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I'm completely lost, and I haven't been able to get anything yet. I looked at some that were similar to this problem, and still got pretty lost.

Arnaldo
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Britton Harsch
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  • One quick example: Map $1/2$ to $0$, then map $3/4$ to $1/2$, $7/8$ to $3/4$, $15/16$ to $7/8$, etc. Everything else gets mapped to itself. – Brian Tung Feb 06 '17 at 20:31

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Consider a sequence $\left(\dfrac{1}{n+1}\right)$ and put $f\left(\dfrac{1}{2}\right)=0$, $f\left(\dfrac{1}{3}\right)=\dfrac{1}{2}$ and so on, i.e. $f\left(\dfrac{1}{n+1}\right)=\dfrac{1}{n}$ for $n=2,3\dots$. For the other $x$ put $f(x)=x$.

szw1710
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