Page "Countable set" Paragraph 1

Some authors use countable set to mean a set with the same cardinality as the set of natural numbers.

The difference between the two definitions is that under the former, finite sets are also considered to be countable, while under the latter definition, they are not considered to be countable.

To resolve this ambiguity, the term at most countable is sometimes used for the former notion, and countably infinite for the latter.

The term denumerable can also be used to mean countably infinite, or countable, in contrast with the term nondenumerable.