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264.16, "end": 290.96, "text": "فواحد على أن ينتمي للـDelta neighborhood للسفر وواحد على أن ينتمي للمجموعة A وبالتالي يجب أن نكون أثبتنا أنه لأي Delta أكبر من السفر أو أي Delta neighborhood للسفر يتقاطع مع A في نقطة مختلفة عن السفر ال X انها جلدها تساوي سفر", "tokens": [5172, 14407, 24401, 15844, 14739, 7251, 29399, 2304, 1829, 24976, 39184, 40848, 1328, 7630, 24976, 3794, 5172, 2288, 4032, 14407, 24401, 15844, 14739, 7251, 29399, 2304, 1829, 5296, 19528, 7435, 2304, 2407, 27884, 316, 46599, 6027, 2655, 6027, 1829, 7251, 7435, 3555, 14739, 8717, 30544, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 5296, 10721, 1829, 18183, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 34051, 36632, 18183, 7630, 24976, 3794, 5172, 2288, 7251, 2655, 4587, 41193, 3615, 20449, 316, 8978, 8717, 47432, 3660, 3714, 46456, 46538, 3660, 18871, 21136, 5172, 2288, 2423, 1783, 16472, 11296, 10874, 1211, 3215, 11296, 6055, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.20975824867217047, "compression_ratio": 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"probability": 0.9747721354166666}, {"start": 276.16, "end": 276.56, "word": " أو", "probability": 0.8564453125}, {"start": 276.56, "end": 278.12, "word": " أي", "probability": 0.412353515625}, {"start": 278.12, "end": 278.58, "word": " Delta", "probability": 0.8779296875}, {"start": 278.58, "end": 279.0, "word": " neighborhood", "probability": 0.869140625}, {"start": 279.0, "end": 279.74, "word": " للسفر", "probability": 0.966064453125}, {"start": 279.74, "end": 280.56, "word": " يتقاطع", "probability": 0.9578125}, {"start": 280.56, "end": 280.84, "word": " مع", "probability": 0.9404296875}, {"start": 280.84, "end": 281.28, "word": " A", "probability": 0.7763671875}, {"start": 281.28, "end": 282.72, "word": " في", "probability": 0.96533203125}, {"start": 282.72, "end": 283.12, "word": " نقطة", "probability": 0.9899088541666666}, {"start": 283.12, "end": 284.02, "word": " مختلفة", "probability": 0.9954833984375}, {"start": 284.02, "end": 284.68, "word": " عن", "probability": 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11933, 15730, 23758, 4724, 12984, 3555, 2655, 2423, 3932, 6024, 48506, 32239, 3224, 19446, 1829, 30544, 8978, 3224, 13630, 2793, 5551, 34740, 7578, 22807], "avg_logprob": -0.3559658971699801, "compression_ratio": 1.5461538461538462, "no_speech_prob": 0.0, "words": [{"start": 292.61, "end": 293.59, "word": "لاتسار", "probability": 0.51513671875}, {"start": 293.59, "end": 294.01, "word": " السفر", "probability": 0.8665364583333334}, {"start": 294.01, "end": 296.49, "word": " وبالتالي", "probability": 0.7202809651692709}, {"start": 296.49, "end": 296.81, "word": " إذا", "probability": 0.489715576171875}, {"start": 296.81, "end": 297.11, "word": " هذا", "probability": 0.67822265625}, {"start": 297.11, "end": 297.69, "word": " بثبت", "probability": 0.8934326171875}, {"start": 297.69, "end": 299.41, "word": " السفر", "probability": 0.8525390625}, {"start": 299.41, "end": 299.93, "word": " is", "probability": 0.78369140625}, {"start": 299.93, "end": 300.29, "word": " a", "probability": 0.90234375}, {"start": 300.29, "end": 300.71, "word": " cluster", "probability": 0.92822265625}, {"start": 300.71, "end": 301.37, "word": " point", "probability": 0.96923828125}, {"start": 301.37, "end": 305.47, "word": " of", "probability": 0.277099609375}, {"start": 305.47, "end": 306.49, "word": " الست", "probability": 0.529541015625}, {"start": 306.49, "end": 307.91, "word": " إذا", "probability": 0.635009765625}, {"start": 307.91, "end": 308.17, "word": " هذا", "probability": 0.83642578125}, {"start": 308.17, "end": 308.69, "word": " بثبت", "probability": 0.9696044921875}, {"start": 308.69, "end": 308.81, "word": " ال", "probability": 0.84375}, {"start": 308.81, "end": 309.15, "word": " claim", "probability": 0.83740234375}, {"start": 309.15, "end": 310.07, "word": " الآن", "probability": 0.6729736328125}, {"start": 310.07, "end": 311.41, "word": " ليه", "probability": 0.955322265625}, {"start": 311.41, "end": 312.09, "word": " مايكون", "probability": 0.7880859375}, {"start": 312.09, "end": 312.31, "word": " فيه", "probability": 0.759033203125}, {"start": 312.31, "end": 312.65, "word": " cluster", "probability": 0.95751953125}, {"start": 312.65, "end": 313.25, "word": " points", "probability": 0.93603515625}, {"start": 313.25, "end": 314.13, "word": " أخرى؟", "probability": 0.9578857421875}], "temperature": 1.0}, {"id": 11, "seek": 34763, "start": 330.49, "end": 347.63, "text": "إذا كانت X لا تساوي سفر، فهي ليست مجموعة من A فحاسيبكم أنتم تكتبوا البرهان", "tokens": [28814, 15730, 25961, 2655, 1783, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 12399, 6156, 3224, 1829, 32239, 14851, 3714, 7435, 2304, 2407, 27884, 9154, 316, 6156, 5016, 32277, 1829, 3555, 24793, 14739, 39237, 6055, 4117, 2655, 3555, 14407, 2423, 26890, 3224, 7649], "avg_logprob": -0.5557528219439767, "compression_ratio": 1.233644859813084, "no_speech_prob": 0.0, "words": [{"start": 330.49, "end": 331.33000000000004, "word": "إذا", "probability": 0.283172607421875}, {"start": 331.33000000000004, "end": 332.17, "word": " كانت", "probability": 0.7763671875}, {"start": 332.17, "end": 332.39, "word": " X", "probability": 0.275634765625}, {"start": 332.39, "end": 332.61, "word": " لا", "probability": 0.63427734375}, {"start": 332.61, "end": 333.09, "word": " تساوي", "probability": 0.8519287109375}, {"start": 333.09, "end": 333.47, "word": " سفر،", "probability": 0.59808349609375}, {"start": 333.47, "end": 333.79, "word": " فهي", "probability": 0.6863606770833334}, {"start": 333.79, "end": 334.07, "word": " ليست", "probability": 0.81005859375}, {"start": 334.07, "end": 334.71, "word": " مجموعة", "probability": 0.5892333984375}, {"start": 334.71, "end": 335.13, "word": " من", "probability": 0.08087158203125}, {"start": 335.13, "end": 341.15, "word": " A", "probability": 0.450927734375}, {"start": 341.15, "end": 346.39, "word": " فحاسيبكم", "probability": 0.7115885416666666}, {"start": 346.39, "end": 346.65, "word": " أنتم", "probability": 0.521728515625}, {"start": 346.65, "end": 347.07, "word": " تكتبوا", "probability": 0.97919921875}, {"start": 347.07, "end": 347.63, "word": " البرهان", "probability": 0.69744873046875}], "temperature": 1.0}, {"id": 12, "seek": 36539, "start": 350.29, "end": 365.39, "text": "هي سفر وهي واحد وهي نص وهي تلت وهي واحد على N وهي واحد على N زائد واحد وهكذا", "tokens": [3224, 1829, 8608, 5172, 2288, 37037, 1829, 36764, 24401, 37037, 1829, 8717, 9381, 37037, 1829, 6055, 1211, 2655, 37037, 1829, 36764, 24401, 15844, 426, 37037, 1829, 36764, 24401, 15844, 426, 30767, 16373, 3215, 36764, 24401, 37037, 4117, 15730], "avg_logprob": -0.22556089361508688, "compression_ratio": 1.736842105263158, "no_speech_prob": 0.0, "words": [{"start": 350.29, "end": 350.63, "word": "هي", "probability": 0.5052490234375}, {"start": 350.63, "end": 351.11, "word": " سفر", "probability": 0.7296549479166666}, {"start": 351.11, "end": 351.43, "word": " وهي", "probability": 0.7412109375}, {"start": 351.43, "end": 