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Chewings72 (talk | contribs) m Adding local short description: "Function from the limited hyperreal to the real numbers", overriding Wikidata description "In non-standard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers." (Shortdesc helper) |
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{{Short description|Function from the limited hyperreal to the real numbers}}
In [[nonstandard analysis]], the '''standard part function''' is a function from the limited (finite) [[hyperreal number]]s to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real. It associates to every such hyperreal <math>x</math>, the unique real <math>x_0</math> infinitely close to it, i.e. <math>x-x_0</math> is [[infinitesimal]]. As such, it is a mathematical implementation of the historical concept of [[adequality]] introduced by [[Pierre de Fermat]],<ref>Karin Usadi Katz and [[Mikhail Katz|Mikhail G. Katz]] (2011) A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography. [[Foundations of Science]]. {{doi|10.1007/s10699-011-9223-1}} [https://doi.org/10.1007%2Fs10699-011-9223-1] See [https://arxiv.org/abs/1104.0375 arxiv]. The authors refer to the Fermat-Robinson standard part.</ref> as well as [[Leibniz]]'s [[Transcendental law of homogeneity]].
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