# Irreducibleness

## irreducible

[ir-i-doo-suh-buhl, -dyoo-]
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
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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

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Medical Dictionary

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.