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\documentclass{exabeamer}
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\usepackage[utf8]{inputenc}
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\begin{document}
\title{Introduction to Analytic Geometry}
\author{Gerhard Kowalewski}
\date{1910}
\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}
