{"segments": [{"id": 1, "seek": 4786, "start": 21.32, "end": 47.86, "text": "هنبدأ ان شاء الله اليوم chapter جديد و هو ال chapter التاني عنوان ال chapter sequences and series المتتاليات و المتسلسلات طبعا الموضوع هذا مار معاكم في تفاضل ألف .. تفاضل با عفوا و درسنا خواص ال sequences بطريقة مختصرة و ال series اتوسعنا فيها", "tokens": [3224, 1863, 44510, 10721, 16472, 13412, 16606, 21984, 45595, 20498, 7187, 10874, 16254, 3215, 4032, 31439, 2423, 7187, 16712, 7649, 1829, 18871, 2407, 7649, 2423, 7187, 22978, 293, 2638, 9673, 2655, 2655, 6027, 1829, 9307, 4032, 9673, 2655, 3794, 1211, 3794, 1211, 9307, 23032, 3555, 3615, 995, 9673, 2407, 11242, 45367, 23758, 3714, 9640, 20449, 995, 24793, 8978, 6055, 5172, 46958, 1211, 5551, 46538, 4386, 6055, 5172, 46958, 1211, 4724, 995, 6225, 5172, 14407, 4032, 11778, 2288, 3794, 8315, 16490, 2407, 33546, 2423, 22978, 4724, 9566, 16572, 28671, 3714, 46456, 9381, 25720, 4032, 2423, 2638, 1975, 2655, 41779, 3615, 8315, 8978, 11296], "avg_logprob": 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هذه", "probability": 0.95068359375}, {"start": 202.2, "end": 202.56, "word": " او", "probability": 0.89794921875}, {"start": 202.56, "end": 203.0, "word": " الصورة", "probability": 0.9850260416666666}, {"start": 203.0, "end": 203.28, "word": " هذه", "probability": 0.955078125}, {"start": 203.28, "end": 204.34, "word": " okay", "probability": 0.67822265625}], "temperature": 1.0}, {"id": 9, "seek": 21735, "start": 206.55, "end": 217.35, "text": "و طبعا ال sequence هذه يعني أسرها هذه أو أي واحدة منهم ممكن نكتبها برضه على الصورة x1, x2, x3 و هكذا", "tokens": [2407, 23032, 3555, 3615, 995, 2423, 8310, 29538, 37495, 22653, 5551, 3794, 2288, 11296, 29538, 34051, 36632, 36764, 24401, 3660, 9154, 16095, 3714, 43020, 8717, 4117, 2655, 3555, 11296, 4724, 43042, 3224, 15844, 31767, 13063, 3660, 2031, 16, 11, 2031, 17, 11, 2031, 18, 4032, 8032, 4117, 15730], "avg_logprob": -0.1257174793554812, "compression_ratio": 1.2348484848484849, "no_speech_prob": 0.0, "words": [{"start": 206.55, "end": 206.81, "word": "و", "probability": 0.91064453125}, {"start": 206.81, "end": 207.19, "word": " طبعا", "probability": 0.8994140625}, {"start": 207.19, "end": 207.31, "word": " ال", "probability": 0.91357421875}, {"start": 207.31, "end": 207.75, "word": " sequence", "probability": 0.94873046875}, {"start": 207.75, "end": 208.19, "word": " هذه", "probability": 0.66796875}, {"start": 208.19, "end": 208.39, "word": " يعني", "probability": 0.818359375}, {"start": 208.39, "end": 208.95, "word": " أسرها", "probability": 0.8748779296875}, {"start": 208.95, "end": 209.35, "word": " هذه", "probability": 0.5166015625}, {"start": 209.35, "end": 209.57, "word": " أو", "probability": 0.84228515625}, {"start": 209.57, "end": 209.75, "word": " أي", "probability": 0.66845703125}, {"start": 209.75, "end": 210.07, "word": " واحدة", "probability": 0.9851888020833334}, {"start": 210.07, "end": 210.49, "word": " منهم", "probability": 0.991943359375}, {"start": 210.49, "end": 211.47, "word": " ممكن", "probability": 0.971435546875}, {"start": 211.47, "end": 211.89, "word": " نكتبها", "probability": 0.99453125}, {"start": 211.89, "end": 212.19, "word": " برضه", "probability": 0.91064453125}, {"start": 212.19, "end": 212.29, "word": " على", "probability": 0.8046875}, {"start": 212.29, "end": 212.73, "word": " الصورة", "probability": 0.9680989583333334}, {"start": 212.73, "end": 213.29, "word": " x1,", "probability": 0.67626953125}, {"start": 213.53, "end": 214.33, "word": " x2,", "probability": 0.93017578125}, {"start": 214.65, "end": 216.29, "word": " x3", "probability": 0.954345703125}, {"start": 216.29, "end": 216.79, "word": " و", "probability": 0.736328125}, {"start": 216.79, "end": 217.35, "word": " هكذا", "probability": 0.9305013020833334}], "temperature": 1.0}, {"id": 10, "seek": 24950, "start": 220.84, "end": 249.5, "text": "فكل الرموز هذه ترمز إلى ال sequence هذه اللي هي ال function f اللي هي ال function f okay إذن أهم شيء في تعريفنا أن ال sequence هي function دلنا وبالتالي لها مجال مجالها العداد الطبيعي المجال المقابل هي المجموعة اللي عناصر ال sequence تنتمي لها ال sequences ممكن أعرفهم بطريقتين", "tokens": [5172, 28820, 34892, 2304, 2407, 11622, 29538, 6055, 2288, 2304, 11622, 30731, 2423, 8310, 29538, 13672, 1829, 39896, 2423, 2445, 283, 13672, 1829, 39896, 2423, 2445, 283, 1392, 11933, 8848, 1863, 5551, 16095, 44049, 38207, 8978, 37279, 16572, 5172, 8315, 14739, 2423, 8310, 39896, 2445, 11778, 1211, 8315, 46599, 6027, 2655, 6027, 1829, 5296, 11296, 3714, 7435, 6027, 3714, 7435, 6027, 11296, 18863, 3215, 18513, 41950, 21292, 3615, 1829, 9673, 7435, 6027, 9673, 4587, 16758, 1211, 39896, 9673, 7435, 2304, 2407, 27884, 13672, 1829, 18871, 33546, 2288, 2423, 8310, 6055, 29399, 2304, 1829, 5296, 