352.01, "word": " واحد", "probability": 0.986328125}, {"start": 352.01, "end": 353.31, "word": " وهي", "probability": 0.877197265625}, {"start": 353.31, "end": 353.77, "word": " نص", "probability": 0.987060546875}, {"start": 353.77, "end": 355.85, "word": " وهي", "probability": 0.81982421875}, {"start": 355.85, "end": 356.45, "word": " تلت", "probability": 0.9313151041666666}, {"start": 356.45, "end": 359.03, "word": " وهي", "probability": 0.9248046875}, {"start": 359.03, "end": 359.67, "word": " واحد", "probability": 0.98876953125}, {"start": 359.67, "end": 359.95, "word": " على", "probability": 0.5859375}, {"start": 359.95, "end": 360.39, "word": " N", "probability": 0.201904296875}, {"start": 360.39, "end": 362.39, "word": " وهي", "probability": 0.784423828125}, {"start": 362.39, "end": 362.89, "word": " واحد", "probability": 0.98974609375}, {"start": 362.89, "end": 363.11, "word": " على", "probability": 0.810546875}, {"start": 363.11, "end": 363.57, "word": " N", "probability": 0.87646484375}, {"start": 363.57, "end": 364.25, "word": " زائد", "probability": 0.8780924479166666}, {"start": 364.25, "end": 364.77, "word": " واحد", "probability": 0.980712890625}, {"start": 364.77, "end": 365.39, "word": " وهكذا", "probability": 0.80419921875}], "temperature": 1.0}, {"id": 13, "seek": 40035, "start": 376.43, "end": 400.35, "text": "فهنا تاندي two cases case one ان x تنتمي الى a و الحلقة التانية case two ان x لا تنتمي الى a ال x دي مستويش السفر احنا already اثبتنا ان السفر cluster point", "tokens": [5172, 3224, 8315, 6055, 7649, 16254, 732, 3331, 1389, 472, 16472, 2031, 6055, 29399, 2304, 1829, 2423, 7578, 257, 4032, 21542, 1211, 28671, 16712, 7649, 10632, 1389, 732, 16472, 2031, 20193, 6055, 29399, 2304, 1829, 2423, 7578, 257, 2423, 2031, 11778, 1829, 3714, 14851, 45865, 8592, 21136, 5172, 2288, 1975, 5016, 8315, 1217, 1975, 12984, 3555, 2655, 8315, 16472, 21136, 5172, 2288, 13630, 935], "avg_logprob": -0.3894230769230769, "compression_ratio": 1.563758389261745, "no_speech_prob": 0.0, "words": [{"start": 376.43, "end": 376.95, "word": "فهنا", "probability": 0.6041666666666666}, {"start": 376.95, "end": 377.53, "word": " تاندي", "probability": 0.2945963541666667}, {"start": 377.53, "end": 377.83, "word": " two", "probability": 0.460693359375}, {"start": 377.83, "end": 378.45, "word": " cases", "probability": 0.9384765625}, {"start": 378.45, "end": 379.59, "word": " case", "probability": 0.485107421875}, {"start": 379.59, "end": 380.01, "word": " one", "probability": 0.7177734375}, {"start": 380.01, "end": 380.87, "word": " ان", "probability": 0.435546875}, {"start": 380.87, "end": 381.27, "word": " x", "probability": 0.3193359375}, {"start": 381.27, "end": 382.03, "word": " تنتمي", "probability": 0.8489990234375}, {"start": 382.03, "end": 382.81, "word": " الى", "probability": 0.6524658203125}, {"start": 382.81, "end": 383.15, "word": " a", "probability": 0.81884765625}, {"start": 383.15, "end": 385.93, "word": " و", "probability": 0.4228515625}, {"start": 385.93, "end": 386.41, "word": " الحلقة", "probability": 0.7900390625}, {"start": 386.41, "end": 386.97, "word": " التانية", "probability": 0.87939453125}, {"start": 386.97, "end": 387.91, "word": " case", "probability": 0.83203125}, {"start": 387.91, "end": 388.35, "word": " two", "probability": 0.8671875}, {"start": 388.35, "end": 389.77, "word": " ان", "probability": 0.73095703125}, {"start": 389.77, "end": 390.19, "word": " x", "probability": 0.62060546875}, {"start": 390.19, "end": 390.41, "word": " لا", "probability": 0.82275390625}, {"start": 390.41, "end": 391.07, "word": " تنتمي", "probability": 0.9161376953125}, {"start": 391.07, "end": 391.21, "word": " الى", "probability": 0.754150390625}, {"start": 391.21, "end": 391.87, "word": " a", "probability": 0.853515625}, {"start": 391.87, "end": 394.41, "word": " ال", "probability": 0.68115234375}, {"start": 394.41, "end": 394.69, "word": " x", "probability": 0.462890625}, {"start": 394.69, "end": 394.91, "word": " دي", "probability": 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كانت ال X واحد من العناصر هدول واحد من العناصر الست فبقدر ألاقي أن يوجد بقدر ألاقي delta neighborhood للعنصر مثلا التلت بقدر ألاقي delta neighborhood", "tokens": [9566, 1829, 3555, 1975, 5172, 43042, 1783, 3714, 14851, 45865, 8592, 8608, 5172, 2288, 11933, 15730, 1783, 3714, 43020, 6055, 3794, 995, 45865, 36764, 24401, 34051, 8717, 9381, 34051, 6055, 1211, 2655, 34051, 36764, 24401, 15844, 426, 337, 512, 426, 20328, 5016, 22807, 3714, 43020, 3714, 9307, 3794, 995, 45865, 8592, 49429, 18871, 9381, 2288, 3714, 43020, 3714, 9307, 30544, 8592, 46811, 46811, 1211, 36632, 3224, 6156, 1211, 2407, 25961, 2655, 2423, 1783, 36764, 24401, 9154, 18863, 1863, 33546, 2288, 8032, 3215, 12610, 36764, 24401, 9154, 18863, 1863, 33546, 2288, 2423, 14851, 6156, 3555, 28543, 2288, 5551, 15040, 38436, 14739, 7251, 29245, 3215, 4724, 28543, 2288, 5551, 15040, 38436, 8289, 7630, 24976, 3615, 1863, 9381, 2288, 50113, 15040, 16712, 1211, 2655, 4724, 28543, 2288, 5551, 15040, 38436, 8289, 7630], "avg_logprob": 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{"start": 423.91, "end": 424.25, "word": " ألاقي", "probability": 0.9690755208333334}, {"start": 424.25, "end": 424.63, "word": " delta", "probability": 0.391357421875}, {"start": 424.63, "end": 425.11, "word": " neighborhood", "probability": 0.7861328125}, {"start": 425.11, "end": 426.97, "word": " للعنصر", "probability": 0.933203125}, {"start": 426.97, "end": 427.45, "word": " مثلا", "probability": 0.96533203125}, {"start": 427.45, "end": 427.99, "word": " التلت", "probability": 0.9158528645833334}, {"start": 427.99, "end": 428.33, "word": " بقدر", "probability": 0.9742838541666666}, {"start": 428.33, "end": 428.61, "word": " ألاقي", "probability": 0.9851888020833334}, {"start": 428.61, "end": 428.99, "word": " delta", "probability": 0.8359375}, {"start": 428.99, "end": 429.49, "word": " neighborhood", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 15, "seek": 45418, "start": 433.86, "end": 454.18, "text": "الأنصر اللي بعد هذا هيكون ربع فباخد المسافة الأصغر بين تلت ربع تلت و نص و باخد نص المسافة ديلتا فبصير عند هنا ديلتا نبرهود للتلت و بتقاطعش مع المجموعة A بالمرة أو في نقطة مختلفة عن التلت", "tokens": [6027, 33456, 9381, 2288, 13672, 1829, 39182, 23758, 39896, 30544, 12602, 3555, 3615, 6156, 3555, 47283, 3215, 9673, 3794, 31845, 3660, 16247, 9381, 17082, 2288, 49374, 6055, 1211, 2655, 12602, 3555, 3615, 6055, 1211, 2655, 4032, 8717, 9381, 4032, 4724, 47283, 3215, 8717, 9381, 9673, 3794, 31845, 3660, 11778, 26895, 2655, 995, 6156, 3555, 9381, 13546, 43242, 34105, 11778, 26895, 2655, 995, 8717, 26890, 3224, 23328, 24976, 2655, 1211, 2655, 4032, 39894, 4587, 41193, 3615, 8592, 20449, 9673, 7435, 2304, 2407, 27884, 316, 20666, 2304, 25720, 34051, 8978, 8717, 47432, 3660, 3714, 46456, 46538, 3660, 18871, 16712, 1211, 2655], "avg_logprob": -0.22749999448657035, "compression_ratio": 1.887005649717514, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 433.86, "end": 434.66, "word": "الأنصر", "probability": 0.7020263671875}, {"start": 434.66, 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تقاطع