diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json"
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+++ "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json"
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+{"segments": [{"id": 1, "seek": 4130, "start": 21.38, "end": 41.3, "text": "بسم الله الرحمن الرحيم اليوم هنكمل .. في الجزء الأول من المحاضرة هنكمل section خمسة واحد و في الوقت المتبقي من المحاضرة هنعطي مجال لكم ل .. لأسئلة على ال homework أو", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 45595, 20498, 8032, 1863, 24793, 1211, 4386, 8978, 25724, 11622, 38207, 16247, 12610, 9154, 9673, 5016, 46958, 25720, 8032, 1863, 24793, 1211, 3541, 16490, 2304, 3794, 3660, 36764, 24401, 4032, 8978, 2423, 30543, 2655, 9673, 2655, 3555, 38436, 9154, 9673, 5016, 46958, 25720, 8032, 1863, 3615, 9566, 1829, 3714, 7435, 6027, 5296, 24793, 5296, 4386, 5296, 10721, 3794, 19986, 37977, 15844, 2423, 14578, 34051], "avg_logprob": -0.11180320925809242, "compression_ratio": 1.6867469879518073, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 21.38, "end": 21.72, "word": "بسم", "probability": 0.9111328125}, {"start": 21.72, "end": 21.9, "word": " الله", "probability": 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هتكون rational number أو irrational number الحالة الأولى case one لو كانت C rational number", "tokens": [19096, 1783, 34051, 383, 6055, 29399, 2304, 1829, 30731, 1249, 34051, 383, 6055, 29399, 2304, 1829, 30731, 497, 3175, 1249, 11933, 15730, 2423, 39184, 383, 23758, 11933, 15042, 8032, 2655, 30544, 15090, 1230, 34051, 39914, 1230, 21542, 6027, 3660, 16247, 12610, 7578, 1389, 472, 45164, 25961, 2655, 383, 15090, 1230], "avg_logprob": -0.2499999953251259, "compression_ratio": 1.5579710144927537, "no_speech_prob": 0.0, "words": [{"start": 189.68, "end": 190.72, "word": "then", "probability": 0.219970703125}, {"start": 190.72, "end": 191.76, "word": " X", "probability": 0.33935546875}, {"start": 191.76, "end": 192.42, "word": " أو", "probability": 0.7255859375}, {"start": 192.42, "end": 192.76, "word": " C", "probability": 0.90478515625}, {"start": 192.76, "end": 193.56, "word": " تنتمي", "probability": 0.961181640625}, {"start": 193.56, "end": 195.88, "word": " إلى", "probability": 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"word": " إما", "probability": 0.80419921875}, {"start": 204.06, "end": 204.44, "word": " هتكون", "probability": 0.7763671875}, {"start": 204.44, "end": 204.8, "word": " rational", "probability": 0.8818359375}, {"start": 204.8, "end": 205.32, "word": " number", "probability": 0.98388671875}, {"start": 205.32, "end": 205.68, "word": " أو", "probability": 0.95068359375}, {"start": 205.68, "end": 206.7, "word": " irrational", "probability": 0.469482421875}, {"start": 206.7, "end": 207.24, "word": " number", "probability": 0.96533203125}, {"start": 207.24, "end": 207.76, "word": " الحالة", "probability": 0.9778645833333334}, {"start": 207.76, "end": 208.8, "word": " الأولى", "probability": 0.9755859375}, {"start": 208.8, "end": 210.06, "word": " case", "probability": 0.7939453125}, {"start": 210.06, "end": 210.48, "word": " one", "probability": 0.64892578125}, {"start": 210.48, "end": 211.4, "word": " لو", "probability": 0.9306640625}, {"start": 211.4, "end": 211.92, "word": " كانت", 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سابقا", "tokens": [995, 34268, 28543, 16472, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 11331, 26108, 3660, 30767, 1829, 29538, 8608, 16758, 4587, 995], "avg_logprob": -0.3614130408867546, "compression_ratio": 1.0454545454545454, "no_speech_prob": 0.0, "words": [{"start": 259.73999999999995, "end": 260.46, "word": "اعتقد", "probability": 0.524169921875}, {"start": 260.46, "end": 260.56, "word": " ان", "probability": 0.8271484375}, {"start": 260.56, "end": 260.74, "word": " احنا", "probability": 0.7574869791666666}, {"start": 260.74, "end": 261.3, "word": " اثبتنا", "probability": 0.923046875}, {"start": 261.3, "end": 261.64, "word": " حاجة", "probability": 0.9083658854166666}, {"start": 261.64, "end": 261.88, "word": " زي", "probability": 0.917236328125}, {"start": 261.88, "end": 262.26, "word": " هذه", "probability": 0.85791015625}, {"start": 262.26, "end": 263.56, "word": " سابقا", "probability": 0.9810791015625}], "temperature": 1.0}, {"id": 10, "seek": 28149, "start": 268.77, "end": 281.49, "text": "حتى لو كان rational فby ال corollary النتيجة تبع ال density theorem ممكن اثبات ان يوجد sequence of irrationals ونهيتها العدد c", "tokens": [33753, 7578, 45164, 25961, 15090, 6156, 2322, 2423, 1181, 1833, 822, 28239, 31371, 7435, 3660, 6055, 3555, 3615, 2423, 10305, 20904, 3714, 43020, 1975, 12984, 3555, 9307, 16472, 7251, 29245, 3215, 8310, 295, 3418, 2405, 1124, 4032, 1863, 3224, 36081, 11296, 18863, 3215, 3215, 269], "avg_logprob": -0.27904212798761285, "compression_ratio": 1.2571428571428571, "no_speech_prob": 0.0, "words": [{"start": 268.77, "end": 269.19, "word": "حتى", "probability": 0.6533203125}, {"start": 269.19, "end": 269.31, "word": " لو", "probability": 0.97119140625}, {"start": 269.31, "end": 269.57, "word": " كان", "probability": 0.9833984375}, {"start": 269.57, "end": 270.07, "word": " rational", "probability": 0.88037109375}, {"start": 270.07, "end": 272.31, "word": " فby", "probability": 0.40966796875}, {"start": 272.31, "end": 272.67, "word": 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"probability": 0.91650390625}, {"start": 336.95, "end": 337.51, "word": " n", "probability": 0.92333984375}, {"start": 337.51, "end": 337.87, "word": " tends", "probability": 0.82568359375}, {"start": 337.87, "end": 338.13, "word": " to", "probability": 0.95703125}, {"start": 338.13, "end": 338.69, "word": " infinity", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 13, "seek": 34414, "start": 340.1, "end": 344.14, "text": "بساوي limit ثابت سفر بساوي سفر", "tokens": [3555, 3794, 995, 45865, 4948, 38637, 16758, 2655, 8608, 5172, 2288, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.2878289505055076, "compression_ratio": 1.0416666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 340.1, "end": 341.2, "word": "بساوي", "probability": 0.7178955078125}, {"start": 341.2, "end": 341.82, "word": " limit", "probability": 0.78759765625}, {"start": 341.82, "end": 342.78, "word": " ثابت", "probability": 0.89501953125}, {"start": 342.78, "end": 343.16, "word": " سفر", "probability": 0.7308756510416666}, {"start": 343.16, "end": 343.62, "word": " بساوي", "probability": 0.8507080078125}, {"start": 343.62, "end": 344.14, "word": " سفر", "probability": 0.9296875}], "temperature": 1.0}, {"id": 14, "seek": 37806, "start": 349.06, "end": 378.06, "text": "وهذا لا يساوي واحد اللي هو f of c ال c rational number ف f and c بيساوي واحد اذا هاي اندي انا اثبتت ان يوجد sequence xn في المجال تبع الدولة اللي هو R و ال sequence هذه converge ل c لكن ال limit لل image لل sequence لا تساوي f of c اذا by divergence criterion", "tokens": [2407, 3224, 15730, 20193, 7251, 3794, 995, 45865, 36764, 24401, 13672, 1829, 31439, 283, 295, 269, 2423, 269, 15090, 1230, 6156, 283, 293, 269, 4724, 1829, 3794, 995, 45865, 36764, 24401, 1975, 15730, 8032, 47302, 16472, 16254, 1975, 8315, 1975, 12984, 3555, 2655, 2655, 16472, 7251, 29245, 3215, 8310, 2031, 77, 8978, 9673, 7435, 6027, 6055, 3555, 3615, 32748, 12610, 3660, 13672, 1829, 31439, 497, 4032, 2423, 8310, 29538, 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" ال", "probability": 0.80615234375}, {"start": 354.5, "end": 354.78, "word": " c", "probability": 0.401611328125}, {"start": 354.78, "end": 355.48, "word": " rational", "probability": 0.4443359375}, {"start": 355.48, "end": 356.08, "word": " number", "probability": 0.97314453125}, {"start": 356.08, "end": 356.86, "word": " ف", "probability": 0.947265625}, {"start": 356.86, "end": 357.12, "word": " f", "probability": 0.27734375}, {"start": 357.12, "end": 357.36, "word": " and", "probability": 0.787109375}, {"start": 357.36, "end": 357.62, "word": " c", "probability": 0.95947265625}, {"start": 357.62, "end": 358.08, "word": " بيساوي", "probability": 0.830810546875}, {"start": 358.08, "end": 358.48, "word": " واحد", "probability": 0.992919921875}, {"start": 358.48, "end": 359.5, "word": " اذا", "probability": 0.70458984375}, {"start": 359.5, "end": 359.74, "word": " هاي", "probability": 0.599609375}, {"start": 359.74, "end": 360.06, "word": " اندي", "probability": 0.5897216796875}, {"start": 360.06, "end": 360.36, "word": " انا", "probability": 0.942138671875}, {"start": 360.36, "end": 361.08, "word": " اثبتت", "probability": 0.96015625}, {"start": 361.08, "end": 361.22, "word": " ان", "probability": 0.92822265625}, {"start": 361.22, "end": 361.8, "word": " يوجد", "probability": 0.8528645833333334}, {"start": 361.8, "end": 362.46, "word": " sequence", "probability": 0.94775390625}, {"start": 362.46, "end": 363.92, "word": " xn", "probability": 0.5916748046875}, {"start": 363.92, "end": 364.64, "word": " في", "probability": 0.87646484375}, {"start": 364.64, "end": 365.14, "word": " المجال", "probability": 0.9700520833333334}, {"start": 365.14, "end": 365.44, "word": " تبع", "probability": 0.8434244791666666}, {"start": 365.44, "end": 365.94, "word": " الدولة", "probability": 0.8899739583333334}, {"start": 365.94, "end": 