ThmDex – An index of mathematical definitions, results, and conjectures.

Result R3506 on D16: Countable set

Finite union of countable sets is countable

Formulation 0

Let $X_1, \dots, X_N$ each be a D16: Countable set.

Then $\bigcup_{n = 1}^N X_n$ is a D16: Countable set.

Proofs

Proof 0

Let $X_1, \dots, X_N$ each be a D16: Countable set.

This is a subresult to R262: Countable union of countable sets is countable. $\square$