Informatica 19 (4):567-596 (2008)

Authors
Yaroslav Sergeyev
Università della Calabria
Abstract
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
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References found in this work BETA

Non-Standard Analysis.A. Robinson - 1961 - North-Holland Publishing Co..
Contributions to the Founding of the Theory of Transfinite Numbers.Cassius J. Keyser - 1916 - Journal of Philosophy, Psychology and Scientific Methods 13 (25):697-697.
Set Theory and the Continuum Hypothesis.Kenneth Kunen - 1966 - Journal of Symbolic Logic 35 (4):591-592.

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