I would like to know how to demonstrate that the real numbers and the interval [-1, 1] are equipotent

Thank you

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- Apr 16th 2014, 09:00 PMYeisonintroduction to real analysis
I would like to know how to demonstrate that the real numbers and the interval [-1, 1] are equipotent

Thank you - Apr 17th 2014, 05:18 PMPlatoRe: introduction to real analysis
Using that $\arctan$ function it is easy to show that $\left( { - 1,1} \right) \approx \mathbb{R}$.

Hence your question comes down to showing that $\left[ { - 1,1} \right] \approx \left( { - 1,1} \right)$

The standard proof for the latter is to construct aof a countable set.**shift**