diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/u5C7kmY6Ltw_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/u5C7kmY6Ltw_raw.json"
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+{"segments": [{"id": 1, "seek": 2532, "start": 20.1, "end": 25.32, "text": "بسم الله الرحمن الرحيم ناخد اليوم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 47283, 3215, 45595, 20498], "avg_logprob": -0.1103515605131785, "compression_ratio": 1.1296296296296295, "no_speech_prob": 0.0, "words": [{"start": 20.1, "end": 21.38, "word": "بسم", "probability": 0.88037109375}, {"start": 21.38, "end": 21.54, "word": " الله", "probability": 0.97412109375}, {"start": 21.54, "end": 21.98, "word": " الرحمن", "probability": 0.9811197916666666}, {"start": 21.98, "end": 22.72, "word": " الرحيم", "probability": 0.9951171875}, {"start": 22.72, "end": 24.78, "word": " ناخد", "probability": 0.7750651041666666}, {"start": 24.78, "end": 25.32, "word": " اليوم", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 2, "seek": 5274, "start": 26.7, "end": 52.74, "text": "الجزء المتعلق بال composition of continuous functions لو كان في عندي اقترانين متصلين فهنشوف ان ال 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اللي هي G ل F of C", "tokens": [1211, 26890, 3224, 7649, 29910, 23275, 8032, 1863, 14851, 9778, 40448, 2423, 39184, 7630, 7123, 295, 23807, 412, 257, 935, 6156, 718, 343, 312, 364, 17889, 7630, 295, 460, 6329, 479, 5296, 383, 13672, 1829, 39896, 460, 5296, 479, 295, 383], "avg_logprob": -0.4866071442763011, "compression_ratio": 1.1958041958041958, "no_speech_prob": 0.0, "words": [{"start": 327.38, "end": 328.78, "word": "لبرهان", "probability": 0.612060546875}, {"start": 328.78, "end": 329.16, "word": " ذلك", "probability": 0.972412109375}, {"start": 329.16, "end": 329.92, "word": " هنستخدم", "probability": 0.74892578125}, {"start": 329.92, "end": 330.9, "word": " الـ", "probability": 0.343017578125}, {"start": 330.9, "end": 331.2, "word": " neighborhood", "probability": 0.431884765625}, {"start": 331.2, "end": 331.92, "word": " definition", "probability": 0.876953125}, {"start": 331.92, "end": 332.68, "word": " of", "probability": 0.92138671875}, {"start": 332.68, "end": 333.38, 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neighborhood للـC اللي هي تنتمي لـA بحيث أنه صورة ال neighborhood هذا subset من الـW neighborhood هنا تعريف ال neighborhood definition للاتصال عن النقطة طيب since", "tokens": [6027, 20292, 39896, 10874, 1829, 1975, 2407, 4724, 1829, 20328, 5016, 22807, 46599, 1863, 12984, 3555, 2655, 14739, 3224, 7251, 29245, 3215, 18183, 7630, 24976, 39184, 34, 13672, 1829, 39896, 6055, 29399, 2304, 1829, 5296, 39184, 32, 4724, 5016, 1829, 12984, 14739, 3224, 20328, 13063, 3660, 2423, 7630, 23758, 25993, 9154, 2423, 39184, 54, 7630, 34105, 37279, 16572, 5172, 2423, 7630, 7123, 24976, 9307, 9381, 6027, 18871, 28239, 47432, 3660, 23032, 1829, 3555, 1670], "avg_logprob": -0.2945833396911621, "compression_ratio": 1.568421052631579, "no_speech_prob": 0.0, "words": [{"start": 356.13, "end": 356.57, "word": "اللي", "probability": 0.48095703125}, {"start": 356.57, "end": 357.23, "word": " هي", "probability": 0.91552734375}, {"start": 357.23, "end": 360.19, "word": " جي", "probability": 0.469818115234375}, 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378.99, "word": " تعريف", "probability": 0.98974609375}, {"start": 378.99, "end": 379.11, "word": " ال", "probability": 0.94384765625}, {"start": 379.11, "end": 379.37, "word": " neighborhood", "probability": 0.734375}, {"start": 379.37, "end": 379.97, "word": " definition", "probability": 0.54248046875}, {"start": 379.97, "end": 381.53, "word": " للاتصال", "probability": 0.971435546875}, {"start": 381.53, "end": 381.71, "word": " عن", "probability": 0.66064453125}, {"start": 381.71, "end": 382.19, "word": " النقطة", "probability": 0.8318684895833334}, {"start": 382.19, "end": 382.73, "word": " طيب", "probability": 0.958984375}, {"start": 382.73, "end": 385.65, "word": " since", "probability": 0.7333984375}], "temperature": 1.0}, {"id": 15, "seek": 41411, "start": 388.45, "end": 414.11, "text": "الفنشن الـ g is continuous at b اللي هي بالساوي f of c تنتمي ل b وهي في عندي w neighborhood w is epsilon neighborhood ل g of b إذا من تعريف الاتصال عن النقطة يوجد", "tokens": [6027, 5172, 1863, 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"probability": 0.48876953125}, {"start": 396.15, "end": 399.01, "word": " اللي", "probability": 0.42791748046875}, {"start": 399.01, "end": 399.23, "word": " هي", "probability": 0.646484375}, {"start": 399.23, "end": 400.09, "word": " بالساوي", "probability": 0.70477294921875}, {"start": 400.09, "end": 400.53, "word": " f", "probability": 0.61181640625}, {"start": 400.53, "end": 400.87, "word": " of", "probability": 0.845703125}, {"start": 400.87, "end": 401.29, "word": " c", "probability": 0.88232421875}, {"start": 401.29, "end": 402.37, "word": " تنتمي", "probability": 0.7918701171875}, {"start": 402.37, "end": 402.53, "word": " ل", "probability": 0.759765625}, {"start": 402.53, "end": 402.85, "word": " b", "probability": 0.435302734375}, {"start": 402.85, "end": 404.35, "word": " وهي", "probability": 0.57177734375}, {"start": 404.35, "end": 404.47, "word": " في", "probability": 0.9091796875}, {"start": 404.47, "end": 404.91, "word": " عندي", "probability": 0.759033203125}, {"start": 404.91, "end": 405.45, "word": " w", "probability": 0.7939453125}, {"start": 405.45, "end": 406.55, "word": " neighborhood", "probability": 0.623046875}, {"start": 406.55, "end": 407.09, "word": " w", "probability": 0.324951171875}, {"start": 407.09, "end": 407.43, "word": " is", "probability": 0.87744140625}, {"start": 407.43, "end": 407.83, "word": " epsilon", "probability": 0.53662109375}, {"start": 407.83, "end": 408.53, "word": " neighborhood", "probability": 0.8515625}, {"start": 408.53, "end": 409.75, "word": " ل", "probability": 0.87158203125}, {"start": 409.75, "end": 410.05, "word": " g", "probability": 0.87109375}, {"start": 410.05, "end": 410.33, "word": " of", "probability": 0.9560546875}, {"start": 410.33, "end": 410.69, "word": " b", "probability": 0.95361328125}, {"start": 410.69, "end": 411.65, "word": " إذا", "probability": 0.5086669921875}, {"start": 411.65, "end": 411.85, "word": " من", "probability": 0.7880859375}, {"start": 411.85, "end": 412.25, "word": " تعريف", "probability": 0.8536783854166666}, {"start": 412.25, "end": 412.81, "word": " الاتصال", "probability": 0.924072265625}, {"start": 412.81, "end": 412.97, "word": " عن", "probability": 0.90771484375}, {"start": 412.97, "end": 413.45, "word": " النقطة", "probability": 0.92822265625}, {"start": 413.45, "end": 414.11, "word": " يوجد", "probability": 0.9524739583333334}], "temperature": 1.0}, {"id": 16, "seek": 44210, "start": 415.46, "end": 442.1, "text": "delta neighborhood نسميه V of ال B بحيث انه لكل Y ينتمي إلى B تقاطع ال V لازم يطلع عندى صورة ال Y", "tokens": [18105, 1328, 7630, 8717, 38251, 1829, 3224, 691, 295, 2423, 363, 4724, 5016, 1829, 12984, 16472, 3224, 5296, 28820, 398, 7251, 29399, 2304, 1829, 30731, 363, 6055, 4587, 41193, 3615, 2423, 691, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 43242, 7578, 20328, 13063, 3660, 2423, 398], "avg_logprob": -0.2253989298292931, "compression_ratio": 1.1951219512195121, "no_speech_prob": 0.0, "words": [{"start": 415.46, "end": 416.54, "word": 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{"start": 434.24, "end": 435.28, "word": " B", "probability": 0.859375}, {"start": 435.28, "end": 437.62, "word": " تقاطع", "probability": 0.9339599609375}, {"start": 437.62, "end": 437.96, "word": " ال", "probability": 0.8740234375}, {"start": 437.96, "end": 438.42, "word": " V", "probability": 0.978515625}, {"start": 438.42, "end": 440.06, "word": " لازم", "probability": 0.9698893229166666}, {"start": 440.06, "end": 440.38, "word": " يطلع", "probability": 0.9891357421875}, {"start": 440.38, "end": 440.86, "word": " عندى", "probability": 0.6448974609375}, {"start": 440.86, "end": 441.52, "word": " صورة", "probability": 0.9871419270833334}, {"start": 441.52, "end": 441.72, "word": " ال", "probability": 0.8271484375}, {"start": 441.72, "end": 442.1, "word": " Y", "probability": 0.9765625}], "temperature": 1.0}, {"id": 17, "seek": 47044, "start": 443.42, "end": 470.44, "text": "G of Y تنتمي لـ W الـ function G continuous عند B في مجالها وبالتالي حسب الاتصال لأي epsilon neighborhood لصورة B", "tokens": [38, 295, 398, 6055, 29399, 2304, 1829, 5296, 39184, 343, 2423, 39184, 2445, 460, 10957, 43242, 363, 8978, 3714, 7435, 6027, 11296, 46599, 6027, 2655, 6027, 1829, 11331, 35457, 2423, 9307, 9381, 6027, 5296, 10721, 1829, 17889, 7630, 5296, 9381, 13063, 3660, 363], "avg_logprob": -0.2869318093765866, "compression_ratio": 1.1510791366906474, "no_speech_prob": 0.0, "words": [{"start": 443.42, "end": 444.0, "word": "G", "probability": 0.1949462890625}, {"start": 444.0, "end": 444.48, "word": " of", "probability": 0.513671875}, {"start": 444.48, "end": 445.0, "word": " Y", "probability": 