Anagram & Information om | Engelska ordet FINITELY

Exempel på hur man kan använda FINITELY i en mening

• Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finitely many".
• Since there are only twenty-six letters in the English alphabet, there are finitely many phrases of under sixty letters, and hence finitely many positive integers that are defined by phrases of under sixty letters.
• This topology differs from another, perhaps more natural-seeming, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.
• A σ-algebra of subsets is a set algebra of subsets; elements of the latter only need to be closed under the union or intersection of finitely many subsets, which is a weaker condition.
• In a union of finitely many sets, the closure of the union and the union of the closures are equal; the union of zero sets is the empty set, and so this statement contains the earlier statement about the closure of the empty set as a special case.
• In a finite (or terminated) continued fraction, the iteration/recursion is stopped after finitely many steps by using an integer in lieu of another continued fraction.
• Every cyclic group is an abelian group (meaning that its group operation is commutative), and every finitely generated abelian group is a direct product of cyclic groups.
• That is, a nonempty set W is a subspace if and only if every linear combination of finitely many elements of W also belongs to W.
• The fundamental theorem of finitely generated abelian groups can be stated two ways, generalizing the two forms of the fundamental theorem of finite abelian groups.
• While it is true that every quotient of a finitely generated group is finitely generated (the images of the generators in the quotient give a finite generating set), a subgroup of a finitely generated group need not be finitely generated.
• The problem is related to the following question: given any two polyhedra of equal volume, is it always possible to cut the first into finitely many polyhedral pieces which can be reassembled to yield the second? Based on earlier writings by Carl Friedrich Gauss, David Hilbert conjectured that this is not always possible.
• Igor Shafarevich conjectured that there are only finitely many isomorphism classes of abelian varieties of fixed dimension and fixed polarization degree over a fixed number field with good reduction outside a fixed finite set of places.
• Whereas it is known that there are infinitely many triples (a, b, c) of coprime positive integers with a + b = c such that q(a, b, c) > 1, the conjecture predicts that only finitely many of those have q > 1.
• In the particular case where the space is a finite-dimensional Euclidean space, each site is a point, there are finitely many points and all of them are different, then the Voronoi cells are convex polytopes and they can be represented in a combinatorial way using their vertices, sides, two-dimensional faces, etc.
• Tarski's circle-squaring problem is the challenge, posed by Alfred Tarski in 1925, to take a disc in the plane, cut it into finitely many pieces, and reassemble the pieces so as to get a square of equal area.
• Although other authors may distinguish them differently (or not at all), Wriggers and Panatiotopoulos (2014) distinguish multivalued functions from set-valued relations (also called set-valued functions) by the fact that multivalued functions only take multiple values at finitely (or denumerably) many points, and otherwise behave like a function.
• The most common version uses the concept of "equidecomposability" of polygons: two polygons are equidecomposable if they can be split into finitely many triangles that only differ by some isometry (in fact only by a combination of a translation and a rotation).
• For finitely generated abelian groups, rank is a strong invariant and every such group is determined up to isomorphism by its rank and torsion subgroup.
• If a field extension is finitely generated and it is also separably generated, then each generating set of the field extension contains a separating transcendence basis.
• This random tree has several equivalent definitions and constructions: using sub-trees generated by finitely many leaves, using a Brownian excursion, Poisson separating a straight line or as a limit of Galton-Watson trees.

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