different between isomorphism vs homogeneous

English

Etymology

iso- +? -morphism

Pronunciation

Noun

isomorphism (plural isomorphisms)

1. Similarity of form
   • 1984 Brigitte Asbach-Schnitker, "Introduction", Mercury or The Secret and Swift Messenger, ?ISBN.

     The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.

   1. (biology) the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology.
   2. (chemistry) the similarity in the crystal structures of similar chemical compounds
      • 1874 C. Rammelsberg, "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.

   3. (sociology) the similarity in the structure or processes of different organizations
2. A one-to-one correspondence
   1. (group algebra) A bijection f such that both f and its inverse f ^?1 are homomorphisms, that is, structure-preserving mappings.
   2. (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
   3. (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).

Synonyms

• (in category theory): iso

Antonyms

• anisomorphism

Related terms

• isomorphic
• isomorphous

Translations

See also

• Isomorphism on Wikipedia.Wikipedia
• Isomorphism on Encyclopedia of Mathematics
• isomorphism on nLab
• Isomorphism on Wolfram MathWorld
• Graph Isomorphism on Wolfram MathWorld
• Natural Isomorphism on Wolfram MathWorld

English

Alternative forms

• homogenous (may be considered incorrect; see usage note at homogenous)

Etymology

From Medieval Latin homogeneus, from Ancient Greek ???????? (homogen?s, “of the same race, family or kind”), from ???? (homós, “same”) + ????? (génos, “kind”). Compare homo- (“same”) and -ous (adjectival suffix).

Pronunciation

• (UK) IPA^(key): /?h?.m?(?)?d?i?.n??s/, /?h??.m?(?)?d?i?.n??s/
• (US) IPA^(key): /?ho?.mo??d?i?.nj?s/, /?ho?.m??d?i?.nj?s/, /?ho?.mo??d??.nj?s/

Adjective

homogeneous (not comparable)

1. Of the same kind; alike, similar.
2. Having the same composition throughout; of uniform make-up.
   • 1946, Bertrand Russell, History of Western Philosophy, I.25:

     Their citizens were not of homogeneous origin, but were from all parts of Greece.

3. (chemistry) in the same state of matter.
4. (mathematics) Of which the properties of a smaller set apply to the whole; scalable.

   The function ${\displaystyle f(x,y)=x^{2}+y^{2}}$ is homogeneous of degree 2 because ${\displaystyle f(\alpha x,\alpha y)=\alpha ^{2}f(x,y)}$.

Antonyms

• heterogeneous

Derived terms

Related terms

• homogeneity
• homogenise, homogenize

Translations

Further reading

• homogeneous in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• homogeneous in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• homogeneous at OneLook Dictionary Search