ال rational numbers then every x تنهي ل I is a cluster point a cluster point of IQ", "tokens": [40, 48, 4724, 3794, 995, 45865, 286, 6055, 4587, 41193, 3615, 2423, 15090, 3547, 550, 633, 2031, 6055, 1863, 3224, 1829, 5296, 286, 307, 257, 13630, 935, 257, 13630, 935, 295, 28921], "avg_logprob": -0.35984848484848486, "compression_ratio": 1.1262135922330097, "no_speech_prob": 0.0, "words": [{"start": 591.2099999999999, "end": 592.5699999999999, "word": "IQ", "probability": 0.528564453125}, {"start": 592.5699999999999, "end": 593.93, "word": " بساوي", "probability": 0.611968994140625}, {"start": 593.93, "end": 594.41, "word": " I", "probability": 0.9296875}, {"start": 594.41, "end": 595.19, "word": " تقاطع", "probability": 0.79364013671875}, {"start": 595.19, "end": 595.39, "word": " ال", "probability": 0.57958984375}, {"start": 595.39, "end": 595.73, "word": " rational", "probability": 0.406494140625}, {"start": 595.73, "end": 596.85, "word": " numbers", "probability": 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613.83, "word": " point", "probability": 0.9736328125}, {"start": 613.83, "end": 614.45, "word": " of", "probability": 0.9736328125}, {"start": 614.45, "end": 615.25, "word": " IQ", "probability": 0.90625}], "temperature": 1.0}, {"id": 22, "seek": 64636, "start": 618.8, "end": 646.36, "text": "إذا I هي الفترة المغلقة من صفر لواحد IQ هي كل الأعداد المسبية الموجودة في الفترة المغلقة من صفر لواحد ممكن إثبات إن كل X في الفترة المغلقة I هي cluster point للمجموعة IQ وذلك باستخدام ال density theorem", "tokens": [28814, 15730, 286, 39896, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 20328, 5172, 2288, 5296, 14407, 24401, 286, 48, 39896, 28242, 16247, 22488, 18513, 9673, 35457, 10632, 9673, 29245, 23328, 3660, 8978, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 20328, 5172, 2288, 5296, 14407, 24401, 3714, 43020, 11933, 12984, 3555, 9307, 36145, 28242, 1783, 8978, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 286, 39896, 13630, 935, 5296, 19528, 7435, 2304, 2407, 27884, 28921, 4032, 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644.66, "word": " وذلك", "probability": 0.8616536458333334}, {"start": 644.66, "end": 645.34, "word": " باستخدام", "probability": 0.9918619791666666}, {"start": 645.34, "end": 645.48, "word": " ال", "probability": 0.841796875}, {"start": 645.48, "end": 645.94, "word": " density", "probability": 0.7783203125}, {"start": 645.94, "end": 646.36, "word": " theorem", "probability": 0.8212890625}], "temperature": 1.0}, {"id": 23, "seek": 67592, "start": 647.76, "end": 675.92, "text": "proof use the density theorem فحاسيبكم انتوا تكتبوا البرهان خدي أي x في I واخدتي انه أي", "tokens": [15690, 764, 264, 10305, 20904, 6156, 5016, 32277, 1829, 3555, 24793, 16472, 2655, 14407, 6055, 4117, 2655, 3555, 14407, 2423, 26890, 3224, 7649, 16490, 16254, 36632, 2031, 8978, 286, 4032, 47283, 3215, 31371, 16472, 3224, 36632], "avg_logprob": -0.33213681143683355, "compression_ratio": 1.1391304347826088, "no_speech_prob": 0.0, "words": [{"start": 647.76, "end": 648.72, "word": "proof", "probability": 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"word": " من", "probability": 0.77490234375}, {"start": 688.22, "end": 688.7, "word": " ملفة", "probability": 0.5900065104166666}, {"start": 688.7, "end": 688.88, "word": " أن", "probability": 0.50146484375}, {"start": 688.88, "end": 689.26, "word": " كل", "probability": 0.80517578125}, {"start": 689.26, "end": 689.72, "word": " X", "probability": 0.81640625}, {"start": 689.72, "end": 691.54, "word": " كل", "probability": 0.469482421875}, {"start": 691.54, "end": 691.84, "word": " X", "probability": 0.9833984375}, {"start": 691.84, "end": 692.18, "word": " فيها", "probability": 0.95654296875}, {"start": 692.18, "end": 692.38, "word": " هو", "probability": 0.755859375}, {"start": 692.38, "end": 692.76, "word": " cluster", "probability": 0.91748046875}, {"start": 692.76, "end": 693.32, "word": " point", "probability": 0.97265625}, {"start": 693.32, "end": 694.74, "word": " لمجموعة", "probability": 0.898681640625}, {"start": 694.74, "end": 695.26, "word": " الأعداد", "probability": 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"word": " و", "probability": 0.59716796875}, {"start": 783.86, "end": 784.12, "word": " هادي", "probability": 0.6969401041666666}, {"start": 784.12, "end": 784.42, "word": " نقطة", "probability": 0.9471028645833334}, {"start": 784.42, "end": 784.8, "word": " سفر", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 28, "seek": 80129, "start": 785.83, "end": 801.29, "text": "الان الفترة هذه بقدر الاقي فيها rational number حسب مباريك الكفافة موجود بين سفر و دلتا و ال rational number هذا موجود في ال unit closed interval", "tokens": [6027, 7649, 27188, 2655, 25720, 29538, 4724, 28543, 2288, 1975, 15040, 38436, 8978, 11296, 15090, 1230, 11331, 35457, 3714, 3555, 9640, 1829, 4117, 33251, 5172, 31845, 3660, 3714, 29245, 23328, 49374, 8608, 5172, 2288, 4032, 11778, 1211, 2655, 995, 4032, 2423, 15090, 1230, 23758, 3714, 29245, 23328, 8978, 2423, 4985, 5395, 15035], "avg_logprob": -0.28832546045195384, "compression_ratio": 1.4342105263157894, "no_speech_prob": 0.0, "words": [{"start": 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"probability": 0.484375}, {"start": 914.31, "end": 915.73, "word": " مجزرة", "probability": 0.7113037109375}, {"start": 915.73, "end": 916.29, "word": " من", "probability": 0.8779296875}, {"start": 916.29, "end": 919.71, "word": " الـ", "probability": 0.1669921875}, {"start": 919.71, "end": 921.61, "word": " set", "probability": 0.650390625}, {"start": 921.61, "end": 922.09, "word": " A", "probability": 0.52978515625}], "temperature": 1.0}, {"id": 34, "seek": 94536, "start": 926.66, "end": 945.36, "text": "المعنى number L هو مقال للمعنى f at x", "tokens": [45340, 3615, 1863, 7578, 1230, 441, 31439, 3714, 4587, 6027, 5296, 19528, 3615, 1863, 7578, 283, 412, 2031], "avg_logprob": -1.0106908020220304, "compression_ratio": 1.0185185185185186, "no_speech_prob": 0.0, "words": [{"start": 926.6600000000001, "end": 928.0600000000001, "word": "المعنى", "probability": 0.398773193359375}, {"start": 928.0600000000001, "end": 929.46, "word": " number", "probability": 0.54931640625}, {"start": 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0.9853515625}, {"start": 1061.46, "end": 1061.62, "word": " و", "probability": 0.87841796875}, {"start": 1061.62, "end": 1061.82, "word": " L", "probability": 0.42578125}, {"start": 1061.82, "end": 1062.42, "word": " أصغر", "probability": 0.98828125}, {"start": 1062.42, "end": 1062.58, "word": " من", "probability": 0.99169921875}, {"start": 1062.58, "end": 1063.06, "word": " إبسلون", "probability": 0.7048583984375}, {"start": 1063.06, "end": 1063.64, "word": " هذا", "probability": 0.171142578125}, {"start": 1063.64, "end": 1064.04, "word": " الكلام", "probability": 0.7639973958333334}, {"start": 1064.04, "end": 1064.56, "word": " اتحقق", "probability": 0.92431640625}, {"start": 1064.56, "end": 1064.98, "word": " لكل", "probability": 0.98193359375}, {"start": 1064.98, "end": 1065.5, "word": " إبسلون", "probability": 0.96455078125}, {"start": 