Gutman A.E.
Infinitesimal analysis
5 publications, 2008–2017

Critical analysis of some papers related to formalization of infinitely small and infinitely large numbers

Within the contemporary infinitesimal analysis, a trivial formalization is given for the basics of a series of papers on a positional numeral system with an infinitely large base.
Algorithmic obstacles are specified to computer implementation of a positional numeral system with an infinitely large base.
A trivial solution is proposed to the problem of reducing the lexicographic order to a numerical order, which does not require any extension of the classical set theory.
The comparative logical and algorithmic status is described of the informal postulates underlying the positional numeral system with an infinitely large base.
The mathematical insignificance is demonstrated of the version of nonstandard analysis based on the quotient of the algebra of sequences by the Fréchet filter.

1.	Gutman A.E., Kutateladze S.S. On the theory of grossone [in Russian] // Sib. Matem. Zh. 2008. V. 49, N 5. P. 1054–1063. Bibliographic record Record in BibTeX format Article (PDF) Cover (PDF) Article on the journal site (PDF) Information on the journal site Information on ResearchGate Journal site English version
	Gutman A.E., Kutateladze S.S. On the theory of grossone // Sib. Math. J. 2008. V. 49, N 5. P. 835–841. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
2.	Gutman A.E., Kutateladze S.S. A trivial formalization of the theory of grossone. Electron. preprint. arXiv.org, 2008. 6 p. (arXiv:0808.1164 [math.GM]) Bibliographic record Record in BibTeX format Electronic preprint (PDF) Preprint on arXiv.org (PDF) Preprint abstract on arXiv.org Information on ResearchGate
3.	Gutman A.E., Kutateladze S.S., Reshetnyak Yu.G. Cofinite numbers, nonstandard analysis, and mechanics [in Russian] // Sib. Zh. Ind. Mat. 2010. V. 13, N 1(41). P. 55–58. Bibliographic record Record in BibTeX format Article (PDF) Information on Math-Net Information on ResearchGate Issue on the journal site Journal site English version
	Gutman A.E., Kutateladze S.S., Reshetnyak Yu.G. Cofinite numbers, nonstandard analysis, and mechanics // J. Appl. Ind. Math. 2010. V. 4, N 2. P. 191–193. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site Russian version
4.	Gutman A.E., Katz M.G., Kudryk T.S., Kutateladze S.S. The Mathematical Intelligencer flunks the Olympics. Electron. preprint. arXiv.org, 2016. 25 p. (arXiv:1606.00160 [math.HO]) Bibliographic record Record in BibTeX format Electronic preprint (PDF) Preprint on arXiv.org (PDF) Preprint abstract on arXiv.org Information on ResearchGate
5.	Gutman A.E., Katz M.G., Kudryk T.S., Kutateladze S.S. The Mathematical Intelligencer flunks the Olympics // Found. Sci. 2017. V. 22, N 3. P. 539–555. Bibliographic record Record in BibTeX format Article (PDF) Information on Springer Link Information on ResearchGate DOI resolution Journal site

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Last updated
June 10, 2020

Gutman A.E.Infinitesimal analysis5 publications, 2008–2017

Gutman A.E.
Infinitesimal analysis
5 publications, 2008–2017