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Cardinality problem

  • Thread starter jav
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jav
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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).

Thanks



Edit: Solved
 
Last edited:

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