File:SemiorderAxiom3.pdf
Summary
| Description |
English: Illustration of 3rd axiom of a semiorder:
For all x, y, z, w x<y and y<z implies x<w or w<x or y<w or w<y or z<w or w<z. — Colors: Dark green: given pairs in <, Light cyan: at least one of these pairs is required to exist in < |
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| Date | ||||
| Source | Own work | |||
| Author | Jochen Burghardt | |||
| Other versions |
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| PDF development |
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(7.000,22.000){\vector(0,1){19.000}}}%
\textcolor{cLess}{\put(5.000,12.000){\makebox(0.000,0.000)[r]{$\vee$}}}%
\textcolor{cLess}{\put(5.000,32.000){\makebox(0.000,0.000)[r]{$\vee$}}}%
% required pair
\textcolor{cExst}{\multiput(7.000,2.000)(1.000,1.000){21}{\makebox(0,0){$\cdot$}}}%
\textcolor{cExst}{\put(7.600,2.600){\vector(-1,-1){0.000}}}%
\textcolor{cExst}{\put(26.400,21.400){\vector(1,1){0.000}}}%
\textcolor{cExst}{\put(19.000,12.000){\makebox(0.000,0.000)[l]{$\lessgtr$}}}%
\textcolor{cExst}{\multiput(7.000,22.000)(1.400,0.000){14}{\makebox(0,0){$\cdot$}}}%
\textcolor{cExst}{\put(8.000,22.000){\vector(-1,0){0.000}}}%
\textcolor{cExst}{\put(26.000,22.000){\vector(1,0){0.000}}}%
\textcolor{cExst}{\put(15.000,23.000){\makebox(0.000,0.000)[b]{$\gtrless$}}}%
\textcolor{cExst}{\multiput(7.000,42.000)(1.000,-1.000){21}{\makebox(0,0){$\cdot$}}}%
\textcolor{cExst}{\put(7.600,41.600){\vector(-1,1){0.000}}}%
\textcolor{cExst}{\put(26.400,22.600){\vector(1,-1){0.000}}}%
\textcolor{cExst}{\put(19.000,32.000){\makebox(0.000,0.000)[l]{$\gtrless$}}}%
% elements
\textcolor{cElem}{\put(7.000,2.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(7.000,22.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(7.000,42.000){\circle*{2.000}}}%
\textcolor{cElem}{\put(27.000,22.000){\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(5.000,42.000){\makebox(0.000,0.000)[r]{$z$}}}%
\textcolor{cElem}{\put(29.000,22.000){\makebox(0.000,0.000)[l]{$w$}}}%
\end{picture}
\end{document}
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