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Math Help - bijective

  1. #1
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    bijective

    Hey i have a question
    f:X--->Y
    X=Z(integers) Y={1,2,3}*Z(integers)

    i have to find a bijective map. So obviously i prove it is injective amd surjective. However i am confused about how because my examples in my notes are different to this. They all give an f(X) Function whereas this does not.
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  2. #2
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    Quote Originally Posted by math_lete View Post
    Hey i have a question
    f:X--->Y
    X=Z(integers) Y={1,2,3}*Z(integers)
    If by {1,2,3}*Z you mean \{ 1,2,3\}  \times \mathbb{Z} then try to show that
    \phi :\mathbb{Z} \mapsto \{ 1,2,3\}  \times \mathbb{Z}\;,\;\phi (z) = \left( {\bmod (z,3) + 1,\left\lceil {\frac{z}{3}} \right\rceil } \right) is a bijection.
    Last edited by Plato; November 9th 2008 at 05:09 AM.
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