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+{"segments": [{"id": 1, "seek": 5008, "start": 21.58, "end": 50.08, "text": "بسم الله الرحمن الرحيم اليوم ان شاء الله هنبدأ chapter خمسة و هذا اخر chapter هناخده في ال course فانواع ال chapter هذا continuous", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 16472, 13412, 16606, 21984, 8032, 1863, 44510, 10721, 7187, 16490, 2304, 3794, 3660, 4032, 23758, 1975, 34740, 7187, 8032, 1863, 47283, 3215, 3224, 8978, 2423, 1164, 6156, 7649, 14407, 3615, 2423, 7187, 23758, 10957], "avg_logprob": -0.12550951022168863, "compression_ratio": 1.4814814814814814, "no_speech_prob": 0.0, "words": [{"start": 21.58, "end": 21.94, "word": "بسم", "probability": 0.938720703125}, {"start": 21.94, "end": 22.18, "word": " الله", "probability": 0.962890625}, {"start": 22.18, "end": 22.66, "word": " الرحمن", "probability": 0.9757486979166666}, {"start": 22.66, "end": 23.38, "word": " الرحيم", "probability": 0.99560546875}, {"start": 23.38, "end": 25.32, "word": " اليوم", 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fails to be continuous at C we say ان F is discontinuous", "tokens": [1211, 2407, 25961, 2655, 2423, 479, 32239, 14851, 44650, 36520, 3660, 43242, 28239, 47432, 3660, 383, 6156, 3555, 1863, 39648, 498, 479, 18199, 281, 312, 10957, 412, 383, 321, 584, 16472, 479, 307, 31420, 12549], "avg_logprob": -0.2510850793785519, "compression_ratio": 1.1300813008130082, "no_speech_prob": 0.0, "words": [{"start": 306.75, "end": 307.09, "word": "لو", "probability": 0.854248046875}, {"start": 307.09, "end": 307.47, "word": " كانت", "probability": 0.8076171875}, {"start": 307.47, "end": 307.59, "word": " ال", "probability": 0.76318359375}, {"start": 307.59, "end": 307.75, "word": " F", "probability": 0.33984375}, {"start": 307.75, "end": 308.21, "word": " ليست", "probability": 0.893798828125}, {"start": 308.21, "end": 308.89, "word": " متصلة", "probability": 0.86181640625}, {"start": 308.89, "end": 309.09, "word": " عند", "probability": 0.97802734375}, {"start": 309.09, "end": 309.99, "word": " 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{"start": 666.76, "end": 667.22, "word": " neighborhood", "probability": 0.875}, {"start": 667.22, "end": 667.82, "word": " هذا", "probability": 0.64697265625}, {"start": 667.82, "end": 670.22, "word": " بـ", "probability": 0.3992919921875}, {"start": 670.22, "end": 670.62, "word": " Delta", "probability": 0.466796875}, {"start": 670.62, "end": 674.58, "word": " يعني", "probability": 0.7003173828125}, {"start": 674.58, "end": 675.96, "word": " أكوّن", "probability": 0.961328125}, {"start": 675.96, "end": 676.32, "word": " Delta", "probability": 0.64013671875}, {"start": 676.32, "end": 676.8, "word": " neighborhood", "probability": 0.9140625}, {"start": 676.8, "end": 677.38, "word": " هنا", "probability": 0.9384765625}, {"start": 677.38, "end": 679.08, "word": " C", "probability": 0.703125}, {"start": 679.08, "end": 679.58, "word": " minus", "probability": 0.44140625}, {"start": 679.58, "end": 680.04, "word": " Delta", "probability": 0.79541015625}, {"start": 680.04, "end": 680.48, 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هو مقاومة مقاومة A ثم F مستمر في X بساوي", "tokens": [28814, 15730, 383, 31439, 3714, 4587, 995, 20498, 3660, 3714, 4587, 995, 20498, 3660, 316, 38637, 2304, 479, 3714, 14851, 29973, 8978, 1783, 4724, 3794, 995, 45865], "avg_logprob": -0.6863839541162763, "compression_ratio": 1.1, "no_speech_prob": 0.0, "words": [{"start": 856.0, "end": 856.48, "word": "إذا", "probability": 0.659423828125}, {"start": 856.48, "end": 857.1, "word": " C", "probability": 0.461181640625}, {"start": 857.1, "end": 857.6, "word": " هو", "probability": 0.29443359375}, {"start": 857.6, "end": 858.4, "word": " مقاومة", "probability": 0.4960693359375}, {"start": 858.4, "end": 862.64, "word": " مقاومة", "probability": 0.624169921875}, {"start": 862.64, "end": 862.64, "word": " A", "probability": 0.1885986328125}, {"start": 862.64, "end": 870.18, "word": " ثم", "probability": 0.56298828125}, {"start": 870.18, "end": 872.64, "word": " F", "probability": 0.548828125}, {"start": 872.64, "end": 873.94, "word": " مستمر", 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"probability": 0.8878580729166666}, {"start": 968.48, "end": 968.84, "word": " الدالة", "probability": 0.9920247395833334}, {"start": 968.84, "end": 969.06, "word": " تكون", "probability": 0.980224609375}, {"start": 969.06, "end": 969.64, "word": " متصلة", "probability": 0.89404296875}, {"start": 969.64, "end": 969.98, "word": " عند", "probability": 0.923828125}, {"start": 969.98, "end": 970.58, "word": " النقطة", "probability": 0.9298502604166666}, {"start": 970.58, "end": 970.78, "word": " c", "probability": 0.74267578125}, {"start": 970.78, "end": 970.98, "word": " في", "probability": 0.95068359375}, {"start": 970.98, "end": 971.56, "word": " مجالها", "probability": 0.9959716796875}], "temperature": 1.0}, {"id": 34, "seek": 97642, "start": 973.54, "end": 976.42, "text": "و لو كانت الـ C هي cluster point طبعا", "tokens": [2407, 45164, 25961, 2655, 2423, 39184, 383, 39896, 13630, 935, 23032, 3555, 3615, 995], "avg_logprob": -0.540625023841858, "compression_ratio": 0.8833333333333333, "no_speech_prob": 0.0, "words": [{"start": 973.54, "end": 974.26, "word": "و", "probability": 0.458251953125}, {"start": 974.26, "end": 974.42, "word": " لو", "probability": 0.2626953125}, {"start": 974.42, "end": 974.8, "word": " كانت", "probability": 0.886962890625}, {"start": 974.8, "end": 974.94, "word": " الـ", "probability": 0.6380615234375}, {"start": 974.94, "end": 975.06, "word": " C", "probability": 0.494873046875}, {"start": 975.06, "end": 975.22, "word": " هي", "probability": 0.244140625}, {"start": 975.22, "end": 975.58, "word": " cluster", "probability": 0.66064453125}, {"start": 975.58, "end": 976.02, "word": " point", "probability": 0.90966796875}, {"start": 976.02, "end": 976.42, "word": " طبعا", "probability": 0.8941650390625}], "temperature": 1.0}, {"id": 35, "seek": 100497, "start": 978.09, "end": 1004.97, "text": "أو حتى لو ماكنتش cluster point فلازم التلاتة صوروطها تتحقق الدالة معرفة عن C طبعا هذا لأن C نقطة في مجال الدالة فلازم تكون معرفة عن ده لازم ال limit ل F عن C تكون موجودة وقيمة ال limit بساوي قيمة الدالة عند النقطة C لو أي واحد ماليش صوروط التلاتة هدول اختل فبنقول ان ال function مش متصلة عند النقطة C", "tokens": [10721, 2407, 11331, 49975, 45164, 19446, 19452, 2655, 8592, 13630, 935, 6156, 1211, 31377, 2304, 16712, 1211, 9307, 3660, 20328, 13063, 2407, 9566, 11296, 6055, 2655, 5016, 4587, 4587, 32748, 6027, 3660, 20449, 28480, 3660, 18871, 383, 23032, 3555, 3615, 995, 23758, 5296, 33456, 383, 8717, 47432, 3660, 8978, 3714, 7435, 6027, 32748, 6027, 3660, 6156, 1211, 31377, 2304, 6055, 30544, 20449, 28480, 3660, 18871, 11778, 3224, 5296, 31377, 2304, 2423, 4948, 5296, 479, 18871, 383, 6055, 30544, 3714, 29245, 23328, 3660, 4032, 4587, 32640, 3660, 2423, 4948, 4724, 3794, 995, 45865, 12174, 32640, 3660, 32748, 6027, 3660, 43242, 28239, 47432, 3660, 383, 45164, 36632, 36764, 24401, 19446, 20292, 8592, 20328, 13063, 2407, 9566, 16712, 1211, 9307, 3660, 8032, 3215, 12610, 1975, 46456, 1211, 6156, 3555, 1863, 39648, 16472, 2423, 2445, 37893, 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{"start": 1023.85, "end": 1024.01, "word": " C", "probability": 0.97900390625}, {"start": 1024.01, "end": 1024.53, "word": " تنتمي", "probability": 0.982177734375}, {"start": 1024.53, "end": 1024.65, "word": " ل", "probability": 0.5595703125}, {"start": 1024.65, "end": 1024.93, "word": " A", "probability": 0.6962890625}, {"start": 1024.93, "end": 1025.51, "word": " اه", "probability": 0.773681640625}, {"start": 1025.51, "end": 1025.89, "word": " طبعا", "probability": 0.98583984375}, {"start": 1025.89, "end": 1026.07, "word": " ال", "probability": 0.9794921875}, {"start": 1026.07, "end": 1026.23, "word": " C", "probability": 0.97705078125}, {"start": 1026.23, "end": 1026.85, "word": " تنتمي", "probability": 0.9820556640625}, {"start": 1026.85, "end": 1026.99, "word": " ل", "probability": 0.94921875}, {"start": 1026.99, "end": 1027.29, "word": " A", "probability": 0.92578125}, {"start": 1027.29, "end": 1029.31, "word": " ال", "probability": 0.246826171875}, {"start": 1029.31, "end": 1029.51, "word": " C", "probability": 0.97607421875}, {"start": 1029.51, "end": 1030.01, "word": " دائما", "probability": 0.86279296875}, {"start": 1030.01, "end": 1030.77, "word": " تنتمي", "probability": 0.990234375}, {"start": 1030.77, "end": 1030.91, "word": " ل", "probability": 0.96923828125}, {"start": 1030.91, "end": 1031.13, "word": " A", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 37, "seek": 106409, "start": 1037.1, "end": 1064.1, "text": "طب لو ماكناش ال c cluster point الملاحظة التانية if c is not يعني لو كان ال c تنتمي طبعا دايما ال c تنتمي ل a is not a cluster point is not cluster point of a", "tokens": [9566, 3555, 45164, 19446, 19452, 33599, 2423, 269, 13630, 935, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632, 