366.1, "word": " اللي", "probability": 0.973876953125}, {"start": 366.1, "end": 366.36, "word": " هو", "probability": 0.95703125}, {"start": 366.36, "end": 366.74, "word": " R", "probability": 0.59814453125}, {"start": 366.74, "end": 367.86, "word": " و", "probability": 0.44873046875}, {"start": 367.86, "end": 368.02, "word": " ال", "probability": 0.69580078125}, {"start": 368.02, "end": 368.36, "word": " sequence", "probability": 0.98681640625}, {"start": 368.36, "end": 368.68, "word": " هذه", "probability": 0.33642578125}, {"start": 368.68, "end": 369.26, "word": " converge", "probability": 0.8994140625}, {"start": 369.26, "end": 369.44, "word": " ل", "probability": 0.9384765625}, {"start": 369.44, "end": 369.8, "word": " c", "probability": 0.477294921875}, {"start": 369.8, "end": 370.86, "word": " لكن", "probability": 0.900390625}, {"start": 370.86, "end": 371.34, "word": " ال", "probability": 0.74462890625}, {"start": 371.34, "end": 371.64, "word": " limit", "probability": 0.97265625}, {"start": 371.64, "end": 371.88, "word": " لل", "probability": 0.88916015625}, {"start": 371.88, "end": 372.18, "word": " image", "probability": 0.80908203125}, {"start": 372.18, "end": 372.42, "word": " لل", "probability": 0.75439453125}, {"start": 372.42, "end": 373.04, "word": " sequence", "probability": 0.984375}, {"start": 373.04, "end": 373.74, "word": " لا", "probability": 0.7099609375}, {"start": 373.74, "end": 374.5, "word": " تساوي", "probability": 0.974853515625}, {"start": 374.5, "end": 374.86, "word": " f", "probability": 0.892578125}, {"start": 374.86, "end": 375.08, "word": " of", "probability": 0.95751953125}, {"start": 375.08, "end": 375.38, "word": " c", "probability": 0.95751953125}, {"start": 375.38, "end": 376.3, "word": " اذا", "probability": 0.876953125}, {"start": 376.3, "end": 376.66, "word": " by", "probability": 0.93994140625}, {"start": 376.66, "end": 377.36, "word": " divergence", "probability": 0.94482421875}, {"start": 377.36, "end": 378.06, "word": " criterion", "probability": 0.951171875}], "temperature": 1.0}, {"id": 15, "seek": 40775, "start": 379.69, "end": 407.75, "text": "أو by discontinuity criterion اذا by discontinuity criterion if is discontinuous is discontinuous at C في الحالة اللي هي C rational number في الحالة التانية", "tokens": [10721, 2407, 538, 31420, 21757, 46691, 1975, 15730, 538, 31420, 21757, 46691, 498, 307, 31420, 12549, 307, 31420, 12549, 412, 383, 8978, 21542, 6027, 3660, 13672, 1829, 39896, 383, 15090, 1230, 8978, 21542, 6027, 3660, 16712, 7649, 10632], "avg_logprob": -0.19310897817978492, "compression_ratio": 1.6379310344827587, "no_speech_prob": 0.0, "words": [{"start": 379.69, "end": 380.53, "word": "أو", "probability": 0.61590576171875}, {"start": 380.53, "end": 380.81, "word": " by", "probability": 0.75146484375}, {"start": 380.81, "end": 381.81, "word": " discontinuity", "probability": 0.921630859375}, {"start": 381.81, "end": 382.49, "word": " criterion", "probability": 0.95263671875}, {"start": 382.49, "end": 382.97, "word": " اذا", "probability": 0.6707763671875}, {"start": 382.97, "end": 384.89, "word": " by", "probability": 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{"start": 423.51, "end": 424.23, "word": " نفسها", "probability": 0.8836263020833334}, {"start": 424.23, "end": 424.67, "word": " use", "probability": 0.6240234375}, {"start": 424.67, "end": 425.33, "word": " density", "probability": 0.931640625}, {"start": 425.33, "end": 426.03, "word": " theorem", "probability": 0.85546875}, {"start": 426.03, "end": 429.13, "word": " to", "probability": 0.92431640625}, {"start": 429.13, "end": 430.05, "word": " choose", "probability": 0.93603515625}, {"start": 430.05, "end": 433.71, "word": " a", "probability": 0.9306640625}, {"start": 433.71, "end": 434.49, "word": " sequence", "probability": 0.98388671875}, {"start": 434.49, "end": 436.43, "word": " x", "probability": 0.75146484375}, {"start": 436.43, "end": 436.97, "word": " in", "probability": 0.45263671875}, {"start": 436.97, "end": 438.15, "word": " contained", "probability": 0.54443359375}], "temperature": 1.0}, {"id": 17, "seek": 46392, "start": 439.76, "end": 463.92, "text": "of rational numbers contained in Q يعني ال sequence هذه عناصرها rational numbers بحيث انه ال limit لل sequence x in as n tends to infinity بساوي c هذا أثبتناه في المحاضرة السابقة وبالتالي so", "tokens": [2670, 15090, 3547, 16212, 294, 1249, 37495, 22653, 2423, 8310, 29538, 18871, 33546, 2288, 11296, 15090, 3547, 4724, 5016, 1829, 12984, 16472, 3224, 2423, 4948, 24976, 8310, 2031, 294, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 269, 23758, 5551, 12984, 3555, 2655, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 46599, 6027, 2655, 6027, 1829, 370], "avg_logprob": -0.24244364167823165, "compression_ratio": 1.4357541899441342, "no_speech_prob": 0.0, "words": [{"start": 439.76, "end": 440.1, "word": "of", "probability": 0.4912109375}, {"start": 440.1, "end": 440.58, "word": " rational", "probability": 0.85107421875}, {"start": 440.58, "end": 441.28, "word": " numbers", "probability": 0.8486328125}, {"start": 441.28, "end": 441.7, "word": " contained", "probability": 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"end": 447.8, "word": " limit", "probability": 0.939453125}, {"start": 447.8, "end": 449.32, "word": " لل", "probability": 0.23046875}, {"start": 449.32, "end": 450.02, "word": " sequence", "probability": 0.96533203125}, {"start": 450.02, "end": 450.44, "word": " x", "probability": 0.61572265625}, {"start": 450.44, "end": 451.02, "word": " in", "probability": 0.476806640625}, {"start": 451.02, "end": 451.56, "word": " as", "probability": 0.82470703125}, {"start": 451.56, "end": 451.88, "word": " n", "probability": 0.626953125}, {"start": 451.88, "end": 452.14, "word": " tends", "probability": 0.73876953125}, {"start": 452.14, "end": 452.28, "word": " to", "probability": 0.857421875}, {"start": 452.28, "end": 452.86, "word": " infinity", "probability": 0.88134765625}, {"start": 452.86, "end": 453.8, "word": " بساوي", "probability": 0.8826904296875}, {"start": 453.8, "end": 454.24, "word": " c", "probability": 0.487060546875}, {"start": 454.24, "end": 454.84, "word": " هذا", "probability": 0.82080078125}, {"start": 454.84, "end": 455.96, "word": " أثبتناه", "probability": 0.8940022786458334}, {"start": 455.96, "end": 456.26, "word": " في", "probability": 0.9599609375}, {"start": 456.26, "end": 456.78, "word": " المحاضرة", "probability": 0.9085693359375}, {"start": 456.78, "end": 457.38, "word": " السابقة", "probability": 0.9855143229166666}, {"start": 457.38, "end": 462.48, "word": " وبالتالي", "probability": 0.890283203125}, {"start": 462.48, "end": 463.92, "word": " so", "probability": 0.814453125}], "temperature": 1.0}, {"id": 18, "seek": 48120, "start": 466.98, "end": 481.2, "text": "أنا عندي بما أنه ال Xn rationals ف F of Xn بتساوي واحد لكل N هذا بيقدي انه limit ل F of Xn as N tends to infinity", "tokens": [10721, 8315, 18871, 16254, 4724, 15042, 14739, 3224, 2423, 1783, 77, 24258, 1124, 6156, 479, 295, 1783, 77, 39894, 3794, 995, 45865, 36764, 24401, 5296, 28820, 426, 23758, 4724, 1829, 4587, 16254, 16472, 3224, 4948, 5296, 479, 295, 1783, 77, 382, 426, 12258, 281, 13202], "avg_logprob": -0.43070652886577276, "compression_ratio": 1.1846153846153846, "no_speech_prob": 0.0, "words": [{"start": 466.98, "end": 467.36, "word": "أنا", "probability": 0.4842529296875}, {"start": 467.36, "end": 467.74, "word": " عندي", "probability": 0.822509765625}, {"start": 467.74, "end": 468.04, "word": " بما", "probability": 0.73388671875}, {"start": 468.04, "end": 468.28, "word": " أنه", "probability": 0.4593505859375}, {"start": 468.28, "end": 468.36, "word": " ال", "probability": 0.77880859375}, {"start": 468.36, "end": 468.82, "word": " Xn", "probability": 0.37158203125}, {"start": 468.82, "end": 469.6, "word": " rationals", "probability": 0.59075927734375}, {"start": 469.6, "end": 469.8, "word": " ف", "probability": 0.2783203125}, {"start": 469.8, "end": 470.22, "word": " F", "probability": 0.2568359375}, {"start": 470.22, "end": 470.46, "word": " of", "probability": 0.499267578125}, {"start": 470.46, "end": 471.22, "word": " Xn", "probability": 0.914794921875}, {"start": 471.22, "end": 472.62, "word": " بتساوي", "probability": 0.556396484375}, {"start": 472.62, "end": 473.12, "word": " واحد", "probability": 0.951416015625}, {"start": 473.12, "end": 473.62, "word": " لكل", "probability": 0.983642578125}, {"start": 473.62, "end": 473.92, "word": " N", "probability": 0.51904296875}, {"start": 473.92, "end": 474.28, "word": " هذا", "probability": 0.60302734375}, {"start": 474.28, "end": 474.9, "word": " بيقدي", "probability": 0.67352294921875}, {"start": 474.9, "end": 475.82, "word": " انه", "probability": 0.6346435546875}, {"start": 475.82, "end": 476.26, "word": " limit", "probability": 0.724609375}, {"start": 476.26, "end": 478.02, "word": " ل", "probability": 0.84765625}, {"start": 478.02, "end": 478.34, "word": " F", "probability": 0.6669921875}, {"start": 478.34, "end": 478.58, "word": " of", "probability": 0.96044921875}, {"start": 478.58, "end": 479.46, "word": " Xn", "probability": 0.93359375}, {"start": 479.46, "end": 479.96, "word": " as", "probability": 0.8125}, {"start": 479.96, "end": 