# countably infinite

A set $S$ is countably infinite if there is a bijection between $S$ and $\mathbb{N}$.

As the name implies, any countably infinite set is both countable and infinite.

Countably infinite sets are also sometimes called denumerable.

Title countably infinite CountablyInfinite 2013-03-22 11:59:05 2013-03-22 11:59:05 vampyr (22) vampyr (22) 7 vampyr (22) Definition msc 03E10 denumerable NumerableSet