A new computational methodology using infinite and infinitesimal numbers
ACRI'10 Proceedings of the 9th international conference on Cellular automata for research and industry
Single-tape and multi-tape Turing machines through the lens of the Grossone methodology
The Journal of Supercomputing
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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.