480.28, "word": " N", "probability": 0.89013671875}, {"start": 480.28, "end": 480.54, "word": " tends", "probability": 0.8115234375}, {"start": 480.54, "end": 480.72, "word": " to", "probability": 0.9423828125}, {"start": 480.72, "end": 481.2, "word": " infinity", "probability": 0.85888671875}], "temperature": 1.0}, {"id": 19, "seek": 50361, "start": 482.29, "end": 503.61, "text": "بساوي limit ثابت واحد بطلع واحد واحد لا يساوي سفر اللي هو ال image ل ال C ال C هنا irrational و من ال definition of the function if and irrational بساوي سفر اذا انا هنا اثبتت ان يوجد sequence", "tokens": [3555, 3794, 995, 45865, 4948, 38637, 16758, 2655, 36764, 24401, 4724, 9566, 1211, 3615, 36764, 24401, 36764, 24401, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 13672, 1829, 31439, 2423, 3256, 5296, 2423, 383, 2423, 383, 34105, 39914, 4032, 9154, 2423, 7123, 295, 264, 2445, 498, 293, 39914, 4724, 3794, 995, 45865, 8608, 5172, 2288, 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"probability": 0.7978515625}, {"start": 487.73, "end": 488.63, "word": " اللي", "probability": 0.781005859375}, {"start": 488.63, "end": 489.05, "word": " هو", "probability": 0.97314453125}, {"start": 489.05, "end": 489.93, "word": " ال", "probability": 0.828125}, {"start": 489.93, "end": 490.31, "word": " image", "probability": 0.861328125}, {"start": 490.31, "end": 490.61, "word": " ل", "probability": 0.5322265625}, {"start": 490.61, "end": 490.91, "word": " ال", "probability": 0.412353515625}, {"start": 490.91, "end": 491.21, "word": " C", "probability": 0.442626953125}, {"start": 491.21, "end": 492.19, "word": " ال", "probability": 0.90087890625}, {"start": 492.19, "end": 492.39, "word": " C", "probability": 0.94287109375}, {"start": 492.39, "end": 492.71, "word": " هنا", "probability": 0.982421875}, {"start": 492.71, "end": 493.17, "word": " irrational", "probability": 0.67578125}, {"start": 493.17, "end": 494.09, "word": " و", "probability": 0.92236328125}, {"start": 494.09, "end": 494.23, "word": " من", "probability": 0.82373046875}, {"start": 494.23, "end": 494.37, "word": " ال", "probability": 0.900390625}, {"start": 494.37, "end": 494.85, "word": " definition", "probability": 0.962890625}, {"start": 494.85, "end": 496.15, "word": " of", "probability": 0.96240234375}, {"start": 496.15, "end": 496.35, "word": " the", "probability": 0.89208984375}, {"start": 496.35, "end": 496.87, "word": " function", "probability": 0.95556640625}, {"start": 496.87, "end": 497.17, "word": " if", "probability": 0.374755859375}, {"start": 497.17, "end": 497.47, "word": " and", "probability": 0.94482421875}, {"start": 497.47, "end": 497.95, "word": " irrational", "probability": 0.7431640625}, {"start": 497.95, "end": 498.35, "word": " بساوي", "probability": 0.8800048828125}, {"start": 498.35, "end": 498.69, "word": " سفر", "probability": 0.9884440104166666}, {"start": 498.69, "end": 498.95, "word": " اذا", "probability": 0.5279541015625}, {"start": 498.95, "end": 499.17, "word": " انا", "probability": 0.654541015625}, {"start": 499.17, "end": 499.45, "word": " هنا", "probability": 0.59228515625}, {"start": 499.45, "end": 500.77, "word": " اثبتت", "probability": 0.96630859375}, {"start": 500.77, "end": 500.93, "word": " ان", "probability": 0.853515625}, {"start": 500.93, "end": 501.73, "word": " يوجد", "probability": 0.8723958333333334}, {"start": 501.73, "end": 503.61, "word": " sequence", "probability": 0.368896484375}], "temperature": 1.0}, {"id": 20, "seek": 53015, "start": 505.71, "end": 530.15, "text": "في مجال الدالة نهايتها c لكن نهاية صورتها لا تساوي صورة ال c كمان مرة hence by discontinuity by discontinuity criterion", "tokens": [41185, 3714, 7435, 6027, 32748, 6027, 3660, 8717, 11296, 36081, 11296, 269, 44381, 8717, 11296, 10632, 20328, 13063, 2655, 11296, 20193, 6055, 3794, 995, 45865, 20328, 13063, 3660, 2423, 269, 9122, 2304, 7649, 3714, 25720, 16678, 538, 31420, 21757, 538, 31420, 21757, 46691], "avg_logprob": -0.12579900195652788, 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512.97, "word": " ال", "probability": 0.8134765625}, {"start": 512.97, "end": 513.27, "word": " c", "probability": 0.603515625}, {"start": 513.27, "end": 515.05, "word": " كمان", "probability": 0.9309895833333334}, {"start": 515.05, "end": 515.51, "word": " مرة", "probability": 0.986572265625}, {"start": 515.51, "end": 517.13, "word": " hence", "probability": 0.57861328125}, {"start": 517.13, "end": 521.75, "word": " by", "probability": 0.92919921875}, {"start": 521.75, "end": 524.57, "word": " discontinuity", "probability": 0.91162109375}, {"start": 524.57, "end": 527.79, "word": " by", "probability": 0.92041015625}, {"start": 527.79, "end": 529.25, "word": " discontinuity", "probability": 0.926513671875}, {"start": 529.25, "end": 530.15, "word": " criterion", "probability": 0.97021484375}], "temperature": 1.0}, {"id": 21, "seek": 56066, "start": 532.89, "end": 560.67, "text": "الـ function f is discontinuous at c لأن بما أن c was arbitrary فالـ function is discontinuous عن كل real number c طبعا في الحالتين لأن هذا بكمل البرهانة لأن هذه ال function هي function من R لR", "tokens": [6027, 39184, 2445, 283, 307, 31420, 12549, 412, 269, 5296, 33456, 4724, 15042, 14739, 269, 390, 23211, 6156, 6027, 39184, 2445, 307, 31420, 12549, 18871, 28242, 957, 1230, 269, 23032, 3555, 3615, 995, 8978, 21542, 6027, 2655, 9957, 5296, 33456, 23758, 4724, 24793, 1211, 2423, 26890, 3224, 7649, 3660, 5296, 33456, 29538, 2423, 2445, 39896, 2445, 9154, 497, 5296, 49], "avg_logprob": -0.31762294104841887, "compression_ratio": 1.5297619047619047, "no_speech_prob": 0.0, "words": [{"start": 532.89, "end": 533.23, "word": "الـ", "probability": 0.5560302734375}, {"start": 533.23, "end": 533.63, "word": " function", "probability": 0.74755859375}, {"start": 533.63, "end": 534.13, "word": " f", "probability": 0.455078125}, {"start": 534.13, "end": 534.77, "word": " is", "probability": 0.87060546875}, {"start": 534.77, "end": 536.83, "word": " discontinuous", "probability": 0.876220703125}, 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566.77, "word": " هذه", "probability": 0.53369140625}, {"start": 566.77, "end": 566.95, "word": " ال", "probability": 0.95654296875}, {"start": 566.95, "end": 567.25, "word": " function", "probability": 0.75146484375}, {"start": 567.25, "end": 567.63, "word": " لها", "probability": 0.6385498046875}, {"start": 567.63, "end": 568.01, "word": " اسم", "probability": 0.90380859375}, {"start": 568.01, "end": 568.73, "word": " ومشهورة", "probability": 0.800048828125}, {"start": 568.73, "end": 569.67, "word": " ومعروفة", "probability": 0.9884440104166666}, {"start": 569.67, "end": 570.45, "word": " اسمها", "probability": 0.97119140625}, {"start": 570.45, "end": 571.03, "word": " Dirichlet", "probability": 0.93408203125}, {"start": 571.03, "end": 572.13, "word": " function", "probability": 0.89892578125}, {"start": 572.13, "end": 575.21, "word": " اذا", "probability": 0.516265869140625}, {"start": 575.21, "end": 575.63, "word": " ال", "probability": 0.84619140625}, {"start": 575.63, "end": 577.25, "word": " function", "probability": 0.68115234375}, {"start": 577.25, "end": 577.79, "word": " هذه", "probability": 0.6484375}, {"start": 577.79, "end": 581.11, "word": " remark", "probability": 0.8017578125}, {"start": 581.11, "end": 586.87, "word": " the", "probability": 0.450439453125}, {"start": 586.87, "end": 588.97, "word": " above", "probability": 0.96044921875}, {"start": 588.97, "end": 589.61, "word": " function", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 23, "seek": 62000, "start": 595.06, "end": 620.0, "text": "function is well-known as Dirichlet Dirichlet دا عالم رياضيات Dirichlet is function او Dirichlet is discontinuous function", "tokens": [22845, 307, 731, 12, 6861, 382, 34422, 480, 2631, 34422, 480, 2631, 11778, 995, 6225, 45340, 12602, 1829, 46958, 1829, 9307, 34422, 480, 2631, 307, 2445, 1975, 2407, 34422, 480, 2631, 307, 31420, 12549, 2445], "avg_logprob": -0.2489149197936058, "compression_ratio": 1.3979591836734695, "no_speech_prob": 0.0, 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" C", "probability": 0.88818359375}, {"start": 724.23, "end": 725.73, "word": " exist", "probability": 0.55615234375}, {"start": 725.73, "end": 725.97, "word": " و", "probability": 0.67529296875}, {"start": 725.97, "end": 726.73, "word": " بساوي", "probability": 0.8067626953125}, {"start": 726.73, "end": 727.13, "word": " F", "probability": 0.95849609375}, {"start": 727.13, "end": 727.35, "word": " of", "probability": 0.6533203125}, {"start": 727.35, "end": 727.67, "word": " C", "probability": 0.958984375}, {"start": 727.67, "end": 728.41, "word": " اللي", "probability": 0.894775390625}, {"start": 728.41, "end": 728.59, "word": " هو", "probability": 0.98583984375}, {"start": 728.59, "end": 729.11, "word": " الشرط", "probability": 0.9510091145833334}, {"start": 729.11, "end": 729.49, "word": " هذا", "probability": 0.8134765625}, {"start": 729.49, "end": 731.03, "word": " هذا", "probability": 0.3935546875}, {"start": 731.03, "end": 731.49, "word": " الشرط", "probability": 0.9609375}, {"start": 731.49, "end": 731.95, "word": " سمنها", "probability": 0.7063802083333334}, {"start": 731.95, "end": 732.43, "word": " تلاتة", "probability": 0.9073486328125}, {"start": 732.43, "end": 