Noun
equivalence relation (plural equivalence relations)
(set theory) A binary relation that is reflexive, symmetric and transitive.
Abstract Algebra, 3rd ed. John Wiley & Sons: 114, Prop. 2. In sum, given an equivalence relation ~ over A, there exists a transformation group G over A whose orbits are the equivalence classes of A under ~. Source: Internet
A finer equivalence relation, Solovay equivalence, can be used to characterize the halting probabilities among the left-c.e. reals. Source: Internet
A preorder that is symmetric is an equivalence relation; it can be thought of as having lost the direction markers on the edges of the graph. Source: Internet
As a corollary of the theorem, any two simply connected open subsets of the Riemann sphere which both lack at least two points of the sphere can be conformally mapped into each other (because conformal equivalence is an equivalence relation). Source: Internet
Explicitly, the Brauer group of the reals consists of two classes, represented by the reals and the quaternions, where the Brauer group is the set of all CSAs, up to equivalence relation of one CSA being a matrix ring over another. Source: Internet
Definition A given binary relation ~ on a set X is said to be an equivalence relation if and only if it is reflexive, symmetric and transitive. Source: Internet