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## Homework Statement

I need to find a bijection between (0,1) and [0,1) in R. It can go in either direction since it is a bijection.

## Homework Equations

I can't think of any equations at all!

## The Attempt at a Solution

Something like f(x) = 1/[(1/x)+1] for x in A

x for x not in A

where A={1/2, 1/3, 1/4, ...}

Having an issue with zero though.