@article { Gutman20080618,
author = "Гутман А.Е. and Кутателадзе С.С.",
title = "О теории гросс-единицы",
journal = "Сиб. матем. журн.",
year = "2008",
volume = "49",
number = "5",
pages = "1054--1063",
annote = "Дана тривиальная формализация неформальных рассуждений серии работ Я.Д.Сергеева о позиционной системе счисления с бесконечно большим основанием (гросс-единицей), произвольно противопоставленной ее автором классическому нестандартному анализу.",
keywords = "нестандартный анализ, инфинитезимальный анализ, позиционная система счисления"
}
@article { Gutman20080619,
author = "Gutman A.E. and Kutateladze S.S.",
title = "On the theory of grossone",
journal = "Sib. Math. J.",
year = "2008",
volume = "49",
number = "5",
pages = "835--841",
doi = "10.1007/s11202-008-0082-0",
annote = "A trivial formalization is given for the informal reasonings presented in 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"
}
@booklet { Gutman20080808,
author = "Gutman A.E. and Kutateladze S.S.",
note = "Electronic preprint / arXiv:0808.1164 [math.GM]",
howpublished = "Electronic",
title = "A trivial formalization of the theory of grossone",
address = "arXiv.org",
year = "2008",
pages = "6",
annote = "A trivial formalization is given for the informal reasonings presented in 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"
}
@article { Gutman20091214,
author = "Гутман А.Е. and Кутателадзе С.С. and Решетняк Ю.Г.",
title = "Кофинитные числа, нестандартный анализ и механика",
journal = "Сиб. журн. индустр. матем.",
year = "2010",
volume = "13",
number = "1(41)",
pages = "55--58",
annote = "Показывается математическая несостоятельность предлагаемых в работах А.Ф.Ревуженко вариантов нестандартного анализа.",
keywords = "нестандартный анализ, Ревуженко, псевдонаука"
}
@article { Gutman20091215,
author = "Gutman A.E. and Kutateladze S.S. and Reshetnyak Yu.G.",
title = "Cofinite numbers, nonstandard analysis, and mechanics",
journal = "J. Appl. Ind. Math.",
year = "2010",
volume = "4",
number = "2",
pages = "191--193",
doi = "10.1134/S1990478910020079",
annote = "We demonstrate the mathematical insignificance of the versions of nonstandard analysis proposed in the articles by A.F.Revuzhenko.",
keywords = "nonstandard analysis, Revuzhenko, pseudoscience"
}
@booklet { Gutman20160601,
author = "Gutman A.E. and Katz M.G. and Kudryk T.S. and Kutateladze S.S.",
note = "Electronic preprint / arXiv:1606.00160 [math.HO]",
howpublished = "Electronic",
title = "The Mathematical Intelligencer flunks the Olympics",
address = "arXiv.org",
year = "2016",
pages = "25",
annote = "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."
}
@article { Gutman20160315,
author = "Gutman A.E. and Katz M.G. and Kudryk T.S. and Kutateladze S.S.",
title = "The Mathematical Intelligencer flunks the Olympics",
journal = "Found. Sci.",
year = "2017",
volume = "22",
number = "3",
pages = "539--555",
doi = "10.1007/s10699-016-9485-8",
annote = "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."
}