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{"start": 539.59, "end": 540.97, "word": " بساوية", "probability": 0.775732421875}, {"start": 540.97, "end": 541.25, "word": " اللي", "probability": 0.966796875}, {"start": 541.25, "end": 541.69, "word": " هو", "probability": 0.96484375}, {"start": 541.69, "end": 543.03, "word": " الصفر", "probability": 0.9436848958333334}, {"start": 543.03, "end": 544.37, "word": " وهذا", "probability": 0.767578125}, {"start": 544.37, "end": 544.73, "word": " هو", "probability": 0.9755859375}, {"start": 544.73, "end": 545.43, "word": " تعريف", "probability": 0.9921875}, {"start": 545.43, "end": 546.09, "word": " من", "probability": 0.98291015625}, {"start": 546.09, "end": 547.31, "word": " ال", "probability": 0.7783203125}, {"start": 547.31, "end": 548.23, "word": " f", "probability": 0.3603515625}, {"start": 548.23, "end": 548.95, "word": " prime", "probability": 0.66650390625}, {"start": 548.95, "end": 549.31, "word": " عند", "probability": 0.9765625}, {"start": 549.31, "end": 549.77, "word": " 0", 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557.33, "end": 557.95, "word": " أثبتنا", "probability": 0.9458984375}], "temperature": 1.0}, {"id": 23, "seek": 58628, "start": 558.36, "end": 586.28, "text": "الـ existence للـ F prime عند الـ zero أي سؤال طيب نيجي الآن نشوف السؤال الثاني خلّال السؤال الأربعة نيجي لسؤال سبعة الان سؤال سبعة اش اللي بقوله سؤال سبعة", "tokens": [6027, 39184, 9123, 24976, 39184, 479, 5835, 43242, 2423, 39184, 4018, 36632, 8608, 33604, 6027, 23032, 1829, 3555, 8717, 1829, 7435, 1829, 6024, 48506, 8717, 8592, 38688, 21136, 33604, 6027, 6024, 104, 7649, 1829, 16490, 1211, 11703, 6027, 21136, 33604, 6027, 16247, 25513, 27884, 8717, 1829, 7435, 1829, 5296, 3794, 33604, 6027, 8608, 3555, 27884, 2423, 7649, 8608, 33604, 6027, 8608, 3555, 27884, 1975, 8592, 13672, 1829, 4724, 39648, 3224, 8608, 33604, 6027, 8608, 3555, 27884], "avg_logprob": -0.2506087662337662, "compression_ratio": 1.7466666666666666, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 558.36, "end": 558.74, "word": "الـ", 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567.4, "end": 568.62, "word": " نشوف", "probability": 0.9650065104166666}, {"start": 568.62, "end": 569.22, "word": " السؤال", "probability": 0.9892578125}, {"start": 569.22, "end": 569.68, "word": " الثاني", "probability": 0.945556640625}, {"start": 569.68, "end": 570.04, "word": " خلّال", "probability": 0.6904296875}, {"start": 570.04, "end": 570.36, "word": " السؤال", "probability": 0.9801432291666666}, {"start": 570.36, "end": 570.84, "word": " الأربعة", "probability": 0.9440104166666666}, {"start": 570.84, "end": 571.18, "word": " نيجي", "probability": 0.95458984375}, {"start": 571.18, "end": 571.9, "word": " لسؤال", "probability": 0.9859619140625}, {"start": 571.9, "end": 572.54, "word": " سبعة", "probability": 0.8798828125}, {"start": 572.54, "end": 584.22, "word": " الان", "probability": 0.5316162109375}, {"start": 584.22, "end": 584.54, "word": " سؤال", "probability": 0.939453125}, {"start": 584.54, "end": 584.96, "word": " سبعة", "probability": 0.9752604166666666}, {"start": 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"probability": 0.91748046875}, {"start": 864.16, "end": 865.36, "word": " absolute", "probability": 0.8798828125}, {"start": 865.36, "end": 865.86, "word": " value", "probability": 0.9873046875}, {"start": 865.86, "end": 865.98, "word": " ل", "probability": 0.401123046875}, {"start": 865.98, "end": 866.16, "word": " F", "probability": 0.346435546875}, {"start": 866.16, "end": 866.34, "word": " of", "probability": 0.59375}, {"start": 866.34, "end": 866.76, "word": " X", "probability": 0.9912109375}, {"start": 866.76, "end": 867.6, "word": " على", "probability": 0.70166015625}, {"start": 867.6, "end": 868.16, "word": " X", "probability": 0.96044921875}, {"start": 868.16, "end": 868.78, "word": " minus", "probability": 0.73388671875}, {"start": 868.78, "end": 869.2, "word": " C", "probability": 0.9853515625}, {"start": 869.2, "end": 869.8, "word": " لما", "probability": 0.89404296875}, {"start": 869.8, "end": 870.02, "word": " X", "probability": 0.98046875}, {"start": 870.02, "end": 870.32, "word": " بتروح", "probability": 0.8341471354166666}, {"start": 870.32, "end": 870.44, "word": " ل", "probability": 0.8330078125}, {"start": 870.44, "end": 870.56, "word": " C", "probability": 0.435791015625}, {"start": 870.56, "end": 870.76, "word": " من", "probability": 0.9365234375}, {"start": 870.76, "end": 871.98, "word": " وين؟", "probability": 0.8779296875}, {"start": 871.98, "end": 872.14, "word": " من", "probability": 0.98828125}, {"start": 872.14, "end": 872.64, "word": " اليمين", "probability": 0.8865559895833334}, {"start": 872.64, "end": 873.36, "word": " يعني", "probability": 0.903076171875}, {"start": 873.36, "end": 874.1, "word": " هذا", "probability": 0.9482421875}, {"start": 874.1, "end": 874.96, "word": " المقدار", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 35, "seek": 89419, "start": 875.57, "end": 894.19, "text": "صار موجود وإيش