1065.5, "end": 1065.86, "word": " أكبر", "probability": 0.9680989583333334}, {"start": 1065.86, "end": 1066.12, "word": " من", "probability": 0.9912109375}, {"start": 1066.12, "end": 1067.22, "word": " الصفر", "probability": 0.7017415364583334}, {"start": 1067.22, "end": 1067.74, "word": " فبنقول", "probability": 0.844970703125}, {"start": 1067.74, "end": 1067.9, "word": " إن", "probability": 0.525390625}, {"start": 1067.9, "end": 1068.36, "word": " العدد", "probability": 0.8977864583333334}, {"start": 1068.36, "end": 1068.7, "word": " L", "probability": 0.85546875}, {"start": 1068.7, "end": 1069.18, "word": " is", "probability": 0.8154296875}, {"start": 1069.18, "end": 1069.88, "word": " a", "probability": 0.75537109375}, {"start": 1069.88, "end": 1070.18, "word": " limit", "probability": 0.96923828125}, {"start": 1070.18, "end": 1070.46, "word": " of", "probability": 0.95947265625}, {"start": 1070.46, "end": 1070.62, "word": " the", "probability": 0.85986328125}, {"start": 1070.62, "end": 1071.0, "word": " function", "probability": 0.96875}, {"start": 1071.0, "end": 1071.3, "word": " f", "probability": 0.8525390625}, {"start": 1071.3, "end": 1071.64, "word": " عند", "probability": 0.74560546875}, {"start": 1071.64, "end": 1072.14, "word": " النقطة", "probability": 0.74951171875}, {"start": 1072.14, "end": 1072.36, "word": " c", "probability": 0.65283203125}], "temperature": 1.0}, {"id": 41, "seek": 110373, "start": 1079.17, "end": 1103.73, "text": "من هذا التعريف بينتج على طول اه طيب in this case in this case we say انه if converges if converges", "tokens": [27842, 23758, 16712, 3615, 16572, 5172, 4724, 9957, 2655, 7435, 15844, 23032, 12610, 1975, 3224, 23032, 1829, 3555, 294, 341, 1389, 294, 341, 1389, 321, 584, 16472, 3224, 498, 9652, 2880, 498, 9652, 2880], "avg_logprob": -0.18962053741727555, "compression_ratio": 1.2403846153846154, "no_speech_prob": 0.0, "words": [{"start": 1079.17, "end": 1079.57, "word": "من", "probability": 0.84765625}, {"start": 1079.57, "end": 1079.85, "word": " هذا", "probability": 0.86962890625}, {"start": 1079.85, "end": 1080.59, "word": " التعريف", "probability": 0.991455078125}, {"start": 1080.59, "end": 1081.39, "word": " بينتج", "probability": 0.7801513671875}, {"start": 1081.39, "end": 1081.59, "word": " على", "probability": 0.8056640625}, {"start": 1081.59, "end": 1082.17, "word": " طول", "probability": 0.993896484375}, {"start": 1082.17, "end": 1084.31, "word": " اه", "probability": 0.615966796875}, {"start": 1084.31, "end": 1084.75, "word": " طيب", "probability": 0.9697265625}, {"start": 1084.75, "end": 1086.15, "word": " in", "probability": 0.72119140625}, {"start": 1086.15, "end": 1086.49, "word": " this", "probability": 0.97314453125}, {"start": 1086.49, "end": 1087.71, "word": " case", "probability": 0.95068359375}, {"start": 1087.71, "end": 1089.69, "word": " in", "probability": 0.52978515625}, {"start": 1089.69, "end": 1090.03, "word": " this", "probability": 0.970703125}, {"start": 1090.03, "end": 1090.63, "word": " case", "probability": 0.94873046875}, {"start": 1090.63, "end": 1093.93, "word": " we", "probability": 0.73974609375}, {"start": 1093.93, "end": 1096.05, "word": " say", "probability": 0.9765625}, {"start": 1096.05, "end": 1096.89, "word": " انه", "probability": 0.887451171875}, {"start": 1096.89, "end": 1097.67, "word": " if", "probability": 0.54443359375}, {"start": 1097.67, "end": 1100.09, "word": " converges", "probability": 0.64208984375}, {"start": 1100.09, "end": 1102.71, "word": " if", "probability": 0.859375}, {"start": 1102.71, "end": 1103.73, "word": " converges", "probability": 0.972900390625}], "temperature": 1.0}, {"id": 42, "seek": 113426, "start": 1105.18, "end": 1134.26, "text": "to the number L at X بساوي C and we write ونكتب الحالة هذه limit ل F of X لما X تقول إلى C بساوي L أو ممكن نكتب limit F as X tends to C بساوي L أو ممكن نكتب", "tokens": [1353, 264, 1230, 441, 412, 1783, 4724, 3794, 995, 45865, 383, 293, 321, 2464, 4032, 1863, 4117, 2655, 3555, 21542, 6027, 3660, 29538, 4948, 5296, 479, 295, 1783, 5296, 15042, 1783, 6055, 39648, 30731, 383, 4724, 3794, 995, 45865, 441, 34051, 3714, 43020, 8717, 4117, 2655, 3555, 4948, 479, 382, 1783, 12258, 281, 383, 4724, 3794, 995, 45865, 441, 34051, 3714, 43020, 8717, 4117, 2655, 3555], "avg_logprob": -0.18435168310777464, "compression_ratio": 1.469387755102041, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1105.18, "end": 1105.44, "word": "to", "probability": 0.1646728515625}, {"start": 1105.44, "end": 1105.6, "word": " the", "probability": 0.693359375}, {"start": 1105.6, "end": 1106.12, "word": " number", "probability": 0.97265625}, {"start": 1106.12, "end": 1106.6, "word": " L", "probability": 0.685546875}, {"start": 1106.6, "end": 1108.44, "word": " at", "probability": 0.763671875}, {"start": 1108.44, "end": 1110.16, "word": " X", "probability": 0.6845703125}, {"start": 1110.16, "end": 1111.02, "word": " بساوي", "probability": 0.69976806640625}, {"start": 1111.02, "end": 1111.52, "word": " C", "probability": 0.8916015625}, {"start": 1111.52, "end": 1112.78, "word": " and", "probability": 0.76318359375}, {"start": 1112.78, "end": 1113.16, "word": " we", "probability": 0.7021484375}, {"start": 1113.16, "end": 1113.72, "word": " write", "probability": 0.939453125}, {"start": 1113.72, "end": 1114.6, "word": " ونكتب", "probability": 0.82412109375}, {"start": 1114.6, "end": 1116.5, "word": " الحالة", "probability": 0.83837890625}, {"start": 1116.5, "end": 1116.84, "word": " هذه", "probability": 0.853515625}, {"start": 1116.84, "end": 1117.4, "word": " limit", "probability": 0.2183837890625}, {"start": 1117.4, "end": 1119.52, "word": " ل", "probability": 0.7109375}, {"start": 1119.52, "end": 1119.92, "word": " F", "probability": 0.5751953125}, {"start": 1119.92, "end": 1120.18, "word": " of", "probability": 0.8505859375}, {"start": 1120.18, "end": 1120.56, "word": " X", "probability": 0.9814453125}, {"start": 1120.56, "end": 1120.92, "word": " لما", "probability": 0.76416015625}, {"start": 1120.92, "end": 1121.24, "word": " X", "probability": 0.974609375}, {"start": 1121.24, "end": 1121.84, "word": " تقول", "probability": 0.90087890625}, {"start": 1121.84, "end": 1122.24, "word": " إلى", "probability": 0.63232421875}, {"start": 1122.24, "end": 1122.6, "word": " C", "probability": 0.9541015625}, {"start": 1122.6, "end": 1123.4, "word": " بساوي", "probability": 0.9530029296875}, {"start": 1123.4, "end": 1123.82, "word": " L", "probability": 0.98779296875}, {"start": 1123.82, "end": 1125.12, "word": " أو", "probability": 0.64794921875}, {"start": 1125.12, "end": 1126.08, "word": " ممكن", "probability": 0.979248046875}, {"start": 1126.08, "end": 1126.52, "word": " نكتب", "probability": 0.9954833984375}, {"start": 1126.52, "end": 1126.94, "word": " limit", "probability": 0.9423828125}, {"start": 1126.94, "end": 1128.56, "word": " F", "probability": 0.85888671875}, {"start": 1128.56, "end": 1129.14, "word": " as", "probability": 0.89111328125}, {"start": 1129.14, "end": 1129.56, "word": " X", "probability": 0.9892578125}, {"start": 1129.56, "end": 