Definition:Asymmetric Relation/Also defined as

Asymmetric Relation: Also defined as
Some sources (possibly erroneously or carelessly) gloss over the differences between this and the definition for an antisymmetric relation, and end up using a definition for antisymmetric which comes too close to one for asymmetric.

An example is :


 * [After having discussed antireflexivity] ... antisymmetry expresses the additional fact that at most one of the possibilities $a \mathrel \RR b$ or $b \mathrel \RR a$ can take place.

Some sources specifically define a relation as anti-symmetric what has been defined on as asymmetric

From : Chapter $0$: Relations:
 * ... the relation $R$ is anti-symmetric iff it is never the case that both $x R y$ and $y R x$.