\begin{definition}[Definition:Lattice (Ordered Set)]
Let $\struct {S, \preceq}$ be an ordered set.
Then $\struct {S, \preceq}$ is a '''lattice''' {{iff}}:
:for all $x, y \in S$, the subset $\set {x, y}$ admits both a supremum and an infimum.
\end{definition}