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

Result R4627 on D16: Countable set
Subresult of R262: Countable union of countable sets is countable

Formulation 0

Let $X_0, X_1, X_2, \ldots$ each be a D16: Countable set such that

(i)	$\bigcup_{n \in \mathbb{N}} X_n$ is the D77: Set union of $X_0, X_1, X_2, \ldots$

Then $\bigcup_{n \in \mathbb{N}} X_n$ is a D16: Countable set.

Proofs

Proof 0

Let $X_0, X_1, X_2, \ldots$ each be a D16: Countable set such that

(i)	$\bigcup_{n \in \mathbb{N}} X_n$ is the D77: Set union of $X_0, X_1, X_2, \ldots$

This result is a particular case of R262: Countable union of countable sets is countable. $\square$