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-%%
-%% An UIT Edition example
-%%
-%% Example 01-02-1 on page 10.
-%%
-%% Copyright (C) 2012 Vo\ss
-%%
-%% 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
-
-%% ====
-\PassOptionsToClass{}{beamer}
-\documentclass{exabeamer}
-\usepackage[utf8]{inputenc}
-
-%\StartShownPreambleCommands
-\documentclass{beamer}
-%\StopShownPreambleCommands
-
-\begin{document}
-\begin{frame}{Negative example}
-We assume that the \textbf{theory} of \textbf{irrational numbers} is known.
-\begin{enumerate}
- \item The \textbf{interval} $\langle a,b\rangle$ contains all \textbf{numbers} $x$ that satisfy
- the condition $a\le x \le b$.
- \item A \textbf{sequence of numbers} or \textbf{sequence} is created by replacing each
- member of the infinite \textbf{sequence of numbers} $1,2,3,\ldots$ by some rational or
- irrational number, i.e.\ each $n$ by a number $x_n$.
- \item $\lim x_n=g$ means that almost all members of the sequence are within each
- \textbf{neighbourhood} of $g$.
- \item \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{enumerate}
-\end{frame}
-\begin{frame}{Positive example}
-We assume that the \emph{theory} of \emph{irrational numbers} is know.
-\begin{enumerate}
- \item The \emph{interval} $\langle a,b\rangle$ contains all \emph{numbers} $x$ that satisfy
- the condition $a\le x \le b$.
- \item A \emph{sequence of numbers} or \emph{sequence} is created by replacing each
- member of the infinite \emph{sequence of numbers} $1,2,3,\ldots$ by some rational or
- irrational number, i.e.\ each $n$ by a number $x_n$.
- \item $\lim x_n=g$ means that almost all members of the sequence are within each
- \emph{neighbourhood} of $g$.
- \item \emph{Convergence criterion}: The sequence $x_1,x_2,x_3,\ldots$ converges
-if and only if \emph{each} sub-sequence $x^\prime_1,x^\prime_2,
-x^\prime_3,\ldots$ satisfies the relation $\lim(x_n-x^\prime_n)=0$.
-\end{enumerate}
-\end{frame}
-\end{document}