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)...

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...

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

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

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

equivalence class contains a unique canonical representative element. The canonical representative is the unique pair (m, n) in the equivalence class...

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

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

{\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...

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

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

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...

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

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...

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...

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...

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]...

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...

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...

"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]...

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...

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...

ordered field. Other common definitions of real numbers include equivalence classes of Cauchy sequences (of rational numbers), Dedekind cuts, and infinite...