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  2. Relation (mathematics) - Wikipedia

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

    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] A function that is surjective.

  3. Finitary relation - Wikipedia

    en.wikipedia.org/wiki/Finitary_relation

    Ternary (3-ary) relations include, for example, the binary functions, which relate two inputs and the output. All three of the domains of a homogeneous ternary relation are the same set. All three of the domains of a homogeneous ternary relation are the same set.

  4. Binary relation - Wikipedia

    en.wikipedia.org/wiki/Binary_relation

    For example, the red and green binary relations in the diagram are functions, but the blue and black ones are not. An injection: a function that is injective. For example, the green relation in the diagram is an injection, but the red one is not; the black and the blue relation is not even a function. A surjection: a function that is surjective ...

  5. Identity function - Wikipedia

    en.wikipedia.org/wiki/Identity_function

    In mathematics, an identity function, also called an identity relation, identity map or identity transformation, is a function that always returns the value that was used as its argument, unchanged. That is, when f is the identity function, the equality f ( x ) = x is true for all values of x to which f can be applied.

  6. Category of relations - Wikipedia

    en.wikipedia.org/wiki/Category_of_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 x R y f ( x ) S f ( y ) , {\displaystyle xRy\implies f(x)Sf(y),} then f is a morphism.

  7. Function (mathematics) - Wikipedia

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

    For example, the relation + + = defines y as an implicit function of x, called the Bring radical, which has as domain and range. The Bring radical cannot be expressed in terms of the four arithmetic operations and n th roots .

  8. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    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.

  9. Converse relation - Wikipedia

    en.wikipedia.org/wiki/Converse_relation

    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 = {(,): = ()}.