binary relation
"Binary relations" are essential in various fields of mathematics, including set theory, logic, and graph theory, for describing relationships between elements of sets.
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Definition
C1Mathematics
(technical, academic)A set of ordered pairs, where each pair consists of one element from one set and one element from another set.
Example
- In the set of real numbers, the 'is greater than' relation can be represented as a binary relation.
- The relation 'is a friend of' in a social network can be modeled as a binary relation.
C2Set Theory
(technical, academic)A subset of the Cartesian product of two sets, defining how elements from one set relate to elements from another set.
Example
- If A and B are sets, then a binary relation from A to B is a subset of the Cartesian product A × B.
Similar
Terms that have similar or relatively close meanings to "binary relation":