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How to define a bijection between $(0,1)$ and $(0,1

Choose an infinite sequence (xn)n⩾1 of distinct elements of (0,1). Let X={xn∣n⩾1}, hence X⊂(0,1). Let x0=1. Define f(xn)=xn+1 for every n⩾0 and f(x)=x ...

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