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Cardinality problem

  1. Sep 29, 2010 #1


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    I have been studying set theory, and come across a few problems that I have not been able to solve. I am trying to prove the bijections exist.

    Let N = Set of all natural numbers
    Let BA = Set of all functions from A to B

    1) Prove |NN x NN| = |NN|

    2) Prove |(NN)N| = |NN|

    Any explanation into the inspiration behind solutions would be greatly appreciated.

    It is simple to consider the identity function going the obvious direction, so I really only need to prove injection (ie. |A| < |B| for the sets in the order stated).


    Edit: Solved
    Last edited: Sep 30, 2010
  2. jcsd
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