File:OmegaPlusOmega.pdf

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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}
\sf
\begin{picture}(210,15)(-5,0)
\color{fA}%
\put(0,5){\line(1,0){100}}%
\NUM{  0}{  0.000}%
\NUM{  1}{  5.000}%
\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}%
\num{ 21}{ 65.944}%
\num{ 22}{ 67.647}%
\num{ 23}{ 69.264}%
\num{ 24}{ 70.801}%
\NUM{ 25}{ 72.261}%
\num{ 26}{ 73.648}%
\num{ 27}{ 74.966}%
\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}%
\num{ 42}{ 88.402}%
\num{ 43}{ 88.982}%
\num{ 44}{ 89.533}%
\num{ 45}{ 90.056}%
\num{ 46}{ 90.553}%
\num{ 47}{ 91.026}%
\num{ 48}{ 91.474}%
\num{ 49}{ 91.901}%
\num{ 50}{ 92.306}%
\num{ 51}{ 92.690}%
\num{ 52}{ 93.056}%
\num{ 53}{ 93.403}%
\num{ 54}{ 93.733}%
\num{ 55}{ 94.046}%
\num{ 56}{ 94.344}%
\num{ 57}{ 94.627}%
\num{ 58}{ 94.895}%
\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}%
\num{ 66}{ 96.613}%
\num{ 67}{ 96.783}%
\num{ 68}{ 96.944}%
\num{ 69}{ 97.096}%
\Num{ 70}{ 97.242}%
\num{ 71}{ 97.380}%
\num{ 72}{ 97.511}%
\num{ 73}{ 97.635}%
\num{ 74}{ 97.753}%
\num{ 75}{ 97.866}%
\num{ 76}{ 97.972}%
\num{ 77}{ 98.074}%
\num{ 78}{ 98.170}%
\num{ 79}{ 98.262}%
\Num{ 80}{ 98.348}%
\num{ 81}{ 98.431}%
\num{ 82}{ 98.509}%
\num{ 83}{ 98.584}%
\num{ 84}{ 98.655}%
\num{ 85}{ 98.722}%
\num{ 86}{ 98.786}%
\num{ 87}{ 98.847}%
\num{ 88}{ 98.904}%
\num{ 89}{ 98.959}%
\Num{ 90}{ 99.011}%
\num{ 91}{ 99.061}%
\num{ 92}{ 99.108}%
\num{ 93}{ 99.152}%
\num{ 94}{ 99.195}%
\num{ 95}{ 99.235}%
\num{ 96}{ 99.273}%
\num{ 97}{ 99.309}%
\num{ 98}{ 99.344}%
\num{ 99}{ 99.377}%
\Num{100}{ 99.408}%
\num{101}{ 99.438}%
\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}%
\num{112}{ 99.680}%
\num{113}{ 99.696}%
\num{114}{ 99.711}%
\num{115}{ 99.726}%
\num{116}{ 99.739}%
\num{117}{ 99.752}%
\num{118}{ 99.765}%
\num{119}{ 99.777}%
\Num{120}{ 99.788}%
\num{121}{ 99.798}%
\num{122}{ 99.808}%
\num{123}{ 99.818}%
\num{124}{ 99.827}%
\num{125}{ 99.836}%
\num{126}{ 99.844}%
\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}%
\num{  7}{130.166}%
\num{  8}{133.658}%
\num{  9}{136.975}%
\NUM{ 10}{140.126}%
\num{ 11}{143.120}%
\num{ 12}{145.964}%
\num{ 13}{148.666}%
\num{ 14}{151.233}%
\NUM{ 15}{153.671}%
\num{ 16}{155.987}%
\num{ 17}{158.188}%
\num{ 18}{160.279}%
\num{ 19}{162.265}%
\NUM{ 20}{164.151}%
\num{ 21}{165.944}%
\num{ 22}{167.647}%
\num{ 23}{169.264}%
\num{ 24}{170.801}%
\NUM{ 25}{172.261}%
