Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Binary_relation> ?p ?o }
- 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 (but with no 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. An example for a ternary relation on Z×Z×Z is "lies between ... and ...", containing e.g. the triples (5,2,8), (5,8,2), and (−4,9,−7).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.".
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- Binary_relation wikiPageWikiLink 4-tuple.
- Binary_relation wikiPageWikiLink Abstract_rewriting_system.
- Binary_relation wikiPageWikiLink Affine_space.
- Binary_relation wikiPageWikiLink Algebraic_structure.
- Binary_relation wikiPageWikiLink Antisymmetric_relation.
- Binary_relation wikiPageWikiLink Arithmetic.
- Binary_relation wikiPageWikiLink Asymmetric_relation.
- Binary_relation wikiPageWikiLink Automata_theory.
- Binary_relation wikiPageWikiLink Axiomatic_set_theory.
- Binary_relation wikiPageWikiLink Bell_number.
- Binary_relation wikiPageWikiLink Bijection.
- Binary_relation wikiPageWikiLink Binary_relation.
- Binary_relation wikiPageWikiLink Boolean_algebra_(structure).
- Binary_relation wikiPageWikiLink Cartesian_product.
- Binary_relation wikiPageWikiLink Category:Mathematical_relations.
- Binary_relation wikiPageWikiLink Category_of_relations.
- Binary_relation wikiPageWikiLink Category_theory.
- Binary_relation wikiPageWikiLink Charles_Sanders_Peirce.
- Binary_relation wikiPageWikiLink Class_(mathematics).
- Binary_relation wikiPageWikiLink Class_(set_theory).
- Binary_relation wikiPageWikiLink Closure_(mathematics).
- Binary_relation wikiPageWikiLink Codomain.
- Binary_relation wikiPageWikiLink Complement_(set_theory).
- Binary_relation wikiPageWikiLink Completeness_(order_theory).
- Binary_relation wikiPageWikiLink Composition_of_functions.
- Binary_relation wikiPageWikiLink Composition_of_relations.
- Binary_relation wikiPageWikiLink Computer_science.
- Binary_relation wikiPageWikiLink Confluence_(abstract_rewriting).
- Binary_relation wikiPageWikiLink Confluence_(term_rewriting).
- Binary_relation wikiPageWikiLink Congruence_(geometry).
- Binary_relation wikiPageWikiLink Coreflexive_relation.
- Binary_relation wikiPageWikiLink Dependency_relation.
- Binary_relation wikiPageWikiLink Directed_graph.
- Binary_relation wikiPageWikiLink Divides.
- Binary_relation wikiPageWikiLink Divisibility.
- Binary_relation wikiPageWikiLink Divisibility_rule.
- Binary_relation wikiPageWikiLink Divisor.
- Binary_relation wikiPageWikiLink Domain_(mathematics).
- Binary_relation wikiPageWikiLink Domain_of_a_function.
- Binary_relation wikiPageWikiLink Duality_(order_theory).
- Binary_relation wikiPageWikiLink Empty_set.
- Binary_relation wikiPageWikiLink Equality_(mathematics).
- Binary_relation wikiPageWikiLink Equivalence_relation.
- Binary_relation wikiPageWikiLink Euclidean_relation.
- Binary_relation wikiPageWikiLink Finitary_relation.
- Binary_relation wikiPageWikiLink Finite_set.
- Binary_relation wikiPageWikiLink Function_(mathematics).
- Binary_relation wikiPageWikiLink Function_composition.
- Binary_relation wikiPageWikiLink Geometry.
- Binary_relation wikiPageWikiLink Graph_(mathematics).
- Binary_relation wikiPageWikiLink Graph_of_a_function.
- Binary_relation wikiPageWikiLink Graph_theory.
- Binary_relation wikiPageWikiLink Greater_than.
- Binary_relation wikiPageWikiLink Greatest_element.
- Binary_relation wikiPageWikiLink Gunther_Schmidt.
- Binary_relation wikiPageWikiLink Hasse_diagram.
- Binary_relation wikiPageWikiLink Incidence_structure.
- Binary_relation wikiPageWikiLink Independency_relation.
- Binary_relation wikiPageWikiLink Indicator_function.
- Binary_relation wikiPageWikiLink Inequality_(mathematics).
- Binary_relation wikiPageWikiLink Infimum_and_supremum.
- Binary_relation wikiPageWikiLink Injective_function.
- Binary_relation wikiPageWikiLink Integer.
- Binary_relation wikiPageWikiLink Intersection_(set_theory).
- Binary_relation wikiPageWikiLink Inverse_relation.
- Binary_relation wikiPageWikiLink Involution_(mathematics).
- Binary_relation wikiPageWikiLink Irreflexive.
- Binary_relation wikiPageWikiLink Irreflexive_relation.
- Binary_relation wikiPageWikiLink Isomorphism.
- Binary_relation wikiPageWikiLink Kernel_(set_theory).
- Binary_relation wikiPageWikiLink Least_element.
- Binary_relation wikiPageWikiLink Less_than.
- Binary_relation wikiPageWikiLink Linear_algebra.
- Binary_relation wikiPageWikiLink Logic_of_relatives.
- Binary_relation wikiPageWikiLink Loop_(graph_theory).
- Binary_relation wikiPageWikiLink Many-sorted.
- Binary_relation wikiPageWikiLink Mathematics.
- Binary_relation wikiPageWikiLink Morse–Kelley_set_theory.
- Binary_relation wikiPageWikiLink Multivalued_function.
- Binary_relation wikiPageWikiLink Noetherian_relation.
- Binary_relation wikiPageWikiLink Order_relation.
- Binary_relation wikiPageWikiLink Order_theory.
- Binary_relation wikiPageWikiLink Ordered_pair.
- Binary_relation wikiPageWikiLink Ordinal_number.
- Binary_relation wikiPageWikiLink Orthogonal.
- Binary_relation wikiPageWikiLink Orthogonality.
- Binary_relation wikiPageWikiLink Parallel_(geometry).
- Binary_relation wikiPageWikiLink Partial_equivalence_relation.
- Binary_relation wikiPageWikiLink Partial_function.
- Binary_relation wikiPageWikiLink Partial_order.
- Binary_relation wikiPageWikiLink Partially_ordered_set.
- Binary_relation wikiPageWikiLink Partition_of_a_set.
- Binary_relation wikiPageWikiLink Pecking_order.
- Binary_relation wikiPageWikiLink Power_set.
- Binary_relation wikiPageWikiLink Preference.