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...on <math>X</math> that contains <math>R.</math> A relation is called {{em|reflexive}} if it relates every element of <math>X</math> to itself. ...>x R y</math> means "<math>x</math> is less than <math>y</math>", then the reflexive closure of <math>R</math> is the relation "<math>x</math> is less than or e ...

...(T)</math> is an [[equivalence relation]]; that is, a [[Reflexive relation|reflexive]], [[Symmetric relation|symmetric]] and [[Transitive relation|transitive]] [[Category:Binary relations]] ...

{{Short description|Math relation that is reflexive and symmetric}} ...erance relation''' on an [[algebraic structure]] is a [[reflexive relation|reflexive]] [[symmetric relation]] that is compatible with all operations of the stru ...

* {{annotated link|Reflexive closure}} [[Category:Binary relations]] ...

{{Short description|Mathematical result on order relations}} ...olds for all <math>x, y \in X.</math> A partial order is, by definition, a reflexive, transitive and antisymmetric relation. A total order is a partial order th ...

...aces are [[stereotype space|stereotype]] and are in the stereotype duality relations with [[Banach space]]s:{{sfn|Akbarov|2003|p=220}}{{sfn|Akbarov|2009|p=467}} ...key space]] if <math>X</math> is [[reflexive space#Reflexive Banach spaces|reflexive as a Banach space]]{{sfn|Akbarov|2003|loc=Example 4.8|p=221}}). ...

...he negation of the pseudo-order <math>x<y</math> of two elements defines a reflexive [[partial order]] <math>y\le x</math>. In these terms, the first condition * ''R'' is [[connex relation|connex]] iff it is [[reflexive relation|reflexive]].<ref group=note>unless the [[domain of a relation|domain]] is a [[singlet ...

=== Preference relations === ...better than B). In this case, the relation should be [[Reflexive relation|reflexive]], that is, <math>A\succeq A</math> always holds. ...

...binary) relations in mathematics|a more in-depth treatment|Binary relation|relations on any number of elements|Finitary relation}} ...mvar|x}} and {{mvar|y}} one often writes {{math|''xRy''}}. For most common relations in mathematics, special symbols are introduced, like "{{math|<}}" for ''"is ...

...ath> is a [[quasi-ordering]] (i.e., a [[preorder]] or [[reflexive relation|reflexive]], [[transitive relation|transitive]] [[binary relation]]) such that any in ...he definition of a WSTS itself says nothing about the computability of the relations <math>\le</math>, <math>\to</math>. ...

...''</sub> if and only if the product ''ef'' exists in ''E''. The following relations can be defined in ''E'': ...atement]] about ''E'' involving the partial binary operation and the above relations in ''E'', one can define the left-right [[Dual (mathematics)|dual]] of ''T' ...

{{stack|{{Binary relations}}}} ...erial relation|serial]], which is also called total. Similarly, connected relations are sometimes called {{em|{{visible anchor|complete|Complete relation}}}},< ...

...ay be empty, expressing the relation is not generally [[reflexive relation|reflexive]]. Arrows amount to equivalence classes of functional relations appropriately respecting the defined equalities. ...

...lation]] <math>R</math> over the individuals of the lowest type, that is [[Reflexive relation|irreflexive]], [[transitive relation|transitive]], and strongly co ...s [[Infinity|infinite]], thus forcing the existence of an infinite set. If relations are defined in terms of [[ordered pair]]s, this axiom requires a prior defi ...

...some authors define the reduction relation → as the indexed union of some relations; for instance if <math>{\rightarrow_1 \cup \rightarrow_2} = {\rightarrow}</ * <math>\stackrel{*}{\rightarrow}</math> is the [[reflexive transitive closure]] of <math>\rightarrow</math>, i.e. the [[transitive clo ...

...g this relation (because <math>\asymp</math> is built out of the symmetric relations <math>\Leftrightarrow</math> {{nowrap|and <math>\parallel</math>),}} and <m ...ces {{nowrap|in <math>X</math>.}} However, there cannot exist reachability relations in both directions between these two components. Therefore, we can define a ...

=== Relations between the interpolation methods === ...h|''X''₀}} and {{math|''X''₁}} are [[Reflexive space|reflexive]], then the dual of the complex interpolation space is obtained by interpol ...

{{term|reflexive}} {{defn|The relative product of two relations is their composition}} ...

...lds related to [[Spatial analysis|computer spatial analysis]]. The spatial relations expressed by the model are invariant to [[Rotation (mathematics)|rotation]] ...classification schemes''. The English language contains about 10 schemes (relations), such as "intersects", "touches" and "equals". When testing two geometries ...

...ned in this way meets the three requirements of a partial order that it be reflexive, antisymmetric, and transitive. ===Quasitransitive relations=== ...