\begin{definition}[Definition:Dual Ordering/Strict/Notation]
To denote the dual of an strict ordering, the conventional technique is to reverse the symbol.
Thus:
:$\succ$ denotes $\prec^{-1}$
and so:
:$a \prec b \iff b \succ a$
Similarly for the standard symbol used to denote a strict ordering on numbers:
:$>$ denotes $<^{-1}$
and so on.
\end{definition}