%% %% 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}