1129.92, "word": " tends", "probability": 0.82177734375}, {"start": 1129.92, "end": 1130.08, "word": " to", "probability": 0.97314453125}, {"start": 1130.08, "end": 1130.38, "word": " C", "probability": 0.9736328125}, {"start": 1130.38, "end": 1131.18, "word": " بساوي", "probability": 0.9593505859375}, {"start": 1131.18, "end": 1131.64, "word": " L", "probability": 0.99365234375}, {"start": 1131.64, "end": 1132.38, "word": " أو", "probability": 0.7548828125}, {"start": 1132.38, "end": 1133.62, "word": " ممكن", "probability": 0.9921875}, {"start": 1133.62, "end": 1134.26, "word": " نكتب", "probability": 0.998291015625}], "temperature": 1.0}, {"id": 43, "seek": 115735, "start": 1141.22, "end": 1157.36, "text": "أو ممكن نكتب f of x tends to L as x tends to c كل هدول معناهم أن العدد L limit لل function f and x سوى c", "tokens": [10721, 2407, 3714, 43020, 8717, 4117, 2655, 3555, 283, 295, 2031, 12258, 281, 441, 382, 2031, 12258, 281, 269, 28242, 8032, 3215, 12610, 20449, 8315, 16095, 14739, 18863, 3215, 3215, 441, 4948, 24976, 2445, 283, 293, 2031, 8608, 2407, 7578, 269], "avg_logprob": -0.25093006023338865, "compression_ratio": 1.1596638655462186, "no_speech_prob": 0.0, "words": [{"start": 1141.22, "end": 1141.62, "word": "أو", "probability": 0.7427978515625}, {"start": 1141.62, "end": 1142.02, "word": " ممكن", "probability": 0.810791015625}, {"start": 1142.02, "end": 1142.7, "word": " نكتب", "probability": 0.9903564453125}, {"start": 1142.7, "end": 1143.48, "word": " f", "probability": 0.2445068359375}, {"start": 1143.48, "end": 1143.76, "word": " of", "probability": 0.215576171875}, {"start": 1143.76, "end": 1144.22, "word": " x", "probability": 0.91162109375}, {"start": 1144.22, "end": 1145.86, "word": " tends", "probability": 0.65673828125}, {"start": 1145.86, "end": 1146.5, "word": " to", "probability": 0.98291015625}, {"start": 1146.5, "end": 1146.88, "word": " L", "probability": 0.73583984375}, {"start": 1146.88, "end": 1148.32, "word": " as", "probability": 0.92236328125}, {"start": 1148.32, "end": 1148.7, "word": " x", "probability": 0.890625}, {"start": 1148.7, "end": 1149.1, "word": " tends", "probability": 0.85205078125}, {"start": 1149.1, "end": 1149.3, "word": " to", "probability": 0.98486328125}, {"start": 1149.3, "end": 1149.7, "word": " c", "probability": 0.61572265625}, {"start": 1149.7, "end": 1151.26, "word": " كل", "probability": 0.7666015625}, {"start": 1151.26, "end": 1151.54, "word": " هدول", "probability": 0.8077799479166666}, {"start": 1151.54, "end": 1152.12, "word": " معناهم", "probability": 0.9612630208333334}, {"start": 1152.12, "end": 1152.38, "word": " أن", "probability": 0.45166015625}, {"start": 1152.38, "end": 1152.88, "word": " العدد", "probability": 0.9256184895833334}, {"start": 1152.88, "end": 1153.22, "word": " L", "probability": 0.7333984375}, {"start": 1153.22, "end": 1154.6, "word": " limit", "probability": 0.7119140625}, {"start": 1154.6, "end": 1154.84, "word": " لل", "probability": 0.765625}, {"start": 1154.84, "end": 1155.22, "word": " function", "probability": 0.43310546875}, {"start": 1155.22, "end": 1155.62, "word": " f", "probability": 0.81396484375}, {"start": 1155.62, "end": 1156.0, "word": " and", "probability": 0.85595703125}, {"start": 1156.0, "end": 1156.36, "word": " x", "probability": 0.93603515625}, {"start": 1156.36, "end": 1157.0, "word": " سوى", "probability": 0.5263671875}, {"start": 1157.0, "end": 1157.36, "word": " c", "probability": 0.7744140625}], "temperature": 1.0}, {"id": 44, "seek": 118558, "start": 1162.85, "end": 1185.59, "text": "ف limit f of x as x tends to c does not exist، يعني مافيش عدد L زي هذا، we say ان ال function f diverges، diverges at x less than c", "tokens": [5172, 4948, 283, 295, 2031, 382, 2031, 12258, 281, 269, 775, 406, 2514, 12399, 37495, 22653, 19446, 41185, 8592, 6225, 3215, 3215, 441, 30767, 1829, 23758, 12399, 321, 584, 16472, 2423, 2445, 283, 18558, 2880, 12399, 18558, 2880, 412, 2031, 1570, 813, 269], "avg_logprob": -0.31196733631870965, "compression_ratio": 1.1729323308270676, "no_speech_prob": 0.0, "words": [{"start": 1162.85, "end": 1163.33, "word": "ف", "probability": 0.35595703125}, {"start": 1163.33, "end": 1163.89, "word": " limit", "probability": 0.424072265625}, {"start": 1163.89, "end": 1165.59, "word": " f", "probability": 0.5439453125}, {"start": 1165.59, "end": 1165.87, "word": " of", "probability": 0.40869140625}, {"start": 1165.87, "end": 1166.27, "word": " x", "probability": 0.94580078125}, {"start": 1166.27, "end": 1166.81, "word": " as", "probability": 0.87744140625}, {"start": 1166.81, "end": 1167.27, "word": " x", "probability": 0.97314453125}, {"start": 1167.27, "end": 1167.61, "word": " tends", "probability": 0.79931640625}, {"start": 1167.61, "end": 1167.75, "word": " to", "probability": 0.98681640625}, {"start": 1167.75, "end": 1168.11, "word": " c", "probability": 0.80029296875}, {"start": 1168.11, "end": 1169.19, "word": " does", "probability": 0.49951171875}, {"start": 1169.19, "end": 1169.47, "word": " not", "probability": 0.9638671875}, {"start": 1169.47, "end": 1170.09, "word": " exist،", "probability": 0.56781005859375}, {"start": 1170.09, "end": 1170.31, "word": " يعني", "probability": 0.90234375}, {"start": 1170.31, "end": 1170.73, "word": " مافيش", "probability": 0.9339192708333334}, {"start": 1170.73, "end": 1171.11, "word": " عدد", "probability": 0.9793294270833334}, {"start": 1171.11, "end": 1171.45, "word": " L", "probability": 0.517578125}, {"start": 1171.45, "end": 1172.93, "word": " زي", "probability": 0.94580078125}, {"start": 1172.93, "end": 1174.07, "word": " هذا،", "probability": 0.717529296875}, {"start": 1174.07, "end": 1175.55, "word": " we", "probability": 0.67236328125}, {"start": 1175.55, "end": 1176.09, "word": " say", "probability": 0.9619140625}, {"start": 1176.09, "end": 1176.35, "word": " ان", "probability": 0.433349609375}, {"start": 1176.35, "end": 1176.55, "word": " ال", "probability": 0.94677734375}, {"start": 1176.55, "end": 1176.95, "word": " function", "probability": 0.81884765625}, {"start": 1176.95, "end": 1177.43, "word": " f", "probability": 0.78369140625}, {"start": 1177.43, "end": 1180.11, "word": " diverges،", "probability": 0.6888020833333334}, {"start": 1180.11, "end": 1182.99, "word": " diverges", "probability": 0.754150390625}, {"start": 1182.99, "end": 1183.51, "word": " at", "probability": 0.97900390625}, {"start": 1183.51, "end": 1184.13, "word": " x", "probability": 0.9794921875}, {"start": 1184.13, "end": 1184.57, "word": " less", "probability": 0.1143798828125}, {"start": 1184.57, "end": 1185.13, "word": " than", "probability": 0.955078125}, {"start": 1185.13, "end": 1185.59, "word": " c", "probability": 0.8427734375}], "temperature": 1.0}, {"id": 45, "seek": 121932, "start": 1190.12, "end": 1219.32, "text": "الان نستطيع ان نثبت ان ال limit لل function هذه النقطة لو كانت موجودة لو كان ال function لها limit فlimit هذه لازم تكون unique ال function if from A to R can have only", "tokens": [6027, 7649, 8717, 14851, 9566, 40228, 16472, 8717, 12984, 3555, 2655, 16472, 2423, 4948, 24976, 2445, 29538, 28239, 47432, 3660, 45164, 25961, 2655, 3714, 