irreducible set

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• Irreducible complexity — This article covers irreducible complexity as used by those who argue for intelligent design. For information on irreducible complexity as used in Systems Theory, see Irreducible complexity (Emergence). Irreducible complexity (IC) is an argument… …   Wikipedia

• Irreducible polynomial — In mathematics, the adjective irreducible means that an object cannot be expressed as a product of at least two non trivial factors in a given set. See also factorization. For any field F , the ring of polynomials with coefficients in F is… …   Wikipedia

• Irreducible component — In mathematics, the concept of irreducible component is used to make formal the idea that a set such as defined by the equation: XY = 0is the union of the two lines: X = 0and : Y = 0.The notion of irreducibility is stronger than connectedness.… …   Wikipedia

• Set-theoretic definition of natural numbers — Several ways have been proposed to define the natural numbers using set theory.The contemporary standardIn standard (ZF) set theory the natural numbersare defined recursively by 0 = {} (the empty set) and n +1 = n ∪ { n }. Then n = {0,1,..., n… …   Wikipedia

• Thin set (Serre) — In mathematics, a thin set in the sense of Serre is a certain kind of subset constructed in algebraic geometry over a given field K , by allowed operations that are in a definite sense unlikely . The two fundamental ones are: solving a polynomial …   Wikipedia

• Algebraic set — In mathematics, an algebraic set over a field K is the set of solutions in K n ( n tuples of elements of K ) of a set of simultaneous equations: P 1( X 1, ..., X n ) = 0: P 2( X 1, ..., X n ) = 0and so on up to: P m ( X 1, ..., X n ) = 0for some… …   Wikipedia

• Maximal independent set — This article is about the combinatorial aspects of maximal independent sets of vertices in a graph. For other aspects of independent vertex sets in graph theory, see Independent set (graph theory). For other kinds of independent sets, see… …   Wikipedia

• Wu's method of characteristic set — Wenjun Wu s method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the late… …   Wikipedia

• Hyperconnected space — In mathematics, a hyperconnected space is a topological space X that cannot be written as the union of two proper closed sets. The name irreducible space is preferred in algebraic geometry.For a topological space X the following conditions are… …   Wikipedia

• Noetherian topological space — In mathematics, a Noetherian topological space is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the… …   Wikipedia

• Generic point — In mathematics, in the fields of general topology and particularly of algebraic geometry, a generic point P of a topological space X is an algebraic way of capturing the notion of a generic property: a generic property is a property of the… …   Wikipedia