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File:Archimedean property for Achilles and Tortoise example.svg

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Summary

Description
English: An illustration of the Archimedean 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 point x 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
Source Created with GeoGebra
Author Sławomir 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 at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free 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 entitled GNU Free Documentation License.
w:en:Creative Commons
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You are free:
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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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Original upload log

The original description page was here. All following user names refer to en.wikipedia.
Date/Time Dimensions User Comment
2017-07-25 11:34:45 533 × 147 Sławomir Biały Uploading a self-made file using [[Wikipedia:File_Upload_Wizard|File Upload Wizard]]

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25 July 2017

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a625ad5fced92768696429a1288cb4bede55f435

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Date/TimeThumbnailDimensionsUserComment
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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