irreducible

[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

irreducibility, irreducibleness, noun
irreducibly, adverb
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World English Dictionary
irreducible (ˌɪrɪˈdjuːsɪbəl)
 
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-dōō'sə-bəl, -dyōō'-)
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
It can produce a sensation of irreducible foreignness.
Creativity comes about whenever you have a collision of ideas, forcing mutually
  irreducible notions to coexist in the same space.
But there is an irreducible psychological dimension to both crises and
  recoveries.
Some phenomena have an irreducible complexity that will defeat any big-idea
  effort at simplification.
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