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 and USA. 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). The new methodology (that is not related to non-standard analysis) evolves ideas of Cantor and Levi-Civita in a more applied way and, among other things, introduces new infinite integers that possess both cardinal and ordinal properties as usual finite numbers. The new methodology has been successfully used in a number of pure and applied areas of mathematics and computer science: measuring infinite sets, studying divergent series, hyperbolic geometry, Turing machines, lexicographic ordering, cellular automata, percolation and biological processes, optimization, numerical differentiation and ODEs, fractals, etc.
The Infinity Calculator using the Infinity Computer technology is presented during the talk.
More information about the new supercomputer at the internet page:
http://www.theinfinitycomputer.com



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