General Mathematics

2509 Submissions

[4] viXra:2509.0126 [pdf] submitted on 2025-09-23 17:24:26

Why a Combination, (N, K), is Always a Natural Number? Different Way to Look at the Answer Accentuates the Generation Process of Factors and Prime Numbers Contained Within a Particular Range of 1 to n.

Authors: Amit Kumar
Comments: 16 Pages. Appendix and supplementary material can be obtained upon the request.

The concept of combination is crucial to layout groundwork for many fundamental sciences, finance and technical domains. There are multiple known methods to show that the combination (binomial coefficient) is integral in nature. This article approaches the same concept with simple non-inductive algebraic steps that can be followed by a wide range of audiences. This article separates an ${n choose k}$ into mutually exclusive and collectively exhaustive cases and then shows for each case that any term in a denominator have at least one corresponding multiple in the numerator. All k for a particular n (for an ${n choose k}$) are visualized through plots to gain better understanding. In the context of the plots, this different way of looking at a Combination ${n choose k}$, gives hindsights into the generation process of factors and prime numbers contained within a particular range of 1 to n.
Category: General Mathematics

[3] viXra:2509.0113 [pdf] submitted on 2025-09-19 18:16:03

On Babylonian Mathematics and Real Numbers

Authors: Lucian M. Ionescu
Comments: 21 Pages. Presentation at Illinois State University Pure and Applied Mathematics Seminar Sept. 18 2025.

Babylonian Algorithm for Square Roots is a precursor of Newton-Cotes numerical method for finding roots, as numerical approximations(perturbative method)."What is a number?" has two complementary aspects: axiomatic viewpoint and as a tool in applications, via mathematical models.Modern 21-st century Mathematics regards Real Numbers as part of Complex Dynamics, in terms of Newton flow, Fatou and Julia sets and fractals, pointing towards their role as trajectories in Dynamics. A brief account is provided.Their relation to Number Fields, theory resulting from the work of Galois and Artin, starts to be apparent via Dirichlet Unit Theorem and the concept of uniformizer (Power Series/Diff. Eq.), extending the correspondence between Number Fields and Function Fields of Algebraic Curves.
Category: General Mathematics

[2] viXra:2509.0105 [pdf] submitted on 2025-09-17 16:40:03

An Essence of Division by Zero

Authors: Hiroshi Okumura
Comments: 22 Pages. 1 Figure (Note by viXra Admin: Further repetition may not be accepted)

We give several pairs of congruent circles arising from a generalized arbelos. A special case, in which the congruent circles are lines, is also considered using division by zero 1/0=0.
Category: General Mathematics

[1] viXra:2509.0036 [pdf] submitted on 2025-09-05 05:12:38

The Structure of First Order Logic

Authors: Martín Alejandro Monzón Marimón
Comments: 1 Page.

The structure of First Order logic will be described here in its verbal, or explicit (Second Order) form, by means of an "apparent" Zeroth Order form, because the actual pure Second Order form is not axiomatizable. Also, another "apparent" Second Order form will be used to make a Zeroth Order description of the structure, which, without the "apparent" Second Order quantification, would remain silent, or implicit, as that is its pure Zeroth Order form.
Category: General Mathematics