Does \Twoheadleftrightarrow exist? How to write my own?

Question

I'm a LaTeX newbie. I am writing a document in which I need to have a two-headed bidirectional arrow. Two-headed like \twoheadleftarrow, bidirectional like \leftrightarrow.

Is there any package that offers something like this? If not, how do I "roll my own"?

Thank you a lot!

Answer 1

\twoheadleftarrow and \twoheadrightarrow can be combined to \twoheadleftrightarrow:

\documentclass{article}
\usepackage{amssymb}

\newcommand*{\twoheadleftrightarrow}{%
  \twoheadleftarrow
  \mathrel{\mkern-15mu}%
  \twoheadrightarrow
}

\begin{document}
\[
  \twoheadleftrightarrow
  \scriptstyle \twoheadleftrightarrow
  \scriptscriptstyle \twoheadleftrightarrow
\]
\end{document}

The symbols can also be combined using \joinrel, which is some negative space that should counteract the side bearings. However, I could see a small gap in \scriptscriptstyle with class option 10pt, thus I have removed another -0.5mu. And the new \longtwoheadleftrightarrow has an optional argument, which allows further adjustment if necessary.

\documentclass{article}
\usepackage{amssymb}

\newcommand*{\longtwoheadleftrightarrow}[1][.5]{%
  \twoheadleftarrow
  \joinrel
  \mathrel{\mkern-#1mu}%
  \twoheadrightarrow
}

\begin{document}
\[
  \longtwoheadleftrightarrow
  \scriptstyle \longtwoheadleftrightarrow
  \scriptscriptstyle \longtwoheadleftrightarrow
\]
\end{document}

An even longer version can be composed with \relbar in the middle.

Also an expandable version can be constructed similar to \xrightarrow:

\documentclass{article}
\usepackage{amsmath,amssymb}

\makeatletter
\newcommand*{\xtwoheadleftrightarrow}[2][]{%
  \ext@arrow 99{10}{10}\twoheadleftrightarrowfill@{#1}{#2}%
}
\newcommand*{\twoheadleftrightarrowfill@}{%
  \arrowfill@\twoheadleftarrow\relbar\twoheadrightarrow
}
\makeatother

\begin{document}
\[
  \xtwoheadleftrightarrow[\text{under}]{\text{over}}
\]
\end{document}