\num{ 26}{173.648}%
\num{ 27}{174.966}%
\num{ 28}{176.217}%
\num{ 29}{177.406}%
\NUM{ 30}{178.536}%
\num{ 31}{179.609}%
\num{ 32}{180.629}%
\num{ 33}{181.597}%
\num{ 34}{182.518}%
\num{ 35}{183.392}%
\num{ 36}{184.222}%
\num{ 37}{185.011}%
\num{ 38}{185.760}%
\num{ 39}{186.472}%
\NUM{ 40}{187.149}%
\num{ 41}{187.791}%
\num{ 42}{188.402}%
\num{ 43}{188.982}%
\num{ 44}{189.533}%
\num{ 45}{190.056}%
\num{ 46}{190.553}%
\num{ 47}{191.026}%
\num{ 48}{191.474}%
\num{ 49}{191.901}%
\num{ 50}{192.306}%
\num{ 51}{192.690}%
\num{ 52}{193.056}%
\num{ 53}{193.403}%
\num{ 54}{193.733}%
\num{ 55}{194.046}%
\num{ 56}{194.344}%
\num{ 57}{194.627}%
\num{ 58}{194.895}%
\num{ 59}{195.151}%
\Num{ 60}{195.393}%
\num{ 61}{195.623}%
\num{ 62}{195.842}%
\num{ 63}{196.050}%
\num{ 64}{196.248}%
\num{ 65}{196.435}%
\num{ 66}{196.613}%
\num{ 67}{196.783}%
\num{ 68}{196.944}%
\num{ 69}{197.096}%
\Num{ 70}{197.242}%
\num{ 71}{197.380}%
\num{ 72}{197.511}%
\num{ 73}{197.635}%
\num{ 74}{197.753}%
\num{ 75}{197.866}%
\num{ 76}{197.972}%
\num{ 77}{198.074}%
\num{ 78}{198.170}%
\num{ 79}{198.262}%
\Num{ 80}{198.348}%
\num{ 81}{198.431}%
\num{ 82}{198.509}%
\num{ 83}{198.584}%
\num{ 84}{198.655}%
\num{ 85}{198.722}%
\num{ 86}{198.786}%
\num{ 87}{198.847}%
\num{ 88}{198.904}%
\num{ 89}{198.959}%
\Num{ 90}{199.011}%
\num{ 91}{199.061}%
\num{ 92}{199.108}%
\num{ 93}{199.152}%
\num{ 94}{199.195}%
\num{ 95}{199.235}%
\num{ 96}{199.273}%
\num{ 97}{199.309}%
\num{ 98}{199.344}%
\num{ 99}{199.377}%
\Num{100}{199.408}%
\num{101}{199.438}%
\num{102}{199.466}%
\num{103}{199.492}%
\num{104}{199.518}%
\num{105}{199.542}%
\num{106}{199.565}%
\num{107}{199.587}%
\num{108}{199.607}%
\num{109}{199.627}%
\Num{100}{199.646}%
\num{111}{199.663}%
\num{112}{199.680}%
\num{113}{199.696}%
\num{114}{199.711}%
\num{115}{199.726}%
\num{116}{199.739}%
\num{117}{199.752}%
\num{118}{199.765}%
\num{119}{199.777}%
\Num{120}{199.788}%
\num{121}{199.798}%
\num{122}{199.808}%
\num{123}{199.818}%
\num{124}{199.827}%
\num{125}{199.836}%
\num{126}{199.844}%
\num{127}{199.852}%
\num{128}{199.859}%
\num{129}{199.866}%
\Num{130}{199.873}%
\end{picture}
\end{document}

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current09:41, 10 February 2020Thumbnail for version as of 09:41, 10 February 20201,268 × 116 (10 KB)Jochen Burghardt (talk | contribs)User created page with UploadWizard

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