Definition:Dual Ordering

Definition
Let $\left({S, \preceq}\right)$ 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 $\preceq$.

By Dual Ordering is Ordering, it is indeed an ordering.

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

Also see

 * Duality Principle (Ordered Sets)