Total Ordering/Examples/Monarchy
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Example of Total 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 total orderings on $K$.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings