David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Informatica 19 (4):567-596 (2008)
A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Examples dealing with divergent series, infinite sets, and limits are given.
|Keywords||Infinite and infinitesimal numbers infinite unite of measure numeral systems infinite sets divergent series|
|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
Yaroslav Sergeyev (2007). Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers. Chaos, Solitons and Fractals 33 (1):50-75.
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 (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). 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 (2010). Counting Systems and the First Hilbert Problem. Nonlinear Analysis Series A 72 (3-4):1701-1708.
Richard Heck (1998). The Finite and the Infinite in Frege's Grundgesetze der Arithmetik. In M. Schirn (ed.), Philosophy of Mathematics Today. OUP
Yaroslav Sergeyev (2009). Numerical Computations and Mathematical Modelling with Infinite and Infinitesimal Numbers. Journal of Applied Mathematics and Computing 29:177-195.
Added to index2009-08-07
Total downloads80 ( #26,139 of 1,700,364 )
Recent downloads (6 months)18 ( #39,449 of 1,700,364 )
How can I increase my downloads?