\begin{definition}[Definition:Dual of Order Type]
Let $\struct {S, \preccurlyeq}$ be an ordered set.
Let $\varrho = \map \ot {S, \preccurlyeq}$ denote the order type of $\struct {S, \preccurlyeq}$.
The '''dual of $\varrho$''' is defined and denoted as:
:$\varrho^* = \map \ot {S, \succcurlyeq}$
where $\struct {S, \succcurlyeq}$ is the dual of $\struct {S, \preccurlyeq}$.
\end{definition}