irreducibility

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
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Based on the Random House Dictionary, © Random House, Inc. 2013.
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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

00:10
Irreducibility is always a great word to know.
So is callithumpian. Does it mean:
a children's mummer's parade, as on the Fourth of July, with prizes for the best costumes.
a printed punctuation mark (‽), available only in some typefaces, designed to combine the question mark (?) and the exclamation point (!), indicating a mixture of query and interjection, as after a rhetorical question.
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
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