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exists delta أكبر من سفر has a derivative مثلا نسميها L has a derivative L at C limited on I if for every Y أكبر من سفر there exists delta أكبر من سفر such that X minus C أكبر من سفر وأصغر من Delta implies اللي هو مين", "tokens": [15456, 8198, 8289, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 575, 257, 13760, 50113, 15040, 8717, 38251, 1829, 11296, 441, 575, 257, 13760, 441, 412, 383, 5567, 322, 286, 498, 337, 633, 398, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 456, 8198, 8289, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 1270, 300, 1783, 3175, 383, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 36725, 9381, 17082, 2288, 9154, 18183, 18779, 13672, 1829, 31439, 3714, 9957], "avg_logprob": -0.24020833810170492, "compression_ratio": 1.6764705882352942, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 828.46, "end": 828.82, "word": "there", "probability": 0.158203125}, {"start": 828.82, "end": 829.36, "word": " exists", "probability": 0.74951171875}, {"start": 829.36, "end": 829.92, 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theorem if F من I لعند R is differentiable at", "tokens": [4587, 16758, 1211, 10632, 2423, 33599, 2655, 4587, 995, 4587, 43242, 8717, 47432, 3660, 37279, 22653, 14739, 32748, 6027, 3660, 44650, 36520, 3660, 43242, 29538, 28239, 47432, 3660, 8717, 8592, 38688, 20904, 498, 479, 9154, 286, 5296, 3615, 41260, 497, 307, 819, 9364, 412], "avg_logprob": -0.13671875529819064, "compression_ratio": 1.2666666666666666, "no_speech_prob": 1.5497207641601562e-06, "words": [{"start": 958.23, "end": 959.19, "word": "قابلية", "probability": 0.9381103515625}, {"start": 959.19, "end": 960.51, "word": " الاشتقاق", "probability": 0.8356119791666666}, {"start": 960.51, "end": 960.93, "word": " عند", "probability": 0.98828125}, {"start": 960.93, "end": 961.91, "word": " نقطة", "probability": 0.9861653645833334}, {"start": 961.91, "end": 963.31, "word": " تعني", "probability": 0.6754150390625}, {"start": 963.31, "end": 965.03, "word": " أن", "probability": 0.7998046875}, {"start": 965.03, "end": 965.65, 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of", "probability": 0.38720703125}, {"start": 2439.3, "end": 2439.72, "word": " X", "probability": 0.94091796875}, {"start": 2439.72, "end": 2440.52, "word": " لما", "probability": 0.842041015625}, {"start": 2440.52, "end": 2440.76, "word": " X", "probability": 0.94921875}, {"start": 2440.76, "end": 2441.1, "word": " تروح", "probability": 0.9698893229166666}, {"start": 2441.1, "end": 2441.44, "word": " للـ", "probability": 0.6650390625}, {"start": 2441.44, "end": 2441.66, "word": " C", "probability": 0.5595703125}, {"start": 2441.66, "end": 2442.32, "word": " بيساوي", "probability": 0.809814453125}, {"start": 2442.32, "end": 2442.62, "word": " G", "probability": 0.8828125}, {"start": 2442.62, "end": 2442.88, "word": " of", "probability": 0.947265625}, {"start": 2442.88, "end": 2444.22, "word": " إيش؟", "probability": 0.7840576171875}, {"start": 2444.22, "end": 2444.56, "word": " of", "probability": 0.37890625}, {"start": 2444.56, "end": 2444.84, "word": " C", "probability": 0.9404296875}, {"start": 2444.84, "end": 2445.14, "word": " الـ", "probability": 