0.96240234375}, {"start": 445.0, "end": 446.12, "word": " تنتمي", "probability": 0.9510498046875}, {"start": 446.12, "end": 448.02, "word": " لـ", "probability": 0.601806640625}, {"start": 448.02, "end": 448.46, "word": " W", "probability": 0.175537109375}, {"start": 448.46, "end": 455.68, "word": " الـ", "probability": 0.565185546875}, {"start": 455.68, "end": 459.46, "word": " function", 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"let let مثال تاني let g2 of x function بيساوي square root of x و x أكبر من أو بيساوي سفر طبعا ده اللي تجد التربيه بس معرفة للأعداد الحقيقية غير السالبة claim g2 أثبتنا احنا ملاش claim by previous exercise", "tokens": [2631, 718, 50113, 6027, 6055, 7649, 1829, 718, 290, 17, 295, 2031, 2445, 4724, 1829, 3794, 995, 45865, 3732, 5593, 295, 2031, 4032, 2031, 5551, 4117, 26890, 9154, 34051, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 23032, 3555, 3615, 995, 11778, 3224, 13672, 1829, 6055, 7435, 3215, 16712, 2288, 21292, 3224, 4724, 3794, 20449, 28480, 3660, 24976, 10721, 22488, 18513, 21542, 38436, 4587, 10632, 32771, 13546, 21136, 6027, 49401, 3932, 290, 17, 5551, 12984, 3555, 2655, 8315, 1975, 5016, 8315, 3714, 1211, 33599, 3932, 538, 3894, 5380], "avg_logprob": -0.24245084537548967, "compression_ratio": 1.473170731707317, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1377.4900000000002, "end": 1378.3300000000002, "word": "let", "probability": 0.205322265625}, {"start": 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316, 550, 538, 12686, 12686, 20904, 4724, 9566, 1211, 3615, 460, 281, 6329, 479, 13672, 1829, 39896, 4724, 3794, 2407, 7578, 10874, 8848, 2288, 2423, 479, 307, 10957, 15844, 9673, 7435, 2304, 2407, 27884, 316], "avg_logprob": -0.2964527027027027, "compression_ratio": 1.1612903225806452, "no_speech_prob": 0.0, "words": [{"start": 1463.23, "end": 1463.73, "word": "on", "probability": 0.45263671875}, {"start": 1463.73, "end": 1464.43, "word": " A", "probability": 0.40673828125}, {"start": 1464.43, "end": 1469.11, "word": " then", "probability": 0.5048828125}, {"start": 1469.11, "end": 1469.59, "word": " by", "probability": 0.89453125}, {"start": 1469.59, "end": 1470.53, "word": " composition", "probability": 0.9033203125}, {"start": 1470.53, "end": 1473.81, "word": " composition", "probability": 0.48046875}, {"start": 1473.81, "end": 1474.77, "word": " theorem", "probability": 0.84423828125}, {"start": 1474.77, "end": 1480.13, "word": " بطلع", "probability": 0.8056640625}, {"start": 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"end": 1509.57, "word": " متصلة", "probability": 0.9427083333333334}, {"start": 1509.57, "end": 1509.73, "word": " على", "probability": 0.92529296875}, {"start": 1509.73, "end": 1510.31, "word": " مجالها", "probability": 0.9969482421875}, {"start": 1510.31, "end": 1511.47, "word": " صح؟", "probability": 0.7972005208333334}, {"start": 1511.47, "end": 1512.01, "word": " وهذا", "probability": 0.52099609375}, {"start": 1512.01, "end": 1512.77, "word": " بيعتبر", "probability": 0.9698486328125}, {"start": 1512.77, "end": 1513.35, "word": " برهان", "probability": 0.9951171875}, {"start": 1513.35, "end": 1514.03, "word": " آخر", "probability": 0.923583984375}, {"start": 1514.03, "end": 1515.67, "word": " غير", "probability": 0.973876953125}, {"start": 1515.67, "end": 1515.87, "word": " عن", "probability": 0.94287109375}, {"start": 1515.87, "end": 1516.35, "word": " البرهان", "probability": 0.9217529296875}, {"start": 1516.35, "end": 1516.49, "word": " اللي", "probability": 0.911376953125}, {"start": 1516.49, "end": 1517.01, "word": " أخدناه", "probability": 0.9255859375}, {"start": 1517.01, "end": 1517.17, "word": " في", "probability": 0.9765625}, {"start": 1517.17, "end": 1517.71, "word": " المحاضرة", "probability": 0.99462890625}, {"start": 1517.71, "end": 1518.23, "word": " السابقة", "probability": 0.9737955729166666}, {"start": 1518.23, "end": 1518.59, "word": " okay", "probability": 0.51123046875}, {"start": 1518.59, "end": 1519.21, "word": " تمام؟", "probability": 0.8896484375}], "temperature": 1.0}, {"id": 54, "seek": 155349, "start": 1529.99, "end": 1553.49, "text": "بثال تلاتة we know ان ال function f of x بساوي sin x is continuous اثبتنا ان الدالي هاد continuous on R صح؟", "tokens": [3555, 12984, 6027, 6055, 1211, 9307, 3660, 321, 458, 16472, 2423, 2445, 283, 295, 2031, 4724, 3794, 995, 45865, 3343, 2031, 307, 10957, 1975, 12984, 3555, 2655, 8315, 16472, 32748, 6027, 1829, 8032, 18513, 10957, 322, 497, 20328, 5016, 22807], "avg_logprob": -0.29306403020533117, "compression_ratio": 1.2393162393162394, "no_speech_prob": 0.0, "words": [{"start": 1529.99, "end": 1530.75, "word": "بثال", "probability": 0.8128255208333334}, {"start": 1530.75, "end": 1531.99, "word": " تلاتة", "probability": 0.8572998046875}, {"start": 1531.99, "end": 1535.23, "word": " we", "probability": 0.1904296875}, {"start": 1535.23, "end": 1535.73, "word": " know", "probability": 0.9130859375}, {"start": 1535.73, "end": 1537.37, "word": " ان", "probability": 0.51611328125}, {"start": 1537.37, "end": 1537.55, "word": " ال", "probability": 0.93798828125}, {"start": 1537.55, "end": 1538.13, "word": " function", "probability": 0.68994140625}, {"start": 1538.13, "end": 1541.31, "word": " f", "probability": 0.75341796875}, {"start": 1541.31, "end": 1541.63, "word": " of", "probability": 0.4599609375}, {"start": 1541.63, "end": 1542.13, "word": " x", "probability": 0.9072265625}, {"start": 1542.13, "end": 1544.45, "word": " بساوي", "probability": 0.892578125}, {"start": 1544.45, "end": 1545.65, "word": " sin", "probability": 0.3603515625}, {"start": 1545.65, "end": 1546.33, "word": " x", "probability": 0.84765625}, {"start": 1546.33, "end": 1547.69, "word": " is", "probability": 0.87060546875}, {"start": 1547.69, "end": 1548.55, "word": " continuous", "probability": 0.9130859375}, {"start": 1548.55, "end": 1549.19, "word": " اثبتنا", "probability": 0.870263671875}, {"start": 1549.19, "end": 1549.33, "word": " ان", "probability": 0.75537109375}, {"start": 1549.33, "end": 1549.69, "word": " الدالي", "probability": 0.7491861979166666}, {"start": 1549.69, "end": 1549.87, "word": " هاد", "probability": 0.4112548828125}, {"start": 1549.87, "end": 1550.41, "word": " continuous", "probability": 0.62158203125}, {"start": 1550.41, "end": 1551.99, "word": " on", "probability": 0.94970703125}, {"start": 1551.99, "end": 1552.43, "word": " R", "probability": 0.82080078125}, {"start": 1552.43, "end": 1553.49, "word": " صح؟", "probability": 0.8818359375}], "temperature": 1.0}, {"id": 55, "seek": 158305, "start": 1558.29, "end": 1583.05, "text": "خلّيني أسميها g of x وفي عندي f of x بساوي واحد على x و x لا يساوي سفر is continuous", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 38251, 1829, 11296, 290, 295, 2031, 4032, 41185, 18871, 16254, 283, 295, 2031, 4724, 3794, 995, 45865, 36764, 24401, 15844, 2031, 4032, 2031, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 307, 10957], "avg_logprob": -0.24804687201976777, "compression_ratio": 1.1775700934579438, "no_speech_prob": 0.0, "words": [{"start": 1558.29, "end": 1558.87, "word": "خلّيني", "probability": 0.6658203125}, {"start": 1558.87, "end": 1559.47, "word": " أسميها", "probability": 0.8709716796875}, {"start": 1559.47, "end": 1559.79, "word": " g", "probability": 0.427978515625}, {"start": 1559.79, "end": 1560.03, "word": " of", "probability": 0.413818359375}, {"start": 1560.03, "end": 1560.43, "word": " x", "probability": 0.927734375}, {"start": 1560.43, "end": 1564.87, "word": " وفي", "probability": 0.517578125}, {"start": 1564.87, "end": 1565.45, "word": " عندي", "probability": 0.83837890625}, {"start": 1565.45, "end": 1568.07, "word": " f", "probability": 0.7099609375}, {"start": 1568.07, "end": 1569.35, "word": " of", "probability": 0.95361328125}, {"start": 1569.35, "end": 1571.67, "word": " x", "probability": 0.96240234375}, {"start": 1571.67, "end": 1573.59, "word": " بساوي", "probability": 0.695068359375}, {"start": 1573.59, "end": 1574.05, "word": " واحد", "probability": 0.947021484375}, {"start": 1574.05, "end": 1574.31, "word": " على", "probability": 0.7470703125}, {"start": 1574.31, "end": 1574.89, "word": " x", "probability": 0.841796875}, {"start": 1574.89, "end": 1578.67, "word": " و", "probability": 0.58251953125}, {"start": 1578.67, "end": 1579.05, "word": " x", "probability": 0.47314453125}, {"start": 1579.05, "end": 1579.33, "word": " لا", "probability": 0.92138671875}, {"start": 1579.33, "end": 1579.95, "word": " يساوي", "probability": 0.9273681640625}, {"start": 1579.95, "end": 1580.55, "word": " سفر", "probability": 0.9192708333333334}, {"start": 1580.55, "end": 1581.05, "word": " is", "probability": 0.7265625}, {"start": 1581.05, "end": 1583.05, "word": " continuous", "probability": 0.939453125}], "temperature": 1.0}, {"id": 56, "seek": 161728, "start": 1589.88, "end": 1617.28, "text": "for all x لا يساوي السفر ده لما اتصل معدى عند السفر صح is continuous on a اللي هي بساوي r معدى السفر hence by composition theorem اللي هو النتيجة