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...

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

In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set (possibly the same) called the...

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

{\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...

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...

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

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...

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...

In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty subset...

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...

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

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

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...

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...

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

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

{5}}.\end{aligned}}} The congruence relation satisfies all the conditions of an equivalence relation: Reflexivity: a ≡ a (mod m) Symmetry: a ≡ b (mod...

characteristics of an equivalence relation: reflexivity, symmetry, and transitivity. Therefore, order isomorphism is an equivalence relation. The class of partially...

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

(1961). Reflexivity presents a problem for science because if a prediction can lead to changes in the system that the prediction is made in relation to, it...

relation is called the arity, adicity or degree of the relation. A relation with n "places" is variously called an n-ary relation, an n-adic relation...

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...

connected relation is symmetric, it is the universal relation. A relation is strongly connected if, and only if, it is connected and reflexive. A connected...

characteristic properties of an equivalence relation (reflexivity, symmetry, and transitivity): Reflexivity Given a set A, the identity function on A is...

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

R)\to X(T)\times X(T)} is an equivalence relation; that is, a reflexive, symmetric and transitive relation. The basic case in practice is when C is the...