equivalence relation
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About Our Definitions: All forms of a word (noun, verb, etc.) are now displayed on one page.equivalence relation
nounDefinition of EQUIVALENCE RELATION
: 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
First Known Use of EQUIVALENCE RELATION
circa 1949
equivalence relation
noun (Concise Encyclopedia)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.
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