At Most Countable Set

Definition

At Most Countable Set

A set is at most countable if there exists an injection :

Thus is either a finite set (including the empty set) or a countably infinite set. Each element can be assigned a distinct natural number; not every natural number needs to be used.
Here denotes aleph-null, the cardinality of .

Terminology

The term countable may mean either at most countable or countably infinite, depending on convention. At most countable explicitly includes finite sets. A set that is not at most countable is uncountable.