MathJax command for `\coloneqq`

Question

Previously, I used $:=$ when defining notation. Until I discovered the preferred $\coloneqq$ or $\colonequals$ command.

This command doesn't work on math.stackexchange. I presume because MathJax doesn't support it.

What would be a good alternative for use on the math.stackexchange website?

Answer 1

This is somewhere half-way between an answer and a long comment, but since I did not want to continue a long discussion with many comments, I have decided to post this as an answer.

I hope that somebody with better knowledge of MathJax, LaTeX (and perhaps Unicode), will post a better answer.

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One possibility I can think of is using Unicode.

If you can find a Unicode character which looks like that, you could use it. But I only find ≔ which looks like this in Math Mode $≔$. (I am not sure whether it is any improvement compared to $\colon=$ $\colon=$ or $:=$ $:=$.)

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Other possibility is to look how it is done in LaTeX and test whether you can make some similar macro in MathJax. (Notice that in MathJax you can use \newcommand.) Of course, not every macro which works in LaTeX will also work in MathJax and another obvious disadvantage is that you would have to add the macro to every post where you want to use it.

Anyway this TeX.SE post mentions several ways how this symbol could by typeset in LaTeX: How to typeset $:=$ correctly?

Since you explicitly mentioned \coloneq I checked how this is defined in mathtools package:

\def\vcentcolon{\mathrel{\mathop\ordinarycolon}}
\providecommand\ordinarycolon{:}
...
\providecommand*\coloneqq{\vcentcolon\mathrel{\mkern-1.2mu}=}

My attempt to replicate this in MathJax looks as follows:
$\newcommand{\ordinarycolon}{:}\newcommand{\vcentcolon}{\mathrel{\mathop\ordinarycolon}}\newcommand{\coloneqqa}{\vcentcolon\mathrel{\mkern-1.2mu}=}$ Unless I am mistaken, this could be simplified to this:
\newcommand{\coloneqqb}{\mathrel{\mathop:}\mathrel{\mkern-1.2mu}=}

Perhaps a reasonable thing to try is also to simply include the "naive solutions" into \mathrel.
\newcommand{\coloneqqc}{\mathrel{:=}}
\newcommand{\coloneqqd}{\mathrel{\colon=}}
\newcommand{\coloneqqe}{\mathrel{≔}}

And this is Davide Cervone's suggestions from a comment:
\newcommand{\coloneqqf}{\mathrel{\vcenter{:}}=}

When I test this, I get the following: $\newcommand{\ordinarycolon}{:}\newcommand{\vcentcolon}{\mathrel{\mathop\ordinarycolon}}\newcommand{\coloneqqa}{\vcentcolon\mathrel{\mkern-1.2mu}=} \newcommand{\coloneqqb}{\mathrel{\mathop:}\mathrel{\mkern-1.2mu}=} \newcommand{\coloneqqc}{\mathrel{:=}} \newcommand{\coloneqqd}{\mathrel{\colon=}} \newcommand{\coloneqqe}{\mathrel{≔}} \newcommand{\coloneqqf}{\mathrel{\vcenter{:}}=} $ $$ \begin{array}{|l|c|} \hline \text{:=} & a:=b \\\hline \text{\colon=} & a\colon=b \\\hline \text{unicode} & a≔b\\\hline \text{\coloneqqa} & a\coloneqqa b\\\hline \text{\coloneqqb} & a\coloneqqb b\\\hline \text{\coloneqqc} & a\coloneqqc b\\\hline \text{\coloneqqd} & a\coloneqqd b\\\hline \text{\coloneqqe} & a\coloneqqe b\\\hline \text{\coloneqqf} & a\coloneqqf b\\\hline \end{array} $$

I am sure there are many other possibilities worth trying if you want to try this way (by creating your own macro).