بساوي بساوي سفر هذا خلّيه لإنه هذا اللي بدنا نصلّه لأن limit صار عندي معنى آخر limit absolute value of f of x على x minus c لما x تروح لل c من اليمين بساوي سفر exist", "tokens": [9381, 9640, 3714, 29245, 23328, 4032, 28814, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 8608, 5172, 2288, 23758, 16490, 1211, 11703, 1829, 3224, 5296, 28814, 1863, 3224, 23758, 13672, 1829, 47525, 8315, 8717, 36520, 11703, 3224, 5296, 33456, 4948, 20328, 9640, 18871, 16254, 20449, 1863, 7578, 19753, 34740, 4948, 8236, 2158, 295, 283, 295, 2031, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 24976, 269, 9154, 2423, 32640, 9957, 4724, 3794, 995, 45865, 8608, 5172, 2288, 2514], "avg_logprob": -0.22025602014668016, "compression_ratio": 1.5274725274725274, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 875.57, "end": 875.95, "word": "صار", "probability": 0.63916015625}, {"start": 875.95, "end": 876.37, "word": " موجود", "probability": 0.9705403645833334}, {"start": 876.37, "end": 876.61, "word": " وإيش", "probability": 0.729736328125}, {"start": 876.61, "end": 877.17, "word": " بساوي", "probability": 0.838134765625}, {"start": 877.17, "end": 878.33, "word": " بساوي", "probability": 0.794189453125}, {"start": 878.33, "end": 878.75, "word": " سفر", "probability": 0.7451171875}, {"start": 878.75, "end": 879.53, "word": " هذا", "probability": 0.638671875}, {"start": 879.53, "end": 880.01, "word": " خلّيه", "probability": 0.83818359375}, {"start": 880.01, "end": 880.19, "word": " لإنه", "probability": 0.7928466796875}, {"start": 880.19, "end": 880.33, "word": " هذا", "probability": 0.8857421875}, {"start": 880.33, "end": 880.45, "word": " اللي", "probability": 0.96875}, {"start": 880.45, "end": 880.63, "word": " بدنا", "probability": 0.88134765625}, {"start": 880.63, "end": 881.19, "word": " نصلّه", "probability": 0.8170166015625}, {"start": 881.19, "end": 881.77, "word": " لأن", "probability": 0.774658203125}, {"start": 881.77, "end": 882.35, "word": " limit", "probability": 0.9052734375}, {"start": 882.35, "end": 882.81, "word": " صار", "probability": 0.9736328125}, {"start": 882.81, "end": 883.09, "word": " عندي", "probability": 0.79931640625}, {"start": 883.09, "end": 883.47, "word": " معنى", "probability": 0.96337890625}, {"start": 883.47, "end": 883.89, "word": " آخر", "probability": 0.9248046875}, {"start": 883.89, "end": 884.85, "word": " limit", "probability": 0.94287109375}, {"start": 884.85, "end": 885.89, "word": " absolute", "probability": 0.63623046875}, {"start": 885.89, "end": 886.35, "word": " value", "probability": 0.9873046875}, {"start": 886.35, "end": 886.55, "word": " of", "probability": 0.394775390625}, {"start": 886.55, "end": 886.77, "word": " f", "probability": 0.65869140625}, {"start": 886.77, "end": 886.93, "word": " of", "probability": 0.44384765625}, {"start": 886.93, "end": 887.31, "word": " x", "probability": 0.68017578125}, {"start": 887.31, "end": 888.33, "word": " على", "probability": 0.68310546875}, {"start": 888.33, "end": 888.73, "word": " x", "probability": 0.83935546875}, {"start": 888.73, 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895.12, "end": 924.72, "text": "لاحظا قاعد رايح لأثبت أن هذا exist ده خد الآن من وين؟ من اليسار خد لأن احسب similarly عندي سفر بساوي absolute value of limit f of x على x minus c لما x تروح ل c من وين؟ من اليسار ويساوي عبارة عن limit absolute value of f of x على absolute value of x minus c لما x تروح ل c من وين؟ من اليسار", "tokens": [15040, 5016, 19913, 995, 12174, 995, 22488, 12602, 47302, 5016, 5296, 10721, 12984, 3555, 2655, 14739, 23758, 2514, 11778, 3224, 16490, 3215, 6024, 48506, 9154, 4032, 9957, 22807, 9154, 45595, 3794, 9640, 16490, 3215, 5296, 33456, 1975, 5016, 35457, 14138, 18871, 16254, 8608, 5172, 2288, 4724, 3794, 995, 45865, 8236, 2158, 295, 4948, 283, 295, 2031, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 5296, 269, 9154, 4032, 9957, 22807, 9154, 45595, 3794, 9640, 4032, 1829, 3794, 995, 45865, 6225, 3555, 9640, 3660, 18871, 4948, 8236, 2158, 295, 283, 295, 2031, 15844, 8236, 2158, 295, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016, 5296, 269, 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{"start": 898.36, "end": 898.5, "word": " من", "probability": 0.94580078125}, {"start": 898.5, "end": 898.88, "word": " وين؟", "probability": 0.7643229166666666}, {"start": 898.88, "end": 898.96, "word": " من", "probability": 0.97265625}, {"start": 898.96, "end": 899.42, "word": " اليسار", "probability": 0.9921875}, {"start": 899.42, "end": 900.3, "word": " خد", "probability": 0.906494140625}, {"start": 900.3, "end": 900.56, "word": " لأن", "probability": 0.763427734375}, {"start": 900.56, "end": 900.98, "word": " احسب", "probability": 0.8865559895833334}, {"start": 900.98, "end": 901.78, "word": " similarly", "probability": 0.5146484375}, {"start": 901.78, "end": 902.7, "word": " عندي", "probability": 0.5999755859375}, {"start": 902.7, "end": 903.52, "word": " سفر", "probability": 0.6846923828125}, {"start": 903.52, "end": 904.06, "word": " بساوي", "probability": 0.8065185546875}, {"start": 