلاد»، الفيلم، ينشف وبعد ذلك طبعًا نسبقها
+
+255
+00:16:59,890 --> 00:17:04,570
+طبعًا في نقاط مهمة جدًا اللي هي عملية الزاوية كل ما
+
+256
+00:17:04,570 --> 00:17:09,530
+زادت الزاوية طبعًا كل ما صار طبعًا الطول أقل ويصير 
+
+257
+00:17:09,530 --> 00:17:13,530
+السمك الـ «thick» أكثر يعني أنا هاي slide أنا
+
+258
+00:17:13,530 --> 00:17:15,610
+ما عنديش اللي كان لو عندي اللي كان الرجل اللي كان
+
+259
+00:17:15,610 --> 00:17:20,370
+فهي عندي سلايدين شايفين بالفيديو تمام؟ عطيت، أنا
+
+260
+00:17:20,370 --> 00:17:23,850
+هذه الزاوية كل ما قلّت الزاوية كان عندي الطول أكثر
+
+261
+00:17:23,850 --> 00:17:29,430
+والسمك ثم أكثر، لو أحط زاوية أكثر بيصير thick
+
+262
+00:17:29,430 --> 00:17:33,210
+فأنا لو بدي إياها thicker أكثر، بدي إيه عشان أعمل؟
+
+263
+00:17:33,210 --> 00:17:36,810
+أزيل الزاوية، تمام؟ التحكم بالزاوية هو اللي
+
+264
+00:17:36,810 --> 00:17:40,470
+بيحكم في نوع السمير و الـquality للسمير  دبعتنا،
+
+265
+00:17:40,470 --> 00:17:45,190
+طبعا هذه الصورة توضيحية بنحط drop، وبعدين بنجيب الـ
+
+266
+00:17:45,190 --> 00:17:48,690
+«سلايد» الثاني بزاوية 30 إلى 40 ونفردها بطريقة
+
+267
+00:17:48,690 --> 00:17:53,810
+سلسة هاي الـSmear، طبعاً، شايفينها، بنخليها تنشف
+
+268
+00:17:53,810 --> 00:17:57,810
+وبعد ذلك بنعملها Fixation بواسطة الـMethanol
+
+269
+00:17:57,810 --> 00:18:04,170
+وبنعملها Staining طبعاً الـArtifacts، أيش يعني
+
+270
+00:18:04,170 --> 00:18:08,460
+Artifacts يا معاذ؟ الآثار تبعتها الـ Artifacts ليه
+
+271
+00:18:08,460 --> 00:18:13,800
+أي شغلة تؤدي لطبعًا ظهور، يعني نحكي الـ «زمير» مش
+
+272
+00:18:13,800 --> 00:18:16,820
+بالـ Quality صح، إن أنا برفضها. لا، يعني مضاعفات،
+
+273
+00:18:16,820 --> 00:18:20,240
+ما بنتحكي عنها. مش، مش، يعني شغلات شوائب، نحكي. هي
+
+274
+00:18:20,240 --> 00:18:23,460
+Artifacts يعني شوائب، تمام؟ أوكي، أوكي. أول شيء،
+
+275
+00:18:23,460 --> 00:18:26,980
+العملية فرد تكون غلط، هتؤدي لظهور Artifacts. أنت
+
+276
+00:18:26,980 --> 00:18:29,500
+جيت فردت، ما عرفت تبعتش زاوية 30 إلى 40، وما عرفت
+
+277
+00:18:29,500 --> 00:18:34,240
+تعمل زاوية مثلًا 50، هتؤدي لظهور «زمير» قصيرة و
+
+278
+00:18:34,240 --> 00:18:38,490
+«very thick»، مش هيكون كويس لقراءة الفيلم. أنت ممكن
+
+279
+00:18:38,490 --> 00:18:42,770
+تكون عندك عملية الـHumidity أدت إلى Slow-drying
+
+280
+00:18:42,770 --> 00:18:47,490
+تؤدي لظهور الـArtifacts عملت الـFixation طولت فيها،
+
+281
+00:18:47,490 --> 00:18:49,630
+روح سفررت بالاسمير وخلت ثانية وعملت الـFixation
+
+282
+00:18:49,630 --> 00:18:53,130
+برضه غلط أصول أول ما تنشف الـSlide عملها
+
+283
+00:18:53,130 --> 00:18:58,330
+الـFixation وجود الماء في الـMethanol إذا كان موجود
+
+284
+00:18:58,330 --> 00:19:02,590
+الماء أكثر من 3% في الحالة هذه لازم أنا أيش برضه أن
+
+285
+00:19:02,590 --> 00:19:05,630
+أتجنب وجود الماء في الماء لأن الماء تعمل Artifacts
+
+286
+00:19:07,460 --> 00:19:10,740
+طبعًا، عندي بعض الحالات المرضية تؤدي لظهور الـ
+
+287
+00:19:10,740 --> 00:19:14,020
+Artifacts زي مثلًا، إذا كان عندك عدد الخلايا الـ
+
+288
+00:19:14,020 --> 00:19:17,080
+lymphocytes عالية أحنا بنعرف إن الـ lymphocytes
+
+289
+00:19:17,080 --> 00:19:23,930
+عبارة عن خلايا بنواة واحدة طبعًا هذه الـ
+
+290
+00:19:23,930 --> 00:19:29,570
+lymphocytes دلوقتي نحكي هشة، fragile مجرد إنك أنت
+
+291
+00:19:29,570 --> 00:19:32,970
+لو كان العدد كبير ومجرد أنك عملت خرد لها ممكن
+
+292
+00:19:32,970 --> 00:19:35,550
+تتكسر إذا كانت بعداد كبيرة أو في بعض الحالات
+
+293
+00:19:35,550 --> 00:19:39,870
+المرضية زي مثلًا اللوكيميا اللي هي CLL-Chronic
+
+294
+00:19:39,870 --> 00:19:42,970
+Lymphocytic Leukemia أو الـAcute Leukemia فهذه
+
+295
+00:19:42,970 --> 00:19:48,470
+تؤدي لظهور Artifacts، فما تتكسر عفوا ما تتكسر في
+
+296
+00:19:48,470 --> 00:19:51,890
+الحالة هذه مش هتظهر عندك خلايا، هتظهر عندك بقايا
+
+297
+00:19:51,890 --> 00:19:57,320
+خلايا اللي هي ممكن تظهر النواة، ممكن تظهر مثلًا
+
+298
+00:19:57,320 --> 00:20:01,500
+الـ«سيتوبلازم» الحال حسب، تمام؟ عندك تغييرات
+
+299
+00:20:01,500 --> 00:20:04,500
+برضه تصير الـGenerative Changes اللي هي بتصير في
+
+300
+00:20:04,500 --> 00:20:08,340
+عملية الـStorage، كيف يعني؟ أنا أخذت عينة الدم،
+
+301
+00:20:08,340 --> 00:20:12,820
+وراح محمد بدل ما يروح يعمل Blood Film منها، راح
+
+302
+00:20:12,820 --> 00:20:16,260
+يشغلها، خلّاها في التلاجة أو خلّاها مثلًا في
+
+303
+00:20:16,260 --> 00:20:20,400
+الغرفة لثاني يوم، ثاني يوم هتلاقي عندك تغييرات على
+
+304
+00:20:20,400 --> 00:20:31,600
+الخلايا، النواة، تمام؟ تمام طبعًا
+
+305
+00:20:33,010 --> 00:20:37,570
+خصائص الـ… الـ «Blood Film» الكويس هذه الخصائص
+
+306
+00:20:37,570 --> 00:20:41,730
+«Blood Film» كويس اللي هي طبعًا خدناها برضه أهم
+
+307
+00:20:41,730 --> 00:20:45,410
+خاصية أنه زي ما حكينا يكون «thick» at one end
+
+308
+00:20:45,410 --> 00:20:48,270
+«thin» at the other end smoothly، يعني كيف يعني؟ أن
+
+309
+00:20:48,270 --> 00:20:51,130
+الـ«Blood Film» بالبداية يكون «thick» وفي النهاية
+
+310
+00:20:51,130 --> 00:20:53,910
+يكون «thin» واحنا بنقرأ، إذا بتذكروا، بنقرأ من
+
+311
+00:20:53,910 --> 00:21:00,110
+المنطقة اللي في الوسط، صحيح سعيد؟ صحيح، صحيح، ده
+
+312
+00:21:00,110 --> 00:21:05,990
+معايا، تمام الشغل الثاني تكون عندك تحتوي يعني Slide
+
+313
+00:21:05,990 --> 00:21:09,790
+ثلثينها تقريبًا موجود للفيلم نفسه الشغل الثالث
+
+314
+00:21:09,790 --> 00:21:14,890
+أنه ما تلمسش الحافة وآخر شيء تكون أن الـ «حواط»
+
+315
+00:21:14,890 --> 00:21:19,210
+ربعها ما فيش فيها شراشين نحكي أنه «margin free»
+
+316
+00:21:19,210 --> 00:21:22,170
+ولا يكون مسك الحواط على اليمين وعلى الشمال يعني يكون
+
+317
+00:21:22,170 --> 00:21:27,630
+بعيد عن الحواط هذه خصائص فيلم اللي كويس هيها
+
+318
+00:21:27,630 --> 00:21:32,250
+«thick» من اثنين إلى اثنين ونص سم، طبعًا إحنا
+
+319
+00:21:32,250 --> 00:21:36,310
+بالمنطقة اللي بقرا فيها اللي هي الـ Advocate Area،
+
+320
+00:21:36,310 --> 00:21:38,210
+الـ Thick Area ما بقراش منها ولا Skin Area بقرا
+
+321
+00:21:38,210 --> 00:21:43,190
+منها، بقرا من منطقة الـ Advocate Area هذه، هذه بعض
+
+322
+00:21:43,190 --> 00:21:47,850
+الـ «الذنوب»، بالنص، مش بالنص، مش شرط بالنص، حسب
+
+323
+00:21:47,850 --> 00:21:51,170
+توتيم البلاد فيلم، حسب الفيلم، بلد فيلم للسوق، أجيتها
+
+324
+00:21:51,170 --> 00:21:55,940
+أنا عندي بعض أنواع الـ Blood Film اللي هي تقريبًا
+
+325
+00:21:55,940 --> 00:21:59,420
+تعتبرش كويسة أنا ممكن أعتبرها كده نوعًا ما كويس،
+
+326
+00:21:59,420 --> 00:22:03,200
+بس مش كتير يعني، تمام؟ فأنتوا شايفينها، شايفها سيد
+
+327
+00:22:03,200 --> 00:22:09,160
+أنتِ؟ آه، آه بإي اي و بي و سي و دي ممتاز اي و بي و
+
+328
+00:22:09,160 --> 00:22:12,480
+سي سيئة جدا، دي نوعًا ما كويسة لكن ما أعتبرهاش كويسة
+
+329
+00:22:12,480 --> 00:22:16,460
+لأنه مش بي .. أنا بالنسبة لي بعتبرها مش كتير، لأن
+
+330
+00:22:16,460 --> 00:22:20,720
+مش بيعطيني finger shape مش ما .. مش طولتين ال
+
+331
+00:22:20,720 --> 00:22:24,160
+سلايد تقريبًا، تمام؟ هو اللي .. اللي إحنا تبقى نوعًا
+
+332
+00:22:24,160 --> 00:22:31,100
+ما أحسن من الواقعين، ما تطلعوا أنتِ إيه؟ كيف؟
+
+333
+00:22:31,100 --> 00:22:35,530
+دي أفضل دي أفضل من القراءة لكن بعتبرها شوية كويسة،
+
+334
+00:22:35,530 --> 00:22:39,230
+بالنسبة لي أنا لو بقيمها بقيمها تقريبًا ثلاثة أو
+
+335
+00:22:39,230 --> 00:22:43,750
+أربعة من خمس بس، فهمنا كيف؟ بس أحسن من الـA و أحسن
+
+336
+00:22:43,750 --> 00:22:44,650
+من الـB و أحسن من الـC
+
+337
+00:22:48,030 --> 00:22:50,750
+بالظبط، هذه أنواع سيئة جدًا كلها من البلاد في
+
+338
+00:22:50,750 --> 00:22:53,870
+الأمور واحدة فيها كويسة، شايفين؟ طبعًا هنا شايفين
+
+339
+00:22:53,870 --> 00:22:56,930
+الـMargins كيف شايفينها، هذه عندي الهواف شرشير بـ12
+
+340
+00:22:56,930 --> 00:23:00,210
+قراءة، هذه جاية متقطعة، فبالتالي ما فيش فيها، نحكي
+
+341
+00:23:00,210 --> 00:23:03,130
+زي «genus» في عملية الـ«thickness»، هذه قصيرة، هذه
+
+342
+00:23:03,130 --> 00:23:09,110
+رفيعة، هذه فيها، نحكي زي الفقاعات تمام، فيها
+
+343
+00:23:09,110 --> 00:23:13,170
+«holes»، وهذه جاية متجنسية، وهذه طبعًا فيها رقم
+
+344
+00:23:13,170 --> 00:23:18,550
+«C» إيش مالها؟ رقم إيش «C»؟ يعني مش معتادة طولها،
+
+345
+00:23:18,550 --> 00:23:20,950
+مش ما زي .. مش جاية أنها .. طبعًا هنا thick، هنا مش زي
+
+346
+00:23:20,950 --> 00:23:24,290
+ثاني كتير، تمام؟ ممكن أنت تقرأها، بدك تقرأ منطقة هاي
+
+347
+00:23:24,290 --> 00:23:26,690
+مش هتعرف تقرأها كويس، بدك منطقة تقرأ بيها كويس،
+
+348
+00:23:26,690 --> 00:23:30,550
+يعني نهاية الرقم C ممكن أنه حط الزاوية عالية شوية،
+
+349
+00:23:30,550 --> 00:23:33,530
+لو نزل الزاوية شوية صغيرة وفرد، الـ smear تضيع
+
+350
+00:23:33,530 --> 00:23:39,550
+أكثر طبعًا طب
+
+351
+00:23:39,550 --> 00:23:45,160
+دكتور بعد إذنك، بس ارجع الصورة اللي قبل شوية أقرأ
+
+352
+00:23:45,160 --> 00:23:49,800
+من الصورة E يعني أحسن هدول كلهم الـ E فيها يا سيد
+
+353
+00:23:49,800 --> 00:23:54,100
+فيها كتير يعني جاية مش خلّي .. يعني شوف المسافة بين
+
+354
+00:23:54,100 --> 00:23:57,140
+الحافة و بينها الدم تقريبًا نفس المسافة دي الدم نفسه
+
+355
+00:23:57,140 --> 00:24:03,220
+هذه تقدر عالم توزيع صح للخلايا آه تمام تمام طيب
+
+356
+00:24:06,410 --> 00:24:09,930
+عندي بعض الحالات اللي ممكن تظهر كأنها حالات مرضية
+
+357
+00:24:09,930 --> 00:24:12,590
+لكنها فعليًا مش حالات مرضية هي حالات نتيجة
+
+358
+00:24:12,590 --> 00:24:14,910
+الـBlood Film نفسها يعني ممكن تظهر في الـThin Area
+
+359
+00:24:14,910 --> 00:24:17,690
+الخلايا تظهر معايا إشي بيسميه الـTargetocytes
+
+360
+00:24:17,690 --> 00:24:21,290
+الـTargetocytes هي عبارة عن خلية حمراء، عبارة عن خلية
+
+361
+00:24:21,290 --> 00:24:26,650
+حمراء طبعًا تظهر فيها، نحكي، مش عارف بتظهر عندنا
+
+362
+00:24:26,650 --> 00:24:29,710
+فراغ اللي هم مجلوبين تقريبًا طوله فراغ وطولها فيه
+
+363
+00:24:29,710 --> 00:24:33,370
+كإنهم مجلوبين، خلايا الحمرة فهي الخلية الحمراء،
+
+364
+00:24:33,370 --> 00:24:34,290
+خليني إذا بقدر أنا
+
+365
+00:24:38,550 --> 00:24:41,790
+المهم الخلايا تظهر فيها حالة بيسموها Spherocytosis
+
+366
+00:24:41,790 --> 00:24:44,950
+طبعا هذه بيكون خلايا حمراء فلاتها ما فيش فيها area
+
+367
+00:24:44,950 --> 00:24:47,410
+اللي يجمعها جلبيها، هذه طبعا في thin area فانا
+
+368
+00:24:47,410 --> 00:24:50,850
+ما بقراش منها، ومنطقة ال thick area تظهر في خلايا
+
+369
+00:24:50,850 --> 00:24:52,890
+كأنها متجمعة ببعض زي الـRouleau Formation،
+
+370
+00:24:52,890 --> 00:24:55,450
+الـRouleau Formation ممكن متخسرة مع بعض لبعض
+
+371
+00:25:04,300 --> 00:25:07,820
+طلع علي، هلجيت الخلايا الحمراء، هي الخلية الحمراء مش
+
+372
+00:25:07,820 --> 00:25:11,100
+عارف ارسمها كتير أنا لأن طبعا هي خلية حمراء هلجيت
+
+373
+00:25:11,100 --> 00:25:16,300
+بنص يكون عندي هجر الإنسان بتلتم مجلوبين، صح؟ فاضية،
+
+374
+00:25:16,300 --> 00:25:24,200
+نصها أبيض، شايفينها؟ خليني
+
+375
+00:25:24,200 --> 00:25:29,400
+أشوف إذا بقدر أجيب تمام، طلع علي، هي خلية حمراء، 
+
+376
+00:25:29,400 --> 00:25:34,120
+نيّح؟ هلّجيت الخلية الحمراء هاي؟ في الـHemoglobin
+
+377
+00:25:34,120 --> 00:25:44,360
+تلتينها تقريبًا شايفين؟
+
+378
+00:25:44,360 --> 00:25:46,660
+شايف يا محمد؟ شايف يا سيد؟ تلتين الـHemoglobin
+
+379
+00:25:46,660 --> 00:25:50,240
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+380
+00:25:50,240 --> 00:25:50,880
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+381
+00:25:50,880 --> 00:25:50,980
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+382
+00:25:50,980 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+383
+00:25:52,640 --> 00:25:56,540
+تمام، تمام،
+
+384
+00:25:56,540 --> 00:25:56,860
+تمام
+
+385
+00:26:03,470 --> 00:26:07,850
+يكون الخلية حمراء، جنبها خلية حمراء، جنبها خلية 
+
+386
+00:26:07,850 --> 00:26:12,430
+حمراء، جنبها خلية حمراء، جنبها خلية حمراء كأنه خلايا
+
+387
+00:26:12,430 --> 00:26:16,150
+متجمعة مع بعض، بيسموه «roller formation» إن الخلايا
+
+388
+00:26:16,150 --> 00:26:20,450
+كأنها ملزقة مع بعض في صمغ أو شغل هيك صح إن أنا
+
+389
+00:26:20,450 --> 00:26:22,210
+الخلية الـ… طبعًا هذه الـ«roller formation» مش أنا
+
+390
+00:26:22,210 --> 00:26:24,510
+اللي سألت صح إن أنت المنطقة البقرة فيها يكون
+
+391
+00:26:24,510 --> 00:26:27,490
+الخلايا الحمراء بالصورة هاي هلّجد؟ لو ظهرت عندي
+
+392
+00:26:27,490 --> 00:26:30,350
+الصورة high في المطبق اللي بقرا فيه بحكي إن شخص
+
+393
+00:26:30,350 --> 00:26:33,510
+عنده roll of formation roll of formation طبعًا في
+
+394
+00:26:33,510 --> 00:26:37,230
+الحالات المرضية خاصة في حالات نحكي زيادة الألبومين
+
+395
+00:26:37,230 --> 00:26:40,230
+البروتينات بتظهر عندي الحالة high فroll of
+
+396
+00:26:40,230 --> 00:26:44,250
+formation طبعًا بتظهر عندي في الحالة high في الـ
+
+397
+00:26:44,250 --> 00:26:47,290
+thick area لكن في الـ adequate area أصلًا ما تظهرش
+
+398
+00:26:47,290 --> 00:26:52,030
+في الحالة normal فيمنا roll of formation؟ في
+
+399
+00:26:52,030 --> 00:26:59,150
+الوقت؟ أه سعيد معاذ طلع من الدادة و بدّيه يدخل مرة
+
+400
+00:26:59,150 --> 00:27:01,630
+ثانية هجاله البرنامج بيقولوا please wait the
+
+401
+00:27:01,630 --> 00:27:04,030
+meeting cost و الـ «لتش» قدروا .. آه آه شوفتوا
+
+402
+00:27:04,030 --> 00:27:09,190
+شوفتوا دايما دخلوا دلوقت صحيح «سيف» سمعناه و كذا
+
+403
+00:27:09,190 --> 00:27:12,870
+بقى معنا «سيف»؟
+
+404
+00:27:12,870 --> 00:27:18,090
+تمام تمام معاكم تمام يا «سيف» أنت مش شايف الشاشة
+
+405
+00:27:18,090 --> 00:27:21,970
+طيبة أيوة
+
+406
+00:27:21,970 --> 00:27:26,250
+شايف طيب فرقتنا، طيب افهم إن أنا رجعت لشو يعني
+
+407
+00:27:26,250 --> 00:27:30,150
+Spherocyte وشو رولوفورميشن؟ بس فادسناك بس دكتور
+
+408
+00:27:30,150 --> 00:27:33,430
+ايه دلّنا اللي هو نقطة ال .. اللي هو الـ formation
+
+409
+00:27:33,430 --> 00:27:37,170
+اللي لما بتظهر؟ طيب أنا بدي أشوف شغل ثاني إن شاء
+
+410
+00:27:37,170 --> 00:27:41,670
+الله إذا أجبرت أشوفها لأ لأ اللي هو ما تبتظهر ما
+
+411
+00:27:41,670 --> 00:27:46,250
+تبتظهر مش مشكلة مش مشكلة خليني أشوف بس أنا اللهم
+
+412
+00:27:46,250 --> 00:27:46,930
+صح يا سيد محمد
+
+413
+00:27:55,570 --> 00:28:00,210
+طب كيف نظام الكوزات هيكون؟ مش مشكلة، نحن نتفق عليها
+
+414
+00:28:00,210 --> 00:28:03,590
+إن شاء الله، تقيل أقول؟ طيب، هذه محاضرة، هناخدها
+
+415
+00:28:03,590 --> 00:28:06,990
+لهم بعدين، طلع معايا هنا، طلعيا سعيد، طلعيا محمد،
+
+416
+00:28:06,990 --> 00:28:11,290
+شايفين؟ هذي الحالة، الـRBC بيكون مع بعض هنا،
+
+417
+00:28:11,290 --> 00:28:14,530
+شايفين الصورة؟ هذي بسبب الـRolling Formation،
+
+418
+00:28:14,530 --> 00:28:20,280
+بيكون الخلايا الحمراء متجمعة مع بعض زي stacks of لو
+
+419
+00:28:20,280 --> 00:28:25,960
+كيف نجيب قطعة نقضية عشرة شكل مع بعض طبعًا وتعملهم
+
+420
+00:28:25,960 --> 00:28:32,800
+جوجب بعض مفتحتش لسه ثواني لسه مفتحتش لسه مفتحتش الـ
+
+421
+00:28:32,800 --> 00:28:40,400
+slide طيب
+
+422
+00:28:40,400 --> 00:28:46,700
+زعيطة تعمل ده؟ معلّق نبين حركي الموسيقى تكتر شوية
+
+423
+00:28:46,700 --> 00:28:52,190
+أنا لازم مفتحتش علاجي أهلا وسهلا يا عزيزي كمان كمان
+
+424
+00:28:52,190 --> 00:28:54,410
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+425
+00:28:54,410 --> 00:28:54,470
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+426
+00:28:54,470 --> 00:28:54,730
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+427
+00:28:54,730 --> 00:29:04,430
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+428
+00:29:04,430 --> 00:29:07,770
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+429
+00:29:07,770 --> 00:29:12,930
+كمان كمان كمان كمان كمان
+
+430
+00:29:12,930 --> 00:29:16,390
+كمان كمان
+
+431
+00:29:16,390 --> 00:29:23,110
+كمان كم طبعًا؟ بعض الحلقات الماضية تكون فيها الـ…
+
+432
+00:29:23,110 --> 00:29:25,530
+اللي يبني الـGlucose عالي فتالي البروتينات عالية
+
+433
+00:29:25,530 --> 00:29:28,950
+تؤدي لـRoller Formations تكون جمعها مع بعض، هذه
+
+434
+00:29:28,950 --> 00:29:31,350
+ممكن تظهر بعض الحلقات الماضية إحنا بتظهر عندما
+
+435
+00:29:31,350 --> 00:29:34,750
+تحكينا، بتظهر معنا في الـ… اللي هي إيه إيش حكينا
+
+436
+00:29:34,750 --> 00:29:39,510
+في حلقات الـThick Film أو في حلقات الـThick Area،
+
+437
+00:29:39,510 --> 00:29:43,410
+طبعًا؟ طيب فهنا عندي Spherocytes تظهر في Thin Area
+
+438
+00:29:43,410 --> 00:29:46,210
+وفي الـThick Area تظهر فيها Roller Formation
+
+439
+00:29:46,210 --> 00:29:48,110
+أبرجيكم مرة الـSpherocytes
+
+440
+00:29:51,890 --> 00:29:59,350
+الـ Spherocytosis زي عندي ..
+
+441
+00:29:59,350 --> 00:30:03,990
+شايفين
+
+442
+00:30:03,990 --> 00:30:08,570
+الخلايا اللي بشوفها؟ شايفين الخلايا هاي الصغيرة؟
+
+443
+00:30:08,570 --> 00:30:09,670
+فتحت عندك السيف؟
+
+444
+00:30:13,230 --> 00:30:15,730
+أه، فتحت، فتحت، يا دكتور شايف الخلايا اللي عليها
+
+445
+00:30:15,730 --> 00:30:17,930
+الـCM، هاي؟ أه، هيفتحت هاي الخلية اللي عليها الـCM
+
+446
+00:30:17,930 --> 00:30:21,030
+مافيش واضح فيها مظاهر Hemoglobin مبينة كأنه خلية
+
+447
+00:30:21,030 --> 00:30:24,710
+متجانسة كاملة، هاي الـSpherocyte بيكون حجمها صغير،
+
+448
+00:30:24,710 --> 00:30:29,910
+بيكون حجمها صغير وكملة الـHemoglobin أه، تبين
+
+449
+00:30:29,910 --> 00:30:32,390
+الـHemoglobin مليها كلها مليانة بالظبط، هذه
+
+450
+00:30:32,390 --> 00:30:35,610
+الـSpherocyte هذه بتظهر في الـThin Area كأنه
+
+451
+00:30:35,610 --> 00:30:38,290
+Spherocyte لكن هي فعليًا مش Spherocyte لكن هي
+
+452
+00:30:38,290 --> 00:30:41,450
+موجودة بسبب إن هي موجودة في الـThin Area طيب،
+
+453
+00:30:41,450 --> 00:30:48,130
+نكمل؟ إذا عندي serocytosis تظهر في حالة thin area و
+
+454
+00:30:48,130 --> 00:30:51,070
+thick area roll of formation لكن هدول حالتهم إيش؟
+
+455
+00:30:51,070 --> 00:30:55,330
+Normal، مش abnormal، لكن لو شوفت الحالتين هدول في
+
+456
+00:30:55,330 --> 00:30:58,750
+adequate area، أني adequate area يا محمد؟ اللي هي
+
+457
+00:30:58,750 --> 00:31:04,070
+بالنص، اللي تقع بيها بالنص، تمام؟ صحيح، هذه الحالة
+
+458
+00:31:04,070 --> 00:31:06,590
+اللي بحكي عنها إيش؟ بحكي إنها حالة مرضية، adequate
+
+459
+00:31:06,590 --> 00:31:08,710
+area، adequate area بالظبط
+
+460
+00:31:13,550 --> 00:31:16,790
+هذه أخدناها، مش هنحكي عليها كتير، لكن هي إيش
+
+461
+00:31:16,790 --> 00:31:22,790
+الحالة تؤدي إلى ظهور نحكي abnormality في عملية
+
+462
+00:31:22,790 --> 00:31:27,430
+الـPoor Blood Smear؟ طبعًا عندك drop too large أو
+
+463
+00:31:27,430 --> 00:31:30,750
+too small، إحنا إذا كنتوا تذكروا جربنا drop 10
+
+464
+00:31:30,750 --> 00:31:34,020
+مايكرو، جربنا 7 مايكرو، عشان تنطقوا معانافي ناس
+
+465
+00:31:34,020 --> 00:31:36,900
+كانت إيد العشرة مايكرون اتخربت، مضبوطش معاها،
+
+466
+00:31:36,900 --> 00:31:40,180
+اعتمدت على سبعة مايكرون، صح؟ فحسب الـ drop نفسها،
+
+467
+00:31:40,180 --> 00:31:43,420
+كل ما زاد الـ drop، كل ما كان عندك بور أكتر تقنيت،
+
+468
+00:31:43,420 --> 00:31:47,040
+عملية الفرد الصحيح ‏- من خمسة لعشرة؟ ‏- احنا حطينا
+
+469
+00:31:47,040 --> 00:31:50,020
+عشرة وما زبطت معايا الأغلبية، فحطينا السبعة عشان
+
+470
+00:31:50,020 --> 00:31:54,340
+إيدك تأخد عليها ‏- ع سبعة كانت تظبط معايا ‏- صحيح،
+
+471
+00:31:54,340 --> 00:31:57,480
+ع سبعة كانت تظبط معايا الأغلبية، لكن مجرد إن إيدك
+
+472
+00:31:57,480 --> 00:32:01,220
+زبطت على سبعة، بعدين لو حطيت عشر أو عشرين، تظبط
+
+473
+00:32:01,220 --> 00:32:06,760
+أكتر، معاك أكتر، لأن إيديك أخدت تقنية نفسها، تمام؟
+
+474
+00:32:06,760 --> 00:32:12,360
+تمام طيب، فرد الـslide مهم جدًا، عشان تنفرد بطريقة
+
+475
+00:32:12,360 --> 00:32:17,220
+مش jerky manner عملية إنك أنت تحافظ على الـedge،
+
+476
+00:32:17,220 --> 00:32:20,860
+تبقى الـedge، وتعمل الـslide بإله دور، الزاوية
+
+477
+00:32:20,860 --> 00:32:24,060
+إلها دور، وعملية الـbush، الـspreader نفسها إلها
+
+478
+00:32:24,060 --> 00:32:28,700
+دور، في عملية تعطيك pour blood، اسمها طبعًا الـ
+
+479
+00:32:28,700 --> 00:32:31,220
+«irregular spiders with a ridge and long tail»
+
+480
+00:32:31,220 --> 00:32:33,920
+برضه نفس الحكاية الـ «Holes» في الـ «Blood Film»
+
+481
+00:32:33,920 --> 00:32:36,920
+كل هذه معنات معناة في ال .. إذا بتفكروا في السمن
+
+482
+00:32:36,920 --> 00:32:41,380
+صور «A» ل«F» وآخرش تغييرات في الخلية الـ «Central
+
+483
+00:32:41,380 --> 00:32:45,020
+Generator» نتيجة أنه أنت طول في عملية «Fixation»
+
+484
+00:32:45,020 --> 00:32:48,220
+نتيجة أنك أنت عملت «Fixing Time» في الميثانول وكان
+
+485
+00:32:48,220 --> 00:32:49,400
+فيه «Contamination» بالوطن
+
+486
+00:32:52,260 --> 00:32:56,520
+عندي حالات طبعًا بيسموها «Biological Causes of
+
+487
+00:32:56,520 --> 00:33:00,620
+Gore Smear» يعني هي سببها أنه عندها حالات بيولوجية
+
+488
+00:33:00,620 --> 00:33:05,500
+مش أنت سبب فيها يعني مثلًا إذا بتذكروا قلتلكم، إذا
+
+489
+00:33:05,500 --> 00:33:10,760
+بتذكروا ميزنا بين، ميزنا بين ال .. حكيتكم الـ
+
+490
+00:33:10,760 --> 00:33:13,320
+«Role Formation» والـ «Agglutination» في الـ slide
+
+491
+00:33:13,320 --> 00:33:16,700
+المرة السابقة، نرجعلها، أبرجكم إياها الـ «Slide
+
+492
+00:33:16,700 --> 00:33:17,180
+High»
+
+493
+00:33:21,140 --> 00:33:25,080
+هذه، شايفينها؟ ‏- أه ‏- هذه في ال .. على اليمين
+
+494
+00:33:25,080 --> 00:33:27,480
+roll-off formation وهذا agglutination الـ roll-off
+
+495
+00:33:27,480 --> 00:33:30,220
+formation، حكينا سببه زيادة البروتينات لكن الـ
+
+496
+00:33:30,220 --> 00:33:33,500
+agglutination سببه هي أجسام مضادة، تمام؟ ممكن
+
+497
+00:33:33,500 --> 00:33:36,660
+أجسام مضادة، حسب، فأنا هذا بيسموه agglutination
+
+498
+00:33:36,660 --> 00:33:39,760
+وهذا roll-off formation طيب، احنا في عندي حالة
+
+499
+00:33:39,760 --> 00:33:42,000
+اللي بيسموها الـ cold agglutination cold
+
+500
+00:33:42,000 --> 00:33:45,320
+agglutination من اسمها cold يعني بارد و الـ 
+
+501
+00:33:45,320 --> 00:33:47,860
+Agglutination بيصير تخثر الدم في الحالات الباردة
+
+502
+00:33:47,860 --> 00:33:52,040
+نتيجة وجود أجسام مضادة طبعا بالحالة هذه الخلايا
+
+503
+00:33:52,040 --> 00:33:55,920
+الحمراء بيصير الكلام مع بعض في الجو البارد لكن لو
+
+504
+00:33:55,920 --> 00:33:58,520
+حاطيتها أنا في الـ water bath كده ترش حالات الـ water
+
+505
+00:33:58,520 --> 00:34:03,020
+bath؟ سبعة و ثلاثين سبعة و ثلاثين فبالتالي بتفك
+
+506
+00:34:03,020 --> 00:34:07,500
+تمام فبالتالي بتفك طب ولا .. ولا أنت بدل زي الدكتور
+
+507
+00:34:07,500 --> 00:34:11,220
+بيسيبني هتفك أنا يعني إيه؟ كيف يا سعيد؟ الـ
+
+508
+00:34:11,220 --> 00:34:13,720
+Antibodies الأجسام المضادة اللي بتكون ماسكة فيها
+
+509
+00:34:13,720 --> 00:34:17,960
+اللي عامل الـ agglutination هذي، تتخيل عنها؟ حسب
+
+510
+00:34:17,960 --> 00:34:21,180
+نوعها، هذي اسمها cold agglutinins cold agglutinins
+
+511
+00:34:21,180 --> 00:34:24,080
+اللي هي أجسام مضادة بتتفعل بدرجة حرارة باردة، يعني
+
+512
+00:34:24,080 --> 00:34:27,800
+نحكي أربعة درجة مئوية، تمام؟ أو نحكي ستة عشر
+
+513
+00:34:27,800 --> 00:34:31,920
+مثلا، هذي من طبيعتها لو حضرتها بدرجة حرارة عالية
+
+514
+00:34:31,920 --> 00:34:36,760
+شويه سبعة و ثلاثين، بتتفعلش، بتفك التفاعل
+
+515
+00:34:36,760 --> 00:34:39,600
+الأجسام المضادة مع الـ Antigens تعتبر تفاعل
+
+516
+00:34:39,600 --> 00:34:43,200
+عكسي الـ Reverse، ممكن أعكسه أنا أجد الـ Warm 
+
+517
+00:34:43,200 --> 00:34:47,520
+Agglutination بتفاعل لدرجة حرارة 37، لدرجة حرارة
+
+518
+00:34:47,520 --> 00:34:49,540
+الجسم لكن الـ Cold Agglutination بتفاعل لدرجة
+
+519
+00:34:49,540 --> 00:34:53,660
+حرارة باردة، أنا بقدر أعالج الحالة هاي، لو مرض ما
+
+520
+00:34:53,660 --> 00:34:56,620
+هي حالة Cold Agglutination، بقدر أعالجها، إن أنا
+
+521
+00:34:56,620 --> 00:35:00,860
+بأخذ العينة، بحطها في Water بقى، خمس دقائق، وبعدين خلال
+
+522
+00:35:00,860 --> 00:35:02,680
+وجود الـ Pottery Barrel بعمل الـ Plug Flow
+
+523
+00:35:02,680 --> 00:35:06,230
+وبفرضه طبعاً بحاول أسخن الـ slides كمان عشان يكون
+
+524
+00:35:06,230 --> 00:35:08,670
+عندي برضه الـ Warm لإن مجرد أسحبها الـ Cold ممكن
+
+525
+00:35:08,670 --> 00:35:13,250
+تقضيها التفاعل تعني حالة تانية سببها الـ biological
+
+526
+00:35:13,250 --> 00:35:16,510
+اللي هي الليبيميا إيش عن الليبيميا يا معاد؟
+
+527
+00:35:16,510 --> 00:35:22,610
+الليبيميا؟ الليبيدات الليبيدات الليبيدات الليبيدات
+
+528
+00:35:22,610 --> 00:35:28,750
+الليبيدات الليبيدات الليبيدات 
+
+529
+00:35:28,750 --> 00:35:31,170
+الليبيدات الليبيدات الليبيدات الليبيدات الليبيدات الليبيدات
+
+530
+00:35:31,170 --> 00:35:34,420
+الليبيدات الليبيدات الليبتبع دهون في الدم، هذه طبعا تؤدي
+
+531
+00:35:34,420 --> 00:35:38,260
+لظهور الـ holes في الاسميرة، إذا كان فيه Slide هي
+
+532
+00:35:38,260 --> 00:35:44,980
+holes، رقم A,B,C,D,E، صح يا محمد؟ Slide E كان
+
+533
+00:35:44,980 --> 00:35:48,640
+فيها holes، الـ holes يعني سبب الترقيم يعني،
+
+534
+00:35:49,380 --> 00:35:51,840
+طبعًا أدى إذا علاج، لأ ما له علاج لأنه أصل هو
+
+535
+00:35:51,840 --> 00:35:54,000
+موجود في جسم الإنسان يعني إنسان جاي يعمل Blood
+
+536
+00:35:54,000 --> 00:35:57,300
+film وكان عنده الدهون عالية أنا ما أقدرش في الحال هاي
+
+537
+00:35:57,300 --> 00:36:00,680
+أني أحكيله لأ، روح نزل دهون تعالي فحنقرأ 
+
+538
+00:36:00,680 --> 00:36:02,880
+الـ Lottery of Lipidemia والـ Roll of formation زي ما
+
+539
+00:36:02,880 --> 00:36:05,760
+حكيت لكم أنه في حال تكون فيها بروتينات عالية شوية
+
+540
+00:36:05,760 --> 00:36:09,460
+عبارة عن Stack of coins، شكل Stack of coins هذه
+
+541
+00:36:09,460 --> 00:36:11,580
+الحالات تؤدي لـ Poor Blood smear في حالة
+
+542
+00:36:11,580 --> 00:36:16,300
+الـ biological cases هيك خلصنا Blood film تقريباً،
+
+543
+00:36:16,300 --> 00:36:22,130
+هندخل للـ Training بالنسبة بس تحدثنا، الـ Rouleaux ارتفاع
+
+544
+00:36:22,130 --> 00:36:25,410
+لبروتينات أي نوع بروتين ولا فيه بروتينات معينة هي
+
+545
+00:36:25,410 --> 00:36:27,810
+اللي بتؤدي للارتفاع اللي هو وجود الـ Rouleaux؟ لأ،
+
+546
+00:36:27,810 --> 00:36:31,070
+ممكن إحنا في الحالة هذه بيصير اختلال، هو غالباً
+
+547
+00:36:31,070 --> 00:36:33,870
+يعني تظهر الـ Rouleaux Formation في حالات مثلًا اللي
+
+548
+00:36:33,870 --> 00:36:38,770
+نحكي تفاعل Immunoglobulins Immunoglobulins طبعًا
+
+549
+00:36:38,770 --> 00:36:42,450
+من أنواع البروتينات الجلوبيولينات، الجلوبيولين، تمام؟
+
+550
+00:36:42,450 --> 00:36:45,010
+فبالحالة هاي بتتفعل، طبعًا Immunoglobulins في حالة
+
+551
+00:36:45,010 --> 00:36:50,240
+مرضية تؤدي إلى ظهور الـ Rouleaux Formation لكن هي
+
+552
+00:36:50,240 --> 00:36:52,960
+بشكل عام، لو ارتفع الألبومين نفس الحكاية، ليش؟ لأن
+
+553
+00:36:52,960 --> 00:36:56,680
+ارتفاع البروتينات يؤدي إلى اختلال في البيئة حول
+
+554
+00:36:56,680 --> 00:36:59,280
+الخلايا الحمراء، طبعاً من شحنات كهربائية وغيرها،
+
+555
+00:36:59,280 --> 00:37:03,680
+وتؤدي بالتالي إلى اختلال البيئة والشحنات إلى
+
+556
+00:37:03,680 --> 00:37:05,920
+اقتراب الخلايا الحمراء من بعض لبعض، يعني الخلايا
+
+557
+00:37:05,920 --> 00:37:10,700
+الحمراء أصلاً، إيش فيها سطحها؟ فيها سطحها شحنات،
+
+558
+00:37:10,700 --> 00:37:13,280
+Lysine هذه تؤدي لتنافر الخلايا الحمراء من
+
+559
+00:37:13,280 --> 00:37:15,600
+بعض، يعني الخلايا الحمراء بتبتعد عن بعض بوجود
+
+560
+00:37:15,600 --> 00:37:20,560
+الشحنات لكن أنا في حالة التفاعل، البروتينات،
+
+561
+00:37:20,560 --> 00:37:24,840
+البيئة اللي حواليها كانت أقرب شوية، خلّيني أتجرب،
+
+562
+00:37:24,840 --> 00:37:28,660
+كانت كأنها صارت Agglutination، إحنا أحد طرق علاج
+
+563
+00:37:28,660 --> 00:37:30,360
+الـ Rouleaux formation أحد طرق علاج الـ Rouleaux
+
+564
+00:37:30,360 --> 00:37:33,960
+formation أن إحنا نشيل من الـ Plasma ونحط بدلها
+
+565
+00:37:33,960 --> 00:37:39,700
+Saline، فبالتالي أنا خففت من الـ… شو اسمه؟ الـ
+
+566
+00:37:39,700 --> 00:37:42,260
+ألبومين أو خففت من البروتينات وبالتالي عملت
+
+567
+00:37:42,260 --> 00:37:45,240
+أدية الخلايا الأمريكية تؤدي لـ تنافر بسبب إيه
+
+568
+00:37:45,240 --> 00:37:48,080
+الشحنتها، تمام؟ تمام
+
+569
+00:37:50,830 --> 00:37:54,310
+طيب الـ Staining، الـ Staining يعني بعد ما تنشف
+
+570
+00:37:54,310 --> 00:37:57,370
+الـ slide و عملت تنشف الـ slide بعمله Staining،
+
+571
+00:37:57,370 --> 00:38:00,230
+طبعا عندي أنواع كثيرة من الـ Staining إحنا ممكن
+
+572
+00:38:00,230 --> 00:38:04,050
+نستخدم طبعا كل الـ Staining تتبع للـ Romanowsky
+
+573
+00:38:04,050 --> 00:38:06,950
+Stains، فعندي Wright Stains، الـ Wright Stains بيسموها
+
+574
+00:38:06,950 --> 00:38:10,460
+Metachromatic Stains ميتاكروماتيك ستينز طبعاً فيها two
+
+575
+00:38:10,460 --> 00:38:15,340
+types of stains طبعاً فيكون فيها صبغة حامضية و صبغة
+
+576
+00:38:15,340 --> 00:38:19,660
+قاعدية طبعاً فيها نوعين من الصبغة فيها مثلاً methylene
+
+577
+00:38:19,660 --> 00:38:23,240
+blue دار و فيها الـ Eosin الحمراء فهي تسبغ لي باللون
+
+578
+00:38:23,240 --> 00:38:27,920
+الأزرق و الأحمر تسبغ لي النواة باللون الأزرق و
+
+579
+00:38:27,920 --> 00:38:35,140
+الخلايا الحمراء تسبغ لي الـ Hemoglobin باللون الأحمر
+
+580
+00:38:35,140 --> 00:38:41,120
+حسب سبب الشحنات طبعاً، بأستخدم الـ Methanol في
+
+581
+00:38:41,120 --> 00:38:47,140
+عملية التثبيت الـ Methylene blue تسبغ لي الـ RNA،
+
+582
+00:38:47,140 --> 00:38:52,460
+تسبغ لي الـ DNA، تسبغ لي كما حكينا، كل الأنوية بالـ
+
+583
+00:38:52,460 --> 00:38:56,160
+Blue-Grey Color بينما الـ Eosin الحمراء تسبغ لي الـ
+
+584
+00:38:56,160 --> 00:38:59,700
+Eosin Granules باللون الأورانج تسبغ لي طبعاً الـ Red blood
+
+585
+00:38:59,700 --> 00:39:06,380
+cells السبغات طبعاً فيها Buffer لإنه يحافظ على الـ
+
+586
+00:39:06,380 --> 00:39:11,060
+pH غالباً الـ pH بيكون من 6.4 لـ 6.7 الـ Buffer
+
+587
+00:39:11,060 --> 00:39:14,960
+مهم جداً جداً جداً يعني إحنا كثيراً مرات معايا
+
+588
+00:39:14,960 --> 00:39:18,140
+بتجربة من ناحية العملية أني أنا أسبغ كنت أسبغ
+
+589
+00:39:18,140 --> 00:39:20,480
+مثلاً بعض الـ Slides ما أعرفش أحكي لكم يا عم
+
+590
+00:39:20,480 --> 00:39:24,100
+بالمخدمة ولا لأ لكن كنت أسبغ Slides في مرة مرات
+
+591
+00:39:24,100 --> 00:39:26,160
+لحد أن معظم الـ Slides اللي أسبغها هتطلع معايا
+
+592
+00:39:26,160 --> 00:39:30,230
+Acidic طبعاً السبب، طبعاً السبب دي عملها Buffer 100%
+
+593
+00:39:30,230 --> 00:39:34,310
+فبعد هيك اكتشفت أن أحد زملائي كان مثلاً يجي
+
+594
+00:39:34,310 --> 00:39:37,990
+يستخدم مثلاً أحد القوارير، يستخدم القارورة و يسيب
+
+595
+00:39:37,990 --> 00:39:41,650
+القارورة مفتوحة نوعاً ما، فبيصير Evaporation للصبغة
+
+596
+00:39:41,650 --> 00:39:44,550
+فيؤدي إلى زيادة صبغة الـ Environment وبالتالي يؤدي
+
+597
+00:39:44,550 --> 00:39:48,530
+إلى زيادة Staining، نحكي الـ Red color Staining أو
+
+598
+00:39:48,530 --> 00:39:51,710
+يصير صبغة أكثر، فهذه الـ Buffer مهم جداً،
+
+599
+00:39:51,710 --> 00:39:54,250
+الـ Atmosphere اللي حواليك مهم، هيعمل اللي يحفظ على
+
+600
+00:39:54,250 --> 00:39:59,240
+الصبغة نفسها طيب، الـ Sealing Procedure مش سهل،
+
+601
+00:39:59,240 --> 00:40:03,480
+هنأخده معنا إحنا بعد ما نجفف السمير لازم نعملها
+
+602
+00:40:03,480 --> 00:40:08,160
+Fixation بواسطة الـ Methanol طبعاً، ممكن أنك أنت
+
+603
+00:40:08,160 --> 00:40:13,460
+تحطها على الـ Rack و تعملها، تحط عليها الـ نحكي الـ
+
+604
+00:40:13,460 --> 00:40:16,120
+Methanol لمدة مثلاً، Two minutes أو Three minutes
+
+605
+00:40:16,120 --> 00:40:19,660
+أو ممكن أنت بواسطة الـ Jar، الـ Sealing Jars
+
+606
+00:40:19,660 --> 00:40:23,300
+تعملها دلوقتي عشر دقائق في الـ Sealing Jars فيها
+
+607
+00:40:23,300 --> 00:40:25,200
+أنا نزلت لكم فيديو، ما أعرف إذا شفتوه
+
+608
+00:40:43,100 --> 00:40:44,500
+‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏
+
+609
+00:40:52,140 --> 00:40:57,140
+الطريقة نفسنا هي استخدام الـ Rack على الـ Sink
+
+610
+00:40:57,140 --> 00:41:00,100
+نفسها وسنقوم بمعالجة السمير ونقوم بعمل دب
+
+611
+00:41:00,100 --> 00:41:05,840
+110 مرة ثم سنضع السمير على الـ Sink لمدة 1-2
+
+612
+00:41:05,840 --> 00:41:09,420
+دقيقة ثم نضيف الـ Buffer بالطبع أن الـ Sink نفسها هي
+
+613
+00:41:09,420 --> 00:41:12,020
+الـ مكس من الـ Eosin والـ Methylene مع
+
+614
+00:41:12,020 --> 00:41:15,200
+بعض سيكون صبغتين وليس منفصلين يعني الـ Wright
+
+615
+00:41:15,200 --> 00:41:18,760
+Stain هي الصبغة الموجودة فيها الـ Methylene مع
+
+616
+00:41:18,760 --> 00:41:22,380
+الـ Eosin هي مسبوغة و جاهزة كنت تقول لنا يا دكتور
+
+617
+00:41:22,380 --> 00:41:25,400
+في المقدمة الحالية هي سبغات موجودة فيها مسبوغة و
+
+618
+00:41:25,400 --> 00:41:30,620
+جاهزة ولا إحنا بنجهزها مسبوغة و جاهزة مش مسبوغة
+
+619
+00:41:30,620 --> 00:41:36,240
+أنا بأسبغها لسه الاسميرة لأ الصبغة جاهزة ولا مثلاً
+
+620
+00:41:36,240 --> 00:41:41,540
+محضرة محضرة و جاهزة ممكن تجيك باودر و أنت تحضرها
+
+621
+00:41:41,540 --> 00:41:46,480
+بالميثانول أو ممكن تجيك مثلاً جاهزة ومتوسطة مباشرة
+
+622
+00:41:46,480 --> 00:41:49,790
+حسب الشركات اللي بتشتري منها طبعاً إحنا بنغمر … حتى
+
+623
+00:41:49,790 --> 00:41:53,270
+بـ … حتى بالشركة أقل إحنا بنغمر السمير لـ One to
+
+624
+00:41:53,270 --> 00:41:56,510
+Two minutes بعد هيك طبعاً بنضيف عليها كمية من الـ
+
+625
+00:41:56,510 --> 00:41:59,730
+Buffer تعادل كمية السمير و بنغمر، بحيث إنه يصير
+
+626
+00:41:59,730 --> 00:42:02,790
+عملية … عملية نفخ يَلْعَب دور كثير في عملية mixing
+
+627
+00:42:02,790 --> 00:42:04,790
+بين الـ buffer و السمير أو بين الميّه داخل الـ
+
+628
+00:42:04,790 --> 00:42:07,090
+water و السمير، إحنا نستخدم distilled water عملية 
+
+629
+00:42:07,090 --> 00:42:11,790
+نفخ، في بعض الصبغات مثلًا، إحنا عزينا Riot وGemsa
+
+630
+00:42:11,790 --> 00:42:15,630
+وفيها نوع كثير من الصبغات Gemsa مثلًا، لو نفختها،
+
+631
+00:42:15,630 --> 00:42:19,550
+هتلاقي إنه ظهر نوع من اللون، بيسموه «هذه طبعاً 
+
+632
+00:42:19,550 --> 00:42:22,770
+بلون حلو كثير رأيك أنك تضمن إن عملت الـ mixing صح
+
+633
+00:42:22,770 --> 00:42:25,770
+ممكن تعمل الـ mixing بالـ pipettes بصير الـ
+
+634
+00:42:25,770 --> 00:42:29,590
+pipettes أو بالنفخ بواسطة سخن مدى المواصع وشغل
+
+635
+00:42:29,590 --> 00:42:33,450
+أيضًا طبعاً إذا نضيف نفس الكمية من الـ buffer على
+
+636
+00:42:33,450 --> 00:42:36,630
+الاسمير و بعدين كبنونه فوق و نخليها two to four
+
+637
+00:42:36,630 --> 00:42:40,070
+minutes نعمل نعمل wash و بعدين نعمل dry الاسمير و
+
+638
+00:42:40,070 --> 00:42:48,470
+نقرأ الاسمير نفسنا طبعاً 90 سنة أعطاني رسالة أن الـ
+
+639
+00:42:48,470 --> 00:42:50,490
+«سيروجيومولوجيا» يبدو بدأ بعد عشر دقائق لإن ما
+
+640
+00:42:50,490 --> 00:42:53,230
+يشبه بعديكم طيب مش مشكلة احنا نحاول نشتغل الـ
+
+641
+00:42:53,230 --> 00:42:57,930
+«سيروجيومولوجيا» ده فكرت الصوت من عندك ساعين، لا،
+
+642
+00:42:57,930 --> 00:43:01,970
+من عندك، طيب، هاي الـstaining، فعندي هنا طبعا two
+
+643
+00:43:01,970 --> 00:43:05,050
+basic، بيكون في المثلين بيقولوا، بيكون هذه طبعا
+
+644
+00:43:05,050 --> 00:43:08,870
+أَذَا أسباب، هذه طبعا أَذَا بشيء، وهذه طبعا two acidic،
+
+645
+00:43:08,870 --> 00:43:09,470
+شايفين؟ 
+
+646
+00:43:12,140 --> 00:43:15,200
+البنافسة دي البربل والأزرق والأحمر بظهرين بشكل
+
+647
+00:43:15,200 --> 00:43:19,700
+متجانس وواضح، مايكونش كلها حمرا ولا كلها زرقا،
+
+648
+00:43:19,700 --> 00:43:22,540
+تشوفين هالخلايا الحمرا كيف؟ هيخلاها حمرا، كلها
+
+649
+00:43:22,540 --> 00:43:25,760
+زرقا، هالخلايا الحمرا كلها حمرا، هنا أيضا أدقوة
+
+650
+00:43:25,760 --> 00:43:31,080
+طبعا أسباب ال .. دكتور هذا الصورة على المجهر؟ إيه؟
+
+651
+00:43:32,750 --> 00:43:35,390
+الصورة هذه هيك هتظهر على المجهر المفروض ولا في
+
+652
+00:43:35,390 --> 00:43:36,730
+العين؟ هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+653
+00:43:36,730 --> 00:43:45,830
+هيك هيك هيك هيك هيك هيك هيك هيك
+
+654
+00:43:45,830 --> 00:43:46,170
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+655
+00:43:46,170 --> 00:43:46,190
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+656
+00:43:46,190 --> 00:43:46,230
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+657
+00:43:46,230 --> 00:43:46,890
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+658
+00:43:46,890 --> 00:43:50,690
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+659
+00:43:50,690 --> 00:43:56,010
+هيك هيك هيك هيك هيك هيك هيك هيك أو إنه character
+
+660
+00:43:56,010 --> 00:44:00,870
+stain عندك بقديمة أو إن البيئة قدش عندك acid زي
+
+661
+00:44:00,870 --> 00:44:03,930
+اللي بحكيلكم، أنا كان زميل يحط استخدام ال acid
+
+662
+00:44:03,930 --> 00:44:08,530
+جنبي، جنب ال swing قد لإنه ترميته stain يعني إذا
+
+663
+00:44:08,530 --> 00:44:11,110
+ظهرت مشكلة هنا في هذا الحالة، هتكون المشكلة من
+
+664
+00:44:11,110 --> 00:44:13,430
+السبغة، مش؟ بالظبط، بيكون المشكلة من السبغة، فإن
+
+665
+00:44:13,430 --> 00:44:18,530
+أنت بدأت تحلها، أه مش من سحبت يعني إنت بالحالة
+
+666
+00:44:18,530 --> 00:44:21,010
+high فكبارا two acidic بدأت تحلها أو two steel
+
+667
+00:44:21,010 --> 00:44:23,610
+alkaline بدأت تحلها، لإن مش هتعرف تقرأ منها أصلاً
+
+668
+00:44:24,090 --> 00:44:31,070
+هتجد الـ two alkaline يعني
+
+669
+00:44:31,070 --> 00:44:35,250
+لو كان عندك ثقيل سمير أو prolong staining يعني إذا
+
+670
+00:44:35,250 --> 00:44:38,510
+كان العكس، ثقيل سمير هتعطيكه أسد أحيانًا two
+
+671
+00:44:38,510 --> 00:44:41,250
+alkaline، thick smear أو prolong staining أو
+
+672
+00:44:41,250 --> 00:44:45,070
+insufficient washing أو alkaline pH طب العلاجاتهم،
+
+673
+00:44:45,070 --> 00:44:47,910
+عرف العلاجاتهم، أنا عند العلاج إذا كان
+
+674
+00:44:48,460 --> 00:44:51,660
+الـSufficient Staining Time، بزوّد الـTime إذا كان
+
+675
+00:44:51,660 --> 00:44:55,380
+الـBH عندي Acidic، بعدّل في الـBH إذا كانت All
+
+676
+00:44:55,380 --> 00:44:59,520
+Stained، بعمل Staining جديدة، تمام؟ الـAlkaline،
+
+677
+00:44:59,520 --> 00:45:02,820
+لو كانت Thick Smear، بحطه Smear كويسة إذا كانت
+
+678
+00:45:02,820 --> 00:45:05,560
+Prolonged Staining، بقلّر من الـTime إذا كانت
+
+679
+00:45:05,560 --> 00:45:08,840
+Sufficient Washing، بعمل Washing صح، يعني مش بحطه
+
+680
+00:45:08,840 --> 00:45:12,560
+تحسين صح وإذا كانت Alkaline BH، بعمل إيش؟ أتشكل
+
+681
+00:45:12,560 --> 00:45:15,860
+الـBH، وبعدّل الـBH، هيك إحنا خلصنا الـStaining
+
+682
+00:45:16,250 --> 00:45:22,390
+وخلصنا الـ «Blood Film» ده عنده جزئية الـ .. طبعا
+
+683
+00:45:22,390 --> 00:45:24,290
+بحكيلك الـ «Manual Differential» اللي على الـ
+
+684
+00:45:24,290 --> 00:45:28,430
+«RBC» وإيش بدهر معاه Normal، تمام؟ عندي طبعا
+
+685
+00:45:28,430 --> 00:45:32,790
+الخلايا الحمرة، أنا إيه الخاطر هذا؟ نواجب .. نواجب
+
+686
+00:45:32,790 --> 00:45:37,870
+احنا هنا إن شاء الله، إيش رأيكوا؟ نواجب هنا، نواجب
+
+687
+00:45:37,870 --> 00:45:42,550
+.. ‏-إيش راجع الفيلم؟ ‏-طايل كثير يا دكتور، طايل
+
+688
+00:45:42,550 --> 00:45:47,420
+كثير مش ضايق الأغربية الصور يعني وأشكال وكيف تتوزين
+
+689
+00:45:47,420 --> 00:45:50,300
+الخلايا الحمراء والخلايا اللي ده إحنا نوقف هنا إن
+
+690
+00:45:50,300 --> 00:45:52,860
+شاء الله ومن السنوات الجاية في لقاء السنوات الجاية
+
+691
+00:45:52,860 --> 00:45:56,200
+بنحاول إن شاء الله نكمل وبناخدكم ده أحاول أبعد
+
+692
+00:45:56,200 --> 00:45:59,340
+بينكم وبين الشباب عشان لو أتأخرنا شوية قدرنا معاكم
+
+693
+00:45:59,340 --> 00:46:00,640
+شوية
+
+694
+00:46:03,210 --> 00:46:06,410
+طبعا، أنا جيت بدي أعمل الـ «Application» بدي أعمل
+
+695
+00:46:06,410 --> 00:46:10,870
+الـ «code» للمحاضرة و أنزلها زي ما حكيتكم، احتمال
+
+696
+00:46:10,870 --> 00:46:14,270
+كبير، إذا حابين الساعة 4، ماعنديش مشكلة احتمال
+
+697
+00:46:14,270 --> 00:46:18,310
+يكون ثابت أو اتنين، طبعا؟ بدي أوزع المعامل بين أنا
+
+698
+00:46:18,310 --> 00:46:20,710
+و تالت و بدي أحاول أعمل وسامة بين كل معمل معمل
+
+699
+00:46:20,710 --> 00:46:24,190
+بحيث أنه يكون عندي ساعة لو اتخلت أنه أقدر أعطيكم
+
+700
+00:46:24,190 --> 00:46:28,310
+كمان راح تفضلوا خلاص، طبعا، إن شاء الله، يلا،
+
+701
+00:46:28,310 --> 00:46:33,070
+أعطيكم العادة، في صفصار في الصبق؟ طبعا، تمام الله
+
+702
+00:46:33,070 --> 00:46:35,690
+يرضى عليك يا دكتور الله يزيد يعطيك العافية يا
+
+703
+00:46:35,690 --> 00:46:39,470
+دكتور ماشي يعطيك العافية يعطيك العافية مع السلامة
+
+704
+00:46:39,470 --> 00:46:39,970
+يعطيك العافية
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_postprocess.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a4ee3295485124be8a3b70ae37ba40b6ecac37f
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_postprocess.srt
@@ -0,0 +1,2816 @@
+1
+00:00:00,000 --> 00:00:05,600
+بس دكتور بعد اسمك بس في نقطة أنا هنا في اني علامة
+
+2
+00:00:05,600 --> 00:00:08,720
+تسجيل بضغط عليها بيقول place as the host و give
+
+3
+00:00:08,720 --> 00:00:10,780
+you ده مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+4
+00:00:10,780 --> 00:00:11,880
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+5
+00:00:11,880 --> 00:00:12,560
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+6
+00:00:12,560 --> 00:00:12,960
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+7
+00:00:12,960 --> 00:00:15,760
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+8
+00:00:15,760 --> 00:00:18,260
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+9
+00:00:18,260 --> 00:00:23,880
+مش مش مش مش مش مش مش مش
+
+10
+00:00:23,880 --> 00:00:30,150
+مش مش مشعلم الدم طبعاً عملت، احنا أخدت في المقاطمة
+
+11
+00:00:30,150 --> 00:00:33,950
+بعض المعامل اللي إلها علاقة بعلم الدم وكان منها
+
+12
+00:00:33,950 --> 00:00:39,290
+طبعاً أخر معمل كنتوا بتذكره أنه هيكون أول معمل في
+
+13
+00:00:39,290 --> 00:00:42,550
+الـ hematology صح ولا لأ؟ فعنا أخر معمل هو كيف
+
+14
+00:00:42,550 --> 00:00:47,170
+نعمل الشريحةوكيف نصبخها، احنا طبعا المعمل الحالي
+
+15
+00:00:47,170 --> 00:00:52,030
+هنعيد كيف نعمل شريحة، كيف نصبخها وكيف بتاني نقرأها
+
+16
+00:00:52,030 --> 00:00:55,190
+إن شاء الله، سواء كانت نوعية طبيعية أو غير طبيعية
+
+17
+00:00:55,190 --> 00:01:01,850
+طبعا بالنسبالي، نحكي الـ Outline تبع المعمل تبعنا،
+
+18
+00:01:01,850 --> 00:01:10,010
+خليني انا أشاركم الشاشة، هل جيت معاي؟ في محمد،
+
+19
+00:01:10,010 --> 00:01:12,250
+شوفين الشاشة حاليا؟ شايفين الشاشة، تمام؟
+
+20
+00:01:20,380 --> 00:01:27,260
+واضح الشاشة عندكم يا شباب؟ واضح، كبرها، عادل نقدر
+
+21
+00:01:27,260 --> 00:01:29,920
+نكبرها من عندنا نكبرها من عندكم، نكبرها من عندنا
+
+22
+00:01:29,920 --> 00:01:33,530
+اللي بتحبه، يعني أنا ماعنديش مشكلتهالأ، إتمام،
+
+23
+00:01:33,530 --> 00:01:35,450
+إتمام، طبعاً «العالم الزمزرريلي» بالنسبة لوعيد
+
+24
+00:01:35,450 --> 00:01:37,590
+المحاضرة إن شاء الله أنا حكيتكم وحددكم زي ما
+
+25
+00:01:37,590 --> 00:01:40,690
+اتفقنا، هكون الساعة 4 بعد العصر، إما السبت أو
+
+26
+00:01:40,690 --> 00:01:45,930
+الإتنين، حسب توزيع الجدول، أنا هوزع جدول بينهم
+
+27
+00:01:45,930 --> 00:01:50,490
+وبين الشباب التانيين طبعا، بالنسبة للمراجع، طبعا
+
+28
+00:01:50,490 --> 00:01:53,510
+فينا كتاب اسمه «Practical Hematology» ل«باربرا»،
+
+29
+00:01:53,510 --> 00:01:57,550
+كتاب خيم جدا، إن شاء الله ممكن أنزلكم نسخة منه PDF
+
+30
+00:01:58,140 --> 00:02:02,900
+طبعًا فينا Color Atlas of Hematology هذا بيحتوي
+
+31
+00:02:02,900 --> 00:02:07,320
+على صور كثيرة طبعًا أهم مرجع أو أكثر مرجع ممكن
+
+32
+00:02:07,320 --> 00:02:10,940
+تستفيد منه اللي هو الـInternet الصور لإن إحنا
+
+33
+00:02:10,940 --> 00:02:14,460
+عملنا معمل عبارة عن خاصة في المعامل الأولى بركزلي
+
+34
+00:02:14,460 --> 00:02:17,300
+على موضوع شكل الخلايا الطبيعية وشكل الخلايا
+
+35
+00:02:17,300 --> 00:02:20,300
+الطبيعية وكيف نميز من خلية طبيعية وخلية طبيعية في
+
+36
+00:02:20,300 --> 00:02:24,520
+حالة الطبيعية والأمراض، تمام؟ ‏- تمام ‏- طبعًا،
+
+37
+00:02:24,520 --> 00:02:27,270
+مراجعة ممكن نلتقطبعًا، احنا هتذكر عن موضوع
+
+38
+00:02:27,270 --> 00:02:30,130
+المحاضرات للـ «سلايدات» اللي بنزلكم بيها على الـ
+
+39
+00:02:30,130 --> 00:02:34,610
+«موديوم» إن شاء الله وطبعًا المجلد المراجعته طبعًا
+
+40
+00:02:34,610 --> 00:02:39,590
+طبعًا يعني كمراجع إفراء أقلكم في تنمية طبعًا
+
+41
+00:02:39,590 --> 00:02:45,200
+المادة أكثر بالنسبة لأقلكمطبعًا المادة زي ما
+
+42
+00:02:45,200 --> 00:02:48,800
+حكيتكم هي عبارة عن دراسة لمكونات الدم والخلايا
+
+43
+00:02:48,800 --> 00:02:51,920
+ودراسة الـ Hemoglobin وأنواع الـ Hemoglobin ودراسة
+
+44
+00:02:51,920 --> 00:02:55,840
+الأمراض المختلفة اللي لها علاقة بالدم زي الأنيميا
+
+45
+00:02:55,840 --> 00:03:01,320
+زي مثلًا مرأة أم الثلاثيميا وأمراض أخرىطبعًا الهدف
+
+46
+00:03:01,320 --> 00:03:03,900
+منها زي ما حكينا الدراسة طبعًا أنتوا هتاخدوا إن
+
+47
+00:03:03,900 --> 00:03:07,420
+شاء الله جزء نظري مع دكتور أحمد سلمي وهيثيركم
+
+48
+00:03:07,420 --> 00:03:11,640
+بنحكي المادة النظرية بشكل كبير جدًا وانا إن شاء
+
+49
+00:03:11,640 --> 00:03:14,840
+الله هنعطيكم جزء عملي بمثالة مع المادة النظرية
+
+50
+00:03:14,840 --> 00:03:18,420
+فهندرس الخلايا، هندرس تشخيص حالات الأنيميا، هندرس
+
+51
+00:03:18,420 --> 00:03:22,560
+اللوكيميا وهندرس طبعًا اللي هي تحضير الأفلام، الدم
+
+52
+00:03:22,560 --> 00:03:26,930
+وكيف نقدر الشخص عنهافعنا طبعاً المعمل الأول اللي
+
+53
+00:03:26,930 --> 00:03:29,870
+هو «Slight Vibration and Staining» حكيتكم إذا
+
+54
+00:03:29,870 --> 00:03:34,030
+بتذكروا إنه هذا المعمل هو يعني كان آخر معمل في
+
+55
+00:03:34,030 --> 00:03:38,510
+المقدمة حيكون إن هو دا أول معمل في الـHematology
+
+56
+00:03:38,510 --> 00:03:42,550
+المعمل الثاني، هندرس طبعاً الخلايا البيضة، كيف
+
+57
+00:03:42,550 --> 00:03:46,190
+نعمل differential بين صفائح دموية وإيش الـ… نحكي
+
+58
+00:03:46,190 --> 00:03:52,630
+الـabnormal morphology فيهاهنعمل برضه لندرس المعمل
+
+59
+00:03:52,630 --> 00:03:54,910
+التالت الـ Abnormal Morphology في الخلايا الحمرة
+
+60
+00:03:54,910 --> 00:03:58,510
+وكيف نشخصها المعمل الرابع هكون عندنا عن
+
+61
+00:03:58,510 --> 00:04:02,230
+Reticulocyte Count المعمل الخامس عن Sickle Cell
+
+62
+00:04:02,230 --> 00:04:06,350
+Anemia المعمل السادس هكون عندنا عن الـ Hemoglobin
+
+63
+00:04:06,350 --> 00:04:09,990
+A2 طبعا أحنا كل دراستنا هكون فترة حالية دراسة
+
+64
+00:04:09,990 --> 00:04:14,750
+نظريةلكن إن شاء الله في أول ما يصير فرصة لنا نروح
+
+65
+00:04:14,750 --> 00:04:19,270
+المعامل، نتغذينا كويس في ناحية النظرية، وندخل
+
+66
+00:04:19,270 --> 00:04:23,170
+العمل المباشرة، ونكون عندنا موضوع اللي إجراء تجربة
+
+67
+00:04:23,170 --> 00:04:27,190
+سهل جدا بإذن الله تعالى طبعا المعمل السابع يكون
+
+68
+00:04:27,190 --> 00:04:32,470
+على الـFeta-Hemoglobinالمعمل الثامن عن الـ
+
+69
+00:04:32,470 --> 00:04:36,950
+Metamoglobin المعمل التاسع عن الـ G6PD Deficiency
+
+70
+00:04:36,950 --> 00:04:41,230
+اللي هو مرض التفول وعنا المعمل العاشر عن الـ
+
+71
+00:04:41,230 --> 00:04:43,550
+Sacrosis السنة والمعمل الأحداشر عن اسم الـ
+
+72
+00:04:43,550 --> 00:04:48,190
+Defragility طبعاً لأن المعمل رقم 12 طبعاً يعتبر
+
+73
+00:04:48,190 --> 00:04:52,170
+معمل مهم جداً هنتكلم عن جهاز الـ CPC اللي بالتأكيد
+
+74
+00:04:52,170 --> 00:04:55,910
+اشتغلته عليه في فترة المقدمة في المعمل المقدمة
+
+75
+00:04:55,910 --> 00:05:00,550
+أكيد احنا عملناأه يا معاد، فضل اشتغلنا عليها و
+
+76
+00:05:00,550 --> 00:05:04,130
+أحكيها أه صحيح، أشتغلنا بتوعها و مشيتوا عينات
+
+77
+00:05:04,130 --> 00:05:07,810
+عليها بس لنعرف أحنا كيف مبدأه، على أي أساس بيشتغل،
+
+78
+00:05:07,810 --> 00:05:10,670
+العين اللي بمشيها في الجهاز، كيف بتروح، و أين
+
+79
+00:05:10,670 --> 00:05:14,330
+بتروح، إيش بيصير فيها، طب كيف بيقرأ الجهاز، كل هذا
+
+80
+00:05:14,330 --> 00:05:17,370
+ندرسه في معمل Automated Hematology Cell Counter
+
+81
+00:05:17,870 --> 00:05:21,830
+طبعًا، وآخر المعاملين، طبعًا هما آخر تلت معاملة
+
+82
+00:05:21,830 --> 00:05:25,570
+دولة أكبر نظرية بحتي، يعني مش ناحية عملية المعامل
+
+83
+00:05:25,570 --> 00:05:29,350
+الأخر، هذا ممكن تاخدوه في نظري أكتر، اللي هو «cell
+
+84
+00:05:29,350 --> 00:05:34,150
+maturation» وطبعًا تشخيص اللوكيميا، الأخر، طبعًا
+
+85
+00:05:34,150 --> 00:05:37,310
+المعاملة هيكون عن أنواع اللوكيميا وكيف نشخصها،
+
+86
+00:05:37,310 --> 00:05:44,290
+الأخرين طبعًا، هذي بشكل أساسي بالنسبة لـ… نحكي
+
+87
+00:05:44,290 --> 00:05:48,580
+المعاملة تبعتناهنوصل إن شاء الله، هتكون عندنا فرصة
+
+88
+00:05:48,580 --> 00:05:52,500
+لتنمية مهاراتنا في معمل الدم إن شاء الله، بدي أسأل
+
+89
+00:05:52,500 --> 00:05:59,760
+«سيف» دخل ولا لسه؟ لسه ما دخلش طب خلاص، يعني هذه
+
+90
+00:05:59,760 --> 00:06:04,280
+إن شاء الله مسجلة، هنحاول قدر مستوطنة إن شاء الله
+
+91
+00:06:04,280 --> 00:06:08,140
+نوصل إلى «سيف» وزي السفصار، ممكن إن شاء الله شرس
+
+92
+00:06:08,140 --> 00:06:14,140
+باق، هنوح لمعملنا حاليا الأولطبعا المعمل هذا أخدنا
+
+93
+00:06:14,140 --> 00:06:17,980
+.. إذا بتذكروا نفس المحاضرة تقريبا يعني في ال ..
+
+94
+00:06:17,980 --> 00:06:24,920
+شو اسمه؟ المقدم يعني دقيقة شباب، ده واقف بتزيل، بس
+
+95
+00:06:24,920 --> 00:06:30,000
+عشان التليفون من شغلها شوف
+
+96
+00:06:30,000 --> 00:06:33,960
+سيف، إيش صار معاه؟
+
+97
+00:06:38,130 --> 00:06:41,650
+وأنا معاك. طيب، أحنا هنكمل إن شاء الله أنا عملت
+
+98
+00:06:41,650 --> 00:06:46,210
+تكميل التسجيل إن شاء الله أنا هروح طبعاً هذه
+
+99
+00:06:46,210 --> 00:06:49,670
+بالنسبة للـOutline للمادة هروح هنا زي ما حكينا
+
+100
+00:06:49,670 --> 00:06:53,970
+المعمل الأول المعمل
+
+101
+00:06:53,970 --> 00:06:57,930
+الأول الـBlood اسمه، شايفين الـScreen معادي، أه؟
+
+102
+00:06:57,930 --> 00:07:02,290
+طيب، طيب، احنا إن شاء الله، بس خليني أنا أعملكم
+
+103
+00:07:02,290 --> 00:07:05,470
+الـ…
+
+104
+00:07:05,470 --> 00:07:10,210
+طيبالـ Blood Smear، طبعًا، هذا المعمل أخدناه في،
+
+105
+00:07:10,210 --> 00:07:13,930
+زي ما حكينا في المقدمة، آخر معمل كان عندنا طبعًا،
+
+106
+00:07:13,930 --> 00:07:17,210
+إذا بتذكروا، قولنا إحنا عندي تلت أنواع طرق في عمل
+
+107
+00:07:17,210 --> 00:07:21,490
+الـBlood Smear إذا بتذكروا، عندي الـCover Glass
+
+108
+00:07:21,490 --> 00:07:24,770
+Smear واللي بيستخدمان فيها الـCover Slide، تمام؟
+
+109
+00:07:24,770 --> 00:07:29,550
+وبيستخدم على Slide طبعًا، هذه الطريقة شوية تقنية
+
+110
+00:07:29,550 --> 00:07:32,670
+أو الـpractice بتاعها شوية صعبة نوعًا ما، عندي
+
+111
+00:07:32,670 --> 00:07:36,730
+الـ…–الكاميرات الصحيفة عنها آه يا معادما كانتش
+
+112
+00:07:36,730 --> 00:07:39,870
+تظبط معنا أساساً ماكانتش تظبط معايا لأنه بتغلب
+
+113
+00:07:39,870 --> 00:07:43,890
+شوية كانت تظبط معايا بس كانت تظبط معايا كشر محمد
+
+114
+00:07:43,890 --> 00:07:46,190
+اللي هي الوجه … اللي هي الولادتين اللي هي
+
+115
+00:07:46,190 --> 00:07:48,610
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+116
+00:07:48,610 --> 00:07:48,630
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+117
+00:07:48,630 --> 00:07:48,750
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+118
+00:07:48,750 --> 00:07:48,770
+هي الولادتين اللي هي الولادتين اللي هي الولادتين
+
+119
+00:07:48,770 --> 00:07:49,270
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+120
+00:07:49,270 --> 00:07:55,110
+الولادتين اللي هي الولادتين
+
+121
+00:07:55,110 --> 00:07:57,730
+اللي هي ال
+
+122
+00:08:00,670 --> 00:08:03,990
+طبعاً هذه كانت تقصد معاكم وإن شاء الله بس نروح على
+
+123
+00:08:03,990 --> 00:08:09,160
+المعامل هنعيد نعملها ونصبغ ال slide ونقرأهاعندي
+
+124
+00:08:09,160 --> 00:08:11,620
+نوع تالت هو «Spun Smear» زي اللي تذكره وقلتلكم هذا
+
+125
+00:08:11,620 --> 00:08:16,080
+عبارة عن استخدام جهاز خاص في الـ «سلايدات» وتحط
+
+126
+00:08:16,080 --> 00:08:19,740
+عليه نقطة دم مع نحكي الـ «كيت» خاص طبعا الـ «كيت»
+
+127
+00:08:19,740 --> 00:08:24,020
+هذا بنحط عليه الـ «سلايد» مع نقطة الدم وهو بفردلي،
+
+128
+00:08:24,020 --> 00:08:27,400
+بعملي الـ «distribution» لفرد الخلايا متجانس 100%
+
+129
+00:08:27,400 --> 00:08:32,220
+طبعا «Spun Smear» كنا نستخدمها أحنا في عملية أنه
+
+130
+00:08:32,220 --> 00:08:35,460
+نقرأ الـ «differential» أو شيء خاصة في حالات في
+
+131
+00:08:35,460 --> 00:08:39,790
+الكيميابتوزع الخلايا بشكل متجانس طبعا في عندي
+
+132
+00:08:39,790 --> 00:08:43,070
+نوعين تانية يستخدموها في حالات خاصة اللي مافي قوة
+
+133
+00:08:43,070 --> 00:08:45,210
+تسمية وهذه في حالة إذا كان عندك بعض الحالات اللي
+
+134
+00:08:45,210 --> 00:08:49,010
+بيكون عندها الخلايا البيضا أقل من ألف كدهش نور
+
+135
+00:08:49,010 --> 00:08:56,170
+مريج لخلايا البيضا سعيد؟ 8000 كدهش؟ 8000 تقريبا من
+
+136
+00:08:56,170 --> 00:09:00,240
+4000 ل 11000فبالحالة اللي كانت عندك Lycopenia إذا
+
+137
+00:09:00,240 --> 00:09:03,840
+بتذكروا Lycopenia هو نقص في خلايا البيضة، الحال هي
+
+138
+00:09:03,840 --> 00:09:06,420
+أنا بستخدم الـBuffie Smear، الـCoat Smear، طبعا
+
+139
+00:09:06,420 --> 00:09:10,420
+باخد العينة، بـCenterها و باخد من الـBuffie Coat،
+
+140
+00:09:10,420 --> 00:09:13,540
+بحطها على الـBlood Film و نفرضها، ممكن إن شاء الله
+
+141
+00:09:13,540 --> 00:09:17,820
+نعملها إحنا، في نوع اللي بيسموه الـThick Blood
+
+142
+00:09:17,820 --> 00:09:20,560
+Smear، هذا بيستخدمها في حالات، إن أنا دول بيشوف
+
+143
+00:09:20,560 --> 00:09:24,000
+حالات الـParasite، خاصة الملارياطبعًا الـ Malaria
+
+144
+00:09:24,000 --> 00:09:27,600
+بنعرف أنه موجود داخل الخلايا الحمراء لو بنتخب الـ
+
+145
+00:09:27,600 --> 00:09:31,280
+Butch Smear فبالتالي أنا مش هقدر أني أنا أشوف
+
+146
+00:09:31,280 --> 00:09:34,420
+البراثايد لأنه هكون عدده قليل وصعب جدًا أني أميزها
+
+147
+00:09:34,420 --> 00:09:39,160
+لكن بالحالة بستخدم الـ Thick Smear بتقدر أني أتميز
+
+148
+00:09:39,160 --> 00:09:43,420
+الخلايا وتقدر أنه لو كان مثلًا نحكي عدد البراثايد
+
+149
+00:09:43,420 --> 00:09:48,620
+قليلة بقدر أني أشخص الحالة الحقيقية، تمام؟طبعًا
+
+150
+00:09:48,620 --> 00:09:51,440
+العينات المستخدمة أحنا في الـWedge Smear اللي هي
+
+151
+00:09:51,440 --> 00:09:54,920
+عينة الـEdita طبعًا هي العين الـCPC نفسها لازم
+
+152
+00:09:54,920 --> 00:09:58,920
+تكون fresh مستخدم خلال ساعتين إلى تلت ساعات طبعًا
+
+153
+00:09:58,920 --> 00:10:03,200
+– زي هذا يا دكتور – هذا لأ، هذا يعتبر Chemistry
+
+154
+00:10:03,200 --> 00:10:05,960
+Tube هذا، مش Edita أنا مش شايف، اللي هو اللي هو
+
+155
+00:10:05,960 --> 00:10:10,880
+أحمر الغطاية، محمد؟ – لأ، الفكرة مكتوبة على Edita
+
+156
+00:10:10,880 --> 00:10:12,860
+– اللي هو Edita صح، اللي هو غطاية غلط، اللي هو
+
+157
+00:10:12,860 --> 00:10:15,600
+غطاية غلط، لازم الغطاية يكون Perpet – لأ، لأ، صح
+
+158
+00:10:15,600 --> 00:10:20,340
+كلامك، صحالغطايب محطوطة غلط، لأنه غالبًا يكون لونه
+
+159
+00:10:20,340 --> 00:10:23,500
+purple أو أزرق، وغالبًا purple، مكتوب على إيده ده
+
+160
+00:10:23,500 --> 00:10:28,880
+صحيح. طبعًا، لأ، فيه إن طبعًا، ليش أنا، ليش أنا
+
+161
+00:10:28,880 --> 00:10:33,940
+أول شي ب .. طبعًا بستخدم فرش اسمه blood، عشان
+
+162
+00:10:33,940 --> 00:10:37,340
+مايصيحش عندي تغيرات في الخلايا الحمرة، يعني نقطة
+
+163
+00:10:37,340 --> 00:10:40,620
+مهمة. وهي وضرف تبعاته. بيصيح تغيرات في خلايا الدم
+
+164
+00:10:40,620 --> 00:10:43,260
+الحمرة، وبيصير زي عملية .. انه بيصير زي
+
+165
+00:10:43,260 --> 00:10:46,950
+Speculated، بيصير زي أكيد إنها من شرية،وهذه، في
+
+166
+00:10:46,950 --> 00:10:50,010
+عندي بعض الحالات بيكون في أصلًا هي عبارة عن سموها
+
+167
+00:10:50,010 --> 00:10:52,830
+«crenated» أو «speculated» طبعًا اللي هي «Spar»
+
+168
+00:10:52,830 --> 00:10:55,830
+وطبعًا هذه الخلايا في حالات مرضية لكن هنا بيكون مش
+
+169
+00:10:55,830 --> 00:11:00,610
+مرضية سببها اللي هي درجة الحرارة أو الـ «old
+
+170
+00:11:00,610 --> 00:11:05,090
+specimen»، تمام؟ طبعًا، متى بيصير هذه الحالات الـ
+
+171
+00:11:05,090 --> 00:11:07,150
+«crenated»؟ تمحك هنا، في حالة إنه عندي
+
+172
+00:11:07,150 --> 00:11:11,510
+الـAnticoagulant كميته أكتر من العينة، كيف يعني؟
+
+173
+00:11:11,780 --> 00:11:15,040
+إحنا بنعرف إحنا عندي مثلا الـ Tube Medical Editor
+
+174
+00:11:15,040 --> 00:11:18,480
+موجود معاك يا محمد، إيش مكتوب عليه كمية الدم؟
+
+175
+00:11:18,480 --> 00:11:22,540
+مكتوب إنك تحط مل تلاتة مل تلاتة مل، هجيت لو حطيت
+
+176
+00:11:22,540 --> 00:11:25,880
+أقل من تلاتة مل، حطيت واحد مل، تسيطر عملية الـ
+
+177
+00:11:25,880 --> 00:11:28,140
+Ratio بين الـAnticoagulant اللي هو الـEditor اللي
+
+178
+00:11:28,140 --> 00:11:31,960
+موجودة في الـTube، و الدم تختلف، فهذه تؤدي لغيرات
+
+179
+00:11:31,960 --> 00:11:36,700
+شكلية في الخلايا نفسها، تمام؟ في نقطة تانية تؤدي
+
+180
+00:11:36,700 --> 00:11:39,880
+لكرينية الـ…………………………………………………………
+
+181
+00:11:41,810 --> 00:11:45,830
+بينفع شجر المنتلات، هشوف عليه، يعني هو مش زي مثلًا
+
+182
+00:11:45,830 --> 00:11:49,410
+إذا معمل مثلًا إن شاء الله لنا نزهب، هنكون عملية
+
+183
+00:11:49,410 --> 00:11:53,090
+ال ratio high مهم جدًا كتير بالنسبة للدم والـ
+
+184
+00:11:53,090 --> 00:11:56,570
+Atomic Aggregate بالنسبة للمعمل الـ Nephematology،
+
+185
+00:11:56,570 --> 00:12:00,530
+هي مهمة، مهمة، يعني لكن مش، يعني بنقدر نتجوزها،
+
+186
+00:12:00,530 --> 00:12:03,650
+لكن مش أنه نتجوزها بشكل كبير، يعني كيف مثلًا، أنا
+
+187
+00:12:03,650 --> 00:12:07,850
+لوعند المطلوب إن أحط تلاتة، وروح وحطيت اتنين ونص،
+
+188
+00:12:07,850 --> 00:12:12,610
+بمشيها عادي عادي، لكن ماحطش واحد، ماحطش نص لأنه
+
+189
+00:12:12,610 --> 00:12:15,170
+مثلا إن أحط نص، لو فرض أن أنا فيها point 2 ml
+
+190
+00:12:15,170 --> 00:12:18,610
+وحطيت نص ال ratio بينهم هيخلف، هتؤدي الاختلاف حتى
+
+191
+00:12:18,610 --> 00:12:21,190
+في توزيع الخلايا وبالتالي، هتؤدي الاختلاف في حجم
+
+192
+00:12:21,190 --> 00:12:25,350
+الخلايا بالنسبة للـ Antibiotic لو تؤدي الاختلاف في
+
+193
+00:12:25,350 --> 00:12:28,250
+عملية القراءة في جهة الـCBC ممكن فهذه النقطة مهم
+
+194
+00:12:28,250 --> 00:12:33,320
+جدا بالنسبة لل ratioعندي السبب التاني اللي يؤدي
+
+195
+00:12:33,320 --> 00:12:36,100
+لـCrenated يعني أحد أسباب اللي يؤدي لـCrenated
+
+196
+00:12:36,100 --> 00:12:40,220
+طبعًا اللي بنسميها أحنا الحالات، مش مرضية هاي،
+
+197
+00:12:40,220 --> 00:12:43,080
+اللي هي Old Specimens في عندي بذلة بحكي عنها برضه
+
+198
+00:12:43,080 --> 00:12:45,780
+الحرارة، في حالة الحرارة تؤدي لـCrenated دور
+
+199
+00:12:45,780 --> 00:12:48,560
+الـCrenated، الثاني تلت أسباب تؤدي لدور
+
+200
+00:12:48,560 --> 00:12:55,720
+الـCrenated طبعًا للحالات الـNormal دكتور، أه محمد
+
+201
+00:12:55,720 --> 00:12:59,020
+–بعدين أتفض على الـslide اللي بتشرح عليها – تمام
+
+202
+00:13:02,780 --> 00:13:07,480
+الثلاث حالات اللي تؤدي للحالات الغير مرضية اللي هي
+
+203
+00:13:07,480 --> 00:13:14,360
+الحالات ال normal هي بالضبط ال old blood
+
+204
+00:13:14,360 --> 00:13:20,280
+و ال ratio تبقى هذا ال ratio amount of blood blood
+
+205
+00:13:20,280 --> 00:13:24,380
+blood blood blood blood blood blood blood blood
+
+206
+00:13:24,380 --> 00:13:24,620
+blood blood blood blood blood blood blood blood
+
+207
+00:13:24,620 --> 00:13:26,860
+blood blood blood blood blood blood blood blood
+
+208
+00:13:26,860 --> 00:13:26,920
+blood blood blood blood blood blood blood blood
+
+209
+00:13:26,920 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+210
+00:13:27,320 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+211
+00:13:27,340 --> 00:13:29,510
+blood blood bloodالـ Cernated بدأت بالحالة أن تكون
+
+212
+00:13:29,510 --> 00:13:33,550
+ملم فيها لأن هذه الحالة سببها مش مرضي طبعاً هذه
+
+213
+00:13:33,550 --> 00:13:36,410
+كيف تعرفها؟ هذه تعرفها إنه مثلا أنا مالاج عامل
+
+214
+00:13:36,410 --> 00:13:40,090
+عصلاية هلاقي إنه عملية الـ Cernated مش مسك لكل RBC
+
+215
+00:13:40,090 --> 00:13:43,870
+هتلاقي بعض المناطق فيها Cernated وبعض المناطق لأ،
+
+216
+00:13:43,870 --> 00:13:46,930
+تمام؟ هتلاقي بعض الخلايا أه وبعض الخلايا لأ، في
+
+217
+00:13:46,930 --> 00:13:48,730
+الحياة المرضية لأ، بيكون معظم الخلايا فيها
+
+218
+00:13:48,730 --> 00:13:52,310
+Cernated في الحياة المرضية ليست بره، تمام؟هل جيت
+
+219
+00:13:52,310 --> 00:13:56,390
+الحلقات اللي نحكي الـ «normal» ويكون أصلًا سببها
+
+220
+00:13:56,390 --> 00:14:00,610
+نحكي خارجي، يعني مش مرضي، اللي هي زي ما حكينا ليه
+
+221
+00:14:00,610 --> 00:14:04,010
+الـRatio Anticagulant للـOil Displacement والـWarm
+
+222
+00:14:04,010 --> 00:14:11,970
+Environment، تمام؟ محمد
+
+223
+00:14:11,970 --> 00:14:17,790
+تمام؟ ما سمع ناس آه
+
+224
+00:14:17,790 --> 00:14:26,180
+سامعدعوتي نرجع للـ slide، فيه عندك سؤال بيها؟
+
+225
+00:14:26,180 --> 00:14:33,260
+بس ما تغيرت ال slide عندى، انا
+
+226
+00:14:33,260 --> 00:14:41,260
+رجعتلها، ما تغيرش انتي عندى، ايه ال slide اللي قمت
+
+227
+00:14:41,260 --> 00:14:42,740
+بإيديك؟
+
+228
+00:14:49,920 --> 00:14:53,500
+محمد slide high؟ لا بتغير الشاشة عندك قاعد كله
+
+229
+00:14:53,500 --> 00:14:59,440
+ثابت عند الكل طب ليش؟ هو عندك كمان ثابت عند ال
+
+230
+00:14:59,440 --> 00:15:06,080
+outline كله موجود عند ال outline عندك؟ آه كله كله
+
+231
+00:15:06,080 --> 00:15:09,060
+عند ال outline الشاشة اللي واضحة عند ال outline
+
+232
+00:15:09,060 --> 00:15:14,980
+أنا ومحمد نفس القصة طب هيك؟ أيوة هيك اتغيرت صحيح؟
+
+233
+00:15:14,980 --> 00:15:18,400
+هيك اتغيرت ناحية ال practical hematology تجيبني
+
+234
+00:15:18,400 --> 00:15:22,010
+على slide B now؟أنواع الـ، شو اسمها؟ الاسمية،
+
+235
+00:15:22,010 --> 00:15:25,610
+شفتوها؟ آه تمام، تمام هاي ال slide دلك يا إمحمد،
+
+236
+00:15:25,610 --> 00:15:29,890
+هاي؟ تمام، هاي، هاي، هاي قدام إيش سؤالك فيها يا
+
+237
+00:15:29,890 --> 00:15:33,110
+إمحمد؟
+
+238
+00:15:33,110 --> 00:15:41,310
+يا إمحمد؟
+
+239
+00:15:41,310 --> 00:15:44,950
+دكتورة
+
+240
+00:15:44,950 --> 00:15:50,370
+آه، معذرعشان بقيتها في الـ Wedge بالـBlood Smear
+
+241
+00:15:50,370 --> 00:15:56,350
+مكتوب «Collected to Mark of You»، إيش يعني؟ ليه؟
+
+242
+00:15:56,350 --> 00:16:00,390
+حكيناها الـRatio، يعني أنت بدك تسحب اللي عندك
+
+243
+00:16:00,390 --> 00:16:04,350
+علامة، في عندك علامة، أه، بدك تسحب اللي عندك علامة
+
+244
+00:16:04,350 --> 00:16:07,470
+أو تحط نفس الكمية ليه 3 ML زي ما موجود عند محمد 3
+
+245
+00:16:07,470 --> 00:16:12,510
+ML، في عندك الـDepartment، أي Mark، يكون 3 ML أو
+
+246
+00:16:12,510 --> 00:16:17,350
+في Mark، يكون علامة، تمام، تمام، فهمت، فهمتطيب،
+
+247
+00:16:17,350 --> 00:16:23,390
+السمير احنا؟ دخل سيف ولا لسه؟ اه دخل، هاي صوت
+
+248
+00:16:23,390 --> 00:16:29,030
+موجود ايه و أيه يا عم، معاكوا هففتح كاميرا غنيه،
+
+249
+00:16:29,030 --> 00:16:33,730
+بياخد أهلا، طيب، احنا .. نسمينا الشباب عشان وقت
+
+250
+00:16:33,730 --> 00:16:39,010
+وعمل وقت طبعا ال procedures أخدناها قبل ذلك، زي ما
+
+251
+00:16:39,010 --> 00:16:43,540
+حكينا، ملحوطعلى الـ «سلايد» إذا تذكرونه، نجيب
+
+252
+00:16:43,540 --> 00:16:48,060
+سلايد ثاني بزاوية تلاتي إلى أربعين درجة، وبعدين
+
+253
+00:16:48,060 --> 00:16:54,100
+نفردها بطريقة طبعا سالسة، مش جيركي مانار، تمام؟
+
+254
+00:16:54,100 --> 00:16:59,890
+نخلّي الـ«بلاد»، الفيلم، ينشفوبعد ذلك طبعًا نسبقها
+
+255
+00:16:59,890 --> 00:17:04,570
+طبعًا في نقاط مهم جدًا اللي هي عملية الزاوية كل ما
+
+256
+00:17:04,570 --> 00:17:09,530
+زادت الزاوية طبعًا كل ما صار طبعًا الطول أقل ويصير
+
+257
+00:17:09,530 --> 00:17:13,530
+السمي ال «thick» أكتر يعني أنا هاي slide أنا
+
+258
+00:17:13,530 --> 00:17:15,610
+ماعنديش اللي كان لو عندي اللي كان الرجل اللي كان
+
+259
+00:17:15,610 --> 00:17:20,370
+فهي عندي slideين شايفين بالفيديو تمام؟عطيت، أنا
+
+260
+00:17:20,370 --> 00:17:23,850
+هذه الزاوية كل ما قلعت الزاوية كان عندي الطول أكتر
+
+261
+00:17:23,850 --> 00:17:29,430
+والسمير ثم أكتر، لو أحط زاوية أكتر بيصير thick
+
+262
+00:17:29,430 --> 00:17:33,210
+فانا لو بدي ديها thicker أكتر، بدي إيه عشان أعمل؟
+
+263
+00:17:33,210 --> 00:17:36,810
+أزيل الزاوية، تمام؟ تحكم بالزاوية وابقى دي اللي
+
+264
+00:17:36,810 --> 00:17:40,470
+بيحكم في نوع السمير و الـquality للسمير دبعتنا،
+
+265
+00:17:40,470 --> 00:17:45,190
+طبعا هذه الصورة توضحيةبنحط drop، وبعدين بنجيب الـ
+
+266
+00:17:45,190 --> 00:17:48,690
+«سلايد» الثاني بزاوية 30 إلى 40 ونفردها بطريقة
+
+267
+00:17:48,690 --> 00:17:53,810
+سلسة هاي الـSmear، طبعاً، شايفينها، بنخليها تنشف
+
+268
+00:17:53,810 --> 00:17:57,810
+وبعد ذلك بنعملها Fixation بواسطة الـMethanol
+
+269
+00:17:57,810 --> 00:18:04,170
+وبنعملها Staining طبعاً الـArtifacts، أيش يعني
+
+270
+00:18:04,170 --> 00:18:08,460
+Artifacts يا معاد؟ الأثار تبعتهاالـ Artifacts ليه
+
+271
+00:18:08,460 --> 00:18:13,800
+أي شغلة تؤدي لطبعًا ظهور، يعني نحكي الـ «زمير» مش
+
+272
+00:18:13,800 --> 00:18:16,820
+بالـ Quality صح، إن أنا برفضها. لا، يعني مضاعفات،
+
+273
+00:18:16,820 --> 00:18:20,240
+ما بنتحكي عنها. مش، مش، يعني شغلات شوائب، نحكي. هي
+
+274
+00:18:20,240 --> 00:18:23,460
+Artifacts يعني شوائب، تمام؟ أوكي، أوكي. أول شي،
+
+275
+00:18:23,460 --> 00:18:26,980
+العملية الفرد تكون غلط، هتؤدي لظهور Artifacts. أنت
+
+276
+00:18:26,980 --> 00:18:29,500
+جيت فردت، ماعرفت تبعتش زاوية 30 إلى 40، وماعرفت
+
+277
+00:18:29,500 --> 00:18:34,240
+تعمل زاوية مثلًا 50، هتؤدي لظهور «زمير» قصيرة و
+
+278
+00:18:34,240 --> 00:18:38,490
+«very thick»، مش هيكون كويس لقراية فيلم.أنت ممكن
+
+279
+00:18:38,490 --> 00:18:42,770
+تكون عندك عملية الـHumidity أدت إلى Slow-drying
+
+280
+00:18:42,770 --> 00:18:47,490
+تؤدي لظهر الـArtifacts عملت الـFixation طولت فيها،
+
+281
+00:18:47,490 --> 00:18:49,630
+روح سفررت بالاسمير وخلت تانية وعملت الـFixation
+
+282
+00:18:49,630 --> 00:18:53,130
+برضه غلط أصول أول ما تنشف الـSlide عملها
+
+283
+00:18:53,130 --> 00:18:58,330
+الـFixation وجود المي في الـMethanol إذا كان موجود
+
+284
+00:18:58,330 --> 00:19:02,590
+المي أكتر من 3% في الحالة هذه لازم أنا أيش برضه أن
+
+285
+00:19:02,590 --> 00:19:05,630
+أتجنب وجود المي في المي لأن المي تعمل Artifacts
+
+286
+00:19:07,460 --> 00:19:10,740
+طبعًا، عندي بعض الحالات المرضية تؤدي لظور الـ
+
+287
+00:19:10,740 --> 00:19:14,020
+Artifacts زي مثلًا، إذا كان عندك عدد الخلايا الـ
+
+288
+00:19:14,020 --> 00:19:17,080
+lymphocytes عالية أحنا بنعرف إن الـ lymphocytes
+
+289
+00:19:17,080 --> 00:19:23,930
+عبارة عن خلايا بنواة واحدةطبعًا هذه الـ
+
+290
+00:19:23,930 --> 00:19:29,570
+lymphocytes دلوقت تحكي هشة، fragile مجرد إنك أنت
+
+291
+00:19:29,570 --> 00:19:32,970
+لو كان العدد كبير ومجرد أنك عملت خرد لإلها ممكن
+
+292
+00:19:32,970 --> 00:19:35,550
+تتكسر إذا كانت بعداد كبيرة أو في بعض الحالات
+
+293
+00:19:35,550 --> 00:19:39,870
+المرضية زي مثلًا اللوكيميا اللي هي CLL-Chronic
+
+294
+00:19:39,870 --> 00:19:42,970
+Lymphocytic Leukemia أو الـAcute Leukemia فهذه
+
+295
+00:19:42,970 --> 00:19:48,470
+تؤدي لظهر Artifacts، فما نتكسر عفوا ما نتكسر في
+
+296
+00:19:48,470 --> 00:19:51,890
+الحالة هذه مش هتظهر عندك خلايا، هتظهر عندك بقايا
+
+297
+00:19:51,890 --> 00:19:57,320
+خلايااللي هي ممكن تظهر النواة، ممكن تظهر مثلًا
+
+298
+00:19:57,320 --> 00:20:01,500
+الـ«سيرفريبلانت» اللحال حسب، تمام؟ عندك تغييرات
+
+299
+00:20:01,500 --> 00:20:04,500
+برضه تصير الـGenerative Changes اللي هي بتصير في
+
+300
+00:20:04,500 --> 00:20:08,340
+عملية الـStorage، كيف يعني؟ أنا أخدت عينيتي الدم،
+
+301
+00:20:08,340 --> 00:20:12,820
+وراح محمد بدل ما يروح يعمل Blood Film منها، راح
+
+302
+00:20:12,820 --> 00:20:16,260
+إشعمال، خلّاها في التلاجة أو خلّاها مثلًا في
+
+303
+00:20:16,260 --> 00:20:20,400
+الغرفة لثاني يوم، ثاني يوم هسيب عندك تغييرات على
+
+304
+00:20:20,400 --> 00:20:31,600
+الخلايا، النواة، تمام؟تمام طبعاً
+
+305
+00:20:33,010 --> 00:20:37,570
+خصائص الـ… الـ «Blood Film» الكويس هذه الخصائص
+
+306
+00:20:37,570 --> 00:20:41,730
+«Blood Film» كويس اللي هي طبعاً خدناها برضه أهم
+
+307
+00:20:41,730 --> 00:20:45,410
+خاصية أنه زي ما حكينا يكون «thick» at one end
+
+308
+00:20:45,410 --> 00:20:48,270
+«thin» out of the smooth، يعني كيف يعني؟ أن
+
+309
+00:20:48,270 --> 00:20:51,130
+الـ«Blood Film» بالبداية يكون «thick» وفي النهاية
+
+310
+00:20:51,130 --> 00:20:53,910
+يكون «thin» واحنا بنقرأ، إذا بتذكروا، بنقرأ من
+
+311
+00:20:53,910 --> 00:21:00,110
+المنطقة اللي في الوسط، صحيح سعيد؟ صحيح، صحيح، ده
+
+312
+00:21:00,110 --> 00:21:05,990
+معايا، تمامالشغل التاني تكون عندك تحتوي يعني Slide
+
+313
+00:21:05,990 --> 00:21:09,790
+تلتينها تقريبًا موجود للفيلم نفسه الشغل التالتة
+
+314
+00:21:09,790 --> 00:21:14,890
+أنه ما تلمسش الحافة وآخر شيء تكون أن الـ «حواط»
+
+315
+00:21:14,890 --> 00:21:19,210
+ربعتها مافيش فيها شراشين نحكي أنه «margin free»
+
+316
+00:21:19,210 --> 00:21:22,170
+ولا يكون مسك الحواط على اليمين وعشمال يعني يكون
+
+317
+00:21:22,170 --> 00:21:27,630
+بعيد عن الحواط هذه خاصات مدفلم اللي كويس هيها
+
+318
+00:21:27,630 --> 00:21:32,250
+«thick»من أثنين إلى أثنين برنامج تانية، طبعًا إحنا
+
+319
+00:21:32,250 --> 00:21:36,310
+بالمنطقة اللي بقرا فيها اللي هي الـ Advocate Area،
+
+320
+00:21:36,310 --> 00:21:38,210
+الـ Thick Area ماقراش منها ولا Skin Area بقرا
+
+321
+00:21:38,210 --> 00:21:43,190
+منها، بقرا من منطقة الـ Advocate Area هذي، هذي بعض
+
+322
+00:21:43,190 --> 00:21:47,850
+الـ «الذنوب»، بالنص، مش بالنص، مش شرط بالنص، حسب
+
+323
+00:21:47,850 --> 00:21:51,170
+توتيم بلاد فيلم، حسب فيلم، بلاد فيلم للسوق، أجيتها
+
+324
+00:21:51,170 --> 00:21:55,940
+أنا عنديبعض أنواع الـ Blood Film اللي هي تقريبًا
+
+325
+00:21:55,940 --> 00:21:59,420
+تعتبرش كويسة أنا ممكن أعتبرها كديه نوعًا ما كويس،
+
+326
+00:21:59,420 --> 00:22:03,200
+بس مش كتير يعني، تمام؟ فأنتوا شايفينها، شايفها سيد
+
+327
+00:22:03,200 --> 00:22:09,160
+أنتي؟ آه، آهبإي اي و بي و سي و دي ممتاز اي و بي و
+
+328
+00:22:09,160 --> 00:22:12,480
+سي سيئة جدا، دي نوعا ما كويسة لكن ماعتبراش كويسة
+
+329
+00:22:12,480 --> 00:22:16,460
+لإنه مش بي .. أنا بالنسبالي بعتبرها مش كتير، لإن
+
+330
+00:22:16,460 --> 00:22:20,720
+مش بيعطياني finger shape مش ما .. مش طولتين ال
+
+331
+00:22:20,720 --> 00:22:24,160
+slide تقريبا، تمام؟ هو اللي .. اللي احنا تبقى نوعا
+
+332
+00:22:24,160 --> 00:22:31,100
+ما أحسن من الواقعين، ما تطلعوا إنتي إيه؟ كيف؟
+
+333
+00:22:31,100 --> 00:22:35,530
+دي أفضلدي أفضل من القراءة لكن بعتبرها شانة كويسة،
+
+334
+00:22:35,530 --> 00:22:39,230
+بالنسبالي أنا لو بقيمها بقيمها تقريبا تلاتة أو
+
+335
+00:22:39,230 --> 00:22:43,750
+أربع من خمس بس، فهمنا كيف؟ بس أحسن من الـA و أحسن
+
+336
+00:22:43,750 --> 00:22:44,650
+من الـB و أحسن من الـC
+
+337
+00:22:48,030 --> 00:22:50,750
+بالظبط، هذه أنواع سيئة جدًا كلها من البلاد في
+
+338
+00:22:50,750 --> 00:22:53,870
+الأمور واحدة فيها كويسة، شايفين؟ طبعًا هنا شايفين
+
+339
+00:22:53,870 --> 00:22:56,930
+الـMargins كيف شايفش، هذه عندي الهواف شرشير بـ12
+
+340
+00:22:56,930 --> 00:23:00,210
+قراءة، هذه جاي متقطعة، فبالتالي مافيش فيها، نحكي
+
+341
+00:23:00,210 --> 00:23:03,130
+زي «genus» في عملية الـ«thickness»، هذه قصيرة، هذه
+
+342
+00:23:03,130 --> 00:23:09,110
+رفيعة، هذه فيها، نحكي زي الفقاعات تمام، فيها
+
+343
+00:23:09,110 --> 00:23:13,170
+«holes»، وهذه بالجاي متجنسية، وهذه طبعًا فيها رقم
+
+344
+00:23:13,170 --> 00:23:18,550
+«C» إيش مالها؟ رقم إيش «C»؟يعني مش معتادة طولتين،
+
+345
+00:23:18,550 --> 00:23:20,950
+مش مازي .. مش جاي أنه .. طبعا هان thick، هان مش زي
+
+346
+00:23:20,950 --> 00:23:24,290
+ثن كتير، تمام؟ ممكن أنت تقرأها، بدك تقرأ منطقة هاي
+
+347
+00:23:24,290 --> 00:23:26,690
+مش هتعرف تقرأها كويس، بدك منطقة تقرأ بيها كويس،
+
+348
+00:23:26,690 --> 00:23:30,550
+يعني نهاية الرقم C ممكن أنه حط الزاوية عالي شوية،
+
+349
+00:23:30,550 --> 00:23:33,530
+لو نزل الزاوية شوية صغيرة وفرد، ال cancer تضمع
+
+350
+00:23:33,530 --> 00:23:39,550
+أكتر طبعا طب
+
+351
+00:23:39,550 --> 00:23:45,160
+دكتور بعد إذنك، بس ارجع الصورة اللي قبل شويةأقرأ
+
+352
+00:23:45,160 --> 00:23:49,800
+من الصورة E يعني أحسن هدولة كلهم الـ E فيها يا سيد
+
+353
+00:23:49,800 --> 00:23:54,100
+فيها كتير يعني جاي مش خلّي .. يعني شوف المسافة بين
+
+354
+00:23:54,100 --> 00:23:57,140
+الحفة و بينها الدم تقريبا نفس المسافة دي الدم نفسه
+
+355
+00:23:57,140 --> 00:24:03,220
+هذه تقدر عالم توزيع صح للخلايا آه تمام تمام طيب
+
+356
+00:24:06,410 --> 00:24:09,930
+عندي بعض الحالات اللي ممكن تظهر كأنها حالات مرضية
+
+357
+00:24:09,930 --> 00:24:12,590
+لكنها فعليًا مش حالات مرضية هي حالات نتيجة
+
+358
+00:24:12,590 --> 00:24:14,910
+الـBlood Firm نفسها يعني ممكن تظهر في الـThin Area
+
+359
+00:24:14,910 --> 00:24:17,690
+الخلايا تظهر معايا إشي بيسميه الـSterocytes
+
+360
+00:24:17,690 --> 00:24:21,290
+الـSterocytes هي عبارة عن خلية حمرة، عبارة عن خلية
+
+361
+00:24:21,290 --> 00:24:26,650
+حمرة طبعًا تظهرش فيها، نحكي، مش عارف بتظهر عندنا
+
+362
+00:24:26,650 --> 00:24:29,710
+فراغ اللي هم مجلوبين تقريبًا طولة فراغ وطولتين فيه
+
+363
+00:24:29,710 --> 00:24:33,370
+كإن هم مجلوبين، خلايا الحمرة فهي الخلية الحمرة،
+
+364
+00:24:33,370 --> 00:24:34,290
+خليني إذا بقدر أنا
+
+365
+00:24:38,550 --> 00:24:41,790
+المهم الخلايا تظهر فيها حالة بيسموها Spherocytosis
+
+366
+00:24:41,790 --> 00:24:44,950
+طبعا هذه بيكون خلايا حمرا فلاتيا مفيش فيها area
+
+367
+00:24:44,950 --> 00:24:47,410
+اللي يجمه جلبيا، هذه طبعا في thin area فانا
+
+368
+00:24:47,410 --> 00:24:50,850
+مابقراعش منها، ومنطقة ال thick area تظهر في خلايا
+
+369
+00:24:50,850 --> 00:24:52,890
+كأنها متجمعة ببعض زي الـRolling Formation،
+
+370
+00:24:52,890 --> 00:24:55,450
+الـRolling Formation ممكن متخسرة مع بعض لبعض
+
+371
+00:25:04,300 --> 00:25:07,820
+طلع علي، هلجيت الخلايا الحمرة، هي الخلية الحمرة مش
+
+372
+00:25:07,820 --> 00:25:11,100
+عارف ارسم بكتير انا لإن طبعا هي خلية حمرة هلجيت
+
+373
+00:25:11,100 --> 00:25:16,300
+بنص يكون عندى هجر لإنسان بتلهم مجلوبين، صح؟ فاضية،
+
+374
+00:25:16,300 --> 00:25:24,200
+نص white، شايفينها؟ خليني
+
+375
+00:25:24,200 --> 00:25:29,400
+أشوف إذا بقدر أجيب ثمام، طلع علي، هي خلية حمرة،
+
+376
+00:25:29,400 --> 00:25:34,120
+نيح؟ هلجيت الخلية الحمرة هاي؟في الـHemoglobin
+
+377
+00:25:34,120 --> 00:25:44,360
+تلتينها تقريبًا شايفين؟
+
+378
+00:25:44,360 --> 00:25:46,660
+شايف يا محمد؟ شايف يا سيد؟ تلتين الـHemoglobin
+
+379
+00:25:46,660 --> 00:25:50,240
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+380
+00:25:50,240 --> 00:25:50,880
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+381
+00:25:50,880 --> 00:25:50,980
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+382
+00:25:50,980 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+383
+00:25:52,640 --> 00:25:56,540
+تمام، تمام،
+
+384
+00:25:56,540 --> 00:25:56,860
+تمام
+
+385
+00:26:03,470 --> 00:26:07,850
+يكون الخلية حمرة، جنبها خلية حمرة، جنبها خلية
+
+386
+00:26:07,850 --> 00:26:12,430
+حمرة، جنبها خلية حمرة، جنبها خلية حمرة كأنه خلايا
+
+387
+00:26:12,430 --> 00:26:16,150
+متجمع مع بعض، بيسموه «roller formation» إن الخلايا
+
+388
+00:26:16,150 --> 00:26:20,450
+كأنها ملزقة مع بعض في صمغ أو شغل هيكا صح إن أنا
+
+389
+00:26:20,450 --> 00:26:22,210
+الخلية الـ… طبعا هذه الـ«roller formation» مش أنا
+
+390
+00:26:22,210 --> 00:26:24,510
+اللي سألت صح إن أنت المنطقة البقرة فيها يكون
+
+391
+00:26:24,510 --> 00:26:27,490
+الخلايا الحمرة بالصورة هايهلجد؟ لو ظهرت عندي
+
+392
+00:26:27,490 --> 00:26:30,350
+الصورة high في المطبق اللي بقرا فيها بحكي إن شخص
+
+393
+00:26:30,350 --> 00:26:33,510
+عنده roll of formation roll of formation طبعا في
+
+394
+00:26:33,510 --> 00:26:37,230
+الحالات المرضية خاصة في حالات نحكي زيادة الألبومين
+
+395
+00:26:37,230 --> 00:26:40,230
+البروتينات بتظهر عندي الحالة high فroll of
+
+396
+00:26:40,230 --> 00:26:44,250
+formation طبعا بتظهر عندي في الحالة high في ال
+
+397
+00:26:44,250 --> 00:26:47,290
+thick area لكن في ال adequate area أصول ما تظهرش
+
+398
+00:26:47,290 --> 00:26:52,030
+في الحالة normal فيمنا roll of formation؟ في
+
+399
+00:26:52,030 --> 00:26:59,150
+الوقت؟ أه سعيدمعاذ طلع من الدادة و بديه يدخل مرة
+
+400
+00:26:59,150 --> 00:27:01,630
+تانية هجاله البرنامج بيقولوا please wait the
+
+401
+00:27:01,630 --> 00:27:04,030
+meeting cost و الـ «لتش» قدروا .. آه آه شوفتوا
+
+402
+00:27:04,030 --> 00:27:09,190
+شوفتوا دايما دخلوا دلوقت صحيح «سيف» سمعناه و كذا
+
+403
+00:27:09,190 --> 00:27:12,870
+بقى معنا «سيف»؟
+
+404
+00:27:12,870 --> 00:27:18,090
+تمام تمام معاكم تمام يا «سيف» أنت مش شايف الشاشة
+
+405
+00:27:18,090 --> 00:27:21,970
+طيبة أيوة
+
+406
+00:27:21,970 --> 00:27:26,250
+شايفطيب فرقتنا، طيب افهم ان انا رجعت لشو يعني
+
+407
+00:27:26,250 --> 00:27:30,150
+Spherocyte وشو رولوفورميشن؟ بس فادسناك بس دكتور
+
+408
+00:27:30,150 --> 00:27:33,430
+ايه دلنا اللي هو نقطة ال .. اللي هو ال formation
+
+409
+00:27:33,430 --> 00:27:37,170
+اللي لما بتظهر؟ طيب انا بدي اشوف شغل تاني ان شاء
+
+410
+00:27:37,170 --> 00:27:41,670
+الله اذا اجبرت اشوفها لأ لأ اللي هو ما تبتظهر ما
+
+411
+00:27:41,670 --> 00:27:46,250
+تبتظهر مش مشكلة مش مشكلة خليني اشوف بس انا اللهم
+
+412
+00:27:46,250 --> 00:27:46,930
+صح يا سيد محمد
+
+413
+00:27:55,570 --> 00:28:00,210
+طب كيف نظام الكوزات هيكون؟ مش مشكلة، نحن نتفق عليا
+
+414
+00:28:00,210 --> 00:28:03,590
+إن شاء الله، تقيل أقول؟ طيب، هذه محاضرة، هناخدها
+
+415
+00:28:03,590 --> 00:28:06,990
+لهم بعدين، طلع معايا هنا، طلعيا سعيد، طلعيا محمد،
+
+416
+00:28:06,990 --> 00:28:11,290
+شايفين؟ هذي الحالة، الـRBC بيكون مع بعض هنا،
+
+417
+00:28:11,290 --> 00:28:14,530
+شايفين الصورة؟ هذي بسبب الـRolling Formation،
+
+418
+00:28:14,530 --> 00:28:20,280
+بيكون الخلايا الحمرة متجمعة مع بعض زي stacks ofلو
+
+419
+00:28:20,280 --> 00:28:25,960
+كيف نجيب قطعة نقضية عشرة شكل مع بعض طبعا وتعملهم
+
+420
+00:28:25,960 --> 00:28:32,800
+جوجب بعض مفتحتش لسه ثواني لسه مفتحتش لسه مفتحتش ال
+
+421
+00:28:32,800 --> 00:28:40,400
+slide طيب
+
+422
+00:28:40,400 --> 00:28:46,700
+زعيطة تعمل ده؟ معلق نبين حركي الموسيقى تكتر شوية
+
+423
+00:28:46,700 --> 00:28:52,190
+أنا لازم مفتحتش علاجيأهلا وسهلا يا عزيزي كمان كمان
+
+424
+00:28:52,190 --> 00:28:54,410
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+425
+00:28:54,410 --> 00:28:54,470
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+426
+00:28:54,470 --> 00:28:54,730
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+427
+00:28:54,730 --> 00:29:04,430
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+428
+00:29:04,430 --> 00:29:07,770
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+429
+00:29:07,770 --> 00:29:12,930
+كمان كمان كمان كمان كمان
+
+430
+00:29:12,930 --> 00:29:16,390
+كمان كمان
+
+431
+00:29:16,390 --> 00:29:23,110
+كمان كمطبعًا؟ بعض الحلقات الماضية تكون فيها الـ…
+
+432
+00:29:23,110 --> 00:29:25,530
+اللي يبني الـGlucose عالي فتالي البروتينات عالية
+
+433
+00:29:25,530 --> 00:29:28,950
+تؤدي لـRoller Formations تكون جمعها مع بعض، هذه
+
+434
+00:29:28,950 --> 00:29:31,350
+ممكن تظهر بعض الحلقات الماضية إحنا بتظهر عندما
+
+435
+00:29:31,350 --> 00:29:34,750
+تحكينا، بتظهر معنا في الـ… اللي هي إيه إيش حكينا
+
+436
+00:29:34,750 --> 00:29:39,510
+في حلقات الـThick Film أو في حلقات الـThick Area،
+
+437
+00:29:39,510 --> 00:29:43,410
+طبعًا؟ طيب فهنا عندي Spherocytes تظهر في Thin Area
+
+438
+00:29:43,410 --> 00:29:46,210
+وفي الـThick Area تظهر فيها Roller Formation
+
+439
+00:29:46,210 --> 00:29:48,110
+أبرجيكم مرة الـSpherocytes
+
+440
+00:29:51,890 --> 00:29:59,350
+الـ Spherocytosis زي عندي ..
+
+441
+00:29:59,350 --> 00:30:03,990
+شايفين
+
+442
+00:30:03,990 --> 00:30:08,570
+الخلايا اللي بشوفها؟ شايفين الخلايا هاي الصغيرة؟
+
+443
+00:30:08,570 --> 00:30:09,670
+فتحت عندك السيف؟
+
+444
+00:30:13,230 --> 00:30:15,730
+أه، فتحت، فتحت، يا دكتور شايف الخلايا اللي عليها
+
+445
+00:30:15,730 --> 00:30:17,930
+الـCM، هاي؟ أه، هيفتحت هاي الخلية اللي عليها الـCM
+
+446
+00:30:17,930 --> 00:30:21,030
+مافيش واضح فيها مظاهر Hemoglobin مبينة كإنة خلية
+
+447
+00:30:21,030 --> 00:30:24,710
+متجانسة كاملة، هاي الـSpherocyte بيكون حجمها صغير،
+
+448
+00:30:24,710 --> 00:30:29,910
+بيكون حجمها صغير وكملة الـHemoglobin أه، تبين
+
+449
+00:30:29,910 --> 00:30:32,390
+الـHemoglobin مليها كلها مليانة بالظبط، هذه
+
+450
+00:30:32,390 --> 00:30:35,610
+الـSpherocyte هذه بتظهر في الـThin Area كإنة
+
+451
+00:30:35,610 --> 00:30:38,290
+Spherocyte لكن هي فعليًا مش Spherocyte لكن هي
+
+452
+00:30:38,290 --> 00:30:41,450
+موجودة بسبب إن هي موجودة في الـThin Area طيب،
+
+453
+00:30:41,450 --> 00:30:48,130
+نكمل؟إذا عندي serocytosis تظهر في حالة thin area و
+
+454
+00:30:48,130 --> 00:30:51,070
+thick area roll of formation لكن هدول حالتهم إيش؟
+
+455
+00:30:51,070 --> 00:30:55,330
+Normal، مش abnormal، لكن لو شوفت الحالتين هدول في
+
+456
+00:30:55,330 --> 00:30:58,750
+adequate area، أني adequate area يا محمد؟ اللي هي
+
+457
+00:30:58,750 --> 00:31:04,070
+بالنص، اللي تقع بيها بالنص، تمام؟ صحيح، هذه الحالة
+
+458
+00:31:04,070 --> 00:31:06,590
+اللي بحكي عنها إيش؟ بحكي إنها حالة مرضية، adequate
+
+459
+00:31:06,590 --> 00:31:08,710
+area، adequate area بالظبط
+
+460
+00:31:13,550 --> 00:31:16,790
+هذه أخدناها، مش هنحكي عليها كتير، لكن هي إيش
+
+461
+00:31:16,790 --> 00:31:22,790
+الحالة تؤدي إلى ظهور نحكي abnormality في عملية
+
+462
+00:31:22,790 --> 00:31:27,430
+الـPoor Blood Smear؟ طبعاً عندك drop too large أو
+
+463
+00:31:27,430 --> 00:31:30,750
+too small، إحنا إذا كنتوا تذكروا جربنا drop 10
+
+464
+00:31:30,750 --> 00:31:34,020
+مايكرو، جربنا 7 مايكرو، عشان تنطقوا معانافي ناس
+
+465
+00:31:34,020 --> 00:31:36,900
+كانت إيد العشرة مايكرون اتخربت، مضبوطش معاها،
+
+466
+00:31:36,900 --> 00:31:40,180
+اعتمدت على سبعة مايكرون، صح؟ فحسب ال drop نفسها،
+
+467
+00:31:40,180 --> 00:31:43,420
+كل ما زاد ال drop، كل ما كان عندك بور أكتر تقنيت،
+
+468
+00:31:43,420 --> 00:31:47,040
+عملية الفرد الصحيح ‏- من خمسة لعشرة؟ ‏- احنا حطينا
+
+469
+00:31:47,040 --> 00:31:50,020
+عشرة وما زبطت معايا الأغلبية، فحطينا السبعة عشان
+
+470
+00:31:50,020 --> 00:31:54,340
+إيدك تأخد عليها ‏- ع سبعة كانت تظبط معايا ‏- صحيح،
+
+471
+00:31:54,340 --> 00:31:57,480
+ع سبعة كانت تظبط معايا الأغلبية، لكن مجرد إن إيدك
+
+472
+00:31:57,480 --> 00:32:01,220
+زبطت على سبعة، بعدين لو حطيت عشر أو عشرين،تظبط
+
+473
+00:32:01,220 --> 00:32:06,760
+أكتر، معاك أكتر، لأن إيديك أخدت تقنية نفسها، تمام؟
+
+474
+00:32:06,760 --> 00:32:12,360
+تمام طيب، فرد الـslide مهم جدا، عشان تنفرد بطريقة
+
+475
+00:32:12,360 --> 00:32:17,220
+مش jerky manner عملية إنك أنت تحافظ على الـedge،
+
+476
+00:32:17,220 --> 00:32:20,860
+تبقى الـedge، وتعمل الـslide بإله دور، الزاوية
+
+477
+00:32:20,860 --> 00:32:24,060
+إلها دور، وعملية الـbush، الـspreader نفسها إلها
+
+478
+00:32:24,060 --> 00:32:28,700
+دور، في عملية تعطيك pour blood، اسمهاطبعًا الـ
+
+479
+00:32:28,700 --> 00:32:31,220
+«irregular spiders with a ridge and long tail»
+
+480
+00:32:31,220 --> 00:32:33,920
+برضه نفس الحكاية الـ «Holes» في الـ «Blood Film»
+
+481
+00:32:33,920 --> 00:32:36,920
+كل هذه معنات معناة في ال .. إذا بتفكروا في السمن
+
+482
+00:32:36,920 --> 00:32:41,380
+صور «A» ل«F» وآخرش تغييرات في الخلية الـ «Central
+
+483
+00:32:41,380 --> 00:32:45,020
+Generator» نتيجة أنه أنت طول في عملية «Fixation»
+
+484
+00:32:45,020 --> 00:32:48,220
+نتيجة أنك أنت عملت «Fixing Time» في الميثانول وكان
+
+485
+00:32:48,220 --> 00:32:49,400
+فيه «Contamination» بالوطن
+
+486
+00:32:52,260 --> 00:32:56,520
+عندي حالات طبعًا بيسموها «Biological Causes of
+
+487
+00:32:56,520 --> 00:33:00,620
+Gore Smear» يعني هي سببها أنه عندها حالات بيولوجية
+
+488
+00:33:00,620 --> 00:33:05,500
+مش أنت سبب فيها يعني مثلًا إذا بتذكروا قلتلكم، إذا
+
+489
+00:33:05,500 --> 00:33:10,760
+بتذكروا ميزنا بين، ميزنا بين ال .. حكيتكم الـ
+
+490
+00:33:10,760 --> 00:33:13,320
+«Role Formation» والـ «Agglutination» في الـ slide
+
+491
+00:33:13,320 --> 00:33:16,700
+المرة السابقة، نرجعلها، أبرجكم إياها الـ «Slide
+
+492
+00:33:16,700 --> 00:33:17,180
+High»
+
+493
+00:33:21,140 --> 00:33:25,080
+هذه، شايفينها؟ ‏- أه ‏- هذه في ال .. على اليمين
+
+494
+00:33:25,080 --> 00:33:27,480
+roll-off formation وهذا agglutination الـ roll-off
+
+495
+00:33:27,480 --> 00:33:30,220
+formation، حكينا سببه زيادة البروتينات لكن الـ
+
+496
+00:33:30,220 --> 00:33:33,500
+agglutination سببه هي أجسام مضادة، تمام؟ ممكن
+
+497
+00:33:33,500 --> 00:33:36,660
+أجسام مضادة، حسب، فأنا هذا بيسموه agglutination
+
+498
+00:33:36,660 --> 00:33:39,760
+وهذا roll-off formation طيب، احنا في عندي حالة
+
+499
+00:33:39,760 --> 00:33:42,000
+اللي بيسموها الـ cold agglutination cold
+
+500
+00:33:42,000 --> 00:33:45,320
+agglutination من اسمها coldيعني بارد و الـ
+
+501
+00:33:45,320 --> 00:33:47,860
+Glutonation بيصير تخفر الدم في الحالات الباردة
+
+502
+00:33:47,860 --> 00:33:52,040
+نتيجة وجود السم مضادة طبعا بالحالة هذه الخلايا
+
+503
+00:33:52,040 --> 00:33:55,920
+الحمراء بيصير الكلام مع بعض في الجو البارد لكن لو
+
+504
+00:33:55,920 --> 00:33:58,520
+حاطيتها أنا في ال water bath كده ترش حالات water
+
+505
+00:33:58,520 --> 00:34:03,020
+bath؟ سبعة و تلاتين سبعة و تلاتين فبالتالي بتفك
+
+506
+00:34:03,020 --> 00:34:07,500
+تمام فبالتالي بتفك طب ولا .. ولا أنت بدل زي دكتورش
+
+507
+00:34:07,500 --> 00:34:11,220
+بيسيبني هتفك أنا يعني إيه؟ كيف يا سعيد؟الـ
+
+508
+00:34:11,220 --> 00:34:13,720
+Antibodies الأجسام المضادة اللي بتكون ماسك فيها
+
+509
+00:34:13,720 --> 00:34:17,960
+اللي عامل الـ agglutination هذي، تتخيل عنها؟ حسب
+
+510
+00:34:17,960 --> 00:34:21,180
+نوعها، هذي اسمها cold agglutinins cold agglutinins
+
+511
+00:34:21,180 --> 00:34:24,080
+اللي هي أجسام مضادة بتتفعل درجة حرارة باردة، يعني
+
+512
+00:34:24,080 --> 00:34:27,800
+نحكي أربعة درجة مقاوية، تمام؟ أو نحكي ستة عشرين
+
+513
+00:34:27,800 --> 00:34:31,920
+مثلا، هذي من طبيبتها لو حضرتها درجة حرارة عالي
+
+514
+00:34:31,920 --> 00:34:36,760
+شويه سبعة و تلاتين، بتتفعلش، بتفكرفالاتفاعل
+
+515
+00:34:36,760 --> 00:34:39,600
+الأجسام المضادة مع الـ «أندجينات» تعتبر اتفاعل
+
+516
+00:34:39,600 --> 00:34:43,200
+عكسي الـ «Reverse»، ممكن أعكسه أنا أجد الـ «Warm
+
+517
+00:34:43,200 --> 00:34:47,520
+Agglutination» بتفاعل لدرجة حرارة 37، لدرجة حرارة
+
+518
+00:34:47,520 --> 00:34:49,540
+الجسم لكن الـ «Cold Agglutination» بتفاعل لدرجة
+
+519
+00:34:49,540 --> 00:34:53,660
+حرارة باردة، أنا بقدر أعالج الحالة هاي، لو مرض ما
+
+520
+00:34:53,660 --> 00:34:56,620
+هي حالة «Cold Agglutination»، بقدر أعالجها، إن أنا
+
+521
+00:34:56,620 --> 00:35:00,860
+باخد العينة، بحط بوتر بقى، خمس دخائط، وبعدين خلال
+
+522
+00:35:00,860 --> 00:35:02,680
+وجود الـ «Pottery Barrel» بعمل الـ «Plug Flow»
+
+523
+00:35:02,680 --> 00:35:06,230
+وبفرضهطبعاً بحاول أسخن ال slides كمان عشان يكون
+
+524
+00:35:06,230 --> 00:35:08,670
+عندى برضه ال war لإن مجرد أسحبها ال cold ممكن
+
+525
+00:35:08,670 --> 00:35:13,250
+تقضيها التفاعل تعني حالة تانية سببها ال biological
+
+526
+00:35:13,250 --> 00:35:16,510
+اللي هي الليبيميا إيش عن الليبيميا يا معاد؟
+
+527
+00:35:16,510 --> 00:35:22,610
+الليبيميا؟ الليبيميا الليبت الليبت الليبت الليبت
+
+528
+00:35:22,610 --> 00:35:28,750
+الليبت الليبت الليبت
+
+529
+00:35:28,750 --> 00:35:31,170
+الليبت الليبت الليبت الليبت الليبت الليبت الليبت
+
+530
+00:35:31,170 --> 00:35:34,420
+الليبت الليبت الليأتبع دهول في الدم، هذه طبعا تؤدي
+
+531
+00:35:34,420 --> 00:35:38,260
+لظهور ال «holes» في الاسميرة، إذا كان فيه slide هي
+
+532
+00:35:38,260 --> 00:35:44,980
+«holes»، رقم A,B,C,D,E، صح يا محمد؟ «slide E» كان
+
+533
+00:35:44,980 --> 00:35:48,640
+فيها «holes»، الـ«holes» يعني سبب الترقيم يعني،
+
+534
+00:35:49,380 --> 00:35:51,840
+طبعًا أدى إذا علاج، لأ مالاش علاج لأنه أصل هو
+
+535
+00:35:51,840 --> 00:35:54,000
+موجود في جسم الإنسان يعني إنسان جاي يعمل blood
+
+536
+00:35:54,000 --> 00:35:57,300
+film وكان عنده الدهون عالية أنا مقدرش في الحال هاي
+
+537
+00:35:57,300 --> 00:36:00,680
+أني أحكيله لأ، روح نزل دهون تعالي فحنقر نقرأ
+
+538
+00:36:00,680 --> 00:36:02,880
+الـLottery of Blipemia والـRoll of formation زي ما
+
+539
+00:36:02,880 --> 00:36:05,760
+حكيتلكم أنه في حال تكون فيها بروتينات عالي شوية
+
+540
+00:36:05,760 --> 00:36:09,460
+عبارة عن stack of coins، شكل stack of coins هذه
+
+541
+00:36:09,460 --> 00:36:11,580
+الحالات تؤدي لبور blood smear في حالة
+
+542
+00:36:11,580 --> 00:36:16,300
+الـbiological cases هيك خلصنا blood film تقريبًا،
+
+543
+00:36:16,300 --> 00:36:22,130
+هندخل للتريننجبالنسبة بس تحدثناك، الـ ReLow ارتفاع
+
+544
+00:36:22,130 --> 00:36:25,410
+لبروتينات أي نوع بروتين و لا فيه بروتينات معينة هي
+
+545
+00:36:25,410 --> 00:36:27,810
+اللي بتقدي الارتفاع اللي هو وجود الـ ReLow؟ لأ،
+
+546
+00:36:27,810 --> 00:36:31,070
+ممكن أحنا في الحالة تهيأ بيصير خدلال، هو غالبًا
+
+547
+00:36:31,070 --> 00:36:33,870
+يعني تظهر الـ Low Formation في حالات مثلًا اللي
+
+548
+00:36:33,870 --> 00:36:38,770
+نحكي اتفاعل immunoglobulins immunoglobulins طبعًا
+
+549
+00:36:38,770 --> 00:36:42,450
+منوع البروتينات الجلوبيلينات، الجلوبيلين، تمام؟
+
+550
+00:36:42,450 --> 00:36:45,010
+فبالحالة هاي بتفع، طبعًا immunoglobulins في حالة
+
+551
+00:36:45,010 --> 00:36:50,240
+مرضية تؤدي إلى شهسمظهور الـ Low Formationلكن هي
+
+552
+00:36:50,240 --> 00:36:52,960
+بشكل عام، لو رتفع الألبومي نفس الحكاية، ليش؟ لأن
+
+553
+00:36:52,960 --> 00:36:56,680
+ارتفاع البروتينات يؤدي إلى اختلال في البيئة حول
+
+554
+00:36:56,680 --> 00:36:59,280
+الخلايا الحمرة، طبعاً من شحنات كورفاية وغيرها،
+
+555
+00:36:59,280 --> 00:37:03,680
+وتؤدي بالتالي إلى اختلال البيئة والشحنات إلى
+
+556
+00:37:03,680 --> 00:37:05,920
+اقتراب الخلايا الحمرة من بعض لبعض، يعني الخلايا
+
+557
+00:37:05,920 --> 00:37:10,700
+الحمرة أصلاً، إيش فيها سطحها؟ فيها سطحها شحنات،
+
+558
+00:37:10,700 --> 00:37:13,280
+Lyseric Acidهذه تؤدي لتنافس الخلايا الحمراء من
+
+559
+00:37:13,280 --> 00:37:15,600
+بعض، يعني الخلايا الحمراء بتتبقى أكتر من بعض بوجود
+
+560
+00:37:15,600 --> 00:37:20,560
+الشحنات لكن انا في حالة التفاعل، البروتينات،
+
+561
+00:37:20,560 --> 00:37:24,840
+البيئة اللي حواليها كانت أقرب شوية، خلّيني أتجرب،
+
+562
+00:37:24,840 --> 00:37:28,660
+كانت كأنها صارت أجلوتينيشن، احنا أحد طرق علاج
+
+563
+00:37:28,660 --> 00:37:30,360
+الـRoll-up formation أحد طرق علاج الـRoll-up
+
+564
+00:37:30,360 --> 00:37:33,960
+formation أن هنا أشيل من الـPlasma وأحط بدلها
+
+565
+00:37:33,960 --> 00:37:39,700
+Saline، فبالتالي أنا خففت منالـ… شو اسمه؟ الـ
+
+566
+00:37:39,700 --> 00:37:42,260
+«البومين» أو النخفة من البروتينات وبالتالي عملت
+
+567
+00:37:42,260 --> 00:37:45,240
+أدية الخلايا الأمريكية تؤدي لـ «تنافر» بسبب إيه
+
+568
+00:37:45,240 --> 00:37:48,080
+الشحنتها، تمام؟ تمام
+
+569
+00:37:50,830 --> 00:37:54,310
+طيب الـ Staining، الـ Staining يعني بعد ما تنشب
+
+570
+00:37:54,310 --> 00:37:57,370
+الـ slide و عملت تنشب الـ slide بعمله Staining،
+
+571
+00:37:57,370 --> 00:38:00,230
+طبعا عندي أنواع كتير من الـ Staining أحنا ممكن
+
+572
+00:38:00,230 --> 00:38:04,050
+نستخدم طبعا كل الـ Staining تتبع للرومان Whiskey
+
+573
+00:38:04,050 --> 00:38:06,950
+Stains، فعندي Rite Stains، الـ Rite Stains بيسموها
+
+574
+00:38:06,950 --> 00:38:10,460
+Metachromic Stainsميدا كوميك ستينز طبعاً فيها two
+
+575
+00:38:10,460 --> 00:38:15,340
+type of stains طبعاً فيكون فيها سبغة حامضية و سبغة
+
+576
+00:38:15,340 --> 00:38:19,660
+قاعدية طبعاً فيها نوعين من السبغة فيها مثلين blue
+
+577
+00:38:19,660 --> 00:38:23,240
+دار و فيها الأيزين الحمراء فهي تسبغلي باللون
+
+578
+00:38:23,240 --> 00:38:27,920
+الأزرق و الأحمر تسبغلي النواء باللون الأزرق و
+
+579
+00:38:27,920 --> 00:38:35,140
+الخلايا الحمراء تسبغلي الهيومكولبين باللون الأحمر
+
+580
+00:38:35,140 --> 00:38:41,120
+حسب سبب الشحناتطبعًا، بأستخدم الـ Methanol في
+
+581
+00:38:41,120 --> 00:38:47,140
+عملية التثبيت الـ Metriblostans تسبغلي الـ RNA،
+
+582
+00:38:47,140 --> 00:38:52,460
+تسبغلي الـ DNA، تسبغلي كما حكينا، كل الأنوية بالـ
+
+583
+00:38:52,460 --> 00:38:56,160
+Blue-Grey Color بينما الـ Eosin الحمراء تسبغلي الـ
+
+584
+00:38:56,160 --> 00:38:59,700
+Eosin Granulesبالأورانج تسبغلي طبعًا الـ Red blood
+
+585
+00:38:59,700 --> 00:39:06,380
+cells السبغات طبعًا فيها buffer لإنه يحافظ على الـ
+
+586
+00:39:06,380 --> 00:39:11,060
+pH غالبًا الـ pH بيكون من 6.4 لـ 6.7 الـ buffer
+
+587
+00:39:11,060 --> 00:39:14,960
+مهم جدًا جدًا جدًا يعني أحنا كتير مرات معايا
+
+588
+00:39:14,960 --> 00:39:18,140
+بتجربة من ناحية العملية أني أنا أسبغ كنت أسبغ
+
+589
+00:39:18,140 --> 00:39:20,480
+مثلًا بعض الـ sliders ماعرفش أحكي لكم يا عم
+
+590
+00:39:20,480 --> 00:39:24,100
+بالمخدمة ولا لأ لكن كنت أسبغ sliders في مرة مرات
+
+591
+00:39:24,100 --> 00:39:26,160
+لحد أن معظم ال sliders اللي أسبغها هتطلع معايا
+
+592
+00:39:26,160 --> 00:39:30,230
+أسيدكطبعًا السبب، طبعًا السبب دي عملها buffer 100%
+
+593
+00:39:30,230 --> 00:39:34,310
+فبعد هيك اكتشفت أن أحد زملائي كان مثلًا ييجي
+
+594
+00:39:34,310 --> 00:39:37,990
+يستخدم مثلًا أحد القخول، يستخدم القخول ويسيب
+
+595
+00:39:37,990 --> 00:39:41,650
+القطار مفتوح نوعًا ما، فبصير evaporation للأسد
+
+596
+00:39:41,650 --> 00:39:44,550
+فيؤدي إلى زيادة أسد ال environment وبالتالي يؤدي
+
+597
+00:39:44,550 --> 00:39:48,530
+إلى زيادة staining، نحكي الـred color staining أو
+
+598
+00:39:48,530 --> 00:39:51,710
+يصير أسدك أكتر، فهذه الـbuffer مهم جدًا،
+
+599
+00:39:51,710 --> 00:39:54,250
+الـatmosphere اللي حواليك مهم، هيعملت اللي حفظ على
+
+600
+00:39:54,250 --> 00:39:59,240
+أسابقها نفسهاطيب، الـ Sealing Procedure مش سهل،
+
+601
+00:39:59,240 --> 00:40:03,480
+هناخده معنا أحنا بعد ما نجفف السمير لازم نعملها
+
+602
+00:40:03,480 --> 00:40:08,160
+Fixation بواسطة الـ Methanol طبعا، ممكن أنك أنت
+
+603
+00:40:08,160 --> 00:40:13,460
+تحطها على الراك وتعملها، تحط عليها الـ نحكي الـ
+
+604
+00:40:13,460 --> 00:40:16,120
+Methanol لمدة مثلا، two minutes أو three minutes
+
+605
+00:40:16,120 --> 00:40:19,660
+أو ممكن أنت بواسطة الـ Jar، الـ Sealing Jars
+
+606
+00:40:19,660 --> 00:40:23,300
+تعملها دلوقتي عشر مرات في الـ Sealing Jars فيها
+
+607
+00:40:23,300 --> 00:40:25,200
+أنا نزلتلكم فيديو، ماعرف إذا شفتوه
+
+608
+00:40:43,100 --> 00:40:44,500
+‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏
+
+609
+00:40:52,140 --> 00:40:57,140
+طريقة نفسنا هي استخدام الـ «راك» على الـ «سينك»
+
+610
+00:40:57,140 --> 00:41:00,100
+نفسها وسنقوم بـ «معالجة» السمير ونقوم بعمل «دب»
+
+611
+00:41:00,100 --> 00:41:05,840
+110 مرات ثم سنضع السمير على الـ «سينك» لمدة 1-2
+
+612
+00:41:05,840 --> 00:41:09,420
+دقيقة ثم نضيف الـ «بافر» بالطبع أن السينك نفسها هي
+
+613
+00:41:09,420 --> 00:41:12,020
+الـ «مكسيك» بين الـ «يوزين» والـ «ميتاليبوه» مع
+
+614
+00:41:12,020 --> 00:41:15,200
+بعض سيكون صبغتين وليس منفصلين يعني الـ «رايتس
+
+615
+00:41:15,200 --> 00:41:18,760
+سينك» هي الصبغة الموجودة فيها الـ «ميتاليبوه» مع
+
+616
+00:41:18,760 --> 00:41:22,380
+الـ «يوزين»هي مسبوغة و جاهزة كنت تقولنا يا دكتور
+
+617
+00:41:22,380 --> 00:41:25,400
+في المقدمة الحالية هي سبغات موجودة فيها مسبوغة و
+
+618
+00:41:25,400 --> 00:41:30,620
+جاهزة و لا احنا مجاهزها مسبوغة و جاهزة مش مسبوغة
+
+619
+00:41:30,620 --> 00:41:36,240
+انا بتسبوغها لسه الاسمية لأ السبغة جاهزة ولا مثلا
+
+620
+00:41:36,240 --> 00:41:41,540
+محضرة محضرة و جاهزة ممكن تجيك باودر و انت تحضرها
+
+621
+00:41:41,540 --> 00:41:46,480
+بالميثانول او ممكن تجيك مثلا جاهزة ومتوسطة مباشرة
+
+622
+00:41:46,480 --> 00:41:49,790
+حسب الشركات اللي بتشتري منهاطبعًا إحنا بنفخ … حتى
+
+623
+00:41:49,790 --> 00:41:53,270
+بـ… حتى بالشركة أقل إحنا بنفخت السمير لـ one to
+
+624
+00:41:53,270 --> 00:41:56,510
+two minutes بعد هيك طبعًا بنضيف عليها كمية من الـ
+
+625
+00:41:56,510 --> 00:41:59,730
+buffer تعادل كمية السمير و بننفخ، بحيث إنه يصير
+
+626
+00:41:59,730 --> 00:42:02,790
+عملية … عملية نفخ يلقى دور كتير في عملية mixing
+
+627
+00:42:02,790 --> 00:42:04,790
+بين الـ buffer و السمير أو بين الميّه داخل الـ
+
+628
+00:42:04,790 --> 00:42:07,090
+water و السمير، إحنا نستخدم distilled water عملية
+
+629
+00:42:07,090 --> 00:42:11,790
+نفخ، في بعض الصبغات مثلًا، إحنا عزينا Riot وGemsa
+
+630
+00:42:11,790 --> 00:42:15,630
+وفيها نوع كتير من الصبغات Gemsa مثلًا، لو نفختها،
+
+631
+00:42:15,630 --> 00:42:19,550
+هتلاقي إنه ظهر نوع من اللون، بيسموه «هذه طبعاً
+
+632
+00:42:19,550 --> 00:42:22,770
+بلون حلو كتير رأيك أنك تضمن إن عملت الـ mixing صح
+
+633
+00:42:22,770 --> 00:42:25,770
+ممكن تعمل الـ mixing بالـ pipettes بصير الـ
+
+634
+00:42:25,770 --> 00:42:29,590
+pipettes أو بالنفخ بواسطة سخن مدى المواصع وشغل
+
+635
+00:42:29,590 --> 00:42:33,450
+أيضاً طبعاً إذا نضيف نفس الكمية من الـ buffer على
+
+636
+00:42:33,450 --> 00:42:36,630
+الاسمير و بعدين كبنونه فوق و نخليها two to four
+
+637
+00:42:36,630 --> 00:42:40,070
+minutes نعمل نعمل wash و بعدين نعمل dry الاسمير و
+
+638
+00:42:40,070 --> 00:42:48,470
+نقرأ الاسمير نفسنا طبعاً 90 سنةأعطاني رسالة أن الـ
+
+639
+00:42:48,470 --> 00:42:50,490
+«سيروجيومولوجيا» يبدو بدأ بعد عشر دقائق لإن ما
+
+640
+00:42:50,490 --> 00:42:53,230
+يشبه بعديكم طيب مش مشكلة احنا نحاول نشتغل الـ
+
+641
+00:42:53,230 --> 00:42:57,930
+«سيروجيومولوجيا» ده فكرت الصوت من عندك ساعين، لا،
+
+642
+00:42:57,930 --> 00:43:01,970
+من عندك، طيب، هاي الـstaining، فعندي هنا طبعا two
+
+643
+00:43:01,970 --> 00:43:05,050
+basic، بيكون في المثلين بيقولوا، بيكون هذه طبعا
+
+644
+00:43:05,050 --> 00:43:08,870
+أذة أسباب، هذه طبعا أذة بشي، وهذه طبعا two acidic،
+
+645
+00:43:08,870 --> 00:43:09,470
+شايفين؟
+
+646
+00:43:12,140 --> 00:43:15,200
+البنافسة دي البربل والأزرق والأحمر بظهرين بشكل
+
+647
+00:43:15,200 --> 00:43:19,700
+متجانس وواضح، مايكونش كلها حمرا ولا كلها زرقا،
+
+648
+00:43:19,700 --> 00:43:22,540
+تشوفين هالخلايا الحمرا كيف؟ هيخلاها حمرا، كلها
+
+649
+00:43:22,540 --> 00:43:25,760
+زرقا، هالخلايا الحمرا كلها حمرا، هنا أيضا أدقوة
+
+650
+00:43:25,760 --> 00:43:31,080
+طبعا أسباب ال .. دكتور هذا الصورة على المجهر؟ إيه؟
+
+651
+00:43:32,750 --> 00:43:35,390
+الصورة هذه هيك هتظهر على المجهر المفروض ولا في
+
+652
+00:43:35,390 --> 00:43:36,730
+العين؟ هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+653
+00:43:36,730 --> 00:43:45,830
+هيك هيك هيك هيك هيك هيك هيك هيك
+
+654
+00:43:45,830 --> 00:43:46,170
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+655
+00:43:46,170 --> 00:43:46,190
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+656
+00:43:46,190 --> 00:43:46,230
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+657
+00:43:46,230 --> 00:43:46,890
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+658
+00:43:46,890 --> 00:43:50,690
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+659
+00:43:50,690 --> 00:43:56,010
+هيك هيك هيك هيك هيك هيك هيك هيكأو إنه character
+
+660
+00:43:56,010 --> 00:44:00,870
+stain عندك بقديمة أو إن البيئة قدش عندك acid زي
+
+661
+00:44:00,870 --> 00:44:03,930
+اللي بحكيلكم، أنا كان زميل يحط استخدام ال acid
+
+662
+00:44:03,930 --> 00:44:08,530
+جنبي، جنب ال swing قد لإنه ترميته stain يعني إذا
+
+663
+00:44:08,530 --> 00:44:11,110
+ظهرت مشكلة هنا في هذا الحالة، هتكون المشكلة من
+
+664
+00:44:11,110 --> 00:44:13,430
+السبغة، مش؟ بالظبط، بيكون المشكلة من السبغة، فإن
+
+665
+00:44:13,430 --> 00:44:18,530
+أنت بدأت تحلها، أه مش من سحبت يعني إنت بالحالة
+
+666
+00:44:18,530 --> 00:44:21,010
+high فكبارا two acidic بدأت تحلها أو two steel
+
+667
+00:44:21,010 --> 00:44:23,610
+alkaline بدأت تحلها، لإن مش هتعرف تقرأ منها أصلاً
+
+668
+00:44:24,090 --> 00:44:31,070
+هتجد الـ two alkaline يعني
+
+669
+00:44:31,070 --> 00:44:35,250
+لو كان عندك ثقيل سمير أو prolong staining يعني إذا
+
+670
+00:44:35,250 --> 00:44:38,510
+كان العكس، ثقيل سمير هتعطيكه أسد أحيانًا two
+
+671
+00:44:38,510 --> 00:44:41,250
+alkaline، thick smear أو prolong staining أو
+
+672
+00:44:41,250 --> 00:44:45,070
+insufficient washing أو alkaline pH طب العلاجاتهم،
+
+673
+00:44:45,070 --> 00:44:47,910
+عرف العلاجاتهم، أنا عند العلاج إذا كان
+
+674
+00:44:48,460 --> 00:44:51,660
+الـSufficient Staining Time، بزوّد الـTime إذا كان
+
+675
+00:44:51,660 --> 00:44:55,380
+الـBH عندي Acidic، بعدّل في الـBH إذا كانت All
+
+676
+00:44:55,380 --> 00:44:59,520
+Stained، بعمل Staining جديدة، تمام؟ الـAlkaline،
+
+677
+00:44:59,520 --> 00:45:02,820
+لو كانت Thick Smear، بحطه Smear كويسة إذا كانت
+
+678
+00:45:02,820 --> 00:45:05,560
+Prolonged Staining، بقلّر من الـTime إذا كانت
+
+679
+00:45:05,560 --> 00:45:08,840
+Sufficient Washing، بعمل Washing صح، يعني مش بحطه
+
+680
+00:45:08,840 --> 00:45:12,560
+تحسين صح وإذا كانت Alkaline BH، بعمل إيش؟ أتشكل
+
+681
+00:45:12,560 --> 00:45:15,860
+الـBH، وبعدّل الـBH، هيك إحنا خلصنا الـStaining
+
+682
+00:45:16,250 --> 00:45:22,390
+وخلصنا الـ «Blood Film» ده عنده جزئية الـ .. طبعا
+
+683
+00:45:22,390 --> 00:45:24,290
+بحكيلك الـ «Manual Differential» اللي على الـ
+
+684
+00:45:24,290 --> 00:45:28,430
+«RBC» وإيش بدهر معاه Normal، تمام؟ عندي طبعا
+
+685
+00:45:28,430 --> 00:45:32,790
+الخلايا الحمرة، أنا إيه الخاطر هذا؟ نواجب .. نواجب
+
+686
+00:45:32,790 --> 00:45:37,870
+احنا هنا إن شاء الله، إيش رأيكوا؟ نواجب هنا، نواجب
+
+687
+00:45:37,870 --> 00:45:42,550
+.. ‏-إيش راجع الفيلم؟ ‏-طايل كتير يا دكتور، طايل
+
+688
+00:45:42,550 --> 00:45:47,420
+كتيرمش ضايق الأغربية الصور يعني وأشكال وكيف تتوزين
+
+689
+00:45:47,420 --> 00:45:50,300
+الخلايا الحمراء والخلايا اللي ده إحنا نوقف هنا إن
+
+690
+00:45:50,300 --> 00:45:52,860
+شاء الله ومن السنوات الجاية في لقاء السنوات الجاية
+
+691
+00:45:52,860 --> 00:45:56,200
+بنحاول إن شاء الله نكمل وبناخدكم ده أحاول أبعد
+
+692
+00:45:56,200 --> 00:45:59,340
+بينكم وبين الشباب عشان لو أتأخرنا شوية قدرنا معاكم
+
+693
+00:45:59,340 --> 00:46:00,640
+شوية
+
+694
+00:46:03,210 --> 00:46:06,410
+طبعا، أنا جيت بدي أعمل الـ «Application» بدي أعمل
+
+695
+00:46:06,410 --> 00:46:10,870
+الـ «code» للمحاضرة و أنزلها زي ما حكيتكم، احتمال
+
+696
+00:46:10,870 --> 00:46:14,270
+كبير، إذا حابين الساعة 4، ماعنديش مشكلة احتمال
+
+697
+00:46:14,270 --> 00:46:18,310
+يكون ثابت أو اتنين، طبعا؟ بدي أوزع المعامل بين انا
+
+698
+00:46:18,310 --> 00:46:20,710
+و تالت و بدي أحاول أعمل وسامة بين كل معمل معمل
+
+699
+00:46:20,710 --> 00:46:24,190
+بحيث أنه يكون عندي ساعة لو اتخلت أنه أقدر أعطيكم
+
+700
+00:46:24,190 --> 00:46:28,310
+كمان راح تفضلوا خلاص، طبعا، إن شاء الله، يلا،
+
+701
+00:46:28,310 --> 00:46:33,070
+أعطيكم العادة، في صفصار في الصبق؟ طبعا، تمامالله
+
+702
+00:46:33,070 --> 00:46:35,690
+يرضى عليك يا دكتور الله يزيد يعطيك العافية يا
+
+703
+00:46:35,690 --> 00:46:39,470
+دكتور ماشي يعطيك العافية يعطيك العافية مع السلامة
+
+704
+00:46:39,470 --> 00:46:39,970
+يعطيك العافية
+
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.json b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9758b560c84cadb8a8fdae411348013a7506aba6
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.json
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غلط، هتؤدي لظهور Artifacts. أنت جيت فردت، ماعرفت تبعتش زاوية 30 إلى 40، وماعرفت تعمل زاوية مثلًا 50، هتؤدي لظهور «زمير» قصيرة و «very thick»، مش هيكون كويس لقراية فيلم.", "tokens": [6027, 39184, 5735, 351, 15295, 32239, 3224, 36632, 13412, 17082, 37977, 6055, 33604, 16254, 5296, 9566, 3555, 3615, 14111, 995, 1357, 116, 3224, 13063, 12399, 37495, 22653, 8717, 5016, 4117, 1829, 2423, 39184, 4657, 11622, 2304, 13546, 5933, 37893, 20666, 39184, 28892, 20328, 5016, 12399, 36145, 41850, 4724, 28480, 11242, 11296, 13, 20193, 12399, 37495, 22653, 3714, 11242, 45761, 5172, 9307, 12399, 19446, 4724, 29399, 5016, 4117, 1829, 18871, 11296, 13, 37893, 12399, 37893, 12399, 37495, 22653, 13412, 17082, 1211, 9307, 13412, 2407, 16373, 3555, 12399, 8717, 5016, 4117, 1829, 13, 39896, 5735, 351, 15295, 37495, 22653, 13412, 2407, 16373, 3555, 12399, 46811, 10943, 22807, 34051, 4117, 1829, 12399, 34051, 4117, 1829, 13, 5551, 12610, 44049, 12399, 18863, 42213, 10632, 27188, 2288, 3215, 6055, 30544, 32771, 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الـHumidity أدت إلى Slow-drying تؤدي لظهر الـArtifacts عملت الـFixation طولت فيها، روح سفررت بالاسمير وخلت تانية وعملت الـFixation برضه غلط أصول أول ما تنشف الـSlide عملها الـFixation وجود المي في الـMethanol إذا كان موجود المي أكتر من 3% في الحالة هذه لازم أنا أيش برضه أن أتجنب وجود المي في المي لأن المي تعمل Artifacts", "tokens": [10721, 29399, 3714, 43020, 6055, 30544, 43242, 4117, 6225, 42213, 10632, 2423, 39184, 39, 449, 17711, 5551, 3215, 2655, 30731, 17703, 12, 67, 19076, 6055, 33604, 16254, 5296, 19913, 3224, 2288, 2423, 39184, 32925, 351, 15295, 6225, 42213, 2655, 2423, 39184, 37, 970, 399, 23032, 12610, 2655, 8978, 11296, 12399, 12602, 2407, 5016, 8608, 5172, 2288, 43500, 20666, 32277, 2304, 13546, 4032, 9778, 1211, 2655, 6055, 7649, 10632, 4032, 25957, 1211, 2655, 2423, 39184, 37, 970, 399, 4724, 43042, 3224, 32771, 1211, 9566, 5551, 9381, 12610, 5551, 12610, 19446, 6055, 1863, 8592, 5172, 2423, 39184, 50, 31264, 6225, 42213, 11296, 2423, 39184, 37, 970, 399, 49610, 23328, 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راح", "probability": 0.40234375}, {"start": 2785.71, "end": 2786.45, "word": " تفضلوا", "probability": 0.4829833984375}, {"start": 2786.45, "end": 2787.03, "word": " خلاص،", "probability": 0.7425537109375}, {"start": 2787.03, "end": 2787.31, "word": " طبعا،", "probability": 0.82314453125}, {"start": 2787.31, "end": 2787.31, "word": " إن", "probability": 0.39453125}, {"start": 2787.31, "end": 2787.41, "word": " شاء", "probability": 0.95166015625}, {"start": 2787.41, "end": 2788.05, "word": " الله،", "probability": 0.7958984375}, {"start": 2788.05, "end": 2788.31, "word": " يلا،", "probability": 0.62744140625}, {"start": 2788.31, "end": 2788.57, "word": " أعطيكم", "probability": 0.6846110026041666}, {"start": 2788.57, "end": 2788.95, "word": " العادة،", "probability": 0.48577880859375}, {"start": 2788.95, "end": 2789.11, "word": " في", "probability": 0.33251953125}, {"start": 2789.11, "end": 2789.59, "word": " صفصار", "probability": 0.6915283203125}, {"start": 2789.59, "end": 2789.75, "word": " في", "probability": 0.98583984375}, {"start": 2789.75, "end": 2791.71, "word": " الصبق؟", "probability": 0.8551025390625}, {"start": 2791.71, "end": 2791.91, "word": " طبعا،", "probability": 0.809521484375}, {"start": 2791.91, "end": 2792.25, "word": " تمام", "probability": 0.670654296875}], "temperature": 1.0}, {"id": 111, "seek": 279997, "start": 2792.83, "end": 2799.97, "text": "الله يرضى عليك يا دكتور الله يزيد يعطيك العافية يا دكتور ماشي يعطيك العافية يعطيك العافية مع السلامة يعطيك العافية", "tokens": [6027, 43761, 7251, 43042, 7578, 25894, 4117, 35186, 11778, 4117, 2655, 13063, 21984, 7251, 11622, 25708, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 35186, 11778, 4117, 2655, 13063, 3714, 33599, 1829, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 37495, 9566, 1829, 4117, 18863, 31845, 10632, 20449, 21136, 37440, 3660, 37495, 9566, 1829, 4117, 18863, 31845, 10632], "avg_logprob": -0.20847040101101524, "compression_ratio": 2.247311827956989, "no_speech_prob": 0.0, "words": [{"start": 2792.83, "end": 2793.07, "word": "الله", "probability": 0.56292724609375}, {"start": 2793.07, "end": 2793.39, "word": " يرضى", "probability": 0.93505859375}, {"start": 2793.39, "end": 2793.65, "word": " عليك", "probability": 0.961181640625}, {"start": 2793.65, "end": 2793.77, "word": " يا", "probability": 0.69091796875}, {"start": 2793.77, "end": 2794.03, "word": " دكتور", "probability": 0.954345703125}, {"start": 2794.03, "end": 2794.23, "word": " الله", "probability": 0.5439453125}, {"start": 2794.23, "end": 2794.57, "word": " يزيد", "probability": 0.6183268229166666}, {"start": 2794.57, "end": 2795.03, "word": " يعطيك", "probability": 0.782562255859375}, {"start": 2795.03, "end": 2795.51, "word": " العافية", "probability": 0.7236328125}, {"start": 2795.51, "end": 2795.69, "word": " يا", "probability": 0.84423828125}, {"start": 2795.69, "end": 2796.09, "word": " دكتور", "probability": 0.9781494140625}, {"start": 2796.09, "end": 2796.53, "word": " ماشي", "probability": 0.7928873697916666}, {"start": 2796.53, "end": 2796.79, "word": " يعطيك", "probability": 0.912841796875}, {"start": 2796.79, "end": 2797.57, "word": " العافية", "probability": 0.9007161458333334}, {"start": 2797.57, "end": 2798.25, "word": " يعطيك", "probability": 0.9271240234375}, {"start": 2798.25, "end": 2798.89, "word": " العافية", "probability": 0.9689127604166666}, {"start": 2798.89, "end": 2799.13, "word": " مع", "probability": 0.28466796875}, {"start": 2799.13, "end": 2799.47, "word": " السلامة", "probability": 0.9383138020833334}, {"start": 2799.47, "end": 2799.63, "word": " يعطيك", "probability": 0.9464111328125}, {"start": 2799.63, "end": 2799.97, "word": " العافية", "probability": 0.9573567708333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2800.4195, "duration_after_vad": 2714.367218749988}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..05c7c55ebabf6029d47f11db4fdbed9d468b3697
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/X8EYD6ZBFD0_raw.srt
@@ -0,0 +1,2924 @@
+1
+00:00:00,000 --> 00:00:05,600
+بس دكتور بعد اسمك بس في نقطة أنا هنا في اني علامة
+
+2
+00:00:05,600 --> 00:00:08,720
+تسجيل بضغط عليها بيقول place as the host و give
+
+3
+00:00:08,720 --> 00:00:10,780
+you ده مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+4
+00:00:10,780 --> 00:00:11,880
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+5
+00:00:11,880 --> 00:00:11,880
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+6
+00:00:11,880 --> 00:00:12,560
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+7
+00:00:12,560 --> 00:00:12,560
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+8
+00:00:12,560 --> 00:00:12,960
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+9
+00:00:12,960 --> 00:00:15,760
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+10
+00:00:15,760 --> 00:00:15,760
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+11
+00:00:15,760 --> 00:00:18,260
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+12
+00:00:18,260 --> 00:00:18,260
+مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش مش
+
+13
+00:00:18,260 --> 00:00:23,880
+مش مش مش مش مش مش مش مش
+
+14
+00:00:23,880 --> 00:00:30,150
+مش مش مشعلم الدم طبعاً عملت، احنا أخدت في المقاطمة
+
+15
+00:00:30,150 --> 00:00:33,950
+بعض المعامل اللي إلها علاقة بعلم الدم وكان منها
+
+16
+00:00:33,950 --> 00:00:39,290
+طبعاً أخر معمل كنتوا بتذكره أنه هيكون أول معمل في
+
+17
+00:00:39,290 --> 00:00:42,550
+الـ hematology صح ولا لأ؟ فعنا أخر معمل هو كيف
+
+18
+00:00:42,550 --> 00:00:47,170
+نعمل الشريحةوكيف نصبخها، احنا طبعا المعمل الحالي
+
+19
+00:00:47,170 --> 00:00:52,030
+هنعيد كيف نعمل شريحة، كيف نصبخها وكيف بتاني نقرأها
+
+20
+00:00:52,030 --> 00:00:55,190
+إن شاء الله، سواء كانت نوعية طبيعية أو غير طبيعية
+
+21
+00:00:55,190 --> 00:01:01,850
+طبعا بالنسبالي، نحكي الـ Outline تبع المعمل تبعنا،
+
+22
+00:01:01,850 --> 00:01:10,010
+خليني انا أشاركم الشاشة، هل جيت معاي؟ في محمد،
+
+23
+00:01:10,010 --> 00:01:12,250
+شوفين الشاشة حاليا؟ شايفين الشاشة، تمام؟
+
+24
+00:01:20,380 --> 00:01:27,260
+واضح الشاشة عندكم يا شباب؟ واضح، كبرها، عادل نقدر
+
+25
+00:01:27,260 --> 00:01:29,920
+نكبرها من عندنا نكبرها من عندكم، نكبرها من عندنا
+
+26
+00:01:29,920 --> 00:01:33,530
+اللي بتحبه، يعني أنا ماعنديش مشكلتهالأ، إتمام،
+
+27
+00:01:33,530 --> 00:01:35,450
+إتمام، طبعاً «العالم الزمزرريلي» بالنسبة لوعيد
+
+28
+00:01:35,450 --> 00:01:37,590
+المحاضرة إن شاء الله أنا حكيتكم وحددكم زي ما
+
+29
+00:01:37,590 --> 00:01:40,690
+اتفقنا، هكون الساعة 4 بعد العصر، إما السبت أو
+
+30
+00:01:40,690 --> 00:01:45,930
+الإتنين، حسب توزيع الجدول، أنا هوزع جدول بينهم
+
+31
+00:01:45,930 --> 00:01:50,490
+وبين الشباب التانيين طبعا، بالنسبة للمراجع، طبعا
+
+32
+00:01:50,490 --> 00:01:53,510
+فينا كتاب اسمه «Practical Hematology» ل«باربرا»،
+
+33
+00:01:53,510 --> 00:01:57,550
+كتاب خيم جدا، إن شاء الله ممكن أنزلكم نسخة منه PDF
+
+34
+00:01:58,140 --> 00:02:02,900
+طبعًا فينا Color Atlas of Hematology هذا بيحتوي
+
+35
+00:02:02,900 --> 00:02:07,320
+على صور كثيرة طبعًا أهم مرجع أو أكثر مرجع ممكن
+
+36
+00:02:07,320 --> 00:02:10,940
+تستفيد منه اللي هو الـInternet الصور لإن إحنا
+
+37
+00:02:10,940 --> 00:02:14,460
+عملنا معمل عبارة عن خاصة في المعامل الأولى بركزلي
+
+38
+00:02:14,460 --> 00:02:17,300
+على موضوع شكل الخلايا الطبيعية وشكل الخلايا
+
+39
+00:02:17,300 --> 00:02:20,300
+الطبيعية وكيف نميز من خلية طبيعية وخلية طبيعية في
+
+40
+00:02:20,300 --> 00:02:24,520
+حالة الطبيعية والأمراض، تمام؟ ‏- تمام ‏- طبعًا،
+
+41
+00:02:24,520 --> 00:02:27,270
+مراجعة ممكن نلتقطبعًا، احنا هتذكر عن موضوع
+
+42
+00:02:27,270 --> 00:02:30,130
+المحاضرات للـ «سلايدات» اللي بنزلكم بيها على الـ
+
+43
+00:02:30,130 --> 00:02:34,610
+«موديوم» إن شاء الله وطبعًا المجلد المراجعته طبعًا
+
+44
+00:02:34,610 --> 00:02:39,590
+طبعًا يعني كمراجع إفراء أقلكم في تنمية طبعًا
+
+45
+00:02:39,590 --> 00:02:45,200
+المادة أكثر بالنسبة لأقلكمطبعًا المادة زي ما
+
+46
+00:02:45,200 --> 00:02:48,800
+حكيتكم هي عبارة عن دراسة لمكونات الدم والخلايا
+
+47
+00:02:48,800 --> 00:02:51,920
+ودراسة الـ Hemoglobin وأنواع الـ Hemoglobin ودراسة
+
+48
+00:02:51,920 --> 00:02:55,840
+الأمراض المختلفة اللي لها علاقة بالدم زي الأنيميا
+
+49
+00:02:55,840 --> 00:03:01,320
+زي مثلًا مرأة أم الثلاثيميا وأمراض أخرىطبعًا الهدف
+
+50
+00:03:01,320 --> 00:03:03,900
+منها زي ما حكينا الدراسة طبعًا أنتوا هتاخدوا إن
+
+51
+00:03:03,900 --> 00:03:07,420
+شاء الله جزء نظري مع دكتور أحمد سلمي وهيثيركم
+
+52
+00:03:07,420 --> 00:03:11,640
+بنحكي المادة النظرية بشكل كبير جدًا وانا إن شاء
+
+53
+00:03:11,640 --> 00:03:14,840
+الله هنعطيكم جزء عملي بمثالة مع المادة النظرية
+
+54
+00:03:14,840 --> 00:03:18,420
+فهندرس الخلايا، هندرس تشخيص حالات الأنيميا، هندرس
+
+55
+00:03:18,420 --> 00:03:22,560
+اللوكيميا وهندرس طبعًا اللي هي تحضير الأفلام، الدم
+
+56
+00:03:22,560 --> 00:03:26,930
+وكيف نقدر الشخص عنهافعنا طبعاً المعمل الأول اللي
+
+57
+00:03:26,930 --> 00:03:29,870
+هو «Slight Vibration and Staining» حكيتكم إذا
+
+58
+00:03:29,870 --> 00:03:34,030
+بتذكروا إنه هذا المعمل هو يعني كان آخر معمل في
+
+59
+00:03:34,030 --> 00:03:38,510
+المقدمة حيكون إن هو دا أول معمل في الـHematology
+
+60
+00:03:38,510 --> 00:03:42,550
+المعمل الثاني، هندرس طبعاً الخلايا البيضة، كيف
+
+61
+00:03:42,550 --> 00:03:46,190
+نعمل differential بين صفائح دموية وإيش الـ… نحكي
+
+62
+00:03:46,190 --> 00:03:52,630
+الـabnormal morphology فيهاهنعمل برضه لندرس المعمل
+
+63
+00:03:52,630 --> 00:03:54,910
+التالت الـ Abnormal Morphology في الخلايا الحمرة
+
+64
+00:03:54,910 --> 00:03:58,510
+وكيف نشخصها المعمل الرابع هكون عندنا عن
+
+65
+00:03:58,510 --> 00:04:02,230
+Reticulocyte Count المعمل الخامس عن Sickle Cell
+
+66
+00:04:02,230 --> 00:04:06,350
+Anemia المعمل السادس هكون عندنا عن الـ Hemoglobin
+
+67
+00:04:06,350 --> 00:04:09,990
+A2 طبعا أحنا كل دراستنا هكون فترة حالية دراسة
+
+68
+00:04:09,990 --> 00:04:14,750
+نظريةلكن إن شاء الله في أول ما يصير فرصة لنا نروح
+
+69
+00:04:14,750 --> 00:04:19,270
+المعامل، نتغذينا كويس في ناحية النظرية، وندخل
+
+70
+00:04:19,270 --> 00:04:23,170
+العمل المباشرة، ونكون عندنا موضوع اللي إجراء تجربة
+
+71
+00:04:23,170 --> 00:04:27,190
+سهل جدا بإذن الله تعالى طبعا المعمل السابع يكون
+
+72
+00:04:27,190 --> 00:04:32,470
+على الـFeta-Hemoglobinالمعمل الثامن عن الـ
+
+73
+00:04:32,470 --> 00:04:36,950
+Metamoglobin المعمل التاسع عن الـ G6PD Deficiency
+
+74
+00:04:36,950 --> 00:04:41,230
+اللي هو مرض التفول وعنا المعمل العاشر عن الـ
+
+75
+00:04:41,230 --> 00:04:43,550
+Sacrosis السنة والمعمل الأحداشر عن اسم الـ
+
+76
+00:04:43,550 --> 00:04:48,190
+Defragility طبعاً لأن المعمل رقم 12 طبعاً يعتبر
+
+77
+00:04:48,190 --> 00:04:52,170
+معمل مهم جداً هنتكلم عن جهاز الـ CPC اللي بالتأكيد
+
+78
+00:04:52,170 --> 00:04:55,910
+اشتغلته عليه في فترة المقدمة في المعمل المقدمة
+
+79
+00:04:55,910 --> 00:05:00,550
+أكيد احنا عملناأه يا معاد، فضل اشتغلنا عليها و
+
+80
+00:05:00,550 --> 00:05:04,130
+أحكيها أه صحيح، أشتغلنا بتوعها و مشيتوا عينات
+
+81
+00:05:04,130 --> 00:05:07,810
+عليها بس لنعرف أحنا كيف مبدأه، على أي أساس بيشتغل،
+
+82
+00:05:07,810 --> 00:05:10,670
+العين اللي بمشيها في الجهاز، كيف بتروح، و أين
+
+83
+00:05:10,670 --> 00:05:14,330
+بتروح، إيش بيصير فيها، طب كيف بيقرأ الجهاز، كل هذا
+
+84
+00:05:14,330 --> 00:05:17,370
+ندرسه في معمل Automated Hematology Cell Counter
+
+85
+00:05:17,870 --> 00:05:21,830
+طبعًا، وآخر المعاملين، طبعًا هما آخر تلت معاملة
+
+86
+00:05:21,830 --> 00:05:25,570
+دولة أكبر نظرية بحتي، يعني مش ناحية عملية المعامل
+
+87
+00:05:25,570 --> 00:05:29,350
+الأخر، هذا ممكن تاخدوه في نظري أكتر، اللي هو «cell
+
+88
+00:05:29,350 --> 00:05:34,150
+maturation» وطبعًا تشخيص اللوكيميا، الأخر، طبعًا
+
+89
+00:05:34,150 --> 00:05:37,310
+المعاملة هيكون عن أنواع اللوكيميا وكيف نشخصها،
+
+90
+00:05:37,310 --> 00:05:44,290
+الأخرين طبعًا، هذي بشكل أساسي بالنسبة لـ… نحكي
+
+91
+00:05:44,290 --> 00:05:48,580
+المعاملة تبعتناهنوصل إن شاء الله، هتكون عندنا فرصة
+
+92
+00:05:48,580 --> 00:05:52,500
+لتنمية مهاراتنا في معمل الدم إن شاء الله، بدي أسأل
+
+93
+00:05:52,500 --> 00:05:59,760
+«سيف» دخل ولا لسه؟ لسه ما دخلش طب خلاص، يعني هذه
+
+94
+00:05:59,760 --> 00:06:04,280
+إن شاء الله مسجلة، هنحاول قدر مستوطنة إن شاء الله
+
+95
+00:06:04,280 --> 00:06:08,140
+نوصل إلى «سيف» وزي السفصار، ممكن إن شاء الله شرس
+
+96
+00:06:08,140 --> 00:06:14,140
+باق، هنوح لمعملنا حاليا الأولطبعا المعمل هذا أخدنا
+
+97
+00:06:14,140 --> 00:06:17,980
+.. إذا بتذكروا نفس المحاضرة تقريبا يعني في ال ..
+
+98
+00:06:17,980 --> 00:06:24,920
+شو اسمه؟ المقدم يعني دقيقة شباب، ده واقف بتزيل، بس
+
+99
+00:06:24,920 --> 00:06:30,000
+عشان التليفون من شغلها شوف
+
+100
+00:06:30,000 --> 00:06:33,960
+سيف، إيش صار معاه؟
+
+101
+00:06:38,130 --> 00:06:41,650
+وأنا معاك. طيب، أحنا هنكمل إن شاء الله أنا عملت
+
+102
+00:06:41,650 --> 00:06:46,210
+تكميل التسجيل إن شاء الله أنا هروح طبعاً هذه
+
+103
+00:06:46,210 --> 00:06:49,670
+بالنسبة للـOutline للمادة هروح هنا زي ما حكينا
+
+104
+00:06:49,670 --> 00:06:53,970
+المعمل الأول المعمل
+
+105
+00:06:53,970 --> 00:06:57,930
+الأول الـBlood اسمه، شايفين الـScreen معادي، أه؟
+
+106
+00:06:57,930 --> 00:07:02,290
+طيب، طيب، احنا إن شاء الله، بس خليني أنا أعملكم
+
+107
+00:07:02,290 --> 00:07:05,470
+الـ…
+
+108
+00:07:05,470 --> 00:07:10,210
+طيبالـ Blood Smear، طبعًا، هذا المعمل أخدناه في،
+
+109
+00:07:10,210 --> 00:07:13,930
+زي ما حكينا في المقدمة، آخر معمل كان عندنا طبعًا،
+
+110
+00:07:13,930 --> 00:07:17,210
+إذا بتذكروا، قولنا إحنا عندي تلت أنواع طرق في عمل
+
+111
+00:07:17,210 --> 00:07:21,490
+الـBlood Smear إذا بتذكروا، عندي الـCover Glass
+
+112
+00:07:21,490 --> 00:07:24,770
+Smear واللي بيستخدمان فيها الـCover Slide، تمام؟
+
+113
+00:07:24,770 --> 00:07:29,550
+وبيستخدم على Slide طبعًا، هذه الطريقة شوية تقنية
+
+114
+00:07:29,550 --> 00:07:32,670
+أو الـpractice بتاعها شوية صعبة نوعًا ما، عندي
+
+115
+00:07:32,670 --> 00:07:36,730
+الـ…–الكاميرات الصحيفة عنها آه يا معادما كانتش
+
+116
+00:07:36,730 --> 00:07:39,870
+تظبط معنا أساساً ماكانتش تظبط معايا لأنه بتغلب
+
+117
+00:07:39,870 --> 00:07:43,890
+شوية كانت تظبط معايا بس كانت تظبط معايا كشر محمد
+
+118
+00:07:43,890 --> 00:07:46,190
+اللي هي الوجه … اللي هي الولادتين اللي هي
+
+119
+00:07:46,190 --> 00:07:48,610
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+120
+00:07:48,610 --> 00:07:48,610
+هي الولادتين اللي هي الولادتين اللي هي الولادتين
+
+121
+00:07:48,610 --> 00:07:48,630
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+122
+00:07:48,630 --> 00:07:48,750
+الولادتين اللي هي الولادتين اللي هي الولادتين اللي
+
+123
+00:07:48,750 --> 00:07:48,770
+هي الولادتين اللي هي الولادتين اللي هي الولادتين
+
+124
+00:07:48,770 --> 00:07:49,270
+اللي هي الولادتين اللي هي الولادتين اللي هي
+
+125
+00:07:49,270 --> 00:07:55,110
+الولادتين اللي هي الولادتين
+
+126
+00:07:55,110 --> 00:07:57,730
+اللي هي ال
+
+127
+00:08:00,670 --> 00:08:03,990
+طبعاً هذه كانت تقصد معاكم وإن شاء الله بس نروح على
+
+128
+00:08:03,990 --> 00:08:09,160
+المعامل هنعيد نعملها ونصبغ ال slide ونقرأهاعندي
+
+129
+00:08:09,160 --> 00:08:11,620
+نوع تالت هو «Spun Smear» زي اللي تذكره وقلتلكم هذا
+
+130
+00:08:11,620 --> 00:08:16,080
+عبارة عن استخدام جهاز خاص في الـ «سلايدات» وتحط
+
+131
+00:08:16,080 --> 00:08:19,740
+عليه نقطة دم مع نحكي الـ «كيت» خاص طبعا الـ «كيت»
+
+132
+00:08:19,740 --> 00:08:24,020
+هذا بنحط عليه الـ «سلايد» مع نقطة الدم وهو بفردلي،
+
+133
+00:08:24,020 --> 00:08:27,400
+بعملي الـ «distribution» لفرد الخلايا متجانس 100%
+
+134
+00:08:27,400 --> 00:08:32,220
+طبعا «Spun Smear» كنا نستخدمها أحنا في عملية أنه
+
+135
+00:08:32,220 --> 00:08:35,460
+نقرأ الـ «differential» أو شيء خاصة في حالات في
+
+136
+00:08:35,460 --> 00:08:39,790
+الكيميابتوزع الخلايا بشكل متجانس طبعا في عندي
+
+137
+00:08:39,790 --> 00:08:43,070
+نوعين تانية يستخدموها في حالات خاصة اللي مافي قوة
+
+138
+00:08:43,070 --> 00:08:45,210
+تسمية وهذه في حالة إذا كان عندك بعض الحالات اللي
+
+139
+00:08:45,210 --> 00:08:49,010
+بيكون عندها الخلايا البيضا أقل من ألف كدهش نور
+
+140
+00:08:49,010 --> 00:08:56,170
+مريج لخلايا البيضا سعيد؟ 8000 كدهش؟ 8000 تقريبا من
+
+141
+00:08:56,170 --> 00:09:00,240
+4000 ل 11000فبالحالة اللي كانت عندك Lycopenia إذا
+
+142
+00:09:00,240 --> 00:09:03,840
+بتذكروا Lycopenia هو نقص في خلايا البيضة، الحال هي
+
+143
+00:09:03,840 --> 00:09:06,420
+أنا بستخدم الـBuffie Smear، الـCoat Smear، طبعا
+
+144
+00:09:06,420 --> 00:09:10,420
+باخد العينة، بـCenterها و باخد من الـBuffie Coat،
+
+145
+00:09:10,420 --> 00:09:13,540
+بحطها على الـBlood Film و نفرضها، ممكن إن شاء الله
+
+146
+00:09:13,540 --> 00:09:17,820
+نعملها إحنا، في نوع اللي بيسموه الـThick Blood
+
+147
+00:09:17,820 --> 00:09:20,560
+Smear، هذا بيستخدمها في حالات، إن أنا دول بيشوف
+
+148
+00:09:20,560 --> 00:09:24,000
+حالات الـParasite، خاصة الملارياطبعًا الـ Malaria
+
+149
+00:09:24,000 --> 00:09:27,600
+بنعرف أنه موجود داخل الخلايا الحمراء لو بنتخب الـ
+
+150
+00:09:27,600 --> 00:09:31,280
+Butch Smear فبالتالي أنا مش هقدر أني أنا أشوف
+
+151
+00:09:31,280 --> 00:09:34,420
+البراثايد لأنه هكون عدده قليل وصعب جدًا أني أميزها
+
+152
+00:09:34,420 --> 00:09:39,160
+لكن بالحالة بستخدم الـ Thick Smear بتقدر أني أتميز
+
+153
+00:09:39,160 --> 00:09:43,420
+الخلايا وتقدر أنه لو كان مثلًا نحكي عدد البراثايد
+
+154
+00:09:43,420 --> 00:09:48,620
+قليلة بقدر أني أشخص الحالة الحقيقية، تمام؟طبعًا
+
+155
+00:09:48,620 --> 00:09:51,440
+العينات المستخدمة أحنا في الـWedge Smear اللي هي
+
+156
+00:09:51,440 --> 00:09:54,920
+عينة الـEdita طبعًا هي العين الـCPC نفسها لازم
+
+157
+00:09:54,920 --> 00:09:58,920
+تكون fresh مستخدم خلال ساعتين إلى تلت ساعات طبعًا
+
+158
+00:09:58,920 --> 00:10:03,200
+– زي هذا يا دكتور – هذا لأ، هذا يعتبر Chemistry
+
+159
+00:10:03,200 --> 00:10:05,960
+Tube هذا، مش Edita أنا مش شايف، اللي هو اللي هو
+
+160
+00:10:05,960 --> 00:10:10,880
+أحمر الغطاية، محمد؟ – لأ، الفكرة مكتوبة على Edita
+
+161
+00:10:10,880 --> 00:10:12,860
+– اللي هو Edita صح، اللي هو غطاية غلط، اللي هو
+
+162
+00:10:12,860 --> 00:10:15,600
+غطاية غلط، لازم الغطاية يكون Perpet – لأ، لأ، صح
+
+163
+00:10:15,600 --> 00:10:20,340
+كلامك، صحالغطايب محطوطة غلط، لأنه غالبًا يكون لونه
+
+164
+00:10:20,340 --> 00:10:23,500
+purple أو أزرق، وغالبًا purple، مكتوب على إيده ده
+
+165
+00:10:23,500 --> 00:10:28,880
+صحيح. طبعًا، لأ، فيه إن طبعًا، ليش أنا، ليش أنا
+
+166
+00:10:28,880 --> 00:10:33,940
+أول شي ب .. طبعًا بستخدم فرش اسمه blood، عشان
+
+167
+00:10:33,940 --> 00:10:37,340
+مايصيحش عندي تغيرات في الخلايا الحمرة، يعني نقطة
+
+168
+00:10:37,340 --> 00:10:40,620
+مهمة. وهي وضرف تبعاته. بيصيح تغيرات في خلايا الدم
+
+169
+00:10:40,620 --> 00:10:43,260
+الحمرة، وبيصير زي عملية .. انه بيصير زي
+
+170
+00:10:43,260 --> 00:10:46,950
+Speculated، بيصير زي أكيد إنها من شرية،وهذه، في
+
+171
+00:10:46,950 --> 00:10:50,010
+عندي بعض الحالات بيكون في أصلًا هي عبارة عن سموها
+
+172
+00:10:50,010 --> 00:10:52,830
+«crenated» أو «speculated» طبعًا اللي هي «Spar»
+
+173
+00:10:52,830 --> 00:10:55,830
+وطبعًا هذه الخلايا في حالات مرضية لكن هنا بيكون مش
+
+174
+00:10:55,830 --> 00:11:00,610
+مرضية سببها اللي هي درجة الحرارة أو الـ «old
+
+175
+00:11:00,610 --> 00:11:05,090
+specimen»، تمام؟ طبعًا، متى بيصير هذه الحالات الـ
+
+176
+00:11:05,090 --> 00:11:07,150
+«crenated»؟ تمحك هنا، في حالة إنه عندي
+
+177
+00:11:07,150 --> 00:11:11,510
+الـAnticoagulant كميته أكتر من العينة، كيف يعني؟
+
+178
+00:11:11,780 --> 00:11:15,040
+إحنا بنعرف إحنا عندي مثلا الـ Tube Medical Editor
+
+179
+00:11:15,040 --> 00:11:18,480
+موجود معاك يا محمد، إيش مكتوب عليه كمية الدم؟
+
+180
+00:11:18,480 --> 00:11:22,540
+مكتوب إنك تحط مل تلاتة مل تلاتة مل، هجيت لو حطيت
+
+181
+00:11:22,540 --> 00:11:25,880
+أقل من تلاتة مل، حطيت واحد مل، تسيطر عملية الـ
+
+182
+00:11:25,880 --> 00:11:28,140
+Ratio بين الـAnticoagulant اللي هو الـEditor اللي
+
+183
+00:11:28,140 --> 00:11:31,960
+موجودة في الـTube، و الدم تختلف، فهذه تؤدي لغيرات
+
+184
+00:11:31,960 --> 00:11:36,700
+شكلية في الخلايا نفسها، تمام؟ في نقطة تانية تؤدي
+
+185
+00:11:36,700 --> 00:11:39,880
+لكرينية الـ…………………………………………………………
+
+186
+00:11:41,810 --> 00:11:45,830
+بينفع شجر المنتلات، هشوف عليه، يعني هو مش زي مثلًا
+
+187
+00:11:45,830 --> 00:11:49,410
+إذا معمل مثلًا إن شاء الله لنا نزهب، هنكون عملية
+
+188
+00:11:49,410 --> 00:11:53,090
+ال ratio high مهم جدًا كتير بالنسبة للدم والـ
+
+189
+00:11:53,090 --> 00:11:56,570
+Atomic Aggregate بالنسبة للمعمل الـ Nephematology،
+
+190
+00:11:56,570 --> 00:12:00,530
+هي مهمة، مهمة، يعني لكن مش، يعني بنقدر نتجوزها،
+
+191
+00:12:00,530 --> 00:12:03,650
+لكن مش أنه نتجوزها بشكل كبير، يعني كيف مثلًا، أنا
+
+192
+00:12:03,650 --> 00:12:07,850
+لوعند المطلوب إن أحط تلاتة، وروح وحطيت اتنين ونص،
+
+193
+00:12:07,850 --> 00:12:12,610
+بمشيها عادي عادي، لكن ماحطش واحد، ماحطش نص لأنه
+
+194
+00:12:12,610 --> 00:12:15,170
+مثلا إن أحط نص، لو فرض أن أنا فيها point 2 ml
+
+195
+00:12:15,170 --> 00:12:18,610
+وحطيت نص ال ratio بينهم هيخلف، هتؤدي الاختلاف حتى
+
+196
+00:12:18,610 --> 00:12:21,190
+في توزيع الخلايا وبالتالي، هتؤدي الاختلاف في حجم
+
+197
+00:12:21,190 --> 00:12:25,350
+الخلايا بالنسبة للـ Antibiotic لو تؤدي الاختلاف في
+
+198
+00:12:25,350 --> 00:12:28,250
+عملية القراءة في جهة الـCBC ممكن فهذه النقطة مهم
+
+199
+00:12:28,250 --> 00:12:33,320
+جدا بالنسبة لل ratioعندي السبب التاني اللي يؤدي
+
+200
+00:12:33,320 --> 00:12:36,100
+لـCrenated يعني أحد أسباب اللي يؤدي لـCrenated
+
+201
+00:12:36,100 --> 00:12:40,220
+طبعًا اللي بنسميها أحنا الحالات، مش مرضية هاي،
+
+202
+00:12:40,220 --> 00:12:43,080
+اللي هي Old Specimens في عندي بذلة بحكي عنها برضه
+
+203
+00:12:43,080 --> 00:12:45,780
+الحرارة، في حالة الحرارة تؤدي لـCrenated دور
+
+204
+00:12:45,780 --> 00:12:48,560
+الـCrenated، الثاني تلت أسباب تؤدي لدور
+
+205
+00:12:48,560 --> 00:12:55,720
+الـCrenated طبعًا للحالات الـNormal دكتور، أه محمد
+
+206
+00:12:55,720 --> 00:12:59,020
+–بعدين أتفض على الـslide اللي بتشرح عليها – تمام
+
+207
+00:13:02,780 --> 00:13:07,480
+الثلاث حالات اللي تؤدي للحالات الغير مرضية اللي هي
+
+208
+00:13:07,480 --> 00:13:14,360
+الحالات ال normal هي بالضبط ال old blood
+
+209
+00:13:14,360 --> 00:13:20,280
+و ال ratio تبقى هذا ال ratio amount of blood blood
+
+210
+00:13:20,280 --> 00:13:24,380
+blood blood blood blood blood blood blood blood
+
+211
+00:13:24,380 --> 00:13:24,620
+blood blood blood blood blood blood blood blood
+
+212
+00:13:24,620 --> 00:13:26,860
+blood blood blood blood blood blood blood blood
+
+213
+00:13:26,860 --> 00:13:26,920
+blood blood blood blood blood blood blood blood
+
+214
+00:13:26,920 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+215
+00:13:27,320 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+216
+00:13:27,320 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+217
+00:13:27,320 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+218
+00:13:27,320 --> 00:13:27,320
+blood blood blood blood blood blood blood blood
+
+219
+00:13:27,320 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+220
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+221
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+222
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+223
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+224
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+225
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+226
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+227
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+228
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+229
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+230
+00:13:27,340 --> 00:13:27,340
+blood blood blood blood blood blood blood blood
+
+231
+00:13:27,340 --> 00:13:29,510
+blood blood bloodالـ Cernated بدأت بالحالة أن تكون
+
+232
+00:13:29,510 --> 00:13:33,550
+ملم فيها لأن هذه الحالة سببها مش مرضي طبعاً هذه
+
+233
+00:13:33,550 --> 00:13:36,410
+كيف تعرفها؟ هذه تعرفها إنه مثلا أنا مالاج عامل
+
+234
+00:13:36,410 --> 00:13:40,090
+عصلاية هلاقي إنه عملية الـ Cernated مش مسك لكل RBC
+
+235
+00:13:40,090 --> 00:13:43,870
+هتلاقي بعض المناطق فيها Cernated وبعض المناطق لأ،
+
+236
+00:13:43,870 --> 00:13:46,930
+تمام؟ هتلاقي بعض الخلايا أه وبعض الخلايا لأ، في
+
+237
+00:13:46,930 --> 00:13:48,730
+الحياة المرضية لأ، بيكون معظم الخلايا فيها
+
+238
+00:13:48,730 --> 00:13:52,310
+Cernated في الحياة المرضية ليست بره، تمام؟هل جيت
+
+239
+00:13:52,310 --> 00:13:56,390
+الحلقات اللي نحكي الـ «normal» ويكون أصلًا سببها
+
+240
+00:13:56,390 --> 00:14:00,610
+نحكي خارجي، يعني مش مرضي، اللي هي زي ما حكينا ليه
+
+241
+00:14:00,610 --> 00:14:04,010
+الـRatio Anticagulant للـOil Displacement والـWarm
+
+242
+00:14:04,010 --> 00:14:11,970
+Environment، تمام؟ محمد
+
+243
+00:14:11,970 --> 00:14:17,790
+تمام؟ ما سمع ناس آه
+
+244
+00:14:17,790 --> 00:14:26,180
+سامعدعوتي نرجع للـ slide، فيه عندك سؤال بيها؟
+
+245
+00:14:26,180 --> 00:14:33,260
+بس ما تغيرت ال slide عندى، انا
+
+246
+00:14:33,260 --> 00:14:41,260
+رجعتلها، ما تغيرش انتي عندى، ايه ال slide اللي قمت
+
+247
+00:14:41,260 --> 00:14:42,740
+بإيديك؟
+
+248
+00:14:49,920 --> 00:14:53,500
+محمد slide high؟ لا بتغير الشاشة عندك قاعد كله
+
+249
+00:14:53,500 --> 00:14:59,440
+ثابت عند الكل طب ليش؟ هو عندك كمان ثابت عند ال
+
+250
+00:14:59,440 --> 00:15:06,080
+outline كله موجود عند ال outline عندك؟ آه كله كله
+
+251
+00:15:06,080 --> 00:15:09,060
+عند ال outline الشاشة اللي واضحة عند ال outline
+
+252
+00:15:09,060 --> 00:15:14,980
+أنا ومحمد نفس القصة طب هيك؟ أيوة هيك اتغيرت صحيح؟
+
+253
+00:15:14,980 --> 00:15:18,400
+هيك اتغيرت ناحية ال practical hematology تجيبني
+
+254
+00:15:18,400 --> 00:15:22,010
+على slide B now؟أنواع الـ، شو اسمها؟ الاسمية،
+
+255
+00:15:22,010 --> 00:15:25,610
+شفتوها؟ آه تمام، تمام هاي ال slide دلك يا إمحمد،
+
+256
+00:15:25,610 --> 00:15:29,890
+هاي؟ تمام، هاي، هاي، هاي قدام إيش سؤالك فيها يا
+
+257
+00:15:29,890 --> 00:15:33,110
+إمحمد؟
+
+258
+00:15:33,110 --> 00:15:41,310
+يا إمحمد؟
+
+259
+00:15:41,310 --> 00:15:44,950
+دكتورة
+
+260
+00:15:44,950 --> 00:15:50,370
+آه، معذرعشان بقيتها في الـ Wedge بالـBlood Smear
+
+261
+00:15:50,370 --> 00:15:56,350
+مكتوب «Collected to Mark of You»، إيش يعني؟ ليه؟
+
+262
+00:15:56,350 --> 00:16:00,390
+حكيناها الـRatio، يعني أنت بدك تسحب اللي عندك
+
+263
+00:16:00,390 --> 00:16:04,350
+علامة، في عندك علامة، أه، بدك تسحب اللي عندك علامة
+
+264
+00:16:04,350 --> 00:16:07,470
+أو تحط نفس الكمية ليه 3 ML زي ما موجود عند محمد 3
+
+265
+00:16:07,470 --> 00:16:12,510
+ML، في عندك الـDepartment، أي Mark، يكون 3 ML أو
+
+266
+00:16:12,510 --> 00:16:17,350
+في Mark، يكون علامة، تمام، تمام، فهمت، فهمتطيب،
+
+267
+00:16:17,350 --> 00:16:23,390
+السمير احنا؟ دخل سيف ولا لسه؟ اه دخل، هاي صوت
+
+268
+00:16:23,390 --> 00:16:29,030
+موجود ايه و أيه يا عم، معاكوا هففتح كاميرا غنيه،
+
+269
+00:16:29,030 --> 00:16:33,730
+بياخد أهلا، طيب، احنا .. نسمينا الشباب عشان وقت
+
+270
+00:16:33,730 --> 00:16:39,010
+وعمل وقت طبعا ال procedures أخدناها قبل ذلك، زي ما
+
+271
+00:16:39,010 --> 00:16:43,540
+حكينا، ملحوطعلى الـ «سلايد» إذا تذكرونه، نجيب
+
+272
+00:16:43,540 --> 00:16:48,060
+سلايد ثاني بزاوية تلاتي إلى أربعين درجة، وبعدين
+
+273
+00:16:48,060 --> 00:16:54,100
+نفردها بطريقة طبعا سالسة، مش جيركي مانار، تمام؟
+
+274
+00:16:54,100 --> 00:16:59,890
+نخلّي الـ«بلاد»، الفيلم، ينشفوبعد ذلك طبعًا نسبقها
+
+275
+00:16:59,890 --> 00:17:04,570
+طبعًا في نقاط مهم جدًا اللي هي عملية الزاوية كل ما
+
+276
+00:17:04,570 --> 00:17:09,530
+زادت الزاوية طبعًا كل ما صار طبعًا الطول أقل ويصير
+
+277
+00:17:09,530 --> 00:17:13,530
+السمي ال «thick» أكتر يعني أنا هاي slide أنا
+
+278
+00:17:13,530 --> 00:17:15,610
+ماعنديش اللي كان لو عندي اللي كان الرجل اللي كان
+
+279
+00:17:15,610 --> 00:17:20,370
+فهي عندي slideين شايفين بالفيديو تمام؟عطيت، أنا
+
+280
+00:17:20,370 --> 00:17:23,850
+هذه الزاوية كل ما قلعت الزاوية كان عندي الطول أكتر
+
+281
+00:17:23,850 --> 00:17:29,430
+والسمير ثم أكتر، لو أحط زاوية أكتر بيصير thick
+
+282
+00:17:29,430 --> 00:17:33,210
+فانا لو بدي ديها thicker أكتر، بدي إيه عشان أعمل؟
+
+283
+00:17:33,210 --> 00:17:36,810
+أزيل الزاوية، تمام؟ تحكم بالزاوية وابقى دي اللي
+
+284
+00:17:36,810 --> 00:17:40,470
+بيحكم في نوع السمير و الـquality للسمير دبعتنا،
+
+285
+00:17:40,470 --> 00:17:45,190
+طبعا هذه الصورة توضحيةبنحط drop، وبعدين بنجيب الـ
+
+286
+00:17:45,190 --> 00:17:48,690
+«سلايد» الثاني بزاوية 30 إلى 40 ونفردها بطريقة
+
+287
+00:17:48,690 --> 00:17:53,810
+سلسة هاي الـSmear، طبعاً، شايفينها، بنخليها تنشف
+
+288
+00:17:53,810 --> 00:17:57,810
+وبعد ذلك بنعملها Fixation بواسطة الـMethanol
+
+289
+00:17:57,810 --> 00:18:04,170
+وبنعملها Staining طبعاً الـArtifacts، أيش يعني
+
+290
+00:18:04,170 --> 00:18:08,460
+Artifacts يا معاد؟ الأثار تبعتهاالـ Artifacts ليه
+
+291
+00:18:08,460 --> 00:18:13,800
+أي شغلة تؤدي لطبعًا ظهور، يعني نحكي الـ «زمير» مش
+
+292
+00:18:13,800 --> 00:18:16,820
+بالـ Quality صح، إن أنا برفضها. لا، يعني مضاعفات،
+
+293
+00:18:16,820 --> 00:18:20,240
+ما بنتحكي عنها. مش، مش، يعني شغلات شوائب، نحكي. هي
+
+294
+00:18:20,240 --> 00:18:23,460
+Artifacts يعني شوائب، تمام؟ أوكي، أوكي. أول شي،
+
+295
+00:18:23,460 --> 00:18:26,980
+العملية الفرد تكون غلط، هتؤدي لظهور Artifacts. أنت
+
+296
+00:18:26,980 --> 00:18:29,500
+جيت فردت، ماعرفت تبعتش زاوية 30 إلى 40، وماعرفت
+
+297
+00:18:29,500 --> 00:18:34,240
+تعمل زاوية مثلًا 50، هتؤدي لظهور «زمير» قصيرة و
+
+298
+00:18:34,240 --> 00:18:38,490
+«very thick»، مش هيكون كويس لقراية فيلم.أنت ممكن
+
+299
+00:18:38,490 --> 00:18:42,770
+تكون عندك عملية الـHumidity أدت إلى Slow-drying
+
+300
+00:18:42,770 --> 00:18:47,490
+تؤدي لظهر الـArtifacts عملت الـFixation طولت فيها،
+
+301
+00:18:47,490 --> 00:18:49,630
+روح سفررت بالاسمير وخلت تانية وعملت الـFixation
+
+302
+00:18:49,630 --> 00:18:53,130
+برضه غلط أصول أول ما تنشف الـSlide عملها
+
+303
+00:18:53,130 --> 00:18:58,330
+الـFixation وجود المي في الـMethanol إذا كان موجود
+
+304
+00:18:58,330 --> 00:19:02,590
+المي أكتر من 3% في الحالة هذه لازم أنا أيش برضه أن
+
+305
+00:19:02,590 --> 00:19:05,630
+أتجنب وجود المي في المي لأن المي تعمل Artifacts
+
+306
+00:19:07,460 --> 00:19:10,740
+طبعًا، عندي بعض الحالات المرضية تؤدي لظور الـ
+
+307
+00:19:10,740 --> 00:19:14,020
+Artifacts زي مثلًا، إذا كان عندك عدد الخلايا الـ
+
+308
+00:19:14,020 --> 00:19:17,080
+lymphocytes عالية أحنا بنعرف إن الـ lymphocytes
+
+309
+00:19:17,080 --> 00:19:23,930
+عبارة عن خلايا بنواة واحدةطبعًا هذه الـ
+
+310
+00:19:23,930 --> 00:19:29,570
+lymphocytes دلوقت تحكي هشة، fragile مجرد إنك أنت
+
+311
+00:19:29,570 --> 00:19:32,970
+لو كان العدد كبير ومجرد أنك عملت خرد لإلها ممكن
+
+312
+00:19:32,970 --> 00:19:35,550
+تتكسر إذا كانت بعداد كبيرة أو في بعض الحالات
+
+313
+00:19:35,550 --> 00:19:39,870
+المرضية زي مثلًا اللوكيميا اللي هي CLL-Chronic
+
+314
+00:19:39,870 --> 00:19:42,970
+Lymphocytic Leukemia أو الـAcute Leukemia فهذه
+
+315
+00:19:42,970 --> 00:19:48,470
+تؤدي لظهر Artifacts، فما نتكسر عفوا ما نتكسر في
+
+316
+00:19:48,470 --> 00:19:51,890
+الحالة هذه مش هتظهر عندك خلايا، هتظهر عندك بقايا
+
+317
+00:19:51,890 --> 00:19:57,320
+خلايااللي هي ممكن تظهر النواة، ممكن تظهر مثلًا
+
+318
+00:19:57,320 --> 00:20:01,500
+الـ«سيرفريبلانت» اللحال حسب، تمام؟ عندك تغييرات
+
+319
+00:20:01,500 --> 00:20:04,500
+برضه تصير الـGenerative Changes اللي هي بتصير في
+
+320
+00:20:04,500 --> 00:20:08,340
+عملية الـStorage، كيف يعني؟ أنا أخدت عينيتي الدم،
+
+321
+00:20:08,340 --> 00:20:12,820
+وراح محمد بدل ما يروح يعمل Blood Film منها، راح
+
+322
+00:20:12,820 --> 00:20:16,260
+إشعمال، خلّاها في التلاجة أو خلّاها مثلًا في
+
+323
+00:20:16,260 --> 00:20:20,400
+الغرفة لثاني يوم، ثاني يوم هسيب عندك تغييرات على
+
+324
+00:20:20,400 --> 00:20:31,600
+الخلايا، النواة، تمام؟تمام طبعاً
+
+325
+00:20:33,010 --> 00:20:37,570
+خصائص الـ… الـ «Blood Film» الكويس هذه الخصائص
+
+326
+00:20:37,570 --> 00:20:41,730
+«Blood Film» كويس اللي هي طبعاً خدناها برضه أهم
+
+327
+00:20:41,730 --> 00:20:45,410
+خاصية أنه زي ما حكينا يكون «thick» at one end
+
+328
+00:20:45,410 --> 00:20:48,270
+«thin» out of the smooth، يعني كيف يعني؟ أن
+
+329
+00:20:48,270 --> 00:20:51,130
+الـ«Blood Film» بالبداية يكون «thick» وفي النهاية
+
+330
+00:20:51,130 --> 00:20:53,910
+يكون «thin» واحنا بنقرأ، إذا بتذكروا، بنقرأ من
+
+331
+00:20:53,910 --> 00:21:00,110
+المنطقة اللي في الوسط، صحيح سعيد؟ صحيح، صحيح، ده
+
+332
+00:21:00,110 --> 00:21:05,990
+معايا، تمامالشغل التاني تكون عندك تحتوي يعني Slide
+
+333
+00:21:05,990 --> 00:21:09,790
+تلتينها تقريبًا موجود للفيلم نفسه الشغل التالتة
+
+334
+00:21:09,790 --> 00:21:14,890
+أنه ما تلمسش الحافة وآخر شيء تكون أن الـ «حواط»
+
+335
+00:21:14,890 --> 00:21:19,210
+ربعتها مافيش فيها شراشين نحكي أنه «margin free»
+
+336
+00:21:19,210 --> 00:21:22,170
+ولا يكون مسك الحواط على اليمين وعشمال يعني يكون
+
+337
+00:21:22,170 --> 00:21:27,630
+بعيد عن الحواط هذه خاصات مدفلم اللي كويس هيها
+
+338
+00:21:27,630 --> 00:21:32,250
+«thick»من أثنين إلى أثنين برنامج تانية، طبعًا إحنا
+
+339
+00:21:32,250 --> 00:21:36,310
+بالمنطقة اللي بقرا فيها اللي هي الـ Advocate Area،
+
+340
+00:21:36,310 --> 00:21:38,210
+الـ Thick Area ماقراش منها ولا Skin Area بقرا
+
+341
+00:21:38,210 --> 00:21:43,190
+منها، بقرا من منطقة الـ Advocate Area هذي، هذي بعض
+
+342
+00:21:43,190 --> 00:21:47,850
+الـ «الذنوب»، بالنص، مش بالنص، مش شرط بالنص، حسب
+
+343
+00:21:47,850 --> 00:21:51,170
+توتيم بلاد فيلم، حسب فيلم، بلاد فيلم للسوق، أجيتها
+
+344
+00:21:51,170 --> 00:21:55,940
+أنا عنديبعض أنواع الـ Blood Film اللي هي تقريبًا
+
+345
+00:21:55,940 --> 00:21:59,420
+تعتبرش كويسة أنا ممكن أعتبرها كديه نوعًا ما كويس،
+
+346
+00:21:59,420 --> 00:22:03,200
+بس مش كتير يعني، تمام؟ فأنتوا شايفينها، شايفها سيد
+
+347
+00:22:03,200 --> 00:22:09,160
+أنتي؟ آه، آهبإي اي و بي و سي و دي ممتاز اي و بي و
+
+348
+00:22:09,160 --> 00:22:12,480
+سي سيئة جدا، دي نوعا ما كويسة لكن ماعتبراش كويسة
+
+349
+00:22:12,480 --> 00:22:16,460
+لإنه مش بي .. أنا بالنسبالي بعتبرها مش كتير، لإن
+
+350
+00:22:16,460 --> 00:22:20,720
+مش بيعطياني finger shape مش ما .. مش طولتين ال
+
+351
+00:22:20,720 --> 00:22:24,160
+slide تقريبا، تمام؟ هو اللي .. اللي احنا تبقى نوعا
+
+352
+00:22:24,160 --> 00:22:31,100
+ما أحسن من الواقعين، ما تطلعوا إنتي إيه؟ كيف؟
+
+353
+00:22:31,100 --> 00:22:35,530
+دي أفضلدي أفضل من القراءة لكن بعتبرها شانة كويسة،
+
+354
+00:22:35,530 --> 00:22:39,230
+بالنسبالي أنا لو بقيمها بقيمها تقريبا تلاتة أو
+
+355
+00:22:39,230 --> 00:22:43,750
+أربع من خمس بس، فهمنا كيف؟ بس أحسن من الـA و أحسن
+
+356
+00:22:43,750 --> 00:22:44,650
+من الـB و أحسن من الـC
+
+357
+00:22:48,030 --> 00:22:50,750
+بالظبط، هذه أنواع سيئة جدًا كلها من البلاد في
+
+358
+00:22:50,750 --> 00:22:53,870
+الأمور واحدة فيها كويسة، شايفين؟ طبعًا هنا شايفين
+
+359
+00:22:53,870 --> 00:22:56,930
+الـMargins كيف شايفش، هذه عندي الهواف شرشير بـ12
+
+360
+00:22:56,930 --> 00:23:00,210
+قراءة، هذه جاي متقطعة، فبالتالي مافيش فيها، نحكي
+
+361
+00:23:00,210 --> 00:23:03,130
+زي «genus» في عملية الـ«thickness»، هذه قصيرة، هذه
+
+362
+00:23:03,130 --> 00:23:09,110
+رفيعة، هذه فيها، نحكي زي الفقاعات تمام، فيها
+
+363
+00:23:09,110 --> 00:23:13,170
+«holes»، وهذه بالجاي متجنسية، وهذه طبعًا فيها رقم
+
+364
+00:23:13,170 --> 00:23:18,550
+«C» إيش مالها؟ رقم إيش «C»؟يعني مش معتادة طولتين،
+
+365
+00:23:18,550 --> 00:23:20,950
+مش مازي .. مش جاي أنه .. طبعا هان thick، هان مش زي
+
+366
+00:23:20,950 --> 00:23:24,290
+ثن كتير، تمام؟ ممكن أنت تقرأها، بدك تقرأ منطقة هاي
+
+367
+00:23:24,290 --> 00:23:26,690
+مش هتعرف تقرأها كويس، بدك منطقة تقرأ بيها كويس،
+
+368
+00:23:26,690 --> 00:23:30,550
+يعني نهاية الرقم C ممكن أنه حط الزاوية عالي شوية،
+
+369
+00:23:30,550 --> 00:23:33,530
+لو نزل الزاوية شوية صغيرة وفرد، ال cancer تضمع
+
+370
+00:23:33,530 --> 00:23:39,550
+أكتر طبعا طب
+
+371
+00:23:39,550 --> 00:23:45,160
+دكتور بعد إذنك، بس ارجع الصورة اللي قبل شويةأقرأ
+
+372
+00:23:45,160 --> 00:23:49,800
+من الصورة E يعني أحسن هدولة كلهم الـ E فيها يا سيد
+
+373
+00:23:49,800 --> 00:23:54,100
+فيها كتير يعني جاي مش خلّي .. يعني شوف المسافة بين
+
+374
+00:23:54,100 --> 00:23:57,140
+الحفة و بينها الدم تقريبا نفس المسافة دي الدم نفسه
+
+375
+00:23:57,140 --> 00:24:03,220
+هذه تقدر عالم توزيع صح للخلايا آه تمام تمام طيب
+
+376
+00:24:06,410 --> 00:24:09,930
+عندي بعض الحالات اللي ممكن تظهر كأنها حالات مرضية
+
+377
+00:24:09,930 --> 00:24:12,590
+لكنها فعليًا مش حالات مرضية هي حالات نتيجة
+
+378
+00:24:12,590 --> 00:24:14,910
+الـBlood Firm نفسها يعني ممكن تظهر في الـThin Area
+
+379
+00:24:14,910 --> 00:24:17,690
+الخلايا تظهر معايا إشي بيسميه الـSterocytes
+
+380
+00:24:17,690 --> 00:24:21,290
+الـSterocytes هي عبارة عن خلية حمرة، عبارة عن خلية
+
+381
+00:24:21,290 --> 00:24:26,650
+حمرة طبعًا تظهرش فيها، نحكي، مش عارف بتظهر عندنا
+
+382
+00:24:26,650 --> 00:24:29,710
+فراغ اللي هم مجلوبين تقريبًا طولة فراغ وطولتين فيه
+
+383
+00:24:29,710 --> 00:24:33,370
+كإن هم مجلوبين، خلايا الحمرة فهي الخلية الحمرة،
+
+384
+00:24:33,370 --> 00:24:34,290
+خليني إذا بقدر أنا
+
+385
+00:24:38,550 --> 00:24:41,790
+المهم الخلايا تظهر فيها حالة بيسموها Spherocytosis
+
+386
+00:24:41,790 --> 00:24:44,950
+طبعا هذه بيكون خلايا حمرا فلاتيا مفيش فيها area
+
+387
+00:24:44,950 --> 00:24:47,410
+اللي يجمه جلبيا، هذه طبعا في thin area فانا
+
+388
+00:24:47,410 --> 00:24:50,850
+مابقراعش منها، ومنطقة ال thick area تظهر في خلايا
+
+389
+00:24:50,850 --> 00:24:52,890
+كأنها متجمعة ببعض زي الـRolling Formation،
+
+390
+00:24:52,890 --> 00:24:55,450
+الـRolling Formation ممكن متخسرة مع بعض لبعض
+
+391
+00:25:04,300 --> 00:25:07,820
+طلع علي، هلجيت الخلايا الحمرة، هي الخلية الحمرة مش
+
+392
+00:25:07,820 --> 00:25:11,100
+عارف ارسم بكتير انا لإن طبعا هي خلية حمرة هلجيت
+
+393
+00:25:11,100 --> 00:25:16,300
+بنص يكون عندى هجر لإنسان بتلهم مجلوبين، صح؟ فاضية،
+
+394
+00:25:16,300 --> 00:25:24,200
+نص white، شايفينها؟ خليني
+
+395
+00:25:24,200 --> 00:25:29,400
+أشوف إذا بقدر أجيب ثمام، طلع علي، هي خلية حمرة،
+
+396
+00:25:29,400 --> 00:25:34,120
+نيح؟ هلجيت الخلية الحمرة هاي؟في الـHemoglobin
+
+397
+00:25:34,120 --> 00:25:44,360
+تلتينها تقريبًا شايفين؟
+
+398
+00:25:44,360 --> 00:25:46,660
+شايف يا محمد؟ شايف يا سيد؟ تلتين الـHemoglobin
+
+399
+00:25:46,660 --> 00:25:50,240
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+400
+00:25:50,240 --> 00:25:50,880
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+401
+00:25:50,880 --> 00:25:50,980
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+402
+00:25:50,980 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+403
+00:25:52,640 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+404
+00:25:52,640 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+405
+00:25:52,640 --> 00:25:52,640
+تمام، تمام، تمام، تمام، تمام، تمام، تمام، تمام،
+
+406
+00:25:52,640 --> 00:25:56,540
+تمام، تمام،
+
+407
+00:25:56,540 --> 00:25:56,860
+تمام
+
+408
+00:26:03,470 --> 00:26:07,850
+يكون الخلية حمرة، جنبها خلية حمرة، جنبها خلية
+
+409
+00:26:07,850 --> 00:26:12,430
+حمرة، جنبها خلية حمرة، جنبها خلية حمرة كأنه خلايا
+
+410
+00:26:12,430 --> 00:26:16,150
+متجمع مع بعض، بيسموه «roller formation» إن الخلايا
+
+411
+00:26:16,150 --> 00:26:20,450
+كأنها ملزقة مع بعض في صمغ أو شغل هيكا صح إن أنا
+
+412
+00:26:20,450 --> 00:26:22,210
+الخلية الـ… طبعا هذه الـ«roller formation» مش أنا
+
+413
+00:26:22,210 --> 00:26:24,510
+اللي سألت صح إن أنت المنطقة البقرة فيها يكون
+
+414
+00:26:24,510 --> 00:26:27,490
+الخلايا الحمرة بالصورة هايهلجد؟ لو ظهرت عندي
+
+415
+00:26:27,490 --> 00:26:30,350
+الصورة high في المطبق اللي بقرا فيها بحكي إن شخص
+
+416
+00:26:30,350 --> 00:26:33,510
+عنده roll of formation roll of formation طبعا في
+
+417
+00:26:33,510 --> 00:26:37,230
+الحالات المرضية خاصة في حالات نحكي زيادة الألبومين
+
+418
+00:26:37,230 --> 00:26:40,230
+البروتينات بتظهر عندي الحالة high فroll of
+
+419
+00:26:40,230 --> 00:26:44,250
+formation طبعا بتظهر عندي في الحالة high في ال
+
+420
+00:26:44,250 --> 00:26:47,290
+thick area لكن في ال adequate area أصول ما تظهرش
+
+421
+00:26:47,290 --> 00:26:52,030
+في الحالة normal فيمنا roll of formation؟ في
+
+422
+00:26:52,030 --> 00:26:59,150
+الوقت؟ أه سعيدمعاذ طلع من الدادة و بديه يدخل مرة
+
+423
+00:26:59,150 --> 00:27:01,630
+تانية هجاله البرنامج بيقولوا please wait the
+
+424
+00:27:01,630 --> 00:27:04,030
+meeting cost و الـ «لتش» قدروا .. آه آه شوفتوا
+
+425
+00:27:04,030 --> 00:27:09,190
+شوفتوا دايما دخلوا دلوقت صحيح «سيف» سمعناه و كذا
+
+426
+00:27:09,190 --> 00:27:12,870
+بقى معنا «سيف»؟
+
+427
+00:27:12,870 --> 00:27:18,090
+تمام تمام معاكم تمام يا «سيف» أنت مش شايف الشاشة
+
+428
+00:27:18,090 --> 00:27:21,970
+طيبة أيوة
+
+429
+00:27:21,970 --> 00:27:26,250
+شايفطيب فرقتنا، طيب افهم ان انا رجعت لشو يعني
+
+430
+00:27:26,250 --> 00:27:30,150
+Spherocyte وشو رولوفورميشن؟ بس فادسناك بس دكتور
+
+431
+00:27:30,150 --> 00:27:33,430
+ايه دلنا اللي هو نقطة ال .. اللي هو ال formation
+
+432
+00:27:33,430 --> 00:27:37,170
+اللي لما بتظهر؟ طيب انا بدي اشوف شغل تاني ان شاء
+
+433
+00:27:37,170 --> 00:27:41,670
+الله اذا اجبرت اشوفها لأ لأ اللي هو ما تبتظهر ما
+
+434
+00:27:41,670 --> 00:27:46,250
+تبتظهر مش مشكلة مش مشكلة خليني اشوف بس انا اللهم
+
+435
+00:27:46,250 --> 00:27:46,930
+صح يا سيد محمد
+
+436
+00:27:55,570 --> 00:28:00,210
+طب كيف نظام الكوزات هيكون؟ مش مشكلة، نحن نتفق عليا
+
+437
+00:28:00,210 --> 00:28:03,590
+إن شاء الله، تقيل أقول؟ طيب، هذه محاضرة، هناخدها
+
+438
+00:28:03,590 --> 00:28:06,990
+لهم بعدين، طلع معايا هنا، طلعيا سعيد، طلعيا محمد،
+
+439
+00:28:06,990 --> 00:28:11,290
+شايفين؟ هذي الحالة، الـRBC بيكون مع بعض هنا،
+
+440
+00:28:11,290 --> 00:28:14,530
+شايفين الصورة؟ هذي بسبب الـRolling Formation،
+
+441
+00:28:14,530 --> 00:28:20,280
+بيكون الخلايا الحمرة متجمعة مع بعض زي stacks ofلو
+
+442
+00:28:20,280 --> 00:28:25,960
+كيف نجيب قطعة نقضية عشرة شكل مع بعض طبعا وتعملهم
+
+443
+00:28:25,960 --> 00:28:32,800
+جوجب بعض مفتحتش لسه ثواني لسه مفتحتش لسه مفتحتش ال
+
+444
+00:28:32,800 --> 00:28:40,400
+slide طيب
+
+445
+00:28:40,400 --> 00:28:46,700
+زعيطة تعمل ده؟ معلق نبين حركي الموسيقى تكتر شوية
+
+446
+00:28:46,700 --> 00:28:52,190
+أنا لازم مفتحتش علاجيأهلا وسهلا يا عزيزي كمان كمان
+
+447
+00:28:52,190 --> 00:28:54,410
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+448
+00:28:54,410 --> 00:28:54,470
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+449
+00:28:54,470 --> 00:28:54,730
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+450
+00:28:54,730 --> 00:29:04,430
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+451
+00:29:04,430 --> 00:29:07,770
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+452
+00:29:07,770 --> 00:29:07,770
+كمان كمان كمان كمان كمان كمان كمان كمان كمان كمان
+
+453
+00:29:07,770 --> 00:29:12,930
+كمان كمان كمان كمان كمان
+
+454
+00:29:12,930 --> 00:29:16,390
+كمان كمان
+
+455
+00:29:16,390 --> 00:29:23,110
+كمان كمطبعًا؟ بعض الحلقات الماضية تكون فيها الـ…
+
+456
+00:29:23,110 --> 00:29:25,530
+اللي يبني الـGlucose عالي فتالي البروتينات عالية
+
+457
+00:29:25,530 --> 00:29:28,950
+تؤدي لـRoller Formations تكون جمعها مع بعض، هذه
+
+458
+00:29:28,950 --> 00:29:31,350
+ممكن تظهر بعض الحلقات الماضية إحنا بتظهر عندما
+
+459
+00:29:31,350 --> 00:29:34,750
+تحكينا، بتظهر معنا في الـ… اللي هي إيه إيش حكينا
+
+460
+00:29:34,750 --> 00:29:39,510
+في حلقات الـThick Film أو في حلقات الـThick Area،
+
+461
+00:29:39,510 --> 00:29:43,410
+طبعًا؟ طيب فهنا عندي Spherocytes تظهر في Thin Area
+
+462
+00:29:43,410 --> 00:29:46,210
+وفي الـThick Area تظهر فيها Roller Formation
+
+463
+00:29:46,210 --> 00:29:48,110
+أبرجيكم مرة الـSpherocytes
+
+464
+00:29:51,890 --> 00:29:59,350
+الـ Spherocytosis زي عندي ..
