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...
12 KB (1,598 words) - 18:48, 12 June 2025
mathematics, an equivalence relation is a binary relation that is reflexive, symmetric, and transitive. The equipollence relation between line segments in...
31 KB (4,473 words) - 10:22, 23 May 2025
Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...
3 KB (311 words) - 08:18, 13 March 2025
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...
62 KB (8,757 words) - 16:57, 9 July 2025
partial order is a relation that is reflexive, antisymmetric, and transitive, an equivalence relation is a relation that is reflexive, symmetric, and transitive...
36 KB (3,768 words) - 22:49, 30 June 2025
{\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...
4 KB (589 words) - 23:03, 2 April 2025
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...
26 KB (2,184 words) - 02:05, 11 May 2025
Closure (mathematics) (redirect from P closure (binary relation))
closure of R {\displaystyle R} on A {\displaystyle A} as the smallest reflexive relation on A {\displaystyle A} that contains R {\displaystyle R} . Symmetry...
13 KB (1,837 words) - 06:17, 16 May 2025
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...
18 KB (2,155 words) - 07:13, 6 July 2025
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...
7 KB (1,183 words) - 14:24, 9 July 2025
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...
10 KB (1,378 words) - 01:20, 18 April 2025
R = RT. Symmetry, along with reflexivity and transitivity, are the three defining properties of an equivalence relation. "is equal to" (equality) (whereas...
4 KB (385 words) - 06:02, 19 August 2024
with a reflexive relationship with its self-identical antecedent Reflexive verb, where a semantic agent and patient are the same Reflexive relation, a relation...
1 KB (212 words) - 23:35, 16 May 2025
Partially ordered set (redirect from Partial ordering relation)
comparable. Formally, a partial order is a homogeneous binary relation that is reflexive, antisymmetric, and transitive. A partially ordered set (poset...
40 KB (5,351 words) - 15:10, 28 June 2025
In grammar, reflexivity is a property of syntactic constructs whereby two arguments (actual or implicit) of an action or relation expressed by a single...
737 bytes (81 words) - 02:38, 11 April 2025
Total order (redirect from Total ordering relation)
corresponding total preorder on that subset. A binary relation that is antisymmetric, transitive, and reflexive (but not necessarily total) is a partial order...
22 KB (3,100 words) - 10:51, 4 June 2025
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...
23 KB (3,386 words) - 02:29, 27 June 2025
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...
2 KB (326 words) - 13:14, 4 May 2025
algebra and lattice theory, a tolerance relation on an algebraic structure is a reflexive symmetric relation that is compatible with all operations of...
14 KB (2,119 words) - 20:14, 28 January 2025
types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...
802 bytes (152 words) - 19:28, 10 August 2021
{5}}.\end{aligned}}} The congruence relation satisfies all the conditions of an equivalence relation: Reflexivity: a ≡ a (mod m) Symmetry: a ≡ b (mod...
29 KB (3,646 words) - 13:08, 26 June 2025
characteristics of an equivalence relation: reflexivity, symmetry, and transitivity. Therefore, order isomorphism is an equivalence relation. The class of partially...
8 KB (1,061 words) - 17:31, 22 December 2024
Equality (mathematics) (redirect from Equality relation)
X} as a binary relation ∼ {\displaystyle \sim } that satisfies the three properties: reflexivity, symmetry, and transitivity. Reflexivity means that every...
68 KB (7,795 words) - 17:53, 4 July 2025
(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...
40 KB (4,989 words) - 07:59, 9 July 2025
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...
18 KB (1,905 words) - 13:30, 9 January 2025
Subset (redirect from Inclusion 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...
11 KB (1,734 words) - 18:05, 12 March 2025
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...
11 KB (1,425 words) - 00:35, 24 March 2025
characteristic properties of an equivalence relation (reflexivity, symmetry, and transitivity): Reflexivity Given a set A, the identity function on A is...
14 KB (1,822 words) - 19:23, 26 May 2025
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector...
12 KB (1,749 words) - 04:42, 9 December 2024
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...
2 KB (353 words) - 18:48, 28 November 2023