Informally, a set is said to be finite if it does not go on for ever. That is, any set whose elements could (theoretically) be named, one by one, in a finite amount of time is finite. Finite sets include the empty set, which has zero elements, and every set with a positive integer number of elements.

Formally, a set is finite if it is the empty set or it can be put into bijection with a set $\{0, 1, 2, \ldots, n\}$ for some nonnegative integer $n$.

See also