[ir-i-doo-suh-buh l, -dyoo-]


not reducible; incapable of being reduced or of being diminished or simplified further: the irreducible minimum.
incapable of being brought into a different condition or form.
  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.

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 Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

Related Words for irreducible

exclusive, clear, remaining, final, excluding, pure, undeductible

Examples from the Web for irreducible

Historical Examples of irreducible

British Dictionary definitions for irreducible



not able to be reduced or lessened
not able to be brought to a simpler or reduced form
  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)
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.

Online Etymology Dictionary, © 2010 Douglas Harper

irreducible in Medicine




Impossible to reduce to a desired, simpler, or smaller form or amount.
Incapable of being made chemically simpler, or of being replaced, hydrogenated, or reduced in positive charge.
Related formsir′re•duc′i•bili•ty′re•duci•bly adv.
The American Heritage® Stedman's Medical Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Company. Published by Houghton Mifflin Company.