Ordering/Examples/American Presidency
Jump to navigation
Jump to search
Example of Ordering
Let $S$ denote the set of American presidents.
Let $\PP$ denote the relation on $S$ defined as:
- $a \mathrel \PP b$ if and only if $a$ was president after or at the same time as $b$.
Because Grover Cleveland was president both before and after Benjamin Harrison, $\PP$ is not an antisymmetric relation.
Thus $\PP$ is not an ordering on $S$.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 14$: Orderings