Definition of equivalence relation in US English:

equivalence relation

noun

Mathematics Logic
  • A relation between elements of a set that is reflexive, symmetric, and transitive. It thus defines exclusive classes whose members bear the relation to each other and not to those in other classes (e.g., “having the same value of a measured property”).

    • ‘In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups.’
    • ‘Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.’
    • ‘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.’
    • ‘You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity.’