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

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?

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Hi John, Welcome to TeX.SE! I edited your question by using the {} button. –  cmhughes Mar 20 '13 at 0:58
Thanks Mico and cmhughes. –  John Mar 20 '13 at 1:06
You can also do \left\{ and \right\} –  dustin Mar 20 '13 at 1:19
@cmhughes - Good one, about using the {} button to edit a question involving { and }... –  Mico Mar 20 '13 at 2:10

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