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 (8,902 words) - 05:57, 20 August 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...
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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...
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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...
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two arguments Binary operation, a mathematical operation that takes two arguments Binary relation, a relation involving two elements Binary-coded decimal...
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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...
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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...
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Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...
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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...
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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...
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mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...
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(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...
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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...
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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'...
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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) - 23:34, 13 August 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...
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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...
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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 ...
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different types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...
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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...
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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...
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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...
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term, as in binary code. For instance, 'hot' gains meaning because of its relation to 'cold,' and vice versa. It is not a contradictory relation but a structural...
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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...
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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...
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Total order (redirect from Total ordering relation)
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...
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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...
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a binary relation is formally defined as a set of pairs, i.e. a subset of the Cartesian product A × B of some sets A and B, so a ternary relation is...
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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...
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equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is...
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