Numerical calculus with infinite and infinitesimal numbers and the Infinity computer

The lecture introduces a new methodology allowing one to execute numerical computations with finite, infinite, and infinitesimal numbers. 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 different from those of the non-standard analysis and surreal numbers. The new approach gives possibility to introduce a new type of a computer - the Infinity Computer - able to operate numerically not only with finite numbers but also with infinite and infinitesimal ones (European Patent has been granted recently). The Infinity Calculator using the Infinity Computer technology is presented during the talk. An additional information can be downloaded from the page www.theinfinitycomputer.com