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Math Help - find a function

  1. #1
    Member pberardi's Avatar
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    find a function

    That maps N onto N bu is not a one to one function. I can create a function that is not one to one on N such as x^2 -2x + 2 but it turns out to not be onto. Can someone try to find a function like this? Also, could you please show that it is indeed onto? I kind of need a good example of an onto proof.

    Thanks,
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by pberardi View Post
    That maps N onto N bu is not a one to one function. I can create a function that is not one to one on N such as x^2 -2x + 2 but it turns out to not be onto. Can someone try to find a function like this? Also, could you please show that it is indeed onto? I kind of need a good example of an onto proof.

    Thanks,
    I assume your definition for \mathbb{N} is the positive integers (that is, it does not include zero).

    f: \mathbb{N} \mapsto \mathbb{N} defined by f(x) = \left \{ \begin{array}{lcl}1 & & \mbox{ if } x = 1 \\ x - 1 & & \mbox{ if } x > 1 \end{array} \right.
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  3. #3
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    You can also use the floor function: \left\lfloor {\frac{n}{2}} \right\rfloor .

    To show onto, note that every integer is one-half of some integer.
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