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Non-standard_calculus abstract "In mathematics, non-standard calculus is the modern application of infinitesimals, in the sense of non-standard analysis, to differential and integral calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.Calculations with infinitesimals were widely used before Karl Weierstrass sought to replace them with the (ε, δ)-definition of limit starting in the 1870s. (See history of calculus.) For almost one hundred years thereafter, mathematicians like Richard Courant viewed infinitesimals as being naive and vague or meaningless.Contrary to such views, Abraham Robinson showed in 1960 that infinitesimals are precise, clear, and meaningful, building upon work by Edwin Hewitt and Jerzy Łoś. According to Jerome Keisler, "Robinson solved a three hundred year old problem by giving a precise treatment of infinitesimals. Robinson's achievement will probably rank as one of the major mathematical advances of the twentieth century."".
Non-standard_calculus wikiPageExternalLink calc.
Non-standard_calculus wikiPageExternalLink calc.html.
Non-standard_calculus wikiPageExternalLink foundations.html.
Non-standard_calculus wikiPageExternalLink calc.html.).
Non-standard_calculus wikiPageID "643021".
Non-standard_calculus wikiPageLength "25179".
Non-standard_calculus wikiPageOutDegree "94".
Non-standard_calculus wikiPageRevisionID "681785899".
Non-standard_calculus wikiPageWikiLink (ε,_δ)-definition_of_limit.
Non-standard_calculus wikiPageWikiLink Abraham_Robinson.
Non-standard_calculus wikiPageWikiLink Adequality.
Non-standard_calculus wikiPageWikiLink Andreas_Blass.
Non-standard_calculus wikiPageWikiLink Archimedes_use_of_infinitesimals.
Non-standard_calculus wikiPageWikiLink Augustin-Louis_Cauchy.
Non-standard_calculus wikiPageWikiLink Augustin_Louis_Cauchy.
Non-standard_calculus wikiPageWikiLink Bonaventura_Cavalieri.
Non-standard_calculus wikiPageWikiLink Calculus.
Non-standard_calculus wikiPageWikiLink Category:Calculus.
Non-standard_calculus wikiPageWikiLink Category:Infinity.
Non-standard_calculus wikiPageWikiLink Category:Non-standard_analysis.
Non-standard_calculus wikiPageWikiLink Cauchy.
Non-standard_calculus wikiPageWikiLink Cavalieris_principle.
Non-standard_calculus wikiPageWikiLink Colin_Maclaurin.
Non-standard_calculus wikiPageWikiLink Continuous_function.
Non-standard_calculus wikiPageWikiLink Cours_dAnalyse.
Non-standard_calculus wikiPageWikiLink Criticism_of_non-standard_analysis.
Non-standard_calculus wikiPageWikiLink Dirichlet_function.
Non-standard_calculus wikiPageWikiLink Edward_Nelson.
Non-standard_calculus wikiPageWikiLink Edwin_Hewitt.
Non-standard_calculus wikiPageWikiLink Elementary_Calculus:_An_Infinitesimal_Approach.
Non-standard_calculus wikiPageWikiLink Epsilon,_delta_technique.
Non-standard_calculus wikiPageWikiLink First-order_logic.
Non-standard_calculus wikiPageWikiLink George_Berkeley.
Non-standard_calculus wikiPageWikiLink Gottfried_Leibniz.
Non-standard_calculus wikiPageWikiLink Gottfried_Wilhelm_Leibniz.
Non-standard_calculus wikiPageWikiLink Heine–Cantor_theorem.
Non-standard_calculus wikiPageWikiLink History_of_calculus.
Non-standard_calculus wikiPageWikiLink Howard_Jerome_Keisler.
Non-standard_calculus wikiPageWikiLink Hyperfinite_set.
Non-standard_calculus wikiPageWikiLink Hyperinteger.
Non-standard_calculus wikiPageWikiLink Hypernatural.
Non-standard_calculus wikiPageWikiLink Hyperreal_number.
Non-standard_calculus wikiPageWikiLink Hyperreals.
Non-standard_calculus wikiPageWikiLink Indivisibles.
