Why don't the curly braces and the mid bar become bigger?

Question

I'm having the following code:

\documentclass[11pt]{article}
\usepackage{amssymb,amsthm,amsmath}
\newcommand{\abs}[1]{\lvert #1 \rvert}
\newcommand{\N}{\mathbb N}
\newcommand{\K}{\mathbb K}

\begin{document}
\begin{displaymath}
l^2 = \{x \doteqdot (x_n)_n \in \K^{\N_0}\mid \sum_{n=1}^{\infty}\abs{x_n}^2 < +\infty\}
\end{displaymath}
\end{document}

I'd like the curly braces and the mid bar to become bigger (they should have the same height as the sum), but they don't want to enlarge.

What did I do wrong?

Answer 1

Here's a solution that doesn't rely on \left, \middle, and \right (since they produce "fences" that are too large for the equation at hand). Instead, I suggest using \biggl\{, \biggm|, and \biggr\}. Observe that the spacing around the \biggm| symbol is the same as for the small \mid symbol.

For more on when not to use automatically-sized fences see, e.g., Is it ever bad to use \left and \right?.

\documentclass[11pt]{article}
\usepackage{amssymb,amsthm,amsmath}
\newcommand{\abs}[1]{\lvert #1 \rvert}
\newcommand{\N}{\mathbb N}
\newcommand{\K}{\mathbb K}
\begin{document}
\begin{displaymath}
l^2 = \biggl\{ x \doteqdot (x_n)_n \in \K^{\N_0} \biggm| 
          \sum_{n=1}^{\infty}\abs{x_n}^2 < +\infty \biggr\}
\end{displaymath}
\end{document}

---

Addendum: From the point of view of LaTeX design philosophy, rather than engage in quasi-visual formatting by using macros such as \biggl\{, \biggm|, and \biggr\} directly in one's code, it's far better to set up macros named, say, \Set and \given, which define the look of a "set" (curly braces...) and of the symbol that indicates conditioning information (a vertical bar). It's straightforward to do so with the tools of the mathtools package (pun intended; see p. 26 of the user guide). Observe that a line break is permitted after the \given symbol. (No screenshot is provided since the resulting is the same as the one shown above; it's just the input syntax that's quite different and, I would claim, much easier to parse.)

\documentclass[11pt]{article}
\usepackage{mathtools} % mathtools loads amsmath in the background
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert} % a modified definition of \abs
\usepackage{amssymb}
\newcommand{\N}{\mathbb N}
\newcommand{\K}{\mathbb K}

%% See p. 26 of the user guide of the mathtools package for the next few macros
\providecommand\given{}  % just to make sure it exists
\newcommand\SetSymbol[1][]{\nonscript\:#1\vert\nonscript\:\allowbreak}
\DeclarePairedDelimiterX\Set[1]\lbrace\rbrace{%
  \renewcommand\given{\SetSymbol[\delimsize]}#1}

\begin{document}
\[
l^2 = \Set[\bigg]{ x \doteqdot (x_n)_n \in \K^{\N_0} \given
                   \sum_{n=1}^{\infty}\abs{x_n}^2 < +\infty }
\]
\end{document}

Answer 2

For braces, you want to use \left\{ and \right\} ... the brace itself still needs to be escaped.

The middle conditional bar can be given with the newcommand \relmiddle from here.

For example:

\documentclass[11pt]{article}
\usepackage{amssymb,amsthm,amsmath}
\newcommand{\abs}[1]{\lvert #1 \rvert}
\newcommand{\N}{\mathbb N} %Natuurlijke getallen
\newcommand{\K}{\mathbb K} %Reële of complexe getallen

\newcommand{\relmiddle}[1]{\mathrel{}\middle#1\mathrel{}}

\begin{document}
\begin{displaymath}
l^2 = \left\{x \doteqdot (x_n)_n \in \K^{\N_0} \relmiddle|  \sum_{n=1}^{\infty}\abs{x_n}^2 < +\infty\right\}
\end{displaymath}
\end{document}

Answer 3

A solution based on the \DeclarePairedDelimiter from the mathtools package. I also use xparse to have a very simple syntax: the set of x such that P(x) is typeset with a \Set{x;P(x)} command. For a fine tuning of the delimiter size, you can use \setwith an optional argument: \big, \Big , \bigg or \Bigg.

I also recall a definition of \abs and norm as defined in the mathtoolsdocumentation. They have an optional argument, and therere is sim![enter image description here][1]ilarly anAbsand a\Norm` command.

\documentclass[12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{fourier}
\usepackage{array}
\usepackage{mathtools}
\newcommand{\N}{\mathbb N}
\newcommand{\K}{\mathbb K}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}%% variable sized absolute value
\def\Abs{\abs*}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}%% variable sized norm
\def\Norm{\norm*}

\usepackage{xparse}
%
\DeclarePairedDelimiterX{\set}[1]{\{}{\}}{\setargs{#1}}
\NewDocumentCommand{\setargs}{>{\SplitArgument{1}{;}}m}
{\setargsaux#1}
\NewDocumentCommand{\setargsaux}{mm}
{\IfNoValueTF{#2}{#1} {#1\,\delimsize|\,#2}}%{#1\:;\:#2}
\def\Set{\set*}%

\begin{document}

\begin{center}
\renewcommand{\arraystretch}{2}
 \begin{tabular}{r >{$\displaystyle}l<{$}}%
\verb+ \Set, \Abs+ : &l^2 = \Set{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\Abs{x_n}^2 < +\infty} \\
\verb+ \set, \abs+ : & l^2 = \set{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\abs{x_n^2} < +\infty} \\
\verb+ \set[\big]+ : & l^2 = \set[\big]{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\abs[big]{x_n}^2 < +\infty} \\
\verb+ \set[\Big]+ : & l^2 = \set[\Big]{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\abs[\Big]{x_n}^2 < +\infty} \\
\verb+ \set[\bigg]+ : & l^2 = \set[\bigg]{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\abs[\bigg]{x_n}^2 < +\infty} \\
\verb+ \set[\Bigg]+ : & l^2 = \set[\Bigg]{x \doteqdot (x_n)_n \in \K^{\N_0} ; \sum_{n=1}^{\infty}\abs[\Bigg]{x_n}^2 < +\infty} \\
 & \Set{\Abs{\dfrac{a}{b}}}_{b\neq 0}
\end{tabular}
\end{center}

\end{document}