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Function theory: Please help!

  1. Apr 12, 2004 #1
    Please help me. I'm trying to find functions where f:N-->N (the set of natural numbers to the set of natural numbers), such that:

    f is surjective but not injective,
    f is neither surjective nor injective

    I'm really not sure how to determine these. Thanks for your consideration.
  2. jcsd
  3. Apr 12, 2004 #2
    errr... now that I look back at my other answers ( i had to find one that is bijective and one that is not surjective but injective), i don't even know if those are right.

    For bijective, could you have f(n) = n ?
    For injective but not surjective, could you have f(n) = 2n + 1 ?

    I'm so confused.
  4. Apr 12, 2004 #3
    OK hehe i think i figured some stuff out, for my first original question, f(n) = (n-5) + 2 works. But I still need help on my last question! please!

    Also, the most recent two questions i asked can be disregarded... haha wow sorry if i confused anyone
  5. Apr 13, 2004 #4
    f: N -> N

    If f(n) = n, f is bijective.
    If f(n) = 2n, f is injective but not surjective (2n+1 also works).
    If f(n) = floor(n/2), f is surjective but not injective.
    If f(n) = constant, f is neither injective nor surjective.

    I think these are all pretty well-known examples.
  6. Apr 13, 2004 #5
    thanks, much appreciated
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