Definition:Complete Lattice/Definition 2

Definition
Let $\left({S, \preceq}\right)$ be a poset.

Then $\left({S, \preceq}\right)$ is said to be a complete poset iff:


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

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

Also see

 * Extended Real Numbers form Complete Poset
 * Definition:Order Completion