<?xml version="1.0" encoding="UTF-8"?>

<record version="2" id="1345">
 <title>linearly ordered</title>
 <name>LinearlyOrdered</name>
 <created>2002-01-05 14:30:45</created>
 <modified>2006-10-28 23:47:19</modified>
 <type>Definition</type>
 <creator id="2" name="akrowne"/>
 <author id="2" name="akrowne"/>
 <classification>
	<category scheme="msc" code="03-00"/>
 </classification>
 <synonyms>
	<synonym concept="linearly ordered" alias="linear ordering"/>
	<synonym concept="linearly ordered" alias="totally ordered"/>
	<synonym concept="linearly ordered" alias="total ordering"/>
 </synonyms>
 <related>
	<object name="chain"/>
 </related>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}
</preamble>
 <content>An ordering $\le$ (or $&lt;$) of $A$ is called \emph{linear} or \emph{total} if any two elements of $A$ are comparable.  The pair $(A,\le)$ is then called a \emph{linearly ordered set}.</content>
</record>