+
+465
+00:29:59,350 --> 00:30:03,990
+شايفين
+
+466
+00:30:03,990 --> 00:30:08,570
+الخلايا اللي بشوفها؟ شايفين الخلايا هاي الصغيرة؟
+
+467
+00:30:08,570 --> 00:30:09,670
+فتحت عندك السيف؟
+
+468
+00:30:13,230 --> 00:30:15,730
+أه، فتحت، فتحت، يا دكتور شايف الخلايا اللي عليها
+
+469
+00:30:15,730 --> 00:30:17,930
+الـCM، هاي؟ أه، هيفتحت هاي الخلية اللي عليها الـCM
+
+470
+00:30:17,930 --> 00:30:21,030
+مافيش واضح فيها مظاهر Hemoglobin مبينة كإنة خلية
+
+471
+00:30:21,030 --> 00:30:24,710
+متجانسة كاملة، هاي الـSpherocyte بيكون حجمها صغير،
+
+472
+00:30:24,710 --> 00:30:29,910
+بيكون حجمها صغير وكملة الـHemoglobin أه، تبين
+
+473
+00:30:29,910 --> 00:30:32,390
+الـHemoglobin مليها كلها مليانة بالظبط، هذه
+
+474
+00:30:32,390 --> 00:30:35,610
+الـSpherocyte هذه بتظهر في الـThin Area كإنة
+
+475
+00:30:35,610 --> 00:30:38,290
+Spherocyte لكن هي فعليًا مش Spherocyte لكن هي
+
+476
+00:30:38,290 --> 00:30:41,450
+موجودة بسبب إن هي موجودة في الـThin Area طيب،
+
+477
+00:30:41,450 --> 00:30:48,130
+نكمل؟إذا عندي serocytosis تظهر في حالة thin area و
+
+478
+00:30:48,130 --> 00:30:51,070
+thick area roll of formation لكن هدول حالتهم إيش؟
+
+479
+00:30:51,070 --> 00:30:55,330
+Normal، مش abnormal، لكن لو شوفت الحالتين هدول في
+
+480
+00:30:55,330 --> 00:30:58,750
+adequate area، أني adequate area يا محمد؟ اللي هي
+
+481
+00:30:58,750 --> 00:31:04,070
+بالنص، اللي تقع بيها بالنص، تمام؟ صحيح، هذه الحالة
+
+482
+00:31:04,070 --> 00:31:06,590
+اللي بحكي عنها إيش؟ بحكي إنها حالة مرضية، adequate
+
+483
+00:31:06,590 --> 00:31:08,710
+area، adequate area بالظبط
+
+484
+00:31:13,550 --> 00:31:16,790
+هذه أخدناها، مش هنحكي عليها كتير، لكن هي إيش
+
+485
+00:31:16,790 --> 00:31:22,790
+الحالة تؤدي إلى ظهور نحكي abnormality في عملية
+
+486
+00:31:22,790 --> 00:31:27,430
+الـPoor Blood Smear؟ طبعاً عندك drop too large أو
+
+487
+00:31:27,430 --> 00:31:30,750
+too small، إحنا إذا كنتوا تذكروا جربنا drop 10
+
+488
+00:31:30,750 --> 00:31:34,020
+مايكرو، جربنا 7 مايكرو، عشان تنطقوا معانافي ناس
+
+489
+00:31:34,020 --> 00:31:36,900
+كانت إيد العشرة مايكرون اتخربت، مضبوطش معاها،
+
+490
+00:31:36,900 --> 00:31:40,180
+اعتمدت على سبعة مايكرون، صح؟ فحسب ال drop نفسها،
+
+491
+00:31:40,180 --> 00:31:43,420
+كل ما زاد ال drop، كل ما كان عندك بور أكتر تقنيت،
+
+492
+00:31:43,420 --> 00:31:47,040
+عملية الفرد الصحيح ‏- من خمسة لعشرة؟ ‏- احنا حطينا
+
+493
+00:31:47,040 --> 00:31:50,020
+عشرة وما زبطت معايا الأغلبية، فحطينا السبعة عشان
+
+494
+00:31:50,020 --> 00:31:54,340
+إيدك تأخد عليها ‏- ع سبعة كانت تظبط معايا ‏- صحيح،
+
+495
+00:31:54,340 --> 00:31:57,480
+ع سبعة كانت تظبط معايا الأغلبية، لكن مجرد إن إيدك
+
+496
+00:31:57,480 --> 00:32:01,220
+زبطت على سبعة، بعدين لو حطيت عشر أو عشرين،تظبط
+
+497
+00:32:01,220 --> 00:32:06,760
+أكتر، معاك أكتر، لأن إيديك أخدت تقنية نفسها، تمام؟
+
+498
+00:32:06,760 --> 00:32:12,360
+تمام طيب، فرد الـslide مهم جدا، عشان تنفرد بطريقة
+
+499
+00:32:12,360 --> 00:32:17,220
+مش jerky manner عملية إنك أنت تحافظ على الـedge،
+
+500
+00:32:17,220 --> 00:32:20,860
+تبقى الـedge، وتعمل الـslide بإله دور، الزاوية
+
+501
+00:32:20,860 --> 00:32:24,060
+إلها دور، وعملية الـbush، الـspreader نفسها إلها
+
+502
+00:32:24,060 --> 00:32:28,700
+دور، في عملية تعطيك pour blood، اسمهاطبعًا الـ
+
+503
+00:32:28,700 --> 00:32:31,220
+«irregular spiders with a ridge and long tail»
+
+504
+00:32:31,220 --> 00:32:33,920
+برضه نفس الحكاية الـ «Holes» في الـ «Blood Film»
+
+505
+00:32:33,920 --> 00:32:36,920
+كل هذه معنات معناة في ال .. إذا بتفكروا في السمن
+
+506
+00:32:36,920 --> 00:32:41,380
+صور «A» ل«F» وآخرش تغييرات في الخلية الـ «Central
+
+507
+00:32:41,380 --> 00:32:45,020
+Generator» نتيجة أنه أنت طول في عملية «Fixation»
+
+508
+00:32:45,020 --> 00:32:48,220
+نتيجة أنك أنت عملت «Fixing Time» في الميثانول وكان
+
+509
+00:32:48,220 --> 00:32:49,400
+فيه «Contamination» بالوطن
+
+510
+00:32:52,260 --> 00:32:56,520
+عندي حالات طبعًا بيسموها «Biological Causes of
+
+511
+00:32:56,520 --> 00:33:00,620
+Gore Smear» يعني هي سببها أنه عندها حالات بيولوجية
+
+512
+00:33:00,620 --> 00:33:05,500
+مش أنت سبب فيها يعني مثلًا إذا بتذكروا قلتلكم، إذا
+
+513
+00:33:05,500 --> 00:33:10,760
+بتذكروا ميزنا بين، ميزنا بين ال .. حكيتكم الـ
+
+514
+00:33:10,760 --> 00:33:13,320
+«Role Formation» والـ «Agglutination» في الـ slide
+
+515
+00:33:13,320 --> 00:33:16,700
+المرة السابقة، نرجعلها، أبرجكم إياها الـ «Slide
+
+516
+00:33:16,700 --> 00:33:17,180
+High»
+
+517
+00:33:21,140 --> 00:33:25,080
+هذه، شايفينها؟ ‏- أه ‏- هذه في ال .. على اليمين
+
+518
+00:33:25,080 --> 00:33:27,480
+roll-off formation وهذا agglutination الـ roll-off
+
+519
+00:33:27,480 --> 00:33:30,220
+formation، حكينا سببه زيادة البروتينات لكن الـ
+
+520
+00:33:30,220 --> 00:33:33,500
+agglutination سببه هي أجسام مضادة، تمام؟ ممكن
+
+521
+00:33:33,500 --> 00:33:36,660
+أجسام مضادة، حسب، فأنا هذا بيسموه agglutination
+
+522
+00:33:36,660 --> 00:33:39,760
+وهذا roll-off formation طيب، احنا في عندي حالة
+
+523
+00:33:39,760 --> 00:33:42,000
+اللي بيسموها الـ cold agglutination cold
+
+524
+00:33:42,000 --> 00:33:45,320
+agglutination من اسمها coldيعني بارد و الـ
+
+525
+00:33:45,320 --> 00:33:47,860
+Glutonation بيصير تخفر الدم في الحالات الباردة
+
+526
+00:33:47,860 --> 00:33:52,040
+نتيجة وجود السم مضادة طبعا بالحالة هذه الخلايا
+
+527
+00:33:52,040 --> 00:33:55,920
+الحمراء بيصير الكلام مع بعض في الجو البارد لكن لو
+
+528
+00:33:55,920 --> 00:33:58,520
+حاطيتها أنا في ال water bath كده ترش حالات water
+
+529
+00:33:58,520 --> 00:34:03,020
+bath؟ سبعة و تلاتين سبعة و تلاتين فبالتالي بتفك
+
+530
+00:34:03,020 --> 00:34:07,500
+تمام فبالتالي بتفك طب ولا .. ولا أنت بدل زي دكتورش
+
+531
+00:34:07,500 --> 00:34:11,220
+بيسيبني هتفك أنا يعني إيه؟ كيف يا سعيد؟الـ
+
+532
+00:34:11,220 --> 00:34:13,720
+Antibodies الأجسام المضادة اللي بتكون ماسك فيها
+
+533
+00:34:13,720 --> 00:34:17,960
+اللي عامل الـ agglutination هذي، تتخيل عنها؟ حسب
+
+534
+00:34:17,960 --> 00:34:21,180
+نوعها، هذي اسمها cold agglutinins cold agglutinins
+
+535
+00:34:21,180 --> 00:34:24,080
+اللي هي أجسام مضادة بتتفعل درجة حرارة باردة، يعني
+
+536
+00:34:24,080 --> 00:34:27,800
+نحكي أربعة درجة مقاوية، تمام؟ أو نحكي ستة عشرين
+
+537
+00:34:27,800 --> 00:34:31,920
+مثلا، هذي من طبيبتها لو حضرتها درجة حرارة عالي
+
+538
+00:34:31,920 --> 00:34:36,760
+شويه سبعة و تلاتين، بتتفعلش، بتفكرفالاتفاعل
+
+539
+00:34:36,760 --> 00:34:39,600
+الأجسام المضادة مع الـ «أندجينات» تعتبر اتفاعل
+
+540
+00:34:39,600 --> 00:34:43,200
+عكسي الـ «Reverse»، ممكن أعكسه أنا أجد الـ «Warm
+
+541
+00:34:43,200 --> 00:34:47,520
+Agglutination» بتفاعل لدرجة حرارة 37، لدرجة حرارة
+
+542
+00:34:47,520 --> 00:34:49,540
+الجسم لكن الـ «Cold Agglutination» بتفاعل لدرجة
+
+543
+00:34:49,540 --> 00:34:53,660
+حرارة باردة، أنا بقدر أعالج الحالة هاي، لو مرض ما
+
+544
+00:34:53,660 --> 00:34:56,620
+هي حالة «Cold Agglutination»، بقدر أعالجها، إن أنا
+
+545
+00:34:56,620 --> 00:35:00,860
+باخد العينة، بحط بوتر بقى، خمس دخائط، وبعدين خلال
+
+546
+00:35:00,860 --> 00:35:02,680
+وجود الـ «Pottery Barrel» بعمل الـ «Plug Flow»
+
+547
+00:35:02,680 --> 00:35:06,230
+وبفرضهطبعاً بحاول أسخن ال slides كمان عشان يكون
+
+548
+00:35:06,230 --> 00:35:08,670
+عندى برضه ال war لإن مجرد أسحبها ال cold ممكن
+
+549
+00:35:08,670 --> 00:35:13,250
+تقضيها التفاعل تعني حالة تانية سببها ال biological
+
+550
+00:35:13,250 --> 00:35:16,510
+اللي هي الليبيميا إيش عن الليبيميا يا معاد؟
+
+551
+00:35:16,510 --> 00:35:22,610
+الليبيميا؟ الليبيميا الليبت الليبت الليبت الليبت
+
+552
+00:35:22,610 --> 00:35:28,750
+الليبت الليبت الليبت
+
+553
+00:35:28,750 --> 00:35:31,170
+الليبت الليبت الليبت الليبت الليبت الليبت الليبت
+
+554
+00:35:31,170 --> 00:35:31,170
+الليبت الليبت الليبت الليبت الليبت الليبت الليبت
+
+555
+00:35:31,170 --> 00:35:31,170
+الليبت الليبت الليبت الليبت الليبت الليبت الليبت
+
+556
+00:35:31,170 --> 00:35:34,420
+الليبت الليبت الليأتبع دهول في الدم، هذه طبعا تؤدي
+
+557
+00:35:34,420 --> 00:35:38,260
+لظهور ال «holes» في الاسميرة، إذا كان فيه slide هي
+
+558
+00:35:38,260 --> 00:35:44,980
+«holes»، رقم A,B,C,D,E، صح يا محمد؟ «slide E» كان
+
+559
+00:35:44,980 --> 00:35:48,640
+فيها «holes»، الـ«holes» يعني سبب الترقيم يعني،
+
+560
+00:35:49,380 --> 00:35:51,840
+طبعًا أدى إذا علاج، لأ مالاش علاج لأنه أصل هو
+
+561
+00:35:51,840 --> 00:35:54,000
+موجود في جسم الإنسان يعني إنسان جاي يعمل blood
+
+562
+00:35:54,000 --> 00:35:57,300
+film وكان عنده الدهون عالية أنا مقدرش في الحال هاي
+
+563
+00:35:57,300 --> 00:36:00,680
+أني أحكيله لأ، روح نزل دهون تعالي فحنقر نقرأ
+
+564
+00:36:00,680 --> 00:36:02,880
+الـLottery of Blipemia والـRoll of formation زي ما
+
+565
+00:36:02,880 --> 00:36:05,760
+حكيتلكم أنه في حال تكون فيها بروتينات عالي شوية
+
+566
+00:36:05,760 --> 00:36:09,460
+عبارة عن stack of coins، شكل stack of coins هذه
+
+567
+00:36:09,460 --> 00:36:11,580
+الحالات تؤدي لبور blood smear في حالة
+
+568
+00:36:11,580 --> 00:36:16,300
+الـbiological cases هيك خلصنا blood film تقريبًا،
+
+569
+00:36:16,300 --> 00:36:22,130
+هندخل للتريننجبالنسبة بس تحدثناك، الـ ReLow ارتفاع
+
+570
+00:36:22,130 --> 00:36:25,410
+لبروتينات أي نوع بروتين و لا فيه بروتينات معينة هي
+
+571
+00:36:25,410 --> 00:36:27,810
+اللي بتقدي الارتفاع اللي هو وجود الـ ReLow؟ لأ،
+
+572
+00:36:27,810 --> 00:36:31,070
+ممكن أحنا في الحالة تهيأ بيصير خدلال، هو غالبًا
+
+573
+00:36:31,070 --> 00:36:33,870
+يعني تظهر الـ Low Formation في حالات مثلًا اللي
+
+574
+00:36:33,870 --> 00:36:38,770
+نحكي اتفاعل immunoglobulins immunoglobulins طبعًا
+
+575
+00:36:38,770 --> 00:36:42,450
+منوع البروتينات الجلوبيلينات، الجلوبيلين، تمام؟
+
+576
+00:36:42,450 --> 00:36:45,010
+فبالحالة هاي بتفع، طبعًا immunoglobulins في حالة
+
+577
+00:36:45,010 --> 00:36:50,240
+مرضية تؤدي إلى شهسمظهور الـ Low Formationلكن هي
+
+578
+00:36:50,240 --> 00:36:52,960
+بشكل عام، لو رتفع الألبومي نفس الحكاية، ليش؟ لأن
+
+579
+00:36:52,960 --> 00:36:56,680
+ارتفاع البروتينات يؤدي إلى اختلال في البيئة حول
+
+580
+00:36:56,680 --> 00:36:59,280
+الخلايا الحمرة، طبعاً من شحنات كورفاية وغيرها،
+
+581
+00:36:59,280 --> 00:37:03,680
+وتؤدي بالتالي إلى اختلال البيئة والشحنات إلى
+
+582
+00:37:03,680 --> 00:37:05,920
+اقتراب الخلايا الحمرة من بعض لبعض، يعني الخلايا
+
+583
+00:37:05,920 --> 00:37:10,700
+الحمرة أصلاً، إيش فيها سطحها؟ فيها سطحها شحنات،
+
+584
+00:37:10,700 --> 00:37:13,280
+Lyseric Acidهذه تؤدي لتنافس الخلايا الحمراء من
+
+585
+00:37:13,280 --> 00:37:15,600
+بعض، يعني الخلايا الحمراء بتتبقى أكتر من بعض بوجود
+
+586
+00:37:15,600 --> 00:37:20,560
+الشحنات لكن انا في حالة التفاعل، البروتينات،
+
+587
+00:37:20,560 --> 00:37:24,840
+البيئة اللي حواليها كانت أقرب شوية، خلّيني أتجرب،
+
+588
+00:37:24,840 --> 00:37:28,660
+كانت كأنها صارت أجلوتينيشن، احنا أحد طرق علاج
+
+589
+00:37:28,660 --> 00:37:30,360
+الـRoll-up formation أحد طرق علاج الـRoll-up
+
+590
+00:37:30,360 --> 00:37:33,960
+formation أن هنا أشيل من الـPlasma وأحط بدلها
+
+591
+00:37:33,960 --> 00:37:39,700
+Saline، فبالتالي أنا خففت منالـ… شو اسمه؟ الـ
+
+592
+00:37:39,700 --> 00:37:42,260
+«البومين» أو النخفة من البروتينات وبالتالي عملت
+
+593
+00:37:42,260 --> 00:37:45,240
+أدية الخلايا الأمريكية تؤدي لـ «تنافر» بسبب إيه
+
+594
+00:37:45,240 --> 00:37:48,080
+الشحنتها، تمام؟ تمام
+
+595
+00:37:50,830 --> 00:37:54,310
+طيب الـ Staining، الـ Staining يعني بعد ما تنشب
+
+596
+00:37:54,310 --> 00:37:57,370
+الـ slide و عملت تنشب الـ slide بعمله Staining،
+
+597
+00:37:57,370 --> 00:38:00,230
+طبعا عندي أنواع كتير من الـ Staining أحنا ممكن
+
+598
+00:38:00,230 --> 00:38:04,050
+نستخدم طبعا كل الـ Staining تتبع للرومان Whiskey
+
+599
+00:38:04,050 --> 00:38:06,950
+Stains، فعندي Rite Stains، الـ Rite Stains بيسموها
+
+600
+00:38:06,950 --> 00:38:10,460
+Metachromic Stainsميدا كوميك ستينز طبعاً فيها two
+
+601
+00:38:10,460 --> 00:38:15,340
+type of stains طبعاً فيكون فيها سبغة حامضية و سبغة
+
+602
+00:38:15,340 --> 00:38:19,660
+قاعدية طبعاً فيها نوعين من السبغة فيها مثلين blue
+
+603
+00:38:19,660 --> 00:38:23,240
+دار و فيها الأيزين الحمراء فهي تسبغلي باللون
+
+604
+00:38:23,240 --> 00:38:27,920
+الأزرق و الأحمر تسبغلي النواء باللون الأزرق و
+
+605
+00:38:27,920 --> 00:38:35,140
+الخلايا الحمراء تسبغلي الهيومكولبين باللون الأحمر
+
+606
+00:38:35,140 --> 00:38:41,120
+حسب سبب الشحناتطبعًا، بأستخدم الـ Methanol في
+
+607
+00:38:41,120 --> 00:38:47,140
+عملية التثبيت الـ Metriblostans تسبغلي الـ RNA،
+
+608
+00:38:47,140 --> 00:38:52,460
+تسبغلي الـ DNA، تسبغلي كما حكينا، كل الأنوية بالـ
+
+609
+00:38:52,460 --> 00:38:56,160
+Blue-Grey Color بينما الـ Eosin الحمراء تسبغلي الـ
+
+610
+00:38:56,160 --> 00:38:59,700
+Eosin Granulesبالأورانج تسبغلي طبعًا الـ Red blood
+
+611
+00:38:59,700 --> 00:39:06,380
+cells السبغات طبعًا فيها buffer لإنه يحافظ على الـ
+
+612
+00:39:06,380 --> 00:39:11,060
+pH غالبًا الـ pH بيكون من 6.4 لـ 6.7 الـ buffer
+
+613
+00:39:11,060 --> 00:39:14,960
+مهم جدًا جدًا جدًا يعني أحنا كتير مرات معايا
+
+614
+00:39:14,960 --> 00:39:18,140
+بتجربة من ناحية العملية أني أنا أسبغ كنت أسبغ
+
+615
+00:39:18,140 --> 00:39:20,480
+مثلًا بعض الـ sliders ماعرفش أحكي لكم يا عم
+
+616
+00:39:20,480 --> 00:39:24,100
+بالمخدمة ولا لأ لكن كنت أسبغ sliders في مرة مرات
+
+617
+00:39:24,100 --> 00:39:26,160
+لحد أن معظم ال sliders اللي أسبغها هتطلع معايا
+
+618
+00:39:26,160 --> 00:39:30,230
+أسيدكطبعًا السبب، طبعًا السبب دي عملها buffer 100%
+
+619
+00:39:30,230 --> 00:39:34,310
+فبعد هيك اكتشفت أن أحد زملائي كان مثلًا ييجي
+
+620
+00:39:34,310 --> 00:39:37,990
+يستخدم مثلًا أحد القخول، يستخدم القخول ويسيب
+
+621
+00:39:37,990 --> 00:39:41,650
+القطار مفتوح نوعًا ما، فبصير evaporation للأسد
+
+622
+00:39:41,650 --> 00:39:44,550
+فيؤدي إلى زيادة أسد ال environment وبالتالي يؤدي
+
+623
+00:39:44,550 --> 00:39:48,530
+إلى زيادة staining، نحكي الـred color staining أو
+
+624
+00:39:48,530 --> 00:39:51,710
+يصير أسدك أكتر، فهذه الـbuffer مهم جدًا،
+
+625
+00:39:51,710 --> 00:39:54,250
+الـatmosphere اللي حواليك مهم، هيعملت اللي حفظ على
+
+626
+00:39:54,250 --> 00:39:59,240
+أسابقها نفسهاطيب، الـ Sealing Procedure مش سهل،
+
+627
+00:39:59,240 --> 00:40:03,480
+هناخده معنا أحنا بعد ما نجفف السمير لازم نعملها
+
+628
+00:40:03,480 --> 00:40:08,160
+Fixation بواسطة الـ Methanol طبعا، ممكن أنك أنت
+
+629
+00:40:08,160 --> 00:40:13,460
+تحطها على الراك وتعملها، تحط عليها الـ نحكي الـ
+
+630
+00:40:13,460 --> 00:40:16,120
+Methanol لمدة مثلا، two minutes أو three minutes
+
+631
+00:40:16,120 --> 00:40:19,660
+أو ممكن أنت بواسطة الـ Jar، الـ Sealing Jars
+
+632
+00:40:19,660 --> 00:40:23,300
+تعملها دلوقتي عشر مرات في الـ Sealing Jars فيها
+
+633
+00:40:23,300 --> 00:40:25,200
+أنا نزلتلكم فيديو، ماعرف إذا شفتوه
+
+634
+00:40:43,100 --> 00:40:44,500
+‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏‏
+
+635
+00:40:52,140 --> 00:40:57,140
+طريقة نفسنا هي استخدام الـ «راك» على الـ «سينك»
+
+636
+00:40:57,140 --> 00:41:00,100
+نفسها وسنقوم بـ «معالجة» السمير ونقوم بعمل «دب»
+
+637
+00:41:00,100 --> 00:41:05,840
+110 مرات ثم سنضع السمير على الـ «سينك» لمدة 1-2
+
+638
+00:41:05,840 --> 00:41:09,420
+دقيقة ثم نضيف الـ «بافر» بالطبع أن السينك نفسها هي
+
+639
+00:41:09,420 --> 00:41:12,020
+الـ «مكسيك» بين الـ «يوزين» والـ «ميتاليبوه» مع
+
+640
+00:41:12,020 --> 00:41:15,200
+بعض سيكون صبغتين وليس منفصلين يعني الـ «رايتس
+
+641
+00:41:15,200 --> 00:41:18,760
+سينك» هي الصبغة الموجودة فيها الـ «ميتاليبوه» مع
+
+642
+00:41:18,760 --> 00:41:22,380
+الـ «يوزين»هي مسبوغة و جاهزة كنت تقولنا يا دكتور
+
+643
+00:41:22,380 --> 00:41:25,400
+في المقدمة الحالية هي سبغات موجودة فيها مسبوغة و
+
+644
+00:41:25,400 --> 00:41:30,620
+جاهزة و لا احنا مجاهزها مسبوغة و جاهزة مش مسبوغة
+
+645
+00:41:30,620 --> 00:41:36,240
+انا بتسبوغها لسه الاسمية لأ السبغة جاهزة ولا مثلا
+
+646
+00:41:36,240 --> 00:41:41,540
+محضرة محضرة و جاهزة ممكن تجيك باودر و انت تحضرها
+
+647
+00:41:41,540 --> 00:41:46,480
+بالميثانول او ممكن تجيك مثلا جاهزة ومتوسطة مباشرة
+
+648
+00:41:46,480 --> 00:41:49,790
+حسب الشركات اللي بتشتري منهاطبعًا إحنا بنفخ … حتى
+
+649
+00:41:49,790 --> 00:41:53,270
+بـ… حتى بالشركة أقل إحنا بنفخت السمير لـ one to
+
+650
+00:41:53,270 --> 00:41:56,510
+two minutes بعد هيك طبعًا بنضيف عليها كمية من الـ
+
+651
+00:41:56,510 --> 00:41:59,730
+buffer تعادل كمية السمير و بننفخ، بحيث إنه يصير
+
+652
+00:41:59,730 --> 00:42:02,790
+عملية … عملية نفخ يلقى دور كتير في عملية mixing
+
+653
+00:42:02,790 --> 00:42:04,790
+بين الـ buffer و السمير أو بين الميّه داخل الـ
+
+654
+00:42:04,790 --> 00:42:07,090
+water و السمير، إحنا نستخدم distilled water عملية
+
+655
+00:42:07,090 --> 00:42:11,790
+نفخ، في بعض الصبغات مثلًا، إحنا عزينا Riot وGemsa
+
+656
+00:42:11,790 --> 00:42:15,630
+وفيها نوع كتير من الصبغات Gemsa مثلًا، لو نفختها،
+
+657
+00:42:15,630 --> 00:42:19,550
+هتلاقي إنه ظهر نوع من اللون، بيسموه «هذه طبعاً
+
+658
+00:42:19,550 --> 00:42:22,770
+بلون حلو كتير رأيك أنك تضمن إن عملت الـ mixing صح
+
+659
+00:42:22,770 --> 00:42:25,770
+ممكن تعمل الـ mixing بالـ pipettes بصير الـ
+
+660
+00:42:25,770 --> 00:42:29,590
+pipettes أو بالنفخ بواسطة سخن مدى المواصع وشغل
+
+661
+00:42:29,590 --> 00:42:33,450
+أيضاً طبعاً إذا نضيف نفس الكمية من الـ buffer على
+
+662
+00:42:33,450 --> 00:42:36,630
+الاسمير و بعدين كبنونه فوق و نخليها two to four
+
+663
+00:42:36,630 --> 00:42:40,070
+minutes نعمل نعمل wash و بعدين نعمل dry الاسمير و
+
+664
+00:42:40,070 --> 00:42:48,470
+نقرأ الاسمير نفسنا طبعاً 90 سنةأعطاني رسالة أن الـ
+
+665
+00:42:48,470 --> 00:42:50,490
+«سيروجيومولوجيا» يبدو بدأ بعد عشر دقائق لإن ما
+
+666
+00:42:50,490 --> 00:42:53,230
+يشبه بعديكم طيب مش مشكلة احنا نحاول نشتغل الـ
+
+667
+00:42:53,230 --> 00:42:57,930
+«سيروجيومولوجيا» ده فكرت الصوت من عندك ساعين، لا،
+
+668
+00:42:57,930 --> 00:43:01,970
+من عندك، طيب، هاي الـstaining، فعندي هنا طبعا two
+
+669
+00:43:01,970 --> 00:43:05,050
+basic، بيكون في المثلين بيقولوا، بيكون هذه طبعا
+
+670
+00:43:05,050 --> 00:43:08,870
+أذة أسباب، هذه طبعا أذة بشي، وهذه طبعا two acidic،
+
+671
+00:43:08,870 --> 00:43:09,470
+شايفين؟
+
+672
+00:43:12,140 --> 00:43:15,200
+البنافسة دي البربل والأزرق والأحمر بظهرين بشكل
+
+673
+00:43:15,200 --> 00:43:19,700
+متجانس وواضح، مايكونش كلها حمرا ولا كلها زرقا،
+
+674
+00:43:19,700 --> 00:43:22,540
+تشوفين هالخلايا الحمرا كيف؟ هيخلاها حمرا، كلها
+
+675
+00:43:22,540 --> 00:43:25,760
+زرقا، هالخلايا الحمرا كلها حمرا، هنا أيضا أدقوة
+
+676
+00:43:25,760 --> 00:43:31,080
+طبعا أسباب ال .. دكتور هذا الصورة على المجهر؟ إيه؟
+
+677
+00:43:32,750 --> 00:43:35,390
+الصورة هذه هيك هتظهر على المجهر المفروض ولا في
+
+678
+00:43:35,390 --> 00:43:36,730
+العين؟ هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+679
+00:43:36,730 --> 00:43:45,830
+هيك هيك هيك هيك هيك هيك هيك هيك
+
+680
+00:43:45,830 --> 00:43:46,170
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+681
+00:43:46,170 --> 00:43:46,190
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+682
+00:43:46,190 --> 00:43:46,230
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+683
+00:43:46,230 --> 00:43:46,890
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+684
+00:43:46,890 --> 00:43:50,690
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+685
+00:43:50,690 --> 00:43:50,690
+هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك هيك
+
+686
+00:43:50,690 --> 00:43:56,010
+هيك هيك هيك هيك هيك هيك هيك هيكأو إنه character
+
+687
+00:43:56,010 --> 00:44:00,870
+stain عندك بقديمة أو إن البيئة قدش عندك acid زي
+
+688
+00:44:00,870 --> 00:44:03,930
+اللي بحكيلكم، أنا كان زميل يحط استخدام ال acid
+
+689
+00:44:03,930 --> 00:44:08,530
+جنبي، جنب ال swing قد لإنه ترميته stain يعني إذا
+
+690
+00:44:08,530 --> 00:44:11,110
+ظهرت مشكلة هنا في هذا الحالة، هتكون المشكلة من
+
+691
+00:44:11,110 --> 00:44:13,430
+السبغة، مش؟ بالظبط، بيكون المشكلة من السبغة، فإن
+
+692
+00:44:13,430 --> 00:44:18,530
+أنت بدأت تحلها، أه مش من سحبت يعني إنت بالحالة
+
+693
+00:44:18,530 --> 00:44:21,010
+high فكبارا two acidic بدأت تحلها أو two steel
+
+694
+00:44:21,010 --> 00:44:23,610
+alkaline بدأت تحلها، لإن مش هتعرف تقرأ منها أصلاً
+
+695
+00:44:24,090 --> 00:44:31,070
+هتجد الـ two alkaline يعني
+
+696
+00:44:31,070 --> 00:44:35,250
+لو كان عندك ثقيل سمير أو prolong staining يعني إذا
+
+697
+00:44:35,250 --> 00:44:38,510
+كان العكس، ثقيل سمير هتعطيكه أسد أحيانًا two
+
+698
+00:44:38,510 --> 00:44:41,250
+alkaline، thick smear أو prolong staining أو
+
+699
+00:44:41,250 --> 00:44:45,070
+insufficient washing أو alkaline pH طب العلاجاتهم،
+
+700
+00:44:45,070 --> 00:44:47,910
+عرف العلاجاتهم، أنا عند العلاج إذا كان
+
+701
+00:44:48,460 --> 00:44:51,660
+الـSufficient Staining Time، بزوّد الـTime إذا كان
+
+702
+00:44:51,660 --> 00:44:55,380
+الـBH عندي Acidic، بعدّل في الـBH إذا كانت All
+
+703
+00:44:55,380 --> 00:44:59,520
+Stained، بعمل Staining جديدة، تمام؟ الـAlkaline،
+
+704
+00:44:59,520 --> 00:45:02,820
+لو كانت Thick Smear، بحطه Smear كويسة إذا كانت
+
+705
+00:45:02,820 --> 00:45:05,560
+Prolonged Staining، بقلّر من الـTime إذا كانت
+
+706
+00:45:05,560 --> 00:45:08,840
+Sufficient Washing، بعمل Washing صح، يعني مش بحطه
+
+707
+00:45:08,840 --> 00:45:12,560
+تحسين صح وإذا كانت Alkaline BH، بعمل إيش؟ أتشكل
+
+708
+00:45:12,560 --> 00:45:15,860
+الـBH، وبعدّل الـBH، هيك إحنا خلصنا الـStaining
+
+709
+00:45:16,250 --> 00:45:22,390
+وخلصنا الـ «Blood Film» ده عنده جزئية الـ .. طبعا
+
+710
+00:45:22,390 --> 00:45:24,290
+بحكيلك الـ «Manual Differential» اللي على الـ
+
+711
+00:45:24,290 --> 00:45:28,430
+«RBC» وإيش بدهر معاه Normal، تمام؟ عندي طبعا
+
+712
+00:45:28,430 --> 00:45:32,790
+الخلايا الحمرة، أنا إيه الخاطر هذا؟ نواجب .. نواجب
+
+713
+00:45:32,790 --> 00:45:37,870
+احنا هنا إن شاء الله، إيش رأيكوا؟ نواجب هنا، نواجب
+
+714
+00:45:37,870 --> 00:45:42,550
+.. ‏-إيش راجع الفيلم؟ ‏-طايل كتير يا دكتور، طايل
+
+715
+00:45:42,550 --> 00:45:47,420
+كتيرمش ضايق الأغربية الصور يعني وأشكال وكيف تتوزين
+
+716
+00:45:47,420 --> 00:45:50,300
+الخلايا الحمراء والخلايا اللي ده إحنا نوقف هنا إن
+
+717
+00:45:50,300 --> 00:45:52,860
+شاء الله ومن السنوات الجاية في لقاء السنوات الجاية
+
+718
+00:45:52,860 --> 00:45:56,200
+بنحاول إن شاء الله نكمل وبناخدكم ده أحاول أبعد
+
+719
+00:45:56,200 --> 00:45:59,340
+بينكم وبين الشباب عشان لو أتأخرنا شوية قدرنا معاكم
+
+720
+00:45:59,340 --> 00:46:00,640
+شوية
+
+721
+00:46:03,210 --> 00:46:06,410
+طبعا، أنا جيت بدي أعمل الـ «Application» بدي أعمل
+
+722
+00:46:06,410 --> 00:46:10,870
+الـ «code» للمحاضرة و أنزلها زي ما حكيتكم، احتمال
+
+723
+00:46:10,870 --> 00:46:14,270
+كبير، إذا حابين الساعة 4، ماعنديش مشكلة احتمال
+
+724
+00:46:14,270 --> 00:46:18,310
+يكون ثابت أو اتنين، طبعا؟ بدي أوزع المعامل بين انا
+
+725
+00:46:18,310 --> 00:46:20,710
+و تالت و بدي أحاول أعمل وسامة بين كل معمل معمل
+
+726
+00:46:20,710 --> 00:46:24,190
+بحيث أنه يكون عندي ساعة لو اتخلت أنه أقدر أعطيكم
+
+727
+00:46:24,190 --> 00:46:28,310
+كمان راح تفضلوا خلاص، طبعا، إن شاء الله، يلا،
+
+728
+00:46:28,310 --> 00:46:33,070
+أعطيكم العادة، في صفصار في الصبق؟ طبعا، تمامالله
+
+729
+00:46:33,070 --> 00:46:35,690
+يرضى عليك يا دكتور الله يزيد يعطيك العافية يا
+
+730
+00:46:35,690 --> 00:46:39,470
+دكتور ماشي يعطيك العافية يعطيك العافية مع السلامة
+
+731
+00:46:39,470 --> 00:46:39,970
+يعطيك العافية
+
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..00e2676a6510cc782850ae388a5b224b263c7fbd
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg.srt
@@ -0,0 +1,1779 @@
+1
+00:00:00,000 --> 00:00:06,900
+أحمد؟ طيب، احنا زي ما حكينا الـWhite pieces
+
+2
+00:00:06,900 --> 00:00:09,880
+morphology هذه الخلايا الطبيعية، هذه خلية 
+
+3
+00:00:09,880 --> 00:00:15,820
+الـNeutrophil الماوس واضح، تمام؟ أيوة، أيوة هذه
+
+4
+00:00:15,820 --> 00:00:19,120
+خلية الـNeutrophil، هذه خلية الـEosinophil هذه خلية 
+
+5
+00:00:19,120 --> 00:00:21,820
+الـLymphocytes، خلية الـMonocytes وخلية
+
+6
+00:00:21,820 --> 00:00:26,220
+الـBasophil طبعا، نفس الخلايا واضحة عندها دهرة
+
+7
+00:00:26,610 --> 00:00:32,010
+الـBand أو الـStaff تسميها؟
+
+8
+00:00:32,010 --> 00:00:35,350
+بكلم
+
+9
+00:00:35,350 --> 00:00:41,940
+جوال يعنيأه ماشي، طيب، هاي خلية دنيا، أكيد،
+
+10
+00:00:41,940 --> 00:00:47,660
+فيزوزين، مونوسايد، مش هنَهجر عنهم، مش هنفنش، نحكي
+
+11
+00:00:47,660 --> 00:00:53,360
+فيهم كتير، حاجينهم جبانية، عمونا لأ تفكر
+
+12
+00:00:53,360 --> 00:00:55,520
+أن لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+13
+00:00:55,520 --> 00:00:55,760
+تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما عندك
+
+14
+00:00:55,760 --> 00:00:56,540
+جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما
+
+15
+00:00:56,540 --> 00:00:57,940
+عندك جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن
+
+16
+00:00:57,940 --> 00:01:02,660
+لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+17
+00:01:02,660 --> 00:01:04,680
+تفكر أن لسه ما عندك جامع
+
+18
+00:01:08,270 --> 00:01:14,470
+هي ميوت يا معاد؟ أفصل أفصل. لأ لأ بس عملتله ميوت
+
+19
+00:01:14,470 --> 00:01:22,870
+طيب الـabnormal shape، الـabnormal shape طبعا أول
+
+20
+00:01:22,870 --> 00:01:27,790
+شغل غراميستيك، غراميستيك طبعا واحد من الشباب سألني
+
+21
+00:01:27,790 --> 00:01:30,130
+قبل هيك يا دكتور ممكن نميز بين عينة المال و الـ
+
+22
+00:01:30,130 --> 00:01:35,670
+female صح ولا لأ؟أه أنا نسألت أه قلتلك أه ممكن على
+
+23
+00:01:35,670 --> 00:01:39,110
+طريق الخلايا النيتروفيل فهذه مميزة على طريق شغلها 
+
+24
+00:01:39,110 --> 00:01:42,910
+طب دراميستيك شايفين الـ .. احنا عندنا خلية هاي في
+
+25
+00:01:42,910 --> 00:01:47,030
+عبارة عن أربع loops شايفين الجزء الطالب البارز هذا
+
+26
+00:01:47,030 --> 00:01:50,810
+اللي عليه الماوس؟
+
+27
+00:01:50,810 --> 00:01:54,910
+أه شايفينههذا عبارة عن «Drumstick» هذا «Drumstick»
+
+28
+00:01:54,910 --> 00:01:58,350
+يعني زي طابلة، كيف عصاية الطابلة؟ هي عصاية طابلة،
+
+29
+00:01:58,350 --> 00:02:01,470
+طبعا «Drumstick» عبارة عن Nuclear Bandage تقريبا
+
+30
+00:02:01,470 --> 00:02:04,770
+واحد ونص مايكرو، طبعا in diameter ويكون attached
+
+31
+00:02:04,770 --> 00:02:08,430
+لـnucleus لإيش؟ لـ X-Chromosome، عشان تظهر وين؟
+
+32
+00:02:08,430 --> 00:02:10,910
+تظهر أكتر الشيء بالـ Female، طبعا الـ X-Chromosome
+
+33
+00:02:10,910 --> 00:02:13,750
+أنواح تيهم، مش الـ Active، الـ Inactive، مع أن
+
+34
+00:02:13,750 --> 00:02:19,460
+مايعرف أن الـ Male عبارة عن إيش؟ XYصح ولا لأ؟ الـ
+
+35
+00:02:19,460 --> 00:02:22,000
+Female XX واحد منهم Active وتاني Inactive فالـ
+
+36
+00:02:22,000 --> 00:02:26,180
+Inactive Form تظهر فيه هاي فإذا الـ Drumstick تظهر
+
+37
+00:02:26,180 --> 00:02:29,160
+في الـ Neutrophil للـ Female تظهر في الـ Male في
+
+38
+00:02:29,160 --> 00:02:31,480
+حالة Klinefelter Syndrome طب ليش تظهر في Klinefelter
+
+39
+00:02:31,480 --> 00:02:33,620
+Syndrome؟ مين بيذكر ليه؟ إيش هذا الـ
+
+40
+00:02:33,620 --> 00:02:40,120
+Syndrome؟ هذا اللي قبل شوية، اللي قبل شوية أجي
+
+41
+00:02:40,120 --> 00:02:47,140
+معانا لأ، Klinefelter Syndrome هذا بيكون عندي XXY
+
+42
+00:02:48,070 --> 00:02:51,110
+فاهميني كيف؟ يعني عنده نسخة إضافية من X يكون طبعاً
+
+43
+00:02:51,110 --> 00:02:56,750
+الـ Male هذا نحكي معاق وفي مشاكل كتير في الجينات
+
+44
+00:02:56,750 --> 00:03:00,850
+فبكون XXY، ففي عنده رسختين X واحدة منهم بتكون A
+
+45
+00:03:00,850 --> 00:03:09,910
+and A أكتر، فهمنا؟ فهمنا، فهمنا، فهمنا،
+
+46
+00:03:09,910 --> 00:03:11,230
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+47
+00:03:11,230 --> 00:03:14,210
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+48
+00:03:14,210 --> 00:03:21,310
+فهمنا، فهمنا، فهمناطيب الـ Dohle bodies نفس الـ
+
+49
+00:03:21,310 --> 00:03:23,150
+«Drumstick» طبعا بتظهر في الـ «Inactive
+
+50
+00:03:23,150 --> 00:03:26,450
+Chromosomes» بس طبعا بيكونش زي اللي جاي عصاية
+
+51
+00:03:26,450 --> 00:03:29,790
+الطابلة بيكون ميته شويسة بيسموها إيه؟ Dohle
+
+52
+00:03:29,790 --> 00:03:34,370
+bodies نفس الأشياء طبعا هنا فيه مميز بينها أربع
+
+53
+00:03:34,370 --> 00:03:36,730
+أنواع Dohle bodies والـ «Drumstick» هنا
+
+54
+00:03:36,730 --> 00:03:39,970
+Drumstick هاي Dohle bodies طبعا هذه بيسموها الـ
+
+55
+00:03:39,970 --> 00:03:43,270
+«حوك» زي الـ «حوك جاي» طبعا فيه تحت الشاشة طبعا بس
+
+56
+00:03:43,270 --> 00:03:46,010
+تدخل على الشاشة الـ«Power Point» هتلاحظوا أسماءهم
+
+57
+00:03:46,010 --> 00:03:49,930
+وتفاصيلهمالـHypersegmentation اللي حكيناها عبارة عن
+
+58
+00:03:49,930 --> 00:03:52,650
+Right Shift تكون عندك نيتروفيل أكثر من 5 loops
+
+59
+00:03:52,650 --> 00:03:56,450
+طبعاً تظهر في حالات طبعاً زي ما حكينا الـ5 to 6
+
+60
+00:03:56,450 --> 00:03:59,170
+loops تظهر في حالات اللي هي Megaloblastic Anemia
+
+61
+00:03:59,170 --> 00:04:01,730
+تظهر في حالة الـIron Deficiency تظهر في حالة
+
+62
+00:04:01,730 --> 00:04:05,210
+Chronic Infection تظهر في حالة Diabetes وفي حالة
+
+63
+00:04:05,210 --> 00:04:05,970
+الـUremia
+
+64
+00:04:08,250 --> 00:04:11,970
+الـ Hyper-segmentation ما حكينا عنها طيب الـ ring
+
+65
+00:04:11,970 --> 00:04:15,290
+-shaped nuclei بيكون النواء أصلا جاي زي ring
+
+66
+00:04:15,290 --> 00:04:20,370
+-shaped بصورة high طبعا بيكون طبعا أو دونات زي
+
+67
+00:04:20,370 --> 00:04:22,410
+الدوناتطبعًا تظهر في حالات برضه الـ Acute
+
+68
+00:04:22,410 --> 00:04:25,010
+Myelogenous Leukemia تظهر في حالة الـ Chronic Myelocytic
+
+69
+00:04:25,010 --> 00:04:28,630
+Leukemia الـ Myelodysplastic Syndromes، في حالة الـ MDS،
+
+70
+00:04:28,630 --> 00:04:32,630
+مالها معناها الـ MDS؟ الـ Myelodysplastic
+
+71
+00:04:32,630 --> 00:04:34,910
+Syndrome، Myelodysplastic Syndrome الحالات المهمة
+
+72
+00:04:34,910 --> 00:04:37,410
+دي كلها هتمور معاكم، و هناخدها إن شاء الله، في جزء
+
+73
+00:04:37,410 --> 00:04:39,910
+ماخدة إحنا عنيكي إشرحانها، و في جزء هتاخدوها مع
+
+74
+00:04:39,910 --> 00:04:44,730
+دكتور أحمد إن شاء الله الـ mouse واضح، شايفي؟ إنه
+
+75
+00:04:44,730 --> 00:04:48,070
+كويسلأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+76
+00:04:48,070 --> 00:04:50,190
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+77
+00:04:50,190 --> 00:04:54,070
+لأ، لأ، لأ، لأ، لأ،
+
+78
+00:04:54,070 --> 00:04:57,010
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+79
+00:04:57,010 --> 00:04:59,930
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+80
+00:04:59,930 --> 00:05:02,390
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأهذه
+
+81
+00:05:02,390 --> 00:05:05,510
+بيسموها «Detached Nuclear Materials» موجودة في
+
+82
+00:05:05,510 --> 00:05:09,070
+الـCytoplasm طبعاً إنتجتها «Dysgranulopoiesis» اللي
+
+83
+00:05:09,070 --> 00:05:11,770
+يعني إن فيه عنده مشكلة في عملية الـGranulation أو
+
+84
+00:05:11,770 --> 00:05:15,730
+طبعا مريض باخد كيموفيرابين، مريض في الـCancer باخد
+
+85
+00:05:15,730 --> 00:05:18,870
+كيموفيرابين أو في حالة الـHIV، هذه بيسموها إيه؟
+
+86
+00:05:18,870 --> 00:05:23,060
+«Detached Nuclear Fragments»طبعًا الـ Toxic
+
+87
+00:05:23,060 --> 00:05:25,400
+Granulation أخدناها أول مرة معناها اللي هي أن
+
+88
+00:05:25,400 --> 00:05:28,100
+خلايا الـ Neutrophil بيكون الـ granules فيها واضحة
+
+89
+00:05:28,100 --> 00:05:31,600
+كتير وكلها أزرق لأسود طبعًا نتيجة الـ infection
+
+90
+00:05:31,600 --> 00:05:34,240
+فالـ Toxic Granulation بيزيد الـ granulation فيها
+
+91
+00:05:34,240 --> 00:05:37,440
+وبيكون لها more basophilic و larger than normal
+
+92
+00:05:37,440 --> 00:05:40,340
+تضرب في حالة severe bacterial infection تضرب في
+
+93
+00:05:40,340 --> 00:05:42,740
+بعض الحالات الـ tissue damage أو الـ type يعني الـ
+
+94
+00:05:42,740 --> 00:05:45,480
+inflammation تضرب في حالة الـ normal pregnancy
+
+95
+00:05:45,480 --> 00:05:49,270
+وتضرب في حالة الـ therapy with cytokinesطبعًا
+
+96
+00:05:49,270 --> 00:05:51,670
+الـCytokines ما هي أسئلة تقرر في عملية إنه يحصل
+
+97
+00:05:51,670 --> 00:05:54,710
+عندي Granulation طبعًا الـHyposegmentation هو
+
+98
+00:05:54,710 --> 00:05:58,310
+واضح عندي الـHypogranulation
+
+99
+00:05:58,310 --> 00:06:01,170
+تظهر إنه بيكون عندي العكس، بيكون Reduced في
+
+100
+00:06:01,170 --> 00:06:04,670
+الـGranulation في النيتروفيل في حالة الـMDS، اللي
+
+101
+00:06:04,670 --> 00:06:09,030
+هي الـMyelodysplastic Syndrome دُه ال bodies
+
+102
+00:06:09,030 --> 00:06:15,660
+شفناها ومرت معنا تمام يا محمد، علمت عليها؟طيب، دُه
+
+103
+00:06:15,660 --> 00:06:18,300
+الـ Bodies اللي فيه أزرق هناك، فالأزرق هي برنامج
+
+104
+00:06:18,300 --> 00:06:23,160
+Small Pale Blue Cytoplasmic Inclusions طبعاً دُه الـ
+
+105
+00:06:23,160 --> 00:06:25,860
+Bodies طبعاً بتكون متكون من الـ Ribosomes والـ
+
+106
+00:06:25,860 --> 00:06:29,540
+Endoplasmic reticulum تظهر في حالات الـ Infective
+
+107
+00:06:29,540 --> 00:06:32,160
+Endocarditis، Inflammatory States، يعني Infection
+
+108
+00:06:32,160 --> 00:06:35,580
+Inflammation، الـ Severe Burn، Tuberculosis، و الـ
+
+109
+00:06:35,580 --> 00:06:37,060
+Postchemotherapy و البريجنالسية
+
+110
+00:06:41,350 --> 00:06:45,210
+وطبعًا في آخر حالة تظهر فيها الـMyoglobin Anomaly
+
+111
+00:06:45,210 --> 00:06:49,970
+الـRussell Body، الـRussell Body طبعًا هي تظهر في
+
+112
+00:06:49,970 --> 00:06:52,570
+الإيزينوفيل، بيكون أصلا، اللي احنا حكينا إن
+
+113
+00:06:52,570 --> 00:06:57,050
+الإيزينوفيل فيها الـgranules حمرة وكبيرة ومسفّطة،
+
+114
+00:06:57,050 --> 00:07:00,350
+بيكون Large, homogeneous, immunoglobulin containing
+
+115
+00:07:00,350 --> 00:07:03,240
+inclusionsطبعًا الـ Immunoglobulins Containing
+
+116
+00:07:03,240 --> 00:07:05,780
+Glucose اللي هي المرتبطة في الـ Immunoglobulins
+
+117
+00:07:05,780 --> 00:07:09,360
+اللي هي الأجسام المضادة طبعًا اللي تظهر في حالة
+
+118
+00:07:09,360 --> 00:07:13,360
+الـ Plasma Cells اللي بيصيرها تطورات طبعًا هي مش
+
+119
+00:07:13,360 --> 00:07:15,400
+تظهر في الـ eosinophil، sorry هي بتظهر في الـ
+
+120
+00:07:15,400 --> 00:07:17,540
+Plasma Cells، اللي خلايا الـ Plasma Cells اللي بقى
+
+121
+00:07:17,540 --> 00:07:20,200
+خلايا الـ lymphocytes مش eosinophil، لكن بتظهر
+
+122
+00:07:20,200 --> 00:07:28,500
+كأنها eosinophil، تمام؟ بتظهر كأنها eosinophil ورا
+
+123
+00:07:28,500 --> 00:07:33,480
+الـأنتوا شايفين العرض اللي راح من عينكم؟ لا
+
+124
+00:07:33,480 --> 00:07:37,200
+شايفينه تمام، تظهر كإنه كإنه إيزينوفي لكن بيكون
+
+125
+00:07:37,200 --> 00:07:40,500
+نوة واحدة زي بلازمس اللي بيسموها وبيكون عليها
+
+126
+00:07:40,500 --> 00:07:43,600
+السيمي الأحمر، شايفين؟ بيكون فيها كإنها جرانيوس
+
+127
+00:07:43,600 --> 00:07:48,560
+كبيرة ولونها أزرق الخلايا اللي حواليها، شايف
+
+128
+00:07:48,560 --> 00:07:52,680
+الخلايا الجنبل عند الماوس هاي؟ والخلايا تحت هاي،
+
+129
+00:07:52,680 --> 00:07:56,180
+هذه عبارة عن خلايا حمراء منوعة نيوكلياتي د ر بي
+
+130
+00:07:56,180 --> 00:07:58,700
+سي،  النيوكلياتي د ر بي سي، كل شيء بيعطيكم إياه،
+
+131
+00:07:58,700 --> 00:08:00,760
+حاولوا تكتبوا جنبه إيش الإسم عشان فيه مبادرة، لو
+
+132
+00:08:00,760 --> 00:08:06,660
+رجعتوله تذكروه،  باشي يا سعيد؟ عيد لسه مبالغة يا
+
+133
+00:08:06,660 --> 00:08:09,900
+دكتور؟ النيوكلياتي د ر بي سي، النيوكلياتي د ر بي 
+
+134
+00:08:09,900 --> 00:08:16,900
+سي، تمام، مش هاي اللي ينفع عنه، هاي، أكتبكم إياها،
+
+135
+00:08:16,900 --> 00:08:23,130
+هذه عبارة عن شايفين الكتابة؟ نعم نعم شايفينها
+
+136
+00:08:23,130 --> 00:08:26,730
+Nucleated
+
+137
+00:08:26,730 --> 00:08:30,890
+RBCs يعني خلايا حمرة منوعة فيها أنوية Nucleated
+
+138
+00:08:30,890 --> 00:08:38,410
+RBCs تمام؟ بس ثواني إيش يا سيد؟ هاتي هاتي رجل هاتي 
+
+139
+00:08:38,410 --> 00:08:43,490
+رجل صوتك باطل شوية يا سيد علي صوتك الراس الفاطس
+
+140
+00:08:43,490 --> 00:08:48,370
+الراس الفاطس الراس الفاطس أه ثواني؟
+
+141
+00:08:49,640 --> 00:08:54,160
+كيف نفرّكها في هي واللي هجت قبل شوية اللي هي
+
+142
+00:08:54,160 --> 00:08:58,600
+الـ Vacuoles؟ الـ Vacuoles بيكون غير منتظمة،
+
+143
+00:08:58,600 --> 00:09:01,460
+الـ Vacuoles غير منتظمة، ما بيكونش Homogeneous،
+
+144
+00:09:01,460 --> 00:09:04,640
+فهذه إن أنا ألاحظ كلمة Homogeneous، أنا عندي هان
+
+145
+00:09:04,640 --> 00:09:07,600
+كلمة Homogeneous ألاحظ كيف مهمة جدا
+
+146
+00:09:11,680 --> 00:09:15,980
+الـ Vacuoles ليست هيموجينية، بيكون بعثرة، حجمها 
+
+147
+00:09:15,980 --> 00:09:19,600
+مختلف من واحدة لواحدة، والـ Vacuoles تظهر في
+
+148
+00:09:19,600 --> 00:09:22,420
+الـ Neutrophil وفي الـ Monocytes، هذه بتظهر في الـ
+
+149
+00:09:22,420 --> 00:09:25,560
+Plasma Cells، البلازما سيلز عبارة عن خلية بصورة
+
+150
+00:09:25,560 --> 00:09:29,560
+High، خلية تكون نواة واحدة تلافية، طبعًا الـ Plasma
+
+151
+00:09:29,560 --> 00:09:32,880
+Cells هي الخلايا المسؤولة عن إنتاج الأجسام
+
+152
+00:09:32,880 --> 00:09:35,940
+المضادة، فيما بعد عشان ذلك بيكون عبارة عن فيها
+
+153
+00:09:35,940 --> 00:09:38,420
+Large Homogeneous Immunoglobulin Immunoglobulin
+
+154
+00:09:38,420 --> 00:09:40,960
+عبارة عن إيه؟ البروتين اللي صنع منه الأجسام
+
+155
+00:09:40,960 --> 00:09:45,280
+المضادة، تمام؟ Inclusions وزي ما حكينا بتظهر في
+
+156
+00:09:45,280 --> 00:09:49,400
+الـ Plasma Cells اللي Undergoing X-Step Synthesis
+
+157
+00:09:49,400 --> 00:09:52,900
+بيكون أنت إنتاج إلها كتير لـ Immunoglobulin فعشان
+
+158
+00:09:52,900 --> 00:09:54,280
+بتظهر الـ Russell Bodies
+
+159
+00:10:01,360 --> 00:10:06,220
+طبعًا… خلّي الـ… هذا فوق شوية الـ Phagocytes بقى
+
+160
+00:10:06,220 --> 00:10:11,940
+Parasites هي خلايا الـ Parasites اللي بتتطفى على
+
+161
+00:10:11,940 --> 00:10:14,960
+جسم الإنسان وتتم بنعمتها طبعًا Phagocytes
+
+162
+00:10:14,960 --> 00:10:19,340
+Parasites اللي هي على طريق الخلايا الحمراء فأكيد
+
+163
+00:10:19,340 --> 00:10:23,680
+سمعتوا في الملاريا، أمام؟ بسبب الملاريا، فطبعًا عند
+
+164
+00:10:23,680 --> 00:10:27,640
+هان، تلاحظون اللي هنا، هاي الخلية هاي، شايفينها؟
+
+165
+00:10:27,640 --> 00:10:37,080
+الخلية هاي، اللي فيها، هي ضاحت عليه دائرة،
+
+166
+00:10:37,080 --> 00:10:40,300
+خلية
+
+167
+00:10:40,300 --> 00:10:42,860
+هاي بالظبط، هاي اللي عند المسعى، المسعى، واي خلية
+
+168
+00:10:42,860 --> 00:10:48,170
+هاي وخلية هاي وخلية هاي، فيها حجم، طب لاحظ، شوف،
+
+169
+00:10:48,170 --> 00:10:51,350
+بقدر أكبر من عندي، فيه ثابتة كبيرة، بس عقلها هي
+
+170
+00:10:51,350 --> 00:10:57,930
+فيها زي ما بتحكيه، فيها زي .. زي إشي زي الخاتم،
+
+171
+00:10:57,930 --> 00:11:00,790
+بيسموه Ring Form Parasite، هاد عبارة عن Malaria،
+
+172
+00:11:00,790 --> 00:11:03,730
+Malaria Parasites، شايفين؟ خليه هاي كمان، خليه
+
+173
+00:11:03,730 --> 00:11:08,630
+هاي، خليه هاي، عليها نقطتين؟ نقطتين وفيه خيط مربط
+
+174
+00:11:08,630 --> 00:11:13,150
+بين أثنين واتنين، زي الخاتم، بيسموه؟ آه، لو كبرت،
+
+175
+00:11:13,150 --> 00:11:17,270
+بيظهر أما بدي أكبر، بدي أروح أكبر مكان تاني، مش
+
+176
+00:11:17,270 --> 00:11:19,930
+مشكلة، إن شاء الله أفرجيكم إياهم عن الأمر واقعي،
+
+177
+00:11:19,930 --> 00:11:24,230
+هيا خليني نشوف من عندنا نقدر نكبر أحنا، شايفين
+
+178
+00:11:24,230 --> 00:11:29,590
+هاي؟ شايف يا سيد؟ أعطيك، أعطيك، أعطيك، أعطيك،
+
+179
+00:11:29,590 --> 00:11:31,530
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+180
+00:11:31,530 --> 00:11:32,090
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+181
+00:11:32,090 --> 00:11:41,790
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+182
+00:11:41,790 --> 00:11:47,350
+أعطيك طبعًا، هذه كما حكيناها بتظهر في حالات
+
+183
+00:11:47,350 --> 00:11:50,870
+الـ Infection بالنصاب بالملاريا طبعًا الـ Phagocyte
+
+184
+00:11:50,870 --> 00:11:55,490
+Platelets العكس بيكون المرحل الذنب اللي عمته اللي
+
+185
+00:11:55,490 --> 00:11:58,190
+هو الـ Platelets تظهر في خلايا الـ Neutrophil
+
+186
+00:11:58,190 --> 00:12:00,590
+الـ Neutrophil بتروح تبلع الـ Platelets نتيجة
+
+187
+00:12:00,590 --> 00:12:03,170
+الـ Infection طبعًا الـ Infection البتوفين بيبقى
+
+188
+00:12:03,170 --> 00:12:05,690
+بيبقى بتبلع بكتيريا لكن نتيجة مثلًا إذا كانت
+
+189
+00:12:05,690 --> 00:12:08,530
+Severe Infection بيصير تروح تبلع ممكن تبقى عند
+
+190
+00:12:08,530 --> 00:12:11,580
+الوقت تبلع الـ Platelets زي بالحالة هذه هي عندي
+
+191
+00:12:11,580 --> 00:12:15,160
+الحالة هاي، شايفين الخلايا ها؟ هي بالعالي Platelets
+
+192
+00:12:15,160 --> 00:12:18,460
+وهان بالعالي Platelets، شايفين هاي؟ النقطة هاي
+
+193
+00:12:18,460 --> 00:12:22,840
+الصغيرة الزرقى، هادي عبارة عن خلية Platelets، هادي
+
+194
+00:12:22,840 --> 00:12:27,420
+عبارة عن هاي، شايفين هاي، هاي الصغيرة، هاي،
+
+195
+00:12:27,420 --> 00:12:30,480
+ما بيضيش أحط بصوم كتير عشان ما تخربطوش كتير، ماشي
+
+196
+00:12:30,480 --> 00:12:34,720
+شفتوها، هادي بيسموها Phagocytes of Platelets طب
+
+197
+00:12:34,720 --> 00:12:36,640
+انتظر في حالات ال Infection، انتظر في حالات ال
+
+198
+00:12:36,640 --> 00:12:36,920
+Infection
+
+199
+00:12:45,010 --> 00:12:54,430
+شوي شباب شوي بس دقيقة سيف
+
+200
+00:12:54,430 --> 00:13:03,870
+أنت في المحاضرة؟
+
+201
+00:13:05,700 --> 00:13:08,400
+طيب، معلش، عشان كان إيش ابني و بدي أحكي معاه في
+
+202
+00:13:08,400 --> 00:13:12,320
+شغلات طيب، هل جيت الفاقوصيات الـ Platelets بيكون
+
+203
+00:13:12,320 --> 00:13:16,000
+خلايا النيتروفيل عاملة الفاقوصيتوشين لـ Platelets
+
+204
+00:13:16,000 --> 00:13:18,860
+في حالة ال Infection؟ هاي الصورة واضحة كتير،
+
+205
+00:13:18,860 --> 00:13:21,860
+شايفينها؟ هاي الخلية النيتروفيل وهي الـ Platelets
+
+206
+00:13:21,860 --> 00:13:28,980
+جواها واضحة يا شباب، أه؟ لأ، مش واضحة دكتور،
+
+207
+00:13:28,980 --> 00:13:32,340
+شايفين الصورة أنتو؟ دكتور، أه شايفين، أه أه
+
+208
+00:13:32,340 --> 00:13:38,920
+شايفين، طب تمام، بس إيش يا سعيد؟ إيش بالنسبة ل ..
+
+209
+00:13:38,920 --> 00:13:44,700
+إيش بالنسبة لهذه؟ في .. في خلايا فوق و تحت هدول
+
+210
+00:13:44,700 --> 00:13:50,860
+Platelets برضه؟ هذه Platelets وهذه Platelets وهذه جوا
+
+211
+00:13:50,860 --> 00:13:55,220
+الخلية دي نيترو فيه Platelets هدول كل اللي عليها دواعي
+
+212
+00:13:55,220 --> 00:13:58,920
+الخضرة Platelets، هذه Platelets، شايفين؟ هذه اللي جت
+
+213
+00:13:58,920 --> 00:14:03,400
+Platelets، شايفها يا سعيد؟ طب هذه يا دكتور؟ أجل، أجل،
+
+214
+00:14:03,400 --> 00:14:05,140
+أجل، أجل علمليها
+
+215
+00:14:08,780 --> 00:14:13,760
+الـ Granules، هذه، هذه تحت Platelets، هذه Hypogranular،
+
+216
+00:14:13,760 --> 00:14:18,000
+بيكون فيه فيها Granules، Hypogranular، طبعًا مرة
+
+217
+00:14:18,000 --> 00:14:20,660
+معنا نوع الـ Platelets، عندي Hypogranular، بيكون
+
+218
+00:14:20,660 --> 00:14:22,980
+Granules خفيف فيها، هذي، هذي الصغيرة هي كمان
+
+219
+00:14:22,980 --> 00:14:26,580
+Platelets، صحيح، تمام؟ ‏- تمام ‏- هذو كل
+
+220
+00:14:26,580 --> 00:14:29,000
+Platelets، بس أنا بهمني في الـ Slide هاي
+
+221
+00:14:29,000 --> 00:14:31,440
+الـ Phagocytes of Platelets، Phagocytes of Platelets، أنا
+
+222
+00:14:31,440 --> 00:14:33,500
+حكيتكم إن هي بثمبة اللي عملتها عن طريق
+
+223
+00:14:33,500 --> 00:14:35,000
+الـ Neutrophil، واضح عندي
+
+224
+00:14:43,050 --> 00:14:47,870
+فيب، نروح لـ Slide البعديها البعديها
+
+225
+00:14:47,870 --> 00:14:49,750
+الـ Phagocytosis of Blood Cells العكس، الـ
+
+226
+00:14:49,750 --> 00:14:53,710
+Neutrophil راح تبقى عادة خلايا حمراء طبعًا، بتظهر
+
+227
+00:14:53,710 --> 00:14:56,610
+في حالات، شايفين أن هي Neutrophil وداخلها خلايا
+
+228
+00:14:56,610 --> 00:15:00,210
+حمراء، واضحة طبعًا، في حالة ال Infection أو الـ
+
+229
+00:15:00,210 --> 00:15:01,990
+Autoimmune Hemorrhagic Anemia أو في حالة
+
+230
+00:15:01,990 --> 00:15:03,570
+الـ Incompatible Blood Transfusion يعني إذا أنا
+
+231
+00:15:03,570 --> 00:15:06,350
+نجلت دم لمريض والدم هتغير متوافق معاه
+
+232
+00:15:06,350 --> 00:15:08,990
+فـ Incompatibility فتصبح الخلايا الـ Neutrophil
+
+233
+00:15:08,990 --> 00:15:13,000
+تتعمل Phagocytosis للخلايا الحمراء، طبعًا ساموها
+
+234
+00:15:13,000 --> 00:15:23,040
+Phagocytosis of Red Blood Cells الـ
+
+235
+00:15:23,040 --> 00:15:23,900
+Slide البعديها
+
+236
+00:15:26,370 --> 00:15:29,490
+هذه طبعًا الـ Phagocytes فهذه الـ Vacuoles
+
+237
+00:15:29,490 --> 00:15:33,050
+هيكون إننا عديد سلايدات، هنتقص فيها شوية الـ
+
+238
+00:15:33,050 --> 00:15:35,090
+Vacuoles، شايفين؟ الـ Vacuoles-T فيها شباب
+
+239
+00:15:35,090 --> 00:15:39,410
+تختلف عن اللي حكينا عنها قبل شوية، الـ Plasma
+
+240
+00:15:39,410 --> 00:15:42,590
+Cells طبعًا لأن الـ Vacuoles أحجامها طبعًا
+
+241
+00:15:42,590 --> 00:15:48,770
+مختلفة، مبترة، مش جايب منتظمة، تمام؟ هاي عندي الـ
+
+242
+00:15:48,770 --> 00:15:50,630
+Auer Rods، حكيناها الـ Auer Rods، الـ Auer Rods
+
+243
+00:15:50,630 --> 00:15:55,140
+عبارة عن طبعًا، زي ما حكينا، بتظهر في حالة الـ
+
+244
+00:15:55,140 --> 00:15:59,140
+Myeloblast و الـ Promyelocyte، يعني في الخلايا بقى
+
+245
+00:15:59,140 --> 00:16:06,980
+بالـ Maturation، أيش يا شباب؟ في حد سأل؟ سعيد،
+
+246
+00:16:06,980 --> 00:16:11,520
+الصوت عنده بيقطع، سعيد طيب، احنا إن شاء الله، زي ما
+
+247
+00:16:11,520 --> 00:16:13,700
+حكيتها سعيد، أنا فيه تسجيل سابق، و أنا هبقى عندكم
+
+248
+00:16:13,700 --> 00:16:17,660
+تسجيل إن شاء الله، فالـ Auer Rods، زي ما حكينا، عندي
+
+249
+00:16:17,660 --> 00:16:20,460
+الـ Auer Rods بتظهر في حالات الـ Acute Myeloid
+
+250
+00:16:20,460 --> 00:16:24,670
+Leukemia الـ M2 و الـ MDS اللي هي Myelodysplastic
+
+251
+00:16:24,670 --> 00:16:26,610
+syndrome ما يُلو dysplastic syndrome، الـ MDS
+
+252
+00:16:26,610 --> 00:16:30,830
+فبتقدر في الحالتين، شايفين النيتروفيل، خليط
+
+253
+00:16:30,830 --> 00:16:35,270
+النيتروفيل؟ خليط النيتروفيل هنا، في زي عصاية صغيرة
+
+254
+00:16:35,270 --> 00:16:40,230
+فيها، هيها، الصورة هي، خليني أحطكم على دائرة، هذه
+
+255
+00:16:40,230 --> 00:16:44,590
+العصاية الصغيرة هذه الصغيرة هنا هي برعم أوروذ، طب
+
+256
+00:16:44,590 --> 00:16:48,030
+انتظر في حالات الـ immature cells إما نحكي
+
+257
+00:16:48,030 --> 00:16:50,370
+mature تكون ناضجة، immature غير ناضجة، فانتظر
+
+258
+00:16:50,370 --> 00:16:53,630
+في حالات غير ناضجة، اللي هي حالات الـ myeloplast
+
+259
+00:16:53,630 --> 00:16:55,470
+والـ promyelocyte، وانتظر في الحالات اللي بحكيها
+
+260
+00:16:55,470 --> 00:16:59,350
+أنا الـ acute myeloplastic leukemia في الـ M2،
+
+261
+00:16:59,350 --> 00:17:03,630
+في إيش بيسميه أن M2، هتمر معنا إن شاء الله يعني،
+
+262
+00:17:03,630 --> 00:17:06,250
+يعني يا دكتور، عادي ممكن أنها تظهر normal أو
+
+263
+00:17:06,250 --> 00:17:10,370
+abnormal؟ لأ، هذه abnormal، هذه المفروضة abnormal،
+
+264
+00:17:10,370 --> 00:17:15,500
+آه الـ Acute Myeloid Leukemia Acute Myeloid Plastic
+
+265
+00:17:15,500 --> 00:17:19,440
+Leukemia الـ AML M2 والـ MDS Myeloid Plastic
+
+266
+00:17:19,440 --> 00:17:23,000
+Syndrome أصلاً
+
+267
+00:17:23,000 --> 00:17:27,680
+هي الخليتين هذولة، يعني الخلية هاي والخلية هاي مش
+
+268
+00:17:27,680 --> 00:17:32,460
+لازم يظهروا في الـ Normal Blood Film لازم يظهروا
+
+269
+00:17:32,460 --> 00:17:34,680
+بالبون مرة، لكن لو ظهروا في الـ Normal Blood Film
+
+270
+00:17:34,680 --> 00:17:36,960
+بحكي أنا عندي حالة مش طبيعية
+
+271
+00:17:41,060 --> 00:17:44,600
+صحيح، هي الـ myeloplast، صحيح مش myeloplast هي مثلًا ما
+
+272
+00:17:44,600 --> 00:17:47,740
+بعد الـ myeloplast الـ myeloplast هذي myeloplast وهذه
+
+273
+00:17:47,740 --> 00:17:53,680
+الـ promyelocytes هاي
+
+274
+00:17:53,680 --> 00:17:56,500
+Auer Rods واضحة، شكل واضح كثير، شايفين الـ Auer
+
+275
+00:17:56,500 --> 00:18:00,480
+Rods؟ حتى هذي بسميها أنا Bundles of Auer Rods
+
+276
+00:18:00,480 --> 00:18:03,780
+يعني Bundles من الجمعة زي العصيات Bundles of Auer
+
+277
+00:18:03,780 --> 00:18:06,860
+Rods هاي اللي هنا، شايفين؟ هذي طبعًا هن الـ Auer
+
+278
+00:18:06,860 --> 00:18:09,840
+Rods عندي، هن في عندي Auer Rods، ظاهرة واضحة
+
+279
+00:18:10,070 --> 00:18:13,870
+طبعًا، يكون الخناية الـ myelocytes كلها هي خلية
+
+280
+00:18:13,870 --> 00:18:16,510
+promyelocytes، هي myelocytes، promyelocytes حدوث ما
+
+281
+00:18:16,510 --> 00:18:19,150
+أنا في حالة الـ maturation إن شاء الله الـ Macro
+
+282
+00:18:19,150 --> 00:18:21,790
+neutrophil، الـ neutrophil بيكون حجم كبير طبعًا،
+
+283
+00:18:21,790 --> 00:18:24,690
+بيكون حجم ضعف، حجم neutrophil عادية طبعًا، هذه
+
+284
+00:18:24,690 --> 00:18:29,050
+نتيجة إنه عندي نشاط في الـ DNA etc. employed of DNA
+
+285
+00:18:29,460 --> 00:18:33,000
+تظهر في حالات طبعًا ممكن تظهر نادر في بعض الحالات
+
+286
+00:18:33,000 --> 00:18:36,780
+الطبيعية لكن قليلة جدًا ممكن تكون وراثية عند الناس،
+
+287
+00:18:36,780 --> 00:18:41,240
+بعض الناس ممكن نتيجة إنه واحد ماخذ مثلًا الـ… نحكي
+
+288
+00:18:41,240 --> 00:18:46,180
+الـ… الـ… الـ Cytokines زي الـ Granulocyte Colony Stimulating
+
+289
+00:18:46,180 --> 00:18:49,900
+Factors هذه المتنشطة النيتروفيل طبعًا أخد
+
+290
+00:18:49,900 --> 00:18:52,300
+الـ Cytokines بتعطيني التنشيط أو تظهر في حالات
+
+291
+00:18:52,300 --> 00:18:54,920
+بَلدِيَّة زي الـ Megaloblastic Anemia أو الـ Chronic
+
+292
+00:18:54,920 --> 00:19:01,930
+Infection تمام؟ مش هذا دكتور يقول الـ G-CSF حسابش هذا
+
+293
+00:19:01,930 --> 00:19:06,710
+الـ factor اللي بنشط؟ هذا الـ factor بنشطني نيتروفيل
+
+294
+00:19:06,710 --> 00:19:08,170
+وبنتجني نيتروفيل، صحيح؟ اللي بيسموه
+
+295
+00:19:08,170 --> 00:19:11,710
+الـ Granulocyte Colony Stimulating Factor اسمها
+
+296
+00:19:11,710 --> 00:19:14,910
+Granulocyte Colony Stimulating Factor طبعا هذا
+
+297
+00:19:14,910 --> 00:19:18,070
+الـ factors بنشطني إنتاج خلايا نيتروفيل
+
+298
+00:19:21,910 --> 00:19:26,090
+طبعًا في الـ Necrobiotic أو الـ «أبوبتك» «أبوبتك»
+
+299
+00:19:26,090 --> 00:19:28,770
+يعني موت الخلايا «أبوبتوس» فيز موت الخلايا، طبعًا
+
+300
+00:19:28,770 --> 00:19:32,310
+«نيكروبيوتيك» طبعًا ما عرف معنى، بيكون اللحظة اللي
+
+301
+00:19:32,310 --> 00:19:36,690
+عنديها النواء في الـ «نيتروفيل» كيف شكلها، يعني
+
+302
+00:19:36,690 --> 00:19:40,650
+تقريبًا فقدت، فقدت مبااعتها وفقدت شكلها اللي
+
+303
+00:19:40,650 --> 00:19:45,680
+فعليًا، بيكون في حالات EH في حالات الفترة، إذا كان
+
+304
+00:19:45,680 --> 00:19:49,520
+عندي طول كثير الدم أو في حالة الـ Acute، ما يلوت
+
+305
+00:19:49,520 --> 00:19:52,880
+بالكيميا طبعاً بيصير الـ Dense Homogenous Nuclei
+
+306
+00:19:52,880 --> 00:19:57,840
+بيكون النواء متشانسة وغامقة كثير وجز، بيسموها
+
+307
+00:19:57,840 --> 00:20:03,600
+Pyknotic، تمام؟ بيسموها Pyknotic يعني
+
+308
+00:20:03,600 --> 00:20:06,300
+زي الـ Necrosis يا دكتور؟ زي الـ Necrosis، هي نقرس،
+
+309
+00:20:06,300 --> 00:20:08,480
+ما حكيت أن هي نقر بيوتك، Necrosis
+
+310
+00:20:11,320 --> 00:20:14,040
+طبعًا شفت لفت حكيناها؟ شفت لفت إنه بيكون أنا عندي
+
+311
+00:20:14,040 --> 00:20:18,220
+خلايا قبل الـ Maturation زي هذه الخلايا طبعًا الـ
+
+312
+00:20:18,220 --> 00:20:22,440
+myeloplast بتظهر عندي، طبعًا بتظهر في حالة
+
+313
+00:20:22,440 --> 00:20:24,920
+الـ Normal Pregnancy، بتظهر في حالة الـ Infection،
+
+314
+00:20:24,920 --> 00:20:27,060
+بتظهر في حالة الـ Pulmonary Fibrosis، وبتظهر في
+
+315
+00:20:27,060 --> 00:20:29,280
+حالة الـ Pulmonary Infiltration By Malignancy، إذا
+
+316
+00:20:29,280 --> 00:20:33,130
+فيندي Malignant Cells بتظهر في حالة أيه في عندي
+
+317
+00:20:33,130 --> 00:20:37,050
+أشياء بيسموها «Pseudo Pelger Huet Anomaly» طبعًا «Pseudo
+
+318
+00:20:37,050 --> 00:20:39,070
+Pelger Huet Anomaly» بيكون الخلايا النيتروفيل اللي
+
+319
+00:20:39,070 --> 00:20:42,370
+احنا حكينا النيتروفيل اللي فيها النواة من 2 إلى 5
+
+320
+00:20:42,370 --> 00:20:45,890
+loops لكن غالبًا تظهر لي بالـ Normal persons 3
+
+321
+00:20:45,890 --> 00:20:49,130
+loops، 4 loops غالبًا لكن لو ظهرت معظم الخلايا 2
+
+322
+00:20:49,130 --> 00:20:51,850
+loops بيكون هذه الحالة اللي سموها «Pseudo Pelger Huet
+
+323
+00:20:51,850 --> 00:20:55,190
+Anomaly» بعبارة عن Bi-looped neutrophil with more
+
+324
+00:20:55,190 --> 00:20:58,630
+condensed chromatin طبعًا تظهر في حالة الـ MDS،
+
+325
+00:20:58,630 --> 00:21:01,850
+تظهر في حالة الـ Idiopathic Myelofibrosis تظهر في
+
+326
+00:21:01,850 --> 00:21:04,730
+حالة الـ Chronic Myelocytic Leukemia أو في حالة
+
+327
+00:21:04,730 --> 00:21:09,550
+العلاج بالـ Colchicine أو الـ Ibuprofen أو في حالة
+
+328
+00:21:09,550 --> 00:21:13,910
+الـ Infection للمونوكلوسس والملاريا والمكسليمة، في
+
+329
+00:21:13,910 --> 00:21:14,650
+حالة الـ CLA
+
+330
+00:21:17,840 --> 00:21:20,120
+الـ Neutrophil Aggregation زي Platelet Aggregation
+
+331
+00:21:20,120 --> 00:21:23,980
+طبعا هذه حالة In Vitro بسبب الإيديتا بتصير عملية
+
+332
+00:21:23,980 --> 00:21:26,600
+Clump للـ Neutrophil مع بعض متخاطرين مع بعض بعض
+
+333
+00:21:26,600 --> 00:21:29,780
+طبعا زي ما حكيت إن هذه عبارة عن حالة In Vitro
+
+334
+00:21:29,780 --> 00:21:34,600
+تتضار في حالات زي ما حكيتها النتيجة إن الإيديتا
+
+335
+00:21:34,600 --> 00:21:38,560
+عندي شوية قديم أو طول كثير أو في بعض الحالات الـ
+
+336
+00:21:38,560 --> 00:21:41,140
+Infectious Mononucleosis أو بعض الحالات الـ Bacterial
+
+337
+00:21:41,140 --> 00:21:45,180
+Infection أو الـ Autoimmune Disease الـ Atypical
+
+338
+00:21:45,180 --> 00:21:47,400
+lymphocyte هي خلايا لينفوسايتز، هنحكي إن خلايا
+
+339
+00:21:47,400 --> 00:21:53,440
+لينفوسايتز عبارة عن حجمين، وبالأحرى ثلاثة، Small و
+
+340
+00:21:53,440 --> 00:21:56,080
+Intermediate و Large الخلايا الـ Atypical
+
+341
+00:21:56,080 --> 00:22:00,660
+lymphocyte بيكون أكبر من Large كمان، وبيكون النواة
+
+342
+00:22:00,660 --> 00:22:05,710
+فيها مش دائرية بيكون شكلها مش منتظم طبعًا هذه بتظهر
+
+343
+00:22:05,710 --> 00:22:07,510
+في حالات الـ infection أكثر إيش هي في
+
+344
+00:22:07,510 --> 00:22:10,770
+الـ Cytomegalovirus أو البشتان بار الفيروس طبعًا
+
+345
+00:22:10,770 --> 00:22:14,410
+Cytomegalovirus يعني بالفيروسات وطبعًا إحنا بنعرف
+
+346
+00:22:14,410 --> 00:22:18,130
+إنه إصابة الفيروس بتأثر أكثر إيش على الـ Lymphocyte
+
+347
+00:22:18,130 --> 00:22:21,370
+إصابة البكتيري بتأثر أكثر إيش على الـ Nitrophil على
+
+348
+00:22:21,370 --> 00:22:24,650
+الأغلب طبعًا فزي ما حكينا، الـ Atypical Lymphocyte
+
+349
+00:22:24,650 --> 00:22:27,810
+عبارة عن بوليومورفيك كبير، والدايمتر بيكون دايمتر
+
+350
+00:22:27,810 --> 00:22:31,130
+15 إلى 30، يعني أكبر من الـ Monocyte نفسها طبعًا،
+
+351
+00:22:31,130 --> 00:22:33,910
+بيكون abundant وبيكون بيزوفيليك، طبعًا الـ Cytoplasm
+
+352
+00:22:33,910 --> 00:22:37,610
+كثير، طبعًا بيزوفيليا وبيكون طبعًا maybe confined
+
+353
+00:22:37,610 --> 00:22:40,030
+with the cytoplasmic margins، بيكون أن الأطراف في
+
+354
+00:22:40,030 --> 00:22:44,380
+الـ Cytoplasm مش منتظمة زي ما حكينا، بتظهر في حالة
+
+355
+00:22:44,380 --> 00:22:48,280
+الـ Viral Infection خاصة الإبشطان بار فيروس أو
+
+356
+00:22:48,280 --> 00:22:50,560
+certain مجال الفيروس أكثر إشي تظهر في حالة الـ
+
+357
+00:22:50,560 --> 00:22:52,460
+Bacterial Infection وأحيانًا الـ Tuberculosis و
+
+358
+00:22:52,460 --> 00:22:57,460
+البروسوليس لأن البروسيلة والـ TB بأثر على الـ
+
+359
+00:22:57,460 --> 00:23:01,320
+lymphocytes ملاريا تظهر في حالة ملاريا ممكن، في
+
+360
+00:23:01,320 --> 00:23:04,920
+حالة الطعيمات ممكن تظهر بالفيروسات هاي أو System
+
+361
+00:23:04,920 --> 00:23:06,560
+ic Lupus اللي موجودة فيها
+
+362
+00:23:09,870 --> 00:23:13,790
+الـ Plasma Cytoid Lymphocyte طبعًا الـ Plasma
+
+363
+00:23:13,790 --> 00:23:16,190
+Cytoid لابد من أن تكون عبارة عن لمفو سايس With
+
+364
+00:23:16,190 --> 00:23:19,430
+basophilic cytoplasm and eccentric nuclei زي هذه
+
+365
+00:23:19,430 --> 00:23:22,690
+أويش الـ cytoplasm واللمفو سايس اللي بتذكره زي هذا
+
+366
+00:23:22,690 --> 00:23:27,350
+عبارة عن blue sky blue أزرق سماوي لكن هنا جانيق
+
+367
+00:23:27,350 --> 00:23:31,310
+أعمق شوية بيكون إيش عبارة عن basophilic كمان إن هو
+
+368
+00:23:31,310 --> 00:23:34,650
+غالبًا يكون الـ Cytoplasm بالنص جاي أو يعني مش
+
+369
+00:23:34,650 --> 00:23:37,970
+طرفية مية مية، بتكون طرفية، طبعًا هذه طبعًا في
+
+370
+00:23:37,970 --> 00:23:40,170
+الحالات اللي بيسموها reactive pneumonia، بيكون
+
+371
+00:23:40,170 --> 00:23:44,630
+نشيط جدًا الـ Cytoplasm، الـ Lymphocytes بتضر في
+
+372
+00:23:44,630 --> 00:23:50,550
+الحالات هذه، بيسموها plasma cytoid lymphocytes،
+
+373
+00:23:50,550 --> 00:23:53,810
+يعني تشبه بحالة إيه؟ بتشبه حالة الـ Plasma cells
+
+374
+00:23:54,880 --> 00:23:57,500
+الـ Mott cells، الـ Mott cells طبعا هي نفس الـ Plasma
+
+375
+00:23:57,500 --> 00:23:59,900
+-Cytoid-Lymphocyte، لكن بيكون فيها granules، بيكون 
+
+376
+00:23:59,900 --> 00:24:03,480
+فيها globular inclusions، اللي هي عبارة عن الـMini 
+
+377
+00:24:03,480 --> 00:24:05,600
+-Globulins، بيكون زي ما حكينا في حالة الـactive 
+
+378
+00:24:05,600 --> 00:24:10,460
+changes للدم. دكتور، هو التسجيل اللي عندك كان وقف،
+
+379
+00:24:10,460 --> 00:24:14,960
+لأنه كان يكتب لأنك بتسجل وهلقيت وقف، بطل؟ لأ،
+
+380
+00:24:14,960 --> 00:24:20,960
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+381
+00:24:20,960 --> 00:24:24,280
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+382
+00:24:24,280 --> 00:24:26,250
+شغال، شغال، شغال، شغال، شفي شيء سببها فيه Side
+
+383
+00:24:26,250 --> 00:24:31,290
+-Effect؟ طيب،
+
+384
+00:24:31,290 --> 00:24:33,650
+الـMod cells زي ما حكينا بتظهر في حالة البلد مثل 
+
+385
+00:24:33,650 --> 00:24:36,290
+ميزايتويت الانفسايز with the globular inclusions
+
+386
+00:24:36,290 --> 00:24:39,030
+composed of hemoglobin بيكون الـHemoglobin في حالة
+
+387
+00:24:39,030 --> 00:24:42,250
+الـReactive lymphocytesالـ Large Granular
+
+388
+00:24:42,250 --> 00:24:45,450
+Lymphocytes طبعًا أهم شيء إنه بيكون هي حجم كبير و
+
+389
+00:24:45,450 --> 00:24:48,610
+Large وفيها Granules، طبعًا حكينا الليمفوكاينس مش
+
+390
+00:24:48,610 --> 00:24:51,290
+فيها Granules أصلا، لكن أحيانًا بتظهر فيها بعض 
+
+391
+00:24:51,290 --> 00:24:53,890
+الـGranules الصغيرة، طبعًا اسمه الـIsonophil
+
+392
+00:24:53,890 --> 00:24:56,690
+Granules أو هذه الخلايا عبارة عن Natural Killer
+
+393
+00:24:56,690 --> 00:24:59,970
+Cells اسمها، وبيكون الـLymphocytes Activated T
+
+394
+00:24:59,970 --> 00:25:03,670
+-Cells يعني بيكون خلايا الليمفوكاينس من نوع تاني
+
+395
+00:25:03,670 --> 00:25:05,090
+اللي بيسموه Natural Killer Cells
+
+396
+00:25:07,950 --> 00:25:10,350
+الـ Monovacculation ما هي معنى وخدناها بيكون
+
+397
+00:25:10,350 --> 00:25:14,050
+«بقلوشان زي دي للإنفكشن في الـ Monocytes» في عندي 
+
+398
+00:25:14,050 --> 00:25:17,970
+شيء بيسموه «Ishidiac Stem Paired Higashi» الأنمالي
+
+399
+00:25:17,970 --> 00:25:23,330
+يكون عندي عبارة عن زي ما يحكي Large Red أو Blue
+
+400
+00:25:23,330 --> 00:25:26,370
+Granules تظهر في السيتوبلازم للـ Granulocyte أو
+
+401
+00:25:26,370 --> 00:25:29,030
+الـ Lymphocyte ممكن أحيانًا أو الـ Monocyte، يعني
+
+402
+00:25:29,030 --> 00:25:31,890
+أي شيء طبعًا هذا Syndrome، هذا Syndrome طبعًا
+
+403
+00:25:31,890 --> 00:25:36,160
+عبارة عن Autosomal Recessive Syndrome زي ما حكينا،
+
+404
+00:25:36,160 --> 00:25:39,560
+ممتاز هذا الـSyndrome إنه بيصير عندي Recurrent
+
+405
+00:25:39,560 --> 00:25:42,360
+Infection طبعًا Recurrent Infection وبيصير عندي
+
+406
+00:25:42,360 --> 00:25:46,540
+البرجة الـOculoptenes Albinism بيكون عندك
+
+407
+00:25:46,540 --> 00:25:49,260
+Proclusive Neurology، في عندك مشكلة عصبية كمان في 
+
+408
+00:25:49,260 --> 00:25:52,420
+الأطراف والـMild Coagulation Defects وبيكون عندك
+
+409
+00:25:52,420 --> 00:25:54,840
+مشكلة في الـCoagulation طبعًا هذا عبارة عن حالة
+
+410
+00:25:54,840 --> 00:25:57,640
+وراثية، طبعا الأهم ميزة زي ما حكينا بيميز إنه
+
+411
+00:25:57,640 --> 00:26:01,740
+بيكون عندي Granules Red أو Blue، بيكون هذه 
+
+412
+00:26:01,740 --> 00:26:07,410
+Granules غير منضمة في الحجم وفي التوزيع اسمها كمان
+
+413
+00:26:07,410 --> 00:26:12,650
+مرة Shidiak Steinberg Higashi Anomaly ده الباقي
+
+414
+00:26:12,650 --> 00:26:15,410
+أخدناه مرة معايا عبارة عن بلوغران نيوز داخل
+
+415
+00:26:15,410 --> 00:26:19,750
+النيتروفيل أنيزو سايتوسون في النيتروفيل أخدناها
+
+416
+00:26:19,750 --> 00:26:21,870
+اللي هي بيكون حجة مختلفة من الحجم، مشايفين
+
+417
+00:26:21,870 --> 00:26:24,490
+نيتروفيل هي حجم كيف؟ وانا كيف حجم مختلف؟
+
+418
+00:26:25,260 --> 00:26:28,920
+وDegeneration of Nucleus بيكون عندي نواة صار
+
+419
+00:26:28,920 --> 00:26:32,080
+لـDegeneration أو بيكونوا تـExcess، زي بيكونوا
+
+420
+00:26:32,080 --> 00:26:35,360
+تـExcess، اختفت طبعا نتيجة أن الـold specimen عينه
+
+421
+00:26:35,360 --> 00:26:39,340
+قديمة جدا، هذا بالنسبالي الـwhite blood cells إن
+
+422
+00:26:39,340 --> 00:26:43,540
+شاء الله مهم حتى الآن، تمام؟ ‏- تمام ‏- الله، أنا
+
+423
+00:26:43,540 --> 00:26:47,840
+كان بقالي أعطيكم الخلايا الحمراء، بس هوقف هنا لأنه
+
+424
+00:26:47,840 --> 00:26:51,380
+بدي أكمل تفتعبوا اللي أخدناه كويس و تدرسوه صح، إيش
+
+425
+00:26:51,380 --> 00:26:55,710
+رأيكم؟ تمام، بس ضروري يا دكتور تنزل المحاضرة اليوم
+
+426
+00:26:55,710 --> 00:26:59,350
+هنزلها إن شاء الله، بس بدي أكم تدرسوا هاي، إن شاء
+
+427
+00:26:59,350 --> 00:27:02,810
+الله موعدنا الجاي بنا نحاول ندرس الخلايا الحمرة و
+
+428
+00:27:02,810 --> 00:27:06,090
+ندرس ال CPC و هذا، طبعا بنا نركز على هذا، بس بدي
+
+429
+00:27:06,090 --> 00:27:10,570
+أكم اللي ما سبق تدرسوه مية مية، هنزله أنا اليوم إن 
+
+430
+00:27:10,570 --> 00:27:13,850
+شاء الله بحاول، ماشي؟ إن شاء الله، الله يحميك طب
+
+431
+00:27:13,850 --> 00:27:15,990
+خلاص، موعدنا الموعد اللي جاي إن شاء الله السبت، أي
+
+432
+00:27:15,990 --> 00:27:19,730
+سيارة حكينا؟ الساعة أحد عشر، ساعة أحد أحد، ماشي يا
+
+433
+00:27:19,730 --> 00:27:23,270
+محمد؟ماشاء الله خلاص سامعه ما شاء الله يلا أعطيكم
+
+434
+00:27:23,270 --> 00:27:25,750
+قبلها، في سؤال قبل ما أطلع؟ في أي سفسارة عن ال
+
+435
+00:27:25,750 --> 00:27:30,650
+slides السابقة كلها؟ بس دكتور التسجيل اللي الورق
+
+436
+00:27:30,650 --> 00:27:35,250
+اللي فات، تتمنين صفحة؟ التسجيل أنا سجلت وحببتكم
+
+437
+00:27:35,250 --> 00:27:37,730
+فيها سعيد، و المرة الأخيرة نزلته، أنا أتأكد منه،
+
+438
+00:27:37,730 --> 00:27:41,730
+شوف كويس، أنا طلعت عليه كويس، التسجيل كان بفتح أو
+
+439
+00:27:41,730 --> 00:27:45,710
+بيفتحش؟ موجود
+
+440
+00:27:45,710 --> 00:27:53,510
+بال model ما هو بدأس عليه بيفتحشليش مفتحاش؟ مش
+
+441
+00:27:53,510 --> 00:27:57,850
+عارف بنجولنا على صفحة من جوجل وبعدين بقولي حميل طب
+
+442
+00:27:57,850 --> 00:28:03,070
+خليني حميل فعلا حميل مش مفتح هو صفحة
+
+443
+00:28:03,070 --> 00:28:06,950
+بيضطجيني طيب بدي اتواصل مع ال IT لان انا نزلته على
+
+444
+00:28:06,950 --> 00:28:09,710
+جوجل درايف و سولومي يدخلوا على يوتيوب انا بتحكي
+
+445
+00:28:09,710 --> 00:28:13,110
+معاهم ان شاء الله ان شاء الله يلا يعطيكم العافية
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_postprocess.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..21a318bf6e97bdac43799758c714a93075c08de3
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_postprocess.srt
@@ -0,0 +1,1780 @@
+1
+00:00:00,000 --> 00:00:06,900
+أحمد؟ طيب، احنا زي ما حكينا الـWhite pieces
+
+2
+00:00:06,900 --> 00:00:09,880
+morphology هذه الخلايا الطبيعية، هذه خلية
+
+3
+00:00:09,880 --> 00:00:15,820
+الـNeutrophil المووس واضح، تمام؟ أيوة، أيوة هذه
+
+4
+00:00:15,820 --> 00:00:19,120
+خلية الـNeutrophil، هذه خلية الـXenophil هذه خلية
+
+5
+00:00:19,120 --> 00:00:21,820
+الـLymphocytes، خلية الـMonocytes وخلية
+
+6
+00:00:21,820 --> 00:00:26,220
+الـBasophil طبعا، نفس الخلايا واضحة عندها دهرة
+
+7
+00:00:26,610 --> 00:00:32,010
+الـBand أو الـStaff تسميها؟
+
+8
+00:00:32,010 --> 00:00:35,350
+بكلم
+
+9
+00:00:35,350 --> 00:00:41,940
+جوال يعنيأه ماشي، طيب، هاي خليه دنيا، أكيد،
+
+10
+00:00:41,940 --> 00:00:47,660
+فيزوزين، مونوسايد، مش هنهجر عنهم، مش هنفنش، نحكي
+
+11
+00:00:47,660 --> 00:00:53,360
+فيهم كتير، حاجينهم جبانية، عمونا لأ تفكر
+
+12
+00:00:53,360 --> 00:00:55,520
+أن لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+13
+00:00:55,520 --> 00:00:55,760
+تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما عندك
+
+14
+00:00:55,760 --> 00:00:56,540
+جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما
+
+15
+00:00:56,540 --> 00:00:57,940
+عندك جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن
+
+16
+00:00:57,940 --> 00:01:02,660
+لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+17
+00:01:02,660 --> 00:01:04,680
+تفكر أن لسه ما عندك جامع
+
+18
+00:01:08,270 --> 00:01:14,470
+هي ميوت يا معاد؟ أفصل أفصل. لأ لأ بس عملتله ميوت
+
+19
+00:01:14,470 --> 00:01:22,870
+طيب ال abnormal shape، ال abnormal shape طبعا أول
+
+20
+00:01:22,870 --> 00:01:27,790
+شغل غراميستيك، غراميستيك طبعا واحد من الشباب سألني
+
+21
+00:01:27,790 --> 00:01:30,130
+قبل هيك يا دكتور ممكن نميز بين عينة المال و ال
+
+22
+00:01:30,130 --> 00:01:35,670
+female صح ولا لأ؟أه أنا نسألت أه قلتلك أه ممكن على
+
+23
+00:01:35,670 --> 00:01:39,110
+طريق الخلايا النيتروفيل فهذه مميزة على طريق شغلهاي
+
+24
+00:01:39,110 --> 00:01:42,910
+طب دراميستك شايفين ال .. احنا عندنا خلية هاي في
+
+25
+00:01:42,910 --> 00:01:47,030
+عبارة عن أربع loops شايفين الجزء الطالب البارز هذا
+
+26
+00:01:47,030 --> 00:01:50,810
+اللي عليه الماوس؟
+
+27
+00:01:50,810 --> 00:01:54,910
+أه شايفينههذا عبارة عن «Dramastic» هذا «Dramastic»
+
+28
+00:01:54,910 --> 00:01:58,350
+يعني زي طابلة، كيف عصاية الطابلة؟ هي عصاية طابلة،
+
+29
+00:01:58,350 --> 00:02:01,470
+طبعا «Dramastic» عبارة عن Nuclear Bandage تقريبا
+
+30
+00:02:01,470 --> 00:02:04,770
+واحد ونص مايكرو، طبعا in diameter ويكون attached
+
+31
+00:02:04,770 --> 00:02:08,430
+لـ nucleus لإيش؟ لـ X-Chromosome، عشان تظهر وين؟
+
+32
+00:02:08,430 --> 00:02:10,910
+تظهر أكتر الشيء بالـ Female، طبعا الـ X-Chromosome
+
+33
+00:02:10,910 --> 00:02:13,750
+أنواح تيهم، مش الـ Active، الـ Inactive، مع أن
+
+34
+00:02:13,750 --> 00:02:19,460
+مايعرف أن الـ Male عبارة عن إيش؟ XYصح ولا لأ؟ الـ
+
+35
+00:02:19,460 --> 00:02:22,000
+Female XX واحد منهم Active وتاني Inactive فالـ
+
+36
+00:02:22,000 --> 00:02:26,180
+Inactive Form تظهر فيه هاي فإذا الـ Dramastic تظهر
+
+37
+00:02:26,180 --> 00:02:29,160
+في الـ Neutrophil للـ Female تظهر في الـ Male في
+
+38
+00:02:29,160 --> 00:02:31,480
+حالة Clean Filter Syndrome طب ليش تظهر في Clean
+
+39
+00:02:31,480 --> 00:02:33,620
+Filter Syndrome؟ مين بيذكر ليه؟ إيش هذا الـ
+
+40
+00:02:33,620 --> 00:02:40,120
+Syndrome؟ هذا اللي قبل شوية، اللي قبل شوية أجي
+
+41
+00:02:40,120 --> 00:02:47,140
+معانا لأ، Clean Filter Syndrome هذا بيكون عندي YXX
+
+42
+00:02:48,070 --> 00:02:51,110
+فاهميني كيف؟ يعني عنده نسخة إضافية من X يكون طبعاً
+
+43
+00:02:51,110 --> 00:02:56,750
+الـ Male هذا نحكي معاق وفي مشاكل كتير في الجينات
+
+44
+00:02:56,750 --> 00:03:00,850
+فبكون Y XX، ففي عنده رسختين X واحدة منهم بتكون A
+
+45
+00:03:00,850 --> 00:03:09,910
+and A أكتر، فهمنا؟ فهمنا، فهمنا، فهمنا،
+
+46
+00:03:09,910 --> 00:03:11,230
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+47
+00:03:11,230 --> 00:03:14,210
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+48
+00:03:14,210 --> 00:03:21,310
+فهمنا، فهمنا، فهمناطيب الـ Cecil's Noodle نفس الـ
+
+49
+00:03:21,310 --> 00:03:23,150
+«دراميستيك» طبعا بتظهر في الـ «Inactive
+
+50
+00:03:23,150 --> 00:03:26,450
+Chromosomes» بس طبعا بيكونش زي اللي جاي عصاية
+
+51
+00:03:26,450 --> 00:03:29,790
+الطابلة بيكون ميته شويسة بيسموها إيه؟ Cecil's
+
+52
+00:03:29,790 --> 00:03:34,370
+Noodles نفس الأشياء طبعا هنا فيه مميز بينها أربع
+
+53
+00:03:34,370 --> 00:03:36,730
+أنواع Cecil's Noodles والـ «دراميستيك» هنا
+
+54
+00:03:36,730 --> 00:03:39,970
+دراميستيك هاي Cecil's Noodles طبعا هذه بيسموها الـ
+
+55
+00:03:39,970 --> 00:03:43,270
+«حوك» زي الـ «حوك جاي» طبعا فيه تحت الشاشة طبعا بس
+
+56
+00:03:43,270 --> 00:03:46,010
+تدخل على الشاشة الـ«Power Point» هتلاحظوا أسماءهم
+
+57
+00:03:46,010 --> 00:03:49,930
+وتفاصيلهمالـHypersegmentة اللي حكيناها عبارة عن
+
+58
+00:03:49,930 --> 00:03:52,650
+Right Shift تكون عندك نيتروفيل أكثر من 5 loops
+
+59
+00:03:52,650 --> 00:03:56,450
+طبعاً تظهر في حالات طبعاً زي ما حكينا الـ5 to 6
+
+60
+00:03:56,450 --> 00:03:59,170
+loops تظهر في حالات اللي هي Megaloplastic Anemia
+
+61
+00:03:59,170 --> 00:04:01,730
+تظهر في حالة الـAerodeficiency تظهر في حالة
+
+62
+00:04:01,730 --> 00:04:05,210
+Chronic Infection تظهر في حالة Diabetes وفي حالة
+
+63
+00:04:05,210 --> 00:04:05,970
+الـUremia
+
+64
+00:04:08,250 --> 00:04:11,970
+الـ Hyper-segmentation ما حكينا عنها طيب الـ ring
+
+65
+00:04:11,970 --> 00:04:15,290
+-shaped nuclei بيكون النواء أصلا جاي زي ring
+
+66
+00:04:15,290 --> 00:04:20,370
+-shaped بصورة high طبعا بيكون طبعا أو دونات زي
+
+67
+00:04:20,370 --> 00:04:22,410
+الدوناتطبعًا تظهر في حالات برضه الـ Acute
+
+68
+00:04:22,410 --> 00:04:25,010
+Myelodigamia تظهر في حالة الـ Chronic Glycemic
+
+69
+00:04:25,010 --> 00:04:28,630
+Glycemia الـ Myeloplastic Anemia، في حالة الـ MDS،
+
+70
+00:04:28,630 --> 00:04:32,630
+مالة معناها الـ MDS؟ الـ EAH Myelodysplastic
+
+71
+00:04:32,630 --> 00:04:34,910
+Syndrome، Myelodysplastic Syndrome الحالات المهمة
+
+72
+00:04:34,910 --> 00:04:37,410
+دي كلها هتمور معاكم، و هناخدها إن شاء الله، في جزء
+
+73
+00:04:37,410 --> 00:04:39,910
+ماخدة إحنا عنيكي إشرحانها، و في جزء هتاخدوها مع
+
+74
+00:04:39,910 --> 00:04:44,730
+دكتور أحمد إن شاء الله الـ mouse واضح، شايفي؟ إنه
+
+75
+00:04:44,730 --> 00:04:48,070
+كويسلأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+76
+00:04:48,070 --> 00:04:50,190
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+77
+00:04:50,190 --> 00:04:54,070
+لأ، لأ، لأ، لأ، لأ،
+
+78
+00:04:54,070 --> 00:04:57,010
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+79
+00:04:57,010 --> 00:04:59,930
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+80
+00:04:59,930 --> 00:05:02,390
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأهذه
+
+81
+00:05:02,390 --> 00:05:05,510
+بيسموها «Detached Nuclear Materials» موجودة في
+
+82
+00:05:05,510 --> 00:05:09,070
+الـCytoplasm طبعاً إنتجتها «Disgranulobiosis» اللي
+
+83
+00:05:09,070 --> 00:05:11,770
+يعني إن فيه عنده مشكلة في عملية الـGranulation أو
+
+84
+00:05:11,770 --> 00:05:15,730
+طبعا مريض باخد كيموفيرابين، مريض في الـCancer باخد
+
+85
+00:05:15,730 --> 00:05:18,870
+كيموفيرابين أو في حالة الـHIV، هذه بيسموها إيه؟
+
+86
+00:05:18,870 --> 00:05:23,060
+«Detached Nuclear Fragments»طبعًا الـ Toxic
+
+87
+00:05:23,060 --> 00:05:25,400
+Granulation أخدناها أول مرة معناها اللي هي أن
+
+88
+00:05:25,400 --> 00:05:28,100
+خلايا الـ Neutrophil بيكون الـ granules فيها واضحة
+
+89
+00:05:28,100 --> 00:05:31,600
+كتير وكلها أزرق لأسود طبعًا نتيجة الـ infection
+
+90
+00:05:31,600 --> 00:05:34,240
+فالـ Toxic Granulation بيزيد الـ granulation فيها
+
+91
+00:05:34,240 --> 00:05:37,440
+وبيكون لها more mesophilic و larger than normal
+
+92
+00:05:37,440 --> 00:05:40,340
+تضرب في حالة severe bacterial infection تضرب في
+
+93
+00:05:40,340 --> 00:05:42,740
+بعض الحالات الـ tissue damage أو الـ type يعني الـ
+
+94
+00:05:42,740 --> 00:05:45,480
+inflammation تضرب في حالة الـ normal البرجنانسي
+
+95
+00:05:45,480 --> 00:05:49,270
+وتضرب في حالة الـ therapy with cytokinesطبعًا
+
+96
+00:05:49,270 --> 00:05:51,670
+الـCytokines ما هي أسئلة تقرر في عملية إنه يحصل
+
+97
+00:05:51,670 --> 00:05:54,710
+عندي Granulation طبعًا الـHydroxygranulation هو
+
+98
+00:05:54,710 --> 00:05:58,310
+واضح عندي الـHypogranulations
+
+99
+00:05:58,310 --> 00:06:01,170
+تظهر إنه بيكون عندي العكس، بيكون Reduced في
+
+100
+00:06:01,170 --> 00:06:04,670
+الـGranulation في النيتروفيل في حالة الـMDS، اللي
+
+101
+00:06:04,670 --> 00:06:09,030
+هي الـMyelodysplastic Syndrome دُه ال bodies
+
+102
+00:06:09,030 --> 00:06:15,660
+شفناها ومرت معنا تمام يا محمد، علمت عليها؟طيب، دُه
+
+103
+00:06:15,660 --> 00:06:18,300
+الـ Bodies اللي فيه أزرق هناك، فالأزرق هي برنامج
+
+104
+00:06:18,300 --> 00:06:23,160
+Small Pale Blue Cytoplasm Infusions طبعاً دُه الـ
+
+105
+00:06:23,160 --> 00:06:25,860
+Bodies طبعاً بتكون متكون من الـ Ribosomes والـ
+
+106
+00:06:25,860 --> 00:06:29,540
+Endoplasmic reticulum تظهر في حالات الـ Infective
+
+107
+00:06:29,540 --> 00:06:32,160
+Inflammation، Inflammatory States، يعني Infection
+
+108
+00:06:32,160 --> 00:06:35,580
+Inflammation، الـ Severe Burn، Tuberculosis، و الـ
+
+109
+00:06:35,580 --> 00:06:37,060
+Postchemotherapy و البريجنالسية
+
+110
+00:06:41,350 --> 00:06:45,210
+وطبعًا في آخر حالة تظهر فيها الـMyogloin Anomaly
+
+111
+00:06:45,210 --> 00:06:49,970
+الـRustle Body، الـRustle Body طبعًا هي تظهر في
+
+112
+00:06:49,970 --> 00:06:52,570
+الإيزينوفيل، بيكون أصلا، اللي احنا حكينا إن
+
+113
+00:06:52,570 --> 00:06:57,050
+الإيزينوفيل فيها الـgranules حمرة وكبيرة ومسفّطة،
+
+114
+00:06:57,050 --> 00:07:00,350
+بيكون Large, homogeneous, immunoglobulin contains
+
+115
+00:07:00,350 --> 00:07:03,240
+inclusionsطبعًا الـ Immunoglobulins Containing
+
+116
+00:07:03,240 --> 00:07:05,780
+Glucose اللي هي المرتبطة في الـ Immunoglobulins
+
+117
+00:07:05,780 --> 00:07:09,360
+اللي هي الأجسام المضادة طبعًا اللي تظهر في حالة
+
+118
+00:07:09,360 --> 00:07:13,360
+الـ Plasma Cells اللي بيصيرها تطورات طبعًا هي مش
+
+119
+00:07:13,360 --> 00:07:15,400
+تظهر في الـ eosinophil، sorry هي بتظهر في الـ
+
+120
+00:07:15,400 --> 00:07:17,540
+Plasma Cells، اللي خلايا الـ Plasma Cells اللي بقى
+
+121
+00:07:17,540 --> 00:07:20,200
+خلايا الـ lymphocytes مش eosinophil، لكن بتظهر
+
+122
+00:07:20,200 --> 00:07:28,500
+كأنها eosinophil، تمام؟ بتظهر كأنها eosinophil ورا
+
+123
+00:07:28,500 --> 00:07:33,480
+الـأنتوا شايفين العرض اللي راح من عينكم؟ لا
+
+124
+00:07:33,480 --> 00:07:37,200
+شايفينه تمام، تظهر كإنه كإنه إيزينوفي لكن بيكون
+
+125
+00:07:37,200 --> 00:07:40,500
+نوة واحدة زي بلازمس اللي بيسموها وبيكون عليها
+
+126
+00:07:40,500 --> 00:07:43,600
+السيمي الأحمر، شايفين؟ بيكون فيها كإنها جرانيوس
+
+127
+00:07:43,600 --> 00:07:48,560
+كبيرة ولونها أزرق الخلايا اللي حواليها، شايف
+
+128
+00:07:48,560 --> 00:07:52,680
+الخلايا الجنبل عند الماوس هاي؟والخلايا تحت هاي،
+
+129
+00:07:52,680 --> 00:07:56,180
+هذه عبارة عن خلايا حمراء منوعة نيوكلياتي د ر بي
+
+130
+00:07:56,180 --> 00:07:58,700
+سي، النيوكلياتي د ر بي سي، كل شي بيعطيكم إياه،
+
+131
+00:07:58,700 --> 00:08:00,760
+حاولوا تكتبوا جنبه إيش الإسم عشان فيه مبادرة، لو
+
+132
+00:08:00,760 --> 00:08:06,660
+رجعتوله تذكروه، باشي يا سعيد؟ عيد لسه مبالغة يا
+
+133
+00:08:06,660 --> 00:08:09,900
+دكتور؟ النيوكلياتي د ر بي سي، النيوكلياتي د ر بي
+
+134
+00:08:09,900 --> 00:08:16,900
+سي، تمام، مش هاي اللي ينفع عنه، هاي، أكتبكم إياها،
+
+135
+00:08:16,900 --> 00:08:23,130
+هذه عبارة عنشايفين الكتابة؟ نعم نعم شايفينها
+
+136
+00:08:23,130 --> 00:08:26,730
+Nucleated
+
+137
+00:08:26,730 --> 00:08:30,890
+RBCs يعني خلايا حمرة منوّة فيها أنوية Nucleated
+
+138
+00:08:30,890 --> 00:08:38,410
+RBCs تمام؟ بس ثواني إيش يا سيد؟ هاتي هاتي رجل هاتي
+
+139
+00:08:38,410 --> 00:08:43,490
+رجل صوتك باطل شوية يا سيد علي صوتك الراس الفاطس
+
+140
+00:08:43,490 --> 00:08:48,370
+الراس الفاطس الراس الفاطس أه ثواني؟
+
+141
+00:08:49,640 --> 00:08:54,160
+كيف نفرّكها في هي واللي هجت قبل شوية اللي هي
+
+142
+00:08:54,160 --> 00:08:58,600
+الـVaculations؟ الـVaculations بيكون غير منتظمة،
+
+143
+00:08:58,600 --> 00:09:01,460
+الـVaculations غير منتظمة، مابيكونش Hemogeneous،
+
+144
+00:09:01,460 --> 00:09:04,640
+فهذه ان انا اتلاحظ كلمة Hemogeneous، انا عندي هان
+
+145
+00:09:04,640 --> 00:09:07,600
+كلمة Hemogeneous اتلاحظ كيف مهم جدا
+
+146
+00:09:11,680 --> 00:09:15,980
+الـ Vacculation ليست هيموجينية، بيكون بعثرة، حجمها
+
+147
+00:09:15,980 --> 00:09:19,600
+مختلف من واحدة لواحدة، والـ Vacculation تظهر في
+
+148
+00:09:19,600 --> 00:09:22,420
+الـ Neutrophil وفي الـ Monocytes، هذه بتظهر في الـ
+
+149
+00:09:22,420 --> 00:09:25,560
+Plasma Cells، البلازما سيلز عبارة عن خلية بصورة
+
+150
+00:09:25,560 --> 00:09:29,560
+high، خلية تكون نواة واحدة تلافيةطبعًا الـ Plasma
+
+151
+00:09:29,560 --> 00:09:32,880
+Cells هي الخلايا المسؤولة عن إنتاج الأجسام
+
+152
+00:09:32,880 --> 00:09:35,940
+المضادة، فيما بعد عشان ذلك بيكون عبارة عن فيها
+
+153
+00:09:35,940 --> 00:09:38,420
+Large Hemogeneous Immunoglobulin Immunoglobulin
+
+154
+00:09:38,420 --> 00:09:40,960
+عبارة عن إيه؟ البروتين اللي صنع منه الأجسام
+
+155
+00:09:40,960 --> 00:09:45,280
+المضادة، تمام؟ Inclusions وزي ما حكينا بتظهر في
+
+156
+00:09:45,280 --> 00:09:49,400
+الـPlasma Cells اللي Undergoing X-Step Synthesis
+
+157
+00:09:49,400 --> 00:09:52,900
+بيكون انت إنتاج إلها كتير لـImmunoglobulin فعشان
+
+158
+00:09:52,900 --> 00:09:54,280
+بتظهر الـRussell Butters
+
+159
+00:10:01,360 --> 00:10:06,220
+طبعًا… خلّي الـ… هذا فوق شوية الـPhagocytes بقى
+
+160
+00:10:06,220 --> 00:10:11,940
+Parasites هي خلايا الـParasites اللي بتتطفى على
+
+161
+00:10:11,940 --> 00:10:14,960
+جسم الإنسان وتتم بنعمتها طبعًا Phagocytes
+
+162
+00:10:14,960 --> 00:10:19,340
+Parasites اللي هي على طريق الخلايا الحمراء فأكيد
+
+163
+00:10:19,340 --> 00:10:23,680
+سمعتوا في الملاريا، أمام؟بسبب الملاريا، فطبعا عند
+
+164
+00:10:23,680 --> 00:10:27,640
+هان، تلاحظون اللي هنا، هاي الخلية هاي، شايفينها؟
+
+165
+00:10:27,640 --> 00:10:37,080
+الخلية هاي، اللي فيها، هي ضاحت عليه دائرة،
+
+166
+00:10:37,080 --> 00:10:40,300
+خلية
+
+167
+00:10:40,300 --> 00:10:42,860
+هاي بالظبط، هاي اللي عند المسعى، المسعى، واي خلية
+
+168
+00:10:42,860 --> 00:10:48,170
+هاي وخلية هاي وخلية هاي، فيهاحجم، طب لاحظ، شوف،
+
+169
+00:10:48,170 --> 00:10:51,350
+بقدر أكبر من عندي، فيه ثابتة كبيرة، بس عقلها هي
+
+170
+00:10:51,350 --> 00:10:57,930
+فيها زي ما بتحكيه، فيها زي .. زي إشي زي الخاتم،
+
+171
+00:10:57,930 --> 00:11:00,790
+بيسموه Ring Form Parasite، هاد عبارة عن malaria،
+
+172
+00:11:00,790 --> 00:11:03,730
+malaria parasites، شايفين؟ خليه هاي كمان، خليه
+
+173
+00:11:03,730 --> 00:11:08,630
+هاي، خليه هاي، عليها نقطين؟ نقطين وفيه خيط مربط
+
+174
+00:11:08,630 --> 00:11:13,150
+بين أثنين واتنين، زي الخاتم، بيسموه؟ آه، لو كبرت،
+
+175
+00:11:13,150 --> 00:11:17,270
+بيظهرأما بدي أكبر، بدي أروح أكبر مكان تاني، مش
+
+176
+00:11:17,270 --> 00:11:19,930
+مشكلة، إن شاء الله أفرجيكم إيهم عن الأمر واقعي،
+
+177
+00:11:19,930 --> 00:11:24,230
+هيا خليني نشوف من عندنا نقدر نكبر أحنا، شايفين
+
+178
+00:11:24,230 --> 00:11:29,590
+هاي؟ شايف يا سيد؟ أعطيك، أعطيك، أعطيك، أعطيك،
+
+179
+00:11:29,590 --> 00:11:31,530
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+180
+00:11:31,530 --> 00:11:32,090
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+181
+00:11:32,090 --> 00:11:41,790
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+182
+00:11:41,790 --> 00:11:47,350
+أعططبعًا، هذه كما حكيناها بتظهر في حالات
+
+183
+00:11:47,350 --> 00:11:50,870
+الـinfection بالنصاب بالملاريا طبعًا الـphagocyte
+
+184
+00:11:50,870 --> 00:11:55,490
+plateless العكس بيكون المرحل الذنب اللي عمته اللي
+
+185
+00:11:55,490 --> 00:11:58,190
+هو الـplateless تظهر في خلايا الـNitrophil
+
+186
+00:11:58,190 --> 00:12:00,590
+الـNitrophil بتروح تبلعلي الـplateless نتيجة
+
+187
+00:12:00,590 --> 00:12:03,170
+الـinfection طبعًا الـinfection البيتوفين بيبقى
+
+188
+00:12:03,170 --> 00:12:05,690
+بيبقى بتبلعلي بكتيريا لكن نتيجة مثلًا إذا كانت
+
+189
+00:12:05,690 --> 00:12:08,530
+severe infection بيصير تروح تبلعلي ممكن تبقى عند
+
+190
+00:12:08,530 --> 00:12:11,580
+الوقت تبلع الـplateless زي بالحالة هذههي عندي
+
+191
+00:12:11,580 --> 00:12:15,160
+الحالة هاي، شايفين الخلايا ها؟ هي بالعالي بليتلس
+
+192
+00:12:15,160 --> 00:12:18,460
+وهان بالعالي بليتلس، شايفين هاي؟ النقطة هاي
+
+193
+00:12:18,460 --> 00:12:22,840
+الصغيرة الزرقى، هادي عبارة عن خلية بليتلس، هادي
+
+194
+00:12:22,840 --> 00:12:27,420
+عبارة عن هاي، شايفين هاي، هاي الصغيرة، هاي،
+
+195
+00:12:27,420 --> 00:12:30,480
+مابيضيش أحط بصوم كتير عشان ما تخربطوش كتير، ماشي
+
+196
+00:12:30,480 --> 00:12:34,720
+شفتوها، هادي بيسموها phagocytes of bletelss طب
+
+197
+00:12:34,720 --> 00:12:36,640
+انتظر في حالات ال infection، انتظر في حالات ال
+
+198
+00:12:36,640 --> 00:12:36,920
+infection
+
+199
+00:12:45,010 --> 00:12:54,430
+شوي شباب شوي بس دقيقة سيف
+
+200
+00:12:54,430 --> 00:13:03,870
+أنت في المحاضرة؟
+
+201
+00:13:05,700 --> 00:13:08,400
+طيب، معلش، عشان كان إيش أبني و بدي أحكي معاه في
+
+202
+00:13:08,400 --> 00:13:12,320
+شغلات طيب، هل جيت الفاقوصيات الـplatelets بيكون
+
+203
+00:13:12,320 --> 00:13:16,000
+خلايا النيتروفيل عاملة الفاقوصيتوشين لـplatelets
+
+204
+00:13:16,000 --> 00:13:18,860
+في حالة الinfection؟ هاي الصورة واضحة كتير،
+
+205
+00:13:18,860 --> 00:13:21,860
+شايفينها؟ هاي الخلاية النيتروفيل وهي الـplatelets
+
+206
+00:13:21,860 --> 00:13:28,980
+جواها واضحة يا شباب، أه؟ لأ، مش واضحة دكتور،
+
+207
+00:13:28,980 --> 00:13:32,340
+شايفين الصورة أنتوا؟ دكتور، أه شايفين، أه أه
+
+208
+00:13:32,340 --> 00:13:38,920
+شايفين، طب تمام، بسإيش يا سعيد؟ إيش بالنسبة ل ..
+
+209
+00:13:38,920 --> 00:13:44,700
+إيش بالنسبة لهذه؟ في .. في خلايا فوق و تحت هدول
+
+210
+00:13:44,700 --> 00:13:50,860
+بليتلس برضه؟ هذه بليتلس و هذه بليتلس و هذه جوا
+
+211
+00:13:50,860 --> 00:13:55,220
+الخلية دي نيتو فيه بليتلس هدول كل اللي عليها دواعي
+
+212
+00:13:55,220 --> 00:13:58,920
+الخضرة بليتلس، هذه بليتلس، شايفين؟ هذه اللي جت
+
+213
+00:13:58,920 --> 00:14:03,400
+بليتلس، شايفها يا سعيد؟ طب هذه يا دكتور؟ أجل، أجل،
+
+214
+00:14:03,400 --> 00:14:05,140
+أجل، أجل علمليها
+
+215
+00:14:08,780 --> 00:14:13,760
+الـGiga، هذه، هذه تحت Plateless، هذه Hypogranular،
+
+216
+00:14:13,760 --> 00:14:18,000
+بيكون فيه فيها Granules، Hypogranular، طبعا مرة
+
+217
+00:14:18,000 --> 00:14:20,660
+معنا نوع الـPlateless، عندي Hypogranular، بيكون
+
+218
+00:14:20,660 --> 00:14:22,980
+Granules خفيف فيها، هذي، هذي الصغيرة هي كمان
+
+219
+00:14:22,980 --> 00:14:26,580
+Plateless، صحيح، تمام؟ ‏- تمام ‏- هذو كل
+
+220
+00:14:26,580 --> 00:14:29,000
+Plateless، بس أنا بهمني في ال slide هاي
+
+221
+00:14:29,000 --> 00:14:31,440
+الـPhagocytes Plateless، Phagocytes Plateless، أنا
+
+222
+00:14:31,440 --> 00:14:33,500
+حكيتكم إن هي بثمبة اللي عملتها عن طريق
+
+223
+00:14:33,500 --> 00:14:35,000
+الـNitrophil، واضح عندي
+
+224
+00:14:43,050 --> 00:14:47,870
+فيب، نروح لـ «سلايت» البعديها البعديها
+
+225
+00:14:47,870 --> 00:14:49,750
+الـ «فاكوسايزر» الـ blood cells العكس، الـ
+
+226
+00:14:49,750 --> 00:14:53,710
+«نيتروفيل» راح تبقى عادة خلايا حمراء طبعا، بتظهر
+
+227
+00:14:53,710 --> 00:14:56,610
+في حالات، شايفين أن هي نيتروفيل وداخلها خلايا
+
+228
+00:14:56,610 --> 00:15:00,210
+حمراء، واضحة طبعا، في حالة ال «infection» أو الـ
+
+229
+00:15:00,210 --> 00:15:01,990
+«autoimmune hemorrhic anemia» أو في حالة
+
+230
+00:15:01,990 --> 00:15:03,570
+الـ«incompatible blood transfusion» يعني إذا أنا
+
+231
+00:15:03,570 --> 00:15:06,350
+نجلت دم لمريض والدم هتغير متوافق معاه
+
+232
+00:15:06,350 --> 00:15:08,990
+ف«incompatibility» فتصبح الخلايا الـ «نيتروفيل»
+
+233
+00:15:08,990 --> 00:15:13,000
+تتعمل فاكوسايدوسين للخلايا الحمراءطبعًا ساموها
+
+234
+00:15:13,000 --> 00:15:23,040
+Phagocytes لـ Red Blood Cells الـ
+
+235
+00:15:23,040 --> 00:15:23,900
+slide البعديها
+
+236
+00:15:26,370 --> 00:15:29,490
+هذه طبعًا الـ Phagocytes فهذه الـ Vacculations
+
+237
+00:15:29,490 --> 00:15:33,050
+هيكون إننا عديد سلايذات، هنتقص فيها شوية الـ
+
+238
+00:15:33,050 --> 00:15:35,090
+Vacculations، شايفين؟ الـ Vacculation-T فيها شباب
+
+239
+00:15:35,090 --> 00:15:39,410
+تختلف عن اللي حكينا عنها قبل سوية، الـ Plasma
+
+240
+00:15:39,410 --> 00:15:42,590
+Cells طبعًا لأن الـ Vacculations أحجامها طبعًا
+
+241
+00:15:42,590 --> 00:15:48,770
+مختلفة، مبترة، مش جايب منتظمة، تمام؟ هاي عندي الـ
+
+242
+00:15:48,770 --> 00:15:50,630
+All Roots، حكيناها الـ All Roots، الـ All Roots
+
+243
+00:15:50,630 --> 00:15:55,140
+عبارة عنطبعًا، زي ما حكينا، بتظهر في حالة الـ
+
+244
+00:15:55,140 --> 00:15:59,140
+Myeloplast و الـ Bromelocyte، يعني في الخلايا بقى
+
+245
+00:15:59,140 --> 00:16:06,980
+بالـ Maturation، أيش يا شباب؟ في حد سأل؟ سعيد،
+
+246
+00:16:06,980 --> 00:16:11,520
+الصوت عنده بجطع، سعيد طيب، احنا ان شاء الله، زي ما
+
+247
+00:16:11,520 --> 00:16:13,700
+حكيتها سعيد، انا فيه تسجيل سابق، و انا هبقى عندكم
+
+248
+00:16:13,700 --> 00:16:17,660
+تسجيل ان شاء الله، فالـ Horrods، زي ما حكينا، عندي
+
+249
+00:16:17,660 --> 00:16:20,460
+الـ Horrods بتظهر في حالات الـ Acute Myeloid
+
+250
+00:16:20,460 --> 00:16:24,670
+الجيمياالـ M2 و الـ MDS اللي ما يلو dysplastic
+
+251
+00:16:24,670 --> 00:16:26,610
+syndrome ما يلو dysplastic syndrome، الـ MDS
+
+252
+00:16:26,610 --> 00:16:30,830
+فبتقدر في الحتين، شايفين النيتروفيل، خليط
+
+253
+00:16:30,830 --> 00:16:35,270
+النيتروفيل؟ خليط النيتروفيل هان، في زي عصاية صغيرة
+
+254
+00:16:35,270 --> 00:16:40,230
+فيها، هيها، الصورة هي، خليني أحطكم علي دائرة، هذه
+
+255
+00:16:40,230 --> 00:16:44,590
+العصاية الصغيرةهذه الصغيرة هنا هي برعن أوروذ، طب
+
+256
+00:16:44,590 --> 00:16:48,030
+انتظر في حالات الـ«immature cells» إما نحكي
+
+257
+00:16:48,030 --> 00:16:50,370
+«mature» تكون ناضجة، «immature» غير ناضجة، فانتظر
+
+258
+00:16:50,370 --> 00:16:53,630
+في حالات غير ناضجة، اللي هي حالات الـ«myeloplast»
+
+259
+00:16:53,630 --> 00:16:55,470
+والـ«bromyelocyte»، وانتظر في الحالات اللي بحكيها
+
+260
+00:16:55,470 --> 00:16:59,350
+أنا الـ«acute myeloplastic leukemia» في الـ«M2»،
+
+261
+00:16:59,350 --> 00:17:03,630
+في إيش بيسميه أن «M2»، هتمر معنا إن شاء الله يعني،
+
+262
+00:17:03,630 --> 00:17:06,250
+يعني يا دكتور، عادي ممكن أنها تظهر normal أو
+
+263
+00:17:06,250 --> 00:17:10,370
+abnormal؟ لأ، هذه abnormal، هذه المفروضة abnormal،
+
+264
+00:17:10,370 --> 00:17:15,500
+آهالـ Acute Myeloid Leukemia Acute Myeloid Plastic
+
+265
+00:17:15,500 --> 00:17:19,440
+Leukemia الـ AML M2 والـ MDS Myeloid Plastic
+
+266
+00:17:19,440 --> 00:17:23,000
+Syndrome أصلاً
+
+267
+00:17:23,000 --> 00:17:27,680
+هي الخليتين هذولة، يعني الخلية هاي والخلية هاي مش
+
+268
+00:17:27,680 --> 00:17:32,460
+لازم يظهروا في الـ Normal Blood Film لازم يظهروا
+
+269
+00:17:32,460 --> 00:17:34,680
+بالبون مرة، لكن لو ظهروا في الـ Normal Blood Film
+
+270
+00:17:34,680 --> 00:17:36,960
+بحكي أنا عندي حالة مش طبيعية
+
+271
+00:17:41,060 --> 00:17:44,600
+صحيح، هي الـMyoplast، صحيح مش Myoplast هي مثلًا ما
+
+272
+00:17:44,600 --> 00:17:47,740
+بعد الـMyoplast الـMyoplast هذي Myoplast وهذه
+
+273
+00:17:47,740 --> 00:17:53,680
+الـBromelocytes هاي
+
+274
+00:17:53,680 --> 00:17:56,500
+All Roots واضحة، شكل واضح كتير، شايفين الـAll
+
+275
+00:17:56,500 --> 00:18:00,480
+Roots؟ حتى هذي بسميها أنا Bundles of All Roots
+
+276
+00:18:00,480 --> 00:18:03,780
+يعني Bundles من الجمعة زي العصيات Bundles of All
+
+277
+00:18:03,780 --> 00:18:06,860
+Roots هاي اللي هنا، شايفين؟ هذي طبعًا هن الـAll
+
+278
+00:18:06,860 --> 00:18:09,840
+Roots عندي، هن في عندي All Roots، ظاهرة واضحة
+
+279
+00:18:10,070 --> 00:18:13,870
+طبعًا، يكون الخناية الـmelocytes كلها هي خلية
+
+280
+00:18:13,870 --> 00:18:16,510
+bromelocytes، هي melocytes، bromelocytes حدوث ما
+
+281
+00:18:16,510 --> 00:18:19,150
+أنا في حالة الـmaturation إن شاء الله الـMacro
+
+282
+00:18:19,150 --> 00:18:21,790
+neutrophil، الـneutrophil بيكون حجم كبير طبعًا،
+
+283
+00:18:21,790 --> 00:18:24,690
+بيكون حجم ضعف، حجم neutrophil عادية طبعًا، هذه
+
+284
+00:18:24,690 --> 00:18:29,050
+نتيجة إنه عندي نشاط في الـDNA etc. employed of DNA
+
+285
+00:18:29,460 --> 00:18:33,000
+تظهر في حالات طبعًا ممكن تظهر نادر في بعض الحالات
+
+286
+00:18:33,000 --> 00:18:36,780
+الطبيعية لكن قليلة جدًا ممكن تكون ورثية عند الناس،
+
+287
+00:18:36,780 --> 00:18:41,240
+بعض الناس ممكن نتيجة إنه واحد ماخد مثلًا الـ… نحكي
+
+288
+00:18:41,240 --> 00:18:46,180
+الـ… الـ… الـCytokines زي الـGranular Coliformic
+
+289
+00:18:46,180 --> 00:18:49,900
+Units هذه المتنشطة النيتروفيل طبعًا أخد
+
+290
+00:18:49,900 --> 00:18:52,300
+الـCytokines بتعطيني التنشيط أو تظهر في حالات
+
+291
+00:18:52,300 --> 00:18:54,920
+بلدية زي الـMegaloplastic Anemia أو الـChronic
+
+292
+00:18:54,920 --> 00:19:01,930
+Infection تمام؟مش هذا دكتور يقول الـGCC حسابش هذا
+
+293
+00:19:01,930 --> 00:19:06,710
+الـfactor اللي بنشط؟ هذا الـfactor بنشطني نيتروفيل
+
+294
+00:19:06,710 --> 00:19:08,170
+وبنتجني نيتروفيل، صحيح؟ اللي بيسموه
+
+295
+00:19:08,170 --> 00:19:11,710
+الـGranulocytic Cholestimulating Factors اسمها
+
+296
+00:19:11,710 --> 00:19:14,910
+Granulocytic Cholestimulating Factors طبعا هذا
+
+297
+00:19:14,910 --> 00:19:18,070
+الـfactors بنشطني إنتاج خلايا نيتروفيل
+
+298
+00:19:21,910 --> 00:19:26,090
+طبعًا في الـ Necrobiotic أو الـ «أبوبتك» «أبوبتك»
+
+299
+00:19:26,090 --> 00:19:28,770
+يعني موت الخلايا «أبوبتوس» فيز موت الخلايا، طبعًا
+
+300
+00:19:28,770 --> 00:19:32,310
+«نيكروبيوتيك» طبعًا ما عرف معنى، بيكون اللحظة اللي
+
+301
+00:19:32,310 --> 00:19:36,690
+عنديها النواء في الـ «نيتروفيل» كيف شكلها، يعني
+
+302
+00:19:36,690 --> 00:19:40,650
+تقريبًا فقدت، فقدت المباعت وفقدت شكلها اللي
+
+303
+00:19:40,650 --> 00:19:45,680
+فعليًا، بيكون في حالات EHفي حالات الفترة، إذا كان
+
+304
+00:19:45,680 --> 00:19:49,520
+عندى طول كتير الدم أو في حالة الـAcute، ما يلوت
+
+305
+00:19:49,520 --> 00:19:52,880
+بالكيميا طبعاً بيصير الـDense Hemogenous Nuclei
+
+306
+00:19:52,880 --> 00:19:57,840
+بيكون النواء متشانسة وغامقة كتير وجز، بيسموها
+
+307
+00:19:57,840 --> 00:20:03,600
+Pycnotec، تمام؟ بيسموها Pycnotec يعني
+
+308
+00:20:03,600 --> 00:20:06,300
+زي الـNecrosis يا دكتور؟ زي الـNecrosis، هي نقرس،
+
+309
+00:20:06,300 --> 00:20:08,480
+ماحكي أن هي نقر بيوتك، Necrosis
+
+310
+00:20:11,320 --> 00:20:14,040
+طبعًا شفت لفت حكيناها؟ شفت لفت إنه بيكون أنا عندي
+
+311
+00:20:14,040 --> 00:20:18,220
+خلايا قبل الـ Maturation زي هذه الخلايا طبعًا الـ
+
+312
+00:20:18,220 --> 00:20:22,440
+Myeloplast بتظهر عندي، طبعًا بتظهر في حالة
+
+313
+00:20:22,440 --> 00:20:24,920
+الـNormal Pregnancy، بتظهر في حالة الـInfection،
+
+314
+00:20:24,920 --> 00:20:27,060
+بتظهر في حالة الـPulmonary Fibrosis، وبتظهر في
+
+315
+00:20:27,060 --> 00:20:29,280
+حالة الـPulmonary Infiltration By Malignancy، إذا
+
+316
+00:20:29,280 --> 00:20:33,130
+فيندي Malignant Cells بتظهر في حالة أيهفي عندي
+
+317
+00:20:33,130 --> 00:20:37,050
+أشياء بيسموها «سيدو بلجر هوت أنومالي» طبعا «سيدو
+
+318
+00:20:37,050 --> 00:20:39,070
+بلجر هوت أنومالي» بيكون الخلايا النيتروفيل اللي
+
+319
+00:20:39,070 --> 00:20:42,370
+احنا حكينا النيتروفيل اللي فيها النواة من 2 إلى 5
+
+320
+00:20:42,370 --> 00:20:45,890
+loops لكن غالبا تظهر لي بالـ Normal persons 3
+
+321
+00:20:45,890 --> 00:20:49,130
+loops، 4 loops غالبا لكن لو ظهرت معظم الخلايا 2
+
+322
+00:20:49,130 --> 00:20:51,850
+loops بيكون هذه الحالة اللي سموها «سيدو بلجر هوت
+
+323
+00:20:51,850 --> 00:20:55,190
+أنومالي» بعبارة عن Bi-looped neutrophil with more
+
+324
+00:20:55,190 --> 00:20:58,630
+condensed chromatinطبعًا تظهر في حالة الـ MDS،
+
+325
+00:20:58,630 --> 00:21:01,850
+تظهر في حالة الـ Adiopathic Myelofibrosis تظهر في
+
+326
+00:21:01,850 --> 00:21:04,730
+حالة الـ Chronic Glycemic Glycemia أو في حالة
+
+327
+00:21:04,730 --> 00:21:09,550
+العلاج بالـ Colchicine أو الـ Ibuprofen أو في حالة
+
+328
+00:21:09,550 --> 00:21:13,910
+الـ Infection للمونوكلوسس والملاريا والمكسليمة، في
+
+329
+00:21:13,910 --> 00:21:14,650
+حالة الـ CLA
+
+330
+00:21:17,840 --> 00:21:20,120
+الـ Neutrophil Aggregation زي Platelet Aggregation
+
+331
+00:21:20,120 --> 00:21:23,980
+طبعا هذه حالة In Vitro بسبب الإيديتا بتصير عملية
+
+332
+00:21:23,980 --> 00:21:26,600
+Clamp للـ Neutrophil مع بعض متخاطرين مع بعض بعض
+
+333
+00:21:26,600 --> 00:21:29,780
+طبعا زي ما حكيت إن هذه عبارة عن حالة In Vitro
+
+334
+00:21:29,780 --> 00:21:34,600
+تتضار في حالات زي ما حكيتها النتيجة إن الإيديتا
+
+335
+00:21:34,600 --> 00:21:38,560
+عندي شوية قديم أو طولة كتير أو في بعض الحالات الـ
+
+336
+00:21:38,560 --> 00:21:41,140
+Infectious Monoclosis أو بعض الحالات الـ Bacterial
+
+337
+00:21:41,140 --> 00:21:45,180
+Infection أو الـ Autoimmune Diseaseالـ Atypical
+
+338
+00:21:45,180 --> 00:21:47,400
+lymphocyte هي خلايا لينفوسايتز، هنحكي إن خلايا
+
+339
+00:21:47,400 --> 00:21:53,440
+لينفوسايتز عبارة عن حجمين، وبالأحرى تلاتة، Small و
+
+340
+00:21:53,440 --> 00:21:56,080
+Intermediate و Large الخلايا الـ Atypical
+
+341
+00:21:56,080 --> 00:22:00,660
+lymphocyte بيكون أكبر من Large كمان، وبيكون النواة
+
+342
+00:22:00,660 --> 00:22:05,710
+فيها مش دائريةبيكون شكلها مش منتظم طبعاً هذه بتظهر
+
+343
+00:22:05,710 --> 00:22:07,510
+في حالات الـinfection أكتر إيش هي في
+
+344
+00:22:07,510 --> 00:22:10,770
+الـCytomegalovirus أو البشتان بير الفيروس طبعاً
+
+345
+00:22:10,770 --> 00:22:14,410
+Cytomegalovirus يعني بالفيروسات وطبعا إحنا بنعرف
+
+346
+00:22:14,410 --> 00:22:18,130
+إنه إصابة الفيروس بتأثر أكتر إش على الـLymphocyte
+
+347
+00:22:18,130 --> 00:22:21,370
+إصابة البكتيري بتأثر أكتر إش على الـNitrophil على
+
+348
+00:22:21,370 --> 00:22:24,650
+الأغلب طبعاًفزي ما حكينا، الـ Atypical Lymphocyte
+
+349
+00:22:24,650 --> 00:22:27,810
+عبارة عن بوليومورفيك كبير، والدايمتر بيكون دايمتر
+
+350
+00:22:27,810 --> 00:22:31,130
+15 إلى 30، يعني أكبر من الـ Monocyte نفسها طبعا،
+
+351
+00:22:31,130 --> 00:22:33,910
+بيكون abundant وبيكون بيزوفيليك، طبعا الـCytoplasm
+
+352
+00:22:33,910 --> 00:22:37,610
+كتير، طبعا بيزوفيليا وبيكون طبعا maybe confined
+
+353
+00:22:37,610 --> 00:22:40,030
+with the cytoplasmic margins، بيكون أن الأطراف في
+
+354
+00:22:40,030 --> 00:22:44,380
+الـCytoplasm مش منتظمةزي ما حكينا، بتظهر في حالة
+
+355
+00:22:44,380 --> 00:22:48,280
+الـ Viral Infection خاصة الإبشطان بار فيروس أو
+
+356
+00:22:48,280 --> 00:22:50,560
+certain مجال الفيروس أكتر إشي تظهر في حالة الـ
+
+357
+00:22:50,560 --> 00:22:52,460
+Bacterial Infection وأحيانًا الـ Tuberculosis و
+
+358
+00:22:52,460 --> 00:22:57,460
+البروسوليس لأن البروسيلة والـ TB بأثر على الـ
+
+359
+00:22:57,460 --> 00:23:01,320
+lymphocytes ملاريا تظهر في حالة ملاريا ممكن، في
+
+360
+00:23:01,320 --> 00:23:04,920
+حالة الطعيمات ممكن تظهر بالفيروسات هاي أو System
+
+361
+00:23:04,920 --> 00:23:06,560
+Globus اللي موجودة فيها
+
+362
+00:23:09,870 --> 00:23:13,790
+الـ Plasma Cytoid Lymphocyte طبعاً الـ Plasma
+
+363
+00:23:13,790 --> 00:23:16,190
+Cytoid لابد من أن تكون عبارة عن لمفو سايس With
+
+364
+00:23:16,190 --> 00:23:19,430
+mesophilic cytoplasm and eccentric nuclei زي هذه
+
+365
+00:23:19,430 --> 00:23:22,690
+أويش الـ cytoplasm واللمفو سايس اللي بتذكره زي هذا
+
+366
+00:23:22,690 --> 00:23:27,350
+عبارة عن blue sky blue أزرق سماوي لكن هنا جانيق
+
+367
+00:23:27,350 --> 00:23:31,310
+أعمق شوية بيكون إيش عبارة عن mesophilicكمان إن هو
+
+368
+00:23:31,310 --> 00:23:34,650
+غالبًا يكون الـCytoplasm بالنص جاي أو يعني مش
+
+369
+00:23:34,650 --> 00:23:37,970
+طرفية مية مية، بتكون طرفية، طبعًا هذه طبعًا في
+
+370
+00:23:37,970 --> 00:23:40,170
+الحالات اللي بيسموها reactive pneumonia، بيكون
+
+371
+00:23:40,170 --> 00:23:44,630
+نشيط جدًا الـCytoplasm، الـLymphocytes بتضر في
+
+372
+00:23:44,630 --> 00:23:50,550
+الحالات هذه، بيسموها plasma cytoid lymphocytes،
+
+373
+00:23:50,550 --> 00:23:53,810
+يعني تشبه بحالة إيه؟ بتشبه حالة الـPlasma cells
+
+374
+00:23:54,880 --> 00:23:57,500
+الـMod cells، الـMod cells طبعا هي نفس الـPlasma
+
+375
+00:23:57,500 --> 00:23:59,900
+-Cytoid-Lipocyte، لكن بيكون فيها granules، بيكون
+
+376
+00:23:59,900 --> 00:24:03,480
+فيها globular inclusions، اللي هي عبارة عن الـMini
+
+377
+00:24:03,480 --> 00:24:05,600
+-Globulins، بيكون زي ما حكينا في حالة الـactive
+
+378
+00:24:05,600 --> 00:24:10,460
+changes للدم. دكتور، هو التسجيل اللي عندك كان وقف،
+
+379
+00:24:10,460 --> 00:24:14,960
+لإنه كان يكتب لإنك بتسجل وهلقيت وقف، بطل؟ لأ،
+
+380
+00:24:14,960 --> 00:24:20,960
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+381
+00:24:20,960 --> 00:24:24,280
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+382
+00:24:24,280 --> 00:24:26,250
+شغال، شغال، شغال، شغال، شفي شيئا سببها فيه Side
+
+383
+00:24:26,250 --> 00:24:31,290
+-Effect؟ طيب،
+
+384
+00:24:31,290 --> 00:24:33,650
+الـMod cells زي ما حكينا بتظهر في حالة البلد مثل
+
+385
+00:24:33,650 --> 00:24:36,290
+ميزايتويت الانفسايز with the globular inclusions
+
+386
+00:24:36,290 --> 00:24:39,030
+composed of hemoglobin بيكون الـHemoglobin في حالة
+
+387
+00:24:39,030 --> 00:24:42,250
+الـReactive lymphocytesالـ Large Granular
+
+388
+00:24:42,250 --> 00:24:45,450
+Lymphocytes طبعًا أهم شيء إنه بيكون هي حجم كبير و
+
+389
+00:24:45,450 --> 00:24:48,610
+Large وفيها Granules، طبعًا حكينا الليمفوكاينس مش
+
+390
+00:24:48,610 --> 00:24:51,290
+فيها Granules أصلا، لكن أحيانًا بتظهر فيها بعض
+
+391
+00:24:51,290 --> 00:24:53,890
+الـGranules الصغيرة، طبعًا اسمه الـIsonophil
+
+392
+00:24:53,890 --> 00:24:56,690
+Granules أو هذه الخلايا عبارة عن Natural Killer
+
+393
+00:24:56,690 --> 00:24:59,970
+Cells اسمها، وبيكون الـLymphocytes Activated T
+
+394
+00:24:59,970 --> 00:25:03,670
+-Cells يعني بيكون خلايا الليمفوكاينس من نوع تاني
+
+395
+00:25:03,670 --> 00:25:05,090
+اللي بيسموه Natural Killer Cells
+
+396
+00:25:07,950 --> 00:25:10,350
+الـ Monovacculation ما هي معنى وخدناها بيكون
+
+397
+00:25:10,350 --> 00:25:14,050
+«بقلوشان زي دي للإنفكشن في الـ Monocytes» في عندي
+
+398
+00:25:14,050 --> 00:25:17,970
+إشي بيسموه «Ishidiac Stem Paired Higashi» الأنمالي
+
+399
+00:25:17,970 --> 00:25:23,330
+يكون عندي عبارة عن زي ما يحكي Large Red أو Blue
+
+400
+00:25:23,330 --> 00:25:26,370
+Granules تظهر في السيطوبلازم للـ Granulocyte أو
+
+401
+00:25:26,370 --> 00:25:29,030
+الـ Lymphocyte ممكن أحيانًا أو الـ Monocyte، يعني
+
+402
+00:25:29,030 --> 00:25:31,890
+أي شيء طبعًا هذا Syndrome، هذا Syndrome طبعًا
+
+403
+00:25:31,890 --> 00:25:36,160
+عبارة عن Autosomal Recessive Syndromeزي ما حكينا،
+
+404
+00:25:36,160 --> 00:25:39,560
+ممتاز هذا الـSyndrome إنه بيصير عندي Recurrent
+
+405
+00:25:39,560 --> 00:25:42,360
+Infection طبعاً Recurrent Infection وبيصير عندي
+
+406
+00:25:42,360 --> 00:25:46,540
+البرجة الـOculoptenes Albinism بيكون عندك
+
+407
+00:25:46,540 --> 00:25:49,260
+Proclusive Neurology، في عندك مشكلة عصبية كمان في
+
+408
+00:25:49,260 --> 00:25:52,420
+الأطراق والـMild Coagulation Defects وبيكون عندك
+
+409
+00:25:52,420 --> 00:25:54,840
+مشكلة في الـCoagulation طبعاً هذا عبارة عن حالة
+
+410
+00:25:54,840 --> 00:25:57,640
+ورافية، طبعا الأهم ميزة زي ما حكينا بيميز إنه
+
+411
+00:25:57,640 --> 00:26:01,740
+بيكون عندي Granules Red أو Blue، بيكون هذه
+
+412
+00:26:01,740 --> 00:26:07,410
+Granules غير منضمةفي الحجم وفي التوزيع اسمها كمان
+
+413
+00:26:07,410 --> 00:26:12,650
+مرة Shidiak Steinberg Higashi Anomaly ده الباقي
+
+414
+00:26:12,650 --> 00:26:15,410
+أخدناه مرة معايا عبارة عن بلوغران نيوز داخل
+
+415
+00:26:15,410 --> 00:26:19,750
+النيتروفيل أنيزو سايتوسون في النيتروفيل أخدناها
+
+416
+00:26:19,750 --> 00:26:21,870
+اللي هي بيكون حجة مختلفة من الحجم، مشايفين
+
+417
+00:26:21,870 --> 00:26:24,490
+نيتروفيل هي حجم كيف؟ وانا كيف حجم مختلف؟
+
+418
+00:26:25,260 --> 00:26:28,920
+وDegeneration of Nucleus بيكون عندي نواة صار
+
+419
+00:26:28,920 --> 00:26:32,080
+لـDegeneration أو بيكونوا تـExcess، زي بيكونوا
+
+420
+00:26:32,080 --> 00:26:35,360
+تـExcess، اختفت طبعا نتيجة أن الـold specimen عينه
+
+421
+00:26:35,360 --> 00:26:39,340
+قديمة جدا، هذا بالنسبالي الـwhite blood cells إن
+
+422
+00:26:39,340 --> 00:26:43,540
+شاء الله مهم حتى الآن، تمام؟ ‏- تمام ‏- الله، أنا
+
+423
+00:26:43,540 --> 00:26:47,840
+كان بقالي أعطيكم الخلايا الحمراء، بس هوقف هنا لأنه
+
+424
+00:26:47,840 --> 00:26:51,380
+بدي أكمل تفتعبوا اللي أخدناه كويس و تدرسوه صح، إيش
+
+425
+00:26:51,380 --> 00:26:55,710
+رأيكم؟تمام، بس ضروري يا دكتور تنزل المحاضرة اليوم
+
+426
+00:26:55,710 --> 00:26:59,350
+هنزلها ان شاء الله، بس بدي أكم تدرسوا هاي، ان شاء
+
+427
+00:26:59,350 --> 00:27:02,810
+الله موعدنا الجاي بنا نحاول ندرس الخلايا الحمرة و
+
+428
+00:27:02,810 --> 00:27:06,090
+ندرس ال CPC و هذا، طبعا بنا نركز على هذا، بس بدي
+
+429
+00:27:06,090 --> 00:27:10,570
+أكم اللي ما سبق تدرسوه مية مية، هنزله انا اليوم ان
+
+430
+00:27:10,570 --> 00:27:13,850
+شاء الله بحاول، ماشي؟ ان شاء الله، الله يحميك طب
+
+431
+00:27:13,850 --> 00:27:15,990
+خلاص، موعدنا الموعد اللي جاي ان شاء الله السبت، أي
+
+432
+00:27:15,990 --> 00:27:19,730
+سيارة حكينا؟ الساعة أحد عشر، ساعة أحد أحد، ماشي يا
+
+433
+00:27:19,730 --> 00:27:23,270
+محمد؟ماشاء الله خلاص سامعه ما شاء الله يلا أعطيكم
+
+434
+00:27:23,270 --> 00:27:25,750
+قبلها، في سؤال قبل ما أطلع؟ في أي سفسارة عن ال
+
+435
+00:27:25,750 --> 00:27:30,650
+slides السابقة كلها؟ بس دكتور التسجيل اللي الورق
+
+436
+00:27:30,650 --> 00:27:35,250
+اللي فات، تتمنين صفحة؟ التسجيل أنا سجلت وحببتكم
+
+437
+00:27:35,250 --> 00:27:37,730
+فيها سعيد، و المرة الأخيرة نزلته، أنا أتأكد منه،
+
+438
+00:27:37,730 --> 00:27:41,730
+شوف كويس، أنا طلعت عليه كويس، التسجيل كان بفتح أو
+
+439
+00:27:41,730 --> 00:27:45,710
+بيفتحش؟ موجود
+
+440
+00:27:45,710 --> 00:27:53,510
+بال model ما هو بدأس عليه بيفتحشليش مفتحاش؟ مش
+
+441
+00:27:53,510 --> 00:27:57,850
+عارف بنجولنا على صفحة من جوجل وبعدين بقولي حميل طب
+
+442
+00:27:57,850 --> 00:28:03,070
+خليني حميل فعلا حميل مش مفتح هو صفحة
+
+443
+00:28:03,070 --> 00:28:06,950
+بيضطجيني طيب بدي اتواصل مع ال IT لان انا نزلته على
+
+444
+00:28:06,950 --> 00:28:09,710
+جوجل درايف و سولومي يدخلوا على يوتيوب انا بتحكي
+
+445
+00:28:09,710 --> 00:28:13,110
+معاهم ان شاء الله ان شاء الله يلا يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.json b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..9c63c4318faea70723a98c71c30398b1219c8041
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.json
@@ -0,0 +1 @@
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{"start": 1649.43, "end": 1650.09, "word": " التسجيل", "probability": 0.930908203125}, {"start": 1650.09, "end": 1650.29, "word": " اللي", "probability": 0.846923828125}, {"start": 1650.29, "end": 1650.65, "word": " الورق", "probability": 0.5011393229166666}, {"start": 1650.65, "end": 1650.77, "word": " اللي", "probability": 0.935302734375}, {"start": 1650.77, "end": 1651.47, "word": " فات،", "probability": 0.6622111002604166}, {"start": 1651.47, "end": 1652.13, "word": " تتمنين", "probability": 0.48101806640625}, {"start": 1652.13, "end": 1653.63, "word": " صفحة؟", "probability": 0.811962890625}, {"start": 1653.63, "end": 1654.09, "word": " التسجيل", "probability": 0.9912109375}, {"start": 1654.09, "end": 1654.37, "word": " أنا", "probability": 0.8427734375}, {"start": 1654.37, "end": 1654.83, "word": " سجلت", "probability": 0.98193359375}, {"start": 1654.83, "end": 1655.25, "word": " وحببتكم", "probability": 0.798095703125}, {"start": 1655.25, "end": 1655.37, "word": " فيها", "probability": 0.4287109375}, {"start": 1655.37, "end": 1655.95, "word": " سعيد،", "probability": 0.874755859375}, {"start": 1655.95, "end": 1656.09, "word": " و", "probability": 0.89501953125}, {"start": 1656.09, "end": 1656.33, "word": " المرة", "probability": 0.6795654296875}, {"start": 1656.33, "end": 1656.49, "word": " الأخيرة", "probability": 0.4932047526041667}, {"start": 1656.49, "end": 1657.05, "word": " نزلته،", "probability": 0.739208984375}, {"start": 1657.05, "end": 1657.15, "word": " أنا", "probability": 0.72802734375}, {"start": 1657.15, "end": 1657.45, "word": " أتأكد", "probability": 0.8955078125}, {"start": 1657.45, "end": 1657.73, "word": " منه،", "probability": 0.8600260416666666}, {"start": 1657.73, "end": 1657.87, "word": " شوف", "probability": 0.745849609375}, {"start": 1657.87, "end": 1658.21, "word": " كويس،", "probability": 0.9202880859375}, {"start": 1658.21, "end": 1658.31, "word": " أنا", "probability": 0.7861328125}, {"start": 1658.31, "end": 1658.73, "word": " طلعت", "probability": 0.7386067708333334}, {"start": 1658.73, "end": 1658.95, "word": " عليه", "probability": 0.86181640625}, {"start": 1658.95, "end": 1659.25, "word": " كويس،", "probability": 0.8023681640625}, {"start": 1659.25, "end": 1659.53, "word": " التسجيل", "probability": 0.86163330078125}, {"start": 1659.53, "end": 1659.79, "word": " كان", "probability": 0.98974609375}, {"start": 1659.79, "end": 1661.61, "word": " بفتح", "probability": 0.72265625}, {"start": 1661.61, "end": 1661.73, "word": " أو", "probability": 0.280029296875}, {"start": 1661.73, "end": 1662.57, "word": " بيفتحش؟", "probability": 0.789306640625}, {"start": 1662.57, "end": 1665.71, "word": " موجود", "probability": 0.8595377604166666}, {"start": 1665.71, "end": 1666.03, "word": " بال", "probability": 0.65966796875}, {"start": 1666.03, "end": 1666.75, "word": " model", "probability": 0.8271484375}, {"start": 1666.75, "end": 1669.31, "word": " ما", "probability": 0.2822265625}, {"start": 1669.31, 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5172, 2655, 5016, 31439, 20328, 5172, 5016, 3660, 4724, 1829, 11242, 9566, 7435, 1829, 22653, 23032, 1829, 3555, 4724, 16254, 1975, 2655, 2407, 33546, 1211, 20449, 2423, 6783, 5296, 7649, 1975, 8315, 8717, 11622, 1211, 47395, 15844, 10874, 29245, 1211, 11778, 23557, 33911, 4032, 8608, 12610, 20498, 1829, 7251, 3215, 9778, 1211, 14407, 15844, 7251, 2407, 31371, 37746, 1975, 8315, 39894, 5016, 4117, 1829, 20449, 995, 16095, 16472, 13412, 16606, 21984, 16472, 13412, 16606, 21984, 7251, 15040, 37495, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.335082122009166, "compression_ratio": 1.9310344827586208, "no_speech_prob": 6.258487701416016e-06, "words": [{"start": 1670.81, "end": 1671.13, "word": "ليش", "probability": 0.81396484375}, {"start": 1671.13, "end": 1673.05, "word": " مفتحاش؟", "probability": 0.7403564453125}, {"start": 1673.05, "end": 1673.51, "word": " مش", "probability": 0.8251953125}, {"start": 1673.51, "end": 1673.93, "word": " عارف", "probability": 0.99658203125}, {"start": 1673.93, "end": 1674.49, "word": " بنجولنا", "probability": 0.5916015625}, {"start": 1674.49, "end": 1674.63, "word": " على", "probability": 0.81494140625}, {"start": 1674.63, "end": 1675.01, "word": " صفحة", "probability": 0.9183349609375}, {"start": 1675.01, "end": 1675.23, "word": " من", "probability": 0.970703125}, {"start": 1675.23, "end": 1675.77, "word": " جوجل", "probability": 0.7239583333333334}, {"start": 1675.77, "end": 1676.09, "word": " وبعدين", "probability": 0.7036946614583334}, {"start": 1676.09, "end": 1676.39, "word": " بقولي", "probability": 0.4508870442708333}, {"start": 1676.39, "end": 1676.95, "word": " حميل", "probability": 0.516845703125}, {"start": 1676.95, "end": 1677.85, "word": " طب", "probability": 0.522125244140625}, {"start": 1677.85, "end": 1678.07, "word": " خليني", "probability": 0.8681640625}, {"start": 1678.07, "end": 1678.35, "word": " حميل", "probability": 0.90185546875}, {"start": 1678.35, "end": 1678.59, "word": " فعلا", "probability": 0.3544108072916667}, {"start": 1678.59, "end": 1678.85, "word": " حميل", "probability": 0.8092447916666666}, {"start": 1678.85, "end": 1678.99, "word": " مش", "probability": 0.859375}, {"start": 1678.99, "end": 1679.19, "word": " مفتح", "probability": 0.678924560546875}, {"start": 1679.19, "end": 1679.43, "word": " هو", "probability": 0.8212890625}, {"start": 1679.43, "end": 1683.07, "word": " صفحة", "probability": 0.780487060546875}, {"start": 1683.07, "end": 1683.85, "word": " بيضطجيني", "probability": 0.7295968191964286}, {"start": 1683.85, "end": 1684.77, "word": " طيب", "probability": 0.833984375}, {"start": 1684.77, "end": 1684.99, "word": " بدي", "probability": 0.6771240234375}, {"start": 1684.99, "end": 1685.39, "word": " اتواصل", "probability": 0.91533203125}, {"start": 1685.39, "end": 1685.51, "word": " مع", "probability": 0.9814453125}, {"start": 1685.51, "end": 1685.61, "word": " ال", "probability": 0.9580078125}, {"start": 1685.61, "end": 1685.85, "word": " IT", "probability": 0.74951171875}, {"start": 1685.85, "end": 1686.09, "word": " لان", "probability": 0.6004638671875}, {"start": 1686.09, "end": 1686.25, "word": " انا", "probability": 0.6915283203125}, {"start": 1686.25, "end": 1686.73, "word": " نزلته", "probability": 0.8599853515625}, {"start": 1686.73, "end": 1686.95, "word": " على", "probability": 0.76708984375}, {"start": 1686.95, "end": 1687.31, "word": " جوجل", "probability": 0.78466796875}, {"start": 1687.31, "end": 1687.65, "word": " درايف", "probability": 0.701171875}, {"start": 1687.65, "end": 1687.75, "word": " و", "probability": 0.5361328125}, {"start": 1687.75, "end": 1688.13, "word": " سولومي", "probability": 0.7430419921875}, {"start": 1688.13, "end": 1688.69, "word": " يدخلوا", "probability": 0.90361328125}, {"start": 1688.69, "end": 1688.85, "word": " على", "probability": 0.6689453125}, {"start": 1688.85, "end": 1689.27, "word": " يوتيوب", "probability": 0.8629150390625}, {"start": 1689.27, "end": 1689.43, "word": " انا", "probability": 0.7861328125}, {"start": 1689.43, "end": 1689.71, "word": " بتحكي", "probability": 0.947998046875}, {"start": 1689.71, "end": 1689.93, "word": " معاهم", "probability": 0.9049479166666666}, {"start": 1689.93, "end": 1690.03, "word": " ان", "probability": 0.77783203125}, {"start": 1690.03, "end": 1690.15, "word": " شاء", "probability": 0.97412109375}, {"start": 1690.15, "end": 1690.33, "word": " الله", "probability": 0.958984375}, {"start": 1690.33, "end": 1691.29, "word": " ان", "probability": 0.1920166015625}, {"start": 1691.29, "end": 1691.61, "word": " شاء", "probability": 0.994873046875}, {"start": 1691.61, "end": 1691.79, "word": " الله", "probability": 0.95849609375}, {"start": 1691.79, "end": 1692.39, "word": " يلا", "probability": 0.6009521484375}, {"start": 1692.39, "end": 1692.71, "word": " يعطيكم", "probability": 0.8348388671875}, {"start": 1692.71, "end": 1693.11, "word": " العافية", "probability": 0.8841145833333334}], "temperature": 1.0}], "language": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.srt b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3247ec787a025e3bbafa7d0aa34f894b8f1af6bc
--- /dev/null
+++ b/PL9fwy3NUQKwYlaku5Rhesb9VDzfHDSqUq/rNT2EZhG1Lg_raw.srt
@@ -0,0 +1,1792 @@
+1
+00:00:00,000 --> 00:00:06,900
+أحمد؟ طيب، احنا زي ما حكينا الـWhite pieces
+
+2
+00:00:06,900 --> 00:00:09,880
+morphology هذه الخلايا الطبيعية، هذه خلية
+
+3
+00:00:09,880 --> 00:00:15,820
+الـNeutrophil المووس واضح، تمام؟ أيوة، أيوة هذه
+
+4
+00:00:15,820 --> 00:00:19,120
+خلية الـNeutrophil، هذه خلية الـXenophil هذه خلية
+
+5
+00:00:19,120 --> 00:00:21,820
+الـLymphocytes، خلية الـMonocytes وخلية
+
+6
+00:00:21,820 --> 00:00:26,220
+الـBasophil طبعا، نفس الخلايا واضحة عندها دهرة
+
+7
+00:00:26,610 --> 00:00:32,010
+الـBand أو الـStaff تسميها؟
+
+8
+00:00:32,010 --> 00:00:35,350
+بكلم
+
+9
+00:00:35,350 --> 00:00:41,940
+جوال يعنيأه ماشي، طيب، هاي خليه دنيا، أكيد،
+
+10
+00:00:41,940 --> 00:00:47,660
+فيزوزين، مونوسايد، مش هنهجر عنهم، مش هنفنش، نحكي
+
+11
+00:00:47,660 --> 00:00:53,360
+فيهم كتير، حاجينهم جبانية، عمونا لأ تفكر
+
+12
+00:00:53,360 --> 00:00:55,520
+أن لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+13
+00:00:55,520 --> 00:00:55,760
+تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما عندك
+
+14
+00:00:55,760 --> 00:00:56,540
+جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن لسه ما
+
+15
+00:00:56,540 --> 00:00:57,940
+عندك جامعات، تفكر أن لسه ما عندك جامعات، تفكر أن
+
+16
+00:00:57,940 --> 00:01:02,660
+لسه ما عندك جامعات، تفكر أن لسه ما عندك جامعات،
+
+17
+00:01:02,660 --> 00:01:04,680
+تفكر أن لسه ما عندك جامع
+
+18
+00:01:08,270 --> 00:01:14,470
+هي ميوت يا معاد؟ أفصل أفصل. لأ لأ بس عملتله ميوت
+
+19
+00:01:14,470 --> 00:01:22,870
+طيب ال abnormal shape، ال abnormal shape طبعا أول
+
+20
+00:01:22,870 --> 00:01:27,790
+شغل غراميستيك، غراميستيك طبعا واحد من الشباب سألني
+
+21
+00:01:27,790 --> 00:01:30,130
+قبل هيك يا دكتور ممكن نميز بين عينة المال و ال
+
+22
+00:01:30,130 --> 00:01:35,670
+female صح ولا لأ؟أه أنا نسألت أه قلتلك أه ممكن على
+
+23
+00:01:35,670 --> 00:01:39,110
+طريق الخلايا النيتروفيل فهذه مميزة على طريق شغلهاي
+
+24
+00:01:39,110 --> 00:01:42,910
+طب دراميستك شايفين ال .. احنا عندنا خلية هاي في
+
+25
+00:01:42,910 --> 00:01:47,030
+عبارة عن أربع loops شايفين الجزء الطالب البارز هذا
+
+26
+00:01:47,030 --> 00:01:50,810
+اللي عليه الماوس؟
+
+27
+00:01:50,810 --> 00:01:54,910
+أه شايفينههذا عبارة عن «Dramastic» هذا «Dramastic»
+
+28
+00:01:54,910 --> 00:01:58,350
+يعني زي طابلة، كيف عصاية الطابلة؟ هي عصاية طابلة،
+
+29
+00:01:58,350 --> 00:02:01,470
+طبعا «Dramastic» عبارة عن Nuclear Bandage تقريبا
+
+30
+00:02:01,470 --> 00:02:04,770
+واحد ونص مايكرو، طبعا in diameter ويكون attached
+
+31
+00:02:04,770 --> 00:02:08,430
+لـ nucleus لإيش؟ لـ X-Chromosome، عشان تظهر وين؟
+
+32
+00:02:08,430 --> 00:02:10,910
+تظهر أكتر الشيء بالـ Female، طبعا الـ X-Chromosome
+
+33
+00:02:10,910 --> 00:02:13,750
+أنواح تيهم، مش الـ Active، الـ Inactive، مع أن
+
+34
+00:02:13,750 --> 00:02:19,460
+مايعرف أن الـ Male عبارة عن إيش؟ XYصح ولا لأ؟ الـ
+
+35
+00:02:19,460 --> 00:02:22,000
+Female XX واحد منهم Active وتاني Inactive فالـ
+
+36
+00:02:22,000 --> 00:02:26,180
+Inactive Form تظهر فيه هاي فإذا الـ Dramastic تظهر
+
+37
+00:02:26,180 --> 00:02:29,160
+في الـ Neutrophil للـ Female تظهر في الـ Male في
+
+38
+00:02:29,160 --> 00:02:31,480
+حالة Clean Filter Syndrome طب ليش تظهر في Clean
+
+39
+00:02:31,480 --> 00:02:33,620
+Filter Syndrome؟ مين بيذكر ليه؟ إيش هذا الـ
+
+40
+00:02:33,620 --> 00:02:40,120
+Syndrome؟ هذا اللي قبل شوية، اللي قبل شوية أجي
+
+41
+00:02:40,120 --> 00:02:47,140
+معانا لأ، Clean Filter Syndrome هذا بيكون عندي YXX
+
+42
+00:02:48,070 --> 00:02:51,110
+فاهميني كيف؟ يعني عنده نسخة إضافية من X يكون طبعاً
+
+43
+00:02:51,110 --> 00:02:56,750
+الـ Male هذا نحكي معاق وفي مشاكل كتير في الجينات
+
+44
+00:02:56,750 --> 00:03:00,850
+فبكون Y XX، ففي عنده رسختين X واحدة منهم بتكون A
+
+45
+00:03:00,850 --> 00:03:09,910
+and A أكتر، فهمنا؟ فهمنا، فهمنا، فهمنا،
+
+46
+00:03:09,910 --> 00:03:11,230
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+47
+00:03:11,230 --> 00:03:11,230
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+48
+00:03:11,230 --> 00:03:11,230
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+49
+00:03:11,230 --> 00:03:14,210
+فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا، فهمنا،
+
+50
+00:03:14,210 --> 00:03:21,310
+فهمنا، فهمنا، فهمناطيب الـ Cecil's Noodle نفس الـ
+
+51
+00:03:21,310 --> 00:03:23,150
+«دراميستيك» طبعا بتظهر في الـ «Inactive
+
+52
+00:03:23,150 --> 00:03:26,450
+Chromosomes» بس طبعا بيكونش زي اللي جاي عصاية
+
+53
+00:03:26,450 --> 00:03:29,790
+الطابلة بيكون ميته شويسة بيسموها إيه؟ Cecil's
+
+54
+00:03:29,790 --> 00:03:34,370
+Noodles نفس الأشياء طبعا هنا فيه مميز بينها أربع
+
+55
+00:03:34,370 --> 00:03:36,730
+أنواع Cecil's Noodles والـ «دراميستيك» هنا
+
+56
+00:03:36,730 --> 00:03:39,970
+دراميستيك هاي Cecil's Noodles طبعا هذه بيسموها الـ
+
+57
+00:03:39,970 --> 00:03:43,270
+«حوك» زي الـ «حوك جاي» طبعا فيه تحت الشاشة طبعا بس
+
+58
+00:03:43,270 --> 00:03:46,010
+تدخل على الشاشة الـ«Power Point» هتلاحظوا أسماءهم
+
+59
+00:03:46,010 --> 00:03:49,930
+وتفاصيلهمالـHypersegmentة اللي حكيناها عبارة عن
+
+60
+00:03:49,930 --> 00:03:52,650
+Right Shift تكون عندك نيتروفيل أكثر من 5 loops
+
+61
+00:03:52,650 --> 00:03:56,450
+طبعاً تظهر في حالات طبعاً زي ما حكينا الـ5 to 6
+
+62
+00:03:56,450 --> 00:03:59,170
+loops تظهر في حالات اللي هي Megaloplastic Anemia
+
+63
+00:03:59,170 --> 00:04:01,730
+تظهر في حالة الـAerodeficiency تظهر في حالة
+
+64
+00:04:01,730 --> 00:04:05,210
+Chronic Infection تظهر في حالة Diabetes وفي حالة
+
+65
+00:04:05,210 --> 00:04:05,970
+الـUremia
+
+66
+00:04:08,250 --> 00:04:11,970
+الـ Hyper-segmentation ما حكينا عنها طيب الـ ring
+
+67
+00:04:11,970 --> 00:04:15,290
+-shaped nuclei بيكون النواء أصلا جاي زي ring
+
+68
+00:04:15,290 --> 00:04:20,370
+-shaped بصورة high طبعا بيكون طبعا أو دونات زي
+
+69
+00:04:20,370 --> 00:04:22,410
+الدوناتطبعًا تظهر في حالات برضه الـ Acute
+
+70
+00:04:22,410 --> 00:04:25,010
+Myelodigamia تظهر في حالة الـ Chronic Glycemic
+
+71
+00:04:25,010 --> 00:04:28,630
+Glycemia الـ Myeloplastic Anemia، في حالة الـ MDS،
+
+72
+00:04:28,630 --> 00:04:32,630
+مالة معناها الـ MDS؟ الـ EAH Myelodysplastic
+
+73
+00:04:32,630 --> 00:04:34,910
+Syndrome، Myelodysplastic Syndrome الحالات المهمة
+
+74
+00:04:34,910 --> 00:04:37,410
+دي كلها هتمور معاكم، و هناخدها إن شاء الله، في جزء
+
+75
+00:04:37,410 --> 00:04:39,910
+ماخدة إحنا عنيكي إشرحانها، و في جزء هتاخدوها مع
+
+76
+00:04:39,910 --> 00:04:44,730
+دكتور أحمد إن شاء الله الـ mouse واضح، شايفي؟ إنه
+
+77
+00:04:44,730 --> 00:04:48,070
+كويسلأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+78
+00:04:48,070 --> 00:04:50,190
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+79
+00:04:50,190 --> 00:04:54,070
+لأ، لأ، لأ، لأ، لأ،
+
+80
+00:04:54,070 --> 00:04:57,010
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+81
+00:04:57,010 --> 00:04:57,010
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+82
+00:04:57,010 --> 00:04:59,930
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+83
+00:04:59,930 --> 00:05:02,390
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأهذه
+
+84
+00:05:02,390 --> 00:05:05,510
+بيسموها «Detached Nuclear Materials» موجودة في
+
+85
+00:05:05,510 --> 00:05:09,070
+الـCytoplasm طبعاً إنتجتها «Disgranulobiosis» اللي
+
+86
+00:05:09,070 --> 00:05:11,770
+يعني إن فيه عنده مشكلة في عملية الـGranulation أو
+
+87
+00:05:11,770 --> 00:05:15,730
+طبعا مريض باخد كيموفيرابين، مريض في الـCancer باخد
+
+88
+00:05:15,730 --> 00:05:18,870
+كيموفيرابين أو في حالة الـHIV، هذه بيسموها إيه؟
+
+89
+00:05:18,870 --> 00:05:23,060
+«Detached Nuclear Fragments»طبعًا الـ Toxic
+
+90
+00:05:23,060 --> 00:05:25,400
+Granulation أخدناها أول مرة معناها اللي هي أن
+
+91
+00:05:25,400 --> 00:05:28,100
+خلايا الـ Neutrophil بيكون الـ granules فيها واضحة
+
+92
+00:05:28,100 --> 00:05:31,600
+كتير وكلها أزرق لأسود طبعًا نتيجة الـ infection
+
+93
+00:05:31,600 --> 00:05:34,240
+فالـ Toxic Granulation بيزيد الـ granulation فيها
+
+94
+00:05:34,240 --> 00:05:37,440
+وبيكون لها more mesophilic و larger than normal
+
+95
+00:05:37,440 --> 00:05:40,340
+تضرب في حالة severe bacterial infection تضرب في
+
+96
+00:05:40,340 --> 00:05:42,740
+بعض الحالات الـ tissue damage أو الـ type يعني الـ
+
+97
+00:05:42,740 --> 00:05:45,480
+inflammation تضرب في حالة الـ normal البرجنانسي
+
+98
+00:05:45,480 --> 00:05:49,270
+وتضرب في حالة الـ therapy with cytokinesطبعًا
+
+99
+00:05:49,270 --> 00:05:51,670
+الـCytokines ما هي أسئلة تقرر في عملية إنه يحصل
+
+100
+00:05:51,670 --> 00:05:54,710
+عندي Granulation طبعًا الـHydroxygranulation هو
+
+101
+00:05:54,710 --> 00:05:58,310
+واضح عندي الـHypogranulations
+
+102
+00:05:58,310 --> 00:06:01,170
+تظهر إنه بيكون عندي العكس، بيكون Reduced في
+
+103
+00:06:01,170 --> 00:06:04,670
+الـGranulation في النيتروفيل في حالة الـMDS، اللي
+
+104
+00:06:04,670 --> 00:06:09,030
+هي الـMyelodysplastic Syndrome دُه ال bodies
+
+105
+00:06:09,030 --> 00:06:15,660
+شفناها ومرت معنا تمام يا محمد، علمت عليها؟طيب، دُه
+
+106
+00:06:15,660 --> 00:06:18,300
+الـ Bodies اللي فيه أزرق هناك، فالأزرق هي برنامج
+
+107
+00:06:18,300 --> 00:06:23,160
+Small Pale Blue Cytoplasm Infusions طبعاً دُه الـ
+
+108
+00:06:23,160 --> 00:06:25,860
+Bodies طبعاً بتكون متكون من الـ Ribosomes والـ
+
+109
+00:06:25,860 --> 00:06:29,540
+Endoplasmic reticulum تظهر في حالات الـ Infective
+
+110
+00:06:29,540 --> 00:06:32,160
+Inflammation، Inflammatory States، يعني Infection
+
+111
+00:06:32,160 --> 00:06:35,580
+Inflammation، الـ Severe Burn، Tuberculosis، و الـ
+
+112
+00:06:35,580 --> 00:06:37,060
+Postchemotherapy و البريجنالسية
+
+113
+00:06:41,350 --> 00:06:45,210
+وطبعًا في آخر حالة تظهر فيها الـMyogloin Anomaly
+
+114
+00:06:45,210 --> 00:06:49,970
+الـRustle Body، الـRustle Body طبعًا هي تظهر في
+
+115
+00:06:49,970 --> 00:06:52,570
+الإيزينوفيل، بيكون أصلا، اللي احنا حكينا إن
+
+116
+00:06:52,570 --> 00:06:57,050
+الإيزينوفيل فيها الـgranules حمرة وكبيرة ومسفّطة،
+
+117
+00:06:57,050 --> 00:07:00,350
+بيكون Large, homogeneous, immunoglobulin contains
+
+118
+00:07:00,350 --> 00:07:03,240
+inclusionsطبعًا الـ Immunoglobulins Containing
+
+119
+00:07:03,240 --> 00:07:05,780
+Glucose اللي هي المرتبطة في الـ Immunoglobulins
+
+120
+00:07:05,780 --> 00:07:09,360
+اللي هي الأجسام المضادة طبعًا اللي تظهر في حالة
+
+121
+00:07:09,360 --> 00:07:13,360
+الـ Plasma Cells اللي بيصيرها تطورات طبعًا هي مش
+
+122
+00:07:13,360 --> 00:07:15,400
+تظهر في الـ eosinophil، sorry هي بتظهر في الـ
+
+123
+00:07:15,400 --> 00:07:17,540
+Plasma Cells، اللي خلايا الـ Plasma Cells اللي بقى
+
+124
+00:07:17,540 --> 00:07:20,200
+خلايا الـ lymphocytes مش eosinophil، لكن بتظهر
+
+125
+00:07:20,200 --> 00:07:28,500
+كأنها eosinophil، تمام؟ بتظهر كأنها eosinophil ورا
+
+126
+00:07:28,500 --> 00:07:33,480
+الـأنتوا شايفين العرض اللي راح من عينكم؟ لا
+
+127
+00:07:33,480 --> 00:07:37,200
+شايفينه تمام، تظهر كإنه كإنه إيزينوفي لكن بيكون
+
+128
+00:07:37,200 --> 00:07:40,500
+نوة واحدة زي بلازمس اللي بيسموها وبيكون عليها
+
+129
+00:07:40,500 --> 00:07:43,600
+السيمي الأحمر، شايفين؟ بيكون فيها كإنها جرانيوس
+
+130
+00:07:43,600 --> 00:07:48,560
+كبيرة ولونها أزرق الخلايا اللي حواليها، شايف
+
+131
+00:07:48,560 --> 00:07:52,680
+الخلايا الجنبل عند الماوس هاي؟والخلايا تحت هاي،
+
+132
+00:07:52,680 --> 00:07:56,180
+هذه عبارة عن خلايا حمراء منوعة نيوكلياتي د ر بي
+
+133
+00:07:56,180 --> 00:07:58,700
+سي، النيوكلياتي د ر بي سي، كل شي بيعطيكم إياه،
+
+134
+00:07:58,700 --> 00:08:00,760
+حاولوا تكتبوا جنبه إيش الإسم عشان فيه مبادرة، لو
+
+135
+00:08:00,760 --> 00:08:06,660
+رجعتوله تذكروه، باشي يا سعيد؟ عيد لسه مبالغة يا
+
+136
+00:08:06,660 --> 00:08:09,900
+دكتور؟ النيوكلياتي د ر بي سي، النيوكلياتي د ر بي
+
+137
+00:08:09,900 --> 00:08:16,900
+سي، تمام، مش هاي اللي ينفع عنه، هاي، أكتبكم إياها،
+
+138
+00:08:16,900 --> 00:08:23,130
+هذه عبارة عنشايفين الكتابة؟ نعم نعم شايفينها
+
+139
+00:08:23,130 --> 00:08:26,730
+Nucleated
+
+140
+00:08:26,730 --> 00:08:30,890
+RBCs يعني خلايا حمرة منوّة فيها أنوية Nucleated
+
+141
+00:08:30,890 --> 00:08:38,410
+RBCs تمام؟ بس ثواني إيش يا سيد؟ هاتي هاتي رجل هاتي
+
+142
+00:08:38,410 --> 00:08:43,490
+رجل صوتك باطل شوية يا سيد علي صوتك الراس الفاطس
+
+143
+00:08:43,490 --> 00:08:48,370
+الراس الفاطس الراس الفاطس أه ثواني؟
+
+144
+00:08:49,640 --> 00:08:54,160
+كيف نفرّكها في هي واللي هجت قبل شوية اللي هي
+
+145
+00:08:54,160 --> 00:08:58,600
+الـVaculations؟ الـVaculations بيكون غير منتظمة،
+
+146
+00:08:58,600 --> 00:09:01,460
+الـVaculations غير منتظمة، مابيكونش Hemogeneous،
+
+147
+00:09:01,460 --> 00:09:04,640
+فهذه ان انا اتلاحظ كلمة Hemogeneous، انا عندي هان
+
+148
+00:09:04,640 --> 00:09:07,600
+كلمة Hemogeneous اتلاحظ كيف مهم جدا
+
+149
+00:09:11,680 --> 00:09:15,980
+الـ Vacculation ليست هيموجينية، بيكون بعثرة، حجمها
+
+150
+00:09:15,980 --> 00:09:19,600
+مختلف من واحدة لواحدة، والـ Vacculation تظهر في
+
+151
+00:09:19,600 --> 00:09:22,420
+الـ Neutrophil وفي الـ Monocytes، هذه بتظهر في الـ
+
+152
+00:09:22,420 --> 00:09:25,560
+Plasma Cells، البلازما سيلز عبارة عن خلية بصورة
+
+153
+00:09:25,560 --> 00:09:29,560
+high، خلية تكون نواة واحدة تلافيةطبعًا الـ Plasma
+
+154
+00:09:29,560 --> 00:09:32,880
+Cells هي الخلايا المسؤولة عن إنتاج الأجسام
+
+155
+00:09:32,880 --> 00:09:35,940
+المضادة، فيما بعد عشان ذلك بيكون عبارة عن فيها
+
+156
+00:09:35,940 --> 00:09:38,420
+Large Hemogeneous Immunoglobulin Immunoglobulin
+
+157
+00:09:38,420 --> 00:09:40,960
+عبارة عن إيه؟ البروتين اللي صنع منه الأجسام
+
+158
+00:09:40,960 --> 00:09:45,280
+المضادة، تمام؟ Inclusions وزي ما حكينا بتظهر في
+
+159
+00:09:45,280 --> 00:09:49,400
+الـPlasma Cells اللي Undergoing X-Step Synthesis
+
+160
+00:09:49,400 --> 00:09:52,900
+بيكون انت إنتاج إلها كتير لـImmunoglobulin فعشان
+
+161
+00:09:52,900 --> 00:09:54,280
+بتظهر الـRussell Butters
+
+162
+00:10:01,360 --> 00:10:06,220
+طبعًا… خلّي الـ… هذا فوق شوية الـPhagocytes بقى
+
+163
+00:10:06,220 --> 00:10:11,940
+Parasites هي خلايا الـParasites اللي بتتطفى على
+
+164
+00:10:11,940 --> 00:10:14,960
+جسم الإنسان وتتم بنعمتها طبعًا Phagocytes
+
+165
+00:10:14,960 --> 00:10:19,340
+Parasites اللي هي على طريق الخلايا الحمراء فأكيد
+
+166
+00:10:19,340 --> 00:10:23,680
+سمعتوا في الملاريا، أمام؟بسبب الملاريا، فطبعا عند
+
+167
+00:10:23,680 --> 00:10:27,640
+هان، تلاحظون اللي هنا، هاي الخلية هاي، شايفينها؟
+
+168
+00:10:27,640 --> 00:10:37,080
+الخلية هاي، اللي فيها، هي ضاحت عليه دائرة،
+
+169
+00:10:37,080 --> 00:10:40,300
+خلية
+
+170
+00:10:40,300 --> 00:10:42,860
+هاي بالظبط، هاي اللي عند المسعى، المسعى، واي خلية
+
+171
+00:10:42,860 --> 00:10:48,170
+هاي وخلية هاي وخلية هاي، فيهاحجم، طب لاحظ، شوف،
+
+172
+00:10:48,170 --> 00:10:51,350
+بقدر أكبر من عندي، فيه ثابتة كبيرة، بس عقلها هي
+
+173
+00:10:51,350 --> 00:10:57,930
+فيها زي ما بتحكيه، فيها زي .. زي إشي زي الخاتم،
+
+174
+00:10:57,930 --> 00:11:00,790
+بيسموه Ring Form Parasite، هاد عبارة عن malaria،
+
+175
+00:11:00,790 --> 00:11:03,730
+malaria parasites، شايفين؟ خليه هاي كمان، خليه
+
+176
+00:11:03,730 --> 00:11:08,630
+هاي، خليه هاي، عليها نقطين؟ نقطين وفيه خيط مربط
+
+177
+00:11:08,630 --> 00:11:13,150
+بين أثنين واتنين، زي الخاتم، بيسموه؟ آه، لو كبرت،
+
+178
+00:11:13,150 --> 00:11:17,270
+بيظهرأما بدي أكبر، بدي أروح أكبر مكان تاني، مش
+
+179
+00:11:17,270 --> 00:11:19,930
+مشكلة، إن شاء الله أفرجيكم إيهم عن الأمر واقعي،
+
+180
+00:11:19,930 --> 00:11:24,230
+هيا خليني نشوف من عندنا نقدر نكبر أحنا، شايفين
+
+181
+00:11:24,230 --> 00:11:29,590
+هاي؟ شايف يا سيد؟ أعطيك، أعطيك، أعطيك، أعطيك،
+
+182
+00:11:29,590 --> 00:11:31,530
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+183
+00:11:31,530 --> 00:11:32,090
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+184
+00:11:32,090 --> 00:11:41,790
+أعطيك، أعطيك، أعطيك، أعطيك، أعطيك،
+
+185
+00:11:41,790 --> 00:11:47,350
+أعططبعًا، هذه كما حكيناها بتظهر في حالات
+
+186
+00:11:47,350 --> 00:11:50,870
+الـinfection بالنصاب بالملاريا طبعًا الـphagocyte
+
+187
+00:11:50,870 --> 00:11:55,490
+plateless العكس بيكون المرحل الذنب اللي عمته اللي
+
+188
+00:11:55,490 --> 00:11:58,190
+هو الـplateless تظهر في خلايا الـNitrophil
+
+189
+00:11:58,190 --> 00:12:00,590
+الـNitrophil بتروح تبلعلي الـplateless نتيجة
+
+190
+00:12:00,590 --> 00:12:03,170
+الـinfection طبعًا الـinfection البيتوفين بيبقى
+
+191
+00:12:03,170 --> 00:12:05,690
+بيبقى بتبلعلي بكتيريا لكن نتيجة مثلًا إذا كانت
+
+192
+00:12:05,690 --> 00:12:08,530
+severe infection بيصير تروح تبلعلي ممكن تبقى عند
+
+193
+00:12:08,530 --> 00:12:11,580
+الوقت تبلع الـplateless زي بالحالة هذههي عندي
+
+194
+00:12:11,580 --> 00:12:15,160
+الحالة هاي، شايفين الخلايا ها؟ هي بالعالي بليتلس
+
+195
+00:12:15,160 --> 00:12:18,460
+وهان بالعالي بليتلس، شايفين هاي؟ النقطة هاي
+
+196
+00:12:18,460 --> 00:12:22,840
+الصغيرة الزرقى، هادي عبارة عن خلية بليتلس، هادي
+
+197
+00:12:22,840 --> 00:12:27,420
+عبارة عن هاي، شايفين هاي، هاي الصغيرة، هاي،
+
+198
+00:12:27,420 --> 00:12:30,480
+مابيضيش أحط بصوم كتير عشان ما تخربطوش كتير، ماشي
+
+199
+00:12:30,480 --> 00:12:34,720
+شفتوها، هادي بيسموها phagocytes of bletelss طب
+
+200
+00:12:34,720 --> 00:12:36,640
+انتظر في حالات ال infection، انتظر في حالات ال
+
+201
+00:12:36,640 --> 00:12:36,920
+infection
+
+202
+00:12:45,010 --> 00:12:54,430
+شوي شباب شوي بس دقيقة سيف
+
+203
+00:12:54,430 --> 00:13:03,870
+أنت في المحاضرة؟
+
+204
+00:13:05,700 --> 00:13:08,400
+طيب، معلش، عشان كان إيش أبني و بدي أحكي معاه في
+
+205
+00:13:08,400 --> 00:13:12,320
+شغلات طيب، هل جيت الفاقوصيات الـplatelets بيكون
+
+206
+00:13:12,320 --> 00:13:16,000
+خلايا النيتروفيل عاملة الفاقوصيتوشين لـplatelets
+
+207
+00:13:16,000 --> 00:13:18,860
+في حالة الinfection؟ هاي الصورة واضحة كتير،
+
+208
+00:13:18,860 --> 00:13:21,860
+شايفينها؟ هاي الخلاية النيتروفيل وهي الـplatelets
+
+209
+00:13:21,860 --> 00:13:28,980
+جواها واضحة يا شباب، أه؟ لأ، مش واضحة دكتور،
+
+210
+00:13:28,980 --> 00:13:32,340
+شايفين الصورة أنتوا؟ دكتور، أه شايفين، أه أه
+
+211
+00:13:32,340 --> 00:13:38,920
+شايفين، طب تمام، بسإيش يا سعيد؟ إيش بالنسبة ل ..
