algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic...

algebra, a branch of mathematics, an Archimedean group is a linearly ordered group for which the Archimedean property holds: every two positive group elements...

Archimedean point Archimedean property Archimedean solid Archimedean spiral Archimedean tiling Archimedean screw Claw of Archimedes The Archimedeans, the mathematical...

non-Archimedean refers to something without the Archimedean property. This includes: Ultrametric space in particular, a domain with non-Archimedean absolute...

include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very...

In mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Such fields will contain infinitesimal...

such a geometry is the Dehn plane. Non-Archimedean geometries may, as the example indicates, have properties significantly different from Euclidean geometry...

The Archimedean spiral (also known as Archimedes' spiral, the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes...

2 {\displaystyle {\sqrt {2}}} is not rational. These properties imply the Archimedean property (which is not implied by other definitions of completeness)...

all 1/10n, where n is a natural number, a property that results immediately from the Archimedean property of the real numbers. There are many other ways...

In geometry, an Archimedean solid is one of 13 convex polyhedra whose faces are regular polygons and whose vertices are all symmetric to each other. They...

critics note that highest median rules violate participation and the Archimedean property; highest median rules can fail to elect a candidate almost-unanimously...

forms of completeness on this page. But Cauchy completeness and the Archimedean property taken together are equivalent to the others. The nested interval...

group. (Elliott, 1976) The Archimedean property of the real numbers can be generalized to partially ordered groups. Property: A partially ordered group...

left-orderable. Otto Hölder showed that every Archimedean group (a bi-ordered group satisfying an Archimedean property) is isomorphic to a subgroup of the additive...

\mathbb {Q} _{p}} of p-adic numbers. p-adic number Valuation (algebra) Archimedean property Multiplicity (mathematics) Ostrowski's theorem Legendre's formula...

A crucially important property of the real numbers is that it is an Archimedean field, meaning it has the Archimedean property that for any real number...

Archimedean principle may refer to: Archimedes' principle, a principle relating buoyancy with displacement Archimedean property, a mathematical property...

structure with a compatible partial order. Archimedean group: a linearly ordered group for which the Archimedean property holds. Topological vector space: a vector...

where l ranges from 1 to U-1. The random variable Z displays fractal properties, resembling the shape distribution akin to Thomae's or Dirichlet function...

In mathematics, a Catalan solid, or Archimedean dual, is a polyhedron that is dual to an Archimedean solid. There are 13 Catalan solids. They are named...

apply to the Archimedean property, because the Archimedean property cannot be stated in first-order logic. In fact, the Archimedean property is false for...

projection property separately imply the principal projection property; and the principal projection property implies the Archimedean property. None of...

space X {\displaystyle X} over the real or complex numbers is called Archimedean if for all x ∈ X , {\displaystyle x\in X,} whenever there exists some...

(n times) equals 0. A t-norm ∗ {\displaystyle *} is called Archimedean if it has the Archimedean property, that is, if for each x, y in the open interval (0, 1)...

Archimedean absolute value Archimedean circle Archimedean copula Archimedean group Archimedean ordered field Archimedean point Archimedean property Archimedean...

and ⋅ {\displaystyle \cdot } is an Archimedean ordered field, meaning the axioms of order and the Archimedean property hold. Let ( I n ) n ∈ N {\displaystyle...

be assumed that does not involve a precise equality, called the Archimedean property. It says that any separation in preference can be maintained under...

, then L ⪯ N {\displaystyle L\preceq N} . convexity/continuity (Archimedean property): If L ⪯ M ⪯ N {\displaystyle L\preceq M\preceq N} , then there is...

theorem stating that every linearly ordered group that satisfies an Archimedean property is isomorphic to a subgroup of the additive group of real numbers...