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. [ 1913 Webster ]

2. (Math.) Incapable of being reduced to a simpler form of expression; as, an irreducible formula. [ 1913 Webster ]

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. [ 1913 Webster ]