File:SemiorderAxiom2.pdf
Summary
| Description |
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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