- Archimedean property
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The property of the set of real numbers, that for any real number there is always a natural number greater than that real number.
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Archimedean property
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Archimedean property — In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some ordered or normed groups, fields, and other algebraic structures. Roughly speaking, it is… … Wikipedia
Archimedean — means of or pertaining to or named in honor of the Greek mathematician Archimedes. These are most commonly:* Archimedean property * Archimedean absolute value * Archimedean solid * Archimedean point * Archimedean tiling * Archimedean spiral *… … Wikipedia
Archimedean field — In mathematics, an Archimedean field is an ordered field with the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse.In an ordered field F we can define the absolute value of an element x in F in the usual… … Wikipedia
Archimedean group — In abstract algebra, a branch of mathematics, an Archimedean group is an algebraic structure consisting of a set together with a binary operation and binary relation satisfying certain axioms detailed below. We can also say that an Archimedean… … Wikipedia
Archimedean — /ahr keuh mee dee euhn, mi dee euhn/, adj. 1. of, pertaining to, or discovered by Archimedes. 2. Math. of or pertaining to any ordered field, as the field of real numbers, having the property that for any two unequal positive elements there is an … Universalium
Non-Archimedean ordered field — In mathematics, a non Archimedean ordered field is an ordered field that does not satisfy the Archimedean property. Examples are the Levi Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational… … Wikipedia
Non-Archimedean — In mathematics and physics, non Archimedean refers to something without the Archimedean property. This includes: Ultrametric space notably, p adic numbers Non Archimedean ordered field, namely: Levi Civita field Hyperreal numbers Surreal numbers… … Wikipedia
Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… … Wikipedia
Axiom of Archimedes — The axiom of Archimedes can be stated in modern notation as follows: Let x be any real number. Then there exists a natural number n such that n > x. In field theory this statement is called the Axiom of Archimedes. The same name is also applied… … Wikipedia
List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A … Wikipedia
