How do I create a vertical version of \not?

Question

If I wanted \not< but with vertical strikethrough rather than a diagonal strikethrough, how would I make it?

Answer 1

What about this:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\newcommand\vnotless{\mathrel{<\mkern-8mu\mid\mkern8mu}}
\begin{document}
    $a \vnotless b$
\end{document}

For sure there are better ways, but this works as a dirty-n-fast method...

Answer 2

A version which more or less scales correctly in math styles (not quite perfect, though...)

\documentclass{article}
\usepackage{amsmath} % for \binrel@
\usepackage{amssymb} % for \lessgtr as test
\makeatletter
\newcommand{\vnot}[2][0]{\def@tempa{\mkern#1mu}\binrel@{#2}\binrel@@{\mathpalette\vnot@{#2}}}
\newcommand{\vnot@}[2]{%
   {\m@th\ooalign{\hidewidth$#1@tempa|$\hidewidth\cr$#1#2$}}%
}
\makeatother
\begin{document}
$a \vnot[1]{<} b$
$\scriptstyle a \vnot[1]{<} b$
$\scriptscriptstyle a \vnot[1]{<} b$
\par
$a<b$
$\scriptstyle a<b$
$\scriptscriptstyle a<b$
\smallskip
$a \vnot{\lessgtr} b$
$\scriptstyle a \vnot{\lessgtr} b$
$\scriptscriptstyle a \vnot{\lessgtr} b$
\par
$a\lessgtr b$
$\scriptstyle a\lessgtr b$
$\scriptscriptstyle a\lessgtr b$
\end{document}

The horizontal placing is tricky, because the "absolute center" might not be optically ideal. I let a small kern to be added through the optional parameter.

$a \vnot{<} b$\par
$a \vnot[1]{<} b$\par
$a \vnot[2]{<} b$