binary relation
Noun
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Noun
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 \langle A,\varrho\rangle consists of a nonvoid set A and a binary relation \varrho on A, such that \varrho 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 non-empty set then by an order on E we mean a binary relation on E that is reflexive, anti-symmetric, 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.
- (order theory) correspondence, dyadic relation, 2-place relation
- French: relation binaire
- Italian: relazione binaria
- Spanish: relación binaria
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004