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A relation between elements of a set which is reflexive, symmetric, and transitive and which defines exclusive classes whose members bear the relation to each other and not to those in other classes.
- ‘You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity.’
- ‘We are almost ready to define an equivalence relation between hyperreal numbers.’
- ‘The ability to use this symmetrically is a part of the full equivalence relation.’
- ‘Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.’
- ‘In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups.’
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