732.55, "word": " في", "probability": 0.90283203125}, {"start": 732.55, "end": 733.01, "word": " واحد", "probability": 0.994384765625}, {"start": 733.01, "end": 733.83, "word": " هذا", "probability": 0.8388671875}, {"start": 733.83, "end": 735.49, "word": " يتضمن", "probability": 0.9912109375}, {"start": 735.49, "end": 735.81, "word": " تلات", "probability": 0.9104817708333334}, {"start": 735.81, "end": 736.23, "word": " شروط", "probability": 0.8484700520833334}, {"start": 736.23, "end": 736.41, "word": " ال", "probability": 0.43896484375}, {"start": 736.41, "end": 736.73, "word": " limit", "probability": 0.94140625}, {"start": 736.73, "end": 736.99, "word": " and", "probability": 0.50244140625}, {"start": 736.99, "end": 737.35, "word": " C", "probability": 0.8095703125}, {"start": 737.35, 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function بتكونش continuous and النقطة c ف sometimes the function can be discontinuous at x بساوي c because", "tokens": [6027, 7649, 45164, 1975, 1829, 36764, 24401, 9154, 16712, 1211, 9307, 25124, 32887, 9566, 8032, 3215, 12610, 1975, 46456, 1211, 6156, 6027, 2445, 39894, 30544, 8592, 10957, 293, 28239, 47432, 3660, 269, 6156, 2171, 264, 2445, 393, 312, 31420, 12549, 412, 2031, 4724, 3794, 995, 45865, 269, 570], "avg_logprob": -0.24346301020408162, "compression_ratio": 1.368421052631579, "no_speech_prob": 0.0, "words": [{"start": 744.59, "end": 745.25, "word": "الان", "probability": 0.705322265625}, {"start": 745.25, "end": 746.25, "word": " لو", "probability": 0.68212890625}, {"start": 746.25, "end": 746.53, "word": " اي", "probability": 0.81689453125}, {"start": 746.53, "end": 746.83, "word": " واحد", "probability": 0.99169921875}, {"start": 746.83, "end": 747.01, "word": " من", "probability": 0.99169921875}, {"start": 747.01, "end": 747.39, "word": " التلات", "probability": 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{"start": 752.69, "end": 753.53, "word": " the", "probability": 0.66259765625}, {"start": 753.53, "end": 754.09, "word": " function", "probability": 0.97998046875}, {"start": 754.09, "end": 756.37, "word": " can", "probability": 0.9150390625}, {"start": 756.37, "end": 758.91, "word": " be", "probability": 0.95849609375}, {"start": 758.91, "end": 762.49, "word": " discontinuous", "probability": 0.81884765625}, {"start": 762.49, "end": 763.09, "word": " at", "probability": 0.92041015625}, {"start": 763.09, "end": 763.73, "word": " x", "probability": 0.845703125}, {"start": 763.73, "end": 764.47, "word": " بساوي", "probability": 0.84326171875}, {"start": 764.47, "end": 764.93, "word": " c", "probability": 0.90380859375}, {"start": 764.93, "end": 766.97, "word": " because", "probability": 0.896484375}], "temperature": 1.0}, {"id": 29, "seek": 79703, "start": 769.45, "end": 797.03, "text": "if is undefined is undefined at C لكن أحيانا أخرى وفي الحالة اللي بقدرش أعمل حاجة بقدرش أعمل حاجة however", "tokens": [351, 307, 674, 5666, 2001, 307, 674, 5666, 2001, 412, 383, 44381, 5551, 5016, 1829, 7649, 995, 5551, 34740, 7578, 4032, 41185, 21542, 6027, 3660, 13672, 1829, 4724, 28543, 2288, 8592, 5551, 25957, 1211, 11331, 26108, 3660, 4724, 28543, 2288, 8592, 5551, 25957, 1211, 11331, 26108, 3660, 4461], "avg_logprob": -0.15369898445752203, "compression_ratio": 1.3893805309734513, "no_speech_prob": 0.0, "words": [{"start": 769.45, "end": 769.99, "word": "if", "probability": 0.3583984375}, {"start": 769.99, "end": 770.65, "word": " is", "probability": 0.921875}, {"start": 770.65, "end": 771.67, "word": " undefined", "probability": 0.8650716145833334}, {"start": 771.67, "end": 773.45, "word": " is", "probability": 0.7373046875}, {"start": 773.45, "end": 775.21, "word": " undefined", "probability": 0.8880208333333334}, {"start": 775.21, "end": 776.11, "word": " at", "probability": 0.9013671875}, {"start": 776.11, "end": 777.85, "word": " C", "probability": 0.53857421875}, 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"probability": 0.939453125}, {"start": 920.59, "end": 921.05, "word": " يعني", "probability": 0.95556640625}, {"start": 921.05, "end": 921.29, "word": " x", "probability": 0.9306640625}, {"start": 921.29, "end": 921.45, "word": " and", "probability": 0.1435546875}, {"start": 921.45, "end": 921.65, "word": " time", "probability": 0.66552734375}, {"start": 921.65, "end": 921.83, "word": " ل", "probability": 0.57568359375}, {"start": 921.83, "end": 921.99, "word": " a", "probability": 0.74072265625}], "temperature": 1.0}, {"id": 34, "seek": 94307, "start": 924.01, "end": 943.07, "text": "فcapital F هي نفسها حسب تعريفها هي small f طب احنا فرضين ان ال limit ل F of X exist و بساوي and C و بساوي L، إذن هذه تطلع موجودة و بساوي L", "tokens": [5172, 9485, 1686, 479, 39896, 8717, 36178, 11296, 11331, 35457, 37279, 16572, 5172, 11296, 39896, 1359, 283, 23032, 3555, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 2423, 4948, 5296, 479, 295, 1783, 2514, 4032, 4724, 3794, 995, 45865, 293, 383, 4032, 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{"start": 1051.55, "end": 1052.23, "word": " اقيد", "probability": 0.8976236979166666}, {"start": 1052.23, "end": 1053.21, "word": " او", "probability": 0.968017578125}, {"start": 1053.21, "end": 1054.01, "word": " احصر", "probability": 0.959716796875}, {"start": 1054.01, "end": 1054.81, "word": " الدولة", "probability": 0.7215983072916666}, {"start": 1054.81, "end": 1055.13, "word": " capital", "probability": 0.6875}, {"start": 1055.13, "end": 1055.35, "word": " F", "probability": 0.9453125}, {"start": 1055.35, "end": 1055.49, "word": " على", "probability": 0.7099609375}, {"start": 1055.49, "end": 1056.03, "word": " المجموعة", "probability": 0.91064453125}, {"start": 1056.03, "end": 1056.25, "word": " a", "probability": 0.88916015625}, {"start": 1056.25, "end": 1056.73, "word": " فقط", "probability": 0.996337890625}, {"start": 1056.73, "end": 1057.77, "word": " فهي", "probability": 0.98681640625}, {"start": 1057.77, "end": 1058.07, "word": " نفس", "probability": 0.996826171875}, {"start": 1058.07, "end": 1058.23, "word": " ال", "probability": 0.7265625}, {"start": 1058.23, "end": 1058.39, "word": " F", "probability": 0.496337890625}, {"start": 1058.39, "end": 1058.65, "word": " هي", "probability": 0.67041015625}, {"start": 1058.65, "end": 1059.65, "word": " لكل", "probability": 0.914306640625}, {"start": 1059.65, "end": 1059.99, "word": " x", "probability": 0.712890625}, {"start": 1059.99, "end": 1060.43, "word": " a", "probability": 0.6181640625}, {"start": 1060.43, "end": 1061.31, "word": " capital", "probability": 0.41064453125}, {"start": 1061.31, "end": 1061.61, "word": " F", "probability": 0.9501953125}, {"start": 1061.61, "end": 1061.79, "word": " هي", "probability": 0.87060546875}, {"start": 1061.79, "end": 1062.13, "word": " small", "probability": 0.91015625}, {"start": 1062.13, "end": 1062.49, "word": " f", "probability": 0.91650390625}], "temperature": 1.0}, {"id": 39, "seek": 107611, "start": 1063.84, "end": 1076.12, "text": "الزيادة ان capital F معرفة عن C و F مش معرفة عن C فهذه الدالة capital F بنسميها توسعة على small f التوسعة هذه متصلة عند النقطة C", "tokens": [6027, 11622, 1829, 18513, 3660, 16472, 4238, 479, 20449, 28480, 3660, 18871, 383, 4032, 479, 37893, 20449, 28480, 3660, 18871, 383, 6156, 3224, 24192, 32748, 6027, 3660, 4238, 479, 44945, 38251, 1829, 11296, 33427, 3794, 27884, 15844, 1359, 283, 16712, 41779, 27884, 29538, 44650, 36520, 3660, 43242, 28239, 47432, 3660, 383], "avg_logprob": -0.2283653783110472, "compression_ratio": 1.4817518248175183, "no_speech_prob": 0.0, "words": [{"start": 1063.8400000000001, "end": 1064.44, "word": "الزيادة", "probability": 0.98076171875}, {"start": 1064.44, "end": 1064.62, "word": " ان", "probability": 0.55419921875}, {"start": 1064.62, "end": 1065.0, "word": " capital", "probability": 0.174560546875}, {"start": 1065.0, "end": 1065.24, "word": " F", "probability": 0.869140625}, {"start": 1065.24, "end": 1065.74, "word": " معرفة", "probability": 0.8994140625}, {"start": 1065.74, 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إذا لو كانت الدالة مش معرفة لو كانت small f مش معرفة عن c لكن نهايتها عن c موجودة وبالساوي عدد L فبقدر أعرف دالة جديدة capital F اللي هي توسعة extension ل small f و ال extension الدالة هذه اللي هي توسعة", "tokens": [39237, 10943, 22807, 11933, 15730, 29538, 5551, 12610, 3714, 15040, 5016, 19913, 3660, 11933, 15730, 45164, 25961, 2655, 32748, 6027, 3660, 37893, 20449, 28480, 3660, 45164, 25961, 2655, 1359, 283, 37893, 20449, 28480, 3660, 18871, 269, 44381, 8717, 11296, 36081, 11296, 18871, 269, 3714, 29245, 23328, 3660, 46599, 6027, 3794, 995, 45865, 6225, 3215, 3215, 441, 6156, 3555, 28543, 2288, 5551, 3615, 28480, 11778, 6027, 3660, 10874, 16254, 41891, 4238, 479, 13672, 1829, 39896, 33427, 3794, 27884, 10320, 5296, 1359, 283, 4032, 2423, 10320, 32748, 6027, 3660, 29538, 13672, 1829, 39896, 33427, 3794, 27884], "avg_logprob": -0.16957237124443053, "compression_ratio": 1.7766990291262137, "no_speech_prob": 0.0, "words": [{"start": 1079.22, "end": 1080.08, "word": "تمام؟", 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1119.62, "text": "بتكون متصلة عند الـ C اننا ناخد قيمتها عند الـ C بساوي قيمة ال limit و عند النقاط ال A هي نفس small if لكن الملاحظة التانية", "tokens": [3555, 2655, 30544, 44650, 36520, 