[Tex/LaTex] LaTeX symbol for “does not divide”

math-moderelation-symbolssymbols

What is the correct way to make the "does not divide" symbol in plain LaTeX 2e?

I'm talking about the symbol that is a vertical bar with a slash through it. I prefer not to install AMS or other packages, but instead to use plain LaTeX.

Best Answer

Try this:

$x\nmid y$

It has been known to 'save the day'.

Related Solutions

[Tex/LaTex] Wedge with vertical bar

This overlaps three things: wedge/vee, shortmid, and shortmid raised to a correct height. The numbers suit cm and lm fonts, for other fonts they might need to be modified.

See here for a quick course on \ooalign.

enter image description here

\documentclass{article}
\usepackage{amssymb}

\makeatletter
\newcommand\@@vertwv[3]{\mathop{\ooalign{%
  $#1#3$\cr
  \hfil$#1\shortmid$\hfil\cr
  \hfil\raisebox{#2}{$#1\shortmid$}\hfil\cr}}}
\newcommand\@vertwv[1]{\mathchoice
  {\@@vertwv{\displaystyle     }{0.38ex}{#1}}%
  {\@@vertwv{\textstyle        }{0.38ex}{#1}}%
  {\@@vertwv{\scriptstyle      }{0.28ex}{#1}}%
  {\@@vertwv{\scriptscriptstyle}{0.21ex}{#1}}}
\newcommand\vertwedge{\@vertwv\wedge}
\newcommand\vertvee  {\@vertwv\vee  }
\makeatother

\begin{document}

\[ a\vertwedge b \neq a\vertvee b \]
\[ \textstyle a\vertwedge b \neq a\vertvee b \]
\[ \scriptstyle a\vertwedge b \neq a\vertvee b \]
\[ \scriptscriptstyle a\vertwedge b \neq a\vertvee b \]

\end{document}

[Tex/LaTex] Not equal sign (≠) with a vertical bar

Equal sign with vertical line

The vertical line | is a little tall for my taste. The following definition for \vneq decreases the total height of the vertical line to match the total height of \neq. Resizing vertical height will not change the line thickness in horizontal direction.

The final witdh and height of the vertical line can be fine-tuned by redefining macros \vneqxscale and \vneqyscale. The default is 1.
\mathpalette allows the symbol to resize automatically.

Example file:

\documentclass{article}

\usepackage{amssymb}% \varnothing

\usepackage{graphicx}% \resizebox
\makeatletter
\newcommand*{\vneq}{%
  \mathrel{%
    \mathpalette\@vneq{=}%
  }%
}
\newcommand*{\@vneq}[2]{%
  % #1: math style (\displaystyle, \textstyle, ...)
  % #2: symbol (=, ...)
  \sbox0{\raisebox{\depth}{$#1\neq$}}%
  \sbox2{\raisebox{\depth}{$#1|\m@th$}}%
  \ifdim\ht2>\ht0 %
    \sbox2{\resizebox{\vneqxscale\width}{\vneqyscale\ht0}{\unhbox2}}%
  \fi
  \sbox2{$\m@th#1\vcenter{\copy2}$}%
  \ooalign{%
    \hfil\phantom{\copy2}\hfil\cr
    \hfil$#1#2\m@th$\hfil\cr
    \hfil\copy2\hfil\cr
  }%
}
\newcommand*{\vneqxscale}{1}
\newcommand*{\vneqyscale}{1}
\makeatother

\begin{document}
\[
  % Comparison \neq vs. vneq
  \varnothing \neq \emptyset \vneq \varnothing \\
\] 
\[ 
  % Check sizes:
  \vneq^{\vneq^{\vneq}} \\
\] 
\[ 
  % Bounding box checks:
  \setlength{\fboxsep}{0pt}
  \setlength{\fboxrule}{.1pt}
  \fbox{$\neq$}\,\fbox{$\vneq$}\,\fbox{$|$}
\]
\end{document}

The height can be further decreased, e.g.

\renewcommand*{\vneqyscale}{.8}

Result for mathabx:

Result for txfonts:

Result for MnSymbol:

Here the vertical line is too thick and the horizontal resizing needs shrinking:

\renewcommand*{\vneqxscale}{.67}

Result for MnSymbol and \vneqxscale = .67:

Alternative to `varnothing`

Instead of changing \neq, the empty set symbol \varnothing could be constructed using \not to match the slope of the slanted vertical lines. However, \circ is too small and \bigcirctoo big. Therefore this method is shown for txfonts that provides \medcirc and MnSymbol with \medcircle.

\documentclass{article}

%\usepackage{txfonts}
%\newcommand*{\varemptysetcircle}{\medcirc}

\usepackage{MnSymbol}
\newcommand*{\varemptysetcircle}{\medcircle}

\makeatletter
\newcommand*{\varemptyset}{%
  {% mathord
    \vphantom{\not=}% correct height and depth of the final symbol
    \mathpalette\@varemptyset\varemptysetcircle
  }%
}
\newcommand*{\@varemptyset}[2]{%
  % #1: math style (\displaystyle, \textstyle, ...)
  % #2: circle
  \ooalign{%
    \hfil$\m@th#1\not\hphantomeq$\hfil\cr
    \hfil$\m@th#1#2$\hfil\cr
  }%
}
% \not can be redefined to take an argument
\newcommand*{\hphantomeq}{%
  \mathrel{\hphantom{=}}%
}
\makeatother

\usepackage{color}

\begin{document}
\[
  \not=\; \color{blue}\neq \varemptyset\; \color{black}\varnothing
\]
\end{document}