29245, 23328, 3660, 45164, 25961, 2423, 2445, 5296, 11296, 4948, 6156, 4197, 270, 29538, 5296, 31377, 2304, 6055, 30544, 3845, 2423, 2445, 498, 490, 316, 281, 497, 393, 362, 787], "avg_logprob": -0.3420454664663835, "compression_ratio": 1.4904458598726114, "no_speech_prob": 0.0, "words": [{"start": 1190.12, "end": 1190.74, "word": "الان", "probability": 0.7587890625}, {"start": 1190.74, "end": 1191.6, "word": " نستطيع", "probability": 0.808349609375}, {"start": 1191.6, "end": 1192.14, "word": " ان", "probability": 0.297119140625}, {"start": 1192.14, "end": 1192.66, "word": " نثبت", "probability": 0.9427490234375}, {"start": 1192.66, "end": 1192.9, "word": " ان", "probability": 0.8447265625}, {"start": 1192.9, "end": 1193.1, "word": " ال", "probability": 0.424560546875}, {"start": 1193.1, 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1330.22, "end": 1330.62, "word": " أننا", "probability": 0.6103515625}, {"start": 1330.62, "end": 1331.28, "word": " فرضين", "probability": 0.9754231770833334}, {"start": 1331.28, "end": 1333.3, "word": " أن", "probability": 0.5791015625}, {"start": 1333.3, "end": 1333.68, "word": " ال", "probability": 0.6162109375}, {"start": 1333.68, "end": 1334.12, "word": " limit", "probability": 0.7900390625}], "temperature": 1.0}, {"id": 50, "seek": 135702, "start": 1336.68, "end": 1357.02, "text": "لأف as x tends to c بالساوي الواحد then by definition by epsilon delta definition of limit there exists delta one depends on epsilon positive number", "tokens": [1211, 10721, 5172, 382, 2031, 12258, 281, 269, 20666, 3794, 995, 45865, 2423, 14407, 24401, 550, 538, 7123, 538, 17889, 8289, 7123, 295, 4948, 456, 8198, 8289, 472, 5946, 322, 17889, 3353, 1230], "avg_logprob": -0.3508731670239392, "compression_ratio": 1.28125, "no_speech_prob": 0.0, "words": [{"start": 1336.68, "end": 1337.6, "word": "لأف", 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"probability": 0.8154296875}, {"start": 1365.19, "end": 1365.67, "word": " أصغر", "probability": 0.980712890625}, {"start": 1365.67, "end": 1365.85, "word": " من", "probability": 0.9931640625}, {"start": 1365.85, "end": 1366.15, "word": " delta", "probability": 0.640625}, {"start": 1366.15, "end": 1366.63, "word": " one", "probability": 0.60302734375}, {"start": 1366.63, "end": 1368.65, "word": " أكبر", "probability": 0.95849609375}, {"start": 1368.65, "end": 1368.89, "word": " من", "probability": 0.99658203125}, {"start": 1368.89, "end": 1369.37, "word": " سفر", "probability": 0.7478841145833334}, {"start": 1369.37, "end": 1369.93, "word": " فهذا", "probability": 0.95947265625}, {"start": 1369.93, "end": 1370.57, "word": " بيقدي", "probability": 0.63531494140625}, {"start": 1370.57, "end": 1371.11, "word": " أن", "probability": 0.79931640625}, {"start": 1371.11, "end": 1371.83, "word": " absolute", "probability": 0.7734375}, {"start": 1371.83, "end": 1374.23, "word": " f", 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{"start": 1400.17, "end": 1400.47, "word": " tends", "probability": 0.470458984375}, {"start": 1400.47, "end": 1400.61, "word": " to", "probability": 0.96875}, {"start": 1400.61, "end": 1400.85, "word": " c", "probability": 0.814453125}, {"start": 1400.85, "end": 1401.43, "word": " بساوي", "probability": 0.71270751953125}, {"start": 1401.43, "end": 1401.89, "word": " عدد", "probability": 0.9287109375}, {"start": 1401.89, "end": 1402.25, "word": " تاني", "probability": 0.9651692708333334}, {"start": 1402.25, "end": 1402.45, "word": " ال", "probability": 0.44677734375}, {"start": 1402.45, "end": 1402.99, "word": " اتنين", "probability": 0.81463623046875}, {"start": 1402.99, "end": 1407.99, "word": " then", "probability": 0.374267578125}, {"start": 1407.99, "end": 1408.65, "word": " for", "probability": 0.96142578125}, {"start": 1408.65, "end": 1409.37, "word": " the", "probability": 0.90380859375}, {"start": 1409.37, "end": 1409.89, "word": " same", "probability": 0.92138671875}, 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تعتمد على Epsilon على 2 وبالتالي على Epsilon عدد موجد بحيث أنه لو كان X ينتمي إلى A و Absolute X minus C أصغر من Delta 2 أكبر من 0", "tokens": [1211, 1863, 36178, 2423, 39184, 462, 16592, 4724, 15042, 14739, 4948, 5296, 479, 295, 1783, 293, 1783, 4724, 3794, 995, 2407, 10632, 383, 4724, 3794, 995, 2407, 10632, 441, 17, 8717, 7435, 3215, 18183, 568, 6055, 34268, 2304, 3215, 15844, 462, 16592, 15844, 568, 46599, 6027, 2655, 6027, 1829, 15844, 462, 16592, 6225, 3215, 3215, 3714, 29245, 3215, 4724, 5016, 1829, 12984, 14739, 3224, 45164, 25961, 1783, 7251, 29399, 2304, 1829, 30731, 316, 4032, 43965, 1169, 1783, 3175, 383, 5551, 9381, 17082, 2288, 9154, 18183, 568, 5551, 4117, 26890, 9154, 1958], "avg_logprob": -0.3077445726679719, "compression_ratio": 1.4653465346534653, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1418.54, "end": 1419.1, "word": "لنفس", "probability": 0.7055257161458334}, {"start": 1419.1, "end": 1419.34, "word": " الـ", "probability": 0.8193359375}, 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"end": 1432.48, "word": " Epsilon", "probability": 0.966796875}, {"start": 1432.48, "end": 1432.88, "word": " عدد", "probability": 0.9407552083333334}, {"start": 1432.88, "end": 1433.42, "word": " موجد", "probability": 0.8634440104166666}, {"start": 1433.42, "end": 1433.94, "word": " بحيث", "probability": 0.9246826171875}, {"start": 1433.94, "end": 1434.42, "word": " أنه", "probability": 0.7119140625}, {"start": 1434.42, "end": 1435.1, "word": " لو", "probability": 0.587890625}, {"start": 1435.1, "end": 1435.46, "word": " كان", "probability": 0.974609375}, {"start": 1435.46, "end": 1435.76, "word": " X", "probability": 0.95556640625}, {"start": 1435.76, "end": 1436.38, "word": " ينتمي", "probability": 0.978759765625}, {"start": 1436.38, "end": 1436.64, "word": " إلى", "probability": 0.93017578125}, {"start": 1436.64, "end": 1437.06, "word": " A", "probability": 0.8203125}, {"start": 1437.06, "end": 1438.02, "word": " و", "probability": 0.537109375}, {"start": 1438.02, "end": 1438.74, "word": " Absolute", "probability": 0.57855224609375}, {"start": 1438.74, "end": 1439.02, "word": " X", "probability": 0.94921875}, {"start": 1439.02, "end": 1439.42, "word": " minus", "probability": 0.826171875}, {"start": 1439.42, "end": 1439.76, "word": " C", "probability": 0.90673828125}, {"start": 1439.76, "end": 1440.3, "word": " أصغر", "probability": 0.981689453125}, {"start": 1440.3, "end": 1440.52, "word": " من", "probability": 0.98779296875}, {"start": 1440.52, "end": 1440.9, "word": " Delta", "probability": 0.9072265625}, {"start": 1440.9, "end": 1441.44, "word": " 2", "probability": 0.90771484375}, {"start": 1441.44, "end": 1442.12, "word": " أكبر", "probability": 0.9231770833333334}, {"start": 1442.12, "end": 1442.36, "word": " من", "probability": 0.9931640625}, {"start": 1442.36, "end": 1442.74, "word": " 0", "probability": 0.6064453125}], "temperature": 1.0}, {"id": 54, "seek": 147123, "start": 1443.79, "end": 1471.23, "text": "فهذا أكيد بيقدّي أنه absolute f of x minus L2 أصغر من epsilon على 2 ال sum ال implication هي D2 الآن بناخد .. بنعرف delta ل L Delta بتساوي