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Math Help - f:\mathbb{N}\to S

  1. #1
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    f:\mathbb{N}\to S

    f:\mathbb{N}\to S

    Where S:\{s\in S| \ s=2p+1, \ p\in\mathbb{Z}\}

    I need to define a 1-1 function.

    f(n)=\begin{cases}n, & \text{when n is odd}\\?, & \text{when n is even}\end{cases}

    I haven't been able to think of something that will produce negative odd integers from even natural numbers.
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  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: f:\mathbb{N}\to S

    Better, one-to-one and onto function from \mathbb{N} to S:

     f(n)=\frac{(-1)^n}{2}(-2n+(-1)^n+1)


    Therefor,  |S|=\aleph_0
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