In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is reflexive if it relates every element of X {\displaystyle X} to itself...

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

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

identity relation. Left quasi-reflexive for all x, y ∈ X, if xRy then xRx. Right quasi-reflexive for all x, y ∈ X, if xRy then yRy. Quasi-reflexive for all...

{\displaystyle a} . An antisymmetric relation R {\displaystyle R} on a set X {\displaystyle X} may be reflexive (that is, a R a {\displaystyle aRa} for...

homogeneous relation over a set X {\displaystyle X} may be subjected to closure operations like: Reflexive closure the smallest reflexive relation over X {\displaystyle...

one element. A transitive relation is asymmetric if and only if it is irreflexive. A transitive relation need not be reflexive. When it is, it is called...

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

mathematics, the reflexive closure of a binary relation R {\displaystyle R} on a set X {\displaystyle X} is the smallest reflexive relation on X {\displaystyle...

} As every intersection of reflexive relations is reflexive, this defines a closure. The reflexive closure of a relation R is thus R ∪ { ( x , x ) ∣...

well-founded relation R on a class X that is extensional, there exists a class C such that (X, R) is isomorphic to (C, ∈). A relation R is said to be reflexive if...

Dually, each right Euclidean relation is right quasi-reflexive, and each right unique and right quasi-reflexive relation is right Euclidean. Fagin, Ronald...

Projection (set theory) Reflexive relation Relation algebra Relational algebra Relational model Relations (philosophy) Codd 1970 "Relation – Encyclopedia of...

is true of every set A that A ⊂ A . {\displaystyle A\subset A.} (a reflexive relation). Other authors prefer to use the symbols ⊂ {\displaystyle \subset...

antecedent Reflexive verb, where a semantic agent and patient are the same Reflexive relation, a relation where elements of a set are self-related Reflexive user...

as a fallback Reflexive pronoun – Anaphoric pronoun Reflexive relation – Binary relation that relates every element to itself Reflexive space – Locally...

associated reflexive relation is its reflexive closure, a (non-strict) partial order ≤ . {\displaystyle \,\leq .} The two associated reflexive relations...

symmetric and transitive. If the relation is also reflexive, then the relation is an equivalence relation. Formally, a relation R {\displaystyle R} on a set...

R = RT. Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas...

as a relation, equality is the archetype of the more general concept of an equivalence relation on a set: those binary relations that are reflexive, symmetric...

a reflexive relation. Binary relations that are both reflexive and Euclidean are equivalence relations. Thus, again implicitly assuming reflexivity, the...

(left-)total relation), then for all x , x R R T x {\displaystyle x,xRR^{\textsf {T}}x} so that R R T {\displaystyle RR^{\textsf {T}}} is a reflexive relation or...

comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset...

Quasi-reflexive may refer to: Quasi-reflexive relation Quasi-reflexive space This disambiguation page lists articles associated with the title Quasi-reflexive...

knowledge, reflexivity refers to circular relationships between cause and effect, especially as embedded in human belief structures. A reflexive relationship...

corresponding total preorder on that subset. A binary relation that is antisymmetric, transitive, and reflexive (but not necessarily total) is a partial order...

especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest that preorders...

a symmetric relation. According to Euclid's tenets, parallelism is not a reflexive relation and thus fails to be an equivalence relation. Nevertheless...

types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...

In grammar, reflexivity is a property of syntactic constructs whereby two arguments (actual or implicit) of an action or relation expressed by a single...