# Is there another symbol that is slightly different from \forall (likewise for \exists)?

## What

Is there a symbol that is slightly different from $\forall$ (e.g. having a second line from upper left to lower middle)? It should obviously mean "for all" but be sufficiently different to not be mistaken for $\forall$.

Similarly, is there a slightly different symbol than $\exists$ (e.g. with two lines downward)?

## Why

I need two different symbols to differentiate whether I'm in some formal logic or on the meta level (talking about the logic). Currently I use "f.a." and "ex.", but I think it's easier to grasp complex descriptions if quantifiers stand out.

## Where

I looked in amssymb and http://www.math.union.edu/~dpvc/jsmath/symbols/welcome.html, but didn't find a suitable symbol.

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Did you try the Comprehensive LaTeX Symbol List? –  Count Zero Oct 18 '12 at 14:53
@Count Zero: Thanks for the comprehensive list. I only found \fgeA from the fge package, and it does not look as good as the answers below (and \fgeE does not exist). –  DaveBall aka user750378 Oct 18 '12 at 15:35
have these variant symbols been used in published journal articles or books? if so, they may be candidates to be considered for inclusion in unicode. citations would be needed; i am the contact person for such material. –  barbara beeton Oct 18 '12 at 17:37

The example defines \eexists and \fforall with the additional lines as requested in the question.

• \eexists: The symbol \eexists is composed of \exists and the vertical line | to get a line with a matching line thickness. The vertical line is scaled to the right height. This vertical scaling does not change the horizontal line width. Finally the line is moved to the right position.

• \fforall: The trick with the vertical line cannot be uses, because the angle is not known exactly. Also the angle depends on the font size. The angle can be estimated from the width and height of the symbol. For this symbol TikZ is used and the line width is guessed from the width of \forall.

Update:

• Decreased distance between the two lines.
• I have removed the case for \scriptscriptstyle, because the symbols have larger side bearings that would need to be compensated. But probably the symbols are not needed at such sizes anyway.
• Of course, the "magic numbers" depend on the used font. A different font might need different settings.

Example file:

\documentclass{article}
\usepackage{graphicx}
\usepackage{tikz}

\makeatletter
\newcommand*{\eexists}{%
{\mathpalette\eexistsAux{}}%
}
\newcommand*{\eexistsAux}[2]{%
\exists
\sbox0{$\m@th#1\exists$}%
\sbox2{\raisebox{\depth}{$\m@th#1|$}}%
\kern-.5\wd2 %
\resizebox{\width}{\ht0}{\copy2}%
\kern-.25\wd2 %
}
\newcommand*{\fforall}{%
{\mathpalette\fforallAux{}}%
}
\newcommand*{\fforallAuxx}[1]{%
\sbox0{$\m@th#1\forall$}%
\sbox2{%
\rlap{%
\raisebox{\depth}{$\m@th#1\backslash$}%
}%
\kern\ht0 %
}%
\sbox2{\resizebox{\ht2}{\height}{\copy2}}%
\sbox2{\resizebox{!}{\ht0}{\copy2}}%
\wd2=0pt %
\copy2
\forall
}
\newsavebox\forallBox
\newdimen\forallLineWidth
\newdimen\forallSep
\newcommand*{\fforallAux}[1]{%
\sbox\forallBox{$\m@th#1\forall$}%
\setlength{\forallLineWidth}{.06\wd\forallBox}%
\setlength{\forallSep}{.09\wd\forallBox}%
\tikz[
inner sep=0pt,
line cap=round,
line width=\forallLineWidth,
]
\draw
(0,0) node (A) {\copy\forallBox}
(A.south) ++(-\forallSep-\forallLineWidth,.4\forallLineWidth)
coordinate (A1)
(A.north west) ++(-\forallSep,-\forallLineWidth)
coordinate (A2)
(A1) -- (A2)
;%
}
\makeatother

\begin{document}
\setlength{\fboxsep}{0pt}
\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{cc}
\fbox{$\forall$} & \fbox{$\exists$}\\
\fbox{$\fforall$} & \fbox{$\eexists$}\\
$\forall^\forall$ & $\exists^\exists$ \\
$\fforall^\fforall$ & $\eexists^\eexists$\\
\end{tabular}
\end{document}


