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- Antisymmetric_relation abstract "In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a and b in Xif R(a,b) and R(b,a), then a = b,or, equivalently,if R(a,b) with a ≠ b, then R(b,a) must not hold.As a simple example, the divisibility order on the natural numbers is an antisymmetric relation. And what antisymmetry means here is that the only way each of two numbers can be divisible by the other is if the two are, in fact, the same number; equivalently, if n and m are distinct and n is a factor of m, then m cannot be a factor of n.In mathematical notation, this is:or, equivalently,The usual order relation ≤ on the real numbers is antisymmetric: if for two real numbers x and y both inequalities x ≤ y and y ≤ x hold then x and y must be equal. Similarly, the subset order ⊆ on the subsets of any given set is antisymmetric: given two sets A and B, if every element in A also is in B and every element in B is also in A, then A and B must contain all the same elements and therefore be equal:Partial and total orders are antisymmetric by definition. A relation can be both symmetric and antisymmetric (e.g., the equality relation), and there are relations which are neither symmetric nor antisymmetric (e.g., the "preys on" relation on biological species).Antisymmetry is different from asymmetry, which requires both antisymmetry and irreflexivity.".
- Antisymmetric_relation thumbnail Even_and_odd_antisymmetric_relation.png?width=300.
- Antisymmetric_relation wikiPageID "1176".
- Antisymmetric_relation wikiPageRevisionID "605092935".
- Antisymmetric_relation hasPhotoCollection Antisymmetric_relation.
- Antisymmetric_relation title "Antisymmetric Relation".
- Antisymmetric_relation urlname "AntisymmetricRelation".
- Antisymmetric_relation subject Category:Mathematical_relations.
- Antisymmetric_relation comment "In mathematics, a binary relation R on a set X is antisymmetric if there is no pair of distinct elements of X each of which is related by R to the other. More formally, R is antisymmetric precisely if for all a and b in Xif R(a,b) and R(b,a), then a = b,or, equivalently,if R(a,b) with a ≠ b, then R(b,a) must not hold.As a simple example, the divisibility order on the natural numbers is an antisymmetric relation.".
- Antisymmetric_relation label "Antisymmetric relation".
- Antisymmetric_relation label "Antisymmetrische Relation".
- Antisymmetric_relation label "Relación antisimétrica".
- Antisymmetric_relation label "Relacja antysymetryczna".
- Antisymmetric_relation label "Relação antissimétrica".
- Antisymmetric_relation label "Антисимметричное отношение".
- Antisymmetric_relation label "反对称关系".
- Antisymmetric_relation label "反対称関係".
- Antisymmetric_relation sameAs Antisymetrická_relace.
- Antisymmetric_relation sameAs Antisymmetrische_Relation.
- Antisymmetric_relation sameAs Relación_antisimétrica.
- Antisymmetric_relation sameAs Antisimetria-erlazio.
- Antisymmetric_relation sameAs 反対称関係.
- Antisymmetric_relation sameAs 반대칭관계.
- Antisymmetric_relation sameAs Relacja_antysymetryczna.
- Antisymmetric_relation sameAs Relação_antissimétrica.
- Antisymmetric_relation sameAs m.0mqp.
- Antisymmetric_relation sameAs Q583760.
- Antisymmetric_relation sameAs Q583760.
- Antisymmetric_relation wasDerivedFrom Antisymmetric_relation?oldid=605092935.
- Antisymmetric_relation depiction Even_and_odd_antisymmetric_relation.png.
- Antisymmetric_relation isPrimaryTopicOf Antisymmetric_relation.