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...

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

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...

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

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

coreflexive relation. The equality relation is the only example of a both reflexive and coreflexive relation, and any coreflexive relation is a subset...

{\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...

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

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

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...

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

binary relation associates elements of one set called the domain with elements of another set called the codomain. Precisely, a binary relation over sets...

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...

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

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...

itself can be formally said to be a "reflexive relation". Just not as relation within ZFC, but as a "meta-relation", within some of metatheory in mathematics...

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

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

In mathematics, an asymmetric relation is a binary relation R {\displaystyle R} on a set X {\displaystyle X} where for all a , b ∈ X , {\displaystyle...

binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of the relation 'child of'...

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...

equivalence relation is a kind of ternary relation analogous to a binary equivalence relation. A ternary equivalence relation is symmetric, reflexive, and transitive...

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

(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 of an antichain is just the identity relation. Approximates relation. See way-below relation. Antisymmetric relation. A homogeneous relation...

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

In mathematics, a binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with...

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...