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...

not yRx. A relation is asymmetric if and only if it is both antisymmetric and irreflexive. For example, > is an asymmetric relation, but ≥ is not. Again...

known about combinations of relation properties, such as "a transitive relation is irreflexive if, and only if, it is asymmetric". Of particular importance...

yRx} . A relation is asymmetric if and only if it is both antisymmetric and irreflexive. For example, > is an asymmetric relation, but ≥ {\displaystyle...

x\in X.} A relation is irreflexive if and only if its complement in X × X {\displaystyle X\times X} is reflexive. An asymmetric relation is necessarily...

asymmetric relation is characterized by a necessary absence of symmetry of the relation in the opposite direction. Inequalities exemplify asymmetric relations...

reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive. The divisibility relation on the natural numbers...

with at most 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...

relation cannot be both symmetric and asymmetric (where if a is related to b, then b cannot be related to a (in the same way)). However, a relation can...

{\overline {R}}} is asymmetric, where U {\displaystyle U} is the universal relation and R ⊤ {\displaystyle R^{\top }} is the converse relation of R . {\displaystyle...

cryptography Asymmetric digital subscriber line, Internet connectivity Asymmetric multiprocessing, in computer architecture Asymmetric relation, in set theory...

effect are of one and the same kind of entity, causality being an asymmetric relation between them. That is to say, it would make good sense grammatically...

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...

strict partial order is a homogeneous relation < on a set P {\displaystyle P} that is irreflexive, asymmetric and transitive; that is, it satisfies the...

ordering of relations by inclusion. If a relation is reflexive, irreflexive, symmetric, antisymmetric, asymmetric, transitive, connected, trichotomous, a...

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

direction 1.  The asymmetric relation between two adjacent vertices in a graph, represented as an arrow. 2.  The asymmetric relation between two vertices...

between each two vertices.) Equivalently, a tournament is a complete asymmetric relation. The name tournament comes from interpreting the graph as the outcome...

International relations theory has recognized that wars may be caused by asymmetric information and that "Most of the great wars of the modern era resulted...

never asymmetric. A preorder can be visualized as a directed graph, with elements of the set corresponding to vertices, and the order relation between...

conception revealed when our hemispheres return to their proper asymmetric relation. In addition to lecturing worldwide, McGilchrist has also been commissioned...

closed fields. Axiom 1 If x < y, then not y < x. [That is, "<" is an asymmetric relation. This implies that "<" is irreflexive, i.e., for all x, not x < x...

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...

is called monotone or order-preserving. Asymmetric relation. A homogeneous relation R on a set X is asymmetric, if x R y implies not y R x, for all elements...

with family rather than a stranger Power relations between parties (asymmetric relation) We are inclined to speak to our social equals differently than those...

entity or relation. DistMult: Since the embedding matrix of the relation is a diagonal matrix, the scoring function can not distinguish asymmetric facts....

be true: x<y, x=y, y<x. A relation is trichotomous if, and only if, it is asymmetric and connected. If a trichotomous relation is also transitive, then...

In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

{R} } , <): Axiom 1. If x < y, then not y < x. That is, "<" is an asymmetric relation. Axiom 2. If x < z, there exists a y such that x < y and y < z. In...

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 sets...