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Irreducibleness

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.

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.

- Irreducible complexity (IC) is the argument that certain biological systems cannot have evolved by successive small modifications to pre-existing functional...

- In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials...

- In philosophy, a phenomenona is governed by the principle of irreducibility when a complete account of an entity is not possible at lower levels of explanation...

- specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...

- In algebraic geometry, an irreducible algebraic set or irreducible variety is an algebraic set that cannot be written as the union of two proper algebraic...

- be irreducible if it is not a product of two non-units, or equivalently, if every factoring of such element contains at least one unit. Irreducible elements...

- Com****tional irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. Wolfram terms the inability to shortcut...

- In mathematics, the concept of irreducibility is used in several ways. A polynomial over a field may be an irreducible polynomial if it cannot be factored...

- Irreducible Mind: Toward a Psychology for the 21st Century is a 2007 psychological book by Edward Francis Kelly, Emily Williams Kelly, Adam Crabtree,...

- especially in the field of ring theory, the term irreducible ring is used in a few different ways. A (meet-)irreducible ring is one in which the intersection of...

- In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials...

- In philosophy, a phenomenona is governed by the principle of irreducibility when a complete account of an entity is not possible at lower levels of explanation...

- specifically in the representation theory of groups and algebras, an irreducible representation ( ρ , V ) {\displaystyle (\rho ,V)} or irrep of an algebraic...

- In algebraic geometry, an irreducible algebraic set or irreducible variety is an algebraic set that cannot be written as the union of two proper algebraic...

- be irreducible if it is not a product of two non-units, or equivalently, if every factoring of such element contains at least one unit. Irreducible elements...

- Com****tional irreducibility is one of the main ideas proposed by Stephen Wolfram in his book A New Kind of Science. Wolfram terms the inability to shortcut...

- In mathematics, the concept of irreducibility is used in several ways. A polynomial over a field may be an irreducible polynomial if it cannot be factored...

- Irreducible Mind: Toward a Psychology for the 21st Century is a 2007 psychological book by Edward Francis Kelly, Emily Williams Kelly, Adam Crabtree,...

- especially in the field of ring theory, the term irreducible ring is used in a few different ways. A (meet-)irreducible ring is one in which the intersection of...

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