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An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself. A reflexive relation is said to have the reflexive property or is said to possess reflexivity. Along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.
A relation is called reflexive if it relates every element of to itself. For example, if X {\displaystyle X} is a set of distinct numbers and x R y {\displaystyle xRy} means " x {\displaystyle x} is less than y {\displaystyle y} ", then the reflexive closure of R {\displaystyle R} is the relation " x {\displaystyle x} is less than or equal to y ...
In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...
In logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the Law of identity), and the substitution property. From those, one can derive the rest of the properties usually needed for equality.
In mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies the following for all a , b {\displaystyle a,b} and c {\displaystyle c} in X {\displaystyle X} :
A reflexive, weak, [1] or non-strict partial order, [2] commonly referred to simply as a partial order, is a homogeneous relation ≤ on a set that is reflexive, antisymmetric, and transitive. That is, for all a , b , c ∈ P , {\displaystyle a,b,c\in P,} it must satisfy:
Reflexive relation, a relation where elements of a set are self-related; Reflexive user interface, an interface that permits its own command verbs and sometimes underlying code to be edited; Reflexive operator algebra, an operator algebra that has enough invariant subspaces to characterize it; Reflexive space, a subset of Banach spaces
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.