0.58270263671875}, {"start": 2445.14, "end": 2445.28, "word": " G", "probability": 0.88916015625}, {"start": 2445.28, "end": 2445.4, "word": " of", "probability": 0.97314453125}, {"start": 2445.4, "end": 2445.52, "word": " C", "probability": 0.9794921875}, {"start": 2445.52, "end": 2445.98, "word": " معناته", "probability": 0.9710286458333334}, {"start": 2445.98, "end": 2446.2, "word": " إيش", "probability": 0.91650390625}, {"start": 2446.2, "end": 2447.12, "word": " ماله؟", "probability": 0.8641357421875}, {"start": 2447.12, "end": 2447.52, "word": " هذا", "probability": 0.30908203125}, {"start": 2447.52, "end": 2448.1, "word": " عدد", "probability": 0.9791666666666666}, {"start": 2448.1, "end": 2448.98, "word": " لا", "probability": 0.51513671875}, {"start": 2448.98, "end": 2449.54, "word": " يساوي", "probability": 0.9652099609375}, {"start": 2449.54, "end": 2449.88, "word": " سفر", "probability": 0.7704264322916666}, {"start": 2449.88, "end": 2450.16, "word": " هيك", "probability": 0.67041015625}, {"start": 2450.16, "end": 2450.36, "word": " جاي", "probability": 0.5487060546875}, {"start": 2450.36, "end": 2450.58, "word": " اللي", "probability": 0.963134765625}, {"start": 2450.58, "end": 2451.02, "word": " هو", "probability": 0.99755859375}, {"start": 2451.02, "end": 2452.14, "word": " مدام", "probability": 0.7809244791666666}, {"start": 2452.14, "end": 2452.28, "word": " لا", "probability": 0.84619140625}, {"start": 2452.28, "end": 2452.58, "word": " يساوي", "probability": 0.9749755859375}, {"start": 2452.58, "end": 2452.9, "word": " سفر", "probability": 0.9931640625}, {"start": 2452.9, "end": 2453.4, "word": " معناته", "probability": 0.9358723958333334}, {"start": 2453.4, "end": 2453.62, "word": " يا", "probability": 0.88232421875}, {"start": 2453.62, "end": 2454.02, "word": " أكبر", "probability": 0.98046875}, {"start": 2454.02, "end": 2454.24, "word": " من", "probability": 0.998046875}, {"start": 2454.24, "end": 2454.7, "word": " سفر", "probability": 0.9850260416666666}, {"start": 2454.7, "end": 2455.34, "word": " يا", "probability": 0.6435546875}, {"start": 2455.34, "end": 2456.6, "word": " إيش؟", "probability": 0.9293212890625}, {"start": 2456.6, "end": 2456.74, "word": " يا", "probability": 0.9501953125}, {"start": 2456.74, "end": 2457.14, "word": " أصغر", "probability": 0.99072265625}, {"start": 2457.14, "end": 2457.38, "word": " من", "probability": 0.998046875}, {"start": 2457.38, "end": 2457.82, "word": " سفر", "probability": 0.9920247395833334}, {"start": 2457.82, "end": 2458.48, "word": " يعني", "probability": 0.941650390625}, {"start": 2458.48, "end": 2458.96, "word": " بمعنى", "probability": 0.9931640625}, {"start": 2458.96, "end": 2459.34, "word": " آخر", "probability": 0.81298828125}, {"start": 2459.34, "end": 2459.6, "word": " there", "probability": 0.58935546875}, {"start": 2459.6, "end": 2460.36, "word": " exist", "probability": 0.73974609375}, {"start": 2460.36, "end": 2461.38, "word": " حسب", "probability": 0.956787109375}, {"start": 2461.38, "end": 2461.92, "word": " النظرية", "probability": 0.9747314453125}, {"start": 2461.92, "end": 2462.36, "word": " هذه", "probability": 0.94189453125}, {"start": 2462.36, "end": 2462.98, "word": " there", "probability": 0.86767578125}, {"start": 2462.98, "end": 2463.44, "word": " exist", "probability": 0.69091796875}, {"start": 2463.44, "end": 2464.04, "word": " neighborhood", "probability": 0.45849609375}], "temperature": 1.0}, {"id": 102, "seek": 248750, "start": 2465.12, "end": 2487.5, "text": "جوار حوالين الـC سميه J هذا جوار لإيه؟ حوالين الـC there exist جوار حوالين الـC طبعاً subset من مين هيكون؟ من الـinterval اللي معرف عليها مين أنا F و G صح ولا لأ؟ there exist G of C subset من I such that G of X", "tokens": [7435, 2407, 9640, 11331, 2407, 6027, 9957, 2423, 39184, 34, 8608, 2304, 1829, 3224, 508, 23758, 10874, 2407, 9640, 5296, 28814, 1829, 3224, 22807, 11331, 2407, 6027, 9957, 2423, 39184, 34, 456, 2514, 10874, 2407, 9640, 11331, 2407, 6027, 9957, 2423, 39184, 34, 23032, 3555, 3615, 995, 14111, 25993, 9154, 3714, 9957, 39896, 30544, 22807, 9154, 2423, 39184, 5106, 3337, 13672, 1829, 20449, 28480, 25894, 11296, 3714, 9957, 41850, 479, 4032, 460, 20328, 5016, 49429, 5296, 10721, 22807, 456, 2514, 460, 295, 383, 25993, 9154, 286, 1270, 300, 460, 295, 1783], "avg_logprob": -0.19667120051124823, "compression_ratio": 1.6774193548387097, "no_speech_prob": 6.80088996887207e-05, "words": [{"start": 2465.12, "end": 2465.98, "word": "جوار", "probability": 0.8670247395833334}, {"start": 2465.98, "end": 2466.84, "word": " حوالين", "probability": 0.9149169921875}, {"start": 2466.84, "end": 2467.14, "word": " الـC", "probability": 0.6878255208333334}, {"start": 2467.14, "end": 2467.74, "word": " سميه", "probability": 0.637451171875}, {"start": 2467.74, "end": 2467.94, "word": " J", "probability": 0.7626953125}, {"start": 2467.94, "end": 2468.84, "word": " هذا", "probability": 0.53759765625}, {"start": 2468.84, "end": 2469.34, "word": " جوار", "probability": 0.9676106770833334}, {"start": 2469.34, "end": 2469.8, "word": " لإيه؟", "probability": 0.6853515625}, {"start": 2469.8, "end": 2470.24, "word": " حوالين", "probability": 0.9031982421875}, {"start": 2470.24, "end": 2470.6, "word": " الـC", "probability": 0.96142578125}, {"start": 2470.6, "end": 2471.24, "word": " there", "probability": 0.4375}, {"start": 2471.24, "end": 2471.68, "word": " exist", "probability": 0.6904296875}, {"start": 2471.68, "end": 2472.22, "word": " جوار", "probability": 0.9580078125}, {"start": 2472.22, "end": 2472.72, "word": " حوالين", "probability": 0.9793701171875}, {"start": 2472.72, "end": 2473.24, "word": " الـC", "probability": 0.9775390625}, {"start": 2473.24, "end": 2474.06, "word": " طبعاً", "probability": 0.8455078125}, {"start": 2474.06, "end": 2474.34, "word": " subset", "probability": 0.85888671875}, {"start": 2474.34, "end": 2474.58, "word": " من", "probability": 0.9951171875}, {"start": 2474.58, "end": 2474.78, "word": " مين", "probability": 0.96240234375}, {"start": 2474.78, "end": 2476.02, "word": " هيكون؟", "probability": 0.6904296875}, {"start": 2476.02, "end": 2476.2, "word": " من", "probability": 0.9873046875}, {"start": 2476.2, "end": 2476.9, "word": " الـinterval", "probability": 0.798828125}, {"start": 2476.9, "end": 2477.08, "word": " اللي", "probability": 0.947998046875}, {"start": 2477.08, "end": 2477.5, "word": " معرف", "probability": 0.931396484375}, {"start": 2477.5, "end": 