Counterexample 2004-10-09 19:08:16 2005-02-28 19:31:13 Definition % 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 A \emph{counterexample} is an example which is used to prove that a statement is false. For instance, to disprove that the statement ``For all $n$, $2^{2^n} + 1$ is prime.'', one could exhibit $5$ as a counterexample; since $2^{2^5} + 1 = 641 \times 6700417$, the statement is false.