Set builder notation

by Nate Soares May 13 2016 updated May 13 2016

$~$\{ 2n \mid n \in \mathbb N \}$~$ denotes the set of all even numbers, using set builder notation. Set builder notation involves an expression on the left and a series of constraints on the right, separated by a pipe and placed between curly braces. The expression on the left makes use of variables that are introduced and constrained on the right. The result denotes the set of all possible values on the left-hand side that obey the constraints on the right-hand side. For example, $~$\{ (x, y) \mid x \in \mathbb R, y \in \mathbb R, x \cdot y = 1 \}$~$ is the set of all pairs of real numbers whose product is 1.