11296, 2423, 22978, 3714, 43020, 5551, 3615, 28480, 16095, 4724, 9566, 16572, 38149, 9957], "avg_logprob": -0.19495412297205095, "compression_ratio": 1.9775784753363228, "no_speech_prob": 0.0, "words": [{"start": 220.84, "end": 221.38, "word": "فكل", "probability": 0.82568359375}, 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0.9923095703125}, {"start": 241.04, "end": 241.26, "word": " هي", "probability": 0.79150390625}, {"start": 241.26, "end": 241.86, "word": " المجموعة", "probability": 0.94990234375}, {"start": 241.86, "end": 242.14, "word": " اللي", "probability": 0.9658203125}, {"start": 242.14, "end": 242.66, "word": " عناصر", "probability": 0.9747721354166666}, {"start": 242.66, "end": 242.78, "word": " ال", "probability": 0.966796875}, {"start": 242.78, "end": 243.28, "word": " sequence", "probability": 0.9931640625}, {"start": 243.28, "end": 244.42, "word": " تنتمي", "probability": 0.9681396484375}, {"start": 244.42, "end": 244.84, "word": " لها", "probability": 0.86376953125}, {"start": 244.84, "end": 246.96, "word": " ال", "probability": 0.9638671875}, {"start": 246.96, "end": 247.5, "word": " sequences", "probability": 0.9541015625}, {"start": 247.5, "end": 247.96, "word": " ممكن", "probability": 0.979736328125}, {"start": 247.96, "end": 248.66, "word": " أعرفهم", "probability": 0.73187255859375}, {"start": 248.66, "end": 249.5, "word": " بطريقتين", "probability": 0.9767578125}], "temperature": 1.0}, {"id": 11, "seek": 26161, "start": 250.49, "end": 261.61, "text": "إذا في الملاحظة هذه sequences can be defined explicitly هذه أحد الطرق ممكن يعرف ال sequence بطريقة صريحة بطريقة بقانون", "tokens": [28814, 15730, 8978, 9673, 15040, 5016, 19913, 3660, 29538, 22978, 393, 312, 7642, 20803, 29538, 5551, 24401, 41950, 2288, 4587, 3714, 43020, 37495, 28480, 2423, 8310, 4724, 9566, 16572, 28671, 20328, 16572, 5016, 3660, 4724, 9566, 16572, 28671, 4724, 4587, 7649, 11536], "avg_logprob": -0.18768168327420257, "compression_ratio": 1.2992700729927007, "no_speech_prob": 0.0, "words": [{"start": 250.49, "end": 250.77, "word": "إذا", "probability": 0.4859619140625}, {"start": 250.77, "end": 250.95, "word": " في", "probability": 0.33544921875}, {"start": 250.95, "end": 251.43, "word": " الملاحظة", "probability": 0.99326171875}, {"start": 251.43, "end": 251.75, "word": " هذه", "probability": 0.84375}, {"start": 251.75, "end": 252.83, "word": " sequences", "probability": 0.4990234375}, {"start": 252.83, "end": 253.33, "word": " can", "probability": 0.93310546875}, {"start": 253.33, "end": 253.59, "word": " be", "probability": 0.9306640625}, {"start": 253.59, "end": 254.29, "word": " defined", "probability": 0.91015625}, {"start": 254.29, "end": 255.97, "word": " explicitly", "probability": 0.75439453125}, {"start": 255.97, "end": 256.51, "word": " هذه", "probability": 0.4599609375}, {"start": 256.51, "end": 256.77, "word": " أحد", "probability": 0.865966796875}, {"start": 256.77, "end": 257.29, "word": " الطرق", "probability": 0.8759765625}, {"start": 257.29, "end": 257.77, "word": " ممكن", "probability": 0.892578125}, {"start": 257.77, "end": 258.21, "word": " يعرف", "probability": 0.73095703125}, {"start": 258.21, "end": 258.35, "word": " ال", "probability": 0.912109375}, {"start": 258.35, "end": 258.75, "word": " sequence", "probability": 0.9541015625}, {"start": 258.75, "end": 259.35, "word": " بطريقة", "probability": 0.9853515625}, {"start": 259.35, "end": 259.91, "word": " صريحة", "probability": 0.972412109375}, {"start": 259.91, "end": 260.61, "word": " بطريقة", "probability": 0.936279296875}, {"start": 260.61, "end": 261.61, "word": " بقانون", "probability": 0.81591796875}], "temperature": 1.0}, {"id": 12, "seek": 28314, "start": 263.47, "end": 283.15, "text": "فمثلا ال sequence if بالساوية عناصرها اتنين اربعة ستة تمانية الاخرى هذه عبارة عن sequence وهي معرفة بطريقة صريحة فهذه عبارة عن sequence of even natural members العداد الطبيعية الزوجية", "tokens": [5172, 2304, 12984, 15040, 2423, 8310, 498, 20666, 3794, 995, 2407, 10632, 18871, 33546, 2288, 11296, 1975, 2655, 1863, 9957, 1975, 25513, 27884, 8608, 2655, 3660, 46811, 7649, 10632, 2423, 47283, 2288, 7578, 29538, 6225, 3555, 9640, 3660, 18871, 8310, 37037, 1829, 20449, 28480, 3660, 4724, 9566, 16572, 28671, 20328, 16572, 5016, 3660, 6156, 3224, 24192, 6225, 3555, 9640, 3660, 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"probability": 0.9820963541666666}, {"start": 269.63, "end": 270.49, "word": " الاخرى", "probability": 0.769287109375}, {"start": 270.49, "end": 271.17, "word": " هذه", "probability": 0.2392578125}, {"start": 271.17, "end": 271.53, "word": " عبارة", "probability": 0.9697265625}, {"start": 271.53, "end": 271.67, "word": " عن", "probability": 0.99755859375}, {"start": 271.67, "end": 