- antisymmetric relation
- мат.антисимметричное отношение
English-Russian scientific dictionary. 2008.
antisymmetric relation
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Antisymmetric relation — In mathematics, a binary relation R on a set X is antisymmetric if, for all a and b in X , if a is R to b and b is R to a , then a = b .In mathematical notation, this is::forall a, b in X, a R b and b R a ; Rightarrow ; a = bor equally, :forall a … Wikipedia
Antisymmetric — In set theory, the adjective antisymmetric usually refers to an antisymmetric relation.The term antisymmetric function is sometimes used for odd function, although some meanings of antisymmetric are essentiality f ( y , x ) = − f ( x , y ). In… … Wikipedia
Relation algebra — is different from relational algebra, a framework developed by Edgar Codd in 1970 for relational databases. In mathematics, a relation algebra is a residuated Boolean algebra supporting an involutary unary operation called converse. The… … Wikipedia
Binary relation — Relation (mathematics) redirects here. For a more general notion of relation, see Finitary relation. For a more combinatorial viewpoint, see Theory of relations. In mathematics, a binary relation on a set A is a collection of ordered pairs of… … Wikipedia
Relation (mathematics) — This article sets out the set theoretic notion of relation. For a more elementary point of view, see binary relations and triadic relations. : For a more combinatorial viewpoint, see theory of relations. In mathematics, especially set theory, and … Wikipedia
antisymmetric — adjective Date: 1923 relating to or being a relation (as “is a subset of”) that implies equality of any two quantities for which it holds in both directions < the relation R is antisymmetric if aRb and bRa implies a = b > … New Collegiate Dictionary
antisymmetric — I. | ̷ ̷(ˌ) ̷ ̷ ̷ ̷| adjective Etymology: anti (I) + symmetric of a square matrix or a tensor : having the sign of every element or component changed by the interchange of any two indices of that element or component II. adjective 1. : relating… … Useful english dictionary
relation — Philosophically relations are interesting because of the historic prejudice, given its most forceful expression by Leibniz, that they are somehow ‘unreal’ compared to the intrinsic, monadic properties of things. A way of putting the idea is that… … Philosophy dictionary
antisymmetric — A relation is antisymmetric if whenever R xy, and R yx, then x = y … Philosophy dictionary
antisymmetric — /an tee si me trik, an tuy /, adj. Math. noting a relation in which one element s dependence on a second implies that the second element is not dependent on the first, as the relation greater than. Also, antisymmetrical. [1920 25; ANTI +… … Universalium
antisymmetric — adjective Of a 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. See Also: symmetric … Wiktionary
