Welcome guest
You're not logged in.
248 users online, thereof 0 logged in

Definition: Equivalence Relation

Let \(V\) be a set and let \(R\subseteq V\times V\) be a relation. \(R\) is called an equivalence relation, if it is reflexive, symmetric and transitive. Elements of $V$ with $aRb$ are called equivalent. Other common notations are \(a\sim_R b\) or \(a\sim b\), if $R$ is known from the context.

| | | | | created: 2014-04-02 23:32:50 | modified: 2018-12-15 19:38:42 | by: bookofproofs | references: [573]

1.Motivation: Significance of Equivalence Relations

2.Example: Examples of Equivalence Relations

3.Proposition: The Equality of Sets Is an Equivalence Relation

4.Definition: Equivalence Class

5.Definition: Quotient Set, Partition

6.Definition: Complete System of Representatives

7.Definition: Canonical Projection

This work was contributed under CC BY-SA 3.0 by:

This work is a derivative of:


Bibliography (further reading)

[573] Schmidt Gunther, Ströhlein Thomas: “Relationen und Graphen”, Springer-Verlag, 1989

FeedsAcknowledgmentsTerms of UsePrivacy PolicyImprint
© 2018 Powered by BooOfProofs, All rights reserved.