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0.9766845703125}, {"start": 336.18, "end": 337.1, "word": " المتبينة", "probability": 0.826220703125}, {"start": 337.1, "end": 337.32, "word": " هذه", "probability": 0.341796875}, {"start": 337.32, "end": 337.46, "word": " في", "probability": 0.94677734375}, {"start": 337.46, "end": 337.82, "word": " U", "probability": 0.95556640625}, {"start": 337.82, "end": 342.72, "word": " وهذا", "probability": 0.7744140625}, {"start": 342.72, "end": 343.46, "word": " بيقدر", "probability": 0.82861328125}, {"start": 343.46, "end": 344.52, "word": " بدوره", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 14, "seek": 37050, "start": 346.64, "end": 370.5, "text": "أبسلوت f of x minus f of u طالع بيساوي أبسلوت واحد على x minus واحد على u هذا بيساوي أبسلوت u minus x على x في u المفروض أحط هنا أبسلوت", "tokens": [10721, 3555, 3794, 1211, 35473, 283, 295, 2031, 3175, 283, 295, 344, 23032, 6027, 3615, 4724, 1829, 3794, 995, 45865, 5551, 3555, 3794, 1211, 35473, 36764, 24401, 15844, 2031, 3175, 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طالع", "probability": 0.5372721354166666}, {"start": 355.4, "end": 356.28, "word": " بيساوي", "probability": 0.78837890625}, {"start": 356.28, "end": 357.44, "word": " أبسلوت", "probability": 0.845166015625}, {"start": 357.44, "end": 359.58, "word": " واحد", "probability": 0.869140625}, {"start": 359.58, "end": 359.76, "word": " على", "probability": 0.505859375}, {"start": 359.76, "end": 360.1, "word": " x", "probability": 0.638671875}, {"start": 360.1, "end": 360.68, "word": " minus", "probability": 0.73095703125}, {"start": 360.68, "end": 361.3, "word": " واحد", "probability": 0.968505859375}, {"start": 361.3, "end": 361.56, "word": " على", "probability": 0.89501953125}, {"start": 361.56, "end": 362.04, "word": " u", "probability": 0.951171875}, {"start": 362.04, "end": 362.52, "word": " هذا", "probability": 0.1822509765625}, {"start": 362.52, "end": 363.06, "word": " بيساوي", "probability": 0.97197265625}, {"start": 363.06, "end": 364.04, "word": " أبسلوت", "probability": 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عناصر في A و A عناصرها كل أعداد موجبة فلا داعي ال absolute value الأن absolute أنا عندي هنا من المتباينة هذه بيطلع عندي المفروض أنه أنا عندي بيطلع U على 2 أصغر من X صح فهذا بيقدي أنه X في", "tokens": [10721, 4117, 3794, 8978, 624, 44381, 2423, 1783, 4032, 2423, 624, 18871, 33546, 2288, 8978, 316, 4032, 316, 18871, 33546, 2288, 11296, 28242, 5551, 22488, 18513, 3714, 29245, 49401, 6156, 15040, 11778, 45761, 1829, 2423, 8236, 2158, 16247, 1863, 8236, 41850, 18871, 16254, 34105, 9154, 9673, 2655, 3555, 995, 9957, 3660, 29538, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 9673, 5172, 32887, 11242, 14739, 3224, 41850, 18871, 16254, 4724, 1829, 9566, 1211, 3615, 624, 15844, 568, 5551, 9381, 17082, 2288, 9154, 1783, 20328, 5016, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 14739, 3224, 1783, 8978], "avg_logprob": -0.24739583333333334, "compression_ratio": 1.6911764705882353, "no_speech_prob": 0.0, "words": [{"start": 371.99, "end": 372.43, "word": "أكس", "probability": 0.5184733072916666}, 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42450, "start": 402.38, "end": 424.5, "text": "أضرب في U، U عدد موجب فبطلع U تربيع اتنين اصغر من X وبالتالي واحد مقلوب XU بطلع اصغر من اتنين على U تربيع اذا مقلوب XU اصغر من اتنين على U تربيع في absolute U minus X", "tokens": [10721, 11242, 25513, 8978, 624, 12399, 624, 6225, 3215, 3215, 3714, 29245, 3555, 6156, 3555, 9566, 1211, 3615, 624, 6055, 2288, 21292, 3615, 1975, 2655, 1863, 9957, 1975, 9381, 17082, 2288, 9154, 1783, 46599, 6027, 2655, 6027, 1829, 36764, 24401, 3714, 4587, 1211, 37746, 1783, 52, 4724, 9566, 1211, 3615, 1975, 9381, 17082, 2288, 9154, 1975, 2655, 1863, 9957, 15844, 624, 6055, 2288, 21292, 3615, 1975, 15730, 3714, 4587, 1211, 37746, 1783, 52, 1975, 9381, 17082, 2288, 9154, 1975, 2655, 1863, 9957, 15844, 624, 6055, 2288, 21292, 3615, 8978, 8236, 624, 3175, 1783], "avg_logprob": -0.19015957002944134, "compression_ratio": 1.8120805369127517, "no_speech_prob": 0.0, "words": [{"start": 402.38, "end": 403.1, "word": "أضرب", "probability": 0.51470947265625}, {"start": 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"seek": 44125, "start": 426.09, "end": 441.25, "text": "و هذي أصغر من دلتا إذاً هذي أصغر من اتنين على U تربية في دلتا طيب الدلتا أنا اختارها ال minimum للقيمة هذه وهذه فبالتالي الدلتا هذه تطلع أصغر من أو ساوي القيمة التانية", "tokens": [2407, 8032, 8848, 1829, 5551, 9381, 17082, 2288, 9154, 11778, 1211, 2655, 995, 11933, 15730, 14111, 8032, 8848, 1829, 5551, 9381, 17082, 2288, 9154, 1975, 2655, 1863, 9957, 15844, 624, 6055, 25513, 10632, 8978, 11778, 1211, 2655, 995, 23032, 1829, 3555, 32748, 1211, 2655, 995, 41850, 1975, 46456, 9640, 11296, 2423, 7285, 5296, 1211, 4587, 32640, 3660, 29538, 37037, 24192, 6156, 3555, 6027, 2655, 6027, 1829, 32748, 1211, 2655, 995, 29538, 6055, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 