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 \coloneqq for this purpose.

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

yields

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.

Answer 4

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

Answer 5

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 6

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 7

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 8

My solution is

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