General Mathematics

2011 Submissions

[3] viXra:2011.0124 [pdf] replaced on 2022-03-10 13:53:38

Discussion of Foundation of Mathematics and Quantum Theory

Authors: Felix M. Lev
Comments: 19 Pages. Published in Open Mathematics, vol. 20, no.1, pp. 94-107 (2022).

Following the results of our recently published book (F. Lev, Finite mathematics as the foundation of classical mathematics and quantum theory. With application to gravity and particle theory. Springer (2020)), we discuss different aspects of classical and finite mathematics and explain why finite mathematics based on a finite ring of characteristic p is more general (fundamental) than classical mathematics: the former does not have foundational problems, and the latter is a special degenerate case of the former in the formal limit p→∞. In particular, quantum theory based on a finite ring of characteristic p is more general than standard quantum theory because the latter is a special degenerate case of the former in the formal limit p→∞ .
Category: General Mathematics

[2] viXra:2011.0020 [pdf] submitted on 2020-11-03 10:24:04

A Demonstration of the Sine Formula of Spherical Trigonometry (in French)

Authors: Abdelmajid Ben Hadj Salem
Comments: 6 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]

In this paper, we give another proof of the formula of sinus of spherical trigonometry.
Category: General Mathematics

[1] viXra:2011.0019 [pdf] submitted on 2020-11-03 10:30:55

A Focus on the Riemann's Hypothesis

Authors: Jean-Max Coranson-Beaudu
Comments: 7 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form] Published in Afr. J. Math. Comput. Sci. Res. Vol. 13(2), pp. 85-91

Riemann's hypothesis, formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin Academy of Mathematic. In that paper, he proposed that this function, called Riemann-zeta function takes values 0 on the complex plane when s=0.5+it. This hypothesis has great significance for the world of mathematics and physics. This solutions would lead to innumerable completions of theorems that rely upon its truth. Over a billion zeros of the function have been calculated by computers and shown that all are on this line s = 0.5+it. In this paper, we initially show that Riemann's (Zêta) function and the analytical extension of this function called (Aleph)) are distinct. After extending this function in the complex plane except the point s=1, we will show the existence and then the uniqueness of real part zeros equal to 1/2.
Category: General Mathematics