+
+212
+00:13:38,920 --> 00:13:44,700
+إيش بالنسبة لهذه؟ في .. في خلايا فوق و تحت هدول
+
+213
+00:13:44,700 --> 00:13:50,860
+بليتلس برضه؟ هذه بليتلس و هذه بليتلس و هذه جوا
+
+214
+00:13:50,860 --> 00:13:55,220
+الخلية دي نيتو فيه بليتلس هدول كل اللي عليها دواعي
+
+215
+00:13:55,220 --> 00:13:58,920
+الخضرة بليتلس، هذه بليتلس، شايفين؟ هذه اللي جت
+
+216
+00:13:58,920 --> 00:14:03,400
+بليتلس، شايفها يا سعيد؟ طب هذه يا دكتور؟ أجل، أجل،
+
+217
+00:14:03,400 --> 00:14:05,140
+أجل، أجل علمليها
+
+218
+00:14:08,780 --> 00:14:13,760
+الـGiga، هذه، هذه تحت Plateless، هذه Hypogranular،
+
+219
+00:14:13,760 --> 00:14:18,000
+بيكون فيه فيها Granules، Hypogranular، طبعا مرة
+
+220
+00:14:18,000 --> 00:14:20,660
+معنا نوع الـPlateless، عندي Hypogranular، بيكون
+
+221
+00:14:20,660 --> 00:14:22,980
+Granules خفيف فيها، هذي، هذي الصغيرة هي كمان
+
+222
+00:14:22,980 --> 00:14:26,580
+Plateless، صحيح، تمام؟ ‏- تمام ‏- هذو كل
+
+223
+00:14:26,580 --> 00:14:29,000
+Plateless، بس أنا بهمني في ال slide هاي
+
+224
+00:14:29,000 --> 00:14:31,440
+الـPhagocytes Plateless، Phagocytes Plateless، أنا
+
+225
+00:14:31,440 --> 00:14:33,500
+حكيتكم إن هي بثمبة اللي عملتها عن طريق
+
+226
+00:14:33,500 --> 00:14:35,000
+الـNitrophil، واضح عندي
+
+227
+00:14:43,050 --> 00:14:47,870
+فيب، نروح لـ «سلايت» البعديها البعديها
+
+228
+00:14:47,870 --> 00:14:49,750
+الـ «فاكوسايزر» الـ blood cells العكس، الـ
+
+229
+00:14:49,750 --> 00:14:53,710
+«نيتروفيل» راح تبقى عادة خلايا حمراء طبعا، بتظهر
+
+230
+00:14:53,710 --> 00:14:56,610
+في حالات، شايفين أن هي نيتروفيل وداخلها خلايا
+
+231
+00:14:56,610 --> 00:15:00,210
+حمراء، واضحة طبعا، في حالة ال «infection» أو الـ
+
+232
+00:15:00,210 --> 00:15:01,990
+«autoimmune hemorrhic anemia» أو في حالة
+
+233
+00:15:01,990 --> 00:15:03,570
+الـ«incompatible blood transfusion» يعني إذا أنا
+
+234
+00:15:03,570 --> 00:15:06,350
+نجلت دم لمريض والدم هتغير متوافق معاه
+
+235
+00:15:06,350 --> 00:15:08,990
+ف«incompatibility» فتصبح الخلايا الـ «نيتروفيل»
+
+236
+00:15:08,990 --> 00:15:13,000
+تتعمل فاكوسايدوسين للخلايا الحمراءطبعًا ساموها
+
+237
+00:15:13,000 --> 00:15:23,040
+Phagocytes لـ Red Blood Cells الـ
+
+238
+00:15:23,040 --> 00:15:23,900
+slide البعديها
+
+239
+00:15:26,370 --> 00:15:29,490
+هذه طبعًا الـ Phagocytes فهذه الـ Vacculations
+
+240
+00:15:29,490 --> 00:15:33,050
+هيكون إننا عديد سلايذات، هنتقص فيها شوية الـ
+
+241
+00:15:33,050 --> 00:15:35,090
+Vacculations، شايفين؟ الـ Vacculation-T فيها شباب
+
+242
+00:15:35,090 --> 00:15:39,410
+تختلف عن اللي حكينا عنها قبل سوية، الـ Plasma
+
+243
+00:15:39,410 --> 00:15:42,590
+Cells طبعًا لأن الـ Vacculations أحجامها طبعًا
+
+244
+00:15:42,590 --> 00:15:48,770
+مختلفة، مبترة، مش جايب منتظمة، تمام؟ هاي عندي الـ
+
+245
+00:15:48,770 --> 00:15:50,630
+All Roots، حكيناها الـ All Roots، الـ All Roots
+
+246
+00:15:50,630 --> 00:15:55,140
+عبارة عنطبعًا، زي ما حكينا، بتظهر في حالة الـ
+
+247
+00:15:55,140 --> 00:15:59,140
+Myeloplast و الـ Bromelocyte، يعني في الخلايا بقى
+
+248
+00:15:59,140 --> 00:16:06,980
+بالـ Maturation، أيش يا شباب؟ في حد سأل؟ سعيد،
+
+249
+00:16:06,980 --> 00:16:11,520
+الصوت عنده بجطع، سعيد طيب، احنا ان شاء الله، زي ما
+
+250
+00:16:11,520 --> 00:16:13,700
+حكيتها سعيد، انا فيه تسجيل سابق، و انا هبقى عندكم
+
+251
+00:16:13,700 --> 00:16:17,660
+تسجيل ان شاء الله، فالـ Horrods، زي ما حكينا، عندي
+
+252
+00:16:17,660 --> 00:16:20,460
+الـ Horrods بتظهر في حالات الـ Acute Myeloid
+
+253
+00:16:20,460 --> 00:16:24,670
+الجيمياالـ M2 و الـ MDS اللي ما يلو dysplastic
+
+254
+00:16:24,670 --> 00:16:26,610
+syndrome ما يلو dysplastic syndrome، الـ MDS
+
+255
+00:16:26,610 --> 00:16:30,830
+فبتقدر في الحتين، شايفين النيتروفيل، خليط
+
+256
+00:16:30,830 --> 00:16:35,270
+النيتروفيل؟ خليط النيتروفيل هان، في زي عصاية صغيرة
+
+257
+00:16:35,270 --> 00:16:40,230
+فيها، هيها، الصورة هي، خليني أحطكم علي دائرة، هذه
+
+258
+00:16:40,230 --> 00:16:44,590
+العصاية الصغيرةهذه الصغيرة هنا هي برعن أوروذ، طب
+
+259
+00:16:44,590 --> 00:16:48,030
+انتظر في حالات الـ«immature cells» إما نحكي
+
+260
+00:16:48,030 --> 00:16:50,370
+«mature» تكون ناضجة، «immature» غير ناضجة، فانتظر
+
+261
+00:16:50,370 --> 00:16:53,630
+في حالات غير ناضجة، اللي هي حالات الـ«myeloplast»
+
+262
+00:16:53,630 --> 00:16:55,470
+والـ«bromyelocyte»، وانتظر في الحالات اللي بحكيها
+
+263
+00:16:55,470 --> 00:16:59,350
+أنا الـ«acute myeloplastic leukemia» في الـ«M2»،
+
+264
+00:16:59,350 --> 00:17:03,630
+في إيش بيسميه أن «M2»، هتمر معنا إن شاء الله يعني،
+
+265
+00:17:03,630 --> 00:17:06,250
+يعني يا دكتور، عادي ممكن أنها تظهر normal أو
+
+266
+00:17:06,250 --> 00:17:10,370
+abnormal؟ لأ، هذه abnormal، هذه المفروضة abnormal،
+
+267
+00:17:10,370 --> 00:17:15,500
+آهالـ Acute Myeloid Leukemia Acute Myeloid Plastic
+
+268
+00:17:15,500 --> 00:17:19,440
+Leukemia الـ AML M2 والـ MDS Myeloid Plastic
+
+269
+00:17:19,440 --> 00:17:23,000
+Syndrome أصلاً
+
+270
+00:17:23,000 --> 00:17:27,680
+هي الخليتين هذولة، يعني الخلية هاي والخلية هاي مش
+
+271
+00:17:27,680 --> 00:17:32,460
+لازم يظهروا في الـ Normal Blood Film لازم يظهروا
+
+272
+00:17:32,460 --> 00:17:34,680
+بالبون مرة، لكن لو ظهروا في الـ Normal Blood Film
+
+273
+00:17:34,680 --> 00:17:36,960
+بحكي أنا عندي حالة مش طبيعية
+
+274
+00:17:41,060 --> 00:17:44,600
+صحيح، هي الـMyoplast، صحيح مش Myoplast هي مثلًا ما
+
+275
+00:17:44,600 --> 00:17:47,740
+بعد الـMyoplast الـMyoplast هذي Myoplast وهذه
+
+276
+00:17:47,740 --> 00:17:53,680
+الـBromelocytes هاي
+
+277
+00:17:53,680 --> 00:17:56,500
+All Roots واضحة، شكل واضح كتير، شايفين الـAll
+
+278
+00:17:56,500 --> 00:18:00,480
+Roots؟ حتى هذي بسميها أنا Bundles of All Roots
+
+279
+00:18:00,480 --> 00:18:03,780
+يعني Bundles من الجمعة زي العصيات Bundles of All
+
+280
+00:18:03,780 --> 00:18:06,860
+Roots هاي اللي هنا، شايفين؟ هذي طبعًا هن الـAll
+
+281
+00:18:06,860 --> 00:18:09,840
+Roots عندي، هن في عندي All Roots، ظاهرة واضحة
+
+282
+00:18:10,070 --> 00:18:13,870
+طبعًا، يكون الخناية الـmelocytes كلها هي خلية
+
+283
+00:18:13,870 --> 00:18:16,510
+bromelocytes، هي melocytes، bromelocytes حدوث ما
+
+284
+00:18:16,510 --> 00:18:19,150
+أنا في حالة الـmaturation إن شاء الله الـMacro
+
+285
+00:18:19,150 --> 00:18:21,790
+neutrophil، الـneutrophil بيكون حجم كبير طبعًا،
+
+286
+00:18:21,790 --> 00:18:24,690
+بيكون حجم ضعف، حجم neutrophil عادية طبعًا، هذه
+
+287
+00:18:24,690 --> 00:18:29,050
+نتيجة إنه عندي نشاط في الـDNA etc. employed of DNA
+
+288
+00:18:29,460 --> 00:18:33,000
+تظهر في حالات طبعًا ممكن تظهر نادر في بعض الحالات
+
+289
+00:18:33,000 --> 00:18:36,780
+الطبيعية لكن قليلة جدًا ممكن تكون ورثية عند الناس،
+
+290
+00:18:36,780 --> 00:18:41,240
+بعض الناس ممكن نتيجة إنه واحد ماخد مثلًا الـ… نحكي
+
+291
+00:18:41,240 --> 00:18:46,180
+الـ… الـ… الـCytokines زي الـGranular Coliformic
+
+292
+00:18:46,180 --> 00:18:49,900
+Units هذه المتنشطة النيتروفيل طبعًا أخد
+
+293
+00:18:49,900 --> 00:18:52,300
+الـCytokines بتعطيني التنشيط أو تظهر في حالات
+
+294
+00:18:52,300 --> 00:18:54,920
+بلدية زي الـMegaloplastic Anemia أو الـChronic
+
+295
+00:18:54,920 --> 00:19:01,930
+Infection تمام؟مش هذا دكتور يقول الـGCC حسابش هذا
+
+296
+00:19:01,930 --> 00:19:06,710
+الـfactor اللي بنشط؟ هذا الـfactor بنشطني نيتروفيل
+
+297
+00:19:06,710 --> 00:19:08,170
+وبنتجني نيتروفيل، صحيح؟ اللي بيسموه
+
+298
+00:19:08,170 --> 00:19:11,710
+الـGranulocytic Cholestimulating Factors اسمها
+
+299
+00:19:11,710 --> 00:19:14,910
+Granulocytic Cholestimulating Factors طبعا هذا
+
+300
+00:19:14,910 --> 00:19:18,070
+الـfactors بنشطني إنتاج خلايا نيتروفيل
+
+301
+00:19:21,910 --> 00:19:26,090
+طبعًا في الـ Necrobiotic أو الـ «أبوبتك» «أبوبتك»
+
+302
+00:19:26,090 --> 00:19:28,770
+يعني موت الخلايا «أبوبتوس» فيز موت الخلايا، طبعًا
+
+303
+00:19:28,770 --> 00:19:32,310
+«نيكروبيوتيك» طبعًا ما عرف معنى، بيكون اللحظة اللي
+
+304
+00:19:32,310 --> 00:19:36,690
+عنديها النواء في الـ «نيتروفيل» كيف شكلها، يعني
+
+305
+00:19:36,690 --> 00:19:40,650
+تقريبًا فقدت، فقدت المباعت وفقدت شكلها اللي
+
+306
+00:19:40,650 --> 00:19:45,680
+فعليًا، بيكون في حالات EHفي حالات الفترة، إذا كان
+
+307
+00:19:45,680 --> 00:19:49,520
+عندى طول كتير الدم أو في حالة الـAcute، ما يلوت
+
+308
+00:19:49,520 --> 00:19:52,880
+بالكيميا طبعاً بيصير الـDense Hemogenous Nuclei
+
+309
+00:19:52,880 --> 00:19:57,840
+بيكون النواء متشانسة وغامقة كتير وجز، بيسموها
+
+310
+00:19:57,840 --> 00:20:03,600
+Pycnotec، تمام؟ بيسموها Pycnotec يعني
+
+311
+00:20:03,600 --> 00:20:06,300
+زي الـNecrosis يا دكتور؟ زي الـNecrosis، هي نقرس،
+
+312
+00:20:06,300 --> 00:20:08,480
+ماحكي أن هي نقر بيوتك، Necrosis
+
+313
+00:20:11,320 --> 00:20:14,040
+طبعًا شفت لفت حكيناها؟ شفت لفت إنه بيكون أنا عندي
+
+314
+00:20:14,040 --> 00:20:18,220
+خلايا قبل الـ Maturation زي هذه الخلايا طبعًا الـ
+
+315
+00:20:18,220 --> 00:20:22,440
+Myeloplast بتظهر عندي، طبعًا بتظهر في حالة
+
+316
+00:20:22,440 --> 00:20:24,920
+الـNormal Pregnancy، بتظهر في حالة الـInfection،
+
+317
+00:20:24,920 --> 00:20:27,060
+بتظهر في حالة الـPulmonary Fibrosis، وبتظهر في
+
+318
+00:20:27,060 --> 00:20:29,280
+حالة الـPulmonary Infiltration By Malignancy، إذا
+
+319
+00:20:29,280 --> 00:20:33,130
+فيندي Malignant Cells بتظهر في حالة أيهفي عندي
+
+320
+00:20:33,130 --> 00:20:37,050
+أشياء بيسموها «سيدو بلجر هوت أنومالي» طبعا «سيدو
+
+321
+00:20:37,050 --> 00:20:39,070
+بلجر هوت أنومالي» بيكون الخلايا النيتروفيل اللي
+
+322
+00:20:39,070 --> 00:20:42,370
+احنا حكينا النيتروفيل اللي فيها النواة من 2 إلى 5
+
+323
+00:20:42,370 --> 00:20:45,890
+loops لكن غالبا تظهر لي بالـ Normal persons 3
+
+324
+00:20:45,890 --> 00:20:49,130
+loops، 4 loops غالبا لكن لو ظهرت معظم الخلايا 2
+
+325
+00:20:49,130 --> 00:20:51,850
+loops بيكون هذه الحالة اللي سموها «سيدو بلجر هوت
+
+326
+00:20:51,850 --> 00:20:55,190
+أنومالي» بعبارة عن Bi-looped neutrophil with more
+
+327
+00:20:55,190 --> 00:20:58,630
+condensed chromatinطبعًا تظهر في حالة الـ MDS،
+
+328
+00:20:58,630 --> 00:21:01,850
+تظهر في حالة الـ Adiopathic Myelofibrosis تظهر في
+
+329
+00:21:01,850 --> 00:21:04,730
+حالة الـ Chronic Glycemic Glycemia أو في حالة
+
+330
+00:21:04,730 --> 00:21:09,550
+العلاج بالـ Colchicine أو الـ Ibuprofen أو في حالة
+
+331
+00:21:09,550 --> 00:21:13,910
+الـ Infection للمونوكلوسس والملاريا والمكسليمة، في
+
+332
+00:21:13,910 --> 00:21:14,650
+حالة الـ CLA
+
+333
+00:21:17,840 --> 00:21:20,120
+الـ Neutrophil Aggregation زي Platelet Aggregation
+
+334
+00:21:20,120 --> 00:21:23,980
+طبعا هذه حالة In Vitro بسبب الإيديتا بتصير عملية
+
+335
+00:21:23,980 --> 00:21:26,600
+Clamp للـ Neutrophil مع بعض متخاطرين مع بعض بعض
+
+336
+00:21:26,600 --> 00:21:29,780
+طبعا زي ما حكيت إن هذه عبارة عن حالة In Vitro
+
+337
+00:21:29,780 --> 00:21:34,600
+تتضار في حالات زي ما حكيتها النتيجة إن الإيديتا
+
+338
+00:21:34,600 --> 00:21:38,560
+عندي شوية قديم أو طولة كتير أو في بعض الحالات الـ
+
+339
+00:21:38,560 --> 00:21:41,140
+Infectious Monoclosis أو بعض الحالات الـ Bacterial
+
+340
+00:21:41,140 --> 00:21:45,180
+Infection أو الـ Autoimmune Diseaseالـ Atypical
+
+341
+00:21:45,180 --> 00:21:47,400
+lymphocyte هي خلايا لينفوسايتز، هنحكي إن خلايا
+
+342
+00:21:47,400 --> 00:21:53,440
+لينفوسايتز عبارة عن حجمين، وبالأحرى تلاتة، Small و
+
+343
+00:21:53,440 --> 00:21:56,080
+Intermediate و Large الخلايا الـ Atypical
+
+344
+00:21:56,080 --> 00:22:00,660
+lymphocyte بيكون أكبر من Large كمان، وبيكون النواة
+
+345
+00:22:00,660 --> 00:22:05,710
+فيها مش دائريةبيكون شكلها مش منتظم طبعاً هذه بتظهر
+
+346
+00:22:05,710 --> 00:22:07,510
+في حالات الـinfection أكتر إيش هي في
+
+347
+00:22:07,510 --> 00:22:10,770
+الـCytomegalovirus أو البشتان بير الفيروس طبعاً
+
+348
+00:22:10,770 --> 00:22:14,410
+Cytomegalovirus يعني بالفيروسات وطبعا إحنا بنعرف
+
+349
+00:22:14,410 --> 00:22:18,130
+إنه إصابة الفيروس بتأثر أكتر إش على الـLymphocyte
+
+350
+00:22:18,130 --> 00:22:21,370
+إصابة البكتيري بتأثر أكتر إش على الـNitrophil على
+
+351
+00:22:21,370 --> 00:22:24,650
+الأغلب طبعاًفزي ما حكينا، الـ Atypical Lymphocyte
+
+352
+00:22:24,650 --> 00:22:27,810
+عبارة عن بوليومورفيك كبير، والدايمتر بيكون دايمتر
+
+353
+00:22:27,810 --> 00:22:31,130
+15 إلى 30، يعني أكبر من الـ Monocyte نفسها طبعا،
+
+354
+00:22:31,130 --> 00:22:33,910
+بيكون abundant وبيكون بيزوفيليك، طبعا الـCytoplasm
+
+355
+00:22:33,910 --> 00:22:37,610
+كتير، طبعا بيزوفيليا وبيكون طبعا maybe confined
+
+356
+00:22:37,610 --> 00:22:40,030
+with the cytoplasmic margins، بيكون أن الأطراف في
+
+357
+00:22:40,030 --> 00:22:44,380
+الـCytoplasm مش منتظمةزي ما حكينا، بتظهر في حالة
+
+358
+00:22:44,380 --> 00:22:48,280
+الـ Viral Infection خاصة الإبشطان بار فيروس أو
+
+359
+00:22:48,280 --> 00:22:50,560
+certain مجال الفيروس أكتر إشي تظهر في حالة الـ
+
+360
+00:22:50,560 --> 00:22:52,460
+Bacterial Infection وأحيانًا الـ Tuberculosis و
+
+361
+00:22:52,460 --> 00:22:57,460
+البروسوليس لأن البروسيلة والـ TB بأثر على الـ
+
+362
+00:22:57,460 --> 00:23:01,320
+lymphocytes ملاريا تظهر في حالة ملاريا ممكن، في
+
+363
+00:23:01,320 --> 00:23:04,920
+حالة الطعيمات ممكن تظهر بالفيروسات هاي أو System
+
+364
+00:23:04,920 --> 00:23:06,560
+Globus اللي موجودة فيها
+
+365
+00:23:09,870 --> 00:23:13,790
+الـ Plasma Cytoid Lymphocyte طبعاً الـ Plasma
+
+366
+00:23:13,790 --> 00:23:16,190
+Cytoid لابد من أن تكون عبارة عن لمفو سايس With
+
+367
+00:23:16,190 --> 00:23:19,430
+mesophilic cytoplasm and eccentric nuclei زي هذه
+
+368
+00:23:19,430 --> 00:23:22,690
+أويش الـ cytoplasm واللمفو سايس اللي بتذكره زي هذا
+
+369
+00:23:22,690 --> 00:23:27,350
+عبارة عن blue sky blue أزرق سماوي لكن هنا جانيق
+
+370
+00:23:27,350 --> 00:23:31,310
+أعمق شوية بيكون إيش عبارة عن mesophilicكمان إن هو
+
+371
+00:23:31,310 --> 00:23:34,650
+غالبًا يكون الـCytoplasm بالنص جاي أو يعني مش
+
+372
+00:23:34,650 --> 00:23:37,970
+طرفية مية مية، بتكون طرفية، طبعًا هذه طبعًا في
+
+373
+00:23:37,970 --> 00:23:40,170
+الحالات اللي بيسموها reactive pneumonia، بيكون
+
+374
+00:23:40,170 --> 00:23:44,630
+نشيط جدًا الـCytoplasm، الـLymphocytes بتضر في
+
+375
+00:23:44,630 --> 00:23:50,550
+الحالات هذه، بيسموها plasma cytoid lymphocytes،
+
+376
+00:23:50,550 --> 00:23:53,810
+يعني تشبه بحالة إيه؟ بتشبه حالة الـPlasma cells
+
+377
+00:23:54,880 --> 00:23:57,500
+الـMod cells، الـMod cells طبعا هي نفس الـPlasma
+
+378
+00:23:57,500 --> 00:23:59,900
+-Cytoid-Lipocyte، لكن بيكون فيها granules، بيكون
+
+379
+00:23:59,900 --> 00:24:03,480
+فيها globular inclusions، اللي هي عبارة عن الـMini
+
+380
+00:24:03,480 --> 00:24:05,600
+-Globulins، بيكون زي ما حكينا في حالة الـactive
+
+381
+00:24:05,600 --> 00:24:10,460
+changes للدم. دكتور، هو التسجيل اللي عندك كان وقف،
+
+382
+00:24:10,460 --> 00:24:14,960
+لإنه كان يكتب لإنك بتسجل وهلقيت وقف، بطل؟ لأ،
+
+383
+00:24:14,960 --> 00:24:20,960
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+384
+00:24:20,960 --> 00:24:24,280
+شغال، شغال، شغال، شغال، شغال، شغال، شغال، شغال،
+
+385
+00:24:24,280 --> 00:24:26,250
+شغال، شغال، شغال، شغال، شفي شيئا سببها فيه Side
+
+386
+00:24:26,250 --> 00:24:31,290
+-Effect؟ طيب،
+
+387
+00:24:31,290 --> 00:24:33,650
+الـMod cells زي ما حكينا بتظهر في حالة البلد مثل
+
+388
+00:24:33,650 --> 00:24:36,290
+ميزايتويت الانفسايز with the globular inclusions
+
+389
+00:24:36,290 --> 00:24:39,030
+composed of hemoglobin بيكون الـHemoglobin في حالة
+
+390
+00:24:39,030 --> 00:24:42,250
+الـReactive lymphocytesالـ Large Granular
+
+391
+00:24:42,250 --> 00:24:45,450
+Lymphocytes طبعًا أهم شيء إنه بيكون هي حجم كبير و
+
+392
+00:24:45,450 --> 00:24:48,610
+Large وفيها Granules، طبعًا حكينا الليمفوكاينس مش
+
+393
+00:24:48,610 --> 00:24:51,290
+فيها Granules أصلا، لكن أحيانًا بتظهر فيها بعض
+
+394
+00:24:51,290 --> 00:24:53,890
+الـGranules الصغيرة، طبعًا اسمه الـIsonophil
+
+395
+00:24:53,890 --> 00:24:56,690
+Granules أو هذه الخلايا عبارة عن Natural Killer
+
+396
+00:24:56,690 --> 00:24:59,970
+Cells اسمها، وبيكون الـLymphocytes Activated T
+
+397
+00:24:59,970 --> 00:25:03,670
+-Cells يعني بيكون خلايا الليمفوكاينس من نوع تاني
+
+398
+00:25:03,670 --> 00:25:05,090
+اللي بيسموه Natural Killer Cells
+
+399
+00:25:07,950 --> 00:25:10,350
+الـ Monovacculation ما هي معنى وخدناها بيكون
+
+400
+00:25:10,350 --> 00:25:14,050
+«بقلوشان زي دي للإنفكشن في الـ Monocytes» في عندي
+
+401
+00:25:14,050 --> 00:25:17,970
+إشي بيسموه «Ishidiac Stem Paired Higashi» الأنمالي
+
+402
+00:25:17,970 --> 00:25:23,330
+يكون عندي عبارة عن زي ما يحكي Large Red أو Blue
+
+403
+00:25:23,330 --> 00:25:26,370
+Granules تظهر في السيطوبلازم للـ Granulocyte أو
+
+404
+00:25:26,370 --> 00:25:29,030
+الـ Lymphocyte ممكن أحيانًا أو الـ Monocyte، يعني
+
+405
+00:25:29,030 --> 00:25:31,890
+أي شيء طبعًا هذا Syndrome، هذا Syndrome طبعًا
+
+406
+00:25:31,890 --> 00:25:36,160
+عبارة عن Autosomal Recessive Syndromeزي ما حكينا،
+
+407
+00:25:36,160 --> 00:25:39,560
+ممتاز هذا الـSyndrome إنه بيصير عندي Recurrent
+
+408
+00:25:39,560 --> 00:25:42,360
+Infection طبعاً Recurrent Infection وبيصير عندي
+
+409
+00:25:42,360 --> 00:25:46,540
+البرجة الـOculoptenes Albinism بيكون عندك
+
+410
+00:25:46,540 --> 00:25:49,260
+Proclusive Neurology، في عندك مشكلة عصبية كمان في
+
+411
+00:25:49,260 --> 00:25:52,420
+الأطراق والـMild Coagulation Defects وبيكون عندك
+
+412
+00:25:52,420 --> 00:25:54,840
+مشكلة في الـCoagulation طبعاً هذا عبارة عن حالة
+
+413
+00:25:54,840 --> 00:25:57,640
+ورافية، طبعا الأهم ميزة زي ما حكينا بيميز إنه
+
+414
+00:25:57,640 --> 00:26:01,740
+بيكون عندي Granules Red أو Blue، بيكون هذه
+
+415
+00:26:01,740 --> 00:26:07,410
+Granules غير منضمةفي الحجم وفي التوزيع اسمها كمان
+
+416
+00:26:07,410 --> 00:26:12,650
+مرة Shidiak Steinberg Higashi Anomaly ده الباقي
+
+417
+00:26:12,650 --> 00:26:15,410
+أخدناه مرة معايا عبارة عن بلوغران نيوز داخل
+
+418
+00:26:15,410 --> 00:26:19,750
+النيتروفيل أنيزو سايتوسون في النيتروفيل أخدناها
+
+419
+00:26:19,750 --> 00:26:21,870
+اللي هي بيكون حجة مختلفة من الحجم، مشايفين
+
+420
+00:26:21,870 --> 00:26:24,490
+نيتروفيل هي حجم كيف؟ وانا كيف حجم مختلف؟
+
+421
+00:26:25,260 --> 00:26:28,920
+وDegeneration of Nucleus بيكون عندي نواة صار
+
+422
+00:26:28,920 --> 00:26:32,080
+لـDegeneration أو بيكونوا تـExcess، زي بيكونوا
+
+423
+00:26:32,080 --> 00:26:35,360
+تـExcess، اختفت طبعا نتيجة أن الـold specimen عينه
+
+424
+00:26:35,360 --> 00:26:39,340
+قديمة جدا، هذا بالنسبالي الـwhite blood cells إن
+
+425
+00:26:39,340 --> 00:26:43,540
+شاء الله مهم حتى الآن، تمام؟ ‏- تمام ‏- الله، أنا
+
+426
+00:26:43,540 --> 00:26:47,840
+كان بقالي أعطيكم الخلايا الحمراء، بس هوقف هنا لأنه
+
+427
+00:26:47,840 --> 00:26:51,380
+بدي أكمل تفتعبوا اللي أخدناه كويس و تدرسوه صح، إيش
+
+428
+00:26:51,380 --> 00:26:55,710
+رأيكم؟تمام، بس ضروري يا دكتور تنزل المحاضرة اليوم
+
+429
+00:26:55,710 --> 00:26:59,350
+هنزلها ان شاء الله، بس بدي أكم تدرسوا هاي، ان شاء
+
+430
+00:26:59,350 --> 00:27:02,810
+الله موعدنا الجاي بنا نحاول ندرس الخلايا الحمرة و
+
+431
+00:27:02,810 --> 00:27:06,090
+ندرس ال CPC و هذا، طبعا بنا نركز على هذا، بس بدي
+
+432
+00:27:06,090 --> 00:27:10,570
+أكم اللي ما سبق تدرسوه مية مية، هنزله انا اليوم ان
+
+433
+00:27:10,570 --> 00:27:13,850
+شاء الله بحاول، ماشي؟ ان شاء الله، الله يحميك طب
+
+434
+00:27:13,850 --> 00:27:15,990
+خلاص، موعدنا الموعد اللي جاي ان شاء الله السبت، أي
+
+435
+00:27:15,990 --> 00:27:19,730
+سيارة حكينا؟ الساعة أحد عشر، ساعة أحد أحد، ماشي يا
+
+436
+00:27:19,730 --> 00:27:23,270
+محمد؟ماشاء الله خلاص سامعه ما شاء الله يلا أعطيكم
+
+437
+00:27:23,270 --> 00:27:25,750
+قبلها، في سؤال قبل ما أطلع؟ في أي سفسارة عن ال
+
+438
+00:27:25,750 --> 00:27:30,650
+slides السابقة كلها؟ بس دكتور التسجيل اللي الورق
+
+439
+00:27:30,650 --> 00:27:35,250
+اللي فات، تتمنين صفحة؟ التسجيل أنا سجلت وحببتكم
+
+440
+00:27:35,250 --> 00:27:37,730
+فيها سعيد، و المرة الأخيرة نزلته، أنا أتأكد منه،
+
+441
+00:27:37,730 --> 00:27:41,730
+شوف كويس، أنا طلعت عليه كويس، التسجيل كان بفتح أو
+
+442
+00:27:41,730 --> 00:27:45,710
+بيفتحش؟ موجود
+
+443
+00:27:45,710 --> 00:27:53,510
+بال model ما هو بدأس عليه بيفتحشليش مفتحاش؟ مش
+
+444
+00:27:53,510 --> 00:27:57,850
+عارف بنجولنا على صفحة من جوجل وبعدين بقولي حميل طب
+
+445
+00:27:57,850 --> 00:28:03,070
+خليني حميل فعلا حميل مش مفتح هو صفحة
+
+446
+00:28:03,070 --> 00:28:06,950
+بيضطجيني طيب بدي اتواصل مع ال IT لان انا نزلته على
+
+447
+00:28:06,950 --> 00:28:09,710
+جوجل درايف و سولومي يدخلوا على يوتيوب انا بتحكي
+
+448
+00:28:09,710 --> 00:28:13,110
+معاهم ان شاء الله ان شاء الله يلا يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8dce7eb8143cbebfca11bc632e170695a716aaa6
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_postprocess.srt
@@ -0,0 +1,1620 @@
+1
+00:00:21,240 --> 00:00:27,440
+لازلنا في شبتر ستة وهو ال isomorphism المرة اللى
+
+2
+00:00:27,440 --> 00:00:33,520
+فاتت عرفنا ال atomorphism وعرفنا انه عبارة عن
+
+3
+00:00:33,520 --> 00:00:37,880
+isomorphism لكن من ال group إلى نفس ال group
+
+4
+00:00:37,880 --> 00:00:43,720
+وبالتالي سمناه atomorphismعرفنا كمان الـ Inner
+
+5
+00:00:43,720 --> 00:00:48,560
+Atomorphism 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 Atomorphism من G الآن لو جمعنا كل
+
+8
+00:01:02,640 --> 00:01:08,570
+الـ Atomorphism في G وسميناهم الستAtomorphism لـ G
+
+9
+00:01:08,570 --> 00:01:14,310
+جمعنا كل ال inner atomorphism وسميناهم ال inner
+
+10
+00:01:14,310 --> 00:01:18,750
+atomorphism of G يفجر الرمز اللي قدام ال
+
+11
+00:01:18,750 --> 00:01:24,110
+atomorphism ل G كل ال atomorphism اللي موجودة في
+
+12
+00:01:24,110 --> 00:01:28,910
+ال group G ال inner atomorphism ل G كل ال inner
+
+13
+00:01:28,910 --> 00:01:34,490
+atomorphism of group G النظرية اللي عندنابتقول لو
+
+14
+00:01:34,490 --> 00:01:38,210
+كانت جي جروب يبقى الاطمورفزم وال 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 تركله .. تركه ملكه as an
+
+18
+00:01:53,170 --> 00:01:57,170
+exercise يعني حطه ال .. ال .. ال .. في التمرين
+
+19
+00:01:57,170 --> 00:02:02,190
+تبعت ميم تبعت الكتاب على أساس اتحله ك exercise
+
+20
+00:02:02,190 --> 00:02:07,070
+احنا هنبره إنه برهان عادييبقى الخطوة الأولى بدي
+
+21
+00:02:07,070 --> 00:02:11,590
+أثبت له ان الاتو مورفزم is a group يعني بدي أثبت
+
+22
+00:02:11,590 --> 00:02:16,150
+ان ال binary operation اللي على الاتو مورفزم اللي
+
+23
+00:02:16,150 --> 00:02:20,150
+جيه is a binary operation associative ال identity
+
+24
+00:02:20,150 --> 00:02:25,050
+element ال inverse element و هكذا نجي للنقطة
+
+25
+00:02:25,050 --> 00:02:31,510
+الأولى لذلك بدي أقوله letفاي واحد وفاي اتنين
+
+26
+00:02:31,510 --> 00:02:39,110
+موجودات في الاتمورفزم اللاجئ يبقى
+
+27
+00:02:39,110 --> 00:02:44,530
+بناء عليه مدام اتمورفزم يبقى كل من فاي واحد وفاي
+
+28
+00:02:44,530 --> 00:02:53,530
+اتنين is one to one and unto يبقى then الواحد وفاي
+
+29
+00:02:53,530 --> 00:03:01,210
+اتنين is one to one and untoهذا بيعطينا من مبادئ
+
+30
+00:03:01,210 --> 00:03:06,910
+الرياضيات ان ال composition فيما بينهما في واحد في
+
+31
+00:03:06,910 --> 00:03:14,510
+اتنين is one to one and one to كذلكمن مبادئ
+
+32
+00:03:14,510 --> 00:03:18,330
+الرياضيات لو كان عندى two functions كل واحدة فيهم
+
+33
+00:03:18,330 --> 00:03:21,730
+one to one and unto يبقى ال composition عليهم
+
+34
+00:03:21,730 --> 00:03:26,450
+بيعطينا one to one and unto function بدى أشوف
+
+35
+00:03:26,450 --> 00:03:31,110
+هالهدى بتخدم خاصية ال isomorphism ولا لأ إن خدمت
+
+36
+00:03:31,110 --> 00:03:36,000
+يبقى بصير هدىهذه موجودة في الاتموفيزم
+
+37
+00:03:44,810 --> 00:03:53,910
+يبقى بناء عليه هذي بتعطينا في وان لفي توف XY ليش
+
+38
+00:03:53,910 --> 00:03:57,970
+هذا تعريف ال composition of functions اللي أخدناه
+
+39
+00:03:57,970 --> 00:04:05,810
+في calculus A هذا الكلام يساوي في واحد امالان في
+
+40
+00:04:05,810 --> 00:04:11,070
+اتنين انا فرضه اتو مورفزم لجي يعني ايزو مورفزم اذا
+
+41
+00:04:11,070 --> 00:04:15,110
+بناء عليه لما يأثر على ال X و Y يبدو يساوي في في
+
+42
+00:04:15,110 --> 00:04:23,790
+تو of X في في تو of Y يبقى في تو of X في في تو of
+
+43
+00:04:23,790 --> 00:04:33,230
+Y ليش؟ since لإن ال في تو is isomorphismطيب هذا
+
+44
+00:04:33,230 --> 00:04:42,890
+الكلام يساوي يساوي فاي وان لفاي two of x وكمان فاي
+
+45
+00:04:42,890 --> 00:04:51,370
+وان لفاي 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
+isomorphismطيب بدا الشغلانة ال composition of
+
+48
+00:05:01,930 --> 00:05:06,930
+functions بده رجعهم الى أصلهم يبقى هذا معناه في
+
+49
+00:05:06,930 --> 00:05:12,890
+واحد في اتنين كله as a function of x و في واحد في
+
+50
+00:05:12,890 --> 00:05:19,290
+اتنين as a function of y يبقى بناء عليه أصبح في
+
+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
+اتومورفزميبقى ال atomorphism ل G is closed under
+
+53
+00:05:30,380 --> 00:05:34,500
+the composition of functions أو ال 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 ال atomorphism
+
+56
+00:05:45,220 --> 00:05:54,740
+atomorphism ل 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 الاتومورفزم 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 ال operation is a binary operationبتقدر
+
+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 ان هذه الخطوة هي الخطوة الأولى في إثبات ال
+
+64
+00:06:34,390 --> 00:06:40,690
+group الخطوة التانية خاصية associativity we know
+
+65
+00:06:40,690 --> 00:06:50,950
+that احنا بنعرف ان 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 ال identity element الآن ال 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
+خلّيني أسألكم السؤال اللي طالع لما أخدتم مبادئ
+
+72
+00:07:24,580 --> 00:07:27,460
+الرياضية ال identity function one to one and unto
+
+73
+00:07:27,460 --> 00:07:34,460
+ولا لأ؟ مظبوط؟ يبقى هذه ال identity function which
+
+74
+00:07:34,460 --> 00:07:44,920
+is one to one and unto مش عجبا هكذا and ال I لو
+
+75
+00:07:44,920 --> 00:07:50,000
+أثرت على ال 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 Yإذا حققت الخاصية تبع الـ isomorphism صار one
+
+78
+00:08:02,520 --> 00:08:08,260
+to one and unto و حقق الخاصية و من ال group لنفسها
+
+79
+00:08:08,260 --> 00:08:15,880
+يبقى هنا ال I موجود في ال atomorphism الجيب يبقى
+
+80
+00:08:15,880 --> 00:08:21,440
+أصبحت ال I عبارة عن atomorphism هذا هو ال 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 الاتمورفزم
+
+83
+00:08:42,320 --> 00:08:49,620
+اللي جيه بدك تعمل تشك تاخد ال identity مع اتمورفزم
+
+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 مشكلةطب الآن بدنا نيجي لمين؟ للمعكوس، الان
+
+86
+00:08:58,900 --> 00:09:09,160
+اف في موجود في ال atom وارفزم لجيبأحاول أن أثبت أن
+
+87
+00:09:09,160 --> 00:09:13,300
+الـPhi Inverse عبارة عن Atomorphism إذا أثبتت أن
+
+88
+00:09:13,300 --> 00:09:16,780
+الـPhi Inverse عبارة عن Atomorphism يبقى أثارة
+
+89
+00:09:16,780 --> 00:09:21,860
+الـAtomorphism 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
+شابتر المقدمة وهو شابتر الـgroup يبقى then Phi is
+
+92
+00:09:34,080 --> 00:09:40,910
+one to one and untoمش على جد هيك مادام في one to
+
+93
+00:09:40,910 --> 00:09:47,350
+one and one to one يبجى معاكسه as one to one and
+
+94
+00:09:47,350 --> 00:09:53,650
+one to كذلك functionيبقى one to one and onto
+
+95
+00:09:53,650 --> 00:09:58,590
+function هذا معناه انه في 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 ان في انفرس is an isomorphism يعني في انفرس
+
+98
+00:10:07,670 --> 00:10:11,250
+of x y هو في انفرس of x وفي انفرس of y اظن
+
+99
+00:10:11,250 --> 00:10:16,590
+اثبتناها في النظرية قبل الماضية او السبع نقاط
+
+100
+00:10:16,590 --> 00:10:20,810
+اثبتناها فيهم طيب و
+
+101
+00:10:23,400 --> 00:10:31,860
+Prove that احنا برهننا كذلك ان في انفرس of x y
+
+102
+00:10:31,860 --> 00:10:40,780
+يسوى في انفرس of x في في انفرس of y برهنها سابقا
+
+103
+00:10:40,780 --> 00:10:47,440
+يبقى صارة في انفرس exist وفي نفس الوقت حققت خاصية
+
+104
+00:10:47,440 --> 00:10:52,570
+ال isomorphism يبقى ه أو ال atomorphismهذا معناه
+
+105
+00:10:52,570 --> 00:10:59,690
+ان في انفرس موجود في الاتموفيزم لمام الاجيه صار
+
+106
+00:10:59,690 --> 00:11:03,510
+الاتموفيزم الاجيه closed under the operation
+
+107
+00:11:03,510 --> 00:11:08,850
+العملية associative ال identity element موجود
+
+108
+00:11:08,850 --> 00:11:15,170
+المعكوس لأي element موجود في الاتموفيزم موجود يبقى
+
+109
+00:11:15,170 --> 00:11:23,170
+الاتموفيزم مالها is a groupيبقى ال atomorphism 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 نجل نقطة ثانية ال inner
+
+113
+00:11:44,830 --> 00:11:50,910
+atom morphism ل G the set of all elements Phi A
+
+114
+00:11:50,910 --> 00:11:58,610
+such that ال Phi A of X بده يساوي ال A X A inverse
+
+115
+00:11:58,610 --> 00:12:05,960
+وهذا الكلام لكل ال X اللي موجودة في Gهذه 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 ال inner atomorphism اللي
+
+119
+00:12:19,960 --> 00:12:25,000
+جي subgroup من ال atomorphism اللي جي مش ال inner
+
+120
+00:12:25,000 --> 00:12:32,000
+بصير groupلأن 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 ال inner atomorphisms اللي جيه هي عبارة عن
+
+123
+00:12:41,540 --> 00:12:45,580
+subgroup من ال atomorphism 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 ان ال 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 ل G
+
+127
+00:13:04,440 --> 00:13:14,920
+ال inner atom morphism ل G is non empty 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 لجي يعني
+
+130
+00:13:27,680 --> 00:13:36,440
+هذا هو ال identity element because and ال Phi E is
+
+131
+00:13:36,440 --> 00:13:47,260
+the identity element element andالـ Inner
+
+132
+00:13:47,260 --> 00:13:49,740
+Atomorphism لـ G
+
+133
+00:14:01,130 --> 00:14:05,330
+انا بتدعي انه ال identity element الان بدى بين ان
+
+134
+00:14:05,330 --> 00:14:10,470
+هذا هو ال identity element تبع ال atomorphism يبقى
+
+135
+00:14:10,470 --> 00:14:17,110
+هذا بدى يعطيني ان ال phi E of X يساوي ال X يساوي
+
+136
+00:14:17,110 --> 00:14:22,410
+شريك ال X هذه لو ضربت في ال identity element تتغير
+
+137
+00:14:22,410 --> 00:14:30,360
+يعني لو قلتلك هذه E X صح ولا غلط؟مية المية طب لو
+
+138
+00:14:30,360 --> 00:14:34,440
+قلتلك كمان ضربت في معكوس ال identity element مين
+
+139
+00:14:34,440 --> 00:14:39,600
+معكوس ال identity element ال identity element نفسه
+
+140
+00:14:39,600 --> 00:14:47,140
+يبقى سعر ال في إيه ده موجود في ال inner atom
+
+141
+00:14:47,140 --> 00:14:51,880
+morphism ل G ومن هنا ال inner atom morphism ل G is
+
+142
+00:14:51,880 --> 00:14:59,450
+non emptyطب كويس الان بدأ اخد two elements موجودات
+
+143
+00:14:59,450 --> 00:15:05,190
+في ال inner و اثبت ان الأول في معكوس الثاني موجود
+
+144
+00:15:05,190 --> 00:15:13,910
+يبقى بداجي اقوله let code لفاي a وفاي بي موجودات
+
+145
+00:15:13,910 --> 00:15:18,750
+في ال inner atomorphism لجيه then
+
+146
+00:15:20,330 --> 00:15:28,470
+بدي اخد فاي ا فاي بي انفرس كله as a function of x
+
+147
+00:15:28,470 --> 00:15:34,330
+وشوف هل هذا موجود في ال inner ولا لأ بمعنى اخر هل
+
+148
+00:15:34,330 --> 00:15:40,430
+بقدر اكتب حصل الضرب هذا على شكل inner atomorphism
+
+149
+00:15:40,430 --> 00:15:47,060
+والله مقدرش هذا ما سنجيب عليهطيب 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 طبعا برهمنا هذا الكلام سابقا فى
+
+152
+00:15:58,700 --> 00:16:03,440
+نظريات السابقة بياننا ان فاي اي انفرس الانفرس
+
+153
+00:16:03,440 --> 00:16:08,720
+بنزله على من؟ على ال element يبقى هاي نزلنا ال
+
+154
+00:16:08,720 --> 00:16:12,470
+inverse على من؟ على ال element اللى جواهذا
+
+155
+00:16:12,470 --> 00:16:20,610
+composition of functions يبقى فاي a لمين لفاي بي
+
+156
+00:16:20,610 --> 00:16:27,150
+انفرس as a function of x يبقى هذه الفاي اللي برا
+
+157
+00:16:27,150 --> 00:16:32,810
+هذه الفاي اللي برا a واللي جوا هذي بده اطبق عليها
+
+158
+00:16:32,810 --> 00:16:38,560
+التعريف اللي احنا جايلينه هنايبقى 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
+ال element A X A inverse يبقى هذا ال element X ال
+
+161
+00:16:51,800 --> 00:16:57,850
+element inverse بالشكل اللي عندنا هذاالان بدي اطبق
+
+162
+00:16:57,850 --> 00:17:04,110
+التعريف كمان مرة يبقى هذا بدي يعطيني ال 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 ال a inverseيبقى 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 ال element ال A inverse الان
+
+167
+00:17:30,030 --> 00:17:35,170
+بالدالي لخاصية ال associativity يبقى بناء عليه هذا
+
+168
+00:17:35,170 --> 00:17:42,120
+بقدر اقول A B inverse في ال X فيهأتطلعلي هذا ال
+
+169
+00:17:42,120 --> 00:17:45,660
+element inverse و هذا ال element inverse بقدر
+
+170
+00:17:45,660 --> 00:17:51,360
+أجمعهم ب inverse واحد بعد ما أغير أو أبدل مواقعهم
+
+171
+00:17:51,360 --> 00:17:57,740
+يبقى هذا الكلام اللي هو ال 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 اتطلعلي
+
+174
+00:18:07,160 --> 00:18:12,120
+للمقدار بين القاوسين هو هذا ولا لايبقى صار ال
+
+175
+00:18:12,120 --> 00:18:18,180
+element هذا هو ال 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 ابتدات ب element في معكوسي ثاني 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 ل G
+
+181
+00:18:55,870 --> 00:19:00,910
+ثبت هنا انه non-empty أخدت ال elements موجودات في
+
+182
+00:19:00,910 --> 00:19:06,350
+ال inner فردت الأول في معكوس الثاني طلع موجود وين
+
+183
+00:19:06,350 --> 00:19:12,810
+في ال inner atomorphism يبقى بناء عليه ال inner
+
+184
+00:19:12,810 --> 00:19:20,150
+atomorphism لجي is a subgroup من ال atomorphism
+
+185
+00:19:20,150 --> 00:19:22,970
+لجي هذا بيعطينا
+
+186
+00:19:48,290 --> 00:19:52,050
+حد لو يتساول 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 انها 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
+انا ادعيت ان هذا هو ال identity element هايو جايلك
+
+191
+00:20:31,150 --> 00:20:34,990
+هذا is identity element ان جيه جيت قولتلك مدام
+
+192
+00:20:34,990 --> 00:20:39,410
+identity يبقى بده يساوي هيكمظبوط تأثيره على ال
+
+193
+00:20:39,410 --> 00:20:43,350
+element بيسوي ال element هذه النتيجة بدي احاول احط
+
+194
+00:20:43,350 --> 00:20:49,510
+على شكل inner atomorphism فروحت قولت الفي يسوي X
+
+195
+00:20:49,510 --> 00:20:54,670
+يسوي 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 بيسوي E X E inverseفاي اي هي ال identity هي
+
+198
+00:21:09,380 --> 00:21:14,840
+جايلك من الأول في اي موجودة وهي ال identity مش ال
+
+199
+00:21:14,840 --> 00:21:19,620
+اي ال اي هو ال identity تبع ال group لكن في اي هو
+
+200
+00:21:19,620 --> 00:21:23,020
+ال identity element تبع ال atom morphism وتبع ال
+
+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 ال elements
+
+203
+00:21:32,580 --> 00:21:36,400
+اللي موجودة وين في نفس ال group اللي عندنا جيهحد
+
+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 الف دي فور بده يساوي ال R نود R تسعين R مية و
+
+207
+00:22:22,400 --> 00:22:35,360
+تمانين R ميتين و سبعين H V D D prime find find او
+
+208
+00:22:35,360 --> 00:22:38,340
+جد ليه ال inner
+
+209
+00:22:41,510 --> 00:22:47,710
+لمان لدي four بدنا ال inner atomorphism لدي four
+
+210
+00:22:47,710 --> 00:22:53,550
+solution
+
+211
+00:23:03,160 --> 00:23:08,840
+تعالى نشوف اللى هو ال elements المختلفة اللى بدنا
+
+212
+00:23:08,840 --> 00:23:13,480
+نجيبها من خلال ال elements اللى عندنا نتكلم احنا
+
+213
+00:23:13,480 --> 00:23:17,620
+على ال inner مدام على ال inner يبقى نتكلم على
+
+214
+00:23:17,620 --> 00:23:23,560
+functions كلها بهذا الشكل تمام؟ بدى أروح أجيب هنا
+
+215
+00:23:23,560 --> 00:23:34,730
+فاي ارتس ارزيرو as a function of xطبعا ال X مين يا
+
+216
+00:23:34,730 --> 00:23:41,130
+شباب ال X اي عنصر من هدول مين ماكان يكون يبقى هذا
+
+217
+00:23:41,130 --> 00:23:45,870
+لكل ال X اللي موجودة في G يبقى هذا حسب ال
+
+218
+00:23:45,870 --> 00:23:52,890
+definition بده يساوي R node X R node inverse حد
+
+219
+00:23:52,890 --> 00:23:59,030
+فيكم يقدر يقولي قداش الناتج؟كداش؟ X لأن هذا هو ال
+
+220
+00:23:59,030 --> 00:24:02,450
+identity element ومعكوس ال identity element ال
+
+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 ال element طيب كويس اذا تأثير في ارنود على
+
+223
+00:24:12,790 --> 00:24:17,350
+جميع أناصر جيه بيعطيني جميع أناصر دي حط على شجرة
+
+224
+00:24:17,350 --> 00:24:24,350
+الان بداجة اخد في ار مية وتمانين as a function of
+
+225
+00:24:24,350 --> 00:24:33,860
+Xيبقى هذا الكلام يبدو يساوي R180 X R180 Inverse
+
+226
+00:24:33,860 --> 00:24:41,360
+السؤال هو قبل مسافر اعطيتكوا ال center تبع ال D4
+
+227
+00:24:41,360 --> 00:24:46,860
+او ال DN قلنا لكوا اذا ال N فردي يبقى ال center
+
+228
+00:24:46,860 --> 00:24:53,340
+مافيه الا ال identity elementوإذا 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
+كميوتس مع جميع عناصر D4 إذا هذه لو بدلتها هنا بصير
+
+232
+00:25:10,100 --> 00:25:14,400
+X R180 IR 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 D4طب من
+
+235
+00:25:27,540 --> 00:25:33,520
+الاتنين هدول إذا الناتج هو نفسه معناته في ار نوت
+
+236
+00:25:33,520 --> 00:25:37,200
+تأثيرها على ال elements بتساوي في ار نوت تأثيرها
+
+237
+00:25:37,200 --> 00:25:40,920
+على الار مية و تمانين تأثيرها على ال elements يبقى
+
+238
+00:25:40,920 --> 00:25:49,640
+أصبح في ار نوت بتساوي في ار مية و تمانين تمام يبقى
+
+239
+00:25:49,640 --> 00:25:53,600
+هدول في ال atom morphism عنصرين ولا عنصر واحد
+
+240
+00:25:54,780 --> 00:26:01,440
+انصرين ولا واحد واحد ممتاز جدا طيب تعالى نشوف فاي
+
+241
+00:26:01,440 --> 00:26:10,120
+R ميتين وسبعين ميتين وسبعين تثيرها على X يبقى هذه
+
+242
+00:26:10,120 --> 00:26:19,700
+R ميتين وسبعين X R ميتين وسبعين inverse وتساويايش
+
+243
+00:26:19,700 --> 00:26:28,240
+رايك ال R270 بقدر اكتبها R180 مضروبة في R90 صحيح
+
+244
+00:26:28,240 --> 00:26:33,500
+ولا لا؟لأن هذه نفسها ال rotation هو نفسه ماعناه مش
+
+245
+00:26:33,500 --> 00:26:39,960
+مشكلة طيب هنا ال X ال R ميتين .. اه هذه R ميتين و
+
+246
+00:26:39,960 --> 00:26:45,220
+سبعين inverse حسب التعريف طبعا يبقى R ميتين و
+
+247
+00:26:45,220 --> 00:26:49,120
+سبعين inverse في ال H مش خليني اسألكوا السؤال
+
+248
+00:26:49,120 --> 00:26:56,640
+التالي R تلتمية و ستين كدهش تساوي يا شباب ارنود
+
+249
+00:26:56,640 --> 00:27:06,420
+طبعاطيب ارنود لو ضربتها في R تسعين انفرس بيصير ال
+
+250
+00:27:06,420 --> 00:27:17,440
+R ميتين و سبعين تساوي ال R تسعين انفرس يعني ضربت
+
+251
+00:27:17,440 --> 00:27:24,200
+الطرفين في مين؟ر تسعين انفرس يبقى بناء عليه الار
+
+252
+00:27:24,200 --> 00:27:30,500
+ميتين وسبعين انفرس الار ميتين وسبعين انفرس لو بدأ
+
+253
+00:27:30,500 --> 00:27:35,660
+اخد الانفرس هنا يقول هيعطيني من الانفرس هنا يبقى
+
+254
+00:27:35,660 --> 00:27:43,180
+الار ميتين وسبعين انفرس بده يساوي الار تسعين طيب
+
+255
+00:27:45,430 --> 00:27:54,010
+هذا الكلام بده يساوي هذه ال R التي هي
+
+256
+00:27:54,010 --> 00:28:02,850
+R تسعين inverse في R مية وتمانين inverseالـ R 180
+
+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 فاي R تسعين يبقى هذه فاي R تسعين as a
+
+261
+00:28:31,640 --> 00:28:39,440
+function of X يبقى بناء عليه أصبح عند هنا مين فاي
+
+262
+00:28:39,440 --> 00:28:48,640
+R ميتين وسبعين بده سوى فاي R تسعين هذه بروزناها
+
+263
+00:28:48,640 --> 00:28:54,030
+وهذه بروزناها النتيجة اللي حصلنا عليهايبقى خلصنا
+
+264
+00:28:54,030 --> 00:28:59,650
+من R نود و من R تسعين و من R مية و تمانين و من R
+
+265
+00:28:59,650 --> 00:29:07,710
+ميتين و سبعين بدنا نجي لامام لفاي H as a function
+
+266
+00:29:07,710 --> 00:29:19,670
+of X يبقى H X H inverse هذا الكلام يساوي بالدجل ال
+
+267
+00:29:19,670 --> 00:29:26,360
+H عندنالو روحت فتحت على الجدول صفحة واحد و تلاتين
+
+268
+00:29:26,360 --> 00:29:33,100
+تابع الكلتاب اللامان لل دي فور صفحة واحد و تلاتين
+
+269
+00:29:33,100 --> 00:29:40,460
+وروح تدور على ح ممكن تساوي هلاجيها R مية و تمانين
+
+270
+00:29:40,460 --> 00:29:47,490
+في Vيبقى ر مية و تمانين في V هي ال H إذا ممكن
+
+271
+00:29:47,490 --> 00:29:56,890
+أشيلها و أكتب ر مية و تمانين V في ال X في ال R مية
+
+272
+00:29:56,890 --> 00:30:05,800
+و تمانين V لكل inverseطب 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 ال R180 كون ال R180 في ال 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
+فى V فى ال X هذه ال inverse اللى 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
+بال identity ايش بصير عندنا هنا VX V inverse يبقى
+
+280
+00:30:48,770 --> 00:30:57,900
+هذه مين هذه Phi V of Xيبقى بناء عليه أصبح عندي فاي
+
+281
+00:30:57,900 --> 00:31:06,700
+H هي عبارة عن فاي V بقى اللي عندي أخر حاجة فاي 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
+Inverseبنفس الطريقة اللى جبت فيها H بدى أروح أجيب
+
+284
+00:31:21,100 --> 00:31:28,460
+D' بروح بفتح الجدول صفحة واحد و تلاتين على ال D'
+
+285
+00:31:29,220 --> 00:31:35,820
+على من؟ على ال D' بدى R مية و تمانين عشان يجيبلي
+
+286
+00:31:35,820 --> 00:31:42,530
+D' بصير R مية و تمانين في Dيبقى بشيلها و بكتب
+
+287
+00:31:42,530 --> 00:31:51,250
+بدالها R مية و تمانين في D في X في ال 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 و تمانين في D
+
+290
+00:32:12,070 --> 00:32:18,930
+يبقى هذه مع هذه بمين بال identity element تمام
+
+291
+00:32:18,930 --> 00:32:26,920
+يبقى النتيجة هتعطيك DX D inverseهذه هي عبارة عن
+
+292
+00:32:26,920 --> 00:32:35,380
+main فايدي of x يبقى بناء عليه أصبح فايدي prime
+
+293
+00:32:35,380 --> 00:32:38,300
+بده يساوي فايدي
+
+294
+00:32:40,110 --> 00:32:45,830
+يبقى التمانية inner atomorphism
+
+295
+00:32:45,830 --> 00:32:54,030
+صاروا كده؟ أربعة وليست تمانية 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 سا ال inner atomorphism ل D for هو عبارة
+
+298
+00:33:19,170 --> 00:33:26,130
+عن ال في R نوت طبعا يسوي في R مية و تمانين والتاني
+
+299
+00:33:26,130 --> 00:33:33,850
+في R تسعين اللي يسوي في R ميتين وسبعين والتالت
+
+300
+00:33:33,850 --> 00:33:39,690
+اللي هو في H والرابع اللي هو main في D بهذا الشكل
+
+301
+00:33:40,480 --> 00:33:46,740
+يبقى هدول ال inner atomorphism لمن؟ لـG السؤال هو
+
+302
+00:33:46,740 --> 00:33:53,380
+هل ال inner atomorphism لـG أقل من ذلك و اللهيهم
+
+303
+00:33:53,380 --> 00:33:58,720
+الأربعة فيش غيرهم بمعنى أخر هل الأربعة هدول بقدر
+
+304
+00:33:58,720 --> 00:34:04,040
+أخسرهم لتلاتة ولا لاتنين تعالوا نشوفوا نتأكد من
+
+305
+00:34:04,040 --> 00:34:09,640
+هذا الكلام أنا أدعي أن هذه الأربعة are destined
+
+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 الفي
+
+308
+00:34:29,580 --> 00:34:31,260
+دي are destiny
+
+309
+00:34:34,120 --> 00:34:38,580
+إذا Destinate معناته إيه؟ معناته إنه فعلا الـ
+
+310
+00:34:38,580 --> 00:34:43,080
+Inner Atomorphism فيه الـD و الـG مافيش فيه إلا
+
+311
+00:34:43,080 --> 00:34:49,600
+الأربع عناصر هدول أو الأربع Inner Atomorphism مشان
+
+312
+00:34:49,600 --> 00:34:54,540
+أثبتهم Destinate يكفيني counter example واحد لكل
+
+313
+00:34:54,540 --> 00:34:59,670
+واحدة فيهم تعالى نشوفالان انا ادعى انهم هذول
+
+314
+00:34:59,670 --> 00:35:06,830
+destinect اذا لو جيت قلت فاي ار نود و بده اخليه
+
+315
+00:35:06,830 --> 00:35:15,910
+اثر مثلا على اتش اخد اتش عشوائيا من ال D4 يبقى هذا
+
+316
+00:35:15,910 --> 00:35:23,290
+بده يسوي ار نود اتش ار نود اللي هو main ب اتشالان
+
+317
+00:35:23,290 --> 00:35:31,170
+بدأ اخد فاي 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 و يساوي
+
+319
+00:35:39,850 --> 00:35:46,370
+برضه بده ارجع للجدول R تسعين H اللي في صفحة واحدة
+
+320
+00:35:46,370 --> 00:35:55,890
+و تلاتين R تسعين HR تسعين تضربها في H بيطلع D
+
+321
+00:35:55,890 --> 00:36:02,590
+Prime يبقى هذي D Prime R تسعين Inverse اللي هي
+
+322
+00:36:02,590 --> 00:36:09,250
+بمين بR ميتين والسبعين يبقى R ميتين والسبعين ال D
+
+323
+00:36:09,250 --> 00:36:13,950
+Prime في ال R ميتين والسبعين عندك D Prime في ال R
+
+324
+00:36:13,950 --> 00:36:20,340
+ميتين والسبعين اللي هو بيعطيلك V بيعطيلك Vهذه
+
+325
+00:36:20,340 --> 00:36:29,460
+اعطتنى H وهذه اعطتنى V إذا لا يمكن لل R لل FI R
+
+326
+00:36:29,460 --> 00:36:37,460
+تسعين انه يساوي مين انه يساوي ال FI R نوت الان
+
+327
+00:36:37,460 --> 00:36:45,240
+بالمثل لو جيت قولت FI R تسعين بدي ابحثها مع مين مع
+
+328
+00:36:45,240 --> 00:36:50,710
+FI H بدي اثبت انه مفيش تساوي فيما بينهمايبقى في ار
+
+329
+00:36:50,710 --> 00:36:57,030
+تسعين مثلا لو خلتها تأثر على ار تسعين يبقاش بيصير
+
+330
+00:36:57,030 --> 00:37:05,510
+ار تسعين ار تسعين ار تسعين انفرس اللي هو بقداش ار
+
+331
+00:37:05,510 --> 00:37:14,770
+تسعين الان بدي انا اخد في اتشر 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 بالداجل ال H R تسعين برضه من
+
+334
+00:37:30,090 --> 00:37:37,710
+صفحة واحدة وتلاتينبدي من؟ بدي ال H R تسعين عندك ال
+
+335
+00:37:37,710 --> 00:37:46,570
+H R تسعين اللي هي ب D دي دي طب و ال H انفرس مش هي
+
+336
+00:37:46,570 --> 00:37:54,720
+H يا شباب ولا لا؟ سكت الشعبالعناصر اللي عندنا هذه
+
+337
+00:37:54,720 --> 00:37:59,260
+هو الراحة H تربيها تساوي V تربيها تساوي D تربيها
+
+338
+00:37:59,260 --> 00:38:03,460
+تساوي D تربيها تساوي ال identity قولنا يبقى الـH
+
+339
+00:38:03,460 --> 00:38:06,900
+والـH inverse DD inverse VV inverse D prime يا D
+
+340
+00:38:06,900 --> 00:38:10,480
+prime inverse، مظبوط؟ إذا اشيلتها وحطيت قيمتها،
+
+341
+00:38:10,480 --> 00:38:16,680
+الآن بدي أشوف الـDH مين هي، يبقى لو جيت لـD في H،
+
+342
+00:38:16,680 --> 00:38:25,460
+D في H باللي بقى 270يبقى هذه بدها تساوي الار متين
+
+343
+00:38:25,460 --> 00:38:30,980
+وسبعين يبقى من الاتنين هدول معناه هذا الكلام اللي
+
+344
+00:38:30,980 --> 00:38:37,780
+هو فاي ار تسعين لا يمكن ان تساوي الفاي اتش اللي
+
+345
+00:38:37,780 --> 00:38:43,590
+عندنا بقى اللي عندنا مين بقى الفايدينالان احنا
+
+346
+00:38:43,590 --> 00:38:47,850
+بياننا هى التنتين الاولى نياتى و هى التنتين
+
+347
+00:38:47,850 --> 00:38:53,850
+التانيات و هى التنتين اللى بعضهم فاي R تسعين برضه
+
+348
+00:38:53,850 --> 00:38:59,770
+بده يخلى يأثر على R تسعين اعطانى R تسعين itself
+
+349
+00:38:59,770 --> 00:39:08,140
+بده اخد اخر واحدة فاي Dلما تأثر على R تسعين يبقى
+
+350
+00:39:08,140 --> 00:39:16,660
+هذا الكلام يساوي DR تسعين D inverseهو يساوي بدي
+
+351
+00:39:16,660 --> 00:39:22,760
+أجيب له ال D R تسعين من الجدول ال D R تسعين عبارة
+
+352
+00:39:22,760 --> 00:39:30,140
+عن V يبقى هذه V و ال D inverse هي عبارة عن D بدي
+
+353
+00:39:30,140 --> 00:39:38,300
+أجيب له ال V في D يبقى ال V في D اللي يبقى R ميتين
+
+354
+00:39:38,300 --> 00:39:46,120
+وسبعينيبقى هذه تساوي R ميتين وسبعين ملي اتنين هدول
+
+355
+00:39:46,120 --> 00:39:54,260
+بس تنتج ان الفاي R تسعين لا يمكن ان تساوي الفاي D
+
+356
+00:39:55,610 --> 00:40:00,970
+اللي عملته انا لسه شغلة اثبت ان الـ Phi R تسعين لا
+
+357
+00:40:00,970 --> 00:40:05,030
+بتساوي هذه ولا بتساوي هذه ولا بتساوي هذه الان انت
+
+358
+00:40:05,030 --> 00:40:09,710
+بكتب ان ال Phi H بساويش هذه Phi H بساويش هذه و Phi
+
+359
+00:40:09,710 --> 00:40:14,590
+H بساويش هذه و بعدين Phi 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 فاي اتش and فاي دي thus و
+
+362
+00:40:28,530 --> 00:40:35,850
+هكذا ال inner atom morphism اللي دي for هو عبارة
+
+363
+00:40:35,850 --> 00:40:46,050
+عن الفاي ار نود و الفاي ار تسعين و الفاي اتش و
+
+364
+00:40:46,050 --> 00:40:55,540
+الفاي ديفقط لا غير طيب بدي أسأل السؤال التالي أنا
+
+365
+00:40:55,540 --> 00:41:01,360
+أخد تأثير ال R node على H و R node على H طب لو
+
+366
+00:41:01,360 --> 00:41:08,060
+غيرت ال H هذه يمكن يطلع اتنين زي بعض اه دير بالك
+
+367
+00:41:08,060 --> 00:41:13,370
+اصبر شوية اصبر عليا شويةانا هنا اثبت له ان الارد
+
+368
+00:41:13,370 --> 00:41:18,690
+نود الارد نود هي الارد مية و تمانين على مين على
+
+369
+00:41:18,690 --> 00:41:25,270
+اكس هل ال X اخترت رمز معين ولا جيت على تمانية رموز
+
+370
+00:41:25,270 --> 00:41:30,770
+على تمانية ممتاز اذاإذا 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 استثناءاذا
+
+375
+00:41:52,620 --> 00:41:58,260
+لو لجيت رمز واحد من التمانية التساوي غير حاصل زي
+
+376
+00:41:58,260 --> 00:42:04,160
+ما شوفت هنا يبقى هدول يمكن ان يتساوى رغم ان 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؟ ايوة مش سامع ايش
+
+379
+00:42:15,720 --> 00:42:18,220
+بتقول هلصوتك
+
+380
+00:42:23,350 --> 00:42:24,650
+مين المتساوين؟
+
+381
+00:42:33,630 --> 00:42:38,550
+ماعنديش مشكلة انا بقولك انه ممكن يحصل تساوي لكن
+
+382
+00:42:38,550 --> 00:42:42,710
+اذا بدك التساوي على جميع العناصر وليس على بعضها
+
+383
+00:42:42,710 --> 00:42:47,130
+عشان يحصل التساوي طبعا اذا انا من التمان عناصر
+
+384
+00:42:47,130 --> 00:42:52,650
+فبعد if لو لجيت عنصر واحد التساوي غير حاصل اذا in
+
+385
+00:42:52,650 --> 00:42:56,670
+general التساوي غير حاصلمشان 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 و لو انه 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 الكمبيوت احسبلي ال atomorphism ل z
+
+394
+00:44:02,000 --> 00:44:04,080
+منين ل z عشرة
+
+395
+00:44:12,500 --> 00:44:17,500
+أنا بدي احسب له كل الاتومورفزم لـ Z10 يعني انا بدي
+
+396
+00:44:17,500 --> 00:44:24,460
+function من Z10 إلى Z10 تبقى وانت وان وانت 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 الاتومورفزم لمين؟ لـ Z10 طبعا
+
+399
+00:44:35,480 --> 00:44:41,590
+هنثبت ان هدول أربعة فقط لغيروهذا ما سيكون في
+
+400
+00:44:41,590 --> 00:44:45,690
+المحاضرة بعض الظهر لإنه ماضلش 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 ان شاء
+
+404
+00:44:58,290 --> 00:45:02,510
+الله بنوضحها لك و بنفهمها لك في المحاضرة القادمة
+
+405
+00:45:02,510 --> 00:45:04,170
+ان شاء الله يعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..c2c023d59fcaee27b7575e4718a4427f83c9a99f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/0riEDI3L2MA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4102, "start": 21.24, "end": 41.02, "text": "لازلنا في شبتر ستة وهو ال isomorphism المرة اللى فاتت عرفنا ال atomorphism وعرفنا انه عبارة عن isomorphism لكن من ال group إلى نفس ال group وبالتالي سمناه atomorphism", "tokens": [1211, 31377, 1211, 8315, 8978, 13412, 3555, 2655, 2288, 8608, 2655, 3660, 37037, 2407, 2423, 307, 32702, 1434, 9673, 25720, 13672, 7578, 6156, 9307, 2655, 6225, 28480, 8315, 2423, 12018, 18191, 1434, 4032, 3615, 28480, 8315, 16472, 3224, 6225, 3555, 9640, 3660, 18871, 307, 32702, 1434, 44381, 9154, 2423, 1594, 30731, 8717, 36178, 2423, 1594, 46599, 6027, 2655, 6027, 1829, 8608, 2304, 8315, 3224, 12018, 18191, 1434], "avg_logprob": -0.2176010957097306, "compression_ratio": 1.6556291390728477, "no_speech_prob": 0.0, "words": [{"start": 21.24, "end": 22.18, "word": "لازلنا", "probability": 0.77392578125}, {"start": 22.18, "end": 22.5, "word": " في", "probability": 0.84423828125}, {"start": 22.5, "end": 23.06, "word": " شبتر", "probability": 0.73773193359375}, {"start": 23.06, "end": 23.72, "word": " ستة", "probability": 0.9016927083333334}, {"start": 23.72, "end": 24.5, "word": " وهو", "probability": 0.7257080078125}, {"start": 24.5, "end": 24.76, "word": " ال", "probability": 0.87841796875}, {"start": 24.76, "end": 26.28, "word": " isomorphism", "probability": 0.6940104166666666}, {"start": 26.28, "end": 27.26, "word": " المرة", "probability": 0.838623046875}, {"start": 27.26, "end": 27.44, "word": " اللى", "probability": 0.604248046875}, {"start": 27.44, "end": 27.82, "word": " فاتت", "probability": 0.8841145833333334}, {"start": 27.82, "end": 28.54, "word": " عرفنا", "probability": 0.8582356770833334}, {"start": 28.54, "end": 28.9, "word": " ال", "probability": 0.9638671875}, {"start": 28.9, "end": 30.08, "word": " atomorphism", "probability": 0.6494140625}, {"start": 30.08, "end": 32.06, "word": " وعرفنا", "probability": 0.8961181640625}, {"start": 32.06, "end": 32.68, "word": " انه", "probability": 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"probability": 0.7236328125}, {"start": 39.84, "end": 41.02, "word": " atomorphism", "probability": 0.9099934895833334}], "temperature": 1.0}, {"id": 2, "seek": 6670, "start": 41.46, "end": 66.7, "text": "عرفنا كمان الـ Inner Atomorphism induced by an element of A group G وقلنا الـ Phi A of X يساوي A X A inverse وسمينا هذا الـ Inner Atomorphism من G الآن لو جمعنا كل الـ Atomorphism في G وسميناهم الست", "tokens": [3615, 28480, 8315, 9122, 2304, 7649, 2423, 39184, 36705, 1711, 32702, 1434, 33991, 538, 364, 4478, 295, 316, 1594, 460, 4032, 4587, 1211, 8315, 2423, 39184, 41435, 316, 295, 1783, 7251, 3794, 995, 45865, 316, 1783, 316, 17340, 4032, 38251, 1829, 8315, 23758, 2423, 39184, 36705, 1711, 32702, 1434, 9154, 460, 6024, 48506, 45164, 10874, 2304, 3615, 8315, 28242, 2423, 39184, 1711, 32702, 1434, 8978, 460, 4032, 38251, 1829, 8315, 16095, 2423, 14851], "avg_logprob": -0.28061654197203145, "compression_ratio": 1.4833333333333334, "no_speech_prob": 0.0, "words": [{"start": 41.46, 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"end": 81.19, "word": " كل", "probability": 0.90576171875}, {"start": 81.19, "end": 81.51, "word": " ال", "probability": 0.95654296875}, {"start": 81.51, "end": 82.97, "word": " atomorphism", "probability": 0.8824869791666666}, {"start": 82.97, "end": 83.43, "word": " اللي", "probability": 0.946533203125}, {"start": 83.43, "end": 83.99, "word": " موجودة", "probability": 0.9715576171875}, {"start": 83.99, "end": 84.11, "word": " في", "probability": 0.93212890625}, {"start": 84.11, "end": 84.25, "word": " ال", "probability": 0.55322265625}, {"start": 84.25, "end": 84.61, "word": " group", "probability": 0.98095703125}, {"start": 84.61, "end": 85.61, "word": " G", "probability": 0.9208984375}, {"start": 85.61, "end": 85.95, "word": " ال", "probability": 0.771484375}, {"start": 85.95, "end": 86.33, "word": " inner", "probability": 0.86962890625}, {"start": 86.33, "end": 87.41, "word": " atomorphism", "probability": 0.91796875}, {"start": 87.41, "end": 87.65, "word": " ل", "probability": 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الاطمورفزم وال inner-automorphism لجروب جي كل واحد فيهم عبارة عن جروب", "tokens": [3555, 2655, 39648, 45164, 25961, 2655, 10874, 1829, 10874, 32887, 3555, 7251, 3555, 4587, 7578, 2423, 41193, 2304, 13063, 5172, 11622, 2304, 16070, 7284, 12, 1375, 32702, 1434, 5296, 7435, 32887, 3555, 10874, 1829, 28242, 36764, 24401, 8978, 16095, 6225, 3555, 9640, 3660, 18871, 10874, 32887, 3555], "avg_logprob": -0.30989584016303223, "compression_ratio": 1.2440944881889764, "no_speech_prob": 0.0, "words": [{"start": 93.69, "end": 94.21, "word": "بتقول", "probability": 0.6785074869791666}, {"start": 94.21, "end": 94.49, "word": " لو", "probability": 0.79345703125}, {"start": 94.49, "end": 95.05, "word": " كانت", "probability": 0.82275390625}, {"start": 95.05, "end": 95.25, "word": " جي", "probability": 0.7010498046875}, {"start": 95.25, "end": 95.79, "word": " جروب", "probability": 0.6910807291666666}, {"start": 95.79, "end": 96.27, "word": " يبقى", "probability": 0.8892822265625}, {"start": 96.27, 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identity element الآن ال I من G إلى G هذه is the identity function", "tokens": [271, 4180, 1166, 7251, 3555, 4587, 7578, 8978, 8592, 11778, 45761, 1829, 5551, 32887, 5016, 8717, 25957, 1211, 11296, 5296, 28814, 1863, 8315, 6225, 9640, 5172, 9957, 36145, 11296, 29538, 7251, 3555, 4587, 7578, 1975, 2655, 5016, 4587, 38149, 9154, 33962, 33546, 10632, 6024, 104, 7649, 10632, 47525, 8315, 8717, 32887, 5016, 8717, 7435, 1829, 3555, 16490, 33546, 10632, 2423, 6575, 4478, 6024, 48506, 2423, 286, 9154, 460, 30731, 460, 29538, 307, 264, 6575, 2445], "avg_logprob": -0.196443253049725, "compression_ratio": 1.540983606557377, "no_speech_prob": 0.0, "words": [{"start": 414.16, "end": 414.88, "word": "is", "probability": 0.59765625}, {"start": 414.88, "end": 416.96, "word": " associative", "probability": 0.9501953125}, {"start": 416.96, "end": 418.22, "word": " يبقى", "probability": 0.7935791015625}, {"start": 418.22, "end": 418.52, "word": " فيش", "probability": 0.4144287109375}, {"start": 418.52, 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"start": 746.48, "end": 772.36, "text": "لأن الـ subgroup هي مجموعة جزئية من المجموعة الأصلية بس تحت نفس العملية إذا لو قدرت أثبت إن ال inner atomorphisms اللي جيه هي عبارة عن subgroup من ال atomorphism اللي جيه بصير هذه group ونكون انتهينا من المسألة هذه يبقى بدنا نروح نثبتها", "tokens": [1211, 33456, 2423, 39184, 1422, 17377, 39896, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 9154, 9673, 7435, 2304, 2407, 27884, 16247, 9381, 1211, 10632, 4724, 3794, 6055, 33753, 8717, 36178, 18863, 42213, 10632, 11933, 15730, 45164, 12174, 3215, 43500, 5551, 12984, 3555, 2655, 36145, 2423, 7284, 12018, 18191, 13539, 13672, 1829, 10874, 1829, 3224, 39896, 6225, 3555, 9640, 3660, 18871, 1422, 17377, 9154, 2423, 12018, 18191, 1434, 13672, 1829, 10874, 1829, 3224, 4724, 9381, 13546, 29538, 1594, 4032, 1863, 30544, 16472, 47395, 1829, 8315, 9154, 9673, 3794, 10721, 37977, 29538, 7251, 3555, 4587, 7578, 47525, 8315, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 11296], "avg_logprob": 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{"start": 754.08, "end": 754.48, "word": " نفس", "probability": 0.997314453125}, {"start": 754.48, "end": 755.16, "word": " العملية", "probability": 0.9881184895833334}, {"start": 755.16, "end": 755.88, "word": " إذا", "probability": 0.76025390625}, {"start": 755.88, "end": 756.12, "word": " لو", "probability": 0.97998046875}, {"start": 756.12, "end": 756.56, "word": " قدرت", "probability": 0.9091796875}, {"start": 756.56, "end": 757.12, "word": " أثبت", "probability": 0.984375}, {"start": 757.12, "end": 757.4, "word": " إن", "probability": 0.443603515625}, {"start": 757.4, "end": 757.64, "word": " ال", "probability": 0.9208984375}, {"start": 757.64, "end": 758.06, "word": " inner", "probability": 0.73046875}, {"start": 758.06, "end": 759.28, "word": " atomorphisms", "probability": 0.47705078125}, {"start": 759.28, "end": 759.74, "word": " اللي", "probability": 0.870361328125}, {"start": 759.74, "end": 760.58, "word": " جيه", "probability": 0.7991536458333334}, {"start": 760.58, "end": 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"word": " a", "probability": 0.900390625}, {"start": 778.26, "end": 778.84, "word": " group", "probability": 0.9716796875}, {"start": 778.84, "end": 779.94, "word": " مشان", "probability": 0.711669921875}, {"start": 779.94, "end": 780.5, "word": " أثبتها", "probability": 0.91396484375}, {"start": 780.5, "end": 780.96, "word": " group", "probability": 0.88623046875}, {"start": 780.96, "end": 781.36, "word": " بدأ", "probability": 0.478515625}, {"start": 781.36, "end": 781.78, "word": " أثبتها", "probability": 0.966796875}, {"start": 781.78, "end": 782.22, "word": " sub", "probability": 0.7861328125}, {"start": 782.22, "end": 782.64, "word": " group", "probability": 0.4873046875}, {"start": 782.64, "end": 782.88, "word": " من", "probability": 0.97314453125}, {"start": 782.88, "end": 783.04, "word": " ال", "probability": 0.87646484375}, {"start": 783.04, "end": 783.3, "word": " atom", "probability": 0.59033203125}, {"start": 783.3, "end": 784.06, "word": " morphism", "probability": 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"tokens": [6027, 39184, 36705, 1711, 32702, 1434, 5296, 39184, 460], "avg_logprob": -0.6718750119209289, "compression_ratio": 0.8611111111111112, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 826.3, "end": 826.88, "word": "الـ", "probability": 0.2869873046875}, {"start": 826.88, "end": 827.26, "word": " Inner", "probability": 0.49853515625}, {"start": 827.26, "end": 828.88, "word": " Atomorphism", "probability": 0.8391927083333334}, {"start": 828.88, "end": 829.56, "word": " لـ", "probability": 0.823486328125}, {"start": 829.56, "end": 829.74, "word": " G", "probability": 0.52880859375}], "temperature": 1.0}, {"id": 36, "seek": 86791, "start": 841.13, "end": 867.91, "text": "انا بتدعي انه ال identity element الان بدى بين ان هذا هو ال identity element تبع ال atomorphism يبقى هذا بدى يعطيني ان ال phi E of X يساوي ال X يساوي شريك ال X هذه لو ضربت في ال identity element تتغير يعني لو قلتلك هذه E X صح ولا غلط؟", "tokens": [7649, 995, 39894, 3215, 3615, 1829, 16472, 3224, 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1156.25, "word": " a", "probability": 0.9248046875}, {"start": 1156.25, "end": 1157.47, "word": " subgroup", "probability": 0.787109375}, {"start": 1157.47, "end": 1158.17, "word": " من", "probability": 0.97998046875}, {"start": 1158.17, "end": 1158.49, "word": " ال", "probability": 0.9384765625}, {"start": 1158.49, "end": 1160.15, "word": " atomorphism", "probability": 0.8961588541666666}, {"start": 1160.15, "end": 1160.91, "word": " لجي", "probability": 0.8260091145833334}, {"start": 1160.91, "end": 1161.91, "word": " هذا", "probability": 0.92333984375}, {"start": 1161.91, "end": 1162.97, "word": " بيعطينا", "probability": 0.8865234375}], "temperature": 1.0}, {"id": 49, "seek": 119205, "start": 1188.29, "end": 1192.05, "text": "حد لو يتساول بالنسبة للنظرية", "tokens": [5016, 3215, 45164, 7251, 2655, 3794, 995, 12610, 20666, 1863, 35457, 3660, 24976, 1863, 19913, 2288, 10632], "avg_logprob": -0.2790798528326882, "compression_ratio": 0.9454545454545454, "no_speech_prob": 0.0, "words": [{"start": 1188.2900000000002, "end": 1189.65, "word": "حد", "probability": 0.50860595703125}, {"start": 1189.65, "end": 1189.89, "word": " لو", "probability": 0.89453125}, {"start": 1189.89, "end": 1190.57, "word": " يتساول", "probability": 0.814013671875}, {"start": 1190.57, "end": 1191.23, "word": " بالنسبة", "probability": 0.91943359375}, {"start": 1191.23, "end": 1192.05, "word": " للنظرية", "probability": 0.96416015625}], "temperature": 1.0}, {"id": 50, "seek": 121781, "start": 1195.71, "end": 1217.81, "text": "علي صوتك شوية عشان نثبت انها non-empty ممتاز تعال هنا تعال تعال الحق الحق قول", "tokens": [3615, 20292, 20328, 35473, 4117, 13412, 2407, 10632, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 16472, 11296, 2107, 12, 4543, 88, 3714, 2304, 2655, 31377, 37279, 6027, 34105, 37279, 6027, 37279, 6027, 1975, 1211, 5016, 4587, 1975, 1211, 5016, 4587, 12174, 12610], "avg_logprob": -0.3793604734332062, "compression_ratio": 1.3232323232323233, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1195.71, "end": 1196.13, "word": "علي", "probability": 0.484375}, {"start": 1196.13, "end": 1196.53, "word": " صوتك", "probability": 0.9938151041666666}, {"start": 1196.53, "end": 1196.97, "word": " شوية", "probability": 0.9222005208333334}, {"start": 1196.97, "end": 1202.03, "word": " عشان", "probability": 0.4839884440104167}, {"start": 1202.03, "end": 1202.51, "word": " نثبت", "probability": 0.9310302734375}, {"start": 1202.51, "end": 1202.77, "word": " انها", "probability": 0.85302734375}, {"start": 1202.77, "end": 1203.09, "word": " non", "probability": 0.6513671875}, {"start": 1203.09, "end": 1203.71, "word": "-empty", "probability": 0.733154296875}, {"start": 1203.71, "end": 1204.23, "word": " ممتاز", "probability": 0.774169921875}, {"start": 1204.23, "end": 1213.11, "word": " تعال", "probability": 0.58770751953125}, {"start": 1213.11, "end": 1213.33, "word": " هنا", "probability": 0.92626953125}, {"start": 1213.33, "end": 1213.69, "word": " تعال", 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{"start": 1249.51, "end": 1250.07, "word": " يسوي", "probability": 0.8937174479166666}, {"start": 1250.07, "end": 1250.53, "word": " E", "probability": 0.7060546875}, {"start": 1250.53, "end": 1250.91, "word": " X", "probability": 0.638671875}, {"start": 1250.91, "end": 1251.21, "word": " E", "probability": 0.96533203125}, {"start": 1251.21, "end": 1251.65, "word": " inverse", "probability": 0.73974609375}, {"start": 1251.65, "end": 1252.69, "word": " هذا", "probability": 0.51220703125}, {"start": 1252.69, "end": 1253.79, "word": " شكل", "probability": 0.915771484375}, {"start": 1253.79, "end": 1254.19, "word": " inner", "probability": 0.869140625}, {"start": 1254.19, "end": 1254.67, "word": " atomorphism", "probability": 0.9041341145833334}, {"start": 1254.67, "end": 1255.39, "word": " وبالتالي", "probability": 0.948828125}, {"start": 1255.39, "end": 1255.77, "word": " هذا", "probability": 0.8935546875}, {"start": 1255.77, "end": 1256.29, "word": " موجود", "probability": 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خلال ال elements اللى عندنا نتكلم احنا على ال inner مدام على ال inner يبقى نتكلم على functions كلها بهذا الشكل تمام؟ بدى أروح أجيب هنا فاي ارتس ارزيرو as a function of x", "tokens": [2655, 3615, 6027, 7578, 8717, 8592, 38688, 13672, 7578, 31439, 2423, 4959, 9673, 46456, 46538, 3660, 13672, 7578, 47525, 8315, 8717, 7435, 1829, 3555, 11296, 9154, 16490, 1211, 6027, 2423, 4959, 13672, 7578, 43242, 8315, 8717, 2655, 4117, 19528, 1975, 5016, 8315, 15844, 2423, 7284, 3714, 3215, 10943, 15844, 2423, 7284, 7251, 3555, 4587, 7578, 8717, 2655, 4117, 19528, 15844, 6828, 28242, 11296, 39627, 15730, 25124, 28820, 46811, 10943, 22807, 47525, 7578, 5551, 32887, 5016, 5551, 7435, 1829, 3555, 34105, 6156, 47302, 1975, 2288, 2655, 3794, 1975, 2288, 11622, 13546, 2407, 382, 257, 2445, 295, 2031], "avg_logprob": -0.18959407708079545, "compression_ratio": 1.806930693069307, "no_speech_prob": 0.0, "words": [{"start": 1383.16, "end": 1383.6, "word": "تعالى", "probability": 0.8062744140625}, {"start": 1383.6, 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تسعين", "probability": 0.9332275390625}, {"start": 2332.85, "end": 2333.85, "word": " برضه", "probability": 0.9840494791666666}, {"start": 2333.85, "end": 2334.27, "word": " بده", "probability": 0.711181640625}, {"start": 2334.27, "end": 2334.59, "word": " يخلى", "probability": 0.6346028645833334}, {"start": 2334.59, "end": 2335.29, "word": " يأثر", "probability": 0.7752278645833334}, {"start": 2335.29, "end": 2335.79, "word": " على", "probability": 0.822265625}, {"start": 2335.79, "end": 2336.23, "word": " R", "probability": 0.814453125}, {"start": 2336.23, "end": 2336.91, "word": " تسعين", "probability": 0.9920654296875}, {"start": 2336.91, "end": 2338.13, "word": " اعطانى", "probability": 0.93056640625}, {"start": 2338.13, "end": 2338.53, "word": " R", "probability": 0.91650390625}, {"start": 2338.53, "end": 2339.13, "word": " تسعين", "probability": 0.9949951171875}, {"start": 2339.13, "end": 2339.77, "word": " itself", "probability": 0.6123046875}, {"start": 2339.77, "end": 2340.63, "word": " بده", "probability": 0.861328125}, {"start": 2340.63, "end": 2341.15, "word": " اخد", "probability": 0.6468098958333334}, {"start": 2341.15, "end": 2341.57, "word": " اخر", "probability": 0.89697265625}, {"start": 2341.57, "end": 2342.15, "word": " واحدة", "probability": 0.9210611979166666}, {"start": 2342.15, "end": 2342.85, "word": " فاي", "probability": 0.722412109375}, {"start": 2342.85, "end": 2343.13, "word": " D", "probability": 0.87158203125}], "temperature": 1.0}, {"id": 97, "seek": 235371, "start": 2343.58, "end": 2353.72, "text": "لما تأثر على R تسعين يبقى هذا الكلام يساوي DR تسعين D inverse", "tokens": [1211, 15042, 6055, 10721, 49115, 15844, 497, 6055, 3794, 3615, 9957, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 12118, 6055, 3794, 3615, 9957, 413, 17340], "avg_logprob": -0.2663810503098272, "compression_ratio": 1.1379310344827587, "no_speech_prob": 0.0, "words": [{"start": 2343.58, "end": 2344.66, "word": "لما", 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0.6337890625}], "temperature": 1.0}, {"id": 98, "seek": 237902, "start": 2355.14, "end": 2379.02, "text": "هو يساوي بدي أجيب له ال D R تسعين من الجدول ال D R تسعين عبارة عن V يبقى هذه V و ال D inverse هي عبارة عن D بدي أجيب له ال V في D يبقى ال V في D اللي يبقى R ميتين وسبعين", "tokens": [3224, 2407, 7251, 3794, 995, 45865, 4724, 16254, 5551, 7435, 1829, 3555, 46740, 2423, 413, 497, 6055, 3794, 3615, 9957, 9154, 25724, 3215, 12610, 2423, 413, 497, 6055, 3794, 3615, 9957, 6225, 3555, 9640, 3660, 18871, 691, 7251, 3555, 4587, 7578, 29538, 691, 4032, 2423, 413, 17340, 39896, 6225, 3555, 9640, 3660, 18871, 413, 4724, 16254, 5551, 7435, 1829, 3555, 46740, 2423, 691, 8978, 413, 7251, 3555, 4587, 7578, 2423, 691, 8978, 413, 13672, 1829, 7251, 3555, 4587, 7578, 497, 3714, 36081, 9957, 4032, 35457, 3615, 9957], "avg_logprob": -0.24644886939363045, "compression_ratio": 1.8079470198675496, "no_speech_prob": 0.0, "words": [{"start": 2355.14, "end": 2355.36, "word": "هو", "probability": 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{"start": 2361.02, "end": 2361.5, "word": " R", "probability": 0.884765625}, {"start": 2361.5, "end": 2362.16, "word": " تسعين", "probability": 0.99267578125}, {"start": 2362.16, "end": 2362.76, "word": " عبارة", "probability": 0.9869384765625}, {"start": 2362.76, "end": 2363.2, "word": " عن", "probability": 0.98779296875}, {"start": 2363.2, "end": 2363.54, "word": " V", "probability": 0.953125}, {"start": 2363.54, "end": 2364.88, "word": " يبقى", "probability": 0.9461669921875}, {"start": 2364.88, "end": 2365.34, "word": " هذه", "probability": 0.3427734375}, {"start": 2365.34, "end": 2365.74, "word": " V", "probability": 0.9755859375}, {"start": 2365.74, "end": 2366.5, "word": " و", "probability": 0.63818359375}, {"start": 2366.5, "end": 2366.7, "word": " ال", "probability": 0.38037109375}, {"start": 2366.7, "end": 2366.92, "word": " D", "probability": 0.97021484375}, {"start": 2366.92, "end": 2367.52, "word": " inverse", "probability": 0.45849609375}, {"start": 2367.52, "end": 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هدول", "probability": 0.8719075520833334}, {"start": 2386.12, "end": 2386.82, "word": " بس", "probability": 0.87646484375}, {"start": 2386.82, "end": 2387.42, "word": " تنتج", "probability": 0.9830729166666666}, {"start": 2387.42, "end": 2387.78, "word": " ان", "probability": 0.8994140625}, {"start": 2387.78, "end": 2388.6, "word": " الفاي", "probability": 0.46441650390625}, {"start": 2388.6, "end": 2389.12, "word": " R", "probability": 0.8974609375}, {"start": 2389.12, "end": 2390.08, "word": " تسعين", "probability": 0.98681640625}, {"start": 2390.08, "end": 2390.76, "word": " لا", "probability": 0.65380859375}, {"start": 2390.76, "end": 2391.4, "word": " يمكن", "probability": 0.82666015625}, {"start": 2391.4, "end": 2391.74, "word": " ان", "probability": 0.791015625}, {"start": 2391.74, "end": 2392.52, "word": " تساوي", "probability": 0.9830322265625}, {"start": 2392.52, "end": 2393.72, "word": " الفاي", "probability": 0.885986328125}, {"start": 2393.72, "end": 2394.26, "word": " D", "probability": 0.80517578125}], "temperature": 1.0}, {"id": 100, "seek": 241591, "start": 2395.61, "end": 2415.91, "text": "اللي عملته انا لسه شغلة اثبت ان الـ Phi R تسعين لا بتساوي هذه ولا بتساوي هذه ولا بتساوي هذه الان انت بكتب ان ال Phi H بساويش هذه Phi H بساويش هذه و Phi H بساويش هذه و بعدين Phi D يبقى بروح بقوله similarly", "tokens": [6027, 20292, 6225, 42213, 47395, 1975, 8315, 5296, 3794, 3224, 13412, 17082, 37977, 1975, 12984, 3555, 2655, 16472, 2423, 39184, 41435, 497, 6055, 3794, 3615, 9957, 20193, 39894, 3794, 995, 45865, 29538, 49429, 39894, 3794, 995, 45865, 29538, 49429, 39894, 3794, 995, 45865, 29538, 2423, 7649, 16472, 2655, 4724, 4117, 2655, 3555, 16472, 2423, 41435, 389, 4724, 3794, 995, 45865, 8592, 29538, 41435, 389, 4724, 3794, 995, 45865, 8592, 29538, 4032, 41435, 389, 4724, 3794, 995, 45865, 8592, 29538, 4032, 39182, 9957, 41435, 413, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 4724, 39648, 3224, 14138], "avg_logprob": -0.24690755099679032, "compression_ratio": 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H", "probability": 0.85400390625}, {"start": 2409.97, "end": 2410.59, "word": " بساويش", "probability": 0.9767578125}, {"start": 2410.59, "end": 2410.83, "word": " هذه", "probability": 0.95458984375}, {"start": 2410.83, "end": 2411.23, "word": " و", "probability": 0.7841796875}, {"start": 2411.23, "end": 2411.63, "word": " بعدين", "probability": 0.914306640625}, {"start": 2411.63, "end": 2411.93, "word": " Phi", "probability": 0.9580078125}, {"start": 2411.93, "end": 2412.63, "word": " D", "probability": 0.99072265625}, {"start": 2412.63, "end": 2413.51, "word": " يبقى", "probability": 0.903076171875}, {"start": 2413.51, "end": 2413.91, "word": " بروح", "probability": 0.9041341145833334}, {"start": 2413.91, "end": 2414.59, "word": " بقوله", "probability": 0.9083658854166666}, {"start": 2414.59, "end": 2415.91, "word": " similarly", "probability": 0.4765625}], "temperature": 1.0}, {"id": 101, "seek": 244783, "start": 2418.41, "end": 2447.83, "text": "similarly for اللي هو فاي اتش and فاي دي thus و هكذا ال inner atom morphism اللي دي for هو عبارة عن الفاي ار نود و الفاي ار تسعين و الفاي اتش و الفاي دي", "tokens": [30937, 2202, 356, 337, 13672, 1829, 31439, 6156, 47302, 1975, 2655, 8592, 293, 6156, 47302, 11778, 1829, 8807, 4032, 8032, 4117, 15730, 2423, 7284, 12018, 25778, 1434, 13672, 1829, 11778, 1829, 337, 31439, 6225, 3555, 9640, 3660, 18871, 27188, 47302, 1975, 2288, 8717, 23328, 4032, 27188, 47302, 1975, 2288, 6055, 3794, 3615, 9957, 4032, 27188, 47302, 1975, 2655, 8592, 4032, 27188, 47302, 11778, 1829], "avg_logprob": -0.28870192307692305, "compression_ratio": 1.6267605633802817, "no_speech_prob": 0.0, "words": [{"start": 2418.41, "end": 2419.81, "word": "similarly", "probability": 0.782958984375}, {"start": 2419.81, "end": 2420.99, "word": " for", "probability": 0.46875}, {"start": 2420.99, "end": 2421.89, "word": " اللي", "probability": 0.5899658203125}, {"start": 2421.89, "end": 2422.27, "word": " هو", "probability": 0.9599609375}, {"start": 2422.27, 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ممتاز اذا", "tokens": [7649, 995, 34105, 1975, 12984, 3555, 2655, 46740, 16472, 2423, 9640, 3215, 8717, 23328, 2423, 9640, 3215, 8717, 23328, 39896, 2423, 9640, 3215, 3714, 10632, 4032, 46811, 7649, 9957, 15844, 3714, 9957, 15844, 1975, 4117, 3794, 8032, 1211, 2423, 1783, 1975, 46456, 43500, 12602, 2304, 11622, 20449, 9957, 49429, 10874, 36081, 15844, 46811, 7649, 10632, 12602, 2304, 2407, 11622, 15844, 46811, 7649, 10632, 3714, 2304, 2655, 31377, 1975, 15730], "avg_logprob": -0.2854910731315613, "compression_ratio": 1.9172932330827068, "no_speech_prob": 0.0, "words": [{"start": 2470.97, "end": 2471.47, "word": "انا", "probability": 0.57977294921875}, {"start": 2471.47, "end": 2471.81, "word": " هنا", "probability": 0.7412109375}, {"start": 2471.81, "end": 2472.47, "word": " اثبت", "probability": 0.96533203125}, {"start": 2472.47, "end": 2472.63, "word": " له", "probability": 0.6591796875}, {"start": 2472.63, "end": 2472.85, "word": " ان", "probability": 0.8837890625}, {"start": 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2604.97, "word": " يبقى", "probability": 0.7921142578125}, {"start": 2604.97, "end": 2605.23, "word": " له", "probability": 0.65185546875}, {"start": 2605.23, "end": 2605.55, "word": " وقت", "probability": 0.88818359375}, {"start": 2605.55, "end": 2607.91, "word": " السؤال", "probability": 0.958984375}, {"start": 2607.91, "end": 2608.65, "word": " الآخر", "probability": 0.9318033854166666}, {"start": 2608.65, "end": 2610.35, "word": " بيقول", "probability": 0.8271484375}, {"start": 2610.35, "end": 2610.61, "word": " ما", "probability": 0.90771484375}, {"start": 2610.61, "end": 2611.73, "word": " يأتي", "probability": 0.8990885416666666}, {"start": 2611.73, "end": 2625.03, "word": " خليه", "probability": 0.3136800130208333}, {"start": 2625.03, "end": 2625.41, "word": " بلكن", "probability": 0.4829915364583333}, {"start": 2625.41, "end": 2626.81, "word": " كمان", "probability": 0.76171875}, {"start": 2626.81, "end": 2627.33, "word": " example", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 110, "seek": 264408, "start": 2631.32, "end": 2644.08, "text": "example بقول الكمبيوت احسبلي ال atomorphism ل z منين ل z عشرة", "tokens": [3121, 335, 781, 4724, 39648, 2423, 24793, 21292, 35473, 1975, 5016, 35457, 20292, 2423, 12018, 284, 950, 1434, 5296, 710, 9154, 9957, 5296, 710, 6225, 8592, 25720], "avg_logprob": -0.3549107110926083, "compression_ratio": 1.0224719101123596, "no_speech_prob": 0.0, "words": [{"start": 2631.3199999999997, "end": 2632.72, "word": "example", "probability": 0.7083333333333334}, {"start": 2632.72, "end": 2634.12, "word": " بقول", "probability": 0.87109375}, {"start": 2634.12, "end": 2635.24, "word": " الكمبيوت", "probability": 0.7412109375}, {"start": 2635.24, "end": 2638.14, "word": " احسبلي", "probability": 0.8818359375}, {"start": 2638.14, "end": 2639.3, "word": " ال", "probability": 0.97900390625}, {"start": 2639.3, "end": 2640.86, "word": " atomorphism", "probability": 0.63702392578125}, {"start": 2640.86, "end": 2641.72, 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6055, 3555, 4587, 7578, 4032, 7649, 2655, 4032, 7649, 4032, 7649, 2655, 4032, 6055, 9778, 40448, 16490, 33546, 10632, 9154, 2423, 39184, 307, 32702, 1434, 28242, 2445, 39627, 24192, 41950, 16572, 28671, 39894, 3555, 4587, 7578, 3714, 29245, 23328, 4032, 9957, 22807, 8978, 2423, 9307, 20498, 13063, 5172, 11622, 2304, 32767, 9957, 22807, 5296, 39184, 1176, 3279, 23032, 3555, 3615, 995, 8032, 1863, 12984, 3555, 2655, 16472, 8032, 3215, 12610, 5551, 25513, 27884, 6156, 47432, 5296, 17082, 13546], "avg_logprob": -0.2816685379615852, "compression_ratio": 1.7045454545454546, "no_speech_prob": 0.0, "words": [{"start": 2652.5, "end": 2652.8, "word": "أنا", "probability": 0.36883544921875}, {"start": 2652.8, "end": 2652.88, "word": " بدي", "probability": 0.3553466796875}, {"start": 2652.88, "end": 2653.9, "word": " احسب", "probability": 0.6416015625}, {"start": 2653.9, "end": 2654.12, "word": " له", "probability": 0.2445068359375}, {"start": 2654.12, "end": 2654.48, "word": " كل", "probability": 0.74169921875}, {"start": 2654.48, "end": 2655.52, "word": " الاتومورفزم", "probability": 0.6215471540178571}, {"start": 2655.52, "end": 2655.88, "word": " لـ", "probability": 0.5394287109375}, {"start": 2655.88, "end": 2656.38, "word": " Z10", "probability": 0.36029052734375}, {"start": 2656.38, "end": 2656.76, "word": " يعني", "probability": 0.852783203125}, {"start": 2656.76, "end": 2657.14, "word": " انا", "probability": 0.766845703125}, {"start": 2657.14, "end": 2657.5, "word": " بدي", "probability": 0.89697265625}, {"start": 2657.5, "end": 2658.32, "word": " function", "probability": 0.56103515625}, {"start": 2658.32, "end": 2659.18, "word": " من", "probability": 0.9609375}, {"start": 2659.18, "end": 2660.04, "word": " Z10", "probability": 0.93115234375}, {"start": 2660.04, "end": 2660.3, "word": " إلى", "probability": 0.64453125}, {"start": 2660.3, "end": 2661.02, "word": " Z10", "probability": 0.9833984375}, {"start": 2661.02, "end": 2661.5, "word": " تبقى", "probability": 0.9564208984375}, {"start": 2661.5, "end": 2661.92, "word": " وانت", "probability": 0.6617838541666666}, {"start": 2661.92, "end": 2662.3, "word": " وان", "probability": 0.672607421875}, {"start": 2662.3, "end": 2663.42, "word": " وانت", "probability": 0.9169921875}, {"start": 2663.42, "end": 2663.9, "word": " و", "probability": 0.50927734375}, {"start": 2663.9, "end": 2664.46, "word": " تخدم", "probability": 0.8499348958333334}, {"start": 2664.46, "end": 2665.22, "word": " خاصية", "probability": 0.97119140625}, {"start": 2665.22, "end": 2665.56, "word": " من", "probability": 0.7666015625}, {"start": 2665.56, "end": 2666.44, "word": " الـ", "probability": 0.48748779296875}, {"start": 2666.44, "end": 2667.42, "word": " isomorphism", "probability": 0.849609375}, {"start": 2667.42, "end": 2668.2, "word": " كل", "probability": 0.8017578125}, {"start": 2668.2, "end": 2668.82, "word": " function", "probability": 0.9248046875}, {"start": 2668.82, "end": 2669.34, "word": " بهذه", "probability": 0.8447265625}, {"start": 2669.34, "end": 2669.8, "word": " الطريقة", "probability": 0.98828125}, {"start": 2669.8, "end": 2670.18, "word": " بتبقى", "probability": 0.888427734375}, {"start": 2670.18, "end": 2670.56, "word": " موجود", "probability": 0.9847005208333334}, {"start": 2670.56, "end": 2671.48, "word": " وين؟", "probability": 0.6455078125}, {"start": 2671.48, "end": 2671.68, "word": " في", "probability": 0.88134765625}, {"start": 2671.68, "end": 2673.44, "word": " الاتومورفزم", "probability": 0.95654296875}, {"start": 2673.44, "end": 2674.32, "word": " لمين؟", "probability": 0.8487955729166666}, {"start": 2674.32, "end": 2674.62, "word": " لـ", "probability": 0.869140625}, {"start": 2674.62, "end": 2675.08, "word": " Z10", "probability": 0.84716796875}, {"start": 2675.08, "end": 2675.48, "word": " طبعا", "probability": 0.96923828125}, {"start": 2675.48, "end": 2676.1, "word": " هنثبت", "probability": 0.89111328125}, {"start": 2676.1, "end": 2676.6, "word": " ان", "probability": 0.677734375}, {"start": 2676.6, "end": 2677.0, "word": " هدول", "probability": 0.8136393229166666}, {"start": 2677.0, "end": 2677.86, "word": " أربعة", "probability": 0.7776692708333334}, {"start": 2677.86, "end": 2678.64, "word": " فقط", "probability": 0.9892578125}, {"start": 2678.64, "end": 2679.46, "word": " لغير", "probability": 0.8211263020833334}], "temperature": 1.0}, {"id": 112, "seek": 270417, "start": 2679.75, "end": 2704.17, "text": "وهذا ما سيكون في المحاضرة بعض الظهر لإنه ماضلش معانا واجد إلا تمام؟ هذا أنا بغششك من الحين إذا معاك الكتاب موجودة في الكتاب تمر عليها ولن تفهم منها إلا القليل أنا متأكد مش هتفهم إن هو كتاب إلا القليل لكن ان شاء الله بنوضحها لك و بنفهمها لك في المحاضرة القادمة ان شاء الله يعطيكوا العفو", "tokens": [2407, 3224, 15730, 19446, 8608, 1829, 30544, 8978, 9673, 5016, 46958, 25720, 45030, 11242, 6024, 116, 3224, 2288, 5296, 28814, 1863, 3224, 19446, 11242, 1211, 8592, 20449, 7649, 995, 4032, 26108, 3215, 11933, 15040, 46811, 10943, 22807, 23758, 41850, 4724, 17082, 8592, 8592, 4117, 9154, 21542, 9957, 11933, 15730, 20449, 995, 4117, 33251, 2655, 16758, 3714, 29245, 23328, 3660, 8978, 33251, 2655, 16758, 6055, 29973, 25894, 11296, 4032, 1211, 1863, 6055, 5172, 16095, 9154, 11296, 11933, 15040, 25062, 20292, 1211, 41850, 44650, 10721, 4117, 3215, 37893, 8032, 2655, 5172, 16095, 36145, 31439, 9122, 2655, 16758, 11933, 15040, 25062, 20292, 1211, 44381, 16472, 13412, 16606, 21984, 44945, 2407, 11242, 5016, 11296, 5296, 4117, 4032, 44945, 5172, 16095, 11296, 5296, 4117, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407], "avg_logprob": -0.1742187530866691, "compression_ratio": 2.1152263374485596, "no_speech_prob": 5.900859832763672e-06, "words": [{"start": 2679.75, "end": 2680.33, "word": "وهذا", "probability": 0.8927408854166666}, {"start": 2680.33, "end": 2680.51, "word": " ما", "probability": 0.91064453125}, {"start": 2680.51, "end": 2681.19, "word": " سيكون", "probability": 0.9606119791666666}, {"start": 2681.19, "end": 2681.59, "word": " في", "probability": 0.890625}, {"start": 2681.59, "end": 2682.15, "word": " المحاضرة", "probability": 0.987548828125}, {"start": 2682.15, "end": 2682.47, "word": " بعض", "probability": 0.7060546875}, {"start": 2682.47, "end": 2682.73, "word": " الظهر", "probability": 0.9139404296875}, {"start": 2682.73, "end": 2683.01, "word": " لإنه", "probability": 0.733642578125}, {"start": 2683.01, "end": 2683.43, "word": " ماضلش", "probability": 0.64599609375}, {"start": 2683.43, "end": 2683.97, "word": " معانا", "probability": 0.9376627604166666}, {"start": 2683.97, "end": 2684.51, "word": " واجد", "probability": 0.6981608072916666}, {"start": 2684.51, "end": 2684.79, "word": " إلا", "probability": 0.6529541015625}, {"start": 2684.79, "end": 2685.69, "word": " تمام؟", "probability": 0.6824544270833334}, {"start": 2685.69, "end": 2685.99, "word": " هذا", "probability": 0.921875}, {"start": 2685.99, "end": 2686.13, "word": " أنا", "probability": 0.2890625}, {"start": 2686.13, "end": 2686.75, "word": " بغششك", "probability": 0.91728515625}, {"start": 2686.75, "end": 2686.91, "word": " من", "probability": 0.9794921875}, {"start": 2686.91, "end": 2687.29, "word": " الحين", "probability": 0.967529296875}, {"start": 2687.29, "end": 2687.85, "word": " إذا", "probability": 0.89306640625}, {"start": 2687.85, "end": 2688.17, "word": " معاك", "probability": 0.9498697916666666}, {"start": 2688.17, "end": 2688.63, "word": " الكتاب", "probability": 0.9549153645833334}, {"start": 2688.63, "end": 2689.13, "word": " موجودة", "probability": 0.9609375}, {"start": 2689.13, "end": 2689.23, "word": " في", "probability": 0.95361328125}, {"start": 2689.23, "end": 2689.65, "word": " الكتاب", "probability": 0.98779296875}, {"start": 2689.65, "end": 2690.27, "word": " تمر", "probability": 0.6156005859375}, {"start": 2690.27, "end": 2691.01, "word": " عليها", "probability": 0.977783203125}, {"start": 2691.01, "end": 2691.79, "word": " ولن", "probability": 0.765625}, {"start": 2691.79, "end": 2692.35, "word": " تفهم", "probability": 0.9931640625}, {"start": 2692.35, "end": 2692.81, "word": " منها", "probability": 0.995849609375}, {"start": 2692.81, "end": 2693.21, "word": " إلا", "probability": 0.987548828125}, {"start": 2693.21, "end": 2693.73, "word": " القليل", "probability": 0.9970703125}, {"start": 2693.73, "end": 2693.89, "word": " أنا", "probability": 0.6865234375}, {"start": 2693.89, "end": 2694.65, "word": " متأكد", "probability": 0.977783203125}, {"start": 2694.65, "end": 2695.29, "word": " مش", "probability": 0.8740234375}, {"start": 2695.29, "end": 2695.79, "word": " هتفهم", "probability": 0.993896484375}, {"start": 2695.79, "end": 2696.03, "word": " إن", "probability": 0.7294921875}, {"start": 2696.03, "end": 2696.23, "word": " هو", "probability": 0.78076171875}, {"start": 2696.23, "end": 2696.77, "word": " كتاب", "probability": 0.8829752604166666}, {"start": 2696.77, "end": 2697.21, "word": " إلا", "probability": 0.96875}, {"start": 2697.21, "end": 2697.57, "word": " القليل", "probability": 0.9873046875}, {"start": 2697.57, "end": 2697.87, "word": " لكن", "probability": 0.8134765625}, {"start": 2697.87, "end": 2698.07, "word": " ان", "probability": 0.58544921875}, {"start": 2698.07, "end": 2698.29, "word": " شاء", "probability": 0.968017578125}, {"start": 2698.29, "end": 2698.49, "word": " الله", "probability": 0.9619140625}, {"start": 2698.49, "end": 2699.53, "word": " بنوضحها", "probability": 0.81611328125}, {"start": 2699.53, "end": 2699.77, "word": " لك", "probability": 0.635009765625}, {"start": 2699.77, "end": 2699.87, "word": " و", "probability": 0.89404296875}, {"start": 2699.87, "end": 2700.37, "word": " بنفهمها", "probability": 0.8997802734375}, {"start": 2700.37, "end": 2700.55, "word": " لك", "probability": 0.986328125}, {"start": 2700.55, "end": 2700.65, "word": " في", "probability": 0.7099609375}, {"start": 2700.65, "end": 2701.33, "word": " المحاضرة", "probability": 0.9971923828125}, {"start": 2701.33, "end": 2702.51, "word": " القادمة", "probability": 0.99267578125}, {"start": 2702.51, "end": 2702.81, "word": " ان", "probability": 0.5869140625}, {"start": 2702.81, "end": 2703.11, "word": " شاء", "probability": 0.994384765625}, {"start": 2703.11, "end": 2703.31, "word": " الله", "probability": 0.96142578125}, {"start": 2703.31, "end": 2703.93, "word": " يعطيكوا", "probability": 0.7422119140625}, {"start": 2703.93, "end": 2704.17, "word": " العفو", "probability": 0.7533365885416666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2705.6355, "duration_after_vad": 2570.5549999999903}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1f9b938427c307633cd456ea31c48262ae850699
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.srt
@@ -0,0 +1,1808 @@
+1
+00:00:21,990 --> 00:00:24,230
+السلام عليكم و رحمة الله بسم الله الرحمن الرحيم
+
+2
+00:00:24,230 --> 00:00:27,590
+اليوم ان شاء الله هنكمل الجزء التالت من مناقشة
+
+3
+00:00:27,590 --> 00:00:31,630
+اللي هو الشبتر الرابع chapter ال cyclic groups
+
+4
+00:00:31,630 --> 00:00:36,310
+المرة الماضية أنهينا سؤال عشرين و اتوقفنا عن سؤال
+
+5
+00:00:36,310 --> 00:00:41,970
+واحد و عشرين سؤال واحد و عشرين سؤال تطبيقى مش صعب
+
+6
+00:00:41,970 --> 00:00:47,250
+كتيرلو جينا نقرأه let g be a group and let a be an
+
+7
+00:00:47,250 --> 00:00:51,390
+element of j لو ال a قص 12 بيساوي ال identity what
+
+8
+00:00:51,390 --> 00:00:55,410
+can you say about the order of a نفس الفكرة في فرع
+
+9
+00:00:55,410 --> 00:00:58,710
+بي لو ال a تقام بيساوي ال identity what can we say
+
+10
+00:00:58,710 --> 00:01:04,750
+about the order of a طبعا الجواب على السؤالين هو
+
+11
+00:01:04,750 --> 00:01:10,330
+جواب واحد ان order ال a في الأول هيقسم ال 12 في
+
+12
+00:01:10,330 --> 00:01:13,050
+الفرع a و في بي هيقسم مين
+
+13
+00:01:16,270 --> 00:01:22,710
+فى الفرع c suppose that ال order لجيب يسوي 24 جيب
+
+14
+00:01:22,710 --> 00:01:27,830
+is cyclic و ال a أُس تمانية لا يساوي ال identity و
+
+15
+00:01:27,830 --> 00:01:31,730
+ال a أُس اتناش لا يساوي ال identity show that ان
+
+16
+00:01:31,730 --> 00:01:38,530
+order ال a او ال generated by a هو الجيب فرع c
+
+17
+00:01:38,530 --> 00:01:45,060
+order الجيب يساوي 24 ال a أُس تمانيةلأ يساوي ال
+
+18
+00:01:45,060 --> 00:01:51,800
+identity و ال a أُس 12 لأ يساوي ال identity طبعا
+
+19
+00:01:51,800 --> 00:01:59,840
+في معلومة أخرى ان ال j is cyclic مدام
+
+20
+00:01:59,840 --> 00:02:06,220
+ال j is cyclic و
+
+21
+00:02:06,220 --> 00:02:12,060
+ال a ينتمي لل j هذا معناته ان order ال a هيقسم
+
+22
+00:02:12,060 --> 00:02:19,240
+order منالـ J هذي احدى الكورلرز على النظرية الاولى
+
+23
+00:02:19,240 --> 00:02:23,300
+انه اي عنصر في الـ cyclic group ال order له بيقسم
+
+24
+00:02:23,300 --> 00:02:26,740
+order ل group في حالة ال finite case هذا معناته
+
+25
+00:02:26,740 --> 00:02:35,840
+order ال A بيقسم ال 24 وبالتالي order ال A يا 1 يا
+
+26
+00:02:35,840 --> 00:02:47,310
+2 يا 3 يا 4 يا 6 يا 8 يا 12ياربع وعشرين تقال نرفض
+
+27
+00:02:47,310 --> 00:02:51,610
+بعضهم since
+
+28
+00:02:51,610 --> 00:02:59,330
+ا ال تمانية لا يساوي ال identity هذا معناته order
+
+29
+00:02:59,330 --> 00:03:04,550
+ال ا لا يساوي واحد لا يساوي اتنين لا يساوي اربع
+
+30
+00:03:04,550 --> 00:03:11,310
+ولا يساوي تمانية اشطب الواحد اشطب الاتنين اشطب
+
+31
+00:03:11,310 --> 00:03:21,130
+الاربع اشطب التمانيةنفس الفكرة also ال a أُس 12 لا
+
+32
+00:03:21,130 --> 00:03:27,550
+يساوي ال identity معناته order ال a لا يساوي تلاتة
+
+33
+00:03:27,550 --> 00:03:34,870
+ولا يساوي ستة ولا يساوي اتناش اشطب التلاتة اشطب
+
+34
+00:03:34,870 --> 00:03:38,290
+الستة اشطب الاتناش ايش حيضل عندك؟ اربع وعشرين
+
+35
+00:03:38,290 --> 00:03:42,690
+وبالتالي order ال a بدي يساوي اربع وعشرين اللي هو
+
+36
+00:03:42,690 --> 00:03:52,600
+order ال jيكبر جيه الانصار
+
+37
+00:03:52,600 --> 00:03:57,140
+اللي اسمه a موجود في الجروب جيه اللي هي cyclic و
+
+38
+00:03:57,140 --> 00:04:02,610
+هي finiteهي group ال order لها 24 يكبر order ل A
+
+39
+00:04:02,610 --> 00:04:06,530
+بيخسم ال 24 يكبر يا واحد يا اتنين يا تلاتة يا اربع
+
+40
+00:04:06,530 --> 00:04:09,890
+يا ستة يا تمانية يا اتناش يا اربع عشرين هيجيت ال A
+
+41
+00:04:09,890 --> 00:04:12,450
+و ال تمانية و ال A و ال اتناش لا يساوي ال identity
+
+42
+00:04:12,450 --> 00:04:15,990
+بستثني ال واحد و التنين و الأربع و التمانية في
+
+43
+00:04:15,990 --> 00:04:19,790
+الأول بعدين بستثني التلاتة و الستة و الأتناش من
+
+44
+00:04:19,790 --> 00:04:27,610
+حيضلان دي خلص السؤال السؤال
+
+45
+00:04:27,610 --> 00:04:33,840
+ال 22Any group of order 3 must be cyclic هذا
+
+46
+00:04:33,840 --> 00:04:36,680
+هيناخدله تعاميم في chapter 7 لما ناخد ال grand
+
+47
+00:04:36,680 --> 00:04:41,300
+theorem ان اي group of prime order لازم تكون
+
+48
+00:04:41,300 --> 00:04:48,020
+cyclic لو كان ال J ال order إيه لها تلاتة ف J is
+
+49
+00:04:48,020 --> 00:04:50,700
+cyclic
+
+50
+00:05:00,270 --> 00:05:09,970
+let جيه بيه فيها تلت عناصر اكيد واحد منهم مين اخد
+
+51
+00:05:09,970 --> 00:05:19,870
+ال a اخد ال b with ا لا يساوي ال a ا لا يساوي ال b
+
+52
+00:05:19,870 --> 00:05:24,710
+ا لا يساوي ال b عشان اقول انه تلت عناصر اشمالهم
+
+53
+00:05:24,710 --> 00:05:27,090
+distinct مختلفات
+
+54
+00:05:29,800 --> 00:05:36,980
+هذا معناته ان a و b وين هيكون في الـ j كم حالة
+
+55
+00:05:36,980 --> 00:05:46,820
+عندك تلاتة cases هذا معناته case واحد ان ال a و b
+
+56
+00:05:46,820 --> 00:05:53,260
+بدت ساوي ايه؟ لو ال a و b بدت ساوي ايه؟ يبقى b بدت
+
+57
+00:05:53,260 --> 00:05:58,060
+ساوي ال identity وهذا مستحيل الحالة التانية
+
+58
+00:06:00,790 --> 00:06:05,990
+إن ال A بيبقى تساوي ال B في هذه الحالة سيصبح ال A
+
+59
+00:06:05,990 --> 00:06:12,270
+بيبقى تساوي ال identity وهذا مستحيل كيس
+
+60
+00:06:12,270 --> 00:06:19,110
+ثلاثة إن ال A بيبقى تساوي ال identity وبالتالي ال
+
+61
+00:06:19,110 --> 00:06:26,070
+B بيبقى تساوي ال A inverse طبعا صارت ال J عبارة عن
+
+62
+00:06:26,070 --> 00:06:28,930
+ال identity و A و A inverse
+
+63
+00:06:33,620 --> 00:06:42,040
+cyclics جيناتك ضايق من انتوا يك ب جيه is cycling
+
+64
+00:06:42,040 --> 00:06:46,000
+وخلص
+
+65
+00:06:46,000 --> 00:07:00,360
+واضح
+
+66
+00:07:00,360 --> 00:07:07,880
+السؤال هذاواضح السؤال هذا طيب سؤال تلاتة عشرين
+
+67
+00:07:07,880 --> 00:07:12,220
+اتكلمنا عنه في سياق الشرح اللي ابقى كنت اشرحه في
+
+68
+00:07:12,220 --> 00:07:17,020
+ال chapter بقولك ال z of ليه عبارة عن ال integers
+
+69
+00:07:17,020 --> 00:07:23,620
+مع الجامع هل كل subgroup من ال z cyclic؟ هل كل
+
+70
+00:07:23,620 --> 00:07:29,260
+subgroup من ال z cyclic؟ لو أخدت H subgroup من ال
+
+71
+00:07:29,260 --> 00:07:32,680
+z ال integers مع الجامع أكيد ال H cyclic
+
+72
+00:07:36,910 --> 00:07:43,350
+ليش؟ since z itself is cyclic مدام الـ z is a
+
+73
+00:07:43,350 --> 00:07:47,710
+cyclic group فكل sub group منه ايش هيكون؟ Cyclic
+
+74
+00:07:47,710 --> 00:07:53,330
+طبعا ال H هتكون generated by some element مثلا M و
+
+75
+00:07:53,330 --> 00:07:59,030
+ال M ينتمي ل z هدا مش معناته هدا معناته هي عبارة
+
+76
+00:07:59,030 --> 00:08:03,930
+عن ال zero موجة بسالب M موجة بسالب اتنين Mموجب
+
+77
+00:08:03,930 --> 00:08:13,230
+سالب تلاتة M الاخرى هذا
+
+78
+00:08:13,230 --> 00:08:16,790
+السؤال
+
+79
+00:08:16,790 --> 00:08:23,010
+23 السؤال 24 find
+
+80
+00:08:23,010 --> 00:08:26,470
+for any element A in any group J prove that انه
+
+81
+00:08:26,470 --> 00:08:30,150
+generated by A is a subgroup من ال centralizer A
+
+82
+00:08:34,580 --> 00:08:43,360
+هذه تريفيال since a في a بيبقى تساوي a في a يكبر
+
+83
+00:08:43,360 --> 00:08:49,720
+ال a أشماله كميوت مع نفسه مادامه كميوت مع نفسه
+
+84
+00:08:49,720 --> 00:08:54,440
+يكبر a موجود في ال centralizer لل a يكبر generated
+
+85
+00:08:54,440 --> 00:09:03,060
+by a sub group من ال centralizer وخلص اثبات خلص
+
+86
+00:09:04,830 --> 00:09:09,990
+خلصوها ال 24 بسرعة أربع
+
+87
+00:09:09,990 --> 00:09:15,370
+أسئلة اللي حليناها واضحة، في أي مشكلة فيها؟ في أي
+
+88
+00:09:15,370 --> 00:09:19,110
+مشكلة في الأسئلة اللي حليناها؟ أي نقطة غير مفهومة؟
+
+89
+00:09:24,500 --> 00:09:28,860
+هو يبدأ بالجنرالتر الـ A بالساقية هذي السبب بقى
+
+90
+00:09:28,860 --> 00:09:32,520
+تبدأ في answer انت بتاخد A تقام بعدين تدبط ان A
+
+91
+00:09:32,520 --> 00:09:38,800
+تقام commute مع ال A عارف تلات تسطر ليش تجي ع راسك
+
+92
+00:09:38,800 --> 00:09:42,140
+بعدين كده بدأت ك A تقام بساقية مش ال A commute مع
+
+93
+00:09:42,140 --> 00:09:46,480
+نفسه فموجود في ال centralizer تبع نفسه و بعدين
+
+94
+00:09:46,480 --> 00:09:48,960
+موجود في ال centralizer تبع نفسه ال centralizer
+
+95
+00:09:48,960 --> 00:09:53,170
+subgroup فال generated by Aهيكون subset من ال
+
+96
+00:09:53,170 --> 00:09:57,490
+centralizer لأنه مدام ال a موجودة يعني فكل powers
+
+97
+00:09:57,490 --> 00:09:58,710
+ال a موجودة يعني
+
+98
+00:10:03,030 --> 00:10:06,690
+سؤال 25 أنا ما طلبتوش لكن هو محلول في الخلف و سهل
+
+99
+00:10:06,690 --> 00:10:12,130
+انت بتشتغل في ال DN ال DN عبارة عن جزءين جزء مكونا
+
+100
+00:10:12,130 --> 00:10:16,490
+من N من العناصر بتكون لل cyclic subgroup generated
+
+101
+00:10:16,490 --> 00:10:23,990
+by R 360 على N و الجزء التاني عبارة عن مجموعة من
+
+102
+00:10:23,990 --> 00:10:27,350
+ال reflections اللي ال order لكل واحد اش في ساوي
+
+103
+00:10:28,270 --> 00:10:32,210
+تنين فعندك صحب الجروب ال order اللي هان فلو كان دي
+
+104
+00:10:32,210 --> 00:10:35,350
+يقسم الان هتلاقي عدد من العناصر ال order اللي هم
+
+105
+00:10:35,350 --> 00:10:40,130
+دي يساوي في الدي بالنسبة لسؤال ستة و عشرين
+
+106
+00:10:40,130 --> 00:10:45,290
+generator ال z قلناهم موجة بسالب واحد generator اي
+
+107
+00:10:45,290 --> 00:10:52,390
+group infinite و cyclic هيكون ال a و a inverse
+
+108
+00:10:52,390 --> 00:10:57,850
+يعني في ال z السؤال ستة و عشرينالـ z ال generator
+
+109
+00:10:57,850 --> 00:11:02,810
+إليها موجب سالب واحد طب لو كان عندك generated by a
+
+110
+00:11:02,810 --> 00:11:07,710
+و order ال a بدي يسوي مالة نهاية مين ال generator
+
+111
+00:11:07,710 --> 00:11:15,410
+هان؟ a و a inverse لأنه أصلا كل .. هنكتشف لاحقا أن
+
+112
+00:11:15,410 --> 00:11:21,650
+كل cyclic group و infinite هتكون copy من ال z
+
+113
+00:11:22,690 --> 00:11:27,450
+السابع و عشرين الـ c star the group of non-zero
+
+114
+00:11:27,450 --> 00:11:31,210
+complex number under multiplication has a cyclic
+
+115
+00:11:31,210 --> 00:11:39,090
+subgroup of order c star عبارة عن اللي هي كل ما
+
+116
+00:11:39,090 --> 00:11:47,330
+عدا ال zero اللي هي ممكن نكتبها زي هيك black c كل
+
+117
+00:11:47,330 --> 00:11:52,780
+ما عدا ال zero مع عملية الضربهذا ما نثبت أنه موجود
+
+118
+00:11:52,780 --> 00:11:58,300
+فيها Cyclic group أو
+
+119
+00:11:58,300 --> 00:12:04,480
+Cyclic subgroup في أوردر n لت ان ينتمي لإنه يشغل
+
+120
+00:12:04,480 --> 00:12:09,180
+number بخط
+
+121
+00:12:09,180 --> 00:12:11,080
+Complex analysis
+
+122
+00:12:14,570 --> 00:12:19,310
+طيب هجيت أي polynomial ال coefficient اللي لها من
+
+123
+00:12:19,310 --> 00:12:25,270
+ال C حلولها وين موجودة؟ اي polynomial ال
+
+124
+00:12:25,270 --> 00:12:28,650
+coefficient اللي هي المعاملات تبعتها من ال complex
+
+125
+00:12:28,650 --> 00:12:32,290
+number ال coefficient تبعتها وين؟ او ال solution
+
+126
+00:12:32,290 --> 00:12:37,250
+تبعتها وين؟برضه في ال complex طبعا هذا سببه ان ال
+
+127
+00:12:37,250 --> 00:12:41,910
+.. ال .. ال .. ال C مع الضرب و الجمع تملي حاجة
+
+128
+00:12:41,910 --> 00:12:44,810
+احنا بنسميها algebraically closed field of
+
+129
+00:12:44,810 --> 00:12:48,610
+characteristics zero طبعا هو اكمل تقريبا اللي هو
+
+130
+00:12:48,610 --> 00:12:51,370
+اكمل ال .. ال .. ال هيئة الجبرية لإن كل ال
+
+131
+00:12:51,370 --> 00:12:57,050
+polynomials بتكون محلولة داخله هجيت السؤال انا بدي
+
+132
+00:12:57,050 --> 00:13:01,730
+اجيب subgroup ال order L, H, N و تكون cyclic في ال
+
+133
+00:13:01,730 --> 00:13:07,500
+C فبدي أنصر يولدهاthe answer يولد هذه ال subgroup
+
+134
+00:13:07,500 --> 00:13:14,040
+طبعا consider the
+
+135
+00:13:14,040 --> 00:13:23,380
+equation x to n بساوي واحد هذه
+
+136
+00:13:23,380 --> 00:13:29,840
+المعادلة we know that
+
+137
+00:13:29,840 --> 00:13:33,380
+this equation
+
+138
+00:13:35,180 --> 00:13:43,600
+أو the solution أو the roots of this أو of this
+
+139
+00:13:43,600 --> 00:13:50,060
+polynomial أو equation are
+
+140
+00:13:50,060 --> 00:14:01,200
+all lies in C ولا
+
+141
+00:14:01,200 --> 00:14:04,240
+واحد منهم يساو Zero none
+
+142
+00:14:06,700 --> 00:14:16,400
+of them is zero ولا واحد منهم
+
+143
+00:14:16,400 --> 00:14:28,660
+ساو صفر let a,n بكل ال X في ال C اللي X أس N بده
+
+144
+00:14:28,660 --> 00:14:29,280
+يساوي واحد
+
+145
+00:14:36,570 --> 00:14:41,190
+بتعلم معايا احنا هن فى ال C و لو واحد منهم صفر
+
+146
+00:14:41,190 --> 00:14:49,150
+فأول هنتقل لل C star using the
+
+147
+00:14:49,150 --> 00:14:53,610
+concepts of
+
+148
+00:14:53,610 --> 00:14:59,830
+complex analysis we
+
+149
+00:14:59,830 --> 00:15:02,870
+can write
+
+150
+00:15:04,970 --> 00:15:12,650
+الان عبارة عن الواحد و و تغبيه لإن و أس ان ماينس
+
+151
+00:15:12,650 --> 00:15:17,110
+واحد where
+
+152
+00:15:17,110 --> 00:15:20,210
+و
+
+153
+00:15:20,210 --> 00:15:23,710
+is a primitive root
+
+154
+00:15:34,970 --> 00:15:45,650
+of unity primitive and root of unity طبعا
+
+155
+00:15:45,650 --> 00:15:48,650
+لو رجعت لل complex analysis احنا بتعرف ان هذه
+
+156
+00:15:48,650 --> 00:15:53,210
+المعادلة كيف بنحلهاهنا x اثنان بدى يسوى واحد او
+
+157
+00:15:53,210 --> 00:15:55,250
+انا بدي احلي المعادلة اللى عبارة عن z اثنان بدى
+
+158
+00:15:55,250 --> 00:15:59,670
+يسوى واحد بروح بجيب الواحد على شكل اللى هو ال ال
+
+159
+00:15:59,670 --> 00:16:04,330
+polar form و بتطلع ال theta تبعته صفر فبجمع صفر
+
+160
+00:16:04,330 --> 00:16:12,130
+زاد اتنين k πاي على n ف ال w عبارة عن اللى هو
+
+161
+00:16:12,130 --> 00:16:22,010
+cosine اتنين πايعلى n زاد i sin 2pi على n هذا من
+
+162
+00:16:22,010 --> 00:16:27,970
+ال complex analysis هيتلاحظ أن باقي العناصر عبارة
+
+163
+00:16:27,970 --> 00:16:31,890
+عن مين هنا
+
+164
+00:16:31,890 --> 00:16:41,370
+unity النتيجة أن a n generated by w
+
+165
+00:16:46,100 --> 00:16:53,520
+and since w أُس n بدأ تساوي واحد طبعاً لما ابدأ
+
+166
+00:16:53,520 --> 00:16:59,920
+أجي أكمل أجيب w أُس n هترجع لمين للواحد w أُس n
+
+167
+00:16:59,920 --> 00:17:04,240
+زاد الواحد هتروح لمين لل w بعدين ال powers تبعين
+
+168
+00:17:04,240 --> 00:17:14,260
+ال w بصير اشمالهم يتكرر النتيجةان ان subgroup من
+
+169
+00:17:14,260 --> 00:17:18,080
+الـ black sea تبعا black sea لما اشهد منصة صفر ده
+
+170
+00:17:18,080 --> 00:17:27,840
+C star و ال order لان بدى يساوي ان and ان is
+
+171
+00:17:27,840 --> 00:17:34,860
+cyclic مشكلة هنا ان اللي بدأ يجيح حل السؤال يكون
+
+172
+00:17:34,860 --> 00:17:40,320
+عنده خلفية عن ال complex analysisلأ لأ مش .. هذه
+
+173
+00:17:40,320 --> 00:17:44,400
+القاعدة انت خدتها في الثانوية المعادلة اللي هي كيف
+
+174
+00:17:44,400 --> 00:17:47,760
+.. كيف .. كيف كنت تجيب جذور ال .. ال .. ال ..
+
+175
+00:17:47,760 --> 00:17:54,440
+الواحد الصحيح ال .. الواحد الصحيح هو بده إجاوب أو
+
+176
+00:17:54,440 --> 00:17:59,580
+صرف إجاوب الوردر لها فاشتغلت علي هذه المعادلةأنا
+
+177
+00:17:59,580 --> 00:18:04,440
+مش هقدر أخد أنصر عشوائي و أضل أرفع فيه الأساس و
+
+178
+00:18:04,440 --> 00:18:08,740
+بعدين أجيبه بواحد إلا لما أكون عارف واحد معين بعرف
+
+179
+00:18:08,740 --> 00:18:18,920
+أنه لما بعرفه هو لأنه بيعطيني واحد عشو
+
+180
+00:18:18,920 --> 00:18:28,090
+فيه بعد 27؟ أو 26؟ 27؟عندي سؤال تسعة و عشرين list
+
+181
+00:18:28,090 --> 00:18:33,550
+all the elements of O أخضر تمانية ان زد تمانتلاف
+
+182
+00:18:33,550 --> 00:18:37,130
+محلول .. محلول السؤال هذا ورا تحلي السؤال اللي
+
+183
+00:18:37,130 --> 00:18:42,700
+بعدهأو حتى لو مش تمانية و تمانية ترليون نفس الفكرة
+
+184
+00:18:42,700 --> 00:18:47,080
+list all elements of order تمانية عشان تشتغل على
+
+185
+00:18:47,080 --> 00:18:50,700
+order تمانية بدك تجيب واحد ال order له تمانية و
+
+186
+00:18:50,700 --> 00:18:52,600
+تكمل بعد هيك عشان تشتغل عشان تشتغل عشان تشتغل عشان
+
+187
+00:18:52,600 --> 00:18:53,280
+تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل
+
+188
+00:18:53,280 --> 00:18:54,720
+عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان
+
+189
+00:18:54,720 --> 00:18:54,980
+تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل
+
+190
+00:18:54,980 --> 00:19:01,340
+عشان تشتغل عشان تشتغل عشان تشتغل
+
+191
+00:19:03,140 --> 00:19:07,240
+بتجيب واحد منهم اللي هو عبارة عن واحد قص تمانية
+
+192
+00:19:07,240 --> 00:19:11,040
+مليون ع تمانية يعني واحد قص مليون عن المليون بترفع
+
+193
+00:19:11,040 --> 00:19:13,880
+على القصص اللي بتكون relative to prime ع تمانية
+
+194
+00:19:13,880 --> 00:19:18,300
+واحد و تلاتة و خمسة و سبعة فهي الأرقام اللي او
+
+195
+00:19:18,300 --> 00:19:21,440
+العناصر اللي في زيد تمانية مليون اللي ال order
+
+196
+00:19:21,440 --> 00:19:24,180
+اللي تمانية هتكون المليون و التلاتة مليون و الخمسة
+
+197
+00:19:24,180 --> 00:19:29,770
+مليون و السبعة مليون نفس الفكرةلو كان ال .. ال
+
+198
+00:19:29,770 --> 00:19:33,230
+يعني copy من ال z تمانية مليون generated by a و ال
+
+199
+00:19:33,230 --> 00:19:38,250
+order ل a تمانية مليون هل السؤال تلاتين؟ ساعات
+
+200
+00:19:38,250 --> 00:19:42,290
+عشرين بتقول ساعات عشرين أحله بحله مع أنه سهل يعني
+
+201
+00:19:42,290 --> 00:19:45,610
+بدك
+
+202
+00:19:45,610 --> 00:19:49,830
+ال .. ال .. ال order لل a بيبقى تساوي تمانية و a
+
+203
+00:19:49,830 --> 00:19:57,430
+ينتمي ل z تمانية مليون أول شي ده number
+
+204
+00:20:00,790 --> 00:20:11,490
+of elements in زد تمانية مليون with order تمانية
+
+205
+00:20:11,490 --> 00:20:16,530
+is five تمانية له بيساوي أربعة because أو since
+
+206
+00:20:16,530 --> 00:20:26,110
+the group is cyclic to find one of them
+
+207
+00:20:32,650 --> 00:20:42,450
+we have that واحد اص تمانية مليون على تمانية اللي
+
+208
+00:20:42,450 --> 00:20:53,590
+واحد اص مليون اللي عبارة عن مليون has order تمانية
+
+209
+00:20:53,590 --> 00:20:57,130
+sure
+
+210
+00:20:59,400 --> 00:21:05,520
+هو بده الارض بده العناصر بلاش اخدها ايه وهنا بقولك
+
+211
+00:21:05,520 --> 00:21:11,040
+find الارض على بيبن ساوة تمانية و ال بي ينتمي بزية
+
+212
+00:21:11,040 --> 00:21:15,460
+تمانية مليون اوجد العناصر بي اللي الارض اغلى
+
+213
+00:21:15,460 --> 00:21:18,720
+تمانية بزية تمانية مليون باق العناصر هالجيتها
+
+214
+00:21:18,720 --> 00:21:26,560
+شهدكون these
+
+215
+00:21:26,560 --> 00:21:27,060
+elements
+
+216
+00:21:33,300 --> 00:21:46,100
+R مليون أس واحد مليون أس ثلاثة مليون أس خمسة و
+
+217
+00:21:46,100 --> 00:21:52,960
+مليون و السبعة اللي هما يبقى عن المليون و التلاتة
+
+218
+00:21:52,960 --> 00:21:58,720
+مليون و الخمسة مليون و السبعة مليون
+
+219
+00:22:02,150 --> 00:22:05,190
+طب انت تكمل السؤال بنفس الطريقة بس بدل الواحد مش
+
+220
+00:22:05,190 --> 00:22:10,650
+هتاخد A فهيصير A أُس مليون A أُس ثلاثة مليون A أُس
+
+221
+00:22:10,650 --> 00:22:16,290
+خمسة مليون أو A أُس سبعة مليون سؤال
+
+222
+00:22:16,290 --> 00:22:20,810
+تلاتين order
+
+223
+00:22:20,810 --> 00:22:32,300
+ال A قد تنين N زي الواحد وA B A inverse بيساوي P
+
+224
+00:22:32,300 --> 00:22:38,240
+inverse show that P
+
+225
+00:22:38,240 --> 00:22:45,800
+تربيع بيساوي ال identity السؤال
+
+226
+00:22:45,800 --> 00:22:48,160
+التلاتين سؤال حلو بيشغل
+
+227
+00:23:26,320 --> 00:23:32,360
+عشان اقول ان ال P تربيه بدي ساوي ال identity لازم
+
+228
+00:23:32,360 --> 00:23:40,180
+اطلع ال P من العلاقة اللي قدامك يعني P A في B في A
+
+229
+00:23:40,180 --> 00:23:43,920
+inverse بدي ساوي P inverse تعالى نخربش على جدب
+
+230
+00:23:43,920 --> 00:23:47,960
+عشان نعرف كيف نبدأ نحل السؤال عشان يكون ال P تربيه
+
+231
+00:23:47,960 --> 00:23:52,650
+بدي ساوي ال identity فP بدي ساوي ايش؟بإنفارس
+
+232
+00:23:52,650 --> 00:23:56,990
+بإنفارس
+
+233
+00:23:56,990 --> 00:24:00,470
+بإنفارس
+
+234
+00:24:00,470 --> 00:24:05,810
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+235
+00:24:05,810 --> 00:24:09,110
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+236
+00:24:09,110 --> 00:24:09,110
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+237
+00:24:09,110 --> 00:24:09,110
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+238
+00:24:09,110 --> 00:24:09,130
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+239
+00:24:09,130 --> 00:24:16,330
+بإنفارس بإنفارس بإنفارس
+
+240
+00:24:16,330 --> 00:24:19,570
+بإنفارس
+
+241
+00:24:19,570 --> 00:24:27,570
+بإCommute تبقى ده ليه طيب فى شفى معضلة لحد تلان ما
+
+242
+00:24:27,570 --> 00:24:32,030
+استعملتوش اللى هو إيش order ال A بدي ساوي odd لما
+
+243
+00:24:32,030 --> 00:24:35,710
+يكون order ال A بدي ساوي odd ف generated by ال A
+
+244
+00:24:35,710 --> 00:24:40,070
+ال order اللي هي إيش تانين إيه أن زاد ال واحد
+
+245
+00:24:40,070 --> 00:24:45,310
+فمعناته generated by ال A هى نفسة generated by ال
+
+246
+00:24:45,310 --> 00:24:45,890
+A تربية
+
+247
+00:24:48,590 --> 00:24:52,770
+طيب لما يكون ال A P بدي ساو P A معناته ال A أنصر
+
+248
+00:24:52,770 --> 00:24:59,670
+وين؟ في ال centralizer ال P ال A أنصر في ال
+
+249
+00:24:59,670 --> 00:25:03,390
+centralizer ال P ف generated by ال A subset من
+
+250
+00:25:03,390 --> 00:25:07,790
+centralizer ال P طب generated by ال A هنافسة
+
+251
+00:25:07,790 --> 00:25:14,120
+generated by ال A تربية فA تربيةأنصر في الـ
+
+252
+00:25:14,120 --> 00:25:19,100
+centralizer الـ P فأنا لو أثبتت أن A تربيع P بيكون
+
+253
+00:25:19,100 --> 00:25:22,440
+حصلت
+
+254
+00:25:22,440 --> 00:25:28,940
+المطلوب بس بي .. A تربية P بيكون حصلت المطلوب بس
+
+255
+00:25:28,940 --> 00:25:32,900
+بي .. A تربية P بيكون حصلت المطلوب بس بي .. A
+
+256
+00:25:32,900 --> 00:25:33,200
+تربية P بيكون حصلت المطلوب بيكون حصلت المطلوب
+
+257
+00:25:33,200 --> 00:25:36,880
+بيكون حصلت المطلوب بيكون حصلت المطلوب بيكون حصلت
+
+258
+00:25:36,880 --> 00:25:36,880
+المطلوب بيكون حصلت المطلوب بيكون حصلت المطلوب
+
+259
+00:25:36,880 --> 00:25:36,880
+بيكون حصلت المطلوب بيكون حصلت المطلوب بيكون حصلت
+
+260
+00:25:36,880 --> 00:25:39,440
+المطلوب بيكون حصلت المطلوب بيكون حصلت المطلوب
+
+261
+00:25:39,440 --> 00:25:47,400
+بيكون حصلعبارة عن A P A inverse لكل inverse اللي
+
+262
+00:25:47,400 --> 00:25:58,980
+يشبه تساوي A P inverse A inverse طيب
+
+263
+00:25:58,980 --> 00:26:07,540
+هذه عبارة عن A A P A inverse في A inverse اللي
+
+264
+00:26:07,540 --> 00:26:13,950
+عبارة عن A P inverse A inverseوبالتالي هذه هي
+
+265
+00:26:13,950 --> 00:26:20,990
+نفسها طبعا أنا بدأت من تحت عشان أفهم نقطة البداية
+
+266
+00:26:20,990 --> 00:26:27,070
+تبعتي مين هي لازم أبدأ بهذه و بهذه هعيد تشكيل الحل
+
+267
+00:26:27,070 --> 00:26:35,850
+و أصل للمطلوب since
+
+268
+00:26:35,850 --> 00:26:39,030
+a
+
+269
+00:26:39,030 --> 00:26:47,890
+p a inverseبدي سوى P inverse خد inverse الطرفين A
+
+270
+00:26:47,890 --> 00:26:54,750
+P A inverse بدي تسوى P inverse ولكل inverse هذه
+
+271
+00:26:54,750 --> 00:27:02,170
+هتصير A P inverse A inverse بدي تسوى P
+
+272
+00:27:10,610 --> 00:27:14,950
+طيب خلّيه على جانب اتذكر ايش الكون اللي بنجيبه
+
+273
+00:27:14,950 --> 00:27:21,770
+احنا بنثبت ان a تربيه b a inverse ايش ده تساوي بي
+
+274
+00:27:21,770 --> 00:27:27,730
+بقى دي اي سالب اتنين هقعد
+
+275
+00:27:27,730 --> 00:27:34,330
+امسك ال a تربيه بي a inverse كيف ده تيجيه also a b
+
+276
+00:27:34,330 --> 00:27:38,690
+inverse a inverse ده تساوي مين بي انفرس
+
+277
+00:27:43,670 --> 00:27:51,510
+أنا أنا أخدت A P Inverse A Inverse ماشي
+
+278
+00:27:51,510 --> 00:27:59,530
+هجيت أضرب A A A B A Inverse A Inverse هد يبقى عنين
+
+279
+00:27:59,530 --> 00:28:10,650
+A P Inverse A Inverse الي مين الي B هي فوق هي
+
+280
+00:28:10,650 --> 00:28:17,330
+فوق Pهذه عبارة عن a تربيع بي a سالب اتنين ايش
+
+281
+00:28:17,330 --> 00:28:27,310
+بيساوي بي يعني a تربيع بي بتساوي بي a تربيع ايش
+
+282
+00:28:27,310 --> 00:28:34,030
+يعني a تربيع بي بتساوي بي a تربيع يعني a تربيع
+
+283
+00:28:34,030 --> 00:28:40,430
+ينتمي ل centralizer ال بي وبالتالي generated by ال
+
+284
+00:28:40,430 --> 00:28:52,240
+a تربيعsome group من الـcentralizer الـB Now order
+
+285
+00:28:52,240 --> 00:29:01,040
+الـA بيساوى 2N زي الواحد odd ايش يعني؟
+
+286
+00:29:01,040 --> 00:29:09,030
+ايش يعني؟ يعني generated by الـA تربيةبدي اساوي
+
+287
+00:29:09,030 --> 00:29:14,650
+generated by الـ A أُس common divisor للتانين
+
+288
+00:29:14,650 --> 00:29:22,610
+والتانين N زاد الواحد اللي هو A أُس واحد يعني
+
+289
+00:29:22,610 --> 00:29:28,700
+generated by الـ Aأحنا خدنا قاعدة انه ال generated
+
+290
+00:29:28,700 --> 00:29:32,800
+by a to m هو نفس ال generated by a أصل grease
+
+291
+00:29:32,800 --> 00:29:38,360
+common divisor لm و order ال a حط ال m اتنين و
+
+292
+00:29:38,360 --> 00:29:42,160
+order ال a اتنين n زادي ال واحد هدولة relatively
+
+293
+00:29:42,160 --> 00:29:45,840
+prime فال grease common divisor له مقداش واحد
+
+294
+00:29:45,840 --> 00:29:50,020
+فgenerated by ال a تربيع هي نفس ال generated by ال
+
+295
+00:29:50,020 --> 00:30:00,670
+a طيب اش يعنييعني generated by ال A صارت sub group
+
+296
+00:30:00,670 --> 00:30:08,170
+من مين؟ من ال centralizer ال B إيش يعني؟ يعني AB
+
+297
+00:30:08,170 --> 00:30:22,110
+بدت ساوي PA AB بدت ساوي PA يعني ABA inverse إيش
+
+298
+00:30:22,110 --> 00:30:29,740
+بدت ساوي؟B بس ABA inverse إيش بتساوي أصلا؟ B
+
+299
+00:30:29,740 --> 00:30:34,040
+inverse يعني B inverse بتساوي B و الخلاصة اللي
+
+300
+00:30:34,040 --> 00:30:40,800
+احنا مطلوب نجيبها أنه B تغبيا بتساوي ال identity
+
+301
+00:30:40,800 --> 00:30:44,840
+واضح؟
+
+302
+00:30:44,840 --> 00:30:47,820
+واضح السؤال يا شباب؟
+
+303
+00:31:04,450 --> 00:31:09,130
+بس وقت فيه .. فيه أفكار يعني طلعت كيف فكرنا في حل
+
+304
+00:31:09,130 --> 00:31:13,710
+و بدأنا من وين؟ من اللي مطلوب نثبته، اشتغلنا
+
+305
+00:31:13,710 --> 00:31:17,550
+ووصلنا لمين؟ للشغل اللي المطلوب احنا نشتغل عليها
+
+306
+00:31:17,550 --> 00:31:25,530
+عشان نصلّى المطلوب بصراحة
+
+307
+00:31:25,530 --> 00:31:25,810
+كتب
+
+308
+00:31:45,950 --> 00:31:50,790
+سنة واحدة و تلاتين على السريع بقولك
+
+309
+00:31:50,790 --> 00:31:58,490
+لو كانت ال order لل J مثلا بيساوي M finite بقولك
+
+310
+00:31:58,490 --> 00:32:04,130
+أثبت أنه يوجد يوجد
+
+311
+00:32:04,130 --> 00:32:08,090
+N such that أن A أُس N بدت ساوي ال identity لكل A
+
+312
+00:32:08,090 --> 00:32:14,280
+في ال J طبعا انا بقولكالـ N هي عبارة عن ال least
+
+313
+00:32:14,280 --> 00:32:19,920
+common multiple ل order A حيث A في الـ G مش شغل
+
+314
+00:32:19,920 --> 00:32:26,100
+على هذه القاعدة خد ال N المطلوبة هي least common
+
+315
+00:32:26,100 --> 00:32:31,320
+multiple ل order العناصر الموجودة فين في الـ G
+
+316
+00:32:31,320 --> 00:32:39,380
+سؤال 32 تبع ال lattice 32 33 34 35 تكلمنا عنهم فضل
+
+317
+00:32:41,970 --> 00:32:46,870
+31 يقولك اثبت انه يوجد عدد بترفع كل عناصر الجي الو
+
+318
+00:32:46,870 --> 00:32:51,170
+بيعطيك ال identity انا بقولك العدد هذا هو ال least
+
+319
+00:32:51,170 --> 00:32:58,450
+common multiple لكل ال orders وبالتالي اي عنصر ال
+
+320
+00:32:58,450 --> 00:33:03,120
+n هذا multiple لل order تبعهفلما ترفع ال a to n
+
+321
+00:33:03,120 --> 00:33:08,840
+هسير ال a او order ال a في رقم ال a مع order ال a
+
+322
+00:33:08,840 --> 00:33:11,180
+بيعطيك ال اد ان انت بتخلص الموضوع طبعا انت عشان
+
+323
+00:33:11,180 --> 00:33:14,600
+تشغل في finite case فالعناصر تبعتي ال a finite
+
+324
+00:33:14,600 --> 00:33:21,060
+يعني عددها محدود وال order الها برضه محدود وبتالي
+
+325
+00:33:21,060 --> 00:33:23,980
+انت بتشغل ال least common multiple العدد محدود من
+
+326
+00:33:23,980 --> 00:33:28,600
+العناصر وكل رقم داخل في الحسبة ايضا محدود فالنتيجة
+
+327
+00:33:28,600 --> 00:33:33,570
+ان رقم اللي هيطلع معاك هو رقمأو عدد طبيعي مش هيكون
+
+328
+00:33:33,570 --> 00:33:37,650
+infinity هان واضح؟
+
+329
+00:33:37,650 --> 00:33:41,950
+طب مش نستفيد منه order ال J بسوا M نستفيد منه هان؟
+
+330
+00:33:41,950 --> 00:33:45,710
+لأ يعني المعضلة أن أنت بتشتغل في finite case فكل
+
+331
+00:33:45,710 --> 00:33:59,970
+ال order تبعت ال J الكبير تبعهم M بفطوش ال M طيب
+
+332
+00:33:59,970 --> 00:34:01,670
+سؤال 36 في شغل برضه
+
+333
+00:34:07,140 --> 00:34:18,500
+ثم اثبت ان الـ j عبارة عن union of a proper صحيح
+
+334
+00:34:18,500 --> 00:34:23,500
+بيجيبوا اركزوا على كلمة proper if and only if j is
+
+335
+00:34:23,500 --> 00:34:35,800
+not cyclic اثبت
+
+336
+00:34:35,800 --> 00:34:42,770
+ان الـ jبارة عن اتحاد proper subgroup if and only
+
+337
+00:34:42,770 --> 00:34:47,650
+if J is not cyclic طب أنا ده الإثبات اتجاهين
+
+338
+00:34:47,650 --> 00:35:01,490
+assume that we can write J بارة عن union H حيث و H
+
+339
+00:35:01,490 --> 00:35:09,120
+proper subgroup من الـ Jان احنا بنقدر نكتب ال j
+
+340
+00:35:09,120 --> 00:35:14,960
+على شكل اتحاد ل subgroups عشان انا اميزها خليها
+
+341
+00:35:14,960 --> 00:35:19,400
+اصغر من ال j ل
+
+342
+00:35:19,400 --> 00:35:27,140
+subgroups proper من ال j ايش بدي اثبت انا ان ال j
+
+343
+00:35:27,140 --> 00:35:30,900
+not cyclic كيف بدي استعمل او اي طريقة بدي استعملها
+
+344
+00:35:30,900 --> 00:35:34,800
+ايش افضل طريقة بدي استعملها
+
+345
+00:35:40,760 --> 00:35:46,760
+شباب كيف بنثبت ان الجروب ليس Cyclic نثبت
+
+346
+00:35:46,760 --> 00:35:54,100
+ان ولا عنصر ال order له بيساوي order للجروب طب
+
+347
+00:35:54,100 --> 00:35:58,780
+انت لا تنساش ان ال j finite ال order لل j بيساوي n
+
+348
+00:35:58,780 --> 00:36:07,780
+finite طب هذه العملية سهلة ولا صعبة؟انت بتاخد عنصر
+
+349
+00:36:07,780 --> 00:36:11,840
+عشوائي بتثبت ان ال order إله لا يساوي n مين
+
+350
+00:36:11,840 --> 00:36:14,860
+الأسهل؟
+
+351
+00:36:14,860 --> 00:36:20,540
+مين الأسهل؟ أستعمل الأسطوب المباشر ولا الغير
+
+352
+00:36:20,540 --> 00:36:26,100
+مباشر؟ أستعمل ال direct ولا ال indirect؟ الأسهل
+
+353
+00:36:26,100 --> 00:36:31,020
+هان أستعمل ال indirect assume that
+
+354
+00:36:31,020 --> 00:36:33,940
+J is cyclic
+
+355
+00:36:37,530 --> 00:36:44,250
+هذا معناته ان الـ J is generated by some A هذا
+
+356
+00:36:44,250 --> 00:36:50,090
+معناته الـ A ينتمي للـ J اللي هي ال union لـ H
+
+357
+00:36:50,090 --> 00:36:56,230
+subgroup من الـ J لـ H لأن الـ G عبارة عن اتحاد
+
+358
+00:36:56,230 --> 00:37:00,210
+بربر subgroups والـ A في الـ J يقبل A موجود في
+
+359
+00:37:00,210 --> 00:37:09,130
+الاتحاد هذا معناته الـ A ينتمي ل some H for someH
+
+360
+00:37:09,130 --> 00:37:14,190
+proper subgroup من الجيه ال A عنصر في proper
+
+361
+00:37:14,190 --> 00:37:20,410
+subgroup من جيه من الجيه هذا معناته انه generated
+
+362
+00:37:20,410 --> 00:37:27,790
+by ال A صارت subgroup من مين من ال H مين generated
+
+363
+00:37:27,790 --> 00:37:30,390
+by ال A يا شباب جيه
+
+364
+00:37:36,010 --> 00:37:44,290
+J subgroup من الـH و الـH أصلا subgroup من مين من
+
+365
+00:37:44,290 --> 00:37:52,190
+الـJ صارت الـJ subgroup من بوبر subgroup منها يعني
+
+366
+00:37:52,190 --> 00:37:59,350
+المبنى اللي انت فيه صار جزء من الغرفة تخيل كيف
+
+367
+00:37:59,350 --> 00:38:04,960
+المبنى طيبة صار جزء من الغرفة اللي انت فيها هناطب
+
+368
+00:38:04,960 --> 00:38:10,700
+و الناس اللي برا الغرفة وين موجودين؟ صارت تناقض
+
+369
+00:38:10,700 --> 00:38:16,000
+لإنه حاسيب معاك ال J بوبر sub group من نفسها و هذا
+
+370
+00:38:16,000 --> 00:38:25,400
+مستحيل تناقض contradiction so J is not cyclic
+
+371
+00:38:25,400 --> 00:38:29,660
+و
+
+372
+00:38:29,660 --> 00:38:33,160
+أصلا ال H بوبر صحيح
+
+373
+00:38:39,820 --> 00:38:46,980
+طيب الجزء التاني لسه شوف
+
+374
+00:38:46,980 --> 00:38:53,600
+قارط سؤال كويس احنا بنثبت ان ال J اتحاد مجموعات
+
+375
+00:38:53,600 --> 00:39:00,240
+جزئية proper منها if and only if هي مش cyclic فلو
+
+376
+00:39:00,240 --> 00:39:04,000
+كانت اتحاد ل proper subgroup اثبتت انها مش cyclic
+
+377
+00:39:04,000 --> 00:39:09,370
+لان لو كانت cyclic هسي في مشكلةيقبل جيه not cyclic
+
+378
+00:39:09,370 --> 00:39:16,590
+حاجة تنتج الاتجاه العكسي نقول assume that
+
+379
+00:39:16,590 --> 00:39:26,530
+جيه is not cyclic اش يعني يعني
+
+380
+00:39:26,530 --> 00:39:34,670
+لكل a في الجيه generated by ال a لا يساوي الجيه اش
+
+381
+00:39:34,670 --> 00:39:41,380
+يعنييعني generated by ال A ال proper subset من
+
+382
+00:39:41,380 --> 00:39:47,720
+مين؟ من ال J هذا
+
+383
+00:39:47,720 --> 00:39:55,560
+معناته الاتحاد A في ال J مش
+
+384
+00:39:55,560 --> 00:40:02,060
+كلهم subset من ال J فالاتحاد تبعه مش هيكون
+
+385
+00:40:05,460 --> 00:40:10,220
+كل واحد من هدول subset من ال j فاتحادهم هيظل
+
+386
+00:40:10,220 --> 00:40:16,020
+subset من ال j طبعا
+
+387
+00:40:16,020 --> 00:40:21,200
+انا بتكلم عليهم كاتحاد ك set مش ك subgroup لإن لو
+
+388
+00:40:21,200 --> 00:40:23,780
+عندك two subgroup الاتحاد تبعه مش ضرر يكون
+
+389
+00:40:23,780 --> 00:40:34,740
+subgroup اعطيها واحد now if a في ال jف a ينتمي ل
+
+390
+00:40:34,740 --> 00:40:41,980
+generated by ال a ف a ينتمي لل union يعني
+
+391
+00:40:41,980 --> 00:40:49,440
+ال j صارت subset من ال union و
+
+392
+00:40:49,440 --> 00:40:56,560
+اعطيها اتنين واحد و اتنين هتصير ال j هي الاتحاد
+
+393
+00:40:59,600 --> 00:41:04,300
+صارت الجي عبارة عن اتحاد subgroup منها وكل واحدة
+
+394
+00:41:04,300 --> 00:41:13,300
+منهم هدولة اشملها with generated
+
+395
+00:41:13,300 --> 00:41:21,140
+by ال a is a proper subgroup of
+
+396
+00:41:21,140 --> 00:41:26,700
+جي لكل a في الجي صارت عبارة عن اتحاد proper
+
+397
+00:41:26,700 --> 00:41:27,420
+subgroup
+
+398
+00:41:31,040 --> 00:41:36,440
+واضحة؟ لأن اثبات السؤال لها .. لأ لها .. هذا ال F
+
+399
+00:41:36,440 --> 00:41:40,000
+and only F لها .. لها .. لها .. لها ال F و لها ال
+
+400
+00:41:40,000 --> 00:41:40,480
+only F
+
+401
+00:42:24,110 --> 00:42:28,890
+37 show that the group of positive rational number
+
+402
+00:42:28,890 --> 00:42:37,850
+under multiplication is not cyclic يعني Q زائد مع
+
+403
+00:42:37,850 --> 00:42:45,270
+ضرب not cyclic Q
+
+404
+00:42:45,270 --> 00:42:54,070
+زائد يعني الأعداد النسبية الموجبةهأقول assume الـ
+
+405
+00:42:54,070 --> 00:43:00,750
+Q generated by some a على b with
+
+406
+00:43:00,750 --> 00:43:06,510
+the greatest common divisor ل a و b بدي يسوي واحد
+
+407
+00:43:06,510 --> 00:43:14,710
+حيث ال a و ال b موجودين في ال initial number طب
+
+408
+00:43:14,710 --> 00:43:19,250
+علشان ماخدتهمش في ال z لإن أنا بتعامل مع مين؟ مع
+
+409
+00:43:19,250 --> 00:43:29,550
+positiveهي التنين بدا تساوي a على b قص
+
+410
+00:43:29,550 --> 00:43:39,730
+أن طبعا .. طبعا clearly أن لا يساوي zero لأن
+
+411
+00:43:39,730 --> 00:43:45,710
+التنين لا يساوي a على b قص صفر ليها واحد also
+
+412
+00:43:47,400 --> 00:43:56,140
+if n بدت ساوي واحد فالتنين بدت ساوي a على b هذا
+
+413
+00:43:56,140 --> 00:44:06,220
+معناته ان ال q star generated by تنين او
+
+414
+00:44:06,220 --> 00:44:11,000
+q زاد generated by تنين هذا معناته ان التلاتة بدت
+
+415
+00:44:11,000 --> 00:44:17,610
+ساوي تنين أسام for someم في الـ z وهذا مستحيل
+
+416
+00:44:17,610 --> 00:44:20,930
+التلقى
+
+417
+00:44:20,930 --> 00:44:27,910
+تلقى تسوى power للتنين طيب if n بدت ساوى سالب واحد
+
+418
+00:44:27,910 --> 00:44:35,730
+يعني ال a على b بدت ساوى نص وبالتالي التلت بدت
+
+419
+00:44:35,730 --> 00:44:41,330
+ساوى نص أُص م والم من ال z يعني التلقى تبدى ساوى
+
+420
+00:44:41,330 --> 00:44:47,950
+تنين أُص م والم من ال z وهذا تناقضيكبى الان لا صفر
+
+421
+00:44:47,950 --> 00:44:53,270
+ولا واحد ولا سالب واحد يكبى يا أكبر من واحد يا
+
+422
+00:44:53,270 --> 00:45:00,430
+أصغر من سالب واحد if n أكبر من الواحد يكبى اتنين
+
+423
+00:45:00,430 --> 00:45:06,590
+بدت ساوي a على b أس n بدت ساوي a أس n على b أس n
+
+424
+00:45:06,590 --> 00:45:13,530
+وبالتالي a أس n بدت ساوي اتنين b أس n
+
+425
+00:45:17,400 --> 00:45:22,520
+هذا معناته تنين تقسم ال a أُس n وبالتالي تنين تقسم
+
+426
+00:45:22,520 --> 00:45:31,640
+ال a يكبر a بدت ساوي تنين k و ال k من ال n يكبر
+
+427
+00:45:31,640 --> 00:45:37,280
+اتنين p أُس n بدت ساوي تنين k أُس n بدت ساوي تنين
+
+428
+00:45:37,280 --> 00:45:42,060
+أُس n k أُس n يكبر p أُس n بدت ساوي تنين n minus
+
+429
+00:45:42,060 --> 00:45:48,600
+واحدك اص ان تنساش ان الان اكبر من الواحد يكبر الان
+
+430
+00:45:48,600 --> 00:45:53,160
+ماينوس الواحد على الاقل واحد يكبر هنا فيه اتنين
+
+431
+00:45:53,160 --> 00:45:57,580
+موجود وبالتالي اتنين تقسم ال بي اص ان يكبر اتنين
+
+432
+00:45:57,580 --> 00:46:05,020
+تقسم ال بي اعطي هذه star وهذه double star هيعطيك
+
+433
+00:46:05,020 --> 00:46:10,480
+ان الجيس common divisor ل a و b اكبر او يسوى اتنين
+
+434
+00:46:10,480 --> 00:46:17,140
+وده مستحيلليش؟ لإن أنا جالي اللي جيزكوا مدفع
+
+435
+00:46:17,140 --> 00:46:22,640
+زورجات دي إيش؟ واحد طبعا لا صفر ولا واحد ولا أكبر
+
+436
+00:46:22,640 --> 00:46:29,560
+من الواحد ولا سالب واحد إيش بيضال عندي؟ if n أقل
+
+437
+00:46:29,560 --> 00:46:39,860
+من سالب واحد نفس الفكرة هسي معاك a على b أسنة بدت
+
+438
+00:46:39,860 --> 00:46:48,200
+ساوي إيش؟ تنين يعنيطبعا ال N أقل من سلب واحد فسلب
+
+439
+00:46:48,200 --> 00:46:57,420
+ال N أكبر من ال واحد معناته A على B طبعا
+
+440
+00:46:57,420 --> 00:47:04,480
+مش هجلبها لغاية هتصير B على A السلب N بدت سوى 2
+
+441
+00:47:04,480 --> 00:47:11,440
+وبالتالي B السلب N بدت سوى 2 A السلب N
+
+442
+00:47:19,340 --> 00:47:24,340
+يكبر تنين تقسم ال B والسالب N يكبر تنين تقسم ال B
+
+443
+00:47:24,340 --> 00:47:30,220
+Similarly تنين
+
+444
+00:47:30,220 --> 00:47:35,260
+هتقسم ال E والسالب N يكبر تنين هتقسم ال A وهذا ما
+
+445
+00:47:35,260 --> 00:47:39,140
+هيعطيك تناقض يكبر لا صفر ولا واحد ولا أكبر من
+
+446
+00:47:39,140 --> 00:47:42,880
+الواحد ولا سالب واحد ولا أصغر من سالب واحد مين
+
+447
+00:47:42,880 --> 00:47:47,420
+ضال؟ So Q
+
+448
+00:47:48,780 --> 00:47:53,720
+زائد is not cyclic
+
+449
+00:47:53,720 --> 00:47:57,440
+يعطيكوا العافية بنجا فان السؤال هذا وحضرة القادمة
+
+450
+00:47:57,440 --> 00:48:02,140
+ان شاء الله هنكمل من سؤال تمانية وتلاتين بس هنحاول
+
+451
+00:48:02,140 --> 00:48:08,080
+انه ننهي المناقشة يعني لن مش هحل كل الأسئلة اللي
+
+452
+00:48:08,080 --> 00:48:10,900
+ضايلة مطلوبة هعطيك فقط هنتائج إليها
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0227cd942936dd8ced76d7faee9e85dabbe9b8cb
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs_postprocess.srt
@@ -0,0 +1,1636 @@
+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 --> 00:03:33,380
+common multiple ل M قص ال least common multiple ل
+
+38
+00:03:33,380 --> 00:03:33,520
+common multiple ل M قص ال least common multiple ل
+
+39
+00:03:33,520 --> 00:03:36,860
+M قص ال least common multiple ل M قص ال least
+
+40
+00:03:36,860 --> 00:03:37,280
+common multiple
+
+41
+00:03:40,270 --> 00:03:47,850
+الـ 0 تنتشر في Z أربعة و عشرين نفس
+
+42
+00:03:47,850 --> 00:03:52,870
+الشيء بعده أربعة عاشر suppose that a cyclic group
+
+43
+00:03:52,870 --> 00:03:56,990
+J has exactly three subgroups J identity and a
+
+44
+00:03:56,990 --> 00:04:03,810
+subgroup of order سبعة what is order J J cyclic
+
+45
+00:04:03,810 --> 00:04:08,690
+generated by ال A اللي هو only
+
+46
+00:04:11,530 --> 00:04:25,630
+subgroups of j are ال identity و ال h حيث order ال
+
+47
+00:04:25,630 --> 00:04:33,250
+h بيساوي سبعة and j itself المطلوب
+
+48
+00:04:33,250 --> 00:04:33,990
+order ال j
+
+49
+00:04:47,620 --> 00:04:53,640
+فكروا انلخص معلوماتنا قولنا لو انا بشتغل في cyclic
+
+50
+00:04:53,640 --> 00:04:59,760
+group ال subgroups كلهم cyclic ال subgroups ال
+
+51
+00:04:59,760 --> 00:05:04,160
+order اللي يقسم ال order لل group وكل قاسم ل order
+
+52
+00:05:04,160 --> 00:05:10,280
+ال group اللي قاسم ال order له هذا القاسم let
+
+53
+00:05:10,280 --> 00:05:17,430
+order الجي بده يساوي nتجمع المعلومات السبعة تقسم
+
+54
+00:05:17,430 --> 00:05:22,730
+الان ليش H subgroup من الجيه و order ال H ودي
+
+55
+00:05:22,730 --> 00:05:34,610
+ساوية سبعة تانية الان لا يساوي سبعة ليش لإن H
+
+56
+00:05:34,610 --> 00:05:40,050
+proper subgroup من الجيه ليش proper لإن جالي فيه
+
+57
+00:05:40,050 --> 00:05:46,930
+ال H و فيه ال جيه و التنتين مختلفةأذا أريد الـ N
+
+58
+00:05:46,930 --> 00:05:56,430
+الـ 7 تقسم الـ N والـ N لا تساوي 7 الـ
+
+59
+00:05:56,430 --> 00:06:03,930
+N مثلا تساوي 7K الـ
+
+60
+00:06:03,930 --> 00:06:14,630
+N ماذا تساوي؟ 7K حيث ك أكبر من 1ليش K أكبر من
+
+61
+00:06:14,630 --> 00:06:23,150
+الواحد؟ لأن الان لا يساوي سبعة But J is cyclic إيش
+
+62
+00:06:23,150 --> 00:06:33,130
+يعني؟ يعني يوجد subgroup T من ال J and other T
+
+63
+00:06:38,280 --> 00:06:42,520
+قدامي تلات خيارات يا إما T بده تساوي ال identity
+
+64
+00:06:42,520 --> 00:06:50,980
+وبالتالي K بده يساوي واحد وهذا تناقض أو
+
+65
+00:06:50,980 --> 00:06:57,580
+T بده تساوي H وبالتالي
+
+66
+00:06:57,580 --> 00:07:03,120
+K بده يساوي سبعة وانا الآن بده يساوي تسعة واربعين
+
+67
+00:07:03,120 --> 00:07:07,080
+وهذا مافيش فيه مشكلة أو
+
+68
+00:07:08,540 --> 00:07:19,940
+كيس واحد هذا كيس اتنين وهذا كيس ثلاثة ال T بتتساوي
+
+69
+00:07:19,940 --> 00:07:25,600
+ال G نفسها هذا
+
+70
+00:07:25,600 --> 00:07:37,640
+ماعنته ان ال K بتتساوي N ايش يعني؟ يعني سبعة Kمش
+
+71
+00:07:37,640 --> 00:07:42,220
+الان بده تساوي 7k وبالتالي واحد بده يساوي سبعة وده
+
+72
+00:07:42,220 --> 00:07:45,520
+عبارة عن ايش؟ من الحالة الوحيدة اللي مافيش فيها
+
+73
+00:07:45,520 --> 00:07:49,240
+تناقض الان
+
+74
+00:07:49,240 --> 00:07:57,580
+بده تساوي تسعة او اربعين وهذا هو الحل السليماني
+
+75
+00:07:57,580 --> 00:08:03,820
+طيب نايد المعطيات تبعت السؤال بيقول لي يوجد ال
+
+76
+00:08:03,820 --> 00:08:10,400
+cyclic groupالها فقط تلاتة subgroup ال identity و
+
+77
+00:08:10,400 --> 00:08:13,700
+subgroup H ال order اللي لها سبعة و ال J نفسها
+
+78
+00:08:13,700 --> 00:08:17,860
+بهيك بيقول لإنه ال J ال order اللي لها أكبر من
+
+79
+00:08:17,860 --> 00:08:23,560
+السبعة و السبعة بتقسم ال order لل J لإن هو J
+
+80
+00:08:23,560 --> 00:08:28,120
+Cyclic بس الآن بدأت تساوي سبعة K و ال K أكبر من
+
+81
+00:08:28,120 --> 00:08:33,800
+الواحد حاجة ال J Cyclic فأكيد لازم تلاقي subgroup
+
+82
+00:08:33,800 --> 00:08:39,250
+ال order اللي لهاK طيب هذه ال sub group يا بده
+
+83
+00:08:39,250 --> 00:08:44,050
+تساوي ال identity انه مافيش غير تلاتها دول وهذا
+
+84
+00:08:44,050 --> 00:08:50,690
+تناقض هيخللي ال K بساوي واحد او ال H بده تساوي او
+
+85
+00:08:50,690 --> 00:08:54,850
+ال T بده تساوي ال H وانا مافيش مشاكل بيعطيني ال
+
+86
+00:08:54,850 --> 00:08:58,950
+Ant سواء باين او ال H هي نفس ال J وانا بيعطيني
+
+87
+00:08:58,950 --> 00:09:03,170
+تناقض يعني بالحالة الوحيدة اللي زبطت معايا هي مين
+
+88
+00:09:03,170 --> 00:09:08,990
+الحالة التانيةوالان بتطلع جديش؟ تسعة واربعين واضحة
+
+89
+00:09:08,990 --> 00:09:19,870
+هذى؟ واضحة يا شباب؟ طيب ايش
+
+90
+00:09:19,870 --> 00:09:26,930
+يا شمش ده؟ ايش .. وان بتكتب؟ هنا؟ احنا بنشد ..
+
+91
+00:09:44,880 --> 00:09:48,500
+حسب النظريات اللي عندي لكل قاسم فيه subgroup الارض
+
+92
+00:09:48,500 --> 00:09:53,820
+لهذه ال subgroup بيساوي القاسم ال
+
+93
+00:09:53,820 --> 00:09:59,640
+K رقم طب و السبعة؟ ال K قاسم تان غير السبعة
+
+94
+00:10:03,160 --> 00:10:07,260
+طيب خمس عشر let j be an appealing group at rest
+
+95
+00:10:07,260 --> 00:10:13,280
+what can you say if سبعة is replaced by بيه ال
+
+96
+00:10:13,280 --> 00:10:20,120
+order ل j هي سوى بيه تربيه لو بنستبدل السبعة بيه
+
+97
+00:10:20,120 --> 00:10:25,220
+هيكون ال order عبارة عن بيه تربيه سؤال خمس عشر
+
+98
+00:10:30,230 --> 00:10:41,970
+suppose that a cyclic group J أو JAB يعني group و
+
+99
+00:10:41,970 --> 00:10:50,570
+ال H عبارة عن كل ال J في ال J حيث ال order ل J
+
+100
+00:10:50,570 --> 00:10:58,850
+يقسم 12 prove that H is a subgroup of Jمطلوب ان
+
+101
+00:10:58,850 --> 00:11:08,770
+اثبت هل ممكن
+
+102
+00:11:08,770 --> 00:11:27,590
+نغير 12 بأي رقم هل ممكن نغير 12 بأي رقم هل ممكن
+
+103
+00:11:27,590 --> 00:11:33,090
+نغير 12 بأي رقمالمجموعة بتمثل subgroup كل العناصر
+
+104
+00:11:33,090 --> 00:11:40,650
+اللي في j اللي ال order اللي هي بيقسم 12 طيب تبدأ
+
+105
+00:11:40,650 --> 00:11:48,910
+تبتنوعش subgroup موضوع تقليدي first H لا يسوى 5
+
+106
+00:11:48,910 --> 00:11:55,430
+since ال identity في ال H since ال order لل
+
+107
+00:11:55,430 --> 00:11:57,310
+identity بيسوى 1 يقسم 12
+
+108
+00:12:00,090 --> 00:12:10,230
+طيب ف a و b ينتمي لل H يعني ال order ل a و ال
+
+109
+00:12:10,230 --> 00:12:16,870
+order ل b كلاهما بيقسم مين ال 12 ايش بدي اشوف انا
+
+110
+00:12:16,870 --> 00:12:23,770
+هذا معناته ان a و 12 بيساوي ال identity بيساوي b و
+
+111
+00:12:23,770 --> 00:12:29,810
+12بغض النظر لو اقدر اتنين، تلاتة، ستة، اربعة،
+
+112
+00:12:29,810 --> 00:12:33,650
+اتناش، لأ بهمني ان ال a أُس اتناش و ال b أُس اتناش
+
+113
+00:12:33,650 --> 00:12:41,070
+بيعطيني مين؟ ال identity for a P inverse اللي هي
+
+114
+00:12:41,070 --> 00:12:49,990
+one step ال a P inverse أُس اتناش عبارة عن a أُس
+
+115
+00:12:49,990 --> 00:12:59,640
+اتناش P inverse أُس اتناش هذا السببعلى سبب ايش؟
+
+116
+00:12:59,640 --> 00:13:06,020
+ليش اقدرت اعمل هذه الحركة؟ عشان ال B يعني طيب ال A
+
+117
+00:13:06,020 --> 00:13:13,180
+وصلة و اتناش identity ال B وصلة و اتناش هذا
+
+118
+00:13:13,180 --> 00:13:17,440
+هيساوة ال identity في B وصلة و اتناش inverse يعني
+
+119
+00:13:17,440 --> 00:13:24,830
+identity inverse هيساوة identity ال A P inverseالـ
+
+120
+00:13:24,830 --> 00:13:31,150
+order اللي بيقسم الـ 12 a,b,in,out ينتمي لمين؟ للـ
+
+121
+00:13:31,150 --> 00:13:38,490
+H فبالتالي الـ H sub group من مين؟ من الـ G هل
+
+122
+00:13:38,490 --> 00:13:45,070
+الرقم 12 special؟ لو بدلت 12 بأي رقم تاني؟ مش
+
+123
+00:13:45,070 --> 00:13:50,630
+ضروري مضعفة لو حطيت 7 بدل 12، في مشكلة؟ لو حطيت
+
+124
+00:13:50,630 --> 00:13:59,680
+1000؟ مافيش مشكلة، 12is not special يعني ممكن تبدل
+
+125
+00:13:59,680 --> 00:14:05,000
+ال 12 بأي رقم مين الحاجة الضرورية هنا ال abelian
+
+126
+00:14:05,000 --> 00:14:13,000
+مش ال 12 لو مش abelian ماقدرتش انا اعمل الفكرة هذه
+
+127
+00:14:13,000 --> 00:14:19,180
+طيب
+
+128
+00:14:20,740 --> 00:14:25,380
+ليش 12 مش special؟ شيل 12 وحط أي رقم بدك إياها،
+
+129
+00:14:25,380 --> 00:14:28,960
+بيفرق معاك؟ طيب، هيك ب 12 مش special
+
+130
+00:14:50,820 --> 00:14:56,200
+أه اللى خلانى أقدر أشتغل هنا بالأسلوب أو و أطلع
+
+131
+00:14:56,200 --> 00:15:05,020
+النتيجة اللى موجودة قدامك هو أنه لجروب قابيل يعنى
+
+132
+00:15:05,020 --> 00:15:10,720
+17 complete the statement order ال A بتيسار order
+
+133
+00:15:10,720 --> 00:15:16,280
+ال A ترمي if and only if order ال A is is ايش
+
+134
+00:15:20,770 --> 00:15:24,890
+17 complete the following statement order A بيسوي
+
+135
+00:15:24,890 --> 00:15:38,950
+order A تربيع if and only if order A is يبسط
+
+136
+00:15:38,950 --> 00:15:47,750
+ال order لإيه؟ طلع معايا نشوف بعض الحلات و نجمعهم
+
+137
+00:15:47,750 --> 00:15:51,940
+عشان نحط كيس واحدةأردر الـ A بيسوي أردر ال A تربيه
+
+138
+00:15:51,940 --> 00:15:58,780
+مين ممكن تلاقي تحت هذا الإطار ممكن نضمه أولا
+
+139
+00:15:58,780 --> 00:16:04,260
+الـidentity أردر ال E بيسوي أردر ال E تربيه بيسوي
+
+140
+00:16:04,260 --> 00:16:09,620
+واحدة اتنين لو
+
+141
+00:16:09,620 --> 00:16:16,460
+أردر ال A infinite برضه
+
+142
+00:16:16,460 --> 00:16:17,580
+أردر ال E تربيه infinite
+
+143
+00:16:22,670 --> 00:16:28,250
+بس ايش بيظل عندي حالة؟ حالة ال finite في ال finite
+
+144
+00:16:28,250 --> 00:16:34,930
+كام كيس عندي؟ فردي و زوجي لو كان أرضر ال a زوجي هل
+
+145
+00:16:34,930 --> 00:16:41,270
+هذا كلام يكون صحيح؟ لو أرضر ال a بدت سوى 2q فأرضر
+
+146
+00:16:41,270 --> 00:16:48,190
+ال a تقريبا بدت سوى q إيه كده؟ بدي أنفذ زوجيطب
+
+147
+00:16:48,190 --> 00:16:53,670
+نشوف الفردي لو order ال A تسوى 2Q زي 1 برضه order
+
+148
+00:16:53,670 --> 00:17:01,370
+ال A تربية 2Q زي 1 ايك بقى ال identity زبطت طب
+
+149
+00:17:01,370 --> 00:17:06,550
+هتنساش ان ال identity ممكن تدخل وين في حالة ال
+
+150
+00:17:06,550 --> 00:17:12,930
+order الفردي ال identity ال order الهيش واحد و ال
+
+151
+00:17:12,930 --> 00:17:17,160
+infiniteيجب الفردي بظبط و ال infinite بظبط مين
+
+152
+00:17:17,160 --> 00:17:23,760
+اللي بظبط ايش يجب ايش نقول if order a is not even
+
+153
+00:17:23,760 --> 00:17:30,840
+if and سبعة عاشر بدك تكملها if and only if order a
+
+154
+00:17:30,840 --> 00:17:34,700
+is not even
+
+155
+00:17:34,700 --> 00:17:39,780
+ركز معايا مافيش infinite even مافيش infinite even
+
+156
+00:17:39,780 --> 00:17:44,910
+و oddالـ Infinite مش فيه even أو odd الـ Infinite
+
+157
+00:17:44,910 --> 00:17:49,570
+Infinite واضح؟
+
+158
+00:17:49,570 --> 00:17:52,850
+يعني هي لو حالة واحدة كانت قولت if and only if
+
+159
+00:17:52,850 --> 00:17:56,890
+order الـ A infinite مثلا لو نفيت هذه وهذه بس أنا
+
+160
+00:17:56,890 --> 00:18:01,230
+نفيت واحدة و أثبتت تنتين فبدل ما أقول if and only
+
+161
+00:18:01,230 --> 00:18:05,150
+if order ال A is infinite أو order ال A is odd
+
+162
+00:18:05,150 --> 00:18:09,190
+بقول لأ not even بغيّر حالي طب كيف الوضع اللي قلت
+
+163
+00:18:09,190 --> 00:18:15,350
+من ال Q يعني؟order a بيبقى اثنين اثنين اثنين اثنين
+
+164
+00:18:15,350 --> 00:18:18,650
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+165
+00:18:18,650 --> 00:18:20,710
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+166
+00:18:20,710 --> 00:18:20,750
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+167
+00:18:20,750 --> 00:18:22,010
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+168
+00:18:22,010 --> 00:18:24,130
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+169
+00:18:24,130 --> 00:18:30,430
+اثنين اثنين ا
+
+170
+00:18:39,470 --> 00:18:45,210
+بتساوي order of a تربيع هجيت قدامي order of a تلت
+
+171
+00:18:45,210 --> 00:18:53,290
+حالات even, odd, infinite هجيت هذه بتظبط وهذه
+
+172
+00:18:53,290 --> 00:19:00,950
+بتظبط وهذه لأ فأوحان في هذه if and only if order
+
+173
+00:19:00,950 --> 00:19:08,530
+of a is not even طيب
+
+174
+00:19:11,590 --> 00:19:17,390
+مش فاهم مش فاهم ال even و ال odd ده مش يعني even
+
+175
+00:19:17,390 --> 00:19:24,990
+طيب فلو كان order ال A بده سوى اتنين Q يعني A أُس
+
+176
+00:19:24,990 --> 00:19:28,610
+اتنين Q بده سوى ال identity يعني A تربيه أُس Q بده
+
+177
+00:19:28,610 --> 00:19:34,250
+سوى ال identity فorder ال A تربيه على الأكثر Q أقل
+
+178
+00:19:34,250 --> 00:19:38,450
+من order ال A إيه؟ فلو كان order ال A even هذه
+
+179
+00:19:38,450 --> 00:19:47,360
+مابتنفعشهذه غير مفيدة، واضحة؟ حجزت، لو كان order
+
+180
+00:19:47,360 --> 00:19:51,120
+الـA بيتساوي ماله نهاية فأكيد order الـA تربيه
+
+181
+00:19:51,120 --> 00:19:58,680
+ماله نهاية يقبل even، مابتنفعش ال infinite بتنفع،
+
+182
+00:19:58,680 --> 00:20:04,160
+بيضال مين؟ ال odd حجزت order الـA بيتساوي un وun
+
+183
+00:20:04,160 --> 00:20:10,990
+odd ف order الـA بيتساوي order الـAقص K حيث ان
+
+184
+00:20:10,990 --> 00:20:16,770
+اجيز common divisor ل K و M يساوي 1 صح ولا لأ؟ طب
+
+185
+00:20:16,770 --> 00:20:24,070
+حط بدل K 2 هل هذا كلام صحيح؟ خلط يجب ان اقضر ل A
+
+186
+00:20:24,070 --> 00:20:30,890
+تربيع لكي اجيز common divisor ل 2 و 1 يساوي 2 و M
+
+187
+00:20:30,890 --> 00:20:34,590
+يساوي 1 بس بسرعة
+
+188
+00:20:38,830 --> 00:20:44,910
+لو في عندك J Cyclic يوجد
+
+189
+00:20:44,910 --> 00:20:51,370
+A في الـ J ال order لـ A يساوي مانا نهاية اكم عنصر
+
+190
+00:20:51,370 --> 00:20:56,630
+ال order له finite في ال J طالع معايا ال A ال
+
+191
+00:20:56,630 --> 00:21:00,570
+order له infinite ف A و A تربية و A تكيب و A أس
+
+192
+00:21:00,570 --> 00:21:05,250
+خمسة و A أس أي حاجة هيكون ال order له infinite بعد
+
+193
+00:21:05,250 --> 00:21:19,540
+مين ال identitythe only element of finite order is
+
+194
+00:21:19,540 --> 00:21:26,120
+E هذا فقط في الـ cyclic لو انت بتشتغل في group مش
+
+195
+00:21:26,120 --> 00:21:30,700
+cyclic ممكن تلاقي عناصر ال order اللي هم finite
+
+196
+00:21:30,700 --> 00:21:36,580
+حتى لو كانت ال group infinite حتى لو كانت ال group
+
+197
+00:21:36,580 --> 00:21:41,020
+infiniteإذا أسمي كل جريس كمان بقايا سلطانة، فالأمر
+
+198
+00:21:41,020 --> 00:21:44,440
+مافيه سواء حد؟
+
+199
+00:21:57,580 --> 00:22:01,480
+عشان يكون ال order ل A أُس K بيساوي order ل A يعني
+
+200
+00:22:01,480 --> 00:22:05,980
+بيساوي N فال N بيساوي N على ال divisor ل K و N
+
+201
+00:22:05,980 --> 00:22:08,680
+يعني ال order ل A أُس K بيساوي order ل A
+
+202
+00:22:22,780 --> 00:22:27,960
+سؤال تسعة عشر سهل بتشوف ال generators للعناصر في U
+
+203
+00:22:27,960 --> 00:22:34,240
+تلاتين او بتمسك العناصر بتشوف ايش بولته سؤال عشرين
+
+204
+00:22:34,240 --> 00:22:37,500
+suppose that J is a pelian group of order خمسة و
+
+205
+00:22:37,500 --> 00:22:39,840
+تلاتين and every element of J satisfies the
+
+206
+00:22:39,840 --> 00:22:43,500
+equation X وخمسة و تلاتين دي ساوي identity proof
+
+207
+00:22:43,500 --> 00:22:49,340
+that J is cyclic order
+
+208
+00:22:49,340 --> 00:22:59,540
+لل J دي ساوي خمسة و تلاتينJ is Abelian لكل
+
+209
+00:22:59,540 --> 00:23:15,800
+X في J X و 35 يساوي ال identity يثبت ان J صحيح هل
+
+210
+00:23:15,800 --> 00:23:18,500
+35 special تعالى نشوف
+
+211
+00:23:24,150 --> 00:23:27,670
+جي أبيليان وكل عنصر فيها بيحقق العلاقة ان اكسوس
+
+212
+00:23:27,670 --> 00:23:38,010
+خمسة و تلاتين بيساوي ال identity هل ال جي Cyclic
+
+213
+00:23:38,010 --> 00:23:43,550
+عشان اثبت ان الجي Cyclic لازم يلاقي عنصر يعني
+
+214
+00:23:43,550 --> 00:23:52,770
+المطلوب prove that يوجد جي في الجي او ا في الجيو
+
+215
+00:23:52,770 --> 00:24:07,990
+اخضر انتي ابني سنة و خمسة و تلاتين هاطوني
+
+216
+00:24:07,990 --> 00:24:15,910
+حلولكم لم احضر السؤال او اعتبوني ماشوفتش السؤال
+
+217
+00:24:15,910 --> 00:24:18,890
+قبل هيك فكوا معايا
+
+218
+00:24:21,730 --> 00:24:29,470
+I'm here و لا انا ايش
+
+219
+00:24:29,470 --> 00:24:36,390
+نعمل ايش الموضوع اللي عندك يا شباب جيابيليان زائد
+
+220
+00:24:36,390 --> 00:24:46,490
+الأخضر خمس و تلاتين طيب زائد ان كل
+
+221
+00:24:46,490 --> 00:24:52,250
+العناصربحقق ان اكسوس خمسة و تلاتين بدي ساوي ال
+
+222
+00:24:52,250 --> 00:24:57,210
+identity انا بدي اثبت انه يوجد عنصر ال order له
+
+223
+00:24:57,210 --> 00:25:08,070
+خمسة و تلاتين كيف؟
+
+224
+00:25:08,070 --> 00:25:12,570
+فكروا
+
+225
+00:25:15,710 --> 00:25:22,530
+أسس الطريقة لإثبات جمل بهذا الشكل هي تنقض هفترض ان
+
+226
+00:25:22,530 --> 00:25:32,730
+لا يوجد عنصر ال order الو 35 تنساش انه ال .. لو
+
+227
+00:25:32,730 --> 00:25:37,730
+بدي اخد اي عنصر هنا و يكون عندك x و 35 يساوي ال
+
+228
+00:25:37,730 --> 00:25:43,490
+identityو X في الـ J معناته order كل العناصر
+
+229
+00:25:43,490 --> 00:25:48,270
+الموجودين في الـ J قواسم للخمس و تلاتين قلنا مافيش
+
+230
+00:25:48,270 --> 00:25:52,070
+عنصر ال order له خمس و تلاتين فكل عنصر انا باخد
+
+231
+00:25:52,070 --> 00:25:58,810
+غير ال identity ال order له اما خمسة
+
+232
+00:25:58,810 --> 00:26:07,610
+او سبعة هجي التواجد العناصر حسب ال order خمسة بيجي
+
+233
+00:26:07,610 --> 00:26:08,890
+في أي شكل
+
+234
+00:26:11,690 --> 00:26:15,170
+عناصر ال order يلهم خمسة، لو كان عند ال X ال order
+
+235
+00:26:15,170 --> 00:26:22,430
+يلهم خمسة أكمل عنصر زي بلاج ال order يلهم خمسة X X
+
+236
+00:26:22,430 --> 00:26:29,570
+تربية X تكييب X أربعةهدولة كلهم ال order اللي هم
+
+237
+00:26:29,570 --> 00:26:33,850
+خمسة لو انا لو أخدت X في هذه لجوب ال order اللي هو
+
+238
+00:26:33,850 --> 00:26:37,770
+خمسة و أخدت ال generated by X اللي هو ال identity
+
+239
+00:26:37,770 --> 00:26:41,550
+هو X و X تربيه و X تكيبه و X أربعة مع هذا ال
+
+240
+00:26:41,550 --> 00:26:45,270
+identity الأربع عناصر هدولة اللي هم فيها الخمسة ال
+
+241
+00:26:45,270 --> 00:26:49,150
+order اللي هم خمسة يجب تواجد ال order الخمسة هيكون
+
+242
+00:26:49,150 --> 00:26:53,810
+في إيش؟ في أربعات شيل ال identity من الخمسة
+
+243
+00:26:53,810 --> 00:27:04,360
+وتلاتين كده هيظلأربعة وتلاتين، شيل كل الأربعات،
+
+244
+00:27:04,360 --> 00:27:11,660
+يجب مش كل العناصر ال order لهم خمسة، بنفس الطريقة
+
+245
+00:27:11,660 --> 00:27:18,020
+ال order سبعة بيجي في ستاتX تربيه لإن X هو الستة
+
+246
+00:27:18,020 --> 00:27:22,940
+شيل الستات من الاربعة وتلاتين بيضال أربعة يكبر مش
+
+247
+00:27:22,940 --> 00:27:26,620
+كل العناصر ال order اللي لهم سبعة مش كل العناصر ال
+
+248
+00:27:26,620 --> 00:27:31,680
+order اللي لهم خمسة فش ال order خمسة و تلاتين يكبر
+
+249
+00:27:31,680 --> 00:27:34,620
+في عنصر ال order اللي له خمسة و في عنصر ال order
+
+250
+00:27:34,620 --> 00:27:40,920
+اللي له سبعة خدها ده A اخدها ده B ال order ل A و B
+
+251
+00:27:40,920 --> 00:27:45,260
+هيكون كده؟ خمسة و تلاتين و هو هيكون ال generator
+
+252
+00:27:46,570 --> 00:27:52,910
+فجهز حالك السؤال ده في شغل Assume
+
+253
+00:27:52,910 --> 00:28:06,930
+that there is no element in J with order خمسة و
+
+254
+00:28:06,930 --> 00:28:13,430
+تلاتين فش أنصر في الـ J ال order الو خمسة و تلاتين
+
+255
+00:28:13,430 --> 00:28:15,110
+since
+
+256
+00:28:16,700 --> 00:28:24,260
+X و 35 يساوي ال identity لكل X في J معناته order X
+
+257
+00:28:24,260 --> 00:28:32,920
+هيقسم 35 لكل X في J order
+
+258
+00:28:32,920 --> 00:28:42,500
+X يساوي 35 لكل X في J if X لا يساوي ال identity
+
+259
+00:28:45,790 --> 00:28:52,070
+Order of X بدي يساوي خمسة Or order of X بدي يساوي
+
+260
+00:28:52,070 --> 00:28:59,910
+سبعة طبعا اكيد order of X لا يساوي خمسة و تلاتين
+
+261
+00:28:59,910 --> 00:29:04,950
+يكبر جميع العناصر مع عدل identity يعني ال order له
+
+262
+00:29:04,950 --> 00:29:12,110
+خمسة او سبعة اجازة اللي هنعمله كانت تالي We will
+
+263
+00:29:12,110 --> 00:29:13,650
+show that
+
+264
+00:29:19,910 --> 00:29:23,490
+أحنا هننفيها عشان نشرع الخمسة و السابعة لحالنا و
+
+265
+00:29:23,490 --> 00:29:28,930
+نصلّى تناقض لهذه الجملة اللي نفنها We will show
+
+266
+00:29:28,930 --> 00:29:35,690
+that there
+
+267
+00:29:35,690 --> 00:29:46,310
+is elements in D with order
+
+268
+00:29:47,650 --> 00:29:58,350
+خمسة and elements with order سبعة هاتبت انه يوجد
+
+269
+00:29:58,350 --> 00:30:02,550
+عناصر ال order له خمسة و يوجد عناصر ال order له
+
+270
+00:30:02,550 --> 00:30:07,930
+ايش سبعة برضه هشغل هالجتنا في داخلي هانفي انه ..
+
+271
+00:30:07,930 --> 00:30:11,610
+يعني هقول انه مافيش order سبعة يعني كل ال order
+
+272
+00:30:11,610 --> 00:30:14,610
+خمسة to show that
+
+273
+00:30:17,330 --> 00:30:25,890
+we will first assume that
+
+274
+00:30:25,890 --> 00:30:43,830
+there is no elements in J with order 7 assume that
+
+275
+00:30:43,830 --> 00:30:46,050
+all
+
+276
+00:30:48,400 --> 00:31:00,780
+x لا يساوي ال identity in j has order خمسة Note
+
+277
+00:31:00,780 --> 00:31:05,080
+that if
+
+278
+00:31:05,080 --> 00:31:10,500
+order ال x بدى يساوي خمسة then order ال x تربع بدى
+
+279
+00:31:10,500 --> 00:31:13,800
+يساوي order ال x تكعي بدى يساوي order ال x أربعة
+
+280
+00:31:13,800 --> 00:31:22,530
+بدى يساوي خمسةطبعا هذه بدأ اثبات prove it اثباتها
+
+281
+00:31:22,530 --> 00:31:30,370
+سهل ال order لexos k بدي ساوي ال o اللي هو n اللي
+
+282
+00:31:30,370 --> 00:31:34,430
+هي خمسة على order لجيسكم و ال divisor ل الخمسة و
+
+283
+00:31:34,430 --> 00:31:41,170
+الكيه في نهاية تصل لكلام هذا هذا معناته the order
+
+284
+00:31:41,170 --> 00:31:46,350
+خمسة is found in
+
+285
+00:31:47,360 --> 00:32:02,040
+J in six contains four elements هذا
+
+286
+00:32:02,040 --> 00:32:10,580
+معناته J هتساوي ال identity اتحاد X1 X1 تربية X2
+
+287
+00:32:10,580 --> 00:32:29,670
+X1 تكييبX1 اقص 4 اتحاد X2 X2 تربيع X2 تكييب لان X2
+
+288
+00:32:29,670 --> 00:32:43,030
+اقص 4 اتحاد وصولا ل XI او XT XT تربيع XT تكييب
+
+289
+00:32:59,740 --> 00:33:04,000
+X لا يساوي X تربيه X لا يساوي X تكيب
+
+290
+00:33:06,760 --> 00:33:12,100
+X تربيه لا يساوي X تكريب X تربيه لا يساوي X أربعة
+
+291
+00:33:12,100 --> 00:33:17,800
+X تكريب لا يساوي X أربعة عشان ماحدش يقولي هدول
+
+292
+00:33:17,800 --> 00:33:22,000
+ممكن يكونوا مكررين ولا واحد من ربعي هذا بيساوي
+
+293
+00:33:22,000 --> 00:33:26,880
+التاني لا هذا بيساوي هدول ولا هذا بيساوي هدول ولا
+
+294
+00:33:26,880 --> 00:33:33,940
+هذا بيساوي هذا هذا معناته order ال J بيساوي أربعة
+
+295
+00:33:33,940 --> 00:33:44,120
+T زاد واحدواحد زياد اربعة زياد اربعة بعد الواحد
+
+296
+00:33:44,120 --> 00:33:48,860
+بصيح تجمع اربعات يعني الخمسة و تلاتين بديوا يساوي
+
+297
+00:33:48,860 --> 00:33:56,360
+ايش اربعة T زياد الواحد تنين T بدي يساوي سبعتعش
+
+298
+00:33:56,360 --> 00:34:02,580
+وهذا تناقض هذا
+
+299
+00:34:02,580 --> 00:34:07,620
+تناقض so not
+
+300
+00:34:08,250 --> 00:34:19,910
+all elements in j has order واحد أو خمسة ايش يعني؟
+
+301
+00:34:19,910 --> 00:34:24,130
+مش الكل واحد مش الكل خمسة، مافيش خمسة و تلاتين،
+
+302
+00:34:24,130 --> 00:34:33,710
+إيش هيضل؟ إيش بقى؟ at least there is a ينتمي لل j
+
+303
+00:34:33,710 --> 00:34:42,620
+and order ال a بدي يساوي سبعةأعطيها نجمة Similarly
+
+304
+00:34:42,620 --> 00:34:49,820
+بنفس الطريقة there
+
+305
+00:34:49,820 --> 00:34:58,440
+is P إذا فيها نكسة لا اطلع فيها اجيت على الواجب
+
+306
+00:34:58,440 --> 00:35:06,300
+فادي there is P أنتمي نرجع with order ال P بدي
+
+307
+00:35:06,300 --> 00:35:11,830
+ساوي خمسةطبعا نفس الطريقة بفترض انه فيش order خمسة
+
+308
+00:35:11,830 --> 00:35:16,310
+فكله يا سبعات يا واحد ال order تبع السبعات بيجي
+
+309
+00:35:16,310 --> 00:35:22,050
+فياش؟ هشيل ال واحد ال order تبع السبعات بيجي فياش؟
+
+310
+00:35:22,050 --> 00:35:26,190
+في شكل مجموعات كل مجموعة فيها ست عناصر بيكون عندك
+
+311
+00:35:26,190 --> 00:35:29,750
+خمسة و تلاتين بيكون ستة T زاد الواحد ستة T بيكون
+
+312
+00:35:29,750 --> 00:35:36,190
+اربعة و تلاتين انا هى السبعة و ايه الخمسة؟ستة T
+
+313
+00:35:36,190 --> 00:35:38,310
+بدت ساوي اربع تلات تلات تلات تلات تلات تلات تلات
+
+314
+00:35:38,310 --> 00:35:38,770
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+315
+00:35:38,770 --> 00:35:39,390
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+316
+00:35:39,390 --> 00:35:47,630
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+317
+00:35:47,630 --> 00:35:53,070
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+318
+00:35:53,070 --> 00:35:54,910
+تلات تلات تلات تلات
+
+319
+00:36:05,570 --> 00:36:10,470
+لأ واحدة تتلاتة اربعة التيش ده تكون، عداد، العداد
+
+320
+00:36:10,470 --> 00:36:18,750
+ينتمي لان مش لل Z كمان طيب claim order
+
+321
+00:36:18,750 --> 00:36:22,990
+ال A B بدي ساوي خمسة و تلاتين طبعا اتباع ال claim
+
+322
+00:36:22,990 --> 00:36:25,710
+بصير تناقض مع مين؟ مع الاسيوم
+
+323
+00:36:31,200 --> 00:36:35,160
+Since ال order ل ال A بدي تسوى خمسة أو ال A بدي
+
+324
+00:36:35,160 --> 00:36:41,620
+تسوى سبعة ال order ل ال B بدي تسوى خمسة لو قلنا ال
+
+325
+00:36:41,620 --> 00:36:46,160
+A بيقص خمسة و تلاتين عبارة عن A أقص خمسة و تلاتين
+
+326
+00:36:46,160 --> 00:36:52,000
+في B أقص خمسة و تلاتين identity في identity ايش
+
+327
+00:36:52,000 --> 00:36:57,640
+بدي تسوى identity هذا معناته order ل ال A بي
+
+328
+00:37:01,460 --> 00:37:10,920
+أشماله يقسم الخمسة و تلاتين خلصناش case واحد order
+
+329
+00:37:10,920 --> 00:37:17,190
+ال AB بدي ساوي واحديكبى a,b بدي يسوى ال identity a
+
+330
+00:37:17,190 --> 00:37:23,290
+بدي يسوى b inverse يكبى o الخمسة بدي تسوى او
+
+331
+00:37:23,290 --> 00:37:27,450
+السبعة بدي تسوى order ال a اللي هو order ال b
+
+332
+00:37:27,450 --> 00:37:30,430
+inverse اللي هو order ال b بدي يسوى خمسة وهذا
+
+333
+00:37:30,430 --> 00:37:39,330
+تناقض case اتنين ال
+
+334
+00:37:39,330 --> 00:37:47,120
+order لل a,bبدي ساوي خمسة ال
+
+335
+00:37:47,120 --> 00:37:51,200
+order لل a,b بدي ساوي خمسة ده اش معناته هذا معناته
+
+336
+00:37:51,200 --> 00:37:59,180
+a,b أس خمسة بدي ساوي ال identity a,b أس خمسة بدي
+
+337
+00:37:59,180 --> 00:38:06,560
+ساوي ال identity اش يعني يعني a أس خمسة,b أس خمسة
+
+338
+00:38:06,560 --> 00:38:10,640
+بدي ساوي ال identity يعني a أس خمسة بدي ساوي ال
+
+339
+00:38:10,640 --> 00:38:17,320
+identityهذا معناته السبعة بديساوي order ال a أقل
+
+340
+00:38:17,320 --> 00:38:26,680
+أو يساوي الخمسة و هذا تناقض case ثلاثة order ال a
+
+341
+00:38:26,680 --> 00:38:31,780
+,b بديساوي سبعة order
+
+342
+00:38:31,780 --> 00:38:36,300
+ال a,b بديساوي سبعة يعني a,b والسبعة بديساوي ال
+
+343
+00:38:36,300 --> 00:38:36,720
+identity
+
+344
+00:38:42,000 --> 00:38:46,340
+ماذا يعني؟ يعني a والسبعة بيه السبعة بدي يسووا ال
+
+345
+00:38:46,340 --> 00:38:50,980
+identity يعني ال identity في بيه الخمسة في بيه
+
+346
+00:38:50,980 --> 00:38:55,020
+تربيه بدي يسووا ال identity بيه تربيه بدي يسووا ال
+
+347
+00:38:55,020 --> 00:39:00,980
+identity هذا معناته خمسة تسوي order ال بيه فقال لو
+
+348
+00:39:00,980 --> 00:39:08,240
+يسووا اتنين تنقض مين ضال؟ الواحد لأ الخمسة لأ
+
+349
+00:39:08,240 --> 00:39:17,150
+السبعة لأهذا معناته order ال a,b يسوى 35 هدف نقض
+
+350
+00:39:17,150 --> 00:39:23,810
+مين contradiction contradiction
+
+351
+00:39:23,810 --> 00:39:29,850
+مع مين مع الفرض اللي انا فرضه ان ال a,b او فيش
+
+352
+00:39:29,850 --> 00:39:38,230
+عنصر اللي orderedه 35 with the assumption that
+
+353
+00:39:38,230 --> 00:39:44,700
+there is noX ينتمي من ال J و أغضر ال X بالساعة 35
+
+354
+00:39:44,700 --> 00:39:48,040
+الفرض
+
+355
+00:39:48,040 --> 00:39:56,220
+اللي أنا فرضه خاطئ، إيش الصواب؟ عكسه طب إيش عكسه؟
+
+356
+00:39:56,220 --> 00:40:02,860
+أنا قولت فش الأغضر 35؟يوجد X ينتمي للـ J Order X
+
+357
+00:40:02,860 --> 00:40:08,540
+يتساوي خمسة وتلاتين Order X يتساوي order جي جي
+
+358
+00:40:08,540 --> 00:40:20,060
+جنيريتد by الـ X جي الصارت
+
+359
+00:40:20,060 --> 00:40:24,340
+طبعا
+
+360
+00:40:24,340 --> 00:40:27,540
+هل الخمسة وتلاتين special
+
+361
+00:40:32,600 --> 00:40:38,240
+لو جربت التلاتة و تلاتين مش هينفع لأ، من التلاتة و
+
+362
+00:40:38,240 --> 00:40:41,700
+تلاتين عندك التلاتة و ال 11 التلاتة بتكون موجودة
+
+363
+00:40:41,700 --> 00:40:49,460
+في إيش؟ في أزواج طيب،
+
+364
+00:40:49,460 --> 00:40:54,320
+معناته ممكن يكون عندك حالة يكون الأرض إلها تلاتة؟
+
+365
+00:40:54,320 --> 00:41:06,180
+إيه الشعير؟هل 35 special ولا لا؟
+
+366
+00:41:06,180 --> 00:41:09,980
+تلاتة
+
+367
+00:41:09,980 --> 00:41:14,660
+وتلاتين هل
+
+368
+00:41:14,660 --> 00:41:23,300
+ايه special؟
+
+369
+00:41:23,300 --> 00:41:29,040
+اه
+
+370
+00:41:29,040 --> 00:41:41,320
+شبابو نعمل تلاتة آلاف تسيتيش حاجة طيب و
+
+371
+00:41:41,320 --> 00:41:47,520
+دم هناخد نظرية تجاوب على السؤال هدا هنشتغل على ال
+
+372
+00:41:47,520 --> 00:41:51,760
+ground theorem هنشتغل على ال factor جوهر بالنسبالي
+
+373
+00:41:51,760 --> 00:41:56,100
+التلاتة و تلاتين انا
+
+374
+00:41:56,100 --> 00:42:01,560
+بقدر اجزم دائماإنه يوجد عنصر الأرض غيله تلاتة إن
+
+375
+00:42:01,560 --> 00:42:04,920
+اشتغلت على إحدى عشات، الإحدى عشات بتتواجد فيها في
+
+376
+00:42:04,920 --> 00:42:09,020
+شكل عشرات فدائما بيظل عنصر الأرض غيله تلاتة طب هل
+
+377
+00:42:09,020 --> 00:42:12,200
+كل العناصر لو اشتغلت على التلاتات، التلاتات
+
+378
+00:42:12,200 --> 00:42:19,800
+يتواجدوا في أزواج فبيظل ال identity لكن هل ده يعني
+
+379
+00:42:19,800 --> 00:42:25,100
+ممكن انا لاي .. بالطريقة اللي اشتغلت فيهاأصل لقنع
+
+380
+00:42:25,100 --> 00:42:31,980
+أنه بقدر يكون كل group الأردن والعصر فيه تلتات هل
+
+381
+00:42:31,980 --> 00:42:35,280
+ممكن أن احصل على group فيها تلت و تلتين عنصر و
+
+382
+00:42:35,280 --> 00:42:38,920
+الأردن غيره تلتات؟
+
+383
+00:42:38,920 --> 00:42:43,960
+ايش رايكو؟ انا
+
+384
+00:42:43,960 --> 00:42:47,260
+مش حاجة تجربك على السؤال هذا لما اتأكد منه بس انا
+
+385
+00:42:47,260 --> 00:42:54,310
+على اعتقادي ان الخمسة و تلتين قد تكون specialيعني
+
+386
+00:42:54,310 --> 00:43:02,050
+ممكن يكون عند جروب ال order إلها P في Q ومش Cyclic
+
+387
+00:43:02,050 --> 00:43:14,890
+تلاتة
+
+388
+00:43:14,890 --> 00:43:20,980
+تلاتين عند تلاتة بيزيدشطب انا يا جد هبطمن ان ال 4
+
+389
+00:43:20,980 --> 00:43:23,720
+جديد و 3 جديد معايا يردوا يطلحوا مش 7 انا انا
+
+390
+00:43:23,720 --> 00:43:29,000
+معايا بحنا يا جد قولنا لو كل 1 و 5 ال 1 و 5
+
+391
+00:43:29,000 --> 00:43:33,460
+هيكونوا على الاكتر جداش تنين و تلاتين زي 1 تلات و
+
+392
+00:43:33,460 --> 00:43:40,260
+تلاتين هيضال عنصرين هدول العنصرين يا 7 يا 35 انا
+
+393
+00:43:40,260 --> 00:43:45,520
+نافل 35 فإيش بيضال عندي سبعة فهي كده انا اجزمت انه
+
+394
+00:43:45,520 --> 00:43:48,950
+في عنصر قدرله سبعةعشان ايه كده ان انا فيت ال 35 في
+
+395
+00:43:48,950 --> 00:43:53,570
+الأول عشان نشر على السبعة لحالي عشان ماقلتش كل
+
+396
+00:43:53,570 --> 00:43:58,030
+شوية جولة أبقى لو ال 35 خلصت لو مش 35 ف7 لأ لما
+
+397
+00:43:58,030 --> 00:44:03,910
+فيت ال 35 ضايحت حالي لما جيت جولة لكل سبعة واحد ال
+
+398
+00:44:03,910 --> 00:44:07,890
+maximum تبقى مجدهاش 31 بيبقى الأربعة أكيد منهم
+
+399
+00:44:07,890 --> 00:44:12,570
+الخمسة فدائما في سبعة دائما في خمسة هات واحد سبعة
+
+400
+00:44:12,570 --> 00:44:16,650
+و واحد خمسة بيطلع ال .. طبعا فادات نهانة كتير مين
+
+401
+00:44:17,540 --> 00:44:21,340
+موضوع ال abelian لو مش abelian بقدرش أشغل الشغل
+
+402
+00:44:21,340 --> 00:44:25,200
+اللي موجود هنا في ال cases اللي موجودين في الحالة
+
+403
+00:44:25,200 --> 00:44:30,160
+اللي موجودة ضمن الكلام واضح؟
+
+404
+00:44:30,160 --> 00:44:36,080
+أي سؤال؟ صحيح
+
+405
+00:44:36,080 --> 00:44:41,580
+قفتلك إياها؟ طب عشان حكينا دلوقتي لأن وكسوس خمسة
+
+406
+00:44:41,580 --> 00:44:46,710
+موجهة identityو X6 برجع ال X و X1 مش الأقدر ال X
+
+407
+00:44:46,710 --> 00:44:55,990
+كمسة ف X5 يبقوا عليا أي سؤال يا شباب؟ أي سؤال؟
+
+408
+00:44:55,990 --> 00:44:58,750
+واضح؟ يا عزيزي يا عزيزي يا شباب من كام اليوم
+
+409
+00:44:58,750 --> 00:44:59,990
+اتنين؟
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..164b23432c32dd3524b0cc727f91d5bd40780c86
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GlbhZeGGWuY_raw.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/MDWmOYiQ1Mk_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f59d12d1be7aff335f853617c1aab9d91b797084
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_raw.srt
@@ -0,0 +1,1728 @@
+1
+00:00:21,500 --> 00:00:25,180
+الرحيم استكملنا محاضرة الصبح اتكلمنا 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 ال permutation ال group ان عيدا اللي ماكنش
+
+4
+00:00:35,240 --> 00:00:39,820
+موجود الفكرة ان انا بدي اروح اصنع group فيه
+
+5
+00:00:39,820 --> 00:00:44,440
+functions مع عملية ال composition فعلشان انا اقدر
+
+6
+00:00:44,440 --> 00:00:49,540
+اتعامل مع الكلام هذا لازم اتعامل ك function بهذا
+
+7
+00:00:49,540 --> 00:00:55,310
+الشكلمن مجموعة لنفسها و عشان عملية ال composition
+
+8
+00:00:55,310 --> 00:00:59,410
+بعد كده لو بدأ أخد J تانية مثلا لو بدأ أقول F من X
+
+9
+00:00:59,410 --> 00:01:03,670
+ل Y لازم J تكون من Y لحاجة تانية و علشان أنا بدأ
+
+10
+00:01:03,670 --> 00:01:07,830
+أشغل بحيث أن أحقق عملية ال .. ال .. اللي هو ال
+
+11
+00:01:07,830 --> 00:01:10,230
+pile يتكون موجودة و تكون العملية مغلقة على
+
+12
+00:01:10,230 --> 00:01:15,120
+المجموعة لازم أثبت شغلي على مجموعة واحدةاللي بتكون
+
+13
+00:01:15,120 --> 00:01:21,160
+من المجموعة لمين لنفسها طبعا ال identity موجود ال
+
+14
+00:01:21,160 --> 00:01:24,680
+associative موجود ال closed موجود بيبقى شغلة ال
+
+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 ال inverse معرف ك function
+
+17
+00:01:32,720 --> 00:01:35,920
+من ال X نفسه لازم يكون ال onto موجود فانا بدي
+
+18
+00:01:35,920 --> 00:01:44,480
+أتكلم عن J بتحتوى من كل ال projections F من X لXو
+
+19
+00:01:44,480 --> 00:01:50,720
+f is bijection و
+
+20
+00:01:50,720 --> 00:01:57,780
+اقول ان ال j مع ال composition تمثل ال group هجيت
+
+21
+00:01:57,780 --> 00:02:03,220
+في هذا ال chapter هروح اقول ان ال 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 undergraduatesفاحنا نتعامل
+
+24
+00:02:12,670 --> 00:02:16,070
+مع الـ finite set و ال functions عليها تكون
+
+25
+00:02:16,070 --> 00:02:24,830
+بيجيكشن ال function اللي بتكون بهذا الشكل بنسميها
+
+26
+00:02:24,830 --> 00:02:29,770
+permutation يعني لما تكون ال 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
+او لجزء اكبر منها بنسميها permutation فحروح اقول
+
+29
+00:02:39,450 --> 00:02:47,760
+ان اي functionمن X ل X في مساقنا ال X finite و
+
+30
+00:02:47,760 --> 00:02:51,740
+تكون one to one هذه هنسميها أيش permutation طبعا
+
+31
+00:02:51,740 --> 00:02:55,100
+في ميزة ان لو كانت ال function one to one على
+
+32
+00:02:55,100 --> 00:02:59,260
+finite set فال on two موجود ال one to one على
+
+33
+00:02:59,260 --> 00:03:04,060
+finite set يؤدي إلى ال on two فتخيل مجموعة محدودة
+
+34
+00:03:04,060 --> 00:03:10,240
+زي هيك مثلا A B C D انا بدي أصنع function من ال X
+
+35
+00:03:10,240 --> 00:03:17,760
+لنفسهاالـ 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 هجت
+
+37
+00:03:25,860 --> 00:03:29,700
+F الـ A و F الـ B و F الـ C و F الـ D هم نفسهم الـ
+
+38
+00:03:29,700 --> 00:03:32,960
+A و الـ B و الـ C و الـ D فالـ F الـ A كم احتمال
+
+39
+00:03:32,960 --> 00:03:43,470
+له؟ لأ أربع يا A يا B يا C يا Dطيب لو ايه اخد F في
+
+40
+00:03:43,470 --> 00:03:47,530
+ايه اخد واحد من هدول يكبر هذا اربع احتمالات F في
+
+41
+00:03:47,530 --> 00:03:51,770
+ال B كم احتمال هيكون له تلاتة لإن واحد واحد فضله
+
+42
+00:03:51,770 --> 00:03:57,590
+تلاتة F في ال C اتنين و F في ال D يكبر كم function
+
+43
+00:03:57,590 --> 00:04:02,370
+بقدر اصنع هنا اربع في تلاتة في اتنين في واحد اربع
+
+44
+00:04:02,370 --> 00:04:07,150
+factorialأنا بقدر أصنع اربعة factorial من
+
+45
+00:04:07,150 --> 00:04:10,970
+الاقترانات على مجموعة فيها اربع عناصر وتكون هذه
+
+46
+00:04:10,970 --> 00:04:13,330
+الاقترانات one to one او one to one او one to one
+
+47
+00:04:13,330 --> 00:04:14,290
+او one to one او one to one او one to one او one
+
+48
+00:04:14,290 --> 00:04:15,250
+to one او one to one او one to one او one to one
+
+49
+00:04:15,250 --> 00:04:15,250
+او one to one او one to one او one to one او one
+
+50
+00:04:15,250 --> 00:04:15,250
+to one او one to one او one to one او one to one
+
+51
+00:04:15,250 --> 00:04:15,250
+او one to one او one to one او one to one او one
+
+52
+00:04:15,250 --> 00:04:15,270
+to one او one to one او one to one او one to one
+
+53
+00:04:15,270 --> 00:04:15,670
+او one to one او one to one او one to one او one
+
+54
+00:04:15,670 --> 00:04:15,670
+to one او one to one او one to one او one to one
+
+55
+00:04:15,670 --> 00:04:15,890
+او one to one او one to one او one to one او one
+
+56
+00:04:15,890 --> 00:04:29,730
+to one او one to one او one
+
+57
+00:04:29,730 --> 00:04:35,250
+to oneما هي مش هتفرق معايا كتير هذا ايه او اي واحد
+
+58
+00:04:35,250 --> 00:04:38,690
+او اي تنين او اي ان كانت قيمته هتظل نفس النتاج
+
+59
+00:04:38,690 --> 00:04:44,990
+متحققة نخلي العناصر هذه بهذا الشكل واحد و اتنين و
+
+60
+00:04:44,990 --> 00:04:51,030
+تلاتة يعني انا باشتغل المجموعة اللي فيها الأقام
+
+61
+00:04:51,030 --> 00:04:55,850
+واحد لانه واخدت جميع الاقترانات اللي بتكون one to
+
+62
+00:04:55,850 --> 00:05:02,600
+one نقنتوا علي هذه المجموعة هحطها فيمجموعة اسمها
+
+63
+00:05:02,600 --> 00:05:12,840
+sn اللي هي the set of all one to one functions on
+
+64
+00:05:12,840 --> 00:05:19,480
+واحد اتنين لعند n هذه الـ sn هنسميها symmetry
+
+65
+00:05:19,480 --> 00:05:25,340
+group او
+
+66
+00:05:25,340 --> 00:05:31,500
+symmetry n group هنظبط تسميها كما شويةهذه هي مجلة
+
+67
+00:05:31,500 --> 00:05:37,220
+شغلنا اليوم سواء كانت على مجموع 1,2,3 ل N أو كانت
+
+68
+00:05:37,220 --> 00:05:41,340
+ال A1,A2 and An مش عارف مين بالظبط هذه اللي انا
+
+69
+00:05:41,340 --> 00:05:45,860
+هسميهم permutation طبعا احنا درسنا شغلة زيها قبل
+
+70
+00:05:45,860 --> 00:05:55,200
+هيك درسنا ل group D3 اش كان فيها؟ R0
+
+71
+00:05:58,110 --> 00:06:03,930
+R120 R240 F1
+
+72
+00:06:03,930 --> 00:06:12,370
+F2 F3 D3 عبارة عن ايش؟ تعامل مع المثلث اذا قلنا 1
+
+73
+00:06:12,370 --> 00:06:24,160
+2 3 ايش ال R0؟بتظل مكاني طيب تعالي أفهمش يعني اظل
+
+74
+00:06:24,160 --> 00:06:28,660
+مكاني الواحد ظل مكانه في الواحد يعني أف الواحد
+
+75
+00:06:28,660 --> 00:06:34,860
+ممكن اعتبره واحد اتنين ظل وين؟ يعني أف التنين و
+
+76
+00:06:34,860 --> 00:06:40,140
+التلاتة ظل وين؟ مكانه يعني أف التلاتة بيساو تلاتة
+
+77
+00:06:40,140 --> 00:06:45,320
+يعني أنا بتكلم عن مين؟ يعني انا بتكلم عن لو خدت
+
+78
+00:06:45,320 --> 00:06:50,030
+مثلا المجموعة Jو اتكلمت عن ال identity function و
+
+79
+00:06:50,030 --> 00:06:59,210
+أخطّلها رمز إبسلون زي هيك طيب لو قلنا ال R Zero
+
+80
+00:06:59,210 --> 00:07:06,170
+هذا هي ال R مية و عشرين أبدا يش دوران بمقدار مية و
+
+81
+00:07:06,170 --> 00:07:11,890
+عشرين درجة في أي اتجاه عكس عقارب الساعة يعني هيك
+
+82
+00:07:11,890 --> 00:07:18,990
+يعني حاسيب معايا واحد اتنينتلاتة وكأنه F الواحد
+
+83
+00:07:18,990 --> 00:07:26,010
+صار تلاتة و F التنين صار واحد و F التلاتة صار
+
+84
+00:07:26,010 --> 00:07:30,010
+اتنين طبعا انا هذا الاقتران واحد اتنين تلاتة
+
+85
+00:07:30,010 --> 00:07:34,730
+الواحد ايش صار تلاتة التلاتة ايش صار
+
+86
+00:07:37,450 --> 00:07:40,430
+ممكن اكتبه بدل من اقول F الواحد يساوي F التانين F
+
+87
+00:07:40,430 --> 00:07:45,210
+التلاتة اكتب الواحد والتانين والتلاتة تغير ترتيبهم
+
+88
+00:07:45,210 --> 00:07:51,630
+لتلاتة واحد اتنين فهذا ال identity عبارة عن ايش
+
+89
+00:07:51,630 --> 00:07:56,370
+الواحد مكانه التانين مكانه التلاتة مكانه يعني هذا
+
+90
+00:07:56,370 --> 00:08:02,970
+هو واحد اتنين تلاتة واحد اتنين تلاتة لكن ال R
+
+91
+00:08:02,970 --> 00:08:08,830
+ميعني عشرينصارت الواحد اتنين تلاتة صارت ايش تلاتة
+
+92
+00:08:08,830 --> 00:08:16,310
+واحد اتنين مش صارت ترتيبة زي هيك طيب هذه بالنسبالي
+
+93
+00:08:16,310 --> 00:08:24,590
+ال R0 ال R 240 كمان لفة واحد اتنين تلاتة يعني F
+
+94
+00:08:24,590 --> 00:08:29,150
+الواحد صارت اتنين F التنين صارت تلاتة F التلاتة
+
+95
+00:08:29,150 --> 00:08:36,050
+صارت ايش واحد يعنيواحد اتنين تلاتة صارت اتنين
+
+96
+00:08:36,050 --> 00:08:42,610
+تلاتة واحد طيب
+
+97
+00:08:42,610 --> 00:08:47,930
+شوية بس مين رجع مكانه؟ محدش هدول رجع مكانه يعني
+
+98
+00:08:47,930 --> 00:08:53,590
+اللي لف التالتة ماهترج على identity اه بس انا خلصت
+
+99
+00:08:53,590 --> 00:08:59,040
+دورانات هفوت على مين هالجير؟ ع reflectionsهي انا
+
+100
+00:08:59,040 --> 00:09:02,900
+لما بدى اجي اعمل هي واحد اتنين تلاتة بدي اعمل
+
+101
+00:09:02,900 --> 00:09:07,560
+reflection بالنسبة للواحد و اجلب هتصير واحد تلاتة
+
+102
+00:09:07,560 --> 00:09:12,880
+اتنين يعني اف الواحد زي ما هي اف التانين تلاتة اف
+
+103
+00:09:12,880 --> 00:09:17,660
+التلاتة اتنين يعني واحد اتنين تلاتة واحد تلاتة
+
+104
+00:09:17,660 --> 00:09:24,150
+اتنين حاجة اقول واحد تلاتة اتنينوهذه بالنسبة لي
+
+105
+00:09:24,150 --> 00:09:27,270
+محايدة، ضالت مكانها الواحد ضال مكانه، مايكبهاش
+
+106
+00:09:27,270 --> 00:09:32,350
+التبديلة صارت تلاتة و اتنين تلاتة و اتنين يعني
+
+107
+00:09:32,350 --> 00:09:36,850
+وكانها تلاتة و اتنين طبعا اللي بعدها هتكون واحد و
+
+108
+00:09:36,850 --> 00:09:42,070
+تلاتة و واحد و اتنين فعليا،
+
+109
+00:09:42,070 --> 00:09:47,190
+طبعا هذه تنساش عبارة عن مين؟S3 ان صارت مجموعة
+
+110
+00:09:47,190 --> 00:09:52,890
+التباديل للمجموعة اللي فيها مين 1 2 3 ال D3 و ال
+
+111
+00:09:52,890 --> 00:10:00,390
+S3 هما واحد هما نفس ال group لكن هذا منطلع إلها من
+
+112
+00:10:00,390 --> 00:10:07,970
+الزاوية وهذا منطلع من زاوية طيب هل ممكن أنعمم هل
+
+113
+00:10:07,970 --> 00:10:18,030
+ال D4 هتصير S4 تعالى نشوف ال D4اكم هنصه فيها ال S4
+
+114
+00:10:18,030 --> 00:10:21,210
+ال
+
+115
+00:10:21,210 --> 00:10:26,710
+D4 مش هي ال S4 لأ هتكون جزء من ال S4 هناخد في مثال
+
+116
+00:10:26,710 --> 00:10:31,110
+كمان شوية كيف هذا الكلام يكون واقعى هنكتب التعريف
+
+117
+00:10:31,110 --> 00:10:37,350
+ناخد أنثلاف بعدك إذا ضال وقت هنصل لمثال ال D4 ان
+
+118
+00:10:37,350 --> 00:10:43,630
+شاء الله كيف؟
+
+119
+00:10:52,890 --> 00:10:59,990
+definition C4 مش الاسفار دي واحد
+
+120
+00:10:59,990 --> 00:11:06,490
+a permutation of
+
+121
+00:11:06,490 --> 00:11:12,730
+a set A زي ما قلنا is a function
+
+122
+00:11:16,040 --> 00:11:33,840
+from A to A that is both one to one and unto كلمة
+
+123
+00:11:33,840 --> 00:11:41,760
+واحدة يعنيش projection تانين الـPermutation group
+
+124
+00:11:44,770 --> 00:11:48,590
+هنا اتكلمنا عن البرموتاشن نفسها البرموتاشن ال
+
+125
+00:11:48,590 --> 00:11:53,810
+group عبارة عن مجموعة بتحتوي برموتاشن مع عملية مين
+
+126
+00:11:53,810 --> 00:11:59,030
+ال composition لان انا بتكلم عن functions و انا
+
+127
+00:11:59,030 --> 00:12:02,370
+اصلا صنعت الموضوع هذا عشان اتناول عملية ال
+
+128
+00:12:02,370 --> 00:12:06,250
+composition و اخليها ضمن ال group ال permutation
+
+129
+00:12:06,250 --> 00:12:13,880
+groupعبارة عن جروب طبعا تحت عملية ال composition
+
+130
+00:12:13,880 --> 00:12:17,700
+العناصر اللي فيها عبارة عن permutation على مجموعة
+
+131
+00:12:17,700 --> 00:12:27,320
+ما permutation group of asset
+
+132
+00:12:27,320 --> 00:12:33,740
+permutation group of asset a is
+
+133
+00:12:40,670 --> 00:12:49,470
+asset of permutations on
+
+134
+00:12:49,470 --> 00:13:02,790
+a that form a group under
+
+135
+00:13:02,790 --> 00:13:06,510
+function
+
+136
+00:13:06,510 --> 00:13:09,010
+composition
+
+137
+00:13:17,160 --> 00:13:22,380
+عبارة عن مجموعة
+
+138
+00:13:22,380 --> 00:13:29,020
+بتعمل جروب مع عملية تركيب الدولة في هذا ال chapter
+
+139
+00:13:29,020 --> 00:13:43,560
+we study here the case where a is finiteيعني في
+
+140
+00:13:43,560 --> 00:13:48,660
+مصراخنا شباب هندرس الحالة اللي بيكون فيها المجموعة
+
+141
+00:13:48,660 --> 00:13:53,200
+مثال ناخد
+
+142
+00:13:53,200 --> 00:13:58,160
+مثال على permutation و بعد هيك ناخد مثال على
+
+143
+00:13:58,160 --> 00:14:03,880
+permutation الجرم كيف؟
+
+144
+00:14:05,440 --> 00:14:10,260
+لأ في هذا المثال تحديدًا هنشتغل يعني ال A عبارة عن
+
+145
+00:14:10,260 --> 00:14:14,680
+واحد اتنين تلاتة لعند N طبعًا انا شراحت في البداية
+
+146
+00:14:14,680 --> 00:14:17,860
+ليش اخترت واحد اتنين تلاتة لعند N لو كان بدل واحد
+
+147
+00:14:17,860 --> 00:14:21,580
+اتنين تلاتة A واحد اتنين لعند AN نفس الخصائص
+
+148
+00:14:21,580 --> 00:14:25,990
+الموجودةممكن تكون موجودة على المجموعة من واحد
+
+149
+00:14:25,990 --> 00:14:31,790
+لاتنين لتلاتة لعندان هي هي انا مش هاهتم كتير عنصر
+
+150
+00:14:31,790 --> 00:14:36,570
+ايش قيمته بدي انا هان خصائص اللي هي التبديل على
+
+151
+00:14:36,570 --> 00:14:41,710
+هذه العناصر فبختار مجموعة سهلة عشان اقدر اتعامل
+
+152
+00:14:41,710 --> 00:14:49,930
+اتكون الكتوبة اسهل طيب ناخد ال اتش اولدت ال ايه
+
+153
+00:14:49,930 --> 00:14:57,160
+عبارة عن الواحد واتنين وتلاتة واربعةlet alpha من a
+
+154
+00:14:57,160 --> 00:15:05,800
+ل a be given as alpha الواحد بدي ساوي تلاتة الف
+
+155
+00:15:05,800 --> 00:15:09,600
+اتنين بدي ساوي واحد الف التلاتة بدي تساوي أربعة
+
+156
+00:15:09,600 --> 00:15:12,640
+والف
+
+157
+00:15:12,640 --> 00:15:17,140
+الأربعة بدي تساوي اتنين
+
+158
+00:15:21,680 --> 00:15:31,740
+بيتا من a ل a be given as بيتا التنين او بيتا
+
+159
+00:15:31,740 --> 00:15:38,260
+الواحد بدت ساوي واحد بيتا التنين بدت ساوي تلاتة
+
+160
+00:15:38,260 --> 00:15:44,060
+بيتا التلاتة بدت ساوي أربعة و بيتا الأربعة بدت
+
+161
+00:15:44,060 --> 00:15:48,100
+ساوي اتنين هيتوا functions clearly
+
+162
+00:15:52,440 --> 00:16:05,880
+الفا and بيتا are permutation on a ليش ال one to
+
+163
+00:16:05,880 --> 00:16:09,700
+one و ال on two واضح من التعريف التعريف موجود عندك
+
+164
+00:16:09,700 --> 00:16:13,760
+بطريقة السرد ولا عنصر بروح ل .. ولا .. مافيش
+
+165
+00:16:13,760 --> 00:16:18,660
+عنصرين بروحوا لنفس القيمة طبعا و لعملية on two
+
+166
+00:16:24,210 --> 00:16:30,290
+طيب ال alpha و ال beta ممكن اكتبهم كتالة we can
+
+167
+00:16:30,290 --> 00:16:40,430
+write ال alpha عبارة عن واحد اتنين تلاتة اربعة ال
+
+168
+00:16:40,430 --> 00:16:46,250
+واحد لمين بيروح لمين بيروح الواحد التانية لمين
+
+169
+00:16:46,250 --> 00:17:01,430
+بيروح التلاتة والاربعةطيب ال beta 1,2,3,4 ال 1,2,3
+
+170
+00:17:01,430 --> 00:17:12,710
+,4,2 هدا هي ال alpha و هدا هي ال beta طيب for
+
+171
+00:17:12,710 --> 00:17:18,390
+alpha beta طبعا انا هجيت هتعامل alpha permutation
+
+172
+00:17:18,390 --> 00:17:22,460
+و beta permutationالعملية اللي بينهم عملية ايش
+
+173
+00:17:22,460 --> 00:17:27,900
+composition المفروض ان يكون Alpha Beta عبارة عن
+
+174
+00:17:27,900 --> 00:17:37,640
+اقتران من A ل A with Alpha Beta ل X عبارة عن Alpha
+
+175
+00:17:37,640 --> 00:17:41,060
+Beta
+
+176
+00:17:41,060 --> 00:17:50,960
+ل X لأن العملية Alpha Beta فعليا هو AlphaComposite
+
+177
+00:17:50,960 --> 00:17:55,980
+Beta طب ليش؟ هذا كانت الزمرة الدليل قال لأ يا عمي
+
+178
+00:17:55,980 --> 00:18:00,380
+هو تعريف العملية أنا مانتش أحط هنا نقطة ال Alpha
+
+179
+00:18:00,380 --> 00:18:03,740
+في Beta عبارة عن أنصف ال group و أنصف ال group
+
+180
+00:18:03,740 --> 00:18:06,540
+العملية اللي بينهم عملية composition بين function
+
+181
+00:18:06,540 --> 00:18:12,880
+و function طيب طب تعالى نشوف Alpha Beta للواحد
+
+182
+00:18:12,880 --> 00:18:19,140
+عبارة عن Alpha Beta الواحد Beta الواحد يا ديش يا
+
+183
+00:18:19,140 --> 00:18:25,470
+شباببيتا الواحد واحد طب الف الواحد جديش تلاتة طب
+
+184
+00:18:25,470 --> 00:18:32,610
+الف بيتا and التنين عبارة عن الف بيتا التنين بيتا
+
+185
+00:18:32,610 --> 00:18:39,210
+التنين جديش تلاتة طب و الف الأربع التلاتة أربع طب
+
+186
+00:18:39,210 --> 00:18:45,850
+الف بيتا and التلاتة عبارة عن الف بيتا التلاتة
+
+187
+00:18:45,850 --> 00:18:52,280
+بيتا التلاتة جديشبيتا التلاتة كده؟ أربعة ألفة
+
+188
+00:18:52,280 --> 00:18:56,160
+الاربعة ألفة
+
+189
+00:18:56,160 --> 00:19:02,640
+بيتا للاربعة عبارة عن ألفة بيتا يعني ألفة التنين
+
+190
+00:19:02,640 --> 00:19:12,060
+ألفة التنين كده؟ واحد طيب هذا معناته أن ألفة بيتا
+
+191
+00:19:12,060 --> 00:19:17,620
+بقدر أكتب زيك واحد اتنين تلاتة أربعة الواحد لمين
+
+192
+00:19:17,620 --> 00:19:26,830
+راح؟الواحد لمين للتلاتة والتنين والتلاتة والاربع
+
+193
+00:19:26,830 --> 00:19:41,870
+للواحد طيب تعالى نشوف beta alpha for beta alpha هو
+
+194
+00:19:41,870 --> 00:19:47,930
+مش قاعدة انهم يتساوي هي مش قاعدة انهم يتساوي تعالى
+
+195
+00:19:47,930 --> 00:19:56,830
+نشوفبيتا ألفة للواحد عبارة
+
+196
+00:19:56,830 --> 00:20:02,330
+عن بيتا ألف الواحد ألف الواحد كده؟ ألف الواحد
+
+197
+00:20:02,330 --> 00:20:09,710
+تلاتة بيتا التلاتة أربع طيب بيتا ألفة للتانين يعني
+
+198
+00:20:09,710 --> 00:20:17,250
+بيتا ألف التانين ألف التانين كده؟ واحد بيتا للواحد
+
+199
+00:20:21,150 --> 00:20:28,410
+بيتا ألفة للتلاتة بيتا ألفة التلاتة بيتا ألفة
+
+200
+00:20:28,410 --> 00:20:35,770
+التلاتة جديش؟ طيب بيتا ألفة للأربعة بيتا ألفة
+
+201
+00:20:35,770 --> 00:20:42,550
+للأربعة ألفة للأربعة جديش؟ اتنين و بيتا التالين
+
+202
+00:20:42,550 --> 00:20:50,610
+بيتا ألفةعبارة عن واحد اتنين تلاتة اربعة الواحد
+
+203
+00:20:50,610 --> 00:20:58,350
+للاربعة تلين الواحد و اتنين و تلاتة ايش بتلاحظ؟ in
+
+204
+00:20:58,350 --> 00:21:05,290
+general Alpha
+
+205
+00:21:05,290 --> 00:21:11,810
+Beta ليسوا Beta Alpha ليش قولت in general؟ قد يكون
+
+206
+00:21:11,810 --> 00:21:12,710
+هناك حالات
+
+207
+00:21:16,150 --> 00:21:20,970
+أو هناك حالات لـ .. لـ .. لت .. ان كل عملية تبدلية
+
+208
+00:21:20,970 --> 00:21:24,650
+هذا
+
+209
+00:21:24,650 --> 00:21:29,690
+مش صورة، هذا مثال مثال لنفهم العملية كده بالتم، بس
+
+210
+00:21:39,190 --> 00:21:43,670
+هل كل مرة يا شباب بدي أقدر أعرفلك Alpha Beta and
+
+211
+00:21:43,670 --> 00:21:46,570
+الواحد يعني Alpha Beta الواحد يعني Alpha مثلا
+
+212
+00:21:46,570 --> 00:21:53,870
+الواحد يعني مستوى تلاتة لأ how to
+
+213
+00:21:53,870 --> 00:22:00,950
+do this using
+
+214
+00:22:00,950 --> 00:22:11,090
+the notation واحد اتنين تلاتةالف الواحد الف التاني
+
+215
+00:22:11,090 --> 00:22:18,170
+الاند الف انا كيف نستعمل ال notation هذا في الحساب
+
+216
+00:22:18,170 --> 00:22:27,490
+نحسب الف بيتا الف بيتا عبارة عن مين هاي الالفة كده
+
+217
+00:22:27,490 --> 00:22:34,530
+الالفة هنا تلاتة واحد اربعة اتنين وبيتا واحد اتنين
+
+218
+00:22:34,530 --> 00:22:39,310
+تلاتة اربعةكداش؟ واحد .. تلاتة .. اربعة .. اتنين
+
+219
+00:22:39,310 --> 00:22:42,990
+كيف بدي اتم الامر هذا؟ هي واحد .. هي اتنين .. هي
+
+220
+00:22:42,990 --> 00:22:48,470
+تلاتة .. هي اربعة؟ بنبدأ من وين؟ الواحد مين اقرب
+
+221
+00:22:48,470 --> 00:22:51,990
+للواحد
+
+222
+00:22:51,990 --> 00:22:57,990
+هنا؟ الالف ولا البيتا؟ البيتا ببدأ البيتا وان
+
+223
+00:22:57,990 --> 00:23:02,670
+بتاخد الواحد؟ للواحد بنجي هنا الالف وان بتاخد
+
+224
+00:23:02,670 --> 00:23:04,850
+الواحد؟ يجب الواحد يروح للتلاتة
+
+225
+00:23:07,750 --> 00:23:11,730
+الواحد باجي من هنا بروح للواحد باجي هنا الواحد لمن
+
+226
+00:23:11,730 --> 00:23:18,510
+بيروح؟ لل تلاتة طيب التنين التلاتة لمن؟ اتنين
+
+227
+00:23:18,510 --> 00:23:23,270
+تلاتة تلاتة اربعة يكبر اتنين للاربعة تلاتة للاربعة
+
+228
+00:23:23,270 --> 00:23:27,490
+اربعة للتنين يكبر تلاتة للتنين اربعة للتنين واتنين
+
+229
+00:23:27,490 --> 00:23:33,190
+للواحد يكبر اربعة لمن؟ للواحد ماشي بس بدون الكتابة
+
+230
+00:23:33,190 --> 00:23:35,930
+هذه كلها بدون الكتابة هذه كلها
+
+231
+00:23:40,500 --> 00:23:45,000
+نبدأ بالواحد الواحد لمين بروح انا؟ بمسك الواحد انا
+
+232
+00:23:45,000 --> 00:23:49,400
+و بطلع فيه فوق لمين هيروح؟ يجب احد لمين؟ انا بتبدأ
+
+233
+00:23:49,400 --> 00:23:54,880
+من ال beta اه من ال beta التاني لمين؟ التلاتة
+
+234
+00:23:54,880 --> 00:23:59,980
+لمين؟ يجب اتنين للاربعة تلاتة اربعة اربعة اتنين
+
+235
+00:23:59,980 --> 00:24:04,300
+يجب تلاتة للتانين اربعة اتنين اتنين واحد يجب اربعة
+
+236
+00:24:04,300 --> 00:24:12,180
+للواحد طيب نفس الطريقة beta alphaواحد اتنين تلاتة
+
+237
+00:24:12,180 --> 00:24:19,240
+اربعة واحد تلاتة اربعة اتنين فيه
+
+238
+00:24:19,240 --> 00:24:26,980
+واحد اتنين تلاتة اربعة تلاتة واحد اربعة اتنين طيب
+
+239
+00:24:26,980 --> 00:24:30,680
+واحد
+
+240
+00:24:30,680 --> 00:24:36,740
+اتنين تلاتة اربعة الواحد لمن بيروح تلاتة لمن هيروح
+
+241
+00:24:36,740 --> 00:24:41,630
+يقبل واحد تلاتة تلاتة اربعة يقبل واحد للاربعةطيب
+
+242
+00:24:41,630 --> 00:24:46,250
+اتنين واحد واحد واحد يكبر اتنين للواحد تلاتة
+
+243
+00:24:46,250 --> 00:24:50,690
+للاربعة واربعة للتانين يكبر تلاتة لمن للتانين
+
+244
+00:24:50,690 --> 00:24:56,490
+اربعة للتانين واتنين للتلاتة يكبر اربعة لمن بيروح
+
+245
+00:24:56,490 --> 00:25:08,910
+بيروح للتلاتة واضح
+
+246
+00:25:18,740 --> 00:25:25,980
+symmetric group etc طبعا المثال هذا شباب اتعاملنا
+
+247
+00:25:25,980 --> 00:25:30,460
+معاه مع ال permutation على شكل عناصر permutation و
+
+248
+00:25:30,460 --> 00:25:32,340
+permutation تانية كيف بنضرب كيف
+
+249
+00:25:32,340 --> 00:25:43,100
+ببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببب
+
+250
+00:25:43,500 --> 00:25:47,360
+يعني ناخد مجموعة تكون جروب و فيها permutation
+
+251
+00:25:47,360 --> 00:25:57,040
+الثلاثة is the set of all طب أنا ماجول all يعني كل
+
+252
+00:25:57,040 --> 00:26:00,160
+ال permutation الممكنة لكن أنا ماجول a set of
+
+253
+00:26:00,160 --> 00:26:03,400
+permutations on يعني مجموعة permutation على
+
+254
+00:26:03,400 --> 00:26:08,840
+المجموعة قد يكونوا كلهم و قد يكون جزء الثلاثة is
+
+255
+00:26:08,840 --> 00:26:11,440
+the set of all permutations
+
+256
+00:26:16,490 --> 00:26:29,850
+on the set واحد اتنين تلاتة which
+
+257
+00:26:29,850 --> 00:26:34,010
+called هذه
+
+258
+00:26:34,010 --> 00:26:44,110
+الأستلاتة بسميها the symmetric الجروب
+
+259
+00:26:45,820 --> 00:26:52,420
+of order تلاتة طب انا بقول هنا of order تلاتة مش
+
+260
+00:26:52,420 --> 00:26:56,280
+القصد انه عدد العناصر تلاتة لأ ال order تلاتة يعني
+
+261
+00:26:56,280 --> 00:27:01,780
+order المجموعة اللي انا اشتغلت عليها مش order ال
+
+262
+00:27:01,780 --> 00:27:08,700
+permutation اللي بيطلع معايا هبدأ بال E عبارة عن
+
+263
+00:27:08,700 --> 00:27:12,600
+واحد اتنين تلاتة واحد اتنين تلاتة اللي هو
+
+264
+00:27:16,300 --> 00:27:19,800
+الـ E نفسه الواحد بيروح للواحد التاني بيروح للتاني
+
+265
+00:27:19,800 --> 00:27:26,400
+التلاتة بتروح لمين و أخد ال alpha واحد اتنين تلاتة
+
+266
+00:27:26,400 --> 00:27:32,360
+و الواحد هيروح للتانين والتانين هيروح للتلاتة
+
+267
+00:27:32,360 --> 00:27:39,620
+والتلاتة هيروح للواحد هذا عبارة عن ايش عن دوران R
+
+268
+00:27:39,620 --> 00:27:46,410
+مياشي و أخد ال betaإبعاداً 1 2 3 أدخل الواحد يذهب
+
+269
+00:27:46,410 --> 00:27:52,070
+لنفسه والتاني يذهب للثالث والثالث للاثنين يعني هذه
+
+270
+00:27:52,070 --> 00:27:56,610
+عبارة عن ال identity ودوران و reflection وانتوا
+
+271
+00:27:56,610 --> 00:28:01,990
+عارفين ان ال DN بتكونه بدوران و reflection و بيصير
+
+272
+00:28:01,990 --> 00:28:06,630
+تعمل دوران تتكرر مع بعضه وكل تكرار متكررات الدوران
+
+273
+00:28:06,630 --> 00:28:11,450
+مع reflection الأولاني يعطيك reflection جديد تعالى
+
+274
+00:28:11,450 --> 00:28:12,450
+نشوف Alpha تربيع
+
+275
+00:28:18,920 --> 00:28:26,320
+Alpha تغبية عبارة عن الـ Alpha في Alpha عشان
+
+276
+00:28:26,320 --> 00:28:29,020
+شرحتنا الكلام في الأول فاحنا فاهمين أنه هذا
+
+277
+00:28:29,020 --> 00:28:32,760
+reflection لكن مفترض أنه أنا أشر عليه و أتفاجأ أنه
+
+278
+00:28:32,760 --> 00:28:38,880
+هذا reflection بس احنا ضيعنا المفاجأة يعني واحد
+
+279
+00:28:38,880 --> 00:28:45,540
+اتنين تلاتة واحد اتنين تلاتة هذا اتنين تلاتة واحد
+
+280
+00:28:45,540 --> 00:28:52,360
+اتنين تلاتة واحدهذا عبارة عن ايش؟ واحد اتنين تلاتة
+
+281
+00:28:52,360 --> 00:28:56,880
+الواحد للتانين والتانين للتلاتة التانين للتلاتة
+
+282
+00:28:56,880 --> 00:29:01,700
+والتلاتة للواحد التلاتة للواحد والواحد للتانين
+
+283
+00:29:01,700 --> 00:29:08,700
+هيبقى بنكتبه بهذا الشكل طيب ال alpha تكايب عبارة
+
+284
+00:29:08,700 --> 00:29:16,400
+عن alpha تغبيه في alpha يعني واحد اتنين تلاتة
+
+285
+00:29:16,400 --> 00:29:25,510
+تلاتة واحد اتنين1 2 3 2 3 1 1 للتانين و تنين
+
+286
+00:29:25,510 --> 00:29:29,050
+للواحد يعني واحد للواحد تنين للتلتة و تلتة للتانين
+
+287
+00:29:29,050 --> 00:29:33,570
+يجب اتنين للتانين تلتة للتلتة اللي هو مين الايتين
+
+288
+00:29:33,570 --> 00:29:41,350
+التانين طيب Beta تربيع يعني
+
+289
+00:29:41,350 --> 00:29:53,170
+1 2 3 و 1 3 2 1 2 3 1 3 2هيعطيك 123 123 اللى هو ال
+
+290
+00:29:53,170 --> 00:30:02,170
+identity سهل هذى لو جينا حسبنا alpha beta يعني 123
+
+291
+00:30:02,170 --> 00:30:06,790
+132
+
+292
+00:30:06,790 --> 00:30:15,430
+او احنا كنا ال alpha في الاول 231 و ال beta 123
+
+293
+00:30:15,430 --> 00:30:22,230
+132يعمل العملية هذه ايش
+
+294
+00:30:22,230 --> 00:30:29,950
+هيعضيك؟ المطلوب يعطينا مركز صحيح واحد لواحد واحد
+
+295
+00:30:29,950 --> 00:30:33,930
+لاتنين يكبر واحد لاتنين تنين لتلاتة و تلاتة لتنين
+
+296
+00:30:33,930 --> 00:30:37,730
+لواحد يكبر تنين لمين؟ لواحد تلاتة لتنين و تلاتة
+
+297
+00:30:37,730 --> 00:30:41,250
+لتلاتة يكبر تلاتة لمين؟ لتلاتة
+
+298
+00:30:50,810 --> 00:30:55,490
+طب على المفروض يا شباب S3 هيكون كام عنصر ستة تعالى
+
+299
+00:30:55,490 --> 00:31:00,870
+نشوف كام عنصر و حصلنا عليه ستة هي الأول هي التاني
+
+300
+00:31:00,870 --> 00:31:08,650
+هي التالت هي الرابع وهي الخامس لإن هي خمس عناصر
+
+301
+00:31:08,650 --> 00:31:12,810
+مختلفة ايه يا ابو عزوز بيتا ألف كيف تجدها ألف بيتا
+
+302
+00:31:12,810 --> 00:31:18,130
+ألف زي ما عملت عمال يضغبها نفس الفكرة تعاشوا ببيتا
+
+303
+00:31:18,130 --> 00:31:18,550
+ألفة
+
+304
+00:31:24,260 --> 00:31:30,780
+واحد اتنين تلاتة واحد اتنين تلاتة ال alpha عبارة
+
+305
+00:31:30,780 --> 00:31:36,260
+عن تلاتة او تنين تلاتة واحد و انا واحد تلاتة اتنين
+
+306
+00:31:36,260 --> 00:31:44,500
+اعمل عملية واحد اتنين تلاتة واحد للتانين تانين
+
+307
+00:31:44,500 --> 00:31:48,380
+للتلاتة واحد للتلاتة تانين للتلاتة و تلاتة للتانين
+
+308
+00:31:48,380 --> 00:31:52,400
+نجمة تانين للتانين تلاتة للواحد هذا أنصار جديد ولا
+
+309
+00:31:52,400 --> 00:31:59,390
+لأ؟بدا نضمن انه مافيش تكرار يعني المفروض احنا
+
+310
+00:31:59,390 --> 00:32:02,870
+هالجيت Alpha Beta المفروض انا احسب Alpha تغبيه
+
+311
+00:32:02,870 --> 00:32:06,350
+Beta Alpha
+
+312
+00:32:06,350 --> 00:32:12,250
+تغبيه Beta عبارة عن ايش ال Alpha تغبيه؟ واحد اتنين
+
+313
+00:32:12,250 --> 00:32:19,630
+تلاتة ايه؟ تلاتة واحد اتنين واحد اتنين تلاتة وال
+
+314
+00:32:19,630 --> 00:32:22,310
+Beta عبارة عن واحد تلاتة اتنين تحسب
+
+315
+00:32:25,380 --> 00:32:30,200
+واحد ل واحد و واحد ل تلاتة تنين ل تلاتة اتنين و
+
+316
+00:32:30,200 --> 00:32:34,700
+تلاتة ل اتنين اللي هو ال main بيتا الفا ايش يعني
+
+317
+00:32:34,700 --> 00:32:43,080
+يعني الف تربية بيتا سوا بيتا الفا يعني انص و واحد
+
+318
+00:32:43,080 --> 00:32:54,200
+يعني كم انص عندي هنا انا
+
+319
+00:32:54,200 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+320
+00:32:54,280 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+321
+00:32:54,280 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+322
+00:32:54,280 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+323
+00:32:54,280 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+324
+00:32:54,280 --> 00:32:55,370
+انا انا انا انا انا انا انا انا انا افيه ال
+
+325
+00:32:55,370 --> 00:33:00,890
+identity وفيه ال alpha وفيه ال alpha تغبيه وفيه ال
+
+326
+00:33:00,890 --> 00:33:07,190
+beta وفيه ال alpha beta وفيه ال alpha تغبيه beta
+
+327
+00:33:07,190 --> 00:33:21,150
+ال S3 فيها كمنصر ست عناصر زي ما انت شايف طيب
+
+328
+00:33:24,580 --> 00:33:27,820
+أيش أهمية القاعدة اللي انا حطيتها غير دي أنه Alpha
+
+329
+00:33:27,820 --> 00:33:33,420
+تربيع Beta بيسوا Beta Alpha؟
+
+330
+00:33:33,420 --> 00:33:38,260
+ايش أهميتها؟
+
+331
+00:33:38,260 --> 00:33:41,440
+هي
+
+332
+00:33:41,440 --> 00:33:46,400
+الأهمية أنا ماكتبتها عبثا يعني أهميتها أنه أنا لما
+
+333
+00:33:46,400 --> 00:33:51,600
+بدي أجي أضغط Powers تانيينهيجيب كل ال powers ال
+
+334
+00:33:51,600 --> 00:33:55,780
+alpha كبير و اتنين و ال beta كبير و واحد يعني
+
+335
+00:33:55,780 --> 00:34:00,760
+alpha تقريب يعني على ال identity و beta تقريب على
+
+336
+00:34:00,760 --> 00:34:07,280
+ال identity تخيل مثلا انا بدي اضرب alpha beta مثلا
+
+337
+00:34:07,280 --> 00:34:13,220
+alpha beta بدي اضربه في alpha تقريب من beta هذا
+
+338
+00:34:13,220 --> 00:34:19,180
+ايش بدي اساوي هذا عبارة عنفى betaف Beta Alpha يعني
+
+339
+00:34:19,180 --> 00:34:24,480
+Alpha Beta تربية طبعا هذه عملية composition وهي
+
+340
+00:34:24,480 --> 00:34:28,720
+associative Beta تربية يبقى بعناش يعني Alpha
+
+341
+00:34:28,720 --> 00:34:34,480
+Identity Alpha Alpha تربية يعني انا لو بدي اعمل
+
+342
+00:34:34,480 --> 00:34:39,100
+هنا multiplication table بقدر من خلال العلاقة هذه
+
+343
+00:34:39,100 --> 00:34:47,320
+انا احصل بهذا الشكل هي ال identity هي ال Alphaهي
+
+344
+00:34:47,320 --> 00:34:52,960
+ال alpha تربيع هى ال beta هى ال beta تربيع او ال
+
+345
+00:34:52,960 --> 00:34:57,280
+alpha beta تربيع او ال alpha beta قصدي و alpha
+
+346
+00:34:57,280 --> 00:35:03,620
+تربيع beta وهنا ال identity وهنا ال alpha وهنا ال
+
+347
+00:35:03,620 --> 00:35:08,580
+alpha تربيع وحط هنا ال alpha beta او ال beta في
+
+348
+00:35:08,580 --> 00:35:15,180
+الأول و ال alpha beta و ال alpha تربيع beta وكمل
+
+349
+00:35:15,180 --> 00:35:15,620
+الجدول
+
+350
+00:35:18,300 --> 00:35:23,640
+تعالى نشوف مش هيطلع معايا طب ال identity نفس
+
+351
+00:35:23,640 --> 00:35:35,560
+العناصر عملت
+
+352
+00:35:35,560 --> 00:35:41,960
+ضغم اللي هو صف بعدين عمود هجت ألفة في ألفة ألفة في
+
+353
+00:35:41,960 --> 00:35:49,810
+ألفة ألف تربيع ألفة في ألف تربيعidentity Alpha في
+
+354
+00:35:49,810 --> 00:35:56,410
+Beta Alpha Beta Alpha في Alpha Beta Alpha تربيع
+
+355
+00:35:56,410 --> 00:36:02,450
+Beta Alpha في Alpha تربيع Beta Alpha تكييب Beta
+
+356
+00:36:02,450 --> 00:36:09,300
+Identity في Beta Beta Alpha تربيع في Alphaidentity
+
+357
+00:36:09,300 --> 00:36:13,180
+ألفة تربية في ألفة تربية ألفة أقصر أربعة أربعة
+
+358
+00:36:13,180 --> 00:36:14,180
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+359
+00:36:14,180 --> 00:36:14,440
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+360
+00:36:14,440 --> 00:36:14,440
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+361
+00:36:14,440 --> 00:36:16,300
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+362
+00:36:16,300 --> 00:36:20,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+363
+00:36:20,360 --> 00:36:22,680
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+364
+00:36:22,680 --> 00:36:24,120
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+365
+00:36:24,120 --> 00:36:28,080
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+366
+00:36:28,080 --> 00:36:37,820
+أرب
+
+367
+00:36:38,830 --> 00:36:51,650
+بيتا ألفة بقالها معايا حاجة بيتا عبارة
+
+368
+00:36:51,650 --> 00:36:56,530
+عن بيتا ألفة ألفة عبارة عن بيتا ألفة عبارة عن أيش
+
+369
+00:36:56,530 --> 00:37:04,050
+ألفة تربية بيتا عبارة عن ألف تربية في ألف تربية
+
+370
+00:37:04,050 --> 00:37:06,950
+بيتا يعني ألف بيتا
+
+371
+00:37:10,200 --> 00:37:14,920
+Beta في Beta Identity
+
+372
+00:37:14,920 --> 00:37:22,000
+Beta في Alpha Beta عبارة عن ايش؟ عبارة عن Alpha
+
+373
+00:37:22,000 --> 00:37:25,460
+تربية Beta في Beta يعني Alpha تربية في ال identity
+
+374
+00:37:25,460 --> 00:37:33,360
+يعني Alpha تربية مين ضال هان؟ ضال ال Alpha طيب
+
+375
+00:37:33,360 --> 00:37:38,880
+Alpha Beta في Alpha وين؟
+
+376
+00:37:48,030 --> 00:37:54,210
+مش فاهمش .. اه .. صحيح
+
+377
+00:37:54,210 --> 00:38:01,690
+.. صحيح .. صحيح .. احنا .. لأ انت خربطني يا شيخ ..
