Definition of equivalence relation in English:

equivalence relation


Mathematics Logic
  • 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.

    • ‘We are almost ready to define an equivalence relation between hyperreal numbers.’
    • ‘In The classification of prime-power groups Hall introduces an equivalence relation called isoclinism to aid the classification of prime power groups.’
    • ‘You can't have a classification without an equivalence relation, and one of the three defining properties of an equivalence relation is transitivity.’
    • ‘Thus, by imposing an adequate equivalence relation on proofs, any deductive system can be turned into a category.’
    • ‘The ability to use this symmetrically is a part of the full equivalence relation.’