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

<record version="2" id="880">
 <title>countable</title>
 <name>Countable</name>
 <created>2001-11-16 00:40:40</created>
 <modified>2002-02-27 23:38:07</modified>
 <type>Definition</type>
 <creator id="22" name="vampyr"/>
 <author id="22" name="vampyr"/>
 <classification>
	<category scheme="msc" code="03E10"/>
 </classification>
 <related>
	<object name="ProofThatTheRationalsAreCountable"/>
	<object name="CantorSet"/>
	<object name="AverageValueOfFunction"/>
	<object name="NumerableSet"/>
 </related>
 <preamble>\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic}</preamble>
 <content>A set $S$ is countable if there exists a bijection between $S$ and some subset of $\mathbb{N}$.

All finite sets are countable.</content>
</record>
