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File:Archimedean property for Achilles and Tortoise example.svg

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File:Archimedean property for Achilles and Tortoise example.svg
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Summary

DescriptionArchimedean property for Achilles and Tortoise example.svg
English: An illustration of theArchimedean property of real numbers. Achilles starts the race at the initial point mathP_0</math>, and the tortoise at mathP_1</math>. They finish the race at the same time. When Achilles reaches mathP_1</math>, the tortoise reaches mathP_2</math>, etc. The Archimedean property is that any pointx in the race lies between two of the P's.The following code was generated using conversion to TiKZ, and manual adjustment so that the generated PDF looks nice.
Date
SourceCreated with GeoGebra
AuthorSławomir Biały
\documentclass[10pt]{article}\usepackage{pgf,tikz}\usepackage{mathrsfs}\usetikzlibrary{arrows}\pagestyle{empty}\begin{document}\definecolor{yqqqqq}{rgb}{0.5019607843137255,0.,0.}\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1.}\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm,scale=10]\clip(-0.12424528781181865,-0.15367169638774447) rectangle (1.379623024945378,0.2598262459990889);\draw [line width=2.pt] (0.,0.)-- (1.,0.);\draw (0.4762485393486732,0.08) node[anchor=north west]{$P_1$};\draw (-0.024162983285070005,0.08) node[anchor=north west]{$P_0$};\draw (0.7185530660976437,0.08) node[anchor=north west]{$P_2$};\draw (0.8370715846161618,0.08) node[anchor=north west]{$P_3$};\draw (0.9081826957272727,0.08) node[anchor=north west]{$P_4$};\draw (0.9481826957272727,0.07) node[anchor=north west]{$\dots$};\draw (0.884478992023569,-0.01) node[anchor=north west]{$x$};\begin{scriptsize}\draw [fill=uuuuuu] (0.,0.) circle (0.25pt);\draw [fill=uuuuuu] (1.,0.) circle (0.25pt);\draw[color=uuuuuu] (1.1188822842046382,0.016204846822132895) node{Finish line};\draw [fill=xdxdff] (0.9108164405832435,0.) circle (0.2pt);\draw [color=yqqqqq, very thick] (0.,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.5,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.75,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.9375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.96875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.984375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.9921875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.99609375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.998046875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.9990234375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.99951171875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.999755859375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.9998779296875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.99993896484375,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\draw [color=yqqqqq, very thick] (0.999969482421875,0.)-- ++(-0.25pt,0 pt) -- ++(0.5pt,0 pt) ++(-0.25pt,-0.25pt) -- ++(0 pt,0.5pt);\end{scriptsize}\end{tikzpicture}\end{document}

Licensing

Sławomir Biały atEnglish Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
GNU headPermission is granted to copy, distribute and/or modify this document under the terms of theGNU Free Documentation License, Version 1.2 or any later version published by theFree Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitledGNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue
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The original description page washere. All following user names refer to en.wikipedia.
Date/TimeDimensionsUserComment
2017-07-25 11:34:45533 × 147Sławomir BiałyUploading a self-made file using [[Wikipedia:File_Upload_Wizard|File Upload Wizard]]

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current03:38, 15 December 2018Thumbnail for version as of 03:38, 15 December 2018533 × 147(34 KB)I love rpgsTransferred from en.wikipedia (MTC!) (1.1.0)

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