Equivalence Relation


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Related to Equivalence Relation: Equivalence class

equivalence relation

[i′kwiv·ə·ləns ri′lā·shən]
(mathematics)
A relation which is reflexive, symmetric, and transitive. Also known as equals functions.

Equivalence Relation

 

a concept in logic and mathematics expressing the presence in different objects of the same characteristics or properties. The objects are indistinguishable—identical, equal, or equivalent—with respect to such shared characteristics. Any of them can serve equally well as a “representative” of the equivalence class to which all objects between which the equivalence relation holds belong. Equivalence relations are reflexive, symmetric, and transitive. Under certain conditions and within certain limits, they possess the property of substitution—that is, objects in an equivalence class can, with certain limitations, perform the same functions and their names, or words designating them, can be substituted for each other in different propositions.


Equivalence Relation

 

an equality-type relation, that is, a binary relation that is reflexive, symmetric, and transitive. For example, if two geometric figures are congruent or similar or if two sets of objects are isomorphic or equipotent, the figures or sets are equal or identical in some regard. Thus, isomorphic sets are indistinguishable in structure if by “structure” is meant the aggregate of the properties with respect to which the sets are isomorphic.

equivalence relation

(mathematics)
A relation R on a set including elements a, b, c, which is reflexive (a R a), symmetric (a R b => b R a) and transitive (a R b R c => a R c). An equivalence relation defines an equivalence class.

See also partial equivalence relation.
References in periodicals archive ?
We do so by putting an equivalence relation on the poset and then ordering the equivalence classes.
An equivalence relation E on t is called arranged if the family of all equivalence classes is arranged.
This research on the RFT approach to language development is based on pioneering work on stimulus equivalence and derived equivalence relations.
r](Q) is a normal subgroup, then the equivalence relation induced by the orbits ofthe right-regular permutation group R([?
An equivalence relation [equivalent to] defined on [A.
It is merely an equivalence relation in which conceptual stimuli are class members.
The widespread use of conditional discriminations in testing an individual's ability to form equivalence relations (e.
Considering that Sidman's (2000) account holds that equivalence relations consist "of ordered pairs of all positive elements that participate in the reinforcement contingency" (Sidman 2000, p.
This emergent performance defines the stimulus equivalence relation (c.
As a whole, these data are consistent with Sidman's suggestion that reinforcing stimuli become a part of the equivalence relation and can suffice to produce class development, expansion, and merger.
These relations have been described in terms of mathematical set theory as documenting the properties of reflexivity (A=A), symmetry (if A=B, then B=A), and transitivity (if A=B and B=C, then the three defining properties of stimulus equivalence relation (Sidman and Tailby 1982).
After participants reached a criterion level of responding for the A-B and B-C relations, they were tested for the untaught C-A equivalence relation, again using all black stimuli (this was designated as the baseline condition in the ABA reversal design).