Abstract
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 […]http://pages.di.unipi.it/fpoloni/files/seminari/Sergeyev_Infinity.pdf