How to get big \{ and \} braces for an equation

Question

How to type big \{ and \} braces in this sentence:

$$P_{n,k}=\{\{x,y\}\in [X]^2: n=\min \{m\in
\omega: B_m(x)\cap B_m(y)=\emptyset\}; (x,y)\notin G_k\}$$

Could somebody help me?

Answer 1

For your particular equation, using \left\{ and \right\} to get larger curly braces won't do you much good, as the material being encased by the braces isn't much taller than a parenthesis. Hence, I suggest you use \bigl\{ and \bigr\} for the inner set of braces (the stuff following \min), and \Bigl\{ and \Bigr\} for the outer set:

\documentclass{article}
\begin{document}
\[ P_{n,k} = \Bigl\{ \{x,y\} \in [X]^2: n= \min 
\bigl\{ m\in\omega : B_m(x) \cap B_m(y)=\emptyset \bigr\} ; 
(x,y) \notin G_k \Bigr\} \]
\end{document}

Incidentally, the use $$ ... $$ to generate display-math equations is heavily deprecated. It's much safer to use \[ and \] (as I do in the example above). For much more on this subject, please see Why is \[ ... \] preferable to $$?