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 $y R x$.