# Cantor’s theorem

Let $X$ be any set and ${\mathcal{P}}(X)$ its power set. Then there is no bijection between $X$ and ${\mathcal{P}}(X)$. Moreover, the cardinality of ${\mathcal{P}}(X)$ is strictly greater than that of $X$; that is, $|X|<|{\mathcal{P}}(X)|$.

Title Cantor’s theorem CantorsTheorem 2013-03-22 12:44:50 2013-03-22 12:44:50 Wkbj79 (1863) Wkbj79 (1863) 8 Wkbj79 (1863) Theorem msc 03E17 msc 03E10 CantorsDiagonalArgument KonigsTheorem