| 释义 |
antisymmetric
antisymmetric (ˌæntɪsɪˈmɛtrɪk) adj1. (Logic) logic (of a relation) never holding between a pair of arguments x and y when it holds between y and x except when x = y, as "…is no younger than…". See nonsymmetric2. (Mathematics) maths symmetric except for a change of sign. Compare asymmetric, symmetric1Translationsantisymmetric
antisymmetric (mathematics)A relation R is antisymmetric if,
for all x and y, x R y and y R x => x == y.
I.e. no two different elements are mutually related.
Partial orders and total orders are antisymmetric. If Ris also symmetric, i.e.
x R y => y R x
then
x R y => x == y
I.e. different elements are not related. |