3660, 43242, 2423, 39184, 383, 16472, 8315, 8717, 47283, 3215, 12174, 32640, 2655, 11296, 43242, 2423, 39184, 383, 4724, 3794, 995, 45865, 12174, 32640, 3660, 2423, 4948, 4032, 43242, 28239, 4587, 41193, 2423, 316, 39896, 8717, 36178, 1359, 498, 44381, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632], "avg_logprob": -0.24262153219293664, "compression_ratio": 1.4539007092198581, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1103.2, "end": 1103.8, "word": "بتكون", "probability": 0.8118489583333334}, {"start": 1103.8, "end": 1104.48, "word": " متصلة", "probability": 0.9034830729166666}, {"start": 1104.48, "end": 1104.64, "word": " عند", "probability": 0.90234375}, {"start": 1104.64, "end": 1104.82, "word": " الـ", "probability": 0.5206298828125}, {"start": 1104.82, "end": 1104.98, 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معرفة عن C يعني هنا sometimes a function g is discontinuous a function g from A to R is discontinuous at C", "tokens": [1211, 2407, 25961, 2655, 2423, 18513, 6027, 3660, 4386, 3714, 43020, 6055, 30544, 2423, 18513, 6027, 3660, 20449, 28480, 3660, 18871, 383, 37495, 22653, 34105, 2171, 257, 2445, 290, 307, 31420, 12549, 257, 2445, 290, 490, 316, 281, 497, 307, 31420, 12549, 412, 383], "avg_logprob": -0.2031250066227383, "compression_ratio": 1.3909774436090225, "no_speech_prob": 0.0, "words": [{"start": 1131.35, "end": 1131.77, "word": "لو", "probability": 0.60491943359375}, {"start": 1131.77, "end": 1132.39, "word": " كانت", "probability": 0.9658203125}, {"start": 1132.39, "end": 1133.35, "word": " الادالة", "probability": 0.75732421875}, {"start": 1133.35, "end": 1133.35, "word": " ..", "probability": 0.357177734375}, {"start": 1133.35, "end": 1133.65, "word": " ممكن", "probability": 0.891357421875}, {"start": 1133.65, "end": 1133.89, "word": " تكون", "probability": 0.981201171875}, 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"text": "بسبب و ال c ممكن تكون موجودة في a او حتى لو مش موجودة في a is discontinuous at c because ال limit ل g of x as x tends to c does not exist يعني ممكن ال g تكون معرفة and ال c لكن", "tokens": [3555, 35457, 3555, 4032, 2423, 269, 3714, 43020, 6055, 30544, 3714, 29245, 23328, 3660, 8978, 257, 1975, 2407, 11331, 49975, 45164, 37893, 3714, 29245, 23328, 3660, 8978, 257, 307, 31420, 12549, 412, 269, 570, 2423, 4948, 5296, 290, 295, 2031, 382, 2031, 12258, 281, 269, 775, 406, 2514, 37495, 22653, 3714, 43020, 2423, 290, 6055, 30544, 20449, 28480, 3660, 293, 2423, 269, 44381], "avg_logprob": -0.21459961216896772, "compression_ratio": 1.4817073170731707, "no_speech_prob": 0.0, "words": [{"start": 1159.59, "end": 1160.35, "word": "بسبب", "probability": 0.5301920572916666}, {"start": 1160.35, "end": 1161.11, "word": " و", "probability": 0.2230224609375}, {"start": 1161.11, "end": 1161.29, "word": " ال", "probability": 0.57958984375}, {"start": 1161.29, "end": 1161.45, "word": " c", 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{"start": 1442.99, "end": 1443.17, "word": " عند", "probability": 0.9345703125}, {"start": 1443.17, "end": 1443.73, "word": " النقطة", "probability": 0.9873046875}, {"start": 1443.73, "end": 1444.91, "word": " فماقدرش", "probability": 0.8609375}, {"start": 1444.91, "end": 1445.51, "word": " أعرف", "probability": 0.7882486979166666}, {"start": 1445.51, "end": 1446.83, "word": " continuous", "probability": 0.9541015625}, {"start": 1446.83, "end": 1447.85, "word": " extension", "probability": 0.97021484375}, {"start": 1447.85, "end": 1449.49, "word": " لدالة", "probability": 0.831787109375}, {"start": 1449.49, "end": 1451.19, "word": " and", "probability": 0.6494140625}, {"start": 1451.19, "end": 1451.99, "word": " النقطة", "probability": 0.9651692708333334}, {"start": 1451.99, "end": 1452.19, "word": " C", "probability": 0.67138671875}], "temperature": 1.0}, {"id": 54, "seek": 148057, "start": 1453.43, "end": 1480.57, "text": "لأن هنا فرضنا أن هناك extension هذا ال extension مش ممكن يكون continuous عند النقطة C لأنه لو كان continuous عند النقطة C سيقدر ان الملمت الدالة small g and c exist وهذا يتناقض مع الفرض تمام، هذا النوع من ال discontinuity لما تكون الدالة discontinuous لعدم", "tokens": [1211, 33456, 34105, 6156, 43042, 8315, 14739, 34105, 4117, 10320, 23758, 2423, 10320, 37893, 3714, 43020, 7251, 30544, 10957, 43242, 28239, 47432, 3660, 383, 5296, 33456, 3224, 45164, 25961, 10957, 43242, 28239, 47432, 3660, 383, 8608, 1829, 4587, 3215, 2288, 16472, 9673, 19528, 2655, 32748, 6027, 3660, 1359, 290, 293, 269, 2514, 37037, 15730, 7251, 2655, 8315, 4587, 11242, 20449, 27188, 43042, 46811, 10943, 12399, 23758, 28239, 45367, 9154, 2423, 31420, 21757, 5296, 15042, 6055, 30544, 32748, 6027, 3660, 31420, 12549, 5296, 22488, 2304], "avg_logprob": -0.36268380950478946, "compression_ratio": 1.8246445497630333, "no_speech_prob": 0.0, "words": [{"start": 1453.43, "end": 1453.85, "word": "لأن", "probability": 0.50653076171875}, {"start": 1453.85, "end": 1454.05, "word": " هنا", "probability": 0.5576171875}, {"start": 1454.05, "end": 1454.53, "word": " فرضنا", "probability": 0.94384765625}, {"start": 1454.53, "end": 1455.23, "word": " أن", "probability": 0.315673828125}, {"start": 1455.23, "end": 1455.61, "word": " هناك", "probability": 0.6806640625}, {"start": 1455.61, "end": 1456.19, "word": " extension", "probability": 0.89501953125}, {"start": 1456.19, "end": 1456.99, "word": " هذا", "probability": 0.244140625}, {"start": 1456.99, "end": 1457.17, "word": " ال", "probability": 0.6826171875}, {"start": 1457.17, "end": 1457.53, "word": " extension", "probability": 0.83984375}, {"start": 1457.53, "end": 1457.85, "word": " مش", "probability": 0.421875}, {"start": 1457.85, "end": 1458.11, "word": " ممكن", "probability": 0.98095703125}, {"start": 1458.11, "end": 1458.39, "word": " يكون", "probability": 0.96337890625}, {"start": 1458.39, "end": 1459.03, "word": " continuous", "probability": 0.94580078125}, {"start": 1459.03, "end": 1459.87, "word": " عند", "probability": 0.861328125}, {"start": 1459.87, "end": 1460.31, "word": " النقطة", "probability": 0.8684895833333334}, {"start": 1460.31, "end": 1460.45, "word": " C", "probability": 0.479248046875}, {"start": 1460.45, "end": 1461.29, "word": " لأنه", "probability": 0.7955729166666666}, {"start": 1461.29, "end": 1461.41, "word": " لو", "probability": 0.85498046875}, {"start": 1461.41, "end": 1461.63, "word": " كان", "probability": 0.9912109375}, {"start": 1461.63, "end": 1462.05, "word": " continuous", "probability": 0.9580078125}, {"start": 1462.05, "end": 1462.35, "word": " عند", "probability": 0.990234375}, {"start": 1462.35, "end": 1462.77, "word": " النقطة", "probability": 0.9783528645833334}, {"start": 1462.77, "end": 1463.05, "word": " C", "probability": 0.921875}, {"start": 1463.05, "end": 1463.97, "word": " سيقدر", "probability": 0.544677734375}, {"start": 1463.97, "end": 1464.09, "word": " ان", "probability": 0.430419921875}, {"start": 1464.09, "end": 1464.51, "word": " الملمت", "probability": 0.4155680338541667}, {"start": 1464.51, "end": 1465.05, "word": " الدالة", "probability": 0.6997884114583334}, {"start": 1465.05, "end": 1465.35, "word": " small", "probability": 0.61962890625}, {"start": 1465.35, "end": 1465.63, "word": " g", "probability": 0.7333984375}, {"start": 1465.63, "end": 1465.87, "word": " and", "probability": 0.2310791015625}, {"start": 1465.87, "end": 1466.15, "word": " c", "probability": 0.81494140625}, {"start": 1466.15, "end": 1466.75, "word": " exist", "probability": 0.490234375}, {"start": 1466.75, "end": 1467.75, "word": " وهذا", "probability": 0.863525390625}, {"start": 1467.75, "end": 1468.49, "word": " يتناقض", "probability": 0.805322265625}, {"start": 1468.49, "end": 1468.77, "word": " مع", "probability": 0.9306640625}, {"start": 1468.77, "end": 1469.55, "word": " الفرض", "probability": 0.81298828125}, {"start": 1469.55, "end": 1471.71, "word": " تمام،", "probability": 0.5166829427083334}, {"start": 1471.71, "end": 1473.21, "word": " هذا", "probability": 0.55859375}, {"start": 1473.21, "end": 1473.73, "word": " النوع", "probability": 0.967529296875}, {"start": 1473.73, "end": 1474.13, "word": " من", "probability": 0.97265625}, {"start": 1474.13, "end": 1474.83, "word": " ال", "probability": 0.9169921875}, {"start": 1474.83, "end": 1475.91, "word": " discontinuity", "probability": 0.932373046875}, {"start": 1475.91, "end": 1477.61, "word": " لما", "probability": 0.701416015625}, {"start": 1477.61, "end": 1477.87, "word": " تكون", "probability": 0.980224609375}, {"start": 1477.87, "end": 1478.35, "word": " الدالة", "probability": 0.98876953125}, {"start": 1478.35, "end": 1479.35, "word": " discontinuous", "probability": 0.93505859375}, {"start": 1479.35, "end": 1480.57, "word": " لعدم", "probability": 0.9308268229166666}], "temperature": 1.0}, {"id": 55, "seek": 148392, "start": 1482.16, "end": 1483.92, "text": "لما تكون الدالة discontinuous", "tokens": [1211, 15042, 6055, 30544, 32748, 6027, 3660, 31420, 12549], "avg_logprob": -0.1455078139901161, "compression_ratio": 0.875, "no_speech_prob": 0.0, "words": [{"start": 1482.16, "end": 1482.5, "word": "لما", "probability": 0.740966796875}, {"start": 1482.5, "end": 1482.74, "word": " تكون", "probability": 0.97119140625}, {"start": 1482.74, "end": 1483.12, "word": " الدالة", "probability": 