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antisymmetric

反对称的

The Free On-line Dictionary of Computing (foldoc)

A {relation} R is antisymmetric if,

for all x and y, x R y and y R x => x == y.

I.e. no two different elements are mutually related.

{Partial orders} and {total orders} are antisymmetric. If R
is also {symmetric}, i.e.

x R y => y R x

then

x R y => x == y

I.e. different elements are not related.

(1995-04-18)

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英文字典中文字典相关资料:

Antisymmetric relation - Wikipedia
In mathematics, a binary relation on a set is antisymmetric if there is no pair of distinct elements of each of which is related by to the other
Antisymmetric Relation Definition - BYJUS
In discrete Maths, a relation is said to be antisymmetric relation for a binary relation R on a set A, if there is no pair of distinct or dissimilar elements of A, each of which is related by R to the other
Antisymmetric Relation - GeeksforGeeks
The properties of antisymmetric relations are listed below: Empty relation on any set is always antisymmetric A relation can be symmetric and antisymmetric at same time If R is an antisymmetric relation, then R-1 is also antisymmetric It R 1 and R 2 are two antisymmetric relations, then R 1 ∩ R 2 is also antisymmetric
ANTISYMMETRIC Definition Meaning - Merriam-Webster
The meaning of ANTISYMMETRIC is relating to or being a relation (such as 'is a subset of') that implies equality of any two quantities for which it holds in both directions How to use antisymmetric in a sentence
Antisymmetric Relations - Mathematics Stack Exchange
Regarding your question, if $(a,b)\in R$ and $(b,a)\in R$ together imply $a=b$, and either one (or both) of $(a,b)\in R$ or $(b,a)\in R$ is false, then the entire statement is true: R is antisymmetric The definition of antisymmetry does not state if $(a,b) \in R$ then $(b,a) \in R$ (that would be the definition of symmetry)
Antisymmetric relation - Cuemath
A relation R on a set A is said to be antisymmetric if there does not exist any pair of distinct elements of A which are related to each other by R Mathematically, it is denoted as: For all a, b $ \in $ A,
Antisymmetric Relation Definition, Condition, Graph Examples
What is Antisymmetric Relation? Antisymmetric relation is one type of relation that can be defined when a set has no ordered pairs having dissimilar elements i e , all the ordered pairs must have the same elements
antisymmetric
Definition: A binary relation R for which a R b and b R a implies a = b See alsosymmetric, irreflexive, partial order Note: The relation "less than or equal to" is antisymmetric: if a ≤ b and b ≤ a, then a=b
Check Anti-Symmetric Relation on a Set - GeeksforGeeks
What is an Anti-Symmetric Relation? A relation R on a set A is called anti-symmetric relation if where R is a subset of (A x A), i e the cartesian product of set A with itself

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