Cantor's theorem

Named after German mathematician George Cantor (1845-1918) who stated and proved this theorem.

Cantor's theorem

1. (set theory) A theorem in set theory which states for any set ${\displaystyle A}$, the set of all subsets of ${\displaystyle A}$ (the power set of ${\displaystyle A}$, denoted by ${\displaystyle {\mathcal {P}}(A)}$) has a strictly greater cardinality than ${\displaystyle A}$ itself.