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

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

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

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

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

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...

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

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

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

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...

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

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)...

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...

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

symmetry and transitivity, reflexivity is one of three properties defining equivalence relations. The word reflexive is originally derived from the Medieval...

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...

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...

smallest transitive relation over X {\displaystyle X} containing R {\displaystyle R} , Equivalence closure the smallest equivalence relation over X {\displaystyle...

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

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

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...

therefore an equivalence relation. Similarly, each left Euclidean and reflexive relation is an equivalence. The range of a right Euclidean relation is always...

partition a set into disjoint equivalence classes. Conversely, every partition defines an equivalence class. The equivalence relation of equality is a special...

associated equivalence relation is defined by saying x ~ y if and only if there exists a g in G with g⋅x = y. The orbits are then the equivalence classes...

kernel of a function f {\displaystyle f} (or equivalence kernel) may be taken to be either the equivalence relation on the function's domain that roughly expresses...

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...

indeed this binary relation has some natural properties, like being an equivalence relation; while the combined ternary relation in general is not studied...

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

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...