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Onto, but not one-to-one

  1. Sep 5, 2007 #1
    [SOLVED] Onto, but not one-to-one

    I need a function

    f: N -> N such that f is onto, but not one-to-one, and I can't think of one to save my life, any suggestions?
     
  2. jcsd
  3. Sep 5, 2007 #2

    EnumaElish

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    f({a,b}) = {x}.

    Sorry, you posted N to N...
     
  4. Sep 5, 2007 #3
    what does {x} stand for?
     
  5. Sep 5, 2007 #4

    EnumaElish

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    f(1) = 2
    f(x) = x for x > 1.

    Doesn't work.

    Hmm...
     
    Last edited: Sep 5, 2007
  6. Sep 5, 2007 #5
    what about

    f(1)=1
    f(2)=1
    f(n) = n-1 for n>2
     
  7. Sep 5, 2007 #6

    EnumaElish

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    I think you have just found one.
     
  8. Sep 5, 2007 #7
    k, well your original post helped me, so thank you!
     
  9. Sep 5, 2007 #8

    mathwonk

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    what about f(x) = 2x? no.....

    or greatest integer not greatER THan x/2, +1?

    or f(x) = x-1, for x >1 and lets see f(!) = ?

    how long did you think about this?
     
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