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From: Webster's Revised Unabridged Dictionary (1913)

 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.
 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.