Ordering/Examples/Monarchy

Example of Ordering

Let $K$ denote the set of British monarchs.

Let $\MM$ denote the relation on $K$ defined as:

$a \mathrel \MM b$ if and only if $a$ was monarch after or at the same time as $b$.


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

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


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


Sources

  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings
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