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  2. Relational operator - Wikipedia

    en.wikipedia.org/wiki/Relational_operator

    When it is desired to associate a numeric value with the result of a comparison between two data items, say a and b, the usual convention is to assign −1 if a < b, 0 if a = b and 1 if a > b. For example, the C function strcmp performs a three-way comparison and returns −1, 0, or 1 according to this convention, and qsort expects the ...

  3. Relation (mathematics) - Wikipedia

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

    In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...

  4. Binary relation - Wikipedia

    en.wikipedia.org/wiki/Binary_relation

    As a relation between some temporal events and some spatial events, hyperbolic orthogonality (as found in split-complex numbers) is a heterogeneous relation. [21] A geometric configuration can be considered a relation between its points and its lines. The relation is expressed as incidence. Finite and infinite projective and affine planes are ...

  5. Equivalence class - Wikipedia

    en.wikipedia.org/wiki/Equivalence_class

    The word "class" in the term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes. For example, "being isomorphic" is an equivalence relation on groups, and the equivalence classes, called isomorphism classes, are not sets.

  6. 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.

  7. Equivalence relation - Wikipedia

    en.wikipedia.org/wiki/Equivalence_relation

    The equality equivalence relation is the finest equivalence relation on any set, while the universal relation, which relates all pairs of elements, is the coarsest. The relation " ∼ {\displaystyle \sim } is finer than ≈ {\displaystyle \approx } " on the collection of all equivalence relations on a fixed set is itself a partial order ...

  8. Category of relations - Wikipedia

    en.wikipedia.org/wiki/Category_of_relations

    In mathematics, the category Rel has the class of sets as objects and binary relations as morphisms. A morphism (or arrow) R : A → B in this category is a relation between the sets A and B, so R ⊆ A × B. The composition of two relations R: A → B and S: B → C is given by (a, c) ∈ S o R ⇔ for some b ∈ B, (a, b) ∈ R and (b, c) ∈ ...

  9. Class (computer programming) - Wikipedia

    en.wikipedia.org/wiki/Class_(computer_programming)

    Classes can be derived from one or more existing classes, thereby establishing a hierarchical relationship between the derived-from classes (base classes, parent classes or superclasses) and the derived class (child class or subclass) . The relationship of the derived class to the derived-from classes is commonly known as an is-a relationship. [21]