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Differential Calculus: a Gross Error in Mathematics

Author:

Kalanov, Temur Z.

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

December 22, 2023

File:

/Research Papers-Mathematics and Applied Mathematics/Download/9774

Downloads:

249

Keywords:

eneral mathematics, foundations of mathematics, differential calculus, integral calculus, methodology of mathematics, philosophy of mathematics, philosophy and mathematics, mathematics education, logic, physics

Abstract:

A detailed proof of the incorrectness of the foundations of the differential calculus is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The proof leads to the following irrefutable statement: differential calculus represents a gross error in mathematics and physics. The proof of this statement is based on the following irrefutable results: (1) the standard theory of infinitesimals and the theory of limits underlying the differential calculus are gross errors. The main error is that infinitesimal (infinitely decreasing) quantities do not take on numerical values in the process of tending to zero. The number “zero” is not a permissible value of infinitesimal quantity. The concepts of “infinitesimal quantity”, “movement”, “process of tendency”, and “limit of tendency” are meaningless concepts in mathematics: they are not mathematical concepts because the mathematical formalism does not contain movement (process).../...

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