ir·re·duc·i·ble

[ir-i-doo-suh-buhl, -dyoo-]
adjective
1.
not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum.
2.
incapable of being brought into a different condition or form.
3.
Mathematics.
a.
of or pertaining to a polynomial that cannot be factored.
b.
of or pertaining to a group that cannot be written as the direct product of two of its subgroups.

Origin:
1625–35; ir-2 + reducible

ir·re·duc·i·bil·i·ty, ir·re·duc·i·ble·ness, noun
ir·re·duc·i·bly, adverb
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2013.
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World English Dictionary
irreducible (ˌɪrɪˈdjuːsɪbəl) [Click for IPA pronunciation guide]
 
adj
1.  not able to be reduced or lessened
2.  not able to be brought to a simpler or reduced form
3.  maths
 a.  (of a polynomial) unable to be factorized into polynomials of lower degree, as (x² + 1)
 b.  (of a radical) incapable of being reduced to a rational expression, as √(x + 1)
 
irreduci'bility
 
n
 
irre'ducibleness
 
n
 
irre'ducibly
 
adv

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Medical Dictionary

irreducible ir·re·duc·i·ble (ĭr'ĭ-d&oomacr;'sə-bəl, -dy&oomacr;'-)
adj.

  1. Impossible to reduce to a desired, simpler, or smaller form or amount.

  2. Incapable of being made chemically simpler, or of being replaced, hydrogenated, or reduced in positive charge.


ir're·duc'i·bil'i·ty or ir're·duc'i·ble·ness n.
ir're·duc'i·bly adv.

The American Heritage® Stedman's Medical Dictionary
Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.
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Example sentences
The evidence from genetic science is overwhelmingly against the case for
  irreducible complexity.
Those cultures are irreducible to the regulatory environment or to economic
  behaviour.
Those cultures are irreducible to the regulatory environment or to economic
  behaviour.
Geology presents its irreducible beauty in raw appearances-and who would
  gainsay it.
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