0.8795572916666666}, {"start": 1483.12, "end": 1483.92, "word": " discontinuous", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 56, "seek": 151196, "start": 1486.76, "end": 1511.96, "text": "السبب في ذلك أنها مش معرفة عند النقطة C لكن نهيتها موجودة عند الـ C فهذا النوع من ال discontinuity من عدم الاتصال بنسميه removable يعني ممكن إزالته أو التخلص منه وهي فعلا اتخلصنا من عدم الاتصال للدالة small f and c بتعريف دالة capital F بالطريقة هذه وشوفنا أن الدالة الجديدة continuous عند ال C", "tokens": [6027, 35457, 3555, 8978, 29910, 23275, 14739, 11296, 37893, 20449, 28480, 3660, 43242, 28239, 47432, 3660, 383, 44381, 8717, 3224, 36081, 11296, 3714, 29245, 23328, 3660, 43242, 2423, 39184, 383, 6156, 3224, 15730, 28239, 45367, 9154, 2423, 31420, 21757, 9154, 6225, 40448, 2423, 9307, 9381, 6027, 44945, 38251, 1829, 3224, 44060, 37495, 22653, 3714, 43020, 11933, 11622, 6027, 47395, 34051, 16712, 9778, 1211, 9381, 9154, 3224, 37037, 1829, 6156, 3615, 15040, 1975, 2655, 9778, 1211, 9381, 8315, 9154, 6225, 40448, 2423, 9307, 9381, 6027, 24976, 3215, 6027, 3660, 1359, 283, 293, 269, 39894, 3615, 16572, 5172, 11778, 6027, 3660, 4238, 479, 20666, 9566, 16572, 28671, 29538, 4032, 8592, 38688, 8315, 14739, 32748, 6027, 3660, 25724, 16254, 41891, 10957, 43242, 2423, 383], "avg_logprob": -0.17597335406014178, "compression_ratio": 1.7518248175182483, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1486.76, "end": 1487.5, "word": "السبب", "probability": 0.7044270833333334}, {"start": 1487.5, "end": 1487.66, "word": " في", "probability": 0.8798828125}, {"start": 1487.66, "end": 1487.94, "word": " ذلك", "probability": 0.9853515625}, {"start": 1487.94, "end": 1488.2, "word": " أنها", "probability": 0.718017578125}, {"start": 1488.2, "end": 1488.44, "word": " مش", "probability": 0.4208984375}, {"start": 1488.44, "end": 1489.08, "word": " معرفة", "probability": 0.8572591145833334}, {"start": 1489.08, "end": 1489.32, "word": " عند", "probability": 0.98193359375}, {"start": 1489.32, "end": 1489.8, "word": " النقطة", "probability": 0.7515462239583334}, {"start": 1489.8, "end": 1490.0, "word": " C", "probability": 0.5888671875}, {"start": 1490.0, "end": 1490.86, "word": " لكن", "probability": 0.81982421875}, {"start": 1490.86, "end": 1491.5, "word": " نهيتها", "probability": 0.8189697265625}, {"start": 1491.5, "end": 1492.14, "word": " موجودة", "probability": 0.9796142578125}, {"start": 1492.14, "end": 1492.36, "word": " عند", "probability": 0.98046875}, {"start": 1492.36, "end": 1492.56, "word": " الـ", "probability": 0.693603515625}, {"start": 1492.56, "end": 1492.72, "word": " C", "probability": 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"probability": 0.981689453125}, {"start": 1498.98, "end": 1499.66, "word": " إزالته", "probability": 0.86407470703125}, {"start": 1499.66, "end": 1500.36, "word": " أو", "probability": 0.87548828125}, {"start": 1500.36, "end": 1500.96, "word": " التخلص", "probability": 0.982666015625}, {"start": 1500.96, "end": 1501.28, "word": " منه", "probability": 0.995849609375}, {"start": 1501.28, "end": 1501.46, "word": " وهي", "probability": 0.517578125}, {"start": 1501.46, "end": 1501.84, "word": " فعلا", "probability": 0.9412434895833334}, {"start": 1501.84, "end": 1503.0, "word": " اتخلصنا", "probability": 0.9759114583333334}, {"start": 1503.0, "end": 1503.16, "word": " من", "probability": 0.99267578125}, {"start": 1503.16, "end": 1503.5, "word": " عدم", "probability": 0.989990234375}, {"start": 1503.5, "end": 1504.28, "word": " الاتصال", "probability": 0.9453125}, {"start": 1504.28, "end": 1505.3, "word": " للدالة", "probability": 0.73358154296875}, {"start": 1505.3, "end": 1505.64, "word": " small", "probability": 0.68994140625}, {"start": 1505.64, "end": 1505.92, "word": " f", "probability": 0.7314453125}, {"start": 1505.92, "end": 1506.18, "word": " and", "probability": 0.76171875}, {"start": 1506.18, "end": 1506.46, "word": " c", "probability": 0.79150390625}, {"start": 1506.46, "end": 1507.12, "word": " بتعريف", "probability": 0.9593505859375}, {"start": 1507.12, "end": 1507.5, "word": " دالة", "probability": 0.78955078125}, {"start": 1507.5, "end": 1507.86, "word": " capital", "probability": 0.740234375}, {"start": 1507.86, "end": 1508.22, "word": " F", "probability": 0.9296875}, {"start": 1508.22, "end": 1509.22, "word": " بالطريقة", "probability": 0.948486328125}, {"start": 1509.22, "end": 1509.48, "word": " هذه", "probability": 0.798828125}, {"start": 1509.48, "end": 1509.88, "word": " وشوفنا", "probability": 0.9234619140625}, {"start": 1509.88, "end": 1510.0, "word": " أن", "probability": 0.59765625}, {"start": 1510.0, "end": 1510.38, "word": " الدالة", "probability": 0.9811197916666666}, {"start": 1510.38, "end": 1510.8, "word": " الجديدة", "probability": 0.9641927083333334}, {"start": 1510.8, "end": 1511.24, "word": " continuous", "probability": 0.92333984375}, {"start": 1511.24, "end": 1511.66, "word": " عند", "probability": 0.78076171875}, {"start": 1511.66, "end": 1511.84, "word": " ال", "probability": 0.68212890625}, {"start": 1511.84, "end": 1511.96, "word": " C", "probability": 0.490478515625}], "temperature": 1.0}, {"id": 57, "seek": 153743, "start": 1512.45, "end": 1537.43, "text": "إذا هذا النوع من عدم الاتصال أو ال discontinuity is called removable يمكن إزالته يمكن تخلص منه أما إذا كانت الدالة discontinuous عند النقطة C لأن نهايتها in C مش موجودة فهذا النوع من عدم الاتصال بنسميه essential يعني أساسي لا يمكن تخلص منه زي ما شفنا في التحليل التحت okay تمام", "tokens": [28814, 15730, 23758, 28239, 45367, 9154, 6225, 40448, 2423, 9307, 9381, 6027, 34051, 2423, 31420, 21757, 307, 1219, 44060, 7251, 43020, 11933, 11622, 6027, 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1513.53, "end": 1513.85, "word": " عدم", "probability": 0.957763671875}, {"start": 1513.85, "end": 1514.39, "word": " الاتصال", "probability": 0.8367919921875}, {"start": 1514.39, "end": 1514.55, "word": " أو", "probability": 0.45458984375}, {"start": 1514.55, "end": 1514.71, "word": " ال", "probability": 0.59375}, {"start": 1514.71, "end": 1515.55, "word": " discontinuity", "probability": 0.808349609375}, {"start": 1515.55, "end": 1516.19, "word": " is", "probability": 0.78466796875}, {"start": 1516.19, "end": 1516.57, "word": " called", "probability": 0.90185546875}, {"start": 1516.57, "end": 1517.11, "word": " removable", "probability": 0.859375}, {"start": 1517.11, "end": 1517.51, "word": " يمكن", "probability": 0.873779296875}, {"start": 1517.51, "end": 1517.97, "word": " إزالته", "probability": 0.8818359375}, {"start": 1517.97, "end": 1518.13, "word": " يمكن", "probability": 0.654296875}, {"start": 1518.13, "end": 1518.61, "word": " تخلص", "probability": 0.8892822265625}, 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{"start": 1695.94, "end": 1696.22, "word": " is", "probability": 0.912109375}, {"start": 1696.22, "end": 1697.24, "word": " undefined", "probability": 0.845703125}], "temperature": 1.0}, {"id": 64, "seek": 172860, "start": 1700.56, "end": 1728.6, "text": "الـ limit شوفنا أنه limit ل f of x لما x تقول ل 0 by squeeze theorem أثبتنا باستخدام squeeze theorem أنه limit هذه بيساوي 0 exist بساوي 0 طبعا إذا هنا f is discontinuous discontinuous at x بساوي 0 لإن أنا مش معرف عند السفر", "tokens": [6027, 39184, 4948, 13412, 38688, 8315, 14739, 3224, 4948, 5296, 283, 295, 2031, 5296, 15042, 2031, 6055, 4587, 2407, 1211, 5296, 1958, 538, 13578, 20904, 5551, 12984, 3555, 2655, 8315, 4724, 995, 14851, 9778, 3215, 10943, 13578, 20904, 14739, 3224, 4948, 29538, 4724, 1829, 3794, 995, 45865, 1958, 2514, 4724, 3794, 995, 45865, 1958, 23032, 3555, 3615, 995, 11933, 15730, 34105, 283, 307, 31420, 12549, 31420, 12549, 412, 2031, 4724, 3794, 995, 45865, 1958, 5296, 28814, 1863, 41850, 37893, 20449, 28480, 43242, 21136, 5172, 2288], "avg_logprob": -0.26344475358031516, "compression_ratio": 1.5477386934673367, "no_speech_prob": 0.0, "words": [{"start": 1700.56, "end": 1700.96, "word": "الـ", "probability": 0.299072265625}, {"start": 1700.96, "end": 1701.2, "word": " limit", "probability": 0.75}, {"start": 1701.2, "end": 1701.68, "word": " شوفنا", "probability": 0.6021321614583334}, {"start": 1701.68, "end": 1701.92, "word": " أنه", "probability": 0.54736328125}, {"start": 1701.92, "end": 1702.28, "word": " limit", "probability": 0.84814453125}, {"start": 1702.28, "end": 1702.52, "word": " ل", "probability": 0.86962890625}, {"start": 1702.52, "end": 1702.82, "word": " f", "probability": 0.317138671875}, {"start": 1702.82, "end": 1703.06, "word": " of", "probability": 0.67041015625}, {"start": 1703.06, "end": 1703.44, "word": " x", "probability": 0.9296875}, {"start": 1703.44, "end": 1704.78, "word": " لما", "probability": 0.849365234375}, {"start": 1704.78, "end": 1705.1, "word": " x", 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"probability": 0.583984375}, {"start": 1711.14, "end": 1711.54, "word": " هذه", "probability": 0.420654296875}, {"start": 1711.54, "end": 1712.5, "word": " بيساوي", "probability": 0.92001953125}, {"start": 1712.5, "end": 1713.1, "word": " 0", "probability": 0.689453125}, {"start": 1713.1, "end": 1714.08, "word": " exist", "probability": 0.6044921875}, {"start": 1714.08, "end": 1714.62, "word": " بساوي", "probability": 0.878662109375}, {"start": 1714.62, "end": 