498, 269, 307, 406, 37495, 22653, 45164, 25961, 2423, 269, 6055, 29399, 2304, 1829, 23032, 3555, 3615, 995, 11778, 47302, 15042, 2423, 269, 6055, 29399, 2304, 1829, 5296, 257, 307, 406, 257, 13630, 935, 307, 406, 13630, 935, 295, 257], 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1062.56, "end": 1063.76, "word": " of", "probability": 0.97705078125}, {"start": 1063.76, "end": 1064.1, "word": " a", "probability": 0.86962890625}], "temperature": 1.0}, {"id": 38, "seek": 108684, "start": 1068.95, "end": 1086.85, "text": "then من تعريف ال cluster point لازم نلاقي delta أكبر من السفر such that a تقاطع v delta of c بساوي singleton c", "tokens": [19096, 9154, 37279, 16572, 5172, 2423, 13630, 935, 5296, 31377, 2304, 8717, 15040, 38436, 8289, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 1270, 300, 257, 6055, 4587, 41193, 3615, 371, 8289, 295, 269, 4724, 3794, 995, 45865, 1522, 14806, 269], "avg_logprob": -0.18206936557118486, "compression_ratio": 1.1732283464566928, "no_speech_prob": 0.0, "words": [{"start": 1068.95, "end": 1069.51, "word": "then", "probability": 0.1217041015625}, {"start": 1069.51, "end": 1070.23, "word": " من", "probability": 0.9619140625}, {"start": 1070.23, "end": 1070.65, "word": " تعريف", "probability": 0.9689127604166666}, {"start": 1070.65, "end": 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{"start": 1105.02, "end": 1105.32, "word": " في", "probability": 0.92431640625}, {"start": 1105.32, "end": 1105.82, "word": " نقطة", "probability": 0.9847005208333334}, {"start": 1105.82, "end": 1106.46, "word": " مختلفة", "probability": 0.97998046875}, {"start": 1106.46, "end": 1106.6, "word": " عن", "probability": 0.96142578125}, {"start": 1106.6, "end": 1106.76, "word": " ال", "probability": 0.56005859375}, {"start": 1106.76, "end": 1107.0, "word": " C", "probability": 0.78076171875}, {"start": 1107.0, "end": 1107.28, "word": " على", "probability": 0.93505859375}, {"start": 1107.28, "end": 1107.78, "word": " الأقل", "probability": 0.9285481770833334}], "temperature": 1.0}, {"id": 40, "seek": 112294, "start": 1108.96, "end": 1122.94, "text": "معناه ان الـ C ما تكونش cluster point معناه ان يوجد delta neighborhood واحد يعني يوجد delta عدد موجب وبالتالي يوجد على الأقل delta neighborhood للـ C وهذا ال delta neighborhood", "tokens": [2304, 3615, 8315, 3224, 16472, 2423, 39184, 383, 19446, 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"probability": 0.67138671875}, {"start": 1307.11, "end": 1314.95, "word": " فكان", "probability": 0.90087890625}, {"start": 1314.95, "end": 1315.11, "word": " في", "probability": 0.93896484375}, {"start": 1315.11, "end": 1315.35, "word": " عندي", "probability": 0.782470703125}, {"start": 1315.35, "end": 1315.85, "word": " sequential", "probability": 0.9453125}, {"start": 1315.85, "end": 1316.71, "word": " criterion", "probability": 0.9521484375}, {"start": 1316.71, "end": 1317.03, "word": " for", "probability": 0.9521484375}, {"start": 1317.03, "end": 1317.59, "word": " limits", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 49, "seek": 134511, "start": 1322.27, "end": 1345.11, "text": "بنفس الطريقة في هنا sequential criterion for continuity للاتصال إذا في عندي هنا sequential criterion for continuity", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 8978, 34105, 42881, 46691, 337, 23807, 24976, 9307, 9381, 6027, 11933, 15730, 8978, 18871, 16254, 34105, 42881, 46691, 337, 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0.970703125}, {"start": 1361.45, "end": 1361.99, "word": " a", "probability": 0.9501953125}, {"start": 1361.99, "end": 1364.43, "word": " then", "probability": 0.7236328125}, {"start": 1364.43, "end": 1366.43, "word": " the", "probability": 0.8544921875}, {"start": 1366.43, "end": 1367.19, "word": " following", "probability": 0.888671875}, {"start": 1367.19, "end": 1368.33, "word": " statements", "probability": 0.89306640625}, {"start": 1368.33, "end": 1370.99, "word": " are", "probability": 0.955078125}, {"start": 1370.99, "end": 1371.71, "word": " equivalent", "probability": 0.9501953125}, {"start": 1371.71, "end": 1376.17, "word": " واحد", "probability": 0.90966796875}, {"start": 1376.17, "end": 1377.95, "word": " if", "probability": 0.56494140625}, {"start": 1377.95, "end": 1378.67, "word": " is", "probability": 0.9306640625}, {"start": 1378.67, "end": 1379.45, "word": " continuous", "probability": 0.89453125}], "temperature": 1.0}, {"id": 51, "seek": 140967, "start": 1381.35, "end": 1409.67, "text": "if is continuous at c for every for every sequence x in contained in a with limit x in بساوي c", "tokens": [351, 307, 10957, 412, 269, 337, 633, 337, 633, 8310, 2031, 294, 16212, 294, 257, 365, 4948, 2031, 294, 4724, 3794, 995, 45865, 269], "avg_logprob": -0.37625000953674315, "compression_ratio": 1.1379310344827587, "no_speech_prob": 0.0, "words": [{"start": 1381.35, "end": 1381.75, "word": "if", "probability": 0.03656005859375}, {"start": 1381.75, "end": 1382.05, "word": " is", "probability": 0.6279296875}, {"start": 1382.05, "end": 1382.59, "word": " continuous", "probability": 0.880859375}, {"start": 1382.59, "end": 1383.27, "word": " at", "probability": 0.94921875}, {"start": 1383.27, "end": 1383.89, "word": " c", "probability": 0.60205078125}, {"start": 1383.89, "end": 1388.01, "word": " for", "probability": 0.338134765625}, {"start": 1388.01, "end": 1388.89, "word": " every", "probability": 0.78955078125}, {"start": 1388.89, "end": 1391.91, "word": " for", "probability": 0.53466796875}, {"start": 1391.91, "end": 1392.75, "word": " every", "probability": 0.80615234375}, {"start": 1392.75, "end": 1393.55, "word": " sequence", "probability": 0.97314453125}, {"start": 1393.55, "end": 1395.65, "word": " x", "probability": 0.89501953125}, {"start": 1395.65, "end": 1396.07, "word": " in", "probability": 0.5087890625}, {"start": 1396.07, "end": 1397.05, "word": " contained", "probability": 0.572265625}, {"start": 1397.05, "end": 1397.33, "word": " in", "probability": 0.94921875}, {"start": 1397.33, "end": 1397.81, "word": " a", "probability": 0.6796875}, {"start": 1397.81, "end": 1402.05, "word": " with", "probability": 0.8896484375}, {"start": 1402.05, "end": 1405.37, "word": " limit", "probability": 0.9638671875}, {"start": 1405.37, "end": 1407.29, "word": " x", "probability": 0.97705078125}, {"start": 1407.29, "end": 1407.95, "word": " in", "probability": 0.62353515625}, {"start": 1407.95, "end": 1409.13, "word": " بساوي", "probability": 0.840576171875}, {"start": 1409.13, "end": 1409.67, "word": " c", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 52, "seek": 142579, "start": 1411.09, "end": 1425.79, "text": "نحن لدينا ان ال limit ل f of x n as n tensor infinity بسوي f of c", "tokens": [1863, 5016, 1863, 5296, 16254, 8315, 16472, 2423, 4948, 5296, 283, 295, 2031, 297, 382, 297, 2064, 539, 81, 13202, 4724, 3794, 2407, 1829, 283, 295, 269], "avg_logprob": -0.5764508779559817, "compression_ratio": 0.9879518072289156, "no_speech_prob": 0.0, "words": [{"start": 1411.09, "end": 1411.71, "word": "نحن", "probability": 0.4895426432291667}, {"start": 1411.71, "end": 1414.13, "word": " لدينا", "probability": 0.6939697265625}, {"start": 1414.13, "end": 1414.63, "word": " ان", "probability": 0.3720703125}, {"start": 1414.63, "end": 1414.81, "word": " ال", "probability": 0.2156982421875}, {"start": 1414.81, "end": 1415.27, "word": " limit", "probability": 0.2066650390625}, {"start": 1415.27, "end": 1417.25, "word": " ل", "probability": 0.84033203125}, {"start": 1417.25, "end": 1417.69, "word": " f", "probability": 0.322998046875}, {"start": 1417.69, "end": 1417.97, "word": " of", "probability": 0.314697265625}, {"start": 1417.97, "end": 1418.57, "word": " x", "probability": 0.9150390625}, {"start": 1418.57, "end": 1419.29, "word": " n", "probability": 0.1751708984375}, {"start": 1419.29, "end": 1420.87, "word": " as", "probability": 0.64111328125}, {"start": 1420.87, "end": 1421.27, "word": " n", "probability": 0.72607421875}, {"start": 1421.27, "end": 1421.71, "word": " tensor", "probability": 0.7649739583333334}, {"start": 1421.71, "end": 1422.33, "word": " infinity", "probability": 0.80517578125}, {"start": 1422.33, "end": 1423.57, "word": " بسوي", "probability": 0.524169921875}, {"start": 1423.57, "end": 1425.23, "word": " f", "probability": 0.81005859375}, {"start": 1425.23, "end": 1425.51, "word": " of", "probability": 0.7861328125}, {"start": 1425.51, "end": 1425.79, "word": " c", "probability": 0.74658203125}], "temperature": 1.0}, {"id": 53, "seek": 145990, "start": 1431.74, "end": 1459.9, "text": "الان الـ sequential criterion for continuity بتقول عشان اثبت ان الدالة F continuous عند نقطة يكفي ان انا اثبت ان لو اخدت اي sequence نهايتها اي sequence في مجال الدالة طبعا كنا في ال limits نشترط ان X in كل انصر في ال sequence مختلف عن ال C هنا لأ ممكن يساوي ال C مش مشكلة هاي الاختلاف بس بين ال sequential criterion for limits", "tokens": [6027, 7649, 2423, 39184, 42881, 46691, 337, 23807, 39894, 39648, 6225, 8592, 7649, 1975, 12984, 3555, 2655, 16472, 