904.06, "end": 904.62, "word": " absolute", "probability": 0.55029296875}, {"start": 904.62, 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0.9881184895833334}, {"start": 909.66, "end": 909.8, "word": " ل", "probability": 0.62646484375}, {"start": 909.8, "end": 909.96, "word": " c", "probability": 0.5986328125}, {"start": 909.96, "end": 910.18, "word": " من", "probability": 0.98486328125}, {"start": 910.18, "end": 911.48, "word": " وين؟", "probability": 0.9677734375}, {"start": 911.48, "end": 911.7, "word": " من", "probability": 0.9794921875}, {"start": 911.7, "end": 912.76, "word": " اليسار", "probability": 0.9978841145833334}, {"start": 912.76, "end": 913.72, "word": " ويساوي", "probability": 0.8728515625}, {"start": 913.72, "end": 914.84, "word": " عبارة", "probability": 0.9930419921875}, {"start": 914.84, "end": 915.1, "word": " عن", "probability": 0.9951171875}, {"start": 915.1, "end": 915.9, "word": " limit", "probability": 0.98486328125}, {"start": 915.9, "end": 917.02, "word": " absolute", "probability": 0.951171875}, {"start": 917.02, "end": 917.46, "word": " value", "probability": 0.98876953125}, {"start": 917.46, "end": 917.62, "word": " of", "probability": 0.64501953125}, {"start": 917.62, "end": 917.82, "word": " f", "probability": 0.939453125}, {"start": 917.82, "end": 918.02, "word": " of", "probability": 0.91455078125}, {"start": 918.02, "end": 918.44, "word": " x", "probability": 0.9912109375}, {"start": 918.44, "end": 919.16, "word": " على", "probability": 0.7431640625}, {"start": 919.16, "end": 919.6, "word": " absolute", "probability": 0.94580078125}, {"start": 919.6, "end": 919.96, "word": " value", "probability": 0.98583984375}, {"start": 919.96, "end": 920.04, "word": " of", "probability": 0.875}, {"start": 920.04, "end": 920.2, "word": " x", "probability": 0.9892578125}, {"start": 920.2, "end": 920.44, "word": " minus", "probability": 0.986328125}, {"start": 920.44, "end": 920.94, "word": " c", "probability": 0.98681640625}, {"start": 920.94, "end": 921.7, "word": " لما", "probability": 0.97802734375}, {"start": 921.7, "end": 921.96, "word": " x", "probability": 0.96923828125}, {"start": 921.96, "end": 922.28, "word": " تروح", "probability": 0.9952799479166666}, {"start": 922.28, "end": 922.42, "word": " ل", "probability": 0.8642578125}, {"start": 922.42, "end": 922.6, "word": " c", "probability": 0.9384765625}, {"start": 922.6, "end": 922.8, "word": " من", "probability": 0.99267578125}, {"start": 922.8, "end": 923.62, "word": " وين؟", "probability": 0.98974609375}, {"start": 923.62, "end": 924.18, "word": " من", "probability": 0.9912109375}, {"start": 924.18, "end": 924.72, "word": " اليسار", "probability": 0.9983723958333334}], "temperature": 1.0}, {"id": 37, "seek": 94102, "start": 925.52, "end": 941.02, "text": "هذه نفسها بساوي limit أو بساوي سالب limit f of x absolute value على x minus c لما x تروح", "tokens": [3224, 24192, 8717, 36178, 11296, 4724, 3794, 995, 45865, 4948, 34051, 4724, 3794, 995, 45865, 8608, 6027, 3555, 4948, 283, 295, 2031, 8236, 2158, 15844, 2031, 3175, 269, 5296, 15042, 2031, 6055, 32887, 5016], "avg_logprob": -0.1620535739830562, "compression_ratio": 1.1401869158878504, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 925.52, "end": 925.9, "word": "هذه", "probability": 0.818115234375}, {"start": 925.9, "end": 926.64, "word": " نفسها", "probability": 0.9835611979166666}, {"start": 926.64, "end": 927.44, "word": " بساوي", "probability": 0.760498046875}, {"start": 927.44, "end": 928.56, "word": " limit", "probability": 0.83740234375}, {"start": 928.56, "end": 929.92, "word": " أو", "probability": 0.6162109375}, {"start": 929.92, "end": 930.42, "word": " بساوي", "probability": 0.957275390625}, {"start": 930.42, "end": 931.38, "word": " سالب", "probability": 0.9080403645833334}, {"start": 931.38, "end": 932.8, "word": " limit", "probability": 0.9296875}, {"start": 932.8, "end": 934.02, "word": " f", "probability": 0.23681640625}, {"start": 934.02, "end": 934.28, "word": " of", "probability": 0.55859375}, {"start": 934.28, "end": 934.58, "word": " x", "probability": 0.794921875}, {"start": 934.58, "end": 934.96, "word": " absolute", "probability": 0.88427734375}, {"start": 934.96, "end": 935.64, "word": " value", "probability": 0.99267578125}, {"start": 935.64, "end": 936.64, "word": " على", "probability": 0.67578125}, {"start": 936.64, "end": 937.58, "word": " x", "probability": 0.83642578125}, {"start": 937.58, "end": 938.1, "word": " minus", "probability": 0.7470703125}, {"start": 938.1, "end": 938.6, "word": " c", "probability": 0.8095703125}, {"start": 938.6, "end": 940.08, "word": " لما", "probability": 0.830810546875}, {"start": 940.08, "end": 940.4, "word": " x", "probability": 0.84765625}, {"start": 940.4, "end": 941.02, "word": " تروح", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 38, "seek": 96921, "start": 941.69, "end": 969.21, "text": "للـ C من اليسار، ليش؟ لأن X أصغر من C، إذا X minus C سالبة إذا الـ absolute value سالب إليها واخدت السالب برا هذا الآن المخضر بيساوي سفر، إذا هذا لحاله برضه إيش ماله؟ سفر، إذا limit absolute value للـ F of X على X minus C، لما X تروح للـ C من اليسار، برضه إيش بيساوي؟ بيساوي سفر، لاحظ إن ال limit من اليمين", "tokens": [1211, 1211, 39184, 383, 9154, 45595, 3794, 9640, 12399, 32239, 8592, 22807, 5296, 33456, 1783, 5551, 9381, 17082, 2288, 9154, 383, 12399, 11933, 15730, 1783, 3175, 383, 8608, 6027, 49401, 11933, 15730, 2423, 39184, 8236, 2158, 8608, 6027, 3555, 11933, 20292, 11296, 4032, 47283, 3215, 2655, 21136, 6027, 3555, 4724, 23557, 23758, 6024, 48506, 9673, 9778, 11242, 2288, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 12399, 11933, 15730, 23758, 5296, 5016, 6027, 3224, 4724, 43042, 3224, 11933, 1829, 8592, 3714, 6027, 3224, 22807, 8608, 5172, 2288, 12399, 11933, 15730, 4948, 8236, 2158, 24976, 39184, 479, 295, 1783, 15844, 1783, 3175, 383, 12399, 5296, 15042, 1783, 6055, 32887, 5016, 24976, 39184, 383, 9154, 45595, 3794, 9640, 12399, 4724, 43042, 3224, 11933, 1829, 8592, 4724, 1829, 3794, 995, 45865, 22807, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 12399, 20193, 5016, 19913, 36145, 2423, 4948, 9154, 45595, 2304, 9957], "avg_logprob": -0.2059563770390197, "compression_ratio": 2.059071729957806, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 941.69, "end": 942.03, "word": "للـ", "probability": 0.6399739583333334}, {"start": 942.03, "end": 942.15, "word": " C", "probability": 0.5087890625}, {"start": 942.15, "end": 942.27, "word": " من", "probability": 0.95751953125}, {"start": 942.27, "end": 942.77, "word": " اليسار،", "probability": 0.82489013671875}, {"start": 942.77, "end": 943.73, "word": " ليش؟", "probability": 0.755126953125}, {"start": 943.73, "end": 944.07, "word": " لأن", "probability": 0.8916015625}, {"start": 944.07, "end": 944.59, "word": " X", "probability": 0.89013671875}, {"start": 944.59, "end": 944.99, "word": " أصغر", "probability": 0.9705810546875}, {"start": 944.99, "end": 945.17, "word": " من", "probability": 0.9931640625}, {"start": 945.17, "end": 945.61, "word": " C،", "probability": 0.669921875}, {"start": 945.61, "end": 945.73, "word": " إذا", "probability": 0.758056640625}, {"start": 945.73, "end": 945.99, "word": " X", "probability": 0.89404296875}, {"start": 945.99, "end": 946.25, "word": " minus", "probability": 0.1668701171875}, {"start": 946.25, "end": 946.47, "word": " C", "probability": 0.9814453125}, {"start": 946.47, "end": 947.03, "word": " سالبة", "probability": 0.7796223958333334}, {"start": 947.03, "end": 947.65, "word": " إذا", "probability": 0.66015625}, {"start": 947.65, "end": 947.75, "word": " الـ", "probability": 0.784423828125}, {"start": 947.75, "end": 948.05, "word": " absolute", "probability": 0.401123046875}, {"start": 948.05, "end": 948.51, "word": " value", "probability": 0.98974609375}, {"start": 948.51, "end": 948.89, "word": " سالب", "probability": 0.9334309895833334}, {"start": 948.89, "end": 949.19, "word": " إليها", "probability": 0.5888671875}, {"start": 949.19, "end": 949.57, "word": " واخدت", "probability": 0.7554931640625}, {"start": 949.57, "end": 949.89, "word": " السالب", "probability": 0.9270833333333334}, {"start": 949.89, "end": 950.23, "word": " برا", "probability": 0.906982421875}, {"start": 950.23, "end": 951.31, "word": " هذا", "probability": 0.767578125}, {"start": 951.31, "end": 951.69, "word": " الآن", "probability": 0.69140625}, {"start": 951.69, "end": 952.17, "word": " المخضر", "probability": 0.74896240234375}, {"start": 952.17, "end": 952.49, "word": " بيساوي", "probability": 0.81640625}, {"start": 952.49, "end": 953.27, "word": " سفر،", "probability": 0.669189453125}, {"start": 953.27, "end": 953.53, "word": " إذا", "probability": 0.92724609375}, {"start": 953.53, "end": 954.01, "word": " هذا", "probability": 0.9501953125}, {"start": 954.01, "end": 954.49, "word": " لحاله", "probability": 0.977294921875}, {"start": 954.49, "end": 954.77, "word": " برضه", "probability": 0.9052734375}, {"start": 954.77, "end": 954.99, "word": " إيش", "probability": 0.8580729166666666}, {"start": 954.99, "end": 955.79, "word": " ماله؟", "probability": 0.82879638671875}, {"start": 955.79, "end": 956.23, "word": " سفر،", "probability": 0.9503173828125}, {"start": 956.23, "end": 956.53, "word": " إذا", "probability": 0.938720703125}, {"start": 956.53, "end": 957.87, "word": " limit", "probability": 0.91552734375}, {"start": 957.87, "end": 958.91, "word": " absolute", "probability": 0.92236328125}, {"start": 958.91, "end": 959.39, "word": " value", "probability": 0.9892578125}, {"start": 959.39, "end": 959.61, "word": " للـ", "probability": 0.5020751953125}, {"start": 959.61, "end": 959.77, "word": " F", "probability": 0.61474609375}, {"start": 959.77, "end": 959.93, "word": " of", "probability": 0.93115234375}, {"start": 959.93, "end": 960.37, "word": " X", "probability": 0.99658203125}, {"start": 960.37, "end": 961.27, "word": " على", "probability": 0.73779296875}, {"start": 961.27, "end": 961.63, "word": " X", "probability": 0.986328125}, {"start": 961.63, "end": 961.95, "word": " minus", "probability": 0.9794921875}, {"start": 961.95, "end": 