Hasse Diagram/Examples/British Monarchs Descent

Example of Hasse Diagram

Recall the partial ordering on the set of people:

Let $P$ denote the set of all people who have ever lived.

Let $\DD$ denote the relation on $P$ defined as:

$a \mathrel \DD b$ if and only if $a$ is a descendant of or the same person as $b$.

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

$a \mathrel {\DD^{-1} } b$ if and only if $a$ is an ancestor of or the same person as $b$.

Then $\DD$ and $\DD^{-1}$ are partial orderings on $P$.

This Hasse diagram illustrates the restriction of $\DD$ to the set of British monarchs such that $x \mathrel \DD \text {Victoria}$.

Source of Name

This entry was named for Helmut Hasse.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings: Exercise $14.2 \ \text{(b)}$