1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Function theory: Please help!
Loading...