Optimization & Numerical Analysis seminars. The Infinity Computer and numerical computations with infinities and in infinitesimals. – Yaroslav D. Sergeyev – Università della Calabria and N.I. Lobachevsky University of Nizhni Novgorod, Russia (Il Seminario si svolgerà nella Sala Seminari Ovest, Dipartimento Informatica, Università di Pisa.)


The lecture presents a recent methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers on a new type of a computer – the Infinity Computer – patented in EU, USA, and Russia (see [23]). The new approach is based on the principle ‘The whole is greater than the part’ (Euclid’s Common Notion 5) that is 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 different from that of the non-standard analysis […]

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