272.15, "word": " sequence", "probability": 0.8720703125}, {"start": 272.15, "end": 272.47, "word": " وهي", "probability": 0.6363525390625}, {"start": 272.47, "end": 273.19, "word": " معرفة", "probability": 0.9527994791666666}, {"start": 273.19, "end": 273.61, "word": " بطريقة", "probability": 0.8929443359375}, {"start": 273.61, "end": 275.75, "word": " صريحة", "probability": 0.87890625}, {"start": 275.75, "end": 277.19, "word": " فهذه", "probability": 0.9142252604166666}, {"start": 277.19, "end": 277.65, "word": " عبارة", "probability": 0.993896484375}, {"start": 277.65, "end": 278.13, "word": " عن", "probability": 0.9970703125}, {"start": 278.13, "end": 279.79, "word": " sequence", "probability": 0.607421875}, {"start": 279.79, "end": 280.31, "word": " of", "probability": 0.9658203125}, {"start": 280.31, "end": 280.69, "word": " even", "probability": 0.87548828125}, {"start": 280.69, "end": 281.25, "word": " natural", "probability": 0.9140625}, {"start": 281.25, "end": 281.65, "word": " members", "probability": 0.56689453125}, {"start": 281.65, "end": 282.11, "word": " العداد", "probability": 0.6011555989583334}, {"start": 282.11, "end": 282.63, "word": " الطبيعية", "probability": 0.84130859375}, {"start": 282.63, "end": 283.15, "word": " الزوجية", "probability": 0.9532470703125}], "temperature": 1.0}, {"id": 13, "seek": 30637, "start": 284.31, "end": 306.37, "text": "ممكن نكتب الحد العام الانف هذا بنسميه الانف term اكس ان هذا هنا بنسميه الانف term الحد النوني الحد النوني او الحد العام فال انف term هنا هو اتنين ان اكس ان بساوي اتنين ان حيث ان عدد طبيعي", "tokens": [2304, 43020, 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375.37, "end": 403.89, "text": "باجي بعبّر عن الحد xn زايد واحد او xn بدلالة الحدود اللي جابله وبستخدم طبعا لهذا formula بنسميها recursive formula او inductive formula كما في المثال التالي يعني انا عند ال sequence 2n هذه انا عند ال sequence xn بساوة 2n", "tokens": [3555, 26108, 1829, 45030, 3555, 11703, 2288, 18871, 21542, 3215, 2031, 77, 30767, 995, 25708, 36764, 24401, 1975, 2407, 2031, 77, 47525, 1211, 6027, 3660, 21542, 3215, 23328, 13672, 1829, 10874, 16758, 43761, 46599, 14851, 9778, 40448, 23032, 3555, 3615, 995, 46740, 15730, 8513, 4724, 1863, 38251, 1829, 11296, 20560, 488, 8513, 1975, 2407, 31612, 488, 8513, 9122, 15042, 8978, 9673, 12984, 6027, 16712, 6027, 1829, 37495, 22653, 1975, 8315, 43242, 2423, 8310, 568, 77, 29538, 1975, 8315, 43242, 2423, 8310, 2031, 77, 4724, 3794, 995, 2407, 3660, 568, 77], "avg_logprob": -0.19110577119575753, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 375.37, "end": 376.01, "word": "باجي", "probability": 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31, "seek": 75460, "start": 735.36, "end": 754.6, "text": "يعني مش اي مجموعة طيب ال .. ان لو في اندي سيكوانس و السيكوانس هاد convergent ف ال limit تبعتها بتطلع unique", "tokens": [40228, 22653, 37893, 1975, 1829, 3714, 7435, 2304, 2407, 27884, 23032, 1829, 3555, 2423, 4386, 16472, 45164, 8978, 16472, 16254, 8608, 1829, 4117, 2407, 7649, 3794, 4032, 21136, 1829, 4117, 2407, 7649, 3794, 8032, 18513, 416, 331, 6930, 6156, 2423, 4948, 6055, 3555, 34268, 11296, 39894, 9566, 1211, 3615, 3845], "avg_logprob": -0.3504901832225276, "compression_ratio": 1.3385826771653544, "no_speech_prob": 0.0, "words": [{"start": 735.36, "end": 735.66, "word": "يعني", "probability": 0.53271484375}, {"start": 735.66, "end": 735.88, "word": " مش", "probability": 0.9423828125}, {"start": 735.88, "end": 736.1, "word": " اي", "probability": 0.6435546875}, {"start": 736.1, "end": 736.72, "word": " مجموعة", "probability": 0.9466796875}, {"start": 736.72, "end": 743.3, "word": " طيب", "probability": 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"end": 832.99, "word": " ل", "probability": 0.89453125}, {"start": 832.99, "end": 833.45, "word": " x", "probability": 0.787109375}, {"start": 833.45, "end": 837.25, "word": " و", "probability": 0.81494140625}, {"start": 837.25, "end": 837.67, "word": " بقدر", "probability": 0.97509765625}, {"start": 837.67, "end": 838.23, "word": " ألاقي", "probability": 0.9650065104166666}, {"start": 838.23, "end": 839.41, "word": " v2", "probability": 0.97998046875}, {"start": 839.41, "end": 845.39, "word": " v2", "probability": 0.7305908203125}, {"start": 845.39, "end": 846.05, "word": " جوار", "probability": 0.9708658854166666}, {"start": 846.05, "end": 846.23, "word": " ل", "probability": 0.9619140625}, {"start": 846.23, "end": 846.61, "word": " y", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 35, "seek": 85712, "start": 849.92, "end": 857.12, "text": "بحيث ان تقاطعهم بساوي five يعني اثنين disjoint", "tokens": [49628, 1829, 12984, 16472, 6055, 4587, 41193, 3615, 16095, 4724, 3794, 995, 45865, 1732, 37495, 22653, 1975, 12984, 1863, 9957, 717, 