هذه", "tokens": [2994, 439, 2031, 20193, 7251, 3794, 995, 45865, 21136, 5172, 2288, 11778, 3224, 5296, 15042, 1975, 2655, 36520, 20449, 3215, 7578, 43242, 21136, 5172, 2288, 20328, 5016, 307, 10957, 322, 257, 13672, 1829, 39896, 4724, 3794, 995, 45865, 367, 20449, 3215, 7578, 21136, 5172, 2288, 16678, 538, 12686, 20904, 13672, 1829, 31439, 28239, 31371, 7435, 3660, 29538], "avg_logprob": -0.3213900903175617, "compression_ratio": 1.4379084967320261, "no_speech_prob": 0.0, "words": 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"probability": 0.7470703125}, {"start": 1607.72, "end": 1609.26, "word": " by", "probability": 0.94677734375}, {"start": 1609.26, "end": 1610.46, "word": " composition", "probability": 0.92578125}, {"start": 1610.46, "end": 1615.96, "word": " theorem", "probability": 0.9609375}, {"start": 1615.96, "end": 1616.16, "word": " اللي", "probability": 0.95556640625}, {"start": 1616.16, "end": 1616.28, "word": " هو", "probability": 0.88134765625}, {"start": 1616.28, "end": 1616.86, "word": " النتيجة", "probability": 0.9459228515625}, {"start": 1616.86, "end": 1617.28, "word": " هذه", "probability": 0.5966796875}], "temperature": 1.0}, {"id": 57, "seek": 164645, "start": 1618.83, "end": 1646.45, "text": "بطلع عندي g circle f of x اللي هو g ل f of x اللي هي بتطلع بالساوي sin واحد على x is continuous على كل الأعداد الحقيقية مع عدد السفر", "tokens": [3555, 9566, 1211, 3615, 18871, 16254, 290, 6329, 283, 295, 2031, 13672, 1829, 31439, 290, 5296, 283, 295, 2031, 13672, 1829, 39896, 39894, 9566, 1211, 3615, 20666, 3794, 995, 45865, 3343, 36764, 24401, 15844, 2031, 307, 10957, 15844, 28242, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 20449, 6225, 3215, 3215, 21136, 5172, 2288], "avg_logprob": -0.2712673533845831, "compression_ratio": 1.4326241134751774, "no_speech_prob": 0.0, "words": [{"start": 1618.83, "end": 1619.49, "word": "بطلع", "probability": 0.65545654296875}, {"start": 1619.49, "end": 1619.83, "word": " عندي", "probability": 0.715087890625}, {"start": 1619.83, "end": 1620.23, "word": " g", "probability": 0.364990234375}, {"start": 1620.23, "end": 1621.03, "word": " circle", "probability": 0.249755859375}, {"start": 1621.03, "end": 1621.51, "word": " f", "probability": 0.50390625}, {"start": 1621.51, "end": 1623.09, "word": " of", "probability": 0.845703125}, {"start": 1623.09, "end": 1623.65, "word": " x", "probability": 0.943359375}, {"start": 1623.65, "end": 1624.07, "word": " اللي", "probability": 0.711669921875}, {"start": 1624.07, "end": 1624.45, "word": " هو", "probability": 0.8505859375}, {"start": 1624.45, "end": 1626.49, "word": " g", "probability": 0.73681640625}, {"start": 1626.49, "end": 1626.79, "word": " ل", "probability": 0.56884765625}, {"start": 1626.79, "end": 1627.21, "word": " f", "probability": 0.625}, {"start": 1627.21, "end": 1627.53, "word": " of", "probability": 0.9599609375}, {"start": 1627.53, "end": 1628.13, "word": " x", "probability": 0.98095703125}, {"start": 1628.13, "end": 1629.49, "word": " اللي", "probability": 0.8955078125}, {"start": 1629.49, "end": 1629.77, "word": " هي", "probability": 0.6826171875}, {"start": 1629.77, "end": 1630.31, "word": " بتطلع", "probability": 0.964599609375}, {"start": 1630.31, "end": 1631.17, "word": " بالساوي", "probability": 0.8011474609375}, {"start": 1631.17, "end": 1632.89, "word": " sin", "probability": 0.443359375}, {"start": 1632.89, "end": 1633.63, "word": " واحد", "probability": 0.845458984375}, {"start": 1633.63, "end": 1633.85, "word": " على", "probability": 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{"start": 1839.68, "end": 1840.08, "word": " لكل", "probability": 0.905517578125}, {"start": 1840.08, "end": 1840.54, "word": " عناصر", "probability": 0.9718424479166666}, {"start": 1840.54, "end": 1840.7, "word": " ال", "probability": 0.904296875}, {"start": 1840.7, "end": 1840.92, "word": " set", "probability": 0.95947265625}, {"start": 1840.92, "end": 1841.32, "word": " هذه", "probability": 0.6396484375}], "temperature": 1.0}, {"id": 64, "seek": 186966, "start": 1842.24, "end": 1869.66, "text": "أصغر من أو يساوي الـ M طيب لو بدى أقول ما معنى أن تكون الدالة unbounded على المجموعة A لأن هنا F from A to R is unbounded", "tokens": [10721, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 2423, 39184, 376, 23032, 1829, 3555, 45164, 47525, 7578, 5551, 39648, 19446, 20449, 1863, 7578, 14739, 6055, 30544, 32748, 6027, 3660, 517, 18767, 292, 15844, 9673, 7435, 2304, 2407, 27884, 316, 5296, 33456, 34105, 479, 490, 316, 281, 497, 307, 517, 18767, 292], "avg_logprob": -0.2854455913658495, 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"word": " معنى", "probability": 0.82373046875}, {"start": 1856.62, "end": 1856.78, "word": " أن", "probability": 0.580078125}, {"start": 1856.78, "end": 1857.38, "word": " تكون", "probability": 0.822509765625}, {"start": 1857.38, "end": 1858.0, "word": " الدالة", "probability": 0.9581705729166666}, {"start": 1858.0, "end": 1859.16, "word": " unbounded", "probability": 0.780517578125}, {"start": 1859.16, "end": 1859.66, "word": " على", "probability": 0.525390625}, {"start": 1859.66, "end": 1860.32, "word": " المجموعة", "probability": 0.905859375}, {"start": 1860.32, "end": 1860.6, "word": " A", "probability": 0.80615234375}, {"start": 1860.6, "end": 1861.42, "word": " لأن", "probability": 0.45758056640625}, {"start": 1861.42, "end": 1861.66, "word": " هنا", "probability": 0.96337890625}, {"start": 1861.66, "end": 1863.34, "word": " F", "probability": 0.374267578125}, {"start": 1863.34, "end": 1864.26, "word": " from", "probability": 0.81103515625}, {"start": 1864.26, "end": 1864.72, "word": " A", "probability": 0.9521484375}, {"start": 1864.72, "end": 1865.0, "word": " to", "probability": 0.97509765625}, {"start": 1865.0, "end": 1865.58, "word": " R", "probability": 0.9921875}, {"start": 1865.58, "end": 1868.44, "word": " is", "probability": 0.89697265625}, {"start": 1868.44, "end": 1869.66, "word": " unbounded", "probability": 0.9601236979166666}], "temperature": 1.0}, {"id": 65, "seek": 189722, "start": 1873.14, "end": 1897.22, "text": "is unbounded on a if الشرط التالي ات��قق خلّينا ننفي الشرط هذا", "tokens": [271, 517, 18767, 292, 322, 257, 498, 25124, 2288, 9566, 16712, 6027, 1829, 1975, 2655, 5016, 4587, 4587, 16490, 1211, 11703, 9957, 995, 8717, 1863, 41185, 25124, 2288, 9566, 23758], "avg_logprob": -0.21711189900675126, "compression_ratio": 1.130952380952381, "no_speech_prob": 0.0, "words": [{"start": 1873.14, "end": 1873.56, "word": "is", "probability": 0.40478515625}, {"start": 1873.56, "end": 1874.96, "word": " unbounded", "probability": 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لكل M عدد موجب يوجد X يوجد X يعتمد على M في مجال الدولة بحيث انه نفي المتبين هذا يتحقق اللي هو absolute F of X", "tokens": [1863, 1863, 41185, 25124, 2288, 4587, 4724, 4587, 7578, 2423, 39184, 37498, 8978, 29245, 3215, 376, 6225, 3215, 3215, 3714, 29245, 3555, 5296, 28820, 4724, 1829, 9381, 13546, 5296, 28820, 376, 6225, 3215, 3215, 3714, 29245, 3555, 7251, 29245, 3215, 1783, 7251, 29245, 3215, 1783, 7251, 34268, 2304, 3215, 15844, 376, 8978, 3714, 7435, 6027, 32748, 12610, 3660, 4724, 5016, 1829, 12984, 16472, 3224, 8717, 41185, 9673, 2655, 3555, 9957, 23758, 7251, 2655, 5016, 4587, 4587, 13672, 1829, 31439, 8236, 479, 295, 1783], "avg_logprob": -0.1971726259660153, "compression_ratio": 1.576470588235294, "no_speech_prob": 0.0, "words": [{"start": 1901.36, "end": 1901.9, "word": "ننفي", "probability": 0.6630045572916666}, {"start": 1901.9, "end": 1902.42, "word": " الشرق", "probability": 0.7377115885416666}, {"start": 1902.42, "end": 1902.64, "word": " بقى", "probability": 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"probability": 0.6295166015625}, {"start": 1920.66, "end": 1921.68, "word": " نفي", "probability": 0.953125}, {"start": 1921.68, "end": 1922.3, "word": " المتبين", "probability": 0.924560546875}, {"start": 1922.3, "end": 1922.5, "word": " هذا", "probability": 0.2095947265625}, {"start": 1922.5, "end": 1923.18, "word": " يتحقق", "probability": 0.97822265625}, {"start": 1923.18, "end": 1923.34, "word": " اللي", "probability": 0.896240234375}, {"start": 1923.34, "end": 1923.6, "word": " هو", "probability": 0.9892578125}, {"start": 1923.6, "end": 1924.18, "word": " absolute", "probability": 0.876953125}, {"start": 1924.18, "end": 1926.54, "word": " F", "probability": 0.339599609375}, {"start": 1926.54, "end": 1926.84, "word": " of", "probability": 0.5625}, {"start": 1926.84, "end": 1927.26, "word": " X", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 67, "seek": 195552, "start": 1928.34, "end": 1955.52, "text": "بطلع أكبر من أو ساوي أكبر من أو ساوي ال M أكبر من أو ساوي ال M هذا معناه أن الدالة ما تكونش bounded على المجال تبعها معناه أنه لأي عدد موجب بقدر ألاقي عنصر يعتمد على عدد الموجب هذا في مجال الدالة والقيمة المطلقة", "tokens": [3555, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 376, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 376, 23758, 20449, 8315, 3224, 14739, 32748, 6027, 3660, 