binary relation

Noun

binary relation (plural binary relations)

1. ("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).
   • 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
   • 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

   Synonyms:

   homogeneous relation

2. ("on" or "between" sets A and B) A subset of the Cartesian product A×B.

   Synonyms:

   heterogeneous relation