Critical Analysis of the Foundations of the Theory of Negative Numbers
Keywords:
Mathematics, Number Theory, Mathematical Physics, Physics, Geometry, Engineering, Formal logic, Philosophy of Science
Abstract
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 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.
References
T.Z.Kalanov, The critical analysis of the foundations of theoretical physics. Crisis in theoretical physics: The problem of scientific truth, Lambert Academic Publishing, (2010).
T.Z.Kalanov, Analysis of the problem of relation between geometry and natural sciences, Prespacetime Journal. 1(5)(2010), 75-87.
T.Z.Kalanov, Logical analysis of the foundations of differential and integral calculus, Bulletin of Pure and Applied Sciences, 30(2)(2011), 327-334.
T.Z.Kalanov, Logical analysis of the foundations of differential and integral calculus, Bulletin of Pure and Applied Sciences. 30(2)(2011), 327-334.
T.Z.Kalanov, Critical analysis of the foundations of differential and integral calculus, MCMS (Ada Lovelace Publications), (2011), 34-40.
T.Z.Kalanov, Critical analysis of the foundations of differential and integral calculus, International Journal of Science and Technology, 1(2)(2012), 80-84.
T.Z.Kalanov, On rationalization of the foundations of differential calculus, Bulletin of Pure and Applied Sciences. 31(1)(2012), 1-7.
T.Z.Kalanov, The logical analysis of the Pythagorean theorem and of the problem of irrational numbers, Asian Journal of Mathematics and Physics. 2013(2013), 1-12.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Global Journal of Advanced Research on Classical and Modern Geometries, 2(2)(2013), 59-68.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Basic Research Journal of Education Research and Review, 2(4)(2013), 59-65.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Bulletin of Pure and Applied Sciences, 32(1)(2013), 1-12.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Research Desk., 2(3)(2013), 249-259.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, International Journal of Scientific Knowledge Computing and Information Technology, 3(2)(2013), 25-30.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Journal of Computer and Mathematical Sciences, 4(4)(2013), 202-321.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Journal of Research in Electrical and Electronics Engineering, 2(5)(2013), 1-5.
T.Z.Kalanov, The foundations of vector calculus: The logical error in mathematics and theoretical physics, Unique Journal of Educational Research, 1(4)(2013), 54-59.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Aryabhatta Journal of Mathematics & Informatics, 5(2)(2013), 227-234.
T.Z.Kalanov, Critical analysis of the mathematical formalism of theoretical physics. II. Foundations of vector calculus, Bulletin of Pure and Applied Sciences, 32(2)(2013), 121-130.
T.Z.Kalanov, On the system analysis of the foundations of trigonometry, International Journal of Science Inventions Today, 3(2)(2014), 119-147.
T.Z.Kalanov, On the system analysis of the foundations of trigonometry, Pure and Applied Mathematics Journal, 3(2)(2014), 26-39.
N.Bourbaki, Elements of the History of Mathematics, Berlin, Heidelberg, New York: Springer-Verlag, (1998).
D.J.Struik, A Concise History of Mathematics, New York: Dover Publications, (1987).
G.Ifrah, The Universal History of Numbers, Harvill Press, London, (1998).
C.B.Boyer, A history of mathematics, (Second ed.), John Wiley & Sons, (1991).
W.R.Hamilton, Theory of conjugate functions, or algebraic couples; with a preliminary and elementary essay on algebra as the science of pure time, Transactions of the Royal Irish Academy, 17(1)(1837), 293-422.
E.Madelung, Die mathematischen hilfsmittel des physikers, Berlin, Gottingen, Heidelberg, Springer-Verlag, (1957).
T.Z.Kalanov, Analysis of the problem of relation between geometry and natural sciences, Prespacetime Journal. 1(5)(2010), 75-87.
T.Z.Kalanov, Logical analysis of the foundations of differential and integral calculus, Bulletin of Pure and Applied Sciences, 30(2)(2011), 327-334.
T.Z.Kalanov, Logical analysis of the foundations of differential and integral calculus, Bulletin of Pure and Applied Sciences. 30(2)(2011), 327-334.
T.Z.Kalanov, Critical analysis of the foundations of differential and integral calculus, MCMS (Ada Lovelace Publications), (2011), 34-40.
T.Z.Kalanov, Critical analysis of the foundations of differential and integral calculus, International Journal of Science and Technology, 1(2)(2012), 80-84.
T.Z.Kalanov, On rationalization of the foundations of differential calculus, Bulletin of Pure and Applied Sciences. 31(1)(2012), 1-7.
T.Z.Kalanov, The logical analysis of the Pythagorean theorem and of the problem of irrational numbers, Asian Journal of Mathematics and Physics. 2013(2013), 1-12.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Global Journal of Advanced Research on Classical and Modern Geometries, 2(2)(2013), 59-68.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Basic Research Journal of Education Research and Review, 2(4)(2013), 59-65.
T.Z.Kalanov, The critical analysis of the Pythagorean theorem and of the problem of irrational numbers, Bulletin of Pure and Applied Sciences, 32(1)(2013), 1-12.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Research Desk., 2(3)(2013), 249-259.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, International Journal of Scientific Knowledge Computing and Information Technology, 3(2)(2013), 25-30.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Journal of Computer and Mathematical Sciences, 4(4)(2013), 202-321.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Journal of Research in Electrical and Electronics Engineering, 2(5)(2013), 1-5.
T.Z.Kalanov, The foundations of vector calculus: The logical error in mathematics and theoretical physics, Unique Journal of Educational Research, 1(4)(2013), 54-59.
T.Z.Kalanov, On the logical analysis of the foundations of vector calculus, Aryabhatta Journal of Mathematics & Informatics, 5(2)(2013), 227-234.
T.Z.Kalanov, Critical analysis of the mathematical formalism of theoretical physics. II. Foundations of vector calculus, Bulletin of Pure and Applied Sciences, 32(2)(2013), 121-130.
T.Z.Kalanov, On the system analysis of the foundations of trigonometry, International Journal of Science Inventions Today, 3(2)(2014), 119-147.
T.Z.Kalanov, On the system analysis of the foundations of trigonometry, Pure and Applied Mathematics Journal, 3(2)(2014), 26-39.
N.Bourbaki, Elements of the History of Mathematics, Berlin, Heidelberg, New York: Springer-Verlag, (1998).
D.J.Struik, A Concise History of Mathematics, New York: Dover Publications, (1987).
G.Ifrah, The Universal History of Numbers, Harvill Press, London, (1998).
C.B.Boyer, A history of mathematics, (Second ed.), John Wiley & Sons, (1991).
W.R.Hamilton, Theory of conjugate functions, or algebraic couples; with a preliminary and elementary essay on algebra as the science of pure time, Transactions of the Royal Irish Academy, 17(1)(1837), 293-422.
E.Madelung, Die mathematischen hilfsmittel des physikers, Berlin, Gottingen, Heidelberg, Springer-Verlag, (1957).
How to Cite
Temur Z. Kalanov. (2015). Critical Analysis of the Foundations of the Theory of Negative Numbers. International Journal of Current Research in Science and Technology, 1(2), 1-12. Retrieved from https://crst.gfer.org/index.php/crst/article/view/6
Issue
Section
Articles
