# Definition:Infinite Set

## Definition

A set which is not finite is called infinite.

That is, it is a set for which there is no bijection between it and any $\N_n$, where $\N_n$ is the the set of all elements of $n$ less than $n$, no matter how big we make $n$.

## Historical Note

The idea of the actual existence of infinite sets as mathematical objects was pioneered by Georg Cantor.