How do I type large set brackets that look like this

Question

How can I get the set brackets to look like this?

Answer 1

You can use \left\{ and \right\}. They autosize your brackets around your content and the item that follows them, in this case \{, is the delimiter.

Answer 2

With mathtools you can define a \set command, which accepts an optional argument: \big, \Big,&c. to control the size of the brackets. The starred version is equivalent of a pair of \left ··· \right around the braces.

As to the separator, @egreg pointed there's a small difference between : and \colon. I propose both, so the choice depends on one's taste:

\documentclass[12pt]{article}

\usepackage{mathtools}
\DeclarePairedDelimiter\set{\{}{\}}
\newcommand\numberset[1]{\mathbf{#1}}
\newcommand\Real{\numberset{R}}

\begin{document}

\begin{align*} 
& \set*{\begin{pmatrix}x + 2y\\x\\-y\end{pmatrix}: x, y\in\Real} \\[3ex]
&\set*{\begin{pmatrix}x + 2y\\x\\-y\end{pmatrix}\colon x, y\in\Real}
\end{align*}

\end{document}