+
+378
+00:38:01,690 --> 00:38:04,250
+صحيح .. بيتا ألفة تربيع .. يعني بيتا ألفة في ألفة
+
+379
+00:38:04,250 --> 00:38:08,250
+.. هذه ألفة .. ألفة تربيع بيتا .. لأ بيصيح ألف
+
+380
+00:38:08,250 --> 00:38:12,560
+تكييب في بيتها .. كل المسلمينهجيت الـ Alpha Beta
+
+381
+00:38:12,560 --> 00:38:17,160
+هادي عبارة عن Alpha تربيع في Beta يعني Alpha أُص
+
+382
+00:38:17,160 --> 00:38:21,680
+أربع في Beta يعني Alpha Beta مين؟
+
+383
+00:38:21,680 --> 00:38:27,440
+في واحدة عملناها اللي بيتا Alpha Beta عبارة عن
+
+384
+00:38:27,440 --> 00:38:34,380
+Alpha تربيع Beta في Beta بتساوي Alpha تربيع مين
+
+385
+00:38:34,380 --> 00:38:39,920
+جاي يعني انها هجيت Alpha Beta في Alpha عبارة عن
+
+386
+00:38:39,920 --> 00:38:47,660
+بدّل هاديBeta Alpha Alpha في Alpha تربيع Beta اللي
+
+387
+00:38:47,660 --> 00:38:58,560
+هي Beta طبعا Alpha Beta في Alpha تربيع عبارة
+
+388
+00:38:58,560 --> 00:39:05,000
+عن أيش Alpha Beta Alpha في Alpha اللي عبارة عن
+
+389
+00:39:05,000 --> 00:39:09,180
+Alpha Alpha تربيع Beta في Alpha عبارة عن Beta
+
+390
+00:39:09,180 --> 00:39:14,170
+Alpha Beta Alpha عبارة عن أيشAlpha تربيع Beta
+
+391
+00:39:14,170 --> 00:39:18,550
+Alpha
+
+392
+00:39:18,550 --> 00:39:23,250
+في Beta في Beta Alpha Alpha Beta في Alpha Beta
+
+393
+00:39:23,250 --> 00:39:26,630
+Alpha
+
+394
+00:39:26,630 --> 00:39:34,170
+Beta Alpha تربيع Alpha Beta Alpha Alpha
+
+395
+00:39:34,170 --> 00:39:36,730
+Beta Alpha Alpha Beta Alpha Alpha Alpha Alpha
+
+396
+00:39:36,730 --> 00:39:38,250
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+397
+00:39:38,250 --> 00:39:40,910
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+398
+00:39:40,910 --> 00:39:41,130
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+399
+00:39:41,130 --> 00:39:41,410
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+400
+00:39:41,410 --> 00:39:41,410
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+401
+00:39:41,410 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+402
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+403
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+404
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+405
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+406
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+407
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+408
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+409
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+410
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+411
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+412
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+413
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+414
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+415
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+416
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+417
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+418
+00:39:41,430 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+419
+00:39:41,430 --> 00:39:46,460
+Alpha Alpha Alphaتنتين هدول بيتا
+
+420
+00:39:46,460 --> 00:39:51,880
+ألف عبارة عن ألف تربيه بيتا بيتا
+
+421
+00:39:51,880 --> 00:39:56,040
+ألف عبارة عن ألف تربيه بيتا ألف ألف مع ألف تربيه
+
+422
+00:39:56,040 --> 00:40:00,380
+identity و بيتا ألف بيظل طبعا الجواب أنها ألف
+
+423
+00:40:00,380 --> 00:40:07,940
+تربيه بيتا ألف بيتا في ألف بيتا عبارة عن ألف ألف
+
+424
+00:40:07,940 --> 00:40:10,100
+تربيه بيتا بيتا بي سوى ال identity
+
+425
+00:40:12,800 --> 00:40:16,640
+و أنا هيظل alpha تربيع طبعا تقدر تكمل الجدول هجت
+
+426
+00:40:16,640 --> 00:40:22,300
+لحالك أنا هيكون identity و أنا alpha أنا alpha
+
+427
+00:40:22,300 --> 00:40:32,160
+تربيع و أنا beta و أنا alpha beta طبعا
+
+428
+00:40:32,160 --> 00:40:35,300
+we
+
+429
+00:40:35,300 --> 00:40:41,020
+will show later that
+
+430
+00:40:43,140 --> 00:40:56,800
+S3 and D3 is the same thing
+
+431
+00:40:56,800 --> 00:41:00,200
+ماشي
+
+432
+00:41:00,200 --> 00:41:05,960
+نفس الحاجة يعطيكوا العفو يا شباب
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..70eaaa47abf70f6699f7c8488cc9bb7c6055686b
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 5167, "start": 22.31, "end": 51.67, "text": "بسم الله الرحمن الرحيم بدأنا المرة الماضية في موضوع ال groups اللي هي المجموعات وعرفنا ان ال set و عليها binary operation بقول عنها group إذا حققتلي ثلاث خاص الخاصية الأولى خاصية ال associativity الخاصية الثانية خاصية ال identity element الخاصية التالتة هي خاصية ال inverse element لأي element موجود في group G", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 4724, 3215, 10721, 8315, 9673, 25720, 9673, 46958, 10632, 8978, 3714, 2407, 11242, 45367, 2423, 3935, 13672, 1829, 39896, 9673, 7435, 2304, 45367, 9307, 4032, 3615, 28480, 8315, 16472, 2423, 992, 4032, 25894, 11296, 17434, 6916, 4724, 39648, 18871, 11296, 1594, 11933, 15730, 11331, 4587, 38149, 20292, 38637, 1211, 5718, 104, 16490, 33546, 33962, 33546, 10632, 16247, 12610, 7578, 16490, 33546, 10632, 2423, 4180, 30142, 33962, 33546, 10632, 6024, 104, 7649, 10632, 16490, 33546, 10632, 2423, 6575, 4478, 33962, 33546, 10632, 16712, 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"probability": 0.9039306640625}, {"start": 235.02, "end": 235.18, "word": " هي", "probability": 0.8154296875}, {"start": 235.18, "end": 235.66, "word": " خمسة", "probability": 0.9908447265625}, {"start": 235.66, "end": 236.02, "word": " زياد", "probability": 0.86181640625}, {"start": 236.02, "end": 236.48, "word": " اتنين", "probability": 0.9429931640625}, {"start": 236.48, "end": 237.0, "word": " و", "probability": 0.69873046875}, {"start": 237.0, "end": 237.62, "word": " هكذا", "probability": 0.9337565104166666}], "temperature": 1.0}, {"id": 10, "seek": 26522, "start": 238.14, "end": 265.22, "text": "طيب نروح لمثال أتقل شوية و أتقل شويات مش شوية بيقول let ال UN be the set of all positive integers less than", "tokens": [9566, 1829, 3555, 8717, 32887, 5016, 32767, 12984, 6027, 5551, 2655, 4587, 1211, 13412, 2407, 10632, 4032, 5551, 2655, 4587, 1211, 13412, 45865, 9307, 37893, 13412, 2407, 10632, 4724, 1829, 39648, 718, 2423, 8229, 312, 264, 992, 295, 439, 3353, 41674, 1570, 813], 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11, "seek": 29538, "start": 267.62, "end": 295.38, "text": "less than ال N less than ال N and relatively prime relatively prime to N then ال U N هذه ال U N", "tokens": [1832, 813, 2423, 426, 1570, 813, 2423, 426, 293, 7226, 5835, 7226, 5835, 281, 426, 550, 2423, 624, 426, 29538, 2423, 624, 426], "avg_logprob": -0.22835286458333334, "compression_ratio": 1.5142857142857142, "no_speech_prob": 0.0, "words": [{"start": 267.62, "end": 268.3, "word": "less", "probability": 0.63232421875}, {"start": 268.3, "end": 269.58, "word": " than", "probability": 0.91455078125}, {"start": 269.58, "end": 270.62, "word": " ال", "probability": 0.88671875}, {"start": 270.62, "end": 271.16, "word": " N", "probability": 0.341064453125}, {"start": 271.16, "end": 272.82, "word": " less", "probability": 0.427001953125}, {"start": 272.82, "end": 273.18, "word": " than", "probability": 0.953125}, {"start": 273.18, "end": 273.4, "word": " ال", "probability": 0.9794921875}, {"start": 273.4, "end": 273.8, "word": " 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{"start": 292.52, "end": 294.68, "word": " ال", "probability": 0.97216796875}, {"start": 294.68, "end": 295.0, "word": " U", "probability": 0.9951171875}, {"start": 295.0, "end": 295.38, "word": " N", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 12, "seek": 31277, "start": 297.4, "end": 312.78, "text": "and the situ in is an abelian group under multiplication modulo n", "tokens": [474, 264, 2054, 294, 307, 364, 410, 338, 952, 1594, 833, 27290, 1072, 13455, 297], "avg_logprob": -0.5175781063735485, "compression_ratio": 1.0655737704918034, "no_speech_prob": 0.0, "words": [{"start": 297.4, "end": 297.72, "word": "and", "probability": 0.04241943359375}, {"start": 297.72, "end": 297.9, "word": " the", "probability": 0.3994140625}, {"start": 297.9, "end": 298.26, "word": " situ", "probability": 0.2724609375}, {"start": 298.26, "end": 298.68, "word": " in", "probability": 0.658203125}, {"start": 298.68, "end": 299.4, "word": " is", "probability": 0.783203125}, {"start": 299.4, 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grasses common divisor يبقى انا بروح بختار المناسب اللي بيخدمني في هذه الحالة", "tokens": [29973, 2655, 25894, 8315, 2423, 10044, 9284, 1975, 5016, 8315, 20328, 5016, 22807, 10044, 9284, 4032, 29973, 25894, 8315, 5296, 49701, 2689, 25974, 284, 7251, 3555, 4587, 7578, 1975, 8315, 4724, 32887, 5016, 4724, 46456, 9640, 9673, 8315, 35457, 13672, 1829, 4724, 1829, 9778, 40448, 22653, 8978, 29538, 21542, 6027, 3660], "avg_logprob": -0.2719350973000893, "compression_ratio": 1.4569536423841059, "no_speech_prob": 0.0, "words": [{"start": 554.48, "end": 555.08, "word": "مرت", "probability": 0.45233154296875}, {"start": 555.08, "end": 555.44, "word": " علينا", "probability": 0.967529296875}, {"start": 555.44, "end": 555.52, "word": " ال", "probability": 0.53955078125}, {"start": 555.52, "end": 555.82, "word": " division", "probability": 0.423583984375}, {"start": 555.82, "end": 556.54, "word": " algorithm", "probability": 0.916015625}, {"start": 556.54, "end": 557.6, "word": " احنا", 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"probability": 0.85546875}, {"start": 917.41, "end": 917.75, "word": " هل", "probability": 0.976806640625}, {"start": 917.75, "end": 918.31, "word": " هذا", "probability": 0.75537109375}, {"start": 918.31, "end": 919.13, "word": " انتجة", "probability": 0.79779052734375}], "temperature": 1.0}, {"id": 38, "seek": 95155, "start": 922.69, "end": 951.55, "text": "طب كيف بده يصير عادي؟ برا ال z ده ده يعني مو صبطتش معاناة أو برا ال UN صحيح؟ يبقى هذا الكلام ليس صحيحا يبقى لو جيه تقولك the inverse of L is X where X is the solution of the equation", "tokens": [9566, 3555, 9122, 33911, 47525, 3224, 7251, 9381, 13546, 6225, 995, 16254, 22807, 4724, 23557, 2423, 710, 11778, 3224, 11778, 3224, 37495, 22653, 3714, 2407, 20328, 3555, 9566, 2655, 8592, 20449, 7649, 995, 3660, 34051, 4724, 23557, 2423, 8229, 20328, 5016, 1829, 5016, 22807, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 32239, 3794, 20328, 5016, 1829, 5016, 995, 7251, 3555, 4587, 7578, 45164, 10874, 1829, 3224, 6055, 39648, 4117, 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"word": " ليس", "probability": 0.971923828125}, {"start": 931.75, "end": 932.65, "word": " صحيحا", "probability": 0.9583984375}, {"start": 932.65, "end": 933.49, "word": " يبقى", "probability": 0.9471435546875}, {"start": 933.49, "end": 933.75, "word": " لو", "probability": 0.93115234375}, {"start": 933.75, "end": 933.99, "word": " جيه", "probability": 0.729248046875}, {"start": 933.99, "end": 934.33, "word": " تقولك", "probability": 0.8216145833333334}, {"start": 934.33, "end": 934.53, "word": " the", "probability": 0.6708984375}, {"start": 934.53, "end": 934.87, "word": " inverse", "probability": 0.96875}, {"start": 934.87, "end": 935.15, "word": " of", "probability": 0.97900390625}, {"start": 935.15, "end": 935.39, "word": " L", "probability": 0.35595703125}, {"start": 935.39, "end": 935.65, "word": " is", "probability": 0.09930419921875}, {"start": 935.65, "end": 937.23, "word": " X", "probability": 0.61376953125}, {"start": 937.23, "end": 939.95, "word": " where", "probability": 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"probability": 0.923828125}, {"start": 976.88, "end": 976.96, "word": " a", "probability": 0.94384765625}, {"start": 976.96, "end": 977.32, "word": " بقدر", "probability": 0.9322916666666666}, {"start": 977.32, "end": 977.56, "word": " أجيب", "probability": 0.8597412109375}, {"start": 977.56, "end": 977.64, "word": " له", "probability": 0.69921875}, {"start": 977.64, "end": 977.74, "word": " ال", "probability": 0.962890625}, {"start": 977.74, "end": 978.02, "word": " x", "probability": 0.9375}, {"start": 978.02, "end": 979.14, "word": " بسهولة", "probability": 0.99345703125}], "temperature": 1.0}, {"id": 40, "seek": 99533, "start": 979.47, "end": 995.33, "text": "و هذه القصة بصير سهلة يبقى هذه صارت appealing group لانها حققت لمن؟ حققت للاربعة شروط يبقى لو اعطيتك مثال for example تفضل قول", "tokens": [2407, 29538, 25062, 9381, 3660, 4724, 9381, 13546, 8608, 3224, 37977, 7251, 3555, 4587, 7578, 29538, 20328, 9640, 2655, 23842, 1594, 5296, 7649, 11296, 11331, 4587, 38149, 5296, 27842, 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"end": 983.75, "word": " appealing", "probability": 0.321044921875}, {"start": 983.75, "end": 984.21, "word": " group", "probability": 0.9111328125}, {"start": 984.21, "end": 984.67, "word": " لانها", "probability": 0.7923990885416666}, {"start": 984.67, "end": 985.17, "word": " حققت", "probability": 0.9625651041666666}, {"start": 985.17, "end": 985.71, "word": " لمن؟", "probability": 0.7083333333333334}, {"start": 985.71, "end": 986.19, "word": " حققت", "probability": 0.96142578125}, {"start": 986.19, "end": 987.41, "word": " للاربعة", "probability": 0.69207763671875}, {"start": 987.41, "end": 988.05, "word": " شروط", "probability": 0.8551432291666666}, {"start": 988.05, "end": 988.73, "word": " يبقى", "probability": 0.9605712890625}, {"start": 988.73, "end": 988.89, "word": " لو", "probability": 0.93896484375}, {"start": 988.89, "end": 989.49, "word": " اعطيتك", "probability": 0.90478515625}, {"start": 989.49, "end": 990.07, "word": " مثال", "probability": 0.776611328125}, {"start": 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0.79608154296875}, {"start": 1102.03, "end": 1102.13, "word": " الـ", "probability": 0.476318359375}, {"start": 1102.13, "end": 1102.67, "word": " identity", "probability": 0.427001953125}, {"start": 1102.67, "end": 1103.25, "word": " element", "probability": 0.93798828125}, {"start": 1103.25, "end": 1104.05, "word": " يبقى", "probability": 0.8408203125}, {"start": 1104.05, "end": 1104.61, "word": " التلاتة", "probability": 0.8759765625}, {"start": 1104.61, "end": 1104.85, "word": " هو", "probability": 0.529296875}, {"start": 1104.85, "end": 1105.47, "word": " معكوس", "probability": 0.8173828125}, {"start": 1105.47, "end": 1106.05, "word": " السبعة", "probability": 0.87939453125}, {"start": 1106.05, "end": 1106.83, "word": " والسبعة", "probability": 0.8619791666666666}, {"start": 1106.83, "end": 1107.09, "word": " هي", "probability": 0.86572265625}, {"start": 1107.09, "end": 1107.61, "word": " معكوس", "probability": 0.8963216145833334}, {"start": 1107.61, "end": 1108.01, "word": " من", "probability": 0.1689453125}, {"start": 1108.01, "end": 1109.19, "word": " الادلي", "probability": 0.5159912109375}, {"start": 1109.19, "end": 1110.01, "word": " والتلاتة", "probability": 0.94462890625}, {"start": 1110.01, "end": 1110.97, "word": " يبقى", "probability": 0.9564208984375}, {"start": 1110.97, "end": 1112.13, "word": " التلاتة", "probability": 0.9114990234375}, {"start": 1112.13, "end": 1112.65, "word": " is", "probability": 0.8486328125}, {"start": 1112.65, "end": 1114.07, "word": " the", "probability": 0.82080078125}, {"start": 1114.07, "end": 1115.35, "word": " inverse", "probability": 0.89404296875}, {"start": 1115.35, "end": 1116.55, "word": " element", "probability": 0.9560546875}, {"start": 1116.55, "end": 1119.43, "word": " of", "probability": 0.9765625}, {"start": 1119.43, "end": 1120.45, "word": " سبعة", "probability": 0.8544921875}], "temperature": 1.0}, {"id": 46, "seek": 114518, "start": 1121.92, "end": 1145.18, "text": "طب التسعة مين معكوسة؟ نفسها لإن التسعة في تسعة و 8 عشرات بظلمين ال identity element and تسعة is the inverse of itself يبجى التسعة هو معكوس لنفسه", "tokens": [9566, 3555, 16712, 3794, 27884, 3714, 9957, 20449, 4117, 41779, 3660, 22807, 8717, 36178, 11296, 5296, 28814, 1863, 16712, 3794, 27884, 8978, 6055, 3794, 27884, 4032, 1649, 6225, 46309, 9307, 4724, 19913, 19528, 9957, 2423, 6575, 4478, 293, 6055, 3794, 27884, 307, 264, 17340, 295, 2564, 7251, 3555, 7435, 7578, 16712, 3794, 27884, 31439, 20449, 4117, 41779, 5296, 1863, 36178, 3224], "avg_logprob": -0.24760585398443283, "compression_ratio": 1.4899328859060403, "no_speech_prob": 0.0, "words": [{"start": 1121.92, "end": 1122.2, "word": "طب", "probability": 0.4609375}, {"start": 1122.2, "end": 1122.64, "word": " التسعة", "probability": 0.91552734375}, {"start": 1122.64, "end": 1122.84, "word": " مين", "probability": 0.914306640625}, {"start": 1122.84, "end": 1124.06, "word": " معكوسة؟", "probability": 0.79873046875}, {"start": 1124.06, "end": 1124.56, "word": " نفسها", "probability": 0.85791015625}, {"start": 1124.56, "end": 1124.72, "word": " لإن", "probability": 0.6829427083333334}, {"start": 1124.72, "end": 1125.06, "word": " التسعة", "probability": 0.8036295572916666}, {"start": 1125.06, "end": 1125.16, "word": " في", "probability": 0.79638671875}, {"start": 1125.16, "end": 1125.7, "word": " تسعة", "probability": 0.9720052083333334}, {"start": 1125.7, "end": 1126.42, "word": " و", "probability": 0.6875}, {"start": 1126.42, "end": 1126.66, "word": " 8", "probability": 0.0819091796875}, {"start": 1126.66, "end": 1127.84, "word": " عشرات", "probability": 0.84716796875}, {"start": 1127.84, "end": 1128.54, "word": " بظلمين", "probability": 0.62896728515625}, {"start": 1128.54, "end": 1129.06, "word": " ال", "probability": 0.93994140625}, {"start": 1129.06, "end": 1129.62, "word": " identity", "probability": 0.8271484375}, {"start": 1129.62, "end": 1130.4, "word": " element", "probability": 0.91259765625}, {"start": 1130.4, "end": 1131.52, "word": " and", "probability": 0.7958984375}, {"start": 1131.52, "end": 1133.52, "word": " تسعة", "probability": 0.9383138020833334}, {"start": 1133.52, "end": 1134.36, "word": " is", "probability": 0.9365234375}, {"start": 1134.36, "end": 1135.48, "word": " the", "probability": 0.84130859375}, {"start": 1135.48, "end": 1137.2, "word": " inverse", "probability": 0.90185546875}, {"start": 1137.2, "end": 1138.52, "word": " of", "probability": 0.9765625}, {"start": 1138.52, "end": 1140.44, "word": " itself", "probability": 0.796875}, {"start": 1140.44, "end": 1142.5, "word": " يبجى", "probability": 0.7955322265625}, {"start": 1142.5, "end": 1143.04, "word": " التسعة", "probability": 0.9923502604166666}, {"start": 1143.04, "end": 1143.36, "word": " هو", "probability": 0.97021484375}, {"start": 1143.36, "end": 1144.12, "word": " معكوس", "probability": 0.9119466145833334}, {"start": 1144.12, "end": 1145.18, "word": " لنفسه", "probability": 0.9765625}], "temperature": 1.0}, {"id": 47, "seek": 117756, "start": 1150.08, "end": 1177.56, "text": "يبقى خريص لقيناله معكوس ولا لا طبعا هذه ال group شباب عليها سنة كتيرة و عليها شغل كتير يبقى هذه ال group very important طيب ننتقل الآن إلى المثال اللي بعده", "tokens": [1829, 3555, 4587, 7578, 16490, 16572, 9381, 5296, 4587, 9957, 6027, 3224, 20449, 4117, 41779, 49429, 20193, 23032, 3555, 3615, 995, 29538, 2423, 1594, 13412, 3555, 16758, 25894, 11296, 8608, 1863, 3660, 9122, 2655, 48923, 4032, 25894, 11296, 13412, 17082, 1211, 9122, 2655, 13546, 7251, 3555, 4587, 7578, 29538, 2423, 1594, 588, 1021, 23032, 1829, 3555, 8717, 29399, 4587, 1211, 6024, 48506, 30731, 9673, 12984, 6027, 13672, 1829, 39182, 3224], "avg_logprob": -0.16857393820520858, "compression_ratio": 1.5389221556886228, "no_speech_prob": 0.0, "words": [{"start": 1150.08, "end": 1150.82, "word": "يبقى", "probability": 0.80804443359375}, {"start": 1150.82, "end": 1151.46, "word": " خريص", "probability": 0.7021484375}, {"start": 1151.46, "end": 1152.3, "word": " لقيناله", "probability": 0.67841796875}, {"start": 1152.3, "end": 1153.22, "word": " معكوس", "probability": 0.9235026041666666}, {"start": 1153.22, "end": 1153.4, "word": " ولا", "probability": 0.89892578125}, {"start": 1153.4, "end": 1153.82, "word": " لا", "probability": 0.54443359375}, {"start": 1153.82, "end": 1163.92, "word": " طبعا", "probability": 0.9122314453125}, {"start": 1163.92, "end": 1164.26, "word": " هذه", "probability": 0.619140625}, {"start": 1164.26, "end": 1165.04, "word": " ال", "probability": 0.740234375}, {"start": 1165.04, "end": 1165.3, "word": " group", "probability": 0.619140625}, {"start": 1165.3, "end": 1165.96, "word": " شباب", "probability": 0.9093424479166666}, {"start": 1165.96, "end": 1167.14, "word": " عليها", "probability": 0.943359375}, {"start": 1167.14, "end": 1167.82, "word": " سنة", "probability": 0.8919270833333334}, {"start": 1167.82, "end": 1168.24, "word": " كتيرة", "probability": 0.8214518229166666}, {"start": 1168.24, "end": 1168.38, "word": " و", 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0.69140625}, {"start": 1175.32, "end": 1175.96, "word": " إلى", "probability": 0.39453125}, {"start": 1175.96, "end": 1176.88, "word": " المثال", "probability": 0.982421875}, {"start": 1176.88, "end": 1177.06, "word": " اللي", "probability": 0.874267578125}, {"start": 1177.06, "end": 1177.56, "word": " بعده", "probability": 0.95751953125}], "temperature": 1.0}, {"id": 48, "seek": 120658, "start": 1177.89, "end": 1206.59, "text": "يبقى مثال سبعة مثال سبعة بيقول the set لو أخدت ال z و عليها عملية الطرح of integers of integers under subtraction", "tokens": [1829, 3555, 4587, 7578, 50113, 6027, 8608, 3555, 27884, 50113, 6027, 8608, 3555, 27884, 4724, 1829, 39648, 264, 992, 45164, 5551, 9778, 3215, 2655, 2423, 710, 4032, 25894, 11296, 6225, 42213, 10632, 41950, 2288, 5016, 295, 41674, 295, 41674, 833, 16390, 313], "avg_logprob": -0.12509083886479222, "compression_ratio": 1.3064516129032258, "no_speech_prob": 0.0, "words": [{"start": 1177.89, "end": 1178.41, "word": "يبقى", "probability": 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0.96435546875}, {"start": 1191.39, "end": 1192.07, "word": " عليها", "probability": 0.89697265625}, {"start": 1192.07, "end": 1192.99, "word": " عملية", "probability": 0.9847005208333334}, {"start": 1192.99, "end": 1194.11, "word": " الطرح", "probability": 0.9609375}, {"start": 1194.11, "end": 1195.49, "word": " of", "probability": 0.9228515625}, {"start": 1195.49, "end": 1198.03, "word": " integers", "probability": 0.92626953125}, {"start": 1198.03, "end": 1199.61, "word": " of", "probability": 0.6650390625}, {"start": 1199.61, "end": 1200.75, "word": " integers", "probability": 0.94580078125}, {"start": 1200.75, "end": 1202.75, "word": " under", "probability": 0.88427734375}, {"start": 1202.75, "end": 1206.59, "word": " subtraction", "probability": 0.7156982421875}], "temperature": 1.0}, {"id": 49, "seek": 122305, "start": 1210.49, "end": 1223.05, "text": "هل يا ترى هذه group ولا ماهياش group؟ اه ده السؤال أنا أدعي is not a group because", "tokens": [3224, 1211, 35186, 6055, 2288, 7578, 29538, 1594, 49429, 19446, 3224, 1829, 33599, 1594, 22807, 1975, 3224, 11778, 3224, 21136, 33604, 6027, 41850, 5551, 3215, 3615, 1829, 307, 406, 257, 1594, 570], "avg_logprob": -0.23378314393939395, "compression_ratio": 1.1226415094339623, "no_speech_prob": 0.0, "words": [{"start": 1210.49, "end": 1210.89, "word": "هل", "probability": 0.979736328125}, {"start": 1210.89, "end": 1211.07, "word": " يا", "probability": 0.19580078125}, {"start": 1211.07, "end": 1211.43, "word": " ترى", "probability": 0.9111328125}, {"start": 1211.43, "end": 1211.75, "word": " هذه", "probability": 0.52392578125}, {"start": 1211.75, "end": 1212.07, "word": " group", "probability": 0.90625}, {"start": 1212.07, "end": 1212.33, "word": " ولا", "probability": 0.81884765625}, {"start": 1212.33, "end": 1212.95, "word": " ماهياش", "probability": 0.8856201171875}, {"start": 1212.95, "end": 1214.13, "word": " group؟", "probability": 0.888916015625}, {"start": 1214.13, "end": 1214.29, "word": " اه", 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لكن هل هذه associative ام لا الله أعلم يبقى هنا because if التلاتة مثلا والخمسة والسبعة موجودة في z then", "tokens": [9566, 3555, 3615, 995, 45164, 23032, 2288, 5016, 2655, 1975, 1829, 18871, 9381, 2288, 9154, 45030, 11242, 8608, 2407, 16606, 23032, 6027, 3615, 16472, 11296, 6055, 7435, 2304, 26895, 49610, 23328, 16070, 43761, 8608, 45340, 8978, 11296, 4032, 2304, 29245, 23328, 8978, 710, 11933, 15730, 6225, 42213, 10632, 41950, 2288, 5016, 15844, 710, 307, 257, 17434, 6916, 19446, 41185, 8592, 8978, 11296, 37893, 28820, 3660, 44381, 8032, 1211, 29538, 4180, 1166, 1975, 2304, 20193, 21984, 5551, 3615, 19528, 7251, 3555, 4587, 7578, 34105, 570, 498, 16712, 1211, 9307, 3660, 50113, 15040, 16070, 9778, 2304, 3794, 3660, 16070, 35457, 27884, 3714, 29245, 23328, 3660, 8978, 710, 550], "avg_logprob": -0.22152452574712095, "compression_ratio": 1.606425702811245, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1227.79, "end": 1228.23, "word": "طبعا", "probability": 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55, "seek": 137616, "start": 1352.28, "end": 1376.16, "text": "six star of non zero real numbers non zero real numbers is a group under the ordinary", "tokens": [35066, 3543, 295, 2107, 4018, 957, 3547, 2107, 4018, 957, 3547, 307, 257, 1594, 833, 264, 10547], "avg_logprob": -0.3528645750549104, "compression_ratio": 1.3076923076923077, "no_speech_prob": 0.0, "words": [{"start": 1352.28, "end": 1352.86, "word": "six", "probability": 0.08599853515625}, {"start": 1352.86, "end": 1353.7, "word": " star", "probability": 0.58154296875}, {"start": 1353.7, "end": 1354.82, "word": " of", "probability": 0.91064453125}, {"start": 1354.82, "end": 1356.56, "word": " non", "probability": 0.88623046875}, {"start": 1356.56, "end": 1358.12, "word": " zero", "probability": 0.3466796875}, {"start": 1358.12, "end": 1359.62, "word": " real", "probability": 0.94384765625}, {"start": 1359.62, "end": 1360.98, "word": " numbers", "probability": 0.7939453125}, {"start": 1360.98, "end": 1364.3, "word": " non", 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0.0, "words": [{"start": 1380.56, "end": 1381.52, "word": "السبق", "probability": 0.6204427083333334}], "temperature": 1.0}, {"id": 57, "seek": 144297, "start": 1419.27, "end": 1442.97, "text": "مرة تانية ال set of real numbers اللي هي اللي بدي أشيل منها ال zero و بدي أسميها R star يبقى مجموعة الأعداد الحقيقية استثنت منها ال zero عرفت عليها عملية الضرب العادية طبعا الأعداد ال real numbers", "tokens": [2304, 25720, 6055, 7649, 10632, 2423, 992, 295, 957, 3547, 13672, 1829, 39896, 13672, 1829, 4724, 16254, 5551, 8592, 26895, 9154, 11296, 2423, 4018, 4032, 4724, 16254, 5551, 38251, 1829, 11296, 497, 3543, 7251, 3555, 4587, 7578, 3714, 7435, 2304, 2407, 27884, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 44713, 12984, 29399, 9154, 11296, 2423, 4018, 6225, 28480, 2655, 25894, 11296, 6225, 42213, 10632, 6024, 114, 25513, 18863, 18513, 10632, 23032, 3555, 3615, 995, 16247, 22488, 18513, 2423, 957, 3547], "avg_logprob": -0.18287037625724886, "compression_ratio": 1.7307692307692308, 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"probability": 0.85888671875}, {"start": 1425.83, "end": 1426.31, "word": " منها", "probability": 0.9931640625}, {"start": 1426.31, "end": 1426.49, "word": " ال", "probability": 0.90966796875}, {"start": 1426.49, "end": 1426.73, "word": " zero", "probability": 0.80615234375}, {"start": 1426.73, "end": 1426.89, "word": " و", "probability": 0.5517578125}, {"start": 1426.89, "end": 1426.99, "word": " بدي", "probability": 0.776611328125}, {"start": 1426.99, "end": 1427.59, "word": " أسميها", "probability": 0.9508056640625}, {"start": 1427.59, "end": 1428.01, "word": " R", "probability": 0.65283203125}, {"start": 1428.01, "end": 1428.49, "word": " star", "probability": 0.116943359375}, {"start": 1428.49, "end": 1429.19, "word": " يبقى", "probability": 0.8646240234375}, {"start": 1429.19, "end": 1429.75, "word": " مجموعة", "probability": 0.9607421875}, {"start": 1429.75, "end": 1430.21, "word": " الأعداد", "probability": 0.74560546875}, {"start": 1430.21, "end": 1430.95, "word": " الحقيقية", 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"end": 1500.18, "text": "we know that احنا بنعرف ان ال multi application is a binary binary associative binary associative operation", "tokens": [826, 458, 300, 1975, 5016, 8315, 44945, 3615, 28480, 16472, 2423, 4825, 3861, 307, 257, 17434, 17434, 4180, 1166, 17434, 4180, 1166, 6916], "avg_logprob": -0.2001953093955914, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 1472.76, "end": 1473.38, "word": "we", "probability": 0.40625}, {"start": 1473.38, "end": 1474.84, "word": " know", "probability": 0.93359375}, {"start": 1474.84, "end": 1475.7, "word": " that", "probability": 0.95654296875}, {"start": 1475.7, "end": 1476.56, "word": " احنا", "probability": 0.9334309895833334}, {"start": 1476.56, "end": 1477.3, "word": " بنعرف", "probability": 0.9327799479166666}, {"start": 1477.3, "end": 1478.14, "word": " ان", "probability": 0.841796875}, {"start": 1478.14, "end": 1479.06, "word": " ال", "probability": 0.90966796875}, {"start": 1479.06, "end": 1479.78, "word": " multi", "probability": 0.7109375}, {"start": 1479.78, "end": 1482.34, "word": " application", "probability": 0.8994140625}, {"start": 1482.34, "end": 1484.94, "word": " is", "probability": 0.94384765625}, {"start": 1484.94, "end": 1486.82, "word": " a", "probability": 0.72900390625}, {"start": 1486.82, "end": 1487.52, "word": " binary", "probability": 0.9072265625}, {"start": 1487.52, "end": 1490.54, "word": " binary", "probability": 0.2039794921875}, {"start": 1490.54, "end": 1493.4, "word": " associative", "probability": 0.976806640625}, {"start": 1493.4, "end": 1495.86, "word": " binary", "probability": 0.64794921875}, {"start": 1495.86, "end": 1498.66, "word": " associative", "probability": 0.9833984375}, {"start": 1498.66, "end": 1500.18, "word": " operation", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 60, "seek": 152701, "start": 1509.63, "end": 1527.01, "text": "بالنسبة للدرب الوحيد هو الـ identity element of R star", "tokens": [3555, 6027, 1863, 35457, 3660, 24976, 3215, 2288, 3555, 2423, 2407, 5016, 25708, 31439, 2423, 39184, 6575, 4478, 295, 497, 3543], "avg_logprob": -0.6395596374164928, "compression_ratio": 0.9871794871794872, "no_speech_prob": 0.0, "words": [{"start": 1509.6299999999999, "end": 1511.03, "word": "بالنسبة", "probability": 0.68060302734375}, {"start": 1511.03, "end": 1512.01, "word": " للدرب", "probability": 0.58502197265625}, {"start": 1512.01, "end": 1513.29, "word": " الوحيد", "probability": 0.493865966796875}, {"start": 1513.29, "end": 1517.03, "word": " هو", "probability": 0.4970703125}, {"start": 1517.03, "end": 1518.77, "word": " الـ", "probability": 0.542724609375}, {"start": 1518.77, "end": 1519.77, "word": " identity", "probability": 0.5185546875}, {"start": 1519.77, "end": 1522.49, "word": " element", "probability": 0.90283203125}, {"start": 1522.49, "end": 1525.05, "word": " of", "probability": 0.7529296875}, {"start": 1525.05, "end": 1526.51, "word": " R", "probability": 0.5439453125}, {"start": 1526.51, 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"text": "طبعا احنا درسنا في الجبر الخطي المصحوفة لنظامها اتنين في اتنين يبجي فيها صفين و عمودين يبجي هذه المصحوفة بقول انه نظامها اتنين في اتنين او ال size تبعها اتنين في اتنين مش اتنين في اتنين يسوى اربعة", "tokens": [9566, 3555, 3615, 995, 1975, 5016, 8315, 11778, 2288, 3794, 8315, 8978, 25724, 26890, 33962, 9566, 1829, 9673, 9381, 5016, 38688, 3660, 5296, 1863, 19913, 10943, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 7251, 3555, 7435, 1829, 8978, 11296, 20328, 5172, 9957, 4032, 6225, 2304, 23328, 9957, 7251, 3555, 7435, 1829, 29538, 9673, 9381, 5016, 38688, 3660, 4724, 39648, 16472, 3224, 8717, 19913, 10943, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 1975, 2407, 2423, 2744, 6055, 3555, 3615, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 37893, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 7251, 3794, 2407, 7578, 1975, 25513, 27884], "avg_logprob": -0.14885602851531335, "compression_ratio": 2.279220779220779, 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matrix multiplication عملية ضرب المصحفات بدعي أنا هذا أن هذا is a group نرجع للجبر الخطي اظن حاصل ضرب تلت مصحفات associative ولا لا اتنين لما نضرب مصحفتين نظامهم اتنين في اتنين تطلع مصحف النظام اربعة في اربعة", "tokens": [5016, 38436, 4587, 10632, 4032, 2304, 24401, 3215, 9307, 11296, 5296, 9307, 3794, 995, 45865, 5551, 3794, 5172, 9640, 995, 6225, 28480, 2655, 25894, 11296, 6225, 42213, 10632, 48812, 25513, 18863, 18513, 10632, 6055, 3555, 3615, 9673, 9381, 5016, 5172, 9307, 833, 8141, 27290, 6225, 42213, 10632, 48812, 25513, 9673, 9381, 5016, 5172, 9307, 47525, 3615, 1829, 41850, 23758, 14739, 23758, 307, 257, 1594, 8717, 47341, 3615, 24976, 7435, 26890, 33962, 9566, 1829, 1975, 19913, 1863, 11331, 33546, 1211, 48812, 25513, 6055, 1211, 2655, 3714, 9381, 5016, 5172, 9307, 4180, 1166, 49429, 20193, 1975, 2655, 1863, 9957, 5296, 15042, 8717, 11242, 25513, 3714, 9381, 5016, 5172, 2655, 9957, 8717, 19913, 10943, 16095, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 6055, 9566, 1211, 3615, 3714, 9381, 5016, 5172, 28239, 19913, 10943, 1975, 25513, 27884, 8978, 1975, 25513, 27884], "avg_logprob": -0.159151791036129, "compression_ratio": 1.8505747126436782, "no_speech_prob": 0.0, "words": [{"start": 1748.6799999999998, "end": 1749.58, "word": "حقيقية", "probability": 0.8743896484375}, {"start": 1749.58, "end": 1750.48, "word": " ومحدداتها", "probability": 0.9307454427083334}, {"start": 1750.48, "end": 1751.26, "word": " لاتساوي", "probability": 0.85673828125}, {"start": 1751.26, "end": 1752.08, "word": " أسفارا", "probability": 0.7529296875}, {"start": 1752.08, "end": 1753.26, "word": " عرفت", "probability": 0.81298828125}, {"start": 1753.26, "end": 1753.6, "word": " عليها", "probability": 0.986328125}, {"start": 1753.6, "end": 1754.22, "word": " عملية", "probability": 0.97412109375}, {"start": 1754.22, "end": 1754.76, "word": " ضرب", "probability": 0.859375}, {"start": 1754.76, "end": 1755.54, "word": " العادية", "probability": 0.9527994791666666}, {"start": 1755.54, "end": 1755.92, "word": " تبع", "probability": 0.8330078125}, {"start": 1755.92, "end": 1756.94, "word": " المصحفات", "probability": 0.78427734375}, {"start": 1756.94, "end": 1757.44, "word": " under", "probability": 0.544921875}, {"start": 1757.44, "end": 1758.62, "word": " matrix", "probability": 0.876953125}, {"start": 1758.62, "end": 1759.78, "word": " multiplication", "probability": 0.89404296875}, {"start": 1759.78, "end": 1760.92, "word": " عملية", "probability": 0.9645182291666666}, {"start": 1760.92, "end": 1761.34, "word": " ضرب", "probability": 0.99755859375}, {"start": 1761.34, "end": 1762.62, "word": " المصحفات", "probability": 0.99404296875}, {"start": 1762.62, "end": 1763.32, "word": " بدعي", "probability": 0.650634765625}, {"start": 1763.32, "end": 1763.6, "word": " أنا", "probability": 0.342529296875}, {"start": 1763.6, "end": 1764.0, "word": " هذا", "probability": 0.418701171875}, {"start": 1764.0, "end": 1764.3, "word": " أن", "probability": 0.36572265625}, {"start": 1764.3, "end": 1764.72, "word": " هذا", "probability": 0.662109375}, {"start": 1764.72, "end": 1765.14, "word": " is", "probability": 0.6904296875}, {"start": 1765.14, "end": 1765.48, "word": " a", "probability": 0.8115234375}, {"start": 1765.48, "end": 1765.84, "word": " group", "probability": 0.728515625}, {"start": 1765.84, "end": 1766.84, "word": " نرجع", "probability": 0.9296875}, {"start": 1766.84, "end": 1767.36, "word": " للجبر", "probability": 0.7967122395833334}, {"start": 1767.36, "end": 1768.02, "word": " الخطي", "probability": 0.77392578125}, {"start": 1768.02, "end": 1768.38, "word": " اظن", "probability": 0.7693684895833334}, {"start": 1768.38, "end": 1768.98, "word": " حاصل", "probability": 0.8221028645833334}, {"start": 1768.98, "end": 1769.26, "word": " ضرب", "probability": 0.995361328125}, {"start": 1769.26, "end": 1769.62, "word": " تلت", "probability": 0.8642578125}, {"start": 1769.62, "end": 1770.22, "word": " مصحفات", "probability": 0.99013671875}, {"start": 1770.22, "end": 1770.9, "word": " associative", "probability": 0.916015625}, {"start": 1770.9, "end": 1771.12, "word": " ولا", "probability": 0.93994140625}, {"start": 1771.12, "end": 1771.44, "word": " لا", "probability": 0.755859375}, {"start": 1771.44, "end": 1772.8, "word": " اتنين", "probability": 0.9031982421875}, {"start": 1772.8, "end": 1773.04, "word": " لما", "probability": 0.902587890625}, {"start": 1773.04, "end": 1773.42, "word": " نضرب", "probability": 0.9954427083333334}, {"start": 1773.42, "end": 1774.18, "word": " مصحفتين", "probability": 0.971923828125}, {"start": 1774.18, "end": 1774.82, "word": " نظامهم", "probability": 0.9840087890625}, {"start": 1774.82, "end": 1775.3, "word": " اتنين", "probability": 0.9732666015625}, {"start": 1775.3, "end": 1775.44, "word": " في", "probability": 0.83837890625}, {"start": 1775.44, "end": 1775.8, "word": " اتنين", "probability": 0.9869384765625}, {"start": 1775.8, "end": 1776.22, "word": " تطلع", "probability": 0.81268310546875}, {"start": 1776.22, "end": 1776.58, "word": " مصحف", "probability": 0.95166015625}, {"start": 1776.58, "end": 1776.92, "word": " النظام", "probability": 0.9646809895833334}, {"start": 1776.92, "end": 1777.34, "word": " اربعة", "probability": 0.8108723958333334}, {"start": 1777.34, "end": 1777.48, "word": " في", "probability": 0.9638671875}, {"start": 1777.48, "end": 1777.88, "word": " اربعة", "probability": 0.9244791666666666}], "temperature": 1.0}, {"id": 71, "seek": 180417, "start": 1778.15, "end": 1804.17, "text": "و الله اتنين في اتنين يبقى اتنين في اتنين كذلك اذا عملية ضرب المصطفات is a binary operation يبقى بقوله النقطة الاولى we know that من الجبر الخاطئ we know from linear algebra that", "tokens": [2407, 21984, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 9122, 8848, 23275, 1975, 15730, 6225, 42213, 10632, 48812, 25513, 9673, 9381, 9566, 5172, 9307, 307, 257, 17434, 6916, 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1781.51, "word": " اتنين", "probability": 0.994140625}, {"start": 1781.51, "end": 1782.13, "word": " كذلك", "probability": 0.9586588541666666}, {"start": 1782.13, "end": 1782.65, "word": " اذا", "probability": 0.786865234375}, {"start": 1782.65, "end": 1783.17, "word": " عملية", "probability": 0.7554524739583334}, {"start": 1783.17, "end": 1783.49, "word": " ضرب", "probability": 0.983154296875}, {"start": 1783.49, "end": 1784.21, "word": " المصطفات", "probability": 0.84404296875}, {"start": 1784.21, "end": 1784.67, "word": " is", "probability": 0.86669921875}, {"start": 1784.67, "end": 1785.27, "word": " a", "probability": 0.96484375}, {"start": 1785.27, "end": 1786.07, "word": " binary", "probability": 0.8828125}, {"start": 1786.07, "end": 1787.59, "word": " operation", "probability": 0.9404296875}, {"start": 1787.59, "end": 1788.61, "word": " يبقى", "probability": 0.9847412109375}, {"start": 1788.61, "end": 1789.15, "word": " بقوله", "probability": 0.8802083333333334}, {"start": 1789.15, "end": 1789.93, "word": " النقطة", "probability": 0.9339192708333334}, {"start": 1789.93, "end": 1791.21, "word": " الاولى", "probability": 0.79345703125}, {"start": 1791.21, "end": 1791.83, "word": " we", "probability": 0.77978515625}, {"start": 1791.83, "end": 1792.45, "word": " know", "probability": 0.91455078125}, {"start": 1792.45, "end": 1793.01, "word": " that", "probability": 0.93798828125}, {"start": 1793.01, "end": 1794.13, "word": " من", "probability": 0.98681640625}, {"start": 1794.13, "end": 1794.61, "word": " الجبر", "probability": 0.7073974609375}, {"start": 1794.61, "end": 1795.15, "word": " الخاطئ", "probability": 0.9166666666666666}, {"start": 1795.15, "end": 1795.39, "word": " we", "probability": 0.65283203125}, {"start": 1795.39, "end": 1795.77, "word": " know", "probability": 0.89404296875}, {"start": 1795.77, "end": 1796.79, "word": " from", "probability": 0.91162109375}, {"start": 1796.79, "end": 1798.83, "word": " linear", "probability": 0.9541015625}, {"start": 1798.83, "end": 1800.75, "word": " algebra", "probability": 0.9267578125}, {"start": 1800.75, "end": 1804.17, "word": " that", "probability": 0.92578125}], "temperature": 1.0}, {"id": 72, "seek": 183305, "start": 1808.51, "end": 1833.05, "text": "matrix multiplication is an associative binary operation on", "tokens": [15677, 6579, 27290, 307, 364, 4180, 1166, 17434, 6916, 322], "avg_logprob": -0.2956321022727273, "compression_ratio": 0.9833333333333333, "no_speech_prob": 0.0, "words": [{"start": 1808.5099999999998, "end": 1809.9099999999999, "word": "matrix", "probability": 0.51409912109375}, {"start": 1809.9099999999999, "end": 1811.31, "word": " multiplication", "probability": 0.8564453125}, {"start": 1811.31, "end": 1816.59, "word": " is", "probability": 0.92822265625}, {"start": 1816.59, "end": 1818.51, "word": " an", "probability": 0.85693359375}, {"start": 1818.51, "end": 1821.09, "word": " associative", "probability": 0.982421875}, {"start": 1821.09, "end": 1825.21, 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"probability": 0.490478515625}, {"start": 2078.1, "end": 2078.48, "word": " binary", "probability": 0.93017578125}, {"start": 2078.48, "end": 2079.1, "word": " operation", "probability": 0.9228515625}, {"start": 2079.1, "end": 2079.92, "word": " أقولك", "probability": 0.8388671875}], "temperature": 1.0}, {"id": 83, "seek": 210803, "start": 2080.15, "end": 2108.03, "text": "ان انا عندى ال determinant لـA لا يساوي 0 و ال determinant لـB لا يساوي 0 صح ولا لأ حسب ال condition اللى هماطينيا الان لو أخدت ال determinant للـA في الـB حسب معلوماتنا من ال linear algebra اللى احنا قلنا عليها ال linear algebra يبقى هذا بده يساوي determinant", "tokens": [7649, 1975, 8315, 43242, 7578, 2423, 41296, 5296, 39184, 32, 20193, 7251, 3794, 995, 45865, 1958, 4032, 2423, 41296, 5296, 39184, 33, 20193, 7251, 3794, 995, 45865, 1958, 20328, 5016, 49429, 5296, 10721, 11331, 35457, 2423, 4188, 13672, 7578, 8032, 2304, 41193, 9957, 25528, 2423, 7649, 45164, 5551, 9778, 3215, 2655, 2423, 41296, 24976, 39184, 32, 8978, 2423, 39184, 33, 11331, 35457, 20449, 1211, 20498, 9307, 8315, 9154, 2423, 8213, 21989, 13672, 7578, 1975, 5016, 8315, 12174, 1211, 8315, 25894, 11296, 2423, 8213, 21989, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 7251, 3794, 995, 45865, 41296], "avg_logprob": -0.2920425159415019, "compression_ratio": 1.8829268292682926, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2080.15, "end": 2080.53, "word": "ان", "probability": 0.14892578125}, {"start": 2080.53, "end": 2080.85, "word": " انا", "probability": 0.664794921875}, {"start": 2080.85, "end": 2081.45, "word": " عندى", "probability": 0.6201171875}, {"start": 2081.45, "end": 2081.45, "word": " ال", "probability": 0.4609375}, {"start": 2081.45, "end": 2082.21, "word": " determinant", "probability": 0.720703125}, {"start": 2082.21, "end": 2083.19, "word": " لـA", "probability": 0.3811442057291667}, {"start": 2083.19, "end": 2084.03, "word": " لا", "probability": 0.72265625}, {"start": 2084.03, "end": 2084.75, "word": " 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"probability": 0.75390625}, {"start": 2091.19, "end": 2091.33, "word": " ال", "probability": 0.94970703125}, {"start": 2091.33, "end": 2091.71, "word": " condition", "probability": 0.95556640625}, {"start": 2091.71, "end": 2091.91, "word": " اللى", "probability": 0.9111328125}, {"start": 2091.91, "end": 2092.75, "word": " هماطينيا", "probability": 0.647216796875}, {"start": 2092.75, "end": 2093.77, "word": " الان", "probability": 0.63232421875}, {"start": 2093.77, "end": 2094.07, "word": " لو", "probability": 0.9755859375}, {"start": 2094.07, "end": 2094.79, "word": " أخدت", "probability": 0.8680419921875}, {"start": 2094.79, "end": 2094.95, "word": " ال", "probability": 0.495361328125}, {"start": 2094.95, "end": 2096.01, "word": " determinant", "probability": 0.98681640625}, {"start": 2096.01, "end": 2097.55, "word": " للـA", "probability": 0.5684407552083334}, {"start": 2097.55, "end": 2097.89, "word": " في", "probability": 0.7041015625}, {"start": 2097.89, "end": 2098.37, "word": " الـB", "probability": 0.8662109375}, {"start": 2098.37, "end": 2099.35, "word": " حسب", "probability": 0.983642578125}, {"start": 2099.35, "end": 2100.23, "word": " معلوماتنا", "probability": 0.95634765625}, {"start": 2100.23, "end": 2100.47, "word": " من", "probability": 0.9833984375}, {"start": 2100.47, "end": 2100.63, "word": " ال", "probability": 0.96728515625}, {"start": 2100.63, "end": 2100.93, "word": " linear", "probability": 0.87646484375}, {"start": 2100.93, "end": 2101.55, "word": " algebra", "probability": 0.83642578125}, {"start": 2101.55, "end": 2101.81, "word": " اللى", "probability": 0.96533203125}, {"start": 2101.81, "end": 2102.11, "word": " احنا", "probability": 0.8932291666666666}, {"start": 2102.11, "end": 2102.57, "word": " قلنا", "probability": 0.8759765625}, {"start": 2102.57, "end": 2103.23, "word": " عليها", "probability": 0.978515625}, {"start": 2103.23, "end": 2103.85, "word": " ال", "probability": 0.66796875}, {"start": 2103.85, "end": 2104.25, "word": " linear", "probability": 0.8583984375}, {"start": 2104.25, "end": 2105.03, "word": " algebra", "probability": 0.90771484375}, {"start": 2105.03, "end": 2105.87, "word": " يبقى", "probability": 0.9810791015625}, {"start": 2105.87, "end": 2106.19, "word": " هذا", "probability": 0.8994140625}, {"start": 2106.19, "end": 2106.61, "word": " بده", "probability": 0.710693359375}, {"start": 2106.61, "end": 2107.17, "word": " يساوي", "probability": 0.96533203125}, {"start": 2107.17, "end": 2108.03, "word": " determinant", "probability": 0.5380859375}], "temperature": 1.0}, {"id": 84, "seek": 213585, "start": 2108.83, "end": 2135.85, "text": "للـ F determinant للـ B تمام؟ يبقى هذا كله ماله لا يساوي Zero معناته حصل الضرب هذا موجود وين؟ موجود في الـ U من هنا هذه صارت binary operation و لا associative يام أخدناها في الثانوية و كذلك أخدناها وين؟ في الجبر الخاطي طيب ممكن نيجي نروح ناخد حالة خاصة", "tokens": [1211, 1211, 39184, 479, 41296, 24976, 39184, 363, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 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0.75390625}, {"start": 2111.23, "end": 2112.35, "word": " للـ", "probability": 0.678466796875}, {"start": 2112.35, "end": 2112.53, "word": " B", "probability": 0.62451171875}, {"start": 2112.53, "end": 2113.91, "word": " تمام؟", "probability": 0.546630859375}, {"start": 2113.91, "end": 2114.35, "word": " يبقى", "probability": 0.956787109375}, {"start": 2114.35, "end": 2114.63, "word": " هذا", "probability": 0.92333984375}, {"start": 2114.63, "end": 2115.11, "word": " كله", "probability": 0.978759765625}, {"start": 2115.11, "end": 2115.57, "word": " ماله", "probability": 0.7892252604166666}, {"start": 2115.57, "end": 2116.23, "word": " لا", "probability": 0.677734375}, {"start": 2116.23, "end": 2116.97, "word": " يساوي", "probability": 0.9097900390625}, {"start": 2116.97, "end": 2117.39, "word": " Zero", "probability": 0.5458984375}, {"start": 2117.39, "end": 2118.35, "word": " معناته", "probability": 0.8483072916666666}, {"start": 2118.35, "end": 2118.97, "word": " حصل", "probability": 0.783447265625}, {"start": 2118.97, "end": 2119.45, "word": " الضرب", "probability": 0.88525390625}, {"start": 2119.45, "end": 2119.71, "word": " هذا", "probability": 0.8798828125}, {"start": 2119.71, "end": 2120.11, "word": " موجود", "probability": 0.98779296875}, {"start": 2120.11, "end": 2120.65, "word": " وين؟", "probability": 0.71728515625}, {"start": 2120.65, "end": 2121.17, "word": " موجود", "probability": 0.96533203125}, {"start": 2121.17, "end": 2121.35, "word": " في", "probability": 0.943359375}, {"start": 2121.35, "end": 2121.49, "word": " الـ", "probability": 0.5091552734375}, {"start": 2121.49, "end": 2121.57, "word": " U", "probability": 0.79345703125}, {"start": 2121.57, "end": 2121.77, "word": " من", "probability": 0.5771484375}, {"start": 2121.77, "end": 2122.11, "word": " هنا", "probability": 0.98583984375}, {"start": 2122.11, "end": 2122.45, "word": " هذه", "probability": 0.53759765625}, {"start": 2122.45, "end": 2122.91, "word": " صارت", "probability": 0.9466145833333334}, {"start": 2122.91, "end": 2123.53, "word": " binary", "probability": 0.521484375}, {"start": 2123.53, "end": 2124.57, "word": " operation", "probability": 0.90625}, {"start": 2124.57, "end": 2124.71, "word": " و", "probability": 0.292724609375}, {"start": 2124.71, "end": 2124.81, "word": " لا", "probability": 0.74853515625}, {"start": 2124.81, "end": 2125.49, "word": " associative", "probability": 0.868896484375}, {"start": 2125.49, "end": 2125.75, "word": " يام", "probability": 0.6119384765625}, {"start": 2125.75, "end": 2126.23, "word": " أخدناها", "probability": 0.80751953125}, {"start": 2126.23, "end": 2126.31, "word": " في", "probability": 0.9560546875}, {"start": 2126.31, "end": 2126.99, "word": " الثانوية", "probability": 0.970703125}, {"start": 2126.99, "end": 2127.45, "word": " و", "probability": 0.96240234375}, {"start": 2127.45, "end": 2127.81, "word": " كذلك", "probability": 0.9627278645833334}, {"start": 2127.81, "end": 2128.29, "word": " أخدناها", "probability": 0.941796875}, {"start": 2128.29, "end": 2128.71, "word": " وين؟", "probability": 0.9625651041666666}, {"start": 2128.71, "end": 2128.83, "word": " في", "probability": 0.82177734375}, {"start": 2128.83, "end": 2129.43, "word": " الجبر", "probability": 0.94970703125}, {"start": 2129.43, "end": 2130.91, "word": " الخاطي", "probability": 0.6236165364583334}, {"start": 2130.91, "end": 2132.91, "word": " طيب", "probability": 0.9794921875}, {"start": 2132.91, "end": 2133.29, "word": " ممكن", "probability": 0.9052734375}, {"start": 2133.29, "end": 2133.65, "word": " نيجي", "probability": 0.8472900390625}, {"start": 2133.65, "end": 2133.95, "word": " نروح", "probability": 0.8528645833333334}, {"start": 2133.95, "end": 2134.41, "word": " ناخد", "probability": 0.9375}, {"start": 2134.41, "end": 2134.97, "word": " حالة", "probability": 0.9908854166666666}, {"start": 2134.97, "end": 2135.85, "word": " خاصة", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 85, "seek": 215785, "start": 2136.17, "end": 2157.85, "text": "من ال general linear group هذه بدل المحدد لا يساوي 0 بدي أقول محدد يساوي 1 صحيح وهذه بسميها ال special linear group of two by two matrices over R وهذه كمان بتلعب دور كبير في عين الجبر عندنا في المسائل المختلفة", "tokens": [27842, 2423, 2674, 8213, 1594, 29538, 47525, 1211, 9673, 24401, 3215, 20193, 7251, 3794, 995, 45865, 1958, 4724, 16254, 5551, 39648, 3714, 24401, 3215, 7251, 3794, 995, 45865, 502, 20328, 5016, 1829, 5016, 37037, 24192, 4724, 38251, 1829, 11296, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 37037, 24192, 9122, 2304, 7649, 39894, 1211, 3615, 3555, 11778, 13063, 9122, 3555, 13546, 8978, 6225, 9957, 25724, 26890, 43242, 8315, 8978, 9673, 3794, 16373, 1211, 9673, 46456, 46538, 3660], "avg_logprob": -0.21508487654320987, "compression_ratio": 1.5643564356435644, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2136.17, "end": 2136.73, "word": "من", "probability": 0.219482421875}, {"start": 2136.73, "end": 2137.29, "word": " ال", "probability": 0.83154296875}, {"start": 2137.29, "end": 2137.69, "word": " general", "probability": 0.54443359375}, {"start": 2137.69, "end": 2138.21, "word": " linear", "probability": 0.8203125}, {"start": 2138.21, "end": 2138.61, "word": " group", "probability": 0.94384765625}, {"start": 2138.61, "end": 2139.03, "word": " هذه", "probability": 0.458251953125}, {"start": 2139.03, "end": 2139.79, "word": " بدل", "probability": 0.8271484375}, {"start": 2139.79, "end": 2140.61, "word": " المحدد", "probability": 0.96875}, {"start": 2140.61, "end": 2140.79, "word": " لا", "probability": 0.7138671875}, {"start": 2140.79, "end": 2141.35, "word": " يساوي", "probability": 0.8709716796875}, {"start": 2141.35, "end": 2141.57, "word": " 0", "probability": 0.199462890625}, {"start": 2141.57, "end": 2141.85, "word": " بدي", "probability": 0.31915283203125}, {"start": 2141.85, "end": 2142.03, "word": " أقول", "probability": 0.760498046875}, {"start": 2142.03, "end": 2142.63, "word": " محدد", "probability": 0.8362630208333334}, {"start": 2142.63, "end": 2143.13, "word": " يساوي", "probability": 0.9783935546875}, {"start": 2143.13, "end": 2143.63, "word": " 1", "probability": 0.771484375}, {"start": 2143.63, "end": 2144.27, "word": " صحيح", "probability": 0.9052734375}, {"start": 2144.27, "end": 2144.97, "word": " وهذه", "probability": 0.7587890625}, {"start": 2144.97, "end": 2145.55, "word": " بسميها", "probability": 0.918701171875}, {"start": 2145.55, "end": 2145.83, "word": " ال", "probability": 0.50830078125}, {"start": 2145.83, "end": 2146.31, "word": " special", "probability": 0.91650390625}, {"start": 2146.31, "end": 2146.89, "word": " linear", "probability": 0.873046875}, {"start": 2146.89, "end": 2147.37, "word": " group", "probability": 0.9580078125}, {"start": 2147.37, "end": 2147.63, "word": " of", "probability": 0.93603515625}, {"start": 2147.63, "end": 2147.89, "word": " two", "probability": 0.49658203125}, {"start": 2147.89, 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2153.97, "word": " الجبر", "probability": 0.86669921875}, {"start": 2153.97, "end": 2154.65, "word": " عندنا", "probability": 0.60693359375}, {"start": 2154.65, "end": 2155.05, "word": " في", "probability": 0.88623046875}, {"start": 2155.05, "end": 2156.09, "word": " المسائل", "probability": 0.9256591796875}, {"start": 2156.09, "end": 2157.85, "word": " المختلفة", "probability": 0.99609375}], "temperature": 1.0}, {"id": 86, "seek": 219794, "start": 2170.9, "end": 2197.94, "text": "نمرة عشرة the set الهي ال special linear a group of two by two matrices over R اللي هي كل المصففات اللي على الشكل اللي عندنا a,b,c,d بحيث ان ال a و ال b و ال c و ال d هذه موجودة", "tokens": [1863, 2304, 25720, 6225, 8592, 25720, 264, 992, 2423, 3224, 1829, 2423, 2121, 8213, 257, 1594, 295, 732, 538, 732, 32284, 670, 497, 13672, 1829, 39896, 28242, 9673, 9381, 5172, 5172, 9307, 13672, 1829, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 257, 11, 65, 11, 66, 11, 67, 4724, 5016, 1829, 12984, 16472, 2423, 257, 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3660, 13672, 1829, 31439, 2423, 8141, 13672, 1829, 39896, 36764, 24401, 30767, 13546, 2407, 30767, 13546, 2407, 36764, 24401, 307, 264, 6575, 4478], "avg_logprob": -0.3737792940810323, "compression_ratio": 1.3958333333333333, "no_speech_prob": 0.0, "words": [{"start": 2392.72, "end": 2394.12, "word": "الواحد", "probability": 0.5744425455729166}, {"start": 2394.12, "end": 2394.86, "word": " هو", "probability": 0.76416015625}, {"start": 2394.86, "end": 2396.92, "word": " المصفوفة", "probability": 0.8412109375}, {"start": 2396.92, "end": 2397.78, "word": " اللي", "probability": 0.65966796875}, {"start": 2397.78, "end": 2398.26, "word": " هو", "probability": 0.9541015625}, {"start": 2398.26, "end": 2400.84, "word": " ال", "probability": 0.82763671875}, {"start": 2400.84, "end": 2401.58, "word": " matrix", "probability": 0.1763916015625}, {"start": 2401.58, "end": 2405.06, "word": " اللي", "probability": 0.844482421875}, {"start": 2405.06, "end": 2405.26, "word": " هي", "probability": 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2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 440, 17340, 295, 2423, 39184, 316, 16070, 39184, 363, 16070, 39184, 383, 16070, 39184, 413, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 2674, 8213, 1594, 295, 732, 538, 732, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284], "avg_logprob": -0.279747595007603, "compression_ratio": 1.7829457364341086, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2416.35, "end": 2417.23, "word": "In", "probability": 0.107421875}, {"start": 2417.23, "end": 2418.11, "word": " the", "probability": 0.405029296875}, {"start": 2418.11, "end": 2418.67, "word": " special", "probability": 0.7294921875}, {"start": 2418.67, "end": 2419.29, "word": " linear", "probability": 0.9013671875}, {"start": 2419.29, "end": 2419.73, "word": " group", "probability": 0.85498046875}, {"start": 2419.73, "end": 2420.05, "word": " of", "probability": 0.9599609375}, {"start": 2420.05, "end": 2420.29, "word": " two", "probability": 0.4453125}, {"start": 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two", "probability": 0.9345703125}, {"start": 2435.79, "end": 2436.07, "word": " by", "probability": 0.98095703125}, {"start": 2436.07, "end": 2436.45, "word": " two", "probability": 0.951171875}, {"start": 2436.45, "end": 2437.13, "word": " ال", "probability": 0.3955078125}, {"start": 2437.13, "end": 2438.01, "word": " special", "probability": 0.7880859375}, {"start": 2438.01, "end": 2439.09, "word": " linear", "probability": 0.90869140625}, {"start": 2439.09, "end": 2439.53, "word": " group", "probability": 0.96435546875}, {"start": 2439.53, "end": 2439.85, "word": " of", "probability": 0.970703125}, {"start": 2439.85, "end": 2440.09, "word": " two", "probability": 0.93310546875}, {"start": 2440.09, "end": 2440.35, "word": " by", "probability": 0.9794921875}, {"start": 2440.35, "end": 2440.69, "word": " two", "probability": 0.93505859375}, {"start": 2440.69, "end": 2441.49, "word": " matrices", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 96, "seek": 246342, "start": 2459.54, "end": 2463.42, "text": "ما ينطبق على R", "tokens": [15042, 7251, 1863, 9566, 3555, 4587, 15844, 497], "avg_logprob": -0.5243055555555556, "compression_ratio": 0.7272727272727273, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2459.54, "end": 2460.94, "word": "ما", "probability": 0.08929443359375}, {"start": 2460.94, "end": 2462.0, "word": " ينطبق", "probability": 0.858984375}, {"start": 2462.0, "end": 2462.62, "word": " على", "probability": 0.8896484375}, {"start": 2462.62, "end": 2463.42, "word": " R", "probability": 0.34814453125}], "temperature": 1.0}, {"id": 97, "seek": 248364, "start": 2463.6, "end": 2483.64, "text": "ينطبق على ال special linear of two by two matrices over q و over c و over zp يبقى this is a true for ال general for ال special", "tokens": [1829, 1863, 9566, 3555, 4587, 15844, 2423, 2121, 8213, 295, 732, 538, 732, 32284, 670, 9505, 4032, 670, 269, 4032, 670, 710, 79, 7251, 3555, 4587, 7578, 341, 307, 257, 2074, 337, 2423, 2674, 337, 2423, 2121], "avg_logprob": -0.26233554043267904, "compression_ratio": 1.2478632478632479, "no_speech_prob": 0.0, "words": [{"start": 2463.6, "end": 2464.96, "word": "ينطبق", "probability": 0.788525390625}, {"start": 2464.96, "end": 2465.5, "word": " على", "probability": 0.8857421875}, {"start": 2465.5, "end": 2465.76, "word": " ال", "probability": 0.810546875}, {"start": 2465.76, "end": 2466.16, "word": " special", "probability": 0.462646484375}, {"start": 2466.16, "end": 2466.48, "word": " linear", "probability": 0.308837890625}, {"start": 2466.48, "end": 2466.84, "word": " of", "probability": 0.76025390625}, {"start": 2466.84, "end": 2467.06, "word": " two", "probability": 0.56103515625}, {"start": 2467.06, "end": 2467.26, "word": " by", "probability": 0.89208984375}, {"start": 2467.26, "end": 2467.46, "word": " two", "probability": 0.94873046875}, {"start": 2467.46, "end": 2467.82, "word": " matrices", "probability": 0.88623046875}, {"start": 2467.82, "end": 2468.22, "word": " over", "probability": 0.7734375}, {"start": 2468.22, "end": 2468.88, "word": " q", "probability": 0.47705078125}, {"start": 2468.88, "end": 2469.7, "word": " و", "probability": 0.87841796875}, {"start": 2469.7, "end": 2470.16, "word": " over", "probability": 0.8203125}, {"start": 2470.16, "end": 2470.9, "word": " c", "probability": 0.58251953125}, {"start": 2470.9, "end": 2471.52, "word": " و", "probability": 0.98779296875}, {"start": 2471.52, "end": 2471.96, "word": " over", "probability": 0.923828125}, {"start": 2471.96, "end": 2472.96, "word": " zp", "probability": 0.8603515625}, {"start": 2472.96, "end": 2474.18, "word": " يبقى", "probability": 0.9697265625}, {"start": 2474.18, "end": 2474.58, "word": " this", "probability": 0.748046875}, {"start": 2474.58, "end": 2475.34, "word": " is", "probability": 0.9619140625}, {"start": 2475.34, "end": 2477.34, "word": " a", "probability": 0.385986328125}, {"start": 2477.34, "end": 2477.78, "word": " true", "probability": 0.9296875}, {"start": 2477.78, "end": 2479.76, "word": " for", "probability": 0.943359375}, {"start": 2479.76, "end": 2480.94, "word": " ال", "probability": 0.83740234375}, {"start": 2480.94, "end": 2481.56, "word": " general", "probability": 0.67041015625}, {"start": 2481.56, "end": 2482.86, "word": " for", "probability": 0.654296875}, {"start": 2482.86, "end": 2483.12, "word": " ال", "probability": 0.85888671875}, {"start": 2483.12, "end": 2483.64, "word": " special", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 98, "seek": 250648, "start": 2485.16, "end": 2506.48, "text": "الـ Special Linear Group of 2x2 matrices over Q والـ Special Linear Group of 2x2 matrices over C والـ Special Linear Group of 2x2 matrices over ZT", "tokens": [6027, 39184, 11863, 14670, 289, 10500, 295, 568, 87, 17, 32284, 670, 1249, 16070, 39184, 11863, 14670, 289, 10500, 295, 568, 87, 17, 32284, 670, 383, 16070, 39184, 11863, 14670, 289, 10500, 295, 568, 87, 17, 32284, 670, 1176, 51], "avg_logprob": -0.24009146341463414, "compression_ratio": 2.242857142857143, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2485.16, "end": 2485.7, "word": "الـ", "probability": 0.2733154296875}, {"start": 2485.7, "end": 2486.28, "word": " Special", "probability": 0.501953125}, {"start": 2486.28, "end": 2487.32, "word": " Linear", "probability": 0.919921875}, {"start": 2487.32, "end": 2487.76, "word": " Group", "probability": 0.8017578125}, {"start": 2487.76, "end": 2488.9, "word": " of", "probability": 0.82177734375}, {"start": 2488.9, "end": 2490.02, "word": " 2x2", "probability": 0.7230631510416666}, {"start": 2490.02, "end": 2490.62, "word": " matrices", "probability": 0.6875}, {"start": 2490.62, "end": 2491.3, "word": " over", "probability": 0.81640625}, {"start": 2491.3, "end": 2492.0, "word": " Q", "probability": 0.87353515625}, {"start": 2492.0, "end": 2492.94, "word": " والـ", "probability": 0.48828125}, {"start": 2492.94, "end": 2493.5, "word": " Special", "probability": 0.81298828125}, {"start": 2493.5, "end": 2494.32, "word": " Linear", "probability": 0.98974609375}, {"start": 2494.32, "end": 2494.68, "word": " Group", "probability": 0.91259765625}, {"start": 2494.68, "end": 2495.12, "word": " of", "probability": 0.97998046875}, {"start": 2495.12, "end": 2496.02, "word": " 2x2", "probability": 0.9959309895833334}, {"start": 2496.02, "end": 2496.82, "word": " matrices", "probability": 0.97314453125}, {"start": 2496.82, "end": 2497.62, "word": " over", "probability": 0.92333984375}, {"start": 2497.62, "end": 2498.26, "word": " C", "probability": 0.75146484375}, {"start": 2498.26, "end": 2499.58, "word": " والـ", "probability": 0.6524658203125}, {"start": 2499.58, "end": 2500.7, "word": " Special", "probability": 0.84423828125}, {"start": 2500.7, "end": 2501.4, "word": " Linear", "probability": 0.9921875}, {"start": 2501.4, "end": 2501.82, "word": " Group", "probability": 0.90576171875}, {"start": 2501.82, "end": 2502.4, "word": " of", "probability": 0.98095703125}, {"start": 2502.4, "end": 2503.18, "word": " 2x2", "probability": 0.9972330729166666}, {"start": 2503.18, "end": 2503.82, "word": " matrices", "probability": 0.982421875}, {"start": 2503.82, "end": 2505.18, "word": " over", "probability": 0.9287109375}, {"start": 2505.18, "end": 2506.48, "word": " ZT", "probability": 0.83251953125}], "temperature": 1.0}, {"id": 99, "seek": 253010, "start": 2508.48, "end": 2530.1, "text": "أظن هدول كلهم طبيعي بسهلات الحسابات لكن تعالى نحسب لك شغلة زى هذه نعطيك مصفوفة موجودة في zp ونشوف ايش اللى حصل for example consider", "tokens": [10721, 19913, 1863, 8032, 3215, 12610, 28242, 16095, 23032, 21292, 3615, 1829, 4724, 3794, 3224, 1211, 9307, 21542, 3794, 16758, 9307, 44381, 37279, 6027, 7578, 8717, 5016, 35457, 5296, 4117, 13412, 17082, 37977, 30767, 7578, 29538, 8717, 3615, 9566, 1829, 4117, 3714, 9381, 5172, 38688, 3660, 3714, 29245, 23328, 3660, 8978, 710, 79, 4032, 1863, 8592, 38688, 1975, 1829, 8592, 13672, 7578, 11331, 36520, 337, 1365, 1949], "avg_logprob": -0.1806066174279241, "compression_ratio": 1.3374233128834356, "no_speech_prob": 0.0, "words": [{"start": 2508.48, "end": 2508.98, "word": "أظن", "probability": 0.7567545572916666}, {"start": 2508.98, "end": 2509.42, "word": " هدول", "probability": 0.72314453125}, {"start": 2509.42, "end": 2510.02, "word": " كلهم", "probability": 0.8779296875}, {"start": 2510.02, "end": 2510.58, "word": " طبيعي", "probability": 0.9560546875}, {"start": 2510.58, "end": 2511.28, "word": " بسهلات", "probability": 0.80380859375}, {"start": 2511.28, "end": 2512.14, "word": " الحسابات", "probability": 0.99072265625}, {"start": 2512.14, "end": 2512.78, "word": " لكن", "probability": 0.70263671875}, {"start": 2512.78, "end": 2513.3, "word": " تعالى", "probability": 0.8142903645833334}, {"start": 2513.3, "end": 2513.7, "word": " نحسب", "probability": 0.9791666666666666}, {"start": 2513.7, "end": 2513.94, "word": " لك", "probability": 0.67919921875}, {"start": 2513.94, "end": 2514.58, "word": " شغلة", "probability": 0.84326171875}, {"start": 2514.58, "end": 2515.24, "word": " زى", "probability": 0.80810546875}, {"start": 2515.24, "end": 2515.66, "word": " هذه", "probability": 0.83203125}, {"start": 2515.66, "end": 2516.56, "word": " نعطيك", "probability": 0.94755859375}, {"start": 2516.56, "end": 2517.28, "word": " مصفوفة", "probability": 0.853515625}, {"start": 2517.28, "end": 2518.16, "word": " موجودة", "probability": 0.976318359375}, {"start": 2518.16, "end": 2518.68, "word": " في", "probability": 0.89501953125}, {"start": 2518.68, "end": 2519.56, "word": " zp", "probability": 0.640869140625}, {"start": 2519.56, "end": 2520.6, "word": " ونشوف", "probability": 0.906494140625}, {"start": 2520.6, "end": 2521.38, "word": " ايش", "probability": 0.78125}, {"start": 2521.38, "end": 2521.58, "word": " اللى", "probability": 0.831787109375}, {"start": 2521.58, "end": 2521.98, "word": " حصل", "probability": 0.972900390625}, {"start": 2521.98, "end": 2522.22, "word": " for", 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لو ضربتها من اليمين او من الشمال بدي يطلع من؟ مصفوفة الوحدة يبقى دير بالك، اي مصفوفة أخرى تاخدها بعد ذلك موجودة في ال especially بقيت عاملها بنفس الطريقة", "tokens": [7649, 995, 1975, 3215, 3615, 1829, 16472, 29538, 9673, 9381, 5172, 38688, 3660, 39896, 20449, 4117, 2407, 12984, 9154, 22807, 20449, 4117, 2407, 12984, 9673, 9381, 5172, 38688, 3660, 16247, 9381, 1211, 10632, 12399, 37893, 7649, 7251, 3555, 4587, 7578, 28242, 10943, 20328, 5016, 1829, 5016, 45164, 48812, 25513, 2655, 11296, 9154, 2423, 32640, 9957, 1975, 2407, 9154, 25124, 2304, 6027, 4724, 16254, 7251, 9566, 1211, 3615, 9154, 22807, 3714, 9381, 5172, 38688, 3660, 2423, 2407, 24401, 3660, 7251, 3555, 4587, 7578, 11778, 13546, 20666, 4117, 12399, 1975, 1829, 3714, 9381, 5172, 38688, 3660, 5551, 34740, 7578, 6055, 47283, 3215, 11296, 39182, 29910, 23275, 3714, 29245, 23328, 3660, 8978, 2423, 2318, 4724, 4587, 36081, 6225, 10943, 1211, 11296, 44945, 36178, 41950, 16572, 28671], "avg_logprob": -0.20022681571783557, 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16490, 2304, 3794, 3660, 8978, 30767, 3215, 8608, 3555, 27884, 8978, 30767, 3215, 5551, 24401, 6225, 8592, 7649, 47525, 4117, 6055, 5016, 35457, 44945, 36178, 41950, 16572, 28671, 13672, 1829, 43242, 8315], "avg_logprob": -0.260863108862014, "compression_ratio": 1.9558823529411764, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3019.97, "end": 3020.57, "word": "موديول", "probability": 0.53765869140625}, {"start": 3020.57, "end": 3021.11, "word": " الخمس", "probability": 0.828125}, {"start": 3021.11, "end": 3021.39, "word": " هنا", "probability": 0.32421875}, {"start": 3021.39, "end": 3022.19, "word": " واحد", "probability": 0.86767578125}, {"start": 3022.19, "end": 3023.21, "word": " زيرو", "probability": 0.5865478515625}, {"start": 3023.21, "end": 3023.95, "word": " وهنا", "probability": 0.61309814453125}, {"start": 3023.95, "end": 3024.59, "word": " زيرو", "probability": 0.7169596354166666}, {"start": 3024.59, "end": 3025.35, "word": " واحد", "probability": 0.951171875}, {"start": 3025.35, "end": 3025.67, "word": " هو", "probability": 0.82421875}, {"start": 3025.67, "end": 3025.97, "word": " ال", "probability": 0.75830078125}, {"start": 3025.97, "end": 3026.77, "word": " identity", "probability": 0.7392578125}, {"start": 3026.77, "end": 3027.55, "word": " matrix", "probability": 0.6279296875}, {"start": 3027.55, "end": 3028.37, "word": " يبقى", "probability": 0.9263916015625}, {"start": 3028.37, "end": 3028.95, "word": " فعلا", "probability": 0.943359375}, {"start": 3028.95, "end": 3029.39, "word": " هذه", "probability": 0.63525390625}, {"start": 3029.39, "end": 3029.73, "word": " هي", "probability": 0.5947265625}, {"start": 3029.73, "end": 3030.61, "word": " هذه", "probability": 0.5654296875}, {"start": 3030.61, "end": 3031.23, "word": " اللي", "probability": 0.790283203125}, {"start": 3031.23, "end": 3031.37, "word": " هي", "probability": 0.8212890625}, {"start": 3031.37, "end": 3032.09, "word": " المصوفة", "probability": 0.81951904296875}, {"start": 3032.09, "end": 3033.39, "word": " ومعكوس", "probability": 0.8599609375}, {"start": 3033.39, "end": 3033.83, "word": " هذه", "probability": 0.92822265625}, {"start": 3033.83, "end": 3034.59, "word": " المصوفة", "probability": 0.977294921875}, {"start": 3034.59, "end": 3034.79, "word": " هي", "probability": 0.9248046875}, {"start": 3034.79, "end": 3035.39, "word": " المصوفة", "probability": 0.9813232421875}, {"start": 3035.39, "end": 3035.49, "word": " اللي", "probability": 0.903076171875}, {"start": 3035.49, "end": 3035.81, "word": " عندنا", "probability": 0.92578125}, {"start": 3035.81, "end": 3036.41, "word": " يبقى", "probability": 0.9481201171875}, {"start": 3036.41, "end": 3036.61, "word": " عند", "probability": 0.88671875}, {"start": 3036.61, "end": 3037.33, "word": " الحسابات", "probability": 0.979736328125}, {"start": 3037.33, "end": 3037.55, "word": " في", "probability": 0.93017578125}, {"start": 3037.55, "end": 3037.81, "word": " زد", "probability": 0.48974609375}, {"start": 3037.81, "end": 3038.35, "word": " خمسة", "probability": 0.9698486328125}, {"start": 3038.35, "end": 3038.47, "word": " في", "probability": 0.94775390625}, {"start": 3038.47, "end": 3038.73, "word": " زد", "probability": 0.969482421875}, {"start": 3038.73, "end": 3039.11, "word": " سبعة", "probability": 0.97412109375}, {"start": 3039.11, "end": 3039.31, "word": " في", "probability": 0.95703125}, {"start": 3039.31, "end": 3039.55, "word": " زد", "probability": 0.97705078125}, {"start": 3039.55, "end": 3039.79, "word": " أحد", "probability": 0.739013671875}, {"start": 3039.79, "end": 3039.99, "word": " عشان", "probability": 0.4517415364583333}, {"start": 3039.99, "end": 3040.35, "word": " بدك", "probability": 0.6319580078125}, {"start": 3040.35, "end": 3040.89, "word": " تحسب", "probability": 0.9773763020833334}, {"start": 3040.89, "end": 3041.45, "word": " بنفس", "probability": 0.97607421875}, {"start": 3041.45, "end": 3042.21, "word": " الطريقة", "probability": 0.9915364583333334}, {"start": 3042.21, "end": 3042.85, "word": " اللي", "probability": 0.960693359375}, {"start": 3042.85, "end": 3043.21, "word": " عندنا", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 122, "seek": 305092, "start": 3044.42, "end": 3050.92, "text": "لازلنا في المحاضرة القادمة مع مزيد من الأمثلة على Legros", "tokens": [1211, 31377, 1211, 8315, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 20449, 3714, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 15844, 7470, 2635], "avg_logprob": -0.18, "compression_ratio": 1.1149425287356323, "no_speech_prob": 0.0, "words": [{"start": 3044.42, "end": 3045.24, "word": "لازلنا", "probability": 0.83154296875}, {"start": 3045.24, "end": 3045.38, "word": " في", "probability": 0.90673828125}, {"start": 3045.38, "end": 3046.06, "word": " المحاضرة", "probability": 0.9888916015625}, {"start": 3046.06, "end": 3046.68, "word": " القادمة", "probability": 0.99072265625}, {"start": 3046.68, "end": 3047.02, "word": " مع", "probability": 0.8525390625}, {"start": 3047.02, "end": 3047.74, "word": " مزيد", "probability": 0.9366861979166666}, {"start": 3047.74, "end": 3048.1, "word": " من", "probability": 0.947265625}, {"start": 3048.1, "end": 3049.14, "word": " الأمثلة", "probability": 0.92822265625}, {"start": 3049.14, "end": 3049.72, "word": " على", "probability": 0.84326171875}, {"start": 3049.72, "end": 3050.92, "word": " Legros", "probability": 0.36602783203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3051.52, "duration_after_vad": 2851.3999999999846}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..04ab5efb890410efb40199d921c9ecd67b837614
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE_raw.srt
@@ -0,0 +1,1808 @@
+1
+00:00:22,310 --> 00:00:26,410
+بسم الله الرحمن الرحيم بدأنا المرة الماضية في
+
+2
+00:00:26,410 --> 00:00:31,130
+موضوع ال groups اللي هي المجموعات وعرفنا ان ال set
+
+3
+00:00:31,130 --> 00:00:34,990
+و عليها binary operation بقول عنها group إذا
+
+4
+00:00:34,990 --> 00:00:39,190
+حققتلي ثلاث خاص الخاصية الأولى خاصية ال
+
+5
+00:00:39,190 --> 00:00:43,650
+associativity الخاصية الثانية خاصية ال identity
+
+6
+00:00:43,650 --> 00:00:47,350
+element الخاصية التالتة هي خاصية ال inverse
+
+7
+00:00:47,350 --> 00:00:53,380
+element لأي element موجود في group Gواخدنا على ذلك
+
+8
+00:00:53,380 --> 00:00:59,440
+بدل المثال أربع وهذا هو المثال رقم خمسة يبقى الـ
+
+9
+00:00:59,440 --> 00:01:04,380
+ZN هي عبارة عن المجموع العناصرها Zero واحد اتنين
+
+10
+00:01:04,380 --> 00:01:10,720
+تلاتة لغاية N ناقص واحد العملية المعرفة عليها اللي
+
+11
+00:01:10,720 --> 00:01:17,560
+هي ال addition modulo Nيبقى العملية اللى على z n
+
+12
+00:01:17,560 --> 00:01:25,440
+هي عملية الجمع العادية بس ايش كل ما يصير n بنهملهم
+
+13
+00:01:25,440 --> 00:01:30,460
+يعني المقياس تبعه هو m هذه عبارة عن ايش عبارة عن
+
+14
+00:01:30,460 --> 00:01:35,440
+group under addition ليش ال a اللى من zero لغاية n
+
+15
+00:01:35,440 --> 00:01:40,180
+ناقص واحدة كلها أعداد عادية بس modulo n ما زاد على
+
+16
+00:01:40,180 --> 00:01:45,140
+ال n ناقص واحد اللى هو n ببدأ من zeroإذا زاد واحد
+
+17
+00:01:45,140 --> 00:01:48,820
+يبدأ واحد وإذا زاد اتنين يصبح اتنين وكذلك يبقى انا
+
+18
+00:01:48,820 --> 00:01:51,940
+عند الاعداد هذه هذه الاعداد لو جمعتها واحد زاد
+
+19
+00:01:51,940 --> 00:01:55,840
+اتنين اتنين زاد واحد اي رقم ان اجمعه بدل ماعناش
+
+20
+00:01:55,840 --> 00:02:01,280
+مشكلة في هذه الحالة اتنين لو جمعت اي عددين يعني
+
+21
+00:02:01,280 --> 00:02:06,160
+هذه ال group a billion لو جمعت اي عددين هيعطيك عدد
+
+22
+00:02:06,160 --> 00:02:14,750
+موجود في هذه الصدرطيب النقطة الثانية لو عملت
+
+23
+00:02:14,750 --> 00:02:19,270
+associative بين أي ثلاثة أعداد منهم فهيطلع نفس
+
+24
+00:02:19,270 --> 00:02:23,770
+العدد مشكلتنا مش هذا مشكلتنا من هو ال identity
+
+25
+00:02:23,770 --> 00:02:28,530
+element تحت عملية الجماعة؟ من؟
+
+26
+00:02:31,650 --> 00:02:36,090
+بدي معكوس أي عنصر موجود فيها
+
+27
+00:02:39,720 --> 00:02:45,260
+هذه بعض الكتب يا شباب بتعبّر عنها ZN هكذا وبتحط
+
+28
+00:02:45,260 --> 00:02:50,680
+لعملية جامع وفي دائرة من حد ما تشوف عملية جامع في
+
+29
+00:02:50,680 --> 00:02:55,280
+دائرة معناته هذه عملية الجامع موديله N مشان
+
+30
+00:02:55,280 --> 00:02:59,700
+يفرجوها ويميزوا بينها و بين عملية الجامع العادية
+
+31
+00:02:59,700 --> 00:03:06,440
+يبقى هنا Zero is the identity
+
+32
+00:03:11,970 --> 00:03:24,010
+the inverse of k الموجود في z in z يعني مين العدد
+
+33
+00:03:24,010 --> 00:03:29,690
+اللى بدي اضيفه لهذا العدد يطلع zero او يطلع in
+
+34
+00:03:29,690 --> 00:03:37,160
+الهمين in minus ال kيبقى the inverse of k المن is
+
+35
+00:03:37,160 --> 00:03:42,080
+n minus الk لإن احنا عندنا عملية جمعة modulo n لو
+
+36
+00:03:42,080 --> 00:03:46,260
+جمعته اتنين هدول بيطلع in اهم ال in بيصير ال zero
+
+37
+00:03:46,260 --> 00:03:51,360
+اللي همين ال identity element طيب هذه جروب بسيطة و
+
+38
+00:03:51,360 --> 00:03:55,660
+زي ما تشوف هي abelian لإنه اتنين زياد خمسة هي خمسة
+
+39
+00:03:55,660 --> 00:04:02,180
+زياد اتنين و هكذاطيب نروح لمثال أتقل شوية و أتقل
+
+40
+00:04:02,180 --> 00:04:14,520
+شويات مش شوية بيقول let ال UN be the set of all
+
+41
+00:04:14,520 --> 00:04:23,500
+positive integers
+
+42
+00:04:23,500 --> 00:04:25,220
+less than
+
+43
+00:04:27,620 --> 00:04:40,840
+less than ال N less than ال N and relatively prime
+
+44
+00:04:40,840 --> 00:04:49,100
+relatively prime to N then
+
+45
+00:04:49,100 --> 00:05:02,620
+ال U N هذه ال U Nand the situ in is an
+
+46
+00:05:02,620 --> 00:05:11,000
+abelian group under
+
+47
+00:05:11,000 --> 00:05:12,780
+multiplication modulo n
+
+48
+00:05:46,170 --> 00:05:55,400
+بسبب نرجع للست UN هذه مين هي ال UN؟بقول ال U N هي
+
+49
+00:05:55,400 --> 00:05:59,700
+set of all positive integers مجموعة الأعداد
+
+50
+00:05:59,700 --> 00:06:05,620
+الصحيحة المجمة واللي عليها شرط تاني less than N
+
+51
+00:06:05,620 --> 00:06:12,160
+يبقى أقل من العدد N وفي نفس الوقت relatively prime
+
+52
+00:06:12,160 --> 00:06:18,500
+مع N طب وقف شوية خلينا نعرف مين هذه الأرقام لو جيت
+
+53
+00:06:18,500 --> 00:06:25,220
+قلتلك بدي ال U خمسةبس الواحد والتلاتة طب والاربعة
+
+54
+00:06:25,220 --> 00:06:33,220
+والاتنين يبقى الاعداد كلهم واحد اتنين تلاتة اربعة
+
+55
+00:06:33,220 --> 00:06:38,180
+كلهم are relatively prime to خمسة يبقى هذي mainly
+
+56
+00:06:38,180 --> 00:06:42,960
+وخمسة لكن لو قلت you ستة you ستة اللي هي واحد
+
+57
+00:06:42,960 --> 00:06:47,580
+وخمسة في غيرهم بس هدول هم اللي relatively prime ل
+
+58
+00:06:47,580 --> 00:06:53,270
+you ستة لو قلتلك you عشرة لك تقول الواحدوالثلاثة
+
+59
+00:06:53,270 --> 00:06:58,870
+والسبعة والتسعة مش غيرهم يبقى هي ال U خمسة الأعداد
+
+60
+00:06:58,870 --> 00:07:03,130
+اللي أقل من الرقم المعطو اللي بيكون relatively
+
+61
+00:07:03,130 --> 00:07:09,990
+prime لهذا الرقم مثلا لو جت ليه خمستاش يبقى الواحد
+
+62
+00:07:09,990 --> 00:07:15,010
+والاتنين والاربعة والسبعة
+
+63
+00:07:16,510 --> 00:07:22,530
+والتمنية تسعة لأ العشر لأ احداش اتناش لأ التلتاش
+
+64
+00:07:22,530 --> 00:07:25,870
+لأ اربعتاش لأ يبقى لغاية تمين لغاية التلتاش وها
+
+65
+00:07:25,870 --> 00:07:30,730
+كده يبقى بجيب الأرقام اللي أقل من الرقم الموطن
+
+66
+00:07:30,730 --> 00:07:34,390
+واللي بيكون relatively prime لهذا الرقم وكلهم
+
+67
+00:07:34,390 --> 00:07:39,210
+أرقام صحيحة موجبة هاي المقصود باليونين يبقى هذه
+
+68
+00:07:39,210 --> 00:07:44,400
+الست يو ام مين ال operation اللي عليهاGallery in
+
+69
+00:07:44,400 --> 00:07:49,040
+the UN is an ability group under multiplication
+
+70
+00:07:49,040 --> 00:07:56,160
+modulo M يبقى العملية عالمية ضرب modulo N يعني
+
+71
+00:07:56,160 --> 00:08:01,280
+المقياس تبعها هو مين هو N أول شيء بدنا نثبت إنه
+
+72
+00:08:01,280 --> 00:08:07,920
+هذي group طيب ال group هذي بدي لسه ما قلتش إنه هذي
+
+73
+00:08:07,920 --> 00:08:14,220
+binary operationاندر مالتفليكيشن موديلو ان هل هذه
+
+74
+00:08:14,220 --> 00:08:19,440
+binary operation على ال UN ام لا لم نقول ذلك لكن
+
+75
+00:08:19,440 --> 00:08:26,280
+انا بدي اخد عددين واضربهم في بعض واشوفهل اتنين
+
+76
+00:08:26,280 --> 00:08:31,940
+هدول modulo N بيكونوا .. ان كان طلع ال remainder
+
+77
+00:08:31,940 --> 00:08:36,860
+تبعهم موجود في ال UN بيكون تم المطلوب؟ ان ما طلعش
+
+78
+00:08:36,860 --> 00:08:41,880
+بصير كلامنا مش صحيح وفيش داعي اروح لبقية الشروط
+
+79
+00:08:41,880 --> 00:08:46,360
+تمامإذا خلّيني أشوف ال condition الأول النقطة
+
+80
+00:08:46,360 --> 00:08:51,480
+الأولى بدي أثبت إنه هذه binary operation لذلك بدي
+
+81
+00:08:51,480 --> 00:08:58,700
+أقوله افترض إن ال A و ال B موجودة في ال UN إيش بدي
+
+82
+00:08:58,700 --> 00:09:03,620
+أثبت إنها binary operation بدي أثبت إن ال A B
+
+83
+00:09:03,620 --> 00:09:08,520
+modulo N موجود وين؟ موجود في ال UN هذا اللي عايز
+
+84
+00:09:08,520 --> 00:09:11,720
+أثبته فبكويس بقوله then
+
+85
+00:09:14,480 --> 00:09:19,740
+مرت علينا ال division algorithm احنا صح؟ division
+
+86
+00:09:19,740 --> 00:09:25,080
+algorithm ومر علينا ل grasses common divisor يبقى
+
+87
+00:09:25,080 --> 00:09:29,140
+انا بروح بختار المناسب اللي بيخدمني في هذه الحالة
+
+88
+00:09:29,410 --> 00:09:34,290
+لو جيها تقولش لك ال grace is common divisor ل ال a
+
+89
+00:09:34,290 --> 00:09:40,090
+و ال n قداش بتقول ايه؟ واحد ليش؟ لأن ال elements
+
+90
+00:09:40,090 --> 00:09:45,870
+اللي موجودة are relatively prime to m يبقى and و
+
+91
+00:09:45,870 --> 00:09:49,910
+في نفس الوقت ال grace is common divisor ل ال b و
+
+92
+00:09:49,910 --> 00:09:55,830
+ال n بتسوي قداش؟إذاً كل واحدة منهم بقدر اكتبها على
+
+93
+00:09:55,830 --> 00:10:03,030
+صيغة linear combination يبقى باجي بقول AS1 زائد
+
+94
+00:10:03,030 --> 00:10:15,640
+NT1 بدل ساوية واحدالـ B S2 زائد ال N T2 بده يساوي
+
+95
+00:10:15,640 --> 00:10:26,580
+1 وهذا for some اللي هو S1 و S2 و T1 و T2 كلها
+
+96
+00:10:26,580 --> 00:10:29,880
+اللي موجودة وين؟ في ال 6 of integers
+
+97
+00:10:32,880 --> 00:10:38,280
+طب انا بدي حصل الضرب a في b modulo n يكون موجودة
+
+98
+00:10:38,280 --> 00:10:42,900
+في ال UN مشان هيك خليني اروح اضربهم في بعض و اشوف
+
+99
+00:10:42,900 --> 00:10:47,860
+كده يكون الناتج اللي عندنا اذا لو جيت اضربهم في
+
+100
+00:10:47,860 --> 00:10:54,400
+بعض فبجي بقول a s one زائد n t one
+
+101
+00:10:57,930 --> 00:11:05,290
+بس2 زائد ال N يساوي واحد في واحد اللي هو واحدطبعا
+
+102
+00:11:05,290 --> 00:11:08,370
+يبقى ضرب في الطرف الشمال في الشمال واليمين في
+
+103
+00:11:08,370 --> 00:11:14,110
+اليمين تعالى فى كحاصل ضرب القوسين هدول يبقى هذا a
+
+104
+00:11:14,110 --> 00:11:20,570
+b s one s two زائد ال element هذا ضربته هنا إذا
+
+105
+00:11:20,570 --> 00:11:27,650
+بدى ضربه في التاني هذا يبقى زائد n a s one t two
+
+106
+00:11:27,650 --> 00:11:36,460
+زائد بدي أضرب هذا هنايبقى زائد n في main في T1 في
+
+107
+00:11:36,460 --> 00:11:45,780
+B في ال S2 زائد في التاني يبقى N تربيع T1 T2 كله
+
+108
+00:11:45,780 --> 00:11:52,040
+بده يسوى واحد صحيح اظن هذا في hash N خليها لحالها
+
+109
+00:11:52,390 --> 00:11:58,730
+يبقى هذا ال a b في ال s one s two زاد شو رايك هدول
+
+110
+00:11:58,730 --> 00:12:04,490
+بدي أخد منهم ان عامل مشترك ايه شو بيظل عندك a s
+
+111
+00:12:04,490 --> 00:12:13,930
+one t two زائد t one b s two زائد n t one t two
+
+112
+00:12:13,930 --> 00:12:20,810
+كله بدي يساوي واحدإيش تفسيرك لهذه العبارة؟ طلع أنا
+
+113
+00:12:20,810 --> 00:12:25,270
+عندي هنا رقم و هنا inيبقى ال a,b و ال n are
+
+114
+00:12:25,270 --> 00:12:28,990
+relatively prime ولا لا او لجريسس common divisor
+
+115
+00:12:28,990 --> 00:12:34,390
+لهم بدي يساوي واحد يبقى هذا معناته ان الجريسس
+
+116
+00:12:34,390 --> 00:12:40,290
+common divisor لل a و ال b و ال n بدي يساوي الواحد
+
+117
+00:12:40,290 --> 00:12:50,050
+هذا بدي يعطيلك ان ال a,b and ال n are relatively
+
+118
+00:12:50,050 --> 00:12:57,000
+primeهذا شو معناه يا شباب هذا معناه ان ال a و b
+
+119
+00:12:57,000 --> 00:13:04,440
+موجودين في ال un يعني عملية ضرب modulo n is a
+
+120
+00:13:04,440 --> 00:13:10,080
+binary operation يبقى هذا معناته ان ال multi
+
+121
+00:13:10,080 --> 00:13:18,900
+application modulo n is
+
+122
+00:13:18,900 --> 00:13:21,100
+a binary
+
+123
+00:13:26,380 --> 00:13:31,700
+Operation بدنا نيجي للنقطة التانية النقطة التانية
+
+124
+00:13:31,700 --> 00:13:38,200
+بدي أخليها عليك تمرني دك فيها في الدعري check that
+
+125
+00:13:38,200 --> 00:13:47,540
+this operation is associative
+
+126
+00:13:50,690 --> 00:13:57,810
+on الـ UN يعني وكذبت لي أنه إيه في B في C بده
+
+127
+00:13:57,810 --> 00:14:04,130
+يساوي إيه لحالها مضروبة في B وC النقطة التالتة مين
+
+128
+00:14:04,130 --> 00:14:10,930
+ال identity element لهذه ال group واحد يبقى واحد
+
+129
+00:14:10,930 --> 00:14:17,010
+is the identity element
+
+130
+00:14:19,980 --> 00:14:26,980
+شو السبب ان لو ضاربته في a modulo n بطلع ال a
+
+131
+00:14:26,980 --> 00:14:38,860
+itself يبقى هذا because واحد في a modulo n بدر
+
+132
+00:14:38,860 --> 00:14:46,240
+يساوي ال a modulo n اللي بدر يساوي ال a itself لكل
+
+133
+00:14:46,240 --> 00:14:48,680
+ال a الموجودة في ال UN
+
+134
+00:14:51,590 --> 00:15:00,510
+طب النقطة الرابعة بد ال inverse the inverse of ايه
+
+135
+00:15:00,510 --> 00:15:07,130
+اللي موجود في ال U N is N
+
+136
+00:15:07,130 --> 00:15:13,070
+مين قال هذا الكلام يعني لما اقول N زائد واحد على N
+
+137
+00:15:13,070 --> 00:15:19,130
+كله مجسوم على N مش هيك على ايه طب هل هذا انتجة
+
+138
+00:15:22,690 --> 00:15:27,290
+طب كيف بده يصير عادي؟ برا ال z ده ده يعني مو صبطتش
+
+139
+00:15:27,290 --> 00:15:31,750
+معاناة أو برا ال UN صحيح؟ يبقى هذا الكلام ليس
+
+140
+00:15:31,750 --> 00:15:37,230
+صحيحا يبقى لو جيه تقولك the inverse of L is X
+
+141
+00:15:37,230 --> 00:15:43,070
+where X
+
+142
+00:15:43,070 --> 00:15:56,700
+is the solution of the equationهو حل المعادلة ax
+
+143
+00:15:56,700 --> 00:16:04,260
+modulo n بده يساوي مين؟ بده يساوي واحد لأن هذا
+
+144
+00:16:04,260 --> 00:16:10,160
+الواحد هو ال identity element يبقى حل المعادلة هذه
+
+145
+00:16:10,160 --> 00:16:15,620
+طبعا هذا بيعتمد على ال a من هي وعلى ال n من هي إذا
+
+146
+00:16:15,620 --> 00:16:20,390
+عرفت ال n وعرفت ال a بقدر أجيب له ال x بسهولةو هذه
+
+147
+00:16:20,390 --> 00:16:24,210
+القصة بصير سهلة يبقى هذه صارت appealing group
+
+148
+00:16:24,210 --> 00:16:29,490
+لانها حققت لمن؟ حققت للاربعة شروط يبقى لو اعطيتك
+
+149
+00:16:29,490 --> 00:16:34,970
+مثال for example تفضل
+
+150
+00:16:34,970 --> 00:16:35,330
+قول
+
+151
+00:16:39,840 --> 00:16:44,360
+أحنا اللي بنقولك الحل تبع هذه المعادلة بيكون هو
+
+152
+00:16:44,360 --> 00:16:50,200
+المعكوس تبع الـA وهذا يختلف من عنصر إلى آخر قد
+
+153
+00:16:50,200 --> 00:16:57,260
+يكون الـA معكوس لنفسه وقد يكون معكوس آخر كما سأريك
+
+154
+00:16:57,260 --> 00:17:02,200
+الآن إن كانت هذه ال group لازم غصب عن و عن ما اسمك
+
+155
+00:17:02,200 --> 00:17:09,400
+أنت ماهر ماهر ايه خريسغصب إن هو عنده مهر يخلص لازم
+
+156
+00:17:09,400 --> 00:17:12,940
+يجي معكوس لهذا الالمطور اللي بس بطل يصير group
+
+157
+00:17:12,940 --> 00:17:17,840
+تمام؟ يبقى ال group لازم كل عنصر في ال group اللي
+
+158
+00:17:17,840 --> 00:17:22,800
+جيه له معكوس طيب يبقى هو حالة نعطي مثال توضح لو
+
+159
+00:17:22,800 --> 00:17:27,920
+أخدت you اللي بدك إياها مش ممكن تدحك أنت you إيش
+
+160
+00:17:27,920 --> 00:17:35,280
+بدك إياها؟ you خمسة دي كم رشد؟ you عشر مثلا، you
+
+161
+00:17:35,280 --> 00:17:44,420
+عشرةعشريش عناصرها الواحد والاتنين التلاتة
+
+162
+00:17:44,420 --> 00:17:54,460
+أربعة خمسة ستة سبعة تمانية تسعة يبقى ماعنديش إلا
+
+163
+00:17:54,460 --> 00:18:01,250
+هذه العناصر تمام الواحد هو ال identity elementيبقى
+
+164
+00:18:01,250 --> 00:18:07,290
+احنا كله modulo عشرة بدي اشوف التلاتة مين معكوسها
+
+165
+00:18:07,290 --> 00:18:12,750
+ماهو العدد اللي بدي اضره في التلاتة modulo عشرة
+
+166
+00:18:12,750 --> 00:18:18,310
+يعطينا الواحد الصحيح مين؟ السبعة سبعة في تلاتة
+
+167
+00:18:18,310 --> 00:18:22,670
+واحد عشرين شيل منهم عشرتينيبقى الـ identity
+
+168
+00:18:22,670 --> 00:18:27,090
+element يبقى التلاتة هو معكوس السبعة والسبعة هي
+
+169
+00:18:27,090 --> 00:18:34,070
+معكوس من الادلي والتلاتة يبقى التلاتة is the
+
+170
+00:18:34,070 --> 00:18:44,560
+inverse element of سبعةطب التسعة مين معكوسة؟ نفسها
+
+171
+00:18:44,560 --> 00:18:49,620
+لإن التسعة في تسعة و 8 عشرات بظلمين ال identity
+
+172
+00:18:49,620 --> 00:19:02,500
+element and تسعة is the inverse of itself يبجى
+
+173
+00:19:02,500 --> 00:19:05,180
+التسعة هو معكوس لنفسه
+
+174
+00:19:10,080 --> 00:19:23,920
+يبقى خريص لقيناله معكوس ولا لا طبعا
+
+175
+00:19:23,920 --> 00:19:29,500
+هذه ال group شباب عليها سنة كتيرة و عليها شغل كتير
+
+176
+00:19:29,500 --> 00:19:35,320
+يبقى هذه ال group very important طيب ننتقل الآن
+
+177
+00:19:35,320 --> 00:19:45,710
+إلى المثال اللي بعدهيبقى مثال سبعة مثال سبعة بيقول
+
+178
+00:19:45,710 --> 00:19:55,490
+the set لو أخدت ال z و عليها عملية الطرح of
+
+179
+00:19:55,490 --> 00:20:06,590
+integers of integers under subtraction
+
+180
+00:20:10,490 --> 00:20:14,950
+هل يا ترى هذه group ولا ماهياش group؟ اه ده السؤال
+
+181
+00:20:14,950 --> 00:20:23,050
+أنا أدعي is not a group because
+
+182
+00:20:27,790 --> 00:20:31,090
+طبعا لو طرحت اي عنصر من بعض سواء طالع انها تجميل
+
+183
+00:20:31,090 --> 00:20:35,370
+وجود والله سالم فيها وموجود في z إذا عملية الطرح
+
+184
+00:20:35,370 --> 00:20:39,250
+على z is a binary operation مافيش فيها مشكلة لكن
+
+185
+00:20:39,250 --> 00:20:44,890
+هل هذه associative ام لا الله أعلم يبقى هنا
+
+186
+00:20:44,890 --> 00:20:52,350
+because if التلاتة مثلا والخمسة والسبعة موجودة في
+
+187
+00:20:52,350 --> 00:21:04,340
+z thenأنا بدى تلاتة ناقص وعندك خمسة ناقص سبعة بدى
+
+188
+00:21:04,340 --> 00:21:08,340
+أستخدم خاصية ال associativity أشوف أصحيها عليها
+
+189
+00:21:08,340 --> 00:21:13,420
+ولا لأ يبقى هذا تلاتة ناقص خمسة ناقص سبعة مقداش يا
+
+190
+00:21:13,420 --> 00:21:19,180
+شباب ناقص اثنين يعني تلاتة زيدي اثنين يسوى مقداش
+
+191
+00:21:19,180 --> 00:21:27,320
+خمسة بطولكن تلاتة ناقص خمسة ناقص سبعة و يساوي
+
+192
+00:21:27,320 --> 00:21:34,420
+تلاتة ناقص خمسة سالب اتنين سالب اتنين سالب سبعة
+
+193
+00:21:35,270 --> 00:21:39,810
+سالب تسعة يبقى هذا الكلام معناه انه العملية
+
+194
+00:21:39,810 --> 00:21:46,390
+associative ولا not associative يبقى هذا معناه انه
+
+195
+00:21:46,390 --> 00:21:57,210
+subtraction عملية الطرح is not associative من هنا
+
+196
+00:21:57,210 --> 00:22:04,380
+زعمنا قبل قليل انها ليست groupإذا عملية الأعداد أو
+
+197
+00:22:04,380 --> 00:22:11,260
+مجموعة الأعداد الصحيحة تحت عملية الطرح مهياش group
+
+198
+00:22:11,260 --> 00:22:21,340
+المثال رقم تمانية بيقول إذا set R star مين هي هذه
+
+199
+00:22:21,340 --> 00:22:30,220
+ال star اللي هي عبارة عن ال set R بدي أشيل منها ال
+
+200
+00:22:30,220 --> 00:22:44,300
+zerosix star of non zero real numbers non
+
+201
+00:22:44,300 --> 00:22:56,160
+zero real numbers is a group under the ordinary
+
+202
+00:23:00,560 --> 00:23:01,520
+السبق
+
+203
+00:23:39,270 --> 00:23:45,230
+مرة تانية ال set of real numbers اللي هي اللي بدي
+
+204
+00:23:45,230 --> 00:23:49,750
+أشيل منها ال zero و بدي أسميها R star يبقى مجموعة
+
+205
+00:23:49,750 --> 00:23:55,450
+الأعداد الحقيقية استثنت منها ال zero عرفت عليها
+
+206
+00:23:55,450 --> 00:24:02,970
+عملية الضرب العادية طبعا الأعداد ال real numbers
+
+207
+00:24:03,810 --> 00:24:07,670
+أضرب اي two real numbers في بعض بيطلع ايه اش ولا
+
+208
+00:24:07,670 --> 00:24:12,910
+بيطلع يعني natural اطلع real تمام يبقى هذا معناته
+
+209
+00:24:12,910 --> 00:24:16,370
+ان ال multiplication is a binary operation اتنين
+
+210
+00:24:16,370 --> 00:24:22,470
+عملية الضرب العادية is associative عالمين على ال
+
+211
+00:24:22,470 --> 00:24:25,970
+set of real numbers يبقى ده اللي عندى بد ال
+
+212
+00:24:25,970 --> 00:24:31,290
+identity element وبد ال inverse element يبقى
+
+213
+00:24:31,290 --> 00:24:39,780
+becausewe know that احنا بنعرف ان ال multi
+
+214
+00:24:39,780 --> 00:24:50,540
+application is a binary binary
+
+215
+00:24:50,540 --> 00:25:00,180
+associative binary associative operation
+
+216
+00:25:09,630 --> 00:25:17,030
+بالنسبة للدرب الوحيد هو
+
+217
+00:25:17,030 --> 00:25:30,340
+الـ identity element of R starطب لو أخدت عنصر A
+
+218
+00:25:30,340 --> 00:25:36,380
+معكوس في R و الله K موجود في R مين معكوسه بيكون؟
+
+219
+00:25:36,380 --> 00:25:40,640
+ممتاز جدا يبقى مقلوبه هو بيكون معكوسه لأن لو ضربت
+
+220
+00:25:40,640 --> 00:25:45,060
+اتنين في بعض بطلع من؟ ال identity element يبقى
+
+221
+00:25:45,060 --> 00:25:57,010
+باجي بقوله the inverse element of Aاللي موجود في R
+
+222
+00:25:57,010 --> 00:26:06,330
+star is واحد على إيه since إيه في واحد على إيه بده
+
+223
+00:26:06,330 --> 00:26:14,010
+يساوي واحد طب السؤال هو ليش استبعد ال zero؟ أيوة
+
+224
+00:26:14,010 --> 00:26:18,610
+يبقى ال zero مالوش معكس لو ضربته في أي رقم لا يمكن
+
+225
+00:26:18,610 --> 00:26:24,410
+يطلع من؟ لا يمكن يطلع الواحد الصحيح على الإطلاق
+
+226
+00:26:26,780 --> 00:26:39,060
+مثال تسعة بيقول الدراسات جي الto over R الgeneral
+
+227
+00:26:39,060 --> 00:26:43,720
+linear group of two by two matrices over R اللي هي
+
+228
+00:26:43,720 --> 00:26:52,760
+كل المصوفات A, B, C, D بحيث أن ال A والB والC والD
+
+229
+00:26:52,760 --> 00:27:00,120
+موجودة في set of real numbers وفي نفس الوقت ال A D
+
+230
+00:27:00,120 --> 00:27:03,820
+نقص B C لا يسوى Zero
+
+231
+00:27:07,870 --> 00:27:13,870
+under matrix multiplication
+
+232
+00:27:13,870 --> 00:27:24,050
+is
+
+233
+00:27:24,050 --> 00:27:26,110
+a group
+
+234
+00:27:41,310 --> 00:27:45,450
+طبعا احنا درسنا في الجبر الخطي المصحوفة لنظامها
+
+235
+00:27:45,450 --> 00:27:49,590
+اتنين في اتنين يبجي فيها صفين و عمودين يبجي هذه
+
+236
+00:27:49,590 --> 00:27:54,490
+المصحوفة بقول انه نظامها اتنين في اتنين او ال size
+
+237
+00:27:54,490 --> 00:27:59,350
+تبعها اتنين في اتنين مش اتنين في اتنين يسوى اربعة
+
+238
+00:27:59,770 --> 00:28:02,750
+الاتنين الأولى يدل على رقم الصفوف والاتنين الثانية
+
+239
+00:28:02,750 --> 00:28:07,670
+يدل على رقم الأعمدة يبقى هذه بدى أسميها ال general
+
+240
+00:28:07,670 --> 00:28:13,130
+linear group of two by two matrices over R هكذا
+
+241
+00:28:13,130 --> 00:28:19,790
+تقرأ general linear group of two by two matrices
+
+242
+00:28:19,790 --> 00:28:25,210
+over R مين هي هذه أنا مهمنيش التسمة بهمني التركيب
+
+243
+00:28:25,210 --> 00:28:29,930
+الداخلي مين هي هذهيبقى هي كل المصففات اللي نظامها
+
+244
+00:28:29,930 --> 00:28:34,550
+اتنين في اتنين و ال elements اللي داخل المصففة
+
+245
+00:28:34,550 --> 00:28:39,150
+كلهم عناصر موجودة فيها سواء كان zero ولا واحد ولا
+
+246
+00:28:39,150 --> 00:28:43,830
+نص ولا تلتبع ولا اي رقم سالب موجب كثير ماعناش
+
+247
+00:28:43,830 --> 00:28:49,660
+مشكلةAnd و في نفس الوقت ال A D ناقص B C ليسوا Zero
+
+248
+00:28:49,660 --> 00:28:56,420
+اتطلعلي A D ناقص B C شو يعني هنا يعني المحدد تبع
+
+249
+00:28:56,420 --> 00:29:01,520
+المصوفة المحدد تبع المصوفة ليسوا Zero يبقى نحنا كل
+
+250
+00:29:01,520 --> 00:29:09,580
+المصوفات اللي عناصرها بيكونوا أعدادحقيقية
+
+251
+00:29:09,580 --> 00:29:14,760
+ومحدداتها لاتساوي أسفارا عرفت عليها عملية ضرب
+
+252
+00:29:14,760 --> 00:29:19,780
+العادية تبع المصحفات under matrix multiplication
+
+253
+00:29:19,780 --> 00:29:25,840
+عملية ضرب المصحفات بدعي أنا هذا أن هذا is a group
+
+254
+00:29:25,840 --> 00:29:30,220
+نرجع للجبر الخطي اظن حاصل ضرب تلت مصحفات
+
+255
+00:29:30,220 --> 00:29:34,820
+associative ولا لا اتنين لما نضرب مصحفتين نظامهم
+
+256
+00:29:34,820 --> 00:29:38,390
+اتنين في اتنين تطلع مصحف النظام اربعة في اربعةو
+
+257
+00:29:38,390 --> 00:29:42,650
+الله اتنين في اتنين يبقى اتنين في اتنين كذلك اذا
+
+258
+00:29:42,650 --> 00:29:48,610
+عملية ضرب المصطفات is a binary operation يبقى
+
+259
+00:29:48,610 --> 00:29:55,150
+بقوله النقطة الاولى we know that من الجبر الخاطئ
+
+260
+00:29:55,150 --> 00:30:04,170
+we know from linear algebra that
+
+261
+00:30:08,510 --> 00:30:16,590
+matrix multiplication is
+
+262
+00:30:16,590 --> 00:30:25,210
+an associative binary
+
+263
+00:30:25,210 --> 00:30:28,390
+operation
+
+264
+00:30:28,390 --> 00:30:33,050
+on
+
+265
+00:30:45,410 --> 00:30:53,190
+النقطة الثانية ال identity element
+
+266
+00:30:55,420 --> 00:31:00,180
+In the general linear group of two by two matrices
+
+267
+00:31:00,180 --> 00:31:06,100
+over R, which is 1,000,000,000,000,000,000,000,000
+
+268
+00:31:06,100 --> 00:31:14,820
+,000,000,000,000,000
+
+269
+00:31:14,820 --> 00:31:16,120
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+270
+00:31:16,120 --> 00:31:17,440
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+271
+00:31:17,440 --> 00:31:18,320
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+272
+00:31:18,320 --> 00:31:20,040
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+273
+00:31:20,040 --> 00:31:20,040
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+274
+00:31:20,040 --> 00:31:20,040
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+275
+00:31:20,040 --> 00:31:20,040
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+276
+00:31:20,040 --> 00:31:20,040
+,000,000,000,000,000,000,000
+
+277
+00:31:42,710 --> 00:31:48,570
+بنبدل عناصر القطر الرئيسي وبنغير إشارات عناصر
+
+278
+00:31:48,570 --> 00:31:58,290
+القطر الثانوييبقى دي واحد على ا دي ناقص بي سي في
+
+279
+00:31:58,290 --> 00:32:04,650
+المصوفة هذه دي بيصير هنا وال ا مكانها بنبدل ال ا
+
+280
+00:32:04,650 --> 00:32:11,070
+وال د مكان بعض وبنغير إشارات عناصر القطر الثانوين
+
+281
+00:32:13,760 --> 00:32:19,640
+يبقى من هنا صارت هذه group السؤال هو is it abelian
+
+282
+00:32:19,640 --> 00:32:26,900
+group ايوة يبقى هنا ال general linear group of two
+
+283
+00:32:26,900 --> 00:32:39,500
+by two matrices is not abelian because السبب ان ال
+
+284
+00:32:39,500 --> 00:32:48,980
+a bلا يساوي BA والA والB موجودات في ال general
+
+285
+00:32:48,980 --> 00:32:53,380
+linear group of two by two matrices over R دير
+
+286
+00:32:53,380 --> 00:32:59,720
+بالك ما كتبتش for all A وB لإنه يمكن يوصف بيحصل
+
+287
+00:32:59,720 --> 00:33:03,380
+أحيان يطلع ال A في B ويسوي ال B في ال A لكن مش
+
+288
+00:33:03,380 --> 00:33:07,340
+دايما يعني لو جيت حالة حالتين تلاتة بيشدوا عن
+
+289
+00:33:07,340 --> 00:33:12,170
+القاعدة لكن ال general الكلام هذا مالهمش صحيح يبقى
+
+290
+00:33:12,170 --> 00:33:17,530
+هذا مثال عملي فعلا ومتعرف عليه واشتغلناه في ال
+
+291
+00:33:17,530 --> 00:33:22,090
+linear algebra ان هذه ال group عبارة عن non
+
+292
+00:33:22,090 --> 00:33:26,850
+abelian group تمام و ال identity element عرفنا
+
+293
+00:33:26,850 --> 00:33:37,290
+ممكن نيجي ناخد منها حالة خاصة يا جباب ايه
+
+294
+00:33:37,290 --> 00:33:38,730
+بيه لا يستوي بيه
+
+295
+00:33:41,490 --> 00:33:49,370
+هي واحد عالى اي
+
+296
+00:33:49,370 --> 00:33:53,030
+دي ناقص بي سي اللي هو المحدد طبعا
+
+297
+00:34:01,350 --> 00:34:06,390
+أنا كان بإمكاني أقول لك هذه matrix is an
+
+298
+00:34:06,390 --> 00:34:11,050
+associative binary operation ال binary operation
+
+299
+00:34:11,050 --> 00:34:15,270
+كان بإمكاني أعملها لك كالتالي أنا عندي شرط إن
+
+300
+00:34:15,270 --> 00:34:20,970
+المحدد لا يساوي zero صح ولا لا إذا لو أخدت مصفتين
+
+301
+00:34:20,970 --> 00:34:26,980
+محددهم لا يساوي zeroلو ضربتهم في بعض و أخدت المحدد
+
+302
+00:34:26,980 --> 00:34:29,740
+تبعهم و دي يطلع معناه لا يساوي ذلك لإن ال
+
+303
+00:34:29,740 --> 00:34:33,220
+determinant لل A في ال B يساوي ال determinant لل A
+
+304
+00:34:33,220 --> 00:34:37,740
+في ال determinant يعني كان بإمكاني ها دي ها ها
+
+305
+00:34:37,740 --> 00:34:41,450
+اللي ال binary operation أقولكان انا عندى ال
+
+306
+00:34:41,450 --> 00:34:48,010
+determinant لـA لا يساوي 0 و ال determinant لـB لا
+
+307
+00:34:48,010 --> 00:34:52,750
+يساوي 0 صح ولا لأ حسب ال condition اللى هماطينيا
+
+308
+00:34:52,750 --> 00:34:59,350
+الان لو أخدت ال determinant للـA في الـB حسب
+
+309
+00:34:59,350 --> 00:35:02,570
+معلوماتنا من ال linear algebra اللى احنا قلنا
+
+310
+00:35:02,570 --> 00:35:07,170
+عليها ال linear algebra يبقى هذا بده يساوي
+
+311
+00:35:07,170 --> 00:35:14,630
+determinantللـ F determinant للـ B تمام؟ يبقى هذا
+
+312
+00:35:14,630 --> 00:35:20,110
+كله ماله لا يساوي Zero معناته حصل الضرب هذا موجود
+
+313
+00:35:20,110 --> 00:35:23,530
+وين؟ موجود في الـ U من هنا هذه صارت binary
+
+314
+00:35:23,530 --> 00:35:26,990
+operation و لا associative يام أخدناها في الثانوية
+
+315
+00:35:26,990 --> 00:35:33,650
+و كذلك أخدناها وين؟ في الجبر الخاطي طيب ممكن نيجي
+
+316
+00:35:33,650 --> 00:35:39,030
+نروح ناخد حالة خاصةمن ال general linear group هذه
+
+317
+00:35:39,030 --> 00:35:44,270
+بدل المحدد لا يساوي 0 بدي أقول محدد يساوي 1 صحيح
+
+318
+00:35:44,270 --> 00:35:48,370
+وهذه بسميها ال special linear group of two by two
+
+319
+00:35:48,370 --> 00:35:53,430
+matrices over R وهذه كمان بتلعب دور كبير في عين
+
+320
+00:35:53,430 --> 00:35:57,850
+الجبر عندنا في المسائل المختلفة
+
+321
+00:36:10,900 --> 00:36:19,600
+نمرة عشرة the set الهي ال special linear a group
+
+322
+00:36:19,600 --> 00:36:26,860
+of two by two matrices over R اللي هي كل المصففات
+
+323
+00:36:26,860 --> 00:36:33,580
+اللي على الشكل اللي عندنا a,b,c,d بحيث ان ال a و
+
+324
+00:36:33,580 --> 00:36:43,020
+ال b و ال c و ال d هذه موجودةموجودة في ال Q أو ال
+
+325
+00:36:43,020 --> 00:37:01,080
+R أو ال C or ZP or ZP and وفي نفس الوقت and
+
+326
+00:37:03,500 --> 00:37:17,060
+الـ and ال a d نقص بي سي يساوي واحد هذه
+
+327
+00:37:17,060 --> 00:37:32,400
+is called the special linear a group of degree
+
+328
+00:37:34,480 --> 00:37:42,220
+of degree two over a يبقى دي بدل مكانة general هنا
+
+329
+00:37:42,220 --> 00:37:47,720
+قولنا special حالة خاصة منها المحدد يساوي واحد و
+
+330
+00:37:47,720 --> 00:37:57,140
+برضه هذه ما لها is هذه a group under matrix
+
+331
+00:37:57,140 --> 00:37:59,100
+multiplication
+
+332
+00:38:11,310 --> 00:38:17,870
+طيب تعالى نتفهم شوية ال general أنا أخدتها بس على
+
+333
+00:38:17,870 --> 00:38:23,330
+set of real numbers هنا إيش كاتب؟ كاتب ال elements
+
+334
+00:38:23,330 --> 00:38:28,470
+هدول ممكن يكونوا rational number و ممكن يكونوا
+
+335
+00:38:28,470 --> 00:38:32,470
+real number و ممكن يكونوا complex number و ممكن
+
+336
+00:38:32,470 --> 00:38:39,290
+يكونوا ZP حيث ال P is prime يبقى ال P هذا شباب هذا
+
+337
+00:38:39,290 --> 00:38:46,600
+primeيعني ممكن أخد العناصر من زد اتنين و من زد
+
+338
+00:38:46,600 --> 00:38:51,020
+تلاتة و من زد خمسة و من زد سبعة و من زد احداش و من
+
+339
+00:38:51,020 --> 00:38:58,440
+زد تلتاش لكن باخدهمش من مينباخدهمش من z6 باخدهمش
+
+340
+00:38:58,440 --> 00:39:03,800
+من z8 باخدهمش من z9 يبقى شرطنا انه zp prime يعني
+
+341
+00:39:03,800 --> 00:39:09,340
+بمعنى اخر ان هذه المصفوفات المجموعة المصفوفات
+
+342
+00:39:09,340 --> 00:39:14,260
+العناصر ممكن يكونوا من ال Q بس والمحدد لا يساوي
+
+343
+00:39:14,260 --> 00:39:18,740
+zero ممكن يكونوا من ال real numbers والمحدد لا
+
+344
+00:39:18,740 --> 00:39:21,360
+يساوي zero ممكن يكونوا من ال complex numbers
+
+345
+00:39:21,670 --> 00:39:26,050
+والمحدد لا يساوي Zero ممكن يكونوا من ال ZP والمحدد
+
+346
+00:39:26,050 --> 00:39:30,510
+ماله لا يساوي Zero الان لو قلت هدول من ال real
+
+347
+00:39:30,510 --> 00:39:34,670
+number بصير هذه حالة خاصة من مين؟ من السؤال اللي
+
+348
+00:39:34,670 --> 00:39:39,030
+جبله ال identity element هو واحد Zero Zero واحد
+
+349
+00:39:39,030 --> 00:39:44,570
+معكوس المصوفة هو نفس المعكوس اللي عندنا هذا بس هذا
+
+350
+00:39:44,570 --> 00:39:49,450
+ايش بصير؟ بروح بواحد لإن المحدد يساوي واحد يبقى
+
+351
+00:39:49,450 --> 00:40:01,580
+باجي بقوله هناالواحد هو المصفوفة اللي هو ال matrix
+
+352
+00:40:01,580 --> 00:40:05,060
+اللي
+
+353
+00:40:05,060 --> 00:40:14,360
+هي واحد زيرو زيرو واحد is the identity element
+
+354
+00:40:16,350 --> 00:40:21,410
+In the special linear group of two by two matrices
+
+355
+00:40:21,410 --> 00:40:31,730
+over R The inverse of الـ A والـ B والـ C والـ D
+
+356
+00:40:31,730 --> 00:40:36,070
+اللي موجودة في ال general linear group of two by
+
+357
+00:40:36,070 --> 00:40:41,490
+two ال special linear group of two by two matrices
+
+358
+00:40:59,540 --> 00:41:07,060
+ما ينطبق على Rينطبق على ال special linear of two
+
+359
+00:41:07,060 --> 00:41:14,180
+by two matrices over q و over c و over zp يبقى
+
+360
+00:41:14,180 --> 00:41:25,700
+this is a true for ال general for ال specialالـ
+
+361
+00:41:25,700 --> 00:41:32,940
+Special Linear Group of 2x2 matrices over Q والـ
+
+362
+00:41:32,940 --> 00:41:39,580
+Special Linear Group of 2x2 matrices over C والـ
+
+363
+00:41:39,580 --> 00:41:46,480
+Special Linear Group of 2x2 matrices over ZT
+
+364
+00:41:48,480 --> 00:41:53,700
+أظن هدول كلهم طبيعي بسهلات الحسابات لكن تعالى نحسب
+
+365
+00:41:53,700 --> 00:42:01,380
+لك شغلة زى هذه نعطيك مصفوفة موجودة في zp ونشوف ايش
+
+366
+00:42:01,380 --> 00:42:10,100
+اللى حصل for example consider
+
+367
+00:42:13,480 --> 00:42:26,520
+زد بي هي زد فايف يبقى
+
+368
+00:42:26,520 --> 00:42:33,500
+then اللي هو غرض واحد zero zero واحد is the
+
+369
+00:42:33,500 --> 00:42:40,020
+identity element
+
+370
+00:42:42,350 --> 00:42:46,330
+طب بنفع يا شباب اقول في زد خمسة في عندنا واحد خمسة
+
+371
+00:42:46,330 --> 00:42:54,070
+تلاتة اربعة واحد خمسة تلاتة اربعة بنفع؟ لأ الخمسة
+
+372
+00:42:54,070 --> 00:43:00,710
+مش موجودة هذا زد خمسة معاك من zero واحد اتنين
+
+373
+00:43:00,710 --> 00:43:06,090
+تلاتة لغاية اربعة اقل من انه بتبدأ من وين؟ بتبدأ
+
+374
+00:43:06,090 --> 00:43:13,020
+من ال zeroيبقى الارقام اللي بدك تاخدها تبقى zero
+
+375
+00:43:13,020 --> 00:43:17,820
+واحد اتنين تلاتة اربعة فقط لغير ما تزيد عليهم هاي
+
+376
+00:43:17,820 --> 00:43:23,220
+واحدة الثانية بد المحدد تبعه يكون كده مشان يكون
+
+377
+00:43:23,220 --> 00:43:27,000
+يكون كلامها صحيح طيب يبقى هذا هو ال identity
+
+378
+00:43:27,000 --> 00:43:30,460
+element لمين لل group هذي
+
+379
+00:43:34,350 --> 00:43:49,710
+the inverse of a b c d is نفس القصة d a ناقص b و
+
+380
+00:43:49,710 --> 00:44:00,380
+هنا ناقص cنعطي مثال عددي غالي يعني ناخد مصفوفة
+
+381
+00:44:00,380 --> 00:44:05,360
+عناصرها من زد خمسة ونشوف كيف بدنا نجبلها من
+
+382
+00:44:05,360 --> 00:44:07,260
+المعكوس
+
+383
+00:44:26,010 --> 00:44:34,470
+تساوي مثلا تلاتة اربعة اربعة اربعة بالشكل اللي
+
+384
+00:44:34,470 --> 00:44:38,230
+عندنا بدأ
+
+385
+00:44:38,230 --> 00:44:46,270
+اشوف هل المصفوفة هذه موجودة في ال special linear
+
+386
+00:44:46,270 --> 00:44:51,030
+group هذي ولا لأ بمعنى اخرالعناصر تبقى تلاتة و
+
+387
+00:44:51,030 --> 00:44:54,970
+أربعة و أربعة و أربعة موجودة في Z خمسة كلام مظبوط
+
+388
+00:44:54,970 --> 00:45:01,770
+اتنين هل المحدد بدي يسوي واحد ام لا ماجي بقوله هذا
+
+389
+00:45:01,770 --> 00:45:11,410
+بدي determinant لل A يبقى تلاتة في أربعة ناقص اللي
+
+390
+00:45:11,410 --> 00:45:16,830
+هو أربعة في أربعة كل هذا موديولو
+
+391
+00:45:19,400 --> 00:45:24,280
+يبقى هذا الكلام يبدو يساوي تلاتة في أربعة باطن عشر
+
+392
+00:45:24,280 --> 00:45:33,440
+ناقص ست عشر مديولو خمسة ويساوي ناقص أربعة مديولو
+
+393
+00:45:33,440 --> 00:45:40,100
+خمسة طيب الناقص أربعة هذه لو ضفت لها المقياس اللي
+
+394
+00:45:40,100 --> 00:45:46,890
+هو خمسة بطلع كده؟ واحديبقى هذه بطلع واحد module
+
+395
+00:45:46,890 --> 00:45:51,870
+وخمسة يعني بواحديبقى بناء عليها شباب ال
+
+396
+00:45:51,870 --> 00:45:56,350
+determinant لإيه سوا إيه سوا احد معناته المصحوفة
+
+397
+00:45:56,350 --> 00:46:03,790
+هذه موجودة يبقى هذا معناه ان المصحوفة تلاتة اربعة
+
+398
+00:46:03,790 --> 00:46:09,490
+اربعة اربعة belongs لل special linear group of two
+
+399
+00:46:09,490 --> 00:46:17,130
+by two matrices over z five طيب بدنا نجيب المعكوس
+
+400
+00:46:17,130 --> 00:46:29,770
+تبعهباجي بقول الان the inverse matrix of اللي هي
+
+401
+00:46:29,770 --> 00:46:37,010
+تلاتة أربعة أربعة أربعة is المحدد بواحد صحيح يبقى
+
+402
+00:46:37,010 --> 00:46:42,110
+بنقسم شعليه يبقى باجي بقوله بصير هنا أربعة و هنا
+
+403
+00:46:42,110 --> 00:46:48,210
+تلاتة بدلنا عناصر القطر الرئيسي مكان بعضعناصر قطر
+
+404
+00:46:48,210 --> 00:46:56,850
+الثروة بيكون بالمن؟ بالصالب بالشكل هذا طيب
+
+405
+00:46:56,850 --> 00:47:02,290
+لو جينا لبعضك و قولنا له طب اربعة في تلاتة باطماش
+
+406
+00:47:02,630 --> 00:47:09,590
+ناقص 16 يظهر ناقص 4 يعني واحد طيب انا بدي اجيبها
+
+407
+00:47:09,590 --> 00:47:15,470
+لك بطريقة اخرى لو جيت قولتلك بالشكل اللي عندنا هنا
+
+408
+00:47:15,470 --> 00:47:20,550
+لان هتيجي تقول ال ZP فش فيها سالب اربعة و سالب
+
+409
+00:47:20,550 --> 00:47:25,790
+اربعةزد P تبدأ من واندي Zero واحد اتنين لغاية P
+
+410
+00:47:25,790 --> 00:47:29,950
+ناقص واحد مانشيفاش عندي سالب طب و السالب هذا كيف
+
+411
+00:47:29,950 --> 00:47:35,510
+جبته بقولك بسيطة جدا الان هذا السالب بدي احوله الى
+
+412
+00:47:35,510 --> 00:47:40,730
+موجب الموجب بخليها زي ما هي السالب انا زد خمسة
+
+413
+00:47:40,730 --> 00:47:46,570
+يبقى المقياس عندي قداش خمسة اذا بدي اروح اضيف خمسة
+
+414
+00:47:46,570 --> 00:47:51,810
+للسالب اربع بطلع قداشواحد يبقى هذا عندنا واحد و
+
+415
+00:47:51,810 --> 00:47:57,590
+هذه واحد و هذه تلاتة تمام؟
+
+416
+00:47:59,780 --> 00:48:06,160
+انا ادعي ان هذه المصفوفة هي معكوث من؟ معكوث
+
+417
+00:48:06,160 --> 00:48:11,920
+المصفوفة الأصلية، مشان يبقى كلام صحيح لو ضربتها من
+
+418
+00:48:11,920 --> 00:48:16,400
+اليمين او من الشمال بدي يطلع من؟ مصفوفة الوحدة
+
+419
+00:48:16,400 --> 00:48:20,540
+يبقى دير بالك، اي مصفوفة أخرى تاخدها بعد ذلك
+
+420
+00:48:20,540 --> 00:48:23,520
+موجودة في ال especially بقيت عاملها بنفس الطريقة
+
+421
+00:48:23,830 --> 00:48:26,990
+يعني انا مش جايبها للناس اللي هو انما مش هنعلمك
+
+422
+00:48:26,990 --> 00:48:33,550
+كيفية الحسابات في ZP بدك تجيب عناصر المصوفة لعناصر
+
+423
+00:48:33,550 --> 00:48:38,830
+اليوم اللي ميكونوا من ZP اثنين النتيجة اللي اتضارب
+
+424
+00:48:38,830 --> 00:48:45,210
+نتيجة اللي اخد المحدد بدك تتقيد بخاصة ZP وشروط ال
+
+425
+00:48:45,210 --> 00:48:48,590
+special linear group ان المحدد تبعها بده يساوي مان
+
+426
+00:48:48,590 --> 00:48:56,450
+بده يساوي واحدالان لو ضربت
+
+427
+00:48:56,450 --> 00:48:59,950
+اتنين في بعض اذا ما طلعش مصمم تلواحدة بصير كلامي
+
+428
+00:48:59,950 --> 00:49:07,160
+غلطأثنين انا لما ادعي ان هذه المعكوس المصوفة هذه
+
+429
+00:49:07,160 --> 00:49:12,240
+لازم العناصر اللي يطلع دول يكون موجودات في Z فيه
+
+430
+00:49:12,240 --> 00:49:15,760
+يبقى الواحد و التلاتة و الأربعة و الواحد كلهم
+
+431
+00:49:15,760 --> 00:49:21,520
+موجودة في Z خمسة مظبوط يبقى كله من Z خمسة الان انا
+
+432
+00:49:21,520 --> 00:49:26,560
+لازم اقول it was كذا because ليش هذه هي المعكوس
+
+433
+00:49:26,560 --> 00:49:32,280
+انا الآن حسبت عمليا بس بدي اثبتها رياضيةلو قلت
+
+434
+00:49:32,280 --> 00:49:35,560
+تلاتة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+435
+00:49:35,560 --> 00:49:37,500
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+436
+00:49:37,500 --> 00:49:38,180
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+437
+00:49:38,180 --> 00:49:41,000
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+438
+00:49:41,000 --> 00:49:43,560
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+439
+00:49:43,560 --> 00:49:44,860
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+440
+00:49:44,860 --> 00:49:44,860
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+441
+00:49:44,860 --> 00:49:45,360
+اربعة اربعة اربعة اربعة اربعة اربعة اربعة اربعة
+
+442
+00:49:45,360 --> 00:49:51,580
+اربعة اربعة اربعة اربعة اربعة اربعة
+
+443
+00:49:53,510 --> 00:49:57,510
+طيب الصفر الثاني في العمود التاني تلاتة واربع في
+
+444
+00:49:57,510 --> 00:50:03,870
+تلاتة باطناش اتناش و تلاتة خمستاش اربع في اربع
+
+445
+00:50:03,870 --> 00:50:11,870
+بستاش واربع عشرين الان اربع في واحد باربع واربع في
+
+446
+00:50:11,870 --> 00:50:18,250
+تلاتة باطناش اللي هي بستاش لكن انا بده هذا كله
+
+447
+00:50:18,250 --> 00:50:24,590
+مديله خمسةموديول الخمس هنا واحد زيرو وهنا زيرو
+
+448
+00:50:24,590 --> 00:50:30,610
+واحد هو ال identity matrix يبقى فعلا هذه هي هذه
+
+449
+00:50:30,610 --> 00:50:35,490
+اللي هي المصوفة ومعكوس هذه المصوفة هي المصوفة اللي
+
+450
+00:50:35,490 --> 00:50:39,310
+عندنا يبقى عند الحسابات في زد خمسة في زد سبعة في
+
+451
+00:50:39,310 --> 00:50:45,240
+زد أحد عشان بدك تحسب بنفس الطريقة اللي عندنالازلنا
+
+452
+00:50:45,240 --> 00:50:50,920
+في المحاضرة القادمة مع مزيد من الأمثلة على Legros
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d37e77184f65f681117663a93ce4600475719cc5
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_postprocess.srt
@@ -0,0 +1,1744 @@
+1
+00:00:21,850 --> 00:00:25,810
+بسم الله الرحمن الرحيم نواصل ما بدأنا فيه في
+
+2
+00:00:25,810 --> 00:00:30,430
+المحاضرة الماضية بدأنا بال normal subgroups أعطينا
+
+3
+00:00:30,430 --> 00:00:34,310
+تعريف لل normal subgroups وعرفنا أن التعريف له
+
+4
+00:00:34,310 --> 00:00:39,230
+أوجه مختلفة بدل وجه تلاتة ثم انتقلنا بعد ذلك إلى
+
+5
+00:00:39,230 --> 00:00:44,970
+ال factor groups وعناصر ال factor groups كلها هي
+
+6
+00:00:44,970 --> 00:00:49,930
+left cosets واخذنا على ذلك مثالا واحدا وهذا هو
+
+7
+00:00:49,930 --> 00:00:55,520
+المثال رقم 2بقول يفترض ان جي هي عبارة عن Z 18
+
+8
+00:00:55,520 --> 00:00:59,600
+واخدنا ال subgroup منها هي ال subgroup generated
+
+9
+00:00:59,600 --> 00:01:06,820
+by 6 العناصر تبعها 0 6 12 الآن السؤال هو هل ال H
+
+10
+00:01:06,820 --> 00:01:15,780
+normal subgroup من Z 18 ام لا؟ بدنا الإجابة Normal
+
+11
+00:01:15,780 --> 00:01:19,220
+ليش؟ لأن جي
+
+12
+00:01:22,380 --> 00:01:27,080
+أول مثال أخدته معاك لو كانت ال group abelian يبقى
+
+13
+00:01:27,080 --> 00:01:31,660
+any subgroup is normal تمام يبقى في هذه الحالة
+
+14
+00:01:31,660 --> 00:01:37,800
+بقوله then ال H is a normal subgroup من Z18
+
+15
+00:01:37,800 --> 00:01:48,050
+because اللي هو Z18 is abelianكويس اذا بدي اروح
+
+16
+00:01:48,050 --> 00:01:52,990
+اكون ال factor group او بدي اعرف ال factor group
+
+17
+00:01:52,990 --> 00:02:00,710
+فيها كم element هذي تمام يبقى ال orderالـ order لـ
+
+18
+00:02:00,710 --> 00:02:09,490
+z 18 الموديولو 11 بده يساوي كله لفتكوه 6 يبقى ال
+
+19
+00:02:09,490 --> 00:02:16,510
+order ل z 18 مقسوما على ال order لل h و اللي هو
+
+20
+00:02:16,510 --> 00:02:25,600
+عبارة عن 18 ع 3 يبقى 6 elementsيبقى ال group هذه
+
+21
+00:02:25,600 --> 00:02:31,460
+فيها ستة عناصر بدي أعرف من هذه العناصر يبقى بروح
+
+22
+00:02:31,460 --> 00:02:41,160
+بقول له the elements of z التمنتاشر module 11 are
+
+23
+00:02:43,100 --> 00:02:49,600
+الأولان هو H itself أو الـ subgroup generated by 6
+
+24
+00:02:49,600 --> 00:02:55,000
+التاني هو واحد زائد ال subgroup generated by 6
+
+25
+00:02:55,000 --> 00:03:00,580
+التالت اتنين زائد ال subgroup generated by 6
+
+26
+00:03:00,580 --> 00:03:06,280
+الرابع هو تلاتة زائد ال subgroup generated by 6
+
+27
+00:03:14,080 --> 00:03:20,300
+السادس والاخير له خمسة زي ال subgroup generated by
+
+28
+00:03:20,300 --> 00:03:26,920
+ستةأي اي اي lift cos 6 بعد ذلك لو جيتلي قولتلي 6
+
+29
+00:03:26,920 --> 00:03:31,040
+زي ال subgroup generated by 6 بقولك هي مين هي
+
+30
+00:03:31,040 --> 00:03:36,640
+الأصلية ال subgroup الأصلية لو جيتلي قولتلي 7 زي
+
+31
+00:03:36,640 --> 00:03:40,000
+ال subgroup generated by 6 بقولك هي الواحد و هكذا
+
+32
+00:03:40,610 --> 00:03:45,190
+الان داخل هذه ال group لو بدى اجمع او بدى اعرف ال
+
+33
+00:03:45,190 --> 00:03:50,610
+order كيف بدى احاسبه يبقى لحد هنا احنا انتهينا من
+
+34
+00:03:50,610 --> 00:03:57,450
+عناصر هذه ال group لو بدى اجي اخد مثلا تلاتة زائد
+
+35
+00:03:57,450 --> 00:04:03,350
+ال sub group generated by ستة بدى اجمع مع مين مع
+
+36
+00:04:03,350 --> 00:04:08,560
+الخمسة زائد ال sub group generated by ستةيعني كأن
+
+37
+00:04:08,560 --> 00:04:14,100
+.. كأن بدي أضرب two left cosets في بعضهم لكن لما
+
+38
+00:04:14,100 --> 00:04:19,000
+كانت العملية عملية جامعة يبقى ضرب بس يتحول إلى
+
+39
+00:04:19,000 --> 00:04:22,720
+جامعة المرة اللي فاتت قلنا ال operation اللي على
+
+40
+00:04:22,720 --> 00:04:28,010
+ال left cosets هذهإن الـ A H مضروب في B H بيكون A
+
+41
+00:04:28,010 --> 00:04:35,270
+B F H يبقى معنى هذا الكلام هذا بيكون تلاتة زائد
+
+42
+00:04:35,270 --> 00:04:40,770
+خمسة زائد ال sub group generated by ستة تلاتة زائد
+
+43
+00:04:40,770 --> 00:04:46,450
+خمسة قداش تمانية تمانية بشيل منهم الستة بظل قداش
+
+44
+00:04:46,450 --> 00:04:51,490
+اتنين يبقى هذا اتنين زائد ال sub group generated
+
+45
+00:04:51,490 --> 00:04:58,110
+by ستة هيهايبقى any two left cosets لو جمعتهم
+
+46
+00:04:58,110 --> 00:05:03,790
+هيعطيني واحدة من الست لإتنين هذول لو بدي أجيب مثلا
+
+47
+00:05:03,790 --> 00:05:08,550
+ال order لأي واحدة منهم يبقى بدي أروح أشوف قدش
+
+48
+00:05:08,550 --> 00:05:13,550
+الرقم اللي بدي أحط اس لهذا ال element بحيث يعطيني
+
+49
+00:05:13,550 --> 00:05:17,590
+main ال identity يعني يعطيني ال subgroup generated
+
+50
+00:05:17,590 --> 00:05:23,420
+by الست بالضبط تمامافمثلًا لو جيت قولت بدي أعرف
+
+51
+00:05:23,420 --> 00:05:27,920
+قداش ال order للي اتنين زيدي ال subgroup generated
+
+52
+00:05:27,920 --> 00:05:34,380
+by ستة بدي بقوله كويس الان مش هنجيب ال order لهذا
+
+53
+00:05:34,380 --> 00:05:39,160
+بدي أروح أرفع لل أس واحد والأس اتنين والأس تلاتة
+
+54
+00:05:39,160 --> 00:05:45,560
+لغاية موصل لمين لل identity element فمثلًالو بد
+
+55
+00:05:45,560 --> 00:05:50,380
+الاتنين زاد ال sub group generated by ستة لكل
+
+56
+00:05:50,380 --> 00:05:56,100
+تربيع تاني اللي هو حاصل ضرب الاتنين يعني حاصل
+
+57
+00:05:56,100 --> 00:06:00,640
+جامعة الاتنين يعني اتنين مضروبة في هذا ال element
+
+58
+00:06:00,640 --> 00:06:05,910
+لأن ال operation عملية جامعةيبقى هذا عبارة عن مين
+
+59
+00:06:05,910 --> 00:06:11,150
+عبارة عن أربعة زي ال sub group generated by ستة لا
+
+60
+00:06:11,150 --> 00:06:15,770
+يساوي ال identity element يبقى بناء عليه بدي أخد
+
+61
+00:06:15,770 --> 00:06:21,410
+اتنين زي ال sub group generated by ستة الكل تكعيب
+
+62
+00:06:21,410 --> 00:06:26,350
+يبقى هذا بدي يساوي ستة زي ال sub group generated
+
+63
+00:06:26,350 --> 00:06:32,940
+by ستة جدش يعطيني هذا؟6 itself يبقى ال order لهذا
+
+64
+00:06:32,940 --> 00:06:37,720
+ال element يساوي تلاتة يبقى هذا الكلام يعطيني ان
+
+65
+00:06:37,720 --> 00:06:42,840
+ال order لإتنين زائد subgroup generated by ستة is
+
+66
+00:06:42,840 --> 00:06:47,600
+equal to three و هكذا يبقى كيف بدنا نضرب كيف بدنا
+
+67
+00:06:47,600 --> 00:06:53,780
+نجمع كيف بدنا نسوي هي مثال قدامك طيب نيجي ناخد
+
+68
+00:06:53,780 --> 00:06:56,160
+مثال example three
+
+69
+00:07:02,940 --> 00:07:13,320
+بقول الات ال G تساوي D4 and ال sub group اللي هي K
+
+70
+00:07:13,320 --> 00:07:20,740
+هي ال sub group generated by R 180 طبعا هذه لا
+
+71
+00:07:20,740 --> 00:07:27,220
+يوجد فيها إلا عنصرين اللي هو ال R نود وال R 180
+
+72
+00:07:27,220 --> 00:07:34,160
+اظن كمان هي هذا ال centerتبع الـ D4 ولا لأ؟ خلّينا
+
+73
+00:07:34,160 --> 00:07:38,620
+نجرب هكذا إنه لو كانت الـ Z لـ D N يا فيها الـ
+
+74
+00:07:38,620 --> 00:07:43,800
+Identity فقط يا إما فيها الـ Identity و الـ 180
+
+75
+00:07:43,800 --> 00:07:49,980
+حسب الـ D هذه هل هي حسب الـ N؟ هل هي odd و لا
+
+76
+00:07:49,980 --> 00:07:57,460
+even؟ يبقى بالشكل اللي عندنا هذا بدنا find the
+
+77
+00:07:57,460 --> 00:08:04,590
+elements ofطبعا في هذا الكلام بده يعطينا مدام هذي
+
+78
+00:08:04,590 --> 00:08:11,650
+هيك بالشكل اللي عندنا هنا Z of D4 السؤال هو هل هذه
+
+79
+00:08:11,650 --> 00:08:17,130
+normal subgroup من D4؟ ليش؟ لأن عناصرها دائما
+
+80
+00:08:17,130 --> 00:08:23,210
+تتعامل مع جميع عناصر الجروم وقد أخذناهم مثلا سابقا
+
+81
+00:08:23,210 --> 00:08:31,840
+يبقى بجي بقوله thenالـ K is normal subgroup في D4
+
+82
+00:08:31,840 --> 00:08:43,840
+يبقى find the elements بدنا عناصر of D4 modulo K
+
+83
+00:08:43,840 --> 00:08:47,720
+يبقى عناصر ال factor group اللي عندنا هذه
+
+84
+00:08:54,650 --> 00:08:58,190
+يبقى بدأ اروح ادور على عناصر ال factor group اللى
+
+85
+00:08:58,190 --> 00:09:02,750
+عندنا هنا الاول شىء بدأ اعرف قداش فيها عناصر قبل
+
+86
+00:09:02,750 --> 00:09:08,850
+ما اروح ادورطب العناصر تبعتها كل ال lift cosets أو
+
+87
+00:09:08,850 --> 00:09:15,050
+كل distance lift cosets يبقى ال order ل D4 modulo
+
+88
+00:09:15,050 --> 00:09:22,990
+K بده سوى ال order ل D4 maximum على ال order ل K
+
+89
+00:09:22,990 --> 00:09:28,790
+هذه تمانيةوهذه اتنين يبقى عدد العناصر فيها يساوي
+
+90
+00:09:28,790 --> 00:09:34,690
+قدرت اربعة عناصر بدي اروح ادور على هذه العناصر
+
+91
+00:09:34,690 --> 00:09:40,790
+يبقى بدي ابدأ بال liftco6 الأولى طبعا ارنود وR180
+
+92
+00:09:40,790 --> 00:09:46,330
+لو ضربتها في K بتظلها كما هي يبقى بقولها صفع شجة و
+
+93
+00:09:46,330 --> 00:09:52,840
+بروح اخد R90 في main في ال Kيبقى بدأ ضربها في
+
+94
+00:09:52,840 --> 00:09:59,920
+العناصر اللي جوا بصير R90 و هذه R90 في R180 اللي
+
+95
+00:09:59,920 --> 00:10:11,200
+يبقى داشر R270 هي بالضبط تماما كمان R278 في K يبقى
+
+96
+00:10:11,200 --> 00:10:14,840
+هدول مش تنتهي ال left coset سواء إنما في الحقيقة
+
+97
+00:10:14,840 --> 00:10:22,280
+left coset واحدةبالمثل بدي اروح اجيب له مين ال H
+
+98
+00:10:22,280 --> 00:10:29,200
+في K هذا الكلام بده يساوي اللي هو لما اضرب ال H في
+
+99
+00:10:29,200 --> 00:10:37,040
+R node بتعطينا H او هنا بتعطينا H في R 180 بالشكل
+
+100
+00:10:37,040 --> 00:10:42,850
+اللي عندنا هذاهذا الكلام بده يساوي ال H هنا عندك
+
+101
+00:10:42,850 --> 00:10:46,990
+في ال جدول في صفحة واحد و تمانين ال H في ال R مية
+
+102
+00:10:46,990 --> 00:10:54,250
+و تمانين اللي هي main of V وتساوي كذلك ال V في K
+
+103
+00:10:54,250 --> 00:10:59,950
+لإن لو ضربت ال V في K بصير هنا V و هنا V بR مية و
+
+104
+00:10:59,950 --> 00:11:04,210
+تمانين اللي هي عبارة عن main ع ال H يبقى صاروا
+
+105
+00:11:04,210 --> 00:11:11,700
+تنتين و ليست واحدةبالمثل لو روحت جبت له ال D في
+
+106
+00:11:11,700 --> 00:11:18,900
+main في ال K يبقى هذه بدها تعطيك D و هنا D في R
+
+107
+00:11:18,900 --> 00:11:25,660
+مية و تمانين هذه بدها تعطيك D و D Prime و اللي هي
+
+108
+00:11:25,660 --> 00:11:31,800
+بدها تساوي D Prime كذلك K يبقى أصبح عندي the
+
+109
+00:11:31,800 --> 00:11:33,740
+elements
+
+110
+00:11:36,580 --> 00:11:43,360
+The elements of D4
+
+111
+00:11:43,360 --> 00:11:50,720
+modulo K R ال element الأول اللي هو ال K itself
+
+112
+00:11:50,720 --> 00:11:57,140
+وال element التاني اللي هو ال R تسعين في ال K اللي
+
+113
+00:11:57,140 --> 00:12:02,720
+بده يساوي R متين وسبعين في K وال element التالت
+
+114
+00:12:02,720 --> 00:12:08,300
+اللي هو ال HKو ال element الرابع والاخير اللي هو
+
+115
+00:12:08,300 --> 00:12:14,220
+dk يبقى هي الأربعة عناصر اللي موجودة عندنا والتي
+
+116
+00:12:14,220 --> 00:12:19,460
+تمثل عناصر ال factor group اللي عندنا بالضبط تماما
+
+117
+00:12:19,460 --> 00:12:26,620
+طيب اللي خاطر أعطيك exercise هك exercise لو قلت لك
+
+118
+00:12:26,620 --> 00:12:35,490
+little g تساوي d for itself andخد لي ال H هي ال
+
+119
+00:12:35,490 --> 00:12:47,270
+sub group generated by R تسعين السؤال هو is ال
+
+120
+00:12:47,270 --> 00:12:59,970
+D for is D for modulo H exist هل هذه موجودة if so
+
+121
+00:13:01,510 --> 00:13:05,110
+if so find it
+
+122
+00:13:07,500 --> 00:13:12,220
+إذا كان الأمر كذلك بدنا إياها طبعا ال subgroup
+
+123
+00:13:12,220 --> 00:13:16,500
+generated by R تسعين فيها جداش كام عنصر؟ أربع
+
+124
+00:13:16,500 --> 00:13:21,420
+عناصر و D4 فيها جداش تمان عناصر يبقى ال index لها
+
+125
+00:13:21,420 --> 00:13:25,800
+جداش مرة اللي فاتت أخدنا لو ال group ال index لها
+
+126
+00:13:25,800 --> 00:13:29,180
+أو ال subgroup ال index لها يساوى اتنين إيش بتكون
+
+127
+00:13:29,180 --> 00:13:33,360
+هذه؟ إيش بتكون؟ normal subgroup مدام normal
+
+128
+00:13:33,360 --> 00:13:38,010
+subgroup يبقى ال factor group existما دام exist
+
+129
+00:13:38,010 --> 00:13:41,670
+هذا جواب السؤال اول يوم نهلك شفوي بدنا نعرف من
+
+130
+00:13:41,670 --> 00:13:47,470
+هالعنصرين فقط اللي موجودين في main في ال factor a
+
+131
+00:13:47,470 --> 00:13:52,190
+group هذا بالنسبة اللي عندنا نيجي ناخد مثال اخر
+
+132
+00:14:11,040 --> 00:14:17,680
+مثال رقم أربعة بيقول
+
+133
+00:14:17,680 --> 00:14:28,420
+little g بدها تساوي A4 and ال H is a subgroup من
+
+134
+00:14:28,420 --> 00:14:38,780
+مين؟ من G where حيث ال H هذه فيها العناصر التالية
+
+135
+00:14:39,460 --> 00:14:47,660
+identity element واحد اتنين تلاتة اربعة العنصر
+
+136
+00:14:47,660 --> 00:14:52,880
+اللي بعده واحد تلاتة اتنين اربعة واحد تلاتة اتنين
+
+137
+00:14:52,880 --> 00:15:00,240
+اربعة العنصر اللي بعده واحد اربعة اتنين تلاتة واحد
+
+138
+00:15:00,240 --> 00:15:06,540
+اربعة اتنين تلاتة بالشكل اللي عندنا هذا number a
+
+139
+00:15:06,540 --> 00:15:16,060
+show thatبيّلي ان ال H is a normal subgroup من من
+
+140
+00:15:16,060 --> 00:15:27,760
+ال G نمرة B show that بيّلي ان ال A for modulo H
+
+141
+00:15:27,760 --> 00:15:31,640
+is cyclic
+
+142
+00:16:01,560 --> 00:16:09,740
+الان مواطين الجيه هي ال a4 من ال a4 هذي ممتاز جدا
+
+143
+00:16:09,740 --> 00:16:14,760
+يبقى هذي the sixth of all even permutations of s4
+
+144
+00:16:14,760 --> 00:16:21,810
+عدد أنصارها كدهش؟12 عنصر تمام يبقى عدد ال A4 12
+
+145
+00:16:21,810 --> 00:16:26,530
+عنصر أخدنا ال subgroup منها ال subgroup اللي هي H
+
+146
+00:16:26,530 --> 00:16:31,710
+زي ما انت شايف بنقل عليه بسأل السؤال هل ال H هذي
+
+147
+00:16:31,710 --> 00:16:37,510
+normal subgroup من G ام لاإن كانت عامة إذا كانت
+
+148
+00:16:37,510 --> 00:16:45,410
+عامة إذا كانت عامة إذا كانت عامة
+
+149
+00:16:45,410 --> 00:16:47,170
+إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+150
+00:16:47,170 --> 00:16:47,450
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+151
+00:16:47,450 --> 00:16:47,470
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+152
+00:16:47,470 --> 00:16:47,730
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+153
+00:16:47,730 --> 00:16:48,330
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+154
+00:16:48,330 --> 00:17:00,070
+عامة إذا كانت عامة إذا كانت عامة إذا
+
+155
+00:17:00,070 --> 00:17:08,110
+كانت عامةقداش ال order لأي element موجود في H او
+
+156
+00:17:08,110 --> 00:17:14,690
+او اربعة او تلاتة يعني اتنين او اربعة او تلاتة
+
+157
+00:17:14,690 --> 00:17:20,970
+عناصر ليليتش هيهم قدامك قداش ال اتنين او اربعة بس
+
+158
+00:17:20,970 --> 00:17:26,850
+اتنين مافيش غير واحد مافيش واحد يعنييبقى ال order
+
+159
+00:17:26,850 --> 00:17:33,370
+إلا واحد أو اتنين ال least common multiple لمين لل
+
+160
+00:17:33,370 --> 00:17:38,230
+cycles اللي عندنا يبقى ال order يا إما واحد يا إما
+
+161
+00:17:38,230 --> 00:17:44,550
+اتنين لا يزيد عن ذلك طبعاهذه ممكن تعمل فيها
+
+162
+00:17:44,550 --> 00:17:47,250
+composition وهذه ممكن تعمل فيها composition ان
+
+163
+00:17:47,250 --> 00:17:51,650
+كانت تقدر طبعا هذه مفيش إمكانية هذه مفيش إمكانية
+
+164
+00:17:51,650 --> 00:17:56,190
+هذه كمان مفيش إمكانية يبقى هؤلاء الارديس جاينت
+
+165
+00:17:56,190 --> 00:17:59,390
+سايكل يبقى ال اسكومة الملطبة اللي طول كل واحدة
+
+166
+00:17:59,390 --> 00:18:02,030
+منهم الاسكومة اللي طول الاتنين والاتنين اللي هو B2
+
+167
+00:18:02,630 --> 00:18:10,430
+يبقى هدول كمان هدول كل العناصر اللي في A4 واللي ال
+
+168
+00:18:10,430 --> 00:18:16,410
+order اللي لهم يساوي اتنين صح يعني انت لو روحت
+
+169
+00:18:16,410 --> 00:18:21,470
+للتفصيلات تبعت A4 في صفحة 107 من الكتاب 107 من
+
+170
+00:18:21,470 --> 00:18:28,330
+الكتاب حطلك كل عناصر ال A4 ل 12 صفهملك صف هدول فقط
+
+171
+00:18:28,630 --> 00:18:33,710
+هم اللي ال order لهم يساوي واحد او اتنين غير هيك
+
+172
+00:18:33,710 --> 00:18:37,430
+ما جابش هايب الأوضة ومعظمها كلهم جابوا مياه قدامهم
+
+173
+00:18:37,430 --> 00:18:47,850
+يبقى أول شغلة observe that observe that لاحظ ان ال
+
+174
+00:18:47,850 --> 00:18:53,610
+elements of
+
+175
+00:18:53,610 --> 00:18:58,290
+h are all
+
+176
+00:19:01,630 --> 00:19:14,830
+الأشياء من A4 التي لديها أردم 2 او 1
+
+177
+00:19:18,250 --> 00:19:23,730
+يبقى عناصر اتش هما كل عناصر a4 اللي ال order لهم
+
+178
+00:19:23,730 --> 00:19:28,050
+يساوي اما اتنين او احد طبعا ال order اللي هذه
+
+179
+00:19:28,050 --> 00:19:30,430
+اتنين ال order اللي هذه اتنين ال order اللي هذه
+
+180
+00:19:30,430 --> 00:19:35,990
+اتنين ال order اللي هذه واحد تمام يبقى هدول كلهم
+
+181
+00:19:35,990 --> 00:19:39,270
+عناصر a4 بلاستيثناء
+
+182
+00:19:42,420 --> 00:19:50,300
+هذا المعلومة لازمان تكون عامة لازمان تكون عامة
+
+183
+00:19:55,440 --> 00:19:58,680
+و اثبت ان حاصر ال element تبع ال G في ال element
+
+184
+00:19:58,680 --> 00:20:02,120
+تبع ال H في معكوس ال element تبع ال G بدي يكون
+
+185
+00:20:02,120 --> 00:20:08,260
+موجود وين في H ممتاز اذا يبقى انا بروح اقوله خدلي
+
+186
+00:20:08,260 --> 00:20:15,080
+Alpha موجودة في ال A4 و ال Alpha does not belong
+
+187
+00:20:15,080 --> 00:20:21,940
+to H بدي اخدها من وين من خارج ال H and ال Beta
+
+188
+00:20:21,940 --> 00:20:29,210
+موجودة وين في Hيبقى انا اخدت alpha موجودة في a4 و
+
+189
+00:20:29,210 --> 00:20:34,710
+خارج h واخدت ال b موجودة في h موجودة في اين؟
+
+190
+00:20:34,710 --> 00:20:43,380
+موجودة في h موجودة في h ولا لا؟ بمعنى اخروالله إن
+
+191
+00:20:43,380 --> 00:20:47,120
+كان ال alpha beta alpha يتشيل كل تربيع يعطاني ال
+
+192
+00:20:47,120 --> 00:20:52,640
+identity إذا ال order يسوى اتنين إذا هتكون واحد من
+
+193
+00:20:52,640 --> 00:20:58,440
+هدول يبقى بتكون one بتكون فائدة يبقى هنا ال order
+
+194
+00:20:58,440 --> 00:21:04,110
+لا بيقدرشتانية لانها موجودة في H لانه في H كل واحد
+
+195
+00:21:04,110 --> 00:21:09,110
+ال order له يساوي اتنين يبقى بداجي اخدله الان
+
+196
+00:21:09,110 --> 00:21:15,430
+Alpha Beta Alpha Inverse لكل تربية هي Alpha Beta
+
+197
+00:21:15,430 --> 00:21:21,440
+Alpha Inverse Alpha Beta Alpha Inverseهذا التربية
+
+198
+00:21:21,440 --> 00:21:26,520
+تبعها الآن من خاصية ال associativity هذه Alpha
+
+199
+00:21:26,520 --> 00:21:33,520
+Beta في Alpha Inverse Alpha في Beta Alpha Inverse
+
+200
+00:21:33,520 --> 00:21:38,060
+خاصية ال associativity دمجت اتنين هدول مالهم مع
+
+201
+00:21:38,060 --> 00:21:41,640
+بعض طب هذا العنصر في المعكس هو مش بيعطينا ال
+
+202
+00:21:41,640 --> 00:21:47,180
+identity يبقى بروح مع السلامة يبقى بصير Alpha Beta
+
+203
+00:21:47,180 --> 00:21:53,500
+تربيع Alpha Inverseبيتا تربية أبجداش لأنها موجودة
+
+204
+00:21:53,500 --> 00:22:00,540
+وين في H يبقى هذا الكلام بده يساوي alpha ال
+
+205
+00:22:00,540 --> 00:22:07,780
+identity في ال alpha inverse السبب because ان ال
+
+206
+00:22:07,780 --> 00:22:14,060
+order ل beta بده يساوي جداش بده يساوي اتنينهذا
+
+207
+00:22:14,060 --> 00:22:18,020
+البرنامج سيعطينا الـ Alpha Alpha Inverse اللي هو
+
+208
+00:22:18,020 --> 00:22:21,000
+الـ Main الـ Identity احنا حطيناها بواحد ولا
+
+209
+00:22:21,000 --> 00:22:25,880
+نغيرها يبقى عدلها بواحد يبقى هذا البرنامج سيعطينا
+
+210
+00:22:25,880 --> 00:22:30,710
+الـ Main اللي هو بواحد صحيح يبقى بناء عليههذا
+
+211
+00:22:30,710 --> 00:22:36,170
+سيعطينا ان ال order ل alpha beta alpha inverse هو
+
+212
+00:22:36,170 --> 00:22:43,370
+اتنين هذا معناه ان ال alpha beta alpha inverse
+
+213
+00:22:43,370 --> 00:22:46,910
+موجودة في normal subgroup
+
+214
+00:22:59,830 --> 00:23:06,380
+هذا الحل اللي حلناه هو المطموب الأول نمرا aالمطموب
+
+215
+00:23:06,380 --> 00:23:12,220
+التاني نمرا بي بيقول لي في نمرا بي اثبتلي ان ال
+
+216
+00:23:12,220 --> 00:23:17,120
+factor group اللي عندنا هذه is a cyclic group
+
+217
+00:23:17,120 --> 00:23:25,220
+بقولك خيص تعالى نشوف قداش ال order لل a for modulo
+
+218
+00:23:25,220 --> 00:23:32,140
+h اللي بقول عليهايبقى هذا بده يساوي ال order لل a4
+
+219
+00:23:32,140 --> 00:23:37,480
+على ال order لل h هذه عبارة عن اتناشر على اربع
+
+220
+00:23:37,480 --> 00:23:42,380
+يساوي كدهش والتلاتة
+
+221
+00:23:42,380 --> 00:23:52,590
+is prime نرجع لمين نرجع لخدنا نظرية مشهورة قلنا في
+
+222
+00:23:52,590 --> 00:23:57,050
+الجبر نظرية الـ grunge و ال crawlers اللي عليها ال
+
+223
+00:23:57,050 --> 00:24:01,870
+crawlers رقمتهم كان بيقولي إذا كان ال order لل
+
+224
+00:24:01,870 --> 00:24:06,550
+group أو لل sub group ال prime number يبقى هي ..
+
+225
+00:24:06,550 --> 00:24:16,750
+هي cyclic group يبقى by her previous crawlery
+
+226
+00:24:19,010 --> 00:24:26,770
+اللي هي اتنين على نظرية Lagrange we have ان ال a4
+
+227
+00:24:26,770 --> 00:24:35,790
+modulo h is cyclic طيب
+
+228
+00:24:35,790 --> 00:24:45,560
+حابب اتعرف على شكل العناصر check thatتأكدلي ان ال
+
+229
+00:24:45,560 --> 00:24:53,820
+a4 modulo h عناصرها اللي هم على الشكل التالي ال h
+
+230
+00:24:53,820 --> 00:25:03,560
+واحد اتنين تلاتة في h واحد تلاتة اتنين في h كيف
+
+231
+00:25:03,560 --> 00:25:12,180
+بدي اعرفها؟يبقى بدي أمسك العناصر من خارج H لإن أي
+
+232
+00:25:12,180 --> 00:25:15,660
+عنصر ما نشتغله في H بده تطلع نفس ال H إذا كتروح
+
+233
+00:25:15,660 --> 00:25:22,100
+اجيب للعناصر اللي ضايلة في A4 صفحة 107 وتضربهم وين
+
+234
+00:25:22,100 --> 00:25:26,800
+تضرب من في العناصر اللي عندك دائما وابنا حيطلع
+
+235
+00:25:26,800 --> 00:25:33,870
+واحد من التلاتة دول إذا لازم أجيبها لكأى حاجة
+
+236
+00:25:33,870 --> 00:25:42,110
+بتلزم كجدول بيجيبوها لك انا بديك تبقى فاهم وليس
+
+237
+00:25:42,110 --> 00:25:47,870
+حافظ تمام يبقى ال a for module h اللي عناصره h
+
+238
+00:25:47,870 --> 00:25:53,690
+واحد اتنين تلاتة h واحد تلاتة اتنين h طب السؤال هو
+
+239
+00:25:53,690 --> 00:25:57,230
+كداش ال order لهذه ال element
+
+240
+00:26:05,570 --> 00:26:17,390
+أربعة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة
+
+241
+00:26:17,390 --> 00:26:21,630
+ستة
+
+242
+00:26:23,010 --> 00:26:27,830
+يا واحد يا تلاتة وغير هيك مافيش فيش بالمرة واحد هي
+
+243
+00:26:27,830 --> 00:26:31,830
+يبقى غصب عني وعنك ال order إلى يسوى تلاتة الحين
+
+244
+00:26:31,830 --> 00:26:35,750
+هذه لم تجد طولها تلاتة المهوض لما تقولي تربية تبدأ
+
+245
+00:26:35,750 --> 00:26:39,610
+تربع هذه وهذه ثابتة تقولي تكعيد الكعب هذه وهذه
+
+246
+00:26:39,610 --> 00:26:43,870
+ثابتة هذه طولها يسوى تلاتة يعني ال order إلى يسوى
+
+247
+00:26:43,870 --> 00:26:48,070
+تلاتة يبقى ال order لكل واحد من هذول تلاتة يبقى كل
+
+248
+00:26:48,070 --> 00:26:53,990
+واحدعبارة عن generator لمن؟ لل group اللي عندنا
+
+249
+00:26:53,990 --> 00:27:03,170
+يعني يبقى باجي بقول clearly كمان انه الواحد اتنين
+
+250
+00:27:03,170 --> 00:27:14,650
+تلاتة each and clearly انه each ofه of الواحد
+
+251
+00:27:14,650 --> 00:27:24,930
+اتنين تلاتة في h and واحد تلاتة اتنين في h is a
+
+252
+00:27:24,930 --> 00:27:36,580
+generator for ال a4 modulo h والسبب becauseإن ال
+
+253
+00:27:36,580 --> 00:27:44,760
+order للواحد اتنين ثلاثة في H بده يساوي ال order
+
+254
+00:27:44,760 --> 00:27:51,780
+للواحد تلاتة اتنين في H بده يساوي كده تلاتة يبقى
+
+255
+00:27:51,780 --> 00:27:55,580
+كل واحد فيهم عبارة عن generator
+
+256
+00:27:59,280 --> 00:28:04,300
+طب خلّيني أسأل كل واحد معكوس لنفسه و الله واحد
+
+257
+00:28:04,300 --> 00:28:10,640
+فيهم معكوس التاني بمعنى هل الواحد اتنين تلاتة و
+
+258
+00:28:10,640 --> 00:28:15,620
+الواحد تلاتة اتنين معكوس لنفسه كل واحد و الله
+
+259
+00:28:15,620 --> 00:28:19,820
+اتنين معكوسة لبعض تعالوا اضربهم في بعض الواحد
+
+260
+00:28:19,820 --> 00:28:24,800
+بيروح لوين و التلاتة بيروح لمين صف على شجر ال
+
+261
+00:28:24,800 --> 00:28:28,850
+identity الواحد را على الواحدبنمسك التلاتة بتروح
+
+262
+00:28:28,850 --> 00:28:34,190
+لمين؟ لاتنين و الاتنين بتروح صف على شج ال identity
+
+263
+00:28:34,190 --> 00:28:37,950
+الاتنين بيروح للواحد و الواحد بيروح لاتنين يبقى ال
+
+264
+00:28:37,950 --> 00:28:43,630
+identity يبقى كل واحد فيهم معكوس للآخر و ليس معكوس
+
+265
+00:28:43,630 --> 00:28:51,040
+لنفسهإذا الـ element هذا في حد ذاته هو معكوس لمن؟
+
+266
+00:28:51,040 --> 00:28:57,480
+لهذا ال element وفي نفس الوقت ال element هذا كله
+
+267
+00:28:57,480 --> 00:29:03,160
+هو معكوس لهذا ال element في ال factor group لأن لو
+
+268
+00:29:03,160 --> 00:29:12,730
+ضربتهم في بعضهم سأحصل على ال identitynot that ان
+
+269
+00:29:12,730 --> 00:29:22,690
+الواحد اتنين تلاتة each is the inverse of الواحد
+
+270
+00:29:22,690 --> 00:29:24,870
+تلاتة اتنين each because
+
+271
+00:29:28,030 --> 00:29:33,110
+لو ضربت في بعض بدي أطين مين ال identity element في
+
+272
+00:29:33,110 --> 00:29:39,630
+H في 1 3 2 H حسب التعريف على ال factor group ال
+
+273
+00:29:39,630 --> 00:29:44,090
+operation قولنا بنضرب ال two elements في بعض يبقى
+
+274
+00:29:44,090 --> 00:29:54,540
+123 132 في H ويساوينمسك الأول مرة تانية الواحد
+
+275
+00:29:54,540 --> 00:30:00,420
+صورته تلاتة والتلاتة صورتها واحد يبقى ماعنديش إلا
+
+276
+00:30:00,420 --> 00:30:05,780
+الواحد نمسك اللي بعده اتنين اتنين صورته واحد
+
+277
+00:30:05,780 --> 00:30:11,540
+والواحد صورته اتنين يبقى جافلة نمسك التلاتة تلاتة
+
+278
+00:30:11,540 --> 00:30:16,930
+صورتها اتنين واتنين صورتها تلاتة يبقى جافلةوهذا
+
+279
+00:30:16,930 --> 00:30:22,850
+الـ main الـ H اللي بتعطيك الـ H itself لأن هذا
+
+280
+00:30:22,850 --> 00:30:28,890
+كله بال identity element يبقى بناء عليه فعلا هذا
+
+281
+00:30:28,890 --> 00:30:33,470
+ال element هو معكوس لمين؟ معكوس لل element اللي
+
+282
+00:30:33,470 --> 00:30:34,550
+عندنا هذا
+
+283
+00:30:52,470 --> 00:31:00,730
+يبقى هذا كان مثال أربعة مثال
+
+284
+00:31:00,730 --> 00:31:01,470
+خمسة
+
+285
+00:31:06,680 --> 00:31:14,420
+بقول لطل جي تده تساوي يوتنين و تلاتين اللي عناصرها
+
+286
+00:31:14,420 --> 00:31:22,540
+طبعا اللي هي واحد و تلاتة و خمسة و سبعة و تمانية
+
+287
+00:31:22,540 --> 00:31:39,910
+تسعة عشرة احداش تلتاش اربعتاش خمستاش15 16 17 19 20
+
+288
+00:31:39,910 --> 00:32:00,830
+21 20 23 بعد 23 24 25 27 28 29 31 مافيش غيرهاطيب
+
+289
+00:32:00,830 --> 00:32:06,930
+هذا بده يعطيني ان ال order لليو اتنين و تلاتين بده
+
+290
+00:32:06,930 --> 00:32:12,030
+يساوي واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+291
+00:32:12,030 --> 00:32:15,550
+تسعة عشر احداشر اتناشر تلاتاشر اربعاشر خمساشر
+
+292
+00:32:15,550 --> 00:32:20,730
+ستاشر عنصر في ال group اللي عندنا هنا بدنا نروح
+
+293
+00:32:20,730 --> 00:32:26,980
+ناخد sub group منها letالـ H هي الـ subgroup
+
+294
+00:32:26,980 --> 00:32:32,420
+generated by خمستاشر واللي مافيش فيها إلا العنصرين
+
+295
+00:32:32,420 --> 00:32:41,000
+واحد وخمستاشر السؤال هو هل الـ H هذي abelian؟ الـ
+
+296
+00:32:41,000 --> 00:32:46,150
+H just a normal subgroup من الـ U تلاتة؟نعم لأن
+
+297
+00:32:46,150 --> 00:32:52,690
+هذيك ال U اتنين و تلاتين is a billion يبقى then ال
+
+298
+00:32:52,690 --> 00:32:59,110
+H is a normal subgroup من ال U اتنين و تلاتين
+
+299
+00:32:59,110 --> 00:33:07,010
+because السبب because ان U اتنين و تلاتين is a
+
+300
+00:33:07,010 --> 00:33:11,990
+billionمعناته بقدر اكوّن ال factor group يعني ال
+
+301
+00:33:11,990 --> 00:33:18,650
+factor group exist يبقى هذا بده يعطيك ان ال U 32
+
+302
+00:33:18,650 --> 00:33:29,290
+modulo H modulo H exist موجودة السؤال هوطب بنقدر
+
+303
+00:33:29,290 --> 00:33:34,730
+نجيب عناصرها قبل السؤال يبقى ال order ليه 32
+
+304
+00:33:34,730 --> 00:33:42,390
+modulo h بده يساوي اللي هو 16 على قداش على 2 و
+
+305
+00:33:42,390 --> 00:33:48,630
+يساوي 8 يبقى هذا ال group هذه فيها ثمانية عناصر
+
+306
+00:33:48,630 --> 00:33:52,230
+اسمع السؤال ال question is
+
+307
+00:33:58,580 --> 00:34:09,400
+السؤال هو هل is الجي موديلو H ايزو مارفك لزد
+
+308
+00:34:09,400 --> 00:34:12,160
+تمانية ولا زد
+
+309
+00:34:35,940 --> 00:34:43,120
+طيب نرجع لسوالنا مرة تانيةبقول لي احنا جه أخدنا ال
+
+310
+00:34:43,120 --> 00:34:47,540
+U32 أخدنا ال subgroup generated by خمساش اللي
+
+311
+00:34:47,540 --> 00:34:53,220
+فيهاش اللي غير عنصرين واحد وخمساش وخمستاشر تربيع
+
+312
+00:34:53,220 --> 00:35:02,080
+متين وخمسة وعشرين اللي هي عبارة عن واحد في U32لأن
+
+313
+00:35:02,080 --> 00:35:09,100
+الـ 224 هي مضاعفات 32 يبقى مافيش فيها إلا عنصرين
+
+314
+00:35:09,100 --> 00:35:13,780
+any subgroup من الabelian group is normal يبقى ال
+
+315
+00:35:13,780 --> 00:35:18,000
+subgroup اللي أخدناها normal subgroup من ال U32
+
+316
+00:35:18,000 --> 00:35:23,420
+يبقى ال factor group exist وفيها ثمانية عناصر
+
+317
+00:35:23,730 --> 00:35:30,010
+السؤال هو هل ال G-modulation isomorphic ل Z8 ولا ل
+
+318
+00:35:30,010 --> 00:35:35,050
+Z4 external product مع Z2 ولا ل Z2 external
+
+319
+00:35:35,050 --> 00:35:40,730
+product مع Z2 external product مع Z2 كذلك أم لا؟
+
+320
+00:35:40,730 --> 00:35:46,920
+هذه تمان عناصر هذه تمان عناصرهذه تمام عناصر تمام
+
+321
+00:35:46,920 --> 00:35:52,680
+التمام بدنا نيجي نشوف مين نستبعد ومين نخليه قداش
+
+322
+00:35:52,680 --> 00:35:57,560
+أكبر order لأي element موجود هنا تمانية تمانية
+
+323
+00:35:57,560 --> 00:36:03,960
+قداش أكبر order لأي element هنا كداش أربعة مزيدش
+
+324
+00:36:03,960 --> 00:36:06,740
+عن أربعة اللي هو least common multiple للأربعة
+
+325
+00:36:06,740 --> 00:36:10,620
+واتنين أو للأربعة والواحد سيام قداش ال maximum
+
+326
+00:36:10,620 --> 00:36:14,510
+order لأي element هنا اتنينيبقى اكبر واحد هناك
+
+327
+00:36:14,510 --> 00:36:19,050
+تمانية اكبر واحد اتنين واكبر واحد هنا اربع طب
+
+328
+00:36:19,050 --> 00:36:24,590
+السؤال هو الجي موديل H فيها ثمانية عناصر لو روحت
+
+329
+00:36:24,590 --> 00:36:29,770
+عناصرها كلهم lift كو ستة لو روحت للأور السبع lift
+
+330
+00:36:29,770 --> 00:36:34,730
+كو ستة و لجيته يساوي تمانية معناته هذا generator
+
+331
+00:36:34,730 --> 00:36:39,470
+وبالتالي isomorphic لزيد تمانية لكن اذا ما لجيتش
+
+332
+00:36:39,470 --> 00:36:44,600
+فيهاولا generator إذا لا يمكن أن تكون isomorphic
+
+333
+00:36:44,600 --> 00:36:49,580
+لميعنى لزيت تمانية بيظل احتمال هنا يا اما لزيت
+
+334
+00:36:49,580 --> 00:36:52,440
+اربعة كسن داية product مع زيت اتنين او زيت اتنين
+
+335
+00:36:52,440 --> 00:36:55,700
+كسن داية product مع زيت اتنين كسن داية product مع
+
+336
+00:36:55,700 --> 00:37:01,600
+زيت اتنين الثانية لذلك هذه العناصر قداميكلها
+
+337
+00:37:01,600 --> 00:37:07,260
+نستطيع ان نحصل على left coset اول واحدة تبقى الاول
+
+338
+00:37:07,260 --> 00:37:11,800
+واحد بتضرب التلاتة في K في H مش هذي left coset
+
+339
+00:37:11,800 --> 00:37:18,600
+كذلك يعني احد عناصر من ال group الان بداجي اقوله
+
+340
+00:37:18,600 --> 00:37:26,880
+تلاتة H هذي موجودة في ال U تنين وتلاتين modulo
+
+341
+00:37:26,880 --> 00:37:35,790
+اللي هو من Hلو جيت تلاتة H هل هذه تساوي H تسلف؟
+
+342
+00:37:35,790 --> 00:37:40,950
+يعني لو ضربت هنا في من في تلاتة بصير تلاتة و تلاتة
+
+343
+00:37:40,950 --> 00:37:45,470
+في خمستاشر بخمسة واربعين شيء اللي بيبقى تلتاش هل
+
+344
+00:37:45,470 --> 00:37:52,790
+هي H؟ لأ اتنين لو جيت قلتلك تلاتة H لكل تربيع
+
+345
+00:37:55,240 --> 00:37:59,440
+أه يعني لو طلع ال identity اتنين هذي بتجسم
+
+346
+00:37:59,440 --> 00:38:03,620
+التمانية يعني ممكن مش في مشكلة هذا الكلام بده
+
+347
+00:38:03,620 --> 00:38:12,460
+يساوي تسعة H هل تسعة H تساوي H اضربها تسعة و هذي
+
+348
+00:38:12,460 --> 00:38:17,400
+تسعة في خمساش إذا لا يمكن أن تساوي مين H أخد تلاتة
+
+349
+00:38:17,400 --> 00:38:24,320
+H تكيبلأ لإن التلاتة لا تقسم مين التمانية يبقى
+
+350
+00:38:24,320 --> 00:38:27,420
+fish element ال order إله يسوي التلاتة يبقى ما
+
+351
+00:38:27,420 --> 00:38:36,620
+تغلبش حالك روح على مينعلى تلاتة H أُس أربعة يبقى
+
+352
+00:38:36,620 --> 00:38:41,060
+هذه عبارة عن قداش تسعة في تسعة بواحد و تمانين H
+
+353
+00:38:41,060 --> 00:38:45,400
+هذا الكلام يساوي تنين و تلاتين و تنين و تلاتين
+
+354
+00:38:45,400 --> 00:38:49,840
+أربعة و ستين من واحد و تمانين ستاشر و واحد و
+
+355
+00:38:49,840 --> 00:38:57,580
+سبعتاشر يبقى هذه سبعتاشر H هل السبعتاشر H بيساوي
+
+356
+00:38:57,580 --> 00:39:03,980
+H؟ لأيبقى سعر ال order لهذا ال element لا يمكن أن
+
+357
+00:39:03,980 --> 00:39:08,800
+يكون أربعة أروح أدور على خمسة وستة وسبعة يبقى
+
+358
+00:39:08,800 --> 00:39:13,020
+automatic ال order له سوى قداش تمانية لأن ال order
+
+359
+00:39:13,020 --> 00:39:16,100
+لل element اللي بيجسم لل order اللي جمده ماتحصل
+
+360
+00:39:16,100 --> 00:39:21,540
+على طول الخطة بنستنتجها يبقى هذا بده يعطينا أن ال
+
+361
+00:39:21,540 --> 00:39:27,480
+order لتلاتة H بده سوى قداش تمانية because
+
+362
+00:39:30,700 --> 00:39:36,000
+the order of
+
+363
+00:39:36,000 --> 00:39:46,880
+the element divide the order of the group
+
+364
+00:39:51,730 --> 00:39:55,870
+لأن ال order لل element بيجسم ال order لل group
+
+365
+00:39:55,870 --> 00:40:02,370
+يبقى لا يمكن ان انا اجد ال order خمسة ولا ستة ولا
+
+366
+00:40:02,370 --> 00:40:07,230
+سبعة اذا ال order يسوى كمان تمانية معناته هذا ال
+
+367
+00:40:07,230 --> 00:40:17,290
+element ماله generator يبقى هنا ال ثلاثة h is a
+
+368
+00:40:17,290 --> 00:40:19,150
+generator
+
+369
+00:40:20,550 --> 00:40:29,770
+Four اللي هو من ال U اتنين و تلاتين modulo H مدام
+
+370
+00:40:29,770 --> 00:40:36,150
+generator يبقى هذه مالها Cyclic يبقى هذا يعطينا ان
+
+371
+00:40:36,150 --> 00:40:45,570
+U اتنين و تلاتين U اتنين و تلاتين modulo 11 is
+
+372
+00:40:45,570 --> 00:40:51,500
+cyclicMadame Cyclic يبقى هل يمكن أن تكون
+
+373
+00:40:51,500 --> 00:40:56,460
+isomorphic لهذه لأن هذا أكبر order لها يساوي اتنين
+
+374
+00:40:56,460 --> 00:41:02,160
+isomorphic لهذه لأ لأن أكبر order عنها مين يساوي
+
+375
+00:41:02,160 --> 00:41:08,980
+أربعة يبقى هنا ال U تنين و تلاتي موديل أحداشر
+
+376
+00:41:08,980 --> 00:41:12,780
+isomorphic لزيد تمانية because
+
+377
+00:41:16,450 --> 00:41:31,430
+زد اربعة external like product مع زد اتنين has
+
+378
+00:41:31,430 --> 00:41:34,490
+no element
+
+379
+00:41:36,400 --> 00:41:43,400
+of order همان مافيش ولا عنصر يبقى هذي صارت
+
+380
+00:41:43,400 --> 00:41:51,220
+isomorphic لمين ل .. ل group اللي عندنا هذي الآن
+
+381
+00:41:51,220 --> 00:41:56,900
+بدنا نيجي لنظرية طبعا أخدت أمثلة لا بأس بها كثيرة
+
+382
+00:41:56,900 --> 00:42:01,700
+على ال normal و على ال factor group بنيجي لأول
+
+383
+00:42:01,700 --> 00:42:08,430
+نظرية في هذا الموضوع بتقولتالـ Center تبع الـ
+
+384
+00:42:08,430 --> 00:42:16,690
+Group G of
+
+385
+00:42:16,690 --> 00:42:22,430
+a
+
+386
+00:42:22,430 --> 00:42:30,570
+group G if الـ G Modulus Center بتبع الـ G is
+
+387
+00:42:30,570 --> 00:42:36,820
+cyclicthen الجي is abelian
+
+388
+00:43:06,770 --> 00:43:07,570
+خلّي بركة
+
+389
+00:43:10,260 --> 00:43:14,500
+عندنا Z of G الـ Center تبع لـ Group G وبنعرف الـ
+
+390
+00:43:14,500 --> 00:43:18,780
+Center اللي بيجمع كل العناصر الكميوس مع جميع عناصر
+
+391
+00:43:18,780 --> 00:43:23,120
+G بالاستثناء يبقى لو كانت الـ G modulo Z Cyclic
+
+392
+00:43:23,120 --> 00:43:29,000
+يبقى بنثبت له إنه G الأصلية is Abelian يبقى
+
+393
+00:43:29,000 --> 00:43:35,800
+المعطيات اللي عندي أ assume that إن الـ G modulo Z
+
+394
+00:43:35,800 --> 00:43:43,120
+of G is Cyclicما دام Cyclic يبقى ايه ايش؟يلها
+
+395
+00:43:43,120 --> 00:43:54,560
+generator ما دام Cyclic يبقى الـG في الـZ of G بـA
+
+396
+00:43:54,560 --> 00:43:56,160
+generator
+
+397
+00:43:57,710 --> 00:44:03,690
+يفترض ان هذا generator اله يعني اي element فيها
+
+398
+00:44:03,690 --> 00:44:11,230
+يكون هذا ال element مرفوع لمين لأس محددة يبقى then
+
+399
+00:44:11,230 --> 00:44:18,190
+ال g modulus center بتبع ال g هي sub group او ال
+
+400
+00:44:18,190 --> 00:44:23,850
+group generated by g في ال z of g بالشكل اللي
+
+401
+00:44:23,850 --> 00:44:30,950
+عندناالان بدي اقول له let ال a و ال b موجودة في g
+
+402
+00:44:30,950 --> 00:44:37,430
+اذا قدرت اثبت له ان ال a في b هي ال b في a بتما
+
+403
+00:44:37,430 --> 00:44:44,990
+المطلوب تمام؟ اذا حاجة اقوله الان ال a موجودة في
+
+404
+00:44:44,990 --> 00:44:50,630
+ال a في ال center بتبع ال g صح ولا لا؟الـ element
+
+405
+00:44:50,630 --> 00:44:57,550
+A موجود في أي lift-go set طب هذا ال element موجود
+
+406
+00:44:57,550 --> 00:45:04,750
+في ال group هذه ولا لا؟ ايه في ال center؟ موجود
+
+407
+00:45:04,750 --> 00:45:08,690
+هنا ولا لا؟ صح؟ مالكه بلعته
+
+408
+00:45:16,880 --> 00:45:28,400
+يبقى هنا هذا الكلام يبقى ميم يبقى ميم
+
+409
+00:45:28,400 --> 00:45:29,320
+ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم
+
+410
+00:45:29,320 --> 00:45:29,380
+يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى
+
+411
+00:45:29,380 --> 00:45:35,820
+ميم يبقىواللي هو بده يساوي GI في ال center اللي
+
+412
+00:45:35,820 --> 00:45:45,210
+تبع ال G for some Iبالمثل الـ B موجود في الـ B في
+
+413
+00:45:45,210 --> 00:45:50,450
+الـ Center بتابع الـ G و اللي هو بده يساوي G في
+
+414
+00:45:50,450 --> 00:45:57,570
+الـ Center بتابع الـ G مرفوع لأخر J وهذا GG للـ
+
+415
+00:45:57,570 --> 00:46:05,970
+Center بتابع الـ Group G for some J الآن خدلي AB
+
+416
+00:46:08,110 --> 00:46:15,830
+يبقى ال a,b بده يساوي ال a,b هذه a موجودة هنا يبقى
+
+417
+00:46:15,830 --> 00:46:21,990
+موجودة هنا مدام موجودة هنا يبقى بقدر اقول ان ال a
+
+418
+00:46:21,990 --> 00:46:31,550
+تساوي g,i,x for some x وهذا بده يعطيني ان b تساوي
+
+419
+00:46:31,550 --> 00:46:42,650
+g,j,y for some yوارسم Y يبقى ال A بي بده يساوي ال
+
+420
+00:46:42,650 --> 00:46:49,630
+A اللي عندي اللي هي main اللي هي GIX وال B اللي هي
+
+421
+00:46:49,630 --> 00:46:52,070
+GJY
+
+422
+00:46:54,390 --> 00:46:59,310
+الإكس والواي والإكس والواي والإكس والواي يا سيدي
+
+423
+00:46:59,310 --> 00:47:03,910
+اللي هم في ال center إذا بقدر أبدل زي ما بدي تمام
+
+424
+00:47:03,910 --> 00:47:12,040
+يبقى هذا بتقدر تقولي GIجي جي في ال X Y بدلت
+
+425
+00:47:12,040 --> 00:47:17,700
+التنتين هذول مع بعض لإن X موجودة في ال center طيب
+
+426
+00:47:17,700 --> 00:47:26,200
+هذه بقدر أبدل كمان بقدر أقول جي جي في جي I وهذه Y
+
+427
+00:47:26,200 --> 00:47:26,860
+في X
+
+428
+00:47:30,120 --> 00:47:34,100
+الان بدي أبدل هدول مع بعض لإن ال X و ال Y في ال
+
+429
+00:47:34,100 --> 00:47:37,980
+center يبدلوا مع بعض دوري يبقى هذا الكلام يبدو
+
+430
+00:47:37,980 --> 00:47:51,200
+يساوي GJ و هنا Y و هنا GIX هذا B وهذا A يبقى G
+
+431
+00:47:51,200 --> 00:47:54,180
+Abelian يبقى هنا Das
+
+432
+00:48:02,290 --> 00:48:10,990
+يبقى من الانفة ساعدا اه
+
+433
+00:48:10,990 --> 00:48:15,070
+طبعا
+
+434
+00:48:15,070 --> 00:48:23,230
+هاي موجودة هنايبقى تساوي GI في element من ال
+
+435
+00:48:23,230 --> 00:48:28,890
+center ال X موجودة في ال center وال Y موجودة في ال
+
+436
+00:48:28,890 --> 00:48:30,590
+center كذلك
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dee92c8ac5cb7555d28bb9a92ff353da4bc64f8c
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc.srt
@@ -0,0 +1,1759 @@
+1
+00:00:22,610 --> 00:00:27,190
+المرة اللي فاتت بدأنا في خواص الـ isomorphism
+
+2
+00:00:27,190 --> 00:00:31,930
+وقسمنا هذه الخواص إلى جزءين، الجزء الأول أخذناه 
+
+3
+00:00:31,930 --> 00:00:35,870
+المرة الماضية، واليوم هناخد الجزء الثاني، الجزء 
+
+4
+00:00:35,870 --> 00:00:40,030
+الأول من خواص الـ isomorphism كان يتحدث عن تأثير الـ
+
+5
+00:00:40,030 --> 00:00:45,650
+isomorphism على عناصر الـ group، وأخذنا على ذلك سبع
+
+6
+00:00:45,650 --> 00:00:50,920
+نقاط، اليوم أربع نقاط تتحدث عن تأثير الـ isomorphism
+
+7
+00:00:50,920 --> 00:00:57,980
+على الشكل العام لمن؟ لـ group دون الخوض في العناصر
+
+8
+00:00:57,980 --> 00:01:01,220
+لأن المرة اللي فاتت كنا في العناصر، مرة هدى في
+
+9
+00:01:01,220 --> 00:01:06,540
+الشكل العام لـ group، يبقى تتكون أو النظرية هذه 
+
+10
+00:01:06,540 --> 00:01:12,500
+تتحدث عن الـ isomorphism acting on groups التي تؤثر
+
+11
+00:01:12,500 --> 00:01:17,000
+على الـ groups، قال افترض أن في هذه عبارة عن
+
+12
+00:01:17,000 --> 00:01:22,920
+isomorphism من الـ group G onto الـ group G bar, then
+
+13
+00:01:23,830 --> 00:01:27,870
+الـ Phi inverse عبارة عن isomorphism، يبقى Phi اللي
+
+14
+00:01:27,870 --> 00:01:32,990
+عندناها دي كانت isomorphism، إذا معكوسة هو عبارة عن
+
+15
+00:01:32,990 --> 00:01:39,670
+isomorphism من G bar onto G، يعني كأنها عملية عكسية
+
+16
+00:01:39,670 --> 00:01:45,470
+تمامًا لمين؟ لـPhi الأصلية، النقطة الثانية لو كان الـG
+
+17
+00:01:45,470 --> 00:01:50,810
+abelian فإن الـG bar abelian، والعكس صحيح، لو كان
+
+18
+00:01:50,810 --> 00:01:53,890
+الـG bar abelian يبقى الـG abelian، يبقى الـG is
+
+19
+00:01:53,890 --> 00:01:57,990
+abelian if and only if الـG bar is abelian، بالمثل
+
+20
+00:01:57,990 --> 00:02:02,390
+الـG is cyclic if and only if الـG bar is cyclic
+
+21
+00:02:02,920 --> 00:02:07,860
+النقطة الرابعة والأخيرة، لو كان K subgroup من G فإن
+
+22
+00:02:07,860 --> 00:02:14,760
+صورة اللي هو الـ K هذه، Phi of capital K هي عبارة عن
+
+23
+00:02:14,760 --> 00:02:20,260
+subgroup كذلك من من من G bar، يبقى لو كان K
+
+24
+00:02:20,260 --> 00:02:25,040
+subgroup من G فإن صورة هذه الـ K اللي هي Phi of K
+
+25
+00:02:25,040 --> 00:02:31,030
+بيبقى subgroup من من من G bar، الآن بدنا نحاول نبرهن
+
+26
+00:02:31,030 --> 00:02:35,330
+النقاط الأربع اللي عندنا، وبدنا نأتي إلى النقطة
+
+27
+00:02:35,330 --> 00:02:41,710
+الأولى، النقطة الأولى بدنا نعتمد في برهانها على ما
+
+28
+00:02:41,710 --> 00:02:47,600
+نعرف من مبادئ الرياضيات، أخذنا في مبادئ الرياضيات إن
+
+29
+00:02:47,600 --> 00:02:52,780
+لو عندي function والـ function هذه كانت one to one
+
+30
+00:02:52,780 --> 00:02:59,340
+and onto فإن المعكوس تبعها exist وفي نفس الوقت
+
+31
+00:02:59,340 --> 00:03:04,120
+one to one and onto، تذكروا هذه أخذناها وراجعناها في
+
+32
+00:03:04,120 --> 00:03:08,760
+أول chapter، إذا هذا العمود الأساسي أو النقطة
+
+33
+00:03:08,760 --> 00:03:12,420
+الأساسية في إثبات أن الـPhi inverse عبارة عن
+
+34
+00:03:12,420 --> 00:03:16,700
+isomorphism، إذا مدام Phi one to one and onto إذا
+
+35
+00:03:16,700 --> 00:03:20,140
+Phi inverse exist وكذلك one to one and onto، إذا ما
+
+36
+00:03:20,140 --> 00:03:25,140
+بضلش علينا إلا خاصية الـ isomorphism لـ Phi of A
+
+37
+00:03:25,140 --> 00:03:28,080
+بيبدوا يسوي Phi of B في Phi of B، بدنا نطبقها
+
+38
+00:03:28,080 --> 00:03:33,970
+عالميًا على Phi inverse، يبقى باجي بقوله هنا since
+
+39
+00:03:33,970 --> 00:03:37,010
+بمعنى
+
+40
+00:03:37,010 --> 00:03:46,710
+فاي is one to one and onto function, then since we
+
+41
+00:03:46,710 --> 00:03:56,790
+have أن الفاي inverse is one to one and onto
+
+42
+00:03:56,790 --> 00:03:58,530
+function
+
+43
+00:04:00,990 --> 00:04:05,070
+يبقى هذه معلومة من مبادئ رياضية من المستوى الثاني
+
+44
+00:04:05,070 --> 00:04:13,550
+يبقاش ضايل عندنا، it remains يبقى that it remains
+
+45
+00:04:13,550 --> 00:04:23,420
+to show that إن فاي انفرس of a,b سيكون فاي انفرس of
+
+46
+00:04:23,420 --> 00:04:30,580
+a في في انفرس of b، هذا الكلام صحيح لكل الـ a والـ b
+
+47
+00:04:30,580 --> 00:04:37,450
+اللي موجودة في G، لذلك بدي اروح اقولكوا consider في
+
+48
+00:04:37,450 --> 00:04:43,210
+انتظار هذا الكلام، consider فاي انفرس لما تأثر
+
+49
+00:04:43,210 --> 00:04:50,490
+على فاي a b نشوف ايش بتعطينا الآن
+
+50
+00:04:50,490 --> 00:04:53,890
+الفاي function والفاي انفرس اللي هو كمان
+
+51
+00:04:53,890 --> 00:04:59,620
+function، بدي ارجع تعريف الـ composition of functions
+
+52
+00:04:59,620 --> 00:05:07,740
+إلى أصله، يبقى هذه بتعطينا في انفرس لفي of a و b
+
+53
+00:05:07,740 --> 00:05:15,020
+تمام، يبقى بناء عليه الدالة ومعكوسها الـ composition
+
+54
+00:05:15,020 --> 00:05:20,660
+تبعهم بيعطينا الـ Identity Function، الـ
+
+55
+00:05:20,660 --> 00:05:25,020
+Identity Function لما تأثر على الـ Element بتعطينا 
+
+56
+00:05:25,020 --> 00:05:30,540
+نفس الـ Element اللي هو A B، تعالى نشوف تأثير الـ
+
+57
+00:05:30,540 --> 00:05:37,340
+Phi Inverse على مين؟ على الـ Phi of A في من؟ في
+
+58
+00:05:37,340 --> 00:05:39,420
+الـ Phi of B
+
+59
+00:05:42,860 --> 00:05:49,440
+تأثير الفاي انفرس على الفاي of a في الفاي of b أو
+
+60
+00:05:49,440 --> 00:05:57,540
+تأثير الفاي على مين؟ على الفاي انفرس الأولين يا
+
+61
+00:05:57,540 --> 00:06:04,490
+شباب، تأثير الفاي على الفاي انفرس عشان اه فايفاي
+
+62
+00:06:04,490 --> 00:06:08,970
+انفرس عشان اه فايفاي انفرس عشان اه فايفاي
+
+63
+00:06:08,970 --> 00:06:17,990
+انفرس عشان اه فايفاي انفرس عشان اه فايفاي
+
+64
+00:06:17,990 --> 00:06:25,020
+انفرس عشان اه فايفاي انفرس عشان اه، يبقى بناء عليه
+
+65
+00:06:25,020 --> 00:06:30,520
+هذا الكلام يساوي، أنا عندي في is an isomorphism
+
+66
+00:06:30,520 --> 00:06:34,660
+معناته في لما تأثر على حاصل ضرب two elements يساوي
+
+67
+00:06:34,660 --> 00:06:38,700
+تأثير الفي على الأولى مضروب في تأثير الفي على
+
+68
+00:06:38,700 --> 00:06:46,560
+الثانية، يبقى هذا بده يعطينا في لفي inverse of a في
+
+69
+00:06:46,560 --> 00:06:55,560
+في لمين؟ لفي inverse of b، الكلام هذا ليش؟ نظرًا لإن
+
+70
+00:06:55,560 --> 00:07:02,160
+الـ Phi is an isomorphism، نظرًا لإن Phi is
+
+71
+00:07:02,160 --> 00:07:05,640
+isomorphism، قدرت أكتبها بالشكل اللي عندنا هذا
+
+72
+00:07:05,640 --> 00:07:10,420
+فبهذا التعريف الـ composition of function يبقى بيظل
+
+73
+00:07:10,420 --> 00:07:19,740
+Phi Phi inverse of A وهنا منوهنا كذلك في لفي انفرس
+
+74
+00:07:19,740 --> 00:07:26,100
+of بي بالشكل اللي عندنا هذا، الكلام يساوي طبعًا في
+
+75
+00:07:26,100 --> 00:07:30,260
+في انفرس، هتطلع الـ identity function، يبقى هنا مش
+
+76
+00:07:30,260 --> 00:07:34,200
+هيضل عندي إلا الـ element a وهنا في في انفرس
+
+77
+00:07:34,200 --> 00:07:37,900
+هيعطينا الـ identity function تأثيره على بي مش
+
+78
+00:07:37,900 --> 00:07:44,290
+هيعطينا إلا من إلا بي، أطلع للنقطة الأولى هذه star
+
+79
+00:07:44,290 --> 00:07:50,870
+والنقطة هذه اللي بدي أسميها double star هذه بتساوي
+
+80
+00:07:50,870 --> 00:07:55,490
+AB، وهذه بتساوي AB، يبقى الطرف الشمال بتساوي من؟
+
+81
+00:07:55,490 --> 00:07:59,570
+الطرف الشمال اللي عندنا هذا، يبقى باجي بقوله هنا
+
+82
+00:07:59,570 --> 00:08:09,460
+from star and double star we have هنحصل على ما يأتي
+
+83
+00:08:09,460 --> 00:08:20,100
+أنه فاي لفاي inverse of a b بدر ساوي فا بدر ساوي
+
+84
+00:08:20,100 --> 00:08:27,500
+مين؟ بدر ساوي فاي لفاي inverse of a في فاي inverse
+
+85
+00:08:27,500 --> 00:08:35,070
+of b بالشكل اللي عندها، طب الآن أنا طلعت قيمتين
+
+86
+00:08:35,070 --> 00:08:40,710
+متساويتين، السؤال هو فاي هدي one to one ولا لأ؟
+
+87
+00:08:40,710 --> 00:08:45,770
+مظبوط، لأنها isomorphism يبقى فاي one to one وعندي
+
+88
+00:08:45,770 --> 00:08:52,230
+صورتين متساويتين يبقى الأصل ماله متساوي، يبقى هذا
+
+89
+00:08:52,230 --> 00:08:58,700
+بده يعطيني مين؟ بده يعطيني أنه في انفرس of a,b اللي
+
+90
+00:08:58,700 --> 00:09:03,560
+هو أصل الطرف الشمال، بدي اسوي أصل الطرف اليمين اللي
+
+91
+00:09:03,560 --> 00:09:10,780
+هو في انفرس of a في في انفرس ماله؟ of b، هذا الكلام
+
+92
+00:09:10,780 --> 00:09:17,580
+ليش؟ because في is one to one، قضينا أثبتنا هنا
+
+93
+00:09:17,580 --> 00:09:24,060
+أثبتنا أن الـ inverse هذا أصبح عبارة عن isomorphism
+
+94
+00:09:24,060 --> 00:09:31,060
+يبقى بروح بقوله thus وهكذا في inverse is an
+
+95
+00:09:31,060 --> 00:09:37,960
+isomorphism وبالتالي أثبتنا النقطة الأولى، النقطة
+
+96
+00:09:37,960 --> 00:09:44,980
+الثانية بيقول جي أبيليان إذا كانت الـG بار أبيليان
+
+97
+00:09:44,980 --> 00:09:51,340
+والعكس بالعكس، إذا أنا بدّي أجي أقوله إن الـG is
+
+98
+00:09:51,340 --> 00:09:58,630
+abelian, for and all F وقتها يجب أن تكون G Ab، يعني إذا
+
+99
+00:09:58,630 --> 00:10:03,330
+كان الـ A بي بدل سوى بي A لكل الـ A والـ B اللي
+
+100
+00:10:03,330 --> 00:10:09,490
+موجودة في G صحيح ولا لأ؟ يبقى for and all F الـ A بي
+
+101
+00:10:09,490 --> 00:10:17,580
+بدل سوى بي A لكل الـ A والـ B اللي موجودة في G، طيب
+
+102
+00:10:17,580 --> 00:10:22,960
+الآن في ايزو مورفزم، مدام ايزو مورفزم يبقى صورة
+
+103
+00:10:22,960 --> 00:10:28,360
+العنصر الأول بدّه تساوي صورة العنصر الثاني، يبقى إذا
+
+104
+00:10:28,360 --> 00:10:38,540
+كان في of a,b بدّه تساوي في of b,a، الكلام هذا صحيح
+
+105
+00:10:38,540 --> 00:10:44,160
+إذا كان الآن في ايزو مورفزم يبقى بقدر أدخل على أي
+
+106
+00:10:44,160 --> 00:10:52,620
+واحدة فيهم، يبقى if and only if في of a في في of b
+
+107
+00:10:52,620 --> 00:11:01,200
+يساوي في of b في في of a، هذا الكلام لماذا؟
+
+108
+00:11:01,200 --> 00:11:09,620
+لأن فاية عشوائية عشوائية عشوائية عشوائية
+
+109
+00:11:09,620 --> 00:11:11,920
+عشوائية عشوائية عشوائية عشوائية عشوائية عشوائية
+
+110
+00:11:11,920 --> 00:11:20,680
+عشوائية عشوائية عشوائية عشوائية
+
+111
+00:11:20,680 --> 00:11:24,020
+عشوائية
+
+112
+00:11:24,020 --> 00:11:27,860
+عشوائية عشوائية عشوائية عشوائية
+
+113
+00:11:35,170 --> 00:11:42,350
+النقطة الثالثة بيقول لي g is cyclic if and only if
+
+114
+00:11:42,350 --> 00:11:50,170
+g bar is cyclic، يبقى بدي أبداله بـ g is cyclic if
+
+115
+00:11:50,170 --> 00:11:58,840
+and only if الـ g is cyclic، لأ كيف؟ أثبتناها للـ
+
+116
+00:11:58,840 --> 00:12:04,940
+elements تمام؟ لكن احنا بنثبتها in general يبقى
+
+117
+00:12:04,940 --> 00:12:08,820
+أنا بقول إن الـ G الـ cyclic عارف أنا عارف تأثيرها
+
+118
+00:12:08,820 --> 00:12:12,500
+اللي بقولنا G تساوي الـ subgroup generated by A if
+
+119
+00:12:12,500 --> 00:12:15,420
+and only if الـ G bar الـ subgroup generated by Phi
+
+120
+00:12:15,420 --> 00:12:19,820
+of A، يعني أثبتناها على العناصر الآن بنثبت in
+
+121
+00:12:19,820 --> 00:12:23,820
+general، G الـ cyclic if and only if الـ G هذه اللي
+
+122
+00:12:23,820 --> 00:12:28,980
+جيتلها ولو generator واحد مظبوط؟ يبقى if and only
+
+123
+00:12:28,980 --> 00:12:37,040
+if الـ G هي الـ group generated by A، يبقى G الصحيح
+
+124
+00:12:37,040 --> 00:12:43,780
+لك إذا كان G قدرت أولدها بعنصر واحد، طب لو حدث ذلك
+
+125
+00:12:43,780 --> 00:12:48,640
+شو العلاقة بين الـ order تبع الـ G والـ order تبع الـ G bar؟ 
+
+126
+00:12:48,640 --> 00:12:57,020
+أ؟ إثنين متساويان يبقى هذا الكلام صحيح if and only if
+
+127
+00:12:57,020 --> 00:13:04,200
+if ال order  للـ A يساوي ال order لـ G طيب هذا الكلام 
+
+128
+00:13:04,200 --> 00:13:11,160
+صحيح if and only if نرجع للمحاضرة اللي فاتت ال
+
+129
+00:13:11,160 --> 00:13:16,620
+order لـ A شو بيساوي النقطة خمسة عندك في المحاضرة
+
+130
+00:13:16,620 --> 00:13:23,080
+الماضية الـ order لـ A بدّه يساوي ال order لـ Phi of A
+
+131
+00:13:23,080 --> 00:13:29,700
+والنقطة رقم سبعة ال order لـ G بدّه يساوي ال order لـ G 
+
+132
+00:13:29,700 --> 00:13:35,720
+bar ليش؟ لأنه Phi isomorphism يبقى if and only if ال
+
+133
+00:13:35,720 --> 00:13:43,160
+order تبع الـ A يساوي ال order لـ Phi of A تمام؟
+
+134
+00:13:44,730 --> 00:13:49,870
+يساوي ال order للـ Phi of A يبقى هذا الكلام صحيح إذا
+
+135
+00:13:49,870 --> 00:13:56,590
+كان ال order لـ A قلنا هو عبارة عن مين؟ ال order لـ G
+
+136
+00:13:56,590 --> 00:14:04,230
+و ال order لـ G هذا هو ال order تبع الـ G bar يبقى
+
+137
+00:14:04,230 --> 00:14:09,930
+بدّه يساوي ال order تبع الـ G bar و هذا بدّه يساوي
+
+138
+00:14:09,930 --> 00:14:18,170
+مدام هذا هو ال order تبع الـ G bar ولا تقول اتلخبط
+
+139
+00:14:18,170 --> 00:14:24,110
+في خطوة واحدة يبقى هذا الكلام صحيح إذا كان هدول
+
+140
+00:14:24,110 --> 00:14:28,750
+إثنين بيساووا بعض هذَا خليته زي ما هو و ال order لـ G
+
+141
+00:14:28,750 --> 00:14:33,350
+بدأت أشتغل شويّة أخذت ال order لـ A بدّه يساوي ال order
+
+142
+00:14:33,350 --> 00:14:39,290
+للـ Phi of A و هذا الكلام بدّه يساوي ال order لـ G
+
+143
+00:14:39,690 --> 00:14:44,170
+يبقى شيلت ال order لـ a و حطيت بداله ال order لـ phi
+
+144
+00:14:44,170 --> 00:14:49,910
+of a و هنا ال order لـ g الآن هذا if and only if
+
+145
+00:14:49,910 --> 00:14:58,750
+طلع لي لهذا ال order للـ phi of a ال order للـ phi of
+
+146
+00:14:58,750 --> 00:15:05,730
+a مالَه؟ الـ order لـ G هو ال order لـ G bar هذا
+
+147
+00:15:05,730 --> 00:15:11,810
+الكلام بدّه يساوي ال order لـ G bar هذا الكلام جبته
+
+148
+00:15:11,810 --> 00:15:17,010
+من وين؟ from سبعة من النقطة السابعة في النظرية
+
+149
+00:15:17,010 --> 00:15:21,310
+السابقة وهذا جبته من وين؟ من النقطة الخامسة في
+
+150
+00:15:21,310 --> 00:15:28,050
+النظرية الماضية يبقى إن حدث ذلك إن ال order لـPhi
+
+151
+00:15:28,050 --> 00:15:34,510
+of A يساوي ال order لـG bar السؤال هو Phi of A هذا
+
+152
+00:15:34,510 --> 00:15:38,590
+موجود في G ولا في G bar؟ طيب ال order له يساوي ال
+
+153
+00:15:38,590 --> 00:15:43,610
+order لـG bar إذا هذا إيش بيكون؟ generator يبقى
+
+154
+00:15:43,610 --> 00:15:50,720
+هذا الكلام if and only if إن الـ G bar بدّه تساوي لـ
+
+155
+00:15:50,720 --> 00:15:57,140
+group generated by Phi of A طب إن حدث ذلك يبقى G
+
+156
+00:15:57,140 --> 00:16:03,340
+bar مالها؟ مال G bar في هذه الحالة if and only if
+
+157
+00:16:03,340 --> 00:16:12,270
+الـ G bar is cyclic وهو المطلوب يبقى اعتمادنا في
+
+158
+00:16:12,270 --> 00:16:18,590
+برهان هذه النظرية على نقطتين من النظرية السابقة
+
+159
+00:16:18,590 --> 00:16:22,450
+وهي ال order لإيه؟ بدّه يساوي ال order لـPhi of V
+
+160
+00:16:22,450 --> 00:16:26,190
+النقطة الأولى النقطة الثانية ال order لـG هو ال
+
+161
+00:16:26,190 --> 00:16:31,050
+order لـG bar كل هذا تحت تأثير أن ال Phi اللي
+
+162
+00:16:31,050 --> 00:16:37,490
+عندها عبارة عن isomorphism بذلك نصل إلى النقطة
+
+163
+00:16:37,490 --> 00:16:41,090
+الرابعة حدّ يبي سؤال هنا قبل أن ننتقل إلى النقطة
+
+164
+00:16:41,090 --> 00:16:49,240
+الرابعة اللي بيحب يسأل سؤال هنا فيش بلاش نجي للنقطة
+
+165
+00:16:49,240 --> 00:16:54,360
+الرابعة بيقول لو كان capital K هو subgroup من J
+
+166
+00:16:54,360 --> 00:17:00,220
+فإن Phi of capital K كل العناصر Phi of small k بحيث
+
+167
+00:17:00,220 --> 00:17:06,000
+k موجود في K كابيتال عبارة عن subgroup من G bar إذا
+
+168
+00:17:06,000 --> 00:17:10,220
+بنحاول نثبت إن الـ Phi اللي عندنا هذه ال subgroup من
+
+169
+00:17:10,220 --> 00:17:17,090
+G bar لما كنا بنثبت ال subgroup كان عندي أكثر من
+
+170
+00:17:17,090 --> 00:17:22,810
+طريقة لإثبات ال subgroup أبسطهم وأسرعهم أني أثبت
+
+171
+00:17:22,810 --> 00:17:27,810
+نقطتين أن الـ Phi اللي عندها دي is non-empty امتى؟ الخطوة
+
+172
+00:17:27,810 --> 00:17:31,960
+الأولى خطوة ثانية لو أخدت منها عنصرين ضربت الأول في
+
+173
+00:17:31,960 --> 00:17:35,960
+المعكوس الثاني اللي جايبتهم فيهم إذا بيصير هذه عبارة
+
+174
+00:17:35,960 --> 00:17:43,980
+عن عبارة عن subgroup طب الآن أنا أدعي أن Phi of K 
+
+175
+00:17:43,980 --> 00:17:55,120
+is non-empty طيب
+
+176
+00:17:55,120 --> 00:18:02,730
+ليش؟ الآن السؤال هو K هذه ال subgroup من G بنفع
+
+177
+00:18:02,730 --> 00:18:08,250
+يكون subgroup وما فيها identity element؟ بنفع؟ لأ
+
+178
+00:18:08,250 --> 00:18:12,910
+يبقى subgroup ال identity element تبع الـ K هو ال
+
+179
+00:18:12,910 --> 00:18:20,780
+identity element تبع من؟ تبع الـ G الأصلية تمام إذا
+
+180
+00:18:20,780 --> 00:18:28,340
+هذه non-empty since ليش؟ لأن الـPhi of ال identity
+
+181
+00:18:28,340 --> 00:18:36,780
+تبع الـG موجود في الـPhi of كابيتال K ليش؟ لأن الـ
+
+182
+00:18:36,780 --> 00:18:42,880
+identity تبع الـ G موجود في كابيتال K هذه يعني هنا
+
+183
+00:18:42,880 --> 00:18:48,980
+that is أي أن هذه Phi of E G من المرة الماضية
+
+184
+00:18:48,980 --> 00:18:55,680
+النقطة الأولى الـ E تبع الـ G bar موجودة في Phi of
+
+185
+00:18:55,680 --> 00:19:03,000
+كابيتال K هذه ههه بالضبط هي هذه أخذنا المرة اللي فاتت
+
+186
+00:19:03,000 --> 00:19:05,980
+أول نقطة في برهان النظرية الماضية كان
+
+187
+00:19:10,840 --> 00:19:17,020
+يبقى Phi of K is non-empty لأنّ نحاول نجد عنصرين في
+
+188
+00:19:17,020 --> 00:19:22,680
+Phi of K ونثبت أن الأول في معكوس الثاني موجود فيها
+
+189
+00:19:22,680 --> 00:19:28,660
+إن حدث ذلك يبقى بقول Phi of K is a subgroup لذلك
+
+190
+00:19:28,660 --> 00:19:34,500
+لو جيت قلت افترض أن X وY موجودات في K
+
+191
+00:19:38,240 --> 00:19:45,760
+أخذت عنصرين موجودات في كابيتال K then الـ phi of x
+
+192
+00:19:45,760 --> 00:19:53,600
+والـ phi of y موجودات هدول وين؟ في مين؟ في G bar
+
+193
+00:19:53,600 --> 00:19:58,660
+صحيح لكن أنا بدي أحصرهم أكثر الـ X والـ Y موجودات
+
+194
+00:19:58,660 --> 00:20:07,100
+في K يبقى Phi of X موجود في Phi of K و Phi of Y
+
+195
+00:20:07,100 --> 00:20:14,120
+موجودة في Phi of K يبقى هذا الكلام موجود في Phi of
+
+196
+00:20:14,120 --> 00:20:20,870
+K بالشكل اللي عندنا يبقى استطعت أن أجد عنصرين
+
+197
+00:20:20,870 --> 00:20:27,210
+وأثبت أنهم موجودين في Phi of k إذا بدي أخذ الأول في معكوس
+
+198
+00:20:27,210 --> 00:20:36,160
+الثاني يبقى بدي أخذ Phi of x في Phi of y inverse إذا
+
+199
+00:20:36,160 --> 00:20:42,520
+قدرت أثبت إن هذا موجود في Phi of K  أثبت Phi of K
+
+200
+00:20:42,520 --> 00:20:47,360
+subgroup وانتهينا من القصة هذه خالص الآن هذا
+
+201
+00:20:47,360 --> 00:20:53,860
+الكلام من الخواص اللي درسناها قبل ذلك Phi of X في
+
+202
+00:20:53,860 --> 00:20:59,870
+Phi of Y inverse الرقم اللي بيكون عندنا هنا أو
+
+203
+00:20:59,870 --> 00:21:04,190
+ينما كان يكون بنزل على العنصر سواء كان هذا
+
+204
+00:21:04,190 --> 00:21:09,650
+رقم موجب أو سالب أو صفر المرة اللي فاتت أخذنا
+
+205
+00:21:09,650 --> 00:21:14,310
+النقطة الثانية اللي Phi of a to the power n بيبقى
+
+206
+00:21:14,310 --> 00:21:19,090
+يساوي Phi of a كلّه to the power n وهذا اللي حاصل
+
+207
+00:21:19,090 --> 00:21:24,500
+عندنا هنا طيب الآن في isomorphism مدام isomorphism
+
+208
+00:21:24,500 --> 00:21:33,040
+بقدر أطبّق عليه هُم بفي واحدة يبقى هذا Phi of x y inverse
+
+209
+00:21:33,040 --> 00:21:44,660
+ليش؟ since الـ Phi is an isomorphism هذا الكلام يساوي
+
+210
+00:21:44,660 --> 00:21:53,300
+Phi of x y inverse هل يا ترى هذا موجود في Phi of
+
+211
+00:21:53,300 --> 00:21:54,400
+كابيتال K؟
+
+212
+00:21:57,290 --> 00:22:03,990
+مش K subgroup وأخذت عنصرين فيها يبقى الأول فيه
+
+213
+00:22:03,990 --> 00:22:07,650
+معكوس الثاني موجودة فيها لأنّ الـ K زي الـ subgroup
+
+214
+00:22:07,650 --> 00:22:15,270
+يبقى موجود since اللي هو من X Y inverse موجودة في
+
+215
+00:22:15,270 --> 00:22:21,160
+capital K وK عبارة عن subgroup من G طيب بناء علي
+
+216
+00:22:21,160 --> 00:22:27,220
+إذا ثبت كلّ الخواص اللازمة لإثبات أن Phi of K is a
+
+217
+00:22:27,220 --> 00:22:33,920
+subgroup مدام ثبتها بروح بقول له غص وهكذا Phi of
+
+218
+00:22:33,920 --> 00:22:42,720
+كابيتال K is a subgroup من G bar وهو المطلوب حدًّا
+
+219
+00:22:42,720 --> 00:22:45,780
+فيكم بيحب يسأل أي سؤال قبل ما أفوت على النقطة اللي
+
+220
+00:22:45,780 --> 00:22:48,760
+بعدها أيّ تساؤل
+
+221
+00:22:53,040 --> 00:22:59,140
+إيش بتقول؟ وين؟
+
+222
+00:22:59,140 --> 00:23:03,320
+تعال هنا على اللوحة شوف تعال بس شوف شرايك إيش
+
+223
+00:23:03,320 --> 00:23:12,760
+بتقول تعال أيوة أه مالَه؟ لأ من الـ A والـ B وين
+
+224
+00:23:12,760 --> 00:23:17,970
+موجودة؟ الـ A والـ B موجودات في G وبالتالي Phi
+
+225
+00:23:17,970 --> 00:23:21,050
+inverse of A وPhi inverse of B هدول موجودات في G
+
+226
+00:23:21,050 --> 00:23:26,530
+bar لكن الأصل أنا ماخذ A وB هدول من وين؟ من G
+
+227
+00:23:26,530 --> 00:23:31,610
+وليس من G bar در بالك اه الكلام هذا سليم فيش فيه
+
+228
+00:23:31,610 --> 00:23:37,470
+لا غبارة عليها حدّ يبي يسأل ثاني؟ طيب ننتقل الآن
+
+229
+00:23:37,470 --> 00:23:40,230
+إلى النقطة التي تليها
+
+230
+00:23:59,000 --> 00:24:09,480
+نقّدم تعريف جديد يبقى Definition of an isomorphism
+
+231
+00:24:09,480 --> 00:24:14,980
+and isomorphism
+
+232
+00:24:14,980 --> 00:24:30,500
+from a group G onto onto
+
+233
+00:24:30,500 --> 00:24:46,240
+itself onto itself نفسها is called is
+
+234
+00:24:46,240 --> 00:24:48,900
+called an
+
+235
+00:24:54,010 --> 00:24:57,410
+Automorphism Automorphism of G
+
+236
+00:25:40,700 --> 00:25:45,060
+احنا لأن موضوعنا موضوع الـ isomorphism الآن بدأنا
+
+237
+00:25:45,060 --> 00:25:51,600
+نخصص شويّة إيش نخصص؟ الـ isomorphism هو function من
+
+238
+00:25:51,600 --> 00:25:55,840
+group إلى group ثانية بحيث الـ function هادي one to
+
+239
+00:25:55,840 --> 00:26:00,840
+one and onto وهو يحقق الخاصية Phi of a b بدّه يساوي Phi
+
+240
+00:26:00,840 --> 00:26:08,660
+of a في Phi of b تمام؟ الآن الآن إيش بنقول؟ بنقول
+
+241
+00:26:08,660 --> 00:26:13,280
+لو كانت الـ function هذه من الـ group لنفس الـ group مش
+
+242
+00:26:13,280 --> 00:26:18,300
+لـ group ثانية إن حدث ذلك باجي بقول إن كانت الـ
+
+243
+00:26:18,300 --> 00:26:22,420
+function هذه من الـ group لنفس الـ group مش لـ group ثانية
+
+244
+00:26:22,420 --> 00:26:27,610
+يبقى بدي اسمّيه إيش؟ Automorphism فالـ definition
+
+245
+00:26:27,610 --> 00:26:32,810
+بيقول لي الـ isomorphism من الـ group G onto itself
+
+246
+00:26:32,810 --> 00:26:38,730
+يبقى من G إلى G نفسها دي is called an
+
+247
+00:26:38,730 --> 00:26:42,770
+Automorphism إيش رأيك؟ احنا أخذنا مثال على الـ
+
+248
+00:26:42,770 --> 00:26:47,960
+Automorphism واحنا مش دارين أخذنا المثال أعتقد رقم
+
+249
+00:26:47,960 --> 00:26:51,160
+خمسة أو رقم أربعة معاك في الأمثلة تبع الـ
+
+250
+00:26:51,160 --> 00:26:59,440
+isomorphism يبقى أول example أخذناه define اللي هو
+
+251
+00:26:59,440 --> 00:27:03,500
+five من الـ special linear group of two by two
+
+252
+00:27:03,500 --> 00:27:09,380
+matrices over R للـ special linear group of two by
+
+253
+00:27:09,380 --> 00:27:19,920
+two matrices over R. Define Phi by عرفنا اللي هو Phi
+
+254
+00:27:19,920 --> 00:27:30,340
+M of A بدي أساوي الـ M A M inverse والـ M هذه
+
+255
+00:27:30,340 --> 00:27:34,820
+مصفوفة نظامها 2 في 2 قد تكون في الـ special و قد لا
+
+256
+00:27:34,820 --> 00:27:40,360
+تكون لكن نظامها 2 في 2. يبقى هاي الـ function اللي
+
+257
+00:27:40,360 --> 00:27:46,240
+عندنا نظرا اثبتناها احنا isomorphism وهيها من الـ
+
+258
+00:27:46,240 --> 00:27:51,460
+group إلى نفس الـ group. يبقى في is an automorphism
+
+259
+00:27:51,460 --> 00:28:02,680
+يبقى هنا بدي بقوله since في M is an isomorphism
+
+260
+00:28:02,680 --> 00:28:09,610
+وهذا previous example مش هنقعد هنا أعيد فيه تاني
+
+261
+00:28:09,610 --> 00:28:18,570
+and الـ phi m من الـ special linear group للـ
+
+262
+00:28:18,570 --> 00:28:28,810
+special linear group هيها نفسها. يبقى we have أنه
+
+263
+00:28:28,810 --> 00:28:33,070
+phi is an automorphism
+
+264
+00:28:35,930 --> 00:28:40,410
+هذا مثال كنا عاملينه و احنا مش عارفينه أو ندريش
+
+265
+00:28:40,410 --> 00:28:45,050
+أنه automorphism. اثبتنا أنه isomorphism وسكتنا لكن
+
+266
+00:28:45,050 --> 00:28:48,810
+لما كان من الـ group إلى نفس الـ group إذا صار هذا
+
+267
+00:28:48,810 --> 00:28:57,450
+معله صار automorphism. نعطي مثال آخر تبقى هذا اعتبره
+
+268
+00:28:57,450 --> 00:29:05,890
+المثال الأول. نجي للمثال رقم اتنين بيقول الاتالـ
+
+269
+00:29:05,890 --> 00:29:13,150
+R تربيع هي عبارة عن كل الـ order pairs A و B بحيث
+
+270
+00:29:13,150 --> 00:29:17,990
+أن الـ A و الـ B موجودة في الـ set of real numbers
+
+271
+00:29:17,990 --> 00:29:27,650
+then الـ R square و عليها عملية الجمع is a group
+
+272
+00:29:27,650 --> 00:29:34,730
+هذا لما تروح في الدار شيكلي عليها وتأكد أنه هذه
+
+273
+00:29:34,730 --> 00:29:41,790
+عبارة عن group. define a
+
+274
+00:29:41,790 --> 00:29:52,150
+function phi من الـ R square للـ R square by phi of
+
+275
+00:29:52,150 --> 00:29:58,810
+A و B بده يساوي الـ B و الـ A
+
+276
+00:30:03,430 --> 00:30:08,090
+show that أن
+
+277
+00:30:08,090 --> 00:30:17,370
+فاي is an automorphism. بيجي لي أن فاي عبارة عن
+
+278
+00:30:17,370 --> 00:30:18,950
+automorphism
+
+279
+00:30:28,120 --> 00:30:32,080
+يبقى احنا الـ function اللي عندنا قال يعرف الـ
+
+280
+00:30:32,080 --> 00:30:36,340
+function. define a function في من R تربيع إلى R
+
+281
+00:30:36,340 --> 00:30:41,980
+تربيع بحيث في of A وB بتقلب وضع اللي هو الـ A و الـ
+
+282
+00:30:41,980 --> 00:30:49,910
+B إلى B و A. وكأننا نقلب عناصر المستوى XY عبر الخط
+
+283
+00:30:49,910 --> 00:30:52,970
+Y تساوي X اللي على الشجة هذه. بنقولها هنا واللي
+
+284
+00:30:52,970 --> 00:30:58,170
+هنا بنقولها على الشجة التانية. جال يبين لي أن الـ
+
+285
+00:30:58,170 --> 00:31:03,310
+Phi هذه عبارة عن اتومورفزم. وواضح أن Phi هيها من
+
+286
+00:31:03,310 --> 00:31:06,710
+وين لوين؟ من R تربيع إلى R تربيع. يعني من الـ group
+
+287
+00:31:06,710 --> 00:31:10,800
+إلى نفسها. يبقى مش ضايق لعيننا نثبت إلا في عبارة عن
+
+288
+00:31:10,800 --> 00:31:14,380
+isomorphism. إن أثبتناها isomorphism بتصير
+
+289
+00:31:14,380 --> 00:31:19,460
+automorphism. بمعنى آخر بدي أثبت إن في one to one
+
+290
+00:31:19,460 --> 00:31:24,220
+and onto. تخدم خاصية الـ isomorphism إذا بدي
+
+291
+00:31:24,220 --> 00:31:31,600
+أبدأ أول شغلة بفي is one to one. يبقى بدي أحاول أثبت
+
+292
+00:31:31,600 --> 00:31:38,600
+أن فاي is one to one. لذلك بروح آخذ صورتين
+
+293
+00:31:38,600 --> 00:31:44,480
+متساويتين وأثبت أن أصلهم متساوي. فبروح بقوله
+
+294
+00:31:44,480 --> 00:31:54,680
+assume افترض that أن فاي of a و b بدي يساوي فاي of
+
+295
+00:31:54,680 --> 00:32:01,240
+c و d. يبقى مطلوب أثبت أن الـ A و الـ B بيبقى ساوية
+
+296
+00:32:01,240 --> 00:32:10,240
+مين؟ بيبقى ساوية C و D. مطلوب نثبت أن الـ A و الـ B
+
+297
+00:32:10,240 --> 00:32:16,180
+بيبقى ساوية CD. ثم الـ
+
+298
+00:32:16,180 --> 00:32:24,090
+Phi of A و B هي عبارة عن مين؟ B و A. الـ5 of C وD هي
+
+299
+00:32:24,090 --> 00:32:32,370
+عبارة عن مين؟ عبارة عن D وC. بناء عليه إذا عندي two
+
+300
+00:32:32,370 --> 00:32:36,010
+ordered pairs are equal. يبقى المركبة الأولى تساوي
+
+301
+00:32:36,010 --> 00:32:40,150
+المركبة الأولى والمركبة الثانية تساوي المركبة
+
+302
+00:32:40,150 --> 00:32:45,490
+الثانية. من الـ linear algebra يبقى هذا يطينا مين؟
+
+303
+00:32:45,670 --> 00:32:52,350
+بدوا يعطينا أن الـ b تساوي الـ d وفي نفس الوقت الـ a
+
+304
+00:32:52,350 --> 00:32:58,370
+بدوا يساوي من الـ c. هذا بدوا يعطينا أنا بدأت أحاول
+
+305
+00:32:58,370 --> 00:33:03,790
+أثبت أن الـ a و الـ b بدوا يساوي .. بدأ .. بدأ أحاول
+
+306
+00:33:03,790 --> 00:33:07,830
+أثبت أن وأنا أخذنا .. بدأ أحاول أثبت أن الـ a و الـ b
+
+307
+00:33:07,830 --> 00:33:13,810
+بدوا يساوي من الـ c و الـ d. إذا لو أخذت الـ a و الـ b
+
+308
+00:33:15,180 --> 00:33:20,240
+الـ A عبارة عن مين؟ C. يبقى بقدر أشيلها وأكتب
+
+309
+00:33:20,240 --> 00:33:26,560
+بدالها C والـ B عبارة عن مين؟ عبارة عن D وهو
+
+310
+00:33:26,560 --> 00:33:30,520
+المطلوب. إذا الـ A و الـ B الـ order pair ساوى الـ
+
+311
+00:33:30,520 --> 00:33:33,520
+order pair التاني الـ C و D. معناه هذا الكلام أنه
+
+312
+00:33:33,520 --> 00:33:39,640
+Phi is one to one. بالدرجة الأقل الـ Phi is onto
+
+313
+00:33:42,100 --> 00:33:49,840
+يبقى بدي أروح آخذ أي element A وB موجود في الـ R²
+
+314
+00:33:49,840 --> 00:33:56,300
+بدي أثبت أنه أي element في المستوى XY له أصل كذلك
+
+315
+00:33:56,300 --> 00:34:07,120
+في المستوى XY. يبقى then الـ A و الـ B لو جلبته إيش
+
+316
+00:34:07,120 --> 00:34:13,230
+بده يصير؟ B و A. بيظل في R تربيع ولا بيطلع برا؟ بيظل
+
+317
+00:34:13,230 --> 00:34:18,610
+في R تربيع. يبقى هنا then بدل ما أقول A و B بدي
+
+318
+00:34:18,610 --> 00:34:28,110
+أقول B و A. كذلك موجود في الـ R تربيع. يبقى and الـ A
+
+319
+00:34:28,110 --> 00:34:41,230
+و الـ B ده بقدر أقول عليه Phi of B و A. في الـ
+
+320
+00:34:41,230 --> 00:34:46,390
+element اللي أخدته في R تربيع لقيت له أصل موجود
+
+321
+00:34:46,390 --> 00:34:51,990
+كذلك في R تربيع اللي هو بي و إيه. يبقى فاي is onto
+
+322
+00:34:51,990 --> 00:34:56,590
+يبقى أي element أخدته في الـ group لقيت له أصل في
+
+323
+00:34:56,590 --> 00:35:02,500
+نفس الـ group. يبقى بناء عليه فاي is onto. ضايل علينا
+
+324
+00:35:02,500 --> 00:35:09,820
+خاصية الـ isomorphism. فاي is an isomorphism. بدا
+
+325
+00:35:09,820 --> 00:35:17,180
+أقول له فاي of بدي آخذ a و b. الـ operation عملية
+
+326
+00:35:17,180 --> 00:35:24,320
+الجامع ل c و d. آخذ تأثير في على main على two
+
+327
+00:35:24,320 --> 00:35:29,290
+elements. والـ two elements موجودات في الـ R². يبقى هذا
+
+328
+00:35:29,290 --> 00:35:40,470
+الكلام بده يساوي في أو يبقى a زائد c و b زائد d
+
+329
+00:35:40,470 --> 00:35:47,190
+كله كـ element واحد. بناء على التعريف هذا الكلام بده
+
+330
+00:35:47,190 --> 00:35:56,060
+يساوي المركبة a ثانية بزائد دي والمركبة الأولى a
+
+331
+00:35:56,060 --> 00:36:03,540
+زائد c بالشكل اللي عندناها. يبقى صورة العنصر هذا
+
+332
+00:36:03,540 --> 00:36:09,600
+بجلب وضع المركبتين. هاي جلبناهم. السؤال هو هل يمكن
+
+333
+00:36:09,600 --> 00:36:17,380
+كتابة الجثة على شكل مجموع قوسين؟ الإجابة نعم. كيف
+
+334
+00:36:17,380 --> 00:36:25,640
+كانت تاليهذا الكلام بقدر أقول b و a زائد d و c
+
+335
+00:36:25,640 --> 00:36:33,840
+طبعا الـ b و الـ a طبقا للـ definition مش هي عبارة عن
+
+336
+00:36:33,840 --> 00:36:41,580
+phi of a و b. والتانية d و c هي عبارة عن phi of
+
+337
+00:36:41,580 --> 00:36:49,470
+c و d. طب إيش اللي عملنا؟ طلع هنا أخذت مجموع اللي هو
+
+338
+00:36:49,470 --> 00:36:54,910
+two ordered pair. لجيت تأثير الفي عليهم يسوى تأثير
+
+339
+00:36:54,910 --> 00:37:00,370
+الفي على الـ element الأول زي تأثير الفي على الـ
+
+340
+00:37:00,370 --> 00:37:06,870
+element الثاني. هنا ظلت النقطة الأخيرة. يبقى since
+
+341
+00:37:07,360 --> 00:37:16,480
+فاي من R تربيع إلى R تربيع is an isomorphism. يبقى
+
+342
+00:37:16,480 --> 00:37:28,040
+الفاي is an automorphism وهو المطلوب. يبقى من الآنفا
+
+343
+00:37:28,040 --> 00:37:34,660
+صاعدا مشان أثبت أنه في اتومورفزم بدي أتأكد أنه
+
+344
+00:37:34,660 --> 00:37:39,120
+لازم تبقى من الـ group لنفس الـ group وبعد هيك ايزو
+
+345
+00:37:39,120 --> 00:37:44,780
+مورفزم. فباقي عندنا في هذه المحاضرة تعريف له علاقة
+
+346
+00:37:44,780 --> 00:37:53,360
+بهذه النقطة. تعريف بقول ما يأتي. definition little
+
+347
+00:37:53,360 --> 00:38:02,420
+group let الـ G be a group and
+
+348
+00:38:02,420 --> 00:38:13,380
+let الـ A موجود في هذه الـ group. define a function
+
+349
+00:38:13,380 --> 00:38:22,820
+فاي A من الـ group G إلى الـ group G by
+
+350
+00:38:25,000 --> 00:38:36,580
+فاي a of x يساوي a x a inverse. لكل
+
+351
+00:38:36,580 --> 00:38:46,740
+الـ x اللي موجود في g. بالاستثناء يبقى then فاي a is
+
+352
+00:38:46,740 --> 00:38:52,120
+called. is called an
+
+353
+00:38:54,790 --> 00:39:01,530
+والله is called the inner the
+
+354
+00:39:01,530 --> 00:39:05,550
+inner automorphism
+
+355
+00:39:05,550 --> 00:39:20,910
+automorphism of g induced by a. ناخد
+
+356
+00:39:20,910 --> 00:39:21,670
+مثال
+
+357
+00:39:25,360 --> 00:39:35,000
+example. let الـ G تساوي D4. D4 عناصرها عارفينهم ر
+
+358
+00:39:35,000 --> 00:39:43,740
+نود و R تسعين و R مية و تمانين و R ميتين و سبعين و
+
+359
+00:39:43,740 --> 00:39:51,400
+H و V و D و D prime. عارفينها من قبل. with
+
+360
+00:39:53,530 --> 00:40:06,890
+R 360 هي الـ R نوت. R 360 هي الـ R نوت. وكذلك الـ H
+
+361
+00:40:06,890 --> 00:40:14,450
+تربيع تساوي الـ V تربيع تساوي الـ D تربيع تساوي
+
+362
+00:40:14,450 --> 00:40:18,630
+الـ D تربيع تساوي الـ D تربيع تساوي من الـ
+
+363
+00:40:18,630 --> 00:40:19,830
+Identity
+
+364
+00:40:26,700 --> 00:40:44,820
+define a function في تسعين من D4 إلى D4 by في
+
+365
+00:40:44,820 --> 00:40:48,800
+تسعين of X ساوي
+
+366
+00:40:50,750 --> 00:41:08,450
+ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين
+
+367
+00:41:08,450 --> 00:41:12,330
+ر تسعين
+
+368
+00:41:24,400 --> 00:41:37,300
+الفاي R تسعين is an inner automorphism
+
+369
+00:41:51,150 --> 00:41:56,130
+العربية. بنرجع لتعريف الـ inner automorphism. جالي جي
+
+370
+00:41:56,130 --> 00:42:00,870
+جروب وخد فيها element. عرف function سماها في a من g
+
+371
+00:42:00,870 --> 00:42:07,050
+إلى g باي في a of x يسوي a x a inverse. الشبيه
+
+372
+00:42:07,050 --> 00:42:12,610
+بمين؟ الشبيه بالتو مثلا احنا اللي في m of a يسوي m
+
+373
+00:42:12,610 --> 00:42:16,830
+a m inverse. بس هنا أخذها على مين؟ على element وليس
+
+374
+00:42:16,830 --> 00:42:20,810
+على مصفوفة. مين ما تكون الـ group سواء مصفوفات ولا
+
+375
+00:42:20,810 --> 00:42:27,030
+غير مصفوفات. يبقى في a x يسوو الـ a x inverse لكل الـ 
+
+376
+00:42:27,030 --> 00:42:31,850
+اللي موجودة في g يبقى في of a بنسميها inner
+
+377
+00:42:31,850 --> 00:42:37,350
+automorphism يعني أكنه automorphism داخلي على مين؟
+
+378
+00:42:37,350 --> 00:42:42,310
+على الـ group الآن أنا أعطي مثال توضيحي أخذنا D4 و
+
+379
+00:42:42,310 --> 00:42:47,310
+كتبنا خواص الـ D4 كما كانت مكتوبة معنا من قبل قال
+
+380
+00:42:47,310 --> 00:42:52,030
+يعرف الـ function Phi R تسعين طبعا هم نقدر نجيب Phi
+
+381
+00:42:52,030 --> 00:42:56,390
+R مية وثمانين و Phi R متين وسبعين و Phi R H و
+
+382
+00:42:56,390 --> 00:43:02,650
+Phi R V و Phi R D و Phi D Prime كلهم نقدر نجيبهم
+
+383
+00:43:02,940 --> 00:43:07,580
+يعني بنقدر نجيب ثمانية automorphism ممكن يكون بعضهم 
+
+384
+00:43:07,580 --> 00:43:11,480
+يساوي بعضه وبالتالي ما تطلعوش ثمانية يطلعوا أقل بس
+
+385
+00:43:11,480 --> 00:43:16,020
+احنا بدنا ناخد فاي ار تسعين وما نعمله عليها بنقدر
+
+386
+00:43:16,020 --> 00:43:22,020
+نعمله لكل العناصر بالاستثناء يبقى هنا show that أن 
+
+387
+00:43:22,020 --> 00:43:28,800
+هذه automorphism باجي بقوله solution بدنا نروح نجيب
+
+388
+00:43:28,800 --> 00:43:37,480
+أول شيء FI R تسعين of الـ R note بدي امسك جميع عناصر
+
+389
+00:43:37,480 --> 00:43:44,100
+الـ D4 ليش؟ لأن فاي هذه around من D4 إلى D4 وأنا جاي
+
+390
+00:43:44,100 --> 00:43:50,720
+ل معرفها أن فاي R90X تساوي R90X لكل الـ X اللي
+
+391
+00:43:50,720 --> 00:43:56,700
+موجودة في D4 يعني هذا الكلام صحيح لكل الـ X اللي
+
+392
+00:43:56,700 --> 00:44:04,190
+موجودة في D4 إذا ميدالي لـ R تسعين R نود هي عبارة عن
+
+393
+00:44:04,190 --> 00:44:13,090
+R تسعين R نود R تسعين inverse الـ R نود مش هدا الـ
+
+394
+00:44:13,090 --> 00:44:18,630
+identity طب والـ R تسعين فيه R تسعين inverse يبقى
+
+395
+00:44:18,630 --> 00:44:26,660
+ده هيطلع الـ R نود itself لن يتغير فيها شيء لو بدى
+
+396
+00:44:26,660 --> 00:44:36,320
+أجيب الآن في ار تسعين يبقى
+
+397
+00:44:36,320 --> 00:44:46,980
+بده يسأل R تسعين R تسعين R تسعين inverse
+
+398
+00:44:46,980 --> 00:44:51,440
+element هذا في الـ inverse شو بيعطينا الـ identity
+
+399
+00:44:51,440 --> 00:44:59,720
+في R تسعين بيعطينا R تسعين itself ما تغيرتش طيب لو
+
+400
+00:44:59,720 --> 00:45:08,100
+بده أروح أجيب الـ فاي R تسعين R مية وثمانين يبقى
+
+401
+00:45:08,100 --> 00:45:16,000
+بيصير عندنا R تسعين R مية وثمانين R تسعين inverse
+
+402
+00:45:16,760 --> 00:45:23,180
+أليس هذه R 180 كمان؟
+
+403
+00:45:23,180 --> 00:45:28,130
+R commute مع نفسها، كل الـ rotation commute مع نفسها طيب
+
+404
+00:45:28,130 --> 00:45:35,910
+لو روحنا جبنا R تسعين أو Phi R تسعين of R متين
+
+405
+00:45:35,910 --> 00:45:44,750
+وسبعين يبقى R تسعين R متين وسبعين R تسعين inverse
+
+406
+00:45:44,750 --> 00:45:50,590
+يبقى كمان R متين وسبعين لأنه بدلناهم مع بعض
+
+407
+00:45:50,590 --> 00:45:55,150
+بنجيب الـ identity ايه المشكلة فيما بعد؟ يبقى بدنا
+
+408
+00:45:55,150 --> 00:46:04,930
+نيجي للـ R تسعين of H يبقى R تسعين H R تسعين
+
+409
+00:46:04,930 --> 00:46:11,950
+inverse طب استنا في الـ هم الشيء R تلت مية وستين
+
+410
+00:46:11,950 --> 00:46:19,210
+بده يساوي الـ R note مظبوط؟ طب لو ضربنا الطرفين في
+
+411
+00:46:19,210 --> 00:46:24,750
+الـ R inverse مش معنى هذا الكلام أن الـ R متين و
+
+412
+00:46:24,750 --> 00:46:33,150
+سبعين بدي أساوي الـ R تسعين inverse ولا لا؟ مظبوط
+
+413
+00:46:33,150 --> 00:46:43,100
+إذا هذه بقدر أكتبها R تسعين H R متين وسبعين بعد ر
+
+414
+00:46:43,100 --> 00:46:52,480
+تسعين اتش ر تسعين
+
+415
+00:46:52,480 --> 00:46:58,980
+اتش قداش تساوي يبقى لو رجعت لهذا الجدول عندك ر
+
+416
+00:46:58,980 --> 00:47:08,940
+تسعين اتش بتعطيك D prime فى R270 ومن نفس الجدول D'
+
+417
+00:47:09,260 --> 00:47:24,160
+فى R270 بتديلك V طيب لو روح جبت فاي R90 V
+
+418
+00:47:24,160 --> 00:47:28,260
+بدي أساوي R90
+
+419
+00:47:29,780 --> 00:47:38,080
+في V في R تسعين inverse ويساوي R تسعين V R تسعين V
+
+420
+00:47:38,080 --> 00:47:48,640
+اللي هي بـ D وهذه بـ R متين وسبعين متين وسبعين وهذه
+
+421
+00:47:48,640 --> 00:47:57,370
+عبارة عن مين عبارة عن H الآن يبقى هاد H بالمثل لو
+
+422
+00:47:57,370 --> 00:48:08,430
+جيبنا فاي R تسعين اللي هو D بدي أساوي R تسعين D R
+
+423
+00:48:08,430 --> 00:48:17,170
+تسعين inverse R تسعين V R تسعين D اللي هي عبارة عن
+
+424
+00:48:17,170 --> 00:48:25,370
+H فى R متين وسبعين والـ H فى R متين وسبعين اللي
+
+425
+00:48:25,370 --> 00:48:32,970
+عبارة عن مين عن D Prime الآن بقيت عندنا الأخيرة
+
+426
+00:48:32,970 --> 00:48:41,410
+Phi R تسعين فى D Prime اختصارا من الآخر هتعطى لك D
+
+427
+00:48:43,390 --> 00:48:47,670
+يبقى بناء عليه هذا الـ inner-automorphism جاب لي
+
+428
+00:48:47,670 --> 00:48:55,510
+مين؟ جاب ليه كل عناصر D4 بلا استثناء تماما يبقى
+
+429
+00:48:55,510 --> 00:49:03,770
+أصبح هنا الساعة اللي هو 5R90
+
+430
+00:49:03,770 --> 00:49:12,280
+لما أنا أثرت على D4 كلها أعطتني D4 كلها أنت ممكن تروح
+
+431
+00:49:12,280 --> 00:49:17,500
+تاخد في ر مية وثمانين وممكن تاخد في ر متين و
+
+432
+00:49:17,500 --> 00:49:23,840
+سبعين وممكن تاخد في ر اتش أو تاخد في اتش وفي دي
+
+433
+00:49:23,840 --> 00:49:28,340
+وفي دي وفي دي prime وطلع كل واحدة على حده ليس
+
+434
+00:49:28,340 --> 00:49:33,840
+بالضرورة أن هجيبلك دي prime لكن لو اتخيلت معكوس الـ
+
+435
+00:49:33,840 --> 00:49:40,340
+R تسعين هجيبلك نفس الـ D prime لكن الباقي لا طيب على
+
+436
+00:49:40,340 --> 00:49:43,880
+أي حال حتى الآن ما انتهناش من هذا الـ section يوم
+
+437
+00:49:43,880 --> 00:49:49,400
+السبت عندك ساعتين فياريت يعني يوم السبت اتحضري أول
+
+438
+00:49:49,400 --> 00:49:54,620
+عشرة أسئلة من التمرين لأن الساعة إن شاء الله بنكمل
+
+439
+00:49:54,620 --> 00:49:58,120
+فيها الـ section والساعة الثانية بناخد فيها مناقشة
+
+440
+00:49:58,120 --> 00:49:58,860
+إن شاء الله
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5f10be4fd22d3c1b80add126ac595e888957bc37
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_raw.srt
@@ -0,0 +1,2028 @@
+1
+00:00:21,190 --> 00:00:26,610
+بسم الله الرحمن الرحيم المرة الماضية بدأنا في خواص
+
+2
+00:00:26,610 --> 00:00:31,330
+ال group الخواص الأولى لل group واخدنا أول خاصية
+
+3
+00:00:31,330 --> 00:00:35,930
+الخاصية الأولى بتقول لو كان عندى identity element
+
+4
+00:00:35,930 --> 00:00:39,980
+في ال group يبقى هذا ال identity element يكونو
+
+5
+00:00:39,980 --> 00:00:43,540
+أثبتنا ان الاتنين مرتبطين و اثبتنا ان الاتنين
+
+6
+00:00:43,540 --> 00:00:45,200
+مرتبطين و اثبتنا ان الاتنين مرتبطين و اثبتنا ان
+
+7
+00:00:45,200 --> 00:00:47,820
+الاتنين مرتبطين و اثبتنا ان الاتنين مرتبطين و
+
+8
+00:00:47,820 --> 00:00:48,960
+اثبتنا ان الاتنين مرتبطين و أثبتنا ان الاتنين
+
+9
+00:00:48,960 --> 00:00:50,300
+مرتبطين و أثبتنا ان الاتنين مرتبطين و أثبتنا ان
+
+10
+00:00:50,300 --> 00:00:52,420
+الاتنين مرتبطين و أثبتنا ان الاتنين مرتبطين و
+
+11
+00:00:52,420 --> 00:00:56,700
+أثبتنا ان الاتنين مرتبطين و أثبتنا ان الاتنين
+
+12
+00:00:56,700 --> 00:01:01,140
+مرتبطين و أثبتنا ان الاتنين مرتبطين و أثبتنا ان
+
+13
+00:01:01,140 --> 00:01:06,290
+الاتنين مرتبطينبلغة أخرى لما نقول بي ايه بده يساوي
+
+14
+00:01:06,290 --> 00:01:12,450
+ca then بيه يساوي c يعني كأنه شاطبنا a مع a وده
+
+15
+00:01:12,450 --> 00:01:18,250
+اسمه قانون الشاطب الأيمن التاني هذا a بيه بده
+
+16
+00:01:18,250 --> 00:01:23,630
+يساوي ac يبقى طالع انه بيه بتساوي c يبقى كأنه
+
+17
+00:01:23,630 --> 00:01:29,510
+شاطبنا من جهة الشماليبقى قانون الشاطب الأيسر قانون
+
+18
+00:01:29,510 --> 00:01:32,810
+الشاطب الأيمن قانون الشاطب الأيسر هذه تسميات
+
+19
+00:01:32,810 --> 00:01:37,310
+بتهمنيش كتير بهمني ان انا نصل الى اثبات هذه
+
+20
+00:01:37,310 --> 00:01:43,170
+العلاقة يبقى بدنا نروح نثبتها فباجي بقوله ل proof
+
+21
+00:01:46,430 --> 00:01:51,850
+الان بي في اه موجود
+
+22
+00:01:51,850 --> 00:01:56,150
+في ال group جي والبي موجود في ال group جي مشان
+
+23
+00:01:56,150 --> 00:02:02,210
+تكون group لازم يكون فيها لكل عنصر معكوس لهذا
+
+24
+00:02:02,210 --> 00:02:07,650
+العنصر اذا بدي افترض انه معكوس لعنصر ا مثلا وليه
+
+25
+00:02:07,650 --> 00:02:12,230
+اكون a prime او اي رمز اخر ونشوف هذا هيوصلنا لوين
+
+26
+00:02:12,230 --> 00:02:14,790
+يبقى حاجة اقوله assume
+
+27
+00:02:34,810 --> 00:02:43,090
+الحين احنا عندنا BA بده يساوي CAبدأ أضرب من جهة
+
+28
+00:02:43,090 --> 00:02:51,850
+اليمين في الـ A' يبقى بي ايه في الـ A' يبقى C A في
+
+29
+00:02:51,850 --> 00:02:59,230
+الـ A' هذا الكلام سيعطينا بدأ أستخدم خاصية ال
+
+30
+00:02:59,230 --> 00:03:03,880
+associativityيبقى من خاصية ال associativity بصير
+
+31
+00:03:03,880 --> 00:03:10,660
+ان بي في a a prime يساوي
+
+32
+00:03:10,660 --> 00:03:17,700
+c في a a prime هذا بدي يعطينا اي عنصر في معكسه شو
+
+33
+00:03:17,700 --> 00:03:22,860
+بيعطيناه عنصر الوحدة ال identity element يبقى بناء
+
+34
+00:03:22,860 --> 00:03:34,390
+عليه هذا هيعطينا ان ال bالـ B في الـ E بدر يساوي
+
+35
+00:03:34,390 --> 00:03:38,890
+مين؟ بدر يساوي الـ C في الـ E طب ال identity
+
+36
+00:03:38,890 --> 00:03:42,870
+element لما أضربه في أي عنصر إيش بيعطينا؟ نفس
+
+37
+00:03:42,870 --> 00:03:49,950
+العنصر يبقى هذا بدر يعطينا B تساوي C هذا هو
+
+38
+00:03:49,950 --> 00:04:01,090
+المطلوب الأول المطلوب الثاني andو كذلك ال a b بده
+
+39
+00:04:01,090 --> 00:04:08,390
+يسوي a c implies ان ال a prime في ال a b بده يسوي
+
+40
+00:04:08,390 --> 00:04:15,350
+ال a prime في ال a c من خاصية ال associativity هذا
+
+41
+00:04:15,350 --> 00:04:18,110
+يعني ان ال a prime a
+
+42
+00:04:26,160 --> 00:04:31,040
+العنصر في معكسه بيعطينا ال identity element دير
+
+43
+00:04:31,040 --> 00:04:34,320
+بالك بس مش عنصر تضرب من اليمين و التاني من الشمال
+
+44
+00:04:34,320 --> 00:04:37,720
+ضربت من الشمال يبقى التاني من الشمال ضربت من
+
+45
+00:04:37,720 --> 00:04:40,960
+اليمين يبقى التاني من اليمين ليش؟ لأنه ماقليش ال
+
+46
+00:04:40,960 --> 00:04:44,780
+group abelianلو قالي لجروب أبيلي ان ضربت واحدة من
+
+47
+00:04:44,780 --> 00:04:47,560
+اليمين و واحدة من الشمال، انت فريقش عننا بس إن كان
+
+48
+00:04:47,560 --> 00:04:49,880
+الضرب من اليمين، الثاني من اليمين، الضرب من
+
+49
+00:04:49,880 --> 00:04:53,280
+الشمال، الطرف التاني من الشمال زي ما أنت شايفلازم
+
+50
+00:04:53,280 --> 00:04:58,420
+نرى الترتيب عند عملية الشغل في ال groups يبقى هذا
+
+51
+00:04:58,420 --> 00:05:03,720
+معناه ان ال identity element في B يسوى ال identity
+
+52
+00:05:03,720 --> 00:05:11,320
+element في C يبقى هذا معناه ان B بيبدأ تسوى C إذا
+
+53
+00:05:11,320 --> 00:05:15,520
+من الآن فصادم قانون الشطب الأيمن وقانون الشطب
+
+54
+00:05:15,520 --> 00:05:23,320
+الأيسر على ال group exist موجود ومتعرف عليهالنقطة
+
+55
+00:05:23,320 --> 00:05:27,880
+الثالثة أو الخاصية التالتة من خواص ال group بيقول
+
+56
+00:05:27,880 --> 00:05:38,920
+for each element for each element لأي عنصر for
+
+57
+00:05:38,920 --> 00:05:47,040
+each element a in a group g
+
+58
+00:05:49,680 --> 00:05:55,360
+لأي عنصر في ال group G there is a unique element
+
+59
+00:05:55,360 --> 00:06:10,620
+there is a unique element there is
+
+60
+00:06:10,620 --> 00:06:17,880
+a unique element B in G such that
+
+61
+00:06:21,290 --> 00:06:29,150
+بعد ذلك اي بي ساوي بي في اي ساوي ال identity
+
+62
+00:06:29,150 --> 00:06:40,070
+element مرة
+
+63
+00:06:40,070 --> 00:06:44,940
+تانيةالمرة اللى فاتت اول خاصية اثبتنا ان عنصر
+
+64
+00:06:44,940 --> 00:06:49,080
+الوحدة يكون وحيدا مافيش غير عنصر واحدة واحدة في ال
+
+65
+00:06:49,080 --> 00:06:53,500
+group كلها من اولها الى اخرها الان بيقول لو اخدت
+
+66
+00:06:53,500 --> 00:07:00,060
+اي عنصر ايه موجود في جيل لازم نلاقي عنصر وحيد لاحظ
+
+67
+00:07:00,060 --> 00:07:05,080
+الكلمة هذه a unique element يبقى عنصرا وحيدا مافيش
+
+68
+00:07:05,080 --> 00:07:10,910
+غيرهوين في جي بي موجود في جي بحيث ان ال a في b
+
+69
+00:07:10,910 --> 00:07:14,710
+بيساوي ال a في b بيساوي ال identity شو معنى هذا
+
+70
+00:07:14,710 --> 00:07:20,990
+الكلام معنى ان المعكوس لكل عنصر يكونه وحيدا مافيش
+
+71
+00:07:20,990 --> 00:07:26,540
+غيرهيعني كل عنصر في موجود في ال group له معكوس لا
+
+72
+00:07:26,540 --> 00:07:31,740
+يشاركه أحد في هذا المعكوس إذا بدنا نروح نثبت هذا
+
+73
+00:07:31,740 --> 00:07:35,840
+الكلام بنفس الفكرة اللي أثبتنا فيها ال identity
+
+74
+00:07:35,840 --> 00:07:39,360
+element يبقى العنصر إيه اللي موجود في ال group بدي
+
+75
+00:07:39,360 --> 00:07:43,960
+أفترض أنه إيه معكوسين و أحاول أثبت أن هذين
+
+76
+00:07:43,960 --> 00:07:49,260
+المعكوسين متساويان يبقى باجي بقوله ال proof
+
+77
+00:07:53,660 --> 00:08:07,940
+Assume افترض ان B وC هم اكتر
+
+78
+00:08:07,940 --> 00:08:18,200
+من الاسم
+
+79
+00:08:18,200 --> 00:08:20,080
+الموجود في G
+
+80
+00:08:26,860 --> 00:08:35,980
+الـ A B بيساوي B A الـ A B بيساوي B A بيساوي ال
+
+81
+00:08:35,980 --> 00:08:44,760
+identity E and الـ A C بيساوي C في A بيساوي ال
+
+82
+00:08:44,760 --> 00:08:50,540
+identity E هذا حسب تعريف من؟ حسب تعريف المعكوس
+
+83
+00:08:50,540 --> 00:08:57,810
+الآن هذا ال elementبدو يساوي ال identity و هذا ال
+
+84
+00:08:57,810 --> 00:09:01,850
+element بدو يساوي ال identity معناته ال two
+
+85
+00:09:01,850 --> 00:09:08,270
+elements are equal يبقى هذا بدو يعطينا ايه انه a
+
+86
+00:09:08,270 --> 00:09:14,230
+في b بدو يساوي ال ac لإنه كل واحد مالهم بدو يساوي
+
+87
+00:09:14,230 --> 00:09:19,310
+ال identity بالخاصية اللي فوق الأولانية رقم اتنين
+
+88
+00:09:19,310 --> 00:09:23,030
+يبقى by property
+
+89
+00:09:29,720 --> 00:09:37,400
+بتساوي الـ C لو أخدنا الجزء الثاني similarly بنفس
+
+90
+00:09:37,400 --> 00:09:38,420
+الطريقة
+
+91
+00:09:40,770 --> 00:09:49,050
+اللي هو BA بده يساوي CA implies ان ال B تساوي C
+
+92
+00:09:49,050 --> 00:09:53,330
+يبقى بناء عليه لو وجد معكوسين ان شاء الله يكونوا
+
+93
+00:09:53,330 --> 00:09:57,970
+عشرة لعنصر ما العشرة هدول لازم يكونوا are equal
+
+94
+00:09:57,970 --> 00:10:02,850
+يعني معنى هذا الكلام ان معكوس العنصر يكونوا ايه؟
+
+95
+00:10:02,850 --> 00:10:05,490
+يكونوا وحيدا مفيش غيره
+
+96
+00:10:13,790 --> 00:10:20,370
+الخاصية الرابعة الرابعة الرابعة الرابعة الرابعة
+
+97
+00:10:20,370 --> 00:10:20,490
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+98
+00:10:20,490 --> 00:10:21,050
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+99
+00:10:21,050 --> 00:10:21,450
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+100
+00:10:21,450 --> 00:10:22,370
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+101
+00:10:22,370 --> 00:10:26,570
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+102
+00:10:26,570 --> 00:10:29,330
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+103
+00:10:29,330 --> 00:10:29,330
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+104
+00:10:29,330 --> 00:10:29,610
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+105
+00:10:29,610 --> 00:10:31,270
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+106
+00:10:31,270 --> 00:10:31,270
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+107
+00:10:31,270 --> 00:10:31,270
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+108
+00:10:31,270 --> 00:10:40,590
+الرابعة الرابعة
+
+109
+00:10:40,590 --> 00:10:46,180
+الروالعكس من جيه
+
+110
+00:10:46,180 --> 00:10:57,840
+هو denoted by جيه انفسيعني يا شباب من الأن فاصاعدا
+
+111
+00:10:57,840 --> 00:11:03,700
+بدنا نبطل نقول let A' B is inverse of A على طول
+
+112
+00:11:03,700 --> 00:11:08,640
+الخط معكوس ال A هقوله A inverse معكوس ال G هو G
+
+113
+00:11:08,640 --> 00:11:20,880
+inverse و هكذا نقطة ثانية if ال N is A positive
+
+114
+00:11:22,440 --> 00:11:32,780
+integer عدد صحيح موجة باللي ال N then ال G to the
+
+115
+00:11:32,780 --> 00:11:40,440
+power N معناته ايه؟ معناته G مضروبة في G مضروبة في
+
+116
+00:11:40,440 --> 00:11:47,800
+G هذا الكلام in times يعني in من المراتيا شباب هنا
+
+117
+00:11:47,800 --> 00:11:50,760
+الدرب هذه النقاط اللي شايفينها مش عملية الدرب
+
+118
+00:11:50,760 --> 00:11:55,860
+العادية يعني g star g g star g star g star g إلى
+
+119
+00:11:55,860 --> 00:11:59,920
+آخرية ال star mean ما كانت تكون بس احنا اختصارا
+
+120
+00:11:59,920 --> 00:12:07,490
+بنكتبها بالشكل هذاالنقطة الثالثة
+
+121
+00:12:07,490 --> 00:12:13,930
+الجي مرفوع للأس زيرو بده يساوي اي element في ال
+
+122
+00:12:13,930 --> 00:12:18,890
+group جي ارفع له الصفر بيعطينا ال identity element
+
+123
+00:12:18,890 --> 00:12:26,550
+يبقى هذا ال E نمره أربع الجي to the power n بقدر
+
+124
+00:12:26,550 --> 00:12:35,520
+اقول جي انفرس أس سالب nلما أقول GN بقدر أكتبها على
+
+125
+00:12:35,520 --> 00:12:36,620
+الشكل التالي
+
+126
+00:12:47,300 --> 00:12:56,760
+بقول ال GM في ال GN بده سوى GM زائد ال N يبقى تجمع
+
+127
+00:12:56,760 --> 00:13:06,260
+الأسس عادي جدا خمسة نمرا ستة نمرا ستة GM كله أس N
+
+128
+00:13:06,260 --> 00:13:14,390
+زي هذه بالضبط تمامايبقى هذه أسس مُركّبة وليست مثل
+
+129
+00:13:14,390 --> 00:13:19,430
+هذه هنا الأساسات هم ال element مرفوعة لنفس الأسس M
+
+130
+00:13:19,430 --> 00:13:24,950
+و N يبقى عند ال operation هذه تجمع الأسس لكن هذه
+
+131
+00:13:24,950 --> 00:13:32,650
+كانها GM Star GM Star GM Star GM يعني إيش يعني N
+
+132
+00:13:32,650 --> 00:13:42,050
+من المراتإذا هذه بالضبط تماما هي GMN أو بقدر أقول
+
+133
+00:13:42,050 --> 00:13:50,250
+GNM ليش؟لأن الان و الام انتجار عملية ضرب العادية
+
+134
+00:13:50,250 --> 00:13:54,910
+للأعداد عملية إبدالية خمسة في ستة هي ستة في خمسة
+
+135
+00:13:54,910 --> 00:14:01,710
+إذا هذه بقدر أروح أكتبها كذلك على الشكل التالي GNM
+
+136
+00:14:01,710 --> 00:14:07,170
+بهمنيش من الأسل ولا على كل الأمرين كله بعطيني نفس
+
+137
+00:14:07,170 --> 00:14:14,580
+النتيجة النقطة السابعةالنقطة السابعة لو قلت a b
+
+138
+00:14:14,580 --> 00:14:23,820
+كله to the power n هل يسوى a n b n يعني
+
+139
+00:14:23,820 --> 00:14:29,680
+لو قلتك اتنين هل ال a b تربيع يسوى a تربيع b تربيع
+
+140
+00:14:29,680 --> 00:14:36,300
+في حالة واحدة لو كانت ال g أبيليا غير هيك بعتلك
+
+141
+00:14:36,300 --> 00:14:41,400
+اللهيبقى هذا الكلام لا يمكن أن يساوي هذا على
+
+142
+00:14:41,400 --> 00:14:49,880
+الاطلاق بروح بستثني و بقول but if g is abelian
+
+143
+00:14:49,880 --> 00:14:58,160
+then اللي هو ال a b to the power n بده يساوي a n b
+
+144
+00:14:58,160 --> 00:15:04,290
+nغير هيك لأ لإنه بقدر أبدل أي عنصر مكان التاني
+
+145
+00:15:04,290 --> 00:15:07,430
+بدون أي مشكلة إن كان تميل لكن if it's not
+
+146
+00:15:07,430 --> 00:15:12,830
+appealing بيصير كلامي هذا كله ليس صحيحا طيب النقطة
+
+147
+00:15:12,830 --> 00:15:23,270
+الثامنة بيقول if ال g و ال plus is a group is a
+
+148
+00:15:23,270 --> 00:15:28,190
+group then
+
+149
+00:15:30,130 --> 00:15:47,370
+الـ inverse of g is minus g that is a n الـ g
+
+150
+00:15:47,370 --> 00:15:53,710
+inverse هي عبارة عن سلب g and
+
+151
+00:15:55,880 --> 00:16:04,480
+الـ G Inverse كل تكييب بده يساوي سالب تلاتة G
+
+152
+00:16:28,420 --> 00:16:34,920
+بترجع مرة تانية لهذه النقاط الأساسية الثمانية لأن
+
+153
+00:16:34,920 --> 00:16:40,000
+هذه الأساسية عندنا بتظل معانا طيلة شغلنا في علم
+
+154
+00:16:40,000 --> 00:16:45,400
+الجبار من الآن فسعدم أن نتفق على هذه النقاط مرة
+
+155
+00:16:45,400 --> 00:16:50,680
+أخرى يبقى النقطة الأخرى احنا بنشغل داخل ال group
+
+156
+00:16:50,680 --> 00:16:55,240
+وليس داخل ال set of real number احنا بنشغل داخل ال
+
+157
+00:16:55,240 --> 00:16:59,380
+group من ما كانت ال group تكون هذهبقول لو كانت جي
+
+158
+00:16:59,380 --> 00:17:04,760
+جروب واخدت عنصر جي موجود في جي يبقى معكوس الجي من
+
+159
+00:17:04,760 --> 00:17:11,040
+الأن فساعدا هنرمزله بالرمز G inverse وليس G أسالب
+
+160
+00:17:11,040 --> 00:17:16,140
+واحد يعني هذه ليست واحد على جي تمام ايوة مشان
+
+161
+00:17:16,140 --> 00:17:22,000
+متوهش بين غسيل اكتب ل G inverse لا تساوي واحد على
+
+162
+00:17:22,000 --> 00:17:26,600
+جييمكن في بعض التعريفات هيها صحيح الـ G inverse
+
+163
+00:17:26,600 --> 00:17:31,920
+واحد على G بس in general الكلام هذا ليس صحيحاً طيب
+
+164
+00:17:31,920 --> 00:17:35,900
+النقطة التانية لو كانت ال N positive integer عدد
+
+165
+00:17:35,900 --> 00:17:41,900
+صحيح موجب يبقى المقصود ب G N هي G star G star G
+
+166
+00:17:41,900 --> 00:17:46,740
+star G N من المرات يعني بدي أطبق ال binary
+
+167
+00:17:46,740 --> 00:17:51,510
+operation على ال element هذا N من المراتالنقطة
+
+168
+00:17:51,510 --> 00:17:56,070
+التالتة الـ A element في ال group G لو حطيت له
+
+169
+00:17:56,070 --> 00:17:59,570
+الأس Zero بدي يعطيني دائما و أبدا ال identity
+
+170
+00:17:59,570 --> 00:18:06,590
+elementلما أقول GN يمكن صياغتها بصياغة أخرى و
+
+171
+00:18:06,590 --> 00:18:11,990
+هتشوفوا و احنا بنبرهن هنضطر نصيغ ال GN بالصياغة
+
+172
+00:18:11,990 --> 00:18:19,070
+هذه يبقى هي G inverse و سالب N هذه و هذه الاتنين
+
+173
+00:18:19,070 --> 00:18:27,180
+are the sameالنقطة الخامسة GM مضروبة في GN يبقى
+
+174
+00:18:27,180 --> 00:18:31,960
+بنجمع الأسس جامعة هذه ليست ضربة وإنما ما المقصود
+
+175
+00:18:31,960 --> 00:18:40,770
+بيها Star GM Star GN يبقى GM زائد Mلو كان الأُس
+
+176
+00:18:40,770 --> 00:18:46,010
+أُسًا مُركّبًا يبقى بنضرب هذه الأُس في بعض يبقى G
+
+177
+00:18:46,010 --> 00:18:52,030
+M N يساوي G أُس M N بدّل ال N و ال M لأن هم هدول
+
+178
+00:18:52,030 --> 00:18:57,470
+integers و اتنين are positive يبقى G N M أو G N
+
+179
+00:18:57,470 --> 00:19:03,240
+أُس M كله are the sameلأ لو جيت لحاصل ضرب a b to
+
+180
+00:19:03,240 --> 00:19:10,360
+the power n لا يساوي a n في b n ولكن هذا يساوي a b
+
+181
+00:19:10,360 --> 00:19:18,160
+a b a b a b a b n من المرات ولا يساوي a n b n لكن
+
+182
+00:19:18,160 --> 00:19:23,100
+إن كانت ال g abelian بقدر أبدل ال a مكان ال b
+
+183
+00:19:23,100 --> 00:19:28,220
+وبالتالي يطلع عند ال a b to the power n يساوي a n
+
+184
+00:19:28,220 --> 00:19:35,950
+b nيبقى دي ربالق اه لو قلتلك a زائد b لكل تربية مش
+
+185
+00:19:35,950 --> 00:19:39,610
+هتقول اه تربية زائد اتنين a b زائد b تربية هذا
+
+186
+00:19:39,610 --> 00:19:44,490
+الكلام غلط a تربية او زائد b تربية صح بس مش اتنين
+
+187
+00:19:44,490 --> 00:19:50,830
+a b يبقى زائد a b زائد b a يعني بهذا الشكل هذا لما
+
+188
+00:19:50,830 --> 00:19:56,770
+اقولك a زائد b لكل تربية لو حبيت اشوفهم هذول في ال
+
+189
+00:19:56,770 --> 00:20:02,110
+group شو شكلهميبقى باجي بقولك هذا a تربية مظبوط و
+
+190
+00:20:02,110 --> 00:20:09,990
+هذا زائد a b و هذا زائد b a و هذا زائد b تربية هيك
+
+191
+00:20:09,990 --> 00:20:14,690
+صح لكن تقوللي a تربية زائد اتنين a b زائد b تربية
+
+192
+00:20:14,690 --> 00:20:19,010
+هذا كلام غلط إلا إذا كانت أبيلا غير هيك يبعتلك
+
+193
+00:20:19,010 --> 00:20:24,580
+الله يبقى دير بالك من الشغل هذهطيب النقطة الثامنة
+
+194
+00:20:24,580 --> 00:20:30,020
+والاخيرة لو كانت العملية ال binary operation معرفة
+
+195
+00:20:30,020 --> 00:20:36,120
+على ال group G هي عملية الجامع يبقى ال G inverse
+
+196
+00:20:36,120 --> 00:20:42,380
+في هذه الحالة هيكون هو سالب G يبقى معكوس ال G هو
+
+197
+00:20:42,380 --> 00:20:47,600
+سالب G that is ال G inverse هي سالب Gوفي هذه
+
+198
+00:20:47,600 --> 00:20:55,100
+الحالة اقول جي انفرس اوس تكييب يعني ايش؟ يعني سالب
+
+199
+00:20:55,100 --> 00:21:01,480
+جي الكل تكييب وهذه تعتبر سالب تلاتة جي لان عند
+
+200
+00:21:01,480 --> 00:21:06,080
+الجامعة بدي اقول سالب جي سالب جي سالب جي بيبقى
+
+201
+00:21:06,080 --> 00:21:13,530
+سالب تلاتة جيوكأنه بيضرب الأسس في بعضها وبنزله تحت
+
+202
+00:21:13,530 --> 00:21:18,110
+بالشكل اللي عنده هذا بيطلع الكلام مائة بالمائة طيب
+
+203
+00:21:18,110 --> 00:21:22,650
+ورسو لو بده أقول جي تكيبه العملية عملية الجامعة
+
+204
+00:21:22,650 --> 00:21:28,750
+يبقى بده أقول جي زائد جي زائد جي وليس تضرب يبقى
+
+205
+00:21:28,750 --> 00:21:33,670
+هذه كلها تساوي من تساوي تلاتة جي يبقى إذا العملية
+
+206
+00:21:33,670 --> 00:21:39,080
+على ال group G هي عملية الجامعة العاديةيبقى جي
+
+207
+00:21:39,080 --> 00:21:44,420
+تكيب هي عبارة عن تلاتة جي جي أس عشرة تعني عشرة جي
+
+208
+00:21:44,420 --> 00:21:50,620
+جي أس ناقص تمانية تعني ناقص تمانية جي and so on و
+
+209
+00:21:50,620 --> 00:21:59,680
+هكذا طيب في الأن بدنا نيجي للنقطة الخامسة if ال a
+
+210
+00:21:59,680 --> 00:22:07,020
+نقطة الخامسة if ال a and ال b belong
+
+211
+00:22:14,690 --> 00:22:24,890
+بالنسبة للمجموع جي ثم اي بي الكل انفرس بدي يسوي بي
+
+212
+00:22:24,890 --> 00:22:37,030
+انفرس اي انفرس خلي
+
+213
+00:22:37,030 --> 00:22:43,070
+بالك هنالأ لو في عنصرين في قلوبه وضربتهم في بعضه
+
+214
+00:22:43,070 --> 00:22:48,230
+بدي أجيب المعكوس تبعهم يبقى المعكوس بقول A B كل
+
+215
+00:22:48,230 --> 00:22:54,110
+inverse عمليا بقدر أقول هذا B inverse A inverse
+
+216
+00:22:54,110 --> 00:22:58,950
+يعني كتبت ال inverse لكل واحد فيهم و جلبت الوضع
+
+217
+00:22:58,950 --> 00:23:04,990
+هروح نبره صحة هذا الكلام احنا قبل قليل أثبتنا ان
+
+218
+00:23:04,990 --> 00:23:09,140
+ال inverse elementوحيد و الله اكتر من واحد الا
+
+219
+00:23:09,140 --> 00:23:14,040
+انصار واحد هو واحد يبقى ال a بي مالوش الا معكوس
+
+220
+00:23:14,040 --> 00:23:20,180
+واحد هدف يقول انه يله جداش اتنين مدام اتنين لازم
+
+221
+00:23:20,180 --> 00:23:25,000
+اتنين يتساوى طبقا للخاصية اللي قبل قليل يبقى انا
+
+222
+00:23:25,000 --> 00:23:30,200
+لو جدرت اثبت ان ال b inverse a inverse هو معكوس ال
+
+223
+00:23:30,200 --> 00:23:32,940
+a بيبتمن المطلوب مظبوط
+
+224
+00:23:37,330 --> 00:23:46,230
+بما ان ال a و ال b موجود في ال g, we have ان حاصل
+
+225
+00:23:46,230 --> 00:23:51,570
+الضرب a,b موجود في gلماذا؟ لمشان ال binary
+
+226
+00:23:51,570 --> 00:23:56,210
+operation a to elements a star b لازم يكون موجود
+
+227
+00:23:56,210 --> 00:24:03,250
+في جي مادام موجود في جي هذا معناته there exists
+
+228
+00:24:03,250 --> 00:24:15,690
+inverse for the element a,b لازم نجيله معكوس that
+
+229
+00:24:15,690 --> 00:24:23,790
+isA B الكل inverse مش شاكب انها رمز المعكوس تبع ال
+
+230
+00:24:23,790 --> 00:24:29,730
+A B A B inverse طيب انا بده اشوف اللي كاتبهلي هذا
+
+231
+00:24:29,730 --> 00:24:34,670
+اذا ضربت في A B من اليمين و من الشمال و طلع ال
+
+232
+00:24:34,670 --> 00:24:39,250
+identity ال ماتيبقى هذا كمان inverse صح ولا لا
+
+233
+00:24:39,250 --> 00:24:48,090
+الان لو جيت و قولتلك consider خدليالـ A B في الـ B
+
+234
+00:24:48,090 --> 00:24:53,590
+inverse A inverse هشوف كده بده يعطيني هذا الان بده
+
+235
+00:24:53,590 --> 00:24:58,450
+أستخدم خاصية ال associativity يبقى هذا بده يعطيني
+
+236
+00:24:58,450 --> 00:25:05,910
+A في B في ال B inverse في ال A inverse ال B في ال
+
+237
+00:25:05,910 --> 00:25:12,210
+B inverse بيعطيني ال identity يبقى ال A في ال E في
+
+238
+00:25:12,210 --> 00:25:17,700
+ال A inverseالـ E أضرب في أي عنصر بيطلع؟ نفس
+
+239
+00:25:17,700 --> 00:25:23,320
+العنصر يبقى هذا A A inverse يبقى بده يساوي ال
+
+240
+00:25:23,320 --> 00:25:28,960
+identity E مانفعش من الشمال و بس و من اليمين لازم
+
+241
+00:25:28,960 --> 00:25:35,410
+يكون من وين؟ من الطرفينيبقى باجي بقوله and ال b
+
+242
+00:25:35,410 --> 00:25:42,670
+inverse a inverse في ال a b بده يساوي b inverse في
+
+243
+00:25:42,670 --> 00:25:50,410
+ال a inverse a في ال a inverse a في من؟ في ال b
+
+244
+00:25:50,410 --> 00:25:56,190
+طيب هذا العنصر و معكوسه بيعطيني من؟ ال identity
+
+245
+00:25:56,190 --> 00:26:02,420
+elementيبقى هذا بدي يعطينا P inverse AB اللي هو
+
+246
+00:26:02,420 --> 00:26:07,200
+بدي يعطينا P inverse P بدي يعطينا من ال identity
+
+247
+00:26:07,200 --> 00:26:12,400
+element بناء عليه هذا ال element P inverse A
+
+248
+00:26:12,400 --> 00:26:18,840
+inverse حقق ليه خاصية معكوس العنصر AB يبقى من
+
+249
+00:26:18,840 --> 00:26:25,940
+الاتنين هدول مع بعضبقدر اقول هذا بده يعطيني ان b
+
+250
+00:26:25,940 --> 00:26:37,140
+inverse a inverse is the inverse element of a,b
+
+251
+00:26:37,140 --> 00:26:41,800
+يبجى هذا العنصر هو معكوس ال a,b لكن احنا عندنا
+
+252
+00:26:41,800 --> 00:26:46,900
+معكوس ال a,b مين هو اللي فاج يبجى دول اتنين معاهم
+
+253
+00:26:47,490 --> 00:26:55,110
+لازم يتساوى فبجي بقوله since بما أن the inverse
+
+254
+00:26:55,110 --> 00:27:05,950
+element of a group G is unique
+
+255
+00:27:13,670 --> 00:27:20,850
+إن ال A بي الكل inverse يساوي B inverse A inverse
+
+256
+00:27:20,850 --> 00:27:24,010
+اللي
+
+257
+00:27:24,010 --> 00:27:28,830
+خاضر أسالكوا هذا السؤال و أشوف إيش رأيكوا فيه طيب
+
+258
+00:27:28,830 --> 00:27:36,510
+يا شباب انا لو بدي A B C كل inverse ايش بده يساوي
+
+259
+00:27:40,480 --> 00:27:44,280
+C inverse B inverse A inverse يعني يبقى شكل من
+
+260
+00:27:44,280 --> 00:27:51,260
+الآخر للأول يبقى هذا الكلام بدي يعطيني C inverse و
+
+261
+00:27:51,260 --> 00:27:56,600
+هنا B inverse و هنا A inverse تلاتة أربعة عشان
+
+262
+00:27:56,600 --> 00:28:01,440
+الله يكونوا مية بدك تبدأ من الآخر و ترجع رجوع يبقى
+
+263
+00:28:01,440 --> 00:28:09,060
+هذا هو المعكوس لمن؟ للعنفر اللي عندناالان في سؤال
+
+264
+00:28:09,060 --> 00:28:15,840
+في الكتاب سؤال تمانتاش برضه بدي اعتبره خاصية مهمة
+
+265
+00:28:15,840 --> 00:28:22,540
+جدا بتلزمنا أثناء الشغل سؤال تمانتاش بيقول لي if G
+
+266
+00:28:22,540 --> 00:28:31,610
+is a group لو كانت ال G group thenالـ A Inverse
+
+267
+00:28:31,610 --> 00:28:39,910
+Inverse بده يساوي A itself هذا الكلام صحيح لكل ال
+
+268
+00:28:39,910 --> 00:28:42,390
+A الموجود في ال group G
+
+269
+00:29:05,530 --> 00:29:11,690
+خلّيني أقول له في ال group G معكوس المعكوس بيعطينا
+
+270
+00:29:11,690 --> 00:29:17,730
+الأصل A inverse انفرس بيعطينا A قبل ما توجد A
+
+271
+00:29:17,730 --> 00:29:23,630
+المعكوس تبعه يبقى من الأن فصاعدا معكوس معكوس ال
+
+272
+00:29:23,630 --> 00:29:28,130
+element بيرجعني لل element itself بدنا نروح نثبت
+
+273
+00:29:28,130 --> 00:29:32,090
+صحة هذا الكلام يبقى باجي بقوله ل ال professor
+
+274
+00:29:38,960 --> 00:29:49,840
+لت ال a موجود في ال group g then a inverse موجود
+
+275
+00:29:49,840 --> 00:29:57,830
+في gمعكوسه موجود في جيه كمان معكوس هذا لازم يكون
+
+276
+00:29:57,830 --> 00:30:06,150
+موجود في جيه صحيح يبقى then and a inverse inverse
+
+277
+00:30:06,150 --> 00:30:12,530
+موجود في جيه ليش لأنه إذا وجد عنصر في ال group
+
+278
+00:30:12,530 --> 00:30:17,610
+لازم يكون معكوسه موجود شو معكوسه اللي هو a inverse
+
+279
+00:30:17,610 --> 00:30:25,060
+inverse طيب مدام هيكلو جيت أخدت ال a inverse
+
+280
+00:30:25,060 --> 00:30:33,820
+inverse inverse مش هذا العنصر و هذا معكوسه حاصل
+
+281
+00:30:33,820 --> 00:30:40,860
+ضربه ما شو بده يطيني ال identity element طيب إيش
+
+282
+00:30:40,860 --> 00:30:47,440
+رأيك لو روحت ضربت من جهة الشمال بالعنصر a اتصلت من
+
+283
+00:30:47,440 --> 00:30:54,760
+جهة الشمال هاهدر بالكيبقى هذا الـ A مضروب في الـ A
+
+284
+00:30:54,760 --> 00:31:02,060
+inverse في الـ A inverse inverse يبقى هذا الـ A
+
+285
+00:31:02,060 --> 00:31:03,360
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+286
+00:31:03,360 --> 00:31:04,500
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+287
+00:31:04,500 --> 00:31:06,880
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+288
+00:31:06,880 --> 00:31:11,880
+مضروب في الـ A inverse inverse يبقى
+
+289
+00:31:11,880 --> 00:31:15,540
+هذا الـ A مضروب في الـ A inverse inverse يبقى هذا
+
+290
+00:31:15,540 --> 00:31:15,540
+الـ A مضروب في الـ A inverse inverse يبقى هذا الـ
+
+291
+00:31:15,540 --> 00:31:15,540
+A مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+292
+00:31:15,540 --> 00:31:15,540
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+293
+00:31:15,540 --> 00:31:15,540
+مضروب في الـ A inverse inverse inverse يبقى هذا
+
+294
+00:31:15,540 --> 00:31:15,540
+الـ A مضروب في الـ A مضروب في الـ A inverse
+
+295
+00:31:15,540 --> 00:31:15,540
+inverse inverse يبقى هذا الـ A مضرو
+
+296
+00:31:26,790 --> 00:31:33,030
+العنصر في المعكوس يعطينا ال identity element يبقى
+
+297
+00:31:33,030 --> 00:31:38,970
+هذا يعطينا ان ال E في A inverse inverse
+
+298
+00:31:41,540 --> 00:31:45,380
+الـ identity element لما نقضبه في أي عنصر بيطلع
+
+299
+00:31:45,380 --> 00:31:51,460
+نفس العنصر يبقى بناء عليه a inverse inverse بده
+
+300
+00:31:51,460 --> 00:31:57,240
+يساوي ال a itself عزيزي و هو المطلوب؟ طيب و هو
+
+301
+00:31:57,240 --> 00:32:02,360
+المطلوب و كنتها هذا ال section و إليكم ال
+
+302
+00:32:02,360 --> 00:32:10,730
+exercises بدنا ياكم تمرني أديكم بسؤال خمسة و ستةو
+
+303
+00:32:10,730 --> 00:32:21,230
+تمانية و عشرة و اتناش و سبعتاش و تسعتاش و اربعة و
+
+304
+00:32:21,230 --> 00:32:30,690
+عشرين و خمسة و عشرين و ستة و عشرين و تلاتة و
+
+305
+00:32:30,690 --> 00:32:39,050
+تلاتين و تلاتة و تلاتين و خمسة و تلاتين و تسعة و
+
+306
+00:32:39,050 --> 00:32:39,730
+تلاتين
+
+307
+00:32:44,920 --> 00:32:49,500
+هذا لا يعني ان بقى الناس مشطوبة لا مش مشطوبة اذا
+
+308
+00:32:49,500 --> 00:32:54,500
+بتحل هدوله كمان جدهم بيكونوا كويس مش غلط لكن انا
+
+309
+00:32:54,500 --> 00:32:59,720
+بهمني هدول انتقنهم انتقان بحيث يغطوا فكرة كثيرة
+
+310
+00:32:59,720 --> 00:33:05,780
+موجودة في التمرين ولذلك هدول من اهم المسائل اللي
+
+311
+00:33:05,780 --> 00:33:10,440
+موجودة في التمرين لعل يكون فيها فكرة جديدة نحاول
+
+312
+00:33:10,440 --> 00:33:15,190
+نستفيد هذه الفكرةطبعا عندكم محاضرة اليوم الاطناشر
+
+313
+00:33:15,190 --> 00:33:20,270
+الواحدة مش حاجة حل الأسئلة لأ حابد محاضرة جديدة
+
+314
+00:33:20,270 --> 00:33:24,710
+لكن الأسئلة ليوم ايش؟ ليوم الإثنين مش هتروح تحل
+
+315
+00:33:24,710 --> 00:33:29,690
+عليك مش هنحل و أنت تنسخ ولا عمرك بتستفيد حاجة بدك
+
+316
+00:33:29,690 --> 00:33:34,510
+تفكر من هنا لبعد بكرة في حل هذه المسألة و تحول تحل
+
+317
+00:33:34,510 --> 00:33:38,430
+بقدر الإمكان و اللي يصعب عليك بعد بكرة ان شاء الله
+
+318
+00:33:38,430 --> 00:33:43,610
+بنحله مهما كان شكل هذا السؤالواضح كلام ايه؟ يعني
+
+319
+00:33:43,610 --> 00:33:47,970
+بديك بعض المكره تيجي جاهز نفسك للنقاش، هيكون في
+
+320
+00:33:47,970 --> 00:33:51,950
+نقاش كتير حسب اللي يمكن اللي يسألكوا كلكوا أو تلت
+
+321
+00:33:51,950 --> 00:33:56,330
+رباعكوا أو نصكوا حسب ما الوقت اللي ايه المتاحيعني
+
+322
+00:33:56,330 --> 00:34:00,050
+كل وحدة انت تتوجهلك السؤال ايش رأيك في السؤال لوين
+
+323
+00:34:00,050 --> 00:34:04,970
+وصلت فيه ايش حلت ايش كده الى اخرين هيك بيصير مخك
+
+324
+00:34:04,970 --> 00:34:10,210
+يفهم اللي هو جبر و بتستطيع انه تمشي معانا ماحلتش
+
+325
+00:34:10,210 --> 00:34:14,250
+والله عمرك ماحتمشي هتضلك جاعد عندنا هنا على طول
+
+326
+00:34:14,250 --> 00:34:21,770
+هاي نعم يبقى الآنحاول بقدر الإمكان تحل هذه المسائل
+
+327
+00:34:21,770 --> 00:34:26,830
+أنا متأكد أنه مش هتعرف تحلهم كلهم لكن على الأقل
+
+328
+00:34:26,830 --> 00:34:32,350
+بتحل شيء كثير منهم ولذلك المناقشة حتى اللي
+
+329
+00:34:32,350 --> 00:34:38,670
+ماعرفناش نحله الروح نحله في محاضرة المناقشةطيب
+
+330
+00:34:38,670 --> 00:34:43,230
+عليكي بكون انتهينا من هذا ال chapter بدنا نروح لل
+
+331
+00:34:43,230 --> 00:34:48,010
+chapter اللي بعده اللي هو chapter تلاتة chapter
+
+332
+00:34:48,010 --> 00:34:54,690
+تلاتة يا شباب اللي هو بتحدث عن ال subgroups يعني
+
+333
+00:34:54,690 --> 00:34:59,110
+احنا كنا بنشتغل في ال groups الآن بدنا نبدأ ناخد
+
+334
+00:34:59,110 --> 00:35:12,310
+مجموعات جزئية منها يبقى chapter تلاتةفاينايت جروبز
+
+335
+00:35:12,310 --> 00:35:20,390
+فاينايت جروبز فاينايت
+
+336
+00:35:20,390 --> 00:35:21,110
+جروبز فاينايت جروبز فاينايت جروبز فاينايت جروبز
+
+337
+00:35:21,110 --> 00:35:22,930
+فاينايت جروبز فاينايت جروبز فاينايت جروبز فاينايت
+
+338
+00:35:22,930 --> 00:35:24,850
+جروبز فاينايت جروبز فاينايت جروبز فاينايت جروبز
+
+339
+00:35:24,850 --> 00:35:24,850
+فاينايت جروبز فاينايت جروبز فاينايت جروبز فاينايت
+
+340
+00:35:24,850 --> 00:35:24,850
+جروبز فاينايت جروبز فاينايت جروبز فاينايت جروبز
+
+341
+00:35:24,850 --> 00:35:26,470
+فاينايت جروبز فاينايت جروبز فاينايت جروبز فاينايت
+
+342
+00:35:26,470 --> 00:35:34,790
+جروبز فاينايت جروبجديدة قبل أن نبدأ في الـ
+
+343
+00:35:34,790 --> 00:35:40,570
+subgroups حاجة اسمة ال order لل group وال order لل
+
+344
+00:35:40,570 --> 00:35:46,090
+element اللي موجود في ال group أول شي بالبلد هيك
+
+345
+00:35:46,090 --> 00:35:50,900
+قبل ما نكتبلو أردت ال order لجروب فأذهب بعد
+
+346
+00:35:50,900 --> 00:35:56,000
+عناصرها جداش ال order لجروب هو عدد العناصر في
+
+347
+00:35:56,000 --> 00:35:59,620
+الجروب جروب فيها أربع عناصر يبقى ال order لها
+
+348
+00:35:59,620 --> 00:36:04,480
+يساوي أربعة جروب فيها عشر عناصر يبقى ال order لها
+
+349
+00:36:04,480 --> 00:36:11,770
+يساوي عشرة و هكذالكن ال order لل element اللي
+
+350
+00:36:11,770 --> 00:36:18,150
+موجود في ال group هو أصغر عدد صحيح موجب بحطه ك أسل
+
+351
+00:36:18,150 --> 00:36:21,170
+هذا ال element بيعطينا ال identity
+
+352
+00:36:26,400 --> 00:36:29,720
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+353
+00:36:29,720 --> 00:36:32,280
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+354
+00:36:32,280 --> 00:36:34,300
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+355
+00:36:34,300 --> 00:36:38,640
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+356
+00:36:38,640 --> 00:36:43,420
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+357
+00:36:43,420 --> 00:36:45,120
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+358
+00:36:45,120 --> 00:36:49,640
+أصغر عدد
+
+359
+00:36:49,640 --> 00:37:01,290
+صحيح موجبG as the number
+
+360
+00:37:01,290 --> 00:37:08,950
+of elements
+
+361
+00:37:08,950 --> 00:37:18,050
+in G which is denoted by
+
+362
+00:37:22,800 --> 00:37:29,120
+by جيه ما بين خطين و تقرأ ال order لجيه مش
+
+363
+00:37:29,120 --> 00:37:34,400
+absolute value لجيه يبقى هذا هو ال order لجيه
+
+364
+00:37:34,400 --> 00:37:39,440
+command definition تاني ال order لل element the
+
+365
+00:37:39,440 --> 00:37:53,720
+order of an element of an elementاللي موجود في G
+
+366
+00:37:53,720 --> 00:38:04,040
+is the smallest positive
+
+367
+00:38:04,040 --> 00:38:07,580
+integer
+
+368
+00:38:37,950 --> 00:38:46,780
+بنروح نكتب ال order لا جي بده يساوي ال inفي عندنا
+
+369
+00:38:46,780 --> 00:38:59,960
+بعض ال notes البسيطة أول واحدة if the operation on
+
+370
+00:38:59,960 --> 00:39:11,100
+g is addition is addition عملية الجامعة then
+
+371
+00:39:30,230 --> 00:39:38,950
+النقطة الثانية is the order of
+
+372
+00:39:38,950 --> 00:39:41,250
+identity
+
+373
+00:39:42,600 --> 00:40:00,500
+Element E is واحدة صحية مقطة تالتة if there is if
+
+374
+00:40:00,500 --> 00:40:10,380
+there is no positive integer in
+
+375
+00:40:11,810 --> 00:40:17,310
+such that الـ
+
+376
+00:40:17,310 --> 00:40:25,310
+G to the power N بده سوى ال identity then ال order
+
+377
+00:40:25,310 --> 00:40:29,270
+لجي is infinite
+
+378
+00:41:00,880 --> 00:41:05,620
+نرجع لهذه التعريفين والملاحظات اللي على التعريفين
+
+379
+00:41:05,620 --> 00:41:10,920
+مرة ثانية بقول the order of a group G is the
+
+380
+00:41:10,920 --> 00:41:16,980
+number of elements in G عدد العناصر في G واللي
+
+381
+00:41:16,980 --> 00:41:22,280
+بتدرمزله بالرمز G ما بين خطين ليست absolute value
+
+382
+00:41:22,280 --> 00:41:28,140
+ل G وإنما ال order ل Gيبقى ال order لcapital G هو
+
+383
+00:41:28,140 --> 00:41:33,360
+عدد العناصر في ال group السؤال هو هل ممكن عدد
+
+384
+00:41:33,360 --> 00:41:37,960
+العناصر يكون محدود يعني رقم و ممكن يكون كذلك
+
+385
+00:41:37,960 --> 00:41:43,760
+infinity ممكن اتنين وردات يعني ال group قد تنتهي
+
+386
+00:41:43,760 --> 00:41:48,700
+وبالتالي عدد العناصر يكون finiteوقد لا تنتهي
+
+387
+00:41:48,700 --> 00:41:54,340
+وبالتالي هذا العناصر in finite زي ال R star اللي
+
+388
+00:41:54,340 --> 00:41:57,760
+هي set of real numbers لما أشيل منها zero تحت
+
+389
+00:41:57,760 --> 00:42:01,680
+عملية الضرب أكم أنصر فيها دي group طبعا أكم أنصر
+
+390
+00:42:01,680 --> 00:42:06,200
+فيها مالا نهاية من العناصر إذا من ال order لل
+
+391
+00:42:06,200 --> 00:42:11,430
+group G في هذه الحالة بيكون in finite لكنلو روحت ل
+
+392
+00:42:11,430 --> 00:42:17,110
+ZN و لا UN و لا كل الأمثلة اللي أخدناهم هذه بيصير
+
+393
+00:42:17,110 --> 00:42:21,630
+مالة finite أربع عناصر ستة عناصر عشرين عنصر حسب
+
+394
+00:42:21,630 --> 00:42:27,110
+قيمة N طيب تعريف التانيبقول ال order of an element
+
+395
+00:42:27,110 --> 00:42:31,850
+g اللي موجود في g is the smallest positive integer
+
+396
+00:42:31,850 --> 00:42:37,870
+in such that ال g n بده يساوي ايه وحدله نفس الرمز
+
+397
+00:42:37,870 --> 00:42:41,750
+ال order لل element g بده يساوي مين؟ بده يساوي ال
+
+398
+00:42:41,750 --> 00:42:46,770
+n استنى شويةطيب انا افترض بقدر اللائك باش كباش
+
+399
+00:42:46,770 --> 00:42:52,290
+تعنصر من ال group مين ما كان يسميته ايه؟ رفعتله أس
+
+400
+00:42:52,290 --> 00:42:57,850
+عشرين لجيته ال identity element إذا ال order لإيه
+
+401
+00:42:57,850 --> 00:43:05,060
+يساوي عشرين؟قد يكون وقد لا يكون كيف قد يكون؟ احنا
+
+402
+00:43:05,060 --> 00:43:08,600
+قلين the smallest positive integer يمكن في رقم تحت
+
+403
+00:43:08,600 --> 00:43:13,320
+العشرين زي عشرة يكون A أُس عشرة يسوى ال identity
+
+404
+00:43:13,320 --> 00:43:17,600
+فإن كان A أُس عشرة يسوى ال identity إذا A أُس
+
+405
+00:43:17,600 --> 00:43:20,720
+عشرين يسوى ال identity A أُس تلاتين يسوى ال
+
+406
+00:43:20,720 --> 00:43:26,800
+identity A أُس خمسين يبقى أصغر رقم إن بحطه كأس
+
+407
+00:43:26,800 --> 00:43:30,990
+لهذا ال element بده يعطيه ال identityان حدث ذلك
+
+408
+00:43:30,990 --> 00:43:35,150
+يبقى هذا الاص هو ال order تبع من؟ تبع هذا ال
+
+409
+00:43:35,150 --> 00:43:39,190
+element يبقى لو قال show that the element of this
+
+410
+00:43:39,190 --> 00:43:45,410
+element is كزواطن رقم تمام احط اص لهذا الرقم يطلع
+
+411
+00:43:45,410 --> 00:43:50,040
+ال identity ماقدرش اقولهذا هو ال order يا ال order
+
+412
+00:43:50,040 --> 00:43:55,380
+يا أقل منه إذا بدأ أستبعد اللي أقل منه يبقى إجباري
+
+413
+00:43:55,380 --> 00:43:59,080
+بيصير هذا ياش هذا هو ال order و هنشوف هذا الكلام
+
+414
+00:43:59,080 --> 00:44:05,000
+من خلال المسائل يبقى بديك تعرف أن ال order لهذا ال
+
+415
+00:44:05,000 --> 00:44:11,040
+element أقل عدد صحيح موجب بحط أس لهذا ال element
+
+416
+00:44:11,040 --> 00:44:15,490
+بتنميةالـ Identity اللى جيت غيره ماليش علاقة فيهم
+
+417
+00:44:15,490 --> 00:44:21,630
+و قدام شوية هنقول لك ان ال order هذا بيقسم اي رقم
+
+418
+00:44:21,630 --> 00:44:25,490
+تاني يحطه كاسئوله و يعطينا ال identity ما علينا
+
+419
+00:44:25,490 --> 00:44:29,870
+لسه بعيد عننا شوية يبقى باجي بقول ال order لل
+
+420
+00:44:29,870 --> 00:44:36,290
+element U هو اصغر smallest و positive integer in
+
+421
+00:44:36,290 --> 00:44:40,290
+such that g to the power n بده يساوي ال ايه و حدله
+
+422
+00:44:40,290 --> 00:44:46,630
+الرمزجي بين خطين وقول الرمز هذا يقرأ ال order لجي
+
+423
+00:44:46,630 --> 00:44:50,690
+وليس ال absolute value لجي absolute للكل كلاص مش
+
+424
+00:44:50,690 --> 00:44:54,930
+للجبر يبقى هنا بنقول اه بنقول ال order لجي يساوي
+
+425
+00:44:54,930 --> 00:45:00,230
+مين؟ يساوي ال n طيب ممكن ل group زي ما شوفنا في
+
+426
+00:45:00,230 --> 00:45:05,160
+الأمثل على group تبقى العملية عملية جامعةطب لو
+
+427
+00:45:05,160 --> 00:45:10,780
+كانت عملية جمع إيش بصير شكل هذا ال element يبقى لو
+
+428
+00:45:10,780 --> 00:45:14,520
+كانت ال operation على G هو الجمع إذا ال element
+
+429
+00:45:14,520 --> 00:45:19,320
+هذا بيصير in G يساوي ال identity element تحت عملية
+
+430
+00:45:19,320 --> 00:45:23,140
+الجمع اللي هو main اللي هو ال zero يبقى ال G to
+
+431
+00:45:23,140 --> 00:45:26,840
+the power in يساوي ال identity بترجم إلى in G
+
+432
+00:45:26,840 --> 00:45:31,480
+يساوي main ال zero بشرط تبقى العملية المعرفة على
+
+433
+00:45:31,480 --> 00:45:36,980
+ال groupهي عملية الجامعة العادية طيب بداج ال
+
+434
+00:45:36,980 --> 00:45:41,900
+identity element ايه بدى اعرف قداش ال order اصغر
+
+435
+00:45:41,900 --> 00:45:46,220
+رقم بحطه لل ايه بطلع ال ايه مين واحد يساوي ايه
+
+436
+00:45:46,220 --> 00:45:50,880
+واحد يساوي مين واحد اذا ال order لأي identity
+
+437
+00:45:50,880 --> 00:45:53,600
+element مهما كان شكل ال group
+
+438
+00:46:11,020 --> 00:46:19,800
+لو لم أجد عدد صحيح فأضعه كأسلجي يعطينا ال identity
+
+439
+00:46:19,800 --> 00:46:25,040
+elementيقول جي أس مية ما طلعش ال identity element
+
+440
+00:46:25,040 --> 00:46:29,100
+يقول جي أس مليون ما طلعش ال identity كل ما يجي
+
+441
+00:46:29,100 --> 00:46:32,740
+ذالي رقم ما يطلعش ال identity element يبقى في هذه
+
+442
+00:46:32,740 --> 00:46:37,820
+الحالة ال order لجي قدش بيكون على نهاية يبقى باجي
+
+443
+00:46:37,820 --> 00:46:42,880
+بقول ال element هذا is of infinite orderيبقى ال
+
+444
+00:46:42,880 --> 00:46:48,820
+order لهذا ال element بيكون infinite وقد تستغربوا
+
+445
+00:46:48,820 --> 00:46:53,000
+انه ممكن يكون و احنا بنشتغل هيك في ال groups
+
+446
+00:46:53,000 --> 00:46:57,720
+element اخده في ال group ال order له finite اتنين
+
+447
+00:46:57,720 --> 00:47:01,520
+تلاتة عشرة جد ما يكونوا element تاني ال order له
+
+448
+00:47:01,520 --> 00:47:07,120
+finite اضرب اتنين في بعض يطلع ال order infinite
+
+449
+00:47:09,630 --> 00:47:13,130
+طبعا انت مش تغربين لكن هنعطيكوا مثال ان شاء الله
+
+450
+00:47:13,130 --> 00:47:16,830
+نوضح فيه هذا الكلام يعني ان كان ال order لل
+
+451
+00:47:16,830 --> 00:47:21,470
+element finite و ال order التاني finite لو ضربت
+
+452
+00:47:21,470 --> 00:47:25,030
+اتنين في بعض بال operation start طلع element جديد
+
+453
+00:47:25,030 --> 00:47:29,910
+ال element جديد ليس بضرورة ان يكون finite و ربما
+
+454
+00:47:29,910 --> 00:47:36,270
+infinite و خاصة في موضوع المصفوفات طيب نبدأ ناخد
+
+455
+00:47:36,270 --> 00:47:42,220
+بعض الأمثلة على هذه التعريفمشان يثبت هذه المعلومات
+
+456
+00:47:42,220 --> 00:47:50,340
+ولو على الأقل مثالا واحدا يبقى examples أول مثال
+
+457
+00:47:50,340 --> 00:47:59,440
+بيقول ال let ال G يساوي U خمستاشر يبقى بدنا عناصر
+
+458
+00:47:59,440 --> 00:48:05,120
+ال U خمستاشر شبه مين ال واحد والاتنين تلاتة منهم
+
+459
+00:48:05,960 --> 00:48:16,160
+الاربعة الخمسة الستة السبعة التمانية التسعة العشرة
+
+460
+00:48:16,160 --> 00:48:25,120
+الاحداشر اتناش تلاتاش وكمان اربعتاش يبقى هاي
+
+461
+00:48:25,120 --> 00:48:32,240
+كتبتله ال U خمستاش طيب بناء عليه ال order ل U
+
+462
+00:48:32,240 --> 00:48:38,520
+خمستاش انا بقول خمستاش ولا لألأ، وش جاب الخمسة؟ عد
+
+463
+00:48:38,520 --> 00:48:41,640
+العناصر واحد، اتنين، تلاتة، اربعة، خمسة، ستة،
+
+464
+00:48:41,640 --> 00:48:46,220
+سبعة، تمانية يبقى ال order اللي أجيبه يسوى تمانية
+
+465
+00:48:46,220 --> 00:48:53,560
+طيب، لو بد أجيب ال order للواحد كدهش؟
+
+466
+00:48:53,560 --> 00:48:57,500
+واحد، لأن هذا هو ال identity element يبقى ال order
+
+467
+00:48:57,500 --> 00:49:03,630
+للواحد يسوى واحد طب، بد ال order لليتنين؟شوف عاد
+
+468
+00:49:03,630 --> 00:49:07,570
