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

<mathematics> Irreducible case, 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. Irredu"cibleness, Irredu"cibly.

(01 Mar 1998)