transitive Transitive 2002-01-23 10:59:21 2004-03-31 15:38:08 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 Let $A$ be a set. $A$ is said to be \emph{transitive} if whenever $x\in A$ then $x\subseteq A$. Equivalently, $A$ is transitive if whenever $x\in A$ and $y\in x$ then $y\in A$.