Isomorphism vs Homogeneous - What's the difference?
isomorphism | homogeneous |
Similarity of form
* 1984 Brigitte Asbach-Schnitker, "Introduction", Mercury or The Secret and Swift Messenger , ISBN 9027232768.
(biology) the similarity in form of organisms of different ancestry
: (chemistry) the similarity in the crystal structures of similar chemical compounds
:* 1874 C. Rammelsberg,
: (sociology) the similarity in the structure or processes of different organizations
: 2. A one-to-one correspondence
: (group algebra) A bijection f'' such that both ''f'' and its inverse ''f −1 are homomorphisms, that is, structure-preserving mappings.
: (computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets
: (category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).
Of the same kind; alike, similar.
Having the same composition throughout; of uniform make-up.
* 1946 , (Bertrand Russell), History of Western Philosophy , I.25:
(chemistry) in the same state of matter.
(mathematics) Of which the properties of a smaller set apply to the whole; scalable.
(proscribed)
As a noun isomorphism
is similarity of form.As an adjective homogeneous is
of the same kind; alike, similar.isomorphism
English
Noun
(en noun)- The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.
"Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides", The Chemical News and Journal of Physical Science , page 197.
- The isomorphism' of compounds does not prove the ' isomorphism of their respective constituents.
Abbreviations
* (in category theory) isoSee also
* ("isomorphism" on Wikipedia)homogeneous
English
Alternative forms
* (proscribed)Adjective
(-)- Their citizens were not of homogeneous origin, but were from all parts of Greece.
- The function ''f(x,y)=x2+y2'' is homogeneous of degree 2 because ''f(''?''x,''?''y)=''?''2f(x,y)''.
