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Isomorphic vs Homogeneous - What's the difference?

isomorphic | homogeneous |

In mathematics|lang=en terms the difference between isomorphic and homogeneous

is that isomorphic is (mathematics) related by an isomorphism; having a structure-preserving one-to-one correspondence while homogeneous is (mathematics) of which the properties of a smaller set apply to the whole; scalable.

As adjectives the difference between isomorphic and homogeneous

is that isomorphic is (mathematics) related by an isomorphism; having a structure-preserving one-to-one correspondence while homogeneous is of the same kind; alike, similar.

isomorphic

English

Adjective

(-)
  • (mathematics) Related by an isomorphism; having a structure-preserving one-to-one correspondence.
  • * 2003 , Bernd Siegfried Walter Schröder, page 254
    • Let A, B be the ordered sets in Figure 10.3. Let C be the direct product of infinitely many copies of the two element chain'' 2'''. ''Then AC is '''isomorphic to BC, but A is not isomorphic to B .
  • (biology) Having a similar structure or function to something that is not related genetically or through evolution.
  • * 1993 , Marcus Jacobson, Foundations of Neuroscience , page 106
    • The fact that different structures can be shown to be functionally isomorphic implies that they are analogous, not homologous.
  • Having identical relevant structure; being structure-preserving while undergoing certain invertible transformations.
  • * 1981 , John Lyons, Language and Linguistics: An Introduction , page 60
    • For example, in so far as written and spoken English are isomorphic (i.e. have the same structure), they are the same language: there is nothing but their structure that they have in common.

    Usage notes

    * (en-usage-equal)

    Derived terms

    * * isomorphically

    Related terms

    * isomorph * isomorphism * isomorphous

    Antonyms

    * *

    Coordinate terms

    * anisomorphic * heteromorphic * homomorphic

    External links

    * (isomorphic keyboard)

    homogeneous

    English

    Alternative forms

    * (proscribed)

    Adjective

    (-)
  • Of the same kind; alike, similar.
  • 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.
  • (chemistry) in the same state of matter.
  • (mathematics) Of which the properties of a smaller set apply to the whole; scalable.
    • The function ''f(x,y)=x2+y2'' is homogeneous of degree 2 because ''f(''?''x,''?''y)=''?''2f(x,y)''.
  • (proscribed)

    • Antonyms

    * heterogeneous

    Related terms

    * homogeneity * homogenise, homogenize

    Derived terms

    * homogeneous mixture * homogeneous broadening * homogeneous catalysis * homogeneous coordinate * homogeneous function * homogeneous ideal * homogeneous number * homogeneous polynomial * homogeneous radiation * homogeneous society * homogeneous space * homogeneous system

    External links

    * * * English words prefixed with homo-