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 class — This article is about equivalency in mathematics; for equivalency in music see equivalence class (music). In mathematics, given a set X and an equivalence relation on X, the equivalence class of an element a in X is the subset of all elements in… … Wikipedia
Equivalence of categories — In category theory, an abstract branch of mathematics, an equivalence of categories is a relation between two categories that establishes that these categories are essentially the same . There are numerous examples of categorical equivalences… … Wikipedia
Equivalence (measure theory) — In mathematics, and specifically in measure theory, equivalence is a notion of two measures being the same . Two measures are equivalent if they have the same null sets.DefinitionLet ( X , Σ) be a measurable space, and let μ , ν : Σ → [0, +∞] be… … Wikipedia
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 — noun Date: circa 1541 1. a. the state or property of being equivalent b. the relation holding between two statements if they are either both true or both false so that to affirm one and to deny the other would result in a contradiction 2. a… … New Collegiate Dictionary
equivalence, equivalency — 1. The property of an element or radical of combining with or displacing, in definite and fixed proportion, another element or radical in a compound. 2. The point in a precipitin test at which antibody and antigen are present in opti … Medical dictionary
equivalence — equiv·a·lence i kwiv( ə) lən(t)s n the state or property of being equivalent * * * equiv·a·lence (e kwivґə ləns) 1. the condition of being equivalent; having equal valence. 2. in immunology, the ratio of antigen to antibody… … Medical dictionary
Mass–energy equivalence — E=MC2 redirects here. For other uses, see E=MC2 (disambiguation). 4 meter tall sculpture of Einstein s 1905 E = mc2 formula at the 2006 Walk of Ideas, Berlin, Germany In physics, mass–energy equivalence is the concept that the … Wikipedia
Morita equivalence — In abstract algebra, Morita equivalence is a relationship defined between rings that preserves many ring theoretic properties. It is named after Japanese mathematician Kiiti Morita who defined equivalence and a similar notion of duality in 1958.… … Wikipedia
