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equivalence relation

Overview page. Subjects: Mathematics — Philosophy.

A relation that is transitive, symmetric, and reflexive. The concept is a convenient generalization or abstraction of equality. It covers most notions of equals, equivalence, and similarity...

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equivalence relation

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 62 words.

A *binary relation ~ on a set S that is *reflexive, *symmetric and *transitive. For an equivalence relation ~, ...

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equivalence relation

Christopher Kirwan.

in The Oxford Companion to Philosophy

January 2005; p ublished online January 2005 .

Reference Entry. Subjects: Philosophy. 50 words.

An equivalence relation is a binary, i.e. two-term, relation that is transitive, symmetric, and (strongly) reflexive; for

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equivalence relation

Overview page. Subjects: Mathematics — Philosophy.

A relation that is transitive, symmetric, and reflexive. The concept is a convenient generalization or abstraction of equality. It covers most notions of equals, equivalence, and similarity...

See overview in Oxford Index

equivalence relation

Edited by Andrew Butterfield, Gerard Ekembe Ngondi and Anne Kerr.

in A Dictionary of Computer Science

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 50 words.

A *relation that is *transitive, *symmetric, and *reflexive. The concept is a convenient generalization or abstraction of equality. It covers most notions of equals, equivalence, and...

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equivalence relation

John Daintith and Edmund Wright.

in A Dictionary of Computing

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 46 words.

A *relation that is *transitive, *symmetric, and *reflexive. The concept is a convenient

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equivalence relation

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 56 words.

A *binary relation ~ on a set S that is *reflexive, *symmetric and *transitive.

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equivalence relation

Simon Blackburn.

in The Oxford Dictionary of Philosophy

January 2016; p ublished online March 2016 .

Reference Entry. Subjects: Philosophy. 129 words.

A *relation which is transitive, symmetric, and reflexive divides its field into exclusive classes of things. Within each class

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equivalence relation

Simon Blackburn.

in The Oxford Dictionary of Philosophy

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Philosophy. 129 words.

A *relation which is transitive, symmetric, and reflexive divides its field into exclusive classes of things. Within each class

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equivalence class

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 84 words.

For an *equivalence relation ~ on a set S, an equivalence class [a] is the set

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residue class (modulo n)

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 170 words.

An *equivalence class for the *equivalence relation of *congruence modulo n. So, two integers are in

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Nerode equivalence

Edited by Andrew Butterfield, Gerard Ekembe Ngondi and Anne Kerr.

in A Dictionary of Computer Science

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 148 words.

An *equivalence relation, =N, arising in *formal language theory. It is defined analogously to the *Myhill equivalence...

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representative

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2009; p ublished online January 2009 .

Reference Entry. Subjects: Pure Mathematics. 46 words.

Given an *equivalence relation on a set, any one of the *equivalence classes can be specified by giving

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equivalence class

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 93 words.

For an *equivalence relation ~ on a set S, an equivalence class [a] is the set of elements of ...

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pattern

Edited by Andrew Butterfield, Gerard Ekembe Ngondi and Anne Kerr.

in A Dictionary of Computer Science

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 253 words.

An *equivalence class associated with a special kind of *relation defined on functions. LetF={f...

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Myhill equivalence

John Daintith and Edmund Wright.

in A Dictionary of Computing

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 214 words.

An *equivalence relation arising in *formal language theory. If L is a language over alphabet Σ (

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Nerode equivalence

John Daintith and Edmund Wright.

in A Dictionary of Computing

January 2008; p ublished online January 2008 .

Reference Entry. Subjects: Computing. 171 words.

An *equivalence relation, =N, arising in *formal language theory. It is defined analogously to

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residue class ((modulo n))

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 151 words.

An *equivalence class for the *equivalence relation of *congruence modulo n. So, two integers are in the same class if they have the same remainder upon division by ...

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representative

Christopher Clapham and James Nicholson.

in The Concise Oxford Dictionary of Mathematics

January 2014; p ublished online September 2014 .

Reference Entry. Subjects: Pure Mathematics. 50 words.

Given an *equivalence relation on a set, any one of the *equivalence classes can be specified by giving one of the elements in it. The particular element ...

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Myhill equivalence

Edited by Andrew Butterfield, Gerard Ekembe Ngondi and Anne Kerr.

in A Dictionary of Computer Science

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 234 words.

An *equivalence relation arising in *formal language theory. If L is a language over alphabet Σ (see...

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equivalence class

Edited by Andrew Butterfield, Gerard Ekembe Ngondi and Anne Kerr.

in A Dictionary of Computer Science

January 2016; p ublished online January 2016 .

Reference Entry. Subjects: Computing. 96 words.

A *subset of a set S (on which an *equivalence relation is defined) that consists of all the elements of ...

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