In the last issue of the prestigious journal EMS Surveys in Mathematical Sciences published by the European Mathematical Society there appeared a 102 pages long paper entitled “Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems” written by Yaroslav D. Sergeyev, Professor at Lobachevsky State University in Nizhni Novgorod, Russia and Distinguished Professor at the University of Calabria, Italy (see his Brief Bio below). The paper describes a recent computational methodology introduced by the author paying a special attention to the separation of mathematical objects from numeral systems involved in their representation. It has been introduced with the intention to allow people to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the part” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The non-contradictory of the approach has been proved by the famous Italian logician Prof. Gabriele Lolli. This computational methodology uses a new kind of supercomputer called the Infinity Computer (patented in USA and EU) working numerically (traditional theories work with infinities and infinitesimals only symbolically) with infinite and infinitesimal numbers that can be written in a positional numeral system with an infinite radix. There exists its working software prototype. The appearance of the Infinity Computer changes drastically the entire panorama of numerical… [Read full story]
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