set builder notation

The set builder notation is used for notating a set, whose elements satisfy a certain condition. This allows convenient conversion from a verbal description of a set to a mathematical one.

A set builder notation typically consists of two parts separated by a colon or a vertical bar. On the right of the separator is the condition, and on the left is how each element will look in the set. For example, we can use set builder to denote a power set: $\mathcal{P}(S)=\{T|T\subseteq S\}$. Words can be used in the condition too, for instance: $\{n\in \mathbb{Z}:n\text{ is even}\}$.