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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)

    Functional programming is the programming paradigm consisting of building programs by using only subroutines that behave like mathematical functions. For example, if_then_else is a function that takes three functions as arguments, and, depending on the result of the first function (true or false), returns the result of either the second or the ...

  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. Category:Mathematical relations - Wikipedia

    en.wikipedia.org/.../Category:Mathematical_relations

    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.

  6. Finitary relation - Wikipedia

    en.wikipedia.org/wiki/Finitary_relation

    For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true. The non-negative integer n that gives the number of "places" in the relation is called the arity, adicity or degree of the relation.

  7. Composition of relations - Wikipedia

    en.wikipedia.org/wiki/Composition_of_relations

    In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R ; S from two given binary relations R and S. In the calculus of relations , the composition of relations is called relative multiplication , [ 1 ] and its result is called a relative product .

  8. Total relation - Wikipedia

    en.wikipedia.org/wiki/Total_relation

    In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with xRy}. Conversely, R is called right total if Y equals the range {y : there is an x with xRy}. When f: X → Y is a function, the domain of f is all of X, hence f is a total relation.

  9. Connected relation - Wikipedia

    en.wikipedia.org/wiki/Connected_relation

    For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by in the "Symmetric" column and in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation R {\displaystyle R} be transitive : for all a , b , c , {\displaystyle a,b,c,} if a R b {\displaystyle ...