19446, 6055, 30544, 8592, 37498, 15844, 9673, 7435, 6027, 6055, 3555, 3615, 11296, 20449, 8315, 3224, 14739, 3224, 5296, 10721, 1829, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 28543, 2288, 5551, 15040, 38436, 18871, 9381, 2288, 7251, 34268, 2304, 3215, 15844, 6225, 3215, 3215, 9673, 29245, 3555, 23758, 8978, 3714, 7435, 6027, 32748, 6027, 3660, 16070, 4587, 32640, 3660, 9673, 9566, 1211, 28671], "avg_logprob": -0.21694711982630766, "compression_ratio": 2.0386740331491713, "no_speech_prob": 0.0, "words": [{"start": 1928.34, "end": 1928.92, "word": "بطلع", "probability": 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{"start": 1939.66, "end": 1939.66, "word": " أو", "probability": 0.97900390625}, {"start": 1939.66, "end": 1939.66, "word": " ساوي", "probability": 0.9620768229166666}, {"start": 1939.66, "end": 1939.66, "word": " ال", "probability": 0.79296875}, {"start": 1939.66, "end": 1939.66, "word": " M", "probability": 0.9716796875}, {"start": 1939.66, "end": 1941.74, "word": " هذا", "probability": 0.480712890625}, {"start": 1941.74, "end": 1942.26, "word": " معناه", "probability": 0.8873697916666666}, {"start": 1942.26, "end": 1942.5, "word": " أن", "probability": 0.5341796875}, {"start": 1942.5, "end": 1943.24, "word": " الدالة", "probability": 0.9368489583333334}, {"start": 1943.24, "end": 1944.2, "word": " ما", "probability": 0.390625}, {"start": 1944.2, "end": 1944.78, "word": " تكونش", "probability": 0.6817626953125}, {"start": 1944.78, "end": 1945.14, "word": " bounded", "probability": 0.52880859375}, {"start": 1945.14, "end": 1945.66, "word": " على", "probability": 0.7890625}, {"start": 1945.66, "end": 1946.24, "word": " المجال", "probability": 0.9690755208333334}, {"start": 1946.24, "end": 1946.76, "word": " تبعها", "probability": 0.8736572265625}, {"start": 1946.76, "end": 1947.26, "word": " معناه", "probability": 0.796142578125}, {"start": 1947.26, "end": 1947.7, "word": " أنه", "probability": 0.6923828125}, {"start": 1947.7, "end": 1947.96, "word": " لأي", "probability": 0.9265950520833334}, {"start": 1947.96, "end": 1948.3, "word": " عدد", "probability": 0.9794921875}, {"start": 1948.3, "end": 1948.8, "word": " موجب", "probability": 0.9894205729166666}, {"start": 1948.8, "end": 1949.64, "word": " بقدر", "probability": 0.9353841145833334}, {"start": 1949.64, "end": 1949.9, "word": " ألاقي", "probability": 0.5994466145833334}, {"start": 1949.9, "end": 1950.46, "word": " عنصر", "probability": 0.9361979166666666}, {"start": 1950.46, "end": 1950.98, "word": " يعتمد", "probability": 0.968017578125}, {"start": 1950.98, "end": 1951.12, "word": " على", "probability": 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34051, 7251, 3794, 995, 45865, 2423, 376, 6156, 2304, 12984, 6027, 15844, 29910, 23275, 8032, 47302, 50113, 6027, 1365, 45164, 5551, 9778, 3215, 2655, 2423, 2445, 283, 295, 2031], "avg_logprob": -0.1850694391462538, "compression_ratio": 1.265625, "no_speech_prob": 0.0, "words": [{"start": 1958.33, "end": 1958.83, "word": "قيمة", "probability": 0.9436848958333334}, {"start": 1958.83, "end": 1959.27, "word": " الدالة", "probability": 0.8727213541666666}, {"start": 1959.27, "end": 1959.43, "word": " عند", "probability": 0.81298828125}, {"start": 1959.43, "end": 1959.97, "word": " العنصر", "probability": 0.8280029296875}, {"start": 1959.97, "end": 1960.43, "word": " أكبر", "probability": 0.8780924479166666}, {"start": 1960.43, "end": 1960.69, "word": " من", "probability": 0.953125}, {"start": 1960.69, "end": 1960.93, "word": " أو", "probability": 0.8427734375}, {"start": 1960.93, "end": 1961.73, "word": " يساوي", "probability": 0.967041015625}, {"start": 1961.73, "end": 1962.03, "word": " ال", "probability": 0.791015625}, {"start": 1962.03, "end": 1962.31, "word": " M", "probability": 0.22216796875}, {"start": 1962.31, "end": 1964.27, "word": " فمثال", "probability": 0.937744140625}, {"start": 1964.27, "end": 1964.49, "word": " على", "probability": 0.828125}, {"start": 1964.49, "end": 1966.87, "word": " ذلك", "probability": 0.992919921875}, {"start": 1966.87, "end": 1971.01, "word": " هاي", "probability": 0.542724609375}, {"start": 1971.01, "end": 1971.57, "word": " مثال", "probability": 0.9697265625}, {"start": 1971.57, "end": 1972.93, "word": " example", "probability": 0.40283203125}, {"start": 1972.93, "end": 1980.45, "word": " لو", "probability": 0.7900390625}, {"start": 1980.45, "end": 1980.99, "word": " أخدت", "probability": 0.9798583984375}, {"start": 1980.99, "end": 1981.15, "word": " ال", "probability": 0.97705078125}, {"start": 1981.15, "end": 1981.71, "word": " function", "probability": 0.96337890625}, {"start": 1981.71, "end": 1983.89, "word": " f", "probability": 0.5927734375}, {"start": 1983.89, "end": 1984.13, "word": " of", "probability": 0.5849609375}, {"start": 1984.13, "end": 1984.49, "word": " x", "probability": 0.78564453125}], "temperature": 1.0}, {"id": 69, "seek": 201232, "start": 1986.14, "end": 2012.32, "text": "show that f of x بيساوي واحد على x و x أكبر من سفر is unbounded على المجموعة a اللي هي الفترة المفتوحة من سفر إلى مانا نهائي", "tokens": [34436, 300, 283, 295, 2031, 4724, 1829, 3794, 995, 45865, 36764, 24401, 15844, 2031, 4032, 2031, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 307, 517, 18767, 292, 15844, 9673, 7435, 2304, 2407, 27884, 257, 13672, 1829, 39896, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 30731, 3714, 7649, 995, 8717, 3224, 16373, 1829], "avg_logprob": -0.2451006391290891, "compression_ratio": 1.3448275862068966, "no_speech_prob": 0.0, "words": [{"start": 1986.14, "end": 1986.76, "word": "show", "probability": 0.205810546875}, {"start": 1986.76, "end": 1987.58, "word": " that", "probability": 0.86376953125}, {"start": 1987.58, "end": 1987.96, "word": " f", "probability": 0.6220703125}, {"start": 1987.96, "end": 1988.22, "word": " of", "probability": 0.471923828125}, {"start": 1988.22, "end": 1988.6, "word": " x", "probability": 0.90576171875}, {"start": 1988.6, "end": 1994.52, "word": " بيساوي", "probability": 0.664697265625}, {"start": 1994.52, "end": 1994.96, "word": " واحد", "probability": 0.906005859375}, {"start": 1994.96, "end": 1995.16, "word": " على", "probability": 0.62646484375}, {"start": 1995.16, "end": 1995.46, "word": " x", "probability": 0.58203125}, {"start": 1995.46, "end": 1995.66, "word": " و", "probability": 0.58251953125}, {"start": 1995.66, "end": 1995.9, "word": " x", "probability": 0.50341796875}, {"start": 1995.9, "end": 1996.38, "word": " أكبر", "probability": 0.87255859375}, {"start": 1996.38, "end": 1996.62, "word": " من", "probability": 0.99609375}, {"start": 1996.62, "end": 1997.16, "word": " سفر", "probability": 0.87744140625}, {"start": 1997.16, "end": 1998.5, "word": " is", "probability": 0.818359375}, {"start": 1998.5, "end": 2002.24, "word": " unbounded", "probability": 0.9563802083333334}, {"start": 2002.24, "end": 2006.5, "word": " على", "probability": 0.48486328125}, {"start": 2006.5, "end": 2007.52, "word": " المجموعة", "probability": 0.97294921875}, {"start": 2007.52, "end": 2007.9, "word": " a", "probability": 0.2247314453125}, {"start": 2007.9, "end": 2008.02, "word": " اللي", "probability": 0.70263671875}, {"start": 2008.02, "end": 2008.24, "word": " هي", "probability": 0.89111328125}, {"start": 2008.24, "end": 2008.74, "word": " الفترة", "probability": 0.9864908854166666}, {"start": 2008.74, "end": 2009.44, "word": " المفتوحة", "probability": 0.98779296875}, {"start": 2009.44, "end": 2009.66, "word": " من", "probability": 0.974609375}, {"start": 2009.66, "end": 2010.36, "word": " سفر", "probability": 0.97900390625}, {"start": 2010.36, "end": 2011.28, "word": " إلى", "probability": 0.8466796875}, {"start": 2011.28, "end": 2011.68, "word": " مانا", "probability": 0.5370279947916666}, {"start": 2011.68, "end": 2012.32, "word": " نهائي", "probability": 0.7449951171875}], "temperature": 1.0}, {"id": 70, "seek": 205623, "start": 2029.08, "end": 2056.24, "text": "proof حسب تعريف ال unboundedness بدي اخد ابدأ let m be an arbitrarily positive number بيه given بدي ارد عليه باكس اعتمد xm بحيث ان المتباين هذا تتحقق ف choose", "tokens": [1424, 29496, 11331, 35457, 37279, 16572, 5172, 2423, 517, 18767, 292, 1287, 4724, 16254, 1975, 9778, 3215, 1975, 44510, 10721, 718, 275, 312, 364, 19071, 3289, 3353, 1230, 4724, 1829, 3224, 2212, 4724, 16254, 1975, 2288, 3215, 47356, 4724, 995, 4117, 3794, 1975, 34268, 2304, 3215, 2031, 76, 4724, 5016, 1829, 12984, 16472, 9673, 2655, 3555, 995, 9957, 23758, 6055, 2655, 5016, 4587, 4587, 6156, 2826], "avg_logprob": -0.2987406582974676, "compression_ratio": 1.304093567251462, "no_speech_prob": 0.0, "words": [{"start": 2029.08, "end": 2030.32, "word": "proof", "probability": 0.50421142578125}, {"start": 2030.32, "end": 2031.56, "word": " حسب", "probability": 0.904541015625}, {"start": 2031.56, "end": 2032.14, "word": " تعريف", "probability": 0.9881184895833334}, {"start": 2032.14, "end": 2032.28, "word": " ال", "probability": 0.8642578125}, {"start": 2032.28, "end": 2033.5, "word": " unboundedness", "probability": 