+نضرب اتنين في نفسه كام مرة حتى يطلع عندى ال
+
+469
+00:49:07,570 --> 00:49:11,230
+identity element طبعا هنا عملية ضرب العادية اتنين
+
+470
+00:49:11,230 --> 00:49:19,370
+في اتنين في اتنين اساس ميارات في اتنين تمانية في
+
+471
+00:49:19,370 --> 00:49:24,070
+اتنين ستة عشر شيله هنا و خمسة عشر بضل اللي يقولوا
+
+472
+00:49:24,070 --> 00:49:29,400
+حد يبقى ال order اللي جديشأربعة يبقى ال order للي
+
+473
+00:49:29,400 --> 00:49:36,220
+اتنين يساوي اربعة because شو السبب انه اتنين اص
+
+474
+00:49:36,220 --> 00:49:42,660
+واحد يساوي اتنين اتنين تربية يساوي اتنين
+
+475
+00:49:42,660 --> 00:49:49,020
+تكيب يساوي تمانية اتنين اص اربعة يساوي ستاشر
+
+476
+00:49:49,020 --> 00:49:55,150
+modulo خمستاشر يبقى هذا الكلام يساوي واحدهذا بدي
+
+477
+00:49:55,150 --> 00:50:00,770
+اعطيك ان ال order للي اتنين هو اربعة طب ال order
+
+478
+00:50:00,770 --> 00:50:08,110
+لاربعة similarly ال order لاربعة بده يساوي اتنين
+
+479
+00:50:08,110 --> 00:50:13,750
+ليش لإنه اربعة في اربعة ستاشر موديله خمس تاشر اين
+
+480
+00:50:13,750 --> 00:50:17,870
+عم يبقى باتنين طيب لو روحتي و قولتلك ال order لي
+
+481
+00:50:17,870 --> 00:50:27,030
+سبعة بدنا نعرف في هذا كدهيبقى بالضبط سبعة اوس واحد
+
+482
+00:50:27,030 --> 00:50:30,290
+يساوي
+
+483
+00:50:30,290 --> 00:50:36,770
+سبعة هو سبعة تربيع يساوي تسعة واربعين موديولو
+
+484
+00:50:36,770 --> 00:50:43,200
+خمستاش خمستاش في تلاتة وخمسة واربعين يطلع أربعةطيب
+
+485
+00:50:43,200 --> 00:50:50,160
+لو جيت قولتلك سبعة تكيب يبقى يساوي سبعة مضروبة في
+
+486
+00:50:50,160 --> 00:50:55,770
+أربعة modulo خمستاشر أربعة في سبعةتمنية وعشرين
+
+487
+00:50:55,770 --> 00:50:57,190
+تمنية وعشرين تمنية وعشرين تمنية وعشرين تمنية
+
+488
+00:50:57,190 --> 00:51:01,690
+وعشرين تمنية وعشرين تمنية وعشرين تمنية تمنية تمنية
+
+489
+00:51:01,690 --> 00:51:06,870
+تمنية تمنية
+
+490
+00:51:06,870 --> 00:51:10,250
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+491
+00:51:10,250 --> 00:51:10,250
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+492
+00:51:10,250 --> 00:51:10,430
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+493
+00:51:10,430 --> 00:51:11,310
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+494
+00:51:11,310 --> 00:51:11,770
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+495
+00:51:11,770 --> 00:51:14,370
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+496
+00:51:14,370 --> 00:51:21,670
+تمنية تمنية تمنية تيبقى بناء عليه ان ال order ل
+
+497
+00:51:21,670 --> 00:51:28,430
+سبعة بده يساوي قداش بده يساوي أربعة و هكذا طيب
+
+498
+00:51:28,430 --> 00:51:35,250
+التمانية تمانية في تمانية أربعة و ستين شيل الستين
+
+499
+00:51:35,250 --> 00:51:39,810
+لأنه مضاعف لخمساش تظل أربعة في تمانية باتنين و
+
+500
+00:51:39,810 --> 00:51:45,130
+تلاتين شيل تلاتين بظل اتنين في تمانية بستعش يبقى
+
+501
+00:51:45,130 --> 00:51:51,460
+ال order ل تمانية بقداش أربعةيبقى similarly كمان
+
+502
+00:51:51,460 --> 00:52:00,140
+ال order ل 8 بده يسوى كذلك 4 و هكذا طب خلينا نسأل
+
+503
+00:52:00,140 --> 00:52:06,740
+ال order ل 11 11
+
+504
+00:52:06,740 --> 00:52:14,040
+و 11 121 121 مش بتكسبها 15 لأنها بتكسبها 30 و 30
+
+505
+00:52:14,040 --> 00:52:20,250
+يبقىيبقى واحد يبقى ال order للإحداش هو اتنين و ال
+
+506
+00:52:20,250 --> 00:52:27,710
+order للإحداش بده يساوي اتنين فقط و هكذا يلا بنكمل
+
+507
+00:52:27,710 --> 00:52:29,070
+ان شاء الله بعد الظهر
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..64a2f3b9e1569e060257cbbf025d28a0cd140614
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4731, "start": 21.21, "end": 47.31, "text": "بسم الله الرحمن الرحيم نكمل ما ابتدأناه في المحاضرة السابقة عرفنا ال isomorphism أخدنا عليه خمسة أمثلة في الفترة الصبحية الآن بدنا نيجي لأول نظرية هذه النظرية نظرية كيلي تنص على ما يتيح أن أي group تبقى isomorphic to a group of permutations", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 6225, 28480, 8315, 2423, 307, 32702, 1434, 5551, 9778, 3215, 8315, 47356, 16490, 2304, 3794, 3660, 5551, 2304, 12984, 37977, 8978, 27188, 2655, 25720, 31767, 49628, 10632, 6024, 48506, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 10721, 12610, 8717, 19913, 2288, 10632, 29538, 28239, 19913, 2288, 10632, 8717, 19913, 2288, 10632, 9122, 1829, 20292, 6055, 1863, 9381, 15844, 19446, 7251, 31371, 5016, 14739, 36632, 1594, 6055, 3555, 4587, 7578, 307, 32702, 299, 281, 257, 1594, 295, 4784, 325, 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0.927001953125}, {"start": 35.53, "end": 36.03, "word": " لأول", "probability": 0.9261067708333334}, {"start": 36.03, "end": 36.61, "word": " نظرية", "probability": 0.988037109375}, {"start": 36.61, "end": 36.97, "word": " هذه", "probability": 0.79541015625}, {"start": 36.97, "end": 37.63, "word": " النظرية", "probability": 0.88427734375}, {"start": 37.63, "end": 38.59, "word": " نظرية", "probability": 0.957275390625}, {"start": 38.59, "end": 39.25, "word": " كيلي", "probability": 0.5183919270833334}, {"start": 39.25, "end": 39.85, "word": " تنص", "probability": 0.8870442708333334}, {"start": 39.85, "end": 40.13, "word": " على", "probability": 0.89599609375}, {"start": 40.13, "end": 40.45, "word": " ما", "probability": 0.80029296875}, {"start": 40.45, "end": 41.15, "word": " يتيح", "probability": 0.6291097005208334}, {"start": 41.15, "end": 41.61, "word": " أن", "probability": 0.341064453125}, {"start": 41.61, "end": 42.15, "word": " أي", "probability": 0.7666015625}, {"start": 42.15, 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"end": 63.21, "word": " permutation", "probability": 0.974853515625}, {"start": 63.21, "end": 63.89, "word": " مش", "probability": 0.79638671875}, {"start": 63.89, "end": 64.25, "word": " مبين", "probability": 0.9440104166666666}, {"start": 64.25, "end": 64.53, "word": " عندي", "probability": 0.957763671875}, {"start": 64.53, "end": 64.71, "word": " ولا", "probability": 0.919921875}, {"start": 64.71, "end": 65.09, "word": " عاجز", "probability": 0.779296875}, {"start": 65.09, "end": 66.17, "word": " لذلك", "probability": 0.9305013020833334}, {"start": 66.17, "end": 66.89, "word": " بدنا", "probability": 0.8408203125}, {"start": 66.89, "end": 67.29, "word": " نبدأ", "probability": 0.9033203125}, {"start": 67.29, "end": 67.89, "word": " البرهان", "probability": 0.8642578125}, {"start": 67.89, "end": 68.69, "word": " كالتالي", "probability": 0.86533203125}, {"start": 68.69, "end": 69.55, "word": " فبجي", "probability": 0.74822998046875}, {"start": 69.55, "end": 70.09, "word": " بقول", "probability": 0.986328125}, {"start": 70.09, "end": 70.83, "word": " let", "probability": 0.70361328125}, {"start": 70.83, "end": 72.37, "word": " G", "probability": 0.564453125}, {"start": 72.37, "end": 73.43, "word": " بي", "probability": 0.648681640625}, {"start": 73.43, "end": 73.99, "word": " أ", "probability": 0.239990234375}, {"start": 73.99, "end": 74.43, "word": " grow", "probability": 0.73193359375}], "temperature": 1.0}, {"id": 3, "seek": 10397, "start": 77.89, "end": 103.97, "text": "for any g اللي موجودة فيه g define a function TG من G إلى G by TG of X بده ساوي GX", "tokens": [2994, 604, 290, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 3224, 290, 6964, 257, 2445, 314, 38, 9154, 460, 30731, 460, 538, 314, 38, 295, 1783, 47525, 3224, 8608, 995, 45865, 460, 55], "avg_logprob": -0.24678309875376084, "compression_ratio": 1.0388349514563107, "no_speech_prob": 0.0, "words": [{"start": 77.89, "end": 78.51, "word": "for", "probability": 0.64453125}, {"start": 78.51, "end": 80.41, 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"end": 96.53, "word": " G", "probability": 0.97607421875}, {"start": 96.53, "end": 97.91, "word": " by", "probability": 0.90625}, {"start": 97.91, "end": 99.99, "word": " TG", "probability": 0.935791015625}, {"start": 99.99, "end": 100.51, "word": " of", "probability": 0.890625}, {"start": 100.51, "end": 101.15, "word": " X", "probability": 0.822265625}, {"start": 101.15, "end": 102.21, "word": " بده", "probability": 0.58740234375}, {"start": 102.21, "end": 102.89, "word": " ساوي", "probability": 0.7415364583333334}, {"start": 102.89, "end": 103.97, "word": " GX", "probability": 0.697021484375}], "temperature": 1.0}, {"id": 4, "seek": 13069, "start": 104.39, "end": 130.69, "text": "لكل الـ X اللي موجود في جي يبقى أنا الأن بدي أسعى إلى أكون من ال group of permutation من ال group اللي موجودة لذلك فرط ال group اللي موجودة عند جي بدي أكون", "tokens": [1211, 28820, 2423, 39184, 1783, 13672, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 7251, 3555, 4587, 7578, 41850, 16247, 1863, 4724, 16254, 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"probability": 0.78033447265625}, {"start": 115.05, "end": 115.35, "word": " أنا", "probability": 0.4990234375}, {"start": 115.35, "end": 115.83, "word": " الأن", "probability": 0.6484375}, {"start": 115.83, "end": 116.33, "word": " بدي", "probability": 0.756591796875}, {"start": 116.33, "end": 117.39, "word": " أسعى", "probability": 0.9378662109375}, {"start": 117.39, "end": 117.97, "word": " إلى", "probability": 0.4443359375}, {"start": 117.97, "end": 118.77, "word": " أكون", "probability": 0.784912109375}, {"start": 118.77, "end": 119.25, "word": " من", "probability": 0.93896484375}, {"start": 119.25, "end": 120.07, "word": " ال", "probability": 0.71044921875}, {"start": 120.07, "end": 120.57, "word": " group", "probability": 0.79052734375}, {"start": 120.57, "end": 121.03, "word": " of", "probability": 0.90185546875}, {"start": 121.03, "end": 122.07, "word": " permutation", "probability": 0.9638671875}, {"start": 122.07, "end": 123.01, "word": " من", "probability": 0.97216796875}, {"start": 123.01, "end": 123.19, "word": " ال", "probability": 0.677734375}, {"start": 123.19, "end": 123.47, "word": " group", "probability": 0.96142578125}, {"start": 123.47, "end": 123.73, "word": " اللي", "probability": 0.967529296875}, {"start": 123.73, "end": 124.43, "word": " موجودة", "probability": 0.98583984375}, {"start": 124.43, "end": 125.75, "word": " لذلك", "probability": 0.9650065104166666}, {"start": 125.75, "end": 126.21, "word": " فرط", "probability": 0.8736979166666666}, {"start": 126.21, "end": 126.39, "word": " ال", "probability": 0.78271484375}, {"start": 126.39, "end": 126.67, "word": " group", "probability": 0.98583984375}, {"start": 126.67, "end": 126.91, "word": " اللي", "probability": 0.98779296875}, {"start": 126.91, "end": 127.59, "word": " موجودة", "probability": 0.9442138671875}, {"start": 127.59, "end": 127.95, "word": " عند", "probability": 0.9326171875}, {"start": 127.95, "end": 128.61, "word": " جي", "probability": 0.836669921875}, {"start": 128.61, 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يجب", "probability": 0.7449544270833334}, {"start": 149.22, "end": 149.22, "word": " أن", "probability": 0.8740234375}, {"start": 149.22, "end": 149.68, "word": " أعرفها", "probability": 0.861328125}, {"start": 149.68, "end": 150.32, "word": " كالتالي", "probability": 0.969140625}, {"start": 150.32, "end": 151.24, "word": " تجي", "probability": 0.9251302083333334}, {"start": 151.24, "end": 151.5, "word": " of", "probability": 0.5126953125}, {"start": 151.5, "end": 151.8, "word": " x", "probability": 0.55712890625}, {"start": 151.8, "end": 152.52, "word": " يساوي", "probability": 0.68951416015625}, {"start": 152.52, "end": 153.0, "word": " جي", "probability": 0.862060546875}, {"start": 153.0, "end": 153.24, "word": " of", "probability": 0.97607421875}, {"start": 153.24, "end": 153.54, "word": " x", "probability": 0.98046875}, {"start": 153.54, "end": 154.14, "word": " لكل", "probability": 0.927978515625}, {"start": 154.14, "end": 154.34, "word": " ال", "probability": 0.734375}, {"start": 154.34, "end": 154.64, "word": " x", "probability": 0.489501953125}, {"start": 154.64, "end": 155.28, "word": " الموجود", "probability": 0.8587239583333334}, {"start": 155.28, "end": 155.44, "word": " في", "probability": 0.95556640625}, {"start": 155.44, "end": 155.72, "word": " جي", "probability": 0.877197265625}], "temperature": 1.0}, {"id": 6, "seek": 18273, "start": 155.97, "end": 182.73, "text": "السؤال هو هل هذا التعريف صحيح ولا غير صحيح الإجابة التعريف صحيح لأن الـTG من G إلى G الـG و الـX موجودات في G إذا حصل ضربهما موجود في G لأنه G closed under multiplication أو ال operation اللي على G هي عبارة عن binary operation يبقى الـG في X موجودة في ال group", "tokens": [6027, 3794, 33604, 6027, 31439, 8032, 1211, 23758, 16712, 3615, 16572, 5172, 20328, 5016, 1829, 5016, 49429, 32771, 13546, 20328, 5016, 1829, 5016, 33688, 7435, 16758, 3660, 16712, 3615, 16572, 5172, 20328, 5016, 1829, 5016, 5296, 33456, 2423, 39184, 51, 38, 9154, 460, 30731, 460, 2423, 39184, 38, 4032, 2423, 39184, 55, 3714, 29245, 23328, 9307, 8978, 460, 11933, 15730, 11331, 36520, 48812, 25513, 3224, 15042, 3714, 29245, 23328, 8978, 460, 5296, 33456, 3224, 460, 5395, 833, 27290, 34051, 2423, 6916, 13672, 1829, 15844, 460, 39896, 6225, 3555, 9640, 3660, 18871, 17434, 6916, 7251, 3555, 4587, 7578, 2423, 39184, 38, 8978, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 1594], "avg_logprob": -0.1391335219144821, "compression_ratio": 1.7210300429184548, "no_speech_prob": 0.0, "words": [{"start": 155.97, "end": 156.79, "word": "السؤال", "probability": 0.8751220703125}, {"start": 156.79, "end": 157.03, "word": " هو", "probability": 0.923828125}, {"start": 157.03, "end": 157.35, "word": " هل", "probability": 0.9091796875}, {"start": 157.35, "end": 157.59, "word": " هذا", "probability": 0.80810546875}, {"start": 157.59, "end": 158.11, "word": " التعريف", "probability": 0.98828125}, {"start": 158.11, "end": 158.65, "word": " صحيح", "probability": 0.99267578125}, {"start": 158.65, "end": 158.89, "word": " ولا", "probability": 0.595703125}, {"start": 158.89, "end": 159.21, "word": " غير", "probability": 0.992919921875}, {"start": 159.21, "end": 159.81, "word": " صحيح", "probability": 0.98828125}, {"start": 159.81, "end": 161.21, "word": " الإجابة", "probability": 0.8231201171875}, {"start": 161.21, "end": 161.99, "word": " التعريف", "probability": 0.9542236328125}, {"start": 161.99, "end": 162.65, "word": " صحيح", "probability": 0.98681640625}, {"start": 162.65, "end": 163.23, "word": " لأن", "probability": 0.734619140625}, {"start": 163.23, "end": 164.03, "word": " الـTG", "probability": 0.55987548828125}, {"start": 164.03, "end": 164.41, "word": " من", "probability": 0.95361328125}, {"start": 164.41, "end": 164.91, "word": " G", "probability": 0.8671875}, {"start": 164.91, "end": 165.25, "word": " إلى", "probability": 0.9384765625}, {"start": 165.25, "end": 165.69, "word": " G", "probability": 0.9716796875}, {"start": 165.69, "end": 166.35, "word": " الـG", "probability": 0.8411458333333334}, {"start": 166.35, "end": 166.53, "word": " و", "probability": 0.51220703125}, {"start": 166.53, "end": 166.99, "word": " الـX", "probability": 0.8245442708333334}, {"start": 166.99, "end": 167.89, "word": " موجودات", "probability": 0.941650390625}, {"start": 167.89, "end": 168.13, "word": " في", "probability": 0.97900390625}, {"start": 168.13, "end": 168.57, "word": " G", "probability": 0.9072265625}, {"start": 168.57, "end": 169.35, "word": " إذا", "probability": 0.88525390625}, {"start": 169.35, "end": 169.95, "word": " حصل", "probability": 0.838134765625}, {"start": 169.95, "end": 170.71, "word": " ضربهما", "probability": 0.8385009765625}, {"start": 170.71, "end": 171.35, "word": " موجود", "probability": 0.9734700520833334}, {"start": 171.35, "end": 171.55, "word": " في", "probability": 0.966796875}, {"start": 171.55, "end": 171.79, "word": " G", "probability": 0.9560546875}, {"start": 171.79, "end": 172.35, "word": " لأنه", "probability": 0.7688802083333334}, {"start": 172.35, "end": 172.61, "word": " G", "probability": 0.791015625}, {"start": 172.61, "end": 173.39, "word": " closed", "probability": 0.51025390625}, {"start": 173.39, "end": 173.77, "word": " under", "probability": 0.865234375}, {"start": 173.77, "end": 174.47, "word": " multiplication", "probability": 0.84814453125}, {"start": 174.47, "end": 175.55, "word": " أو", "probability": 0.9111328125}, {"start": 175.55, "end": 175.75, "word": " ال", "probability": 0.927734375}, {"start": 175.75, "end": 176.37, "word": " operation", "probability": 0.51953125}, {"start": 176.37, "end": 176.73, "word": " اللي", "probability": 0.935546875}, {"start": 176.73, "end": 176.95, "word": " على", "probability": 0.888671875}, {"start": 176.95, "end": 177.21, "word": " G", "probability": 0.9501953125}, {"start": 177.21, "end": 177.47, "word": " هي", "probability": 0.7734375}, {"start": 177.47, "end": 177.87, "word": " عبارة", "probability": 0.974853515625}, {"start": 177.87, "end": 178.07, "word": " عن", "probability": 0.9833984375}, {"start": 178.07, "end": 178.55, "word": " binary", "probability": 0.85693359375}, {"start": 178.55, "end": 179.67, "word": " operation", "probability": 0.94970703125}, {"start": 179.67, "end": 180.61, "word": " يبقى", "probability": 0.9862060546875}, {"start": 180.61, "end": 180.95, "word": " الـG", "probability": 0.9013671875}, {"start": 180.95, "end": 181.15, "word": " في", "probability": 0.9775390625}, {"start": 181.15, "end": 181.49, "word": " X", "probability": 0.9521484375}, {"start": 181.49, "end": 182.15, "word": " موجودة", "probability": 0.9888916015625}, {"start": 182.15, "end": 182.31, "word": " في", "probability": 0.98583984375}, {"start": 182.31, "end": 182.43, "word": " ال", "probability": 0.81982421875}, {"start": 182.43, "end": 182.73, "word": " group", "probability": 0.66845703125}], "temperature": 1.0}, {"id": 7, "seek": 21166, "start": 183.14, "end": 211.66, "text": "اللي عندنا يبقى تعريفي هذا صحيح الان انا ادعي ان هذه ال function is a permutation انا ادعي ان تيجي هذه عبارة عن permutation طيب هي ال permutation عبارة عن ايش؟ function و ال function بتكبر one to one and on two اذا طلعت هذه ال function one to one and on two يبقى بال فهي تكون permutation مظبوط؟", "tokens": [6027, 20292, 6225, 41260, 8315, 7251, 3555, 4587, 7578, 37279, 16572, 5172, 1829, 23758, 20328, 5016, 1829, 5016, 2423, 7649, 1975, 8315, 1975, 3215, 3615, 1829, 16472, 29538, 2423, 2445, 307, 257, 4784, 11380, 1975, 8315, 1975, 3215, 3615, 1829, 16472, 6055, 1829, 7435, 1829, 29538, 6225, 3555, 9640, 3660, 18871, 4784, 11380, 23032, 1829, 3555, 39896, 2423, 4784, 11380, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 22807, 2445, 4032, 2423, 2445, 39894, 4117, 3555, 2288, 472, 281, 472, 293, 322, 732, 1975, 15730, 23032, 1211, 34268, 29538, 2423, 2445, 472, 281, 472, 293, 322, 732, 7251, 3555, 4587, 7578, 20666, 6156, 3224, 1829, 6055, 30544, 4784, 11380, 3714, 19913, 3555, 2407, 9566, 22807], "avg_logprob": -0.22669720110194436, "compression_ratio": 2.053921568627451, "no_speech_prob": 0.0, "words": [{"start": 183.14, "end": 183.5, "word": "اللي", "probability": 0.48046875}, {"start": 183.5, "end": 183.84, "word": " عندنا", "probability": 0.4351399739583333}, {"start": 183.84, "end": 184.2, "word": " يبقى", "probability": 0.78900146484375}, {"start": 184.2, "end": 184.76, "word": " تعريفي", "probability": 0.72406005859375}, {"start": 184.76, "end": 185.06, "word": " هذا", "probability": 0.81689453125}, {"start": 185.06, "end": 185.54, "word": " صحيح", "probability": 0.975341796875}, {"start": 185.54, "end": 186.06, "word": " الان", "probability": 0.501739501953125}, {"start": 186.06, "end": 187.08, "word": " انا", "probability": 0.880615234375}, {"start": 187.08, "end": 187.94, "word": " ادعي", "probability": 0.7777099609375}, {"start": 187.94, "end": 188.68, "word": " ان", "probability": 0.9345703125}, {"start": 188.68, "end": 189.16, "word": " هذه", "probability": 0.8544921875}, {"start": 189.16, "end": 189.38, "word": " ال", "probability": 0.9423828125}, {"start": 189.38, "end": 189.8, "word": " function", "probability": 0.67333984375}, {"start": 189.8, "end": 190.48, "word": " is", "probability": 0.70703125}, {"start": 190.48, "end": 191.08, "word": " a", "probability": 0.9345703125}, {"start": 191.08, "end": 192.14, "word": " permutation", "probability": 0.975341796875}, {"start": 192.14, "end": 193.46, "word": " انا", "probability": 0.850341796875}, {"start": 193.46, "end": 194.24, "word": " ادعي", "probability": 0.9300537109375}, {"start": 194.24, "end": 194.8, "word": " ان", "probability": 0.95263671875}, {"start": 194.8, "end": 195.54, "word": " تيجي", "probability": 0.83349609375}, {"start": 195.54, "end": 195.9, "word": " هذه", "probability": 0.66943359375}, {"start": 195.9, "end": 196.36, "word": " عبارة", "probability": 0.978515625}, {"start": 196.36, "end": 196.54, "word": " عن", "probability": 0.99267578125}, {"start": 196.54, "end": 197.42, "word": " permutation", "probability": 0.988525390625}, {"start": 197.42, "end": 198.38, "word": " طيب", "probability": 0.953125}, {"start": 198.38, "end": 198.72, "word": " هي", "probability": 0.78662109375}, {"start": 198.72, "end": 198.92, "word": " ال", "probability": 0.9296875}, {"start": 198.92, "end": 199.52, "word": " permutation", "probability": 0.973388671875}, {"start": 199.52, "end": 199.98, "word": " عبارة", "probability": 0.9954833984375}, {"start": 199.98, "end": 200.14, "word": " عن", "probability": 0.99072265625}, {"start": 200.14, "end": 200.44, "word": " ايش؟", "probability": 0.7821044921875}, {"start": 200.44, "end": 201.24, "word": " function", "probability": 0.6796875}, {"start": 201.24, "end": 201.82, "word": " و", "probability": 0.447265625}, {"start": 201.82, "end": 201.96, "word": " ال", "probability": 0.78173828125}, {"start": 201.96, "end": 202.38, "word": " function", "probability": 0.9521484375}, {"start": 202.38, "end": 203.02, "word": " بتكبر", "probability": 0.69342041015625}, {"start": 203.02, "end": 203.36, "word": " one", "probability": 0.78857421875}, {"start": 203.36, "end": 203.56, "word": " to", "probability": 0.90478515625}, {"start": 203.56, "end": 203.78, "word": " one", "probability": 0.95263671875}, {"start": 203.78, "end": 204.1, "word": " and", "probability": 0.9521484375}, {"start": 204.1, "end": 204.34, "word": " on", "probability": 0.42041015625}, {"start": 204.34, "end": 204.56, "word": " two", "probability": 0.7119140625}, {"start": 204.56, "end": 205.22, "word": " اذا", "probability": 0.83349609375}, {"start": 205.22, "end": 205.68, "word": " طلعت", "probability": 0.99169921875}, {"start": 205.68, "end": 205.96, "word": " هذه", "probability": 0.92236328125}, {"start": 205.96, "end": 206.14, "word": " ال", "probability": 0.978515625}, {"start": 206.14, "end": 206.56, "word": " function", "probability": 0.96044921875}, {"start": 206.56, "end": 206.92, "word": " one", "probability": 0.94287109375}, {"start": 206.92, "end": 207.12, "word": " to", "probability": 0.9716796875}, {"start": 207.12, "end": 207.32, "word": " one", "probability": 0.9462890625}, {"start": 207.32, "end": 207.62, "word": " and", "probability": 0.95703125}, {"start": 207.62, "end": 207.86, "word": " on", "probability": 0.939453125}, {"start": 207.86, "end": 207.96, "word": " two", "probability": 0.96044921875}, {"start": 207.96, "end": 208.38, "word": " يبقى", "probability": 0.9713134765625}, {"start": 208.38, "end": 208.64, "word": " بال", "probability": 0.22216796875}, {"start": 208.64, "end": 209.04, "word": " فهي", "probability": 0.7267252604166666}, {"start": 209.04, "end": 209.48, "word": " تكون", "probability": 0.79248046875}, {"start": 209.48, "end": 210.48, "word": " permutation", "probability": 0.98193359375}, {"start": 210.48, "end": 211.66, "word": " مظبوط؟", "probability": 0.854248046875}], "temperature": 1.0}, {"id": 8, "seek": 23274, "start": 211.9, "end": 232.74, "text": "يبقى هنا باجي بقول now ال TG is a permutation طبعا؟ طيب ليش؟ because السبب النقطة الأولى", "tokens": [1829, 3555, 4587, 7578, 34105, 4724, 26108, 1829, 4724, 39648, 586, 2423, 314, 38, 307, 257, 4784, 11380, 23032, 3555, 3615, 995, 22807, 23032, 1829, 3555, 32239, 8592, 22807, 570, 21136, 3555, 3555, 28239, 47432, 3660, 16247, 12610, 7578], "avg_logprob": -0.16933594420552253, "compression_ratio": 1.1074380165289257, "no_speech_prob": 0.0, "words": [{"start": 211.9, "end": 212.5, "word": "يبقى", "probability": 0.90185546875}, {"start": 212.5, "end": 212.82, "word": " هنا", "probability": 0.9775390625}, {"start": 212.82, "end": 213.28, "word": " باجي", "probability": 0.91162109375}, {"start": 213.28, "end": 213.84, "word": " بقول", "probability": 0.952880859375}, {"start": 213.84, "end": 215.32, "word": " now", "probability": 0.330078125}, {"start": 215.32, "end": 216.8, "word": " ال", "probability": 0.66552734375}, {"start": 216.8, "end": 217.72, "word": " TG", "probability": 0.662353515625}, {"start": 217.72, "end": 218.72, "word": " is", "probability": 0.8876953125}, {"start": 218.72, "end": 219.8, "word": " a", "probability": 0.98095703125}, {"start": 219.8, "end": 221.78, "word": " permutation", "probability": 0.975341796875}, {"start": 221.78, "end": 225.08, "word": " طبعا؟", "probability": 0.7009765625}, {"start": 225.08, "end": 226.18, "word": " طيب", "probability": 0.94384765625}, {"start": 226.18, "end": 227.08, "word": " ليش؟", "probability": 0.9490559895833334}, {"start": 227.08, "end": 228.02, "word": " because", "probability": 0.73583984375}, {"start": 228.02, "end": 230.88, "word": " السبب", "probability": 0.9347330729166666}, {"start": 230.88, "end": 232.22, "word": " النقطة", "probability": 0.90234375}, {"start": 232.22, "end": 232.74, "word": " الأولى", "probability": 0.9733072916666666}], "temperature": 1.0}, {"id": 9, "seek": 26086, "start": 234.12, "end": 260.86, "text": "الـ TG هادي is one to one الـ TG is one to one بدنا نثبت صحة هذا الكلام يبقى باجي بقوله let الـ TG of X يساوي TG of Y then حسب التعريف الـ TG of X بده يساوي الـ G في X", "tokens": [6027, 39184, 314, 38, 8032, 995, 16254, 307, 472, 281, 472, 2423, 39184, 314, 38, 307, 472, 281, 472, 47525, 8315, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 2423, 28820, 10943, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 718, 2423, 39184, 314, 38, 295, 1783, 7251, 3794, 995, 45865, 314, 38, 295, 398, 550, 11331, 35457, 16712, 3615, 16572, 5172, 2423, 39184, 314, 38, 295, 1783, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 460, 8978, 1783], "avg_logprob": -0.21341463941626432, "compression_ratio": 1.5947712418300655, "no_speech_prob": 0.0, "words": [{"start": 234.12, "end": 234.54, "word": "الـ", "probability": 0.7939453125}, {"start": 234.54, "end": 235.0, "word": " TG", "probability": 0.7021484375}, {"start": 235.0, "end": 235.48, "word": " هادي", "probability": 0.4947916666666667}, {"start": 235.48, "end": 235.74, "word": " is", "probability": 0.424560546875}, {"start": 235.74, "end": 236.1, "word": 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"end": 354.91, "word": " لإيش؟", "probability": 0.66767578125}, {"start": 354.91, "end": 355.19, "word": " لأن", "probability": 0.880126953125}, {"start": 355.19, "end": 355.41, "word": " الـ", "probability": 0.739013671875}, {"start": 355.41, "end": 355.55, "word": " G", "probability": 0.74951171875}, {"start": 355.55, "end": 355.91, "word": " G", "probability": 0.29345703125}, {"start": 355.91, "end": 356.49, "word": " inverse", "probability": 0.908203125}, {"start": 356.49, "end": 356.91, "word": " هو", "probability": 0.93896484375}, {"start": 356.91, "end": 357.17, "word": " ال", "probability": 0.955078125}, {"start": 357.17, "end": 358.15, "word": " identity", "probability": 0.748046875}, {"start": 358.15, "end": 358.93, "word": " element", "probability": 0.97802734375}, {"start": 358.93, "end": 359.53, "word": " و", "probability": 0.406982421875}, {"start": 359.53, "end": 359.67, "word": " ال", "probability": 0.9541015625}, {"start": 359.67, "end": 360.21, "word": " identity", "probability": 0.90966796875}, {"start": 360.21, "end": 360.69, "word": " element", "probability": 0.98583984375}, {"start": 360.69, "end": 361.23, "word": " تضربه", "probability": 0.8751220703125}, {"start": 361.23, "end": 361.35, "word": " في", "probability": 0.98095703125}, {"start": 361.35, "end": 361.53, "word": " أي", "probability": 0.9189453125}, {"start": 361.53, "end": 361.89, "word": " element", "probability": 0.96826171875}, {"start": 361.89, "end": 362.47, "word": " بيعطيك", "probability": 0.809716796875}, {"start": 362.47, "end": 362.77, "word": " نفس", "probability": 0.998779296875}, {"start": 362.77, "end": 362.99, "word": " ال", "probability": 0.9814453125}, {"start": 362.99, "end": 363.31, "word": " element", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 15, "seek": 37049, "start": 363.89, "end": 370.49, "text": "إذا بقدر أقول هذه G في G inverse Y", "tokens": [28814, 15730, 4724, 28543, 2288, 5551, 39648, 29538, 460, 8978, 460, 17340, 398], "avg_logprob": 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إذا العنصر هذا شيلته و حاطه بدله مين؟ إكس طيب جي إكس هذه عبارة عن مين؟ عبارة عن تجي of إكس", "tokens": [5172, 3555, 33599, 12602, 10721, 1829, 4117, 23758, 13672, 1829, 49374, 12174, 9381, 13546, 3224, 22807, 4724, 16254, 5551, 38251, 1829, 3224, 36632, 18871, 9381, 2288, 19753, 34740, 24976, 3794, 3224, 12610, 3660, 11933, 15730, 4724, 28543, 2288, 5551, 39648, 29538, 10874, 1829, 11933, 4117, 3794, 50113, 15040, 11933, 15730, 18863, 1863, 9381, 2288, 23758, 13412, 26895, 47395, 4032, 11331, 41193, 3224, 47525, 1211, 3224, 3714, 9957, 22807, 11933, 4117, 3794, 23032, 1829, 3555, 10874, 1829, 11933, 4117, 3794, 29538, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 6225, 3555, 9640, 3660, 18871, 6055, 7435, 1829, 295, 11933, 4117, 3794], "avg_logprob": -0.2577351461542715, "compression_ratio": 1.782122905027933, "no_speech_prob": 0.0, "words": [{"start": 373.17, "end": 373.77, "word": "فباش", "probability": 0.2833251953125}, {"start": 373.77, "end": 374.19, "word": " رأيك", 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{"start": 380.51, "end": 381.11, "word": " أقول", "probability": 0.886474609375}, {"start": 381.11, "end": 381.73, "word": " هذه", "probability": 0.568359375}, {"start": 381.73, "end": 382.55, "word": " جي", "probability": 0.583251953125}, {"start": 382.55, "end": 383.13, "word": " إكس", "probability": 0.8272298177083334}, {"start": 383.13, "end": 383.95, "word": " مثلا", "probability": 0.97216796875}, {"start": 383.95, "end": 384.99, "word": " إذا", "probability": 0.845947265625}, {"start": 384.99, "end": 385.69, "word": " العنصر", "probability": 0.901611328125}, {"start": 385.69, "end": 386.03, "word": " هذا", "probability": 0.96044921875}, {"start": 386.03, "end": 386.55, "word": " شيلته", "probability": 0.80615234375}, {"start": 386.55, "end": 386.63, "word": " و", "probability": 0.98095703125}, {"start": 386.63, "end": 386.99, "word": " حاطه", "probability": 0.6181640625}, {"start": 386.99, "end": 387.49, "word": " بدله", "probability": 0.8515625}, {"start": 387.49, "end": 388.11, "word": " مين؟", "probability": 0.7631022135416666}, {"start": 388.11, "end": 389.05, "word": " إكس", "probability": 0.7926432291666666}, {"start": 389.05, "end": 390.05, "word": " طيب", "probability": 0.8907877604166666}, {"start": 390.05, "end": 390.53, "word": " جي", "probability": 0.904052734375}, {"start": 390.53, "end": 391.03, "word": " إكس", "probability": 0.9871419270833334}, {"start": 391.03, "end": 391.33, "word": " هذه", "probability": 0.6494140625}, {"start": 391.33, "end": 391.75, "word": " عبارة", "probability": 0.9942626953125}, {"start": 391.75, "end": 391.99, "word": " عن", "probability": 0.9873046875}, {"start": 391.99, "end": 392.93, "word": " مين؟", "probability": 0.9562174479166666}, {"start": 392.93, "end": 393.77, "word": " عبارة", "probability": 0.991943359375}, {"start": 393.77, "end": 394.53, "word": " عن", "probability": 0.9931640625}, {"start": 394.53, "end": 396.41, "word": " تجي", "probability": 0.6478678385416666}, {"start": 396.41, "end": 397.15, 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الجروب جاب لي permutation اسمها مين اسمها TG الآن بده لم هدول كل ال permutation و بده حطهم في set يبقى الآن", "tokens": [3615, 3555, 9640, 3660, 18871, 472, 281, 472, 293, 322, 281, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 2423, 314, 38, 8032, 8848, 1829, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 4784, 11380, 7251, 3555, 4587, 7578, 2423, 4478, 460, 9154, 25724, 32887, 3555, 10874, 16758, 32239, 4784, 11380, 24525, 2304, 11296, 3714, 9957, 24525, 2304, 11296, 314, 38, 6024, 48506, 47525, 3224, 32767, 8032, 3215, 12610, 28242, 2423, 4784, 11380, 4032, 47525, 3224, 11331, 9566, 16095, 8978, 992, 7251, 3555, 4587, 7578, 6024, 48506], "avg_logprob": -0.28178879858433514, "compression_ratio": 1.707182320441989, "no_speech_prob": 0.0, "words": [{"start": 421.05, "end": 421.83, "word": "عبارة", "probability": 0.74322509765625}, {"start": 421.83, "end": 421.95, "word": " عن", "probability": 0.98486328125}, {"start": 421.95, "end": 422.21, "word": " one", "probability": 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437.69, "word": " اسمها", "probability": 0.9510091145833334}, {"start": 437.69, "end": 438.09, "word": " مين", "probability": 0.587158203125}, {"start": 438.09, "end": 438.95, "word": " اسمها", "probability": 0.9436848958333334}, {"start": 438.95, "end": 440.31, "word": " TG", "probability": 0.8740234375}, {"start": 440.31, "end": 441.49, "word": " الآن", "probability": 0.63330078125}, {"start": 441.49, "end": 441.95, "word": " بده", "probability": 0.652099609375}, {"start": 441.95, "end": 442.25, "word": " لم", "probability": 0.19482421875}, {"start": 442.25, "end": 443.27, "word": " هدول", "probability": 0.7586263020833334}, {"start": 443.27, "end": 443.87, "word": " كل", "probability": 0.95947265625}, {"start": 443.87, "end": 444.13, "word": " ال", "probability": 0.87890625}, {"start": 444.13, "end": 445.07, "word": " permutation", "probability": 0.7373046875}, {"start": 445.07, "end": 445.51, "word": " و", "probability": 0.88330078125}, {"start": 445.51, "end": 445.87, "word": " بده", "probability": 0.717041015625}, {"start": 445.87, "end": 446.43, "word": " حطهم", "probability": 0.8639322916666666}, {"start": 446.43, "end": 446.73, "word": " في", "probability": 0.9453125}, {"start": 446.73, "end": 447.35, "word": " set", "probability": 0.5341796875}, {"start": 447.35, "end": 448.65, "word": " يبقى", "probability": 0.988525390625}, {"start": 448.65, "end": 449.19, "word": " الآن", "probability": 0.71533203125}], "temperature": 1.0}, {"id": 19, "seek": 47255, "start": 449.89, "end": 472.55, "text": "consider جي بار جي بار هذي بتعطيها الرمز SG مين ال SG هذي كل ت جي بحيث الجي موجودة في جي يعني", "tokens": [21190, 1438, 10874, 1829, 4724, 9640, 10874, 1829, 4724, 9640, 8032, 8848, 1829, 39894, 3615, 9566, 1829, 11296, 34892, 2304, 11622, 34520, 3714, 9957, 2423, 34520, 8032, 8848, 1829, 28242, 6055, 10874, 1829, 4724, 5016, 1829, 12984, 25724, 1829, 3714, 29245, 23328, 3660, 8978, 10874, 1829, 37495, 22653], "avg_logprob": -0.2531887657788335, "compression_ratio": 1.3539823008849559, "no_speech_prob": 0.0, "words": [{"start": 449.89, "end": 451.03, "word": "consider", "probability": 0.6343994140625}, {"start": 451.03, "end": 454.75, "word": " جي", "probability": 0.70751953125}, {"start": 454.75, "end": 455.09, "word": " بار", "probability": 0.802978515625}, {"start": 455.09, "end": 456.45, "word": " جي", "probability": 0.61248779296875}, {"start": 456.45, "end": 456.85, "word": " بار", "probability": 0.986572265625}, {"start": 456.85, "end": 457.55, "word": " هذي", "probability": 0.4564615885416667}, {"start": 457.55, "end": 458.33, "word": " بتعطيها", "probability": 0.84599609375}, {"start": 458.33, "end": 459.05, "word": " الرمز", "probability": 0.95166015625}, {"start": 459.05, "end": 460.13, "word": " SG", "probability": 0.8330078125}, {"start": 460.13, "end": 461.93, "word": " مين", "probability": 0.83154296875}, {"start": 461.93, "end": 462.11, "word": " ال", "probability": 0.96142578125}, {"start": 462.11, "end": 462.75, "word": " SG", "probability": 0.9736328125}, {"start": 462.75, "end": 463.65, "word": " هذي", "probability": 0.79931640625}, {"start": 463.65, "end": 464.13, "word": " كل", "probability": 0.9365234375}, {"start": 464.13, "end": 464.65, "word": " ت", "probability": 0.29052734375}, {"start": 464.65, "end": 465.83, "word": " جي", "probability": 0.7451171875}, {"start": 465.83, "end": 466.59, "word": " بحيث", "probability": 0.978271484375}, {"start": 466.59, "end": 467.21, "word": " الجي", "probability": 0.821533203125}, {"start": 467.21, "end": 468.07, "word": " موجودة", "probability": 0.950439453125}, {"start": 468.07, "end": 468.25, "word": " في", "probability": 0.935546875}, {"start": 468.25, "end": 468.95, "word": " جي", "probability": 0.843017578125}, {"start": 468.95, "end": 472.55, "word": " يعني", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 20, "seek": 50165, "start": 473.31, "end": 501.65, "text": "لو جينا قولنا الـ G هذه فيها خمسين elements مثلا يبقى ابو دي اطلع هنا كم element عندى؟ خمسين elements لإنه TG1, TG2, TG3, TG4 لغاية مكمله الخمسين يبقى ال SG هذي mean the set of all permutations اللي محطوطة على ال group G هذه the set", "tokens": [1211, 2407, 10874, 1829, 8315, 12174, 12610, 8315, 2423, 39184, 460, 29538, 8978, 11296, 16490, 2304, 3794, 9957, 4959, 50113, 15040, 7251, 3555, 4587, 7578, 48127, 2407, 11778, 1829, 1975, 9566, 1211, 3615, 34105, 9122, 2304, 4478, 43242, 7578, 22807, 16490, 2304, 3794, 9957, 4959, 5296, 28814, 1863, 3224, 314, 38, 16, 11, 314, 38, 17, 11, 314, 38, 18, 11, 314, 38, 19, 5296, 17082, 995, 10632, 3714, 24793, 1211, 3224, 33962, 2304, 3794, 9957, 7251, 3555, 4587, 7578, 2423, 318, 38, 8032, 8848, 1829, 914, 264, 992, 295, 439, 4784, 325, 763, 13672, 1829, 3714, 5016, 9566, 2407, 9566, 3660, 15844, 2423, 1594, 460, 29538, 264, 992], "avg_logprob": -0.27329546348615125, "compression_ratio": 1.54337899543379, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 473.31, "end": 473.73, "word": "لو", "probability": 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{"start": 479.47, "end": 479.79, "word": " اطلع", "probability": 0.8251953125}, {"start": 479.79, "end": 479.97, "word": " هنا", "probability": 0.95556640625}, {"start": 479.97, "end": 480.35, "word": " كم", "probability": 0.6732177734375}, {"start": 480.35, "end": 480.83, "word": " element", "probability": 0.76708984375}, {"start": 480.83, "end": 482.03, "word": " عندى؟", "probability": 0.60986328125}, {"start": 482.03, "end": 482.91, "word": " خمسين", "probability": 0.9381103515625}, {"start": 482.91, "end": 483.79, "word": " elements", "probability": 0.5419921875}, {"start": 483.79, "end": 484.63, "word": " لإنه", "probability": 0.78857421875}, {"start": 484.63, "end": 485.37, "word": " TG1,", "probability": 0.6484375}, {"start": 485.53, "end": 486.15, "word": " TG2,", "probability": 0.8955078125}, {"start": 486.31, "end": 486.93, "word": " TG3,", "probability": 0.9427083333333334}, {"start": 487.05, "end": 487.65, "word": " TG4", "probability": 0.9436848958333334}, {"start": 487.65, "end": 487.95, "word": " لغاية", "probability": 0.9617919921875}, {"start": 487.95, "end": 488.57, "word": " مكمله", "probability": 0.76226806640625}, {"start": 488.57, "end": 489.35, "word": " الخمسين", "probability": 0.93896484375}, {"start": 489.35, "end": 490.39, "word": " يبقى", "probability": 0.9566650390625}, {"start": 490.39, "end": 490.57, "word": " ال", "probability": 0.9638671875}, {"start": 490.57, "end": 491.31, "word": " SG", "probability": 0.3768310546875}, {"start": 491.31, "end": 491.81, "word": " هذي", "probability": 0.584716796875}, {"start": 491.81, "end": 492.15, "word": " mean", "probability": 0.311767578125}, {"start": 492.15, "end": 492.75, "word": " the", "probability": 0.68115234375}, {"start": 492.75, "end": 493.11, "word": " set", "probability": 0.96044921875}, {"start": 493.11, "end": 493.53, "word": " of", "probability": 0.97900390625}, {"start": 493.53, "end": 494.39, "word": " all", "probability": 0.939453125}, {"start": 494.39, "end": 495.87, "word": " permutations", "probability": 0.9122721354166666}, {"start": 495.87, "end": 496.37, "word": " اللي", "probability": 0.8662109375}, {"start": 496.37, "end": 496.97, "word": " محطوطة", "probability": 0.81640625}, {"start": 496.97, "end": 497.15, "word": " على", "probability": 0.81689453125}, {"start": 497.15, "end": 497.33, "word": " ال", "probability": 0.77880859375}, {"start": 497.33, "end": 497.67, "word": " group", "probability": 0.9453125}, {"start": 497.67, "end": 498.15, "word": " G", "probability": 0.9619140625}, {"start": 498.15, "end": 499.23, "word": " هذه", "probability": 0.5029296875}, {"start": 499.23, "end": 500.21, "word": " the", "probability": 0.60546875}, {"start": 500.21, "end": 501.65, "word": " set", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 21, "seek": 52328, "start": 502.6, "end": 523.28, "text": "of all permutations of G كل ال permutations اللي على G الان انا هتدعي ان SG هدى is a group", "tokens": [2670, 439, 4784, 325, 763, 295, 460, 28242, 2423, 4784, 325, 763, 13672, 1829, 15844, 460, 2423, 7649, 1975, 8315, 8032, 2655, 3215, 3615, 1829, 16472, 34520, 8032, 3215, 7578, 307, 257, 1594], "avg_logprob": -0.2649356477400836, "compression_ratio": 1.2291666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 502.6, "end": 503.28, "word": "of", "probability": 0.546875}, {"start": 503.28, "end": 504.96, "word": " all", "probability": 0.9306640625}, {"start": 504.96, "end": 508.3, "word": " permutations", "probability": 0.9244791666666666}, {"start": 508.3, "end": 512.06, "word": " of", "probability": 0.9716796875}, {"start": 512.06, "end": 513.18, "word": " G", "probability": 0.638671875}, {"start": 513.18, "end": 514.42, "word": " كل", "probability": 0.71435546875}, {"start": 514.42, "end": 514.68, "word": " ال", "probability": 0.7900390625}, {"start": 514.68, "end": 515.76, "word": " permutations", "probability": 0.89208984375}, {"start": 515.76, "end": 516.32, "word": " اللي", "probability": 0.96142578125}, {"start": 516.32, "end": 516.58, "word": " على", "probability": 0.6171875}, {"start": 516.58, "end": 516.92, "word": " G", "probability": 0.927734375}, {"start": 516.92, "end": 518.16, "word": " الان", "probability": 0.61083984375}, {"start": 518.16, "end": 519.16, "word": " انا", "probability": 0.792236328125}, {"start": 519.16, "end": 520.28, "word": " هتدعي", "probability": 0.86845703125}, {"start": 520.28, "end": 520.64, "word": " ان", "probability": 0.85400390625}, {"start": 520.64, "end": 521.3, "word": " SG", "probability": 0.377685546875}, {"start": 521.3, "end": 521.9, "word": " هدى", "probability": 0.6189778645833334}, {"start": 521.9, "end": 522.28, "word": " is", "probability": 0.85205078125}, {"start": 522.28, "end": 522.68, "word": " a", "probability": 0.94140625}, {"start": 522.68, "end": 523.28, "word": " group", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 22, "seek": 54819, "start": 524.05, "end": 548.19, "text": "وبنفعش تدعى يا صاحبي بدك تبين انه فعلا انه SG هذه ايه هي group لانه اذا اثبتت انها group وصلت للنص اللى انا بقول عنه كل group isomorphic الى permutation group او ال group of permutation تمام يبقى الخطوة التالية بعد ما خلقت", "tokens": [37746, 1863, 5172, 3615, 8592, 6055, 3215, 3615, 7578, 35186, 20328, 39319, 21292, 47525, 4117, 6055, 3555, 9957, 16472, 3224, 6156, 3615, 15040, 16472, 3224, 34520, 29538, 1975, 1829, 3224, 39896, 1594, 5296, 7649, 3224, 1975, 15730, 1975, 12984, 3555, 2655, 2655, 16472, 11296, 1594, 4032, 36520, 2655, 24976, 1863, 9381, 13672, 7578, 1975, 8315, 4724, 39648, 18871, 3224, 28242, 1594, 307, 32702, 299, 2423, 7578, 4784, 11380, 1594, 1975, 2407, 2423, 1594, 295, 4784, 11380, 46811, 10943, 7251, 3555, 4587, 7578, 33962, 9566, 2407, 3660, 16712, 6027, 10632, 39182, 19446, 16490, 1211, 38149], "avg_logprob": -0.23914473966548316, "compression_ratio": 1.6473429951690821, "no_speech_prob": 0.0, "words": [{"start": 524.05, "end": 524.77, "word": "وبنفعش", "probability": 0.7581298828125}, {"start": 524.77, "end": 525.29, "word": " تدعى", "probability": 0.8262939453125}, {"start": 525.29, "end": 525.43, "word": " يا", "probability": 0.9482421875}, {"start": 525.43, "end": 525.85, "word": " صاحبي", "probability": 0.7486165364583334}, {"start": 525.85, "end": 526.31, "word": " بدك", "probability": 0.63623046875}, {"start": 526.31, "end": 527.05, "word": " تبين", "probability": 0.8894856770833334}, {"start": 527.05, "end": 527.45, "word": " انه", "probability": 0.41552734375}, {"start": 527.45, "end": 528.01, "word": " فعلا", "probability": 0.7250162760416666}, {"start": 528.01, "end": 528.79, "word": " انه", "probability": 0.4322509765625}, {"start": 528.79, "end": 529.33, "word": " SG", "probability": 0.76416015625}, {"start": 529.33, "end": 529.93, "word": " هذه", "probability": 0.572265625}, {"start": 529.93, "end": 530.27, "word": " ايه", "probability": 0.896484375}, {"start": 530.27, "end": 530.45, "word": " هي", "probability": 0.7119140625}, {"start": 530.45, "end": 530.93, "word": " group", "probability": 0.900390625}, {"start": 530.93, "end": 531.89, "word": " لانه", "probability": 0.7832845052083334}, {"start": 531.89, "end": 532.09, "word": " اذا", "probability": 0.874755859375}, {"start": 532.09, "end": 532.61, "word": " اثبتت", "probability": 0.83662109375}, {"start": 532.61, "end": 532.81, "word": " انها", "probability": 0.96240234375}, {"start": 532.81, "end": 533.33, "word": " group", "probability": 0.98486328125}, {"start": 533.33, "end": 534.51, "word": " وصلت", "probability": 0.9537760416666666}, {"start": 534.51, "end": 535.13, "word": " للنص", "probability": 0.884765625}, {"start": 535.13, "end": 535.47, "word": " اللى", "probability": 0.7705078125}, {"start": 535.47, "end": 535.77, "word": " انا", "probability": 0.812255859375}, {"start": 535.77, "end": 536.23, "word": " بقول", "probability": 0.9833984375}, {"start": 536.23, "end": 536.79, "word": " عنه", "probability": 0.7010498046875}, {"start": 536.79, "end": 537.57, "word": " كل", "probability": 0.89501953125}, {"start": 537.57, "end": 538.15, "word": " group", "probability": 0.98876953125}, {"start": 538.15, "end": 539.37, "word": " isomorphic", "probability": 0.908203125}, {"start": 539.37, "end": 539.73, "word": " الى", "probability": 0.780517578125}, {"start": 539.73, "end": 540.61, "word": " permutation", "probability": 0.953857421875}, {"start": 540.61, "end": 541.13, "word": " group", "probability": 0.7392578125}, {"start": 541.13, "end": 541.41, "word": " او", "probability": 0.895751953125}, {"start": 541.41, "end": 541.51, "word": " ال", "probability": 0.447509765625}, {"start": 541.51, "end": 541.89, "word": " group", "probability": 0.92431640625}, {"start": 541.89, "end": 542.21, "word": " of", "probability": 0.95654296875}, {"start": 542.21, "end": 543.57, "word": " permutation", "probability": 0.6170654296875}, {"start": 543.57, "end": 544.57, "word": " تمام", "probability": 0.78271484375}, {"start": 544.57, "end": 545.35, "word": " يبقى", "probability": 0.9146728515625}, {"start": 545.35, "end": 546.05, "word": " الخطوة", "probability": 0.9775390625}, {"start": 546.05, "end": 546.65, "word": " التالية", "probability": 0.9933268229166666}, {"start": 546.65, "end": 547.05, "word": " بعد", "probability": 0.966796875}, {"start": 547.05, "end": 547.27, "word": " ما", "probability": 0.93017578125}, {"start": 547.27, "end": 548.19, "word": " خلقت", "probability": 0.8782552083333334}], "temperature": 1.0}, {"id": 23, "seek": 55539, "start": 548.59, "end": 555.39, "text": "permutations لكل عنصر موجود في دي خلقتله permutation اقبله", "tokens": [610, 38326, 763, 5296, 28820, 18871, 9381, 2288, 3714, 29245, 23328, 8978, 11778, 1829, 16490, 1211, 38149, 43761, 4784, 11380, 1975, 4587, 36150, 3224], "avg_logprob": -0.2859375, "compression_ratio": 1.0897435897435896, "no_speech_prob": 0.0, "words": [{"start": 548.59, "end": 550.19, "word": "permutations", "probability": 0.670166015625}, {"start": 550.19, "end": 551.43, "word": " لكل", "probability": 0.83837890625}, {"start": 551.43, "end": 552.21, "word": " عنصر", "probability": 0.9599609375}, {"start": 552.21, "end": 552.75, "word": " موجود", "probability": 0.9254557291666666}, {"start": 552.75, "end": 552.91, "word": " في", "probability": 0.880859375}, {"start": 552.91, "end": 553.27, "word": " دي", "probability": 0.5238037109375}, {"start": 553.27, "end": 553.95, "word": " خلقتله", "probability": 0.7061767578125}, {"start": 553.95, "end": 554.67, "word": " permutation", "probability": 0.7705078125}, {"start": 554.67, "end": 555.39, "word": " اقبله", "probability": 0.8316650390625}], "temperature": 1.0}, {"id": 24, "seek": 58203, "start": 555.89, "end": 582.03, "text": "الـ Perimotations حطيتهم في ست واحدة سميتها G bar أو سميتها SG من العناصر تبعتها كل الـ Perimotations اللي خلقتهم على ال group G الآن أنا بتدعي ان SG هذه is a group يبقى بدى أشوف هل ال SG بتحقق شروط ال group ولا لا", "tokens": [6027, 39184, 3026, 332, 310, 763, 11331, 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558.23, "word": " ست", "probability": 0.50872802734375}, {"start": 558.23, "end": 558.63, "word": " واحدة", "probability": 0.9661458333333334}, {"start": 558.63, "end": 559.25, "word": " سميتها", "probability": 0.8675537109375}, {"start": 559.25, "end": 559.51, "word": " G", "probability": 0.55078125}, {"start": 559.51, "end": 559.89, "word": " bar", "probability": 0.41845703125}, {"start": 559.89, "end": 560.21, "word": " أو", "probability": 0.794921875}, {"start": 560.21, "end": 561.23, "word": " سميتها", "probability": 0.932373046875}, {"start": 561.23, "end": 562.01, "word": " SG", "probability": 0.85595703125}, {"start": 562.01, "end": 563.23, "word": " من", "probability": 0.796875}, {"start": 563.23, "end": 564.03, "word": " العناصر", "probability": 0.947265625}, {"start": 564.03, "end": 564.93, "word": " تبعتها", "probability": 0.9088134765625}, {"start": 564.93, "end": 565.69, "word": " كل", "probability": 0.9384765625}, {"start": 565.69, "end": 566.05, "word": " الـ", "probability": 0.765869140625}, {"start": 566.05, "end": 567.07, "word": " Perimotations", "probability": 0.7939453125}, {"start": 567.07, "end": 567.49, "word": " اللي", "probability": 0.931884765625}, {"start": 567.49, "end": 568.55, "word": " خلقتهم", "probability": 0.8939208984375}, {"start": 568.55, "end": 568.89, "word": " على", "probability": 0.765625}, {"start": 568.89, "end": 569.09, "word": " ال", "probability": 0.7470703125}, {"start": 569.09, "end": 569.61, "word": " group", "probability": 0.65771484375}, {"start": 569.61, "end": 570.19, "word": " G", "probability": 0.876953125}, {"start": 570.19, "end": 571.51, "word": " الآن", "probability": 0.596435546875}, {"start": 571.51, "end": 571.91, "word": " أنا", "probability": 0.81591796875}, {"start": 571.91, "end": 572.63, "word": " بتدعي", "probability": 0.853271484375}, {"start": 572.63, "end": 572.93, "word": " ان", "probability": 0.44287109375}, {"start": 572.93, "end": 573.55, "word": " SG", "probability": 0.8017578125}, {"start": 573.55, "end": 574.09, "word": " هذه", "probability": 0.419921875}, {"start": 574.09, "end": 574.75, "word": " is", "probability": 0.439453125}, {"start": 574.75, "end": 575.51, "word": " a", "probability": 0.91748046875}, {"start": 575.51, "end": 576.11, "word": " group", "probability": 0.9599609375}, {"start": 576.11, "end": 576.83, "word": " يبقى", "probability": 0.935302734375}, {"start": 576.83, "end": 577.19, "word": " بدى", "probability": 0.5091552734375}, {"start": 577.19, "end": 577.51, "word": " أشوف", "probability": 0.8587239583333334}, {"start": 577.51, "end": 577.83, "word": " هل", "probability": 0.7354736328125}, {"start": 577.83, "end": 578.01, "word": " ال", "probability": 0.78515625}, {"start": 578.01, "end": 578.91, "word": " SG", "probability": 0.9658203125}, {"start": 578.91, "end": 580.29, "word": " بتحقق", "probability": 0.935791015625}, {"start": 580.29, "end": 580.79, "word": " شروط", "probability": 0.9767252604166666}, {"start": 580.79, "end": 580.97, "word": " ال", "probability": 0.70751953125}, {"start": 580.97, "end": 581.41, "word": " group", "probability": 0.955078125}, {"start": 581.41, "end": 581.83, "word": " ولا", "probability": 0.935546875}, {"start": 581.83, "end": 582.03, "word": " لا", "probability": 0.56103515625}], "temperature": 1.0}, {"id": 25, "seek": 61119, "start": 582.57, "end": 611.19, "text": "يبقى أول شيء ال operation اللي عليها madam permutation هو ال composition of functions الآن ال composition of functions بدي أثبت إنها binary operation إيش يعني binary operation؟ يعني لو جبت composition بين two permutations بدي أعطيني مين؟ permutation واحدة إن حدث ذلك يبقى فعلا تبقى ال operation اللي عليها هي binary", "tokens": [1829, 3555, 4587, 7578, 5551, 12610, 44049, 38207, 2423, 6916, 13672, 1829, 25894, 11296, 28882, 4784, 11380, 31439, 2423, 12686, 295, 6828, 6024, 48506, 2423, 12686, 295, 6828, 4724, 16254, 5551, 12984, 3555, 2655, 36145, 11296, 17434, 6916, 11933, 1829, 8592, 37495, 22653, 17434, 6916, 22807, 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0.9739583333333334}, {"start": 599.95, "end": 600.69, "word": " composition", "probability": 0.94287109375}, {"start": 600.69, "end": 601.13, "word": " بين", "probability": 0.9580078125}, {"start": 601.13, "end": 601.43, "word": " two", "probability": 0.9443359375}, {"start": 601.43, "end": 602.19, "word": " permutations", "probability": 0.9173177083333334}, {"start": 602.19, "end": 602.49, "word": " بدي", "probability": 0.77490234375}, {"start": 602.49, "end": 602.89, "word": " أعطيني", "probability": 0.69384765625}, {"start": 602.89, "end": 604.01, "word": " مين؟", "probability": 0.8592122395833334}, {"start": 604.01, "end": 604.97, "word": " permutation", "probability": 0.896240234375}, {"start": 604.97, "end": 605.83, "word": " واحدة", "probability": 0.9866536458333334}, {"start": 605.83, "end": 606.19, "word": " إن", "probability": 0.70849609375}, {"start": 606.19, "end": 606.67, "word": " حدث", "probability": 0.9969075520833334}, {"start": 606.67, "end": 607.29, "word": " ذلك", "probability": 0.967041015625}, {"start": 607.29, "end": 608.13, "word": " يبقى", "probability": 0.92626953125}, {"start": 608.13, "end": 608.51, "word": " فعلا", "probability": 0.9378255208333334}, {"start": 608.51, "end": 609.01, "word": " تبقى", "probability": 0.856201171875}, {"start": 609.01, "end": 609.21, "word": " ال", "probability": 0.966796875}, {"start": 609.21, "end": 609.77, "word": " operation", "probability": 0.974609375}, {"start": 609.77, "end": 610.03, "word": " اللي", "probability": 0.991455078125}, {"start": 610.03, "end": 610.35, "word": " عليها", "probability": 0.9384765625}, {"start": 610.35, "end": 610.59, "word": " هي", "probability": 0.38232421875}, {"start": 610.59, "end": 611.19, "word": " binary", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 26, "seek": 63910, "start": 611.8, "end": 639.1, "text": "operation يبقى we a claim that اكليم يدعي ان ال SG is a group under the composition of functions", "tokens": [43493, 7251, 3555, 4587, 7578, 321, 257, 3932, 300, 1975, 4117, 20292, 2304, 7251, 3215, 3615, 1829, 16472, 2423, 34520, 307, 257, 1594, 833, 264, 12686, 295, 6828], "avg_logprob": -0.4730603530489165, "compression_ratio": 1.0560747663551402, "no_speech_prob": 0.0, "words": [{"start": 611.8, "end": 612.78, "word": "operation", "probability": 0.041107177734375}, {"start": 612.78, "end": 614.88, "word": " يبقى", "probability": 0.9515380859375}, {"start": 614.88, "end": 615.6, "word": " we", "probability": 0.5712890625}, {"start": 615.6, "end": 617.66, "word": " a", "probability": 0.187744140625}, {"start": 617.66, "end": 618.52, "word": " claim", "probability": 0.96826171875}, {"start": 618.52, "end": 619.92, "word": " that", "probability": 0.83642578125}, {"start": 619.92, "end": 620.58, "word": " اكليم", "probability": 0.488555908203125}, {"start": 620.58, "end": 621.46, "word": " يدعي", "probability": 0.5919189453125}, {"start": 621.46, "end": 622.3, "word": " ان", "probability": 0.826171875}, {"start": 622.3, "end": 622.62, "word": " ال", "probability": 0.9560546875}, {"start": 622.62, "end": 623.8, "word": " SG", "probability": 0.334228515625}, {"start": 623.8, "end": 625.38, "word": " is", "probability": 0.8662109375}, {"start": 625.38, "end": 626.68, "word": " a", "probability": 0.95263671875}, {"start": 626.68, "end": 627.62, "word": " group", "probability": 0.978515625}, {"start": 627.62, "end": 629.3, "word": " under", "probability": 0.84716796875}, {"start": 629.3, "end": 632.52, "word": " the", "probability": 0.8486328125}, {"start": 632.52, "end": 634.34, "word": " composition", "probability": 0.93701171875}, {"start": 634.34, "end": 638.24, "word": " of", "probability": 0.9736328125}, {"start": 638.24, "end": 639.1, "word": " functions", "probability": 0.86279296875}], "temperature": 1.0}, {"id": 27, "seek": 66419, "start": 641.91, "end": 664.19, "text": "انا هتدعي ان اس جي هدى is a group تحت عملية تحصيل او تركيب من ال function بيدروح اثبت هذا الكلام يبقى باجي بقوله for all جي و H اللى موجودة في جي we have", "tokens": [7649, 995, 8032, 2655, 3215, 3615, 1829, 16472, 24525, 10874, 1829, 8032, 3215, 7578, 307, 257, 1594, 6055, 33753, 6225, 42213, 10632, 6055, 5016, 9381, 26895, 1975, 2407, 6055, 31747, 1829, 3555, 9154, 2423, 2445, 4724, 25708, 32887, 5016, 1975, 12984, 3555, 2655, 23758, 2423, 28820, 10943, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 337, 439, 10874, 1829, 4032, 389, 13672, 7578, 3714, 29245, 23328, 3660, 8978, 10874, 1829, 321, 362], "avg_logprob": -0.2679166595141093, "compression_ratio": 1.4210526315789473, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 641.91, "end": 642.35, "word": "انا", "probability": 0.6884765625}, {"start": 642.35, "end": 643.01, "word": " هتدعي", "probability": 0.75009765625}, {"start": 643.01, "end": 643.41, "word": " ان", "probability": 0.79443359375}, {"start": 643.41, "end": 643.79, "word": " اس", "probability": 0.1552734375}, {"start": 643.79, "end": 644.11, "word": " جي", "probability": 0.83642578125}, {"start": 644.11, "end": 644.59, "word": " هدى", "probability": 0.5365397135416666}, {"start": 644.59, "end": 644.95, "word": " is", "probability": 0.84130859375}, {"start": 644.95, "end": 645.33, "word": " a", "probability": 0.9580078125}, {"start": 645.33, "end": 645.81, "word": " group", "probability": 0.97216796875}, {"start": 645.81, "end": 646.61, "word": " تحت", "probability": 0.985595703125}, {"start": 646.61, "end": 647.19, "word": " عملية", "probability": 0.98876953125}, {"start": 647.19, "end": 647.89, "word": " تحصيل", "probability": 0.9609375}, {"start": 647.89, "end": 648.23, "word": " او", "probability": 0.799072265625}, {"start": 648.23, "end": 648.75, "word": " تركيب", "probability": 0.9925537109375}, {"start": 648.75, "end": 649.11, "word": " من", "probability": 0.282958984375}, {"start": 649.11, "end": 649.67, "word": " ال", "probability": 0.90283203125}, {"start": 649.67, "end": 650.19, "word": " function", "probability": 0.67724609375}, {"start": 650.19, "end": 651.25, "word": " بيدروح", "probability": 0.560546875}, {"start": 651.25, "end": 651.99, "word": " اثبت", "probability": 0.9288330078125}, {"start": 651.99, "end": 652.99, "word": " هذا", "probability": 0.97021484375}, {"start": 652.99, "end": 653.77, "word": " الكلام", "probability": 0.9396158854166666}, {"start": 653.77, "end": 654.69, "word": " يبقى", "probability": 0.9532470703125}, {"start": 654.69, "end": 655.09, "word": " باجي", "probability": 0.7146809895833334}, {"start": 655.09, "end": 655.81, "word": " بقوله", "probability": 0.94677734375}, {"start": 655.81, "end": 656.13, "word": " for", "probability": 0.9296875}, {"start": 656.13, "end": 657.19, "word": " all", "probability": 0.9384765625}, {"start": 657.19, "end": 659.97, "word": " جي", "probability": 0.6524658203125}, {"start": 659.97, "end": 660.47, "word": " و", "probability": 0.9462890625}, {"start": 660.47, "end": 661.01, "word": " H", "probability": 0.26318359375}, {"start": 661.01, "end": 661.69, "word": " اللى", "probability": 0.785888671875}, {"start": 661.69, "end": 662.37, "word": " موجودة", "probability": 0.9713134765625}, {"start": 662.37, "end": 662.57, "word": " في", "probability": 0.9013671875}, {"start": 662.57, "end": 662.99, "word": " جي", "probability": 0.8291015625}, {"start": 662.99, "end": 663.65, "word": " we", "probability": 0.58349609375}, {"start": 663.65, "end": 664.19, "word": " have", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 28, "seek": 68484, "start": 680.2, "end": 684.84, "text": "البيانات مضربات ضرب لكن في الحقيقة هي عبارة عن", "tokens": [6027, 21292, 7649, 9307, 3714, 11242, 25513, 9307, 48812, 25513, 44381, 8978, 21542, 38436, 28671, 39896, 6225, 3555, 9640, 3660, 18871], "avg_logprob": -0.30468750406395306, "compression_ratio": 1.1666666666666667, "no_speech_prob": 0.0, "words": [{"start": 680.2, "end": 681.0, "word": "البيانات", "probability": 0.557037353515625}, {"start": 681.0, "end": 681.62, "word": " مضربات", "probability": 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"end": 1409.66, "text": "تمام إذا تي جي لما تأثر على أي element بده يسوى تأثير تي إتش على أي element سواء كان ال element هذا ال identity element أو أي element موجود في ال group يعني لو قلت لك تي جي of اي أو قلت لك تي جي of اكسيان هذه والله هذه الاتنين هيأديني إلى نفس النتيجة", "tokens": [2655, 15042, 2304, 11933, 15730, 6055, 1829, 10874, 1829, 5296, 15042, 6055, 10721, 49115, 15844, 36632, 4478, 47525, 3224, 7251, 3794, 2407, 7578, 6055, 10721, 12984, 13546, 6055, 1829, 11933, 2655, 8592, 15844, 36632, 4478, 8608, 2407, 16606, 25961, 2423, 4478, 23758, 2423, 6575, 4478, 34051, 36632, 4478, 3714, 29245, 23328, 8978, 2423, 1594, 37495, 22653, 45164, 12174, 1211, 2655, 5296, 4117, 6055, 1829, 10874, 1829, 295, 1975, 1829, 34051, 12174, 1211, 2655, 5296, 4117, 6055, 1829, 10874, 1829, 295, 1975, 4117, 3794, 1829, 7649, 29538, 16070, 43761, 29538, 2423, 9307, 1863, 9957, 39896, 10721, 3215, 9957, 1829, 30731, 8717, 36178, 28239, 31371, 7435, 3660], "avg_logprob": -0.24189268994443822, 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"probability": 0.67401123046875}, {"start": 1633.48, "end": 1634.24, "word": " أعيدها", "probability": 0.9278564453125}, {"start": 1634.24, "end": 1634.5, "word": " لكم", "probability": 0.873046875}, {"start": 1634.5, "end": 1634.9, "word": " مرة", "probability": 0.9521484375}, {"start": 1634.9, "end": 1635.32, "word": " تانية", "probability": 0.9913736979166666}, {"start": 1635.32, "end": 1635.8, "word": " حتى", "probability": 0.843994140625}, {"start": 1635.8, "end": 1636.52, "word": " نثبت", "probability": 0.9833984375}, {"start": 1636.52, "end": 1636.86, "word": " هذه", "probability": 0.97412109375}, {"start": 1636.86, "end": 1637.92, "word": " المعلومات", "probability": 0.9906005859375}, {"start": 1637.92, "end": 1638.6, "word": " عندكم", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 67, "seek": 166248, "start": 1640.3, "end": 1662.48, "text": "طبعا هي من أطول النظريات برهانة اللى موجودة فى الكتاب ليش لأنها تحدث عن نقطة واحدة وليس عن مجموعة من النقاط النظرية بتقول ما يأتي every group is isomorphic to group if permutation هو هذا اللى ما قلناه فى الآخر", "tokens": [9566, 3555, 3615, 995, 39896, 9154, 5551, 9566, 12610, 28239, 19913, 16572, 9307, 4724, 2288, 3224, 7649, 3660, 13672, 7578, 3714, 29245, 23328, 3660, 6156, 7578, 33251, 2655, 16758, 32239, 8592, 5296, 33456, 11296, 6055, 24401, 12984, 18871, 8717, 47432, 3660, 36764, 24401, 3660, 4032, 20292, 3794, 18871, 3714, 7435, 2304, 2407, 27884, 9154, 28239, 4587, 41193, 28239, 19913, 2288, 10632, 39894, 39648, 19446, 7251, 10721, 31371, 633, 1594, 307, 307, 32702, 299, 281, 1594, 498, 4784, 11380, 31439, 23758, 13672, 7578, 19446, 12174, 1211, 8315, 3224, 6156, 7578, 6024, 95, 34740], "avg_logprob": -0.15927419611202773, "compression_ratio": 1.5529953917050692, "no_speech_prob": 0.0, "words": [{"start": 1640.3, "end": 1640.76, "word": "طبعا", "probability": 0.8826904296875}, {"start": 1640.76, "end": 1640.94, "word": " هي", "probability": 0.52099609375}, {"start": 1640.94, "end": 1641.16, "word": 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1662.02, "end": 1662.14, "word": " فى", "probability": 0.922119140625}, {"start": 1662.14, "end": 1662.48, "word": " الآخر", "probability": 0.7598470052083334}], "temperature": 1.0}, {"id": 68, "seek": 169141, "start": 1662.91, "end": 1691.41, "text": "إنه ال group G isomorphic لل set of all permutations اللي كوّنها على G اللي وعطناها الرمز من SD لما أنا قاعد أقرا النص هذا بقول group G ماشي لكن ال group permutation مش عارف الشكلها يبقى أنا بدأ أخلق ال group هذي وبعد هيك نبدأ نتفاهم على حكاية من ال isomorphism", "tokens": [28814, 1863, 3224, 2423, 1594, 460, 307, 32702, 299, 24976, 992, 295, 439, 4784, 325, 763, 13672, 1829, 9122, 2407, 11703, 1863, 11296, 15844, 460, 13672, 1829, 4032, 3615, 9566, 8315, 11296, 34892, 2304, 11622, 9154, 14638, 5296, 15042, 41850, 12174, 995, 22488, 5551, 4587, 23557, 28239, 9381, 23758, 4724, 39648, 1594, 460, 3714, 33599, 1829, 44381, 2423, 1594, 4784, 11380, 37893, 6225, 9640, 5172, 25124, 28820, 11296, 7251, 3555, 4587, 7578, 41850, 47525, 10721, 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"word": " permutation", "probability": 0.951416015625}, {"start": 1681.69, "end": 1681.97, "word": " مش", "probability": 0.9287109375}, {"start": 1681.97, "end": 1682.37, "word": " عارف", "probability": 0.9943033854166666}, {"start": 1682.37, "end": 1683.25, "word": " الشكلها", "probability": 0.5196126302083334}, {"start": 1683.25, "end": 1684.25, "word": " يبقى", "probability": 0.9500732421875}, {"start": 1684.25, "end": 1684.69, "word": " أنا", "probability": 0.77490234375}, {"start": 1684.69, "end": 1685.19, "word": " بدأ", "probability": 0.601318359375}, {"start": 1685.19, "end": 1685.73, "word": " أخلق", "probability": 0.870849609375}, {"start": 1685.73, "end": 1685.91, "word": " ال", "probability": 0.486572265625}, {"start": 1685.91, "end": 1686.23, "word": " group", "probability": 0.984375}, {"start": 1686.23, "end": 1686.85, "word": " هذي", "probability": 0.7327473958333334}, {"start": 1686.85, "end": 1687.47, "word": " وبعد", "probability": 0.736083984375}, {"start": 1687.47, "end": 1687.69, "word": " هيك", "probability": 0.643798828125}, {"start": 1687.69, "end": 1688.03, "word": " نبدأ", "probability": 0.8611653645833334}, {"start": 1688.03, "end": 1688.67, "word": " نتفاهم", "probability": 0.892578125}, {"start": 1688.67, "end": 1688.89, "word": " على", "probability": 0.52734375}, {"start": 1688.89, "end": 1689.31, "word": " حكاية", "probability": 0.94775390625}, {"start": 1689.31, "end": 1689.69, "word": " من", "probability": 0.66162109375}, {"start": 1689.69, "end": 1690.43, "word": " ال", "probability": 0.88232421875}, {"start": 1690.43, "end": 1691.41, "word": " isomorphism", "probability": 0.9090169270833334}], "temperature": 1.0}, {"id": 69, "seek": 171853, "start": 1694.91, "end": 1718.53, "text": "أخذ أي عنصر جي موجود في جي من مكان يكون عرفت عليه function TG من جي إلى جي by TG of X ساوية G of X التعريف هذا صحيح لأن X و G موجودات في الجي والجي group closed under multiplication يبقى فعلا ال element هذا موجود في جي", "tokens": [10721, 9778, 8848, 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"end": 1698.21, "word": " موجود", "probability": 0.8251953125}, {"start": 1698.21, "end": 1698.35, "word": " في", "probability": 0.94189453125}, {"start": 1698.35, "end": 1698.61, "word": " جي", "probability": 0.76904296875}, {"start": 1698.61, "end": 1698.87, "word": " من", "probability": 0.6982421875}, {"start": 1698.87, "end": 1699.35, "word": " مكان", "probability": 0.90673828125}, {"start": 1699.35, "end": 1699.81, "word": " يكون", "probability": 0.9150390625}, {"start": 1699.81, "end": 1701.31, "word": " عرفت", "probability": 0.6831868489583334}, {"start": 1701.31, "end": 1701.69, "word": " عليه", "probability": 0.99072265625}, {"start": 1701.69, "end": 1702.33, "word": " function", "probability": 0.442138671875}, {"start": 1702.33, "end": 1703.27, "word": " TG", "probability": 0.573486328125}, {"start": 1703.27, "end": 1703.51, "word": " من", "probability": 0.90185546875}, {"start": 1703.51, "end": 1703.87, "word": " جي", "probability": 0.699462890625}, {"start": 1703.87, "end": 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78, "seek": 189999, "start": 1882.15, "end": 1899.99, "text": "وجروب تانية بقدر اعمل ال isomorphism ما بين الاتنين طب سؤال هامشي هيه جاب المكمل بنفع اعمل isomorphism ما بين جروب و ما بين set؟ بنفع", "tokens": [2407, 7435, 32887, 3555, 6055, 7649, 10632, 4724, 28543, 2288, 1975, 25957, 1211, 2423, 307, 32702, 1434, 19446, 49374, 2423, 9307, 1863, 9957, 23032, 3555, 8608, 33604, 6027, 8032, 10943, 8592, 1829, 39896, 3224, 10874, 16758, 9673, 24793, 1211, 44945, 5172, 3615, 1975, 25957, 1211, 307, 32702, 1434, 19446, 49374, 10874, 32887, 3555, 4032, 19446, 49374, 992, 22807, 44945, 5172, 3615], "avg_logprob": -0.26008065765903843, "compression_ratio": 1.6119402985074627, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1882.15, "end": 1882.89, "word": "وجروب", "probability": 0.72821044921875}, {"start": 1882.89, "end": 1883.39, "word": " تانية", "probability": 0.9923502604166666}, {"start": 1883.39, "end": 1883.93, "word": " بقدر", "probability": 0.9767252604166666}, 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1900.76, "end": 1926.02, "text": "لا يمكن ينفع لأن هذه عليها binary operation وهذه ما عليها اش احنا بيقول isomorphism الأولى والتانية كله لهم نفس القواصة الرياضية فكيف علي هذه binary operation وهذه لأ إذا لا يمكن أن يكون هناك isomorphism ما بين group ما بين set لازم يكون التنتين are groups طيب نرجع الأن لل SG أنا أدعى", "tokens": [15040, 7251, 43020, 7251, 1863, 5172, 3615, 5296, 33456, 29538, 25894, 11296, 17434, 6916, 37037, 24192, 19446, 25894, 11296, 1975, 8592, 1975, 5016, 8315, 4724, 1829, 39648, 307, 32702, 1434, 16247, 12610, 7578, 4032, 6027, 2655, 7649, 10632, 28242, 3224, 5296, 16095, 8717, 36178, 25062, 2407, 33546, 3660, 2423, 16572, 46958, 10632, 6156, 4117, 33911, 25894, 29538, 17434, 6916, 4032, 3224, 24192, 5296, 10721, 11933, 15730, 20193, 7251, 43020, 14739, 7251, 30544, 34105, 4117, 307, 32702, 1434, 19446, 49374, 1594, 19446, 49374, 992, 5296, 31377, 2304, 7251, 30544, 16712, 29399, 9957, 366, 3935, 23032, 1829, 3555, 8717, 47341, 3615, 16247, 1863, 24976, 34520, 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{"start": 1991.22, "end": 1991.82, "word": " عندنا", "probability": 0.83837890625}, {"start": 1991.82, "end": 1992.54, "word": " binary", "probability": 0.1922607421875}, {"start": 1992.54, "end": 1993.22, "word": " operation", "probability": 0.5849609375}, {"start": 1993.22, "end": 1993.78, "word": " كمان", "probability": 0.79736328125}, {"start": 1993.78, "end": 1993.92, "word": " ال", "probability": 0.6572265625}, {"start": 1993.92, "end": 1994.42, "word": " composition", "probability": 0.87744140625}, {"start": 1994.42, "end": 1994.68, "word": " of", "probability": 0.73291015625}, {"start": 1994.68, "end": 1994.8, "word": " a", "probability": 0.265625}, {"start": 1994.8, "end": 1995.06, "word": " function", "probability": 0.962890625}, {"start": 1995.06, "end": 1995.32, "word": " ثم", "probability": 0.55731201171875}, {"start": 1995.32, "end": 1995.58, "word": " نعرف", "probability": 0.9137369791666666}, {"start": 1995.58, "end": 1995.8, "word": " انها", "probability": 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2002.58, "end": 2018.78, "text": "انا ادعي ان TA هو ال identity element وروح نثبتنا ان هو ال identity element اتدعيت ان تجي انفرس بالضبط هو ت وال انفرس بحطه على ال element", "tokens": [7649, 995, 1975, 3215, 3615, 1829, 16472, 20094, 31439, 2423, 6575, 4478, 4032, 32887, 5016, 8717, 12984, 3555, 2655, 8315, 16472, 31439, 2423, 6575, 4478, 1975, 2655, 3215, 3615, 36081, 16472, 6055, 7435, 1829, 16472, 5172, 2288, 3794, 20666, 11242, 3555, 9566, 31439, 6055, 16070, 16472, 5172, 2288, 3794, 4724, 5016, 9566, 3224, 15844, 2423, 4478], "avg_logprob": -0.3670504511448375, "compression_ratio": 1.6, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 2002.5800000000002, "end": 2003.7, "word": "انا", "probability": 0.498046875}, {"start": 2003.7, "end": 2004.4, "word": " ادعي", "probability": 0.6866455078125}, {"start": 2004.4, "end": 2005.12, "word": " ان", "probability": 0.5361328125}, {"start": 2005.12, "end": 2005.74, "word": " TA", "probability": 0.132080078125}, {"start": 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0.89697265625}, {"start": 2226.18, "end": 2226.74, "word": " هذه", "probability": 0.221923828125}, {"start": 2226.74, "end": 2233.68, "word": " example", "probability": 0.861328125}], "temperature": 1.0}, {"id": 95, "seek": 228454, "start": 2268.3, "end": 2284.54, "text": "find الاجرب SG where ال G بدأت ساوي ال U عشرة", "tokens": [35072, 2423, 26108, 25513, 34520, 689, 2423, 460, 47525, 10721, 2655, 8608, 995, 45865, 2423, 624, 6225, 8592, 25720], "avg_logprob": -0.45546873956918715, "compression_ratio": 0.9710144927536232, "no_speech_prob": 0.0, "words": [{"start": 2268.2999999999997, "end": 2269.7, "word": "find", "probability": 0.27978515625}, {"start": 2269.7, "end": 2271.1, "word": " الاجرب", "probability": 0.4938557942708333}, {"start": 2271.1, "end": 2274.06, "word": " SG", "probability": 0.447265625}, {"start": 2274.06, "end": 2276.56, "word": " where", "probability": 0.83740234375}, {"start": 2276.56, "end": 2279.76, "word": " ال", "probability": 0.46484375}, {"start": 2279.76, "end": 2280.26, "word": " G", "probability": 0.396728515625}, {"start": 2280.26, "end": 2281.88, "word": " بدأت", "probability": 0.681640625}, {"start": 2281.88, "end": 2282.54, "word": " ساوي", "probability": 0.7317708333333334}, {"start": 2282.54, "end": 2283.52, "word": " ال", "probability": 0.8544921875}, {"start": 2283.52, "end": 2283.92, "word": " U", "probability": 0.97216796875}, {"start": 2283.92, "end": 2284.54, "word": " عشرة", "probability": 0.8772786458333334}], "temperature": 1.0}, {"id": 96, "seek": 232680, "start": 2297.14, "end": 2326.8, "text": "أظهر لو وجدنا عناصر SG بيصير الجيل الأصلي اللي هي U10 isomorphic لمين؟ للـ SG حسب نظرية كلب الأن لو جيت للـU10 مين عناصرها؟ الواحد، اتنين، تلاتة، أربعة، خمسة، ستة، سبعة، تسعة، في غيرهم؟", "tokens": [10721, 19913, 3224, 2288, 45164, 49610, 3215, 8315, 18871, 33546, 2288, 34520, 4724, 1829, 9381, 13546, 25724, 26895, 16247, 9381, 20292, 13672, 1829, 39896, 624, 3279, 307, 32702, 299, 32767, 9957, 22807, 24976, 39184, 34520, 11331, 35457, 8717, 19913, 2288, 10632, 28242, 3555, 16247, 1863, 45164, 10874, 36081, 24976, 39184, 52, 3279, 3714, 9957, 18871, 33546, 2288, 11296, 22807, 2423, 14407, 24401, 12399, 1975, 2655, 1863, 9957, 12399, 6055, 1211, 9307, 3660, 12399, 5551, 25513, 27884, 12399, 16490, 2304, 3794, 3660, 12399, 8608, 2655, 3660, 12399, 8608, 3555, 27884, 12399, 6055, 3794, 27884, 12399, 8978, 32771, 13546, 16095, 22807], "avg_logprob": -0.2190625025331974, "compression_ratio": 1.5771144278606966, "no_speech_prob": 0.0, "words": [{"start": 2297.14, "end": 2297.62, "word": "أظهر", "probability": 0.651031494140625}, {"start": 2297.62, "end": 2297.86, "word": " لو", "probability": 0.923828125}, {"start": 2297.86, "end": 2298.46, "word": " وجدنا", "probability": 0.9715169270833334}, {"start": 2298.46, "end": 2299.24, "word": " عناصر", "probability": 0.9622395833333334}, {"start": 2299.24, "end": 2300.34, "word": " SG", "probability": 0.74072265625}, {"start": 2300.34, "end": 2302.04, "word": " بيصير", "probability": 0.8199462890625}, {"start": 2302.04, "end": 2302.44, "word": " الجيل", "probability": 0.5810546875}, {"start": 2302.44, "end": 2303.14, "word": " الأصلي", "probability": 0.8167317708333334}, {"start": 2303.14, "end": 2303.42, "word": " اللي", "probability": 0.776611328125}, {"start": 2303.42, "end": 2303.66, "word": " هي", "probability": 0.75341796875}, {"start": 2303.66, "end": 2304.34, "word": " U10", "probability": 0.904541015625}, {"start": 2304.34, "end": 2305.62, "word": " isomorphic", "probability": 0.7462565104166666}, {"start": 2305.62, "end": 2306.4, "word": " لمين؟", "probability": 0.7478841145833334}, {"start": 2306.4, "end": 2306.84, "word": " للـ", "probability": 0.6444091796875}, {"start": 2306.84, "end": 2307.24, "word": " SG", "probability": 0.84814453125}, {"start": 2307.24, "end": 2308.1, "word": " حسب", "probability": 0.875244140625}, {"start": 2308.1, "end": 2308.76, "word": " نظرية", "probability": 0.9598388671875}, {"start": 2308.76, "end": 2309.26, "word": " كلب", "probability": 0.524169921875}, {"start": 2309.26, "end": 2310.4, "word": " الأن", "probability": 0.456268310546875}, {"start": 2310.4, "end": 2310.6, "word": " لو", "probability": 0.984375}, {"start": 2310.6, "end": 2310.88, "word": " جيت", "probability": 0.788330078125}, {"start": 2310.88, "end": 2311.94, "word": " للـU10", "probability": 0.8255615234375}, {"start": 2311.94, "end": 2314.52, "word": " مين", "probability": 0.85107421875}, {"start": 2314.52, "end": 2316.42, "word": " عناصرها؟", "probability": 0.94560546875}, {"start": 2316.42, "end": 2317.6, "word": " الواحد،", "probability": 0.82257080078125}, {"start": 2317.6, "end": 2319.0, "word": " اتنين،", "probability": 0.809912109375}, {"start": 2319.0, "end": 2320.34, "word": " تلاتة،", "probability": 0.94921875}, {"start": 2320.34, "end": 2321.56, "word": " أربعة،", "probability": 0.8621826171875}, {"start": 2321.56, "end": 2322.46, "word": " خمسة،", "probability": 0.98349609375}, {"start": 2322.46, "end": 2323.52, "word": " ستة،", "probability": 0.978759765625}, {"start": 2323.52, "end": 2324.66, "word": " سبعة،", "probability": 0.92578125}, {"start": 2324.66, "end": 2325.44, "word": " تسعة،", "probability": 0.9000244140625}, {"start": 2325.44, "end": 2326.04, "word": " في", "probability": 0.6640625}, {"start": 2326.04, "end": 2326.8, "word": " غيرهم؟", "probability": 0.970947265625}], "temperature": 1.0}, {"id": 97, "seek": 235594, "start": 2328.07, "end": 2355.95, "text": "طيب يبقى بناء عليه ال S G ال S G أو ال S U عشرة بدها تساوي T واحد و T تلاتة و T سبعة و T تسعة بس مين T واحد و T تلاتة و T سبعة مش عارفين بدنا نعرف تمام باجي بقولهم where", "tokens": [9566, 1829, 3555, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 2423, 318, 460, 2423, 318, 460, 34051, 2423, 318, 624, 6225, 8592, 25720, 47525, 11296, 6055, 3794, 995, 45865, 314, 36764, 24401, 4032, 314, 6055, 1211, 9307, 3660, 4032, 314, 8608, 3555, 27884, 4032, 314, 6055, 3794, 27884, 4724, 3794, 3714, 9957, 314, 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"word": " T", "probability": 0.64111328125}, {"start": 2342.25, "end": 2343.05, "word": " تلاتة", "probability": 0.8831787109375}, {"start": 2343.05, "end": 2343.79, "word": " و", "probability": 0.97607421875}, {"start": 2343.79, "end": 2344.07, "word": " T", "probability": 0.87548828125}, {"start": 2344.07, "end": 2344.81, "word": " سبعة", "probability": 0.94970703125}, {"start": 2344.81, "end": 2345.45, "word": " و", "probability": 0.99072265625}, {"start": 2345.45, "end": 2345.65, "word": " T", "probability": 0.896484375}, {"start": 2345.65, "end": 2346.83, "word": " تسعة", "probability": 0.9851888020833334}, {"start": 2346.83, "end": 2347.95, "word": " بس", "probability": 0.96044921875}, {"start": 2347.95, "end": 2348.21, "word": " مين", "probability": 0.914306640625}, {"start": 2348.21, "end": 2348.43, "word": " T", "probability": 0.9072265625}, {"start": 2348.43, "end": 2348.91, "word": " واحد", "probability": 0.9853515625}, {"start": 2348.91, "end": 2349.11, "word": " و", 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"language": "ar", "language_probability": 1.0, "duration": 2660.914, "duration_after_vad": 2535.4112499999906}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f2c7a9f361aa103bc1ccafa0151d5b3e84f18c6d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.json
@@ -0,0 +1 @@
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" القادمة.", "probability": 0.9915364583333334}], "temperature": 1.0}, {"id": 13, "seek": 29989, "start": 275.6, "end": 299.9, "text": "يبقى في انفرس جي برايم يبقى مين يسوى جي في الكرنة اللي في هذا اللي عايزين ان تبدو هدول two sets are equal يبقى بدي اروح اخد element هنا اثبت انه موجود هنا و اعمل الأعمال العكسية اخد element هنا و اثبت انه موجود هنا يبقى مشان هيك بداجي اقوله let ال X موجودة في في انفرس جي برايم", "tokens": [1829, 3555, 4587, 7578, 8978, 16472, 5172, 2288, 3794, 10874, 1829, 4724, 23557, 32640, 7251, 3555, 4587, 7578, 3714, 9957, 7251, 3794, 2407, 7578, 10874, 1829, 8978, 2423, 37983, 1863, 3660, 13672, 1829, 8978, 23758, 13672, 1829, 6225, 47302, 11622, 9957, 16472, 6055, 44510, 2407, 8032, 3215, 12610, 732, 6352, 366, 2681, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 32887, 5016, 1975, 9778, 3215, 4478, 34105, 1975, 12984, 3555, 2655, 16472, 3224, 3714, 29245, 23328, 34105, 4032, 1975, 25957, 1211, 16247, 25957, 6027, 18863, 4117, 3794, 10632, 1975, 9778, 3215, 4478, 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مُعطَى من الرأس المسألة؟ G prime يبقى هذا Phi of G بده يساوي G prime طيب Phi of K كدهش؟ طلع ليه هنا، احنا جيبناها من وين الـK هذا؟", "tokens": [6027, 9566, 28480, 25124, 2304, 6027, 41435, 295, 1783, 41950, 28480, 2423, 32640, 9957, 41435, 295, 460, 9122, 3215, 3224, 8592, 3714, 10859, 3615, 9566, 6808, 7578, 9154, 34892, 10721, 3794, 9673, 3794, 10721, 37977, 22807, 460, 5835, 7251, 3555, 4587, 7578, 23758, 41435, 295, 460, 47525, 3224, 7251, 3794, 995, 45865, 460, 5835, 23032, 1829, 3555, 41435, 295, 591, 9122, 3215, 3224, 8592, 22807, 23032, 1211, 3615, 32239, 3224, 34105, 12399, 1975, 5016, 8315, 10874, 1829, 3555, 8315, 11296, 9154, 4032, 9957, 2423, 39184, 42, 23758, 22807], "avg_logprob": -0.3114466158191809, "compression_ratio": 1.6022727272727273, "no_speech_prob": 0.0, "words": [{"start": 524.22, "end": 524.82, "word": "الطرف", "probability": 0.8663736979166666}, {"start": 524.82, "end": 525.46, "word": " الشمال", "probability": 0.98193359375}, {"start": 525.46, "end": 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{"start": 539.94, "end": 540.3, "word": " Phi", "probability": 0.88623046875}, {"start": 540.3, "end": 540.6, "word": " of", "probability": 0.97509765625}, {"start": 540.6, "end": 540.8, "word": " K", "probability": 0.97900390625}, {"start": 540.8, "end": 544.9, "word": " كدهش؟", "probability": 0.7915283203125}, {"start": 544.9, "end": 545.52, "word": " طلع", "probability": 0.84619140625}, {"start": 545.52, "end": 545.74, "word": " ليه", "probability": 0.7064208984375}, {"start": 545.74, "end": 546.16, "word": " هنا،", "probability": 0.6627197265625}, {"start": 546.16, "end": 546.32, "word": " احنا", "probability": 0.8831380208333334}, {"start": 546.32, "end": 546.7, "word": " جيبناها", "probability": 0.823974609375}, {"start": 546.7, "end": 546.86, "word": " من", "probability": 0.869140625}, {"start": 546.86, "end": 547.12, "word": " وين", "probability": 0.883544921875}, {"start": 547.12, "end": 547.52, "word": " الـK", "probability": 0.7097981770833334}, {"start": 547.52, "end": 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648.67, "end": 649.27, "word": " وانت", "probability": 0.9983723958333334}, {"start": 649.27, "end": 649.27, "word": " وانت", "probability": 0.9983723958333334}, {"start": 649.27, "end": 649.39, "word": " وانت", "probability": 0.9983723958333334}, {"start": 649.39, "end": 649.99, "word": " وانت", "probability": 0.9983723958333334}, {"start": 649.99, "end": 650.47, "word": " وانت", "probability": 0.9983723958333334}, {"start": 650.47, "end": 650.53, "word": " وانت", "probability": 0.99853515625}, {"start": 650.53, "end": 650.59, "word": " وانت", "probability": 0.99853515625}, {"start": 650.59, "end": 650.65, "word": " وانت", "probability": 0.99853515625}, {"start": 650.65, "end": 654.77, "word": " وانت", "probability": 0.99853515625}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.99853515625}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.99853515625}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9983723958333334}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9983723958333334}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9983723958333334}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9983723958333334}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9982096354166666}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.998046875}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.998046875}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9978841145833334}, {"start": 654.77, "end": 654.77, "word": " وانت", "probability": 0.9977213541666666}], "temperature": 1.0}, {"id": 29, "seek": 68851, "start": 662.63, "end": 688.51, "text": "اللي هو subset من مين من الـ Phi inverse of G prime وهذه العلاقة رقم اتنين يبقى باجي بقول from واحد and اتنين we have ان ال Phi inverse of G prime بده يساوي G في الكيرن للـ Phi", "tokens": [6027, 20292, 31439, 25993, 9154, 3714, 9957, 9154, 2423, 39184, 41435, 17340, 295, 460, 5835, 37037, 24192, 18863, 15040, 28671, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 321, 362, 16472, 2423, 41435, 17340, 295, 460, 5835, 47525, 3224, 7251, 3794, 995, 45865, 460, 8978, 33251, 13546, 1863, 24976, 39184, 41435], "avg_logprob": -0.31204042671357884, "compression_ratio": 1.4912280701754386, "no_speech_prob": 0.0, "words": [{"start": 662.63, "end": 662.99, "word": "اللي", "probability": 0.4285888671875}, {"start": 662.99, "end": 663.25, "word": " هو", "probability": 0.916015625}, {"start": 663.25, "end": 663.89, "word": " subset", "probability": 0.5244140625}, {"start": 663.89, "end": 664.29, "word": " من", "probability": 0.9814453125}, {"start": 664.29, "end": 664.65, "word": " مين", "probability": 0.60467529296875}, {"start": 664.65, "end": 665.25, "word": " من", "probability": 0.62353515625}, {"start": 665.25, "end": 665.61, "word": " الـ", "probability": 0.803466796875}, {"start": 665.61, "end": 665.93, "word": " Phi", "probability": 0.26171875}, {"start": 665.93, "end": 666.75, "word": " inverse", "probability": 0.7607421875}, {"start": 666.75, "end": 667.37, "word": " of", "probability": 0.95556640625}, {"start": 667.37, "end": 667.71, "word": " G", "probability": 0.84326171875}, {"start": 667.71, "end": 668.23, "word": " prime", "probability": 0.2529296875}, {"start": 668.23, "end": 669.03, "word": " وهذه", "probability": 0.4793701171875}, {"start": 669.03, "end": 669.57, "word": " العلاقة", "probability": 0.9098307291666666}, {"start": 669.57, "end": 670.13, "word": " رقم", "probability": 0.9375}, {"start": 670.13, "end": 670.79, "word": " اتنين", "probability": 0.890380859375}, {"start": 670.79, "end": 671.65, "word": " يبقى", "probability": 0.905517578125}, {"start": 671.65, "end": 671.99, "word": " باجي", "probability": 0.85107421875}, {"start": 671.99, "end": 672.43, "word": " بقول", "probability": 0.877685546875}, {"start": 672.43, "end": 672.99, "word": " from", "probability": 0.73095703125}, {"start": 672.99, "end": 674.41, "word": " واحد", "probability": 0.961181640625}, {"start": 674.41, "end": 676.03, "word": " and", "probability": 0.87158203125}, {"start": 676.03, "end": 677.73, "word": " اتنين", "probability": 0.978271484375}, {"start": 677.73, "end": 678.39, "word": " we", "probability": 0.261474609375}, {"start": 678.39, "end": 679.29, "word": " have", "probability": 0.97216796875}, {"start": 679.29, "end": 681.47, "word": " ان", "probability": 0.65380859375}, {"start": 681.47, "end": 681.77, "word": " ال", "probability": 0.5556640625}, {"start": 681.77, "end": 682.23, "word": " Phi", "probability": 0.62841796875}, {"start": 682.23, "end": 683.01, "word": " inverse", "probability": 0.83544921875}, {"start": 683.01, "end": 683.49, "word": " of", "probability": 0.9775390625}, {"start": 683.49, "end": 683.81, "word": " G", "probability": 0.98486328125}, {"start": 683.81, "end": 684.33, "word": " prime", "probability": 0.82861328125}, {"start": 684.33, "end": 685.17, "word": " بده", "probability": 0.551025390625}, {"start": 685.17, "end": 685.65, "word": " يساوي", "probability": 0.7962646484375}, {"start": 685.65, "end": 686.37, "word": " G", "probability": 0.90185546875}, {"start": 686.37, "end": 686.79, "word": " في", "probability": 0.90869140625}, {"start": 686.79, "end": 687.91, "word": " الكيرن", "probability": 0.6388346354166666}, {"start": 687.91, "end": 688.33, "word": " للـ", "probability": 0.599609375}, {"start": 688.33, "end": 688.51, "word": " Phi", "probability": 0.70361328125}], "temperature": 1.0}, {"id": 30, "seek": 71911, "start": 694.71, "end": 719.11, "text": "نعطيك مثال توضيح على ذلك لإن هي خلصت النظرية example بقول suppose that افترض ان الفاي من z تلاتين الى z تلاتين", "tokens": [1863, 3615, 9566, 1829, 4117, 50113, 6027, 6055, 2407, 11242, 1829, 5016, 15844, 29910, 23275, 5296, 28814, 1863, 39896, 16490, 1211, 9381, 2655, 28239, 19913, 2288, 10632, 1365, 4724, 39648, 7297, 300, 1975, 5172, 2655, 43042, 16472, 27188, 47302, 9154, 710, 6055, 1211, 9307, 9957, 2423, 7578, 710, 6055, 1211, 9307, 9957], "avg_logprob": -0.2995283041360243, "compression_ratio": 1.3161764705882353, "no_speech_prob": 0.0, "words": [{"start": 694.71, "end": 695.47, "word": "نعطيك", "probability": 0.79912109375}, {"start": 695.47, "end": 696.07, "word": " مثال", "probability": 0.944091796875}, {"start": 696.07, "end": 696.55, "word": " توضيح", "probability": 0.87421875}, {"start": 696.55, "end": 696.71, "word": " على", "probability": 0.84228515625}, {"start": 696.71, "end": 697.07, "word": " ذلك", "probability": 0.988525390625}, {"start": 697.07, "end": 697.27, "word": " لإن", "probability": 0.724365234375}, {"start": 697.27, "end": 697.43, "word": " هي", "probability": 0.491943359375}, {"start": 697.43, "end": 698.11, "word": " خلصت", "probability": 0.8768310546875}, {"start": 698.11, "end": 698.89, "word": " النظرية", "probability": 0.842529296875}, {"start": 698.89, "end": 700.41, "word": " example", "probability": 0.28515625}, {"start": 700.41, "end": 704.87, "word": " بقول", "probability": 0.5660400390625}, {"start": 704.87, "end": 705.35, "word": " suppose", "probability": 0.2822265625}, {"start": 705.35, "end": 709.61, "word": " that", "probability": 0.90966796875}, {"start": 709.61, "end": 710.87, "word": " افترض", "probability": 0.84747314453125}, {"start": 710.87, "end": 711.31, "word": " ان", "probability": 0.55419921875}, {"start": 711.31, "end": 713.05, "word": " الفاي", "probability": 0.3577880859375}, {"start": 713.05, "end": 714.73, "word": " من", "probability": 0.96044921875}, {"start": 714.73, "end": 715.53, "word": " z", "probability": 0.60009765625}, {"start": 715.53, "end": 716.85, "word": " تلاتين", "probability": 0.81378173828125}, {"start": 716.85, "end": 717.41, "word": " الى", "probability": 0.71728515625}, {"start": 717.41, "end": 718.05, "word": " z", "probability": 0.9599609375}, {"start": 718.05, "end": 719.11, "word": " تلاتين", "probability": 0.9813232421875}], "temperature": 1.0}, {"id": 31, "seek": 73903, "start": 720.85, "end": 739.03, "text": "A homomorphism suppose that فاي is a homomorphism and الكيرنل للفاي هي العناصر zero و عشرة و عشرين", "tokens": [32, 3655, 32702, 1434, 7297, 300, 6156, 47302, 307, 257, 3655, 32702, 1434, 293, 33251, 13546, 1863, 1211, 24976, 5172, 47302, 39896, 18863, 1863, 33546, 2288, 4018, 4032, 6225, 8592, 25720, 4032, 6225, 46309, 9957], "avg_logprob": -0.4275173528326882, "compression_ratio": 1.2201834862385321, "no_speech_prob": 0.0, "words": [{"start": 720.85, "end": 721.13, "word": "A", "probability": 0.05706787109375}, {"start": 721.13, "end": 722.17, "word": " homomorphism", "probability": 0.8933919270833334}, {"start": 722.17, "end": 722.73, "word": " suppose", "probability": 0.17724609375}, {"start": 722.73, "end": 723.29, "word": " that", "probability": 0.82373046875}, {"start": 723.29, "end": 723.77, "word": " فاي", "probability": 0.3916015625}, {"start": 723.77, "end": 724.47, "word": " is", "probability": 0.77587890625}, {"start": 724.47, "end": 725.27, "word": " a", "probability": 0.892578125}, {"start": 725.27, "end": 727.73, "word": " homomorphism", "probability": 0.97900390625}, {"start": 727.73, "end": 729.43, "word": " and", "probability": 0.82275390625}, {"start": 729.43, "end": 732.51, "word": " الكيرنل", "probability": 0.6412353515625}, {"start": 732.51, "end": 733.45, "word": " للفاي", "probability": 0.8331705729166666}, {"start": 733.45, "end": 733.95, "word": " هي", "probability": 0.392333984375}, {"start": 733.95, "end": 735.15, "word": " العناصر", "probability": 0.945556640625}, {"start": 735.15, "end": 736.21, "word": " zero", "probability": 0.302734375}, {"start": 736.21, "end": 736.85, "word": " و", "probability": 0.67919921875}, {"start": 736.85, "end": 737.63, "word": " عشرة", "probability": 0.7615559895833334}, {"start": 737.63, "end": 738.09, "word": " و", "probability": 0.98974609375}, {"start": 738.09, "end": 739.03, "word": " عشرين", "probability": 0.8323567708333334}], "temperature": 1.0}, {"id": 32, "seek": 75851, "start": 740.51, "end": 758.51, "text": "بيقول لـ F إذا كان الـ Phi لـ 23 هي عبارة عن 9 السؤال هو determine all", "tokens": [3555, 1829, 39648, 5296, 39184, 479, 11933, 15730, 25961, 2423, 39184, 41435, 5296, 39184, 6673, 39896, 6225, 3555, 9640, 3660, 18871, 1722, 21136, 33604, 6027, 31439, 6997, 439], "avg_logprob": -0.30845904761347276, "compression_ratio": 1.05, "no_speech_prob": 0.0, "words": [{"start": 740.51, "end": 741.09, "word": "بيقول", "probability": 0.5686848958333334}, {"start": 741.09, "end": 741.35, "word": " لـ", "probability": 0.28302001953125}, {"start": 741.35, "end": 741.77, "word": " F", "probability": 0.64501953125}, {"start": 741.77, "end": 742.39, "word": " إذا", "probability": 0.939208984375}, {"start": 742.39, "end": 743.05, "word": " كان", "probability": 0.99365234375}, {"start": 743.05, "end": 743.57, "word": " الـ", "probability": 0.89453125}, {"start": 743.57, "end": 743.97, "word": " Phi", "probability": 0.182373046875}, {"start": 743.97, "end": 744.75, "word": " لـ", "probability": 0.8515625}, {"start": 744.75, "end": 745.77, "word": " 23", "probability": 0.7626953125}, {"start": 745.77, "end": 747.07, "word": " هي", "probability": 0.84423828125}, {"start": 747.07, "end": 747.77, "word": " عبارة", "probability": 0.9962158203125}, {"start": 747.77, "end": 748.15, "word": " عن", "probability": 0.99560546875}, {"start": 748.15, "end": 748.65, "word": " 9", "probability": 0.728515625}, {"start": 748.65, "end": 749.89, "word": " السؤال", "probability": 0.9212239583333334}, {"start": 749.89, "end": 750.29, "word": " هو", "probability": 0.970703125}, {"start": 750.29, "end": 753.99, "word": " determine", "probability": 0.58056640625}, {"start": 753.99, "end": 758.51, "word": " all", "probability": 0.8447265625}], "temperature": 1.0}, {"id": 33, "seek": 78754, "start": 761.76, "end": 787.54, "text": "Elements that map maps to تسعة كل ال elements اللي هم maps to تسعة السؤال مرة تانية فيها النفاي من Z تلاتين ل Z تلاتين homomorphism", "tokens": [36, 17988, 300, 4471, 11317, 281, 6055, 3794, 27884, 28242, 2423, 4959, 13672, 1829, 8032, 2304, 11317, 281, 6055, 3794, 27884, 21136, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 8978, 11296, 28239, 5172, 47302, 9154, 1176, 6055, 1211, 9307, 9957, 5296, 1176, 6055, 1211, 9307, 9957, 3655, 32702, 1434], "avg_logprob": -0.3265624976158142, "compression_ratio": 1.46875, "no_speech_prob": 0.0, "words": [{"start": 761.7600000000001, "end": 762.8000000000001, "word": "Elements", "probability": 0.481719970703125}, {"start": 762.8000000000001, "end": 763.84, "word": " that", "probability": 0.70556640625}, {"start": 763.84, "end": 765.86, "word": " map", "probability": 0.30859375}, {"start": 765.86, "end": 767.84, "word": " maps", "probability": 0.67626953125}, {"start": 767.84, "end": 768.34, "word": " to", "probability": 0.9560546875}, {"start": 768.34, "end": 769.6, "word": " تسعة", "probability": 0.8429361979166666}, {"start": 769.6, "end": 770.48, "word": " كل", "probability": 0.302978515625}, {"start": 770.48, "end": 770.66, "word": " ال", "probability": 0.85791015625}, {"start": 770.66, "end": 771.02, "word": " elements", "probability": 0.693359375}, {"start": 771.02, "end": 771.3, "word": " اللي", "probability": 0.85107421875}, {"start": 771.3, "end": 771.5, "word": " هم", "probability": 0.5579833984375}, {"start": 771.5, "end": 771.92, "word": " maps", "probability": 0.74658203125}, {"start": 771.92, "end": 772.16, "word": " to", "probability": 0.9208984375}, {"start": 772.16, "end": 772.68, "word": " تسعة", "probability": 0.9762369791666666}, {"start": 772.68, "end": 782.04, "word": " السؤال", "probability": 0.9407552083333334}, {"start": 782.04, "end": 782.32, "word": " مرة", "probability": 0.868408203125}, {"start": 782.32, "end": 782.84, "word": " تانية", "probability": 0.9767252604166666}, {"start": 782.84, "end": 784.02, "word": " فيها", "probability": 0.571044921875}, {"start": 784.02, "end": 784.56, "word": " النفاي", "probability": 0.66015625}, {"start": 784.56, "end": 784.8, "word": " من", "probability": 0.89990234375}, {"start": 784.8, "end": 784.9, "word": " Z", "probability": 0.362548828125}, {"start": 784.9, "end": 785.52, "word": " تلاتين", "probability": 0.81207275390625}, {"start": 785.52, "end": 785.64, "word": " ل", "probability": 0.9423828125}, {"start": 785.64, "end": 785.8, "word": " Z", "probability": 0.461181640625}, {"start": 785.8, "end": 786.48, "word": " تلاتين", "probability": 0.9853515625}, {"start": 786.48, "end": 787.54, "word": " homomorphism", "probability": 0.8087565104166666}], "temperature": 1.0}, {"id": 34, "seek": 81129, "start": 788.21, "end": 811.29, "text": "وهذا حسبنا له كيرن اللي جينا كيرنه zero وعشرة وعشرين هذه معلومة وزيادة على ذلك five of تلاتة وعشرين يساوي تسعة قال لي هاتلي كل ال elements اللي maps to تسعة يعني بدي كل العناصر اللي في زد تلاتين واللي صارتهم بتكون مان تسعة يعني مش ع جد تلاتة وعشرين", "tokens": [2407, 3224, 15730, 11331, 35457, 8315, 46740, 9122, 13546, 1863, 13672, 1829, 10874, 1829, 8315, 9122, 13546, 1863, 3224, 4018, 4032, 3615, 8592, 25720, 4032, 3615, 46309, 9957, 29538, 20449, 1211, 20498, 3660, 4032, 11622, 1829, 18513, 3660, 15844, 29910, 23275, 1732, 295, 6055, 1211, 9307, 3660, 4032, 3615, 46309, 9957, 7251, 3794, 995, 45865, 6055, 3794, 27884, 50239, 32239, 8032, 9307, 20292, 28242, 2423, 4959, 13672, 1829, 11317, 281, 6055, 3794, 27884, 37495, 22653, 4724, 16254, 28242, 18863, 1863, 33546, 2288, 13672, 1829, 8978, 30767, 3215, 6055, 1211, 9307, 9957, 4032, 6027, 20292, 20328, 9640, 2655, 16095, 39894, 30544, 3714, 7649, 6055, 3794, 27884, 37495, 22653, 37893, 6225, 10874, 3215, 6055, 1211, 9307, 3660, 4032, 3615, 46309, 9957], "avg_logprob": -0.23593749701976777, "compression_ratio": 1.8968609865470851, "no_speech_prob": 0.0, "words": [{"start": 788.21, "end": 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"text": "لو كانت الـ H is a normal subgroup من G then Phi of H is a normal subgroup من Phi of G النقطة الخامسة", "tokens": [1211, 2407, 25961, 2655, 2423, 39184, 389, 307, 257, 2710, 1422, 17377, 9154, 460, 550, 41435, 295, 389, 307, 257, 2710, 1422, 17377, 9154, 41435, 295, 460, 28239, 47432, 3660, 33962, 10943, 3794, 3660], "avg_logprob": -0.23928571087973458, "compression_ratio": 1.3229166666666667, "no_speech_prob": 0.0, "words": [{"start": 1089.08, "end": 1089.6, "word": "لو", "probability": 0.85595703125}, {"start": 1089.6, "end": 1090.28, "word": " كانت", "probability": 0.912353515625}, {"start": 1090.28, "end": 1090.7, "word": " الـ", "probability": 0.82421875}, {"start": 1090.7, "end": 1091.16, "word": " H", "probability": 0.56396484375}, {"start": 1091.16, "end": 1092.34, "word": " is", "probability": 0.350830078125}, {"start": 1092.34, "end": 1092.72, "word": " a", "probability": 0.96142578125}, {"start": 1092.72, "end": 1093.26, "word": " normal", "probability": 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1102.04, "end": 1103.58, "word": " Phi", "probability": 0.19091796875}, {"start": 1103.58, "end": 1105.2, "word": " of", "probability": 0.86376953125}, {"start": 1105.2, "end": 1105.6, "word": " G", "probability": 0.9951171875}, {"start": 1105.6, "end": 1108.62, "word": " النقطة", "probability": 0.9441731770833334}, {"start": 1108.62, "end": 1110.02, "word": " الخامسة", "probability": 0.98486328125}], "temperature": 1.0}, {"id": 47, "seek": 113608, "start": 1111.32, "end": 1136.08, "text": "إذا كانت أعضاء كيرنال فيا هي نة ثم فيا ثم فيا هي نة إلى واحدة نة إلى واحدة مابينج من", "tokens": [28814, 15730, 25961, 2655, 5551, 3615, 11242, 16606, 9122, 13546, 1863, 6027, 8978, 995, 39896, 8717, 3660, 38637, 2304, 8978, 995, 38637, 2304, 8978, 995, 39896, 8717, 3660, 30731, 36764, 24401, 3660, 8717, 3660, 30731, 36764, 24401, 3660, 3714, 16758, 9957, 7435, 9154], "avg_logprob": -0.6889204626733606, "compression_ratio": 1.6195652173913044, "no_speech_prob": 0.0, "words": [{"start": 1111.32, "end": 1111.98, "word": "إذا", "probability": 0.684326171875}, {"start": 1111.98, "end": 1113.32, "word": " كانت", "probability": 0.3858642578125}, {"start": 1113.32, "end": 1113.9, "word": " أعضاء", "probability": 0.4471893310546875}, {"start": 1113.9, "end": 1115.02, "word": " كيرنال", "probability": 0.392242431640625}, {"start": 1115.02, "end": 1115.8, "word": " فيا", "probability": 0.3675537109375}, {"start": 1115.8, "end": 1116.16, "word": " هي", "probability": 0.060089111328125}, {"start": 1116.16, "end": 1118.12, "word": " نة", "probability": 0.3851318359375}, {"start": 1118.12, "end": 1119.06, "word": " ثم", "probability": 0.5997314453125}, {"start": 1119.06, "end": 1121.22, "word": " فيا", "probability": 0.744873046875}, {"start": 1121.22, "end": 1122.54, "word": " ثم", "probability": 0.741943359375}, {"start": 1122.54, "end": 1123.42, "word": " فيا", "probability": 0.85302734375}, {"start": 1123.42, "end": 1124.12, "word": " هي", "probability": 0.5380859375}, {"start": 1124.12, "end": 1127.04, "word": " نة", "probability": 0.806396484375}, {"start": 1127.04, "end": 1128.08, "word": " إلى", "probability": 0.1119384765625}, {"start": 1128.08, "end": 1129.54, "word": " واحدة", "probability": 0.8357747395833334}, {"start": 1129.54, "end": 1130.76, "word": " نة", "probability": 0.668212890625}, {"start": 1130.76, "end": 1130.76, "word": " إلى", "probability": 0.890625}, {"start": 1130.76, "end": 1131.12, "word": " واحدة", "probability": 0.9869791666666666}, {"start": 1131.12, "end": 1132.44, "word": " مابينج", "probability": 0.481689453125}, {"start": 1132.44, "end": 1136.08, "word": " من", "probability": 0.51904296875}], "temperature": 1.0}, {"id": 48, "seek": 116742, "start": 1138.3, "end": 1167.42, "text": "from g to phi of g النقطة السادسة بيقول if ال order لل H كان يسوى N then ال order لل phi of H بده يقسم", "tokens": [69, 340, 76, 290, 281, 13107, 295, 290, 28239, 47432, 3660, 21136, 18513, 3794, 3660, 4724, 1829, 39648, 498, 2423, 1668, 24976, 389, 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"word": " if", "probability": 0.529296875}, {"start": 1154.3, "end": 1155.64, "word": " ال", "probability": 0.275634765625}, {"start": 1155.64, "end": 1156.16, "word": " order", "probability": 0.8466796875}, {"start": 1156.16, "end": 1156.56, "word": " لل", "probability": 0.6630859375}, {"start": 1156.56, "end": 1157.04, "word": " H", "probability": 0.380859375}, {"start": 1157.04, "end": 1157.7, "word": " كان", "probability": 0.93994140625}, {"start": 1157.7, "end": 1158.58, "word": " يسوى", "probability": 0.841064453125}, {"start": 1158.58, "end": 1159.04, "word": " N", "probability": 0.48046875}, {"start": 1159.04, "end": 1160.36, "word": " then", "probability": 0.439453125}, {"start": 1160.36, "end": 1162.48, "word": " ال", "probability": 0.6875}, {"start": 1162.48, "end": 1163.16, "word": " order", "probability": 0.96533203125}, {"start": 1163.16, "end": 1164.12, "word": " لل", "probability": 0.77978515625}, {"start": 1164.12, "end": 1164.62, "word": " phi", "probability": 0.6044921875}, {"start": 1164.62, "end": 1165.1, "word": " of", "probability": 0.94140625}, {"start": 1165.1, "end": 1165.58, "word": " H", "probability": 0.880859375}, {"start": 1165.58, "end": 1166.52, "word": " بده", "probability": 0.556640625}, {"start": 1166.52, "end": 1167.42, "word": " يقسم", "probability": 0.984375}], "temperature": 1.0}, {"id": 49, "seek": 119068, "start": 1169.96, "end": 1190.68, "text": "الـ N النقطة السابعة بيقول لي if ال K bar if ال K bar is a subgroup من ال G bar then", "tokens": [6027, 39184, 426, 28239, 47432, 3660, 21136, 16758, 27884, 4724, 1829, 39648, 32239, 498, 2423, 591, 2159, 498, 2423, 591, 2159, 307, 257, 1422, 17377, 9154, 2423, 460, 2159, 550], "avg_logprob": -0.32862903610352545, "compression_ratio": 1.2365591397849462, "no_speech_prob": 0.0, "words": [{"start": 1169.96, "end": 1170.46, "word": "الـ", "probability": 0.5174560546875}, {"start": 1170.46, "end": 1170.76, "word": " N", "probability": 0.60205078125}, {"start": 1170.76, "end": 1173.98, "word": " النقطة", "probability": 0.94189453125}, {"start": 1173.98, "end": 1175.7, "word": " السابعة", "probability": 0.9197591145833334}, {"start": 1175.7, "end": 1177.32, "word": " بيقول", "probability": 0.74853515625}, {"start": 1177.32, "end": 1177.58, "word": " لي", "probability": 0.268310546875}, {"start": 1177.58, "end": 1178.08, "word": " if", "probability": 0.216064453125}, {"start": 1178.08, "end": 1180.18, "word": " ال", "probability": 0.7216796875}, {"start": 1180.18, "end": 1180.62, "word": " K", "probability": 0.419189453125}, {"start": 1180.62, "end": 1181.24, "word": " bar", "probability": 0.62353515625}, {"start": 1181.24, "end": 1183.24, "word": " if", "probability": 0.568359375}, {"start": 1183.24, "end": 1183.54, "word": " ال", "probability": 0.9306640625}, {"start": 1183.54, "end": 1183.82, "word": " K", "probability": 0.97314453125}, {"start": 1183.82, "end": 1184.42, "word": " bar", "probability": 0.90771484375}, {"start": 1184.42, "end": 1185.68, "word": " is", "probability": 0.90234375}, {"start": 1185.68, "end": 1186.0, "word": " a", "probability": 0.97216796875}, {"start": 1186.0, "end": 1187.16, "word": " subgroup", "probability": 0.754150390625}, {"start": 1187.16, "end": 1188.0, "word": " من", "probability": 0.99365234375}, {"start": 1188.0, "end": 1188.38, "word": " ال", "probability": 0.85107421875}, {"start": 1188.38, "end": 1188.64, "word": " G", "probability": 0.857421875}, {"start": 1188.64, "end": 1189.22, "word": " bar", "probability": 0.9052734375}, {"start": 1189.22, "end": 1190.68, "word": " then", "probability": 0.7802734375}], "temperature": 1.0}, {"id": 50, "seek": 121300, "start": 1192.1, "end": 1213.0, "text": "الـ Phi inverse of الـ K bar اللي هو كل ال K اللي موجودة في G such that Phi of K Phi of K موجودة في ال K bar", "tokens": [6027, 39184, 41435, 17340, 295, 2423, 39184, 591, 2159, 13672, 1829, 31439, 28242, 2423, 591, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 460, 1270, 300, 41435, 295, 591, 41435, 295, 591, 3714, 29245, 23328, 3660, 8978, 2423, 591, 2159], "avg_logprob": -0.275000012665987, "compression_ratio": 1.4747474747474747, "no_speech_prob": 0.0, "words": [{"start": 1192.1, "end": 1192.6, "word": "الـ", "probability": 0.5380859375}, {"start": 1192.6, "end": 1192.94, "word": " Phi", "probability": 0.34716796875}, {"start": 1192.94, "end": 1193.96, "word": " inverse", "probability": 0.5966796875}, {"start": 1193.96, "end": 1194.9, "word": " of", "probability": 0.921875}, {"start": 1194.9, "end": 1195.3, "word": " الـ", "probability": 0.58349609375}, {"start": 1195.3, "end": 1195.62, "word": " K", "probability": 0.57373046875}, {"start": 1195.62, "end": 1196.36, "word": " bar", "probability": 0.6650390625}, {"start": 1196.36, "end": 1197.82, "word": " اللي", "probability": 0.659423828125}, {"start": 1197.82, "end": 1198.04, "word": " هو", "probability": 0.96337890625}, {"start": 1198.04, "end": 1198.92, "word": " كل", "probability": 0.92626953125}, {"start": 1198.92, "end": 1200.34, "word": " ال", "probability": 0.71484375}, {"start": 1200.34, "end": 1200.76, "word": " K", "probability": 0.460205078125}, {"start": 1200.76, "end": 1201.58, "word": " اللي", "probability": 0.872802734375}, {"start": 1201.58, "end": 1202.34, "word": " موجودة", "probability": 0.97900390625}, {"start": 1202.34, "end": 1202.62, "word": " في", "probability": 0.970703125}, {"start": 1202.62, "end": 1203.14, "word": " G", "probability": 0.82470703125}, {"start": 1203.14, "end": 1204.1, "word": " such", "probability": 0.6953125}, {"start": 1204.1, "end": 1204.74, "word": " that", "probability": 0.94482421875}, {"start": 1204.74, "end": 1205.94, "word": " Phi", "probability": 0.7578125}, {"start": 1205.94, "end": 1207.02, "word": " of", "probability": 0.953125}, {"start": 1207.02, "end": 1207.62, "word": " K", "probability": 0.98388671875}, {"start": 1207.62, "end": 1208.56, "word": " Phi", "probability": 0.269287109375}, {"start": 1208.56, "end": 1209.0, "word": " of", "probability": 0.97509765625}, {"start": 1209.0, "end": 1209.48, "word": " K", "probability": 0.9833984375}, {"start": 1209.48, "end": 1211.0, "word": " موجودة", "probability": 0.9849853515625}, {"start": 1211.0, "end": 1211.64, "word": " في", "probability": 0.97021484375}, {"start": 1211.64, "end": 1211.96, "word": " ال", "probability": 0.80029296875}, {"start": 1211.96, "end": 1212.36, "word": " K", "probability": 0.6650390625}, {"start": 1212.36, "end": 1213.0, "word": " bar", "probability": 0.90380859375}], "temperature": 1.0}, {"id": 51, "seek": 124301, "start": 1213.43, "end": 1243.01, "text": "ما لها هذه is a subgroup of G يبقى هذه is a subgroup of G النقطة الثامنة بقول لو كان ال K bar is a normal subgroup if ال K bar is a normal subgroup من ال G bar then", "tokens": [15042, 5296, 11296, 29538, 307, 257, 1422, 17377, 295, 460, 7251, 3555, 4587, 7578, 29538, 307, 257, 1422, 17377, 295, 460, 28239, 47432, 3660, 6024, 104, 10943, 1863, 3660, 4724, 39648, 45164, 25961, 2423, 591, 2159, 307, 257, 2710, 1422, 17377, 498, 2423, 591, 2159, 307, 257, 2710, 1422, 17377, 9154, 2423, 460, 2159, 550], "avg_logprob": -0.20633370615541935, "compression_ratio": 1.6587301587301588, "no_speech_prob": 7.212162017822266e-06, "words": [{"start": 1213.43, "end": 1213.79, "word": "ما", "probability": 0.5439453125}, {"start": 1213.79, "end": 1214.17, "word": " لها", "probability": 0.72900390625}, {"start": 1214.17, "end": 1214.71, "word": " هذه", "probability": 0.60498046875}, {"start": 1214.71, "end": 1215.95, "word": " is", "probability": 0.07861328125}, {"start": 1215.95, "end": 1216.41, "word": " a", "probability": 0.91845703125}, {"start": 1216.41, "end": 1217.41, "word": " subgroup", "probability": 0.833984375}, {"start": 1217.41, "end": 1217.85, "word": " of", "probability": 0.97802734375}, {"start": 1217.85, "end": 1218.15, "word": " G", "probability": 0.6259765625}, {"start": 1218.15, "end": 1219.35, "word": " يبقى", "probability": 0.8656005859375}, {"start": 1219.35, "end": 1219.67, "word": " هذه", "probability": 0.8251953125}, {"start": 1219.67, "end": 1220.35, "word": " is", "probability": 0.78466796875}, {"start": 1220.35, "end": 1221.21, "word": " a", "probability": 0.97265625}, {"start": 1221.21, "end": 1222.87, "word": " subgroup", "probability": 0.952392578125}, {"start": 1222.87, "end": 1225.23, "word": " of", "probability": 0.9541015625}, {"start": 1225.23, "end": 1226.35, "word": " G", "probability": 0.97216796875}, {"start": 1226.35, "end": 1228.39, "word": " النقطة", "probability": 0.9638671875}, {"start": 1228.39, "end": 1229.63, "word": " الثامنة", "probability": 0.9541015625}, {"start": 1229.63, "end": 1232.07, "word": " بقول", "probability": 0.804931640625}, {"start": 1232.07, "end": 1232.33, "word": " لو", "probability": 0.88623046875}, {"start": 1232.33, "end": 1232.91, "word": " كان", "probability": 0.96728515625}, {"start": 1232.91, "end": 1233.27, "word": " ال", "probability": 0.662109375}, {"start": 1233.27, "end": 1233.53, "word": " K", "probability": 0.638671875}, {"start": 1233.53, "end": 1233.77, "word": " bar", "probability": 0.77783203125}, {"start": 1233.77, "end": 1234.07, "word": " is", "probability": 0.9365234375}, {"start": 1234.07, "end": 1234.31, "word": " a", "probability": 0.9755859375}, {"start": 1234.31, "end": 1234.67, "word": " normal", "probability": 0.82861328125}, {"start": 1234.67, "end": 1235.37, "word": " subgroup", "probability": 0.95068359375}, {"start": 1235.37, "end": 1236.01, "word": " if", "probability": 0.464111328125}, {"start": 1236.01, "end": 1236.97, "word": " ال", "probability": 0.68603515625}, {"start": 1236.97, "end": 1237.27, "word": " K", "probability": 0.94482421875}, {"start": 1237.27, "end": 1237.89, "word": " bar", "probability": 0.923828125}, {"start": 1237.89, "end": 1238.83, "word": " is", "probability": 0.9658203125}, {"start": 1238.83, "end": 1239.27, "word": " a", "probability": 0.98779296875}, {"start": 1239.27, "end": 1239.79, "word": " normal", "probability": 0.87060546875}, {"start": 1239.79, "end": 1240.67, "word": " subgroup", "probability": 0.96875}, {"start": 1240.67, "end": 1240.95, "word": " من", "probability": 0.99169921875}, {"start": 1240.95, "end": 1241.25, "word": " ال", "probability": 0.76318359375}, {"start": 1241.25, "end": 1241.49, "word": " G", "probability": 0.96533203125}, {"start": 1241.49, "end": 1242.01, "word": " bar", "probability": 0.93798828125}, {"start": 1242.01, "end": 1243.01, "word": " then", "probability": 0.7822265625}], "temperature": 1.0}, {"id": 52, "seek": 126761, "start": 1245.86, "end": 1267.62, "text": "then الـ Phi inverse of K bar هذه كل العناصر K اللي موجودة في G بحيث ان Phi of K موجود في K bar", "tokens": [19096, 2423, 39184, 41435, 17340, 295, 591, 2159, 29538, 28242, 18863, 1863, 33546, 2288, 591, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 460, 4724, 5016, 1829, 12984, 16472, 41435, 295, 591, 3714, 29245, 23328, 8978, 591, 2159], "avg_logprob": -0.33326479714167745, 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"probability": 0.8681640625}], "temperature": 1.0}, {"id": 53, "seek": 129602, "start": 1284.44, "end": 1296.02, "text": "النقطة التاسعة والاخيرة بقول لو كانت الفاي is onto f الفاي is onto", "tokens": [6027, 1863, 47432, 3660, 16712, 32277, 27884, 16070, 47283, 48923, 4724, 39648, 45164, 25961, 2655, 27188, 47302, 307, 3911, 283, 27188, 47302, 307, 3911], "avg_logprob": -0.48406248092651366, "compression_ratio": 1.2298850574712643, "no_speech_prob": 0.0, "words": [{"start": 1284.4399999999998, "end": 1285.84, "word": "النقطة", "probability": 0.7023162841796875}, {"start": 1285.84, "end": 1286.44, "word": " التاسعة", "probability": 0.9850260416666666}, {"start": 1286.44, "end": 1287.98, "word": " والاخيرة", "probability": 0.7488606770833334}, {"start": 1287.98, "end": 1289.22, "word": " بقول", "probability": 0.5511474609375}, {"start": 1289.22, "end": 1289.52, "word": " لو", "probability": 0.681640625}, {"start": 1289.52, "end": 1290.16, "word": " كانت", "probability": 0.811767578125}, {"start": 1290.16, "end": 1290.66, "word": " الفاي", "probability": 0.360595703125}, {"start": 1290.66, "end": 1291.08, "word": " is", "probability": 0.6552734375}, {"start": 1291.08, "end": 1291.72, "word": " onto", "probability": 0.478515625}, {"start": 1291.72, "end": 1292.58, "word": " f", "probability": 0.27734375}, {"start": 1292.58, "end": 1294.12, "word": " الفاي", "probability": 0.8076171875}, {"start": 1294.12, "end": 1295.16, "word": " is", "probability": 0.8642578125}, {"start": 1295.16, "end": 1296.02, "word": " onto", "probability": 0.8408203125}], "temperature": 1.0}, {"id": 54, "seek": 130911, "start": 1296.72, "end": 1309.12, "text": "لو كانت الـphi صندوق الـ and الكيرنل للـphi بده يساوي الـ identity element تبع الـG", "tokens": [1211, 2407, 25961, 2655, 2423, 39184, 950, 72, 20328, 41260, 30543, 2423, 39184, 293, 33251, 13546, 1863, 1211, 24976, 39184, 950, 72, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 6575, 4478, 6055, 3555, 3615, 2423, 39184, 38], "avg_logprob": -0.5312500061132969, "compression_ratio": 1.2450980392156863, "no_speech_prob": 0.0, "words": [{"start": 1296.72, "end": 1297.18, "word": "لو", "probability": 0.75927734375}, {"start": 1297.18, "end": 1297.66, "word": " كانت", "probability": 0.7412109375}, {"start": 1297.66, "end": 1297.98, "word": " الـphi", "probability": 0.5568695068359375}, {"start": 1297.98, "end": 1298.3, "word": " صندوق", "probability": 0.4552205403645833}, {"start": 1298.3, "end": 1298.58, "word": " الـ", "probability": 0.7138671875}, {"start": 1298.58, "end": 1299.24, "word": " and", "probability": 0.321533203125}, {"start": 1299.24, "end": 1302.26, "word": " الكيرنل", "probability": 0.60162353515625}, {"start": 1302.26, "end": 1304.08, "word": " للـphi", "probability": 0.64373779296875}, {"start": 1304.08, "end": 1304.82, "word": " بده", "probability": 0.486083984375}, {"start": 1304.82, "end": 1305.54, "word": " يساوي", "probability": 0.9600830078125}, {"start": 1305.54, "end": 1306.08, "word": " الـ", "probability": 0.660400390625}, {"start": 1306.08, "end": 1306.98, "word": " identity", "probability": 0.75146484375}, {"start": 1306.98, "end": 1307.84, "word": " element", "probability": 0.9833984375}, {"start": 1307.84, "end": 1308.42, "word": " تبع", "probability": 0.9134114583333334}, {"start": 1308.42, "end": 1309.12, "word": " الـG", "probability": 0.77685546875}], "temperature": 1.0}, {"id": 55, "seek": 133698, "start": 1323.46, "end": 1336.98, "text": "من اين الى اين من جيه لجيه بار من جيه لجيه بار", "tokens": [27842, 1975, 9957, 2423, 7578, 1975, 9957, 9154, 10874, 1829, 3224, 5296, 7435, 1829, 3224, 4724, 9640, 9154, 10874, 1829, 3224, 5296, 7435, 1829, 3224, 4724, 9640], "avg_logprob": -0.371930792927742, "compression_ratio": 1.8409090909090908, "no_speech_prob": 0.0, "words": [{"start": 1323.4600000000003, "end": 1324.8000000000002, "word": "من", "probability": 0.09478759765625}, {"start": 1324.8000000000002, "end": 1326.14, "word": " اين", "probability": 0.5526123046875}, {"start": 1326.14, "end": 1326.38, "word": " الى", "probability": 0.738525390625}, {"start": 1326.38, "end": 1326.68, "word": " اين", "probability": 0.924072265625}, {"start": 1326.68, "end": 1328.02, "word": " من", "probability": 0.49951171875}, {"start": 1328.02, "end": 1328.52, "word": " جيه", "probability": 0.7353515625}, {"start": 1328.52, "end": 1329.0, "word": " لجيه", "probability": 0.844482421875}, {"start": 1329.0, "end": 1329.22, "word": " بار", "probability": 0.60443115234375}, {"start": 1329.22, "end": 1329.82, "word": " من", "probability": 0.51904296875}, {"start": 1329.82, "end": 1334.14, "word": " جيه", "probability": 0.9773763020833334}, {"start": 1334.14, "end": 1336.24, "word": " لجيه", "probability": 0.962646484375}, {"start": 1336.24, "end": 1336.98, "word": " بار", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 56, "seek": 138551, "start": 1361.15, "end": 1385.51, "text": "Nigel will prove the parts الواحد واتنين and تلاتة are identical to", "tokens": [45, 328, 338, 486, 7081, 264, 3166, 2423, 14407, 24401, 4032, 9307, 1863, 9957, 293, 6055, 1211, 9307, 3660, 366, 14800, 281], "avg_logprob": -0.4021739000859468, "compression_ratio": 0.9655172413793104, "no_speech_prob": 0.0, "words": [{"start": 1361.15, "end": 1361.67, "word": "Nigel", "probability": 0.3531697591145833}, {"start": 1361.67, "end": 1361.85, "word": " will", "probability": 0.25439453125}, {"start": 1361.85, "end": 1362.45, "word": " prove", "probability": 0.56787109375}, {"start": 1362.45, "end": 1368.85, "word": " the", "probability": 0.385498046875}, {"start": 1368.85, "end": 1370.21, "word": " parts", "probability": 0.900390625}, {"start": 1370.21, "end": 1372.17, "word": " الواحد", "probability": 0.9549153645833334}, {"start": 1372.17, "end": 1374.45, "word": " واتنين", "probability": 0.7603759765625}, {"start": 1374.45, "end": 1375.99, "word": " and", "probability": 0.80029296875}, {"start": 1375.99, "end": 1377.89, "word": " تلاتة", "probability": 0.9110107421875}, {"start": 1377.89, "end": 1379.75, "word": " are", "probability": 0.87939453125}, {"start": 1379.75, "end": 1382.99, "word": " identical", "probability": 0.93212890625}, {"start": 1382.99, "end": 1385.51, "word": " to", "probability": 0.9697265625}], "temperature": 1.0}, {"id": 57, "seek": 141242, "start": 1387.26, "end": 1412.42, "text": "are identical to the probes of أربعة واتنين and واحد of theorem of theorem", "tokens": [543, 14800, 281, 264, 1239, 279, 295, 5551, 25513, 27884, 4032, 9307, 1863, 9957, 293, 36764, 24401, 295, 20904, 295, 20904], "avg_logprob": -0.2881747118451379, "compression_ratio": 1.072289156626506, "no_speech_prob": 0.0, "words": [{"start": 1387.26, "end": 1387.64, "word": "are", "probability": 0.163818359375}, {"start": 1387.64, "end": 1388.4, "word": " identical", "probability": 0.93115234375}, {"start": 1388.4, "end": 1389.14, "word": " to", "probability": 0.98291015625}, {"start": 1389.14, "end": 1390.38, "word": " the", "probability": 0.90478515625}, {"start": 1390.38, "end": 1392.2, "word": " probes", "probability": 0.61334228515625}, {"start": 1392.2, "end": 1394.5, "word": " of", "probability": 0.97119140625}, {"start": 1394.5, "end": 1397.74, "word": " أربعة", "probability": 0.8421223958333334}, {"start": 1397.74, "end": 1400.06, "word": " واتنين", "probability": 0.80126953125}, {"start": 1400.06, "end": 1401.6, "word": " and", "probability": 0.80908203125}, {"start": 1401.6, "end": 1403.7, "word": " واحد", "probability": 0.980224609375}, {"start": 1403.7, "end": 1407.64, "word": " of", "probability": 0.9541015625}, {"start": 1407.64, "end": 1409.58, "word": " theorem", "probability": 0.849609375}, {"start": 1409.58, "end": 1411.74, "word": " of", "probability": 0.82373046875}, {"start": 1411.74, "end": 1412.42, "word": " theorem", "probability": 0.85107421875}], "temperature": 1.0}, {"id": 58, "seek": 142454, "start": 1413.18, "end": 1424.54, "text": "ستة تلاتة بصفحات مية وسبعة وعشرين respectively", "tokens": [3794, 2655, 3660, 6055, 1211, 9307, 3660, 4724, 9381, 5172, 5016, 9307, 3714, 10632, 4032, 35457, 27884, 4032, 3615, 46309, 9957, 25009], "avg_logprob": -0.35326087474823, "compression_ratio": 1.0277777777777777, "no_speech_prob": 0.0, "words": [{"start": 1413.18, "end": 1414.22, "word": "ستة", "probability": 0.662353515625}, {"start": 1414.22, "end": 1416.56, "word": " تلاتة", "probability": 0.8623046875}, {"start": 1416.56, "end": 1420.06, "word": " بصفحات", "probability": 0.545703125}, {"start": 1420.06, "end": 1420.98, "word": " مية", "probability": 0.791259765625}, {"start": 1420.98, "end": 1421.82, "word": " وسبعة", "probability": 0.884765625}, {"start": 1421.82, "end": 1422.74, "word": " وعشرين", "probability": 0.912109375}, {"start": 1422.74, "end": 1424.54, "word": " respectively", "probability": 0.68017578125}], "temperature": 1.0}, {"id": 59, "seek": 147935, "start": 1452.85, "end": 1479.35, "text": "نرجع تاني للنظرية اللى احنا كاتبينها حاول نقرأها كمان مرة نتفهم كل ما فيها بعد هيك بنروح الى البرهان المرة اللى فاتت النظرية اللى فاتت كانت بيشتغل على ال elements homomorphism على ال elements هنا ال subgroups under ال homomorphism يجيب جال ال homomorphism يشتغل عالميا على ال subgroups وليس على ال elements", "tokens": [1863, 47341, 3615, 6055, 7649, 1829, 24976, 1863, 19913, 2288, 10632, 13672, 7578, 1975, 5016, 8315, 9122, 9307, 3555, 9957, 11296, 11331, 995, 12610, 8717, 4587, 2288, 10721, 11296, 9122, 2304, 7649, 3714, 25720, 8717, 2655, 5172, 16095, 28242, 19446, 8978, 11296, 39182, 39896, 4117, 44945, 32887, 5016, 2423, 7578, 2423, 26890, 3224, 7649, 9673, 25720, 13672, 7578, 6156, 9307, 2655, 28239, 19913, 2288, 10632, 13672, 7578, 6156, 9307, 2655, 25961, 2655, 4724, 1829, 8592, 2655, 17082, 1211, 15844, 2423, 4959, 3655, 32702, 1434, 15844, 2423, 4959, 34105, 2423, 1422, 17377, 82, 833, 2423, 3655, 32702, 1434, 7251, 7435, 1829, 3555, 10874, 6027, 2423, 3655, 32702, 1434, 7251, 8592, 2655, 17082, 1211, 6225, 45340, 25528, 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elements", "probability": 0.91650390625}, {"start": 1469.99, "end": 1470.83, "word": " هنا", "probability": 0.923828125}, {"start": 1470.83, "end": 1471.03, "word": " ال", "probability": 0.46728515625}, {"start": 1471.03, "end": 1472.55, "word": " subgroups", "probability": 0.6394856770833334}, {"start": 1472.55, "end": 1472.87, "word": " under", "probability": 0.50341796875}, {"start": 1472.87, "end": 1473.13, "word": " ال", "probability": 0.88525390625}, {"start": 1473.13, "end": 1474.01, "word": " homomorphism", "probability": 0.9759114583333334}, {"start": 1474.01, "end": 1474.33, "word": " يجيب", "probability": 0.5635986328125}, {"start": 1474.33, "end": 1474.59, "word": " جال", "probability": 0.43896484375}, {"start": 1474.59, "end": 1474.69, "word": " ال", "probability": 0.8525390625}, {"start": 1474.69, "end": 1475.25, "word": " homomorphism", "probability": 0.9765625}, {"start": 1475.25, "end": 1475.73, "word": " يشتغل", "probability": 0.784228515625}, {"start": 1475.73, "end": 1476.19, "word": " عالميا", "probability": 0.9207356770833334}, {"start": 1476.19, "end": 1476.81, "word": " على", "probability": 0.8349609375}, {"start": 1476.81, "end": 1476.97, "word": " ال", "probability": 0.7880859375}, {"start": 1476.97, "end": 1477.71, "word": " subgroups", "probability": 0.9446614583333334}, {"start": 1477.71, "end": 1478.23, "word": " وليس", "probability": 0.8693033854166666}, {"start": 1478.23, "end": 1478.63, "word": " على", "probability": 0.93212890625}, {"start": 1478.63, "end": 1479.03, "word": " ال", "probability": 0.97119140625}, {"start": 1479.03, "end": 1479.35, "word": " elements", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 60, "seek": 149520, "start": 1479.8, "end": 1495.2, "text": "مقول لو كانت فاي من جي إلى جي بار هي hemomorphism وكانت ال H subgroup من جي then فاي of H، H هذه sub set من مين او subgroup من جي إذا صورتها", "tokens": [2304, 39648, 45164, 25961, 2655, 6156, 47302, 9154, 10874, 1829, 30731, 10874, 1829, 4724, 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{"start": 1744.58, "end": 1745.5, "word": " موجود", "probability": 0.9807942708333334}, {"start": 1745.5, "end": 1745.76, "word": " في", "probability": 0.99072265625}, {"start": 1745.76, "end": 1746.08, "word": " G", "probability": 0.85546875}], "temperature": 1.0}, {"id": 72, "seek": 175871, "start": 1746.75, "end": 1758.71, "text": "واخدنا ال H موجود في H then ايه شرايك في ال GHG inverse؟", "tokens": [2407, 47283, 3215, 8315, 2423, 389, 3714, 29245, 23328, 8978, 389, 550, 1975, 1829, 3224, 13412, 23557, 1829, 4117, 8978, 2423, 40690, 38, 17340, 22807], "avg_logprob": -0.3569711572848834, "compression_ratio": 1.05, "no_speech_prob": 0.0, "words": [{"start": 1746.75, "end": 1748.15, "word": "واخدنا", "probability": 0.872802734375}, {"start": 1748.15, "end": 1748.69, "word": " ال", "probability": 0.89404296875}, {"start": 1748.69, "end": 1749.35, "word": " H", "probability": 0.330322265625}, {"start": 1749.35, "end": 1750.73, "word": " موجود", "probability": 0.9742838541666666}, 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اخدت ال phi of GHG inverse هيكون موجود في ال phi of H", "tokens": [3555, 9957, 39237, 1829, 32767, 9957, 22807, 1975, 1829, 2407, 3660, 7251, 3555, 4587, 7578, 23758, 12953, 281, 389, 21136, 3555, 3555, 570, 16472, 2423, 389, 307, 257, 2710, 1422, 17377, 9154, 460, 23032, 3555, 1975, 5016, 8315, 5296, 15042, 8717, 2655, 4117, 19528, 15844, 8978, 9307, 7251, 3555, 4587, 7578, 8717, 44510, 10721, 8717, 47283, 3215, 27188, 1829, 9307, 34105, 7251, 3555, 4587, 7578, 45164, 12602, 2407, 33753, 1975, 9778, 3215, 2655, 2423, 13107, 295, 40690, 38, 17340, 39896, 30544, 3714, 29245, 23328, 8978, 2423, 13107, 295, 389], "avg_logprob": -0.21215277877118852, "compression_ratio": 1.5, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1762.66, "end": 1763.32, "word": "بينتمي", "probability": 0.72088623046875}, {"start": 1763.32, "end": 1763.78, "word": " لمين؟", "probability": 0.7176106770833334}, {"start": 1763.78, "end": 1765.1, "word": " ايوة", "probability": 0.659332275390625}, 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Phi of G لكل Inverse موجود في Phi of H تعالى نشوف تعالى نشوف هذا وين موجود يا شباب؟", "tokens": [3224, 15730, 3714, 29245, 23328, 8978, 3714, 9957, 22807, 8978, 2423, 39184, 41435, 295, 389, 23032, 1829, 3555, 12399, 5551, 1211, 3794, 995, 23758, 41435, 295, 460, 41435, 295, 389, 41435, 295, 460, 5296, 28820, 682, 4308, 3714, 29245, 23328, 8978, 41435, 295, 389, 37279, 6027, 7578, 8717, 8592, 38688, 37279, 6027, 7578, 8717, 8592, 38688, 23758, 4032, 9957, 3714, 29245, 23328, 35186, 13412, 3555, 16758, 22807], "avg_logprob": -0.22863051295280457, "compression_ratio": 1.6544117647058822, "no_speech_prob": 0.0, "words": [{"start": 1807.63, "end": 1808.13, "word": "هذا", "probability": 0.880126953125}, {"start": 1808.13, "end": 1808.93, "word": " موجود", "probability": 0.953125}, {"start": 1808.93, "end": 1809.55, "word": " في", "probability": 0.89404296875}, {"start": 1809.55, "end": 1810.01, "word": " مين؟", "probability": 0.5768229166666666}, {"start": 1810.01, "end": 1810.17, "word": " 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0.61171875}, {"start": 1962.48, "end": 1962.88, "word": " مازالة", "probability": 0.43743896484375}, {"start": 1962.88, "end": 1962.96, "word": " مازالة", "probability": 0.67822265625}, {"start": 1962.96, "end": 1962.96, "word": " مازالة", "probability": 0.7237548828125}, {"start": 1962.96, "end": 1962.96, "word": " مازالة", "probability": 0.69281005859375}, {"start": 1962.96, "end": 1963.06, "word": " مازالة", "probability": 0.68341064453125}, {"start": 1963.06, "end": 1963.28, "word": " مازالة", "probability": 0.688690185546875}, {"start": 1963.28, "end": 1963.78, "word": " مازالة", "probability": 0.726043701171875}, {"start": 1963.78, "end": 1963.86, "word": " مازالة", "probability": 0.775146484375}, {"start": 1963.86, "end": 1963.92, "word": " مازالة", "probability": 0.81512451171875}, {"start": 1963.92, "end": 1963.92, "word": " مازالة", "probability": 0.84747314453125}, {"start": 1963.92, "end": 1963.92, "word": " مازالة", "probability": 0.8699951171875}, {"start": 1963.92, "end": 1963.92, "word": " مازالة", "probability": 0.8887939453125}, {"start": 1963.92, "end": 1963.92, "word": " مازالة", "probability": 0.9039306640625}, {"start": 1963.92, "end": 1963.92, "word": " مازالة", "probability": 0.9169921875}, {"start": 1963.92, "end": 1965.3, "word": " مازالة", "probability": 0.92578125}, {"start": 1965.3, "end": 1965.46, "word": " مازالة", "probability": 0.93603515625}, {"start": 1965.46, "end": 1967.74, "word": " مازالة", "probability": 0.94140625}, {"start": 1967.74, "end": 1968.06, "word": " مازالة", "probability": 0.947265625}, {"start": 1968.06, "end": 1968.84, "word": " مازالة", "probability": 0.9520263671875}, {"start": 1968.84, "end": 1968.96, "word": " مازالة", "probability": 0.9593505859375}, {"start": 1968.96, "end": 1969.02, "word": " مازالة", "probability": 0.9627685546875}, {"start": 1969.02, "end": 1969.06, "word": " مازالة", "probability": 0.967529296875}, {"start": 1969.06, "end": 1969.22, "word": " مازالة", "probability": 0.969970703125}, {"start": 1969.22, "end": 1969.22, "word": " مازالة", "probability": 0.9722900390625}, {"start": 1969.22, "end": 1969.22, "word": " مازالة", "probability": 0.974609375}, {"start": 1969.22, "end": 1969.22, "word": " مازالة", "probability": 0.9774169921875}, {"start": 1969.22, "end": 1969.28, "word": " مازالة", "probability": 0.978759765625}, {"start": 1969.28, "end": 1969.28, "word": " مازالة", "probability": 0.9805908203125}, {"start": 1969.28, "end": 1969.32, "word": " مازالة", "probability": 0.9815673828125}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.9827880859375}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.984130859375}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.98583984375}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.9864501953125}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.9869384765625}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.98779296875}, {"start": 1969.32, "end": 1969.32, "word": " مازالة", "probability": 0.9879150390625}, {"start": 1969.32, "end": 1969.78, "word": " مازالة", "probability": 0.9876708984375}, {"start": 1969.78, "end": 1970.26, "word": " مازال", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 82, "seek": 199655, "start": 1970.63, "end": 1996.55, "text": "يبقى let الكلام then هذا ايش معناه؟ معناه ان الـPhi of الـidentity element تبع الـG بده يساوي الـidentity element تبع الـG bar والـPhi of G1 بده يساوي الـidentity element تبع الـG bar والـPhi of G2 بده يساوي الـidentity element تبع الـG bar", "tokens": [1829, 3555, 4587, 7578, 718, 2423, 28820, 10943, 550, 23758, 1975, 1829, 8592, 20449, 8315, 3224, 22807, 20449, 8315, 3224, 16472, 2423, 39184, 47, 4954, 295, 2423, 39184, 1078, 507, 4478, 6055, 3555, 3615, 2423, 39184, 38, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 1078, 507, 4478, 6055, 3555, 3615, 2423, 39184, 38, 2159, 16070, 39184, 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"seek": 202544, "start": 1996.78, "end": 2025.44, "text": "والـ Phi of G N minus الـ one بده يساوي الـ identity تبع الـ G bar يبقى أنا صار عندي N من العناصر لهم صورة واحدة يبقى الـ Phi is into one يبقى هذا this means that ان الـ Phi is into one", "tokens": [2407, 6027, 39184, 41435, 295, 460, 426, 3175, 2423, 39184, 472, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 6575, 6055, 3555, 3615, 2423, 39184, 460, 2159, 7251, 3555, 4587, 7578, 41850, 20328, 9640, 43242, 1829, 426, 9154, 18863, 1863, 33546, 2288, 5296, 16095, 20328, 13063, 3660, 36764, 24401, 3660, 7251, 3555, 4587, 7578, 2423, 39184, 41435, 307, 666, 472, 7251, 3555, 4587, 7578, 23758, 341, 1355, 300, 16472, 2423, 39184, 41435, 307, 666, 472], "avg_logprob": -0.28104441926667567, "compression_ratio": 1.5470588235294118, "no_speech_prob": 0.0, "words": [{"start": 1996.78, "end": 1997.62, "word": "والـ", "probability": 0.5892740885416666}, {"start": 1997.62, "end": 1998.0, "word": " Phi", "probability": 0.2071533203125}, {"start": 1998.0, "end": 1998.56, "word": " of", "probability": 0.6591796875}, {"start": 1998.56, "end": 1999.08, "word": " G", "probability": 0.50341796875}, {"start": 1999.08, "end": 1999.64, "word": " N", "probability": 0.302734375}, {"start": 1999.64, "end": 2000.2, "word": " minus", "probability": 0.33935546875}, {"start": 2000.2, "end": 2000.56, "word": " الـ", "probability": 0.76318359375}, {"start": 2000.56, "end": 2000.82, "word": " one", "probability": 0.21044921875}, {"start": 2000.82, "end": 2001.56, "word": " بده", "probability": 0.33587646484375}, {"start": 2001.56, "end": 2002.04, "word": " يساوي", "probability": 0.910888671875}, {"start": 2002.04, "end": 2002.26, "word": " الـ", "probability": 0.640380859375}, {"start": 2002.26, "end": 2002.98, "word": " identity", "probability": 0.6708984375}, {"start": 2002.98, "end": 2003.6, "word": " تبع", "probability": 0.92529296875}, {"start": 2003.6, "end": 2003.9, "word": " الـ", "probability": 0.930908203125}, {"start": 2003.9, "end": 2004.1, "word": " G", "probability": 0.90673828125}, {"start": 2004.1, "end": 2004.7, "word": " bar", "probability": 0.58251953125}, {"start": 2004.7, "end": 2005.88, "word": " يبقى", "probability": 0.9417724609375}, {"start": 2005.88, "end": 2006.26, "word": " أنا", "probability": 0.7021484375}, {"start": 2006.26, "end": 2006.6, "word": " صار", "probability": 0.881591796875}, {"start": 2006.6, "end": 2007.2, "word": " عندي", "probability": 0.598876953125}, {"start": 2007.2, "end": 2007.54, "word": " N", "probability": 0.86962890625}, {"start": 2007.54, "end": 2007.84, "word": " من", "probability": 0.98046875}, {"start": 2007.84, "end": 2008.62, "word": " العناصر", "probability": 0.9068603515625}, {"start": 2008.62, "end": 2008.98, "word": " لهم", "probability": 0.7724609375}, {"start": 2008.98, "end": 2009.46, "word": " صورة", "probability": 0.9851888020833334}, {"start": 2009.46, "end": 2009.82, "word": " واحدة", "probability": 0.9817708333333334}, {"start": 2009.82, "end": 2010.1, "word": " يبقى", "probability": 0.9769287109375}, {"start": 2010.1, "end": 2010.32, "word": " الـ", "probability": 0.767578125}, {"start": 2010.32, "end": 2010.54, "word": " Phi", "probability": 0.79541015625}, {"start": 2010.54, "end": 2010.98, "word": " is", "probability": 0.900390625}, {"start": 2010.98, "end": 2011.72, "word": " into", "probability": 0.51806640625}, {"start": 2011.72, "end": 2012.26, "word": " one", "probability": 0.94091796875}, {"start": 2012.26, "end": 2013.56, "word": " يبقى", "probability": 0.98095703125}, {"start": 2013.56, "end": 2014.08, "word": " هذا", "probability": 0.96240234375}, {"start": 2014.08, "end": 2014.8, "word": " this", "probability": 0.54736328125}, {"start": 2014.8, "end": 2017.14, "word": " means", "probability": 0.78662109375}, {"start": 2017.14, "end": 2019.06, "word": " that", "probability": 0.83740234375}, {"start": 2019.06, "end": 2020.18, "word": " ان", "probability": 0.440185546875}, {"start": 2020.18, "end": 2020.6, "word": " الـ", "probability": 0.715087890625}, {"start": 2020.6, "end": 2021.08, "word": " Phi", "probability": 0.87890625}, {"start": 2021.08, "end": 2021.96, "word": " is", "probability": 0.9658203125}, {"start": 2021.96, "end": 2023.56, "word": " into", "probability": 0.60986328125}, {"start": 2023.56, "end": 2025.44, "word": " one", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 84, "seek": 204486, "start": 2032.04, "end": 2044.86, "text": "يبقى هايات مثلا من جي لجي من from جي to جي بار ولم اقول unto جي بار", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 9307, 50113, 15040, 9154, 10874, 1829, 5296, 7435, 1829, 9154, 490, 10874, 1829, 281, 10874, 1829, 4724, 9640, 4032, 19528, 1975, 39648, 16521, 10874, 1829, 4724, 9640], "avg_logprob": -0.39889705444083495, "compression_ratio": 1.2857142857142858, "no_speech_prob": 0.0, "words": [{"start": 2032.04, "end": 2033.28, "word": "يبقى", "probability": 0.7457733154296875}, {"start": 2033.28, "end": 2033.7, "word": " هايات", "probability": 0.5222981770833334}, {"start": 2033.7, "end": 2033.96, "word": " مثلا", "probability": 0.82958984375}, {"start": 2033.96, "end": 2034.46, "word": " من", "probability": 0.85498046875}, {"start": 2034.46, "end": 2035.9, "word": " جي", "probability": 0.495361328125}, {"start": 2035.9, "end": 2036.28, "word": " لجي", "probability": 0.75390625}, {"start": 2036.28, "end": 2036.66, "word": " من", "probability": 0.71337890625}, {"start": 2036.66, "end": 2037.76, "word": " from", "probability": 0.6474609375}, {"start": 2037.76, "end": 2039.82, "word": " جي", "probability": 0.707275390625}, {"start": 2039.82, "end": 2040.46, "word": " to", "probability": 0.69970703125}, {"start": 2040.46, "end": 2041.8, "word": " جي", "probability": 0.923095703125}, {"start": 2041.8, "end": 2042.04, "word": " بار", "probability": 0.972900390625}, {"start": 2042.04, "end": 2042.44, "word": " ولم", "probability": 0.83056640625}, {"start": 2042.44, "end": 2043.06, "word": " اقول", "probability": 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{"start": 2333.3, "end": 2333.98, "word": " بيخليهاش", "probability": 0.8487955729166666}, {"start": 2333.98, "end": 2334.14, "word": " على", "probability": 0.951171875}, {"start": 2334.14, "end": 2334.62, "word": " أطلقها،", "probability": 0.5835774739583334}, {"start": 2334.62, "end": 2335.0, "word": " بس", "probability": 0.873291015625}, {"start": 2335.0, "end": 2335.24, "word": " على", "probability": 0.90771484375}, {"start": 2335.24, "end": 2335.78, "word": " عناصر", "probability": 0.9715169270833334}, {"start": 2335.78, "end": 2336.38, "word": " إيش،", "probability": 0.506591796875}, {"start": 2336.38, "end": 2336.7, "word": " يبقى", "probability": 0.9586181640625}, {"start": 2336.7, "end": 2336.82, "word": " يا", "probability": 0.258056640625}, {"start": 2336.82, "end": 2337.08, "word": " ريت", "probability": 0.89599609375}, {"start": 2337.08, "end": 2337.22, "word": " من", "probability": 0.92041015625}, {"start": 2337.22, "end": 2337.82, "word": " الكتاب", "probability": 0.9899088541666666}, {"start": 2337.82, "end": 2338.3, "word": " تروح", "probability": 0.87841796875}, {"start": 2338.3, "end": 2338.86, "word": " تجرها", "probability": 0.8472900390625}, {"start": 2338.86, "end": 2339.92, "word": " وترتب", "probability": 0.8269856770833334}, {"start": 2339.92, "end": 2340.4, "word": " أمورها", "probability": 0.984619140625}], "temperature": 1.0}, {"id": 97, "seek": 235508, "start": 2340.88, "end": 2355.08, "text": "الان كي بار سابق روب من جي بار يبقى في انفرست اوف كي بده اثبتها السابق روب من مين؟ من الجي طيب مشان اثبتها السابق روب بده اثبته conditions", "tokens": [6027, 7649, 9122, 1829, 4724, 9640, 8608, 16758, 4587, 12602, 37746, 9154, 10874, 1829, 4724, 9640, 7251, 3555, 4587, 7578, 8978, 16472, 5172, 2288, 14851, 1975, 38688, 9122, 1829, 47525, 3224, 1975, 12984, 3555, 2655, 11296, 21136, 16758, 4587, 12602, 37746, 9154, 3714, 9957, 22807, 9154, 25724, 1829, 23032, 1829, 3555, 37893, 7649, 1975, 12984, 3555, 2655, 11296, 21136, 16758, 4587, 12602, 37746, 47525, 3224, 1975, 12984, 3555, 2655, 3224, 4487], "avg_logprob": -0.3543836805555556, "compression_ratio": 1.816793893129771, "no_speech_prob": 0.0, "words": [{"start": 2340.88, "end": 2341.5, "word": "الان", "probability": 0.660400390625}, {"start": 2341.5, "end": 2342.3, "word": " كي", "probability": 0.4075927734375}, {"start": 2342.3, "end": 2342.58, "word": " بار", "probability": 0.6876220703125}, {"start": 2342.58, "end": 2343.08, "word": " سابق", "probability": 0.4612630208333333}, {"start": 2343.08, "end": 2343.38, "word": " روب", "probability": 0.622314453125}, {"start": 2343.38, "end": 2343.66, "word": " من", "probability": 0.88037109375}, {"start": 2343.66, "end": 2344.1, "word": " جي", "probability": 0.897705078125}, {"start": 2344.1, "end": 2344.46, "word": " بار", "probability": 0.98974609375}, {"start": 2344.46, "end": 2345.54, "word": " يبقى", "probability": 0.9072265625}, {"start": 2345.54, "end": 2345.84, "word": " في", "probability": 0.56396484375}, {"start": 2345.84, "end": 2346.74, "word": " انفرست", "probability": 0.7325439453125}, {"start": 2346.74, "end": 2347.02, "word": " اوف", "probability": 0.3460693359375}, {"start": 2347.02, "end": 2347.36, "word": " كي", "probability": 0.933837890625}, {"start": 2347.36, "end": 2347.66, "word": " بده", "probability": 0.33917236328125}, {"start": 2347.66, "end": 2348.02, "word": " اثبتها", "probability": 0.821923828125}, {"start": 2348.02, "end": 2348.58, "word": " السابق", "probability": 0.7143147786458334}, {"start": 2348.58, "end": 2348.78, "word": " روب", "probability": 0.803466796875}, {"start": 2348.78, "end": 2348.98, "word": " من", "probability": 0.94482421875}, {"start": 2348.98, "end": 2349.6, "word": " مين؟", "probability": 0.5185953776041666}, {"start": 2349.6, "end": 2350.24, "word": " من", "probability": 0.8916015625}, {"start": 2350.24, "end": 2351.12, "word": " الجي", "probability": 0.7490234375}, {"start": 2351.12, "end": 2352.02, "word": " طيب", "probability": 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"probability": 0.483642578125}, {"start": 2365.16, "end": 2365.96, "word": " Phi", "probability": 0.2154541015625}, {"start": 2365.96, "end": 2366.86, "word": " inverse", "probability": 0.415771484375}, {"start": 2366.86, "end": 2368.08, "word": " subgroup", "probability": 0.718505859375}, {"start": 2368.08, "end": 2368.34, "word": " من", "probability": 0.9609375}, {"start": 2368.34, "end": 2369.14, "word": " مين؟", "probability": 0.806884765625}, {"start": 2369.14, "end": 2369.6, "word": " من", "probability": 0.96044921875}, {"start": 2369.6, "end": 2370.3, "word": " الـG", "probability": 0.7169596354166666}, {"start": 2370.3, "end": 2370.96, "word": " هذا", "probability": 0.845703125}, {"start": 2370.96, "end": 2371.16, "word": " اللي", "probability": 0.97412109375}, {"start": 2371.16, "end": 2371.7, "word": " عايزيني", "probability": 0.820947265625}, {"start": 2371.7, "end": 2372.06, "word": " أثبته", "probability": 0.901611328125}, {"start": 2372.06, "end": 2372.62, "word": " مشان", "probability": 0.92333984375}, {"start": 2372.62, "end": 2373.02, "word": " هيك", "probability": 0.7010498046875}, {"start": 2373.02, "end": 2373.54, "word": " بدي", "probability": 0.9189453125}, {"start": 2373.54, "end": 2374.06, "word": " أثبتله", "probability": 0.86162109375}, {"start": 2374.06, "end": 2374.2, "word": " أن", "probability": 0.40625}, {"start": 2374.2, "end": 2374.52, "word": " هذه", "probability": 0.57421875}, {"start": 2374.52, "end": 2374.78, "word": " non", "probability": 0.375244140625}, {"start": 2374.78, "end": 2375.46, "word": "-empty", "probability": 0.7900390625}, {"start": 2375.46, "end": 2375.76, "word": " و", "probability": 0.7939453125}, {"start": 2375.76, "end": 2375.94, "word": " لو", "probability": 0.64990234375}, {"start": 2375.94, "end": 2376.3, "word": " أخدت", "probability": 0.74871826171875}, {"start": 2376.3, "end": 2376.88, "word": " عنصرين", "probability": 0.8736572265625}, {"start": 2376.88, "end": 2377.14, "word": " منها", "probability": 0.991455078125}, {"start": 2377.14, "end": 2377.38, "word": " بدي", "probability": 0.93359375}, {"start": 2377.38, "end": 2377.78, "word": " أثبت", "probability": 0.994384765625}, {"start": 2377.78, "end": 2377.92, "word": " أن", "probability": 0.67236328125}, {"start": 2377.92, "end": 2378.26, "word": " الأول", "probability": 0.989013671875}, {"start": 2378.26, "end": 2378.4, "word": " في", "probability": 0.96875}, {"start": 2378.4, "end": 2379.0, "word": " معكوسي", "probability": 0.876708984375}, {"start": 2379.0, "end": 2379.48, "word": " الثاني", "probability": 0.94580078125}, {"start": 2379.48, "end": 2380.22, "word": " موجود", "probability": 0.9724934895833334}, {"start": 2380.22, "end": 2380.52, "word": " فيها", "probability": 0.981201171875}, {"start": 2380.52, "end": 2381.02, "word": " وبالتالي", "probability": 0.9419921875}, {"start": 2381.02, "end": 2381.5, "word": " بيصير", "probability": 0.8084716796875}, {"start": 2381.5, "end": 2381.84, "word": " a", "probability": 0.71533203125}, {"start": 2381.84, "end": 2383.02, "word": " subgroup", "probability": 0.903076171875}], "temperature": 1.0}, {"id": 99, "seek": 241417, "start": 2385.06, "end": 2414.18, "text": "يبقى بضاجي أقول له assume أفترض أن الـK bar هي عبارة عن subgroup من الـG bar يبقى هذه subgroup من الـG bar then الـPhi inverse of K bar is non-empty", "tokens": [1829, 3555, 4587, 7578, 4724, 11242, 26108, 1829, 5551, 39648, 46740, 6552, 5551, 5172, 2655, 43042, 14739, 2423, 39184, 42, 2159, 39896, 6225, 3555, 9640, 3660, 18871, 1422, 17377, 9154, 2423, 39184, 38, 2159, 7251, 3555, 4587, 7578, 29538, 1422, 17377, 9154, 2423, 39184, 38, 2159, 550, 2423, 39184, 47, 4954, 17340, 295, 591, 2159, 307, 2107, 12, 4543, 88], "avg_logprob": -0.35399589382234165, "compression_ratio": 1.3557046979865772, "no_speech_prob": 0.0, "words": [{"start": 2385.06, "end": 2385.46, "word": "يبقى", "probability": 0.744171142578125}, {"start": 2385.46, "end": 2386.0, "word": " بضاجي", "probability": 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0.97705078125}, {"start": 2394.84, "end": 2396.7, "word": " الـG", "probability": 0.6382649739583334}, {"start": 2396.7, "end": 2397.32, "word": " bar", "probability": 0.85791015625}, {"start": 2397.32, "end": 2401.6, "word": " يبقى", "probability": 0.90966796875}, {"start": 2401.6, "end": 2401.88, "word": " هذه", "probability": 0.810546875}, {"start": 2401.88, "end": 2402.78, "word": " subgroup", "probability": 0.755859375}, {"start": 2402.78, "end": 2403.04, "word": " من", "probability": 0.98486328125}, {"start": 2403.04, "end": 2403.44, "word": " الـG", "probability": 0.8531901041666666}, {"start": 2403.44, "end": 2403.78, "word": " bar", "probability": 0.90869140625}, {"start": 2403.78, "end": 2405.04, "word": " then", "probability": 0.48876953125}, {"start": 2405.04, "end": 2407.46, "word": " الـPhi", "probability": 0.65069580078125}, {"start": 2407.46, "end": 2408.78, "word": " inverse", "probability": 0.5859375}, {"start": 2408.78, "end": 2409.46, "word": " of", "probability": 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"word": " of", "probability": 0.94775390625}, {"start": 2525.09, "end": 2526.57, "word": " الكوان", "probability": 0.7533365885416666}], "temperature": 1.0}, {"id": 105, "seek": 255434, "start": 2526.76, "end": 2554.34, "text": "في الـ Phi inverse of K2 لكل inverse يبقى هذا الكلام بده يساوي هذا الكلام بده يساوي Phi inverse of K1 في Phi inverse of K2 inverse", "tokens": [41185, 2423, 39184, 41435, 17340, 295, 591, 17, 5296, 28820, 17340, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 41435, 17340, 295, 591, 16, 8978, 41435, 17340, 295, 591, 17, 17340], "avg_logprob": -0.1891276016831398, "compression_ratio": 1.8350515463917525, "no_speech_prob": 0.0, "words": [{"start": 2526.76, "end": 2527.2, "word": "في", "probability": 0.55712890625}, {"start": 2527.2, "end": 2527.54, "word": " الـ", "probability": 0.69775390625}, {"start": 2527.54, "end": 2527.92, "word": " Phi", "probability": 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0.9703776041666666}, {"start": 2546.1, "end": 2546.5, "word": " بده", "probability": 0.934814453125}, {"start": 2546.5, "end": 2547.0, "word": " يساوي", "probability": 0.9814453125}, {"start": 2547.0, "end": 2547.58, "word": " Phi", "probability": 0.58544921875}, {"start": 2547.58, "end": 2548.34, "word": " inverse", "probability": 0.78466796875}, {"start": 2548.34, "end": 2549.1, "word": " of", "probability": 0.97119140625}, {"start": 2549.1, "end": 2549.92, "word": " K1", "probability": 0.9833984375}, {"start": 2549.92, "end": 2550.6, "word": " في", "probability": 0.89599609375}, {"start": 2550.6, "end": 2551.14, "word": " Phi", "probability": 0.93115234375}, {"start": 2551.14, "end": 2551.9, "word": " inverse", "probability": 0.796875}, {"start": 2551.9, "end": 2552.42, "word": " of", "probability": 0.98583984375}, {"start": 2552.42, "end": 2553.76, "word": " K2", "probability": 0.99462890625}, {"start": 2553.76, "end": 2554.34, "word": " inverse", "probability": 0.75927734375}], "temperature": 1.0}, {"id": 106, "seek": 256365, "start": 2555.45, "end": 2563.65, "text": "هذا الكلام بده يساوي في انفرس of K1 K2 انفرس", "tokens": [3224, 15730, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 8978, 16472, 5172, 2288, 3794, 295, 591, 16, 591, 17, 16472, 5172, 2288, 3794], "avg_logprob": -0.3377403777379256, "compression_ratio": 1.042857142857143, "no_speech_prob": 0.0, "words": [{"start": 2555.45, "end": 2555.95, "word": "هذا", "probability": 0.822021484375}, {"start": 2555.95, "end": 2556.53, "word": " الكلام", "probability": 0.89697265625}, {"start": 2556.53, "end": 2557.01, "word": " بده", "probability": 0.354736328125}, {"start": 2557.01, "end": 2557.69, "word": " يساوي", "probability": 0.9654541015625}, {"start": 2557.69, "end": 2558.23, "word": " في", "probability": 0.288330078125}, {"start": 2558.23, "end": 2559.47, "word": " انفرس", "probability": 0.7252197265625}, {"start": 2559.47, "end": 2559.99, "word": " of", "probability": 0.317138671875}, {"start": 2559.99, "end": 2560.87, "word": " K1", "probability": 0.701416015625}, {"start": 2560.87, "end": 2562.71, "word": " K2", "probability": 0.839111328125}, {"start": 2562.71, "end": 2563.65, "word": " انفرس", "probability": 0.912353515625}], "temperature": 1.0}, {"id": 107, "seek": 258990, "start": 2564.44, "end": 2589.9, "text": "هذا كله مين؟ اللي هو الـ X Y inverse هل هذا الان موجود في الـ Phi inverse of K bar؟ ليش؟ لأن هدول حاصل ضربهم موجود في K bar لأن أول ما جينا كنا K bar ما لها subgroup من G بقى closed under multiplication", "tokens": [3224, 15730, 28242, 3224, 3714, 9957, 22807, 13672, 1829, 31439, 2423, 39184, 1783, 398, 17340, 8032, 1211, 23758, 2423, 7649, 3714, 29245, 23328, 8978, 2423, 39184, 41435, 17340, 295, 591, 2159, 22807, 32239, 8592, 22807, 5296, 33456, 8032, 3215, 12610, 11331, 33546, 1211, 48812, 25513, 16095, 3714, 29245, 23328, 8978, 591, 2159, 5296, 33456, 5551, 12610, 19446, 10874, 1829, 8315, 9122, 8315, 591, 2159, 19446, 5296, 11296, 1422, 17377, 9154, 460, 4724, 4587, 7578, 5395, 833, 27290], "avg_logprob": -0.3397435935644003, "compression_ratio": 1.5025641025641026, "no_speech_prob": 0.0, "words": [{"start": 2564.44, "end": 2564.86, "word": "هذا", "probability": 0.7705078125}, {"start": 2564.86, "end": 2565.26, "word": " كله", "probability": 0.907470703125}, {"start": 2565.26, "end": 2565.9, "word": " مين؟", "probability": 0.3667805989583333}, {"start": 2565.9, "end": 2566.16, "word": " اللي", "probability": 0.73876953125}, {"start": 2566.16, "end": 2566.36, "word": " هو", "probability": 0.9765625}, {"start": 2566.36, "end": 2566.58, "word": " الـ", "probability": 0.781494140625}, {"start": 2566.58, "end": 2566.88, "word": " X", "probability": 0.2861328125}, {"start": 2566.88, "end": 2567.42, "word": " Y", "probability": 0.5927734375}, {"start": 2567.42, "end": 2568.06, "word": " inverse", "probability": 0.3994140625}, {"start": 2568.06, "end": 2569.64, "word": " هل", "probability": 0.7115478515625}, {"start": 2569.64, "end": 2570.1, "word": " هذا", "probability": 0.9453125}, {"start": 2570.1, "end": 2570.6, "word": " الان", "probability": 0.660400390625}, {"start": 2570.6, "end": 2571.64, "word": " موجود", "probability": 0.9881184895833334}, {"start": 2571.64, "end": 2574.54, "word": " في", "probability": 0.47021484375}, {"start": 2574.54, "end": 2574.9, "word": " الـ", "probability": 0.6748046875}, {"start": 2574.9, "end": 2575.42, "word": " Phi", "probability": 0.306884765625}, {"start": 2575.42, "end": 2576.52, "word": " inverse", "probability": 0.796875}, {"start": 2576.52, "end": 2577.32, "word": " of", "probability": 0.92529296875}, {"start": 2577.32, "end": 2577.98, "word": " K", "probability": 0.7431640625}, {"start": 2577.98, "end": 2579.16, "word": " bar؟", "probability": 0.6142578125}, {"start": 2579.16, "end": 2580.08, "word": " ليش؟", "probability": 0.6920572916666666}, {"start": 2580.08, "end": 2580.46, "word": " لأن", "probability": 0.87109375}, {"start": 2580.46, "end": 2580.82, "word": " هدول", "probability": 0.67626953125}, {"start": 2580.82, "end": 2581.52, "word": " حاصل", "probability": 0.8860677083333334}, {"start": 2581.52, "end": 2581.98, "word": " ضربهم", "probability": 0.9072265625}, {"start": 2581.98, "end": 2582.38, "word": " موجود", "probability": 0.9680989583333334}, {"start": 2582.38, "end": 2582.54, "word": " في", "probability": 0.94677734375}, {"start": 2582.54, "end": 2582.86, "word": " K", "probability": 0.93017578125}, {"start": 2582.86, "end": 2583.24, "word": " bar", "probability": 0.86181640625}, {"start": 2583.24, "end": 2583.86, "word": " لأن", "probability": 0.876220703125}, {"start": 2583.86, "end": 2584.26, "word": " أول", "probability": 0.7626953125}, {"start": 2584.26, "end": 2584.42, "word": " ما", "probability": 0.446044921875}, {"start": 2584.42, "end": 2584.74, "word": " جينا", "probability": 0.9676106770833334}, {"start": 2584.74, "end": 2585.06, "word": " كنا", "probability": 0.6497802734375}, {"start": 2585.06, "end": 2585.46, "word": " K", "probability": 0.4169921875}, {"start": 2585.46, "end": 2585.9, "word": " bar", "probability": 0.87890625}, {"start": 2585.9, "end": 2586.12, "word": " ما", "probability": 0.611328125}, {"start": 2586.12, "end": 2586.44, "word": " لها", "probability": 0.7181396484375}, {"start": 2586.44, "end": 2587.48, "word": " subgroup", "probability": 0.694580078125}, {"start": 2587.48, "end": 2587.74, "word": " من", "probability": 0.97998046875}, {"start": 2587.74, "end": 2588.0, "word": " G", "probability": 0.7724609375}, {"start": 2588.0, "end": 2588.22, "word": " بقى", "probability": 0.7091471354166666}, {"start": 2588.22, "end": 2588.84, "word": " closed", "probability": 0.87060546875}, {"start": 2588.84, "end": 2589.22, "word": " under", "probability": 0.826171875}, {"start": 2589.22, "end": 2589.9, "word": " multiplication", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 108, "seek": 261888, "start": 2590.56, "end": 2618.88, "text": "يبقى هذا موجود في الـPhi inverse of K bar يبقى بناء عليه الـPhi inverse of K bar is a subgroup من جيه؟ من جيه وانتهينا منها بدنا نروح للنقطة اللي بعدها وهي خاصية ال normality ايوة عرف لو ماكنتش homomorphism", "tokens": [1829, 3555, 4587, 7578, 23758, 3714, 29245, 23328, 8978, 2423, 39184, 47, 4954, 17340, 295, 591, 2159, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 2423, 39184, 47, 4954, 17340, 295, 591, 2159, 307, 257, 1422, 17377, 9154, 10874, 1829, 3224, 22807, 9154, 10874, 1829, 3224, 4032, 7649, 47395, 1829, 8315, 9154, 11296, 47525, 8315, 8717, 32887, 5016, 24976, 1863, 47432, 3660, 13672, 1829, 39182, 11296, 37037, 1829, 16490, 33546, 10632, 2423, 2026, 1860, 1975, 1829, 2407, 3660, 6225, 28480, 45164, 19446, 19452, 2655, 8592, 3655, 32702, 1434], "avg_logprob": -0.24378551661290906, "compression_ratio": 1.545, "no_speech_prob": 0.0, "words": [{"start": 2590.56, "end": 2591.08, "word": "يبقى", "probability": 0.89990234375}, {"start": 2591.08, "end": 2591.42, "word": " هذا", "probability": 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2605.8, "end": 2606.9, "word": " بدنا", "probability": 0.766357421875}, {"start": 2606.9, "end": 2607.16, "word": " نروح", "probability": 0.9933268229166666}, {"start": 2607.16, "end": 2607.88, "word": " للنقطة", "probability": 0.9237060546875}, {"start": 2607.88, "end": 2608.06, "word": " اللي", "probability": 0.882080078125}, {"start": 2608.06, "end": 2608.62, "word": " بعدها", "probability": 0.91064453125}, {"start": 2608.62, "end": 2609.06, "word": " وهي", "probability": 0.82421875}, {"start": 2609.06, "end": 2609.92, "word": " خاصية", "probability": 0.9817708333333334}, {"start": 2609.92, "end": 2610.22, "word": " ال", "probability": 0.87060546875}, {"start": 2610.22, "end": 2611.04, "word": " normality", "probability": 0.720703125}, {"start": 2611.04, "end": 2612.18, "word": " ايوة", "probability": 0.68756103515625}, {"start": 2612.18, "end": 2616.84, "word": " عرف", "probability": 0.28839111328125}, {"start": 2616.84, "end": 2617.06, "word": " لو", "probability": 0.92236328125}, {"start": 2617.06, "end": 2617.72, "word": " ماكنتش", "probability": 0.9527587890625}, {"start": 2617.72, "end": 2618.88, "word": " homomorphism", "probability": 0.9344075520833334}], "temperature": 1.0}, {"id": 109, "seek": 264767, "start": 2619.71, "end": 2647.67, "text": "أمرها ما بيصير كلامها ده صحيح وحسب التعريف اللي عندك حسب التعريف يعني أعرفنا الـPhi Inverse وين أعرفناه و الله مسحنا .. مسحنا .. لا أيوة أيوة كل الـK اللي موجودة في جبهات الـPhi of K موجودة وين؟ في الـK bar أيوة", "tokens": [10721, 29973, 11296, 19446, 4724, 1829, 9381, 13546, 28242, 10943, 11296, 11778, 3224, 20328, 5016, 1829, 5016, 4032, 5016, 35457, 16712, 3615, 16572, 5172, 13672, 1829, 43242, 4117, 11331, 35457, 16712, 3615, 16572, 5172, 37495, 22653, 5551, 3615, 28480, 8315, 2423, 39184, 47, 4954, 682, 4308, 4032, 9957, 5551, 3615, 28480, 8315, 3224, 4032, 21984, 47524, 5016, 8315, 4386, 47524, 5016, 8315, 4386, 20193, 36632, 2407, 3660, 36632, 2407, 3660, 28242, 2423, 39184, 42, 13672, 1829, 3714, 29245, 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تمام", "probability": 0.990478515625}, {"start": 2926.66, "end": 2927.7, "word": " واخدنا", "probability": 0.9417724609375}, {"start": 2927.7, "end": 2928.06, "word": " x", "probability": 0.42041015625}, {"start": 2928.06, "end": 2928.48, "word": " y", "probability": 0.669921875}, {"start": 2928.48, "end": 2929.3, "word": " inverse", "probability": 0.896484375}, {"start": 2929.3, "end": 2930.0, "word": " و", "probability": 0.6943359375}, {"start": 2930.0, "end": 2930.6, "word": " أثرنا", "probability": 0.6949869791666666}, {"start": 2930.6, "end": 2931.02, "word": " عليها", "probability": 0.979736328125}, {"start": 2931.02, "end": 2931.56, "word": " بفاية", "probability": 0.5115966796875}, {"start": 2931.56, "end": 2931.72, "word": " و", "probability": 0.978515625}, {"start": 2931.72, "end": 2932.16, "word": " طلع", "probability": 0.8068033854166666}, {"start": 2932.16, "end": 2932.46, "word": " ك", "probability": 0.46044921875}, {"start": 2932.46, "end": 2933.18, "word": " واحد", 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Phi of K صحيح يبقى بنقول هنا النقطة الأخيرة ان ال X Y inverse هذه موجودة في ال Phi inverse في ال Phi inverse في ال Phi inverse of K بار", "tokens": [3555, 1863, 28543, 2288, 8717, 39648, 1783, 398, 17340, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 41435, 8978, 2423, 41435, 295, 591, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 44945, 39648, 34105, 28239, 47432, 3660, 16247, 9778, 48923, 16472, 2423, 1783, 398, 17340, 29538, 3714, 29245, 23328, 3660, 8978, 2423, 41435, 17340, 8978, 2423, 41435, 17340, 8978, 2423, 41435, 17340, 295, 591, 4724, 9640], "avg_logprob": -0.26941287923942914, "compression_ratio": 1.8391608391608392, "no_speech_prob": 0.0, "words": [{"start": 2938.47, "end": 2939.35, "word": "بنقدر", "probability": 0.67974853515625}, {"start": 2939.35, "end": 2939.65, "word": " نقول", "probability": 0.93359375}, {"start": 2939.65, "end": 2940.11, "word": " X", "probability": 0.11480712890625}, {"start": 2940.11, "end": 2940.63, "word": " Y", "probability": 0.73779296875}, 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{"id": 125, "seek": 300616, "start": 2979.36, "end": 3006.16, "text": "هذه الخطوة زيادة تمام يبقى موجودة في الـ Phi inverse of K bar يبقى بناء اللي عليه Phi inverse of K bar is a subgroup يبقى هنا Phi inverse of K bar is a subgroup من مين؟ من ال G بدنا نيجي للنقطة الثامنة خلي بالك معايا", "tokens": [3224, 24192, 33962, 9566, 2407, 3660, 30767, 1829, 18513, 3660, 46811, 10943, 7251, 3555, 4587, 7578, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 41435, 17340, 295, 591, 2159, 7251, 3555, 4587, 7578, 44945, 16606, 13672, 1829, 47356, 41435, 17340, 295, 591, 2159, 307, 257, 1422, 17377, 7251, 3555, 4587, 7578, 34105, 41435, 17340, 295, 591, 2159, 307, 257, 1422, 17377, 9154, 3714, 9957, 22807, 9154, 2423, 460, 47525, 8315, 8717, 1829, 7435, 1829, 24976, 1863, 47432, 3660, 6024, 104, 10943, 1863, 3660, 16490, 20292, 20666, 4117, 20449, 995, 25528], "avg_logprob": -0.2604166782564587, "compression_ratio": 1.6935483870967742, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2979.36, "end": 2979.76, "word": "هذه", "probability": 0.6328125}, {"start": 2979.76, "end": 2980.24, "word": " الخطوة", "probability": 0.8792724609375}, {"start": 2980.24, "end": 2980.84, "word": " زيادة", "probability": 0.90625}, {"start": 2980.84, "end": 2981.82, "word": " تمام", "probability": 0.6846923828125}, {"start": 2981.82, "end": 2982.52, "word": " يبقى", "probability": 0.8685302734375}, {"start": 2982.52, "end": 2983.04, "word": " موجودة", "probability": 0.9652099609375}, {"start": 2983.04, "end": 2983.14, "word": " في", "probability": 0.97021484375}, {"start": 2983.14, "end": 2983.34, "word": " الـ", "probability": 0.619140625}, {"start": 2983.34, "end": 2983.48, "word": " Phi", "probability": 0.157958984375}, {"start": 2983.48, "end": 2983.92, "word": " inverse", "probability": 0.7958984375}, {"start": 2983.92, "end": 2984.28, "word": " of", "probability": 0.96484375}, {"start": 2984.28, "end": 2984.62, "word": " K", "probability": 0.59912109375}, {"start": 2984.62, "end": 2985.0, "word": " bar", "probability": 0.71435546875}, {"start": 2985.0, "end": 2985.66, "word": " يبقى", "probability": 0.9390869140625}, {"start": 2985.66, "end": 2986.0, "word": " بناء", "probability": 0.51318359375}, {"start": 2986.0, "end": 2986.32, "word": " اللي", "probability": 0.600341796875}, {"start": 2986.32, "end": 2986.76, "word": " عليه", "probability": 0.787109375}, {"start": 2986.76, "end": 2987.16, "word": " Phi", "probability": 0.6337890625}, {"start": 2987.16, "end": 2987.58, "word": " inverse", "probability": 0.83203125}, {"start": 2987.58, "end": 2987.94, "word": " of", "probability": 0.9755859375}, {"start": 2987.94, "end": 2988.58, "word": " K", "probability": 0.8701171875}, {"start": 2988.58, "end": 2988.98, "word": " bar", "probability": 0.8818359375}, {"start": 2988.98, "end": 2989.64, "word": " is", "probability": 0.8154296875}, {"start": 2989.64, "end": 2990.06, "word": " a", "probability": 0.9755859375}, {"start": 2990.06, "end": 2990.92, "word": " subgroup", "probability": 0.71337890625}, {"start": 2990.92, "end": 2991.86, "word": " يبقى", "probability": 0.9749755859375}, {"start": 2991.86, "end": 2992.2, "word": " هنا", "probability": 0.984375}, {"start": 2992.2, "end": 2993.24, "word": " Phi", "probability": 0.5712890625}, {"start": 2993.24, "end": 2994.42, "word": " inverse", "probability": 0.85546875}, {"start": 2994.42, "end": 2995.0, "word": " of", "probability": 0.9794921875}, {"start": 2995.0, "end": 2995.8, "word": " K", "probability": 0.958984375}, {"start": 2995.8, "end": 2996.46, "word": " bar", "probability": 0.927734375}, {"start": 2996.46, "end": 2997.4, "word": " is", "probability": 0.85888671875}, {"start": 2997.4, "end": 2998.12, "word": " a", "probability": 0.93408203125}, {"start": 2998.12, "end": 2998.88, "word": " subgroup", "probability": 0.9580078125}, {"start": 2998.88, "end": 2999.1, "word": " من", "probability": 0.97998046875}, {"start": 2999.1, "end": 2999.84, "word": " مين؟", "probability": 0.5887044270833334}, {"start": 2999.84, "end": 3000.22, "word": " من", "probability": 0.9609375}, {"start": 3000.22, "end": 3000.54, "word": " ال", "probability": 0.51611328125}, {"start": 3000.54, "end": 3000.72, "word": " G", "probability": 0.412109375}, {"start": 3000.72, "end": 3002.12, "word": " بدنا", "probability": 0.405517578125}, {"start": 3002.12, "end": 3002.3, "word": " نيجي", "probability": 0.9017333984375}, {"start": 3002.3, "end": 3002.92, "word": " للنقطة", "probability": 0.8953857421875}, {"start": 3002.92, "end": 3004.02, "word": " الثامنة", "probability": 0.95009765625}, {"start": 3004.02, "end": 3005.54, "word": " خلي", "probability": 0.77490234375}, {"start": 3005.54, "end": 3005.84, "word": " بالك", "probability": 0.73876953125}, {"start": 3005.84, "end": 3006.16, "word": " معايا", "probability": 0.7639973958333334}], "temperature": 1.0}, {"id": 126, "seek": 302822, "start": 3006.8, "end": 3028.22, "text": "النقطة الثامنة اللى جبناها هذه الـ subgroup من G بنا نثبت انها normal بس بشرط ان ال K bar normal من G يبقى باجي بقوله assume افترض ان ال K bar is a normal subgroup من G bar", "tokens": [6027, 1863, 47432, 3660, 6024, 104, 10943, 1863, 3660, 13672, 7578, 10874, 3555, 8315, 11296, 29538, 2423, 39184, 1422, 17377, 9154, 460, 4724, 8315, 8717, 12984, 3555, 2655, 16472, 11296, 2710, 4724, 3794, 4724, 46309, 9566, 16472, 2423, 591, 2159, 2710, 9154, 460, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 591, 2159, 307, 257, 2710, 1422, 17377, 9154, 460, 2159], "avg_logprob": -0.25990318244611715, "compression_ratio": 1.5923566878980893, "no_speech_prob": 0.0, "words": [{"start": 3006.8, "end": 3007.46, "word": "النقطة", "probability": 0.8819580078125}, {"start": 3007.46, "end": 3008.06, "word": " الثامنة", "probability": 0.90556640625}, {"start": 3008.06, "end": 3008.72, "word": " اللى", "probability": 0.5433349609375}, {"start": 3008.72, "end": 3009.36, "word": " جبناها", "probability": 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0.89599609375}, {"start": 3015.2, "end": 3015.48, "word": " ال", "probability": 0.6826171875}, {"start": 3015.48, "end": 3015.76, "word": " K", "probability": 0.445068359375}, {"start": 3015.76, "end": 3016.16, "word": " bar", "probability": 0.529296875}, {"start": 3016.16, "end": 3016.62, "word": " normal", "probability": 0.5517578125}, {"start": 3016.62, "end": 3017.04, "word": " من", "probability": 0.99267578125}, {"start": 3017.04, "end": 3017.36, "word": " G", "probability": 0.95458984375}, {"start": 3017.36, "end": 3018.32, "word": " يبقى", "probability": 0.9334716796875}, {"start": 3018.32, "end": 3018.64, "word": " باجي", "probability": 0.8323567708333334}, {"start": 3018.64, "end": 3019.24, "word": " بقوله", "probability": 0.87353515625}, {"start": 3019.24, "end": 3020.2, "word": " assume", "probability": 0.1451416015625}, {"start": 3020.2, "end": 3021.82, "word": " افترض", "probability": 0.9495849609375}, {"start": 3021.82, "end": 3022.64, "word": " ان", "probability": 0.95654296875}, {"start": 3022.64, "end": 3022.94, "word": " ال", "probability": 0.837890625}, {"start": 3022.94, "end": 3023.32, "word": " K", "probability": 0.9267578125}, {"start": 3023.32, "end": 3023.86, "word": " bar", "probability": 0.88427734375}, {"start": 3023.86, "end": 3024.28, "word": " is", "probability": 0.8818359375}, {"start": 3024.28, "end": 3024.62, "word": " a", "probability": 0.96875}, {"start": 3024.62, "end": 3025.1, "word": " normal", "probability": 0.86962890625}, {"start": 3025.1, "end": 3026.36, "word": " subgroup", "probability": 0.945068359375}, {"start": 3026.36, "end": 3027.12, "word": " من", "probability": 0.9931640625}, {"start": 3027.12, "end": 3027.82, "word": " G", "probability": 0.97607421875}, {"start": 3027.82, "end": 3028.22, "word": " bar", "probability": 0.869140625}], "temperature": 1.0}, {"id": 127, "seek": 304958, "start": 3028.92, "end": 3049.58, "text": "بالدالي اثبت ان الفاي انفرس of K bar is a normal subgroup من من من ال G", "tokens": [3555, 6027, 3215, 6027, 1829, 1975, 12984, 3555, 2655, 16472, 27188, 47302, 16472, 5172, 2288, 3794, 295, 591, 2159, 307, 257, 2710, 1422, 17377, 9154, 9154, 9154, 2423, 460], "avg_logprob": -0.5359374841054281, "compression_ratio": 1.1590909090909092, "no_speech_prob": 0.0, "words": [{"start": 3028.92, "end": 3029.58, "word": "بالدالي", "probability": 0.505712890625}, {"start": 3029.58, "end": 3030.24, "word": " اثبت", "probability": 0.84075927734375}, {"start": 3030.24, "end": 3030.84, "word": " ان", "probability": 0.9189453125}, {"start": 3030.84, "end": 3038.52, "word": " الفاي", "probability": 0.281585693359375}, {"start": 3038.52, "end": 3039.74, "word": " انفرس", "probability": 0.84521484375}, {"start": 3039.74, "end": 3040.18, "word": " of", "probability": 0.4052734375}, {"start": 3040.18, "end": 3041.08, "word": " K", "probability": 0.410400390625}, {"start": 3041.08, "end": 3041.82, "word": " bar", "probability": 0.58203125}, {"start": 3041.82, "end": 3042.46, "word": " is", "probability": 0.4130859375}, {"start": 3042.46, "end": 3042.92, "word": " a", "probability": 0.9140625}, {"start": 3042.92, "end": 3043.4, "word": " normal", "probability": 0.8291015625}, {"start": 3043.4, "end": 3044.8, "word": " subgroup", "probability": 0.76904296875}, {"start": 3044.8, "end": 3045.28, "word": " من", "probability": 0.978515625}, {"start": 3045.28, "end": 3047.82, "word": " من", "probability": 0.361328125}, {"start": 3047.82, "end": 3048.4, "word": " من", "probability": 0.7001953125}, {"start": 3048.4, "end": 3049.3, "word": " ال", "probability": 0.3544921875}, {"start": 3049.3, "end": 3049.58, "word": " G", "probability": 0.54296875}], "temperature": 1.0}, {"id": 128, "seek": 307177, "start": 3050.95, "end": 3071.77, "text": "كويس لذلك بدروع اخد let الجي موجودة في جي and ال X موجود في الفاي انفرس of الكبار then الجي موجودة في الجي", "tokens": [4117, 45865, 3794, 5296, 8848, 23275, 4724, 3215, 2288, 45367, 1975, 9778, 3215, 718, 25724, 1829, 3714, 29245, 23328, 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"end": 3058.15, "word": " جي", "probability": 0.784423828125}, {"start": 3058.15, "end": 3058.85, "word": " and", "probability": 0.865234375}, {"start": 3058.85, "end": 3059.85, "word": " ال", "probability": 0.81982421875}, {"start": 3059.85, "end": 3060.27, "word": " X", "probability": 0.60400390625}, {"start": 3060.27, "end": 3060.95, "word": " موجود", "probability": 0.98388671875}, {"start": 3060.95, "end": 3061.15, "word": " في", "probability": 0.888671875}, {"start": 3061.15, "end": 3061.75, "word": " الفاي", "probability": 0.4217529296875}, {"start": 3061.75, "end": 3062.75, "word": " انفرس", "probability": 0.7340087890625}, {"start": 3062.75, "end": 3063.57, "word": " of", "probability": 0.8037109375}, {"start": 3063.57, "end": 3065.11, "word": " الكبار", "probability": 0.74169921875}, {"start": 3065.11, "end": 3067.27, "word": " then", "probability": 0.66748046875}, {"start": 3067.27, "end": 3070.27, "word": " الجي", "probability": 0.944580078125}, {"start": 3070.27, "end": 3071.01, "word": " موجودة", "probability": 0.96337890625}, {"start": 3071.01, "end": 3071.21, "word": " في", "probability": 0.9853515625}, {"start": 3071.21, "end": 3071.77, "word": " الجي", "probability": 0.960693359375}], "temperature": 1.0}, {"id": 129, "seek": 308315, "start": 3072.83, "end": 3083.15, "text": "والـ X هذه بدها تساوي في انفرس في انفرس of K على سبيل المثال", "tokens": [2407, 6027, 39184, 1783, 29538, 47525, 11296, 6055, 3794, 995, 45865, 8978, 16472, 5172, 2288, 3794, 8978, 16472, 5172, 2288, 3794, 295, 591, 15844, 8608, 21292, 1211, 9673, 12984, 6027], "avg_logprob": -0.27494958331508024, "compression_ratio": 1.197674418604651, "no_speech_prob": 0.0, "words": [{"start": 3072.83, "end": 3073.57, "word": "والـ", "probability": 0.517578125}, {"start": 3073.57, "end": 3073.99, "word": " X", "probability": 0.59375}, {"start": 3073.99, "end": 3074.61, "word": " هذه", "probability": 0.5634765625}, {"start": 3074.61, "end": 3075.53, "word": " بدها", "probability": 0.76025390625}, {"start": 3075.53, "end": 3076.29, "word": " تساوي", "probability": 0.84014892578125}, {"start": 3076.29, "end": 3076.77, "word": " في", "probability": 0.1591796875}, {"start": 3076.77, "end": 3078.33, "word": " انفرس", "probability": 0.7880859375}, {"start": 3078.33, "end": 3079.13, "word": " في", "probability": 0.69482421875}, {"start": 3079.13, "end": 3079.93, "word": " انفرس", "probability": 0.9849853515625}, {"start": 3079.93, "end": 3080.37, "word": " of", "probability": 0.7646484375}, {"start": 3080.37, "end": 3080.95, "word": " K", "probability": 0.79248046875}, {"start": 3080.95, "end": 3081.73, "word": " على", "probability": 0.88916015625}, {"start": 3081.73, "end": 3082.47, "word": " سبيل", "probability": 0.9755859375}, {"start": 3082.47, "end": 3083.15, "word": " المثال", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 130, "seek": 310540, "start": 3083.94, "end": 3105.4, "text": "يبقى هذا معناه ان جي موجود في جي and فاي of اكس فاي of اكس بده يساوي كم؟ بده يساوي كم طب لو أخدت الجي اكس جي انفرس مشان اثبات ال normality", "tokens": [1829, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 10874, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 293, 6156, 47302, 295, 1975, 4117, 3794, 6156, 47302, 295, 1975, 4117, 3794, 47525, 3224, 7251, 3794, 995, 45865, 9122, 2304, 22807, 47525, 3224, 7251, 3794, 995, 45865, 9122, 2304, 23032, 3555, 45164, 5551, 9778, 3215, 2655, 25724, 1829, 1975, 4117, 3794, 10874, 1829, 16472, 5172, 2288, 3794, 37893, 7649, 1975, 12984, 3555, 9307, 2423, 2026, 1860], "avg_logprob": -0.3229166634877523, "compression_ratio": 1.5472972972972974, "no_speech_prob": 0.0, "words": [{"start": 3083.94, "end": 3085.44, "word": "يبقى", "probability": 0.83892822265625}, {"start": 3085.44, "end": 3085.78, "word": " هذا", "probability": 0.84130859375}, {"start": 3085.78, "end": 3086.48, "word": " معناه", "probability": 0.8640950520833334}, {"start": 3086.48, "end": 3086.86, "word": " ان", "probability": 0.54833984375}, 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{"start": 3095.2, "end": 3095.62, "word": " يساوي", "probability": 0.814697265625}, {"start": 3095.62, "end": 3096.2, "word": " كم؟", "probability": 0.5665690104166666}, {"start": 3096.2, "end": 3096.7, "word": " بده", "probability": 0.6649169921875}, {"start": 3096.7, "end": 3097.36, "word": " يساوي", "probability": 0.9361572265625}, {"start": 3097.36, "end": 3097.9, "word": " كم", "probability": 0.76171875}, {"start": 3097.9, "end": 3098.72, "word": " طب", "probability": 0.73486328125}, {"start": 3098.72, "end": 3098.94, "word": " لو", "probability": 0.98046875}, {"start": 3098.94, "end": 3100.04, "word": " أخدت", "probability": 0.8505859375}, {"start": 3100.04, "end": 3100.88, "word": " الجي", "probability": 0.7171630859375}, {"start": 3100.88, "end": 3101.76, "word": " اكس", "probability": 0.8995768229166666}, {"start": 3101.76, "end": 3102.64, "word": " جي", "probability": 0.847900390625}, {"start": 3102.64, "end": 3103.64, "word": " انفرس", "probability": 0.849853515625}, {"start": 3103.64, "end": 3104.12, "word": " مشان", "probability": 0.56103515625}, {"start": 3104.12, "end": 3104.54, "word": " اثبات", "probability": 0.8905029296875}, {"start": 3104.54, "end": 3104.7, "word": " ال", "probability": 0.79296875}, {"start": 3104.7, "end": 3105.4, "word": " normality", "probability": 0.77880859375}], "temperature": 1.0}, {"id": 131, "seek": 313478, "start": 3106.28, "end": 3134.78, "text": "واخد تأثير الـ Phi عليها يبقى هذا الكلام بدل يساوي Phi of G Phi of X Phi of G inverse يبقى هذا الكلام بدل يساوي Phi of G Phi of X اللي هي main اللي هي اب K Phi of X اللي هي و ال K normal اللي هو K", "tokens": [2407, 47283, 3215, 6055, 10721, 12984, 13546, 2423, 39184, 41435, 25894, 11296, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 1211, 7251, 3794, 995, 45865, 41435, 295, 460, 41435, 295, 1783, 41435, 295, 460, 17340, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 1211, 7251, 3794, 995, 45865, 41435, 295, 460, 41435, 295, 1783, 13672, 1829, 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{"start": 3111.38, "end": 3111.84, "word": " يساوي", "probability": 0.76617431640625}, {"start": 3111.84, "end": 3112.36, "word": " Phi", "probability": 0.82373046875}, {"start": 3112.36, "end": 3112.84, "word": " of", "probability": 0.91015625}, {"start": 3112.84, "end": 3113.2, "word": " G", "probability": 0.9111328125}, {"start": 3113.2, "end": 3114.26, "word": " Phi", "probability": 0.88623046875}, {"start": 3114.26, "end": 3114.82, "word": " of", "probability": 0.982421875}, {"start": 3114.82, "end": 3115.36, "word": " X", "probability": 0.98486328125}, {"start": 3115.36, "end": 3116.52, "word": " Phi", "probability": 0.935546875}, {"start": 3116.52, "end": 3117.1, "word": " of", "probability": 0.98291015625}, {"start": 3117.1, "end": 3117.72, "word": " G", "probability": 0.98486328125}, {"start": 3117.72, "end": 3118.46, "word": " inverse", "probability": 0.572265625}, {"start": 3118.46, "end": 3119.7, "word": " يبقى", "probability": 0.973876953125}, {"start": 3119.7, "end": 3120.0, "word": " هذا", "probability": 0.97900390625}, {"start": 3120.0, "end": 3120.6, "word": " الكلام", "probability": 0.9816080729166666}, {"start": 3120.6, "end": 3121.0, "word": " بدل", "probability": 0.972412109375}, {"start": 3121.0, "end": 3121.72, "word": " يساوي", "probability": 0.9892578125}, {"start": 3121.72, "end": 3122.48, "word": " Phi", "probability": 0.9677734375}, {"start": 3122.48, "end": 3123.38, "word": " of", "probability": 0.9765625}, {"start": 3123.38, "end": 3123.7, "word": " G", "probability": 0.98193359375}, {"start": 3123.7, "end": 3124.94, "word": " Phi", "probability": 0.9619140625}, {"start": 3124.94, "end": 3125.34, "word": " of", "probability": 0.98193359375}, {"start": 3125.34, "end": 3125.8, "word": " X", "probability": 0.99609375}, {"start": 3125.8, "end": 3126.18, "word": " اللي", "probability": 0.6409912109375}, {"start": 3126.18, "end": 3126.42, "word": " هي", "probability": 0.890625}, {"start": 3126.42, "end": 3126.76, "word": " main", "probability": 0.4111328125}, {"start": 3126.76, "end": 3127.22, "word": " اللي", "probability": 0.94140625}, {"start": 3127.22, "end": 3127.62, "word": " هي", "probability": 0.9716796875}, {"start": 3127.62, "end": 3128.12, "word": " اب", "probability": 0.2061767578125}, {"start": 3128.12, "end": 3128.6, "word": " K", "probability": 0.4345703125}, {"start": 3128.6, "end": 3129.6, "word": " Phi", "probability": 0.93603515625}, {"start": 3129.6, "end": 3130.02, "word": " of", "probability": 0.9814453125}, {"start": 3130.02, "end": 3130.74, "word": " X", "probability": 0.99560546875}, {"start": 3130.74, "end": 3131.22, "word": " اللي", "probability": 0.94873046875}, {"start": 3131.22, "end": 3131.46, "word": " هي", "probability": 0.8408203125}, {"start": 3131.46, "end": 3131.6, "word": " و", "probability": 0.499267578125}, {"start": 3131.6, "end": 3131.72, "word": " ال", "probability": 0.630859375}, {"start": 3131.72, "end": 3131.92, "word": " K", "probability": 0.7568359375}, {"start": 3131.92, "end": 3132.4, "word": " normal", "probability": 0.174560546875}, {"start": 3132.4, "end": 3133.78, "word": " اللي", "probability": 0.992431640625}, {"start": 3133.78, "end": 3134.22, "word": " هو", "probability": 0.9853515625}, {"start": 3134.22, "end": 3134.78, "word": " K", "probability": 0.94189453125}], "temperature": 1.0}, {"id": 132, "seek": 314598, "start": 3135.98, "end": 3145.98, "text": "والـ Phi هذه of G لكل inverse بالشكل اللي عندنا هنا تمام؟ الحين هذه موجودة في G", "tokens": [2407, 6027, 39184, 41435, 29538, 295, 460, 5296, 28820, 17340, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 46811, 10943, 22807, 21542, 9957, 29538, 3714, 29245, 23328, 3660, 8978, 460], "avg_logprob": -0.3230846793420853, "compression_ratio": 1.1636363636363636, "no_speech_prob": 0.0, "words": [{"start": 3135.98, "end": 3136.86, "word": "والـ", "probability": 0.491455078125}, {"start": 3136.86, "end": 3137.22, "word": " Phi", "probability": 0.1900634765625}, {"start": 3137.22, "end": 3137.84, "word": " هذه", "probability": 0.58642578125}, {"start": 3137.84, "end": 3138.48, "word": " of", "probability": 0.69287109375}, {"start": 3138.48, "end": 3138.92, "word": " G", "probability": 0.75537109375}, {"start": 3138.92, "end": 3139.72, "word": " لكل", "probability": 0.921875}, {"start": 3139.72, "end": 3140.4, "word": " inverse", "probability": 0.57470703125}, {"start": 3140.4, "end": 3141.0, "word": " بالشكل", "probability": 0.9627278645833334}, {"start": 3141.0, "end": 3141.2, "word": " اللي", "probability": 0.941650390625}, {"start": 3141.2, "end": 3141.62, "word": " عندنا", "probability": 0.923583984375}, {"start": 3141.62, "end": 3141.92, "word": " هنا", "probability": 0.79296875}, {"start": 3141.92, "end": 3143.98, "word": " تمام؟", "probability": 0.535888671875}, {"start": 3143.98, "end": 3144.42, "word": " الحين", "probability": 0.794921875}, {"start": 3144.42, "end": 3144.74, "word": " هذه", "probability": 0.8994140625}, {"start": 3144.74, "end": 3145.42, "word": " موجودة", "probability": 0.9765625}, {"start": 3145.42, "end": 3145.64, "word": " في", "probability": 0.97119140625}, {"start": 3145.64, "end": 3145.98, "word": " G", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 133, "seek": 317332, "start": 3146.9, "end": 3173.32, "text": "وهذه موجودة في الـPhi inverse of K وهذه موجودة في G أخدنا تأثير الـPhi عليهم وطلع عندنا هذا الـElement وهذا وهذا الـK bar أنا جال عليها normal يبقى لو أخدت element من G bar هذا موجود في G bar", "tokens": [2407, 3224, 24192, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 47, 4954, 17340, 295, 591, 37037, 24192, 3714, 29245, 23328, 3660, 8978, 460, 5551, 9778, 3215, 8315, 6055, 10721, 12984, 13546, 2423, 39184, 47, 4954, 25894, 16095, 4032, 9566, 1211, 3615, 43242, 8315, 23758, 2423, 39184, 36, 3054, 37037, 15730, 37037, 15730, 2423, 39184, 42, 2159, 41850, 10874, 6027, 25894, 11296, 2710, 7251, 3555, 4587, 7578, 45164, 5551, 9778, 3215, 2655, 4478, 9154, 460, 2159, 23758, 3714, 29245, 23328, 8978, 460, 2159], "avg_logprob": -0.2624246987951807, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 3146.9, "end": 3147.68, "word": "وهذه", "probability": 0.6336263020833334}, {"start": 3147.68, "end": 3148.62, "word": " موجودة", "probability": 0.85418701171875}, {"start": 3148.62, "end": 3149.08, "word": " في", "probability": 0.9443359375}, {"start": 3149.08, "end": 3149.6, "word": " الـPhi", "probability": 0.619964599609375}, {"start": 3149.6, "end": 3150.34, "word": " inverse", "probability": 0.53955078125}, {"start": 3150.34, "end": 3150.88, "word": " of", "probability": 0.88623046875}, {"start": 3150.88, "end": 3151.38, "word": " K", "probability": 0.72119140625}, {"start": 3151.38, "end": 3152.4, "word": " وهذه", "probability": 0.89697265625}, {"start": 3152.4, "end": 3154.64, "word": " موجودة", "probability": 0.9783935546875}, {"start": 3154.64, "end": 3154.78, "word": " في", "probability": 0.900390625}, {"start": 3154.78, "end": 3155.22, "word": " G", "probability": 0.44287109375}, {"start": 3155.22, "end": 3156.24, "word": " أخدنا", "probability": 0.737548828125}, {"start": 3156.24, "end": 3156.86, "word": " تأثير", "probability": 0.879638671875}, {"start": 3156.86, "end": 3157.38, "word": " الـPhi", "probability": 0.7939453125}, {"start": 3157.38, "end": 3158.04, "word": " عليهم", "probability": 0.972900390625}, {"start": 3158.04, "end": 3158.88, "word": " وطلع", "probability": 0.88232421875}, {"start": 3158.88, "end": 3159.54, "word": " عندنا", "probability": 0.921142578125}, {"start": 3159.54, "end": 3160.16, "word": " هذا", "probability": 0.91748046875}, {"start": 3160.16, "end": 3160.88, "word": " الـElement", "probability": 0.822021484375}, {"start": 3160.88, "end": 3161.72, "word": " وهذا", "probability": 0.800048828125}, {"start": 3161.72, "end": 3162.42, "word": " وهذا", "probability": 0.8359375}, {"start": 3162.42, "end": 3164.5, "word": " الـK", "probability": 0.6560872395833334}, {"start": 3164.5, "end": 3165.56, "word": " bar", "probability": 0.408203125}, {"start": 3165.56, "end": 3165.84, "word": " أنا", "probability": 0.54443359375}, {"start": 3165.84, "end": 3166.08, "word": " جال", "probability": 0.694091796875}, {"start": 3166.08, "end": 3166.48, "word": " عليها", "probability": 0.89990234375}, {"start": 3166.48, "end": 3167.34, "word": " normal", "probability": 0.407470703125}, {"start": 3167.34, "end": 3168.3, "word": " يبقى", "probability": 0.873046875}, {"start": 3168.3, "end": 3168.5, "word": " لو", "probability": 0.8515625}, {"start": 3168.5, "end": 3169.1, "word": " أخدت", "probability": 0.934326171875}, {"start": 3169.1, "end": 3169.66, "word": " element", "probability": 0.41455078125}, {"start": 3169.66, "end": 3170.14, "word": " من", "probability": 0.97802734375}, {"start": 3170.14, "end": 3170.72, "word": " G", "probability": 0.8037109375}, {"start": 3170.72, "end": 3171.18, "word": " bar", "probability": 0.60009765625}, {"start": 3171.18, "end": 3171.56, "word": " هذا", "probability": 0.59765625}, {"start": 3171.56, "end": 3172.42, "word": " موجود", "probability": 0.9755859375}, {"start": 3172.42, "end": 3172.62, "word": " في", "probability": 0.96826171875}, {"start": 3172.62, "end": 3172.94, "word": " G", "probability": 0.85400390625}, {"start": 3172.94, "end": 3173.32, "word": " bar", "probability": 0.80908203125}], "temperature": 1.0}, {"id": 134, "seek": 320150, "start": 3173.86, "end": 3201.5, "text": "وهذا موجود في جي بار وهذا موجود في الفاي انفرس هذا موجود في الفاي انفرس of K إذا هذا كله موجود في الفاي انفرس of K بار بالشكل اللي عندنا K بار يبقى بناء عليه الفاي", "tokens": [2407, 3224, 15730, 3714, 29245, 23328, 8978, 10874, 1829, 4724, 9640, 37037, 15730, 3714, 29245, 23328, 8978, 27188, 47302, 16472, 5172, 2288, 3794, 23758, 3714, 29245, 23328, 8978, 27188, 47302, 16472, 5172, 2288, 3794, 295, 591, 11933, 15730, 23758, 28242, 3224, 3714, 29245, 23328, 8978, 27188, 47302, 16472, 5172, 2288, 3794, 295, 591, 4724, 9640, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 591, 4724, 9640, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 27188, 47302], "avg_logprob": -0.24583333015441894, "compression_ratio": 2.3278688524590163, "no_speech_prob": 0.0, "words": [{"start": 3173.86, "end": 3175.38, "word": "وهذا", "probability": 0.6133219401041666}, {"start": 3175.38, "end": 3176.28, "word": " موجود", "probability": 0.8487955729166666}, {"start": 3176.28, "end": 3176.58, "word": " في", "probability": 0.9345703125}, {"start": 3176.58, "end": 3177.68, "word": " جي", "probability": 0.60498046875}, {"start": 3177.68, "end": 3178.14, "word": " بار", "probability": 0.948486328125}, {"start": 3178.14, "end": 3179.28, "word": " وهذا", "probability": 0.697509765625}, {"start": 3179.28, "end": 3180.96, "word": " موجود", "probability": 0.8390299479166666}, {"start": 3180.96, "end": 3181.16, "word": " في", "probability": 0.98046875}, {"start": 3181.16, "end": 3181.66, "word": " الفاي", "probability": 0.53076171875}, {"start": 3181.66, "end": 3182.52, "word": " انفرس", "probability": 0.7943115234375}, {"start": 3182.52, "end": 3183.12, "word": " هذا", "probability": 0.38232421875}, {"start": 3183.12, "end": 3183.76, "word": " موجود", "probability": 0.9518229166666666}, {"start": 3183.76, "end": 3184.0, "word": " في", "probability": 0.978515625}, {"start": 3184.0, "end": 3184.62, "word": " الفاي", "probability": 0.768798828125}, {"start": 3184.62, "end": 3185.52, "word": " انفرس", "probability": 0.982177734375}, {"start": 3185.52, "end": 3185.94, "word": " of", "probability": 0.783203125}, {"start": 3185.94, "end": 3186.3, "word": " K", "probability": 0.47998046875}, {"start": 3186.3, "end": 3186.96, "word": " إذا", "probability": 0.6253662109375}, {"start": 3186.96, "end": 3187.36, "word": " هذا", "probability": 0.77197265625}, {"start": 3187.36, "end": 3187.9, "word": " كله", "probability": 0.978515625}, {"start": 3187.9, "end": 3188.5, "word": " موجود", "probability": 0.9861653645833334}, {"start": 3188.5, "end": 3188.76, "word": " في", "probability": 0.98291015625}, {"start": 3188.76, "end": 3189.38, "word": " الفاي", "probability": 0.8193359375}, {"start": 3189.38, "end": 3190.46, "word": " انفرس", "probability": 0.9833984375}, {"start": 3190.46, "end": 3191.36, "word": " of", "probability": 0.91162109375}, {"start": 3191.36, "end": 3192.68, "word": " K", "probability": 0.75634765625}, {"start": 3192.68, "end": 3193.64, "word": " بار", "probability": 0.8291015625}, {"start": 3193.64, "end": 3194.2, "word": " بالشكل", "probability": 0.84765625}, {"start": 3194.2, "end": 3194.36, "word": " اللي", "probability": 0.94384765625}, {"start": 3194.36, "end": 3195.02, "word": " عندنا", "probability": 0.8486328125}, {"start": 3195.02, "end": 3195.42, "word": " K", "probability": 0.5263671875}, {"start": 3195.42, "end": 3195.94, "word": " بار", "probability": 0.869873046875}, {"start": 3195.94, "end": 3196.62, "word": " يبقى", "probability": 0.96826171875}, {"start": 3196.62, "end": 3197.02, "word": " بناء", "probability": 0.786376953125}, {"start": 3197.02, "end": 3197.68, "word": " عليه", "probability": 0.90283203125}, {"start": 3197.68, "end": 3201.5, "word": " الفاي", "probability": 0.50946044921875}], "temperature": 1.0}, {"id": 135, "seek": 321027, "start": 3201.89, "end": 3210.27, "text": "إنفرست من K بار هو عضو عام من جيه", "tokens": [28814, 1863, 5172, 2288, 14851, 9154, 591, 4724, 9640, 31439, 6225, 11242, 2407, 6225, 10943, 9154, 10874, 1829, 3224], "avg_logprob": -0.9921874523162841, "compression_ratio": 0.95, "no_speech_prob": 0.0, "words": [{"start": 3201.89, "end": 3202.89, "word": "إنفرست", "probability": 0.403851318359375}, {"start": 3202.89, "end": 3203.65, "word": " من", "probability": 0.380615234375}, {"start": 3203.65, "end": 3204.27, "word": " K", "probability": 0.2288818359375}, {"start": 3204.27, "end": 3205.11, "word": " بار", "probability": 0.6375732421875}, {"start": 3205.11, "end": 3205.79, "word": " هو", "probability": 0.158203125}, {"start": 3205.79, "end": 3206.47, "word": " عضو", "probability": 0.3853759765625}, {"start": 3206.47, "end": 3206.53, "word": " عام", "probability": 0.5020751953125}, {"start": 3206.53, "end": 3207.61, "word": " من", "probability": 0.91796875}, {"start": 3207.61, "end": 3210.27, "word": " جيه", "probability": 0.4012858072916667}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3211.1805, "duration_after_vad": 3048.463749999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f3bba5daea3e59790f289c7eb2f361863f742d32
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_raw.srt
@@ -0,0 +1,1980 @@
+1
+00:00:20,690 --> 00:00:24,770
+بسم الله الرحمن الرحيم عودنا على بدأ في المحاضر في
+
+2
+00:00:24,770 --> 00:00:29,010
+الفترة الصباحية كتبنا نظرية نظرية عبارة عن ست نقاط
+
+3
+00:00:29,010 --> 00:00:33,450
+نقطتين كانوا مبرهنات 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 انه five of a بدو يساوي five of b if
+
+6
+00:00:42,430 --> 00:00:46,990
+and only if ال a في ال kernel بدو يساوي بي في ال
+
+7
+00:00:46,990 --> 00:00:52,660
+kernelيبقى بدنا نبرهن صحة هذه النقطة فباجي بقوله
+
+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 ifلو ضربنا في المعكوث
+
+10
+00:01:06,210 --> 00:01:11,990
+تبعها هذه من جهة الشمال بيكون مين؟ بيكون في of بي
+
+11
+00:01:11,990 --> 00:01:18,190
+لكل inverse في في of a بدي ساوي ال identity
+
+12
+00:01:18,190 --> 00:01:25,690
+element تبع من؟ تبع الـG bar لأن في of a وفي of b
+
+13
+00:01:25,690 --> 00:01:32,440
+موجودة تاتوين في الـG barالكلام 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 ifالـ Phi أول ما أخدناها 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¯أيش تفسيرك
+
+18
+00:02:08,650 --> 00:02:13,810
+لهذه العبارة فاي 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 الفايمعنى هذا الكلام أن الـP 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 الـP 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 P في الkernel للـPhi أظن و هو المطلوب
+
+27
+00:02:56,130 --> 00:03:05,820
+النقطة السادسةالنقطة السادسة بتقول ما يأتي لو كان
+
+28
+00:03:05,820 --> 00:03:12,220
+الـ Phi of G بده ساوي الـ G Prime ال Phi of G بده
+
+29
+00:03:12,220 --> 00:03:20,470
+ساوي ال G PrimeالـPhi Inverse of G' بدي يساوي الـG
+
+30
+00:03:20,470 --> 00:03:24,430
+في الـKernel للـPhi وراح المعرفة هذه كل الـX اللى
+
+31
+00:03:24,430 --> 00:03:27,750
+موجودة في G بيحيط الـPhi of X بدي يساوي مين؟ بدي
+
+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
+تعالى نشوف ايش مفهومها قبل ما نبرهن بدنا نفهم ما
+
+34
+00:03:38,030 --> 00:03:42,770
+هو موضوع هذه النقطة شوف يا سيديأحنا عندنا فاي من
+
+35
+00:03:42,770 --> 00:03:48,150
+ال group G إلى ال group G bar تمام قال لي فاي of G
+
+36
+00:03:48,150 --> 00:03:52,200
+بده يسوي G prime يقولي G prime وين موجودةفي الـG
+
+37
+00:03:52,200 --> 00:03:56,840
+بار والـG هذه موجودة في الـG طيب كويس إذا هذه
+
+38
+00:03:56,840 --> 00:04:02,140
+معلومة الآن ايش بقولي بقي بدي يكون الـPhi inverse
+
+39
+00:04:02,140 --> 00:04:07,960
+للـG prime تسوي G مضربة في الكنز يعني لما ناخد Phi
+
+40
+00:04:07,960 --> 00:04:11,260
+inverse للطرفين مش هروح اقول Phi inverse of G
+
+41
+00:04:11,260 --> 00:04:16,930
+prime تسوي G ليش؟ ليش؟ لأ وكانت one to one صحيحهذا
+
+42
+00:04:16,930 --> 00:04:20,250
+ليس إيزو مورفزم، 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 في انفرس جي برايم يبقى مين
+
+47
+00:04:38,420 --> 00:04:41,680
+يسوى جي في الكرنة اللي في هذا اللي عايزين ان تبدو
+
+48
+00:04:41,680 --> 00:04:45,340
+هدول two sets are equal يبقى بدي اروح اخد element
+
+49
+00:04:45,340 --> 00:04:48,800
+هنا اثبت انه موجود هنا و اعمل الأعمال العكسية اخد
+
+50
+00:04:48,800 --> 00:04:52,840
+element هنا و اثبت انه موجود هنا يبقى مشان هيك
+
+51
+00:04:52,840 --> 00:04:59,900
+بداجي اقوله let ال X موجودة في في انفرس جي برايم
+
+52
+00:05:01,340 --> 00:05:09,260
+طبعا يبقى لو أثرت بمين بفاي على الطرفين بصير فاي
+
+53
+00:05:09,260 --> 00:05:17,880
+of X بدها تساوي G prime طيب هذا معناه انه فاي of X
+
+54
+00:05:17,880 --> 00:05:24,500
+يساوي اظن G prime مواطعه مقدرش بفاي of G يبقى هذا
+
+55
+00:05:24,500 --> 00:05:31,090
+فاي of G بالشكل اللي عندنا هنا طيب لو روحتمن 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 main 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 main تبع ال g بعضبنفس المفهوم
+
+60
+00:05:56,610 --> 00:06:02,810
+هذا ايش معناه؟ معناه انه Phi of G inverse في Phi
+
+61
+00:06:02,810 --> 00:06:08,310
+of X بده ساوي ال identity element تبع ال G bar او
+
+62
+00:06:08,310 --> 00:06:15,250
+انشئتم فقولوا Phi of G inverse X بده ساوي ال
+
+63
+00:06:15,250 --> 00:06:20,470
+identity element تبع ال G barمعنى هذا الكلام أن
+
+64
+00:06:20,470 --> 00:06:24,690
+هذا الـElement بين القوسين وين موجود في الـKernel
+
+65
+00:06:24,690 --> 00:06:29,690
+لأنه صورته الـIdentity يبقى بده يصير G inverse X
+
+66
+00:06:29,690 --> 00:06:36,490
+موجود في الـKernel للـPhi طب لو ضربت الطرفين في G
+
+67
+00:06:36,490 --> 00:06:42,130
+من جهة الشمال يبقى بظل X موجود في الـG في
+
+68
+00:06:42,130 --> 00:06:48,480
+الـKernel للـPhiيبقى انا اخدت X موجود في الـPhi
+
+69
+00:06:48,480 --> 00:06:53,940
+inverse للـG' لقيته موجود وين؟ في G في الـkernel
+
+70
+00:06:53,940 --> 00:07:00,020
+معناته الست الأولانية subset من الست التانية يبقى
+
+71
+00:07:00,020 --> 00:07:08,060
+هنا سا Phi inverse of G' subset من مين؟ من الـG في
+
+72
+00:07:08,060 --> 00:07:13,580
+ال kernel للـPhiاعتبر هذه هي النقطة الأولى بالدرجة
+
+73
+00:07:13,580 --> 00:07:21,300
+للنقطة التانية on the other hand بالدرجة
+
+74
+00:07:21,300 --> 00:07:28,940
+ياخد X موجودة في الـG في الكيرن للـPhiخُد للـ X
+
+75
+00:07:28,940 --> 00:07:35,380
+موجودة في الـ G في الكيرنل للـ Phi إذا كنت أثبت إن
+
+76
+00:07:35,380 --> 00:07:39,700
+الـ X هذه موجودة هنا بيكون تم المطلوب يكون انتهينا
+
+77
+00:07:39,700 --> 00:07:45,600
+من المسألة اللي عندنا يبقى then الـ X هذه يا شباب
+
+78
+00:07:45,600 --> 00:07:51,200
+بقدر أقول هي الـ G مضروبة في element من مين؟ من
+
+79
+00:07:51,200 --> 00:07:59,080
+الكيرنل تبع الـ Phi وليكن اللي هو Kيبقى x بدأ
+
+80
+00:07:59,080 --> 00:08:09,660
+تساوي gk for some for some k اللي موجودة في الكيرن
+
+81
+00:08:09,660 --> 00:08:17,100
+لفاي طيب شو رأيك أثر على تنتين بفاي يبقى ايش بده
+
+82
+00:08:17,100 --> 00:08:25,960
+يصير بده يصير في of x بده يساوي في of g في kيعني
+
+83
+00:08:25,960 --> 00:08:32,540
+معنى هذا الكلام أنه Phi of X بدر 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
+بدر يعطيناالطرف الشمال Phi of X الطرف اليمين Phi
+
+86
+00:08:49,680 --> 00:08:55,860
+of G كدهش مُعطَى من الرأس 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 كدهش؟
+
+88
+00:09:04,900 --> 00:09:10,080
+طلع ليه هنا، احنا جيبناها من وين الـK هذا؟موجودة
+
+89
+00:09:10,080 --> 00:09:13,200
+في الـ Kernel for some K الموجودة في الـ Kernel
+
+90
+00:09:13,200 --> 00:09:18,880
+يبقى Phi of K بقداش بال Identity يبقى هذا بال
+
+91
+00:09:18,880 --> 00:09:27,880
+Identity تبع الـ G ليش؟ since اللي هو الـ K هذه
+
+92
+00:09:27,880 --> 00:09:33,300
+موجودة في ال Kernel للـ Phiالنظر اللي موجودة هنا
+
+93
+00:09:33,300 --> 00:09:39,400
+تعطينا الـ Identity Element يبقى هنا الساعة الـ
+
+94
+00:09:39,400 --> 00:09:45,860
+Phi of X بده يساوي من الـ G' ليش ان الـ G' موجودة
+
+95
+00:09:45,860 --> 00:09:50,380
+في G' و الـ Identity هي تبع الـ G' يبقى حاصل الدرب
+
+96
+00:09:50,380 --> 00:09:58,050
+يعطينا من G' يبقى معنى هذا الكلام ان الـ Xبتكون
+
+97
+00:09:58,050 --> 00:10:06,270
+موجودة في الـPhi inverse of G' لاحظ ما يأتي اش
+
+98
+00:10:06,270 --> 00:10:11,070
+كتبت أنا السطر الأخير انا 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'أيش روحت كتبتي يبقى ال X ما كتبتش تساوي في
+
+101
+00:10:22,230 --> 00:10:27,490
+انفرس of G' كتبت ال X موجودة في ال في انفرس of G'
+
+102
+00:10:27,890 --> 00:10:33,270
+ليش ان ال في انفرس of G' عدت نقات مش نقطة واحدة لو
+
+103
+00:10:33,270 --> 00:10:39,650
+كانت نقطة واحدة لكتبت ايش لكتبت اليساوي تمام اذا X
+
+104
+00:10:41,450 --> 00:10:43,270
+ماشي و لو 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 وانت
+
+106
+00:10:44,270 --> 00:10:44,630
+وانت 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 وانت
+
+108
+00:10:45,630 --> 00:10:47,230
+وانت 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 وانت
+
+110
+00:10:50,470 --> 00:10:54,770
+وانت وانت وانت وانت
+
+111
+00:10:54,770 --> 00:10:54,770
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+112
+00:10:54,770 --> 00:10:54,770
+وانت
+
+113
+00:11:02,630 --> 00:11:07,710
+اللي هو subset من مين من الـ Phi inverse of G
+
+114
+00:11:07,710 --> 00:11:12,990
+prime وهذه العلاقة رقم اتنين يبقى باجي بقول from
+
+115
+00:11:12,990 --> 00:11:23,810
+واحد and اتنين we have ان ال Phi inverse of G
+
+116
+00:11:23,810 --> 00:11:28,510
+prime بده يساوي G في الكيرن للـ Phi
+
+117
+00:11:34,710 --> 00:11:38,890
+نعطيك مثال توضيح على ذلك لإن هي خلصت النظرية
+
+118
+00:11:38,890 --> 00:11:44,870
+example بقول
+
+119
+00:11:44,870 --> 00:11:49,610
+suppose that
+
+120
+00:11:49,610 --> 00:12:01,130
+افترض ان الفاي من z تلاتين الى z تلاتينA
+
+121
+00:12:01,130 --> 00:12:07,730
+homomorphism suppose that فاي is a homomorphism
+
+122
+00:12:07,730 --> 00:12:12,510
+and الكيرنل
+
+123
+00:12:12,510 --> 00:12:22,390
+للفاي هي العناصر zero و عشرة و عشرينبيقول لـ F إذا
+
+124
+00:12:22,390 --> 00:12:30,290
+كان الـ Phi لـ 23 هي عبارة عن 9 السؤال هو
+
+125
+00:12:30,290 --> 00:12:33,990
+determine
+
+126
+00:12:33,990 --> 00:12:38,510
+all
+
+127
+00:12:41,760 --> 00:12:51,300
+Elements that map maps to تسعة كل ال elements اللي
+
+128
+00:12:51,300 --> 00:13:02,040
+هم maps to تسعة السؤال
+
+129
+00:13:02,040 --> 00:13:06,480
+مرة تانية فيها النفاي من Z تلاتين ل Z تلاتين
+
+130
+00:13:06,480 --> 00:13:10,870
+homomorphismوهذا حسبنا له كيرن اللي جينا كيرنه
+
+131
+00:13:10,870 --> 00:13:16,190
+zero وعشرة وعشرين هذه معلومة وزيادة على ذلك five
+
+132
+00:13:16,190 --> 00:13:20,590
+of تلاتة وعشرين يساوي تسعة قال لي هاتلي كل ال
+
+133
+00:13:20,590 --> 00:13:25,250
+elements اللي maps to تسعة يعني بدي كل العناصر
+
+134
+00:13:25,250 --> 00:13:29,810
+اللي في زد تلاتين واللي صارتهم بتكون مان تسعة يعني
+
+135
+00:13:29,810 --> 00:13:33,750
+مش ع جد تلاتة وعشرينبقى باقي ال elements اللي
+
+136
+00:13:33,750 --> 00:13:39,990
+وصرتهم بتكون تسعة تطلعلي في النقطة الأخيرة رقم ستة
+
+137
+00:13:39,990 --> 00:13:45,270
+وخليها في دماغك انا عندي في of G يسوى G prime كأنه
+
+138
+00:13:45,270 --> 00:13:50,030
+G هدى main تلاتة وعشرين وال G prime هي main التسعة
+
+139
+00:13:50,030 --> 00:13:55,510
+يبقى ال في inverse of G prime بده سوى ال G في ال
+
+140
+00:13:55,510 --> 00:14:00,750
+kernel للفييبقى بناء عليه انا عندي فاي of تلاتة
+
+141
+00:14:00,750 --> 00:14:07,250
+وعشرين يساوي تسعة شو رايك اخد معكوس الفاي للطرفين
+
+142
+00:14:07,250 --> 00:14:14,370
+يبقى ايش بصير عندي بصير الفاي inverse of تسعة بده
+
+143
+00:14:14,370 --> 00:14:18,930
+يساوي ال element اللي عندنا اللي هو تلاتة وعشرين
+
+144
+00:14:18,930 --> 00:14:27,530
+في ال kernel للفايتمام؟ لكن لما كانت العملية عملية
+
+145
+00:14:27,530 --> 00:14:31,890
+جامعة إذا ما بكتبش تلاتة وعشرين مضروبة في ال
+
+146
+00:14:31,890 --> 00:14:37,990
+kernel وإنما بكتب تلاتة وعشرين زائد ال kernel لمن؟
+
+147
+00:14:37,990 --> 00:14:44,890
+لل في يبقى هذا الكلام بدرساوي تلاتة وعشرين زائد ال
+
+148
+00:14:44,890 --> 00:14:53,110
+kernel لل في هي موجود فوق يبقى zero وعشرة وعشرينمش
+
+149
+00:14:53,110 --> 00:14:57,070
+تروح تقول هنا فاينفرس وتسعة الفاينفرس وتضرع
+
+150
+00:14:57,070 --> 00:14:57,650
+الفاينفرس وتضرع الفاينفرس تضرع الفاينفرس تضرع
+
+151
+00:14:57,650 --> 00:14:57,950
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+152
+00:14:57,950 --> 00:14:58,630
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+153
+00:14:58,630 --> 00:14:59,010
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+154
+00:14:59,010 --> 00:15:01,730
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+155
+00:15:01,730 --> 00:15:07,210
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+156
+00:15:07,210 --> 00:15:14,830
+الفاينفرس تضرع الفاينفرس
+
+157
+00:15:14,830 --> 00:15:18,880
+تفي المثل لأن ال operation عملية جمع هذا الكلام
+
+158
+00:15:18,880 --> 00:15:22,460
+بده يساوي بده يجمع كل عنصر مع اناظره يبقى هذا
+
+159
+00:15:22,460 --> 00:15:27,460
+تلاتة وعشرين تلاتة وعشرين وعشرة تلاتة وتلاتين في
+
+160
+00:15:27,460 --> 00:15:32,980
+زد تلاتين بطلع تلاتةتلاتة واربعين في زي التلاتين
+
+161
+00:15:32,980 --> 00:15:37,340
+بيطلع تلاتاش بيطلع تلاتاش إذا العناصر لو صرتهم
+
+162
+00:15:37,340 --> 00:15:42,140
+تسعة هي تلاتة وعشرين وهي معطاة وكذلك في of تلاتة
+
+163
+00:15:42,140 --> 00:15:46,160
+وفي of تلاتاش هي اللي بتساومهم هي اللي بتساوي تسعة
+
+164
+00:15:46,160 --> 00:15:52,240
+يبقى دير بالك من هذه النقطة ننتقل الآن إلى النظرية
+
+165
+00:15:52,240 --> 00:15:56,480
+التالية يبقى بالداجي ل theorem
+
+166
+00:15:59,090 --> 00:16:07,770
+هذه نظرية بتتحدث عن properties of
+
+167
+00:16:07,770 --> 00:16:15,270
+subgroups under
+
+168
+00:16:15,270 --> 00:16:18,470
+homomorphism
+
+169
+00:16:27,200 --> 00:16:36,600
+تنص على مياتي لت الفاي ب homomorphism
+
+170
+00:16:36,600 --> 00:16:47,240
+from a group g to a group g bar
+
+171
+00:17:02,150 --> 00:17:10,650
+النقطة الأولى فاي اف اتش كابتل اتش اللي هي كل
+
+172
+00:17:10,650 --> 00:17:19,080
+العناصر في اف اتش بحيث الاتش موجودة في الاتشis a
+
+173
+00:17:19,080 --> 00:17:24,240
+subgroup من الـ G bar يبقى هذه ال subgroup من ال G
+
+174
+00:17:24,240 --> 00:17:34,120
+bar النقطة الثانية لو كانت ال H Cyclic F ال H is
+
+175
+00:17:34,120 --> 00:17:43,340
+Cyclic لو كانت ال H Cyclic then Phi of H صورتها is
+
+176
+00:17:43,340 --> 00:17:56,420
+Cyclicالنقطة التالتة لو كانت ال h is abelian then
+
+177
+00:17:56,420 --> 00:18:04,740
+لو five of h is abelian five of h is abelian
+
+178
+00:18:04,740 --> 00:18:14,120
+النقطة الرابعةلو كانت الـ H is a normal subgroup
+
+179
+00:18:14,120 --> 00:18:25,200
+من G then Phi of H is a normal subgroup من Phi of
+
+180
+00:18:25,200 --> 00:18:28,620
+G النقطة
+
+181
+00:18:28,620 --> 00:18:42,540
+الخامسةإذا كانت أعضاء كيرنال فيا هي نة ثم فيا ثم
+
+182
+00:18:42,540 --> 00:18:56,080
+فيا هي نة إلى واحدة نة إلى واحدة مابينج من
+
+183
+00:18:58,300 --> 00:19:10,500
+from g to phi of g النقطة
+
+184
+00:19:10,500 --> 00:19:22,480
+السادسة بيقول if ال order لل H كان يسوى N then ال
+
+185
+00:19:22,480 --> 00:19:27,420
+order لل phi of H بده يقسم
+
+186
+00:19:29,960 --> 00:19:33,980
+الـ N النقطة
+
+187
+00:19:33,980 --> 00:19:46,000
+السابعة بيقول لي if ال K bar if ال K bar is a
+
+188
+00:19:46,000 --> 00:19:55,620
+subgroup من ال G bar thenالـ Phi inverse of الـ K
+
+189
+00:19:55,620 --> 00:20:05,940
+bar اللي هو كل ال K اللي موجودة في G such that Phi
+
+190
+00:20:05,940 --> 00:20:16,410
+of K Phi of K موجودة في ال K barما لها هذه is a
+
+191
+00:20:16,410 --> 00:20:28,390
+subgroup of G يبقى هذه is a subgroup of G النقطة
+
+192
+00:20:28,390 --> 00:20:35,370
+الثامنة بقول لو كان ال K bar is a normal subgroup
+
+193
+00:20:35,370 --> 00:20:43,010
+if ال K bar is a normal subgroup من ال G bar then
+
+194
+00:20:45,860 --> 00:20:54,920
+then الـ Phi inverse of K bar هذه
+
+195
+00:20:54,920 --> 00:21:04,360
+كل العناصر K اللي موجودة في G بحيث ان Phi of K
+
+196
+00:21:04,360 --> 00:21:07,620
+موجود في K bar
+
+197
+00:21:24,440 --> 00:21:31,720
+النقطة التاسعة والاخيرة بقول لو كانت الفاي is onto
+
+198
+00:21:31,720 --> 00:21:39,240
+f الفاي is ontoلو كانت الـphi صندوق الـ and
+
+199
+00:21:39,240 --> 00:21:42,260
+الكيرنل
+
+200
+00:21:42,260 --> 00:21:49,120
+للـphi بده يساوي الـ identity element تبع الـG
+
+201
+00:22:03,460 --> 00:22:14,140
+من اين الى اين من جيه لجيه بار من جيه
+
+202
+00:22:14,140 --> 00:22:16,980
+لجيه بار
+
+203
+00:22:41,150 --> 00:22:48,850
+Nigel will prove the
+
+204
+00:22:48,850 --> 00:23:02,990
+parts الواحد واتنين and تلاتة are identical
+
+205
+00:23:02,990 --> 00:23:05,510
+to
+
+206
+00:23:07,260 --> 00:23:17,740
+are identical to the probes of أربعة
+
+207
+00:23:17,740 --> 00:23:27,640
+واتنين and واحد of
+
+208
+00:23:27,640 --> 00:23:40,060
+theorem of theoremستة تلاتة بصفحات
+
+209
+00:23:40,060 --> 00:23:44,540
+مية وسبعة وعشرين respectively
+
+210
+00:24:12,850 --> 00:24:16,630
+نرجع تاني للنظرية اللى احنا كاتبينها حاول نقرأها
+
+211
+00:24:16,630 --> 00:24:21,250
+كمان مرة نتفهم كل ما فيها بعد هيك بنروح الى
+
+212
+00:24:21,250 --> 00:24:26,610
+البرهان المرة اللى فاتت النظرية اللى فاتت كانت
+
+213
+00:24:26,610 --> 00:24:29,610
+بيشتغل على ال elements homomorphism على ال
+
+214
+00:24:29,610 --> 00:24:34,010
+elements هنا ال subgroups under ال homomorphism
+
+215
+00:24:34,010 --> 00:24:36,970
+يجيب جال ال homomorphism يشتغل عالميا على ال
+
+216
+00:24:36,970 --> 00:24:41,500
+subgroups وليس على ال elementsمقول لو كانت فاي من
+
+217
+00:24:41,500 --> 00:24:46,180
+جي إلى جي بار هي hemomorphism وكانت ال H subgroup
+
+218
+00:24:46,180 --> 00:24:52,620
+من جي then فاي of H، H هذه sub set من مين او
+
+219
+00:24:52,620 --> 00:24:56,260
+subgroup من جي إذا صورتهاأذا كنت أريد أن تكون
+
+220
+00:24:56,260 --> 00:25:02,380
+موجودة في جي بار في جي بار في جي بار في جي بار في
+
+221
+00:25:02,380 --> 00:25:06,980
+جي بار في جي بار في جي بار في جي بار في جي بار في
+
+222
+00:25:06,980 --> 00:25:13,870
+جي بارمن الجيل المقابل يبقى ال subgroup صورتها
+
+223
+00:25:13,870 --> 00:25:18,130
+subgroup أخرى تحت تأثير ال homomorphism الناحية
+
+224
+00:25:18,130 --> 00:25:22,650
+التانية لو كانت هذه ال subgroup cyclic يبقى صورتها
+
+225
+00:25:22,650 --> 00:25:27,570
+كمان cyclic يعني ليست فقط subgroup و كذلك cycle
+
+226
+00:25:27,570 --> 00:25:32,530
+group طب لو كانت ال H abelian يبقى صورتها كذلك ما
+
+227
+00:25:32,530 --> 00:25:37,520
+لها abelian groupهذول واحد واتنين وتلاتة برهنهم
+
+228
+00:25:37,520 --> 00:25:43,680
+قبل هيك في النظرية اللي في صفحة 127 نظرية 6 3 لذلك
+
+229
+00:25:43,680 --> 00:25:48,000
+النقطة الأولى مكافئة هي نفس النقطة 4 في النظرية
+
+230
+00:25:48,000 --> 00:25:53,670
+النقطة 2 هي 2 النقطة 3 هي نقطة 1لو رجعنا لهذه
+
+231
+00:25:53,670 --> 00:25:57,530
+النظرية في صحفة 127 من الكتاب نجد التلاتة اللي
+
+232
+00:25:57,530 --> 00:26:01,410
+عندنا هذا نجي للربع الرابع بيقول لو كانت ال H
+
+233
+00:26:01,410 --> 00:26:06,990
+normal subgroup يجي صورتها normal في صورة ال G
+
+234
+00:26:06,990 --> 00:26:12,810
+كلها لأن ال Phi of G ليس بالضرورة ان تغطيلي كل
+
+235
+00:26:12,810 --> 00:26:17,730
+عناصر G برشوية منهم و ممكن تغطيهم كلهم سيان سواء
+
+236
+00:26:17,730 --> 00:26:21,840
+كان لكن احنا in general بيقول لأطيب يبقى لو كانت
+
+237
+00:26:21,840 --> 00:26:27,620
+هذه normal صورتها normal في صورة G طب لو كان ال
+
+238
+00:26:27,620 --> 00:26:33,200
+kernel في N من العناصر ال order له يساوي N يبقى ال
+
+239
+00:26:33,200 --> 00:26:35,300
+N هدول بدهم يروحوا لوين؟
+
+240
+00:26:37,710 --> 00:26:42,050
+لوين؟ للـ identity، ممتاز جدا يبقى أثار ال
+
+241
+00:26:42,050 --> 00:26:47,010
+homomorphism N to 1 التلاتة أو الأربعة أو العشرة
+
+242
+00:26:47,010 --> 00:26:50,490
+راحوا العنصر واحد يبقى بقول عشرة to one مش one to
+
+243
+00:26:50,490 --> 00:26:54,950
+one بقول الأربعة to one أو الخمسة to one أو الستة
+
+244
+00:26:54,950 --> 00:26:59,950
+جدما يكون ال order one to one mapping من ال G on
+
+245
+00:26:59,950 --> 00:27:04,840
+twoانتوا هادى، دي البالك مش هنقول انتوا انه وخلاص
+
+246
+00:27:04,840 --> 00:27:09,280
+وننسى لابد تغطي جميع أناصر five of G وهذا اللي
+
+247
+00:27:09,280 --> 00:27:12,540
+مطلوب مش روح نبره ان هدى وننسى هدى، لأ لأ لأ هدول
+
+248
+00:27:12,540 --> 00:27:18,020
+نقطتين وليست نقطة واحدة السادسة لو كان ال order ل
+
+249
+00:27:18,020 --> 00:27:23,620
+in بده يساوي ال H يبقى ال order للصورة بده يقسم ال
+
+250
+00:27:23,620 --> 00:27:28,640
+order تبع من؟ تبع ال H أظن حلينا مثال شبيه بو قبل
+
+251
+00:27:28,640 --> 00:27:36,540
+شويةالان لو كانت كيابار subgroup من جيبار يبقى
+
+252
+00:27:36,540 --> 00:27:40,780
+صورتها subgroup و لو كانت هذه ال subgroup normal
+
+253
+00:27:40,780 --> 00:27:46,400
+يبقى صورتها normal اتنين هذول بنقدر ندمجهم ب band
+
+254
+00:27:46,400 --> 00:27:47,060
+واحد
+
+255
+00:28:06,500 --> 00:28:12,150
+النقطة الأخيرة لو كانت Phi is ontoوالـ Kernel
+
+256
+00:28:12,150 --> 00:28:15,930
+مافيش فيه إلا الـ Identity Element يبقى الـ Phi
+
+257
+00:28:15,930 --> 00:28:20,970
+عبارة عن إيش؟ Isomorphism طب هيا أعطاني Phi أنتوا
+
+258
+00:28:20,970 --> 00:28:25,710
+و أعطاني هنا Phi همومورفزم بقى عليه باسمين يعني لو
+
+259
+00:28:25,710 --> 00:28:29,470
+أثبتت أن Phi one to one بيكون خلصنا من الموضوع
+
+260
+00:28:29,470 --> 00:28:33,910
+بيكون خلاص انتهينا منه يبقى بس مطلوب أثبت أن Phi
+
+261
+00:28:33,910 --> 00:28:38,240
+one to one طيب نيجي للبرهاميبقى أول ثلاث نقاط
+
+262
+00:28:38,240 --> 00:28:42,260
+تفاجئنا عليهم نجي للرابعة الربعة H Normal بدي أثبت
+
+263
+00:28:42,260 --> 00:28:46,760
+ان الـ Phi of H هذي ايه اللي همالها normal
+
+264
+00:28:46,760 --> 00:28:51,700
+subgroup من main من الـ Phi of G لذلك بدي أروح
+
+265
+00:28:51,700 --> 00:28:57,080
+أخدلي element في H و أخد element من G و أشوف لوين
+
+266
+00:28:57,080 --> 00:29:03,160
+بده اتوصل هالدنيا هذه يبقى باجي بقوله هنا لو أخدنا
+
+267
+00:29:03,160 --> 00:29:15,050
+الـ G موجود في Gواخدنا ال H موجود في H then ايه
+
+268
+00:29:15,050 --> 00:29:18,710
+شرايك في ال GHG inverse؟
+
+269
+00:29:22,660 --> 00:29:29,260
+بينتمي لمين؟ ايوة يبقى هذا belongs to H السبب
+
+270
+00:29:29,260 --> 00:29:35,860
+because ان ال H is a normal subgroup من G طب احنا
+
+271
+00:29:35,860 --> 00:29:40,260
+لما نتكلم على فيات يبقى نبدأ ناخد الفيات هنا يبقى
+
+272
+00:29:40,260 --> 00:29:47,560
+لو روحت اخدت ال phi of GHG inverse هيكون موجود في
+
+273
+00:29:47,560 --> 00:29:55,310
+ال phi of Hطب الـ Phi homomorphism يبقى بدي افك
+
+274
+00:29:55,310 --> 00:30:04,710
+هدول يبقاش بصير انها Phi of G Phi of H Phi of G
+
+275
+00:30:04,710 --> 00:30:14,450
+inverseهذا موجود في مين؟ في الـ Phi of H طيب، ألسا
+
+276
+00:30:14,450 --> 00:30:23,910
+هذا Phi of G Phi of H Phi of G لكل Inverse موجود
+
+277
+00:30:23,910 --> 00:30:30,950
+في Phi of H تعالى نشوف تعالى نشوف هذا وين موجود يا
+
+278
+00:30:30,950 --> 00:30:37,790
+شباب؟في الـ Phi of G يبقى هذا belongs to Phi of G
+
+279
+00:30:37,790 --> 00:30:46,670
+طيب هذا Phi of H belongs to Phi of H هذا بelongs
+
+280
+00:30:46,670 --> 00:30:54,540
+to Phi of G صح؟طيب ممتاز جدا يبقى الان انا هاي
+
+281
+00:30:54,540 --> 00:30:59,000
+اللي بدفتها ال normality يبقى اخدت element من هنا
+
+282
+00:30:59,000 --> 00:31:03,220
+و element من هنا ضربت ال element من هنا في ال
+
+283
+00:31:03,220 --> 00:31:07,180
+element من هنا في معكوس هذا ال element لجته موجود
+
+284
+00:31:07,180 --> 00:31:12,760
+في Phi H يبقى ايش تفتيرك لهذا الكلام ان Phi H is
+
+285
+00:31:12,760 --> 00:31:18,830
+normalيبقى هذا بده يعطينا الـPhi of H is a normal
+
+286
+00:31:18,830 --> 00:31:24,670
+subgroup من من الـPhi of G طبعا رب واحد فيكوا قاعد
+
+287
+00:31:24,670 --> 00:31:28,910
+بيفكر هك وقال لي طب استنى شوية انت جيبت نص البرهان
+
+288
+00:31:28,910 --> 00:31:32,890
+و اين النص التاني بقوله ايش النص التاني قال لي ال
+
+289
+00:31:32,890 --> 00:31:36,070
+Phi of H is a subgroup بقوله اه ما هيوا عندك رقم
+
+290
+00:31:36,070 --> 00:31:40,110
+واحدهذا مطلوب، هيبقى باعتباره مثبت، هيبقى مثبت
+
+291
+00:31:40,110 --> 00:31:45,790
+معاك وإن لم يكن مثبتًا، لأثبتناه أولًا، ثم أثبتنا
+
+292
+00:31:45,790 --> 00:31:50,430
+مين؟ الـNormality يبقى هي الكلام صحيح، هذا النقطة
+
+293
+00:31:50,430 --> 00:31:55,370
+أربعة بدنا نروح للنقطة رقم خمسة النقطة رقم خمسة
+
+294
+00:31:55,370 --> 00:31:58,770
+بتقول لي لو كان assume
+
+295
+00:32:23,000 --> 00:32:24,960
+إذا أردت أن أردت أن أردت أن أردت أن أردت أن أردت
+
+296
+00:32:24,960 --> 00:32:25,500
+أن أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+297
+00:32:25,500 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+298
+00:32:25,840 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+299
+00:32:25,840 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+300
+00:32:25,840 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+301
+00:32:25,840 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+302
+00:32:25,840 --> 00:32:30,720
+أردت أن أردت أن أرالـ Kernel لـ Phi يجب أن يساوي،
+
+303
+00:32:30,720 --> 00:32:34,320
+يجب أن أضع فيه N من العناصر، أظن أن الـ Identity
+
+304
+00:32:34,320 --> 00:32:41,520
+تبع الـ G منهم يبقى G منهم، ويجب أن أقول G1 وG2
+
+305
+00:32:41,520 --> 00:32:43,280
+ويبقى مازالة مازالة مازالة مازالة مازالة مازالة
+
+306
+00:32:43,280 --> 00:32:43,920
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+307
+00:32:43,920 --> 00:32:48,960
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+308
+00:32:48,960 --> 00:32:49,280
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+309
+00:32:49,280 --> 00:32:49,320
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+310
+00:32:49,320 --> 00:32:53,270
+مازالة مازالة مازالة مازاليبقى let الكلام then هذا
+
+311
+00:32:53,270 --> 00:32:59,450
+ايش معناه؟ معناه ان الـPhi of الـidentity element
+
+312
+00:32:59,450 --> 00:33:03,510
+تبع الـG بده يساوي الـidentity element تبع الـG
+
+313
+00:33:03,510 --> 00:33:09,430
+bar والـPhi of G1 بده يساوي الـidentity element
+
+314
+00:33:09,430 --> 00:33:15,110
+تبع الـG bar والـPhi of G2 بده يساوي الـidentity
+
+315
+00:33:15,110 --> 00:33:20,820
+element تبع الـG barوالـ Phi of G N minus الـ one
+
+316
+00:33:20,820 --> 00:33:26,600
+بده يساوي الـ identity تبع الـ G bar يبقى أنا صار
+
+317
+00:33:26,600 --> 00:33:30,980
+عندي N من العناصر لهم صورة واحدة يبقى الـ Phi is
+
+318
+00:33:30,980 --> 00:33:41,960
+into one يبقى هذا this means that ان الـ Phi is
+
+319
+00:33:41,960 --> 00:33:45,440
+into one
+
+320
+00:33:52,040 --> 00:34:02,440
+يبقى هايات مثلا من جي لجي من from جي to جي بار ولم
+
+321
+00:34:02,440 --> 00:34:09,970
+اقول unto جي باريبقى دلت قصة الـ onto هذه بدها
+
+322
+00:34:09,970 --> 00:34:15,270
+إثبات يبقى بدأ أروح أخد element في five of G و
+
+323
+00:34:15,270 --> 00:34:24,870
+أثبت أنه له أصل وين في G طيب كويس أه مش بدنا نثبت
+
+324
+00:34:24,870 --> 00:34:30,760
+أنها ontoلأ جي بار لأ في of جي هي من عناصر جي بار
+
+325
+00:34:30,760 --> 00:34:35,380
+جزء منها لكن هل تسويها او لا تسويها قد يكون و قد
+
+326
+00:34:35,380 --> 00:34:41,120
+لا يكون يعني يا شباب لو اتخيلنا ان هذه كلها هي جي
+
+327
+00:34:41,120 --> 00:34:49,500
+بار وانا عندي في من الجي من الجي الى الجي بار يمكن
+
+328
+00:34:49,500 --> 00:34:57,460
+هدولهذا كله يطلع هو في of جي لكن هذا هنا مافيش ولا
+
+329
+00:34:57,460 --> 00:35:04,100
+عنصر تمام يبقى جزء بقول لذلك انا مركز على في of جي
+
+330
+00:35:04,100 --> 00:35:10,160
+on to في of جي يعني كل element في هذه ال set بدي
+
+331
+00:35:10,160 --> 00:35:15,580
+اثبت انه له اصل وين في جي كويس لذلك مضاجي اقوله
+
+332
+00:35:15,580 --> 00:35:25,360
+خدلي yالان بدي اثبتله ان فاي is onto يبقى بداجة
+
+333
+00:35:25,360 --> 00:35:34,880
+اقوله let مثلا y belongs to فاي of g فاي of كابتل
+
+334
+00:35:34,880 --> 00:35:44,120
+جي تمام؟ then ال y هذه بدها تسوي فاي of g for some
+
+335
+00:35:44,120 --> 00:35:52,310
+g اللي موجودة في جيمصبوط هيك يبقى انا اخدت element
+
+336
+00:35:52,310 --> 00:35:56,610
+في الصورة و روحت اخدت element من هنا يبقى ال five
+
+337
+00:35:56,610 --> 00:36:02,890
+ده سواء five of g for some ايوة طيب انا بدي ايش ال
+
+338
+00:36:02,890 --> 00:36:07,490
+element اللي اخدته في ال five of g بدي اثبت انه له
+
+339
+00:36:07,490 --> 00:36:13,810
+اصل في g او له اصولممكن يكون أصول مش أصل ممكن يكون
+
+340
+00:36:13,810 --> 00:36:20,230
+كتار انتوا أثبتنا ان انتوا يبقى أصول وليس أصل تمام
+
+341
+00:36:20,230 --> 00:36:29,110
+يبقى الفي انفرس يبقى بناء على لو أخدت الفي انفرس
+
+342
+00:36:29,110 --> 00:36:35,230
+of Y يبقى الفي انفرس of Y عشان بده يساويG في الـ
+
+343
+00:36:35,230 --> 00:36:40,450
+Kernel ها دي ربالك يبقى هذا بده يساوي الـ Phi
+
+344
+00:36:40,450 --> 00:36:46,970
+inverse of Y بده يساوي الـ G في ال Kernel لمين؟ في
+
+345
+00:36:46,970 --> 00:36:52,490
+ال Kernel للـ Phi معناه هذا الكلام أنه طبعا Phi
+
+346
+00:36:52,490 --> 00:36:57,850
+inverse of Y مش عنصر واحد لو بدي أشتغل حرفي لو
+
+347
+00:36:57,850 --> 00:37:02,830
+بقول عنصر واحدلكن هذه عناصر وبالتالي كثير من
+
+348
+00:37:02,830 --> 00:37:08,390
+العناصر اللي هو الـ Y هذه قد يكون هو صورتها فبجي
+
+349
+00:37:08,390 --> 00:37:15,650
+بقوله يبقى ال order للـ Phi inverse of Y بده يساوي
+
+350
+00:37:15,650 --> 00:37:22,990
+ال order للـ G في ال kernel للـ Phi. مظبوط ولا لا؟
+
+351
+00:37:22,990 --> 00:37:29,150
+طب ايش العلاقة؟ الآن هذا ليس left cosetجي في
+
+352
+00:37:29,150 --> 00:37:33,350
+الكيرن الفاي مش left coset صح ولا لا؟ طب إذا ال
+
+353
+00:37:33,350 --> 00:37:37,990
+order إيه اللي هيسوي ال order ل ال subgroup نفسه
+
+354
+00:37:37,990 --> 00:37:43,090
+يبقى هذا الكلام بدي يسوي ال order للكيرن الفاي
+
+355
+00:37:43,090 --> 00:37:49,190
+اللي هو جداش ال N يعني معنى هذا الكلام إن ال Y
+
+356
+00:37:49,190 --> 00:37:55,770
+اللي عندي أخدت هذه لجتلها أصول عددهم N تمام يبقى
+
+357
+00:37:55,770 --> 00:38:04,900
+on twoيبقى this means that .. يبقى this means that
+
+358
+00:38:04,900 --> 00:38:08,240
+ان
+
+359
+00:38:08,240 --> 00:38:16,600
+الفاي maps in elements from
+
+360
+00:38:18,360 --> 00:38:26,080
+جي تو واي اللي موجود وين في جي بار او موجود في في
+
+361
+00:38:26,080 --> 00:38:37,560
+of جي بالتحديد موجود في في of جي so في is ontoطيب،
+
+362
+00:38:37,560 --> 00:38:43,320
+هذه النقطة أيه؟ النقطة الخامسة اللي خاطر مدام حلنا
+
+363
+00:38:43,320 --> 00:38:48,680
+زيها يبقى النقطة السادسة هذه أقولكوا exercise طبعا
+
+364
+00:38:48,680 --> 00:38:52,780
+مبرهنة في الكتاب، بس بعمل restriction على الـfi
+
+365
+00:38:52,780 --> 00:38:56,700
+يعني بيخليهاش على أطلقها، بس على عناصر إيش، يبقى
+
+366
+00:38:56,700 --> 00:39:02,300
+يا ريت من الكتاب تروح تجرها وترتب أمورهاالان كي
+
+367
+00:39:02,300 --> 00:39:07,660
+بار سابق روب من جي بار يبقى في انفرست اوف كي بده
+
+368
+00:39:07,660 --> 00:39:12,780
+اثبتها السابق روب من مين؟ من الجي طيب مشان اثبتها
+
+369
+00:39:12,780 --> 00:39:18,600
+السابق روب بده اثبته conditionsيبقى بدي أروح لمين؟
+
+370
+00:39:18,600 --> 00:39:24,620
+للنقطة السابعة مشان أروح للنقطة السابعة بدي أثبت
+
+371
+00:39:24,620 --> 00:39:31,160
+هذه Phi inverse subgroup من مين؟ من الـG هذا اللي
+
+372
+00:39:31,160 --> 00:39:35,460
+عايزيني أثبته مشان هيك بدي أثبتله أن هذه non-empty
+
+373
+00:39:35,460 --> 00:39:39,000
+و لو أخدت عنصرين منها بدي أثبت أن الأول في معكوسي
+
+374
+00:39:39,000 --> 00:39:43,020
+الثاني موجود فيها وبالتالي بيصير a subgroup
+
+375
+00:39:45,060 --> 00:39:52,840
+يبقى بضاجي أقول له assume أفترض أن الـK bar هي
+
+376
+00:39:52,840 --> 00:40:01,600
+عبارة عن subgroup من الـG bar يبقى
+
+377
+00:40:01,600 --> 00:40:10,020
+هذه subgroup من الـG bar then الـPhi inverse of K
+
+378
+00:40:10,020 --> 00:40:14,180
+bar is non-empty
+
+379
+00:40:20,320 --> 00:40:25,200
+الـ Phi of الـ Identity تبع الـ G بده يعطيني مين
+
+380
+00:40:25,200 --> 00:40:33,300
+الـ Identity تبع من؟ تبع الـ G bar يعني إيش؟ هذا
+
+381
+00:40:33,300 --> 00:40:43,430
+بده يعطيلكإن الـ Phi Inverse of الـ Identity تبع
+
+382
+00:40:43,430 --> 00:40:48,190
+الـ G Bar بدي سوى الـ Identity Element تبع الـ G
+
+383
+00:40:48,190 --> 00:40:55,030
+مظبوط؟ يبقى معنا هذا الكلام إن الـ Identity تبع
+
+384
+00:40:55,030 --> 00:41:02,830
+الـ G موجود في الـ Phi Inverse of الـ K Bar بعد
+
+385
+00:41:02,830 --> 00:41:10,120
+هيك بتروح أخد two elementsالـ X و الـ Y موجودة في
+
+386
+00:41:10,120 --> 00:41:18,780
+الـ Phi inverse of الـ K bar معنى هذا الكلام ان
+
+387
+00:41:18,780 --> 00:41:28,520
+الـ X بده يساوي Phi inverse of K1 مثلا و الـ Y بده
+
+388
+00:41:28,520 --> 00:41:32,800
+يساوي Phi inverse of K2
+
+389
+00:41:36,280 --> 00:41:42,310
+كويسيبقى بدي أروح أخد الـ X Y inverse أشوف هل
+
+390
+00:41:42,310 --> 00:41:45,930
+موجودة هنا ولا لأ إذا طلعت موجودة بيكون كفى الله
+
+391
+00:41:45,930 --> 00:41:53,370
+المؤمنين يبقى بدي أروح أخد له الـ X Y inverse يبقى
+
+392
+00:41:53,370 --> 00:41:59,190
+او الـ Phi خلّي
+
+393
+00:41:59,190 --> 00:42:03,610
+أشوف الـ X Y inverse يبقى الـ X اللي عبارة عن Phi
+
+394
+00:42:03,610 --> 00:42:12,100
+inverse of الكوانفي الـ Phi inverse of K2 لكل
+
+395
+00:42:12,100 --> 00:42:25,400
+inverse يبقى هذا الكلام بده يساوي هذا
+
+396
+00:42:25,400 --> 00:42:31,900
+الكلام بده يساوي Phi inverse of K1 في Phi inverse
+
+397
+00:42:31,900 --> 00:42:40,870
+of K2 inverseهذا الكلام بده يساوي في انفرس of K1
+
+398
+00:42:40,870 --> 00:42:49,640
+K2 انفرسهذا كله مين؟ اللي هو الـ X Y inverse هل
+
+399
+00:42:49,640 --> 00:43:00,080
+هذا الان موجود في الـ Phi inverse of K bar؟ ليش؟
+
+400
+00:43:00,080 --> 00:43:04,740
+لأن هدول حاصل ضربهم موجود في K bar لأن أول ما جينا
+
+401
+00:43:04,740 --> 00:43:09,220
+كنا K bar ما لها subgroup من G بقى closed under
+
+402
+00:43:09,220 --> 00:43:13,480
+multiplicationيبقى هذا موجود في الـPhi inverse of
+
+403
+00:43:13,480 --> 00:43:22,060
+K bar يبقى بناء عليه الـPhi inverse of K bar is a
+
+404
+00:43:22,060 --> 00:43:27,160
+subgroup من جيه؟ من جيه وانتهينا منها بدنا نروح
+
+405
+00:43:27,160 --> 00:43:36,840
+للنقطة اللي بعدها وهي خاصية ال normality ايوة عرف
+
+406
+00:43:36,840 --> 00:43:42,730
+لو ماكنتش homomorphismأمرها ما بيصير كلامها ده
+
+407
+00:43:42,730 --> 00:43:51,470
+صحيح وحسب
+
+408
+00:43:51,470 --> 00:43:55,670
+التعريف اللي عندك حسب التعريف يعني أعرفنا الـPhi
+
+409
+00:43:55,670 --> 00:44:00,210
+Inverse وين أعرفناه و الله مسحنا .. مسحنا .. لا
+
+410
+00:44:00,210 --> 00:44:04,230
+أيوة أيوة كل الـK اللي موجودة في جبهات الـPhi of K
+
+411
+00:44:04,230 --> 00:44:07,670
+موجودة وين؟ في الـK bar أيوة
+
+412
+00:44:14,620 --> 00:44:30,300
+تاني تاني سؤالك سطر التاني هنا لفوق اه اه
+
+413
+00:44:30,300 --> 00:44:37,200
+هذا يا ابني انا بقول يساوي ال identity تبع ال جي
+
+414
+00:44:37,200 --> 00:44:42,220
+بار اثر على الطرفين بالفاي انفرستلا مانعثرنا بفعل
+
+415
+00:44:42,220 --> 00:44:46,900
+مش هتاطنين ال identity يعنياللي هو .. هذا لو كنت
+
+416
+00:44:46,900 --> 00:44:51,000
+أريد مورفزم، عنصر واحد. أنا بهمني العنصر، بدي أجيب
+
+417
+00:44:51,000 --> 00:44:55,000
+عنصر، بديش أجيب كتير، بكفيني منك عنصر، هذا همش أن
+
+418
+00:44:55,000 --> 00:45:02,260
+أثبت أنها non-empty، تمام؟ طيب، أنا إلي وجهة نظر
+
+419
+00:45:02,260 --> 00:45:07,980
+أخرى، إلي وجهة نظر أخرى في هذا الكلام، يعني لو
+
+420
+00:45:07,980 --> 00:45:12,820
+بدنا نشك في هذا هل هو homomorphism ولا لا، بنقدر
+
+421
+00:45:12,820 --> 00:45:18,450
+نقول الخطوة هذه استني شوية،الحين لو جيت هنا فاي of
+
+422
+00:45:18,450 --> 00:45:26,950
+ال X Y inverse أليست هي فاي لفاي inverse of K1 K2
+
+423
+00:45:26,950 --> 00:45:35,530
+inverse صح ولا لا أثر هنا بفاي و أثر هنا بفاييبقى
+
+424
+00:45:35,530 --> 00:45:40,250
+النتيجة
+
+425
+00:45:40,250 --> 00:45:47,640
+K1 K2 Inverse اللي موجودة في الـK barصح ولا لا
+
+426
+00:45:47,640 --> 00:45:55,440
+يبقى صار عندك اللي هو ال X Y inverse موجودة ال X Y
+
+427
+00:45:55,440 --> 00:46:05,560
+inverse بدها تساوي اللي بدها تساوي او هذه مو ..
