Countably infinite set

Definition

A set $A$ is countably infinite when there is a bijective function $f \colon \mathbb{N} \to A$.

Remarks

Another name is denumerable. Its cardinality is aleph-null. Examples are $\mathbb{N}$, $\mathbb{Z}$ and $\mathbb{Q}$, and also the set of primes. A set is countably infinite exactly when it is countable and infinite.

Explanations

L1 human

A countably infinite set can be listed as $a_0, a_1, a_2, \dots$ without end, and each element appears exactly one time. The integers have such a list: $0, 1, -1, 2, -2, \dots$.