How to typeset $:=$ correctly?

Question

I like to use $:=$ for "is defined to be equal to", but this is never typeset with the symmetry one would like, as the colon is always too low relatively to the equals sign. Is there any way of getting this to appear correctly?

Answer 1

See the mathtools package, which offers the macro \coloneq for this purpose.

\documentclass{standalone}
\usepackage{mathtools}
\begin{document}
\( b := 10 \) \emph{versus} \( b \coloneq 10 \).
\end{document}

yields

Click image or right here to see it at full size (1600×133).

Note that the colon is slightly too low on the left, but vertically centered on the right.

---

Edit: as of 2022, \coloneq replaces legacy \coloneqq (which is still supported, but now labeled a 'Legacy duplicate name' in the mathtools docs' colon symbols list)

Answer 2

This answer is an attempt to make Matthew happy, who doesn't like that the dots in the colon are so far apart. (@Matthew: I do understand that you don't like it.)

\makeatletter
\newcommand*{\defeq}{\mathrel{\rlap{%
                     \raisebox{0.3ex}{$\m@th\cdot$}}%
                     \raisebox{-0.3ex}{$\m@th\cdot$}}%
                     =}
\makeatother

EDIT:

To make Matthew even happier, I provide yet another answer that uses a different approach (motivated by the definition of \vdots) where the dots are smaller:

\newcommand*{\defeq}{\mathrel{\vcenter{\baselineskip0.5ex \lineskiplimit0pt
                     \hbox{\scriptsize.}\hbox{\scriptsize.}}}%
                     =}

Answer 3

I prefer Donald Arseneau's hack that can be found on the TeX FAQ (sorry, this links to a page in German):

\mathchardef\ordinarycolon\mathcode`\:
\mathcode`\:=\string"8000
\begingroup \catcode`\:=\active
  \gdef:{\mathrel{\mathop\ordinarycolon}}
\endgroup

Just put this code into your preamble. Then you can use := as usual, and you'll get horizontal symmetry. Much easier to use than \coloneqq, in my opinion.

Per @Will Robertson's comment, there is also a feature of mathtools to change the vertical alignment of all colons in math mode.

\mathtoolsset{centercolon}

Answer 4

Obligatory ConTeXt solution: \colonequals; which uses a composed character in MkII and the proper unicode math character in MkIV

Answer 5

There is also a package by Heiko Oberdiek: colonequals

Some fonts have dedicated characters for these symbols. Unfortunately, there are name clashes concerning \coloneq, which may refer to :- or to ≔ (U+2254, :=).

Answer 6

A way to get this with pxfonts without including the whole package:

\DeclareSymbolFont{symbolsC}{U}{pxsyc}{m}{n}
\DeclareMathSymbol{\coloneqq}{\mathrel}{symbolsC}{"42}

and you get:

Answer 7

I tried quite some of the solutions given here but none of those seemed satisfactory to me. Most of them only solve the problem of the vertical alignment of the colon but do not respect the length of all the other binary relations, that is ":=" is much longer than "=" and the like.

My suggestion hence is the following:

\newcommand{\eqcolon}{\mathrel{\resizebox{\widthof{$\mathord{=}$}}{\height}{ $\!\!=\!\!\resizebox{1.2\width}{0.8\height}{\raisebox{0.23ex}{$\mathop{:}$}}\!\!$ }}}
\newcommand{\coloneq}{\mathrel{\resizebox{\widthof{$\mathord{=}$}}{\height}{ $\!\!\resizebox{1.2\width}{0.8\height}{\raisebox{0.23ex}{$\mathop{:}$}}\!\!=\!\!$ }}}

This will result in ":=" beeing equally long as "=" so it will align properly in multiline math equations. Below is a comparisson of the approach \newcommand{\eqcolon}{\ensuremath{\mathrel{=\!\!\mathop{:}}}} with my suggestion. Note how the lines align properly in amsmath align environments.

Before:

After:

Answer 8

I actually think that symbol looks ugly. It would be OK if the spacing between the dots were the same as that between the lines of the equals. But I use

\newcommand{\defeq}{\stackrel{\text{def}}{=}}

instead.

Answer 9

My solution is

\def\defeq{\mathrel{\mathop:}=}

Answer 10

You may try \coloneq (as well as \eqcolon) from unicode-math package:

Note that unicode-math requires XeLaTeX/LuaLaTeX.

Answer 11

I use \vcentcolon= from the mathtools package. I like it better than \coloneqq because with the former, there is more spacing between the colon and the equals sign.

Answer 12

Edit: I didn't know this at the time of writing this answer, but commath is not a well designed package, and it can lead to obscure problems. I would stay away from it and use a solution from another answer.

---

The commath package automatically fixes the alignment of := and =: in math mode.

...
\usepackage{commath}
...
\begin{gather*}
a := b \\
b =: a
\end{gather*}
...