Irreducible

Quick meaning: Irreducible is an adjective meaning Not able to be reduced or lessened.

Meaning

Not able to be reduced or lessened.

More Meanings

1. Not able to be brought to a simpler or reduced form.
2. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x² + 1).
3. (number theory, of a fraction) Whose numerator and denominator share no common factor greater than 1.
4. (number theory, of an integer) Unable to be factored into smaller integers; prime.
5. (algebra, of an element of a ring) Whose only divisors are units and associates.
6. (algebraic geometry, of an algebraic variety) Inexpressible as the union of two proper algebraic subvarieties.
7. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.

Example Sentences

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.

Word Forms

• irreducibles

Antonyms for irreducible

Common opposites include reducible, unincreasable.

Related Words

Related dictionary entries include inescapable, intractable, must-see, unavoidable, basic, hardline.

Related Dictionary Tools