Search results
Results from the WOW.Com Content Network
A partial order is a relation that is reflexive, antisymmetric, and transitive, [3] an equivalence relation is a relation that is reflexive, symmetric, and transitive, [4] a function is a relation that is right-unique and left-total (see below).
A multivariate function, multivariable function, or function of several variables is a function that depends on several arguments. Such functions are commonly encountered. For example, the position of a car on a road is a function of the time travelled and its average speed.
Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
The equivalence relations on any set X, when ordered by set inclusion, form a complete lattice, called Con X by convention. The canonical map ker : X^X → Con X, relates the monoid X^X of all functions on X and Con X. ker is surjective but not injective. Less formally, the equivalence relation ker on X, takes each function f : X → X to its ...
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.
David Rydeheard and Rod Burstall consider Rel to have objects that are homogeneous relations. For example, A is a set and R ⊆ A × A is a binary relation on A.The morphisms of this category are functions between sets that preserve a relation: Say S ⊆ B × B is a second relation and f: A → B is a function such that () (), then f is a morphism.
Mathematical relations fall into various types according to their specific properties, often as expressed in the axioms or definitions that they satisfy. Many of these types of relations are listed below.
A function is invertible if and only if its converse relation is a function, in which case the converse relation is the inverse function. The converse relation of a function : is the relation defined by the = {(,): = ()}.