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.