File:OmegaPlusOmega.pdf
Summary
| Description |
English: Illustration of the ordinal number , obtained as disjoint union { (0,n) : n∈ℕ } ∪ { (1,n) : n∈ℕ } , ordered lexicographically. Numbers refer to the second component of pairs; the first can be obtained from color. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:OmegaPlusOmega.pdf * File:OmegaPlusOmega svg.svg * File:TwoTimesOmega.pdf * File:TwoTimesOmega svg.svg |
LaTeX source code |
|---|
\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\usepackage[paperwidth=215mm,paperheight=20mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{215mm}
\setlength{\textheight}{20mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
% colors
\definecolor{fA} {rgb}{0.50,0.00,0.00} % lower omega
\definecolor{fB} {rgb}{0.00,0.00,0.50} % higher omega
\newcommand{\NUM}[2]{%
\put(#2,3){\line(0,1){4}}%
\put(#2,8){\makebox(0,0)[b]{$#1$}}%
}
\newcommand{\Num}[2]{%
\put(#2,3){\line(0,1){4}}%
%\put(#2,8){\makebox(0,0)[b]{$#1$}}%
}
\newcommand{\num}[2]{%
\put(#2,3){\line(0,1){4}}%
%\put(#2,8){\makebox(0,0)[b]{$#1$}}%
}
\begin{document}
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\NUM{ 2}{ 9.750}%
\NUM{ 3}{ 14.262}%
\NUM{ 4}{ 18.549}%
\NUM{ 5}{ 22.622}%
\num{ 6}{ 26.491}%
\num{ 7}{ 30.166}%
\num{ 8}{ 33.658}%
\num{ 9}{ 36.975}%
\NUM{ 10}{ 40.126}%
\num{ 11}{ 43.120}%
\num{ 12}{ 45.964}%
\num{ 13}{ 48.666}%
\num{ 14}{ 51.233}%
\NUM{ 15}{ 53.671}%
\num{ 16}{ 55.987}%
\num{ 17}{ 58.188}%
\num{ 18}{ 60.279}%
\num{ 19}{ 62.265}%
\NUM{ 20}{ 64.151}%
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\num{ 28}{ 76.217}%
\num{ 29}{ 77.406}%
\NUM{ 30}{ 78.536}%
\num{ 31}{ 79.609}%
\num{ 32}{ 80.629}%
\num{ 33}{ 81.597}%
\num{ 34}{ 82.518}%
\num{ 35}{ 83.392}%
\num{ 36}{ 84.222}%
\num{ 37}{ 85.011}%
\num{ 38}{ 85.760}%
\num{ 39}{ 86.472}%
\NUM{ 40}{ 87.149}%
\num{ 41}{ 87.791}%
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\num{ 59}{ 95.151}%
\Num{ 60}{ 95.393}%
\num{ 61}{ 95.623}%
\num{ 62}{ 95.842}%
\num{ 63}{ 96.050}%
\num{ 64}{ 96.248}%
\num{ 65}{ 96.435}%
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\num{ 89}{ 98.959}%
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\num{ 94}{ 99.195}%
\num{ 95}{ 99.235}%
\num{ 96}{ 99.273}%
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\num{102}{ 99.466}%
\num{103}{ 99.492}%
\num{104}{ 99.518}%
\num{105}{ 99.542}%
\num{106}{ 99.565}%
\num{107}{ 99.587}%
\num{108}{ 99.607}%
\num{109}{ 99.627}%
\Num{100}{ 99.646}%
\num{111}{ 99.663}%
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\num{127}{ 99.852}%
\num{128}{ 99.859}%
\num{129}{ 99.866}%
\Num{130}{ 99.873}%
\color{fB}%
\put(100,5){\line(1,0){100}}%
\NUM{ 0}{100.000}%
\NUM{ 1}{105.000}%
\NUM{ 2}{109.750}%
\NUM{ 3}{114.262}%
\NUM{ 4}{118.549}%
\NUM{ 5}{122.622}%
\num{ 6}{126.491}%
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\num{ 24}{170.801}%
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\num{ 29}{177.406}%
\NUM{ 30}{178.536}%
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\num{123}{199.818}%
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\num{127}{199.852}%
\num{128}{199.859}%
\num{129}{199.866}%
\Num{130}{199.873}%
\end{picture}
\end{document}
|
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