32748, 6027, 3660, 479, 10957, 43242, 8717, 47432, 3660, 7251, 4117, 41185, 16472, 1975, 8315, 1975, 12984, 3555, 2655, 16472, 45164, 1975, 9778, 3215, 2655, 1975, 1829, 8310, 8717, 11296, 36081, 11296, 1975, 1829, 8310, 8978, 3714, 7435, 6027, 32748, 6027, 3660, 23032, 3555, 3615, 995, 9122, 8315, 8978, 2423, 10406, 8717, 8592, 2655, 2288, 9566, 16472, 1783, 294, 28242, 16472, 9381, 2288, 8978, 2423, 8310, 3714, 46456, 46538, 18871, 2423, 383, 34105, 5296, 10721, 3714, 43020, 7251, 3794, 995, 45865, 2423, 383, 37893, 37893, 28820, 3660, 8032, 47302, 2423, 47283, 2655, 15040, 5172, 4724, 3794, 49374, 2423, 42881, 46691, 337, 10406], "avg_logprob": -0.2040289305458384, "compression_ratio": 1.8615384615384616, "no_speech_prob": 0.0, "words": [{"start": 1431.74, "end": 1432.14, "word": "الان", "probability": 0.153717041015625}, {"start": 1432.14, "end": 1432.38, "word": " الـ", "probability": 0.4952392578125}, {"start": 1432.38, "end": 1432.74, "word": " sequential", "probability": 0.70849609375}, {"start": 1432.74, "end": 1433.46, "word": " criterion", "probability": 0.91845703125}, {"start": 1433.46, "end": 1433.92, "word": " for", "probability": 0.93017578125}, {"start": 1433.92, "end": 1434.54, "word": " continuity", "probability": 0.80126953125}, {"start": 1434.54, "end": 1434.94, "word": " بتقول", "probability": 0.877685546875}, {"start": 1434.94, "end": 1435.48, "word": " عشان", "probability": 0.77783203125}, {"start": 1435.48, "end": 1436.52, "word": " اثبت", "probability": 0.8707275390625}, {"start": 1436.52, "end": 1436.68, "word": " ان", "probability": 0.81005859375}, {"start": 1436.68, "end": 1437.12, "word": " الدالة", "probability": 0.7762044270833334}, {"start": 1437.12, "end": 1437.32, "word": " F", "probability": 0.47607421875}, {"start": 1437.32, "end": 1437.86, "word": " continuous", "probability": 0.8056640625}, {"start": 1437.86, "end": 1438.26, "word": " عند", "probability": 0.896484375}, {"start": 1438.26, "end": 1438.8, "word": " نقطة", "probability": 0.7805989583333334}, {"start": 1438.8, "end": 1440.22, "word": " يكفي", "probability": 0.9192708333333334}, {"start": 1440.22, "end": 1440.38, "word": " ان", "probability": 0.826171875}, {"start": 1440.38, "end": 1440.52, "word": " انا", "probability": 0.76318359375}, {"start": 1440.52, "end": 1441.04, "word": " اثبت", "probability": 0.9725341796875}, {"start": 1441.04, "end": 1441.24, "word": " ان", "probability": 0.9248046875}, {"start": 1441.24, "end": 1441.42, "word": " لو", "probability": 0.71630859375}, {"start": 1441.42, "end": 1441.88, "word": " اخدت", "probability": 0.891845703125}, {"start": 1441.88, "end": 1442.12, "word": " اي", "probability": 0.83544921875}, {"start": 1442.12, "end": 1442.7, "word": " sequence", "probability": 0.9150390625}, {"start": 1442.7, "end": 1443.58, "word": " نهايتها", "probability": 0.9227294921875}, {"start": 1443.58, "end": 1444.9, "word": " اي", "probability": 0.901123046875}, {"start": 1444.9, "end": 1445.36, "word": " sequence", "probability": 0.9755859375}, {"start": 1445.36, "end": 1445.52, "word": " في", "probability": 0.90869140625}, {"start": 1445.52, "end": 1445.86, "word": " مجال", "probability": 0.9964192708333334}, {"start": 1445.86, "end": 1446.4, "word": " الدالة", "probability": 0.9915364583333334}, {"start": 1446.4, "end": 1446.72, "word": " طبعا", "probability": 0.9638671875}, {"start": 1446.72, "end": 1446.96, "word": " كنا", "probability": 0.9814453125}, {"start": 1446.96, "end": 1447.12, "word": " في", "probability": 0.845703125}, {"start": 1447.12, "end": 1447.24, "word": " ال", "probability": 0.900390625}, {"start": 1447.24, "end": 1447.66, "word": " limits", "probability": 0.96826171875}, {"start": 1447.66, "end": 1449.06, "word": " نشترط", "probability": 0.6869140625}, {"start": 1449.06, "end": 1449.22, "word": " ان", "probability": 0.916015625}, {"start": 1449.22, "end": 1449.52, "word": " X", "probability": 0.73388671875}, {"start": 1449.52, "end": 1449.84, "word": " in", "probability": 0.3447265625}, {"start": 1449.84, "end": 1450.34, "word": " كل", "probability": 0.96630859375}, {"start": 1450.34, "end": 1450.7, "word": " انصر", "probability": 0.6695149739583334}, {"start": 1450.7, "end": 1450.82, "word": " في", "probability": 0.9345703125}, {"start": 1450.82, "end": 1450.88, "word": " ال", "probability": 0.96044921875}, {"start": 1450.88, "end": 1451.28, "word": " sequence", "probability": 0.9833984375}, {"start": 1451.28, "end": 1451.94, "word": " مختلف", "probability": 0.986328125}, {"start": 1451.94, "end": 1452.66, "word": " عن", "probability": 0.9794921875}, {"start": 1452.66, "end": 1452.86, "word": " ال", "probability": 0.8125}, {"start": 1452.86, "end": 1453.02, "word": " C", "probability": 0.7490234375}, {"start": 1453.02, "end": 1453.28, "word": " هنا", "probability": 0.81591796875}, {"start": 1453.28, "end": 1453.52, "word": " لأ", "probability": 0.930419921875}, {"start": 1453.52, "end": 1453.82, "word": " ممكن", "probability": 0.96826171875}, {"start": 1453.82, "end": 1454.18, "word": " يساوي", "probability": 0.7977294921875}, {"start": 1454.18, "end": 1454.32, "word": " ال", "probability": 0.75830078125}, {"start": 1454.32, "end": 1454.42, "word": " C", "probability": 0.92236328125}, {"start": 1454.42, "end": 1454.62, "word": " مش", "probability": 0.94775390625}, {"start": 1454.62, "end": 1455.18, "word": " مشكلة", "probability": 0.9514973958333334}, {"start": 1455.18, "end": 1456.42, "word": " هاي", "probability": 0.698974609375}, {"start": 1456.42, "end": 1456.92, "word": " الاختلاف", "probability": 0.88662109375}, {"start": 1456.92, "end": 1457.2, "word": " بس", "probability": 0.98681640625}, {"start": 1457.2, "end": 1457.48, "word": " بين", "probability": 0.91845703125}, {"start": 1457.48, "end": 1457.8, "word": " ال", "probability": 0.97119140625}, {"start": 1457.8, "end": 1458.24, "word": " sequential", "probability": 0.94921875}, {"start": 1458.24, "end": 1458.9, "word": " criterion", "probability": 0.95703125}, {"start": 1458.9, "end": 1459.4, "word": " for", "probability": 0.9560546875}, {"start": 1459.4, "end": 1459.9, "word": " limits", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 54, "seek": 147869, "start": 1460.65, "end": 1478.69, "text": "و Sequential criterion for continuity إنه لكل sequence x in في مجال الدالة و نهايتها بتساوي c لازم اطلع عندي نهاية ال image تبعت ال sequence x in بتساوي العدد f و c", "tokens": [2407, 46859, 2549, 46691, 337, 23807, 36145, 3224, 5296, 28820, 8310, 2031, 294, 8978, 3714, 7435, 6027, 32748, 6027, 3660, 4032, 8717, 11296, 36081, 11296, 39894, 3794, 995, 45865, 269, 5296, 31377, 2304, 1975, 9566, 1211, 3615, 18871, 16254, 8717, 11296, 10632, 2423, 3256, 6055, 3555, 34268, 2423, 8310, 2031, 294, 39894, 3794, 995, 45865, 18863, 3215, 3215, 283, 4032, 269], "avg_logprob": -0.23828125, "compression_ratio": 1.4444444444444444, "no_speech_prob": 0.0, "words": [{"start": 1460.65, "end": 1460.85, "word": "و", "probability": 0.69677734375}, {"start": 1460.85, "end": 1461.43, "word": " Sequential", "probability": 0.565185546875}, {"start": 1461.43, "end": 1461.97, "word": " criterion", "probability": 0.77734375}, {"start": 1461.97, "end": 1462.37, "word": " for", "probability": 0.94189453125}, {"start": 1462.37, "end": 1463.21, "word": " continuity", "probability": 0.80078125}, {"start": 1463.21, "end": 1464.47, "word": " إنه", "probability": 0.29693603515625}, {"start": 1464.47, "end": 1464.89, "word": " لكل", "probability": 0.755859375}, {"start": 1464.89, "end": 1465.39, "word": " sequence", "probability": 0.77685546875}, {"start": 1465.39, "end": 1465.65, "word": " x", "probability": 0.5986328125}, {"start": 1465.65, "end": 1465.85, "word": " in", "probability": 0.556640625}, {"start": 1465.85, "end": 1466.03, "word": " في", "probability": 0.890625}, {"start": 1466.03, "end": 1466.41, "word": " مجال", "probability": 0.9925130208333334}, {"start": 1466.41, "end": 1467.11, "word": " الدالة", "probability": 0.9724934895833334}, {"start": 1467.11, "end": 1467.61, "word": " و", "probability": 0.908203125}, {"start": 1467.61, "end": 1468.41, "word": " نهايتها", "probability": 0.8529052734375}, {"start": 1468.41, "end": 1469.79, "word": " بتساوي", "probability": 0.8492431640625}, {"start": 1469.79, "end": 1470.13, "word": " c", "probability": 0.349609375}, {"start": 1470.13, "end": 1471.83, "word": " لازم", "probability": 0.9332682291666666}, {"start": 1471.83, "end": 1472.19, "word": " اطلع", "probability": 0.82647705078125}, {"start": 1472.19, "end": 1472.55, "word": " عندي", "probability": 0.6900634765625}, {"start": 1472.55, "end": 1473.35, "word": " نهاية", "probability": 0.9646809895833334}, {"start": 1473.35, "end": 1474.25, "word": " ال", "probability": 0.92578125}, {"start": 1474.25, "end": 1474.55, "word": " image", "probability": 0.84912109375}, {"start": 1474.55, "end": 1474.95, "word": " تبعت", "probability": 0.8271484375}, {"start": 1474.95, "end": 1475.09, "word": " ال", "probability": 0.70263671875}, {"start": 1475.09, "end": 