25062, 32640, 3660, 16712, 7649, 10632], "avg_logprob": -0.27283654108152283, "compression_ratio": 1.8198757763975155, "no_speech_prob": 0.0, "words": [{"start": 426.09, "end": 426.33, "word": "و", "probability": 0.5458984375}, {"start": 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1191.94, "word": " ذلك", "probability": 0.986083984375}], "temperature": 1.0}, {"id": 46, "seek": 122003, "start": 1193.13, "end": 1220.03, "text": "أفرضي أن F uniformly continuous إذا اشترتها تتحقق تبع الـ Uniform Continuous الآن لإثبات أن F continuous على A بتثبت أن F continuous at every U ينتمي لـ A يعني بتثبت أنه لأي epsilon و لأي U فـ let epsilon be given و let U be fixed element في A", "tokens": [10721, 5172, 43042, 1829, 14739, 479, 48806, 10957, 11933, 15730, 1975, 8592, 2655, 43500, 11296, 6055, 2655, 5016, 4587, 4587, 6055, 3555, 3615, 2423, 39184, 1156, 8629, 14674, 12549, 6024, 48506, 5296, 28814, 12984, 3555, 9307, 14739, 479, 10957, 15844, 316, 39894, 12984, 3555, 2655, 14739, 479, 10957, 412, 633, 624, 7251, 29399, 2304, 1829, 5296, 39184, 316, 37495, 22653, 39894, 12984, 3555, 2655, 14739, 3224, 5296, 10721, 1829, 17889, 4032, 5296, 10721, 1829, 624, 6156, 39184, 718, 17889, 312, 2212, 4032, 718, 624, 312, 6806, 4478, 8978, 316], "avg_logprob": -0.3899305436346266, "compression_ratio": 1.565217391304348, "no_speech_prob": 0.0, "words": [{"start": 1193.13, "end": 1193.77, "word": "أفرضي", "probability": 0.5455169677734375}, {"start": 1193.77, "end": 1193.93, "word": " أن", "probability": 0.53173828125}, {"start": 1193.93, "end": 1194.35, "word": " F", "probability": 0.298583984375}, {"start": 1194.35, "end": 1196.13, "word": " uniformly", "probability": 0.101318359375}, {"start": 1196.13, "end": 1197.03, "word": " continuous", "probability": 0.8955078125}, {"start": 1197.03, "end": 1198.07, "word": " إذا", "probability": 0.4730224609375}, {"start": 1198.07, "end": 1198.65, "word": " اشترتها", "probability": 0.7288330078125}, {"start": 1198.65, "end": 1199.43, "word": " تتحقق", "probability": 0.75078125}, {"start": 1199.43, "end": 1200.27, "word": " تبع", "probability": 0.7052408854166666}, {"start": 1200.27, "end": 1200.77, "word": " الـ", "probability": 0.582763671875}, {"start": 1200.77, "end": 1201.23, "word": " Uniform", "probability": 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{"start": 1213.23, "end": 1213.57, "word": " لأي", "probability": 0.9069010416666666}, {"start": 1213.57, "end": 1214.01, "word": " U", "probability": 0.986328125}, {"start": 1214.01, "end": 1216.27, "word": " فـ", "probability": 0.3890380859375}, {"start": 1216.27, "end": 1216.43, "word": " let", "probability": 0.716796875}, {"start": 1216.43, "end": 1216.87, "word": " epsilon", "probability": 0.716796875}, {"start": 1216.87, "end": 1217.09, "word": " be", "probability": 0.81640625}, {"start": 1217.09, "end": 1217.47, "word": " given", "probability": 0.84326171875}, {"start": 1217.47, "end": 1217.67, "word": " و", "probability": 0.86328125}, {"start": 1217.67, "end": 1217.93, "word": " let", "probability": 0.88671875}, {"start": 1217.93, "end": 1218.23, "word": " U", "probability": 0.9482421875}, {"start": 1218.23, "end": 1218.47, "word": " be", "probability": 0.8671875}, {"start": 1218.47, "end": 1219.03, "word": " fixed", "probability": 0.7919921875}, {"start": 1219.03, "end": 1219.49, "word": " element", "probability": 0.9453125}, {"start": 1219.49, "end": 1219.83, "word": " في", "probability": 0.96435546875}, {"start": 1219.83, "end": 1220.03, "word": " A", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 47, "seek": 124967, "start": 1222.93, "end": 1249.67, "text": "من هنا لهذه الـ Epsilon من هنا بما أن هذا الشرط متحقق لأن خد ال Delta لأي ال Epsilon هادي given خد ال Delta اللي هي هذه موجودة في ال uniform continuous اللي بتعتمد على Epsilon فقط خديها هي ال Delta هذه فطبعا هذه ال Delta بتخلي ال implication هذه تتحقق نظرت؟ لو هذه متحققة فهذه متحققة", "tokens": [27842, 34105, 46740, 24192, 2423, 39184, 462, 16592, 9154, 34105, 4724, 15042, 14739, 23758, 25124, 2288, 9566, 44650, 5016, 4587, 4587, 5296, 33456, 16490, 3215, 2423, 18183, 5296, 10721, 1829, 2423, 462, 16592, 8032, 18513, 1829, 2212, 16490, 3215, 2423, 18183, 13672, 1829, 39896, 29538, 3714, 29245, 23328, 3660, 8978, 2423, 9452, 10957, 13672, 1829, 39894, 34268, 2304, 3215, 15844, 462, 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1234.95, "end": 1235.33, "word": " continuous", "probability": 0.0985107421875}, {"start": 1235.33, "end": 1235.53, "word": " اللي", "probability": 0.964111328125}, {"start": 1235.53, "end": 1235.97, "word": " بتعتمد", "probability": 0.9552001953125}, {"start": 1235.97, "end": 1236.11, "word": " على", "probability": 0.8251953125}, {"start": 1236.11, "end": 1236.43, "word": " Epsilon", "probability": 0.902587890625}, {"start": 1236.43, "end": 1236.85, "word": " فقط", "probability": 0.948486328125}, {"start": 1236.85, "end": 1238.23, "word": " خديها", "probability": 0.8186848958333334}, {"start": 