Zermelo's well-ordering theorem ZermelosWellOrderingTheorem 2002-08-25 14:58:03 2002-08-25 15:06:35 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 If $X$ is any set whatsoever, then there exists a well-ordering of $X$. The well-ordering theorem is equivalent to the Axiom of Choice.