equivalence relation

Math.a relation that is reflexive, symmetrical, and transitive, as equality.[194550]
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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.* * *
Universalium. 2010.
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Equivalence relation — In mathematics, an equivalence relation is a binary relation between two elements of a set which groups them together as being equivalent in some way. Let a , b , and c be arbitrary elements of some set X . Then a b or a ≡ b denotes that a is… … Wikipedia
equivalence relation — noun A binary relation that is reflexive, symmetric and transitive. See Also: equivalence class, setoid, ≡, equivalence relation … Wiktionary
equivalence relation — (or equivalence class ) A relation which is transitive, symmetric, and reflexive divides its field into exclusive classes of things. Within each class everything bears the relation to everything else, and nothing bears it to anything in a… … Philosophy dictionary
equivalence relation — /əˈkwɪvələns rəˌleɪʃən/ (say uh kwivuhluhns ruh.layshuhn) noun Mathematics, Logic a reflexive, symmetric and transitive relation, that establishes any two elements in the set as equivalent or non equivalent. Also, equivalence … Australian English dictionary
equivalence relation — noun Mathematics & Logic a relation between elements of a set which is reflexive, symmetric, and transitive and which defines exclusive classes whose members bear the relation to each other and not to those in other classes … English new terms dictionary
equivalence relation — noun Date: circa 1949 a relation (as equality) between elements of a set (as the real numbers) that is symmetric, reflexive, and transitive and for any two elements either holds or does not hold … New Collegiate Dictionary
equivalence relation — noun : a relation (as equality) between elements of a set (as the real numbers) that is symmetric, reflexive, and transitive and for any two elements either holds or does not hold … Useful english dictionary
Adequate equivalence relation — In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well working theory of such cycles, and in particular, well defined… … Wikipedia
Partial equivalence relation — In mathematics, a partial equivalence relation (often abbreviated as PER) R on a set X is a relation which is symmetric and transitive . In other words, it holds for all a, b and c in X that:# (Symmetry) if a R b then b R a # (Transitivity) if a… … Wikipedia
Borel equivalence relation — In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X times; X (in the product topology).Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one… … Wikipedia