What context can I use each word in?
Learn when and how to use these words with these examples!
isomorphism
Example
The isomorphism between the two groups shows that they are structurally identical. [isomorphism: noun]
Example
The theorem states that any two finite-dimensional vector spaces over the same field are isomorphic. [isomorphic: adjective]
homomorphism
Example
The homomorphism between the two rings preserves the addition and multiplication operations. [homomorphism: noun]
Example
The group homomorphism maps the elements of one group to another while preserving the group structure. [homomorphic: adjective]
Good things to know
Which word is more common?
Homomorphism is more commonly used than isomorphism in everyday mathematical language. Homomorphism is a more general term that applies to a wider range of structures, while isomorphism is a more specific term used to show that two structures are identical.
Whatโs the difference in the tone of formality between isomorphism and homomorphism?
Both isomorphism and homomorphism are formal terms used in advanced mathematics. They are not commonly used in everyday language and are typically only used in academic or technical contexts.
