Reducible vs. Irreducible — What's the Difference?

To bring down, as in extent, amount, or degree; diminish.

Impossible to reduce to a desired, simpler, or smaller form or amount

To gain control of; subject or conquer

Not able to be reduced or lessened.

To subject to destruction

Not able to be brought to a simpler or reduced form.

To bring to a specified undesirable state, as of weakness or helplessness

Unable to be factorized into polynomials of lower degree, as (x² + 1).

To compel to desperate acts

Whose numerator and denominator share no common factor greater than 1.

To lower in rank or grade; demote.

Unable to be factored into smaller integers; prime.

To thicken or intensify the flavor of (a sauce, for example) by slow boiling.

That its only divisors are units and associates.

To lower the price of

Not containing a sphere of codimension 1 that is not the boundary of a ball.

To decrease the viscosity of (paint, for example), as by adding a solvent.

Impossible to divide further into representations of lower dimension by means of any similarity transformation.

To put in a simpler or more systematic form; simplify or codify

(mathematics) Such a polynomial

To turn into powder; pulverize.

Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.

To decrease the valence of (an atom) by adding electrons.

Incapable of being reduced to a simpler form of expression; as, an irreducible formula.

To remove oxygen from (a compound).

Incapable of being made smaller or simpler;

To add hydrogen to (a compound).

To change to a metallic state by removing nonmetallic constituents; smelt.

(Mathematics) To simplify the form of (an expression, such as a fraction) without changing the value.

(Medicine) To restore (a fractured or displaced body part) to a normal condition or position.

(Linguistics) To pronounce (a stressed vowel) as the unstressed version of that vowel or as schwa.

To become diminished.

To lose weight, as by dieting.

(Biology) To undergo meiosis.

Capable of being reduced.

Able to be factored into polynomials of lower degree, as $x^2-1$.

Able to be factored into smaller integers; composite.

Containing a sphere of codimension 1 that is not the boundary of a ball.

Capable of being reduced.

Capable of being reduced;