Logical Analysis of the Foundations of Differential and Integral Calculus

摘要

Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. The methodological basis of the analysis is the unity of formal logic and rational dialectics. It is shown that the generally accepted foundations are based on the logically and practically erroneous concepts 'increment as variable quantity', 'infinitesimal quantity (uninterruptedly diminishing quantity)', 'derivative' and, consequently, represent an incorrect basis for mathematics.