1475.47, "word": " sequence", "probability": 0.97509765625}, {"start": 1475.47, "end": 1475.83, "word": " x", "probability": 0.95166015625}, {"start": 1475.83, "end": 1476.17, "word": " in", "probability": 0.87548828125}, {"start": 1476.17, "end": 1477.35, "word": " بتساوي", "probability": 0.883056640625}, {"start": 1477.35, "end": 1477.99, "word": " العدد", "probability": 0.9348958333333334}, {"start": 1477.99, "end": 1478.27, "word": " f", "probability": 0.7490234375}, {"start": 1478.27, "end": 1478.47, "word": " و", "probability": 0.962890625}, {"start": 1478.47, "end": 1478.69, "word": " c", "probability": 0.77685546875}], "temperature": 1.0}, {"id": 55, "seek": 150774, "start": 1480.02, "end": 1507.74, "text": "وبرهان النظرية هذه زي برهان sequential criterion for limits مع تعديلات طفيفة مع التعديلات الطفيفة في التعريفين او في التعريف تبع الاتصال اذا ال proof similar to proof of", "tokens": [2407, 26890, 3224, 7649, 28239, 19913, 2288, 10632, 29538, 30767, 1829, 4724, 2288, 3224, 7649, 42881, 46691, 337, 10406, 20449, 37279, 16254, 1211, 9307, 23032, 5172, 33911, 3660, 20449, 16712, 3615, 16254, 1211, 9307, 41950, 5172, 33911, 3660, 8978, 16712, 3615, 16572, 5172, 9957, 1975, 2407, 8978, 16712, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 9307, 9381, 6027, 1975, 15730, 2423, 8177, 2531, 281, 8177, 295], "avg_logprob": 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2058.71, "word": " أربعة", "probability": 0.6745198567708334}, {"start": 2058.71, "end": 2059.33, "word": " واحد", "probability": 0.963134765625}, {"start": 2059.33, "end": 2060.53, "word": " ان", "probability": 0.583984375}, {"start": 2060.53, "end": 2060.99, "word": " limit", "probability": 0.490478515625}, {"start": 2060.99, "end": 2061.47, "word": " F", "probability": 0.291748046875}, {"start": 2061.47, "end": 2061.73, "word": " of", "probability": 0.64599609375}, {"start": 2061.73, "end": 2062.13, "word": " X", "probability": 0.95458984375}, {"start": 2062.13, "end": 2063.19, "word": " لما", "probability": 0.79541015625}, {"start": 2063.19, "end": 2063.53, "word": " X", "probability": 0.95947265625}, {"start": 2063.53, "end": 2063.95, "word": " تقول", "probability": 0.510986328125}, {"start": 2063.95, "end": 2064.39, "word": " C", "probability": 0.51171875}, {"start": 2064.39, "end": 2064.85, "word": " طلعت", "probability": 0.8732096354166666}, {"start": 2064.85, "end": 2065.33, 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continuous", "probability": 0.92626953125}, {"start": 2073.39, "end": 2075.21, "word": " at", "probability": 0.943359375}, {"start": 2075.21, "end": 2075.61, "word": " C", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 75, "seek": 210373, "start": 2079.86, "end": 2103.74, "text": "و بما انه c arbitrary element اذا ال F يكون continuous at every c ينتمي ال R وبالتالي continuous على كل ال R ممكن برضه", "tokens": [2407, 4724, 15042, 16472, 3224, 269, 23211, 4478, 1975, 15730, 2423, 479, 7251, 30544, 10957, 412, 633, 269, 7251, 29399, 2304, 1829, 2423, 497, 46599, 6027, 2655, 6027, 1829, 10957, 15844, 28242, 2423, 497, 3714, 43020, 4724, 43042, 3224], "avg_logprob": -0.3755859464406967, "compression_ratio": 1.251908396946565, "no_speech_prob": 0.0, "words": [{"start": 2079.86, "end": 2080.22, "word": "و", "probability": 0.461181640625}, {"start": 2080.22, "end": 2080.66, "word": " بما", "probability": 0.70849609375}, {"start": 2080.66, "end": 2081.22, "word": " انه", 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اثبتنا ان ال limit ل ال function f and c بالساوية c في section اربعة واحدة انا ممكن اثبت يعني استخدم تعريف epsilon دلتا مباشرة و اقول let if fix اول حاجة fix c تنتمي ل R to show", "tokens": [1863, 14851, 9778, 40448, 37279, 16572, 5172, 17889, 11778, 1211, 2655, 995, 3714, 3555, 33599, 25720, 4724, 1211, 33599, 8717, 39648, 16472, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 16472, 2423, 4948, 5296, 2423, 2445, 283, 293, 269, 20666, 3794, 995, 2407, 10632, 269, 8978, 3541, 1975, 25513, 27884, 36764, 24401, 3660, 1975, 8315, 3714, 43020, 1975, 12984, 3555, 2655, 37495, 22653, 44713, 9778, 40448, 37279, 16572, 5172, 17889, 11778, 1211, 2655, 995, 3714, 3555, 33599, 25720, 4032, 1975, 39648, 718, 498, 3191, 1975, 12610, 11331, 26108, 3660, 3191, 269, 6055, 29399, 2304, 1829, 5296, 497, 281, 855], "avg_logprob": -0.28937500923871995, "compression_ratio": 1.7241379310344827, "no_speech_prob": 0.0, "words": [{"start": 2105.0, "end": 2105.82, "word": "نستخدم", "probability": 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at c let epsilon أكبر من السفر be given it shows .. زي ما عملنا في ال limits it shows delta بساوي epsilon لذن هي يوجد delta تعتمد على epsilon", "tokens": [351, 307, 10957, 412, 269, 718, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 312, 2212, 309, 3110, 4386, 30767, 1829, 19446, 6225, 42213, 8315, 8978, 2423, 10406, 309, 3110, 8289, 4724, 3794, 995, 45865, 17889, 5296, 8848, 1863, 39896, 7251, 29245, 3215, 8289, 6055, 34268, 2304, 3215, 15844, 17889], "avg_logprob": -0.3155637313337887, "compression_ratio": 1.3246753246753247, "no_speech_prob": 0.0, "words": [{"start": 2130.38, "end": 2130.88, "word": "if", "probability": 0.061187744140625}, {"start": 2130.88, "end": 2132.18, "word": " is", "probability": 0.75439453125}, {"start": 2132.18, "end": 2133.2, "word": " continuous", "probability": 0.8876953125}, {"start": 2133.2, "end": 2134.96, "word": " at", "probability": 0.833984375}, {"start": 2134.96, "end": 2135.4, "word": " c", "probability": 0.66796875}, {"start": 2135.4, 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2235.89, "text": "at C since C تنتمي ل R was arbitrary اذا F is continuous على كل الأعداد الحقيقية تمام؟ اذا هذا ممكن استخدم تعريف Epsilon Delta مباشرة", "tokens": [267, 383, 1670, 383, 6055, 29399, 2304, 1829, 5296, 497, 390, 23211, 1975, 15730, 479, 307, 10957, 15844, 28242, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 46811, 10943, 22807, 1975, 15730, 23758, 3714, 43020, 44713, 9778, 40448, 37279, 16572, 5172, 462, 16592, 18183, 3714, 3555, 33599, 25720], "avg_logprob": -0.27376303014655906, "compression_ratio": 1.204968944099379, "no_speech_prob": 0.0, "words": [{"start": 2216.73, "end": 2217.63, "word": "at", "probability": 0.11419677734375}, {"start": 2217.63, "end": 2218.39, "word": " C", "probability": 0.53857421875}, {"start": 2218.39, "end": 2220.81, "word": " since", "probability": 0.5205078125}, {"start": 2220.81, "end": 2221.27, "word": " C", "probability": 0.92138671875}, {"start": 2221.27, "end": 2221.85, "word": " تنتمي", "probability": 0.9354248046875}, {"start": 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2313.31, "word": " صفر", "probability": 0.7333984375}, {"start": 2313.31, "end": 2314.21, "word": " و", "probability": 0.875}, {"start": 2314.21, "end": 2314.97, "word": " بنجيب", "probability": 0.904541015625}, {"start": 2314.97, "end": 2315.39, "word": " دلتا", "probability": 0.843505859375}, {"start": 2315.39, "end": 2315.61, "word": " زي", "probability": 0.980224609375}, {"start": 2315.61, "end": 2315.71, "word": " ما", "probability": 0.9638671875}, {"start": 2315.71, "end": 2316.11, "word": " عملنا", "probability": 0.9903971354166666}, {"start": 2316.11, "end": 2316.23, "word": " في", "probability": 0.8603515625}, {"start": 2316.23, "end": 2316.49, "word": " section", "probability": 0.84521484375}, {"start": 2316.49, "end": 2316.89, "word": " اربعة", "probability": 0.6676432291666666}, {"start": 2316.89, "end": 2317.27, "word": " واحد", "probability": 0.966796875}, {"start": 2317.27, "end": 2317.65, "word": " دلتا", "probability": 0.942138671875}, {"start": 2317.65, "end": 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لو", "probability": 0.86669921875}, {"start": 2332.32, "end": 2332.66, "word": " طلب", "probability": 0.92822265625}, {"start": 2332.66, "end": 2333.12, "word": " منكم", "probability": 0.9697265625}, {"start": 2333.12, "end": 2334.14, "word": " استخدام", "probability": 0.9283447265625}, {"start": 2334.14, "end": 2334.58, "word": " تعريف", "probability": 0.9947916666666666}, {"start": 2334.58, "end": 2334.96, "word": " epsilon", "probability": 0.38232421875}, {"start": 2334.96, "end": 2335.3, "word": " delta", "probability": 0.289794921875}, {"start": 2335.3, "end": 2335.82, "word": " لإثبات", "probability": 0.9251953125}, {"start": 2335.82, "end": 2335.94, "word": " أن", "probability": 0.6201171875}, {"start": 2335.94, "end": 2336.28, "word": " الدالة", "probability": 0.81298828125}, {"start": 2336.28, "end": 2336.46, "word": " هذه", "probability": 0.638671875}, {"start": 2336.46, "end": 2337.06, "word": " مقتصرة", "probability": 0.81201171875}, {"start": 2337.06, "end": 2337.24, 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2375.85, "end": 2376.59, "word": " تربية", "probability": 0.7816162109375}, {"start": 2376.59, "end": 2377.29, "word": " اللي", "probability": 0.88427734375}, {"start": 2377.29, "end": 2377.55, "word": " هي", "probability": 0.88427734375}, {"start": 2377.55, "end": 2377.95, "word": " F", "probability": 