# 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.