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.(adsbygoogle = window.adsbygoogle || []).push({});

Let N = Set of all natural numbers

Let B^{A}= Set of all functions from A to B

1) Prove |N^{N}x N^{N}| = |N^{N}|

2) Prove |(N^{N})^{N}| = |N^{N}|

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

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# Homework Help: Cardinality problem

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