Critical Analysis of the Foundations of Differential and Integral Calculus

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Author(s) Temur Z. Kalanov
Pages 80-84
Volume 1
Issue 2
Date February, 2012
Keywords Differential and integral calculus, foundations of mathematics, philosophy of mathematics.

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 “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative”, “derivative as function of variable quantity” and, consequently, represent incorrect basis of mathematics.

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