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Problem 2. Prove that open interval (-1, 1) and closed interval [-1,1] are bijective. (Open interval does not include endpoint, and closed interval does include endpoints.)

          Problem 2. Prove that open interval (-1, 1) and closed interval [-1,1] are bijective.
(Open interval does not include endpoint, and closed interval does include endpoints.)
        
Problem 2. Prove that open interval (-1, 1) and closed interval [-1,1] are bijective.
(Open interval does not include endpoint, and closed interval does include endpoints.)

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Problem 2. Prove that open interval (-1,1 and closed interval [-1,1] are bijective (Open interval does not include endpoint, and closed interval does include endpoints.)
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Consider two sets A and B and a function f: A to B between them. Find a bijection from the half-open interval [0,1) to the closed interval [0,1] and show that it is bijective, or else show why it is impossible.

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Transcript

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00:01 Hello everyone, so here the function is if a2b to 01, where f x is equal to x minus a by b minus a where x belongs to ab.
00:13 Now for x1 x2 belongs to a b, let f x1 is equal to fx2.
00:24 So here x1 minus a by b minus a is equal to xx2.
00:30 X 2 minus a by b minus a so here x 1 is equal to x2 therefore f is injective now let alpha belongs to 0 1 and f beta is equal to alpha so here beta minus alpha a by b minus a is equal to alpha so here beta is equal to a plus alpha b minus a therefore beta belongs to ab.
01:09 So for any if, xylene belongs to 01, beta belongs to 0b such that f beta is equal to alpha...
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