Last Updated
：2025/11/22
antisymmetric
Adjective
not-comparable
of a binary relation R on a set S
of a matrix
of certain mathematical objects
of a tensor
of a bilinear form
Japanese Meaning
反対称的：集合S上の2項関係Rが、任意の異なる2要素について、少なくとも一方が他方と関係していない、もしくは逆に、どちらか一方が他方と関係しているときは、必ず両者が同一である（すなわち、xRyかつyRxならばx=yとなる）という性質を持つこと。
Sense（1）
Sense（3）
Quizzes for review
(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.
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See correct answer
antisymmetric
In the poset example, the relation R is antisymmetric, so if aRb and bRa hold then a and b must be equal.
See correct answer
In the poset example, the relation R is antisymmetric, so if aRb and bRa hold then a and b must be equal.
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