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- Binary_relation abstract "In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B. The terms correspondence, dyadic relation and 2-place relation are synonyms for binary relation.An example is the "divides" relation between the set of prime numbers P and the set of integers Z, in which every prime p is associated with every integer z that is a multiple of p (and not with any integer that is not a multiple of p). In this relation, for instance, the prime 2 is associated with numbers that include −4, 0, 6, 10, but not 1 or 9; and the prime 3 is associated with numbers that include 0, 6, and 9, but not 4 or 13.Binary relations are used in many branches of mathematics to model concepts like "is greater than", "is equal to", and "divides" in arithmetic, "is congruent to" in geometry, "is adjacent to" in graph theory, "is orthogonal to" in linear algebra and many more. The concept of function is defined as a special kind of binary relation. Binary relations are also heavily used in computer science.A binary relation is the special case n = 2 of an n-ary relation R ⊆ A1 × … × An, that is, a set of n-tuples where the jth component of each n-tuple is taken from the jth domain Aj of the relation.In some systems of axiomatic set theory, relations are extended to classes, which are generalizations of sets. This extension is needed for, among other things, modeling the concepts of "is an element of" or "is a subset of" in set theory, without running into logical inconsistencies such as Russell's paradox.".
- Binary_relation wikiPageID "3931".
- Binary_relation wikiPageRevisionID "603584684".
- Binary_relation date "July 2013".
- Binary_relation hasPhotoCollection Binary_relation.
- Binary_relation id "p/b016380".
- Binary_relation reason "In a directed graph, usually multiple edges may exist between two nodes x and y. However, a binary relation can relate x and y at most once.".
- Binary_relation reason "It seems that there may be several minimal relations having the same transitive closure as R. If this is true, it should be stated explicitly. In that case 'transitive reduction' is not an 'operation' on binary relations in a strict sense, as it doesn't have a unique result.".
- Binary_relation reason "Why is the notation 'R∘S' more ambigous than 'S∘R'? Isn't the order merely a matter of taste, and of compatibility with other notations?".
- Binary_relation title "Binary relation".
- Binary_relation subject Category:Mathematical_relations.
- Binary_relation comment "In mathematics, a binary relation on a set A is a collection of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2 = A × A. More generally, a binary relation between two sets A and B is a subset of A × B.".
- Binary_relation label "Binary relation".
- Binary_relation label "Relación binaria".
- Binary_relation label "Relacja dwuargumentowa".
- Binary_relation label "Relation binaire".
- Binary_relation label "Relazione binaria".
- Binary_relation label "Relação binária".
- Binary_relation label "Tweeplaatsige relatie".
- Binary_relation label "Бинарное отношение".
- Binary_relation label "علاقة ثنائية".
- Binary_relation label "二元关系".
- Binary_relation label "二項関係".
- Binary_relation sameAs Binární_relace.
- Binary_relation sameAs Relación_binaria.
- Binary_relation sameAs Erlazio_bitar.
- Binary_relation sameAs Relation_binaire.
- Binary_relation sameAs Relasi_biner.
- Binary_relation sameAs Relazione_binaria.
- Binary_relation sameAs 二項関係.
- Binary_relation sameAs 이항관계.
- Binary_relation sameAs Tweeplaatsige_relatie.
- Binary_relation sameAs Relacja_dwuargumentowa.
- Binary_relation sameAs Relação_binária.
- Binary_relation sameAs m.018yh.
- Binary_relation sameAs Q130901.
- Binary_relation sameAs Q130901.
- Binary_relation wasDerivedFrom Binary_relation?oldid=603584684.
- Binary_relation isPrimaryTopicOf Binary_relation.