48613], "avg_logprob": -0.25577445133872656, "compression_ratio": 0.948051948051948, "no_speech_prob": 0.0, "words": [{"start": 849.92, "end": 850.72, "word": "بحيث", "probability": 0.9514973958333334}, {"start": 850.72, "end": 851.08, "word": " ان", "probability": 0.497314453125}, {"start": 851.08, "end": 853.16, "word": " تقاطعهم", "probability": 0.9087890625}, {"start": 853.16, "end": 854.56, "word": " بساوي", "probability": 0.8455810546875}, {"start": 854.56, "end": 855.1, "word": " five", "probability": 0.57080078125}, {"start": 855.1, "end": 856.06, "word": " يعني", "probability": 0.853271484375}, {"start": 856.06, "end": 856.5, "word": " اثنين", "probability": 0.779052734375}, {"start": 856.5, "end": 857.12, "word": " disjoint", "probability": 0.532470703125}], "temperature": 1.0}, {"id": 36, "seek": 88186, "start": 859.26, "end": 881.86, "text": "تمام؟ لو كان في عندي عددين حققين x لا يساوي y بقدر ألاقي جوار v1 ل x و جوار v2 ل y و الجوارين هدول منفصلين بعتقد حلنا السؤال هذا اه فقولنا خدي epsilon بساوي نص المسافة بين x و y", "tokens": [39237, 10943, 22807, 45164, 25961, 8978, 18871, 16254, 6225, 3215, 3215, 9957, 11331, 4587, 4587, 9957, 2031, 20193, 7251, 3794, 995, 45865, 288, 4724, 28543, 2288, 5551, 15040, 38436, 10874, 2407, 9640, 371, 16, 5296, 2031, 4032, 10874, 2407, 9640, 371, 17, 5296, 288, 4032, 25724, 2407, 9640, 9957, 8032, 3215, 12610, 9154, 5172, 36520, 9957, 4724, 34268, 28543, 11331, 1211, 8315, 21136, 33604, 6027, 23758, 1975, 3224, 6156, 39648, 8315, 16490, 16254, 17889, 4724, 3794, 995, 45865, 8717, 9381, 9673, 3794, 31845, 3660, 49374, 2031, 4032, 288], "avg_logprob": -0.18872893124483944, "compression_ratio": 1.6054054054054054, "no_speech_prob": 0.0, "words": [{"start": 859.26, "end": 860.06, "word": "تمام؟", "probability": 0.6532389322916666}, {"start": 860.06, "end": 860.36, "word": " لو", "probability": 0.8212890625}, {"start": 860.36, "end": 860.64, "word": " كان", 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" و", "probability": 0.9775390625}, {"start": 881.48, "end": 881.86, "word": " y", "probability": 0.93115234375}], "temperature": 1.0}, {"id": 37, "seek": 90103, "start": 883.39, "end": 901.03, "text": "و هد خلّي x زاد y و النقطة هد x سالب y هد عبارة عن y neighborhood ل x وبالتالي neighborhood ل x و خدي هنا برضه هد عبارة عن y سالب y و النقطة هد y زاد y", "tokens": [2407, 8032, 3215, 16490, 1211, 11703, 1829, 2031, 30767, 18513, 288, 4032, 28239, 47432, 3660, 8032, 3215, 2031, 8608, 6027, 3555, 288, 8032, 3215, 6225, 3555, 9640, 3660, 18871, 288, 7630, 5296, 2031, 46599, 6027, 2655, 6027, 1829, 7630, 5296, 2031, 4032, 16490, 16254, 34105, 4724, 43042, 3224, 8032, 3215, 6225, 3555, 9640, 3660, 18871, 288, 8608, 6027, 3555, 288, 4032, 28239, 47432, 3660, 8032, 3215, 288, 30767, 18513, 288], "avg_logprob": -0.2136883790224371, "compression_ratio": 1.7348484848484849, "no_speech_prob": 0.0, "words": [{"start": 883.39, "end": 883.73, "word": "و", "probability": 0.61767578125}, {"start": 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{"start": 893.83, "end": 894.69, "word": " برضه", "probability": 0.95068359375}, {"start": 894.69, "end": 895.57, "word": " هد", "probability": 0.94921875}, {"start": 895.57, "end": 895.99, "word": " عبارة", "probability": 0.994384765625}, {"start": 895.99, "end": 896.25, "word": " عن", "probability": 0.994140625}, {"start": 896.25, "end": 896.75, "word": " y", "probability": 0.9541015625}, {"start": 896.75, "end": 897.51, "word": " سالب", "probability": 0.9742838541666666}, {"start": 897.51, "end": 897.87, "word": " y", "probability": 0.9453125}, {"start": 897.87, "end": 898.11, "word": " و", "probability": 0.931640625}, {"start": 898.11, "end": 898.51, "word": " النقطة", "probability": 0.9812825520833334}, {"start": 898.51, "end": 898.81, "word": " هد", "probability": 0.914306640625}, {"start": 898.81, "end": 900.05, "word": " y", "probability": 0.953125}, {"start": 900.05, "end": 900.59, "word": " زاد", "probability": 0.96240234375}, {"start": 900.59, "end": 901.03, "word": " y", 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"probability": 0.78729248046875}, {"start": 1100.11, "end": 1100.39, "word": " Y", "probability": 0.81298828125}, {"start": 1100.39, "end": 1101.19, "word": " وبالتالي", "probability": 0.89951171875}, {"start": 1101.19, "end": 1102.17, "word": " ال", "probability": 0.5625}, {"start": 1102.17, "end": 1102.97, "word": " limit", "probability": 0.86181640625}, {"start": 1102.97, "end": 1103.21, "word": " لل", "probability": 0.59228515625}, {"start": 1103.21, "end": 1103.85, "word": " sequence", "probability": 0.94970703125}, {"start": 1103.85, "end": 1104.59, "word": " لازم", "probability": 0.98193359375}, {"start": 1104.59, "end": 1104.97, "word": " تكون", "probability": 0.98388671875}, {"start": 