Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of 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 incorrect basis of mathematics.
Foundations of mathematics, Philosophy of mathematics
