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Homework Help: Discrete Math Question

  1. Mar 9, 2004 #1
    Hi,

    Does there exist a function f: Z+ --> Z which is onto?

    I had been told there such funciton exists, since both Z+ and Z are countable infinite series. Thus there exists some transformation that could map Z+ to every single Z

    However, I still can't shake off the idea that since Z+ is a subset of Z, there just aren't "enough" Z+ to cover every single Z, and the 0 in Z is giving me trouble as well


    Thanks for any input
     
  2. jcsd
  3. Mar 10, 2004 #2

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    After goofing around with pencil and paper,

    If N is a positive integer, it seems like this does the trick:

    f(N)= (N/2)(-1)^N + 1/4 + (1/4)(-1)^(N+1).

    This gives:
    f(1)=0
    f(2)=1
    f(3)=-1
    f(4)=2
    f(5)=-2
    f(6)=3
    f(7)=-3

    and so on. Is that the sort of function that you are talking about?
     
  4. Mar 10, 2004 #3
    Oh wow, that looks like it.

    Now I'm a firm believer of countable infinity. :smile:


    Your equation will do, thanks!

    I'm wondering if there is any easier function. This question isn't suppose to be a tough one.
     
  5. Mar 10, 2004 #4

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    I'll bet there is one that looks less messy, given that I just kludged that one up by trial & error.
     
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