irreducibility
|ir-re-duc-i-bil-i-ty|
/ˌɪrɪdʌkˈsɪbɪlɪti/
not able to be reduced
Etymology
'irreducibility' is formed in English by adding the negative prefix 'ir-' to 'reducibility' (itself from 'reducible' + '-ity').
'irreducibility' developed from English 'reducibility' (Middle English/Old French influence) to which the prefix 'ir-' (from Latin 'in-' via assimilation before 'r') was attached, yielding the modern noun 'irreducibility'.
Originally the root notion came from Latin 'reducere' meaning 'to lead back', and the compound originally conveyed 'not able to be led back'; over time it specialized to mean 'not able to be reduced' or 'not factorable/simplifiable' in modern usage.
Meanings by Part of Speech
Noun 1
the quality or state of being not reducible; not able to be made simpler or broken down into smaller parts.
The irreducibility of the mechanism meant engineers could not simplify its design further.
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Noun 2
in mathematics, the property of an object (for example, a polynomial or an element of a ring) that cannot be factored into a product of two non-unit elements in a given domain.
The irreducibility of the polynomial over Q was established by Eisenstein's criterion.
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Noun 3
in chemistry or physics, resistance to being reduced (in the redox sense) or to being broken into simpler components; sometimes used metaphorically in other sciences to denote non-reducibility of explanations.
The irreducibility of the compound under those conditions made the reaction pathway unlikely.
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Last updated: 2025/11/10 23:13