+
+428
+00:46:05,560 --> 00:46:11,190
+استنى شويةبدي ألغي هذه ألغيتها بمين أثرت عليها فهي
+
+429
+00:46:11,190 --> 00:46:16,070
+أصبح X Y inverse بدي أجيبها هنا يبقى بدها تساوي
+
+430
+00:46:16,070 --> 00:46:24,030
+الـ Phi of الـ K واحد K اتنين inverse اللي هي هذه
+
+431
+00:46:24,030 --> 00:46:32,490
+موجودة في المين في ال Phi of Phi of K وPhi of K
+
+432
+00:46:32,490 --> 00:46:43,590
+Phi of Kلأ احنا احنا خليك معايا احنا خليك .. هاي
+
+433
+00:46:43,590 --> 00:46:49,270
+اللي وصلنا X Y inverse بده يساوي في انفرست ل K1 K2
+
+434
+00:46:49,270 --> 00:46:53,830
+بده اثر هنا بفي و اثر هنا بفي هاي اثرنا بفي و
+
+435
+00:46:53,830 --> 00:46:59,390
+اثرنا هنا بفي هذه هتلغي التانية بصير اللي هو X Y
+
+436
+00:46:59,390 --> 00:47:06,100
+inverse بده يساوي في of K1 K2 inverse تمام؟يبقى
+
+437
+00:47:06,100 --> 00:47:20,100
+هذه موجودة في Phi of K و Phi of K لحظة
+
+438
+00:47:20,100 --> 00:47:25,880
+شوية عندك اعتراض على هذه العبارة؟الخطوة اللى بعدها
+
+439
+00:47:25,880 --> 00:47:31,680
+تمام انا جيت اثره بفاي على XY inverse طب هدى تساوي
+
+440
+00:47:31,680 --> 00:47:35,460
+هدى مشينا لغاية هنا لو قلنا مش عارفين هى
+
+441
+00:47:35,460 --> 00:47:40,240
+homomorphism ولا لأ يبقى كان صار كل الشغل هدى مش
+
+442
+00:47:40,240 --> 00:47:45,350
+صحيحإذا هي homomorphism غصب على ما يرضى وإلا كان
+
+443
+00:47:45,350 --> 00:47:48,530
+هذا الكلام .. لقد قلت ال inverse صح لكن مصير هذا
+
+444
+00:47:48,530 --> 00:47:52,910
+الكلام صحيح ليس صحيحا إلا إذا كانت homomorphism
+
+445
+00:47:52,910 --> 00:48:00,130
+تمام؟ على .. ايوة ال homomorphism مش ضروري يكون
+
+446
+00:48:00,130 --> 00:48:04,010
+مدبن صحيح لما تجيب في انفص بطل افتران أصلا مصير
+
+447
+00:48:04,010 --> 00:48:08,490
+الواحد اللي عند الصور مظبوطمش متبطل اختراع اصلا مش
+
+448
+00:48:08,490 --> 00:48:12,350
+متبطل homomorphism متبطل اختراع معرف اصلا تصير
+
+449
+00:48:12,350 --> 00:48:15,470
+الصورة العنصر اللي هو اكتر من الصورة فكيف انت
+
+450
+00:48:15,470 --> 00:48:18,130
+بتاخد اللي هو اكتر من الصورة العنصر اللي هو اكتر
+
+451
+00:48:18,130 --> 00:48:21,210
+من الصورة احنا بنحكي homomorphism وليس function
+
+452
+00:48:21,210 --> 00:48:27,050
+اذا قلنا function ماهو isomorphism function يعني
+
+453
+00:48:27,050 --> 00:48:30,230
+مية المية بس ال homomorphism قد يكون و قد لا يكون
+
+454
+00:48:31,440 --> 00:48:36,400
+أه قد يكون و قد لا يكون تمام طيب احنا هذه النقطة
+
+455
+00:48:36,400 --> 00:48:42,740
+رقم قداش هي سبعة النقطة هذه رقم سبعة رقم سبعة
+
+456
+00:48:42,740 --> 00:48:50,600
+ماشيين كله صح وهذه تمام واخدنا x y inverse و أثرنا
+
+457
+00:48:50,600 --> 00:48:55,180
+عليها بفاية و طلع ك واحد كتنين اللي موجودة في ك
+
+458
+00:48:55,180 --> 00:49:01,270
+مظبوط يبقى من هذا الكلامبنقدر نقول X Y inverse
+
+459
+00:49:01,270 --> 00:49:08,490
+موجودة في الـ Phi في ال Phi of K صحيح يبقى بنقول
+
+460
+00:49:08,490 --> 00:49:16,550
+هنا النقطة الأخيرة ان ال X Y inverse هذه موجودة في
+
+461
+00:49:16,550 --> 00:49:25,650
+ال Phi inverse في ال Phi inverse في ال Phi inverse
+
+462
+00:49:25,650 --> 00:49:31,360
+of K باراللي فوق بالظبط تماما خلاص يبقى ليش يعيدها
+
+463
+00:49:31,360 --> 00:49:36,220
+هذي كلها مالاش نزول هي ال X Y انفرست موجودة في
+
+464
+00:49:36,220 --> 00:49:40,840
+الفاي انفرست هذا كله زيادة صوتناهذه الخطوة زيادة
+
+465
+00:49:40,840 --> 00:49:45,660
+تمام يبقى موجودة في الـ Phi inverse of K bar يبقى
+
+466
+00:49:45,660 --> 00:49:50,920
+بناء اللي عليه Phi inverse of K bar is a subgroup
+
+467
+00:49:50,920 --> 00:49:59,100
+يبقى هنا Phi inverse of K bar is a subgroup من
+
+468
+00:49:59,100 --> 00:50:05,840
+مين؟ من ال G بدنا نيجي للنقطة الثامنة خلي بالك
+
+469
+00:50:05,840 --> 00:50:10,900
+معاياالنقطة الثامنة اللى جبناها هذه الـ subgroup
+
+470
+00:50:10,900 --> 00:50:16,160
+من G بنا نثبت انها normal بس بشرط ان ال K bar
+
+471
+00:50:16,160 --> 00:50:23,320
+normal من G يبقى باجي بقوله assume افترض ان ال K
+
+472
+00:50:23,320 --> 00:50:30,840
+bar is a normal subgroup من G barبالدالي اثبت ان
+
+473
+00:50:30,840 --> 00:50:38,520
+الفاي
+
+474
+00:50:38,520 --> 00:50:49,580
+انفرس of K bar is a normal subgroup من من من ال G
+
+475
+00:50:50,950 --> 00:51:00,270
+كويس لذلك بدروع اخد let الجي موجودة في جي and ال X
+
+476
+00:51:00,270 --> 00:51:11,210
+موجود في الفاي انفرس of الكبار then الجي موجودة في
+
+477
+00:51:11,210 --> 00:51:20,950
+الجيوالـ X هذه بدها تساوي في انفرس في انفرس of K
+
+478
+00:51:20,950 --> 00:51:29,760
+على سبيل المثاليبقى هذا معناه ان جي موجود في جي
+
+479
+00:51:29,760 --> 00:51:37,360
+and فاي of اكس فاي of اكس بده يساوي كم؟ بده يساوي
+
+480
+00:51:37,360 --> 00:51:44,700
+كم طب لو أخدت الجي اكس جي انفرس مشان اثبات ال
+
+481
+00:51:44,700 --> 00:51:51,000
+normalityواخد تأثير الـ Phi عليها يبقى هذا الكلام
+
+482
+00:51:51,000 --> 00:51:59,700
+بدل يساوي Phi of G Phi of X Phi of G inverse يبقى
+
+483
+00:51:59,700 --> 00:52:06,420
+هذا الكلام بدل يساوي Phi of G Phi of X اللي هي
+
+484
+00:52:06,420 --> 00:52:12,400
+main اللي هي اب K Phi of X اللي هي و ال K normal
+
+485
+00:52:12,400 --> 00:52:21,200
+اللي هو Kوالـ Phi هذه of G لكل inverse بالشكل اللي
+
+486
+00:52:21,200 --> 00:52:28,620
+عندنا هنا تمام؟ الحين هذه موجودة في Gوهذه موجودة
+
+487
+00:52:28,620 --> 00:52:36,240
+في الـPhi inverse of K وهذه موجودة في G أخدنا
+
+488
+00:52:36,240 --> 00:52:41,720
+تأثير الـPhi عليهم وطلع عندنا هذا الـElement وهذا
+
+489
+00:52:41,720 --> 00:52:49,100
+وهذا الـK bar أنا جال عليها normal يبقى لو أخدت
+
+490
+00:52:49,100 --> 00:52:56,580
+element من G bar هذا موجود في G barوهذا موجود في
+
+491
+00:52:56,580 --> 00:53:04,000
+جي بار وهذا موجود في الفاي انفرس هذا موجود في
+
+492
+00:53:04,000 --> 00:53:10,460
+الفاي انفرس of K إذا هذا كله موجود في الفاي انفرس
+
+493
+00:53:10,460 --> 00:53:17,680
+of K بار بالشكل اللي عندنا K بار يبقى بناء عليه
+
+494
+00:53:17,680 --> 00:53:21,500
+الفاي
+
+495
+00:53:21,890 --> 00:53:30,270
+إنفرست من K بار هو عضو عام من جيه
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d9771ad247c60af74841c47aaeecefe234d5d85c
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/bNy_YGVobck_postprocess.srt
@@ -0,0 +1,1492 @@
+1
+00:00:20,970 --> 00:00:25,690
+بسم الله الرحمن الرحيم مواصل ما ابتدأنا به في ال
+
+2
+00:00:25,690 --> 00:00:29,650
+chapter الأول وهو ال chapter المقدمة التاسيس
+
+3
+00:00:29,650 --> 00:00:35,190
+لموضوع ال groups وصلنا إلى النقطة الأخيرة من هذا
+
+4
+00:00:35,190 --> 00:00:39,170
+ال chapter وهي موضوع ال functions أو ال mapping
+
+5
+00:00:39,170 --> 00:00:45,310
+يعني الدوال أو الاقتراناتطبعا الدالة أخدنا تعريف
+
+6
+00:00:45,310 --> 00:00:50,230
+في Calculus A واخدنا إيش معنى one to one function
+
+7
+00:00:50,230 --> 00:00:54,970
+و بعد ذلك على مبادئ الرياضيات رجعنا أخدنا تعريف ال
+
+8
+00:00:54,970 --> 00:00:58,330
+function كمان مرة وعرفنا ما هي ال one to one
+
+9
+00:00:58,330 --> 00:01:02,890
+function وما هي ال one to functionو ال composition
+
+10
+00:01:02,890 --> 00:01:07,590
+ما بين two functions اليوم نظرة لإهمية الموضوع
+
+11
+00:01:07,590 --> 00:01:14,270
+لموضوع الذي ساعدته الموضوعين سيأتياني فيما بعد و
+
+12
+00:01:14,270 --> 00:01:19,030
+خاصة موضوع ال isomorphism و ال homomorphism بدنا
+
+13
+00:01:19,030 --> 00:01:24,350
+نرجع نؤسس مرة تانيةأو انذكر ايه اللي ناسي بما سبق
+
+14
+00:01:24,350 --> 00:01:29,050
+دراسته فباجي اول شي لتعريف ال function فباجي بقول
+
+15
+00:01:29,050 --> 00:01:34,490
+في من ال set A الى ال set B is a rule that assigns
+
+16
+00:01:34,490 --> 00:01:40,290
+تعين او تخصص لكل أنصر موجود في ال set A بالضبط
+
+17
+00:01:40,290 --> 00:01:45,650
+أنصر واحد فقط لا غير بي موجود في ال set B وبروح
+
+18
+00:01:45,650 --> 00:01:49,910
+نكتب انه في of a بدها تساوي مين بدها تساوي بي
+
+19
+00:01:49,910 --> 00:01:55,380
+خليني اتوقفعشان نقف
+
+20
+00:01:55,380 --> 00:02:00,640
+على كل نقطة في هذا التعريف بيقول لي هادي في من ال
+
+21
+00:02:00,640 --> 00:02:07,280
+6a إلى ال 6b بقول عليها function لو هدي خصصة لكل
+
+22
+00:02:07,280 --> 00:02:13,860
+عنصر من ال 6a يبقى في هتأثر على جميع أنصر ال 6a
+
+23
+00:02:13,860 --> 00:02:20,700
+ولا على بعضها دون البعض الأخر على من؟ع الكل؟ والله
+
+24
+00:02:20,700 --> 00:02:26,560
+على بعضهم على الكل نجلي to each element لكل عنصر
+
+25
+00:02:26,560 --> 00:02:31,460
+في ال set A إذا ال fi ستؤثر على جميع عناصر ال set
+
+26
+00:02:31,460 --> 00:02:36,940
+A ال set A هدى هسميها domain ال function المجال
+
+27
+00:02:36,940 --> 00:02:41,100
+تبع ال 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 Bيبقى
+
+29
+00:02:47,670 --> 00:02:53,650
+عنصرا واحدا بالظبط في الست بي تمام هذا بدي اطرح
+
+30
+00:02:53,650 --> 00:02:59,130
+لنا مجموعة من المسائل السؤال الاول هل يمكن لعنصر
+
+31
+00:02:59,130 --> 00:03:05,590
+من الست ايه ان تكون له صورتان في الست بيلأ لانه
+
+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 ال set B سنجد له صورة واحدة فقط في ال set B لو
+
+34
+00:03:16,590 --> 00:03:21,610
+حصل ان العنصر لاجي ناله صورتين يبقى هذه ليست
+
+35
+00:03:21,610 --> 00:03:26,790
+function طب السؤال الثاني هل يمكن لعنصرين من ال
+
+36
+00:03:26,790 --> 00:03:34,260
+set A ان يشترك في صورة واحدة من ال set B؟صحيح لأنه
+
+37
+00:03:34,260 --> 00:03:39,420
+لم يشترط ذلك إذا يمكن لعمصرين وممكن تلاتة وممكن
+
+38
+00:03:39,420 --> 00:03:43,440
+أربعة وممكن كل عناصر ايه تطلع لهم نفس الصورة عادي
+
+39
+00:03:43,440 --> 00:03:47,780
+جدا زي ايش مثلا لو جيها تقول لك انا عندي function
+
+40
+00:03:47,780 --> 00:03:52,200
+من الست of real numbers للست of real numbers معرفة
+
+41
+00:03:52,200 --> 00:03:56,060
+كتلة f of x يساوي خمسة اللي الكونوصان function
+
+42
+00:03:56,060 --> 00:03:59,600
+يبقى جميع عناصر الست of real numbers بدها تروح
+
+43
+00:03:59,600 --> 00:04:06,260
+لمينإذا عنصر واحد ظهر كصورة لجميع عناصر الست
+
+44
+00:04:06,260 --> 00:04:09,620
+الأولى اللي هو ال 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 لهسورتان
+
+47
+00:04:21,420 --> 00:04:27,060
+ممتاز جدا طيب هل اشترط في هذا التعريف ان جميع
+
+48
+00:04:27,060 --> 00:04:33,340
+عناصر بيظهروا كصور لعناصر ايه لا لم يقول ذلك مجالش
+
+49
+00:04:33,340 --> 00:04:39,800
+ذلك ولذلك لما اقول انا عندي في من الست ايه للست
+
+50
+00:04:39,800 --> 00:04:45,400
+بيه يعني لو جيت قلت هذه الست ايه وهذه مثلا الست
+
+51
+00:04:45,400 --> 00:04:50,340
+بيه على سبيل المثالاذا لو افترضت انه ماعنديش الا
+
+52
+00:04:50,340 --> 00:04:56,960
+تلت عناصر هنا و هنا عندى مجموعة من العناصر والتكن
+
+53
+00:04:56,960 --> 00:05:01,900
+خمسة اذا التلاتة هدول ممكن تطلعلهم صورة واحدة و
+
+54
+00:05:01,900 --> 00:05:06,760
+ممكن صورتين و ممكن تلات صور اكتر من هيك ممكنما فيش
+
+55
+00:05:06,760 --> 00:05:12,000
+إمكانية إذا ممكن هذا العنصر تطلع صورته هذه و هذا
+
+56
+00:05:12,000 --> 00:05:16,320
+العنصر تطلع صورته هذه و هذا العنصر تطلع صورته هذه
+
+57
+00:05:16,320 --> 00:05:21,980
+إذا اتنين اللي في النص دول ما لهم لم يظهر كصور
+
+58
+00:05:21,980 --> 00:05:29,160
+لعناصر من ال set A إذا هذه ال set B بسميها ال code
+
+59
+00:05:29,160 --> 00:05:33,820
+domain المجال المصاحب أو المجال المناظر لمهم
+
+60
+00:05:35,850 --> 00:05:42,590
+العناصر التي أظهرت كوصور بسميها ال range المدى تبع
+
+61
+00:05:42,590 --> 00:05:47,610
+من تبع ال function فاي يبجي هذه كل أسئلة 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 ال domain
+
+64
+00:05:57,140 --> 00:06:02,020
+والـ B بسميه main ال code main لل function Phi
+
+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 ال F
+
+68
+00:06:20,620 --> 00:06:26,960
+of Aيبقى ال element بي اللي موجود في بي بسميه
+
+69
+00:06:26,960 --> 00:06:33,980
+image of a under في يعني صورة العمصر a تحت تأثير
+
+70
+00:06:33,980 --> 00:06:39,220
+ال function في في لما أثرت على العمصر a اللي عندنا
+
+71
+00:06:39,220 --> 00:06:46,640
+هذا خلت صورته منب مين هي بي هي f of a يبقى هى
+
+72
+00:06:46,640 --> 00:06:52,640
+العنصر اللى نتجه نتيجة لتأثير الفي على العنصر a
+
+73
+00:06:52,640 --> 00:06:58,320
+اللى موجود وين فى domain اذا بي هي ال image تبعت
+
+74
+00:06:58,320 --> 00:07:01,380
+ليه يعنى هى صورة العنصر a
+
+75
+00:07:05,090 --> 00:07:11,830
+الان لو جيت اخدت كل الصور تبعت عناصر ايه بطلع عند
+
+76
+00:07:11,830 --> 00:07:16,770
+من؟ بطلع عند ال range تبع الفاي يبقى انا عند
+
+77
+00:07:16,770 --> 00:07:20,110
+العناصر التالتة ال range عندهم التلت عناصر هدول
+
+78
+00:07:20,110 --> 00:07:23,770
+يبقى التلت عناصر اللي من بيها هدول بسميهم ايه؟
+
+79
+00:07:23,770 --> 00:07:29,470
+بسميهم ال range تبع من؟ تبع ال function فايهذا
+
+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 ال set A إلى ال set B و Epsilon B إلى C
+
+82
+00:07:38,030 --> 00:07:42,910
+عبارة عن functions بدى أكوّن من ال 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 ال composite functionيبقى هذول بدي اكوّم
+
+85
+00:07:53,160 --> 00:07:56,460
+منهم دلّة اسم الـ Composite Function اللي هي
+
+86
+00:07:56,460 --> 00:08:01,180
+الدلّة المحاصلة أو الدلّة التركيبية و بديها الرمز
+
+87
+00:08:01,180 --> 00:08:07,820
+Epsi Composition Phi واختصارا هقول Epsi Phi بدون
+
+88
+00:08:07,820 --> 00:08:11,710
+منطق كلمة ال composition لكن بديك تفهمان هذي
+
+89
+00:08:11,710 --> 00:08:16,610
+محاصلة الـ two function مش حاصل ضربهما حاصل ضرب
+
+90
+00:08:16,610 --> 00:08:19,530
+two function غير ال composition of two function
+
+91
+00:08:19,530 --> 00:08:22,770
+انا مش هتكلم اللي هو حاصل ضرب function كلام عتيجي
+
+92
+00:08:22,770 --> 00:08:26,590
+هذا في calculus ايه انا بهمن ال composition of two
+
+93
+00:08:26,590 --> 00:08:31,650
+functionيبقى في من a إلى b إبصي من b إلى c بدي
+
+94
+00:08:31,650 --> 00:08:36,790
+أجيب المحصلة تبعتهم اللي إبصي في هتكون من الست a
+
+95
+00:08:36,790 --> 00:08:41,810
+إلى الست c يبقى في من الست a إلى الست t is defined
+
+96
+00:08:41,810 --> 00:08:47,470
+by فيبصي في of a يساوي اللي في domain مين؟
+
+97
+00:08:49,760 --> 00:08:55,760
+فى دمين الفاي لإن هاي فاي هنا من a إلى بيبقى ال a
+
+98
+00:08:55,760 --> 00:09:01,540
+small موجود وين؟ فى ال a كفترة إذا العنصر a موجود
+
+99
+00:09:01,540 --> 00:09:07,200
+فى دمين الفاي وبالتالي الفاي هتقدر تأثر عليه بيبقى
+
+100
+00:09:07,200 --> 00:09:13,480
+هذا بيبقى يسوى إبساي لفاي of aف I of A كلها بيصير
+
+101
+00:09:13,480 --> 00:09:17,560
+عنصر في domain I بس I يبقى ال I بس I بتقدر تأثر
+
+102
+00:09:17,560 --> 00:09:20,700
+عليه كيف عنصر في domain اللي هو ال I بس I
+
+103
+00:09:26,170 --> 00:09:32,150
+العنصر اللي موجود في a صار صورت في b تمام بي هي ال
+
+104
+00:09:32,150 --> 00:09:36,610
+domain تبع مين تبع ليه بصي اذا بصي تقدر تأثر على
+
+105
+00:09:36,610 --> 00:09:41,690
+هذا العنصر يبقى بصي لفاي of a لكل ال a اللي موجود
+
+106
+00:09:41,690 --> 00:09:47,990
+في ال set A تعريف اخر بنعرف حاجة اسم ال one to one
+
+107
+00:09:47,990 --> 00:09:53,300
+functionيبقى الفي من الست A الى الست 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 نخر
+
+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 اي كتاب
+
+113
+00:10:15,460 --> 00:10:20,140
+جبر الكلمة injective function تفهم منها ايش 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 طبعاإذا كان ال a واحد لا
+
+116
+00:10:31,710 --> 00:10:35,810
+يساوي ال a اتنين يبقى then ال f of واحد لا يساوي
+
+117
+00:10:35,810 --> 00:10:41,970
+ال f of اتنين بالبلد هيك بجينا نقول في كل كلاصية
+
+118
+00:10:41,970 --> 00:10:44,470
+أول ما جيتوا على الجامعة بجينا نقول العناصر
+
+119
+00:10:44,470 --> 00:10:51,290
+المختلفةلها صور مختلفة يبقى ال a1 لا يساوي a2
+
+120
+00:10:51,290 --> 00:10:57,210
+imply الصورة ال 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
+equivalentlyيعني في تعريف أخر مكافئ لهذا التعريف
+
+123
+00:11:10,940 --> 00:11:19,300
+وهو لو كانت صورتان متساويتان فإن أصلهما متساوين
+
+124
+00:11:19,620 --> 00:11:25,380
+يعني F of F of F واحد of A واحد بده يساوي F of A
+
+125
+00:11:25,380 --> 00:11:29,640
+اتنين يبجى اذا ان ال A واحد بده يساوي مين يعني
+
+126
+00:11:29,640 --> 00:11:33,460
+بالبلد هيك زي ما اخدت في مبادئ الرياضيات ال
+
+127
+00:11:33,460 --> 00:11:37,300
+counter positive يعني انا بده امشي في الاتجاه من
+
+128
+00:11:37,300 --> 00:11:43,080
+العكس اطلعا واحد لا يساوي ا اتنين هذا بيطلب افه في
+
+129
+00:11:43,080 --> 00:11:47,220
+ا واحد لا يساوي افه في اتنين يبقى لو نفيت هذه بده
+
+130
+00:11:47,220 --> 00:11:52,260
+يعطيني مين نفي هذه هذه المكافئة نفي لهذه اللي هو
+
+131
+00:11:52,260 --> 00:11:57,760
+التساوي يبقى هايهم بيساوي بعض بده يعطيني التساوي
+
+132
+00:11:57,760 --> 00:12:02,600
+هذه تماما يعني عكس هذه بده يعطيك عكس هذه هذا اللي
+
+133
+00:12:02,600 --> 00:12:06,770
+كنا في مادة الرياضة بيسميه ال contrapositiveطيب
+
+134
+00:12:06,770 --> 00:12:14,350
+تعرف اللي هو الأخير بيقول ال function Phi من A إلى
+
+135
+00:12:14,350 --> 00:12:19,190
+B is said to be onto أنتوا بالعربي يعني ده الفوقية
+
+136
+00:12:19,190 --> 00:12:24,230
+فوقية يعني بمعنى آخر بتغطي جميع أنصر ال code
+
+137
+00:12:24,230 --> 00:12:28,870
+domain هنا في الرسم هذه مغطتش جميع أنصر مغطت بعضهم
+
+138
+00:12:28,870 --> 00:12:34,750
+إذا مشان تبقى onto لازم تمر على جميع أنصر ال B بلا
+
+139
+00:12:34,750 --> 00:12:41,640
+إستثناءهذه الانتو بعض الكتب بتكتبها surjective
+
+140
+00:12:41,640 --> 00:12:45,360
+يبقى
+
+141
+00:12:45,360 --> 00:12:50,640
+انتو او انتو كما هي يبقى ده شو تعريفة يبقى ده لفاي
+
+142
+00:12:50,640 --> 00:12:57,500
+من a الى b بسميها انتو إذا كان كل عنصر في b بدي
+
+143
+00:12:57,500 --> 00:13:03,060
+يظهر كصورة لمينالعنصر 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 Phi 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
+يشتري ك .. 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
+اتنين، تلاتة، أربعة موجودات وينموجودات في الـ set
+
+150
+00:13:28,360 --> 00:13:32,800
+A يبقى لو قال لي اثبت ان هذه ال function اللي عندي
+
+151
+00:13:32,800 --> 00:13:37,960
+هي onto function بروح بجيبله element عشوائي اي
+
+152
+00:13:37,960 --> 00:13:42,360
+element من ال code domain وبحاول اثبت انه له أصل
+
+153
+00:13:42,360 --> 00:13:46,480
+في ال domainإن حدث ذلك يبقى هذه الـ function بصير
+
+154
+00:13:46,480 --> 00:13:52,100
+مالها onto functions that is أي أنه بدي أعيد صياغة
+
+155
+00:13:52,100 --> 00:13:56,100
+التعريف بقول الـPhi 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 بدي يسوى من إيه؟
+
+158
+00:14:07,560 --> 00:14:12,050
+الـPhi of Aيبقى ال element هذا اللي أخدته من b
+
+159
+00:14:12,050 --> 00:14:17,430
+اللي جاتله أصل فيه a capital اللي هو a small بحيث
+
+160
+00:14:17,430 --> 00:14:22,630
+انه five of a بده ساوين بده ساوي ال b خلّك
+
+161
+00:14:22,630 --> 00:14:27,450
+الملاحظة دي الآن لو ال function من a لبيت كانت one
+
+162
+00:14:27,450 --> 00:14:31,570
+to one and unto يبقى حققت التعريف اللي عندها و
+
+163
+00:14:31,570 --> 00:14:35,770
+التعريف اللي فوق اتنين في آن واحد يبقاش بسميها ال
+
+164
+00:14:35,770 --> 00:14:41,890
+functionone to one correspondence طب السؤال هو ال
+
+165
+00:14:41,890 --> 00:14:47,970
+one to one بنسميها injective والانتوا سيريجيكتف ال
+
+166
+00:14:47,970 --> 00:14:53,570
+one to one correspondence بايجيكتف يبقى هادي هاي
+
+167
+00:14:53,570 --> 00:14:57,950
+ال one to one من راحة ت correspondence هادي بسميها
+
+168
+00:14:57,950 --> 00:15:00,090
+بايجيكتف
+
+169
+00:15:01,970 --> 00:15:06,050
+يبقى لو لجيت في الكتاب عند اي لحظة تمام by
+
+170
+00:15:06,050 --> 00:15:10,510
+adjective بدك تفهم انها one to one and unto 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
+unto و ال one to one cross bonders الدالة يا شباب
+
+173
+00:15:19,730 --> 00:15:24,060
+يمكن تبقى one to one لكن ما تكونش untoوممكن تكون
+
+174
+00:15:24,060 --> 00:15:30,760
+one to one وممكن تكون one to one and unto في نفس
+
+175
+00:15:30,760 --> 00:15:35,800
+الوقت كل احتمالات واردة عنها نعطي المثال الأول
+
+176
+00:15:35,800 --> 00:15:46,540
+define عرفلي ال function define ال f من ال set of
+
+177
+00:15:46,540 --> 00:15:52,180
+integers z لset of integers z by
+
+178
+00:15:54,160 --> 00:16:06,120
+ف by f of x f of x يساوي اتنين x 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 عنصرين يشتركوا في نفس الصورة مش ممكنية على
+
+181
+00:16:15,600 --> 00:16:20,620
+الإطلاق هذه one to one السؤال هو هل هي one toلأ
+
+182
+00:16:20,620 --> 00:16:25,220
+لإن كل الأعداد الفردية متظهرش ليه ال X لو كان فردي
+
+183
+00:16:25,220 --> 00:16:28,200
+و لا زوجي تضربه في اتنابه و تصبح زوجي يبقى كل
+
+184
+00:16:28,200 --> 00:16:34,060
+الأعداد الفردية مش هتظهر كصور لعناصر من اللي هو Z
+
+185
+00:16:34,060 --> 00:16:44,640
+يبقى هذه is one to one but not unto because
+
+186
+00:16:44,640 --> 00:16:57,280
+مثلا for exampleكمثال بسيط انه التلاتة does not
+
+187
+00:16:57,280 --> 00:17:05,980
+image ماهواش 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
+انزد مشان تنفي هذا كلام الشباب يا بنجيب counter
+
+190
+00:17:25,100 --> 00:17:29,060
+example يا بنبرهن احنا جيبنا counter example بسيط
+
+191
+00:17:29,060 --> 00:17:35,620
+يؤكد 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 byG of X بده يساوي احد امرين يا اما ال X if ال X
+
+196
+00:18:18,640 --> 00:18:33,040
+is odd يا اما ال X على اتنين 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؟ تلاتة و ستة تلاتة فردة، G of
+
+199
+00:18:53,970 --> 00:18:58,710
+تلاتة بده يسوى تلاتة، G of ستة زوجي، ستة على اتنين
+
+200
+00:18:58,710 --> 00:19:03,150
+بطلع تلاتة، إذا وصلت التلاتة وصلت الستة نفس الشيء،
+
+201
+00:19:03,150 --> 00:19:06,410
+يبقى الـ not one to one طب، Z on two؟
+
+202
+00:19:11,290 --> 00:19:17,070
+معقول؟ طيب تمانية على اتنين مقداش؟ اربعة على اتنين
+
+203
+00:19:17,070 --> 00:19:22,130
+يبقى ظهروا even ولا لا؟ يبقى هذي on to but not one
+
+204
+00:19:22,130 --> 00:19:32,050
+to one يبقى هذي G is on to 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 تلاتة بدها تساوي الـG of ستة
+
+207
+00:19:42,280 --> 00:19:50,500
+والتي بدها تساوي كم؟ بدها تساوي تلاتة and التلاتة
+
+208
+00:19:50,500 --> 00:19:56,080
+لا تساوي ستة هاي جيب 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 خدلي مثال تلاتةلو أخدت five من ال
+
+211
+00:20:09,880 --> 00:20:17,980
+set of real numbers define اللي هو five من ال set
+
+212
+00:20:17,980 --> 00:20:25,240
+of real number ل set of real number مثلا by five
+
+213
+00:20:25,240 --> 00:20:32,940
+of x يساوي حط أي دالة خطية بدكيها أي دالة خطية تجي
+
+214
+00:20:32,940 --> 00:20:40,180
+في بالك مثلاأتنين X زي التلاتة السؤال هو هذه one
+
+215
+00:20:40,180 --> 00:20:45,740
+to one ولا لأ انتوا ولا لأ يبقى انتوا كمان لإن
+
+216
+00:20:45,740 --> 00:20:49,260
+مايبقى ليش عندي ولا element إيش ما تكون ال X تكون
+
+217
+00:20:49,260 --> 00:21:01,580
+يبقى هذه then الفاي is one to one and انتوا طيب خد
+
+218
+00:21:01,580 --> 00:21:11,070
+مثال أربعة لو قلتلك دي فاي5 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 5 of X دي سوى E of X ال exponential
+
+222
+00:21:30,190 --> 00:21:32,390
+function تبع ال calculus بيه
+
+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 هك هذا محور X هذا محور Y هذا نقطة
+
+225
+00:21:48,630 --> 00:21:54,520
+الأصل الدالة بتيجي ماشية هكوعند الـ zero بتبقى هذه
+
+226
+00:21:54,520 --> 00:21:59,580
+النقطة اللي هي zero أو واحد احداثية النقطة هذه
+
+227
+00:21:59,580 --> 00:22:05,940
+وهذه الدالة اللي هي EOSX ال domain تبعها بياخد كل
+
+228
+00:22:05,940 --> 00:22:09,840
+ال real lineوالـ Range تبعها بياخد من و لا و اين
+
+229
+00:22:09,840 --> 00:22:14,680
+من Zero ل Infinity يبقى one to one and one to ولا
+
+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 اي horizontal line ممنوع يقطع المنحنة الا في
+
+232
+00:22:25,840 --> 00:22:30,460
+نقطتين واحدة فلو قطع في نقطتين او اكثر بالبطالسية
+
+233
+00:22:30,460 --> 00:22:37,580
+one to one اذا هذه ال function كذلك one to oneيبقى
+
+234
+00:22:37,580 --> 00:22:45,440
+then اللي هو ال five is one to one and unto كذلك
+
+235
+00:22:46,030 --> 00:22:50,730
+يبقى يعطيناك العديد من الأمثلة ممكن تبقى one to
+
+236
+00:22:50,730 --> 00:22:56,710
+one وما تبقاش on two وممكن تكون on two وما تكونش
+
+237
+00:22:56,710 --> 00:23:02,290
+one to one وممكن تكون one to one and on two وهكذا
+
+238
+00:23:02,290 --> 00:23:07,410
+وانا جابتلك دوال بسيطة ماهياش دوال معقدة لان انا
+
+239
+00:23:07,410 --> 00:23:15,980
+بدي المفهوم يثبت عندكطيب ننتقل الان الى 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 الدوار
+
+243
+00:23:41,350 --> 00:23:58,170
+بقول الف الالفة من a إلى b and بيتا من b إلى c و
+
+244
+00:23:58,170 --> 00:24:11,110
+جامع من c إلى d and جامع من c إلى d من c إلى dare
+
+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 alpha beta عفوا جامعة جامعة beta alpha
+
+247
+00:24:41,110 --> 00:24:55,730
+النقطة الثانية if alpha and beta are one to one
+
+248
+00:24:55,730 --> 00:25:06,830
+are one to one then beta alpha isone to one نمرة
+
+249
+00:25:06,830 --> 00:25:20,830
+تلاتة if alpha and beta are onto are
+
+250
+00:25:20,830 --> 00:25:36,900
+onto then beta alpha is onto نقطة الرابعةإذا كانت
+
+251
+00:25:36,900 --> 00:25:45,580
+ألفة واحدة واحدة وانتوا 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 ان ال alpha inverse alpha of a بدر ساوي a لكل
+
+255
+00:26:15,570 --> 00:26:20,090
+ال a الموجودة في ال 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 الفand on to one to one and on to and alpha
+
+262
+00:26:58,680 --> 00:27:05,960
+of a بدى يساوي ال b then ال
+
+263
+00:27:05,960 --> 00:27:09,720
+a يساوي alpha inverse of b
+
+264
+00:27:46,960 --> 00:27:50,800
+الان بدنا نجي لبعض الخواص الخاصة بال functions و
+
+265
+00:27:50,800 --> 00:27:57,320
+التي درست في مبادئ الرياضية 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 القصية هذه؟في علم الرياضيات جابر
+
+270
+00:28:18,130 --> 00:28:25,550
+الخاطي اش اسمها؟ خاصية ايش؟ واحد بدي يحكي رفع يده،
+
+271
+00:28:25,550 --> 00:28:28,710
+بدي واحد يرى يرفع يده باسم ويحكي يقولي، 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، و هذه خاصية ال
+
+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 ال 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 ال functions كما تنطبق على ضرب
+
+278
+00:29:02,900 --> 00:29:07,960
+المصحفات كما تنطبق على جمع المصحفات إلى آخرين 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 و جيبنا ال composition ما بين beta و alpha
+
+281
+00:29:15,220 --> 00:29:21,020
+هذا هيعطينا مينهيعطيني one to one يمكن واحد يسألني
+
+282
+00:29:21,020 --> 00:29:25,240
+طب يقولي 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 existعلى 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 ال composition تبعهم one to one بالمثل
+
+286
+00:29:38,290 --> 00:29:42,070
+لو كانوا on two يبقى ال composition تبعهم معله on
+
+287
+00:29:42,070 --> 00:29:47,090
+two الان النقطة الرابعة لو كانت alpha one to one
+
+288
+00:29:47,090 --> 00:29:52,990
+and on two نرجع ل calculus ايه الشرط ال existence
+
+289
+00:29:52,990 --> 00:29:59,740
+لمعكوس الدالةتبقى دولة one to one مظبوط يبقى one
+
+290
+00:29:59,740 --> 00:30:05,580
+to one وعناصر بيه كلهم يظهروا كصور لعناصري 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 one 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 واحدألفا 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 يسوى ماين ال a يعني ال
+
+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
+يسوى ماين بده يساوي ال a لكل ال a اللي موجودة في a
+
+299
+00:30:40,840 --> 00:30:45,860
+طبعا ال a في domain مين يا شباب هناأيه؟ 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 بدل يساوي B
+
+302
+00:30:54,220 --> 00:30:58,820
+لكل الـ B اللي موجودة في ال domain الـ Alpha
+
+303
+00:30:58,820 --> 00:31:03,210
+Inverseالأن 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
+ال b لو بده اجيب العنصر a بأثر على الطرفين بمين ب
+
+306
+00:31:13,010 --> 00:31:18,620
+alpha inverse بصير alpha inverseالفا انفرس او الفا
+
+307
+00:31:18,620 --> 00:31:22,820
+انفرس او الفا انفرس او الفا انفرس او الفا انفرس او
+
+308
+00:31:22,820 --> 00:31:35,180
+الفا انفرس او الفا 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 ستراهن خلال دراستنا الآن بدنا نروح
+
+311
+00:31:44,020 --> 00:31:48,480
+الى ال chapter 2 اللي هو الجديد chapter ل groups
+
+312
+00:31:48,480 --> 00:31:56,700
+يبقى chapter 2 اللي هو ل 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 ستis a function a start من g cross ال g إلى g
+
+320
+00:32:39,170 --> 00:32:48,190
+that is ان it
+
+321
+00:32:48,190 --> 00:32:58,750
+is a rule it is a rule that ascends 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 ال g an
+
+324
+00:33:26,500 --> 00:33:27,340
+element
+
+325
+00:33:31,010 --> 00:33:35,910
+A Star B N 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، أخد
+
+330
+00:34:39,420 --> 00:34:44,300
+ورتمات، أخد جذور، أي عملية رياضيةالعملية 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 ال 6 g cross ال g إلى gيبقى
+
+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 مالهموجود في جيبجا مشان تكون
+
+341
+00:35:38,470 --> 00:35:44,890
+binary operation تحت هذه العملية نتيجة لجمع انصرين
+
+342
+00:35:44,890 --> 00:35:49,990
+لطرح انصرين لضربهم او 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 ان حدث ذلك بقول يبقى هذه ال operation ما
+
+345
+00:35:58,950 --> 00:36:03,420
+لها binary operationهعطيك 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
+و أحيان بتكونش binary operations أول مثال لو جيت
+
+348
+00:36:11,700 --> 00:36:20,040
+قولت خدلي set g هي set of integer z define عرفلي
+
+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 هدوليعني مجموع two integers بيظل
+
+351
+00:36:50,040 --> 00:36:55,980
+انتجر ولا بيصير complex مجموع two integers ايش
+
+352
+00:36:55,980 --> 00:37:00,340
+بيظل انتجر 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
+أسطار 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 listar is a binary operation is a
+
+360
+00:38:15,740 --> 00:38:27,770
+binary operation on the sets اللي هو الكيو andالـ
+
+361
+00:38:27,770 --> 00:38:31,910
+R يعني على مجموعة الاعداد النسبية و كذلك مجموعة
+
+362
+00:38:31,910 --> 00:38:37,370
+الاعداد الحقيقية طب مثال اتنين ايه اش رايك؟
+
+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
+لأ 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 نقرص ال N إلى N by
+
+369
+00:39:33,680 --> 00:39:37,440
+أربعة و سبعة موجودة في N
+
+370
+00:39:41,310 --> 00:39:48,690
+أنا جالس بتركشن طرح أربعة ناقص سبعة يسوي قداش ناقص
+
+371
+00:39:48,690 --> 00:39:53,210
+ثلاثة هل هذه موجودة في ال N مش موجودة في ال 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/cZhfo9e7d48.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d5a6a94f8b1679cfbce3300708bc69313194e9e7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cZhfo9e7d48.srt
@@ -0,0 +1,1787 @@
+1
+00:00:21,800 --> 00:00:25,620
+بسم الله الرحمن الرحيم المرة اللي فاتت انتهينا من
+
+2
+00:00:25,620 --> 00:00:30,520
+chapter 6 كنظري والآن 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 لـ 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 automorphism لـ z لو
+
+7
+00:00:54,340 --> 00:01:03,160
+جيت قولتك خدلي alpha من z إلى z بيان automorphism
+
+8
+00:01:03,160 --> 00:01:06,620
+الآن
+
+9
+00:01:06,620 --> 00:01:11,460
+بدي أعرف إيه الشكل الـ automorphism هدول السؤال هو
+
+10
+00:01:11,460 --> 00:01:14,560
+الـ z هذا فيها كام generator
+
+11
+00:01:21,280 --> 00:01:30,020
+يبقى الآن لو جيت لـ alpha لما أتأثر على أي 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 one يبقى أي automorphism بدي يعتمد على
+
+14
+00:01:45,710 --> 00:01:51,510
+شكل مين؟ على شكل الـ alpha of one إذا بدنا نعرف شكل
+
+15
+00:01:51,510 --> 00:02:00,830
+الـ alpha of one الآن الواحد generator for
+
+16
+00:02:00,830 --> 00:02:08,070
+z يبقى هذا معناه أن الـ alpha of one is a
+
+17
+00:02:08,070 --> 00:02:14,280
+generator مش غدناها نظرية لو كان عندك الـ group
+
+18
+00:02:14,280 --> 00:02:18,580
+الأولى فيها generator يبقى صورتها وهو generator
+
+19
+00:02:18,580 --> 00:02:22,460
+لمن الـ group التانية يبقى alpha of one is a
+
+20
+00:02:22,460 --> 00:02:31,320
+generator لمن؟ للـ automorphism لـ z طب
+
+21
+00:02:31,320 --> 00:02:38,260
+مدام هيك يبقى الـ alpha of one كم generator فيه في
+
+22
+00:02:38,260 --> 00:02:38,480
+z
+
+23
+00:02:42,310 --> 00:02:47,290
+يبقى الـ alpha of one احتمال أنها تكون واحد و
+
+24
+00:02:47,290 --> 00:02:54,610
+احتمال أنها تكون سالب واحد يبقى لو كان الـ
+
+25
+00:02:54,610 --> 00:03:00,650
+alpha of one يساوي الـ one يبقى معناه أن الـ alpha
+
+26
+00:03:00,650 --> 00:03:07,080
+of n يساوي الـ n يعني هذا الـ identity function لو
+
+27
+00:03:07,080 --> 00:03:13,220
+كان الـ alpha of one يساوي ناقص one يبقى الـ alpha
+
+28
+00:03:13,220 --> 00:03:19,400
+of n هيساوي كده؟ سالب n معناه هو كم automorphism
+
+29
+00:03:19,400 --> 00:03:25,240
+في عندي؟ اتنين فقط لا غير يبقى هنا
+
+30
+00:03:27,820 --> 00:03:36,600
+automorphisms لمين؟ لـ Z هذي has two limits
+
+31
+00:03:42,590 --> 00:03:48,630
+بس عنصرين العنصر الأول هو alpha of n يساوي الـ n
+
+32
+00:03:48,630 --> 00:03:54,150
+والتاني alpha of n يساوي ناقص n يعني two autom
+
+33
+00:03:54,150 --> 00:03:58,010
+orphisms فقط يعني two functions one to one and
+
+34
+00:03:58,010 --> 00:04:03,410
+onto وبتخدم خاصية الـ isomorphism طب خليني أسأل كمان
+
+35
+00:04:03,410 --> 00:04:07,870
+سؤال ما لهوش علاقة بسؤال الكتاب لكن يعتمد على اللي
+
+36
+00:04:07,870 --> 00:04:14,310
+قدامنا هذه حد فيكم بقدر يقولي automorphism لـ Z isomorphic
+
+37
+00:04:14,310 --> 00:04:18,730
+لـ مين؟
+
+38
+00:04:18,730 --> 00:04:25,710
+عنصرين بس بدي جروب فيها عنصرين فقط لا غير هي من
+
+39
+00:04:25,710 --> 00:04:29,510
+أبسط العناصر، المرة اللي فاتت في نظرية 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
+وبرأيي 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 automorphism هذه زيادة لـ Z isomorphic فقط
+
+44
+00:04:56,350 --> 00:05:05,330
+لـ Z2 فقط لا غير طب هذا كان السؤال الثاني السؤال
+
+45
+00:05:05,330 --> 00:05:09,950
+اللي بعده السؤال الرابع بيقول لي إن U8 ليست
+
+46
+00:05:09,950 --> 00:05:17,770
+isomorphic لـ U10 يبقى السؤال الرابع U8 is not
+
+47
+00:05:17,770 --> 00:05:24,770
+isomorphic لـ U10 بدنا نثبت صحة هذا الكلام الآن لو
+
+48
+00:05:24,770 --> 00:05:31,250
+جيت لعناصر الـ U8 هو عبارة عن واحد و ثلاثة و خمسة و
+
+49
+00:05:31,250 --> 00:05:39,490
+سبعة تمام؟ وعناصر الـ U10 هو عبارة عن واحد و ثلاثة
+
+50
+00:05:39,490 --> 00:05:48,280
+و سبعة و تسعة مش هنثبت إن اتنين ليسوا isomorphic
+
+51
+00:05:48,280 --> 00:05:52,520
+بدي أجيب counter example يعني شغلة متحققة في إحدى
+
+52
+00:05:52,520 --> 00:05:56,820
+الـ groups و غير متحققة في الـ group التاني لو جيت
+
+53
+00:05:56,820 --> 00:06:03,390
+لـ ثمانية هل الثلاثة هذا generator؟ ثلاثة مضروبة
+
+54
+00:06:03,390 --> 00:06:08,250
+بواحد، ثلاثة مضروبة بواحد بتلاتة ثلاثة 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 ثمانية Cyclic؟ لأ، U ثمانية is not
+
+57
+00:06:24,070 --> 00:06:32,360
+cyclic يعني ما فيهاش ولا generator عشرة ثلاثة مضروبة
+
+58
+00:06:32,360 --> 00:06:38,800
+بواحد ثلاثة و واحد بواحد ثلاثة تربيع بتسعة ثلاثة
+
+59
+00:06:38,800 --> 00:06:44,520
+تكعيب بسبعة يبقى جايبة كل العناصر ثلاثة و واحد أربعة
+
+60
+00:06:44,520 --> 00:06:49,190
+ليهم مين؟ بواحد تسعة فتسعة و واحد ثمانية يبقى هذه الـ
+
+61
+00:06:49,190 --> 00:06:55,110
+cyclic والثلاثة generator is not cyclic but اللي
+
+62
+00:06:55,110 --> 00:07:00,570
+هو U عشرة بدها تساوي الـ group generated by ثلاثة
+
+63
+00:07:00,570 --> 00:07:05,190
+اللي هي الـ cyclic معناه هل ممكن اتنين يكونوا هدول
+
+64
+00:07:05,190 --> 00:07:10,990
+isomorphic طبعا لأ لأن واحدة cyclic والتانية لأ
+
+65
+00:07:10,990 --> 00:07:19,320
+يبقى هنا سواء الـ U ثمانية الـ U8 is not isomorphic
+
+66
+00:07:19,320 --> 00:07:27,140
+لمين؟ لـ U10 ممكن مش بضرورة الـ cyclic ممكن تجيب لي
+
+67
+00:07:27,140 --> 00:07:31,140
+هنا مثلا two elements الـ order اللي لهم يساوي
+
+68
+00:07:31,140 --> 00:07:34,600
+اتنين هنا تجيب لي two elements ولا أربعة elements
+
+69
+00:07:34,600 --> 00:07:37,940
+الـ order اللي لهم يساوي اتنين يعني عدد عناصر اللي
+
+70
+00:07:37,940 --> 00:07:40,880
+لهم الـ order هنا يختلف عن عدد عناصر اللي لهم الـ
+
+71
+00:07:40,880 --> 00:07:45,590
+order هنا وبالتالي ما فيش isomorphism ما بين الاتنين
+
+72
+00:07:45,590 --> 00:07:52,210
+هذا كان السؤال الرابع وبعدين السؤال السادس G
+
+73
+00:07:52,210 --> 00:07:58,590
+isomorphic لـ H و H isomorphic لـ K السؤال السادس
+
+74
+00:07:59,750 --> 00:08:07,470
+عندك G isomorphic لـ H و الـ H isomorphic لـ K بدنا
+
+75
+00:08:07,470 --> 00:08:16,020
+نثبت إن الـ G isomorphic لمين؟ لـ K وهذه نسميها
+
+76
+00:08:16,020 --> 00:08:21,560
+الـtransitive property خاصية النقل أو نقول الـ
+
+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 الـtransitive لو كان الـG isomorphic لـH وH
+
+79
+00:08:30,780 --> 00:08:37,540
+نفسها isomorphic لـK يبقى الـG isomorphic لمين؟ لـK
+
+80
+00:08:38,160 --> 00:08:45,500
+يبقى بدي أجي أقول solution معناه بدنا نفترض assume
+
+81
+00:08:45,500 --> 00:08:56,940
+أن في Phi واحد من g إلى h is an isomorphism and وفي
+
+82
+00:08:56,940 --> 00:09:07,540
+نفس الوقت في Phi اتنين من الـ 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 هتطلع isomorphism مدام هذا isomorphism و
+
+85
+00:09:21,230 --> 00:09:30,110
+هذا isomorphism معناه أن الـPhi 1 و Phi 2 هم 1 to
+
+86
+00:09:30,110 --> 00:09:36,710
+1 and onto كويس
+
+87
+00:09:37,460 --> 00:09:42,700
+يبقى في is one to one and onto معناه هذا الكلام إن
+
+88
+00:09:42,700 --> 00:09:49,060
+الـ composition تبعهم في 2 في 1 is one to one
+
+89
+00:09:49,060 --> 00:09:56,800
+and onto في نفس الوقت طيب إذا طلع في 2 في 1 عبارة
+
+90
+00:09:56,800 --> 00:10:02,920
+عن isomorphism بتم المطلب طيب السؤال هو هل الـ في 2
+
+91
+00:10:02,920 --> 00:10:09,540
+في 1 هي function من G إلى K؟ Calculus إيه هذا؟
+
+92
+00:10:09,540 --> 00:10:13,840
+ما لهوش دعوة بالجبر أنا عندي في function من هنا لهنا
+
+93
+00:10:13,840 --> 00:10:19,700
+يعني لو بنجي نقول لو أخدنا هذه الـ G وهذه الـ H
+
+94
+00:10:19,700 --> 00:10:26,480
+وهذه الـ 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 لـ في one
+
+97
+00:10:39,280 --> 00:10:45,840
+of x والـ X موجودة في جروب G يبقى بدي يعطيني Phi
+
+98
+00:10:45,840 --> 00:10:50,700
+one of X يبقى موجودة في H إذا هذه صارت domain
+
+99
+00:10:50,700 --> 00:10:55,140
+element في ضمن الـ Phi 2 يبقى Phi 2 بتقدر تأثر عليها
+
+100
+00:10:55,140 --> 00:11:00,700
+وبالتالي بصير Phi 2 و Phi 2 هي function من مين؟ من G
+
+101
+00:11:00,700 --> 00:11:08,440
+إلى K مباشرة يبقى أنا أثبت له أن Phi 2 و Phi 2 يبقى هنا
+
+102
+00:11:10,490 --> 00:11:18,070
+Phi 2 في 1 هي function من g إلى k إذا قلت أثبت
+
+103
+00:11:18,070 --> 00:11:21,410
+إنها بتخدم خاصية الـ isomorphism بتتم المطلوب أن
+
+104
+00:11:21,410 --> 00:11:28,790
+يثبت إنها 1 to 1 and onto لذلك بتروح أخد Phi 2 في
+
+105
+00:11:28,790 --> 00:11:38,370
+1 هذه كلها اللي عندنا as a function of x في y هل
+
+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
+Phi 2 لـ Phi 1 of x في y هذا بدل يساوي Phi 2 والآن Phi 1
+
+108
+00:11:51,610 --> 00:11:59,150
+عبارة عن isomorphism إذا تقدر تدخل على كل من الـ x
+
+109
+00:11:59,150 --> 00:12:08,380
+وكذلك تدخل على الـ y بالمثل Phi 2 isomorphism و Phi
+
+110
+00:12:08,380 --> 00:12:14,020
+1 of x و Phi 1 اللي موجودة وين؟ في H مدام الـ H يبقى
+
+111
+00:12:14,020 --> 00:12:19,720
+Phi 2 بتقدر تدخل عليهم يبقى هذا الكلام بده يساوي
+
+112
+00:12:19,720 --> 00:12:28,180
+Phi 2 لـ Phi 1 of X وهنا Phi 2 لـ Phi 1 of Y
+
+113
+00:12:30,800 --> 00:12:36,200
+طيب هذا الكلام لو جيت رجعتها إلى أصلها هذا تعريف الـ
+
+114
+00:12:36,200 --> 00:12:41,400
+composition of functions يبقى Phi 2 Phi 1 of x
+
+115
+00:12:41,400 --> 00:12:49,160
+والتانية Phi 2 Phi 1 of y يبقى صارت isomorphism
+
+116
+00:12:49,160 --> 00:12:57,020
+يبقى هذا بده يعطينا إن الـ G isomorphic لـ K 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
+transitive أنا عندي isomorphism من الـ 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
+الثالثة إذا بصير عندي isomorphism من الأولى إلى
+
+121
+00:13:14,020 --> 00:13:22,810
+الثالثة هذا كان سؤال ستة سؤال سبعة بيقول لي بيقول لي
+
+122
+00:13:22,810 --> 00:13:34,110
+أن الـ S4 is not isomorphic لـ D12 سؤال 7 S4
+
+123
+00:13:34,110 --> 00:13:38,550
+is not isomorphic لـ D12
+
+124
+00:13:40,360 --> 00:13:48,300
+هذا يجعلني أسأل السؤال التالي الـ S4 هذه الـ 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 دول الاربعة، تلاتة ولا واحد،
+
+128
+00:14:08,430 --> 00:14:15,310
+اتنين واتنين، اتنين وواحد، قداش أعلى order؟ قداش؟
+
+129
+00:14:15,310 --> 00:14:20,710
+أعلى order للـ S، أربعة مش جيبنا أعلى order للـ S7 و
+
+130
+00:14:20,710 --> 00:14:26,470
+S6 بالمثل بده يجيب أعلى order للـ S4 يبقى بده يشوف
+
+131
+00:14:26,470 --> 00:14:32,890
+قداش أكبر cycle في S4 اللي طولها أربعة 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
+أعلى order يعني في S4 الحين صار قداش؟ أربعة، ما فيش
+
+135
+00:14:45,080 --> 00:14:58,840
+غيره يبقى هنا الـ maximum order of elements of S
+
+136
+00:14:58,840 --> 00:15:04,560
+أربعة is أربعة طيب، بالدجلة دي اتناش 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 أربعة كم element فيها تمانية
+
+139
+00:15:13,420 --> 00:15:17,560
+يعني قدها مرتين يبقى دي اتناش كم element فيها
+
+140
+00:15:17,560 --> 00:15:23,240
+أربعة وعشرين element لما أقول دي أربعة هي E و R
+
+141
+00:15:23,240 --> 00:15:27,300
+تسعين و R مية وثمانين و R متين وسبعين و H و V و
+
+142
+00:15:27,300 --> 00:15:33,220
+D و D prime مظبوط يعني كأنه بدي أقول إن دي أربعة E
+
+143
+00:15:33,220 --> 00:15:38,410
+و رو و رو تربيه 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
+أقوله إيه وراه وراه تربيه وراه تكيب لما أتموصل
+
+146
+00:15:46,490 --> 00:15:52,370
+لروح داش يبقى أعلى element في دي اتناش الـ 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
+isomorphic لا 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 ما فيش
+
+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 ما مروش
+
+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 element كذلك طيب
+
+155
+00:16:49,230 --> 00:16:53,350
+هذا السؤال سبعة السؤال ثمانية بيقول لي اللي الـ
+
+156
+00:16:53,350 --> 00:16:58,270
+group الـ function a بالستوي اللوغاريتمي is an
+
+157
+00:16:58,270 --> 00:17:05,590
+isomorphism لـ R plus under multiplication to R
+
+158
+00:17:05,590 --> 00:17:12,700
+under addition هذه من الـ R plus يبقى احنا عن هذا
+
+159
+00:17:12,700 --> 00:17:22,530
+السؤال ثمانية عن فاينمان من الـ R plus إذا أنا 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
+إلى R تحت عملية من تحت عملية الجمع معرفة بالتالي
+
+162
+00:17:39,230 --> 00:17:45,790
+Phi of A بده يساوي لوغاريتم الـ a للأساس عشرة؟ يساوي
+
+163
+00:17:45,790 --> 00:17:50,170
+اللوغاريتم الـ a 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؟ الآن الـ operation هنا عملية ضرب على
+
+166
+00:18:10,490 --> 00:18:14,750
+مجموعة الأعداد الحقيقية الموجبة هنا الـ operation
+
+167
+00:18:14,750 --> 00:18:17,510
+عملية جمع على مجموعة الأعداد الحقيقية 
+
+168
+00:18:17,510 --> 00:18:22,090
+و السالبة و الصفر كلّه الأعداد الحقيقية كلها عرفنا
+
+169
+00:18:22,090 --> 00:18:25,450
+function بالـ Phi of a يساوي لوغاريتم الـ a للأساس عشرة
+
+170
+00:18:25,450 --> 00:18:30,670
+بدي أثبت إن هذا عبارة عن isomorphism مشان أثبت إن
+
+171
+00:18:30,670 --> 00:18:36,560
+هو isomorphism بدي أثبت إن Phi is one to one لذلك
+
+172
+00:18:36,560 --> 00:18:44,220
+بتروح آخذ صورتين متساويتين assume إن فاي of a
+
+173
+00:18:44,220 --> 00:18:50,460
+بتساوي فاي of b then طب لما أخدت صورتين متساويتين
+
+174
+00:18:50,460 --> 00:18:55,880
+إمشانات بينها one to one إيش عايز أثبت؟ إن الـ A
+
+175
+00:18:55,880 --> 00:19:02,740
+تساوي الـ B يبقى بناء عليه Phi of A هي لوغاريتم الـ A
+
+176
+00:19:02,740 --> 00:19:09,660
+للأساس عشرة و الـ Phi of B هو لوغاريتم الـ B للأساس عشرة
+
+177
+00:19:10,420 --> 00:19:16,940
+معنى هذا الكلام هذي بقدر أكتبها بدلالة لن يبقى لن
+
+178
+00:19:16,940 --> 00:19:24,800
+الـ a على لن على لن العشرة و هذي بدي يساوي لن الـ b
+
+179
+00:19:24,800 --> 00:19:30,830
+على لن العشرة لو ضربت الطرفين في لن العشرة لأن لن
+
+180
+00:19:30,830 --> 00:19:37,070
+العشرة مقدار ثابت يبقى بده يصير لن الـ A بده يساوي
+
+181
+00:19:37,070 --> 00:19:44,990
+لن الـ B لو رفعت كل واحد فيهم كأس للعدد A يبقى هوصل
+
+182
+00:19:44,990 --> 00:19:51,740
+إن الـ A بده يساوي بده يساوي الـ B وبناء عليه الـ FI
+
+183
+00:19:51,740 --> 00:19:57,940
+is one to one بدي أحاول أثبت له الآن إن الـ FI is
+
+184
+00:19:57,940 --> 00:20:05,080
+onto مشان هيك بدي أقعد آخذ الـ Y موجودة في من؟
+
+185
+00:20:05,080 --> 00:20:13,100
+موجودة في R أو خليني آخذ الـ B خليني الـ A و B خدلي
+
+186
+00:20:13,100 --> 00:20:19,350
+الـ B موجودة في R إذا 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 بالضبط أقول له if الـ B أكبر من الـ 0 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 الـ B هذه تساوي أو then؟ there exist اللي هو A
+
+196
+00:21:09,790 --> 00:21:17,150
+بحيث الـ A يكون أكبر من الـ 1 such that .. such
+
+197
+00:21:17,150 --> 00:21:25,330
+that إن الـ B يساوي لوغاريتم الـ A للأساس عشرة هل 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 لـ Calculus بي
+
+200
+00:21:35,410 --> 00:21:41,250
+منحنا الآن كان بالشكل اللي عندك كده IY تساوي لن الـ
+
+201
+00:21:41,250 --> 00:21:46,730
+X وهذا النقطة واحدة وهي Zero احنا بنقول لو كان الـ
+
+202
+00:21:46,730 --> 00:21:54,280
+B موجبة يبقى الـ B تساوي لوغاريتم عدد ده مظبوط و اجتاش
+
+203
+00:21:54,280 --> 00:21:59,820
+اللوغاريتم 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 الـ 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 A طيب هذا لو كانت
+
+207
+00:22:18,920 --> 00:22:25,140
+الـ B موجبة كلامنا صح طب لو كانت الـ B بـ 0 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
+الـ B تساوي 0 then بدي
+
+210
+00:22:36,600 --> 00:22:43,920
+آخذ الـ A بـ 1 then اللي هو الـ zero هذا بده يساوي
+
+211
+00:22:43,920 --> 00:22:53,000
+لين أو بده يساوي لوغاريتم الواحد للأساس عشرة كيف؟
+
+212
+00:22:55,210 --> 00:22:59,930
+لوغاريتم أو لن اتنين نفس الرسمة كلّه يمر بهذه
+
+213
+00:22:59,930 --> 00:23:05,590
+النقطة بس بيجرب على المحور أو بيبعد عنها مديش غلبك
+
+214
+00:23:05,590 --> 00:23:12,870
+هذا log X للأساس عشرة خليها هي ماشي ماهي الـ log هي
+
+215
+00:23:12,870 --> 00:23:19,520
+الـ ln بس بتنضر في مقدار ثابت فقط لا غير طيب يبقى
+
+216
+00:23:19,520 --> 00:23:25,520
+صار الـ zero بده يساوي log الواحد للأساس عشرة يعني
+
+217
+00:23:25,520 --> 00:23:33,160
+هذا log الـ a للأساس عشرة اللي هو بده يساوي في of a
+
+218
+00:23:33,160 --> 00:23:41,400
+و الـ a تساوي 1 يبقى صارت في is onto طب لو كانت
+
+219
+00:23:41,400 --> 00:23:53,810
+سالبة يبقى f الـ b أقل من الـ 0 then الـ b تساوي أو
+
+220
+00:23:53,810 --> 00:24:02,370
+then there exist لازم ألاقي a أكبر من الـ 0 أقل
+
+221
+00:24:02,370 --> 00:24:07,620
+من الـ 1 طلالي على الفترة هذه الفترة هذه لما
+
+222
+00:24:07,620 --> 00:24:12,240
+تأخذ الـ log لأي رقم هنا إيش بيطلع قيمة موجبة و
+
+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 1 such that بحيث إن الـ b هذي
+
+225
+00:24:26,800 --> 00:24:33,990
+بده يساوي log a للعساس عشرة اللي هو five of a يبقى
+
+226
+00:24:33,990 --> 00:24:39,250
+ليه جميع قيم b الموجبة و السالبة و الصفر لقيت اللي
+
+227
+00:24:39,250 --> 00:24:44,650
+هي أصل اسمه Phi of A يبقى Phi of A أو Phi is
+
+228
+00:24:44,650 --> 00:24:52,990
+onto يبقى هنا ف Phi is onto بقيت عند النقطة
+
+229
+00:24:52,990 --> 00:24:57,230
+الأخيرة لإنه أثبت له الآن إن في one to one
+
+230
+00:24:57,230 --> 00:25:02,210
+و أثبت له إن في is onto مش ضايل عندنا إلا نثبت
+
+231
+00:25:02,210 --> 00:25:09,750
+خاصية من الـ isomorphism الآن بدى أروح آخذ له الـ في
+
+232
+00:25:09,750 --> 00:25:16,910
+of x في y طبعا كون الـ في من الست اللي عليها الضرب
+
+233
+00:25:16,910 --> 00:25:22,510
+بدى أروح للست اللي عليها من الجامعة يبقى حسب الـ
+
+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 الـ log الـ log لحاصل الضرب يساوي
+
+236
+00:25:36,930 --> 00:25:43,310
+حاصل جمع الـ 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 y يبقى بناء عليه
+
+239
+00:25:57,560 --> 00:26:08,060
+بقوله غص وهكذا ف I of A يساوي لج الـ A للأساس عشرة
+
+240
+00:26:08,060 --> 00:26:18,200
+لج الـ A للأساس عشرة is an isomorphism
+
+241
+00:26:45,420 --> 00:26:51,760
+هذا كان سؤال ثمانية سؤال تسعة أثبتناه في المحاضرة
+
+242
+00:26:51,760 --> 00:26:59,600
+السؤال العاشر بيقول لي إن جي جروب from the mapping
+
+243
+00:26:59,600 --> 00:27:09,200
+اللي هي the mapping Alpha G بتساوي G inverse for
+
+244
+00:27:09,200 --> 00:27:13,960
+all G is an atomorphism if and only if الـ G is
+
+245
+00:27:13,960 --> 00:27:24,640
+abelian يبقى هذا سؤال عشرة سؤال عشرة Alpha of G بده
+
+246
+00:27:24,640 --> 00:27:32,820
+يساوي G inverse هذا معنى لكل الـ G اللي معنى is
+
+247
+00:27:32,820 --> 00:27:41,540
+atomorphism is atomorphism if and only if الـ G is
+
+248
+00:27:41,540 --> 00:27:52,100
+abelian الـ G is 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
+الـ function اللي هي Alpha من G إلى G يعني Alpha
+
+252
+00:28:05,940 --> 00:28:12,120
+هذه من G إلى G المعرفة alpha G ساوي G inverse
+
+253
+00:28:12,120 --> 00:28:17,800
+سابارع أن اتومورفزم إذا كانت الـ G is abelian
+
+254
+00:28:17,800 --> 00:28:22,240
+if and only if تعني أن البرهان سيصير في اتجاهين
+
+255
+00:28:22,240 --> 00:28:29,360
+تفكير بده اروح اخدني اتجاهي الأول assume that أن 
+
+256
+00:28:29,360 --> 00:28:35,620
+الـ alpha of G بده يساوي G inverse is an
+
+257
+00:28:35,620 --> 00:28:40,800
+automorphism ايش بده نثبت؟
+
+258
+00:28:44,150 --> 00:28:48,310
+أنا بدي أثبت أن G1 G2 يستوي G2 G1
+
+259
+00:28:48,310 --> 00:28:54,890
+واحد for all G1 و G2 اللي موجودة في G
+
+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 G1 G2 هذا الكلام بقدر أقول alpha of G
+
+262
+00:29:07,980 --> 00:29:13,880
+واحد في alpha of G2 صحيح هذا يا شباب صحيح لأن
+
+263
+00:29:13,880 --> 00:29:19,160
+أنا فرضت أن alpha عبارة عن ايش automorphism يعني
+
+264
+00:29:19,160 --> 00:29:25,660
+isomorphism هذا الكلام صحيح since alpha is an
+
+265
+00:29:25,660 --> 00:29:33,400
+isomorphism طيب بطء ولكن الـ alpha of G1 G
+
+266
+00:29:33,400 --> 00:29:34,020
+2
+
+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 G1 طب 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
+الـ alpha هذا إيش فرضه أنا؟ automorphism يعني isomorphism
+
+274
+00:30:34,060 --> 00:30:39,780
+مورفزم إذا بده ارجع كل واحد الى اصله يبقى هذا
+
+275
+00:30:39,780 --> 00:30:48,980
+معناته أن alpha of G1 G2 بده يساوي alpha of G2 G1
+
+276
+00:30:48,980 --> 00:30:55,120
+طب الـ alpha ايش جايل عليها أنا؟ automorphism يعني
+
+277
+00:30:55,120 --> 00:31:05,830
+one to one يبقى باطل ولكن الـ alpha is one to one إذا
+
+278
+00:31:05,830 --> 00:31:12,570
+صورتين متساويتين يبقى G1 G2 بتساوي G
+
+279
+00:31:12,570 --> 00:31:19,490
+2 G1 لكل الـ G1 و G2 اللي موجودات
+
+280
+00:31:19,490 --> 00:31:26,340
+فيه G ايش معنى هذا الكلام أن G is abelian يبقى
+
+281
+00:31:26,340 --> 00:31:34,580
+هنا الـ G is abelian الآن هذا الاتجاه الأول بروح
+
+282
+00:31:34,580 --> 00:31:44,920
+نقوله conversely assume افترض that أن الـ G is
+
+283
+00:31:44,920 --> 00:31:50,020
+abelian افترض
+
+284
+00:31:50,020 --> 00:31:56,670
+أن الـ G is abelian ايش بده نثبت؟ هذا isomorphism
+
+285
+00:31:56,670 --> 00:32:02,010
+يعني بدي أثبت أنه one to one وانتوا ويخدم خاصية
+
+286
+00:32:02,010 --> 00:32:08,650
+مين الـ isomorphism بعدين بقوله كويس يبقى بدي أروح
+
+287
+00:32:08,650 --> 00:32:16,150
+أخدله اللي هو الـ alpha is one to one بدي أحاول
+
+288
+00:32:16,150 --> 00:32:25,720
+أثبتها لذلك بدي أقوله assume افترض أن alpha of G1
+
+289
+00:32:25,720 --> 00:32:34,460
+يساوي alpha of G2 إذا قدرت اثبت له أن G1 يساوي G2
+
+290
+00:32:34,460 --> 00:32:39,280
+يكون اثبتنا أن 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 الـ identity صح؟
+
+295
+00:33:11,110 --> 00:33:17,670
+طب بدي اضرب من جهة الشمال في G1 يبقى هذا معناته
+
+296
+00:33:17,670 --> 00:33:27,630
+أن G2 بده يساوي الـ G1 أظن و هو المطلوب طيب ضايق
+
+297
+00:33:27,630 --> 00:33:33,230
+نثبت علينا الآن أن الـ 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 الـ element اللي أخدته هنا هنا له
+
+301
+00:34:01,110 --> 00:34:09,620
+أصل موجود هنا يبقى روحت أخدت الـ Y موجود في G then
+
+302
+00:34:09,620 --> 00:34:17,320
+الـ Y بقدر أكتبها كيف؟
+
+303
+00:34:17,320 --> 00:34:21,440
+G
+
+304
+00:34:21,440 --> 00:34:22,200
+group أيوة
+
+305
+00:34:25,220 --> 00:34:29,380
+هذا يعني G اللي موجود في G له معكوس لكن أنا بدأ
+
+306
+00:34:29,380 --> 00:34:36,320
+أثبت أن هذا المعكوس هو يساوي phi of شغله، مظبوط؟
+
+307
+00:34:36,320 --> 00:34:42,900
+هذا ليش اللي عايزين تفهمه؟ يبقى أنا اخدت Y، then Y
+
+308
+00:34:42,900 --> 00:34:49,420
+inverse هذا بدي يكون موجود في G، ليش؟ لأن الـ G is
+
+309
+00:34:49,420 --> 00:34:50,340
+a group
+
+310
+00:34:56,530 --> 00:35:07,090
+طيب الآن الـ y هذه بقدر أكتبها y inverse inverse
+
+311
+00:35:07,090 --> 00:35:15,310
+بنفعله ما نفعش 100% ايش رأيك y inverse بدي اكتبها x
+
+312
+00:35:15,310 --> 00:35:20,570
+inverse يعني بدي اشيل اللي بين قوسين و اكتب بدلها x
+
+313
+00:35:20,570 --> 00:35:29,800
+طب بين هي هذه مش هي alpha of x صح ولا لأ يبقى الـ
+
+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 الـ 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 of G1 G2 يساوي اللي هو الـ 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؟ آه لماذا؟ لأنه فارض أنا أن G 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 الـ G is abelian مدام
+
+323
+00:36:40,480 --> 00:36:51,040
+abelian يبقى الأول alpha of G1 و الثاني alpha of G2
+
+324
+00:36:51,040 --> 00:36:57,700
+يبقى sir alpha of G1 G2 هو alpha of G1 G2 بناء أن
+
+325
+00:36:57,700 --> 00:37:02,800
+على الـ alpha أنا ماخدها من G إلى G أن الـ alpha
+
+326
+00:37:02,800 --> 00:37:09,860
+عبارة عن automorphism thus الـ alpha is an
+
+327
+00:37:09,860 --> 00:37:12,520
+automorphism
+
+328
+00:37:41,820 --> 00:37:46,500
+طيب هذا كان سؤال عشرة من الكتاب السؤال اثنا عشر for
+
+329
+00:37:46,500 --> 00:37:51,160
+two groups G and ليش ساطجات الـ G ليست isomorphic
+
+330
+00:37:51,160 --> 00:37:57,880
+يعني بدنا two groups بحيث الـ G ماهواش isomorphic لا
+
+331
+00:37:57,880 --> 00:38:07,600
+H سؤال اثنا عشر بدنا G ماهياش isomorphic لا H but
+
+332
+00:38:07,600 --> 00:38:15,480
+ولكن ولكن الـ automorphism لـ G isomorphic للـ
+
+333
+00:38:15,480 --> 00:38:25,240
+automorphism بطل automorphism للـ G isomorphic للـ
+
+334
+00:38:25,240 --> 00:38:32,960
+automorphism للـ H للـ automorphism للـ H اللي عندنا
+
+335
+00:38:32,960 --> 00:38:37,200
+هذا القصة
+
+336
+00:38:37,200 --> 00:38:44,420
+بسيطة جدا و لا نبعد كثير و نحاول نستخدم ما درسناه
+
+337
+00:38:44,420 --> 00:38:49,280
+في آخر نظرية أخدناها في الـ chapter آخر نظرية قلنا
+
+338
+00:38:49,280 --> 00:38:56,720
+automorphic لـ ZN isomorphic لمين؟ للـ UN الآن لو جيت
+
+339
+00:38:56,720 --> 00:39:05,980
+قلت لك أخدت solution لو أخدت الـ G تساوي الـ Z6 and
+
+340
+00:39:06,790 --> 00:39:12,990
+الـ H اللي هي بدها تساوي الـ Z3 هل الاثنين
+
+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؟ ثلاثة يبقى then الـ then الـ order اللي
+
+343
+00:39:27,490 --> 00:39:34,420
+هجيه بده يساوي ستة و الـ order لـ H بدي يساوي ثلاثة هذا
+
+344
+00:39:34,420 --> 00:39:43,000
+بده يعطينا أن الـ G is not isomorphic لمين؟ لـ H but
+
+345
+00:39:43,000 --> 00:39:54,760
+ولكن الـ automorphism لـ Z6 isomorphic لمين يا شباب؟ لـ
+
+346
+00:39:54,760 --> 00:40:05,600
+U6 U6 من عناصر واحد، ثلاثة، أربعة، خمسة، و ... الآن
+
+347
+00:40:05,600 --> 00:40:15,360
+الـ automorphism لـ Z3 isomorphic لـ U3 U3 اللي هو
+
+348
+00:40:15,360 --> 00:40:23,480
+واحد و اثنين 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 للـ identity الآن هل
+
+351
+00:40:36,600 --> 00:40:41,950
+اثنين generator ليه ثلاثة؟ هو برضه عملية ضرب اثنين
+
+352
+00:40:41,950 --> 00:40:46,010
+في اثنين بأربعة بيطلع واحد الـ identity و هكذا يبقى
+
+353
+00:40:46,010 --> 00:40:49,010
+اثنين هذول كل واحدة فيها اثنين و هنا اثنين
+
+354
+00:40:49,010 --> 00:40:52,810
+identity identity generator generator الـ order
+
+355
+00:40:52,810 --> 00:40:57,910
+الأول يساوي يبقى اثنين 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 الموضوع يعني ممكن هذا مثال هيعطينا أن two
+
+358
+00:41:26,250 --> 00:41:31,830
+groups ليست isomorphic لكن الـ automorphism على الـ
+
+359
+00:41:31,830 --> 00:41:35,050
+group الأولى و الـ automorphism على الـ group الثانية
+
+360
+00:41:35,050 --> 00:41:40,890
+اثنين are isomorphic هذا سؤال اثنا عشر السؤال
+
+361
+00:41:40,890 --> 00:41:46,430
+الاربعة عشر الشفوي قال لي هاتي الـ automorphism لمن؟ لـ
+
+362
+00:41:46,430 --> 00:41:52,950
+Z6 عظم زد ستة الـ automorphism لـ زد ستة عرفنا الـ
+
+363
+00:41:52,950 --> 00:41:56,010
+isomorphism اللي يعني مافيش فيها إلا ايه؟ two
+
+364
+00:41:56,010 --> 00:42:02,110
+elements معناته كم isomorphism في في automorphism لـ زد
+
+365
+00:42:02,110 --> 00:42:07,310
+ستة كم واحد؟ اثنين يبقى الأول يا إما الـ alpha of
+
+366
+00:42:07,310 --> 00:42:11,770
+one بده يساوي الـ one يا إما الـ alpha one بده يساوي
+
+367
+00:42:11,770 --> 00:42:17,480
+الخمسة يبقى اثنين فقط يبقى السؤال الاربعة عشر اللي هو
+
+368
+00:42:17,480 --> 00:42:25,140
+shuffling الآن السؤال ستة عشر الـ proof ان الـ mapping
+
+369
+00:42:25,140 --> 00:42:30,540
+من U16 الى الـ self given by عبارة عن automorphism
+
+370
+00:42:30,540 --> 00:42:39,300
+و ماذا عن و ماذا عن أعمم يبقى الآن بدنا نيجي للسؤال
+
+371
+00:42:39,300 --> 00:42:49,350
+تبع ستة عشر بيقول ما يأتي الـ mapping في من U16
+
+372
+00:42:49,350 --> 00:42:58,390
+إلى U16 من U16 إلى U16 is given by اللي هو
+
+373
+00:42:58,390 --> 00:43:08,360
+given by phi of x يساوي الـ x تكعب و is an
+
+374
+00:43:08,360 --> 00:43:16,120
+automorphism is automorphism what about
+
+375
+00:43:17,650 --> 00:43:27,990
+phi of x يساوي x أس خمسة و phi of x يساوي x أس 
+
+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 جنرلايز 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 الآن أنا عندي من U16 إلى U16
+
+380
+00:43:54,540 --> 00:43:58,880
+مطابق فيوفيكسي يساوي X<sup>3</sup> 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 U16 يا جماعة من عناصرها الواحد والتالتة
+
+386
+00:44:26,460 --> 00:44:36,920
+والخمسة، ستة، سبعة، ثمانية، تسعة، عشرة، أحد عشر،
+
+387
+00:44:36,920 --> 00:44:48,540
+اثنا عشر، ثلاثة عشر، أربعة عشر، خمسة عشر هذه
+
+388
+00:44:48,540 --> 00:44:55,600
+العناصر هي ثمان عناصر الـ U16 أنا عندي five من U
+
+389
+00:44:55,600 --> 00:45:02,220
+16 إلى U 16 مطابق X<sup>3</sup> شوفوا لي بالله ثلاثة 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 --> 00:45:29,460
+تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة
+
+398
+00:45:29,460 --> 00:45:40,120
+أربعة تسعة أربعة تسعة أربعة تسعة أربعة تسعة أربعة
+
+399
+00:45:40,120 --> 00:45:48,850
+تسعة property الخاصية التالية أن الـ x<sup>4</sup> بده
+
+400
+00:45:48,850 --> 00:45:54,610
+يشوّن identity element خلّي هذه المعلومة في دماغك و
+
+401
+00:45:54,610 --> 00:46:01,130
+بدنا نحاول نستفيد منها متى لازم الأمر و وقت أشي
+
+402
+00:46:01,130 --> 00:46:07,050
+بيلزم بدنا نحاول نستفيد منها طيب احنا بدنا نيجي
+
+403
+00:46:07,050 --> 00:46:16,190
+الـΦ of X يساوي X<sup>3</sup> بدي أثبت أن الـΦ is one
+
+404
+00:46:16,190 --> 00:46:22,870
+to one يبقى بالدرجة أقول له assume افترض أنه five
+
+405
+00:46:22,870 --> 00:46:30,510
+of x يساوي five of y يعني معناته أن ال x<sup>3</sup> بده
+
+406
+00:46:30,510 --> 00:46:36,530
+يساوي ال y<sup>3</sup> معناته ال x بده يساوي main بده يساوي 
+
+407
+00:46:36,530 --> 00:46:46,610
+ال y بعدين ال five is onto افترض أن ال Y موجودة في 
+
+408
+00:46:46,610 --> 00:47:00,550
+U 16 يبقى ال Y<sup>4</sup> تساوي كم؟ تساوي واحد بدي أثبت
+
+409
+00:47:00,550 --> 00:47:07,820
+أن ال Y هذه لها أصل في U 16 بقول له كويس إيش رأيك
+
+410
+00:47:07,820 --> 00:47:13,540
+هذه بدل Y<sup>4</sup> بدي آخذ Y واحدة يعني إيش أعمل
+
+411
+00:47:13,540 --> 00:47:21,640
+في المعادلة بدي أضرب في Y<sup>-3</sup> أو Y inverse
+
+412
+00:47:21,640 --> 00:47:28,660
+تكعيب أو Y تكعيب inverse يبقى هذا بده يعطيك أن y
+
+413
+00:47:28,660 --> 00:47:35,480
+<sup>4</sup> ل y<sup>-3</sup> بده يساوي ال y<sup>-3</sup>
+
+414
+00:47:35,480 --> 00:47:41,300
+يعني ضربنا الطرفين y<sup>-3</sup> هذا معناه إيش أن
+
+415
+00:47:41,300 --> 00:47:50,640
+ال y يساوي y inverse تكعيب ال y inverse بقدر أقول
+
+416
+00:47:50,640 --> 00:47:59,550
+عليها x تكعيب اللي بقدر أقول عليها في of X يبقى ال
+
+417
+00:47:59,550 --> 00:48:05,270
+element اللي أخدته Y اللي جيت له أصل هنا X يبقى في
+
+418
+00:48:05,270 --> 00:48:10,630
+is onto بالخاصية هذه أنا لما كتبتها ما كتبتاش بلاش
+
+419
+00:48:10,630 --> 00:48:17,230
+لزمت لي ولما لزمت لي روحت استخدمتها تمام يبقى في
+
+420
+00:48:17,230 --> 00:48:21,490
+one to one and onto مش ضايل إلا خاصية من ال
+
+421
+00:48:21,490 --> 00:48:30,430
+isomorphism يبقى بدي أخد finally أخيرًا finally بدي
+
+422
+00:48:30,430 --> 00:48:38,090
+آخذ ال five of XY يبقى هذا الكلام بدي يساوي XY لكل
+
+423
+00:48:38,090 --> 00:48:44,130
+تكعيب السؤال هو هل بقدر أكتب X تكعيب Y تكعيب ولا
+
+424
+00:48:44,130 --> 00:48:56,080
+لا؟ بقدر أكتب هك؟ بقدر؟ طب ليش؟ بقدر أكتب بالشكل
+
+425
+00:48:56,080 --> 00:49:01,520
+يعني هذا لإنه فاهم من وين لوين طب ال U16 أبيلين
+
+426
+00:49:01,520 --> 00:49:08,140
+ولا non abelian ال UN in general أبيلين ولا non
+
+427
+00:49:08,140 --> 00:49:13,650
+abelian أبيليان ضرب أعداد عادي يبقى أبيليان يبقى
+
+428
+00:49:13,650 --> 00:49:20,470
+هذا الكلام صحيح since U16 is abelian لو
+
+429
+00:49:20,470 --> 00:49:25,870
+ماكنتش أبيليان بصير هذا كلام ما له مش صحيح يبقى هذا
+
+430
+00:49:25,870 --> 00:49:33,410
+الكلام بدي أعطيك في of x في في of y يبقى دص وهكذا
+
+431
+00:49:33,410 --> 00:49:37,770
+الفي is an automorphism
+
+432
+00:49:38,960 --> 00:49:43,920
+يقول لي إيش رأيك في هذا وإيش رأيك في هذا بنفس
+
+433
+00:49:43,920 --> 00:49:52,020
+الطريقة بنفس الطريقة يبقى similarly بنفس الطريقة
+
+434
+00:49:52,020 --> 00:50:00,400
+اللي هو five of x يساوي ال x<sup>5</sup> and five of x
+
+435
+00:50:00,400 --> 00:50:06,720
+يساوي ال x<sup>7</sup> are automorphism
+
+436
+00:50:08,830 --> 00:50:16,510
+جالي عمّم مدام عمّم يبقى بده أقول له يبقى الـΦ of
+
+437
+00:50:16,510 --> 00:50:24,510
+X يساوي الـX بدك تخلي الأس فردي تقدر تقول 2N
+
+438
+00:50:24,510 --> 00:50:32,430
+زائد واحد is an Automorphism دير بالك في حالة الـX
+
+439
+00:50:32,430 --> 00:50:39,060
+السابعة ها ديها ها بدي أجيب identity فبصير لما
+
+440
+00:50:39,060 --> 00:50:43,220
+أقول لك x<sup>4</sup> بال identity بصير x<sup>8</sup>
+
+441
+00:50:43,220 --> 00:50:49,200
+بجداش بال identity يبقى لما أجي أقول له ال x<sup> </sup>
+
+442
+00:50:49,200 --> 00:50:54,820
+<sup>8</sup> اللي هي عبارة عن x في x<sup>7</sup> أو بدي x
+
+443
+00:50:54,820 --> 00:51:00,200
+لحالها بضرب في x<sup>-7</sup> بصير ال x هو x<sup> </sup>
+
+444
+00:51:00,200 --> 00:51:04,750
+<sup>-7</sup> وهكذا تمام؟ يعني نفس ال tactic اللي
+
+445
+00:51:04,750 --> 00:51:10,230
+عملنا هنا للحالة الأولى بنروح نعمله لمين؟ للحالة
+
+446
+00:51:10,230 --> 00:51:14,130
+التالتة والحالة التانية وبالتالي عبارة عن
+
+447
+00:51:14,130 --> 00:51:15,630
+automorphism 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..119e1bebcbb222bffd3d5595afdc93b36785c9ae
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_raw.json
@@ -0,0 +1 @@
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ايش قيمتها شو تساوي ماهو نوع هذه ال function فبجي بقول الان لو كان ال k موجود في z عشرة then", "tokens": [2304, 8592, 7649, 39896, 4117, 12602, 2407, 33753, 1975, 5172, 2655, 43042, 16472, 2423, 8961, 9154, 710, 6225, 8592, 25720, 2423, 7578, 710, 6225, 8592, 25720, 7251, 3555, 4587, 7578, 1975, 3615, 1863, 7578, 12018, 18191, 1434, 13412, 2407, 13412, 28820, 2423, 8961, 21984, 1975, 3615, 19528, 46811, 10943, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 44945, 49628, 12984, 12174, 3215, 33599, 2423, 8961, 11778, 1829, 1975, 2407, 1975, 1829, 8592, 12174, 32640, 2655, 11296, 13412, 2407, 6055, 3794, 995, 45865, 19446, 3224, 2407, 8717, 45367, 29538, 2423, 2445, 6156, 3555, 7435, 1829, 4724, 39648, 2423, 7649, 45164, 25961, 2423, 350, 3714, 29245, 23328, 8978, 710, 6225, 8592, 25720, 550], "avg_logprob": -0.25591216914288634, "compression_ratio": 1.6968325791855203, "no_speech_prob": 1.1920928955078125e-06, "words": [{"start": 32.21, "end": 32.77, "word": "مشان", "probability": 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"text": "يبقى باجي بقوله و ال alpha of one موجودة في z عشرة طيب باجي بقول كمان in z عشرة قداش ال order للواحد قداش ال order للواحد في z عشرة مين ال operation اللي على z عشرة", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 4032, 2423, 8961, 295, 472, 3714, 29245, 23328, 3660, 8978, 710, 6225, 8592, 25720, 23032, 1829, 3555, 4724, 26108, 1829, 4724, 39648, 9122, 2304, 7649, 294, 710, 6225, 8592, 25720, 12174, 3215, 33599, 2423, 1668, 24976, 14407, 24401, 12174, 3215, 33599, 2423, 1668, 24976, 14407, 24401, 8978, 710, 6225, 8592, 25720, 3714, 9957, 2423, 6916, 13672, 1829, 15844, 710, 6225, 8592, 25720], "avg_logprob": -0.1337756816654989, "compression_ratio": 1.748299319727891, "no_speech_prob": 0.0, "words": [{"start": 142.58, "end": 143.08, "word": "يبقى", "probability": 0.84307861328125}, {"start": 143.08, "end": 143.42, "word": " باجي", "probability": 0.7428385416666666}, {"start": 143.42, "end": 144.52, "word": " بقوله", "probability": 0.8020833333333334}, 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0.93701171875}, {"start": 163.36, "end": 163.52, "word": " z", "probability": 0.96826171875}, {"start": 163.52, "end": 164.2, "word": " عشرة", "probability": 0.9772135416666666}, {"start": 164.2, "end": 166.64, "word": " مين", "probability": 0.7039794921875}, {"start": 166.64, "end": 166.78, "word": " ال", "probability": 0.98779296875}, {"start": 166.78, "end": 167.32, "word": " operation", "probability": 0.916015625}, {"start": 167.32, "end": 167.64, "word": " اللي", "probability": 0.899658203125}, {"start": 167.64, "end": 167.84, "word": " على", "probability": 0.77783203125}, {"start": 167.84, "end": 168.14, "word": " z", "probability": 0.9775390625}, {"start": 168.14, "end": 168.76, "word": " عشرة", "probability": 0.9811197916666666}], "temperature": 1.0}, {"id": 7, "seek": 19922, "start": 169.64, "end": 199.22, "text": "أزايد الجامعة مظبوط الجامعة هي ال operation الموجودة على ز عشرة إذا الواحد قداش ال order له الواحد لو أشبهك كام مرة بيعطيني ال zero عشر مرات يعني ال order للواحد يسوى قداش يسوى عشرة يبقى ال order للواحد يسوى عشرة هذا بده يعطينا أن ال order لل alpha of واحد", "tokens": [10721, 11622, 995, 25708, 25724, 10943, 27884, 3714, 19913, 3555, 2407, 9566, 25724, 10943, 27884, 39896, 2423, 6916, 9673, 29245, 23328, 3660, 15844, 30767, 6225, 8592, 25720, 11933, 15730, 2423, 14407, 24401, 12174, 3215, 33599, 2423, 1668, 46740, 2423, 14407, 24401, 45164, 5551, 8592, 3555, 3224, 4117, 9122, 10943, 3714, 25720, 4724, 1829, 3615, 9566, 1829, 22653, 2423, 4018, 6225, 46309, 3714, 2288, 9307, 37495, 22653, 2423, 1668, 24976, 14407, 24401, 7251, 3794, 2407, 7578, 12174, 3215, 33599, 7251, 3794, 2407, 7578, 6225, 8592, 25720, 7251, 3555, 4587, 7578, 2423, 1668, 24976, 14407, 24401, 7251, 3794, 2407, 7578, 6225, 8592, 25720, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 14739, 2423, 1668, 24976, 8961, 295, 36764, 24401], "avg_logprob": -0.22582799094355005, "compression_ratio": 2.0585365853658537, "no_speech_prob": 9.5367431640625e-07, "words": [{"start": 169.64, 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"probability": 0.9931640625}, {"start": 216.5, "end": 216.84, "word": " phi", "probability": 0.4501953125}, {"start": 216.84, "end": 217.28, "word": " ايزو", "probability": 0.731201171875}, {"start": 217.28, "end": 217.9, "word": " مورفزم", "probability": 0.75390625}, {"start": 217.9, "end": 218.6, "word": " انا", "probability": 0.86962890625}, {"start": 218.6, "end": 218.94, "word": " افرض", "probability": 0.7819010416666666}, {"start": 218.94, "end": 219.2, "word": " ان", "probability": 0.9033203125}, {"start": 219.2, "end": 220.3, "word": " اتومورفزم", "probability": 0.747802734375}, {"start": 220.3, "end": 220.66, "word": " هو", "probability": 0.61328125}, {"start": 220.66, "end": 221.24, "word": " ايزو", "probability": 0.951171875}, {"start": 221.24, "end": 221.92, "word": " مورفزم", "probability": 0.98310546875}, {"start": 221.92, "end": 222.6, "word": " من", "probability": 0.90576171875}, {"start": 222.6, "end": 222.78, "word": " ال", "probability": 0.62890625}, {"start": 222.78, "end": 223.22, "word": " group", "probability": 0.95458984375}, {"start": 223.22, "end": 223.64, "word": " الى", "probability": 0.70751953125}, {"start": 223.64, "end": 224.46, "word": " نفسه", "probability": 0.8966471354166666}, {"start": 224.46, "end": 224.86, "word": " هذا", "probability": 0.85400390625}, {"start": 224.86, "end": 225.7, "word": " بيعطينا", "probability": 0.8429361979166666}, {"start": 225.7, "end": 225.94, "word": " ان", "probability": 0.916015625}, {"start": 225.94, "end": 226.38, "word": " هذا", "probability": 0.92919921875}, {"start": 226.38, "end": 227.02, "word": " بيساوي", "probability": 0.846484375}, {"start": 227.02, "end": 227.72, "word": " عشرة", "probability": 0.9130859375}, {"start": 227.72, "end": 228.62, "word": " because", "probability": 0.875}], "temperature": 1.0}, {"id": 9, "seek": 23878, "start": 230.02, "end": 238.78, "text": "إن الـ order للـ A بدي سوى ال order لـ Phi of A هذا previous theorem", "tokens": [28814, 1863, 2423, 39184, 1668, 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"temperature": 1.0}, {"id": 12, "seek": 32766, "start": 298.28, "end": 327.66, "text": "one او تلاتة او سبعة او تسعة because السبب each of واحد و تلاتة و سبعة و تسعة is of order عشر كويس مادام alpha of one ساوت يا واحد يا تلاتة يا سبعة يا تسعة معناته اكم اوتومورفزم عندى", "tokens": [546, 1975, 2407, 6055, 1211, 9307, 3660, 1975, 2407, 8608, 3555, 27884, 1975, 2407, 6055, 3794, 27884, 570, 21136, 3555, 3555, 1184, 295, 36764, 24401, 4032, 6055, 1211, 9307, 3660, 4032, 8608, 3555, 27884, 4032, 6055, 3794, 27884, 307, 295, 1668, 6225, 46309, 9122, 45865, 3794, 3714, 18513, 10943, 8961, 295, 472, 8608, 995, 35473, 35186, 36764, 24401, 35186, 6055, 1211, 9307, 3660, 35186, 8608, 3555, 27884, 35186, 6055, 3794, 27884, 20449, 8315, 47395, 1975, 24793, 1975, 35473, 20498, 13063, 5172, 11622, 2304, 43242, 7578], "avg_logprob": -0.20621366798877716, "compression_ratio": 1.7682926829268293, "no_speech_prob": 0.0, "words": [{"start": 298.28, "end": 298.92, "word": "one", "probability": 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"end": 868.58, "word": " من", "probability": 0.5654296875}, {"start": 868.58, "end": 869.86, "word": " alpha", "probability": 0.2288818359375}, {"start": 869.86, "end": 870.76, "word": " 7", "probability": 0.78173828125}, {"start": 870.76, "end": 871.6, "word": " and", "probability": 0.84912109375}, {"start": 871.6, "end": 872.4, "word": " alpha", "probability": 0.7783203125}, {"start": 872.4, "end": 873.32, "word": " 9", "probability": 0.982421875}, {"start": 873.32, "end": 874.42, "word": " are", "probability": 0.83544921875}, {"start": 874.42, "end": 877.9, "word": " automorphisms", "probability": 0.6727294921875}, {"start": 877.9, "end": 881.94, "word": " where", "probability": 0.798828125}, {"start": 881.94, "end": 883.76, "word": " كذلك", "probability": 0.9658203125}, {"start": 883.76, "end": 884.66, "word": " حيثهم", "probability": 0.76739501953125}, {"start": 884.66, "end": 885.38, "word": " اللي", "probability": 0.97412109375}, {"start": 885.38, "end": 885.56, "word": " هو", "probability": 0.9951171875}, {"start": 885.56, "end": 885.8, "word": " ال", "probability": 0.8701171875}, {"start": 885.8, "end": 886.32, "word": " alpha", "probability": 0.87890625}, {"start": 886.32, "end": 886.92, "word": " 1", "probability": 0.52099609375}, {"start": 886.92, "end": 888.04, "word": " is", "probability": 0.93798828125}, {"start": 888.04, "end": 889.12, "word": " the", "probability": 0.833984375}, {"start": 889.12, "end": 891.08, "word": " identity", "probability": 0.931640625}], "temperature": 1.0}, {"id": 35, "seek": 89257, "start": 892.01, "end": 892.57, "text": "Animal", "tokens": [7828, 10650], "avg_logprob": -0.5908203125, "compression_ratio": 0.42857142857142855, "no_speech_prob": 0.0, "words": [{"start": 892.01, "end": 892.57, "word": "Animal", "probability": 0.566650390625}], "temperature": 1.0}, {"id": 36, "seek": 90602, "start": 895.76, "end": 906.02, "text": "identity element يبقى الأن اثبتنا ان الاتومورفيزم لزد عشرة بالضبط", "tokens": [1078, 507, 4478, 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"probability": 0.9246419270833334}, {"start": 933.22, "end": 933.5, "word": " فيها", "probability": 0.980712890625}, {"start": 933.5, "end": 933.76, "word": " الا", "probability": 0.31494140625}, {"start": 933.76, "end": 934.28, "word": " اربعة", "probability": 0.77001953125}, {"start": 934.28, "end": 934.84, "word": " عناصر", "probability": 0.9518229166666666}, {"start": 934.84, "end": 935.6, "word": " وكل", "probability": 0.92138671875}, {"start": 935.6, "end": 936.08, "word": " عنصر", "probability": 0.99169921875}, {"start": 936.08, "end": 936.42, "word": " منها", "probability": 0.84765625}, {"start": 936.42, "end": 936.68, "word": " دول", "probability": 0.79345703125}, {"start": 936.68, "end": 937.18, "word": " عبارة", "probability": 0.989013671875}, {"start": 937.18, "end": 937.54, "word": " عن", "probability": 0.99462890625}, {"start": 937.54, "end": 939.4, "word": " اتومورفزم", "probability": 0.8868582589285714}, {"start": 939.4, "end": 940.76, "word": " طيب", "probability": 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"probability": 0.6728515625}, {"start": 967.14, "end": 967.64, "word": " التانية،", "probability": 0.83544921875}, {"start": 967.64, "end": 968.02, "word": " هل", "probability": 0.989990234375}, {"start": 968.02, "end": 968.66, "word": " بتبقى", "probability": 0.9488525390625}, {"start": 968.66, "end": 969.16, "word": " closed", "probability": 0.84326171875}, {"start": 969.16, "end": 969.62, "word": " فعلا", "probability": 0.9422200520833334}, {"start": 969.62, "end": 969.9, "word": " ولا", "probability": 0.87451171875}, {"start": 969.9, "end": 970.64, "word": " لأ؟", "probability": 0.8963216145833334}, {"start": 970.64, "end": 970.9, "word": " بس", "probability": 0.992431640625}, {"start": 970.9, "end": 971.6, "word": " مجرد", "probability": 0.99462890625}, {"start": 971.6, "end": 972.32, "word": " معلومات", "probability": 0.97802734375}, {"start": 972.32, "end": 972.8, "word": " كيف", "probability": 0.908203125}, {"start": 972.8, "end": 973.36, "word": " بدنا", "probability": 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"seek": 129907, "start": 1270.87, "end": 1299.07, "text": "إذا لو جيت لل group هذي و حسبت ال key ل table لكل منها يبقى ملاحظة هذي remark from", "tokens": [28814, 15730, 45164, 10874, 36081, 24976, 1594, 8032, 8848, 1829, 4032, 11331, 35457, 2655, 2423, 2141, 5296, 3199, 5296, 28820, 9154, 11296, 7251, 3555, 4587, 7578, 3714, 15040, 5016, 19913, 3660, 8032, 8848, 1829, 7942, 490], "avg_logprob": -0.305320955611564, "compression_ratio": 1.1081081081081081, "no_speech_prob": 0.0, "words": [{"start": 1270.87, "end": 1271.27, "word": "إذا", "probability": 0.736328125}, {"start": 1271.27, "end": 1271.61, "word": " لو", "probability": 0.98828125}, {"start": 1271.61, "end": 1271.95, "word": " جيت", "probability": 0.9755859375}, {"start": 1271.95, "end": 1272.21, "word": " لل", "probability": 0.6162109375}, {"start": 1272.21, "end": 1272.83, "word": " group", "probability": 0.68017578125}, {"start": 1272.83, "end": 1273.63, "word": " هذي", "probability": 0.5071614583333334}, {"start": 1273.63, 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{"start": 1766.02, "end": 1767.14, "word": " المثال", "probability": 0.9803059895833334}, {"start": 1767.14, "end": 1768.1, "word": " لاحظنا", "probability": 0.9600830078125}, {"start": 1768.1, "end": 1768.78, "word": " ان", "probability": 0.49072265625}, {"start": 1768.78, "end": 1769.34, "word": " قيمة", "probability": 0.98095703125}, {"start": 1769.34, "end": 1769.8, "word": " Alpha", "probability": 0.15673828125}, {"start": 1769.8, "end": 1770.58, "word": " تعتمد", "probability": 0.9495849609375}, {"start": 1770.58, "end": 1770.82, "word": " على", "probability": 0.81005859375}, {"start": 1770.82, "end": 1772.2, "word": " قيمة", "probability": 0.7433268229166666}, {"start": 1772.2, "end": 1772.6, "word": " Alpha", "probability": 0.89697265625}, {"start": 1772.6, "end": 1773.26, "word": " of", "probability": 0.9033203125}, {"start": 1773.26, "end": 1773.68, "word": " 1", "probability": 0.44921875}, {"start": 1773.68, "end": 1774.86, "word": " Alpha", "probability": 0.5537109375}, 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inverse هذي بدي اسميها مثلا star يبقى بداجي اقوله multiply multi", "tokens": [2304, 2304, 2655, 31377, 10874, 28259, 7251, 3555, 4587, 7578, 34105, 4724, 26108, 1829, 4724, 39648, 3224, 1670, 497, 3714, 29245, 23328, 3660, 8978, 2423, 8229, 321, 362, 16472, 2423, 497, 17340, 3714, 29245, 23328, 3660, 8978, 2423, 8229, 1975, 1829, 8592, 12602, 47302, 4117, 9673, 3615, 18513, 37977, 8032, 8848, 1829, 4724, 16254, 1975, 11242, 25513, 11296, 8978, 497, 17340, 8032, 8848, 1829, 4724, 16254, 24525, 2304, 1829, 11296, 50113, 15040, 3543, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 3224, 12972, 4825], "avg_logprob": -0.19840116937493169, "compression_ratio": 1.6557377049180328, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2271.1, "end": 2271.82, "word": "ممتاز", "probability": 0.8719482421875}, {"start": 2271.82, "end": 2272.22, "word": " جدا", "probability": 0.958740234375}, {"start": 2272.22, "end": 2273.24, "word": " يبقى", "probability": 0.8782958984375}, 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{"start": 2296.44, "end": 2297.36, "word": " multiply", "probability": 0.9150390625}, {"start": 2297.36, "end": 2299.9, "word": " multi", "probability": 0.64208984375}], "temperature": 1.0}, {"id": 94, "seek": 232566, "start": 2302.08, "end": 2325.66, "text": "ply star by R inverse we get لو ضربنا هنا في R inverse بتروح معاها S واحد ناقص S اتنين موديولو N بده يساوي Zero في R inverse اللي هو من من Zero", "tokens": [2724, 3543, 538, 497, 17340, 321, 483, 45164, 48812, 25513, 8315, 34105, 8978, 497, 17340, 39894, 32887, 5016, 20449, 995, 11296, 318, 36764, 24401, 8717, 995, 4587, 9381, 318, 1975, 2655, 1863, 9957, 3714, 2407, 16254, 12610, 2407, 426, 47525, 3224, 7251, 3794, 995, 45865, 17182, 8978, 497, 17340, 13672, 1829, 31439, 9154, 9154, 17182], "avg_logprob": -0.38002231025270056, "compression_ratio": 1.3666666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2302.0800000000004, "end": 2303.28, "word": "ply", "probability": 0.03717041015625}, {"start": 2303.28, "end": 2304.48, "word": " star", "probability": 0.2415771484375}, {"start": 2304.48, "end": 2305.68, "word": " by", "probability": 0.796875}, {"start": 2305.68, "end": 2306.58, "word": " R", "probability": 0.72509765625}, {"start": 2306.58, "end": 2307.46, "word": " inverse", "probability": 0.86474609375}, {"start": 2307.46, "end": 2308.24, "word": " we", "probability": 0.5966796875}, {"start": 2308.24, "end": 2308.92, "word": " get", "probability": 0.9453125}, {"start": 2308.92, "end": 2310.82, "word": " لو", "probability": 0.499267578125}, {"start": 2310.82, "end": 2311.42, "word": " ضربنا", "probability": 0.9609375}, {"start": 2311.42, "end": 2311.74, "word": " هنا", "probability": 0.92431640625}, {"start": 2311.74, "end": 2311.96, "word": " في", "probability": 0.8935546875}, {"start": 2311.96, "end": 2312.2, "word": " R", "probability": 0.916015625}, {"start": 2312.2, "end": 2312.76, "word": " inverse", "probability": 0.8798828125}, {"start": 2312.76, "end": 2313.38, "word": " بتروح", "probability": 0.9007161458333334}, {"start": 2313.38, "end": 2313.8, "word": " معاها", "probability": 0.8953450520833334}, {"start": 2313.8, "end": 2314.04, "word": " S", "probability": 0.169677734375}, {"start": 2314.04, "end": 2316.78, "word": " واحد", "probability": 0.7890625}, {"start": 2316.78, "end": 2317.88, "word": " ناقص", "probability": 0.95849609375}, {"start": 2317.88, "end": 2318.34, "word": " S", "probability": 0.68798828125}, {"start": 2318.34, "end": 2319.06, "word": " اتنين", "probability": 0.79302978515625}, {"start": 2319.06, "end": 2320.56, "word": " موديولو", "probability": 0.727587890625}, {"start": 2320.56, "end": 2320.92, "word": " N", "probability": 0.7861328125}, {"start": 2320.92, "end": 2321.8, "word": " بده", "probability": 0.3580322265625}, {"start": 2321.8, "end": 2322.2, "word": " يساوي", "probability": 0.871337890625}, {"start": 2322.2, "end": 2322.5, "word": " Zero", "probability": 0.415283203125}, {"start": 2322.5, "end": 2322.72, "word": " في", "probability": 0.9189453125}, {"start": 2322.72, "end": 2322.96, "word": " R", "probability": 0.97314453125}, {"start": 2322.96, "end": 2323.38, "word": " inverse", "probability": 0.89892578125}, {"start": 2323.38, "end": 2323.58, "word": " اللي", "probability": 0.74072265625}, {"start": 2323.58, "end": 2323.74, "word": " هو", "probability": 0.91943359375}, {"start": 2323.74, "end": 2323.9, "word": " من", "probability": 0.361083984375}, {"start": 2323.9, "end": 2324.98, "word": " من", "probability": 0.24365234375}, {"start": 2324.98, "end": 2325.66, "word": " Zero", "probability": 0.724609375}], "temperature": 1.0}, {"id": 95, "seek": 234566, "start": 2326.74, "end": 2345.66, "text": "طيب هذه بقدر افكها و احولها الى S1 modulo N بده يساوي ال S2 modulo N يبقى هذا معناه ان ال S1 هي نفس ال S2", "tokens": [9566, 1829, 3555, 29538, 4724, 28543, 2288, 1975, 5172, 4117, 11296, 4032, 1975, 5016, 12610, 11296, 2423, 7578, 318, 16, 1072, 13455, 426, 47525, 3224, 7251, 3794, 995, 45865, 2423, 318, 17, 1072, 13455, 426, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 16472, 2423, 318, 16, 39896, 8717, 36178, 2423, 318, 17], "avg_logprob": -0.19849537561337152, "compression_ratio": 1.3471074380165289, "no_speech_prob": 0.0, "words": [{"start": 2326.74, "end": 2327.3, "word": "طيب", "probability": 0.7032877604166666}, {"start": 2327.3, "end": 2327.7, "word": " هذه", "probability": 0.291259765625}, {"start": 2327.7, "end": 2328.1, "word": " بقدر", "probability": 0.8203125}, {"start": 2328.1, "end": 2328.62, "word": " افكها", "probability": 0.8311767578125}, {"start": 2328.62, "end": 2328.78, "word": " و", "probability": 0.95361328125}, {"start": 2328.78, "end": 2329.72, "word": " احولها", "probability": 0.9110107421875}, {"start": 2329.72, "end": 2330.58, "word": " الى", "probability": 0.8740234375}, {"start": 2330.58, "end": 2331.74, "word": " S1", "probability": 0.841796875}, {"start": 2331.74, "end": 2332.96, "word": " modulo", "probability": 0.5361328125}, {"start": 2332.96, "end": 2333.44, "word": " N", "probability": 0.86376953125}, {"start": 2333.44, "end": 2334.34, "word": " بده", "probability": 0.5517578125}, {"start": 2334.34, "end": 2334.78, "word": " يساوي", "probability": 0.8323974609375}, {"start": 2334.78, "end": 2335.0, "word": " ال", "probability": 0.69189453125}, {"start": 2335.0, "end": 2336.36, "word": " S2", "probability": 0.93017578125}, {"start": 2336.36, "end": 2337.74, "word": " modulo", "probability": 0.8857421875}, {"start": 2337.74, "end": 2338.32, "word": " N", "probability": 0.9873046875}, {"start": 2338.32, "end": 2340.06, "word": " يبقى", "probability": 0.92333984375}, {"start": 2340.06, "end": 2340.4, "word": " هذا", "probability": 0.9111328125}, {"start": 2340.4, "end": 2341.38, "word": " معناه", "probability": 0.9617513020833334}, {"start": 2341.38, "end": 2341.74, "word": " ان", "probability": 0.8486328125}, {"start": 2341.74, "end": 2342.02, "word": " ال", "probability": 0.814453125}, {"start": 2342.02, "end": 2343.22, "word": " S1", "probability": 0.972412109375}, {"start": 2343.22, "end": 2343.88, "word": " هي", "probability": 0.85693359375}, {"start": 2343.88, "end": 2344.42, "word": " نفس", "probability": 0.993408203125}, {"start": 2344.42, "end": 2344.72, "word": " ال", "probability": 0.97119140625}, {"start": 2344.72, "end": 2345.66, "word": " S2", "probability": 0.983642578125}], "temperature": 1.0}, {"id": 96, "seek": 237462, "start": 2346.7, "end": 2374.62, "text": "طبعا يبقى هك اثبت ان ال alpha is one to one بدنا نثبت ان ال alpha is on الان ال alpha is on هو ال alpha من وين لوين", "tokens": [9566, 3555, 3615, 995, 7251, 3555, 4587, 7578, 8032, 4117, 1975, 12984, 3555, 2655, 16472, 2423, 8961, 307, 472, 281, 472, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 2423, 8961, 307, 322, 2423, 7649, 2423, 8961, 307, 322, 31439, 2423, 8961, 9154, 4032, 9957, 5296, 2407, 9957], "avg_logprob": -0.33626302269597846, "compression_ratio": 1.690721649484536, "no_speech_prob": 0.0, "words": 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"word": " ال", "probability": 0.82666015625}, {"start": 2373.48, "end": 2373.8, "word": " alpha", "probability": 0.90673828125}, {"start": 2373.8, "end": 2374.0, "word": " من", "probability": 0.9609375}, {"start": 2374.0, "end": 2374.24, "word": " وين", "probability": 0.3638916015625}, {"start": 2374.24, "end": 2374.62, "word": " لوين", "probability": 0.7134602864583334}], "temperature": 1.0}, {"id": 97, "seek": 239371, "start": 2376.29, "end": 2393.71, "text": "من ZN إلى Z وانا أخدت هنا S موجودة في ZN يبقى باجي بقوله F ال S موجودة في ZN then ال S تساوي", "tokens": [27842, 1176, 45, 30731, 1176, 4032, 7649, 995, 5551, 9778, 3215, 2655, 34105, 318, 3714, 29245, 23328, 3660, 8978, 1176, 45, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 479, 2423, 318, 3714, 29245, 23328, 3660, 8978, 1176, 45, 550, 2423, 318, 6055, 3794, 995, 45865], "avg_logprob": -0.15824298955956284, "compression_ratio": 1.3644859813084111, "no_speech_prob": 0.0, "words": [{"start": 2376.29, "end": 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باجي", "probability": 0.650634765625}, {"start": 2385.39, "end": 2386.19, "word": " بقوله", "probability": 0.8587239583333334}, {"start": 2386.19, "end": 2386.77, "word": " F", "probability": 0.92724609375}, {"start": 2386.77, "end": 2387.67, "word": " ال", "probability": 0.8583984375}, {"start": 2387.67, "end": 2388.19, "word": " S", "probability": 0.78515625}, {"start": 2388.19, "end": 2389.19, "word": " موجودة", "probability": 0.98681640625}, {"start": 2389.19, "end": 2389.43, "word": " في", "probability": 0.9814453125}, {"start": 2389.43, "end": 2390.45, "word": " ZN", "probability": 0.98046875}, {"start": 2390.45, "end": 2391.39, "word": " then", "probability": 0.497802734375}, {"start": 2391.39, "end": 2392.15, "word": " ال", "probability": 0.90625}, {"start": 2392.15, "end": 2392.61, "word": " S", "probability": 0.962890625}, {"start": 2392.61, "end": 2393.71, "word": " تساوي", "probability": 0.9718017578125}], "temperature": 1.0}, {"id": 98, "seek": 242237, "start": 2396.35, "end": 2422.37, "text": "عشان رايك بقدر اكتبها هذه S مثلا في ال R inverse R منفع الله مانفعش ايه انا السما عندي لسه بجمعش كويس حتى اللحظة علي صوتك عشرين ايه", "tokens": [3615, 8592, 7649, 12602, 47302, 4117, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 29538, 318, 50113, 15040, 8978, 2423, 497, 17340, 497, 3714, 1863, 5172, 3615, 21984, 3714, 7649, 5172, 3615, 8592, 1975, 1829, 3224, 1975, 8315, 21136, 15042, 18871, 16254, 5296, 3794, 3224, 4724, 7435, 2304, 3615, 8592, 9122, 45865, 3794, 11331, 49975, 13672, 5016, 19913, 3660, 6225, 20292, 20328, 35473, 4117, 6225, 46309, 9957, 1975, 1829, 3224], "avg_logprob": -0.23899648391025166, "compression_ratio": 1.4610389610389611, "no_speech_prob": 0.0, "words": [{"start": 2396.35, "end": 2396.85, "word": "عشان", "probability": 0.62744140625}, {"start": 2396.85, "end": 2397.29, "word": " رايك", "probability": 0.6715494791666666}, {"start": 2397.29, "end": 2398.55, "word": " بقدر", "probability": 0.8681640625}, {"start": 2398.55, "end": 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أثبت ان T is onto", "tokens": [10721, 8315, 12174, 1211, 2655, 4724, 3794, 16472, 2655, 19446, 47283, 3215, 2655, 8592, 20666, 4117, 1975, 8315, 16247, 1863, 1975, 1829, 8592, 4724, 16254, 5551, 12984, 3555, 2655, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 314, 307, 3911], "avg_logprob": -0.2513671875, "compression_ratio": 1.3222222222222222, "no_speech_prob": 0.0, "words": [{"start": 2542.27, "end": 2542.59, "word": "أنا", "probability": 0.704345703125}, {"start": 2542.59, "end": 2542.83, "word": " قلت", "probability": 0.89404296875}, {"start": 2542.83, "end": 2543.03, "word": " بس", "probability": 0.876953125}, {"start": 2543.03, "end": 2543.21, "word": " انت", "probability": 0.6427001953125}, {"start": 2543.21, "end": 2543.73, "word": " مااخدتش", "probability": 0.8791015625}, {"start": 2543.73, "end": 2544.25, "word": " بالك", "probability": 0.974365234375}, {"start": 2544.25, "end": 2545.41, "word": " انا", "probability": 0.7230224609375}, {"start": 2545.41, "end": 2545.73, 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"word": " لأ", "probability": 0.91015625}, {"start": 2576.42, "end": 2577.18, "word": " حتى", "probability": 0.904296875}, {"start": 2577.18, "end": 2577.58, "word": " هذه", "probability": 0.974609375}, {"start": 2577.58, "end": 2578.04, "word": " اللحظة", "probability": 0.993408203125}, {"start": 2578.04, "end": 2578.22, "word": " لم", "probability": 0.97119140625}, {"start": 2578.22, "end": 2578.68, "word": " اثبت", "probability": 0.95751953125}, {"start": 2578.68, "end": 2579.04, "word": " انها", "probability": 0.87841796875}, {"start": 2579.04, "end": 2579.84, "word": " atomorphism", "probability": 0.9656575520833334}], "temperature": 1.0}, {"id": 106, "seek": 260046, "start": 2580.54, "end": 2600.46, "text": "مظبوط واذا طلعت atomorphism بدي بيجيلك ان صورتها R اللى عندنا وبالتالي يكون حلنا المشكلة واضحة تمام واضحة يا شباب هيك طيب يبقى انا اخدت S موجودة في Z ان ال S بقدر اكتبها SR inverse R modulo N عادي جدا", "tokens": [2304, 19913, 3555, 2407, 9566, 4032, 45636, 995, 23032, 1211, 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"end": 2611.13, "word": " هي", "probability": 0.6259765625}, {"start": 2611.13, "end": 2611.89, "word": " Alpha", "probability": 0.51708984375}, {"start": 2611.89, "end": 2612.53, "word": " of", "probability": 0.9140625}, {"start": 2612.53, "end": 2613.27, "word": " S1", "probability": 0.988525390625}], "temperature": 1.0}, {"id": 108, "seek": 264461, "start": 2614.71, "end": 2644.61, "text": "مش هي ال alpha of S يساوي SR modulo N طلعناها S1R يبقى alpha of S1 يبقى صار ال element S اللي أخدته في Z in لجتله أصل اسمه ايش اسمه S1 يبقى ال alpha انتوا ولا لا يبقى ال alpha انتوا يبقى أثبت الآن ان ال alpha اللي أخدتها دي one to one and انتوا شو ضايل عندى", "tokens": [2304, 8592, 39896, 2423, 8961, 295, 318, 7251, 3794, 995, 45865, 20840, 1072, 13455, 426, 23032, 1211, 3615, 8315, 11296, 318, 16, 49, 7251, 3555, 4587, 7578, 8961, 295, 318, 16, 7251, 3555, 4587, 7578, 20328, 9640, 2423, 4478, 318, 13672, 1829, 5551, 9778, 3215, 47395, 8978, 1176, 294, 5296, 7435, 2655, 43761, 5551, 36520, 24525, 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"probability": 0.690185546875}, {"start": 2633.11, "end": 2634.01, "word": " اسمه", "probability": 0.92431640625}, {"start": 2634.01, "end": 2634.61, "word": " S1", "probability": 0.9755859375}, {"start": 2634.61, "end": 2635.25, "word": " يبقى", "probability": 0.9718017578125}, {"start": 2635.25, "end": 2635.41, "word": " ال", "probability": 0.8974609375}, {"start": 2635.41, "end": 2635.77, "word": " alpha", "probability": 0.8154296875}, {"start": 2635.77, "end": 2636.29, "word": " انتوا", "probability": 0.5547688802083334}, {"start": 2636.29, "end": 2636.47, "word": " ولا", "probability": 0.90087890625}, {"start": 2636.47, "end": 2636.81, "word": " لا", "probability": 0.5693359375}, {"start": 2636.81, "end": 2637.79, "word": " يبقى", "probability": 0.928955078125}, {"start": 2637.79, "end": 2637.97, "word": " ال", "probability": 0.82666015625}, {"start": 2637.97, "end": 2638.39, "word": " alpha", "probability": 0.90966796875}, {"start": 2638.39, "end": 2638.79, "word": " انتوا", "probability": 0.9148763020833334}, {"start": 2638.79, "end": 2639.03, "word": " يبقى", "probability": 0.9664306640625}, {"start": 2639.03, "end": 2639.41, "word": " أثبت", "probability": 0.80303955078125}, {"start": 2639.41, "end": 2639.89, "word": " الآن", "probability": 0.74365234375}, {"start": 2639.89, "end": 2640.53, "word": " ان", "probability": 0.662109375}, {"start": 2640.53, "end": 2640.69, "word": " ال", "probability": 0.830078125}, {"start": 2640.69, "end": 2640.95, "word": " alpha", "probability": 0.8837890625}, {"start": 2640.95, "end": 2641.09, "word": " اللي", "probability": 0.961669921875}, {"start": 2641.09, "end": 2641.59, "word": " أخدتها", "probability": 0.8396484375}, {"start": 2641.59, "end": 2641.71, "word": " دي", "probability": 0.7115478515625}, {"start": 2641.71, "end": 2641.97, "word": " one", "probability": 0.75732421875}, {"start": 2641.97, "end": 2642.29, "word": " to", "probability": 0.912109375}, {"start": 2642.29, "end": 2642.75, "word": " one", "probability": 0.95556640625}, {"start": 2642.75, "end": 2643.21, "word": " and", "probability": 0.7978515625}, {"start": 2643.21, "end": 2643.55, "word": " انتوا", "probability": 0.8681640625}, {"start": 2643.55, "end": 2643.79, "word": " شو", "probability": 0.87841796875}, {"start": 2643.79, "end": 2644.05, "word": " ضايل", "probability": 0.798583984375}, {"start": 2644.05, "end": 2644.61, "word": " عندى", "probability": 0.762939453125}], "temperature": 1.0}, {"id": 109, "seek": 267393, "start": 2645.37, "end": 2673.93, "text": "أثبت أنه بتخدم خاصية ال isomorphism لذلك بتروح أخد alpha of مثلا a زائد ال .. او S1 زائد S2 خليها نفس الرمز خليها S1 و S2 S1 زائد S2 بده يساوي ال S1 و ال S2 أرقام هذه", "tokens": [10721, 12984, 3555, 2655, 14739, 3224, 39894, 9778, 40448, 16490, 33546, 10632, 2423, 307, 32702, 1434, 5296, 8848, 23275, 39894, 32887, 5016, 5551, 9778, 3215, 8961, 295, 50113, 15040, 257, 30767, 16373, 3215, 2423, 4386, 1975, 2407, 318, 16, 30767, 16373, 3215, 318, 17, 16490, 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"word": " بتروح", "probability": 0.8636067708333334}, {"start": 2650.35, "end": 2650.93, "word": " أخد", "probability": 0.8216145833333334}, {"start": 2650.93, "end": 2651.85, "word": " alpha", "probability": 0.5}, {"start": 2651.85, "end": 2652.75, "word": " of", "probability": 0.54833984375}, {"start": 2652.75, "end": 2653.51, "word": " مثلا", "probability": 0.921630859375}, {"start": 2653.51, "end": 2653.95, "word": " a", "probability": 0.55810546875}, {"start": 2653.95, "end": 2654.57, "word": " زائد", "probability": 0.7571614583333334}, {"start": 2654.57, "end": 2654.79, "word": " ال", "probability": 0.166259765625}, {"start": 2654.79, "end": 2655.09, "word": " ..", "probability": 0.460205078125}, {"start": 2655.09, "end": 2656.99, "word": " او", "probability": 0.762939453125}, {"start": 2656.99, "end": 2657.69, "word": " S1", "probability": 0.7333984375}, {"start": 2657.69, "end": 2658.23, "word": " زائد", "probability": 0.8411458333333334}, {"start": 2658.23, "end": 2658.99, "word": " S2", "probability": 0.992431640625}, {"start": 2658.99, "end": 2659.45, "word": " خليها", "probability": 0.8177083333333334}, {"start": 2659.45, "end": 2659.77, "word": " نفس", "probability": 0.997314453125}, {"start": 2659.77, "end": 2660.39, "word": " الرمز", "probability": 0.8404947916666666}, {"start": 2660.39, "end": 2661.27, "word": " خليها", "probability": 0.8186848958333334}, {"start": 2661.27, "end": 2661.85, "word": " S1", "probability": 0.98486328125}, {"start": 2661.85, "end": 2662.03, "word": " و", "probability": 0.94287109375}, {"start": 2662.03, "end": 2662.63, "word": " S2", "probability": 0.83642578125}, {"start": 2662.63, "end": 2664.05, "word": " S1", "probability": 0.899169921875}, {"start": 2664.05, "end": 2665.17, "word": " زائد", "probability": 0.9544270833333334}, {"start": 2665.17, "end": 2666.13, "word": " S2", "probability": 0.993896484375}, {"start": 2666.13, "end": 2666.91, "word": " بده", "probability": 0.52880859375}, {"start": 2666.91, "end": 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"probability": 0.911376953125}, {"start": 2678.52, "end": 2678.86, "word": " زي", "probability": 0.96533203125}, {"start": 2678.86, "end": 2679.0, "word": " ما", "probability": 0.9013671875}, {"start": 2679.0, "end": 2679.36, "word": " بدي", "probability": 0.7274169921875}, {"start": 2679.36, "end": 2680.38, "word": " او", "probability": 0.9716796875}, {"start": 2680.38, "end": 2681.5, "word": " خلينا", "probability": 0.7457275390625}, {"start": 2681.5, "end": 2682.12, "word": " بلاشي", "probability": 0.9385986328125}, {"start": 2682.12, "end": 2682.88, "word": " نغلط", "probability": 0.70159912109375}, {"start": 2682.88, "end": 2683.56, "word": " شوية", "probability": 0.9202473958333334}, {"start": 2683.56, "end": 2684.84, "word": " هذه", "probability": 0.57177734375}, {"start": 2684.84, "end": 2685.72, "word": " قولنا", "probability": 0.8642578125}, {"start": 2685.72, "end": 2685.98, "word": " is", "probability": 0.8525390625}, {"start": 2685.98, "end": 2686.36, "word": " on", "probability": 0.529296875}, {"start": 2686.36, "end": 2686.82, "word": " to", "probability": 0.470947265625}, {"start": 2686.82, "end": 2687.7, "word": " خلصنا", "probability": 0.9766845703125}, {"start": 2687.7, "end": 2688.2, "word": " منها", "probability": 0.993896484375}, {"start": 2688.2, "end": 2689.08, "word": " S1", "probability": 0.519775390625}, {"start": 2689.08, "end": 2689.3, "word": " و", "probability": 0.94189453125}, {"start": 2689.3, "end": 2690.36, "word": " S2", "probability": 0.80224609375}, {"start": 2690.36, "end": 2691.34, "word": " مظبوط", "probability": 0.74833984375}, {"start": 2691.34, "end": 2691.84, "word": " حسب", "probability": 0.954345703125}, {"start": 2691.84, "end": 2692.02, "word": " ال", "probability": 0.96728515625}, {"start": 2692.02, "end": 2692.62, "word": " definition", "probability": 0.84619140625}, {"start": 2692.62, "end": 2693.94, "word": " هذه", "probability": 0.85546875}, {"start": 2693.94, "end": 2694.44, "word": " بدها", "probability": 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واحد وهذه Alpha of S اتنى؟ يبقى بناء عليها صارت هذه ايش؟ صارت Atomorphism لأنها من ال group إلى نفسها يبقى هنا Sir Alpha is an Atomorphism", "tokens": [3224, 1211, 10721, 1829, 14851, 29538, 13672, 1829, 31439, 20588, 295, 318, 36764, 24401, 37037, 24192, 20588, 295, 318, 1975, 2655, 1863, 7578, 22807, 7251, 3555, 4587, 7578, 44945, 16606, 25894, 11296, 20328, 9640, 2655, 29538, 1975, 1829, 8592, 22807, 20328, 9640, 2655, 1711, 32702, 1434, 5296, 33456, 11296, 9154, 2423, 1594, 30731, 8717, 36178, 11296, 7251, 3555, 4587, 7578, 34105, 6144, 20588, 307, 364, 1711, 32702, 1434], "avg_logprob": -0.32042571081631427, "compression_ratio": 1.5121951219512195, "no_speech_prob": 0.0, "words": [{"start": 2725.68, "end": 2726.52, "word": "هلأيست", "probability": 0.62137451171875}, {"start": 2726.52, "end": 2727.22, "word": " هذه", "probability": 0.8291015625}, {"start": 2727.22, "end": 2727.9, "word": " اللي", "probability": 0.6441650390625}, {"start": 2727.9, "end": 2728.08, "word": " هو", 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فماعناش مشكلة", "tokens": [1829, 3555, 4587, 7578, 29538, 39896, 314, 295, 33286, 16070, 2655, 7649, 10632, 39896, 314, 295, 20588, 7251, 3555, 4587, 7578, 5551, 12984, 3555, 2655, 8315, 46740, 14739, 314, 295, 33286, 20588, 39896, 314, 33286, 20588, 45164, 12602, 2407, 33753, 24976, 4117, 2655, 16758, 39896, 30544, 10874, 46152, 2423, 2407, 11242, 3615, 5551, 9778, 3215, 5296, 4117, 314, 20588, 33286, 4032, 3224, 8315, 6055, 39648, 5296, 4117, 314, 20588, 314, 6156, 15042, 3615, 1863, 33599, 37893, 28820, 3660], "avg_logprob": -0.24841771774654148, "compression_ratio": 1.6204819277108433, "no_speech_prob": 0.0, "words": [{"start": 3104.44, "end": 3105.18, "word": "يبقى", "probability": 0.846435546875}, {"start": 3105.18, "end": 3105.66, "word": " هذه", "probability": 0.64404296875}, {"start": 3105.66, "end": 3106.34, "word": " هي", "probability": 0.5185546875}, {"start": 3106.34, "end": 3107.12, "word": " T", "probability": 0.7470703125}, {"start": 3107.12, "end": 3108.12, "word": " 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0.92138671875}, {"start": 3115.36, "end": 3115.82, "word": " Beta", "probability": 0.9306640625}, {"start": 3115.82, "end": 3116.46, "word": " Alpha", "probability": 0.923828125}, {"start": 3116.46, "end": 3117.04, "word": " هي", "probability": 0.94091796875}, {"start": 3117.04, "end": 3117.5, "word": " T", "probability": 0.95556640625}, {"start": 3117.5, "end": 3118.26, "word": " Beta", "probability": 0.88818359375}, {"start": 3118.26, "end": 3118.84, "word": " Alpha", "probability": 0.98388671875}, {"start": 3118.84, "end": 3119.46, "word": " لو", "probability": 0.84521484375}, {"start": 3119.46, "end": 3119.82, "word": " روحت", "probability": 0.7859700520833334}, {"start": 3119.82, "end": 3120.64, "word": " للكتاب", "probability": 0.96875}, {"start": 3120.64, "end": 3121.24, "word": " هيكون", "probability": 0.6712646484375}, {"start": 3121.24, "end": 3121.6, "word": " جلب", "probability": 0.672119140625}, {"start": 3121.6, "end": 3122.04, "word": " الوضع", "probability": 0.990234375}, {"start": 3122.04, "end": 3122.46, "word": " أخد", "probability": 0.7042643229166666}, {"start": 3122.46, "end": 3122.64, "word": " لك", "probability": 0.6240234375}, {"start": 3122.64, "end": 3122.86, "word": " T", "probability": 0.93115234375}, {"start": 3122.86, "end": 3123.26, "word": " Alpha", "probability": 0.77490234375}, {"start": 3123.26, "end": 3123.72, "word": " Beta", "probability": 0.9150390625}, {"start": 3123.72, "end": 3124.52, "word": " وهنا", "probability": 0.7311197916666666}, {"start": 3124.52, "end": 3124.78, "word": " تقول", "probability": 0.5318603515625}, {"start": 3124.78, "end": 3124.98, "word": " لك", "probability": 0.82666015625}, {"start": 3124.98, "end": 3125.3, "word": " T", "probability": 0.88671875}, {"start": 3125.3, "end": 3126.02, "word": " Alpha", "probability": 0.96240234375}, {"start": 3126.02, "end": 3126.32, "word": " T", "probability": 0.58154296875}, {"start": 3126.32, "end": 3127.06, "word": " فماعناش", "probability": 0.718603515625}, {"start": 3127.06, "end": 3127.58, "word": " مشكلة", "probability": 0.9803059895833334}], "temperature": 1.0}, {"id": 129, "seek": 315573, "start": 3127.83, "end": 3155.73, "text": "بس بدل ما اقول لك ان alpha of one times بقول لك beta of one time اذا لا مشكلة انا اتعمد اجيبك بشكل هذا حتى تتعرف انه ليس بالضرورة قرآن كريم لكن احنا فهمنا هذا الكلام يبقى .. يبقى بناء عليه so T is an isomorphism هذا بدي اعطيلك ان ال atomorphism", "tokens": [3555, 3794, 47525, 1211, 19446, 1975, 39648, 5296, 4117, 16472, 8961, 295, 472, 1413, 4724, 39648, 5296, 4117, 9861, 295, 472, 565, 1975, 15730, 20193, 37893, 28820, 3660, 1975, 8315, 1975, 2655, 25957, 3215, 1975, 7435, 1829, 3555, 4117, 4724, 8592, 28820, 23758, 11331, 49975, 6055, 2655, 3615, 28480, 16472, 3224, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 12174, 2288, 148, 48506, 9122, 16572, 2304, 44381, 1975, 5016, 8315, 6156, 16095, 8315, 23758, 2423, 28820, 10943, 7251, 3555, 4587, 7578, 4386, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 370, 314, 307, 364, 307, 32702, 1434, 23758, 4724, 16254, 1975, 3615, 9566, 1829, 23275, 16472, 2423, 12018, 18191, 1434], "avg_logprob": -0.20326835573266405, "compression_ratio": 1.6725663716814159, "no_speech_prob": 0.0, "words": [{"start": 3127.83, "end": 3128.13, "word": "بس", "probability": 0.8779296875}, {"start": 3128.13, "end": 3128.41, "word": " بدل", "probability": 0.97705078125}, {"start": 3128.41, "end": 3128.53, "word": " ما", "probability": 0.6171875}, {"start": 3128.53, "end": 3128.71, "word": " اقول", "probability": 0.7088623046875}, {"start": 3128.71, "end": 3128.87, "word": " لك", "probability": 0.62890625}, {"start": 3128.87, "end": 3129.03, "word": " ان", "probability": 0.434814453125}, {"start": 3129.03, "end": 3129.19, "word": " alpha", "probability": 0.125244140625}, {"start": 3129.19, "end": 3129.41, "word": " of", "probability": 0.75732421875}, {"start": 3129.41, "end": 3129.55, "word": " one", "probability": 0.92138671875}, {"start": 3129.55, "end": 3129.85, "word": " times", "probability": 0.5498046875}, {"start": 3129.85, "end": 3130.13, "word": " بقول", "probability": 0.852294921875}, {"start": 3130.13, "end": 3130.33, "word": " لك", "probability": 0.90234375}, {"start": 3130.33, "end": 3130.83, "word": " beta", "probability": 0.69775390625}, {"start": 3130.83, "end": 3131.27, "word": " of", "probability": 0.978515625}, {"start": 3131.27, "end": 3131.73, "word": " one", "probability": 0.95849609375}, {"start": 3131.73, "end": 3132.53, "word": " time", "probability": 0.51123046875}, {"start": 3132.53, "end": 3133.15, "word": " اذا", "probability": 0.7059326171875}, {"start": 3133.15, "end": 3133.41, "word": " لا", "probability": 0.86474609375}, {"start": 3133.41, "end": 3133.89, "word": " مشكلة", "probability": 0.97802734375}, {"start": 3133.89, "end": 3134.11, "word": " انا", "probability": 0.90283203125}, {"start": 3134.11, "end": 3134.71, "word": " اتعمد", "probability": 0.906494140625}, {"start": 3134.71, "end": 3135.15, "word": " اجيبك", "probability": 0.95615234375}, {"start": 3135.15, "end": 3135.49, "word": " بشكل", "probability": 0.9593098958333334}, {"start": 3135.49, "end": 3135.87, "word": " هذا", "probability": 0.97119140625}, {"start": 3135.87, "end": 3136.41, "word": " حتى", "probability": 0.88037109375}, {"start": 3136.41, "end": 3136.77, "word": " تتعرف", "probability": 0.79925537109375}, {"start": 3136.77, "end": 3137.09, "word": " انه", "probability": 0.9267578125}, {"start": 3137.09, "end": 3137.49, "word": " ليس", "probability": 0.9560546875}, {"start": 3137.49, "end": 3138.27, "word": " بالضرورة", "probability": 0.97294921875}, {"start": 3138.27, "end": 3138.97, "word": " قرآن", "probability": 0.8763427734375}, {"start": 3138.97, "end": 3139.45, "word": " كريم", "probability": 0.9601236979166666}, {"start": 3139.45, "end": 3139.77, "word": " لكن", "probability": 0.892578125}, {"start": 3139.77, "end": 3140.25, "word": " احنا", "probability": 0.9873046875}, {"start": 3140.25, "end": 3141.13, "word": " فهمنا", "probability": 0.98486328125}, {"start": 3141.13, "end": 3141.57, "word": " هذا", "probability": 0.9716796875}, {"start": 3141.57, "end": 3142.23, "word": " الكلام", "probability": 0.9384765625}, {"start": 3142.23, "end": 3143.47, "word": " يبقى", "probability": 0.9710693359375}, {"start": 3143.47, "end": 3143.49, "word": " ..", "probability": 0.321044921875}, {"start": 3143.49, "end": 3144.23, "word": " يبقى", "probability": 0.9835205078125}, {"start": 3144.23, "end": 3144.69, "word": " بناء", "probability": 0.9189453125}, {"start": 3144.69, "end": 3145.31, "word": " عليه", "probability": 0.9765625}, {"start": 3145.31, "end": 3146.37, "word": " so", "probability": 0.21923828125}, {"start": 3146.37, "end": 3147.87, "word": " T", "probability": 0.13525390625}, {"start": 3147.87, "end": 3149.07, "word": " is", "probability": 0.89501953125}, {"start": 3149.07, "end": 3150.07, "word": " an", "probability": 0.79638671875}, {"start": 3150.07, "end": 3151.57, "word": " isomorphism", "probability": 0.96728515625}, {"start": 3151.57, "end": 3152.23, "word": " هذا", "probability": 0.95166015625}, {"start": 3152.23, "end": 3152.59, "word": " بدي", "probability": 0.753662109375}, {"start": 3152.59, "end": 3153.29, "word": " اعطيلك", "probability": 0.8755859375}, {"start": 3153.29, "end": 3154.01, "word": " ان", "probability": 0.90576171875}, {"start": 3154.01, "end": 3154.35, "word": " ال", "probability": 0.9677734375}, {"start": 3154.35, "end": 3155.73, "word": " atomorphism", "probability": 0.6238606770833334}], "temperature": 1.0}, {"id": 130, "seek": 316323, "start": 3155.91, "end": 3163.23, "text": "لزد ان ايزو مارفك ل يو ان من الآن فصاعدا", "tokens": [1211, 11622, 3215, 16472, 1975, 1829, 11622, 2407, 3714, 9640, 5172, 4117, 5296, 7251, 2407, 16472, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995], "avg_logprob": -0.37749999046325683, "compression_ratio": 1.0597014925373134, "no_speech_prob": 0.0, "words": [{"start": 3155.91, "end": 3157.05, "word": "لزد", "probability": 0.5244140625}, {"start": 3157.05, "end": 3157.47, "word": " ان", "probability": 0.50927734375}, {"start": 3157.47, "end": 3158.51, "word": " ايزو", "probability": 0.74981689453125}, {"start": 3158.51, "end": 3159.27, "word": " مارفك", "probability": 0.8822021484375}, {"start": 3159.27, "end": 3159.85, "word": " ل", "probability": 0.7373046875}, {"start": 3159.85, "end": 3160.29, "word": " يو", "probability": 0.5504150390625}, {"start": 3160.29, "end": 3160.63, "word": " ان", "probability": 0.79443359375}, {"start": 3160.63, "end": 3161.29, "word": " من", "probability": 0.9658203125}, {"start": 3161.29, "end": 3161.97, "word": " الآن", "probability": 0.6368408203125}, {"start": 3161.97, "end": 3163.23, "word": " فصاعدا", "probability": 0.9107421875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3165.62275, "duration_after_vad": 3032.512499999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ec1a76d80de6bafa3473918d51e602821c51023a
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_postprocess.srt
@@ -0,0 +1,1740 @@
+1
+00:00:21,280 --> 00:00:24,820
+بسم الله الرحمن الرحيم المرة اللى فاتت و اللى
+
+2
+00:00:24,820 --> 00:00:29,380
+قبلها أخدنا تعريف ل group و بدأنا ناخد أمثلة على
+
+3
+00:00:29,380 --> 00:00:35,340
+ذلك و أخدنا عشرة من الأمثلة و الآن بنكمل برضه بدل
+
+4
+00:00:35,340 --> 00:00:39,360
+المثال اتنين على نفس الموضوع المثال الرقم أحداشر
+
+5
+00:00:39,360 --> 00:00:47,210
+بيقول افترض جي كل ال X اللى موجودة في ال Qفي ال
+
+6
+00:00:47,210 --> 00:00:52,010
+set of rational numbers وليس فقط كل ال X الموجودة
+
+7
+00:00:52,010 --> 00:00:57,390
+في ال IQ بحيث ال X لا تساوي واحد يبقى احنا عندنا
+
+8
+00:00:57,390 --> 00:01:04,070
+اعداد 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 يسوى a زائد b
+
+11
+00:01:13,540 --> 00:01:19,500
+ناقص ال a b يبقى مجموع العددين ناقص حاصل ضربهم
+
+12
+00:01:19,500 --> 00:01:23,500
+كلها على بعضها هذه بدي أسميها ال operation star
+
+13
+00:01:23,500 --> 00:01:30,860
+لكل ال a و b الموجودة في gهل الـ G و الـ Star هدى
+
+14
+00:01:30,860 --> 00:01:36,260
+اي group ولا لأ يبقى انا بروح بسبحة ثمانة الثلاثة
+
+15
+00:01:36,260 --> 00:01:40,320
+شروط لإعطانيها binary operation بدي أشوف هل الـ
+
+16
+00:01:40,320 --> 00:01:44,380
+Star هدى associative هل ال identity element موجود
+
+17
+00:01:44,380 --> 00:01:50,320
+هل المعكوس لكل عنصر موجود ام 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 أخد تلت عناصر موجودة في ال group G يبقى
+
+20
+00:02:04,740 --> 00:02:10,280
+بداجي أقوله let ال A والB والC موجودة في G then
+
+21
+00:02:11,170 --> 00:02:18,770
+بتروح اخد a star b star c اشوف كده شو ساوي بدي اجي
+
+22
+00:02:18,770 --> 00:02:23,950
+الان ل a star b a star b هي معرفة يبقى بدي اشيلها
+
+23
+00:02:23,950 --> 00:02:29,950
+و احط اللي هي القيمة تبعتها يبقى a زائد ال b ناقص
+
+24
+00:02:29,950 --> 00:02:38,060
+ال a b هي ال star و هي cالان هذا كله صار عنصر جديد
+
+25
+00:02:38,060 --> 00:02:44,940
+في ال group اللي عندنا جي او في الست اللي عندنا جي
+
+26
+00:02:44,940 --> 00:02:50,280
+يبقى هذا العنصر بدي اعمله star مع c ال star بين
+
+27
+00:02:50,280 --> 00:02:54,960
+two عنصر يمكن اقول الاول زائد التاني ناقص حصل ضرب
+
+28
+00:02:54,960 --> 00:03:00,900
+الاول في الثاني اذا هذا بدي يساوي الاول زائد b
+
+29
+00:03:00,900 --> 00:03:09,000
+ناقص الabزائد الثاني اللي هو C تمام ناقص حاصل
+
+30
+00:03:09,000 --> 00:03:15,900
+ضربهما يبقى ناقص A زائد B ناقص ال A و ال B كله في
+
+31
+00:03:15,900 --> 00:03:20,540
+مين؟ في ال C يبقى هاي طبق لل start طبق لل
+
+32
+00:03:20,540 --> 00:03:25,370
+definition اللي فوقبدي اشوف 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 عفوا
+
+34
+00:03:37,230 --> 00:03:49,420
+ناقص ac ac بالترتيب ناقص bc زائد abcهذا ال term
+
+35
+00:03:49,420 --> 00:03:55,520
+الأول بده أشوف ال term التاني بده أشوف ال a star b
+
+36
+00:03:55,520 --> 00:04:01,670
+star c شو بده يعطينييبقى بدروح أحسبله بي ستار سي
+
+37
+00:04:01,670 --> 00:04:08,410
+يبقى هذا ال a اللي برا وهذا ال star وهيجوز بي زائد
+
+38
+00:04:08,410 --> 00:04:15,690
+سي ناقص بي سي طبق ال definition اللي عرفناها ال
+
+39
+00:04:15,690 --> 00:04:20,100
+operation أو ال binary operation اللي عندنابتطبق
+
+40
+00:04:20,100 --> 00:04:24,680
+ال binary operation كمان مرة يبقى الأول زائد
+
+41
+00:04:24,680 --> 00:04:29,600
+التاني ناقص حاصل ضرب الأول في الثاني يبقى هذا
+
+42
+00:04:29,600 --> 00:04:38,720
+الأول زائد التاني بزائد c ناقص bc ناقص حاصل ضرب
+
+43
+00:04:38,720 --> 00:04:48,280
+الأول في الثاني بزائد c ناقص bc هذا الكلام يساوي a
+
+44
+00:04:49,470 --> 00:05:02,190
+A زائد B زائد C ناقص BC ناقص AB ناقص AC زائد ABC
+
+45
+00:05:02,190 --> 00:05:10,430
+طلعلي هذه رقم واحد وهذه رقم اتنينتعالى نطلع على
+
+46
+00:05:10,430 --> 00:05:14,370
+رقم واحد و رقم اتنين هل اتنين 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
+التلاتة دول هم هما زائد حصل ضرب التلاتة زائد حصل
+
+50
+00:05:32,970 --> 00:05:38,950
+ضرب التلاتةيبقى بناء علي اتنين هذول مالهم بيسووا
+
+51
+00:05:38,950 --> 00:05:47,930
+بعض يبقى بروح بقوله هنا from واحد and اتنين we
+
+52
+00:05:47,930 --> 00:06:00,720
+have ان ال a star bstar c بده يساوي a star b star
+
+53
+00:06:00,720 --> 00:06:06,600
+c يبقى هذا معناته ان ال star مالها is associative
+
+54
+00:06:06,600 --> 00:06:18,360
+يبقى هنا so ال 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 خلّصنا النقطة الأولى بدي أجل النقطة التانية
+
+57
+00:06:32,280 --> 00:06:40,240
+بدي أثبت أنه في عندي identity element وطبقا لهذه
+
+58
+00:06:40,240 --> 00:06:44,040
+العملية بدي أعرفش إيه شكل هذا ال identity element
+
+59
+00:06:44,040 --> 00:06:50,120
+إذا أنا هفترض أن عندي identity element E وشوف ال E
+
+60
+00:06:50,120 --> 00:06:54,450
+بقدر أجيب له قيمة ولا بقدرشإذا قدرنا نجيب له قيمة
+
+61
+00:06:54,450 --> 00:06:58,330
+معناته موجود ماقدرنا معناته 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
+ال E is the identity element of
+
+64
+00:07:19,170 --> 00:07:26,450
+Gافترض ان ايه ال identity element في g افترض كمان
+
+65
+00:07:26,450 --> 00:07:42,690
+ان ال a موجود في g يبقى then ال e star a بدي اعرف
+
+66
+00:07:42,690 --> 00:07:50,190
+ايه شكل ال e هذي لذلك بروح اخد اي واحدة من هذولأذا
+
+67
+00:07:50,190 --> 00:07:58,010
+لو أخدت ال E star ايه يسوى ايه امبليزه؟ بدي أطبخ
+
+68
+00:07:58,010 --> 00:08:02,250
+تعريف ال star اللي عندنا هذه على الجزء اللي عندنا
+
+69
+00:08:02,250 --> 00:08:10,290
+هذا يبقى الأول زائدي الثاني ناقص حاصل ضرب الأول في
+
+70
+00:08:10,290 --> 00:08:18,590
+الثاني كل هذا بده سوى مين؟ بده سوى ال A itselfطيب
+
+71
+00:08:18,590 --> 00:08:24,110
+احنا بنشتغل في مين؟ في rational numbers اعداد
+
+72
+00:08:24,110 --> 00:08:30,770
+جذرية عادية اذا هذا لو جبت عند هذا بروح اذا هذا
+
+73
+00:08:30,770 --> 00:08:37,490
+هيعطيني ما يأتي ان ال E نقص ال E في ايه؟ بيكون سوى
+
+74
+00:08:37,490 --> 00:08:39,490
+كده؟ بيكون سوى Zero
+
+75
+00:08:45,960 --> 00:08:52,440
+يبقى هذا معناه ان ال E في واحد ناقص ال A يبقى يسوى
+
+76
+00:08:52,440 --> 00:08:57,320
+Zero يبقى هذا معناه ان ال E يسوى Zero على واحد
+
+77
+00:08:57,320 --> 00:08:58,440
+ناقص ال 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 معناته كم؟ Zero يبقى هنا سواء الـ E Identity
+
+80
+00:09:17,900 --> 00:09:31,780
+Element of GS الـ E بده يساوي Zeroطيب يبقى صار ال
+
+81
+00:09:31,780 --> 00:09:36,700
+identity element exist الان بدنا نثبت ان ال
+
+82
+00:09:36,700 --> 00:09:43,100
+inverse element كذلك ماله exist لذلك بداجي اقول
+
+83
+00:09:43,100 --> 00:09:53,060
+هنا النقطة الثالثة والاخيرة 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 يسوى b star a
+
+86
+00:10:08,190 --> 00:10:13,990
+يسوى ال identity element اللي هو مين ال zero هاخد
+
+87
+00:10:13,990 --> 00:10:22,910
+أي واحدة فيهميبقى a star بي بدي ساوي a زائد بي
+
+88
+00:10:22,910 --> 00:10:29,430
+ناقص ال a بي بدي ساوي قداش بدي ساوي zero طلعلي
+
+89
+00:10:29,430 --> 00:10:35,510
+لهذه أنا ببحث عن مين عن بي إذا بدي أخلي بي في
+
+90
+00:10:35,510 --> 00:10:40,180
+ناحية والباقي كله في ناحية تانيةيبقى هذه ايش
+
+91
+00:10:40,180 --> 00:10:48,890
+هتعطيني هتعطيني ان ال a يساوي a في b ناقص bأو الـ
+
+92
+00:10:48,890 --> 00:10:56,590
+A بدي ساوي اللي هو A ناقص واحد في B أو الـ B بدي
+
+93
+00:10:56,590 --> 00:11:03,390
+ساوي A على A ناقص واحد يبقى هذا الشكل ال inverse
+
+94
+00:11:03,390 --> 00:11:12,150
+element يبقى B تساوي A على A ناقص واحد 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 ايش رأيك انا جبت
+
+97
+00:11:26,860 --> 00:11:31,160
+ال zero element و جبت ال inverse element حابب
+
+98
+00:11:31,160 --> 00:11:37,220
+اتأكد شغلي هذا صح ولا لأ انا بدعي انه صح 100% لكن
+
+99
+00:11:37,220 --> 00:11:43,020
+حابب اتأكد حابب اتأكد كيف لو جبت a star zero لازم
+
+100
+00:11:43,020 --> 00:11:48,470
+يعطيني mainالـ 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 أصح أو لا؟ الـ A
+
+102
+00:11:48,690 --> 00:11:50,030
+أصح أو لا؟ الـ A 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 أصح أو لا؟ الـ A
+
+104
+00:11:53,870 --> 00:11:53,970
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+105
+00:11:53,970 --> 00:11:57,170
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+106
+00:11:57,170 --> 00:12:01,620
+أصح أو لا؟ الـ A أصح أو لايبقى أنا بناء عليه بقدر
+
+107
+00:12:01,620 --> 00:12:11,480
+أقول رص و هكذا ال g و ال star is a group لكن لو
+
+108
+00:12:11,480 --> 00:12:16,280
+جيت في ال ه مش هيك بدأ أتأكد من صحة كلامي بداجي
+
+109
+00:12:16,280 --> 00:12:23,600
+أخد a star is zeroهذا لازم يطلع جداش a مشانيك
+
+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 zeroطبعا هدف zero و هدف 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 ال zero star a بده يساوي ال a
+
+114
+00:12:50,860 --> 00:12:59,860
+and بده اخد a star bأنا ادعيت ان ب هو معكوس ال a
+
+115
+00:12:59,860 --> 00:13:03,740
+يبقى لما انا اعمل star في مابينهما لازم يطلع ال
+
+116
+00:13:03,740 --> 00:13:08,100
+identity element اللي هو mean ال zero يبقى هذا
+
+117
+00:13:08,100 --> 00:13:15,820
+الكلام بده يساوي a star ب هي موجودة عندى a على a
+
+118
+00:13:15,820 --> 00:13:21,800
+minus ال oneيبقى 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 يساويلو حتى المقامات
+
+121
+00:13:39,370 --> 00:13:46,370
+للكل بصير a ناقص واحد بصير هنا a في a ناقص واحد
+
+122
+00:13:46,370 --> 00:13:55,280
+زائد ال a ناقص ال a تربيةهذه لو فكيتها بيصير a
+
+123
+00:13:55,280 --> 00:14:03,580
+تربيع ناقص ال a زائد ال a ناقص ال a تربيع كله على
+
+124
+00:14:03,580 --> 00:14:12,340
+a ناقص واحد أظن كده البسط هذا بيطلع0 على a-1 يبقى
+
+125
+00:14:12,340 --> 00:14:17,560
+يساوي 0 يبقى فعلا هذا هو معكوس ال element اللي
+
+126
+00:14:17,560 --> 00:14:21,800
+موجود هنا طبعا لم ناخد في الأمثلة السابقة العشرة
+
+127
+00:14:21,800 --> 00:14:27,020
+أمثلة السابقة ولا مثال أخدنا بهذا الشكل لأن كان من
+
+128
+00:14:27,020 --> 00:14:30,720
+السهل أو بكل بساطةكان ممكن نجيب ال identity
+
+129
+00:14:30,720 --> 00:14:34,700
+element و ال inverse element بس لما صارت ال
+
+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 ال tacticبعد ذلك تفترض ان عندك ال identity
+
+134
+00:14:51,680 --> 00:14:56,400
+element تستنتج ما هو شكله بعد ذلك تفترض ان عندك
+
+135
+00:14:56,400 --> 00:15:01,760
+inverse element وتستنتج ما هو شكل هذا ال 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 الخاصةالان بنعطي مثال
+
+138
+00:15:17,700 --> 00:15:24,040
+اخر على ال 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 او
+
+140
+00:15:28,500 --> 00:15:32,840
+معلومة على هذا المثال او ما إلى ذلك المثال هذا
+
+141
+00:15:32,840 --> 00:15:40,320
+بنسميه symmetry of a square او 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 اتنين في اربعة اللي هو
+
+145
+00:16:29,480 --> 00:16:30,800
+بده يسوى تمانية
+
+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 2Nيعني الرقم
+
+150
+00:17:06,420 --> 00:17:11,140
+اللي عندك هدا دائما و قبلها بتضربه في كده؟ في
+
+151
+00:17:11,140 --> 00:17:16,080
+اتنين اللي انا بدنا نشوف ليش سمناها symmetries of
+
+152
+00:17:16,080 --> 00:17:22,380
+a² هذي ال group انت 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 ثناء السطوحيعني 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 أخد مربع المربع هذا بالشكل اللي عندنا
+
+157
+00:17:49,340 --> 00:17:54,140
+هنا و بدي أعطيه تسميات مشان نتقيد بالتسمية اللي
+
+158
+00:17:54,140 --> 00:17:59,820
+بالكتاب مشان ماصيرش 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 بدى اعمل فيه دورانات يعني انت قدامك وجه
+
+161
+00:18:16,690 --> 00:18:21,890
+مظبوط لكن الوجه في ناحية التانية احيانا بدى اخلي
+
+162
+00:18:21,890 --> 00:18:26,590
+هذا الوجه يبين و احيانا بدى اخلي الوجه الثاني و
+
+163
+00:18:26,590 --> 00:18:34,100
+احيانا بدى اخلي نفس الوجه بس بدى اغير مواقعيبقى
+
+164
+00:18:34,100 --> 00:18:40,860
+هنا لو جيت قلت عملت rotation بزاوية مقدرها zero
+
+165
+00:18:40,860 --> 00:18:48,720
+درجة هل سيتغير وضع هذا المربع؟ لأ يبقى بداجي أسمي
+
+166
+00:18:48,720 --> 00:18:57,140
+حاجة عندي R node روتيشن
+
+167
+00:18:57,140 --> 00:19:05,570
+of zero درجةrotation of zero درجة يبقى دوران بزيرو
+
+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
+مافيش تغيير في المكان no change in position مافيش
+
+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 Gهذا P وهذا W وهذا R نوت
+
+172
+00:19:34,480 --> 00:19:39,200
+يعني ماصارش دوران يبقى بدي أسبب هذا الوضع الأساسي
+
+173
+00:19:39,200 --> 00:19:47,400
+طيب بدي أجي ل R تسعين R تسعين درجة هو rotation of
+
+174
+00:19:47,400 --> 00:19:53,380
+تسعين درجة بس تسعين ممكن مع أقارب الساعة وممكن ضد
+
+175
+00:19:53,380 --> 00:19:58,980
+أقارب الساعة أنا بدي أمشي counter clockwiseيبقى
+
+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 اتحركتبزاوية تسعين درجة يبقى
+
+179
+00:20:23,920 --> 00:20:29,940
+الشكل المربع هيصير على الشكل اللي عندنا ال P هتيجي
+
+180
+00:20:29,940 --> 00:20:36,780
+مكان G و G هتيجي مكان P و P مكان ال W و ال W مكان
+
+181
+00:20:36,780 --> 00:20:42,500
+مين مكان ال P يبقى ال P هتيجي هنا و ال G هتيجي هنا
+
+182
+00:20:42,500 --> 00:20:49,650
+و ال P هتيجي هنا و ال W هتيجي هنايبقى 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 ال Bو هذه ال W وهنا Rotation بزاوية
+
+188
+00:21:21,430 --> 00:21:29,090
+مقدرها 180 درجة بدي اجي عند المربع التالي من هنا
+
+189
+00:21:29,090 --> 00:21:33,170
+لهنا قولنا بقداش تسعين اذا بدي امشي كمان من هنا
+
+190
+00:21:33,170 --> 00:21:39,370
+كمان تسعين اذا P بدي اتيجي هنا تمام؟ الان P بدي
+
+191
+00:21:39,370 --> 00:21:45,070
+اتيجي هنا يبقى G بعد ال P يبقى ال G بدي اتيجي 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
+روتيشن ب 270 counter clockwise يبقى هذا المربع
+
+195
+00:22:05,680 --> 00:22:14,850
+اللي عندنا الأصلي هذا P وهذا Gوهذا P وهذا W يصير
+
+196
+00:22:14,850 --> 00:22:25,090
+بالشكل اللي عندنا هذا نتيجة لل R 270 درجة P لما جت
+
+197
+00:22:25,090 --> 00:22:31,310
+هنا كان 180 270 بدنا ايه؟ كمان واحدة إذا ال P بدها
+
+198
+00:22:31,310 --> 00:22:35,970
+تيجي هناالـ G لما جت هنا كان مية و تمانية يبقى
+
+199
+00:22:35,970 --> 00:22:41,450
+بتيجي مكان ال P يبقى هنا بده يجين ال G و هنا بده
+
+200
+00:22:41,450 --> 00:22:48,470
+يجين ال P ال P و هنا ال W يبقى هاي ال متين
+
+201
+00:22:48,470 --> 00:22:53,710
+والسبعين درجة طب لو تلتنية و ستين درجة برجع كما
+
+202
+00:22:53,710 --> 00:23:00,740
+كنت مظبوطيبقى بتطلع الارنود اللى فوق طب انا بدى
+
+203
+00:23:00,740 --> 00:23:08,160
+اعمل شغل تانى بدى الان اخد دوران حول خط أفقى
+
+204
+00:23:08,160 --> 00:23:14,840
+ودوران حول خط رأسى ودوران حول من؟ حول الأقطار
+
+205
+00:23:32,710 --> 00:23:40,710
+واللي بقى لكن الان بدي أخد 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 الهيمين ال H بدي أجيك
+
+211
+00:24:20,260 --> 00:24:26,490
+المربع اللي عندك هناخلّي بالك هنا انا بدي ادخلي
+
+212
+00:24:26,490 --> 00:24:32,050
+الدوران افو الدوران horizontal حوالين الخط الأحمر
+
+213
+00:24:32,050 --> 00:24:39,690
+هذا بزاوية قداش rotation مية و تمانين درجة مية و
+
+214
+00:24:39,690 --> 00:24:45,250
+تمانين درجة about a horizontal line يبقى انا لما
+
+215
+00:24:45,250 --> 00:24:50,630
+اجي مية و تمانين درجة ال G وين بتصير مكان ال P و
+
+216
+00:24:50,630 --> 00:24:58,330
+ال B و ال Wيعني بده يظهر الوجه الآخر للمربع السطح
+
+217
+00:24:58,330 --> 00:25:01,470
+اللي اقبلنا هذا بده يصير هذا في الناحية التانية و
+
+218
+00:25:01,470 --> 00:25:04,550
+اللي كان الناحية التانية بده يصير في وجهنا هو من
+
+219
+00:25:04,550 --> 00:25:10,210
+هنا سمناه dihydral ثنائي السطوح السطح اللي كان مش
+
+220
+00:25:10,210 --> 00:25:13,570
+ظاهر بده يصير هو الظاهر والسطح اللي كان ظاهر بده
+
+221
+00:25:13,570 --> 00:25:18,620
+يصير ماله مش ظاهر سمناه من هنا ثنائي السطوحيبقى
+
+222
+00:25:18,620 --> 00:25:23,780
+دوران حوال الخط بده يصير عندنا مين؟ بده يصير هذه G
+
+223
+00:25:23,780 --> 00:25:35,000
+وتحت هنا P وهنا B وهنا W طيب مافيش أحسن حد من حد
+
+224
+00:25:35,000 --> 00:25:40,140
+مدام صورة دوران أفق بده يخلي دوران حوال الخط
+
+225
+00:25:40,140 --> 00:25:45,880
+الرأسي يبقى لو جيت سميت ال verticalاللي هو
+
+226
+00:25:45,880 --> 00:25:55,740
+rotation بمية و تمانين 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 الرأسيالـ
+
+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 ال P بدي تيجي مكان ال W و ال W مكان ال P
+
+232
+00:26:30,120 --> 00:26:35,820
+يعني بدي نجلي برأسي تمام؟ يعني زي ما تقول هاي هذا
+
+233
+00:26:35,820 --> 00:26:40,860
+المربع لما نجلي برأسي حوالين نص بدي أصير دوران فوق
+
+234
+00:26:40,860 --> 00:26:44,670
+و تحتقبل كان دوران اللي قبل هي أمين و أشمال لكن هي
+
+235
+00:26:44,670 --> 00:26:49,510
+منذ عامة الدوران فوق أو تحت معناته ال P بده تيجي
+
+236
+00:26:49,510 --> 00:26:58,590
+مكان ال W و ال W مكان ال P تمام؟ و ال B بده تيجي
+
+237
+00:26:58,590 --> 00:27:04,930
+مكان ال G و ال G مكان ال B يبقى هذا اسمه vertical
+
+238
+00:27:04,930 --> 00:27:12,390
+rotation ب180 درجةطيب 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 mean 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 Bهنا 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 هميبقى هذه بيبقى P و هذه بي كما هي
+
+250
+00:28:33,620 --> 00:28:39,920
+مافيش تغيير هالتغيير بيصير بين مين ومين يبقى ال W
+
+251
+00:28:39,920 --> 00:28:45,300
+بتيجي هنا و ال 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 الآخريبقى باجي بقوله هذا
+
+254
+00:28:59,000 --> 00:29:09,540
+المربع و هذا ال P G P G و هنا اللي هي ال P و هنا
+
+255
+00:29:09,540 --> 00:29:16,440
+من ال W يبقى هذه اللي هو D Prime المربع سيأخذ
+
+256
+00:29:16,440 --> 00:29:23,180
+الشكل التالي الدوران حوالين القطر الأخر اللي هو
+
+257
+00:29:23,180 --> 00:29:30,070
+القطر اللي عندنا هذا يبقى ال Gو ال P و ال W عند
+
+258
+00:29:30,070 --> 00:29:36,130
+الدوران تبقى كما هي اللى بده يتغير بس مين ال P و
+
+259
+00:29:36,130 --> 00:29:42,750
+ال B يبقى بده يصير ال P و هنا مين و هنا ال P
+
+260
+00:29:42,750 --> 00:29:49,410
+العناصر اللى شايفهم قدامك بيكونولي ال dihydral
+
+261
+00:29:49,410 --> 00:29:55,610
+group D4 و زى ما انت شايف فيها ستة و اتنين ثمانية
+
+262
+00:29:55,610 --> 00:30:03,440
+عناصريبقى الان الديهيدرالي جروب D4 عناصرها ال
+
+263
+00:30:03,440 --> 00:30:11,240
+identity element اللي حدله الرمز R0 و بعدها R90 و
+
+264
+00:30:11,240 --> 00:30:12,560
+R180
+
+265
+00:30:16,180 --> 00:30:25,640
+وR2O70 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 كله ضرب في اتنين
+
+267
+00:30:31,140 --> 00:30:36,020
+دي عشرة فيها عشرين عنصر دي تلاتين فيها ستين عنصر و
+
+268
+00:30:36,020 --> 00:30:42,040
+هكذا تمام يبقى هذه ايه هذه ال 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 ال identity element R تسعين هذي
+
+271
+00:30:55,470 --> 00:31:01,870
+بدي اعمل كم مرة بهذه الطريقة حتى ارجع للاصل اربع
+
+272
+00:31:01,870 --> 00:31:07,050
+مرات يبقى هذه معناته R أس أربع عارف تسعين أس أربع
+
+273
+00:31:07,050 --> 00:31:14,610
+بدي أساوي من ال identityطيب و الـ 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 default
+
+276
+00:31:28,510 --> 00:31:35,910
+الخاصية الأولى ان R تسعين أس أربعة هي R ميتين
+
+277
+00:31:35,910 --> 00:31:40,850
+وسبعين أس أربعة اللي تساوي ال identity اللي هو
+
+278
+00:31:40,850 --> 00:31:49,790
+main R node الخاصية الثانية R مية و تمانين تربيع
+
+279
+00:31:54,620 --> 00:31:59,400
+أرنود الأصلية اتش
+
+280
+00:31:59,400 --> 00:32:07,020
+تربيع ارنود الأصلية برضه الرد بترجع كما كانت مظبوط
+
+281
+00:32:07,020 --> 00:32:14,520
+طيب ادي تربيع ال V تربيع نفسها
+
+282
+00:32:14,520 --> 00:32:22,480
+ال identity طب ادي تربيع طيب ادي prime تربيع
+
+283
+00:32:25,950 --> 00:32:29,690
+يبقى الار مية و تمانية تربيع هي ال identity اللى
+
+284
+00:32:29,690 --> 00:32:35,790
+قلت بديش اعطيها ايه بدي اسميها ارنود تمام طيب و ال
+
+285
+00:32:35,790 --> 00:32:39,610
+H تربيع بتسوي ارنود و ال V تربيع ليش ان 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 بالارنود طيب ايش رايكلو جيت قلت ال R مية
+
+288
+00:32:51,510 --> 00:32:57,190
+و تمانين تربية بده يساوي ال identity وضربت الطرفين
+
+289
+00:32:57,190 --> 00:33:03,190
+في R مية و تمانين inverse قداش بطلع يعني لما أقول
+
+290
+00:33:03,190 --> 00:33:08,950
+G تربية يساوي E يبقى لو ضربت inverse الطرفين بصير
+
+291
+00:33:08,950 --> 00:33:14,780
+الطرف اليمين G inverse و الطرف الشمالجي واحدة بس
+
+292
+00:33:14,780 --> 00:33:18,700
+يبقى بصير جي يساوي جي انفرست معناته ال element
+
+293
+00:33:18,700 --> 00:33:24,540
+يساوي مين؟ يساوي معكوسه إذا للعناصر اللي عندك واحد
+
+294
+00:33:24,540 --> 00:33:29,780
+اتنين تلاتة اربعة خمسة كل عنصر يساوي ايه؟ يساوي
+
+295
+00:33:29,780 --> 00:33:38,580
+معكوسه يبقى هذا معناه ان ال R مية و تمانينيساوي
+
+296
+00:33:38,580 --> 00:33:44,700
+الار مية و تمانين inverse واللي بعدها ال H بده
+
+297
+00:33:44,700 --> 00:33:50,720
+يساوي ال H inverse و ال V بده يساوي ال V inverse و
+
+298
+00:33:50,720 --> 00:33:55,280
+ال D بده يساوي ال D inverse و ال 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
+كويسهذه المعلومات ديلوا بالك منها ان شاء الله ال
+
+301
+00:34:07,760 --> 00:34:11,580
+section جاي نبدأ ال order لل element و ال order لل
+
+302
+00:34:11,580 --> 00:34:17,300
+group ال order لل element أقل رقم بيرفعه عدد صحيح
+
+303
+00:34:17,300 --> 00:34:21,260
+موجة بيرفعه نقص بيعطيني ال identity يعني معناته
+
+304
+00:34:21,260 --> 00:34:25,340
+بعد قليل المحاضرة القادمة يمكن ندخلها و يمكن لأ
+
+305
+00:34:39,090 --> 00:34:47,530
+طيب بدنا نروح لخاصية تالتة غير هذه الخواصلو ضربت
+
+306
+00:34:47,530 --> 00:34:52,470
+او قبل ان اضرب ايش رأيك هدول الاربع واحد اتنين
+
+307
+00:34:52,470 --> 00:34:57,470
+تلات اربع اليست هذه حركة دورانية counter clockwise
+
+308
+00:34:57,470 --> 00:35:08,310
+يبقى هدول الاربع حالات كلهم بسميهم rotation دوران
+
+309
+00:35:09,580 --> 00:35:14,720
+و ممكن اختصارا اديهم الرمز R طب والاربع حالات اللي
+
+310
+00:35:14,720 --> 00:35:21,300
+بعدهم الاتنين هدول و الاتنين هدول اسم من عكاس
+
+311
+00:35:21,300 --> 00:35:29,140
+reflection يبقى هدول بسميهم reflection و هدول
+
+312
+00:35:29,140 --> 00:35:36,760
+اتنين كمان reflection تمام
+
+313
+00:35:36,760 --> 00:35:45,190
+تمام طيبعشان نختار دوران مع reflection اشوف ايه
+
+314
+00:35:45,190 --> 00:35:49,750
+يعطينا دوران يعني حاصل ضرب اي دوران من الدورانات
+
+315
+00:35:49,750 --> 00:35:53,790
+هدول في اي reflection من ال reflections الأربعة
+
+316
+00:35:53,790 --> 00:35:58,990
+اشوف ايه يعطينا دوران هل بيعطينا rotation دوران و
+
+317
+00:35:58,990 --> 00:36:04,730
+الله بيعطينا reflection تعالي ناخد اختارلك اي رقم
+
+318
+00:36:04,730 --> 00:36:08,970
+من الدورانات اللي عندناو بدي اختار اي reflection
+
+319
+00:36:08,970 --> 00:36:14,210
+منهم و اضرب اتنين في بعض ابسط الحالات لو اخد ر
+
+320
+00:36:14,210 --> 00:36:19,230
+تسعين بدي
+
+321
+00:36:19,230 --> 00:36:25,480
+اضربها مثلا في Hفي أول دوران أشوف إيش بيعطينا وين
+
+322
+00:36:25,480 --> 00:36:31,320
+ال H اللي عندي طلع لل H هي ال H يبقى هذه ال 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 ال 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 TGGوهنا 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 تعالي نطلع نشوف نشوف
+
+329
+00:37:06,410 --> 00:37:12,590
+تعالي ال 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 ال H خدلي ال V هشوف إيش بده يعطيني هذا
+
+333
+00:37:32,100 --> 00:37:37,180
+حاصل الضرب بقوله أه وين ال V هاي ال V اللي عندي
+
+334
+00:37:37,180 --> 00:37:45,610
+تمام؟ال V هذه بدي اهي ال V بدي اعملها 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 التالف هذه ال B وهذه ال G وهذه ال P اعلي 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 ال V هاي ال V تمام يبقى هاد ال V
+
+339
+00:38:15,500 --> 00:38:20,080
+بده أشوف إيش بده يصير لها يبقى هاد بده أصير بالشكل
+
+340
+00:38:20,080 --> 00:38:23,820
+اللي عندنا هنا بده أعملها دوران تسعين يبقى ال W
+
+341
+00:38:23,820 --> 00:38:30,020
+هتيجي هنا و ال P هتيجي هنا و ال G هتيجي هنا و ال P
+
+342
+00:38:30,020 --> 00:38:36,880
+هتيجي هنا بده أشوف هاد مين منهم ديوارينا نشوف يبقى
+
+343
+00:38:36,880 --> 00:38:42,140
+و ب هي تحت و P و G مظبوط يبقى هذا حصلت ضرب بده
+
+344
+00:38:42,140 --> 00:38:46,660
+يعطينا D يبقى هذا reflection و هذا كمان reflection
+
+345
+00:38:46,660 --> 00:38:55,740
+طيب لو جيت أخدت ال R تسعين في من في ال D هذه بده
+
+346
+00:38:55,740 --> 00:39:01,440
+يساوي يبقى وين ال 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 Gوين ال P و ال W يبقى H ممتاز
+
+349
+00:39:20,240 --> 00:39:25,540
+يدن يبقى هذا ال P W و G P مظبوط يبقى هذا الكلام
+
+350
+00:39:25,540 --> 00:39:32,420
+بده يساوي H بده يساوي H طيب لو جيت قولتلك N R
+
+351
+00:39:32,420 --> 00:39:39,160
+تسعين في D Primeراحة ال H و راحة ال D و هتظلش إلا
+
+352
+00:39:39,160 --> 00:39:44,300
+ال V مظبوط يبقى ده هتلاقيه بده ساوي V يبقى الآن
+
+353
+00:39:44,300 --> 00:39:48,540
+حاصل ضرب rotation ف reflection بيعطينا reflection
+
+354
+00:39:48,540 --> 00:39:53,740
+و أنت بتجري وهي كله دليل عدالة قدامك حتى لو أخدت
+
+355
+00:39:53,740 --> 00:39:59,640
+ال R مية و تمانين 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 بد
+
+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 ساوي؟
+
+362
+00:40:41,980 --> 00:40:47,260
+ايوة هذا تربيع كدهش؟
+
+363
+00:40:47,260 --> 00:40:52,760
+ارنول مش هذا reflection صار reflection يعني قد اده
+
+364
+00:40:52,760 --> 00:40:56,040
+D prime D prime تربيع بال identity على طول الخط
+
+365
+00:40:56,340 --> 00:40:59,960
+يبقى هذا تربيه بال identity هذا تربيه بال identity
+
+366
+00:40:59,960 --> 00:41:03,580
+هذا تربيه بال identity هذا تربيه بال identity على
+
+367
+00:41:03,580 --> 00:41:07,900
+طول الخط و انت بتجيبها كده يعني هذه هنطلع منها اشي
+
+368
+00:41:07,900 --> 00:41:12,800
+كتير لسه احنا هذه بس نكشات بسيطة مشان تعرف يعني لو
+
+369
+00:41:12,800 --> 00:41:18,880
+قلتلك اي بدي اجي اضرب مثلا R270 في D مثلا كيف بدي
+
+370
+00:41:18,880 --> 00:41:22,950
+اضرب R270 في D؟ بنروح على ال Dو انا دى هى دى
+
+371
+00:41:22,950 --> 00:41:26,910
+ارمتين و سبعين بتخليها تلف اللى هو التلت اماكن و
+
+372
+00:41:26,910 --> 00:41:30,670
+انا بتوصل بشوف مين من هدول بكون جبت الجواب دورى
+
+373
+00:41:30,670 --> 00:41:35,870
+على اى حال هادى راح عمل ليه فيها جدول فى صفحه واحد
+
+374
+00:41:35,870 --> 00:41:39,600
+و تلاتينهدا فيكم معاه كتاب اللى معاه كتاب يفتحلى
+
+375
+00:41:39,600 --> 00:41:43,220
+على صفحة واحد و تلاتين اللى قبل ما ندخل في ال
+
+376
+00:41:43,220 --> 00:41:46,120
+group الشابتر اللى مرضيش هجيبلكم سيطة و أقولكم
+
+377
+00:41:46,120 --> 00:41:49,920
+هعطيكميها من خلال الشابتر القادر يعني مش خليه
+
+378
+00:41:49,920 --> 00:41:54,700
+أفصله لحاله يبقى هذا هو ايه هذا هو من الشابتر
+
+379
+00:41:54,700 --> 00:41:58,610
+السابقلإن ال chapter اللى قبله ماكناش ماخدين حاجة
+
+380
+00:41:58,610 --> 00:42:03,390
+اسم مجروم لكن الأن أخدت هذه كحالة اللى من ال
+
+381
+00:42:03,390 --> 00:42:06,750
+holography جدول عندك في صفحه تواعى و تلاتين حطت
+
+382
+00:42:06,750 --> 00:42:12,110
+التمن عناصر و التمن عناصر و حاصل ضربهم كله يبقى يا
+
+383
+00:42:12,110 --> 00:42:15,730
+ريت هذا تطلعلي على الجدول اللى بتعرف النتائج الدرب
+
+384
+00:42:15,730 --> 00:42:22,870
+كلها بلا استثناء يبقى بداجة أقولك هنا lock the
+
+385
+00:42:22,870 --> 00:42:24,430
+table
+
+386
+00:42:30,080 --> 00:42:36,940
+تعرف باقى الضربيات و كل الشغلات هذه حد
+
+387
+00:42:36,940 --> 00:42:40,800
+بتسأل 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
+اعطي نقاط فيها النقطة الأولى ن 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 groupقلنا لجروب فيها
+
+396
+00:44:25,460 --> 00:44:29,240
+identity element لكن ماقلناش هما اتنين هو تلاتة هو
+
+397
+00:44:29,240 --> 00:44:33,760
+واحد الاخري تمام يبقى الخاصية الأولى من خاصة
+
+398
+00:44:33,760 --> 00:44:38,060
+الجروب بتقولي ال identity element في الجروب يكون
+
+399
+00:44:38,060 --> 00:44:42,490
+وحيدايعني ال group الواحدة لا يوجد فيها الا
+
+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 تاذا الكلام مشان نثبت صحة تاذا الكلام مفرض انه
+
+403
+00:44:56,850 --> 00:45:01,410
+عنده ايش اتنين و بثبت ان اتنين هدول مالهم are
+
+404
+00:45:01,410 --> 00:45:10,330
+equal يبقى هنا بداجي اقول assume افترض thatإن الـ
+
+405
+00:45:10,330 --> 00:45:25,050
+E and الـ 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
+ال
+
+408
+00:45:33,830 --> 00:45:42,880
+A star Eبتساوي 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 الان 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 elementيبقى 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 الأن لو افترت أن الـ E' هو
+
+417
+00:46:25,620 --> 00:46:36,400
+identity element يبقى and الـ E' أستارلأ 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
+elementيبقى هذا بده يعطينا ايه لكل اللي موجودة في
+
+424
+00:47:11,850 --> 00:47:19,090
+فيجيالأن 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 اتنين هذول الطرف الشمال مش هو
+
+427
+00:47:32,530 --> 00:47:38,210
+نفسه إذا الطرف اليمين هو نفسه إذا هذا بده يعطيلك
+
+428
+00:47:38,210 --> 00:47:45,400
+إن ال E تساوي مينالـ 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 مافيش غيره إن قلت هو ال zero هو ال identity
+
+431
+00:47:54,680 --> 00:47:58,590
+element إذا لا يوجد غير هذا الصفرإن جدش ال group
+
+432
+00:47:58,590 --> 00:48:02,230
+فيها الواحد ال identity element يبقى الواحد مافيش
+
+433
+00:48:02,230 --> 00:48:09,170
+غيره و هكذا تمام؟ في كمان نقطة تانية 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 و نكمل المحاضرة القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..660b413515fc179fe898eb3f53373f2be50b870d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nAC2Rz1Zado_raw.json
@@ -0,0 +1 @@
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"end": 201.62, "word": " عشان", "probability": 0.9781901041666666}, {"start": 201.62, "end": 202.02, "word": " ارجع", "probability": 0.73388671875}, {"start": 202.02, "end": 202.98, "word": " العنصر", "probability": 0.9384765625}, {"start": 202.98, "end": 204.14, "word": " لمكانه", "probability": 0.9147135416666666}, {"start": 204.14, "end": 206.18, "word": " بحتاج", "probability": 0.9773763020833334}, {"start": 206.18, "end": 206.5, "word": " ايش", "probability": 0.9246419270833334}], "temperature": 1.0}, {"id": 8, "seek": 23562, "start": 207.36, "end": 235.62, "text": "ان من الدورات لان هنا a بيروح ل a1 ل a2 و a2 بيروح ل a3 لما أعمل الف في الف فهيصير a1 يروح لمين ل a3 كمان لف a1 هيروح ل a4 بعد ان من اللفات a1 هيصير يروح لمين ل a1 و هيرجع مكانه طيب هذه انا هثبتها ل two cycles و بعد هيك التعميم تبعها بسيرة القائمة we will", "tokens": [7649, 9154, 32748, 13063, 9307, 5296, 7649, 34105, 257, 4724, 13546, 2407, 5016, 5296, 257, 16, 5296, 257, 17, 4032, 257, 17, 4724, 13546, 2407, 5016, 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208.68, "word": " لان", "probability": 0.3743896484375}, {"start": 208.68, "end": 209.0, "word": " هنا", "probability": 0.5576171875}, {"start": 209.0, "end": 209.22, "word": " a", "probability": 0.497802734375}, {"start": 209.22, "end": 209.6, "word": " بيروح", "probability": 0.7021484375}, {"start": 209.6, "end": 209.74, "word": " ل", "probability": 0.68359375}, {"start": 209.74, "end": 210.14, "word": " a1", "probability": 0.58056640625}, {"start": 210.14, "end": 210.32, "word": " ل", "probability": 0.79248046875}, {"start": 210.32, "end": 210.84, "word": " a2", "probability": 0.974853515625}, {"start": 210.84, "end": 211.34, "word": " و", "probability": 0.6708984375}, {"start": 211.34, "end": 211.54, "word": " a2", "probability": 0.5113525390625}, {"start": 211.54, "end": 211.74, "word": " بيروح", "probability": 0.9791259765625}, {"start": 211.74, "end": 211.82, "word": " ل", "probability": 0.97802734375}, {"start": 211.82, "end": 212.28, "word": " a3", "probability": 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"probability": 0.912109375}, {"start": 223.0, "end": 223.78, "word": " ل", "probability": 0.900390625}, {"start": 223.78, "end": 224.18, "word": " a1", "probability": 0.9775390625}, {"start": 224.18, "end": 224.26, "word": " و", "probability": 0.8212890625}, {"start": 224.26, "end": 224.78, "word": " هيرجع", "probability": 0.8868815104166666}, {"start": 224.78, "end": 226.06, "word": " مكانه", "probability": 0.8347981770833334}, {"start": 226.06, "end": 226.5, "word": " طيب", "probability": 0.7268880208333334}, {"start": 226.5, "end": 226.96, "word": " هذه", "probability": 0.53369140625}, {"start": 226.96, "end": 227.14, "word": " انا", "probability": 0.848388671875}, {"start": 227.14, "end": 227.98, "word": " هثبتها", "probability": 0.93525390625}, {"start": 227.98, "end": 228.86, "word": " ل", "probability": 0.97412109375}, {"start": 228.86, "end": 229.36, "word": " two", "probability": 0.8310546875}, {"start": 229.36, "end": 230.18, "word": " cycles", "probability": 0.88671875}, {"start": 230.18, "end": 231.88, "word": " و", "probability": 0.6728515625}, {"start": 231.88, "end": 232.1, "word": " بعد", "probability": 0.93896484375}, {"start": 232.1, "end": 232.38, "word": " هيك", "probability": 0.935302734375}, {"start": 232.38, "end": 232.9, "word": " التعميم", "probability": 0.89697265625}, {"start": 232.9, "end": 233.2, "word": " تبعها", "probability": 0.7252197265625}, {"start": 233.2, "end": 233.56, "word": " بسيرة", "probability": 0.73583984375}, {"start": 233.56, "end": 234.06, "word": " القائمة", "probability": 0.5179850260416666}, {"start": 234.06, "end": 234.34, "word": " we", "probability": 0.8017578125}, {"start": 234.34, "end": 235.62, "word": " will", "probability": 0.89794921875}], "temperature": 1.0}, {"id": 9, "seek": 26577, "start": 236.86, "end": 265.78, "text": "proof this result for a permutation consists of two disjoint cycles يعني", "tokens": [15690, 341, 1874, 337, 257, 4784, 11380, 14689, 295, 732, 717, 48613, 17796, 37495, 22653], "avg_logprob": -0.21557616535574198, "compression_ratio": 0.9743589743589743, "no_speech_prob": 0.0, "words": [{"start": 236.86, "end": 237.48, "word": "proof", "probability": 0.2364501953125}, {"start": 237.48, "end": 242.2, "word": " this", "probability": 0.7392578125}, {"start": 242.2, "end": 244.68, "word": " result", "probability": 0.9619140625}, {"start": 244.68, "end": 247.12, "word": " for", "probability": 0.92138671875}, {"start": 247.12, "end": 249.12, "word": " a", "probability": 0.9609375}, {"start": 249.12, "end": 249.98, "word": " permutation", "probability": 0.98779296875}, {"start": 249.98, "end": 253.14, "word": " consists", "probability": 0.41796875}, {"start": 253.14, "end": 255.76, "word": " of", "probability": 0.9833984375}, {"start": 255.76, "end": 256.5, "word": " two", "probability": 0.9296875}, {"start": 256.5, "end": 259.94, "word": " disjoint", "probability": 0.879150390625}, {"start": 259.94, "end": 263.28, "word": " cycles", "probability": 0.890625}, {"start": 263.28, "end": 265.78, "word": " يعني", "probability": 0.940673828125}], "temperature": 1.0}, {"id": 10, "seek": 29424, "start": 270.1, "end": 294.24, "text": "we show that if order للألفة بدي ساوي M order للبيتا بدي ساوي N then order للألفة في بيتا بدي ساوي least common multiple ل M1 طبعا لو انا اثبتت تلتين تين لما بدي اجيب واحدة تالتة", "tokens": [826, 855, 300, 498, 1668, 24976, 10721, 46538, 3660, 4724, 16254, 8608, 995, 45865, 376, 1668, 24976, 21292, 2655, 995, 4724, 16254, 8608, 995, 45865, 426, 550, 1668, 24976, 10721, 46538, 3660, 8978, 4724, 36081, 995, 4724, 16254, 8608, 995, 45865, 1935, 2689, 3866, 5296, 376, 16, 23032, 3555, 3615, 995, 45164, 1975, 8315, 1975, 12984, 3555, 2655, 2655, 6055, 1211, 2655, 9957, 6055, 9957, 5296, 15042, 4724, 16254, 1975, 7435, 1829, 3555, 36764, 24401, 3660, 6055, 6027, 2655, 3660], "avg_logprob": -0.22299382421705458, "compression_ratio": 1.592814371257485, "no_speech_prob": 0.0, "words": [{"start": 270.1, "end": 271.06, "word": "we", "probability": 0.063232421875}, {"start": 271.06, "end": 272.02, "word": " show", "probability": 0.9267578125}, {"start": 272.02, "end": 272.56, "word": " that", "probability": 0.93115234375}, {"start": 272.56, "end": 274.76, "word": " if", "probability": 0.83642578125}, {"start": 274.76, "end": 275.48, "word": " order", "probability": 0.923828125}, {"start": 275.48, "end": 276.14, "word": " للألفة", "probability": 0.719482421875}, {"start": 276.14, "end": 276.38, "word": " بدي", "probability": 0.333587646484375}, {"start": 276.38, "end": 276.76, "word": " ساوي", "probability": 0.8621419270833334}, {"start": 276.76, "end": 277.0, "word": " M", "probability": 0.57568359375}, {"start": 277.0, "end": 277.98, "word": " order", "probability": 0.81005859375}, {"start": 277.98, "end": 278.74, "word": " للبيتا", "probability": 0.8787841796875}, {"start": 278.74, "end": 279.9, "word": " بدي", "probability": 0.966796875}, {"start": 279.9, "end": 280.3, "word": " ساوي", "probability": 0.9627278645833334}, {"start": 280.3, "end": 280.62, "word": " N", "probability": 0.892578125}, {"start": 280.62, "end": 282.02, "word": " then", "probability": 0.6630859375}, {"start": 282.02, "end": 282.56, "word": " order", "probability": 0.9677734375}, {"start": 282.56, "end": 283.32, "word": " للألفة", "probability": 0.9168701171875}, {"start": 283.32, "end": 283.46, "word": " في", "probability": 0.79345703125}, {"start": 283.46, "end": 283.9, "word": " بيتا", "probability": 0.8059895833333334}, {"start": 283.9, "end": 284.32, "word": " بدي", "probability": 0.966552734375}, {"start": 284.32, "end": 284.58, "word": " ساوي", "probability": 0.9446614583333334}, {"start": 284.58, "end": 285.06, "word": " least", "probability": 0.50390625}, {"start": 285.06, "end": 285.44, "word": " common", "probability": 0.96044921875}, {"start": 285.44, "end": 286.06, "word": " multiple", "probability": 0.88427734375}, {"start": 286.06, "end": 287.2, "word": " ل", "probability": 0.91259765625}, {"start": 287.2, "end": 287.68, "word": " M1", "probability": 0.67431640625}, {"start": 287.68, "end": 289.98, "word": " طبعا", "probability": 0.978515625}, {"start": 289.98, "end": 290.1, "word": " لو", "probability": 0.93212890625}, {"start": 290.1, "end": 290.26, "word": " انا", "probability": 0.7235107421875}, {"start": 290.26, "end": 290.74, "word": " اثبتت", "probability": 0.817724609375}, {"start": 290.74, "end": 291.1, "word": " تلتين", "probability": 0.8023681640625}, {"start": 291.1, "end": 291.5, "word": " تين", "probability": 0.765869140625}, {"start": 291.5, "end": 293.0, "word": " لما", "probability": 0.811767578125}, {"start": 293.0, "end": 293.16, "word": " بدي", "probability": 0.7059326171875}, {"start": 293.16, "end": 293.4, "word": " اجيب", "probability": 0.928955078125}, {"start": 293.4, "end": 293.74, "word": " واحدة", "probability": 0.9606119791666666}, {"start": 293.74, "end": 294.24, "word": " تالتة", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 11, "seek": 31944, "start": 296.58, "end": 319.44, "text": "بأخد ال least common multiple التنتين مع التالتة لو بدنا نضيف واحدة رابعة بيصير عملية عملية تكرارية assume that ان order ال alpha بيتا بيدي ساوي T وان ال least common multiple ل M و N بيساوي K", "tokens": [3555, 10721, 9778, 3215, 2423, 1935, 2689, 3866, 16712, 29399, 9957, 20449, 16712, 6027, 2655, 3660, 45164, 47525, 8315, 8717, 11242, 33911, 36764, 24401, 3660, 12602, 16758, 27884, 4724, 1829, 9381, 13546, 6225, 42213, 10632, 6225, 42213, 10632, 6055, 37983, 9640, 10632, 6552, 300, 16472, 1668, 2423, 8961, 4724, 36081, 995, 4724, 1829, 16254, 8608, 995, 45865, 314, 4032, 7649, 2423, 1935, 2689, 3866, 5296, 376, 4032, 426, 4724, 1829, 3794, 995, 45865, 591], "avg_logprob": -0.31604166666666667, "compression_ratio": 1.574585635359116, "no_speech_prob": 0.0, "words": [{"start": 296.58, "end": 297.02, "word": "بأخد", "probability": 0.62213134765625}, {"start": 297.02, "end": 297.12, "word": " ال", "probability": 0.6708984375}, {"start": 297.12, "end": 297.26, "word": " least", "probability": 0.69482421875}, {"start": 297.26, "end": 297.46, "word": " common", "probability": 0.89404296875}, {"start": 297.46, "end": 297.78, "word": " multiple", "probability": 0.92578125}, {"start": 297.78, "end": 298.38, "word": " التنتين", "probability": 0.6525065104166666}, {"start": 298.38, "end": 299.04, "word": " مع", "probability": 0.92431640625}, {"start": 299.04, "end": 299.62, "word": " التالتة", "probability": 0.9146728515625}, {"start": 299.62, "end": 300.24, "word": " لو", "probability": 0.71826171875}, {"start": 300.24, "end": 300.54, "word": " بدنا", "probability": 0.338623046875}, {"start": 300.54, "end": 300.72, "word": " نضيف", "probability": 0.9798177083333334}, {"start": 300.72, "end": 301.04, "word": " واحدة", "probability": 0.9322916666666666}, {"start": 301.04, "end": 301.36, "word": " رابعة", "probability": 0.9275716145833334}, {"start": 301.36, "end": 301.74, "word": " بيصير", "probability": 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"end": 399.93, "text": "ال K عبارة عن ال least م multiple ل M و N يعني ال K عبارة عن multiple ل M مثلا M في اختارة في R وهي نفسها ال N في S يكبر Alpha Beta أس K عبارة عن إيش؟", "tokens": [6027, 591, 6225, 3555, 9640, 3660, 18871, 2423, 1935, 3714, 3866, 5296, 376, 4032, 426, 37495, 22653, 2423, 591, 6225, 3555, 9640, 3660, 18871, 3866, 5296, 376, 50113, 15040, 376, 8978, 1975, 46456, 9640, 3660, 8978, 497, 37037, 1829, 8717, 36178, 11296, 2423, 426, 8978, 318, 7251, 4117, 3555, 2288, 20588, 33286, 5551, 3794, 591, 6225, 3555, 9640, 3660, 18871, 11933, 1829, 8592, 22807], "avg_logprob": -0.3485576923076923, "compression_ratio": 1.4932432432432432, "no_speech_prob": 0.0, "words": [{"start": 379.67, "end": 379.99, "word": "ال", "probability": 0.82080078125}, {"start": 379.99, "end": 380.25, "word": " K", "probability": 0.257568359375}, {"start": 380.25, "end": 380.71, "word": " عبارة", "probability": 0.8939208984375}, {"start": 380.71, "end": 380.93, "word": " عن", "probability": 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"عن Alpha أُس K Beta أُس K يعني Alpha أُس MR في Beta أُس N S يعني Alpha أُس M أُس R Beta أُس N أُس S يعني Identity أُس R في Identity أُس S إيش بيعطيني؟ معناته ال Alpha Beta أُس K", "tokens": [3615, 1863, 20588, 5551, 10859, 3794, 591, 33286, 5551, 10859, 3794, 591, 37495, 22653, 20588, 5551, 10859, 3794, 9808, 8978, 33286, 5551, 10859, 3794, 426, 318, 37495, 22653, 20588, 5551, 10859, 3794, 376, 5551, 10859, 3794, 497, 33286, 5551, 10859, 3794, 426, 5551, 10859, 3794, 318, 37495, 22653, 25905, 507, 5551, 10859, 3794, 497, 8978, 25905, 507, 5551, 10859, 3794, 318, 11933, 1829, 8592, 4724, 40228, 9566, 1829, 22653, 22807, 20449, 8315, 47395, 2423, 20588, 33286, 5551, 10859, 3794, 591], "avg_logprob": -0.18624614786218713, "compression_ratio": 2.008130081300813, "no_speech_prob": 0.0, "words": [{"start": 401.61, "end": 402.03, "word": "عن", "probability": 0.8603515625}, {"start": 402.03, "end": 402.41, "word": " Alpha", "probability": 0.45751953125}, {"start": 402.41, "end": 402.77, "word": " أُس", "probability": 0.580078125}, {"start": 402.77, "end": 402.95, "word": " K", "probability": 0.873046875}, {"start": 402.95, "end": 403.65, "word": " Beta", "probability": 0.314208984375}, {"start": 403.65, "end": 404.01, "word": " أُس", "probability": 0.9762369791666666}, {"start": 404.01, "end": 404.23, "word": " K", "probability": 0.94970703125}, {"start": 404.23, "end": 405.05, "word": " يعني", "probability": 0.732666015625}, {"start": 405.05, "end": 405.49, "word": " Alpha", "probability": 0.9501953125}, {"start": 405.49, "end": 406.11, "word": " أُس", "probability": 0.9529622395833334}, {"start": 406.11, "end": 406.59, "word": " MR", "probability": 0.398681640625}, {"start": 406.59, "end": 407.75, "word": " في", "probability": 0.84423828125}, {"start": 407.75, "end": 408.07, "word": " Beta", "probability": 0.9248046875}, {"start": 408.07, "end": 408.43, "word": " أُس", "probability": 0.9873046875}, {"start": 408.43, "end": 408.67, "word": " N", "probability": 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0.93408203125}, {"start": 448.63, "end": 448.87, "word": " ال", "probability": 0.9697265625}, {"start": 448.87, "end": 449.25, "word": " alpha", "probability": 0.775390625}, {"start": 449.25, "end": 449.77, "word": " beta", "probability": 0.9248046875}, {"start": 449.77, "end": 450.35, "word": " عبارة", "probability": 0.994873046875}, {"start": 450.35, "end": 450.55, "word": " عن", "probability": 0.99267578125}, {"start": 450.55, "end": 451.07, "word": " مين؟", "probability": 0.919921875}], "temperature": 1.0}, {"id": 17, "seek": 48119, "start": 452.27, "end": 481.19, "text": "عن الـ T يعني الـ Alpha Beta أس T بدي يساوي ال identity يعني Alpha أس T لاحظ انه انهم disjoint هو اللي سهل عملية رفع للأس T و رفع للأس K هذا بدي يساوي ايش identity يعني ال Alpha أس T بدي يساوي Beta أس ثالث T طيب", "tokens": [3615, 1863, 2423, 39184, 314, 37495, 22653, 2423, 39184, 20588, 33286, 5551, 3794, 314, 4724, 16254, 7251, 3794, 995, 45865, 2423, 6575, 37495, 22653, 20588, 5551, 3794, 314, 20193, 5016, 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{"start": 461.47, "end": 461.85, "word": " انه", "probability": 0.46875}, {"start": 461.85, "end": 462.97, "word": " انهم", "probability": 0.82666015625}, {"start": 462.97, "end": 463.73, "word": " disjoint", "probability": 0.573486328125}, {"start": 463.73, "end": 464.35, "word": " هو", "probability": 0.90771484375}, {"start": 464.35, "end": 464.53, "word": " اللي", "probability": 0.9658203125}, {"start": 464.53, "end": 464.87, "word": " سهل", "probability": 0.9759114583333334}, {"start": 464.87, "end": 465.53, "word": " عملية", "probability": 0.7170003255208334}, {"start": 465.53, "end": 466.35, "word": " رفع", "probability": 0.8958333333333334}, {"start": 466.35, "end": 466.73, "word": " للأس", "probability": 0.70361328125}, {"start": 466.73, "end": 466.99, "word": " T", "probability": 0.9716796875}, {"start": 466.99, "end": 467.63, "word": " و", "probability": 0.9609375}, {"start": 467.63, "end": 467.89, "word": " رفع", "probability": 0.81298828125}, {"start": 467.89, "end": 468.49, "word": " للأس", "probability": 0.9293619791666666}, {"start": 468.49, "end": 469.31, "word": " K", "probability": 0.97021484375}, {"start": 469.31, "end": 470.49, "word": " هذا", "probability": 0.7353515625}, {"start": 470.49, "end": 470.71, "word": " بدي", "probability": 0.983642578125}, {"start": 470.71, "end": 471.01, "word": " يساوي", "probability": 0.9468994140625}, {"start": 471.01, "end": 471.33, "word": " ايش", "probability": 0.7889811197916666}, {"start": 471.33, "end": 472.37, "word": " identity", "probability": 0.273681640625}, {"start": 472.37, "end": 473.33, "word": " يعني", "probability": 0.94482421875}, {"start": 473.33, "end": 473.49, "word": " ال", "probability": 0.65087890625}, {"start": 473.49, "end": 473.83, "word": " Alpha", "probability": 0.83837890625}, {"start": 473.83, "end": 474.17, "word": " أس", "probability": 0.986083984375}, {"start": 474.17, "end": 474.51, "word": " T", "probability": 0.99267578125}, {"start": 474.51, "end": 475.19, "word": " بدي", "probability": 0.98193359375}, {"start": 475.19, "end": 475.47, "word": " يساوي", "probability": 0.9793701171875}, {"start": 475.47, "end": 475.95, "word": " Beta", "probability": 0.83203125}, {"start": 475.95, "end": 477.59, "word": " أس", "probability": 0.97265625}, {"start": 477.59, "end": 477.85, "word": " ثالث", "probability": 0.6814778645833334}, {"start": 477.85, "end": 478.07, "word": " T", "probability": 0.83056640625}, {"start": 478.07, "end": 481.19, "word": " طيب", "probability": 0.9334309895833334}], "temperature": 1.0}, {"id": 18, "seek": 50254, "start": 484.5, "end": 502.54, "text": "Alpha and beta are disjoint لما يكون عندك two cycles و disjoint يعني عناصر ال alpha غير عناصر ال beta", "tokens": [9171, 7211, 293, 9861, 366, 717, 48613, 5296, 15042, 7251, 30544, 43242, 4117, 732, 17796, 4032, 717, 48613, 37495, 22653, 18871, 33546, 2288, 2423, 8961, 32771, 13546, 18871, 33546, 2288, 2423, 9861], "avg_logprob": -0.18584280303030304, "compression_ratio": 1.2641509433962264, "no_speech_prob": 0.0, "words": [{"start": 484.5, "end": 485.64, "word": "Alpha", "probability": 0.699462890625}, {"start": 485.64, "end": 486.78, "word": " and", "probability": 0.85205078125}, {"start": 486.78, "end": 487.26, "word": " beta", "probability": 0.322021484375}, {"start": 487.26, "end": 488.58, "word": " are", "probability": 0.9521484375}, {"start": 488.58, "end": 491.0, "word": " disjoint", "probability": 0.900146484375}, {"start": 491.0, "end": 494.72, "word": " لما", "probability": 0.8330078125}, {"start": 494.72, "end": 494.92, "word": " يكون", "probability": 0.939697265625}, {"start": 494.92, "end": 495.34, "word": " عندك", "probability": 0.975341796875}, {"start": 495.34, "end": 495.82, "word": " two", "probability": 0.8720703125}, {"start": 495.82, "end": 496.96, "word": " cycles", "probability": 0.87060546875}, {"start": 496.96, "end": 497.24, "word": " و", "probability": 0.76318359375}, {"start": 497.24, "end": 498.12, "word": " disjoint", "probability": 0.7222900390625}, {"start": 498.12, "end": 499.16, "word": " يعني", "probability": 0.8916015625}, {"start": 499.16, "end": 499.74, "word": " عناصر", "probability": 0.9807942708333334}, {"start": 499.74, "end": 499.88, "word": " ال", "probability": 0.6923828125}, {"start": 499.88, "end": 500.32, "word": " alpha", "probability": 0.381591796875}, {"start": 500.32, "end": 501.54, "word": " غير", "probability": 0.989501953125}, {"start": 501.54, "end": 502.1, "word": " عناصر", "probability": 0.98779296875}, {"start": 502.1, "end": 502.26, "word": " ال", "probability": 0.9765625}, {"start": 502.26, "end": 502.54, "word": " beta", "probability": 0.9365234375}], "temperature": 1.0}, {"id": 19, "seek": 52270, "start": 503.6, "end": 522.7, "text": "فجد ما تلف ال alpha و تلف ال beta مش هتلاقي عناصر مشتركة إلا في حالة واحدة لما هاد تلف و تصل ال identity و هاد تلف و تصل ال identity So we must have that", "tokens": [5172, 7435, 3215, 19446, 6055, 46538, 2423, 8961, 4032, 6055, 46538, 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506.2, "word": " ال", "probability": 0.98779296875}, {"start": 506.2, "end": 506.56, "word": " beta", "probability": 0.90869140625}, {"start": 506.56, "end": 507.44, "word": " مش", "probability": 0.60498046875}, {"start": 507.44, "end": 507.88, "word": " هتلاقي", "probability": 0.967529296875}, {"start": 507.88, "end": 508.34, "word": " عناصر", "probability": 0.978515625}, {"start": 508.34, "end": 508.92, "word": " مشتركة", "probability": 0.9666748046875}, {"start": 508.92, "end": 509.12, "word": " إلا", "probability": 0.8701171875}, {"start": 509.12, "end": 509.28, "word": " في", "probability": 0.8427734375}, {"start": 509.28, "end": 509.52, "word": " حالة", "probability": 0.9931640625}, {"start": 509.52, "end": 510.04, "word": " واحدة", "probability": 0.9617513020833334}, {"start": 510.04, "end": 510.72, "word": " لما", "probability": 0.8037109375}, {"start": 510.72, "end": 510.92, "word": " هاد", "probability": 0.5045166015625}, {"start": 510.92, "end": 511.24, "word": " تلف", "probability": 0.9755859375}, {"start": 511.24, "end": 511.36, "word": " و", "probability": 0.70263671875}, {"start": 511.36, "end": 511.6, "word": " تصل", "probability": 0.97119140625}, {"start": 511.6, "end": 511.74, "word": " ال", "probability": 0.5869140625}, {"start": 511.74, "end": 512.32, "word": " identity", "probability": 0.92626953125}, {"start": 512.32, "end": 513.04, "word": " و", "probability": 0.5888671875}, {"start": 513.04, "end": 513.22, "word": " هاد", "probability": 0.9375}, {"start": 513.22, "end": 513.54, "word": " تلف", "probability": 0.98095703125}, {"start": 513.54, "end": 513.7, "word": " و", "probability": 0.97607421875}, {"start": 513.7, "end": 513.98, "word": " تصل", "probability": 0.985595703125}, {"start": 513.98, "end": 514.26, "word": " ال", "probability": 0.57275390625}, {"start": 514.26, "end": 515.74, "word": " identity", "probability": 0.8212890625}, {"start": 515.74, "end": 516.64, "word": " So", "probability": 0.1641845703125}, {"start": 516.64, "end": 518.32, "word": " we", "probability": 0.5478515625}, {"start": 518.32, "end": 521.14, "word": " must", "probability": 0.8759765625}, {"start": 521.14, "end": 521.64, "word": " have", "probability": 0.96337890625}, {"start": 521.64, "end": 522.7, "word": " that", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 20, "seek": 55313, "start": 523.75, "end": 553.13, "text": "الـ α أُس T بيبقى تساوي الـ Beta أُس سالب T بيبقى تساوي الـ Identity Alpha أُس T بيبقى تساوي الـ Identity Beta أُس T أُس سالب T بيبقى تساوي الـ Identity Alpha أُس T بـ Identity Beta أُس T بـ Identity يقبل M بيقسم الـ T Order الـ Alpha بيبقى تساوي M بيقسم الـ T Order ال Beta", "tokens": [6027, 39184, 5691, 5551, 10859, 3794, 314, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 995, 45865, 2423, 39184, 33286, 5551, 10859, 3794, 8608, 6027, 3555, 314, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 995, 45865, 2423, 39184, 25905, 507, 20588, 5551, 10859, 3794, 314, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 995, 45865, 2423, 39184, 25905, 507, 33286, 5551, 10859, 3794, 314, 5551, 10859, 3794, 8608, 6027, 3555, 314, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 995, 45865, 2423, 39184, 25905, 507, 20588, 5551, 10859, 3794, 314, 4724, 39184, 25905, 507, 33286, 5551, 10859, 3794, 314, 4724, 39184, 25905, 507, 7251, 4587, 36150, 376, 4724, 1829, 4587, 38251, 2423, 39184, 314, 16321, 2423, 39184, 20588, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 995, 45865, 376, 4724, 1829, 4587, 38251, 2423, 39184, 314, 16321, 2423, 33286], "avg_logprob": -0.2509191248785047, "compression_ratio": 3.015151515151515, "no_speech_prob": 0.0013551712036132812, "words": [{"start": 523.75, "end": 524.27, "word": "الـ", "probability": 0.7119140625}, {"start": 524.27, "end": 524.57, "word": " α", "probability": 0.40771484375}, {"start": 524.57, "end": 524.89, "word": " أُس", "probability": 0.6145426432291666}, {"start": 524.89, "end": 525.09, "word": " T", "probability": 0.74462890625}, {"start": 525.09, "end": 525.85, "word": " بيبقى", "probability": 0.52373046875}, {"start": 525.85, "end": 526.19, "word": " تساوي", "probability": 0.734130859375}, {"start": 526.19, "end": 526.33, "word": " الـ", "probability": 0.7978515625}, {"start": 526.33, "end": 526.55, "word": " Beta", "probability": 0.458740234375}, {"start": 526.55, "end": 526.89, "word": " أُس", "probability": 0.8525390625}, {"start": 526.89, "end": 527.21, "word": " سالب", "probability": 0.7342936197916666}, {"start": 527.21, "end": 527.41, "word": " T", "probability": 0.86376953125}, {"start": 527.41, "end": 527.73, "word": " بيبقى", "probability": 0.81552734375}, {"start": 527.73, "end": 527.99, "word": " تساوي", "probability": 0.9202880859375}, {"start": 527.99, "end": 528.35, "word": " الـ", "probability": 0.684326171875}, {"start": 528.35, "end": 529.29, "word": " Identity", "probability": 0.809326171875}, {"start": 529.29, "end": 530.13, "word": " Alpha", "probability": 0.65869140625}, {"start": 530.13, "end": 530.53, "word": " أُس", "probability": 0.95849609375}, {"start": 530.53, "end": 530.67, "word": " T", "probability": 0.98828125}, {"start": 530.67, "end": 530.97, "word": " بيبقى", "probability": 0.949609375}, {"start": 530.97, "end": 531.13, "word": " تساوي", "probability": 0.9573974609375}, {"start": 531.13, "end": 531.27, "word": " الـ", "probability": 0.855224609375}, {"start": 531.27, "end": 531.87, "word": " Identity", "probability": 0.9189453125}, {"start": 531.87, "end": 532.95, "word": " Beta", "probability": 0.8525390625}, {"start": 532.95, "end": 533.37, "word": " أُس", "probability": 0.9889322916666666}, {"start": 533.37, "end": 533.71, "word": " T", "probability": 0.99169921875}, {"start": 533.71, "end": 535.59, "word": " أُس", "probability": 0.7874348958333334}, {"start": 535.59, "end": 535.85, "word": " سالب", "probability": 0.98779296875}, {"start": 535.85, "end": 535.99, "word": " T", "probability": 0.9833984375}, {"start": 535.99, "end": 536.13, "word": " بيبقى", "probability": 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" هتقدر", "probability": 0.989501953125}, {"start": 905.87, "end": 906.21, "word": " تضيفي", "probability": 0.947998046875}, {"start": 906.21, "end": 907.31, "word": " شيء", "probability": 0.6512451171875}, {"start": 907.31, "end": 907.75, "word": " يكبر", "probability": 0.6790771484375}], "temperature": 1.0}, {"id": 34, "seek": 93258, "start": 908.9, "end": 932.58, "text": "لو كان عندك permutation تلاتة تقدر تخليها permutation اتنين مثلا واحد اتنين تلاتة الواحد اتنين تلاتة انا ممكن اخليها واحد تلاتة واحد اتنين و جرب واحد بيروح للتنين و اتنين بيروح للنفس يجب واحد ده التنين تنين بيروح للواحد واحد بيروح للتلاتة و اتنين بيروح للتلاتة تلاتة لنفسه و تلاتة للواحد يجب تلاتة للواحد", "tokens": [1211, 2407, 25961, 43242, 4117, 4784, 11380, 6055, 1211, 9307, 3660, 6055, 28543, 2288, 6055, 9778, 20292, 11296, 4784, 11380, 1975, 2655, 1863, 9957, 50113, 15040, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 2423, 14407, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 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"word": " للواحد", "probability": 0.9729817708333334}, {"start": 927.96, "end": 928.18, "word": " واحد", "probability": 0.85009765625}, {"start": 928.18, "end": 928.3, "word": " بيروح", "probability": 0.970458984375}, {"start": 928.3, "end": 928.66, "word": " للتلاتة", "probability": 0.9369140625}, {"start": 928.66, "end": 928.76, "word": " و", "probability": 0.1590576171875}, {"start": 928.76, "end": 928.96, "word": " اتنين", "probability": 0.92919921875}, {"start": 928.96, "end": 929.16, "word": " بيروح", "probability": 0.9642333984375}, {"start": 929.16, "end": 929.82, "word": " للتلاتة", "probability": 0.9771484375}, {"start": 929.82, "end": 930.38, "word": " تلاتة", "probability": 0.9708251953125}, {"start": 930.38, "end": 930.82, "word": " لنفسه", "probability": 0.8521728515625}, {"start": 930.82, "end": 930.9, "word": " و", "probability": 0.92236328125}, {"start": 930.9, "end": 931.14, "word": " تلاتة", "probability": 0.9632568359375}, {"start": 931.14, "end": 931.54, "word": " 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"probability": 0.9541015625}, {"start": 1165.01, "end": 1165.33, "word": " وهذه", "probability": 0.5345458984375}, {"start": 1165.33, "end": 1165.85, "word": " جاهزة", "probability": 0.974853515625}], "temperature": 1.0}, {"id": 43, "seek": 117803, "start": 1168.51, "end": 1178.03, "text": "أدوش محتاجة حسابات لما", "tokens": [10721, 3215, 2407, 8592, 3714, 33753, 26108, 3660, 11331, 3794, 16758, 9307, 5296, 15042], "avg_logprob": -0.3614583452542623, "compression_ratio": 0.8913043478260869, "no_speech_prob": 0.0, "words": [{"start": 1168.51, "end": 1168.91, "word": "أدوش", "probability": 0.62506103515625}, {"start": 1168.91, "end": 1169.63, "word": " محتاجة", "probability": 0.8975830078125}, {"start": 1169.63, "end": 1170.55, "word": " حسابات", "probability": 0.8223876953125}, {"start": 1170.55, "end": 1178.03, "word": " لما", "probability": 0.5126953125}], "temperature": 1.0}, {"id": 44, "seek": 122136, "start": 1196.27, "end": 1221.37, "text": "هذه اللمة هناخدها بدون اثبات هنحتاجها في اثبات شغلة قادمة او نظرية لبعدها اللمة هذه بتقول ال identity لو جدرت تكتب على شكل two cycles فعدد ال two cycles هذا لازم يكون زوجي ال identity لو جدرت تكتب على شكل two cycles عدد ال two cycles هدول هيكون زوجي if", "tokens": [3224, 24192, 13672, 46007, 8032, 1863, 47283, 3215, 11296, 47525, 11536, 1975, 12984, 3555, 9307, 8032, 1863, 33753, 26108, 11296, 8978, 1975, 12984, 3555, 9307, 13412, 17082, 37977, 12174, 18513, 46007, 1975, 2407, 8717, 19913, 2288, 10632, 5296, 3555, 22488, 11296, 13672, 46007, 29538, 39894, 39648, 2423, 6575, 45164, 10874, 3215, 43500, 6055, 4117, 2655, 3555, 15844, 13412, 28820, 732, 17796, 6156, 22488, 3215, 2423, 732, 17796, 23758, 5296, 31377, 2304, 7251, 30544, 30767, 29245, 1829, 2423, 6575, 45164, 10874, 3215, 43500, 6055, 4117, 2655, 3555, 15844, 13412, 28820, 732, 17796, 6225, 3215, 3215, 2423, 732, 17796, 8032, 3215, 12610, 39896, 30544, 30767, 29245, 1829, 498], "avg_logprob": -0.13529497997783055, "compression_ratio": 2.0670103092783507, "no_speech_prob": 0.0, "words": [{"start": 1196.27, "end": 1196.61, "word": "هذه", "probability": 0.903076171875}, {"start": 1196.61, "end": 1196.95, "word": " اللمة", "probability": 0.6124267578125}, {"start": 1196.95, "end": 1197.61, "word": " هناخدها", "probability": 0.798828125}, {"start": 1197.61, "end": 1197.89, "word": " بدون", "probability": 0.983642578125}, {"start": 1197.89, "end": 1198.45, "word": " اثبات", "probability": 0.8802490234375}, {"start": 1198.45, "end": 1199.23, "word": " هنحتاجها", "probability": 0.733447265625}, {"start": 1199.23, "end": 1199.35, "word": " في", "probability": 0.740234375}, {"start": 1199.35, "end": 1199.99, "word": " اثبات", "probability": 0.9688720703125}, {"start": 1199.99, "end": 1200.93, "word": " شغلة", "probability": 0.7607421875}, {"start": 1200.93, "end": 1201.83, "word": " قادمة", "probability": 0.9938151041666666}, {"start": 1201.83, "end": 1202.65, "word": " او", "probability": 0.855712890625}, {"start": 1202.65, "end": 1203.03, "word": " نظرية", "probability": 0.9688720703125}, {"start": 1203.03, "end": 1203.55, "word": " لبعدها", "probability": 0.867919921875}, {"start": 1203.55, "end": 1203.95, "word": " اللمة", "probability": 0.873046875}, {"start": 1203.95, "end": 1204.15, "word": " هذه", "probability": 0.720703125}, {"start": 1204.15, "end": 1204.51, "word": " بتقول", "probability": 0.96728515625}, {"start": 1204.51, "end": 1204.63, "word": " ال", "probability": 0.9609375}, {"start": 1204.63, "end": 1205.27, "word": " identity", "probability": 0.82958984375}, {"start": 1205.27, "end": 1206.23, "word": " لو", "probability": 0.8525390625}, {"start": 1206.23, "end": 1206.65, "word": " جدرت", "probability": 0.7061360677083334}, {"start": 1206.65, "end": 1207.11, "word": " تكتب", "probability": 0.9810791015625}, {"start": 1207.11, "end": 1207.31, "word": " على", "probability": 0.76708984375}, {"start": 1207.31, "end": 1207.75, "word": " شكل", "probability": 0.982177734375}, {"start": 1207.75, "end": 1208.15, "word": " two", "probability": 0.89697265625}, {"start": 1208.15, "end": 1208.99, "word": " cycles", "probability": 0.83837890625}, {"start": 1208.99, "end": 1209.69, "word": " فعدد", "probability": 0.94921875}, {"start": 1209.69, "end": 1209.83, "word": " ال", "probability": 0.91650390625}, {"start": 1209.83, "end": 1209.99, "word": " two", "probability": 0.9228515625}, {"start": 1209.99, "end": 1210.41, "word": " cycles", "probability": 0.86962890625}, {"start": 1210.41, "end": 1210.65, "word": " هذا", "probability": 0.6845703125}, {"start": 1210.65, "end": 1210.99, "word": " لازم", "probability": 0.9874674479166666}, {"start": 1210.99, "end": 1211.21, "word": " يكون", "probability": 0.992431640625}, {"start": 1211.21, "end": 1211.71, "word": " زوجي", "probability": 0.9637044270833334}, {"start": 1211.71, "end": 1213.31, "word": " ال", "probability": 0.9296875}, {"start": 1213.31, "end": 1213.85, "word": " identity", "probability": 0.94970703125}, {"start": 1213.85, "end": 1214.57, "word": " لو", "probability": 0.84228515625}, {"start": 1214.57, "end": 1215.31, "word": " جدرت", "probability": 0.9881184895833334}, {"start": 1215.31, "end": 1215.79, "word": " تكتب", "probability": 0.9971923828125}, {"start": 1215.79, "end": 1216.01, "word": " على", "probability": 0.93701171875}, {"start": 1216.01, "end": 1216.37, "word": " شكل", "probability": 0.976318359375}, {"start": 1216.37, "end": 1216.67, "word": " two", "probability": 0.95703125}, {"start": 1216.67, "end": 1217.35, "word": " cycles", "probability": 0.873046875}, {"start": 1217.35, "end": 1218.27, "word": " عدد", "probability": 0.96533203125}, {"start": 1218.27, "end": 1218.41, "word": " ال", "probability": 0.94140625}, {"start": 1218.41, "end": 1218.55, "word": " two", "probability": 0.9638671875}, {"start": 1218.55, "end": 1219.03, "word": " cycles", "probability": 0.8603515625}, {"start": 1219.03, "end": 1219.43, "word": " هدول", "probability": 0.9248046875}, {"start": 1219.43, "end": 1220.07, "word": " هيكون", "probability": 0.881591796875}, {"start": 1220.07, "end": 1220.99, "word": " زوجي", "probability": 0.9812825520833334}, {"start": 1220.99, "end": 1221.37, "word": " if", "probability": 0.6328125}], "temperature": 1.0}, {"id": 45, "seek": 125247, "start": 1222.81, "end": 1252.47, "text": "الـ identity عبارة عن ألف واحد ألف اتنين لعند ألف مثلا R is a product of two cycles then R is even لو جدرت تكتب عيد ال identity على شكل two cycles فعدد ال two cycles هدون لازم يكون", "tokens": [6027, 39184, 6575, 6225, 3555, 9640, 3660, 18871, 5551, 46538, 36764, 24401, 5551, 46538, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 5551, 46538, 50113, 15040, 497, 307, 257, 1674, 295, 732, 17796, 550, 497, 307, 754, 45164, 10874, 3215, 43500, 6055, 4117, 2655, 3555, 6225, 25708, 2423, 6575, 15844, 13412, 28820, 732, 17796, 6156, 22488, 3215, 2423, 732, 17796, 8032, 3215, 11536, 5296, 31377, 2304, 7251, 30544], "avg_logprob": -0.24999999693211386, "compression_ratio": 1.5088757396449703, "no_speech_prob": 0.0, "words": [{"start": 1222.81, "end": 1223.09, "word": "الـ", "probability": 0.39129638671875}, {"start": 1223.09, "end": 1223.49, "word": " identity", "probability": 0.55908203125}, {"start": 1223.49, "end": 1224.09, "word": " عبارة", "probability": 0.972412109375}, {"start": 1224.09, "end": 1224.49, "word": " عن", "probability": 0.99560546875}, {"start": 1224.49, "end": 1225.09, "word": " ألف", "probability": 0.6201171875}, {"start": 1225.09, "end": 1225.65, "word": " واحد", "probability": 0.80859375}, {"start": 1225.65, "end": 1226.11, "word": " ألف", "probability": 0.6993408203125}, {"start": 1226.11, "end": 1226.55, "word": " اتنين", "probability": 0.93212890625}, {"start": 1226.55, "end": 1227.19, "word": " لعند", "probability": 0.6619466145833334}, {"start": 1227.19, "end": 1227.65, "word": " ألف", "probability": 0.766845703125}, {"start": 1227.65, "end": 1229.27, "word": " مثلا", "probability": 0.821044921875}, {"start": 1229.27, "end": 1229.79, "word": " R", "probability": 0.1632080078125}, {"start": 1229.79, "end": 1231.91, "word": " is", "probability": 0.6162109375}, {"start": 1231.91, "end": 1232.75, "word": " a", "probability": 0.8212890625}, {"start": 1232.75, "end": 1233.43, "word": " product", "probability": 0.96826171875}, {"start": 1233.43, "end": 1235.85, "word": " of", "probability": 0.95458984375}, {"start": 1235.85, "end": 1236.29, "word": " two", "probability": 0.8994140625}, {"start": 1236.29, "end": 1238.49, "word": " cycles", "probability": 0.83837890625}, {"start": 1238.49, "end": 1239.33, "word": " then", "probability": 0.638671875}, {"start": 1239.33, "end": 1240.99, "word": " R", "probability": 0.94140625}, {"start": 1240.99, "end": 1241.35, "word": " is", "probability": 0.958984375}, {"start": 1241.35, "end": 1241.93, "word": " even", "probability": 0.888671875}, {"start": 1241.93, "end": 1246.05, "word": " لو", "probability": 0.8408203125}, {"start": 1246.05, "end": 1246.37, "word": " جدرت", "probability": 0.7724609375}, {"start": 1246.37, "end": 1246.79, "word": " تكتب", "probability": 0.9805908203125}, {"start": 1246.79, "end": 1247.31, "word": " عيد", "probability": 0.5419921875}, {"start": 1247.31, "end": 1247.55, "word": " ال", "probability": 0.97998046875}, {"start": 1247.55, "end": 1247.99, "word": " identity", "probability": 0.6298828125}, {"start": 1247.99, "end": 1248.23, "word": " على", "probability": 0.73291015625}, {"start": 1248.23, "end": 1248.61, "word": " شكل", "probability": 0.979736328125}, {"start": 1248.61, "end": 1248.91, "word": " two", "probability": 0.89697265625}, {"start": 1248.91, "end": 1249.55, "word": " cycles", "probability": 0.900390625}, {"start": 1249.55, "end": 1250.59, "word": " فعدد", "probability": 0.9812825520833334}, {"start": 1250.59, "end": 1250.71, "word": " ال", "probability": 0.90478515625}, {"start": 1250.71, "end": 1250.89, "word": " two", "probability": 0.8544921875}, {"start": 1250.89, "end": 1251.25, "word": " cycles", "probability": 0.890625}, {"start": 1251.25, "end": 1251.61, "word": " هدون", "probability": 0.7195638020833334}, {"start": 1251.61, "end": 1251.99, "word": " لازم", "probability": 0.98974609375}, {"start": 1251.99, "end": 1252.47, "word": " يكون", "probability": 0.992919921875}], "temperature": 1.0}, {"id": 46, "seek": 128042, "start": 1253.46, "end": 1280.42, "text": "زوجي أهميتها هي نظرية 5-5 theorem 5-5 في نظرية 5-5 لو جدرت تكتب permutation بطريقتين على شكل two cycles لو جدرت تكتب permutation على شكل two cycles بطريقتين", "tokens": [11622, 29245, 1829, 5551, 16095, 36081, 11296, 39896, 8717, 19913, 2288, 10632, 1025, 12, 20, 20904, 1025, 12, 20, 8978, 8717, 19913, 2288, 10632, 1025, 12, 20, 45164, 10874, 3215, 43500, 6055, 4117, 2655, 3555, 4784, 11380, 4724, 9566, 16572, 38149, 9957, 15844, 13412, 28820, 732, 17796, 45164, 10874, 3215, 43500, 6055, 4117, 2655, 3555, 4784, 11380, 15844, 13412, 28820, 732, 17796, 4724, 9566, 16572, 38149, 9957], "avg_logprob": -0.19852940760114612, "compression_ratio": 1.6715328467153285, "no_speech_prob": 0.0, "words": [{"start": 1253.46, "end": 1254.04, "word": "زوجي", "probability": 0.641845703125}, {"start": 1254.04, "end": 1255.48, "word": " أهميتها", "probability": 0.84014892578125}, {"start": 1255.48, "end": 1255.8, "word": " هي", "probability": 0.1549072265625}, {"start": 1255.8, "end": 1256.22, "word": " نظرية", "probability": 0.9498291015625}, {"start": 1256.22, "end": 1256.46, "word": " 5", "probability": 0.474365234375}, {"start": 1256.46, "end": 1256.88, "word": "-5", "probability": 0.6209716796875}, {"start": 1256.88, "end": 1258.6, "word": " theorem", "probability": 0.40478515625}, {"start": 1258.6, "end": 1262.56, "word": " 5", "probability": 0.472900390625}, {"start": 1262.56, "end": 1263.1, "word": "-5", "probability": 0.91455078125}, {"start": 1263.1, "end": 1264.22, "word": " في", "probability": 0.6767578125}, {"start": 1264.22, "end": 1264.62, "word": " نظرية", "probability": 0.9888916015625}, {"start": 1264.62, "end": 1264.88, "word": " 5", "probability": 0.98974609375}, {"start": 1264.88, "end": 1265.36, "word": "-5", "probability": 0.994384765625}, {"start": 1265.36, "end": 1267.4, "word": " لو", "probability": 0.74853515625}, {"start": 1267.4, "end": 1267.96, "word": " جدرت", "probability": 0.6756998697916666}, {"start": 1267.96, "end": 1268.56, "word": " تكتب", "probability": 0.9915771484375}, {"start": 1268.56, "end": 1269.34, "word": " permutation", "probability": 0.95556640625}, {"start": 1269.34, "end": 1272.0, "word": " بطريقتين", "probability": 0.95478515625}, {"start": 1272.0, "end": 1273.4, "word": " على", "probability": 0.8447265625}, {"start": 1273.4, "end": 1273.82, "word": " شكل", "probability": 0.977783203125}, {"start": 1273.82, "end": 1274.12, "word": " two", "probability": 0.8349609375}, {"start": 1274.12, "end": 1275.0, "word": " cycles", "probability": 0.86376953125}, {"start": 1275.0, "end": 1276.42, "word": " لو", "probability": 0.734375}, {"start": 1276.42, "end": 1276.7, "word": " جدرت", "probability": 0.9957682291666666}, {"start": 1276.7, "end": 1277.04, "word": " تكتب", "probability": 0.9969482421875}, {"start": 1277.04, "end": 1277.68, "word": " permutation", "probability": 0.99169921875}, {"start": 1277.68, "end": 1278.38, "word": " على", "probability": 0.8203125}, {"start": 1278.38, "end": 1278.68, "word": " شكل", "probability": 0.94921875}, {"start": 1278.68, "end": 1278.96, "word": " two", "probability": 0.943359375}, {"start": 1278.96, "end": 1279.46, "word": " cycles", "probability": 0.89990234375}, {"start": 1279.46, "end": 1280.42, "word": " بطريقتين", "probability": 0.97197265625}], "temperature": 1.0}, {"id": 47, "seek": 131178, "start": 1283.02, "end": 1311.78, "text": "و عديت ال two cycles في الطريقة الأولى و عديت ال two cycles في الطريقة التانية ياتنين even ياتنين odd if Alpha عبارة عن Alpha 1 Alpha 2 لعند Alpha R وهي نفسها Beta 1 Beta 2 لعند Beta S where", "tokens": [2407, 6225, 16254, 2655, 2423, 732, 17796, 8978, 41950, 16572, 28671, 16247, 12610, 7578, 4032, 6225, 16254, 2655, 2423, 732, 17796, 8978, 41950, 16572, 28671, 16712, 7649, 10632, 7251, 9307, 1863, 9957, 754, 7251, 9307, 1863, 9957, 7401, 498, 20588, 6225, 3555, 9640, 3660, 18871, 20588, 502, 20588, 568, 5296, 3615, 41260, 20588, 497, 37037, 1829, 8717, 36178, 11296, 33286, 502, 33286, 568, 5296, 3615, 41260, 33286, 318, 689], "avg_logprob": -0.18995535224676133, "compression_ratio": 1.6875, "no_speech_prob": 0.0, "words": [{"start": 1283.02, "end": 1283.24, "word": "و", "probability": 0.61865234375}, {"start": 1283.24, "end": 1283.94, "word": " عديت", "probability": 0.7898763020833334}, {"start": 1283.94, "end": 1284.14, "word": " ال", "probability": 0.931640625}, {"start": 1284.14, "end": 1284.3, "word": " two", "probability": 0.81005859375}, {"start": 1284.3, "end": 1284.8, "word": " cycles", "probability": 0.86328125}, {"start": 1284.8, "end": 1284.98, "word": " في", "probability": 0.7939453125}, {"start": 1284.98, "end": 1285.34, "word": " الطريقة", "probability": 0.9791666666666666}, {"start": 1285.34, "end": 1285.9, "word": " الأولى", "probability": 0.9558919270833334}, {"start": 1285.9, "end": 1286.24, "word": " و", "probability": 0.76953125}, {"start": 1286.24, "end": 1286.84, "word": " عديت", "probability": 0.9560546875}, {"start": 1286.84, "end": 1286.98, "word": " ال", "probability": 0.95556640625}, {"start": 1286.98, "end": 1287.18, "word": " two", "probability": 0.9609375}, {"start": 1287.18, "end": 1287.6, "word": " cycles", "probability": 0.90234375}, {"start": 1287.6, "end": 1287.8, "word": " في", "probability": 0.9365234375}, {"start": 1287.8, "end": 1288.12, "word": " الطريقة", "probability": 0.9856770833333334}, {"start": 1288.12, "end": 1289.14, "word": " التانية", "probability": 0.9661458333333334}, {"start": 1289.14, "end": 1292.32, "word": " ياتنين", "probability": 0.6748046875}, {"start": 1292.32, "end": 1292.72, "word": " even", "probability": 0.77392578125}, {"start": 1292.72, "end": 1294.04, "word": " ياتنين", "probability": 0.913818359375}, {"start": 1294.04, "end": 1294.34, "word": " odd", "probability": 0.6513671875}, {"start": 1294.34, "end": 1296.86, "word": " if", "probability": 0.57861328125}, {"start": 1296.86, "end": 1299.06, "word": " Alpha", "probability": 0.2098388671875}, {"start": 1299.06, "end": 1299.66, "word": " عبارة", "probability": 0.984619140625}, {"start": 1299.66, "end": 1300.04, "word": " عن", "probability": 0.98681640625}, {"start": 1300.04, "end": 1300.88, "word": " Alpha", "probability": 0.6640625}, {"start": 1300.88, "end": 1301.3, "word": " 1", "probability": 0.54150390625}, {"start": 1301.3, "end": 1301.7, "word": " Alpha", "probability": 0.6552734375}, {"start": 1301.7, "end": 1302.04, "word": " 2", "probability": 0.970703125}, {"start": 1302.04, "end": 1302.42, "word": " لعند", "probability": 0.75048828125}, {"start": 1302.42, "end": 1302.84, "word": " Alpha", "probability": 0.96484375}, {"start": 1302.84, "end": 1304.26, "word": " R", "probability": 0.5712890625}, {"start": 1304.26, "end": 1304.62, "word": " وهي", "probability": 0.685302734375}, {"start": 1304.62, "end": 1305.38, "word": " نفسها", "probability": 0.9791666666666666}, {"start": 1305.38, "end": 1305.8, "word": " Beta", "probability": 0.77001953125}, {"start": 1305.8, "end": 1306.36, "word": " 1", "probability": 0.97705078125}, {"start": 1306.36, "end": 1307.22, "word": " Beta", "probability": 0.79736328125}, {"start": 1307.22, "end": 1307.78, "word": " 2", "probability": 0.98876953125}, {"start": 1307.78, "end": 1308.8, "word": " لعند", "probability": 0.9775390625}, {"start": 1308.8, "end": 1309.14, "word": " Beta", "probability": 0.91064453125}, {"start": 1309.14, "end": 1309.78, "word": " S", "probability": 0.95458984375}, {"start": 1309.78, "end": 1311.78, "word": " where", "probability": 0.716796875}], "temperature": 1.0}, {"id": 48, "seek": 134170, "start": 1313.3, "end": 1341.7, "text": "أو is a product of two cycles in two ways then both are and is even or both are odd", "tokens": [10721, 2407, 307, 257, 1674, 295, 732, 17796, 294, 732, 2098, 550, 1293, 366, 293, 307, 754, 420, 1293, 366, 7401], "avg_logprob": -0.2501775554635308, "compression_ratio": 1.0759493670886076, "no_speech_prob": 0.0, "words": [{"start": 1313.3, "end": 1313.58, "word": "أو", "probability": 0.6876220703125}, {"start": 1313.58, "end": 1313.9, "word": " is", "probability": 0.9189453125}, {"start": 1313.9, "end": 1315.1, "word": " a", "probability": 0.93017578125}, {"start": 1315.1, "end": 1315.72, "word": " product", "probability": 0.95703125}, {"start": 1315.72, "end": 1317.94, "word": " of", "probability": 0.97216796875}, {"start": 1317.94, "end": 1319.14, "word": " two", "probability": 0.95556640625}, {"start": 1319.14, "end": 1320.68, "word": " cycles", "probability": 0.884765625}, {"start": 1320.68, "end": 1321.6, "word": " in", "probability": 0.96533203125}, {"start": 1321.6, "end": 1323.52, "word": " two", "probability": 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كتبت ال permutation على شكل two cycles وضعتها زيكي لكي أميزها بطريقتين فعدد ال two cycles في الأولى وعدد ال two cycles في التانية يا اتنين زوجي يا اتنين فردي ولا حاجة since Alpha بدي ساوي Alpha واحد Alpha اتنين لعند Alpha R هو نفسه Beta واحد Beta اتنين", "tokens": [40228, 22653, 45164, 9122, 2655, 3555, 2655, 2423, 4784, 11380, 15844, 13412, 28820, 732, 17796, 4032, 11242, 34268, 11296, 30767, 1829, 4117, 1829, 5296, 4117, 1829, 5551, 2304, 1829, 11622, 11296, 4724, 9566, 16572, 38149, 9957, 6156, 22488, 3215, 2423, 732, 17796, 8978, 16247, 12610, 7578, 4032, 22488, 3215, 2423, 732, 17796, 8978, 16712, 7649, 10632, 35186, 1975, 2655, 1863, 9957, 30767, 29245, 1829, 35186, 1975, 2655, 1863, 9957, 6156, 2288, 16254, 49429, 11331, 26108, 3660, 1670, 20588, 4724, 16254, 8608, 995, 45865, 20588, 36764, 24401, 20588, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 20588, 497, 31439, 8717, 36178, 3224, 33286, 36764, 24401, 33286, 1975, 2655, 1863, 9957], "avg_logprob": -0.22434059687710683, 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1371.92, "word": " Beta", "probability": 0.6328125}, {"start": 1371.92, "end": 1372.36, "word": " واحد", "probability": 0.9658203125}, {"start": 1372.36, "end": 1372.7, "word": " Beta", "probability": 0.7119140625}, {"start": 1372.7, "end": 1373.22, "word": " اتنين", "probability": 0.9813232421875}], "temperature": 1.0}, {"id": 50, "seek": 140019, "start": 1375.45, "end": 1400.19, "text": "لأن BTS أجد شباب ال two cycle الأخضر غير هجد دياش اتنين since Alpha I عبارة عن a1i a2i", "tokens": [1211, 33456, 17951, 5551, 7435, 3215, 13412, 3555, 16758, 2423, 732, 6586, 16247, 9778, 11242, 2288, 32771, 13546, 8032, 7435, 3215, 11778, 1829, 33599, 1975, 2655, 1863, 9957, 1670, 20588, 286, 6225, 3555, 9640, 3660, 18871, 257, 16, 72, 257, 17, 72], "avg_logprob": -0.3844476633293684, "compression_ratio": 1.0413223140495869, "no_speech_prob": 0.0, "words": [{"start": 1375.45, "end": 1375.83, "word": "لأن", "probability": 0.76953125}, {"start": 1375.83, "end": 1376.49, "word": " BTS", "probability": 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"probability": 0.35498046875}, {"start": 1393.15, "end": 1393.61, "word": " I", "probability": 0.88916015625}, {"start": 1393.61, "end": 1394.69, "word": " عبارة", "probability": 0.9664306640625}, {"start": 1394.69, "end": 1396.19, "word": " عن", "probability": 0.99169921875}, {"start": 1396.19, "end": 1398.55, "word": " a1i", "probability": 0.5978190104166666}, {"start": 1398.55, "end": 1400.19, "word": " a2i", "probability": 0.86572265625}], "temperature": 1.0}, {"id": 51, "seek": 142800, "start": 1401.2, "end": 1428.0, "text": "وبيتا جي عبارة عن بي واحد جي بيتينين جي النتيجة order لالف اي بيسوي order لبيتا جي بيسوي اتنين لكل اي اقل او يسوي ار جي اقل او يسوي اس هذا معناته ان الف اي بيسوي الف اي inverse وبيتا جي بيسوي بيتا جي inverse", "tokens": [37746, 36081, 995, 10874, 1829, 6225, 3555, 9640, 3660, 18871, 4724, 1829, 36764, 24401, 10874, 1829, 4724, 36081, 9957, 9957, 10874, 1829, 28239, 31371, 7435, 3660, 1668, 5296, 6027, 5172, 1975, 1829, 4724, 1829, 3794, 45865, 1668, 5296, 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"word": " بيسوي", "probability": 0.833251953125}, {"start": 1413.84, "end": 1414.18, "word": " اتنين", "probability": 0.912109375}, {"start": 1414.18, "end": 1414.66, "word": " لكل", "probability": 0.972412109375}, {"start": 1414.66, "end": 1415.0, "word": " اي", "probability": 0.93603515625}, {"start": 1415.0, "end": 1415.42, "word": " اقل", "probability": 0.9563802083333334}, {"start": 1415.42, "end": 1415.58, "word": " او", "probability": 0.973876953125}, {"start": 1415.58, "end": 1415.94, "word": " يسوي", "probability": 0.9072265625}, {"start": 1415.94, "end": 1416.28, "word": " ار", "probability": 0.38604736328125}, {"start": 1416.28, "end": 1416.5, "word": " جي", "probability": 0.964599609375}, {"start": 1416.5, "end": 1416.82, "word": " اقل", "probability": 0.9866536458333334}, {"start": 1416.82, "end": 1416.98, "word": " او", "probability": 0.9912109375}, {"start": 1416.98, "end": 1417.34, "word": " يسوي", "probability": 0.9441731770833334}, {"start": 1417.34, "end": 1417.68, 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0.890625}, {"start": 2011.22, "end": 2011.48, "word": " مين", "probability": 0.91015625}, {"start": 2011.48, "end": 2011.84, "word": " هي", "probability": 0.80615234375}, {"start": 2011.84, "end": 2013.92, "word": " نفسها", "probability": 0.8785807291666666}, {"start": 2013.92, "end": 2017.88, "word": " و", "probability": 0.87841796875}, {"start": 2017.88, "end": 2018.08, "word": " 2", "probability": 0.61181640625}, {"start": 2018.08, "end": 2018.44, "word": " 4", "probability": 0.9931640625}, {"start": 2018.44, "end": 2018.66, "word": " 3", "probability": 0.99169921875}, {"start": 2018.66, "end": 2018.98, "word": " 5", "probability": 0.9931640625}, {"start": 2018.98, "end": 2019.54, "word": " inverse", "probability": 0.8984375}, {"start": 2019.54, "end": 2020.9, "word": " خمسة", "probability": 0.862060546875}, {"start": 2020.9, "end": 2021.66, "word": " تلاتة", "probability": 0.76776123046875}, {"start": 2021.66, "end": 2022.0, "word": " اربعة", "probability": 0.80029296875}, {"start": 2022.0, "end": 2022.44, "word": " اتنين", "probability": 0.9678955078125}, {"start": 2022.44, "end": 2026.62, "word": " خيال", "probability": 0.6861979166666666}], "temperature": 1.0}, {"id": 73, "seek": 205577, "start": 2028.31, "end": 2055.77, "text": "و هدى صارت عندك أهمية تانية لكتابة ال permutation على شكل two cycles دى theorem خمسة ستة بيجي السؤال هل جيت ال Sn فيها permutation even و فيها permutation odd", "tokens": [2407, 8032, 3215, 7578, 20328, 9640, 2655, 43242, 4117, 5551, 16095, 10632, 6055, 7649, 10632, 5296, 4117, 2655, 16758, 3660, 2423, 4784, 11380, 15844, 13412, 28820, 732, 17796, 11778, 7578, 20904, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 4724, 1829, 7435, 1829, 21136, 33604, 6027, 8032, 1211, 10874, 36081, 2423, 9264, 8978, 11296, 4784, 11380, 754, 4032, 8978, 11296, 4784, 11380, 7401], "avg_logprob": -0.245535714758767, "compression_ratio": 1.43125, "no_speech_prob": 0.0, "words": [{"start": 2028.31, "end": 2028.53, "word": "و", "probability": 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"probability": 0.81396484375}, {"start": 2034.77, "end": 2043.47, "word": " دى", "probability": 0.22442626953125}, {"start": 2043.47, "end": 2044.01, "word": " theorem", "probability": 0.6572265625}, {"start": 2044.01, "end": 2044.43, "word": " خمسة", "probability": 0.7734375}, {"start": 2044.43, "end": 2045.09, "word": " ستة", "probability": 0.9412434895833334}, {"start": 2045.09, "end": 2049.55, "word": " بيجي", "probability": 0.91357421875}, {"start": 2049.55, "end": 2049.85, "word": " السؤال", "probability": 0.982421875}, {"start": 2049.85, "end": 2050.05, "word": " هل", "probability": 0.834228515625}, {"start": 2050.05, "end": 2050.29, "word": " جيت", "probability": 0.93310546875}, {"start": 2050.29, "end": 2051.31, "word": " ال", "probability": 0.728515625}, {"start": 2051.31, "end": 2051.91, "word": " Sn", "probability": 0.1929931640625}, {"start": 2051.91, "end": 2052.71, "word": " فيها", "probability": 0.798583984375}, {"start": 2052.71, "end": 2053.37, "word": " permutation", "probability": 0.98779296875}, {"start": 2053.37, "end": 2053.89, "word": " even", "probability": 0.9091796875}, {"start": 2053.89, "end": 2054.43, "word": " و", "probability": 0.69091796875}, {"start": 2054.43, "end": 2054.65, "word": " فيها", "probability": 0.8056640625}, {"start": 2054.65, "end": 2055.25, "word": " permutation", "probability": 0.98828125}, {"start": 2055.25, "end": 2055.77, "word": " odd", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 74, "seek": 207667, "start": 2059.31, "end": 2076.67, "text": "هل ال odd مع بعض بيعملولي subgroup؟ بيجي هانا السؤال هل ال even مع بعض بيعملولي subgroup؟ والله لأ نظرية خمسة ستة بتقولك أنه لو أخدت ال even مع بعض هيعملوا subgroup", "tokens": [3224, 1211, 2423, 7401, 20449, 45030, 11242, 4724, 1829, 25957, 1211, 12610, 1829, 1422, 17377, 22807, 4724, 1829, 7435, 1829, 8032, 7649, 995, 21136, 33604, 6027, 8032, 1211, 2423, 754, 20449, 45030, 11242, 4724, 1829, 25957, 1211, 12610, 1829, 1422, 17377, 22807, 16070, 43761, 5296, 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{"start": 2064.37, "end": 2064.59, "word": " هانا", "probability": 0.4337565104166667}, {"start": 2064.59, "end": 2064.95, "word": " السؤال", "probability": 0.98388671875}, {"start": 2064.95, "end": 2067.27, "word": " هل", "probability": 0.8076171875}, {"start": 2067.27, "end": 2067.45, "word": " ال", "probability": 0.9912109375}, {"start": 2067.45, "end": 2067.71, "word": " even", "probability": 0.95166015625}, {"start": 2067.71, "end": 2067.95, "word": " مع", "probability": 0.990234375}, {"start": 2067.95, "end": 2068.27, "word": " بعض", "probability": 0.996337890625}, {"start": 2068.27, "end": 2068.81, "word": " بيعملولي", "probability": 0.9877115885416666}, {"start": 2068.81, "end": 2070.27, "word": " subgroup؟", "probability": 0.9130859375}, {"start": 2070.27, "end": 2070.47, "word": " والله", "probability": 0.80126953125}, {"start": 2070.47, "end": 2070.75, "word": " لأ", "probability": 0.84912109375}, {"start": 2070.75, "end": 2072.69, "word": " نظرية", "probability": 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0.978271484375}], "temperature": 1.0}, {"id": 75, "seek": 210546, "start": 2077.92, "end": 2105.46, "text": "إن الـ odd مع بعض ما بيعملش subgroup هذا عبارة عن counter .. محتاج counter example انه مش هيعمل subgroup موجود ضمن الأسئلة هنثبت في نظرية ان ال even بيعملوا subgroup و بنستعطيها اسم اسم ال alternating group of degree theorem 5-6 that's it of all even permutations", "tokens": [28814, 1863, 2423, 39184, 7401, 20449, 45030, 11242, 19446, 4724, 1829, 25957, 1211, 8592, 1422, 17377, 23758, 6225, 3555, 9640, 3660, 18871, 5682, 4386, 3714, 33753, 26108, 5682, 1365, 16472, 3224, 37893, 39896, 25957, 1211, 1422, 17377, 3714, 29245, 23328, 48812, 27842, 16247, 3794, 19986, 37977, 8032, 1863, 12984, 3555, 2655, 8978, 8717, 19913, 2288, 10632, 16472, 2423, 754, 4724, 1829, 25957, 1211, 14407, 1422, 17377, 4032, 44945, 14851, 3615, 9566, 1829, 11296, 24525, 2304, 24525, 2304, 2423, 40062, 1594, 295, 4314, 20904, 1025, 12, 21, 300, 311, 309, 295, 439, 754, 4784, 325, 763], "avg_logprob": 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{"start": 2101.44, "end": 2102.3, "word": " even", "probability": 0.849609375}, {"start": 2102.3, "end": 2105.46, "word": " permutations", "probability": 0.9388020833333334}], "temperature": 1.0}, {"id": 76, "seek": 213419, "start": 2111.48, "end": 2134.2, "text": "ن أسن form a subgroup of أسن بتبقى سهل let أن عبارة عن كل الألف حيث ألف ينتمي لأسن و ألف is even", "tokens": [1863, 5551, 3794, 1863, 1254, 257, 1422, 17377, 295, 5551, 3794, 1863, 39894, 3555, 4587, 7578, 8608, 3224, 1211, 718, 14739, 6225, 3555, 9640, 3660, 18871, 28242, 16247, 46538, 11331, 1829, 12984, 5551, 46538, 7251, 29399, 2304, 1829, 5296, 10721, 3794, 1863, 4032, 5551, 46538, 307, 754], "avg_logprob": -0.23649088914195696, "compression_ratio": 1.2478632478632479, "no_speech_prob": 0.0, "words": [{"start": 2111.48, "end": 2112.88, "word": "ن", "probability": 0.21728515625}, {"start": 2112.88, "end": 2114.28, "word": " أسن", "probability": 0.4939982096354167}, {"start": 2114.28, "end": 2115.9, "word": " form", 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step", "tokens": [6027, 39184, 25905, 507, 7251, 29399, 2304, 1829, 5296, 7649, 46599, 6027, 2655, 6027, 1829, 2423, 7649, 20193, 7251, 3794, 9640, 6156, 3615, 15040, 23032, 3555, 3615, 995, 34105, 337, 364, 5551, 4117, 26890, 9154, 2423, 14407, 24401, 5296, 33456, 45164, 364, 4724, 1829, 3794, 9640, 36764, 24401, 19446, 41185, 8592, 32771, 13546, 18871, 9381, 2288, 36764, 24401, 31439, 2423, 6575, 36632, 8592, 4724, 1829, 19913, 1211, 5551, 12984, 3555, 2655, 14739, 11296, 10874, 9307, 22807, 16472, 39896, 8592, 8032, 8848, 1829, 19362, 8978, 2423, 19362, 7251, 4117, 41185, 8717, 1829, 33599, 13412, 2288, 9566, 36764, 24401, 13672, 1829, 31439, 2423, 472, 1823], "avg_logprob": -0.31580527843191075, "compression_ratio": 1.705069124423963, "no_speech_prob": 0.0, "words": [{"start": 2139.34, "end": 2139.68, "word": "الـ", "probability": 0.509033203125}, {"start": 2139.68, "end": 2140.18, "word": " Identity", "probability": 0.6387939453125}, {"start": 2140.18, "end": 2140.7, "word": " ينتمي", "probability": 0.7921142578125}, {"start": 2140.7, "end": 2141.06, "word": " لان", "probability": 0.57720947265625}, {"start": 2141.06, "end": 2141.98, "word": " وبالتالي", "probability": 0.849072265625}, {"start": 2141.98, "end": 2142.74, "word": " الان", "probability": 0.67431640625}, {"start": 2142.74, "end": 2144.3, "word": " لا", "probability": 0.54931640625}, {"start": 2144.3, "end": 2144.6, "word": " يسار", "probability": 0.6029459635416666}, {"start": 2144.6, "end": 2145.24, "word": " فعلا", "probability": 0.6363932291666666}, {"start": 2145.24, "end": 2146.26, "word": " طبعا", "probability": 0.92236328125}, {"start": 2146.26, "end": 2146.42, "word": " هنا", "probability": 0.712890625}, {"start": 2146.42, "end": 2146.72, "word": " for", "probability": 0.890625}, {"start": 2146.72, "end": 2146.96, "word": " an", "probability": 0.232421875}, {"start": 2146.96, "end": 2147.44, "word": " أكبر", "probability": 0.95556640625}, {"start": 2147.44, "end": 2147.58, "word": " من", "probability": 0.99072265625}, {"start": 2147.58, "end": 2148.1, "word": " الواحد", "probability": 0.94873046875}, {"start": 2148.1, "end": 2150.08, "word": " لأن", "probability": 0.7509765625}, {"start": 2150.08, "end": 2150.26, "word": " لو", "probability": 0.734375}, {"start": 2150.26, "end": 2150.42, "word": " an", "probability": 0.36083984375}, {"start": 2150.42, "end": 2150.7, "word": " بيسار", "probability": 0.898681640625}, {"start": 2150.7, "end": 2150.9, "word": " واحد", "probability": 0.980712890625}, {"start": 2150.9, "end": 2151.18, "word": " مافيش", "probability": 0.8719075520833334}, {"start": 2151.18, "end": 2151.3, "word": " غير", "probability": 0.768310546875}, {"start": 2151.3, "end": 2151.58, "word": " عنصر", "probability": 0.8723958333333334}, {"start": 2151.58, "end": 2151.8, "word": " واحد", "probability": 0.99267578125}, {"start": 2151.8, "end": 2151.94, "word": " هو", "probability": 0.97314453125}, {"start": 2151.94, "end": 2152.04, "word": " ال", "probability": 0.9833984375}, {"start": 2152.04, "end": 2152.5, "word": " identity", "probability": 0.81494140625}, {"start": 2152.5, "end": 2155.18, "word": " أيش", "probability": 0.59820556640625}, {"start": 2155.18, "end": 2155.42, "word": " بيظل", "probability": 0.8192138671875}, {"start": 2155.42, "end": 2155.76, "word": " أثبت", "probability": 0.976318359375}, {"start": 2155.76, "end": 2155.96, "word": " أنها", "probability": 0.718017578125}, {"start": 2155.96, "end": 2158.96, "word": " جات؟", "probability": 0.4239908854166667}, {"start": 2158.96, "end": 2160.22, "word": " ان", "probability": 0.35400390625}, {"start": 2160.22, "end": 2160.56, "word": " هيش", "probability": 0.584716796875}, {"start": 2160.56, "end": 2162.58, "word": " هذي", "probability": 0.3912760416666667}, {"start": 2162.58, "end": 2163.04, "word": " finite", "probability": 0.94384765625}, {"start": 2163.04, "end": 2163.68, "word": " في", "probability": 0.76513671875}, {"start": 2163.68, "end": 2163.8, "word": " ال", "probability": 0.9013671875}, {"start": 2163.8, "end": 2164.12, "word": " finite", "probability": 0.87255859375}, {"start": 2164.12, "end": 2164.44, "word": " يكفي", "probability": 0.8720703125}, {"start": 2164.44, "end": 2164.86, "word": " نياش", "probability": 0.8759765625}, {"start": 2164.86, "end": 2166.64, "word": " شرط", "probability": 0.95556640625}, {"start": 2166.64, "end": 2166.98, "word": " واحد", "probability": 0.990234375}, {"start": 2166.98, "end": 2167.12, "word": " اللي", "probability": 0.6314697265625}, {"start": 2167.12, "end": 2167.26, "word": " هو", "probability": 0.97216796875}, {"start": 2167.26, "end": 2167.78, "word": " ال", "probability": 0.8701171875}, {"start": 2167.78, "end": 2167.96, "word": " one", "probability": 0.84130859375}, {"start": 2167.96, "end": 2168.36, "word": " step", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 78, "seek": 219927, "start": 2169.85, "end": 2199.27, "text": "لأ انه closed انه اي عنصرين بتاخدهم يكون حاصل ضربه معاها let alpha و beta ينتمي ل a,n معناته alpha و beta is even يعني alpha عبارة عن ال alpha واحد ال alpha اتنين اللي عند ال alpha اتنين ام beta بتساوي beta واحد beta تنين اللي عند ال beta تنين", "tokens": [1211, 10721, 16472, 3224, 5395, 16472, 3224, 1975, 1829, 18871, 9381, 2288, 9957, 39894, 47283, 3215, 16095, 7251, 30544, 11331, 33546, 1211, 48812, 25513, 3224, 20449, 995, 11296, 718, 8961, 4032, 9861, 7251, 29399, 2304, 1829, 5296, 257, 11, 77, 20449, 8315, 47395, 8961, 4032, 9861, 307, 754, 37495, 22653, 8961, 6225, 3555, 9640, 3660, 18871, 2423, 8961, 36764, 24401, 2423, 8961, 1975, 2655, 1863, 9957, 13672, 1829, 43242, 2423, 8961, 1975, 2655, 1863, 9957, 1975, 2304, 9861, 4724, 2655, 3794, 995, 45865, 9861, 36764, 24401, 9861, 6055, 1863, 9957, 13672, 1829, 43242, 2423, 9861, 6055, 1863, 9957], "avg_logprob": -0.32244318663471877, "compression_ratio": 1.9361702127659575, "no_speech_prob": 0.0, "words": [{"start": 2169.85, "end": 2170.25, "word": "لأ", "probability": 0.9248046875}, {"start": 2170.25, "end": 2170.65, "word": " انه", "probability": 0.706787109375}, {"start": 2170.65, "end": 2171.25, "word": " closed", "probability": 0.46826171875}, {"start": 2171.25, "end": 2172.33, "word": " انه", "probability": 0.59814453125}, {"start": 2172.33, "end": 2172.51, "word": " اي", "probability": 0.77880859375}, {"start": 2172.51, "end": 2172.99, "word": " عنصرين", "probability": 0.729766845703125}, {"start": 2172.99, "end": 2173.63, "word": " بتاخدهم", "probability": 0.9730224609375}, {"start": 2173.63, "end": 2174.47, "word": " يكون", "probability": 0.784423828125}, {"start": 2174.47, "end": 2174.79, "word": " حاصل", "probability": 0.95166015625}, {"start": 2174.79, "end": 2175.13, "word": " ضربه", "probability": 0.8091634114583334}, {"start": 2175.13, "end": 2175.43, "word": " معاها", "probability": 0.302490234375}, {"start": 2175.43, "end": 2175.99, "word": " let", "probability": 0.6416015625}, {"start": 2175.99, "end": 2178.01, "word": " alpha", "probability": 0.48095703125}, {"start": 2178.01, "end": 2178.29, "word": " و", "probability": 0.9609375}, {"start": 2178.29, "end": 2178.71, "word": " beta", "probability": 0.921875}, {"start": 2178.71, "end": 2180.87, "word": " ينتمي", "probability": 0.9735107421875}, {"start": 2180.87, "end": 2181.01, "word": " ل", "probability": 0.86474609375}, {"start": 2181.01, "end": 2181.19, "word": " a", "probability": 0.291259765625}, {"start": 2181.19, "end": 2181.47, "word": ",n", "probability": 0.3310546875}, {"start": 2181.47, "end": 2182.49, "word": " معناته", "probability": 0.7984212239583334}, {"start": 2182.49, "end": 2182.87, "word": " alpha", "probability": 0.71435546875}, {"start": 2182.87, "end": 2183.11, "word": " و", "probability": 0.98388671875}, {"start": 2183.11, "end": 2183.55, "word": " beta", "probability": 0.9384765625}, {"start": 2183.55, "end": 2186.11, "word": " is", "probability": 0.91943359375}, {"start": 2186.11, "end": 2186.57, "word": " even", "probability": 0.91259765625}, {"start": 2186.57, "end": 2188.23, "word": " يعني", "probability": 0.932373046875}, {"start": 2188.23, "end": 2188.73, "word": " alpha", "probability": 0.63818359375}, {"start": 2188.73, "end": 2189.65, "word": " عبارة", "probability": 0.871826171875}, {"start": 2189.65, "end": 2189.83, "word": " عن", "probability": 0.9873046875}, {"start": 2189.83, "end": 2189.93, "word": " ال", "probability": 0.67236328125}, {"start": 2189.93, "end": 2190.17, "word": " alpha", "probability": 0.67578125}, {"start": 2190.17, "end": 2190.61, "word": " واحد", "probability": 0.9306640625}, {"start": 2190.61, "end": 2190.77, "word": " ال", "probability": 0.2440185546875}, {"start": 2190.77, "end": 2190.97, "word": " alpha", "probability": 0.837890625}, {"start": 2190.97, "end": 2191.27, "word": " اتنين", "probability": 0.9014892578125}, {"start": 2191.27, "end": 2191.43, "word": " اللي", "probability": 0.6534423828125}, {"start": 2191.43, "end": 2191.59, "word": " عند", "probability": 0.9921875}, {"start": 2191.59, "end": 2191.75, "word": " ال", "probability": 0.60107421875}, {"start": 2191.75, "end": 2192.07, "word": " alpha", "probability": 0.79931640625}, {"start": 2192.07, "end": 2193.21, "word": " اتنين", "probability": 0.97412109375}, {"start": 2193.21, "end": 2193.63, "word": " ام", "probability": 0.710205078125}, {"start": 2193.63, "end": 2194.83, "word": " beta", "probability": 0.41650390625}, {"start": 2194.83, "end": 2195.37, "word": " بتساوي", "probability": 0.63125}, {"start": 2195.37, "end": 2195.73, "word": " beta", "probability": 0.51513671875}, {"start": 2195.73, "end": 2196.21, "word": " واحد", "probability": 0.96826171875}, {"start": 2196.21, "end": 2196.61, "word": " beta", "probability": 0.357666015625}, {"start": 2196.61, "end": 2196.95, "word": " تنين", "probability": 0.8479817708333334}, {"start": 2196.95, "end": 2197.09, "word": " اللي", "probability": 0.978759765625}, {"start": 2197.09, "end": 2197.27, "word": " عند", "probability": 0.994140625}, {"start": 2197.27, "end": 2197.77, "word": " ال", "probability": 0.491943359375}, {"start": 2197.77, "end": 2197.77, "word": " beta", "probability": 0.94873046875}, {"start": 2197.77, "end": 2199.27, "word": " تنين", "probability": 0.9694010416666666}], "temperature": 1.0}, {"id": 79, "seek": 222644, "start": 2201.61, "end": 2226.45, "text": "مش هما even فعبارة عن where alpha i and beta j اشملهم are two cycles تعالوا تقبلي alpha في beta", "tokens": [2304, 8592, 8032, 15042, 754, 6156, 3615, 3555, 9640, 3660, 18871, 689, 8961, 741, 293, 9861, 361, 1975, 8592, 2304, 1211, 16095, 366, 732, 17796, 37279, 6027, 14407, 6055, 4587, 36150, 1829, 8961, 8978, 9861], "avg_logprob": -0.3148871453271972, "compression_ratio": 1.1238938053097345, "no_speech_prob": 0.0, "words": [{"start": 2201.61, "end": 2201.99, "word": "مش", "probability": 0.69677734375}, {"start": 2201.99, "end": 2202.29, "word": " هما", "probability": 0.80859375}, {"start": 2202.29, "end": 2202.69, "word": " even", "probability": 0.853515625}, {"start": 2202.69, "end": 2203.59, "word": " فعبارة", "probability": 0.8953125}, {"start": 2203.59, "end": 2204.05, "word": " عن", "probability": 0.97412109375}, {"start": 2204.05, "end": 2205.07, "word": " where", "probability": 0.666015625}, {"start": 2205.07, "end": 2208.47, "word": " alpha", "probability": 0.479736328125}, {"start": 2208.47, "end": 2208.87, "word": " i", "probability": 0.439697265625}, {"start": 2208.87, "end": 2210.31, "word": " and", "probability": 0.8798828125}, {"start": 2210.31, "end": 2210.67, "word": " beta", "probability": 0.828125}, {"start": 2210.67, "end": 2211.17, "word": " j", "probability": 0.91748046875}, {"start": 2211.17, "end": 2212.83, "word": " اشملهم", "probability": 0.7263671875}, {"start": 2212.83, "end": 2214.67, "word": " are", "probability": 0.88623046875}, {"start": 2214.67, "end": 2215.13, "word": " two", "probability": 0.93505859375}, {"start": 2215.13, "end": 2218.87, "word": " cycles", "probability": 0.88671875}, {"start": 2218.87, "end": 2225.55, "word": " تعالوا", "probability": 0.7314453125}, {"start": 2225.55, "end": 2225.81, "word": " تقبلي", "probability": 0.55889892578125}, {"start": 2225.81, "end": 2226.01, "word": " alpha", "probability": 0.29833984375}, {"start": 2226.01, "end": 2226.19, "word": " في", "probability": 0.84912109375}, {"start": 2226.19, "end": 2226.45, "word": " beta", "probability": 0.83544921875}], "temperature": 1.0}, {"id": 80, "seek": 225806, "start": 2230.32, "end": 2258.06, "text": "الف في بيتا يبقى عن الف واحد الف اتنين لعند الف اتنين ك بيتا واحد بيتا اتنين لعند بيتا اتنين ام في الاول اتنين ام و اتنين ك كده اش عدد هدول اتنين ام زائد ك من ال two cycles اش يعني الف بيتا is even يبقى الف بيتا وان موجود", "tokens": [6027, 5172, 8978, 4724, 36081, 995, 7251, 3555, 4587, 7578, 18871, 27188, 36764, 24401, 27188, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 27188, 1975, 2655, 1863, 9957, 9122, 4724, 36081, 995, 36764, 24401, 4724, 36081, 995, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 4724, 36081, 995, 1975, 2655, 1863, 9957, 1975, 2304, 8978, 42963, 12610, 1975, 2655, 1863, 9957, 1975, 2304, 4032, 1975, 2655, 1863, 9957, 9122, 9122, 3215, 3224, 1975, 8592, 6225, 3215, 3215, 8032, 3215, 12610, 1975, 2655, 1863, 9957, 1975, 2304, 30767, 16373, 3215, 9122, 9154, 2423, 732, 17796, 1975, 8592, 37495, 22653, 27188, 4724, 36081, 995, 307, 754, 7251, 3555, 4587, 7578, 27188, 4724, 36081, 995, 4032, 7649, 3714, 29245, 23328], "avg_logprob": -0.24326508286698112, "compression_ratio": 2.2574850299401197, "no_speech_prob": 0.0, "words": [{"start": 2230.32, "end": 2230.8, "word": "الف", "probability": 0.745849609375}, {"start": 2230.8, "end": 2230.98, "word": " في", "probability": 0.623046875}, {"start": 2230.98, "end": 2231.28, "word": " بيتا", "probability": 0.6383463541666666}, {"start": 2231.28, "end": 2231.6, "word": " يبقى", "probability": 0.8531494140625}, {"start": 2231.6, "end": 2231.8, "word": " عن", "probability": 0.66162109375}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sITeKhKUP3A_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sITeKhKUP3A_raw.srt
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@@ -0,0 +1,1928 @@
+1
+00:00:21,680 --> 00:00:25,760
+بسم الله الرحمن الرحيم المرة اللي فاتبا جينا
+
+2
+00:00:25,760 --> 00:00:31,020
+بنعملنا discussion على chapter 9ووصلنا الى سؤال 46
+
+3
+00:00:31,020 --> 00:00:36,000
+ودخل علينا الوقت وطلعنا وخلنا لليوم ان شاء الله و
+
+4
+00:00:36,000 --> 00:00:39,220
+تعالى طبعا هنحل كمان سؤالين غيره ان شاء الله و
+
+5
+00:00:39,220 --> 00:00:44,000
+بعدين ندخل فى الشابتر الجديد اللى هو شابتر 10 على
+
+6
+00:00:44,000 --> 00:00:46,960
+اي حال السؤال كان بيقولى لو كان ال index تبع ال
+
+7
+00:00:46,960 --> 00:00:50,860
+center تبع ال group G فى ال G هو عبارة عن اربعة
+
+8
+00:00:50,860 --> 00:00:56,140
+بييلى ان ال G modulo ال center isomorphic ال Z to
+
+9
+00:00:56,140 --> 00:01:05,460
+X product مع مينمع z2 المرة اللى فاتت قولنا ال
+
+10
+00:01:05,460 --> 00:01:13,790
+order لل g لل z of g بدى يساوي اربعة impliesما
+
+11
+00:01:13,790 --> 00:01:18,190
+يأتي انه عدد ال left cosets هو عبارة عن ماين عن
+
+12
+00:01:18,190 --> 00:01:23,290
+أربعة left cosets وبالتالي هذا بيخلي ال group اللي
+
+13
+00:01:23,290 --> 00:01:30,610
+عندنا اللي هي G modulus center بتابع ال G Z of G
+
+14
+00:01:30,610 --> 00:01:36,650
+isomorphic يا إما لزد أربعة يا إما لزد اتنين
+
+15
+00:01:36,650 --> 00:01:41,710
+external like product مع ماين مع زد اتنين مع هذه
+
+16
+00:01:41,710 --> 00:01:47,280
+أو هذهالان قال لي اثبت ان هذا ايزو مورفك لزد اتنين
+
+17
+00:01:47,280 --> 00:01:51,880
+اكسيرون ضايكابرودك زد اتنين يجب ان نحاول نستبعد زد
+
+18
+00:01:51,880 --> 00:01:56,340
+اربعة ان استبعدنا زد اربعة بيفضل عندنا اللي هو زد
+
+19
+00:01:56,340 --> 00:02:01,200
+اتنين اكسيرون ضايكابرودك مع مين مع زد اتنين طيب
+
+20
+00:02:01,200 --> 00:02:07,960
+باجي بقول لو كان اللي هو الجي موديولوس سينتر بتابع
+
+21
+00:02:07,960 --> 00:02:14,820
+الجي ايزو مورفك لزد اربعة دمزد اربعة هذي Cyclic
+
+22
+00:02:14,820 --> 00:02:20,660
+إذا هذي ال group بصير ما لها Cyclic يبقى then ال G
+
+23
+00:02:20,660 --> 00:02:27,280
+module ال center بتابع ال G is Cyclicمدام Cyclic
+
+24
+00:02:27,280 --> 00:02:34,060
+بالنظرية اللى أخدناها في هذا الشبطر يبقى
+
+25
+00:02:34,060 --> 00:02:42,000
+الـ G is abelian طيب مدام الـ G is abelian يبقى في
+
+26
+00:02:42,000 --> 00:02:46,750
+هذه الحالةأي جروب .. والله لا مش في ال normal هذه
+
+27
+00:02:46,750 --> 00:02:52,550
+يبقى .. يبقى اي .. اي جروب في هذه الحلقة بتبقى ..
+
+28
+00:02:52,550 --> 00:02:58,790
+بتبقى normal subgroup تمام؟ مدام جي is abelian
+
+29
+00:02:58,790 --> 00:03:04,710
+يبقى معنى هذا الكلام انه ايش؟ ان ال center بتابع
+
+30
+00:03:04,710 --> 00:03:10,190
+لجروب جي بده يساوي جي itself كله مدام الجي abelian
+
+31
+00:03:11,240 --> 00:03:16,880
+يبقى معنى هذا الكلام ان ال index بتابع ال center
+
+32
+00:03:16,880 --> 00:03:23,440
+of G ال center تابع ال G بده يساوي ال order تابع
+
+33
+00:03:23,440 --> 00:03:28,360
+ال G على ال order تابع ال Z of G اللي هو ال order
+
+34
+00:03:28,360 --> 00:03:32,340
+بتابع ال G على ال order بتابع ال G يساوي كده؟
+
+35
+00:03:32,340 --> 00:03:38,200
+يساوي واحد طب هو جايلي ال index كده؟كداش ال index
+
+36
+00:03:38,200 --> 00:03:44,100
+ماطة؟ أربعة طلع كداش أن واحد معناته اللي أخدنا خطأ
+
+37
+00:03:44,100 --> 00:03:51,220
+وعكسه هو من الصح يبقى هذا this is contradiction
+
+38
+00:03:52,760 --> 00:03:57,820
+يبقى هذا تناقض ليش؟ لأن ال index فوق يبقى داش؟
+
+39
+00:03:57,820 --> 00:04:03,100
+يبقى أربعة معناته اللي أخدنا هذا ليس صحيحا والآخر
+
+40
+00:04:03,100 --> 00:04:08,500
+هو الصحيح يعني معنى هذا الكلام أن ال G modulus
+
+41
+00:04:08,500 --> 00:04:14,660
+center of G is not isomorphic لمين إلى زد أربعة
+
+42
+00:04:14,660 --> 00:04:24,160
+يبقى it remainsذات يبقى انه الـ G-modulus center
+
+43
+00:04:24,160 --> 00:04:30,380
+بتبع الـ G-isomorphic لمن؟ لزد اتنين Extended
+
+44
+00:04:30,380 --> 00:04:34,020
+product مع من؟ مع زد اتنين
+
+45
+00:04:36,750 --> 00:04:40,670
+هذا اللي كان اخر سؤال كتبناه المرة اللي فاتت ولم
+
+46
+00:04:40,670 --> 00:04:47,390
+نتمكن من حله بسبب ضيق الوقت ننتقل الى سؤال اخر
+
+47
+00:04:47,390 --> 00:04:54,670
+وليكن سؤال ستة وخمسين سؤال ستة وخمسين بيقول ما
+
+48
+00:04:54,670 --> 00:05:00,600
+ياتي انه m normal subgroupsالـ N normal subgroup
+
+49
+00:05:00,600 --> 00:05:08,220
+من G والـ M normal subgroup من G prove that انه
+
+50
+00:05:08,220 --> 00:05:17,160
+هادي normal subgroup prove ان ال N في M is a
+
+51
+00:05:17,160 --> 00:05:23,810
+normal subgroup من G هاد اللي عايزين نثبتهخلّي
+
+52
+00:05:23,810 --> 00:05:29,770
+بالك هنا قال لي N normal subgroup من G و M normal
+
+53
+00:05:29,770 --> 00:05:35,390
+subgroup من G اثبتلي ان حاصل ضرب ال N في M هو
+
+54
+00:05:35,390 --> 00:05:40,850
+normal subgroup من Gإذا إحنا هنا بدنا نثبت شغلتين
+
+55
+00:05:40,850 --> 00:05:45,170
+الشغل الأولى بدنا نثبت إنه حصل الضرب هذا ال
+
+56
+00:05:45,170 --> 00:05:49,690
+subgroup قبل كل شيء لإنه مامرش علينا قبل هيك أن
+
+57
+00:05:49,690 --> 00:05:54,370
+حصل ضرب two subgroups is a subgroup وطبعا in
+
+58
+00:05:54,370 --> 00:05:55,830
+general ماهوش subgroup
+
+59
+00:06:05,300 --> 00:06:13,660
+الخطوة الأولى يبقى firstlyWe show that
+
+60
+00:06:13,660 --> 00:06:20,000
+ان الـ N في M is a subgroup من G هذا اللي عزيزي
+
+61
+00:06:20,000 --> 00:06:25,920
+نثبته في الأول انها subgroup من G لذلك، بدا اقول
+
+62
+00:06:25,920 --> 00:06:35,440
+النقطة الأولى الـ N في M is non-empty ليش؟ since
+
+63
+00:06:35,440 --> 00:06:43,620
+او becauseالـ E موجودة في الـ N والـ E نفسها كمان
+
+64
+00:06:43,620 --> 00:06:49,860
+موجودة في الـ M إذا هذا الكلام بده يساوي E موجودة
+
+65
+00:06:49,860 --> 00:06:57,300
+في N Mيبقى الـ N Subgroup و الـ M Subgroup يبقى كل
+
+66
+00:06:57,300 --> 00:07:01,280
+واحدة فيهم تحتوي على الـ Identity Element حاصل
+
+67
+00:07:01,280 --> 00:07:05,560
+ضارهم بالـ Identity يبقى هذا موجود وان في الـ N M
+
+68
+00:07:05,560 --> 00:07:10,360
+الان بدي اروح اثبت ان هذا الـ Subgroup يبقى بداجي
+
+69
+00:07:10,360 --> 00:07:21,290
+اقوله let ال X و ال Y موجودة في الـ N M thenالـ X
+
+70
+00:07:21,290 --> 00:07:27,750
+هذه بدها تساوي N1 M1 على شكل حاصل ضرب Element من N
+
+71
+00:07:27,750 --> 00:07:37,170
+و Element من M و كذلك ال Y هتساوي عنصر تاني N2 M2
+
+72
+00:07:38,140 --> 00:07:42,860
+طب انا ايش بده اثبت؟ بده اثبت ان ال X Y inverse
+
+73
+00:07:42,860 --> 00:07:48,880
+موجود في ال N M لو استطعت ذلك لأصبحت ال N M عبارة
+
+74
+00:07:48,880 --> 00:07:56,340
+عن subgroup اذا بدهاجي اخد ال X Y inverse ال X N 1
+
+75
+00:07:56,340 --> 00:08:04,530
+M 1هذا الانفرس
+
+76
+00:08:04,530 --> 00:08:13,530
+يبقى M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2
+
+77
+00:08:13,530 --> 00:08:16,150
+M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M2 M1 M2 M2 M1
+
+78
+00:08:16,150 --> 00:08:18,870
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+79
+00:08:18,870 --> 00:08:19,070
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+80
+00:08:19,070 --> 00:08:19,070
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+81
+00:08:19,070 --> 00:08:19,190
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+82
+00:08:19,190 --> 00:08:27,900
+M2 M2 M2 M2 M2 M2 Mفي M إذا بدأت تبدأ اللي هم
+
+83
+00:08:27,900 --> 00:08:36,220
+بعنصر تالت يبقى لو جيت قلت هذا الكلام دي سوى N1 M3
+
+84
+00:08:36,220 --> 00:08:46,160
+N2 inverse و ال M3 اللي هي عبارة عن M1 M2 inverse
+
+85
+00:08:46,400 --> 00:08:51,180
+الشكل اللي عندنا هنا اذا انا استبدلت العنصر اللي
+
+86
+00:08:51,180 --> 00:08:57,480
+اتنين هدول بعنصر بدالهم من من من اللي هو ال M يبقى
+
+87
+00:08:57,480 --> 00:09:01,700
+أصبحت على الشكل اللي عندنا هنا طيب كويس استأنى
+
+88
+00:09:01,700 --> 00:09:07,320
+شويةبتذكروا أول ما أخدنا ال normal subgroup لما
+
+89
+00:09:07,320 --> 00:09:10,420
+أخدنا ال normal subgroup أخدنا التعريف تبعها جون
+
+90
+00:09:10,420 --> 00:09:14,760
+ال left coset يسوى ال right coset جون هذا لا يعني
+
+91
+00:09:14,760 --> 00:09:20,400
+أن ال a في h بدي يسوى ال h في a كsmall لكن هذا
+
+92
+00:09:20,400 --> 00:09:27,440
+يعني أن ال a h one بدي يسوى h two في a يبقى إذا
+
+93
+00:09:27,440 --> 00:09:35,890
+هذا الكلام بقدر أقول يساوييساوي N1 زي ما هى هدها
+
+94
+00:09:35,890 --> 00:09:41,490
+ها بدي استبدله برقم اخر و اعمله تبديل مع مين مع ال
+
+95
+00:09:41,490 --> 00:09:50,910
+M يبقى هذا بدي يعطيني N3 M3 ليش هذا الكلام because
+
+96
+00:09:50,910 --> 00:09:59,380
+اللي هو ال N is a normal subgroup من Gمن تعريف الـ
+
+97
+00:09:59,380 --> 00:10:03,860
+Normality لما تبقى ال N Normal هذا element موجود
+
+98
+00:10:03,860 --> 00:10:07,540
+في G يبقى هذا ال element في هذا ال element بقدر
+
+99
+00:10:07,540 --> 00:10:12,140
+استبدله ب element تاني من هذا و هذا زي ما هو و
+
+100
+00:10:12,140 --> 00:10:18,940
+بنجلب وضعهم يبقى قلت N تلاتة M تلاتة ليش؟ لأن ال N
+
+101
+00:10:18,940 --> 00:10:23,780
+عبارة عن Normal Subgroup من G طب N واحد في N تلاتة
+
+102
+00:10:23,780 --> 00:10:30,040
+وين موجود؟وهذا الوضع موجود في الـM ويبقى هذا الوضع
+
+103
+00:10:30,040 --> 00:10:38,560
+كله موجود في الـNM مدام موجود في الـNM أخد عنصرين
+
+104
+00:10:38,560 --> 00:10:42,200
+موجودات في الـNM واخدت الأول في المعكس التاني
+
+105
+00:10:42,200 --> 00:10:49,700
+وجدته موجود في الـNM يبقى سائل الـNM is a subgroup
+
+106
+00:10:49,700 --> 00:10:56,890
+من Gبقى الآن نثبت خاصية ال normality يبقى باجي
+
+107
+00:10:56,890 --> 00:11:07,010
+بقوله هنا if ال G موجود في G and ال X موجود في ال
+
+108
+00:11:07,010 --> 00:11:15,760
+N M او بقدر اقول دغري هكذا ولا X ولا غيره thenعلى
+
+109
+00:11:15,760 --> 00:11:23,800
+طول الخط IG في N M إذا قلت أثبت إن هذا يسوي N M في
+
+110
+00:11:23,800 --> 00:11:29,980
+G بتم المطلوب طب الكلام هذا بده يساوي بقدر أقول
+
+111
+00:11:29,980 --> 00:11:32,480
+هذا NGM
+
+112
+00:11:34,870 --> 00:11:42,310
+نقدر؟ ليش؟ لأن N is normal يبقى هذا because ال N
+
+113
+00:11:42,310 --> 00:11:47,550
+is a normal subgroup من G طب بدأجي للاتنين هدول
+
+114
+00:11:47,550 --> 00:11:53,370
+يبقى هذا الكلام هاي ال N زي ما هيهذه الـ M في G
+
+115
+00:11:53,370 --> 00:11:58,410
+لأن الـ M مجلد عام من جهة جديدة من جهة جديدة من
+
+116
+00:11:58,410 --> 00:11:59,470
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+117
+00:11:59,470 --> 00:12:01,390
+من جهة جديدة من جهة جديدة من جهة جديدة من جهة
+
+118
+00:12:01,390 --> 00:12:01,850
+جديدة من جهة جديدة من جهة جديدة من جهة جديدة من
+
+119
+00:12:01,850 --> 00:12:03,790
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+120
+00:12:03,790 --> 00:12:03,790
+من جهة جديدة من جهة جديدة من جهة جديدة من جهة
+
+121
+00:12:03,790 --> 00:12:07,930
+جديدة من جهة جديدة من جهة جديدة من جهة جديدة من
+
+122
+00:12:07,930 --> 00:12:11,250
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+123
+00:12:11,250 --> 00:12:15,170
+من جهة جديدة من جهيعني يبقى يا شباب لما يقولك خدلي
+
+124
+00:12:15,170 --> 00:12:18,830
+هست و اثبتلي انها normal subgroup بدك تثبت اولا
+
+125
+00:12:18,830 --> 00:12:24,550
+انها subgroup و بعدين بتثبت انها normal وبالتالي
+
+126
+00:12:24,550 --> 00:12:28,890
+بيكون اجبت سؤالك اجابة كاملة يعني يمكن لو طلبت
+
+127
+00:12:28,890 --> 00:12:31,470
+سؤال زي هيك اقولك show that نمرا واحد انها
+
+128
+00:12:31,470 --> 00:12:36,790
+subgroup نمرا اتنين انها normal subgroup من main
+
+129
+00:12:36,790 --> 00:12:45,780
+من Gكمان سؤال أخر يبقى سؤال تسعة وستين سؤال تسعة
+
+130
+00:12:45,780 --> 00:12:50,200
+وستين بيقول لي لو كان ال order ل G بده يساوي
+
+131
+00:12:50,200 --> 00:12:56,440
+تلاتين و ال order لل center بتابع ال G بده يساوي
+
+132
+00:12:56,440 --> 00:13:04,480
+خمسة بيقول لي what is the structure
+
+133
+00:13:11,390 --> 00:13:19,620
+Structure of LG Modulus Center بتابع LGأريد أن
+
+134
+00:13:19,620 --> 00:13:24,380
+أعرف جيه موديلوس سنتر بتابع الجيه عبارة عن مين أو
+
+135
+00:13:24,380 --> 00:13:30,320
+أي قدرة تتطلع ان ايزو مورفك لمين بتم المطلب يبقى
+
+136
+00:13:30,320 --> 00:13:34,600
+عندنا ال order لجيه تلاتين وال order للسنتر يسوى
+
+137
+00:13:34,600 --> 00:13:39,260
+خمسة بقولوا شو ال structure هذا تابع مين تابع ال
+
+138
+00:13:39,260 --> 00:13:46,930
+center اللي عندنا طب كويس قال لي بلا كدهالحين احنا
+
+139
+00:13:46,930 --> 00:13:51,670
+لو جينا كونا ال factor group اللى عندنا اللى هى ال
+
+140
+00:13:51,670 --> 00:13:58,250
+G موديولو ال center بتبع ال G وروحت اخدت ال order
+
+141
+00:13:58,250 --> 00:14:03,510
+لها يبقى هذا بدى يساوي ال order لل G على ال order
+
+142
+00:14:03,510 --> 00:14:11,090
+لمين ل ال center بتبع ال Gهذا بده يعطيني تلاتين
+
+143
+00:14:11,090 --> 00:14:17,970
+على خمسة ويسوى كدهاش؟ ستة طب الستة أليست اتنين في
+
+144
+00:14:17,970 --> 00:14:27,130
+تلاتة؟ يعني كأنها ايش؟ كأنها اتنين P وال P أكبر من
+
+145
+00:14:27,130 --> 00:14:27,650
+اتنين
+
+146
+00:14:30,510 --> 00:14:38,530
+في عنا نظرية في صفحة 144 النظرية في صفحة 144 بتقول
+
+147
+00:14:38,530 --> 00:14:44,930
+إذا كان ال order لجروب 2P يبقى هذي الجروب اللي
+
+148
+00:14:44,930 --> 00:14:59,330
+عندنا Z of G isomorphic لزد 2P او لD او لDP
+
+149
+00:15:01,780 --> 00:15:04,920
+طبعا نظرية هذه اعطيناها لكم بس مابرهنهاش اقول لكم
+
+150
+00:15:04,920 --> 00:15:10,320
+مابندهاش البرهان تمام يبقى الجي موديولوس سنتر اذا
+
+151
+00:15:10,320 --> 00:15:15,620
+امرك لزد اتنين P او ل دي P طبعا ال P عندنا بقداش
+
+152
+00:15:15,620 --> 00:15:22,680
+تلاتة طب كويس اذا استبعدنا هذه بيكون حصلنا على هذه
+
+153
+00:15:22,680 --> 00:15:29,570
+او اذا استبعدنا هذه بيكون حصلنا على هذهيعني هذه
+
+154
+00:15:29,570 --> 00:15:35,720
+اتنين في تلاتة وهذه دي تلاتةلأننا قلنا ال P عندنا
+
+155
+00:15:35,720 --> 00:15:41,260
+هذه اللي هي F تلاتة كويس يبقى هذه لو كانت
+
+156
+00:15:41,260 --> 00:15:49,260
+isomorphic لل 2 في 3 يعني 6 يبقى هنا F ال G
+
+157
+00:15:49,260 --> 00:15:55,740
+modulus center بتابع ال G isomorphic ل Z 2 في 3
+
+158
+00:15:55,740 --> 00:16:02,760
+يعني اللي هي Z 6 then ال G modulus center ايش
+
+159
+00:16:02,760 --> 00:16:11,990
+بتكونCyclic مدام Cyclic يبقى G مالها Abelian مدام
+
+160
+00:16:11,990 --> 00:16:17,650
+Abelian يعني ال center تبع ال group بده يساوي ال
+
+161
+00:16:17,650 --> 00:16:24,280
+group itselfيعني ال order لل group بده يساوي ال
+
+162
+00:16:24,280 --> 00:16:29,800
+order لل center هذا بده يعطيك ان ال order لل
+
+163
+00:16:29,800 --> 00:16:34,920
+center بده يساوي ال order لل G لكن احنا المعطى
+
+164
+00:16:34,920 --> 00:16:40,510
+عندنا عاشرتلاتين وخمس هل التلاتين بتساوي الخمسة؟
+
+165
+00:16:40,510 --> 00:16:45,910
+لا يمكن هذا الكلام this is يعني that is التلاتين
+
+166
+00:16:45,910 --> 00:16:54,270
+بتساوي الخمسة يبقى this is impossible أو هذا تناقض
+
+167
+00:16:54,270 --> 00:17:00,670
+غير ممكنمدام غير ممكن إذا بنستبعد هذا بضالمين يبقى
+
+168
+00:17:00,670 --> 00:17:07,110
+هنا ساعة ال G يعني نفس سكرة السؤال ذاك تقريبا G
+
+169
+00:17:07,110 --> 00:17:14,510
+modulus center بتابع ال G isomorphic ل D3
+
+170
+00:17:17,120 --> 00:17:21,980
+إذا الـ structure تبع ال group اللي عندنا هو نفس
+
+171
+00:17:21,980 --> 00:17:27,320
+ال structure تبع مين؟ تبع ال D3 وD3 فيها كم عنصر؟
+
+172
+00:17:27,320 --> 00:17:33,700
+ستة عناصر ضعف الرقم اللي عندنا دائما و أبدا
+
+173
+00:17:43,650 --> 00:17:48,090
+ننتقل لآخر chapter اللي هو chapter عشرة اللي هو
+
+174
+00:17:48,090 --> 00:17:55,130
+group homomorphism
+
+175
+00:17:55,130 --> 00:17:59,570
+بدنا
+
+176
+00:17:59,570 --> 00:18:05,030
+نعطي تعريف لل group homomorphism وبعد ذلك نبدأ
+
+177
+00:18:05,030 --> 00:18:10,950
+ناخد بعض الأمثلة المتعلقة بيهم يبقى definition
+
+178
+00:18:13,450 --> 00:18:18,670
+a homomorphism a homomorphism
+
+179
+00:18:18,670 --> 00:18:27,870
+في من الـ g إلى الـ g bar is a mapping is a
+
+180
+00:18:27,870 --> 00:18:36,070
+mapping يبقى هو عبارة عن دل أو function from from
+
+181
+00:18:36,070 --> 00:18:41,130
+the group g
+
+182
+00:18:43,030 --> 00:18:49,590
+توزع جروب جي
+
+183
+00:18:49,590 --> 00:19:01,050
+بارthat satisfies that satisfies the condition
+
+184
+00:19:01,050 --> 00:19:06,070
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+185
+00:19:06,070 --> 00:19:06,550
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+186
+00:19:06,550 --> 00:19:08,550
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+187
+00:19:08,550 --> 00:19:09,610
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+188
+00:19:09,610 --> 00:19:09,610
+التي تحقق الشرط اللي تحقق الشرط اللي تحقق الشرط
+
+189
+00:19:09,610 --> 00:19:09,610
+اللي تحقق الشرط اللي تحقق الشرط اللي تحقق الشرط
+
+190
+00:19:09,610 --> 00:19:09,610
+اللي تحقق الشرط اللي تحقق الشرط اللي تحقق الشرط
+
+191
+00:19:09,610 --> 00:19:09,850
+اللي تحقق الشرط اللي تحقق الشرط اللي تحقق الشرط
+
+192
+00:19:09,850 --> 00:19:15,270
+اللي تحقق الشرط اللي تحقق
+
+193
+00:19:18,520 --> 00:19:26,580
+اللي موجودات في جي كمان definition آخر the kernel
+
+194
+00:19:26,580 --> 00:19:31,980
+of
+
+195
+00:19:31,980 --> 00:19:47,660
+a homomorphism في from جي from a groupG from a
+
+196
+00:19:47,660 --> 00:20:02,700
+group G to a group G bar is the set is the set
+
+197
+00:20:05,710 --> 00:20:11,090
+هديلة اختصرها الى care الـ Phi كل العناصر اللي
+
+198
+00:20:11,090 --> 00:20:18,250
+موجودة في جيه بحيث Phi of X بده يساوي ال identity
+
+199
+00:20:18,250 --> 00:20:21,050
+بتابع من ال جيه بقى
+
+200
+00:20:42,690 --> 00:20:47,990
+نرجع لتعريفين اللي كتبناه حاول نفهم كل تعريف ما هو
+
+201
+00:20:47,990 --> 00:20:55,930
+المقصود منه a homomorphism phi من g إلى g bar is a
+
+202
+00:20:55,930 --> 00:21:00,720
+mapping a يبقى عبارة عن functionمن الـ group G إلى
+
+203
+00:21:00,720 --> 00:21:06,020
+الـ group G bar والذي يحقق ال condition Phi of A
+
+204
+00:21:06,020 --> 00:21:11,140
+بيبقى سوى Phi of A في Phi of B لكل الـ A والـ B
+
+205
+00:21:11,140 --> 00:21:16,970
+اللي موجودة في الـ Gعملية جامع يبقى باجي بقوله في
+
+206
+00:21:16,970 --> 00:21:23,530
+of a زائد ال b بيسوي في of a زائد ال في of b إذا
+
+207
+00:21:23,530 --> 00:21:26,690
+كانت ال operation زائد على ال group التانى وإذا
+
+208
+00:21:26,690 --> 00:21:33,090
+كان ضرب بيكون في of a في في of bيعني يا شباب هذا
+
+209
+00:21:33,090 --> 00:21:38,270
+حاصل ضربته elements في الـG بار بس هذا اللي بنقصين
+
+210
+00:21:38,270 --> 00:21:43,290
+حاصل ضربته elements موجود في G يبقى كل elements
+
+211
+00:21:43,290 --> 00:21:46,850
+وين موقعهم يخضعوا للعملية اللي على من؟ اللي على ال
+
+212
+00:21:46,850 --> 00:21:50,290
+group السؤال اللي بدأ أسأله بما ياتي احنا أخدنا
+
+213
+00:21:50,290 --> 00:21:54,590
+isomorphism قبل هيك وال isomorphism كان فيه ثلاث
+
+214
+00:21:54,590 --> 00:22:01,300
+خواصة اظن هذه الخاصية التالتةبناء عليه اي ايزو
+
+215
+00:22:01,300 --> 00:22:07,240
+مورفزم هو هومو مورفزم لكن العكس صحيح العكس ليس
+
+216
+00:22:07,240 --> 00:22:12,600
+صحيحا ليس بدرورة ان يكون كل هومو مورفزم هو ايزو
+
+217
+00:22:12,600 --> 00:22:16,520
+مورفزم لانه لسه بدي one to one and on to نحققوا
+
+218
+00:22:16,520 --> 00:22:19,910
+تلات شروط عشان نصير ايزو مورفزميبقى any
+
+219
+00:22:19,910 --> 00:22:24,830
+isomorphism is a homomorphism but the converse is
+
+220
+00:22:24,830 --> 00:22:29,410
+not necessarily تقول ليس بضرورته صحيحة هذه واحدة
+
+221
+00:22:29,410 --> 00:22:33,710
+نروح لل definition التاني الان بدأ يجي لقلب ال
+
+222
+00:22:33,710 --> 00:22:39,650
+homomorphism ال kern ofthe homomorphism في من جي
+
+223
+00:22:39,650 --> 00:22:44,510
+إلى جي بار باعرفه بالشكل التالي كيرنل هاختصلها إلى
+
+224
+00:22:44,510 --> 00:22:50,050
+كير و ال homomorphism هقول كيرنل للفي حسب التعريف
+
+225
+00:22:50,050 --> 00:22:55,230
+بيقولي كل ال X في اللي موجودة في جي بي حيث صورتها
+
+226
+00:22:55,230 --> 00:22:59,370
+بده تعطيني ال identity element تبع من ال جي بار
+
+227
+00:22:59,370 --> 00:23:06,540
+هذا بده يخليني أطرح أكثر من سؤال السؤال الأوللما
+
+228
+00:23:06,540 --> 00:23:10,840
+أقول كيرنا لفاي كل ال X اللي موجودة في G بحيث فاي
+
+229
+00:23:10,840 --> 00:23:16,320
+of X يساوي ال identity element هل هذا يعني ان
+
+230
+00:23:16,320 --> 00:23:21,680
+الكيرنا لفاي هو ال identity element تبع ال G bar؟
+
+231
+00:23:21,680 --> 00:23:30,540
+يعني كلام غلط هذا الكلام اللي أنا بقوله واحد
+
+232
+00:23:30,540 --> 00:23:32,060
+واحد يعني كيف؟
+
+233
+00:23:35,390 --> 00:23:40,930
+يعني .. يعني أنا قصدت هل ال kernel هو ال identity
+
+234
+00:23:40,930 --> 00:23:46,710
+تبع ال G bar؟ لأ الإجابة خطأ، طيب السؤال الثاني هل
+
+235
+00:23:46,710 --> 00:23:53,040
+ال kernel subset من ال G bar؟ برضه لألأ لإيش؟ لأن
+
+236
+00:23:53,040 --> 00:23:59,240
+كل ال X اللي موجودة في G يعني ال kernel subset من
+
+237
+00:23:59,240 --> 00:24:03,540
+من من ال G وليس من ال G bar بس مين ال subset؟ كل
+
+238
+00:24:03,540 --> 00:24:12,130
+العناصر اللي موجودة في G اللي صورتهمهذا يجعلني
+
+239
+00:24:12,130 --> 00:24:18,170
+أطرح كمان تساؤل لو كان عندي isomorphism فتح كويس
+
+240
+00:24:18,170 --> 00:24:22,010
+معايا ايزو مورفزم وبدي ال kernel لهذا ال
+
+241
+00:24:22,010 --> 00:24:27,470
+isomorphism اكم عنصر بقدر اللاجي فيهوحد بس ليش
+
+242
+00:24:27,470 --> 00:24:31,110
+حكاية ال one to one مافيش عنصرين بيشتركوا في نفس
+
+243
+00:24:31,110 --> 00:24:34,870
+الصورة لكن لما انا اقول ال kernel ال phi كل ال x
+
+244
+00:24:34,870 --> 00:24:38,390
+اللي في بحيث ال phi of x بدها تساوي ال identity
+
+245
+00:24:38,390 --> 00:24:43,010
+معناته عندي عدة عناصر بيشتركوا في نفس الصورة اللي
+
+246
+00:24:43,010 --> 00:24:46,810
+هي ال identity تبعي ال G bar يرجى ال kernel هو
+
+247
+00:24:46,810 --> 00:24:51,290
+حضرة العناصر اللي عندي هدول اللي من G واضح؟يبقى
+
+248
+00:24:51,290 --> 00:24:55,970
+بدك تفهم شغل احطهالي في دماغك ان الكيرنل تبع الفاي
+
+249
+00:24:55,970 --> 00:25:02,350
+هو ال subset من جي وليس من جي بار مين هم هدول هم
+
+250
+00:25:02,350 --> 00:25:06,590
+العناصر اللي موجودات في جي و اللي صرتهم بتكون ال
+
+251
+00:25:06,590 --> 00:25:12,990
+identity تبع من تبع الجي بار تمام نبدأ ناخد امثلة
+
+252
+00:25:12,990 --> 00:25:14,690
+يبقى examples
+
+253
+00:25:19,440 --> 00:25:25,180
+أول مثال بدي أطرحه اللي هو الـ isomorphism يبقى
+
+254
+00:25:25,180 --> 00:25:35,440
+any isomorphism في من جي إلى جي بار is a
+
+255
+00:25:35,440 --> 00:25:40,680
+homomorphism بدون لشته ولا حاجة لإنه فاهمين
+
+256
+00:25:40,680 --> 00:25:46,760
+isomorphism يعني ثلاثة شروط andلو قلنا لك هات لي
+
+257
+00:25:46,760 --> 00:25:53,060
+مين؟ هات لي ال kernel تبع هذا ال isomorphism ال
+
+258
+00:25:53,060 --> 00:26:00,680
+kernel بتبع ال Phi يساوي مين؟ ال identity تبع ال G
+
+259
+00:26:00,680 --> 00:26:08,720
+bar ولا تبع ال G؟تبع الـ G فقط لغير ليش because
+
+260
+00:26:08,720 --> 00:26:15,360
+أنه five is one to one ولو واحد هيشترك مع ال
+
+261
+00:26:15,360 --> 00:26:18,880
+identity element تبع ال G في الصورة يبقى ال kernel
+
+262
+00:26:18,880 --> 00:26:24,000
+في هذه الحالة يساوي ال identity يبقى هذا أبسط
+
+263
+00:26:24,000 --> 00:26:29,260
+أنواع الأمثلة أروح لمثال ثاني مثال ثاني بيقول
+
+264
+00:26:29,260 --> 00:26:29,900
+define
+
+265
+00:26:32,490 --> 00:26:38,790
+A function فاي من
+
+266
+00:26:38,790 --> 00:26:42,830
+ال general linear group of two by two matrices
+
+267
+00:26:42,830 --> 00:26:49,470
+over R لمن لست of real numbers لما أشيل منها ال
+
+268
+00:26:49,470 --> 00:26:57,830
+zero تحت عملية الضرب by فاي of A بدو سوى ال
+
+269
+00:26:57,830 --> 00:27:05,610
+determinant لل Aيبقى show that show المطلوب الأول
+
+270
+00:27:05,610 --> 00:27:12,950
+نمره a show that phi is homomorphism هذا المطلوب
+
+271
+00:27:12,950 --> 00:27:21,470
+الأول المطلوب التاني نمره b find الكيرن ال main لل
+
+272
+00:27:21,470 --> 00:27:21,890
+phi
+
+273
+00:27:30,810 --> 00:27:37,750
+خلّي بالا كدا الان مرة ثانية عرفنا function من ال
+
+274
+00:27:37,750 --> 00:27:41,430
+general linear group of two by two matrices over R
+
+275
+00:27:41,430 --> 00:27:45,470
+لل R minus Zero مجموعة الاعداد الحقيقية شيلت منها
+
+276
+00:27:45,470 --> 00:27:49,490
+الصفر وعرفنا عليها عملية الضرب سابقا اثبتنا انها
+
+277
+00:27:49,490 --> 00:27:55,010
+group by Phi of A يسوى ال determinant لل A الان ال
+
+278
+00:27:55,010 --> 00:28:00,880
+A هى عبارة عن مين؟مصوفة نظامها 2 في 2 ومحددها لا
+
+279
+00:28:00,880 --> 00:28:05,920
+يساوي الصفر رقم جد ما يكون يكون بعد ذلك ودناها
+
+280
+00:28:05,920 --> 00:28:10,320
+لوان determinant ليها داري ال number يبقى
+
+281
+00:28:10,320 --> 00:28:15,160
+determinant لأ موجود في ال R ناقص ال zero يبقى
+
+282
+00:28:15,160 --> 00:28:19,420
+determinant لل A بحيث هذا ال determinant بدي
+
+283
+00:28:19,420 --> 00:28:24,880
+يعطيني رقم غير من الصفر لأن الصفر هنا ماله مستبعد
+
+284
+00:28:25,200 --> 00:28:28,560
+قال يثبت لي أن فاي هذا هو هذا هو عبارة عن
+
+285
+00:28:28,560 --> 00:28:33,400
+homomorphism بقوله كويس إذا بدي أروح أطبق الخاصية
+
+286
+00:28:33,400 --> 00:28:38,640
+اللي فوق عندنا هنا يبقى بدي أخد فاي لحاصل ضرب
+
+287
+00:28:38,640 --> 00:28:44,640
+مصفوف تينأريد أن أثبت أن هذا الكلام يسوى فاي of a
+
+288
+00:28:44,640 --> 00:28:49,300
+في فاي of b يبقى حسب ال definition هذا ال
+
+289
+00:28:49,300 --> 00:28:55,360
+determinant لل a في ال b من ال linear algebra هذا
+
+290
+00:28:55,360 --> 00:28:57,300
+عبارة عن ال determinant
+
+291
+00:29:23,250 --> 00:29:30,030
+يبقى معناه كيف؟ما هو الهيزمورفزم كانت تلت شغلات و
+
+292
+00:29:30,030 --> 00:29:37,230
+ده شغلة واحدة فقط لا غير يبقى أصبح ال Phi of A بي
+
+293
+00:29:37,230 --> 00:29:40,670
+هي Phi of A في Phi of B لكل ال A و ال B اللي
+
+294
+00:29:40,670 --> 00:29:43,550
+موجودة في ال general linear group of two by two
+
+295
+00:29:43,550 --> 00:29:48,570
+matrices over R يبقى Phi عبارة عن همومورفزمنمرا بي
+
+296
+00:29:48,570 --> 00:29:53,250
+قال لي هاتلي ال kernel يبقى بداجي أطبقله التعريف
+
+297
+00:29:53,250 --> 00:29:58,850
+تبع ال kernel يبقى باجي بقوله ال kernel ل الفاي هو
+
+298
+00:29:58,850 --> 00:30:03,690
+كل المصفوفات اللي موجودة في ال general linear
+
+299
+00:30:03,690 --> 00:30:09,490
+group of two by two matrices over Rsuch that ان
+
+300
+00:30:09,490 --> 00:30:16,990
+الـ Phi of A بده يساوي ال identity تبع ال R minus
+
+301
+00:30:16,990 --> 00:30:24,450
+ال 0 ال R minus ال 0 تمام؟
+
+302
+00:30:30,650 --> 00:30:35,590
+مرة تانية بقول الان انا كتبت تعريف ال kernel الذي
+
+303
+00:30:35,590 --> 00:30:40,490
+يناسب وضع المثلة كل المصففات اللي موجودة في ال
+
+304
+00:30:40,490 --> 00:30:43,690
+general linear group of two by two matrices over R
+
+305
+00:30:43,690 --> 00:30:50,840
+بحيث ال Phi of A بده يسوى من ال I identityطيب الان
+
+306
+00:30:50,840 --> 00:30:56,580
+لما اقول هذا الكلام كل المصفوفات اللى موجودة في ال
+
+307
+00:30:56,580 --> 00:31:00,920
+general linear group of two by two matrices over R
+
+308
+00:31:00,920 --> 00:31:06,760
+such that الـ Phi of A هو مين ال determinant لل A
+
+309
+00:31:07,370 --> 00:31:14,710
+بدو يساوي ال identity في هذا ال human الواحد طيب
+
+310
+00:31:14,710 --> 00:31:18,950
+المصطفات ال determinant اللي هي عبارة عن مين ال
+
+311
+00:31:18,950 --> 00:31:24,550
+special يبقى هذا الكلام بيساوي ال special linear
+
+312
+00:31:24,550 --> 00:31:32,290
+group of two by two matrices over Rيبقى أصبح الـ
+
+313
+00:31:32,290 --> 00:31:38,550
+Kern كل المصرفات المحددة يساوي كم؟ يساوي الواحد
+
+314
+00:31:38,550 --> 00:31:49,630
+الصحيح مثال رقم تلاتة بيقول define برضه a function
+
+315
+00:31:49,630 --> 00:31:57,420
+في منالـ set of real numbers ناقص الـ zero تحت
+
+316
+00:31:57,420 --> 00:32:03,340
+عملية الضرب الى نفس ال group الى ال set of real
+
+317
+00:32:03,340 --> 00:32:09,160
+numbers ناقص ال zero تحت عملية الضرب بالضبط تماما
+
+318
+00:32:09,160 --> 00:32:19,170
+نهيها by فاي of X بده يسوي absolute value ل Xبرضه
+
+319
+00:32:19,170 --> 00:32:26,810
+بدي اعمل نفس اللي مطلوب هنا نمرة a show that phi
+
+320
+00:32:26,810 --> 00:32:36,470
+is a homomorphism نمرة b find الكيرن اللي من للphi
+
+321
+00:32:36,470 --> 00:32:40,050
+شكل اللي عندنا هنا الان solution
+
+322
+00:32:45,300 --> 00:32:51,380
+العملية عملية ضرب يبقى بيقول XY حسب التعريف يبقى
+
+323
+00:32:51,380 --> 00:32:56,860
+absolute value لل X في Y لو راجعنا إلى ال calculus
+
+324
+00:32:56,860 --> 00:33:00,640
+هذا absolute value لل X في ال absolute value
+
+325
+00:33:00,640 --> 00:33:06,180
+لماذا؟للـ Y الـ absolute value لل X هي Phi of X
+
+326
+00:33:06,180 --> 00:33:11,500
+والـ absolute value لل Y Phi of Y هذا لكل ال X
+
+327
+00:33:11,500 --> 00:33:17,440
+والـ Y اللي موجودة في الـ R ناقص الـ Zero لذلك Phi
+
+328
+00:33:17,440 --> 00:33:22,360
+is a homomorphism يبقى هذه النقطة الأولى بداجة
+
+329
+00:33:22,360 --> 00:33:29,040
+للنقطة الثانية بدنا الكيرن للـ Phiيبقى كل العناصر
+
+330
+00:33:29,040 --> 00:33:35,040
+اللي موجودة في الـR ناقص الـ0 بحيث Phi of X بده
+
+331
+00:33:35,040 --> 00:33:39,840
+يساوي مين؟ بده يساوي الـ0 ولا الـ1؟ بده يساوي
+
+332
+00:33:39,840 --> 00:33:45,340
+الـ1، تمام يعني كل العناصر X اللي موجودة في الـR
+
+333
+00:33:45,340 --> 00:33:51,080
+ناقص الـ0، وصتتش ذات Absolute value للـX بده يساوي
+
+334
+00:33:51,080 --> 00:33:57,460
+1 طب مين العناصر هنا الـAbsolute فيها يساوي 1؟بس
+
+335
+00:33:57,460 --> 00:34:01,020
+واحد و سالب واحد في غيرهم يبقى الكيرن اللي لا
+
+336
+00:34:01,020 --> 00:34:06,420
+يحتوي إلا على two elements اللي هي سالب واحد واحد
+
+337
+00:34:06,420 --> 00:34:09,800
+فقط لغاية ال absolute value للواحد هي بواحد ال
+
+338
+00:34:09,800 --> 00:34:15,660
+absolute value لسالب واحد هي اللي هي بواحد طب مثال
+
+339
+00:34:15,660 --> 00:34:25,310
+رقم أربع بيقول define a mappingبدنا نعرف كمان
+
+340
+00:34:25,310 --> 00:34:34,470
+function فاي من ال R وعليها عملية الجامعة الى ال R
+
+341
+00:34:34,470 --> 00:34:40,630
+plus وعليها عملية الضرب يبقى اختلفت العمليتين بين
+
+342
+00:34:40,630 --> 00:34:50,190
+المجمعتين by فاي of X يساوي ال E أس X لكل ال X
+
+343
+00:34:50,190 --> 00:34:56,890
+اللي موجودة في Rيبقى برضه نفس المطلوب نمرا a show
+
+344
+00:34:56,890 --> 00:35:05,030
+that بييل لي أن فاي is homomorphism نمرا بي find
+
+345
+00:35:05,030 --> 00:35:09,190
+ال kern ال mainly الفاي
+
+346
+00:35:13,790 --> 00:35:20,870
+فكر في الموضوع كويس و بدنا نيجي نثبت أو نوجد له
+
+347
+00:35:20,870 --> 00:35:29,110
+المطلبين اللي طلبهم في هذه المسألة طبعا لما درسنا
+
+348
+00:35:29,110 --> 00:35:33,750
+ال isomorphism ماجيبناش سيرة ال kernel على الإطلاق
+
+349
+00:35:33,750 --> 00:35:37,530
+لكن أجلنا لل homomorphism كيف؟
+
+350
+00:35:40,170 --> 00:35:45,650
+لانه فش غير عنصر واحد طيب الان بدى نبين ان هذا هو
+
+351
+00:35:45,650 --> 00:35:51,650
+homomorphism فباجى بقوله بدي اخد في of بدي اشوف x
+
+352
+00:35:51,650 --> 00:36:02,080
+زائد y والله x في yيبقى عملية جامعة فاي اف اكس
+
+353
+00:36:02,080 --> 00:36:03,320
+زائد واي
+
+354
+00:36:17,560 --> 00:36:24,240
+هذا يعني إن الـ E أُس X في الـ E أُس Y عند الضرب
+
+355
+00:36:24,240 --> 00:36:29,600
+تجمع من الأسس معلومات Calculus تمام؟ هذا الكلام
+
+356
+00:36:29,600 --> 00:36:37,240
+يساوي Phi of X وهذا Phi of Y وهذا كله صحيح لكل الـ
+
+357
+00:36:37,240 --> 00:36:42,250
+X والـ Y اللي موجودة ويناللي موجودة في الـR يبقى
+
+358
+00:36:42,250 --> 00:36:47,870
+هي أثبتناله في عبارة عن homomorphism نمرأ بيه بدنا
+
+359
+00:36:47,870 --> 00:36:54,070
+نجيب ال kernel للـFi ال kernel للـFi كل ال X اللي
+
+360
+00:36:54,070 --> 00:37:03,040
+موجودة في الـRالـ Phi of X بده يساوي ال identity
+
+361
+00:37:03,040 --> 00:37:09,760
+element
+
+362
+00:37:09,760 --> 00:37:18,820
+تبع ال R plusبقوله كويس كل ال X اللي موجودة في R
+
+363
+00:37:18,820 --> 00:37:25,780
+بحيث ان Phi of X هي مين إيقص X تمام؟ وهذا ال
+
+364
+00:37:25,780 --> 00:37:33,570
+identity element اللي هو واحد صحيح في غيره؟ممتاز
+
+365
+00:37:33,570 --> 00:37:40,790
+جدا يبقى هذه هها بدها تساوي Zero فقط يعني X التي
+
+366
+00:37:40,790 --> 00:37:46,130
+تساوي Zero اللي موجودة في R هي حل المعادلة هذه
+
+367
+00:37:46,130 --> 00:37:54,430
+because X تساوي Zero
+
+368
+00:37:54,430 --> 00:38:09,740
+isthe only solution of the equation EO6 تساوي مين؟
+
+369
+00:38:09,740 --> 00:38:15,340
+تساوي واحد هذا هو الحل الوحيد اللي ماعناش غيره
+
+370
+00:38:15,340 --> 00:38:23,900
+نعطي كمان مثال خمسة نمرة A بيقول define
+
+371
+00:38:47,220 --> 00:38:58,890
+السؤال هوفاي a homomorphism والإجابة نعم او لا بدك
+
+372
+00:38:58,890 --> 00:39:11,950
+تقولي why نمر بي define a function في من زد اتناش
+
+373
+00:39:12,610 --> 00:39:21,230
+الى زد اتناش بي فاي of اكس بده يساوي تلاتة اكس
+
+374
+00:39:21,230 --> 00:39:32,490
+show that show that فاي is homomorphism
+
+375
+00:39:32,490 --> 00:39:38,990
+and find ال kernel للفاي
+
+376
+00:39:50,090 --> 00:39:56,690
+المعارف function φي من الار بلس وعليها عملية الضرب
+
+377
+00:39:56,690 --> 00:40:00,070
+لار بلس وعليها عملية الضرب يبقى من مجموعة العدد
+
+378
+00:40:00,070 --> 00:40:04,750
+الحقيقية الموجبة إلى مجموعة العدد الحقيقية الموجبة
+
+379
+00:40:04,750 --> 00:40:08,430
+by five of x سوى التلاتة اكس ويقول هل هذه
+
+380
+00:40:08,430 --> 00:40:13,010
+homomorphism ولا لأ إن كان نعم لماذا وإن كان لا
+
+381
+00:40:13,010 --> 00:40:19,200
+لماذاوالله ما احنا عارفين بنجيجي نشوف في of x في y
+
+382
+00:40:19,200 --> 00:40:25,300
+يبقى عملية ضرب فاخدت في of x في y حسب التعريف
+
+383
+00:40:25,300 --> 00:40:33,900
+تلاتة x y يعني هذه تلاتة x في مين في ال y في of x
+
+384
+00:40:33,900 --> 00:40:43,030
+في ال y وليس في في of yطيب خدلي الان في of x في في
+
+385
+00:40:43,030 --> 00:40:49,850
+of y اللي هي تلاتة x في تلاتة y يعني قدشته ساوي
+
+386
+00:40:49,850 --> 00:40:57,490
+تسعة x y المعنى هذا الكلام ان ال في of x y لا
+
+387
+00:40:57,490 --> 00:41:07,810
+يساوي في of x في في of y يبقى هنا ال في is not
+
+388
+00:41:09,550 --> 00:41:15,850
+Homomorphism تعال خدلي نمر بيه نمر بيه بنفس
+
+389
+00:41:15,850 --> 00:41:23,330
+الطريقة بس ال operation هنا شباباشجمع يبقى في of x
+
+390
+00:41:23,330 --> 00:41:30,270
+زائد ال y يسوى تلاتة في x زائد y يبقى تلاتة x زائد
+
+391
+00:41:30,270 --> 00:41:38,270
+تلاتة y يبقى في of x زائد في of y هذا كله صحيح لكل
+
+392
+00:41:38,270 --> 00:41:43,970
+ال x و ال y اللي موجودة في z main اتناش يبقى هنا
+
+393
+00:41:43,970 --> 00:41:53,530
+في is a homomorphismجالي هاتلي ال kernel يبقى
+
+394
+00:41:53,530 --> 00:42:00,670
+بالداجي اقوله ال kernel بتبع ال five كل ال X اللي
+
+395
+00:42:00,670 --> 00:42:07,130
+موجودة في Z12 بحيث ال five of X بديه يسوى ال
+
+396
+00:42:07,130 --> 00:42:15,130
+identity تبع Z12 اللي هم هنا شباب ال zero تمام؟طيب
+
+397
+00:42:15,130 --> 00:42:21,330
+بدا اتي اشوف تحت تأثير ال homomorphism اللي هو
+
+398
+00:42:21,330 --> 00:42:28,570
+five of x بده يساوي تلاتة x من ال elements اللي
+
+399
+00:42:28,570 --> 00:42:33,330
+صورتها دائما و أبدا ال zero اللي عندها طبعا أكيد
+
+400
+00:42:33,330 --> 00:42:38,230
+ال zero لإنه تلاتة في zero ب zero طبعا طب من كمان؟
+
+401
+00:42:38,500 --> 00:42:43,420
+والاربعة لان تلاتة في اربعة باطناش تعني مين؟ تعني
+
+402
+00:42:43,420 --> 00:42:50,580
+Zero في كمان تمانية تمانية في تلاتة باربعة وعشرين
+
+403
+00:42:50,580 --> 00:42:56,900
+جد اتناش مرتين يبقى تمانية في غيرهم؟ لأ يبقى الكرن
+
+404
+00:42:56,900 --> 00:43:01,200
+اللي فيه تلاتة اللي من الصفر اربعة تمانية فقط لا
+
+405
+00:43:01,200 --> 00:43:01,820
+غير
+
+406
+00:43:18,750 --> 00:43:26,610
+طب اننا نجي لأول نظرية على هذا ال isomorphism وهذه
+
+407
+00:43:26,610 --> 00:43:32,890
+تتحدث عن علاقة ال isomorphism بال elements يبقى
+
+408
+00:43:32,890 --> 00:43:37,770
+هنا theorem اللي
+
+409
+00:43:37,770 --> 00:43:48,130
+هي ال properties of elements under
+
+410
+00:43:59,930 --> 00:44:08,430
+homomorphisms نظرية بتقول let في من جي إلى جي بار
+
+411
+00:44:08,430 --> 00:44:14,790
+بأقرب
+
+412
+00:44:14,790 --> 00:44:17,370
+homomorphism
+
+413
+00:44:18,770 --> 00:44:24,550
+a group homomorphism let and
+
+414
+00:44:24,550 --> 00:44:36,390
+let الجي موجودة في الجي then النقطة الأولى اللي هي
+
+415
+00:44:36,390 --> 00:44:41,530
+five of ال identity element تبع الجي قد يقين ال
+
+416
+00:44:41,530 --> 00:44:47,180
+identity element تبع الجي بقىالنقطة الثانية يبقى
+
+417
+00:44:47,180 --> 00:44:53,860
+هذه هي النقطة الأولى النقطة الثانية five of g to
+
+418
+00:44:53,860 --> 00:45:02,700
+the power n يسوى five of g to the power n for all
+
+419
+00:45:02,700 --> 00:45:09,140
+in اللي موجودة في زد يعني أعداد صحيحةالنقطة
+
+420
+00:45:09,140 --> 00:45:18,380
+الثالثة if ال order لل G is finite لو كان هذا
+
+421
+00:45:18,380 --> 00:45:26,840
+finite then ال order لل phi of G divides ال order
+
+422
+00:45:26,840 --> 00:45:37,080
+لمين ال order ل G النقطة الرابعة ال kernelللـ Phi
+
+423
+00:45:37,080 --> 00:45:47,520
+is a subgroup من مين؟ من G النقطة الخامسة Phi of A
+
+424
+00:45:47,520 --> 00:45:56,240
+بده يساوي Phi of B if and only if ال A في الكيرن
+
+425
+00:45:56,240 --> 00:46:05,940
+للـ Phi بده يساوي ال Bالنقطة السادسة والاخيرة if
+
+426
+00:46:05,940 --> 00:46:13,400
+الـ phi of G بدي ساوي الـ G prime then الـ phi
+
+427
+00:46:13,400 --> 00:46:19,200
+inverse of G primeفاينفرس في جي برايم اللي هو كل
+
+428
+00:46:19,200 --> 00:46:26,520
+ال X اللي موجودة في جي بحيث ان فاي اف X بدر ساوي
+
+429
+00:46:26,520 --> 00:46:32,180
+جي برايم واللي هي بدها تساوي جي في كيرن للفاي
+
+430
+00:46:58,070 --> 00:47:02,290
+أظن الأولى والتانية برهنهم في حالة ال isomorphism
+
+431
+00:47:02,290 --> 00:47:07,210
+وبالتالي انبرهانات مافيش مالناشن ضايع فيه يقوموا
+
+432
+00:47:07,210 --> 00:47:13,170
+.. يبقى واحد and اتنين و approved
+
+433
+00:47:17,210 --> 00:47:25,250
+Rowed in chapter سبعة أظن ستة in chapter ستة يبقى
+
+434
+00:47:25,250 --> 00:47:32,110
+بترجعهم نفس البرهان حرفية بنجي لتلاتة تلاتة بيقول
+
+435
+00:47:32,110 --> 00:47:36,170
+لو كان ال order اللي جي يبقى بالداجة أقوله assume
+
+436
+00:47:36,170 --> 00:47:44,170
+ان ال order اللي جي بده يساوي n و ال n is finite
+
+437
+00:47:46,550 --> 00:47:54,210
+that is يعني ان الـG to the power N بده ساوى من؟
+
+438
+00:47:54,210 --> 00:48:00,330
+بده ساوى ال identity بدي اثبت ان ال order للصورة
+
+439
+00:48:00,330 --> 00:48:05,400
+تبعت ال G بيقسم ال order تبع من ال Gإحنا أثبتنا
+
+440
+00:48:05,400 --> 00:48:10,340
+هذا الكلام في حالة الـ isomorphism إنه 2 are equal
+
+441
+00:48:10,340 --> 00:48:14,200
+ال order للصورة بيعطينا ال order للأصل نفسه ال
+
+442
+00:48:14,200 --> 00:48:18,440
+order لل G هو ال order لل Phi of G هذا في حالة لو
+
+443
+00:48:18,440 --> 00:48:22,580
+كانت Phi isomorphism لكن هنا homomorphism بدي أثبت
+
+444
+00:48:22,580 --> 00:48:27,280
+ان ال order للصورة بيقسم من ال order تبع الأصل
+
+445
+00:48:27,280 --> 00:48:32,140
+بقوله بسيطة فرضنا ال order اللي G بده يساوي N يعني
+
+446
+00:48:32,140 --> 00:48:40,490
+finiteيعني G أُس N بده يسوي ال identity بده يقسم
+
+447
+00:48:40,490 --> 00:48:50,430
+ال N لذلك لو جيت قلت لخدلي ال Phi خدلي ال Phi of G
+
+448
+00:48:50,430 --> 00:48:58,360
+كله to the power Nحسب الخصية رقم اتنين هذا بدي
+
+449
+00:48:58,360 --> 00:49:06,240
+يعطيني في of GN طيب في of GN اللي هي عبارة عن ال
+
+450
+00:49:06,240 --> 00:49:13,430
+identity element بتابعي ال Gفاي لما اتأثر على الـ
+
+451
+00:49:13,430 --> 00:49:16,770
+identity element تبع الـG من النقطة الأولى بدي
+
+452
+00:49:16,770 --> 00:49:21,710
+اعطينا من الـ identity element تبع الـG بقى اذا
+
+453
+00:49:21,710 --> 00:49:27,210
+انا في of G رفعتها كأسل عدد طالع ال identity يبقى
+
+454
+00:49:27,210 --> 00:49:34,370
+ال order تبعهايا بيكون N يا أقل من N ويقسمين ويقسم
+
+455
+00:49:34,370 --> 00:49:38,810
+ال N على كل الأمرين ال N بتقسم نفسها صحيح لو كان
+
+456
+00:49:38,810 --> 00:49:44,670
+أصغر منها برضه بدي أقسم منها ال N يبقى هذا يعني أن
+
+457
+00:49:44,670 --> 00:49:54,260
+ال order تبع ال Phi of G ماله divide ال Nأظن
+
+458
+00:49:54,260 --> 00:50:00,220
+كرولري على Lagrange theorem طيب هذا الكلام يعني ان
+
+459
+00:50:00,220 --> 00:50:06,480
+ال order ل phi of G divide ال order ل G وهو
+
+460
+00:50:06,480 --> 00:50:12,240
+المطلوبهذه النقطة التالتة النقطة الرابعة ال kernel
+
+461
+00:50:12,240 --> 00:50:17,920
+subgroup هذه النقطة الرابعة اول شي ال kernel
+
+462
+00:50:25,280 --> 00:50:29,780
+اللي هو الـ Phi of الـ Identity بتابع الـ G بدي
+
+463
+00:50:29,780 --> 00:50:34,060
+أسوأ الـ Identity تابع الـ G bar هذا يعني أن الـ
+
+464
+00:50:34,060 --> 00:50:38,560
+Identity تابع الـ G موجودة في الـ Kernel للـ Phi
+
+465
+00:50:38,560 --> 00:50:46,720
+الآن لو قلت لك خدلي XY موجودة في الـ Kernel للـ
+
+466
+00:50:46,720 --> 00:50:52,850
+Phi thenالـ Phi of X بده يساوي الـ Identity تبع
+
+467
+00:50:52,850 --> 00:50:58,690
+الـ G bar وفي نفس الوقت الـ Phi of Y بده يساوي الـ
+
+468
+00:50:58,690 --> 00:51:05,580
+Identity Element تبع الـ G bar هذا بده يعنيإن
+
+469
+00:51:05,580 --> 00:51:13,260
+الـPhi of Y الكل انفرس اللي هو عبارة عن Phi of Y
+
+470
+00:51:13,260 --> 00:51:19,640
+انفرس بدر يساوي ال identity element تبع الـG bar
+
+471
+00:51:19,640 --> 00:51:25,040
+انفرس اللي هو الـG barطب انا بدي اثبت ان ال X في
+
+472
+00:51:25,040 --> 00:51:34,220
+ال Y انفرس موجود في الكيرنل لذلك بدي اخد الان فاي
+
+473
+00:51:34,220 --> 00:51:40,660
+اف X Y انفرسوالله إذا طلع يسوى ال identity يبقى
+
+474
+00:51:40,660 --> 00:51:47,160
+هذا موجود يبقى هذا الكلام بدي يعطيني في of X في في
+
+475
+00:51:47,160 --> 00:51:52,800
+of Y inverse في of X عندي بقداش بال identity
+
+476
+00:51:52,800 --> 00:51:58,640
+element تبع ال G bar وفي of Y inverse كمان بمين
+
+477
+00:51:58,640 --> 00:52:04,120
+بال identity تبع ال G bar يبقى هذا الكلام بدي سوى
+
+478
+00:52:04,120 --> 00:52:09,530
+ال identity تبع مينتبع الـ G bar مدام هيك معناته
+
+479
+00:52:09,530 --> 00:52:14,930
+الـ X Y inverse موجود في الكيرن اللي الفاي هذا
+
+480
+00:52:14,930 --> 00:52:20,910
+معناه ان الكيرن اللي الفاي is a subgroup من مين؟
+
+481
+00:52:20,910 --> 00:52:28,230
+من G وبعد شوية هنتبهتلك هي انه normal للمحاضرة
+
+482
+00:52:28,230 --> 00:52:30,910
+القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e68c8d1cf513108ac80a6c141509716f26c085bb
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_raw.srt
@@ -0,0 +1,1828 @@
+1
+00:00:20,990 --> 00:00:24,830
+بسم الله الرحمن الرحيم نرجع لمحاضرة ابتدناها في
+
+2
+00:00:24,830 --> 00:00:29,010
+الفترة الصباحية و هو أنه بدأنا في chapter 3 اللي
+
+3
+00:00:29,010 --> 00:00:38,030
+بتحدث عن ال subgroups طبعا أعطينا تعريف لل order
+
+4
+00:00:38,030 --> 00:00:42,370
+لل group و order لل element اللي موجود داخل ال
+
+5
+00:00:42,370 --> 00:00:46,120
+groupوعرفنا ان ال order لل group هو عدد العناصر في
+
+6
+00:00:46,120 --> 00:00:49,900
+ال group و ال order لل element هو أصغر عدد صحيح
+
+7
+00:00:49,900 --> 00:00:53,000
+موجب أحط ال cos لل element بيعطينا main ال
+
+8
+00:00:53,000 --> 00:00:56,980
+identity element و أخدنا على ذلك مثالا واحدة وهي
+
+9
+00:00:56,980 --> 00:01:02,020
+قدامنا المثالة رقم اتنين يبقى لو أخدت g هي ال z
+
+10
+00:01:02,020 --> 00:01:06,900
+تمانية لما أحط زائد في دائرة صغيرة ليست عملية
+
+11
+00:01:06,900 --> 00:01:11,140
+الضرب العاديةلو كان عملية الضرب العادية بحط زائد
+
+12
+00:01:11,140 --> 00:01:15,200
+بدون دائرة حول الناس يبقى هذا المقصود ان الجامعه
+
+13
+00:01:15,200 --> 00:01:20,720
+modulo 8 هي المقصود العملية هذه يبقى زاده في دائرة
+
+14
+00:01:20,720 --> 00:01:25,000
+حسب الرقم اللي عندى بكون هذا modulo هذا main هذا
+
+15
+00:01:25,000 --> 00:01:29,780
+الرقميعني زد تمانية وعليها عملية الجمع مدينة
+
+16
+00:01:29,780 --> 00:01:34,620
+تمانية عناصرها من صفر لغاية سبعة يبقى بناء عليه ال
+
+17
+00:01:34,620 --> 00:01:39,240
+order اللي جيه كده شو ساوي تمانية فيها تمان عناصر
+
+18
+00:01:39,240 --> 00:01:45,900
+الصفر من ضمنهم يبقى then ال order اللي جيه بده
+
+19
+00:01:45,900 --> 00:01:51,990
+يساوي تمانيةزيرو هو ال identity element لما نضيف
+
+20
+00:01:51,990 --> 00:01:55,250
+زيرو لأي element مديره تمانية بيبقى نفس ال element
+
+21
+00:01:55,250 --> 00:02:00,450
+يبقى zero هو ال identity element الان لو بد ال
+
+22
+00:02:00,450 --> 00:02:09,890
+order مثلا للواحد كده ال order للواحدتحت عملية
+
+23
+00:02:09,890 --> 00:02:15,230
+الجمعة يعني واحد تربيع يعني واحد زائد واحد موديله
+
+24
+00:02:15,230 --> 00:02:20,030
+تمانى له جداش اتنين زائد واحد زائد واحد يعني جداش
+
+25
+00:02:20,030 --> 00:02:27,870
+ال order ايه له تلاتة سبعة ودي يطلع ال zero ها ال
+
+26
+00:02:27,870 --> 00:02:32,210
+zero هو ال identity تمانية طيب يجي ال order للواحد
+
+27
+00:02:32,210 --> 00:02:36,950
+بده يساوي تمانية طيب ال order ليه تلاتة
+
+28
+00:02:40,210 --> 00:02:47,450
+تلاتة تلاتة و تلاتة ستة و تلاتة تسعة و تلاتة اتناش
+
+29
+00:02:47,450 --> 00:02:54,390
+و تلاتة خمستاش و تلاتة تمانتاش و تلاتة واحد و
+
+30
+00:02:54,390 --> 00:03:00,190
+عشرين و تلاتة يبقى هذا ال zero يبقى كدهش تمانية
+
+31
+00:03:00,190 --> 00:03:07,910
+كذلك يبقى هذا هو ال order كمان لتلاتة طيب أليس هو
+
+32
+00:03:07,910 --> 00:03:09,710
+ال order كمان لخمسة
+
+33
+00:03:12,610 --> 00:03:19,170
+خمسة وخمسة عشر هبقى اتنين وكمان خمسة سبعة وكمان
+
+34
+00:03:19,170 --> 00:03:25,210
+خمسة بصير اتناشر وكمان خمسة سبعة طيب هتلاقي كمان
+
+35
+00:03:25,210 --> 00:03:30,750
+تمانية و ال order ليه سبعة كمان هو تمانية يبقى هذا
+
+36
+00:03:30,750 --> 00:03:35,790
+يساوي كمان ال order ليه سبعة كل هذا الكلام بده
+
+37
+00:03:35,790 --> 00:03:41,790
+يساوي قداش تمانية طب لو جيت ال order لل zero قداش
+
+38
+00:03:41,790 --> 00:03:47,230
+يا شبابواحد لأن هو ال identity element طب ال order
+
+39
+00:03:47,230 --> 00:03:53,070
+للي اتنين اتنين
+
+40
+00:03:53,070 --> 00:03:57,230
+زيدي اتنين زيدي اتنين زيدي اتنين ب zero يبقى اربعة
+
+41
+00:03:57,230 --> 00:04:02,250
+يبقى ال order ل اتنين بده يساوي اربعة طيب لو بده
+
+42
+00:04:02,250 --> 00:04:08,130
+يقولك ال order ل الأربعة اتنين طب ال order لستة
+
+43
+00:04:12,200 --> 00:04:16,980
+أربعة بالضبط صحيح ستة و ستة اتناش كمان ستة تمانتاش
+
+44
+00:04:16,980 --> 00:04:20,920
+كمان ستة اربع عشرين اللي هو تلف تمانية يبقى هذا
+
+45
+00:04:20,920 --> 00:04:26,200
+بده يساوي الأربعة يبقى بناء عليه جيبنا ال order لل
+
+46
+00:04:26,200 --> 00:04:30,950
+group G اللي هو تمانيةوجبنا ال order لكل element
+
+47
+00:04:30,950 --> 00:04:34,090
+موجود في ال group ال order لل identity element هو
+
+48
+00:04:34,090 --> 00:04:39,530
+بواحد صحيح الباقي بعضهم يساوي تمانية وبعضهم يساوي
+
+49
+00:04:39,530 --> 00:04:42,950
+اتنين زي ما طلع لنا الأربعة و الباقي ال order لهم
+
+50
+00:04:42,950 --> 00:04:48,010
+يساوي كده؟ أربعة طيب خليني أسأل سؤال كامشي ايش
+
+51
+00:04:48,010 --> 00:04:51,670
+بتلاحظوا عن ال order تبع ال element و ال order تبع
+
+52
+00:04:51,670 --> 00:04:54,870
+ال group؟ في علاقة بينهم؟
+
+53
+00:04:58,210 --> 00:05:04,790
+معلومة تانية مضاعفة ال order لل element دائما لو
+
+54
+00:05:04,790 --> 00:05:10,270
+أبدا بيكسب ال order لل group كله ال group finite
+
+55
+00:05:10,270 --> 00:05:14,830
+إذا ال order لل elementهتلاقي السؤال هذا بس قدامي
+
+56
+00:05:14,830 --> 00:05:18,510
+شوية مش الحين كويس يبقى ال order للإيمين دائما و
+
+57
+00:05:18,510 --> 00:05:22,850
+أبدا بيجسم ال order لل group وكمان هتلاقي كمان ان
+
+58
+00:05:22,850 --> 00:05:27,290
+ال order لل sub group بيجسم ال order لل group بس
+
+59
+00:05:27,290 --> 00:05:31,730
+لقدامي شوية بس معلومة هيك على الله مش هادر طيب نجي
+
+60
+00:05:31,730 --> 00:05:38,430
+ناخد كمان مثال تلاتة يبقى مثال تلاتة يقول خدلي
+
+61
+00:05:38,430 --> 00:05:47,320
+الأن the groupاللي هو the group R star من ال R
+
+62
+00:05:47,320 --> 00:05:52,460
+star هي عبارة عن ال R بدي أشيل منها ال zero و بدي
+
+63
+00:05:52,460 --> 00:05:58,940
+أخد عليها عملية الضرب قداش ال order هذه اللي هي يا
+
+64
+00:05:58,940 --> 00:06:09,360
+شباب تمام يبقى هذه is of infinite order
+
+65
+00:06:11,050 --> 00:06:16,010
+هذا الـ order لها سيكون كمية ما لا نهاية السؤال هو
+
+66
+00:06:16,010 --> 00:06:21,690
+إذا أخذت أي عنصر فيها مثل 2 مثل 3 مثل نص مثل قمس
+
+67
+00:06:21,690 --> 00:06:26,730
+مثل سدس مثل جذر تلاتة مثلا كمية ال order لهذه
+
+68
+00:06:26,730 --> 00:06:36,630
+العناص؟ هل يعرف؟ ال order مثلا لإتنين هل أجد رقم
+
+69
+00:06:36,630 --> 00:06:40,610
+أضعه كأس لإتنين يظهر ال identity اللي هو واحد؟
+
+70
+00:06:48,260 --> 00:06:55,360
+is of infinite order يعني إذا ما لقيتش رقم أحطه
+
+71
+00:06:55,360 --> 00:06:59,760
+كأس لهذا العدد يطلع ال identity element يبقى في
+
+72
+00:06:59,760 --> 00:07:04,420
+هذه الحالة order لهذا ال element يساوي infinite
+
+73
+00:07:04,420 --> 00:07:10,750
+طيب السؤال هوالزيرو مافيش سيبلي الواحد والسالب
+
+74
+00:07:10,750 --> 00:07:16,850
+واحد امسك بعد الواحد وقبل السالب واحد وما بين
+
+75
+00:07:16,850 --> 00:07:20,830
+الزيرو والواحد وما بين الزيرو والسالب واحد خدلي اي
+
+76
+00:07:20,830 --> 00:07:25,690
+رقم عمرك بتلاقي عدد ان تحطه كأسئلة ويطلع الواحد
+
+77
+00:07:25,690 --> 00:07:31,740
+الصحيحأي رقم ينجز صحيح كثري ايراشيونال ايراشيونال
+
+78
+00:07:31,740 --> 00:07:35,720
+بدكية تربيتك اي بوس خمسة واس عشرة واس مانيا اوس
+
+79
+00:07:35,720 --> 00:07:41,180
+مليون كذا الاخرى عمره بطلع واحد صحيح ساكتيه
+
+80
+00:07:41,180 --> 00:07:46,940
+الولادة خد اي رقم وربع شوفه بزيد ولا بينجس مثل
+
+81
+00:07:46,940 --> 00:07:51,220
+افترض انه عدد صحيح زي ما قلتلك اتنين بقدر الاقي
+
+82
+00:07:51,220 --> 00:07:54,820
+اوس ان عدد صحيح احطه له يطلع ال identity اللي هو
+
+83
+00:07:54,820 --> 00:07:59,070
+واحد صحيحيعني بقدر اتنين اضربها في نفسه ان من
+
+84
+00:07:59,070 --> 00:08:03,290
+المرات يطلع واحد صحيح عمره شو بيحصل يبقى اتنين of
+
+85
+00:08:03,290 --> 00:08:05,570
+of of of of of of of of of of of of of of of of of
+
+86
+00:08:05,570 --> 00:08:07,050
+of of of of of of of of of of of of of of of of of
+
+87
+00:08:07,050 --> 00:08:07,130
+of of of of of of of of of of of of of of of of of
+
+88
+00:08:07,130 --> 00:08:07,490
+of of of of of of of of of of of of of of of of of
+
+89
+00:08:07,490 --> 00:08:07,610
+of of of of of of of of of of of of of of of of of
+
+90
+00:08:07,610 --> 00:08:08,110
+of of of of of of of of of of of of of of of of of
+
+91
+00:08:08,110 --> 00:08:08,110
+of of of of of of of of of of of of of of of of of
+
+92
+00:08:08,110 --> 00:08:08,130
+of of of of of of of of of of of of of of of of of
+
+93
+00:08:08,130 --> 00:08:08,130
+of of of of of of of of of of of of of of of of of
+
+94
+00:08:08,130 --> 00:08:08,130
+of of of of of of of of of of of of of of of of of
+
+95
+00:08:08,130 --> 00:08:15,390
+of
+
+96
+00:08:15,390 --> 00:08:15,850
+of of of
+
+97
+00:08:24,530 --> 00:08:30,170
+ألاقي اشي بالكسور هذه are of infinite order مين
+
+98
+00:08:30,170 --> 00:08:33,750
+ضايق اللي عندى؟ الواحد والسالب الواحد all order
+
+99
+00:08:33,750 --> 00:08:37,290
+وقداش واحد لأن هو ال identity element طب والسالب
+
+100
+00:08:37,290 --> 00:08:42,450
+واحد اتنين اتنين في شغلنا هدول اتنين فقط في ال
+
+101
+00:08:42,450 --> 00:08:48,130
+group هذه هم لل order انهم finite اما ما خل ذلك كل
+
+102
+00:08:48,130 --> 00:08:51,630
+ال elements اللي باقي ال order انهم is infinite
+
+103
+00:08:51,630 --> 00:08:56,090
+تمام؟وأحد يقول لي طب هذا متناقض مع كلمة اللي تو
+
+104
+00:08:56,090 --> 00:08:59,830
+ايش كلمة اللي تو انا قلت ال order لل element بيقسم
+
+105
+00:08:59,830 --> 00:09:05,010
+ال order للي group بشرط ان ال group تبقى finite
+
+106
+00:09:05,010 --> 00:09:09,930
+order مش infinite هذا ال order يتقدش infinity ل
+
+107
+00:09:09,930 --> 00:09:20,000
+group تمام يبقى باجي بقوله الواحد andالواحد and
+
+108
+00:09:20,000 --> 00:09:28,680
+الواحد and سلب واحد are of finite order
+
+109
+00:09:34,140 --> 00:09:39,760
+الـ order للواحد يساوي الواحد and ال order لسالب
+
+110
+00:09:39,760 --> 00:09:43,660
+واحد يساوي اتنين لأن السالب واحد تربيه تاني و
+
+111
+00:09:43,660 --> 00:09:46,480
+السالب واحد يسالي واحد اللي هو بال identity بواحد
+
+112
+00:09:46,480 --> 00:09:50,180
+يبقى ال order اللي يساوي اتنين يبقى باروح بقوله
+
+113
+00:09:50,180 --> 00:09:57,280
+the other elements of
+
+114
+00:09:58,740 --> 00:10:07,860
+R star are of infinite order
+
+115
+00:10:07,860 --> 00:10:12,120
+يبقى هذول ال order اللي بقى ال element كله ب
+
+116
+00:10:12,120 --> 00:10:19,360
+infinite خدلي هذا المثال وتعالى نشوف اللي هو ايش
+
+117
+00:10:19,360 --> 00:10:23,300
+الموضوع بالظبط الان مثالة رقم أربعة
+
+118
+00:10:27,260 --> 00:10:31,240
+الآن لو أخدت ال order لل general linear group of
+
+119
+00:10:31,240 --> 00:10:34,220
+two by two matrices over R
+
+120
+00:10:40,910 --> 00:10:46,670
+أكم مصفوفة عندى بيطلع محددهم لا يساوي zero نظامهم
+
+121
+00:10:46,670 --> 00:10:51,850
+اتنين في اتنين كدهش infinity كده ما بدك تاخد
+
+122
+00:10:51,850 --> 00:10:56,690
+مصفوفة تغير الأرقام زى ما بدك لإن الأرقام عددهما
+
+123
+00:10:56,690 --> 00:11:01,270
+لنهاية set of real number بقدر أخلي الأربع أرقام
+
+124
+00:11:01,270 --> 00:11:05,360
+زى بعضها وشوف أكم مصفوفة يطلع كيف لما أغيرهميبقى
+
+125
+00:11:05,360 --> 00:11:09,560
+infinity يبقى ال order لهذه اللي هو بده يساوي
+
+126
+00:11:09,560 --> 00:11:15,100
+infinity طب بتاخد فيها بعض ال elements وشوف قداش
+
+127
+00:11:15,100 --> 00:11:22,320
+ال order لهم يبقى هذا ال order infinity but ال
+
+128
+00:11:22,320 --> 00:11:29,440
+a تساوي اللي هو zero واحد و سالب واحد و سالب واحد
+
+129
+00:11:29,440 --> 00:11:42,080
+andوالتانية هي الـ main المصوفة بي تساوي بي تساوي
+
+130
+00:11:42,080 --> 00:11:48,840
+الـ zero والسالب واحد واحد و zero هذه موجودة في
+
+131
+00:11:48,840 --> 00:11:51,380
+الـ general group
+
+132
+00:11:54,820 --> 00:12:00,480
+ليش موجودة؟ لأن محددها لا يساوي Zero Zero زائد
+
+133
+00:12:00,480 --> 00:12:05,080
+واحد بيطلع واحد موجودة فيها هذه Zero زائد واحد
+
+134
+00:12:05,080 --> 00:12:08,560
+بيطلع واحد يبقى موجودة فيها يبقى اتنين موجودات في
+
+135
+00:12:08,560 --> 00:12:11,080
+ال general linear group of two by two matrices
+
+136
+00:12:11,080 --> 00:12:16,540
+over R بدي أدور على ال order تبع ال A يبقى بدي
+
+137
+00:12:16,540 --> 00:12:22,430
+أروح أقوله ال A تربيعيبقى الـ A تربيع الـ 0 1 سالب
+
+138
+00:12:22,430 --> 00:12:28,050
+واحد سالب واحد 0 1 سالب واحد سالب واحد و يسوى
+
+139
+00:12:37,780 --> 00:12:43,100
+الصف الأول في العمود الثاني هو zero وبطلع هنا كمان
+
+140
+00:12:43,100 --> 00:12:47,620
+سالب واحد طب الصف الثاني في العمود الأول بطلع واحد
+
+141
+00:12:47,620 --> 00:12:53,060
+الصف الثاني في العمود الثاني سالب واحد وهنا زائد
+
+142
+00:12:53,060 --> 00:12:57,680
+واحد بطلع كم؟ بطلع zero لا يسوى ال identity
+
+143
+00:12:57,680 --> 00:13:03,560
+element طيب إيش رأيك لو روحت ضربت كمان في ايه بصير
+
+144
+00:13:03,560 --> 00:13:09,390
+عندي كم؟ اتكيبطيب لو جيت قولت هذا بده يعطينا انه
+
+145
+00:13:09,390 --> 00:13:15,810
+ايه تكييب بده يساوي اللي هو من Zero و واحد و سالب
+
+146
+00:13:15,810 --> 00:13:22,370
+واحد و سالب واحد في سالب واحد سالب واحد واحد Zero
+
+147
+00:13:22,370 --> 00:13:27,650
+و يساوي الصف الأول في العمود الأول يبقى Zero و هنا
+
+148
+00:13:27,650 --> 00:13:35,060
+واحد هنا Zero و هنا Zero اللي هو ب Zero تمامهنا هي
+
+149
+00:13:35,060 --> 00:13:40,080
+واحد وهنا سالب واحد يبقى zero الصف هذا في هذا
+
+150
+00:13:40,080 --> 00:13:45,820
+بيطلع واحد وهنا واحد فقط لا غير يبقى ال order
+
+151
+00:13:45,820 --> 00:13:50,980
+لإيه؟ تلاتة لإن هذه ال identity matrix يبقى
+
+152
+00:13:50,980 --> 00:13:59,970
+similarlyبنفس الطريقة similarly ال
+
+153
+00:13:59,970 --> 00:14:07,070
+b square يساوي ال b square يبقى بدأ اضرب zero سالب
+
+154
+00:14:07,070 --> 00:14:14,310
+واحد واحد zero في zero سالب واحد واحد zero ويساوي
+
+155
+00:14:14,310 --> 00:14:18,330
+الصف الأول في العامل الأول zero سالب واحد بسالب
+
+156
+00:14:18,330 --> 00:14:25,950
+واحدزيرو وزيرو أب زيرو صف التاني زيرو وزيرو أب
+
+157
+00:14:25,950 --> 00:14:31,750
+زيرو و هنا سالب واحد شكلنا ماطلعش ال identity
+
+158
+00:14:31,750 --> 00:14:38,650
+element لكن الشافوي طلعلي هذه لو ضربت في نفسي مين
+
+159
+00:14:38,650 --> 00:14:45,770
+بطلع مين تتوقع يطلعالـ Identity Matrix على طول
+
+160
+00:14:45,770 --> 00:14:52,350
+الخط يبقى لو روحت جبت ال بي أس أربع اوتوماتيك
+
+161
+00:14:52,350 --> 00:14:57,800
+هيطلع واحد زيرو زيرو واحدبناء ان عليه هذا بدي
+
+162
+00:14:57,800 --> 00:15:04,520
+يقولك ان ال order ل a بدي ساوي تلاتة and ال order
+
+163
+00:15:04,520 --> 00:15:10,160
+ل b بدي ساوي كده اربعة طيب ايش رايك لو ضربت
+
+164
+00:15:10,160 --> 00:15:14,420
+التنتين في بعض و بدي اشوف ال order ايه الشطعة تبعه
+
+165
+00:15:14,420 --> 00:15:21,790
+الا لو اخدتاللي هو ال A في B يساوي وين ال A اللي
+
+166
+00:15:21,790 --> 00:15:27,270
+عندنا هذا ال A اللي هي Zero واحد سالب واحد سالب
+
+167
+00:15:27,270 --> 00:15:32,710
+واحد في B اللي هي Zero سالب واحد واحد Zero بده
+
+168
+00:15:32,710 --> 00:15:37,280
+يشوف كده يصنعالصف الأول في العمود الأول بيطلع
+
+169
+00:15:37,280 --> 00:15:44,580
+بواحد الصف الأول في العمود الثاني بيطلع zero الصف
+
+170
+00:15:44,580 --> 00:15:49,700
+الثاني في العمود الأول بيطلع سالب واحد الصف الثاني
+
+171
+00:15:49,700 --> 00:15:55,380
+في العمود الثاني بيطلع له كمان قداش اللي هو واحد
+
+172
+00:15:55,380 --> 00:16:00,680
+بالشكل اللي عندنا هذا ال a في bالأن لو ال a في b
+
+173
+00:16:00,680 --> 00:16:06,260
+تضربها في نفسها مائة مرة لا يمكن يطلع ال identity
+
+174
+00:16:06,260 --> 00:16:13,120
+مثال و ذلك لو روحت أخدت ال a بي الكل ترميةيبقى
+
+175
+00:16:13,120 --> 00:16:22,360
+واحد زيرو سالب واحد واحد هذا الكلام يساوي في واحد
+
+176
+00:16:22,360 --> 00:16:27,620
+زيرو سالب واحد واحد ويساوي الصف الأول في العمود
+
+177
+00:16:27,620 --> 00:16:33,860
+الأول بواحد الصف الأول في العمود الثاني بزيرو الصف
+
+178
+00:16:33,860 --> 00:16:38,960
+الثاني في العمود الأول بسالب اتنين الصف الثاني في
+
+179
+00:16:38,960 --> 00:16:43,650
+العمود الثاني بواحدأيش اللى تغير عن حصل الضرب
+
+180
+00:16:43,650 --> 00:16:49,630
+المصوفة الأصلية ؟ ثلاثة عناصر هدول هما يتغيرون بس
+
+181
+00:16:49,630 --> 00:16:55,150
+السالب واحد صار باتنين يبقى بناء عليه لو جيت قلتلك
+
+182
+00:16:55,150 --> 00:17:01,630
+يبقى ال a b to the power nأيش بيتقولي واحد زير و
+
+183
+00:17:01,630 --> 00:17:09,010
+واحد و هنا كده؟ سالب M طيب بتقدر تلاقي رقم تحطه ك
+
+184
+00:17:09,010 --> 00:17:14,310
+أس ل a,b يطلع ال identity؟ مفيش إمكانية يبقى ال a
+
+185
+00:17:14,310 --> 00:17:19,310
+,b كدهش ال order اللي لها infinity يبقى هذا بده
+
+186
+00:17:19,310 --> 00:17:27,390
+يعطيلي ان ال a,b is of infinite order
+
+187
+00:17:28,710 --> 00:17:34,670
+يبقى هذا مثال جميل جدا لو سألك قالك انت عندك group
+
+188
+00:17:34,670 --> 00:17:39,630
+فيها two elements كل واحد بفيهم finite order هل
+
+189
+00:17:39,630 --> 00:17:44,890
+حاصل الضرب بديكون finite ولا infinite لاحتمالين
+
+190
+00:17:44,890 --> 00:17:49,210
+وردات قد يكون حاصل الضرب finite وقد يكون حاصل
+
+191
+00:17:49,210 --> 00:17:54,690
+الضرب infiniteهي طلع ال order لكل واحدة فيهم
+
+192
+00:17:54,690 --> 00:17:58,790
+finite لكن ال order لحاصل الدربع التاني infinite
+
+193
+00:18:00,400 --> 00:18:06,500
+هذا مثال جميل جدا حكيتلكوا الصبح عنه و نحنا قد
+
+194
+00:18:06,500 --> 00:18:11,780
+أعطيناكم هذا المثال طب بدنا نخش الأن للموضوع اللي
+
+195
+00:18:11,780 --> 00:18:15,040
+احنا كنا رافعينه اللي هو انتبعنا اللي لسه
+
+196
+00:18:15,040 --> 00:18:20,880
+ماتحدثناش فيه لغمين ال subgroups المجموعات الجزئية
+
+197
+00:18:20,880 --> 00:18:26,550
+لمجموعة ماالـ definition بيقول ما يأتي definition
+
+198
+00:18:26,550 --> 00:18:40,650
+let الـ H be a subset of G الـ
+
+199
+00:18:40,650 --> 00:18:53,780
+H is called هذي بنسميها a subgroup ofG subgroup من
+
+200
+00:18:53,780 --> 00:19:09,380
+G F L H is a group is a group under the same
+
+201
+00:19:09,380 --> 00:19:19,540
+operation under the same operation of
+
+202
+00:19:20,800 --> 00:19:33,080
+G We write بروح نكتب ان ال H هي ال sub group من جي
+
+203
+00:19:33,080 --> 00:19:37,460
+بالشكل اللي عندنا Notes
+
+204
+00:19:37,460 --> 00:19:49,740
+بعض الملاحظات اول ملاحظة F ال H لا تساوي G We
+
+205
+00:19:49,740 --> 00:20:03,150
+writeبنروح نكتب ان ال H subgroup من G and ال H is
+
+206
+00:20:03,150 --> 00:20:11,290
+called بنروح نسميها a proper
+
+207
+00:20:11,290 --> 00:20:18,330
+subgroup نقطة
+
+208
+00:20:18,330 --> 00:20:19,070
+ثانية
+
+209
+00:20:21,440 --> 00:20:32,180
+ست إي فقط لغير is called a
+
+210
+00:20:32,180 --> 00:20:38,960
+trivial subgroup of
+
+211
+00:20:38,960 --> 00:20:40,300
+G
+
+212
+00:20:47,700 --> 00:20:56,780
+the others and the other subgroups
+
+213
+00:20:56,780 --> 00:21:03,400
+are called
+
+214
+00:21:03,400 --> 00:21:07,860
+the
+
+215
+00:21:07,860 --> 00:21:11,340
+non
+
+216
+00:21:11,340 --> 00:21:15,740
+-atrivial subgroups
+
+217
+00:21:22,890 --> 00:21:24,670
+R G
+
+218
+00:22:07,520 --> 00:22:10,640
+نرجع للتعريف اللى احنا كنا نقوله تعريف ال subgroup
+
+219
+00:22:10,640 --> 00:22:16,120
+فباجي بقول لو كانت ال H هي ال subset من G بس مش
+
+220
+00:22:16,120 --> 00:22:20,820
+حيالها subset في شغلة بتتحقق عليها يبقى ال H is
+
+221
+00:22:20,820 --> 00:22:25,380
+called subgroup من G إذا كانت ال H باقية هي group
+
+222
+00:22:25,380 --> 00:22:31,980
+under the same operation of G يعني اعتبر الطلاب
+
+223
+00:22:31,980 --> 00:22:36,060
+اللى عندي في هذه القاعة كلهم groupلو أخدت هذه
+
+224
+00:22:36,060 --> 00:22:41,080
+المجموعة منهم يبقى هذه بسميها ال subgroup إذا طلعت
+
+225
+00:22:41,080 --> 00:22:45,400
+هذه group تحت نفسي العملية المعرفة عليه ال group
+
+226
+00:22:45,400 --> 00:22:49,780
+الأصلية إيش يعني group؟ يعني هذه فيهم ال identity
+
+227
+00:22:49,780 --> 00:22:55,440
+element وعناصرهم associative مع بعضهم وكل عنصر له
+
+228
+00:22:55,440 --> 00:23:00,500
+معكوسيبقى ان حدث ذلك بقول يبقى هذه الجديدة group
+
+229
+00:23:00,500 --> 00:23:05,040
+ان حد ذلك يبقى بقول هذه ال sub group من من من ال
+
+230
+00:23:05,040 --> 00:23:09,240
+group الأصلية يبقى ال H sub group من ال group
+
+231
+00:23:09,240 --> 00:23:13,980
+الأصلية إذا كانت هي group تحت نفس العملية وبدل
+
+232
+00:23:13,980 --> 00:23:18,040
+مكتوب sub group من الأنفا ساعدا هكتب ال sub group
+
+233
+00:23:18,040 --> 00:23:23,220
+H is a sub group من جيه مش H أقل من أو يساوي جيه
+
+234
+00:23:23,580 --> 00:23:27,200
+هذا أقل من سوى للاعداد العادية بس هذا رمز عندنا
+
+235
+00:23:27,200 --> 00:23:31,860
+يدل طيلة الكتاب على ميم على ال subgroup بيبقى كلمة
+
+236
+00:23:31,860 --> 00:23:36,520
+subgroup بدي أختصرها إلى الرمز اللي عندنا هذا و
+
+237
+00:23:36,520 --> 00:23:42,590
+تقرأ subgroup اتش subgroup من Gالـ H هذه يا شباب
+
+238
+00:23:42,590 --> 00:23:48,450
+ممكن تساوي جي وممكن ما تساويش الجي إذا الـ H هذه
+
+239
+00:23:48,450 --> 00:23:53,410
+ما سواتش الجي بنكتب H subgroup من جي وبنشيل
+
+240
+00:23:53,410 --> 00:23:55,210
+اليساوي اللي عندنا
+
+241
+00:23:57,730 --> 00:24:01,550
+الـ HP في هذه الحالة بسميها proper subgroup يعني
+
+242
+00:24:01,550 --> 00:24:06,370
+انا لو أخدت subgroup و لاقيتها لا تساوي لجروب
+
+243
+00:24:06,370 --> 00:24:10,750
+الأصلية لأنه بناعرف احنا any set is a subset of
+
+244
+00:24:10,750 --> 00:24:16,730
+itself صحيح ولا لأ؟ هي مجموعة جزئية من نفسها طلعت
+
+245
+00:24:16,730 --> 00:24:21,750
+المجموعة هذه الجزئية أقل من نفسهالاتساوي الأصلية
+
+246
+00:24:21,750 --> 00:24:28,170
+يبقى في هذه الحالة بسميها proper subgroup طبعا طيب
+
+247
+00:24:28,170 --> 00:24:32,050
+طب لو كده تلاقيتش تساوي جيه طبعا تلاقيتش جد الجيه
+
+248
+00:24:32,050 --> 00:24:37,630
+بالضبط تماما يبقى بسميها بسميها improper subgroup
+
+249
+00:24:37,630 --> 00:24:42,670
+هذه اسمها improper بقوم بلغيها زي ما نقول إن هذا
+
+250
+00:24:42,670 --> 00:24:48,240
+possible ممكن ننفيها بنقول impossible غير ممكنيبقى
+
+251
+00:24:48,240 --> 00:24:55,380
+هذي ممكن احطها لك ملاحظة رقم تلاتة if ال H تساوي G
+
+252
+00:24:55,380 --> 00:25:09,380
+then ال H is called improper subgroup
+
+253
+00:25:09,380 --> 00:25:13,020
+يبقى
+
+254
+00:25:13,020 --> 00:25:17,810
+هذي مسميها improper subgroupلو رحت أخدت ال
+
+255
+00:25:17,810 --> 00:25:23,630
+identity وحدة لحاله و حطيته داخل set يبقى السعر
+
+256
+00:25:23,630 --> 00:25:28,610
+عندي set لا يوجد فيها إلا ال identity element هل
+
+257
+00:25:28,610 --> 00:25:33,570
+هذه ال subgroup في الأول؟ subgroup ليش؟ لأن ال
+
+258
+00:25:33,570 --> 00:25:37,870
+identity موجودلو ضربت ال identity في نفسه بيطلع ال
+
+259
+00:25:37,870 --> 00:25:42,690
+identity موجود معكس ال identity هو ال identity
+
+260
+00:25:42,690 --> 00:25:48,010
+نفسه إذا موجود يبقى هذا صارت subgroup إن حدث ذلك
+
+261
+00:25:48,010 --> 00:25:52,310
+يبقى بسميها هذا ال subgroup ال trivial subgroup
+
+262
+00:25:52,600 --> 00:25:58,140
+يعني المجموع الجزئي البدي هي أو التافية أبسط أنواع
+
+263
+00:25:58,140 --> 00:26:02,720
+ال subgroups يبقى هذه ال set عبارة عن subgroup من
+
+264
+00:26:02,720 --> 00:26:06,580
+من من ال group الأصلي بسميها ال trivial subgroup
+
+265
+00:26:06,580 --> 00:26:11,220
+سيبنا هذه وروح تاخد كل ال subgroups الباقية كلهم
+
+266
+00:26:11,220 --> 00:26:15,840
+بسميهم non trivial subgroups يبقى هنا and the
+
+267
+00:26:15,840 --> 00:26:19,160
+other subgroups are called the non trivial
+
+268
+00:26:19,160 --> 00:26:25,080
+subgroupsof g يبقى صار undetriable subgroup, non
+
+269
+00:26:25,080 --> 00:26:28,360
+-detriable subgroup, proper subgroup, improper
+
+270
+00:26:28,360 --> 00:26:34,640
+subgroup, improper يبقى
+
+271
+00:26:34,640 --> 00:26:39,260
+أقل من الأصلية بشوية طبعا جد ما يكون يكون ان شاء
+
+272
+00:26:39,260 --> 00:26:45,560
+الله يكون عنصرين طب خليني أسألك طب هذه بنفع أقول
+
+273
+00:26:45,560 --> 00:26:51,210
+عليها properبنفع proper على كل خط بس لدرجة انها
+
+274
+00:26:51,210 --> 00:26:54,570
+مسمية trivial subgroup وبالتالي مقولش عليها proper
+
+275
+00:26:54,570 --> 00:26:59,710
+subgroup بدأ ناخد بعض الأمثلة التوضيحية على ذلك
+
+276
+00:26:59,710 --> 00:27:09,730
+قبل أن ندخل إلى أول نظرية يبقى examples أول
+
+277
+00:27:09,730 --> 00:27:16,510
+مثل بيقول z in under
+
+278
+00:27:19,250 --> 00:27:28,150
+addition modulo n اللي هي توسعة رمز نالها بالرمز z
+
+279
+00:27:28,150 --> 00:27:36,250
+in وعليها عملية الجمع modulo n هذه ماالها is not a
+
+280
+00:27:36,250 --> 00:27:44,090
+subgroup of
+
+281
+00:27:44,090 --> 00:27:45,890
+z
+
+282
+00:27:47,150 --> 00:27:53,850
+هو عليها عملية الجمع العادية هذه
+
+283
+00:27:53,850 --> 00:27:58,990
+مش subgroup طب زد n عناصرها zero واحد واثنين
+
+284
+00:27:58,990 --> 00:28:04,210
+وتلاتة لغاية n ناقص واحد زد هذه الموجب والسالب
+
+285
+00:28:04,210 --> 00:28:09,830
+والصفر يبقى zn هي subset من من؟ subset من z
+
+286
+00:28:09,830 --> 00:28:14,090
+بيتداعي هنا بيقول ماهياش subgroup حد بيقول لي ليش؟
+
+287
+00:28:14,090 --> 00:28:20,350
+ايوةأيوة اختلفت العملية حسب التعريف اللي كتبناه
+
+288
+00:28:20,350 --> 00:28:23,650
+لازم تبقى العملية على ال group الأصلية هي نفس
+
+289
+00:28:23,650 --> 00:28:28,390
+العملية على من؟ على ال subset يبقى هنا Z under
+
+290
+00:28:28,390 --> 00:28:38,730
+that is not a subgroup because the two operations
+
+291
+00:28:41,770 --> 00:28:50,570
+on zed in and الـ zed are different تختلف عن
+
+292
+00:28:50,570 --> 00:28:55,170
+التانية ولا واحدة فيهم زي التانية يبقى هذا نقض
+
+293
+00:28:55,170 --> 00:29:02,650
+التعريف لذلك هذا ماهياش subgroup خدلي مثال ثاني
+
+294
+00:29:02,650 --> 00:29:11,070
+خدلي الـ G هي عبارة عن ليكيو و عليها عملية الجمع
+
+295
+00:29:11,910 --> 00:29:20,830
+and ال h هي عبارة عن ال z و عليها عملية الجمع
+
+296
+00:29:20,830 --> 00:29:29,670
+السؤال هو هل هذه صبست من هذه صحيح لأن any integer
+
+297
+00:29:29,670 --> 00:29:33,210
+is a rational number ال operation نفسي ال
+
+298
+00:29:33,210 --> 00:29:40,450
+operation ال identity هنا مينوهنا نفس الـ identity
+
+299
+00:29:40,450 --> 00:29:45,490
+element المعكوس لل element هنا a عبارة عن مين؟
+
+300
+00:29:45,490 --> 00:29:49,850
+سالب a، المعكوس لهنا، مثل نفس الشيء، إذا هذه
+
+301
+00:29:49,850 --> 00:29:56,110
+subgroup من مين؟ من هنا، يبقى let g and then ال H
+
+302
+00:29:56,110 --> 00:30:02,710
+is a subgroup من g على طول الخط، مافيش أي تناقضما
+
+303
+00:30:02,710 --> 00:30:08,590
+بين الأثنين لا عملية ولا identity ولا معكوس طيب
+
+304
+00:30:08,590 --> 00:30:16,550
+السؤال الثالث لو أخدت ال Q plus تحت عملية الضرب
+
+305
+00:30:16,550 --> 00:30:27,810
+العادية and ال Q تحت عملية الجمع groups and all
+
+306
+00:30:29,450 --> 00:30:34,470
+group صحيح بس هل هذه subgroup من هذه أو العكس هل
+
+307
+00:30:34,470 --> 00:30:40,070
+هذه subgroup من هذه برضه لأ ليش لإنه ال operation
+
+308
+00:30:40,070 --> 00:30:47,050
+هنا ضربه هناك جامعة تختلف كليا and then
+
+309
+00:30:48,500 --> 00:30:56,320
+الـ q plus تحت عملية الجامعة is not a subgroup من
+
+310
+00:30:56,320 --> 00:31:07,900
+ال q و ال plus because السبب the two operations
+
+311
+00:31:07,900 --> 00:31:20,340
+العمليتين on ال q andالـ Q plus are different ولا
+
+312
+00:31:20,340 --> 00:31:27,780
+واحدة فيهم زي التانية طيب نبدأ في أول نظرية اظن ان
+
+313
+00:31:27,780 --> 00:31:32,160
+كان كل مرة بدنا نقعد نفحص ان هذه ال subgroup
+
+314
+00:31:32,160 --> 00:31:37,240
+العملية نفس العملية قصتنا هذه طويلةلكن نحاول ناخد
+
+315
+00:31:37,240 --> 00:31:41,940
+نظرية بواسطها نقدر نحكم على ال subset اللى أخدنا
+
+316
+00:31:41,940 --> 00:31:47,480
+منه هل هو subgroup أم لا بطريقة أسهل يبقى بإذن
+
+317
+00:31:47,480 --> 00:31:52,460
+الله نأتي لأول نظرية very important على ال
+
+318
+00:31:52,460 --> 00:32:02,300
+subgroup فالنظرية بتقول ما يأتي letالـ H بـ A non
+
+319
+00:32:02,300 --> 00:32:10,120
+empty subset of
+
+320
+00:32:10,120 --> 00:32:14,760
+a group G
+
+321
+00:32:20,070 --> 00:32:24,270
+الـ H is
+
+322
+00:32:24,270 --> 00:32:33,330
+a subgroup من G
+
+323
+00:32:33,330 --> 00:32:36,710
+الـ
+
+324
+00:32:36,710 --> 00:32:43,970
+A B inverse belongs to H whenever
+
+325
+00:32:47,020 --> 00:32:54,920
+عندما ال A and ال B are in H
+
+326
+00:33:19,250 --> 00:33:26,150
+مرة تانية انا عندى group اخدت منها subset ال
+
+327
+00:33:26,150 --> 00:33:31,770
+subset هذا وقتش بقدر اقول عنه subgroup اذا تحقق
+
+328
+00:33:31,770 --> 00:33:37,630
+شرطا الشرط الاول ان ال H اللي اخدت هذا تبقى non
+
+329
+00:33:37,630 --> 00:33:43,290
+-empty subset من Gالشرط التاني لو أخدت عمصرين
+
+330
+00:33:43,290 --> 00:33:48,370
+موجودات في H بدي أكون حاصل ضرب الأول في معكوس
+
+331
+00:33:48,370 --> 00:33:53,370
+الثاني موجود في H ان حد ذلك تبقى ال H هذه بقول
+
+332
+00:33:53,370 --> 00:33:58,870
+عليها subgroup تمام طب قبل ما برهن بدي أبرهن صحة
+
+333
+00:33:58,870 --> 00:34:03,590
+هذا الكلام مش حيال اللهالـ a b inverse هذه موجودة
+
+334
+00:34:03,590 --> 00:34:08,330
+في اتش لو كان شباب ال operation اللي على g عملية
+
+335
+00:34:08,330 --> 00:34:16,930
+الجامعة هذا الشرط كيف بكتبه a ناقص b موجود في اتش
+
+336
+00:34:16,930 --> 00:34:27,950
+يبقى هنا هذه كملاحظة بس يبقى if the operation if
+
+337
+00:34:27,950 --> 00:34:28,990
+the operation
+
+338
+00:34:35,690 --> 00:34:50,090
+on g is addition then الو a b inverse belongs to h
+
+339
+00:34:50,090 --> 00:34:56,130
+is written is
+
+340
+00:34:56,130 --> 00:35:03,620
+written as a minus b كل هذا موجود في hكل ال
+
+341
+00:35:03,620 --> 00:35:10,880
+element هذا موجود في ال proof مرة
+
+342
+00:35:10,880 --> 00:35:17,280
+تانيةبقول لو كان الـH هي الـnon-empty subset of A
+
+343
+00:35:17,280 --> 00:35:22,300
+group G، هاي ال condition الأول، then الـH is a
+
+344
+00:35:22,300 --> 00:35:27,100
+subgroup of G if الـA, B inverse موجود في H
+
+345
+00:35:27,100 --> 00:35:32,540
+whenever A وB are in H يبقى حسب التعريف الـsubset
+
+346
+00:35:32,540 --> 00:35:39,480
+اللي خدت بتبقى subgroup لو بقيت group تحت نفس
+
+347
+00:35:39,480 --> 00:35:44,330
+العمليةتعالى نشوف هل هذا الكلام بيحقق خاصية ال
+
+348
+00:35:44,330 --> 00:35:48,530
+group تحت نفس العملية ولا لأ؟ الآن ال H هذه ال
+
+349
+00:35:48,530 --> 00:35:53,510
+subset من مين؟ من G و ال operation اللي ع G
+
+350
+00:35:53,510 --> 00:35:58,490
+associative binary operation صح ولا لأ؟ يبقى هل
+
+351
+00:35:58,490 --> 00:36:02,390
+اختلفوا عناصر H؟ يعني صار على رأسهم ريشة لما
+
+352
+00:36:02,390 --> 00:36:06,910
+أخدناهم من G؟ لأ ما ينطبق على عناصر G ينطبق عليهم
+
+353
+00:36:07,270 --> 00:36:12,230
+إذا ال operation على H is associative binary
+
+354
+00:36:12,230 --> 00:36:17,330
+operation تمام ليش؟ لأن H هي ال subset من G يعني
+
+355
+00:36:17,330 --> 00:36:22,950
+ما ينطبق على عناصر G ينطبق تماما على عناصر من؟ على
+
+356
+00:36:22,950 --> 00:36:28,700
+عناصر H لكن هل ال identity هو نفسه؟ الله أعلمهل
+
+357
+00:36:28,700 --> 00:36:33,780
+معكوس العنصر اللى بده ياخده من إتش بده يكون في إتش
+
+358
+00:36:33,780 --> 00:36:39,280
+ولا برا الله أعلم هل لو أخدت عنصرين من إتش وضربتهم
+
+359
+00:36:39,280 --> 00:36:44,300
+في بعض بده يكون داخل إتش ولا لأ إن تحققت خواصة
+
+360
+00:36:44,300 --> 00:36:48,080
+التلاتة دي بيصير هذه الصعبة بالرومما تحقق واحد
+
+361
+00:36:48,080 --> 00:36:52,360
+منهم يبقى برا بتبطل يصير subgroup يبقى هو حاط ل
+
+362
+00:36:52,360 --> 00:36:57,660
+condition بدي أحاول أستفيد منه يبقى البرهان النقطة
+
+363
+00:36:57,660 --> 00:37:13,280
+الأولى الان the operation on H is an associative
+
+364
+00:37:13,280 --> 00:37:15,480
+binary
+
+365
+00:37:25,220 --> 00:37:31,680
+بسبب ان الـ H مالها subset من G
+
+366
+00:37:37,990 --> 00:37:41,710
+يبقى هذه ال associative binary operation متحققة
+
+367
+00:37:41,710 --> 00:37:46,890
+بالنسبة للخاصية الثانية الخاصية التانية بتقول انت
+
+368
+00:37:46,890 --> 00:37:51,670
+كل اللي عندي ان لو أخدت أنصرين من H بدي يكون حاصل
+
+369
+00:37:51,670 --> 00:38:00,090
+ضرب الأول فيه الثاني موجود في H صح ولا لا الان let
+
+370
+00:38:00,090 --> 00:38:11,010
+ال A و ال B موجودة في ال H thenالـ A B إنفرس موجود
+
+371
+00:38:11,010 --> 00:38:19,350
+في الـ H هذا in general هذا مواطع من نص النظرية طب
+
+372
+00:38:19,350 --> 00:38:26,240
+إيش رايك؟ بنفع أخد A تساوي B؟ بنفع ولا مانفعش؟هذا
+
+373
+00:38:26,240 --> 00:38:33,520
+ينفع لجميع الانصار ان ايه ممنوع يساوي بيه فانا
+
+374
+00:38:33,520 --> 00:38:36,180
+ممكن اخد اي انصار اذا انا ممكن اخد اي انصار اذا
+
+375
+00:38:36,180 --> 00:38:36,320
+انا ممكن اخد اي انصار اذا انا ممكن اخد اي انصار
+
+376
+00:38:36,320 --> 00:38:38,200
+اذا انا ممكن اخد اي انصار اذا انا ممكن اخد اي
+
+377
+00:38:38,200 --> 00:38:38,540
+انصار اذا انا ممكن اخد اي انصار اذا انا ممكن اخد
+
+378
+00:38:38,540 --> 00:38:41,580
+اي انصار اذا انا ممكن اخد اي انصار اذا انا ممكن
+
+379
+00:38:41,580 --> 00:38:43,340
+اخد اي انصار اذا انا ممكن اخد اي انصار اذا انا
+
+380
+00:38:43,340 --> 00:38:48,420
+ممكن اخد اي انصار اذا انا ممكن اخد اي انصار اذا
+
+381
+00:38:48,420 --> 00:38:51,660
+انا ممكن اخد اي انصار ا
+
+382
+00:38:53,490 --> 00:38:59,210
+الـ A B Inverse بدي ساوي ال X في ال X Inverse
+
+383
+00:38:59,210 --> 00:39:00,290
+موجودة في H
+
+384
+00:39:08,810 --> 00:39:15,790
+هذا يعني أن الـ E موجود في الـ H يبقى الـ H فيها
+
+385
+00:39:15,790 --> 00:39:20,070
+الـ identity element تبع من؟ تبع الـ group الأصلي
+
+386
+00:39:20,070 --> 00:39:23,490
+صار الـ identity في الـ group الأصلي اللي هو E
+
+387
+00:39:23,490 --> 00:39:29,310
+نفسه هو هو موجود في من؟ في ال subset اللي هي H حتى
+
+388
+00:39:29,310 --> 00:39:33,610
+لما أقول subset ما أقول subgroupموجود هو هو يبقى
+
+389
+00:39:33,610 --> 00:39:38,110
+ال X X inverse هذا موجود في G و هذا موجود في G إذا
+
+390
+00:39:38,110 --> 00:39:42,410
+ال element هذا صار موجود في H لإنه حصل ضاربه ما
+
+391
+00:39:42,410 --> 00:39:46,450
+موجود في H ال identity هذا هو تبع G الأصلية
+
+392
+00:39:46,450 --> 00:39:55,470
+ماغيرتشها طيب بدنا نيجي لل condition التالت F
+
+393
+00:40:06,200 --> 00:40:12,120
+معكوس العنصر هذا موجود لأنه في جيه بس موجود في H
+
+394
+00:40:12,120 --> 00:40:17,980
+والله برة H انا مش عارف انا بدي اثبت ان معكوس هذا
+
+395
+00:40:17,980 --> 00:40:20,640
+العنصر موجود في H
+
+396
+00:40:24,680 --> 00:40:30,080
+الان ايه شفتنا هنا يا شباب ان ال E موجود في H بدي
+
+397
+00:40:30,080 --> 00:40:38,180
+اخد هذا ال E هو A و ال B inverse يبقى هنا A في ال
+
+398
+00:40:38,180 --> 00:40:45,760
+B inverse موجود في H implies بدي اخدي ال A في ال B
+
+399
+00:40:45,760 --> 00:40:50,140
+inverse بدي اكون موجود في H صح ولا لا طبق لل
+
+400
+00:40:50,140 --> 00:40:56,510
+condition اللي عندي كويسيبقى هذا ايش معناه ان ال P
+
+401
+00:40:56,510 --> 00:41:01,430
+inverse موجود في H هل ال P اللي أخدته في H عليه
+
+402
+00:41:01,430 --> 00:41:06,250
+قيود والله اي عنصر موجود في H اي عنصر موجود في H
+
+403
+00:41:06,250 --> 00:41:11,650
+يبقى اي عنصر موجود في H اللي جات المعكوث تبعه
+
+404
+00:41:11,650 --> 00:41:16,650
+موجود وين موجود في H يبقى ضايق لنا بس النقطة
+
+405
+00:41:16,650 --> 00:41:17,490
+الأخيرة
+
+406
+00:41:20,560 --> 00:41:26,300
+إن لو أخدت عنصرين من H بدي أثبت أن حاصل ضربهما
+
+407
+00:41:26,300 --> 00:41:32,500
+موجود في H بس هاي كل اللي بديها ان تم ذلك بصير
+
+408
+00:41:32,500 --> 00:41:37,200
+عندنا هذا الـ H is a subgroup وبصير نستخدم هذه
+
+409
+00:41:37,200 --> 00:41:41,120
+النظرية في الحكم على ال subsets المختلفة هل هي
+
+410
+00:41:41,120 --> 00:41:47,860
+subgroup ام لاأنا بدي أخد عنصرين موجودات في H و
+
+411
+00:41:47,860 --> 00:41:56,060
+بدي أثبت أن حاصل ضربه موجود في H يبقى هنا F A و B
+
+412
+00:41:56,060 --> 00:42:01,580
+موجودات في H let
+
+413
+00:42:01,580 --> 00:42:12,480
+A تساوي X و B تساوي Y inverse مثلاوخد الـ P يبدو
+
+414
+00:42:12,480 --> 00:42:19,040
+يساوي Y inverse then ايش
+
+415
+00:42:19,040 --> 00:42:22,120
+رأيك لو اخدت ال X في Y؟
+
+416
+00:42:24,710 --> 00:42:30,250
+الـ X في Y أشوف إيش بيساوي هنا X وهنا B تساوي Y
+
+417
+00:42:30,250 --> 00:42:36,510
+inverse يعني ال Y هذه موجودة في G موجودة في G بدي
+
+418
+00:42:36,510 --> 00:42:44,550
+أخد ال X في Y مين ال X؟ أو ملاش يساوي X في ال Y
+
+419
+00:42:44,550 --> 00:42:50,850
+بقدر أكتبها Y inverse inverse مظبوط؟
+
+420
+00:42:51,360 --> 00:42:57,100
+هذا الكلام يستوي ال X انا افرضها بقداش؟ ب A وال Y
+
+421
+00:42:57,100 --> 00:42:59,600
+inverse ب مين؟ ب B
+
+422
+00:43:03,070 --> 00:43:09,370
+يبقى هذا موجود في h طبقا لل condition يعني حاصل
+
+423
+00:43:09,370 --> 00:43:14,930
+ضرب any two elements موجودة وين في h يبقى هذا
+
+424
+00:43:14,930 --> 00:43:21,650
+بيعطينا ان x و y موجود في h for all x و y اللي
+
+425
+00:43:21,650 --> 00:43:27,000
+موجودة وينموجودة في H يعني ال H is closed under
+
+426
+00:43:27,000 --> 00:43:31,020
+multiplication يبقى تحققت أو هذه اللي كنا نسميها
+
+427
+00:43:31,020 --> 00:43:35,700
+binary operation أنه تاخد two elements أثر واحد
+
+428
+00:43:35,700 --> 00:43:39,120
+على التاني يعطيك عنصر يديد هذا العنصر موجود في من؟
+
+429
+00:43:39,120 --> 00:43:45,920
+في H يبقى بناء عليه بروح بقوله thus و هكذا ال H is
+
+430
+00:43:45,920 --> 00:43:51,740
+a subgroup من G وبالتالي برهن النظرية اللي موجودة
+
+431
+00:43:51,740 --> 00:43:57,960
+عندنامن الانفة الصاعدة يا شباب لو اعطاني group
+
+432
+00:43:57,960 --> 00:44:03,280
+واعطاني set من ال group وقال يثبتلي ان ال set هذه
+
+433
+00:44:03,280 --> 00:44:10,210
+is a sub group بدي اعمله خطوتين لثالثة لهماالخطوة
+
+434
+00:44:10,210 --> 00:44:18,790
+الأولى هي أن أثبت له أن الـH هي non-empty يبقى هذه
+
+435
+00:44:18,790 --> 00:44:23,830
+فيها عناصر و لو تثبت أن فيها عنصر واحد يكفي منك
+
+436
+00:44:23,830 --> 00:44:26,870
+الله يعطيك العفو بس أثبت أن فيها عنصر واحد يبقى
+
+437
+00:44:26,870 --> 00:44:30,030
+non-empty خلصنا من ال condition الأولىالـ
+
+438
+00:44:30,030 --> 00:44:34,830
+condition الثاني لو رحت أخدت أي two elements في
+
+439
+00:44:34,830 --> 00:44:40,430
+هذه ال subset وقدرت تثبت أن الأول في معكوس الثاني
+
+440
+00:44:40,430 --> 00:44:45,510
+موجود في h double h subgroupخلصنا يبقى من الآن
+
+441
+00:44:45,510 --> 00:44:52,670
+فصاعدا لو أخد subset من group G ال subset هذا بدي
+
+442
+00:44:52,670 --> 00:44:58,510
+أثبت أنه subgroup معطوب منك تثبت شرطين إذا أثبتهم
+
+443
+00:44:58,510 --> 00:45:04,210
+صحيح بيصير هذا subgroup كيف؟ يعني بيكتثبت أولا أن
+
+444
+00:45:04,210 --> 00:45:08,970
+ال subset اللي أخدتها non-empty على الأقليجب أن
+
+445
+00:45:08,970 --> 00:45:14,270
+تظهر أن هناك عنصر موجود في هذه الـ subset اثنين لو
+
+446
+00:45:14,270 --> 00:45:17,250
+أخذت أي احد من الـ two elements في هذا الـ subset
+
+447
+00:45:17,250 --> 00:45:21,350
+يجب أن تثبت أنه حصل ضرب الأول في معكوس الثاني
+
+448
+00:45:21,350 --> 00:45:25,330
+موجود فيه إذا أثبتت ذلك يبقى هذا سيصبح معناه
+
+449
+00:45:25,330 --> 00:45:31,070
+subgroup يعني شغلنا بعد ذلك في الأمثلة يجب أن
+
+450
+00:45:31,070 --> 00:45:35,030
+يعطيني group يعطيني ال subset من هنا يقول يثبت أن
+
+451
+00:45:35,030 --> 00:45:38,940
+هذه subgroup أو ما هيشالسابقروب يعني ما قلت ماهياش
+
+452
+00:45:38,940 --> 00:45:43,180
+سابقروب بدك تجيبله counter example قلت له group
+
+453
+00:45:43,180 --> 00:45:47,800
+بدك تروح اياش اتبرهنها والله بنفع اجيب example بس
+
+454
+00:45:47,800 --> 00:45:50,920
+كده عدد يثبت انها group .. انها سابقروب بالفعل
+
+455
+00:45:50,920 --> 00:45:54,460
+بنفعش لكن counter example اه بثبت انه ماهيش
+
+456
+00:45:54,460 --> 00:46:00,180
+سابقروب بس ديك لازم اتبرهنها برهانة طيب الآن ماضلش
+
+457
+00:46:00,180 --> 00:46:04,780
+وقت الحقيقة كان أخدنا الآن بعض الأمثلة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ba09282602463a942326aabe9d23f295060af234
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8.srt
@@ -0,0 +1,1602 @@
+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 الجبر اللي
+
+3
+00:00:31,750 --> 00:00:36,670
+سندرسه واليوم إن شاء الله سنتعرض إلى 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
+الرياضيات، هنعطي 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 إن شاء الله، بنبدأ بال
+
+9
+00:01:00,000 --> 00:01:04,140
+equivalence relations اللي هي علاقات التكافؤ
+
+10
+00:01:04,140 --> 00:01:08,630
+بدنا نعرف علاقات التكافؤ، وبعدين أنا آخذ مثال و
+
+11
+00:01:08,630 --> 00:01:13,310
+أوضّحها عليه، بقول little s ب a6، يبقى أخذنا s
+
+12
+00:01:13,310 --> 00:01:19,970
+كمجموعة، جالي a subset R of s cross ال s، يبقى أنا
+
+13
+00:01:19,970 --> 00:01:25,150
+على ال 6s بدي أعمل direct product ما بين ال s وال
+
+14
+00:01:25,150 --> 00:01:29,910
+s itself، بيصير كل element في ال s cross ال s عبارة
+
+15
+00:01:29,910 --> 00:01:36,620
+عن ordered pair، زوج مرتب، يبقى 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
+transitive، تعال نشوف شو يعني معنى reflexive
+
+20
+00:01:55,020 --> 00:02:00,400
+property، بيقول ال a وال a موجودة في R، يعني لو
+
+21
+00:02:00,400 --> 00:02:05,900
+أخذت a موجود في S، لازم يكون ال element a و a ك
+
+22
+00:02:05,900 --> 00:02:11,340
+ordered pair موجود و a موجود في R، يعني العنصر مرتبط
+
+23
+00:02:11,340 --> 00:02:17,520
+مع مين؟ مع نفسه بهذه ال relation، يقبل 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 أخذت أي element من ال 6S، يكون هذا
+
+26
+00:02:26,640 --> 00:02:31,460
+ال element مربوط مع نفسه بالعلاقة من ال 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 الخاصية العاكسة، الشرط التاني أو
+
+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 التماثل، الأمر الثالث والأخير، لو كان ال ordered
+
+37
+00:03:25,510 --> 00:03:30,410
+pair A وB موجود في R وال 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 وال C موجود وإن
+
+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 تحقق هذه الخاصية بسميها علاقة
+
+42
+00:03:50,090 --> 00:03:54,240
+ناقلة، إذا ال 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
+relation، هذا 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 واحد، مثال، وذلك لو قلنا ال R هي equivalence
+
+52
+00:04:37,240 --> 00:04:43,360
+relation على ال 6S، بالروح نكتب أن 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 أن ال A وال B مرتبطات
+
+55
+00:04:52,920 --> 00:04:58,430
+مع بعض بالعلاقة R، instead of بدلا من قول إن الراجل
+
+56
+00:04:58,430 --> 00:05:02,810
+مرتّب a و b موجود في ال R، 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، وأحيانا بيعبروا بحكاية
+
+60
+00:05:18,750 --> 00:05:23,490
+اليساوي، وأحيانا بثلاثة، اللي هي زي التكافؤ 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 التكافؤ اللي
+
+64
+00:05:37,730 --> 00:05:43,680
+هي reflexive و symmetric and transitive، طيب العلاقة
+
+65
+00:05:43,680 --> 00:05:48,080
+اللي عندنا هذه لما نجي على ال set اللي عندنا هذه
+
+66
+00:05:48,080 --> 00:05:52,640
+ونقول عندنا العلاقة هذه، العلاقة هذه بتعملي مجموعة
+
+67
+00:05:52,640 --> 00:05:57,780
+من ال equivalence classes اللي همين فصول التكافؤ
+
+68
+00:05:57,780 --> 00:06:02,660
+إيه قصة فصول التكافؤ هذا؟ تعال نشوف دي، لو كان أن
+
+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، واخذ 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 واللي بتكون مربوطة مع هذا
+
+73
+00:06:24,340 --> 00:06:28,800
+العنصر فقط، وماليش دعوة في الباقي، يعني 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 التكافؤ لهذا العنصر، يبقى لما نشوف element a
+
+78
+00:06:47,970 --> 00:06:53,390
+ومحطوط بين قوسين، كبارك 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 واللي
+
+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
+أخذته، 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 بالإضافة إلى مجموعة من
+
+87
+00:07:28,510 --> 00:07:33,120
+العناصر الأخرى، نعطي مثال على ال equivalence
+
+88
+00:07:33,120 --> 00:07:36,140
+relation
+
+89
+00:07:36,140 --> 00:07:40,520
+وبعد ذلك نذهب نجيب ال equivalence class لأي
+
+90
+00:07:40,520 --> 00:07:45,960
+element موجود داخل ال set اللي بدنا ناخدها، بقول لو
+
+91
+00:07:45,960 --> 00:07:52,000
+أخذت ال set of integers، يبقى ال S هدفين ليه ال Z
+
+92
+00:07:52,000 --> 00:07:56,740
+مجموعة الأعداد الصحيحة، الموجبة والسالمة والصفر، يعني
+
+93
+00:07:56,740 --> 00:08:02,620
+هذه صارت يا مين؟ هي ال 6z اللي عرفنالكوا في أول
+
+94
+00:08:02,620 --> 00:08:07,860
+محاضرة، قولنالكوا ال 6 اللي هي 6 of integer، لت ال n
+
+95
+00:08:07,860 --> 00:08:12,660
+بيه positive integer، أخذت ال n أي عدد صحيح موجب، ب 2
+
+96
+00:08:12,660 --> 00:08:19,800
+3، 10، 20 قد ما يكون، تمام، بناخد عنصرين موجودة في ال set
+
+97
+00:08:19,800 --> 00:08:23,840
+S، يعني ال A وال B integers، يمكن يكونوا اتنين
+
+98
+00:08:23,840 --> 00:08:26,020
+بالموجب، يمكن يكونوا اتنين بالسالب، يمكن يكونوا واحد
+
+99
+00:08:26,020 --> 00:08:30,220
+موجب وواحد سالب، مهمنيش، ماليهمش قيود، بدنا نروح و
+
+100
+00:08:30,220 --> 00:08:35,970
+نعرف أن ال A مرتبط مع ال B إذا كان ال 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 اليساوي، يعني ال
+
+105
+00:08:53,710 --> 00:08:57,110
+remainder تبع ال A يبقى يساوي ال remainder تبع
+
+106
+00:08:57,110 --> 00:09:02,670
+الباقي نتيجة لقسمة ال A على M، نفس الباقي لو قسمنا
+
+107
+00:09:02,670 --> 00:09:08,850
+ال B على M، that is بدي أترجم هذا الكلام بصياغة
+
+108
+00:09:08,850 --> 00:09:15,730
+أخرى، بعدين بقول ال A مرتبطة مع بي إذا هذا أخذنا صيغة
+
+109
+00:09:15,730 --> 00:09:20,410
+مكافئة إلو وهي N، بدأ تقسم الفرق ما بين ال A وال
+
+110
+00:09:20,410 --> 00:09:24,070
+لي بياخذه 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 الأولى، أنا 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، الآن بده تقسمين الفرق في ما بينهما، يبقى بدي
+
+122
+00:10:13,460 --> 00:10:20,300
+آخذ أول حاجة، خاصية ال reflex، يبقى باجي بقوله بدي
+
+123
+00:10:20,300 --> 00:10:25,760
+آجي أقوله الآن ال a are related مع a، مرتبط مع a، شو
+
+124
+00:10:25,760 --> 00:10:34,380
+السبب؟ because إن 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
+هل الـ N بتقسم الـ zero صحيح أم لا؟ هل الـ N بتقسم الـ
+
+127
+00:10:46,660 --> 00:10:50,960
+Zero؟ هل الـ Zero على N جد حاصلها Zero أو 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 الـ N بتقسم الـ Zero، يبقى هذا العنصر مرتبط مع
+
+130
+00:11:00,400 --> 00:11:07,960
+نفسه، وهذه هي اللي سميها reflexive property، طيب نيجي
+
+131
+00:11:07,960 --> 00:11:11,620
+للخاصية الثانية F
+
+132
+00:11:21,910 --> 00:11:33,070
+لما نقول إن الـ N بدأت تقسم الـ A ناقص الـ B، هذا
+
+133
+00:11:33,070 --> 00:11:40,070
+معناه إن الـ A ناقص الـ B بده يساوي الـ N في الـ Q
+
+134
+00:11:44,970 --> 00:11:51,910
+طيب إيش رأيك لو ضربت الطرفين في إشارة سالب؟ انفك و
+
+135
+00:11:51,910 --> 00:11:56,350
+لو ضربت الاثنين في إشارة سالب، إيش بده يصير؟ بده يصير الـ B
+
+136
+00:11:56,350 --> 00:12:03,030
+بالموجب و الـ A بالسالب، يبقى هذا بده يصير B ناقص الـ A
+
+137
+00:12:03,030 --> 00:12:10,640
+هنا بقدر أقول N ناقص Q ماذا يعني هذا الكلام؟
+
+138
+00:12:10,640 --> 00:12:17,940
+معناته إن بتقسم من؟ الـ B ناقص الـ A، هذا معناه إن الـ
+
+139
+00:12:17,940 --> 00:12:24,000
+N بتقسم الـ B ناقص الـ A، مدام هيك يبقى هذا معناه إن
+
+140
+00:12:24,000 --> 00:12:30,340
+الـ 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 الآن تحققت الخاصية الثانية، بتروح
+
+143
+00:12:40,340 --> 00:12:46,760
+لمين؟ للخاصية الثالثة، يبقى بالعامية للخاصية الثالثة
+
+144
+00:12:46,760 --> 00:12:55,280
+assume، افترض أن الـ A are related with B and الـ B
+
+145
+00:12:55,280 --> 00:13:02,940
+are related with C، و الـ A و الـ B و الـ C موجودات في
+
+146
+00:13:02,940 --> 00:13:12,090
+الـ Z اللي هو integers، then بقدر أقول إن الـ N
+
+147
+00:13:12,090 --> 00:13:22,110
+divides الـ A ناقص الـ B and الـ N divides الـ B ناقص
+
+148
+00:13:22,110 --> 00:13:22,650
+الـ C
+
+149
+00:13:25,490 --> 00:13:28,110
+مش هيك تعريف الـ equivalence relation أو الـ
+
+150
+00:13:28,110 --> 00:13:32,310
+relation اللي عندنا؟ يبقى الـ N بتقسم الـ A ناقص الـ B
+
+151
+00:13:32,310 --> 00:13:38,270
+وفي نفس الوقت الـ N بتقسم الـ B ناقص الـ C، هذا معناه
+
+152
+00:13:38,270 --> 00:13:53,680
+إن هناك Q1 و Q2 موجودة في Z such that بحيث إن الـ A
+
+153
+00:13:53,680 --> 00:14:03,600
+ناقص الـ B يساوي Q واحد في N and الـ B ناقص الـ C
+
+154
+00:14:03,600 --> 00:14:07,720
+بده يساوي Q اثنين في N
+
+155
+00:14:11,650 --> 00:14:18,370
+طيب أنا إيش بدي؟ بدي الخاصية الثالثة، بدي A مرتبطة
+
+156
+00:14:18,370 --> 00:14:23,310
+مع مين؟ مع الـ C، يبقى بدي الـ A تكون مرتبطة مع الـ C
+
+157
+00:14:23,310 --> 00:14:28,220
+باجي بقول كويسة، بدي أطلع في هذه وهذه، أظن لو جمعنا
+
+158
+00:14:28,220 --> 00:14:34,060
+الاثنين بده يطلع من عنده الـ A و الـ C، يبقى هذا يعطيك
+
+159
+00:14:34,060 --> 00:14:41,700
+لو جينا جمعنا هدول بده يصير عندنا الـ A ناقص الـ C يساوي Q
+
+160
+00:14:41,700 --> 00:14:47,880
+واحد زائد Q اثنين، كله مضروب في مين؟ مضروب في N
+
+161
+00:14:48,090 --> 00:14:55,310
+معنى هذا الكلام إن الـ N بتقسم الـ A ناقص الـ C، هذا
+
+162
+00:14:55,310 --> 00:15:04,300
+معناه إن الـ N بتقسم الـ A ناقص الـ C، مدام الـ N بتقسم 
+163
+00:15:04,300 --> 00:15:06,720
+الـ A بتقسم الـ C بتقسم الـ A بتقسم الـ C
+
+164
+00:15:06,720 --> 00:15:08,960
+بتقسم الـ A بتقسم الـ C بتقسم الـ A بتقسم الـ
+
+165
+00:15:08,960 --> 00:15:10,680
+C بتقسم الـ A بتقسم الـ C بتقسم الـ C بتقسم
+
+166
+00:15:10,680 --> 00:15:16,940
+الـ A بتقسم الـ C بتقسم الـ A بتقسم الـ C
+
+167
+00:15:16,940 --> 00:15:20,500
+بتقسم الـ C بتقسم الـ C بتقسم الـ C بتقسم الـ
+
+168
+00:15:20,500 --> 00:15:23,220
+C بتقسم الـ C بتقسم الـ C بتقسم الـ C بتقسم
+
+169
+00:15:23,220 --> 00:15:24,400
+الـ C بتقسم الـ C بتقسم الـ C بتقسم الـ C
+
+170
+00:15:24,400 --> 00:15:29,300
+بتقسم الـ C، إذا تحققت الشروط الثلاثة اللي عندنا
+
+171
+00:15:29,300 --> 00:15:33,400
+يبقى الـ relation هذي مالها؟ is an equivalence
+
+172
+00:15:33,400 --> 00:15:39,280
+relation، يبقى بقى دي بقول له ده وهكذا إن الـ
+
+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
+طيب كويس، يبقى يعطينا مثال على الـ equivalence
+
+175
+00:15:58,170 --> 00:16:03,390
+relation، بدنا نيجي نحسب الـ equivalence class لأي
+
+176
+00:16:03,390 --> 00:16:09,610
+element موجود عندنا، يعني بدي أروح آخذ عنصر من Z وأجيبه
+
+177
+00:16:09,610 --> 00:16:14,770
+أجيب كل العناصر اللي مرتبطة مع هذا العنصر طبق الـ
+
+178
+00:16:14,770 --> 00:16:19,930
+main طبق الـ definition اللي إحنا 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 الـ 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 إن الـ X are related with A، طيب
+
+183
+00:16:55,310 --> 00:17:00,140
+إحنا أخذنا هنا لما جينا عرفناها قيل لنا إن الـ A
+
+184
+00:17:00,140 --> 00:17:06,840
+مرتبطة مع B إذا كانت الـ N بتقسم الـ A ناقص الـ B
+
+185
+00:17:06,840 --> 00:17:13,140
+يبقى الـ N بدي آخده كم؟ قياس Modulo N بدي آخذ
+
+186
+00:17:13,140 --> 00:17:18,740
+الأرقام هذه كلها Modulo M، بس إن هذا الرقم شائع بياخد
+
+187
+00:17:18,740 --> 00:17:23,880
+ماله نهاية من القيام، أنا بقدر أحسب لرقم محدد، أختار
+
+188
+00:17:23,880 --> 00:17:30,430
+لك رقم يجي في بالك قداش؟ خمسة، ممتاز جدا، يبقى صاحبنا
+
+189
+00:17:30,430 --> 00:17:38,570
+أخذ الرقم خمسة، بقول له 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 that
+
+191
+00:17:43,950 --> 00:17:50,830
+الـ X مرتبط مع مين؟ مع الخمسة، طيب كويس، يعني هذا كل
+
+192
+00:17:50,830 --> 00:17:57,370
+العناصر X اللي موجودة في Z such that الـ X بده
+
+193
+00:17:57,370 --> 00:18:02,930
+يساوي، أنت حتى المقياس خمسة، والله المقياس قداش؟
+
+194
+00:18:02,930 --> 00:18:06,690
+خمسة برضه؟ لأ، إذا بنأخذ المقياس خمسة بدنا نأخذ رقم
+
+195
+00:18:06,690 --> 00:18:10,690
+ثاني، مثلا بدي آخذ 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
+الـ X الموجودة في Z بحيث X يساوي 9 زائد الرقم مضروب
+
+198
+00:18:41,550 --> 00:18:47,270
+في خمسة قد ما يكون يكون، تمام، يبقى بالعامية أقول Q
+
+199
+00:18:47,270 --> 00:18:55,080
+مضروب في خمسة، يبقى هذا بيجيب لي كل العناصر من أول الـ
+
+200
+00:18:55,080 --> 00:18:59,660
+Z إلى آخرها اللي مرتبطة مع مين؟ مع التسعة، طيب أنا
+
+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، وباجي بحط الرقم اللي عندنا اللي
+
+203
+00:19:09,060 --> 00:19:14,060
+هو تسعة في النص، وبصير أضيف له خمسات وأطرح منه
+
+204
+00:19:14,060 --> 00:19:22,370
+خمسات، لإنه قلت تسعة زي ما هي زائد لـ Q في خمسة، ليه Q
+
+205
+00:19:22,370 --> 00:19:29,130
+موجودة في Z، يعني Q integer، باجي بقول له لو التسعة
+
+206
+00:19:29,130 --> 00:19:37,420
+حطيت له خمسة قداش بده يصير؟ أربعة عشر، وكمان خمسة، وكمان خمسة
+
+207
+00:19:37,420 --> 00:19:42,600
+بده يصير تسعة عشر، وكمان خمسة بده يصير أربعة وعشرين، وكمان
+
+208
+00:19:42,600 --> 00:19:47,140
+خمسة بده يصير 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 قداش؟ أربعة
+
+210
+00:19:52,300 --> 00:19:58,220
+بيظل سالب واحد، بيظل سالب ستة، بيظل سالب أحد عشر، وهكذا
+
+211
+00:19:58,780 --> 00:20:04,160
+يبقى هي عناصر الـ equivalency class، كل العناصر هدول
+
+212
+00:20:04,160 --> 00:20:09,740
+أخذوا جزء من الست و الـ integer بس مش كلها، أخذوا جزء
+
+213
+00:20:09,740 --> 00:20:13,880
+منها، هذا الجزء أو هذه المجموعة هي اللي بنسميها الـ
+
+214
+00:20:13,880 --> 00:20:18,540
+equivalency class، يبقى الـ 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 منهم، طيب إيش رأيك الـ equivalence relation
+
+217
+00:20:30,690 --> 00:20:36,730
+بتعمل partition للست اللي عندها أو للـ Z اللي
+
+218
+00:20:36,730 --> 00:20:41,310
+عندنا، إيش يعني partition؟ لو رجعنا لمبادئ رياضات
+
+219
+00:20:41,310 --> 00:20:46,390
+بقول لك لو عندي set وعليها partition، partition يعني
+
+220
+00:20:46,390 --> 00:20:53,390
+مجموعة من الـ subset اللي بتحقق شرطين، الشرط الأول
+
+221
+00:20:53,390 --> 00:20:58,810
+لو أخذت الـ union على كل الـ subsets هذي بده يطلع main
+
+222
+00:20:58,810 --> 00:21:04,510
+set الأصل، يتنام لو عملت intersection على كل الـ
+
+223
+00:21:04,510 --> 00:21:10,590
+subsets هذي بده يطلع Ø، خلّيني أذكر بتعريف الـ
+
+224
+00:21:10,590 --> 00:21:16,370
+partition وبعد هيك نحسبه للبعض، يبقى بدنا نيجي
+
+225
+00:21:16,370 --> 00:21:21,450
+لحاجة اسمها اللي هو الـ 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
+S whose union is
+
+234
+00:22:54,040 --> 00:23:00,620
+S itself، طيب
+
+235
+00:23:00,620 --> 00:23:07,220
+كويس، تعال نوضح هذا المفهوم، افترض إن أنا عندي الـ S
+
+236
+00:23:07,220 --> 00:23:13,940
+والـ S بالشكل هذا، هذا الـ S، قسمتها إلى مجموعة من الـ
+
+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 وهكذا تمام، سميتها S1 S2 S3 وظلت ماشي
+
+239
+00:23:30,220 --> 00:23:38,100
+للاخيرة اللي هي الـ S N، تمام، يبقى الـ partition
+
+240
+00:23:38,100 --> 00:23:45,660
+هديله الرمز بيه، هو عبارة عن مجموعة S1 و S2 و
+
+241
+00:23:45,660 --> 00:23:55,070
+لغاية S N، بس بشرط، طلع هسه 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 وهنا في عندي
+
+244
+00:24:06,910 --> 00:24:11,470
+عناصر وهنا في عناصر وهنا في عناصر وهكذا، يبقى كل
+
+245
+00:24:11,470 --> 00:24:15,970
+مجموعة لازم يكون على الأقل فيها ولو عنصر 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 الـ intersection
+
+249
+00:24:32,150 --> 00:24:39,650
+على الـ S I و I تساوي واحد لغاية الـ N بدي يساوي
+
+250
+00:24:39,650 --> 00:24:44,920
+قداش؟ Ø، 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 إن حدث ذلك يبقى بقول هذا
+
+254
+00:25:03,320 --> 00:25:11,890
+بسمي partition على مين على S يبقى ال partition على
+
+255
+00:25:11,890 --> 00:25:16,810
+set معينة هو تجزئة ال set هذه إلى مجموعة من ال
+
+256
+00:25:16,810 --> 00:25:21,210
+subsets بحيث ال subsets هدول بدوني محققي شرطين
+
+257
+00:25:21,210 --> 00:25:25,670
+مافيش تداخل بين أي subset و الثانية يعني ال
+
+258
+00:25:25,670 --> 00:25:30,410
+intersection بين أي subset و الثانية بده يساوي قداش
+
+259
+00:25:30,410 --> 00:25:36,310
+five إذا أخذت ال union عليهم كلهم بدي يعطينا نفس ال
+
+260
+00:25:36,310 --> 00:25:41,590
+S 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 للـ S 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 هيك بدنا 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 ثانية بنرجع الكلام اللي 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 للـ S اللي ال union تبعهم بدي
+
+285
+00:29:20,570 --> 00:29:25,030
+يساوي مين S بالبلد هيك ال intersection على كل ال
+
+286
+00:29:25,030 --> 00:29:28,750
+subsets بدي يساوي Phi و ال union بدي يساوي 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 الـ S هدول
+
+289
+00:29:38,700 --> 00:29:44,420
+بيكونوا لي partition لمن؟ للـ 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 بيكونوا لي partition على الـ S العملية
+
+292
+00:29:52,540 --> 00:29:57,950
+العكسية قال لي conversely لأي partition P على ست S
+
+293
+00:29:57,950 --> 00:30:03,210
+هم
+
+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 وعكسها صحيحة لو كان عندي
+
+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 اللي عندنا الآن الي خاطر أوضح
+
+300
+00:30:31,110 --> 00:30:35,770
+هذا الكلام عمليا عمليا من وين أنا أخذ ال relation
+
+301
+00:30:35,770 --> 00:30:40,410
+اللي عندنا احنا أخذنا اللي هو قلنا العنصر تسعة
+
+302
+00:30:40,410 --> 00:30:45,490
+وأخذنا المقياس مين اللي هو خمسة طب أنا لما أخذ
+
+303
+00:30:45,490 --> 00:30:50,800
+المقياس خمسة لما نأخذ المقياس خمسة يبقى العناصر
+
+304
+00:30:50,800 --> 00:30:56,820
+Zero واحد واثنين وثلاثة وأربعة وخمسة بترجع مين؟
+
+305
+00:30:56,820 --> 00:31:01,960
+Zero ستة بترجع واحد سبعة بترجع اثنين ثمانية بترجع
+
+306
+00:31:01,960 --> 00:31:07,520
+ثلاثة تسعة بترجع أربعة وهكذا نوضح هذا الكلام يبقى
+
+307
+00:31:07,520 --> 00:31:20,450
+for example كمثال على ذلك from the above 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 والـ N أو and الـ 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
+classes are اللي هو الـ Zero والواحد والاثنين
+
+312
+00:31:55,780 --> 00:32:05,240
+والثلاثة والأربعة 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 Zero بجي بقول هي الـ zero
+
+315
+00:32:17,840 --> 00:32:25,460
+حط الـ zero ضيف له خمسات يبقى بصير خمسة وعشرة وخمسة عشر
+
+316
+00:32:25,460 --> 00:32:32,700
+و تضلك ماشي سالب خمسة سالب عشرة سالب خمسة عشر و تضلك
+
+317
+00:32:32,700 --> 00:32:37,910
+ماشية بعد ذلك يبدأ ال equivalence class للواحد يبقى
+
+318
+00:32:37,910 --> 00:32:43,290
+بالدرجة أقول له هذه واحد وخمسة ستة وخمسة أحد عشر
+
+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 مازال تمام؟ طيب لو بدي ال equivalence class للـ 
+
+327
+00:33:04,460 --> 00:33:12,000
+اثنين هو عبارة عن اثنين وخمسة سبعة واثنا عشر وسبعة عشر
+
+328
+00:33:12,000 --> 00:33:17,700
+إلى ما شاء الله أضيف سالب خمسة بصير سالب ثلاثة
+
+329
+00:33:17,700 --> 00:33:23,880
+سالب ثمانية سالب ثلاثة عشر إلى ما شاء الله بدي ال
+
+330
+00:33:23,880 --> 00:33:29,260
+equivalence class لمن؟ للثلاثة يبقى باجي بقول له هذه
+
+331
+00:33:29,260 --> 00:33:36,380
+الثلاثة وخمسة ثمانية وثلاثة عشر وثمانية عشر إلى ما شاء الله
+
+332
+00:33:36,380 --> 00:33:42,020
+و هنا نضيف سالب خمسة بصير السالب اثنين و هنا سالب
+
+333
+00:33:42,020 --> 00:33:47,700
+سبعة و هنا سالب اثنا عشر إلى ما شاء الله بنوصل للعنصر
+
+334
+00:33:47,700 --> 00:33:52,510
+اللي هو مين؟ أربعة يبقى العنصر أربعة، يبقى هذه
+
+335
+00:33:52,510 --> 00:33:59,150
+الأربعة وخمسة تسعة وأربعة عشر وتسعة عشر 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 وهكذا طيب هذه العناصر اللي حطيتها من قبل
+
+338
+00:34:12,860 --> 00:34:17,680
+طيب بده أجي لخمسة يبقى بده أحط خمسة يبقى بده أحط
+
+339
+00:34:17,680 --> 00:34:26,380
+خمسة وخمسة وخمسة هي هذه وسالب خمسة زيرو وسالب
+
+340
+00:34:26,380 --> 00:34:30,260
+خمسة وسالب عشرة هي هذه ولا لا طيب لو جيت بعد
+
+341
+00:34:30,260 --> 00:34:36,260
+الخمسة بتأخذ الستة يبقى بتبدأ بستة وخمسة أحد عشر
+
+342
+00:34:36,260 --> 00:34:41,260
+هي ستة وخمسة أحد عشر وكمان خمسة بيطلع هذه يبقى
+
+343
+00:34:41,260 --> 00:34:46,000
+الستة هتطلع الواحد والسبعة هتطلع اثنين والثمانية
+
+344
+00:34:46,000 --> 00:34:50,660
+هتطلع الثلاثة والتسعة تطلع الأربعة والعشرة ترجع
+
+345
+00:34:50,660 --> 00:34:57,410
+لزيرو وهكذا طيب 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
+جبت لي أي equivalency class آخر لأن الـ Z فيها
+
+349
+00:35:13,810 --> 00:35:18,570
+ملانة من العناصر أي واحد فيهم هيطلع واحد من هدول
+
+350
+00:35:19,130 --> 00:35:24,790
+يبقى ما عنديش إلا مين إلا الخمسة هدول فقط لغاية في
+
+351
+00:35:24,790 --> 00:35:31,190
+علم الجبر خلي بالك في علم الجبر 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 واثنين وثلاثة وأربعة دائما وأبدا طيب 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 أي رقم يجي في بالك من الزد هتلاقيه
+
+356
+00:36:05,220 --> 00:36:08,880
+موجود في واحد من الخمسة هدول أي 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 أي عنصر في أي equivalency class موجود في
+
+359
+00:36:19,230 --> 00:36:24,910
+الثاني ما فيش بالمرة طب لو عملت union عليهم كلهم
+
+360
+00:36:24,910 --> 00:36:30,400
+بيعطيني الذد الأصلية طلع هي عندك هنا كده الـ zero هي
+
+361
+00:36:30,400 --> 00:36:35,080
+واحد اثنين ثلاثة أربعة وهييجي خمسة ستة سبعة ثمانية
+
+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 وهي الأحد عشر وهي اثنا عشر
+
+364
+00:36:42,440 --> 00:36:46,860
+ثلاثة عشر أربعة عشر خمسة عشر والسالب زيها يبقى هتلاقي
+
+365
+00:36:46,860 --> 00:36:52,720
+كل الأرقام هذه لو أخذتهم ال union بيعطيني مين الـ Z
+
+366
+00:36:52,720 --> 00:36:58,700
+الأصلية اثنين 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 هنا هو 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 أنا جبت بس
+
+372
+00:37:21,080 --> 00:37:24,100
+العنصر مرتبطة مع مين مع العنصر اللي بقى يعني أنا
+
+373
+00:37:24,100 --> 00:37:29,570
+لما أقول zero بدي العناصر المرتبطة مع الـ zero تحت
+
+374
+00:37:29,570 --> 00:37:33,130
+أثر ال relation اللي هو modulo خمسة غير هيك ما ليش
+
+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 اتنين لا 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
+الواحد 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 كم عنصر هيطلع عندي؟ سبع عناصر أولى واحد
+
+390
+00:38:53,260 --> 00:38:56,990
+في اشتراك بينه وبين التاني 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 إن 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 أنا اختصارا
+
+395
+00:39:15,530 --> 00:39:18,630
+مكتوبهم زي هيك أما 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 وهكذا هذه الجروب إن شاء الله
+
+398
+00:39:23,820 --> 00:39:27,820
+هتلعب دور كبير عندنا في ال chapter القادم إن شاء
+
+399
+00:39:27,820 --> 00:39:31,640
+الله و تعالى طبعا الآن 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/vg_8OS-lDhg.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..34f732f52c8c513f0ea3db62ca786b34e5a77eb6
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg.srt
@@ -0,0 +1,1639 @@
+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 السابعة والثامنة، بدي أحاول أدمج
+
+4
+00:00:35,140 --> 00:00:41,260
+النقطتين بنقطة واحدة، النقطة الواحدة تتلخص 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 الـ group G، إذا أثبت نقطتين، النقطة
+
+7
+00:00:49,810 --> 00:00:56,090
+الأولى بدي 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 بقول له Phi inverse of K bar is non-empty
+
+11
+00:01:18,030 --> 00:01:27,430
+لأنه ليش since أو 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 بدها تساوي 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 بدها تساوي Phi Inverse of الـ Identity Element
+
+16
+00:01:48,880 --> 00:01:55,580
+تبع الـ G bar، وهذا الـ Element موجود في الـ group
+
+17
+00:01:55,580 --> 00:02:01,820
+اللي عندنا، وهذا 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
+أن الـ X و الـ Y موجودة في Phi inverse of K bar، يبقى
+
+20
+00:02:16,740 --> 00:02:25,720
+then الـ X هذي بدها تساوي في في انفرس of K1 for
+
+21
+00:02:25,720 --> 00:02:34,630
+some K1 اللي موجودة في K bar، والـ y بدها تساوي 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
+بدها تساوي k1 اللي موجودة في k bar، and فاي واي بدها
+
+25
+00:03:02,090 --> 00:03:12,190
+تساوي كتو اللي موجودة في ك بار، طيب 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 بار، طيب
+
+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 inverse، الـ 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 بار، يبقى 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
+G، باقي علينا أن نثبت النقطة الثامنة وهي خاصية ال
+
+38
+00:04:47,510 --> 00:04:57,630
+normality، يبقى افترض 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 إيه؟ معناها أن جي موجودة في جي، جي
+
+41
+00:05:16,810 --> 00:05:27,140
+موجودة في جي، and في of اكس موجودة في كي بار، طب لو
+
+42
+00:05:27,140 --> 00:05:35,000
+أخدت له في of g x g inverse، يبقى هذه بدها 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 homomorphism، يبقى 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 الآن، في اف جي، هذا ال element وين موجود؟ ال
+
+47
+00:06:11,020 --> 00:06:17,330
+element الأول هذا في اي group؟ في جي ولا 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 بار، 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؟ because لإن ال K bar عبارة
+
+55
+00:07:09,160 --> 00:07:15,860
+عن subgroup من ال G bar، معطى، طيب، إذا 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 bar، يبقى 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 النقطة، يبقى ده مقتصر النقطة السابعة
+
+61
+00:07:53,300 --> 00:08:02,040
+والثامنة مرة ثانية، بدنا نيجي للنقطة التاسعة، النقطة
+
+62
+00:08:02,040 --> 00:08:09,540
+التاسعة بتقول لي ما يأتي، لو كانت في is onto، في is
+
+63
+00:08:09,540 --> 00:08:18,880
+onto، والكرنل للفي بدها تساوي ال identity element، ثم
+
+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 بار، أنا 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، بقول له كويسة، انتوا هيوم، اعطيني اياها، تمام
+
+69
+00:08:45,820 --> 00:08:51,020
+الفي، قلت 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 that اللي 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 بدنا نروح أخد صورتين متساويتين لاثنين
+
+75
+00:09:23,670 --> 00:09:29,870
+وأثبت أن أصلهم متساوين، يبقى بناء عليه بالداجة اقول له
+
+76
+00:09:29,870 --> 00:09:40,900
+assume أنه في of X بدها تساوي في of Y، طبعا إذا
+
+77
+00:09:40,900 --> 00:09:45,500
+قررت أثبت أن ال X تساوي الفي، بكون تم المطلوب عندنا
+
+78
+00:09:45,500 --> 00:09:49,780
+then الآن
+
+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 أن Phi of X في Phi of Y inverse بدها تساوي الـ
+
+83
+00:10:15,850 --> 00:10:22,540
+Identity تبع الـ G bar، في همومورفزم، إذا برجع هذا
+
+84
+00:10:22,540 --> 00:10:28,880
+الى أصله، في of x y inverse بدها تساوي 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 أن ال x y inverse موجودة وين؟ في
+
+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 أن 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 تساوي؟ الـ Identity، يبقى
+
+91
+00:11:03,780 --> 00:11:08,900
+بناء عليه تصير الـ X تساوي 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 isomorphism، one 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، بتقول
+
+99
+00:12:00,860 --> 00:12:11,200
+الـ Phi، الـ Phi من G إلى G bar بـ
+
+100
+00:12:11,200 --> 00:12:21,960
+homomorphism، homomorphism، ثم الكيرنل 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 ثانية، 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 إنه normal
+
+106
+00:12:49,610 --> 00:12:53,570
+subgroup من جي، يبقى لو عندي homomorphism إيش 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 هو هذا، أنا
+
+109
+00:13:03,560 --> 00:13:07,180
+بدي أثبت إنه normal subgroup، يعني إيش بدي أثبت؟
+
+110
+00:13:07,180 --> 00:13:11,920
+subgroup أولا، ثم normal، أظن subgroup اثبتناها في
+
+111
+00:13:11,920 --> 00:13:16,420
+النقطة الرابعة من النظرية الأولى، شكله كان اثبت ان ال
+
+112
+00:13:16,420 --> 00:13:27,630
+kernel subgroup، يبقى هنا we approved that أثبتنا إن
+
+113
+00:13:27,630 --> 00:13:38,690
+الـ kernel للـ Phi is a subgroup من جي، بـ 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 الأولى، يبقى ليش يظل عليه نصف باتمين بس
+
+117
+00:13:54,830 --> 00:14:02,790
+normality، يبقى بدها تروح تاخد ال G موجودة في G، and
+
+118
+00:14:02,790 --> 00:14:13,190
+ال X موجودة في كيرن ال 5، أحاول 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؟ أن جي موجودة في جي، أن
+
+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
+طبعا الجي بار، طيب الآن بدي أخد ال جي اكس جي انفرس
+
+124
+00:14:42,790 --> 00:14:49,290
+وأخد 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  في of جي انفرس أو انشئته فاقوله فاي اف جي
+
+127
+00:15:08,050 --> 00:15:17,710
+فاي اف جي طب الفاي اف اكس 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 inverse طيب 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 أنا أثرت
+
+131
+00:15:39,320 --> 00:15:43,740
+على حصل الضرب ال three elements أعطاني 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 في يبقى 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؟ أخذت 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 معناه إن 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 تمانتاشر 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 تسعة النقطة 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 function هي 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
+أو 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 للواحد والـ 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 Zero بس والله هذا مش real
+
+181
+00:21:20,170 --> 00:21:24,010
+number عادية أنت بتشتغل في group وليس في real
+
+182
+00:21:24,010 --> 00:21:30,590
+number عادية إذا هذا بده يساوي zero لأن التلاتة في
+
+183
+00:21:30,590 --> 00:21:35,890
+zero تساوي zero وكمان 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
+إثناش لإنه تلاتة في إثناش ستة و تلاتين جدت تمانتاش
+
+186
+00:21:46,510 --> 00:21:52,250
+مرتين يبقى ال zero في غيرهم لأن ماعنديش يبقى هذا
+
+187
+00:21:52,250 --> 00:21:58,170
+الكيرن للـ Phi يبقى يا شباب هدول تلت عناصر أيش
+
+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 ستة أول امبارح أخذنا 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 kernel أو 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 احنا 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
+X يبقى تلاتة X يسوى ستة إذا ال X بده يسوى قداش
+
+205
+00:23:49,180 --> 00:23:56,860
+إثنين 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 إثنين زائد ال kernel ال
+
+207
+00:24:02,820 --> 00:24:08,000
+kernel حسبناه اللي هو Zero وستة وإثناش يبقى
+
+208
+00:24:08,000 --> 00:24:15,890
+النتيجة إثنين و تمانية و أربعتاش يبقى 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
+إثنين و الثمانية و الاربعتاش يبقى five of إثنين
+
+211
+00:24:25,090 --> 00:24:29,370
+يساوي ستة و five of ثمانية يساوي ستة و five of
+
+212
+00:24:29,370 --> 00:24:35,320
+أربعتاش 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 قداش
+
+217
+00:24:55,240 --> 00:25:01,830
+إثنين إذا Phi inverse of 6 يساوي إثنين، 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 إثناش 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 تلاتة في الـ subgroup generated
+
+229
+00:26:00,460 --> 00:26:05,360
+by تلاتة اللي هو الـ zero تلاتة و ستة و تسعة و
+
+230
+00:26:05,360 --> 00:26:12,480
+إثناش و خمستاشر تمام؟ طيب نشوف هذه مين بدها تعطينا
+
+231
+00:26:12,480 --> 00:26:18,350
+تلاتة في zero بقداش على الجامعة، ماشي، بس هذه ضرب
+
+232
+00:26:18,350 --> 00:26:23,930
+تلاتة في ايه؟ لما أقول 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 ثمان عشرة تسعة ثمان عشرة تسعة ثمان عشرة تسعة
+
+252
+00:27:36,140 --> 00:27:37,120
+ثمان عشرة تسعة ثمان عشرة تسعة ثمان عشرة تسعة ثمان عشرة
+
+253
+00:27:37,120 --> 00:27:39,960
+ثمان عشرة تسعة ثمان عشرة تسعة ثمان عشرة تسعة ثمان عشرة
+
+254
+00:27:39,960 --> 00:27:49,290
+تسعة ثمان عشرة تسعة ثمان عشرة تسعة.النقطة الخامسة بيقول
+
+255
+00:27:49,290 --> 00:27:52,990
+find the order للـ one والـ order للـ five of one ال
+
+256
+00:27:52,990 --> 00:27:59,010
+one هذا وين موجود زي الـ 18 الـ one هذا موجود في
+
+257
+00:27:59,010 --> 00:28:03,970
+الـ z ثمان عشرة يبقى الـ order للـ one قداش تحت عملية
+
+258
+00:28:03,970 --> 00:28:09,510
+الجمل هو ثمان عشرة طيب نيجي للي بعده بدنا الـ order
+
+259
+00:28:09,510 --> 00:28:14,090
+للـ five of one السؤال هو ما علاقة الـ order بالـ
+
+260
+00:28:14,090 --> 00:28:18,190
+five of one بيقسم يبقى الـ order تبع الـ five of one
+
+261
+00:28:18,190 --> 00:28:22,970
+بدي يقسم الـ order تبع الـ one يعني بدي يكون قاسم للـ
+
+262
+00:28:22,970 --> 00:28:27,440
+ثمان عشرة يبقى الـ order للـ five of one يا واحد، يا
+
+263
+00:28:27,440 --> 00:28:33,260
+اثنين، يا ثلاثة، يا ستة، يا تسعة، يا ثمان عشرة، واحد
+
+264
+00:28:33,260 --> 00:28:37,080
+من هدول طب واحد اللي هو بدي أعرف منه و بنقول له
+
+265
+00:28:37,080 --> 00:28:43,860
+بسيط جدا عندك أنت الـ five of one قداشه سوى ثلاثة
+
+266
+00:28:43,860 --> 00:28:48,690
+في one اللي هو بثلاثة مش هيك التعريف تبع الـ five يبقى
+
+267
+00:28:48,690 --> 00:28:55,110
+الثلاثة ثلاثة وين موجودة كمان في Z 18 موجودة في
+
+268
+00:28:55,110 --> 00:29:01,870
+Z 18 يبقى هذا بدي أعطيك إن الـ order للـ five of one
+
+269
+00:29:01,870 --> 00:29:06,990
+هو الـ order للثلاثة هو قداش
+
+270
+00:29:09,110 --> 00:29:14,130
+القصة التي تضعها تدور بضعف ستة يبقى الـ order يساوي
+
+271
+00:29:14,130 --> 00:29:19,430
+كم؟ يساوي ستة لأنه ستة في ثلاثة أو ثلاثة أست ستة
+
+272
+00:29:19,430 --> 00:29:24,270
+تعني ستة في ثلاثة اللي هو بقى داشر بثمان عشرة اللي هو
+
+273
+00:29:24,270 --> 00:29:29,050
+الـ identity element الـ zero يبقى هذا هو أول رقم
+
+274
+00:29:29,050 --> 00:29:33,050
+بحطه قصة الثلاثة بيطلع الـ identity يبقى الـ order
+
+275
+00:29:33,050 --> 00:29:39,800
+يساوي ستة وزي ما أنت شايف الستة بتجسمين بتجسم 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 الـ first theorem اللي
+
+278
+00:29:55,560 --> 00:30:03,040
+هي الـ 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 أساوي الـ Phi
+
+286
+00:31:15,460 --> 00:31:26,520
+of G يبقى هذا كله بدي أساوي الـ Phi of G is an
+
+287
+00:31:26,520 --> 00:31:36,710
+isomorphism that is إن الـ G موديول الكيرني للـ Phi
+
+288
+00:31:36,710 --> 00:31:42,410
+ايزو مورف أكلمين للـ Phi of capital G
+
+289
+00:32:39,840 --> 00:32:45,640
+طيب نرجع للنظرية مرة ثانية 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 لـ G bar ما قالت G و G bar groups هدول لكن أنا
+
+292
+00:33:00,900 --> 00:33:05,400
+بفهم إنه groups من خلال قولي group homomorphism
+
+293
+00:33:05,400 --> 00:33:09,900
+يعني مش function بين two sets، بين two groups يبقى
+
+294
+00:33:09,900 --> 00:33:14,020
+لو قلت الـ Phi بـ a group homomorphism من G لـ G bar أو
+
+295
+00:33:14,020 --> 00:33:18,640
+قلت Phi بـ a homomorphism from the group G to the
+
+296
+00:33:18,640 --> 00:33:22,940
+group G bar اثنين نفس النص تمام؟ يبقى then the
+
+297
+00:33:22,940 --> 00:33:27,780
+mapping ابصي من الـ G kernel Phi للـ Phi of G معرفة
+
+298
+00:33:27,780 --> 00:33:33,760
+بـ Phi of الـ left coset الجي في الـ kernel للـ Phi
+
+299
+00:33:33,760 --> 00:33:38,300
+بده يساوي Phi of G is an isomorphism يعني اثنين
+
+300
+00:33:38,300 --> 00:33:43,480
+هدول are isomorphic لبعض وهي الـ function معرفة
+
+301
+00:33:43,480 --> 00:33:48,280
+عندنا بالشكل اللي عندنا هذا طبعا واضح إن جي في
+
+302
+00:33:48,280 --> 00:33:52,280
+الكيرن اللي هو left coset إذا موجود في الـ group
+
+303
+00:33:52,280 --> 00:33:58,780
+هذه في of small جي موجود في في كابتل أو في في of
+
+304
+00:33:58,780 --> 00:34:05,520
+جي كابتل لأن جي small موجودة في جي كابتل سنثبت 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 إن هذه الـ 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 سليما  مباشر
+
+309
+00:34:32,390 --> 00:34:41,350
+هيك بروح آخذ عنصرين متساويين أفترض أفترض
+
+310
+00:34:41,350 --> 00:34:50,670
+أن الـ X في الـ kernel للـ five بدي يساوي الـ Y في الـ kernel
+
+311
+00:34:50,670 --> 00:34:56,910
+للـ five إذا كنت أثبت إن five of X بدي يساوي five of Y
+
+312
+00:34:56,910 --> 00:35:01,290
+بتتم المطلوب يبقى then
+
+313
+00:35:06,420 --> 00:35:13,420
+يبقى لو جيت هنا ضربت من جهة اليمين في Y inverse أو
+
+314
+00:35:13,420 --> 00:35:18,340
+في X inverse سايان الاثنين نفس الشيء يبقى لو ضربت
+
+315
+00:35:18,340 --> 00:35:25,120
+في Y inverse بيصير Y inverse X في Kernel الفاي بده
+
+316
+00:35:25,120 --> 00:35:32,300
+يساوي Kernel الفاي ايش تفسيرك لهذه العبارة؟ يبقى
+
+317
+00:35:32,300 --> 00:35:39,920
+then اللي هو main Y inverse X موجود في Kernel الـ Phi
+
+318
+00:35:39,920 --> 00:35:47,760
+يعني معناه هذا الكلام إن Phi of Y inverse X بديه
+
+319
+00:35:47,760 --> 00:35:55,210
+يساوي الـ Identity element تبع الـ G bar هذا معناه
+
+320
+00:35:55,210 --> 00:36:04,190
+ايه؟ معناه إن الـ Phi of Y inverse في الـ Phi of X
+
+321
+00:36:04,190 --> 00:36:09,830
+بدي يساوي الـ Identity Element تبع الـ G bar هذا
+
+322
+00:36:09,830 --> 00:36:17,830
+معناه إن Phi of Y الكل inverse في الـ Phi of X بدي
+
+323
+00:36:17,830 --> 00:36:25,220
+يساوي الـ Identity Element تبع الـ G bar هذا معناه إن
+
+324
+00:36:25,220 --> 00:36:32,000
+أضرب من جهة اليمين في الـ Phi 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
+اليمين في Phi of Y هذه 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 أصبح عندي Phi of X بدي يساوي Phi of Y يبقى
+
+330
+00:36:59,250 --> 00:37:05,160
+بناء عليه الدالة معرفة تعريفا سليما أريد أن أثبت له
+
+331
+00:37:05,160 --> 00:37:10,760
+إن الـ Psi is one to one يعني إنه يريد أن يذهب
+
+332
+00:37:10,760 --> 00:37:21,600
+ويأخذ صورتين متساويتين أعتبر ذلك الـ Psi أو جي في
+
+333
+00:37:21,600 --> 00:37:29,100
+الكيرن للـ five يبدا يساوي .. والله خلّيها X X في ال
+
+334
+00:37:29,100 --> 00:37:35,340
+kernel لفاي بده يساوي A بصي في الـ Y في الـ kernel
+
+335
+00:37:35,340 --> 00:37:41,220
+لفاي إذا استطعنا إنه نثبت X في الـ kernel تساوي Y
+
+336
+00:37:41,220 --> 00:37:45,860
+في الـ kernel بيكون الـ A بصي صارت معاها one to one
+
+337
+00:37:45,860 --> 00:37:55,640
+يبقى then هذه معناها إن الـ Phi of X دي ساوية الـ Phi
+
+338
+00:37:55,640 --> 00:38:05,120
+of Y هذا معناه لو ضربت في معكوس الـ Phi of Y يبقى
+
+339
+00:38:05,120 --> 00:38:12,620
+ايه بيصير عندي الـ Phi of X في الـ Phi of Y الكل
+
+340
+00:38:12,620 --> 00:38:17,600
+inverse بدي يساوي الـ identity element تبع الـ G bar
+
+341
+00:38:18,390 --> 00:38:26,390
+أو اللي هو main هكذا يصبح XY inverse في الـ A 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 اليمين وليس من جهة اليسار عشان تظبط معناة
+
+344
+00:38:39,950 --> 00:38:47,060
+هي بدي أضربها من جهة اليمين يبقى بدي آخذ الان في of
+
+345
+00:38:47,060 --> 00:38:53,680
+Y الكل inverse في في of X دي يساوي الـ identity
+
+346
+00:38:53,680 --> 00:38:59,940
+element تبع الـ G bar هذا بده يعطينا هذه نقدر ننزلها
+
+347
+00:38:59,940 --> 00:39:08,240
+جوا يبقى بيصير في Phi of Y inverse في Phi of X يساوي
+
+348
+00:39:08,240 --> 00:39:15,800
+الـ Identity Element تبع الـ G bar هذا معناه إن
+
+349
+00:39:15,800 --> 00:39:23,980
+Phi of Y inverse في X يساوي الـ Identity Element
+
+350
+00:39:23,980 --> 00:39:29,590
+تبع الـ G bar لأن Phi عبارة عن Homomorphism هذا
+
+351
+00:39:29,590 --> 00:39:37,130
+معناه ايه؟ معناه إن الـ Y inverse X موجودة في الـ
+
+352
+00:39:37,130 --> 00:39:41,530
+kernel تبع الـ Phi لأن صورتها بتعطينا الـ
+
+353
+00:39:41,530 --> 00:39:46,040
+identity element تبع الـ G bar ما دام موجودة في الـ
+
+354
+00:39:46,040 --> 00:39:52,560
+Kernel يبقى بيصير Y inverse X في الـ Kernel للـ Phi
+
+355
+00:39:52,560 --> 00:39:58,260
+بده يساوي الـ Kernel للـ Phi نفسه لأن الـ subgroup
+
+356
+00:39:58,260 --> 00:40:02,920
+لما أضربها بـ element منها بتعطيني نفس الـ subgroup
+
+357
+00:40:02,920 --> 00:40:09,280
+طيب نضرب الطرفين في Y يبقى X في الـ Kernel للـ Phi
+
+358
+00:40:09,280 --> 00:40:17,020
+بده يساوي Y في الـ Kern المهم للـ Phi وهو المطلوب
+
+359
+00:40:17,020 --> 00:40:26,520
+يبقى بنا نيجي لـ Psi as all يبقى بالداجة أقوله احنا
+
+360
+00:40:26,520 --> 00:40:33,950
+عندنا الـ Psi ما هو طابلات الـ 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 Capital يبقى الـ X اللي أخذتها
+
+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 و Unto معرفة ضال عندي آخر 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 بتاخذ Psi لحاصل ضرب عددين الأول two
+
+369
+00:41:28,170 --> 00:41:34,850
+elements X في الكرن للـ five في الـ Y في الـ Kernel
+
+370
+00:41:34,850 --> 00:41:40,090
+للـ Phi مش عددين وإنما two elements موجودات في
+
+371
+00:41:40,090 --> 00:41:45,510
+الـ Factor A group هذا الكلام بده يساوي بـ Psi of
+
+372
+00:41:45,510 --> 00:41:50,290
+هذا الـ Left Cosetة وهذا الـ Left Cosetة وقبل شوية
+
+373
+00:41:50,290 --> 00:41:54,770
+قلنا الـ Kernel هي normal subgroup إذا بناء عليه
+
+374
+00:41:54,770 --> 00:42:02,590
+بيصير الـ XY في الـ Kernel للـ Phi طيب بـ Psi لما تؤثر
+
+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 عن اللي 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 module للـ
+
+381
+00:42:41,660 --> 00:42:46,800
+Kernel للـ Phi of G عبارة عن أيش؟ Isomorphism في
+
+382
+00:42:46,800 --> 00:42:56,920
+نتيجة بسيطة عليها Krull's theorem 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
+finite group
+
+386
+00:43:21,220 --> 00:43:32,900
+G to G bar then then
+
+387
+00:43:32,900 --> 00:43:42,380
+the order of Phi of G the order of Phi 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 خلي
+
+390
+00:44:14,280 --> 00:44:22,310
+برا كده الآن 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
+divides the 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 module the kernel 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 G مقسوما على ال order تبع الكرنل للفاي
+
+402
+00:45:36,880 --> 00:45:45,480
+بدي أساوي 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 G بدي أساوي 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
+divides the 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/wwhcAnUFnP8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..724dafba1317ede4dce043bf98d1be38612aaef7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8_postprocess.srt
@@ -0,0 +1,1272 @@
+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 locosets and