962.37, "word": " C،", "probability": 0.752197265625}, {"start": 962.37, "end": 962.53, "word": " لما", "probability": 0.955322265625}, {"start": 962.53, "end": 962.77, "word": " X", "probability": 0.9677734375}, {"start": 962.77, "end": 963.05, "word": " تروح", "probability": 0.9830729166666666}, {"start": 963.05, "end": 963.29, "word": " للـ", "probability": 0.748291015625}, {"start": 963.29, "end": 963.39, "word": " C", "probability": 0.82958984375}, {"start": 963.39, "end": 963.53, "word": " من", "probability": 0.9892578125}, {"start": 963.53, "end": 964.39, "word": " اليسار،", "probability": 0.8795166015625}, {"start": 964.39, "end": 964.67, "word": " برضه", "probability": 0.9876302083333334}, {"start": 964.67, "end": 964.87, "word": " إيش", "probability": 0.9547526041666666}, {"start": 964.87, "end": 965.73, "word": " بيساوي؟", "probability": 0.9657389322916666}, {"start": 965.73, "end": 966.13, "word": " بيساوي", "probability": 0.96962890625}, {"start": 966.13, "end": 966.85, "word": " سفر،", "probability": 0.887939453125}, {"start": 966.85, "end": 967.57, "word": " لاحظ", "probability": 0.9208984375}, {"start": 967.57, "end": 967.73, "word": " إن", "probability": 0.72509765625}, {"start": 967.73, "end": 967.87, "word": " ال", "probability": 0.86669921875}, {"start": 967.87, "end": 968.23, "word": " limit", "probability": 0.38671875}, {"start": 968.23, "end": 968.53, "word": " من", "probability": 0.99609375}, {"start": 968.53, "end": 969.21, "word": " اليمين", "probability": 0.79541015625}], "temperature": 1.0}, {"id": 39, "seek": 99903, "start": 970.01, "end": 999.03, "text": "والـ limit من اليسار موجود وبساوي 0 متساويين يعني الآن ال limit هذا صار ايش بساوي بساوي 0 إذا الان هذا الآن بنقوله كله تحت هذا وبقول hence اللي هو g prime of c بساوي limit of g of x نقص g of c على x minus c", "tokens": [2407, 6027, 39184, 4948, 9154, 45595, 3794, 9640, 3714, 29245, 23328, 4032, 3555, 3794, 995, 45865, 1958, 44650, 3794, 995, 45865, 9957, 37495, 22653, 6024, 48506, 2423, 4948, 23758, 20328, 9640, 1975, 1829, 8592, 4724, 3794, 995, 45865, 4724, 3794, 995, 45865, 1958, 11933, 15730, 2423, 7649, 23758, 6024, 48506, 44945, 39648, 3224, 28242, 3224, 6055, 33753, 23758, 46599, 39648, 16678, 13672, 1829, 31439, 290, 5835, 295, 269, 4724, 3794, 995, 45865, 4948, 295, 290, 295, 2031, 8717, 4587, 9381, 290, 295, 269, 15844, 2031, 3175, 269], "avg_logprob": -0.24751421639865095, "compression_ratio": 1.7043010752688172, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 970.01, "end": 970.45, "word": "والـ", "probability": 0.6056315104166666}, {"start": 970.45, "end": 970.67, "word": " limit", "probability": 0.68310546875}, {"start": 970.67, "end": 970.85, "word": " من", "probability": 0.90380859375}, {"start": 970.85, "end": 971.61, "word": " اليسار", "probability": 0.9835611979166666}, {"start": 971.61, "end": 972.77, "word": " موجود", "probability": 0.9698893229166666}, {"start": 972.77, "end": 973.21, "word": " وبساوي", "probability": 0.709423828125}, {"start": 973.21, "end": 973.63, "word": " 0", "probability": 0.52587890625}, {"start": 973.63, "end": 974.91, "word": " متساويين", "probability": 0.893359375}, {"start": 974.91, "end": 975.53, "word": " يعني", "probability": 0.9140625}, {"start": 975.53, "end": 975.89, "word": " الآن", "probability": 0.6639404296875}, {"start": 975.89, "end": 976.13, "word": " ال", "probability": 0.89404296875}, {"start": 976.13, "end": 976.49, "word": " limit", "probability": 0.64306640625}, {"start": 976.49, "end": 977.25, "word": " هذا", "probability": 0.93212890625}, {"start": 977.25, "end": 978.63, "word": " صار", "probability": 0.7008056640625}, {"start": 978.63, "end": 978.83, "word": " ايش", "probability": 0.7079264322916666}, {"start": 978.83, "end": 979.43, "word": " بساوي", "probability": 0.856201171875}, {"start": 979.43, "end": 980.31, "word": " بساوي", "probability": 0.8302001953125}, {"start": 980.31, "end": 980.61, "word": " 0", "probability": 0.82080078125}, {"start": 980.61, "end": 981.27, "word": " إذا", "probability": 0.4676513671875}, {"start": 981.27, "end": 982.17, "word": " الان", "probability": 0.6007080078125}, {"start": 982.17, "end": 983.13, "word": " هذا", "probability": 0.90478515625}, {"start": 983.13, "end": 983.59, "word": " الآن", "probability": 0.6695556640625}, {"start": 983.59, "end": 984.19, "word": " بنقوله", "probability": 0.6448567708333334}, {"start": 984.19, "end": 984.47, "word": " كله", "probability": 0.9765625}, {"start": 984.47, "end": 984.83, "word": " تحت", "probability": 0.9814453125}, {"start": 984.83, "end": 985.35, "word": " هذا", "probability": 0.9794921875}, {"start": 985.35, "end": 986.55, "word": " وبقول", "probability": 0.7257080078125}, {"start": 986.55, "end": 987.25, "word": " hence", "probability": 0.89501953125}, {"start": 987.25, "end": 988.57, "word": " اللي", "probability": 0.863525390625}, {"start": 988.57, "end": 988.99, "word": " هو", "probability": 0.982421875}, {"start": 988.99, "end": 989.87, "word": " g", "probability": 0.43212890625}, {"start": 989.87, "end": 990.37, "word": " prime", "probability": 