AskDefine | Define irreducible

Dictionary Definition

irreducible adj : incapable of being made smaller or simpler; "an irreducible minimum"; "an irreducible formula"; "an irreducible hernia" [ant: reducible]

User Contributed Dictionary



  • /ˌɪrɪˈdjuːsɪbəl/


  1. Not able to be reduced or lessened.
  2. Not able to be brought to a simpler or reduced form.
  3. Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
  4. mathematics of an integer Unable to be factored into smaller integers; prime.
  5. Not containing a sphere of codimension 1 that is not the boundary of a ball.
  6. impossible to divide further into representations of lower dimension by means of any similarity transformation


Derived terms

Extensive Definition

Irreducible may be used to refer to many different things.
  • In mathematics, the term "irreducible" is used in many different, unrelated fields; its use often follows from the denotative meaning of the word "irreducible".
  • irreducible (philosophy)
  • Irreducible complexity is an argument about certain biological systems that are too complex to have evolved from simpler predecessors.
  • In inorganic chemistry, an irreducible representation is the basic representation of a symmetry operation in a given point group.

Synonyms, Antonyms and Related Words

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