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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 B

1) Prove |N

2) Prove |(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|

Thanks

Let N = Set of all natural numbers

Let B

^{A}= Set of all functions from A to B1) 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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