Prove that there is a bijection between (0,1) and (b,infinity) for any real number b. A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea?
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Originally Posted by TitaniumX Prove that there is a bijection between (0,1) and (b,infinity) for any real number b. A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea? How about f(x) = b - 1 + 1/x?
Originally Posted by TitaniumX Prove that there is a bijection between (0,1) and (b,infinity) for any real number b. A function is needed. I've though about the function f(x)=b/x but it won't work if b<=0. Any idea? is (I believe) standard for expanding to , so I would use this. This can be relatively easily manipulated to give you the function you want. (Half it to give you a bijection between and , then scale).
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