equivalence relation

In mathematics, a generalization of the idea of equality between elements of a set. All equivalence relations (e.g., that symbolized by the equals sign) obey three conditions: reflexivity (every element is in the relation to itself), symmetry (element A has the same relation to element B that B has to A), and transitivity (see transitive law). Congruence of triangles is an equivalence relation in geometry. Members of a set are said to be in the same equivalence class if they have an equivalence relation.

equivalence relation [i′kwiv·ə·ləns ri′lā·shən]

(mathematics)

A relation which is reflexive, symmetric, and transitive. Also known as equals functions.

(mathematics)

equivalence relation - 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.

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.

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No references found	of North Texas) presents a study of equivalence relations and classification problems that includes an introduction to basic concepts as well as a review of classical descriptions of set theory. Invariant descriptive set theory by SciTech Book News Likewise, the variable that best shows the importance of studying equivalence relations is its capacity to improve the learning process (e. Equivalence-equivalence responding: training conditions involved in ... by Garcia, Andres; Bohorquez, Cristobal; Perez, Vicente; Gutierrez, Maria Teresa; Gomez, Jesus / The Psychological Record Others state that the formation of equivalence relations requires no such mediation and that the formation of these classes plays a role in the development of language (Sidman, 1994), (see Fields & Nevin, 1993; Hayes, 1989; Horne & Lowe, 1996, 1997; and Sidman 1994 for reviews of this literature from differing viewpoints). Equivalence relations, the assessment of basic learning abilities and ... by Jackson, Marianne; Williams, W. Larry; Biesbrouck, Jeremy / The Journal of Speech-Language Pathology and Applied Behavior Analysis	Equisetum equisignal equisignal localizer equisignal radio-range beacon equisignal surface equisignal zone equitable equitangential curve equitant equitation equitempered scale Equites Equity equity crude equivalence equivalence class equivalence class partitioning equivalence classes equivalence element equivalence gate equivalence law of ordered sampling equivalence partitioning equivalence point equivalence principle Equivalence Relation Equivalence relations equivalence transformation equivalence zone Equivalence, Principle of Equivalent equivalent absorption area equivalent airspeed Equivalent and Equidecomposable Figures equivalent angles equivalent annual rate equivalent barotropic model equivalent bending moment equivalent binary digits equivalent blackbody temperature equivalent circuit equivalent conductance equivalent continued fractions equivalent continuous sound level equivalent diameter equivalent duct diameter equivalent electrons equivalent elements equivalent embedment length Equivalent Equations equivalent evaporation equivalent focal length	Equiv equiv. equivalence equivalence equivalence equivalence Equivalence class equivalence class partitioning Equivalence class representative Equivalence Class Unification Equivalence classes equivalence element equivalence gate equivalence law of ordered sampling Equivalence of inertial frames Equivalence of Input Equivalence partition Equivalence partitioning Equivalence point Equivalence principle Equivalence principle Equivalence principle of gravitation Equivalence principle of gravitation Equivalence principle of special relativity Equivalence principle of special relativity Equivalence Ratio equivalence relation equivalence relation equivalence relation equivalence relation Equivalence relations equivalence transformation equivalence trial equivalence zone equivalence zone Equivalence, Principle of Equivalences Equivalences Equivalences Equivalences Equivalencia Equivalencia de rendimiento equivalencies equivalencies equivalencies equivalencies equivalency equivalency equivalency equivalency equivalent equivalent equivalent equivalent equivalent Equivalent (chemistry) Equivalent (chemistry) Equivalent (chemistry) Equivalent a Temps Plein equivalent absorption area Equivalent Advertising Value

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of North Texas) presents a study of equivalence relations and classification problems that includes an introduction to basic concepts as well as a review of classical descriptions of set theory.

Invariant descriptive set theory by SciTech Book News

Likewise, the variable that best shows the importance of studying equivalence relations is its capacity to improve the learning process (e.

Equivalence-equivalence responding: training conditions involved in ... by Garcia, Andres; Bohorquez, Cristobal; Perez, Vicente; Gutierrez, Maria Teresa; Gomez, Jesus / The Psychological Record

Others state that the formation of equivalence relations requires no such mediation and that the formation of these classes plays a role in the development of language (Sidman, 1994), (see Fields & Nevin, 1993; Hayes, 1989; Horne & Lowe, 1996, 1997; and Sidman 1994 for reviews of this literature from differing viewpoints).

Equivalence relations, the assessment of basic learning abilities and ... by Jackson, Marianne; Williams, W. Larry; Biesbrouck, Jeremy / The Journal of Speech-Language Pathology and Applied Behavior Analysis

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equisignal localizer

equisignal radio-range beacon