Irreducible case(Alg.), a particular case in the solution of a cubic equation, in which the formula commonly employed contains an imaginary quantity, and therefore fails in its application.

Ir`re*du"ci*ble*ness, n. — — Ir`re*du"ci*bly, adv.

Irreflection
(Ir`re*flec"tion) n. Want of reflection.

Irreflective
(Ir`re*flect"ive) a. Not reflective. De Quincey.

Irreformable
(Ir`re*form"a*ble) a. Incapable of being reformed; incorrigible. Joseph Cook.

Irrefragability
(Ir*ref`ra*ga*bil"i*ty) n. The quality or state of being irrefragable; incapability of being refuted.

Irrefragable
(Ir*ref"ra*ga*ble) a. [F. irréfragable, L. irrefragabilis. See Refragable.] Not refragable; not to be gainsaid or denied; not to be refuted or overthrown; unanswerable; incontestable; undeniable; as, an irrefragable argument; irrefragable evidence.Ir*ref"ra*ga*ble*ness, n.Ir*ref"ra*ga*bly, adv.

Syn. — Incontrovertible; unanswerable; indisputable; unquestionable; incontestable; indubitable; undeniable; irrefutable.

Irrefrangibility
(Ir`re*fran`gi*bil"i*ty) n. The quality or state of being irrefrangible; irrefrangibleness.

Irrefrangible
(Ir`re*fran"gi*ble) a. Not refrangible; that can not be refracted in passing from one medium to another.Ir`re*fran"gi*ble*ness, n.

Irrefutable
(Ir`re*fut"a*ble) a. [L. irrefutabilis: cf. F. irréfutable. See Refute.] Incapable of being refuted or disproved; indisputable.Ir`re*fut"a*ble*ness, n.Ir`re*fut"a*bly, adv.

Irregeneracy
(Ir`re*gen"er*a*cy) n. Unregeneracy.

Irregeneration
(Ir`re*gen`er*a"tion) n. An unregenerate state. [Obs.]

Irregular
(Ir*reg"u*lar) a. [Pref. ir- not + regular: cf. F. irrégulier.] Not regular; not conforming to a law, method, or usage recognized as the general rule; not according to common form; not conformable to nature, to the rules of moral rectitude, or to established principles; not normal; unnatural; immethodical; unsymmetrical; erratic; no

Irrecusable
(Ir`re*cu"sa*ble) a. [L. irrecusabilis; pref. ir— not + recusabilis that should be rejected, fr. recusare to reject: cf. F. irrécusable.] Not liable to exception or rejection. Sir W. Hamilton.

Irredeemability
(Ir`re*deem`a*bil"i*ty) n. The state or quality of being irredeemable; irredeemableness.

Irredeemable
(Ir`re*deem"a*ble) a. Not redeemable; that can not be redeemed; not payable in gold or silver, as a bond; — used especially of such government notes, issued as currency, as are not convertible into coin at the pleasure of the holder.Ir`re*deem"a*ble*ness, adv.

Irreducibility
(Ir`re*du`ci*bil"i*ty) n. The state or quality of being irreducible.

Irreducible
(Ir`re*du"ci*ble) a.

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

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


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