0.731536865234375}, {"start": 2033.5, "end": 2036.0, "word": " بدي", "probability": 0.627685546875}, {"start": 2036.0, "end": 2036.76, "word": " اخد", "probability": 0.7088216145833334}, {"start": 2036.76, "end": 2037.32, "word": " ابدأ", "probability": 0.71923828125}, {"start": 2037.32, "end": 2037.82, "word": " let", "probability": 0.75390625}, {"start": 2037.82, "end": 2040.56, "word": " m", "probability": 0.4404296875}, {"start": 2040.56, "end": 2041.1, "word": " be", "probability": 0.41748046875}, {"start": 2041.1, "end": 2041.32, "word": " an", "probability": 0.35595703125}, {"start": 2041.32, "end": 2041.84, "word": " arbitrarily", "probability": 0.776123046875}, {"start": 2041.84, "end": 2042.26, "word": " positive", "probability": 0.89697265625}, {"start": 2042.26, "end": 2042.88, "word": " number", "probability": 0.978515625}, {"start": 2042.88, "end": 2043.64, "word": " بيه", "probability": 0.6090494791666666}, {"start": 2043.64, "end": 2043.98, "word": " given", "probability": 0.6220703125}, {"start": 2043.98, "end": 2046.96, "word": " بدي", "probability": 0.871337890625}, {"start": 2046.96, "end": 2047.42, "word": " ارد", "probability": 0.9588216145833334}, {"start": 2047.42, "end": 2048.04, "word": " عليه", "probability": 0.982421875}, {"start": 2048.04, "end": 2048.9, "word": " باكس", "probability": 0.724334716796875}, {"start": 2048.9, "end": 2049.78, "word": " اعتمد", "probability": 0.8880615234375}, {"start": 2049.78, "end": 2050.54, "word": " xm", "probability": 0.61279296875}, {"start": 2050.54, "end": 2052.86, "word": " بحيث", "probability": 0.9808349609375}, {"start": 2052.86, "end": 2052.98, "word": " ان", "probability": 0.83837890625}, {"start": 2052.98, "end": 2053.52, "word": " المتباين", "probability": 0.8689453125}, {"start": 2053.52, "end": 2053.7, "word": " هذا", "probability": 0.23583984375}, {"start": 2053.7, "end": 2054.44, "word": " تتحقق", "probability": 0.976953125}, {"start": 2054.44, "end": 2055.56, "word": " ف", "probability": 0.8994140625}, {"start": 2055.56, "end": 2056.24, "word": " choose", "probability": 0.7568359375}], "temperature": 1.0}, {"id": 71, "seek": 208417, "start": 2058.02, "end": 2084.18, "text": "إذاً لهذا العدد الموجب هختار XM X يعتمد على M على إنه واحد على M زائد واحد فهذا بالتأكيد عدد موجب لأن M عدد موجب صح؟ فبالتالي هذا ينتبه للفترة المفتوحة من صفر إلى ملد يعني اللي هي ال A", "tokens": [28814, 15730, 14111, 46740, 15730, 18863, 3215, 3215, 9673, 29245, 3555, 8032, 46456, 9640, 1783, 44, 1783, 7251, 34268, 2304, 3215, 15844, 376, 15844, 36145, 3224, 36764, 24401, 15844, 376, 30767, 16373, 3215, 36764, 24401, 6156, 3224, 15730, 20666, 2655, 10721, 4117, 25708, 6225, 3215, 3215, 3714, 29245, 3555, 5296, 33456, 376, 6225, 3215, 3215, 3714, 29245, 3555, 20328, 5016, 22807, 6156, 3555, 6027, 2655, 6027, 1829, 23758, 7251, 29399, 3555, 3224, 24976, 5172, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 20328, 5172, 2288, 30731, 3714, 1211, 3215, 37495, 22653, 13672, 1829, 39896, 2423, 316], "avg_logprob": -0.24410076971564973, "compression_ratio": 1.8295454545454546, "no_speech_prob": 0.0, "words": [{"start": 2058.02, "end": 2058.46, "word": "إذاً", "probability": 0.4223225911458333}, {"start": 2058.46, "end": 2058.78, "word": " لهذا", "probability": 0.946533203125}, {"start": 2058.78, "end": 2059.1, "word": " العدد", "probability": 0.9031575520833334}, {"start": 2059.1, "end": 2059.64, "word": " الموجب", "probability": 0.9695638020833334}, {"start": 2059.64, "end": 2061.12, "word": " هختار", "probability": 0.6787109375}, {"start": 2061.12, "end": 2063.18, "word": " XM", "probability": 0.2821044921875}, {"start": 2063.18, "end": 2063.6, "word": " X", "probability": 0.6279296875}, {"start": 2063.6, "end": 2064.16, "word": " يعتمد", "probability": 0.923828125}, {"start": 2064.16, "end": 2064.32, "word": " على", "probability": 0.90283203125}, {"start": 2064.32, "end": 2064.72, "word": " M", "probability": 0.90478515625}, {"start": 2064.72, "end": 2065.96, "word": " على", "probability": 0.74609375}, {"start": 2065.96, "end": 2066.62, "word": " إنه", "probability": 0.74169921875}, {"start": 2066.62, "end": 2067.34, "word": " واحد", "probability": 0.9306640625}, {"start": 2067.34, "end": 2067.68, "word": " على", "probability": 0.68310546875}, {"start": 2067.68, "end": 2068.36, "word": " M", "probability": 0.841796875}, {"start": 2068.36, "end": 2069.38, "word": " زائد", "probability": 0.8587239583333334}, {"start": 2069.38, "end": 2069.8, "word": " واحد", "probability": 0.982421875}, {"start": 2069.8, "end": 2070.94, "word": " فهذا", "probability": 0.7916666666666666}, {"start": 2070.94, "end": 2071.92, "word": " بالتأكيد", "probability": 0.990625}, {"start": 2071.92, "end": 2073.6, "word": " عدد", "probability": 0.8126627604166666}, {"start": 2073.6, "end": 2074.08, "word": " موجب", "probability": 0.9864908854166666}, {"start": 2074.08, "end": 2074.46, "word": " لأن", "probability": 0.828125}, {"start": 2074.46, "end": 2074.72, "word": " M", "probability": 0.8505859375}, {"start": 2074.72, "end": 2075.02, "word": " عدد", "probability": 0.9850260416666666}, {"start": 2075.02, "end": 2075.44, "word": " موجب", "probability": 0.9874674479166666}, {"start": 2075.44, "end": 2077.3, "word": " صح؟", "probability": 0.671630859375}, {"start": 2077.3, "end": 2078.36, "word": " فبالتالي", "probability": 0.97509765625}, {"start": 2078.36, "end": 2078.66, "word": " هذا", "probability": 0.857421875}, {"start": 2078.66, "end": 2079.44, "word": " ينتبه", "probability": 0.9178466796875}, {"start": 2079.44, "end": 2080.14, "word": " للفترة", "probability": 0.8565673828125}, {"start": 2080.14, "end": 2080.82, "word": " المفتوحة", "probability": 0.9773763020833334}, {"start": 2080.82, "end": 2081.02, "word": " من", "probability": 0.97998046875}, {"start": 2081.02, "end": 2081.44, "word": " صفر", "probability": 0.7306315104166666}, {"start": 2081.44, "end": 2081.6, "word": " إلى", "probability": 0.93701171875}, {"start": 2081.6, "end": 2081.94, "word": " ملد", "probability": 0.4217936197916667}, {"start": 2081.94, "end": 2082.38, "word": " يعني", "probability": 0.701904296875}, {"start": 2082.38, "end": 2083.56, "word": " اللي", "probability": 0.87548828125}, {"start": 2083.56, "end": 2083.8, "word": " هي", "probability": 0.94873046875}, {"start": 2083.8, "end": 2084.0, "word": " ال", "probability": 0.63916015625}, {"start": 2084.0, "end": 2084.18, "word": " A", "probability": 0.23388671875}], "temperature": 1.0}, {"id": 72, "seek": 211554, "start": 2087.86, "end": 2115.54, "text": "يعني هاي لأي عدد موجب يعني وجدت there exist xm ينتمي للمجال تبع الدالة وهذا يثبت أنه بحقق المتباين هذا then absolute f of xm بساوي absolute مقلوب", "tokens": [40228, 22653, 8032, 47302, 5296, 10721, 1829, 6225, 3215, 3215, 3714, 29245, 3555, 37495, 22653, 49610, 3215, 2655, 456, 2514, 2031, 76, 7251, 29399, 2304, 1829, 5296, 19528, 7435, 6027, 6055, 3555, 3615, 32748, 6027, 3660, 37037, 15730, 7251, 12984, 3555, 2655, 14739, 3224, 4724, 5016, 4587, 4587, 9673, 2655, 3555, 995, 9957, 23758, 550, 8236, 283, 295, 2031, 76, 4724, 3794, 995, 45865, 8236, 3714, 4587, 1211, 37746], "avg_logprob": -0.2819196454116276, "compression_ratio": 1.4394904458598725, "no_speech_prob": 0.0, "words": [{"start": 2087.86, "end": 2088.12, "word": "يعني", "probability": 0.5965576171875}, {"start": 2088.12, "end": 2088.54, "word": " هاي", "probability": 0.40972900390625}, {"start": 2088.54, "end": 2088.86, "word": " لأي", "probability": 0.8839518229166666}, {"start": 2088.86, "end": 2089.2, "word": " عدد", "probability": 0.9772135416666666}, {"start": 2089.2, "end": 2089.68, "word": " موجب", "probability": 0.89306640625}, {"start": 2089.68, "end": 2090.02, "word": " يعني", "probability": 0.50408935546875}, {"start": 2090.02, "end": 2090.96, "word": " وجدت", "probability": 0.9090169270833334}, {"start": 2090.96, "end": 2091.18, "word": " there", "probability": 0.325927734375}, {"start": 2091.18, "end": 2091.72, "word": " exist", "probability": 0.63134765625}, {"start": 2091.72, "end": 2093.38, "word": " xm", "probability": 0.5064697265625}, {"start": 2093.38, "end": 2094.82, "word": " ينتمي", "probability": 0.810302734375}, {"start": 2094.82, "end": 2095.5, "word": " للمجال", "probability": 0.8438720703125}, {"start": 2095.5, "end": 2095.84, "word": " تبع", "probability": 0.8805338541666666}, {"start": 2095.84, "end": 2096.58, "word": " الدالة", "probability": 0.8562825520833334}, {"start": 2096.58, "end": 2098.36, "word": " وهذا", "probability": 0.8544921875}, {"start": 2098.36, "end": 2099.22, "word": " يثبت", "probability": 0.8812255859375}, {"start": 2099.22, "end": 2099.38, "word": " أنه", "probability": 0.39501953125}, {"start": 2099.38, "end": 2099.8, "word": " بحقق", "probability": 0.91552734375}, {"start": 2099.8, "end": 2100.44, "word": " المتباين", "probability": 0.89169921875}, {"start": 2100.44, "end": 2100.84, "word": " هذا", "probability": 0.54052734375}, {"start": 2100.84, "end": 2104.34, "word": " then", "probability": 0.5986328125}, {"start": 