irreducible adj : incapable of being made smaller or simpler; "an irreducible minimum"; "an irreducible formula"; "an irreducible hernia" [ant: reducible]
- Not able to be reduced or lessened.
- Not able to be brought to a simpler or reduced form.
- Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
- mathematics of an integer Unable to be factored into smaller integers; prime.
- Not containing a sphere of codimension 1 that is not the boundary of a ball.
- impossible to divide further into representations of lower dimension by means of any similarity transformation
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.
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