1238.23, "end": 1238.47, "word": " هي", "probability": 0.93798828125}, {"start": 1238.47, "end": 1238.65, "word": " ال", "probability": 0.9697265625}, {"start": 1238.65, "end": 1238.93, "word": " Delta", "probability": 0.8447265625}, {"start": 1238.93, "end": 1239.33, "word": " هذه", "probability": 0.7236328125}, {"start": 1239.33, "end": 1241.97, "word": " فطبعا", "probability": 0.98740234375}, {"start": 1241.97, "end": 1242.23, "word": " هذه", "probability": 0.5224609375}, {"start": 1242.23, "end": 1242.37, "word": " ال", "probability": 0.96240234375}, {"start": 1242.37, "end": 1242.57, "word": " Delta", "probability": 0.91943359375}, {"start": 1242.57, "end": 1243.15, "word": " بتخلي", "probability": 0.9005533854166666}, {"start": 1243.15, "end": 1243.31, "word": " ال", "probability": 0.9697265625}, {"start": 1243.31, "end": 1243.73, "word": " implication", "probability": 0.98828125}, {"start": 1243.73, "end": 1244.09, "word": " هذه", "probability": 0.486083984375}, {"start": 1244.09, "end": 1244.89, "word": " تتحقق", "probability": 0.8908203125}, {"start": 1244.89, "end": 1246.95, "word": " نظرت؟", "probability": 0.594757080078125}, {"start": 1246.95, "end": 1247.93, "word": " لو", "probability": 0.8876953125}, {"start": 1247.93, "end": 1248.15, "word": " هذه", "probability": 0.61767578125}, {"start": 1248.15, "end": 1248.77, "word": " متحققة", "probability": 0.9334716796875}, {"start": 1248.77, "end": 1249.07, "word": " فهذه", "probability": 0.94873046875}, {"start": 1249.07, "end": 1249.67, "word": " متحققة", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 48, "seek": 127757, "start": 1251.09, "end": 1277.57, "text": "إذن هيك واضح إن ال uniform continuous إذا الواحدة بيقدر أن f continuous and u لما أن u واظهر بترة إذا f continuous and كل على كل المجموعية لكن العكس مش صحيح إذا العكس المواحدة التانية العكس مش صحيح but not conversely", "tokens": [28814, 8848, 1863, 39896, 4117, 4032, 46958, 5016, 36145, 2423, 9452, 10957, 11933, 15730, 2423, 14407, 24401, 3660, 4724, 1829, 28543, 2288, 14739, 283, 10957, 293, 344, 5296, 15042, 14739, 344, 4032, 5718, 116, 3224, 2288, 4724, 2655, 25720, 11933, 15730, 283, 10957, 293, 28242, 15844, 28242, 9673, 7435, 2304, 45367, 10632, 44381, 18863, 4117, 3794, 37893, 20328, 5016, 1829, 5016, 11933, 15730, 18863, 4117, 3794, 9673, 14407, 24401, 3660, 16712, 7649, 10632, 18863, 4117, 3794, 37893, 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"word": " few", "probability": 0.943359375}, {"start": 1354.72, "end": 1359.1, "word": " minutes", "probability": 0.92431640625}, {"start": 1359.1, "end": 1361.36, "word": " كما", "probability": 0.6468505859375}, {"start": 1361.36, "end": 1361.98, "word": " سنرى", "probability": 0.87890625}, {"start": 1361.98, "end": 1362.34, "word": " بعد", "probability": 0.96826171875}, {"start": 1362.34, "end": 1362.98, "word": " لحظات", "probability": 0.990234375}, {"start": 1362.98, "end": 1363.6, "word": " الدالة", "probability": 0.6708984375}, {"start": 1363.6, "end": 1363.78, "word": " هذه", "probability": 0.72314453125}, {"start": 1363.78, "end": 1364.1, "word": " ليست", "probability": 0.86279296875}, {"start": 1364.1, "end": 1364.9, "word": " متصلة", "probability": 0.8362630208333334}], "temperature": 1.0}, {"id": 52, "seek": 139312, "start": 1365.3, "end": 1393.12, "text": "إتصالا منتظم هنأخر المرحلة ده شوية و هنبرهنه فلكن في الأول خلينا من التعريف تبع ال uniform continuity نستنتج non uniform continuity criterion من هنا non uniform", "tokens": [28814, 2655, 9381, 6027, 995, 9154, 2655, 19913, 2304, 8032, 1863, 10721, 34740, 9673, 2288, 5016, 37977, 11778, 3224, 13412, 2407, 10632, 4032, 8032, 1863, 26890, 3224, 1863, 3224, 6156, 1211, 19452, 8978, 16247, 12610, 16490, 1211, 9957, 995, 9154, 16712, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 9452, 23807, 8717, 14851, 29399, 7435, 2107, 9452, 23807, 46691, 9154, 34105, 2107, 9452], "avg_logprob": -0.22445436366020688, "compression_ratio": 1.515923566878981, "no_speech_prob": 0.0, "words": [{"start": 1365.3, "end": 1366.16, "word": "إتصالا", "probability": 0.764013671875}, {"start": 1366.16, "end": 1366.72, "word": " منتظم", "probability": 0.7056884765625}, {"start": 1366.72, "end": 1367.48, "word": " هنأخر", "probability": 0.712188720703125}, {"start": 1367.48, "end": 1367.94, "word": " المرحلة", "probability": 0.732177734375}, {"start": 1367.94, "end": 1368.12, "word": " ده", "probability": 0.968505859375}, {"start": 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"end": 1379.56, "word": " continuity", "probability": 0.7197265625}, {"start": 1379.56, "end": 1381.68, "word": " نستنتج", "probability": 0.966552734375}, {"start": 1381.68, "end": 1383.48, "word": " non", "probability": 0.82470703125}, {"start": 1383.48, "end": 1384.16, "word": " uniform", "probability": 0.7958984375}, {"start": 1384.16, "end": 1385.02, "word": " continuity", "probability": 0.74755859375}, {"start": 1385.02, "end": 1385.84, "word": " criterion", "probability": 