\documentclass[11pt]{article}
\usepackage{amssymb}
\usepackage{epsfig}

\pagestyle{empty}
\setlength{\textwidth}{6.5in} 
\setlength{\textheight}{9in} 
\setlength{\headheight}{0in} 
\setlength{\evensidemargin}{0in}
\setlength{\oddsidemargin}{0in}
\setlength{\topmargin}{0in}
\input{/home/jeff/tex/shortcuts.tex}

\begin{document}
\begin{center}
{\bf Supplementary problems (assigned 9/5/03)}
\end{center}
\vspace*{.3in}

\begin{enumerate}
\item Prove that every open interval $(a,b)\subset\R$ is uncountable.
\item Prove that a finite union of finite sets is finite.
\item Consider the set $S$ of all subsets of $\N$.  Show that $S$ is 
uncountable. (Hint: there is a close relationship between $S$ and 
the set $2^\N$ discussed in class.)
\item Consider the set $S$ of all finite subsets of $\N$.  Show that
$S$ is countable.
\end{enumerate}

\end{document}
\end
