nonprincipal ideal

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• Ideal number — In mathematics an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind s definition of ideals for rings. An ideal in the ring …   Wikipedia

• Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is …   Wikipedia

• Filter (mathematics) — The powerset algebra of the set {1,2,3,4} with the upset colored green. The green elements make a principal ultrafilter on the lattice. In mathematics, a filter is a special subset of a partially ordered set. A frequently used special case is the …   Wikipedia

• 0.999... — In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0 …   Wikipedia

• Property of Baire — A subset A of a topological space X has the property of Baire (Baire property) if it differs from an open set by a meager set; that is, if there is an open: Usubseteq Xsuch that: ADelta Uis meager (here, Delta; denotes the symmetric… …   Wikipedia

• Piecewise syndetic set — In mathematics, piecewise syndeticity is a notion of largeness of subsets of the natural numbers. Let mathcal{P} f(mathbb{N}) denote the set of finite subsets of mathbb{N}. Then a set S sub mathbb{N} is called piecewise syndetic if there exists G …   Wikipedia