irreducible en · ADJ
Pronunciation
- (US) audio
- /ˌɪɹɪˈdjuːsɪbəl/
Etymology
Etymology tree Proto-Indo-European *né Proto-Indo-European *n̥- Proto-Italic *n̥- Latin in-bor. Middle English in- English ir- English reduce Proto-Indo-European *-dʰlom Proto-Italic *-ðlom Proto-Italic *-ðlis Latin -bilis Latin -ibilis Old French -ibleder. Middle English -ible English -ible English reducible English irreducible From ir- + reducible.
Meanings
-
(not-comparable) Not able to be reduced or lessened.
With each reduction in the number of railways, there must come, eventually, a decline in interest, if only through reduction in variety; and when it comes to one nationalised railway only we have reached the irreducible minimum.
1948 January and February, Cecil J. Allen, “British Locomotive Practice and Performance”, in Railway Magazine, page 48:
- (not-comparable) Not able to be brought to a simpler or reduced form.
- (not-comparable, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
- (not-comparable, of a fraction) Whose numerator and denominator share no common factor greater than 1.
- (not-comparable, of an integer) Unable to be factored into smaller integers; prime.
- (not-comparable, of an element of a ring) Whose only divisors are units and associates.
- (not-comparable, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
- (not-comparable, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
- (not-comparable, of a representation) Impossible to divide further into representations of lower dimension by means of any similarity transformation.
Antonyms
Deriveds
irreducibly · irreducibility · irrep · irreducibleness · irreducible complexity
Translations (24)
pl nieredukowalny (not able to be reduced or lessened) · mk нескратлив ((mathematics, of an integer) unable to be factored into smaller integers) · ja 減らせない (not able to be reduced or lessened) · mk несведлив (not able to be reduced or lessened) · fr irréductible ((mathematics, of an integer) unable to be factored into smaller integers) · it irriducibile (not able to be reduced or lessened) · kk келтірілмейтін ((mathematics, of an integer) unable to be factored into smaller integers) · ga dochloíte (not able to be reduced or lessened) · nl onherleidbaar (not able to be reduced or lessened) · pl nieredukowalny ((mathematics, of an integer) unable to be factored into smaller integers) · eo nereduktebla ((mathematics, of an integer) unable to be factored into smaller integers) · fr irréductible (not able to be reduced or lessened) · fi jaoton ((mathematics, of an integer) unable to be factored into smaller integers) · pt irredutível (not able to be reduced or lessened) · ga dosháraithe (not able to be reduced or lessened) · ca irreductible (not able to be reduced or lessened) · ru неприводимый ((mathematics, of an integer) unable to be factored into smaller integers) · es irreductible (not able to be reduced or lessened) · es irreducible ((mathematics, of an integer) unable to be factored into smaller integers) · nl onherleidbaar ((mathematics, of an integer) unable to be factored into smaller integers) · ja 既約の ((mathematics, of an integer) unable to be factored into smaller integers) · bg неподлежащ на намаление (not able to be reduced or lessened) · bg несъкратим ((mathematics, of an integer) unable to be factored into smaller integers) · fi vähenemätön (not able to be reduced or lessened)