1104.97, "end": 1105.43, "word": " واحدة", "probability": 0.9270833333333334}, {"start": 1105.43, "end": 1106.01, "word": " unique", "probability": 0.60498046875}, {"start": 1106.01, "end": 1107.33, "word": " تمام؟", "probability": 0.79052734375}, {"start": 1107.33, "end": 1107.61, "word": " واضح", "probability": 0.9637044270833334}, {"start": 1107.61, "end": 1108.71, "word": " البرهان؟", "probability": 0.847900390625}, {"start": 1108.71, "end": 1108.83, "word": " في", "probability": 0.88037109375}, {"start": 1108.83, "end": 1108.99, "word": " أي", "probability": 0.85009765625}, {"start": 1108.99, "end": 1113.99, "word": " استفسار؟", "probability": 0.8951416015625}, {"start": 1113.99, "end": 1116.67, "word": " في", "probability": 0.8603515625}, {"start": 1116.67, "end": 1116.87, "word": " أي", "probability": 0.86865234375}, {"start": 1116.87, "end": 1117.51, "word": " سؤال؟", "probability": 0.9874267578125}], "temperature": 1.0}, {"id": 47, "seek": 115524, "start": 1130.08, "end": 1155.24, "text": "النظرية التانية تعطيني شروط متكافئة لتعريف ال convergence للسيكوينس فلو في عندي سيكوينس of real numbers وعندي real number x the following are equivalent", "tokens": [6027, 1863, 19913, 2288, 10632, 16712, 7649, 10632, 6055, 3615, 9566, 9957, 1829, 13412, 32887, 9566, 44650, 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{"start": 1152.84, "end": 1153.22, "word": " x", "probability": 0.49951171875}, {"start": 1153.22, "end": 1153.98, "word": " the", "probability": 0.1658935546875}, {"start": 1153.98, "end": 1154.36, "word": " following", "probability": 0.88232421875}, {"start": 1154.36, "end": 1154.72, "word": " are", "probability": 0.93896484375}, {"start": 1154.72, "end": 1155.24, "word": " equivalent", "probability": 0.94384765625}], "temperature": 1.0}, {"id": 48, "seek": 118481, "start": 1156.19, "end": 1184.81, "text": "هذا اختصار الكلمات the following are equivalent الاعبارات التالية متكافئة اول عبارة x in converge ل x هذا معناه حسب تعريف ال convergence ال neighborhood definition ان for every neighborhood V of X of X there exists capital N يعتمد على V", "tokens": [3224, 15730, 1975, 46456, 9381, 9640, 33251, 19528, 9307, 264, 3480, 366, 10344, 42963, 3615, 3555, 9640, 9307, 16712, 6027, 10632, 44650, 4117, 31845, 19986, 3660, 1975, 12610, 6225, 3555, 9640, 3660, 2031, 294, 41881, 5296, 2031, 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{"start": 1161.15, "end": 1161.53, "word": " التالية", "probability": 0.98291015625}, {"start": 1161.53, "end": 1162.45, "word": " متكافئة", "probability": 0.95615234375}, {"start": 1162.45, "end": 1163.21, "word": " اول", "probability": 0.799560546875}, {"start": 1163.21, "end": 1163.75, "word": " عبارة", "probability": 0.97509765625}, {"start": 1163.75, "end": 1164.01, "word": " x", "probability": 0.53076171875}, {"start": 1164.01, "end": 1164.27, "word": " in", "probability": 0.394775390625}, {"start": 1164.27, "end": 1164.91, "word": " converge", "probability": 0.95361328125}, {"start": 1164.91, "end": 1165.09, "word": " ل", "probability": 0.8955078125}, {"start": 1165.09, "end": 1165.47, "word": " x", "probability": 0.662109375}, {"start": 1165.47, "end": 1165.85, "word": " هذا", "probability": 0.7587890625}, {"start": 1165.85, "end": 1167.17, "word": " معناه", "probability": 0.9801432291666666}, {"start": 1167.17, "end": 1167.67, "word": " حسب", "probability": 0.970703125}, 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هاي معناه xn converge ل x الان هذا ال neighborhood definition لل convergence بيكافئ العبارة بي وهذا بنسميها ال epsilon neighborhood definition لل convergence", "tokens": [3615, 3215, 3215, 23032, 21292, 3615, 1829, 4724, 5016, 1829, 12984, 14739, 3224, 45164, 25961, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 23758, 4724, 1829, 4587, 3215, 2288, 16472, 2031, 77, 7251, 29399, 2304, 1829, 30731, 272, 8032, 47302, 20449, 8315, 3224, 2031, 77, 41881, 5296, 2031, 2423, 7649, 23758, 2423, 7630, 7123, 24976, 32181, 4724, 1829, 4117, 31845, 19986, 18863, 3555, 9640, 3660, 4724, 1829, 37037, 15730, 44945, 38251, 1829, 11296, 2423, 17889, 7630, 7123, 24976, 32181], "avg_logprob": -0.25150601978761605, "compression_ratio": 1.6298076923076923, "no_speech_prob": 0.0, "words": [{"start": 1185.99, "end": 1186.57, "word": "عدد", "probability": 0.791015625}, {"start": 1186.57, "end": 1187.49, "word": " طبيعي", "probability": 0.9276123046875}, {"start": 1187.49, "end": 1189.13, 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{"start": 1237.35, "end": 1237.47, "word": " على", "probability": 0.765625}, {"start": 1237.47, "end": 1237.55, "word": " ال", "probability": 0.9658203125}, {"start": 1237.55, "end": 1237.95, "word": " epsilon", "probability": 0.8017578125}, {"start": 1237.95, "end": 