2477.9, "word": " عليها", "probability": 0.958251953125}, {"start": 2477.9, "end": 2478.14, "word": " مين", "probability": 0.9765625}, {"start": 2478.14, "end": 2478.56, "word": " أنا", "probability": 0.90869140625}, {"start": 2478.56, "end": 2479.64, "word": " F", "probability": 0.271484375}, {"start": 2479.64, "end": 2479.82, "word": " و", "probability": 0.80859375}, {"start": 2479.82, "end": 2480.08, "word": " G", "probability": 0.490478515625}, {"start": 2480.08, "end": 2480.74, "word": " صح", "probability": 0.9208984375}, {"start": 2480.74, "end": 2480.9, "word": " ولا", "probability": 0.94189453125}, {"start": 2480.9, "end": 2481.94, "word": " لأ؟", "probability": 0.8929036458333334}, {"start": 2481.94, "end": 2482.12, "word": " there", "probability": 0.8720703125}, {"start": 2482.12, "end": 2482.46, "word": " exist", "probability": 0.82177734375}, {"start": 2482.46, "end": 2482.76, "word": " G", "probability": 0.71044921875}, {"start": 2482.76, "end": 2482.96, "word": " of", "probability": 0.84130859375}, {"start": 2482.96, "end": 2483.26, "word": " C", "probability": 0.9658203125}, {"start": 2483.26, "end": 2483.74, "word": " subset", "probability": 0.94775390625}, {"start": 2483.74, "end": 2484.0, "word": " من", "probability": 0.9931640625}, {"start": 2484.0, "end": 2484.36, "word": " I", "probability": 0.98828125}, {"start": 2484.36, "end": 2485.16, "word": " such", "probability": 0.89599609375}, {"start": 2485.16, "end": 2485.74, "word": " that", "probability": 0.9599609375}, {"start": 2485.74, "end": 2486.8, "word": " G", "probability": 0.4296875}, {"start": 2486.8, "end": 2487.06, "word": " of", "probability": 0.927734375}, {"start": 2487.06, "end": 2487.5, "word": " X", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 103, "seek": 250637, "start": 2488.49, "end": 2506.37, "text": "إذا كانت هذا أكبر من صفر تكون أكبر من صفر إذا كان أصغر من صفر تكون أشماله أصغر من صفر قلنا there exist gc اللي هو عبارة عن neighborhood حوالين الـC جزء طبعا من I اللي هي ال interval معرفة عليها G", "tokens": [28814, 15730, 25961, 2655, 23758, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 6055, 30544, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 11933, 15730, 25961, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 6055, 30544, 5551, 8592, 2304, 6027, 3224, 5551, 9381, 17082, 2288, 9154, 20328, 5172, 2288, 12174, 1211, 8315, 456, 2514, 290, 66, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 7630, 11331, 2407, 6027, 9957, 2423, 39184, 34, 10874, 11622, 38207, 23032, 3555, 3615, 995, 9154, 286, 13672, 1829, 39896, 2423, 15035, 20449, 28480, 3660, 25894, 11296, 460], "avg_logprob": -0.20793269787515914, "compression_ratio": 1.7065217391304348, "no_speech_prob": 2.5033950805664062e-06, "words": [{"start": 2488.49, "end": 2488.79, "word": "إذا", "probability": 0.88671875}, {"start": 2488.79, "end": 2489.13, "word": " كانت", "probability": 0.814697265625}, {"start": 2489.13, "end": 2489.33, "word": " هذا", "probability": 0.431884765625}, {"start": 2489.33, "end": 2489.65, "word": " أكبر", "probability": 0.9471028645833334}, {"start": 2489.65, "end": 2489.83, "word": " من", "probability": 0.9951171875}, {"start": 2489.83, "end": 2490.29, "word": " صفر", "probability": 