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Math Help - introduction to real analysis

  1. #1
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    introduction to real analysis

    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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  2. #2
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    Re: introduction to real analysis

    Quote Originally Posted by Yeison View Post
    I would like to know how to demonstrate that the real numbers and the interval [-1, 1] are equipotent.
    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 a shift of a countable set.
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