Cofinite numbers, nonstandard analysis, and mechanics
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 1, pp. 55-58 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show the mathematical insignificance of the versions of nonstandard analysis proposed by A. F. Revuzhenko.
Keywords: nonstandard analysis
Mots-clés : Revuzhenko, pseudoscience.
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A. E. Gutman; S. S. Kutateladze; Yu. G. Reshetnyak. Cofinite numbers, nonstandard analysis, and mechanics. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 1, pp. 55-58. http://geodesic.mathdoc.fr/item/SJIM_2010_13_1_a4/

[1] Revuzhenko A. F., Mekhanika uprugo-plasticheskikh sred i nestandartnyi analiz, izd. NGU, Novosibirsk, 2000

[2] Revuzhenko A. F., “Ob ispolzovanii v mekhanike tverdogo tela kontseptsii prostranstva, nadelennogo ierarkhiei strukturnykh urovnei”, Fizicheskaya mezomekhanika, 6:4 (2003), 73–83

[3] Revuzhenko A. F. i dr., “Kontseptsiya nearkhimedova mnogomasshtabnogo prostranstva i modeli plasticheskikh sred so strukturoi”, Fizicheskaya mezomekhanika, 11:3 (2008), 45–60

[4] Macintyre A. J., “Abraham Robinson, 1918–1974”, Bull. Amer. Math. Soc., 83 (1977), 646–666 | DOI | MR | Zbl

[5] Robinson A., Aerofoil Theory of a Flat Delta Wing at Supersonic Speeds, Ministry of Supply, Aeronautical Research Council, London, 1946 | MR

[6] Robinson A., Laurmann J. A., Wing Theory, Univ. Press, Cambridge, 1956 | MR | Zbl

[7] Robinson A., “Non-standard analysis”, Indag. Math., 23 (1961), 423–440 | MR

[8] Robinson A., Non-standard Analysis, North-Holland, Amsterdam, 1974 | MR

[9] Kanovei V. G., “O korrektnosti eilerova metoda razlozheniya sinusa v beskonechnoe proizvedenie”, Uspekhi mat. nauk, 43:4(262) (1988), 57–81 | MR | Zbl

[10] Chwistek L., The Limits of Science, Kegan Paul, London, 1948

[11] Lakatos I., “Cauchy and the continuum: The significance of non-standard analysis for the history and philosophy of mathematics”, Math. Intelligencer, 1 (1978), 151–161 | DOI | MR | Zbl

[12] Capinski M., Cutland N. J., Nonstandard Methods for Stochastic Fluid Mechanics, World Sci. Publ., Singapore et al., 1995 | MR | Zbl

[13] Rubio J. E., Optimization and Nonstandard Analysis, Marcel Dekker, New York–London, 1994 | MR | Zbl

[14] Cutland N., Loeb Measures in Practice: Recent Advances, Springer Verl., Berlin et al., 2001 | MR

[15] Gordon E. I., Kusraev A. G., Kutateladze S. S., Infinitezimalnyi analiz, Izd-vo Instituta matematiki, Novosibirsk, 2006

[16] The Strength of Nonstandard Analysis, Springer Verl., Wienn, 2007

[17] Maslov V. P., “Nonstandard analysis, parastatistics, and fractals”, Theor. Math. Physics, 153:2 (2007), 1575–1581 | DOI | MR | Zbl

[18] Nelson E., “Internal set theory: A new approach to nonstandard analysis”, Bull. Amer. Math. Soc., 83:6 (1977), 1165–1198 | DOI | MR | Zbl

[19] Gordon E. I., “Otnositelno standartnye elementy v teorii vnutrennikh mnozhestv E. Nelsona”, Sib. mat. zhurn., 30:1 (1989), 89–95 | MR | Zbl