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+{"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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نهائية إذا هنا أنا بعرف ال sequence برص حدودها أول تلات حدود إلى و هكذا أو بكتب قاعدة لحد العام xn و طبعا n أدى الطبيعي فمقدر من القاعدة هذه أجيب كل الحد��د إذا هذا explicit definition of a sequence هذا تعريف صريح لل sequence", "tokens": [10721, 2407, 3714, 43020, 8717, 4117, 2655, 3555, 2423, 8310, 15844, 20328, 13063, 3660, 568, 77, 9154, 297, 20666, 3794, 995, 27884, 36764, 24401, 30731, 3714, 15040, 8717, 3224, 16373, 10632, 11933, 15730, 34105, 41850, 45030, 28480, 2423, 8310, 4724, 2288, 9381, 11331, 3215, 23328, 11296, 5551, 12610, 6055, 1211, 9307, 11331, 3215, 23328, 30731, 4032, 8032, 4117, 15730, 34051, 4724, 4117, 2655, 3555, 12174, 995, 22488, 3660, 5296, 24401, 18863, 10943, 2031, 77, 4032, 23032, 3555, 3615, 995, 297, 5551, 3215, 7578, 41950, 21292, 3615, 1829, 6156, 2304, 28543, 2288, 9154, 25062, 995, 22488, 3660, 29538, 5551, 7435, 1829, 3555, 28242, 21542, 3215, 23328, 11933, 15730, 23758, 13691, 7123, 295, 257, 8310, 23758, 37279, 16572, 5172, 20328, 16572, 5016, 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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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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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