Definition:Lattice (Ordered Set)

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Then $\struct {S, \preceq}$ is a lattice :
 * for all $x, y \in S$, the subset $\set {x, y}$ admits both a supremum and an infimum.

Also see

 * Definition:Lattice: an abstraction of this definition in a more general context