1239.41, "word": " عدد", "probability": 0.9537760416666666}, {"start": 1239.41, "end": 1239.99, "word": " طبيعي", "probability": 0.9761962890625}], "temperature": 1.0}, {"id": 51, "seek": 124698, "start": 1241.24, "end": 1246.98, "text": "بحيث أنه لكل N أكبر من أوسعه capital N بطلع XN ينتمي لبي نفس العادل", "tokens": [49628, 1829, 12984, 14739, 3224, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 4238, 426, 4724, 9566, 1211, 3615, 1783, 45, 7251, 29399, 2304, 1829, 5296, 21292, 8717, 36178, 18863, 18513, 1211], "avg_logprob": -0.3287760333882438, "compression_ratio": 1.09, "no_speech_prob": 0.0, "words": [{"start": 1241.24, "end": 1241.88, "word": "بحيث", "probability": 0.8517252604166666}, {"start": 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1269.7, "word": " جزء", "probability": 0.9088541666666666}, {"start": 1269.7, "end": 1271.06, "word": " هنستخدمه", "probability": 0.9641927083333334}, {"start": 1271.06, "end": 1271.82, "word": " في", "probability": 0.9521484375}, {"start": 1271.82, "end": 1273.02, "word": " إثبات", "probability": 0.883056640625}, {"start": 1273.02, "end": 1273.18, "word": " ال", "probability": 0.98095703125}, {"start": 1273.18, "end": 1273.76, "word": " convergence", "probability": 0.94482421875}, {"start": 1273.76, "end": 1275.22, "word": " لsequences", "probability": 0.7164306640625}, {"start": 1275.22, "end": 1275.84, "word": " معينة", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 53, "seek": 128650, "start": 1276.62, "end": 1286.5, "text": "هذا بيسميه epsilon capital N definition of convergence", "tokens": [3224, 15730, 4724, 1829, 38251, 1829, 3224, 17889, 4238, 426, 7123, 295, 32181], "avg_logprob": -0.3976004549435207, "compression_ratio": 0.8873239436619719, "no_speech_prob": 0.0, 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استعماله شائع اكتر من العبارات السابقة", "tokens": [7649, 995, 8978, 43242, 7578, 1975, 8315, 27188, 2288, 4587, 316, 23758, 6225, 3555, 9640, 3660, 18871, 17889, 6225, 3555, 9640, 3660, 18871, 7630, 7123, 295, 32181, 27188, 2288, 4587, 363, 44945, 38251, 1829, 3224, 2423, 17889, 7630, 7123, 24976, 32181, 27188, 2288, 4587, 383, 44945, 38251, 1829, 3224, 17889, 4238, 426, 7123, 295, 32181, 23758, 39896, 30544, 44713, 25957, 6027, 3224, 13412, 16373, 3615, 1975, 4117, 2655, 2288, 9154, 18863, 3555, 9640, 9307, 21136, 16758, 28671], "avg_logprob": -0.1896033642383722, "compression_ratio": 1.876923076923077, "no_speech_prob": 0.0, "words": [{"start": 1290.35, "end": 1290.69, "word": "انا", "probability": 0.25128173828125}, {"start": 1290.69, "end": 1290.85, "word": " في", "probability": 0.5400390625}, {"start": 1290.85, "end": 1291.21, "word": " عندى", "probability": 0.7734375}, {"start": 1291.21, "end": 1291.51, "word": " انا", "probability": 0.822998046875}, {"start": 1291.51, "end": 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0.956298828125}, {"start": 1304.93, "end": 1305.37, "word": " epsilon", "probability": 0.81884765625}, {"start": 1305.37, "end": 1305.93, "word": " capital", "probability": 0.7353515625}, {"start": 1305.93, "end": 1306.21, "word": " N", "probability": 0.9287109375}, {"start": 1306.21, "end": 1306.69, "word": " definition", "probability": 0.9580078125}, {"start": 1306.69, "end": 1306.93, "word": " of", "probability": 0.94677734375}, {"start": 1306.93, "end": 1307.53, "word": " convergence", "probability": 0.95751953125}, {"start": 1307.53, "end": 1308.21, "word": " هذا", "probability": 0.79248046875}, {"start": 1308.21, "end": 1308.63, "word": " هيكون", "probability": 0.83837890625}, {"start": 1308.63, "end": 1309.27, "word": " استعماله", "probability": 0.98388671875}, {"start": 1309.27, "end": 1309.77, "word": " شائع", "probability": 0.97509765625}, {"start": 1309.77, "end": 1310.23, "word": " اكتر", "probability": 0.9627685546875}, {"start": 1310.23, "end": 1310.51, "word": " من", "probability": 0.9951171875}, {"start": 1310.51, "end": 1312.33, "word": " العبارات", "probability": 0.83642578125}, {"start": 1312.33, "end": 1312.89, "word": " السابقة", "probability": 0.990234375}], "temperature": 1.0}, {"id": 55, "seek": 133583, "start": 1315.03, "end": 1335.83, "text": "البرهان ان هذا ال تلاتة إبراهيم بتكافئ بعض هنثبت ان a implies b و b implies c و بعد هيك هنثبت ان c implies a وبالتالي هيك بيطلع التلاتة متكافئة حسب قوانين ال logic مظبوط صح؟", "tokens": [6027, 26890, 3224, 7649, 16472, 23758, 2423, 6055, 1211, 9307, 3660, 11933, 3555, 23557, 3224, 32640, 39894, 4117, 31845, 19986, 45030, 11242, 8032, 1863, 12984, 3555, 2655, 16472, 257, 18779, 272, 4032, 272, 18779, 269, 4032, 39182, 39896, 4117, 8032, 1863, 12984, 3555, 2655, 16472, 269, 18779, 257, 46599, 6027, 2655, 6027, 1829, 39896, 4117, 4724, 1829, 9566, 1211, 3615, 16712, 1211, 9307, 3660, 44650, 4117, 31845, 19986, 3660, 