binary relation

A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A, alternatively written as A²).

Noun

  1. A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A, alternatively written as A²).
    • A partially ordered set #92;langleA,#92;varrho#92;rangle consists of a nonvoid set A and a binary relation #92;varrho on A, such that #92;varrho satisfies properties (P1)-(P3). - 1978, George Grätzer, General Lattice...
    • 1.30. Corollary. If P is a binary relation which is asymmetric and negatively transitive, then P is also transitive. It should be noted that a binary relation may be irreflexive and negatively transitive without being...
    • Definition If E is a non-empty set then by an order on E we mean a binary relation on E that is reflexive, anti-symmetric, and transitive. - 2005, T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer, page 1:

    Synonyms: homogeneous relation

  2. A subset of the Cartesian product A×B.

    Synonyms: heterogeneous relation

Forms

binary relations

Synonyms

correspondence dyadic relation 2-place relation

Hyponyms

dependency relation equivalence relation

Related

nil relation universal relation