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
Canonical name	CantorsTheorem
Date of creation	2013-03-22 12:44:50
Last modified on	2013-03-22 12:44:50
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	8
Author	Wkbj79 (1863)
Entry type	Theorem
Classification	msc 03E17
Classification	msc 03E10
Related topic	CantorsDiagonalArgument
Related topic	KonigsTheorem