2104.34, "end": 2105.72, "word": " absolute", "probability": 0.8837890625}, {"start": 2105.72, "end": 2107.7, "word": " f", "probability": 0.6572265625}, {"start": 2107.7, "end": 2108.0, "word": " of", "probability": 0.4833984375}, {"start": 2108.0, "end": 2109.0, "word": " xm", "probability": 0.90185546875}, {"start": 2109.0, "end": 2111.22, "word": " بساوي", "probability": 0.8096923828125}, {"start": 2111.22, "end": 2113.16, "word": " absolute", "probability": 0.90966796875}, {"start": 2113.16, "end": 2115.54, "word": " مقلوب", "probability": 0.949951171875}], "temperature": 1.0}, {"id": 73, "seek": 214373, "start": 2117.15, "end": 2143.73, "text": "الـ Xm هو absolute واحد على Xm وهذا بيساوي M زياد واحد هو مفروض اكتب absolute M زياد واحد اللي هو M زياد واحد لأن M عدد موجة وهذا أكبر من M لأن هذه المتباينة اتحققت أكبر من M", "tokens": [6027, 39184, 1783, 76, 31439, 8236, 36764, 24401, 15844, 1783, 76, 37037, 15730, 4724, 1829, 3794, 995, 45865, 376, 30767, 1829, 18513, 36764, 24401, 31439, 3714, 5172, 32887, 11242, 1975, 4117, 2655, 3555, 8236, 376, 30767, 1829, 18513, 36764, 24401, 13672, 1829, 31439, 376, 30767, 1829, 18513, 36764, 24401, 5296, 33456, 376, 6225, 3215, 3215, 3714, 29245, 3660, 37037, 15730, 5551, 4117, 26890, 9154, 376, 5296, 33456, 29538, 9673, 2655, 3555, 995, 9957, 3660, 1975, 2655, 5016, 4587, 38149, 5551, 4117, 26890, 9154, 376], "avg_logprob": -0.32058824931873997, "compression_ratio": 1.7530864197530864, "no_speech_prob": 0.0, "words": [{"start": 2117.15, "end": 2117.55, "word": "الـ", "probability": 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0.35107421875}, {"start": 2127.17, "end": 2127.39, "word": " مفروض", "probability": 0.711883544921875}, {"start": 2127.39, "end": 2127.71, "word": " اكتب", "probability": 0.8489990234375}, {"start": 2127.71, "end": 2128.23, "word": " absolute", "probability": 0.90234375}, {"start": 2128.23, "end": 2128.57, "word": " M", "probability": 0.8701171875}, {"start": 2128.57, "end": 2128.95, "word": " زياد", "probability": 0.9138997395833334}, {"start": 2128.95, "end": 2129.35, "word": " واحد", "probability": 0.994140625}, {"start": 2129.35, "end": 2131.49, "word": " اللي", "probability": 0.82373046875}, {"start": 2131.49, "end": 2131.79, "word": " هو", "probability": 0.97216796875}, {"start": 2131.79, "end": 2132.29, "word": " M", "probability": 0.94384765625}, {"start": 2132.29, "end": 2132.79, "word": " زياد", "probability": 0.9679361979166666}, {"start": 2132.79, "end": 2133.21, "word": " واحد", "probability": 0.996337890625}, {"start": 2133.21, "end": 2133.59, "word": " لأن", 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{"start": 2164.29, "end": 2164.41, "word": " ال", "probability": 0.91943359375}, {"start": 2164.41, "end": 2164.85, "word": " remark", "probability": 0.93994140625}, {"start": 2164.85, "end": 2165.35, "word": " بنطلع", "probability": 0.8160400390625}, {"start": 2165.35, "end": 2165.47, "word": " ال", "probability": 0.93701171875}, {"start": 2165.47, "end": 2165.79, "word": " function", "probability": 0.93017578125}, {"start": 2165.79, "end": 2166.45, "word": " تبعتي", "probability": 0.8079833984375}, {"start": 2166.45, "end": 2168.05, "word": " unbounded", "probability": 0.8365885416666666}, {"start": 2168.05, "end": 2168.39, "word": " على", "probability": 0.884765625}, {"start": 2168.39, "end": 2169.05, "word": " الفترة", "probability": 0.986328125}, {"start": 2169.05, "end": 2169.65, "word": " المفتوحة", "probability": 0.9781087239583334}, {"start": 2169.65, "end": 2169.83, "word": " من", "probability": 0.97802734375}, {"start": 2169.83, "end": 2170.29, "word": " صفر", "probability": 0.689208984375}, {"start": 2170.29, "end": 2170.55, "word": " إلى", "probability": 0.892578125}, {"start": 2170.55, "end": 2170.83, "word": " ملا", "probability": 0.476806640625}, {"start": 2170.83, "end": 2171.45, "word": " نهائي", "probability": 0.795654296875}, {"start": 2171.45, "end": 2172.63, "word": " تمام", "probability": 0.91748046875}], "temperature": 1.0}, {"id": 75, "seek": 220121, "start": 2175.08, "end": 2201.22, "text": "الان في عندي boundedness theorem في نظرية مهمة اسمها boundedness theorem boundedness", "tokens": [6027, 7649, 8978, 18871, 16254, 37498, 1287, 20904, 8978, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 24525, 2304, 11296, 37498, 1287, 20904, 37498, 1287], "avg_logprob": -0.20671875, "compression_ratio": 1.3095238095238095, "no_speech_prob": 0.0, "words": [{"start": 2175.08, "end": 2175.62, "word": "الان", "probability": 0.80322265625}, {"start": 2175.62, "end": 2175.86, "word": " في", "probability": 0.4208984375}, {"start": 2175.86, "end": 2176.38, "word": " عندي", "probability": 0.78369140625}, {"start": 2176.38, "end": 2177.6, "word": " boundedness", "probability": 0.5927734375}, {"start": 2177.6, "end": 2178.1, "word": " theorem", "probability": 0.90869140625}, {"start": 2178.1, "end": 2188.84, "word": " في", "probability": 0.54638671875}, {"start": 2188.84, "end": 2189.4, "word": " نظرية", "probability": 0.9803466796875}, {"start": 2189.4, "end": 2190.82, "word": " مهمة", "probability": 0.9811197916666666}, {"start": 2190.82, "end": 2191.64, "word": " اسمها", "probability": 0.921875}, {"start": 2191.64, "end": 2192.54, "word": " boundedness", "probability": 0.949462890625}, {"start": 2192.54, "end": 2193.48, "word": " theorem", "probability": 0.92919921875}, {"start": 2193.48, "end": 2201.22, "word": " boundedness", "probability": 0.94091796875}], "temperature": 1.0}, {"id": 76, "seek": 223650, "start": 2207.4, "end": 2236.5, "text": "bound this theorem let خلينا ناخد I let I be closed and bounded interval be closed and bounded interval", "tokens": [18767, 341, 20904, 718, 16490, 1211, 9957, 995, 8717, 47283, 3215, 286, 718, 286, 312, 5395, 293, 37498, 15035, 312, 5395, 293, 37498, 15035], "avg_logprob": -0.31390625953674317, "compression_ratio": 1.382716049382716, "no_speech_prob": 0.0, "words": [{"start": 2207.4, "end": 2207.86, "word": "bound", "probability": 0.45166015625}, {"start": 2207.86, "end": 2208.26, "word": " this", "probability": 0.1793212890625}, {"start": 2208.26, "end": 2208.78, "word": " theorem", "probability": 0.482177734375}, {"start": 2208.78, "end": 2214.56, "word": " let", "probability": 0.62646484375}, {"start": 2214.56, "end": 2216.1, "word": " خلينا", "probability": 0.6165771484375}, {"start": 2216.1, "end": 2216.74, "word": " ناخد", "probability": 0.9757486979166666}, {"start": 2216.74, "end": 2217.26, "word": " I", "probability": 0.7451171875}, {"start": 2217.26, "end": 2217.82, "word": " let", "probability": 0.7197265625}, {"start": 2217.82, "end": 2220.22, "word": " I", "probability": 0.94970703125}, {"start": 2220.22, "end": 2220.62, "word": " be", "probability": 0.83740234375}, {"start": 2220.62, "end": 2221.54, "word": " closed", "probability": 0.91357421875}, {"start": 2221.54, "end": 2223.36, "word": " and", "probability": 0.95751953125}, {"start": 2223.36, "end": 2223.88, "word": " bounded", "probability": 0.9619140625}, {"start": 2223.88, "end": 2224.58, "word": " interval", "probability": 0.98046875}, {"start": 2224.58, "end": 2225.1, "word": " be", "probability": 0.493896484375}, {"start": 2225.1, "end": 2226.04, "word": " closed", "probability": 0.92333984375}, {"start": 2226.04, "end": 2230.74, "word": " and", "probability": 0.95654296875}, {"start": 2230.74, "end": 2231.58, "word": " bounded", "probability": 0.95068359375}, {"start": 2231.58, "end": 2236.5, "word": " interval", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 77, "seek": 226769, "start": 2238.72, "end": 2267.7, "text": "لو كانت F F from I to R is continuous is continuous on I then F is bounded on I لإن لو كان مجلة ده close bounded interval", "tokens": [1211, 2407, 25961, 2655, 479, 479, 490, 286, 281, 497, 307, 10957, 307, 10957, 322, 286, 550, 479, 307, 37498, 322, 286, 5296, 28814, 1863, 45164, 25961, 3714, 7435, 37977, 11778, 3224, 1998, 37498, 15035], "avg_logprob": -0.3328993047277133, "compression_ratio": 1.2589285714285714, "no_speech_prob": 0.0, "words": [{"start": 2238.72, "end": 2239.18, "word": "لو", "probability": 0.833251953125}, {"start": 2239.18, "end": 2239.94, "word": " كانت", "probability": 0.94287109375}, {"start": 2239.94, "end": 2240.3, "word": " F", "probability": 0.239013671875}, {"start": 2240.3, "end": 2240.84, "word": " F", "probability": 0.404541015625}, {"start": 2240.84, "end": 2242.38, "word": " from", "probability": 0.74462890625}, {"start": 2242.38, "end": 2242.92, "word": " I", "probability": 0.94921875}, {"start": 2242.92, "end": 2243.24, "word": " to", "probability": 0.9462890625}, {"start": 2243.24, "end": 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"probability": 0.9970703125}, {"start": 2262.82, "end": 2265.16, "word": " لإن", "probability": 0.658447265625}, {"start": 2265.16, "end": 2265.4, "word": " لو", "probability": 0.97021484375}, {"start": 2265.4, "end": 2265.58, "word": " كان", "probability": 0.99560546875}, {"start": 2265.58, "end": 2266.02, "word": " مجلة", "probability": 