\begin{definition}[Definition:Lattice/Definition 1]
Let $\struct {S, \preceq}$ be an ordered set.
Suppose that $S$ admits all finite non-empty suprema and finite non-empty infima.
Denote with $\vee$ and $\wedge$ the join and meet operations on $S$, respectively.
Then the ordered structure $\struct {S, \vee, \wedge, \preceq}$ is called a '''lattice'''.
\end{definition}