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Wow, very sophisticated solution (+1). Are you typographically educated and chose the large distance of the separate lines from the original quantifiers on purpose? To me, a little closer looks sweeter... –  DaveBall aka user750378 Oct 18 '12 at 22:06
@DaveBallakauser750378 I have updated the answer. –  Heiko Oberdiek Oct 18 '12 at 22:28
This is even better than what I was thinking about. Thus this is my (final?) accepted answer. –  DaveBall aka user750378 Oct 19 '12 at 7:41
Just put it into my text and zoomed all the way in. It's beautiful, man! Thx again. –  DaveBall aka user750378 Oct 19 '12 at 9:56
\documentclass{article}
\usepackage{graphicx,amsmath,amssymb}
\newcommand{\myexists}{\ensuremath\exists\kern-.7em\exists}
\newcommand{\myforall}{\kern.05em\ensuremath\forall\kern-.9em\rotatebox{110}{\ensuremath-}}
\newcommand{\myforalll}{\ensuremath\forall\kern-.5em\forall}

\begin{document}
\noindent
\verb|\myexists|: $\myexists$ \\
\verb|\myforall|: $\myforall$ \\
\verb|\myforalll|: $\myforalll$
\end{document}


Adjusting the length of \myforall

\documentclass{article}
\usepackage{graphicx,amsmath,amssymb}
\newcommand{\myexists}{\ensuremath\exists\kern-.7em\exists}
\newcommand{\myforall}{\kern.05em\ensuremath\forall\kern-.63em\rotatebox{110}{\rule{.73em}{.4pt}}}
\newcommand{\myforalll}{\ensuremath\forall\kern-.5em\forall}

\begin{document}
\noindent
\verb|\myexists|: $\myexists$ \\
\verb|\myforall|: $\myforall$ \\
\verb|\myforalll|: $\myforalll$
\end{document}


Using these techniques, you can customize your quantifiers in many ways, for instance:

\newcommand{\fa}{\kern.05em\ensuremath\forall\kern-.22em\rotatebox{69}{\rule{.73em}{.4pt}}}
\newcommand{\ex}{\kern.05em\ensuremath\exists\kern-.03em\rotatebox{90}{\rule{.68em}{.35pt}}}


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Thanks for the anser (+1). \myforall would be great if the additional line was a bit longer. Any ideas how to do that? –  DaveBall aka user750378 Oct 18 '12 at 15:47
@DaveBallakauser750378: See the updated answer. –  Harish Kumar Oct 18 '12 at 16:00
This was exactly what I was thinking about. Thus this was my second accepted answer. –  DaveBall aka user750378 Oct 19 '12 at 7:40

You could make something along these lines by rotating \mathbb{A} and reflecting \mathbb{E}.

\documentclass{article}
\usepackage{amssymb}
\usepackage{graphicx}
\begin{document}
\rotatebox[origin=c]{180}{$\mathbb{A}$} $\forall$
\reflectbox{$\mathbb{E}$} $\exists$
\end{document}


That way, you can experiment and pick the font you like best, e.g., mathrm:

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Nice solution (+1). This was my first accepted answer... –  DaveBall aka user750378 Oct 19 '12 at 7:39

Here is a version of \exist that has a double line:

\documentclass{article}
\newcommand{\eexists}{\ooalign{$\exists\,$\cr$\,\exists$}}
\begin{document}
Let's assume $\exists\mathcal{X}$ or $\eexists\mathcal{Y}$.
\end{document}


\eexists is an overlay of two \exists with some space inbetween.

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