Finite Product of Finite Sets is Finite

Theorem

Let $\sequence {S_n}$ be a sequence of finite sets.

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

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

Proof

This theorem requires a proof. In particular: Boring induction from Product of Finite Sets is Finite You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

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