\begin{definition}[Definition:Ordered Set]
An '''ordered set''' is a relational structure $\struct {S, \preceq}$ such that the relation $\preceq$ is an ordering.
Such a structure may be:
:A partially ordered set (poset)
:A totally ordered set (toset)
:A well-ordered set (woset)
depending on whether the ordering $\preceq$ is:
:A partial ordering
:A total ordering
:A well-ordering.
\end{definition}