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# irreducible

[ir-i-doo-suh-buh l, -dyoo-] /ˌɪr ɪˈdu sə bəl, -ˈdyu-/
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.
Origin of irreducible
1625-1635
First recorded in 1625-35; ir-2 + reducible
Related forms
irreducibility, irreducibleness, noun
Dictionary.com Unabridged
Based on the Random House 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.

• 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.

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

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

Henry Atkinson
• This much at least the after history demands as the irreducible minimum.

W. E. Orchard
• But it would have confined it to its essential and irreducible minimum.

Walter Lyon Blease
• The borderland of the unknown or the irreducible is its realm.

George Edward Woodberry
• Or are they irreducible events, and units of mechanism by themselves?

George Santayana
• For from what source could an irreducible relativity be produced in it?

Edouard le Roy
British Dictionary definitions for irreducible

## irreducible

/ˌɪrɪˈdjuːsɪbəl/
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 (x² + 1)
2. (of a radical) incapable of being reduced to a rational expression, as √(x + 1)
Derived Forms
irreducibility, irreducibleness, noun
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
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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
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irreducible in Medicine

irreducible ir·re·duc·i·ble (ĭr'ĭ-dōō'sə-bəl, -dyōō'-)

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.