File:SemiorderAxiom2.pdf
SemiorderAxiom2.pdf (222 × 283 pixels, file size: 29 KB, MIME type: application/pdf)
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DescriptionSemiorderAxiom2.pdf |
English: Illustration of 2nd axiom of a semiorder: "For all x, y, z, w: x<y and y~z and z<w implies x<w". — The incomparability relation ~ is defined by "a~b if neither a<b nor b<a". — Colors: Dark green: given pairs in <, Dark red: given pair in ~, Light cyan: required existing pair in < |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions | File:SemiorderAxiom2 svg.svg Svg version |
LaTeX source code |
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\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\usepackage[paperwidth=38\unitlength,paperheight=48\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{38\unitlength}
\setlength{\textheight}{48\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
\definecolor{cElem} {rgb}{0.00,0.00,0.00}
\definecolor{cLess} {rgb}{0.00,0.50,0.00}
\definecolor{cIncm} {rgb}{0.50,0.00,0.00}
\definecolor{cExst} {rgb}{0.00,0.99,0.50}
\begin{document}
\begin{picture}(34,44)
% given pairs
\textcolor{cLess}{\put(7.000,2.000){\vector(0,1){19.000}}}%
\textcolor{cLess}{\put(27.000,22.000){\vector(0,1){19.000}}}%
\textcolor{cLess}{\put(5.000,12.000){\makebox(0.000,0.000)[r]{$\vee$}}}%
\textcolor{cLess}{\put(29.000,32.000){\makebox(0.000,0.000)[l]{$\vee$}}}%
% given incomparability
\textcolor{cIncm}{\multiput(7.000,22.000)(1.000,0.000){21}{\makebox(0.000,0.000){$\scriptscriptstyle\mid$}}}%
\textcolor{cIncm}{\put(20.000,20.000){\makebox(0.000,0.000)[t]{$\sim$}}}%
% required pair
\textcolor{cExst}{\multiput(7.000,2.000)(0.700,1.400){30}{\makebox(0,0){$\cdot$}}}%
\textcolor{cExst}{\put(26.500,41.000){\vector(1,2){0.000}}}%
\textcolor{cExst}{\put(17.000,25.000){\makebox(0.000,0.000)[b]{$\vee$}}}%
% elements
\textcolor{cElem}{\put(7.000,2.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(7.000,22.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(27.000,22.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(27.000,42.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(5.000,2.000){\makebox(0.000,0.000)[r]{$x$}}}%
\textcolor{cElem}{\put(5.000,22.000){\makebox(0.000,0.000)[r]{$y$}}}%
\textcolor{cElem}{\put(29.000,22.000){\makebox(0.000,0.000)[l]{$z$}}}%
\textcolor{cElem}{\put(29.000,42.000){\makebox(0.000,0.000)[l]{$w$}}}%
\end{picture}
\end{document}
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Licensing edit
I, the copyright holder of this work, hereby publish it under the following license:
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.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:27, 17 April 2018 | 222 × 283 (29 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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Software used | TeX |
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Conversion program | pdfTeX-1.40.18 |
Encrypted | no |
Page size | 107.716 x 136.062 pts |
Version of PDF format | 1.5 |