0.9228515625}, {"start": 2377.95, "end": 2378.21, "word": " of", "probability": 0.92138671875}, {"start": 2378.21, "end": 2378.49, "word": " C", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 86, "seek": 239419, "start": 2381.21, "end": 2394.19, "text": "حسب تعريف الاتصال على النقطة بيطلع أي شرط تلاتة في واحد متحقق وبالتاني if is continuous at c okay تمام", "tokens": [5016, 35457, 37279, 16572, 5172, 2423, 9307, 9381, 6027, 15844, 28239, 47432, 3660, 4724, 1829, 9566, 1211, 3615, 36632, 13412, 2288, 9566, 6055, 1211, 9307, 3660, 8978, 36764, 24401, 44650, 5016, 4587, 4587, 46599, 6027, 2655, 7649, 1829, 498, 307, 10957, 412, 269, 1392, 46811, 10943], "avg_logprob": 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0.994384765625}, {"start": 2385.47, "end": 2386.19, "word": " متحقق", "probability": 0.79052734375}, {"start": 2386.19, "end": 2387.35, "word": " وبالتاني", "probability": 0.8630859375}, {"start": 2387.35, "end": 2387.55, "word": " if", "probability": 0.57958984375}, {"start": 2387.55, "end": 2387.77, "word": " is", "probability": 0.56591796875}, {"start": 2387.77, "end": 2388.51, "word": " continuous", "probability": 0.91552734375}, {"start": 2388.51, "end": 2390.31, "word": " at", "probability": 0.9287109375}, {"start": 2390.31, "end": 2391.13, "word": " c", "probability": 0.5263671875}, {"start": 2391.13, "end": 2393.69, "word": " okay", "probability": 0.313232421875}, {"start": 2393.69, "end": 2394.19, "word": " تمام", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 87, "seek": 242392, "start": 2397.19, "end": 2423.93, "text": "وطبعاً بما أن الـ C تنتمي الـ R was arbitrary إذن الدالة F continuous على كل الـ R okay إذا دامت ياندي إما نستخدم نتائج section 4-1 أو نعيد البرهان باستخدام تعريف epsilon Delta زي ما عملنا في المثال الأخير أو زي ما عملنا في section 4-1 الدالة كمان عندي الدالة", "tokens": [2407, 9566, 3555, 3615, 995, 14111, 4724, 15042, 14739, 2423, 39184, 383, 6055, 29399, 2304, 1829, 2423, 39184, 497, 390, 23211, 11933, 8848, 1863, 32748, 6027, 3660, 479, 10957, 15844, 28242, 2423, 39184, 497, 1392, 11933, 15730, 11778, 10943, 2655, 7251, 7649, 16254, 11933, 15042, 8717, 14851, 9778, 40448, 8717, 2655, 16373, 7435, 3541, 1017, 12, 16, 34051, 8717, 3615, 25708, 2423, 26890, 3224, 7649, 4724, 995, 14851, 9778, 3215, 10943, 37279, 16572, 5172, 17889, 18183, 30767, 1829, 19446, 6225, 42213, 8315, 8978, 9673, 12984, 6027, 16247, 9778, 13546, 34051, 30767, 1829, 19446, 6225, 42213, 8315, 8978, 3541, 1017, 12, 16, 32748, 6027, 3660, 9122, 2304, 7649, 18871, 16254, 32748, 6027, 3660], "avg_logprob": -0.279314171951429, "compression_ratio": 1.6571428571428573, "no_speech_prob": 0.0, "words": [{"start": 2397.19, "end": 2397.83, "word": "وطبعاً", 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" F", "probability": 0.42919921875}, {"start": 2400.77, "end": 2401.31, "word": " continuous", "probability": 0.5634765625}, {"start": 2401.31, "end": 2401.73, "word": " على", "probability": 0.9189453125}, {"start": 2401.73, "end": 2402.19, "word": " كل", "probability": 0.93798828125}, {"start": 2402.19, "end": 2402.57, "word": " الـ", "probability": 0.76025390625}, {"start": 2402.57, "end": 2402.83, "word": " R", "probability": 0.73193359375}, {"start": 2402.83, "end": 2403.21, "word": " okay", "probability": 0.1417236328125}, {"start": 2403.21, "end": 2403.49, "word": " إذا", "probability": 0.65625}, {"start": 2403.49, "end": 2403.97, "word": " دامت", "probability": 0.6162109375}, {"start": 2403.97, "end": 2404.41, "word": " ياندي", "probability": 0.8631184895833334}, {"start": 2404.41, "end": 2405.55, "word": " إما", "probability": 0.768310546875}, {"start": 2405.55, "end": 2406.79, "word": " نستخدم", "probability": 0.978271484375}, {"start": 2406.79, "end": 2407.25, "word": " 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"probability": 0.966796875}, {"start": 2704.73, "end": 2706.29, "word": " tends", "probability": 0.8212890625}, {"start": 2706.29, "end": 2706.47, "word": " to", "probability": 0.984375}, {"start": 2706.47, "end": 2706.97, "word": " zero", "probability": 0.82470703125}, {"start": 2706.97, "end": 2707.37, "word": " does", "probability": 0.85009765625}, {"start": 2707.37, "end": 2707.69, "word": " not", "probability": 0.96728515625}, {"start": 2707.69, "end": 2708.29, "word": " exist", "probability": 0.9580078125}, {"start": 2708.29, "end": 2710.11, "word": " أثبتنا", "probability": 0.9673828125}, {"start": 2710.11, "end": 2710.29, "word": " إن", "probability": 0.34912109375}, {"start": 2710.29, "end": 2710.67, "word": " الـ", "probability": 0.5570068359375}, {"start": 2710.67, "end": 2710.95, "word": " function", "probability": 0.90185546875}, {"start": 2710.95, "end": 2711.37, "word": " هذه", "probability": 0.51513671875}, {"start": 2711.37, "end": 2711.49, "word": " ما", "probability": 0.53076171875}, {"start": 2711.49, "end": 2711.79, "word": " لهاش", "probability": 0.653564453125}, {"start": 2711.79, "end": 2712.03, "word": " limit", "probability": 0.9306640625}, {"start": 2712.03, "end": 2712.35, "word": " عند", "probability": 0.98974609375}, {"start": 2712.35, "end": 2712.85, "word": " السفر", "probability": 0.8251953125}], "temperature": 1.0}, {"id": 98, "seek": 274255, "start": 2715.83, "end": 2742.55, "text": "فا استخدمنا ال divergence criterion ا شفنا ان هناك sequence اللى هى واحد عال ان converge للسفر but limit ال image لل sequence واحد على ان as n tends to infinity بساوي limit in بساوي infinity does not exist in R", "tokens": [5172, 995, 44713, 9778, 40448, 8315, 2423, 47387, 46691, 1975, 13412, 5172, 8315, 16472, 34105, 4117, 8310, 13672, 7578, 8032, 7578, 36764, 24401, 6225, 6027, 16472, 41881, 24976, 3794, 5172, 2288, 457, 4948, 2423, 3256, 24976, 8310, 36764, 24401, 15844, 16472, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 4948, 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0.430908203125}, {"start": 2737.81, "end": 2738.77, "word": " بساوي", "probability": 0.90185546875}, {"start": 2738.77, "end": 2739.39, "word": " infinity", "probability": 0.8642578125}, {"start": 2739.39, "end": 2739.85, "word": " does", "probability": 0.51123046875}, {"start": 2739.85, "end": 2740.17, "word": " not", "probability": 0.970703125}, {"start": 2740.17, "end": 2740.87, "word": " exist", "probability": 0.9482421875}, {"start": 2740.87, "end": 2742.17, "word": " in", "probability": 0.96728515625}, {"start": 2742.17, "end": 2742.55, "word": " R", "probability": 0.80712890625}], "temperature": 1.0}, {"id": 99, "seek": 277265, "start": 2744.21, "end": 2772.65, "text": "وبالتالي by divergence criterion ال function هذه مالهاش limit وبالتالي مش ممكن تكون continuous so if I can't be continuous at x بساوي سفر تمام؟ لأن واحد من الشروط التلاتة تبعت الاتصال عن نقطة غير متحققة تمام؟", "tokens": [37746, 6027, 2655, 6027, 1829, 538, 47387, 46691, 2423, 2445, 29538, 19446, 43761, 33599, 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section", "probability": 0.8525390625}, {"start": 2840.93, "end": 2841.39, "word": " أربعة", "probability": 0.6333821614583334}, {"start": 2841.39, "end": 2841.93, "word": " واحد", "probability": 0.96875}, {"start": 2841.93, "end": 2842.93, "word": " انه", "probability": 0.58984375}, {"start": 2842.93, "end": 2843.33, "word": " limit", "probability": 0.79833984375}, {"start": 2843.33, "end": 2843.55, "word": " ل", "probability": 0.89013671875}, {"start": 2843.55, "end": 2844.41, "word": " signum", "probability": 0.6656494140625}, {"start": 2844.41, "end": 2845.45, "word": " x", "probability": 0.7236328125}, {"start": 2845.45, "end": 2846.83, "word": " لما", "probability": 0.884521484375}, {"start": 2846.83, "end": 2847.17, "word": " x", "probability": 0.9130859375}, {"start": 2847.17, "end": 2847.87, "word": " تقول", "probability": 0.963134765625}, {"start": 2847.87, "end": 2848.43, "word": " إلى", "probability": 0.437255859375}, {"start": 2848.43, "end": 2849.19, "word": " سفر", "probability": 0.8865559895833334}, {"start": 2849.19, "end": 2850.63, "word": " does", "probability": 0.7373046875}, {"start": 2850.63, "end": 2850.93, "word": " not", "probability": 0.9716796875}, {"start": 2850.93, "end": 2851.49, "word": " exist", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 103, "seek": 288758, "start": 2860.56, "end": 2887.58, "text": "اللي هي ان ال limit لل signal function عند السفر does not exist شوفنا ان ال limit من اليمين واحد عند السفر و ال limit و ال limit عند السفر مليار ساعة سالف واحد وبالتالي مش متساوي اتين اذا ال limit عند السفر does not exist okay تمام اذا ال ال function هذه ماهياش متصلة عند السفر لعدم نظرا لعدم وجود ال limit عند السفر", "tokens": [6027, 20292, 39896, 16472, 2423, 4948, 24976, 6358, 2445, 43242, 21136, 5172, 2288, 775, 406, 2514, 13412, 38688, 8315, 16472, 2423, 4948, 9154, 45595, 2304, 9957, 36764, 24401, 43242, 21136, 5172, 2288, 4032, 2423, 4948, 4032, 2423, 4948, 43242, 21136, 5172, 2288, 3714, 20292, 9640, 8608, 995, 27884, 8608, 6027, 5172, 36764, 24401, 46599, 6027, 2655, 6027, 1829, 37893, 44650, 3794, 995, 45865, 