0.7099609375}, {"start": 990.37, "end": 990.65, "word": " of", "probability": 0.96630859375}, {"start": 990.65, "end": 991.09, "word": " c", "probability": 0.72412109375}, {"start": 991.09, "end": 992.17, "word": " بساوي", "probability": 0.8878173828125}, {"start": 992.17, "end": 992.81, "word": " limit", "probability": 0.9775390625}, {"start": 992.81, "end": 993.93, "word": " of", "probability": 0.94482421875}, {"start": 993.93, "end": 994.29, "word": " g", "probability": 0.94921875}, {"start": 994.29, "end": 994.45, "word": " of", "probability": 0.78515625}, {"start": 994.45, "end": 994.93, "word": " x", "probability": 0.95849609375}, {"start": 994.93, "end": 996.53, "word": " نقص", "probability": 0.8427734375}, {"start": 996.53, "end": 996.73, "word": " g", "probability": 0.91455078125}, {"start": 996.73, "end": 996.91, "word": " of", "probability": 0.95263671875}, {"start": 996.91, "end": 997.31, "word": " c", "probability": 0.93017578125}, {"start": 997.31, "end": 998.03, "word": " على", "probability": 0.7041015625}, {"start": 998.03, "end": 998.31, "word": " x", "probability": 0.95849609375}, {"start": 998.31, "end": 998.61, "word": " minus", "probability": 0.91259765625}, {"start": 998.61, "end": 999.03, "word": " c", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 40, "seek": 102393, "start": 999.39, "end": 1023.93, "text": "as x → c بساوي حسب اللي عندى من هنا و من هنا و من هنا هيساوي سفر الان conversely بتأفترض طبعا ان ال conversely هيكون الخطوات كثير مشابهه لللي هنا يعني كثير اللي استخدمته هنا هستخدمه في اللي بعدها", "tokens": [296, 2031, 41600, 269, 4724, 3794, 995, 45865, 11331, 35457, 13672, 1829, 43242, 7578, 9154, 34105, 4032, 9154, 34105, 4032, 9154, 34105, 39896, 3794, 995, 45865, 8608, 5172, 2288, 2423, 7649, 2615, 736, 39894, 10721, 5172, 2655, 43042, 23032, 3555, 3615, 995, 16472, 2423, 2615, 736, 39896, 30544, 33962, 9566, 2407, 9307, 9122, 12984, 13546, 37893, 16758, 3224, 3224, 24976, 20292, 34105, 37495, 22653, 9122, 12984, 13546, 13672, 1829, 44713, 9778, 40448, 47395, 34105, 8032, 14851, 9778, 40448, 3224, 8978, 13672, 1829, 39182, 11296], "avg_logprob": -0.3641544215819415, "compression_ratio": 1.7923497267759563, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 999.39, "end": 999.71, "word": "as", "probability": 0.43115234375}, {"start": 999.71, "end": 999.93, "word": " x", "probability": 0.61083984375}, {"start": 999.93, "end": 1000.21, "word": " →", "probability": 0.06488037109375}, {"start": 1000.21, "end": 1000.75, "word": " c", "probability": 0.7978515625}, {"start": 1000.75, "end": 1002.01, "word": " بساوي", "probability": 0.6122970581054688}, {"start": 1002.01, "end": 1002.99, "word": " حسب", "probability": 0.888671875}, {"start": 1002.99, "end": 1003.31, "word": " اللي", "probability": 0.519775390625}, {"start": 1003.31, "end": 1004.53, "word": " عندى", "probability": 0.594482421875}, {"start": 1004.53, "end": 1006.19, "word": " من", "probability": 0.7734375}, {"start": 1006.19, "end": 1006.45, "word": " هنا", "probability": 0.5595703125}, {"start": 1006.45, "end": 1006.69, "word": " و", "probability": 0.826171875}, {"start": 1006.69, "end": 1006.87, "word": " من", "probability": 0.732421875}, {"start": 1006.87, "end": 1007.15, "word": " هنا", "probability": 0.98974609375}, {"start": 1007.15, "end": 1007.33, "word": " و", "probability": 0.95458984375}, {"start": 1007.33, "end": 1007.47, "word": " من", "probability": 0.96875}, {"start": 1007.47, "end": 1007.79, "word": " هنا", "probability": 0.9912109375}, {"start": 1007.79, "end": 1008.99, "word": " هيساوي", "probability": 0.6663818359375}, {"start": 1008.99, "end": 1009.89, "word": " سفر", "probability": 0.85546875}, {"start": 1009.89, "end": 1011.45, "word": " الان", "probability": 0.65771484375}, {"start": 1011.45, "end": 1012.27, "word": " conversely", "probability": 0.82080078125}, {"start": 1012.27, "end": 1015.31, "word": " بتأفترض", "probability": 0.46146240234375}, {"start": 1015.31, "end": 1015.67, "word": " طبعا", "probability": 0.8831787109375}, {"start": 1015.67, "end": 1015.79, "word": " ان", "probability": 0.3798828125}, {"start": 1015.79, "end": 1015.97, "word": " ال", "probability": 0.74267578125}, {"start": 1015.97, "end": 1016.33, "word": " conversely", "probability": 0.5279541015625}, {"start": 1016.33, "end": 1016.73, "word": " هيكون", "probability": 0.859130859375}, {"start": 1016.73, "end": 1017.19, "word": " الخطوات", "probability": 0.9783935546875}, {"start": 1017.19, "end": 1017.53, "word": " كثير", "probability": 0.7532552083333334}, {"start": 1017.53, "end": 1018.09, "word": " مشابهه", "probability": 0.83551025390625}, {"start": 1018.09, "end": 1018.41, "word": " لللي", "probability": 0.7587890625}, {"start": 1018.41, "end": 1018.63, "word": " هنا", "probability": 0.2490234375}, {"start": 1018.63, "end": 1019.77, "word": " يعني", "probability": 0.881591796875}, {"start": 1019.77, "end": 1020.09, "word": " كثير", "probability": 0.88427734375}, {"start": 1020.09, "end": 1020.17, "word": " اللي", "probability": 0.84326171875}, {"start": 