binary relation
Contents
EnglishEdit
NounEdit
binary relation (plural binary relations)
 (set theory, order theory, "on" a set A) A subset of the Cartesian product A×A (the set of ordered pairs (a, b) of elements of A).
 1978, George Grätzer, General Lattice Theory, Academic Press, page 1,
 A partially ordered set consists of a nonvoid set and a binary relation on , such that satisfies properties (P1)(P3).
 1999, James C. Moore, Mathematical Methods for Economic Theory 1, Springer, page 24,
 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 (≠).
 2005, T. S. Blyth, Lattices and Ordered Algebraic Structures, Springer, page 1,
 Definition If E is a nonempty set then by an order on E we mean a binary relation on E that is reflexive, antisymmetric, and transitive.
 1978, George Grätzer, General Lattice Theory, Academic Press, page 1,
 (set theory, order theory, "on" or "between" sets A and B) A subset of the Cartesian product A×B.
Usage notesEdit
For a binary relation , the notation signifies that , and one may say that is in binary relation to .
SynonymsEdit
 (order theory): correspondence, dyadic relation, 2place relation
HyponymsEdit
 (order theory): dependency relation, equivalence relation
TranslationsEdit
order theory


See alsoEdit
 nil relation (the empty set)
 universal relation (the entire set A×A)
Further readingEdit
 Finitary relation on Wikipedia.Wikipedia
 Order theory on Wikipedia.Wikipedia
 Binary relation on Encyclopedia of Mathematics
 Binary Relation on Wolfram MathWorld