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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. 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 .

  4. 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.

  5. 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 ...

  6. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  7. List of types of functions - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_functions

    Nowhere continuous function: is not continuous at any point of its domain; for example, the Dirichlet function. Homeomorphism: is a bijective function that is also continuous, and whose inverse is continuous. Open function: maps open sets to open sets. Closed function: maps closed sets to closed sets.

  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. Equivalence relation - Wikipedia

    en.wikipedia.org/wiki/Equivalence_relation

    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 ...