Cantor's theorem CantorsTheorem 2002-06-05 23:09:34 2007-08-08 23:04:36 Theorem % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \def\P{{\mathcal P}} Let $X$ be any set and $\P(X)$ its power set. 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, $|X|<|\P(X)|$.