antisymmetric relation

For example, consider the property of being an antisymmetric relation.

As opposed to the former, the latter is antisymmetric relation and a total order.

As a simple example, the divisibility order on the natural numbers is an antisymmetric relation.

Antisymmetric relation in mathematics (also see below).

In set theory, the adjective 'antisymmetric' usually refers to an antisymmetric relation.

The less-than-or-equal-to relation on the real numbers is an example of an antisymmetric relation, because whenever and , it is true that .

In the definition of an antisymmetric relation, "minus" is replaced by "not", and the condition is necessarily relaxed, to be required only in the case x y. The corresponding 2D set has a special kind of geometric "symmetry".