Definition:Complete Lattice/Definition 2

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

Then $\left({S, \preceq}\right)$ is a complete ordered set :


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

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

Also see

 * Extended Real Numbers form Complete Ordered Set
 * Definition:Order Completion


 * Definition:Dedekind Complete Set
 * Definition:Chain Complete Set