IEVref:102-01-08ID:
Language:enStatus: Standard
Term: equivalence relation
Synonym1: equivalence
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Definition: binary relation ℛ between elements a and b of a given set having the following properties:

  • reflexivity: aℛa,

  • symmetry: if aℛb then bℛa,

  • transitivity: if aℛb and bℛc then aℛc for any elements a, b and c of the given set

Note 1 to entry: Examples are the equality of elements of a set, the parallelism of straight lines in a point space, the relation between integers whose difference is even.


Publication date:2008-08
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Internal notes:2017-02-20: Editorial revisions in accordance with the information provided in C00019 (IEV 102) - evaluation. JGO
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