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Possible Duplicate:
Proving $\mathbb{N}^k$ is countable

I would like to prove that if S is countable then for any positive integer n the set $S^n$ (the n-fold Cartesian product of S with itself) is countable using mathematical induction.

I think I should initialize it at n=0 but I don't know where to go from there.

Thanks so much for the help

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    I made it with your help. Many thanks !2012-05-01

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Brian gave me some excellent advise and I found a way to do it. Showing that the cartesian $S^n \times S$