# Category:Axiom of Countable Choice

This category contains results about Axiom of Countable Choice.
Definitions specific to this category can be found in Definitions/Axiom of Countable Choice.

### Form 1

Let $\sequence {S_n}_{n \mathop \in \N}$ be a sequence of non-empty sets.

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

$\sequence {x_n}_{n \mathop \in \N}$

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.