0.72998046875}, {"start": 2266.02, "end": 2266.26, "word": " ده", "probability": 0.869384765625}, {"start": 2266.26, "end": 2266.64, "word": " close", "probability": 0.1302490234375}, {"start": 2266.64, "end": 2267.12, "word": " bounded", "probability": 0.84814453125}, {"start": 2267.12, "end": 2267.7, "word": " interval", "probability": 0.9912109375}], "temperature": 1.0}, {"id": 78, "seek": 229433, "start": 2268.37, "end": 2294.33, "text": "وكانت ال function continuous على I فلابد انها تطلع bounded على الفترة I ولبرهان ذلك البرهان سهل proof برهان بالتناقض assume on contrary", "tokens": [2407, 41361, 2655, 2423, 2445, 10957, 15844, 286, 6156, 15040, 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2460.49, "end": 2463.77, "word": " contained", "probability": 0.82470703125}, {"start": 2463.77, "end": 2467.99, "word": " in", "probability": 0.9560546875}, {"start": 2467.99, "end": 2468.53, "word": " I", "probability": 0.78515625}], "temperature": 1.0}, {"id": 85, "seek": 249963, "start": 2471.61, "end": 2499.63, "text": "والـ I عبارة عن الفترة المغلقة من A ل B إذا X in is bounded لأن كل حدود ال sequence محصورة X in أكبر من أو ساوي A أصفر من أو ساوي B لكل M هذه ال sequence محدودة من أسفل ومحدودة من أعلى كل حدودها محصورة بين A وB إذا ال sequence هذه bounded صح؟", "tokens": [2407, 6027, 39184, 286, 6225, 3555, 9640, 3660, 18871, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 316, 5296, 363, 11933, 15730, 1783, 294, 307, 37498, 5296, 33456, 28242, 11331, 3215, 23328, 2423, 8310, 3714, 5016, 9381, 13063, 3660, 1783, 294, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 316, 5551, 9381, 5172, 2288, 9154, 34051, 8608, 995, 45865, 363, 5296, 28820, 376, 29538, 2423, 8310, 3714, 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0.9765625}, {"start": 2489.59, "end": 2489.81, "word": " B", "probability": 0.98095703125}, {"start": 2489.81, "end": 2490.25, "word": " لكل", "probability": 0.988037109375}, {"start": 2490.25, "end": 2490.55, "word": " M", "probability": 0.352783203125}, {"start": 2490.55, "end": 2491.95, "word": " هذه", "probability": 0.4501953125}, {"start": 2491.95, "end": 2492.07, "word": " ال", "probability": 0.91357421875}, {"start": 2492.07, "end": 2492.39, "word": " sequence", "probability": 0.95751953125}, {"start": 2492.39, "end": 2492.97, "word": " محدودة", "probability": 0.97900390625}, {"start": 2492.97, "end": 2493.09, "word": " من", "probability": 0.9912109375}, {"start": 2493.09, "end": 2493.51, "word": " أسفل", "probability": 0.93798828125}, {"start": 2493.51, "end": 2493.95, "word": " ومحدودة", "probability": 0.93623046875}, {"start": 2493.95, "end": 2494.09, "word": " من", "probability": 0.9931640625}, {"start": 2494.09, "end": 2494.43, "word": " أعلى", "probability": 0.9405924479166666}, {"start": 2494.43, "end": 2494.77, "word": " كل", "probability": 0.79931640625}, {"start": 2494.77, "end": 2495.35, "word": " حدودها", "probability": 0.994873046875}, {"start": 2495.35, "end": 2496.39, "word": " محصورة", "probability": 0.9919921875}, {"start": 2496.39, "end": 2496.59, "word": " بين", "probability": 0.9072265625}, {"start": 2496.59, "end": 2496.77, "word": " A", "probability": 0.970703125}, {"start": 2496.77, "end": 2497.15, "word": " وB", "probability": 0.808837890625}, {"start": 2497.15, "end": 2497.81, "word": " إذا", "probability": 0.90966796875}, {"start": 2497.81, "end": 2497.99, "word": " ال", "probability": 0.82177734375}, {"start": 2497.99, "end": 2498.35, "word": " sequence", "probability": 0.96630859375}, {"start": 2498.35, "end": 2498.63, "word": " هذه", "probability": 0.6630859375}, {"start": 2498.63, "end": 2498.95, "word": " bounded", "probability": 0.9287109375}, {"start": 2498.95, "end": 2499.63, "word": " صح؟", "probability": 0.9029947916666666}], "temperature": 1.0}, {"id": 86, "seek": 252894, "start": 2500.27, "end": 2528.95, "text": "وبالتالي So by Bolzano-Weierstrass theorem نظرية Bolzano-Weierstrass بتقول كل bounded sequence has a convergent subsequence لإن هنا there exists a subsequence سمية X in R of a sequence X in", "tokens": [37746, 6027, 2655, 6027, 1829, 407, 538, 14331, 89, 3730, 12, 4360, 811, 9733, 640, 20904, 8717, 19913, 2288, 10632, 14331, 89, 3730, 12, 4360, 811, 9733, 640, 39894, 39648, 28242, 37498, 8310, 575, 257, 9652, 6930, 13924, 655, 5296, 28814, 1863, 34105, 456, 8198, 257, 13924, 655, 8608, 2304, 10632, 1783, 294, 497, 295, 257, 8310, 1783, 294], "avg_logprob": -0.34192709624767303, "compression_ratio": 1.3518518518518519, "no_speech_prob": 0.0, "words": [{"start": 2500.27, "end": 2501.57, "word": "وبالتالي", "probability": 0.92353515625}, {"start": 2501.57, "end": 2504.81, "word": " So", "probability": 0.068359375}, {"start": 2504.81, "end": 2505.59, "word": " by", 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"end": 2515.41, "word": " a", "probability": 0.974609375}, {"start": 2515.41, "end": 2515.91, "word": " convergent", "probability": 0.770263671875}, {"start": 2515.91, "end": 2517.05, "word": " subsequence", "probability": 0.984619140625}, {"start": 2517.05, "end": 2517.87, "word": " لإن", "probability": 0.4503987630208333}, {"start": 2517.87, "end": 2518.25, "word": " هنا", "probability": 0.9853515625}, {"start": 2518.25, "end": 2518.85, "word": " there", "probability": 0.58740234375}, {"start": 2518.85, "end": 2519.39, "word": " exists", "probability": 0.5234375}, {"start": 2519.39, "end": 2519.79, "word": " a", "probability": 0.96435546875}, {"start": 2519.79, "end": 2521.61, "word": " subsequence", "probability": 0.9951171875}, {"start": 2521.61, "end": 2523.33, "word": " سمية", "probability": 0.7051595052083334}, {"start": 2523.33, "end": 2523.79, "word": " X", "probability": 0.7177734375}, {"start": 2523.79, "end": 2524.29, "word": " in", "probability": 0.251220703125}, {"start": 2524.29, "end": 2524.93, "word": " R", "probability": 0.98779296875}, {"start": 2524.93, "end": 2526.83, "word": " of", "probability": 0.92919921875}, {"start": 2526.83, "end": 2527.17, "word": " a", "probability": 0.33984375}, {"start": 2527.17, "end": 2527.83, "word": " sequence", "probability": 0.9716796875}, {"start": 2527.83, "end": 2528.49, "word": " X", "probability": 0.96142578125}, {"start": 2528.49, "end": 2528.95, "word": " in", "probability": 0.89990234375}], "temperature": 1.0}, {"id": 87, "seek": 255679, "start": 2532.27, "end": 2556.79, "text": "which converges وهذه الـ subsequence converges say خلّينا نفترض إنه limit لـ subsequence x in R as R tends to infinity بساوي x تمام؟ since", "tokens": [13690, 9652, 2880, 37037, 24192, 2423, 39184, 13924, 655, 9652, 2880, 584, 16490, 1211, 11703, 9957, 995, 8717, 5172, 2655, 43042, 36145, 3224, 4948, 5296, 39184, 13924, 655, 2031, 294, 497, 382, 497, 12258, 281, 13202, 4724, 3794, 995, 45865, 2031, 46811, 10943, 22807, 1670], "avg_logprob": -0.39436140138169995, "compression_ratio": 1.2127659574468086, "no_speech_prob": 0.0, "words": [{"start": 2532.2699999999995, "end": 2533.5899999999997, "word": "which", "probability": 0.06304931640625}, {"start": 2533.5899999999997, "end": 2534.91, "word": " converges", "probability": 0.6531982421875}, {"start": 2534.91, "end": 2535.97, "word": " وهذه", "probability": 0.5712890625}, {"start": 2535.97, "end": 2536.25, "word": " الـ", "probability": 0.40625}, {"start": 2536.25, "end": 2537.11, "word": " subsequence", "probability": 0.9306640625}, {"start": 2537.11, "end": 2538.79, "word": " converges", "probability": 0.7685546875}, {"start": 2538.79, "end": 2539.59, "word": " say", "probability": 0.300048828125}, {"start": 2539.59, "end": 2541.87, "word": " خلّينا", "probability": 0.80556640625}, {"start": 2541.87, "end": 2542.35, "word": " نفترض", "probability": 0.9779052734375}, {"start": 2542.35, "end": 2542.71, "word": " إنه", "probability": 0.39599609375}, {"start": 2542.71, "end": 2543.15, "word": " limit", "probability": 0.78515625}, {"start": 2543.15, "end": 2544.67, "word": " لـ", "probability": 0.421142578125}, {"start": 2544.67, "end": 2545.49, "word": " subsequence", "probability": 0.97802734375}, {"start": 2545.49, "end": 2545.79, "word": " x", "probability": 0.57666015625}, {"start": 2545.79, "end": 2546.15, "word": " in", "probability": 0.83251953125}, {"start": 2546.15, "end": 2546.67, "word": " R", "probability": 0.9482421875}, {"start": 2546.67, "end": 2547.19, "word": " as", "probability": 0.78955078125}, {"start": 2547.19, "end": 2547.55, "word": " R", "probability": 0.93603515625}, {"start": 2547.55, "end": 2547.89, "word": " tends", "probability": 0.377685546875}, {"start": 2547.89, "end": 2548.05, "word": " to", "probability": 0.8779296875}, {"start": 2548.05, "end": 2548.73, "word": " infinity", "probability": 0.84423828125}, {"start": 2548.73, "end": 2550.79, "word": " بساوي", "probability": 0.8634033203125}, {"start": 2550.79, "end": 2551.45, "word": " x", "probability": 0.66015625}, {"start": 2551.45, "end": 2554.15, "word": " تمام؟", "probability": 0.8098958333333334}, {"start": 2554.15, "end": 2556.79, "word": " since", "probability": 0.8564453125}], "temperature": 