Asymmetric relation

In mathematics, an asymmetric relation is a binary relation on a set X where:

In mathematical notation, this is:

An example is the "less than" relation < between real numbers: if x < y, then necessarily y is not less than x.The "less than or equal" relation ≤, on the other hand, is not asymmetric, because reversing x ≤ x produces x ≤ x and both are true. In general, any relation in which x R x holds for some x (that is, which is not irreflexive) is also not asymmetric.

Asymmetry is not the same thing as "not symmetric": the less-than-or-equal relation is an example of a relation that is neither symmetric nor asymmetric. The empty relation is the only relation that is (vacuously) both symmetric and asymmetric.

...
Wikipedia