Relation (mathematics)

Definition

In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. 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, and likewise between 3 and 4, but not between the values 3 and 1 nor between 4 and 4, that is, 3 < 1 and 4 < 4 both evaluate to false. As another example, "is sister of" is a relation on the set of all people, it holds e.g. between Marie Curie and Bronisława Dłuska, and likewise vice versa. Set members may not be in relation "to a certain degree" – either they are in relation or they are not.

Related concepts

Academic Press Addison-Wesley Affine space Algebra of sets Algebraic function Alphabetical order Analytic function Antisymmetric relation Asymmetric relation Bijection Binary relation Boolean-valued function Boolean function Boolean matrix Bronisława Dłuska C. I. Lewis Calculus of relations Cambridge University Press Cartesian coordinates Charles Sanders Peirce Class (mathematics)Complement (set theory)Complex-valued function Composition of functions Composition of relations Connected relation Constant function Continuous function Converse relation Dependency relation Directed graph Directed path Divides Edgar F. Codd Eike Best Ellipse Equality (mathematics)Equivalence relation Ernst Schröder (mathematician)Finitary relation Function (mathematics)Function composition Function of a complex variable Function of a real variable Function of several complex variables Function of several real variables Function space Functor Greater than Gunther Schmidt Hasse diagram Herbert Enderton Heterogeneous relation Higher-order function History of the function concept Identity element Identity function Implicit function Incidence structure Independency relation Infinite set Infix notation Injective function Integer-valued function Internet Archive Intersection (set theory)Inverse function Irreflexive relation Isomorphism Kinship Lambda calculus Less than Line (geometry)Linear map List of mathematical functions Marie Curie Mathematical object Mathematics Measurable function Morphism Multivalued function Naive Set Theory (book)Natural number Nontrivial divisor Order relation Order theory Ordered pair Parallel (geometry)Partial function Partial order Partially ordered set Pierre Curie Plot (graphics)Point (geometry)Polynomial Rational function Rational number Real-valued function Real number Reflexive relation Relation algebra Relative product Restriction (mathematics)Sequence Serial relation Set-valued function Set (mathematics)Smooth function Strict order Strict weak order Subset Surjective function Symmetric relation Tolerance relation Total order Transitive closure Transitive relation Trichotomy (mathematics)Union (set theory)Vacuous truth Walter de Gruyter

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