Abstract
A new computational methodology for computations 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 observed in the physical world. It is applied to all sets and processes (finite and infinite) and all numbers (finite, infinite, and infinitesimal). It is shown that it becomes possible to work with all of them in a unique framework (different from non-standard analysis) allowing one to easily manage mathematical situations that traditionally create difficulties (divergences of various kind, indeterminate forms, etc.) and to construct mathematical models of physical phenomena of a new type.
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