1975, 2655, 9957, 1975, 15730, 2423, 4948, 43242, 21136, 5172, 2288, 775, 406, 2514, 1392, 46811, 10943, 1975, 15730, 2423, 2423, 2445, 29538, 19446, 3224, 1829, 33599, 44650, 36520, 3660, 43242, 21136, 5172, 2288, 5296, 22488, 2304, 8717, 19913, 23557, 5296, 22488, 2304, 49610, 23328, 2423, 4948, 43242, 21136, 5172, 2288], "avg_logprob": -0.2604619674060656, "compression_ratio": 2.238532110091743, "no_speech_prob": 0.0, "words": [{"start": 2860.56, "end": 2860.84, "word": "اللي", "probability": 0.3155517578125}, {"start": 2860.84, "end": 2860.94, "word": " هي", "probability": 0.469482421875}, {"start": 2860.94, "end": 2861.08, "word": " ان", "probability": 0.394287109375}, {"start": 2861.08, "end": 2861.2, "word": " ال", "probability": 0.59326171875}, {"start": 2861.2, "end": 2861.44, "word": " limit", "probability": 0.82763671875}, {"start": 2861.44, "end": 2861.66, "word": " 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" من", "probability": 0.9736328125}, {"start": 2865.64, "end": 2866.06, "word": " اليمين", "probability": 0.8009440104166666}, {"start": 2866.06, "end": 2866.58, "word": " واحد", "probability": 0.8359375}, {"start": 2866.58, "end": 2866.8, "word": " عند", "probability": 0.98486328125}, {"start": 2866.8, "end": 2867.34, "word": " السفر", "probability": 0.9860026041666666}, {"start": 2867.34, "end": 2867.98, "word": " و", "probability": 0.51611328125}, {"start": 2867.98, "end": 2868.06, "word": " ال", "probability": 0.482666015625}, {"start": 2868.06, "end": 2868.4, "word": " limit", "probability": 0.96044921875}, {"start": 2868.4, "end": 2868.62, "word": " و", "probability": 0.35595703125}, {"start": 2868.62, "end": 2868.74, "word": " ال", "probability": 0.80224609375}, {"start": 2868.74, "end": 2868.96, "word": " limit", "probability": 0.9765625}, {"start": 2868.96, "end": 2869.24, "word": " عند", "probability": 0.9853515625}, {"start": 2869.24, "end": 2869.68, "word": " السفر", 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عند", "probability": 0.951171875}, {"start": 2873.74, "end": 2874.04, "word": " السفر", "probability": 0.9900716145833334}, {"start": 2874.04, "end": 2874.26, "word": " does", "probability": 0.8193359375}, {"start": 2874.26, "end": 2874.52, "word": " not", "probability": 0.96435546875}, {"start": 2874.52, "end": 2874.98, "word": " exist", "probability": 0.955078125}, {"start": 2874.98, "end": 2876.82, "word": " okay", "probability": 0.392822265625}, {"start": 2876.82, "end": 2878.64, "word": " تمام", "probability": 0.948486328125}, {"start": 2878.64, "end": 2879.06, "word": " اذا", "probability": 0.6634521484375}, {"start": 2879.06, "end": 2879.46, "word": " ال", "probability": 0.95751953125}, {"start": 2879.46, "end": 2880.0, "word": " ال", "probability": 0.560546875}, {"start": 2880.0, "end": 2880.38, "word": " function", "probability": 0.85546875}, {"start": 2880.38, "end": 2880.68, "word": " هذه", "probability": 0.7138671875}, {"start": 2880.68, "end": 2881.2, "word": " ماهياش", "probability": 0.9508056640625}, {"start": 2881.2, "end": 2881.84, "word": " متصلة", "probability": 0.9246419270833334}, {"start": 2881.84, "end": 2882.04, "word": " عند", "probability": 0.98876953125}, {"start": 2882.04, "end": 2882.58, "word": " السفر", "probability": 0.9933268229166666}, {"start": 2882.58, "end": 2883.86, "word": " لعدم", "probability": 0.9368489583333334}, {"start": 2883.86, "end": 2884.24, "word": " نظرا", "probability": 0.70751953125}, {"start": 2884.24, "end": 2884.7, "word": " لعدم", "probability": 0.94921875}, {"start": 2884.7, "end": 2885.12, "word": " وجود", "probability": 0.955078125}, {"start": 2885.12, "end": 2885.28, "word": " ال", "probability": 0.59716796875}, {"start": 2885.28, "end": 2885.64, "word": " limit", "probability": 0.98681640625}, {"start": 2885.64, "end": 2886.92, "word": " عند", "probability": 0.96630859375}, {"start": 2886.92, "end": 2887.58, "word": " السفر", "probability": 0.9923502604166666}], "temperature": 1.0}, {"id": 104, "seek": 291285, "start": 2888.83, "end": 2912.85, "text": "رغم أن الدالة هذه معرفة عند السفر، الـSignum للسفر هي معرفة عند السفر بساوي سفر تمام؟ طيب، لكن ممكن اثبات أن الـSignum function متصلة عند كل X لا يساوي سفر", "tokens": [2288, 17082, 2304, 14739, 32748, 6027, 3660, 29538, 20449, 28480, 3660, 43242, 21136, 5172, 2288, 12399, 2423, 39184, 50, 788, 449, 24976, 3794, 5172, 2288, 39896, 20449, 28480, 3660, 43242, 21136, 5172, 2288, 4724, 3794, 995, 45865, 8608, 5172, 2288, 46811, 10943, 22807, 23032, 1829, 3555, 12399, 44381, 3714, 43020, 1975, 12984, 3555, 9307, 14739, 2423, 39184, 50, 788, 449, 2445, 44650, 36520, 3660, 43242, 28242, 1783, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.24259868813188454, "compression_ratio": 1.6560509554140128, "no_speech_prob": 0.0, "words": [{"start": 2888.83, "end": 2889.29, "word": "رغم", "probability": 0.83251953125}, {"start": 2889.29, "end": 2889.53, "word": " أن", "probability": 0.60546875}, {"start": 2889.53, "end": 2890.03, 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2897.31, "end": 2897.73, "word": " سفر", "probability": 0.85546875}, {"start": 2897.73, "end": 2904.93, "word": " تمام؟", "probability": 0.6940104166666666}, {"start": 2904.93, "end": 2906.37, "word": " طيب،", "probability": 0.851806640625}, {"start": 2906.37, "end": 2907.35, "word": " لكن", "probability": 0.76123046875}, {"start": 2907.35, "end": 2907.77, "word": " ممكن", "probability": 0.96240234375}, {"start": 2907.77, "end": 2908.41, "word": " اثبات", "probability": 0.83892822265625}, {"start": 2908.41, "end": 2908.67, "word": " أن", "probability": 0.6484375}, {"start": 2908.67, "end": 2909.19, "word": " الـSignum", "probability": 0.8892578125}, {"start": 2909.19, "end": 2909.57, "word": " function", "probability": 0.74755859375}, {"start": 2909.57, "end": 2910.71, "word": " متصلة", "probability": 0.892578125}, {"start": 2910.71, "end": 2911.11, "word": " عند", "probability": 0.8701171875}, {"start": 2911.11, "end": 2911.43, "word": " كل", "probability": 0.99072265625}, {"start": 2911.43, "end": 2911.81, "word": " X", "probability": 0.75048828125}, {"start": 2911.81, "end": 2912.05, "word": " لا", "probability": 0.8154296875}, {"start": 2912.05, "end": 2912.49, "word": " يساوي", "probability": 0.83575439453125}, {"start": 2912.49, "end": 2912.85, "word": " سفر", "probability": 0.9840494791666666}], "temperature": 1.0}, {"id": 105, "seek": 294946, "start": 2925.1, "end": 2949.46, "text": "However، الـ signum الـ signum function is continuous at every x لا يساوي سفر لأنه", "tokens": [6462, 1054, 12399, 2423, 39184, 1465, 449, 2423, 39184, 1465, 449, 2445, 307, 10957, 412, 633, 2031, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 33456, 3224], "avg_logprob": -0.34455817732317695, "compression_ratio": 1.0842105263157895, "no_speech_prob": 0.0, "words": [{"start": 2925.1, "end": 2926.42, "word": "However،", "probability": 0.4700113932291667}, {"start": 2926.42, "end": 2926.5, "word": " الـ", "probability": 0.798095703125}, {"start": 2926.5, "end": 2927.02, "word": " signum", "probability": 0.59619140625}, {"start": 2927.02, "end": 2929.38, "word": " الـ", "probability": 0.448974609375}, {"start": 2929.38, "end": 2929.72, "word": " signum", "probability": 0.793212890625}, {"start": 2929.72, "end": 2930.28, "word": " function", "probability": 0.9375}, {"start": 2930.28, "end": 2932.44, "word": " is", "probability": 0.71923828125}, {"start": 2932.44, "end": 2933.46, "word": " continuous", "probability": 0.92138671875}, {"start": 2933.46, "end": 2939.28, "word": " at", "probability": 0.869140625}, {"start": 2939.28, "end": 2939.94, "word": " every", "probability": 0.8046875}, {"start": 2939.94, "end": 2941.7, "word": " x", "probability": 0.703125}, {"start": 2941.7, "end": 2942.04, "word": " لا", "probability": 0.84326171875}, {"start": 2942.04, "end": 2942.66, "word": " يساوي", "probability": 0.898193359375}, {"start": 2942.66, "end": 2943.1, "word": " سفر", "probability": 0.8219401041666666}, {"start": 2943.1, "end": 2949.46, "word": " لأنه", "probability": 0.88037109375}], "temperature": 1.0}, {"id": 106, "seek": 298929, "start": 2962.23, "end": 2989.29, "text": "proof fix c لا تنتمي لار وc لا يساوي ستة تمام then absolute signum x minus signum", "tokens": [15690, 3191, 269, 20193, 6055, 29399, 2304, 1829, 5296, 9640, 4032, 66, 20193, 7251, 3794, 995, 45865, 8608, 2655, 3660, 46811, 10943, 550, 8236, 1465, 449, 2031, 3175, 1465, 449], "avg_logprob": -0.37676410328957344, "compression_ratio": 1.127659574468085, "no_speech_prob": 0.0, "words": [{"start": 2962.23, "end": 2963.63, "word": "proof", "probability": 0.26513671875}, {"start": 2963.63, "end": 2965.03, "word": " fix", "probability": 0.40771484375}, {"start": 2965.03, "end": 2967.33, "word": " c", "probability": 0.367431640625}, {"start": 2967.33, "end": 2967.97, "word": " لا", "probability": 0.78955078125}, {"start": 2967.97, "end": 2970.17, "word": " تنتمي", "probability": 0.8448486328125}, {"start": 2970.17, "end": 2970.85, "word": " لار", "probability": 