0.97021484375}, {"start": 1385.84, "end": 1389.72, "word": " من", "probability": 0.442626953125}, {"start": 1389.72, "end": 1389.96, "word": " هنا", "probability": 0.99462890625}, {"start": 1389.96, "end": 1390.66, "word": " non", "probability": 0.73388671875}, {"start": 1390.66, "end": 1393.12, "word": " uniform", "probability": 0.94677734375}], "temperature": 1.0}, {"id": 53, "seek": 142124, "start": 1395.38, "end": 1421.24, "text": "non uniform continuity criteria let f from a to r be a function then", "tokens": [30092, 9452, 23807, 11101, 718, 283, 490, 257, 281, 367, 312, 257, 2445, 550], "avg_logprob": -0.44583332935969033, "compression_ratio": 1.0793650793650793, "no_speech_prob": 0.0, "words": [{"start": 1395.38, "end": 1395.82, "word": "non", "probability": 0.0750732421875}, {"start": 1395.82, "end": 1396.32, "word": " uniform", "probability": 0.50537109375}, {"start": 1396.32, "end": 1397.84, "word": " continuity", "probability": 0.7119140625}, {"start": 1397.84, "end": 1402.56, "word": " criteria", "probability": 0.79345703125}, {"start": 1402.56, "end": 1413.94, "word": " let", "probability": 0.28759765625}, {"start": 1413.94, "end": 1414.44, "word": " f", "probability": 0.64111328125}, {"start": 1414.44, "end": 1416.3, "word": " from", "probability": 0.880859375}, {"start": 1416.3, "end": 1416.76, "word": " a", "probability": 0.6513671875}, {"start": 1416.76, "end": 1416.96, "word": " to", "probability": 0.9697265625}, {"start": 1416.96, "end": 1417.44, "word": " r", 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"probability": 0.5379638671875}, {"start": 1737.51, "end": 1737.75, "word": " هي", "probability": 0.82275390625}, {"start": 1737.75, "end": 1738.19, "word": " الفافرة", "probability": 0.9090169270833334}, {"start": 1738.19, "end": 1738.75, "word": " مفتوحة", "probability": 0.9805501302083334}, {"start": 1738.75, "end": 1738.93, "word": " من", "probability": 0.9775390625}, {"start": 1738.93, "end": 1739.35, "word": " صفر", "probability": 0.7818196614583334}, {"start": 1739.35, "end": 1739.63, "word": " لما", "probability": 0.41455078125}, {"start": 1739.63, "end": 1739.75, "word": " لا", "probability": 0.459228515625}, {"start": 1739.75, "end": 1740.43, "word": " نهاية", "probability": 0.8460286458333334}, {"start": 1740.43, "end": 1741.75, "word": " we", "probability": 0.63232421875}, {"start": 1741.75, "end": 1742.29, "word": " use", "probability": 0.90185546875}, {"start": 1742.29, "end": 1747.01, "word": " non", "probability": 0.482666015625}, {"start": 1747.01, "end": 1749.27, "word": " uniform", "probability": 0.6455078125}], "temperature": 1.0}, {"id": 67, "seek": 176189, "start": 1751.05, "end": 1761.89, "text": "Non-uniform continuity criteria", "tokens": [47914, 12, 409, 8629, 23807, 11101], "avg_logprob": -0.6696428571428571, "compression_ratio": 0.7948717948717948, "no_speech_prob": 0.0, "words": [{"start": 1751.05, "end": 1751.53, "word": "Non", "probability": 0.2325439453125}, {"start": 1751.53, "end": 1752.35, "word": "-uniform", "probability": 0.7232259114583334}, {"start": 1752.35, "end": 1756.39, "word": " continuity", "probability": 0.6533203125}, {"start": 1756.39, "end": 1761.89, "word": " criteria", "probability": 0.8134765625}], "temperature": 1.0}, {"id": 68, "seek": 178987, "start": 1777.15, "end": 1789.87, "text": "يوجد أبسلون زيرو يوجد عدد أبسلون زيرو موجد", "tokens": [1829, 29245, 3215, 5551, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 7251, 29245, 3215, 6225, 3215, 3215, 5551, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 3714, 29245, 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خيار ثاني UN بساوي واحد على ان زايد واحد", "tokens": [2655, 46456, 9640, 16490, 1829, 9640, 1783, 76, 4724, 3794, 995, 45865, 36764, 24401, 15844, 16472, 1975, 4117, 25708, 29538, 2423, 8310, 5304, 8978, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 19528, 15040, 8717, 11296, 10632, 20328, 5016, 22807, 293, 9122, 2304, 7649, 6055, 46456, 9640, 16490, 1829, 9640, 38637, 7649, 1829, 8229, 4724, 3794, 995, 45865, 36764, 24401, 15844, 16472, 30767, 995, 25708, 36764, 24401], "avg_logprob": -0.441300668023728, "compression_ratio": 1.6134969325153374, "no_speech_prob": 0.0, "words": [{"start": 1807.55, "end": 1808.53, "word": "تختار", "probability": 0.5718180338541666}, {"start": 1808.53, "end": 1809.51, "word": " خيار", "probability": 0.607421875}, {"start": 1809.51, "end": 1810.65, "word": " Xm", "probability": 0.26171875}, {"start": 1810.65, "end": 1813.09, "word": " بساوي", "probability": 0.4987640380859375}, {"start": 1813.09, "end": 1813.63, 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{"start": 1828.21, "end": 1828.41, "word": " على", "probability": 0.7802734375}, {"start": 1828.41, "end": 1828.77, "word": " ان", "probability": 0.84033203125}, {"start": 1828.77, "end": 1829.23, "word": " زايد", "probability": 0.754638671875}, {"start": 1829.23, "end": 1829.65, "word": " واحد", "probability": 0.989013671875}], "temperature": 1.0}, {"id": 