Could one give me a bijection between $[0,1]$ and $[0,1)$ ?
I am trying to find a function $f:[0,2]\to[0,2]$ such that $\forall0\le x\le2,f^{-1}(x)$ is a tuple (2 elements), and such a bijection would give me an answer easily.
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4A very small modification in this answer or this answer to a very similar question will do the trick. – Brian M. Scott Jan 05 '15 at 19:35
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How about sending $$\frac1n\mapsto\frac1{n+1}$$ where $n\ge 1$ is an integer. Leave the rest unchanged.
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