'Irreducible case' definitions:

Definition of 'Irreducible case'

From: GCIDE
  • 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. [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]