I am sorry if this question is not for mathoverflow. I asked the same question in tex stackexchange and got an answer that this question is out of topic. If it's the same here, please let me know.


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 compare
$$\{x : \lvert x \rvert = 1\}$$
and
$$\{x \mid \lvert x \rvert = 1\}.$$


Can I use both the vertical bar and the colon in one article to make it more readable?
Or should I choose one notation to be consistent?



Can I use both of setbuilder notations in one article?
As the author, such things are generally up to you. It would not be the first time an author chose clarity over consistency of notation. I think many readers appreciate such tradeoffs, although I am sure there is someone who doesn't. If you are going to use inconsistent notation, it is polite to make a footnote or something about why you have done so, but this case is probably transparent enough to make that unnecessary.


If using both really bothers you, you could use \big to do things like $\{ x\ \big\vert\ \lvert x\rvert = 1\}$, which is slightly more readable than when all the symbols are the same size.


