Set-Builder Notation

A way to describe a Set by stating a property its elements satisfy, instead of listing them.

General form:

$$\{x\in S\mid \text{ condition on }x\}$$

Read as “the set of all $x$ in $S$ such that (condition).”

Example

$$\{(x,y)\in {\mathbb{R}}^2\mid x^2+y^2\le 1\}$$

Refers to all points in or on the unit-circle.