# Text in a set comprehension

What is the proper way to typeset this set comprehension that has a lot of words in it? Is \textrm with manual spaces really the only way?

$$D = (S, \{(a,b) \,|\, \exists s,x,y\in S^* \textrm{ and } i < j \textrm{ such that } w^i = sax \textrm{ and } w^j = sby\})$$

• just text{...}. and instead of  is better to use $... ] or \begin{equation*} ... \end{equation*}. – Zarko Sep 28 '16 at 2:54 • I would use \textnormal rather than \textrm or \text, or may be define \newcommand*\mathwords{\textnormal} and use \mathwords{ such that }, etc. Also a macro \given rather than writing directly \,|\,. There are multiple questions in this site where a nice of \set{ .. \given .. } is in the answers. – Manuel Sep 28 '16 at 5:27 ## 2 Answers With that answer, I'm concentrating on the "that has a lot of words in it" part on the question. The solution that is often used is \text{...} with ... snippets for the math parts inside of it, just as you would use in normal text mode. You example might then look like this: \[ D = (S, \{(a,b) \mid \text{\exists s,x,y\in S^* and i < j such that w^i = sax and w^j = sby}\})$

• +1. The only thing I'd change is to replace \,|\, with \mid. (\mid is a relational operator and thus inserts thickspace, not thinspace, on either side of the vertical bar.) – Mico Sep 28 '16 at 5:56
• @Mico \mid is indeed better, I added it to the answer – siracusa Sep 28 '16 at 6:31
• I'd say that \mid is not good in general as it cannot be scaled. It is fine in most cases, but annoying when you want it scaled. – daleif Sep 28 '16 at 6:34
• @daleif - Note that I did not say that "\mid is good in general". I was merely pointing out that for the formula at hand, using \mid was better than \,|\,. (If there was need to resize the vertical bar, I would have provided a different suggestion...) – Mico Sep 28 '16 at 8:34
• my point is just that, many people use these pages as a guide as what to do, thus taking for granted that an ad hoc solution is the solution. – daleif Sep 28 '16 at 8:47

The idea is to keep set descriptions as short as possible. That long description hides the main parts at the end, where the reader will have a hard time to end at.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Here is a possibility
$D = (S, \{(a,b) \mid w^i=sax, w^j=sby \text{ for some s,x,y\in S^*, i < j}\}$
but probably it is better if you describe the set in words.

For $w\in S$, define $T_{w}$ as the set of pairs $(a,b)\in S\times S$
such that there exist $s,x,y\in S^{*}$ and $i<j$ so that $w^i=sax$ and
$w^j=sby$. Set $D=(S,T_w)$; then ...

\end{document}
`