Definition:Lattice (Ordered Set)

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

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

Also see

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