Dictionary

binary relation en · NOUN

Pronunciation

• /ˈbaɪ.ner.i rɪˈleɪ.ʃən/ (General-American)
• (General-American) audio

Meanings

1. (qualifier:"on" a set A) A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A, alternatively written as A²).
   • 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 transitive; as an example, consider the standard inequality relation (≠). 1999, James C. Moore, Mathematical Methods for Economic Theory 1, Springer, page 24:
   • 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 Theory, Academic Press, page 1:
   • 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:
2. (qualifier:"on" or "between" sets A and B) A subset of the Cartesian product A×B.

Forms

Hyponyms

equivalence relation · dependency relation

Relateds

universal relation · nil relation

Synonyms

homogeneous relation · 2-place relation · heterogeneous relation · dyadic relation · correspondence

Translations (12)

es relación binaria (order theory) · pl relacja dwuczłonowa (order theory) · ja 二項関係 (order theory) · is tvístæð vensl (order theory) · cs binární relace (order theory) · fi binäärirelaatio (order theory) · pl relacja binarna (order theory) · ro relație binară (order theory) · it relazione binaria (order theory) · hu kétváltozós reláció (order theory) · fr relation binaire (order theory) · pl relacja dwuargumentowa (order theory)