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## 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]

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