1020.17, "end": 1020.71, "word": " استخدمته", "probability": 0.9327392578125}, {"start": 1020.71, "end": 1020.87, "word": " هنا", "probability": 0.9052734375}, {"start": 1020.87, "end": 1021.81, "word": " هستخدمه", "probability": 0.89150390625}, {"start": 1021.81, "end": 1023.35, "word": " في", "probability": 0.75341796875}, {"start": 1023.35, "end": 1023.47, "word": " اللي", "probability": 0.963623046875}, {"start": 1023.47, "end": 1023.93, "word": " بعدها", "probability": 0.70556640625}], "temperature": 1.0}, {"id": 41, "seek": 105991, "start": 1032.67, "end": 1059.91, "text": "Conversely suppose that g of x سواء absolute value او f of x اللي هو is differentiable at c بدا وجدلك الان اثبتلك ان f prime of c ايش ما لها بتساوي سفر يعني بدا اثبت 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" x", "probability": 0.869140625}, {"start": 1040.05, "end": 1040.97, "word": " سواء", "probability": 0.4903157552083333}, {"start": 1040.97, "end": 1041.29, "word": " absolute", "probability": 0.213623046875}, {"start": 1041.29, "end": 1041.75, "word": " value", "probability": 0.97705078125}, {"start": 1041.75, "end": 1041.89, "word": " او", "probability": 0.71484375}, {"start": 1041.89, "end": 1042.07, "word": " f", "probability": 0.414306640625}, {"start": 1042.07, "end": 1042.23, "word": " of", "probability": 0.85693359375}, {"start": 1042.23, "end": 1042.71, "word": " x", "probability": 0.90478515625}, {"start": 1042.71, "end": 1045.89, "word": " اللي", "probability": 0.5924072265625}, {"start": 1045.89, "end": 1046.13, "word": " هو", "probability": 0.9931640625}, {"start": 1046.13, "end": 1046.63, "word": " is", "probability": 0.74609375}, {"start": 1046.63, "end": 1048.85, "word": " differentiable", "probability": 0.962646484375}, {"start": 1048.85, "end": 1050.19, "word": " at", "probability": 0.9453125}, {"start": 1050.19, "end": 1050.47, "word": " c", "probability": 0.51953125}, {"start": 1050.47, "end": 1052.19, "word": " بدا", "probability": 0.27655029296875}, {"start": 1052.19, "end": 1052.63, "word": " وجدلك", "probability": 0.6331380208333334}, {"start": 1052.63, "end": 1052.99, "word": " الان", "probability": 0.58343505859375}, {"start": 1052.99, "end": 1053.43, "word": " اثبتلك", "probability": 0.83046875}, {"start": 1053.43, "end": 1053.55, "word": " ان", "probability": 0.90234375}, {"start": 1053.55, "end": 1053.75, "word": " f", "probability": 0.242431640625}, {"start": 1053.75, "end": 1054.07, "word": " prime", "probability": 0.693359375}, {"start": 1054.07, "end": 1054.27, "word": " of", "probability": 0.96337890625}, {"start": 1054.27, "end": 1054.47, "word": " c", "probability": 0.89892578125}, {"start": 1054.47, "end": 1054.71, "word": " ايش", "probability": 0.7001139322916666}, {"start": 1054.71, "end": 1054.85, "word": " ما", 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" ناقص", "probability": 0.6781005859375}, {"start": 1092.39, "end": 1092.49, "word": " ال", "probability": 0.6025390625}, {"start": 1092.49, "end": 1092.81, "word": " absolute", "probability": 0.54296875}, {"start": 1092.81, "end": 1093.23, "word": " value", "probability": 0.99072265625}, {"start": 1093.23, "end": 1093.37, "word": " of", "probability": 0.89501953125}, {"start": 1093.37, "end": 1093.53, "word": " f", "probability": 0.78271484375}, {"start": 1093.53, "end": 1093.77, "word": " of", "probability": 0.94775390625}, {"start": 1093.77, "end": 1094.05, "word": " c", "probability": 0.66259765625}, {"start": 1094.05, "end": 1095.41, "word": " صفر", "probability": 0.7096354166666666}, {"start": 1095.41, "end": 1096.17, "word": " على", "probability": 0.6201171875}, {"start": 1096.17, "end": 1098.57, "word": " x", "probability": 0.7900390625}, {"start": 1098.57, "end": 1098.95, "word": " minus", "probability": 0.75732421875}, {"start": 1098.95, "end": 1099.41, "word": " c", 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"start": 1446.41, "end": 1474.97, "text": "بتكون الـ function الـ G prime إيه شمالها is even انحل واحدة من هنا والتانية similarly زيها الآن لنفترض F من عند R لعند R be an odd differentiable function ماشي الحال show that", "tokens": [3555, 2655, 30544, 2423, 39184, 2445, 2423, 39184, 460, 5835, 11933, 1829, 3224, 13412, 2304, 6027, 11296, 307, 754, 16472, 5016, 1211, 36764, 24401, 3660, 9154, 34105, 16070, 2655, 7649, 10632, 1034, 2202, 356, 30767, 1829, 11296, 6024, 48506, 5296, 1863, 5172, 2655, 43042, 479, 9154, 43242, 497, 5296, 3615, 41260, 497, 312, 364, 7401, 819, 9364, 2445, 3714, 33599, 1829, 21542, 6027, 855, 300], "avg_logprob": -0.2904829473206491, "compression_ratio": 1.358695652173913, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1446.41, "end": 1447.01, "word": "بتكون", "probability": 0.67919921875}, {"start": 1447.01, "end": 1447.19, "word": " الـ", "probability": 0.821533203125}, {"start": 1447.19, "end": 1447.51, "word": " function", "probability": 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limit f of xₙ as n goes to infinity بساوي برضه الـ", "tokens": [3555, 30544, 43242, 7578, 36632, 8310, 2031, 37781, 247, 39894, 32887, 5016, 24976, 