Abstract. The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev's claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev's grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.
A trivial formalization is given for the informal reasonings of a series of papers by Ya. D. Sergeyev on a positional numeral system with an infinitely large base, grossone; the system which is groundlessly opposed by its originator to the classical nonstandard analysis.Keywords: nonstandard analysis, infinitesimal analysis, positional numeral system In recent years Sergeyev has published a series of papers [1][2][3][4][5] in which a positional numeral system is advanced related to the notion of grossone. ‡) Sergeyev opposes his system to nonstandard analysis and regards the former as resting on different mathematical, philosophical, etc. doctrines. The aim of the present note is to properly position the papers by Sergeyev on developing numeral systems. It turns out that a model of Sergeyev's system is provided by the initial segment {1, 2, . . . , ν!} of the nonstandard natural scale up to the factorial ν! of an arbitrary actual infinitely large natural ν. Such a factorial serves as a model of Sergeyev's grossone, thus demonstrating the place occupying by the numeral system he proposed.As the main source we have chosen [4], the latest available paper by Sergeyev, which contains a detailed description of his basic ideas.
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