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(a) Show that the function g: (0,1)→(0,∞)with g(x) =(1−x)/x is a bijection (b)Show that the natural...

(a) Show that the function g: (0,1)→(0,∞)with g(x) =(1−x)/x is a bijection

(b)Show that the natural logarithm ln: (0,∞)→R is a bijection

(c) Show that R has the same cardinality as the interval (0,1)

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Answer #1

For part a and b, hope you can easily understand the solutions. For part c if you don't know the Schroder Bernstein theorem then you can take help from any cardinality book. ?

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