\begin{definition}[Definition:Complete Lattice/Definition 2]
Let $\struct {S, \preceq}$ be an ordered set.
Then $\struct {S, \preceq}$ is a '''complete lattice''' {{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.
\end{definition}