EveryOrderedFieldWithTheLeastUpperBoundPropertyIsIsomorphicToTheRealNumbers 2004-02-20 13:53:19 2004-02-20 13:53:19 Theorem real number % 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 Let $F$ be an ordered field. If $F$ satisfies the least upper bound property then $F$ is isomorphic as an ordered field to the real numbers $\mathbb{R}$.