39184, 383, 5296, 31377, 2304, 7251, 2655, 5016, 4587, 4587, 5296, 11296, 4948, 283, 295, 2031, 37781, 247, 382, 297, 1709, 281, 13202, 4724, 3794, 995, 45865, 4724, 43042, 3224, 2423, 39184], "avg_logprob": -0.26460598344388214, "compression_ratio": 1.1044776119402986, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1845.7, "end": 1846.14, "word": "بكون", "probability": 0.7431640625}, {"start": 1846.14, "end": 1846.94, "word": " عندى", "probability": 0.75390625}, {"start": 1846.94, "end": 1847.32, "word": " أي", "probability": 0.443603515625}, {"start": 1847.32, "end": 1848.24, "word": " sequence", "probability": 0.7919921875}, {"start": 1848.24, "end": 1849.42, "word": " xₙ", "probability": 0.4777933756510417}, {"start": 1849.42, "end": 1850.62, "word": " بتروح", "probability": 0.9111328125}, {"start": 1850.62, "end": 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0.876708984375}, {"start": 2023.21, "end": 2023.53, "word": " بيقول", "probability": 0.9908854166666666}, {"start": 2023.53, "end": 2024.11, "word": " if", "probability": 0.9091796875}, {"start": 2024.11, "end": 2025.39, "word": " f", "probability": 0.475341796875}, {"start": 2025.39, "end": 2025.95, "word": " برا", "probability": 0.5985107421875}, {"start": 2025.95, "end": 2026.31, "word": " اللي", "probability": 0.815185546875}, {"start": 2026.31, "end": 2026.53, "word": " هو", "probability": 0.9833984375}, {"start": 2026.53, "end": 2027.03, "word": " limit", "probability": 0.96240234375}, {"start": 2027.03, "end": 2028.85, "word": " f", "probability": 0.73828125}, {"start": 2028.85, "end": 2030.07, "word": " of", "probability": 0.92529296875}, {"start": 2030.07, "end": 2030.47, "word": " c", "probability": 0.8193359375}, {"start": 2030.47, "end": 2030.97, "word": " زاد", "probability": 0.6021728515625}, {"start": 2030.97, "end": 2031.51, "word": " واحدة", "probability": 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2036.51, "end": 2036.73, "word": " goes", "probability": 0.91650390625}, {"start": 2036.73, "end": 2036.87, "word": " to", "probability": 0.91162109375}, {"start": 2036.87, "end": 2037.35, "word": " infinity", "probability": 0.892578125}, {"start": 2037.35, "end": 2038.69, "word": " exist", "probability": 0.495361328125}, {"start": 2038.69, "end": 2041.13, "word": " if", "probability": 0.7333984375}, {"start": 2041.13, "end": 2041.61, "word": " كده", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 80, "seek": 206992, "start": 2042.5, "end": 2069.92, "text": "then f prime at c need not be exist اصلا مش انه يكون بيسوي هذا او لا need not to be اشمله exist لان لو كان exist على طول بيسوي اما need not to be exist ومااخد مثال جالي consider consider consider f of x", "tokens": [19096, 283, 5835, 412, 269, 643, 406, 312, 2514, 1975, 9381, 15040, 37893, 16472, 3224, 7251, 30544, 4724, 1829, 3794, 45865, 23758, 1975, 2407, 20193, 643, 406, 281, 312, 1975, 8592, 2304, 43761, 2514, 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"probability": 0.8857421875}], "temperature": 1.0}, {"id": 81, "seek": 209973, "start": 2070.66, "end": 2099.74, "text": "بساوي ال absolute value لل X وخد عند ال C أش بتساوي سفر واضح F prime of 0 does not exist لأنها عبارة عن corner point، انتوا عارفين احنا اللي هو ال F prime عند ال zero لل absolute value does not exist لكن هذه متحققة، ليش؟ but limit", "tokens": [3555, 3794, 995, 45865, 2423, 8236, 2158, 24976, 1783, 4032, 9778, 3215, 43242, 2423, 383, 5551, 8592, 39894, 3794, 995, 45865, 8608, 5172, 2288, 4032, 46958, 5016, 479, 5835, 295, 1958, 775, 406, 2514, 5296, 33456, 11296, 6225, 3555, 9640, 3660, 18871, 4538, 935, 12399, 16472, 2655, 14407, 6225, 9640, 5172, 9957, 1975, 5016, 8315, 13672, 1829, 31439, 2423, 479, 5835, 43242, 2423, 4018, 24976, 8236, 2158, 775, 406, 2514, 44381, 29538, 44650, 5016, 4587, 28671, 12399, 32239, 8592, 22807, 457, 4948], "avg_logprob": -0.2682605292423662, "compression_ratio": 1.4703196347031964, "no_speech_prob": 2.682209014892578e-06, "words": 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2090.64, "word": " zero", "probability": 0.438232421875}, {"start": 2090.64, "end": 2090.86, "word": " لل", "probability": 0.65673828125}, {"start": 2090.86, "end": 2091.64, "word": " absolute", "probability": 0.89501953125}, {"start": 2091.64, "end": 2092.06, "word": " value", "probability": 0.990234375}, {"start": 2092.06, "end": 2092.26, "word": " does", "probability": 0.5595703125}, {"start": 2092.26, "end": 2092.48, "word": " not", "probability": 0.96875}, {"start": 2092.48, "end": 2092.96, "word": " exist", "probability": 0.9736328125}, {"start": 2092.96, "end": 2094.62, "word": " لكن", "probability": 0.93603515625}, {"start": 2094.62, "end": 2095.16, "word": " هذه", "probability": 0.837890625}, {"start": 2095.16, "end": 2096.66, "word": " متحققة،", "probability": 0.866015625}, {"start": 2096.66, "end": 2097.34, "word": " ليش؟", "probability": 0.8447265625}, {"start": 2097.34, "end": 2097.76, "word": " but", "probability": 0.62939453125}, {"start": 2097.76, "end": 2099.74, 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