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...

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

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)...

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

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...

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...

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

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

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

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...

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

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...

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

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

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...

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

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...

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...

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

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

then given by |U| / |R| as a set of equivalence classes. Let Y be an algebraic space defined by an equivalence relation S ⊂ V × V. The set Hom(Y, X) of morphisms...

Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...

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

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...

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

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

apartness relation is an equivalence relation, as the above three conditions become reflexivity, symmetry, and transitivity. If this equivalence relation is...

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...