11331, 35457, 12174, 2407, 7649, 9957, 2423, 9952, 3714, 19913, 3555, 2407, 9566, 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{"start": 1357.97, "end": 1358.13, "word": " ان", "probability": 0.70361328125}, {"start": 1358.13, "end": 1358.33, "word": " b", "probability": 0.58251953125}, {"start": 1358.33, "end": 1359.15, "word": " صحيح", "probability": 0.9969482421875}, {"start": 1359.15, "end": 1360.09, "word": " ناخد", "probability": 0.9768880208333334}, {"start": 1360.09, "end": 1360.37, "word": " أي", "probability": 0.4638671875}, {"start": 1360.37, "end": 1360.83, "word": " epsilon", "probability": 0.91943359375}, {"start": 1360.83, "end": 1361.39, "word": " neighborhood", "probability": 0.8515625}, {"start": 1361.39, "end": 1362.09, "word": " ل", "probability": 0.97216796875}, {"start": 1362.09, "end": 1362.51, "word": " x", "probability": 0.73193359375}], "temperature": 1.0}, {"id": 57, "seek": 138331, "start": 1363.99, "end": 1383.31, "text": "طب احنا لما درسنا ال neighborhoods قلنا ان كل epsilon neighborhood .. every epsilon neighborhood على الصورة هذه ل X هو ايضا neighborhood ل X صح؟ هذه حقيقة معروفة .. كل epsilon neighborhood ل X is also a neighborhood of X", "tokens": [9566, 3555, 1975, 5016, 8315, 5296, 15042, 11778, 2288, 3794, 8315, 2423, 20052, 12174, 1211, 8315, 16472, 28242, 17889, 7630, 4386, 633, 17889, 7630, 15844, 31767, 13063, 3660, 29538, 5296, 1783, 31439, 1975, 1829, 11242, 995, 7630, 5296, 1783, 20328, 5016, 22807, 29538, 11331, 38436, 28671, 20449, 32887, 5172, 3660, 4386, 28242, 17889, 7630, 5296, 1783, 307, 611, 257, 7630, 295, 1783], "avg_logprob": -0.1625744000313774, "compression_ratio": 1.6904761904761905, "no_speech_prob": 0.0, "words": [{"start": 1363.99, "end": 1364.27, "word": "طب", "probability": 0.8935546875}, {"start": 1364.27, "end": 1364.51, "word": " احنا", "probability": 0.94287109375}, {"start": 1364.51, "end": 1364.69, "word": " لما", "probability": 0.9580078125}, {"start": 1364.69, "end": 1365.13, "word": " درسنا", "probability": 0.917724609375}, {"start": 1365.13, "end": 1365.23, "word": " ال", "probability": 0.87548828125}, {"start": 1365.23, 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"temperature": 1.0}, {"id": 60, "seek": 148220, "start": 1453.9, "end": 1482.2, "text": "لو أخدت أي epsilon أكبر من السفر for any epsilon أكبر من السفر take v epsilon of x اللي هو عبارة عن ال epsilon neighborhood ل x فهذا is epsilon neighborhood of x صح؟", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 36632, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 337, 604, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 747, 371, 17889, 295, 2031, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 2423, 17889, 7630, 5296, 2031, 6156, 3224, 15730, 307, 17889, 7630, 295, 2031, 20328, 5016, 22807], "avg_logprob": -0.21889204437082463, "compression_ratio": 1.5683453237410072, "no_speech_prob": 0.0, "words": [{"start": 1453.9, "end": 1454.24, "word": "لو", "probability": 0.893798828125}, {"start": 1454.24, "end": 1454.74, "word": " أخدت", "probability": 0.95849609375}, {"start": 1454.74, "end": 1455.0, "word": " أي", "probability": 0.88818359375}, {"start": 1455.0, "end": 1455.46, "word": " 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absolute xn minus x أصغر من epsilon إذن هين أثبتنا إن لو كان b صحيح", "tokens": [3224, 15730, 2423, 39184, 2031, 77, 7251, 29399, 2304, 1829, 24976, 5172, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 29538, 20449, 8315, 47395, 23758, 2423, 28820, 10943, 20328, 5016, 23758, 20449, 8315, 3224, 2031, 77, 3175, 2031, 5551, 9381, 17082, 2288, 9154, 17889, 5551, 4117, 26890, 9154, 8608, 6027, 3555, 17889, 23758, 20449, 8315, 3224, 8236, 2031, 77, 3175, 2031, 5551, 9381, 17082, 2288, 9154, 17889, 11933, 8848, 1863, 8032, 9957, 5551, 12984, 3555, 2655, 8315, 36145, 45164, 25961, 272, 20328, 5016, 1829, 5016], "avg_logprob": -0.1646075648970382, "compression_ratio": 1.7383720930232558, "no_speech_prob": 0.0, "words": [{"start": 1544.55, "end": 1544.93, "word": "هذا", "probability": 0.75927734375}, {"start": 1544.93, "end": 1545.07, "word": " الـ", "probability": 0.671630859375}, {"start": 1545.07, "end": 1545.67, "word": " xn", "probability": 0.5205078125}, {"start": 1545.67, "end": 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" xn", "probability": 0.5274658203125}, {"start": 1583.16, "end": 1583.66, "word": " minus", "probability": 0.5341796875}, {"start": 1583.66, "end": 1584.18, "word": " x", "probability": 0.9853515625}, {"start": 1584.18, "end": 1585.16, "word": " أصغر", "probability": 0.9820556640625}, {"start": 1585.16, "end": 1585.32, "word": " من", "probability": 0.9921875}, {"start": 1585.32, "end": 1586.1, "word": " يبسلون", "probability": 0.97861328125}, {"start": 