Axiom:Axiom of Countable Choice

Axiom
Let $\left\langle{S_n}\right\rangle_{n \in \N}$ be a sequence of non-empty sets.

The axiom of countable choice states that there exists a sequence:
 * $\left\langle{x_n}\right\rangle_{n \in \N}$

such that $x_n \in S_n$ for all $n \in \N$.

This axiom can be abbreviated $\mathrm{ACC}$, $\mathrm{AC}_\omega$, or $\mathrm{AC}_\N$.

Also see
This axiom is a weaker form of the axiom of dependent choice, as shown in Axiom of Dependent Choice Implies Axiom of Countable Choice.