File:Cantor's first uncountability proof Case 1.pdf

Summary

Description
English: Used to illustrate case 1 of en:Cantor's first uncountability proof.
Date
Source Own work; after a specification of en:User:RJGray
Author Jochen Burghardt
Other versions The remaining cases are shown in File:Cantor's first uncountability proof Case 2.pdf and File:Cantor's first uncountability proof Case 3.pdf. Svg versions of all three files are found at File:Cantor's first uncountability proof Case 1 svg.svg, File:Cantor's first uncountability proof Case 2 svg.svg, and File:Cantor's first uncountability proof Case 3 svg.svg.
LaTeX source
\documentclass[12pt]{article}
\setlength{\unitlength}{0.75mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=125\unitlength,paperheight=25\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{125\unitlength}
\setlength{\textheight}{25\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}

% parantheses heights
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\newlength{\parantB}
\setlength{\parantA}{00.0mm}
\setlength{\parantB}{03.4mm}

% colors
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\definecolor{cGvn}      {rgb}{0.00,0.00,0.50}   % given interval
\definecolor{cISq}      {rgb}{0.80,0.80,0.80}   % interval sequence
\definecolor{cWit}      {rgb}{0.00,0.40,0.00}   % witness point
\definecolor{cLmt}      {rgb}{0.00,0.40,0.00}   % limit / innermost interval
\definecolor{cCns}      {rgb}{0.40,0.00,0.00}   % considered interval
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% which case to render (select by defining as #1)
\newcommand{\caseI}[1]{#1}
\newcommand{\caseII}[1]{}
\newcommand{\caseIII}[1]{}

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% standard math fonts
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%
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% interval limit
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%\textcolor{cLmt}{\put(54.645,0){\makebox(0.000,0.000)[b]{$\a_\infty \!=\! \b_\infty$}}}%
%
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%
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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% label (debug only)
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% interval lower bound sequence
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%
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% interval upper bound sequence
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%
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%\textcolor{cISq}{\put(100.550,0.000){\makebox(0.000,0.000)[b]{$\b_3$}}}%
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% interval limits
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%
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}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\end{picture}
\end{document}

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Category:CC-BY-SA-4.0#Cantor's%20first%20uncountability%20proof%20Case%201.pdf
Category:Self-published work Category:Files by User:Jochen Burghardt Category:Countable sets Category:Images with LaTeX source code
Category:CC-BY-SA-4.0 Category:Countable sets Category:Files by User:Jochen Burghardt Category:Images with LaTeX source code Category:Self-published work