Definition of a Countable Set

It is equivalent to a subset of the positive integers

Explanation

A set \(A\) is countable if \(A \sim J_n\) for some finite \(J_n\) (i.e., \(A\) is finite) or \(A \sim \mathbb{N}\) (i.e., \(A\) is countably infinite). Both cases fall under: \(A\) is equivalent to a subset of \(\mathbb{N}\). Countably infinite sets are also called enumerable or denumerable.