Definition, Meaning & Synonyms

antisymmetric

adjective

/ˌan(t)ɪˈsɪmɛtrɪk/

Definition

A property of a binary relation that states if one element is related to another, then the reverse relation cannot hold unless both are the same element.

Examples

In mathematics, the relation ‘≤’ (less than or equal to) is antisymmetric because if a ≤ b and b ≤ a, then a must equal b.
The concept of antisymmetry can also be observed in certain matrices, where the transposed matrix is the negative of the original matrix.

Meaning

In mathematics, particularly in set theory and relation theory, a relation R on a set A is antisymmetric if for any elements a and b in A, if a is related to b and b is related to a, then a must be equal to b.