Definition:Complete Lattice/Definition 2

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

Then $\struct {S, \preceq}$ is a complete lattice :


 * $\forall S' \subseteq S: \inf S', \sup S' \in S$

That is, all subsets of $S$ have both a supremum and an infimum.

Also see

 * Equivalence of Definitions of Complete Lattice