1714.94, "word": " 0", "probability": 0.6943359375}, {"start": 1714.94, "end": 1717.4, "word": " طبعا", "probability": 0.9638671875}, {"start": 1717.4, "end": 1717.64, "word": " إذا", "probability": 0.654296875}, {"start": 1717.64, "end": 1718.1, "word": " هنا", "probability": 0.9833984375}, {"start": 1718.1, "end": 1719.18, "word": " f", "probability": 0.56982421875}, {"start": 1719.18, "end": 1719.88, "word": " is", "probability": 0.9560546875}, {"start": 1719.88, "end": 1721.06, "word": " discontinuous", "probability": 0.909423828125}, {"start": 1721.06, "end": 1723.86, "word": " discontinuous", "probability": 0.826171875}, {"start": 1723.86, "end": 1724.48, "word": " at", "probability": 0.91748046875}, {"start": 1724.48, "end": 1725.68, "word": " x", "probability": 0.98291015625}, {"start": 1725.68, "end": 1726.32, "word": " بساوي", "probability": 0.9434814453125}, {"start": 1726.32, "end": 1726.78, "word": " 0", "probability": 0.89306640625}, {"start": 1726.78, "end": 1727.02, "word": " لإن", "probability": 0.696533203125}, {"start": 1727.02, "end": 1727.18, "word": " أنا", "probability": 0.80029296875}, {"start": 1727.18, "end": 1727.36, "word": " مش", "probability": 0.96875}, {"start": 1727.36, "end": 1727.84, "word": " معرف", "probability": 0.94970703125}, {"start": 1727.84, "end": 1728.14, "word": " عند", "probability": 0.56787109375}, {"start": 1728.14, "end": 1728.6, "word": " السفر", "probability": 0.7236735026041666}], "temperature": 1.0}, {"id": 65, "seek": 175122, "start": 1729.72, "end": 1751.22, "text": "لكن بما ان ال limit تبقى عند السفر موجودة we can define a continuous extension of f at سفر as follows", "tokens": [1211, 19452, 4724, 15042, 16472, 2423, 4948, 6055, 3555, 4587, 7578, 43242, 21136, 5172, 2288, 3714, 29245, 23328, 3660, 321, 393, 6964, 257, 10957, 10320, 295, 283, 412, 8608, 5172, 2288, 382, 10002], "avg_logprob": -0.28033087534063, "compression_ratio": 1.11864406779661, "no_speech_prob": 0.0, "words": [{"start": 1729.72, "end": 1730.18, "word": "لكن", "probability": 0.6304931640625}, {"start": 1730.18, "end": 1730.74, "word": " بما", "probability": 0.9404296875}, {"start": 1730.74, "end": 1730.96, "word": " ان", "probability": 0.455810546875}, {"start": 1730.96, "end": 1731.1, "word": " ال", "probability": 0.51513671875}, {"start": 1731.1, "end": 1731.36, "word": " limit", "probability": 0.837890625}, {"start": 1731.36, "end": 1731.58, "word": " تبقى", "probability": 0.78271484375}, {"start": 1731.58, "end": 1731.92, "word": " عند", "probability": 0.62353515625}, {"start": 1731.92, "end": 1732.32, "word": " السفر", "probability": 0.770263671875}, {"start": 1732.32, "end": 1733.94, "word": " موجودة", "probability": 0.978271484375}, {"start": 1733.94, "end": 1734.36, "word": " we", "probability": 0.2093505859375}, {"start": 1734.36, "end": 1734.98, "word": " can", "probability": 0.97119140625}, {"start": 1734.98, "end": 1738.32, "word": " define", "probability": 0.9775390625}, {"start": 1738.32, "end": 1740.6, "word": " a", "probability": 0.97314453125}, {"start": 1740.6, "end": 1741.72, "word": " continuous", "probability": 0.869140625}, {"start": 1741.72, "end": 1743.54, "word": " extension", "probability": 0.95166015625}, {"start": 1743.54, "end": 1747.32, "word": " of", "probability": 0.96923828125}, {"start": 1747.32, "end": 1747.9, "word": " f", "probability": 0.344970703125}, {"start": 1747.9, "end": 1749.48, "word": " at", "probability": 0.6611328125}, {"start": 1749.48, "end": 1750.02, "word": " سفر", "probability": 0.8522135416666666}, {"start": 1750.02, "end": 1750.68, "word": " as", "probability": 0.96044921875}, {"start": 1750.68, "end": 1751.22, "word": " follows", "probability": 0.8623046875}], "temperature": 1.0}, {"id": 66, "seek": 177856, "start": 1754.8, "end": 1778.56, "text": "فعندى capital F of X بنعرفها على أنها بالساوى السفر اللى هو limit لل function عند السفر إذا كان ال X بساوى السفر و بالساوى small f of X إذا كان X تنتمي ل domain الدالة اللى هو", "tokens": [5172, 3615, 41260, 7578, 4238, 479, 295, 1783, 44945, 3615, 28480, 11296, 15844, 14739, 11296, 20666, 3794, 995, 2407, 7578, 21136, 5172, 2288, 13672, 7578, 31439, 4948, 24976, 2445, 43242, 21136, 5172, 2288, 11933, 15730, 25961, 2423, 1783, 4724, 3794, 995, 2407, 7578, 21136, 5172, 2288, 4032, 20666, 3794, 995, 2407, 7578, 1359, 283, 295, 1783, 11933, 15730, 25961, 1783, 6055, 29399, 2304, 1829, 5296, 9274, 32748, 6027, 3660, 13672, 7578, 31439], "avg_logprob": -0.22838185258107643, "compression_ratio": 1.7, "no_speech_prob": 0.0, "words": [{"start": 1754.8, "end": 1755.56, "word": "فعندى", "probability": 0.48114013671875}, {"start": 1755.56, "end": 1755.94, "word": " capital", "probability": 0.62451171875}, {"start": 1755.94, "end": 1756.44, "word": " F", "probability": 0.78173828125}, {"start": 1756.44, "end": 1757.96, "word": " of", "probability": 0.89599609375}, {"start": 1757.96, "end": 1758.44, "word": " X", "probability": 0.69140625}, {"start": 1758.44, "end": 1759.44, "word": " بنعرفها", "probability": 0.7857666015625}, {"start": 1759.44, "end": 1759.62, "word": " على", "probability": 0.78125}, {"start": 1759.62, "end": 1760.5, "word": " أنها", "probability": 0.7025146484375}, {"start": 1760.5, "end": 1761.98, "word": " بالساوى", "probability": 0.74375}, {"start": 1761.98, "end": 1762.48, "word": " السفر", "probability": 0.8362630208333334}, {"start": 1762.48, "end": 1762.84, "word": " اللى", "probability": 0.882080078125}, {"start": 1762.84, "end": 1763.02, "word": " هو", "probability": 0.92333984375}, {"start": 1763.02, "end": 1763.34, "word": " limit", "probability": 0.66357421875}, {"start": 1763.34, "end": 1763.54, "word": " لل", "probability": 0.75390625}, {"start": 1763.54, "end": 1763.9, "word": " function", "probability": 0.65625}, {"start": 1763.9, "end": 1764.14, "word": " عند", "probability": 0.939453125}, {"start": 1764.14, "end": 1764.74, "word": " السفر", "probability": 0.9462890625}, {"start": 1764.74, "end": 1765.6, "word": " إذا", "probability": 0.78515625}, {"start": 1765.6, "end": 1766.04, "word": " كان", "probability": 0.99560546875}, {"start": 1766.04, "end": 1766.36, "word": " ال", "probability": 0.89111328125}, {"start": 1766.36, "end": 1766.74, "word": " X", "probability": 0.90087890625}, {"start": 1766.74, "end": 1767.72, "word": " بساوى", "probability": 0.94033203125}, {"start": 1767.72, "end": 1768.18, "word": " السفر", "probability": 0.88330078125}, {"start": 1768.18, "end": 1769.04, "word": " و", "probability": 0.421875}, {"start": 1769.04, "end": 1769.56, "word": " بالساوى", "probability": 0.9080078125}, {"start": 1769.56, "end": 1770.02, "word": " small", "probability": 0.912109375}, {"start": 1770.02, "end": 1770.36, "word": " f", "probability": 0.57958984375}, {"start": 1770.36, "end": 1770.62, "word": " of", "probability": 0.9443359375}, {"start": 1770.62, "end": 1771.02, "word": " X", "probability": 0.9384765625}, {"start": 1771.02, "end": 1772.42, "word": " إذا", "probability": 0.939453125}, {"start": 1772.42, "end": 1772.94, "word": " كان", "probability": 0.9951171875}, {"start": 1772.94, "end": 1774.96, "word": " X", "probability": 0.9736328125}, {"start": 1774.96, "end": 1776.28, "word": " تنتمي", "probability": 0.83978271484375}, {"start": 1776.28, "end": 1776.38, "word": " ل", "probability": 0.97216796875}, {"start": 1776.38, "end": 1776.66, "word": " domain", "probability": 0.72509765625}, {"start": 1776.66, "end": 1777.44, "word": " الدالة", "probability": 0.9319661458333334}, {"start": 1777.44, "end": 1777.8, "word": " اللى", "probability": 0.8544921875}, {"start": 1777.8, "end": 1778.56, "word": " هو", "probability": 0.896484375}], "temperature": 1.0}, {"id": 67, "seek": 180558, "start": 1779.74, "end": 1805.58, "text": "اللي هو ر مع ده سفر ر مع ده سفر مش هذا هو ال domain تبع الدالة الانف دالة if now you can verify انه capital F is continuous is continuous at x بساوي سفر", "tokens": [6027, 20292, 31439, 12602, 20449, 11778, 3224, 8608, 5172, 2288, 12602, 20449, 11778, 3224, 8608, 5172, 2288, 37893, 23758, 31439, 2423, 9274, 6055, 3555, 3615, 32748, 6027, 3660, 2423, 7649, 5172, 11778, 6027, 3660, 498, 586, 291, 393, 16888, 16472, 3224, 4238, 479, 307, 10957, 307, 10957, 412, 2031, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.29084429406283197, "compression_ratio": 1.4620689655172414, "no_speech_prob": 0.0, "words": [{"start": 1779.74, "end": 1780.1, "word": "اللي", "probability": 0.4739990234375}, {"start": 1780.1, "end": 1780.4, "word": " هو", "probability": 0.95263671875}, {"start": 1780.4, "end": 1780.68, "word": " ر", "probability": 0.1220703125}, {"start": 1780.68, "end": 1780.9, "word": " مع", "probability": 0.9423828125}, {"start": 1780.9, "end": 1781.12, "word": " ده", "probability": 0.703369140625}, {"start": 1781.12, "end": 1781.5, "word": " سفر", "probability": 0.8621419270833334}, {"start": 1781.5, "end": 1782.26, "word": " ر", "probability": 0.1702880859375}, {"start": 1782.26, "end": 1783.34, "word": " مع", "probability": 0.9091796875}, {"start": 1783.34, "end": 1783.66, "word": " ده", "probability": 0.976318359375}, {"start": 1783.66, "end": 1783.96, "word": " سفر", "probability": 0.9899088541666666}, {"start": 1783.96, "end": 1784.12, "word": " مش", "probability": 0.876953125}, {"start": 1784.12, "end": 1784.32, "word": " هذا", "probability": 