Ordering/Examples/American Presidency

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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 $S$.


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