Total Ordering/Examples/Monarchy

Example of Total Ordering
Let $K$ denote the set of.

Let $\MM$ denote the relation on $K$ defined as:
 * $a \mathrel \MM b$ $a$ was  after or at the same time as $b$.

Its dual $\MM^{-1}$ is defined as:


 * $a \mathrel {\MM^{-1} } b$ $a$ was  before or at the same time as $b$.

Then $\MM$ and $\MM^{-1}$ are total orderings on $K$.