Countable set

A set $A$ is countable if there exists an injective function $f\colon A\to\mathbb{N}$.

Equivalently, $A$ is countable if it is finite or there exists a bijection $f\colon A\to\mathbb{N}$. In terms of cardinality , this says $|A|\le|\mathbb{N}|$.

Examples:

• $\mathbb{N}$ and $\mathbb{Z}$ are countable.
• The set of rational numbers $\mathbb{Q}$ is countable.
• Any finite set is countable.