Locking size of character to that of another character?

Question

I have a command for setbuilder notation,

\newcommand{\set}[2]{\left\{ #1 \ \big| \ #2 \right\}}

Pretty simple stuff. I have issues, however, when I want larger characters in the set, for example summations, fractions, and whatnot as the vertical bar doesn't scale. Is there a way its height can be tied to the outside brackets?

Answer 1

You might do like this:

\documentclass{article}
\usepackage{amsmath}

\newcommand{\set}[2]{\left\{ {#1}\vphantom{\big|} \;\middle|\; #2 \right\}}

\begin{document}

\begin{gather*}
\set{x\in A}{x^{-1}=x^2} \\
\set{x\in A}{\frac{1}{x}=x^2}
\end{gather*}

\end{document}

The \vphantom{\big|} is meant to use at least \big size.

However, you should take into account that \left and \right will in most cases choose too big a size. The documentation of mathtools shows alternative approaches.

Answer 2

The TeX primitive \middle is here just for these cases. It was introduced in eTeX extension of TeX (sometime in the nineties). Its argument is an extensible parenthesis/fence like arguments of \left and \right primitives. It can be used only somewhere inside the group given by \left...\right and it gets the same size.

Your macro can be defined as

 \def\set#1#2{\left\{ #1 \vbox to.85em{} \;\middle|\; #2  \right\}}

the \vbox to.85em{} is a strut which is equal to \big size.