Antisymmetric is a term that is commonly used in mathematics, physics, and other scientific fields. It is a concept that helps to describe the properties of various objects and systems. In this article, we will explore the definition and meaning of antisymmetric, its origin, synonyms, and antonyms, as well as its associations and usage in different contexts.
Definitions
Antisymmetric is a term that is used to describe a relation between two objects or elements. It is a property that states that if two objects are related in a certain way, then the reverse relation is not possible. In other words, if A is related to B, then B cannot be related to A in the same way.
In mathematics, antisymmetric is often used to describe a relation between two sets. For example, if set A is a subset of set B, then set B cannot be a subset of set A. This is because the relation of subset is antisymmetric.
In physics, antisymmetric is used to describe the properties of certain physical systems. For example, the wave function of a system of identical particles must be antisymmetric in order to satisfy the Pauli exclusion principle.
Origin
The term antisymmetric has its roots in the Greek language. The prefix “anti-” means “opposite” or “against,” while “symmetric” refers to a property of objects that have the same shape or arrangement on both sides. The term was first used in mathematics in the early 20th century.
Meaning in different dictionaries
According to the Merriam-Webster dictionary, antisymmetric means “having a relationship in which if one element is related to a second element, the second element is not related in the same way to the first element.”
The Oxford English Dictionary defines antisymmetric as “having a property such that if one element is related to another in a certain way, then the reverse relation is not possible.”
Associations
Antisymmetric is often associated with the concept of symmetry. It is a property that describes the absence of symmetry in a relation or system. Antisymmetric relations are also often associated with partial orders, which are a type of mathematical structure that describes a relation between elements of a set.
Synonyms
Some synonyms of antisymmetric include:
- Asymmetric.
- Non-symmetric.
- Unsymmetric.
- Non-reciprocal.
Antonyms
Some antonyms of antisymmetric include:
- Symmetric.
- Reciprocal.
- Bi-directional.
- Mutual.
The same root words
Some words that share the same root as antisymmetric include:
- Symmetry.
- Asymmetry.
- Symphonic.
Example Sentences
Here are some example sentences that use the term antisymmetric:
- The relation of “less than or equal to” is antisymmetric, meaning that if a is less than or equal to b, and b is less than or equal to a, then a must be equal to b.
- The wave function of a system of identical fermions must be antisymmetric in order to satisfy the Pauli exclusion principle.
- The relationship between a parent and child is not antisymmetric, as a parent is always related to their child, but a child is not necessarily related to their parent in the same way.
- The relation of “is a factor of” is not antisymmetric, as if a is a factor of b, then b is not necessarily a factor of a.