\begin{definition}[Definition:Greatest/Ordered Set]
Let $\struct {S, \preceq}$ be an ordered set.
An element $x \in S$ is '''the greatest element (of $S$)''' {{iff}}:
:$\forall y \in S: y \preceq x$
That is, every element of $S$ '''precedes, or is equal to,''' $x$.
The Greatest Element is Unique, so calling it '''''the'' greatest element''' is justified.
Thus for an element $x$ to be the '''greatest element''', all $y \in S$ must be comparable to $x$.
\end{definition}