# Cartesian product proof

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Cartesian product of finitely many countable sets is countable.

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##### Solution Summary

This is a proof regarding the Cartesian product of countable sets.

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First let's state the counting theorem:

"The Counting Theorem":

Let S be a set. The following are equivalent.

(i) S is either finite or a countably infinite set.

(ii) Either S = Null or there is a surjective map alpha: N ---> S.

(iii) There is an injective map beta: S ---> N.

If any of these three equivalent conditions hold, then we say

that S is a countable set.

This theorem has a ...

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