(set theory, order theory, of a binary relation R on a set S) Having the property that, for any two distinct elements of S, at least one is not related to the other via R; equivalently, having the property that, for any x, y ∈ S, if both xRy and yRx then x=y.

An adjective "antisymmetric" describes mathematical objects, such as matrices, tensors, and bilinear forms, that exhibit a change in sign when subjected to a matrix transpose or index interchange.