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  2. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    A function [d] A relation that is functional and total. For example, the red and green relations in the diagram are functions, but the blue and black ones are not. An injection [d] A function that is injective. For example, the green relation in the diagram is an injection, but the red, blue and black ones are not. A surjection [d]

  3. Finitary relation - Wikipedia

    en.wikipedia.org/wiki/Finitary_relation

    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.

  4. Function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Function_(mathematics)

    In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.

  5. Category of relations - Wikipedia

    en.wikipedia.org/wiki/Category_of_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.

  6. Composition of relations - Wikipedia

    en.wikipedia.org/wiki/Composition_of_relations

    In the calculus of relations, the composition of relations is called relative multiplication, [1] and its result is called a relative product. [2]: 40 Function composition is the special case of composition of relations where all relations involved are functions.

  7. Set theory - Wikipedia

    en.wikipedia.org/wiki/Set_theory

    Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects.Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole.

  8. Total relation - Wikipedia

    en.wikipedia.org/wiki/Total_relation

    Total relations can be characterized algebraically by equalities and inequalities involving compositions of relations.To this end, let , be two sets, and let . For any two sets ,, let , = be the universal relation between and , and let = {(,):} be the identity relation on .

  9. Converse relation - Wikipedia

    en.wikipedia.org/wiki/Converse_relation

    In the monoid of binary endorelations on a set (with the binary operation on relations being the composition of relations), the converse relation does not satisfy the definition of an inverse from group theory, that is, if is an arbitrary relation on , then does not equal the identity relation on in general.