- UN SEMPLICE MODO PER TRATTARE LE GRANDEZZE INFINITE ED INFINITESIME.Yaroslav Sergeyev - 2015 - la Matematica Nella Società E Nella Cultura: Rivista Dell’Unione Matematica Italiana, Serie I 8:111-147.details
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Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.details
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The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.details
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An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.details
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Higher order numerical differentiation on the Infinity Computer.Yaroslav Sergeyev - 2011 - Optimization Letters 5 (4):575-585.details
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Exact and Approximate Arithmetic in an Amazonian Indigene Group.Pierre Pica, Cathy Lemer, Véronique Izard & Stanislas Dehaene - 2004 - Science 306 (5695):499-503.details
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Observability of Turing Machines: a refinement of the theory of computation.Yaroslav Sergeyev & Alfredo Garro - 2010 - Informatica 21 (3):425–454.details
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On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.details
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Numerical computations and mathematical modelling with infinite and infinitesimal numbers.Yaroslav Sergeyev - 2009 - Journal of Applied Mathematics and Computing 29:177-195.details
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The Olympic medals ranks, lexicographic ordering and numerical infinities.Yaroslav Sergeyev - 2015 - The Mathematical Intelligencer 37 (2):4-8.details
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A Study of Mathematical Determination through Bertrand’s Paradox.Davide Rizza - 2018 - Philosophia Mathematica 26 (3):375-395.details
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(1 other version)Finite combinatory processes—formulation.Emil L. Post - 1936 - Journal of Symbolic Logic 1 (3):103-105.details
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Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.details
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Using blinking fractals for mathematical modelling of processes of growth in biological systems.Yaroslav Sergeyev - 2011 - Informatica 22 (4):559–576.details
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Interpretation of percolation in terms of infinity computations.Yaroslav Sergeyev, Dmitri Iudin & Masaschi Hayakawa - 2012 - Applied Mathematics and Computation 218 (16):8099-8111.details
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Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers.Yaroslav Sergeyev - 2007 - Chaos, Solitons and Fractals 33 (1):50-75.details
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Counting systems and the First Hilbert problem.Yaroslav Sergeyev - 2010 - Nonlinear Analysis Series A 72 (3-4):1701-1708.details
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A new applied approach for executing computations with infinite and infinitesimal quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.details
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ontributions to the Founding of the Theory of Transfinite Numbers. [REVIEW]Georg Cantor - 1916 - Ancient Philosophy (Misc) 26:638.details
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Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.details
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Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.details
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Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge.Yaroslav Sergeyev - 2009 - Chaos, Solitons and Fractals 42: 3042–3046.details
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On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.details
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(2 other versions)J. P. Mayberry. The foundations of mathematics in the theory of sets. Encyclopedia of mathematics and its applications, vol. 82. Cambridge University Press, Cambridge 2000, New York 2001, etc., xx + 424 pp. [REVIEW]W. W. Tait - 2002 - Bulletin of Symbolic Logic 8 (3):424-426.details
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Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.details
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(2 other versions)Contributions to the Founding of the Theory of Transfinite Numbers. [REVIEW]Cassius J. Keyser - 1916 - Journal of Philosophy, Psychology and Scientific Methods 13 (25):697-697.details
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The Consistency of the Continuum Hypothesis.Kurt Gödel - 1940 - Princeton University Press.details
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[Omnibus Review].C. Smorynski - 1979 - Journal of Symbolic Logic 44 (1):116-119.details
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