Indian Journal of Science and Technology

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Title Logical analysis of the foundations of differential and integral calculus
Author Temur Z. Kalanov
Abstract
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 erroneous concepts of “increment as variable quantity”, “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative” and, consequently,  represent   incorrect  basis of mathematics.
Citation
References
1. Luzin NN (1952) Differential calculus. Moscow.
2. Polya G (1954) Mathematics and plausible reasoning. 
Princeton.
3. Smirnov VI (1974) Course of  higher mathematics. 
Moscow.  
Keywords Foundations of mathematics, Philosophy of science
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