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In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
In mathematics, a finitary relation over a sequence of sets X 1, ..., X n is a subset of the Cartesian product X 1 × ... × X n; that is, it is a set of n-tuples (x 1, ..., x n), each being a sequence of elements x i in the corresponding X i. [1] [2] [3] Typically, the relation describes a possible connection between the elements of an n-tuple.
A finitary or n-ary relation is a set of n-tuples. Specific types of relations include: Relation (mathematics) (an elementary treatment of binary relations) Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation; Homogeneous relation; Reflexive relation; Serial relation
A relation R is called intransitive if it is not transitive, that is, if xRy and yRz, but not xRz, for some x, y, z. In contrast, a relation R is called antitransitive if xRy and yRz always implies that xRz does not hold. For example, the relation defined by xRy if xy is an even number is intransitive, [13] but not antitransitive. [14]
In mathematics, a binary relation associates elements of one set called the domain with elements of another set called the codomain. [1] Precisely, ...
Mathematical relations fall into various types according to their specific properties, often as expressed in the axioms or definitions that they satisfy. Many of ...
In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R ; S from two given binary relations R and S.In the calculus of relations, the composition of relations is called relative multiplication, [1] and its result is called a relative product.