a binary relation associates elements of one set called the domain with elements of another set called the codomain. Precisely, a binary relation over...

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...

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...

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...

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...

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...

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...

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...

two arguments Binary operation, a mathematical operation that takes two arguments Binary relation, a relation involving two elements Binary-coded decimal...

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...

mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in...

Binary relation (or diadic relation – a more in-depth treatment of binary relations) Equivalence relation Homogeneous relation Reflexive relation Serial...

(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...

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...

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...

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'...

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...

different types of binary relation. One specific variation of weak ordering, a total preorder (= a connected, reflexive and transitive relation), is also sometimes...

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...

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 ...

arguments. Mathematics portal Philosophy portal Logic of relatives Binary relation Ternary relation Theory of relations Signature (logic) Parameter p-adic number...

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...

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...

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...

partial order without incomparable pairs Total relation, which may also mean connected relation (a binary relation in which any two elements are comparable)...

equivalence relation (often abbreviated as PER, in older literature also called restricted equivalence relation) is a homogeneous binary relation that is...

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...

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...

nontransitivity) is a property of binary relations that are not transitive relations. This may include any relation that is not transitive, or the stronger...

single binary operation, satisfying certain axioms. If G {\displaystyle G} is a group with operation ∗ {\displaystyle \ast } , a congruence relation on G...