# doc/beamerug-tutorial.tex

\item<1-> Suppose $p$ were the largest prime number.

\item<2-> Let $q$ be the product of the first $p$ numbers.

\item<3-> Then $q + 1$ is not divisible by any of them.

- \item<1-> Thus $q + 1$ is also prime and greater than $p$.\qedhere

+ \item<1-> But $q + 1$ is greater than $1$, thus divisible by some prime

+ number not in the first $p$ numbers.\qedhere

\uncover<4->{The proof used \textit{reductio ad absurdum}.}

\item<1-| alert@1> Suppose $p$ were the largest prime number.

\item<2-> Let $q$ be the product of the first $p$ numbers.

\item<3-> Then $q+1$ is not divisible by any of them.

- \item<1-> Thus $q+1$ is also prime and greater than $p$.\qedhere

+ \item<1-> But $q + 1$ is greater than $1$, thus divisible by some prime

+ number not in the first $p$ numbers.\qedhere

Copyright 2003--2007 by Till Tantau

- Copyright 2010 by Joseph Wright and Vedran Mileti\'c

+ Copyright 2010,2011 by Joseph Wright and Vedran Mileti\'c

Permission is granted to copy, distribute and/or modify \emph{the documentation} under the terms of the \textsc{gnu} Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled \textsc{gnu} Free Documentation License.