Non-standard_calculus wikiPageWikiLink Infinitesimal.
Non-standard_calculus wikiPageWikiLink Infinitesimal_calculus.
Non-standard_calculus wikiPageWikiLink Infinitesimals.
Non-standard_calculus wikiPageWikiLink Intermediate_value_theorem.
Non-standard_calculus wikiPageWikiLink Internal_set.
Non-standard_calculus wikiPageWikiLink Isaac_Barrow.
Non-standard_calculus wikiPageWikiLink Isaac_Newton.
Non-standard_calculus wikiPageWikiLink Jean_le_Rond_dAlembert.
Non-standard_calculus wikiPageWikiLink Jerzy_Łoś.
Non-standard_calculus wikiPageWikiLink John_Wallis.
Non-standard_calculus wikiPageWikiLink Karl_Weierstrass.
Non-standard_calculus wikiPageWikiLink Kevin_Houston_(mathematician).
Non-standard_calculus wikiPageWikiLink Limit_of_a_function.
Non-standard_calculus wikiPageWikiLink Mathematical_logic.
Non-standard_calculus wikiPageWikiLink Mathematics.
Non-standard_calculus wikiPageWikiLink Michel_Rolle.
Non-standard_calculus wikiPageWikiLink Microcontinuity.
Non-standard_calculus wikiPageWikiLink Microcontinuous.
Non-standard_calculus wikiPageWikiLink Non-classical_analysis.
Non-standard_calculus wikiPageWikiLink Non-standard_analysis.
Non-standard_calculus wikiPageWikiLink Non-standard_calculus.
Non-standard_calculus wikiPageWikiLink Nowhere_continuous_function.
Non-standard_calculus wikiPageWikiLink Overspill.
Non-standard_calculus wikiPageWikiLink Pierre_de_Fermat.
Non-standard_calculus wikiPageWikiLink Predicate_logic.
Non-standard_calculus wikiPageWikiLink Quantifier_(logic).
Non-standard_calculus wikiPageWikiLink René_Descartes.
Non-standard_calculus wikiPageWikiLink Richard_Courant.
Non-standard_calculus wikiPageWikiLink Standard_part_function.
Non-standard_calculus wikiPageWikiLink The_Analyst.
Non-standard_calculus wikiPageWikiLink The_Method_of_Mechanical_Theorems.
Non-standard_calculus wikiPageWikiLink Transfer_principle.
Non-standard_calculus wikiPageWikiLink Uniform_continuity.
Non-standard_calculus wikiPageWikiLink ZFC.
Non-standard_calculus wikiPageWikiLink Zermelo-Fraenkel_set_theory.
Non-standard_calculus wikiPageWikiLink Zermelo–Fraenkel_set_theory.
Non-standard_calculus wikiPageWikiLinkText "Non-standard calculus".
Non-standard_calculus wikiPageWikiLinkText "definition of limit".
Non-standard_calculus wikiPageWikiLinkText "infinitesimal calculus".
Non-standard_calculus wikiPageWikiLinkText "modern infinitesimal theory".
Non-standard_calculus wikiPageWikiLinkText "non-standard calculus".
Non-standard_calculus wikiPageWikiLinkText "uniform continuity".
Non-standard_calculus hasPhotoCollection Non-standard_calculus.
Non-standard_calculus id "p/i050950".
Non-standard_calculus title "Infinitesimal calculus".
Non-standard_calculus wikiPageUsesTemplate Template:Citation.
Non-standard_calculus wikiPageUsesTemplate Template:Harv.
Non-standard_calculus wikiPageUsesTemplate Template:Harvtxt.
Non-standard_calculus wikiPageUsesTemplate Template:Infinitesimals.
Non-standard_calculus wikiPageUsesTemplate Template:Reflist.
Non-standard_calculus wikiPageUsesTemplate Template:Springer.
Non-standard_calculus subject Category:Calculus.
Non-standard_calculus subject Category:Infinity.
Non-standard_calculus subject Category:Non-standard_analysis.
Non-standard_calculus hypernym Application.