• synonyms


[ir-i-doo-suh-buh l, -dyoo-]
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  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.
    1. of or relating to a polynomial that cannot be factored.
    2. of or relating to a group that cannot be written as the direct product of two of its subgroups.
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Origin of irreducible

First recorded in 1625–35; ir-2 + reducible
Related formsir·re·duc·i·bil·i·ty, ir·re·duc·i·ble·ness, nounir·re·duc·i·bly, adverb
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

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Examples from the Web for irreducible

Historical Examples

  • The one-third of the French law seemed to be the irreducible minimum.

    Notes on Life and Letters

    Joseph Conrad

  • For all that, we trust that the irreducible minimum has now been reached.

  • We know that this form of association is not primary and irreducible.

  • The art of building bungalows is reduced in California to the irreducible.

  • It is an irreducible minimum in connection with the Reward System.

British Dictionary definitions for irreducible


  1. not able to be reduced or lessened
  2. not able to be brought to a simpler or reduced form
  3. maths
    1. (of a polynomial) unable to be factorized into polynomials of lower degree, as (x ² + 1)
    2. (of a radical) incapable of being reduced to a rational expression, as √(x + 1)
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Derived Formsirreducibility or irreducibleness, nounirreducibly, adverb
Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Word Origin and History for irreducible


1530s, from assimilated form of in- (1) "not, opposite of" + reducible. Related: Irreducibly; irreducibility.

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Online Etymology Dictionary, © 2010 Douglas Harper

irreducible in Medicine


  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.
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Related formsir′re•duc′i•bili•ty n.ir′re•duci•bly adv.
The American Heritage® Stedman's Medical Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.