binary relation
nounUS /ˈbaɪ.ner.i rɪˈleɪ.ʃən/
1
Mathematics, Order theory, Sciences, Set theory 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:
1 more example
- 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:
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Mathematics, Order theory, Sciences, Set theory A subset of the Cartesian product A×B.
"on" or "between" sets A and B
- Synonyms
- correspondence, dyadic relation, 2-place relation
- Related terms
- nil relation, universal relation
- Hyponyms
- dependency relation, equivalence relation