\begin{definition}[Definition:Dual Ordering]
Let $\struct {S, \preceq}$ be an ordered set.
Let $\succeq$ be the inverse relation to $\preceq$.
That is, for all $a, b \in S$:
:$a \succeq b$ {{iff}} $b \preceq a$
Then $\succeq$ is called the '''dual ordering of $\preceq$'''.
\end{definition}