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IEVref: | 102-01-08 | ID: | |

Language: | en | Status: 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:
*a*ℛ*a*, - symmetry: if
*a*ℛ*b*then*b*ℛ*a*, - transitivity: if
*a*ℛ*b*and*b*ℛ*c*then*a*ℛ*c*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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VT remarks: | |||

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Domain5: |

- reflexivity:
*a*ℛ*a*, - symmetry: if
*a*ℛ*b*then*b*ℛ*a*, - transitivity: if
*a*ℛ*b*and*b*ℛ*c*then*a*ℛ*c*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.