Noun
equivalence class (plural equivalence classes)
(set theory) Any one of the subsets into which an equivalence relation partitions a set, each of these subsets containing all the elements of the set that are equivalent under the equivalence relation.
A cardinal is defined to be an equivalence class of similar classes (as opposed to ZFC, where a cardinal is a special sort of von Neumann ordinal). Source: Internet
A comparison y ≤ c between a form y and a surreal number c is performed by choosing a form z from the equivalence class c and evaluating y ≤ z; and likewise for c ≤ x and for comparison b ≤ c between two surreal numbers. Source: Internet
All elements of X equivalent to each other are also elements of the same equivalence class. Source: Internet
Consider the embedding D → P(D) by z → U(z,1) where U(z,1) is the equivalence class of (z,1). Source: Internet
Equivalence classes of numeric forms The numeric forms are placed in equivalence classes; each such equivalence class is a surreal number. Source: Internet
Every equivalence class has a unique member that is of the form (n,0) or (0,n) (or both at once). Source: Internet