# 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

## English

### Pronunciation

- /ˌɪrɪˈdjuːsɪbəl/

### Adjective

- 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

#### Antonyms

- sense all senses reducible

#### 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

a certain, an, any, any one, atomic, austere, bare, basic, called for, chaste, deep-seated, either, elementary, esoteric, essential, exclusive, fundamental, homely, homespun, homogeneous, immanent, implanted, implicit, inalienable, indicated, indispensable, individual, indivisible, indwelling, inextricable, infixed, ingrained, inherent, inner, integral, internal, intrinsic, inward, inwrought, irreductible, irreplaceable, lone, mere, monadic, monistic, monolithic, necessary, needed, needful, of a piece, one, plain, prerequisite, primal, primary, private, pure, pure and simple, required, requisite, resident, secret, severe, simon-pure, simple, single, singular, sole, solid, solitary, spare, stark, subjective, unadorned, unalienable, unanalyzable, unchallengeable,
uncluttered,
undifferenced,
undifferentiated,
undivided, unforgoable, uniform, unique, unitary, unquestionable, unsolvable, vital, wanted, whole