Finite Product of Finite Sets is Finite

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Theorem

Let $\langle S_n \rangle$ be a sequence of finite sets.

Let $\displaystyle \prod_{k \mathop = 1}^n S_k$ be their Cartesian product.


Then $\displaystyle \prod_{k \mathop = 1}^n S_k$ is also a finite set.


Proof


Sources