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...

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...

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...

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...

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...

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

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)...

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...

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"...

"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]...

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...

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...

exactly one subset. Every equivalence relation on a set defines a partition of this set, and every partition defines an equivalence relation. A set equipped...

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...

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

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...

given a symmetry class and a dimension of the Brillouin zone, what are all the equivalence classes of Hamiltonians. Each equivalence class can be labeled...

{\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...

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

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...

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...

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...

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...

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...

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]...

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