Hyperreal Numbers for Infinite Divergent Series
نویسندگان
چکیده
منابع مشابه
Ultraproducts and Hyperreal Numbers
Notions of infinite and infinitesimal numbers have been around since the earliest days of calculus; in particular, Leibniz found them a great inspiration in his co-invention of calculus. Later generations of analysts, including Weierstrass, frowned upon such notions, pointing out the lack of rigor in many of their arguments. Yet even Cauchy, who was largely known for his efforts to ‘clean up’ a...
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This paper presents new concepts in the use of infinite and infinitesimal numbers in real analysis. The theory is based upon the hyperreal number system developed by Abraham Robinson in the 1960's in his invention of “nonstandard analysis”. The paper begins with a short exposition of the construction of the hyperreal number system and the fundamental results of nonstandard analysis which are us...
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We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2019
ISSN: 1556-5068
DOI: 10.2139/ssrn.3459243