Definition:Dual Ordering

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Let $\succeq$ be the inverse relation to $\preceq$.

That is, for all $a, b \in S$:


 * $a \succeq b$ $b \preceq a$

Then $\succeq$ is called the dual ordering of $\preceq$.

Also known as
The dual ordering is also known as the opposite ordering or inverse ordering.

The dual ordering of an ordering $\preccurlyeq$ can also be referred to as the dual of $\preccurlyeq$.

Also see

 * Dual Ordering is Ordering demonstrating that a dual ordering is itself indeed also an ordering.


 * Duality Principle (Ordered Sets)