# How to automatically resize the vertical bar in a set comprehension?

I have a simple command which I use to write set comprehensions so that the braces automatically resize with respect to size of the enclosed arguments, e.g.

\usepackage{amsmath}
\newcommand{\set}[1]{\left\lbrace #1\right\rbrace}

\begin{equation*}
\set{x \in X \mid x > \frac{1}{2}}
\end{equation*}
% Produces something like: { x : X | x > 1/2 }


However, the \mid vertical bar wont resize like the braces { .. } do. How can I get the \mid to resize as well?

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## 5 Answers

You can use \middle| instead of \mid like

$\left\{ x \in X \middle| x > \frac{1}{2}\right\}$


or with better spacing

$\left\{ x \in X \,\middle|\, x > \frac{1}{2}\right\}$


(I think this requires a somewhat modern TeX-distribution.)

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@Andrew: It is an eTeX primitive (not included in the original TeX). But nowadays LaTeX always is run on the pdftex engine, which includes the eTeX stuff. – Paŭlo Ebermann Aug 15 '11 at 13:34

I think the best idea is to use the braket package, which provides markup for these sorts of constructions, for which the brackets and "pipes" expand where necessary.

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Thanks. Leaving a comment here for future reference: Braket lets you write \Set{ x | 0<x<5} etc., expanding the | as necessary. – ShreevatsaR Jul 29 '10 at 12:28

There is the \middle command, it is like \left and \right but for the middle =)

However, LaTeX does not consider \mid to be a delimiter, so you have to use pipe instead (or vertical bar).

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Here is a nice solution using mathtools, which is quite versatile and produces the right spacing (thin space withing braces, and thick space around the mid symbol):

\usepackage{mathtools}
\DeclarePairedDelimiterX\setc[2]{\{}{\}}{\,#1 \;\delimsize\vert\; #2\,}


Now if you use the starred version of the macro you get the desired result:

\setc*{x \in X}{x > \frac{1}{2}}


You can even adjust to a different size if you think that the braces are too big, with the syntax

\setc[\Big]{x \in X}{x > \frac{1}{2}}


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This seems to work for me, possibly the horizontal spacing around the bar needs adjusting.

\documentclass{article}

\usepackage{amssymb}

\makeatletter
\newcommand{\my@set}[1]{\left\lbrace #1\right\rbrace}
\newcommand{\my@cset}[2]{%
\left\lbrace #1\vphantom{#2}\right\vert%
\left.\vphantom{#1}#2\right\rbrace}

\def\my@first#1|#2\relax{#1}
\def\my@second#1|#2\relax{#2}
\newcommand{\set}[1]{%
\edef\my@given{#1}
\edef\my@start{\my@first #1|\relax}%
\ifx\my@start\my@given
\my@set{#1}
\else
\edef\my@last{\my@second #1\relax}%
\my@cset{\my@start}{\my@last}%
\fi}

\begin{document}

$\set{x \in X \int_0^1 | y \in Y} \; \set{x \in X \int_0^1 y \in Y}$

$\set{x | y} \set{a b}$

\end{document}

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