Kalanov, Temur Z.
Mathematics and Applied Mathematics
December 30, 2014
mathematics, number theory, mathematical physics, physics, geometry, engineering, formal logic, philosophy of science
Critical analysis of the foundations of the theory of negative numbers is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of the theory of negative numbers contradict practice and contain formal-logical errors. The main results are as follows: a) the concept “number sign” is an inadmissible one because it represents a formal-logical error; b) all the numbers are neutral ones because the
number “zero” is a neutral one; c) signs “plus” and “minus” are only symbols of mathematical operations. The obtained results are the sufficient reason for the following statement. The existence of logical errors in the theory of negative numbers determines the essence of the theory: the theory is a false one.