Source : Webster's Revised Unabridged Dictionary (1913)

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.

   {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.

Source : WordNet®

irreducible
     adj : incapable of being made smaller or simpler; "an irreducible
           minimum"; "an irreducible formula"; "an irreducible
           hernia" [ant: {reducible}]