ال minimum ل delta واحد و delta اتنين", "tokens": [5172, 3224, 15730, 5551, 4117, 25708, 4724, 1829, 28543, 11703, 1829, 14739, 3224, 8236, 283, 295, 2031, 3175, 441, 17, 5551, 9381, 17082, 2288, 9154, 17889, 15844, 568, 2423, 2408, 2423, 37814, 39896, 413, 17, 6024, 48506, 44945, 47283, 3215, 4386, 44945, 3615, 28480, 8289, 5296, 441, 18183, 39894, 3794, 995, 45865, 2423, 7285, 5296, 8289, 36764, 24401, 4032, 8289, 1975, 2655, 1863, 9957], "avg_logprob": -0.41057692307692306, "compression_ratio": 1.308108108108108, "no_speech_prob": 0.0, "words": [{"start": 1443.79, "end": 1444.85, "word": "فهذا", "probability": 0.7021891276041666}, {"start": 1444.85, "end": 1445.31, "word": " أكيد", "probability": 0.785888671875}, {"start": 1445.31, "end": 1446.03, "word": " بيقدّي", "probability": 0.6501953125}, {"start": 1446.03, "end": 1446.65, "word": " أنه", "probability": 0.32122802734375}, {"start": 1446.65, "end": 1447.35, "word": " absolute", "probability": 0.66455078125}, {"start": 1447.35, "end": 1448.53, "word": " f", "probability": 0.52587890625}, {"start": 1448.53, "end": 1448.77, "word": " of", "probability": 0.299072265625}, {"start": 1448.77, "end": 1449.05, "word": " x", "probability": 0.88134765625}, {"start": 1449.05, "end": 1449.75, "word": " minus", "probability": 0.6611328125}, {"start": 1449.75, "end": 1450.55, "word": " L2", "probability": 0.6634521484375}, {"start": 1450.55, "end": 1451.35, "word": " أصغر", "probability": 0.9615478515625}, {"start": 1451.35, "end": 1451.55, "word": " من", "probability": 0.99072265625}, {"start": 1451.55, "end": 1452.09, "word": " epsilon", "probability": 0.375244140625}, {"start": 1452.09, "end": 1452.41, "word": " على", "probability": 0.59130859375}, {"start": 1452.41, "end": 1452.67, "word": " 2", "probability": 0.7587890625}, {"start": 1452.67, "end": 1454.03, "word": " ال", "probability": 0.385009765625}, {"start": 1454.03, 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"word": " فإن", "probability": 0.472900390625}, {"start": 1670.84, "end": 1672.06, "word": " إبسلون", "probability": 0.859375}, {"start": 1672.06, "end": 1672.42, "word": " أكبر", "probability": 0.978515625}, {"start": 1672.42, "end": 1672.6, "word": " من", "probability": 0.99365234375}, {"start": 1672.6, "end": 1673.06, "word": " السفر", "probability": 0.8621419270833334}, {"start": 1673.06, "end": 1673.5, "word": " فهذا", "probability": 0.9295247395833334}, {"start": 1673.5, "end": 1673.94, "word": " بيقدي", "probability": 0.52813720703125}, {"start": 1673.94, "end": 1674.08, "word": " أن", "probability": 0.62939453125}, {"start": 1674.08, "end": 1674.36, "word": " a", "probability": 0.50732421875}, {"start": 1674.36, "end": 1674.86, "word": " بيساوي", "probability": 0.7553955078125}, {"start": 1674.86, "end": 1675.34, "word": " سفر", "probability": 0.9156901041666666}], "temperature": 1.0}, {"id": 63, "seek": 170194, "start": 1676.36, "end": 1701.94, "text": "أخد ايه هنا الـ absolute value ل L1 minus L2 فحسب النمة هذه هيطلع عندى هذا بقدر اللي قدر انه absolute L1 minus L2 بالساوية سفر وبالتالي بطلع عندى L1 بساوية L2 وهو المطلوب", "tokens": [10721, 9778, 3215, 1975, 1829, 3224, 34105, 2423, 39184, 8236, 2158, 5296, 441, 16, 3175, 441, 17, 6156, 5016, 35457, 28239, 2304, 3660, 29538, 8032, 1829, 9566, 1211, 3615, 43242, 7578, 23758, 4724, 28543, 2288, 13672, 1829, 12174, 3215, 2288, 16472, 3224, 8236, 441, 16, 3175, 441, 17, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 4724, 9566, 1211, 3615, 43242, 7578, 441, 16, 4724, 3794, 995, 2407, 10632, 441, 17, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.37255270150770625, "compression_ratio": 1.5808383233532934, "no_speech_prob": 0.0, "words": [{"start": 1676.36, "end": 1676.94, "word": "أخد", "probability": 0.443115234375}, {"start": 1676.94, "end": 1677.2, "word": " ايه", "probability": 0.56787109375}, {"start": 1677.2, "end": 1677.5, "word": " هنا", "probability": 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{"start": 1687.36, "end": 1688.36, "word": " هذا", "probability": 0.471923828125}, {"start": 1688.36, "end": 1688.86, "word": " بقدر", "probability": 0.728515625}, {"start": 1688.86, "end": 1689.14, "word": " اللي", "probability": 0.607177734375}, {"start": 1689.14, "end": 1689.72, "word": " قدر", "probability": 0.4324544270833333}, {"start": 1689.72, "end": 1690.1, "word": " انه", "probability": 0.34747314453125}, {"start": 1690.1, "end": 1690.6, "word": " absolute", "probability": 0.853515625}, {"start": 1690.6, "end": 1691.62, "word": " L1", "probability": 0.94677734375}, {"start": 1691.62, "end": 1692.24, "word": " minus", "probability": 0.9755859375}, {"start": 1692.24, "end": 1693.56, "word": " L2", "probability": 0.99609375}, {"start": 1693.56, "end": 1694.16, "word": " بالساوية", "probability": 0.759326171875}, {"start": 1694.16, "end": 1694.62, "word": " سفر", "probability": 0.8128255208333334}, {"start": 1694.62, "end": 1695.6, "word": " وبالتالي", "probability": 0.89091796875}, {"start": 1695.6, "end": 1696.72, "word": " بطلع", "probability": 0.820068359375}, {"start": 1696.72, "end": 1697.12, "word": " عندى", "probability": 0.885009765625}, {"start": 1697.12, "end": 1697.74, "word": " L1", "probability": 0.979248046875}, {"start": 1697.74, "end": 1699.32, "word": " بساوية", "probability": 0.91044921875}, {"start": 1699.32, "end": 1700.52, "word": " L2", "probability": 0.977783203125}, {"start": 1700.52, "end": 1701.22, "word": " وهو", "probability": 0.78466796875}, {"start": 1701.22, "end": 1701.94, "word": " المطلوب", "probability": 0.9871826171875}], "temperature": 1.0}, {"id": 64, "seek": 172320, "start": 1703.24, "end": 1723.2, "text": "إذا أنا فرقت إن الـ function إلها two limits عن نقطة فطلع الـ two limits متساوياتين وبالتالي لو كانت الـ function إلها limit عن نقطة فال limit تطلع وحيدة unique، بقى ده؟ في أي سؤال أو أي سؤال على البرهانة؟", "tokens": [28814, 15730, 41850, 6156, 2288, 38149, 36145, 2423, 39184, 2445, 11933, 1211, 11296, 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0.8802490234375}, {"start": 1715.8, "end": 1717.24, "word": " unique،", "probability": 0.3751220703125}, {"start": 1717.24, "end": 1717.74, "word": " بقى", "probability": 0.6735026041666666}, {"start": 1717.74, "end": 1718.48, "word": " ده؟", "probability": 0.93359375}, {"start": 1718.48, "end": 1720.68, "word": " في", "probability": 0.61328125}, {"start": 1720.68, "end": 1720.9, "word": " أي", "probability": 0.8203125}, {"start": 1720.9, "end": 1721.44, "word": " سؤال", "probability": 0.6903483072916666}, {"start": 1721.44, "end": 1721.72, "word": " أو", "probability": 0.82470703125}, {"start": 1721.72, "end": 1721.94, "word": " أي", "probability": 0.372314453125}, {"start": 1721.94, "end": 1722.28, "word": " سؤال", "probability": 0.8927408854166666}, {"start": 1722.28, "end": 1722.42, "word": " على", "probability": 0.75537109375}, {"start": 1722.42, "end": 1723.2, "word": " البرهانة؟", "probability": 0.8846842447916666}], "temperature": 1.0}, {"id": 65, "seek": 176927, "start": 1742.29, "end": 1769.27, "text": "ناخد ملاحظة هنا الـ epsilon delta definition of limit of a function f from a to