Cantor’s theorem

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