The Collaborative International Dictionary
Irreducibleness
Irreducible \Ir`re*du"ci*ble\, a.
Incapable of being reduced, or brought into a different state; incapable of restoration to its proper or normal condition; as, an irreducible hernia.
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(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.
Wiktionary
irreducibleness
n. The quality of being irreducible.