0.456298828125}, {"start": 2970.85, "end": 2971.65, "word": " وc", "probability": 0.568359375}, {"start": 2971.65, "end": 2971.91, "word": " لا", "probability": 0.8974609375}, {"start": 2971.91, "end": 2972.57, "word": " يساوي", "probability": 0.9361572265625}, {"start": 2972.57, "end": 2973.51, "word": " ستة", "probability": 0.7147623697916666}, {"start": 2973.51, "end": 2975.31, "word": " تمام", "probability": 0.6937255859375}, {"start": 2975.31, "end": 2982.61, "word": " then", "probability": 0.408203125}, {"start": 2982.61, "end": 2984.67, "word": " absolute", "probability": 0.8701171875}, {"start": 2984.67, "end": 2985.93, "word": " signum", "probability": 0.778076171875}, {"start": 2985.93, "end": 2986.93, "word": " x", "probability": 0.734375}, {"start": 2986.93, "end": 2988.33, "word": " minus", "probability": 0.97314453125}, {"start": 2988.33, "end": 2989.29, "word": " signum", "probability": 0.9765625}], "temperature": 1.0}, {"id": 107, "seek": 301516, "start": 2990.32, "end": 3015.16, "text": "الـ C بساوي absolute X على absolute X أو بلاش", "tokens": [6027, 39184, 383, 4724, 3794, 995, 45865, 8236, 1783, 15844, 8236, 1783, 34051, 4724, 1211, 33599], "avg_logprob": -0.18772977941176472, "compression_ratio": 1.0508474576271187, "no_speech_prob": 0.0, "words": [{"start": 2990.32, "end": 2990.8, "word": "الـ", "probability": 0.898681640625}, {"start": 2990.8, "end": 2991.24, "word": " C", "probability": 0.58251953125}, {"start": 2991.24, "end": 2992.28, "word": " بساوي", "probability": 0.74005126953125}, {"start": 2992.28, "end": 2993.46, "word": " absolute", "probability": 0.6279296875}, {"start": 2993.46, "end": 2997.42, "word": " X", "probability": 0.84619140625}, {"start": 2997.42, "end": 2997.92, "word": " على", "probability": 0.7666015625}, {"start": 2997.92, "end": 2998.74, "word": " absolute", "probability": 0.94580078125}, {"start": 2998.74, "end": 2999.96, "word": " X", "probability": 0.6279296875}, {"start": 2999.96, "end": 3014.64, "word": " أو", "probability": 0.8681640625}, {"start": 3014.64, "end": 3015.16, "word": " بلاش", "probability": 0.9685872395833334}], "temperature": 1.0}, {"id": 108, "seek": 304563, "start": 3019.85, "end": 3045.63, "text": "then ال limit ل sigma x لما x تقول إلى c بساوي لما x تقول إلى c فهذا عبارة عن limit x على absolute x لما x تقول إلى c", "tokens": [19096, 2423, 4948, 5296, 12771, 2031, 5296, 15042, 2031, 6055, 39648, 30731, 269, 4724, 3794, 995, 45865, 5296, 15042, 2031, 6055, 39648, 30731, 269, 6156, 3224, 15730, 6225, 3555, 9640, 3660, 18871, 4948, 2031, 15844, 8236, 2031, 5296, 15042, 2031, 6055, 39648, 30731, 269], "avg_logprob": -0.24739583598242865, "compression_ratio": 1.6095238095238096, "no_speech_prob": 0.0, "words": [{"start": 3019.85, "end": 3020.33, "word": "then", "probability": 0.1683349609375}, {"start": 3020.33, "end": 3020.65, "word": " ال", "probability": 0.354248046875}, {"start": 3020.65, "end": 3021.03, "word": " limit", "probability": 0.90380859375}, {"start": 3021.03, "end": 3022.67, "word": " ل", "probability": 0.904296875}, {"start": 3022.67, "end": 3023.51, "word": " sigma", "probability": 0.3125}, {"start": 3023.51, "end": 3026.73, "word": " x", "probability": 0.7685546875}, {"start": 3026.73, "end": 3027.09, "word": " لما", "probability": 0.87060546875}, {"start": 3027.09, "end": 3027.43, "word": " x", "probability": 0.96630859375}, {"start": 3027.43, "end": 3027.99, "word": " تقول", "probability": 0.885009765625}, {"start": 3027.99, "end": 3028.49, "word": " إلى", "probability": 0.59423828125}, {"start": 3028.49, "end": 3029.21, "word": " c", "probability": 0.7431640625}, {"start": 3029.21, "end": 3034.39, "word": " بساوي", "probability": 0.80908203125}, {"start": 3034.39, "end": 3037.99, "word": " لما", "probability": 0.6973876953125}, {"start": 3037.99, "end": 3038.39, "word": " x", "probability": 0.2783203125}, {"start": 3038.39, "end": 3038.77, "word": " تقول", "probability": 0.97998046875}, {"start": 3038.77, "end": 3039.01, "word": " إلى", "probability": 0.720703125}, {"start": 3039.01, "end": 3039.29, "word": " c", "probability": 0.9287109375}, {"start": 3039.29, "end": 3039.83, "word": " فهذا", "probability": 0.8347981770833334}, {"start": 3039.83, "end": 3040.15, "word": " عبارة", "probability": 0.991455078125}, {"start": 3040.15, "end": 3040.37, "word": " عن", "probability": 0.99560546875}, {"start": 3040.37, "end": 3040.81, "word": " limit", "probability": 0.98046875}, {"start": 3040.81, "end": 3042.21, "word": " x", "probability": 0.9365234375}, {"start": 3042.21, "end": 3042.47, "word": " على", "probability": 0.6787109375}, {"start": 3042.47, "end": 3043.05, "word": " absolute", "probability": 0.62890625}, {"start": 3043.05, "end": 3043.67, "word": " x", "probability": 0.97998046875}, {"start": 3043.67, "end": 3044.03, "word": " لما", "probability": 0.97265625}, {"start": 3044.03, "end": 3044.39, "word": " x", "probability": 0.990234375}, {"start": 3044.39, "end": 3044.83, "word": " تقول", "probability": 0.9638671875}, {"start": 3044.83, "end": 3045.13, "word": " إلى", "probability": 0.96044921875}, {"start": 3045.13, "end": 3045.63, "word": " c", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 109, "seek": 307801, "start": 3063.05, "end": 3078.01, "text": "فده كانت ال X لا تساوي سفر فاما ال X موجة بقى أو سالي بقى then C أكبر من السفر or C أصغر من سفر", "tokens": [5172, 3215, 3224, 25961, 2655, 2423, 1783, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 6156, 10943, 995, 2423, 1783, 3714, 29245, 3660, 4724, 4587, 7578, 34051, 8608, 6027, 1829, 4724, 4587, 7578, 550, 383, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 420, 383, 5551, 9381, 17082, 2288, 9154, 8608, 5172, 2288], "avg_logprob": -0.20931603211276936, "compression_ratio": 1.3220338983050848, "no_speech_prob": 0.0, "words": [{"start": 3063.0499999999997, "end": 3063.97, "word": "فده", "probability": 0.5834147135416666}, {"start": 3063.97, "end": 3064.33, "word": " كانت", "probability": 0.93017578125}, {"start": 3064.33, "end": 3064.49, "word": " ال", "probability": 0.8671875}, {"start": 3064.49, "end": 3064.67, "word": " X", "probability": 0.70263671875}, {"start": 3064.67, "end": 3064.93, "word": " لا", "probability": 0.79052734375}, {"start": 3064.93, "end": 3065.47, "word": " تساوي", "probability": 0.9249267578125}, {"start": 3065.47, "end": 3066.41, "word": " سفر", "probability": 0.755859375}, {"start": 3066.41, "end": 3067.67, "word": " فاما", "probability": 0.7452799479166666}, {"start": 3067.67, "end": 3067.77, "word": " ال", "probability": 0.95751953125}, {"start": 3067.77, "end": 3067.99, "word": " X", "probability": 0.97705078125}, {"start": 3067.99, "end": 3068.47, "word": " موجة", "probability": 0.9334309895833334}, {"start": 3068.47, "end": 3068.59, "word": " بقى", "probability": 0.8416341145833334}, {"start": 3068.59, "end": 3068.75, "word": " أو", "probability": 0.6474609375}, {"start": 3068.75, "end": 3069.23, "word": " سالي", "probability": 0.66845703125}, {"start": 3069.23, "end": 3072.89, "word": " بقى", "probability": 0.9837239583333334}, {"start": 3072.89, "end": 3073.75, "word": " then", "probability": 0.677734375}, {"start": 3073.75, "end": 3074.55, "word": " C", "probability": 0.80126953125}, {"start": 3074.55, "end": 3075.13, "word": " أكبر", "probability": 0.9597981770833334}, {"start": 3075.13, "end": 3075.33, "word": " من", "probability": 0.99462890625}, {"start": 3075.33, "end": 3075.97, "word": " السفر", "probability": 0.90234375}, {"start": 3075.97, "end": 3076.35, "word": " or", "probability": 0.361083984375}, {"start": 3076.35, "end": 3076.79, "word": " C", "probability": 0.91357421875}, {"start": 3076.79, "end": 3077.35, "word": " أصغر", "probability": 0.9912109375}, {"start": 3077.35, "end": 3077.55, "word": " من", "probability": 0.998046875}, {"start": 3077.55, "end": 3078.01, "word": " سفر", "probability": 0.9514973958333334}], "temperature": 1.0}, {"id": 110, "seek": 311098, "start": 3083.04, "end": 3110.98, "text": "الـ C هتكون أكبر من السفر الـ C هنا لأ تساوي سفر إذا أما C أكبر من السفر أو أصغر من السفر case one لو كانت C أكبر من سفر فهذا بقد أنه limit signum X as X tends to C بساوي limit X على absolute X", "tokens": [6027, 39184, 383, 8032, 2655, 30544, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 2423, 39184, 383, 34105, 5296, 10721, 6055, 3794, 995, 45865, 8608, 5172, 2288, 11933, 15730, 5551, 15042, 383, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 34051, 5551, 9381, 17082, 2288, 9154, 21136, 5172, 2288, 1389, 472, 45164, 25961, 2655, 383, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 6156, 3224, 15730, 4724, 4587, 3215, 14739, 3224, 4948, 1465, 449, 1783, 382, 1783, 12258, 281, 383, 4724, 3794, 995, 45865, 4948, 1783, 15844, 8236, 1783], "avg_logprob": -0.2194683849811554, "compression_ratio": 1.6628571428571428, "no_speech_prob": 0.0, "words": [{"start": 3083.04, "end": 3083.64, "word": "الـ", "probability": 0.690185546875}, {"start": 3083.64, "end": 3083.82, "word": " C", "probability": 0.40869140625}, {"start": 