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File:Standard part function with two continua.svg

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Original file (SVG file, nominally 646 × 436 pixels, file size: 16 KB)

Summary

Description
English: The standard part function mapping hyperreal numbers from an infinitesimal-enriched continuum to their standard parts in a classical one.
Date
Source Self-made; converted to SVG using latex st.tex && dvisvgm -n -c1.75 st.dvi.
Author User:Kephir

TeX source

\documentclass{article}
 
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{tikz}
\usepackage{scalefnt}
 
\begin{document}
\pagestyle{empty}

\def\lineticktop#1#2{
  \draw[-] ({#1},3.075) node [anchor=south] {#2} -- (#1,2.925) ;
}

\def\linetickbot#1#2{
  \draw[-] ({#1},-0.075) node [anchor=north] {#2} -- (#1,0.075) ;
}

\def\microscope#1{
  \draw [thick,-         ] (#1 -0.25,2.15) -- (#1+0,3) -- (#1 +0.25,2.15) ;
  \draw [thick,fill=white] (#1 +0.00,1.50) circle (1) ;  
  \fill [white           ] (#1 -0.25,2.15) -- (#1+0,3) -- (#1 +0.25,2.15) ;
  \draw [thick,blue,->   ](#1-0.95,1.5) -- (#1+0.95,1.5) ;
}

\def\microtick#1#2#3#4#5#6{
  \draw [-,#5] (#1+0.375*#2,1.5+#3) node [anchor=#6,font=\small] {#4} -- (#1+0.375*#2,1.5-#3) ;
  \draw [red,thin] (#1+0.375*#2,1.3) to [out=-90,in=90] (#1+0.00,0.6);
}

\begin {tikzpicture} [scale=2]
  \draw[blue,thick,->]      (-1.1,3) -- (4.1,3) coordinate (x axis);
  
  \microscope    {1.41}
  \microtick     {1.41}{-0.2}{0.1}{$r$}{}{south}
  \microtick     {1.41}{ 0.7}{0.05}{\tiny $r+\epsilon$}{blue}{south}
  \microtick     {1.41}{ 2.1}{0.05}{\tiny $r+\gamma$}  {blue}{south}
  \microtick     {1.41}{-1.7}{0.05}{\tiny $r+\eta$}    {blue}{south}
  \draw[red,->] (1.41,0.6) -- (1.41,0.325) node [anchor=west] {$\scriptstyle \operatorname{st}$} -- (1.41,0.15) ;

  \lineticktop{-1}{$-1$}
  \linetickbot{-1}{$-1$}
  \lineticktop{ 0}{$ 0$}
  \linetickbot{ 0}{$ 0$}
  \lineticktop{+1}{$ 1$}
  \linetickbot{+1}{$ 1$}
  \lineticktop{+2}{$ 2$}
  \linetickbot{+2}{$ 2$}
  \lineticktop{+3}{$ 3$}
  \linetickbot{+3}{$ 3$}
  \lineticktop{+4}{$ 4$}
  \linetickbot{+4}{$ 4$}

  \lineticktop{+1.41}{}
  \linetickbot{+1.41}{$ r$}

  \draw[->]      (-1.1,0) -- (4.1,0) coordinate (x axis);
\end {tikzpicture}

\end{document}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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30 December 2013

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Date/TimeThumbnailDimensionsUserComment
current16:56, 30 December 2013Thumbnail for version as of 16:56, 30 December 2013646 × 436 (16 KB)Kephir== {{int:filedesc}} == {{Information |Description={{en|The standard part function mapping hyperreal numbers from an infinitesimal-enriched continuum to their standard parts in a classical one.}} |Source=Self-made; converted...

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