%% %% An UIT Edition example %% %% Example 04-01-4 on page 71. %% %% 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) 1,2,3 %% ==== \PassOptionsToClass{}{beamer} \documentclass{exabeamer} \title{Introduction to Analytic Geometry} \author{Gerhard Kowalewski} \date{1910} %\StartShownPreambleCommands \usefonttheme{structureitalicserif} %\StopShownPreambleCommands \begin{document} \frame{\maketitle} \section{Research and studies} \begin{frame}{The integral and its geometric applications.} We assume that the theory of irrational numbers is known. \begin{enumerate}[<+->] \item The \emph{interval} $\langle a,b\rangle$ consists of all 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 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 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} \end{document}