isomorphism Definition
- 1the quality or state of being isomorphic; correspondence in form, structure, or appearance.
- 2a one-to-one correspondence between the elements of two sets such that the result of an operation on elements of one set corresponds to the result of the analogous operation on their images in the other set.
Using isomorphism: Examples
Take a moment to familiarize yourself with how "isomorphism" can be used in various situations through the following examples!
Example
The isomorphism between the two languages made translation easy.
Example
The isomorphism between the two mathematical structures allowed for a simple proof.
Example
The isomorphism between the two companies' organizational structures was striking.
isomorphism Synonyms and Antonyms
Synonyms for isomorphism
Phrases with isomorphism
a type of isomorphism that occurs when two or more systems have the same underlying structure, despite differences in their surface features
Example
There is a structural isomorphism between the human brain and the neural network of a deep learning algorithm.
a theorem in mathematics that states that if two mathematical structures are isomorphic, then any property that can be expressed in terms of the structure is true for both structures
Example
The isomorphism theorem allowed us to prove that the two groups were equivalent.
a set of mathematical structures that are isomorphic to each other
Example
The isomorphism class of finite groups is well-studied in algebra.
Origins of isomorphism
from Greek 'isos', meaning 'equal', and 'morphē', meaning 'form'
Summary: isomorphism in Brief
Isomorphism [ahy-suh-mawr-fiz-uhm] refers to the correspondence in form, structure, or appearance between two sets. It is often used in mathematics to describe a one-to-one correspondence between the elements of two sets. For example, 'The isomorphism between the two languages made translation easy.' Isomorphism can also refer to structural isomorphism, isomorphism theorem, and isomorphism class.
