# Axiom:Axiom of Countable Choice

## Contents

## Axiom

### Form 1

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

The **axiom of countable choice** states that there exists a sequence:

- $\left\langle{x_n}\right\rangle_{n \mathop \in \N}$

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

### Form 2

Let $S$ be a countable set of non-empty sets.

Then $S$ has a choice function.

## Also known as

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