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...

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

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...

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...

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"...

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)...

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

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...

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...

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

by Carl Friedrich Gauss, a composition law was defined on certain equivalence classes of forms. This gave a finite abelian group, as was recognised at...

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]...

be an equivalence relation on X . {\displaystyle X.} The quotient set Y = X / ∼ {\displaystyle Y=X/{\sim }} is the set of equivalence classes of elements...

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...

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

matrix equivalence a generalization of row equivalence. The rank property yields an intuitive canonical form for matrices of the equivalence class of rank...

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...

{\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...

rational number.) So strictly speaking, the surreal numbers are equivalence classes of representations of the form { L | R } that designate the same...

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...

in the same equivalence class. There are three fundamental approaches to constructing measures of network similarity: structural equivalence, automorphic...

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...

X} , together with a partial order on the set of equivalence class. Like partial orders and equivalence relations, preorders (on a nonempty set) are never...

the equivalence class of the result depends only on the equivalences classes of the summands, and thus that this defines an addition of equivalence classes...

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...

the size of the ideal class group of a number ring Class number (binary quadratic forms), the number of equivalence classes of binary quadratic forms...