70, "seek": 185747, "start": 1831.19, "end": 1857.47, "text": "برضه هذه ال sequence حدودها كلها موزبة وبالتالي مجموعة جزئية من الفترة المفتوحة من سفر لملنغا Clearly واضح ان ال limit ل xn minus un as n times infinity بساوي limit", "tokens": [3555, 43042, 3224, 29538, 2423, 8310, 11331, 3215, 23328, 11296, 28242, 11296, 3714, 2407, 11622, 49401, 46599, 6027, 2655, 6027, 1829, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 9154, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 42213, 1863, 17082, 995, 24120, 4032, 46958, 5016, 16472, 2423, 4948, 5296, 2031, 77, 3175, 517, 382, 297, 1413, 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2049.65, "text": "إذا لو قلنا لكم prove or disprove continuity implies continuity .. ال uniform .. continuity implies uniform continuity هتقولي هذا ال statement false و ال counter example هو هذا هذا مثال على function continuous لكن ليست uniformly continuous تمام؟ طيب، كويس", "tokens": [28814, 15730, 45164, 12174, 1211, 8315, 5296, 24793, 7081, 420, 717, 46955, 23807, 18779, 23807, 4386, 2423, 9452, 4386, 23807, 18779, 9452, 23807, 8032, 2655, 39648, 1829, 23758, 2423, 5629, 7908, 4032, 2423, 5682, 1365, 31439, 23758, 23758, 50113, 6027, 15844, 2445, 10957, 44381, 32239, 14851, 48806, 10957, 46811, 10943, 22807, 23032, 1829, 3555, 12399, 9122, 45865, 3794], "avg_logprob": -0.2499999949487589, "compression_ratio": 1.6391752577319587, "no_speech_prob": 0.0, "words": [{"start": 2024.49, "end": 2024.83, "word": "إذا", "probability": 0.6036376953125}, {"start": 2024.83, "end": 2025.01, "word": " لو", "probability": 0.904296875}, {"start": 2025.01, "end": 2025.27, "word": " قلنا", "probability": 0.9200846354166666}, {"start": 2025.27, "end": 2025.67, "word": " لكم", "probability": 0.8095703125}, {"start": 2025.67, "end": 2027.13, "word": " prove", "probability": 0.86474609375}, {"start": 2027.13, "end": 2027.39, "word": " or", "probability": 0.9208984375}, {"start": 2027.39, "end": 2028.15, "word": " disprove", "probability": 0.931884765625}, {"start": 2028.15, "end": 2031.33, "word": " continuity", "probability": 0.5224609375}, {"start": 2031.33, "end": 2032.21, "word": " implies", "probability": 0.9599609375}, {"start": 2032.21, "end": 2033.03, "word": " continuity", "probability": 0.51025390625}, {"start": 2033.03, "end": 2033.29, "word": " ..", "probability": 0.1546630859375}, {"start": 2033.29, "end": 2033.63, "word": " ال", "probability": 0.4443359375}, {"start": 2033.63, "end": 2033.93, "word": " uniform", "probability": 0.7607421875}, {"start": 2033.93, "end": 2034.33, "word": " ..", "probability": 0.47900390625}, {"start": 2034.33, "end": 2035.01, "word": " continuity", "probability": 0.88720703125}, {"start": 2035.01, "end": 2035.69, "word": " implies", "probability": 0.96875}, {"start": 2035.69, "end": 2036.15, "word": " uniform", "probability": 0.978515625}, {"start": 2036.15, "end": 2036.93, "word": " continuity", "probability": 0.77734375}, {"start": 2036.93, "end": 2038.27, "word": " هتقولي", "probability": 0.8328857421875}, {"start": 2038.27, "end": 2038.45, "word": " هذا", "probability": 0.880859375}, {"start": 2038.45, "end": 2038.63, "word": " ال", "probability": 0.95654296875}, {"start": 2038.63, "end": 2038.97, "word": " statement", "probability": 0.94482421875}, {"start": 2038.97, "end": 2039.85, "word": " false", "probability": 0.68359375}, {"start": 2039.85, "end": 2040.73, "word": " و", "probability": 0.52734375}, {"start": 2040.73, "end": 2040.81, "word": " ال", "probability": 0.7705078125}, {"start": 2040.81, "end": 2041.09, "word": " counter", "probability": 0.54931640625}, {"start": 2041.09, "end": 2041.63, "word": " example", "probability": 0.96875}, {"start": 2041.63, "end": 2041.99, "word": " هو", "probability": 0.97314453125}, {"start": 2041.99, "end": 2042.35, "word": " هذا", "probability": 0.95703125}, {"start": 2042.35, "end": 2043.57, "word": " هذا", "probability": 0.55322265625}, {"start": 2043.57, "end": 2043.97, "word": " مثال", "probability": 0.985107421875}, {"start": 2043.97, "end": 2044.15, "word": " على", "probability": 0.89453125}, {"start": 2044.15, "end": 2044.57, "word": " function", "probability": 0.96240234375}, {"start": 2044.57, "end": 2045.29, "word": " continuous", "probability": 0.91796875}, {"start": 2045.29, "end": 2045.63, "word": " لكن", "probability": 0.8515625}, {"start": 2045.63, "end": 2046.15, "word": " ليست", "probability": 0.76171875}, {"start": 2046.15, "end": 2046.79, "word": " uniformly", "probability": 0.9775390625}, {"start": 2046.79, "end": 2047.57, "word": " continuous", "probability": 0.91455078125}, {"start": 2047.57, "end": 2048.73, "word": " تمام؟", "probability": 0.77587890625}, {"start": 2048.73, "end": 2049.27, "word": " طيب،", "probability": 0.83203125}, {"start": 2049.27, "end": 2049.65, "word": " كويس", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 78, "seek": 208016, "start": 2051.0, "end": 2080.16, "text": "خلّينا الآن نثبت بعض النظريات المهمة اللي بتخص uniform continuity ومن أهم النظريات التي هي النظرية التالية theorem اسمها uniform continuity continuity theorem", "tokens": [9778, 1211, 11703, 9957, 995, 6024, 48506, 8717, 12984, 3555, 2655, 45030, 11242, 28239, 19913, 16572, 9307, 9673, 16095, 3660, 13672, 1829, 39894, 9778, 9381, 9452, 23807, 4032, 27842, 5551, 16095, 28239, 19913, 16572, 9307, 38392, 39896, 28239, 19913, 2288, 10632, 16712, 6027, 10632, 20904, 24525, 2304, 11296, 9452, 23807, 23807, 20904], "avg_logprob": -0.18337263926020209, "compression_ratio": 1.6388888888888888, "no_speech_prob": 0.0, "words": [{"start": 2051.0, "end": 2051.52, "word": "خلّينا", "probability": 0.861328125}, {"start": 2051.52, "end": 2051.9, "word": " الآن", "probability": 0.6181640625}, {"start": 2051.9, "end": 2054.18, "word": " نثبت", "probability": 0.9813232421875}, {"start": 2054.18, "end": 2054.56, "word": " بعض", "probability": 0.93212890625}, {"start": 2054.56, "end": 2057.82, "word": " النظريات", "probability": 0.8553466796875}, {"start": 2057.82, "end": 2060.16, "word": " المهمة", "probability": 0.9895833333333334}, {"start": 2060.16, "end": 2060.44, "word": " اللي", "probability": 0.85302734375}, {"start": 2060.44, "end": 2061.96, "word": " بتخص", "probability": 0.94677734375}, {"start": 2061.96, "end": 2062.54, "word": " uniform", "probability": 0.505859375}, {"start": 2062.54, "end": 2063.44, "word": " continuity", "probability": 0.611328125}, {"start": 2063.44, "end": 2063.9, "word": " ومن", "probability": 0.87451171875}, {"start": 2063.9, "end": 2064.3, "word": " أهم", "probability": 0.916015625}, {"start": 2064.3, "end": 2065.06, "word": " النظريات", "probability": 0.9520263671875}, {"start": 2065.06, "end": 2065.38, "word": " التي", "probability": 0.1800537109375}, {"start": 2065.38, "end": 2066.56, "word": " هي", "probability": 0.84814453125}, {"start": 2066.56, "end": 2067.3, "word": " النظرية", "probability": 0.9376220703125}, {"start": 2067.3, "end": 2067.92, "word": " التالية", "probability": 0.98974609375}, {"start": 2067.92, "end": 2068.54, "word": " theorem", "probability": 0.576171875}, {"start": 2068.54, "end": 2072.68, "word": " اسمها", "probability": 0.9558919270833334}, {"start": 2072.68, "end": 2073.28, "word": " uniform", "probability": 0.90625}, {"start": 2073.28, "end": 2076.66, "word": " continuity", "probability": 0.728515625}, {"start": 2076.66, "end": 2077.82, "word": " continuity", "probability": 0.426513671875}, {"start": 2077.82, "end": 2080.16, "word": " theorem", "probability": 0.8896484375}], "temperature": 1.0}, {"id": 79, "seek": 211623, "start": 2089.43, "end": 2116.23, "text": "let I بساوي be a closed and bounded interval اذا I عبارة عن closed and bounded interval لو كان", "tokens": [2631, 286, 4724, 3794, 995, 45865, 312, 257, 5395, 293, 37498, 15035, 1975, 15730, 286, 6225, 3555, 9640, 3660, 18871, 5395, 293, 37498, 15035, 45164, 25961], "avg_logprob": -0.25708911816279095, "compression_ratio": 1.2391304347826086, "no_speech_prob": 0.0, "words": [{"start": 2089.43, "end": 2089.99, "word": "let", "probability": 0.71435546875}, {"start": 2089.99, "end": 2091.67, "word": " I", "probability": 0.75732421875}, {"start": 2091.67, "end": 2092.75, "word": " بساوي", "probability": 0.674102783203125}, {"start": 2092.75, "end": 2096.77, "word": " be", "probability": 0.347412109375}, {"start": 2096.77, "end": 2098.87, "word": " a", "probability": 0.478759765625}, {"start": 2098.87, "end": 2099.45, "word": " closed", "probability": 0.90673828125}, {"start": 2099.45, "end": 2101.61, "word": " and", "probability": 0.955078125}, {"start": 2101.61, "end": 2102.41, "word": " bounded", "probability": 0.95068359375}, {"start": 2102.41, "end": 2105.57, "word": " interval", "probability": 0.98046875}, {"start": 2105.57, "end": 2109.35, "word": " اذا", "probability": 0.5235595703125}, {"start": 2109.35, "end": 2109.75, "word": " I", "probability": 0.61376953125}, {"start": 2109.75, "end": 2110.13, "word": " عبارة", "probability": 0.9866943359375}, {"start": 2110.13, "end": 2110.29, "word": " عن", "probability": 0.98974609375}, {"start": 2110.29, "end": 2110.99, "word": " closed", "probability": 0.654296875}, {"start": 2110.99, "end": 2112.85, "word": " and", "probability": 0.95166015625}, {"start": 2112.85, "end": 2113.43, "word": " bounded", "probability": 0.95166015625}, {"start": 2113.43, "end": 2114.11, "word": " interval", "probability": 0.9833984375}, {"start": 2114.11, "end": 2115.71, "word": " لو", "probability": 0.86328125}, {"start": 2115.71, "end": 2116.23, "word": " كان", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 80, "seek": 214362, "start": 2117.02, "end": 2143.62, "text": "لو كانت الـ function f continuous، if f from I to R is continuous on I، then f is uniformly .. uniformly continuous on I", "tokens": [1211, 2407, 25961, 2655, 2423, 39184, 2445, 283, 10957, 12399, 498, 283, 490, 286, 281, 497, 307, 10957, 322, 286, 12399, 550, 283, 307, 48806, 4386, 48806, 10957, 322, 286], "avg_logprob": -0.3140120929287326, "compression_ratio": 