ON RATIONALIZATION OF THE FOUNDATIONS OF DIFFERENTIAL CALCULUS

摘要

Logical analysis of different?al, calculus for ?he purpose of rationalization of the foundations of mathematics is proposed. Methodological basis for analysis is the unity of formal logic and rational dialectics. It is shown thatthe Standard definitions of the concepts "variable quantity", "infinitesimal (infinitely diminishing) quantity", and "infinitely large (infinitely increas?ng) quantity" represent logical errors because these definitions are based on the concept of mathematical process. The correct definition of the concept "variable quantity" and the unified mathematical definition relating?to both extreme ca??? of values of variable quantity (i.e. to the case of arbitrarily smaìl values of the variable quantity and the case of arbitrarily large values of the variable quantity) and the case of arbitrary values of the variable quantity are proposed.