1.0}, {"id": 88, "seek": 258031, "start": 2558.33, "end": 2580.31, "text": "الـ X in R أكبر من أو ساوي A أصغر من أو ساوي B لكل R في N الـ sequence X in contained in I وهذه subsequence منها لأن علاصتها موجودة في I بالتالي محصورة بين A وB والsequence هذه converge ل X", "tokens": [6027, 39184, 1783, 294, 497, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 316, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 363, 5296, 28820, 497, 8978, 426, 2423, 39184, 8310, 1783, 294, 16212, 294, 286, 37037, 24192, 13924, 655, 9154, 11296, 5296, 33456, 11203, 33546, 2655, 11296, 3714, 29245, 23328, 3660, 8978, 286, 20666, 2655, 6027, 1829, 3714, 5016, 9381, 13063, 3660, 49374, 316, 4032, 33, 16070, 11834, 655, 29538, 41881, 5296, 1783], "avg_logprob": 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{"start": 2563.07, "end": 2563.29, "word": " أو", "probability": 0.96142578125}, {"start": 2563.29, "end": 2563.77, "word": " ساوي", "probability": 0.970703125}, {"start": 2563.77, "end": 2564.17, "word": " B", "probability": 0.95703125}, {"start": 2564.17, "end": 2565.57, "word": " لكل", "probability": 0.9609375}, {"start": 2565.57, "end": 2566.09, "word": " R", "probability": 0.8994140625}, {"start": 2566.09, "end": 2566.47, "word": " في", "probability": 0.9267578125}, {"start": 2566.47, "end": 2566.89, "word": " N", "probability": 0.8974609375}, {"start": 2566.89, "end": 2568.61, "word": " الـ", "probability": 0.58251953125}, {"start": 2568.61, "end": 2568.97, "word": " sequence", "probability": 0.68310546875}, {"start": 2568.97, "end": 2569.33, "word": " X", "probability": 0.89404296875}, {"start": 2569.33, "end": 2569.59, "word": " in", "probability": 0.8291015625}, {"start": 2569.59, "end": 2570.11, "word": " contained", "probability": 0.6669921875}, {"start": 2570.11, "end": 2570.33, "word": " in", "probability": 0.89794921875}, {"start": 2570.33, "end": 2570.63, "word": " I", "probability": 0.9814453125}, {"start": 2570.63, "end": 2571.19, "word": " وهذه", "probability": 0.822509765625}, {"start": 2571.19, "end": 2571.97, "word": " subsequence", "probability": 0.5933837890625}, {"start": 2571.97, "end": 2572.41, "word": " منها", "probability": 0.9814453125}, {"start": 2572.41, "end": 2573.27, "word": " لأن", "probability": 0.652587890625}, {"start": 2573.27, "end": 2573.71, "word": " علاصتها", "probability": 0.674072265625}, {"start": 2573.71, "end": 2574.31, "word": " موجودة", "probability": 0.986083984375}, {"start": 2574.31, "end": 2574.45, "word": " في", "probability": 0.96728515625}, {"start": 2574.45, "end": 2574.69, "word": " I", "probability": 0.9833984375}, {"start": 2574.69, "end": 2575.09, "word": " بالتالي", "probability": 0.79583740234375}, {"start": 2575.09, "end": 2575.63, "word": " محصورة", "probability": 0.96025390625}, {"start": 2575.63, "end": 2575.83, "word": " بين", "probability": 0.8994140625}, {"start": 2575.83, "end": 2576.05, "word": " A", "probability": 0.96923828125}, {"start": 2576.05, "end": 2576.43, "word": " وB", "probability": 0.756103515625}, {"start": 2576.43, "end": 2578.49, "word": " والsequence", "probability": 0.5984700520833334}, {"start": 2578.49, "end": 2578.81, "word": " هذه", "probability": 0.65771484375}, {"start": 2578.81, "end": 2579.31, "word": " converge", "probability": 0.74658203125}, {"start": 2579.31, "end": 2579.87, "word": " ل", "probability": 0.9443359375}, {"start": 2579.87, "end": 2580.31, "word": " X", "probability": 0.60205078125}], "temperature": 1.0}, {"id": 89, "seek": 260831, "start": 2581.35, "end": 2608.31, "text": "إذا حسب نظرية سابقة لما تكون ال sequence محصورة بين a و b وconvergent فنهايتها أيضا we get from previous theorem أن x تنتمي إلى I أو تنتمي للفترة المغلقة من a إلى b اللي هي I تمام", "tokens": [28814, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 8608, 16758, 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"compression_ratio": 1.1666666666666667, "no_speech_prob": 0.0, "words": [{"start": 2767.5499999999997, "end": 2768.95, "word": "by", "probability": 0.1370849609375}, {"start": 2768.95, "end": 2769.79, "word": " our", "probability": 0.54296875}, {"start": 2769.79, "end": 2770.41, "word": " chameleon", "probability": 0.8555908203125}, {"start": 2770.41, "end": 2771.49, "word": " by", "probability": 0.039825439453125}, {"start": 2771.49, "end": 2779.17, "word": " our", "probability": 0.88427734375}, {"start": 2779.17, "end": 2781.49, "word": " chameleon", "probability": 0.92724609375}, {"start": 2781.49, "end": 2782.61, "word": " property", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 96, "seek": 281281, "start": 2784.45, "end": 2812.81, "text": "يوجد R ينتمي إلى N أو خلّيني أسميه R0 ينتمي إلى N بحيث أنه R0 أكبر من M صح؟ لأي عدد حقيقي سواء موجب أو سالب فيه دائما عدد طبيعي أكبر منه now by star", "tokens": [1829, 29245, 3215, 497, 7251, 29399, 2304, 1829, 30731, 426, 34051, 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{"start": 2805.69, "end": 2806.37, "word": " طبيعي", "probability": 0.985107421875}, {"start": 2806.37, "end": 2806.91, "word": " أكبر", "probability": 0.97998046875}, {"start": 2806.91, "end": 2807.73, "word": " منه", "probability": 0.981201171875}, {"start": 2807.73, "end": 2809.51, "word": " now", "probability": 0.349609375}, {"start": 2809.51, "end": 2812.09, "word": " by", "probability": 0.83544921875}, {"start": 2812.09, "end": 2812.81, "word": " star", "probability": 0.5810546875}], "temperature": 1.0}, {"id": 97, "seek": 284150, "start": 2814.14, "end": 2841.5, "text": "and double star we have لدينا انه ال M أكبر من أو يساوي absolute F of X in R0 صح؟ هاي من هنا خدي R بساوي R0 فهذا الكلام صحيح هذا من double star", "tokens": [474, 3834, 3543, 321, 362, 5296, 16254, 8315, 16472, 3224, 2423, 376, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 8236, 479, 295, 1783, 294, 497, 15, 20328, 5016, 22807, 8032, 47302, 9154, 34105, 16490, 16254, 497, 4724, 3794, 995, 45865, 497, 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2845.61, "end": 2847.67, "word": " هذا", "probability": 0.37158203125}, {"start": 2847.67, "end": 2848.37, "word": " أكبر", "probability": 0.84619140625}, {"start": 2848.37, "end": 2848.67, "word": " من", "probability": 0.9736328125}, {"start": 2848.67, "end": 2848.79, "word": " ..", "probability": 0.1739501953125}, {"start": 2848.79, "end": 2848.99, "word": " إذا", "probability": 0.6043701171875}, {"start": 2848.99, "end": 2849.25, "word": " من", "probability": 0.98681640625}, {"start": 2849.25, "end": 2849.87, "word": " star", "probability": 0.53759765625}, {"start": 2849.87, "end": 2850.83, "word": " f", "probability": 0.489990234375}, {"start": 2850.83, "end": 2851.09, "word": " of", "probability": 0.396240234375}, {"start": 2851.09, "end": 2851.41, "word": " x", "probability": 0.8681640625}, {"start": 2851.41, "end": 2851.91, "word": " in", "probability": 0.306640625}, {"start": 2851.91, "end": 2852.97, "word": " R0", "probability": 0.47894287109375}, {"start": 2852.97, "end": 2854.09, "word": " أكب��", "probability": 0.9684244791666666}, {"start": 2854.09, "end": 2854.45, "word": " من", "probability": 0.99658203125}, {"start": 2854.45, "end": 2854.89, "word": " in", "probability": 0.31591796875}, {"start": 2854.89, "end": 2856.15, "word": " R0", "probability": 0.971923828125}, {"start": 2856.15, "end": 2858.77, "word": " هذا", "probability": 0.8193359375}, {"start": 2858.77, "end": 2859.31, "word": " صحيح", "probability": 0.998046875}, {"start": 2859.31, "end": 2859.75, "word": " لكل", "probability": 0.979248046875}, {"start": 2859.75, "end": 2860.23, "word": " عناصر", "probability": 0.9747721354166666}, {"start": 2860.23, "end": 2860.37, "word": " ال", "probability": 0.82763671875}, {"start": 2860.37, "end": 2860.67, "word": " sequence", "probability": 0.892578125}, {"start": 2860.67, "end": 2861.11, "word": " x", "probability": 0.92822265625}, {"start": 2861.11, "end": 2861.45, "word": " in", "probability": 0.88525390625}, {"start": 2861.45, "end": 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"text": "طيب ناخد احنا شوية break نكتفي بهذا القدر و هناخد ان شاء الله break و نواصل في اللقاء القادم", "tokens": [9566, 1829, 3555, 8717, 47283, 3215, 1975, 5016, 8315, 13412, 2407, 10632, 1821, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 4032, 8032, 1863, 47283, 3215, 16472, 13412, 16606, 21984, 1821, 4032, 8717, 2407, 33546, 1211, 8978, 13672, 4587, 16606, 25062, 18513, 2304], "avg_logprob": -0.0470052076710595, "compression_ratio": 1.4444444444444444, "no_speech_prob": 0.0, "words": [{"start": 2927.09, "end": 2927.51, "word": "طيب", "probability": 0.9913736979166666}, {"start": 2927.51, "end": 2927.97, "word": " ناخد", "probability": 0.9825846354166666}, {"start": 2927.97, "end": 2928.37, "word": " احنا", "probability": 0.97216796875}, {"start": 2928.37, "end": 2929.01, "word": " شوية", "probability": 0.9625651041666666}, {"start": 2929.01, "end": 2929.61, "word": " break", "probability": 0.99658203125}, {"start": 2929.61, "end": 2933.65, "word": " نكتفي", 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