Equivalence relation - Wikipedia, the free encyclopedia
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In mathematics, an equivalence relation is, loosely, a binary relation on a set that specifies how to split up (i.e. partition) the set into subsets such that every element of the larger set is in e...
en.wikipedia.org/wiki/Equivalence_relation
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Encyclopedia information on Equivalence Relation ... Elementary Examples of Equivalence Relation; There are two obvious equivalence relations on a set, X, that follow easily from the definition: the relation of equality and the Cartesian product.
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www.iscid.org/encyclopedia/Equivalence_Relation
www.iscid.org/encyclopedia/Equivalence_Relation
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Equivalence relations and partitions ... The concept of equivalence relation is an abstraction of the idea of two math objects being like each other in some respect. ...
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www.abstractmath.org/MM/MMEquivalenceRelations.htm
www.abstractmath.org/MM/MMEquivalenceRelations.htm
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Determine whether the given relation is an equivalence relation on the set. Describe the partition arising from each equivalence relations. 1. x is Related to y in Real number if |x| = |y|. 2. n is Related to m in Z+ if n and m have ... Math Central is supported by the University of Regina and the Imperial Oil Foundation.
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mathcentral.uregina.ca/QQ/database/QQ.09.06/h/jim4.html
mathcentral.uregina.ca/QQ/database/QQ.09.06/h/jim4.html
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RELATIONS AND EQUIVALENCE RELATIONS; A "relation" might be an intuitive notion, but it is rather hard to make precise what is meant by the word. (It is questionable whether kids should be forced to deal with such abstractions before they are ready for it.
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mathcentral.uregina.ca/QQ/database/QQ.09.98/megan1.html
mathcentral.uregina.ca/QQ/database/QQ.09.98/megan1.html
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A relation on A is an equivalence relation if it is reflexive, symmetric and transitive. An example of such is equality on a set. One might think of equivalence as a way to glob together elements that can be considered the same relative to ... Next: Congruence modulo n Up: NOTES ON RELATIONS Previous: Relations on a set...
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www.math.csusb.edu/notes/rel/node3.html
www.math.csusb.edu/notes/rel/node3.html
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L. A. Harrington, A. S. Kechris, A. Louveau. A Glimm -- Effros dichotomy for Borel equivalence relations. J. Amer. Math. Soc. 1990, 3, no 4, p. 903 --928. ... A Glimm -- Effros dichotomy for Borel equivalence relations. J. Amer. Math. Soc. 1990, 3, no 4, p. 903 --928. Online articles have much greater impact More...
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citeseer.ist.psu.edu/context/126703/0
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(with B.D. Miller) Means on equivalence relations, Israel. J. Math. 163 (2008), 241-262. ... (with S. Jackson and A. Louveau) Countable Borel equivalence relations, J. Math. Logic 2(1) (2002), 1-80.
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www.math.caltech.edu/people/kechris.html
www.math.caltech.edu/people/kechris.html
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An equivalence relation on a set induces a partition on it. Conversely, any partition induces an equivalence relation. Equivalence relations are important, because often the set $S$ can be 'transformed' into another set (quotient space) by considering each equivalence class as a single unit. ... Math for the people,
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planetmath.org/encyclopedia/EquivalenceClass2.html
planetmath.org/encyclopedia/EquivalenceClass2.html
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