r", "tokens": [1863, 47283, 3215, 3714, 15040, 5016, 19913, 3660, 34105, 2423, 39184, 17889, 8289, 7123, 295, 4948, 295, 257, 2445, 283, 490, 257, 281, 367], "avg_logprob": -0.29593749046325685, "compression_ratio": 1.065934065934066, "no_speech_prob": 0.0, "words": [{"start": 1742.29, "end": 1742.83, "word": "ناخد", "probability": 0.77294921875}, {"start": 1742.83, "end": 1743.45, "word": " ملاحظة", "probability": 0.97578125}, {"start": 1743.45, "end": 1744.73, "word": " هنا", "probability": 0.86474609375}, {"start": 1744.73, "end": 1755.59, "word": " الـ", "probability": 0.558349609375}, {"start": 1755.59, "end": 1755.83, "word": " epsilon", "probability": 0.5283203125}, {"start": 1755.83, "end": 1756.39, "word": " delta", "probability": 0.2235107421875}, {"start": 1756.39, "end": 1758.43, "word": " definition", "probability": 0.8125}, {"start": 1758.43, "end": 1761.13, 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سفر", "tokens": [3322, 16970, 9673, 2655, 3555, 995, 9957, 3660, 13672, 1829, 39896, 8236, 2031, 3175, 269, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 11778, 12610, 2655, 7649, 1355, 11331, 26108, 2655, 9957, 25724, 11622, 38207, 23758, 20449, 8315, 3224, 14739, 8236, 2031, 3175, 269, 20193, 7251, 3794, 995, 2407, 7578, 8608, 5172, 2288], "avg_logprob": -0.31519396397574195, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 1772.6699999999998, "end": 1774.07, "word": "the", "probability": 0.1690673828125}, {"start": 1774.07, "end": 1775.47, "word": " inequality", "probability": 0.9287109375}, {"start": 1775.47, "end": 1780.25, "word": " المتباينة", "probability": 0.7985432942708334}, {"start": 1780.25, "end": 1781.39, "word": " اللي", "probability": 0.472381591796875}, {"start": 1781.39, "end": 1781.95, "word": " هي", "probability": 0.95068359375}, {"start": 1781.95, "end": 1782.97, "word": " absolute", "probability": 0.81591796875}, 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absolute X minus C أصغر من Delta هذه بتكافئ أن X minus C أصغر من Delta أكبر من ثالث Delta صح؟", "tokens": [37746, 6027, 2655, 6027, 1829, 1783, 20193, 7251, 3794, 995, 45865, 383, 11933, 15730, 14111, 23758, 37495, 22653, 14739, 1783, 20193, 6055, 3794, 995, 45865, 383, 9673, 2655, 3555, 995, 9957, 3660, 16712, 7649, 10632, 13672, 1829, 39896, 8236, 1783, 3175, 383, 5551, 9381, 17082, 2288, 9154, 18183, 29538, 39894, 4117, 31845, 19986, 14739, 1783, 3175, 383, 5551, 9381, 17082, 2288, 9154, 18183, 5551, 4117, 26890, 9154, 38637, 6027, 12984, 18183, 20328, 5016, 22807], "avg_logprob": -0.2362500043710073, "compression_ratio": 1.6097560975609757, "no_speech_prob": 0.0, "words": [{"start": 1803.09, "end": 1804.11, "word": "وبالتالي", "probability": 0.89130859375}, {"start": 1804.11, "end": 1805.03, "word": " X", "probability": 0.423583984375}, {"start": 1805.03, "end": 1805.29, "word": " لا", "probability": 0.90576171875}, {"start": 1805.29, "end": 1806.03, "word": " يساوي", 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"probability": 0.92041015625}, {"start": 1883.69, "end": 1885.17, "word": " كذلك", "probability": 0.9661458333333334}, {"start": 1885.17, "end": 1886.29, "word": " المتباينة", "probability": 0.986572265625}, {"start": 1886.29, "end": 1889.57, "word": " also", "probability": 0.69873046875}], "temperature": 1.0}, {"id": 70, "seek": 191283, "start": 1893.07, "end": 1912.83, "text": "الإي نكواليتي المتباينة اللي هي absolute f of x minus L أصغر من إبسلون means لو جينا الحل المتباينة هذه في f of x", "tokens": [6027, 28814, 1829, 8717, 4117, 2407, 6027, 1829, 31371, 9673, 2655, 3555, 995, 9957, 3660, 13672, 1829, 39896, 8236, 283, 295, 2031, 3175, 441, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 1355, 45164, 10874, 1829, 8315, 21542, 1211, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8978, 283, 295, 2031], "avg_logprob": -0.35259433962264153, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1893.07, "end": 1893.59, "word": "الإي", 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"word": " من", "probability": 0.986328125}, {"start": 1902.63, "end": 1903.45, "word": " إبسلون", "probability": 0.82783203125}, {"start": 1903.45, "end": 1906.49, "word": " means", "probability": 0.072509765625}, {"start": 1906.49, "end": 1907.73, "word": " لو", "probability": 0.78125}, {"start": 1907.73, "end": 1908.09, "word": " جينا", "probability": 0.9915364583333334}, {"start": 1908.09, "end": 1908.51, "word": " الحل", "probability": 0.749267578125}, {"start": 1908.51, "end": 1909.43, "word": " المتباينة", "probability": 0.9156901041666666}, {"start": 1909.43, "end": 1909.87, "word": " هذه", "probability": 0.564453125}, {"start": 1909.87, "end": 1911.93, "word": " في", "probability": 0.91796875}, {"start": 1911.93, "end": 1912.23, "word": " f", "probability": 0.71875}, {"start": 1912.23, "end": 1912.43, "word": " of", "probability": 0.9521484375}, {"start": 1912.43, "end": 1912.83, "word": " x", "probability": 0.94140625}], "temperature": 1.0}, {"id": 71, "seek": 195138, "start": 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بالساوي بيه سالب ال limit اللي هي بيه فهذا بيطلع أبسليوت السفر بيطلع سفر والسفر هذا أصغر من أي إبسلون موجة", "tokens": [3224, 1211, 23758, 4724, 1829, 28543, 2288, 5296, 10721, 3555, 3794, 1211, 1829, 35473, 283, 295, 2031, 3175, 272, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 20666, 2655, 10721, 4117, 25708, 41850, 18871, 16254, 283, 295, 2031, 20666, 3794, 995, 45865, 4724, 1829, 3224, 8608, 6027, 3555, 2423, 4948, 13672, 1829, 39896, 4724, 1829, 3224, 6156, 3224, 15730, 4724, 1829, 9566, 1211, 3615, 5551, 3555, 3794, 20292, 35473, 21136, 5172, 2288, 4724, 1829, 9566, 1211, 3615, 8608, 5172, 2288, 16070, 3794, 5172, 2288, 23758, 5551, 9381, 17082, 2288, 9154, 36632, 11933, 3555, 3794, 1211, 11536, 3714, 29245, 3660], "avg_logprob": -0.22794118231418087, "compression_ratio": 1.7965116279069768, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2617.41, "end": 2617.89, "word": "هل", "probability": 0.901123046875}, {"start": 2617.89, "end": 2618.13, 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2820.83, "end": 2821.23, "word": " epsilon", "probability": 0.257080078125}, {"start": 2821.23, "end": 2823.79, "word": " وبالتالي", "probability": 0.873876953125}, {"start": 2823.79, "end": 2823.97, "word": " by", "probability": 0.80029296875}, {"start": 2823.97, "end": 2824.57, "word": " definition", "probability": 0.95458984375}, {"start": 2824.57, "end": 2824.99, "word": " بطلع", "probability": 0.6610107421875}, {"start": 2824.99, "end": 2825.23, "word": " عندي", "probability": 0.630615234375}, {"start": 2825.23, "end": 2825.67, "word": " limit", "probability": 0.9384765625}, {"start": 2825.67, "end": 2826.69, "word": " ال", "probability": 0.859375}, {"start": 2826.69, "end": 2827.07, "word": " function", "probability": 0.70556640625}, {"start": 2827.07, "end": 2827.39, "word": " f", "probability": 0.8037109375}, {"start": 2827.39, "end": 2827.61, "word": " of", "probability": 0.392333984375}, {"start": 2827.61, "end": 2827.83, "word": " x", "probability": 0.90869140625}, {"start": 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