How do I write $\notin$ backwards?

Question

I write $P \niton x$, but it does not work. How can I write the symbol $\notin$ backwards?

Answer 1

After consulting The Comprehensive LaTeX Symbol List a few fonts provide such a symbol:

• txfonts, newtxmath and pxfonts have $\notni$.
• mathabx has $\notowner$ and $\varnotowner$
• MnSymbol has $\nowns$
• mathdesign has a small version $\notsmallowns$, but no normal sized one.
• kpfonts has $\notowns$

Note however that using one of these packages changes the complete font set. Of course you can rip this single symbol from a font that has it, let's try with $\notni$ from txfonts, surrounded by Latin Modern:

\DeclareSymbolFont{symbolsC}{U}{txsyc}{m}{n}
\DeclareMathSymbol{\notniFromTxfonts}{\mathrel}{symbolsC}{61}
...
$x \notin P \notniFromTxfonts x$

but the result is not convincing:

Answer 2

If the math fonts you use don't have the symbol, you can say

\newcommand{\niton}{\not\owns}

Here's a complete example, showing that the symbol will change size in subscripts:

\documentclass{article}
\newcommand{\niton}{\not\owns}
\begin{document}
$A\niton x_{B\niton y}$
\end{document}

If your fonts don't have \owns (that is, the reverse of \in) you can emulate it by loading graphicx and amsmath:

\usepackage{graphicx}
\usepackage{amsmath}
\newcommand{\niton}{\not\mathrel{\text{\reflectbox{$\in$}}}}

---

A possibly better definition, that uses the same slash as \notin, can be the following:

\documentclass{article}

\makeatletter
\newcommand\niton{\mathrel{\m@th\mathpalette\canc@l\owns}}
\newcommand\canc@l[2]{{\ooalign{$\hfil#1/\mkern1mu\hfil$\crcr$#1#2$}}}
\makeatother

\begin{document}
$A\niton x_{B\niton y}$

$A\notin x_{B\notin y}$
\end{document}

Answer 3

\documentclass{memoir}
\usepackage{graphicx}
\begin{document}

$\notin$ \reflectbox{$\notin$}

\end{document}

Answer 4

I believe that \rotatebox is more proper than \reflectbox, I suggest this solution:

\documentclass{article}

\usepackage{rotating}

\makeatletter
\newcommand\@notni[2]{\mathrel{\rotatebox[y=#1]{180}{$#2\notin$}}}
\newcommand\notni{
\mathchoice
  {\@notni{0.57ex}\displaystyle}
  {\@notni{0.57ex}\textstyle}
  {\@notni{0.39ex}\scriptstyle}
  {\@notni{0.26ex}\scriptscriptstyle}
}
\makeatother

\begin{document}

\[
    L\notni x
\quad
    x\notin L
\quad
    \sum_{L\notni x} f(L)
\quad
    \sum_{Z_{L\notni x}} 1
\]

\end{document}