+
+3
+00:00:30,320 --> 00:00:34,180
+lagrange theorem في الفترة الصباحية اعطينا اربع
+
+4
+00:00:34,180 --> 00:00:38,700
+crawlers على نظرية Lagrange وعطينا على ذلك بعض
+
+5
+00:00:38,700 --> 00:00:44,790
+الأمثلةالان صح برضه حكينا ان 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 ان 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
+خمسةالان في نظرية بعض اللي هي نظرية اللي قدامنا
+
+10
+00:01:02,680 --> 00:01:05,740
+هذه بيقول اللي قلت جي بي ا group of order اتنين بي
+
+11
+00:01:05,740 --> 00:01:09,960
+حيث بي is a prime greater than two then الجي
+
+12
+00:01:09,960 --> 00:01:16,040
+isomorphic لزد بي or دي بي طب ليش قال هذول التنتين
+
+13
+00:01:16,040 --> 00:01:20,380
+فيهم نفس العدد من العناصر ولا بيختلفوا عن بعض زد
+
+14
+00:01:20,380 --> 00:01:24,820
+اتنين بي و دي بي عدد عناصرهم كانت بعض ولا بيختلفوا
+
+15
+00:01:24,820 --> 00:01:29,580
+عن بعض هدولجت بعض على طول خاطر لأن دي بي عدد
+
+16
+00:01:29,580 --> 00:01:33,820
+عناصرها اتنين بي و زد بي عدد عناصرها اتنين بي طب
+
+17
+00:01:33,820 --> 00:01:40,380
+ليش قال زد اتنين بي اللي هو دي بي 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
+زد اتنين بي لحالها بس؟ او قال اللي هو دي بي لحالها
+
+20
+00:01:52,840 --> 00:01:54,780
+بس؟ ليش قال هذه او هذه؟
+
+21
+00:01:58,360 --> 00:02:06,480
+هذا بقدر افكر يقول ليش؟ مية لمية تمام هذا الان
+
+22
+00:02:06,480 --> 00:02:10,500
+عندي ال cyclic group يبقى لو كانت جيل أصلية ال
+
+23
+00:02:10,500 --> 00:02:15,490
+cyclic automatic هتكون isomorphic لمينلزد بي
+
+24
+00:02:15,490 --> 00:02:20,850
+مباشرة لو كانت هذه ماهياش Cyclic إذا هتبقى
+
+25
+00:02:20,850 --> 00:02:25,290
+isomorphic لمين لDP لإن دي بي not cyclic group
+
+26
+00:02:25,290 --> 00:02:29,070
+تمام يبقى لما نقل التنتين والتنتين اللي هما نفس ال
+
+27
+00:02:29,070 --> 00:02:33,410
+order يبقى isomorphic لزد اتنين بي إذا كانت ال G
+
+28
+00:02:33,410 --> 00:02:38,560
+Cyclicيبقى إجباري هتكون isomorphic لمام لزد اتنين
+
+29
+00:02:38,560 --> 00:02:43,060
+P وإذا ماكنتش Cyclic يبقى إجباري isomorphic لDP
+
+30
+00:02:43,060 --> 00:02:46,080
+الحقيقة برهان طويل فام سامحينكوا بدك تطلي عليه
+
+31
+00:02:46,080 --> 00:02:49,540
+ماعنديش مشكلة روح تطلي عليه من الكتاب بيبنيش
+
+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 تلاتين من الشبطر تبع خمسة وحليته لكوا يه على
+
+35
+00:03:03,320 --> 00:03:07,010
+اللوحيناو اثبت ان ال stabilizer هو عبارة عن
+
+36
+00:03:07,010 --> 00:03:10,690
+subgroup كان السؤال يثبت ان 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
+little g ب group of permutation of a6sأي element I
+
+39
+00:03:22,650 --> 00:03:26,590
+موجود في الاسلسل Stabilizer تبع الـ I 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 ال I يعني ليه تثبت ال I؟ يعني صورة ال I بتكون
+
+42
+00:03:35,370 --> 00:03:42,520
+من؟الـ I itself يبقى ال stabilizer لل I يعني كل ال
+
+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 وصورة ال I بتبقى ال I نفسه لو قلت بدل
+
+45
+00:03:51,520 --> 00:03:55,400
+ال I واحد يبقى صوت ال واحد هي واحد لو قلت بدل ال I
+
+46
+00:03:55,400 --> 00:03:59,720
+قلت عشرة يبقى صوت 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 ا
+
+48
+00:04:05,020 --> 00:04:10,260
+ثابتا يعني بيعطيني نفس ال element صورته نفسه فقلنا
+
+49
+00:04:10,260 --> 00:04:16,360
+ال stabilizer ل ال I اللي موجود في G لعلى G هو كل
+
+50
+00:04:16,360 --> 00:04:20,240
+ال Phi يعني كل ال permutation اللي موجودة في G
+
+51
+00:04:20,240 --> 00:04:26,620
+بحيث أن صورة I هي من ال I itselfطبعا ال stabilizer
+
+52
+00:04:26,620 --> 00:04:31,360
+is a subgroup و هذا أنا برهنتهلكوا سابقا اللي هو
+
+53
+00:04:31,360 --> 00:04:34,040
+السؤال واحد و ثلاثين من شفض 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 ان في شغل
+
+56
+00:04:41,740 --> 00:04:46,900
+متعلق فيه و في نظرية مرتبطة فيه بعد قليلبعد ذلك
+
+57
+00:04:46,900 --> 00:04:51,220
+قال لليلتل جي بيه a group of permutations of a set
+
+58
+00:04:51,220 --> 00:04:55,340
+S بدنا نعرف تعريف جديد هذا ماشوفنهوش قبل هيك
+
+59
+00:04:55,340 --> 00:04:59,960
+التعريف بيقولولي كل S موجود في S بدنا نعرف حاجة ال
+
+60
+00:04:59,960 --> 00:05:04,800
+orbit تبع ال S ال orbit يعني بالعربي ايه؟مدار مسار
+
+61
+00:05:04,800 --> 00:05:10,680
+كويس يبقى المدار تبع ال 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 وانا عندي G هذه بطلع من ال permutations
+
+65
+00:05:25,920 --> 00:05:31,630
+اللي الواحد له صورة و بروح باخد هذه الصورةطلع ايش
+
+66
+00:05:31,630 --> 00:05:36,790
+بقوله بقول ال orbit ل S كل ال Phi of S يعني صورة
+
+67
+00:05:36,790 --> 00:05:40,830
+main صورة هذا ال S بحيث ال Phi موجودة في جيب يعني
+
+68
+00:05:40,830 --> 00:05:43,930
+انا بتطلع على كل ال permutations اللي موجودة في ال
+
+69
+00:05:43,930 --> 00:05:50,370
+group قلت بد ال orbit مثلا لتلاتةبجيب اطلع وين
+
+70
+00:05:50,370 --> 00:05:54,250
+تلاتة كانت موجود 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 اذا هذول أرقام عادية تماميبقى في هذه الحالة
+
+74
+00:06:06,790 --> 00:06:11,970
+ال orbit لل S هو كل ال Phi of S يعني الصور ال S
+
+75
+00:06:11,970 --> 00:06:15,590
+بحيث ال Phi هي permutation موجود وين؟ موجود في G
+
+76
+00:06:15,590 --> 00:06:20,770
+يعني يا شباب احنا بدنا نطبق موضوع ال courses 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 ل S على Gوحط الخطين اللي بقيتنا نسميهم order
+
+81
+00:06:38,240 --> 00:06:43,620
+لجيه طبعا ال order درجة العادة ان نقوله group او
+
+82
+00:06:43,620 --> 00:06:47,940
+sub group او element بس هذا ال order ماقولناش sub
+
+83
+00:06:47,940 --> 00:06:52,240
+group ماقولناش حتى اقول 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 لجيهبنعطي مثال من خلال هذا المثال بدي
+
+86
+00:07:01,780 --> 00:07:05,760
+أحسب ال stabilizer لأعداد مختلفة وبدي أحسب ال
+
+87
+00:07:05,760 --> 00:07:10,720
+order ل الأعداد المختلفة نجي الأقل ال stabilizer
+
+88
+00:07:10,720 --> 00:07:16,800
+لمين للواحد حسب التعريف تبع ال stabilizer كل ال
+
+89
+00:07:16,800 --> 00:07:20,760
+permutations اللي فيهم الواحد fixed أيش يعني
+
+90
+00:07:20,760 --> 00:07:25,000
+الواحد fixed يعني الصورة الواحد بتعطيني مين الواحد
+
+91
+00:07:25,000 --> 00:07:30,440
+itselfأظن الـ identity permutation منهم صح الواحد
+
+92
+00:07:30,440 --> 00:07:33,400
+صورته واحد اتنين صورته اتنين تلاته صورته تلاته اذا
+
+93
+00:07:33,400 --> 00:07:39,600
+الواحد هذي منهم الان الواحد صورته ايش يبقى هذي ال
+
+94
+00:07:39,600 --> 00:07:43,800
+permutation منها لأ لإن ماثبتتاش 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؟مضربات في بعض ضرب الواحد صرت تلاتة
+
+98
+00:07:58,320 --> 00:08:03,660
+هنا هذه منهم لا يبقى ماعنديش إلا الأخيرة اتنين
+
+99
+00:08:03,660 --> 00:08:08,540
+واربع وخمسة يعني كل ال permutation اللي بيظهر فيهم
+
+100
+00:08:08,540 --> 00:08:14,040
+الواحد انسى الموضوع ما هذا ال identityيبقى اتنين
+
+101
+00:08:14,040 --> 00:08:21,140
+اربعة خمسة ستة يبقى اتنين اربعة هنا خمسة ستة
+
+102
+00:08:21,140 --> 00:08:26,100
+بالشكل اللي عندنا هنا طب بدي اجيب ال orbit لمن
+
+103
+00:08:26,100 --> 00:08:32,960
+للواحد على جي ويسوي بدي اجيب صورة الان في ال
+
+104
+00:08:32,960 --> 00:08:38,320
+permutation الاولى ايش صورة الواحد واحد itself هنا
+
+105
+00:08:38,320 --> 00:08:45,940
+صورة الواحد ثلاثة صورة الواحد اتنينهنا صورة الواحد
+
+106
+00:08:45,940 --> 00:08:52,260
+أخدناها بكرراش 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 العنصرلو بده اجيب ال
+
+110
+00:09:10,540 --> 00:09:18,620
+stabilizer على جيل ال element مثلا تلاتة طيب
+
+111
+00:09:18,620 --> 00:09:22,340
+هذه منهم صحيح لان هذه ال identity الصورة التلاتة
+
+112
+00:09:22,340 --> 00:09:27,460
+بتلاتة يبقى هذه منهم نيجي الان 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
+fixedالتلاتة 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 تلاتأريد أن أشاهد
+
+121
+00:10:03,700 --> 00:10:07,900
+صور العناصر التلاتة في الـPermutations 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
+التلاتةأما أخدناها هايه صورة التلاتة اتنين أخدناها
+
+126
+00:10:36,110 --> 00:10:41,750
+هايه صورة التلاتة تلاتة هي أخدناها في الأول يبقى
+
+127
+00:10:41,750 --> 00:10:46,770
+انتهينا من الشغل هذه تمام؟ في خمسة خد ال orbit لل
+
+128
+00:10:46,770 --> 00:10:52,790
+stabilizer للخمسة مثلا ال stabilizer عالجي للخمسة
+
+129
+00:10:52,790 --> 00:10:59,390
+ويساوي طبعا صورة الخمسة اللي هي الخمسة نيجي هنا
+
+130
+00:11:01,020 --> 00:11:07,900
+الستابلازر اللى هو الواحد اللى هو الواحد مش ال
+
+131
+00:11:07,900 --> 00:11:12,180
+orbit اللى هو الواحد طبعا 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
+بداجي اقوله واحد اتنين تلاتة اربعة وكمانهنا الخمسة
+
+134
+00:11:24,410 --> 00:11:29,490
+ستة يبقى انسى هنا ظهرت لأ يبقى واحد تلاتة اتنين
+
+135
+00:11:29,490 --> 00:11:36,290
+اربعة يبقى واحد تلاتة اتنين اربعة خلصنا منها هنا
+
+136
+00:11:36,290 --> 00:11:40,750
+الخمسة صورتها ستة ماهياش fixed الخمسة صورتها ستة
+
+137
+00:11:40,750 --> 00:11:45,690
+ماعرف كده يبقى واحد اربعة اتنين تلاتة يبقى واحد
+
+138
+00:11:45,690 --> 00:11:52,670
+اربعةأتنين تلاتة خلصنا منها واحد اربع اتنين تلاتة
+
+139
+00:11:52,670 --> 00:11:58,650
+هنا ماهياش fixed يبقى انت 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 Gكويس 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 ستةصورة الخمسة خمسة
+
+144
+00:12:27,120 --> 00:12:32,060
+أخدناها صورة الخمسة ستة أخدناها صورة الخمسة ستة
+
+145
+00:12:32,060 --> 00:12:37,040
+أخدناها صورة الخمسة خمسة أخدناها صورة الخمسة ستة
+
+146
+00:12:37,040 --> 00:12:43,960
+أخدناها 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 يليه ثيرم let
+
+151
+00:13:31,830 --> 00:13:36,630
+الـGP
+
+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 Sof 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 Sالشكل 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 ان هذا النحيا خلاص يبقى
+
+161
+00:15:16,560 --> 00:15:17,660
+مرة تانية 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 أخدت أي element I موجود في S
+
+165
+00:15:37,360 --> 00:15:42,780
+من خلال هذا الكلام اثبت ان ال order لل G هو عبارة
+
+166
+00:15:42,780 --> 00:15:48,350
+عنعدد 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 لإن ال stabilizer ال subgroup لكن هذه
+
+169
+00:15:56,230 --> 00:16:02,690
+ماهياش subgroup طيب البرهان كان التالي احنا الآن
+
+170
+00:16:02,690 --> 00:16:04,650
+اقوِن
+
+171
+00:16:06,510 --> 00:16:13,530
+أحنا 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؟ معناته إن ال order لل
+
+173
+00:16:19,970 --> 00:16:30,000
+stabilizer على G لل I يقسم ال order ل Gيعني معنى
+
+174
+00:16:30,000 --> 00:16:36,360
+هذا الكلام ان 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 ساوي the number
+
+176
+00:16:45,060 --> 00:16:50,600
+of lift cassettes
+
+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
+تانيةأحنا عارفين أن ال stabilizer هو subgroup من G
+
+179
+00:17:11,490 --> 00:17:16,370
+وقلنا لك هذا السؤال 31 من شهدر خمسة و قبل 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 main ال left distinct اللي هو cosets of h
+
+187
+00:17:52,290 --> 00:17:57,710
+and 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
+cossets of the stabilizer تبع ال HNG يبقى هذا
+
+190
+00:18:05,890 --> 00:18:09,910
+بيعطيني عدد ال lift cossets اللي ولا واحدة فيهم
+
+191
+00:18:09,910 --> 00:18:17,510
+مالها زي التانية طيب كويس الان انا لو جدرت اثبت ان
+
+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 اثبتإنه عدد اللي هو الرقم اللي
+
+194
+00:18:29,260 --> 00:18:37,380
+عندنا هذا عدد ال lift cos 6 اللي عندي من ال
+
+195
+00:18:37,380 --> 00:18:42,820
+stabilizer في ال group G أثبته انه 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 بنضر بضاربة تبذل
+
+198
+00:18:50,320 --> 00:18:55,790
+يكون برهن هذا الكلامعشان اثبت ان هذا العدد يساوي
+
+199
+00:18:55,790 --> 00:19:00,340
+هذا العدديعني معناته بدي أعرف function من الـ 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 on two خلاص بصير
+
+202
+00:19:09,600 --> 00:19:14,360
+العدد قال بعض و لو وصلنا لإيه وصلنا للمطلوب بسهولة
+
+203
+00:19:14,360 --> 00:19:20,680
+طبعا 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 سوى ال order لهذا
+
+205
+00:19:24,140 --> 00:19:28,500
+عرفنا functionيعني أخدنا نظرية في لف الكوسيطس أن
+
+206
+00:19:28,500 --> 00:19:35,300
+ال order للـH بدي يساوي ال order للـBH يعني عدل
+
+207
+00:19:35,300 --> 00:19:38,920
+عناصر يساوي عدل عناصر هنا عرفنا function فيه ما
+
+208
+00:19:38,920 --> 00:19:43,760
+بينهما و أثبتنا إنها one to one and أنتم يبقى الأن
+
+209
+00:19:43,760 --> 00:19:56,380
+أنا بدي أعمل نفس القصة define a functiont from the
+
+210
+00:19:56,380 --> 00:20:08,020
+set of all left-destinate left
+
+211
+00:20:08,020 --> 00:20:15,440
+-destinate cosets of stabilizer
+
+212
+00:20:18,540 --> 00:20:26,560
+الـ I على G in G يبقى من هذه الـ set to بدّى مين
+
+213
+00:20:26,560 --> 00:20:35,700
+بدّيها الـ set of elements في ال orbit لمن؟ to the
+
+214
+00:20:35,700 --> 00:20:47,480
+orbit على I للـ G أو the set of numbers in the
+
+215
+00:20:47,480 --> 00:20:56,220
+orbitالى مجموعة الأعداد اللى موجودة في ال orbit by
+
+216
+00:20:56,220 --> 00:20:59,400
+T
+
+217
+00:20:59,400 --> 00:21:06,750
+offأنا قلت left cosets و ال subgroup هي ال
+
+218
+00:21:06,750 --> 00:21:11,190
+stabilizer يبقى بدي أخد 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 Phi مضروب في
+
+221
+00:21:21,550 --> 00:21:29,310
+ال stabilizer لمن؟ لل I على Gهذه الـ set اللي
+
+222
+00:21:29,310 --> 00:21:34,290
+عندنا عناصرها lift coset من ال stabilizer يعني
+
+223
+00:21:34,290 --> 00:21:38,890
+element من G مضروب في ال stabilizer بدي اودي لل
+
+224
+00:21:38,890 --> 00:21:48,960
+set هذه يبقى T of كذا بدي ساوي Phi of Iلأن الـ
+
+225
+00:21:48,960 --> 00:21:54,220
+Orbit عرفناها قبل قليل صور الـ Phi of I حيث الـ I
+
+226
+00:21:54,220 --> 00:21:59,420
+موجودة وين؟ موجودة في S طب أول شي بنشوف هل هذه
+
+227
+00:21:59,420 --> 00:22:04,120
+فعلا هي دالة ولا ماهياش دالة وبعدين بشوف الحكاية
+
+228
+00:22:04,120 --> 00:22:12,380
+ال one to one and unto فبجي بقوله الآن T is well
+
+229
+00:22:12,380 --> 00:22:18,460
+definedمشان اثبت حكاية الولد فاني بدي امشي عكس ال
+
+230
+00:22:18,460 --> 00:22:25,080
+one to one يعني بدي اجي اخد عنصرين متساوين و اثبت
+
+231
+00:22:25,080 --> 00:22:31,520
+ان صورتهم عليها بتكون متساوين الان ماشي بدي اجي
+
+232
+00:22:31,520 --> 00:22:40,970
+اقوله assumeإن Alpha في ال stabilizer ل I على G
+
+233
+00:22:40,970 --> 00:22:50,670
+يسوى Beta في ال stabilizer ل I على main على G يعني
+
+234
+00:22:50,670 --> 00:22:57,970
+افرط ان عندي two left cosets are equal يبقى then
+
+235
+00:23:05,810 --> 00:23:12,450
+معكوس الالفة موجود في الـ 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 سوى Alpha
+
+238
+00:23:23,420 --> 00:23:31,100
+inverse مضروبة في B في ال stabilizer لل I على G
+
+239
+00:23:31,730 --> 00:23:35,690
+أضرب الطرفين في alpha inverse يصبح هنا ال identity
+
+240
+00:23:35,690 --> 00:23:39,810
+اضربها في ال stabilizer يصبح ال stabilizer أضرب
+
+241
+00:23:39,810 --> 00:23:43,430
+alpha inverse هنا يصبح alpha inverse بي في ال
+
+242
+00:23:43,430 --> 00:23:48,890
+stabilizer طيب نرجع بالذاكرة قليلا إلى ال left
+
+243
+00:23:48,890 --> 00:23:56,700
+costals لما اقول H يساوي AH ايش يعني معناهاعندما
+
+244
+00:23:56,700 --> 00:24:01,980
+أقول H يساوي A H مايعني هذا بيحصل إذا كان ال A
+
+245
+00:24:01,980 --> 00:24:07,280
+موجود في H يبقى هذا معناه إن ال alpha inverse B
+
+246
+00:24:07,280 --> 00:24:13,600
+موجودة في ال stabilizer يبقى هذا معناه إن ال alpha
+
+247
+00:24:13,600 --> 00:24:22,900
+inverse B موجودة في ال stabilizer لل I على Gما دام
+
+248
+00:24:22,900 --> 00:24:28,000
+موجودة هنا يبقى ال alpha 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 ان alpha inverse
+
+252
+00:24:42,340 --> 00:24:51,180
+beta of I ساوي Iطيب مادام Alpha يعني بدي أثر على
+
+253
+00:24:51,180 --> 00:24:56,180
+الطرفين بAlpha يبقى هذا إيش بيعطينا؟ بيعطينا إنه
+
+254
+00:24:56,180 --> 00:25:04,960
+Beta تأثيرها على I يسوى 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 ان بيتا في
+
+257
+00:25:19,570 --> 00:25:27,350
+ال stabilizer لل I على G بديه يسوي Alpha في ال
+
+258
+00:25:27,350 --> 00:25:37,580
+stabilizer ل I على Gمصبوط هكذا؟ طيب أنا جايل 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 واناأحنا أثبتنا
+
+261
+00:25:50,630 --> 00:25:57,850
+إن 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 و أثبت 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
+إن T of Alpha في الـ Stabilizer لـ I على G بده
+
+267
+00:26:30,330 --> 00:26:37,550
+ساوي 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 انا بدى اثبت ان ال Alpha
+
+272
+00:27:01,740 --> 00:27:04,580
+في ال stabilizer بدى 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 القيمتانمتساويتا يبقى هذا معناته انه Alpha
+
+275
+00:27:15,840 --> 00:27:23,680
+في ال stabilizer على I لجيه بده يساوي 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
+تاشر one to one الان بدنا نثبت ان T is unto كويس
+
+278
+00:27:41,580 --> 00:27:47,020
+الان بدي اجي على ال orbit مش هذه موجودة في ال
+
+279
+00:27:47,020 --> 00:27:52,240
+orbit يبقى بدي افترض ان 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 سوى 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 Sلأنه 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 Gنعم يبقى سارة T is one to one and unto يبقى
+
+288
+00:28:56,750 --> 00:29:06,090
+هنا سارة T is one to one and unto بدأ من one to
+
+289
+00:29:06,090 --> 00:29:10,630
+one and unto يبقى عدد العناصر عدد ال lift 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 lift destined cassettes
+
+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
+إن ال order اللي جيه على ال order اللي لسه
+
+297
+00:30:12,940 --> 00:30:18,140
+بالأضافة بتسوية 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 ان that
+
+299
+00:30:25,420 --> 00:30:34,680
+is اللي هو العدد تبع ال orbit لل I على Gهذه
+
+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 و أكتب القيمة
+
+303
+00:30:51,360 --> 00:30:57,620
+بتبعتها سميلي هذه star اللي بتقدر تقولي الصواب اسم
+
+304
+00:30:57,620 --> 00:31:08,860
+تت يوتin 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 Gلو ضربنا ضرب
+
+307
+00:31:23,920 --> 00:31:31,560
+تبادلي بصير ال order لل G بيساوي العدد 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 وابدا 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
+اتعرف function ما بين اتين اتين و تثبت ان هذه one
+
+313
+00:31:57,330 --> 00:32:03,110
+to one and unto 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 شغلالموضوع اللى بدنا نشيها اللى 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 المسائد على هذا ال section ان
+
+318
+00:32:20,560 --> 00:32:22,120
+شاء الله تبارك وتعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1d4c5215d1bb45de8de1be919350f32769f2b0c0
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/wwhcAnUFnP8_raw.srt
@@ -0,0 +1,1276 @@
+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 locosets and
+
+3
+00:00:30,320 --> 00:00:34,180
+lagrange theorem في الفترة الصباحية اعطينا اربع
+
+4
+00:00:34,180 --> 00:00:38,700
+crawlers على نظرية Lagrange وعطينا على ذلك بعض
+
+5
+00:00:38,700 --> 00:00:44,790
+الأمثلةالان صح برضه حكينا ان 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 ان 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
+خمسةالان في نظرية بعض اللي هي نظرية اللي قدامنا
+
+10
+00:01:02,680 --> 00:01:05,740
+هذه بيقول اللي قلت جي بي ا group of order اتنين بي
+
+11
+00:01:05,740 --> 00:01:09,960
+حيث بي is a prime greater than two then الجي
+
+12
+00:01:09,960 --> 00:01:16,040
+isomorphic لزد بي or دي بي طب ليش قال هذول التنتين
+
+13
+00:01:16,040 --> 00:01:20,380
+فيهم نفس العدد من العناصر ولا بيختلفوا عن بعض زد
+
+14
+00:01:20,380 --> 00:01:24,820
+اتنين بي و دي بي عدد عناصرهم كانت بعض ولا بيختلفوا
+
+15
+00:01:24,820 --> 00:01:29,580
+عن بعض هدولجت بعض على طول خاطر لأن دي بي عدد
+
+16
+00:01:29,580 --> 00:01:33,820
+عناصرها اتنين بي و زد بي عدد عناصرها اتنين بي طب
+
+17
+00:01:33,820 --> 00:01:40,380
+ليش قال زد اتنين بي اللي هو دي بي 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
+زد اتنين بي لحالها بس؟ او قال اللي هو دي بي لحالها
+
+20
+00:01:52,840 --> 00:01:54,780
+بس؟ ليش قال هذه او هذه؟
+
+21
+00:01:58,360 --> 00:02:06,480
+هذا بقدر افكر يقول ليش؟ مية لمية تمام هذا الان
+
+22
+00:02:06,480 --> 00:02:10,500
+عندي ال cyclic group يبقى لو كانت جيل أصلية ال
+
+23
+00:02:10,500 --> 00:02:15,490
+cyclic automatic هتكون isomorphic لمينلزد بي
+
+24
+00:02:15,490 --> 00:02:20,850
+مباشرة لو كانت هذه ماهياش Cyclic إذا هتبقى
+
+25
+00:02:20,850 --> 00:02:25,290
+isomorphic لمين لDP لإن دي بي not cyclic group
+
+26
+00:02:25,290 --> 00:02:29,070
+تمام يبقى لما نقل التنتين والتنتين اللي هما نفس ال
+
+27
+00:02:29,070 --> 00:02:33,410
+order يبقى isomorphic لزد اتنين بي إذا كانت ال G
+
+28
+00:02:33,410 --> 00:02:38,560
+Cyclicيبقى إجباري هتكون isomorphic لمام لزد اتنين
+
+29
+00:02:38,560 --> 00:02:43,060
+P وإذا ماكنتش Cyclic يبقى إجباري isomorphic لDP
+
+30
+00:02:43,060 --> 00:02:46,080
+الحقيقة برهان طويل فام سامحينكوا بدك تطلي عليه
+
+31
+00:02:46,080 --> 00:02:49,540
+ماعنديش مشكلة روح تطلي عليه من الكتاب بيبنيش
+
+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 تلاتين من الشبطر تبع خمسة وحليته لكوا يه على
+
+35
+00:03:03,320 --> 00:03:07,010
+اللوحيناو اثبت ان ال stabilizer هو عبارة عن
+
+36
+00:03:07,010 --> 00:03:10,690
+subgroup كان السؤال يثبت ان 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
+little g ب group of permutation of a6sأي element I
+
+39
+00:03:22,650 --> 00:03:26,590
+موجود في الاسلسل Stabilizer تبع الـ I 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 ال I يعني ليه تثبت ال I؟ يعني صورة ال I بتكون
+
+42
+00:03:35,370 --> 00:03:42,520
+من؟الـ I itself يبقى ال stabilizer لل I يعني كل ال
+
+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 وصورة ال I بتبقى ال I نفسه لو قلت بدل
+
+45
+00:03:51,520 --> 00:03:55,400
+ال I واحد يبقى صوت ال واحد هي واحد لو قلت بدل ال I
+
+46
+00:03:55,400 --> 00:03:59,720
+قلت عشرة يبقى صوت 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 ا
+
+48
+00:04:05,020 --> 00:04:10,260
+ثابتا يعني بيعطيني نفس ال element صورته نفسه فقلنا
+
+49
+00:04:10,260 --> 00:04:16,360
+ال stabilizer ل ال I اللي موجود في G لعلى G هو كل
+
+50
+00:04:16,360 --> 00:04:20,240
+ال Phi يعني كل ال permutation اللي موجودة في G
+
+51
+00:04:20,240 --> 00:04:26,620
+بحيث أن صورة I هي من ال I itselfطبعا ال stabilizer
+
+52
+00:04:26,620 --> 00:04:31,360
+is a subgroup و هذا أنا برهنتهلكوا سابقا اللي هو
+
+53
+00:04:31,360 --> 00:04:34,040
+السؤال واحد و ثلاثين من شفض 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 ان في شغل
+
+56
+00:04:41,740 --> 00:04:46,900
+متعلق فيه و في نظرية مرتبطة فيه بعد قليلبعد ذلك
+
+57
+00:04:46,900 --> 00:04:51,220
+قال لليلتل جي بيه a group of permutations of a set
+
+58
+00:04:51,220 --> 00:04:55,340
+S بدنا نعرف تعريف جديد هذا ماشوفنهوش قبل هيك
+
+59
+00:04:55,340 --> 00:04:59,960
+التعريف بيقولولي كل S موجود في S بدنا نعرف حاجة ال
+
+60
+00:04:59,960 --> 00:05:04,800
+orbit تبع ال S ال orbit يعني بالعربي ايه؟مدار مسار
+
+61
+00:05:04,800 --> 00:05:10,680
+كويس يبقى المدار تبع ال 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 وانا عندي G هذه بطلع من ال permutations
+
+65
+00:05:25,920 --> 00:05:31,630
+اللي الواحد له صورة و بروح باخد هذه الصورةطلع ايش
+
+66
+00:05:31,630 --> 00:05:36,790
+بقوله بقول ال orbit ل S كل ال Phi of S يعني صورة
+
+67
+00:05:36,790 --> 00:05:40,830
+main صورة هذا ال S بحيث ال Phi موجودة في جيب يعني
+
+68
+00:05:40,830 --> 00:05:43,930
+انا بتطلع على كل ال permutations اللي موجودة في ال
+
+69
+00:05:43,930 --> 00:05:50,370
+group قلت بد ال orbit مثلا لتلاتةبجيب اطلع وين
+
+70
+00:05:50,370 --> 00:05:54,250
+تلاتة كانت موجود 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 اذا هذول أرقام عادية تماميبقى في هذه الحالة
+
+74
+00:06:06,790 --> 00:06:11,970
+ال orbit لل S هو كل ال Phi of S يعني الصور ال S
+
+75
+00:06:11,970 --> 00:06:15,590
+بحيث ال Phi هي permutation موجود وين؟ موجود في G
+
+76
+00:06:15,590 --> 00:06:20,770
+يعني يا شباب احنا بدنا نطبق موضوع ال courses 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 ل S على Gوحط الخطين اللي بقيتنا نسميهم order
+
+81
+00:06:38,240 --> 00:06:43,620
+لجيه طبعا ال order درجة العادة ان نقوله group او
+
+82
+00:06:43,620 --> 00:06:47,940
+sub group او element بس هذا ال order ماقولناش sub
+
+83
+00:06:47,940 --> 00:06:52,240
+group ماقولناش حتى اقول 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 لجيهبنعطي مثال من خلال هذا المثال بدي
+
+86
+00:07:01,780 --> 00:07:05,760
+أحسب ال stabilizer لأعداد مختلفة وبدي أحسب ال
+
+87
+00:07:05,760 --> 00:07:10,720
+order ل الأعداد المختلفة نجي الأقل ال stabilizer
+
+88
+00:07:10,720 --> 00:07:16,800
+لمين للواحد حسب التعريف تبع ال stabilizer كل ال
+
+89
+00:07:16,800 --> 00:07:20,760
+permutations اللي فيهم الواحد fixed أيش يعني
+
+90
+00:07:20,760 --> 00:07:25,000
+الواحد fixed يعني الصورة الواحد بتعطيني مين الواحد
+
+91
+00:07:25,000 --> 00:07:30,440
+itselfأظن الـ identity permutation منهم صح الواحد
+
+92
+00:07:30,440 --> 00:07:33,400
+صورته واحد اتنين صورته اتنين تلاته صورته تلاته اذا
+
+93
+00:07:33,400 --> 00:07:39,600
+الواحد هذي منهم الان الواحد صورته ايش يبقى هذي ال
+
+94
+00:07:39,600 --> 00:07:43,800
+permutation منها لأ لإن ماثبتتاش 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؟مضربات في بعض ضرب الواحد صرت تلاتة
+
+98
+00:07:58,320 --> 00:08:03,660
+هنا هذه منهم لا يبقى ماعنديش إلا الأخيرة اتنين
+
+99
+00:08:03,660 --> 00:08:08,540
+واربع وخمسة يعني كل ال permutation اللي بيظهر فيهم
+
+100
+00:08:08,540 --> 00:08:14,040
+الواحد انسى الموضوع ما هذا ال identityيبقى اتنين
+
+101
+00:08:14,040 --> 00:08:21,140
+اربعة خمسة ستة يبقى اتنين اربعة هنا خمسة ستة
+
+102
+00:08:21,140 --> 00:08:26,100
+بالشكل اللي عندنا هنا طب بدي اجيب ال orbit لمن
+
+103
+00:08:26,100 --> 00:08:32,960
+للواحد على جي ويسوي بدي اجيب صورة الان في ال
+
+104
+00:08:32,960 --> 00:08:38,320
+permutation الاولى ايش صورة الواحد واحد itself هنا
+
+105
+00:08:38,320 --> 00:08:45,940
+صورة الواحد ثلاثة صورة الواحد اتنينهنا صورة الواحد
+
+106
+00:08:45,940 --> 00:08:52,260
+أخدناها بكرراش 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 العنصرلو بده اجيب ال
+
+110
+00:09:10,540 --> 00:09:18,620
+stabilizer على جيل ال element مثلا تلاتة طيب
+
+111
+00:09:18,620 --> 00:09:22,340
+هذه منهم صحيح لان هذه ال identity الصورة التلاتة
+
+112
+00:09:22,340 --> 00:09:27,460
+بتلاتة يبقى هذه منهم نيجي الان 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
+fixedالتلاتة 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 --> 00:09:52,180
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+119
+00:09:52,180 --> 00:09:53,520
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+120
+00:09:53,520 --> 00:09:54,760
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+121
+00:09:54,760 --> 00:10:03,700
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتأريد أن أشاهد
+
+122
+00:10:03,700 --> 00:10:07,900
+صور العناصر التلاتة في الـPermutations المختلفة
+
+123
+00:10:07,900 --> 00:10:13,840
+صورة التلاتة هنا كم؟ تلاتة يبقى تلاتة منهم لأنه
+
+124
+00:10:13,840 --> 00:10:22,880
+مقرر صورة التلاتة أربعة صورة التلاتة مكررة صورة
+
+125
+00:10:22,880 --> 00:10:30,140
+التلاتة خلصنا من هذا صورة التلاتة اتنين صورة
+
+126
+00:10:30,140 --> 00:10:36,110
+التلاتةأما أخدناها هايه صورة التلاتة اتنين أخدناها
+
+127
+00:10:36,110 --> 00:10:41,750
+هايه صورة التلاتة تلاتة هي أخدناها في الأول يبقى
+
+128
+00:10:41,750 --> 00:10:46,770
+انتهينا من الشغل هذه تمام؟ في خمسة خد ال orbit لل
+
+129
+00:10:46,770 --> 00:10:52,790
+stabilizer للخمسة مثلا ال stabilizer عالجي للخمسة
+
+130
+00:10:52,790 --> 00:10:59,390
+ويساوي طبعا صورة الخمسة اللي هي الخمسة نيجي هنا
+
+131
+00:11:01,020 --> 00:11:07,900
+الستابلازر اللى هو الواحد اللى هو الواحد مش ال
+
+132
+00:11:07,900 --> 00:11:12,180
+orbit اللى هو الواحد طبعا طيب الستابلازر مثبت على
+
+133
+00:11:12,180 --> 00:11:17,240
+الخمسة الخمسة ظاهرة هنا يبقى هنا الخمسة fixed يبقى
+
+134
+00:11:17,240 --> 00:11:24,410
+بداجي اقوله واحد اتنين تلاتة اربعة وكمانهنا الخمسة
+
+135
+00:11:24,410 --> 00:11:29,490
+ستة يبقى انسى هنا ظهرت لأ يبقى واحد تلاتة اتنين
+
+136
+00:11:29,490 --> 00:11:36,290
+اربعة يبقى واحد تلاتة اتنين اربعة خلصنا منها هنا
+
+137
+00:11:36,290 --> 00:11:40,750
+الخمسة صورتها ستة ماهياش fixed الخمسة صورتها ستة
+
+138
+00:11:40,750 --> 00:11:45,690
+ماعرف كده يبقى واحد اربعة اتنين تلاتة يبقى واحد
+
+139
+00:11:45,690 --> 00:11:52,670
+اربعةأتنين تلاتة خلصنا منها واحد اربع اتنين تلاتة
+
+140
+00:11:52,670 --> 00:11:58,650
+هنا ماهياش fixed يبقى انت هنا منها يبقى هذا ال
+
+141
+00:11:58,650 --> 00:12:06,910
+orbit لمين ال stabilizer للخمسة بد ال orbit للخمسة
+
+142
+00:12:06,910 --> 00:12:14,360
+على ال group Gكويس يعني بده صورة العدد خمسة صورة
+
+143
+00:12:14,360 --> 00:12:20,740
+خمسة هنا بخمسة itself طيب وصورة الخمسة هنا خمسة
+
+144
+00:12:20,740 --> 00:12:27,120
+itself صورة الخمسة هنا هي ستةصورة الخمسة خمسة
+
+145
+00:12:27,120 --> 00:12:32,060
+أخدناها صورة الخمسة ستة أخدناها صورة الخمسة ستة
+
+146
+00:12:32,060 --> 00:12:37,040
+أخدناها صورة الخمسة خمسة أخدناها صورة الخمسة ستة
+
+147
+00:12:37,040 --> 00:12:43,960
+أخدناها يبقى بس two elements تمام؟ يبقى عرفنا كيف
+
+148
+00:12:43,960 --> 00:12:48,840
+بنحسب ال orbit و ال stabilizer تمام؟ الحين بدنا
+
+149
+00:12:48,840 --> 00:12:51,860
+نجيب نظرية تربط ما بين ال order
+
+150
+00:12:59,360 --> 00:13:03,800
+هذا الموضوع النظرية التالية
+
+151
+00:13:21,170 --> 00:13:31,830
+يبقى هذه نظرية نصف على ما يليه ثيرم let
+
+152
+00:13:31,830 --> 00:13:36,630
+الـGP
+
+153
+00:13:36,630 --> 00:13:44,650
+a finite group of
+
+154
+00:13:44,650 --> 00:13:52,200
+permutations of a set Sof permutations
+
+155
+00:13:52,200 --> 00:13:59,680
+of a set capital
+
+156
+00:13:59,680 --> 00:14:03,480
+S then
+
+157
+00:14:03,480 --> 00:14:08,100
+for
+
+158
+00:14:08,100 --> 00:14:20,000
+then for any I اللي موجودة في capital Sالشكل اللي
+
+159
+00:14:20,000 --> 00:14:24,400
+عندنا هنا هو عدد
+
+160
+00:14:24,400 --> 00:14:29,500
+العناصر في ال orbit على بورت I على G
+
+161
+00:14:53,700 --> 00:15:16,560
+عظم ان هذا النحيا خلاص يبقى
+
+162
+00:15:16,560 --> 00:15:17,660
+مرة تانية بقول
+
+163
+00:15:24,280 --> 00:15:28,700
+عندنا g finite group of permutations يعني لازلنا
+
+164
+00:15:28,700 --> 00:15:32,180
+في موضوع ال group of permutations وهذه ال
+
+165
+00:15:32,180 --> 00:15:37,360
+permutations على ست S أخدت أي element I موجود في S
+
+166
+00:15:37,360 --> 00:15:42,780
+من خلال هذا الكلام اثبت ان ال order لل G هو عبارة
+
+167
+00:15:42,780 --> 00:15:48,350
+عنعدد العناصر في ال orbit لل I على G مضروب في ال
+
+168
+00:15:48,350 --> 00:15:52,810
+order تبع من؟ تبع ال stabilizer قلت ال order لل
+
+169
+00:15:52,810 --> 00:15:56,230
+stabilizer لإن ال stabilizer ال subgroup لكن هذه
+
+170
+00:15:56,230 --> 00:16:02,690
+ماهياش subgroup طيب البرهان كان التالي احنا الآن
+
+171
+00:16:02,690 --> 00:16:04,650
+اقوِن
+
+172
+00:16:06,510 --> 00:16:13,530
+أحنا بنعرف إن ال stabilizer لل I على G is a
+
+173
+00:16:13,530 --> 00:16:19,970
+subgroup من G هذا معناه إيش؟ معناته إن ال order لل
+
+174
+00:16:19,970 --> 00:16:30,000
+stabilizer على G لل I يقسم ال order ل Gيعني معنى
+
+175
+00:16:30,000 --> 00:16:36,360
+هذا الكلام ان ال order ل G مقسوم على ال order لل
+
+176
+00:16:36,360 --> 00:16:45,060
+stabilizer على I لل G هذا كله بدي ساوي the number
+
+177
+00:16:45,060 --> 00:16:50,600
+of lift cassettes
+
+178
+00:16:52,010 --> 00:17:05,750
+of the stabilizer ل I على G مرة
+
+179
+00:17:05,750 --> 00:17:11,490
+تانيةأحنا عارفين أن ال stabilizer هو subgroup من G
+
+180
+00:17:11,490 --> 00:17:16,370
+وقلنا لك هذا السؤال 31 من شهدر خمسة و قبل ذلك
+
+181
+00:17:16,370 --> 00:17:19,990
+أثبتناه إذا ال stabilizer هو subgroup من G حسب
+
+182
+00:17:19,990 --> 00:17:25,170
+نظرية Lagrange ال order لل stabilizer بده يقسم من
+
+183
+00:17:25,170 --> 00:17:26,750
+ال order لل G
+
+184
+00:17:30,470 --> 00:17:36,990
+يبقى ال order ل ال stabilizer بده يقسم ال order ل
+
+185
+00:17:36,990 --> 00:17:41,970
+ال g لما ال order ل ال h بده يقسم ال order ل ال g
+
+186
+00:17:41,970 --> 00:17:45,670
+يبقى لو قسمت ال order ل ال g على ال order ل ال h
+
+187
+00:17:45,670 --> 00:17:52,290
+بيعطيني main ال left distinct اللي هو cosets of h
+
+188
+00:17:52,290 --> 00:17:57,710
+and g يبقى هذا بدي يعطيني the number of left
+
+189
+00:17:57,710 --> 00:17:59,170
+distinct
+
+190
+00:18:01,470 --> 00:18:05,890
+cossets of the stabilizer تبع ال HNG يبقى هذا
+
+191
+00:18:05,890 --> 00:18:09,910
+بيعطيني عدد ال lift cossets اللي ولا واحدة فيهم
+
+192
+00:18:09,910 --> 00:18:17,510
+مالها زي التانية طيب كويس الان انا لو جدرت اثبت ان
+
+193
+00:18:17,510 --> 00:18:22,890
+هذا الرقم اللي عندي هو عدد عناصر في ال orbit بتما
+
+194
+00:18:22,890 --> 00:18:29,260
+المطلوب يعني لو اثبتإنه عدد اللي هو الرقم اللي
+
+195
+00:18:29,260 --> 00:18:37,380
+عندنا هذا عدد ال lift cos 6 اللي عندي من ال
+
+196
+00:18:37,380 --> 00:18:42,820
+stabilizer في ال group G أثبته انه يساوي اللي هو
+
+197
+00:18:42,820 --> 00:18:46,780
+عدد العناصر اللي موجودة في ال orbit باسم المطابق
+
+198
+00:18:46,780 --> 00:18:50,320
+بيبقى أشيل هذا و أضع عدد العناصر بنضر بضاربة تبذل
+
+199
+00:18:50,320 --> 00:18:55,790
+يكون برهن هذا الكلامعشان اثبت ان هذا العدد يساوي
+
+200
+00:18:55,790 --> 00:19:00,340
+هذا العدديعني معناته بدي أعرف function من الـ left
+
+201
+00:19:00,340 --> 00:19:05,080
+cosets للصور اللي عندنا هذه إذا ال function هذه
+
+202
+00:19:05,080 --> 00:19:09,600
+كنت أثبت إنها one to one and on two خلاص بصير
+
+203
+00:19:09,600 --> 00:19:14,360
+العدد قال بعض و لو وصلنا لإيه وصلنا للمطلوب بسهولة
+
+204
+00:19:14,360 --> 00:19:20,680
+طبعا احنا مر علينا جزء من نظرية مثل هذه قبل ذلك
+
+205
+00:19:20,680 --> 00:19:24,140
+بشأن نثبت أن ال order لهذا بدي سوى ال order لهذا
+
+206
+00:19:24,140 --> 00:19:28,500
+عرفنا functionيعني أخدنا نظرية في لف الكوسيطس أن
+
+207
+00:19:28,500 --> 00:19:35,300
+ال order للـH بدي يساوي ال order للـBH يعني عدل
+
+208
+00:19:35,300 --> 00:19:38,920
+عناصر يساوي عدل عناصر هنا عرفنا function فيه ما
+
+209
+00:19:38,920 --> 00:19:43,760
+بينهما و أثبتنا إنها one to one and أنتم يبقى الأن
+
+210
+00:19:43,760 --> 00:19:56,380
+أنا بدي أعمل نفس القصة define a functiont from the
+
+211
+00:19:56,380 --> 00:20:08,020
+set of all left-destinate left
+
+212
+00:20:08,020 --> 00:20:15,440
+-destinate cosets of stabilizer
+
+213
+00:20:18,540 --> 00:20:26,560
+الـ I على G in G يبقى من هذه الـ set to بدّى مين
+
+214
+00:20:26,560 --> 00:20:35,700
+بدّيها الـ set of elements في ال orbit لمن؟ to the
+
+215
+00:20:35,700 --> 00:20:47,480
+orbit على I للـ G أو the set of numbers in the
+
+216
+00:20:47,480 --> 00:20:56,220
+orbitالى مجموعة الأعداد اللى موجودة في ال orbit by
+
+217
+00:20:56,220 --> 00:20:59,400
+T
+
+218
+00:20:59,400 --> 00:21:06,750
+offأنا قلت left cosets و ال subgroup هي ال
+
+219
+00:21:06,750 --> 00:21:11,190
+stabilizer يبقى بدي أخد element من G ال elements
+
+220
+00:21:11,190 --> 00:21:15,650
+اللي فيها كلهم permutations لأن ال G set of all
+
+221
+00:21:15,650 --> 00:21:21,550
+permutations يبقى بدي يكون ال element Phi مضروب في
+
+222
+00:21:21,550 --> 00:21:29,310
+ال stabilizer لمن؟ لل I على Gهذه الـ set اللي
+
+223
+00:21:29,310 --> 00:21:34,290
+عندنا عناصرها lift coset من ال stabilizer يعني
+
+224
+00:21:34,290 --> 00:21:38,890
+element من G مضروب في ال stabilizer بدي اودي لل
+
+225
+00:21:38,890 --> 00:21:48,960
+set هذه يبقى T of كذا بدي ساوي Phi of Iلأن الـ
+
+226
+00:21:48,960 --> 00:21:54,220
+Orbit عرفناها قبل قليل صور الـ Phi of I حيث الـ I
+
+227
+00:21:54,220 --> 00:21:59,420
+موجودة وين؟ موجودة في S طب أول شي بنشوف هل هذه
+
+228
+00:21:59,420 --> 00:22:04,120
+فعلا هي دالة ولا ماهياش دالة وبعدين بشوف الحكاية
+
+229
+00:22:04,120 --> 00:22:12,380
+ال one to one and unto فبجي بقوله الآن T is well
+
+230
+00:22:12,380 --> 00:22:18,460
+definedمشان اثبت حكاية الولد فاني بدي امشي عكس ال
+
+231
+00:22:18,460 --> 00:22:25,080
+one to one يعني بدي اجي اخد عنصرين متساوين و اثبت
+
+232
+00:22:25,080 --> 00:22:31,520
+ان صورتهم عليها بتكون متساوين الان ماشي بدي اجي
+
+233
+00:22:31,520 --> 00:22:40,970
+اقوله assumeإن Alpha في ال stabilizer ل I على G
+
+234
+00:22:40,970 --> 00:22:50,670
+يسوى Beta في ال stabilizer ل I على main على G يعني
+
+235
+00:22:50,670 --> 00:22:57,970
+افرط ان عندي two left cosets are equal يبقى then
+
+236
+00:23:05,810 --> 00:23:12,450
+معكوس الالفة موجود في الـ group of all
+
+237
+00:23:12,450 --> 00:23:13,550
+permutations
+
+238
+00:23:16,760 --> 00:23:23,420
+بصير عند ال stabilizer لل I على G بدل سوى Alpha
+
+239
+00:23:23,420 --> 00:23:31,100
+inverse مضروبة في B في ال stabilizer لل I على G
+
+240
+00:23:31,730 --> 00:23:35,690
+أضرب الطرفين في alpha inverse يصبح هنا ال identity
+
+241
+00:23:35,690 --> 00:23:39,810
+اضربها في ال stabilizer يصبح ال stabilizer أضرب
+
+242
+00:23:39,810 --> 00:23:43,430
+alpha inverse هنا يصبح alpha inverse بي في ال
+
+243
+00:23:43,430 --> 00:23:48,890
+stabilizer طيب نرجع بالذاكرة قليلا إلى ال left
+
+244
+00:23:48,890 --> 00:23:56,700
+costals لما اقول H يساوي AH ايش يعني معناهاعندما
+
+245
+00:23:56,700 --> 00:24:01,980
+أقول H يساوي A H مايعني هذا بيحصل إذا كان ال A
+
+246
+00:24:01,980 --> 00:24:07,280
+موجود في H يبقى هذا معناه إن ال alpha inverse B
+
+247
+00:24:07,280 --> 00:24:13,600
+موجودة في ال stabilizer يبقى هذا معناه إن ال alpha
+
+248
+00:24:13,600 --> 00:24:22,900
+inverse B موجودة في ال stabilizer لل I على Gما دام
+
+249
+00:24:22,900 --> 00:24:28,000
+موجودة هنا يبقى ال alpha inverse بتأثيرها على I
+
+250
+00:24:28,000 --> 00:24:32,140
+نفسه
+
+251
+00:24:32,140 --> 00:24:37,680
+ما دام موجودة في ال stabilizer ما دام هذه
+
+252
+00:24:37,680 --> 00:24:42,340
+موجودة في ال stabilizer هذا معناه ان alpha inverse
+
+253
+00:24:42,340 --> 00:24:51,180
+beta of I ساوي Iطيب مادام Alpha يعني بدي أثر على
+
+254
+00:24:51,180 --> 00:24:56,180
+الطرفين بAlpha يبقى هذا إيش بيعطينا؟ بيعطينا إنه
+
+255
+00:24:56,180 --> 00:25:04,960
+Beta تأثيرها على I يسوى Alpha تأثيرها على I تمام؟
+
+256
+00:25:04,960 --> 00:25:09,900
+طيب إيش رأيك بدي أضرب ال stabilizer في الطرفين من
+
+257
+00:25:09,900 --> 00:25:19,570
+جهات اليمين؟ يعني هذا بيعطيك مين؟بيعطيك ان بيتا في
+
+258
+00:25:19,570 --> 00:25:27,350
+ال stabilizer لل I على G بديه يسوي Alpha في ال
+
+259
+00:25:27,350 --> 00:25:37,580
+stabilizer ل I على Gمصبوط هكذا؟ طيب أنا جايل أخدت
+
+260
+00:25:37,580 --> 00:25:43,520
+عنصرين متساوين لجيت .. احنا استنى .. استنى ..
+
+261
+00:25:43,520 --> 00:25:50,630
+استنى شوية، لا لا لا استناشي لسا واناأحنا أثبتنا
+
+262
+00:25:50,630 --> 00:25:57,850
+إن الـ Beta I بدها تساوي Alpha I وهو المطلوب
+
+263
+00:25:57,850 --> 00:26:03,250
+انتهينا من الشغل يعني يبقى T is well defined بداجي
+
+264
+00:26:03,250 --> 00:26:08,890
+الآن T is one to one يبقى بدي أعمل العملية العكسية
+
+265
+00:26:08,890 --> 00:26:15,330
+بدي أخد صورتين متساويتين و أثبت أن أصلهم متساوي
+
+266
+00:26:15,330 --> 00:26:18,310
+يبقى بداجي أقول Assume
+
+267
+00:26:20,190 --> 00:26:30,330
+إن T of Alpha في الـ Stabilizer لـ I على G بده
+
+268
+00:26:30,330 --> 00:26:37,550
+ساوي T of Beta في الـ Stabilizer على I لـ Main لـ
+
+269
+00:26:37,550 --> 00:26:39,850
+G itself بشكل عام
+
+270
+00:26:42,820 --> 00:26:47,620
+يبقى معنى هذا الكلام هذا الصورة اللي هو Alpha I
+
+271
+00:26:47,620 --> 00:26:56,120
+بدها تساوي Beta I حسب التعريف اللي احنا قايله طبعا
+
+272
+00:26:56,120 --> 00:27:01,740
+ما دام حسب التعريف الحين انا بدى اثبت ان ال Alpha
+
+273
+00:27:01,740 --> 00:27:04,580
+في ال stabilizer بدى تساوي Beta في ال stabilizer
+
+274
+00:27:04,580 --> 00:27:09,040
+معناته هذه لو جيت ضربت كل واحدة فيهم ال stabilizer
+
+275
+00:27:09,040 --> 00:27:15,840
+هتطلع القيمتانمتساويتا يبقى هذا معناته انه Alpha
+
+276
+00:27:15,840 --> 00:27:23,680
+في ال stabilizer على I لجيه بده يساوي Beta في ال
+
+277
+00:27:23,680 --> 00:27:30,220
+stabilizer على I لمين لجيه وهو المطلوب يبقى T سارة
+
+278
+00:27:30,220 --> 00:27:40,160
+تاشر one to one الان بدنا نثبت ان T is unto كويس
+
+279
+00:27:41,580 --> 00:27:47,020
+الان بدي اجي على ال orbit مش هذه موجودة في ال
+
+280
+00:27:47,020 --> 00:27:52,240
+orbit يبقى بدي افترض ان عندي عنصر موجود في ال
+
+281
+00:27:52,240 --> 00:28:00,240
+orbit يبقى let ال X موجود في ال orbit على I ل G
+
+282
+00:28:00,240 --> 00:28:10,630
+then ال X هذا بدي سوى Phi of I صح؟يبقى الـ x hat
+
+283
+00:28:10,630 --> 00:28:18,610
+of I of I for some I
+
+284
+00:28:18,610 --> 00:28:25,930
+اللي موجودة في
+
+285
+00:28:25,930 --> 00:28:34,640
+capital Sلأنه قال في نص النظرية قال لأي
+
+286
+00:28:34,640 --> 00:28:40,080
+ست له كامتل S يبقى ال I موجود وين في كامتل S طيب
+
+287
+00:28:40,080 --> 00:28:48,800
+ال Phi of I أليس تهيأ T ل Phi في ال stabilizer على
+
+288
+00:28:48,800 --> 00:28:56,750
+I ل Gنعم يبقى سارة T is one to one and unto يبقى
+
+289
+00:28:56,750 --> 00:29:06,090
+هنا سارة T is one to one and unto بدأ من one to
+
+290
+00:29:06,090 --> 00:29:10,630
+one and unto يبقى عدد العناصر عدد ال lift cosets
+
+291
+00:29:10,630 --> 00:29:17,550
+يبقى عدد العناصر في ال orbit يبقى هذا يعطينا مين
+
+292
+00:29:18,540 --> 00:29:29,560
+the number of lift destined cassettes
+
+293
+00:29:29,560 --> 00:29:44,020
+of the stabilizer لل I على G in G equal to equal
+
+294
+00:29:44,020 --> 00:29:46,640
+to the number
+
+295
+00:29:49,250 --> 00:30:00,230
+of equal to the number of elements in the orbit of
+
+296
+00:30:00,230 --> 00:30:03,130
+I على G
+
+297
+00:30:09,860 --> 00:30:12,940
+إن ال order اللي جيه على ال order اللي لسه
+
+298
+00:30:12,940 --> 00:30:18,140
+بالأضافة بتسوية عدد من عدد ال left cosets هنا the
+
+299
+00:30:18,140 --> 00:30:25,420
+number of elements in اللي هو that is يعني ان that
+
+300
+00:30:25,420 --> 00:30:34,680
+is اللي هو العدد تبع ال orbit لل I على Gهذه
+
+301
+00:30:34,680 --> 00:30:40,160
+المقصود فيها يعني صار إيش عدد ال left cosets اللي
+
+302
+00:30:40,160 --> 00:30:46,160
+ولا واحدة زي التانية يساوي من يساوي العدد تبع
+
+303
+00:30:46,160 --> 00:30:51,360
+العناصر هنا إذا بقدر أشيل هذه و أكتب القيمة
+
+304
+00:30:51,360 --> 00:30:57,620
+بتبعتها سميلي هذه star اللي بتقدر تقولي الصواب اسم
+
+305
+00:30:57,620 --> 00:31:08,860
+تت يوتin a star we get ال order لل G على ال order
+
+306
+00:31:08,860 --> 00:31:17,000
+لل stabilizer ل I على G بيساوي عدد العناصر أو عدد
+
+307
+00:31:17,000 --> 00:31:23,920
+ال elements في ال orbit تبع ال I على Gلو ضربنا ضرب
+
+308
+00:31:23,920 --> 00:31:31,560
+تبادلي بصير ال order لل G بيساوي العدد العناصر في
+
+309
+00:31:31,560 --> 00:31:39,900
+ال orbit لل I على G في ال order لل stabilizer لل I
+
+310
+00:31:39,900 --> 00:31:42,320
+على G وهو المطلوب
+
+311
+00:31:44,870 --> 00:31:48,970
+دائما وابدا لما نقول لك بدي عدل العناصر في الست
+
+312
+00:31:48,970 --> 00:31:53,370
+الأولى يساوي عدل العناصر في الستات التانية بتروح
+
+313
+00:31:53,370 --> 00:31:57,330
+اتعرف function ما بين اتين اتين و تثبت ان هذه one
+
+314
+00:31:57,330 --> 00:32:03,110
+to one and unto إذا أثبتتها بيكون هك تمام لحد هيك
+
+315
+00:32:03,110 --> 00:32:07,810
+بيكون انتهينا من الجزء النظري تبع هذا section طبعا
+
+316
+00:32:07,810 --> 00:32:11,940
+في شغلالموضوع اللى بدنا نشيها اللى هو دوران المكعب
+
+317
+00:32:11,940 --> 00:32:15,800
+وما إلى ذلك امسح هناك فيها لحد هنا stop يوم
+
+318
+00:32:15,800 --> 00:32:20,560
+الأثنين بنناقش بعض المسائد على هذا ال section ان
+
+319
+00:32:20,560 --> 00:32:22,120
+شاء الله تبارك وتعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7a8bac8734a91b518589ae144b928fb333daf504
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2674, "start": 21.7, "end": 26.74, "text": "بسم الله الرحمن الرحيم عودة على بدء المرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 6225, 23328, 3660, 15844, 47525, 38207, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.19456844954263597, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 21.7, "end": 22.04, "word": "بسم", "probability": 0.5836181640625}, {"start": 22.04, "end": 22.32, "word": " الله", "probability": 0.974609375}, {"start": 22.32, "end": 22.76, "word": " الرحمن", "probability": 0.9449869791666666}, {"start": 22.76, "end": 23.58, "word": " الرحيم", "probability": 0.99365234375}, {"start": 23.58, "end": 24.74, "word": " عودة", "probability": 0.7731119791666666}, {"start": 24.74, "end": 24.94, "word": " على", "probability": 0.7529296875}, {"start": 24.94, "end": 25.52, "word": " بدء", "probability": 0.626220703125}, {"start": 25.52, "end": 26.12, "word": " المرة", "probability": 0.865234375}, {"start": 26.12, "end": 26.74, "word": " الماضية", "probability": 0.9860026041666666}], "temperature": 1.0}, {"id": 2, "seek": 5542, "start": 27.12, "end": 55.42, "text": "عطينا تعريف للـ isomorphism وعطينا بعض الأمثلة على ال isomorphism ثم برهننا نظرية وهي أي group isomorphic إلى ال group of permutations وعطينا علامة ذلك مثلا واحدة المرة الماضية ووصلنا إلى خواص ال isomorphism يبقى أنا كاتب عنوان properties of isomorphism بخواص التشكل النمطي", "tokens": [3615, 9566, 1829, 8315, 37279, 16572, 5172, 24976, 39184, 307, 32702, 1434, 4032, 3615, 9566, 1829, 8315, 45030, 11242, 16247, 2304, 12984, 37977, 15844, 2423, 307, 32702, 1434, 38637, 2304, 4724, 2288, 3224, 1863, 8315, 8717, 19913, 2288, 10632, 37037, 1829, 36632, 1594, 307, 32702, 299, 30731, 2423, 1594, 295, 4784, 325, 763, 4032, 3615, 9566, 1829, 8315, 11203, 10943, 3660, 29910, 23275, 50113, 15040, 36764, 24401, 3660, 9673, 25720, 9673, 46958, 10632, 4032, 2407, 36520, 8315, 30731, 16490, 14407, 9381, 2423, 307, 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"probability": 0.9599609375}, {"start": 32.12, "end": 33.34, "word": " isomorphism", "probability": 0.802734375}, {"start": 33.34, "end": 34.42, "word": " ثم", "probability": 0.971923828125}, {"start": 34.42, "end": 35.5, "word": " برهننا", "probability": 0.7625}, {"start": 35.5, "end": 36.34, "word": " نظرية", "probability": 0.984375}, {"start": 36.34, "end": 37.04, "word": " وهي", "probability": 0.67724609375}, {"start": 37.04, "end": 37.3, "word": " أي", "probability": 0.72802734375}, {"start": 37.3, "end": 37.64, "word": " group", "probability": 0.875}, {"start": 37.64, "end": 38.62, "word": " isomorphic", "probability": 0.9417317708333334}, {"start": 38.62, "end": 38.94, "word": " إلى", "probability": 0.88232421875}, {"start": 38.94, "end": 39.16, "word": " ال", "probability": 0.52392578125}, {"start": 39.16, "end": 39.46, "word": " group", "probability": 0.9189453125}, {"start": 39.46, "end": 39.74, "word": " of", "probability": 0.947265625}, {"start": 39.74, "end": 40.7, "word": " permutations", "probability": 0.88916015625}, {"start": 40.7, "end": 41.68, "word": " وعطينا", "probability": 0.9669921875}, {"start": 41.68, "end": 42.1, "word": " علامة", "probability": 0.6905110677083334}, {"start": 42.1, "end": 42.46, "word": " ذلك", "probability": 0.989990234375}, {"start": 42.46, "end": 43.16, "word": " مثلا", "probability": 0.867431640625}, {"start": 43.16, "end": 43.7, "word": " واحدة", "probability": 0.7835286458333334}, {"start": 43.7, "end": 44.04, "word": " المرة", "probability": 0.959228515625}, {"start": 44.04, "end": 45.02, "word": " الماضية", "probability": 0.99609375}, {"start": 45.02, "end": 45.94, "word": " ووصلنا", "probability": 0.9837646484375}, {"start": 45.94, "end": 46.28, "word": " إلى", "probability": 0.908203125}, {"start": 46.28, "end": 46.92, "word": " خواص", "probability": 0.86474609375}, {"start": 46.92, "end": 47.12, "word": " ال", "probability": 0.9873046875}, {"start": 47.12, "end": 48.2, "word": " isomorphism", "probability": 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عناصر ال group والخاصية التانية حينما يعمل isomorphism على الشكل العام لل group وبالتالي هيكون عندنا نظريتين هذه النظرية الأولى مكونة من سبع نقاط والنظرية الثانية مكونة من أربع نقاط ان شاء الله تعالى", "tokens": [3224, 1863, 4587, 38251, 29538, 33962, 14407, 9381, 30731, 10874, 11622, 38207, 9957, 25724, 11622, 38207, 16247, 12610, 33962, 14407, 9381, 11331, 9957, 7251, 25957, 1211, 2423, 307, 32702, 1434, 15844, 18871, 33546, 2288, 2423, 1594, 16070, 9778, 33546, 10632, 16712, 7649, 10632, 11331, 9957, 15042, 7251, 25957, 1211, 307, 32702, 1434, 15844, 25124, 28820, 18863, 10943, 24976, 1594, 46599, 6027, 2655, 6027, 1829, 39896, 30544, 43242, 8315, 8717, 19913, 16572, 2655, 9957, 29538, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 3714, 30544, 3660, 9154, 8608, 3555, 3615, 8717, 4587, 41193, 16070, 1863, 19913, 2288, 10632, 6024, 104, 7649, 10632, 3714, 30544, 3660, 9154, 5551, 25513, 3615, 8717, 4587, 41193, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": 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{"start": 71.61, "end": 72.35, "word": " العام", "probability": 0.98974609375}, {"start": 72.35, "end": 72.63, "word": " لل", "probability": 0.54052734375}, {"start": 72.63, "end": 73.17, "word": " group", "probability": 0.98681640625}, {"start": 73.17, "end": 74.25, "word": " وبالتالي", "probability": 0.94970703125}, {"start": 74.25, "end": 74.79, "word": " هيكون", "probability": 0.718017578125}, {"start": 74.79, "end": 75.17, "word": " عندنا", "probability": 0.993896484375}, {"start": 75.17, "end": 75.97, "word": " نظريتين", "probability": 0.91181640625}, {"start": 75.97, "end": 76.63, "word": " هذه", "probability": 0.8056640625}, {"start": 76.63, "end": 77.19, "word": " النظرية", "probability": 0.94873046875}, {"start": 77.19, "end": 77.63, "word": " الأولى", "probability": 0.9646809895833334}, {"start": 77.63, "end": 78.25, "word": " مكونة", "probability": 0.8606770833333334}, {"start": 78.25, "end": 78.45, "word": " من", "probability": 0.99072265625}, {"start": 78.45, "end": 78.85, "word": " سبع", "probability": 0.900390625}, {"start": 78.85, "end": 79.51, "word": " نقاط", "probability": 0.9747721354166666}, {"start": 79.51, "end": 80.51, "word": " والنظرية", "probability": 0.94111328125}, {"start": 80.51, "end": 80.89, "word": " الثانية", "probability": 0.90283203125}, {"start": 80.89, "end": 81.69, "word": " مكونة", "probability": 0.9637044270833334}, {"start": 81.69, "end": 82.11, "word": " من", "probability": 0.9951171875}, {"start": 82.11, "end": 82.89, "word": " أربع", "probability": 0.908203125}, {"start": 82.89, "end": 83.55, "word": " نقاط", "probability": 0.9920247395833334}, {"start": 83.55, "end": 83.87, "word": " ان", "probability": 0.65234375}, {"start": 83.87, "end": 84.15, "word": " شاء", "probability": 0.981201171875}, {"start": 84.15, "end": 84.37, "word": " الله", "probability": 0.94189453125}, {"start": 84.37, "end": 84.89, "word": " تعالى", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 4, "seek": 10130, "start": 85.34, "end": 101.3, "text": "نبدأ بالنظرية الأولى وهي الـ properties of isomorphism acting on elements يبقى خواص ال isomorphism إن كان يعمل عالميا على العناصر اللي موجودة في ال group", "tokens": [1863, 44510, 10721, 20666, 1863, 19913, 2288, 10632, 16247, 12610, 7578, 37037, 1829, 2423, 39184, 7221, 295, 307, 32702, 1434, 6577, 322, 4959, 7251, 3555, 4587, 7578, 16490, 2407, 33546, 2423, 307, 32702, 1434, 36145, 25961, 7251, 25957, 1211, 6225, 45340, 25528, 15844, 18863, 1863, 33546, 2288, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 1594], "avg_logprob": -0.1689967063435337, "compression_ratio": 1.3614457831325302, "no_speech_prob": 0.0, "words": [{"start": 85.34, "end": 86.02, "word": "نبدأ", "probability": 0.8816731770833334}, {"start": 86.02, "end": 86.76, "word": " بالنظرية", "probability": 0.95068359375}, {"start": 86.76, "end": 87.64, "word": " الأولى", "probability": 0.974609375}, {"start": 87.64, "end": 88.18, "word": " وهي", "probability": 0.710693359375}, {"start": 88.18, 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"probability": 0.99169921875}, {"start": 95.84, "end": 96.36, "word": " يعمل", "probability": 0.8876953125}, {"start": 96.36, "end": 96.96, "word": " عالميا", "probability": 0.83740234375}, {"start": 96.96, "end": 98.06, "word": " على", "probability": 0.845703125}, {"start": 98.06, "end": 99.6, "word": " العناصر", "probability": 0.8720703125}, {"start": 99.6, "end": 99.84, "word": " اللي", "probability": 0.723388671875}, {"start": 99.84, "end": 100.54, "word": " موجودة", "probability": 0.99169921875}, {"start": 100.54, "end": 100.78, "word": " في", "probability": 0.95166015625}, {"start": 100.78, "end": 100.9, "word": " ال", "probability": 0.7861328125}, {"start": 100.9, "end": 101.3, "word": " group", "probability": 0.87890625}], "temperature": 1.0}, {"id": 5, "seek": 12875, "start": 101.89, "end": 128.75, "text": "بقول يفترض أن الـ Phi عبارة عن isomorphism من الآن فالساعدة هختصر كلمة isomorphism إلى ISO اللي هي أول تلت حروف من كلمة isomorphism يبقى Phi isomorphism من ال group G on to G bar يبقى one to one و on to و يختم خاصية اللي هو ال isomorphism بالإضافة إلى أن ال Phi عبارة عن function", "tokens": [3555, 39648, 7251, 5172, 2655, 43042, 14739, 2423, 39184, 41435, 6225, 3555, 9640, 3660, 18871, 307, 32702, 1434, 9154, 6024, 48506, 6156, 6027, 3794, 995, 22488, 3660, 8032, 46456, 9381, 2288, 9122, 19528, 3660, 307, 32702, 1434, 30731, 25042, 13672, 1829, 39896, 5551, 12610, 6055, 1211, 2655, 11331, 32887, 5172, 9154, 9122, 19528, 3660, 307, 32702, 1434, 7251, 3555, 4587, 7578, 41435, 307, 32702, 1434, 9154, 2423, 1594, 460, 322, 281, 460, 2159, 7251, 3555, 4587, 7578, 472, 281, 472, 4032, 322, 281, 4032, 7251, 9778, 39237, 16490, 33546, 10632, 13672, 1829, 31439, 2423, 307, 32702, 1434, 20666, 28814, 11242, 31845, 3660, 30731, 14739, 2423, 41435, 6225, 3555, 9640, 3660, 18871, 2445], "avg_logprob": -0.203816369571517, "compression_ratio": 1.8227272727272728, "no_speech_prob": 0.0, "words": [{"start": 101.89, "end": 102.35, "word": "بقول", "probability": 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العنصر معناته ايه له معكوس معناته هذا العنصر اللى هو معكوس فى جى بار بيدروح اضرب الطرفين فى هذا المعكوس يبقى لو روحت ضربت الطرفين فى هذا المعكوس بيصير في of ال identity تبع الجى فى في of ال identity تبع الجى فى في of ال identity تبع الجى بس الكل inverse", "tokens": [5172, 7578, 10874, 7578, 4724, 9640, 23032, 3555, 10874, 7578, 4724, 9640, 1975, 1829, 8592, 12174, 1211, 8315, 25894, 11296, 1594, 18863, 1863, 9381, 2288, 20449, 8315, 47395, 1975, 1829, 3224, 46740, 20449, 4117, 41779, 20449, 8315, 47395, 23758, 18863, 1863, 9381, 2288, 13672, 7578, 31439, 20449, 4117, 41779, 6156, 7578, 10874, 7578, 4724, 9640, 4724, 25708, 32887, 5016, 1975, 11242, 25513, 41950, 28480, 9957, 6156, 7578, 23758, 9673, 3615, 4117, 41779, 7251, 3555, 4587, 7578, 45164, 12602, 2407, 33753, 48812, 25513, 2655, 41950, 28480, 9957, 6156, 7578, 23758, 9673, 3615, 4117, 41779, 4724, 1829, 9381, 13546, 8978, 295, 2423, 6575, 6055, 3555, 3615, 25724, 7578, 6156, 7578, 8978, 295, 2423, 6575, 6055, 3555, 3615, 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" group", "probability": 0.798828125}, {"start": 441.06, "end": 442.06, "word": " العنصر", "probability": 0.925048828125}, {"start": 442.06, "end": 442.58, "word": " معناته", "probability": 0.9488932291666666}, {"start": 442.58, "end": 443.0, "word": " ايه", "probability": 0.6343180338541666}, {"start": 443.0, "end": 443.14, "word": " له", "probability": 0.5439453125}, {"start": 443.14, "end": 444.0, "word": " معكوس", "probability": 0.8660481770833334}, {"start": 444.0, "end": 445.0, "word": " معناته", "probability": 0.93994140625}, {"start": 445.0, "end": 445.32, "word": " هذا", "probability": 0.939453125}, {"start": 445.32, "end": 445.98, "word": " العنصر", "probability": 0.99609375}, {"start": 445.98, "end": 446.16, "word": " اللى", "probability": 0.5484619140625}, {"start": 446.16, "end": 446.32, "word": " هو", "probability": 0.82421875}, {"start": 446.32, "end": 446.96, "word": " معكوس", "probability": 0.8678385416666666}, {"start": 446.96, "end": 447.18, "word": " فى", "probability": 0.86669921875}, {"start": 447.18, "end": 447.48, "word": " جى", "probability": 0.971435546875}, {"start": 447.48, "end": 447.7, "word": " بار", "probability": 0.994140625}, {"start": 447.7, "end": 448.24, "word": " بيدروح", "probability": 0.6431884765625}, {"start": 448.24, "end": 448.78, "word": " اضرب", "probability": 0.9313151041666666}, {"start": 448.78, "end": 449.56, "word": " الطرفين", "probability": 0.9427083333333334}, {"start": 449.56, "end": 449.84, "word": " فى", "probability": 0.914306640625}, {"start": 449.84, "end": 450.36, "word": " هذا", "probability": 0.91552734375}, {"start": 450.36, "end": 451.44, "word": " المعكوس", "probability": 0.97119140625}, {"start": 451.44, "end": 452.4, "word": " يبقى", "probability": 0.97802734375}, {"start": 452.4, "end": 452.58, "word": " لو", "probability": 0.94091796875}, {"start": 452.58, "end": 452.92, "word": " روحت", "probability": 0.83544921875}, {"start": 452.92, "end": 453.44, "word": " ضربت", "probability": 0.96630859375}, {"start": 453.44, "end": 454.1, "word": " الطرفين", "probability": 0.986328125}, {"start": 454.1, "end": 454.38, "word": " فى", "probability": 0.92333984375}, {"start": 454.38, "end": 454.68, "word": " هذا", "probability": 0.962890625}, {"start": 454.68, "end": 455.28, "word": " المعكوس", "probability": 0.89892578125}, {"start": 455.28, "end": 455.84, "word": " بيصير", "probability": 0.9302978515625}, {"start": 455.84, "end": 456.2, "word": " في", "probability": 0.88037109375}, {"start": 456.2, "end": 456.6, "word": " of", "probability": 0.5390625}, {"start": 456.6, "end": 456.82, "word": " ال", "probability": 0.93359375}, {"start": 456.82, "end": 457.56, "word": " identity", "probability": 0.90869140625}, {"start": 457.56, "end": 458.08, "word": " تبع", "probability": 0.9632161458333334}, {"start": 458.08, "end": 458.6, "word": " الجى", "probability": 0.61083984375}, {"start": 458.6, "end": 459.28, "word": " فى", "probability": 0.89306640625}, {"start": 459.28, "end": 459.64, "word": " في", "probability": 0.623046875}, {"start": 459.64, "end": 460.02, "word": " of", "probability": 0.9716796875}, {"start": 460.02, "end": 460.3, "word": " ال", "probability": 0.986328125}, {"start": 460.3, "end": 461.04, "word": " identity", "probability": 0.947265625}, {"start": 461.04, "end": 461.62, "word": " تبع", "probability": 0.9895833333333334}, {"start": 461.62, "end": 462.22, "word": " الجى", "probability": 0.9287109375}, {"start": 462.22, "end": 462.86, "word": " فى", "probability": 0.9462890625}, {"start": 462.86, "end": 463.26, "word": " في", "probability": 0.9189453125}, {"start": 463.26, "end": 463.6, "word": " of", "probability": 0.9833984375}, {"start": 463.6, "end": 463.86, "word": " ال", "probability": 0.99462890625}, {"start": 463.86, "end": 464.7, "word": " identity", "probability": 0.9599609375}, {"start": 464.7, "end": 465.3, "word": " تبع", "probability": 0.9925130208333334}, {"start": 465.3, "end": 465.76, "word": " الجى", "probability": 0.92578125}, {"start": 465.76, "end": 466.12, "word": " بس", "probability": 0.9892578125}, {"start": 466.12, "end": 466.82, "word": " الكل", "probability": 0.89306640625}, {"start": 466.82, "end": 467.7, "word": " inverse", "probability": 0.50048828125}], "temperature": 1.0}, {"id": 22, "seek": 49409, "start": 468.11, "end": 494.09, "text": "بدي ساوي الـ Phi of ال identity تبع ال G في Phi of ال identity تبع ال G لكل inverse يبقى ضاربت المعادلة اللي عندنا هذه من جهتي اليمين في ال element Phi of G inverse طب ال element هذا في هذا مش هذا ال element و معكوسه؟ قدش بيعطيني؟", "tokens": [3555, 16254, 8608, 995, 45865, 2423, 39184, 41435, 295, 2423, 6575, 6055, 3555, 3615, 2423, 460, 8978, 41435, 295, 2423, 6575, 6055, 3555, 3615, 2423, 460, 5296, 28820, 17340, 7251, 3555, 4587, 7578, 48812, 9640, 3555, 2655, 9673, 3615, 18513, 37977, 13672, 1829, 43242, 8315, 29538, 9154, 10874, 3224, 31371, 2423, 32640, 9957, 8978, 2423, 4478, 41435, 295, 460, 17340, 23032, 3555, 2423, 4478, 23758, 8978, 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471.99, "end": 472.23, "word": " G", "probability": 0.44873046875}, {"start": 472.23, "end": 472.77, "word": " في", "probability": 0.8310546875}, {"start": 472.77, "end": 473.23, "word": " Phi", "probability": 0.92431640625}, {"start": 473.23, "end": 473.59, "word": " of", "probability": 0.98291015625}, {"start": 473.59, "end": 473.83, "word": " ال", "probability": 0.982421875}, {"start": 473.83, "end": 474.65, "word": " identity", "probability": 0.927734375}, {"start": 474.65, "end": 475.47, "word": " تبع", "probability": 0.9775390625}, {"start": 475.47, "end": 475.73, "word": " ال", "probability": 0.8037109375}, {"start": 475.73, "end": 476.19, "word": " G", "probability": 0.953125}, {"start": 476.19, "end": 477.09, "word": " لكل", "probability": 0.906494140625}, {"start": 477.09, "end": 477.91, "word": " inverse", "probability": 0.5224609375}, {"start": 477.91, "end": 479.41, "word": " يبقى", "probability": 0.9549560546875}, {"start": 479.41, "end": 480.17, "word": " ضاربت", "probability": 0.7933349609375}, {"start": 480.17, "end": 481.19, "word": " المعادلة", "probability": 0.8719482421875}, {"start": 481.19, "end": 481.37, "word": " اللي", "probability": 0.885986328125}, {"start": 481.37, "end": 481.75, "word": " عندنا", "probability": 0.65380859375}, {"start": 481.75, "end": 482.01, "word": " هذه", "probability": 0.357177734375}, {"start": 482.01, "end": 482.33, "word": " من", "probability": 0.97607421875}, {"start": 482.33, "end": 482.93, "word": " جهتي", "probability": 0.9602864583333334}, {"start": 482.93, "end": 483.71, "word": " اليمين", "probability": 0.8173014322916666}, {"start": 483.71, "end": 484.23, "word": " في", "probability": 0.91357421875}, {"start": 484.23, "end": 484.37, "word": " ال", "probability": 0.96142578125}, {"start": 484.37, "end": 484.91, "word": " element", "probability": 0.95263671875}, {"start": 484.91, "end": 485.53, "word": " Phi", "probability": 0.88818359375}, {"start": 485.53, "end": 486.01, "word": " of", "probability": 0.966796875}, {"start": 486.01, "end": 486.51, "word": " G", "probability": 0.9677734375}, {"start": 486.51, "end": 487.25, "word": " inverse", "probability": 0.88818359375}, {"start": 487.25, "end": 488.03, "word": " طب", "probability": 0.78125}, {"start": 488.03, "end": 488.25, "word": " ال", "probability": 0.97314453125}, {"start": 488.25, "end": 488.79, "word": " element", "probability": 0.986328125}, {"start": 488.79, "end": 489.27, "word": " هذا", "probability": 0.78955078125}, {"start": 489.27, "end": 489.49, "word": " في", "probability": 0.94287109375}, {"start": 489.49, "end": 489.93, "word": " هذا", "probability": 0.97998046875}, {"start": 489.93, "end": 491.23, "word": " مش", "probability": 0.7890625}, {"start": 491.23, "end": 491.45, "word": " هذا", "probability": 0.90673828125}, {"start": 491.45, "end": 491.59, "word": " ال", "probability": 0.98046875}, {"start": 491.59, "end": 491.89, "word": " element", "probability": 0.9873046875}, {"start": 491.89, "end": 492.11, "word": " و", "probability": 0.69677734375}, {"start": 492.11, "end": 493.01, "word": " معكوسه؟", "probability": 0.714111328125}, {"start": 493.01, "end": 493.37, "word": " قدش", "probability": 0.7185872395833334}, {"start": 493.37, "end": 494.09, "word": " بيعطيني؟", "probability": 0.8006417410714286}], "temperature": 1.0}, {"id": 23, "seek": 50913, "start": 494.71, "end": 509.13, "text": "تبع مين؟ تبع الـ G bar في الـ Phi of EG بيعطيني مين؟ لا بيعطيني Phi of EG دغلي لإن Phi of EG element في G bar", "tokens": [2655, 3555, 3615, 3714, 9957, 22807, 6055, 3555, 3615, 2423, 39184, 460, 2159, 8978, 2423, 39184, 41435, 295, 462, 38, 4724, 1829, 3615, 9566, 1829, 22653, 3714, 9957, 22807, 20193, 4724, 1829, 3615, 9566, 1829, 22653, 41435, 295, 462, 38, 11778, 17082, 20292, 5296, 28814, 1863, 41435, 295, 462, 38, 4478, 8978, 460, 2159], "avg_logprob": -0.4170454437082464, "compression_ratio": 1.471698113207547, "no_speech_prob": 0.0, "words": [{"start": 494.71, "end": 495.15, "word": "تبع", "probability": 0.5723775227864584}, {"start": 495.15, "end": 495.73, "word": " مين؟", "probability": 0.4875691731770833}, {"start": 495.73, "end": 496.63, "word": " تبع", "probability": 0.90234375}, {"start": 496.63, "end": 496.83, "word": " الـ", "probability": 0.753662109375}, {"start": 496.83, "end": 496.97, "word": " G", "probability": 0.465576171875}, {"start": 496.97, "end": 497.39, "word": " bar", "probability": 0.438720703125}, {"start": 497.39, "end": 497.95, "word": " في", "probability": 0.73046875}, {"start": 497.95, "end": 498.21, "word": " الـ", "probability": 0.5712890625}, {"start": 498.21, "end": 498.45, "word": " Phi", "probability": 0.25244140625}, {"start": 498.45, "end": 498.91, "word": " of", "probability": 0.9287109375}, {"start": 498.91, "end": 499.63, "word": " EG", "probability": 0.737060546875}, {"start": 499.63, "end": 500.27, "word": " بيعطيني", "probability": 0.6942545572916666}, {"start": 500.27, "end": 502.73, "word": " مين؟", "probability": 0.8898111979166666}, {"start": 502.73, "end": 504.39, "word": " لا", "probability": 0.415283203125}, {"start": 504.39, "end": 504.87, "word": " بيعطيني", "probability": 0.8008626302083334}, {"start": 504.87, "end": 505.11, "word": " Phi", "probability": 0.79150390625}, {"start": 505.11, "end": 505.41, "word": " of", "probability": 0.95703125}, {"start": 505.41, "end": 505.91, "word": " EG", "probability": 0.974365234375}, {"start": 505.91, "end": 506.33, "word": " دغلي", "probability": 0.5605061848958334}, {"start": 506.33, "end": 506.59, "word": " لإن", "probability": 0.7279459635416666}, {"start": 506.59, "end": 506.89, "word": " Phi", "probability": 0.85400390625}, {"start": 506.89, "end": 507.13, "word": " of", "probability": 0.96142578125}, {"start": 507.13, "end": 507.41, "word": " EG", "probability": 0.9873046875}, {"start": 507.41, "end": 508.09, "word": " element", "probability": 0.322021484375}, {"start": 508.09, "end": 508.47, "word": " في", "probability": 0.9716796875}, {"start": 508.47, "end": 508.71, "word": " G", "probability": 0.89306640625}, {"start": 508.71, "end": 509.13, "word": " bar", "probability": 0.83056640625}], "temperature": 1.0}, {"id": 24, "seek": 52573, "start": 509.57, "end": 525.73, "text": "ويعني هذا بدي يعطيني مين؟ بدي يعطيني الـPhi of ال identity تبع الـG في ال identity element تبع الـG bar وهذا بدي يعطيني ال identity element تبع مين؟ تبع الـG bar", "tokens": [2407, 40228, 22653, 23758, 4724, 16254, 37495, 9566, 1829, 22653, 3714, 9957, 22807, 4724, 16254, 37495, 9566, 1829, 22653, 2423, 39184, 47, 4954, 295, 2423, 6575, 6055, 3555, 3615, 2423, 39184, 38, 8978, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 39184, 38, 2159, 37037, 15730, 4724, 16254, 37495, 9566, 1829, 22653, 2423, 6575, 4478, 6055, 3555, 3615, 3714, 9957, 22807, 6055, 3555, 3615, 2423, 39184, 38, 2159], "avg_logprob": -0.2506893474389525, "compression_ratio": 2.142857142857143, "no_speech_prob": 0.0, "words": [{"start": 509.57, "end": 510.39, "word": 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"probability": 0.7892252604166666}, {"start": 516.59, "end": 516.85, "word": " في", "probability": 0.81494140625}, {"start": 516.85, "end": 517.07, "word": " ال", "probability": 0.98486328125}, {"start": 517.07, "end": 517.79, "word": " identity", "probability": 0.75341796875}, {"start": 517.79, "end": 518.39, "word": " element", "probability": 0.98876953125}, {"start": 518.39, "end": 518.89, "word": " تبع", "probability": 0.9864908854166666}, {"start": 518.89, "end": 519.33, "word": " الـG", "probability": 0.9391276041666666}, {"start": 519.33, "end": 519.61, "word": " bar", "probability": 0.66796875}, {"start": 519.61, "end": 520.55, "word": " وهذا", "probability": 0.8154296875}, {"start": 520.55, "end": 520.87, "word": " بدي", "probability": 0.95849609375}, {"start": 520.87, "end": 521.49, "word": " يعطيني", "probability": 0.9136962890625}, {"start": 521.49, "end": 521.75, "word": " ال", "probability": 0.98388671875}, {"start": 521.75, "end": 522.61, "word": " identity", "probability": 0.84765625}, {"start": 522.61, "end": 523.57, "word": " element", "probability": 0.990234375}, {"start": 523.57, "end": 524.05, "word": " تبع", "probability": 0.9772135416666666}, {"start": 524.05, "end": 524.61, "word": " مين؟", "probability": 0.8971354166666666}, {"start": 524.61, "end": 525.03, "word": " تبع", "probability": 0.99072265625}, {"start": 525.03, "end": 525.41, "word": " الـG", "probability": 0.9436848958333334}, {"start": 525.41, "end": 525.73, "word": " bar", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 25, "seek": 54979, "start": 526.58, "end": 549.8, "text": "طب هذا element في G bar لأن صورة ال identity element تبع ال G و هذا ال identity element تبع ال G bar حصل ضربهما شو بيعطيني ال phi of EG نفسه لأن ال identity element اضرب في أي عنصر في ال group بيعطيني نفس العنصر إذا بناء عليه هذا بده يعطيني", "tokens": [9566, 3555, 23758, 4478, 8978, 460, 2159, 5296, 33456, 20328, 13063, 3660, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 460, 4032, 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هذا سيعطينا ان ال statement صحيح في حالة الان تساوي واحد", "tokens": [1829, 3555, 4587, 7578, 25724, 2304, 37977, 31767, 5016, 1829, 5016, 3660, 8978, 11331, 6027, 3660, 2423, 7649, 6055, 3794, 995, 45865, 36764, 24401, 23758, 8608, 40228, 9566, 1829, 8315, 16472, 2423, 5629, 20328, 5016, 1829, 5016, 8978, 11331, 6027, 3660, 2423, 7649, 6055, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.3556249910593033, "compression_ratio": 1.6634615384615385, "no_speech_prob": 0.0, "words": [{"start": 692.8900000000001, "end": 693.8100000000001, "word": "يبقى", "probability": 0.6201629638671875}, {"start": 693.8100000000001, "end": 694.73, "word": " الجملة", "probability": 0.7027994791666666}, {"start": 694.73, "end": 695.57, "word": " الصحيحة", "probability": 0.9087890625}, {"start": 695.57, "end": 695.71, "word": " في", "probability": 0.81005859375}, {"start": 695.71, "end": 696.25, "word": " حالة", "probability": 0.9871419270833334}, {"start": 696.25, "end": 696.61, "word": " الان", 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{"start": 1312.3, "end": 1312.8, "word": " هنجي", "probability": 0.63958740234375}, {"start": 1312.8, "end": 1313.34, "word": " للشجة", "probability": 0.8712158203125}, {"start": 1313.34, "end": 1313.66, "word": " دي", "probability": 0.635498046875}, {"start": 1313.66, "end": 1313.84, "word": " يعني", "probability": 0.601806640625}, {"start": 1313.84, "end": 1314.36, "word": " خلصنا", "probability": 0.9801025390625}, {"start": 1314.36, "end": 1314.68, "word": " نقطة", "probability": 0.8914388020833334}, {"start": 1314.68, "end": 1315.14, "word": " تالتة", "probability": 0.76556396484375}, {"start": 1315.14, "end": 1315.56, "word": " بنروح", "probability": 0.822021484375}, {"start": 1315.56, "end": 1316.14, "word": " للرابع", "probability": 0.8570556640625}, {"start": 1316.14, "end": 1316.9, "word": " الان", "probability": 0.6162109375}, {"start": 1316.9, "end": 1317.22, "word": " بدنا", "probability": 0.840087890625}, {"start": 1317.22, "end": 1317.5, "word": " نجي", "probability": 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بقول هذا من ناحية الفهم", "tokens": [6027, 7435, 1863, 16572, 2655, 2288, 8978, 10874, 1829, 3224, 31439, 10874, 1863, 16572, 2655, 2288, 32767, 9957, 5296, 7435, 1829, 3224, 4724, 9640, 45030, 3555, 9640, 3660, 5551, 34740, 7578, 4724, 1829, 39648, 25724, 1863, 16572, 2655, 2288, 6055, 3555, 3615, 5296, 7435, 32887, 3555, 10874, 1829, 3224, 20328, 13063, 47395, 31439, 25724, 1863, 16572, 2655, 2288, 32767, 9957, 5296, 7435, 32887, 3555, 10874, 1829, 3224, 4724, 9640, 20449, 8315, 3224, 16472, 1975, 8315, 4724, 39648, 23758, 9154, 8717, 39319, 10632, 27188, 16095], "avg_logprob": -0.1677389712894664, "compression_ratio": 1.9787234042553192, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1339.91, "end": 1341.23, "word": "الجنريتر", "probability": 0.7711588541666666}, {"start": 1341.23, "end": 1341.47, "word": " في", "probability": 0.94482421875}, {"start": 1341.47, "end": 1342.09, "word": " جيه", "probability": 0.7184244791666666}, {"start": 1342.09, "end": 1342.75, 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ال sub group generated by a اللي صورته من؟ صورته في of a طب كويس الان لو جيت اخد العنصر اللي موجود في جي مين ما يكون يكون يبقى لو جيت يقولش لك little a belongs to g then", "tokens": [9566, 3555, 9122, 45865, 3794, 1975, 8315, 6156, 43042, 16472, 10874, 1829, 4724, 9640, 2655, 2407, 8608, 995, 45865, 8978, 295, 257, 4724, 16254, 1975, 5016, 995, 12610, 1975, 12984, 3555, 2655, 16472, 25724, 1829, 39896, 2423, 1422, 1594, 10833, 538, 257, 13672, 1829, 20328, 13063, 47395, 9154, 22807, 20328, 13063, 47395, 8978, 295, 257, 23032, 3555, 9122, 45865, 3794, 2423, 7649, 45164, 10874, 36081, 1975, 9778, 3215, 18863, 1863, 9381, 2288, 13672, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 3714, 9957, 19446, 7251, 30544, 7251, 30544, 7251, 3555, 4587, 7578, 45164, 10874, 36081, 7251, 39648, 8592, 5296, 4117, 707, 257, 12953, 281, 290, 550], "avg_logprob": -0.2433667409251321, "compression_ratio": 1.705069124423963, "no_speech_prob": 0.0, "words": [{"start": 1734.6, "end": 1734.96, "word": "طب", 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"word": " sub", "probability": 0.83837890625}, {"start": 1810.01, "end": 1810.61, "word": " set", "probability": 0.78515625}, {"start": 1810.61, "end": 1810.95, "word": " من", "probability": 0.97216796875}, {"start": 1810.95, "end": 1811.29, "word": " من", "probability": 0.331787109375}, {"start": 1811.29, "end": 1812.57, "word": " جيب", "probability": 0.7965494791666666}, {"start": 1812.57, "end": 1813.17, "word": " وهذه", "probability": 0.56591796875}, {"start": 1813.17, "end": 1814.11, "word": " النقطة", "probability": 0.9676106770833334}, {"start": 1814.11, "end": 1815.41, "word": " الأولى", "probability": 0.9698893229166666}, {"start": 1815.41, "end": 1815.77, "word": " اللى", "probability": 0.71240234375}, {"start": 1815.77, "end": 1816.09, "word": " بدى", "probability": 0.685791015625}, {"start": 1816.09, "end": 1816.91, "word": " أسميها", "probability": 0.82318115234375}, {"start": 1816.91, "end": 1817.69, "word": " شرطة", "probability": 0.9757080078125}, {"start": 1817.69, 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"probability": 0.7578125}, {"start": 2082.05, "end": 2082.29, "word": " to", "probability": 0.85986328125}, {"start": 2082.29, "end": 2082.57, "word": " the", "probability": 0.91845703125}, {"start": 2082.57, "end": 2083.13, "word": " power", "probability": 0.9169921875}, {"start": 2083.13, "end": 2084.07, "word": " k", "probability": 0.65673828125}, {"start": 2084.07, "end": 2085.87, "word": " مدام", "probability": 0.6944986979166666}, {"start": 2085.87, "end": 2086.19, "word": " a", "probability": 0.92919921875}, {"start": 2086.19, "end": 2086.37, "word": " to", "probability": 0.9736328125}, {"start": 2086.37, "end": 2086.61, "word": " the", "probability": 0.9228515625}, {"start": 2086.61, "end": 2086.99, "word": " power", "probability": 0.908203125}, {"start": 2086.99, "end": 2087.31, "word": " k", "probability": 0.96484375}, {"start": 2087.31, "end": 2087.79, "word": " يبقى", "probability": 0.9718017578125}, {"start": 2087.79, "end": 2087.89, "word": " ال", "probability": 0.87060546875}, {"start": 2087.89, "end": 2088.27, "word": " a", "probability": 0.92919921875}, {"start": 2088.27, "end": 2088.47, "word": " to", "probability": 0.97119140625}, {"start": 2088.47, "end": 2088.73, "word": " the", "probability": 0.92578125}, {"start": 2088.73, "end": 2089.17, "word": " power", "probability": 0.9072265625}, {"start": 2089.17, "end": 2089.59, "word": " k", "probability": 0.9658203125}, {"start": 2089.59, "end": 2090.37, "word": " موجودة", "probability": 0.981689453125}, {"start": 2090.37, "end": 2090.55, "word": " في", "probability": 0.96142578125}, {"start": 2090.55, "end": 2090.73, "word": " ال", "probability": 0.74609375}, {"start": 2090.73, "end": 2090.99, "word": " sub", "probability": 0.7744140625}, {"start": 2090.99, "end": 2091.41, "word": " group", "probability": 0.5810546875}, {"start": 2091.41, "end": 2092.11, "word": " generated", "probability": 0.83349609375}, {"start": 2092.11, "end": 2092.57, "word": " by", "probability": 0.978515625}, {"start": 2092.57, "end": 2092.97, "word": " a", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 92, "seek": 211646, "start": 2093.7, "end": 2116.46, "text": "ممتاز اذا اخدنا بي موجود في جي اثبتنا ان بي موجود في subgroup generated by a هذا معناه ان جي is a subset milligroup generated by a اطلعلي للأولى واطلعلي للتانية هذه هي", "tokens": [2304, 2304, 2655, 31377, 1975, 15730, 1975, 9778, 3215, 8315, 4724, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 1975, 12984, 3555, 2655, 8315, 16472, 4724, 1829, 3714, 29245, 23328, 8978, 1422, 17377, 10833, 538, 257, 23758, 20449, 8315, 3224, 16472, 10874, 1829, 307, 257, 25993, 1728, 328, 81, 1250, 10833, 538, 257, 1975, 9566, 1211, 3615, 20292, 24976, 10721, 12610, 7578, 4032, 41193, 1211, 3615, 20292, 24976, 2655, 7649, 10632, 29538, 39896], "avg_logprob": -0.2870291095890411, "compression_ratio": 1.608974358974359, "no_speech_prob": 0.0, "words": [{"start": 2093.7, "end": 2094.5, "word": "ممتاز", "probability": 0.8746337890625}, {"start": 2094.5, "end": 2094.74, "word": " اذا", "probability": 0.6033935546875}, {"start": 2094.74, "end": 2095.44, "word": " اخدنا", "probability": 0.67388916015625}, {"start": 2095.44, "end": 2095.78, "word": " بي", "probability": 0.6549072265625}, {"start": 2095.78, "end": 2096.36, "word": " موجود", "probability": 0.9484049479166666}, {"start": 2096.36, "end": 2096.64, "word": " في", "probability": 0.9453125}, {"start": 2096.64, "end": 2097.12, "word": " جي", "probability": 0.72802734375}, {"start": 2097.12, "end": 2098.36, "word": " اثبتنا", "probability": 0.89609375}, {"start": 2098.36, "end": 2098.62, "word": " ان", "probability": 0.89208984375}, {"start": 2098.62, "end": 2098.96, "word": " بي", "probability": 0.962890625}, {"start": 2098.96, "end": 2099.36, "word": " موجود", "probability": 0.9871419270833334}, {"start": 2099.36, "end": 2099.78, "word": " في", "probability": 0.71435546875}, {"start": 2099.78, "end": 2101.16, "word": " subgroup", "probability": 0.41448974609375}, {"start": 2101.16, "end": 2101.78, "word": " generated", "probability": 0.623046875}, {"start": 2101.78, "end": 2102.28, "word": " by", "probability": 0.9658203125}, {"start": 2102.28, "end": 2102.72, "word": " a", "probability": 0.496826171875}, {"start": 2102.72, "end": 2103.5, "word": " هذا", "probability": 0.69384765625}, {"start": 2103.5, "end": 2104.32, "word": " معناه", "probability": 0.8670247395833334}, {"start": 2104.32, "end": 2105.22, "word": " ان", "probability": 0.9462890625}, {"start": 2105.22, "end": 2105.94, "word": " جي", "probability": 0.898681640625}, {"start": 2105.94, "end": 2106.46, "word": " is", "probability": 0.2149658203125}, {"start": 2106.46, "end": 2106.92, "word": " a", "probability": 0.9287109375}, {"start": 2106.92, "end": 2107.68, "word": " subset", "probability": 0.93603515625}, {"start": 2107.68, "end": 2109.22, "word": " milligroup", "probability": 0.739501953125}, {"start": 2109.22, "end": 2110.02, "word": " generated", 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{"start": 2121.81, "end": 2122.31, "word": " بقدر", "probability": 0.9490559895833334}, {"start": 2122.31, "end": 2122.65, "word": " أقول", "probability": 0.811279296875}, {"start": 2122.65, "end": 2126.13, "word": " الآن", "probability": 0.669921875}, {"start": 2126.13, "end": 2135.03, "word": " بقدر", "probability": 0.96923828125}, {"start": 2135.03, "end": 2135.29, "word": " أقول", "probability": 0.9736328125}, {"start": 2135.29, "end": 2135.89, "word": " from", "probability": 0.900390625}, {"start": 2135.89, "end": 2138.13, "word": " اللي", "probability": 0.977294921875}, {"start": 2138.13, "end": 2138.53, "word": " هو", "probability": 0.99462890625}, {"start": 2138.53, "end": 2138.99, "word": " ال", "probability": 0.67822265625}, {"start": 2138.99, "end": 2139.37, "word": " star", "probability": 0.327880859375}, {"start": 2139.37, "end": 2140.25, "word": " الأولى", "probability": 0.9742838541666666}, {"start": 2140.25, "end": 2141.75, "word": " ال", "probability": 0.8525390625}, {"start": 2141.75, "end": 2142.35, "word": " star", "probability": 0.8974609375}, {"start": 2142.35, "end": 2143.29, "word": " التانية", "probability": 0.9851888020833334}, {"start": 2143.29, "end": 2144.19, "word": " we", "probability": 0.5595703125}, {"start": 2144.19, "end": 2145.09, "word": " have", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 94, "seek": 217117, "start": 2146.8, "end": 2171.18, "text": "إن الـ G بيكون ساوية لـ group generated by A يبقى هي أثبتنا A اللي هو النظرية يعني يبقى بناء عليه الـ G بيكون ساوية لـ subgroup generated by A if and only if الـ G برثة والsubgroup generated by Phi of A بيبقى تفهيمي من الآن فصاعدا", "tokens": [28814, 1863, 2423, 39184, 460, 4724, 1829, 30544, 8608, 995, 2407, 10632, 5296, 39184, 1594, 10833, 538, 316, 7251, 3555, 4587, 7578, 39896, 5551, 12984, 3555, 2655, 8315, 316, 13672, 1829, 31439, 28239, 19913, 2288, 10632, 37495, 22653, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 2423, 39184, 460, 4724, 1829, 30544, 8608, 995, 2407, 10632, 5296, 39184, 1422, 17377, 10833, 538, 316, 498, 293, 787, 498, 2423, 39184, 460, 4724, 2288, 12984, 3660, 16070, 30131, 17377, 10833, 538, 41435, 295, 316, 4724, 1829, 3555, 4587, 7578, 6055, 5172, 3224, 32640, 1829, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995], "avg_logprob": -0.35437498658895494, "compression_ratio": 1.75, "no_speech_prob": 0.0, "words": [{"start": 2146.8, "end": 2147.3, "word": "إن", "probability": 0.5020751953125}, {"start": 2147.3, "end": 2148.36, "word": " الـ", "probability": 0.61962890625}, {"start": 2148.36, "end": 2148.7, "word": " G", "probability": 0.456787109375}, {"start": 2148.7, "end": 2149.56, "word": " بيكون", "probability": 0.2830047607421875}, {"start": 2149.56, "end": 2150.02, "word": " ساوية", "probability": 0.65020751953125}, {"start": 2150.02, "end": 2150.18, "word": " لـ", "probability": 0.532958984375}, {"start": 2150.18, "end": 2150.6, "word": " group", "probability": 0.32666015625}, {"start": 2150.6, "end": 2151.36, "word": " generated", "probability": 0.74951171875}, {"start": 2151.36, "end": 2152.1, "word": " by", "probability": 0.966796875}, {"start": 2152.1, "end": 2152.66, "word": " A", "probability": 0.84375}, {"start": 2152.66, "end": 2155.94, "word": " يبقى", "probability": 0.79205322265625}, {"start": 2155.94, "end": 2156.1, "word": " هي", "probability": 0.171142578125}, {"start": 2156.1, "end": 2156.96, "word": " أثبتنا", "probability": 0.9390625}, {"start": 2156.96, "end": 2157.56, "word": " A", "probability": 0.3759765625}, {"start": 2157.56, "end": 2158.0, "word": " اللي", "probability": 0.8193359375}, {"start": 2158.0, "end": 2158.4, "word": " هو", "probability": 0.95947265625}, {"start": 2158.4, "end": 2159.54, "word": " النظرية", "probability": 0.9525146484375}, {"start": 2159.54, "end": 2159.88, "word": " يعني", "probability": 0.6380615234375}, {"start": 2159.88, "end": 2160.66, "word": " يبقى", "probability": 0.9351806640625}, {"start": 2160.66, "end": 2161.04, "word": " بناء", 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" لمين؟", "probability": 0.5757649739583334}, {"start": 2179.4, "end": 2180.26, "word": " للجروب", "probability": 0.8460693359375}, {"start": 2180.26, "end": 2181.02, "word": " الثاني", "probability": 0.919921875}, {"start": 2181.02, "end": 2182.0, "word": " يبقى", "probability": 0.8934326171875}, {"start": 2182.0, "end": 2182.28, "word": " هذا", "probability": 0.7099609375}, {"start": 2182.28, "end": 2182.84, "word": " النقطة", "probability": 0.9671223958333334}, {"start": 2182.84, "end": 2183.34, "word": " الرابعة", "probability": 0.9703776041666666}, {"start": 2183.34, "end": 2183.76, "word": " بدنا", "probability": 0.6484375}, {"start": 2183.76, "end": 2184.04, "word": " نروح", "probability": 0.9923502604166666}, {"start": 2184.04, "end": 2185.24, "word": " للنقطة", "probability": 0.9188232421875}, {"start": 2185.24, "end": 2186.6, "word": " الخامسة", "probability": 0.988525390625}], "temperature": 1.0}, {"id": 96, "seek": 221375, "start": 2188.11, "end": 2213.75, "text": "النقطة الخامسة بتقول ان ال order ل a بده يسوى ال order ل fi of a لكل ال a اللي موجود في جيه يبقى بقى داجي اقول له assume ان ال order ل a بده يسوى m and ال m is finite and", "tokens": [6027, 1863, 47432, 3660, 33962, 10943, 3794, 3660, 39894, 39648, 16472, 2423, 1668, 5296, 257, 47525, 3224, 7251, 3794, 2407, 7578, 2423, 1668, 5296, 15848, 295, 257, 5296, 28820, 2423, 257, 13672, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 3224, 7251, 3555, 4587, 7578, 4724, 4587, 7578, 11778, 26108, 1829, 1975, 39648, 46740, 6552, 16472, 2423, 1668, 5296, 257, 47525, 3224, 7251, 3794, 2407, 7578, 275, 293, 2423, 275, 307, 19362, 293], "avg_logprob": -0.32684076322268135, "compression_ratio": 1.6979865771812082, "no_speech_prob": 0.0, "words": [{"start": 2188.11, "end": 2188.79, "word": "النقطة", "probability": 0.9091796875}, {"start": 2188.79, "end": 2189.39, "word": " الخامسة", "probability": 0.96484375}, {"start": 2189.39, "end": 2189.93, "word": " بتقول", "probability": 0.88037109375}, {"start": 2189.93, "end": 2190.61, "word": " ان", "probability": 0.477783203125}, {"start": 2190.61, "end": 2190.89, "word": " ال", "probability": 0.6396484375}, {"start": 2190.89, "end": 2191.35, "word": " order", "probability": 0.7197265625}, {"start": 2191.35, "end": 2191.71, "word": " ل", "probability": 0.8154296875}, {"start": 2191.71, "end": 2192.03, "word": " a", "probability": 0.1812744140625}, {"start": 2192.03, "end": 2192.47, "word": " بده", "probability": 0.2928466796875}, {"start": 2192.47, "end": 2192.83, "word": " يسوى", "probability": 0.66033935546875}, {"start": 2192.83, "end": 2192.95, "word": " ال", "probability": 0.72216796875}, {"start": 2192.95, "end": 2193.35, "word": " order", "probability": 0.97265625}, {"start": 2193.35, "end": 2193.61, "word": " ل", "probability": 0.9169921875}, {"start": 2193.61, "end": 2193.91, "word": " fi", "probability": 0.1353759765625}, {"start": 2193.91, "end": 2194.15, "word": " of", "probability": 0.73876953125}, {"start": 2194.15, "end": 2194.35, "word": " a", "probability": 0.962890625}, {"start": 2194.35, "end": 2195.11, "word": " لكل", "probability": 0.828125}, {"start": 2195.11, "end": 2195.39, "word": " ال", "probability": 0.62841796875}, {"start": 2195.39, "end": 2195.65, "word": " a", "probability": 0.88623046875}, {"start": 2195.65, "end": 2195.77, "word": " اللي", "probability": 0.72900390625}, {"start": 2195.77, "end": 2196.19, "word": " موجود", "probability": 0.9715169270833334}, {"start": 2196.19, "end": 2196.75, "word": " في", "probability": 0.55615234375}, {"start": 2196.75, "end": 2197.75, "word": " جيه", "probability": 0.5775553385416666}, {"start": 2197.75, "end": 2198.43, "word": " يبقى", "probability": 0.8341064453125}, {"start": 2198.43, "end": 2198.65, "word": " بقى", "probability": 0.6338704427083334}, {"start": 2198.65, "end": 2199.15, "word": " داجي", "probability": 0.6931966145833334}, {"start": 2199.15, "end": 2199.59, "word": " اقول", "probability": 0.77197265625}, {"start": 2199.59, "end": 2199.87, "word": " له", "probability": 0.171875}, {"start": 2199.87, "end": 2200.61, "word": " assume", "probability": 0.80078125}, {"start": 2200.61, "end": 2202.59, "word": " ان", "probability": 0.8388671875}, {"start": 2202.59, "end": 2202.87, "word": " ال", "probability": 0.99072265625}, {"start": 2202.87, "end": 2203.41, "word": " order", "probability": 0.9833984375}, {"start": 2203.41, "end": 2203.81, "word": " ل", "probability": 0.96826171875}, {"start": 2203.81, "end": 2204.27, "word": " a", "probability": 0.95654296875}, {"start": 2204.27, "end": 2205.37, "word": " بده", "probability": 0.955322265625}, {"start": 2205.37, "end": 2205.93, "word": " يسوى", "probability": 0.927001953125}, {"start": 2205.93, "end": 2206.51, "word": " m", "probability": 0.46630859375}, {"start": 2206.51, "end": 2207.77, "word": " and", "probability": 0.66552734375}, {"start": 2207.77, "end": 2208.73, "word": " ال", "probability": 0.88623046875}, {"start": 2208.73, "end": 2209.21, "word": " m", "probability": 0.92919921875}, {"start": 2209.21, "end": 2210.39, "word": " is", "probability": 0.9072265625}, {"start": 2210.39, "end": 2211.23, "word": " finite", "probability": 0.99169921875}, {"start": 2211.23, "end": 2213.75, "word": " and", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 97, "seek": 223739, "start": 2215.11, "end": 2237.39, "text": "الـ Order لـ Phi of A بدل سوء الـ N مثلا مرة تانية مطلوب أني أثبت أن الـ Order لـ A بدل سوء الـ Order لـ Phi A في حالة إذا كان Phi isomorphism", "tokens": [6027, 39184, 16321, 5296, 39184, 41435, 295, 316, 47525, 1211, 8608, 2407, 38207, 2423, 39184, 426, 50113, 15040, 3714, 25720, 6055, 7649, 10632, 3714, 9566, 1211, 37746, 14739, 1829, 5551, 12984, 3555, 2655, 14739, 2423, 39184, 16321, 5296, 39184, 316, 47525, 1211, 8608, 2407, 38207, 2423, 39184, 16321, 5296, 39184, 41435, 316, 8978, 11331, 6027, 3660, 11933, 15730, 25961, 41435, 307, 32702, 1434], "avg_logprob": -0.3479003836400807, "compression_ratio": 1.5217391304347827, "no_speech_prob": 0.0, "words": [{"start": 2215.11, "end": 2215.61, "word": "الـ", "probability": 0.32110595703125}, {"start": 2215.61, "end": 2216.17, "word": " Order", "probability": 0.18408203125}, {"start": 2216.17, "end": 2217.13, "word": " لـ", "probability": 0.82177734375}, {"start": 2217.13, "end": 2217.71, "word": " Phi", "probability": 0.367431640625}, {"start": 2217.71, "end": 2219.41, "word": " of", "probability": 0.6689453125}, {"start": 2219.41, "end": 2220.01, "word": " A", "probability": 0.82421875}, {"start": 2220.01, "end": 2220.81, "word": " بدل", "probability": 0.22772216796875}, {"start": 2220.81, "end": 2221.35, "word": " سوء", "probability": 0.5677897135416666}, {"start": 2221.35, "end": 2221.61, "word": " الـ", "probability": 0.5467529296875}, {"start": 2221.61, "end": 2221.93, "word": " N", "probability": 0.7080078125}, {"start": 2221.93, "end": 2223.87, "word": " مثلا", "probability": 0.936767578125}, {"start": 2223.87, "end": 2227.89, "word": " مرة", "probability": 0.923828125}, {"start": 2227.89, "end": 2228.33, "word": " تانية", "probability": 0.9632161458333334}, {"start": 2228.33, "end": 2229.59, "word": " مطلوب", "probability": 0.8145751953125}, {"start": 2229.59, "end": 2229.91, "word": " أني", "probability": 0.4007568359375}, {"start": 2229.91, "end": 2230.39, "word": " أثبت", "probability": 0.9422607421875}, {"start": 2230.39, "end": 2230.57, "word": " أن", "probability": 0.736328125}, {"start": 2230.57, "end": 2230.79, "word": " الـ", "probability": 0.52587890625}, {"start": 2230.79, "end": 2231.15, "word": " Order", "probability": 0.830078125}, {"start": 2231.15, "end": 2231.49, "word": " لـ", "probability": 0.65380859375}, {"start": 2231.49, "end": 2231.59, "word": " A", "probability": 0.85791015625}, {"start": 2231.59, "end": 2231.89, "word": " بدل", "probability": 0.928466796875}, {"start": 2231.89, "end": 2232.13, "word": " سوء", "probability": 0.9830729166666666}, {"start": 2232.13, "end": 2232.35, "word": " الـ", "probability": 0.728759765625}, {"start": 2232.35, "end": 2232.69, "word": " Order", "probability": 0.85302734375}, {"start": 2232.69, "end": 2233.25, "word": " لـ", "probability": 0.829345703125}, {"start": 2233.25, "end": 2233.59, "word": " Phi", "probability": 0.7919921875}, {"start": 2233.59, "end": 2234.19, "word": " A", "probability": 0.76611328125}, {"start": 2234.19, "end": 2234.49, "word": " في", "probability": 0.87939453125}, {"start": 2234.49, "end": 2235.11, "word": " حالة", "probability": 0.99658203125}, {"start": 2235.11, "end": 2235.43, "word": " إذا", "probability": 0.932861328125}, {"start": 2235.43, "end": 2235.77, "word": " كان", "probability": 0.99267578125}, {"start": 2235.77, "end": 2236.07, "word": " Phi", "probability": 0.92578125}, {"start": 2236.07, "end": 2237.39, "word": " isomorphism", "probability": 0.702392578125}], "temperature": 1.0}, {"id": 98, "seek": 226717, "start": 2238.33, "end": 2267.17, "text": "يبقى باجي بقول افترض ان ال order ليه يسوى m و ال m finite لان ال order قد يكون infinite يبقى انا بدأ اخد حالة ال finite ال m is finite واخدت ال order لفا يو فيه يسوى ال n ايش بدى اثبت ان ال m بدها ساوى ال n اذا جدت اثبت ان ال m اقل من او يسوى ال n و ال n اقل من او يسوى ال m", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 1975, 5172, 2655, 43042, 16472, 2423, 1668, 32239, 3224, 7251, 3794, 2407, 7578, 275, 4032, 2423, 275, 19362, 5296, 7649, 2423, 1668, 12174, 3215, 7251, 30544, 13785, 7251, 3555, 4587, 7578, 1975, 8315, 47525, 10721, 1975, 9778, 3215, 11331, 6027, 3660, 2423, 19362, 2423, 275, 307, 19362, 4032, 47283, 3215, 2655, 2423, 1668, 5296, 5172, 995, 7251, 2407, 8978, 3224, 7251, 3794, 2407, 7578, 2423, 297, 1975, 1829, 8592, 47525, 7578, 1975, 12984, 3555, 2655, 16472, 2423, 275, 47525, 11296, 8608, 995, 2407, 7578, 2423, 297, 1975, 15730, 10874, 3215, 2655, 1975, 12984, 3555, 2655, 16472, 2423, 275, 1975, 4587, 1211, 9154, 1975, 2407, 7251, 3794, 2407, 7578, 2423, 297, 4032, 2423, 297, 1975, 4587, 1211, 9154, 1975, 2407, 7251, 3794, 2407, 7578, 2423, 275], "avg_logprob": -0.21539351719397085, "compression_ratio": 2.1907216494845363, "no_speech_prob": 0.01085662841796875, "words": [{"start": 2238.33, "end": 2238.85, "word": "يبقى", "probability": 0.664642333984375}, {"start": 2238.85, "end": 2239.23, "word": " باجي", "probability": 0.6341959635416666}, {"start": 2239.23, "end": 2239.55, "word": " بقول", "probability": 0.814208984375}, {"start": 2239.55, "end": 2240.07, "word": " افترض", "probability": 0.913330078125}, {"start": 2240.07, "end": 2240.39, "word": " ان", "probability": 0.6923828125}, {"start": 2240.39, "end": 2240.59, "word": " ال", "probability": 0.86328125}, {"start": 2240.59, "end": 2241.01, "word": " order", "probability": 0.89306640625}, {"start": 2241.01, "end": 2241.39, "word": " ليه", "probability": 0.77734375}, {"start": 2241.39, "end": 2241.89, "word": " يسوى", "probability": 0.822509765625}, {"start": 2241.89, "end": 2242.11, "word": " m", "probability": 0.2607421875}, {"start": 2242.11, "end": 2242.29, "word": " و", "probability": 0.65625}, {"start": 2242.29, "end": 2242.39, "word": " ال", "probability": 0.76171875}, {"start": 2242.39, "end": 2242.65, "word": " m", "probability": 0.73681640625}, {"start": 2242.65, "end": 2243.13, "word": " finite", "probability": 0.91552734375}, {"start": 2243.13, "end": 2243.47, "word": " لان", "probability": 0.6812744140625}, {"start": 2243.47, "end": 2243.59, "word": " ال", "probability": 0.97509765625}, {"start": 2243.59, "end": 2243.81, "word": " order", "probability": 0.970703125}, {"start": 2243.81, "end": 2244.27, "word": " قد", "probability": 0.979248046875}, {"start": 2244.27, "end": 2245.03, "word": " يكون", "probability": 0.97314453125}, {"start": 2245.03, "end": 2245.97, "word": " infinite", "probability": 0.6484375}, {"start": 2245.97, "end": 2247.13, "word": " يبقى", "probability": 0.904052734375}, {"start": 2247.13, "end": 2247.37, "word": " انا", "probability": 0.87451171875}, {"start": 2247.37, "end": 2247.67, "word": " بدأ", "probability": 0.5748291015625}, {"start": 2247.67, "end": 2247.91, "word": " اخد", "probability": 0.7999674479166666}, {"start": 2247.91, "end": 2248.53, "word": " حالة", "probability": 0.99169921875}, {"start": 2248.53, "end": 2248.77, "word": " ال", "probability": 0.80615234375}, {"start": 2248.77, "end": 2249.27, "word": " finite", "probability": 0.98486328125}, {"start": 2249.27, "end": 2250.17, "word": " ال", "probability": 0.939453125}, {"start": 2250.17, "end": 2250.51, "word": " m", "probability": 0.86474609375}, {"start": 2250.51, "end": 2250.85, "word": " is", "probability": 0.7626953125}, {"start": 2250.85, "end": 2251.53, "word": " finite", "probability": 0.98876953125}, {"start": 2251.53, "end": 2252.29, "word": " واخدت", "probability": 0.90966796875}, {"start": 2252.29, "end": 2252.45, "word": " ال", "probability": 0.98974609375}, {"start": 2252.45, "end": 2252.79, "word": " order", "probability": 0.96826171875}, {"start": 2252.79, "end": 2253.25, "word": " لفا", "probability": 0.5423990885416666}, {"start": 2253.25, "end": 2253.49, "word": " يو", "probability": 0.546142578125}, {"start": 2253.49, "end": 2253.67, "word": " فيه", "probability": 0.809326171875}, {"start": 2253.67, "end": 2254.41, "word": " يسوى", "probability": 0.9178466796875}, {"start": 2254.41, "end": 2254.57, "word": " ال", "probability": 0.93701171875}, {"start": 2254.57, "end": 2254.75, "word": " n", "probability": 0.744140625}, {"start": 2254.75, "end": 2255.01, "word": " ايش", "probability": 0.7596028645833334}, {"start": 2255.01, "end": 2255.29, "word": " بدى", "probability": 0.6650390625}, {"start": 2255.29, "end": 2255.91, "word": " اثبت", "probability": 0.901611328125}, {"start": 2255.91, "end": 2257.01, "word": " ان", "probability": 0.900390625}, {"start": 2257.01, "end": 2257.33, "word": " ال", "probability": 0.9697265625}, {"start": 2257.33, "end": 2257.59, "word": " m", "probability": 0.9541015625}, {"start": 2257.59, "end": 2257.95, "word": " بدها", "probability": 0.76513671875}, {"start": 2257.95, "end": 2258.71, "word": " ساوى", "probability": 0.697509765625}, {"start": 2258.71, "end": 2258.95, "word": " ال", "probability": 0.96875}, {"start": 2258.95, "end": 2259.41, "word": " n", "probability": 0.95068359375}, {"start": 2259.41, "end": 2260.03, "word": " اذا", "probability": 0.9140625}, {"start": 2260.03, "end": 2260.43, "word": " جدت", "probability": 0.8811848958333334}, {"start": 2260.43, "end": 2261.03, "word": " اثبت", "probability": 0.960693359375}, {"start": 2261.03, "end": 2261.75, "word": " ان", "probability": 0.9306640625}, {"start": 2261.75, "end": 2262.01, "word": " ال", "probability": 0.98046875}, {"start": 2262.01, "end": 2262.35, "word": " m", "probability": 0.978515625}, {"start": 2262.35, "end": 2263.09, "word": " اقل", "probability": 0.8572591145833334}, {"start": 2263.09, "end": 2263.35, "word": " من", "probability": 0.98486328125}, {"start": 2263.35, "end": 2263.63, "word": " او", "probability": 0.811279296875}, {"start": 2263.63, "end": 2264.19, "word": " يسوى", "probability": 0.9576416015625}, {"start": 2264.19, "end": 2264.37, "word": " ال", "probability": 0.97412109375}, {"start": 2264.37, "end": 2264.63, "word": " n", "probability": 0.75341796875}, {"start": 2264.63, "end": 2264.85, "word": " و", "probability": 0.78173828125}, {"start": 2264.85, "end": 2265.09, "word": " ال", "probability": 0.96875}, {"start": 2265.09, "end": 2265.37, "word": " n", "probability": 0.7294921875}, {"start": 2265.37, "end": 2266.01, "word": " اقل", "probability": 0.9715169270833334}, {"start": 2266.01, "end": 2266.21, "word": " من", "probability": 0.99462890625}, {"start": 2266.21, "end": 2266.45, "word": " او", "probability": 0.947021484375}, {"start": 2266.45, "end": 2266.91, "word": " يسوى", "probability": 0.97998046875}, {"start": 2266.91, "end": 2267.01, "word": " ال", "probability": 0.97216796875}, {"start": 2267.01, "end": 2267.17, "word": " m", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 99, "seek": 229323, "start": 2268.42, "end": 2293.24, "text": "اريكل بلغة مبادئ الرياضية كويس بأجي بقوله consider خدلي الـPhi of A كله اسم يساوي هذا عبارة عن Phi of A M من أين جبت المعلومة هذه؟", "tokens": [9640, 1829, 28820, 4724, 1211, 17082, 3660, 3714, 3555, 18513, 19986, 2423, 16572, 46958, 10632, 9122, 45865, 3794, 4724, 10721, 7435, 1829, 4724, 39648, 3224, 1949, 16490, 3215, 20292, 2423, 39184, 47, 4954, 295, 316, 28242, 3224, 24525, 2304, 7251, 3794, 995, 45865, 23758, 6225, 3555, 9640, 3660, 18871, 41435, 295, 316, 376, 9154, 5551, 9957, 10874, 3555, 2655, 9673, 30241, 20498, 3660, 29538, 22807], "avg_logprob": -0.3077651515151515, "compression_ratio": 1.33125, "no_speech_prob": 0.0, "words": [{"start": 2268.42, "end": 2269.48, "word": "اريكل", "probability": 0.6053059895833334}, {"start": 2269.48, "end": 2270.34, "word": " بلغة", "probability": 0.84393310546875}, {"start": 2270.34, "end": 2271.0, "word": " مبادئ", 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"temperature": 1.0}, {"id": 102, "seek": 237862, "start": 2350.18, "end": 2378.62, "text": "يبقى ال N أقل من M لإن ال N أصغر عدد صحيح موجه بارفع أسل وبيعطينا ال identity يبقى هنا هذا بده يعطينا إن ال N أقل من أو يساوي ال M وهذا اعتبر هالي هنا Star أغششك أكتر؟ لو كان عندك ال order لإيه هو N", "tokens": [1829, 3555, 4587, 7578, 2423, 426, 5551, 4587, 1211, 9154, 376, 5296, 28814, 1863, 2423, 426, 5551, 9381, 17082, 2288, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3224, 4724, 9640, 5172, 3615, 5551, 3794, 1211, 4032, 21292, 3615, 9566, 1829, 8315, 2423, 6575, 7251, 3555, 4587, 7578, 34105, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 36145, 2423, 426, 5551, 4587, 1211, 9154, 34051, 7251, 3794, 995, 45865, 2423, 376, 37037, 15730, 1975, 34268, 26890, 8032, 6027, 1829, 34105, 5705, 5551, 17082, 8592, 8592, 4117, 5551, 4117, 2655, 2288, 22807, 45164, 25961, 43242, 4117, 2423, 1668, 5296, 28814, 1829, 3224, 31439, 426], "avg_logprob": -0.2220552946225955, "compression_ratio": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ydybodWcOkM_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ydybodWcOkM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e2b33b63bfa33c17b9133c92f039a1d08a6d52a5
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ydybodWcOkM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4923, "start": 21.45, "end": 49.23, "text": "بسم الله الرحمن الرحيم بنتابع الآن حل الأسئلة على هذا الموضوع بعد انقطاع الكهرباء لمدة نصف ساعة فبنواصل عملية التصوير مع حل المسائل السؤال بيقول ايه show that show that ان ال order lay in is even", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 44945, 2655, 16758, 3615, 6024, 48506, 11331, 1211, 16247, 3794, 19986, 37977, 15844, 23758, 9673, 2407, 11242, 45367, 39182, 16472, 47432, 45761, 33251, 3224, 25513, 16606, 32767, 41891, 8717, 9381, 5172, 8608, 995, 27884, 6156, 3555, 1863, 2407, 33546, 1211, 6225, 42213, 10632, 16712, 9381, 2407, 13546, 20449, 11331, 1211, 9673, 3794, 16373, 1211, 21136, 33604, 6027, 4724, 1829, 39648, 1975, 1829, 3224, 855, 300, 855, 300, 16472, 2423, 1668, 2360, 294, 307, 754], "avg_logprob": -0.11337425293666976, "compression_ratio": 1.61, "no_speech_prob": 0.0, "words": [{"start": 21.45, "end": 21.77, "word": "بسم", "probability": 0.895751953125}, 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"probability": 0.970703125}, {"start": 147.77, "end": 148.15, "word": " الو", "probability": 0.86376953125}, {"start": 148.15, "end": 148.63, "word": " يساو", "probability": 0.9794921875}, {"start": 148.63, "end": 149.17, "word": " اتنين", "probability": 0.9891357421875}, {"start": 149.17, "end": 150.17, "word": " بمعنى", "probability": 0.7681640625}, {"start": 150.17, "end": 150.73, "word": " ان", "probability": 0.91162109375}, {"start": 150.73, "end": 151.09, "word": " هذا", "probability": 0.61328125}, {"start": 151.09, "end": 151.25, "word": " ال", "probability": 0.986328125}, {"start": 151.25, "end": 151.57, "word": " element", "probability": 0.97998046875}, {"start": 151.57, "end": 151.93, "word": " لو", "probability": 0.86962890625}, {"start": 151.93, "end": 152.61, "word": " ربعته", "probability": 0.9659423828125}, {"start": 152.61, "end": 153.15, "word": " بيطلع", "probability": 0.753125}, {"start": 153.15, "end": 153.25, "word": " ال", "probability": 0.9775390625}, {"start": 153.25, "end": 153.81, "word": " identity", "probability": 0.8876953125}, {"start": 153.81, "end": 154.13, "word": " اللي", "probability": 0.873291015625}, {"start": 154.13, "end": 154.37, "word": " هو", "probability": 0.98779296875}, {"start": 154.37, "end": 155.01, "word": " واحد", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 7, "seek": 17954, "start": 155.82, "end": 179.54, "text": "الان ناقص واحد تعالى نشوف الان ناقص واحد الكلام يقوله صح ولا غلط الان انا باجي للحلقة التالية يبقى فده يقوله solution احنا عندنا ال M ناقص واحد كل هذا ال element belongs to UM", "tokens": [6027, 7649, 8717, 995, 4587, 9381, 36764, 24401, 6055, 3615, 6027, 7578, 8717, 8592, 38688, 2423, 7649, 8717, 995, 4587, 9381, 36764, 24401, 2423, 28820, 10943, 7251, 39648, 3224, 20328, 5016, 49429, 32771, 1211, 9566, 2423, 7649, 1975, 8315, 4724, 26108, 1829, 24976, 5016, 1211, 28671, 16712, 6027, 10632, 7251, 3555, 4587, 7578, 6156, 3215, 3224, 7251, 39648, 3224, 3827, 1975, 5016, 8315, 43242, 8315, 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"text": "طيب ماشي كلامك صح اللي حكيته لكن احنا بنجيبه بطريقة تناسب هذا الشبتر اللي هو ال order لل element بيقسم ال order لل group صحيح طيب الان بدي اشوف اكم عنصر هنا موجود في هذا ال intersection", "tokens": [9566, 1829, 3555, 3714, 33599, 1829, 28242, 10943, 4117, 20328, 5016, 13672, 1829, 11331, 4117, 36081, 3224, 44381, 1975, 5016, 8315, 44945, 7435, 1829, 3555, 3224, 4724, 9566, 16572, 28671, 6055, 8315, 35457, 23758, 25124, 3555, 2655, 2288, 13672, 1829, 31439, 2423, 1668, 24976, 4478, 4724, 1829, 4587, 38251, 2423, 1668, 24976, 1594, 20328, 5016, 1829, 5016, 23032, 1829, 3555, 2423, 7649, 4724, 16254, 1975, 8592, 38688, 1975, 24793, 18871, 9381, 2288, 34105, 3714, 29245, 23328, 8978, 23758, 2423, 15236], "avg_logprob": -0.18528164168934763, "compression_ratio": 1.5625, "no_speech_prob": 0.0, "words": [{"start": 454.9, "end": 455.38, "word": "طيب", "probability": 0.6632486979166666}, {"start": 455.38, "end": 456.32, "word": " ماشي", "probability": 0.6855875651041666}, {"start": 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موجود في H و لازم يكون موجود وين؟ في K يعني ال order تبعه بدي يقسم ل 12 و ال order تبعه بدي يقسم ل 35 يبقى انا لو جيت للحلقة التالية و روحت قلت له the divisors of 12R", "tokens": [2304, 8592, 7649, 7251, 30544, 18863, 1863, 9381, 2288, 3714, 29245, 23328, 8978, 2423, 15236, 37495, 22653, 18863, 1863, 9381, 2288, 13672, 1829, 5296, 31377, 2304, 7251, 30544, 3714, 29245, 23328, 8978, 389, 4032, 5296, 31377, 2304, 7251, 30544, 3714, 29245, 23328, 4032, 9957, 22807, 8978, 591, 37495, 22653, 2423, 1668, 6055, 3555, 3615, 3224, 4724, 16254, 7251, 4587, 38251, 5296, 2272, 4032, 2423, 1668, 6055, 3555, 3615, 3224, 4724, 16254, 7251, 4587, 38251, 5296, 6976, 7251, 3555, 4587, 7578, 1975, 8315, 45164, 10874, 36081, 24976, 5016, 1211, 28671, 16712, 6027, 10632, 4032, 12602, 2407, 33753, 12174, 1211, 2655, 46740, 264, 25974, 830, 295, 2272, 49], "avg_logprob": -0.15216121606737654, "compression_ratio": 1.838235294117647, "no_speech_prob": 0.0, "words": [{"start": 474.25, "end": 474.81, "word": 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موجود", "probability": 0.96484375}, {"start": 478.63, "end": 478.83, "word": " في", "probability": 0.97119140625}, {"start": 478.83, "end": 479.29, "word": " H", "probability": 0.66064453125}, {"start": 479.29, "end": 479.83, "word": " و", "probability": 0.81103515625}, {"start": 479.83, "end": 480.19, "word": " لازم", "probability": 0.8458658854166666}, {"start": 480.19, "end": 480.41, "word": " يكون", "probability": 0.98681640625}, {"start": 480.41, "end": 480.81, "word": " موجود", "probability": 0.9724934895833334}, {"start": 480.81, "end": 481.65, "word": " وين؟", "probability": 0.633056640625}, {"start": 481.65, "end": 481.81, "word": " في", "probability": 0.8369140625}, {"start": 481.81, "end": 482.21, "word": " K", "probability": 0.9384765625}, {"start": 482.21, "end": 483.01, "word": " يعني", "probability": 0.928955078125}, {"start": 483.01, "end": 483.23, "word": " ال", "probability": 0.89013671875}, {"start": 483.23, "end": 483.67, "word": " order", "probability": 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divisors", "probability": 0.9716796875}, {"start": 497.27, "end": 499.75, "word": " of", "probability": 0.9697265625}, {"start": 499.75, "end": 501.95, "word": " 12R", "probability": 0.786865234375}], "temperature": 1.0}, {"id": 21, "seek": 52551, "start": 502.87, "end": 525.51, "text": "الواحد والاتنين والتلاتة والاربع والست واطمعاش بدي اجيب ال divisors كمان of الخمسة وتلاتين are واحد وخمسة وسبعة وخمسة وتلاتين في غيرهم؟", "tokens": [6027, 14407, 24401, 16070, 9307, 1863, 9957, 16070, 2655, 1211, 9307, 3660, 16070, 9640, 3555, 3615, 16070, 14851, 4032, 41193, 2304, 3615, 33599, 4724, 16254, 1975, 7435, 1829, 3555, 2423, 25974, 830, 9122, 2304, 7649, 295, 33962, 2304, 3794, 3660, 4032, 2655, 1211, 9307, 9957, 366, 36764, 24401, 4032, 9778, 2304, 3794, 3660, 4032, 35457, 27884, 4032, 9778, 2304, 3794, 3660, 4032, 2655, 1211, 9307, 9957, 8978, 32771, 13546, 16095, 22807], "avg_logprob": -0.20713975259827244, "compression_ratio": 1.6857142857142857, "no_speech_prob": 0.0, "words": 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{"start": 514.03, "end": 515.45, "word": " الخمسة", "probability": 0.942138671875}, {"start": 515.45, "end": 516.59, "word": " وتلاتين", "probability": 0.766162109375}, {"start": 516.59, "end": 517.39, "word": " are", "probability": 0.346435546875}, {"start": 517.39, "end": 520.11, "word": " واحد", "probability": 0.9267578125}, {"start": 520.11, "end": 521.59, "word": " وخمسة", "probability": 0.985546875}, {"start": 521.59, "end": 522.71, "word": " وسبعة", "probability": 0.9700520833333334}, {"start": 522.71, "end": 523.83, "word": " وخمسة", "probability": 0.9869140625}, {"start": 523.83, "end": 524.43, "word": " وتلاتين", "probability": 0.91298828125}, {"start": 524.43, "end": 524.61, "word": " في", "probability": 0.37353515625}, {"start": 524.61, "end": 525.51, "word": " غيرهم؟", "probability": 0.905029296875}], "temperature": 1.0}, {"id": 22, "seek": 55308, "start": 525.94, "end": 553.08, "text": "طيب الان العنصر مشان يكون في ال intersection في كل منها في التنتين إذا في كل منها يعني 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بده يساوي bk one inverse يعني k one inverse b inverse لإنه مجليش قبيل يعني طب سيب هالمعلومة هذه ع الشجة و تعالي .. و تعالي نشوف أشي اللي بدنا احنا بدنا نثبت ان h هذه subset من k", "tokens": [1829, 3555, 4587, 7578, 34105, 45164, 5551, 9778, 3215, 2655, 2423, 257, 17340, 47525, 3224, 7251, 3794, 995, 45865, 2423, 272, 74, 4386, 47525, 3224, 7251, 3794, 995, 45865, 272, 74, 472, 17340, 37495, 22653, 350, 472, 17340, 272, 17340, 5296, 28814, 1863, 3224, 3714, 7435, 20292, 8592, 12174, 21292, 1211, 37495, 22653, 23032, 3555, 8608, 1829, 3555, 8032, 45340, 30241, 20498, 3660, 29538, 6225, 25124, 7435, 3660, 4032, 37279, 6027, 1829, 4386, 4032, 37279, 6027, 1829, 8717, 8592, 38688, 5551, 8592, 1829, 13672, 1829, 47525, 8315, 1975, 5016, 8315, 47525, 8315, 8717, 12984, 3555, 2655, 16472, 276, 29538, 25993, 9154, 350], "avg_logprob": -0.3328276675881691, "compression_ratio": 1.7537688442211055, "no_speech_prob": 0.0, "words": [{"start": 869.69, "end": 870.53, "word": "يبقى", "probability": 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بتابع ال HNG بده ساوي ال index بتابع ال KNG مضروبا في ال index بتابع ال HNK", "tokens": [7649, 2423, 8186, 39894, 16758, 3615, 2423, 389, 30237, 47525, 3224, 8608, 995, 45865, 2423, 8186, 39894, 16758, 3615, 2423, 26967, 38, 3714, 11242, 32887, 3555, 995, 8978, 2423, 8186, 39894, 16758, 3615, 2423, 389, 45, 42], "avg_logprob": -0.3009868295569169, "compression_ratio": 1.6794871794871795, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1192.22, "end": 1193.0, "word": "ان", "probability": 0.0712890625}, {"start": 1193.0, "end": 1193.98, "word": " ال", "probability": 0.431396484375}, {"start": 1193.98, "end": 1194.82, "word": " index", "probability": 0.70361328125}, {"start": 1194.82, "end": 1196.22, "word": " بتابع", "probability": 0.7786458333333334}, {"start": 1196.22, "end": 1196.42, "word": " ال", "probability": 0.68701171875}, {"start": 1196.42, "end": 1198.26, "word": " HNG", "probability": 0.51422119140625}, {"start": 1198.26, "end": 1199.5, "word": " بده", 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0.95361328125}, {"start": 1234.87, "end": 1235.57, "word": " index", "probability": 0.91162109375}, {"start": 1235.57, "end": 1236.89, "word": " بتابع", "probability": 0.8037109375}, {"start": 1236.89, "end": 1237.47, "word": " ال", "probability": 0.6484375}, {"start": 1237.47, "end": 1237.97, "word": " K", "probability": 0.634765625}, {"start": 1237.97, "end": 1238.31, "word": " في", "probability": 0.8818359375}, {"start": 1238.31, "end": 1238.73, "word": " G", "probability": 0.91845703125}, {"start": 1238.73, "end": 1239.43, "word": " في", "probability": 0.65478515625}, {"start": 1239.43, "end": 1239.67, "word": " ال", "probability": 0.908203125}, {"start": 1239.67, "end": 1240.33, "word": " index", "probability": 0.95068359375}, {"start": 1240.33, "end": 1241.33, "word": " بتابع", "probability": 0.9729817708333334}, {"start": 1241.33, "end": 1241.51, "word": " ال", "probability": 0.95849609375}, {"start": 1241.51, "end": 1242.03, "word": " H", "probability": 0.9365234375}, {"start": 1242.03, "end": 1242.37, "word": " في", "probability": 0.9873046875}, {"start": 1242.37, "end": 1242.89, "word": " وين", "probability": 0.7086181640625}, {"start": 1242.89, "end": 1243.43, "word": " في", "probability": 0.94384765625}, {"start": 1243.43, "end": 1243.89, "word": " K", "probability": 0.88623046875}, {"start": 1243.89, "end": 1244.51, "word": " بالشكل", "probability": 0.9641927083333334}, {"start": 1244.51, "end": 1244.69, "word": " اللي", "probability": 0.984130859375}, {"start": 1244.69, "end": 1245.03, "word": " عندنا", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 52, "seek": 127172, "start": 1245.96, "end": 1271.72, "text": "حسب تعريف ال index هذا كم بيساوي ال order تبع ال G على ال order تبع ال K هذا ال order بتبع ال G على ال order بتبع ال K مضروب في هذا بنفس الطريقة ال order بتبع ال K على ال order بتبع ال H ال order هذا أرقام real number", "tokens": [5016, 35457, 37279, 16572, 5172, 2423, 8186, 23758, 9122, 2304, 4724, 1829, 3794, 995, 45865, 2423, 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"word": " مضروب", "probability": 0.907958984375}, {"start": 1261.72, "end": 1261.94, "word": " في", "probability": 0.95068359375}, {"start": 1261.94, "end": 1262.74, "word": " هذا", "probability": 0.578125}, {"start": 1262.74, "end": 1263.26, "word": " بنفس", "probability": 0.958984375}, {"start": 1263.26, "end": 1263.94, "word": " الطريقة", "probability": 0.9855143229166666}, {"start": 1263.94, "end": 1264.14, "word": " ال", "probability": 0.873046875}, {"start": 1264.14, "end": 1264.66, "word": " order", "probability": 0.97119140625}, {"start": 1264.66, "end": 1265.44, "word": " بتبع", "probability": 0.9640299479166666}, {"start": 1265.44, "end": 1265.72, "word": " ال", "probability": 0.8828125}, {"start": 1265.72, "end": 1266.1, "word": " K", "probability": 0.9443359375}, {"start": 1266.1, "end": 1266.9, "word": " على", "probability": 0.84814453125}, {"start": 1266.9, "end": 1267.26, "word": " ال", "probability": 0.955078125}, {"start": 1267.26, "end": 1267.76, "word": " order", "probability": 0.9580078125}, {"start": 1267.76, "end": 1268.42, "word": " بتبع", "probability": 0.97021484375}, {"start": 1268.42, "end": 1268.56, "word": " ال", "probability": 0.98779296875}, {"start": 1268.56, "end": 1268.94, "word": " H", "probability": 0.96240234375}, {"start": 1268.94, "end": 1269.78, "word": " ال", "probability": 0.93310546875}, {"start": 1269.78, "end": 1270.12, "word": " order", "probability": 0.9755859375}, {"start": 1270.12, "end": 1270.4, "word": " هذا", "probability": 0.41259765625}, {"start": 1270.4, "end": 1270.96, "word": " أرقام", "probability": 0.8675537109375}, {"start": 1270.96, "end": 1271.2, "word": " real", "probability": 0.673828125}, {"start": 1271.2, "end": 1271.72, "word": " number", "probability": 0.73046875}], "temperature": 1.0}, {"id": 53, "seek": 129645, "start": 1272.07, "end": 1296.45, "text": "أو positive real number يبقى هذا مع هذا الله يسهل عليه يبقى بيظل ال order لل G على ال order لمين لل H ال order لل G على ال R هو تعريف ال index اللي احنا قاعدين ندور عليه يبقى هذا الكلام بده يساوي ال index تبع ال H in G وهو المطلوب", "tokens": [10721, 2407, 3353, 957, 1230, 7251, 3555, 4587, 7578, 23758, 20449, 23758, 21984, 7251, 3794, 3224, 1211, 47356, 7251, 3555, 4587, 7578, 4724, 1829, 19913, 1211, 2423, 1668, 24976, 460, 15844, 2423, 1668, 32767, 9957, 24976, 389, 2423, 1668, 24976, 460, 15844, 2423, 497, 31439, 37279, 16572, 5172, 2423, 8186, 13672, 1829, 1975, 5016, 8315, 12174, 995, 22488, 9957, 8717, 3215, 13063, 47356, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 2423, 8186, 6055, 3555, 3615, 2423, 389, 294, 460, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.18968413786221577, "compression_ratio": 1.8214285714285714, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1272.07, "end": 1272.31, "word": "أو", "probability": 0.528472900390625}, {"start": 1272.31, "end": 1272.67, "word": " positive", "probability": 0.7626953125}, {"start": 1272.67, "end": 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G abelian و ال N بيه positive integer و relative ل prime لل order بتابع ال G يبقى سؤال اربعين أسيوم افترض ان ال order ل G بده يساوي ال M تمام؟", "tokens": [3555, 16095, 13412, 2288, 9640, 1829, 2423, 39184, 460, 410, 338, 952, 4032, 2423, 426, 4724, 1829, 3224, 3353, 24922, 4032, 4972, 5296, 5835, 24976, 1668, 39894, 16758, 3615, 2423, 460, 7251, 3555, 4587, 7578, 8608, 33604, 6027, 1975, 25513, 3615, 9957, 5551, 3794, 1829, 20498, 1975, 5172, 2655, 43042, 16472, 2423, 1668, 5296, 460, 47525, 3224, 7251, 3794, 995, 45865, 2423, 376, 46811, 10943, 22807], "avg_logprob": -0.29244402985074625, "compression_ratio": 1.349112426035503, "no_speech_prob": 0.0, "words": [{"start": 1308.96, "end": 1309.54, "word": "بهم", "probability": 0.682861328125}, {"start": 1309.54, "end": 1310.38, "word": " شراري", "probability": 0.47918701171875}, {"start": 1310.38, "end": 1310.78, "word": " الـ", "probability": 0.609619140625}, {"start": 1310.78, "end": 1311.14, "word": " G", "probability": 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0.8465169270833334}, {"start": 1578.49, "end": 1578.61, "word": " دغري", "probability": 0.9158528645833334}, {"start": 1578.61, "end": 1578.89, "word": " لكن", "probability": 0.8173828125}, {"start": 1578.89, "end": 1579.27, "word": " قص", "probability": 0.70166015625}, {"start": 1579.27, "end": 1579.57, "word": " ان", "probability": 0.56494140625}, {"start": 1579.57, "end": 1579.93, "word": " الله", "probability": 0.95263671875}, {"start": 1579.93, "end": 1580.45, "word": " أعلم", "probability": 0.8507486979166666}, {"start": 1580.45, "end": 1581.41, "word": " يبقى", "probability": 0.9791259765625}, {"start": 1581.41, "end": 1581.61, "word": " هنا", "probability": 0.97412109375}, {"start": 1581.61, "end": 1581.97, "word": " بصير", "probability": 0.7289225260416666}, {"start": 1581.97, "end": 1582.57, "word": " العملية", "probability": 0.9768880208333334}, {"start": 1582.57, "end": 1583.33, "word": " شاقة", "probability": 0.9720052083333334}, {"start": 1583.33, "end": 1583.99, "word": " شوية", "probability": 0.80126953125}, {"start": 1583.99, "end": 1584.61, "word": " على", "probability": 0.875}, {"start": 1584.61, "end": 1584.79, "word": " اي", "probability": 0.783447265625}, {"start": 1584.79, "end": 1585.21, "word": " حال", "probability": 0.99853515625}, {"start": 1585.21, "end": 1586.17, "word": " ضلت", "probability": 0.4972330729166667}, {"start": 1586.17, "end": 1586.57, "word": " الحكاية", "probability": 0.81072998046875}, {"start": 1586.57, "end": 1586.77, "word": " on", "probability": 0.268310546875}, {"start": 1586.77, "end": 1586.89, "word": " two", "probability": 0.5341796875}, {"start": 1586.89, "end": 1587.29, "word": " سهلة", "probability": 0.9632161458333334}, {"start": 1587.29, "end": 1587.59, "word": " جدا", "probability": 0.99072265625}, {"start": 1587.59, "end": 1587.99, "word": " مدام", "probability": 0.8211263020833334}, {"start": 1587.99, "end": 1588.23, "word": " هي", "probability": 0.93017578125}, {"start": 1588.23, "end": 1588.65, "word": " ال", "probability": 0.90576171875}, {"start": 1588.65, "end": 1588.85, "word": " G", "probability": 0.59228515625}, {"start": 1588.85, "end": 1589.35, "word": " finite", "probability": 0.8837890625}, {"start": 1589.35, "end": 1590.27, "word": " one", "probability": 0.83740234375}, {"start": 1590.27, "end": 1590.53, "word": " to", "probability": 0.9716796875}, {"start": 1590.53, "end": 1590.71, "word": " one", "probability": 0.9541015625}, {"start": 1590.71, "end": 1591.19, "word": " يبقى", "probability": 0.9896240234375}, {"start": 1591.19, "end": 1591.53, "word": " on", "probability": 0.88232421875}, {"start": 1591.53, "end": 1591.67, "word": " two", "probability": 0.94677734375}, {"start": 1591.67, "end": 1592.39, "word": " طبيعي", "probability": 0.9473876953125}, {"start": 1592.39, "end": 1593.13, "word": " خاصية", "probability": 0.85302734375}, {"start": 1593.13, "end": 1593.25, "word": " ال", "probability": 0.454345703125}, {"start": 1593.25, "end": 1593.93, "word": " isomorphism", "probability": 0.7972005208333334}, {"start": 1593.93, "end": 1594.27, "word": " phi", "probability": 0.2247314453125}, {"start": 1594.27, "end": 1594.63, "word": " of", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 68, "seek": 160313, "start": 1594.75, "end": 1603.13, "text": "اب لكل N يسوى ANBN يبقى Phi of A في Phi of B وانتهينا من القصة هذه", "tokens": [16758, 5296, 28820, 426, 7251, 3794, 2407, 7578, 5252, 32006, 7251, 3555, 4587, 7578, 41435, 295, 316, 8978, 41435, 295, 363, 4032, 7649, 47395, 1829, 8315, 9154, 25062, 9381, 3660, 29538], "avg_logprob": -0.36938475258648396, "compression_ratio": 1.125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1594.75, "end": 1595.07, "word": "اب", "probability": 0.03863525390625}, {"start": 1595.07, "end": 1595.59, "word": " لكل", "probability": 0.6368408203125}, {"start": 1595.59, "end": 1595.89, "word": " N", "probability": 0.2362060546875}, {"start": 1595.89, "end": 1596.73, "word": " يسوى", "probability": 0.7139892578125}, {"start": 1596.73, "end": 1597.83, "word": " ANBN", "probability": 0.50537109375}, {"start": 1597.83, "end": 1598.31, "word": " يبقى", "probability": 0.9600830078125}, {"start": 1598.31, "end": 1598.53, "word": " Phi", "probability": 0.30322265625}, {"start": 1598.53, "end": 1598.77, "word": " of", "probability": 0.78564453125}, {"start": 1598.77, "end": 1599.05, "word": " A", "probability": 0.93310546875}, {"start": 1599.05, "end": 1599.17, "word": " في", "probability": 0.80029296875}, {"start": 1599.17, "end": 1599.57, "word": " Phi", "probability": 0.935546875}, {"start": 1599.57, "end": 1599.89, "word": " of", "probability": 0.97314453125}, {"start": 1599.89, "end": 1600.09, "word": " B", "probability": 0.9892578125}, {"start": 1600.09, "end": 1600.87, "word": " وانتهينا", "probability": 0.9646484375}, {"start": 1600.87, "end": 1601.69, "word": " من", "probability": 0.98388671875}, {"start": 1601.69, "end": 1602.75, "word": " القصة", "probability": 0.7767740885416666}, {"start": 1602.75, "end": 1603.13, "word": " هذه", "probability": 0.8505859375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1604.54525, "duration_after_vad": 1498.962499999998}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bc99f01610cc0891f5a822e52b7f1b1d686ea16f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060_postprocess.srt
@@ -0,0 +1,2000 @@
+1
+00:00:20,700 --> 00:00:26,660
+بسم الله الرحمن الرحيم المرة الماضية كانت المحاضرة
+
+2
+00:00:26,660 --> 00:00:32,010
+discussionو نقشنا الأسئلة المطلوبة و بقى سؤالان
+
+3
+00:00:32,010 --> 00:00:40,070
+سؤال 35 و سؤال 39 سؤال 35 يقول اثبت ان لو كانت جي
+
+4
+00:00:40,070 --> 00:00:45,350
+جروب و عليها خاصية الخاصية بتقول the square of
+
+5
+00:00:45,350 --> 00:00:52,930
+every element is the identity then g is abelian
+
+6
+00:00:52,930 --> 00:01:02,730
+يبقى سؤال 35بقول ما يأتي لو كانت ال G كل العناصر X
+
+7
+00:01:02,730 --> 00:01:10,070
+بحيث ان X تربيع يسوى ال identity بدي أثبت هذا هو
+
+8
+00:01:10,070 --> 00:01:18,370
+المطلوب ان G is abelian هذا هو المطلوب طبعا اذا
+
+9
+00:01:18,370 --> 00:01:25,510
+بيقول لي لو كانت ال group G فيها خاصية هذه الخاصية
+
+10
+00:01:25,860 --> 00:01:31,460
+بتقول انه اي element x لو رفعته للأس اتنين بدي
+
+11
+00:01:31,460 --> 00:01:36,660
+يعطيني ال identity بدي أثبت ان هذه هي abelian
+
+12
+00:01:36,660 --> 00:01:41,440
+group abelian group لو أخدت any two elements فيها
+
+13
+00:01:41,440 --> 00:01:46,520
+معناته ان ال a في b بدي أسوأ بي في a for all a و b
+
+14
+00:01:46,520 --> 00:01:53,080
+اللي belongs to g يبقى لأثبت انه g abelian يبقى
+
+15
+00:01:53,080 --> 00:02:05,010
+هنا fالـ A والـ B موجودة في G و shall shall ذات
+
+16
+00:02:05,010 --> 00:02:11,910
+بدنا نحاول نثبت ان ال A في B بده سوى B في A لكل ال
+
+17
+00:02:11,910 --> 00:02:17,290
+A و B اللي belongs تماما ل G يعني ابقى بقالي بقوله
+
+18
+00:02:17,290 --> 00:02:18,850
+الحل كتالي
+
+19
+00:02:23,490 --> 00:02:28,890
+مطلوب لثبت تحت هذا ال condition أن G أبليان a
+
+20
+00:02:28,890 --> 00:02:34,850
+group فبتروح أخد two elements موجودات في G يبقى لو
+
+21
+00:02:34,850 --> 00:02:41,130
+كان ال A و ال B موجودة في G thenمربع اي واحد فيهم
+
+22
+00:02:41,130 --> 00:02:46,990
+او a star a اللي هي main اللي هي a تربية بده يساوي
+
+23
+00:02:46,990 --> 00:02:52,290
+ال identity and ال b تربية بده يساوي ال identity
+
+24
+00:02:52,290 --> 00:02:57,690
+طبق لمين طبق للمعطيات اللي موجودة عندنا هنا طب
+
+25
+00:02:57,690 --> 00:03:02,690
+خليني اسأل السؤال التالي طب لو كان a في b لكل
+
+26
+00:03:02,690 --> 00:03:07,980
+تربية كده ايش بده يعطينا؟برضه ال identity لإن ال a
+
+27
+00:03:07,980 --> 00:03:11,920
+في b هو element موجود في ال group لإن ال group is
+
+28
+00:03:11,920 --> 00:03:16,040
+closed under the given operation يبقى بناء عليه
+
+29
+00:03:16,040 --> 00:03:21,840
+هذا كمان هيعطينا ال identity element طب الآن لو
+
+30
+00:03:21,840 --> 00:03:29,420
+جيت ال a تربيع هذه أليست هي a في a يعني عند ال a
+
+31
+00:03:29,420 --> 00:03:35,820
+تربيع هذا معناهإن الـ A تربية بي تربية بدي يسوى A
+
+32
+00:03:35,820 --> 00:03:39,520
+بي الكل تربية اللي هو ال identity هذا بيسوى ال
+
+33
+00:03:39,520 --> 00:03:42,180
+identity و هذا بيسوى ال identity و هذا بيسوى ال
+
+34
+00:03:42,180 --> 00:03:47,820
+identity يبقى بناء عليه هذا كله بدي يعطيني ال
+
+35
+00:03:47,820 --> 00:03:54,860
+identity element لكن ال A تربية هذه هي عبارة عن A
+
+36
+00:03:54,860 --> 00:04:01,090
+في A و ال B اللي هي عبارة عن B في Bوالـ AB تربيه
+
+37
+00:04:01,090 --> 00:04:07,710
+اللي هي عبارة عن AB في AB مظبوط اخدنا احنا ال
+
+38
+00:04:07,710 --> 00:04:10,770
+right cancellation law و ال left cancellation law
+
+39
+00:04:10,770 --> 00:04:16,970
+مظبوط يعني معنى هذا الكلام انه ممكن اضرب من جهة
+
+40
+00:04:16,970 --> 00:04:21,630
+الشمال في A inverse و اضرب من جهة اليمين في B
+
+41
+00:04:21,630 --> 00:04:26,730
+inverse و لن تكون هناك اي مشكلة بس بدك ترى الدقة
+
+42
+00:04:26,730 --> 00:04:31,570
+عندما تضرب من جهة الشمالفي ال a inverse يبقى a
+
+43
+00:04:31,570 --> 00:04:38,910
+inverse a a b كمان b بدي اضربها في ال b inverse
+
+44
+00:04:38,910 --> 00:04:43,570
+بدي ساوي زي ما ضربت في ال a inverse من جهة الشمال
+
+45
+00:04:43,570 --> 00:04:49,530
+يبقى بدي اضرب في ال a inverse من جهة الشمال a b a
+
+46
+00:04:49,530 --> 00:04:54,650
+b كمان في ال b inverse من جهة الشمال طيب تمام هذا
+
+47
+00:04:54,650 --> 00:05:00,980
+كدهش بيعطينا ال identityهذا كم يعطينا ال identity
+
+48
+00:05:00,980 --> 00:05:04,260
+وهذا كم يعطينا ال identity وهذا كم يعطينا ال
+
+49
+00:05:04,260 --> 00:05:04,640
+identity وهذا كم يعطينا ال identity وهذا كم يعطينا
+
+50
+00:05:04,640 --> 00:05:05,440
+ال identity وهذا كم يعطينا ال identity وهذا كم
+
+51
+00:05:05,440 --> 00:05:08,080
+يعطينا ال identity وهذا كم يعطينا ال identity وهذا
+
+52
+00:05:08,080 --> 00:05:11,200
+كم يعطينا ال identity وهذا كم يعطينا ال identity
+
+53
+00:05:11,200 --> 00:05:13,740
+وهذا كم يعطينا ال identity وهذا كم يعطينا ال
+
+54
+00:05:13,740 --> 00:05:13,760
+identity وهذا كم يعطينا ال identity وهذا كم يعطينا
+
+55
+00:05:13,760 --> 00:05:14,520
+ال identity وهذا كم يعطينا ال identity وهذا كم
+
+56
+00:05:14,520 --> 00:05:16,880
+كم يعطينا ال identity وهذا كم يعطينا ال identity
+
+57
+00:05:16,880 --> 00:05:18,540
+وهذا كم يعطينا ال identity وهذا كم يعطينا ال
+
+58
+00:05:18,540 --> 00:05:25,360
+identity وهذا كم يعطينا
+
+59
+00:05:25,360 --> 00:05:31,160
+ال identity وهذا كمبـ A شو تفسير كل هذا Abelian
+
+60
+00:05:31,160 --> 00:05:36,580
+طبعا هذا كلام صحي لإن ماخدتش عنصرين محددين بعينهم
+
+61
+00:05:36,580 --> 00:05:41,940
+أو إنا ماخدت any two elements يعني اختياري يبقى
+
+62
+00:05:41,940 --> 00:05:46,780
+هذا معناه صحيح لكل ال A و ال B اللي موجودة في G
+
+63
+00:05:46,780 --> 00:05:55,320
+هذا بدي أقولك إن G is abelian وهو المصمم سؤال تسعة
+
+64
+00:05:55,320 --> 00:05:55,980
+وتلاتين
+
+65
+00:05:58,680 --> 00:06:06,100
+سؤال تسعة وتلاتين بيقول ما يأتي خدلي ال G كل
+
+66
+00:06:06,100 --> 00:06:14,060
+المصفوفات يبقى خدلي G هي عبارة عن كل المصفوفات
+
+67
+00:06:14,060 --> 00:06:22,360
+اللي على الشكل التالي A A Aأيه بحيث الـ A موجود في
+
+68
+00:06:22,360 --> 00:06:27,640
+الـ R Star مظبوط هيك بحيث الـ G موجود و لا موجودة
+
+69
+00:06:27,640 --> 00:06:32,400
+في R A موجودة في R و A لا تساوي Zero يعني A موجودة
+
+70
+00:06:32,400 --> 00:06:37,320
+في R Star يعني لا يمكن أن تساوي Zero سواء قلنا
+
+71
+00:06:37,320 --> 00:06:43,030
+الصيغة هذه أو قلنا أن A موجودة في Rوالـ A لا يساوي
+
+72
+00:06:43,030 --> 00:06:48,450
+0 إذا ممنوع الـ A يساوي الـ 0 يبقى كل المصوفات
+
+73
+00:06:48,450 --> 00:06:52,910
+اللي على الشكل اللي عندنا هذا بيقول يبين الـ G is
+
+74
+00:06:52,910 --> 00:06:57,910
+a group under matrix multiplication X plan Y each
+
+75
+00:06:57,910 --> 00:07:02,710
+element of G has an inverse رغم كذا كذا طيب على أي
+
+76
+00:07:02,710 --> 00:07:08,210
+حالالان هذه مجموعة المصحفات اللي على الشكل هذا
+
+77
+00:07:08,210 --> 00:07:12,870
+يعني اللي جميع العناصر الأربعة في ال two by two
+
+78
+00:07:12,870 --> 00:07:17,650
+matrix are equal1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+79
+00:07:17,650 --> 00:07:19,870
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+80
+00:07:19,870 --> 00:07:23,510
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+81
+00:07:23,510 --> 00:07:25,090
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+82
+00:07:25,090 --> 00:07:29,950
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+83
+00:07:29,950 --> 00:07:30,430
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+84
+00:07:30,430 --> 00:07:31,070
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+85
+00:07:31,070 --> 00:07:32,830
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+86
+00:07:32,830 --> 00:07:39,930
+1 1 1 1
+
+87
+00:07:39,930 --> 00:07:44,210
+1 1 1عبارة عن مجموعة تحت عملية ضرب المصوفات احنا
+
+88
+00:07:44,210 --> 00:07:47,850
+بنعرف ان عملية ضرب المصوفات لأي أنواع المصوفات
+
+89
+00:07:47,850 --> 00:07:52,410
+عبارة عن associative binary operation يعني لو ضرت
+
+90
+00:07:52,410 --> 00:07:56,150
+مصوفتين اتنين في اتنين في بعض بيطلع نفس النظام له
+
+91
+00:07:56,150 --> 00:08:01,350
+اتنين في اتنين غير هيك عملية الضرب عملية ادماجية
+
+92
+00:08:01,350 --> 00:08:05,290
+يبقى باجي بقوله solution و
+
+93
+00:08:09,510 --> 00:08:18,350
+know that لبنعرف ان ال matrix multiplication
+
+94
+00:08:18,350 --> 00:08:23,470
+is
+
+95
+00:08:23,470 --> 00:08:32,990
+an associative binary
+
+96
+00:08:32,990 --> 00:08:33,770
+operation
+
+97
+00:08:41,390 --> 00:08:46,050
+يبقى هذه هي النقطة الأولى بدنا نيجي للنقطة الثانية
+
+98
+00:08:46,050 --> 00:08:53,310
+النقطة الثانية بدنا نثبت ان هذه المصوفات لها عنصر
+
+99
+00:08:53,310 --> 00:08:58,790
+واحدة طبعا كيف عنصر واحدة بحيث هذا العنصر لو ضربته
+
+100
+00:08:58,790 --> 00:09:03,190
+في أي مصوفة بدي يطلع من نفس المصوفة انا شو شكله
+
+101
+00:09:03,190 --> 00:09:08,770
+انا مش عارف لذلك هعطيها رمزو روح اطلع شو شكل هذا
+
+102
+00:09:08,770 --> 00:09:20,890
+الرمز فبجي بقول assume افترض ان ال B بي بي بي is
+
+103
+00:09:20,890 --> 00:09:32,130
+the identity element طبعا يا شباب ال B هنا مالها
+
+104
+00:09:33,180 --> 00:09:37,840
+لاتساوي الـ zero لأن كلها موجودة في الـ R plus
+
+105
+00:09:37,840 --> 00:09:45,040
+افترض ان هذا هو ال identity element ال identity
+
+106
+00:09:45,040 --> 00:09:54,000
+element بي بي بي بي لو ضربته في a a a بيطلع نفس ال
+
+107
+00:09:54,000 --> 00:09:59,920
+element اللي هو a a a بالشكل عنهاضربت من اليمين و
+
+108
+00:09:59,920 --> 00:10:04,080
+الشمال لإتنين are the same لأنه مادام identity
+
+109
+00:10:04,080 --> 00:10:07,180
+element اذا ضربت من اليمين و لا ضربت من الشمال كله
+
+110
+00:10:07,180 --> 00:10:11,980
+سيؤدي إلى نفس النتيجة يبقى هذا ايش بيعطينا هذا
+
+111
+00:10:11,980 --> 00:10:15,600
+بيعطينا مثلا بدي أضرب الصف الأول في العمود الأول
+
+112
+00:10:15,600 --> 00:10:24,720
+يبقى BA و هنا BA يبقى اتنين BA يبقى هذا اتنين BA و
+
+113
+00:10:24,720 --> 00:10:31,450
+هنا اتنين BAتنين بي إيه تنين بي إيه كله بده يساوي
+
+114
+00:10:31,450 --> 00:10:38,410
+ال a في ال a في ال a طبعا عندي مصفتين بيساووا بعض
+
+115
+00:10:38,410 --> 00:10:45,490
+إذا العناصر المتناضرة مالها متساوية يبقى هذا معناه
+
+116
+00:10:45,490 --> 00:10:53,170
+إيه معناته أنه تنين بي إيه بده يساوي ال a itself
+
+117
+00:10:54,340 --> 00:10:59,320
+بنقدر نجسم الطرفين على a نجسم الطرفين على a او بال
+
+118
+00:10:59,320 --> 00:11:03,380
+right cancellation لأن ال a و ال b هدور real
+
+119
+00:11:03,380 --> 00:11:08,500
+numbers بس لا يسووا أصفرة يبقى ال a لا يسووا zero
+
+120
+00:11:08,500 --> 00:11:12,740
+إذا معناه هذا الكلام أنه اتنين بيبدوا يسووا جداش
+
+121
+00:11:12,740 --> 00:11:20,160
+واحد هذا معناه أنه بيسووا نص يبقى أصبح اللي هو ال
+
+122
+00:11:20,160 --> 00:11:21,860
+identity element
+
+123
+00:11:24,530 --> 00:11:36,770
+identity element is نص نص نص نص نص نص
+
+124
+00:11:36,770 --> 00:11:40,070
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+125
+00:11:40,070 --> 00:11:40,490
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+126
+00:11:40,490 --> 00:11:40,610
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+127
+00:11:40,610 --> 00:11:41,790
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+128
+00:11:41,790 --> 00:11:44,930
+نص نص
+
+129
+00:11:47,890 --> 00:11:53,890
+بدي افترض ان عندي مصوفة وهذه المصوفة هي معكوس
+
+130
+00:11:53,890 --> 00:12:02,890
+المصوفة a a a يبقى هنا باجي بقول assume افترض ان c
+
+131
+00:12:02,890 --> 00:12:12,290
+c c c is the inverse element of
+
+132
+00:12:15,130 --> 00:12:23,770
+اللي موجودة في جيل أصلي افترض ان هذا ال element هو
+
+133
+00:12:23,770 --> 00:12:28,290
+المعكوس اذا الحاصل ضربهما سواء من اليمين و الله مش
+
+134
+00:12:28,290 --> 00:12:32,650
+ملش و بده يعطينيالـ identity element اللي هو
+
+135
+00:12:32,650 --> 00:12:40,050
+المصوفة نص نص نص يبقى باجي بقوله إذا ال C C بالشكل
+
+136
+00:12:40,050 --> 00:12:45,370
+اللي عندنا هذا مضروبة في ال A A A كل هذا الكلام
+
+137
+00:12:45,370 --> 00:12:51,870
+بده يساوي نص نص نص طيب
+
+138
+00:12:51,870 --> 00:12:57,390
+هذا الكلام بده يساويالان بدي اضرب المصفات هدول ضرب
+
+139
+00:12:57,390 --> 00:13:08,310
+في بعض يبقى CA و CA ب 2 CA يبقى هنا اتنين CA اتنين
+
+140
+00:13:08,310 --> 00:13:15,890
+CA اتنين CA اتنين CA اتنين CA اتنين CA اتنين CA
+
+141
+00:13:15,890 --> 00:13:21,350
+اتنين CA اتنين CA اتنين CA اتنين CA اتنين CA اتنين
+
+142
+00:13:21,350 --> 00:13:22,250
+CA اتنين CA اتنين CA اتنين CA اتنين CA اتنين CA
+
+143
+00:13:22,250 --> 00:13:24,090
+اتنين CA اتنين CA اتنين CA اتنين CA اتنين CA اتنين
+
+144
+00:13:24,090 --> 00:13:24,390
+CA اتنين CA اتنين CA اتنين CA اتنين CA اتنين CA
+
+145
+00:13:24,390 --> 00:13:26,420
+CA اتنين CA اتنين CA اتنين CAيبقى لو قررنا العناصر
+
+146
+00:13:26,420 --> 00:13:32,480
+المتنظرة في الطرفين بصير عندى اتنين CA بده يسوى
+
+147
+00:13:32,480 --> 00:13:38,480
+قداش مصر والباقي كله بنفس الطريقة انا عندى المجهول
+
+148
+00:13:38,480 --> 00:13:45,980
+مين C يبقى C بده يسوى واحد على أربعة A يبقى باجي
+
+149
+00:13:45,980 --> 00:13:55,600
+بقوله هذا بده يعطينا the inverse ofاللي هو a و a و
+
+150
+00:13:55,600 --> 00:14:05,140
+a is واحد على اربعة a واحد على اربعة a واحد على
+
+151
+00:14:05,140 --> 00:14:11,640
+اربعة a واحد على اربعة a بهذا الشكل هذا هو المعكوس
+
+152
+00:14:11,640 --> 00:14:15,040
+لمهم للمصوفة اللي عندنا
+
+153
+00:14:17,940 --> 00:14:23,620
+إذا صار كل element له معكوس و ال identity موجود و
+
+154
+00:14:23,620 --> 00:14:28,300
+binary أو associative binary operation يبقى تحققت
+
+155
+00:14:28,300 --> 00:14:33,260
+كل الشروط اللي عندنا معناته جهة دمالها group يبقى
+
+156
+00:14:33,260 --> 00:14:39,620
+باجي بقوله thus و هكذا that's it اللي عندنا هذه
+
+157
+00:14:39,620 --> 00:14:46,320
+اللي على الشكل اللي عندنا هذا بحيث انهالـA موجود
+
+158
+00:14:46,320 --> 00:14:55,260
+في الـR*) هذي is a group اللي خاطرة اتناقش هنا
+
+159
+00:14:55,260 --> 00:15:00,560
+وياكوا في هذا السؤال هذا بعض المناقشات البسيطة
+
+160
+00:15:00,560 --> 00:15:05,580
+السؤال الأول هل ال group اللي احنا هذي قايلينها
+
+161
+00:15:05,580 --> 00:15:09,640
+موجودة في ال general linear group of two by two
+
+162
+00:15:09,640 --> 00:15:18,690
+matrices over R؟ مش ممكنيةهذه المحددة لا يساوي 0
+
+163
+00:15:18,690 --> 00:15:23,530
+هل هي في ال special linear group of 2x2 matrices
+
+164
+00:15:23,530 --> 00:15:28,310
+over R؟ لأ لأن هذه المحددة لا يساوي 0
+
+165
+00:15:35,700 --> 00:15:41,900
+إذا المعكوث تبع المصفوف العادية بيختلف عن المعكوث
+
+166
+00:15:41,900 --> 00:15:45,860
+في حالة من؟ في حالة الجروب، مش يعني دايما زي ما هو
+
+167
+00:15:45,860 --> 00:15:49,280
+مطلوع في دماغنا واحد، zero, zero, zero، لا، لا،
+
+168
+00:15:49,280 --> 00:15:52,940
+لا، لا، بتختلف، دلوقت هذا السؤال أنا جبته في إحدى
+
+169
+00:15:52,940 --> 00:15:58,880
+الامتحانات قبل خمستاشر سنة، أه، اللي جيته في كتاب
+
+170
+00:15:58,880 --> 00:16:01,240
+هندي، ماكنش موجود في كتابنا، موجود في الطبعة
+
+171
+00:16:01,240 --> 00:16:05,160
+الجديدة بس، زمان ماكنش موجود في هذه الطبعةلا
+
+172
+00:16:05,160 --> 00:16:10,380
+الأولى ولا التانية ولا حتى التالتة طبعا فلجيت
+
+173
+00:16:10,380 --> 00:16:15,180
+السؤال فكر فيه عجبنت الفكرة فجم جايبه ايه؟ جايبه
+
+174
+00:16:15,180 --> 00:16:19,420
+في الامتحان طبعا ليه؟ عشان انه طالع هيستغرب لأول و
+
+175
+00:16:19,420 --> 00:16:23,000
+هيقولك محدده لا يساوي زير محدده يساوي زير و يبقى
+
+176
+00:16:23,000 --> 00:16:27,220
+مافيش لكن اللي بيقولوا اثبت ان هذه group يعني رصبا
+
+177
+00:16:27,220 --> 00:16:30,360
+عنك بدك تجيب ال identity element او بدك تجيب ال
+
+178
+00:16:30,360 --> 00:16:32,180
+inverse element لكن ال associative binary
+
+179
+00:16:32,180 --> 00:16:35,430
+operation هذه مشهورة على المصففاتو احنا في التنوية
+
+180
+00:16:35,430 --> 00:16:40,190
+قبل ما نجي على الجامعة تمام لحد هنا stop بدنا نروح
+
+181
+00:16:40,190 --> 00:16:46,170
+نكمل محاضرات كما كنا في المحاضرة قبل الماضي في
+
+182
+00:16:46,170 --> 00:16:52,090
+المحاضرة قبل الماضي بدنا بموضوع ال subgroups و قبل
+
+183
+00:16:52,090 --> 00:16:56,450
+ان نبدأ بال subgroups روحنا جيبنا عرفنا ال
+
+184
+00:16:56,450 --> 00:17:01,350
+identity لل group و ال identity لل element اللي في
+
+185
+00:17:01,350 --> 00:17:09,330
+ال group و بعد ذلكروحنا لمين الى ال subgroups الأن
+
+186
+00:17:09,330 --> 00:17:15,470
+بدأ ألخص شفاوي هيك ما درسناه في الشابتر الجديد حتى
+
+187
+00:17:15,470 --> 00:17:22,170
+نكمل عليه معلوماتنا شوف يا سيد في الجزء النظري
+
+188
+00:17:22,170 --> 00:17:27,070
+اللي أخدناه في الشابتر تلاتة هذا ذكرنا ال order لل
+
+189
+00:17:27,070 --> 00:17:32,370
+group وقولنا ال order لل group هو عبارة عن عن ايش؟
+
+190
+00:17:32,370 --> 00:17:37,350
+حد بيعرف؟عدد العناصر اللي موجودة في ال group طب
+
+191
+00:17:37,350 --> 00:17:40,730
+كويس هذا التعريف الأول التعريف الثاني بدنا ال
+
+192
+00:17:40,730 --> 00:17:47,150
+order للعنصر اللي موجود في ال group ها حد بيعرف ال
+
+193
+00:17:47,150 --> 00:17:48,210
+order للعنصر
+
+194
+00:17:53,330 --> 00:17:58,430
+بالشرط يكون أصغر أُس يبقى هو the smallest positive
+
+195
+00:17:58,430 --> 00:18:03,410
+integer such that ال G to the power n بدو يسوي ال
+
+196
+00:18:03,410 --> 00:18:09,310
+identity يبقى ال n هذه بقول عليها هي ال order لمين
+
+197
+00:18:09,310 --> 00:18:15,800
+هي ال order لل group تماميبقى ال order لل element
+
+198
+00:18:15,800 --> 00:18:22,520
+هو أصغر عدد موجب برفعه ك أس لمن؟ برفعه ك أس لل
+
+199
+00:18:22,520 --> 00:18:26,580
+element بيعطيني ال identity وممكن ألاقي غيره أكبر
+
+200
+00:18:26,580 --> 00:18:29,380
+منه برضه بيعطيني ال identity لكن بهمنيش أنا بهمني
+
+201
+00:18:29,380 --> 00:18:34,860
+أصغر أس بحطه لل element بيعطيني من ال identity
+
+202
+00:18:34,860 --> 00:18:38,770
+يبقى هذا الفرق ما بين ال order لل groupوال order
+
+203
+00:18:38,770 --> 00:18:42,490
+لل element اللى موجود فى ال group واخدنا على ذلك
+
+204
+00:18:42,490 --> 00:18:47,870
+بعض الأمثلة ثم دخلنا إلى موضوع ال subgroup وقلنا
+
+205
+00:18:47,870 --> 00:18:52,490
+لو أخدت subset من ال group ال subset دى اللى
+
+206
+00:18:52,490 --> 00:18:57,010
+أخدتها من ال group بقول عليها ال subgroup إذا لجأت
+
+207
+00:18:57,010 --> 00:19:02,010
+ال subset دى باقية group جديدة تحت نفس العملية تبع
+
+208
+00:19:02,010 --> 00:19:06,590
+ال group الأصلية مش هاجو بعدين قولنا هذه قصة طويلة
+
+209
+00:19:06,590 --> 00:19:12,110
+روحنا أخدنا عليها نظرية النظرية بتقول لو أخدت ال H
+
+210
+00:19:12,110 --> 00:19:16,050
+subset من ال group يبقى هذه ال H بقول على ال
+
+211
+00:19:16,050 --> 00:19:21,590
+subgroup إذا تحقق شرطان الشرط الأول إنه H non
+
+212
+00:19:21,590 --> 00:19:27,050
+-empty والشرط الثاني لو أخدت عنصرين موجودات في H
+
+213
+00:19:27,050 --> 00:19:31,950
+فحصل ضرب الأول في معكوس الثاني بيكون وين؟في اتش
+
+214
+00:19:31,950 --> 00:19:34,630
+هذي اخر حاجة خدناها المرة الماضية لكن ماخدناش
+
+215
+00:19:34,630 --> 00:19:39,380
+امتلة، مظبوط؟ولا خدنا .. إذا نجي ناخد أمثلة تطبيق
+
+216
+00:19:39,380 --> 00:19:45,020
+على هذه النظرية يبقى باختصار جاب المبدأ مشان تبقى
+
+217
+00:19:45,020 --> 00:19:53,820
+ال H subgroup من G لازم يتحقق شرطين الشرط الأولاني
+
+218
+00:19:53,820 --> 00:19:59,780
+ان ال H لا تسوى Phi أو non-empty يابا نقول عليها
+
+219
+00:19:59,780 --> 00:20:05,730
+non-emptyيابن قول عليها الـ H لا تساوي في هذا
+
+220
+00:20:05,730 --> 00:20:11,870
+الأمر الأول الأمر الثاني لو كان ال A و ال B
+
+221
+00:20:11,870 --> 00:20:18,150
+موجودات في ال H then ال A B inverse موجود في ال H
+
+222
+00:20:18,150 --> 00:20:24,050
+يبقى هذه أخر نظرية خدناها المرة الماضية بدنا الآن
+
+223
+00:20:24,050 --> 00:20:29,230
+على هذه النظرية نعطي عليها مجموعة منالأمثلة
+
+224
+00:20:29,230 --> 00:20:40,750
+التطبيقية أول مثال يبقى example أول مثال بيقول let
+
+225
+00:20:40,750 --> 00:20:47,870
+ال g be an abelian group let ال g be an abelian
+
+226
+00:20:47,870 --> 00:20:52,710
+group define
+
+227
+00:20:52,710 --> 00:21:01,170
+عرف ال hDefine الـ H بدها تساوي كل العناصر X اللي
+
+228
+00:21:01,170 --> 00:21:06,610
+موجودة في الـ group G بحيث ان الـ X تربيع بده
+
+229
+00:21:06,610 --> 00:21:12,290
+يساوي الـ identity element السؤال هو هل الـ H هذه
+
+230
+00:21:12,290 --> 00:21:19,570
+ال subgroup او ماهياش subgroup يبقى prove or
+
+231
+00:21:19,570 --> 00:21:21,550
+disapprove
+
+232
+00:21:23,500 --> 00:21:30,680
+الـ H هي الـ subgroup من هنا يمكن أن تثبت أن الـ H
+
+233
+00:21:30,680 --> 00:21:33,960
+هي subgroup أو يمكن أن تثبت أن الـ H ليس موجودة في
+
+234
+00:21:33,960 --> 00:21:40,860
+الـ subgroup يمكن أن تثبت أن الـ H هي subgroup من
+
+235
+00:21:40,860 --> 00:21:41,060
+هنا
+
+236
+00:21:45,720 --> 00:21:50,320
+باجي بقوله و الله إذا تحقق الشرطان اللي فوق يبقى
+
+237
+00:21:50,320 --> 00:21:55,040
+ال H subgroup تحقق واحد و التاني لأ يبقى ماهياش
+
+238
+00:21:55,040 --> 00:22:00,160
+subgroup أو ينجيب counter example إن أمكنها ذلك
+
+239
+00:22:00,160 --> 00:22:04,360
+يبقى بداجي أشوف أقوله ال H هل هي empty ولا non
+
+240
+00:22:04,360 --> 00:22:12,080
+-empty أنا أزعم أن ال H is non-empty non-empty
+
+241
+00:22:12,080 --> 00:22:20,980
+ليه؟ لأنهبيقولي عناصر H هما كل العناصر اللي مربعهم
+
+242
+00:22:20,980 --> 00:22:25,480
+بيساوي من؟ ال identity طب ال identity نفسه مربع
+
+243
+00:22:25,480 --> 00:22:31,460
+وقداش؟ ال identity يبقى ال H is non-empty sense
+
+244
+00:22:31,460 --> 00:22:42,150
+حيث ال E هو ال E تربية وهذا موجود في Hأي subgroup
+
+245
+00:22:42,150 --> 00:22:44,530
+من المرة الماضية يقول إنه لازم يكون ال identity
+
+246
+00:22:44,530 --> 00:22:48,690
+element و ال inverse element موجود يبقى سرعتنا
+
+247
+00:22:48,690 --> 00:22:53,570
+ننفي إذا انتحقق ال condition الأول يبقى هذا ال
+
+248
+00:22:53,570 --> 00:22:57,510
+condition الأول بدي أجي لل condition الثاني بدي
+
+249
+00:22:57,510 --> 00:23:07,410
+أخد عنصرين موجودات في each then مربع
+
+250
+00:23:07,410 --> 00:23:14,480
+الأول كده؟ والتاني؟الـ identity يبقى then a تربية
+
+251
+00:23:14,480 --> 00:23:19,320
+بده يساوي ال identity and b تربية بده يساوي ال
+
+252
+00:23:19,320 --> 00:23:26,500
+identity طيب لو جيت قولتك طيب قداش ال a و ال b كل
+
+253
+00:23:26,500 --> 00:23:37,720
+تربية قداش برضه بال identity ليش؟ لأنه because انه
+
+254
+00:23:37,720 --> 00:23:46,540
+ال ..لأن الـ X تربية ساوية الـ E لكل X الموجودة في
+
+255
+00:23:46,540 --> 00:23:51,980
+الـ H طيب
+
+256
+00:23:51,980 --> 00:23:56,120
+هذا الآن بيساوي ال identity وهذا الآن بيساوي ال
+
+257
+00:23:56,120 --> 00:24:03,960
+identity لو ضربت ال A تربية في ال B تربية كده ايش
+
+258
+00:24:03,960 --> 00:24:10,440
+بيطلع اي في اي اللي هو بال identityيبقى هذا الكلام
+
+259
+00:24:10,440 --> 00:24:17,080
+بده يساوي a b كذلك لكل تربيع اللي كل واحد فيهم
+
+260
+00:24:17,080 --> 00:24:22,700
+بيساوي ال identity element طيب هذا الكلام بده
+
+261
+00:24:22,700 --> 00:24:27,600
+يعطينا ان ال
+
+262
+00:24:27,600 --> 00:24:36,360
+a في ال a في ال b في ال b بده يساوي a b في ال a b
+
+263
+00:24:39,230 --> 00:24:43,090
+لكن احنا ايش بدنا بدنا ال a b inverse ولا لا اه
+
+264
+00:24:43,090 --> 00:24:47,350
+ثانى شوية يبقى خلينا نجيب ال a b بلاش الخطوة هذه
+
+265
+00:24:47,350 --> 00:24:52,970
+نيجي ناخد ال a b inverse طيب مدام هيك انا ماخد ال
+
+266
+00:24:52,970 --> 00:24:57,230
+a و ال b موجودة في h then ال a تربيع بده يساوي b
+
+267
+00:24:57,230 --> 00:25:03,110
+تربيع بده يساوي ال a لو اخدت من .. لو اخدت من ..
+
+268
+00:25:03,110 --> 00:25:09,400
+بده اخد ال .. ال b inverseخلّي بالك معايا تاني
+
+269
+00:25:09,400 --> 00:25:13,400
+خلّي بالك معايا تاني والله بس نعيد الخطوة هذه من
+
+270
+00:25:13,400 --> 00:25:18,460
+جديد انا ماخد ال a و ال b موجودة في h يبقى a تربية
+
+271
+00:25:18,460 --> 00:25:21,400
+بده يساوي ال identity و ال b تربية بده يساوي ال
+
+272
+00:25:21,400 --> 00:25:30,200
+identity طيب لو جيت اخدت هنا من معكوس ال b يبقى لو
+
+273
+00:25:30,200 --> 00:25:39,540
+كان f ال a بده يساوي ال x andالـ B بده يساوي Y
+
+274
+00:25:39,540 --> 00:25:44,000
+inverse على سبيل المثال ال Y بده يساوي B inverse
+
+275
+00:25:44,000 --> 00:25:49,400
+على سبيل المثال و ال Y بده يساوي B inverse على
+
+276
+00:25:49,400 --> 00:25:56,920
+سبيل المثاليبقى أخدت ال A بده يساوي ال X وال Y بده
+
+277
+00:25:56,920 --> 00:26:02,660
+يساوي B inverse مثلا انا عايز أثبت ان ال A B
+
+278
+00:26:02,660 --> 00:26:08,160
+inverse موجود وين؟ موجود في H، مظبوط؟ طيب إذا لو
+
+279
+00:26:08,160 --> 00:26:16,840
+جيت أخد ال A B inverse الكل
+
+280
+00:26:16,840 --> 00:26:22,910
+ترابيعيبقى هذا الكلام يبدو يساوي a b inverse في ال
+
+281
+00:26:22,910 --> 00:26:31,470
+a b inverse مظبوط طيب هذا الكلام بدي يكون ماله بدي
+
+282
+00:26:31,470 --> 00:26:37,510
+يكون موجود في H لإن هذا بدي يساوي ال identity هذا
+
+283
+00:26:37,510 --> 00:26:43,920
+بدي يساوي من ال identity طيب كويسيبقى انا بدى حاول
+
+284
+00:26:43,920 --> 00:26:50,320
+هذا بدى ساوي ال identity لانه كمية لأ انا بدى اثبت
+
+285
+00:26:50,320 --> 00:26:54,540
+انه بدى ساوي ال identity مش هيك لأ انا بدى اثبت
+
+286
+00:26:54,540 --> 00:26:58,980
+انه بدى ساوي ال identity element لان مربع ال
+
+287
+00:26:58,980 --> 00:27:03,560
+element بده يكون وين موجود بده يكون موجود في itأذا
+
+288
+00:27:03,560 --> 00:27:08,740
+لما أقول a b inverse في ال a بي انفرس بدي أثبت أن
+
+289
+00:27:08,740 --> 00:27:13,620
+هذا يسوى من ال identity element كويسة الحين يا
+
+290
+00:27:13,620 --> 00:27:17,060
+جماعة لما أقول ال a تربيه بده يسوى ال e و ال b
+
+291
+00:27:17,060 --> 00:27:22,160
+تربيه كمان بده يسوى من .. بده يسوى ال a طب أنا
+
+292
+00:27:22,160 --> 00:27:30,140
+أخدت ال x في y يبقى ال x y تربيه
+
+293
+00:27:34,120 --> 00:27:42,080
+سنة سنة شوية لو اخدت انا بدي اثبت ايش بدي اثبت بدي
+
+294
+00:27:42,080 --> 00:27:47,200
+اثبت لا جي أبيليان اه صحيح مواطع انا نفسي مش شايف
+
+295
+00:27:47,200 --> 00:27:52,480
+ان جي هدي is abelian جي أبيليان جروب وعرفنا بدي
+
+296
+00:27:52,480 --> 00:27:56,100
+اثبت هذا انها subgroup اه سنة خلصنا حلت مشكلتنا
+
+297
+00:27:57,080 --> 00:28:01,340
+انحلت المشكلة، يبقى مش ماخد بالله بالي ان جي is
+
+298
+00:28:01,340 --> 00:28:06,140
+أبيلا، خلي بالك يعني، خلاص خلاص خلاص، انحلت خلاص،
+
+299
+00:28:06,140 --> 00:28:10,440
+فرطت كل شيءيبقى صارت ايه؟ صارت a تربيع بده يساوي
+
+300
+00:28:10,440 --> 00:28:12,720
+ال identity و ال b تربيع بده يساوي ال identity انا
+
+301
+00:28:12,720 --> 00:28:18,640
+بدي اثبت ان ال a b inverse بده يساوي ال كل تربيع
+
+302
+00:28:18,640 --> 00:28:22,880
+بده يساوي ايه؟ ان اثبت ذلك يبقى على طول الخط بصير
+
+303
+00:28:22,880 --> 00:28:26,520
+ايه؟ بصير ال a b inverse موجودة في h و التالي ال h
+
+304
+00:28:26,520 --> 00:28:30,880
+subgroup تبقى لمين؟ ده الكلام اللي عندنا هذا يبقى
+
+305
+00:28:30,880 --> 00:28:38,560
+بضعكي اخد a b inverse الكل تربيعهذا الكلام بده
+
+306
+00:28:38,560 --> 00:28:48,820
+يساوي a b inverse في ال a b inverse هذا الكلام
+
+307
+00:28:48,820 --> 00:28:59,420
+بده يساوي a b n a في a في ال b inverse في ال b
+
+308
+00:28:59,420 --> 00:29:00,180
+inverse
+
+309
+00:29:02,610 --> 00:29:08,770
+يبقى هذا الكلام بده يساوي A تربيع B inverse تربيع
+
+310
+00:29:08,770 --> 00:29:20,030
+هذا الكلام بده يساوي A تربيع B أسالب اتنين او هذا
+
+311
+00:29:20,030 --> 00:29:27,350
+الكلام بده يساوي A تربيع B تربيع inverse الشكل
+
+312
+00:29:27,350 --> 00:29:33,450
+اللي عندنا هذاأخدنا g to the power of m n هي g m n
+
+313
+00:29:33,450 --> 00:29:38,490
+جلبناهم يبقى هي تطبيق مباشر الان هذا بيعطينا من ال
+
+314
+00:29:38,490 --> 00:29:43,490
+identity و البين جثين بيعطينا ال identity وهي ال
+
+315
+00:29:43,490 --> 00:29:47,650
+inverse اللي برا يبقى هذا ايش معناه معناه ال
+
+316
+00:29:47,650 --> 00:29:55,310
+identity itself بناء عليه ال a b inverse موجود وين
+
+317
+00:29:55,310 --> 00:30:01,140
+في ال Hهذا بدى يعطيك ان ال HSA sub group من ال
+
+318
+00:30:01,140 --> 00:30:09,160
+main من الجيل انها حققت الشرطين طب نعطي مثالة رقم
+
+319
+00:30:09,160 --> 00:30:16,460
+اتنين example two
+
+320
+00:30:16,460 --> 00:30:22,960
+بيقول
+
+321
+00:30:22,960 --> 00:30:33,080
+الالـ G Be An Abelian Group برضه هذه Abelian Group
+
+322
+00:30:33,080 --> 00:30:46,120
+و let ال H بدها تساوي كل العناصر X تربيع بحيث ان X
+
+323
+00:30:46,120 --> 00:30:51,420
+موجودة في G show
+
+324
+00:30:51,420 --> 00:31:01,910
+thatبيّلني ان الـ H is a subgroup من G
+
+325
+00:31:01,910 --> 00:31:12,170
+جي
+
+326
+00:31:12,170 --> 00:31:20,620
+أبيليان أخدنا ست منها H مين هي هذه الـ H؟كل X
+
+327
+00:31:20,620 --> 00:31:25,140
+تربية بحيث X موجودة في جي يعني انا بدي اجي على
+
+328
+00:31:25,140 --> 00:31:30,020
+عناصر جي بدي امسك كل عنصر و اربعه ايش بطلع بدي
+
+329
+00:31:30,020 --> 00:31:35,980
+موجودة دوان بـH بدي اثبت ان الـH هو subgroup يبقى
+
+330
+00:31:35,980 --> 00:31:44,060
+بدي اجي للخطوة الأولى الـH is non-empty حد بيقدر
+
+331
+00:31:44,060 --> 00:31:52,480
+يجيبلي فيها answer؟ اه ليش؟ becauseالـ E موجودة في
+
+332
+00:31:52,480 --> 00:32:00,380
+G الـ E موجودة في G and الـ E بيساوي الـ E تربية
+
+333
+00:32:00,380 --> 00:32:07,160
+اللي موجودة في H لأن مربع الـ E هو E تربية وانا كل
+
+334
+00:32:07,160 --> 00:32:11,440
+العناصر تبعت الـ H اللي هو العناصر المربعة تبعت
+
+335
+00:32:11,440 --> 00:32:18,510
+الـ G بيبقى G non-empty بعد ذلك بدي أفترضإن ال A و
+
+336
+00:32:18,510 --> 00:32:27,610
+ال B موجودة في ال H ثم كل واحد فيهم بيكون على شكل
+
+337
+00:32:27,610 --> 00:32:33,970
+A على شكل كمية مردعةيبقى باجي بقول ال a و ال b
+
+338
+00:32:33,970 --> 00:32:41,810
+then ال x هذا بدي يكون ال a بدي يكون على شكل x
+
+339
+00:32:41,810 --> 00:32:52,610
+تربية and ال b بدي يكون على شكل y تربية for some x
+
+340
+00:32:52,610 --> 00:33:03,480
+و y اللي موجودة في g مرة تانيةمرة تانية انا خدت a
+
+341
+00:33:03,480 --> 00:33:10,020
+وb موجودات في h يبقى كل واحد هنا بدى يكون شكله يا
+
+342
+00:33:10,020 --> 00:33:14,840
+اما x تربيع يا اما y تربيع لان كل عنصر في h هو
+
+343
+00:33:14,840 --> 00:33:19,540
+مربعات main مربعات ال g انا ماخد هدول في h اذا
+
+344
+00:33:19,540 --> 00:33:25,640
+اصلا هدول موجودات في g اذا كل واحد فيهم على الشكل
+
+345
+00:33:25,640 --> 00:33:31,630
+اللى عندنا هذاالان بداجي اخد a b inverse ان قدرت
+
+346
+00:33:31,630 --> 00:33:37,890
+اثبت ان موجود موجود في h بتم المطلوب يبقى بداجي
+
+347
+00:33:37,890 --> 00:33:45,490
+اخد هنا ال a b inverse يبقى هذا الكلام ال a هي x
+
+348
+00:33:45,490 --> 00:33:53,010
+تربيع و ال b اللي هي y تربيع و هذا ال inverse فوق
+
+349
+00:33:56,320 --> 00:34:05,800
+هذا الكلام يساوي X تربيع في Y سالي باتنين هذا
+
+350
+00:34:05,800 --> 00:34:08,800
+الكلام
+
+351
+00:34:08,800 --> 00:34:18,000
+يساوي X تربيع Y انفرس لكل تربيع
+
+352
+00:34:23,270 --> 00:34:29,410
+مدام abelian إذا هذا بقدر أقول x y inverse لكل
+
+353
+00:34:29,410 --> 00:34:34,990
+تاربيع بدون مشاكل لأنك لو ماكنتش abelian بدي أجلب
+
+354
+00:34:34,990 --> 00:34:40,430
+مكان واحد الواحد مكان التاني يبقى هذا الكلام بتكتب
+
+355
+00:34:40,430 --> 00:34:46,150
+ليه جنبه because يعني كتبناه بهذا الشكل g is
+
+356
+00:34:46,150 --> 00:34:54,240
+abelian طيب السؤال هو هذا موجود في h ولا لا؟موجود
+
+357
+00:34:54,240 --> 00:35:01,160
+في H لأنه على شكل كمية مربعة لعنصر من مين من G
+
+358
+00:35:01,160 --> 00:35:06,260
+يبقى مادام صار كمية مربعة إذا هذا موجود في H معناه
+
+359
+00:35:06,260 --> 00:35:14,800
+هذا الكلام أنه A B inverse belongs to Hبإنفرس هذه
+
+360
+00:35:14,800 --> 00:35:21,320
+اللي طلعناها مربع هذا العنصر موجود في H إذا تحققت
+
+361
+00:35:21,320 --> 00:35:26,360
+الخاصية الثانية من خواص ال subgroup non-empty أخدت
+
+362
+00:35:26,360 --> 00:35:32,320
+عنصرين من H أثبت أن حاصل ضرب الأول في معكوس الثاني
+
+363
+00:35:32,320 --> 00:35:38,500
+موجود في H طبقا للنظرية هذا معناه إن ال H is a
+
+364
+00:35:38,500 --> 00:35:41,640
+subgroup من G
+
+365
+00:35:42,940 --> 00:35:47,580
+يعني المقصود من ذلك إحنا بدنا نحقق الخاصيت اللي
+
+366
+00:35:47,580 --> 00:35:53,240
+اتنين تبعها ال subgroup بأي وسيلة رياضية صحيحة طيب
+
+367
+00:35:53,240 --> 00:36:04,780
+المثال الثالث بيقول show that show that بيّلليإن
+
+368
+00:36:04,780 --> 00:36:08,920
+ال special linear group of two by two matrices
+
+369
+00:36:08,920 --> 00:36:15,020
+over R عبارة عن subgroup من ال general linear
+
+370
+00:36:15,020 --> 00:36:19,140
+group of two by two matrices over R
+
+371
+00:36:23,240 --> 00:36:28,420
+بايل لي ان ال special linear group هي sub group من
+
+372
+00:36:28,420 --> 00:36:31,420
+ال general linear group طبعا المرة الماضية احنا و
+
+373
+00:36:31,420 --> 00:36:34,300
+احنا بناخد امثلة مش الماضية اللي جبلها و اللي
+
+374
+00:36:34,300 --> 00:36:38,860
+جبلها اثبتنا ان ال general linear group هي عبارة
+
+375
+00:36:38,860 --> 00:36:42,880
+عن group و اثبتنا كذلك ان ال special linear group
+
+376
+00:36:42,880 --> 00:36:46,960
+هي عبارة عن group اليوم بنثبت ان ال special هي
+
+377
+00:36:46,960 --> 00:36:51,780
+subset من من ال general ما الفرق ما بين الاتنين
+
+378
+00:36:52,400 --> 00:36:56,480
+إتنين مصوفة ومربعة نظامها اتنين في اتنين لكن في
+
+379
+00:36:56,480 --> 00:37:01,200
+حالة ال general المحدد لا يساوي zero مين ما يكون
+
+380
+00:37:01,200 --> 00:37:05,820
+الرقم يكون لكن في الثانية المحدد يساوي كده؟ واحد
+
+381
+00:37:05,820 --> 00:37:11,180
+صحيح أيه الفرق ما بين الاتنين يعني احنا ال special
+
+382
+00:37:11,180 --> 00:37:14,440
+linear group solution
+
+383
+00:37:16,210 --> 00:37:20,990
+الـ Special Linear Group of 2x2 matrices over R كل
+
+384
+00:37:20,990 --> 00:37:32,550
+المصفات A وB وC وD بحيث أن الـ A وB وC وD موجودة
+
+385
+00:37:32,550 --> 00:37:37,230
+في set of real numbers والـ A D ناقص وB C موجودة
+
+386
+00:37:37,230 --> 00:37:42,020
+في set of real numbersهذه اللي هي شغلة عند الان
+
+387
+00:37:42,020 --> 00:37:47,680
+مكان ال H بدي أثبت أن هذه ال sub group الأن أنا
+
+388
+00:37:47,680 --> 00:37:54,600
+أدعي أن هذه non-empty non-empty ليش؟ لأن على الأقل
+
+389
+00:37:54,600 --> 00:37:59,570
+فيها من؟مصفوفة الوحدة المحددة تبعها يساوي واحد
+
+390
+00:37:59,570 --> 00:38:05,250
+صحيح يبقى باجي بقوله النقطة الأولى ال special
+
+391
+00:38:05,250 --> 00:38:11,110
+linear group of two by two matrices over R is non
+
+392
+00:38:11,110 --> 00:38:20,590
+empty السبب becauseاللي هو واحد زيرو زيرو واحد
+
+393
+00:38:20,590 --> 00:38:25,810
+موجودة في ال special linear group of two by two
+
+394
+00:38:25,810 --> 00:38:34,750
+matrices over R since ال
+
+395
+00:38:34,750 --> 00:38:39,310
+determinant لواحد زيرو زيرو واحد بده يساوي من
+
+396
+00:38:39,310 --> 00:38:47,230
+الواحدبعد ذلك اختار مصففين موجودة في ال special لت
+
+397
+00:38:47,230 --> 00:38:52,530
+ال a و ال b موجودة في ال special linear group of
+
+398
+00:38:52,530 --> 00:38:59,490
+two by two matrices over R ثم كم محدد الأولى يا
+
+399
+00:38:59,490 --> 00:39:05,650
+شباب؟ واحد و كم محدد التانية؟
+
+400
+00:39:07,830 --> 00:39:13,010
+يساوي واحد طب انا بدي اثبت انه الاولى في معكوس
+
+401
+00:39:13,010 --> 00:39:18,410
+الثانية موجودة في ال special بمعنى اخر بدي اثبت
+
+402
+00:39:18,410 --> 00:39:23,250
+انه محدد الاولى في معكوس الثانية يساوي واحد ان كنت
+
+403
+00:39:23,250 --> 00:39:27,710
+اثبت واحد معناته حصل الضرب هذا موجود وام موجود في
+
+404
+00:39:27,710 --> 00:39:30,730
+ال special وبالتالي ال special صارت sub group من
+
+405
+00:39:30,730 --> 00:39:33,990
+ال main group من ال group الأساسي اللي هي ال
+
+406
+00:39:33,990 --> 00:39:39,360
+general linear group على اي حاللو جيت قلتلك بالله
+
+407
+00:39:39,360 --> 00:39:47,320
+قداش ال determinant لل A B inverse ورجعنا بذاكرة
+
+408
+00:39:47,320 --> 00:39:52,280
+الى الوراء الى الجبري الخاطى يبقى هذا بدي يعطينا
+
+409
+00:39:52,280 --> 00:39:58,240
+ال determinant ل A في ال determinant لل B inverse
+
+410
+00:39:58,240 --> 00:40:02,800
+طب انا ال determinant لل B inverse ماهواش عندي
+
+411
+00:40:02,800 --> 00:40:07,970
+ماعرفوش لكن بنقدر نعرفه قداشه ساوي1 على
+
+412
+00:40:07,970 --> 00:40:14,610
+determinant ل a من أين جبتها اه لو ضربنا المصوفة
+
+413
+00:40:14,610 --> 00:40:19,130
+في معكس بيعطينا مصوفة من الواحدة الواحدة جداش محدد
+
+414
+00:40:19,130 --> 00:40:23,570
+مصوفة الواحدة واحد ال determinant لل بي بي انفرس
+
+415
+00:40:23,570 --> 00:40:26,890
+يساوي واحد يبقى صار ال determinant ل بي في ال
+
+416
+00:40:26,890 --> 00:40:29,890
+determinant ل بي انفرس يساوي واحد اذا ال
+
+417
+00:40:29,890 --> 00:40:32,630
+determinant ل بي انفرس يساوي واحد على ال
+
+418
+00:40:32,630 --> 00:40:38,440
+determinant ل بيإذا هذا الكلام بدي يساوي
+
+419
+00:40:38,440 --> 00:40:49,220
+determinant للـA في واحد على determinant للـB الان
+
+420
+00:40:49,220 --> 00:40:53,560
+determinant للـA بواحد و هذا واحد على واحد يبقى
+
+421
+00:40:53,560 --> 00:40:58,380
+النتيجة كدهش؟ النتيجة واحدة صحيح ايش تفسيرك لهذا
+
+422
+00:40:58,380 --> 00:41:03,300
+الكلام؟ ان ال A B inverse belong لل special linear
+
+423
+00:41:03,300 --> 00:41:11,250
+groupيبقى هنا سا ال a b inverse belongs ل ال
+
+424
+00:41:11,250 --> 00:41:16,410
+special linear group of two by two matrices over R
+
+425
+00:41:16,410 --> 00:41:22,610
+وبالتالي تحقق ال two conditions يبقى باجي بقول له
+
+426
+00:41:22,610 --> 00:41:27,170
+هذه من هنا هي النقطة التانية يا شبابمن هنا بدأت
+
+427
+00:41:27,170 --> 00:41:32,950
+النقطة الثانية يبقى الاصل special linear group of
+
+428
+00:41:32,950 --> 00:41:38,230
+two by two matrices over R عبارة عن subgroup من ال
+
+429
+00:41:38,230 --> 00:41:44,150
+general linear group of two by two matrices over R
+
+430
+00:41:44,150 --> 00:41:53,550
+حد أيه له أي سؤال هنا؟ بالنسبة ليه؟ ايوة ماله هذا؟
+
+431
+00:41:54,660 --> 00:42:02,440
+أخد دراسة جابر خطي ولا لا؟ زمان بسأل درست ولا لا؟
+
+432
+00:42:02,440 --> 00:42:08,160
+درست درست درست يعني طار بفعل زمان؟ شوف يا سيد
+
+433
+00:42:08,160 --> 00:42:15,360
+الحين المصفوفة بيه المصفوفة بيه inverse كدهش
+
+434
+00:42:15,360 --> 00:42:21,940
+بتعطيه لك؟ المصفوفة الوحدة صح؟ طيب المصفوفة الوحدة
+
+435
+00:42:21,940 --> 00:42:27,000
+اخد المحدد للي اتنينDeterminant للـ B طبعا كله
+
+436
+00:42:27,000 --> 00:42:30,380
+نظامه اتنين في اتنين Determinant للـ B في
+
+437
+00:42:30,380 --> 00:42:36,260
+Determinant للـ B inverse يسوى Determinant لمصفوفة
+
+438
+00:42:36,260 --> 00:42:40,940
+الواحدة يبقى قداشة Determinant لمصفوفة الواحدة؟ هي
+
+439
+00:42:40,940 --> 00:42:48,560
+واحد يبقى هذا بواحد يبقى بصير Determinant للـ B
+
+440
+00:42:48,560 --> 00:42:53,180
+inverse يسوى واحد على Determinant
+
+441
+00:43:11,200 --> 00:43:21,240
+المثال الرقم 4 بيقول
+
+442
+00:43:24,060 --> 00:43:32,080
+الـ G هي الـ general linear group of two by two
+
+443
+00:43:32,080 --> 00:43:42,220
+matrices over R and let ال H تساوي كل المصفوفات
+
+444
+00:43:42,220 --> 00:43:52,450
+اللي على الصيغة اللي هي A, 0, 0, Bبحيث ان ال a و
+
+445
+00:43:52,450 --> 00:44:01,450
+ال b موجودة في الارس تاع بقول prove or
+
+446
+00:44:01,450 --> 00:44:09,970
+disprove prove or disprove that ان ال h هي ال sub
+
+447
+00:44:09,970 --> 00:44:14,810
+group من مين sub group من جي هذا من الكتاب السؤال
+
+448
+00:44:14,810 --> 00:44:18,590
+من الكتاب رقمه اللي هو خمسة و خمسين
+
+449
+00:44:24,260 --> 00:44:28,220
+مرة تانية مايعطينا ال general linear group اللي هي
+
+450
+00:44:28,220 --> 00:44:33,810
+كل المصفات اللي محددها لا يساوي zeroبعد ذلك أخد H
+
+451
+00:44:33,810 --> 00:44:40,530
+كل المصفوفة للقطر الرئيسي عناصر لاتساوي أسفارا
+
+452
+00:44:40,530 --> 00:44:45,790
+جالي ال A والB موجودة في R*) R*) هي R minus Zero
+
+453
+00:44:45,790 --> 00:44:50,950
+يعني لا يمكن ل A تساوي Zero ولا يمكن ل B تساوي
+
+454
+00:44:50,950 --> 00:44:58,160
+Zero لكن للقطر الثانوي كل عناصره أسفارايبقى هدول
+
+455
+00:44:58,160 --> 00:45:03,440
+لايمكن في أي يوم من الأيام أن يكون أسفارا لكن هدول
+
+456
+00:45:03,440 --> 00:45:07,760
+أسفارة على طول الخطب بيقول لي شوفلي بالله الإتش
+
+457
+00:45:07,760 --> 00:45:11,640
+هذي ممكن تكون subgroup والله ممكن ما تكونش
+
+458
+00:45:11,640 --> 00:45:17,180
+subgroup السؤال هو هل هذي non-empty تقدر تجيبولي
+
+459
+00:45:17,180 --> 00:45:22,000
+عنصر فيها identity matrix الرئيسي واحد واحد لايسوي
+
+460
+00:45:22,000 --> 00:45:30,310
+أسفارة والباقى أسفارة يبقى لقربهو ال solution ال H
+
+461
+00:45:30,310 --> 00:45:43,950
+is non-empty because السبب because مصفوفة
+
+462
+00:45:43,950 --> 00:45:52,430
+الوحدة اللي هي 1001 موجودة في H تمام يبقى هذه non
+
+463
+00:45:52,430 --> 00:46:00,780
+-emptyالان اخد مصفتين موجودات هنا و اضرب الأول في
+
+464
+00:46:00,780 --> 00:46:05,020
+معكوس الثاني و الله ان طلع على الشكل هذا تبع ال H
+
+465
+00:46:05,020 --> 00:46:08,600
+يقول خلاص كلامنا صحيح و هذي صح بجروح ما طلع
+
+466
+00:46:08,600 --> 00:46:15,880
+بجمهياش صح بجروح يبقى بداجي اقول له ال H ال A و ال
+
+467
+00:46:15,880 --> 00:46:21,920
+B مصفتين موجودات في H then ايه الشكل ال A يا شباب
+
+468
+00:46:25,230 --> 00:46:31,410
+A00B والـ B تساوي ها بدنا نغيرها ليس بالضرورة انها
+
+469
+00:46:31,410 --> 00:46:34,850
+ممكن C000D
+
+470
+00:46:34,850 --> 00:46:40,090
+والـ A والـ B والـ C والـ D كلهم موجودات وين؟ في R
+
+471
+00:46:40,090 --> 00:46:46,910
+Star طيب مشان هيك بدروح اجيب معكوس المصوفة B يبقى
+
+472
+00:46:46,910 --> 00:46:54,750
+بد اروحله اجيبله الـ B Inverse تساويواحد على محدد
+
+473
+00:46:54,750 --> 00:47:03,990
+المصفوفة كداش المحدد تبعها CD يبقى واحد على CD و
+
+474
+00:47:03,990 --> 00:47:08,530
+باجي على المصفوفة دي و ببدل عناصر القطر الثانوي
+
+475
+00:47:08,530 --> 00:47:14,050
+مكان بعض و بغير إشارات عناصر القطر الرئيسي يبقى لو
+
+476
+00:47:14,050 --> 00:47:23,090
+جيت قلت هنا D و هنا C و هنا Zero و هنا Zeroبمشكلة
+
+477
+00:47:23,090 --> 00:47:27,050
+فاش مشكلة تمام الرئيس ما هو ال zero و الله سالب
+
+478
+00:47:27,050 --> 00:47:30,790
+zero هو ب zero يبقى اتغير ولا ماتغير ولا كل شي زي
+
+479
+00:47:30,790 --> 00:47:36,000
+ما هو طيب بدنا نشوف ايه الشكل هذه بالضبطهذا يعتبر
+
+480
+00:47:36,000 --> 00:47:40,840
+real number مضروب في المصوفة إذا مضروب في كل أنصر
+
+481
+00:47:40,840 --> 00:47:47,880
+من عناصر المصوفة إذا لو ضربناها هذا سيصبح D على CD
+
+482
+00:47:58,200 --> 00:48:03,800
+هذا الكلام ممكن اختصر D مع D و يظهر كده 1 على C و
+
+483
+00:48:03,800 --> 00:48:09,220
+هنا Zero زي ماهي و هنا زي ماهي و هنا واحد على D
+
+484
+00:48:09,220 --> 00:48:15,020
+هذا من ال B inverse الان انا بدي اشوف ال A في ال B
+
+485
+00:48:15,020 --> 00:48:20,000
+inverse هل هو موجود في H ولا لأ يبقى بتروح اخدله
+
+486
+00:48:20,000 --> 00:48:26,950
+ال A B inverseالـ A عندنا اللي هي A 00B والـ B
+
+487
+00:48:26,950 --> 00:48:36,590
+inverse واحد على C 001 على D ويسوىالصف الأول في
+
+488
+00:48:36,590 --> 00:48:42,530
+العمود الأول يبقى a على c زائد zero الصف الأول في
+
+489
+00:48:42,530 --> 00:48:47,630
+العمود الثاني بزيرو الصف الثاني في العمود الأول
+
+490
+00:48:47,630 --> 00:48:54,730
+بزيرو الصف الثاني في العمود الثاني بي على دي يبقى
+
+491
+00:48:54,730 --> 00:48:59,590
+هي القطر الرئيسي لا يسوى أصفرا والقطر الثانوي
+
+492
+00:48:59,590 --> 00:49:07,480
+بأصفر يبقى كل هذا موجود في Hبناء عليه تحققت
+
+493
+00:49:07,480 --> 00:49:11,740
+الخاصية من أين من هنا تبدأ الخاصية التانية من هنا
+
+494
+00:49:11,740 --> 00:49:16,920
+تبدأ الخاصية التانية وهذه هي الخاصية الأولى إذا
+
+495
+00:49:16,920 --> 00:49:21,460
+تبقى النظرية اللي عندنا تحققت الخاصيتين الأثنين أو
+
+496
+00:49:21,460 --> 00:49:25,100
+المعطيات الأثنين تبع النظرية يبقى بناء عليه
+
+497
+00:49:25,100 --> 00:49:30,400
+المصوفة الموطنة هي subgroup من ال general linear a
+
+498
+00:49:30,400 --> 00:49:32,500
+group يبقى هنا by
+
+499
+00:49:39,830 --> 00:49:45,910
+بالنظرية السابقة الـ H is a subgroup من ال general
+
+500
+00:49:45,910 --> 00:49:50,610
+linear group of two by two matrices over R
+