Definition:Dual Ordering/Notation

Definition
To denote the dual of an ordering, the conventional technique is to reverse the symbol.

Thus:
 * $\succeq$ denotes $\preceq^{-1}$
 * $\succcurlyeq$ denotes $\preccurlyeq^{-1}$
 * $\curlyeqsucc$ denotes $\curlyeqprec^{-1}$

and so:
 * $a \preceq b \iff b \succeq a$
 * $a \preccurlyeq b \iff b \succcurlyeq a$
 * $a \curlyeqprec b \iff b \curlyeqsucc a$

Similarly for the standard symbols used to denote an ordering on numbers:
 * $\ge$ denotes $\le^{-1}$
 * $\geqslant$ denotes $\leqslant^{-1}$
 * $\eqslantgtr$ denotes $\eqslantless^{-1}$

and so on.