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Math Help - Finding a Bijection

  1. #1
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    Finding a Bijection

    Given: A = [0,1] B = [0,1)

    I'm needing to find a bijection between the two sets to show they are equinumerous. My understanding of what is being asked is to find some function f such that f: A -> B and f: B -> A

    Am I on the correct track? Other ideas or ways of looking at the problem?

    Thanks.

    Edit: I figured it out. I'm needing to show that A is injective and surjective of B by some function f
    Last edited by spruancejr; February 29th 2012 at 07:31 AM.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Finding a Bijection

    Quote Originally Posted by spruancejr View Post
    Given: A = [0,1] B = [0,1) I'm needing to find a bijection between the two sets to show they are equinumerous.
    f(x)=\begin{Bmatrix} x & \mbox{ if }& x\not\in\{1,\;1/2,\;1/4,\;1/8,\;\ldots\}\\x/2 & \mbox{if}& x\in\{1,\;1/2,\;1/4,\;1/8,\;\ldots\}\end{matrix}

    is a bijection between [0,1] and [0,1).
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