# 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

- 2000: James R. Munkres:
*Topology*(2nd ed.) ... (previous) ... (next): $1$: Set Theory and Logic: $\S 6$: Finite Sets: Corollary $6.8$