1.297029702970297, "no_speech_prob": 0.0, "words": [{"start": 2117.02, "end": 2117.36, "word": "لو", "probability": 0.853759765625}, {"start": 2117.36, "end": 2117.72, "word": " كانت", "probability": 0.94775390625}, {"start": 2117.72, "end": 2117.84, "word": " الـ", "probability": 0.636962890625}, {"start": 2117.84, "end": 2118.22, "word": " function", "probability": 0.8564453125}, {"start": 2118.22, "end": 2118.64, "word": " f", "probability": 0.316162109375}, {"start": 2118.64, "end": 2120.58, "word": " continuous،", "probability": 0.44769287109375}, {"start": 2120.58, "end": 2120.84, "word": " if", 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"end": 2133.98, "word": " uniformly", "probability": 0.962890625}, {"start": 2133.98, "end": 2134.04, "word": " ..", "probability": 0.40283203125}, {"start": 2134.04, "end": 2136.1, "word": " uniformly", "probability": 0.9453125}, {"start": 2136.1, "end": 2138.66, "word": " continuous", "probability": 0.8876953125}, {"start": 2138.66, "end": 2143.06, "word": " on", "probability": 0.90771484375}, {"start": 2143.06, "end": 2143.62, "word": " I", "probability": 0.9990234375}], "temperature": 1.0}, {"id": 81, "seek": 217207, "start": 2146.19, "end": 2172.07, "text": "والبرهان السهل prove by contradiction اذا ان بكل بساطة نظرية هذه رغم بساطة بساطة ال statement تبعها اللي انا من اهم النظريات بكل بساطة النظرية اللي بيقول لو كان في عندك function متصل على المجال تبعها والمجال تبعها closed bounded interval اذا الاتصال العادي يصبح اتصال منتظم", "tokens": [2407, 6027, 26890, 3224, 7649, 21136, 3224, 1211, 7081, 538, 34937, 1975, 15730, 16472, 4724, 28820, 4724, 3794, 41193, 3660, 8717, 19913, 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" closed", "probability": 0.7265625}, {"start": 2167.27, "end": 2167.61, "word": " bounded", "probability": 0.91357421875}, {"start": 2167.61, "end": 2168.23, "word": " interval", "probability": 0.9755859375}, {"start": 2168.23, "end": 2168.55, "word": " اذا", "probability": 0.787353515625}, {"start": 2168.55, "end": 2169.37, "word": " الاتصال", "probability": 0.899658203125}, {"start": 2169.37, "end": 2169.87, "word": " العادي", "probability": 0.8184407552083334}, {"start": 2169.87, "end": 2170.99, "word": " يصبح", "probability": 0.9910481770833334}, {"start": 2170.99, "end": 2171.51, "word": " اتصال", "probability": 0.9918212890625}, {"start": 2171.51, "end": 2172.07, "word": " منتظم", "probability": 0.75823974609375}], "temperature": 1.0}, {"id": 82, "seek": 219967, "start": 2173.11, "end": 2199.67, "text": "إن ان هذه الحالة الوحيدة اللي او يعني احد الحالات اللي فيها بيكون الاتصال العادى بقدر الاتصال المنظم ان احنا اضافنا شرط ان مجال تبع الدالة مايكونش اي set لازم يكون closed 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"probability": 0.95751953125}, {"start": 2479.73, "end": 2482.43, "word": " to", "probability": 0.2783203125}, {"start": 2482.43, "end": 2482.73, "word": " see", "probability": 0.890625}, {"start": 2482.73, "end": 2483.35, "word": " this", "probability": 0.9599609375}, {"start": 2483.35, "end": 2485.39, "word": " note", "probability": 0.66552734375}, {"start": 2485.39, "end": 2488.25, "word": " that", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 95, "seek": 251926, "start": 2491.68, "end": 2519.26, "text": "بنقدر اخل الفرق بين unk و z أصغر من أي epsilon فهذا أصغر من أو ساوي unk minus xnk زاد absolute xnk minus z", "tokens": [3555, 1863, 28543, 2288, 1975, 9778, 1211, 27188, 2288, 4587, 49374, 517, 74, 4032, 710, 5551, 9381, 17082, 2288, 9154, 36632, 17889, 6156, 3224, 15730, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 517, 74, 3175, 2031, 77, 74, 30767, 18513, 8236, 2031, 77, 74, 3175, 710], "avg_logprob": -0.29129464285714285, "compression_ratio": 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2507.58, "word": " فهذا", "probability": 0.7556966145833334}, {"start": 2507.58, "end": 2507.96, "word": " أصغر", "probability": 0.968994140625}, {"start": 2507.96, "end": 2508.04, "word": " من", "probability": 0.90478515625}, {"start": 2508.04, "end": 2508.2, "word": " أو", "probability": 0.78076171875}, {"start": 2508.2, "end": 2508.66, "word": " ساوي", "probability": 0.8513997395833334}, {"start": 2508.66, "end": 2510.62, "word": " unk", "probability": 0.71630859375}, {"start": 2510.62, "end": 2511.48, "word": " minus", "probability": 0.459716796875}, {"start": 2511.48, "end": 2513.94, "word": " xnk", "probability": 0.8761393229166666}, {"start": 2513.94, "end": 2515.86, "word": " زاد", "probability": 0.7958984375}, {"start": 2515.86, "end": 2516.36, "word": " absolute", "probability": 0.89404296875}, {"start": 2516.36, "end": 2518.02, "word": " xnk", "probability": 0.9737955729166666}, {"start": 2518.02, "end": 2518.86, "word": " minus", "probability": 0.94775390625}, {"start": 2518.86, "end": 2519.26, "word": " z", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 96, "seek": 254544, "start": 2521.24, "end": 2545.44, "text": "هو في الأصل أن أنا