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There are two setbuilder notations, the vertical bar and the colon. In some cases, it is better to make a choice. For example, compare
\{f \mid f\colon M \rightarrow N \text{ is continuous}\}
and
\{f : f\colon M \rightarrow N \text{ is continuous}\}.
Also,
\{x : \lvert x \rvert = 1\}
and
\{x \mid \lvert x \rvert = 1\}.
But I feel uneasy because I was not consistent with the notation. Is it OK if I use both of them in one article?
This isn't really a TeX question (and so might get closed as off topic) but if you think your users may be worried that the different nations actually mean something different then it would be better to stick to one. If for example you stick to \mid you could avoid the clash of notation by using \abs(x) rather than |x| (after defining \abs with \DeclareMathOperator)
\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator\abs{abs}
\begin{document}
\[
\{f \mid f\colon M \rightarrow N \text{ is continuous}\}
\]
and
\[
\{x \mid \abs(x) = 1\}.
\]
\end{document}
abs(x) to write just that (not $\lvert x \rvert$) when using \mid for sets.
\log) rather than using |x|.
Apr 23, 2013 at 19:01
I think consistency is better. What you can do is to emphasise the differences between your vertical bars, or your colons, with spacing as in
$\bigl\{ f\colon M \to N \; : \; \text{$f$ is continuous} \bigr\}$
or delimiter resizing, as in
$\bigl\{ x \;\big|\; \lvert x \rvert = 1 \bigr\}$
(In the latter case, I would be tempted to use \Bigl, \Big, and \Bigr, but this would work less well for inline math inside a paragraph of prose.)
I find that whitespace and larger delimiters help to reinforce the distinction between different levels of mathematical syntax when manually (or is that optically?) parsing it, and that this can be helpful when there is repetition of similar symbols in different roles.
;throughout!