General Mathematics

2404 Submissions

[3] viXra:2404.0078 [pdf] submitted on 2024-04-15 23:29:58

On a Combinatorial Problem of Existing Matchings

Authors: Wladislaw Zlatjkovic Petrovescu
Comments: 2 Pages. (Abstract added by viXra Admin as required - Please conform)

In this paper we prove a classic combinatorial result on matchings.
Category: General Mathematics

[2] viXra:2404.0018 [pdf] submitted on 2024-04-03 20:46:31

Foundations of Differential Calculus: Does the Theory Satisfy the Criterion of Truth?

Authors: Temur Z. Kalanov
Comments: 16 Pages.

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 unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable statement: differential calculus represents an incorrect theory 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 incorrect theories. The concepts of "infinitesimal quantity", "movement", "process of tendency", and "limit of tendency" are meaningless concepts in mathematics; (2) the concepts of "increment of argument" and "increment of function" as the starting point of the differential calculus are not defined correctly; (3) the definition of the derivative of a function is an incorrect because the following logical contradiction arises: the increment of the argument is both not equal to zero and equal to zero; (4) the differentials of the argument and the function - as infinitesimal quantities - do not take on numerical values. This means that the differentials of quantities have neither quantitative nor qualitative determinacy; (5) the definition of the total differential of a function of two (many) variables does not satisfy the formal-logical law of the lack (absence) of contradiction; (6) the theory of proportions completely refutes the theory of differential calculus. Thus, differential calculus does not satisfy the criterion of truth and is not correct scientific (mathematical) theory.
Category: General Mathematics

[1] viXra:2404.0012 [pdf] submitted on 2024-04-02 11:51:48

A Power Series Divergent at Half Pi Yields a Sequence Briskly Convergent to Pi

Authors: Steven Kenneth Kauffmann
Comments: 2 Pages.

The tangent function's Taylor expansion about zero is a series of odd powers with positive coefficients; it converges when the absolute value of its argument is less than half pi, and diverges to positive infinity when its argument equals half pi, so with the aid of the ratio test it is seen that twice the square root of the ratio of its successive coefficients is a sequence which converges to pi. The odd derivatives of the tangent function are polynomials in powers of its square with positive integer coefficients, so a recursion of positive integers can be found from which the coefficients of the series described above may be successively obtained. Its related sequence which converges to pi does so monotonically from above, and appears to refine its approximation to pi by about one significant decimal figure per successive term.
Category: General Mathematics