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- Overspill abstract "In non-standard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers. By applying the induction principle for the standard integers N and the transfer principle we get the principle of internal induction:For any internal subset A of *N, if 1 is an element of A, and for every element n of A, n + 1 also belongs to A,thenA = *NIf N were an internal set, then instantiating the internal induction principle with N, it would follow N = *N which is known not to be the case.The overspill principle has a number of useful consequences: The set of standard hyperreals is not internal. The set of bounded hyperreals is not internal. The set of infinitesimal hyperreals is not internal.In particular: If an internal set contains all infinitesimal non-negative hyperreals, it contains a positive non-infinitesimal (or appreciable) hyperreal. If an internal set contains N it contains an unlimited (infinite) element of *N.".
- Overspill wikiPageID "636621".
- Overspill wikiPageLength "2745".
- Overspill wikiPageOutDegree "11".
- Overspill wikiPageRevisionID "573834412".
- Overspill wikiPageWikiLink Category:Non-standard_analysis.
- Overspill wikiPageWikiLink Hyperinteger.
- Overspill wikiPageWikiLink Infinitesimal.
- Overspill wikiPageWikiLink Internal_set.
- Overspill wikiPageWikiLink Mathematical_induction.
- Overspill wikiPageWikiLink Mathematics.
- Overspill wikiPageWikiLink Microcontinuity.
- Overspill wikiPageWikiLink Natural_number.
- Overspill wikiPageWikiLink Non-standard_analysis.
- Overspill wikiPageWikiLink Robert_Goldblatt.
- Overspill wikiPageWikiLink Transfer_principle.
- Overspill wikiPageWikiLinkText "Overspill".
- Overspill wikiPageWikiLinkText "overspill".
- Overspill hasPhotoCollection Overspill.
- Overspill wikiPageUsesTemplate Template:About.
- Overspill wikiPageUsesTemplate Template:Infinitesimals.
- Overspill subject Category:Non-standard_analysis.
- Overspill type Field.
- Overspill comment "In non-standard analysis, a branch of mathematics, overspill (referred to as overflow by Goldblatt (1998, p. 129)) is a widely used proof technique. It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers.".
- Overspill label "Overspill".
- Overspill sameAs m.02z73p.
- Overspill sameAs Q7113981.
- Overspill sameAs Q7113981.
- Overspill wasDerivedFrom Overspill?oldid=573834412.
- Overspill isPrimaryTopicOf Overspill.