1586.1, "end": 1588.32, "word": " وبالتالي", "probability": 0.941796875}, {"start": 1588.32, "end": 1589.04, "word": " العبارة", "probability": 0.9847412109375}, {"start": 1589.04, "end": 1589.24, "word": " C", "probability": 0.5517578125}, {"start": 1589.24, "end": 1589.92, "word": " صحيحة", "probability": 0.9671875}, {"start": 1589.92, "end": 1590.64, "word": " متحققة", "probability": 0.8316650390625}, {"start": 1590.64, "end": 1591.38, "word": " okay", "probability": 0.459716796875}, {"start": 1591.38, "end": 1592.84, "word": " 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{"start": 1786.53, "end": 1786.87, "word": " in", "probability": 0.89013671875}, {"start": 1786.87, "end": 1787.61, "word": " فنرجع", "probability": 0.9744873046875}, {"start": 1787.61, "end": 1788.11, "word": " لتعريف", "probability": 0.92333984375}, {"start": 1788.11, "end": 1788.25, "word": " ال", "probability": 0.87548828125}, {"start": 1788.25, "end": 1788.65, "word": " neighborhood", "probability": 0.85888671875}, {"start": 1788.65, "end": 1789.97, "word": " definition", "probability": 0.8212890625}, {"start": 1789.97, "end": 1790.19, "word": " of", "probability": 0.671875}, {"start": 1790.19, "end": 1790.73, "word": " convergence", "probability": 0.962890625}, {"start": 1790.73, "end": 1791.91, "word": " نبدأ", "probability": 0.900390625}, {"start": 1791.91, "end": 1792.01, "word": " ب", "probability": 0.4169921875}, {"start": 1792.01, "end": 1792.39, "word": " neighborhood", "probability": 0.67431640625}, {"start": 1792.39, "end": 1792.77, "word": " ل", "probability": 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"end": 1814.1, "text": "الان من C .. C بيقول لي إذا في عندك إبسلون موجبة تقدر تلاقي capital N يعتمد عليها بحيث أنه لكل N أكبر من ما يساوي capital N المسافة هذه أصغر من إبسلون", "tokens": [6027, 7649, 9154, 383, 4386, 383, 4724, 1829, 39648, 32239, 11933, 15730, 8978, 43242, 4117, 11933, 3555, 3794, 1211, 11536, 3714, 29245, 49401, 6055, 28543, 2288, 6055, 15040, 38436, 4238, 426, 7251, 34268, 2304, 3215, 25894, 11296, 4724, 5016, 1829, 12984, 14739, 3224, 5296, 28820, 426, 5551, 4117, 26890, 9154, 19446, 7251, 3794, 995, 45865, 4238, 426, 9673, 3794, 31845, 3660, 29538, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.20772688846065573, "compression_ratio": 1.496969696969697, "no_speech_prob": 0.0, "words": [{"start": 1800.98, "end": 1801.52, "word": "الان", "probability": 0.818603515625}, {"start": 1801.52, "end": 1801.84, "word": " من", "probability": 0.88720703125}, {"start": 1801.84, "end": 1802.14, "word": " C", "probability": 0.50830078125}, {"start": 1802.14, "end": 1802.96, "word": 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N", "probability": 0.98046875}, {"start": 1812.28, "end": 1812.94, "word": " المسافة", "probability": 0.9263916015625}, {"start": 1812.94, "end": 1813.16, "word": " هذه", "probability": 0.72021484375}, {"start": 1813.16, "end": 1813.52, "word": " أصغر", "probability": 0.986083984375}, {"start": 1813.52, "end": 1813.64, "word": " من", "probability": 0.994140625}, {"start": 1813.64, "end": 1814.1, "word": " إبسلون", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 74, "seek": 183058, "start": 1815.58, "end": 1830.58, "text": "طب هذه ال implication الأخيرة هي N أكبر من أو ساوي capital N بتقدي في حل المتباين هذه في Xn فبطلع Xn ينتمي إلى X سالب Y و X فاللي هو هذا ال epsilon neighborhood اللي هو", "tokens": [9566, 3555, 29538, 2423, 37814, 16247, 9778, 48923, 39896, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 39894, 4587, 16254, 8978, 11331, 1211, 9673, 2655, 3555, 995, 9957, 29538, 8978, 1783, 77, 6156, 3555, 9566, 1211, 3615, 1783, 77, 7251, 29399, 2304, 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capital", "probability": 0.81640625}, {"start": 2142.27, "end": 2142.73, "word": " N", "probability": 0.9677734375}, {"start": 2142.73, "end": 2143.31, "word": " مطروح", "probability": 0.9041748046875}, {"start": 2143.31, "end": 2143.93, "word": " منها", "probability": 0.985107421875}, {"start": 2143.93, "end": 2145.19, "word": " capital", "probability": 0.8857421875}, {"start": 2145.19, "end": 2145.59, "word": " M", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 88, "seek": 216556, "start": 2146.58, "end": 2165.56, "text": "طبعا هنا capital N احنا اختارناها اكبر من M فالفرق هذا موجب وهذا عدد طبيعي وهذا عدد طبيعي اذا الفرق عدد صحيح موجب يعني عدد طبيعي هذا عدد ثابت وهذا يعتمد على epsilon اذا N prime الفرق بينهم يعتمد على epsilon تمام؟", "tokens": [9566, 3555, 3615, 995, 34105, 4238, 426, 1975, 5016, 8315, 1975, 46456, 9640, 8315, 11296, 1975, 4117, 26890, 9154, 376, 6156, 6027, 5172, 2288, 4587, 23758, 3714, 29245, 3555, 37037, 15730, 6225, 3215, 3215, 23032, 21292, 3615, 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