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Mindboggling set of set of functions

  1. Oct 24, 2012 #1
    For two sets X and Y let X^Y be the set of functions from Y to X.

    Prove that there is a bijection between (X^Y)^Z and X^(Y x Z).

    Attempt: These all are so confusing that I don't even know how to start.
     
  2. jcsd
  3. Oct 24, 2012 #2

    haruspex

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    Start by considering what an element of (X^Y)^Z would be like. What would it do?
     
  4. Oct 25, 2012 #3
    It's elements are the ordered pairs (z,(y,x)) aren't they? Where z€Z etc. and if this is true then the elements of X^(Y x Z) are similarly the ordered pairs ((y,z),x). Am I correct?
     
  5. Oct 28, 2012 #4

    haruspex

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    No. It would be a function from Z to X^Y, right? So for each zεZ it would pick out a function from Y to X. And if you supply that function with an element of Y it will give you an element of X. So in total, giving that function from Z to X^Y both an element of Z and an element of Y you find an element of X. Do you see it now?
     
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