\begin{definition}[Definition:Dual Ordering/Dual Ordered Set]
Let $\struct {S, \preceq}$ be an ordered set.
Let $\succeq$ be the dual ordering of $\preceq$.
The ordered set $\struct {S, \succeq}$ is called the '''dual ordered set''' (or just '''dual''') '''of $\struct {S, \preceq}$'''.
That it indeed is an ordered set is a consequence of Dual Ordering is Ordering.
\end{definition}