3083.82, "end": 3084.32, "word": " هتكون", "probability": 0.7647298177083334}, {"start": 3084.32, "end": 3084.7, "word": " أكبر", "probability": 0.8645833333333334}, {"start": 3084.7, "end": 3084.9, "word": " من", "probability": 0.99072265625}, {"start": 3084.9, "end": 3085.38, "word": " السفر", "probability": 0.7901204427083334}, {"start": 3085.38, "end": 3085.82, "word": " الـ", "probability": 0.6046142578125}, {"start": 3085.82, "end": 3086.0, "word": " C", "probability": 0.7392578125}, {"start": 3086.0, "end": 3086.2, "word": " هنا", "probability": 0.958984375}, {"start": 3086.2, "end": 3086.4, "word": " لأ", "probability": 0.687255859375}, {"start": 3086.4, "end": 3086.8, "word": " تساوي", "probability": 0.875732421875}, {"start": 3086.8, "end": 3087.12, "word": " سفر", "probability": 0.95068359375}, {"start": 3087.12, "end": 3087.34, "word": " إذا", "probability": 0.64111328125}, {"start": 3087.34, "end": 3087.62, "word": " أما", "probability": 0.677734375}, {"start": 3087.62, "end": 3087.92, "word": " C", "probability": 0.8173828125}, {"start": 3087.92, "end": 3088.3, "word": " أكبر", "probability": 0.9763997395833334}, {"start": 3088.3, "end": 3088.48, "word": " من", "probability": 0.98876953125}, {"start": 3088.48, "end": 3088.96, "word": " السفر", "probability": 0.9484049479166666}, {"start": 3088.96, "end": 3089.58, "word": " أو", "probability": 0.9306640625}, {"start": 3089.58, "end": 3089.96, "word": " أصغر", "probability": 0.98291015625}, {"start": 3089.96, "end": 3090.14, "word": " من", "probability": 0.98828125}, {"start": 3090.14, "end": 3090.54, "word": " السفر", "probability": 0.9581705729166666}, {"start": 3090.54, "end": 3092.1, "word": " case", "probability": 0.5703125}, {"start": 3092.1, "end": 3093.24, "word": " one", "probability": 0.55126953125}, {"start": 3093.24, "end": 3094.8, "word": " لو", "probability": 0.9052734375}, {"start": 3094.8, "end": 3095.34, "word": " كانت", "probability": 0.96435546875}, {"start": 3095.34, "end": 3095.54, "word": " C", "probability": 0.90625}, {"start": 3095.54, "end": 3096.0, "word": " أكبر", "probability": 0.9778645833333334}, {"start": 3096.0, "end": 3096.22, "word": " من", "probability": 0.998046875}, {"start": 3096.22, "end": 3096.64, "word": " سفر", "probability": 0.8639322916666666}, {"start": 3096.64, "end": 3097.02, "word": " فهذا", "probability": 0.9314778645833334}, {"start": 3097.02, "end": 3097.4, "word": " بقد", "probability": 0.6541341145833334}, {"start": 3097.4, "end": 3097.68, "word": " أنه", "probability": 0.686279296875}, {"start": 3097.68, "end": 3098.0, "word": " limit", "probability": 0.953125}, {"start": 3098.0, "end": 3100.54, "word": " signum", "probability": 0.528533935546875}, {"start": 3100.54, "end": 3101.0, "word": " X", "probability": 0.685546875}, {"start": 3101.0, "end": 3101.74, "word": " as", "probability": 0.77783203125}, {"start": 3101.74, "end": 3102.14, "word": " X", "probability": 0.9873046875}, {"start": 3102.14, "end": 3102.5, "word": " tends", "probability": 0.8173828125}, {"start": 3102.5, "end": 3102.68, "word": " to", "probability": 0.97412109375}, {"start": 3102.68, "end": 3103.94, "word": " C", "probability": 0.87255859375}, {"start": 3103.94, "end": 3106.24, "word": " بساوي", "probability": 0.8160400390625}, {"start": 3106.24, "end": 3107.12, "word": " limit", "probability": 0.97265625}, {"start": 3107.12, "end": 3109.38, "word": " X", "probability": 0.9599609375}, {"start": 3109.38, "end": 3109.7, "word": " على", "probability": 0.88525390625}, {"start": 3109.7, "end": 3110.28, "word": " absolute", "probability": 0.87939453125}, {"start": 3110.28, "end": 3110.98, "word": " X", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 111, "seek": 314470, "start": 3119.94, "end": 3144.7, "text": "و طبعا ال X أكبر من ال C أكبر من السفر ف absolute .. فهذا بيساوي واحد بيساوي limit واحد as X tends to C بيساوي واحد بيساوي F and C", "tokens": [2407, 23032, 3555, 3615, 995, 2423, 1783, 5551, 4117, 26890, 9154, 2423, 383, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 6156, 8236, 4386, 6156, 3224, 15730, 4724, 1829, 3794, 995, 45865, 36764, 24401, 4724, 1829, 3794, 995, 45865, 4948, 36764, 24401, 382, 1783, 12258, 281, 383, 4724, 1829, 3794, 995, 45865, 36764, 24401, 4724, 1829, 3794, 995, 45865, 479, 293, 383], "avg_logprob": -0.16078629657145468, "compression_ratio": 1.5634920634920635, "no_speech_prob": 0.0, "words": [{"start": 3119.9399999999996, "end": 3120.74, "word": "و", "probability": 0.62841796875}, {"start": 3120.74, "end": 3121.08, "word": " طبعا", "probability": 0.8746337890625}, {"start": 3121.08, "end": 3121.22, "word": " ال", "probability": 0.904296875}, {"start": 3121.22, "end": 3121.5, "word": " X", "probability": 0.60888671875}, {"start": 3121.5, "end": 3122.12, "word": " أكبر", "probability": 0.9422200520833334}, {"start": 3122.12, "end": 3122.44, "word": " من", "probability": 0.98095703125}, {"start": 3122.44, "end": 3125.66, "word": " ال", "probability": 0.85400390625}, {"start": 3125.66, "end": 3125.9, "word": " C", "probability": 0.6611328125}, {"start": 3125.9, "end": 3126.36, "word": " أكبر", "probability": 0.9703776041666666}, {"start": 3126.36, "end": 3126.56, "word": " من", "probability": 0.99658203125}, {"start": 3126.56, "end": 3127.12, "word": " السفر", "probability": 0.8352864583333334}, {"start": 3127.12, "end": 3129.76, "word": " ف", "probability": 0.935546875}, {"start": 3129.76, "end": 3130.38, "word": " absolute", "probability": 0.56591796875}, {"start": 3130.38, "end": 3130.64, "word": " ..", "probability": 0.254150390625}, {"start": 3130.64, "end": 3130.96, "word": " فهذا", "probability": 0.8434244791666666}, {"start": 3130.96, "end": 3131.46, "word": " بيساوي", "probability": 0.85263671875}, {"start": 3131.46, "end": 3131.86, "word": " واحد", "probability": 0.9775390625}, {"start": 3131.86, "end": 3132.44, "word": " بيساوي", "probability": 0.90224609375}, {"start": 3132.44, "end": 3132.86, "word": " limit", "probability": 0.95166015625}, {"start": 3132.86, "end": 3134.54, "word": " واحد", "probability": 0.916748046875}, {"start": 3134.54, "end": 3134.92, "word": " as", "probability": 0.9189453125}, {"start": 3134.92, "end": 3135.26, "word": " X", "probability": 0.755859375}, {"start": 3135.26, "end": 3135.52, "word": " tends", "probability": 0.245361328125}, {"start": 3135.52, "end": 3135.64, "word": " to", "probability": 0.9599609375}, {"start": 3135.64, "end": 3136.18, "word": " C", "probability": 0.876953125}, {"start": 3136.18, "end": 3138.02, "word": " بيساوي", "probability": 0.97119140625}, {"start": 3138.02, "end": 3141.44, "word": " واحد", "probability": 0.9443359375}, {"start": 3141.44, "end": 3143.64, "word": " بيساوي", "probability": 0.964453125}, {"start": 3143.64, "end": 3144.04, "word": " F", "probability": 0.9345703125}, {"start": 3144.04, "end": 3144.38, "word": " and", "probability": 0.9384765625}, {"start": 3144.38, "end": 3144.7, "word": " C", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 112, "seek": 316391, "start": 3147.29, "end": 3163.91, "text": "أو signum C لأن ال C موجبة فلما ال C تكون موجبة ف absolute ال C بساوي ال C بطلع المخضر هذا بطلع واحد", "tokens": [10721, 2407, 1465, 449, 383, 5296, 33456, 2423, 383, 3714, 29245, 49401, 6156, 1211, 15042, 2423, 383, 6055, 30544, 3714, 29245, 49401, 6156, 8236, 2423, 383, 4724, 3794, 995, 45865, 2423, 383, 4724, 9566, 1211, 3615, 9673, 9778, 11242, 2288, 23758, 4724, 9566, 1211, 3615, 36764, 24401], "avg_logprob": -0.2887369903425376, "compression_ratio": 1.3166666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3147.29, "end": 3147.63, "word": "أو", "probability": 0.5682373046875}, {"start": 3147.63, "end": 3148.19, "word": " signum", "probability": 0.6112060546875}, {"start": 3148.19, "end": 3148.51, "word": " C", "probability": 0.5791015625}, {"start": 3148.51, "end": 3152.49, "word": " لأن", "probability": 0.76513671875}, {"start": 3152.49, "end": 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بساوي", "probability": 0.8609619140625}, {"start": 3160.69, "end": 3161.17, "word": " ال", "probability": 0.7568359375}, {"start": 3161.17, "end": 3161.49, "word": " C", "probability": 0.9384765625}, {"start": 3161.49, "end": 3162.11, "word": " بطلع", "probability": 0.74859619140625}, {"start": 3162.11, "end": 3163.09, "word": " المخضر", "probability": 0.7437744140625}, {"start": 3163.09, "end": 3163.27, "word": " هذا", "probability": 0.8837890625}, {"start": 3163.27, "end": 3163.63, "word": " بطلع", "probability": 0.9365234375}, {"start": 3163.63, "end": 3163.91, "word": " واحد", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 113, "seek": 319195, "start": 3165.97, "end": 3191.95, "text": "و بالتالي إذا ال signal x is continuous at c case 2 إذا كانت ال c أصغر من سفر ف similar to case 1 في الحالة هذه", "tokens": [2407, 20666, 2655, 6027, 1829, 11933, 15730, 2423, 6358, 2031, 307, 10957, 412, 269, 1389, 568, 11933, 15730, 25961, 2655, 2423, 269, 5551, 9381, 17082, 2288, 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