notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S {\displaystyle S} into equivalence classes. These equivalence...

{\displaystyle a=c} (transitive). Each equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given...

Equivalence partitioning or equivalence class partitioning (ECP) is a software testing technique that divides the input data of a software unit into partitions...

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...

A forwarding equivalence class (FEC) is a term used in Multiprotocol Label Switching (MPLS) to describe a set of packets with similar or identical characteristics...

Enharmonic equivalence In music theory, equivalence class is an equality (=) or equivalence between properties of sets (unordered) or twelve-tone rows...

(mathematics) Equivalence relation Equivalence class Equivalence of categories, in category theory Equivalent infinitesimal Identity Matrix equivalence in linear...

intended to be defined as an isomorphism class of well-ordered sets: that is, as an equivalence class for the equivalence relation of "being order-isomorphic"...

states. Fiber-homotopy equivalence (relative version of a homotopy equivalence) Homeotopy Homotopy type theory Mapping class group Poincaré conjecture...

shown that this is an equivalence relation. The equivalence classes are called the ideal classes of R {\displaystyle R} . Ideal classes can be multiplied:...

If x is a pitch class, the inversion with index number n is written In = n - x mod 12. "For a relation in set S to be an equivalence relation [in algebra]...

write x ≡ y for "x and y are topologically indistinguishable". The equivalence class of x will be denoted by [x]. By definition, any two distinct points...

independent of the choice of representatives of the equivalence classes. Every equivalence class has a unique member that is of the form (n,0) or (0,n)...

Unicode equivalence is the specification by the Unicode character encoding standard that some sequences of code points represent essentially the same...

1-forms yield linearly equivalent divisors. Any divisor in this linear equivalence class is called the canonical divisor of X, KX. The genus g of X can be...

called "equal up to an equivalence relation R" if a and b are related by R, that is, if aRb holds, that is, if the equivalence classes of a and b with respect...

sheaves. Let X be a set and consider some equivalence relation on it. Let Q be the set of all equivalence classes in X. Then the map q : X → Q {\displaystyle...

{\displaystyle X} comprises a single class, and we wish to express this class (i.e., this subset) using the equivalence classes induced by attribute subset P...

numbers can be formally defined as equivalence classes of pairs of integers (p, q) with q ≠ 0, using the equivalence relation defined as follows: ( p 1...

called the conformal factor. An equivalence class of such metrics is known as a conformal metric or conformal class. Thus, a conformal metric may be...

identification of an element x of M' with the equivalence class of sequences in M converging to x (i.e., the equivalence class containing the sequence with constant...

partitioned into equivalence classes, called classes of quadratic forms. A class invariant can mean either a function defined on equivalence classes of forms...

v\leq u} is an equivalence relation on the monomorphisms with codomain A {\displaystyle A} , and the corresponding equivalence classes of these monomorphisms...

is a class function. This matrix transformation is clearly an equivalence relation, that is, all such equivalent matrices form an equivalence class. In...

the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures their shared...

all equivalence classes. Each equivalence class is considered as a single point, or, in other words, a point is defined as being an equivalence class. If...

"there are two isomorphism classes of non-Abelian groups of order 8". Referring to an equivalence class of an equivalence relation by x instead of [x]...

vectors in N {\displaystyle N} get mapped into the equivalence class of the zero vector. The equivalence class – or, in this case, the coset – of x {\displaystyle...

In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent...

group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor...