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[14] viXra:2201.0185 [pdf] submitted on 2022-01-26 19:13:37
Authors: Imad El Ghazi
Comments: 7 Pages.
We prove in this short paper that the stochastic process defined by: $$Y_{t} := \frac{X_{t+1}}{\mathbb{E}\left[ X_{t+1}\right]},\; t\geq a > 1,$$
is an increasing process for the convex order,
where $ X_{t}$ a random variable taking values in $\mathbb{N}$ with probability $\mathbb{P}(X_{t}= n) = \frac{n^{-t}}{\zeta(t)}$ and $\zeta(t) = \sum \limits_{k=1}^{+\infty} \frac{1}{k^{t}}, \;\; \forall t> 1$.
Category: General Mathematics
[13] viXra:2201.0176 [pdf] submitted on 2022-01-25 19:42:33
Authors: Adriaan van der Walt
Comments: Pages. This document is the text of a book that contains background to the article “Leibnizian Mathematics” which is available on viXra at http://viXra.org/abs/2201.0175.
This book is a description of the examples and ideas that trace the progress of the author’s view of Mathematics from being subjected to the Scientific Method in division three, to being a technique of Ontology in section one. Section three was posted on the link http://vixra.org/abs/1501.0153 on VIXRA in 2015.
The scientific Method requires that any model should be as near as possible to perceived reality. PART ONE of DIVISION THREE is concerned with the concept of “infinite decimal fraction” as used by Cantor in his well-known diagonal proof. This concept is contrasted to the same concept in perceived reality by exploring the differences between Cantor’s arguments and perceived reality, resulting in a rejection of the validity of Cantor’s proof.
Next an analyses of the discrepancy between the cases where a line is assumed to be a string of points, and thus more than countable many points are required so that their lengths can add up to one, and the case where the points are limits of partitions of the interval and the lengths of only countable many points are required to add up to one.
The standard number system is then extended to the Cauchy Numbers which comprises infinitesimal numbers, rated numbers and infinite numbers. Infinitesimals are also defined. The concept of cascades of differentials is introduced and the fundamental theorem of Calculus is derived for this context. It is then pointed out that the approach of Parmenides of Elea is in line with the system in which Cantor’s argument is invalid. The implications for Physics and the possibility of uniting the two approaches to the divisibility of Space is investigated.
In DIVISION TWO the dichotomy, or discrepancy, studied in DIVISION THREE is further developed resulting in the introduction of the Euclidean Cosmology and the Leibnizian Cosmology. Leibnizian Cosmology required a closer look at the process of using numerals for depicting irrational numbers. This then resulted in a closer look at the concept of “infinity” in these two cosmologies.
In DIVISION ONE The results of DIVISION TWO are refined to define an alternative paradigm to Abstract Mathematics. It is a transitional step towards the document “LEIBNIZIAN MATHEMATICS” that includes further insights of the author, and which extends the current paradigm of Mathematics to include Leibnizian Mathematics as complementary, and not an alternative, to Euclidean Mathematics.
Category: General Mathematics
[12] viXra:2201.0175 [pdf] submitted on 2022-01-25 01:45:20
Authors: Adriaan van der Walt
Comments: 52 Pages. This document introduces Leibnizian Mathematics to complement Euclidean Mathematics. The background to this, [1], can be downloaded on http://viXra.org/abs/2201.0176
The document starts with a prologue discussing the Ontological aspects of the concept of Space to indicate where in the scheme of human endeavour this work fits. The prologue is followed by a prospectus intended to mitigate the strangeness of the concepts by offering a “bird’s eye view” of some concepts and arguments. This is then followed by a note to the reader containing some background information and precepts.
The main discourse “LEIBNIZIAN COSMOLOGY and LEIBNIZIAN MATHEMATICS”, which consists of nine sections, then follows.
It starts by introducing the core difference between the Leibnizian Cosmology and the Euclidean Cosmology by way of an example showing that the real line can contain only countable many real numbers in the Leibnizian Cosmology. Though the two cosmologies are formally stated only in paragraphs four and five, the main relevant difference is introduced by replacing the Euclidean assumption that points exist and that a line is a string of points with the Leibnizian assumption that lines exist and that points are merely the ends of lines.
Then follows a discussion of some relevant properties of perceived space and how they impact on Ontology. This is followed by an analysis of the basic assumptions of the Euclidean approach showing that these assumptions imply that a line must be formed from more than countable many points and that it is possible to perform infinitely many operations to completion.
The relevant basic assumptions of the Leibnizian Cosmology, including the Axiom of Parmenides, are then introduced.
Thereafter the basics of Leibnizian Mathematics are developed. Firstly, the standard argument for obtaining the gradient of a straight line to a curve is analysed to come to the concept of infinitesimal as it was introduced by Leibniz. The rule of L’Hospital is transcribed into a form in which the concept of limit is not present and so to come to a definition of an infinitesimal number. The number concept is then extended to the Cauchy Numbers. A special case of the Riemann integral is then analysed to motivate the definition of an infinitesimal.
The Fundamental Theorem of Calculus is next analysed from the perspective of Leibnizian Mathematics. The Dirac δ-function is presented as an example of a function that can have an infinite Cauchy number as value.
Category: General Mathematics
[11] viXra:2201.0156 [pdf] submitted on 2022-01-24 17:53:54
Authors: Mohit Gaur
Comments: 9 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
This research paper discusses the shortcomings of the currently prevalent definition of multiplication, and according to this paper, the definition of Multiplication is not complete and has many Errors as it does not apply to all types of examples such as negative*negative
Rather, the new definition given by us applies well to all examples and also defines
the multiplication of negative numbers more efficiently than the current definition
The correctness of this new definition means that we should not write 2*2=2+2, but in the new format, although in this example both definitions are correct, but in the example of negative numbers, only the new definition works.
Therefore, whether it is positive or negative, the same definition and format should be used which is more perfect because in mathematics a definition will be considered complete only if it works in all types of example numbers and charge According to the mathematics of the Vedic period, multiplication is somewhat different from modern mathematics, and modern mathematics took the basics from ancient Indian mathematics but was not flawless. I found the real meaning of multiplication by doing deep research on
Brahmagupta's Mathematics, Vedic Mathematics,Rashi vigyan, Brahmasiddhanta, Upanishads, Rigveda and other Ganit Shashtras Apart from this, we have also explained the correct definition of zero and its actual form which is mentioned in Indian Sanskrit texts.Through the real property and
basic nature of zero, we have also given a new dimension to understand the basics
of negative and positive number's operation
Category: General Mathematics
[10] viXra:2201.0153 [pdf] submitted on 2022-01-24 17:47:26
Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 5 Pages. In this note, we will state the definitions of the division by zero and division by zero calculus for popular using for the sake of their generality and great applications to mathematical sciences and the universe containing our basic ideas. In particular
In this note, we will state the definitions of the division by zero and division by zero calculus for popular using for the sake of their generality and great applications to mathematical sciences and the universe containing our basic ideas. In particular, we consider the value of the function $f(x,a)/\log a$ at $a=1$.
Category: General Mathematics
[9] viXra:2201.0117 [pdf] submitted on 2022-01-19 17:38:55
Authors: Ronald Danilo Chávez Calderón
Comments: 2 Pages.
In this present paper we will show you some interesting identity involving combina-
torial symbols and a proof of it as a theorem. The theorem was a discovery from the
times when I was studying Calculus at USAC/CUNOC University in Quetzaltenango,
Guatemala around 2004 year.
Category: General Mathematics
[8] viXra:2201.0101 [pdf] submitted on 2022-01-17 17:19:32
Authors: Saburou Saitoh, Yoshinori Saitoh
Comments: 5 Pages.
In this note, we will refer to the simple identity $(1/(x-1)) + (1/(x -2)) = (2x -3)/((x -1)(x- 2))$ and the expression that $g(z,a) + \log |z - a| $ is harmonic around $z=a$ from the viewpoint of the division by zero calculus that are very popular expressions in elementary mathematics. With these simple and very popular expressions, we would like to show clearly the importance of the division by zero calculus for some general people in a self-contained way.
Category: General Mathematics
[7] viXra:2201.0090 [pdf] replaced on 2022-02-06 14:59:08
Authors: Timothy W. Jones
Comments: 16 Pages. Some awkward prose corrected. Additional bibliography added.
Texas Instruments have added coding in Python to their TI-83 family of calculators. The question this paper attempts to address is why. This investigation starts by considering the programming language of Python and its benefits, especially as contrasted with TI-83 Basic (the standard language for these calculators). It then considers the implementation issues that confront the idea. As an example, Python is highly extensible, but calculators are by their nature highly proprietary, not extensible. And then there is the interface with its other products Smartview and Connect. These are designed to aid teachers and programmers respectively by porting calculator features to PC programs. Does Python inter-phase with these? How well? These concerns are motivated and organized by a concrete programming challenge: seek to code the quadratic formula (we'll define what that means) in Python and attempt to port it to a calculator -- as easily as possible, if possible, noting issues and problems as we go along.
Category: General Mathematics
[6] viXra:2201.0077 [pdf] submitted on 2022-01-13 04:28:52
Authors: Timothy W. Jones
Comments: 3 Pages.
Synthetic division is easily accomplished with a spreadsheet, but it gets complicated. In contrast, a TI-84's list feature with its dynamic dimension feature is ideal. We provide the code and an easy test case.
Category: General Mathematics
[5] viXra:2201.0071 [pdf] submitted on 2022-01-12 05:36:19
Authors: Edgar Valdebenito
Comments: 2 Pages.
In this note we give some relations between u and Pi.
Category: General Mathematics
[4] viXra:2201.0055 [pdf] submitted on 2022-01-10 09:44:30
Authors: Zhi Li, Hua Li
Comments: 7 Pages.
In this paper, it is found that there is an error in the calculation of multi-layer radicals by solving a higher degree algebraic equation of one variable, and the order of power roots is higher and the number of layers of the power roots is larger, the error is bigger. The analysis shows that this phenomenon is uncertain, and hence the multi-layer radical number is defined as inaccurate numbers. The discovery and definition of inaccurate numbers after irrational and imaginary numbers enriches people's cognition of numbers.
Using the experimental observation of the established mathematical models, the calculation error of the inaccurate numbers is -0.0004~5.57‰ under the model conditions.
Category: General Mathematics
[3] viXra:2201.0052 [pdf] submitted on 2022-01-10 20:03:50
Authors: Edgar Valdebenito
Comments: 3 Pages.
We present a family of infinite series.
Category: General Mathematics
[2] viXra:2201.0038 [pdf] replaced on 2022-08-15 21:11:38
Authors: Vincenzo Nardozza
Comments: 57 Pages.
In these notes I present all beginner methods I have used to solve the cubes I own. These notes are for myself, as a reference for the algorithm I have used and to have these algorithms at hand when I pick up a cube I have not solved for a long time. However, these notes are available for anybody interested in it.
Category: General Mathematics
[1] viXra:2201.0003 [pdf] replaced on 2022-02-24 00:38:51
Authors: Kyumin Nam
Comments: 2 Pages.
In this paper, we provide definitions and proof of the Zero-over-Zero Theorem. This theorem would be some help for the 0/0 problem.
Category: General Mathematics
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