Set builder notation is a notation for describing a set by stating the properties that it's elements must satisfy.

The set builder notation has three parts, a variable a vertical bar separator "", and a predicate, all three of these parts are contained in curly brackets. For example:

Additionally, the domain of can be explicitly stated on either the left or right side of the separator:

Domain expressed on the left side of the separator

Domain expressed on the right side of the separator, using a logical conjunction with the predicate.

In both of these examples represents set membership.

Example

The set of all even integers can be defined as follows using set builder notation and the existential quantifier: