Explore: Equivalence Classes (set Theory)

term "equivalence class" may generally be considered as a synonym of "set", although some equivalence classes are not sets but proper classes. For example

One branch of musical set theory deals with collections (sets and permutations) of pitches and pitch classes (pitch-class set theory), which may be ordered

(transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent

hand, can have proper classes as members. ZF set theory does not formalize the notion of classes, so each formula with classes must be reduced syntactically

relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped with an equivalence relation or a

In mathematical logic, descriptive set theory (DST) is the study of certain classes of "well-behaved" subsets of the real line and other Polish spaces

b=gag^{-1}.} This is an equivalence relation whose equivalence classes are called conjugacy classes. In other words, each conjugacy class is closed under b

Frege defined cardinal numbers as equivalence classes of sets under equinumerosity. However, Frege's approach to set theory was later shown to be flawed.

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in

larger than sets, such as the class of all sets and the class of all ordinals. Morse–Kelley set theory (MK) allows classes to be defined by formulas whose