The Infinity Computer and Numerical Computations with Infinite and Infinitesimal Numbers

摘要

A new computational methodology for executing calculations with infinite and infinitesimal quantities is described. 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. The new methodology has allowed us to introduce the Infinity Computer working with such numbers (its simulator has already been realized). Numerous examples are givea