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...

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

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

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

closure of R {\displaystyle R} on A {\displaystyle A} as the smallest reflexive relation on A {\displaystyle A} that contains R {\displaystyle R} . Symmetry...

example of a both reflexive and coreflexive relation, and any coreflexive relation is a subset of the identity relation. Left quasi-reflexive for all x, y...

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...

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

{\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...

reflexive as well as transitive, another preorder, R = { (1,2), (2,3), (1,3) } is transitive, but not reflexive. As a counter example, the relation <...

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...

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

with a reflexive relationship with its self-identical antecedent Reflexive verb, where a semantic agent and patient are the same Reflexive relation, a relation...

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...

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...

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

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...

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...

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

≤ {\displaystyle \leq } on X {\displaystyle X} (a transitive and reflexive relation on X {\displaystyle X} ) that is strongly connected (meaning that...

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

complement is. Similarly, a relation is quasitransitive if, and only if, its converse is. Intransitivity Reflexive relation Robert Duncan Luce (Apr 1956)...

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

algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of...

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...

X} as a binary relation ∼ {\displaystyle \sim } that satisfies the three properties: reflexivity, symmetry, and transitivity. Reflexivity means that every...

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

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