Definition:Infinite Set

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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 $n$.

Also see

  • Results about infinite sets can be found here.

Historical Note

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