In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments...

partial equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that...

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

algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties...

In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...

areas of mathematics, a hyperfinite equivalence relation on a standard Borel space X is a Borel equivalence relation E with countable classes, that can...

to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, inequality and equality among real numbers...

a ternary equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric...

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

index number n is written In = n - x mod 12. "For a relation in set S to be an equivalence relation [in algebra], it has to satisfy three conditions: it...

preorder is an equivalence relation. Moreover, a preorder on a set X {\displaystyle X} can equivalently be defined as an equivalence relation on X {\displaystyle...

In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X × X (in the product topology)...

reflexivity is one of three properties defining equivalence relations. Let R {\displaystyle R} be a binary relation on a set X , {\displaystyle X,} which by...

reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas "is less than" is not symmetric)...

strict chain, is a relation that is irreflexive, antisymmetric, transitive and connected. A partial equivalence relation is a relation that is symmetric...

mathematics, given a category C, a quotient of an object X by an equivalence relation f : R → X × X {\displaystyle f:R\to X\times X} is a coequalizer for...

properties. A partial order is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric...

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...

formulation of thermodynamics. It makes the relation of thermal equilibrium between systems an equivalence relation, which can represent equality of some quantity...

transitive relation over X containing R, Equivalence closure the smallest equivalence relation over X containing R. In mathematics, a heterogeneous relation is...

The fundamental concept of ECP comes from equivalence class which in turn comes from equivalence relation. A software system is in effect a computable...

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 , q...

property this "incomparability relation" needs in order to be an equivalence relation. Define also an induced homogeneous relation ≲ {\displaystyle \,\lesssim...

g:A\rightarrow C} . Special cases include: Setoids: sets that come with an equivalence relation, G-sets: sets equipped with an action of a group G {\displaystyle...

In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle...

through e and g. Therefore, this is an equivalence relation, and it can be used to partition the edges into equivalence classes, subsets of edges with the...

Nida formulated the distinction originally in relation to Bible translations. The "Formal-equivalence" approach emphasizes fidelity to the lexical details...

mathematics, a setoid (X, ~) is a set (or type) X equipped with an equivalence relation ~. A setoid may also be called E-set, Bishop set, or extensional...

as described by the energy–momentum relation, were later developed by other physicists. Mass–energy equivalence states that all objects having mass,...

mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set...