Set builder notation

\(\{ 2n \mid n \in \mathbb N \}\) 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.


  • Set

    An unordered collection of distinct objects.