0.50390625}, {"start": 1784.32, "end": 1784.48, "word": " هو", "probability": 0.97607421875}, {"start": 1784.48, "end": 1784.6, "word": " ال", "probability": 0.89306640625}, {"start": 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8608, 2407, 7578, 8608, 5172, 2288, 5296, 28820, 297, 8978, 297], "avg_logprob": -0.3085171475129969, "compression_ratio": 1.4224137931034482, "no_speech_prob": 0.0, "words": [{"start": 2197.41, "end": 2197.75, "word": "ما", "probability": 0.2071533203125}, {"start": 2197.75, "end": 2198.27, "word": " بنجمع", "probability": 0.9305419921875}, {"start": 2198.27, "end": 2198.97, "word": " مش", "probability": 0.51318359375}, {"start": 2198.97, "end": 2199.35, "word": " عاملة", "probability": 0.82763671875}, {"start": 2199.35, "end": 2199.83, "word": " اتجمع", "probability": 0.815234375}, {"start": 2199.83, "end": 2201.17, "word": " الان", "probability": 0.7802734375}, {"start": 2201.17, "end": 2201.45, "word": " في", "probability": 0.8203125}, {"start": 2201.45, "end": 2201.83, "word": " اندي", "probability": 0.6220703125}, {"start": 2201.83, "end": 2202.15, "word": " انا", "probability": 0.891845703125}, {"start": 2202.15, "end": 2202.67, "word": " لحظة", "probability": 0.7462158203125}, {"start": 2202.67, "end": 2202.95, "word": " انت", "probability": 0.679443359375}, {"start": 2202.95, "end": 2203.95, "word": " عندك", "probability": 0.973876953125}, {"start": 2203.95, "end": 2205.13, "word": " من", "probability": 0.96337890625}, {"start": 2205.13, "end": 2205.71, "word": " الفرض", "probability": 0.92138671875}, {"start": 2205.71, "end": 2207.27, "word": " xn", "probability": 0.463134765625}, {"start": 2207.27, "end": 2207.99, "word": " أكبر", "probability": 0.84423828125}, {"start": 2207.99, "end": 2208.21, "word": " من", "probability": 0.96435546875}, {"start": 2208.21, "end": 2208.41, "word": " أو", "probability": 0.828125}, {"start": 2208.41, "end": 2208.85, "word": " سوى", "probability": 0.7776692708333334}, {"start": 2208.85, "end": 2209.27, "word": " سفر", "probability": 0.8196614583333334}, {"start": 2209.27, "end": 2209.81, "word": " لكل", "probability": 0.984375}, {"start": 2209.81, "end": 2210.15, "word": " n", "probability": 0.5927734375}, {"start": 2210.15, "end": 2210.33, "word": " في", "probability": 0.91162109375}, {"start": 2210.33, "end": 2210.53, "word": " n", "probability": 0.1585693359375}], "temperature": 1.0}, {"id": 82, "seek": 224312, "start": 2215.48, "end": 2243.12, "text": "فبالتالي إذا x2n سالب واحد أكبر من أوسعه سفر لكل n وكذلك x2n برضه أكبر من أوسعه سفر لكل n صح؟ أصبت؟ وبالتالي إذا ال limit ل x2n سالب واحد تطلع أكبر من أوسعه سفر", "tokens": [5172, 3555, 6027, 2655, 6027, 1829, 11933, 15730, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288, 5296, 28820, 297, 4032, 4117, 8848, 23275, 2031, 17, 77, 4724, 43042, 3224, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288, 5296, 28820, 297, 20328, 5016, 22807, 5551, 9381, 3555, 2655, 22807, 46599, 6027, 2655, 6027, 1829, 11933, 15730, 2423, 4948, 5296, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 6055, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288], "avg_logprob": -0.1402994718713065, "compression_ratio": 2.0, "no_speech_prob": 0.0, "words": [{"start": 2215.48, "end": 2216.48, "word": "فبالتالي", "probability": 0.872314453125}, {"start": 2216.48, "end": 2216.86, "word": " إذا", "probability": 0.544677734375}, {"start": 2216.86, "end": 2219.02, "word": " x2n", "probability": 0.6661783854166666}, {"start": 2219.02, "end": 2219.54, "word": " سالب", "probability": 0.6663004557291666}, {"start": 2219.54, "end": 2219.94, "word": " واحد", "probability": 0.960693359375}, {"start": 2219.94, "end": 2220.4, "word": " أكبر", "probability": 0.9500325520833334}, {"start": 2220.4, "end": 2220.54, "word": " من", "probability": 0.9765625}, {"start": 2220.54, "end": 2221.04, "word": " أوسعه", "probability": 0.6634521484375}, {"start": 2221.04, "end": 2221.44, "word": " سفر", "probability": 0.8971354166666666}, {"start": 2221.44, "end": 2222.94, "word": " لكل", "probability": 0.98291015625}, {"start": 2222.94, "end": 2223.28, "word": " n", "probability": 0.77783203125}, {"start": 2223.28, "end": 2225.04, "word": " وكذلك", "probability": 0.923828125}, {"start": 2225.04, "end": 2226.58, "word": " x2n", "probability": 0.9830729166666666}, {"start": 2226.58, "end": 2228.12, "word": " برضه", "probability": 0.9296875}, {"start": 2228.12, "end": 2229.12, "word": " أكبر", "probability": 0.9768880208333334}, {"start": 2229.12, "end": 2229.34, "word": " من", "probability": 0.99658203125}, {"start": 2229.34, "end": 2229.9, "word": " أوسعه", "probability": 0.9757080078125}, {"start": 2229.9, "end": 2230.3, "word": " سفر", "probability": 0.9925130208333334}, {"start": 2230.3, "end": 2230.74, "word": " لكل", "probability": 0.990478515625}, {"start": 2230.74, "end": 2231.12, "word": " n", "probability": 0.97216796875}, {"start": 2231.12, "end": 2233.6, "word": " صح؟", "probability": 0.7501627604166666}, {"start": 2233.6, "end": 2235.82, "word": " أصبت؟", "probability": 0.743603515625}, {"start": 2235.82, "end": 2236.84, "word": " وبالتالي", "probability": 0.891650390625}, {"start": 2236.84, "end": 2237.1, "word": " إذا", "probability": 0.88818359375}, {"start": 2237.1, "end": 2237.28, "word": " ال", "probability": 0.93359375}, {"start": 2237.28, "end": 2237.66, "word": " limit", "probability": 0.95166015625}, {"start": 2237.66, "end": 2239.14, "word": " ل", "probability": 0.9287109375}, {"start": 2239.14, "end": 2240.24, "word": " x2n", "probability": 0.89990234375}, {"start": 2240.24, "end": 2240.76, "word": " سالب", "probability": 0.9716796875}, {"start": 2240.76, "end": 2241.06, "word": " واحد", "probability": 0.98974609375}, {"start": 2241.06, "end": 2241.54, "word": " تطلع", "probability": 0.978271484375}, {"start": 2241.54, "end": 2242.04, "word": " أكبر", "probability": 0.978515625}, {"start": 2242.04, "end": 2242.24, "word": " من", "probability": 0.99560546875}, {"start": 2242.24, "end": 2242.74, "word": " أوسعه", "probability": 0.97412109375}, {"start": 2242.74, "end": 2243.12, "word": " سفر", "probability": 0.9933268229166666}], "temperature": 1.0}, {"id": 83, "seek": 227189, "start": 2244.31, "end": 2271.89, "text": "و ال limit ل x2n تطلع أكبر من أوي ساوي سفر هذه نظرية أخدناها صح؟ أخدناها نظرية بتقول لو كانت ال sequence كل حدوة ده غير سالبة و ال limit تبعتها exist فال limit تبعتها تطلع غير سالبة صح؟ فال limit هنا هي حسبناها سالم x و ال limit هنا طلعت x", "tokens": [2407, 2423, 4948, 5296, 2031, 17, 77, 6055, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 1829, 8608, 995, 45865, 8608, 5172, 2288, 29538, 8717, 19913, 2288, 10632, 5551, 9778, 3215, 8315, 11296, 20328, 5016, 22807, 5551, 9778, 3215, 8315, 11296, 8717, 19913, 2288, 10632, 39894, 39648, 45164, 25961, 2655, 2423, 8310, 28242, 11331, 3215, 2407, 3660, 11778, 3224, 32771, 13546, 8608, 6027, 49401, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 2514, 6156, 6027, 4948, 6055, 3555, 34268, 11296, 6055, 9566, 1211, 3615, 32771, 13546, 8608, 6027, 49401, 20328, 5016, 22807, 6156, 6027, 4948, 34105, 39896, 11331, 35457, 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2268.53, "word": " x", "probability": 0.9541015625}, {"start": 2268.53, "end": 2270.01, "word": " و", "probability": 0.84423828125}, {"start": 2270.01, "end": 2270.15, "word": " ال", "probability": 0.9365234375}, {"start": 2270.15, "end": 2270.41, "word": " limit", "probability": 0.9853515625}, {"start": 2270.41, "end": 2270.75, "word": " هنا", "probability": 0.99365234375}, {"start": 2270.75, "end": 2271.45, "word": " طلعت", "probability": 0.93017578125}, {"start": 2271.45, "end": 2271.89, "word": " x", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 84, "seek": 229504, "start": 2273.2, "end": 2295.04, "text": "إذا أنا في عندي سالب X أكبر من أو ساوي سفر and X أكبر من أو ساوي سفر هذا بيقدر ان X أصغر من أو ساوي سفر and X أكبر من أو ساوي سفر هذا بيقدر ان X بساوي سفر", "tokens": [28814, 15730, 41850, 8978, 18871, 16254, 8608, 6027, 3555, 1783, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288, 293, 1783, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 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2277.72, "end": 2277.96, "word": " من", "probability": 0.98779296875}, {"start": 2277.96, "end": 2278.16, "word": " أو", "probability": 0.9658203125}, {"start": 2278.16, "end": 2278.56, "word": " ساوي", "probability": 0.9319661458333334}, {"start": 2278.56, "end": 2279.06, "word": " سفر", "probability": 0.8445638020833334}, {"start": 2279.06, "end": 2279.84, "word": " and", "probability": 0.87744140625}, {"start": 2279.84, "end": 2281.24, "word": " X", "probability": 0.982421875}, {"start": 2281.24, "end": 2281.74, "word": " أكبر", "probability": 0.98486328125}, {"start": 2281.74, "end": 2281.92, "word": " من", "probability": 0.99755859375}, {"start": 2281.92, "end": 2282.16, "word": " أو", "probability": 0.9892578125}, {"start": 2282.16, "end": 2282.46, "word": " ساوي", "probability": 0.9801432291666666}, {"start": 2282.46, "end": 2282.84, "word": " سفر", "probability": 0.99267578125}, {"start": 2282.84, "end": 2283.2, "word": " هذا", "probability": 0.7626953125}, {"start": 2283.2, 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