A few remarks on philosophical foundations of a new applied approach to Infinity

Traditional computers are able to execute operations only with finite numbers. Operations with infinite and infinitesimal quantities could not be realized. Thus, situations where the usage of infinite or infinitesimal quantities is required are studied only theoretically. In this paper, a new positional system with infinite radix proposed recently in [Sergeyev] is discussed. This system allows one to write down finite, infinite, and infinitesimal numbers as particular cases of a unique framework and to realize calculations at a new calculating device – Infinity Computer. Thus the problem of infinity is considered from a new – applied – point of view. The new approach both gives possibilities to execute numerical calculations of a new type and simplifies fields of mathematics where usage of infinity and/or infinitesimals is necessary. In this paper, we make a few remarks on philosophical (and physical) foundations of the new approach and give some illustrative examples.