Antisymmetric Relation/Examples/Partial Ordering

Example of Antisymmetric Relation

Let $\preccurlyeq$ be a partial ordering on a set $S$.

Then $\preccurlyeq$ is an antisymmetric relation on $S$.

Proof

This follows directly from the definition of partial ordering.

$\blacksquare$

Sources

• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): antisymmetric relation