equivalence relation

(redirected from Equivalence relations)
Also found in: Encyclopedia.
Related to Equivalence relations: Equivalence classes

equivalence relation

n.
A reflexive, symmetric, and transitive relationship between elements of a set, such as congruence for the set of all triangles in a plane.

equivalence relation

n
(Logic) logic maths a relation that is reflexive, symmetric, and transitive: it imposes a partition on its domain of definition so that two elements belong to the same subset if and only if the relation holds between them
Translations
relace ekvivalence
relacija ekvivalencije
References in periodicals archive ?
Overtraining increases the strength of equivalence relations.
This paper proposes equivalence relations as a criterion (standard of inclusion) to integrate the different functions of research activities into analytical categories, such as those raised by Ribes (2003) and to structure the field of knowledge or discipline.
She covers language, logic, and proof; techniques of proof; induction; sets ; functions; an introduction to number theory; equivalence relations and partitions; finite and infinite sets; and foundations of analysis.
We also defined symmetric, transitive, reflexive and equivalence relations on the NP-soft sets.
The necessary tests to determine this relationship are derived from the mathematical definition of equivalence relations (Sidman & Tailby, 1982), which specifies three properties: reflexivity, symmetry, and transitivity.
This internal category will be a groupoid precisely when the given reflexive and transitive relation R is symmetric, so that if in C every internal category is an internal groupoid, then all of its internal reflexive and transitive relations are equivalence relations.
While lower division mathematics courses focus on techniques, he says, upper division courses treat theory, in particular logic, set theory, the use of functions, equivalence relations, and so on.
On any nonempty closed subset t of r, we can obtain as many time scales as the number of arranged equivalence relations defined on t and the number of values of [alpha] [member of] S [union] {inf T, sup t}.
These theories have two things in common: (a) they assume verbal behavior or symbolic behavior to be fundamentally implied in the emergence of equivalence relations and (b) they contend that, equivalence relations and verbal behavior (whatever the specificities of their relations), are the product of operant conditioning processes.
This research on the RFT approach to language development is based on pioneering work on stimulus equivalence and derived equivalence relations.