KnowraArchimedean propertyLinked fromLinked fromThe 8 pages that link to Archimedean property, each with the reason it gives.All 8Related 6Compared with 2Real numberRelated: It rules out infinitely large or infinitesimal real numbers.Rational numberRelated: Rational numbers have no infinitely large or infinitesimal elements under their usual order.InfinitesimalCompared with: This property rules out nonzero infinitesimals inside the real numbers.Method of exhaustionRelated: This principle ensures a sufficiently fine subdivision can make a fixed error bound impossible.Completeness of the real numbersRelated: It is distinct from completeness: ordered fields can be Archimedean yet incomplete.Hyperreal numberCompared with: The real numbers satisfy this property; hyperreal fields with infinitesimals do not.Cantor–Dedekind axiomRelated: It is a separate order condition often included when characterizing the real number system.Ostrowski's theoremRelated: Absolute values with Archimedean behavior fall into the usual class on the rationals.