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

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...

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

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

single element under ideal operations is called a principal ideal. A binary relation R {\displaystyle R} on a set A {\displaystyle A} is a subset of A ×...

(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...

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, an asymmetric relation is a binary relation R {\displaystyle R} on a set X {\displaystyle X} where for all a , b ∈ X , {\displaystyle...

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...

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...

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 {\displaystyle R} on a set X {\displaystyle X} is antisymmetric if there is no pair of distinct elements of X {\displaystyle...

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...

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...

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 ⊆ 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...

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...

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

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...

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...

establishes a relation between the elements of the domain and some (possibly all) elements of the codomain. Mathematically, a binary relation between two...

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...

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 ...

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...

A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols...

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...

Cartesian product of two sets is called a binary relation or correspondence; thus, a correspondence here is a relation that is defined by algebraic equations...

A congruence relation is a tolerance relation that also forms a set partition. Let ∼ {\displaystyle \sim } be a tolerance binary relation on an algebraic...

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

elements and an interpretation of the ∈ {\displaystyle \in } relation as a binary relation on these elements. A {\displaystyle {\mathcal {A}}} is called...