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单词 antisymmetric
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, symmetric1
Translations
αντισυμμετρικός

antisymmetric


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.
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更新时间:2024/11/14 19:07:35