a binary relation associates elements of one set called the domain with elements of another set called the codomain. Precisely, a binary relation over...
63 KB (8,832 words) - 17:38, 7 September 2024
In mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian...
22 KB (2,177 words) - 16:30, 29 September 2024
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...
10 KB (1,334 words) - 01:01, 10 September 2024
A symmetric relation is a type of binary relation. Formally, a binary relation R over a set X is symmetric if: ∀ a , b ∈ X ( a R b ⇔ b R a ) , {\displaystyle...
4 KB (385 words) - 06:02, 19 August 2024
In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates...
17 KB (2,092 words) - 16:24, 29 September 2024
In mathematics, a binary relation R {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle...
4 KB (589 words) - 16:30, 24 January 2024
two arguments Binary operation, a mathematical operation that takes two arguments Binary relation, a relation involving two elements Binary-coded decimal...
3 KB (358 words) - 04:54, 23 September 2024
Rx1⋯xn and using postfix notation by x1⋯xnR. In the case where R is a binary relation, those statements are also denoted using infix notation by x1Rx2. The...
18 KB (1,905 words) - 09:28, 29 September 2024
Closure (mathematics) (redirect from P closure (binary relation))
single element under ideal operations is called a principal ideal. A binary relation on a set A can be defined as a subset R of A × A , {\displaystyle A\times...
12 KB (1,786 words) - 22:36, 14 August 2024
mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...
30 KB (4,424 words) - 12:58, 8 September 2024
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...
6 KB (833 words) - 05:22, 21 February 2024
Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...
2 KB (301 words) - 18:04, 26 February 2024
(finitary relation, like "person x lives in town y at time z"), and relations between classes (like "is an element of" on the class of all sets, see Binary relation...
36 KB (3,758 words) - 05:39, 22 August 2024
a 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'...
13 KB (1,725 words) - 01:03, 3 June 2024
Continuous function (redirect from Continuous binary relation)
canonically identified with the quotient topology under the equivalence relation defined by f. Dually, for a function f from a set S to a topological space...
60 KB (9,404 words) - 10:25, 11 September 2024
Logical matrix (redirect from Binary matrix)
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a...
14 KB (1,939 words) - 03:02, 14 September 2024
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...
10 KB (1,382 words) - 11:23, 31 January 2024
different 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
Arity (redirect from K-ary relation)
arguments. Mathematics portal Philosophy portal Logic of relatives Binary relation Ternary relation Theory of relations Signature (logic) Parameter p-adic number...
13 KB (1,396 words) - 22:56, 22 August 2024
A\triangleleft R} of a binary relation R {\displaystyle R} between E {\displaystyle E} and F {\displaystyle F} may be defined as a relation having domain A ...
11 KB (1,924 words) - 04:32, 1 February 2024
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...
4 KB (608 words) - 15:30, 7 February 2024
Transitive closure (category Binary relations)
mathematics, the transitive closure R+ of a homogeneous binary relation R on a set X is the smallest relation on X that contains R and is transitive. For finite...
17 KB (2,306 words) - 12:10, 8 September 2024
case of a logical matrix representing a binary relation R, the transpose corresponds to the converse relation RT. The transpose of a matrix A, denoted...
20 KB (2,525 words) - 12:30, 8 May 2024
Preorder (category Properties of binary relations)
mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant to suggest...
23 KB (3,351 words) - 13:50, 21 July 2024
partial order without incomparable pairs Total relation, which may also mean connected relation (a binary relation in which any two elements are comparable)...
2 KB (255 words) - 10:02, 7 May 2024
axiomatization of a calculus of relations. Roughly, a relation algebra is to a system of binary relations on a set containing the empty (0), universal...
25 KB (2,546 words) - 13:46, 21 June 2024
Glossary of order theory (redirect from Acyclic relation)
0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Acyclic. A binary relation is acyclic if it contains no "cycles": equivalently, its transitive...
29 KB (4,210 words) - 23:05, 23 April 2023
equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is...
7 KB (1,164 words) - 07:53, 5 July 2024
single binary operation, satisfying certain axioms. If G {\displaystyle G} is a group with operation ∗ {\displaystyle \ast } , a congruence relation on G...
12 KB (1,702 words) - 04:49, 29 June 2024
Intransitivity (redirect from Intransitive relation)
nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger...
12 KB (1,592 words) - 19:22, 7 March 2024