المفروض أكتب انا اشعر بالإضطراحة x in k و رجعتها و استخدمت ال triangle inequality طيب هذا صحيح لكل k ينتمي إلى n طيب أنا عندي limit x in minus u in بالساوية سفر", "tokens": [3224, 2407, 8978, 16247, 36520, 14739, 41850, 9673, 5172, 32887, 11242, 5551, 4117, 2655, 3555, 1975, 8315, 1975, 8592, 3615, 2288, 20666, 28814, 11242, 9566, 23557, 5016, 3660, 2031, 294, 350, 4032, 12602, 7435, 34268, 11296, 4032, 44713, 9778, 40448, 2655, 2423, 13369, 16970, 23032, 1829, 3555, 23758, 20328, 5016, 1829, 5016, 5296, 28820, 350, 7251, 29399, 2304, 1829, 30731, 297, 23032, 1829, 3555, 41850, 18871, 16254, 4948, 2031, 294, 3175, 344, 294, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288], "avg_logprob": -0.2747713432806294, "compression_ratio": 1.4659685863874345, "no_speech_prob": 0.0, "words": [{"start": 2521.24, "end": 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"word": " tends", "probability": 0.57177734375}, {"start": 2559.95, "end": 2560.09, "word": " to", "probability": 0.9423828125}, {"start": 2560.09, "end": 2560.61, "word": " infinity", "probability": 0.86328125}, {"start": 2560.61, "end": 2561.97, "word": " وعندي", "probability": 0.7996826171875}, {"start": 2561.97, "end": 2562.27, "word": " أنا", "probability": 0.40185546875}, {"start": 2562.27, "end": 2563.35, "word": " برضه", "probability": 0.8958333333333334}, {"start": 2563.35, "end": 2563.75, "word": " u", "probability": 0.84375}, {"start": 2563.75, "end": 2564.11, "word": " ال", "probability": 0.884765625}, {"start": 2564.11, "end": 2565.37, "word": " x", "probability": 0.62158203125}, {"start": 2565.37, "end": 2565.67, "word": " in", "probability": 0.9345703125}, {"start": 2565.67, "end": 2566.03, "word": " k", "probability": 0.990234375}, {"start": 2566.03, "end": 2566.53, "word": " جلنا", "probability": 0.5712076822916666}, {"start": 2566.53, "end": 2568.29, "word": " تقول", "probability": 0.808837890625}, {"start": 2568.29, "end": 2568.59, "word": " إلى", "probability": 0.59130859375}, {"start": 2568.59, "end": 2568.93, "word": " z", "probability": 0.84228515625}, {"start": 2568.93, "end": 2569.81, "word": " فبالتالي", "probability": 0.976806640625}, {"start": 2569.81, "end": 2569.93, "word": " ال", "probability": 0.81103515625}, {"start": 2569.93, "end": 2570.29, "word": " absolute", "probability": 0.8681640625}, {"start": 2570.29, "end": 2570.65, "word": " value", "probability": 0.99267578125}, {"start": 2570.65, "end": 2570.85, "word": " هذه", "probability": 0.19482421875}, {"start": 2570.85, "end": 2571.31, "word": " بتروح", "probability": 0.88037109375}, {"start": 2571.31, "end": 2571.93, "word": " لسفر", "probability": 0.8782958984375}, {"start": 2571.93, "end": 2573.43, "word": " as", "probability": 0.9619140625}, {"start": 2573.43, "end": 2573.77, "word": " k", "probability": 0.970703125}, {"start": 2573.77, "end": 2574.15, "word": " tends", "probability": 0.7666015625}, {"start": 2574.15, "end": 2574.31, "word": " to", "probability": 0.9736328125}, {"start": 2574.31, "end": 2574.71, "word": " infinity", "probability": 0.892578125}], "temperature": 1.0}, {"id": 98, "seek": 259477, "start": 2576.09, "end": 2594.77, "text": "وهذا أكبر من سفر، إذن by squeeze theorem ال sequence هذه محصورة بين ال sequence هذه بالسفر ومجموعة two sequences بيقولوا للسفر", "tokens": [2407, 3224, 15730, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 12399, 11933, 8848, 1863, 538, 13578, 20904, 2423, 8310, 29538, 3714, 5016, 9381, 13063, 3660, 49374, 2423, 8310, 29538, 20666, 3794, 5172, 2288, 4032, 2304, 7435, 2304, 2407, 27884, 732, 22978, 4724, 1829, 39648, 14407, 24976, 3794, 5172, 2288], "avg_logprob": -0.256718755364418, "compression_ratio": 1.3955223880597014, "no_speech_prob": 0.0, "words": [{"start": 2576.09, "end": 2576.63, "word": "وهذا", "probability": 0.6790364583333334}, {"start": 2576.63, "end": 2577.11, "word": " أكبر", "probability": 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299859, "start": 2977.05, "end": 2998.59, "text": "Okay إذا بنوقف ان شاء الله هنا عند نهاية البرهان هذا و بيكون هيك احنا يعني خلصنا جزء مش بسيط في section خمسة أربعة و نكتفي بهذا القدر و يعطيكم ألف عافية و شكرا لحصن أصغائكم", "tokens": [8297, 11933, 15730, 44945, 30543, 5172, 16472, 13412, 16606, 21984, 34105, 43242, 8717, 11296, 10632, 2423, 26890, 3224, 7649, 23758, 4032, 4724, 1829, 30544, 39896, 4117, 1975, 5016, 8315, 37495, 22653, 16490, 1211, 9381, 8315, 10874, 11622, 38207, 37893, 4724, 3794, 1829, 9566, 8978, 3541, 16490, 2304, 3794, 3660, 5551, 25513, 27884, 4032, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 4032, 37495, 9566, 1829, 24793, 5551, 46538, 6225, 31845, 10632, 4032, 13412, 4117, 23557, 5296, 5016, 9381, 1863, 5551, 9381, 17082, 16373, 24793], "avg_logprob": -0.14089752941630607, "compression_ratio": 1.544041450777202, "no_speech_prob": 0.0, "words": [{"start": 2977.05, "end": 2977.53, "word": "Okay", "probability": 0.91162109375}, {"start": 2977.53, 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