[Tex/LaTex] the purpose of : in math mode

math-modepunctuation

What is the purpose of $:$ ?

We know that in math mode one should write in natural language and not being so strict with math notation.

For example: $f:A\to B$ is not "correct", the correct way would be $f\colon A\to B$ (and variants).

I do not remember any math book that uses the colon as part of a sentence in math mode.

The only 2 uses I can give to $:$ are when learning about divisions ( $2:4=1:2$ ) and scales ( $1:2$ ).

Does (La)TeX give a meaning of : in math mode?

Best Answer

The : is a relational symbol in TeX. In the TeXbook it is used in conjunction with =.

Plain \TeX\ treats the four characters |=|, |<|, |>|, and |:|\ as
``^{relations}'' because they express a relationship between two
quantities. For example, `${x<y}$' means that $x$~is less than~$y$.
Such relationships have a rather different meaning from binary
operations like $+$, and the symbols are typeset somewhat differently:
\beginmathdemo
|$x=y>z$|&x=y>z\cr
|$x:=y$|&x:=y\cr
|$x\le y\ne z$|&x\le y\ne z\cr
|$x\sim y\simeq z$|&x\sim y\simeq z\cr
|$x\equiv y\not\equiv z$|&x\equiv y\not\equiv z\cr
|$x\subset y\subseteq z$|&x\subset y\subseteq z\cr
\endmathdemo

In the comments, egreg pointed out another example in the TeXbook, where : is used to separate the condition from the set variable.

\beginmathdemo
|$\{\,x\mid x>5\,\}$|&\{\,x\mid x>5\,\}\cr
|$\{\,x:x>5\,\}$|&\{\,x:x>5\,\}\cr
\endmathdemo
(Some authors prefer to use a ^{colon} instead of `$\mid$', as in the second
example here.)

The colon has the exact same meaning in Plain TeX and LaTeX, as can be verified using this simple document:

\showthe\mathcode`:
\csname @@end\endcsname
\bye

The output is

$ pdftex test.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdftex)
 restricted \write18 enabled.
entering extended mode
(./test.tex
> 12346.
l.1 \showthe\mathcode`:

? 
 )
No pages of output.
Transcript written on test.log.
$ pdflatex test.tex
This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex)
 restricted \write18 enabled.
entering extended mode
(./test.tex
LaTeX2e <2018-12-01>
> 12346.
l.1 \showthe\mathcode`:

? 
 )
No pages of output.
Transcript written on test.log.

Here the same table rendered in LaTeX:

\documentclass{article}
\usepackage{array}
\usepackage{amsmath}
\usepackage{listings}
\lstset{basicstyle=\ttfamily}
\begin{document}
\lstMakeShortInline|
\begin{tabular}{l>{$}l<{$}}
|$x=y>z$|                 & x=y>z                 \\
|$x:=y$|                  & x:=y                  \\
|$x\le y\ne z$|           & x\le y\ne z           \\
|$x\sim y\simeq z$|       & x\sim y\simeq z       \\
|$x\equiv y\not\equiv z$| & x\equiv y\not\equiv z \\
|$x\subset y\subseteq z$| & x\subset y\subseteq z \\
\end{tabular}
\end{document}

Related Solutions

[Tex/LaTex] What are semantically correct alternatives to \text in math mode

I'm afraid you hit no correct choice. ;-)

$\fT_\text{triv} = \Set{\emptyset, X}$ : incorrect. Define
```
\newcommand{\ts}[1]{\textnormal{#1}} % textual subscript
```
and use $\fT_{\ts{triv}}. You can later change your mind about the typesetting of \ts. With \text you're not guaranteed to get upright shape, for example in the statement of a theorem.
$g \circ f = \text{id}_X$ : incorrect. Define
```
\newcommand{\id}{\textnormal{id}}
```
(or with \textit, which I'd prefer).
$\text{Isom}(X)$ : incorrect. It's an operator, so $\operatorname{Isom}(X)$ . Defining a command with \DeclareMathOperator is of course a good choice. The same considerations hold for “grad”, “cov”, ”sgn” and ”Gal”.
\[ \text{Let } x = \text{ number of cats} \]: incorrect. “Let” should not go in the displayed equation. So
```
Let
\[
x=\text{number of cats}
\]
```
with no space before “number”.

The longer one should be

\begin{align*}
U \subseteq \mathbb{R}^n \text{ offen} \Leftrightarrow 
  &\text{für jedes $x \in U$ gibt es $r > 0$,}\\
  &\text{sodass $\fB_r(x) = \Set{y \in \mdr^n | d(x,y) < r} \subseteq U$}
\end{align*}

so you don't have to think where spaces are necessary.

I wouldn't use a macro \Set with delimited argument, preferring

\newcommand{\Set}[2]{\{\,#1\mid #2\,\}}

and \Set{y \in \mdr^n}{d(x,y) < r}. This is more consistent with LaTeX syntax. If your \Set macro has just one normal argument, then use \mid and not |.

[Tex/LaTex] Does the comma look the same within/without the dollar signs

Under the normal setting, the math code for comma is "613B as it results from

\mathcode`\,="613B

in Plain TeX and

\DeclareMathSymbol{,}{\mathpunct}{letters}{"3B}

in LaTeX (precisely in fontmath.ltx). This means that the comma is a punctuation symbol (class 6), and that it's taken from the font specialized for math letters (family 1, where the math italic letters are the main object).

The glyph's shape therefore depends on how the fonts are designed: there may be a difference, particularly if the text and math font don't match (which would be a typographical error anyway). Why is the symbol “different”? Let's look with the standard setting:

\documentclass{article}
\begin{document}
\fboxsep=0pt \fboxrule=0.1pt % no padding, hairline box

\fbox{,} \fbox{$,$}

\makebox[0pt][l]{\fbox{,}}\fbox{$,$}

\end{document}

enter image description here

Looking at the first line seems to hint that the result is identica, which is confirmed by the second line.

However, a difference can be seen if NewTX is loaded; the same input as before, with the addition of \usepackage{newtxtext,newtxmath} produces

enter image description here

where we see that the math comma has no left sidebearing. Design decision.

Best Answer

Related Solutions

[Tex/LaTex] What are semantically correct alternatives to \text in math mode

[Tex/LaTex] Does the comma look the same within/without the dollar signs

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