Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Archimedean_property> ?p ?o }
- Archimedean_property abstract "In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. Roughly speaking, it is the property of having no infinitely large or infinitely small elements. It was Otto Stolz who gave the axiom of Archimedes its name because it appears as Axiom V of Archimedes’ On the Sphere and Cylinder.The notion arose from the theory of magnitudes of Ancient Greece; it still plays an important role in modern mathematics such as David Hilbert's axioms for geometry, and the theories of ordered groups, ordered fields, and local fields.An algebraic structure in which any two non-zero elements are comparable, in the sense that neither of them is infinitesimal with respect to the other, is said to be Archimedean. A structure which has a pair of non-zero elements, one of which is infinitesimal with respect to the other, is said to be non-Archimedean. For example, a linearly ordered group that is Archimedean is an Archimedean group.This can be made precise in various contexts with slightly different ways of formulation. For example, in the context of ordered fields, one has the axiom of Archimedes which formulates this property, where the field of real numbers is Archimedean, but that of rational functions in real coefficients is not.".
- Archimedean_property thumbnail Archimedean_property.png?width=300.
- Archimedean_property wikiPageID "264158".
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- Archimedean_property wikiPageRevisionID "675005487".
- Archimedean_property wikiPageWikiLink Abstract_algebra.
- Archimedean_property wikiPageWikiLink Algebraic_structure.
- Archimedean_property wikiPageWikiLink Analysis.
- Archimedean_property wikiPageWikiLink Ancient_Greece.
- Archimedean_property wikiPageWikiLink Archimedean_group.
- Archimedean_property wikiPageWikiLink Archimedes.
- Archimedean_property wikiPageWikiLink Archimedess_use_of_infinitesimals.
- Archimedean_property wikiPageWikiLink Axiomatic_theory_of_real_numbers.
- Archimedean_property wikiPageWikiLink Category:Field_theory.
- Archimedean_property wikiPageWikiLink Category:Ordered_groups.
- Archimedean_property wikiPageWikiLink Category:Real_algebraic_geometry.
- Archimedean_property wikiPageWikiLink Coefficient.
- Archimedean_property wikiPageWikiLink Cofinal_(mathematics).
- Archimedean_property wikiPageWikiLink Construction_of_the_real_numbers.
- Archimedean_property wikiPageWikiLink Constructive_analysis.
- Archimedean_property wikiPageWikiLink David_Hilbert.
- Archimedean_property wikiPageWikiLink Dense_set.
- Archimedean_property wikiPageWikiLink Euclids_Elements.
- Archimedean_property wikiPageWikiLink Eudoxus_of_Cnidus.
- Archimedean_property wikiPageWikiLink Field_(mathematics).
- Archimedean_property wikiPageWikiLink Group_(algebra).
- Archimedean_property wikiPageWikiLink Group_(mathematics).
- Archimedean_property wikiPageWikiLink Heuristic.
- Archimedean_property wikiPageWikiLink Hilberts_axioms.
- Archimedean_property wikiPageWikiLink Infimum.
- Archimedean_property wikiPageWikiLink Infimum_and_supremum.
- Archimedean_property wikiPageWikiLink Infinitesimal.
- Archimedean_property wikiPageWikiLink Leading_coefficient.
- Archimedean_property wikiPageWikiLink Least-upper-bound_property.
- Archimedean_property wikiPageWikiLink Least_upper_bound.
- Archimedean_property wikiPageWikiLink Least_upper_bound_property.
- Archimedean_property wikiPageWikiLink Linearly_ordered_group.
- Archimedean_property wikiPageWikiLink Local_field.
- Archimedean_property wikiPageWikiLink Local_fields.
- Archimedean_property wikiPageWikiLink Magnitude_(mathematics).
- Archimedean_property wikiPageWikiLink Mathematical_proof.
- Archimedean_property wikiPageWikiLink Monoid.
- Archimedean_property wikiPageWikiLink Natural_number.
- Archimedean_property wikiPageWikiLink On_the_Sphere_and_Cylinder.
- Archimedean_property wikiPageWikiLink Order_type.
- Archimedean_property wikiPageWikiLink Ordered_field.
- Archimedean_property wikiPageWikiLink Ostrowskis_theorem.
- Archimedean_property wikiPageWikiLink Otto_Stolz.
- Archimedean_property wikiPageWikiLink P-adic_number.
- Archimedean_property wikiPageWikiLink Polynomial.
- Archimedean_property wikiPageWikiLink Proof_by_contradiction.
- Archimedean_property wikiPageWikiLink Rational_function.
- Archimedean_property wikiPageWikiLink Rational_functions.
- Archimedean_property wikiPageWikiLink Real_number.
- Archimedean_property wikiPageWikiLink Ring_(mathematics).
- Archimedean_property wikiPageWikiLink Syracuse,_Italy.
- Archimedean_property wikiPageWikiLink Syracuse,_Sicily.
- Archimedean_property wikiPageWikiLink The_Method_of_Mechanical_Theorems.
- Archimedean_property wikiPageWikiLink Triangle_inequality.
- Archimedean_property wikiPageWikiLink Ultrametric.
- Archimedean_property wikiPageWikiLink Ultrametric_space.
- Archimedean_property wikiPageWikiLink Upper_and_lower_bounds.
- Archimedean_property wikiPageWikiLink Upper_bound.
- Archimedean_property wikiPageWikiLink Valuation_ring.
- Archimedean_property wikiPageWikiLink File:Archimedean_property.png.
- Archimedean_property wikiPageWikiLinkText "Archimedean property".
- Archimedean_property wikiPageWikiLinkText "Archimedean".
- Archimedean_property wikiPageWikiLinkText "Archimedean_property#Ordered_fields".
- Archimedean_property wikiPageWikiLinkText "archimedean".
- Archimedean_property wikiPageWikiLinkText "non-Archimedean".
- Archimedean_property wikiPageWikiLinkText "nonarchimedean".
- Archimedean_property hasPhotoCollection Archimedean_property.
- Archimedean_property wikiPageUsesTemplate Template:Cite_book.
- Archimedean_property wikiPageUsesTemplate Template:Main.
- Archimedean_property wikiPageUsesTemplate Template:Math.
- Archimedean_property wikiPageUsesTemplate Template:Mvar.
- Archimedean_property wikiPageUsesTemplate Template:Open-open.
- Archimedean_property wikiPageUsesTemplate Template:Quote.
- Archimedean_property wikiPageUsesTemplate Template:Refbegin.
- Archimedean_property wikiPageUsesTemplate Template:Refend.
- Archimedean_property wikiPageUsesTemplate Template:Reflist.
- Archimedean_property subject Category:Field_theory.
- Archimedean_property subject Category:Ordered_groups.
- Archimedean_property subject Category:Real_algebraic_geometry.
- Archimedean_property hypernym Property.
- Archimedean_property type Building.
- Archimedean_property type Group.
- Archimedean_property type Group.
- Archimedean_property type Structure.
- Archimedean_property comment "In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. Roughly speaking, it is the property of having no infinitely large or infinitely small elements.".
- Archimedean_property label "Archimedean property".
- Archimedean_property sameAs Archimedisches_Axiom.
- Archimedean_property sameAs خاصية_أرخميدس.
- Archimedean_property sameAs Axioma_dArquimedes.
- Archimedean_property sameAs Archimedisches_Axiom.
- Archimedean_property sameAs Αξίωμα_Ευδόξου-Αρχιμήδη.
- Archimedean_property sameAs Arkimeda_propraĵo.
- Archimedean_property sameAs Axioma_de_Arquímedes.
- Archimedean_property sameAs Arkhimedeen_lause.