David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Applied Mathematics and Computing 29:177-195 (2009)
Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers numerically. This can be done on a new kind of a computer – the Infinity Computer – able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Kenneth L. Manders (1986). What Numbers Are Real? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:253 - 269.
Yaroslav Sergeyev (2007). Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers. Chaos, Solitons and Fractals 33 (1):50-75.
Yaroslav Sergeyev (2010). Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals. Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
Yaroslav Sergeyev (2009). Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains. Nonlinear Analysis Series A 71 (12):e1688-e1707.
Yaroslav Sergeyev (2009). Evaluating the Exact Infinitesimal Values of Area of Sierpinski's Carpet and Volume of Menger's Sponge. Chaos, Solitons and Fractals 42: 3042–3046.
Jeremy Gwiazda (2012). On Infinite Number and Distance. Constructivist Foundations 7 (2):126-130.
Yaroslav Sergeyev & Alfredo Garro (2010). Observability of Turing Machines: A Refinement of the Theory of Computation. Informatica 21 (3):425–454.
Yaroslav Sergeyev (2010). Counting Systems and the First Hilbert Problem. Nonlinear Analysis Series A 72 (3-4):1701-1708.
Added to index2009-12-03
Total downloads12 ( #150,301 of 1,692,788 )
Recent downloads (6 months)2 ( #108,992 of 1,692,788 )
How can I increase my downloads?