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+%%
+%% An UIT Edition example
+%%
+%% 1st edition
+%%
+%% Example 04-03-2 on page 76.
+%%
+%% Copyright (C) 2012 Herbert Voss
+%%
+%% It may be distributed and/or modified under the conditions
+%% of the LaTeX Project Public License, either version 1.3
+%% of this license or (at your option) any later version.
+%%
+%% See http://www.latex-project.org/lppl.txt for details.
+%%
+%%
+%% ====
+% Show page(s) 1,2
+%%
+%%
+\documentclass[a5paper,12pt]{exaarticle}
+\pagestyle{empty}
+\setlength\textwidth{192.32402pt}
+\usepackage[british]{babel}
+\usepackage[utf8]{inputenc}
+%\StartShownPreambleCommands
+\documentclass[a5paper,12pt]{article}
+\usepackage[envcountsect]{beamerarticle}
+\mode<article>{% only article mode
+ \usepackage{fullpage} \usepackage[linktocpage]{hyperref} }
+\mode<presentation>{% only slides
+ \setbeamertemplate{background canvas}[vertical shading][bottom=red!10,top=blue!10]
+ \usetheme{Warsaw} \usefonttheme[onlysmall]{structurebold} }
+%\StopShownPreambleCommands
+\begin{document}
+\title{Introduction to analytic geometry}
+\author{Gerhard Kowalewski} \date{1910}
+\frame{\titlepage}
+\section<presentation>*{Overview}
+\begin{frame}{Overview} \tableofcontents[part=1,pausesections] \end{frame}
+\AtBeginSubsection[]{\begin{frame}<beamer>
+ \frametitle{Overview} \tableofcontents[current,currentsubsection] \end{frame} }
+\part<presentation>{Main part}
+\section{Research and studies}
+\begin{frame}{The integral and its geometric applications.}
+We assume that the theory of irrational numbers is known.
+\end{frame}
+\subsection{Interval}
+\begin{frame}{Definition}
+The \emph{interval} $\langle a,b\rangle$ consists of all numbers $x$ that
+satisfy the condition $a\le x\le b$.
+\end{frame}
+\subsection{Sequence of numbers}
+\begin{frame}{Definition of a sequence}
+A \emph{sequence of numbers} or \emph{sequence} is created by replacing each member
+of the infinite sequence of numbers $1,2,3,\ldots$ by some rational or irrational
+number, i.e.\ each $n$ by a number $x_n$.
+\end{frame}
+\subsection{Limits}
+\begin{frame}{Definition of a limit}
+$\lim x_n=g$ means that almost all members of the sequence are within each neighbourhood of $g$.
+\end{frame}
+\subsection{Convergence criterion}
+\begin{frame}{Definition of convergence}
+\textbf{Convergence criterion}: The sequence $x_1,x_2,x_3,\ldots$ converges if and
+only if \textbf{each} sub-sequence $x^\prime_1,x^\prime_2, x^\prime_3,\ldots$
+satisfies the relation $\lim(x_n-x^\prime_n)=0$.
+\end{frame}
+\end{document}