# Category: Mathematical relations

Composition of relations
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
Idempotence
Idempotence (UK: /ˌɪdɛmˈpoʊtəns/, US: /ˈaɪdəm-/) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond
Bidirectional transformation
In computer programming, bidirectional transformations (bx) are programs in which a single piece of code can be run in several ways, such that the same data are sometimes considered as input, and some
Relation construction
In logic and mathematics, relation construction and relational constructibility have to do with the ways that one relation is determined by an indexed family or a sequence of other relations, called t
Ternary equivalence relation
In mathematics, a ternary equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric, reflexive, and transitive. The cla
Inverse trigonometric functions
In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric func
Difunctional
No description available.
Near sets
In mathematics, near sets are either spatially close or descriptively close. Spatially close sets have nonempty intersection. In other words, spatially close sets are not disjoint sets, since they alw
Ternary relation
In mathematics, a ternary relation or triadic relation is a finitary relation in which the number of places in the relation is three. Ternary relations may also be referred to as 3-adic, 3-ary, 3-dime
Bijection, injection and surjection
In mathematics, injections, surjections, and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from
Reduct
In universal algebra and in model theory, a reduct of an algebraic structure is obtained by omitting some of the operations and relations of that structure. The opposite of "reduct" is "expansion."
Cointerpretability
In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the lang
Hypostatic abstraction
Hypostatic abstraction in mathematical logic, also known as hypostasis or subjectal abstraction, is a formal operation that transforms a predicate into a relation; for example "Honey is sweet" is tran
Propositional function
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x
Contour set
In mathematics, contour sets generalize and formalize the everyday notions of * everything superior to something * everything superior or equivalent to something * everything inferior to something
Relation (mathematics)
In mathematics, a relation on a set may, or may not, hold between two given set members.For example, "is less than" is a relation on the set of natural numbers; it holds e.g. between 1 and 3 (denoted
Quasi-commutative property
In mathematics, the quasi-commutative property is an extension or generalization of the general commutative property. This property is used in specific applications with various definitions.
Representation (mathematics)
In mathematics, a representation is a very general relationship that expresses similarities (or equivalences) between mathematical objects or structures. Roughly speaking, a collection Y of mathematic
Alternating multilinear map
In mathematics, more specifically in multilinear algebra, an alternating multilinear map is a multilinear map with all arguments belonging to the same vector space (for example, a bilinear form or a m
List of set identities and relations
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
Allegory (mathematics)
In the mathematical field of category theory, an allegory is a category that has some of the structure of the category Rel of sets and binary relations between them. Allegories can be used as an abstr
Relation algebra
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation algebra is
Surjective function
In mathematics, a surjective function (also known as surjection, or onto function) is a function f that every element y can be mapped from element x so that f(x) = y. In other words, every element of
Demonic composition
In mathematics, demonic composition is an operation on binary relations that is somewhat comparable to ordinary composition of relations but is robust to refinement of the relations into (partial) fun
Unimodality
In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object.
Finitary relation
In mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, t
Jouanolou's trick
In algebraic geometry, Jouanolou's trick is a theorem that asserts, for an algebraic variety X, the existence of a surjection with affine fibers from an affine variety W to X. The variety W is therefo
Property (mathematics)
In mathematics, a property is any characteristic that applies to a given set. Rigorously, a property p defined for all elements of a set X is usually defined as a function p: X → {true, false}, that i
Bijection
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is pai
Sequential composition
No description available.
Fiber (mathematics)
In mathematics, the term fiber (US English) or fibre (British English) can have two meanings, depending on the context: 1. * In naive set theory, the fiber of the element in the set under a map is th
Exceptional isomorphism
In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members ai and bj of two families, usually infinite, of mathematical objects, that is not a
Partial function
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the dom