0.7455240885416666}, {"start": 2490.29, "end": 2491.05, "word": " تكون", "probability": 0.7296142578125}, {"start": 2491.05, "end": 2491.33, "word": " أكبر", "probability": 0.9716796875}, {"start": 2491.33, "end": 2491.49, "word": " من", "probability": 0.99462890625}, {"start": 2491.49, "end": 2491.93, "word": " صفر", "probability": 0.9910481770833334}, {"start": 2491.93, "end": 2492.47, "word": " إذا", "probability": 0.8466796875}, {"start": 2492.47, "end": 2492.69, "word": " كان", "probability": 0.99560546875}, {"start": 2492.69, "end": 2492.97, "word": " أصغر", "probability": 0.9744873046875}, {"start": 2492.97, "end": 2493.09, "word": " من", "probability": 0.9873046875}, {"start": 2493.09, "end": 2493.33, "word": " صفر", "probability": 0.9798177083333334}, {"start": 2493.33, "end": 2493.57, "word": " تكون", "probability": 0.7275390625}, {"start": 2493.57, "end": 2494.31, "word": " أشماله", "probability": 0.771142578125}, {"start": 2494.31, "end": 2495.27, "word": " أصغر", "probability": 0.9854736328125}, {"start": 2495.27, "end": 2495.43, "word": " من", "probability": 0.998046875}, {"start": 2495.43, "end": 2495.93, "word": " صفر", "probability": 0.9755859375}, {"start": 2495.93, "end": 2496.93, "word": " قلنا", "probability": 0.6245930989583334}, {"start": 2496.93, "end": 2497.09, "word": " there", "probability": 0.59521484375}, {"start": 2497.09, "end": 2497.45, "word": " exist", "probability": 0.376953125}, {"start": 2497.45, "end": 2499.63, "word": " gc", "probability": 0.3399658203125}, {"start": 2499.63, "end": 2499.97, "word": " اللي", "probability": 0.653076171875}, {"start": 2499.97, "end": 2500.13, "word": " هو", "probability": 0.8828125}, {"start": 2500.13, "end": 2500.45, "word": " عبارة", "probability": 0.993408203125}, {"start": 2500.45, "end": 2500.61, "word": " عن", "probability": 0.9853515625}, {"start": 2500.61, "end": 2500.95, "word": " neighborhood", "probability": 0.468994140625}, {"start": 2500.95, "end": 2501.63, "word": " حوالين", "probability": 0.9234619140625}, {"start": 2501.63, "end": 2501.99, "word": " الـC", "probability": 0.6195475260416666}, {"start": 2501.99, "end": 2502.79, "word": " جزء", "probability": 0.9763997395833334}, {"start": 2502.79, "end": 2503.17, "word": " طبعا", "probability": 0.8980712890625}, {"start": 2503.17, "end": 2503.37, "word": " من", "probability": 0.95458984375}, {"start": 2503.37, "end": 2503.69, "word": " I", "probability": 0.95458984375}, {"start": 2503.69, "end": 2503.85, "word": " اللي", "probability": 0.949462890625}, {"start": 2503.85, "end": 2504.17, "word": " هي", "probability": 0.81689453125}, {"start": 2504.17, "end": 2504.89, "word": " ال", "probability": 0.958984375}, {"start": 2504.89, "end": 2505.31, "word": " interval", "probability": 0.416748046875}, {"start": 2505.31, "end": 2505.87, "word": " معرفة", "probability": 0.726806640625}, {"start": 2505.87, "end": 2506.13, "word": " عليها", "probability": 0.988525390625}, {"start": 2506.13, "end": 2506.37, "word": " G", "probability": 0.70458984375}], "temperature": 1.0}, {"id": 104, "seek": 252937, "start": 2507.59, "end": 2529.37, "text": "such that الـ g of x أشماله لا يسوى أيضًا سفر طبعًا أنا جاعت ليش أعمل تهيأك 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