Hi, I'm trying to map all the reals into the interval [0,1]. I figured out that you can map all the numbers in the open interval (0,1) to all the reals by the function tan(pi(x-.5)) (so if I wanted a function from all the reals to (0,1) I could just take the inverse). But this problem is much harder when you consider the closed interval. Is there a way to modify the tangent function I gave to make another bijective function that hits the end points 0 and 1? Would I have to create some sort of peicewise function to remedy this problem?(adsbygoogle = window.adsbygoogle || []).push({});

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# Bijection problem

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